Consider the following premises. forall x_5: P_5(x_5) -> T_4(x_5). forall x_5: P_5(x_5). forall x_5: Q_5(x_5) -> T_4(x_5). Can we infer exists x_5: ~(T_4(x_5) or Q(x_5)) from them?
 From forall x_5: P_5(x_5) we can infer forall x_5: P_5(x_5) or Q_5(x_5). From forall x_5: P_5(x_5) -> T_4(x_5), forall x_5: Q_5(x_5) -> T_4(x_5), forall x_5: P_5(x_5) or Q_5(x_5) we can infer forall x_5: T_4(x_5). Finally, from forall x_5: T_4(x_5) we can infer forall x_5: T_4(x_5) or Q(x_5), which contradicts exists x_5: ~(T_4(x_5) or Q(x_5)). Therefore, the answer is no.