Consider the following premises. u_1 -> w. w -> t. t -> w. ~t. w <-> u_1. Can we infer u_1 from them?
 From w -> t, t -> w we can infer w <-> t. From w <-> u_1 we can infer w -> u_1. From w -> u_1, u_1 -> w we can infer w <-> u_1. From w <-> t, ~t we can infer ~w. Finally, from w <-> u_1, ~w we can infer ~u_1, which contradicts u_1. Therefore, the answer is no.