Consider the following premises. forall x_12: P_12(x_12). forall x_15: P_1(x_15) and Q_15(x_15). Can we infer exists x_15: P_1(x_15) from them?
 From forall x_15: P_1(x_15) and Q_15(x_15) we can infer forall x_15: P_1(x_15). From forall x_12: P_12(x_12) we can infer P_12(c). From P_12(c) we can infer exists x_15: P_12(x_15). From forall x_15: P_1(x_15), exists x_15: P_12(x_15) we can infer exists x_15: P_1(x_15) and P_12(x_15). Finally, from exists x_15: P_1(x_15) and P_12(x_15) we can infer exists x_15: P_1(x_15). Therefore, the answer is yes.