A major challenge to understanding glass-forming materials is obtaining equilibrium data far below the laboratory glass transition temperature Tg. The challenge arises because it takes geologic aging times to achieve the equilibrium glassy state when temperatures are well below Tg. Here, we finesse this problem through measurements on an ultrastable amorphous Teflon with fictive temperature Tf near to its Kauzmann temperature TK. In the window between Tf and Tg, the material has a lower molecular mobility than the equilibrium state because of its low specific volume and enthalpy. Our measurements show that the determined scaled relaxation times deviate strongly from the classical expectation of divergence of time scales at a finite temperature. The results challenge the view of an ideal glass transition at or near to TK.