Consider the following premises. forall x: W(x) -> S(x). exists x: T_1(x) <-> W(x). forall x: T_1(x) -> W(x). forall x: S(x) -> T_1(x). Can we infer forall x: ~(W(x) <-> T_1(x)) from them?
 From forall x: W(x) -> S(x), forall x: S(x) -> T_1(x) we can infer forall x: W(x) -> T_1(x). Finally, from forall x: T_1(x) -> W(x), forall x: W(x) -> T_1(x) we can infer forall x: T_1(x) <-> W(x), which contradicts forall x: ~(W(x) <-> T_1(x)). Therefore, the answer is no.