Consider the following premises. exists x_9: T_4(x_9) <-> Q_9(x_9). forall x_9: Q_9(x_9) -> R_1(x_9). forall x_9: T_4(x_9). Can we infer exists x_9: R_1(x_9) from them? If possible, name the inference rules being used at each step.
 From exists x_9: T_4(x_9) <-> Q_9(x_9) we can infer exists x_9: T_4(x_9) -> Q_9(x_9) via existential biconditional elimination. From exists x_9: T_4(x_9) -> Q_9(x_9), forall x_9: Q_9(x_9) -> R_1(x_9) we can infer exists x_9: T_4(x_9) -> R_1(x_9) via existential transitivity. Finally, from exists x_9: T_4(x_9) -> R_1(x_9), forall x_9: T_4(x_9) we can infer exists x_9: R_1(x_9) via existential modus ponens. Therefore, the answer is yes.