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