I am looking at something where there are two conjectures, Conjecture A and Conjecture B.
I have Example X. It isn't a counterexample for Conjecture A or for Conjecture B but it is a counterexample for "Conjecture A and Conjecture B".
That is, if Conjecture A is true, then Example X is a counterexample to Conjecture B; and if Conjecture B is true, then Example X is a counterexample to Conjecture A.
It is (alas) not true that Example X implies that Conjecture A exclusive-or Conjecture B is true.
It probably isn't natural to bundle Conjectures A and B into Conjecture C, and call Example X a counterexample to Conjecture C.
Is there a name for such a counterexample?
I have a short note and it would be nice to have a nice title and an answer to the question might help.