Consider the following premises. exists x_10: T(x_10). forall x_10: T_1(x_10). forall x_10: Q_10(x_10) -> Q_1(x_10). forall x_10: T(x_10) -> Q_1(x_10). Can we infer forall x_10: ~(Q_1(x_10) and T_1(x_10)) from them? If possible, name the inference rules being used at each step.
 From exists x_10: T(x_10) we can infer exists x_10: T(x_10) or Q_10(x_10) via existential addition. From forall x_10: T(x_10) -> Q_1(x_10), forall x_10: Q_10(x_10) -> Q_1(x_10), exists x_10: T(x_10) or Q_10(x_10) we can infer exists x_10: Q_1(x_10) via existential disjunction elimination. Finally, from exists x_10: Q_1(x_10), forall x_10: T_1(x_10) we can infer exists x_10: Q_1(x_10) and T_1(x_10) via existential conjunction, which contradicts forall x_10: ~(Q_1(x_10) and T_1(x_10)). Therefore, the answer is no.