Consider the following premises. forall z: Q(z) -> R(z). forall z: R(z) -> R_3(z). forall z: R_2(z) or Q(z). exists z: R_2(z) -> R_3(z). Can we infer exists z: R_3(z) from them?
 From forall z: Q(z) -> R(z), forall z: R(z) -> R_3(z) we can infer forall z: Q(z) -> R_3(z). Finally, from exists z: R_2(z) -> R_3(z), forall z: Q(z) -> R_3(z), forall z: R_2(z) or Q(z) we can infer exists z: R_3(z). Therefore, the answer is yes.