I am looking for a closed statement (i.e. not depending on any parameter objects) which is true in the internal logic of the topos of simplicial sets, but is not an intuitionistic tautology. Ideally, I would like it to be a simple universal statement of propositional logic (e.g. "for all propositions P, Q, and R, blah blah", like LEM or de Morgan's law).

(To clarify: this has nothing to do with higher topoi or homotopy type theory; it's purely a question about ordinary 1-categorical 1-topos theory.)