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(despite roughdraft's comments about gumballs... as in right in front of you that you can see subject to different standards than the idea of God or Gods)
We are discussing the simple idea of "I don't believe this" & "I don't believe that". The topic of belief is really beside the point. We can be discussing gumballs, god or anything else and the point stands.
The direct logical negation of "I believe the gumballs are odd" isn't "I believe the gum balls are even". It's actually "I believe the gumballs are not odd."
In this exact same sense, the direct logical negation of "I believe gods exist" is not "I believe there are no gods" but instead "I don't believe gods exist."
Denying the first position only tells you the direct logical negation of the phrase. You would have to make assumptions to draw anything else from it.