Consider the following premises. p_10 or u_3. ~p_10 or q_2. q_2 -> q_1. ~q_1. ~u_3 or q. Can we infer ~q from them? If possible, name the inference rules being used at each step.
 From p_10 or u_3, ~p_10 or q_2 we can infer u_3 or q_2 via resolution. From u_3 or q_2, ~u_3 or q we can infer q_2 or q via resolution. From q_2 -> q_1, ~q_1 we can infer ~q_2 via modus tollens. Finally, from q_2 or q, ~q_2 we can infer q via disjunctive syllogism, which contradicts ~q. Therefore, the answer is no.