premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
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|---|---|---|---|---|---|---|---|
Everyone who is not tall is tall or not kind and vice versa. If susan is both not calm and not quiet then someone is not old or not wise. Everyone who is not calm is wise or not tall and vice versa. If someone is not strong then john is either not curious or happy and vice versa. If alice is wise or patient then mary is both tall and old and vice versa. If someone is humble or not humble then someone is humble and vice versa. Everyone who is both tall and not old is both happy and strong. If fred is creative then someone is tall or not patient and vice versa. Everyone who is both generous and not humble is happy or creative and vice versa. If someone is not calm then someone is either patient or not creative. Everyone who is either kind or funny is calm and vice versa. Everyone who is not humble is either not tall or quiet and vice versa. If john is not rich or kind then someone is both brave and not creative. Everyone who is either generous or quiet is strong or brave and vice versa. Everyone who is both quiet and not happy is rich or quiet. Fred is both rich and wise. Someone is either generous or wise. Someone is brave. Mary is both not generous and not wise. | Fred is generous. | entailment | (![X]:(~tall(X)<=>(tall(X)|~kind(X))))&
(((~calm(susan)&~quiet(susan)))=>(?[X]:((~old(X)|~wise(X)))))&
(![X]:(~calm(X)<=>(wise(X)|~tall(X))))&
((?[X]:(~strong(X)))<=>((~curious(john)<~>happy(john))))&
(((wise(alice)|patient(alice)))<=>((tall(mary)&old(mary))))&
((?[X]:((humble(X)|~humble(X))))<=>(?[X]:(humble(X))))&
(![X]:((tall(X)&~old(X))=>(happy(X)&strong(X))))&
((creative(fred))<=>(?[X]:((tall(X)|~patient(X)))))&
(![X]:((generous(X)&~humble(X))<=>(happy(X)|creative(X))))&
((?[X]:(~calm(X)))=>(?[X]:((patient(X)<~>~creative(X)))))&
(![X]:((kind(X)<~>funny(X))<=>calm(X)))&
(![X]:(~humble(X)<=>(~tall(X)<~>quiet(X))))&
(((~rich(john)|kind(john)))=>(?[X]:((brave(X)&~creative(X)))))&
(![X]:((generous(X)<~>quiet(X))<=>(strong(X)|brave(X))))&
(![X]:((quiet(X)&~happy(X))=>(rich(X)|quiet(X))))&
((rich(fred)&wise(fred)))&
(?[X]:((generous(X)<~>wise(X))))&
(?[X]:(brave(X)))&
((~generous(mary)&~wise(mary))) | generous(fred) | [
"p0",
"p4",
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 4890042013841484885579567
% SZS output start Proof for 4890042013841484885579567
1. ! [X0] : (~tall(X0) <=> (~kind(X0) | tall(X0))) [input p0]
5. (patient(alice) | wise(alice)) <=> (old(mary) & tall(mary)) [input p4]
8. creative(fred) <=> ? [X0] : (~patient(X0) | tall(X0)) [input p7]
9. ! [X0] : ((~humble(X0) & generous(X0)) <=> (creative(X0) | happy(X0))) [input p8]
20. ~generous(fred) [input hypothesis]
32. ! [X0] : ((~tall(X0) | (kind(X0) & ~tall(X0))) & ((~kind(X0) | tall(X0)) | tall(X0))) [nnf transformation 1]
33. ! [X0] : ((~tall(X0) | (kind(X0) & ~tall(X0))) & (~kind(X0) | tall(X0) | tall(X0))) [flattening 32]
42. ((patient(alice) | wise(alice)) | (~old(mary) | ~tall(mary))) & ((old(mary) & tall(mary)) | (~patient(alice) & ~wise(alice))) [nnf transformation 5]
43. (patient(alice) | wise(alice) | ~old(mary) | ~tall(mary)) & ((old(mary) & tall(mary)) | (~patient(alice) & ~wise(alice))) [flattening 42]
49. (creative(fred) | ! [X0] : (patient(X0) & ~tall(X0))) & (? [X0] : (~patient(X0) | tall(X0)) | ~creative(fred)) [nnf transformation 8]
50. (creative(fred) | ! [X0] : (patient(X0) & ~tall(X0))) & (? [X1] : (~patient(X1) | tall(X1)) | ~creative(fred)) [rectify 49]
51. ? [X1] : (~patient(X1) | tall(X1)) => (~patient(sK4) | tall(sK4)) [choice axiom]
52. (creative(fred) | ! [X0] : (patient(X0) & ~tall(X0))) & ((~patient(sK4) | tall(sK4)) | ~creative(fred)) [skolemisation 50,51]
53. ! [X0] : (((~humble(X0) & generous(X0)) | (~creative(X0) & ~happy(X0))) & ((creative(X0) | happy(X0)) | (humble(X0) | ~generous(X0)))) [nnf transformation 9]
54. ! [X0] : (((~humble(X0) & generous(X0)) | (~creative(X0) & ~happy(X0))) & (creative(X0) | happy(X0) | humble(X0) | ~generous(X0))) [flattening 53]
71. ~tall(X0) | ~tall(X0) [cnf transformation 33]
82. tall(mary) | ~patient(alice) [cnf transformation 43]
93. creative(fred) | patient(X0) [cnf transformation 52]
96. ~creative(X0) | generous(X0) [cnf transformation 54]
123. ~generous(fred) [cnf transformation 20]
125. ~tall(X0) [duplicate literal removal 71]
165. 9 <=> patient(alice) [avatar definition]
167. ~patient(alice) <- (~9) [avatar component clause 165]
178. ~patient(alice) [subsumption resolution 82,125]
179. ~9 [avatar split clause 178,165]
195. 15 <=> ! [X0] : patient(X0) [avatar definition]
196. patient(X0) <- (15) [avatar component clause 195]
198. 16 <=> creative(fred) [avatar definition]
200. creative(fred) <- (16) [avatar component clause 198]
201. 15 | 16 [avatar split clause 93,198,195]
234. $false <- (~9, 15) [subsumption resolution 167,196]
235. 9 | ~15 [avatar contradiction clause 234]
236. generous(fred) <- (16) [resolution 96,200]
237. $false <- (16) [subsumption resolution 236,123]
238. ~16 [avatar contradiction clause 237]
239. $false [avatar sat refutation 179,201,235,238]
% SZS output end Proof for 4890042013841484885579567
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not humble or not rich is brave or not kind and vice versa.
If someone is not generous then someone is patient.
Everyone who is either not funny or patient is old or not generous.
If someone is quiet or patient then someone is either wise or funny.
If someone is both not generous and old then paul is patient.
If someone is both not brave and old then someone is either kind or not patient and vice versa.
Everyone who is not patient or not old is not funny or wise and vice versa.
Everyone who is not creative is both not wise and tall and vice versa.
Everyone who is both not patient and not calm is both not creative and not brave.
Everyone who is rich is either calm or rich.
If mary is not brave then susan is funny or not calm and vice versa.
Everyone who is either not humble or funny is both generous and not generous.
Everyone who is both creative and not kind is not humble.
If susan is not kind then susan is not funny or patient.
If someone is either brave or not rich then someone is not curious and vice versa.
John is either not tall or not kind.
Someone is either tall or rich.
Someone is both funny and not brave.
Someone is not generous or not patient.
Someone is either not curious or not tall.
Someone is both not old and not curious.
Someone is generous or not quiet.
Fred is either not creative or not calm. | Paul is not creative. | neutral | (![X]:((~humble(X)<~>~rich(X))<=>(brave(X)|~kind(X))))&
((?[X]:(~generous(X)))=>(?[X]:(patient(X))))&
(![X]:((~funny(X)<~>patient(X))=>(old(X)|~generous(X))))&
((?[X]:((quiet(X)|patient(X))))=>(?[X]:((wise(X)<~>funny(X)))))&
((?[X]:((~generous(X)&old(X))))=>(patient(paul)))&
((?[X]:((~brave(X)&old(X))))<=>(?[X]:((kind(X)<~>~patient(X)))))&
(![X]:((~patient(X)|~old(X))<=>(~funny(X)|wise(X))))&
(![X]:(~creative(X)<=>(~wise(X)&tall(X))))&
(![X]:((~patient(X)&~calm(X))=>(~creative(X)&~brave(X))))&
(![X]:(rich(X)=>(calm(X)<~>rich(X))))&
((~brave(mary))<=>((funny(susan)|~calm(susan))))&
(![X]:((~humble(X)<~>funny(X))=>(generous(X)&~generous(X))))&
(![X]:((creative(X)&~kind(X))=>~humble(X)))&
((~kind(susan))=>((~funny(susan)|patient(susan))))&
((?[X]:((brave(X)<~>~rich(X))))<=>(?[X]:(~curious(X))))&
((~tall(john)<~>~kind(john)))&
(?[X]:((tall(X)<~>rich(X))))&
(?[X]:((funny(X)&~brave(X))))&
(?[X]:((~generous(X)|~patient(X))))&
(?[X]:((~curious(X)<~>~tall(X))))&
(?[X]:((~old(X)&~curious(X))))&
(?[X]:((generous(X)|~quiet(X))))&
((~creative(fred)<~>~calm(fred))) | ~creative(paul) | [] | null | 0 |
If alice is not wise then lucy is humble or not strong and vice versa. Everyone who is rich is not humble or wise and vice versa. Everyone who is wise is either not kind or not patient and vice versa. Everyone who is either not strong or not tall is either not strong or not calm and vice versa. Everyone who is not patient or not calm is rich or tall. Everyone who is kind is not generous or not quiet and vice versa. If someone is either not generous or rich then someone is wise or generous and vice versa. Everyone who is wise or not rich is both wise and not creative. If someone is not strong or wise then someone is either not patient or not humble. If john is not funny then mary is not funny and vice versa. If lucy is both curious and old then john is not brave. If someone is either not wise or not tall then someone is not generous or tall and vice versa. Everyone who is both creative and not happy is either not strong or brave. Everyone who is tall or kind is either not calm or not happy. If alice is both tall and not quiet then someone is rich or old and vice versa. If susan is either humble or not creative then someone is not happy or not creative. Someone is brave. John is both calm and not creative. Paul is rich or generous. Someone is either not happy or curious. Alice is either not happy or not humble. Someone is not happy or rich. Someone is either not old or funny. Someone is happy. | Alice is not wise. | contradiction | ((~wise(alice))<=>((humble(lucy)|~strong(lucy))))&
(![X]:(rich(X)<=>(~humble(X)|wise(X))))&
(![X]:(wise(X)<=>(~kind(X)<~>~patient(X))))&
(![X]:((~strong(X)<~>~tall(X))<=>(~strong(X)<~>~calm(X))))&
(![X]:((~patient(X)|~calm(X))=>(rich(X)|tall(X))))&
(![X]:(kind(X)<=>(~generous(X)|~quiet(X))))&
((?[X]:((~generous(X)<~>rich(X))))<=>(?[X]:((wise(X)|generous(X)))))&
(![X]:((wise(X)|~rich(X))=>(wise(X)&~creative(X))))&
((?[X]:((~strong(X)|wise(X))))=>(?[X]:((~patient(X)<~>~humble(X)))))&
((~funny(john))<=>(~funny(mary)))&
(((curious(lucy)&old(lucy)))=>(~brave(john)))&
((?[X]:((~wise(X)<~>~tall(X))))<=>(?[X]:((~generous(X)|tall(X)))))&
(![X]:((creative(X)&~happy(X))=>(~strong(X)<~>brave(X))))&
(![X]:((tall(X)|kind(X))=>(~calm(X)<~>~happy(X))))&
(((tall(alice)&~quiet(alice)))<=>(?[X]:((rich(X)|old(X)))))&
(((humble(susan)<~>~creative(susan)))=>(?[X]:((~happy(X)|~creative(X)))))&
(?[X]:(brave(X)))&
((calm(john)&~creative(john)))&
((rich(paul)|generous(paul)))&
(?[X]:((~happy(X)<~>curious(X))))&
((~happy(alice)<~>~humble(alice)))&
(?[X]:((~happy(X)|rich(X))))&
(?[X]:((~old(X)<~>funny(X))))&
(?[X]:(happy(X))) | ~wise(alice) | [
"p1",
"p3",
"p7",
"p13",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 9052718544489112415317427
% SZS output start Proof for 9052718544489112415317427
2. ! [X0] : (rich(X0) <=> (wise(X0) | ~humble(X0))) [input p1]
4. ! [X0] : ((~strong(X0) <~> ~tall(X0)) <=> (~strong(X0) <~> ~calm(X0))) [input p3]
8. ! [X0] : ((~rich(X0) | wise(X0)) => (~creative(X0) & wise(X0))) [input p7]
14. ! [X0] : ((kind(X0) | tall(X0)) => (~calm(X0) <~> ~happy(X0))) [input p13]
15. (~quiet(alice) & tall(alice)) <=> ? [X0] : (old(X0) | rich(X0)) [input p14]
21. ~happy(alice) <~> ~humble(alice) [input p20]
25. ~wise(alice) [input hypothesis]
31. ! [X0] : ((~creative(X0) & wise(X0)) | (rich(X0) & ~wise(X0))) [ennf transformation 8]
37. ! [X0] : ((~calm(X0) <~> ~happy(X0)) | (~kind(X0) & ~tall(X0))) [ennf transformation 14]
41. ! [X0] : ((rich(X0) | (~wise(X0) & humble(X0))) & ((wise(X0) | ~humble(X0)) | ~rich(X0))) [nnf transformation 2]
42. ! [X0] : ((rich(X0) | (~wise(X0) & humble(X0))) & (wise(X0) | ~humble(X0) | ~rich(X0))) [flattening 41]
44. ! [X0] : ((((tall(X0) | strong(X0)) & (~tall(X0) | ~strong(X0))) | ((~strong(X0) | calm(X0)) & (~calm(X0) | strong(X0)))) & (((calm(X0) | strong(X0)) & (~calm(X0) | ~strong(X0))) | ((~strong(X0) | tall(X0)) & (~tall(X0) | strong(X0))))) [nnf transformation 4]
63. ! [X0] : (((happy(X0) | calm(X0)) & (~happy(X0) | ~calm(X0))) | (~kind(X0) & ~tall(X0))) [nnf transformation 37]
64. ((~quiet(alice) & tall(alice)) | ! [X0] : (~old(X0) & ~rich(X0))) & (? [X0] : (old(X0) | rich(X0)) | (quiet(alice) | ~tall(alice))) [nnf transformation 15]
65. ((~quiet(alice) & tall(alice)) | ! [X0] : (~old(X0) & ~rich(X0))) & (? [X0] : (old(X0) | rich(X0)) | quiet(alice) | ~tall(alice)) [flattening 64]
66. ((~quiet(alice) & tall(alice)) | ! [X0] : (~old(X0) & ~rich(X0))) & (? [X1] : (old(X1) | rich(X1)) | quiet(alice) | ~tall(alice)) [rectify 65]
67. ? [X1] : (old(X1) | rich(X1)) => (old(sK5) | rich(sK5)) [choice axiom]
68. ((~quiet(alice) & tall(alice)) | ! [X0] : (~old(X0) & ~rich(X0))) & ((old(sK5) | rich(sK5)) | quiet(alice) | ~tall(alice)) [skolemisation 66,67]
77. (humble(alice) | happy(alice)) & (~humble(alice) | ~happy(alice)) [nnf transformation 21]
88. ~rich(X0) | ~humble(X0) | wise(X0) [cnf transformation 42]
90. ~wise(X0) | rich(X0) [cnf transformation 42]
96. ~calm(X0) | ~strong(X0) | ~strong(X0) | tall(X0) [cnf transformation 44]
97. calm(X0) | strong(X0) | ~tall(X0) | strong(X0) [cnf transformation 44]
100. ~tall(X0) | ~strong(X0) | ~strong(X0) | calm(X0) [cnf transformation 44]
101. tall(X0) | strong(X0) | ~calm(X0) | strong(X0) [cnf transformation 44]
115. wise(X0) | rich(X0) [cnf transformation 31]
133. ~happy(X0) | ~calm(X0) | ~tall(X0) [cnf transformation 63]
138. tall(alice) | ~rich(X0) [cnf transformation 68]
151. humble(alice) | happy(alice) [cnf transformation 77]
156. ~wise(alice) [cnf transformation 25]
157. ~calm(X0) | ~strong(X0) | tall(X0) [duplicate literal removal 96]
158. calm(X0) | strong(X0) | ~tall(X0) [duplicate literal removal 97]
159. ~tall(X0) | ~strong(X0) | calm(X0) [duplicate literal removal 100]
160. tall(X0) | strong(X0) | ~calm(X0) [duplicate literal removal 101]
166. 2 <=> wise(alice) [avatar definition]
168. ~wise(alice) <- (~2) [avatar component clause 166]
176. ~tall(X0) | calm(X0) [subsumption resolution 158,159]
177. ~calm(X0) | tall(X0) [subsumption resolution 157,160]
213. rich(X0) [subsumption resolution 115,90]
286. ~happy(X0) | ~calm(X0) [subsumption resolution 133,177]
298. 30 <=> tall(alice) [avatar definition]
300. tall(alice) <- (30) [avatar component clause 298]
302. tall(alice) [subsumption resolution 138,213]
303. 30 [avatar split clause 302,298]
333. 37 <=> happy(alice) [avatar definition]
335. happy(alice) <- (37) [avatar component clause 333]
337. 38 <=> humble(alice) [avatar definition]
339. humble(alice) <- (38) [avatar component clause 337]
340. 37 | 38 [avatar split clause 151,337,333]
352. ~2 [avatar split clause 156,166]
359. calm(alice) <- (30) [resolution 176,300]
365. ~calm(alice) <- (37) [resolution 286,335]
366. $false <- (30, 37) [subsumption resolution 365,359]
367. ~30 | ~37 [avatar contradiction clause 366]
370. ~humble(X1) | wise(X1) [resolution 88,213]
371. wise(alice) <- (38) [resolution 370,339]
372. $false <- (~2, 38) [subsumption resolution 371,168]
373. 2 | ~38 [avatar contradiction clause 372]
374. $false [avatar sat refutation 303,340,352,367,373]
% SZS output end Proof for 9052718544489112415317427
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not humble or not creative is not creative.
Everyone who is both rich and not old is either wise or not calm and vice versa.
If someone is both not tall and calm then alice is not curious or not patient.
If susan is rich or creative then susan is both curious and generous and vice versa.
Everyone who is creative or not wise is not creative.
If lucy is not funny then paul is old and vice versa.
Everyone who is tall or strong is both not kind and creative.
Everyone who is either not brave or not funny is both not humble and generous and vice versa.
If john is either not wise or not rich then someone is not rich or patient.
Everyone who is both not brave and creative is either not rich or not creative and vice versa.
Everyone who is either calm or not tall is either old or not generous and vice versa.
If someone is quiet or generous then paul is not patient and vice versa.
If paul is strong then paul is humble or curious and vice versa.
Everyone who is both not brave and not creative is both not brave and happy.
Everyone who is both not strong and humble is either kind or not creative.
Everyone who is old is both brave and not funny.
Fred is wise or curious.
Mary is both not quiet and not kind.
Someone is both not calm and not old.
Someone is both not patient and not funny.
Someone is old or not old.
Someone is both generous and happy.
John is either not funny or wise.
Someone is not brave. | Lucy is tall. | contradiction | (![X]:((~humble(X)<~>~creative(X))=>~creative(X)))&
(![X]:((rich(X)&~old(X))<=>(wise(X)<~>~calm(X))))&
((?[X]:((~tall(X)&calm(X))))=>((~curious(alice)|~patient(alice))))&
(((rich(susan)|creative(susan)))<=>((curious(susan)&generous(susan))))&
(![X]:((creative(X)|~wise(X))=>~creative(X)))&
((~funny(lucy))<=>(old(paul)))&
(![X]:((tall(X)|strong(X))=>(~kind(X)&creative(X))))&
(![X]:((~brave(X)<~>~funny(X))<=>(~humble(X)&generous(X))))&
(((~wise(john)<~>~rich(john)))=>(?[X]:((~rich(X)|patient(X)))))&
(![X]:((~brave(X)&creative(X))<=>(~rich(X)<~>~creative(X))))&
(![X]:((calm(X)<~>~tall(X))<=>(old(X)<~>~generous(X))))&
((?[X]:((quiet(X)|generous(X))))<=>(~patient(paul)))&
((strong(paul))<=>((humble(paul)|curious(paul))))&
(![X]:((~brave(X)&~creative(X))=>(~brave(X)&happy(X))))&
(![X]:((~strong(X)&humble(X))=>(kind(X)<~>~creative(X))))&
(![X]:(old(X)=>(brave(X)&~funny(X))))&
((wise(fred)|curious(fred)))&
((~quiet(mary)&~kind(mary)))&
(?[X]:((~calm(X)&~old(X))))&
(?[X]:((~patient(X)&~funny(X))))&
(?[X]:((old(X)|~old(X))))&
(?[X]:((generous(X)&happy(X))))&
((~funny(john)<~>wise(john)))&
(?[X]:(~brave(X))) | tall(lucy) | [
"p4",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 5244315500742475667263746
% SZS output start Proof for 5244315500742475667263746
5. ! [X0] : ((~wise(X0) | creative(X0)) => ~creative(X0)) [input p4]
7. ! [X0] : ((strong(X0) | tall(X0)) => (creative(X0) & ~kind(X0))) [input p6]
25. tall(lucy) [input hypothesis]
31. ! [X0] : (~creative(X0) | (wise(X0) & ~creative(X0))) [ennf transformation 5]
32. ! [X0] : ((creative(X0) & ~kind(X0)) | (~strong(X0) & ~tall(X0))) [ennf transformation 7]
85. ~creative(X0) | ~creative(X0) [cnf transformation 31]
91. creative(X0) | ~tall(X0) [cnf transformation 32]
138. tall(lucy) [cnf transformation 25]
141. ~creative(X0) [duplicate literal removal 85]
187. ~tall(X0) [subsumption resolution 91,141]
251. $false [subsumption resolution 138,187]
% SZS output end Proof for 5244315500742475667263746
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is generous is both not happy and not patient and vice versa.
If someone is either wise or not quiet then fred is both tall and calm and vice versa.
If alice is either not quiet or not old then someone is both rich and not calm and vice versa.
Everyone who is both curious and not humble is either kind or not happy and vice versa.
Everyone who is not kind or tall is humble or not rich and vice versa.
If someone is not brave then paul is both not rich and humble and vice versa.
Everyone who is either not calm or not tall is not brave.
If someone is not humble or funny then lucy is not kind or wise.
If someone is both not wise and generous then someone is not kind and vice versa.
Everyone who is either not brave or not tall is either happy or not wise.
Everyone who is either rich or not funny is both creative and rich and vice versa.
If susan is both patient and not patient then someone is patient and vice versa.
If someone is generous then paul is creative or not funny.
If susan is both rich and old then paul is either generous or not humble.
Everyone who is not patient is not curious or not patient and vice versa.
If someone is not brave then susan is either generous or not quiet and vice versa.
Paul is calm or not happy.
Alice is both not curious and not rich.
Someone is not quiet.
Mary is brave or quiet.
Someone is both calm and humble.
Lucy is not rich. | Paul is not kind. | neutral | (![X]:(generous(X)<=>(~happy(X)&~patient(X))))&
((?[X]:((wise(X)<~>~quiet(X))))<=>((tall(fred)&calm(fred))))&
(((~quiet(alice)<~>~old(alice)))<=>(?[X]:((rich(X)&~calm(X)))))&
(![X]:((curious(X)&~humble(X))<=>(kind(X)<~>~happy(X))))&
(![X]:((~kind(X)|tall(X))<=>(humble(X)|~rich(X))))&
((?[X]:(~brave(X)))<=>((~rich(paul)&humble(paul))))&
(![X]:((~calm(X)<~>~tall(X))=>~brave(X)))&
((?[X]:((~humble(X)|funny(X))))=>((~kind(lucy)|wise(lucy))))&
((?[X]:((~wise(X)&generous(X))))<=>(?[X]:(~kind(X))))&
(![X]:((~brave(X)<~>~tall(X))=>(happy(X)<~>~wise(X))))&
(![X]:((rich(X)<~>~funny(X))<=>(creative(X)&rich(X))))&
(((patient(susan)&~patient(susan)))<=>(?[X]:(patient(X))))&
((?[X]:(generous(X)))=>((creative(paul)|~funny(paul))))&
(((rich(susan)&old(susan)))=>((generous(paul)<~>~humble(paul))))&
(![X]:(~patient(X)<=>(~curious(X)|~patient(X))))&
((?[X]:(~brave(X)))<=>((generous(susan)<~>~quiet(susan))))&
((calm(paul)|~happy(paul)))&
((~curious(alice)&~rich(alice)))&
(?[X]:(~quiet(X)))&
((brave(mary)|quiet(mary)))&
(?[X]:((calm(X)&humble(X))))&
(~rich(lucy)) | ~kind(paul) | [] | null | 0 |
Everyone who is either quiet or not wise is both not old and kind. If someone is either not kind or quiet then someone is not happy and vice versa. Everyone who is not happy is either curious or not curious and vice versa. Everyone who is both not funny and not happy is not happy or not tall. If paul is not creative or not funny then someone is both not generous and not creative. Everyone who is both quiet and not happy is funny. Everyone who is either not funny or old is not calm. Everyone who is not tall is both strong and not patient and vice versa. If someone is old or not happy then paul is both not curious and brave. Everyone who is patient or not funny is strong or not humble. Everyone who is either not rich or strong is not strong or not generous. If someone is both patient and not tall then someone is not brave or tall. If paul is either quiet or old then alice is not old or humble and vice versa. If someone is happy then someone is either calm or not wise. Everyone who is curious is either quiet or strong and vice versa. Everyone who is either tall or not brave is both generous and not funny and vice versa. Someone is rich or not wise. Someone is either not curious or not tall. Someone is not rich or quiet. Mary is not brave. Someone is not wise or wise. Someone is rich. Someone is both curious and not humble. John is either not rich or brave. | Mary is curious. | neutral | (![X]:((quiet(X)<~>~wise(X))=>(~old(X)&kind(X))))&
((?[X]:((~kind(X)<~>quiet(X))))<=>(?[X]:(~happy(X))))&
(![X]:(~happy(X)<=>(curious(X)<~>~curious(X))))&
(![X]:((~funny(X)&~happy(X))=>(~happy(X)|~tall(X))))&
(((~creative(paul)|~funny(paul)))=>(?[X]:((~generous(X)&~creative(X)))))&
(![X]:((quiet(X)&~happy(X))=>funny(X)))&
(![X]:((~funny(X)<~>old(X))=>~calm(X)))&
(![X]:(~tall(X)<=>(strong(X)&~patient(X))))&
((?[X]:((old(X)|~happy(X))))=>((~curious(paul)&brave(paul))))&
(![X]:((patient(X)|~funny(X))=>(strong(X)|~humble(X))))&
(![X]:((~rich(X)<~>strong(X))=>(~strong(X)|~generous(X))))&
((?[X]:((patient(X)&~tall(X))))=>(?[X]:((~brave(X)|tall(X)))))&
(((quiet(paul)<~>old(paul)))<=>((~old(alice)|humble(alice))))&
((?[X]:(happy(X)))=>(?[X]:((calm(X)<~>~wise(X)))))&
(![X]:(curious(X)<=>(quiet(X)<~>strong(X))))&
(![X]:((tall(X)<~>~brave(X))<=>(generous(X)&~funny(X))))&
(?[X]:((rich(X)|~wise(X))))&
(?[X]:((~curious(X)<~>~tall(X))))&
(?[X]:((~rich(X)|quiet(X))))&
(~brave(mary))&
(?[X]:((~wise(X)|wise(X))))&
(?[X]:(rich(X)))&
(?[X]:((curious(X)&~humble(X))))&
((~rich(john)<~>brave(john))) | curious(mary) | [] | null | 0 |
Everyone who is not creative or strong is either kind or wise. Everyone who is either wise or funny is either not old or old. Everyone who is tall is creative. If someone is both old and not happy then john is not rich or not patient. Everyone who is creative is curious and vice versa. If someone is generous or not patient then paul is either not curious or not creative. Everyone who is brave or not patient is not brave or brave. Everyone who is both brave and humble is not calm and vice versa. If someone is not humble or humble then mary is either not rich or not happy. Everyone who is both not patient and funny is both calm and not kind and vice versa. If alice is both not kind and not wise then mary is either not quiet or humble and vice versa. Everyone who is not humble is not generous. If paul is strong or curious then someone is not kind. If john is both generous and not generous then someone is tall or not funny. If someone is not quiet then fred is funny and vice versa. If someone is not tall then someone is not curious. Someone is not quiet. Fred is both not humble and happy. Paul is rich. Someone is creative. Someone is not rich or not generous. Someone is not quiet or strong. | John is curious. | neutral | (![X]:((~creative(X)|strong(X))=>(kind(X)<~>wise(X))))&
(![X]:((wise(X)<~>funny(X))=>(~old(X)<~>old(X))))&
(![X]:(tall(X)=>creative(X)))&
((?[X]:((old(X)&~happy(X))))=>((~rich(john)|~patient(john))))&
(![X]:(creative(X)<=>curious(X)))&
((?[X]:((generous(X)|~patient(X))))=>((~curious(paul)<~>~creative(paul))))&
(![X]:((brave(X)|~patient(X))=>(~brave(X)|brave(X))))&
(![X]:((brave(X)&humble(X))<=>~calm(X)))&
((?[X]:((~humble(X)|humble(X))))=>((~rich(mary)<~>~happy(mary))))&
(![X]:((~patient(X)&funny(X))<=>(calm(X)&~kind(X))))&
(((~kind(alice)&~wise(alice)))<=>((~quiet(mary)<~>humble(mary))))&
(![X]:(~humble(X)=>~generous(X)))&
(((strong(paul)|curious(paul)))=>(?[X]:(~kind(X))))&
(((generous(john)&~generous(john)))=>(?[X]:((tall(X)|~funny(X)))))&
((?[X]:(~quiet(X)))<=>(funny(fred)))&
((?[X]:(~tall(X)))=>(?[X]:(~curious(X))))&
(?[X]:(~quiet(X)))&
((~humble(fred)&happy(fred)))&
(rich(paul))&
(?[X]:(creative(X)))&
(?[X]:((~rich(X)|~generous(X))))&
(?[X]:((~quiet(X)|strong(X)))) | curious(john) | [] | null | 0 |
Everyone who is either not funny or old is both tall and not funny and vice versa.
If mary is strong then lucy is rich or creative.
If someone is humble or old then fred is either quiet or not happy and vice versa.
If susan is either not kind or wise then someone is both not rich and not humble and vice versa.
Everyone who is not old is rich and vice versa.
Everyone who is generous is curious and vice versa.
Everyone who is not old or kind is either quiet or not strong and vice versa.
Everyone who is either not creative or not kind is either generous or rich.
Everyone who is both curious and not generous is both not old and not rich and vice versa.
Everyone who is strong is old and vice versa.
Everyone who is either not strong or curious is happy or not old.
If someone is either not wise or not old then someone is either not wise or not tall.
Everyone who is curious or old is not generous or not patient.
Everyone who is creative or rich is either not kind or not generous and vice versa.
If someone is both patient and kind then alice is both tall and creative and vice versa.
If mary is not quiet then someone is not tall.
Someone is either strong or rich.
Someone is either funny or not quiet.
Someone is both not generous and brave.
Susan is rich or not creative.
Fred is quiet.
Someone is either not quiet or generous.
Someone is happy.
Someone is both not tall and old. | Fred is rich. | contradiction | (![X]:((~funny(X)<~>old(X))<=>(tall(X)&~funny(X))))&
((strong(mary))=>((rich(lucy)|creative(lucy))))&
((?[X]:((humble(X)|old(X))))<=>((quiet(fred)<~>~happy(fred))))&
(((~kind(susan)<~>wise(susan)))<=>(?[X]:((~rich(X)&~humble(X)))))&
(![X]:(~old(X)<=>rich(X)))&
(![X]:(generous(X)<=>curious(X)))&
(![X]:((~old(X)|kind(X))<=>(quiet(X)<~>~strong(X))))&
(![X]:((~creative(X)<~>~kind(X))=>(generous(X)<~>rich(X))))&
(![X]:((curious(X)&~generous(X))<=>(~old(X)&~rich(X))))&
(![X]:(strong(X)<=>old(X)))&
(![X]:((~strong(X)<~>curious(X))=>(happy(X)|~old(X))))&
((?[X]:((~wise(X)<~>~old(X))))=>(?[X]:((~wise(X)<~>~tall(X)))))&
(![X]:((curious(X)|old(X))=>(~generous(X)|~patient(X))))&
(![X]:((creative(X)|rich(X))<=>(~kind(X)<~>~generous(X))))&
((?[X]:((patient(X)&kind(X))))<=>((tall(alice)&creative(alice))))&
((~quiet(mary))=>(?[X]:(~tall(X))))&
(?[X]:((strong(X)<~>rich(X))))&
(?[X]:((funny(X)<~>~quiet(X))))&
(?[X]:((~generous(X)&brave(X))))&
((rich(susan)|~creative(susan)))&
(quiet(fred))&
(?[X]:((~quiet(X)<~>generous(X))))&
(?[X]:(happy(X)))&
(?[X]:((~tall(X)&old(X)))) | rich(fred) | [
"p4",
"p6",
"p9",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 151577886033283994345642
% SZS output start Proof for 151577886033283994345642
5. ! [X0] : (~old(X0) <=> rich(X0)) [input p4]
7. ! [X0] : ((kind(X0) | ~old(X0)) <=> (quiet(X0) <~> ~strong(X0))) [input p6]
10. ! [X0] : (strong(X0) <=> old(X0)) [input p9]
21. quiet(fred) [input p20]
25. rich(fred) [input hypothesis]
47. ! [X0] : ((~old(X0) | ~rich(X0)) & (rich(X0) | old(X0))) [nnf transformation 5]
49. ! [X0] : (((kind(X0) | ~old(X0)) | ((quiet(X0) | strong(X0)) & (~strong(X0) | ~quiet(X0)))) & (((strong(X0) | ~quiet(X0)) & (~strong(X0) | quiet(X0))) | (~kind(X0) & old(X0)))) [nnf transformation 7]
50. ! [X0] : ((kind(X0) | ~old(X0) | ((quiet(X0) | strong(X0)) & (~strong(X0) | ~quiet(X0)))) & (((strong(X0) | ~quiet(X0)) & (~strong(X0) | quiet(X0))) | (~kind(X0) & old(X0)))) [flattening 49]
54. ! [X0] : ((strong(X0) | ~old(X0)) & (old(X0) | ~strong(X0))) [nnf transformation 10]
104. ~rich(X0) | ~old(X0) [cnf transformation 47]
109. ~quiet(X0) | strong(X0) | old(X0) [cnf transformation 50]
121. ~strong(X0) | old(X0) [cnf transformation 54]
148. quiet(fred) [cnf transformation 21]
154. rich(fred) [cnf transformation 25]
175. 5 <=> quiet(fred) [avatar definition]
177. quiet(fred) <- (5) [avatar component clause 175]
304. 5 [avatar split clause 148,175]
317. ~old(fred) [resolution 104,154]
363. strong(fred) | old(fred) <- (5) [resolution 109,177]
365. strong(fred) <- (5) [subsumption resolution 363,317]
368. old(fred) <- (5) [resolution 365,121]
369. $false <- (5) [subsumption resolution 368,317]
370. ~5 [avatar contradiction clause 369]
371. $false [avatar sat refutation 304,370]
% SZS output end Proof for 151577886033283994345642
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If someone is either rich or not old then someone is both generous and not creative. If someone is both happy and creative then someone is humble and vice versa. Everyone who is not happy is both not creative and not happy and vice versa. If someone is either not humble or not kind then paul is either not kind or humble and vice versa. Everyone who is both calm and not kind is either not funny or calm and vice versa. If paul is either happy or not patient then john is either not quiet or not patient and vice versa. If someone is not patient or not calm then fred is both not rich and old and vice versa. Everyone who is not patient is both not curious and not old. If someone is not tall then someone is either not rich or not quiet and vice versa. Everyone who is not funny is patient or not generous. Everyone who is either humble or generous is both not humble and wise and vice versa. Everyone who is patient is either wise or quiet and vice versa. Everyone who is not rich or not quiet is not tall or not funny. Everyone who is both not funny and not happy is patient or not tall and vice versa. Everyone who is brave is not humble and vice versa. If alice is funny or not calm then paul is either old or kind. Someone is either not creative or not quiet. Lucy is not calm. Someone is rich or not tall. Someone is not brave. Paul is both not happy and wise. Mary is both not calm and creative. Someone is either not patient or patient. Alice is both rich and funny. | Paul is not old. | entailment | ((?[X]:((rich(X)<~>~old(X))))=>(?[X]:((generous(X)&~creative(X)))))&
((?[X]:((happy(X)&creative(X))))<=>(?[X]:(humble(X))))&
(![X]:(~happy(X)<=>(~creative(X)&~happy(X))))&
((?[X]:((~humble(X)<~>~kind(X))))<=>((~kind(paul)<~>humble(paul))))&
(![X]:((calm(X)&~kind(X))<=>(~funny(X)<~>calm(X))))&
(((happy(paul)<~>~patient(paul)))<=>((~quiet(john)<~>~patient(john))))&
((?[X]:((~patient(X)|~calm(X))))<=>((~rich(fred)&old(fred))))&
(![X]:(~patient(X)=>(~curious(X)&~old(X))))&
((?[X]:(~tall(X)))<=>(?[X]:((~rich(X)<~>~quiet(X)))))&
(![X]:(~funny(X)=>(patient(X)|~generous(X))))&
(![X]:((humble(X)<~>generous(X))<=>(~humble(X)&wise(X))))&
(![X]:(patient(X)<=>(wise(X)<~>quiet(X))))&
(![X]:((~rich(X)|~quiet(X))=>(~tall(X)|~funny(X))))&
(![X]:((~funny(X)&~happy(X))<=>(patient(X)|~tall(X))))&
(![X]:(brave(X)<=>~humble(X)))&
(((funny(alice)|~calm(alice)))=>((old(paul)<~>kind(paul))))&
(?[X]:((~creative(X)<~>~quiet(X))))&
(~calm(lucy))&
(?[X]:((rich(X)|~tall(X))))&
(?[X]:(~brave(X)))&
((~happy(paul)&wise(paul)))&
((~calm(mary)&creative(mary)))&
(?[X]:((~patient(X)<~>patient(X))))&
((rich(alice)&funny(alice))) | ~old(paul) | [
"p4",
"p7",
"p13",
"p15",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 5152462422993369487459492
% SZS output start Proof for 5152462422993369487459492
5. ! [X0] : ((~kind(X0) & calm(X0)) <=> (~funny(X0) <~> calm(X0))) [input p4]
8. ! [X0] : (~patient(X0) => (~old(X0) & ~curious(X0))) [input p7]
14. ! [X0] : ((~happy(X0) & ~funny(X0)) <=> (~tall(X0) | patient(X0))) [input p13]
16. (~calm(alice) | funny(alice)) => (old(paul) <~> kind(paul)) [input p15]
24. funny(alice) & rich(alice) [input p23]
25. old(paul) [input hypothesis]
30. ! [X0] : (~patient(X0) => ~old(X0)) [pure predicate removal 8]
32. ! [X0] : (~old(X0) | patient(X0)) [ennf transformation 30]
38. (old(paul) <~> kind(paul)) | (calm(alice) & ~funny(alice)) [ennf transformation 16]
54. ! [X0] : (((~kind(X0) & calm(X0)) | ((~funny(X0) | ~calm(X0)) & (calm(X0) | funny(X0)))) & (((~calm(X0) | funny(X0)) & (calm(X0) | ~funny(X0))) | (kind(X0) | ~calm(X0)))) [nnf transformation 5]
55. ! [X0] : (((~kind(X0) & calm(X0)) | ((~funny(X0) | ~calm(X0)) & (calm(X0) | funny(X0)))) & (((~calm(X0) | funny(X0)) & (calm(X0) | ~funny(X0))) | kind(X0) | ~calm(X0))) [flattening 54]
70. ! [X0] : (((~happy(X0) & ~funny(X0)) | (tall(X0) & ~patient(X0))) & ((~tall(X0) | patient(X0)) | (happy(X0) | funny(X0)))) [nnf transformation 14]
71. ! [X0] : (((~happy(X0) & ~funny(X0)) | (tall(X0) & ~patient(X0))) & (~tall(X0) | patient(X0) | happy(X0) | funny(X0))) [flattening 70]
72. ((~kind(paul) | ~old(paul)) & (kind(paul) | old(paul))) | (calm(alice) & ~funny(alice)) [nnf transformation 38]
102. ~calm(X0) | funny(X0) | kind(X0) | ~calm(X0) [cnf transformation 55]
103. calm(X0) | calm(X0) | funny(X0) [cnf transformation 55]
120. ~old(X0) | patient(X0) [cnf transformation 32]
139. ~patient(X0) | ~funny(X0) [cnf transformation 71]
146. ~kind(paul) | ~old(paul) | ~funny(alice) [cnf transformation 72]
160. funny(alice) [cnf transformation 24]
161. old(paul) [cnf transformation 25]
164. ~calm(X0) | funny(X0) | kind(X0) [duplicate literal removal 102]
165. funny(X0) | calm(X0) [duplicate literal removal 103]
210. 11 <=> kind(paul) [avatar definition]
212. ~kind(paul) <- (~11) [avatar component clause 210]
235. funny(X0) | kind(X0) [subsumption resolution 164,165]
249. 19 <=> patient(paul) [avatar definition]
251. patient(paul) <- (19) [avatar component clause 249]
317. 33 <=> old(paul) [avatar definition]
318. old(paul) <- (33) [avatar component clause 317]
322. 34 <=> funny(alice) [avatar definition]
325. ~34 | ~33 | ~11 [avatar split clause 146,210,317,322]
348. 34 [avatar split clause 160,322]
349. 33 [avatar split clause 161,317]
367. patient(paul) <- (33) [resolution 120,318]
370. 19 | ~33 [avatar split clause 367,317,249]
371. ~funny(paul) <- (19) [resolution 139,251]
385. kind(paul) <- (19) [resolution 235,371]
386. $false <- (~11, 19) [subsumption resolution 385,212]
387. 11 | ~19 [avatar contradiction clause 386]
388. $false [avatar sat refutation 325,348,349,370,387]
% SZS output end Proof for 5152462422993369487459492
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not generous and not wise is not wise or not kind and vice versa. If someone is not brave or kind then someone is not rich. If someone is either happy or not wise then paul is both strong and quiet and vice versa. If someone is not calm or not brave then someone is not funny. Everyone who is both rich and not generous is not calm and vice versa. Everyone who is both strong and kind is old. If someone is either patient or not curious then paul is tall and vice versa. Everyone who is not funny or tall is both funny and not wise. If someone is either not patient or old then someone is both not funny and rich. If john is either not curious or not strong then someone is strong and vice versa. If someone is kind then paul is either not strong or humble and vice versa. If someone is either not tall or wise then someone is kind and vice versa. If alice is calm then john is either kind or wise and vice versa. If paul is both not patient and not wise then someone is not creative or quiet and vice versa. Everyone who is both wise and brave is strong or not happy and vice versa. If someone is not happy then susan is either old or humble. Someone is both not kind and old. Mary is generous or brave. Someone is not kind or funny. Someone is not rich or not kind. Someone is either happy or not old. Paul is not curious. Someone is either quiet or rich. | John is rich. | contradiction | (![X]:((~generous(X)&~wise(X))<=>(~wise(X)|~kind(X))))&
((?[X]:((~brave(X)|kind(X))))=>(?[X]:(~rich(X))))&
((?[X]:((happy(X)<~>~wise(X))))<=>((strong(paul)&quiet(paul))))&
((?[X]:((~calm(X)|~brave(X))))=>(?[X]:(~funny(X))))&
(![X]:((rich(X)&~generous(X))<=>~calm(X)))&
(![X]:((strong(X)&kind(X))=>old(X)))&
((?[X]:((patient(X)<~>~curious(X))))<=>(tall(paul)))&
(![X]:((~funny(X)|tall(X))=>(funny(X)&~wise(X))))&
((?[X]:((~patient(X)<~>old(X))))=>(?[X]:((~funny(X)&rich(X)))))&
(((~curious(john)<~>~strong(john)))<=>(?[X]:(strong(X))))&
((?[X]:(kind(X)))<=>((~strong(paul)<~>humble(paul))))&
((?[X]:((~tall(X)<~>wise(X))))<=>(?[X]:(kind(X))))&
((calm(alice))<=>((kind(john)<~>wise(john))))&
(((~patient(paul)&~wise(paul)))<=>(?[X]:((~creative(X)|quiet(X)))))&
(![X]:((wise(X)&brave(X))<=>(strong(X)|~happy(X))))&
((?[X]:(~happy(X)))=>((old(susan)<~>humble(susan))))&
(?[X]:((~kind(X)&old(X))))&
((generous(mary)|brave(mary)))&
(?[X]:((~kind(X)|funny(X))))&
(?[X]:((~rich(X)|~kind(X))))&
(?[X]:((happy(X)<~>~old(X))))&
(~curious(paul))&
(?[X]:((quiet(X)<~>rich(X)))) | rich(john) | [
"p0",
"p3",
"p4",
"p7",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 3619490561764493442254825
% SZS output start Proof for 3619490561764493442254825
1. ! [X0] : ((~wise(X0) & ~generous(X0)) <=> (~kind(X0) | ~wise(X0))) [input p0]
4. ? [X0] : (~brave(X0) | ~calm(X0)) => ? [X0] : ~funny(X0) [input p3]
5. ! [X0] : ((~generous(X0) & rich(X0)) <=> ~calm(X0)) [input p4]
8. ! [X0] : ((tall(X0) | ~funny(X0)) => (~wise(X0) & funny(X0))) [input p7]
13. calm(alice) <=> (kind(john) <~> wise(john)) [input p12]
24. rich(john) [input hypothesis]
26. ? [X0] : (~brave(X0) | ~calm(X0)) => ? [X1] : ~funny(X1) [rectify 4]
30. ? [X1] : ~funny(X1) | ! [X0] : (brave(X0) & calm(X0)) [ennf transformation 26]
33. ! [X0] : ((~wise(X0) & funny(X0)) | (~tall(X0) & funny(X0))) [ennf transformation 8]
36. ! [X0] : (((~wise(X0) & ~generous(X0)) | (kind(X0) & wise(X0))) & ((~kind(X0) | ~wise(X0)) | (wise(X0) | generous(X0)))) [nnf transformation 1]
37. ! [X0] : (((~wise(X0) & ~generous(X0)) | (kind(X0) & wise(X0))) & (~kind(X0) | ~wise(X0) | wise(X0) | generous(X0))) [flattening 36]
46. ? [X0] : ~funny(X0) | ! [X1] : (brave(X1) & calm(X1)) [rectify 30]
47. ? [X0] : ~funny(X0) => ~funny(sK2) [choice axiom]
48. ~funny(sK2) | ! [X1] : (brave(X1) & calm(X1)) [skolemisation 46,47]
49. ! [X0] : (((~generous(X0) & rich(X0)) | calm(X0)) & (~calm(X0) | (generous(X0) | ~rich(X0)))) [nnf transformation 5]
50. ! [X0] : (((~generous(X0) & rich(X0)) | calm(X0)) & (~calm(X0) | generous(X0) | ~rich(X0))) [flattening 49]
72. (calm(alice) | ((kind(john) | ~wise(john)) & (wise(john) | ~kind(john)))) & (((~wise(john) | ~kind(john)) & (wise(john) | kind(john))) | ~calm(alice)) [nnf transformation 13]
94. ~generous(X0) | wise(X0) [cnf transformation 37]
97. ~wise(X0) | kind(X0) [cnf transformation 37]
106. ~funny(sK2) | calm(X1) [cnf transformation 48]
108. ~calm(X0) | generous(X0) | ~rich(X0) [cnf transformation 50]
116. funny(X0) | funny(X0) [cnf transformation 33]
137. ~wise(john) | ~kind(john) | ~calm(alice) [cnf transformation 72]
162. rich(john) [cnf transformation 24]
163. funny(X0) [duplicate literal removal 116]
205. 10 <=> funny(sK2) [avatar definition]
207. ~funny(sK2) <- (~10) [avatar component clause 205]
210. 11 <=> ! [X1] : calm(X1) [avatar definition]
211. calm(X1) <- (11) [avatar component clause 210]
212. 11 | ~10 [avatar split clause 106,205,210]
307. 31 <=> wise(john) [avatar definition]
308. ~wise(john) <- (~31) [avatar component clause 307]
311. 32 <=> calm(alice) [avatar definition]
312. ~calm(alice) <- (~32) [avatar component clause 311]
315. ~wise(john) | ~calm(alice) [subsumption resolution 137,97]
316. ~32 | ~31 [avatar split clause 315,307,311]
398. $false <- (~10) [subsumption resolution 207,163]
399. 10 [avatar contradiction clause 398]
401. $false <- (11, ~32) [resolution 312,211]
402. ~11 | 32 [avatar contradiction clause 401]
427. ~rich(X1) | generous(X1) <- (11) [resolution 108,211]
430. generous(john) <- (11) [resolution 427,162]
433. wise(john) <- (11) [resolution 430,94]
434. $false <- (11, ~31) [subsumption resolution 433,308]
435. ~11 | 31 [avatar contradiction clause 434]
436. $false [avatar sat refutation 212,316,399,402,435]
% SZS output end Proof for 3619490561764493442254825
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy and strong is not wise or not calm.
If fred is both not brave and not humble then someone is not quiet or calm.
Everyone who is both curious and generous is not curious.
If someone is kind or funny then john is either strong or kind.
If susan is calm then someone is not funny or not quiet.
If someone is both not kind and creative then someone is both generous and brave.
Everyone who is both wise and not happy is both not tall and happy and vice versa.
Everyone who is brave is both not rich and brave and vice versa.
Everyone who is wise is both not rich and generous.
Everyone who is generous or quiet is either brave or not curious and vice versa.
If someone is either patient or not generous then susan is old or humble.
Everyone who is either not funny or quiet is not humble.
If someone is patient or not creative then fred is humble.
If paul is either not strong or strong then paul is either tall or old and vice versa.
Everyone who is either not rich or not quiet is both not old and quiet and vice versa.
If someone is not tall then someone is both old and quiet.
John is happy.
Paul is happy or patient.
Someone is both not rich and calm.
Fred is either happy or not kind.
John is either not kind or patient.
Susan is both not generous and old.
Susan is not old or not curious.
Someone is not brave or old. | John is not tall. | contradiction | (![X]:((~happy(X)&strong(X))=>(~wise(X)|~calm(X))))&
(((~brave(fred)&~humble(fred)))=>(?[X]:((~quiet(X)|calm(X)))))&
(![X]:((curious(X)&generous(X))=>~curious(X)))&
((?[X]:((kind(X)|funny(X))))=>((strong(john)<~>kind(john))))&
((calm(susan))=>(?[X]:((~funny(X)|~quiet(X)))))&
((?[X]:((~kind(X)&creative(X))))=>(?[X]:((generous(X)&brave(X)))))&
(![X]:((wise(X)&~happy(X))<=>(~tall(X)&happy(X))))&
(![X]:(brave(X)<=>(~rich(X)&brave(X))))&
(![X]:(wise(X)=>(~rich(X)&generous(X))))&
(![X]:((generous(X)|quiet(X))<=>(brave(X)<~>~curious(X))))&
((?[X]:((patient(X)<~>~generous(X))))=>((old(susan)|humble(susan))))&
(![X]:((~funny(X)<~>quiet(X))=>~humble(X)))&
((?[X]:((patient(X)|~creative(X))))=>(humble(fred)))&
(((~strong(paul)<~>strong(paul)))<=>((tall(paul)<~>old(paul))))&
(![X]:((~rich(X)<~>~quiet(X))<=>(~old(X)&quiet(X))))&
((?[X]:(~tall(X)))=>(?[X]:((old(X)&quiet(X)))))&
(happy(john))&
((happy(paul)|patient(paul)))&
(?[X]:((~rich(X)&calm(X))))&
((happy(fred)<~>~kind(fred)))&
((~kind(john)<~>patient(john)))&
((~generous(susan)&old(susan)))&
((~old(susan)|~curious(susan)))&
(?[X]:((~brave(X)|old(X)))) | ~tall(john) | [
"p6",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 6493654172915104250542637
% SZS output start Proof for 6493654172915104250542637
7. ! [X0] : ((~happy(X0) & wise(X0)) <=> (happy(X0) & ~tall(X0))) [input p6]
17. happy(john) [input p16]
25. ~tall(john) [input hypothesis]
51. ! [X0] : (((~happy(X0) & wise(X0)) | (~happy(X0) | tall(X0))) & ((happy(X0) & ~tall(X0)) | (happy(X0) | ~wise(X0)))) [nnf transformation 7]
52. ! [X0] : (((~happy(X0) & wise(X0)) | ~happy(X0) | tall(X0)) & ((happy(X0) & ~tall(X0)) | happy(X0) | ~wise(X0))) [flattening 51]
84. ~happy(X0) | ~happy(X0) | tall(X0) [cnf transformation 52]
118. happy(john) [cnf transformation 17]
130. ~tall(john) [cnf transformation 25]
138. ~happy(X0) | tall(X0) [duplicate literal removal 84]
298. tall(john) [resolution 138,118]
300. $false [subsumption resolution 298,130]
% SZS output end Proof for 6493654172915104250542637
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or not kind is both not wise and brave.
Everyone who is not curious or not quiet is either not patient or humble.
If paul is not wise or generous then fred is either not strong or not tall.
Everyone who is both brave and generous is either rich or kind and vice versa.
If fred is both not calm and not rich then someone is not strong or quiet and vice versa.
Everyone who is not calm or not creative is not tall.
Everyone who is wise is either not strong or calm.
Everyone who is not brave or creative is either humble or not creative.
If someone is not funny then john is humble or tall and vice versa.
Everyone who is both rich and not creative is funny or not tall.
If someone is quiet then lucy is tall.
Everyone who is not calm is not quiet or happy.
Everyone who is tall is curious and vice versa.
Everyone who is either tall or humble is curious and vice versa.
If paul is not happy or wise then paul is either humble or not strong and vice versa.
If lucy is either not kind or not funny then fred is both wise and not rich and vice versa.
Alice is not funny or calm.
Someone is brave.
Someone is both brave and not kind.
Susan is not generous or not funny.
Susan is rich or not generous.
Someone is not humble or not tall. | Fred is quiet. | contradiction | (![X]:((funny(X)|~kind(X))=>(~wise(X)&brave(X))))&
(![X]:((~curious(X)|~quiet(X))=>(~patient(X)<~>humble(X))))&
(((~wise(paul)|generous(paul)))=>((~strong(fred)<~>~tall(fred))))&
(![X]:((brave(X)&generous(X))<=>(rich(X)<~>kind(X))))&
(((~calm(fred)&~rich(fred)))<=>(?[X]:((~strong(X)|quiet(X)))))&
(![X]:((~calm(X)|~creative(X))=>~tall(X)))&
(![X]:(wise(X)=>(~strong(X)<~>calm(X))))&
(![X]:((~brave(X)|creative(X))=>(humble(X)<~>~creative(X))))&
((?[X]:(~funny(X)))<=>((humble(john)|tall(john))))&
(![X]:((rich(X)&~creative(X))=>(funny(X)|~tall(X))))&
((?[X]:(quiet(X)))=>(tall(lucy)))&
(![X]:(~calm(X)=>(~quiet(X)|happy(X))))&
(![X]:(tall(X)<=>curious(X)))&
(![X]:((tall(X)<~>humble(X))<=>curious(X)))&
(((~happy(paul)|wise(paul)))<=>((humble(paul)<~>~strong(paul))))&
(((~kind(lucy)<~>~funny(lucy)))<=>((wise(fred)&~rich(fred))))&
((~funny(alice)|calm(alice)))&
(?[X]:(brave(X)))&
(?[X]:((brave(X)&~kind(X))))&
((~generous(susan)|~funny(susan)))&
((rich(susan)|~generous(susan)))&
(?[X]:((~humble(X)|~tall(X)))) | quiet(fred) | [
"p5",
"p7",
"p10",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5867477123302851900354217
% SZS output start Proof for 5867477123302851900354217
6. ! [X0] : ((~creative(X0) | ~calm(X0)) => ~tall(X0)) [input p5]
8. ! [X0] : ((creative(X0) | ~brave(X0)) => (humble(X0) <~> ~creative(X0))) [input p7]
11. ? [X0] : quiet(X0) => tall(lucy) [input p10]
13. ! [X0] : (tall(X0) <=> curious(X0)) [input p12]
14. ! [X0] : ((tall(X0) <~> humble(X0)) <=> curious(X0)) [input p13]
23. quiet(fred) [input hypothesis]
27. ! [X0] : (~tall(X0) | (creative(X0) & calm(X0))) [ennf transformation 6]
29. ! [X0] : ((humble(X0) <~> ~creative(X0)) | (~creative(X0) & brave(X0))) [ennf transformation 8]
32. tall(lucy) | ! [X0] : ~quiet(X0) [ennf transformation 11]
45. ! [X0] : (((creative(X0) | ~humble(X0)) & (~creative(X0) | humble(X0))) | (~creative(X0) & brave(X0))) [nnf transformation 29]
51. ! [X0] : ((tall(X0) | ~curious(X0)) & (curious(X0) | ~tall(X0))) [nnf transformation 13]
52. ! [X0] : ((((~humble(X0) | ~tall(X0)) & (humble(X0) | tall(X0))) | ~curious(X0)) & (curious(X0) | ((tall(X0) | ~humble(X0)) & (humble(X0) | ~tall(X0))))) [nnf transformation 14]
87. ~tall(X0) | creative(X0) [cnf transformation 27]
91. ~creative(X0) | humble(X0) | ~creative(X0) [cnf transformation 45]
98. tall(lucy) | ~quiet(X0) [cnf transformation 32]
100. ~tall(X0) | curious(X0) [cnf transformation 51]
105. ~humble(X0) | ~tall(X0) | ~curious(X0) [cnf transformation 52]
125. quiet(fred) [cnf transformation 23]
126. ~creative(X0) | humble(X0) [duplicate literal removal 91]
150. 5 <=> ! [X0] : ~quiet(X0) [avatar definition]
151. ~quiet(X0) <- (5) [avatar component clause 150]
195. 15 <=> tall(lucy) [avatar definition]
197. tall(lucy) <- (15) [avatar component clause 195]
198. 5 | 15 [avatar split clause 98,195,150]
199. ~tall(X0) | ~humble(X0) [subsumption resolution 105,100]
260. $false <- (5) [resolution 151,125]
261. ~5 [avatar contradiction clause 260]
265. creative(lucy) <- (15) [resolution 87,197]
269. humble(lucy) <- (15) [resolution 126,265]
274. ~humble(lucy) <- (15) [resolution 199,197]
277. $false <- (15) [subsumption resolution 274,269]
278. ~15 [avatar contradiction clause 277]
279. $false [avatar sat refutation 198,261,278]
% SZS output end Proof for 5867477123302851900354217
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either creative or not happy then fred is not kind or strong. Everyone who is not tall is not kind and vice versa. Everyone who is curious is both rich and not patient and vice versa. Everyone who is not quiet is either not tall or calm. If someone is both calm and curious then john is either strong or not kind and vice versa. Everyone who is not wise is creative or funny and vice versa. If someone is wise then someone is wise or kind and vice versa. If someone is not brave or patient then john is either brave or happy. If someone is both wise and not patient then someone is both wise and calm and vice versa. Everyone who is both calm and not humble is both happy and not calm and vice versa. If someone is either not wise or patient then someone is either not wise or funny. If someone is both quiet and not quiet then someone is both not creative and not wise and vice versa. Everyone who is either brave or not creative is either not rich or kind and vice versa. Everyone who is wise is rich or not brave. Everyone who is not humble or not funny is both not brave and not quiet and vice versa. Everyone who is generous is either not brave or strong and vice versa. Alice is not happy or rich. Lucy is not humble or not happy. Alice is not patient or not old. Someone is both not kind and not humble. Fred is both not old and not kind. Alice is not patient. Someone is either not calm or generous. Someone is either not rich or strong. | Lucy is happy. | contradiction | ((?[X]:((creative(X)<~>~happy(X))))=>((~kind(fred)|strong(fred))))&
(![X]:(~tall(X)<=>~kind(X)))&
(![X]:(curious(X)<=>(rich(X)&~patient(X))))&
(![X]:(~quiet(X)=>(~tall(X)<~>calm(X))))&
((?[X]:((calm(X)&curious(X))))<=>((strong(john)<~>~kind(john))))&
(![X]:(~wise(X)<=>(creative(X)|funny(X))))&
((?[X]:(wise(X)))<=>(?[X]:((wise(X)|kind(X)))))&
((?[X]:((~brave(X)|patient(X))))=>((brave(john)<~>happy(john))))&
((?[X]:((wise(X)&~patient(X))))<=>(?[X]:((wise(X)&calm(X)))))&
(![X]:((calm(X)&~humble(X))<=>(happy(X)&~calm(X))))&
((?[X]:((~wise(X)<~>patient(X))))=>(?[X]:((~wise(X)<~>funny(X)))))&
((?[X]:((quiet(X)&~quiet(X))))<=>(?[X]:((~creative(X)&~wise(X)))))&
(![X]:((brave(X)<~>~creative(X))<=>(~rich(X)<~>kind(X))))&
(![X]:(wise(X)=>(rich(X)|~brave(X))))&
(![X]:((~humble(X)|~funny(X))<=>(~brave(X)&~quiet(X))))&
(![X]:(generous(X)<=>(~brave(X)<~>strong(X))))&
((~happy(alice)|rich(alice)))&
((~humble(lucy)|~happy(lucy)))&
((~patient(alice)|~old(alice)))&
(?[X]:((~kind(X)&~humble(X))))&
((~old(fred)&~kind(fred)))&
(~patient(alice))&
(?[X]:((~calm(X)<~>generous(X))))&
(?[X]:((~rich(X)<~>strong(X)))) | happy(lucy) | [
"p9",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 5315522643150644633952788
% SZS output start Proof for 5315522643150644633952788
10. ! [X0] : ((~humble(X0) & calm(X0)) <=> (~calm(X0) & happy(X0))) [input p9]
18. ~happy(lucy) | ~humble(lucy) [input p17]
25. happy(lucy) [input hypothesis]
61. ! [X0] : (((~humble(X0) & calm(X0)) | (calm(X0) | ~happy(X0))) & ((~calm(X0) & happy(X0)) | (humble(X0) | ~calm(X0)))) [nnf transformation 10]
62. ! [X0] : (((~humble(X0) & calm(X0)) | calm(X0) | ~happy(X0)) & ((~calm(X0) & happy(X0)) | humble(X0) | ~calm(X0))) [flattening 61]
114. ~calm(X0) | humble(X0) | ~calm(X0) [cnf transformation 62]
115. calm(X0) | calm(X0) | ~happy(X0) [cnf transformation 62]
144. ~happy(lucy) | ~humble(lucy) [cnf transformation 18]
153. happy(lucy) [cnf transformation 25]
154. ~calm(X0) | humble(X0) [duplicate literal removal 114]
155. ~happy(X0) | calm(X0) [duplicate literal removal 115]
303. 33 <=> humble(lucy) [avatar definition]
305. ~humble(lucy) <- (~33) [avatar component clause 303]
307. 34 <=> happy(lucy) [avatar definition]
308. happy(lucy) <- (34) [avatar component clause 307]
310. ~33 | ~34 [avatar split clause 144,307,303]
332. 34 [avatar split clause 153,307]
338. calm(lucy) <- (34) [resolution 155,308]
339. humble(lucy) <- (34) [resolution 338,154]
340. $false <- (~33, 34) [subsumption resolution 339,305]
341. 33 | ~34 [avatar contradiction clause 340]
342. $false [avatar sat refutation 310,332,341]
% SZS output end Proof for 5315522643150644633952788
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not patient or brave is both not rich and rich.
Everyone who is both not curious and happy is either old or funny.
Everyone who is either not rich or not strong is not curious or wise and vice versa.
Everyone who is not strong or curious is wise.
Everyone who is not generous or not brave is both not quiet and not patient.
If mary is not funny or not creative then mary is not funny or calm.
If someone is either not humble or patient then someone is brave or not tall and vice versa.
If susan is not rich then susan is not calm and vice versa.
If someone is funny or tall then mary is both not creative and quiet.
If susan is not tall or not rich then lucy is not old.
Everyone who is brave or creative is brave.
Everyone who is both not wise and not old is not funny and vice versa.
Everyone who is both not patient and creative is not curious or not kind and vice versa.
If someone is not curious or not old then someone is either not happy or not old and vice versa.
If someone is either calm or humble then someone is either old or not tall.
Everyone who is not strong or happy is not calm and vice versa.
John is either humble or not brave.
Someone is not old or not calm.
Mary is patient or funny.
Alice is quiet or patient.
Fred is both generous and not curious. | Mary is creative. | contradiction | (![X]:((~patient(X)<~>brave(X))=>(~rich(X)&rich(X))))&
(![X]:((~curious(X)&happy(X))=>(old(X)<~>funny(X))))&
(![X]:((~rich(X)<~>~strong(X))<=>(~curious(X)|wise(X))))&
(![X]:((~strong(X)|curious(X))=>wise(X)))&
(![X]:((~generous(X)|~brave(X))=>(~quiet(X)&~patient(X))))&
(((~funny(mary)|~creative(mary)))=>((~funny(mary)|calm(mary))))&
((?[X]:((~humble(X)<~>patient(X))))<=>(?[X]:((brave(X)|~tall(X)))))&
((~rich(susan))<=>(~calm(susan)))&
((?[X]:((funny(X)|tall(X))))=>((~creative(mary)&quiet(mary))))&
(((~tall(susan)|~rich(susan)))=>(~old(lucy)))&
(![X]:((brave(X)|creative(X))=>brave(X)))&
(![X]:((~wise(X)&~old(X))<=>~funny(X)))&
(![X]:((~patient(X)&creative(X))<=>(~curious(X)|~kind(X))))&
((?[X]:((~curious(X)|~old(X))))<=>(?[X]:((~happy(X)<~>~old(X)))))&
((?[X]:((calm(X)<~>humble(X))))=>(?[X]:((old(X)<~>~tall(X)))))&
(![X]:((~strong(X)|happy(X))<=>~calm(X)))&
((humble(john)<~>~brave(john)))&
(?[X]:((~old(X)|~calm(X))))&
((patient(mary)|funny(mary)))&
((quiet(alice)|patient(alice)))&
((generous(fred)&~curious(fred))) | creative(mary) | [
"p3",
"p8",
"p11",
"p12",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 8982382309147636529165695
% SZS output start Proof for 8982382309147636529165695
4. ! [X0] : ((curious(X0) | ~strong(X0)) => wise(X0)) [input p3]
9. ? [X0] : (tall(X0) | funny(X0)) => (quiet(mary) & ~creative(mary)) [input p8]
12. ! [X0] : ((~old(X0) & ~wise(X0)) <=> ~funny(X0)) [input p11]
13. ! [X0] : ((creative(X0) & ~patient(X0)) <=> (~kind(X0) | ~curious(X0))) [input p12]
19. funny(mary) | patient(mary) [input p18]
22. creative(mary) [input hypothesis]
31. ! [X0] : (wise(X0) | (~curious(X0) & strong(X0))) [ennf transformation 4]
35. (quiet(mary) & ~creative(mary)) | ! [X0] : (~tall(X0) & ~funny(X0)) [ennf transformation 9]
49. ! [X0] : (((~old(X0) & ~wise(X0)) | funny(X0)) & (~funny(X0) | (old(X0) | wise(X0)))) [nnf transformation 12]
50. ! [X0] : (((~old(X0) & ~wise(X0)) | funny(X0)) & (~funny(X0) | old(X0) | wise(X0))) [flattening 49]
51. ! [X0] : (((creative(X0) & ~patient(X0)) | (kind(X0) & curious(X0))) & ((~kind(X0) | ~curious(X0)) | (~creative(X0) | patient(X0)))) [nnf transformation 13]
52. ! [X0] : (((creative(X0) & ~patient(X0)) | (kind(X0) & curious(X0))) & (~kind(X0) | ~curious(X0) | ~creative(X0) | patient(X0))) [flattening 51]
80. ~curious(X0) | wise(X0) [cnf transformation 31]
93. ~creative(mary) | ~funny(X0) [cnf transformation 35]
102. ~wise(X0) | funny(X0) [cnf transformation 50]
105. ~patient(X0) | curious(X0) [cnf transformation 52]
125. funny(mary) | patient(mary) [cnf transformation 19]
128. creative(mary) [cnf transformation 22]
133. 1 <=> creative(mary) [avatar definition]
137. 2 <=> funny(mary) [avatar definition]
138. funny(mary) <- (2) [avatar component clause 137]
181. 11 <=> ! [X0] : ~funny(X0) [avatar definition]
182. ~funny(X0) <- (11) [avatar component clause 181]
185. 11 | ~1 [avatar split clause 93,133,181]
259. 28 <=> patient(mary) [avatar definition]
261. patient(mary) <- (28) [avatar component clause 259]
262. 28 | 2 [avatar split clause 125,137,259]
272. 1 [avatar split clause 128,133]
275. curious(mary) <- (28) [resolution 105,261]
277. wise(mary) <- (28) [resolution 275,80]
278. funny(mary) <- (28) [resolution 277,102]
279. $false <- (11, 28) [subsumption resolution 278,182]
280. ~11 | ~28 [avatar contradiction clause 279]
281. $false <- (2, 11) [subsumption resolution 138,182]
282. ~2 | ~11 [avatar contradiction clause 281]
283. $false [avatar sat refutation 185,262,272,280,282]
% SZS output end Proof for 8982382309147636529165695
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If susan is either not quiet or funny then someone is both funny and not brave.
