Consider the following premises. forall z_4: Q(z_4). forall z_4: U(z_4) <-> Q_3(z_4). forall z_4: U(z_4). Can we infer exists z_4: ~(Q(z_4) and Q_3(z_4)) from them?
 From forall z_4: U(z_4) <-> Q_3(z_4) we can infer forall z_4: U(z_4) -> Q_3(z_4). From forall z_4: U(z_4) -> Q_3(z_4), forall z_4: U(z_4) we can infer forall z_4: Q_3(z_4). Finally, from forall z_4: Q(z_4), forall z_4: Q_3(z_4) we can infer forall z_4: Q(z_4) and Q_3(z_4), which contradicts exists z_4: ~(Q(z_4) and Q_3(z_4)). Therefore, the answer is no.