Finding shortest path of undirected weighted graph in prolog

Question

I am trying to do a shortest path for a London underground system inside prolog, and I'm stuck I've managed to get the code to return lists of all the possible routes however I need it to print the shortest weighted route an example of the desired outcome would be: [aaa,bbb,ccc,ddd,eee,40] where aaa,bbb etc. are stations in the knowledge base Here is my code

edge(chrc,embk,3).
edge(embk,wtrl,6).
edge(kksp,angl,16).
edge(angl,olds,20).
edge(olds,mrgt,9).
edge(mrgt,monm,9).
edge(monm,lnbg,6).
edge(lnbg,borg,9).
edge(wtrl,bank,33).

%go(leic,wtrl,R,D).

connected(X,Y,L) :-
    edge(X,Y,L).
connected(X,Y,L) :-
    edge(Y,X,L).
    
connected(X,Y,L) :- connected(X,Z,L),connected(Z,Y,L).
connected(Y,X,L) :- connected(Y,Z,L),connected(Z,X,L).

path3(Routes, Destination, Route):-
    shortest(Routes, Shortest, RestRoutes),
    proceed(Shortest, Destination, RestRoutes, Route).
    
proceed(r(Distance, Route), Destination, _, Route):-
    Route = [Destination|_].

proceed(r(Distance, [Last|Trail]), Destination, Routes, Route):-
    findall(r(D1, [Z,Last|Trail]),
    legalnode(Last, Trail, Z, Distance, D1), List),
    append(List, Routes, NewRoutes),
    path3(NewRoutes, Destination, Route).
    
shortest([Route|Routes], Shortest, [Route|Rest]) :-
    shortest(Routes, Shortest, Rest),
    shorter(Shortest, Route),
    !.

shortest([Route|Rest], Route, Rest).
    shorter(r(M1,_), r(M2,_)) :- M1 < M2.
    
legal(X, []).
legal(X, [H|T]) :- not(X = H), legal(X,T).

legalnode(X, Trail, Y, Distance, NewDistance) :-
    (edge(X,Y, Cost); edge(Y,X, Cost)),
    legal(Y, Trail),
    NewDistance is Distance + Cost.
    
go(Start, Destination, Route) :-
    path3([r(0, [Start])], Destination, R),
    reverse(R, Route).

There are more edges defined but it takes too much space