Consider the following premises. forall x_5: U_4(x_5) or ~U(x_5). exists x_5: U_4(x_5) -> Q_5(x_5). forall x_5: ~Q_5(x_5). Can we infer forall x_5: U(x_5) from them? If possible, name the inference rules being used at each step.
 From exists x_5: U_4(x_5) -> Q_5(x_5), forall x_5: ~Q_5(x_5) we can infer exists x_5: ~U_4(x_5) via existential modus tollens. From forall x_5: U_4(x_5) or ~U(x_5) we can infer forall x_5: U(x_5) -> U_4(x_5) via universal rewriting. Finally, from forall x_5: U(x_5) -> U_4(x_5), exists x_5: ~U_4(x_5) we can infer exists x_5: ~U(x_5) via existential modus tollens, which contradicts forall x_5: U(x_5). Therefore, the answer is no.