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