Consider the following premises. exists x_12: U_4(x_12) and Q_12(x_12). forall x_12: Q_5(x_12) -> R_4(x_12). forall x_12: P_5(x_12) -> R_4(x_12). forall x_12: P_5(x_12). Can we infer forall x_12: ~(U_4(x_12) and R_4(x_12)) from them?
 From exists x_12: U_4(x_12) and Q_12(x_12) we can infer exists x_12: U_4(x_12). From forall x_12: P_5(x_12) we can infer forall x_12: P_5(x_12) or Q_5(x_12). From forall x_12: P_5(x_12) -> R_4(x_12), forall x_12: Q_5(x_12) -> R_4(x_12), forall x_12: P_5(x_12) or Q_5(x_12) we can infer forall x_12: R_4(x_12). Finally, from exists x_12: U_4(x_12), forall x_12: R_4(x_12) we can infer exists x_12: U_4(x_12) and R_4(x_12), which contradicts forall x_12: ~(U_4(x_12) and R_4(x_12)). Therefore, the answer is no.