Before revision:  In the course of this investigation, we show that monotone instances of Planar 3-SAT with  three distinct variables per clause are always satisfiable, thus settling the question by Darmann, D\"ocker, and Dorn on the complexity of this problem variant in a surprising way.
After revision:  In the course of this investigation, we show that monotone instances of Planar 3-SAT with exactly three distinct variables per clause are always satisfiable, thus settling the question by Darmann, D\"ocker, and Dorn on the complexity of this problem variant in a surprising way.