Consider the following premises. T(d). forall z_4: U_4(z_4). Can we infer forall z_4: ~(T(z_4) and U_4(z_4)) from them? If possible, name the inference rules being used at each step.
 From T(d) we can infer exists z_4: T(z_4) via existential generalization. Finally, from exists z_4: T(z_4), forall z_4: U_4(z_4) we can infer exists z_4: T(z_4) and U_4(z_4) via existential conjunction, which contradicts forall z_4: ~(T(z_4) and U_4(z_4)). Therefore, the answer is no.