\begin{verbatim}

 obj(a).
 obj(b).
 obj(c).
 obj(d).

 prec(X,Y) :- obj(X), obj(Y), not prec(Y,X),  neq(X,Y).
 prec(X,Y) :- obj(X), obj(Y), obj(Z), prec(X,Z), prec(Z,Y).
%It works even if the previous rule is removed.

 not_succ(X,Z) :- obj(X), obj(Z), prec(Z,X).
 not_succ(X,Z) :- obj(X), obj(Y), obj(Z), prec(X,Y), prec(Y,Z).
 not_succ(X,Y) :- obj(X), obj(Y), eq(X,Y).
 succ(X,Y) :- obj(X), obj(Y), not  not_succ(X,Y).

 not_first(X) :- obj(X), obj(Y), prec(Y,X).
 first(X) :- obj(X), not not_first(X).

 not_last(X) :-  obj(X), obj(Y), prec(X,Y).
 last(X) :- obj(X), not not_last(X).

 reachable(X) :- obj(X), first(X).
 reachable(Y) :- obj(X), obj(Y), reachable(X), succ(X,Y).

 linear :- obj(X), reachable(X), last(X).
 inconsistent :- not inconsistent, not linear.

 hide obj(X).
 hide prec(X,Y).
 hide not_succ(X,Y).
 hide not_first(X).
 hide not_last(X).
 hide reachable(X).
 hide linear.
 hide inconsistent.

\end{verbatim}