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