Consider the following premises. forall x_3: P_3(x_3) -> P_2(x_3). forall x_3: U(x_3). exists x_3: P_3(x_3). Can we infer forall x_3: ~(P_2(x_3) and U(x_3)) from them? If possible, name the inference rules being used at each step.
 From forall x_3: P_3(x_3) -> P_2(x_3), exists x_3: P_3(x_3) we can infer exists x_3: P_2(x_3) via existential modus ponens. Finally, from exists x_3: P_2(x_3), forall x_3: U(x_3) we can infer exists x_3: P_2(x_3) and U(x_3) via existential conjunction, which contradicts forall x_3: ~(P_2(x_3) and U(x_3)). Therefore, the answer is no.