Consider the following premises. forall x_12: Q(x_12) or ~P(x_12). forall x_12: P_7(x_12) or P(x_12). exists x_12: ~P_7(x_12) or S_2(x_12). forall x_12: S_2(x_12) -> Q(x_12). forall x_12: Q(x_12) -> S_2(x_12). Can we infer forall x_12: ~Q(x_12) from them?
 From forall x_12: S_2(x_12) -> Q(x_12), forall x_12: Q(x_12) -> S_2(x_12) we can infer forall x_12: S_2(x_12) <-> Q(x_12). From forall x_12: Q(x_12) or ~P(x_12) we can infer forall x_12: P(x_12) -> Q(x_12). From forall x_12: P_7(x_12) or P(x_12), exists x_12: ~P_7(x_12) or S_2(x_12) we can infer exists x_12: P(x_12) or S_2(x_12). From forall x_12: S_2(x_12) <-> Q(x_12) we can infer forall x_12: S_2(x_12) -> Q(x_12). Finally, from forall x_12: P(x_12) -> Q(x_12), forall x_12: S_2(x_12) -> Q(x_12), exists x_12: P(x_12) or S_2(x_12) we can infer exists x_12: Q(x_12), which contradicts forall x_12: ~Q(x_12). Therefore, the answer is no.