  Constructive theories usually have interesting metamathematical properties
where explicit witnesses can be extracted from proofs of existential sentences.
For relational theories, probably the most natural of these is the existence
property, EP, sometimes referred to as the set existence property. This states
that whenever (\exists x)\phi(x) is provable, there is a formula \chi(x) such
that (\exists ! x)\phi(x) \wedge \chi(x) is provable. It has been known since
the 80's that EP holds for some intuitionistic set theories and yet fails for
IZF. Despite this, it has remained open until now whether EP holds for the most
well known constructive set theory, CZF. In this paper we show that EP fails
for CZF.
