Automatic Theorem Proving with Built-in Theories Including Equality, Partial Ordering, and Sets
Journal of the ACM (JACM)
Variable Elimination and Chaining in a Resolution-based Prover for Inequalities
Proceedings of the 5th Conference on Automated Deduction
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A modified version of PHR-resolution comprising negative hyper-resolution and paramodulation is introduced to reduce the search of statements that contain transitive relations. Let R be a symbol of transitive relation and let a nucleus contain the literal tRp, and let a factor of an electron be of the form C V nt, Rt2. Moreover let us suppose that tU=t, U, where U is a simultaneous most general unifier for the corresponding clash. Then the resolvent of this clash contains the subclause (C V pRt2)U. This rule of deduction is said to Be TPHR-rule. It is shown that TPHR-resolution is complete. More precisely, it is shown that the empty clause a can be deduced from a set G of clauses which contains the axiom of transitivity Tr for the relation R by using PHR - resolution iff can be deduced from the set G-{Tr} by using TPHR"-resolution. The efficiency of the use of TPHR-rule is illustrated by examples.