Consider the following premises. forall z: W_3(z) -> R_2(z). forall z: T_3(z) -> P(z). exists z: R(z) -> W_3(z). forall z: R_2(z) -> T_3(z). Can we infer exists z: R(z) -> P(z) from them? If possible, name the inference rules being used at each step.
 From forall z: R_2(z) -> T_3(z), forall z: T_3(z) -> P(z) we can infer forall z: R_2(z) -> P(z) via universal transitivity. From exists z: R(z) -> W_3(z), forall z: W_3(z) -> R_2(z) we can infer exists z: R(z) -> R_2(z) via existential transitivity. Finally, from exists z: R(z) -> R_2(z), forall z: R_2(z) -> P(z) we can infer exists z: R(z) -> P(z) via existential transitivity. Therefore, the answer is yes.