Consider the following premises. w or q. p <-> s_1. ~q. ~w or s_1. Can we infer ~p from them?
 From w or q, ~w or s_1 we can infer q or s_1. From p <-> s_1 we can infer s_1 -> p. From q or s_1, ~q we can infer s_1. Finally, from s_1 -> p, s_1 we can infer p, which contradicts ~p. Therefore, the answer is no.