Consider the following premises. forall x_10: P_5(x_10) or Q_4(x_10). forall x_10: P_5(x_10) -> Q_10(x_10). forall x_10: P_10(x_10) or ~Q_10(x_10). forall x_10: Q_4(x_10) -> P_10(x_10). exists x_10: R(x_10). Can we infer forall x_10: ~(R(x_10) and P_10(x_10)) from them?
 From forall x_10: P_10(x_10) or ~Q_10(x_10) we can infer forall x_10: Q_10(x_10) -> P_10(x_10). From forall x_10: P_5(x_10) -> Q_10(x_10), forall x_10: Q_10(x_10) -> P_10(x_10) we can infer forall x_10: P_5(x_10) -> P_10(x_10). From forall x_10: P_5(x_10) -> P_10(x_10), forall x_10: Q_4(x_10) -> P_10(x_10), forall x_10: P_5(x_10) or Q_4(x_10) we can infer forall x_10: P_10(x_10). Finally, from exists x_10: R(x_10), forall x_10: P_10(x_10) we can infer exists x_10: R(x_10) and P_10(x_10), which contradicts forall x_10: ~(R(x_10) and P_10(x_10)). Therefore, the answer is no.