  Monte Carlo generators which were tuned for energies up to that of the
Tevatron, are found wanting when extended to LHC energies. We construct a model
that satisfies the theoretical requisites of high energy soft interactions,
based on two conjectures: (i) the results of the Ads/CDF correspondence for N =
4 SYM, and (ii) the requirement of matching with high energy QCD. In keeping
with these postulates, we assume that the soft Pomeron intercept is relatively
large, and the slope of the Pomeron trajectory is equal to zero. We derive
analytical formulae that sum both the enhanced and semi-enhanced diagrams for
elastic and diffractive amplitudes. Parameters of the model are obtained by
fitting to experimental data, up to and including the Tevatron energies, and we
predict cross sections at all energies accessible at the LHC and beyond.
  Predictions of the model are in agreement with measured values obtained by
CMS, ATLAS and ALICE for inelastic and inclusive cross sections. We compare our
results with experimental data and competing models.
