Consider the following premises. exists z_3: W_1(z_3) -> S(z_3). forall z_3: R_3(z_3) <-> U(z_3). forall z_3: S(z_3) -> U(z_3). Can we infer exists z_3: W_1(z_3) -> R_3(z_3) from them? If possible, name the inference rules being used at each step.
 From forall z_3: R_3(z_3) <-> U(z_3) we can infer forall z_3: U(z_3) -> R_3(z_3) via universal biconditional elimination. From forall z_3: S(z_3) -> U(z_3), forall z_3: U(z_3) -> R_3(z_3) we can infer forall z_3: S(z_3) -> R_3(z_3) via universal transitivity. Finally, from exists z_3: W_1(z_3) -> S(z_3), forall z_3: S(z_3) -> R_3(z_3) we can infer exists z_3: W_1(z_3) -> R_3(z_3) via existential transitivity. Therefore, the answer is yes.