Consider the following premises. forall y: U(y) -> S_2(y). forall y: S_2(y) or ~S_4(y). forall y: ~T_2(y) or S_4(y). forall y: T_2(y) or U(y). Can we infer exists y: ~S_2(y) from them?
 From forall y: T_2(y) or U(y), forall y: ~T_2(y) or S_4(y) we can infer forall y: U(y) or S_4(y). From forall y: S_2(y) or ~S_4(y) we can infer forall y: S_4(y) -> S_2(y). Finally, from forall y: U(y) -> S_2(y), forall y: S_4(y) -> S_2(y), forall y: U(y) or S_4(y) we can infer forall y: S_2(y), which contradicts exists y: ~S_2(y). Therefore, the answer is no.