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