Consider the following premises. u_4 -> w. w or ~q_11. u_4 or q_11. Can we infer ~w from them? If possible, name the inference rules being used at each step.
 From w or ~q_11 we can infer q_11 -> w via rewriting. Finally, from u_4 -> w, q_11 -> w, u_4 or q_11 we can infer w via disjunction elimination, which contradicts ~w. Therefore, the answer is no.