Currently I'm dealing with two floors, one on top of the other. The top is sheet vinyl, about 15 years old and the bottom layer is sheet true linoleum, made from linseed oil. The linoleum is original to the house, circa 1964. So, for better or for worse, it is cracking as I take it up in pieces. I have this old manure scraper... yes manure scraper. It was used a long time ago to scrap barn floors to remove, yes, manure. I have been successful in scraping the linoleum and vinyl layers away, but keep the angle low enough as to not dig into the subflooring... Good luck!