if the pithead is a quadratic then the southeast is both not aptitudinal and a Baptist.
sent1: the pithead is a quadratic if the fact that the stipendiary is an antitoxin and is not a Baptist is false. sent2: the stipendiary is an antitoxin. sent3: that the southeast is aptitudinal and a Baptist is not incorrect if the pithead is quadratic. sent4: the southeast is a Baptist. sent5: if the fact that that the stipendiary is an antitoxin but it is not a Baptist is false is not false then the pithead is not a kind of a quadratic. sent6: if the stipendiary is not a kind of an antitoxin the pithead is not quadratic. sent7: the southeast is non-aptitudinal thing that is a Baptist if the stipendiary is not a Baptist.
void -> assump2: Let's assume that the pithead is not non-quadratic.; void -> assump1: Let's assume that that the stipendiary is an antitoxin but it is not a Baptist does not hold.; sent5 & assump1 -> int1: the pithead is not quadratic.; assump2 & int1 -> int2: this is contradiction.; [assump1] & int2 -> int3: the stipendiary is an antitoxin but it is not a kind of a Baptist.; int3 -> int4: the stipendiary is not a Baptist.; sent7 & int4 -> int5: the southeast is not aptitudinal but a Baptist.; [assump2] & int5 -> hypothesis;
$hypothesis$ = if the pithead is a quadratic then the southeast is both not aptitudinal and a Baptist. ; $context$ = sent1: the pithead is a quadratic if the fact that the stipendiary is an antitoxin and is not a Baptist is false. sent2: the stipendiary is an antitoxin. sent3: that the southeast is aptitudinal and a Baptist is not incorrect if the pithead is quadratic. sent4: the southeast is a Baptist. sent5: if the fact that that the stipendiary is an antitoxin but it is not a Baptist is false is not false then the pithead is not a kind of a quadratic. sent6: if the stipendiary is not a kind of an antitoxin the pithead is not quadratic. sent7: the southeast is non-aptitudinal thing that is a Baptist if the stipendiary is not a Baptist. ; $proof$ = 
void -> assump2: Let's assume that the pithead is not non-quadratic.; void -> assump1: Let's assume that that the stipendiary is an antitoxin but it is not a Baptist does not hold.; sent5 & assump1 -> int1: the pithead is not quadratic.; assump2 & int1 -> int2: this is contradiction.; [assump1] & int2 -> int3: the stipendiary is an antitoxin but it is not a kind of a Baptist.; int3 -> int4: the stipendiary is not a Baptist.; sent7 & int4 -> int5: the southeast is not aptitudinal but a Baptist.; [assump2] & int5 -> hypothesis; __PROVED__