NAE-3SAT is the width-three restriction of NAE-SAT: a CNF structure is a yes-instance when every clause has at most three literal occurrences, the promise 3SAT uses, and some assignment gives every clause both a true and a false literal. Both reductions are the interpretations of the SAT and 3SAT pair applied unchanged: membership through the identity-like reduction to NAE-SAT, hardness through the clause-splitting ordered reduction from NAE-SAT, whose chain of pieces also works for the not-all-equal reading. Its value in the catalog is as a reduction source, for Max Cut and for job sequencing.