Computational complexity of the 3-partition problem with distinct numbers
It is proved in [1, Corollary 7], that 3-partition is strongly NP-hard when the integers $a_1, \ldots, a_n$ are all distinct. The bounds $B/4 &lt; a_i &lt; B/2$ are not imposed in [1], but this should not make a difference.

[1]: Heather Hulett, Todd G. Will, Gerhard J. Woeginger: Multigraph realizations of degree sequences: Maximization is easy, minimization is hard. Oper. Res. Lett. 36(5): 594-596 (2008). DOI