#show match/3.

% Let the choice to have a triplet in the match or not
unmatch(X,Y,Z) :- tri(X,Y,Z), not match(X,Y,Z).
match(X,Y,Z) :- tri(X,Y,Z), not unmatch(X,Y,Z).

% every letter in domain must be used
:- dom(X), not match(X,_,_).

% cannot have different matching with same first letter
:- match(X,Y,Z), match(X,Y1,Z1), Z != Z1.
:- match(X,Y,Z), match(X,Y1,Z1), Y1 != Y.

% cannot have different matching with same second letter
:- match(X,Y,Z), match(X1,Y,Z1), X1 != X.
:- match(X,Y,Z), match(X1,Y,Z1), Z != Z1.

% cannot have different matching with same third letter
:- match(X,Y,Z), match(X1,Y1,Z), X != X1.
:- match(X,Y,Z), match(X1,Y1,Z), Y1 != Y.