Consider the following premises. forall x_6: Q_6(x_6) -> Q(x_6). exists x_6: ~Q_1(x_6). forall x_6: Q_1(x_6) -> Q_6(x_6). forall x_6: Q_1(x_6) or ~Q(x_6). Can we infer exists x_6: ~Q(x_6) from them?
 From forall x_6: Q_1(x_6) -> Q_6(x_6), forall x_6: Q_6(x_6) -> Q(x_6) we can infer forall x_6: Q_1(x_6) -> Q(x_6). From forall x_6: Q_1(x_6) or ~Q(x_6) we can infer forall x_6: Q(x_6) -> Q_1(x_6). From forall x_6: Q_1(x_6) -> Q(x_6), forall x_6: Q(x_6) -> Q_1(x_6) we can infer forall x_6: Q_1(x_6) <-> Q(x_6). Finally, from forall x_6: Q_1(x_6) <-> Q(x_6), exists x_6: ~Q_1(x_6) we can infer exists x_6: ~Q(x_6). Therefore, the answer is yes.