Consider the following premises. forall x_9: P_2(x_9) -> T(x_9). exists x_9: Q_9(x_9). forall x_9: T(x_9) -> P_2(x_9). forall x_9: T(x_9) -> ~Q_9(x_9). Can we infer forall x_9: P_2(x_9) from them? If possible, name the inference rules being used at each step.
 From forall x_9: T(x_9) -> ~Q_9(x_9), exists x_9: Q_9(x_9) we can infer exists x_9: ~T(x_9) via existential modus tollens. From forall x_9: T(x_9) -> P_2(x_9), forall x_9: P_2(x_9) -> T(x_9) we can infer forall x_9: T(x_9) <-> P_2(x_9) via universal biconditional introduction. From forall x_9: T(x_9) <-> P_2(x_9) we can infer forall x_9: P_2(x_9) -> T(x_9) via universal biconditional elimination. Finally, from forall x_9: P_2(x_9) -> T(x_9), exists x_9: ~T(x_9) we can infer exists x_9: ~P_2(x_9) via existential modus tollens, which contradicts forall x_9: P_2(x_9). Therefore, the answer is no.