Consider the following premises. forall x_10: P_10(x_10) -> ~Q_10(x_10). forall x_10: S(x_10) and Q_3(x_10). forall x_10: Q_10(x_10). forall x_10: P_10(x_10) or Q_6(x_10). Can we infer exists x_10: ~(S(x_10) and Q_6(x_10)) from them?
 From forall x_10: P_10(x_10) -> ~Q_10(x_10), forall x_10: Q_10(x_10) we can infer forall x_10: ~P_10(x_10). From forall x_10: P_10(x_10) or Q_6(x_10), forall x_10: ~P_10(x_10) we can infer forall x_10: Q_6(x_10). From forall x_10: S(x_10) and Q_3(x_10) we can infer forall x_10: S(x_10). Finally, from forall x_10: S(x_10), forall x_10: Q_6(x_10) we can infer forall x_10: S(x_10) and Q_6(x_10), which contradicts exists x_10: ~(S(x_10) and Q_6(x_10)). Therefore, the answer is no.