| ?- sat(X + Y).
sat(X=\=_A*Y#Y)
illustrates three facts. First, any accumulated constraints affecting
the top-level variables are displayed floundered
goals, since the query is not true for all X and
Y. Secondly, accumulated constraints are displayed as
sat(V=:=Expr) or sat(V=\=Expr)
where V is a variable and Expr is a “polynomial”,
i.e. an exclusive or of conjunctions of variables and
constants. Thirdly, _A had to be introduced as an artificial
variable, since Y cannot be expressed as a function of
X. That is, X + Y is true iff there exists an _A
such that X=\=_A*Y#Y. Let's check it!
| ?- taut(_A ^ (X=\=_A*Y#Y) =:= X + Y, T).
T = 1
verifies the above answer. Notice that the formula in this query is a tautology, and so it is entailed by an empty set of constraints.