Consider the following premises. forall z_3: R_2(z_3) -> Q_4(z_3). forall z_3: Q_4(z_3) -> S(z_3). forall z_3: ~R_2(z_3). forall z_3: S(z_3) -> Q_4(z_3). forall z_3: Q_4(z_3) -> R_2(z_3). Can we infer forall z_3: ~S(z_3) from them?
 From forall z_3: Q_4(z_3) -> R_2(z_3), forall z_3: R_2(z_3) -> Q_4(z_3) we can infer forall z_3: Q_4(z_3) <-> R_2(z_3). From forall z_3: Q_4(z_3) <-> R_2(z_3), forall z_3: ~R_2(z_3) we can infer forall z_3: ~Q_4(z_3). From forall z_3: Q_4(z_3) -> S(z_3), forall z_3: S(z_3) -> Q_4(z_3) we can infer forall z_3: Q_4(z_3) <-> S(z_3). Finally, from forall z_3: Q_4(z_3) <-> S(z_3), forall z_3: ~Q_4(z_3) we can infer forall z_3: ~S(z_3). Therefore, the answer is yes.