Consider the following premises. t -> p_4. t or ~p. p_4 -> p. Can we infer ~(p <-> t) from them? If possible, name the inference rules being used at each step.
 From t or ~p we can infer p -> t via rewriting. From t -> p_4, p_4 -> p we can infer t -> p via transitivity. Finally, from p -> t, t -> p we can infer p <-> t via biconditional introduction, which contradicts ~(p <-> t). Therefore, the answer is no.