Why is it not possible to prove a system itself doesn't conflict?
For a strong enough system, there is "If this system conflicts, then this system doesn't conflict", so "this system doesn't conflict", no matter what it actually is.
Or that's because the system doesn't know itself?

What type of system are you talking about? A computer system? A language system? A political system? Do you have an example of what you mean?

Aomething from Gödel's_incompleteness_theorems