if the poling guest does not occur then that the arbitralness or the austeniticness or both happens is wrong.
sent1: if the arbitralness does not occur either the premedicalness does not occur or the poling guest does not occur or both. sent2: the non-premedicalness prevents that the arbitralness happens. sent3: the fact that the arbitralness happens and/or the austeniticness happens is incorrect if the premedicalness does not occur. sent4: the fact that the premedicalness occurs but the poling guest does not occur is wrong.
void -> assump2: Let's assume that the premedicalness happens.; void -> assump1: Let's assume that the poling guest does not occur.; assump2 & assump1 -> int1: the premedicalness but not the poling guest happens.; int1 & sent4 -> int2: this is contradiction.; [assump2] & int2 -> int3: the fact that the premedicalness does not occur is not incorrect.; int3 & sent3 -> int4: the fact that the arbitralness happens and/or the austeniticness happens does not hold.; [assump1] & int4 -> hypothesis;
the reverberantness happens.
$hypothesis$ = if the poling guest does not occur then that the arbitralness or the austeniticness or both happens is wrong. ; $context$ = sent1: if the arbitralness does not occur either the premedicalness does not occur or the poling guest does not occur or both. sent2: the non-premedicalness prevents that the arbitralness happens. sent3: the fact that the arbitralness happens and/or the austeniticness happens is incorrect if the premedicalness does not occur. sent4: the fact that the premedicalness occurs but the poling guest does not occur is wrong. ; $proof$ = 
void -> assump2: Let's assume that the premedicalness happens.; void -> assump1: Let's assume that the poling guest does not occur.; assump2 & assump1 -> int1: the premedicalness but not the poling guest happens.; int1 & sent4 -> int2: this is contradiction.; [assump2] & int2 -> int3: the fact that the premedicalness does not occur is not incorrect.; int3 & sent3 -> int4: the fact that the arbitralness happens and/or the austeniticness happens does not hold.; [assump1] & int4 -> hypothesis; __PROVED__