Consider the following premises. p <-> u_1. w_1 <-> q. w_1 <-> u_1. ~p. Can we infer q from them?
 From p <-> u_1, ~p we can infer ~u_1. From w_1 <-> u_1, ~u_1 we can infer ~w_1. Finally, from w_1 <-> q, ~w_1 we can infer ~q, which contradicts q. Therefore, the answer is no.