Everyone who is both not quiet and rich is both wise and not quiet.
Everyone who is both creative and not curious is both brave and curious and vice versa.
If someone is creative then lucy is both not quiet and not creative.
Everyone who is curious is not patient and vice versa.
If someone is both wise and generous then someone is either strong or old and vice versa.
If alice is not old then fred is old or humble and vice versa.
If someone is both not tall and not generous then someone is old.
Everyone who is not curious is not old or not generous and vice versa.
Everyone who is either not brave or patient is both creative and not generous.
Everyone who is either not patient or not generous is either not patient or generous.
Everyone who is both kind and not rich is brave or tall.
Everyone who is not creative is either not curious or old.
Everyone who is not calm is either not rich or not funny.
Everyone who is either not tall or not generous is both humble and not old and vice versa.
If someone is wise or not tall then someone is both quiet and not kind and vice versa.
Someone is either humble or kind.
Someone is both not kind and not strong.
Someone is either calm or not rich.
John is not wise.
Someone is patient.
Someone is both not old and not funny.
Someone is not old or generous. | Alice is creative. | contradiction | (((~quiet(susan)<~>funny(susan)))=>(?[X]:((funny(X)&~brave(X)))))&
(![X]:((~quiet(X)&rich(X))=>(wise(X)&~quiet(X))))&
(![X]:((creative(X)&~curious(X))<=>(brave(X)&curious(X))))&
((?[X]:(creative(X)))=>((~quiet(lucy)&~creative(lucy))))&
(![X]:(curious(X)<=>~patient(X)))&
((?[X]:((wise(X)&generous(X))))<=>(?[X]:((strong(X)<~>old(X)))))&
((~old(alice))<=>((old(fred)|humble(fred))))&
((?[X]:((~tall(X)&~generous(X))))=>(?[X]:(old(X))))&
(![X]:(~curious(X)<=>(~old(X)|~generous(X))))&
(![X]:((~brave(X)<~>patient(X))=>(creative(X)&~generous(X))))&
(![X]:((~patient(X)<~>~generous(X))=>(~patient(X)<~>generous(X))))&
(![X]:((kind(X)&~rich(X))=>(brave(X)|tall(X))))&
(![X]:(~creative(X)=>(~curious(X)<~>old(X))))&
(![X]:(~calm(X)=>(~rich(X)<~>~funny(X))))&
(![X]:((~tall(X)<~>~generous(X))<=>(humble(X)&~old(X))))&
((?[X]:((wise(X)|~tall(X))))<=>(?[X]:((quiet(X)&~kind(X)))))&
(?[X]:((humble(X)<~>kind(X))))&
(?[X]:((~kind(X)&~strong(X))))&
(?[X]:((calm(X)<~>~rich(X))))&
(~wise(john))&
(?[X]:(patient(X)))&
(?[X]:((~old(X)&~funny(X))))&
(?[X]:((~old(X)|generous(X)))) | creative(alice) | [
"p2",
"p4",
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 6398533857616955733339053
% SZS output start Proof for 6398533857616955733339053
3. ! [X0] : ((~curious(X0) & creative(X0)) <=> (curious(X0) & brave(X0))) [input p2]
5. ! [X0] : (curious(X0) <=> ~patient(X0)) [input p4]
9. ! [X0] : (~curious(X0) <=> (~generous(X0) | ~old(X0))) [input p8]
11. ! [X0] : ((~patient(X0) <~> ~generous(X0)) => (~patient(X0) <~> generous(X0))) [input p10]
24. creative(alice) [input hypothesis]
34. ! [X0] : ((~patient(X0) <~> generous(X0)) | (~patient(X0) <=> ~generous(X0))) [ennf transformation 11]
42. ! [X0] : (((~curious(X0) & creative(X0)) | (~curious(X0) | ~brave(X0))) & ((curious(X0) & brave(X0)) | (curious(X0) | ~creative(X0)))) [nnf transformation 3]
43. ! [X0] : (((~curious(X0) & creative(X0)) | ~curious(X0) | ~brave(X0)) & ((curious(X0) & brave(X0)) | curious(X0) | ~creative(X0))) [flattening 42]
44. ! [X0] : ((curious(X0) | patient(X0)) & (~patient(X0) | ~curious(X0))) [nnf transformation 5]
55. ! [X0] : ((~curious(X0) | (generous(X0) & old(X0))) & ((~generous(X0) | ~old(X0)) | curious(X0))) [nnf transformation 9]
56. ! [X0] : ((~curious(X0) | (generous(X0) & old(X0))) & (~generous(X0) | ~old(X0) | curious(X0))) [flattening 55]
58. ! [X0] : (((~generous(X0) | patient(X0)) & (generous(X0) | ~patient(X0))) | ((~patient(X0) | generous(X0)) & (~generous(X0) | patient(X0)))) [nnf transformation 34]
89. curious(X0) | curious(X0) | ~creative(X0) [cnf transformation 43]
94. ~patient(X0) | ~curious(X0) [cnf transformation 44]
95. patient(X0) | curious(X0) [cnf transformation 44]
108. ~curious(X0) | generous(X0) [cnf transformation 56]
114. generous(X0) | ~patient(X0) | ~patient(X0) | generous(X0) [cnf transformation 58]
115. ~generous(X0) | patient(X0) | ~generous(X0) | patient(X0) [cnf transformation 58]
144. creative(alice) [cnf transformation 24]
145. ~patient(X0) | generous(X0) [duplicate literal removal 114]
146. ~generous(X0) | patient(X0) [duplicate literal removal 115]
147. ~creative(X0) | curious(X0) [duplicate literal removal 89]
301. generous(X0) | curious(X0) [resolution 145,95]
302. generous(X0) [subsumption resolution 301,108]
304. patient(X0) [resolution 302,146]
305. curious(alice) [resolution 147,144]
312. ~curious(X1) [resolution 304,94]
316. $false [resolution 312,305]
% SZS output end Proof for 6398533857616955733339053
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or not calm is either humble or calm and vice versa. Everyone who is either not quiet or not happy is strong or not quiet and vice versa. Everyone who is either not curious or not quiet is either old or tall. Everyone who is both not strong and not creative is both generous and not kind and vice versa. If someone is either creative or not rich then someone is either not old or not strong. If mary is either patient or not humble then someone is both not kind and calm and vice versa. Everyone who is both rich and happy is both not patient and not strong. Everyone who is either not happy or brave is quiet and vice versa. Everyone who is happy or calm is either rich or humble. Everyone who is either kind or rich is strong. Everyone who is either funny or happy is either brave or funny and vice versa. Everyone who is both not happy and tall is not generous. If lucy is wise then john is either calm or not patient. If someone is both not happy and not creative then someone is rich or calm and vice versa. If lucy is either not tall or calm then someone is patient or not funny. Everyone who is either creative or strong is both not kind and not creative and vice versa. Fred is either strong or tall. Lucy is either not wise or not tall. John is not kind. Lucy is both not happy and not wise. Lucy is not curious or not creative. Someone is old or not creative. Alice is not happy. Someone is generous. | Fred is happy. | contradiction | (![X]:((~curious(X)|~calm(X))<=>(humble(X)<~>calm(X))))&
(![X]:((~quiet(X)<~>~happy(X))<=>(strong(X)|~quiet(X))))&
(![X]:((~curious(X)<~>~quiet(X))=>(old(X)<~>tall(X))))&
(![X]:((~strong(X)&~creative(X))<=>(generous(X)&~kind(X))))&
((?[X]:((creative(X)<~>~rich(X))))=>(?[X]:((~old(X)<~>~strong(X)))))&
(((patient(mary)<~>~humble(mary)))<=>(?[X]:((~kind(X)&calm(X)))))&
(![X]:((rich(X)&happy(X))=>(~patient(X)&~strong(X))))&
(![X]:((~happy(X)<~>brave(X))<=>quiet(X)))&
(![X]:((happy(X)|calm(X))=>(rich(X)<~>humble(X))))&
(![X]:((kind(X)<~>rich(X))=>strong(X)))&
(![X]:((funny(X)<~>happy(X))<=>(brave(X)<~>funny(X))))&
(![X]:((~happy(X)&tall(X))=>~generous(X)))&
((wise(lucy))=>((calm(john)<~>~patient(john))))&
((?[X]:((~happy(X)&~creative(X))))<=>(?[X]:((rich(X)|calm(X)))))&
(((~tall(lucy)<~>calm(lucy)))=>(?[X]:((patient(X)|~funny(X)))))&
(![X]:((creative(X)<~>strong(X))<=>(~kind(X)&~creative(X))))&
((strong(fred)<~>tall(fred)))&
((~wise(lucy)<~>~tall(lucy)))&
(~kind(john))&
((~happy(lucy)&~wise(lucy)))&
((~curious(lucy)|~creative(lucy)))&
(?[X]:((old(X)|~creative(X))))&
(~happy(alice))&
(?[X]:(generous(X))) | happy(fred) | [
"p1",
"p3",
"p7",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 408974101305877177880087
% SZS output start Proof for 408974101305877177880087
2. ! [X0] : ((~quiet(X0) <~> ~happy(X0)) <=> (~quiet(X0) | strong(X0))) [input p1]
4. ! [X0] : ((~creative(X0) & ~strong(X0)) <=> (~kind(X0) & generous(X0))) [input p3]
8. ! [X0] : ((~happy(X0) <~> brave(X0)) <=> quiet(X0)) [input p7]
11. ! [X0] : ((funny(X0) <~> happy(X0)) <=> (brave(X0) <~> funny(X0))) [input p10]
16. ! [X0] : ((creative(X0) <~> strong(X0)) <=> (~creative(X0) & ~kind(X0))) [input p15]
25. happy(fred) [input hypothesis]
40. ! [X0] : ((((happy(X0) | quiet(X0)) & (~happy(X0) | ~quiet(X0))) | (quiet(X0) & ~strong(X0))) & ((~quiet(X0) | strong(X0)) | ((~quiet(X0) | happy(X0)) & (~happy(X0) | quiet(X0))))) [nnf transformation 2]
41. ! [X0] : ((((happy(X0) | quiet(X0)) & (~happy(X0) | ~quiet(X0))) | (quiet(X0) & ~strong(X0))) & (~quiet(X0) | strong(X0) | ((~quiet(X0) | happy(X0)) & (~happy(X0) | quiet(X0))))) [flattening 40]
43. ! [X0] : (((~creative(X0) & ~strong(X0)) | (kind(X0) | ~generous(X0))) & ((~kind(X0) & generous(X0)) | (creative(X0) | strong(X0)))) [nnf transformation 4]
44. ! [X0] : (((~creative(X0) & ~strong(X0)) | kind(X0) | ~generous(X0)) & ((~kind(X0) & generous(X0)) | creative(X0) | strong(X0))) [flattening 43]
53. ! [X0] : ((((~brave(X0) | happy(X0)) & (brave(X0) | ~happy(X0))) | ~quiet(X0)) & (quiet(X0) | ((~happy(X0) | ~brave(X0)) & (brave(X0) | happy(X0))))) [nnf transformation 8]
56. ! [X0] : ((((~happy(X0) | ~funny(X0)) & (happy(X0) | funny(X0))) | ((brave(X0) | ~funny(X0)) & (funny(X0) | ~brave(X0)))) & (((~funny(X0) | ~brave(X0)) & (funny(X0) | brave(X0))) | ((funny(X0) | ~happy(X0)) & (happy(X0) | ~funny(X0))))) [nnf transformation 11]
66. ! [X0] : ((((~strong(X0) | ~creative(X0)) & (strong(X0) | creative(X0))) | (creative(X0) | kind(X0))) & ((~creative(X0) & ~kind(X0)) | ((creative(X0) | ~strong(X0)) & (strong(X0) | ~creative(X0))))) [nnf transformation 16]
67. ! [X0] : ((((~strong(X0) | ~creative(X0)) & (strong(X0) | creative(X0))) | creative(X0) | kind(X0)) & ((~creative(X0) & ~kind(X0)) | ((creative(X0) | ~strong(X0)) & (strong(X0) | ~creative(X0))))) [flattening 66]
82. ~strong(X0) | ~quiet(X0) | ~happy(X0) [cnf transformation 41]
85. happy(X0) | quiet(X0) | quiet(X0) [cnf transformation 41]
91. ~kind(X0) | creative(X0) | strong(X0) [cnf transformation 44]
107. quiet(X0) | ~happy(X0) | ~brave(X0) [cnf transformation 53]
109. ~brave(X0) | happy(X0) | ~quiet(X0) [cnf transformation 53]
117. funny(X0) | brave(X0) | funny(X0) | ~happy(X0) [cnf transformation 56]
123. ~happy(X0) | ~funny(X0) | brave(X0) | ~funny(X0) [cnf transformation 56]
136. ~creative(X0) | strong(X0) | ~creative(X0) [cnf transformation 67]
138. strong(X0) | creative(X0) | creative(X0) | kind(X0) [cnf transformation 67]
151. happy(fred) [cnf transformation 25]
152. ~creative(X0) | strong(X0) [duplicate literal removal 136]
153. strong(X0) | creative(X0) | kind(X0) [duplicate literal removal 138]
154. funny(X0) | brave(X0) | ~happy(X0) [duplicate literal removal 117]
157. ~happy(X0) | ~funny(X0) | brave(X0) [duplicate literal removal 123]
159. happy(X0) | quiet(X0) [duplicate literal removal 85]
206. ~brave(X0) | happy(X0) [subsumption resolution 109,159]
207. ~brave(X0) | quiet(X0) [subsumption resolution 107,206]
209. ~happy(X0) | brave(X0) [subsumption resolution 154,157]
272. creative(X0) | strong(X0) [subsumption resolution 153,91]
273. strong(X0) [subsumption resolution 152,272]
307. brave(X0) | quiet(X0) [resolution 209,159]
308. quiet(X0) [subsumption resolution 307,207]
325. ~quiet(X1) | ~happy(X1) [resolution 82,273]
326. ~happy(X1) [subsumption resolution 325,308]
331. $false [resolution 326,151]
% SZS output end Proof for 408974101305877177880087
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or old is rich and vice versa. Everyone who is both calm and not brave is not generous or not old. If someone is not humble or happy then someone is either happy or not patient. If john is both not old and tall then paul is old and vice versa. Everyone who is both not old and not generous is not calm or calm and vice versa. Everyone who is either creative or not old is not humble or strong and vice versa. Everyone who is not tall or not rich is not creative and vice versa. Everyone who is rich is either rich or happy and vice versa. Everyone who is not humble or happy is calm and vice versa. If alice is either funny or not wise then alice is either generous or not tall. If fred is curious or kind then someone is both quiet and not quiet. If fred is humble or calm then someone is old or creative and vice versa. Everyone who is both happy and not quiet is funny or not patient and vice versa. If john is either strong or not tall then susan is both not wise and funny and vice versa. Everyone who is not wise is either not humble or curious and vice versa. If paul is happy or kind then someone is both not creative and not brave. Someone is either not curious or not quiet. Alice is quiet or not rich. Mary is not wise. Alice is not quiet. Someone is not curious or old. Someone is not old. | Mary is not curious. | contradiction | (![X]:((quiet(X)<~>old(X))<=>rich(X)))&
(![X]:((calm(X)&~brave(X))=>(~generous(X)|~old(X))))&
((?[X]:((~humble(X)|happy(X))))=>(?[X]:((happy(X)<~>~patient(X)))))&
(((~old(john)&tall(john)))<=>(old(paul)))&
(![X]:((~old(X)&~generous(X))<=>(~calm(X)|calm(X))))&
(![X]:((creative(X)<~>~old(X))<=>(~humble(X)|strong(X))))&
(![X]:((~tall(X)|~rich(X))<=>~creative(X)))&
(![X]:(rich(X)<=>(rich(X)<~>happy(X))))&
(![X]:((~humble(X)|happy(X))<=>calm(X)))&
(((funny(alice)<~>~wise(alice)))=>((generous(alice)<~>~tall(alice))))&
(((curious(fred)|kind(fred)))=>(?[X]:((quiet(X)&~quiet(X)))))&
(((humble(fred)|calm(fred)))<=>(?[X]:((old(X)|creative(X)))))&
(![X]:((happy(X)&~quiet(X))<=>(funny(X)|~patient(X))))&
(((strong(john)<~>~tall(john)))<=>((~wise(susan)&funny(susan))))&
(![X]:(~wise(X)<=>(~humble(X)<~>curious(X))))&
(((happy(paul)|kind(paul)))=>(?[X]:((~creative(X)&~brave(X)))))&
(?[X]:((~curious(X)<~>~quiet(X))))&
((quiet(alice)|~rich(alice)))&
(~wise(mary))&
(~quiet(alice))&
(?[X]:((~curious(X)|old(X))))&
(?[X]:(~old(X))) | ~curious(mary) | [
"p2",
"p7",
"p12",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 8703905818485120640441971
% SZS output start Proof for 8703905818485120640441971
3. ? [X0] : (happy(X0) | ~humble(X0)) => ? [X0] : (happy(X0) <~> ~patient(X0)) [input p2]
8. ! [X0] : (rich(X0) <=> (rich(X0) <~> happy(X0))) [input p7]
13. ! [X0] : ((~quiet(X0) & happy(X0)) <=> (~patient(X0) | funny(X0))) [input p12]
15. ! [X0] : (~wise(X0) <=> (~humble(X0) <~> curious(X0))) [input p14]
19. ~wise(mary) [input p18]
23. ~curious(mary) [input hypothesis]
24. ? [X0] : (happy(X0) | ~humble(X0)) => ? [X1] : (happy(X1) <~> ~patient(X1)) [rectify 3]
29. ? [X1] : (happy(X1) <~> ~patient(X1)) | ! [X0] : (~happy(X0) & humble(X0)) [ennf transformation 24]
34. ? [X1] : ((patient(X1) | ~happy(X1)) & (~patient(X1) | happy(X1))) | ! [X0] : (~happy(X0) & humble(X0)) [nnf transformation 29]
35. ? [X0] : ((patient(X0) | ~happy(X0)) & (~patient(X0) | happy(X0))) | ! [X1] : (~happy(X1) & humble(X1)) [rectify 34]
36. ? [X0] : ((patient(X0) | ~happy(X0)) & (~patient(X0) | happy(X0))) => ((patient(sK0) | ~happy(sK0)) & (~patient(sK0) | happy(sK0))) [choice axiom]
37. ((patient(sK0) | ~happy(sK0)) & (~patient(sK0) | happy(sK0))) | ! [X1] : (~happy(X1) & humble(X1)) [skolemisation 35,36]
46. ! [X0] : ((rich(X0) | ((rich(X0) | ~happy(X0)) & (happy(X0) | ~rich(X0)))) & (((~happy(X0) | ~rich(X0)) & (happy(X0) | rich(X0))) | ~rich(X0))) [nnf transformation 8]
57. ! [X0] : (((~quiet(X0) & happy(X0)) | (patient(X0) & ~funny(X0))) & ((~patient(X0) | funny(X0)) | (quiet(X0) | ~happy(X0)))) [nnf transformation 13]
58. ! [X0] : (((~quiet(X0) & happy(X0)) | (patient(X0) & ~funny(X0))) & (~patient(X0) | funny(X0) | quiet(X0) | ~happy(X0))) [flattening 57]
61. ! [X0] : ((~wise(X0) | ((~humble(X0) | ~curious(X0)) & (curious(X0) | humble(X0)))) & (((~curious(X0) | humble(X0)) & (curious(X0) | ~humble(X0))) | wise(X0))) [nnf transformation 15]
76. ~patient(sK0) | happy(sK0) | humble(X1) [cnf transformation 37]
98. ~happy(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 46]
100. rich(X0) | rich(X0) | ~happy(X0) [cnf transformation 46]
116. patient(X0) | happy(X0) [cnf transformation 58]
125. ~humble(X0) | curious(X0) | wise(X0) [cnf transformation 61]
134. ~wise(mary) [cnf transformation 19]
138. ~curious(mary) [cnf transformation 23]
139. ~happy(X0) | ~rich(X0) [duplicate literal removal 98]
140. ~happy(X0) | rich(X0) [duplicate literal removal 100]
142. 1 <=> ! [X1] : ~happy(X1) [avatar definition]
143. ~happy(X1) <- (1) [avatar component clause 142]
145. 2 <=> happy(sK0) [avatar definition]
146. happy(sK0) <- (2) [avatar component clause 145]
149. 3 <=> patient(sK0) [avatar definition]
150. ~patient(sK0) <- (~3) [avatar component clause 149]
154. 4 <=> ! [X1] : humble(X1) [avatar definition]
155. humble(X1) <- (4) [avatar component clause 154]
158. 4 | 2 | ~3 [avatar split clause 76,149,145,154]
179. ~happy(X0) [subsumption resolution 139,140]
180. 1 [avatar split clause 179,142]
290. happy(sK0) <- (~3) [resolution 116,150]
293. $false <- (1, ~3) [subsumption resolution 290,143]
294. ~1 | 3 [avatar contradiction clause 293]
295. $false <- (1, 2) [subsumption resolution 146,143]
296. ~1 | ~2 [avatar contradiction clause 295]
310. curious(X0) | wise(X0) <- (4) [resolution 125,155]
317. wise(mary) <- (4) [resolution 310,138]
320. $false <- (4) [subsumption resolution 317,134]
321. ~4 [avatar contradiction clause 320]
322. $false [avatar sat refutation 158,180,294,296,321]
% SZS output end Proof for 8703905818485120640441971
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not creative and strong is quiet or not creative and vice versa.
If someone is not generous or brave then mary is either humble or not curious.
If someone is funny or wise then susan is generous.
If alice is not creative or not quiet then someone is wise.
If someone is not quiet then mary is both not brave and not strong and vice versa.
If someone is not wise then someone is not happy or happy and vice versa.
Everyone who is either not humble or curious is both not calm and not brave.
If someone is not kind then someone is quiet or generous and vice versa.
Everyone who is funny is not creative or creative.
Everyone who is both not curious and brave is either curious or tall and vice versa.
Everyone who is not kind or not brave is either not rich or curious and vice versa.
Everyone who is happy is tall or rich and vice versa.
If someone is either not kind or not patient then paul is either not funny or brave.
Everyone who is both not humble and not brave is not rich and vice versa.
Everyone who is humble or not funny is both quiet and strong and vice versa.
If alice is not patient or calm then someone is not funny or not strong and vice versa.
Lucy is either not patient or rich.
Lucy is not tall or not wise.
Someone is not generous.
Someone is not curious.
Mary is rich.
Mary is strong or tall.
Someone is strong or not wise.
Someone is either quiet or not happy. | Mary is not creative. | entailment | (![X]:((~creative(X)&strong(X))<=>(quiet(X)|~creative(X))))&
((?[X]:((~generous(X)|brave(X))))=>((humble(mary)<~>~curious(mary))))&
((?[X]:((funny(X)|wise(X))))=>(generous(susan)))&
(((~creative(alice)|~quiet(alice)))=>(?[X]:(wise(X))))&
((?[X]:(~quiet(X)))<=>((~brave(mary)&~strong(mary))))&
((?[X]:(~wise(X)))<=>(?[X]:((~happy(X)|happy(X)))))&
(![X]:((~humble(X)<~>curious(X))=>(~calm(X)&~brave(X))))&
((?[X]:(~kind(X)))<=>(?[X]:((quiet(X)|generous(X)))))&
(![X]:(funny(X)=>(~creative(X)|creative(X))))&
(![X]:((~curious(X)&brave(X))<=>(curious(X)<~>tall(X))))&
(![X]:((~kind(X)|~brave(X))<=>(~rich(X)<~>curious(X))))&
(![X]:(happy(X)<=>(tall(X)|rich(X))))&
((?[X]:((~kind(X)<~>~patient(X))))=>((~funny(paul)<~>brave(paul))))&
(![X]:((~humble(X)&~brave(X))<=>~rich(X)))&
(![X]:((humble(X)|~funny(X))<=>(quiet(X)&strong(X))))&
(((~patient(alice)|calm(alice)))<=>(?[X]:((~funny(X)|~strong(X)))))&
((~patient(lucy)<~>rich(lucy)))&
((~tall(lucy)|~wise(lucy)))&
(?[X]:(~generous(X)))&
(?[X]:(~curious(X)))&
(rich(mary))&
((strong(mary)|tall(mary)))&
(?[X]:((strong(X)|~wise(X))))&
(?[X]:((quiet(X)<~>~happy(X)))) | ~creative(mary) | [
"p0",
"p1",
"p4",
"p10",
"p14",
"p18",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6077258146067386823218970
% SZS output start Proof for 6077258146067386823218970
1. ! [X0] : ((strong(X0) & ~creative(X0)) <=> (~creative(X0) | quiet(X0))) [input p0]
2. ? [X0] : (brave(X0) | ~generous(X0)) => (humble(mary) <~> ~curious(mary)) [input p1]
5. ? [X0] : ~quiet(X0) <=> (~strong(mary) & ~brave(mary)) [input p4]
11. ! [X0] : ((~brave(X0) | ~kind(X0)) <=> (~rich(X0) <~> curious(X0))) [input p10]
15. ! [X0] : ((~funny(X0) | humble(X0)) <=> (strong(X0) & quiet(X0))) [input p14]
19. ? [X0] : ~generous(X0) [input p18]
21. rich(mary) [input p20]
25. creative(mary) [input hypothesis]
28. (humble(mary) <~> ~curious(mary)) | ! [X0] : (~brave(X0) & generous(X0)) [ennf transformation 2]
35. ! [X0] : (((strong(X0) & ~creative(X0)) | (creative(X0) & ~quiet(X0))) & ((~creative(X0) | quiet(X0)) | (~strong(X0) | creative(X0)))) [nnf transformation 1]
36. ! [X0] : (((strong(X0) & ~creative(X0)) | (creative(X0) & ~quiet(X0))) & (~creative(X0) | quiet(X0) | ~strong(X0) | creative(X0))) [flattening 35]
37. ((curious(mary) | ~humble(mary)) & (~curious(mary) | humble(mary))) | ! [X0] : (~brave(X0) & generous(X0)) [nnf transformation 28]
40. (? [X0] : ~quiet(X0) | (strong(mary) | brave(mary))) & ((~strong(mary) & ~brave(mary)) | ! [X0] : quiet(X0)) [nnf transformation 5]
41. (? [X0] : ~quiet(X0) | strong(mary) | brave(mary)) & ((~strong(mary) & ~brave(mary)) | ! [X0] : quiet(X0)) [flattening 40]
42. (? [X0] : ~quiet(X0) | strong(mary) | brave(mary)) & ((~strong(mary) & ~brave(mary)) | ! [X1] : quiet(X1)) [rectify 41]
43. ? [X0] : ~quiet(X0) => ~quiet(sK1) [choice axiom]
44. (~quiet(sK1) | strong(mary) | brave(mary)) & ((~strong(mary) & ~brave(mary)) | ! [X1] : quiet(X1)) [skolemisation 42,43]
58. ! [X0] : (((~brave(X0) | ~kind(X0)) | ((~rich(X0) | ~curious(X0)) & (curious(X0) | rich(X0)))) & (((~curious(X0) | rich(X0)) & (curious(X0) | ~rich(X0))) | (brave(X0) & kind(X0)))) [nnf transformation 11]
59. ! [X0] : ((~brave(X0) | ~kind(X0) | ((~rich(X0) | ~curious(X0)) & (curious(X0) | rich(X0)))) & (((~curious(X0) | rich(X0)) & (curious(X0) | ~rich(X0))) | (brave(X0) & kind(X0)))) [flattening 58]
65. ! [X0] : (((~funny(X0) | humble(X0)) | (~strong(X0) | ~quiet(X0))) & ((strong(X0) & quiet(X0)) | (funny(X0) & ~humble(X0)))) [nnf transformation 15]
66. ! [X0] : ((~funny(X0) | humble(X0) | ~strong(X0) | ~quiet(X0)) & ((strong(X0) & quiet(X0)) | (funny(X0) & ~humble(X0)))) [flattening 65]
73. ? [X0] : ~generous(X0) => ~generous(sK7) [choice axiom]
74. ~generous(sK7) [skolemisation 19,73]
83. ~quiet(X0) | ~creative(X0) [cnf transformation 36]
87. ~curious(mary) | humble(mary) | generous(X0) [cnf transformation 37]
95. ~brave(mary) | quiet(X1) [cnf transformation 44]
96. ~strong(mary) | quiet(X1) [cnf transformation 44]
116. ~rich(X0) | curious(X0) | brave(X0) [cnf transformation 59]
133. ~humble(X0) | strong(X0) [cnf transformation 66]
143. ~generous(sK7) [cnf transformation 74]
145. rich(mary) [cnf transformation 21]
150. creative(mary) [cnf transformation 25]
157. 2 <=> humble(mary) [avatar definition]
158. humble(mary) <- (2) [avatar component clause 157]
161. 3 <=> curious(mary) [avatar definition]
166. 4 <=> ! [X0] : generous(X0) [avatar definition]
167. generous(X0) <- (4) [avatar component clause 166]
170. 4 | 2 | ~3 [avatar split clause 87,161,157,166]
198. 11 <=> brave(mary) [avatar definition]
199. ~brave(mary) <- (~11) [avatar component clause 198]
202. 12 <=> strong(mary) [avatar definition]
203. ~strong(mary) <- (~12) [avatar component clause 202]
211. 14 <=> ! [X1] : quiet(X1) [avatar definition]
212. quiet(X1) <- (14) [avatar component clause 211]
213. 14 | ~12 [avatar split clause 96,202,211]
214. 14 | ~11 [avatar split clause 95,198,211]
379. $false <- (4) [resolution 167,143]
380. ~4 [avatar contradiction clause 379]
382. ~creative(X1) <- (14) [resolution 212,83]
396. curious(mary) | brave(mary) [resolution 116,145]
401. curious(mary) <- (~11) [subsumption resolution 396,199]
402. 3 | 11 [avatar split clause 401,198,161]
408. strong(mary) <- (2) [resolution 158,133]
424. $false <- (14) [resolution 382,150]
425. ~14 [avatar contradiction clause 424]
428. $false <- (2, ~12) [subsumption resolution 408,203]
429. ~2 | 12 [avatar contradiction clause 428]
431. $false [avatar sat refutation 170,213,214,380,402,425,429]
% SZS output end Proof for 6077258146067386823218970
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave is either not wise or not kind and vice versa. Everyone who is either not wise or not curious is either not brave or funny and vice versa. If susan is either not generous or strong then someone is either patient or not funny and vice versa. If someone is not curious or brave then john is either not happy or not generous. If john is not old or generous then paul is patient or old. Everyone who is generous is both strong and not patient. Everyone who is quiet or kind is happy or funny and vice versa. Everyone who is both generous and wise is not humble and vice versa. If someone is both not tall and not old then someone is brave or not generous and vice versa. If susan is kind then someone is both funny and patient and vice versa. Everyone who is not quiet is both creative and funny and vice versa. Everyone who is not kind or not humble is not generous or not curious. If john is not curious then someone is wise or not rich. If someone is kind then someone is both curious and not kind. Everyone who is kind or quiet is both strong and patient and vice versa. Everyone who is both kind and calm is quiet. Someone is either creative or not curious. Paul is both creative and wise. Someone is rich. | Susan is generous. | contradiction | (![X]:(brave(X)<=>(~wise(X)<~>~kind(X))))&
(![X]:((~wise(X)<~>~curious(X))<=>(~brave(X)<~>funny(X))))&
(((~generous(susan)<~>strong(susan)))<=>(?[X]:((patient(X)<~>~funny(X)))))&
((?[X]:((~curious(X)|brave(X))))=>((~happy(john)<~>~generous(john))))&
(((~old(john)|generous(john)))=>((patient(paul)|old(paul))))&
(![X]:(generous(X)=>(strong(X)&~patient(X))))&
(![X]:((quiet(X)|kind(X))<=>(happy(X)|funny(X))))&
(![X]:((generous(X)&wise(X))<=>~humble(X)))&
((?[X]:((~tall(X)&~old(X))))<=>(?[X]:((brave(X)|~generous(X)))))&
((kind(susan))<=>(?[X]:((funny(X)&patient(X)))))&
(![X]:(~quiet(X)<=>(creative(X)&funny(X))))&
(![X]:((~kind(X)|~humble(X))=>(~generous(X)|~curious(X))))&
((~curious(john))=>(?[X]:((wise(X)|~rich(X)))))&
((?[X]:(kind(X)))=>(?[X]:((curious(X)&~kind(X)))))&
(![X]:((kind(X)|quiet(X))<=>(strong(X)&patient(X))))&
(![X]:((kind(X)&calm(X))=>quiet(X)))&
(?[X]:((creative(X)<~>~curious(X))))&
((creative(paul)&wise(paul)))&
(?[X]:(rich(X))) | generous(susan) | [
"p2",
"p5",
"p9",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8302592813681074267467611
% SZS output start Proof for 8302592813681074267467611
3. (~generous(susan) <~> strong(susan)) <=> ? [X0] : (patient(X0) <~> ~funny(X0)) [input p2]
6. ! [X0] : (generous(X0) => (~patient(X0) & strong(X0))) [input p5]
10. kind(susan) <=> ? [X0] : (patient(X0) & funny(X0)) [input p9]
11. ! [X0] : (~quiet(X0) <=> (funny(X0) & creative(X0))) [input p10]
15. ! [X0] : ((quiet(X0) | kind(X0)) <=> (patient(X0) & strong(X0))) [input p14]
20. generous(susan) [input hypothesis]
28. ! [X0] : ((~patient(X0) & strong(X0)) | ~generous(X0)) [ennf transformation 6]
37. (((~strong(susan) | generous(susan)) & (strong(susan) | ~generous(susan))) | ! [X0] : ((patient(X0) | funny(X0)) & (~funny(X0) | ~patient(X0)))) & (? [X0] : ((funny(X0) | ~patient(X0)) & (~funny(X0) | patient(X0))) | ((~generous(susan) | ~strong(susan)) & (strong(susan) | generous(susan)))) [nnf transformation 3]
38. (((~strong(susan) | generous(susan)) & (strong(susan) | ~generous(susan))) | ! [X0] : ((patient(X0) | funny(X0)) & (~funny(X0) | ~patient(X0)))) & (? [X1] : ((funny(X1) | ~patient(X1)) & (~funny(X1) | patient(X1))) | ((~generous(susan) | ~strong(susan)) & (strong(susan) | generous(susan)))) [rectify 37]
39. ? [X1] : ((funny(X1) | ~patient(X1)) & (~funny(X1) | patient(X1))) => ((funny(sK0) | ~patient(sK0)) & (~funny(sK0) | patient(sK0))) [choice axiom]
40. (((~strong(susan) | generous(susan)) & (strong(susan) | ~generous(susan))) | ! [X0] : ((patient(X0) | funny(X0)) & (~funny(X0) | ~patient(X0)))) & (((funny(sK0) | ~patient(sK0)) & (~funny(sK0) | patient(sK0))) | ((~generous(susan) | ~strong(susan)) & (strong(susan) | generous(susan)))) [skolemisation 38,39]
49. (kind(susan) | ! [X0] : (~patient(X0) | ~funny(X0))) & (? [X0] : (patient(X0) & funny(X0)) | ~kind(susan)) [nnf transformation 10]
50. (kind(susan) | ! [X0] : (~patient(X0) | ~funny(X0))) & (? [X1] : (patient(X1) & funny(X1)) | ~kind(susan)) [rectify 49]
51. ? [X1] : (patient(X1) & funny(X1)) => (patient(sK3) & funny(sK3)) [choice axiom]
52. (kind(susan) | ! [X0] : (~patient(X0) | ~funny(X0))) & ((patient(sK3) & funny(sK3)) | ~kind(susan)) [skolemisation 50,51]
53. ! [X0] : ((~quiet(X0) | (~funny(X0) | ~creative(X0))) & ((funny(X0) & creative(X0)) | quiet(X0))) [nnf transformation 11]
54. ! [X0] : ((~quiet(X0) | ~funny(X0) | ~creative(X0)) & ((funny(X0) & creative(X0)) | quiet(X0))) [flattening 53]
60. ! [X0] : (((quiet(X0) | kind(X0)) | (~patient(X0) | ~strong(X0))) & ((patient(X0) & strong(X0)) | (~quiet(X0) & ~kind(X0)))) [nnf transformation 15]
61. ! [X0] : ((quiet(X0) | kind(X0) | ~patient(X0) | ~strong(X0)) & ((patient(X0) & strong(X0)) | (~quiet(X0) & ~kind(X0)))) [flattening 60]
80. ~funny(sK0) | patient(sK0) | ~generous(susan) | ~strong(susan) [cnf transformation 40]
82. funny(sK0) | ~patient(sK0) | ~generous(susan) | ~strong(susan) [cnf transformation 40]
93. ~generous(X0) | strong(X0) [cnf transformation 28]
94. ~patient(X0) | ~generous(X0) [cnf transformation 28]
107. kind(susan) | ~patient(X0) | ~funny(X0) [cnf transformation 52]
109. quiet(X0) | funny(X0) [cnf transformation 54]
118. ~kind(X0) | patient(X0) [cnf transformation 61]
119. ~quiet(X0) | patient(X0) [cnf transformation 61]
126. generous(susan) [cnf transformation 20]
128. 1 <=> ! [X0] : (patient(X0) | funny(X0)) [avatar definition]
129. patient(X0) | funny(X0) <- (1) [avatar component clause 128]
131. 2 <=> generous(susan) [avatar definition]
133. generous(susan) <- (2) [avatar component clause 131]
135. 3 <=> strong(susan) [avatar definition]
140. 4 <=> ! [X0] : (~funny(X0) | ~patient(X0)) [avatar definition]
141. ~patient(X0) | ~funny(X0) <- (4) [avatar component clause 140]
146. 5 <=> patient(sK0) [avatar definition]
147. patient(sK0) <- (5) [avatar component clause 146]
148. ~patient(sK0) <- (~5) [avatar component clause 146]
150. 6 <=> funny(sK0) [avatar definition]
152. funny(sK0) <- (6) [avatar component clause 150]
153. ~3 | ~2 | ~5 | 6 [avatar split clause 82,150,146,131,135]
155. ~3 | ~2 | 5 | ~6 [avatar split clause 80,150,146,131,135]
217. 20 <=> kind(susan) [avatar definition]
219. kind(susan) <- (20) [avatar component clause 217]
220. 4 | 20 [avatar split clause 107,217,140]
267. 2 [avatar split clause 126,131]
268. strong(susan) <- (2) [resolution 93,133]
273. patient(X0) | funny(X0) [resolution 119,109]
275. 1 [avatar split clause 273,128]
277. funny(sK0) <- (1, ~5) [resolution 129,148]
281. 3 | ~2 [avatar split clause 268,131,135]
282. 6 | ~1 | 5 [avatar split clause 277,146,128,150]
286. ~funny(sK0) <- (4, 5) [resolution 141,147]
288. $false <- (4, 5, 6) [subsumption resolution 286,152]
289. ~4 | ~5 | ~6 [avatar contradiction clause 288]
292. patient(susan) <- (20) [resolution 219,118]
305. ~generous(susan) <- (20) [resolution 292,94]
306. $false <- (2, 20) [subsumption resolution 305,133]
307. ~2 | ~20 [avatar contradiction clause 306]
308. $false [avatar sat refutation 153,155,220,267,275,281,282,289,307]
% SZS output end Proof for 8302592813681074267467611
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not creative and humble is old. If lucy is both strong and generous then paul is kind and vice versa. Everyone who is both not brave and quiet is humble and vice versa. Everyone who is not rich or calm is both wise and humble and vice versa. If someone is either kind or not wise then paul is old or not kind. If someone is either not rich or not strong then john is calm. If someone is either not tall or not generous then someone is not kind or happy. Everyone who is either creative or generous is either not patient or not strong and vice versa. If mary is both tall and not patient then paul is both not patient and not wise and vice versa. If alice is both not quiet and generous then someone is either rich or not rich. Everyone who is not calm or not kind is not old and vice versa. Everyone who is both patient and not happy is either old or generous. If someone is quiet then alice is both not tall and generous. Everyone who is not wise is both happy and funny and vice versa. If mary is both patient and not funny then someone is either generous or calm. Everyone who is happy or rich is both not quiet and not kind and vice versa. Someone is both not generous and not quiet. Alice is not generous. Fred is both patient and happy. Alice is wise. Someone is either not happy or not humble. Alice is either not creative or not old. Lucy is not rich or not humble. Someone is either generous or rich. | Fred is not rich. | contradiction | (![X]:((~creative(X)&humble(X))=>old(X)))&
(((strong(lucy)&generous(lucy)))<=>(kind(paul)))&
(![X]:((~brave(X)&quiet(X))<=>humble(X)))&
(![X]:((~rich(X)|calm(X))<=>(wise(X)&humble(X))))&
((?[X]:((kind(X)<~>~wise(X))))=>((old(paul)|~kind(paul))))&
((?[X]:((~rich(X)<~>~strong(X))))=>(calm(john)))&
((?[X]:((~tall(X)<~>~generous(X))))=>(?[X]:((~kind(X)|happy(X)))))&
(![X]:((creative(X)<~>generous(X))<=>(~patient(X)<~>~strong(X))))&
(((tall(mary)&~patient(mary)))<=>((~patient(paul)&~wise(paul))))&
(((~quiet(alice)&generous(alice)))=>(?[X]:((rich(X)<~>~rich(X)))))&
(![X]:((~calm(X)|~kind(X))<=>~old(X)))&
(![X]:((patient(X)&~happy(X))=>(old(X)<~>generous(X))))&
((?[X]:(quiet(X)))=>((~tall(alice)&generous(alice))))&
(![X]:(~wise(X)<=>(happy(X)&funny(X))))&
(((patient(mary)&~funny(mary)))=>(?[X]:((generous(X)<~>calm(X)))))&
(![X]:((happy(X)|rich(X))<=>(~quiet(X)&~kind(X))))&
(?[X]:((~generous(X)&~quiet(X))))&
(~generous(alice))&
((patient(fred)&happy(fred)))&
(wise(alice))&
(?[X]:((~happy(X)<~>~humble(X))))&
((~creative(alice)<~>~old(alice)))&
((~rich(lucy)|~humble(lucy)))&
(?[X]:((generous(X)<~>rich(X)))) | ~rich(fred) | [
"p2",
"p3",
"p12",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 7363988395352682030447628
% SZS output start Proof for 7363988395352682030447628
3. ! [X0] : ((quiet(X0) & ~brave(X0)) <=> humble(X0)) [input p2]
4. ! [X0] : ((calm(X0) | ~rich(X0)) <=> (humble(X0) & wise(X0))) [input p3]
13. ? [X0] : quiet(X0) => (generous(alice) & ~tall(alice)) [input p12]
18. ~generous(alice) [input p17]
25. ~rich(fred) [input hypothesis]
37. (generous(alice) & ~tall(alice)) | ! [X0] : ~quiet(X0) [ennf transformation 13]
42. ! [X0] : (((quiet(X0) & ~brave(X0)) | ~humble(X0)) & (humble(X0) | (~quiet(X0) | brave(X0)))) [nnf transformation 3]
43. ! [X0] : (((quiet(X0) & ~brave(X0)) | ~humble(X0)) & (humble(X0) | ~quiet(X0) | brave(X0))) [flattening 42]
44. ! [X0] : (((calm(X0) | ~rich(X0)) | (~humble(X0) | ~wise(X0))) & ((humble(X0) & wise(X0)) | (~calm(X0) & rich(X0)))) [nnf transformation 4]
45. ! [X0] : ((calm(X0) | ~rich(X0) | ~humble(X0) | ~wise(X0)) & ((humble(X0) & wise(X0)) | (~calm(X0) & rich(X0)))) [flattening 44]
83. ~humble(X0) | quiet(X0) [cnf transformation 43]
86. rich(X0) | humble(X0) [cnf transformation 45]
115. generous(alice) | ~quiet(X0) [cnf transformation 37]
128. ~generous(alice) [cnf transformation 18]
139. ~rich(fred) [cnf transformation 25]
216. 18 <=> ! [X0] : ~quiet(X0) [avatar definition]
217. ~quiet(X0) <- (18) [avatar component clause 216]
219. 19 <=> generous(alice) [avatar definition]
222. 18 | 19 [avatar split clause 115,219,216]
242. ~19 [avatar split clause 128,219]
283. humble(fred) [resolution 86,139]
287. quiet(fred) [resolution 283,83]
288. $false <- (18) [subsumption resolution 287,217]
289. ~18 [avatar contradiction clause 288]
290. $false [avatar sat refutation 222,242,289]
% SZS output end Proof for 7363988395352682030447628
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is creative or not calm is either quiet or not happy.
Everyone who is both funny and not strong is generous or happy and vice versa.
Everyone who is both not curious and calm is both creative and not quiet.
Everyone who is not tall or funny is wise or not rich and vice versa.
If fred is not generous or not patient then someone is wise or calm.
Everyone who is not rich is generous and vice versa.
Everyone who is brave or happy is both curious and creative.
Everyone who is wise or not humble is not creative.
If someone is calm then someone is happy or kind and vice versa.
If john is not wise then paul is funny.
Everyone who is both not quiet and creative is humble.
Everyone who is either not happy or curious is not funny and vice versa.
Everyone who is not calm is both not old and not quiet and vice versa.
If paul is either humble or brave then someone is either not tall or patient.
If lucy is not kind then susan is both humble and strong.
If alice is brave or rich then someone is not old or generous.
Alice is either not generous or not funny.
Mary is not generous or humble.
Someone is either wise or quiet.
Paul is both not brave and not strong.
John is not creative.
Someone is generous or not generous.
Someone is tall. | Susan is not quiet. | neutral | (![X]:((creative(X)|~calm(X))=>(quiet(X)<~>~happy(X))))&
(![X]:((funny(X)&~strong(X))<=>(generous(X)|happy(X))))&
(![X]:((~curious(X)&calm(X))=>(creative(X)&~quiet(X))))&
(![X]:((~tall(X)|funny(X))<=>(wise(X)|~rich(X))))&
(((~generous(fred)|~patient(fred)))=>(?[X]:((wise(X)|calm(X)))))&
(![X]:(~rich(X)<=>generous(X)))&
(![X]:((brave(X)|happy(X))=>(curious(X)&creative(X))))&
(![X]:((wise(X)|~humble(X))=>~creative(X)))&
((?[X]:(calm(X)))<=>(?[X]:((happy(X)|kind(X)))))&
((~wise(john))=>(funny(paul)))&
(![X]:((~quiet(X)&creative(X))=>humble(X)))&
(![X]:((~happy(X)<~>curious(X))<=>~funny(X)))&
(![X]:(~calm(X)<=>(~old(X)&~quiet(X))))&
(((humble(paul)<~>brave(paul)))=>(?[X]:((~tall(X)<~>patient(X)))))&
((~kind(lucy))=>((humble(susan)&strong(susan))))&
(((brave(alice)|rich(alice)))=>(?[X]:((~old(X)|generous(X)))))&
((~generous(alice)<~>~funny(alice)))&
((~generous(mary)|humble(mary)))&
(?[X]:((wise(X)<~>quiet(X))))&
((~brave(paul)&~strong(paul)))&
(~creative(john))&
(?[X]:((generous(X)|~generous(X))))&
(?[X]:(tall(X))) | ~quiet(susan) | [] | null | 0 |
Everyone who is both not calm and humble is not generous or kind. If someone is both wise and not strong then susan is humble or wise and vice versa. Everyone who is not kind is not curious and vice versa. Everyone who is funny is tall and vice versa. Everyone who is not patient is either rich or not generous and vice versa. Everyone who is not curious or not humble is either curious or wise. Everyone who is calm or not patient is old or not curious. If john is either not curious or not generous then someone is happy and vice versa. If someone is not funny then someone is not calm. If someone is either not brave or not generous then someone is both quiet and not wise. Everyone who is both not calm and quiet is old or not tall. Everyone who is both patient and wise is creative. Everyone who is not brave is patient or old and vice versa. Everyone who is not creative is quiet and vice versa. Everyone who is both not tall and not creative is strong or not old and vice versa. Everyone who is both not generous and creative is either not patient or humble and vice versa. Someone is not kind or tall. Someone is not brave. Susan is either not calm or not patient. Someone is either quiet or creative. Fred is rich or creative. Fred is either quiet or tall. Someone is not strong or humble. | Fred is not wise. | neutral | (![X]:((~calm(X)&humble(X))=>(~generous(X)|kind(X))))&
((?[X]:((wise(X)&~strong(X))))<=>((humble(susan)|wise(susan))))&
(![X]:(~kind(X)<=>~curious(X)))&
(![X]:(funny(X)<=>tall(X)))&
(![X]:(~patient(X)<=>(rich(X)<~>~generous(X))))&
(![X]:((~curious(X)|~humble(X))=>(curious(X)<~>wise(X))))&
(![X]:((calm(X)|~patient(X))=>(old(X)|~curious(X))))&
(((~curious(john)<~>~generous(john)))<=>(?[X]:(happy(X))))&
((?[X]:(~funny(X)))=>(?[X]:(~calm(X))))&
((?[X]:((~brave(X)<~>~generous(X))))=>(?[X]:((quiet(X)&~wise(X)))))&
(![X]:((~calm(X)&quiet(X))=>(old(X)|~tall(X))))&
(![X]:((patient(X)&wise(X))=>creative(X)))&
(![X]:(~brave(X)<=>(patient(X)|old(X))))&
(![X]:(~creative(X)<=>quiet(X)))&
(![X]:((~tall(X)&~creative(X))<=>(strong(X)|~old(X))))&
(![X]:((~generous(X)&creative(X))<=>(~patient(X)<~>humble(X))))&
(?[X]:((~kind(X)|tall(X))))&
(?[X]:(~brave(X)))&
((~calm(susan)<~>~patient(susan)))&
(?[X]:((quiet(X)<~>creative(X))))&
((rich(fred)|creative(fred)))&
((quiet(fred)<~>tall(fred)))&
(?[X]:((~strong(X)|humble(X)))) | ~wise(fred) | [] | null | 0 |
If someone is brave or curious then mary is not rich.
If fred is both brave and patient then paul is both curious and calm and vice versa.
If mary is not funny then john is either not curious or happy.
Everyone who is both calm and not strong is old or wise and vice versa.
Everyone who is both happy and not calm is patient or not happy.
Everyone who is not curious or not happy is both creative and not kind.
Everyone who is both curious and happy is not kind or strong and vice versa.
Everyone who is humble is either not generous or kind and vice versa.
If someone is both old and not creative then someone is not rich or funny.
Everyone who is not curious or strong is not kind.
Everyone who is both wise and not happy is both not funny and not tall and vice versa.
Everyone who is kind or strong is either quiet or not patient and vice versa.
Everyone who is both brave and funny is creative.
If fred is both wise and not old then alice is strong or tall and vice versa.
Everyone who is not humble is quiet and vice versa.
Everyone who is either not wise or not calm is either not curious or wise.
Someone is not old.
Mary is both strong and not rich.
Someone is kind or old.
Someone is both not rich and patient.
Someone is creative or not funny.
Alice is either creative or not brave.
Someone is both wise and rich. | Mary is generous. | entailment | ((?[X]:((brave(X)|curious(X))))=>(~rich(mary)))&
(((brave(fred)&patient(fred)))<=>((curious(paul)&calm(paul))))&
((~funny(mary))=>((~curious(john)<~>happy(john))))&
(![X]:((calm(X)&~strong(X))<=>(old(X)|wise(X))))&
(![X]:((happy(X)&~calm(X))=>(patient(X)|~happy(X))))&
(![X]:((~curious(X)|~happy(X))=>(creative(X)&~kind(X))))&
(![X]:((curious(X)&happy(X))<=>(~kind(X)|strong(X))))&
(![X]:(humble(X)<=>(~generous(X)<~>kind(X))))&
((?[X]:((old(X)&~creative(X))))=>(?[X]:((~rich(X)|funny(X)))))&
(![X]:((~curious(X)|strong(X))=>~kind(X)))&
(![X]:((wise(X)&~happy(X))<=>(~funny(X)&~tall(X))))&
(![X]:((kind(X)|strong(X))<=>(quiet(X)<~>~patient(X))))&
(![X]:((brave(X)&funny(X))=>creative(X)))&
(((wise(fred)&~old(fred)))<=>((strong(alice)|tall(alice))))&
(![X]:(~humble(X)<=>quiet(X)))&
(![X]:((~wise(X)<~>~calm(X))=>(~curious(X)<~>wise(X))))&
(?[X]:(~old(X)))&
((strong(mary)&~rich(mary)))&
(?[X]:((kind(X)|old(X))))&
(?[X]:((~rich(X)&patient(X))))&
(?[X]:((creative(X)|~funny(X))))&
((creative(alice)<~>~brave(alice)))&
(?[X]:((wise(X)&rich(X)))) | generous(mary) | [
"p3",
"p4",
"p5",
"p6",
"p7",
"p9",
"p11",
"p14",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 3347425272357712072408237
% SZS output start Proof for 3347425272357712072408237
4. ! [X0] : ((~strong(X0) & calm(X0)) <=> (wise(X0) | old(X0))) [input p3]
5. ! [X0] : ((~calm(X0) & happy(X0)) => (~happy(X0) | patient(X0))) [input p4]
6. ! [X0] : ((~happy(X0) | ~curious(X0)) => (~kind(X0) & creative(X0))) [input p5]
7. ! [X0] : ((happy(X0) & curious(X0)) <=> (strong(X0) | ~kind(X0))) [input p6]
8. ! [X0] : (humble(X0) <=> (~generous(X0) <~> kind(X0))) [input p7]
10. ! [X0] : ((strong(X0) | ~curious(X0)) => ~kind(X0)) [input p9]
12. ! [X0] : ((strong(X0) | kind(X0)) <=> (quiet(X0) <~> ~patient(X0))) [input p11]
15. ! [X0] : (~humble(X0) <=> quiet(X0)) [input p14]
16. ! [X0] : ((~wise(X0) <~> ~calm(X0)) => (~curious(X0) <~> wise(X0))) [input p15]
18. ~rich(mary) & strong(mary) [input p17]
24. ~generous(mary) [input hypothesis]
28. ! [X0] : ((~happy(X0) | patient(X0)) | (calm(X0) | ~happy(X0))) [ennf transformation 5]
29. ! [X0] : (~happy(X0) | patient(X0) | calm(X0) | ~happy(X0)) [flattening 28]
30. ! [X0] : ((~kind(X0) & creative(X0)) | (happy(X0) & curious(X0))) [ennf transformation 6]
32. ! [X0] : (~kind(X0) | (~strong(X0) & curious(X0))) [ennf transformation 10]
35. ! [X0] : ((~curious(X0) <~> wise(X0)) | (~wise(X0) <=> ~calm(X0))) [ennf transformation 16]
39. ! [X0] : (((~strong(X0) & calm(X0)) | (~wise(X0) & ~old(X0))) & ((wise(X0) | old(X0)) | (strong(X0) | ~calm(X0)))) [nnf transformation 4]
40. ! [X0] : (((~strong(X0) & calm(X0)) | (~wise(X0) & ~old(X0))) & (wise(X0) | old(X0) | strong(X0) | ~calm(X0))) [flattening 39]
41. ! [X0] : (((happy(X0) & curious(X0)) | (~strong(X0) & kind(X0))) & ((strong(X0) | ~kind(X0)) | (~happy(X0) | ~curious(X0)))) [nnf transformation 7]
42. ! [X0] : (((happy(X0) & curious(X0)) | (~strong(X0) & kind(X0))) & (strong(X0) | ~kind(X0) | ~happy(X0) | ~curious(X0))) [flattening 41]
43. ! [X0] : ((humble(X0) | ((~generous(X0) | ~kind(X0)) & (kind(X0) | generous(X0)))) & (((~kind(X0) | generous(X0)) & (kind(X0) | ~generous(X0))) | ~humble(X0))) [nnf transformation 8]
49. ! [X0] : (((strong(X0) | kind(X0)) | ((quiet(X0) | patient(X0)) & (~patient(X0) | ~quiet(X0)))) & (((patient(X0) | ~quiet(X0)) & (~patient(X0) | quiet(X0))) | (~strong(X0) & ~kind(X0)))) [nnf transformation 12]
50. ! [X0] : ((strong(X0) | kind(X0) | ((quiet(X0) | patient(X0)) & (~patient(X0) | ~quiet(X0)))) & (((patient(X0) | ~quiet(X0)) & (~patient(X0) | quiet(X0))) | (~strong(X0) & ~kind(X0)))) [flattening 49]
53. ! [X0] : ((~humble(X0) | ~quiet(X0)) & (quiet(X0) | humble(X0))) [nnf transformation 15]
54. ! [X0] : (((~wise(X0) | curious(X0)) & (wise(X0) | ~curious(X0))) | ((~wise(X0) | calm(X0)) & (~calm(X0) | wise(X0)))) [nnf transformation 35]
78. ~wise(X0) | ~strong(X0) [cnf transformation 40]
79. ~happy(X0) | patient(X0) | calm(X0) | ~happy(X0) [cnf transformation 29]
82. ~kind(X0) | curious(X0) [cnf transformation 30]
83. ~kind(X0) | happy(X0) [cnf transformation 30]
84. strong(X0) | ~kind(X0) | ~happy(X0) | ~curious(X0) [cnf transformation 42]
85. curious(X0) | kind(X0) [cnf transformation 42]
87. happy(X0) | kind(X0) [cnf transformation 42]
91. generous(X0) | kind(X0) | humble(X0) [cnf transformation 43]
95. ~kind(X0) | ~strong(X0) [cnf transformation 32]
101. ~strong(X0) | quiet(X0) | ~patient(X0) [cnf transformation 50]
113. ~quiet(X0) | ~humble(X0) [cnf transformation 53]
114. wise(X0) | ~curious(X0) | ~calm(X0) | wise(X0) [cnf transformation 54]
119. strong(mary) [cnf transformation 18]
129. ~generous(mary) [cnf transformation 24]
130. wise(X0) | ~curious(X0) | ~calm(X0) [duplicate literal removal 114]
132. ~happy(X0) | patient(X0) | calm(X0) [duplicate literal removal 79]
179. happy(X0) [subsumption resolution 87,83]
180. curious(X0) [subsumption resolution 85,82]
181. strong(X0) | ~kind(X0) | ~curious(X0) [subsumption resolution 84,179]
182. ~kind(X0) | strong(X0) [subsumption resolution 181,180]
195. ~kind(X0) [subsumption resolution 95,182]
220. ~calm(X0) | wise(X0) [subsumption resolution 130,180]
262. kind(mary) | humble(mary) [resolution 91,129]
265. humble(mary) [subsumption resolution 262,195]
269. quiet(mary) | ~patient(mary) [resolution 101,119]
271. 22 <=> patient(mary) [avatar definition]
275. 23 <=> quiet(mary) [avatar definition]
277. quiet(mary) <- (23) [avatar component clause 275]
278. ~22 | 23 [avatar split clause 269,275,271]
281. calm(X0) | patient(X0) [resolution 132,179]
283. wise(X0) | patient(X0) [resolution 281,220]
291. ~strong(X0) | patient(X0) [resolution 283,78]
294. patient(mary) [resolution 291,119]
297. 22 [avatar split clause 294,271]
303. ~humble(mary) <- (23) [resolution 277,113]
304. $false <- (23) [subsumption resolution 303,265]
305. ~23 [avatar contradiction clause 304]
306. $false [avatar sat refutation 278,297,305]
% SZS output end Proof for 3347425272357712072408237
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is strong is either not creative or tall.
Everyone who is both not strong and generous is both creative and quiet.
Everyone who is both not tall and kind is both not curious and not rich.
Everyone who is not strong is humble or curious.
If someone is not old or not tall then john is either not generous or not curious.
If someone is both creative and rich then susan is both old and kind.
Everyone who is humble is either not brave or not rich and vice versa.
Everyone who is generous or not funny is not old and vice versa.
If someone is rich or kind then alice is both curious and humble.
Everyone who is strong is both rich and not old and vice versa.
If susan is not curious or brave then someone is both wise and not quiet.
Everyone who is either not humble or rich is patient or wise.
If someone is both quiet and not tall then someone is kind and vice versa.
If paul is creative or not quiet then someone is wise or calm and vice versa.
If someone is both not brave and not patient then john is both generous and not generous.
Everyone who is not funny is generous or not funny.
Paul is funny or kind.
Alice is both curious and happy.
Lucy is wise.
Someone is not calm or not strong.
Someone is either happy or not kind.
Someone is both not creative and tall.
Mary is both quiet and brave.
Susan is not old. | John is kind. | neutral | (![X]:(strong(X)=>(~creative(X)<~>tall(X))))&
(![X]:((~strong(X)&generous(X))=>(creative(X)&quiet(X))))&
(![X]:((~tall(X)&kind(X))=>(~curious(X)&~rich(X))))&
(![X]:(~strong(X)=>(humble(X)|curious(X))))&
((?[X]:((~old(X)|~tall(X))))=>((~generous(john)<~>~curious(john))))&
((?[X]:((creative(X)&rich(X))))=>((old(susan)&kind(susan))))&
(![X]:(humble(X)<=>(~brave(X)<~>~rich(X))))&
(![X]:((generous(X)|~funny(X))<=>~old(X)))&
((?[X]:((rich(X)|kind(X))))=>((curious(alice)&humble(alice))))&
(![X]:(strong(X)<=>(rich(X)&~old(X))))&
(((~curious(susan)|brave(susan)))=>(?[X]:((wise(X)&~quiet(X)))))&
(![X]:((~humble(X)<~>rich(X))=>(patient(X)|wise(X))))&
((?[X]:((quiet(X)&~tall(X))))<=>(?[X]:(kind(X))))&
(((creative(paul)|~quiet(paul)))<=>(?[X]:((wise(X)|calm(X)))))&
((?[X]:((~brave(X)&~patient(X))))=>((generous(john)&~generous(john))))&
(![X]:(~funny(X)=>(generous(X)|~funny(X))))&
((funny(paul)|kind(paul)))&
((curious(alice)&happy(alice)))&
(wise(lucy))&
(?[X]:((~calm(X)|~strong(X))))&
(?[X]:((happy(X)<~>~kind(X))))&
(?[X]:((~creative(X)&tall(X))))&
((quiet(mary)&brave(mary)))&
(~old(susan)) | kind(john) | [] | null | 0 |
If someone is both not brave and calm then someone is both not rich and rich and vice versa. If someone is both rich and not happy then someone is not tall or generous and vice versa. If paul is patient then john is happy and vice versa. If susan is not old then lucy is not creative or not kind and vice versa. Everyone who is happy or humble is not generous or not tall. If someone is humble or not brave then alice is not patient or curious. Everyone who is both calm and not calm is not brave. Everyone who is either generous or calm is either tall or wise. If someone is generous then alice is either rich or creative and vice versa. Everyone who is either not calm or not tall is old. If someone is not creative or old then someone is old or not funny and vice versa. Everyone who is both not generous and not brave is curious or tall. If someone is both not patient and not kind then paul is both creative and strong and vice versa. If mary is both humble and not generous then mary is rich. If someone is either patient or rich then someone is not strong or not tall and vice versa. Everyone who is either kind or funny is not wise or not humble and vice versa. Alice is either patient or generous. Mary is either not humble or creative. Mary is either not patient or not strong. Someone is rich or patient. Alice is both not tall and creative. Alice is not tall. Someone is both rich and generous. Someone is not patient or not happy. | Alice is not tall. | entailment | ((?[X]:((~brave(X)&calm(X))))<=>(?[X]:((~rich(X)&rich(X)))))&
((?[X]:((rich(X)&~happy(X))))<=>(?[X]:((~tall(X)|generous(X)))))&
((patient(paul))<=>(happy(john)))&
((~old(susan))<=>((~creative(lucy)|~kind(lucy))))&
(![X]:((happy(X)|humble(X))=>(~generous(X)|~tall(X))))&
((?[X]:((humble(X)|~brave(X))))=>((~patient(alice)|curious(alice))))&
(![X]:((calm(X)&~calm(X))=>~brave(X)))&
(![X]:((generous(X)<~>calm(X))=>(tall(X)<~>wise(X))))&
((?[X]:(generous(X)))<=>((rich(alice)<~>creative(alice))))&
(![X]:((~calm(X)<~>~tall(X))=>old(X)))&
((?[X]:((~creative(X)|old(X))))<=>(?[X]:((old(X)|~funny(X)))))&
(![X]:((~generous(X)&~brave(X))=>(curious(X)|tall(X))))&
((?[X]:((~patient(X)&~kind(X))))<=>((creative(paul)&strong(paul))))&
(((humble(mary)&~generous(mary)))=>(rich(mary)))&
((?[X]:((patient(X)<~>rich(X))))<=>(?[X]:((~strong(X)|~tall(X)))))&
(![X]:((kind(X)<~>funny(X))<=>(~wise(X)|~humble(X))))&
((patient(alice)<~>generous(alice)))&
((~humble(mary)<~>creative(mary)))&
((~patient(mary)<~>~strong(mary)))&
(?[X]:((rich(X)|patient(X))))&
((~tall(alice)&creative(alice)))&
(~tall(alice))&
(?[X]:((rich(X)&generous(X))))&
(?[X]:((~patient(X)|~happy(X)))) | ~tall(alice) | [
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4603052246198614730943584
% SZS output start Proof for 4603052246198614730943584
21. creative(alice) & ~tall(alice) [input p20]
25. tall(alice) [input hypothesis]
140. ~tall(alice) [cnf transformation 21]
146. tall(alice) [cnf transformation 25]
368. $false [subsumption resolution 146,140]
% SZS output end Proof for 4603052246198614730943584
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny is both not patient and not curious and vice versa.
Everyone who is either old or not quiet is both strong and brave and vice versa.
Everyone who is either not tall or not creative is funny or generous.
Everyone who is not kind is both funny and not happy.
Everyone who is either not tall or happy is both brave and funny and vice versa.
Everyone who is old or not calm is calm or not quiet and vice versa.
Everyone who is not generous or not humble is either kind or not tall and vice versa.
Everyone who is not curious is either not happy or happy and vice versa.
Everyone who is both not curious and not happy is humble.
If someone is both brave and not patient then someone is not wise or not patient and vice versa.
Everyone who is either kind or patient is not humble or brave.
If fred is either not patient or not rich then fred is both not patient and rich.
