Consider the following premises. forall x_10: W_3(x_10) or S_3(x_10). forall x_10: R_1(x_10) <-> W_3(x_10). forall x_10: P_10(x_10) or ~R_1(x_10). forall x_10: ~P_10(x_10). Can we infer forall x_10: S_3(x_10) from them? If possible, name the inference rules being used at each step.
 From forall x_10: P_10(x_10) or ~R_1(x_10) we can infer forall x_10: R_1(x_10) -> P_10(x_10) via universal rewriting. From forall x_10: R_1(x_10) -> P_10(x_10), forall x_10: ~P_10(x_10) we can infer forall x_10: ~R_1(x_10) via universal modus tollens. From forall x_10: R_1(x_10) <-> W_3(x_10), forall x_10: ~R_1(x_10) we can infer forall x_10: ~W_3(x_10) via universal biconditional elimination. Finally, from forall x_10: W_3(x_10) or S_3(x_10), forall x_10: ~W_3(x_10) we can infer forall x_10: S_3(x_10) via universal disjunctive syllogism. Therefore, the answer is yes.