Consider the following premises. forall z: Q_2(z) -> P_4(z). exists z: P_4(z) -> S(z). forall z: Q_2(z) or ~S(z). Can we infer exists z: Q_2(z) -> S(z) from them?
 From forall z: Q_2(z) or ~S(z) we can infer forall z: S(z) -> Q_2(z). Finally, from forall z: Q_2(z) -> P_4(z), exists z: P_4(z) -> S(z) we can infer exists z: Q_2(z) -> S(z). Therefore, the answer is yes.