Results in complexity theory such as $P \neq NP$.

Philosophically, it makes sense that there is a difference between verification and search, and no-one has discovered a counterexample.

(Note, that this result is not strictly speaking known to be correct. However, it is believed to be correct and routinely used as if it were simply true. No one, as far as I can tell, would ever begin a proof in complexity theory by assuming $P = NP$. )