Consider the following premises. exists y: Q(y) -> U_3(y). forall y: ~U_3(y). forall y: P(y) -> Q(y). forall y: Q(y) -> P(y). Can we infer forall y: P(y) from them? If possible, name the inference rules being used at each step.
 From forall y: Q(y) -> P(y), forall y: P(y) -> Q(y) we can infer forall y: Q(y) <-> P(y) via universal biconditional introduction. From exists y: Q(y) -> U_3(y), forall y: ~U_3(y) we can infer exists y: ~Q(y) via existential modus tollens. Finally, from forall y: Q(y) <-> P(y), exists y: ~Q(y) we can infer exists y: ~P(y) via existential biconditional elimination, which contradicts forall y: P(y). Therefore, the answer is no.