Brute-force sudoku solver

sudoku.pl

% Define digits from 1 to 9
digit(1).
digit(2).
digit(3).
digit(4).
digit(5).
digit(6).
digit(7).
digit(8).
digit(9).

% Decrement rules
decrement(2,1).
decrement(3,2).
decrement(4,3).
decrement(5,4).
decrement(6,5).
decrement(7,6).
decrement(8,7).
decrement(9,8).

% Define is_not_one
is_not_one(2).
is_not_one(A) :- decrement(A, AA), is_not_one(AA).

% Define less_than
less_than(1,A) :- is_not_one(A).
less_than(A,B) :- decrement(A, AA), decrement(B, BB), less_than(AA, BB).

% Define greater_than
greater_than(A,1) :- is_not_one(A).
greater_than(A,B) :- decrement(A, AA), decrement(B, BB), greater_than(AA, BB).

% Define is_different
is_different(A,B) :- less_than(A,B).
is_different(A,B) :- greater_than(A,B).

% Ensure nine different digits
different9(A,B,C,D,E,F,G,H,I) :-
    is_different(A,B), is_different(A,C), is_different(A,D), is_different(A,E), is_different(A,F), is_different(A,G), is_different(A,H), is_different(A,I),
    is_different(B,C), is_different(B,D), is_different(B,E), is_different(B,F), is_different(B,G), is_different(B,H), is_different(B,I),
    is_different(C,D), is_different(C,E), is_different(C,F), is_different(C,G), is_different(C,H), is_different(C,I),
    is_different(D,E), is_different(D,F), is_different(D,G), is_different(D,H), is_different(D,I),
    is_different(E,F), is_different(E,G), is_different(E,H), is_different(E,I),
    is_different(F,G), is_different(F,H), is_different(F,I),
    is_different(G,H), is_different(G,I),
    is_different(H,I).

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

  % Ensure all Rows have distinct values
  different9(A1,A2,A3,A4,A5,A6,A7,A8,A9),
  different9(B1,B2,B3,B4,B5,B6,B7,B8,B9),
  different9(C1,C2,C3,C4,C5,C6,C7,C8,C9),
  different9(D1,D2,D3,D4,D5,D6,D7,D8,D9),
  different9(E1,E2,E3,E4,E5,E6,E7,E8,E9),
  different9(F1,F2,F3,F4,F5,F6,F7,F8,F9),
  different9(G1,G2,G3,G4,G5,G6,G7,G8,G9),
  different9(H1,H2,H3,H4,H5,H6,H7,H8,H9),
  different9(I1,I2,I3,I4,I5,I6,I7,I8,I9),

  % Ensure all Columns have distinct values
  different9(A1,B1,C1,D1,E1,F1,G1,H1,I1),
  different9(A2,B2,C2,D2,E2,F2,G2,H2,I2),
  different9(A3,B3,C3,D3,E3,F3,G3,H3,I3),
  different9(A4,B4,C4,D4,E4,F4,G4,H4,I4),
  different9(A5,B5,C5,D5,E5,F5,G5,H5,I5),
  different9(A6,B6,C6,D6,E6,F6,G6,H6,I6),
  different9(A7,B7,C7,D7,E7,F7,G7,H7,I7),
  different9(A8,B8,C8,D8,E8,F8,G8,H8,I8),
  different9(A9,B9,C9,D9,E9,F9,G9,H9,I9),

  % Ensure all Subgrids have distinct values
  different9(A1,A2,A3,B1,B2,B3,C1,C2,C3),
  different9(A4,A5,A6,B4,B5,B6,C4,C5,C6),
  different9(A7,A8,A9,B7,B8,B9,C7,C8,C9),
  different9(D1,D2,D3,E1,E2,E3,F1,F2,F3),
  different9(D4,D5,D6,E4,E5,E6,F4,F5,F6),
  different9(D7,D8,D9,E7,E8,E9,F7,F8,F9),
  different9(G1,G2,G3,H1,H2,H3,I1,I2,I3),
  different9(G4,G5,G6,H4,H5,H6,I4,I5,I6),
  different9(G7,G8,G9,H7,H8,H9,I7,I8,I9).

Usage example:

sudoku(4,3,5, 2,6,9, 7,8,A9, % 1
    6,B2,2, 5,7,1, 4,9,3, % 8
    C1,9,7, 8,3,4, 5,6,2, % 1
    8,2,6, D4,9,5, 3,4,7, % 1
    3,7,4, 6,8,2, E7,1,5, % 9
    9,5,F3, 7,4,3, 6,2,8, % 1
    5,1,9, 3,2,6, G7,7,4, % 8
    2,4,8, 9,5,H6, 1,3,6, % 7
    7,6,3, I4,1,8, 2,5,9) % 4