:- table p/1.
p(b).
p(c) :- tnot p(a).
p(X) :- t(X,Y,Z), tnot p(Y), tnot p(Z).

t(a,b,a). t(a,a,b). t(c,c,c).

/*

tnot/1 vs.  ${\tt '\backslash+'/1}$

Subject to some semantic restrictions, an XSB programmer can intermix the use of tabled negation ( tnot/1) with Prolog's 
   negation (  ${\tt '\backslash+'/1}$, or equivalently fail_if/1 or not/1). These restrictions are discussed in detail below 
  -- for now we focus on differences in behavior or these two predicates in stratified programs. Recall that  
   ${\tt '\backslash+'(S)}$ calls $S$ and if $S$ has a solution, Prolog , executes a cut over the subtree created by  ${\tt '\backslash+'(S)}$, 
   and fails. tnot/1 on the other hand, does not execute a cut, so that all subgoals in the computation path begun by the 
   negative call will be completely evaluated. The major reason for not executing the cut is to insure that XSB evaluates ground queries 
   to Datalog programs with negation with polynomial data complexity. As seen in Section 5.2, this 
   property cannot be preserved if negation ``cuts'' over tables.

There are other small differences between tnot/1 and  ${\tt '\backslash+'/1}$ illustrated in the following exercise.

Exercise 5.3.3   In general, making a call to non-ground negative subgoal in Prolog may be unsound (cf. [29]), 
but the following program illustrates a case in which non-ground negation is sound.

 See http://www3.cs.stonybrook.edu/~sbprolog/manual1/node74.html#sec:control

*/

ngr_p:- \+ ngr_p(_).

ngr_p(a).
% Its tabled analog is

:- table ngr_tp/1.

ngr_tp:- tnot(ngr_tp(_)).
ngr_tp(a).