The formula should read soap, warm water and... time (of course, it helps if the time is used for moderately vigorous scrubbing).

Viruses are enclosed in a lipid (fat) layer and once the soap weakens, or dissolves, this layer of protection for the virus, they die. Warm water makes the soap work better. A popular mistake I have seen in the industrial environment is people practically scalding and grinding their skin with such hot water and harsh soaps so much that it also removes the protective oils from their skin. Afterwards, chemicals and biological agents get an easier path into your body.