Consider the following premises. exists x_7: P_5(x_7) <-> R_7(x_7). forall x_7: P_7(x_7) or U_2(x_7). forall x_7: U_2(x_7) -> P_5(x_7). forall x_7: ~P_7(x_7) or R_7(x_7). Can we infer exists x_7: P_5(x_7) from them?
 From forall x_7: P_7(x_7) or U_2(x_7), forall x_7: ~P_7(x_7) or R_7(x_7) we can infer forall x_7: U_2(x_7) or R_7(x_7). From exists x_7: P_5(x_7) <-> R_7(x_7) we can infer exists x_7: R_7(x_7) -> P_5(x_7). Finally, from forall x_7: U_2(x_7) -> P_5(x_7), exists x_7: R_7(x_7) -> P_5(x_7), forall x_7: U_2(x_7) or R_7(x_7) we can infer exists x_7: P_5(x_7). Therefore, the answer is yes.