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Conference Paper

Superposition Theorem Proving for Abelian Groups Represented as Integer Modules


Stuber,  Jürgen
Programming Logics, MPI for Informatics, Max Planck Society;

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Stuber, J. (1996). Superposition Theorem Proving for Abelian Groups Represented as Integer Modules. In H. Ganzinger (Ed.), Rewriting Techniques and Applications, 7th International Conference, RTA-96 (pp. 33-47). Berlin, Germany: Springer.

Cite as:
We define a superposition calculus specialized for abelian groups represented as integer modules, and show its refutational completeness. This allows to substantially reduce the number of inferences compared to a standard superposition prover which applies the axioms directly. Specifically, equational literals are simplified, so that only the maximal term of the sums is on the left-hand side. Only certain minimal superpositions need to be considered; other superpositions which a standard prover would consider become redundant. This not only reduces the number of inferences, but also reduces the size of the AC-unification problems which are generated. That is, AC-unification is not necessary at the top of a term, only below some non-AC-symbol. Further, we consider situations where the axioms give rise to variable overlaps and develop techniques to avoid these explosive cases where possible.