Consider the following premises. ~r_3 or t. t -> u_3. r_3 or w. ~w or q_3. u_3 -> r. q_3 -> r. Can we infer ~r from them? If possible, name the inference rules being used at each step.
 From t -> u_3, u_3 -> r we can infer t -> r via transitivity. From r_3 or w, ~r_3 or t we can infer w or t via resolution. From w or t, ~w or q_3 we can infer t or q_3 via resolution. Finally, from t -> r, q_3 -> r, t or q_3 we can infer r via disjunction elimination, which contradicts ~r. Therefore, the answer is no.