  It has become standard that, when a SAT solver decides that a CNF $\Gamma$ is
unsatisfiable, it produces a certificate of unsatisfiability in the form of a
refutation of $\Gamma$ in some proof system. The system typically used is DRAT,
which is equivalent to extended resolution (ER) -- for example, until this year
DRAT refutations were required in the annual SAT competition. Recently
[Bogaerts et al.~2023] introduced a new proof system, associated with the tool
VeriPB, which is at least as strong as DRAT and is further able to handle
certain symmetry-breaking techniques. We show that this system simulates the
proof system $G_1$, which allows limited reasoning with QBFs and forms the
first level above ER in a natural hierarchy of proof systems. This hierarchy is
not known to be strict, but nevertheless this is evidence that the system of
[Bogaerts et al. 2023] is plausibly strictly stronger than ER and DRAT. In the
other direction, we show that symmetry-breaking for a single symmetry can be
handled inside ER.
