  We consider Grand Unified Theories based on $SO(10)$ which originate from $M$
theory on $G_2$ manifolds. In this framework we are naturally led to a novel
solution of the doublet-triplet splitting problem involving an extra
$\overline{{\bf 16}}_X+{\bf 16}_X$ vector-like pair by considering discrete
symmetries of the extra dimensions and preserving unification. Since Wilson
line breaking preserves the rank of the gauge group, the necessary $U(1)$ gauge
breaking is generated from extra multiplets. The main prediction of the
approach is the existence of light states with the quantum numbers of a
$\overline{{\bf 16}}_X+{\bf 16}_X$ vector-like pair which could show up in
future LHC searches.
