Well, you start off by asking for a very very durable flooring, and by the time I got to the end of the post I figured you'd already decided that the most durable flooring was ceramic or porcelain tile.
Ceramic and porcelain tile make for a durable floor, but you're selling yourself short by not considering synthetic rubber flooring. I have synthetic rubber stair treads in my front and back stair wells, and about the only thing that will damage this material is a razor and a firm intent to damage the floor.
Synthetic rubber comes in both 12 inch square tiles and 24 inch square tiles, and Johnsonite makes it in about 75 colours and eleven different raised patterns, and each colour and raised pattern can come either marbelized or speckled with any of the other 74 colours, so you can play interior designer and really make a mess. By ordering some extra tiles, you can repair your floor by replacing damaged tiles. But, as I say, about the only way you can damage one is by intentionally cutting it with a razor. Or, perhaps by scratching it up by sitting on a chair that's missing the feet from it's steel tube legs, but that would scratch up tile as well.
Strong solvents like acetone (nail polish remover) or lacquer thinner (toluene) will, if left on for long enough, start to soften it, but you have to do that intentionally because those solvents would typically evaporate before they did any damage. When I was installing my stair treads, I would use xylene to clean the mold release agent off the treads so that the polyurethane caulk I used on them would stick. I started off using acetone and lacquer thinner, but was told by the factory that xylene works just as well, and doesn't evaporate nearly as fast, so you use less of it and inhale less solvent as well.
I don't know of anything that stains synthetic rubber, and I don't think you can stain a porcelain tile either.
You rarely see rubber tile flooring in residential settings because, quite frankly, it's expensive and much more durable than one would ever need in a house. Typically, you find it in commercial settings, and often in gymnasiums because rubber flooring will stand up to a 40 pound steel weight being dropped on it from shoulder height or an exercise machine pounding on it 8 hours per day, 363 days per year. So, it certainly meets the requirements specified in your post. About the only flooring more durable than rubber flooring that I can think of are the thick rubber mats between the rink and change rooms in hockey rinks that players walk on with their newly sharpened skates.
So, ceramic tile can be damaged by dropping something hard on it and causing the tile to chip or crack, and that's about the only risk. Rubber flooring can be damaged by cutting it with a very sharp knife like a razor, and that's about the only risk. Ceramic tile is cold to walk on in bare feet, too. Both will stand up to a lit cigarette being put out on them.
I know Roppe and Bengard also make rubber and vinyl moldings for floors, but I don't know if they also make rubber floor tiles or not. Certainly, Johnsonite is the biggest name in synthetic rubber flooring.
http://www.johnsonite.com/en/floorin...ubberflooring/
http://www.johnsonite.com/NR/rdonlyr...2RubberBro.pdf
Material to use for replacing linoleum (glued down).
Linear Mode
