Consider the following premises. forall x_5: P_5(x_5) or ~Q_5(x_5). forall x_5: P_5(x_5) -> Q_5(x_5). ~Q_5(a_2). Can we infer P_5(a_2) from them?
 From forall x_5: P_5(x_5) or ~Q_5(x_5) we can infer forall x_5: Q_5(x_5) -> P_5(x_5). From forall x_5: Q_5(x_5) -> P_5(x_5), forall x_5: P_5(x_5) -> Q_5(x_5) we can infer forall x_5: Q_5(x_5) <-> P_5(x_5). From forall x_5: Q_5(x_5) <-> P_5(x_5) we can infer Q_5(a_2) <-> P_5(a_2). Finally, from Q_5(a_2) <-> P_5(a_2), ~Q_5(a_2) we can infer ~P_5(a_2), which contradicts P_5(a_2). Therefore, the answer is no.