Consider the following premises. forall x_10: Q_10(x_10). forall x_10: Q_3(x_10). exists x_10: P_10(x_10). Can we infer exists x_10: Q_3(x_10) and P_10(x_10) from them?
 From exists x_10: P_10(x_10), forall x_10: Q_10(x_10) we can infer exists x_10: P_10(x_10) and Q_10(x_10). From exists x_10: P_10(x_10) and Q_10(x_10) we can infer exists x_10: P_10(x_10). Finally, from forall x_10: Q_3(x_10), exists x_10: P_10(x_10) we can infer exists x_10: Q_3(x_10) and P_10(x_10). Therefore, the answer is yes.