Garey and Johnson (1975) originally proved 3-Partition to be NP-complete, by a reduction from [[3-dimensional matching]].<ref>{{cite journal|author=[[Michael Garey|Garey, Michael R.]] and [[David S. Johnson]]|year=1975|title=Complexity (1979),results ''Computersfor andmultiprocessor Intractability;scheduling Aunder Guideresource toconstraints|journal=SIAM theJournal Theoryon of NP-Completeness''Computing|volume=4|issue=4|pages=397–411|doi=10. {{ISBN|0-7167-1045-51137/0204035}}. Pages 96–105 and 224.</ref> The classic reference by Garey and Johnson (1979) describes an NP-completeness proof, reducing from 3-dimensional matching to 4-partition to 3-partition.<ref>{{cite journal|author=[[Michael Garey|Garey, Michael R.]] and [[David S. Johnson]]|year=1975|title=Complexityresults(1979), for''Computers multiprocessorand schedulingIntractability; underA resourceGuide constraints|journal=SIAMto Journalthe onTheory Computing|volume=4|issue=4|pages=397–411|doi=10of NP-Completeness''.1137/0204035 {{ISBN|0-7167-1045-5}}. Pages 96–105 and 224.</ref> Logically, the reduction can be partitioned into several steps.
=== Reduction from 3d-matching to ABCD-partition ===
