Consider the following premises. forall x_10: P(x_10) or Q_10(x_10). forall x_10: Q(x_10) or ~Q_10(x_10). forall x_10: P(x_10) -> Q(x_10). forall x_10: Q_1(x_10) or ~Q(x_10). Can we infer exists x_10: ~Q_1(x_10) from them?
 From forall x_10: Q(x_10) or ~Q_10(x_10) we can infer forall x_10: Q_10(x_10) -> Q(x_10). From forall x_10: Q_1(x_10) or ~Q(x_10) we can infer forall x_10: Q(x_10) -> Q_1(x_10). From forall x_10: P(x_10) -> Q(x_10), forall x_10: Q_10(x_10) -> Q(x_10), forall x_10: P(x_10) or Q_10(x_10) we can infer forall x_10: Q(x_10). Finally, from forall x_10: Q(x_10) -> Q_1(x_10), forall x_10: Q(x_10) we can infer forall x_10: Q_1(x_10), which contradicts exists x_10: ~Q_1(x_10). Therefore, the answer is no.