sudoku aids

:- use_module(library(clpfd)).

valid([]).
valid([Head|Tail]) :- all_distinct(Head), valid(Tail).

valid_domain(List, Min, Max) :- List ins Min..Max.

sudoku(Puzzle, Solution) :-
    Solution = Puzzle,

    Puzzle = [S11,S12,S13,S14,S15,S16,S17,S18,S19,
              S21,S22,S23,S24,S25,S26,S27,S28,S29,
              S31,S32,S33,S34,S35,S36,S37,S38,S39,
              S41,S42,S43,S44,S45,S46,S47,S48,S49,
              S51,S52,S53,S54,S55,S56,S57,S58,S59,
              S61,S62,S63,S64,S65,S66,S67,S68,S69,
              S71,S72,S73,S74,S75,S76,S77,S78,S79,
              S81,S82,S83,S84,S85,S86,S87,S88,S89,
              S91,S92,S93,S94,S95,S96,S97,S98,S99],

    Row1 = [S11,S12,S13,S14,S15,S16,S17,S18,S19],
    Row2 = [S21,S22,S23,S24,S25,S26,S27,S28,S29],
    Row3 = [S31,S32,S33,S34,S35,S36,S37,S38,S39],
    Row4 = [S41,S42,S43,S44,S45,S46,S47,S48,S49],
    Row5 = [S51,S52,S53,S54,S55,S56,S57,S58,S59],
    Row6 = [S61,S62,S63,S64,S65,S66,S67,S68,S69],
    Row7 = [S71,S72,S73,S74,S75,S76,S77,S78,S79],
    Row8 = [S81,S82,S83,S84,S85,S86,S87,S88,S89],
    Row9 = [S91,S92,S93,S94,S95,S96,S97,S98,S99],

    Col1 = [S11,S21,S31,S41,S51,S61,S71,S81,S91],
    Col2 = [S12,S22,S32,S42,S52,S62,S72,S82,S92],
    Col3 = [S13,S23,S33,S43,S53,S63,S73,S83,S93],
    Col4 = [S14,S24,S34,S44,S54,S64,S74,S84,S94],
    Col5 = [S15,S25,S35,S45,S55,S65,S75,S85,S95],
    Col6 = [S16,S26,S36,S46,S56,S66,S76,S86,S96],
    Col7 = [S17,S27,S37,S47,S57,S67,S77,S87,S97],
    Col8 = [S18,S28,S38,S48,S58,S68,S78,S88,S98],
    Col9 = [S19,S29,S39,S49,S59,S69,S79,S89,S99],

    Squ1 = [S11,S12,S13,S21,S22,S23,S31,S32,S33],
    Squ2 = [S14,S15,S16,S24,S25,S26,S34,S35,S36],
    Squ3 = [S17,S18,S19,S27,S28,S29,S37,S38,S39],
    Squ4 = [S41,S42,S43,S51,S52,S53,S61,S62,S63],
    Squ5 = [S44,S45,S46,S54,S55,S56,S64,S65,S66],
    Squ6 = [S47,S48,S49,S57,S58,S59,S67,S68,S69],
    Squ7 = [S71,S72,S73,S81,S82,S83,S91,S92,S93],
    Squ8 = [S74,S75,S76,S84,S85,S86,S94,S95,S96],
    Squ9 = [S77,S78,S79,S87,S88,S89,S97,S98,S99],

    valid([Row1,Row2,Row3,Row4,Row5,Row6,Row7,Row8,Row9,
           Col1,Col2,Col3,Col4,Col5,Col6,Col7,Col8,Col9,
           Squ1,Squ2,Squ3,Squ4,Squ5,Squ6,Squ7,Squ8,Squ9]),

    valid_domain(Puzzle, 1, 9).