The code attached is incomplete. It handles only "half" the cases.
I'll re-submit after it's fixed.
The repertoire of Mathematica boolean functions is most impressive, though I often find the documentation insufficient.
Attached is a boolean function "finger exercise" that I would like to 1) improve, and 2) generalize.
It finds 2-ary boolean functions that are 1st-order independent.
Enjoy, -- Mark