Solve 4x4 sudoku in prolog stupidly

Query

?- sudoku44(A1,2,3,A4,B1,B2,B3,2,1,C2,C3,C4,D1,4,1,D4).

    1 2   3 4
  -------------
A | . 2 | 3 . |
B | . . | . 2 |
  -------------
C | 1 . | . . |
D | . 4 | 1 . |
  -------------

A1 = B3, B3 = C4, C4 = 4,
A4 = B2, B2 = 1,
B1 = C2, C2 = D4, D4 = 3,
C3 = D1, D1 = 2

sudoku.pl

% I'm very new to prolog lol

unique(1,2,3,4).
unique(1,2,4,3).
unique(1,3,2,4).
unique(1,3,4,2).
unique(1,4,2,3).
unique(1,4,3,2).
unique(2,1,3,4).
unique(2,1,4,3).
unique(2,3,1,4).
unique(2,3,4,1).
unique(2,4,1,3).
unique(2,4,3,1).
unique(3,1,2,4).
unique(3,1,4,2).
unique(3,2,1,4).
unique(3,2,4,1).
unique(3,4,1,2).
unique(3,4,2,1).
unique(4,1,2,3).
unique(4,1,3,2).
unique(4,2,1,3).
unique(4,2,3,1).
unique(4,3,1,2).
unique(4,3,2,1).

sudoku44(A1,A2,A3,A4,B1,B2,B3,B4,C1,C2,C3,C4,D1,D2,D3,D4) :-
    unique(A1,A2,A3,A4),
    unique(B1,B2,B3,B4),
    unique(C1,C2,C3,C4),
    unique(D1,D2,D3,D4),
    unique(A1,A2,B1,B2),
    unique(A3,A4,B3,B4),
    unique(C1,C2,D1,D2),
    unique(C3,C4,D3,D4),
    unique(A1,B1,C1,D1),
    unique(A2,B2,C2,D2),
    unique(A3,B3,C3,D3),
    unique(A4,B4,C4,D4).