Evidence for atheism

[Jackalope]

It's not a statement within the realm of classical logic.

No shit...lol, I should have been more precise (and I forget sometimes that people better educated than I approach this with standardized and classical terminology), mea culpa "not p" was a poor choice of words on my part, I was describing a state, not a rule of inference. "Not p" in the context of a statement which might be made by...say, a creationist. As in, "If such and such is true, than" whereby you state "such and such is not true". The requirement that each component be sound.

OK so I think the source of our mutual confusion has become apparent.

So you're asking about this:

If P then Q
Not P
Therefore, not Q.

That's a fallacy of the inverse (denying the antecedent)