Consider the following premises. forall x_10: Q_10(x_10) -> W(x_10). forall x_10: Q_9(x_10). forall x_10: Q_2(x_10). forall x_10: Q_2(x_10) -> Q_10(x_10). forall x_10: T(x_10). Can we infer forall x_10: T(x_10) and W(x_10) from them? If possible, name the inference rules being used at each step.
 From forall x_10: Q_2(x_10) -> Q_10(x_10), forall x_10: Q_10(x_10) -> W(x_10) we can infer forall x_10: Q_2(x_10) -> W(x_10) via universal transitivity. From forall x_10: Q_2(x_10), forall x_10: Q_9(x_10) we can infer forall x_10: Q_2(x_10) and Q_9(x_10) via universal conjunction. From forall x_10: Q_2(x_10) and Q_9(x_10) we can infer forall x_10: Q_2(x_10) via universal simplification. From forall x_10: Q_2(x_10) -> W(x_10), forall x_10: Q_2(x_10) we can infer forall x_10: W(x_10) via universal modus ponens. Finally, from forall x_10: T(x_10), forall x_10: W(x_10) we can infer forall x_10: T(x_10) and W(x_10) via universal conjunction. Therefore, the answer is yes.