Reduce $\overline{K}$ to the set of pairs of natural numbers codifying programs such that the domain of the function computed by the machine codified by the first one is strictly included into the domain of the function computed by the machine codified by the second one, which in turn is strictly included into the image of the function computed by the machine codified by the first one (roughly, the set of pairs of programs such that the domain of the function computed by the first one is strictly included into the domain of the function computed by the second one, which in turn is strictly included into the image of the function computed by the first one), in order to prove that such set is not semi-decidable (not recursively enumerable).