Consider the following premises. forall x: ~R_4(x). R_4(i) or ~w. Can we infer w from them? If possible, name the inference rules being used at each step.
 From forall x: ~R_4(x) we can infer ~R_4(i) via universal instantiation. From R_4(i) or ~w we can infer w -> R_4(i) via rewriting. Finally, from w -> R_4(i), ~R_4(i) we can infer ~w via modus tollens, which contradicts w. Therefore, the answer is no.