Catalysis of the reaction: [(2->1)-beta-D-fructosyl](n) = [(2->1)-beta-D-fructosyl](n-1) + alpha-D-fructofuranose-beta-D-fructofuranose 1,2':1,2'-dianhydride. This reaction is the production of alpha-D-fructofuranose beta-D-fructofuranose 1,2':2,1'-dianhydride (DFA I) by successively eliminating the diminishing (2->1)-beta-D-fructan (inulin) chain from the terminal D-fructosyl-D-fructosyl disaccharide.