Consider the following premises. p -> P_7(a_5). forall x_7: P_7(x_7) or ~Q_7(x_7). p or Q_7(a_5). Can we infer P_7(a_5) from them?
 From forall x_7: P_7(x_7) or ~Q_7(x_7) we can infer forall x_7: Q_7(x_7) -> P_7(x_7). From forall x_7: Q_7(x_7) -> P_7(x_7) we can infer Q_7(a_5) -> P_7(a_5). Finally, from p -> P_7(a_5), Q_7(a_5) -> P_7(a_5), p or Q_7(a_5) we can infer P_7(a_5). Therefore, the answer is yes.