Consider the following premises. forall x_12: P_5(x_12). forall x_12: P_5(x_12) -> Q_12(x_12). forall x_12: T(x_12) <-> Q_12(x_12). Can we infer exists x_12: ~(T(x_12) or Q(x_12)) from them?
 From forall x_12: T(x_12) <-> Q_12(x_12) we can infer forall x_12: Q_12(x_12) -> T(x_12). From forall x_12: P_5(x_12) -> Q_12(x_12), forall x_12: P_5(x_12) we can infer forall x_12: Q_12(x_12). From forall x_12: Q_12(x_12) -> T(x_12), forall x_12: Q_12(x_12) we can infer forall x_12: T(x_12). Finally, from forall x_12: T(x_12) we can infer forall x_12: T(x_12) or Q(x_12), which contradicts exists x_12: ~(T(x_12) or Q(x_12)). Therefore, the answer is no.