Consider the following premises. u_1 -> w_4. q. w_4 -> r_10. q -> q_15. ~r_10. Can we infer u_1 from them? If possible, name the inference rules being used at each step.
 From q -> q_15, q we can infer q_15 via modus ponens. From u_1 -> w_4, w_4 -> r_10 we can infer u_1 -> r_10 via transitivity. Finally, from u_1 -> r_10, ~r_10 we can infer ~u_1 via modus tollens, which contradicts u_1. Therefore, the answer is no.