Consider the following premises. forall x_5: Q_1(x_5) -> P_5(x_5). forall x_5: P_5(x_5) or ~U(x_5). exists x_5: U(x_5). Can we infer exists x_5: P_5(x_5) from them?
 From forall x_5: P_5(x_5) or ~U(x_5) we can infer forall x_5: U(x_5) -> P_5(x_5). From exists x_5: U(x_5) we can infer exists x_5: U(x_5) or Q_1(x_5). Finally, from forall x_5: U(x_5) -> P_5(x_5), forall x_5: Q_1(x_5) -> P_5(x_5), exists x_5: U(x_5) or Q_1(x_5) we can infer exists x_5: P_5(x_5). Therefore, the answer is yes.