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The failure of cut-elimination in cyclic proof for first-order logic with inductive definitions (2106.11798v4)
Published 22 Jun 2021 in cs.LO and math.LO
Abstract: A cyclic proof system is a proof system whose proof figure is a tree with cycles. The cut-elimination in a proof system is fundamental. It is conjectured that the cut-elimination in the cyclic proof system for first-order logic with inductive definitions does not hold. This paper shows that the conjecture is correct by giving a sequent not provable without the cut rule but provable in the cyclic proof system.