If lucy is not kind then lucy is wise.
Everyone who is calm is both not funny and not rich.
Everyone who is quiet is kind.
If fred is not curious then alice is wise or not rich and vice versa.
Someone is brave.
Fred is not brave or rich.
Mary is creative or not wise.
Someone is quiet.
Someone is both not patient and not calm.
John is not happy or tall.
Mary is not brave or happy. | Lucy is not old. | neutral | (![X]:(funny(X)<=>(~patient(X)&~curious(X))))&
(![X]:((old(X)<~>~quiet(X))<=>(strong(X)&brave(X))))&
(![X]:((~tall(X)<~>~creative(X))=>(funny(X)|generous(X))))&
(![X]:(~kind(X)=>(funny(X)&~happy(X))))&
(![X]:((~tall(X)<~>happy(X))<=>(brave(X)&funny(X))))&
(![X]:((old(X)|~calm(X))<=>(calm(X)|~quiet(X))))&
(![X]:((~generous(X)|~humble(X))<=>(kind(X)<~>~tall(X))))&
(![X]:(~curious(X)<=>(~happy(X)<~>happy(X))))&
(![X]:((~curious(X)&~happy(X))=>humble(X)))&
((?[X]:((brave(X)&~patient(X))))<=>(?[X]:((~wise(X)|~patient(X)))))&
(![X]:((kind(X)<~>patient(X))=>(~humble(X)|brave(X))))&
(((~patient(fred)<~>~rich(fred)))=>((~patient(fred)&rich(fred))))&
((~kind(lucy))=>(wise(lucy)))&
(![X]:(calm(X)=>(~funny(X)&~rich(X))))&
(![X]:(quiet(X)=>kind(X)))&
((~curious(fred))<=>((wise(alice)|~rich(alice))))&
(?[X]:(brave(X)))&
((~brave(fred)|rich(fred)))&
((creative(mary)|~wise(mary)))&
(?[X]:(quiet(X)))&
(?[X]:((~patient(X)&~calm(X))))&
((~happy(john)|tall(john)))&
((~brave(mary)|happy(mary))) | ~old(lucy) | [] | null | 0 |
If mary is both rich and not brave then mary is generous.
Everyone who is calm or happy is both not rich and not wise.
Everyone who is not humble is calm and vice versa.
If someone is patient then someone is creative.
If someone is both generous and not creative then lucy is not old.
Everyone who is not tall or brave is either brave or not humble.
Everyone who is not strong or calm is humble or funny.
If someone is not brave or brave then someone is quiet or generous.
Everyone who is both not brave and curious is rich or not funny.
If someone is either old or wise then susan is not curious or strong.
Everyone who is kind is both not happy and not humble and vice versa.
Everyone who is not tall is funny.
Everyone who is either not calm or not humble is not strong or brave and vice versa.
If someone is both wise and not generous then john is either not happy or creative and vice versa.
Everyone who is generous or creative is not funny or not creative.
Everyone who is both not curious and not quiet is not wise or old and vice versa.
Fred is kind or not rich.
Someone is not patient.
Paul is kind.
Fred is rich or not strong.
Paul is either rich or not happy.
Someone is either strong or patient.
Someone is both strong and quiet. | Mary is not creative. | neutral | (((rich(mary)&~brave(mary)))=>(generous(mary)))&
(![X]:((calm(X)|happy(X))=>(~rich(X)&~wise(X))))&
(![X]:(~humble(X)<=>calm(X)))&
((?[X]:(patient(X)))=>(?[X]:(creative(X))))&
((?[X]:((generous(X)&~creative(X))))=>(~old(lucy)))&
(![X]:((~tall(X)|brave(X))=>(brave(X)<~>~humble(X))))&
(![X]:((~strong(X)|calm(X))=>(humble(X)|funny(X))))&
((?[X]:((~brave(X)|brave(X))))=>(?[X]:((quiet(X)|generous(X)))))&
(![X]:((~brave(X)&curious(X))=>(rich(X)|~funny(X))))&
((?[X]:((old(X)<~>wise(X))))=>((~curious(susan)|strong(susan))))&
(![X]:(kind(X)<=>(~happy(X)&~humble(X))))&
(![X]:(~tall(X)=>funny(X)))&
(![X]:((~calm(X)<~>~humble(X))<=>(~strong(X)|brave(X))))&
((?[X]:((wise(X)&~generous(X))))<=>((~happy(john)<~>creative(john))))&
(![X]:((generous(X)|creative(X))=>(~funny(X)|~creative(X))))&
(![X]:((~curious(X)&~quiet(X))<=>(~wise(X)|old(X))))&
((kind(fred)|~rich(fred)))&
(?[X]:(~patient(X)))&
(kind(paul))&
((rich(fred)|~strong(fred)))&
((rich(paul)<~>~happy(paul)))&
(?[X]:((strong(X)<~>patient(X))))&
(?[X]:((strong(X)&quiet(X)))) | ~creative(mary) | [] | null | 0 |
If john is either not patient or old then someone is either not creative or humble.
Everyone who is both not wise and not patient is either strong or old and vice versa.
Everyone who is calm or not creative is either not old or not curious.
Everyone who is both not wise and not old is both not humble and not kind.
Everyone who is not brave or not funny is not calm.
If someone is not generous or not kind then lucy is not funny and vice versa.
If paul is not patient or humble then someone is patient or not funny and vice versa.
Everyone who is both happy and not wise is both rich and happy.
Everyone who is both not curious and not creative is generous.
If paul is either brave or not quiet then susan is not rich or not strong and vice versa.
Everyone who is either creative or not happy is not tall or wise and vice versa.
If susan is not wise then someone is not strong or not patient.
If someone is either not old or not quiet then someone is both funny and not curious and vice versa.
If fred is both not wise and patient then alice is either strong or not wise and vice versa.
Everyone who is both quiet and not kind is brave or not happy and vice versa.
Someone is either not happy or kind.
Paul is old.
John is not happy or not calm.
Mary is either not tall or generous.
Mary is brave.
Someone is not old.
John is tall.
Alice is both not old and humble. | Susan is patient. | neutral | (((~patient(john)<~>old(john)))=>(?[X]:((~creative(X)<~>humble(X)))))&
(![X]:((~wise(X)&~patient(X))<=>(strong(X)<~>old(X))))&
(![X]:((calm(X)|~creative(X))=>(~old(X)<~>~curious(X))))&
(![X]:((~wise(X)&~old(X))=>(~humble(X)&~kind(X))))&
(![X]:((~brave(X)|~funny(X))=>~calm(X)))&
((?[X]:((~generous(X)|~kind(X))))<=>(~funny(lucy)))&
(((~patient(paul)|humble(paul)))<=>(?[X]:((patient(X)|~funny(X)))))&
(![X]:((happy(X)&~wise(X))=>(rich(X)&happy(X))))&
(![X]:((~curious(X)&~creative(X))=>generous(X)))&
(((brave(paul)<~>~quiet(paul)))<=>((~rich(susan)|~strong(susan))))&
(![X]:((creative(X)<~>~happy(X))<=>(~tall(X)|wise(X))))&
((~wise(susan))=>(?[X]:((~strong(X)|~patient(X)))))&
((?[X]:((~old(X)<~>~quiet(X))))<=>(?[X]:((funny(X)&~curious(X)))))&
(((~wise(fred)&patient(fred)))<=>((strong(alice)<~>~wise(alice))))&
(![X]:((quiet(X)&~kind(X))<=>(brave(X)|~happy(X))))&
(?[X]:((~happy(X)<~>kind(X))))&
(old(paul))&
((~happy(john)|~calm(john)))&
((~tall(mary)<~>generous(mary)))&
(brave(mary))&
(?[X]:(~old(X)))&
(tall(john))&
((~old(alice)&humble(alice))) | patient(susan) | [] | null | 0 |
Everyone who is calm or not rich is either quiet or not curious.
Everyone who is not kind is both not wise and not curious and vice versa.
Everyone who is either old or not happy is both not wise and kind.
Everyone who is happy is curious or not curious.
Everyone who is strong or not generous is both patient and not happy.
Everyone who is both not wise and generous is either patient or not kind and vice versa.
Everyone who is either kind or not kind is either not funny or not tall and vice versa.
If someone is strong or not curious then john is not kind.
Everyone who is either not patient or not rich is brave and vice versa.
Everyone who is not strong is not old or funny.
Everyone who is both not creative and not funny is quiet or not rich and vice versa.
If alice is not quiet then someone is both humble and kind.
If someone is either tall or rich then lucy is both not strong and patient.
Everyone who is either curious or not happy is both funny and old and vice versa.
If someone is either not tall or curious then someone is not humble.
Everyone who is not humble is both not generous and not rich and vice versa.
Paul is strong or not happy. | Paul is not generous. | contradiction | (![X]:((calm(X)|~rich(X))=>(quiet(X)<~>~curious(X))))&
(![X]:(~kind(X)<=>(~wise(X)&~curious(X))))&
(![X]:((old(X)<~>~happy(X))=>(~wise(X)&kind(X))))&
(![X]:(happy(X)=>(curious(X)|~curious(X))))&
(![X]:((strong(X)|~generous(X))=>(patient(X)&~happy(X))))&
(![X]:((~wise(X)&generous(X))<=>(patient(X)<~>~kind(X))))&
(![X]:((kind(X)<~>~kind(X))<=>(~funny(X)<~>~tall(X))))&
((?[X]:((strong(X)|~curious(X))))=>(~kind(john)))&
(![X]:((~patient(X)<~>~rich(X))<=>brave(X)))&
(![X]:(~strong(X)=>(~old(X)|funny(X))))&
(![X]:((~creative(X)&~funny(X))<=>(quiet(X)|~rich(X))))&
((~quiet(alice))=>(?[X]:((humble(X)&kind(X)))))&
((?[X]:((tall(X)<~>rich(X))))=>((~strong(lucy)&patient(lucy))))&
(![X]:((curious(X)<~>~happy(X))<=>(funny(X)&old(X))))&
((?[X]:((~tall(X)<~>curious(X))))=>(?[X]:(~humble(X))))&
(![X]:(~humble(X)<=>(~generous(X)&~rich(X))))&
((strong(paul)|~happy(paul))) | ~generous(paul) | [
"p1",
"p2",
"p4",
"p5",
"p6",
"p10",
"p13",
"p14",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 6461872342714345859104104
% SZS output start Proof for 6461872342714345859104104
2. ! [X0] : (~kind(X0) <=> (~curious(X0) & ~wise(X0))) [input p1]
3. ! [X0] : ((old(X0) <~> ~happy(X0)) => (kind(X0) & ~wise(X0))) [input p2]
5. ! [X0] : ((~generous(X0) | strong(X0)) => (~happy(X0) & patient(X0))) [input p4]
6. ! [X0] : ((generous(X0) & ~wise(X0)) <=> (patient(X0) <~> ~kind(X0))) [input p5]
7. ! [X0] : ((kind(X0) <~> ~kind(X0)) <=> (~funny(X0) <~> ~tall(X0))) [input p6]
11. ! [X0] : ((~funny(X0) & ~creative(X0)) <=> (~rich(X0) | quiet(X0))) [input p10]
14. ! [X0] : ((curious(X0) <~> ~happy(X0)) <=> (old(X0) & funny(X0))) [input p13]
15. ? [X0] : (~tall(X0) <~> curious(X0)) => ? [X0] : ~humble(X0) [input p14]
16. ! [X0] : (~humble(X0) <=> (~rich(X0) & ~generous(X0))) [input p15]
17. ~happy(paul) | strong(paul) [input p16]
18. ~generous(paul) [input hypothesis]
19. ? [X0] : (~tall(X0) <~> curious(X0)) => ? [X1] : ~humble(X1) [rectify 15]
22. ! [X0] : ((kind(X0) & ~wise(X0)) | (old(X0) <=> ~happy(X0))) [ennf transformation 3]
25. ! [X0] : ((~happy(X0) & patient(X0)) | (generous(X0) & ~strong(X0))) [ennf transformation 5]
31. ? [X1] : ~humble(X1) | ! [X0] : (~tall(X0) <=> curious(X0)) [ennf transformation 19]
33. ! [X0] : ((~kind(X0) | (curious(X0) | wise(X0))) & ((~curious(X0) & ~wise(X0)) | kind(X0))) [nnf transformation 2]
34. ! [X0] : ((~kind(X0) | curious(X0) | wise(X0)) & ((~curious(X0) & ~wise(X0)) | kind(X0))) [flattening 33]
35. ! [X0] : ((kind(X0) & ~wise(X0)) | ((old(X0) | happy(X0)) & (~happy(X0) | ~old(X0)))) [nnf transformation 22]
36. ! [X0] : (((generous(X0) & ~wise(X0)) | ((patient(X0) | kind(X0)) & (~kind(X0) | ~patient(X0)))) & (((kind(X0) | ~patient(X0)) & (~kind(X0) | patient(X0))) | (~generous(X0) | wise(X0)))) [nnf transformation 6]
37. ! [X0] : (((generous(X0) & ~wise(X0)) | ((patient(X0) | kind(X0)) & (~kind(X0) | ~patient(X0)))) & (((kind(X0) | ~patient(X0)) & (~kind(X0) | patient(X0))) | ~generous(X0) | wise(X0))) [flattening 36]
38. ! [X0] : ((((kind(X0) | ~kind(X0)) & (~kind(X0) | kind(X0))) | ((~funny(X0) | tall(X0)) & (~tall(X0) | funny(X0)))) & (((tall(X0) | funny(X0)) & (~tall(X0) | ~funny(X0))) | ((kind(X0) | kind(X0)) & (~kind(X0) | ~kind(X0))))) [nnf transformation 7]
39. ! [X0] : (((~funny(X0) & ~creative(X0)) | (rich(X0) & ~quiet(X0))) & ((~rich(X0) | quiet(X0)) | (funny(X0) | creative(X0)))) [nnf transformation 11]
40. ! [X0] : (((~funny(X0) & ~creative(X0)) | (rich(X0) & ~quiet(X0))) & (~rich(X0) | quiet(X0) | funny(X0) | creative(X0))) [flattening 39]
44. ! [X0] : ((((happy(X0) | ~curious(X0)) & (~happy(X0) | curious(X0))) | (~old(X0) | ~funny(X0))) & ((old(X0) & funny(X0)) | ((curious(X0) | happy(X0)) & (~happy(X0) | ~curious(X0))))) [nnf transformation 14]
45. ! [X0] : ((((happy(X0) | ~curious(X0)) & (~happy(X0) | curious(X0))) | ~old(X0) | ~funny(X0)) & ((old(X0) & funny(X0)) | ((curious(X0) | happy(X0)) & (~happy(X0) | ~curious(X0))))) [flattening 44]
46. ? [X1] : ~humble(X1) | ! [X0] : ((~tall(X0) | ~curious(X0)) & (curious(X0) | tall(X0))) [nnf transformation 31]
47. ? [X0] : ~humble(X0) | ! [X1] : ((~tall(X1) | ~curious(X1)) & (curious(X1) | tall(X1))) [rectify 46]
48. ? [X0] : ~humble(X0) => ~humble(sK1) [choice axiom]
49. ~humble(sK1) | ! [X1] : ((~tall(X1) | ~curious(X1)) & (curious(X1) | tall(X1))) [skolemisation 47,48]
50. ! [X0] : ((~humble(X0) | (rich(X0) | generous(X0))) & ((~rich(X0) & ~generous(X0)) | humble(X0))) [nnf transformation 16]
51. ! [X0] : ((~humble(X0) | rich(X0) | generous(X0)) & ((~rich(X0) & ~generous(X0)) | humble(X0))) [flattening 50]
55. ~curious(X0) | kind(X0) [cnf transformation 34]
59. ~happy(X0) | kind(X0) | ~old(X0) [cnf transformation 35]
60. happy(X0) | old(X0) | kind(X0) [cnf transformation 35]
63. patient(X0) | generous(X0) [cnf transformation 25]
64. ~strong(X0) | ~happy(X0) [cnf transformation 25]
65. ~happy(X0) | generous(X0) [cnf transformation 25]
70. generous(X0) | ~kind(X0) | ~patient(X0) [cnf transformation 37]
72. ~tall(X0) | ~funny(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 38]
73. ~tall(X0) | ~funny(X0) | kind(X0) | kind(X0) [cnf transformation 38]
87. ~funny(X0) | rich(X0) [cnf transformation 40]
95. funny(X0) | curious(X0) | happy(X0) [cnf transformation 45]
100. ~humble(sK1) | curious(X1) | tall(X1) [cnf transformation 49]
102. ~generous(X0) | humble(X0) [cnf transformation 51]
103. ~rich(X0) | humble(X0) [cnf transformation 51]
105. ~happy(paul) | strong(paul) [cnf transformation 17]
106. ~generous(paul) [cnf transformation 18]
107. ~tall(X0) | ~funny(X0) | ~kind(X0) [duplicate literal removal 72]
108. ~tall(X0) | ~funny(X0) | kind(X0) [duplicate literal removal 73]
111. ~kind(X0) | generous(X0) [subsumption resolution 70,63]
116. ~tall(X0) | ~funny(X0) [subsumption resolution 107,108]
165. 12 <=> humble(sK1) [avatar definition]
167. ~humble(sK1) <- (~12) [avatar component clause 165]
170. 13 <=> ! [X1] : (curious(X1) | tall(X1)) [avatar definition]
171. tall(X1) | curious(X1) <- (13) [avatar component clause 170]
172. 13 | ~12 [avatar split clause 100,165,170]
173. ~happy(paul) [subsumption resolution 105,64]
204. old(X2) | kind(X2) | generous(X2) [resolution 60,65]
207. 18 <=> kind(paul) [avatar definition]
208. ~kind(paul) <- (~18) [avatar component clause 207]
209. kind(paul) <- (18) [avatar component clause 207]
215. generous(X2) | old(X2) [subsumption resolution 204,111]
217. generous(paul) <- (18) [resolution 209,111]
223. 21 <=> curious(paul) [avatar definition]
224. ~curious(paul) <- (~21) [avatar component clause 223]
225. curious(paul) <- (21) [avatar component clause 223]
227. $false <- (18) [subsumption resolution 217,106]
228. ~18 [avatar contradiction clause 227]
240. happy(X0) | curious(X0) | rich(X0) [resolution 95,87]
268. humble(X0) | old(X0) [resolution 215,102]
336. curious(X2) | rich(X2) | kind(X2) | ~old(X2) [resolution 240,59]
344. ~old(X2) | kind(X2) | rich(X2) [subsumption resolution 336,55]
346. kind(paul) <- (21) [resolution 225,55]
352. $false <- (~18, 21) [subsumption resolution 346,208]
353. 18 | ~21 [avatar contradiction clause 352]
427. 44 <=> rich(sK1) [avatar definition]
429. rich(sK1) <- (44) [avatar component clause 427]
431. 45 <=> kind(sK1) [avatar definition]
433. kind(sK1) <- (45) [avatar component clause 431]
437. 46 <=> generous(sK1) [avatar definition]
439. generous(sK1) <- (46) [avatar component clause 437]
446. ~funny(X2) | curious(X2) <- (13) [resolution 171,116]
452. curious(X0) | curious(X0) | happy(X0) <- (13) [resolution 446,95]
455. happy(X0) | curious(X0) <- (13) [duplicate literal removal 452]
515. curious(paul) <- (13) [resolution 455,173]
521. $false <- (13, ~21) [subsumption resolution 515,224]
522. ~13 | 21 [avatar contradiction clause 521]
544. old(sK1) <- (~12) [resolution 167,268]
590. kind(sK1) | rich(sK1) <- (~12) [resolution 544,344]
612. humble(sK1) <- (44) [resolution 429,103]
622. $false <- (~12, 44) [subsumption resolution 612,167]
623. 12 | ~44 [avatar contradiction clause 622]
624. 44 | 45 | 12 [avatar split clause 590,165,431,427]
627. generous(sK1) <- (45) [resolution 433,111]
628. 46 | ~45 [avatar split clause 627,431,437]
629. humble(sK1) <- (46) [resolution 439,102]
630. $false <- (~12, 46) [subsumption resolution 629,167]
631. 12 | ~46 [avatar contradiction clause 630]
632. $false [avatar sat refutation 172,228,353,522,623,624,628,631]
% SZS output end Proof for 6461872342714345859104104
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is not humble is both not strong and not creative and vice versa.
If alice is not wise then susan is brave or not old and vice versa.
Everyone who is both not strong and not rich is either not tall or funny and vice versa.
If susan is not calm then alice is either not calm or not funny and vice versa.
Everyone who is tall or brave is not wise and vice versa.
If someone is not calm then someone is not tall or not rich.
If alice is either wise or not brave then someone is both generous and not wise and vice versa.
If someone is calm then someone is calm or not funny and vice versa.
Everyone who is patient is tall or not old and vice versa.
Everyone who is generous is both rich and not quiet and vice versa.
Everyone who is not funny is either not old or patient and vice versa.
If someone is not tall then someone is not brave or not generous and vice versa.
Everyone who is either curious or not quiet is both not patient and not rich.
If fred is either generous or not patient then fred is not brave.
Everyone who is old is both creative and not funny and vice versa.
Everyone who is both not quiet and not curious is wise or not funny and vice versa.
Mary is either calm or patient.
Someone is brave.
John is either not funny or tall.
Susan is not curious.
Someone is tall. | Mary is patient. | entailment | (![X]:(~humble(X)<=>(~strong(X)&~creative(X))))&
((~wise(alice))<=>((brave(susan)|~old(susan))))&
(![X]:((~strong(X)&~rich(X))<=>(~tall(X)<~>funny(X))))&
((~calm(susan))<=>((~calm(alice)<~>~funny(alice))))&
(![X]:((tall(X)|brave(X))<=>~wise(X)))&
((?[X]:(~calm(X)))=>(?[X]:((~tall(X)|~rich(X)))))&
(((wise(alice)<~>~brave(alice)))<=>(?[X]:((generous(X)&~wise(X)))))&
((?[X]:(calm(X)))<=>(?[X]:((calm(X)|~funny(X)))))&
(![X]:(patient(X)<=>(tall(X)|~old(X))))&
(![X]:(generous(X)<=>(rich(X)&~quiet(X))))&
(![X]:(~funny(X)<=>(~old(X)<~>patient(X))))&
((?[X]:(~tall(X)))<=>(?[X]:((~brave(X)|~generous(X)))))&
(![X]:((curious(X)<~>~quiet(X))=>(~patient(X)&~rich(X))))&
(((generous(fred)<~>~patient(fred)))=>(~brave(fred)))&
(![X]:(old(X)<=>(creative(X)&~funny(X))))&
(![X]:((~quiet(X)&~curious(X))<=>(wise(X)|~funny(X))))&
((calm(mary)<~>patient(mary)))&
(?[X]:(brave(X)))&
((~funny(john)<~>tall(john)))&
(~curious(susan))&
(?[X]:(tall(X))) | patient(mary) | [
"p8",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2508410048821915412887869
% SZS output start Proof for 2508410048821915412887869
9. ! [X0] : (patient(X0) <=> (~old(X0) | tall(X0))) [input p8]
11. ! [X0] : (~funny(X0) <=> (~old(X0) <~> patient(X0))) [input p10]
15. ! [X0] : (old(X0) <=> (~funny(X0) & creative(X0))) [input p14]
22. ~patient(mary) [input hypothesis]
48. ! [X0] : ((patient(X0) | (old(X0) & ~tall(X0))) & ((~old(X0) | tall(X0)) | ~patient(X0))) [nnf transformation 9]
49. ! [X0] : ((patient(X0) | (old(X0) & ~tall(X0))) & (~old(X0) | tall(X0) | ~patient(X0))) [flattening 48]
52. ! [X0] : ((~funny(X0) | ((~old(X0) | ~patient(X0)) & (patient(X0) | old(X0)))) & (((~patient(X0) | old(X0)) & (patient(X0) | ~old(X0))) | funny(X0))) [nnf transformation 11]
60. ! [X0] : ((old(X0) | (funny(X0) | ~creative(X0))) & ((~funny(X0) & creative(X0)) | ~old(X0))) [nnf transformation 15]
61. ! [X0] : ((old(X0) | funny(X0) | ~creative(X0)) & ((~funny(X0) & creative(X0)) | ~old(X0))) [flattening 60]
98. patient(X0) | old(X0) [cnf transformation 49]
102. patient(X0) | ~old(X0) | funny(X0) [cnf transformation 52]
103. ~patient(X0) | old(X0) | funny(X0) [cnf transformation 52]
116. ~funny(X0) | ~old(X0) [cnf transformation 61]
130. ~patient(mary) [cnf transformation 22]
216. funny(X0) | old(X0) [subsumption resolution 103,98]
217. patient(X0) | funny(X0) [subsumption resolution 102,216]
261. 29 <=> patient(mary) [avatar definition]
263. ~patient(mary) <- (~29) [avatar component clause 261]
276. ~29 [avatar split clause 130,261]
281. old(mary) <- (~29) [resolution 98,263]
287. funny(mary) <- (~29) [resolution 217,263]
302. ~old(mary) <- (~29) [resolution 287,116]
312. $false <- (~29) [subsumption resolution 302,281]
313. 29 [avatar contradiction clause 312]
314. $false [avatar sat refutation 276,313]
% SZS output end Proof for 2508410048821915412887869
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient is both wise and not tall and vice versa.
Everyone who is brave is wise or calm.
If paul is not creative or calm then someone is not strong and vice versa.
If someone is both tall and not creative then someone is both not curious and wise and vice versa.
If someone is both not kind and not wise then mary is either not tall or kind and vice versa.
Everyone who is both not patient and kind is curious and vice versa.
If susan is either not humble or calm then paul is both not rich and not brave.
Everyone who is both not patient and patient is not humble or funny and vice versa.
Everyone who is generous or happy is not strong or generous.
Everyone who is either not quiet or not kind is either not old or not generous.
Everyone who is kind is either not quiet or happy.
If someone is brave then someone is both not quiet and not humble.
Everyone who is not curious is either not curious or not wise and vice versa.
Everyone who is both brave and humble is humble or not rich.
Everyone who is not rich or quiet is both not happy and wise.
If susan is curious then mary is quiet or old.
Fred is curious or patient.
Fred is not patient or not calm.
Someone is both not old and not brave.
Mary is generous or not funny.
Someone is either not creative or tall.
Someone is rich. | Mary is generous. | neutral | (![X]:(~patient(X)<=>(wise(X)&~tall(X))))&
(![X]:(brave(X)=>(wise(X)|calm(X))))&
(((~creative(paul)|calm(paul)))<=>(?[X]:(~strong(X))))&
((?[X]:((tall(X)&~creative(X))))<=>(?[X]:((~curious(X)&wise(X)))))&
((?[X]:((~kind(X)&~wise(X))))<=>((~tall(mary)<~>kind(mary))))&
(![X]:((~patient(X)&kind(X))<=>curious(X)))&
(((~humble(susan)<~>calm(susan)))=>((~rich(paul)&~brave(paul))))&
(![X]:((~patient(X)&patient(X))<=>(~humble(X)|funny(X))))&
(![X]:((generous(X)|happy(X))=>(~strong(X)|generous(X))))&
(![X]:((~quiet(X)<~>~kind(X))=>(~old(X)<~>~generous(X))))&
(![X]:(kind(X)=>(~quiet(X)<~>happy(X))))&
((?[X]:(brave(X)))=>(?[X]:((~quiet(X)&~humble(X)))))&
(![X]:(~curious(X)<=>(~curious(X)<~>~wise(X))))&
(![X]:((brave(X)&humble(X))=>(humble(X)|~rich(X))))&
(![X]:((~rich(X)|quiet(X))=>(~happy(X)&wise(X))))&
((curious(susan))=>((quiet(mary)|old(mary))))&
((curious(fred)|patient(fred)))&
((~patient(fred)|~calm(fred)))&
(?[X]:((~old(X)&~brave(X))))&
((generous(mary)|~funny(mary)))&
(?[X]:((~creative(X)<~>tall(X))))&
(?[X]:(rich(X))) | generous(mary) | [] | null | 0 |
Everyone who is not brave or calm is old or creative.
If someone is not kind or not generous then lucy is both not old and not strong.
Everyone who is not creative or funny is either not rich or tall.
If alice is either not kind or generous then someone is both quiet and patient and vice versa.
Everyone who is not old is brave or wise.
Everyone who is both wise and not funny is not generous and vice versa.
If john is both not strong and tall then alice is happy.
Everyone who is either tall or humble is kind and vice versa.
If susan is not rich or strong then someone is wise and vice versa.
Everyone who is not funny or not kind is quiet or curious.
If alice is either happy or not funny then someone is either not brave or not old and vice versa.
Everyone who is generous is both not old and curious.
Everyone who is not old is rich.
If someone is humble or not curious then someone is calm or not calm.
Everyone who is either not curious or not generous is both creative and not brave and vice versa.
Everyone who is either curious or not patient is humble and vice versa.
Fred is both not kind and not humble.
Lucy is curious or not curious.
Someone is not brave or not funny.
Someone is not kind.
Someone is generous.
John is either not creative or not rich.
Someone is not generous.
Someone is both generous and not tall. | John is creative. | neutral | (![X]:((~brave(X)|calm(X))=>(old(X)|creative(X))))&
((?[X]:((~kind(X)|~generous(X))))=>((~old(lucy)&~strong(lucy))))&
(![X]:((~creative(X)|funny(X))=>(~rich(X)<~>tall(X))))&
(((~kind(alice)<~>generous(alice)))<=>(?[X]:((quiet(X)&patient(X)))))&
(![X]:(~old(X)=>(brave(X)|wise(X))))&
(![X]:((wise(X)&~funny(X))<=>~generous(X)))&
(((~strong(john)&tall(john)))=>(happy(alice)))&
(![X]:((tall(X)<~>humble(X))<=>kind(X)))&
(((~rich(susan)|strong(susan)))<=>(?[X]:(wise(X))))&
(![X]:((~funny(X)|~kind(X))=>(quiet(X)|curious(X))))&
(((happy(alice)<~>~funny(alice)))<=>(?[X]:((~brave(X)<~>~old(X)))))&
(![X]:(generous(X)=>(~old(X)&curious(X))))&
(![X]:(~old(X)=>rich(X)))&
((?[X]:((humble(X)|~curious(X))))=>(?[X]:((calm(X)|~calm(X)))))&
(![X]:((~curious(X)<~>~generous(X))<=>(creative(X)&~brave(X))))&
(![X]:((curious(X)<~>~patient(X))<=>humble(X)))&
((~kind(fred)&~humble(fred)))&
((curious(lucy)|~curious(lucy)))&
(?[X]:((~brave(X)|~funny(X))))&
(?[X]:(~kind(X)))&
(?[X]:(generous(X)))&
((~creative(john)<~>~rich(john)))&
(?[X]:(~generous(X)))&
(?[X]:((generous(X)&~tall(X)))) | creative(john) | [] | null | 0 |
If fred is both humble and not calm then paul is both strong and humble.
If someone is either not old or not funny then paul is quiet.
Everyone who is both not kind and quiet is either happy or not brave and vice versa.
If alice is both not generous and not curious then susan is not rich.
If fred is happy or creative then mary is either tall or not creative.
Everyone who is patient is both funny and old.
If someone is either not quiet or not wise then john is both not happy and old.
Everyone who is either not patient or not quiet is both strong and generous.
Everyone who is old is both not creative and not old and vice versa.
If someone is either brave or humble then someone is both old and funny and vice versa.
If someone is both strong and tall then someone is not generous or brave and vice versa.
If john is creative then someone is both brave and calm and vice versa.
Everyone who is tall or generous is both kind and creative and vice versa.
If paul is not quiet then someone is both brave and not strong and vice versa.
Everyone who is either not calm or not tall is funny and vice versa.
Everyone who is both old and not curious is not kind or happy and vice versa.
Someone is curious or creative.
Someone is not creative or strong.
Susan is either not creative or not tall.
Someone is either not patient or curious.
Someone is both tall and wise.
Someone is rich or curious. | John is not creative. | contradiction | (((humble(fred)&~calm(fred)))=>((strong(paul)&humble(paul))))&
((?[X]:((~old(X)<~>~funny(X))))=>(quiet(paul)))&
(![X]:((~kind(X)&quiet(X))<=>(happy(X)<~>~brave(X))))&
(((~generous(alice)&~curious(alice)))=>(~rich(susan)))&
(((happy(fred)|creative(fred)))=>((tall(mary)<~>~creative(mary))))&
(![X]:(patient(X)=>(funny(X)&old(X))))&
((?[X]:((~quiet(X)<~>~wise(X))))=>((~happy(john)&old(john))))&
(![X]:((~patient(X)<~>~quiet(X))=>(strong(X)&generous(X))))&
(![X]:(old(X)<=>(~creative(X)&~old(X))))&
((?[X]:((brave(X)<~>humble(X))))<=>(?[X]:((old(X)&funny(X)))))&
((?[X]:((strong(X)&tall(X))))<=>(?[X]:((~generous(X)|brave(X)))))&
((creative(john))<=>(?[X]:((brave(X)&calm(X)))))&
(![X]:((tall(X)|generous(X))<=>(kind(X)&creative(X))))&
((~quiet(paul))<=>(?[X]:((brave(X)&~strong(X)))))&
(![X]:((~calm(X)<~>~tall(X))<=>funny(X)))&
(![X]:((old(X)&~curious(X))<=>(~kind(X)|happy(X))))&
(?[X]:((curious(X)|creative(X))))&
(?[X]:((~creative(X)|strong(X))))&
((~creative(susan)<~>~tall(susan)))&
(?[X]:((~patient(X)<~>curious(X))))&
(?[X]:((tall(X)&wise(X))))&
(?[X]:((rich(X)|curious(X)))) | ~creative(john) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 625515324817408126824006
% SZS output start Proof for 625515324817408126824006
9. ! [X0] : (old(X0) <=> (~old(X0) & ~creative(X0))) [input p8]
23. ~creative(john) [input hypothesis]
41. ! [X0] : ((old(X0) | (old(X0) | creative(X0))) & ((~old(X0) & ~creative(X0)) | ~old(X0))) [nnf transformation 9]
42. ! [X0] : ((old(X0) | old(X0) | creative(X0)) & ((~old(X0) & ~creative(X0)) | ~old(X0))) [flattening 41]
104. ~old(X0) | ~old(X0) [cnf transformation 42]
105. old(X0) | old(X0) | creative(X0) [cnf transformation 42]
146. ~creative(john) [cnf transformation 23]
147. ~old(X0) [duplicate literal removal 104]
148. creative(X0) | old(X0) [duplicate literal removal 105]
280. 30 <=> creative(john) [avatar definition]
281. ~creative(john) <- (~30) [avatar component clause 280]
349. ~30 [avatar split clause 146,280]
362. old(john) <- (~30) [resolution 148,281]
366. $false <- (~30) [subsumption resolution 362,147]
367. 30 [avatar contradiction clause 366]
370. $false [avatar sat refutation 349,367]
% SZS output end Proof for 625515324817408126824006
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
If susan is curious or tall then someone is either not humble or not patient and vice versa.
If someone is either calm or wise then someone is both not humble and humble and vice versa.
If someone is strong or not calm then someone is either not funny or not wise and vice versa.
Everyone who is either curious or not generous is humble or brave and vice versa.
Everyone who is both not happy and kind is brave or not tall and vice versa.
Everyone who is not humble is both kind and calm.
Everyone who is either kind or not tall is not patient and vice versa.
Everyone who is not humble is either not funny or not brave.
If someone is not rich then fred is either wise or funny.
Everyone who is not happy or old is not tall and vice versa.
Everyone who is both not patient and not tall is either strong or not tall.
Everyone who is patient or curious is wise and vice versa.
Everyone who is both funny and not rich is not calm or patient and vice versa.
If paul is not strong or not old then someone is both funny and brave.
Everyone who is both rich and happy is not brave or strong and vice versa.
Everyone who is both not generous and strong is either tall or funny.
Lucy is either patient or not humble.
Paul is not calm or wise.
Lucy is curious or not wise.
Someone is either rich or humble.
Someone is not kind or not creative.
Susan is either not brave or patient.
Someone is either generous or not brave.
Someone is either not wise or rich. | Susan is not curious. | contradiction | (((curious(susan)|tall(susan)))<=>(?[X]:((~humble(X)<~>~patient(X)))))&
((?[X]:((calm(X)<~>wise(X))))<=>(?[X]:((~humble(X)&humble(X)))))&
((?[X]:((strong(X)|~calm(X))))<=>(?[X]:((~funny(X)<~>~wise(X)))))&
(![X]:((curious(X)<~>~generous(X))<=>(humble(X)|brave(X))))&
(![X]:((~happy(X)&kind(X))<=>(brave(X)|~tall(X))))&
(![X]:(~humble(X)=>(kind(X)&calm(X))))&
(![X]:((kind(X)<~>~tall(X))<=>~patient(X)))&
(![X]:(~humble(X)=>(~funny(X)<~>~brave(X))))&
((?[X]:(~rich(X)))=>((wise(fred)<~>funny(fred))))&
(![X]:((~happy(X)|old(X))<=>~tall(X)))&
(![X]:((~patient(X)&~tall(X))=>(strong(X)<~>~tall(X))))&
(![X]:((patient(X)|curious(X))<=>wise(X)))&
(![X]:((funny(X)&~rich(X))<=>(~calm(X)|patient(X))))&
(((~strong(paul)|~old(paul)))=>(?[X]:((funny(X)&brave(X)))))&
(![X]:((rich(X)&happy(X))<=>(~brave(X)|strong(X))))&
(![X]:((~generous(X)&strong(X))=>(tall(X)<~>funny(X))))&
((patient(lucy)<~>~humble(lucy)))&
((~calm(paul)|wise(paul)))&
((curious(lucy)|~wise(lucy)))&
(?[X]:((rich(X)<~>humble(X))))&
(?[X]:((~kind(X)|~creative(X))))&
((~brave(susan)<~>patient(susan)))&
(?[X]:((generous(X)<~>~brave(X))))&
(?[X]:((~wise(X)<~>rich(X)))) | ~curious(susan) | [
"p0",
"p1",
"p3",
"p4",
"p5",
"p6",
"p7",
"p8",
"p9",
"p11",
"p12",
"p14",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 5716836769095703905648075
% SZS output start Proof for 5716836769095703905648075
1. (tall(susan) | curious(susan)) <=> ? [X0] : (~humble(X0) <~> ~patient(X0)) [input p0]
2. ? [X0] : (calm(X0) <~> wise(X0)) <=> ? [X0] : (humble(X0) & ~humble(X0)) [input p1]
4. ! [X0] : ((curious(X0) <~> ~generous(X0)) <=> (brave(X0) | humble(X0))) [input p3]
5. ! [X0] : ((kind(X0) & ~happy(X0)) <=> (~tall(X0) | brave(X0))) [input p4]
6. ! [X0] : (~humble(X0) => (calm(X0) & kind(X0))) [input p5]
7. ! [X0] : ((kind(X0) <~> ~tall(X0)) <=> ~patient(X0)) [input p6]
8. ! [X0] : (~humble(X0) => (~funny(X0) <~> ~brave(X0))) [input p7]
9. ? [X0] : ~rich(X0) => (wise(fred) <~> funny(fred)) [input p8]
10. ! [X0] : ((old(X0) | ~happy(X0)) <=> ~tall(X0)) [input p9]
12. ! [X0] : ((curious(X0) | patient(X0)) <=> wise(X0)) [input p11]
13. ! [X0] : ((~rich(X0) & funny(X0)) <=> (patient(X0) | ~calm(X0))) [input p12]
15. ! [X0] : ((happy(X0) & rich(X0)) <=> (strong(X0) | ~brave(X0))) [input p14]
22. ~brave(susan) <~> patient(susan) [input p21]
25. ~curious(susan) [input hypothesis]
26. ? [X0] : (calm(X0) <~> wise(X0)) <=> ? [X1] : (humble(X1) & ~humble(X1)) [rectify 2]
29. ! [X0] : ((calm(X0) & kind(X0)) | humble(X0)) [ennf transformation 6]
30. ! [X0] : ((~funny(X0) <~> ~brave(X0)) | humble(X0)) [ennf transformation 8]
31. (wise(fred) <~> funny(fred)) | ! [X0] : rich(X0) [ennf transformation 9]
37. ((tall(susan) | curious(susan)) | ! [X0] : ((~humble(X0) | patient(X0)) & (~patient(X0) | humble(X0)))) & (? [X0] : ((patient(X0) | humble(X0)) & (~patient(X0) | ~humble(X0))) | (~tall(susan) & ~curious(susan))) [nnf transformation 1]
38. (tall(susan) | curious(susan) | ! [X0] : ((~humble(X0) | patient(X0)) & (~patient(X0) | humble(X0)))) & (? [X0] : ((patient(X0) | humble(X0)) & (~patient(X0) | ~humble(X0))) | (~tall(susan) & ~curious(susan))) [flattening 37]
39. (tall(susan) | curious(susan) | ! [X0] : ((~humble(X0) | patient(X0)) & (~patient(X0) | humble(X0)))) & (? [X1] : ((patient(X1) | humble(X1)) & (~patient(X1) | ~humble(X1))) | (~tall(susan) & ~curious(susan))) [rectify 38]
40. ? [X1] : ((patient(X1) | humble(X1)) & (~patient(X1) | ~humble(X1))) => ((patient(sK0) | humble(sK0)) & (~patient(sK0) | ~humble(sK0))) [choice axiom]
41. (tall(susan) | curious(susan) | ! [X0] : ((~humble(X0) | patient(X0)) & (~patient(X0) | humble(X0)))) & (((patient(sK0) | humble(sK0)) & (~patient(sK0) | ~humble(sK0))) | (~tall(susan) & ~curious(susan))) [skolemisation 39,40]
42. (? [X0] : ((~wise(X0) | ~calm(X0)) & (wise(X0) | calm(X0))) | ! [X1] : (~humble(X1) | humble(X1))) & (? [X1] : (humble(X1) & ~humble(X1)) | ! [X0] : ((calm(X0) | ~wise(X0)) & (wise(X0) | ~calm(X0)))) [nnf transformation 26]
43. (? [X0] : ((~wise(X0) | ~calm(X0)) & (wise(X0) | calm(X0))) | ! [X1] : (~humble(X1) | humble(X1))) & (? [X2] : (humble(X2) & ~humble(X2)) | ! [X3] : ((calm(X3) | ~wise(X3)) & (wise(X3) | ~calm(X3)))) [rectify 42]
44. ? [X0] : ((~wise(X0) | ~calm(X0)) & (wise(X0) | calm(X0))) => ((~wise(sK1) | ~calm(sK1)) & (wise(sK1) | calm(sK1))) [choice axiom]
45. ? [X2] : (humble(X2) & ~humble(X2)) => (humble(sK2) & ~humble(sK2)) [choice axiom]
46. (((~wise(sK1) | ~calm(sK1)) & (wise(sK1) | calm(sK1))) | ! [X1] : (~humble(X1) | humble(X1))) & ((humble(sK2) & ~humble(sK2)) | ! [X3] : ((calm(X3) | ~wise(X3)) & (wise(X3) | ~calm(X3)))) [skolemisation 43,45,44]
52. ! [X0] : ((((generous(X0) | ~curious(X0)) & (~generous(X0) | curious(X0))) | (~brave(X0) & ~humble(X0))) & ((brave(X0) | humble(X0)) | ((curious(X0) | generous(X0)) & (~generous(X0) | ~curious(X0))))) [nnf transformation 4]
53. ! [X0] : ((((generous(X0) | ~curious(X0)) & (~generous(X0) | curious(X0))) | (~brave(X0) & ~humble(X0))) & (brave(X0) | humble(X0) | ((curious(X0) | generous(X0)) & (~generous(X0) | ~curious(X0))))) [flattening 52]
54. ! [X0] : (((kind(X0) & ~happy(X0)) | (tall(X0) & ~brave(X0))) & ((~tall(X0) | brave(X0)) | (~kind(X0) | happy(X0)))) [nnf transformation 5]
55. ! [X0] : (((kind(X0) & ~happy(X0)) | (tall(X0) & ~brave(X0))) & (~tall(X0) | brave(X0) | ~kind(X0) | happy(X0))) [flattening 54]
56. ! [X0] : ((((tall(X0) | ~kind(X0)) & (~tall(X0) | kind(X0))) | patient(X0)) & (~patient(X0) | ((kind(X0) | tall(X0)) & (~tall(X0) | ~kind(X0))))) [nnf transformation 7]
57. ! [X0] : (((brave(X0) | funny(X0)) & (~brave(X0) | ~funny(X0))) | humble(X0)) [nnf transformation 30]
58. ((~funny(fred) | ~wise(fred)) & (funny(fred) | wise(fred))) | ! [X0] : rich(X0) [nnf transformation 31]
59. ! [X0] : (((old(X0) | ~happy(X0)) | tall(X0)) & (~tall(X0) | (~old(X0) & happy(X0)))) [nnf transformation 10]
60. ! [X0] : ((old(X0) | ~happy(X0) | tall(X0)) & (~tall(X0) | (~old(X0) & happy(X0)))) [flattening 59]
62. ! [X0] : (((curious(X0) | patient(X0)) | ~wise(X0)) & (wise(X0) | (~curious(X0) & ~patient(X0)))) [nnf transformation 12]
63. ! [X0] : ((curious(X0) | patient(X0) | ~wise(X0)) & (wise(X0) | (~curious(X0) & ~patient(X0)))) [flattening 62]
64. ! [X0] : (((~rich(X0) & funny(X0)) | (~patient(X0) & calm(X0))) & ((patient(X0) | ~calm(X0)) | (rich(X0) | ~funny(X0)))) [nnf transformation 13]
65. ! [X0] : (((~rich(X0) & funny(X0)) | (~patient(X0) & calm(X0))) & (patient(X0) | ~calm(X0) | rich(X0) | ~funny(X0))) [flattening 64]
68. ! [X0] : (((happy(X0) & rich(X0)) | (~strong(X0) & brave(X0))) & ((strong(X0) | ~brave(X0)) | (~happy(X0) | ~rich(X0)))) [nnf transformation 15]
69. ! [X0] : (((happy(X0) & rich(X0)) | (~strong(X0) & brave(X0))) & (strong(X0) | ~brave(X0) | ~happy(X0) | ~rich(X0))) [flattening 68]
75. (~patient(susan) | brave(susan)) & (patient(susan) | ~brave(susan)) [nnf transformation 22]
87. tall(susan) | curious(susan) | ~humble(X0) | patient(X0) [cnf transformation 41]
88. ~humble(sK2) | wise(X3) | ~calm(X3) [cnf transformation 46]
90. humble(sK2) | wise(X3) | ~calm(X3) [cnf transformation 46]
100. ~generous(X0) | humble(X0) | brave(X0) | ~curious(X0) [cnf transformation 53]
104. ~humble(X0) | ~curious(X0) | generous(X0) [cnf transformation 53]
105. ~brave(X0) | ~curious(X0) | generous(X0) [cnf transformation 53]
107. ~happy(X0) | ~brave(X0) [cnf transformation 55]
110. kind(X0) | tall(X0) [cnf transformation 55]
112. calm(X0) | humble(X0) [cnf transformation 29]
116. tall(X0) | ~kind(X0) | patient(X0) [cnf transformation 56]
118. brave(X0) | funny(X0) | humble(X0) [cnf transformation 57]
120. ~funny(fred) | ~wise(fred) | rich(X0) [cnf transformation 58]
121. ~tall(X0) | happy(X0) [cnf transformation 60]
126. ~patient(X0) | wise(X0) [cnf transformation 63]
128. ~wise(X0) | patient(X0) | curious(X0) [cnf transformation 63]
131. ~patient(X0) | funny(X0) [cnf transformation 65]
132. ~rich(X0) | calm(X0) [cnf transformation 65]
133. ~rich(X0) | ~patient(X0) [cnf transformation 65]
139. rich(X0) | brave(X0) [cnf transformation 69]
151. patient(susan) | ~brave(susan) [cnf transformation 75]
152. ~patient(susan) | brave(susan) [cnf transformation 75]
157. ~curious(susan) [cnf transformation 25]
160. 1 <=> ! [X0] : (~humble(X0) | patient(X0)) [avatar definition]
161. ~humble(X0) | patient(X0) <- (1) [avatar component clause 160]
163. 2 <=> curious(susan) [avatar definition]
164. ~curious(susan) <- (~2) [avatar component clause 163]
167. 3 <=> tall(susan) [avatar definition]
169. tall(susan) <- (3) [avatar component clause 167]
170. 1 | 2 | 3 [avatar split clause 87,167,163,160]
191. 8 <=> humble(sK2) [avatar definition]
196. 9 <=> ! [X3] : (wise(X3) | ~calm(X3)) [avatar definition]
197. ~calm(X3) | wise(X3) <- (9) [avatar component clause 196]
198. 9 | 8 [avatar split clause 90,191,196]
200. 9 | ~8 [avatar split clause 88,191,196]
235. patient(X0) | tall(X0) [subsumption resolution 116,110]
238. 18 <=> ! [X0] : rich(X0) [avatar definition]
239. rich(X0) <- (18) [avatar component clause 238]
241. 19 <=> wise(fred) [avatar definition]
242. wise(fred) <- (19) [avatar component clause 241]
243. ~wise(fred) <- (~19) [avatar component clause 241]
245. 20 <=> funny(fred) [avatar definition]
247. ~funny(fred) <- (~20) [avatar component clause 245]
248. 18 | ~19 | ~20 [avatar split clause 120,245,241,238]
309. 33 <=> brave(susan) [avatar definition]
310. ~brave(susan) <- (~33) [avatar component clause 309]
313. 34 <=> patient(susan) [avatar definition]
314. patient(susan) <- (34) [avatar component clause 313]
315. ~patient(susan) <- (~34) [avatar component clause 313]
316. 33 | ~34 [avatar split clause 152,313,309]
317. ~33 | 34 [avatar split clause 151,313,309]
338. ~2 [avatar split clause 157,163]
343. happy(susan) <- (3) [resolution 121,169]
346. ~brave(susan) <- (3) [resolution 343,107]
352. brave(X1) | calm(X1) [resolution 139,132]
363. wise(X0) | humble(X0) <- (9) [resolution 197,112]
367. funny(X0) | tall(X0) [resolution 235,131]
473. funny(X1) | humble(X1) | ~curious(X1) | generous(X1) [resolution 118,105]
495. ~curious(X1) | funny(X1) | generous(X1) [subsumption resolution 473,104]
497. ~33 | ~3 [avatar split clause 346,167,309]
546. patient(fred) | curious(fred) <- (19) [resolution 128,242]
549. 60 <=> curious(fred) [avatar definition]
551. curious(fred) <- (60) [avatar component clause 549]
553. 61 <=> patient(fred) [avatar definition]
555. patient(fred) <- (61) [avatar component clause 553]
556. 60 | 61 | ~19 [avatar split clause 546,241,553,549]
632. calm(susan) <- (~33) [resolution 352,310]
665. tall(fred) <- (~20) [resolution 367,247]
686. funny(fred) | generous(fred) <- (60) [resolution 495,551]
689. generous(fred) <- (~20, 60) [subsumption resolution 686,247]
728. happy(fred) <- (~20) [resolution 665,121]
732. humble(fred) | brave(fred) | ~curious(fred) <- (~20, 60) [resolution 689,100]
734. humble(fred) | brave(fred) <- (~20, 60) [subsumption resolution 732,551]
736. 74 <=> brave(fred) [avatar definition]
738. brave(fred) <- (74) [avatar component clause 736]
740. 75 <=> humble(fred) [avatar definition]
742. humble(fred) <- (75) [avatar component clause 740]
743. 74 | 75 | 20 | ~60 [avatar split clause 734,549,245,740,736]
836. wise(susan) <- (9, ~33) [resolution 632,197]
845. ~brave(fred) <- (~20) [resolution 728,107]
846. $false <- (~20, 74) [subsumption resolution 845,738]
847. 20 | ~74 [avatar contradiction clause 846]
865. humble(fred) <- (9, ~19) [resolution 243,363]
867. 75 | ~9 | 19 [avatar split clause 865,241,196,740]
939. patient(susan) | curious(susan) <- (9, ~33) [resolution 836,128]
941. curious(susan) <- (9, ~33, ~34) [subsumption resolution 939,315]
942. $false <- (~2, 9, ~33, ~34) [subsumption resolution 941,164]
943. 2 | ~9 | 33 | 34 [avatar contradiction clause 942]
972. patient(fred) <- (1, 75) [resolution 161,742]
979. 61 | ~1 | ~75 [avatar split clause 972,740,160,553]
996. funny(fred) <- (61) [resolution 555,131]
997. wise(fred) <- (61) [resolution 555,126]
1000. 19 | ~61 [avatar split clause 997,553,241]
1004. 20 | ~61 [avatar split clause 996,553,245]
1010. ~patient(X0) <- (18) [resolution 239,133]
1069. $false <- (18, 34) [resolution 1010,314]
1070. $false <- (18, 61) [resolution 1010,555]
1075. ~18 | ~61 [avatar contradiction clause 1070]
1076. ~18 | ~34 [avatar contradiction clause 1069]
1077. $false [avatar sat refutation 170,198,200,248,316,317,338,497,556,743,847,867,943,979,1000,1004,1075,1076]
% SZS output end Proof for 5716836769095703905648075
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5500
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is either generous or humble then someone is not funny or not generous and vice versa.
If mary is either not wise or not patient then someone is both curious and not quiet and vice versa.
Everyone who is tall is either not rich or not creative and vice versa.
If someone is not generous or strong then someone is either not quiet or brave and vice versa.
If someone is both not rich and not quiet then someone is not generous and vice versa.
If someone is happy then someone is either kind or not funny and vice versa.
If someone is both not funny and not quiet then susan is happy and vice versa.
If mary is either tall or wise then someone is not calm or not old.
If someone is not wise or curious then someone is both strong and not old and vice versa.
If someone is both generous and humble then someone is humble or calm.
Everyone who is not funny or not humble is not strong.
If someone is either humble or funny then someone is both tall and not kind and vice versa.
If lucy is both not old and not wise then someone is either tall or curious.
If john is both rich and funny then mary is not curious or wise.
Everyone who is not generous is not happy or not wise.
If someone is both patient and not patient then john is both not quiet and not calm and vice versa.
Fred is old or quiet.
Someone is not brave or curious.
Someone is both brave and creative.
Lucy is either happy or calm.
Someone is not funny or strong.
Someone is not old.
Lucy is either old or brave.
Someone is not rich or not humble. | Mary is not patient. | neutral | (((generous(lucy)<~>humble(lucy)))<=>(?[X]:((~funny(X)|~generous(X)))))&
(((~wise(mary)<~>~patient(mary)))<=>(?[X]:((curious(X)&~quiet(X)))))&
(![X]:(tall(X)<=>(~rich(X)<~>~creative(X))))&
((?[X]:((~generous(X)|strong(X))))<=>(?[X]:((~quiet(X)<~>brave(X)))))&
((?[X]:((~rich(X)&~quiet(X))))<=>(?[X]:(~generous(X))))&
((?[X]:(happy(X)))<=>(?[X]:((kind(X)<~>~funny(X)))))&
((?[X]:((~funny(X)&~quiet(X))))<=>(happy(susan)))&
(((tall(mary)<~>wise(mary)))=>(?[X]:((~calm(X)|~old(X)))))&
((?[X]:((~wise(X)|curious(X))))<=>(?[X]:((strong(X)&~old(X)))))&
((?[X]:((generous(X)&humble(X))))=>(?[X]:((humble(X)|calm(X)))))&
(![X]:((~funny(X)|~humble(X))=>~strong(X)))&
((?[X]:((humble(X)<~>funny(X))))<=>(?[X]:((tall(X)&~kind(X)))))&
(((~old(lucy)&~wise(lucy)))=>(?[X]:((tall(X)<~>curious(X)))))&
(((rich(john)&funny(john)))=>((~curious(mary)|wise(mary))))&
(![X]:(~generous(X)=>(~happy(X)|~wise(X))))&
((?[X]:((patient(X)&~patient(X))))<=>((~quiet(john)&~calm(john))))&
((old(fred)|quiet(fred)))&
(?[X]:((~brave(X)|curious(X))))&
(?[X]:((brave(X)&creative(X))))&
((happy(lucy)<~>calm(lucy)))&
(?[X]:((~funny(X)|strong(X))))&
(?[X]:(~old(X)))&
((old(lucy)<~>brave(lucy)))&
(?[X]:((~rich(X)|~humble(X)))) | ~patient(mary) | [] | null | 0 |
If alice is not curious or kind then paul is calm. Everyone who is strong is either not curious or funny. Everyone who is funny or quiet is funny and vice versa. If lucy is both not happy and not tall then paul is kind or not calm and vice versa. Everyone who is happy is both not patient and creative. Everyone who is wise is generous and vice versa. Everyone who is not curious is not strong or quiet. Everyone who is not happy or kind is not brave or not rich. Everyone who is both rich and not funny is funny or brave and vice versa. Everyone who is either patient or kind is creative. If someone is either quiet or not strong then lucy is either not generous or not kind. Everyone who is not tall is generous. If paul is strong or not funny then fred is both not creative and not rich and vice versa. Everyone who is either not brave or kind is either not quiet or not old and vice versa. If alice is either tall or not tall then someone is not wise or patient. Everyone who is not happy or not humble is not happy. Paul is wise. Someone is either tall or not strong. Someone is both not old and not kind. Mary is both not wise and not humble. Someone is not old or not funny. John is either old or creative. | Alice is calm. | neutral | (((~curious(alice)|kind(alice)))=>(calm(paul)))&
(![X]:(strong(X)=>(~curious(X)<~>funny(X))))&
(![X]:((funny(X)|quiet(X))<=>funny(X)))&
(((~happy(lucy)&~tall(lucy)))<=>((kind(paul)|~calm(paul))))&
(![X]:(happy(X)=>(~patient(X)&creative(X))))&
(![X]:(wise(X)<=>generous(X)))&
(![X]:(~curious(X)=>(~strong(X)|quiet(X))))&
(![X]:((~happy(X)|kind(X))=>(~brave(X)|~rich(X))))&
(![X]:((rich(X)&~funny(X))<=>(funny(X)|brave(X))))&
(![X]:((patient(X)<~>kind(X))=>creative(X)))&
((?[X]:((quiet(X)<~>~strong(X))))=>((~generous(lucy)<~>~kind(lucy))))&
(![X]:(~tall(X)=>generous(X)))&
(((strong(paul)|~funny(paul)))<=>((~creative(fred)&~rich(fred))))&
(![X]:((~brave(X)<~>kind(X))<=>(~quiet(X)<~>~old(X))))&
(((tall(alice)<~>~tall(alice)))=>(?[X]:((~wise(X)|patient(X)))))&
(![X]:((~happy(X)|~humble(X))=>~happy(X)))&
(wise(paul))&
(?[X]:((tall(X)<~>~strong(X))))&
(?[X]:((~old(X)&~kind(X))))&
((~wise(mary)&~humble(mary)))&
(?[X]:((~old(X)|~funny(X))))&
((old(john)<~>creative(john))) | calm(alice) | [] | null | 0 |
Everyone who is generous is both funny and rich.
Everyone who is either humble or old is both generous and funny.
Everyone who is humble is calm and vice versa.
Everyone who is humble is generous and vice versa.
If someone is either happy or not humble then someone is either patient or not creative.
Everyone who is both not strong and not creative is not brave or tall and vice versa.
Everyone who is calm or not quiet is generous or patient and vice versa.
Everyone who is not strong is either not kind or funny and vice versa.
Everyone who is not happy or brave is either not brave or not creative and vice versa.
If alice is old then paul is both not happy and generous.
Everyone who is generous is both brave and strong.
Everyone who is either humble or strong is both curious and not creative.
Everyone who is both not strong and not creative is either brave or not calm and vice versa.
Everyone who is both not old and tall is patient.
Everyone who is old or tall is both not strong and happy.
If lucy is either not calm or not old then someone is either quiet or not brave and vice versa.
Fred is not wise or not old.
Someone is not calm or old.
Someone is either patient or rich.
John is both kind and not tall.
Susan is rich or not generous.
Mary is both not strong and not generous.
Someone is either not humble or funny. | Alice is not creative. | entailment | (![X]:(generous(X)=>(funny(X)&rich(X))))&
(![X]:((humble(X)<~>old(X))=>(generous(X)&funny(X))))&
(![X]:(humble(X)<=>calm(X)))&
(![X]:(humble(X)<=>generous(X)))&
((?[X]:((happy(X)<~>~humble(X))))=>(?[X]:((patient(X)<~>~creative(X)))))&
(![X]:((~strong(X)&~creative(X))<=>(~brave(X)|tall(X))))&
(![X]:((calm(X)|~quiet(X))<=>(generous(X)|patient(X))))&
(![X]:(~strong(X)<=>(~kind(X)<~>funny(X))))&
(![X]:((~happy(X)|brave(X))<=>(~brave(X)<~>~creative(X))))&
((old(alice))=>((~happy(paul)&generous(paul))))&
(![X]:(generous(X)=>(brave(X)&strong(X))))&
(![X]:((humble(X)<~>strong(X))=>(curious(X)&~creative(X))))&
(![X]:((~strong(X)&~creative(X))<=>(brave(X)<~>~calm(X))))&
(![X]:((~old(X)&tall(X))=>patient(X)))&
(![X]:((old(X)|tall(X))=>(~strong(X)&happy(X))))&
(((~calm(lucy)<~>~old(lucy)))<=>(?[X]:((quiet(X)<~>~brave(X)))))&
((~wise(fred)|~old(fred)))&
(?[X]:((~calm(X)|old(X))))&
(?[X]:((patient(X)<~>rich(X))))&
((kind(john)&~tall(john)))&
((rich(susan)|~generous(susan)))&
((~strong(mary)&~generous(mary)))&
(?[X]:((~humble(X)<~>funny(X)))) | ~creative(alice) | [
"p5",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 3565373961582489823822564
% SZS output start Proof for 3565373961582489823822564
6. ! [X0] : ((~creative(X0) & ~strong(X0)) <=> (tall(X0) | ~brave(X0))) [input p5]
9. ! [X0] : ((brave(X0) | ~happy(X0)) <=> (~brave(X0) <~> ~creative(X0))) [input p8]
24. creative(alice) [input hypothesis]
44. ! [X0] : (((~creative(X0) & ~strong(X0)) | (~tall(X0) & brave(X0))) & ((tall(X0) | ~brave(X0)) | (creative(X0) | strong(X0)))) [nnf transformation 6]
45. ! [X0] : (((~creative(X0) & ~strong(X0)) | (~tall(X0) & brave(X0))) & (tall(X0) | ~brave(X0) | creative(X0) | strong(X0))) [flattening 44]
49. ! [X0] : (((brave(X0) | ~happy(X0)) | ((~brave(X0) | creative(X0)) & (~creative(X0) | brave(X0)))) & (((creative(X0) | brave(X0)) & (~creative(X0) | ~brave(X0))) | (~brave(X0) & happy(X0)))) [nnf transformation 9]
50. ! [X0] : ((brave(X0) | ~happy(X0) | ((~brave(X0) | creative(X0)) & (~creative(X0) | brave(X0)))) & (((creative(X0) | brave(X0)) & (~creative(X0) | ~brave(X0))) | (~brave(X0) & happy(X0)))) [flattening 49]
83. ~creative(X0) | brave(X0) [cnf transformation 45]
94. ~creative(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 50]
134. creative(alice) [cnf transformation 24]
135. ~creative(X0) | ~brave(X0) [duplicate literal removal 94]
156. ~creative(X0) [subsumption resolution 135,83]
234. $false [subsumption resolution 134,156]
% SZS output end Proof for 3565373961582489823822564
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either kind or funny is not humble or wise and vice versa.
Everyone who is not tall or not brave is both rich and old and vice versa.
If lucy is not humble then alice is not brave and vice versa.
Everyone who is humble or curious is funny and vice versa.
Everyone who is either not humble or not wise is kind and vice versa.
Everyone who is both not brave and not kind is either not creative or not brave.
Everyone who is not kind or humble is both old and not calm.
If fred is not strong then john is both brave and calm and vice versa.
If someone is calm then someone is creative.
If someone is either not tall or not curious then someone is either humble or not happy and vice versa.
If someone is either wise or strong then john is not happy and vice versa.
Everyone who is either happy or not wise is not creative or not strong and vice versa.
Everyone who is both not rich and tall is curious or rich and vice versa.
If susan is not curious or not old then someone is either not strong or generous.
Everyone who is not patient is not curious or quiet and vice versa.
If fred is both wise and funny then fred is both not curious and not kind and vice versa.
Someone is both not generous and patient.
Alice is not funny or not generous.
Mary is either funny or calm.
