Consider the following premises. u -> w. ~p_5 or p. p_5 or q_5. p <-> w. ~q_5 or u. Can we infer ~w from them? If possible, name the inference rules being used at each step.
 From p <-> w we can infer p -> w via biconditional elimination. From p_5 or q_5, ~p_5 or p we can infer q_5 or p via resolution. From q_5 or p, ~q_5 or u we can infer p or u via resolution. Finally, from p -> w, u -> w, p or u we can infer w via disjunction elimination, which contradicts ~w. Therefore, the answer is no.