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