I might not have used the optimal wording there. The important difference between the two prolog implementations is that the "longer" version is implemented by

I might not have used the optimal wording there. The important difference between the two prolog implementations is that the "longer" version is implemented by (recursive) iteration over a list of [peak] values (and comparing it to a reference list), whereas in the shorter one, the reference values are specified as separate conditions in the prolog rule, combined with logical AND. The separate conditions enables "shortcut" of the match-testing, in a way that the recursive list-parsing did not: As soon as one of the conditions is not met, the current spectrum will be rejected and the backtracking will go on with the next item, while with the recursive list-parsing version each item of the list of values will be compared to the reference [value-]list regardless of whether the current spectra has already been rejected or not. The "shorter" prolog version, with separate conditions, thus enables to order the conditions according so that statistically rare peak values come first (thus, "heuristically"), so that a spectrum can be rejected as soon as possible. Being a heuristic solution, the performance would of course depend on the prior knowledge of the values in the data. But as can be seen from figure 15, both prolog versions beat Jena and Pellet by a large margin, though the "shorter" version did so well that it is even hard to notice an increase of the running time linear to the number of triples in the triplestore, in the diagram. Hope that made it a tad clearer!