Consider the following premises. forall x_8: P_8(x_8) or U(x_8). ~U(g) or w. forall x_8: ~P_8(x_8) or R_8(x_8). ~R_8(g). Can we infer ~w from them? If possible, name the inference rules being used at each step.
 From forall x_8: P_8(x_8) or U(x_8), forall x_8: ~P_8(x_8) or R_8(x_8) we can infer forall x_8: U(x_8) or R_8(x_8) via universal resolution. From forall x_8: U(x_8) or R_8(x_8) we can infer U(g) or R_8(g) via universal instantiation. From U(g) or R_8(g), ~U(g) or w we can infer R_8(g) or w via resolution. Finally, from R_8(g) or w, ~R_8(g) we can infer w via disjunctive syllogism, which contradicts ~w. Therefore, the answer is no.