Consider the following premises. R(a_5). forall x_7: P_7(x_7) or ~R(x_7). Can we infer P_7(a_5) from them?
 From forall x_7: P_7(x_7) or ~R(x_7) we can infer forall x_7: R(x_7) -> P_7(x_7). From forall x_7: R(x_7) -> P_7(x_7) we can infer R(a_5) -> P_7(a_5). Finally, from R(a_5) -> P_7(a_5), R(a_5) we can infer P_7(a_5). Therefore, the answer is yes.