Consider the following premises. forall x: T_3(x) or ~W_3(x). forall x: W_3(x) -> T_3(x). exists x: T_3(x) -> W_3(x). Can we infer forall x: ~(T_3(x) <-> W_3(x)) from them?
 From exists x: T_3(x) -> W_3(x), forall x: W_3(x) -> T_3(x) we can infer exists x: T_3(x) <-> W_3(x). From forall x: T_3(x) or ~W_3(x) we can infer forall x: W_3(x) -> T_3(x). From exists x: T_3(x) <-> W_3(x) we can infer exists x: T_3(x) -> W_3(x). Finally, from exists x: T_3(x) -> W_3(x), forall x: W_3(x) -> T_3(x) we can infer exists x: T_3(x) <-> W_3(x), which contradicts forall x: ~(T_3(x) <-> W_3(x)). Therefore, the answer is no.