Without understanding the meaning of the term, you boldly provided links to multiple posts wherein you claimed instantiations were provided? Is this your preferred method of building credibility? It is not working.
What you are doing is this:
"{} = {}" is a tautology.
"{X}$X OR {X}$X" is a tautology.
Since tautology = tautology, "{} = {}" is indistinguishable of "{X}$X OR {X}$X".
This is a trivial way of reasoning.
A non-trivial way of reasoning enables to distinguish between "{} = {}" and "{X}$X OR {X}$X" as follows:
"{} = {}"
can't be used in order to define optional (non-essential) properties of mathematical objects, according to their relations with each other.
"{X}$X OR {X}$X"
can be used in order to define optional (non-essential) properties of mathematical objects according to their relations with each other, where
http://www.internationalskeptics.com/forums/showpost.php?p=11285851&postcount=1535 is a concrete example of such non-trivial reasoning.
What you call
instantiation is simply another name to force {X} to be a successor of X by using the wff "Y$Z <=> Y = {Z}", as if being a successor is an essential (non-optional) property of {X}.
By the way, instantiation is a common enough term in Mathematics. You asked about it once before, and I told you what it meant once before.
Yes teacher, I'm a naughty naughty boy.