Inconsistency of Carnot's theorem's proof by William Thomson

William Thomson proved Carnot's theorem basing on postulate: "It is impossible, by means of inanimate material agency, to derive mechanical effect from any portion of matter by cooling it below the temperature of the coldest of the surrounding objects". The present paper demonstrates that Carnot's theorem can be proved based on the contrary Thomson's postulate: "It is impossible to use the mechanical effect to the heating the coldest of surrounding objects". A conclusion that Carnot's theorem does not follow from the Thomson's postulate has been drawn.