In the original paper All Possible Symmetries of the S-Matrix, by S. Coleman and J. Mandula, they prove their famous 'no go' theorem regarding the possible extensions of Poincaré symmetry. The loophole that allows for supersymmetry is their assumption that the generators are bosonic, as it is often said in modern introductory courses to SUSY. But I have not been able to pinpoint this precise statement in their original paper.
Could the fifth requirement be that assumption, that the generators are bosonic? If so, I do not see why demanding that the generators be integral operators is equivalent to demanding they be bosonic, as opposed to fermionic generators with spinor indices which satisfy anti-commutation relations. Perhaps the statement, often quoted in lectures, that the assumption is that they are 'bosonic,' is a gross simplification, or inaccuracy?