Split line at regular intervals in shapely

Question

I have been trying to use Shapely to split a shapefile with multiple features at regular intervals. I have used the split function to do this. I can easily create the points at which the lines should be split, but when I then split nothing happens.

What am I missing?

import fiona
import shapely
from shapely.ops import split
from shapely.geometry import *

schema = {
'geometry': 'MultiLineString',
'properties': {'id': 'int'},
 }

with fiona.open("./test_depth.shp") as inp:
    with fiona.open('result3.shp', 'w', 'ESRI Shapefile', schema) as out:
        for line in inp:
            geom = shape(line['geometry'])
            length = geom.length
            for i, distance in enumerate(range(0, int(length), 10)):
                point = geom.interpolate(distance)
                split_line = shapely.geometry.MultiLineString(split(geom,point))
                print(split_line)
                out.write({'geometry': mapping(split_line),'properties': {'id': 1}})