  We study varieties with a term-definable poset structure, "po-groupoids". It
is known that connected posets have the "strict refinement property" (SRP). In
[arXiv:0808.1860v1 [math.LO]] it is proved that semidegenerate varieties with
the SRP have definable factor congruences and if the similarity type is finite,
directly indecomposables are axiomatizable by a set of first-order sentences.
We obtain such a set for semidegenerate varieties of connected po-groupoids and
show its quantifier complexity is bounded in general.
