Consider the following premises. exists z: R_3(z) -> P_3(z). forall z: ~R_3(z). forall z: P_3(z) -> R_3(z). Can we infer exists z: ~P_3(z) from them?
 From exists z: R_3(z) -> P_3(z), forall z: P_3(z) -> R_3(z) we can infer exists z: R_3(z) <-> P_3(z). From exists z: R_3(z) <-> P_3(z) we can infer exists z: P_3(z) -> R_3(z). Finally, from exists z: P_3(z) -> R_3(z), forall z: ~R_3(z) we can infer exists z: ~P_3(z). Therefore, the answer is yes.