Consider the following premises. forall x_16: P_2(x_16) or S(x_16). forall x_16: W_4(x_16) and Q_7(x_16). forall x_16: P_16(x_16) -> R_16(x_16). forall x_16: P_2(x_16) -> ~R_16(x_16). forall x_16: Q_16(x_16) -> R_16(x_16). forall x_16: P_16(x_16) or Q_16(x_16). Can we infer forall x_16: W_4(x_16) and S(x_16) from them? If possible, name the inference rules being used at each step.
 From forall x_16: P_16(x_16) -> R_16(x_16), forall x_16: Q_16(x_16) -> R_16(x_16), forall x_16: P_16(x_16) or Q_16(x_16) we can infer forall x_16: R_16(x_16) via universal disjunction elimination. From forall x_16: P_2(x_16) -> ~R_16(x_16), forall x_16: R_16(x_16) we can infer forall x_16: ~P_2(x_16) via universal modus tollens. From forall x_16: W_4(x_16) and Q_7(x_16) we can infer forall x_16: W_4(x_16) via universal simplification. From forall x_16: P_2(x_16) or S(x_16), forall x_16: ~P_2(x_16) we can infer forall x_16: S(x_16) via universal disjunctive syllogism. Finally, from forall x_16: W_4(x_16), forall x_16: S(x_16) we can infer forall x_16: W_4(x_16) and S(x_16) via universal conjunction. Therefore, the answer is yes.