Peterofthecorn, can you name any entity other than your god, the existence of which is "proved" by using "logic" in this manner? We never see physicists publishing papers that start out with "If existing faster-than-light neutrinos exist, then faster-than-light neutrinos exist..." Why not? Because scientists set up their claims in such a way that they can be validated or falsified
by appeal to reality itself, rather than carefully-arranged human verbiage. But, if you prefer to argue in syllogisms...
1) An existing god should have consequences in reality that a non-existing god will not.
2) An existing god that has no consequences in reality is indistinguishable from a non-existing god.
3) Per Anselm's Ontological argument, a god that exists is greater than a god that does not exist.
4) An existing god that is indistinguishable from a non-existing god cannot be the Greatest Conceivable Being, therefore it cannot be God.
5) Therefore, an existing God would have consequences in reality that would not be present if there was no existing God.
So, what consequences in reality can you cite as manifestations of the presence of an existing God? Per #2 above, the consequences in question have to be something atheistic/naturalistic world-view would
not anticipate as part of how reality would behave. If the proposed consequence is something both world-views agree on ("There are clouds."), then it is not an effect that distinguishes between "There is an existing god" and "There is no existing god." Miraculous healings of amputees would be one such consequence, if they occurred, hence the title of this Forum.
However, the very fact that you try to prove your god's existence by "pure logic" (and dodgy "logic" at that!) rather than any real consequences of his presence strongly implies that you
anticipate in advance that there will be no such consequences. Which means: when it comes to anticipating how reality will behave, you expect it to behave the way it would if no gods exist. You live in the same godless Universe we do,
and you know it. The purpose then, of the sort of pseudo-syllogism-as-summoning-incantation you use here isn't an attempt to show that your proposed god is real--you already know better than that. What it does, is serve as a way to tell yourself and others that you possess a belief-in-god. When it comes to anticipating reality's behavior, you don't actually have one of those. What you have is a
belief in belief in god. In other words, you believe in the value of the
belief, not in the real existence of the god.
Having a belief-in-god makes you a good person. It says that your life has meaning and purpose, and is your passport to membership in your community of faith. In order to acquire those benefits, you have to
signal to yourself and others that you have belief-in-god. One way to reconcile the contradiction between professing to have a belief-in-god while anticipating the consequences of god's non-existence, is to structure the contents of your belief-in-god so that it is completely divorced from reality. In your case, you have set out to place your god solely in a realm of "pure logic," where he can be summoned into "existence" (in that realm) by the simple trick of inserting "existing" into a premise to modify "god."
Nutshell: The whole method and structure of your "argument" would be neither necessary nor desirable if your god actually existed in reality. The only reason you have to present this sort of "argument" is if, on the level of your understanding of the behavior of reality, you anticipate as if there is no real god.