\begin{verbatim}

const total=8.
const max=50.

num(1..total).
numm(1..max).
number(0..total).

vertex(v1).
vertex(v2).
%vertex(v3).
%vertex(v4).

col(c1).
col(c2).
col(c3).

colored(V,C) :-
    vertex(V),
    col(C),
    not not_colored(V,C).

not_colored(V,C) :-
   vertex(V),
        col(C),
        not colored(V,C).


%%%%%%%%%%%%%%%%%%%%%%%

not_assg(X,Y,J) :-
    vertex(X),
    col(Y),
    col(YY),
    colored(X,Y),
    colored(X,YY),
    num(J),
    assg(X,YY,J),
    neq(Y,YY).

not_assg(X,Y,J) :-
    vertex(X),
    col(Y),
    col(YY),
    colored(X,Y),
    num(J),
    num(JJ),
    assg(X,Y,JJ),
    neq(J,JJ).

assg(X,Y,J) :-
    vertex(X),
    col(Y),
    colored(X,Y),
    num(J),
    not not_assg(X,Y,J).

numbered(X,J) :-
    num(J),
    vertex(X),
    col(Y),
    colored(X,Y),
    assg(X,Y,J).

:-  num(J),
    vertex(X),
    col(Y),
    colored(X,Y),
    numbered(X,J+1),
    not numbered(X,J).

one_is_assigned(X) :-
    vertex(X),
    col(Y),
    colored(X,Y),
    assg(X,Y,1).

:-  vertex(X),
    col(Y),
    colored(X,Y),
    not one_is_assigned(X).

initialize(count,X,1):-
    vertex(X),
    col(Y),
    colored(X,Y),
    assg(X,Y,1).

update(count, W, Y, W+1) :-
    numm(W),
    col(Y).

aggr(count,1,X,1) :-
    vertex(X),
    col(Y),
    colored(X,Y),
    initialize(count,X,1).

aggr(count,J+1,X,Z) :-
    num(J),
    0 < J,
    J <= total-1,
    numm(W),
    vertex(X),
    col(Y),
    colored(X,Y),
    aggr(count,J,X,W),
    assg(X,Y,J+1),
    update(count,W,Y,Z).

last_number(X,J) :-
    num(J),
    vertex(X),
    col(Y),
    colored(X,Y),
    numbered(X,J),
    not numbered(X,J+1).

count_color(X,Q) :-
    vertex(X),
    num(J),
    numm(Q),
    last_number(X,J),
    aggr(count,J,X,Q).

%%%%%%%%%%%%%%%%%%%%%%%%

has_color(V) :-
    vertex(V),
    col(C),
        colored(V,C).

count_color(V,0)    :-
    vertex(V),
    not has_color(V).


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%    :-  vertex(V),
%        number(N),
%        count_color(V,N),
%        neq(N,1).

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

:-  vertex(V),
        number(N),
        count_color(V,N),
        N>2.

:-  vertex(V),
        number(N),
        count_color(V,N),
        N<1.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

hide num(X).
hide numm(X).
hide number(X).
hide numbered(X,J).
hide one_is_assigned(X).
hide initialize(X,Y,Z).
hide update(X,Y,Z,T).
hide aggr(U,V,W,X).
hide last_number(X,Y).
hide not_assg(X,Y,J).
hide assg(X,Y,J).

hide vertex(X).
hide col(C).
hide not_colored(X,Y).
hide count_color(V,N).
hide has_color(X).

\end{verbatim}