Consider the following premises. forall z: R(z). forall z: R(z) -> T_3(z). Can we infer exists x_4: T_3(x_4) from them? If possible, name the inference rules being used at each step.
 From forall z: R(z) -> T_3(z), forall z: R(z) we can infer forall z: T_3(z) via universal modus ponens. From forall z: T_3(z) we can infer T_3(f) via universal instantiation. Finally, from T_3(f) we can infer exists x_4: T_3(x_4) via existential generalization. Therefore, the answer is yes.