Consider the following premises. exists y: ~P(y). forall y: Q_1(y) -> P(y). forall y: Q_1(y) or ~U_1(y). Can we infer forall y: U_1(y) from them? If possible, name the inference rules being used at each step.
 From forall y: Q_1(y) -> P(y), exists y: ~P(y) we can infer exists y: ~Q_1(y) via existential modus tollens. From forall y: Q_1(y) or ~U_1(y) we can infer forall y: U_1(y) -> Q_1(y) via universal rewriting. Finally, from forall y: U_1(y) -> Q_1(y), exists y: ~Q_1(y) we can infer exists y: ~U_1(y) via existential modus tollens, which contradicts forall y: U_1(y). Therefore, the answer is no.