Also, SWI-Prolog is not exactly the fastest prolog available and its clpfd module is not exactly the fastest CLP(FD) library either... I would not be surprised if some other prolog could run the same program more than an order of magnitude faster!

Here it goes the same program adapted for GNU Prolog. In my machine in runs on five seconds, finding the solutions for the ten pairs of input rows!

different_lists([A|TA], [B|TB]) :-
        (   A #\= B
        ;   A #= B,
            different_lists(TA, TB) ).

all_different_lists([]).
all_different_lists([A|T]) :-
        all_different_lists(T, A),
        all_different_lists(T).

all_different_lists([], _).
all_different_lists([B|T], A) :-
        different_lists(A, B),
        all_different_lists(T, A).

list_sequence([]).
list_sequence([H|T]) :-
        list_sequence(T, H).

list_sequence([], _).
list_sequence([B|T], A) :-
        list_lt(A, B),
        list_sequence(T, B).
    
list_lt([A|TA], [B|TB]) :-
        (   A #< B
        ;   A #= B,
            list_lt(TA, TB) ).

domain_from_global_cardinality([], []).
domain_from_global_cardinality([Val-_|ET], [Val|DT]) :-
        domain_from_global_cardinality(ET, DT).

global_cardinality(L, Exactly) :-
        domain_from_global_cardinality(Exactly, Domain),
        fd_domain(L, Domain),
        global_cardinality1(Exactly, L).

global_cardinality1([], _).
global_cardinality1([Val-Rep|T], L) :-
        fd_exactly(Rep, L, Val),
        global_cardinality1(T, L).

solve([Row1, Row2, Row3, Row4, Row5, Row6, Row7]) :-
    
        Row1 = [A1, A2, A3, A4, A5, A6, A7],
        Row2 = [B1, B2, B3, B4, B5, B6, B7],
        Row3 = [C1, C2, C3, C4, C5, C6, C7],
        Row4 = [D1, D2, D3, D4, D5, D6, D7],
        Row5 = [E1, E2, E3, E4, E5, E6, E7],
        Row6 = [F1, F2, F3, F4, F5, F6, F7],
        Row7 = [G1, G2, G3, G4, G5, G6, G7],

        Col1 = [A1, B1, C1, D1, E1, F1, G1],
        Col2 = [A2, B2, C2, D2, E2, F2, G2],
        Col3 = [A3, B3, C3, D3, E3, F3, G3],
        Col4 = [A4, B4, C4, D4, E4, F4, G4],
        Col5 = [A5, B5, C5, D5, E5, F5, G5],
        Col6 = [A6, B6, C6, D6, E6, F6, G6],
        Col7 = [A7, B7, C7, D7, E7, F7, G7],

        global_cardinality(Row1, [0-2, 1-2, 2-3]),
        global_cardinality(Row2, [0-2, 1-2, 2-3]),
        global_cardinality(Row3, [0-2, 1-2, 2-3]),
        global_cardinality(Row4, [0-2, 1-2, 2-3]),
        global_cardinality(Row5, [0-2, 1-2, 2-3]),
        global_cardinality(Row6, [0-2, 1-2, 2-3]),
        global_cardinality(Row7, [0-2, 1-2, 2-3]),

        global_cardinality(Col1, [0-2, 1-2, 2-3]),
        global_cardinality(Col2, [0-2, 1-2, 2-3]),
        global_cardinality(Col3, [0-2, 1-2, 2-3]),
        global_cardinality(Col4, [0-2, 1-2, 2-3]),
        global_cardinality(Col5, [0-2, 1-2, 2-3]),
        global_cardinality(Col6, [0-2, 1-2, 2-3]),
        global_cardinality(Col7, [0-2, 1-2, 2-3]),

        all_different_lists([Row3, Row4, Row5, Row6, Row7], Row1),
        all_different_lists([Row3, Row4, Row5, Row6, Row7], Row2),

        list_sequence([Row3, Row4, Row5, Row6, Row7]),
        
        all_different_lists([Col1, Col2, Col3, Col4, Col5, Col6, Col7]
+),

        fd_labeling([A1, A2, A3, A4, A5, A6, A7, B1, B2, B3, B4, B5,
                     B6, B7, C1, C2, C3, C4, C5, C6, C7, D1, D2, D3,
                     D4, D5, D6, D7, E1, E2, E3, E4, E5, E6, E7, F1,
                     F2, F3, F4, F5, F6, F7, G1, G2, G3, G4, G5, G6,
                     G7]).

time(G) :-
        cpu_time(Start),
        call(G),
        cpu_time(End),
        S is End - Start,
        write(time(goal(G), ms(S))), nl.

solve(R1, R2, L) :-
        findall(-, solve([R1, R2 | _]), All),
        length(All, L).

tryme([]).
tryme([H|T]) :-
        H = [R1, R2],
        write('searching...'), nl,
        time(solve(R1, R2, L)),
        L120 is L * 120,
        write(solve(R1, R2, L, L120)), nl,
        tryme(T).

tryme :-
        tryme([[[2, 1, 0, 0, 2, 2, 1], [0, 2, 2, 1, 1, 0, 2]],
               [[2, 0, 0, 2, 2, 1, 1], [2, 0, 1, 2, 2, 1, 0]],
               [[2, 1, 0, 1, 2, 0, 2], [2, 2, 1, 1, 2, 0, 0]],
               [[2, 1, 0, 1, 2, 2, 0], [1, 2, 0, 2, 1, 2, 0]],
               [[0, 2, 0, 1, 2, 1, 2], [1, 2, 0, 2, 1, 0, 2]],
               [[2, 0, 0, 1, 2, 2, 1], [2, 1, 1, 0, 2, 2, 0]],
               [[1, 2, 2, 0, 0, 2, 1], [2, 0, 1, 0, 1, 2, 2]],
               [[2, 2, 1, 1, 0, 2, 0], [1, 0, 2, 1, 2, 0, 2]],
               [[2, 0, 1, 1, 2, 0, 2], [0, 1, 2, 2, 0, 1, 2]],
               [[0, 2, 2, 0, 1, 2, 1], [1, 0, 1, 2, 2, 2, 0]]]).
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