We consider a combined satisfiability problem where an instance is given in two parts: a set of traditional clauses extended with a set of parity (xor) constraints. To solve such problems without translation to CNF, we develop a parity constraint reasoning method that can be integrated to a clause learning solver. The idea is to devise a module that offers a decision procedure and implied literal detection for parity constraints and also provides clausal explanations for implied literals and conflicts. We have implemented the method and integrated it to a state-of-the-art clause learning solver. The resulting system is experimentally evaluated and compared to state-of-the-art solvers.
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