Consider the following premises. forall y_4: Q_1(y_4) -> W(y_4). forall x_10: P_10(x_10) or Q_10(x_10). forall x_10: P_10(x_10) -> Q_1(x_10). forall x_10: Q_10(x_10) -> Q_1(x_10). Can we infer W(f) from them? If possible, name the inference rules being used at each step.
 From forall x_10: P_10(x_10) -> Q_1(x_10), forall x_10: Q_10(x_10) -> Q_1(x_10), forall x_10: P_10(x_10) or Q_10(x_10) we can infer forall x_10: Q_1(x_10) via universal disjunction elimination. From forall x_10: Q_1(x_10) we can infer Q_1(f) via universal instantiation. From forall y_4: Q_1(y_4) -> W(y_4) we can infer Q_1(f) -> W(f) via universal instantiation. Finally, from Q_1(f) -> W(f), Q_1(f) we can infer W(f) via modus ponens. Therefore, the answer is yes.