  In analogy with GRB 190114C, we here analyze the ultrarelativistic prompt
emission (UPE) of GRB 180720B observed in the rest-frame time interval $t_{\rm
rf}=4.84$--$10.89$~s by Fermi-GBM. We reveal the UPE hierarchical structure
from the time-resolved spectral analysis performed in time sub-intervals: the
spectrum in each shorter time interval is always fitted by a composite
blackbody plus cutoff power-law model. We explain this structure with the
\textit{inner engine} of binary-driven hypernova (BdHN) model operating in a
quantum electrodynamics (QED) regime. In this regime, the electric field
induced by the gravitomagnetic interaction of the newborn Kerr BH with the
surrounding magnetic field is overcritical, i.e., $|{\bf E}|\geq E_c$, where
$E_c=m_e^2 c^3/(e\hbar)$. The overcritical field polarizes the vacuum leading
to an $e^+~e^-$ pair plasma that loads baryons from the surroundings during its
expansion. We calculate the dynamics of the self-acceleration of the
pair-electromagnetic-baryon (PEMB) pulses to their point of transparency. We
characterize the quantum vacuum polarization process in the sequences of
decreasing time bins of the UPE by determining the radiation timescale, Lorentz
factors, and transparency radius of the PEMB pulses. We also estimate the
strength of the surrounding magnetic field $\sim 10^{14}$ G, and obtain a lower
limit to the BH mass, $M=2.4~M_\odot$, and correspondingly an upper limit to
the spin, $\alpha = 0.6$, from the conditions that the UPE is powered by the
Kerr BH extractable energy and its mass is bound from below by the NS critical
mass.
