Consider the following premises. w_3 -> s_4. s_4 -> s. w <-> s. Can we infer ~(w_3 -> w) from them?
 From w <-> s we can infer s -> w. From w_3 -> s_4, s_4 -> s we can infer w_3 -> s. Finally, from w_3 -> s, s -> w we can infer w_3 -> w, which contradicts ~(w_3 -> w). Therefore, the answer is no.