To 'zero sum' and cease to exist is impossible, as there will always be leftover 'data' (if you will) which is capable of rebuilding itself (by itself) into a new coherent existence.
If we were somehow able to prove to ourselves beyond a doubt that we don't exist, the aspects of our mind other than the one's which had proven non-existence would rebuild a new coherent reality that, by forced coincidence, would overpower the aspects of the mind that believed in non-existence.