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