Consider the following premises. w_4 -> t. t -> r. w_4 or ~r. Can we infer ~(w_4 <-> r) from them?
 From w_4 or ~r we can infer r -> w_4. From w_4 -> t, t -> r we can infer w_4 -> r. Finally, from w_4 -> r, r -> w_4 we can infer w_4 <-> r, which contradicts ~(w_4 <-> r). Therefore, the answer is no.