Consider the following premises. forall x_5: P_5(x_5) -> T(x_5). forall x_5: P_5(x_5) -> T(x_5). forall x_5: T(x_5) -> P_5(x_5). Can we infer exists x_5: ~(T(x_5) <-> P_5(x_5)) from them?
 From forall x_5: P_5(x_5) -> T(x_5), forall x_5: T(x_5) -> P_5(x_5) we can infer forall x_5: P_5(x_5) <-> T(x_5). From forall x_5: P_5(x_5) <-> T(x_5) we can infer forall x_5: T(x_5) -> P_5(x_5). Finally, from forall x_5: T(x_5) -> P_5(x_5), forall x_5: P_5(x_5) -> T(x_5) we can infer forall x_5: T(x_5) <-> P_5(x_5), which contradicts exists x_5: ~(T(x_5) <-> P_5(x_5)). Therefore, the answer is no.