there is something such that the fact that it is not beakless and/or is anacoluthic does not hold.
sent1: there is something such that that it is not a Lascaux and snowballs rushlight does not hold. sent2: the Haida snowballs rushlight if it is schismatic. sent3: if there exists something such that that it is not a Lascaux and snowballs rushlight does not hold the Haida does not snowballs rushlight. sent4: the fact that the antigen is not beakless and/or it is anacoluthic is wrong if there exists something such that it is not schismatic.
void -> assump1: Let's assume that the Haida is schismatic.; sent2 & assump1 -> int1: the Haida snowballs rushlight.; sent1 & sent3 -> int2: the fact that the Haida does not snowball rushlight is right.; int1 & int2 -> int3: this is contradiction.; [assump1] & int3 -> int4: the Haida is not schismatic.; int4 -> int5: there exists something such that the fact that it is non-schismatic is not incorrect.; int5 & sent4 -> int6: the fact that the antigen is not beakless or is anacoluthic or both is incorrect.; int6 -> hypothesis;
$hypothesis$ = there is something such that the fact that it is not beakless and/or is anacoluthic does not hold. ; $context$ = sent1: there is something such that that it is not a Lascaux and snowballs rushlight does not hold. sent2: the Haida snowballs rushlight if it is schismatic. sent3: if there exists something such that that it is not a Lascaux and snowballs rushlight does not hold the Haida does not snowballs rushlight. sent4: the fact that the antigen is not beakless and/or it is anacoluthic is wrong if there exists something such that it is not schismatic. ; $proof$ = 
void -> assump1: Let's assume that the Haida is schismatic.; sent2 & assump1 -> int1: the Haida snowballs rushlight.; sent1 & sent3 -> int2: the fact that the Haida does not snowball rushlight is right.; int1 & int2 -> int3: this is contradiction.; [assump1] & int3 -> int4: the Haida is not schismatic.; int4 -> int5: there exists something such that the fact that it is non-schismatic is not incorrect.; int5 & sent4 -> int6: the fact that the antigen is not beakless or is anacoluthic or both is incorrect.; int6 -> hypothesis; __PROVED__