Consider this:

1. I declare some function y =f(x)

2. I hypothesize that y = 1 when X = 2

3. I use physics to build a mathematical model to prove that the hypothesis is true

4. The model is physically valid, however, it is not renormalizable

5. Since all proofs are equivalent, any proof of the hypothesis must validate this non renormalizable model

6. Therefore all proofs of this hypothesis are non renormalizable and undecidable

Is this valid reasoning? If you disagree give a counterexample.