Consider the following premises. T(f_2) <-> r_1. forall y: T(y) <-> R(y). forall y: ~R(y). Can we infer r_1 from them? If possible, name the inference rules being used at each step.
 From forall y: T(y) <-> R(y), forall y: ~R(y) we can infer forall y: ~T(y) via universal biconditional elimination. From forall y: ~T(y) we can infer ~T(f_2) via universal instantiation. Finally, from T(f_2) <-> r_1, ~T(f_2) we can infer ~r_1 via biconditional elimination, which contradicts r_1. Therefore, the answer is no.