Consider the following premises. forall x_7: Q_2(x_7) -> P_5(x_7). forall x_7: ~P_7(x_7) or Q_2(x_7). forall x_7: P_7(x_7) or U(x_7). exists x_7: P_5(x_7) <-> U(x_7). Can we infer exists x_7: P_5(x_7) from them?
 From forall x_7: P_7(x_7) or U(x_7), forall x_7: ~P_7(x_7) or Q_2(x_7) we can infer forall x_7: U(x_7) or Q_2(x_7). From exists x_7: P_5(x_7) <-> U(x_7) we can infer exists x_7: U(x_7) -> P_5(x_7). Finally, from exists x_7: U(x_7) -> P_5(x_7), forall x_7: Q_2(x_7) -> P_5(x_7), forall x_7: U(x_7) or Q_2(x_7) we can infer exists x_7: P_5(x_7). Therefore, the answer is yes.