It is the active belief that there is no God, based either on faith or on a lack of empirical evidence.
That's a very narrow definition of "atheism," that neither reflects the literal meaning of the word ("without atheism"), nor a common belief (few atheists actively believe there is certainly no God; agnostic atheism is much more common than "hard" atheism).
Most people would claim that there's not rational reason to believe in God, but that is not the same as "active belief that there is no God" -- we are, after all, talking about a metaphysical subject.
I was responding to Afleitch's assertion that atheism is "simply a non-belief in God", which is not true.
Now you're literally citing doctrines and defining denominations of this supposed "unreligion".
As for homeopathy...you can claim it has been rejected and that many treatments it prescribes ineffective...but you'd have a hard time arguing "successful homeopathy doesn't exist at all."