Consider the following premises. forall z_1: ~W(z_1). forall z_1: T_4(z_1) -> W(z_1). exists z_1: S_2(z_1) <-> T_4(z_1). forall z_1: S_2(z_1) -> U(z_1). forall z_1: U(z_1) -> S_2(z_1). forall z_1: W(z_1) -> T_4(z_1). Can we infer forall z_1: U(z_1) from them?
 From forall z_1: W(z_1) -> T_4(z_1), forall z_1: T_4(z_1) -> W(z_1) we can infer forall z_1: W(z_1) <-> T_4(z_1). From forall z_1: W(z_1) <-> T_4(z_1), forall z_1: ~W(z_1) we can infer forall z_1: ~T_4(z_1). From forall z_1: S_2(z_1) -> U(z_1), forall z_1: U(z_1) -> S_2(z_1) we can infer forall z_1: S_2(z_1) <-> U(z_1). From exists z_1: S_2(z_1) <-> T_4(z_1), forall z_1: ~T_4(z_1) we can infer exists z_1: ~S_2(z_1). Finally, from forall z_1: S_2(z_1) <-> U(z_1), exists z_1: ~S_2(z_1) we can infer exists z_1: ~U(z_1), which contradicts forall z_1: U(z_1). Therefore, the answer is no.