if the bookshelf is not nonrepresentative and it is not a broadbill that the bosc is not Lusitanian is correct.
sent1: the bosc is non-Lusitanian if something is both representative and not a broadbill. sent2: the bookshelf is non-Lusitanian if a non-nonrepresentative thing is not a kind of a broadbill. sent3: if the bookshelf is not nonrepresentative and is a broadbill the bosc is not Lusitanian. sent4: the bookshelf is not a broadbill and is not Lusitanian.
void -> assump1: Let's assume that the bookshelf is not nonrepresentative and it is not a kind of a broadbill.; assump1 -> int1: something is not nonrepresentative and is not a kind of a broadbill.; int1 & sent1 -> int2: the bosc is not Lusitanian.; [assump1] & int2 -> hypothesis;
$hypothesis$ = if the bookshelf is not nonrepresentative and it is not a broadbill that the bosc is not Lusitanian is correct. ; $context$ = sent1: the bosc is non-Lusitanian if something is both representative and not a broadbill. sent2: the bookshelf is non-Lusitanian if a non-nonrepresentative thing is not a kind of a broadbill. sent3: if the bookshelf is not nonrepresentative and is a broadbill the bosc is not Lusitanian. sent4: the bookshelf is not a broadbill and is not Lusitanian. ; $proof$ = 
void -> assump1: Let's assume that the bookshelf is not nonrepresentative and it is not a kind of a broadbill.; assump1 -> int1: something is not nonrepresentative and is not a kind of a broadbill.; int1 & sent1 -> int2: the bosc is not Lusitanian.; [assump1] & int2 -> hypothesis; __PROVED__