Consider the following premises. forall z: R_4(z) or P(z). forall z: P(z) -> T(z). exists z: S_4(z) <-> R_4(z). forall z: T(z) -> S_4(z). Can we infer exists z: S_4(z) from them?
 From forall z: P(z) -> T(z), forall z: T(z) -> S_4(z) we can infer forall z: P(z) -> S_4(z). From exists z: S_4(z) <-> R_4(z) we can infer exists z: R_4(z) -> S_4(z). Finally, from exists z: R_4(z) -> S_4(z), forall z: P(z) -> S_4(z), forall z: R_4(z) or P(z) we can infer exists z: S_4(z). Therefore, the answer is yes.