Abstract.
The simultaneous rigid E-unification problem arises naturally in theorem proving with equality. This problem has recently been shown to be undecidable. This raises the question whether simultaneous rigid E-unification can usefully be applied to equality theorem proving. We give some evidence in the affirmative, by presenting a number of common special cases in which a decidable version of this problem suffices for theorem proving with equality. We also present some general decidable methods of a rigid nature that can be used for equality theorem proving and discuss their complexity. Finally, we give a new proof of undecidability of simultaneous rigid E-unification which is based on Post's Correspondence Problem, and has the interesting feature that all the positive equations used are ground equations (that is, contain no variables).
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Received: March 6, 1997; revised version: August 13, 1999
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Plaisted, D. Special Cases and Substitutes for Rigid E-Unification. AAECC 10, 97–152 (2000). https://doi.org/10.1007/s002000050001
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DOI: https://doi.org/10.1007/s002000050001