Consider the following premises. forall x_14: P_3(x_14) and Q_3(x_14). exists x_14: P_1(x_14). forall x_14: Q_14(x_14). Can we infer exists x_14: P_1(x_14) and P_3(x_14) from them?
 From exists x_14: P_1(x_14), forall x_14: Q_14(x_14) we can infer exists x_14: P_1(x_14) and Q_14(x_14). From exists x_14: P_1(x_14) and Q_14(x_14) we can infer exists x_14: P_1(x_14). From forall x_14: P_3(x_14) and Q_3(x_14) we can infer forall x_14: P_3(x_14). Finally, from exists x_14: P_1(x_14), forall x_14: P_3(x_14) we can infer exists x_14: P_1(x_14) and P_3(x_14). Therefore, the answer is yes.