Consider the following premises. q_11 -> w. w_3 -> q_11. p_2 or ~r. w -> r. Can we infer ~(w_3 -> p_2) from them? If possible, name the inference rules being used at each step.
 From w_3 -> q_11, q_11 -> w we can infer w_3 -> w via transitivity. From w_3 -> w, w -> r we can infer w_3 -> r via transitivity. From p_2 or ~r we can infer r -> p_2 via rewriting. Finally, from w_3 -> r, r -> p_2 we can infer w_3 -> p_2 via transitivity, which contradicts ~(w_3 -> p_2). Therefore, the answer is no.