[Kranar]

You are absolutely correct and you have discovered Rice's Theorem [1]. The fact that you generalized the halting problem on your own is a very good indication that you fundamentally understand it.

[1] https://en.wikipedia.org/wiki/Rice%27s_theorem

[6gvONxR4sf7o]

I certainly do feel like I understand it better now. Thanks again for the pointers!