Consider the following premises. w. ~t. p <-> t. t or ~p. Can we infer p from them?
 From p <-> t we can infer t -> p. From t or ~p we can infer p -> t. From p -> t, t -> p we can infer p <-> t. Finally, from p <-> t, ~t we can infer ~p, which contradicts p. Therefore, the answer is no.