Consider the following premises. forall x_12: Q_8(x_12) -> R_8(x_12). forall x_12: P(x_12) <-> Q_12(x_12). forall x_12: P_8(x_12) or Q_8(x_12). forall x_12: P_8(x_12) -> R_8(x_12). forall x_12: Q_4(x_12) -> P(x_12). forall x_12: Q_12(x_12) or Q_4(x_12). Can we infer exists x_12: ~(P(x_12) and R_8(x_12)) from them?
 From forall x_12: P(x_12) <-> Q_12(x_12) we can infer forall x_12: Q_12(x_12) -> P(x_12). From forall x_12: P_8(x_12) -> R_8(x_12), forall x_12: Q_8(x_12) -> R_8(x_12), forall x_12: P_8(x_12) or Q_8(x_12) we can infer forall x_12: R_8(x_12). From forall x_12: Q_12(x_12) -> P(x_12), forall x_12: Q_4(x_12) -> P(x_12), forall x_12: Q_12(x_12) or Q_4(x_12) we can infer forall x_12: P(x_12). Finally, from forall x_12: P(x_12), forall x_12: R_8(x_12) we can infer forall x_12: P(x_12) and R_8(x_12), which contradicts exists x_12: ~(P(x_12) and R_8(x_12)). Therefore, the answer is no.