Given are two forms of one mathematical problem :
(ambivalent) Find either a proof that statement S is true, or a proof that statement S is false.
(definite) Find a proof of statement S.
For example, S could be a plausible conjecture, or a problem on an examination.
Is there a term with a precise formal interpretation, such as generalization, disambiguation, restriction, or lazy (as in "lazy evaluation") that correctly describes the relationship between the two formulations?
Dichotomies that are imprecise (such as strong/weak, or definite/indefinite) or describe each of the two types of question alone without stating a precise relationship between them (such as ambivalent/unequivocal, bivalent/univalent, or stereo/mono) do not satisfy the criterion. The bivalent version of the problem about proving X, and the unequivocal task of proving Y, are indeed of different types but I am asking about the case X=Y where a term such as subproblem might describe how to get from one version to the other.