Consider the following premises. exists x_12: P_12(x_12) or ~Q_12(x_12). forall x_12: P_8(x_12) or Q_12(x_12). forall x_12: P(x_12) -> ~P_12(x_12). forall x_12: P_8(x_12) -> P_12(x_12). Can we infer exists x_12: ~P(x_12) from them?
 From exists x_12: P_12(x_12) or ~Q_12(x_12) we can infer exists x_12: Q_12(x_12) -> P_12(x_12). From forall x_12: P_8(x_12) -> P_12(x_12), exists x_12: Q_12(x_12) -> P_12(x_12), forall x_12: P_8(x_12) or Q_12(x_12) we can infer exists x_12: P_12(x_12). Finally, from forall x_12: P(x_12) -> ~P_12(x_12), exists x_12: P_12(x_12) we can infer exists x_12: ~P(x_12). Therefore, the answer is yes.