the kylie is grammatical.
sent1: if the vinegar is congestive then the wicker is appellate. sent2: if the wicker is appellate the kylie is grammatical. sent3: the windmill gladdens and it is a AFRL. sent4: the vinegar is congestive if there is something such that it does gladden and it is a AFRL.
sent3 -> int1: there is something such that it does gladden and is a kind of a AFRL.; int1 & sent4 -> int2: the fact that the vinegar is congestive hold.; sent1 & int2 -> int3: the wicker is appellate.; sent2 & int3 -> hypothesis;
$hypothesis$ = the kylie is grammatical. ; $context$ = sent1: if the vinegar is congestive then the wicker is appellate. sent2: if the wicker is appellate the kylie is grammatical. sent3: the windmill gladdens and it is a AFRL. sent4: the vinegar is congestive if there is something such that it does gladden and it is a AFRL. ; $proof$ = 
sent3 -> int1: there is something such that it does gladden and is a kind of a AFRL.; int1 & sent4 -> int2: the fact that the vinegar is congestive hold.; sent1 & int2 -> int3: the wicker is appellate.; sent2 & int3 -> hypothesis; __PROVED__