Paul is either old or not funny. | Lucy is rich. | contradiction | (![X]:((kind(X)<~>funny(X))<=>(~humble(X)|wise(X))))&
(![X]:((~tall(X)|~brave(X))<=>(rich(X)&old(X))))&
((~humble(lucy))<=>(~brave(alice)))&
(![X]:((humble(X)|curious(X))<=>funny(X)))&
(![X]:((~humble(X)<~>~wise(X))<=>kind(X)))&
(![X]:((~brave(X)&~kind(X))=>(~creative(X)<~>~brave(X))))&
(![X]:((~kind(X)|humble(X))=>(old(X)&~calm(X))))&
((~strong(fred))<=>((brave(john)&calm(john))))&
((?[X]:(calm(X)))=>(?[X]:(creative(X))))&
((?[X]:((~tall(X)<~>~curious(X))))<=>(?[X]:((humble(X)<~>~happy(X)))))&
((?[X]:((wise(X)<~>strong(X))))<=>(~happy(john)))&
(![X]:((happy(X)<~>~wise(X))<=>(~creative(X)|~strong(X))))&
(![X]:((~rich(X)&tall(X))<=>(curious(X)|rich(X))))&
(((~curious(susan)|~old(susan)))=>(?[X]:((~strong(X)<~>generous(X)))))&
(![X]:(~patient(X)<=>(~curious(X)|quiet(X))))&
(((wise(fred)&funny(fred)))<=>((~curious(fred)&~kind(fred))))&
(?[X]:((~generous(X)&patient(X))))&
((~funny(alice)|~generous(alice)))&
((funny(mary)<~>calm(mary)))&
((old(paul)<~>~funny(paul))) | rich(lucy) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 6989986824937200338729036
% SZS output start Proof for 6989986824937200338729036
13. ! [X0] : ((tall(X0) & ~rich(X0)) <=> (rich(X0) | curious(X0))) [input p12]
21. rich(lucy) [input hypothesis]
57. ! [X0] : (((tall(X0) & ~rich(X0)) | (~rich(X0) & ~curious(X0))) & ((rich(X0) | curious(X0)) | (~tall(X0) | rich(X0)))) [nnf transformation 13]
58. ! [X0] : (((tall(X0) & ~rich(X0)) | (~rich(X0) & ~curious(X0))) & (rich(X0) | curious(X0) | ~tall(X0) | rich(X0))) [flattening 57]
118. ~rich(X0) | ~rich(X0) [cnf transformation 58]
137. rich(lucy) [cnf transformation 21]
139. ~rich(X0) [duplicate literal removal 118]
288. $false [subsumption resolution 137,139]
% SZS output end Proof for 6989986824937200338729036
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either brave or not calm then someone is either not patient or rich. If mary is quiet or strong then someone is both not rich and quiet and vice versa. If alice is strong then mary is either tall or humble. If someone is either funny or not old then alice is quiet or strong. Everyone who is not brave is both happy and not calm. Everyone who is either not brave or calm is both not old and not generous. If mary is kind or not wise then fred is not wise or kind and vice versa. If lucy is not humble then alice is both tall and funny and vice versa. Everyone who is humble is both not tall and quiet and vice versa. Everyone who is old or not happy is not quiet or not generous and vice versa. Everyone who is either not humble or quiet is both tall and not old and vice versa. Everyone who is not curious is not brave or not happy and vice versa. If paul is both strong and not rich then paul is happy or humble. If paul is not funny then someone is old. Everyone who is curious or humble is not old and vice versa. Everyone who is either generous or not curious is not creative. Fred is either not kind or not curious. Fred is patient or creative. John is not generous or not rich. Mary is either humble or kind. Fred is not funny. Someone is strong or not brave. | John is not calm. | entailment | ((?[X]:((brave(X)<~>~calm(X))))=>(?[X]:((~patient(X)<~>rich(X)))))&
(((quiet(mary)|strong(mary)))<=>(?[X]:((~rich(X)&quiet(X)))))&
((strong(alice))=>((tall(mary)<~>humble(mary))))&
((?[X]:((funny(X)<~>~old(X))))=>((quiet(alice)|strong(alice))))&
(![X]:(~brave(X)=>(happy(X)&~calm(X))))&
(![X]:((~brave(X)<~>calm(X))=>(~old(X)&~generous(X))))&
(((kind(mary)|~wise(mary)))<=>((~wise(fred)|kind(fred))))&
((~humble(lucy))<=>((tall(alice)&funny(alice))))&
(![X]:(humble(X)<=>(~tall(X)&quiet(X))))&
(![X]:((old(X)|~happy(X))<=>(~quiet(X)|~generous(X))))&
(![X]:((~humble(X)<~>quiet(X))<=>(tall(X)&~old(X))))&
(![X]:(~curious(X)<=>(~brave(X)|~happy(X))))&
(((strong(paul)&~rich(paul)))=>((happy(paul)|humble(paul))))&
((~funny(paul))=>(?[X]:(old(X))))&
(![X]:((curious(X)|humble(X))<=>~old(X)))&
(![X]:((generous(X)<~>~curious(X))=>~creative(X)))&
((~kind(fred)<~>~curious(fred)))&
((patient(fred)|creative(fred)))&
((~generous(john)|~rich(john)))&
((humble(mary)<~>kind(mary)))&
(~funny(fred))&
(?[X]:((strong(X)|~brave(X)))) | ~calm(john) | [
"p4",
"p5",
"p8",
"p9",
"p10",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1812543776007540356725205
% SZS output start Proof for 1812543776007540356725205
5. ! [X0] : (~brave(X0) => (~calm(X0) & happy(X0))) [input p4]
6. ! [X0] : ((~brave(X0) <~> calm(X0)) => (~generous(X0) & ~old(X0))) [input p5]
9. ! [X0] : (humble(X0) <=> (quiet(X0) & ~tall(X0))) [input p8]
10. ! [X0] : ((~happy(X0) | old(X0)) <=> (~generous(X0) | ~quiet(X0))) [input p9]
11. ! [X0] : ((~humble(X0) <~> quiet(X0)) <=> (~old(X0) & tall(X0))) [input p10]
12. ! [X0] : (~curious(X0) <=> (~happy(X0) | ~brave(X0))) [input p11]
15. ! [X0] : ((humble(X0) | curious(X0)) <=> ~old(X0)) [input p14]
23. calm(john) [input hypothesis]
29. ! [X0] : ((~calm(X0) & happy(X0)) | brave(X0)) [ennf transformation 5]
30. ! [X0] : ((~generous(X0) & ~old(X0)) | (~brave(X0) <=> calm(X0))) [ennf transformation 6]
46. ! [X0] : ((~generous(X0) & ~old(X0)) | ((~brave(X0) | ~calm(X0)) & (calm(X0) | brave(X0)))) [nnf transformation 30]
51. ! [X0] : ((humble(X0) | (~quiet(X0) | tall(X0))) & ((quiet(X0) & ~tall(X0)) | ~humble(X0))) [nnf transformation 9]
52. ! [X0] : ((humble(X0) | ~quiet(X0) | tall(X0)) & ((quiet(X0) & ~tall(X0)) | ~humble(X0))) [flattening 51]
53. ! [X0] : (((~happy(X0) | old(X0)) | (generous(X0) & quiet(X0))) & ((~generous(X0) | ~quiet(X0)) | (happy(X0) & ~old(X0)))) [nnf transformation 10]
54. ! [X0] : ((~happy(X0) | old(X0) | (generous(X0) & quiet(X0))) & (~generous(X0) | ~quiet(X0) | (happy(X0) & ~old(X0)))) [flattening 53]
55. ! [X0] : ((((~quiet(X0) | humble(X0)) & (quiet(X0) | ~humble(X0))) | (old(X0) | ~tall(X0))) & ((~old(X0) & tall(X0)) | ((~humble(X0) | ~quiet(X0)) & (quiet(X0) | humble(X0))))) [nnf transformation 11]
56. ! [X0] : ((((~quiet(X0) | humble(X0)) & (quiet(X0) | ~humble(X0))) | old(X0) | ~tall(X0)) & ((~old(X0) & tall(X0)) | ((~humble(X0) | ~quiet(X0)) & (quiet(X0) | humble(X0))))) [flattening 55]
57. ! [X0] : ((~curious(X0) | (happy(X0) & brave(X0))) & ((~happy(X0) | ~brave(X0)) | curious(X0))) [nnf transformation 12]
58. ! [X0] : ((~curious(X0) | (happy(X0) & brave(X0))) & (~happy(X0) | ~brave(X0) | curious(X0))) [flattening 57]
61. ! [X0] : (((humble(X0) | curious(X0)) | old(X0)) & (~old(X0) | (~humble(X0) & ~curious(X0)))) [nnf transformation 15]
62. ! [X0] : ((humble(X0) | curious(X0) | old(X0)) & (~old(X0) | (~humble(X0) & ~curious(X0)))) [flattening 61]
82. ~calm(X0) | brave(X0) [cnf transformation 29]
84. ~old(X0) | ~brave(X0) | ~calm(X0) [cnf transformation 46]
94. ~humble(X0) | ~tall(X0) [cnf transformation 52]
95. ~humble(X0) | quiet(X0) [cnf transformation 52]
96. ~quiet(X0) | humble(X0) | tall(X0) [cnf transformation 52]
99. ~happy(X0) | old(X0) | quiet(X0) [cnf transformation 54]
101. tall(X0) | quiet(X0) | humble(X0) [cnf transformation 56]
102. tall(X0) | ~humble(X0) | ~quiet(X0) [cnf transformation 56]
103. ~old(X0) | quiet(X0) | humble(X0) [cnf transformation 56]
104. ~old(X0) | ~humble(X0) | ~quiet(X0) [cnf transformation 56]
106. ~quiet(X0) | humble(X0) | old(X0) | ~tall(X0) [cnf transformation 56]
109. ~curious(X0) | happy(X0) [cnf transformation 58]
114. curious(X0) | humble(X0) | old(X0) [cnf transformation 62]
125. calm(john) [cnf transformation 23]
196. ~old(X0) | ~calm(X0) [subsumption resolution 84,82]
233. ~quiet(X0) | humble(X0) | old(X0) [subsumption resolution 106,96]
234. ~old(X0) | ~humble(X0) [subsumption resolution 104,95]
235. ~old(X0) | quiet(X0) [subsumption resolution 103,234]
236. ~quiet(X0) | tall(X0) [subsumption resolution 102,96]
237. humble(X0) | tall(X0) [subsumption resolution 101,236]
310. tall(X0) | quiet(X0) [resolution 237,95]
313. tall(X0) [subsumption resolution 310,236]
329. happy(X1) | old(X1) | humble(X1) [resolution 114,109]
356. old(X2) | humble(X2) | old(X2) | quiet(X2) [resolution 329,99]
357. old(X2) | humble(X2) | quiet(X2) [duplicate literal removal 356]
359. humble(X2) | quiet(X2) [subsumption resolution 357,235]
360. quiet(X2) [subsumption resolution 359,95]
361. old(X0) | humble(X0) [resolution 360,233]
372. ~calm(X3) | humble(X3) [resolution 361,196]
377. humble(john) [resolution 372,125]
379. ~tall(john) [resolution 377,94]
380. $false [subsumption resolution 379,313]
% SZS output end Proof for 1812543776007540356725205
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is patient or kind is either not quiet or wise and vice versa. Everyone who is wise is either old or wise. Everyone who is both not strong and not funny is both not quiet and not wise and vice versa. Everyone who is both not old and quiet is curious. If paul is generous or not brave then lucy is both generous and happy and vice versa. Everyone who is tall or creative is both kind and not funny. Everyone who is happy is either not calm or rich and vice versa. Everyone who is both not brave and not generous is either not patient or tall. Everyone who is not humble or tall is not tall. Everyone who is not brave or creative is funny and vice versa. Everyone who is not tall or not humble is either not generous or strong and vice versa. Everyone who is either creative or rich is not brave and vice versa. If fred is either creative or curious then lucy is curious and vice versa. If someone is happy then someone is either not patient or calm and vice versa. Everyone who is patient is not humble. Everyone who is not kind is both creative and humble and vice versa. Paul is either not generous or calm. Paul is wise. Paul is both brave and not funny. Someone is both not quiet and not strong. Someone is either not creative or patient. Someone is generous or old. John is either not wise or wise. | Lucy is not funny. | neutral | (![X]:((patient(X)|kind(X))<=>(~quiet(X)<~>wise(X))))&
(![X]:(wise(X)=>(old(X)<~>wise(X))))&
(![X]:((~strong(X)&~funny(X))<=>(~quiet(X)&~wise(X))))&
(![X]:((~old(X)&quiet(X))=>curious(X)))&
(((generous(paul)|~brave(paul)))<=>((generous(lucy)&happy(lucy))))&
(![X]:((tall(X)|creative(X))=>(kind(X)&~funny(X))))&
(![X]:(happy(X)<=>(~calm(X)<~>rich(X))))&
(![X]:((~brave(X)&~generous(X))=>(~patient(X)<~>tall(X))))&
(![X]:((~humble(X)|tall(X))=>~tall(X)))&
(![X]:((~brave(X)|creative(X))<=>funny(X)))&
(![X]:((~tall(X)|~humble(X))<=>(~generous(X)<~>strong(X))))&
(![X]:((creative(X)<~>rich(X))<=>~brave(X)))&
(((creative(fred)<~>curious(fred)))<=>(curious(lucy)))&
((?[X]:(happy(X)))<=>(?[X]:((~patient(X)<~>calm(X)))))&
(![X]:(patient(X)=>~humble(X)))&
(![X]:(~kind(X)<=>(creative(X)&humble(X))))&
((~generous(paul)<~>calm(paul)))&
(wise(paul))&
((brave(paul)&~funny(paul)))&
(?[X]:((~quiet(X)&~strong(X))))&
(?[X]:((~creative(X)<~>patient(X))))&
(?[X]:((generous(X)|old(X))))&
((~wise(john)<~>wise(john))) | ~funny(lucy) | [] | null | 0 |
Everyone who is tall is not calm.
Everyone who is calm is either calm or humble and vice versa.
If someone is not quiet then fred is wise or not calm and vice versa.
If someone is both kind and not rich then someone is either not funny or not rich.
If fred is both calm and wise then someone is not creative or not quiet.
Everyone who is brave or not wise is curious and vice versa.
Everyone who is either rich or not kind is not strong.
If lucy is not wise or funny then someone is curious.
If fred is either patient or not curious then someone is tall and vice versa.
If someone is not funny then someone is patient.
If someone is both rich and not wise then someone is not kind and vice versa.
Everyone who is not strong or brave is not patient and vice versa.
If fred is both not humble and strong then someone is not wise and vice versa.
Everyone who is either not strong or not humble is both tall and wise and vice versa.
If someone is both not generous and rich then paul is both not calm and not old and vice versa.
If someone is not brave or kind then someone is not humble or not curious.
Someone is either brave or funny.
Someone is quiet.
Someone is either not generous or not patient.
Alice is generous or not tall.
Someone is kind or not curious.
Paul is generous or patient. | Lucy is kind. | entailment | (![X]:(tall(X)=>~calm(X)))&
(![X]:(calm(X)<=>(calm(X)<~>humble(X))))&
((?[X]:(~quiet(X)))<=>((wise(fred)|~calm(fred))))&
((?[X]:((kind(X)&~rich(X))))=>(?[X]:((~funny(X)<~>~rich(X)))))&
(((calm(fred)&wise(fred)))=>(?[X]:((~creative(X)|~quiet(X)))))&
(![X]:((brave(X)|~wise(X))<=>curious(X)))&
(![X]:((rich(X)<~>~kind(X))=>~strong(X)))&
(((~wise(lucy)|funny(lucy)))=>(?[X]:(curious(X))))&
(((patient(fred)<~>~curious(fred)))<=>(?[X]:(tall(X))))&
((?[X]:(~funny(X)))=>(?[X]:(patient(X))))&
((?[X]:((rich(X)&~wise(X))))<=>(?[X]:(~kind(X))))&
(![X]:((~strong(X)|brave(X))<=>~patient(X)))&
(((~humble(fred)&strong(fred)))<=>(?[X]:(~wise(X))))&
(![X]:((~strong(X)<~>~humble(X))<=>(tall(X)&wise(X))))&
((?[X]:((~generous(X)&rich(X))))<=>((~calm(paul)&~old(paul))))&
((?[X]:((~brave(X)|kind(X))))=>(?[X]:((~humble(X)|~curious(X)))))&
(?[X]:((brave(X)<~>funny(X))))&
(?[X]:(quiet(X)))&
(?[X]:((~generous(X)<~>~patient(X))))&
((generous(alice)|~tall(alice)))&
(?[X]:((kind(X)|~curious(X))))&
((generous(paul)|patient(paul))) | kind(lucy) | [
"p1",
"p5",
"p8",
"p10",
"p11",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4453061417301444794468826
% SZS output start Proof for 4453061417301444794468826
2. ! [X0] : (calm(X0) <=> (calm(X0) <~> humble(X0))) [input p1]
6. ! [X0] : ((~wise(X0) | brave(X0)) <=> curious(X0)) [input p5]
9. (patient(fred) <~> ~curious(fred)) <=> ? [X0] : tall(X0) [input p8]
11. ? [X0] : (~wise(X0) & rich(X0)) <=> ? [X0] : ~kind(X0) [input p10]
12. ! [X0] : ((brave(X0) | ~strong(X0)) <=> ~patient(X0)) [input p11]
13. (strong(fred) & ~humble(fred)) <=> ? [X0] : ~wise(X0) [input p12]
14. ! [X0] : ((~strong(X0) <~> ~humble(X0)) <=> (wise(X0) & tall(X0))) [input p13]
23. ~kind(lucy) [input hypothesis]
26. ? [X0] : (~wise(X0) & rich(X0)) <=> ? [X1] : ~kind(X1) [rectify 11]
35. ! [X0] : ((calm(X0) | ((calm(X0) | ~humble(X0)) & (humble(X0) | ~calm(X0)))) & (((~humble(X0) | ~calm(X0)) & (humble(X0) | calm(X0))) | ~calm(X0))) [nnf transformation 2]
45. ! [X0] : (((~wise(X0) | brave(X0)) | ~curious(X0)) & (curious(X0) | (wise(X0) & ~brave(X0)))) [nnf transformation 6]
46. ! [X0] : ((~wise(X0) | brave(X0) | ~curious(X0)) & (curious(X0) | (wise(X0) & ~brave(X0)))) [flattening 45]
50. (((curious(fred) | ~patient(fred)) & (~curious(fred) | patient(fred))) | ! [X0] : ~tall(X0)) & (? [X0] : tall(X0) | ((patient(fred) | curious(fred)) & (~curious(fred) | ~patient(fred)))) [nnf transformation 9]
51. (((curious(fred) | ~patient(fred)) & (~curious(fred) | patient(fred))) | ! [X0] : ~tall(X0)) & (? [X1] : tall(X1) | ((patient(fred) | curious(fred)) & (~curious(fred) | ~patient(fred)))) [rectify 50]
52. ? [X1] : tall(X1) => tall(sK3) [choice axiom]
53. (((curious(fred) | ~patient(fred)) & (~curious(fred) | patient(fred))) | ! [X0] : ~tall(X0)) & (tall(sK3) | ((patient(fred) | curious(fred)) & (~curious(fred) | ~patient(fred)))) [skolemisation 51,52]
57. (? [X0] : (~wise(X0) & rich(X0)) | ! [X1] : kind(X1)) & (? [X1] : ~kind(X1) | ! [X0] : (wise(X0) | ~rich(X0))) [nnf transformation 26]
58. (? [X0] : (~wise(X0) & rich(X0)) | ! [X1] : kind(X1)) & (? [X2] : ~kind(X2) | ! [X3] : (wise(X3) | ~rich(X3))) [rectify 57]
59. ? [X0] : (~wise(X0) & rich(X0)) => (~wise(sK5) & rich(sK5)) [choice axiom]
60. ? [X2] : ~kind(X2) => ~kind(sK6) [choice axiom]
61. ((~wise(sK5) & rich(sK5)) | ! [X1] : kind(X1)) & (~kind(sK6) | ! [X3] : (wise(X3) | ~rich(X3))) [skolemisation 58,60,59]
62. ! [X0] : (((brave(X0) | ~strong(X0)) | patient(X0)) & (~patient(X0) | (~brave(X0) & strong(X0)))) [nnf transformation 12]
63. ! [X0] : ((brave(X0) | ~strong(X0) | patient(X0)) & (~patient(X0) | (~brave(X0) & strong(X0)))) [flattening 62]
64. ((strong(fred) & ~humble(fred)) | ! [X0] : wise(X0)) & (? [X0] : ~wise(X0) | (~strong(fred) | humble(fred))) [nnf transformation 13]
65. ((strong(fred) & ~humble(fred)) | ! [X0] : wise(X0)) & (? [X0] : ~wise(X0) | ~strong(fred) | humble(fred)) [flattening 64]
66. ((strong(fred) & ~humble(fred)) | ! [X0] : wise(X0)) & (? [X1] : ~wise(X1) | ~strong(fred) | humble(fred)) [rectify 65]
67. ? [X1] : ~wise(X1) => ~wise(sK7) [choice axiom]
68. ((strong(fred) & ~humble(fred)) | ! [X0] : wise(X0)) & (~wise(sK7) | ~strong(fred) | humble(fred)) [skolemisation 66,67]
69. ! [X0] : ((((humble(X0) | strong(X0)) & (~humble(X0) | ~strong(X0))) | (~wise(X0) | ~tall(X0))) & ((wise(X0) & tall(X0)) | ((~strong(X0) | humble(X0)) & (~humble(X0) | strong(X0))))) [nnf transformation 14]
70. ! [X0] : ((((humble(X0) | strong(X0)) & (~humble(X0) | ~strong(X0))) | ~wise(X0) | ~tall(X0)) & ((wise(X0) & tall(X0)) | ((~strong(X0) | humble(X0)) & (~humble(X0) | strong(X0))))) [flattening 69]
91. ~humble(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 35]
93. calm(X0) | calm(X0) | ~humble(X0) [cnf transformation 35]
99. ~brave(X0) | curious(X0) [cnf transformation 46]
101. ~curious(X0) | brave(X0) | ~wise(X0) [cnf transformation 46]
108. ~curious(fred) | patient(fred) | ~tall(X0) [cnf transformation 53]
109. curious(fred) | ~patient(fred) | ~tall(X0) [cnf transformation 53]
113. ~wise(sK5) | kind(X1) [cnf transformation 61]
115. ~patient(X0) | ~brave(X0) [cnf transformation 63]
116. ~strong(X0) | brave(X0) | patient(X0) [cnf transformation 63]
119. strong(fred) | wise(X0) [cnf transformation 68]
121. tall(X0) | ~strong(X0) | humble(X0) [cnf transformation 70]
123. wise(X0) | ~strong(X0) | humble(X0) [cnf transformation 70]
140. ~kind(lucy) [cnf transformation 23]
141. ~humble(X0) | ~calm(X0) [duplicate literal removal 91]
142. ~humble(X0) | calm(X0) [duplicate literal removal 93]
143. ~humble(X0) [subsumption resolution 141,142]
154. 3 <=> wise(fred) [avatar definition]
155. wise(fred) <- (3) [avatar component clause 154]
190. 11 <=> ! [X0] : ~tall(X0) [avatar definition]
191. ~tall(X0) <- (11) [avatar component clause 190]
193. 12 <=> patient(fred) [avatar definition]
194. patient(fred) <- (12) [avatar component clause 193]
195. ~patient(fred) <- (~12) [avatar component clause 193]
197. 13 <=> curious(fred) [avatar definition]
198. ~curious(fred) <- (~13) [avatar component clause 197]
199. curious(fred) <- (13) [avatar component clause 197]
200. 11 | ~12 | 13 [avatar split clause 109,197,193,190]
201. 11 | 12 | ~13 [avatar split clause 108,197,193,190]
217. 17 <=> ! [X1] : kind(X1) [avatar definition]
218. kind(X1) <- (17) [avatar component clause 217]
220. 18 <=> wise(sK5) [avatar definition]
222. ~wise(sK5) <- (~18) [avatar component clause 220]
223. 17 | ~18 [avatar split clause 113,220,217]
238. 22 <=> ! [X0] : wise(X0) [avatar definition]
239. wise(X0) <- (22) [avatar component clause 238]
241. 23 <=> strong(fred) [avatar definition]
243. strong(fred) <- (23) [avatar component clause 241]
244. 22 | 23 [avatar split clause 119,241,238]
252. ~strong(X0) | wise(X0) [subsumption resolution 123,143]
253. ~strong(X0) | tall(X0) [subsumption resolution 121,143]
325. $false <- (17) [resolution 218,140]
326. ~17 [avatar contradiction clause 325]
327. $false <- (~18, 22) [subsumption resolution 222,239]
328. 18 | ~22 [avatar contradiction clause 327]
337. wise(fred) <- (23) [resolution 252,243]
339. 3 | ~23 [avatar split clause 337,241,154]
340. tall(fred) <- (23) [resolution 253,243]
342. $false <- (11, 23) [subsumption resolution 340,191]
343. ~11 | ~23 [avatar contradiction clause 342]
346. ~brave(fred) <- (12) [resolution 194,115]
349. brave(fred) | ~wise(fred) <- (13) [resolution 101,199]
352. ~wise(fred) <- (12, 13) [subsumption resolution 349,346]
353. $false <- (3, 12, 13) [subsumption resolution 352,155]
354. ~3 | ~12 | ~13 [avatar contradiction clause 353]
373. brave(fred) | patient(fred) <- (23) [resolution 116,243]
375. brave(fred) <- (~12, 23) [subsumption resolution 373,195]
376. curious(fred) <- (~12, 23) [resolution 375,99]
377. $false <- (~12, ~13, 23) [subsumption resolution 376,198]
378. 12 | 13 | ~23 [avatar contradiction clause 377]
379. $false [avatar sat refutation 200,201,223,244,326,328,339,343,354,378]
% SZS output end Proof for 4453061417301444794468826
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or not quiet is not kind or not quiet. If susan is kind then john is wise or not funny and vice versa. Everyone who is not funny is either creative or happy and vice versa. Everyone who is patient or not tall is both not patient and quiet and vice versa. Everyone who is not creative or old is quiet. If fred is either patient or not humble then someone is kind or not funny and vice versa. Everyone who is either not creative or not calm is quiet and vice versa. If susan is not generous or not creative then someone is both humble and not happy. Everyone who is calm or brave is both quiet and not creative and vice versa. Everyone who is both not strong and not tall is funny or rich. If lucy is both not funny and not tall then someone is not patient or generous. If john is either not funny or not humble then someone is both strong and not happy. Everyone who is calm or generous is both old and humble and vice versa. If someone is both not wise and kind then someone is old or not brave. If alice is either not wise or funny then someone is old or quiet. Everyone who is patient is either brave or not wise. Someone is not happy or not humble. Someone is not patient or calm. Mary is both not happy and not generous. John is not curious. Lucy is not generous or humble. Someone is quiet. Someone is strong. | John is quiet. | entailment | (![X]:((~tall(X)|~quiet(X))=>(~kind(X)|~quiet(X))))&
((kind(susan))<=>((wise(john)|~funny(john))))&
(![X]:(~funny(X)<=>(creative(X)<~>happy(X))))&
(![X]:((patient(X)|~tall(X))<=>(~patient(X)&quiet(X))))&
(![X]:((~creative(X)|old(X))=>quiet(X)))&
(((patient(fred)<~>~humble(fred)))<=>(?[X]:((kind(X)|~funny(X)))))&
(![X]:((~creative(X)<~>~calm(X))<=>quiet(X)))&
(((~generous(susan)|~creative(susan)))=>(?[X]:((humble(X)&~happy(X)))))&
(![X]:((calm(X)|brave(X))<=>(quiet(X)&~creative(X))))&
(![X]:((~strong(X)&~tall(X))=>(funny(X)|rich(X))))&
(((~funny(lucy)&~tall(lucy)))=>(?[X]:((~patient(X)|generous(X)))))&
(((~funny(john)<~>~humble(john)))=>(?[X]:((strong(X)&~happy(X)))))&
(![X]:((calm(X)|generous(X))<=>(old(X)&humble(X))))&
((?[X]:((~wise(X)&kind(X))))=>(?[X]:((old(X)|~brave(X)))))&
(((~wise(alice)<~>funny(alice)))=>(?[X]:((old(X)|quiet(X)))))&
(![X]:(patient(X)=>(brave(X)<~>~wise(X))))&
(?[X]:((~happy(X)|~humble(X))))&
(?[X]:((~patient(X)|calm(X))))&
((~happy(mary)&~generous(mary)))&
(~curious(john))&
((~generous(lucy)|humble(lucy)))&
(?[X]:(quiet(X)))&
(?[X]:(strong(X))) | quiet(john) | [
"p4",
"p6",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 5047116462686419765432241
% SZS output start Proof for 5047116462686419765432241
5. ! [X0] : ((old(X0) | ~creative(X0)) => quiet(X0)) [input p4]
7. ! [X0] : ((~creative(X0) <~> ~calm(X0)) <=> quiet(X0)) [input p6]
9. ! [X0] : ((brave(X0) | calm(X0)) <=> (~creative(X0) & quiet(X0))) [input p8]
24. ~quiet(john) [input hypothesis]
32. ! [X0] : (quiet(X0) | (~old(X0) & creative(X0))) [ennf transformation 5]
49. ! [X0] : ((((calm(X0) | creative(X0)) & (~calm(X0) | ~creative(X0))) | ~quiet(X0)) & (quiet(X0) | ((~creative(X0) | calm(X0)) & (~calm(X0) | creative(X0))))) [nnf transformation 7]
52. ! [X0] : (((brave(X0) | calm(X0)) | (creative(X0) | ~quiet(X0))) & ((~creative(X0) & quiet(X0)) | (~brave(X0) & ~calm(X0)))) [nnf transformation 9]
53. ! [X0] : ((brave(X0) | calm(X0) | creative(X0) | ~quiet(X0)) & ((~creative(X0) & quiet(X0)) | (~brave(X0) & ~calm(X0)))) [flattening 52]
88. quiet(X0) | creative(X0) [cnf transformation 32]
97. quiet(X0) | ~creative(X0) | calm(X0) [cnf transformation 49]
99. calm(X0) | creative(X0) | ~quiet(X0) [cnf transformation 49]
104. quiet(X0) | ~calm(X0) [cnf transformation 53]
128. ~quiet(john) [cnf transformation 24]
170. calm(X0) | creative(X0) [subsumption resolution 99,88]
171. quiet(X0) | calm(X0) [subsumption resolution 97,170]
192. quiet(X0) [subsumption resolution 104,171]
224. $false [subsumption resolution 128,192]
% SZS output end Proof for 5047116462686419765432241
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both strong and not creative is both patient and not quiet and vice versa.
If someone is either not tall or happy then paul is not curious or not wise.
If someone is patient then lucy is either not humble or wise.
Everyone who is both patient and not tall is either patient or not generous and vice versa.
If someone is old then john is curious or calm and vice versa.
Everyone who is curious or not kind is both creative and not quiet and vice versa.
Everyone who is either not rich or not kind is wise.
If someone is wise or not calm then paul is brave.
Everyone who is either quiet or generous is both not tall and not creative and vice versa.
Everyone who is both not funny and not happy is both happy and not curious and vice versa.
Everyone who is either calm or not generous is patient or not strong and vice versa.
If john is both happy and patient then john is either not rich or not calm.
Everyone who is humble is both not strong and not patient and vice versa.
If fred is old then john is old and vice versa.
Everyone who is not strong is both not tall and generous.
If paul is not kind or funny then john is both not old and humble.
Someone is not strong.
Someone is both creative and not rich.
Someone is wise or quiet.
Alice is not patient.
Someone is brave.
Fred is either not generous or not patient.
Paul is strong. | Alice is not curious. | entailment | (![X]:((strong(X)&~creative(X))<=>(patient(X)&~quiet(X))))&
((?[X]:((~tall(X)<~>happy(X))))=>((~curious(paul)|~wise(paul))))&
((?[X]:(patient(X)))=>((~humble(lucy)<~>wise(lucy))))&
(![X]:((patient(X)&~tall(X))<=>(patient(X)<~>~generous(X))))&
((?[X]:(old(X)))<=>((curious(john)|calm(john))))&
(![X]:((curious(X)|~kind(X))<=>(creative(X)&~quiet(X))))&
(![X]:((~rich(X)<~>~kind(X))=>wise(X)))&
((?[X]:((wise(X)|~calm(X))))=>(brave(paul)))&
(![X]:((quiet(X)<~>generous(X))<=>(~tall(X)&~creative(X))))&
(![X]:((~funny(X)&~happy(X))<=>(happy(X)&~curious(X))))&
(![X]:((calm(X)<~>~generous(X))<=>(patient(X)|~strong(X))))&
(((happy(john)&patient(john)))=>((~rich(john)<~>~calm(john))))&
(![X]:(humble(X)<=>(~strong(X)&~patient(X))))&
((old(fred))<=>(old(john)))&
(![X]:(~strong(X)=>(~tall(X)&generous(X))))&
(((~kind(paul)|funny(paul)))=>((~old(john)&humble(john))))&
(?[X]:(~strong(X)))&
(?[X]:((creative(X)&~rich(X))))&
(?[X]:((wise(X)|quiet(X))))&
(~patient(alice))&
(?[X]:(brave(X)))&
((~generous(fred)<~>~patient(fred)))&
(strong(paul)) | ~curious(alice) | [
"p0",
"p3",
"p5",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 5583909724028842763874538
% SZS output start Proof for 5583909724028842763874538
1. ! [X0] : ((~creative(X0) & strong(X0)) <=> (~quiet(X0) & patient(X0))) [input p0]
4. ! [X0] : ((~tall(X0) & patient(X0)) <=> (patient(X0) <~> ~generous(X0))) [input p3]
6. ! [X0] : ((~kind(X0) | curious(X0)) <=> (~quiet(X0) & creative(X0))) [input p5]
9. ! [X0] : ((quiet(X0) <~> generous(X0)) <=> (~creative(X0) & ~tall(X0))) [input p8]
24. curious(alice) [input hypothesis]
35. ! [X0] : (((~creative(X0) & strong(X0)) | (quiet(X0) | ~patient(X0))) & ((~quiet(X0) & patient(X0)) | (creative(X0) | ~strong(X0)))) [nnf transformation 1]
36. ! [X0] : (((~creative(X0) & strong(X0)) | quiet(X0) | ~patient(X0)) & ((~quiet(X0) & patient(X0)) | creative(X0) | ~strong(X0))) [flattening 35]
39. ! [X0] : (((~tall(X0) & patient(X0)) | ((patient(X0) | generous(X0)) & (~generous(X0) | ~patient(X0)))) & (((generous(X0) | ~patient(X0)) & (~generous(X0) | patient(X0))) | (tall(X0) | ~patient(X0)))) [nnf transformation 4]
40. ! [X0] : (((~tall(X0) & patient(X0)) | ((patient(X0) | generous(X0)) & (~generous(X0) | ~patient(X0)))) & (((generous(X0) | ~patient(X0)) & (~generous(X0) | patient(X0))) | tall(X0) | ~patient(X0))) [flattening 39]
46. ! [X0] : (((~kind(X0) | curious(X0)) | (quiet(X0) | ~creative(X0))) & ((~quiet(X0) & creative(X0)) | (kind(X0) & ~curious(X0)))) [nnf transformation 6]
47. ! [X0] : ((~kind(X0) | curious(X0) | quiet(X0) | ~creative(X0)) & ((~quiet(X0) & creative(X0)) | (kind(X0) & ~curious(X0)))) [flattening 46]
49. ! [X0] : ((((~generous(X0) | ~quiet(X0)) & (generous(X0) | quiet(X0))) | (creative(X0) | tall(X0))) & ((~creative(X0) & ~tall(X0)) | ((quiet(X0) | ~generous(X0)) & (generous(X0) | ~quiet(X0))))) [nnf transformation 9]
50. ! [X0] : ((((~generous(X0) | ~quiet(X0)) & (generous(X0) | quiet(X0))) | creative(X0) | tall(X0)) & ((~creative(X0) & ~tall(X0)) | ((quiet(X0) | ~generous(X0)) & (generous(X0) | ~quiet(X0))))) [flattening 49]
69. ~patient(X0) | quiet(X0) | ~creative(X0) [cnf transformation 36]
77. patient(X0) | patient(X0) | generous(X0) [cnf transformation 40]
83. ~curious(X0) | creative(X0) [cnf transformation 47]
85. ~curious(X0) | ~quiet(X0) [cnf transformation 47]
93. ~generous(X0) | quiet(X0) | ~creative(X0) [cnf transformation 50]
127. curious(alice) [cnf transformation 24]
131. generous(X0) | patient(X0) [duplicate literal removal 77]
242. creative(alice) [resolution 83,127]
243. ~quiet(alice) [resolution 85,127]
298. quiet(X1) | ~creative(X1) | patient(X1) [resolution 93,131]
302. ~creative(X1) | quiet(X1) [subsumption resolution 298,69]
304. quiet(alice) [resolution 302,242]
305. $false [subsumption resolution 304,243]
% SZS output end Proof for 5583909724028842763874538
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not kind or not brave is either old or not kind and vice versa.
Everyone who is not rich or curious is generous or patient.
Everyone who is either tall or wise is not patient and vice versa.
Everyone who is tall or not strong is either not wise or calm and vice versa.
If someone is not rich then someone is either not strong or quiet.
Everyone who is patient is both not quiet and rich and vice versa.
If someone is happy or wise then someone is humble or not happy.
If someone is generous or not curious then someone is not humble or strong and vice versa.
If paul is quiet then someone is not tall.
Everyone who is old is not rich or kind.
If someone is both not patient and not creative then someone is patient or not strong.
Everyone who is either not tall or not patient is either wise or tall and vice versa.
If someone is both not humble and not kind then someone is both not patient and rich and vice versa.
If paul is not generous then mary is either not calm or not happy and vice versa.
Everyone who is creative or wise is not brave or kind and vice versa.
Everyone who is humble or not wise is not old.
Lucy is either not tall or not happy.
Someone is not tall or humble.
Mary is both tall and brave.
Someone is not kind or happy.
Someone is not generous.
Someone is both funny and not happy.
Mary is not creative.
Someone is both not wise and humble. | Mary is quiet. | neutral | (![X]:((~kind(X)<~>~brave(X))<=>(old(X)<~>~kind(X))))&
(![X]:((~rich(X)|curious(X))=>(generous(X)|patient(X))))&
(![X]:((tall(X)<~>wise(X))<=>~patient(X)))&
(![X]:((tall(X)|~strong(X))<=>(~wise(X)<~>calm(X))))&
((?[X]:(~rich(X)))=>(?[X]:((~strong(X)<~>quiet(X)))))&
(![X]:(patient(X)<=>(~quiet(X)&rich(X))))&
((?[X]:((happy(X)|wise(X))))=>(?[X]:((humble(X)|~happy(X)))))&
((?[X]:((generous(X)|~curious(X))))<=>(?[X]:((~humble(X)|strong(X)))))&
((quiet(paul))=>(?[X]:(~tall(X))))&
(![X]:(old(X)=>(~rich(X)|kind(X))))&
((?[X]:((~patient(X)&~creative(X))))=>(?[X]:((patient(X)|~strong(X)))))&
(![X]:((~tall(X)<~>~patient(X))<=>(wise(X)<~>tall(X))))&
((?[X]:((~humble(X)&~kind(X))))<=>(?[X]:((~patient(X)&rich(X)))))&
((~generous(paul))<=>((~calm(mary)<~>~happy(mary))))&
(![X]:((creative(X)|wise(X))<=>(~brave(X)|kind(X))))&
(![X]:((humble(X)|~wise(X))=>~old(X)))&
((~tall(lucy)<~>~happy(lucy)))&
(?[X]:((~tall(X)|humble(X))))&
((tall(mary)&brave(mary)))&
(?[X]:((~kind(X)|happy(X))))&
(?[X]:(~generous(X)))&
(?[X]:((funny(X)&~happy(X))))&
(~creative(mary))&
(?[X]:((~wise(X)&humble(X)))) | quiet(mary) | [] | null | 0 |
Everyone who is not humble or not old is not wise or wise and vice versa.
If someone is either happy or brave then someone is funny and vice versa.
Everyone who is not old is creative and vice versa.
If someone is both brave and not brave then someone is curious and vice versa.
Everyone who is patient or creative is both not patient and funny.
Everyone who is either tall or not tall is either not kind or not funny.
Everyone who is not generous or not funny is either not calm or not funny and vice versa.
If someone is either wise or not wise then lucy is not patient and vice versa.
Everyone who is tall or creative is both rich and not patient.
Everyone who is either not brave or not happy is brave or not patient and vice versa.
Everyone who is both rich and not humble is either patient or tall.
Everyone who is either not rich or strong is both not quiet and calm and vice versa.
If mary is both patient and curious then john is both not generous and rich and vice versa.
Everyone who is strong is wise or not strong.
Everyone who is curious or tall is not creative or humble and vice versa.
Someone is either calm or rich.
Someone is not calm.
Someone is tall.
Someone is either wise or kind.
Lucy is tall.
John is rich or strong.
Fred is kind. | Lucy is brave. | neutral | (![X]:((~humble(X)|~old(X))<=>(~wise(X)|wise(X))))&
((?[X]:((happy(X)<~>brave(X))))<=>(?[X]:(funny(X))))&
(![X]:(~old(X)<=>creative(X)))&
((?[X]:((brave(X)&~brave(X))))<=>(?[X]:(curious(X))))&
(![X]:((patient(X)|creative(X))=>(~patient(X)&funny(X))))&
(![X]:((tall(X)<~>~tall(X))=>(~kind(X)<~>~funny(X))))&
(![X]:((~generous(X)|~funny(X))<=>(~calm(X)<~>~funny(X))))&
((?[X]:((wise(X)<~>~wise(X))))<=>(~patient(lucy)))&
(![X]:((tall(X)|creative(X))=>(rich(X)&~patient(X))))&
(![X]:((~brave(X)<~>~happy(X))<=>(brave(X)|~patient(X))))&
(![X]:((rich(X)&~humble(X))=>(patient(X)<~>tall(X))))&
(![X]:((~rich(X)<~>strong(X))<=>(~quiet(X)&calm(X))))&
(((patient(mary)&curious(mary)))<=>((~generous(john)&rich(john))))&
(![X]:(strong(X)=>(wise(X)|~strong(X))))&
(![X]:((curious(X)|tall(X))<=>(~creative(X)|humble(X))))&
(?[X]:((calm(X)<~>rich(X))))&
(?[X]:(~calm(X)))&
(?[X]:(tall(X)))&
(?[X]:((wise(X)<~>kind(X))))&
(tall(lucy))&
((rich(john)|strong(john)))&
(kind(fred)) | brave(lucy) | [] | null | 0 |
If paul is creative or brave then someone is either old or kind and vice versa. Everyone who is tall is both quiet and not rich and vice versa. Everyone who is not calm is not patient and vice versa. If paul is either not quiet or patient then fred is both brave and not kind. If someone is quiet or tall then someone is not brave or humble. Everyone who is tall or happy is not wise. Everyone who is strong or not rich is not quiet or not funny and vice versa. Everyone who is calm or generous is wise or not creative. Everyone who is rich or curious is both not brave and not funny and vice versa. Everyone who is not creative or not kind is either not happy or humble and vice versa. Everyone who is humble or not rich is either old or not funny. Everyone who is not funny or patient is not old and vice versa. If fred is either not quiet or generous then someone is both humble and not funny and vice versa. Everyone who is not funny is both tall and not patient. If paul is happy then someone is either old or patient. Everyone who is generous is wise or not calm. Someone is patient or tall. John is either curious or tall. Someone is not tall or not happy. Someone is not wise or rich. Fred is both happy and not old. Paul is old or rich. | Fred is not curious. | entailment | (((creative(paul)|brave(paul)))<=>(?[X]:((old(X)<~>kind(X)))))&
(![X]:(tall(X)<=>(quiet(X)&~rich(X))))&
(![X]:(~calm(X)<=>~patient(X)))&
(((~quiet(paul)<~>patient(paul)))=>((brave(fred)&~kind(fred))))&
((?[X]:((quiet(X)|tall(X))))=>(?[X]:((~brave(X)|humble(X)))))&
(![X]:((tall(X)|happy(X))=>~wise(X)))&
(![X]:((strong(X)|~rich(X))<=>(~quiet(X)|~funny(X))))&
(![X]:((calm(X)|generous(X))=>(wise(X)|~creative(X))))&
(![X]:((rich(X)|curious(X))<=>(~brave(X)&~funny(X))))&
(![X]:((~creative(X)|~kind(X))<=>(~happy(X)<~>humble(X))))&
(![X]:((humble(X)|~rich(X))=>(old(X)<~>~funny(X))))&
(![X]:((~funny(X)|patient(X))<=>~old(X)))&
(((~quiet(fred)<~>generous(fred)))<=>(?[X]:((humble(X)&~funny(X)))))&
(![X]:(~funny(X)=>(tall(X)&~patient(X))))&
((happy(paul))=>(?[X]:((old(X)<~>patient(X)))))&
(![X]:(generous(X)=>(wise(X)|~calm(X))))&
(?[X]:((patient(X)|tall(X))))&
((curious(john)<~>tall(john)))&
(?[X]:((~tall(X)|~happy(X))))&
(?[X]:((~wise(X)|rich(X))))&
((happy(fred)&~old(fred)))&
((old(paul)|rich(paul))) | ~curious(fred) | [
"p1",
"p3",
"p6",
"p8",
"p11",
"p13",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 3006391760354811706413303
% SZS output start Proof for 3006391760354811706413303
2. ! [X0] : (tall(X0) <=> (~rich(X0) & quiet(X0))) [input p1]
4. (~quiet(paul) <~> patient(paul)) => (~kind(fred) & brave(fred)) [input p3]
7. ! [X0] : ((~rich(X0) | strong(X0)) <=> (~funny(X0) | ~quiet(X0))) [input p6]
9. ! [X0] : ((curious(X0) | rich(X0)) <=> (~funny(X0) & ~brave(X0))) [input p8]
12. ! [X0] : ((patient(X0) | ~funny(X0)) <=> ~old(X0)) [input p11]
14. ! [X0] : (~funny(X0) => (~patient(X0) & tall(X0))) [input p13]
22. rich(paul) | old(paul) [input p21]
23. curious(fred) [input hypothesis]
27. (~kind(fred) & brave(fred)) | (~quiet(paul) <=> patient(paul)) [ennf transformation 4]
33. ! [X0] : ((~patient(X0) & tall(X0)) | funny(X0)) [ennf transformation 14]
42. ! [X0] : ((tall(X0) | (rich(X0) | ~quiet(X0))) & ((~rich(X0) & quiet(X0)) | ~tall(X0))) [nnf transformation 2]
43. ! [X0] : ((tall(X0) | rich(X0) | ~quiet(X0)) & ((~rich(X0) & quiet(X0)) | ~tall(X0))) [flattening 42]
44. (~kind(fred) & brave(fred)) | ((~quiet(paul) | ~patient(paul)) & (patient(paul) | quiet(paul))) [nnf transformation 27]
48. ! [X0] : (((~rich(X0) | strong(X0)) | (funny(X0) & quiet(X0))) & ((~funny(X0) | ~quiet(X0)) | (rich(X0) & ~strong(X0)))) [nnf transformation 7]
49. ! [X0] : ((~rich(X0) | strong(X0) | (funny(X0) & quiet(X0))) & (~funny(X0) | ~quiet(X0) | (rich(X0) & ~strong(X0)))) [flattening 48]
50. ! [X0] : (((curious(X0) | rich(X0)) | (funny(X0) | brave(X0))) & ((~funny(X0) & ~brave(X0)) | (~curious(X0) & ~rich(X0)))) [nnf transformation 9]
51. ! [X0] : ((curious(X0) | rich(X0) | funny(X0) | brave(X0)) & ((~funny(X0) & ~brave(X0)) | (~curious(X0) & ~rich(X0)))) [flattening 50]
55. ! [X0] : (((patient(X0) | ~funny(X0)) | old(X0)) & (~old(X0) | (~patient(X0) & funny(X0)))) [nnf transformation 12]
56. ! [X0] : ((patient(X0) | ~funny(X0) | old(X0)) & (~old(X0) | (~patient(X0) & funny(X0)))) [flattening 55]
78. ~rich(X0) | ~tall(X0) [cnf transformation 43]
81. brave(fred) | patient(paul) | quiet(paul) [cnf transformation 44]
90. ~funny(X0) | ~quiet(X0) | rich(X0) [cnf transformation 49]
96. ~curious(X0) | ~brave(X0) [cnf transformation 51]
97. ~funny(X0) | ~rich(X0) [cnf transformation 51]
110. ~old(X0) | funny(X0) [cnf transformation 56]
111. ~patient(X0) | ~old(X0) [cnf transformation 56]
119. funny(X0) | tall(X0) [cnf transformation 33]
131. rich(paul) | old(paul) [cnf transformation 22]
132. curious(fred) [cnf transformation 23]
162. 7 <=> patient(paul) [avatar definition]
163. patient(paul) <- (7) [avatar component clause 162]
166. 8 <=> quiet(paul) [avatar definition]
167. quiet(paul) <- (8) [avatar component clause 166]
176. 10 <=> brave(fred) [avatar definition]
180. 8 | 7 | 10 [avatar split clause 81,176,162,166]
274. 31 <=> old(paul) [avatar definition]
276. old(paul) <- (31) [avatar component clause 274]
278. 32 <=> rich(paul) [avatar definition]
280. rich(paul) <- (32) [avatar component clause 278]
281. 31 | 32 [avatar split clause 131,278,274]
284. ~brave(fred) [resolution 96,132]
286. ~10 [avatar split clause 284,176]
290. funny(paul) <- (31) [resolution 110,276]
291. ~old(paul) <- (7) [resolution 111,163]
293. $false <- (7, 31) [subsumption resolution 291,276]
294. ~7 | ~31 [avatar contradiction clause 293]
295. tall(X0) | ~rich(X0) [resolution 119,97]
298. ~rich(X0) [subsumption resolution 295,78]
342. ~quiet(paul) | rich(paul) <- (31) [resolution 90,290]
344. rich(paul) <- (8, 31) [subsumption resolution 342,167]
345. $false <- (8, 31) [subsumption resolution 344,298]
346. ~8 | ~31 [avatar contradiction clause 345]
349. $false <- (32) [subsumption resolution 280,298]
350. ~32 [avatar contradiction clause 349]
351. $false [avatar sat refutation 180,281,286,294,346,350]
% SZS output end Proof for 3006391760354811706413303
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious is not brave or old. Everyone who is either strong or not brave is both not patient and kind. If someone is both creative and wise then paul is either not humble or generous. Everyone who is either brave or humble is creative. If alice is both creative and calm then fred is old. If susan is either not funny or not generous then fred is kind and vice versa. If someone is either not curious or creative then someone is quiet and vice versa. Everyone who is not brave or not calm is both brave and not brave. If someone is not old then someone is either not wise or happy. If someone is both humble and not funny then alice is both not humble and tall and vice versa. If someone is either not brave or not patient then fred is either not brave or quiet and vice versa. Everyone who is either not curious or not kind is either not rich or creative. Everyone who is both not generous and kind is funny or creative and vice versa. If someone is either not funny or funny then someone is either quiet or not brave and vice versa. Everyone who is not generous or funny is not creative. Everyone who is both strong and not old is not happy or wise. Someone is either not kind or patient. Paul is not happy. Someone is either creative or not rich. Susan is either kind or old. Someone is humble. | Susan is not humble. | contradiction | (![X]:(~curious(X)=>(~brave(X)|old(X))))&
(![X]:((strong(X)<~>~brave(X))=>(~patient(X)&kind(X))))&
((?[X]:((creative(X)&wise(X))))=>((~humble(paul)<~>generous(paul))))&
(![X]:((brave(X)<~>humble(X))=>creative(X)))&
(((creative(alice)&calm(alice)))=>(old(fred)))&
(((~funny(susan)<~>~generous(susan)))<=>(kind(fred)))&
((?[X]:((~curious(X)<~>creative(X))))<=>(?[X]:(quiet(X))))&
(![X]:((~brave(X)|~calm(X))=>(brave(X)&~brave(X))))&
((?[X]:(~old(X)))=>(?[X]:((~wise(X)<~>happy(X)))))&
((?[X]:((humble(X)&~funny(X))))<=>((~humble(alice)&tall(alice))))&
((?[X]:((~brave(X)<~>~patient(X))))<=>((~brave(fred)<~>quiet(fred))))&
(![X]:((~curious(X)<~>~kind(X))=>(~rich(X)<~>creative(X))))&
(![X]:((~generous(X)&kind(X))<=>(funny(X)|creative(X))))&
((?[X]:((~funny(X)<~>funny(X))))<=>(?[X]:((quiet(X)<~>~brave(X)))))&
(![X]:((~generous(X)|funny(X))=>~creative(X)))&
(![X]:((strong(X)&~old(X))=>(~happy(X)|wise(X))))&
(?[X]:((~kind(X)<~>patient(X))))&
(~happy(paul))&
(?[X]:((creative(X)<~>~rich(X))))&
((kind(susan)<~>old(susan)))&
(?[X]:(humble(X))) | ~humble(susan) | [
"p3",
"p7",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 370961065040298251314720
% SZS output start Proof for 370961065040298251314720
4. ! [X0] : ((brave(X0) <~> humble(X0)) => creative(X0)) [input p3]
8. ! [X0] : ((~calm(X0) | ~brave(X0)) => (~brave(X0) & brave(X0))) [input p7]
13. ! [X0] : ((kind(X0) & ~generous(X0)) <=> (creative(X0) | funny(X0))) [input p12]
15. ! [X0] : ((funny(X0) | ~generous(X0)) => ~creative(X0)) [input p14]
22. ~humble(susan) [input hypothesis]
30. ! [X0] : (creative(X0) | (brave(X0) <=> humble(X0))) [ennf transformation 4]
33. ! [X0] : ((~brave(X0) & brave(X0)) | (calm(X0) & brave(X0))) [ennf transformation 8]
36. ! [X0] : (~creative(X0) | (~funny(X0) & generous(X0))) [ennf transformation 15]
41. ! [X0] : (creative(X0) | ((brave(X0) | ~humble(X0)) & (humble(X0) | ~brave(X0)))) [nnf transformation 30]
62. ! [X0] : (((kind(X0) & ~generous(X0)) | (~creative(X0) & ~funny(X0))) & ((creative(X0) | funny(X0)) | (~kind(X0) | generous(X0)))) [nnf transformation 13]
63. ! [X0] : (((kind(X0) & ~generous(X0)) | (~creative(X0) & ~funny(X0))) & (creative(X0) | funny(X0) | ~kind(X0) | generous(X0))) [flattening 62]
85. ~brave(X0) | humble(X0) | creative(X0) [cnf transformation 41]
96. brave(X0) | brave(X0) [cnf transformation 33]
120. ~generous(X0) | ~creative(X0) [cnf transformation 63]
131. ~creative(X0) | generous(X0) [cnf transformation 36]
142. ~humble(susan) [cnf transformation 22]
147. brave(X0) [duplicate literal removal 96]
283. ~creative(X0) [subsumption resolution 131,120]
312. humble(X0) | creative(X0) [resolution 85,147]
313. humble(X0) [subsumption resolution 312,283]
319. $false [resolution 313,142]
% SZS output end Proof for 370961065040298251314720
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong is brave or wise. Everyone who is both not old and not quiet is either not funny or old and vice versa. If someone is not strong then lucy is not calm or rich and vice versa. Everyone who is both not old and wise is either not tall or not rich. Everyone who is either not old or not happy is not brave or not funny and vice versa. If someone is either not strong or not quiet then mary is both not humble and not strong and vice versa. Everyone who is either curious or not tall is curious. If fred is either wise or not funny then someone is both creative and kind and vice versa. Everyone who is both not brave and not wise is either strong or not wise and vice versa. Everyone who is both not rich and not funny is not wise or not funny and vice versa. If someone is both not quiet and patient then someone is both patient and old. Everyone who is both not patient and not tall is either patient or not happy. Everyone who is either rich or not patient is not kind or not strong. If someone is both generous and humble then lucy is both not generous and tall. If someone is creative then fred is curious and vice versa. If john is both tall and not humble then fred is both creative and happy and vice versa. Lucy is both not creative and not patient. Someone is humble or strong. Someone is not humble. Someone is either not humble or creative. Someone is either patient or brave. Susan is tall. John is both not calm and rich. Susan is either not happy or patient. | Lucy is not calm. | neutral | (![X]:(~strong(X)=>(brave(X)|wise(X))))&
(![X]:((~old(X)&~quiet(X))<=>(~funny(X)<~>old(X))))&
((?[X]:(~strong(X)))<=>((~calm(lucy)|rich(lucy))))&
(![X]:((~old(X)&wise(X))=>(~tall(X)<~>~rich(X))))&
(![X]:((~old(X)<~>~happy(X))<=>(~brave(X)|~funny(X))))&
((?[X]:((~strong(X)<~>~quiet(X))))<=>((~humble(mary)&~strong(mary))))&
(![X]:((curious(X)<~>~tall(X))=>curious(X)))&
(((wise(fred)<~>~funny(fred)))<=>(?[X]:((creative(X)&kind(X)))))&
(![X]:((~brave(X)&~wise(X))<=>(strong(X)<~>~wise(X))))&
(![X]:((~rich(X)&~funny(X))<=>(~wise(X)|~funny(X))))&
((?[X]:((~quiet(X)&patient(X))))=>(?[X]:((patient(X)&old(X)))))&
(![X]:((~patient(X)&~tall(X))=>(patient(X)<~>~happy(X))))&
(![X]:((rich(X)<~>~patient(X))=>(~kind(X)|~strong(X))))&
((?[X]:((generous(X)&humble(X))))=>((~generous(lucy)&tall(lucy))))&
((?[X]:(creative(X)))<=>(curious(fred)))&
(((tall(john)&~humble(john)))<=>((creative(fred)&happy(fred))))&
((~creative(lucy)&~patient(lucy)))&
(?[X]:((humble(X)|strong(X))))&
(?[X]:(~humble(X)))&
(?[X]:((~humble(X)<~>creative(X))))&
(?[X]:((patient(X)<~>brave(X))))&
(tall(susan))&
((~calm(john)&rich(john)))&
((~happy(susan)<~>patient(susan))) | ~calm(lucy) | [] | null | 0 |
Everyone who is both curious and not curious is not calm and vice versa.
Everyone who is both not humble and not funny is both not calm and humble and vice versa.
If lucy is either funny or kind then mary is not kind or not tall and vice versa.
Everyone who is not strong or not tall is either patient or strong and vice versa.
Everyone who is both generous and not generous is both not brave and not patient and vice versa.
Everyone who is not curious is not old or not humble.
If someone is not tall or not kind then john is not calm or not kind and vice versa.
If someone is either creative or not tall then someone is both funny and not generous.
If someone is either not curious or happy then fred is not humble or calm and vice versa.
If susan is either not creative or not patient then paul is either not patient or not wise and vice versa.
If someone is both not generous and creative then mary is both not generous and not calm.
Everyone who is wise is both happy and not wise and vice versa.
Everyone who is both kind and not creative is not calm and vice versa.
Everyone who is not patient or quiet is both rich and generous.
If john is either brave or not calm then alice is either old or not brave.
Everyone who is humble or tall is quiet or not humble and vice versa.
Alice is not rich or not tall.
Lucy is not old or not strong.
Susan is either rich or not patient.
Someone is both tall and not curious.
Someone is not patient or happy. | Mary is kind. | neutral | (![X]:((curious(X)&~curious(X))<=>~calm(X)))&
(![X]:((~humble(X)&~funny(X))<=>(~calm(X)&humble(X))))&
(((funny(lucy)<~>kind(lucy)))<=>((~kind(mary)|~tall(mary))))&
(![X]:((~strong(X)|~tall(X))<=>(patient(X)<~>strong(X))))&
(![X]:((generous(X)&~generous(X))<=>(~brave(X)&~patient(X))))&
(![X]:(~curious(X)=>(~old(X)|~humble(X))))&
((?[X]:((~tall(X)|~kind(X))))<=>((~calm(john)|~kind(john))))&
((?[X]:((creative(X)<~>~tall(X))))=>(?[X]:((funny(X)&~generous(X)))))&
((?[X]:((~curious(X)<~>happy(X))))<=>((~humble(fred)|calm(fred))))&
(((~creative(susan)<~>~patient(susan)))<=>((~patient(paul)<~>~wise(paul))))&
((?[X]:((~generous(X)&creative(X))))=>((~generous(mary)&~calm(mary))))&
(![X]:(wise(X)<=>(happy(X)&~wise(X))))&
(![X]:((kind(X)&~creative(X))<=>~calm(X)))&
(![X]:((~patient(X)|quiet(X))=>(rich(X)&generous(X))))&
(((brave(john)<~>~calm(john)))=>((old(alice)<~>~brave(alice))))&
(![X]:((humble(X)|tall(X))<=>(quiet(X)|~humble(X))))&
((~rich(alice)|~tall(alice)))&
((~old(lucy)|~strong(lucy)))&
((rich(susan)<~>~patient(susan)))&
(?[X]:((tall(X)&~curious(X))))&
(?[X]:((~patient(X)|happy(X)))) | kind(mary) | [] | null | 0 |
If paul is either funny or generous then paul is not rich.
If someone is tall then paul is kind or not curious.
If lucy is generous or not generous then someone is kind or not calm.
Everyone who is either not quiet or rich is calm or rich.
Everyone who is either rich or not old is either not tall or not old and vice versa.
If alice is strong or patient then alice is generous and vice versa.
Everyone who is either generous or rich is either not happy or not wise.
If someone is either quiet or not creative then someone is either not generous or not wise.
Everyone who is calm or creative is generous or tall and vice versa.
Everyone who is either generous or not creative is both not curious and old.
If someone is both curious and creative then someone is both not wise and curious and vice versa.
Everyone who is both wise and calm is wise or strong and vice versa.
If fred is either not generous or not tall then someone is either brave or patient.
Everyone who is creative or generous is not kind.
If someone is either wise or happy then alice is brave or curious and vice versa.
Paul is not humble.
Paul is tall or old.
Mary is not happy or not humble.
Someone is not brave or not happy.
John is not wise or happy. | Alice is not curious. | neutral | (((funny(paul)<~>generous(paul)))=>(~rich(paul)))&
((?[X]:(tall(X)))=>((kind(paul)|~curious(paul))))&
(((generous(lucy)|~generous(lucy)))=>(?[X]:((kind(X)|~calm(X)))))&
(![X]:((~quiet(X)<~>rich(X))=>(calm(X)|rich(X))))&
(![X]:((rich(X)<~>~old(X))<=>(~tall(X)<~>~old(X))))&
(((strong(alice)|patient(alice)))<=>(generous(alice)))&
(![X]:((generous(X)<~>rich(X))=>(~happy(X)<~>~wise(X))))&
((?[X]:((quiet(X)<~>~creative(X))))=>(?[X]:((~generous(X)<~>~wise(X)))))&
(![X]:((calm(X)|creative(X))<=>(generous(X)|tall(X))))&
(![X]:((generous(X)<~>~creative(X))=>(~curious(X)&old(X))))&
((?[X]:((curious(X)&creative(X))))<=>(?[X]:((~wise(X)&curious(X)))))&
(![X]:((wise(X)&calm(X))<=>(wise(X)|strong(X))))&
(((~generous(fred)<~>~tall(fred)))=>(?[X]:((brave(X)<~>patient(X)))))&
(![X]:((creative(X)|generous(X))=>~kind(X)))&
((?[X]:((wise(X)<~>happy(X))))<=>((brave(alice)|curious(alice))))&
(~humble(paul))&
((tall(paul)|old(paul)))&
((~happy(mary)|~humble(mary)))&
(?[X]:((~brave(X)|~happy(X))))&
((~wise(john)|happy(john))) | ~curious(alice) | [] | null | 0 |
Everyone who is wise or happy is both not kind and tall and vice versa.
Everyone who is either not creative or not rich is either creative or not patient and vice versa.
Everyone who is both curious and kind is either not old or not calm.
If someone is either not curious or not creative then mary is both not funny and rich.
Everyone who is either not brave or brave is not brave or strong.
Everyone who is not strong is both not happy and not calm.
Everyone who is either quiet or humble is either not strong or funny.
Everyone who is either curious or strong is humble and vice versa.
If someone is curious then someone is either creative or wise.
Everyone who is not wise or not old is either patient or not brave.
Everyone who is either rich or not wise is either not patient or curious and vice versa.
If someone is either not strong or rich then someone is either not brave or not kind and vice versa.
If lucy is not creative or not generous then someone is either rich or not quiet.
Everyone who is both not happy and not quiet is either not strong or tall and vice versa.
If susan is calm or not funny then fred is not rich or wise and vice versa.
If alice is funny then someone is curious or generous and vice versa.
Someone is both patient and quiet.
Someone is wise or rich.
John is not happy or old.
Someone is funny.
Someone is both not brave and not creative.
Paul is both humble and generous.
Someone is old.
Fred is both creative and wise. | John is happy. | contradiction | (![X]:((wise(X)|happy(X))<=>(~kind(X)&tall(X))))&
(![X]:((~creative(X)<~>~rich(X))<=>(creative(X)<~>~patient(X))))&
(![X]:((curious(X)&kind(X))=>(~old(X)<~>~calm(X))))&
((?[X]:((~curious(X)<~>~creative(X))))=>((~funny(mary)&rich(mary))))&
(![X]:((~brave(X)<~>brave(X))=>(~brave(X)|strong(X))))&
(![X]:(~strong(X)=>(~happy(X)&~calm(X))))&
(![X]:((quiet(X)<~>humble(X))=>(~strong(X)<~>funny(X))))&
(![X]:((curious(X)<~>strong(X))<=>humble(X)))&
((?[X]:(curious(X)))=>(?[X]:((creative(X)<~>wise(X)))))&
(![X]:((~wise(X)|~old(X))=>(patient(X)<~>~brave(X))))&
(![X]:((rich(X)<~>~wise(X))<=>(~patient(X)<~>curious(X))))&
((?[X]:((~strong(X)<~>rich(X))))<=>(?[X]:((~brave(X)<~>~kind(X)))))&
(((~creative(lucy)|~generous(lucy)))=>(?[X]:((rich(X)<~>~quiet(X)))))&
(![X]:((~happy(X)&~quiet(X))<=>(~strong(X)<~>tall(X))))&
(((calm(susan)|~funny(susan)))<=>((~rich(fred)|wise(fred))))&
((funny(alice))<=>(?[X]:((curious(X)|generous(X)))))&
(?[X]:((patient(X)&quiet(X))))&
(?[X]:((wise(X)|rich(X))))&
((~happy(john)|old(john)))&
(?[X]:(funny(X)))&
(?[X]:((~brave(X)&~creative(X))))&
((humble(paul)&generous(paul)))&
(?[X]:(old(X)))&
((creative(fred)&wise(fred))) | happy(john) | [
"p0",
"p5",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5624962833188970828338032
% SZS output start Proof for 5624962833188970828338032
1. ! [X0] : ((happy(X0) | wise(X0)) <=> (tall(X0) & ~kind(X0))) [input p0]
6. ! [X0] : (~strong(X0) => (~calm(X0) & ~happy(X0))) [input p5]
14. ! [X0] : ((~quiet(X0) & ~happy(X0)) <=> (~strong(X0) <~> tall(X0))) [input p13]
25. happy(john) [input hypothesis]
33. ! [X0] : ((~calm(X0) & ~happy(X0)) | strong(X0)) [ennf transformation 6]
38. ! [X0] : (((happy(X0) | wise(X0)) | (~tall(X0) | kind(X0))) & ((tall(X0) & ~kind(X0)) | (~happy(X0) & ~wise(X0)))) [nnf transformation 1]
39. ! [X0] : ((happy(X0) | wise(X0) | ~tall(X0) | kind(X0)) & ((tall(X0) & ~kind(X0)) | (~happy(X0) & ~wise(X0)))) [flattening 38]
60. ! [X0] : (((~quiet(X0) & ~happy(X0)) | ((~strong(X0) | ~tall(X0)) & (tall(X0) | strong(X0)))) & (((~tall(X0) | strong(X0)) & (tall(X0) | ~strong(X0))) | (quiet(X0) | happy(X0)))) [nnf transformation 14]
61. ! [X0] : (((~quiet(X0) & ~happy(X0)) | ((~strong(X0) | ~tall(X0)) & (tall(X0) | strong(X0)))) & (((~tall(X0) | strong(X0)) & (tall(X0) | ~strong(X0))) | quiet(X0) | happy(X0))) [flattening 60]
81. tall(X0) | ~happy(X0) [cnf transformation 39]
99. ~happy(X0) | strong(X0) [cnf transformation 33]
138. ~happy(X0) | ~strong(X0) | ~tall(X0) [cnf transformation 61]
160. happy(john) [cnf transformation 25]
261. ~happy(X0) | ~strong(X0) [subsumption resolution 138,81]
262. ~happy(X0) [subsumption resolution 261,99]
313. $false [subsumption resolution 160,262]
% SZS output end Proof for 5624962833188970828338032
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy is not humble. If lucy is both not brave and curious then fred is patient and vice versa. Everyone who is either rich or brave is both kind and happy. Everyone who is not rich or rich is both not calm and not strong and vice versa. Everyone who is not funny or not strong is not quiet and vice versa. Everyone who is both not humble and kind is either rich or not generous and vice versa. If fred is either not humble or patient then alice is either not brave or not wise and vice versa. If paul is not brave or curious then someone is not strong. Everyone who is rich is not wise and vice versa. If john is not strong then susan is not rich or generous and vice versa. Everyone who is both strong and quiet is either curious or rich. Everyone who is either wise or quiet is wise. Everyone who is either quiet or not tall is not calm or not quiet. Everyone who is not old or happy is strong or not curious and vice versa. Everyone who is both not wise and generous is creative. Someone is both happy and not tall. Someone is not wise or patient. Someone is patient. Someone is both not rich and happy. Someone is either not kind or patient. | Alice is tall. | neutral | (![X]:((old(X)|happy(X))=>~humble(X)))&
(((~brave(lucy)&curious(lucy)))<=>(patient(fred)))&
(![X]:((rich(X)<~>brave(X))=>(kind(X)&happy(X))))&
(![X]:((~rich(X)|rich(X))<=>(~calm(X)&~strong(X))))&
(![X]:((~funny(X)|~strong(X))<=>~quiet(X)))&
(![X]:((~humble(X)&kind(X))<=>(rich(X)<~>~generous(X))))&
(((~humble(fred)<~>patient(fred)))<=>((~brave(alice)<~>~wise(alice))))&
(((~brave(paul)|curious(paul)))=>(?[X]:(~strong(X))))&
(![X]:(rich(X)<=>~wise(X)))&
((~strong(john))<=>((~rich(susan)|generous(susan))))&
(![X]:((strong(X)&quiet(X))=>(curious(X)<~>rich(X))))&
(![X]:((wise(X)<~>quiet(X))=>wise(X)))&
(![X]:((quiet(X)<~>~tall(X))=>(~calm(X)|~quiet(X))))&
(![X]:((~old(X)|happy(X))<=>(strong(X)|~curious(X))))&
(![X]:((~wise(X)&generous(X))=>creative(X)))&
(?[X]:((happy(X)&~tall(X))))&
(?[X]:((~wise(X)|patient(X))))&
(?[X]:(patient(X)))&
(?[X]:((~rich(X)&happy(X))))&
(?[X]:((~kind(X)<~>patient(X)))) | tall(alice) | [] | null | 0 |
Everyone who is not curious is not wise or not old.
