the.com/process of elimination

means A method of reaching the correct answer by systematically ruling out every incorrect possibility until just one remains.

from Straightforward compound logic rather than a single coined phrase: 'process' comes from Latin 'processus' (a going forward, progress), from 'procedere' (to proceed), while 'elimination' traces to Latin 'eliminare' — literally 'to turn out of doors,' built from 'e-' (out) and 'limen' (threshold). So the phrase is etymologically a march (process) of throwing things out the door (elimination) one by one, which is a remarkably literal match for what the method actually does.