Consider the following premises. forall x_8: P_8(x_8) -> Q_8(x_8). ~P_8(a_2). forall x_8: Q_8(x_8) -> P_8(x_8). forall x_8: Q_8(x_8) -> P_8(x_8). Can we infer ~Q_8(a_2) from them?
 From forall x_8: P_8(x_8) -> Q_8(x_8), forall x_8: Q_8(x_8) -> P_8(x_8) we can infer forall x_8: P_8(x_8) <-> Q_8(x_8). From forall x_8: P_8(x_8) <-> Q_8(x_8) we can infer forall x_8: P_8(x_8) -> Q_8(x_8). From forall x_8: Q_8(x_8) -> P_8(x_8), forall x_8: P_8(x_8) -> Q_8(x_8) we can infer forall x_8: Q_8(x_8) <-> P_8(x_8). From forall x_8: Q_8(x_8) <-> P_8(x_8) we can infer Q_8(a_2) <-> P_8(a_2). Finally, from Q_8(a_2) <-> P_8(a_2), ~P_8(a_2) we can infer ~Q_8(a_2). Therefore, the answer is yes.