If someone is either brave or not funny then lucy is rich.
If someone is generous or creative then someone is both not tall and not kind and vice versa.
Everyone who is both not old and old is generous.
Everyone who is generous is not wise and vice versa.
Everyone who is old is not tall or not humble.
If john is both not kind and wise then someone is not rich.
Everyone who is not happy or not brave is not rich.
Everyone who is either humble or not generous is either not generous or not old.
If paul is either old or curious then susan is both quiet and not old.
Everyone who is not tall or not creative is both humble and wise.
Everyone who is tall is humble or wise and vice versa.
Everyone who is either creative or tall is humble.
Everyone who is either humble or curious is not rich or not tall.
Everyone who is old or not funny is funny or generous.
Everyone who is funny or brave is rich and vice versa.
Alice is not quiet or not happy.
Susan is not strong or not generous.
Someone is curious.
Someone is not old or curious. | Alice is not happy. | contradiction | (![X]:(~curious(X)=>(~wise(X)|~old(X))))&
((?[X]:((brave(X)<~>~funny(X))))=>(rich(lucy)))&
((?[X]:((generous(X)|creative(X))))<=>(?[X]:((~tall(X)&~kind(X)))))&
(![X]:((~old(X)&old(X))=>generous(X)))&
(![X]:(generous(X)<=>~wise(X)))&
(![X]:(old(X)=>(~tall(X)|~humble(X))))&
(((~kind(john)&wise(john)))=>(?[X]:(~rich(X))))&
(![X]:((~happy(X)|~brave(X))=>~rich(X)))&
(![X]:((humble(X)<~>~generous(X))=>(~generous(X)<~>~old(X))))&
(((old(paul)<~>curious(paul)))=>((quiet(susan)&~old(susan))))&
(![X]:((~tall(X)|~creative(X))=>(humble(X)&wise(X))))&
(![X]:(tall(X)<=>(humble(X)|wise(X))))&
(![X]:((creative(X)<~>tall(X))=>humble(X)))&
(![X]:((humble(X)<~>curious(X))=>(~rich(X)|~tall(X))))&
(![X]:((old(X)|~funny(X))=>(funny(X)|generous(X))))&
(![X]:((funny(X)|brave(X))<=>rich(X)))&
((~quiet(alice)|~happy(alice)))&
((~strong(susan)|~generous(susan)))&
(?[X]:(curious(X)))&
(?[X]:((~old(X)|curious(X)))) | ~happy(alice) | [
"p2",
"p4",
"p7",
"p10",
"p11",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3279152981060623575601906
% SZS output start Proof for 3279152981060623575601906
3. ? [X0] : (creative(X0) | generous(X0)) <=> ? [X0] : (~kind(X0) & ~tall(X0)) [input p2]
5. ! [X0] : (generous(X0) <=> ~wise(X0)) [input p4]
8. ! [X0] : ((~brave(X0) | ~happy(X0)) => ~rich(X0)) [input p7]
11. ! [X0] : ((~creative(X0) | ~tall(X0)) => (wise(X0) & humble(X0))) [input p10]
12. ! [X0] : (tall(X0) <=> (wise(X0) | humble(X0))) [input p11]
15. ! [X0] : ((~funny(X0) | old(X0)) => (generous(X0) | funny(X0))) [input p14]
16. ! [X0] : ((brave(X0) | funny(X0)) <=> rich(X0)) [input p15]
21. ~happy(alice) [input hypothesis]
22. ? [X0] : (creative(X0) | generous(X0)) <=> ? [X1] : (~kind(X1) & ~tall(X1)) [rectify 3]
33. ! [X0] : (~rich(X0) | (brave(X0) & happy(X0))) [ennf transformation 8]
36. ! [X0] : ((wise(X0) & humble(X0)) | (creative(X0) & tall(X0))) [ennf transformation 11]
40. ! [X0] : ((generous(X0) | funny(X0)) | (funny(X0) & ~old(X0))) [ennf transformation 15]
41. ! [X0] : (generous(X0) | funny(X0) | (funny(X0) & ~old(X0))) [flattening 40]
43. (? [X0] : (creative(X0) | generous(X0)) | ! [X1] : (kind(X1) | tall(X1))) & (? [X1] : (~kind(X1) & ~tall(X1)) | ! [X0] : (~creative(X0) & ~generous(X0))) [nnf transformation 22]
44. (? [X0] : (creative(X0) | generous(X0)) | ! [X1] : (kind(X1) | tall(X1))) & (? [X2] : (~kind(X2) & ~tall(X2)) | ! [X3] : (~creative(X3) & ~generous(X3))) [rectify 43]
45. ? [X0] : (creative(X0) | generous(X0)) => (creative(sK0) | generous(sK0)) [choice axiom]
46. ? [X2] : (~kind(X2) & ~tall(X2)) => (~kind(sK1) & ~tall(sK1)) [choice axiom]
47. ((creative(sK0) | generous(sK0)) | ! [X1] : (kind(X1) | tall(X1))) & ((~kind(sK1) & ~tall(sK1)) | ! [X3] : (~creative(X3) & ~generous(X3))) [skolemisation 44,46,45]
48. ! [X0] : ((generous(X0) | wise(X0)) & (~wise(X0) | ~generous(X0))) [nnf transformation 5]
53. ! [X0] : ((tall(X0) | (~wise(X0) & ~humble(X0))) & ((wise(X0) | humble(X0)) | ~tall(X0))) [nnf transformation 12]
54. ! [X0] : ((tall(X0) | (~wise(X0) & ~humble(X0))) & (wise(X0) | humble(X0) | ~tall(X0))) [flattening 53]
57. ! [X0] : (((brave(X0) | funny(X0)) | ~rich(X0)) & (rich(X0) | (~brave(X0) & ~funny(X0)))) [nnf transformation 16]
58. ! [X0] : ((brave(X0) | funny(X0) | ~rich(X0)) & (rich(X0) | (~brave(X0) & ~funny(X0)))) [flattening 57]
66. ~tall(sK1) | ~generous(X3) [cnf transformation 47]
72. ~generous(X0) | ~wise(X0) [cnf transformation 48]
73. generous(X0) | wise(X0) [cnf transformation 48]
76. ~rich(X0) | happy(X0) [cnf transformation 33]
88. tall(X0) | wise(X0) [cnf transformation 36]
92. tall(X0) | ~wise(X0) [cnf transformation 54]
98. generous(X0) | funny(X0) | funny(X0) [cnf transformation 41]
99. ~funny(X0) | rich(X0) [cnf transformation 58]
105. ~happy(alice) [cnf transformation 21]
106. generous(X0) | funny(X0) [duplicate literal removal 98]
142. 9 <=> ! [X3] : ~generous(X3) [avatar definition]
143. ~generous(X3) <- (9) [avatar component clause 142]
146. 10 <=> tall(sK1) [avatar definition]
148. ~tall(sK1) <- (~10) [avatar component clause 146]
150. 9 | ~10 [avatar split clause 66,146,142]
184. tall(X0) [subsumption resolution 92,88]
193. 19 <=> happy(alice) [avatar definition]
195. ~happy(alice) <- (~19) [avatar component clause 193]
206. ~19 [avatar split clause 105,193]
207. $false <- (~10) [subsumption resolution 148,184]
208. 10 [avatar contradiction clause 207]
210. wise(X1) <- (9) [resolution 73,143]
215. funny(X0) | ~wise(X0) [resolution 106,72]
217. funny(X0) <- (9) [subsumption resolution 215,210]
218. rich(X0) <- (9) [resolution 217,99]
221. happy(X1) <- (9) [resolution 218,76]
234. $false <- (9, ~19) [resolution 221,195]
235. ~9 | 19 [avatar contradiction clause 234]
236. $false [avatar sat refutation 150,206,208,235]
% SZS output end Proof for 3279152981060623575601906
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is tall is either generous or wise. Everyone who is either not humble or not rich is happy or funny and vice versa. If someone is either old or not wise then paul is creative or wise. Everyone who is generous is both not strong and creative. Everyone who is old is both not rich and happy and vice versa. If someone is not old then someone is both not quiet and not rich. Everyone who is quiet is not funny and vice versa. Everyone who is both tall and creative is old and vice versa. Everyone who is wise is both not funny and kind. Everyone who is either generous or not calm is not kind or tall. If someone is either humble or creative then someone is tall. Everyone who is not happy is either not rich or generous and vice versa. Everyone who is either generous or calm is either wise or kind. Everyone who is humble or not patient is both not curious and quiet. If someone is both not quiet and humble then someone is not funny. Everyone who is both wise and not curious is curious or wise. Mary is either not old or humble. Someone is either not patient or not creative. Fred is not curious. Someone is both not rich and not brave. Fred is either not creative or humble. Someone is not kind. | Paul is curious. | contradiction | (![X]:(tall(X)=>(generous(X)<~>wise(X))))&
(![X]:((~humble(X)<~>~rich(X))<=>(happy(X)|funny(X))))&
((?[X]:((old(X)<~>~wise(X))))=>((creative(paul)|wise(paul))))&
(![X]:(generous(X)=>(~strong(X)&creative(X))))&
(![X]:(old(X)<=>(~rich(X)&happy(X))))&
((?[X]:(~old(X)))=>(?[X]:((~quiet(X)&~rich(X)))))&
(![X]:(quiet(X)<=>~funny(X)))&
(![X]:((tall(X)&creative(X))<=>old(X)))&
(![X]:(wise(X)=>(~funny(X)&kind(X))))&
(![X]:((generous(X)<~>~calm(X))=>(~kind(X)|tall(X))))&
((?[X]:((humble(X)<~>creative(X))))=>(?[X]:(tall(X))))&
(![X]:(~happy(X)<=>(~rich(X)<~>generous(X))))&
(![X]:((generous(X)<~>calm(X))=>(wise(X)<~>kind(X))))&
(![X]:((humble(X)|~patient(X))=>(~curious(X)&quiet(X))))&
((?[X]:((~quiet(X)&humble(X))))=>(?[X]:(~funny(X))))&
(![X]:((wise(X)&~curious(X))=>(curious(X)|wise(X))))&
((~old(mary)<~>humble(mary)))&
(?[X]:((~patient(X)<~>~creative(X))))&
(~curious(fred))&
(?[X]:((~rich(X)&~brave(X))))&
((~creative(fred)<~>humble(fred)))&
(?[X]:(~kind(X))) | curious(paul) | [
"p1",
"p4",
"p5",
"p6",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 543387063240458388089501
% SZS output start Proof for 543387063240458388089501
2. ! [X0] : ((~humble(X0) <~> ~rich(X0)) <=> (funny(X0) | happy(X0))) [input p1]
5. ! [X0] : (old(X0) <=> (happy(X0) & ~rich(X0))) [input p4]
6. ? [X0] : ~old(X0) => ? [X0] : (~rich(X0) & ~quiet(X0)) [input p5]
7. ! [X0] : (quiet(X0) <=> ~funny(X0)) [input p6]
14. ! [X0] : ((~patient(X0) | humble(X0)) => (quiet(X0) & ~curious(X0))) [input p13]
23. curious(paul) [input hypothesis]
24. ? [X0] : ~old(X0) => ? [X1] : (~rich(X1) & ~quiet(X1)) [rectify 6]
33. ? [X1] : (~rich(X1) & ~quiet(X1)) | ! [X0] : old(X0) [ennf transformation 24]
39. ! [X0] : ((quiet(X0) & ~curious(X0)) | (patient(X0) & ~humble(X0))) [ennf transformation 14]
44. ! [X0] : ((((rich(X0) | humble(X0)) & (~rich(X0) | ~humble(X0))) | (~funny(X0) & ~happy(X0))) & ((funny(X0) | happy(X0)) | ((~humble(X0) | rich(X0)) & (~rich(X0) | humble(X0))))) [nnf transformation 2]
45. ! [X0] : ((((rich(X0) | humble(X0)) & (~rich(X0) | ~humble(X0))) | (~funny(X0) & ~happy(X0))) & (funny(X0) | happy(X0) | ((~humble(X0) | rich(X0)) & (~rich(X0) | humble(X0))))) [flattening 44]
47. ! [X0] : ((old(X0) | (~happy(X0) | rich(X0))) & ((happy(X0) & ~rich(X0)) | ~old(X0))) [nnf transformation 5]
48. ! [X0] : ((old(X0) | ~happy(X0) | rich(X0)) & ((happy(X0) & ~rich(X0)) | ~old(X0))) [flattening 47]
49. ? [X0] : (~rich(X0) & ~quiet(X0)) | ! [X1] : old(X1) [rectify 33]
50. ? [X0] : (~rich(X0) & ~quiet(X0)) => (~rich(sK0) & ~quiet(sK0)) [choice axiom]
51. (~rich(sK0) & ~quiet(sK0)) | ! [X1] : old(X1) [skolemisation 49,50]
52. ! [X0] : ((quiet(X0) | funny(X0)) & (~funny(X0) | ~quiet(X0))) [nnf transformation 7]
80. ~happy(X0) | humble(X0) | rich(X0) [cnf transformation 45]
81. ~funny(X0) | humble(X0) | rich(X0) [cnf transformation 45]
85. ~old(X0) | ~rich(X0) [cnf transformation 48]
86. ~old(X0) | happy(X0) [cnf transformation 48]
88. ~quiet(sK0) | old(X1) [cnf transformation 51]
89. ~rich(sK0) | old(X1) [cnf transformation 51]
91. quiet(X0) | funny(X0) [cnf transformation 52]
109. ~curious(X0) | ~humble(X0) [cnf transformation 39]
111. ~humble(X0) | quiet(X0) [cnf transformation 39]
124. curious(paul) [cnf transformation 23]
143. 5 <=> ! [X1] : old(X1) [avatar definition]
144. old(X1) <- (5) [avatar component clause 143]
146. 6 <=> rich(sK0) [avatar definition]
148. ~rich(sK0) <- (~6) [avatar component clause 146]
149. 5 | ~6 [avatar split clause 89,146,143]
151. 7 <=> quiet(sK0) [avatar definition]
153. ~quiet(sK0) <- (~7) [avatar component clause 151]
154. 5 | ~7 [avatar split clause 88,151,143]
201. funny(sK0) <- (~7) [resolution 91,153]
204. ~humble(paul) [resolution 109,124]
225. humble(sK0) | rich(sK0) <- (~7) [resolution 81,201]
226. humble(sK0) <- (~6, ~7) [subsumption resolution 225,148]
228. quiet(sK0) <- (~6, ~7) [resolution 226,111]
229. $false <- (~6, ~7) [subsumption resolution 228,153]
230. 6 | 7 [avatar contradiction clause 229]
234. happy(X2) <- (5) [resolution 144,86]
235. ~rich(X3) <- (5) [resolution 144,85]
251. humble(X1) | rich(X1) <- (5) [resolution 234,80]
253. humble(X1) <- (5) [subsumption resolution 251,235]
263. $false <- (5) [resolution 253,204]
264. ~5 [avatar contradiction clause 263]
265. $false [avatar sat refutation 149,154,230,264]
% SZS output end Proof for 543387063240458388089501
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not creative or old then john is both old and not wise and vice versa.
Everyone who is either patient or not brave is funny and vice versa.
Everyone who is patient is not humble and vice versa.
Everyone who is curious or old is rich or curious.
If someone is strong then john is both not generous and not brave.
If someone is both not generous and not kind then someone is either funny or not happy and vice versa.
Everyone who is not generous is both not curious and not happy and vice versa.
Everyone who is either rich or not creative is both not wise and not brave and vice versa.
If paul is not kind or generous then someone is not kind and vice versa.
Everyone who is not creative or tall is not happy or not funny.
Everyone who is both patient and creative is old and vice versa.
If someone is both not funny and not quiet then paul is either happy or not rich and vice versa.
Everyone who is not rich or not happy is either funny or old and vice versa.
Everyone who is calm is either patient or humble.
If someone is rich then john is tall.
If paul is not rich then someone is either not curious or not generous and vice versa.
Someone is not patient.
Someone is either not wise or not brave.
Someone is both curious and quiet.
Fred is either not humble or calm.
John is not tall or old.
Someone is both not humble and funny.
Lucy is not brave.
Someone is generous or not strong. | John is rich. | entailment | ((?[X]:((~creative(X)<~>old(X))))<=>((old(john)&~wise(john))))&
(![X]:((patient(X)<~>~brave(X))<=>funny(X)))&
(![X]:(patient(X)<=>~humble(X)))&
(![X]:((curious(X)|old(X))=>(rich(X)|curious(X))))&
((?[X]:(strong(X)))=>((~generous(john)&~brave(john))))&
((?[X]:((~generous(X)&~kind(X))))<=>(?[X]:((funny(X)<~>~happy(X)))))&
(![X]:(~generous(X)<=>(~curious(X)&~happy(X))))&
(![X]:((rich(X)<~>~creative(X))<=>(~wise(X)&~brave(X))))&
(((~kind(paul)|generous(paul)))<=>(?[X]:(~kind(X))))&
(![X]:((~creative(X)|tall(X))=>(~happy(X)|~funny(X))))&
(![X]:((patient(X)&creative(X))<=>old(X)))&
((?[X]:((~funny(X)&~quiet(X))))<=>((happy(paul)<~>~rich(paul))))&
(![X]:((~rich(X)|~happy(X))<=>(funny(X)<~>old(X))))&
(![X]:(calm(X)=>(patient(X)<~>humble(X))))&
((?[X]:(rich(X)))=>(tall(john)))&
((~rich(paul))<=>(?[X]:((~curious(X)<~>~generous(X)))))&
(?[X]:(~patient(X)))&
(?[X]:((~wise(X)<~>~brave(X))))&
(?[X]:((curious(X)&quiet(X))))&
((~humble(fred)<~>calm(fred)))&
((~tall(john)|old(john)))&
(?[X]:((~humble(X)&funny(X))))&
(~brave(lucy))&
(?[X]:((generous(X)|~strong(X)))) | rich(john) | [
"p0",
"p1",
"p2",
"p7",
"p10",
"p12",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 7651457452385893955361233
% SZS output start Proof for 7651457452385893955361233
1. ? [X0] : (~creative(X0) <~> old(X0)) <=> (~wise(john) & old(john)) [input p0]
2. ! [X0] : ((patient(X0) <~> ~brave(X0)) <=> funny(X0)) [input p1]
3. ! [X0] : (patient(X0) <=> ~humble(X0)) [input p2]
8. ! [X0] : ((rich(X0) <~> ~creative(X0)) <=> (~brave(X0) & ~wise(X0))) [input p7]
11. ! [X0] : ((creative(X0) & patient(X0)) <=> old(X0)) [input p10]
13. ! [X0] : ((~happy(X0) | ~rich(X0)) <=> (funny(X0) <~> old(X0))) [input p12]
22. ? [X0] : (funny(X0) & ~humble(X0)) [input p21]
25. ~rich(john) [input hypothesis]
35. (? [X0] : ((~old(X0) | creative(X0)) & (old(X0) | ~creative(X0))) | (wise(john) | ~old(john))) & ((~wise(john) & old(john)) | ! [X0] : ((~creative(X0) | ~old(X0)) & (old(X0) | creative(X0)))) [nnf transformation 1]
36. (? [X0] : ((~old(X0) | creative(X0)) & (old(X0) | ~creative(X0))) | wise(john) | ~old(john)) & ((~wise(john) & old(john)) | ! [X0] : ((~creative(X0) | ~old(X0)) & (old(X0) | creative(X0)))) [flattening 35]
37. (? [X0] : ((~old(X0) | creative(X0)) & (old(X0) | ~creative(X0))) | wise(john) | ~old(john)) & ((~wise(john) & old(john)) | ! [X1] : ((~creative(X1) | ~old(X1)) & (old(X1) | creative(X1)))) [rectify 36]
38. ? [X0] : ((~old(X0) | creative(X0)) & (old(X0) | ~creative(X0))) => ((~old(sK0) | creative(sK0)) & (old(sK0) | ~creative(sK0))) [choice axiom]
39. (((~old(sK0) | creative(sK0)) & (old(sK0) | ~creative(sK0))) | wise(john) | ~old(john)) & ((~wise(john) & old(john)) | ! [X1] : ((~creative(X1) | ~old(X1)) & (old(X1) | creative(X1)))) [skolemisation 37,38]
40. ! [X0] : ((((brave(X0) | ~patient(X0)) & (~brave(X0) | patient(X0))) | ~funny(X0)) & (funny(X0) | ((patient(X0) | brave(X0)) & (~brave(X0) | ~patient(X0))))) [nnf transformation 2]
41. ! [X0] : ((patient(X0) | humble(X0)) & (~humble(X0) | ~patient(X0))) [nnf transformation 3]
49. ! [X0] : ((((creative(X0) | ~rich(X0)) & (~creative(X0) | rich(X0))) | (brave(X0) | wise(X0))) & ((~brave(X0) & ~wise(X0)) | ((rich(X0) | creative(X0)) & (~creative(X0) | ~rich(X0))))) [nnf transformation 8]
50. ! [X0] : ((((creative(X0) | ~rich(X0)) & (~creative(X0) | rich(X0))) | brave(X0) | wise(X0)) & ((~brave(X0) & ~wise(X0)) | ((rich(X0) | creative(X0)) & (~creative(X0) | ~rich(X0))))) [flattening 49]
56. ! [X0] : (((creative(X0) & patient(X0)) | ~old(X0)) & (old(X0) | (~creative(X0) | ~patient(X0)))) [nnf transformation 11]
57. ! [X0] : (((creative(X0) & patient(X0)) | ~old(X0)) & (old(X0) | ~creative(X0) | ~patient(X0))) [flattening 56]
62. ! [X0] : (((~happy(X0) | ~rich(X0)) | ((funny(X0) | ~old(X0)) & (old(X0) | ~funny(X0)))) & (((~old(X0) | ~funny(X0)) & (old(X0) | funny(X0))) | (happy(X0) & rich(X0)))) [nnf transformation 13]
63. ! [X0] : ((~happy(X0) | ~rich(X0) | ((funny(X0) | ~old(X0)) & (old(X0) | ~funny(X0)))) & (((~old(X0) | ~funny(X0)) & (old(X0) | funny(X0))) | (happy(X0) & rich(X0)))) [flattening 62]
77. ? [X0] : (funny(X0) & ~humble(X0)) => (funny(sK9) & ~humble(sK9)) [choice axiom]
78. funny(sK9) & ~humble(sK9) [skolemisation 22,77]
79. old(john) | old(X1) | creative(X1) [cnf transformation 39]
80. old(john) | ~creative(X1) | ~old(X1) [cnf transformation 39]
82. ~wise(john) | ~creative(X1) | ~old(X1) [cnf transformation 39]
85. ~brave(X0) | funny(X0) | ~patient(X0) [cnf transformation 40]
90. humble(X0) | patient(X0) [cnf transformation 41]
106. ~creative(X0) | rich(X0) | brave(X0) | wise(X0) [cnf transformation 50]
113. ~patient(X0) | ~creative(X0) | old(X0) [cnf transformation 57]
114. ~old(X0) | patient(X0) [cnf transformation 57]
115. ~old(X0) | creative(X0) [cnf transformation 57]
124. ~funny(X0) | ~old(X0) | rich(X0) [cnf transformation 63]
143. ~humble(sK9) [cnf transformation 78]
146. ~rich(john) [cnf transformation 25]
148. 1 <=> old(john) [avatar definition]
149. old(john) <- (1) [avatar component clause 148]
152. 2 <=> wise(john) [avatar definition]
153. ~wise(john) <- (~2) [avatar component clause 152]
166. 5 <=> ! [X1] : (~creative(X1) | ~old(X1)) [avatar definition]
167. ~creative(X1) | ~old(X1) <- (5) [avatar component clause 166]
168. 5 | ~2 [avatar split clause 82,152,166]
170. 6 <=> ! [X1] : (old(X1) | creative(X1)) [avatar definition]
171. old(X1) | creative(X1) <- (6) [avatar component clause 170]
173. 5 | 1 [avatar split clause 80,148,166]
174. 6 | 1 [avatar split clause 79,148,170]
296. creative(X1) <- (6) [subsumption resolution 171,115]
297. ~old(X1) <- (5, 6) [subsumption resolution 167,296]
298. patient(sK9) [resolution 90,143]
364. ~creative(sK9) | old(sK9) [resolution 113,298]
366. old(sK9) <- (6) [subsumption resolution 364,296]
367. $false <- (5, 6) [subsumption resolution 366,297]
368. ~5 | ~6 [avatar contradiction clause 367]
412. ~old(X1) <- (5) [subsumption resolution 167,115]
413. $false <- (1, 5) [subsumption resolution 149,412]
414. ~1 | ~5 [avatar contradiction clause 413]
430. creative(john) <- (1) [resolution 149,115]
431. patient(john) <- (1) [resolution 149,114]
435. 47 <=> funny(john) [avatar definition]
436. funny(john) <- (47) [avatar component clause 435]
509. rich(john) | brave(john) | wise(john) <- (1) [resolution 106,430]
516. brave(john) | wise(john) <- (1) [subsumption resolution 509,146]
517. brave(john) <- (1, ~2) [subsumption resolution 516,153]
652. funny(john) | ~patient(john) <- (1, ~2) [resolution 517,85]
656. funny(john) <- (1, ~2) [subsumption resolution 652,431]
657. 47 | ~1 | 2 [avatar split clause 656,152,148,435]
659. ~old(john) | rich(john) <- (47) [resolution 436,124]
665. rich(john) <- (1, 47) [subsumption resolution 659,149]
666. $false <- (1, 47) [subsumption resolution 665,146]
667. ~1 | ~47 [avatar contradiction clause 666]
668. $false [avatar sat refutation 168,173,174,368,414,657,667]
% SZS output end Proof for 7651457452385893955361233
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not rich or patient is not curious or happy and vice versa. Everyone who is either generous or funny is patient and vice versa. Everyone who is not patient or happy is tall and vice versa. If alice is both not old and not tall then someone is either patient or humble and vice versa. Everyone who is both not happy and not calm is generous or brave. Everyone who is not calm or happy is either not creative or not quiet and vice versa. If someone is both old and not wise then someone is both not kind and not quiet. If someone is either not tall or patient then fred is both not kind and strong and vice versa. Everyone who is not rich is tall and vice versa. If someone is generous then someone is either not curious or not humble. If someone is strong then mary is not wise. If fred is both calm and creative then susan is either not strong or calm. If someone is both patient and not quiet then someone is creative and vice versa. If someone is both wise and not brave then lucy is both not patient and not funny and vice versa. If someone is humble then paul is both generous and not funny and vice versa. If someone is both curious and not strong then someone is not creative or wise. Fred is either not funny or not old. Alice is both not strong and kind. Lucy is either wise or not creative. Someone is old. Alice is creative or curious. Paul is not rich. Susan is both funny and strong. | Mary is humble. | contradiction | (![X]:((~rich(X)<~>patient(X))<=>(~curious(X)|happy(X))))&
(![X]:((generous(X)<~>funny(X))<=>patient(X)))&
(![X]:((~patient(X)|happy(X))<=>tall(X)))&
(((~old(alice)&~tall(alice)))<=>(?[X]:((patient(X)<~>humble(X)))))&
(![X]:((~happy(X)&~calm(X))=>(generous(X)|brave(X))))&
(![X]:((~calm(X)|happy(X))<=>(~creative(X)<~>~quiet(X))))&
((?[X]:((old(X)&~wise(X))))=>(?[X]:((~kind(X)&~quiet(X)))))&
((?[X]:((~tall(X)<~>patient(X))))<=>((~kind(fred)&strong(fred))))&
(![X]:(~rich(X)<=>tall(X)))&
((?[X]:(generous(X)))=>(?[X]:((~curious(X)<~>~humble(X)))))&
((?[X]:(strong(X)))=>(~wise(mary)))&
(((calm(fred)&creative(fred)))=>((~strong(susan)<~>calm(susan))))&
((?[X]:((patient(X)&~quiet(X))))<=>(?[X]:(creative(X))))&
((?[X]:((wise(X)&~brave(X))))<=>((~patient(lucy)&~funny(lucy))))&
((?[X]:(humble(X)))<=>((generous(paul)&~funny(paul))))&
((?[X]:((curious(X)&~strong(X))))=>(?[X]:((~creative(X)|wise(X)))))&
((~funny(fred)<~>~old(fred)))&
((~strong(alice)&kind(alice)))&
((wise(lucy)<~>~creative(lucy)))&
(?[X]:(old(X)))&
((creative(alice)|curious(alice)))&
(~rich(paul))&
((funny(susan)&strong(susan))) | humble(mary) | [
"p0",
"p1",
"p2",
"p8",
"p14",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 8468650732517492748780631
% SZS output start Proof for 8468650732517492748780631
1. ! [X0] : ((~rich(X0) <~> patient(X0)) <=> (happy(X0) | ~curious(X0))) [input p0]
2. ! [X0] : ((generous(X0) <~> funny(X0)) <=> patient(X0)) [input p1]
3. ! [X0] : ((happy(X0) | ~patient(X0)) <=> tall(X0)) [input p2]
9. ! [X0] : (~rich(X0) <=> tall(X0)) [input p8]
15. ? [X0] : humble(X0) <=> (~funny(paul) & generous(paul)) [input p14]
22. ~rich(paul) [input p21]
24. humble(mary) [input hypothesis]
37. ! [X0] : ((((~patient(X0) | rich(X0)) & (patient(X0) | ~rich(X0))) | (~happy(X0) & curious(X0))) & ((happy(X0) | ~curious(X0)) | ((~rich(X0) | ~patient(X0)) & (patient(X0) | rich(X0))))) [nnf transformation 1]
38. ! [X0] : ((((~patient(X0) | rich(X0)) & (patient(X0) | ~rich(X0))) | (~happy(X0) & curious(X0))) & (happy(X0) | ~curious(X0) | ((~rich(X0) | ~patient(X0)) & (patient(X0) | rich(X0))))) [flattening 37]
39. ! [X0] : ((((~funny(X0) | ~generous(X0)) & (funny(X0) | generous(X0))) | ~patient(X0)) & (patient(X0) | ((generous(X0) | ~funny(X0)) & (funny(X0) | ~generous(X0))))) [nnf transformation 2]
40. ! [X0] : (((happy(X0) | ~patient(X0)) | ~tall(X0)) & (tall(X0) | (~happy(X0) & patient(X0)))) [nnf transformation 3]
41. ! [X0] : ((happy(X0) | ~patient(X0) | ~tall(X0)) & (tall(X0) | (~happy(X0) & patient(X0)))) [flattening 40]
57. ! [X0] : ((~rich(X0) | ~tall(X0)) & (tall(X0) | rich(X0))) [nnf transformation 9]
73. (? [X0] : humble(X0) | (funny(paul) | ~generous(paul))) & ((~funny(paul) & generous(paul)) | ! [X0] : ~humble(X0)) [nnf transformation 15]
74. (? [X0] : humble(X0) | funny(paul) | ~generous(paul)) & ((~funny(paul) & generous(paul)) | ! [X0] : ~humble(X0)) [flattening 73]
75. (? [X0] : humble(X0) | funny(paul) | ~generous(paul)) & ((~funny(paul) & generous(paul)) | ! [X1] : ~humble(X1)) [rectify 74]
76. ? [X0] : humble(X0) => humble(sK7) [choice axiom]
77. (humble(sK7) | funny(paul) | ~generous(paul)) & ((~funny(paul) & generous(paul)) | ! [X1] : ~humble(X1)) [skolemisation 75,76]
90. ~happy(X0) | rich(X0) | ~patient(X0) [cnf transformation 38]
91. ~generous(X0) | funny(X0) | patient(X0) [cnf transformation 39]
97. ~tall(X0) | ~patient(X0) | happy(X0) [cnf transformation 41]
119. tall(X0) | rich(X0) [cnf transformation 57]
133. generous(paul) | ~humble(X1) [cnf transformation 77]
134. ~funny(paul) | ~humble(X1) [cnf transformation 77]
145. ~rich(paul) [cnf transformation 22]
148. humble(mary) [cnf transformation 24]
299. 34 <=> generous(paul) [avatar definition]
300. generous(paul) <- (34) [avatar component clause 299]
303. 35 <=> funny(paul) [avatar definition]
304. ~funny(paul) <- (~35) [avatar component clause 303]
312. 37 <=> ! [X1] : ~humble(X1) [avatar definition]
313. ~humble(X1) <- (37) [avatar component clause 312]
314. 37 | ~35 [avatar split clause 134,303,312]
315. 37 | 34 [avatar split clause 133,299,312]
402. funny(paul) | patient(paul) <- (34) [resolution 91,300]
403. patient(paul) <- (34, ~35) [subsumption resolution 402,304]
470. ~patient(X0) | happy(X0) | rich(X0) [resolution 97,119]
474. ~patient(X0) | rich(X0) [subsumption resolution 470,90]
701. rich(paul) <- (34, ~35) [resolution 474,403]
704. $false <- (34, ~35) [subsumption resolution 701,145]
705. ~34 | 35 [avatar contradiction clause 704]
706. $false <- (37) [resolution 313,148]
717. ~37 [avatar contradiction clause 706]
718. $false [avatar sat refutation 314,315,705,717]
% SZS output end Proof for 8468650732517492748780631
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not curious is not generous or strong. If someone is either humble or not brave then someone is both funny and not humble and vice versa. If lucy is tall or strong then susan is generous and vice versa. Everyone who is not humble or kind is either rich or not curious. Everyone who is either not rich or calm is both not rich and calm and vice versa. Everyone who is both not calm and not happy is strong and vice versa. Everyone who is either generous or not patient is not curious. If someone is not tall or tall then john is either patient or old and vice versa. If someone is generous then alice is not creative and vice versa. If mary is rich or not tall then mary is either rich or wise and vice versa. If alice is both not quiet and happy then john is both not strong and not old and vice versa. Everyone who is creative is either humble or not calm. Everyone who is both not old and not curious is funny or not creative and vice versa. Everyone who is either not humble or humble is either brave or rich and vice versa. Everyone who is both patient and generous is either not funny or calm. Someone is either funny or not calm. Susan is either not happy or funny. Someone is curious or not kind. Fred is not quiet. Someone is old or not generous. Someone is either not curious or wise. | Susan is humble. | entailment | (![X]:(~curious(X)=>(~generous(X)|strong(X))))&
((?[X]:((humble(X)<~>~brave(X))))<=>(?[X]:((funny(X)&~humble(X)))))&
(((tall(lucy)|strong(lucy)))<=>(generous(susan)))&
(![X]:((~humble(X)|kind(X))=>(rich(X)<~>~curious(X))))&
(![X]:((~rich(X)<~>calm(X))<=>(~rich(X)&calm(X))))&
(![X]:((~calm(X)&~happy(X))<=>strong(X)))&
(![X]:((generous(X)<~>~patient(X))=>~curious(X)))&
((?[X]:((~tall(X)|tall(X))))<=>((patient(john)<~>old(john))))&
((?[X]:(generous(X)))<=>(~creative(alice)))&
(((rich(mary)|~tall(mary)))<=>((rich(mary)<~>wise(mary))))&
(((~quiet(alice)&happy(alice)))<=>((~strong(john)&~old(john))))&
(![X]:(creative(X)=>(humble(X)<~>~calm(X))))&
(![X]:((~old(X)&~curious(X))<=>(funny(X)|~creative(X))))&
(![X]:((~humble(X)<~>humble(X))<=>(brave(X)<~>rich(X))))&
(![X]:((patient(X)&generous(X))=>(~funny(X)<~>calm(X))))&
(?[X]:((funny(X)<~>~calm(X))))&
((~happy(susan)<~>funny(susan)))&
(?[X]:((curious(X)|~kind(X))))&
(~quiet(fred))&
(?[X]:((old(X)|~generous(X))))&
(?[X]:((~curious(X)<~>wise(X)))) | humble(susan) | [
"p1",
"p3",
"p4",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7857847659719462161183659
% SZS output start Proof for 7857847659719462161183659
2. ? [X0] : (humble(X0) <~> ~brave(X0)) <=> ? [X0] : (~humble(X0) & funny(X0)) [input p1]
4. ! [X0] : ((kind(X0) | ~humble(X0)) => (rich(X0) <~> ~curious(X0))) [input p3]
5. ! [X0] : ((~rich(X0) <~> calm(X0)) <=> (calm(X0) & ~rich(X0))) [input p4]
13. ! [X0] : ((~curious(X0) & ~old(X0)) <=> (~creative(X0) | funny(X0))) [input p12]
14. ! [X0] : ((~humble(X0) <~> humble(X0)) <=> (brave(X0) <~> rich(X0))) [input p13]
22. ~humble(susan) [input hypothesis]
23. ? [X0] : (humble(X0) <~> ~brave(X0)) <=> ? [X1] : (~humble(X1) & funny(X1)) [rectify 2]
25. ! [X0] : (~humble(X0) => (rich(X0) <~> ~curious(X0))) [pure predicate removal 4]
28. ! [X0] : ((rich(X0) <~> ~curious(X0)) | humble(X0)) [ennf transformation 25]
33. (? [X0] : ((brave(X0) | ~humble(X0)) & (~brave(X0) | humble(X0))) | ! [X1] : (humble(X1) | ~funny(X1))) & (? [X1] : (~humble(X1) & funny(X1)) | ! [X0] : ((humble(X0) | brave(X0)) & (~brave(X0) | ~humble(X0)))) [nnf transformation 23]
34. (? [X0] : ((brave(X0) | ~humble(X0)) & (~brave(X0) | humble(X0))) | ! [X1] : (humble(X1) | ~funny(X1))) & (? [X2] : (~humble(X2) & funny(X2)) | ! [X3] : ((humble(X3) | brave(X3)) & (~brave(X3) | ~humble(X3)))) [rectify 33]
35. ? [X0] : ((brave(X0) | ~humble(X0)) & (~brave(X0) | humble(X0))) => ((brave(sK0) | ~humble(sK0)) & (~brave(sK0) | humble(sK0))) [choice axiom]
36. ? [X2] : (~humble(X2) & funny(X2)) => (~humble(sK1) & funny(sK1)) [choice axiom]
37. (((brave(sK0) | ~humble(sK0)) & (~brave(sK0) | humble(sK0))) | ! [X1] : (humble(X1) | ~funny(X1))) & ((~humble(sK1) & funny(sK1)) | ! [X3] : ((humble(X3) | brave(X3)) & (~brave(X3) | ~humble(X3)))) [skolemisation 34,36,35]
40. ! [X0] : (((curious(X0) | ~rich(X0)) & (~curious(X0) | rich(X0))) | humble(X0)) [nnf transformation 28]
41. ! [X0] : ((((~calm(X0) | rich(X0)) & (calm(X0) | ~rich(X0))) | (~calm(X0) | rich(X0))) & ((calm(X0) & ~rich(X0)) | ((~rich(X0) | ~calm(X0)) & (calm(X0) | rich(X0))))) [nnf transformation 5]
42. ! [X0] : ((((~calm(X0) | rich(X0)) & (calm(X0) | ~rich(X0))) | ~calm(X0) | rich(X0)) & ((calm(X0) & ~rich(X0)) | ((~rich(X0) | ~calm(X0)) & (calm(X0) | rich(X0))))) [flattening 41]
59. ! [X0] : (((~curious(X0) & ~old(X0)) | (creative(X0) & ~funny(X0))) & ((~creative(X0) | funny(X0)) | (curious(X0) | old(X0)))) [nnf transformation 13]
60. ! [X0] : (((~curious(X0) & ~old(X0)) | (creative(X0) & ~funny(X0))) & (~creative(X0) | funny(X0) | curious(X0) | old(X0))) [flattening 59]
61. ! [X0] : ((((~humble(X0) | humble(X0)) & (humble(X0) | ~humble(X0))) | ((brave(X0) | ~rich(X0)) & (rich(X0) | ~brave(X0)))) & (((~rich(X0) | ~brave(X0)) & (rich(X0) | brave(X0))) | ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0))))) [nnf transformation 14]
74. funny(sK1) | humble(X3) | brave(X3) [cnf transformation 37]
76. ~humble(sK1) | humble(X3) | brave(X3) [cnf transformation 37]
83. ~rich(X0) | curious(X0) | humble(X0) [cnf transformation 40]
86. calm(X0) | calm(X0) | rich(X0) [cnf transformation 42]
89. ~calm(X0) | rich(X0) | ~calm(X0) | rich(X0) [cnf transformation 42]
118. ~funny(X0) | ~curious(X0) [cnf transformation 60]
122. ~rich(X0) | ~brave(X0) | humble(X0) | humble(X0) [cnf transformation 61]
123. ~rich(X0) | ~brave(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 61]
138. ~humble(susan) [cnf transformation 22]
141. ~rich(X0) | ~brave(X0) | humble(X0) [duplicate literal removal 122]
142. ~rich(X0) | ~brave(X0) | ~humble(X0) [duplicate literal removal 123]
146. calm(X0) | rich(X0) [duplicate literal removal 86]
147. ~calm(X0) | rich(X0) [duplicate literal removal 89]
162. 4 <=> ! [X3] : (humble(X3) | brave(X3)) [avatar definition]
163. humble(X3) | brave(X3) <- (4) [avatar component clause 162]
165. 5 <=> humble(sK1) [avatar definition]
167. ~humble(sK1) <- (~5) [avatar component clause 165]
168. 4 | ~5 [avatar split clause 76,165,162]
170. 6 <=> ! [X3] : (~brave(X3) | ~humble(X3)) [avatar definition]
171. ~brave(X3) | ~humble(X3) <- (6) [avatar component clause 170]
174. 7 <=> funny(sK1) [avatar definition]
176. funny(sK1) <- (7) [avatar component clause 174]
177. 4 | 7 [avatar split clause 74,174,162]
194. rich(X0) [subsumption resolution 146,147]
257. ~brave(X0) | ~humble(X0) [subsumption resolution 142,194]
258. 6 [avatar split clause 257,170]
259. ~brave(X0) | humble(X0) [subsumption resolution 141,194]
291. ~brave(X3) <- (6) [subsumption resolution 171,259]
297. ~curious(sK1) <- (7) [resolution 118,176]
313. humble(X0) | curious(X0) [resolution 83,194]
318. curious(sK1) <- (~5) [resolution 313,167]
319. $false <- (~5, 7) [subsumption resolution 318,297]
320. 5 | ~7 [avatar contradiction clause 319]
321. humble(X3) <- (4, 6) [subsumption resolution 163,291]
322. $false <- (4, 6) [resolution 321,138]
327. ~4 | ~6 [avatar contradiction clause 322]
328. $false [avatar sat refutation 168,177,258,320,327]
% SZS output end Proof for 7857847659719462161183659
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either curious or old is generous or not generous and vice versa. If susan is brave then paul is generous or not rich and vice versa. Everyone who is either tall or not kind is both patient and strong and vice versa. Everyone who is generous is both not tall and old and vice versa. If lucy is old or not strong then susan is both old and not curious. If susan is not kind then someone is creative and vice versa. If someone is generous or not old then someone is not kind and vice versa. Everyone who is not funny is kind and vice versa. If someone is wise or not generous then john is both kind and not brave and vice versa. Everyone who is both kind and not strong is not old and vice versa. If someone is both funny and not quiet then alice is not curious or not patient and vice versa. If fred is wise then lucy is not happy. If john is not humble or not quiet then paul is both not old and not creative and vice versa. If lucy is quiet then someone is both quiet and not happy. Everyone who is either not strong or strong is funny. Fred is either generous or not strong. Mary is either not calm or not strong. Someone is both not tall and not wise. Someone is calm. Susan is either not humble or not creative. Someone is not kind. | Paul is strong. | entailment | (![X]:((curious(X)<~>old(X))<=>(generous(X)|~generous(X))))&
((brave(susan))<=>((generous(paul)|~rich(paul))))&
(![X]:((tall(X)<~>~kind(X))<=>(patient(X)&strong(X))))&
(![X]:(generous(X)<=>(~tall(X)&old(X))))&
(((old(lucy)|~strong(lucy)))=>((old(susan)&~curious(susan))))&
((~kind(susan))<=>(?[X]:(creative(X))))&
((?[X]:((generous(X)|~old(X))))<=>(?[X]:(~kind(X))))&
(![X]:(~funny(X)<=>kind(X)))&
((?[X]:((wise(X)|~generous(X))))<=>((kind(john)&~brave(john))))&
(![X]:((kind(X)&~strong(X))<=>~old(X)))&
((?[X]:((funny(X)&~quiet(X))))<=>((~curious(alice)|~patient(alice))))&
((wise(fred))=>(~happy(lucy)))&
(((~humble(john)|~quiet(john)))<=>((~old(paul)&~creative(paul))))&
((quiet(lucy))=>(?[X]:((quiet(X)&~happy(X)))))&
(![X]:((~strong(X)<~>strong(X))=>funny(X)))&
((generous(fred)<~>~strong(fred)))&
((~calm(mary)<~>~strong(mary)))&
(?[X]:((~tall(X)&~wise(X))))&
(?[X]:(calm(X)))&
((~humble(susan)<~>~creative(susan)))&
(?[X]:(~kind(X))) | strong(paul) | [
"p2",
"p3",
"p7",
"p8",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 9154547714870314724992025
% SZS output start Proof for 9154547714870314724992025
3. ! [X0] : ((tall(X0) <~> ~kind(X0)) <=> (strong(X0) & patient(X0))) [input p2]
4. ! [X0] : (generous(X0) <=> (old(X0) & ~tall(X0))) [input p3]
8. ! [X0] : (~funny(X0) <=> kind(X0)) [input p7]
9. ? [X0] : (~generous(X0) | wise(X0)) <=> (~brave(john) & kind(john)) [input p8]
15. ! [X0] : ((~strong(X0) <~> strong(X0)) => funny(X0)) [input p14]
22. ~strong(paul) [input hypothesis]
28. ! [X0] : (funny(X0) | (~strong(X0) <=> strong(X0))) [ennf transformation 15]
33. ! [X0] : ((((kind(X0) | ~tall(X0)) & (~kind(X0) | tall(X0))) | (~strong(X0) | ~patient(X0))) & ((strong(X0) & patient(X0)) | ((tall(X0) | kind(X0)) & (~kind(X0) | ~tall(X0))))) [nnf transformation 3]
34. ! [X0] : ((((kind(X0) | ~tall(X0)) & (~kind(X0) | tall(X0))) | ~strong(X0) | ~patient(X0)) & ((strong(X0) & patient(X0)) | ((tall(X0) | kind(X0)) & (~kind(X0) | ~tall(X0))))) [flattening 33]
35. ! [X0] : ((generous(X0) | (~old(X0) | tall(X0))) & ((old(X0) & ~tall(X0)) | ~generous(X0))) [nnf transformation 4]
36. ! [X0] : ((generous(X0) | ~old(X0) | tall(X0)) & ((old(X0) & ~tall(X0)) | ~generous(X0))) [flattening 35]
46. ! [X0] : ((~funny(X0) | ~kind(X0)) & (kind(X0) | funny(X0))) [nnf transformation 8]
47. (? [X0] : (~generous(X0) | wise(X0)) | (brave(john) | ~kind(john))) & ((~brave(john) & kind(john)) | ! [X0] : (generous(X0) & ~wise(X0))) [nnf transformation 9]
48. (? [X0] : (~generous(X0) | wise(X0)) | brave(john) | ~kind(john)) & ((~brave(john) & kind(john)) | ! [X0] : (generous(X0) & ~wise(X0))) [flattening 47]
49. (? [X0] : (~generous(X0) | wise(X0)) | brave(john) | ~kind(john)) & ((~brave(john) & kind(john)) | ! [X1] : (generous(X1) & ~wise(X1))) [rectify 48]
50. ? [X0] : (~generous(X0) | wise(X0)) => (~generous(sK3) | wise(sK3)) [choice axiom]
51. ((~generous(sK3) | wise(sK3)) | brave(john) | ~kind(john)) & ((~brave(john) & kind(john)) | ! [X1] : (generous(X1) & ~wise(X1))) [skolemisation 49,50]
63. ! [X0] : (funny(X0) | ((~strong(X0) | ~strong(X0)) & (strong(X0) | strong(X0)))) [nnf transformation 28]
85. strong(X0) | tall(X0) | kind(X0) [cnf transformation 34]
88. ~tall(X0) | ~generous(X0) [cnf transformation 36]
101. ~funny(X0) | ~kind(X0) [cnf transformation 46]
103. kind(john) | generous(X1) [cnf transformation 51]
121. funny(X0) | strong(X0) | strong(X0) [cnf transformation 63]
122. funny(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 63]
133. ~strong(paul) [cnf transformation 22]
134. funny(X0) | strong(X0) [duplicate literal removal 121]
135. ~strong(X0) | funny(X0) [duplicate literal removal 122]
211. 17 <=> kind(john) [avatar definition]
212. kind(john) <- (17) [avatar component clause 211]
228. 21 <=> ! [X1] : generous(X1) [avatar definition]
229. generous(X1) <- (21) [avatar component clause 228]
235. 21 | 17 [avatar split clause 103,211,228]
291. funny(X0) [subsumption resolution 134,135]
323. ~kind(X1) [resolution 101,291]
325. $false <- (17) [resolution 323,212]
326. ~17 [avatar contradiction clause 325]
366. tall(paul) | kind(paul) [resolution 85,133]
370. tall(paul) [subsumption resolution 366,323]
374. ~generous(paul) [resolution 370,88]
375. $false <- (21) [subsumption resolution 374,229]
376. ~21 [avatar contradiction clause 375]
377. $false [avatar sat refutation 235,326,376]
% SZS output end Proof for 9154547714870314724992025
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If lucy is calm or rich then someone is both not curious and funny and vice versa.
Everyone who is calm or strong is either not tall or not kind and vice versa.
If someone is humble then paul is funny or brave and vice versa.
If john is both tall and not creative then lucy is both not quiet and strong and vice versa.
If fred is not kind or not calm then john is not old or brave and vice versa.
If mary is brave or not old then lucy is funny or wise.
Everyone who is both not brave and not patient is patient or generous.
Everyone who is both strong and not patient is old and vice versa.
Everyone who is funny is both not tall and not patient.
Everyone who is not curious or patient is generous and vice versa.
If paul is not kind or funny then someone is curious.
If someone is old then fred is both not kind and rich and vice versa.
Everyone who is either creative or brave is not wise and vice versa.
Everyone who is both old and not tall is both curious and happy and vice versa.
Everyone who is either tall or not kind is either not creative or not curious and vice versa.
Everyone who is creative or not kind is not quiet.
Someone is not quiet or creative.
Alice is not tall or brave.
Fred is brave or not creative.
Someone is either generous or wise.
Susan is both not tall and brave.
Someone is both not calm and happy.
Fred is both kind and brave.
Someone is humble. | Fred is not creative. | neutral | (((calm(lucy)|rich(lucy)))<=>(?[X]:((~curious(X)&funny(X)))))&
(![X]:((calm(X)|strong(X))<=>(~tall(X)<~>~kind(X))))&
((?[X]:(humble(X)))<=>((funny(paul)|brave(paul))))&
(((tall(john)&~creative(john)))<=>((~quiet(lucy)&strong(lucy))))&
(((~kind(fred)|~calm(fred)))<=>((~old(john)|brave(john))))&
(((brave(mary)|~old(mary)))=>((funny(lucy)|wise(lucy))))&
(![X]:((~brave(X)&~patient(X))=>(patient(X)|generous(X))))&
(![X]:((strong(X)&~patient(X))<=>old(X)))&
(![X]:(funny(X)=>(~tall(X)&~patient(X))))&
(![X]:((~curious(X)|patient(X))<=>generous(X)))&
(((~kind(paul)|funny(paul)))=>(?[X]:(curious(X))))&
((?[X]:(old(X)))<=>((~kind(fred)&rich(fred))))&
(![X]:((creative(X)<~>brave(X))<=>~wise(X)))&
(![X]:((old(X)&~tall(X))<=>(curious(X)&happy(X))))&
(![X]:((tall(X)<~>~kind(X))<=>(~creative(X)<~>~curious(X))))&
(![X]:((creative(X)|~kind(X))=>~quiet(X)))&
(?[X]:((~quiet(X)|creative(X))))&
((~tall(alice)|brave(alice)))&
((brave(fred)|~creative(fred)))&
(?[X]:((generous(X)<~>wise(X))))&
((~tall(susan)&brave(susan)))&
(?[X]:((~calm(X)&happy(X))))&
((kind(fred)&brave(fred)))&
(?[X]:(humble(X))) | ~creative(fred) | [] | null | 0 |
If someone is both not happy and not strong then someone is not kind. If fred is not generous or creative then fred is either not old or tall. Everyone who is quiet is not brave or curious and vice versa. Everyone who is not funny or creative is both not old and not curious and vice versa. If someone is either not old or strong then someone is both not kind and not generous. Everyone who is brave is both not funny and not brave and vice versa. Everyone who is both not quiet and old is not kind or not patient. Everyone who is creative or not brave is brave or not patient. If someone is kind or tall then someone is both not tall and strong and vice versa. If someone is either funny or kind then paul is either patient or generous. Everyone who is both happy and not rich is not brave or not strong. Everyone who is either strong or not rich is not strong or patient and vice versa. Everyone who is not happy is either not tall or curious and vice versa. Everyone who is both tall and curious is not funny or not curious and vice versa. If alice is not happy or not rich then someone is either funny or old and vice versa. If lucy is either creative or not generous then someone is both generous and not curious. Susan is either not tall or creative. Someone is either rich or not generous. Alice is not happy or curious. Alice is either not humble or not funny. Fred is either not creative or not funny. Someone is not generous or brave. | Paul is not humble. | neutral | ((?[X]:((~happy(X)&~strong(X))))=>(?[X]:(~kind(X))))&
(((~generous(fred)|creative(fred)))=>((~old(fred)<~>tall(fred))))&
(![X]:(quiet(X)<=>(~brave(X)|curious(X))))&
(![X]:((~funny(X)|creative(X))<=>(~old(X)&~curious(X))))&
((?[X]:((~old(X)<~>strong(X))))=>(?[X]:((~kind(X)&~generous(X)))))&
(![X]:(brave(X)<=>(~funny(X)&~brave(X))))&
(![X]:((~quiet(X)&old(X))=>(~kind(X)|~patient(X))))&
(![X]:((creative(X)|~brave(X))=>(brave(X)|~patient(X))))&
((?[X]:((kind(X)|tall(X))))<=>(?[X]:((~tall(X)&strong(X)))))&
((?[X]:((funny(X)<~>kind(X))))=>((patient(paul)<~>generous(paul))))&
(![X]:((happy(X)&~rich(X))=>(~brave(X)|~strong(X))))&
(![X]:((strong(X)<~>~rich(X))<=>(~strong(X)|patient(X))))&
(![X]:(~happy(X)<=>(~tall(X)<~>curious(X))))&
(![X]:((tall(X)&curious(X))<=>(~funny(X)|~curious(X))))&
(((~happy(alice)|~rich(alice)))<=>(?[X]:((funny(X)<~>old(X)))))&
(((creative(lucy)<~>~generous(lucy)))=>(?[X]:((generous(X)&~curious(X)))))&
((~tall(susan)<~>creative(susan)))&
(?[X]:((rich(X)<~>~generous(X))))&
((~happy(alice)|curious(alice)))&
((~humble(alice)<~>~funny(alice)))&
((~creative(fred)<~>~funny(fred)))&
(?[X]:((~generous(X)|brave(X)))) | ~humble(paul) | [] | null | 0 |
If someone is curious then someone is not tall or patient.
Everyone who is both old and tall is both wise and kind and vice versa.
Everyone who is both not humble and brave is creative or not humble.
If someone is not humble or not old then someone is not rich or not kind and vice versa.
Everyone who is old or not tall is both not old and not rich and vice versa.
Everyone who is not old is humble and vice versa.
If lucy is either not brave or calm then someone is both happy and patient.
If john is strong then lucy is not patient or not humble and vice versa.
Everyone who is both brave and not old is both not funny and not creative and vice versa.
If fred is both rich and not creative then alice is not rich or wise.
If someone is patient then someone is both funny and quiet and vice versa.
Everyone who is not rich or curious is both old and not creative.
Everyone who is not quiet is not patient or not tall and vice versa.
If someone is not tall or not kind then someone is both brave and not kind and vice versa.
Everyone who is not calm or happy is both not strong and quiet.
Lucy is not wise.
Someone is not wise or not generous.
John is both funny and not patient.
Someone is not wise.
Someone is strong or not wise.
Fred is either not curious or calm.
Susan is wise or curious. | Fred is old. | contradiction | ((?[X]:(curious(X)))=>(?[X]:((~tall(X)|patient(X)))))&
(![X]:((old(X)&tall(X))<=>(wise(X)&kind(X))))&
(![X]:((~humble(X)&brave(X))=>(creative(X)|~humble(X))))&
((?[X]:((~humble(X)|~old(X))))<=>(?[X]:((~rich(X)|~kind(X)))))&
(![X]:((old(X)|~tall(X))<=>(~old(X)&~rich(X))))&
(![X]:(~old(X)<=>humble(X)))&
(((~brave(lucy)<~>calm(lucy)))=>(?[X]:((happy(X)&patient(X)))))&
((strong(john))<=>((~patient(lucy)|~humble(lucy))))&
(![X]:((brave(X)&~old(X))<=>(~funny(X)&~creative(X))))&
(((rich(fred)&~creative(fred)))=>((~rich(alice)|wise(alice))))&
((?[X]:(patient(X)))<=>(?[X]:((funny(X)&quiet(X)))))&
(![X]:((~rich(X)|curious(X))=>(old(X)&~creative(X))))&
(![X]:(~quiet(X)<=>(~patient(X)|~tall(X))))&
((?[X]:((~tall(X)|~kind(X))))<=>(?[X]:((brave(X)&~kind(X)))))&
(![X]:((~calm(X)|happy(X))=>(~strong(X)&quiet(X))))&
(~wise(lucy))&
(?[X]:((~wise(X)|~generous(X))))&
((funny(john)&~patient(john)))&
(?[X]:(~wise(X)))&
(?[X]:((strong(X)|~wise(X))))&
((~curious(fred)<~>calm(fred)))&
((wise(susan)|curious(susan))) | old(fred) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 4015531709969462825310621
% SZS output start Proof for 4015531709969462825310621
5. ! [X0] : ((~tall(X0) | old(X0)) <=> (~rich(X0) & ~old(X0))) [input p4]
23. old(fred) [input hypothesis]
47. ! [X0] : (((~tall(X0) | old(X0)) | (rich(X0) | old(X0))) & ((~rich(X0) & ~old(X0)) | (tall(X0) & ~old(X0)))) [nnf transformation 5]
48. ! [X0] : ((~tall(X0) | old(X0) | rich(X0) | old(X0)) & ((~rich(X0) & ~old(X0)) | (tall(X0) & ~old(X0)))) [flattening 47]
84. ~old(X0) | ~old(X0) [cnf transformation 48]
130. old(fred) [cnf transformation 23]
131. ~old(X0) [duplicate literal removal 84]
313. $false [subsumption resolution 130,131]
% SZS output end Proof for 4015531709969462825310621
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either kind or old then john is either brave or calm and vice versa.
Everyone who is not humble is humble.
If lucy is both curious and tall then someone is strong or not patient and vice versa.
Everyone who is happy is both rich and not kind and vice versa.
Everyone who is not strong or not happy is not funny or calm and vice versa.
If fred is rich or wise then mary is both not tall and not calm and vice versa.
Everyone who is not generous is calm or brave and vice versa.
If fred is not creative then lucy is quiet and vice versa.
Everyone who is either not quiet or not calm is tall or not patient and vice versa.
If someone is both brave and not tall then someone is both curious and strong and vice versa.
If mary is either happy or not kind then lucy is either funny or brave and vice versa.
If someone is kind or not generous then someone is quiet.
If fred is both not funny and tall then lucy is funny.
If lucy is curious then someone is both not quiet and kind.
If someone is creative or kind then someone is not humble and vice versa.
Everyone who is calm or not happy is either not humble or not old.
Someone is either old or not brave.
Someone is not curious or not strong.
Mary is not old.
John is either patient or quiet.
Mary is either rich or not wise.
Mary is not curious.
Someone is either rich or calm.
John is not tall or not strong. | Fred is strong. | contradiction | ((?[X]:((kind(X)<~>old(X))))<=>((brave(john)<~>calm(john))))&
(![X]:(~humble(X)=>humble(X)))&
(((curious(lucy)&tall(lucy)))<=>(?[X]:((strong(X)|~patient(X)))))&
(![X]:(happy(X)<=>(rich(X)&~kind(X))))&
(![X]:((~strong(X)|~happy(X))<=>(~funny(X)|calm(X))))&
(((rich(fred)|wise(fred)))<=>((~tall(mary)&~calm(mary))))&
(![X]:(~generous(X)<=>(calm(X)|brave(X))))&
((~creative(fred))<=>(quiet(lucy)))&
(![X]:((~quiet(X)<~>~calm(X))<=>(tall(X)|~patient(X))))&
((?[X]:((brave(X)&~tall(X))))<=>(?[X]:((curious(X)&strong(X)))))&
(((happy(mary)<~>~kind(mary)))<=>((funny(lucy)<~>brave(lucy))))&
((?[X]:((kind(X)|~generous(X))))=>(?[X]:(quiet(X))))&
(((~funny(fred)&tall(fred)))=>(funny(lucy)))&
((curious(lucy))=>(?[X]:((~quiet(X)&kind(X)))))&
((?[X]:((creative(X)|kind(X))))<=>(?[X]:(~humble(X))))&
(![X]:((calm(X)|~happy(X))=>(~humble(X)<~>~old(X))))&
(?[X]:((old(X)<~>~brave(X))))&
(?[X]:((~curious(X)|~strong(X))))&
(~old(mary))&
((patient(john)<~>quiet(john)))&
((rich(mary)<~>~wise(mary)))&
(~curious(mary))&
(?[X]:((rich(X)<~>calm(X))))&
((~tall(john)|~strong(john))) | strong(fred) | [
"p1",
"p2",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5246200152168780442685016
% SZS output start Proof for 5246200152168780442685016
2. ! [X0] : (~humble(X0) => humble(X0)) [input p1]
3. (tall(lucy) & curious(lucy)) <=> ? [X0] : (~patient(X0) | strong(X0)) [input p2]
14. curious(lucy) => ? [X0] : (kind(X0) & ~quiet(X0)) [input p13]
15. ? [X0] : (kind(X0) | creative(X0)) <=> ? [X0] : ~humble(X0) [input p14]
25. strong(fred) [input hypothesis]
28. ? [X0] : (kind(X0) | creative(X0)) <=> ? [X1] : ~humble(X1) [rectify 15]
30. ! [X0] : (humble(X0) | humble(X0)) [ennf transformation 2]
35. ? [X0] : (kind(X0) & ~quiet(X0)) | ~curious(lucy) [ennf transformation 14]
41. ((tall(lucy) & curious(lucy)) | ! [X0] : (patient(X0) & ~strong(X0))) & (? [X0] : (~patient(X0) | strong(X0)) | (~tall(lucy) | ~curious(lucy))) [nnf transformation 3]
42. ((tall(lucy) & curious(lucy)) | ! [X0] : (patient(X0) & ~strong(X0))) & (? [X0] : (~patient(X0) | strong(X0)) | ~tall(lucy) | ~curious(lucy)) [flattening 41]
43. ((tall(lucy) & curious(lucy)) | ! [X0] : (patient(X0) & ~strong(X0))) & (? [X1] : (~patient(X1) | strong(X1)) | ~tall(lucy) | ~curious(lucy)) [rectify 42]
44. ? [X1] : (~patient(X1) | strong(X1)) => (~patient(sK1) | strong(sK1)) [choice axiom]
45. ((tall(lucy) & curious(lucy)) | ! [X0] : (patient(X0) & ~strong(X0))) & ((~patient(sK1) | strong(sK1)) | ~tall(lucy) | ~curious(lucy)) [skolemisation 43,44]
64. ? [X0] : (kind(X0) & ~quiet(X0)) => (kind(sK5) & ~quiet(sK5)) [choice axiom]
65. (kind(sK5) & ~quiet(sK5)) | ~curious(lucy) [skolemisation 35,64]
66. (? [X0] : (kind(X0) | creative(X0)) | ! [X1] : humble(X1)) & (? [X1] : ~humble(X1) | ! [X0] : (~kind(X0) & ~creative(X0))) [nnf transformation 28]
67. (? [X0] : (kind(X0) | creative(X0)) | ! [X1] : humble(X1)) & (? [X2] : ~humble(X2) | ! [X3] : (~kind(X3) & ~creative(X3))) [rectify 66]
68. ? [X0] : (kind(X0) | creative(X0)) => (kind(sK6) | creative(sK6)) [choice axiom]
69. ? [X2] : ~humble(X2) => ~humble(sK7) [choice axiom]
70. ((kind(sK6) | creative(sK6)) | ! [X1] : humble(X1)) & (~humble(sK7) | ! [X3] : (~kind(X3) & ~creative(X3))) [skolemisation 67,69,68]
90. humble(X0) | humble(X0) [cnf transformation 30]
92. curious(lucy) | ~strong(X0) [cnf transformation 45]
134. kind(sK5) | ~curious(lucy) [cnf transformation 65]
136. ~humble(sK7) | ~kind(X3) [cnf transformation 70]
154. strong(fred) [cnf transformation 25]
155. humble(X0) [duplicate literal removal 90]
195. 9 <=> ! [X0] : ~strong(X0) [avatar definition]
196. ~strong(X0) <- (9) [avatar component clause 195]
199. 10 <=> curious(lucy) [avatar definition]
203. 9 | 10 [avatar split clause 92,199,195]
305. 31 <=> ! [X1] : ~kind(X1) [avatar definition]
306. ~kind(X1) <- (31) [avatar component clause 305]
318. 34 <=> kind(sK5) [avatar definition]
320. kind(sK5) <- (34) [avatar component clause 318]
321. ~10 | 34 [avatar split clause 134,318,199]
327. ~kind(X3) [subsumption resolution 136,155]
328. 31 [avatar split clause 327,305]
392. $false <- (9) [resolution 196,154]
393. ~9 [avatar contradiction clause 392]
394. $false <- (31, 34) [subsumption resolution 320,306]
395. ~31 | ~34 [avatar contradiction clause 394]
398. $false [avatar sat refutation 203,321,328,393,395]
% SZS output end Proof for 5246200152168780442685016
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old is not funny. If susan is patient then john is either not old or happy and vice versa. If someone is happy or wise then mary is both not generous and humble and vice versa. Everyone who is either not quiet or not creative is either creative or not tall and vice versa. Everyone who is either calm or generous is not old and vice versa. Everyone who is happy is not calm. Everyone who is both not tall and not happy is not strong or humble. If john is either not curious or wise then lucy is both not happy and not patient. Everyone who is not calm is either not brave or rich and vice versa. If alice is rich then alice is creative. Everyone who is not tall or old is either not strong or not kind. Everyone who is kind is both happy and not humble. Everyone who is not brave is either not curious or not quiet. Everyone who is both calm and tall is both not calm and quiet. If someone is generous or not wise then lucy is both happy and not calm and vice versa. Everyone who is either funny or kind is creative and vice versa. Susan is not tall or not patient. Someone is both not happy and patient. Paul is not patient. Paul is both generous and not old. Someone is either brave or not funny. Mary is strong. Someone is not happy. Paul is either not kind or not creative. | Paul is not calm. | entailment | (![X]:((~strong(X)&old(X))=>~funny(X)))&
((patient(susan))<=>((~old(john)<~>happy(john))))&
((?[X]:((happy(X)|wise(X))))<=>((~generous(mary)&humble(mary))))&
(![X]:((~quiet(X)<~>~creative(X))<=>(creative(X)<~>~tall(X))))&
(![X]:((calm(X)<~>generous(X))<=>~old(X)))&
(![X]:(happy(X)=>~calm(X)))&
(![X]:((~tall(X)&~happy(X))=>(~strong(X)|humble(X))))&
(((~curious(john)<~>wise(john)))=>((~happy(lucy)&~patient(lucy))))&
(![X]:(~calm(X)<=>(~brave(X)<~>rich(X))))&
((rich(alice))=>(creative(alice)))&
(![X]:((~tall(X)|old(X))=>(~strong(X)<~>~kind(X))))&
(![X]:(kind(X)=>(happy(X)&~humble(X))))&
(![X]:(~brave(X)=>(~curious(X)<~>~quiet(X))))&
(![X]:((calm(X)&tall(X))=>(~calm(X)&quiet(X))))&
((?[X]:((generous(X)|~wise(X))))<=>((happy(lucy)&~calm(lucy))))&
(![X]:((funny(X)<~>kind(X))<=>creative(X)))&
((~tall(susan)|~patient(susan)))&
(?[X]:((~happy(X)&patient(X))))&
(~patient(paul))&
((generous(paul)&~old(paul)))&
(?[X]:((brave(X)<~>~funny(X))))&
(strong(mary))&
(?[X]:(~happy(X)))&
((~kind(paul)<~>~creative(paul))) | ~calm(paul) | [
"p4",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 99878885267688448228856
% SZS output start Proof for 99878885267688448228856
5. ! [X0] : ((calm(X0) <~> generous(X0)) <=> ~old(X0)) [input p4]
20. ~old(paul) & generous(paul) [input p19]
25. calm(paul) [input hypothesis]
45. ! [X0] : ((((~generous(X0) | ~calm(X0)) & (generous(X0) | calm(X0))) | old(X0)) & (~old(X0) | ((calm(X0) | ~generous(X0)) & (generous(X0) | ~calm(X0))))) [nnf transformation 5]
85. ~calm(X0) | ~generous(X0) | old(X0) [cnf transformation 45]
120. generous(paul) [cnf transformation 20]
121. ~old(paul) [cnf transformation 20]
128. calm(paul) [cnf transformation 25]
301. ~generous(paul) | old(paul) [resolution 85,128]
304. old(paul) [subsumption resolution 301,120]
305. $false [subsumption resolution 304,121]
% SZS output end Proof for 99878885267688448228856
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not curious and not calm then someone is tall or not tall.
