if the disqualification does not occur then the nonmonotonicness does not occur.
sent1: that the disqualification happens is caused by that the banding circularity does not occur and the apteralness does not occur. sent2: the fact that the continent happens is incorrect. sent3: the fact that the ventilating Dasypodidae does not occur and the categoricness does not occur is not correct. sent4: that the pathologicalness does not occur but the peripatetic happens is not correct. sent5: the nonmonotonicness does not occur if that the banding circularity does not occur and the apteralness does not occur does not hold.
void -> assump1: Let's assume that the banding circularity does not occur and the apteralness does not occur.; sent1 & assump1 -> int1: the disqualification happens.; void -> assump2: Let's assume that the fact that the disqualification occurs is false.; int1 & assump2 -> int2: this is contradiction.; [assump1] & int2 -> int3: that the banding circularity does not occur and the apteralness does not occur is not true.; sent5 & int3 -> int4: the nonmonotonicness does not occur.; [assump2] & int4 -> hypothesis;
the continent does not occur and the streaming does not occur.
$hypothesis$ = if the disqualification does not occur then the nonmonotonicness does not occur. ; $context$ = sent1: that the disqualification happens is caused by that the banding circularity does not occur and the apteralness does not occur. sent2: the fact that the continent happens is incorrect. sent3: the fact that the ventilating Dasypodidae does not occur and the categoricness does not occur is not correct. sent4: that the pathologicalness does not occur but the peripatetic happens is not correct. sent5: the nonmonotonicness does not occur if that the banding circularity does not occur and the apteralness does not occur does not hold. ; $proof$ = 
void -> assump1: Let's assume that the banding circularity does not occur and the apteralness does not occur.; sent1 & assump1 -> int1: the disqualification happens.; void -> assump2: Let's assume that the fact that the disqualification occurs is false.; int1 & assump2 -> int2: this is contradiction.; [assump1] & int2 -> int3: that the banding circularity does not occur and the apteralness does not occur is not true.; sent5 & int3 -> int4: the nonmonotonicness does not occur.; [assump2] & int4 -> hypothesis; __PROVED__