Consider the following premises. u -> p_11. p_11 or ~u_1. u. r_1 -> ~p_11. Can we infer r_1 from them? If possible, name the inference rules being used at each step.
 From u we can infer u or u_1 via addition. From p_11 or ~u_1 we can infer u_1 -> p_11 via rewriting. From u -> p_11, u_1 -> p_11, u or u_1 we can infer p_11 via disjunction elimination. Finally, from r_1 -> ~p_11, p_11 we can infer ~r_1 via modus tollens, which contradicts r_1. Therefore, the answer is no.