Everyone who is either quiet or not brave is either not funny or tall and vice versa.
If paul is rich or not strong then mary is either strong or not funny and vice versa.
If someone is both not generous and humble then fred is both rich and curious.
If paul is not curious then someone is not creative and vice versa.
If someone is both strong and not old then alice is not creative or old and vice versa.
If paul is curious or not humble then someone is both not happy and not strong and vice versa.
If mary is generous or creative then someone is either not humble or happy.
Everyone who is not funny is brave or not tall and vice versa.
Everyone who is both strong and not happy is not brave and vice versa.
If someone is both quiet and not humble then someone is both funny and not calm.
Everyone who is humble is either tall or calm.
Everyone who is either calm or funny is not creative and vice versa.
Everyone who is both funny and creative is either rich or not funny and vice versa.
Everyone who is either not kind or wise is rich or calm and vice versa.
Everyone who is both not brave and generous is not patient or rich and vice versa.
Someone is rich.
Mary is not wise.
Paul is humble or funny.
Mary is tall.
Someone is either not old or not kind.
Someone is both not brave and not creative.
Someone is happy or kind.
Someone is rich or creative. | Alice is not generous. | neutral | ((?[X]:((~curious(X)&~calm(X))))=>(?[X]:((tall(X)|~tall(X)))))&
(![X]:((quiet(X)<~>~brave(X))<=>(~funny(X)<~>tall(X))))&
(((rich(paul)|~strong(paul)))<=>((strong(mary)<~>~funny(mary))))&
((?[X]:((~generous(X)&humble(X))))=>((rich(fred)&curious(fred))))&
((~curious(paul))<=>(?[X]:(~creative(X))))&
((?[X]:((strong(X)&~old(X))))<=>((~creative(alice)|old(alice))))&
(((curious(paul)|~humble(paul)))<=>(?[X]:((~happy(X)&~strong(X)))))&
(((generous(mary)|creative(mary)))=>(?[X]:((~humble(X)<~>happy(X)))))&
(![X]:(~funny(X)<=>(brave(X)|~tall(X))))&
(![X]:((strong(X)&~happy(X))<=>~brave(X)))&
((?[X]:((quiet(X)&~humble(X))))=>(?[X]:((funny(X)&~calm(X)))))&
(![X]:(humble(X)=>(tall(X)<~>calm(X))))&
(![X]:((calm(X)<~>funny(X))<=>~creative(X)))&
(![X]:((funny(X)&creative(X))<=>(rich(X)<~>~funny(X))))&
(![X]:((~kind(X)<~>wise(X))<=>(rich(X)|calm(X))))&
(![X]:((~brave(X)&generous(X))<=>(~patient(X)|rich(X))))&
(?[X]:(rich(X)))&
(~wise(mary))&
((humble(paul)|funny(paul)))&
(tall(mary))&
(?[X]:((~old(X)<~>~kind(X))))&
(?[X]:((~brave(X)&~creative(X))))&
(?[X]:((happy(X)|kind(X))))&
(?[X]:((rich(X)|creative(X)))) | ~generous(alice) | [] | null | 0 |
If paul is funny or humble then lucy is both not generous and not strong and vice versa.
If someone is old then john is either not happy or brave.
If someone is both humble and not generous then john is old or curious and vice versa.
If someone is either not humble or generous then someone is not kind or calm and vice versa.
If fred is both happy and patient then someone is calm or happy.
Everyone who is kind is both creative and wise and vice versa.
Everyone who is not calm is not quiet or not curious.
If someone is either quiet or strong then alice is either not funny or not wise and vice versa.
Everyone who is either not humble or quiet is patient and vice versa.
If someone is not brave then someone is either not patient or not brave.
Everyone who is both not rich and quiet is not wise and vice versa.
Everyone who is not brave is not brave or not happy.
If fred is calm then someone is patient or not quiet and vice versa.
Everyone who is both quiet and funny is not strong or calm and vice versa.
If alice is both not humble and not old then susan is either tall or not strong.
Everyone who is both not kind and old is not curious and vice versa.
Alice is either not calm or rich.
Someone is humble or not kind.
Lucy is both not rich and not brave.
Someone is patient.
Someone is either happy or calm.
John is either calm or quiet. | Alice is kind. | neutral | (((funny(paul)|humble(paul)))<=>((~generous(lucy)&~strong(lucy))))&
((?[X]:(old(X)))=>((~happy(john)<~>brave(john))))&
((?[X]:((humble(X)&~generous(X))))<=>((old(john)|curious(john))))&
((?[X]:((~humble(X)<~>generous(X))))<=>(?[X]:((~kind(X)|calm(X)))))&
(((happy(fred)&patient(fred)))=>(?[X]:((calm(X)|happy(X)))))&
(![X]:(kind(X)<=>(creative(X)&wise(X))))&
(![X]:(~calm(X)=>(~quiet(X)|~curious(X))))&
((?[X]:((quiet(X)<~>strong(X))))<=>((~funny(alice)<~>~wise(alice))))&
(![X]:((~humble(X)<~>quiet(X))<=>patient(X)))&
((?[X]:(~brave(X)))=>(?[X]:((~patient(X)<~>~brave(X)))))&
(![X]:((~rich(X)&quiet(X))<=>~wise(X)))&
(![X]:(~brave(X)=>(~brave(X)|~happy(X))))&
((calm(fred))<=>(?[X]:((patient(X)|~quiet(X)))))&
(![X]:((quiet(X)&funny(X))<=>(~strong(X)|calm(X))))&
(((~humble(alice)&~old(alice)))=>((tall(susan)<~>~strong(susan))))&
(![X]:((~kind(X)&old(X))<=>~curious(X)))&
((~calm(alice)<~>rich(alice)))&
(?[X]:((humble(X)|~kind(X))))&
((~rich(lucy)&~brave(lucy)))&
(?[X]:(patient(X)))&
(?[X]:((happy(X)<~>calm(X))))&
((calm(john)<~>quiet(john))) | kind(alice) | [] | null | 0 |
Everyone who is either not kind or funny is both old and happy and vice versa.
If someone is either calm or not brave then someone is not calm or not creative and vice versa.
Everyone who is either wise or not patient is both not calm and not quiet and vice versa.
If paul is both not curious and tall then john is either curious or not patient and vice versa.
If someone is either rich or wise then someone is both old and quiet and vice versa.
Everyone who is either tall or happy is either not creative or not happy.
Everyone who is either patient or not generous is both not patient and not rich and vice versa.
Everyone who is either not tall or happy is both happy and wise.
If someone is both not tall and creative then someone is funny and vice versa.
Everyone who is either curious or not old is not rich or not generous and vice versa.
Everyone who is either quiet or generous is both tall and old and vice versa.
If someone is not kind or not generous then fred is either kind or brave.
If susan is not funny then mary is both old and not tall and vice versa.
Everyone who is both not generous and not tall is not kind or quiet and vice versa.
If mary is not patient then someone is either brave or strong and vice versa.
If paul is strong or brave then mary is both not creative and humble and vice versa.
Someone is not brave.
Someone is funny or happy.
Alice is not calm.
Susan is either not happy or not calm.
Someone is both not funny and creative.
Lucy is not happy or not funny.
Someone is either kind or not happy.
John is wise or not quiet. | Mary is not generous. | entailment | (![X]:((~kind(X)<~>funny(X))<=>(old(X)&happy(X))))&
((?[X]:((calm(X)<~>~brave(X))))<=>(?[X]:((~calm(X)|~creative(X)))))&
(![X]:((wise(X)<~>~patient(X))<=>(~calm(X)&~quiet(X))))&
(((~curious(paul)&tall(paul)))<=>((curious(john)<~>~patient(john))))&
((?[X]:((rich(X)<~>wise(X))))<=>(?[X]:((old(X)&quiet(X)))))&
(![X]:((tall(X)<~>happy(X))=>(~creative(X)<~>~happy(X))))&
(![X]:((patient(X)<~>~generous(X))<=>(~patient(X)&~rich(X))))&
(![X]:((~tall(X)<~>happy(X))=>(happy(X)&wise(X))))&
((?[X]:((~tall(X)&creative(X))))<=>(?[X]:(funny(X))))&
(![X]:((curious(X)<~>~old(X))<=>(~rich(X)|~generous(X))))&
(![X]:((quiet(X)<~>generous(X))<=>(tall(X)&old(X))))&
((?[X]:((~kind(X)|~generous(X))))=>((kind(fred)<~>brave(fred))))&
((~funny(susan))<=>((old(mary)&~tall(mary))))&
(![X]:((~generous(X)&~tall(X))<=>(~kind(X)|quiet(X))))&
((~patient(mary))<=>(?[X]:((brave(X)<~>strong(X)))))&
(((strong(paul)|brave(paul)))<=>((~creative(mary)&humble(mary))))&
(?[X]:(~brave(X)))&
(?[X]:((funny(X)|happy(X))))&
(~calm(alice))&
((~happy(susan)<~>~calm(susan)))&
(?[X]:((~funny(X)&creative(X))))&
((~happy(lucy)|~funny(lucy)))&
(?[X]:((kind(X)<~>~happy(X))))&
((wise(john)|~quiet(john))) | ~generous(mary) | [
"p5",
"p7",
"p8",
"p10",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 218895174253989825875446
% SZS output start Proof for 218895174253989825875446
6. ! [X0] : ((tall(X0) <~> happy(X0)) => (~creative(X0) <~> ~happy(X0))) [input p5]
8. ! [X0] : ((~tall(X0) <~> happy(X0)) => (wise(X0) & happy(X0))) [input p7]
9. ? [X0] : (creative(X0) & ~tall(X0)) <=> ? [X0] : funny(X0) [input p8]
11. ! [X0] : ((quiet(X0) <~> generous(X0)) <=> (old(X0) & tall(X0))) [input p10]
13. ~funny(susan) <=> (~tall(mary) & old(mary)) [input p12]
14. ! [X0] : ((~tall(X0) & ~generous(X0)) <=> (quiet(X0) | ~kind(X0))) [input p13]
25. generous(mary) [input hypothesis]
28. ? [X0] : (creative(X0) & ~tall(X0)) <=> ? [X1] : funny(X1) [rectify 9]
29. ! [X0] : ((~creative(X0) <~> ~happy(X0)) | (tall(X0) <=> happy(X0))) [ennf transformation 6]
30. ! [X0] : ((wise(X0) & happy(X0)) | (~tall(X0) <=> happy(X0))) [ennf transformation 8]
48. ! [X0] : (((happy(X0) | creative(X0)) & (~happy(X0) | ~creative(X0))) | ((tall(X0) | ~happy(X0)) & (happy(X0) | ~tall(X0)))) [nnf transformation 29]
51. ! [X0] : ((wise(X0) & happy(X0)) | ((~tall(X0) | ~happy(X0)) & (happy(X0) | tall(X0)))) [nnf transformation 30]
52. (? [X0] : (creative(X0) & ~tall(X0)) | ! [X1] : ~funny(X1)) & (? [X1] : funny(X1) | ! [X0] : (~creative(X0) | tall(X0))) [nnf transformation 28]
53. (? [X0] : (creative(X0) & ~tall(X0)) | ! [X1] : ~funny(X1)) & (? [X2] : funny(X2) | ! [X3] : (~creative(X3) | tall(X3))) [rectify 52]
54. ? [X0] : (creative(X0) & ~tall(X0)) => (creative(sK4) & ~tall(sK4)) [choice axiom]
55. ? [X2] : funny(X2) => funny(sK5) [choice axiom]
56. ((creative(sK4) & ~tall(sK4)) | ! [X1] : ~funny(X1)) & (funny(sK5) | ! [X3] : (~creative(X3) | tall(X3))) [skolemisation 53,55,54]
59. ! [X0] : ((((~generous(X0) | ~quiet(X0)) & (generous(X0) | quiet(X0))) | (~old(X0) | ~tall(X0))) & ((old(X0) & tall(X0)) | ((quiet(X0) | ~generous(X0)) & (generous(X0) | ~quiet(X0))))) [nnf transformation 11]
60. ! [X0] : ((((~generous(X0) | ~quiet(X0)) & (generous(X0) | quiet(X0))) | ~old(X0) | ~tall(X0)) & ((old(X0) & tall(X0)) | ((quiet(X0) | ~generous(X0)) & (generous(X0) | ~quiet(X0))))) [flattening 59]
62. (~funny(susan) | (tall(mary) | ~old(mary))) & ((~tall(mary) & old(mary)) | funny(susan)) [nnf transformation 13]
63. (~funny(susan) | tall(mary) | ~old(mary)) & ((~tall(mary) & old(mary)) | funny(susan)) [flattening 62]
64. ! [X0] : (((~tall(X0) & ~generous(X0)) | (~quiet(X0) & kind(X0))) & ((quiet(X0) | ~kind(X0)) | (tall(X0) | generous(X0)))) [nnf transformation 14]
65. ! [X0] : (((~tall(X0) & ~generous(X0)) | (~quiet(X0) & kind(X0))) & (quiet(X0) | ~kind(X0) | tall(X0) | generous(X0))) [flattening 64]
113. ~happy(X0) | ~creative(X0) | tall(X0) | ~happy(X0) [cnf transformation 48]
122. happy(X0) | happy(X0) | tall(X0) [cnf transformation 51]
127. ~tall(sK4) | ~funny(X1) [cnf transformation 56]
128. creative(sK4) | ~funny(X1) [cnf transformation 56]
136. ~generous(X0) | quiet(X0) | tall(X0) [cnf transformation 60]
146. ~tall(mary) | funny(susan) [cnf transformation 63]
150. ~generous(X0) | ~quiet(X0) [cnf transformation 65]
173. generous(mary) [cnf transformation 25]
174. tall(X0) | happy(X0) [duplicate literal removal 122]
177. ~creative(X0) | ~happy(X0) | tall(X0) [duplicate literal removal 113]
267. 20 <=> ! [X1] : ~funny(X1) [avatar definition]
268. ~funny(X1) <- (20) [avatar component clause 267]
270. 21 <=> creative(sK4) [avatar definition]
272. creative(sK4) <- (21) [avatar component clause 270]
273. 20 | 21 [avatar split clause 128,270,267]
275. 22 <=> tall(sK4) [avatar definition]
278. 20 | ~22 [avatar split clause 127,275,267]
310. 30 <=> tall(mary) [avatar definition]
314. 31 <=> funny(susan) [avatar definition]
315. funny(susan) <- (31) [avatar component clause 314]
318. 31 | ~30 [avatar split clause 146,310,314]
414. ~quiet(mary) [resolution 150,173]
498. quiet(mary) | tall(mary) [resolution 136,173]
499. tall(mary) [subsumption resolution 498,414]
502. 30 [avatar split clause 499,310]
589. ~happy(sK4) | tall(sK4) <- (21) [resolution 177,272]
594. tall(sK4) <- (21) [subsumption resolution 589,174]
595. 22 | ~21 [avatar split clause 594,270,275]
596. $false <- (20, 31) [resolution 268,315]
599. ~20 | ~31 [avatar contradiction clause 596]
600. $false [avatar sat refutation 273,278,318,502,595,599]
% SZS output end Proof for 218895174253989825875446
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
If someone is calm or not rich then someone is both not strong and not creative and vice versa.
Everyone who is patient or generous is both not brave and not calm and vice versa.
Everyone who is both funny and not funny is not humble or calm.
If someone is brave then mary is either curious or old and vice versa.
If mary is quiet then fred is happy.
If john is either humble or funny then mary is both brave and creative.
If alice is either funny or humble then someone is not quiet or wise.
If someone is either curious or not creative then mary is quiet.
Everyone who is not funny or not curious is both humble and funny and vice versa.
If someone is not calm then someone is both not quiet and kind and vice versa.
If susan is either not happy or humble then someone is not strong and vice versa.
Everyone who is either generous or not calm is not generous or not quiet and vice versa.
Everyone who is either not humble or generous is curious or strong and vice versa.
Everyone who is rich is not funny or not old.
Everyone who is both not quiet and humble is not happy or humble and vice versa.
Everyone who is not old is wise or not curious and vice versa.
John is either not funny or not creative.
Fred is wise or not humble.
Susan is not humble or kind.
Alice is not tall. | Fred is not generous. | entailment | ((?[X]:((calm(X)|~rich(X))))<=>(?[X]:((~strong(X)&~creative(X)))))&
(![X]:((patient(X)|generous(X))<=>(~brave(X)&~calm(X))))&
(![X]:((funny(X)&~funny(X))=>(~humble(X)|calm(X))))&
((?[X]:(brave(X)))<=>((curious(mary)<~>old(mary))))&
((quiet(mary))=>(happy(fred)))&
(((humble(john)<~>funny(john)))=>((brave(mary)&creative(mary))))&
(((funny(alice)<~>humble(alice)))=>(?[X]:((~quiet(X)|wise(X)))))&
((?[X]:((curious(X)<~>~creative(X))))=>(quiet(mary)))&
(![X]:((~funny(X)|~curious(X))<=>(humble(X)&funny(X))))&
((?[X]:(~calm(X)))<=>(?[X]:((~quiet(X)&kind(X)))))&
(((~happy(susan)<~>humble(susan)))<=>(?[X]:(~strong(X))))&
(![X]:((generous(X)<~>~calm(X))<=>(~generous(X)|~quiet(X))))&
(![X]:((~humble(X)<~>generous(X))<=>(curious(X)|strong(X))))&
(![X]:(rich(X)=>(~funny(X)|~old(X))))&
(![X]:((~quiet(X)&humble(X))<=>(~happy(X)|humble(X))))&
(![X]:(~old(X)<=>(wise(X)|~curious(X))))&
((~funny(john)<~>~creative(john)))&
((wise(fred)|~humble(fred)))&
((~humble(susan)|kind(susan)))&
(~tall(alice)) | ~generous(fred) | [
"p1",
"p8",
"p11",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7220989080242555696395232
% SZS output start Proof for 7220989080242555696395232
2. ! [X0] : ((generous(X0) | patient(X0)) <=> (~calm(X0) & ~brave(X0))) [input p1]
9. ! [X0] : ((~curious(X0) | ~funny(X0)) <=> (funny(X0) & humble(X0))) [input p8]
12. ! [X0] : ((generous(X0) <~> ~calm(X0)) <=> (~quiet(X0) | ~generous(X0))) [input p11]
13. ! [X0] : ((~humble(X0) <~> generous(X0)) <=> (strong(X0) | curious(X0))) [input p12]
15. ! [X0] : ((humble(X0) & ~quiet(X0)) <=> (humble(X0) | ~happy(X0))) [input p14]
21. generous(fred) [input hypothesis]
38. ! [X0] : (((generous(X0) | patient(X0)) | (calm(X0) | brave(X0))) & ((~calm(X0) & ~brave(X0)) | (~generous(X0) & ~patient(X0)))) [nnf transformation 2]
39. ! [X0] : ((generous(X0) | patient(X0) | calm(X0) | brave(X0)) & ((~calm(X0) & ~brave(X0)) | (~generous(X0) & ~patient(X0)))) [flattening 38]
49. ! [X0] : (((~curious(X0) | ~funny(X0)) | (~funny(X0) | ~humble(X0))) & ((funny(X0) & humble(X0)) | (curious(X0) & funny(X0)))) [nnf transformation 9]
50. ! [X0] : ((~curious(X0) | ~funny(X0) | ~funny(X0) | ~humble(X0)) & ((funny(X0) & humble(X0)) | (curious(X0) & funny(X0)))) [flattening 49]
60. ! [X0] : ((((calm(X0) | ~generous(X0)) & (~calm(X0) | generous(X0))) | (quiet(X0) & generous(X0))) & ((~quiet(X0) | ~generous(X0)) | ((generous(X0) | calm(X0)) & (~calm(X0) | ~generous(X0))))) [nnf transformation 12]
61. ! [X0] : ((((calm(X0) | ~generous(X0)) & (~calm(X0) | generous(X0))) | (quiet(X0) & generous(X0))) & (~quiet(X0) | ~generous(X0) | ((generous(X0) | calm(X0)) & (~calm(X0) | ~generous(X0))))) [flattening 60]
62. ! [X0] : ((((~generous(X0) | humble(X0)) & (generous(X0) | ~humble(X0))) | (~strong(X0) & ~curious(X0))) & ((strong(X0) | curious(X0)) | ((~humble(X0) | ~generous(X0)) & (generous(X0) | humble(X0))))) [nnf transformation 13]
63. ! [X0] : ((((~generous(X0) | humble(X0)) & (generous(X0) | ~humble(X0))) | (~strong(X0) & ~curious(X0))) & (strong(X0) | curious(X0) | ((~humble(X0) | ~generous(X0)) & (generous(X0) | humble(X0))))) [flattening 62]
64. ! [X0] : (((humble(X0) & ~quiet(X0)) | (~humble(X0) & happy(X0))) & ((humble(X0) | ~happy(X0)) | (~humble(X0) | quiet(X0)))) [nnf transformation 15]
65. ! [X0] : (((humble(X0) & ~quiet(X0)) | (~humble(X0) & happy(X0))) & (humble(X0) | ~happy(X0) | ~humble(X0) | quiet(X0))) [flattening 64]
77. ~generous(X0) | ~calm(X0) [cnf transformation 39]
94. curious(X0) | humble(X0) [cnf transformation 50]
110. calm(X0) | ~generous(X0) | quiet(X0) [cnf transformation 61]
115. ~generous(X0) | humble(X0) | ~curious(X0) [cnf transformation 63]
120. ~quiet(X0) | ~humble(X0) [cnf transformation 65]
130. generous(fred) [cnf transformation 21]
279. ~generous(X0) | quiet(X0) [subsumption resolution 110,77]
283. ~generous(X0) | humble(X0) [subsumption resolution 115,94]
292. 34 <=> humble(fred) [avatar definition]
334. quiet(fred) [resolution 279,130]
335. ~humble(fred) [resolution 334,120]
337. humble(fred) [resolution 283,130]
340. 34 [avatar split clause 337,292]
341. ~34 [avatar split clause 335,292]
342. $false [avatar sat refutation 340,341]
% SZS output end Proof for 7220989080242555696395232
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not wise is both funny and not creative and vice versa.
Everyone who is not calm or funny is not creative and vice versa.
If someone is both curious and not happy then susan is either not old or not tall and vice versa.
Everyone who is not creative is generous and vice versa.
Everyone who is both creative and happy is both not happy and not rich and vice versa.
If someone is either strong or not tall then susan is brave.
Everyone who is both not happy and not rich is either not patient or tall.
If someone is not wise then lucy is both curious and kind.
If someone is either kind or not strong then someone is wise.
If someone is either not creative or curious then lucy is both not funny and strong and vice versa.
Everyone who is old or not generous is both not old and not brave and vice versa.
If someone is either tall or patient then alice is both not strong and wise and vice versa.
Everyone who is humble or wise is either not strong or quiet.
Everyone who is both not patient and not humble is either not brave or humble and vice versa.
Everyone who is either not tall or strong is both wise and not generous.
If mary is both creative and tall then someone is not patient.
Someone is not funny or not kind.
Fred is either old or quiet.
Susan is patient or not patient.
Susan is calm.
John is both not wise and tall.
Paul is not funny or not curious.
Someone is both brave and not strong.
Susan is not funny or not rich. | Susan is not calm. | contradiction | (![X]:(~wise(X)<=>(funny(X)&~creative(X))))&
(![X]:((~calm(X)|funny(X))<=>~creative(X)))&
((?[X]:((curious(X)&~happy(X))))<=>((~old(susan)<~>~tall(susan))))&
(![X]:(~creative(X)<=>generous(X)))&
(![X]:((creative(X)&happy(X))<=>(~happy(X)&~rich(X))))&
((?[X]:((strong(X)<~>~tall(X))))=>(brave(susan)))&
(![X]:((~happy(X)&~rich(X))=>(~patient(X)<~>tall(X))))&
((?[X]:(~wise(X)))=>((curious(lucy)&kind(lucy))))&
((?[X]:((kind(X)<~>~strong(X))))=>(?[X]:(wise(X))))&
((?[X]:((~creative(X)<~>curious(X))))<=>((~funny(lucy)&strong(lucy))))&
(![X]:((old(X)|~generous(X))<=>(~old(X)&~brave(X))))&
((?[X]:((tall(X)<~>patient(X))))<=>((~strong(alice)&wise(alice))))&
(![X]:((humble(X)|wise(X))=>(~strong(X)<~>quiet(X))))&
(![X]:((~patient(X)&~humble(X))<=>(~brave(X)<~>humble(X))))&
(![X]:((~tall(X)<~>strong(X))=>(wise(X)&~generous(X))))&
(((creative(mary)&tall(mary)))=>(?[X]:(~patient(X))))&
(?[X]:((~funny(X)|~kind(X))))&
((old(fred)<~>quiet(fred)))&
((patient(susan)|~patient(susan)))&
(calm(susan))&
((~wise(john)&tall(john)))&
((~funny(paul)|~curious(paul)))&
(?[X]:((brave(X)&~strong(X))))&
((~funny(susan)|~rich(susan))) | ~calm(susan) | [
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 1238058425542526673356787
% SZS output start Proof for 1238058425542526673356787
20. calm(susan) [input p19]
25. ~calm(susan) [input hypothesis]
138. calm(susan) [cnf transformation 20]
145. ~calm(susan) [cnf transformation 25]
312. $false [subsumption resolution 145,138]
% SZS output end Proof for 1238058425542526673356787
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is either wise or not funny then lucy is quiet or not happy and vice versa.
If paul is curious or brave then someone is humble.
Everyone who is both wise and not humble is both calm and wise.
Everyone who is both old and not funny is both funny and strong and vice versa.
Everyone who is kind is both funny and not strong.
Everyone who is both rich and not curious is both not creative and creative and vice versa.
Everyone who is both not tall and not happy is not kind and vice versa.
If someone is not patient or generous then someone is both not strong and not funny.
Everyone who is both not quiet and not humble is not rich or not calm and vice versa.
Everyone who is curious or patient is either not funny or not happy.
Everyone who is either rich or not strong is either not curious or tall.
Everyone who is either not rich or strong is either not funny or not rich and vice versa.
If lucy is strong or not brave then susan is either not strong or not happy.
If paul is both not kind and not calm then someone is creative and vice versa.
Everyone who is wise or generous is rich or creative and vice versa.
Everyone who is either not creative or not strong is either calm or not calm.
Lucy is either strong or brave.
Someone is not generous.
Fred is humble.
Someone is curious or not humble.
Fred is not curious or funny.
Someone is either not happy or not creative. | Lucy is funny. | entailment | (((wise(lucy)<~>~funny(lucy)))<=>((quiet(lucy)|~happy(lucy))))&
(((curious(paul)|brave(paul)))=>(?[X]:(humble(X))))&
(![X]:((wise(X)&~humble(X))=>(calm(X)&wise(X))))&
(![X]:((old(X)&~funny(X))<=>(funny(X)&strong(X))))&
(![X]:(kind(X)=>(funny(X)&~strong(X))))&
(![X]:((rich(X)&~curious(X))<=>(~creative(X)&creative(X))))&
(![X]:((~tall(X)&~happy(X))<=>~kind(X)))&
((?[X]:((~patient(X)|generous(X))))=>(?[X]:((~strong(X)&~funny(X)))))&
(![X]:((~quiet(X)&~humble(X))<=>(~rich(X)|~calm(X))))&
(![X]:((curious(X)|patient(X))=>(~funny(X)<~>~happy(X))))&
(![X]:((rich(X)<~>~strong(X))=>(~curious(X)<~>tall(X))))&
(![X]:((~rich(X)<~>strong(X))<=>(~funny(X)<~>~rich(X))))&
(((strong(lucy)|~brave(lucy)))=>((~strong(susan)<~>~happy(susan))))&
(((~kind(paul)&~calm(paul)))<=>(?[X]:(creative(X))))&
(![X]:((wise(X)|generous(X))<=>(rich(X)|creative(X))))&
(![X]:((~creative(X)<~>~strong(X))=>(calm(X)<~>~calm(X))))&
((strong(lucy)<~>brave(lucy)))&
(?[X]:(~generous(X)))&
(humble(fred))&
(?[X]:((curious(X)|~humble(X))))&
((~curious(fred)|funny(fred)))&
(?[X]:((~happy(X)<~>~creative(X)))) | funny(lucy) | [
"p4",
"p6",
"p7",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 4551871142652752713384661
% SZS output start Proof for 4551871142652752713384661
5. ! [X0] : (kind(X0) => (~strong(X0) & funny(X0))) [input p4]
7. ! [X0] : ((~happy(X0) & ~tall(X0)) <=> ~kind(X0)) [input p6]
8. ? [X0] : (generous(X0) | ~patient(X0)) => ? [X0] : (~funny(X0) & ~strong(X0)) [input p7]
10. ! [X0] : ((patient(X0) | curious(X0)) => (~funny(X0) <~> ~happy(X0))) [input p9]
12. ! [X0] : ((~rich(X0) <~> strong(X0)) <=> (~funny(X0) <~> ~rich(X0))) [input p11]
23. ~funny(lucy) [input hypothesis]
24. ? [X0] : (generous(X0) | ~patient(X0)) => ? [X1] : (~funny(X1) & ~strong(X1)) [rectify 8]
28. ! [X0] : ((~strong(X0) & funny(X0)) | ~kind(X0)) [ennf transformation 5]
29. ? [X1] : (~funny(X1) & ~strong(X1)) | ! [X0] : (~generous(X0) & patient(X0)) [ennf transformation 24]
30. ! [X0] : ((~funny(X0) <~> ~happy(X0)) | (~patient(X0) & ~curious(X0))) [ennf transformation 10]
42. ! [X0] : (((~happy(X0) & ~tall(X0)) | kind(X0)) & (~kind(X0) | (happy(X0) | tall(X0)))) [nnf transformation 7]
43. ! [X0] : (((~happy(X0) & ~tall(X0)) | kind(X0)) & (~kind(X0) | happy(X0) | tall(X0))) [flattening 42]
44. ? [X0] : (~funny(X0) & ~strong(X0)) | ! [X1] : (~generous(X1) & patient(X1)) [rectify 29]
45. ? [X0] : (~funny(X0) & ~strong(X0)) => (~funny(sK1) & ~strong(sK1)) [choice axiom]
46. (~funny(sK1) & ~strong(sK1)) | ! [X1] : (~generous(X1) & patient(X1)) [skolemisation 44,45]
49. ! [X0] : (((happy(X0) | funny(X0)) & (~happy(X0) | ~funny(X0))) | (~patient(X0) & ~curious(X0))) [nnf transformation 30]
51. ! [X0] : ((((~strong(X0) | rich(X0)) & (strong(X0) | ~rich(X0))) | ((~funny(X0) | rich(X0)) & (~rich(X0) | funny(X0)))) & (((rich(X0) | funny(X0)) & (~rich(X0) | ~funny(X0))) | ((~rich(X0) | ~strong(X0)) & (strong(X0) | rich(X0))))) [nnf transformation 12]
83. ~kind(X0) | funny(X0) [cnf transformation 28]
91. ~happy(X0) | kind(X0) [cnf transformation 43]
92. ~strong(sK1) | patient(X1) [cnf transformation 46]
94. ~funny(sK1) | patient(X1) [cnf transformation 46]
104. ~patient(X0) | funny(X0) | happy(X0) [cnf transformation 49]
111. rich(X0) | funny(X0) | strong(X0) | rich(X0) [cnf transformation 51]
113. strong(X0) | ~rich(X0) | ~rich(X0) | funny(X0) [cnf transformation 51]
140. ~funny(lucy) [cnf transformation 23]
142. rich(X0) | funny(X0) | strong(X0) [duplicate literal removal 111]
143. strong(X0) | ~rich(X0) | funny(X0) [duplicate literal removal 113]
156. 3 <=> funny(lucy) [avatar definition]
157. ~funny(lucy) <- (~3) [avatar component clause 156]
188. 9 <=> funny(sK1) [avatar definition]
193. 10 <=> ! [X1] : patient(X1) [avatar definition]
194. patient(X1) <- (10) [avatar component clause 193]
195. 10 | ~9 [avatar split clause 94,188,193]
197. 11 <=> strong(sK1) [avatar definition]
199. ~strong(sK1) <- (~11) [avatar component clause 197]
201. 10 | ~11 [avatar split clause 92,197,193]
204. strong(X0) | funny(X0) [subsumption resolution 142,143]
273. ~3 [avatar split clause 140,156]
285. funny(sK1) <- (~11) [resolution 204,199]
291. 9 | 11 [avatar split clause 285,197,188]
307. happy(X0) | funny(X0) <- (10) [resolution 104,194]
309. funny(X1) | kind(X1) <- (10) [resolution 307,91]
314. funny(X1) <- (10) [subsumption resolution 309,83]
315. $false <- (~3, 10) [resolution 314,157]
320. 3 | ~10 [avatar contradiction clause 315]
321. $false [avatar sat refutation 195,201,273,291,320]
% SZS output end Proof for 4551871142652752713384661
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either strong or not humble is not old or strong and vice versa.
Everyone who is either creative or funny is both kind and not generous and vice versa.
If susan is either generous or happy then someone is either not tall or not funny.
If someone is old then paul is either not calm or old.
Everyone who is not old is both not brave and wise.
Everyone who is both not curious and not quiet is either kind or not wise.
If someone is either generous or old then fred is both not tall and not wise.
If paul is not curious or not humble then someone is either happy or not strong and vice versa.
If lucy is both not calm and wise then someone is curious and vice versa.
Everyone who is either calm or not humble is not curious and vice versa.
If someone is not brave then fred is either not creative or rich.
If someone is either not quiet or old then alice is patient or not rich and vice versa.
If susan is humble or rich then someone is either not generous or not tall.
If someone is tall then mary is either not generous or not wise and vice versa.
Everyone who is not old or not curious is both happy and not brave.
Everyone who is creative is funny or not brave and vice versa.
Mary is either humble or not tall.
Paul is funny or not humble.
Someone is both strong and not patient.
Someone is both not patient and not generous.
Alice is wise or old.
Someone is quiet or not generous.
Alice is both not quiet and curious. | Paul is brave. | contradiction | (![X]:((strong(X)<~>~humble(X))<=>(~old(X)|strong(X))))&
(![X]:((creative(X)<~>funny(X))<=>(kind(X)&~generous(X))))&
(((generous(susan)<~>happy(susan)))=>(?[X]:((~tall(X)<~>~funny(X)))))&
((?[X]:(old(X)))=>((~calm(paul)<~>old(paul))))&
(![X]:(~old(X)=>(~brave(X)&wise(X))))&
(![X]:((~curious(X)&~quiet(X))=>(kind(X)<~>~wise(X))))&
((?[X]:((generous(X)<~>old(X))))=>((~tall(fred)&~wise(fred))))&
(((~curious(paul)|~humble(paul)))<=>(?[X]:((happy(X)<~>~strong(X)))))&
(((~calm(lucy)&wise(lucy)))<=>(?[X]:(curious(X))))&
(![X]:((calm(X)<~>~humble(X))<=>~curious(X)))&
((?[X]:(~brave(X)))=>((~creative(fred)<~>rich(fred))))&
((?[X]:((~quiet(X)<~>old(X))))<=>((patient(alice)|~rich(alice))))&
(((humble(susan)|rich(susan)))=>(?[X]:((~generous(X)<~>~tall(X)))))&
((?[X]:(tall(X)))<=>((~generous(mary)<~>~wise(mary))))&
(![X]:((~old(X)|~curious(X))=>(happy(X)&~brave(X))))&
(![X]:(creative(X)<=>(funny(X)|~brave(X))))&
((humble(mary)<~>~tall(mary)))&
((funny(paul)|~humble(paul)))&
(?[X]:((strong(X)&~patient(X))))&
(?[X]:((~patient(X)&~generous(X))))&
((wise(alice)|old(alice)))&
(?[X]:((quiet(X)|~generous(X))))&
((~quiet(alice)&curious(alice))) | brave(paul) | [
"p0",
"p3",
"p4",
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 766433209147262230153043
% SZS output start Proof for 766433209147262230153043
1. ! [X0] : ((strong(X0) <~> ~humble(X0)) <=> (strong(X0) | ~old(X0))) [input p0]
4. ? [X0] : old(X0) => (~calm(paul) <~> old(paul)) [input p3]
5. ! [X0] : (~old(X0) => (wise(X0) & ~brave(X0))) [input p4]
10. ! [X0] : ((calm(X0) <~> ~humble(X0)) <=> ~curious(X0)) [input p9]
15. ! [X0] : ((~curious(X0) | ~old(X0)) => (~brave(X0) & happy(X0))) [input p14]
24. brave(paul) [input hypothesis]
26. (~calm(paul) <~> old(paul)) | ! [X0] : ~old(X0) [ennf transformation 4]
27. ! [X0] : ((wise(X0) & ~brave(X0)) | old(X0)) [ennf transformation 5]
33. ! [X0] : ((~brave(X0) & happy(X0)) | (curious(X0) & old(X0))) [ennf transformation 15]
34. ! [X0] : ((((humble(X0) | ~strong(X0)) & (~humble(X0) | strong(X0))) | (~strong(X0) & old(X0))) & ((strong(X0) | ~old(X0)) | ((strong(X0) | humble(X0)) & (~humble(X0) | ~strong(X0))))) [nnf transformation 1]
35. ! [X0] : ((((humble(X0) | ~strong(X0)) & (~humble(X0) | strong(X0))) | (~strong(X0) & old(X0))) & (strong(X0) | ~old(X0) | ((strong(X0) | humble(X0)) & (~humble(X0) | ~strong(X0))))) [flattening 34]
41. ((~old(paul) | calm(paul)) & (old(paul) | ~calm(paul))) | ! [X0] : ~old(X0) [nnf transformation 26]
54. ! [X0] : ((((humble(X0) | ~calm(X0)) & (~humble(X0) | calm(X0))) | curious(X0)) & (~curious(X0) | ((calm(X0) | humble(X0)) & (~humble(X0) | ~calm(X0))))) [nnf transformation 10]
78. strong(X0) | ~old(X0) | strong(X0) | humble(X0) [cnf transformation 35]
82. humble(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 35]
94. ~old(paul) | calm(paul) | ~old(X0) [cnf transformation 41]
95. ~brave(X0) | old(X0) [cnf transformation 27]
112. ~curious(X0) | ~humble(X0) | ~calm(X0) [cnf transformation 54]
135. ~brave(X0) | curious(X0) [cnf transformation 33]
150. brave(paul) [cnf transformation 24]
151. strong(X0) | ~old(X0) | humble(X0) [duplicate literal removal 78]
152. ~strong(X0) | humble(X0) [duplicate literal removal 82]
153. ~old(X0) | humble(X0) [subsumption resolution 151,152]
175. 5 <=> ! [X0] : ~old(X0) [avatar definition]
176. ~old(X0) <- (5) [avatar component clause 175]
178. 6 <=> calm(paul) [avatar definition]
182. 7 <=> old(paul) [avatar definition]
183. old(paul) <- (7) [avatar component clause 182]
185. 5 | 6 | ~7 [avatar split clause 94,182,178,175]
209. 13 <=> curious(paul) [avatar definition]
210. curious(paul) <- (13) [avatar component clause 209]
213. 14 <=> humble(paul) [avatar definition]
214. humble(paul) <- (14) [avatar component clause 213]
357. old(paul) [resolution 95,150]
360. 7 [avatar split clause 357,182]
364. curious(paul) [resolution 135,150]
365. 13 [avatar split clause 364,209]
370. humble(paul) <- (7) [resolution 153,183]
377. 14 | ~7 [avatar split clause 370,182,213]
395. ~humble(paul) | ~calm(paul) <- (13) [resolution 112,210]
398. ~calm(paul) <- (13, 14) [subsumption resolution 395,214]
419. ~6 | ~13 | ~14 [avatar split clause 398,213,209,178]
420. $false <- (5, 7) [resolution 176,183]
425. ~5 | ~7 [avatar contradiction clause 420]
426. $false [avatar sat refutation 185,360,365,377,419,425]
% SZS output end Proof for 766433209147262230153043
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either funny or rich is both brave and not strong.
If someone is not tall or not kind then alice is both not quiet and not patient and vice versa.
If lucy is either not happy or not humble then susan is creative.
If someone is either not patient or curious then someone is wise or not patient.
Everyone who is either funny or happy is either strong or not happy and vice versa.
Everyone who is creative or quiet is either not brave or not old.
Everyone who is not generous is curious.
Everyone who is either not humble or not calm is wise and vice versa.
If someone is both quiet and not old then someone is curious.
If someone is not humble then john is old.
Everyone who is both not calm and not quiet is old or patient and vice versa.
If susan is either strong or creative then someone is not strong or happy.
If lucy is both not patient and happy then fred is either not happy or humble.
Everyone who is either not patient or quiet is both not wise and quiet and vice versa.
If someone is both funny and patient then mary is either tall or not calm.
If someone is both kind and quiet then susan is both creative and old and vice versa.
Someone is rich.
Alice is either not creative or not happy.
John is either not wise or calm.
Lucy is tall.
Someone is not calm.
Lucy is not wise.
Someone is old or tall.
Someone is both strong and generous. | Lucy is calm. | contradiction | (![X]:((funny(X)<~>rich(X))=>(brave(X)&~strong(X))))&
((?[X]:((~tall(X)|~kind(X))))<=>((~quiet(alice)&~patient(alice))))&
(((~happy(lucy)<~>~humble(lucy)))=>(creative(susan)))&
((?[X]:((~patient(X)<~>curious(X))))=>(?[X]:((wise(X)|~patient(X)))))&
(![X]:((funny(X)<~>happy(X))<=>(strong(X)<~>~happy(X))))&
(![X]:((creative(X)|quiet(X))=>(~brave(X)<~>~old(X))))&
(![X]:(~generous(X)=>curious(X)))&
(![X]:((~humble(X)<~>~calm(X))<=>wise(X)))&
((?[X]:((quiet(X)&~old(X))))=>(?[X]:(curious(X))))&
((?[X]:(~humble(X)))=>(old(john)))&
(![X]:((~calm(X)&~quiet(X))<=>(old(X)|patient(X))))&
(((strong(susan)<~>creative(susan)))=>(?[X]:((~strong(X)|happy(X)))))&
(((~patient(lucy)&happy(lucy)))=>((~happy(fred)<~>humble(fred))))&
(![X]:((~patient(X)<~>quiet(X))<=>(~wise(X)&quiet(X))))&
((?[X]:((funny(X)&patient(X))))=>((tall(mary)<~>~calm(mary))))&
((?[X]:((kind(X)&quiet(X))))<=>((creative(susan)&old(susan))))&
(?[X]:(rich(X)))&
((~creative(alice)<~>~happy(alice)))&
((~wise(john)<~>calm(john)))&
(tall(lucy))&
(?[X]:(~calm(X)))&
(~wise(lucy))&
(?[X]:((old(X)|tall(X))))&
(?[X]:((strong(X)&generous(X)))) | calm(lucy) | [
"p10",
"p13",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 8791859567395783964434886
% SZS output start Proof for 8791859567395783964434886
11. ! [X0] : ((~quiet(X0) & ~calm(X0)) <=> (patient(X0) | old(X0))) [input p10]
14. ! [X0] : ((~patient(X0) <~> quiet(X0)) <=> (quiet(X0) & ~wise(X0))) [input p13]
22. ~wise(lucy) [input p21]
25. calm(lucy) [input hypothesis]
57. ! [X0] : (((~quiet(X0) & ~calm(X0)) | (~patient(X0) & ~old(X0))) & ((patient(X0) | old(X0)) | (quiet(X0) | calm(X0)))) [nnf transformation 11]
58. ! [X0] : (((~quiet(X0) & ~calm(X0)) | (~patient(X0) & ~old(X0))) & (patient(X0) | old(X0) | quiet(X0) | calm(X0))) [flattening 57]
63. ! [X0] : ((((~quiet(X0) | patient(X0)) & (quiet(X0) | ~patient(X0))) | (~quiet(X0) | wise(X0))) & ((quiet(X0) & ~wise(X0)) | ((~patient(X0) | ~quiet(X0)) & (quiet(X0) | patient(X0))))) [nnf transformation 14]
64. ! [X0] : ((((~quiet(X0) | patient(X0)) & (quiet(X0) | ~patient(X0))) | ~quiet(X0) | wise(X0)) & ((quiet(X0) & ~wise(X0)) | ((~patient(X0) | ~quiet(X0)) & (quiet(X0) | patient(X0))))) [flattening 63]
114. ~calm(X0) | ~patient(X0) [cnf transformation 58]
116. ~patient(X0) | ~quiet(X0) [cnf transformation 58]
123. quiet(X0) | quiet(X0) | patient(X0) [cnf transformation 64]
126. ~quiet(X0) | patient(X0) | ~quiet(X0) | wise(X0) [cnf transformation 64]
140. ~wise(lucy) [cnf transformation 22]
143. calm(lucy) [cnf transformation 25]
144. patient(X0) | quiet(X0) [duplicate literal removal 123]
145. ~quiet(X0) | patient(X0) | wise(X0) [duplicate literal removal 126]
240. 21 <=> patient(lucy) [avatar definition]
241. ~patient(lucy) <- (~21) [avatar component clause 240]
253. ~quiet(X0) | wise(X0) [subsumption resolution 145,116]
319. ~patient(lucy) [resolution 114,143]
320. ~21 [avatar split clause 319,240]
325. quiet(lucy) <- (~21) [resolution 144,241]
340. wise(lucy) <- (~21) [resolution 253,325]
342. $false <- (~21) [subsumption resolution 340,140]
343. 21 [avatar contradiction clause 342]
345. $false [avatar sat refutation 320,343]
% SZS output end Proof for 8791859567395783964434886
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not kind is tall or not curious.
Everyone who is creative or not patient is not kind and vice versa.
If someone is not funny then susan is both not wise and patient and vice versa.
If someone is either curious or tall then someone is either not happy or not generous and vice versa.
Everyone who is creative or not humble is curious.
If john is both not creative and not curious then mary is both not curious and not humble.
Everyone who is humble is both creative and not curious and vice versa.
Everyone who is both old and not creative is both calm and not strong and vice versa.
Everyone who is both not quiet and brave is not creative or old and vice versa.
Everyone who is not quiet is happy or tall.
If someone is calm or funny then someone is both humble and strong.
If someone is both not creative and generous then someone is not generous or happy.
If mary is not funny then john is both generous and creative and vice versa.
Everyone who is both not calm and not wise is not creative.
If someone is not tall or not strong then someone is brave or not tall.
Someone is not old.
Fred is not humble or old.
Fred is strong.
Mary is either not funny or not creative.
Someone is both curious and not calm.
Someone is not curious or not generous.
Alice is either happy or rich.
Someone is either not rich or not brave. | Alice is not calm. | entailment | (![X]:(~kind(X)=>(tall(X)|~curious(X))))&
(![X]:((creative(X)|~patient(X))<=>~kind(X)))&
((?[X]:(~funny(X)))<=>((~wise(susan)&patient(susan))))&
((?[X]:((curious(X)<~>tall(X))))<=>(?[X]:((~happy(X)<~>~generous(X)))))&
(![X]:((creative(X)|~humble(X))=>curious(X)))&
(((~creative(john)&~curious(john)))=>((~curious(mary)&~humble(mary))))&
(![X]:(humble(X)<=>(creative(X)&~curious(X))))&
(![X]:((old(X)&~creative(X))<=>(calm(X)&~strong(X))))&
(![X]:((~quiet(X)&brave(X))<=>(~creative(X)|old(X))))&
(![X]:(~quiet(X)=>(happy(X)|tall(X))))&
((?[X]:((calm(X)|funny(X))))=>(?[X]:((humble(X)&strong(X)))))&
((?[X]:((~creative(X)&generous(X))))=>(?[X]:((~generous(X)|happy(X)))))&
((~funny(mary))<=>((generous(john)&creative(john))))&
(![X]:((~calm(X)&~wise(X))=>~creative(X)))&
((?[X]:((~tall(X)|~strong(X))))=>(?[X]:((brave(X)|~tall(X)))))&
(?[X]:(~old(X)))&
((~humble(fred)|old(fred)))&
(strong(fred))&
((~funny(mary)<~>~creative(mary)))&
(?[X]:((curious(X)&~calm(X))))&
(?[X]:((~curious(X)|~generous(X))))&
((happy(alice)<~>rich(alice)))&
(?[X]:((~rich(X)<~>~brave(X)))) | ~calm(alice) | [
"p4",
"p6",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 6066892359468438994957817
% SZS output start Proof for 6066892359468438994957817
5. ! [X0] : ((~humble(X0) | creative(X0)) => curious(X0)) [input p4]
7. ! [X0] : (humble(X0) <=> (~curious(X0) & creative(X0))) [input p6]
11. ? [X0] : (funny(X0) | calm(X0)) => ? [X0] : (strong(X0) & humble(X0)) [input p10]
24. calm(alice) [input hypothesis]
26. ? [X0] : (funny(X0) | calm(X0)) => ? [X1] : (strong(X1) & humble(X1)) [rectify 11]
33. ! [X0] : (curious(X0) | (humble(X0) & ~creative(X0))) [ennf transformation 5]
38. ? [X1] : (strong(X1) & humble(X1)) | ! [X0] : (~funny(X0) & ~calm(X0)) [ennf transformation 26]
53. ! [X0] : ((humble(X0) | (curious(X0) | ~creative(X0))) & ((~curious(X0) & creative(X0)) | ~humble(X0))) [nnf transformation 7]
54. ! [X0] : ((humble(X0) | curious(X0) | ~creative(X0)) & ((~curious(X0) & creative(X0)) | ~humble(X0))) [flattening 53]
59. ? [X0] : (strong(X0) & humble(X0)) | ! [X1] : (~funny(X1) & ~calm(X1)) [rectify 38]
60. ? [X0] : (strong(X0) & humble(X0)) => (strong(sK3) & humble(sK3)) [choice axiom]
61. (strong(sK3) & humble(sK3)) | ! [X1] : (~funny(X1) & ~calm(X1)) [skolemisation 59,60]
95. ~creative(X0) | curious(X0) [cnf transformation 33]
96. humble(X0) | curious(X0) [cnf transformation 33]
99. ~humble(X0) | creative(X0) [cnf transformation 54]
100. ~humble(X0) | ~curious(X0) [cnf transformation 54]
112. humble(sK3) | ~calm(X1) [cnf transformation 61]
135. calm(alice) [cnf transformation 24]
215. 18 <=> ! [X1] : ~calm(X1) [avatar definition]
216. ~calm(X1) <- (18) [avatar component clause 215]
219. 19 <=> humble(sK3) [avatar definition]
221. humble(sK3) <- (19) [avatar component clause 219]
223. 18 | 19 [avatar split clause 112,219,215]
311. $false <- (18) [resolution 216,135]
312. ~18 [avatar contradiction clause 311]
320. creative(X0) | curious(X0) [resolution 99,96]
322. curious(X0) [subsumption resolution 320,95]
326. ~curious(sK3) <- (19) [resolution 100,221]
328. $false <- (19) [subsumption resolution 326,322]
329. ~19 [avatar contradiction clause 328]
330. $false [avatar sat refutation 223,312,329]
% SZS output end Proof for 6066892359468438994957817
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not curious and kind is happy and vice versa.
If lucy is both brave and humble then someone is patient or wise.
Everyone who is rich is either creative or not calm and vice versa.
If someone is either curious or creative then susan is either calm or creative.
If mary is generous then someone is not brave or not patient and vice versa.
Everyone who is either not wise or not happy is kind or patient and vice versa.
Everyone who is either not tall or not calm is not rich.
Everyone who is both rich and not patient is tall or curious.
Everyone who is not creative is both not quiet and happy.
If someone is brave or strong then someone is either not tall or happy and vice versa.
Everyone who is not wise or not kind is happy.
If fred is either not calm or tall then lucy is not brave or kind.
Everyone who is not curious or generous is curious and vice versa.
Everyone who is either not happy or not calm is not tall and vice versa.
Everyone who is either tall or not quiet is either wise or not funny and vice versa.
Susan is not happy.
Fred is not patient.
Mary is brave or curious.
Someone is patient.
Susan is calm or not rich. | Susan is not strong. | entailment | (![X]:((~curious(X)&kind(X))<=>happy(X)))&
(((brave(lucy)&humble(lucy)))=>(?[X]:((patient(X)|wise(X)))))&
(![X]:(rich(X)<=>(creative(X)<~>~calm(X))))&
((?[X]:((curious(X)<~>creative(X))))=>((calm(susan)<~>creative(susan))))&
((generous(mary))<=>(?[X]:((~brave(X)|~patient(X)))))&
(![X]:((~wise(X)<~>~happy(X))<=>(kind(X)|patient(X))))&
(![X]:((~tall(X)<~>~calm(X))=>~rich(X)))&
(![X]:((rich(X)&~patient(X))=>(tall(X)|curious(X))))&
(![X]:(~creative(X)=>(~quiet(X)&happy(X))))&
((?[X]:((brave(X)|strong(X))))<=>(?[X]:((~tall(X)<~>happy(X)))))&
(![X]:((~wise(X)|~kind(X))=>happy(X)))&
(((~calm(fred)<~>tall(fred)))=>((~brave(lucy)|kind(lucy))))&
(![X]:((~curious(X)|generous(X))<=>curious(X)))&
(![X]:((~happy(X)<~>~calm(X))<=>~tall(X)))&
(![X]:((tall(X)<~>~quiet(X))<=>(wise(X)<~>~funny(X))))&
(~happy(susan))&
(~patient(fred))&
((brave(mary)|curious(mary)))&
(?[X]:(patient(X)))&
((calm(susan)|~rich(susan))) | ~strong(susan) | [
"p0",
"p2",
"p6",
"p8",
"p9",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 366417170627980887364333
% SZS output start Proof for 366417170627980887364333
1. ! [X0] : ((kind(X0) & ~curious(X0)) <=> happy(X0)) [input p0]
3. ! [X0] : (rich(X0) <=> (creative(X0) <~> ~calm(X0))) [input p2]
7. ! [X0] : ((~tall(X0) <~> ~calm(X0)) => ~rich(X0)) [input p6]
9. ! [X0] : (~creative(X0) => (happy(X0) & ~quiet(X0))) [input p8]
10. ? [X0] : (strong(X0) | brave(X0)) <=> ? [X0] : (~tall(X0) <~> happy(X0)) [input p9]
13. ! [X0] : ((generous(X0) | ~curious(X0)) <=> curious(X0)) [input p12]
14. ! [X0] : ((~happy(X0) <~> ~calm(X0)) <=> ~tall(X0)) [input p13]
21. strong(susan) [input hypothesis]
22. ? [X0] : (strong(X0) | brave(X0)) <=> ? [X1] : (~tall(X1) <~> happy(X1)) [rectify 10]
23. ! [X0] : ((creative(X0) <~> ~calm(X0)) => rich(X0)) [unused predicate definition removal 3]
25. ! [X0] : (rich(X0) | (creative(X0) <=> ~calm(X0))) [ennf transformation 23]
27. ! [X0] : (~rich(X0) | (~tall(X0) <=> ~calm(X0))) [ennf transformation 7]
30. ! [X0] : ((happy(X0) & ~quiet(X0)) | creative(X0)) [ennf transformation 9]
34. ! [X0] : (((kind(X0) & ~curious(X0)) | ~happy(X0)) & (happy(X0) | (~kind(X0) | curious(X0)))) [nnf transformation 1]
35. ! [X0] : (((kind(X0) & ~curious(X0)) | ~happy(X0)) & (happy(X0) | ~kind(X0) | curious(X0))) [flattening 34]
36. ! [X0] : (rich(X0) | ((creative(X0) | calm(X0)) & (~calm(X0) | ~creative(X0)))) [nnf transformation 25]
44. ! [X0] : (~rich(X0) | ((~tall(X0) | calm(X0)) & (~calm(X0) | tall(X0)))) [nnf transformation 27]
45. (? [X0] : (strong(X0) | brave(X0)) | ! [X1] : ((~tall(X1) | ~happy(X1)) & (happy(X1) | tall(X1)))) & (? [X1] : ((~happy(X1) | tall(X1)) & (happy(X1) | ~tall(X1))) | ! [X0] : (~strong(X0) & ~brave(X0))) [nnf transformation 22]
46. (? [X0] : (strong(X0) | brave(X0)) | ! [X1] : ((~tall(X1) | ~happy(X1)) & (happy(X1) | tall(X1)))) & (? [X2] : ((~happy(X2) | tall(X2)) & (happy(X2) | ~tall(X2))) | ! [X3] : (~strong(X3) & ~brave(X3))) [rectify 45]
47. ? [X0] : (strong(X0) | brave(X0)) => (strong(sK1) | brave(sK1)) [choice axiom]
48. ? [X2] : ((~happy(X2) | tall(X2)) & (happy(X2) | ~tall(X2))) => ((~happy(sK2) | tall(sK2)) & (happy(sK2) | ~tall(sK2))) [choice axiom]
49. ((strong(sK1) | brave(sK1)) | ! [X1] : ((~tall(X1) | ~happy(X1)) & (happy(X1) | tall(X1)))) & (((~happy(sK2) | tall(sK2)) & (happy(sK2) | ~tall(sK2))) | ! [X3] : (~strong(X3) & ~brave(X3))) [skolemisation 46,48,47]
51. ! [X0] : (((generous(X0) | ~curious(X0)) | ~curious(X0)) & (curious(X0) | (~generous(X0) & curious(X0)))) [nnf transformation 13]
52. ! [X0] : ((generous(X0) | ~curious(X0) | ~curious(X0)) & (curious(X0) | (~generous(X0) & curious(X0)))) [flattening 51]
53. ! [X0] : ((((calm(X0) | happy(X0)) & (~calm(X0) | ~happy(X0))) | tall(X0)) & (~tall(X0) | ((~happy(X0) | calm(X0)) & (~calm(X0) | happy(X0))))) [nnf transformation 14]
58. ~happy(X0) | ~curious(X0) [cnf transformation 35]
60. ~calm(X0) | rich(X0) | ~creative(X0) [cnf transformation 36]
75. ~calm(X0) | ~rich(X0) | tall(X0) [cnf transformation 44]
79. creative(X0) | happy(X0) [cnf transformation 30]
81. happy(sK2) | ~tall(sK2) | ~strong(X3) [cnf transformation 49]
90. curious(X0) | curious(X0) [cnf transformation 52]
96. tall(X0) | happy(X0) | calm(X0) [cnf transformation 53]
110. strong(susan) [cnf transformation 21]
111. curious(X0) [duplicate literal removal 90]
171. 14 <=> ! [X3] : ~strong(X3) [avatar definition]
172. ~strong(X3) <- (14) [avatar component clause 171]
174. 15 <=> tall(sK2) [avatar definition]
175. ~tall(sK2) <- (~15) [avatar component clause 174]
178. 16 <=> happy(sK2) [avatar definition]
179. happy(sK2) <- (16) [avatar component clause 178]
180. ~happy(sK2) <- (~16) [avatar component clause 178]
186. 14 | ~15 | 16 [avatar split clause 81,178,174,171]
242. ~curious(sK2) <- (16) [resolution 179,58]
243. $false <- (16) [subsumption resolution 242,111]
244. ~16 [avatar contradiction clause 243]
246. 19 <=> calm(sK2) [avatar definition]
248. calm(sK2) <- (19) [avatar component clause 246]
250. 20 <=> rich(sK2) [avatar definition]
252. ~rich(sK2) <- (~20) [avatar component clause 250]
256. $false <- (14) [resolution 172,110]
257. ~14 [avatar contradiction clause 256]
261. happy(sK2) | calm(sK2) <- (~15) [resolution 175,96]
262. calm(sK2) <- (~15, ~16) [subsumption resolution 261,180]
265. 19 | 15 | 16 [avatar split clause 262,178,174,246]
269. ~rich(sK2) | tall(sK2) <- (19) [resolution 248,75]
270. rich(sK2) | ~creative(sK2) <- (19) [resolution 248,60]
271. ~creative(sK2) <- (19, ~20) [subsumption resolution 270,252]
272. happy(sK2) <- (19, ~20) [resolution 271,79]
273. $false <- (~16, 19, ~20) [subsumption resolution 272,180]
274. 16 | ~19 | 20 [avatar contradiction clause 273]
280. ~rich(sK2) <- (~15, 19) [subsumption resolution 269,175]
281. ~20 | 15 | ~19 [avatar split clause 280,246,174,250]
282. $false [avatar sat refutation 186,244,257,265,274,281]
% SZS output end Proof for 366417170627980887364333
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not creative and quiet then someone is either not tall or not kind.
Everyone who is strong or not rich is not quiet or not calm and vice versa.
Everyone who is both happy and brave is both not happy and strong and vice versa.
Everyone who is old or not funny is not curious or happy and vice versa.
Everyone who is not generous or not humble is not calm or not generous and vice versa.
If fred is both not generous and quiet then mary is not quiet or not wise.
Everyone who is not quiet is curious or not patient and vice versa.
If someone is both not happy and not rich then mary is both not strong and quiet and vice versa.
Everyone who is either quiet or not generous is not happy.
If fred is not calm or generous then someone is either not strong or old.
If susan is happy then fred is either not calm or not strong.
If john is not generous or not brave then john is either brave or not rich.
Everyone who is both not rich and not strong is not strong or rich.
Everyone who is brave or patient is not old or patient and vice versa.
If someone is not patient then lucy is either curious or calm and vice versa.
If someone is either not curious or funny then alice is both wise and not kind and vice versa.
Someone is not curious.
Lucy is tall or kind.
Someone is both not generous and not quiet.
Someone is both wise and quiet.
John is both creative and not curious.
Someone is funny or not tall.
Fred is both not tall and strong.
Someone is both humble and not patient. | Mary is not patient. | contradiction | ((?[X]:((~creative(X)&quiet(X))))=>(?[X]:((~tall(X)<~>~kind(X)))))&
(![X]:((strong(X)|~rich(X))<=>(~quiet(X)|~calm(X))))&
(![X]:((happy(X)&brave(X))<=>(~happy(X)&strong(X))))&
(![X]:((old(X)|~funny(X))<=>(~curious(X)|happy(X))))&
(![X]:((~generous(X)|~humble(X))<=>(~calm(X)|~generous(X))))&
(((~generous(fred)&quiet(fred)))=>((~quiet(mary)|~wise(mary))))&
(![X]:(~quiet(X)<=>(curious(X)|~patient(X))))&
((?[X]:((~happy(X)&~rich(X))))<=>((~strong(mary)&quiet(mary))))&
(![X]:((quiet(X)<~>~generous(X))=>~happy(X)))&
(((~calm(fred)|generous(fred)))=>(?[X]:((~strong(X)<~>old(X)))))&
((happy(susan))=>((~calm(fred)<~>~strong(fred))))&
(((~generous(john)|~brave(john)))=>((brave(john)<~>~rich(john))))&
(![X]:((~rich(X)&~strong(X))=>(~strong(X)|rich(X))))&
(![X]:((brave(X)|patient(X))<=>(~old(X)|patient(X))))&
((?[X]:(~patient(X)))<=>((curious(lucy)<~>calm(lucy))))&
((?[X]:((~curious(X)<~>funny(X))))<=>((wise(alice)&~kind(alice))))&
(?[X]:(~curious(X)))&
((tall(lucy)|kind(lucy)))&
(?[X]:((~generous(X)&~quiet(X))))&
(?[X]:((wise(X)&quiet(X))))&
((creative(john)&~curious(john)))&
(?[X]:((funny(X)|~tall(X))))&
((~tall(fred)&strong(fred)))&
(?[X]:((humble(X)&~patient(X)))) | ~patient(mary) | [
"p1",
"p2",
"p6",
"p7",
"p8",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 6780116167121385120912164
% SZS output start Proof for 6780116167121385120912164
2. ! [X0] : ((~rich(X0) | strong(X0)) <=> (~calm(X0) | ~quiet(X0))) [input p1]
3. ! [X0] : ((brave(X0) & happy(X0)) <=> (strong(X0) & ~happy(X0))) [input p2]
7. ! [X0] : (~quiet(X0) <=> (~patient(X0) | curious(X0))) [input p6]
8. ? [X0] : (~rich(X0) & ~happy(X0)) <=> (quiet(mary) & ~strong(mary)) [input p7]
9. ! [X0] : ((quiet(X0) <~> ~generous(X0)) => ~happy(X0)) [input p8]
19. ? [X0] : (~quiet(X0) & ~generous(X0)) [input p18]
25. ~patient(mary) [input hypothesis]
31. ! [X0] : (~happy(X0) | (quiet(X0) <=> ~generous(X0))) [ennf transformation 9]
37. ! [X0] : (((~rich(X0) | strong(X0)) | (calm(X0) & quiet(X0))) & ((~calm(X0) | ~quiet(X0)) | (rich(X0) & ~strong(X0)))) [nnf transformation 2]
38. ! [X0] : ((~rich(X0) | strong(X0) | (calm(X0) & quiet(X0))) & (~calm(X0) | ~quiet(X0) | (rich(X0) & ~strong(X0)))) [flattening 37]
39. ! [X0] : (((brave(X0) & happy(X0)) | (~strong(X0) | happy(X0))) & ((strong(X0) & ~happy(X0)) | (~brave(X0) | ~happy(X0)))) [nnf transformation 3]
40. ! [X0] : (((brave(X0) & happy(X0)) | ~strong(X0) | happy(X0)) & ((strong(X0) & ~happy(X0)) | ~brave(X0) | ~happy(X0))) [flattening 39]
45. ! [X0] : ((~quiet(X0) | (patient(X0) & ~curious(X0))) & ((~patient(X0) | curious(X0)) | quiet(X0))) [nnf transformation 7]
46. ! [X0] : ((~quiet(X0) | (patient(X0) & ~curious(X0))) & (~patient(X0) | curious(X0) | quiet(X0))) [flattening 45]
47. (? [X0] : (~rich(X0) & ~happy(X0)) | (~quiet(mary) | strong(mary))) & ((quiet(mary) & ~strong(mary)) | ! [X0] : (rich(X0) | happy(X0))) [nnf transformation 8]
48. (? [X0] : (~rich(X0) & ~happy(X0)) | ~quiet(mary) | strong(mary)) & ((quiet(mary) & ~strong(mary)) | ! [X0] : (rich(X0) | happy(X0))) [flattening 47]
49. (? [X0] : (~rich(X0) & ~happy(X0)) | ~quiet(mary) | strong(mary)) & ((quiet(mary) & ~strong(mary)) | ! [X1] : (rich(X1) | happy(X1))) [rectify 48]
50. ? [X0] : (~rich(X0) & ~happy(X0)) => (~rich(sK0) & ~happy(sK0)) [choice axiom]
51. ((~rich(sK0) & ~happy(sK0)) | ~quiet(mary) | strong(mary)) & ((quiet(mary) & ~strong(mary)) | ! [X1] : (rich(X1) | happy(X1))) [skolemisation 49,50]
52. ! [X0] : (~happy(X0) | ((quiet(X0) | generous(X0)) & (~generous(X0) | ~quiet(X0)))) [nnf transformation 31]
71. ? [X0] : (~quiet(X0) & ~generous(X0)) => (~quiet(sK5) & ~generous(sK5)) [choice axiom]
72. ~quiet(sK5) & ~generous(sK5) [skolemisation 19,71]
81. ~rich(X0) | strong(X0) | quiet(X0) [cnf transformation 38]
85. happy(X0) | ~strong(X0) | happy(X0) [cnf transformation 40]
98. ~quiet(X0) | patient(X0) [cnf transformation 46]
100. quiet(mary) | rich(X1) | happy(X1) [cnf transformation 51]
104. ~happy(X0) | quiet(X0) | generous(X0) [cnf transformation 52]
132. ~generous(sK5) [cnf transformation 72]
133. ~quiet(sK5) [cnf transformation 72]
142. ~patient(mary) [cnf transformation 25]
146. ~strong(X0) | happy(X0) [duplicate literal removal 85]
156. 3 <=> quiet(mary) [avatar definition]
157. quiet(mary) <- (3) [avatar component clause 156]
179. 8 <=> ! [X1] : (rich(X1) | happy(X1)) [avatar definition]
180. happy(X1) | rich(X1) <- (8) [avatar component clause 179]
181. 8 | 3 [avatar split clause 100,156,179]
291. patient(mary) <- (3) [resolution 98,157]
292. $false <- (3) [subsumption resolution 291,142]
293. ~3 [avatar contradiction clause 292]
337. generous(X0) | quiet(X0) | rich(X0) <- (8) [resolution 104,180]
425. quiet(sK5) | rich(sK5) <- (8) [resolution 337,132]
428. rich(sK5) <- (8) [subsumption resolution 425,133]
606. strong(sK5) | quiet(sK5) <- (8) [resolution 428,81]
612. 71 <=> strong(sK5) [avatar definition]
614. strong(sK5) <- (71) [avatar component clause 612]
616. strong(sK5) <- (8) [subsumption resolution 606,133]
617. 71 | ~8 [avatar split clause 616,179,612]
711. happy(sK5) <- (71) [resolution 614,146]
713. 81 <=> happy(sK5) [avatar definition]
715. happy(sK5) <- (81) [avatar component clause 713]
721. 81 | ~71 [avatar split clause 711,612,713]
766. quiet(sK5) | generous(sK5) <- (81) [resolution 715,104]
767. generous(sK5) <- (81) [subsumption resolution 766,133]
768. $false <- (81) [subsumption resolution 767,132]
769. ~81 [avatar contradiction clause 768]
770. $false [avatar sat refutation 181,293,617,721,769]
% SZS output end Proof for 6780116167121385120912164
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not kind or kind is both not brave and calm and vice versa.
