  Symmetry and dominance breaking can be crucial for solving hard combinatorial
search and optimisation problems, but the correctness of these techniques
sometimes relies on subtle arguments. For this reason, it is desirable to
produce efficient, machine-verifiable certificates that solutions have been
computed correctly. Building on the cutting planes proof system, we develop a
certification method for optimisation problems in which symmetry and dominance
breaking are easily expressible. Our experimental evaluation demonstrates that
we can efficiently verify fully general symmetry breaking in Boolean
satisfiability (SAT) solving, thus providing, for the first time, a unified
method to certify a range of advanced SAT techniques that also includes XOR and
cardinality reasoning. In addition, we apply our method to maximum clique
solving and constraint programming as a proof of concept that the approach
applies to a wider range of combinatorial problems.
