Consider the following premises. t_2 -> p_1. u_1 -> p_1. ~p_11 or t_2. p_11 or u_1. Can we infer ~p_1 from them? If possible, name the inference rules being used at each step.
 From p_11 or u_1, ~p_11 or t_2 we can infer u_1 or t_2 via resolution. Finally, from u_1 -> p_1, t_2 -> p_1, u_1 or t_2 we can infer p_1 via disjunction elimination, which contradicts ~p_1. Therefore, the answer is no.