We solve the hypernetted-chain (HNC) and Rogers-Young (RY) integral equations for the pair structure of a system of two weakly coupled replicae of a soft-sphere fluid, in order to detect signatures of an equilibrium transition to an "ideal glass". Both integral equations predict, in addition to the supercooled-liquid branch, the appearance of a new disordered state characterized by different pair correlations, over a range of temperatures. The ideal-glass transition temperature T-DJ, identified by a discontinuous jump in the inter-replica pair correlation function, is predicted to be substantially higher with RY compared to HNC theory. The internal energy is predicted to undergo a weak discontinuity at T-DJ.
