Consider the following premises. forall x_9: T(x_9) -> R(x_9). forall x_9: P(x_9). forall x_9: R(x_9) -> T(x_9). exists x_9: T(x_9) -> ~P(x_9). Can we infer exists x_9: ~R(x_9) from them? If possible, name the inference rules being used at each step.
 From forall x_9: R(x_9) -> T(x_9), forall x_9: T(x_9) -> R(x_9) we can infer forall x_9: R(x_9) <-> T(x_9) via universal biconditional introduction. From exists x_9: T(x_9) -> ~P(x_9), forall x_9: P(x_9) we can infer exists x_9: ~T(x_9) via existential modus tollens. Finally, from forall x_9: R(x_9) <-> T(x_9), exists x_9: ~T(x_9) we can infer exists x_9: ~R(x_9) via existential biconditional elimination. Therefore, the answer is yes.