The conjecture was: is closed under finite intersections.
The counter-example follows: , .
It is easy to show that but .
This result is discouraging, because (as it seems) it probably follows that using plain funcoids approach to singularity theory fails and we need to invent something more sophisticated.
Also note that is a rather counter-intuitive result (draw a graph to see it), despite of the fact that it can be easily proved.