if the conjugation does not occur the fact that the loop does not occur and/or the concordance does not occur is not true.
sent1: that the looping does not occur or the concordance happens or both yields the conjugation. sent2: the looping occurs. sent3: the loop happens if the conjugation does not occur. sent4: the looping does not occur and/or the concordance does not occur if the conjugation does not occur. sent5: the conjugation occurs if either the looping does not occur or the concordance does not occur or both.
void -> assump2: Let's assume that the loop does not occur or the concordance does not occur or both.; sent5 & assump2 -> int1: the conjugation occurs.; void -> assump1: Let's assume that the conjugation does not occur.; int1 & assump1 -> int2: this is contradiction.; [assump2] & int2 -> int3: that the loop does not occur or the concordance does not occur or both does not hold.; [assump1] & int3 -> hypothesis;
$hypothesis$ = if the conjugation does not occur the fact that the loop does not occur and/or the concordance does not occur is not true. ; $context$ = sent1: that the looping does not occur or the concordance happens or both yields the conjugation. sent2: the looping occurs. sent3: the loop happens if the conjugation does not occur. sent4: the looping does not occur and/or the concordance does not occur if the conjugation does not occur. sent5: the conjugation occurs if either the looping does not occur or the concordance does not occur or both. ; $proof$ = 
void -> assump2: Let's assume that the loop does not occur or the concordance does not occur or both.; sent5 & assump2 -> int1: the conjugation occurs.; void -> assump1: Let's assume that the conjugation does not occur.; int1 & assump1 -> int2: this is contradiction.; [assump2] & int2 -> int3: that the loop does not occur or the concordance does not occur or both does not hold.; [assump1] & int3 -> hypothesis; __PROVED__