When Symmetry Yields NP-Hardness: Affine ML-SAT on S5 Frames

Hemaspaandra~et~al.~[JCSS 2010] conjectured that satisfiability for multi-modal logic restricted to the connectives XOR and 1, over frame classes T, S4, and S5, is solvable in polynomial time. We refute this for S5 frames, by proving NP-hardness.