Consider the following premises. w <-> r_1. ~r_1. r <-> w. w -> r_1. Can we infer r from them?
 From w <-> r_1 we can infer r_1 -> w. From w -> r_1, r_1 -> w we can infer w <-> r_1. From w <-> r_1, ~r_1 we can infer ~w. Finally, from r <-> w, ~w we can infer ~r, which contradicts r. Therefore, the answer is no.