Consider the following premises. forall x_8: P_8(x_8) -> Q_8(x_8). forall x_8: Q_8(x_8) -> P_8(x_8). p_1 -> P_8(a_7). Q_8(a_7) or p_1. Can we infer ~P_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) <-> Q_8(a_7) we can infer Q_8(a_7) -> P_8(a_7). Finally, from Q_8(a_7) -> P_8(a_7), p_1 -> P_8(a_7), Q_8(a_7) or p_1 we can infer P_8(a_7), which contradicts ~P_8(a_7). Therefore, the answer is no.