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