Consider the following premises. forall x: T_4(x) <-> S_3(x). forall x: T_4(x) -> ~S(x). exists x: S_3(x) <-> U_2(x). forall x: S(x). Can we infer forall x: U_2(x) from them?
 From forall x: T_4(x) -> ~S(x), forall x: S(x) we can infer forall x: ~T_4(x). From forall x: T_4(x) <-> S_3(x), forall x: ~T_4(x) we can infer forall x: ~S_3(x). Finally, from exists x: S_3(x) <-> U_2(x), forall x: ~S_3(x) we can infer exists x: ~U_2(x), which contradicts forall x: U_2(x). Therefore, the answer is no.