Consider the belief:

MAXCSP classic ( belief (R,ar) , confidence)
[offerer claims there is a problem where ar CANNOT be satisfied]
with approximation ratio ar

If this belief is discounted, offerer should offer :
the complemented (negated) belief:

MAXCSP classic complement ( belief (R,ar) , confidence)
[offerer claims there is a solution satisfying ar]

The negated belief records the discounting event? 
Forces the offerer to defend the opposite when the complemented 
belief is accepted.
Should the successful discounter offer the complemented belief?
Would be in better position to defend it.