First of all, I should have wrote "logically inconsistent", but "factually incorrect" sounded better. :) More importantly, it is possible that I misinterpreted what you wrote:

here is an empirical fact : only the present exists, other instants (past or future) do not exist.

I interpreted this as a positive statement that an observer-independent present does actually exist, hundred percent. This is in contradiction with special relativity, as someone else already noted. Reading other comments from you in this thread, it seems like this is not what you meant. It is more like you choose the second option of my dichotomy: the frog's view instead of the bird's view. I have no problem with that.