if the daemon is obfuscated, there is no efficient procedure which takes the daemon circuit as input and produces a smaller circuit that still solves the problem.
So we can’t find any efficient constructive argument. That rules out most of the obvious strategies.
I don’t think the procedure needs to be efficient to solve the problem, since we only care about existence of a smaller circuit (not an efficient way to produce it).
I don’t think the procedure needs to be efficient to solve the problem, since we only care about existence of a smaller circuit (not an efficient way to produce it).