Consider the following premises. q -> p_2. q. p -> ~w_4. p_2 -> w_4. Can we infer p from them? If possible, name the inference rules being used at each step.
 From q -> p_2, p_2 -> w_4 we can infer q -> w_4 via transitivity. From q -> w_4, q we can infer w_4 via modus ponens. Finally, from p -> ~w_4, w_4 we can infer ~p via modus tollens, which contradicts p. Therefore, the answer is no.