## Completion and Equational Theorem Proving using Taxonomic Constraints

• We present an approach to prove several theorems in slightly different axiomsystems simultaneously. We represent the different problems as a taxonomy, i.e.a tree in which each node inherits all knowledge of its predecessors, and solve theproblems using inference steps on rules and equations with simple constraints,i.e. words identifying nodes in the taxonomy. We demonstrate that a substantialgain can be achieved by using taxonomic constraints, not only by avoiding therepetition of inference steps in the different problems but also by achieving runtimes that are much shorter than the accumulated run times when proving eachproblem separately.

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