Consider the following premises. r_2 -> p. p -> r_3. ~r_3. w and w_4. Can we infer ~w from them? If possible, name the inference rules being used at each step.
 From p -> r_3, ~r_3 we can infer ~p via modus tollens. From r_2 -> p, ~p we can infer ~r_2 via modus tollens. Finally, from w and w_4 we can infer w via simplification, which contradicts ~w. Therefore, the answer is no.