SAT solvers are nowadays used in many applications where the UNSAT result has a special meaning that is at time critical. SAT instances sometimes exhibit symmetries which can be exploited to produce short proofs that would have been exponential for resolution alone. However, current unsatisfiability proof formats do not support symmetrical learning on which dynamic symmetry handling is based. We present in this paper a new proof format called DSRUP (Delete Symmetry Reverse Unit Propagation) which is an extension of DRUP (Delete Reverse Unit Propagation) and that is devised to certify UNSAT claims of SAT solvers implementing symmetrical learning. We first show that the problem of verifying symmetries of a CNF formula is Turing NP-hard. This led us to the definition of a new type of symmetry called RUP-symmetry, a class of symmetries more general than syntactic symmetries that can be efficiently checked. The DSRUP proof format is formally described and a verification algorithm is provided to validate DSRUP certificates. Finally, we provide experimental results obtained with the state-of-the-art dynamic symmetry-handling-based SAT solvers on unsatisfiable symmetric benchmarks drawn from SAT competitions, using an implementation of the DSRUP checking algorithm.

如今，SAT解算器被用于许多应用中，其中UNSAT结果具有特殊的意义，这在时间上很关键。SAT实例有时会表现出对称性，可以利用这些对称性来生成简短的证明，而这些证明对于单独的解决而言将是指数级的。但是，当前的不满足证明格式不支持动态对称处理所基于的对称学习。我们在本文中提出了一种称为DSRUP（删除对称反向单元传播）的新证明格式，该格式是DRUP（删除反向单元传播）的扩展，旨在证明采用对称学习的SAT解算器的UNSAT要求。我们首先表明，验证CNF公式的对称性的问题是图灵NP-困难的。这导致我们定义了一种新型的对称性，称为RUP对称性，比可以有效检查的句法对称性更通用的一类对称性。正式描述了DSRUP证明格式，并提供了一种验证算法来验证DSRUP证书。最后，我们使用DSRUP检查算法的实现，提供了基于最新动态对称处理的SAT求解器的实验结果，这些求解器是从SAT竞赛中获得的无法满足的对称基准。