Consider the following premises. forall x_12: P_12(x_12) or Q_12(x_12). forall x_12: Q_5(x_12) -> P_3(x_12). forall x_12: P_12(x_12) -> R_12(x_12). forall x_12: Q_12(x_12) -> R_12(x_12). forall x_12: R_12(x_12) -> Q_5(x_12). Can we infer ~P_3(j) from them?
 From forall x_12: P_12(x_12) -> R_12(x_12), forall x_12: Q_12(x_12) -> R_12(x_12), forall x_12: P_12(x_12) or Q_12(x_12) we can infer forall x_12: R_12(x_12). From forall x_12: R_12(x_12) -> Q_5(x_12), forall x_12: R_12(x_12) we can infer forall x_12: Q_5(x_12). Finally, from forall x_12: Q_5(x_12) -> P_3(x_12), forall x_12: Q_5(x_12) we can infer forall x_12: P_3(x_12), which contradicts ~P_3(j). Therefore, the answer is no.