Cutting surface with curves in grasshopper

Hi, I need to cut a surface with a curve.
i projected the curve on the surface and i used split surface to trim it, but it doesn’t work!
I attach the file
please find an answer
trim surface problem.3dm (607.1 KB)
trim surface (12.8 KB)

Your curve is not closed.
Close it.
You can use “Connect curves” with Close(L)=true.

thank you very much