Consider the following premises. forall x_6: Q_1(x_6) or R(x_6). forall x_6: P_6(x_6) or ~Q_1(x_6). forall x_6: P_6(x_6) or ~R(x_6). Can we infer exists x_6: ~P_6(x_6) from them?
 From forall x_6: P_6(x_6) or ~R(x_6) we can infer forall x_6: R(x_6) -> P_6(x_6). From forall x_6: P_6(x_6) or ~Q_1(x_6) we can infer forall x_6: Q_1(x_6) -> P_6(x_6). Finally, from forall x_6: Q_1(x_6) -> P_6(x_6), forall x_6: R(x_6) -> P_6(x_6), forall x_6: Q_1(x_6) or R(x_6) we can infer forall x_6: P_6(x_6), which contradicts exists x_6: ~P_6(x_6). Therefore, the answer is no.