If paul is either strong or not humble then someone is both not strong and not brave.
Everyone who is both not old and generous is either not old or patient and vice versa.
Everyone who is not brave is either kind or curious.
If mary is rich or not wise then someone is both patient and not tall.
If someone is tall then susan is curious.
If someone is not brave or generous then alice is either not old or not tall and vice versa.
If fred is both tall and not kind then susan is creative and vice versa.
Everyone who is happy is not quiet.
Everyone who is both patient and kind is not patient or patient.
Everyone who is both not tall and not humble is not wise and vice versa.
Everyone who is not happy or not patient is both not happy and generous.
If mary is patient then someone is both creative and not kind and vice versa.
Everyone who is not patient is wise and vice versa.
Everyone who is not strong or not generous is not strong or not brave and vice versa.
If someone is generous then someone is not funny or generous and vice versa.
Someone is not patient or calm.
Paul is either quiet or brave.
Fred is either not strong or not brave.
Lucy is either rich or not generous.
Someone is happy or not strong.
Alice is not generous or creative.
Someone is either patient or not tall.
Someone is creative. | Fred is not patient. | contradiction | (![X]:((~kind(X)<~>kind(X))<=>(~brave(X)&calm(X))))&
(((strong(paul)<~>~humble(paul)))=>(?[X]:((~strong(X)&~brave(X)))))&
(![X]:((~old(X)&generous(X))<=>(~old(X)<~>patient(X))))&
(![X]:(~brave(X)=>(kind(X)<~>curious(X))))&
(((rich(mary)|~wise(mary)))=>(?[X]:((patient(X)&~tall(X)))))&
((?[X]:(tall(X)))=>(curious(susan)))&
((?[X]:((~brave(X)|generous(X))))<=>((~old(alice)<~>~tall(alice))))&
(((tall(fred)&~kind(fred)))<=>(creative(susan)))&
(![X]:(happy(X)=>~quiet(X)))&
(![X]:((patient(X)&kind(X))=>(~patient(X)|patient(X))))&
(![X]:((~tall(X)&~humble(X))<=>~wise(X)))&
(![X]:((~happy(X)|~patient(X))=>(~happy(X)&generous(X))))&
((patient(mary))<=>(?[X]:((creative(X)&~kind(X)))))&
(![X]:(~patient(X)<=>wise(X)))&
(![X]:((~strong(X)|~generous(X))<=>(~strong(X)|~brave(X))))&
((?[X]:(generous(X)))<=>(?[X]:((~funny(X)|generous(X)))))&
(?[X]:((~patient(X)|calm(X))))&
((quiet(paul)<~>brave(paul)))&
((~strong(fred)<~>~brave(fred)))&
((rich(lucy)<~>~generous(lucy)))&
(?[X]:((happy(X)|~strong(X))))&
((~generous(alice)|creative(alice)))&
(?[X]:((patient(X)<~>~tall(X))))&
(?[X]:(creative(X))) | ~patient(fred) | [
"p0",
"p11",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 2798434136187994612515601
% SZS output start Proof for 2798434136187994612515601
1. ! [X0] : ((~kind(X0) <~> kind(X0)) <=> (calm(X0) & ~brave(X0))) [input p0]
12. ! [X0] : ((~patient(X0) | ~happy(X0)) => (generous(X0) & ~happy(X0))) [input p11]
15. ! [X0] : ((~generous(X0) | ~strong(X0)) <=> (~brave(X0) | ~strong(X0))) [input p14]
19. ~strong(fred) <~> ~brave(fred) [input p18]
25. ~patient(fred) [input hypothesis]
34. ! [X0] : ((generous(X0) & ~happy(X0)) | (patient(X0) & happy(X0))) [ennf transformation 12]
35. ! [X0] : ((((~kind(X0) | kind(X0)) & (kind(X0) | ~kind(X0))) | (~calm(X0) | brave(X0))) & ((calm(X0) & ~brave(X0)) | ((~kind(X0) | ~kind(X0)) & (kind(X0) | kind(X0))))) [nnf transformation 1]
36. ! [X0] : ((((~kind(X0) | kind(X0)) & (kind(X0) | ~kind(X0))) | ~calm(X0) | brave(X0)) & ((calm(X0) & ~brave(X0)) | ((~kind(X0) | ~kind(X0)) & (kind(X0) | kind(X0))))) [flattening 35]
58. ! [X0] : (((~generous(X0) | ~strong(X0)) | (brave(X0) & strong(X0))) & ((~brave(X0) | ~strong(X0)) | (generous(X0) & strong(X0)))) [nnf transformation 15]
59. ! [X0] : ((~generous(X0) | ~strong(X0) | (brave(X0) & strong(X0))) & (~brave(X0) | ~strong(X0) | (generous(X0) & strong(X0)))) [flattening 58]
68. (brave(fred) | strong(fred)) & (~brave(fred) | ~strong(fred)) [nnf transformation 19]
77. ~brave(X0) | kind(X0) | kind(X0) [cnf transformation 36]
78. ~brave(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 36]
117. patient(X0) | generous(X0) [cnf transformation 34]
126. ~generous(X0) | ~strong(X0) | brave(X0) [cnf transformation 59]
134. brave(fred) | strong(fred) [cnf transformation 68]
142. ~patient(fred) [cnf transformation 25]
146. ~brave(X0) | kind(X0) [duplicate literal removal 77]
147. ~brave(X0) | ~kind(X0) [duplicate literal removal 78]
151. ~brave(X0) [subsumption resolution 146,147]
247. ~generous(X0) | ~strong(X0) [subsumption resolution 126,151]
267. strong(fred) [subsumption resolution 134,151]
309. generous(fred) [resolution 117,142]
320. ~strong(fred) [resolution 247,309]
324. $false [subsumption resolution 320,267]
% SZS output end Proof for 2798434136187994612515601
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not happy or curious is not curious and vice versa.
If someone is both generous and not curious then someone is either old or generous and vice versa.
Everyone who is both strong and not curious is either funny or calm and vice versa.
If fred is not strong then someone is both brave and not patient and vice versa.
Everyone who is not strong is both not kind and not patient.
Everyone who is both happy and not quiet is either kind or not tall and vice versa.
Everyone who is either brave or humble is strong or creative.
Everyone who is both not tall and patient is funny or patient.
If alice is tall or old then paul is not old and vice versa.
Everyone who is both wise and generous is strong and vice versa.
If someone is not funny then someone is either humble or happy.
If lucy is both strong and tall then susan is either not funny or not old and vice versa.
Everyone who is funny is not wise.
Everyone who is both creative and tall is old or funny.
If someone is either patient or not humble then someone is either not curious or not kind.
If mary is not brave then alice is patient.
Someone is not brave.
Paul is either not quiet or not curious.
Lucy is both not generous and not funny.
Someone is both wise and not brave.
Lucy is both not brave and not curious.
Someone is both not humble and creative.
Lucy is not generous.
Fred is quiet. | Paul is not old. | neutral | (![X]:((~happy(X)<~>curious(X))<=>~curious(X)))&
((?[X]:((generous(X)&~curious(X))))<=>(?[X]:((old(X)<~>generous(X)))))&
(![X]:((strong(X)&~curious(X))<=>(funny(X)<~>calm(X))))&
((~strong(fred))<=>(?[X]:((brave(X)&~patient(X)))))&
(![X]:(~strong(X)=>(~kind(X)&~patient(X))))&
(![X]:((happy(X)&~quiet(X))<=>(kind(X)<~>~tall(X))))&
(![X]:((brave(X)<~>humble(X))=>(strong(X)|creative(X))))&
(![X]:((~tall(X)&patient(X))=>(funny(X)|patient(X))))&
(((tall(alice)|old(alice)))<=>(~old(paul)))&
(![X]:((wise(X)&generous(X))<=>strong(X)))&
((?[X]:(~funny(X)))=>(?[X]:((humble(X)<~>happy(X)))))&
(((strong(lucy)&tall(lucy)))<=>((~funny(susan)<~>~old(susan))))&
(![X]:(funny(X)=>~wise(X)))&
(![X]:((creative(X)&tall(X))=>(old(X)|funny(X))))&
((?[X]:((patient(X)<~>~humble(X))))=>(?[X]:((~curious(X)<~>~kind(X)))))&
((~brave(mary))=>(patient(alice)))&
(?[X]:(~brave(X)))&
((~quiet(paul)<~>~curious(paul)))&
((~generous(lucy)&~funny(lucy)))&
(?[X]:((wise(X)&~brave(X))))&
((~brave(lucy)&~curious(lucy)))&
(?[X]:((~humble(X)&creative(X))))&
(~generous(lucy))&
(quiet(fred)) | ~old(paul) | [] | null | 0 |
Everyone who is either not patient or wise is not curious and vice versa.
Everyone who is patient or old is both not tall and brave and vice versa.
Everyone who is either not tall or creative is both not curious and happy and vice versa.
Everyone who is not funny is not wise.
Everyone who is not quiet is happy or tall and vice versa.
Everyone who is curious or old is either not wise or curious.
If john is not patient or old then someone is not creative or not humble and vice versa.
Everyone who is not strong or not old is not curious or not brave.
Everyone who is either not funny or not quiet is not curious.
If someone is either not creative or not rich then someone is either not tall or creative and vice versa.
Everyone who is both patient and old is either tall or not kind.
Everyone who is not quiet or not rich is either not old or wise.
If susan is both not happy and not funny then someone is not calm or calm and vice versa.
If someone is both not creative and not humble then lucy is both not funny and not kind.
Everyone who is happy or not strong is both funny and creative and vice versa.
Everyone who is both creative and not tall is kind and vice versa.
Someone is either not old or not generous.
Someone is both not strong and not humble.
Someone is not rich.
Someone is not generous or funny.
Fred is both not happy and not brave.
Someone is both kind and humble.
Someone is either rich or not old.
Someone is patient or curious. | Lucy is funny. | neutral | (![X]:((~patient(X)<~>wise(X))<=>~curious(X)))&
(![X]:((patient(X)|old(X))<=>(~tall(X)&brave(X))))&
(![X]:((~tall(X)<~>creative(X))<=>(~curious(X)&happy(X))))&
(![X]:(~funny(X)=>~wise(X)))&
(![X]:(~quiet(X)<=>(happy(X)|tall(X))))&
(![X]:((curious(X)|old(X))=>(~wise(X)<~>curious(X))))&
(((~patient(john)|old(john)))<=>(?[X]:((~creative(X)|~humble(X)))))&
(![X]:((~strong(X)|~old(X))=>(~curious(X)|~brave(X))))&
(![X]:((~funny(X)<~>~quiet(X))=>~curious(X)))&
((?[X]:((~creative(X)<~>~rich(X))))<=>(?[X]:((~tall(X)<~>creative(X)))))&
(![X]:((patient(X)&old(X))=>(tall(X)<~>~kind(X))))&
(![X]:((~quiet(X)|~rich(X))=>(~old(X)<~>wise(X))))&
(((~happy(susan)&~funny(susan)))<=>(?[X]:((~calm(X)|calm(X)))))&
((?[X]:((~creative(X)&~humble(X))))=>((~funny(lucy)&~kind(lucy))))&
(![X]:((happy(X)|~strong(X))<=>(funny(X)&creative(X))))&
(![X]:((creative(X)&~tall(X))<=>kind(X)))&
(?[X]:((~old(X)<~>~generous(X))))&
(?[X]:((~strong(X)&~humble(X))))&
(?[X]:(~rich(X)))&
(?[X]:((~generous(X)|funny(X))))&
((~happy(fred)&~brave(fred)))&
(?[X]:((kind(X)&humble(X))))&
(?[X]:((rich(X)<~>~old(X))))&
(?[X]:((patient(X)|curious(X)))) | funny(lucy) | [] | null | 0 |
If alice is not strong or not curious then someone is either not wise or creative and vice versa.
If lucy is not generous then someone is quiet or rich and vice versa.
If mary is both not happy and not generous then alice is either strong or happy and vice versa.
If someone is either happy or not humble then lucy is brave or not rich.
Everyone who is both not curious and calm is either not generous or not brave and vice versa.
Everyone who is kind is not calm and vice versa.
Everyone who is both happy and calm is both happy and not rich.
Everyone who is both brave and not humble is not brave.
Everyone who is both not rich and kind is not creative or not happy and vice versa.
If someone is either not brave or creative then someone is brave.
Everyone who is funny is quiet or not curious and vice versa.
Everyone who is funny is not creative and vice versa.
If someone is quiet then paul is not curious or kind and vice versa.
Everyone who is not kind or not brave is rich.
If lucy is tall then someone is creative.
Everyone who is either not creative or not old is both funny and creative and vice versa.
Alice is not curious.
Lucy is quiet or not funny.
Fred is both not funny and not calm.
Someone is patient or generous.
Lucy is either not wise or happy.
Alice is both humble and not curious.
Mary is tall.
Paul is not happy or not curious. | Alice is old. | contradiction | (((~strong(alice)|~curious(alice)))<=>(?[X]:((~wise(X)<~>creative(X)))))&
((~generous(lucy))<=>(?[X]:((quiet(X)|rich(X)))))&
(((~happy(mary)&~generous(mary)))<=>((strong(alice)<~>happy(alice))))&
((?[X]:((happy(X)<~>~humble(X))))=>((brave(lucy)|~rich(lucy))))&
(![X]:((~curious(X)&calm(X))<=>(~generous(X)<~>~brave(X))))&
(![X]:(kind(X)<=>~calm(X)))&
(![X]:((happy(X)&calm(X))=>(happy(X)&~rich(X))))&
(![X]:((brave(X)&~humble(X))=>~brave(X)))&
(![X]:((~rich(X)&kind(X))<=>(~creative(X)|~happy(X))))&
((?[X]:((~brave(X)<~>creative(X))))=>(?[X]:(brave(X))))&
(![X]:(funny(X)<=>(quiet(X)|~curious(X))))&
(![X]:(funny(X)<=>~creative(X)))&
((?[X]:(quiet(X)))<=>((~curious(paul)|kind(paul))))&
(![X]:((~kind(X)|~brave(X))=>rich(X)))&
((tall(lucy))=>(?[X]:(creative(X))))&
(![X]:((~creative(X)<~>~old(X))<=>(funny(X)&creative(X))))&
(~curious(alice))&
((quiet(lucy)|~funny(lucy)))&
((~funny(fred)&~calm(fred)))&
(?[X]:((patient(X)|generous(X))))&
((~wise(lucy)<~>happy(lucy)))&
((humble(alice)&~curious(alice)))&
(tall(mary))&
((~happy(paul)|~curious(paul))) | old(alice) | [
"p10",
"p11",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 2579316309076546291667248
% SZS output start Proof for 2579316309076546291667248
11. ! [X0] : (funny(X0) <=> (~curious(X0) | quiet(X0))) [input p10]
12. ! [X0] : (funny(X0) <=> ~creative(X0)) [input p11]
16. ! [X0] : ((~creative(X0) <~> ~old(X0)) <=> (creative(X0) & funny(X0))) [input p15]
22. ~curious(alice) & humble(alice) [input p21]
25. old(alice) [input hypothesis]
58. ! [X0] : ((funny(X0) | (curious(X0) & ~quiet(X0))) & ((~curious(X0) | quiet(X0)) | ~funny(X0))) [nnf transformation 11]
59. ! [X0] : ((funny(X0) | (curious(X0) & ~quiet(X0))) & (~curious(X0) | quiet(X0) | ~funny(X0))) [flattening 58]
60. ! [X0] : ((funny(X0) | creative(X0)) & (~creative(X0) | ~funny(X0))) [nnf transformation 12]
68. ! [X0] : ((((old(X0) | creative(X0)) & (~old(X0) | ~creative(X0))) | (~creative(X0) | ~funny(X0))) & ((creative(X0) & funny(X0)) | ((~creative(X0) | old(X0)) & (~old(X0) | creative(X0))))) [nnf transformation 16]
69. ! [X0] : ((((old(X0) | creative(X0)) & (~old(X0) | ~creative(X0))) | ~creative(X0) | ~funny(X0)) & ((creative(X0) & funny(X0)) | ((~creative(X0) | old(X0)) & (~old(X0) | creative(X0))))) [flattening 68]
108. funny(X0) | curious(X0) [cnf transformation 59]
109. ~funny(X0) | ~creative(X0) [cnf transformation 60]
119. creative(X0) | ~old(X0) | creative(X0) [cnf transformation 69]
130. ~curious(alice) [cnf transformation 22]
133. old(alice) [cnf transformation 25]
134. ~old(X0) | creative(X0) [duplicate literal removal 119]
145. 3 <=> curious(alice) [avatar definition]
147. ~curious(alice) <- (~3) [avatar component clause 145]
277. ~3 [avatar split clause 130,145]
292. ~creative(X0) | curious(X0) [resolution 109,108]
300. creative(alice) [resolution 134,133]
386. curious(alice) [resolution 292,300]
387. $false <- (~3) [subsumption resolution 386,147]
388. 3 [avatar contradiction clause 387]
389. $false [avatar sat refutation 277,388]
% SZS output end Proof for 2579316309076546291667248
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or not old then mary is not wise.
If mary is both old and curious then john is either not tall or calm.
If someone is not kind then someone is both patient and not patient and vice versa.
If someone is brave or not generous then someone is not brave or not rich and vice versa.
Everyone who is not kind is both happy and strong.
If someone is both not patient and not tall then someone is either kind or not brave and vice versa.
Everyone who is both rich and tall is strong or humble and vice versa.
Everyone who is rich or not humble is either creative or old.
If someone is not old then someone is both not curious and kind and vice versa.
Everyone who is both patient and funny is either patient or not humble.
Everyone who is both not rich and wise is either not wise or generous.
If someone is happy then mary is humble and vice versa.
Everyone who is both rich and old is either not humble or humble and vice versa.
Everyone who is both not calm and patient is both not rich and strong and vice versa.
If someone is either strong or not quiet then paul is not patient and vice versa.
Everyone who is both quiet and not creative is both funny and not generous and vice versa.
Paul is kind.
Susan is either not humble or curious.
Someone is either rich or tall.
Someone is both happy and tall.
Someone is not calm.
Someone is rich or generous.
Paul is not calm or kind. | Susan is not curious. | contradiction | ((?[X]:((curious(X)|~old(X))))=>(~wise(mary)))&
(((old(mary)&curious(mary)))=>((~tall(john)<~>calm(john))))&
((?[X]:(~kind(X)))<=>(?[X]:((patient(X)&~patient(X)))))&
((?[X]:((brave(X)|~generous(X))))<=>(?[X]:((~brave(X)|~rich(X)))))&
(![X]:(~kind(X)=>(happy(X)&strong(X))))&
((?[X]:((~patient(X)&~tall(X))))<=>(?[X]:((kind(X)<~>~brave(X)))))&
(![X]:((rich(X)&tall(X))<=>(strong(X)|humble(X))))&
(![X]:((rich(X)|~humble(X))=>(creative(X)<~>old(X))))&
((?[X]:(~old(X)))<=>(?[X]:((~curious(X)&kind(X)))))&
(![X]:((patient(X)&funny(X))=>(patient(X)<~>~humble(X))))&
(![X]:((~rich(X)&wise(X))=>(~wise(X)<~>generous(X))))&
((?[X]:(happy(X)))<=>(humble(mary)))&
(![X]:((rich(X)&old(X))<=>(~humble(X)<~>humble(X))))&
(![X]:((~calm(X)&patient(X))<=>(~rich(X)&strong(X))))&
((?[X]:((strong(X)<~>~quiet(X))))<=>(~patient(paul)))&
(![X]:((quiet(X)&~creative(X))<=>(funny(X)&~generous(X))))&
(kind(paul))&
((~humble(susan)<~>curious(susan)))&
(?[X]:((rich(X)<~>tall(X))))&
(?[X]:((happy(X)&tall(X))))&
(?[X]:(~calm(X)))&
(?[X]:((rich(X)|generous(X))))&
((~calm(paul)|kind(paul))) | ~curious(susan) | [
"p2",
"p8",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2187453031467473799301212
% SZS output start Proof for 2187453031467473799301212
3. ? [X0] : ~kind(X0) <=> ? [X0] : (~patient(X0) & patient(X0)) [input p2]
9. ? [X0] : ~old(X0) <=> ? [X0] : (kind(X0) & ~curious(X0)) [input p8]
13. ! [X0] : ((old(X0) & rich(X0)) <=> (~humble(X0) <~> humble(X0))) [input p12]
24. ~curious(susan) [input hypothesis]
25. ? [X0] : ~kind(X0) <=> ? [X1] : (~patient(X1) & patient(X1)) [rectify 3]
28. ? [X0] : ~old(X0) <=> ? [X1] : (kind(X1) & ~curious(X1)) [rectify 9]
39. (? [X0] : ~kind(X0) | ! [X1] : (patient(X1) | ~patient(X1))) & (? [X1] : (~patient(X1) & patient(X1)) | ! [X0] : kind(X0)) [nnf transformation 25]
40. (? [X0] : ~kind(X0) | ! [X1] : (patient(X1) | ~patient(X1))) & (? [X2] : (~patient(X2) & patient(X2)) | ! [X3] : kind(X3)) [rectify 39]
41. ? [X0] : ~kind(X0) => ~kind(sK0) [choice axiom]
42. ? [X2] : (~patient(X2) & patient(X2)) => (~patient(sK1) & patient(sK1)) [choice axiom]
43. (~kind(sK0) | ! [X1] : (patient(X1) | ~patient(X1))) & ((~patient(sK1) & patient(sK1)) | ! [X3] : kind(X3)) [skolemisation 40,42,41]
57. (? [X0] : ~old(X0) | ! [X1] : (~kind(X1) | curious(X1))) & (? [X1] : (kind(X1) & ~curious(X1)) | ! [X0] : old(X0)) [nnf transformation 28]
58. (? [X0] : ~old(X0) | ! [X1] : (~kind(X1) | curious(X1))) & (? [X2] : (kind(X2) & ~curious(X2)) | ! [X3] : old(X3)) [rectify 57]
59. ? [X0] : ~old(X0) => ~old(sK6) [choice axiom]
60. ? [X2] : (kind(X2) & ~curious(X2)) => (kind(sK7) & ~curious(sK7)) [choice axiom]
61. (~old(sK6) | ! [X1] : (~kind(X1) | curious(X1))) & ((kind(sK7) & ~curious(sK7)) | ! [X3] : old(X3)) [skolemisation 58,60,59]
68. ! [X0] : (((old(X0) & rich(X0)) | ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0)))) & (((~humble(X0) | humble(X0)) & (humble(X0) | ~humble(X0))) | (~old(X0) | ~rich(X0)))) [nnf transformation 13]
69. ! [X0] : (((old(X0) & rich(X0)) | ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0)))) & (((~humble(X0) | humble(X0)) & (humble(X0) | ~humble(X0))) | ~old(X0) | ~rich(X0))) [flattening 68]
92. patient(sK1) | kind(X3) [cnf transformation 43]
93. ~patient(sK1) | kind(X3) [cnf transformation 43]
118. ~old(sK6) | ~kind(X1) | curious(X1) [cnf transformation 61]
129. old(X0) | humble(X0) | humble(X0) [cnf transformation 69]
130. old(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 69]
153. ~curious(susan) [cnf transformation 24]
156. old(X0) | humble(X0) [duplicate literal removal 129]
157. old(X0) | ~humble(X0) [duplicate literal removal 130]
161. 1 <=> ! [X0] : old(X0) [avatar definition]
162. old(X0) <- (1) [avatar component clause 161]
191. 8 <=> ! [X3] : kind(X3) [avatar definition]
192. kind(X3) <- (8) [avatar component clause 191]
194. 9 <=> patient(sK1) [avatar definition]
197. 8 | ~9 [avatar split clause 93,194,191]
198. 8 | 9 [avatar split clause 92,194,191]
263. 25 <=> ! [X1] : (~kind(X1) | curious(X1)) [avatar definition]
264. ~kind(X1) | curious(X1) <- (25) [avatar component clause 263]
266. 26 <=> old(sK6) [avatar definition]
268. ~old(sK6) <- (~26) [avatar component clause 266]
269. 25 | ~26 [avatar split clause 118,266,263]
293. old(X0) [subsumption resolution 156,157]
294. 1 [avatar split clause 293,161]
324. 38 <=> curious(susan) [avatar definition]
326. ~curious(susan) <- (~38) [avatar component clause 324]
348. ~38 [avatar split clause 153,324]
353. $false <- (1, ~26) [resolution 268,162]
354. ~1 | 26 [avatar contradiction clause 353]
355. curious(X1) <- (8, 25) [subsumption resolution 264,192]
357. $false <- (8, 25, ~38) [resolution 355,326]
358. ~8 | ~25 | 38 [avatar contradiction clause 357]
360. $false [avatar sat refutation 197,198,269,294,348,354,358]
% SZS output end Proof for 2187453031467473799301212
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not curious or not happy is either kind or not happy and vice versa. Everyone who is creative is both not patient and wise and vice versa. Everyone who is both patient and not brave is both not happy and brave. If mary is both kind and not tall then fred is creative or not old. Everyone who is either strong or not calm is rich and vice versa. If mary is both happy and not patient then someone is funny or not funny. Everyone who is not funny or humble is brave and vice versa. Everyone who is not tall is humble or not curious. Everyone who is either happy or patient is not rich or not old and vice versa. If someone is strong then john is not old or curious. Everyone who is either creative or not humble is wise or happy and vice versa. If mary is not calm then susan is either generous or kind and vice versa. Everyone who is both brave and not strong is both calm and humble and vice versa. Everyone who is not strong is either funny or humble. If paul is not humble or not patient then someone is happy or not brave and vice versa. Everyone who is kind or happy is not old and vice versa. Someone is curious or not tall. Someone is both not happy and not wise. Fred is creative. Paul is both not creative and not wise. Paul is not quiet. John is not tall or not creative. Susan is not calm or not strong. Fred is humble. | Fred is not rich. | entailment | (![X]:((~curious(X)|~happy(X))<=>(kind(X)<~>~happy(X))))&
(![X]:(creative(X)<=>(~patient(X)&wise(X))))&
(![X]:((patient(X)&~brave(X))=>(~happy(X)&brave(X))))&
(((kind(mary)&~tall(mary)))=>((creative(fred)|~old(fred))))&
(![X]:((strong(X)<~>~calm(X))<=>rich(X)))&
(((happy(mary)&~patient(mary)))=>(?[X]:((funny(X)|~funny(X)))))&
(![X]:((~funny(X)|humble(X))<=>brave(X)))&
(![X]:(~tall(X)=>(humble(X)|~curious(X))))&
(![X]:((happy(X)<~>patient(X))<=>(~rich(X)|~old(X))))&
((?[X]:(strong(X)))=>((~old(john)|curious(john))))&
(![X]:((creative(X)<~>~humble(X))<=>(wise(X)|happy(X))))&
((~calm(mary))<=>((generous(susan)<~>kind(susan))))&
(![X]:((brave(X)&~strong(X))<=>(calm(X)&humble(X))))&
(![X]:(~strong(X)=>(funny(X)<~>humble(X))))&
(((~humble(paul)|~patient(paul)))<=>(?[X]:((happy(X)|~brave(X)))))&
(![X]:((kind(X)|happy(X))<=>~old(X)))&
(?[X]:((curious(X)|~tall(X))))&
(?[X]:((~happy(X)&~wise(X))))&
(creative(fred))&
((~creative(paul)&~wise(paul)))&
(~quiet(paul))&
((~tall(john)|~creative(john)))&
((~calm(susan)|~strong(susan)))&
(humble(fred)) | ~rich(fred) | [
"p4",
"p6",
"p12",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 8493942971150335347774702
% SZS output start Proof for 8493942971150335347774702
5. ! [X0] : ((strong(X0) <~> ~calm(X0)) <=> rich(X0)) [input p4]
7. ! [X0] : ((humble(X0) | ~funny(X0)) <=> brave(X0)) [input p6]
13. ! [X0] : ((~strong(X0) & brave(X0)) <=> (humble(X0) & calm(X0))) [input p12]
24. humble(fred) [input p23]
25. rich(fred) [input hypothesis]
42. ! [X0] : ((((calm(X0) | ~strong(X0)) & (~calm(X0) | strong(X0))) | ~rich(X0)) & (rich(X0) | ((strong(X0) | calm(X0)) & (~calm(X0) | ~strong(X0))))) [nnf transformation 5]
45. ! [X0] : (((humble(X0) | ~funny(X0)) | ~brave(X0)) & (brave(X0) | (~humble(X0) & funny(X0)))) [nnf transformation 7]
46. ! [X0] : ((humble(X0) | ~funny(X0) | ~brave(X0)) & (brave(X0) | (~humble(X0) & funny(X0)))) [flattening 45]
52. ! [X0] : (((~strong(X0) & brave(X0)) | (~humble(X0) | ~calm(X0))) & ((humble(X0) & calm(X0)) | (strong(X0) | ~brave(X0)))) [nnf transformation 13]
53. ! [X0] : (((~strong(X0) & brave(X0)) | ~humble(X0) | ~calm(X0)) & ((humble(X0) & calm(X0)) | strong(X0) | ~brave(X0))) [flattening 52]
80. ~rich(X0) | strong(X0) | ~calm(X0) [cnf transformation 42]
81. ~rich(X0) | ~strong(X0) | calm(X0) [cnf transformation 42]
84. ~humble(X0) | brave(X0) [cnf transformation 46]
104. ~brave(X0) | strong(X0) | calm(X0) [cnf transformation 53]
107. ~humble(X0) | ~strong(X0) | ~calm(X0) [cnf transformation 53]
125. humble(fred) [cnf transformation 24]
126. rich(fred) [cnf transformation 25]
233. brave(fred) [resolution 84,125]
250. strong(fred) | ~calm(fred) [resolution 80,126]
254. ~strong(fred) | calm(fred) [resolution 81,126]
266. strong(fred) | calm(fred) [resolution 104,233]
271. 24 <=> calm(fred) [avatar definition]
273. calm(fred) <- (24) [avatar component clause 271]
275. 25 <=> strong(fred) [avatar definition]
277. strong(fred) <- (25) [avatar component clause 275]
278. 24 | 25 [avatar split clause 266,275,271]
279. 24 | ~25 [avatar split clause 254,275,271]
280. ~24 | 25 [avatar split clause 250,275,271]
293. ~strong(fred) | ~calm(fred) [resolution 107,125]
295. ~calm(fred) <- (25) [subsumption resolution 293,277]
296. $false <- (24, 25) [subsumption resolution 295,273]
297. ~24 | ~25 [avatar contradiction clause 296]
307. $false [avatar sat refutation 278,279,280,297]
% SZS output end Proof for 8493942971150335347774702
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is generous or creative is either old or not curious.
If alice is both not brave and funny then someone is either not rich or brave and vice versa.
Everyone who is both old and not kind is quiet or wise.
Everyone who is humble or curious is both not calm and old and vice versa.
If fred is either happy or not patient then fred is either brave or not strong.
Everyone who is either old or not generous is either strong or old.
If mary is not strong or not quiet then john is not patient.
Everyone who is both not patient and patient is old or calm and vice versa.
If someone is generous then lucy is either happy or tall and vice versa.
Everyone who is either old or not happy is both quiet and not old.
Everyone who is either old or not old is both funny and not happy.
Everyone who is either curious or old is brave and vice versa.
Everyone who is either not quiet or not humble is not rich.
If john is both not quiet and brave then someone is either not wise or quiet and vice versa.
If someone is both not wise and not strong then fred is both not old and not kind.
Everyone who is quiet is both not curious and not patient.
Lucy is kind.
Fred is either wise or quiet.
Mary is not kind.
Paul is quiet or not humble.
Someone is both strong and not generous.
Susan is quiet or not patient.
Mary is patient or not brave. | Fred is not strong. | entailment | (![X]:((generous(X)|creative(X))=>(old(X)<~>~curious(X))))&
(((~brave(alice)&funny(alice)))<=>(?[X]:((~rich(X)<~>brave(X)))))&
(![X]:((old(X)&~kind(X))=>(quiet(X)|wise(X))))&
(![X]:((humble(X)|curious(X))<=>(~calm(X)&old(X))))&
(((happy(fred)<~>~patient(fred)))=>((brave(fred)<~>~strong(fred))))&
(![X]:((old(X)<~>~generous(X))=>(strong(X)<~>old(X))))&
(((~strong(mary)|~quiet(mary)))=>(~patient(john)))&
(![X]:((~patient(X)&patient(X))<=>(old(X)|calm(X))))&
((?[X]:(generous(X)))<=>((happy(lucy)<~>tall(lucy))))&
(![X]:((old(X)<~>~happy(X))=>(quiet(X)&~old(X))))&
(![X]:((old(X)<~>~old(X))=>(funny(X)&~happy(X))))&
(![X]:((curious(X)<~>old(X))<=>brave(X)))&
(![X]:((~quiet(X)<~>~humble(X))=>~rich(X)))&
(((~quiet(john)&brave(john)))<=>(?[X]:((~wise(X)<~>quiet(X)))))&
((?[X]:((~wise(X)&~strong(X))))=>((~old(fred)&~kind(fred))))&
(![X]:(quiet(X)=>(~curious(X)&~patient(X))))&
(kind(lucy))&
((wise(fred)<~>quiet(fred)))&
(~kind(mary))&
((quiet(paul)|~humble(paul)))&
(?[X]:((strong(X)&~generous(X))))&
((quiet(susan)|~patient(susan)))&
((patient(mary)|~brave(mary))) | ~strong(fred) | [
"p4",
"p7",
"p9",
"p10",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6784901556308390475854797
% SZS output start Proof for 6784901556308390475854797
5. (happy(fred) <~> ~patient(fred)) => (brave(fred) <~> ~strong(fred)) [input p4]
8. ! [X0] : ((patient(X0) & ~patient(X0)) <=> (calm(X0) | old(X0))) [input p7]
10. ! [X0] : ((old(X0) <~> ~happy(X0)) => (~old(X0) & quiet(X0))) [input p9]
11. ! [X0] : ((old(X0) <~> ~old(X0)) => (~happy(X0) & funny(X0))) [input p10]
12. ! [X0] : ((curious(X0) <~> old(X0)) <=> brave(X0)) [input p11]
16. ! [X0] : (quiet(X0) => (~patient(X0) & ~curious(X0))) [input p15]
24. strong(fred) [input hypothesis]
29. (brave(fred) <~> ~strong(fred)) | (happy(fred) <=> ~patient(fred)) [ennf transformation 5]
32. ! [X0] : ((~old(X0) & quiet(X0)) | (old(X0) <=> ~happy(X0))) [ennf transformation 10]
33. ! [X0] : ((~happy(X0) & funny(X0)) | (old(X0) <=> ~old(X0))) [ennf transformation 11]
36. ! [X0] : ((~patient(X0) & ~curious(X0)) | ~quiet(X0)) [ennf transformation 16]
45. ((strong(fred) | ~brave(fred)) & (~strong(fred) | brave(fred))) | ((happy(fred) | patient(fred)) & (~patient(fred) | ~happy(fred))) [nnf transformation 29]
47. ! [X0] : (((patient(X0) & ~patient(X0)) | (~calm(X0) & ~old(X0))) & ((calm(X0) | old(X0)) | (~patient(X0) | patient(X0)))) [nnf transformation 8]
48. ! [X0] : (((patient(X0) & ~patient(X0)) | (~calm(X0) & ~old(X0))) & (calm(X0) | old(X0) | ~patient(X0) | patient(X0))) [flattening 47]
53. ! [X0] : ((~old(X0) & quiet(X0)) | ((old(X0) | happy(X0)) & (~happy(X0) | ~old(X0)))) [nnf transformation 32]
54. ! [X0] : ((~happy(X0) & funny(X0)) | ((old(X0) | old(X0)) & (~old(X0) | ~old(X0)))) [nnf transformation 33]
55. ! [X0] : ((((~old(X0) | ~curious(X0)) & (old(X0) | curious(X0))) | ~brave(X0)) & (brave(X0) | ((curious(X0) | ~old(X0)) & (old(X0) | ~curious(X0))))) [nnf transformation 12]
80. ~strong(fred) | brave(fred) | happy(fred) | patient(fred) [cnf transformation 45]
90. ~patient(X0) | ~old(X0) [cnf transformation 48]
92. ~old(X0) | patient(X0) [cnf transformation 48]
99. quiet(X0) | old(X0) | happy(X0) [cnf transformation 53]
105. ~happy(X0) | old(X0) | old(X0) [cnf transformation 54]
108. old(X0) | curious(X0) | ~brave(X0) [cnf transformation 55]
120. ~quiet(X0) | ~curious(X0) [cnf transformation 36]
121. ~patient(X0) | ~quiet(X0) [cnf transformation 36]
131. strong(fred) [cnf transformation 24]
135. ~happy(X0) | old(X0) [duplicate literal removal 105]
168. 7 <=> patient(fred) [avatar definition]
170. patient(fred) <- (7) [avatar component clause 168]
172. 8 <=> happy(fred) [avatar definition]
174. happy(fred) <- (8) [avatar component clause 172]
176. 9 <=> brave(fred) [avatar definition]
177. brave(fred) <- (9) [avatar component clause 176]
180. 10 <=> strong(fred) [avatar definition]
185. 7 | 8 | 9 | ~10 [avatar split clause 80,180,176,172,168]
202. ~old(X0) [subsumption resolution 90,92]
222. happy(X0) | quiet(X0) [subsumption resolution 99,202]
223. ~happy(X0) [subsumption resolution 135,202]
225. ~brave(X0) | curious(X0) [subsumption resolution 108,202]
291. 10 [avatar split clause 131,180]
292. ~quiet(fred) <- (7) [resolution 121,170]
293. quiet(X0) [resolution 222,223]
295. ~curious(X0) [resolution 293,120]
302. $false <- (7) [subsumption resolution 292,293]
303. ~7 [avatar contradiction clause 302]
305. curious(fred) <- (9) [resolution 177,225]
306. $false <- (9) [subsumption resolution 305,295]
307. ~9 [avatar contradiction clause 306]
308. $false <- (8) [subsumption resolution 174,223]
309. ~8 [avatar contradiction clause 308]
310. $false [avatar sat refutation 185,291,303,307,309]
% SZS output end Proof for 6784901556308390475854797
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not curious or not old is kind.
If mary is both humble and not creative then someone is not creative.
If mary is either tall or not patient then lucy is curious or humble and vice versa.
If someone is both not generous and tall then lucy is patient or not curious.
If someone is not patient then lucy is strong and vice versa.
If someone is not brave or generous then lucy is tall or not old and vice versa.
Everyone who is both curious and not funny is funny or tall and vice versa.
Everyone who is both generous and not funny is both humble and generous.
Everyone who is not wise or not curious is not kind and vice versa.
Everyone who is funny is both old and funny.
If lucy is either not happy or creative then someone is either generous or strong.
Everyone who is not funny or curious is both not strong and not brave.
Everyone who is not calm is not creative or creative and vice versa.
If susan is either calm or not generous then someone is either creative or not humble.
If someone is not calm or happy then susan is either not creative or wise and vice versa.
If susan is funny or not creative then someone is wise or not kind.
Alice is either not humble or not wise.
Someone is either quiet or not curious.
Someone is not calm or calm.
Someone is both quiet and rich.
Mary is old.
Lucy is not curious or creative.
Someone is not calm. | Lucy is not strong. | entailment | (![X]:((~curious(X)<~>~old(X))=>kind(X)))&
(((humble(mary)&~creative(mary)))=>(?[X]:(~creative(X))))&
(((tall(mary)<~>~patient(mary)))<=>((curious(lucy)|humble(lucy))))&
((?[X]:((~generous(X)&tall(X))))=>((patient(lucy)|~curious(lucy))))&
((?[X]:(~patient(X)))<=>(strong(lucy)))&
((?[X]:((~brave(X)|generous(X))))<=>((tall(lucy)|~old(lucy))))&
(![X]:((curious(X)&~funny(X))<=>(funny(X)|tall(X))))&
(![X]:((generous(X)&~funny(X))=>(humble(X)&generous(X))))&
(![X]:((~wise(X)|~curious(X))<=>~kind(X)))&
(![X]:(funny(X)=>(old(X)&funny(X))))&
(((~happy(lucy)<~>creative(lucy)))=>(?[X]:((generous(X)<~>strong(X)))))&
(![X]:((~funny(X)|curious(X))=>(~strong(X)&~brave(X))))&
(![X]:(~calm(X)<=>(~creative(X)|creative(X))))&
(((calm(susan)<~>~generous(susan)))=>(?[X]:((creative(X)<~>~humble(X)))))&
((?[X]:((~calm(X)|happy(X))))<=>((~creative(susan)<~>wise(susan))))&
(((funny(susan)|~creative(susan)))=>(?[X]:((wise(X)|~kind(X)))))&
((~humble(alice)<~>~wise(alice)))&
(?[X]:((quiet(X)<~>~curious(X))))&
(?[X]:((~calm(X)|calm(X))))&
(?[X]:((quiet(X)&rich(X))))&
(old(mary))&
((~curious(lucy)|creative(lucy)))&
(?[X]:(~calm(X))) | ~strong(lucy) | [
"p6",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 7368548486030259386762992
% SZS output start Proof for 7368548486030259386762992
7. ! [X0] : ((~funny(X0) & curious(X0)) <=> (tall(X0) | funny(X0))) [input p6]
12. ! [X0] : ((curious(X0) | ~funny(X0)) => (~brave(X0) & ~strong(X0))) [input p11]
24. strong(lucy) [input hypothesis]
35. ! [X0] : ((~brave(X0) & ~strong(X0)) | (~curious(X0) & funny(X0))) [ennf transformation 12]
52. ! [X0] : (((~funny(X0) & curious(X0)) | (~tall(X0) & ~funny(X0))) & ((tall(X0) | funny(X0)) | (funny(X0) | ~curious(X0)))) [nnf transformation 7]
53. ! [X0] : (((~funny(X0) & curious(X0)) | (~tall(X0) & ~funny(X0))) & (tall(X0) | funny(X0) | funny(X0) | ~curious(X0))) [flattening 52]
99. ~funny(X0) | ~funny(X0) [cnf transformation 53]
112. ~strong(X0) | funny(X0) [cnf transformation 35]
140. strong(lucy) [cnf transformation 24]
142. ~funny(X0) [duplicate literal removal 99]
248. ~strong(X0) [subsumption resolution 112,142]
304. $false [subsumption resolution 140,248]
% SZS output end Proof for 7368548486030259386762992
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall then john is both not generous and not old and vice versa.
If someone is wise or generous then lucy is both rich and patient.
If susan is both strong and curious then susan is not happy and vice versa.
If someone is strong or generous then someone is not old and vice versa.
If someone is happy then someone is either creative or not brave and vice versa.
Everyone who is either not wise or patient is not kind and vice versa.
If someone is not generous or not tall then lucy is not tall or funny.
Everyone who is not old is patient or rich.
If someone is old then someone is not happy or wise and vice versa.
Everyone who is both funny and curious is both happy and not kind and vice versa.
If fred is both quiet and tall then mary is not rich or funny.
Everyone who is calm is either not humble or wise and vice versa.
If fred is both kind and wise then someone is old or not old.
If someone is either not quiet or not strong then someone is both not happy and not tall.
If paul is rich then someone is either quiet or funny and vice versa.
Everyone who is either generous or brave is not old or old.
Mary is not funny.
Someone is not humble or not strong.
John is either generous or quiet.
Someone is either not tall or not creative.
Paul is both not happy and not funny.
Someone is funny.
Alice is either tall or not funny.
Someone is both tall and wise. | John is generous. | contradiction | ((?[X]:(tall(X)))<=>((~generous(john)&~old(john))))&
((?[X]:((wise(X)|generous(X))))=>((rich(lucy)&patient(lucy))))&
(((strong(susan)&curious(susan)))<=>(~happy(susan)))&
((?[X]:((strong(X)|generous(X))))<=>(?[X]:(~old(X))))&
((?[X]:(happy(X)))<=>(?[X]:((creative(X)<~>~brave(X)))))&
(![X]:((~wise(X)<~>patient(X))<=>~kind(X)))&
((?[X]:((~generous(X)|~tall(X))))=>((~tall(lucy)|funny(lucy))))&
(![X]:(~old(X)=>(patient(X)|rich(X))))&
((?[X]:(old(X)))<=>(?[X]:((~happy(X)|wise(X)))))&
(![X]:((funny(X)&curious(X))<=>(happy(X)&~kind(X))))&
(((quiet(fred)&tall(fred)))=>((~rich(mary)|funny(mary))))&
(![X]:(calm(X)<=>(~humble(X)<~>wise(X))))&
(((kind(fred)&wise(fred)))=>(?[X]:((old(X)|~old(X)))))&
((?[X]:((~quiet(X)<~>~strong(X))))=>(?[X]:((~happy(X)&~tall(X)))))&
((rich(paul))<=>(?[X]:((quiet(X)<~>funny(X)))))&
(![X]:((generous(X)<~>brave(X))=>(~old(X)|old(X))))&
(~funny(mary))&
(?[X]:((~humble(X)|~strong(X))))&
((generous(john)<~>quiet(john)))&
(?[X]:((~tall(X)<~>~creative(X))))&
((~happy(paul)&~funny(paul)))&
(?[X]:(funny(X)))&
((tall(alice)<~>~funny(alice)))&
(?[X]:((tall(X)&wise(X)))) | generous(john) | [
"p0",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 8104138232075368785615745
% SZS output start Proof for 8104138232075368785615745
1. ? [X0] : tall(X0) <=> (~old(john) & ~generous(john)) [input p0]
24. ? [X0] : (wise(X0) & tall(X0)) [input p23]
25. generous(john) [input hypothesis]
43. (? [X0] : tall(X0) | (old(john) | generous(john))) & ((~old(john) & ~generous(john)) | ! [X0] : ~tall(X0)) [nnf transformation 1]
44. (? [X0] : tall(X0) | old(john) | generous(john)) & ((~old(john) & ~generous(john)) | ! [X0] : ~tall(X0)) [flattening 43]
45. (? [X0] : tall(X0) | old(john) | generous(john)) & ((~old(john) & ~generous(john)) | ! [X1] : ~tall(X1)) [rectify 44]
46. ? [X0] : tall(X0) => tall(sK0) [choice axiom]
47. (tall(sK0) | old(john) | generous(john)) & ((~old(john) & ~generous(john)) | ! [X1] : ~tall(X1)) [skolemisation 45,46]
86. ? [X0] : (wise(X0) & tall(X0)) => (wise(sK12) & tall(sK12)) [choice axiom]
87. wise(sK12) & tall(sK12) [skolemisation 24,86]
88. ~generous(john) | ~tall(X1) [cnf transformation 47]
141. tall(sK12) [cnf transformation 87]
143. generous(john) [cnf transformation 25]
145. 1 <=> generous(john) [avatar definition]
158. 4 <=> ! [X1] : ~tall(X1) [avatar definition]
159. ~tall(X1) <- (4) [avatar component clause 158]
161. 4 | ~1 [avatar split clause 88,145,158]
362. 1 [avatar split clause 143,145]
365. $false <- (4) [resolution 159,141]
366. ~4 [avatar contradiction clause 365]
367. $false [avatar sat refutation 161,362,366]
% SZS output end Proof for 8104138232075368785615745
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble then lucy is either happy or creative. If mary is either patient or not generous then someone is not old or funny and vice versa. If someone is both not wise and creative then someone is not strong. Everyone who is both not calm and not old is not quiet or curious. Everyone who is creative or not kind is either calm or patient and vice versa. If someone is not creative then mary is either not brave or not tall and vice versa. Everyone who is either not old or not tall is not wise and vice versa. Everyone who is not generous is not tall or not brave. Everyone who is either curious or calm is not patient or calm. If someone is funny or not quiet then someone is either not funny or curious. Everyone who is wise or funny is either wise or not kind. Everyone who is old is both happy and funny and vice versa. Everyone who is both not rich and not quiet is either not quiet or not rich and vice versa. Everyone who is not humble or not strong is either creative or kind. Everyone who is creative is not funny or patient and vice versa. Everyone who is humble or creative is either not quiet or creative. Someone is both not tall and brave. Someone is not tall. John is not tall. Lucy is generous or strong. Paul is not creative or humble. Someone is not happy or wise. Paul is either not humble or not generous. Lucy is funny. | Lucy is funny. | entailment | ((?[X]:(humble(X)))=>((happy(lucy)<~>creative(lucy))))&
(((patient(mary)<~>~generous(mary)))<=>(?[X]:((~old(X)|funny(X)))))&
((?[X]:((~wise(X)&creative(X))))=>(?[X]:(~strong(X))))&
(![X]:((~calm(X)&~old(X))=>(~quiet(X)|curious(X))))&
(![X]:((creative(X)|~kind(X))<=>(calm(X)<~>patient(X))))&
((?[X]:(~creative(X)))<=>((~brave(mary)<~>~tall(mary))))&
(![X]:((~old(X)<~>~tall(X))<=>~wise(X)))&
(![X]:(~generous(X)=>(~tall(X)|~brave(X))))&
(![X]:((curious(X)<~>calm(X))=>(~patient(X)|calm(X))))&
((?[X]:((funny(X)|~quiet(X))))=>(?[X]:((~funny(X)<~>curious(X)))))&
(![X]:((wise(X)|funny(X))=>(wise(X)<~>~kind(X))))&
(![X]:(old(X)<=>(happy(X)&funny(X))))&
(![X]:((~rich(X)&~quiet(X))<=>(~quiet(X)<~>~rich(X))))&
(![X]:((~humble(X)|~strong(X))=>(creative(X)<~>kind(X))))&
(![X]:(creative(X)<=>(~funny(X)|patient(X))))&
(![X]:((humble(X)|creative(X))=>(~quiet(X)<~>creative(X))))&
(?[X]:((~tall(X)&brave(X))))&
(?[X]:(~tall(X)))&
(~tall(john))&
((generous(lucy)|strong(lucy)))&
((~creative(paul)|humble(paul)))&
(?[X]:((~happy(X)|wise(X))))&
((~humble(paul)<~>~generous(paul)))&
(funny(lucy)) | funny(lucy) | [
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 6446893681498588454167614
% SZS output start Proof for 6446893681498588454167614
24. funny(lucy) [input p23]
25. ~funny(lucy) [input hypothesis]
140. funny(lucy) [cnf transformation 24]
141. ~funny(lucy) [cnf transformation 25]
265. $false [subsumption resolution 141,140]
% SZS output end Proof for 6446893681498588454167614
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong is both curious and not quiet and vice versa.
If someone is old or not old then someone is quiet and vice versa.
Everyone who is not funny or not rich is both humble and not curious and vice versa.
If someone is not creative or strong then mary is not strong or not funny and vice versa.
Everyone who is either happy or wise is both kind and not patient and vice versa.
Everyone who is either not happy or not creative is not funny and vice versa.
Everyone who is not strong is both creative and kind and vice versa.
Everyone who is both not patient and not creative is curious or not curious.
If mary is either not strong or not wise then fred is not wise or strong and vice versa.
If mary is strong or not strong then paul is either not tall or brave and vice versa.
Everyone who is kind is both not patient and quiet and vice versa.
If someone is either not calm or quiet then someone is wise.
If lucy is both not calm and happy then fred is both not patient and funny.
If paul is not funny then someone is either not kind or not funny and vice versa.
John is either quiet or not wise.
Someone is not patient.
Fred is both not calm and not generous.
Someone is either rich or old.
Someone is both not generous and not brave.
Someone is patient or old.
Someone is creative. | Paul is not patient. | entailment | (![X]:(strong(X)<=>(curious(X)&~quiet(X))))&
((?[X]:((old(X)|~old(X))))<=>(?[X]:(quiet(X))))&
(![X]:((~funny(X)|~rich(X))<=>(humble(X)&~curious(X))))&
((?[X]:((~creative(X)|strong(X))))<=>((~strong(mary)|~funny(mary))))&
(![X]:((happy(X)<~>wise(X))<=>(kind(X)&~patient(X))))&
(![X]:((~happy(X)<~>~creative(X))<=>~funny(X)))&
(![X]:(~strong(X)<=>(creative(X)&kind(X))))&
(![X]:((~patient(X)&~creative(X))=>(curious(X)|~curious(X))))&
(((~strong(mary)<~>~wise(mary)))<=>((~wise(fred)|strong(fred))))&
(((strong(mary)|~strong(mary)))<=>((~tall(paul)<~>brave(paul))))&
(![X]:(kind(X)<=>(~patient(X)&quiet(X))))&
((?[X]:((~calm(X)<~>quiet(X))))=>(?[X]:(wise(X))))&
(((~calm(lucy)&happy(lucy)))=>((~patient(fred)&funny(fred))))&
((~funny(paul))<=>(?[X]:((~kind(X)<~>~funny(X)))))&
((quiet(john)<~>~wise(john)))&
(?[X]:(~patient(X)))&
((~calm(fred)&~generous(fred)))&
(?[X]:((rich(X)<~>old(X))))&
(?[X]:((~generous(X)&~brave(X))))&
(?[X]:((patient(X)|old(X))))&
(?[X]:(creative(X))) | ~patient(paul) | [
"p0",
"p2",
"p6",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4347011192651648159526289
% SZS output start Proof for 4347011192651648159526289
1. ! [X0] : (strong(X0) <=> (~quiet(X0) & curious(X0))) [input p0]
3. ! [X0] : ((~rich(X0) | ~funny(X0)) <=> (~curious(X0) & humble(X0))) [input p2]
7. ! [X0] : (~strong(X0) <=> (kind(X0) & creative(X0))) [input p6]
11. ! [X0] : (kind(X0) <=> (quiet(X0) & ~patient(X0))) [input p10]
14. ~funny(paul) <=> ? [X0] : (~kind(X0) <~> ~funny(X0)) [input p13]
22. patient(paul) [input hypothesis]
32. ! [X0] : ((strong(X0) | (quiet(X0) | ~curious(X0))) & ((~quiet(X0) & curious(X0)) | ~strong(X0))) [nnf transformation 1]
33. ! [X0] : ((strong(X0) | quiet(X0) | ~curious(X0)) & ((~quiet(X0) & curious(X0)) | ~strong(X0))) [flattening 32]
39. ! [X0] : (((~rich(X0) | ~funny(X0)) | (curious(X0) | ~humble(X0))) & ((~curious(X0) & humble(X0)) | (rich(X0) & funny(X0)))) [nnf transformation 3]
40. ! [X0] : ((~rich(X0) | ~funny(X0) | curious(X0) | ~humble(X0)) & ((~curious(X0) & humble(X0)) | (rich(X0) & funny(X0)))) [flattening 39]
49. ! [X0] : ((~strong(X0) | (~kind(X0) | ~creative(X0))) & ((kind(X0) & creative(X0)) | strong(X0))) [nnf transformation 7]
50. ! [X0] : ((~strong(X0) | ~kind(X0) | ~creative(X0)) & ((kind(X0) & creative(X0)) | strong(X0))) [flattening 49]
55. ! [X0] : ((kind(X0) | (~quiet(X0) | patient(X0))) & ((quiet(X0) & ~patient(X0)) | ~kind(X0))) [nnf transformation 11]
56. ! [X0] : ((kind(X0) | ~quiet(X0) | patient(X0)) & ((quiet(X0) & ~patient(X0)) | ~kind(X0))) [flattening 55]
61. (~funny(paul) | ! [X0] : ((~kind(X0) | funny(X0)) & (~funny(X0) | kind(X0)))) & (? [X0] : ((funny(X0) | kind(X0)) & (~funny(X0) | ~kind(X0))) | funny(paul)) [nnf transformation 14]
62. (~funny(paul) | ! [X0] : ((~kind(X0) | funny(X0)) & (~funny(X0) | kind(X0)))) & (? [X1] : ((funny(X1) | kind(X1)) & (~funny(X1) | ~kind(X1))) | funny(paul)) [rectify 61]
63. ? [X1] : ((funny(X1) | kind(X1)) & (~funny(X1) | ~kind(X1))) => ((funny(sK4) | kind(sK4)) & (~funny(sK4) | ~kind(sK4))) [choice axiom]
64. (~funny(paul) | ! [X0] : ((~kind(X0) | funny(X0)) & (~funny(X0) | kind(X0)))) & (((funny(sK4) | kind(sK4)) & (~funny(sK4) | ~kind(sK4))) | funny(paul)) [skolemisation 62,63]
77. ~strong(X0) | curious(X0) [cnf transformation 33]
85. ~curious(X0) | funny(X0) [cnf transformation 40]
103. kind(X0) | strong(X0) [cnf transformation 50]
118. ~patient(X0) | ~kind(X0) [cnf transformation 56]
127. ~funny(paul) | ~funny(X0) | kind(X0) [cnf transformation 64]
138. patient(paul) [cnf transformation 22]
241. 23 <=> funny(paul) [avatar definition]
242. funny(paul) <- (23) [avatar component clause 241]
243. ~funny(paul) <- (~23) [avatar component clause 241]
246. 24 <=> ! [X0] : (~funny(X0) | kind(X0)) [avatar definition]
247. ~funny(X0) | kind(X0) <- (24) [avatar component clause 246]
248. 24 | ~23 [avatar split clause 127,241,246]
303. ~kind(paul) [resolution 118,138]
305. strong(paul) [resolution 303,103]
309. kind(paul) <- (23, 24) [resolution 247,242]
312. $false <- (23, 24) [subsumption resolution 309,303]
313. ~23 | ~24 [avatar contradiction clause 312]
526. curious(paul) [resolution 305,77]
683. funny(paul) [resolution 526,85]
684. $false <- (~23) [subsumption resolution 683,243]
685. 23 [avatar contradiction clause 684]
686. $false [avatar sat refutation 248,313,685]
% SZS output end Proof for 4347011192651648159526289
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
If paul is either not tall or not funny then someone is either not tall or funny and vice versa.
Everyone who is not kind is humble or not generous.
If someone is not wise or not old then someone is not kind.
If someone is curious or not quiet then someone is creative or happy.
Everyone who is not wise or not brave is either funny or not humble.
Everyone who is either not kind or strong is quiet or not creative and vice versa.
Everyone who is rich or not patient is not humble.
Everyone who is not tall or not wise is strong or calm.
If someone is not rich then paul is brave or happy.
Everyone who is both tall and not humble is brave or creative.
Everyone who is both not kind and not creative is not quiet or not funny and vice versa.
Everyone who is both creative and not wise is both creative and not old.
Everyone who is not brave is both not curious and kind and vice versa.
If john is either not quiet or not wise then susan is not calm or not patient.
Everyone who is old or not generous is either happy or not rich.
If someone is not patient then someone is not generous.
Lucy is kind.
Someone is strong or not patient.
Lucy is not curious.
Lucy is both not curious and tall.
Susan is both rich and not humble.
Alice is not rich or generous.
Lucy is either rich or not wise.
Someone is not strong or not rich. | Lucy is funny. | entailment | (((~tall(paul)<~>~funny(paul)))<=>(?[X]:((~tall(X)<~>funny(X)))))&
(![X]:(~kind(X)=>(humble(X)|~generous(X))))&
((?[X]:((~wise(X)|~old(X))))=>(?[X]:(~kind(X))))&
((?[X]:((curious(X)|~quiet(X))))=>(?[X]:((creative(X)|happy(X)))))&
(![X]:((~wise(X)|~brave(X))=>(funny(X)<~>~humble(X))))&
(![X]:((~kind(X)<~>strong(X))<=>(quiet(X)|~creative(X))))&
(![X]:((rich(X)|~patient(X))=>~humble(X)))&
(![X]:((~tall(X)|~wise(X))=>(strong(X)|calm(X))))&
((?[X]:(~rich(X)))=>((brave(paul)|happy(paul))))&
(![X]:((tall(X)&~humble(X))=>(brave(X)|creative(X))))&
(![X]:((~kind(X)&~creative(X))<=>(~quiet(X)|~funny(X))))&
(![X]:((creative(X)&~wise(X))=>(creative(X)&~old(X))))&
(![X]:(~brave(X)<=>(~curious(X)&kind(X))))&
(((~quiet(john)<~>~wise(john)))=>((~calm(susan)|~patient(susan))))&
(![X]:((old(X)|~generous(X))=>(happy(X)<~>~rich(X))))&
((?[X]:(~patient(X)))=>(?[X]:(~generous(X))))&
(kind(lucy))&
(?[X]:((strong(X)|~patient(X))))&
(~curious(lucy))&
((~curious(lucy)&tall(lucy)))&
((rich(susan)&~humble(susan)))&
((~rich(alice)|generous(alice)))&
((rich(lucy)<~>~wise(lucy)))&
(?[X]:((~strong(X)|~rich(X)))) | funny(lucy) | [
"p10",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 4266618751438231387626243
% SZS output start Proof for 4266618751438231387626243
11. ! [X0] : ((~creative(X0) & ~kind(X0)) <=> (~funny(X0) | ~quiet(X0))) [input p10]
17. kind(lucy) [input p16]
25. ~funny(lucy) [input hypothesis]
63. ! [X0] : (((~creative(X0) & ~kind(X0)) | (funny(X0) & quiet(X0))) & ((~funny(X0) | ~quiet(X0)) | (creative(X0) | kind(X0)))) [nnf transformation 11]
64. ! [X0] : (((~creative(X0) & ~kind(X0)) | (funny(X0) & quiet(X0))) & (~funny(X0) | ~quiet(X0) | creative(X0) | kind(X0))) [flattening 63]
106. ~kind(X0) | funny(X0) [cnf transformation 64]
119. kind(lucy) [cnf transformation 17]
130. ~funny(lucy) [cnf transformation 25]
268. funny(lucy) [resolution 106,119]
269. $false [subsumption resolution 268,130]
% SZS output end Proof for 4266618751438231387626243
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or not old is tall and vice versa.
If john is not tall then someone is either not calm or quiet.
Everyone who is not kind is not funny.
If lucy is either kind or quiet then someone is both generous and not patient.
Everyone who is not rich or not creative is not humble and vice versa.
If someone is both not creative and not generous then mary is not old or not kind and vice versa.
Everyone who is both not humble and brave is both wise and not quiet and vice versa.
Everyone who is either not happy or tall is either not tall or strong and vice versa.
If paul is both not calm and rich then someone is humble and vice versa.
Everyone who is tall is calm or brave.
Everyone who is not quiet or not humble is either generous or not humble and vice versa.
Everyone who is either not happy or not creative is wise or not curious and vice versa.
Everyone who is either rich or not funny is either curious or not curious and vice versa.
Everyone who is not strong or not generous is brave and vice versa.
Everyone who is not happy or tall is not rich or funny.
Everyone who is not funny is not calm and vice versa.
Someone is creative or patient.
Someone is wise or not creative.
Someone is both patient and not funny.
Someone is not wise or not calm.
