that the overcoat is a kind of a ecclesiasticism is correct.
sent1: if there is something such that the fact that it does not dump allies and is not a ticket is not true the overcoat is a ecclesiasticism. sent2: the favor is not a rifle. sent3: the fact that the favor does not dump allies and is not a ticket is incorrect if it is not a rifle.
sent3 & sent2 -> int1: that the favor does not dump allies and it does not ticket is incorrect.; int1 -> int2: there exists something such that that it does not dump allies and is not a ticket is not right.; int2 & sent1 -> hypothesis;
$hypothesis$ = that the overcoat is a kind of a ecclesiasticism is correct. ; $context$ = sent1: if there is something such that the fact that it does not dump allies and is not a ticket is not true the overcoat is a ecclesiasticism. sent2: the favor is not a rifle. sent3: the fact that the favor does not dump allies and is not a ticket is incorrect if it is not a rifle. ; $proof$ = 
sent3 & sent2 -> int1: that the favor does not dump allies and it does not ticket is incorrect.; int1 -> int2: there exists something such that that it does not dump allies and is not a ticket is not right.; int2 & sent1 -> hypothesis; __PROVED__