Consider the following premises. forall x_8: P_2(x_8) -> Q_8(x_8). forall x_8: P_8(x_8) -> P_2(x_8). exists x_8: P_8(x_8) or ~Q_8(x_8). Can we infer forall x_8: ~(P_8(x_8) <-> P_2(x_8)) from them?
 From exists x_8: P_8(x_8) or ~Q_8(x_8) we can infer exists x_8: Q_8(x_8) -> P_8(x_8). From forall x_8: P_2(x_8) -> Q_8(x_8), exists x_8: Q_8(x_8) -> P_8(x_8) we can infer exists x_8: P_2(x_8) -> P_8(x_8). Finally, from forall x_8: P_8(x_8) -> P_2(x_8), exists x_8: P_2(x_8) -> P_8(x_8) we can infer exists x_8: P_8(x_8) <-> P_2(x_8), which contradicts forall x_8: ~(P_8(x_8) <-> P_2(x_8)). Therefore, the answer is no.