solve(Configuration, []) :- final(Configuration).

solve(Configuration, [Move | R]) :- 
    \+marked(Configuration),
    assert(marked(Configuration)),
    valid(Configuration, Move, Newconfiguration), 
    solve(Newconfiguration, R).

valid([[T | R1], P2, P3], peg1toPeg2, [R1, [T | P2], P3]) :- 
    sorted([T | P2]).

valid([[T | R1], P2, P3], peg1toPeg3, [R1, P2, [T | P3]]) :-
    sorted([T | P3]).

valid([P1, [T | R2], P3], peg2toPeg1, [[T | P1], R2, P3]) :-
    sorted([T | P1]).

valid([P1, [T | R2], P3], peg2toPeg3, [P1, R2, [T | P3]]) :-
    sorted([T | P3]).

valid([P1, P2, [T | R3]], peg3toPeg1, [[T | P1], P2, R3]) :-
    sorted([T | P1]).

valid([P1, P2, [T | R3]], 32, [P1, [T | P2], R3]) :-
    sorted([T | P2]).

sorted([]).

sorted([_]).

sorted([D1, D2 | R]) :- D1 < D2, sorted([D2 | R]). 

final([[], [], P3]) :- sorted(P3).

:- dynamic marked/1.