Belief does not entail a reasoning disposition

Are there any dispositions one must have if one believes p? A widespread answer emphasizes the role of beliefs in reasoning and holds that if one believes p, one must be disposed to treat p as true (rely on p/use p as a premise) in one's reasoning. I argue that this answer is subject to counterexamples.

Automated summary

Believing in something does not necessarily mean using it as a premise in reasoning.