Consider the following premises. forall z_3: R(z_3) or U(z_3). forall z_3: ~R(z_3). exists z_3: W_4(z_3) or P(z_3). forall z_3: ~W_4(z_3). Can we infer forall z_3: ~(P(z_3) and U(z_3)) from them? If possible, name the inference rules being used at each step.
 From forall z_3: R(z_3) or U(z_3), forall z_3: ~R(z_3) we can infer forall z_3: U(z_3) via universal disjunctive syllogism. From exists z_3: W_4(z_3) or P(z_3), forall z_3: ~W_4(z_3) we can infer exists z_3: P(z_3) via existential disjunctive syllogism. Finally, from exists z_3: P(z_3), forall z_3: U(z_3) we can infer exists z_3: P(z_3) and U(z_3) via existential conjunction, which contradicts forall z_3: ~(P(z_3) and U(z_3)). Therefore, the answer is no.