Consider the following premises. forall z_1: ~P(z_1). forall z_1: W(z_1) -> P(z_1). exists z_1: U_3(z_1) <-> S_3(z_1). forall z_1: U_3(z_1) <-> W(z_1). Can we infer forall z_1: S_3(z_1) from them?
 From forall z_1: W(z_1) -> P(z_1), forall z_1: ~P(z_1) we can infer forall z_1: ~W(z_1). From forall z_1: U_3(z_1) <-> W(z_1), forall z_1: ~W(z_1) we can infer forall z_1: ~U_3(z_1). Finally, from exists z_1: U_3(z_1) <-> S_3(z_1), forall z_1: ~U_3(z_1) we can infer exists z_1: ~S_3(z_1), which contradicts forall z_1: S_3(z_1). Therefore, the answer is no.