Consider the following premises. p_11 or ~s_1. w -> p_11. s_1 or w. Can we infer ~p_11 from them? If possible, name the inference rules being used at each step.
 From p_11 or ~s_1 we can infer s_1 -> p_11 via rewriting. Finally, from s_1 -> p_11, w -> p_11, s_1 or w we can infer p_11 via disjunction elimination, which contradicts ~p_11. Therefore, the answer is no.