Existence & the Contrary

I'd like to examine & query the intelligibility of a series of words placed together with the intent of forming a structure that imparts coherent meaning. The verbal structure I had in mind is the following: "It does not exist." My claim is that this is an absurdity based on thoughts hopefully successfully expressed in the very near future.
What I am disputing here is the "it" bit in relation to the not existing bit. "It" refers to something that exists; if it didn't, then it wouldn't be an it. To put it another way, an "it" requires an "is." I can't refer to something that isn't in terms of being an it. Its non-existence means it may be more accurately decribed as a not-it. Though even here, "Its non-existence" is fraught with unintelligibility as its very non-existence means it isn't an it with which to have a non-existence.
So to re-cap, the sentence should read, "It does exist," unless it doesn't, in which case the less said the better.