if the discoursing occurs that the quadraticness happens is correct.
sent1: if the quadrupedalness does not occur and the covert happens then the discourse does not occur. sent2: the non-nonimitativeness and the chemotherapy happens. sent3: the covertness occurs. sent4: that the covertness does not occur prevents that the quadraticness does not occur. sent5: that not the easement but the arbitrativeness happens does not hold if the quadratic does not occur. sent6: that not the quadrupedalness but the covert occurs prevents that the discourse does not occur. sent7: the quadratic happens if that the quadrupedalness does not occur but the covert happens does not hold.
void -> assump1: Let's assume that the non-quadrupedalness and the covert occurs.; sent1 & assump1 -> int1: the discoursing does not occur.; void -> assump2: Let's assume that the discoursing occurs.; int1 & assump2 -> int2: this is contradiction.; [assump1] & int2 -> int3: that the quadrupedalness does not occur and the covertness happens is wrong.; int3 & sent7 -> int4: the quadratic occurs.; [assump2] & int4 -> hypothesis;
the fact that the easement does not occur but the arbitrativeness occurs is false.
$hypothesis$ = if the discoursing occurs that the quadraticness happens is correct. ; $context$ = sent1: if the quadrupedalness does not occur and the covert happens then the discourse does not occur. sent2: the non-nonimitativeness and the chemotherapy happens. sent3: the covertness occurs. sent4: that the covertness does not occur prevents that the quadraticness does not occur. sent5: that not the easement but the arbitrativeness happens does not hold if the quadratic does not occur. sent6: that not the quadrupedalness but the covert occurs prevents that the discourse does not occur. sent7: the quadratic happens if that the quadrupedalness does not occur but the covert happens does not hold. ; $proof$ = 
void -> assump1: Let's assume that the non-quadrupedalness and the covert occurs.; sent1 & assump1 -> int1: the discoursing does not occur.; void -> assump2: Let's assume that the discoursing occurs.; int1 & assump2 -> int2: this is contradiction.; [assump1] & int2 -> int3: that the quadrupedalness does not occur and the covertness happens is wrong.; int3 & sent7 -> int4: the quadratic occurs.; [assump2] & int4 -> hypothesis; __PROVED__