An algorithm based on equivalence classes for tableau with equality

This paper introduces an algorithm based on equivalence classes for tableau with equality - CECA, which use the method based on the transformation into disjunctions of inequalities and the calculation of equivalence classes. It restricts equality applications and avoids the generation of useless new formula. It is possible to restrict search space. In the same time, to study the effectiveness of the algorithm, an example is made to analyze and compare its performance with Fitting's approach and Jeffrey's approach. In addition, we have implemented the algorithm on a PC workstation using PROLOG. The results show tableau based on equivalence classes is superior to that of other algorithms.