Abstract
We show how to prove formulas of the form ∀ x∃ yΦ(x, y) in the initial model of an equational variety by using purely algebraic simplifications. This allows to tackle theorems whose proofs requires complicated noetherian induction. We also give a disproof theorem, which is not only useful to prove that a conjecture is false but is also used to shorten the proof search of a theorem. We show applications of the method to fragments of arithmetic.
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© 1994 Springer-Verlag Berlin Heidelberg
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Chazarain, J., Kounalis, E. (1994). Mechanizable inductive proofs for a class of ∀ ∃ formulas. In: Bundy, A. (eds) Automated Deduction — CADE-12. CADE 1994. Lecture Notes in Computer Science, vol 814. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58156-1_9
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DOI: https://doi.org/10.1007/3-540-58156-1_9
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