Consider the following premises. forall x_12: ~P(x_12). forall x_12: P_4(x_12) -> Q_7(x_12). exists x_12: Q_7(x_12) -> Q_12(x_12). forall x_12: P(x_12) or ~Q_12(x_12). Can we infer exists x_12: ~P_4(x_12) from them?
 From forall x_12: P(x_12) or ~Q_12(x_12) we can infer forall x_12: Q_12(x_12) -> P(x_12). From forall x_12: P_4(x_12) -> Q_7(x_12), exists x_12: Q_7(x_12) -> Q_12(x_12) we can infer exists x_12: P_4(x_12) -> Q_12(x_12). From exists x_12: P_4(x_12) -> Q_12(x_12), forall x_12: Q_12(x_12) -> P(x_12) we can infer exists x_12: P_4(x_12) -> P(x_12). Finally, from exists x_12: P_4(x_12) -> P(x_12), forall x_12: ~P(x_12) we can infer exists x_12: ~P_4(x_12). Therefore, the answer is yes.