German says that he will not try.

Is there a difference between these two?
- I won't try to refute your theses.
- I will try not to refute your theses.

won't is the same as will not- much like how can't is the same as cannot and so forth.

Yes, but I meant the different word order.
(Thinking it over, I am pretty sure there is a difference)

I think you could have "I will not try to refute your theses" as well as "I will try not to refute your theses " but I don't think it adds any ambiguity to meaning

In this example, it's hard to imagine a substantial difference, but I’m not really convinced the meaning of these two is exactly the same.

"I will try not to refute your theses" means something "I feel the urge to refute your theses, but for some reason I'll try not to do it." The point is that I restrain myself from doing it.
"I will not try to refute your theses" means something like "For some reason (maybe I know it's not possible or very difficult) I will not take the effort. It's more neutral, it doesn’t mean I have to restrain myself.

I, too, have the feeling that it should be “I won’t/will not try to refute your theses”, as what you wrote in the sentence above would be “Ich werde versuchen, Ihre Thesen nicht zu widerlegen”, which is different.

I'll change it then

Thank you