could try this:
x is Father Christmas
(and not, of course, $x[[CxÙ"y[Cy®x=y]]Ù¬$yy=x])
answers the question, but it doesn't do something else we might
like. Our sentence poses a certain problem. On the one hand it is
obviously true; but on the other hand "Father Christmas"
appears to be a referring expression. But, if it were a referring
expression, it seems that the sentence would not be true.
what is the role of the expression? One possible answer is
this. It is really a disguised definite description, and if we paraphrase
the sentence using Russell's theory of descriptions being careful
about scope, we will see how the sentence can be unproblematically
true. (This was Russell's own answer.)
But what is the definite description which is disguised as "Father
Christmas"? Evidently we can't answer this question
by saying, "the thing which is Father Christmas", because
that repeats the expression "Father Christmas", with the
disguise still in place. In fact the question of how to understand
sentences such as this (innocent as it looks) has a long history
and no simple answer.