Consider the following premises. forall x_11: P_2(x_11) -> Q_11(x_11). forall x_11: T(x_11) -> P_2(x_11). forall x_11: Q_11(x_11) -> P_11(x_11). exists x_11: P_11(x_11) -> Q_11(x_11). Can we infer exists x_11: T(x_11) -> P_11(x_11) from them? If possible, name the inference rules being used at each step.
 From exists x_11: P_11(x_11) -> Q_11(x_11), forall x_11: Q_11(x_11) -> P_11(x_11) we can infer exists x_11: P_11(x_11) <-> Q_11(x_11) via existential biconditional introduction. From exists x_11: P_11(x_11) <-> Q_11(x_11) we can infer exists x_11: Q_11(x_11) -> P_11(x_11) via existential biconditional elimination. From forall x_11: P_2(x_11) -> Q_11(x_11), exists x_11: Q_11(x_11) -> P_11(x_11) we can infer exists x_11: P_2(x_11) -> P_11(x_11) via existential transitivity. Finally, from forall x_11: T(x_11) -> P_2(x_11), exists x_11: P_2(x_11) -> P_11(x_11) we can infer exists x_11: T(x_11) -> P_11(x_11) via existential transitivity. Therefore, the answer is yes.