Consider the following premises. w_2 <-> w. w_2 <-> q_1. q_4 <-> q_1. ~q_4. Can we infer w from them?
 From q_4 <-> q_1, ~q_4 we can infer ~q_1. From w_2 <-> q_1, ~q_1 we can infer ~w_2. Finally, from w_2 <-> w, ~w_2 we can infer ~w, which contradicts w. Therefore, the answer is no.