if that the yaws does not occur is correct then the Neanderthalness but not the necklessness happens.
sent1: that the yaws happens is triggered by that the necklessness occurs. sent2: if that the Neanderthalness but not the necklessness happens is false then the yaws occurs. sent3: the yawing occurs if both the Neanderthalness and the non-necklessness happens. sent4: the necklessness does not occur. sent5: that the necklessness does not occur is true if the yaws does not occur.
void -> assump2: Let's assume that the fact that the Neanderthalness and the non-necklessness occurs is incorrect.; sent2 & assump2 -> int1: the yaws occurs.; void -> assump1: Let's assume that the yawing does not occur.; int1 & assump1 -> int2: this is contradiction.; [assump2] & int2 -> int3: both the Neanderthalness and the neckedness happens.; [assump1] & int3 -> hypothesis;
$hypothesis$ = if that the yaws does not occur is correct then the Neanderthalness but not the necklessness happens. ; $context$ = sent1: that the yaws happens is triggered by that the necklessness occurs. sent2: if that the Neanderthalness but not the necklessness happens is false then the yaws occurs. sent3: the yawing occurs if both the Neanderthalness and the non-necklessness happens. sent4: the necklessness does not occur. sent5: that the necklessness does not occur is true if the yaws does not occur. ; $proof$ = 
void -> assump2: Let's assume that the fact that the Neanderthalness and the non-necklessness occurs is incorrect.; sent2 & assump2 -> int1: the yaws occurs.; void -> assump1: Let's assume that the yawing does not occur.; int1 & assump1 -> int2: this is contradiction.; [assump2] & int2 -> int3: both the Neanderthalness and the neckedness happens.; [assump1] & int3 -> hypothesis; __PROVED__