User blog comment:Ubersketch/Uncomputable function/@comment-35470197-20190618223755/@comment-35470197-20190619005558

As I pointed out twice, you have not defined how to encode a statement as a variable. Therefore it does not work, even if you want it to default to 0.

> saying it can solve any decision problem in a single step.

In order to define "decision problem", you need to fix a computation model and encode problems into natural numbers, because you are considering problems beyond recursive computation,

Then according to your assumption, it can solve the decision problem on itself. Contradiction.

> Anyways how do I define the notion of a proof?

It depends on what you want to do. Since you are considering the notion of a proof in your original context, which is different from the usual syntax, you need to define it by yourself. As I recommended, you should not use stuffs if you do not understand the precise formalisation.