there exists something such that if it is not nonassociative then it is not inaudible and not desirable.
sent1: the pyralid is both an undesirable and a graduate. sent2: something is nonassociative if it is a kind of a Bethlehem. sent3: the pyralid is an audible if it is not a Bethlehem and it does not sound party. sent4: something is nonassociative if that it is not a Bethlehem and it does not sound party is not right.
sent4 -> int1: the pyralid is nonassociative if that it is not a Bethlehem and does not sound party is false.; void -> assump2: Let's assume that that the pyralid is not a Bethlehem and it does not sound party does not hold.; int1 & assump2 -> int2: the fact that the pyralid is nonassociative is right.; void -> assump1: Let's assume that the pyralid is not nonassociative.; int2 & assump1 -> int3: this is contradiction.; [assump2] & int3 -> int4: the pyralid is not a kind of a Bethlehem and does not sound party.; int4 & sent3 -> int5: the pyralid is an audible.; sent1 -> int6: the pyralid is an undesirable.; int5 & int6 -> int7: the pyralid is a kind of an audible and it is an undesirable.; [assump1] & int7 -> int8: if that the pyralid is not nonassociative is not incorrect it is audible and an undesirable.; int8 -> hypothesis;
$hypothesis$ = there exists something such that if it is not nonassociative then it is not inaudible and not desirable. ; $context$ = sent1: the pyralid is both an undesirable and a graduate. sent2: something is nonassociative if it is a kind of a Bethlehem. sent3: the pyralid is an audible if it is not a Bethlehem and it does not sound party. sent4: something is nonassociative if that it is not a Bethlehem and it does not sound party is not right. ; $proof$ = 
sent4 -> int1: the pyralid is nonassociative if that it is not a Bethlehem and does not sound party is false.; void -> assump2: Let's assume that that the pyralid is not a Bethlehem and it does not sound party does not hold.; int1 & assump2 -> int2: the fact that the pyralid is nonassociative is right.; void -> assump1: Let's assume that the pyralid is not nonassociative.; int2 & assump1 -> int3: this is contradiction.; [assump2] & int3 -> int4: the pyralid is not a kind of a Bethlehem and does not sound party.; int4 & sent3 -> int5: the pyralid is an audible.; sent1 -> int6: the pyralid is an undesirable.; int5 & int6 -> int7: the pyralid is a kind of an audible and it is an undesirable.; [assump1] & int7 -> int8: if that the pyralid is not nonassociative is not incorrect it is audible and an undesirable.; int8 -> hypothesis; __PROVED__