Consider the following premises. forall y: W(y) <-> T(y). forall y: T(y) or R_1(y). forall y: R_1(y) -> W(y). forall y: W(y) -> R_1(y). Can we infer ~W(e) from them? If possible, name the inference rules being used at each step.
 From forall y: R_1(y) -> W(y), forall y: W(y) -> R_1(y) we can infer forall y: R_1(y) <-> W(y) via universal biconditional introduction. From forall y: R_1(y) <-> W(y) we can infer forall y: R_1(y) -> W(y) via universal biconditional elimination. From forall y: W(y) <-> T(y) we can infer forall y: T(y) -> W(y) via universal biconditional elimination. Finally, from forall y: T(y) -> W(y), forall y: R_1(y) -> W(y), forall y: T(y) or R_1(y) we can infer forall y: W(y) via universal disjunction elimination, which contradicts ~W(e). Therefore, the answer is no.