Consider the following premises. exists x_4: T_3(x_4) -> S(x_4). forall x_4: S(x_4) -> T_3(x_4). forall x_4: T_3(x_4) or ~S(x_4). Can we infer forall x_4: ~(S(x_4) <-> T_3(x_4)) from them?
 From forall x_4: S(x_4) -> T_3(x_4), exists x_4: T_3(x_4) -> S(x_4) we can infer exists x_4: S(x_4) <-> T_3(x_4). From exists x_4: S(x_4) <-> T_3(x_4) we can infer exists x_4: T_3(x_4) -> S(x_4). From forall x_4: T_3(x_4) or ~S(x_4) we can infer forall x_4: S(x_4) -> T_3(x_4). Finally, from forall x_4: S(x_4) -> T_3(x_4), exists x_4: T_3(x_4) -> S(x_4) we can infer exists x_4: S(x_4) <-> T_3(x_4), which contradicts forall x_4: ~(S(x_4) <-> T_3(x_4)). Therefore, the answer is no.