The conjecture that no finitely axiomatized consistent Vaught theory is Enayat

Let $U$ be a Vaught theory, meaning a theory with the relevant direct interpretation properties described in the paper. Call $U$ Enayat when it interprets itself together with the Tarski biconditionals. Vaught Enayat-theory conjecture. No finitely axiomatized consistent Vaught theory is Enayat. This is the general Vaught-theory version of the sequential conjecture; the paper gives no resolution.