Consider the following premises. forall z_1: Q_3(z_1) or ~S(z_1). exists z_1: Q_3(z_1) <-> S(z_1). Can we infer forall z_1: ~(Q_3(z_1) <-> S(z_1)) from them?
 From exists z_1: Q_3(z_1) <-> S(z_1) we can infer exists z_1: Q_3(z_1) -> S(z_1). From forall z_1: Q_3(z_1) or ~S(z_1) we can infer forall z_1: S(z_1) -> Q_3(z_1). Finally, from exists z_1: Q_3(z_1) -> S(z_1), forall z_1: S(z_1) -> Q_3(z_1) we can infer exists z_1: Q_3(z_1) <-> S(z_1), which contradicts forall z_1: ~(Q_3(z_1) <-> S(z_1)). Therefore, the answer is no.