Consider the following premises. w_2 <-> r_2. ~r_2. w_2 <-> u_4. Can we infer u_4 from them?
 From w_2 <-> r_2, ~r_2 we can infer ~w_2. From w_2 <-> u_4 we can infer u_4 -> w_2. Finally, from u_4 -> w_2, ~w_2 we can infer ~u_4, which contradicts u_4. Therefore, the answer is no.