Someone is not generous or quiet. | John is not wise. | contradiction | (![X]:((~funny(X)<~>~old(X))<=>tall(X)))&
((~tall(john))=>(?[X]:((~calm(X)<~>quiet(X)))))&
(![X]:(~kind(X)=>~funny(X)))&
(((kind(lucy)<~>quiet(lucy)))=>(?[X]:((generous(X)&~patient(X)))))&
(![X]:((~rich(X)|~creative(X))<=>~humble(X)))&
((?[X]:((~creative(X)&~generous(X))))<=>((~old(mary)|~kind(mary))))&
(![X]:((~humble(X)&brave(X))<=>(wise(X)&~quiet(X))))&
(![X]:((~happy(X)<~>tall(X))<=>(~tall(X)<~>strong(X))))&
(((~calm(paul)&rich(paul)))<=>(?[X]:(humble(X))))&
(![X]:(tall(X)=>(calm(X)|brave(X))))&
(![X]:((~quiet(X)|~humble(X))<=>(generous(X)<~>~humble(X))))&
(![X]:((~happy(X)<~>~creative(X))<=>(wise(X)|~curious(X))))&
(![X]:((rich(X)<~>~funny(X))<=>(curious(X)<~>~curious(X))))&
(![X]:((~strong(X)|~generous(X))<=>brave(X)))&
(![X]:((~happy(X)|tall(X))=>(~rich(X)|funny(X))))&
(![X]:(~funny(X)<=>~calm(X)))&
(?[X]:((creative(X)|patient(X))))&
(?[X]:((wise(X)|~creative(X))))&
(?[X]:((patient(X)&~funny(X))))&
(?[X]:((~wise(X)|~calm(X))))&
(?[X]:((~generous(X)|quiet(X)))) | ~wise(john) | [
"p6",
"p8",
"p10",
"p12",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 462567934594269848164860
% SZS output start Proof for 462567934594269848164860
7. ! [X0] : ((brave(X0) & ~humble(X0)) <=> (~quiet(X0) & wise(X0))) [input p6]
9. (rich(paul) & ~calm(paul)) <=> ? [X0] : humble(X0) [input p8]
11. ! [X0] : ((~humble(X0) | ~quiet(X0)) <=> (generous(X0) <~> ~humble(X0))) [input p10]
13. ! [X0] : ((rich(X0) <~> ~funny(X0)) <=> (curious(X0) <~> ~curious(X0))) [input p12]
14. ! [X0] : ((~generous(X0) | ~strong(X0)) <=> brave(X0)) [input p13]
16. ! [X0] : (~funny(X0) <=> ~calm(X0)) [input p15]
22. ~wise(john) [input hypothesis]
44. ! [X0] : (((brave(X0) & ~humble(X0)) | (quiet(X0) | ~wise(X0))) & ((~quiet(X0) & wise(X0)) | (~brave(X0) | humble(X0)))) [nnf transformation 7]
45. ! [X0] : (((brave(X0) & ~humble(X0)) | quiet(X0) | ~wise(X0)) & ((~quiet(X0) & wise(X0)) | ~brave(X0) | humble(X0))) [flattening 44]
47. ((rich(paul) & ~calm(paul)) | ! [X0] : ~humble(X0)) & (? [X0] : humble(X0) | (~rich(paul) | calm(paul))) [nnf transformation 9]
48. ((rich(paul) & ~calm(paul)) | ! [X0] : ~humble(X0)) & (? [X0] : humble(X0) | ~rich(paul) | calm(paul)) [flattening 47]
49. ((rich(paul) & ~calm(paul)) | ! [X0] : ~humble(X0)) & (? [X1] : humble(X1) | ~rich(paul) | calm(paul)) [rectify 48]
50. ? [X1] : humble(X1) => humble(sK3) [choice axiom]
51. ((rich(paul) & ~calm(paul)) | ! [X0] : ~humble(X0)) & (humble(sK3) | ~rich(paul) | calm(paul)) [skolemisation 49,50]
52. ! [X0] : (((~humble(X0) | ~quiet(X0)) | ((generous(X0) | humble(X0)) & (~humble(X0) | ~generous(X0)))) & (((humble(X0) | ~generous(X0)) & (~humble(X0) | generous(X0))) | (humble(X0) & quiet(X0)))) [nnf transformation 11]
53. ! [X0] : ((~humble(X0) | ~quiet(X0) | ((generous(X0) | humble(X0)) & (~humble(X0) | ~generous(X0)))) & (((humble(X0) | ~generous(X0)) & (~humble(X0) | generous(X0))) | (humble(X0) & quiet(X0)))) [flattening 52]
56. ! [X0] : ((((funny(X0) | ~rich(X0)) & (~funny(X0) | rich(X0))) | ((curious(X0) | curious(X0)) & (~curious(X0) | ~curious(X0)))) & (((curious(X0) | ~curious(X0)) & (~curious(X0) | curious(X0))) | ((rich(X0) | funny(X0)) & (~funny(X0) | ~rich(X0))))) [nnf transformation 13]
57. ! [X0] : (((~generous(X0) | ~strong(X0)) | ~brave(X0)) & (brave(X0) | (generous(X0) & strong(X0)))) [nnf transformation 14]
58. ! [X0] : ((~generous(X0) | ~strong(X0) | ~brave(X0)) & (brave(X0) | (generous(X0) & strong(X0)))) [flattening 57]
59. ! [X0] : ((~funny(X0) | calm(X0)) & (~calm(X0) | funny(X0))) [nnf transformation 16]
89. ~brave(X0) | wise(X0) | humble(X0) [cnf transformation 45]
102. ~calm(paul) | ~humble(X0) [cnf transformation 51]
103. rich(paul) | ~humble(X0) [cnf transformation 51]
108. humble(X0) | ~generous(X0) | humble(X0) [cnf transformation 53]
123. funny(X0) | ~rich(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 56]
124. funny(X0) | ~rich(X0) | curious(X0) | curious(X0) [cnf transformation 56]
126. brave(X0) | generous(X0) [cnf transformation 58]
131. ~funny(X0) | calm(X0) [cnf transformation 59]
138. ~wise(john) [cnf transformation 22]
141. funny(X0) | ~rich(X0) | ~curious(X0) [duplicate literal removal 123]
142. funny(X0) | ~rich(X0) | curious(X0) [duplicate literal removal 124]
143. ~generous(X0) | humble(X0) [duplicate literal removal 108]
210. 13 <=> ! [X0] : ~humble(X0) [avatar definition]
211. ~humble(X0) <- (13) [avatar component clause 210]
213. 14 <=> rich(paul) [avatar definition]
215. rich(paul) <- (14) [avatar component clause 213]
216. 13 | 14 [avatar split clause 103,213,210]
218. 15 <=> calm(paul) [avatar definition]
220. ~calm(paul) <- (~15) [avatar component clause 218]
221. 13 | ~15 [avatar split clause 102,218,210]
227. ~rich(X0) | funny(X0) [subsumption resolution 141,142]
269. wise(X0) | humble(X0) | generous(X0) [resolution 89,126]
270. wise(X0) | generous(X0) <- (13) [subsumption resolution 269,211]
271. generous(john) <- (13) [resolution 270,138]
274. humble(john) <- (13) [resolution 271,143]
275. $false <- (13) [subsumption resolution 274,211]
276. ~13 [avatar contradiction clause 275]
288. funny(paul) <- (14) [resolution 215,227]
293. calm(paul) <- (14) [resolution 288,131]
304. $false <- (14, ~15) [subsumption resolution 293,220]
305. ~14 | 15 [avatar contradiction clause 304]
306. $false [avatar sat refutation 216,221,276,305]
% SZS output end Proof for 462567934594269848164860
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not happy or not wise then paul is either patient or generous and vice versa. If mary is old then lucy is not happy or brave. Everyone who is tall or not old is not generous. Everyone who is both not curious and not wise is quiet or generous and vice versa. If fred is both patient and curious then someone is not funny. Everyone who is either brave or not kind is both not tall and generous. Everyone who is quiet or not generous is both rich and not kind. Everyone who is not funny is wise. If john is not brave or not generous then susan is both not creative and not funny and vice versa. Everyone who is both tall and not happy is rich and vice versa. If someone is not funny then fred is both not wise and not old. Everyone who is both curious and happy is both not tall and calm. If someone is not old then someone is either calm or happy and vice versa. If mary is not brave or not patient then alice is both tall and kind. Everyone who is not tall or happy is either tall or not wise. Everyone who is funny is both not calm and generous and vice versa. Lucy is either humble or rich. Someone is both not happy and not humble. Someone is generous. Someone is either wise or not creative. Someone is not brave or not rich. Someone is not tall or not happy. | John is brave. | entailment | ((?[X]:((~happy(X)|~wise(X))))<=>((patient(paul)<~>generous(paul))))&
((old(mary))=>((~happy(lucy)|brave(lucy))))&
(![X]:((tall(X)|~old(X))=>~generous(X)))&
(![X]:((~curious(X)&~wise(X))<=>(quiet(X)|generous(X))))&
(((patient(fred)&curious(fred)))=>(?[X]:(~funny(X))))&
(![X]:((brave(X)<~>~kind(X))=>(~tall(X)&generous(X))))&
(![X]:((quiet(X)|~generous(X))=>(rich(X)&~kind(X))))&
(![X]:(~funny(X)=>wise(X)))&
(((~brave(john)|~generous(john)))<=>((~creative(susan)&~funny(susan))))&
(![X]:((tall(X)&~happy(X))<=>rich(X)))&
((?[X]:(~funny(X)))=>((~wise(fred)&~old(fred))))&
(![X]:((curious(X)&happy(X))=>(~tall(X)&calm(X))))&
((?[X]:(~old(X)))<=>(?[X]:((calm(X)<~>happy(X)))))&
(((~brave(mary)|~patient(mary)))=>((tall(alice)&kind(alice))))&
(![X]:((~tall(X)|happy(X))=>(tall(X)<~>~wise(X))))&
(![X]:(funny(X)<=>(~calm(X)&generous(X))))&
((humble(lucy)<~>rich(lucy)))&
(?[X]:((~happy(X)&~humble(X))))&
(?[X]:(generous(X)))&
(?[X]:((wise(X)<~>~creative(X))))&
(?[X]:((~brave(X)|~rich(X))))&
(?[X]:((~tall(X)|~happy(X)))) | brave(john) | [
"p2",
"p7",
"p8",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4137959268062036136461728
% SZS output start Proof for 4137959268062036136461728
3. ! [X0] : ((~old(X0) | tall(X0)) => ~generous(X0)) [input p2]
8. ! [X0] : (~funny(X0) => wise(X0)) [input p7]
9. (~generous(john) | ~brave(john)) <=> (~funny(susan) & ~creative(susan)) [input p8]
11. ? [X0] : ~funny(X0) => (~old(fred) & ~wise(fred)) [input p10]
16. ! [X0] : (funny(X0) <=> (generous(X0) & ~calm(X0))) [input p15]
23. ~brave(john) [input hypothesis]
27. ! [X0] : (~generous(X0) | (old(X0) & ~tall(X0))) [ennf transformation 3]
32. ! [X0] : (wise(X0) | funny(X0)) [ennf transformation 8]
33. (~old(fred) & ~wise(fred)) | ! [X0] : funny(X0) [ennf transformation 11]
47. ((~generous(john) | ~brave(john)) | (funny(susan) | creative(susan))) & ((~funny(susan) & ~creative(susan)) | (generous(john) & brave(john))) [nnf transformation 9]
48. (~generous(john) | ~brave(john) | funny(susan) | creative(susan)) & ((~funny(susan) & ~creative(susan)) | (generous(john) & brave(john))) [flattening 47]
57. ! [X0] : ((funny(X0) | (~generous(X0) | calm(X0))) & ((generous(X0) & ~calm(X0)) | ~funny(X0))) [nnf transformation 16]
58. ! [X0] : ((funny(X0) | ~generous(X0) | calm(X0)) & ((generous(X0) & ~calm(X0)) | ~funny(X0))) [flattening 57]
79. ~generous(X0) | old(X0) [cnf transformation 27]
94. funny(X0) | wise(X0) [cnf transformation 32]
97. ~funny(susan) | brave(john) [cnf transformation 48]
103. ~wise(fred) | funny(X0) [cnf transformation 33]
104. ~old(fred) | funny(X0) [cnf transformation 33]
120. ~funny(X0) | generous(X0) [cnf transformation 58]
131. ~brave(john) [cnf transformation 23]
192. 14 <=> funny(susan) [avatar definition]
193. ~funny(susan) <- (~14) [avatar component clause 192]
196. 15 <=> brave(john) [avatar definition]
205. 15 | ~14 [avatar split clause 97,192,196]
209. 17 <=> ! [X0] : funny(X0) [avatar definition]
210. funny(X0) <- (17) [avatar component clause 209]
212. 18 <=> old(fred) [avatar definition]
214. ~old(fred) <- (~18) [avatar component clause 212]
215. 17 | ~18 [avatar split clause 104,212,209]
217. 19 <=> wise(fred) [avatar definition]
219. ~wise(fred) <- (~19) [avatar component clause 217]
220. 17 | ~19 [avatar split clause 103,217,209]
304. ~15 [avatar split clause 131,196]
311. $false <- (~14, 17) [resolution 210,193]
312. 14 | ~17 [avatar contradiction clause 311]
326. generous(X0) | wise(X0) [resolution 120,94]
454. old(X2) | wise(X2) [resolution 326,79]
544. wise(fred) <- (~18) [resolution 454,214]
546. $false <- (~18, ~19) [subsumption resolution 544,219]
547. 18 | 19 [avatar contradiction clause 546]
548. $false [avatar sat refutation 205,215,220,304,312,547]
% SZS output end Proof for 4137959268062036136461728
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old is both not generous and not kind and vice versa.
Everyone who is both not kind and not calm is both funny and tall.
If someone is either rich or happy then someone is calm and vice versa.
If someone is not humble then someone is generous or not creative.
Everyone who is not generous or not tall is either not quiet or curious and vice versa.
Everyone who is both not creative and not rich is both not brave and humble and vice versa.
If someone is strong or old then john is brave or not tall.
Everyone who is both brave and not calm is either not strong or not tall.
If someone is old or quiet then lucy is both not rich and patient and vice versa.
Everyone who is not strong is both not calm and not rich and vice versa.
Everyone who is humble or tall is both calm and curious.
Everyone who is either not quiet or humble is rich.
Everyone who is not patient or tall is both brave and not curious.
Everyone who is both calm and creative is not brave or not calm and vice versa.
If someone is strong or creative then someone is both not rich and calm.
Everyone who is happy is both wise and not strong and vice versa.
Alice is both not kind and calm.
Someone is calm or not calm.
Someone is both not rich and wise.
Alice is quiet.
Lucy is either not happy or rich.
Someone is strong.
Someone is not funny. | John is curious. | neutral | (![X]:(~old(X)<=>(~generous(X)&~kind(X))))&
(![X]:((~kind(X)&~calm(X))=>(funny(X)&tall(X))))&
((?[X]:((rich(X)<~>happy(X))))<=>(?[X]:(calm(X))))&
((?[X]:(~humble(X)))=>(?[X]:((generous(X)|~creative(X)))))&
(![X]:((~generous(X)|~tall(X))<=>(~quiet(X)<~>curious(X))))&
(![X]:((~creative(X)&~rich(X))<=>(~brave(X)&humble(X))))&
((?[X]:((strong(X)|old(X))))=>((brave(john)|~tall(john))))&
(![X]:((brave(X)&~calm(X))=>(~strong(X)<~>~tall(X))))&
((?[X]:((old(X)|quiet(X))))<=>((~rich(lucy)&patient(lucy))))&
(![X]:(~strong(X)<=>(~calm(X)&~rich(X))))&
(![X]:((humble(X)|tall(X))=>(calm(X)&curious(X))))&
(![X]:((~quiet(X)<~>humble(X))=>rich(X)))&
(![X]:((~patient(X)|tall(X))=>(brave(X)&~curious(X))))&
(![X]:((calm(X)&creative(X))<=>(~brave(X)|~calm(X))))&
((?[X]:((strong(X)|creative(X))))=>(?[X]:((~rich(X)&calm(X)))))&
(![X]:(happy(X)<=>(wise(X)&~strong(X))))&
((~kind(alice)&calm(alice)))&
(?[X]:((calm(X)|~calm(X))))&
(?[X]:((~rich(X)&wise(X))))&
(quiet(alice))&
((~happy(lucy)<~>rich(lucy)))&
(?[X]:(strong(X)))&
(?[X]:(~funny(X))) | curious(john) | [] | null | 0 |
If someone is old then paul is both not calm and quiet and vice versa. Everyone who is not tall or old is quiet. If someone is both not quiet and quiet then someone is strong or not humble and vice versa. If john is either not patient or wise then alice is kind. Everyone who is curious is kind or old. Everyone who is not humble or happy is not patient and vice versa. Everyone who is either curious or not rich is both funny and old and vice versa. Everyone who is quiet or not happy is both strong and not quiet and vice versa. Everyone who is not old is not patient or not funny and vice versa. If fred is humble then someone is either tall or not creative. If paul is either not happy or wise then someone is not rich and vice versa. If someone is either generous or not kind then someone is not patient or not kind and vice versa. Everyone who is either calm or curious is either tall or funny. If paul is either not calm or not wise then someone is not tall or not patient and vice versa. Everyone who is either not curious or not kind is either creative or not quiet. If susan is not curious or not funny then lucy is kind or humble and vice versa. Alice is creative or curious. Someone is either not tall or tall. John is tall or creative. Someone is either not quiet or not calm. John is either happy or not kind. Lucy is wise or not rich. Someone is either calm or not quiet. | Lucy is not kind. | neutral | ((?[X]:(old(X)))<=>((~calm(paul)&quiet(paul))))&
(![X]:((~tall(X)|old(X))=>quiet(X)))&
((?[X]:((~quiet(X)&quiet(X))))<=>(?[X]:((strong(X)|~humble(X)))))&
(((~patient(john)<~>wise(john)))=>(kind(alice)))&
(![X]:(curious(X)=>(kind(X)|old(X))))&
(![X]:((~humble(X)|happy(X))<=>~patient(X)))&
(![X]:((curious(X)<~>~rich(X))<=>(funny(X)&old(X))))&
(![X]:((quiet(X)|~happy(X))<=>(strong(X)&~quiet(X))))&
(![X]:(~old(X)<=>(~patient(X)|~funny(X))))&
((humble(fred))=>(?[X]:((tall(X)<~>~creative(X)))))&
(((~happy(paul)<~>wise(paul)))<=>(?[X]:(~rich(X))))&
((?[X]:((generous(X)<~>~kind(X))))<=>(?[X]:((~patient(X)|~kind(X)))))&
(![X]:((calm(X)<~>curious(X))=>(tall(X)<~>funny(X))))&
(((~calm(paul)<~>~wise(paul)))<=>(?[X]:((~tall(X)|~patient(X)))))&
(![X]:((~curious(X)<~>~kind(X))=>(creative(X)<~>~quiet(X))))&
(((~curious(susan)|~funny(susan)))<=>((kind(lucy)|humble(lucy))))&
((creative(alice)|curious(alice)))&
(?[X]:((~tall(X)<~>tall(X))))&
((tall(john)|creative(john)))&
(?[X]:((~quiet(X)<~>~calm(X))))&
((happy(john)<~>~kind(john)))&
((wise(lucy)|~rich(lucy)))&
(?[X]:((calm(X)<~>~quiet(X)))) | ~kind(lucy) | [] | null | 0 |
Everyone who is not strong or not funny is either not patient or not curious and vice versa.
If someone is either not patient or not old then someone is either quiet or rich and vice versa.
Everyone who is strong or curious is both not wise and not brave.
Everyone who is not funny is both not generous and quiet and vice versa.
If someone is happy or not curious then susan is either calm or rich and vice versa.
If someone is either not calm or calm then someone is both rich and old.
If someone is either funny or old then alice is not old.
Everyone who is either brave or tall is patient or not calm and vice versa.
Everyone who is creative is old.
If paul is curious then someone is generous.
Everyone who is not old is curious or not kind and vice versa.
If someone is curious or not generous then someone is both humble and rich and vice versa.
If someone is both not tall and tall then someone is strong or funny.
If someone is either wise or not quiet then susan is not old or not creative and vice versa.
Everyone who is both not happy and not curious is both funny and not calm and vice versa.
If someone is not funny then paul is not tall or not curious and vice versa.
Alice is both not generous and not creative.
Fred is not patient or not curious.
Someone is either brave or kind.
Susan is creative.
Alice is not happy or not generous.
Someone is tall or not kind.
Someone is both not rich and not kind.
Susan is humble. | Fred is curious. | neutral | (![X]:((~strong(X)|~funny(X))<=>(~patient(X)<~>~curious(X))))&
((?[X]:((~patient(X)<~>~old(X))))<=>(?[X]:((quiet(X)<~>rich(X)))))&
(![X]:((strong(X)|curious(X))=>(~wise(X)&~brave(X))))&
(![X]:(~funny(X)<=>(~generous(X)&quiet(X))))&
((?[X]:((happy(X)|~curious(X))))<=>((calm(susan)<~>rich(susan))))&
((?[X]:((~calm(X)<~>calm(X))))=>(?[X]:((rich(X)&old(X)))))&
((?[X]:((funny(X)<~>old(X))))=>(~old(alice)))&
(![X]:((brave(X)<~>tall(X))<=>(patient(X)|~calm(X))))&
(![X]:(creative(X)=>old(X)))&
((curious(paul))=>(?[X]:(generous(X))))&
(![X]:(~old(X)<=>(curious(X)|~kind(X))))&
((?[X]:((curious(X)|~generous(X))))<=>(?[X]:((humble(X)&rich(X)))))&
((?[X]:((~tall(X)&tall(X))))=>(?[X]:((strong(X)|funny(X)))))&
((?[X]:((wise(X)<~>~quiet(X))))<=>((~old(susan)|~creative(susan))))&
(![X]:((~happy(X)&~curious(X))<=>(funny(X)&~calm(X))))&
((?[X]:(~funny(X)))<=>((~tall(paul)|~curious(paul))))&
((~generous(alice)&~creative(alice)))&
((~patient(fred)|~curious(fred)))&
(?[X]:((brave(X)<~>kind(X))))&
(creative(susan))&
((~happy(alice)|~generous(alice)))&
(?[X]:((tall(X)|~kind(X))))&
(?[X]:((~rich(X)&~kind(X))))&
(humble(susan)) | curious(fred) | [] | null | 0 |
Everyone who is not creative is not creative or not quiet. If alice is not humble then someone is both rich and happy. Everyone who is not patient is rich or not calm. If john is not humble or calm then mary is funny and vice versa. If mary is not funny then fred is both not funny and not tall. If someone is humble or calm then paul is not strong or not kind. If alice is not quiet or patient then lucy is creative. If someone is either not calm or not creative then someone is quiet or calm and vice versa. Everyone who is strong or not old is creative and vice versa. Everyone who is quiet is rich and vice versa. Everyone who is not funny or not wise is not tall or not funny. If someone is not happy then john is not creative. Everyone who is either curious or not generous is curious or happy. Everyone who is quiet or not kind is either generous or not quiet and vice versa. If susan is either brave or not generous then someone is either happy or not rich and vice versa. If someone is either old or not tall then someone is either not rich or tall and vice versa. Fred is either not kind or not creative. Paul is not creative. John is not humble or old. John is either curious or brave. John is generous or not happy. Paul is not calm. Lucy is not creative or not tall. Fred is tall or not calm. | Susan is not rich. | neutral | (![X]:(~creative(X)=>(~creative(X)|~quiet(X))))&
((~humble(alice))=>(?[X]:((rich(X)&happy(X)))))&
(![X]:(~patient(X)=>(rich(X)|~calm(X))))&
(((~humble(john)|calm(john)))<=>(funny(mary)))&
((~funny(mary))=>((~funny(fred)&~tall(fred))))&
((?[X]:((humble(X)|calm(X))))=>((~strong(paul)|~kind(paul))))&
(((~quiet(alice)|patient(alice)))=>(creative(lucy)))&
((?[X]:((~calm(X)<~>~creative(X))))<=>(?[X]:((quiet(X)|calm(X)))))&
(![X]:((strong(X)|~old(X))<=>creative(X)))&
(![X]:(quiet(X)<=>rich(X)))&
(![X]:((~funny(X)|~wise(X))=>(~tall(X)|~funny(X))))&
((?[X]:(~happy(X)))=>(~creative(john)))&
(![X]:((curious(X)<~>~generous(X))=>(curious(X)|happy(X))))&
(![X]:((quiet(X)|~kind(X))<=>(generous(X)<~>~quiet(X))))&
(((brave(susan)<~>~generous(susan)))<=>(?[X]:((happy(X)<~>~rich(X)))))&
((?[X]:((old(X)<~>~tall(X))))<=>(?[X]:((~rich(X)<~>tall(X)))))&
((~kind(fred)<~>~creative(fred)))&
(~creative(paul))&
((~humble(john)|old(john)))&
((curious(john)<~>brave(john)))&
((generous(john)|~happy(john)))&
(~calm(paul))&
((~creative(lucy)|~tall(lucy)))&
((tall(fred)|~calm(fred))) | ~rich(susan) | [] | null | 0 |
Everyone who is creative is both not quiet and not calm and vice versa.
If paul is not creative then someone is either strong or calm.
Everyone who is either humble or not funny is tall or not generous and vice versa.
Everyone who is not kind is rich.
If paul is patient or not generous then someone is either not rich or kind and vice versa.
Everyone who is happy is both quiet and wise.
If someone is both not happy and tall then someone is not creative or patient.
Everyone who is tall or funny is happy or not kind and vice versa.
If fred is both not calm and not generous then someone is both not calm and wise and vice versa.
Everyone who is funny is rich and vice versa.
Everyone who is either not kind or funny is not old and vice versa.
Everyone who is not calm is either quiet or happy and vice versa.
If alice is not kind then alice is either not humble or funny and vice versa.
Everyone who is not old or not calm is not brave and vice versa.
Everyone who is both kind and not brave is kind or funny and vice versa.
If alice is either humble or calm then someone is either strong or patient and vice versa.
Lucy is rich.
Mary is both old and not happy.
Someone is both not strong and humble.
Someone is either not old or wise.
Someone is not patient.
Someone is tall or curious. | Paul is not wise. | neutral | (![X]:(creative(X)<=>(~quiet(X)&~calm(X))))&
((~creative(paul))=>(?[X]:((strong(X)<~>calm(X)))))&
(![X]:((humble(X)<~>~funny(X))<=>(tall(X)|~generous(X))))&
(![X]:(~kind(X)=>rich(X)))&
(((patient(paul)|~generous(paul)))<=>(?[X]:((~rich(X)<~>kind(X)))))&
(![X]:(happy(X)=>(quiet(X)&wise(X))))&
((?[X]:((~happy(X)&tall(X))))=>(?[X]:((~creative(X)|patient(X)))))&
(![X]:((tall(X)|funny(X))<=>(happy(X)|~kind(X))))&
(((~calm(fred)&~generous(fred)))<=>(?[X]:((~calm(X)&wise(X)))))&
(![X]:(funny(X)<=>rich(X)))&
(![X]:((~kind(X)<~>funny(X))<=>~old(X)))&
(![X]:(~calm(X)<=>(quiet(X)<~>happy(X))))&
((~kind(alice))<=>((~humble(alice)<~>funny(alice))))&
(![X]:((~old(X)|~calm(X))<=>~brave(X)))&
(![X]:((kind(X)&~brave(X))<=>(kind(X)|funny(X))))&
(((humble(alice)<~>calm(alice)))<=>(?[X]:((strong(X)<~>patient(X)))))&
(rich(lucy))&
((old(mary)&~happy(mary)))&
(?[X]:((~strong(X)&humble(X))))&
(?[X]:((~old(X)<~>wise(X))))&
(?[X]:(~patient(X)))&
(?[X]:((tall(X)|curious(X)))) | ~wise(paul) | [] | null | 0 |
Everyone who is generous or not kind is either not old or not strong and vice versa.
Everyone who is either quiet or strong is both not tall and not wise and vice versa.
Everyone who is strong or not wise is both not humble and kind and vice versa.
Everyone who is either generous or not calm is not strong.
Everyone who is both not kind and not rich is both creative and not brave.
Everyone who is happy or brave is rich.
If alice is either rich or not curious then alice is both tall and not creative.
Everyone who is either not curious or not rich is either not kind or quiet and vice versa.
If alice is both patient and not kind then fred is both calm and patient and vice versa.
Everyone who is not happy is not creative or generous.
Everyone who is either tall or not generous is not rich and vice versa.
Everyone who is both quiet and not brave is either brave or not old and vice versa.
Everyone who is both brave and not wise is kind or not old and vice versa.
If someone is both not quiet and not creative then john is not tall.
Everyone who is either not funny or not wise is not quiet and vice versa.
If someone is not generous then alice is tall or not creative and vice versa.
John is old.
Alice is either humble or not kind.
Someone is old.
Someone is not generous or not patient.
Paul is calm or happy.
Someone is generous.
Someone is both not tall and old.
Mary is not curious. | John is wise. | entailment | (![X]:((generous(X)|~kind(X))<=>(~old(X)<~>~strong(X))))&
(![X]:((quiet(X)<~>strong(X))<=>(~tall(X)&~wise(X))))&
(![X]:((strong(X)|~wise(X))<=>(~humble(X)&kind(X))))&
(![X]:((generous(X)<~>~calm(X))=>~strong(X)))&
(![X]:((~kind(X)&~rich(X))=>(creative(X)&~brave(X))))&
(![X]:((happy(X)|brave(X))=>rich(X)))&
(((rich(alice)<~>~curious(alice)))=>((tall(alice)&~creative(alice))))&
(![X]:((~curious(X)<~>~rich(X))<=>(~kind(X)<~>quiet(X))))&
(((patient(alice)&~kind(alice)))<=>((calm(fred)&patient(fred))))&
(![X]:(~happy(X)=>(~creative(X)|generous(X))))&
(![X]:((tall(X)<~>~generous(X))<=>~rich(X)))&
(![X]:((quiet(X)&~brave(X))<=>(brave(X)<~>~old(X))))&
(![X]:((brave(X)&~wise(X))<=>(kind(X)|~old(X))))&
((?[X]:((~quiet(X)&~creative(X))))=>(~tall(john)))&
(![X]:((~funny(X)<~>~wise(X))<=>~quiet(X)))&
((?[X]:(~generous(X)))<=>((tall(alice)|~creative(alice))))&
(old(john))&
((humble(alice)<~>~kind(alice)))&
(?[X]:(old(X)))&
(?[X]:((~generous(X)|~patient(X))))&
((calm(paul)|happy(paul)))&
(?[X]:(generous(X)))&
(?[X]:((~tall(X)&old(X))))&
(~curious(mary)) | wise(john) | [
"p2",
"p11",
"p12",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 5189981131757969217829404
% SZS output start Proof for 5189981131757969217829404
3. ! [X0] : ((~wise(X0) | strong(X0)) <=> (kind(X0) & ~humble(X0))) [input p2]
12. ! [X0] : ((~brave(X0) & quiet(X0)) <=> (brave(X0) <~> ~old(X0))) [input p11]
13. ! [X0] : ((~wise(X0) & brave(X0)) <=> (~old(X0) | kind(X0))) [input p12]
17. old(john) [input p16]
25. ~wise(john) [input hypothesis]
38. ! [X0] : (((~wise(X0) | strong(X0)) | (~kind(X0) | humble(X0))) & ((kind(X0) & ~humble(X0)) | (wise(X0) & ~strong(X0)))) [nnf transformation 3]
39. ! [X0] : ((~wise(X0) | strong(X0) | ~kind(X0) | humble(X0)) & ((kind(X0) & ~humble(X0)) | (wise(X0) & ~strong(X0)))) [flattening 38]
46. ! [X0] : (((~brave(X0) & quiet(X0)) | ((brave(X0) | old(X0)) & (~old(X0) | ~brave(X0)))) & (((old(X0) | ~brave(X0)) & (~old(X0) | brave(X0))) | (brave(X0) | ~quiet(X0)))) [nnf transformation 12]
47. ! [X0] : (((~brave(X0) & quiet(X0)) | ((brave(X0) | old(X0)) & (~old(X0) | ~brave(X0)))) & (((old(X0) | ~brave(X0)) & (~old(X0) | brave(X0))) | brave(X0) | ~quiet(X0))) [flattening 46]
48. ! [X0] : (((~wise(X0) & brave(X0)) | (old(X0) & ~kind(X0))) & ((~old(X0) | kind(X0)) | (wise(X0) | ~brave(X0)))) [nnf transformation 13]
49. ! [X0] : (((~wise(X0) & brave(X0)) | (old(X0) & ~kind(X0))) & (~old(X0) | kind(X0) | wise(X0) | ~brave(X0))) [flattening 48]
80. wise(X0) | kind(X0) [cnf transformation 39]
113. ~brave(X0) | ~old(X0) | ~brave(X0) [cnf transformation 47]
116. ~kind(X0) | brave(X0) [cnf transformation 49]
128. old(john) [cnf transformation 17]
138. ~wise(john) [cnf transformation 25]
140. ~brave(X0) | ~old(X0) [duplicate literal removal 113]
224. kind(john) [resolution 80,138]
225. brave(john) [resolution 116,224]
230. ~old(john) [resolution 140,225]
232. $false [subsumption resolution 230,128]
% SZS output end Proof for 5189981131757969217829404
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or not rich is both wise and not happy and vice versa. If someone is strong or happy then someone is either not patient or not wise. Everyone who is either strong or old is both not humble and not strong. If someone is not generous then susan is either not quiet or not kind. Everyone who is both creative and rich is either calm or not tall and vice versa. Everyone who is either curious or not tall is humble and vice versa. Everyone who is generous is not creative or not patient and vice versa. Everyone who is old is both happy and generous. If someone is quiet then someone is either not funny or not humble. Everyone who is either not generous or wise is not calm. If someone is funny then someone is both humble and not strong and vice versa. If lucy is not brave or humble then someone is not generous. If mary is not happy then john is both not happy and quiet and vice versa. If paul is either generous or not quiet then alice is either not wise or wise. Everyone who is curious or patient is both humble and not rich. Everyone who is both not calm and humble is not curious or tall and vice versa. Someone is not old. Someone is either not old or not creative. Someone is both tall and creative. Susan is not humble or funny. Someone is both not old and kind. Paul is not quiet. Someone is either not curious or wise. | Susan is funny. | entailment | (![X]:((~tall(X)|~rich(X))<=>(wise(X)&~happy(X))))&
((?[X]:((strong(X)|happy(X))))=>(?[X]:((~patient(X)<~>~wise(X)))))&
(![X]:((strong(X)<~>old(X))=>(~humble(X)&~strong(X))))&
((?[X]:(~generous(X)))=>((~quiet(susan)<~>~kind(susan))))&
(![X]:((creative(X)&rich(X))<=>(calm(X)<~>~tall(X))))&
(![X]:((curious(X)<~>~tall(X))<=>humble(X)))&
(![X]:(generous(X)<=>(~creative(X)|~patient(X))))&
(![X]:(old(X)=>(happy(X)&generous(X))))&
((?[X]:(quiet(X)))=>(?[X]:((~funny(X)<~>~humble(X)))))&
(![X]:((~generous(X)<~>wise(X))=>~calm(X)))&
((?[X]:(funny(X)))<=>(?[X]:((humble(X)&~strong(X)))))&
(((~brave(lucy)|humble(lucy)))=>(?[X]:(~generous(X))))&
((~happy(mary))<=>((~happy(john)&quiet(john))))&
(((generous(paul)<~>~quiet(paul)))=>((~wise(alice)<~>wise(alice))))&
(![X]:((curious(X)|patient(X))=>(humble(X)&~rich(X))))&
(![X]:((~calm(X)&humble(X))<=>(~curious(X)|tall(X))))&
(?[X]:(~old(X)))&
(?[X]:((~old(X)<~>~creative(X))))&
(?[X]:((tall(X)&creative(X))))&
((~humble(susan)|funny(susan)))&
(?[X]:((~old(X)&kind(X))))&
(~quiet(paul))&
(?[X]:((~curious(X)<~>wise(X)))) | funny(susan) | [
"p14",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 5618302733184605274980608
% SZS output start Proof for 5618302733184605274980608
15. ! [X0] : ((patient(X0) | curious(X0)) => (~rich(X0) & humble(X0))) [input p14]
16. ! [X0] : ((humble(X0) & ~calm(X0)) <=> (tall(X0) | ~curious(X0))) [input p15]
20. funny(susan) | ~humble(susan) [input p19]
24. ~funny(susan) [input hypothesis]
37. ! [X0] : ((~rich(X0) & humble(X0)) | (~patient(X0) & ~curious(X0))) [ennf transformation 15]
66. ! [X0] : (((humble(X0) & ~calm(X0)) | (~tall(X0) & curious(X0))) & ((tall(X0) | ~curious(X0)) | (~humble(X0) | calm(X0)))) [nnf transformation 16]
67. ! [X0] : (((humble(X0) & ~calm(X0)) | (~tall(X0) & curious(X0))) & (tall(X0) | ~curious(X0) | ~humble(X0) | calm(X0))) [flattening 66]
125. humble(X0) | ~curious(X0) [cnf transformation 37]
132. humble(X0) | curious(X0) [cnf transformation 67]
139. funny(susan) | ~humble(susan) [cnf transformation 20]
145. ~funny(susan) [cnf transformation 24]
236. humble(X0) [subsumption resolution 132,125]
247. funny(susan) [subsumption resolution 139,236]
258. $false [subsumption resolution 145,247]
% SZS output end Proof for 5618302733184605274980608
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or not quiet is both kind and quiet.
If someone is quiet or not happy then mary is happy.
If susan is either not kind or not generous then lucy is generous.
Everyone who is not generous or calm is creative.
Everyone who is calm is not generous or not tall and vice versa.
Everyone who is rich is both not curious and not brave and vice versa.
Everyone who is curious or calm is both humble and generous and vice versa.
Everyone who is old or not kind is both not strong and not creative.
If someone is not creative then someone is rich and vice versa.
If someone is both not curious and not humble then someone is either brave or rich and vice versa.
Everyone who is tall or brave is both humble and not old and vice versa.
Everyone who is either tall or not funny is both not generous and strong.
Everyone who is not kind or curious is not patient.
If someone is not curious then fred is either not humble or not brave.
If someone is both not happy and kind then susan is either not patient or not funny.
Everyone who is humble or not quiet is rich or quiet and vice versa.
Alice is either not patient or not creative.
Someone is creative or not tall.
Someone is happy.
Paul is not old or kind. | Mary is curious. | entailment | (![X]:((patient(X)|~quiet(X))=>(kind(X)&quiet(X))))&
((?[X]:((quiet(X)|~happy(X))))=>(happy(mary)))&
(((~kind(susan)<~>~generous(susan)))=>(generous(lucy)))&
(![X]:((~generous(X)|calm(X))=>creative(X)))&
(![X]:(calm(X)<=>(~generous(X)|~tall(X))))&
(![X]:(rich(X)<=>(~curious(X)&~brave(X))))&
(![X]:((curious(X)|calm(X))<=>(humble(X)&generous(X))))&
(![X]:((old(X)|~kind(X))=>(~strong(X)&~creative(X))))&
((?[X]:(~creative(X)))<=>(?[X]:(rich(X))))&
((?[X]:((~curious(X)&~humble(X))))<=>(?[X]:((brave(X)<~>rich(X)))))&
(![X]:((tall(X)|brave(X))<=>(humble(X)&~old(X))))&
(![X]:((tall(X)<~>~funny(X))=>(~generous(X)&strong(X))))&
(![X]:((~kind(X)|curious(X))=>~patient(X)))&
((?[X]:(~curious(X)))=>((~humble(fred)<~>~brave(fred))))&
((?[X]:((~happy(X)&kind(X))))=>((~patient(susan)<~>~funny(susan))))&
(![X]:((humble(X)|~quiet(X))<=>(rich(X)|quiet(X))))&
((~patient(alice)<~>~creative(alice)))&
(?[X]:((creative(X)|~tall(X))))&
(?[X]:(happy(X)))&
((~old(paul)|kind(paul))) | curious(mary) | [
"p0",
"p5",
"p9",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3866067751774587958904089
% SZS output start Proof for 3866067751774587958904089
1. ! [X0] : ((~quiet(X0) | patient(X0)) => (quiet(X0) & kind(X0))) [input p0]
6. ! [X0] : (rich(X0) <=> (~brave(X0) & ~curious(X0))) [input p5]
10. ? [X0] : (~humble(X0) & ~curious(X0)) <=> ? [X0] : (brave(X0) <~> rich(X0)) [input p9]
16. ! [X0] : ((~quiet(X0) | humble(X0)) <=> (quiet(X0) | rich(X0))) [input p15]
21. ~curious(mary) [input hypothesis]
23. ? [X0] : (~humble(X0) & ~curious(X0)) <=> ? [X1] : (brave(X1) <~> rich(X1)) [rectify 10]
27. ! [X0] : ((quiet(X0) & kind(X0)) | (quiet(X0) & ~patient(X0))) [ennf transformation 1]
37. ! [X0] : ((rich(X0) | (brave(X0) | curious(X0))) & ((~brave(X0) & ~curious(X0)) | ~rich(X0))) [nnf transformation 6]
38. ! [X0] : ((rich(X0) | brave(X0) | curious(X0)) & ((~brave(X0) & ~curious(X0)) | ~rich(X0))) [flattening 37]
46. (? [X0] : (~humble(X0) & ~curious(X0)) | ! [X1] : ((brave(X1) | ~rich(X1)) & (rich(X1) | ~brave(X1)))) & (? [X1] : ((~rich(X1) | ~brave(X1)) & (rich(X1) | brave(X1))) | ! [X0] : (humble(X0) | curious(X0))) [nnf transformation 23]
47. (? [X0] : (~humble(X0) & ~curious(X0)) | ! [X1] : ((brave(X1) | ~rich(X1)) & (rich(X1) | ~brave(X1)))) & (? [X2] : ((~rich(X2) | ~brave(X2)) & (rich(X2) | brave(X2))) | ! [X3] : (humble(X3) | curious(X3))) [rectify 46]
48. ? [X0] : (~humble(X0) & ~curious(X0)) => (~humble(sK2) & ~curious(sK2)) [choice axiom]
49. ? [X2] : ((~rich(X2) | ~brave(X2)) & (rich(X2) | brave(X2))) => ((~rich(sK3) | ~brave(sK3)) & (rich(sK3) | brave(sK3))) [choice axiom]
50. ((~humble(sK2) & ~curious(sK2)) | ! [X1] : ((brave(X1) | ~rich(X1)) & (rich(X1) | ~brave(X1)))) & (((~rich(sK3) | ~brave(sK3)) & (rich(sK3) | brave(sK3))) | ! [X3] : (humble(X3) | curious(X3))) [skolemisation 47,49,48]
55. ! [X0] : (((~quiet(X0) | humble(X0)) | (~quiet(X0) & ~rich(X0))) & ((quiet(X0) | rich(X0)) | (quiet(X0) & ~humble(X0)))) [nnf transformation 16]
56. ! [X0] : ((~quiet(X0) | humble(X0) | (~quiet(X0) & ~rich(X0))) & (quiet(X0) | rich(X0) | (quiet(X0) & ~humble(X0)))) [flattening 55]
63. quiet(X0) | quiet(X0) [cnf transformation 27]
72. ~brave(X0) | ~rich(X0) [cnf transformation 38]
73. brave(X0) | rich(X0) | curious(X0) [cnf transformation 38]
89. ~humble(sK2) | rich(X1) | ~brave(X1) [cnf transformation 50]
90. ~humble(sK2) | brave(X1) | ~rich(X1) [cnf transformation 50]
107. ~quiet(X0) | humble(X0) | ~quiet(X0) [cnf transformation 56]
112. ~curious(mary) [cnf transformation 21]
114. ~quiet(X0) | humble(X0) [duplicate literal removal 107]
115. quiet(X0) [duplicate literal removal 63]
133. 4 <=> ! [X1] : ~rich(X1) [avatar definition]
134. ~rich(X1) <- (4) [avatar component clause 133]
148. ~humble(sK2) | ~rich(X1) [subsumption resolution 90,72]
150. 8 <=> humble(sK2) [avatar definition]
152. ~humble(sK2) <- (~8) [avatar component clause 150]
153. 4 | ~8 [avatar split clause 148,150,133]
154. ~humble(sK2) | ~brave(X1) [subsumption resolution 89,72]
156. 9 <=> ! [X1] : ~brave(X1) [avatar definition]
157. ~brave(X1) <- (9) [avatar component clause 156]
158. 9 | ~8 [avatar split clause 154,150,156]
169. 11 <=> ! [X3] : humble(X3) [avatar definition]
170. humble(X3) <- (11) [avatar component clause 169]
184. 14 <=> ! [X0] : curious(X0) [avatar definition]
185. curious(X0) <- (14) [avatar component clause 184]
197. humble(X0) [subsumption resolution 114,115]
198. 11 [avatar split clause 197,169]
230. $false <- (~8, 11) [subsumption resolution 152,170]
231. 8 | ~11 [avatar contradiction clause 230]
236. $false <- (14) [resolution 185,112]
237. ~14 [avatar contradiction clause 236]
261. rich(X2) | curious(X2) <- (9) [resolution 73,157]
262. curious(X2) <- (4, 9) [subsumption resolution 261,134]
263. 14 | ~4 | ~9 [avatar split clause 262,156,133,184]
264. $false [avatar sat refutation 153,158,198,231,237,263]
% SZS output end Proof for 3866067751774587958904089
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both generous and not calm then mary is either happy or not funny and vice versa.
Everyone who is either happy or not humble is both rich and not strong.
If someone is generous or not curious then someone is either old or generous.
Everyone who is funny is either not old or strong.
If fred is either not old or not creative then lucy is both not old and patient and vice versa.
Everyone who is both old and not kind is both brave and old and vice versa.
If lucy is wise then someone is old or not curious and vice versa.
Everyone who is not generous is either not generous or old and vice versa.
Everyone who is curious or humble is both not humble and calm.
Everyone who is not old or kind is both not patient and wise.
Everyone who is both not happy and curious is both not humble and kind and vice versa.
Everyone who is not funny is both not humble and quiet and vice versa.
If lucy is generous or not wise then someone is quiet or creative and vice versa.
Everyone who is brave is humble and vice versa.
Everyone who is not happy or rich is not kind or brave.
If someone is happy or not patient then fred is either not happy or patient.
Alice is not generous.
Mary is both wise and not curious.
Lucy is curious.
Paul is both not kind and not calm.
Lucy is patient or not tall.
Mary is not rich.
John is not brave. | Fred is not strong. | entailment | ((?[X]:((generous(X)&~calm(X))))<=>((happy(mary)<~>~funny(mary))))&
(![X]:((happy(X)<~>~humble(X))=>(rich(X)&~strong(X))))&
((?[X]:((generous(X)|~curious(X))))=>(?[X]:((old(X)<~>generous(X)))))&
(![X]:(funny(X)=>(~old(X)<~>strong(X))))&
(((~old(fred)<~>~creative(fred)))<=>((~old(lucy)&patient(lucy))))&
(![X]:((old(X)&~kind(X))<=>(brave(X)&old(X))))&
((wise(lucy))<=>(?[X]:((old(X)|~curious(X)))))&
(![X]:(~generous(X)<=>(~generous(X)<~>old(X))))&
(![X]:((curious(X)|humble(X))=>(~humble(X)&calm(X))))&
(![X]:((~old(X)|kind(X))=>(~patient(X)&wise(X))))&
(![X]:((~happy(X)&curious(X))<=>(~humble(X)&kind(X))))&
(![X]:(~funny(X)<=>(~humble(X)&quiet(X))))&
(((generous(lucy)|~wise(lucy)))<=>(?[X]:((quiet(X)|creative(X)))))&
(![X]:(brave(X)<=>humble(X)))&
(![X]:((~happy(X)|rich(X))=>(~kind(X)|brave(X))))&
((?[X]:((happy(X)|~patient(X))))=>((~happy(fred)<~>patient(fred))))&
(~generous(alice))&
((wise(mary)&~curious(mary)))&
(curious(lucy))&
((~kind(paul)&~calm(paul)))&
((patient(lucy)|~tall(lucy)))&
(~rich(mary))&
(~brave(john)) | ~strong(fred) | [
"p1",
"p7",
"p8",
"p9",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2890760567389919931672137
% SZS output start Proof for 2890760567389919931672137
2. ! [X0] : ((happy(X0) <~> ~humble(X0)) => (~strong(X0) & rich(X0))) [input p1]
8. ! [X0] : (~generous(X0) <=> (~generous(X0) <~> old(X0))) [input p7]
9. ! [X0] : ((humble(X0) | curious(X0)) => (calm(X0) & ~humble(X0))) [input p8]
10. ! [X0] : ((kind(X0) | ~old(X0)) => (wise(X0) & ~patient(X0))) [input p9]
16. ? [X0] : (~patient(X0) | happy(X0)) => (~happy(fred) <~> patient(fred)) [input p15]
24. strong(fred) [input hypothesis]
27. ! [X0] : ((~strong(X0) & rich(X0)) | (happy(X0) <=> ~humble(X0))) [ennf transformation 2]
30. ! [X0] : ((calm(X0) & ~humble(X0)) | (~humble(X0) & ~curious(X0))) [ennf transformation 9]
31. ! [X0] : ((wise(X0) & ~patient(X0)) | (~kind(X0) & old(X0))) [ennf transformation 10]
34. (~happy(fred) <~> patient(fred)) | ! [X0] : (patient(X0) & ~happy(X0)) [ennf transformation 16]
39. ! [X0] : ((~strong(X0) & rich(X0)) | ((happy(X0) | humble(X0)) & (~humble(X0) | ~happy(X0)))) [nnf transformation 27]
53. ! [X0] : ((~generous(X0) | ((~generous(X0) | ~old(X0)) & (old(X0) | generous(X0)))) & (((~old(X0) | generous(X0)) & (old(X0) | ~generous(X0))) | generous(X0))) [nnf transformation 8]
64. ((~patient(fred) | happy(fred)) & (patient(fred) | ~happy(fred))) | ! [X0] : (patient(X0) & ~happy(X0)) [nnf transformation 34]
74. ~strong(X0) | happy(X0) | humble(X0) [cnf transformation 39]
95. ~old(X0) | generous(X0) | generous(X0) [cnf transformation 53]
97. ~generous(X0) | ~generous(X0) | ~old(X0) [cnf transformation 53]
99. ~humble(X0) | ~humble(X0) [cnf transformation 30]
102. ~patient(X0) | old(X0) [cnf transformation 31]
121. patient(fred) | ~happy(fred) | ~happy(X0) [cnf transformation 64]
133. strong(fred) [cnf transformation 24]
134. ~humble(X0) [duplicate literal removal 99]
135. ~old(X0) | generous(X0) [duplicate literal removal 95]
136. ~old(X0) | ~generous(X0) [duplicate literal removal 97]
208. 15 <=> ! [X0] : ~old(X0) [avatar definition]
209. ~old(X0) <- (15) [avatar component clause 208]
220. ~old(X0) [subsumption resolution 135,136]
221. 15 [avatar split clause 220,208]
255. 24 <=> happy(fred) [avatar definition]
257. happy(fred) <- (24) [avatar component clause 255]
259. 25 <=> patient(fred) [avatar definition]
260. patient(fred) <- (25) [avatar component clause 259]
264. 26 <=> ! [X0] : ~happy(X0) [avatar definition]
265. ~happy(X0) <- (26) [avatar component clause 264]
268. 26 | ~24 | 25 [avatar split clause 121,259,255,264]
296. happy(fred) | humble(fred) [resolution 74,133]
300. happy(fred) [subsumption resolution 296,134]
301. 24 [avatar split clause 300,255]
302. $false <- (24, 26) [subsumption resolution 257,265]
303. ~24 | ~26 [avatar contradiction clause 302]
309. old(fred) <- (25) [resolution 260,102]
310. $false <- (15, 25) [subsumption resolution 309,209]
311. ~15 | ~25 [avatar contradiction clause 310]
312. $false [avatar sat refutation 221,268,301,303,311]
% SZS output end Proof for 2890760567389919931672137
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If susan is either old or quiet then someone is old or not strong and vice versa. If mary is either not curious or generous then mary is either tall or happy. If someone is not curious or tall then someone is humble or calm. If someone is not strong or strong then mary is patient or not wise and vice versa. If someone is both calm and not kind then someone is not wise and vice versa. If paul is wise then paul is both not humble and strong. If paul is either not old or humble then lucy is either quiet or tall. Everyone who is old or not old is either not tall or humble and vice versa. If lucy is either not calm or not kind then someone is either not kind or strong and vice versa. Everyone who is not happy is either not creative or curious and vice versa. Everyone who is both generous and not happy is both patient and not generous. If someone is tall or not old then paul is both not happy and not patient. Everyone who is both funny and curious is either not happy or creative and vice versa. Everyone who is both kind and not happy is either rich or not creative and vice versa. If someone is not happy or not creative then alice is not old or creative. Everyone who is either generous or not brave is not humble and vice versa. Someone is either not humble or not happy. Paul is either humble or patient. Alice is not tall. Someone is happy. Someone is humble. Paul is both tall and not happy. Someone is either kind or not funny. Someone is either not generous or not old. | Paul is brave. | entailment | (((old(susan)<~>quiet(susan)))<=>(?[X]:((old(X)|~strong(X)))))&
(((~curious(mary)<~>generous(mary)))=>((tall(mary)<~>happy(mary))))&
((?[X]:((~curious(X)|tall(X))))=>(?[X]:((humble(X)|calm(X)))))&
((?[X]:((~strong(X)|strong(X))))<=>((patient(mary)|~wise(mary))))&
((?[X]:((calm(X)&~kind(X))))<=>(?[X]:(~wise(X))))&
((wise(paul))=>((~humble(paul)&strong(paul))))&
(((~old(paul)<~>humble(paul)))=>((quiet(lucy)<~>tall(lucy))))&
(![X]:((old(X)|~old(X))<=>(~tall(X)<~>humble(X))))&
(((~calm(lucy)<~>~kind(lucy)))<=>(?[X]:((~kind(X)<~>strong(X)))))&
(![X]:(~happy(X)<=>(~creative(X)<~>curious(X))))&
(![X]:((generous(X)&~happy(X))=>(patient(X)&~generous(X))))&
((?[X]:((tall(X)|~old(X))))=>((~happy(paul)&~patient(paul))))&
(![X]:((funny(X)&curious(X))<=>(~happy(X)<~>creative(X))))&
(![X]:((kind(X)&~happy(X))<=>(rich(X)<~>~creative(X))))&
((?[X]:((~happy(X)|~creative(X))))=>((~old(alice)|creative(alice))))&
(![X]:((generous(X)<~>~brave(X))<=>~humble(X)))&
(?[X]:((~humble(X)<~>~happy(X))))&
((humble(paul)<~>patient(paul)))&
(~tall(alice))&
(?[X]:(happy(X)))&
(?[X]:(humble(X)))&
((tall(paul)&~happy(paul)))&
(?[X]:((kind(X)<~>~funny(X))))&
(?[X]:((~generous(X)<~>~old(X)))) | brave(paul) | [
"p10",
"p11",
"p15",
"p17",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 7337198448647845750742996
% SZS output start Proof for 7337198448647845750742996
11. ! [X0] : ((~happy(X0) & generous(X0)) => (~generous(X0) & patient(X0))) [input p10]
12. ? [X0] : (~old(X0) | tall(X0)) => (~patient(paul) & ~happy(paul)) [input p11]
16. ! [X0] : ((generous(X0) <~> ~brave(X0)) <=> ~humble(X0)) [input p15]
18. humble(paul) <~> patient(paul) [input p17]
22. ~happy(paul) & tall(paul) [input p21]
25. ~brave(paul) [input hypothesis]
32. ! [X0] : ((~generous(X0) & patient(X0)) | (happy(X0) | ~generous(X0))) [ennf transformation 11]
33. ! [X0] : ((~generous(X0) & patient(X0)) | happy(X0) | ~generous(X0)) [flattening 32]
34. (~patient(paul) & ~happy(paul)) | ! [X0] : (old(X0) & ~tall(X0)) [ennf transformation 12]
67. ! [X0] : ((((brave(X0) | ~generous(X0)) & (~brave(X0) | generous(X0))) | humble(X0)) & (~humble(X0) | ((generous(X0) | brave(X0)) & (~brave(X0) | ~generous(X0))))) [nnf transformation 16]
71. (~patient(paul) | ~humble(paul)) & (patient(paul) | humble(paul)) [nnf transformation 18]
126. ~generous(X0) | happy(X0) | ~generous(X0) [cnf transformation 33]
129. ~patient(paul) | ~tall(X0) [cnf transformation 34]
146. ~humble(X0) | generous(X0) | brave(X0) [cnf transformation 67]
151. patient(paul) | humble(paul) [cnf transformation 71]
156. tall(paul) [cnf transformation 22]
157. ~happy(paul) [cnf transformation 22]
162. ~brave(paul) [cnf transformation 25]
163. ~generous(X0) | happy(X0) [duplicate literal removal 126]
213. 11 <=> ! [X1] : ~tall(X1) [avatar definition]
214. ~tall(X1) <- (11) [avatar component clause 213]
272. 25 <=> humble(paul) [avatar definition]
273. humble(paul) <- (25) [avatar component clause 272]
328. 36 <=> patient(paul) [avatar definition]
332. 11 | ~36 [avatar split clause 129,328,213]
334. 37 <=> happy(paul) [avatar definition]
336. ~happy(paul) <- (~37) [avatar component clause 334]
372. 25 | 36 [avatar split clause 151,328,272]
373. ~37 [avatar split clause 157,334]
492. generous(paul) | brave(paul) <- (25) [resolution 146,273]
496. generous(paul) <- (25) [subsumption resolution 492,162]
524. $false <- (11) [resolution 214,156]
527. ~11 [avatar contradiction clause 524]
531. happy(paul) <- (25) [resolution 496,163]
532. $false <- (25, ~37) [subsumption resolution 531,336]
533. ~25 | 37 [avatar contradiction clause 532]
534. $false [avatar sat refutation 332,372,373,527,533]
% SZS output end Proof for 7337198448647845750742996
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is both curious and not tall then someone is not creative or not curious and vice versa. If someone is old or rich then john is either creative or curious. If susan is both not curious and not calm then someone is tall or not quiet and vice versa. Everyone who is either not patient or not rich is not rich or not strong and vice versa. Everyone who is either not generous or not old is both brave and generous and vice versa. Everyone who is not wise or not brave is both not patient and not humble and vice versa. If someone is both not humble and not kind then fred is not quiet or old and vice versa. If someone is rich or not calm then fred is either not humble or old and vice versa. Everyone who is generous or humble is either not funny or patient and vice versa. If someone is old then someone is both brave and not old. If someone is both happy and wise then someone is both not generous and funny. If alice is either humble or funny then alice is quiet or kind. Everyone who is not curious or not quiet is not strong and vice versa. Everyone who is not creative is both not patient and happy and vice versa. Everyone who is rich or happy is not creative or kind and vice versa. Everyone who is both not curious and creative is patient and vice versa. Someone is curious. Fred is tall. Fred is kind. Alice is not strong. Alice is not rich or not old. Alice is not old or humble. Someone is both generous and not old. | Paul is not quiet. | entailment | (((curious(paul)&~tall(paul)))<=>(?[X]:((~creative(X)|~curious(X)))))&
((?[X]:((old(X)|rich(X))))=>((creative(john)<~>curious(john))))&
(((~curious(susan)&~calm(susan)))<=>(?[X]:((tall(X)|~quiet(X)))))&
(![X]:((~patient(X)<~>~rich(X))<=>(~rich(X)|~strong(X))))&
(![X]:((~generous(X)<~>~old(X))<=>(brave(X)&generous(X))))&
(![X]:((~wise(X)|~brave(X))<=>(~patient(X)&~humble(X))))&
((?[X]:((~humble(X)&~kind(X))))<=>((~quiet(fred)|old(fred))))&
((?[X]:((rich(X)|~calm(X))))<=>((~humble(fred)<~>old(fred))))&
(![X]:((generous(X)|humble(X))<=>(~funny(X)<~>patient(X))))&
((?[X]:(old(X)))=>(?[X]:((brave(X)&~old(X)))))&
((?[X]:((happy(X)&wise(X))))=>(?[X]:((~generous(X)&funny(X)))))&
(((humble(alice)<~>funny(alice)))=>((quiet(alice)|kind(alice))))&
(![X]:((~curious(X)|~quiet(X))<=>~strong(X)))&
(![X]:(~creative(X)<=>(~patient(X)&happy(X))))&
(![X]:((rich(X)|happy(X))<=>(~creative(X)|kind(X))))&
(![X]:((~curious(X)&creative(X))<=>patient(X)))&
(?[X]:(curious(X)))&
(tall(fred))&
(kind(fred))&
(~strong(alice))&
((~rich(alice)|~old(alice)))&
((~old(alice)|humble(alice)))&
(?[X]:((generous(X)&~old(X)))) | ~quiet(paul) | [
"p0",
"p1",
"p3",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7709471583341252264685096
% SZS output start Proof for 7709471583341252264685096
1. (~tall(paul) & curious(paul)) <=> ? [X0] : (~curious(X0) | ~creative(X0)) [input p0]
2. ? [X0] : (rich(X0) | old(X0)) => (creative(john) <~> curious(john)) [input p1]
4. ! [X0] : ((~patient(X0) <~> ~rich(X0)) <=> (~strong(X0) | ~rich(X0))) [input p3]
13. ! [X0] : ((~quiet(X0) | ~curious(X0)) <=> ~strong(X0)) [input p12]
16. ! [X0] : ((creative(X0) & ~curious(X0)) <=> patient(X0)) [input p15]
24. quiet(paul) [input hypothesis]
27. (creative(john) <~> curious(john)) | ! [X0] : (~rich(X0) & ~old(X0)) [ennf transformation 2]
32. ((~tall(paul) & curious(paul)) | ! [X0] : (curious(X0) & creative(X0))) & (? [X0] : (~curious(X0) | ~creative(X0)) | (tall(paul) | ~curious(paul))) [nnf transformation 1]
33. ((~tall(paul) & curious(paul)) | ! [X0] : (curious(X0) & creative(X0))) & (? [X0] : (~curious(X0) | ~creative(X0)) | tall(paul) | ~curious(paul)) [flattening 32]
34. ((~tall(paul) & curious(paul)) | ! [X0] : (curious(X0) & creative(X0))) & (? [X1] : (~curious(X1) | ~creative(X1)) | tall(paul) | ~curious(paul)) [rectify 33]
35. ? [X1] : (~curious(X1) | ~creative(X1)) => (~curious(sK0) | ~creative(sK0)) [choice axiom]
36. ((~tall(paul) & curious(paul)) | ! [X0] : (curious(X0) & creative(X0))) & ((~curious(sK0) | ~creative(sK0)) | tall(paul) | ~curious(paul)) [skolemisation 34,35]
37. ((~curious(john) | ~creative(john)) & (curious(john) | creative(john))) | ! [X0] : (~rich(X0) & ~old(X0)) [nnf transformation 27]
43. ! [X0] : ((((rich(X0) | patient(X0)) & (~rich(X0) | ~patient(X0))) | (strong(X0) & rich(X0))) & ((~strong(X0) | ~rich(X0)) | ((~patient(X0) | rich(X0)) & (~rich(X0) | patient(X0))))) [nnf transformation 4]
44. ! [X0] : ((((rich(X0) | patient(X0)) & (~rich(X0) | ~patient(X0))) | (strong(X0) & rich(X0))) & (~strong(X0) | ~rich(X0) | ((~patient(X0) | rich(X0)) & (~rich(X0) | patient(X0))))) [flattening 43]
67. ! [X0] : (((~quiet(X0) | ~curious(X0)) | strong(X0)) & (~strong(X0) | (quiet(X0) & curious(X0)))) [nnf transformation 13]
68. ! [X0] : ((~quiet(X0) | ~curious(X0) | strong(X0)) & (~strong(X0) | (quiet(X0) & curious(X0)))) [flattening 67]
73. ! [X0] : (((creative(X0) & ~curious(X0)) | ~patient(X0)) & (patient(X0) | (~creative(X0) | curious(X0)))) [nnf transformation 16]
74. ! [X0] : (((creative(X0) & ~curious(X0)) | ~patient(X0)) & (patient(X0) | ~creative(X0) | curious(X0))) [flattening 73]
80. curious(paul) | creative(X0) [cnf transformation 36]
81. curious(paul) | curious(X0) [cnf transformation 36]
87. ~curious(john) | ~creative(john) | ~rich(X0) [cnf transformation 37]
93. ~strong(X0) | ~rich(X0) | ~rich(X0) | patient(X0) [cnf transformation 44]
97. rich(X0) | patient(X0) | rich(X0) [cnf transformation 44]
135. ~quiet(X0) | ~curious(X0) | strong(X0) [cnf transformation 68]
144. ~patient(X0) | ~curious(X0) [cnf transformation 74]
154. quiet(paul) [cnf transformation 24]
157. ~strong(X0) | ~rich(X0) | patient(X0) [duplicate literal removal 93]
158. patient(X0) | rich(X0) [duplicate literal removal 97]
160. 1 <=> ! [X0] : curious(X0) [avatar definition]
161. curious(X0) <- (1) [avatar component clause 160]
168. 3 <=> ! [X0] : creative(X0) [avatar definition]
169. creative(X0) <- (3) [avatar component clause 168]
172. 4 <=> curious(paul) [avatar definition]
174. curious(paul) <- (4) [avatar component clause 172]
175. 1 | 4 [avatar split clause 81,172,160]
176. 3 | 4 [avatar split clause 80,172,168]
187. 7 <=> ! [X0] : ~rich(X0) [avatar definition]
188. ~rich(X0) <- (7) [avatar component clause 187]
190. 8 <=> creative(john) [avatar definition]
192. ~creative(john) <- (~8) [avatar component clause 190]
194. 9 <=> curious(john) [avatar definition]
196. ~curious(john) <- (~9) [avatar component clause 194]
197. 7 | ~8 | ~9 [avatar split clause 87,194,190,187]
231. ~strong(X0) | patient(X0) [subsumption resolution 157,158]
328. ~curious(X0) | rich(X0) [resolution 158,144]
359. ~curious(paul) | strong(paul) [resolution 135,154]
360. strong(paul) <- (4) [subsumption resolution 359,174]
361. patient(paul) <- (4) [resolution 360,231]
366. ~curious(paul) <- (4) [resolution 361,144]
370. $false <- (4) [subsumption resolution 366,174]
371. ~4 [avatar contradiction clause 370]
377. rich(X0) <- (1) [resolution 161,328]
378. $false <- (1, ~9) [resolution 161,196]
383. ~1 | 9 [avatar contradiction clause 378]
384. $false <- (1, 7) [subsumption resolution 188,377]
385. ~1 | ~7 [avatar contradiction clause 384]
386. $false <- (3, ~8) [subsumption resolution 192,169]
387. ~3 | 8 [avatar contradiction clause 386]
388. $false [avatar sat refutation 175,176,197,371,383,385,387]
% SZS output end Proof for 7709471583341252264685096
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or happy is not humble. If lucy is both not brave and curious then fred is patient and vice versa. Everyone who is either rich or brave is both kind and happy. Everyone who is not rich or rich is both not calm and not strong and vice versa. Everyone who is not funny or not strong is not quiet and vice versa. Everyone who is both not humble and kind is either rich or not generous and vice versa. If fred is either not humble or patient then alice is either not brave or not wise and vice versa. If paul is not brave or curious then someone is not strong. Everyone who is rich is not wise and vice versa. If john is not strong then susan is not rich or generous and vice versa. Everyone who is both strong and quiet is either curious or rich. Everyone who is either wise or quiet is wise. Everyone who is either quiet or not tall is not calm or not quiet. Everyone who is not old or happy is strong or not curious and vice versa. Everyone who is both not wise and generous is creative. Someone is both happy and not tall. Someone is not wise or patient. Someone is patient. Someone is both not rich and happy. Someone is either not kind or patient. | Fred is not generous. | neutral | (![X]:((old(X)|happy(X))=>~humble(X)))&
(((~brave(lucy)&curious(lucy)))<=>(patient(fred)))&
(![X]:((rich(X)<~>brave(X))=>(kind(X)&happy(X))))&
(![X]:((~rich(X)|rich(X))<=>(~calm(X)&~strong(X))))&
(![X]:((~funny(X)|~strong(X))<=>~quiet(X)))&
(![X]:((~humble(X)&kind(X))<=>(rich(X)<~>~generous(X))))&
(((~humble(fred)<~>patient(fred)))<=>((~brave(alice)<~>~wise(alice))))&
(((~brave(paul)|curious(paul)))=>(?[X]:(~strong(X))))&
(![X]:(rich(X)<=>~wise(X)))&
((~strong(john))<=>((~rich(susan)|generous(susan))))&
(![X]:((strong(X)&quiet(X))=>(curious(X)<~>rich(X))))&
(![X]:((wise(X)<~>quiet(X))=>wise(X)))&
(![X]:((quiet(X)<~>~tall(X))=>(~calm(X)|~quiet(X))))&
(![X]:((~old(X)|happy(X))<=>(strong(X)|~curious(X))))&
(![X]:((~wise(X)&generous(X))=>creative(X)))&
(?[X]:((happy(X)&~tall(X))))&
(?[X]:((~wise(X)|patient(X))))&
(?[X]:(patient(X)))&
(?[X]:((~rich(X)&happy(X))))&
(?[X]:((~kind(X)<~>patient(X)))) | ~generous(fred) | [] | null | 0 |
Subsets and Splits