Consider the following premises. forall x_5: S_3(x_5). forall x_5: Q_5(x_5) -> U_4(x_5). forall x_5: P_5(x_5) -> Q_5(x_5). forall x_5: P_5(x_5) or Q_4(x_5). forall x_5: Q_4(x_5) -> U_4(x_5). Can we infer exists x_5: ~(S_3(x_5) and U_4(x_5)) from them?
 From forall x_5: P_5(x_5) -> Q_5(x_5), forall x_5: Q_5(x_5) -> U_4(x_5) we can infer forall x_5: P_5(x_5) -> U_4(x_5). From forall x_5: P_5(x_5) -> U_4(x_5), forall x_5: Q_4(x_5) -> U_4(x_5), forall x_5: P_5(x_5) or Q_4(x_5) we can infer forall x_5: U_4(x_5). Finally, from forall x_5: S_3(x_5), forall x_5: U_4(x_5) we can infer forall x_5: S_3(x_5) and U_4(x_5), which contradicts exists x_5: ~(S_3(x_5) and U_4(x_5)). Therefore, the answer is no.