Consider the following premises. s_2 -> w. w -> p. q -> p_2. p -> p_2. s_2 or q. Can we infer ~p_2 from them?
 From s_2 -> w, w -> p we can infer s_2 -> p. From s_2 -> p, p -> p_2 we can infer s_2 -> p_2. Finally, from s_2 -> p_2, q -> p_2, s_2 or q we can infer p_2, which contradicts ~p_2. Therefore, the answer is no.