Consider the following premises. w <-> s_1. w_1 or ~w. Can we infer ~(s_1 -> w_1) from them? If possible, name the inference rules being used at each step.
 From w_1 or ~w we can infer w -> w_1 via rewriting. From w <-> s_1 we can infer s_1 -> w via biconditional elimination. Finally, from s_1 -> w, w -> w_1 we can infer s_1 -> w_1 via transitivity, which contradicts ~(s_1 -> w_1). Therefore, the answer is no.