Right now there's only a 2x2 solver, and it finds solutions in ~45s on my machine with SWI-Prolog. I intend to add a 3x3 solver eventually, but feel that I should probably find a way to optimize my general algorithm such that it will finish before the heat death of the universe.
Use this image as a general guide:
The top face is "A", left face is "B", and the right face is "C". One each side, the four tiles are labeled 1-4 clockwise from the top-left. Not shown in the image, but the face opposite of "A" is "F", the face opposite of "B" is "D", and the face opposite of "C" is "F".
After loading the program [two_by_two]., you will use the newsolve/2 clause to solve your cube like so:
newsolve(Moves, Matrix).
The Matrix variable should be a description of the cube; faces should be entered in letter order (A, then B, then C, ...) and tiles in number order (1, then 2, then 3, ...). Each tile's color is represented by a one-letter atom; y for yellow, o for orange, etc.
For instance, if your cube looks like this:
Then you would write:
newsolve(Moves, [[y, o, b, y], [b, w, b, b], [r, y, r, y], ..., ..., ...]).
The ... for the last three lists are because the other three faces aren't visible and I haven't determined yet what they are.