You are probably better off going with a computability theorem (such as the halting problem) instead of incompleteness. However, I suspect both will get you to the same place. Namely, there exists a program whose behavior cannot be predicted.

There is no theory that says that there does not exist a program whose behavior can be predicted. We have just criminally underfunded research into formal verification; and somehow decided that even computationally limited, code is law programs handling millions of dollars don't need any type of formal verification