## A proof-producing decision procedure for real arithmetic (2005)

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Venue: | Automated deduction – CADE-20. 20th international conference on automated deduction |

Citations: | 24 - 3 self |

### BibTeX

@INPROCEEDINGS{Mclaughlin05aproof-producing,

author = {Sean Mclaughlin and John Harrison},

title = {A proof-producing decision procedure for real arithmetic},

booktitle = {Automated deduction – CADE-20. 20th international conference on automated deduction},

year = {2005},

pages = {295--314},

publisher = {Springer-Verlag}

}

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### Abstract

Abstract. We present a fully proof-producing implementation of a quantifier elimination procedure for real closed fields. To our knowledge, this is the first generally useful proof-producing implementation of such an algorithm. While many problems within the domain are intractable, we demonstrate convincing examples of its value in interactive theorem proving. 1 Overview and related work Arguably the first automated theorem prover ever written was for a theory of linear arithmetic [8]. Nowadays many theorem proving systems, even those normally classified as ‘interactive ’ rather than ‘automatic’, contain procedures to automate routine arithmetical reasoning over some of the supported number systems like N, Z, Q, R and C. Experience shows that such automated support is invaluable in relieving users of what would otherwise be tedious low-level proofs. We can identify several very common limitations of such procedures: – Often they are restricted to proving purely universal formulas rather than dealing with arbitrary quantifier structure and performing general quantifier elimination.