Consider the following premises. forall z_1: U_3(z_1). forall z_1: W_4(z_1). exists z_1: U(z_1) -> ~U_3(z_1). Can we infer exists z_1: ~U(z_1) from them? If possible, name the inference rules being used at each step.
 From forall z_1: U_3(z_1), forall z_1: W_4(z_1) we can infer forall z_1: U_3(z_1) and W_4(z_1) via universal conjunction. From forall z_1: U_3(z_1) and W_4(z_1) we can infer forall z_1: U_3(z_1) via universal simplification. Finally, from exists z_1: U(z_1) -> ~U_3(z_1), forall z_1: U_3(z_1) we can infer exists z_1: ~U(z_1) via existential modus tollens. Therefore, the answer is yes.