Proper term for someone who actively believes there is no god?

[Lehrling]

Although "atheism" is simply a disbelief (not a belief) the "atheist", the person who "holds" that disbelief, automatically has to defer to the antithesis of "god exists" (i.e. "god does NOT exist").
The dictionary is simply supplying us with the logical outcome of atheism.

"... automatically has to defer" is wrong. You are implicitly asserting that one must hold a position on whether there is a god. I see no reason why this should be the case. Someone who knew nothing of religion would not even understand the question if you asked them whether god existed. Knowing about a hypothesis (in this case, god) does not necessarily imply that one must agree or disagree with it.

I am simply trying to harmonize what atheism is with what the dictionary says an atheist is.
Atheism is not a belief. But the dictionary clearly says the atheist (not "anti-theist", or "gnostic atheist", but "atheist") believes there is no god.
If you have a better way for us to agree with the objective authority on the english language while still maintaining the proper definition of atheism, then I am happy to hear it.

Atheists such as myself prefer to disassociate ourselves from such atheists, calling them "strong atheists", and ourselves "weak atheists".

I take mild offence to this statement. I wouldn't class myself as a strong atheist, but I don't agree with this either: "Most atheists are quite open to hearing evidence for god; we have not rejected the possibility that god exists". I also think this part of your post is preachy and snooty.

Is it inaccurate?
Are all atheists automatically ruling out the possibility of god?

The "proper term for someone who actively believes there is no god" is gnostic atheist. The proper term for someone who does not believe in a god is agnostic atheist. "Atheist" on its own is non specific as to whether one believes actively in anything at all.

I agree with the last part.
But to be "gnostic" is to actually "know" something.
It has to do with knowledge, not belief.
A gnostic theist is someone who both knows AND believes that god exists.
An agnostic atheist is someone who does not know if god exists or not, but determines that being an atheist is the most logical choice.