sudoku riddle Prolog solver

% This is a verbose but straightforward formulation of Sudoku
% using constraint logic programming for finite domains.
% credit https://github.com/fatuhoku/prolog-sudoku/blob/master/sudoku.pl
% sudoku([[_,_,_,_,_,_,_,_,_],[_,_,_,_,_,_,_,_,_],[_,_,_,_,_,_,_,_,_],[_,_,_,_,_,_,_,_,_],[_,_,_,_,_,_,_,_,_],[_,_,_,_,_,_,_,_,_],[_,_,_,_,_,_,_,_,_],[_,_,_,_,_,_,_,_,_],[_,_,_,_,_,_,_,_,_]])
% sudoku([A,B,C,D,E,F,G,H,I]).
% run as "sudoku([A,B,C,D,E,F,G,H,I])." or "solve(P)."
:- use_module(library(clpfd)).

solve(P):-
    sudoku(P),
    forall(member(R,P), (print(R),nl)).

sudoku([[A1,B1,C1,D1,E1,F1,G1,H1,I1],
        [A2,B2,C2,D2,E2,F2,G2,H2,I2],
        [A3,B3,C3,D3,E3,F3,G3,H3,I3],
        [A4,B4,C4,D4,E4,F4,G4,H4,I4],
        [A5,B5,C5,D5,E5,F5,G5,H5,I5],
        [A6,B6,C6,D6,E6,F6,G6,H6,I6],
        [A7,B7,C7,D7,E7,F7,G7,H7,I7],
        [A8,B8,C8,D8,E8,F8,G8,H8,I8],
        [A9,B9,C9,D9,E9,F9,G9,H9,I9]]):-
    Vars = [A1,B1,C1,D1,E1,F1,G1,H1,I1,
            A2,B2,C2,D2,E2,F2,G2,H2,I2,
            A3,B3,C3,D3,E3,F3,G3,H3,I3,
            A4,B4,C4,D4,E4,F4,G4,H4,I4,
            A5,B5,C5,D5,E5,F5,G5,H5,I5,
            A6,B6,C6,D6,E6,F6,G6,H6,I6,
            A7,B7,C7,D7,E7,F7,G7,H7,I7,
            A8,B8,C8,D8,E8,F8,G8,H8,I8,
            A9,B9,C9,D9,E9,F9,G9,H9,I9],
    Vars ins 1..9,
    % Rows
    all_different([A1,B1,C1,D1,E1,F1,G1,H1,I1]),
    all_different([A2,B2,C2,D2,E2,F2,G2,H2,I2]),
    all_different([A3,B3,C3,D3,E3,F3,G3,H3,I3]),
    all_different([A4,B4,C4,D4,E4,F4,G4,H4,I4]),
    all_different([A5,B5,C5,D5,E5,F5,G5,H5,I5]),
    all_different([A6,B6,C6,D6,E6,F6,G6,H6,I6]),
    all_different([A7,B7,C7,D7,E7,F7,G7,H7,I7]),
    all_different([A8,B8,C8,D8,E8,F8,G8,H8,I8]),
    all_different([A9,B9,C9,D9,E9,F9,G9,H9,I9]),

    % Column
    all_different([A1,A2,A3,A4,A5,A6,A7,A8,A9]),
    all_different([B1,B2,B3,B4,B5,B6,B7,B8,B9]),
    all_different([C1,C2,C3,C4,C5,C6,C7,C8,C9]),
    all_different([D1,D2,D3,D4,D5,D6,D7,D8,D9]),
    all_different([E1,E2,E3,E4,E5,E6,E7,E8,E9]),
    all_different([F1,F2,F3,F4,F5,F6,F7,F8,F9]),
    all_different([G1,G2,G3,G4,G5,G6,G7,G8,G9]),
    all_different([H1,H2,H3,H4,H5,H6,H7,H8,H9]),
    all_different([I1,I2,I3,I4,I5,I6,I7,I8,I9]),

    %Squares
    all_different([A1,A2,A3,B1,B2,B3,C1,C2,C3]),
    all_different([D1,D2,D3,E1,E2,E3,F1,F2,F3]),
    all_different([G1,G2,G3,H1,H2,H3,I1,I2,I3]),

    all_different([A4,A5,A6,B4,B5,B6,C4,C5,C6]),
    all_different([D4,D5,D6,E4,E5,E6,F4,F5,F6]),
    all_different([G4,G5,G6,H4,H5,H6,I4,I5,I6]),

    all_different([A7,A8,A9,B7,B8,B9,C7,C8,C9]),
    all_different([D7,D8,D9,E7,E8,E9,F7,F8,F9]),
    all_different([G7,G8,G9,H7,H8,H9,I7,I8,I9]),
    C1 + C2 + D1 + D2 #= 12,
    D1 + D2 + E1 + E2 #= 25,
    E1 + E2 + F1 + F2 #= 28,
    F1 + F2 + G1 + G2 #= 23,
    G2 + G3 + H2 + H3 #= 25,
    H3 + I3 + H4 + I4 #= 28,
    H4 + I4 + H5 + I5 #= 25,
    H5 + I5 + H6 + I6 #= 19,
    H6 + I6 + H7 + I7 #= 12,
    G7 + H7 + G8 + H8 #= 12,
    C8 + C9 + D8 + D9 #= 28,
    D8 + D9 + E8 + E9 #= 20,
    E8 + E9 + F8 + F9 #= 12,
    F8 + F9 + G8 + G9 #= 12,
    B7 + B8 + C7 + C8 #= 19,
    A3 + B3 + A4 + B4 #= 12,
    A4 + B4 + A5 + B5 #= 15,
    A5 + B5 + A6 + B6 #= 23,
    A6 + B6 + A7 + B7 #= 25,
    B2 + C2 + B3 + C3 #= 12,
    label(Vars).