"you are mistaken. You say that a belief is not a fact. However, it is a fact. "
A thing that is indisputably the case.
Information used as evidence or as part of a report or news article.
An acceptance that a statement is true or that something exists.
Something one accepts as true or real; a firmly held opinion or conviction.
You're going to have to offer some evidence for that assertion, as the definition of the two words seems to refute your premise.