Consider the following premises. forall y: T(y) <-> S(y). forall y: U_1(y) or T(y). forall y: ~U_1(y). Can we infer exists y: ~S(y) from them?
 From forall y: U_1(y) or T(y), forall y: ~U_1(y) we can infer forall y: T(y). From forall y: T(y) <-> S(y) we can infer forall y: T(y) -> S(y). Finally, from forall y: T(y) -> S(y), forall y: T(y) we can infer forall y: S(y), which contradicts exists y: ~S(y). Therefore, the answer is no.