# The cutting plane proof system with bounded degree of falsity

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## Abstract

The cutting plane proof system for proving the unsatisfiability of propositional formulas in conjunctive normalform is based on a natural representation of formulas as systems of integer inequalities. We define a restriction of this system, the cutting plane system with bounded degree of falsity, and show the results: This system *p*-simulates resolution and has polynomial size proofs for the pigeonhole formulas. The formulas from [ 9] only have superpolynomially long proofs in the system. Our system is the only known system with provably superpolynomial proof size, but polynomial size proofs for the pigeonhole formulas.

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© Springer-Verlag Berlin Heidelberg 1992