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$\overline{K}\;\leq\;\{ p \mid M_p(1){\downarrow} \,\wedge\, M_p(2){\uparrow} \}$
Reduce $\overline{K}$ to the set of natural numbers such that the program
codified by them halt with input $1$ and do not halt with input $2$ (roughly,
the set of programs that halt with input $1$ and do not halt with input $2$),
in order to prove that such set is not semi-decidable (not recursively
enumerable).
Authors: Carles Creus, Guillem Godoy
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