A proof system and a decision procedure for equality logic

Equality Logic with uninterpreted functions is used for proving the equivalense or refinement between systems (hardware verification, compiler translation, etc). Current approaches for deciding this type of formulas use a transformation of an equality formula to the propositional one of larger size, and then any standard SAT checker can be applied. We give an approach for deciding satisfiability of equality logic formulas (E-SAT) in conjunctive normal form. Central in our approach is a single proof rule called ER. For this single rule we prove soundness and completeness. Based on this rule we propose a complete procedure for E-SAT and prove its correctness. Applying our procedure on a variation of the pigeon hole formula yields a polynomial complexity contrary to earlier approaches to E-SAT.