Consider the following premises. forall x_8: ~P_8(x_8) or R_8(x_8). forall x_8: ~R_8(x_8). forall x_8: ~Q_8(x_8) or W(x_8). forall x_8: P_8(x_8) or Q_8(x_8). Can we infer ~W(d) from them? If possible, name the inference rules being used at each step.
 From forall x_8: P_8(x_8) or Q_8(x_8), forall x_8: ~P_8(x_8) or R_8(x_8) we can infer forall x_8: Q_8(x_8) or R_8(x_8) via universal resolution. From forall x_8: Q_8(x_8) or R_8(x_8), forall x_8: ~Q_8(x_8) or W(x_8) we can infer forall x_8: R_8(x_8) or W(x_8) via universal resolution. Finally, from forall x_8: R_8(x_8) or W(x_8), forall x_8: ~R_8(x_8) we can infer forall x_8: W(x_8) via universal disjunctive syllogism, which contradicts ~W(d). Therefore, the answer is no.