Consider the following premises. r_6 -> ~u_1. u -> q_6. q_6 -> r_6. u_1. Can we infer u from them? If possible, name the inference rules being used at each step.
 From u -> q_6, q_6 -> r_6 we can infer u -> r_6 via transitivity. From r_6 -> ~u_1, u_1 we can infer ~r_6 via modus tollens. Finally, from u -> r_6, ~r_6 we can infer ~u via modus tollens, which contradicts u. Therefore, the answer is no.