Consider the following premises. w -> s_2. r <-> s_2. s_2 -> u_1. ~r. u_1 -> w. Can we infer w from them?
 From s_2 -> u_1, u_1 -> w we can infer s_2 -> w. From r <-> s_2, ~r we can infer ~s_2. From s_2 -> w, w -> s_2 we can infer s_2 <-> w. Finally, from s_2 <-> w, ~s_2 we can infer ~w, which contradicts w. Therefore, the answer is no.