Consider the following premises. U_2(i) -> r. T(i) -> r. forall z_2: T(z_2) or U_2(z_2). r -> U_2(i). Can we infer r from them? If possible, name the inference rules being used at each step.
 From forall z_2: T(z_2) or U_2(z_2) we can infer T(i) or U_2(i) via universal instantiation. From r -> U_2(i), U_2(i) -> r we can infer r <-> U_2(i) via biconditional introduction. From r <-> U_2(i) we can infer U_2(i) -> r via biconditional elimination. Finally, from T(i) -> r, U_2(i) -> r, T(i) or U_2(i) we can infer r via disjunction elimination. Therefore, the answer is yes.