Consider the following premises. forall z_4: U_3(z_4). forall z_4: U_1(z_4). exists z_4: S_3(z_4). Can we infer forall z_4: ~S_3(z_4) from them? If possible, name the inference rules being used at each step.
 From forall z_4: U_1(z_4), forall z_4: U_3(z_4) we can infer forall z_4: U_1(z_4) and U_3(z_4) via universal conjunction. From forall z_4: U_1(z_4) and U_3(z_4) we can infer forall z_4: U_1(z_4) via universal simplification. From exists z_4: S_3(z_4), forall z_4: U_1(z_4) we can infer exists z_4: S_3(z_4) and U_1(z_4) via existential conjunction. Finally, from exists z_4: S_3(z_4) and U_1(z_4) we can infer exists z_4: S_3(z_4) via existential simplification, which contradicts forall z_4: ~S_3(z_4). Therefore, the answer is no.