Consider the following premises. forall x_4: W(x_4) or Q_4(x_4). forall x_4: Q_4(x_4) -> T(x_4). forall x_4: U_4(x_4). forall x_4: W(x_4) -> T(x_4). Can we infer exists x_4: ~(T(x_4) and U_4(x_4)) from them?
 From forall x_4: W(x_4) -> T(x_4), forall x_4: Q_4(x_4) -> T(x_4), forall x_4: W(x_4) or Q_4(x_4) we can infer forall x_4: T(x_4). Finally, from forall x_4: T(x_4), forall x_4: U_4(x_4) we can infer forall x_4: T(x_4) and U_4(x_4), which contradicts exists x_4: ~(T(x_4) and U_4(x_4)). Therefore, the answer is no.