Example request for Monotone 1 in 3 SAT

I know that monotone 3SAT is NPComplete. Also, 1 in 3SAT is NPComplete. I think both conditions together also leave the problem NP Complete (need confirmation).

If possible can someone please help with the smallest non trivial problem of this form that is unsatisfiable. Would be grateful.

How about $(x_1 \lor x_2 \lor x_3) \land (\bar{x}_1 \lor \bar{x}_2 \lor \bar{x}_3)$?