Consider the following premises. r. forall x_8: P_8(x_8) -> Q_8(x_8). P_8(a_7) -> ~r. forall x_8: Q_8(x_8) -> P_8(x_8). Can we infer ~Q_8(a_7) 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 P_8(a_7) <-> Q_8(a_7). From P_8(a_7) -> ~r, r we can infer ~P_8(a_7). Finally, from P_8(a_7) <-> Q_8(a_7), ~P_8(a_7) we can infer ~Q_8(a_7). Therefore, the answer is yes.