Consider the following premises. ~w. p_2 -> p. w or ~p. Can we infer p_2 from them? If possible, name the inference rules being used at each step.
 From w or ~p we can infer p -> w via rewriting. From p -> w, ~w we can infer ~p via modus tollens. Finally, from p_2 -> p, ~p we can infer ~p_2 via modus tollens, which contradicts p_2. Therefore, the answer is no.