Consider the following premises. exists z_3: Q(z_3) -> S(z_3). forall z_3: Q(z_3) -> S(z_3). forall z_3: S(z_3) -> Q(z_3). forall z_3: ~S(z_3). Can we infer forall z_3: Q(z_3) from them?
 From exists z_3: Q(z_3) -> S(z_3), forall z_3: S(z_3) -> Q(z_3) we can infer exists z_3: Q(z_3) <-> S(z_3). From exists z_3: Q(z_3) <-> S(z_3) we can infer exists z_3: S(z_3) -> Q(z_3). From exists z_3: S(z_3) -> Q(z_3), forall z_3: Q(z_3) -> S(z_3) we can infer exists z_3: S(z_3) <-> Q(z_3). Finally, from exists z_3: S(z_3) <-> Q(z_3), forall z_3: ~S(z_3) we can infer exists z_3: ~Q(z_3), which contradicts forall z_3: Q(z_3). Therefore, the answer is no.