Hi, I'm trying to get a plan working to solve a predefined 8 Puzzle. The issue i'm having is that it will only solve if I remove the is_movable and at(empty,X) constraint. Otherwise it just seems to loop continuously.

Heres the code:

% Simple Prolog Planner for the 8 Puzzle Problem

% This predicate initialises the problem states. The first argument
% of solve/3 is the initial state, the 2nd the goal state, and the
% third the plan that will be produced.

test(Plan):-
    write('Initial state:'),nl,
    Init= [at(tile4,1), at(tile3,2), at(tile8,3), at(empty,4), at(tile2,5), at(tile6,6), at(tile5,7), at(tile1,8), at(tile7,9)],
    write_sol(Init),
    Goal= [at(tile1,1), at(tile2,2), at(tile3,3), at(tile4,4), at(empty,5), at(tile5,6), at(tile6,7), at(tile7,8), at(tile8,9)],
    nl,write('Goal state:'),nl,
    write(Goal),nl,nl,
    solve(Init,Goal,Plan).

solve(State, Goal, Plan):-
    solve(State, Goal, [], Plan).
    
%Determines whether Current and Destination tiles are a valid move.     
is_movable(X1,Y1) :- (1 is X1 - Y1) ; (-1 is X1 - Y1) ; (3 is X1 - Y1) ; (-3 is X1 - Y1).

    
% This predicate produces the plan. Once the Goal list is a subset
% of the current State the plan is complete and it is written to
% the screen using write_sol/1.

solve(State, Goal, Plan, Plan):-
    is_subset(Goal, State), nl,
    write_sol(Plan).

solve(State, Goal, Sofar, Plan):-
    act(Action, Preconditions, Delete, Add),
    is_subset(Preconditions, State),
    \+ member(Action, Sofar),
    delete_list(Delete, State, Remainder),
    append(Add, Remainder, NewState),
    solve(NewState, Goal, [Action|Sofar], Plan).
   
% The problem has three operators.
% 1st arg = name
% 2nd arg = preconditions
% 3rd arg = delete list
% 4th arg = add list.

% Tile can move to new position only if the destination tile is empty & Manhattan distance = 1
act(move(X,Y,Z),
    [at(X,Y), at(empty,Z), is_movable(Y,Z)],
    [at(X,Y), at(empty,Z)],
    [at(X,Z), at(empty,Y)]).


% Utility predicates.

% Check is first list is a subset of the second

is_subset([H|T], Set):-
    member(H, Set),
    is_subset(T, Set).
is_subset([], _).

% Remove all elements of 1st list from second to create third.

delete_list([H|T], Curstate, Newstate):-
    remove(H, Curstate, Remainder),
    delete_list(T, Remainder, Newstate).
delete_list([], Curstate, Curstate).
    
remove(X, [X|T], T).
remove(X, [H|T], [H|R]):-
    remove(X, T, R).

write_sol([]).
write_sol([H|T]):-
    write_sol(T),
    write(H), nl.
                 
append([H|T], L1, [H|L2]):-
    append(T, L1, L2).
append([], L, L).

member(X, [X|_]).
member(X, [_|T]):-
    member(X, T).