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In this paper we describe the rules of the SET-VAR prover, which is an extension of resolution and which handles theorems in a subset of second-order logic. We also give example proofs using the system and show that the rules are sound. We conjecture that the prover, defined by these SET-VAR...
At CADE-10 Ross Overbeek proposed a two-part contest to stimulate and reward work in automated theorem proving. The first part consists of seven theorems to be proved with resolution, and the second part of equational theorems. Our theorem proversOtter and its parallel childRoo proved all of the...
This paper reports the detailed computer proofs of nine equality problems in Overbeek's competition obtained by Herky, a completion-based theorem prover developed by the author. Advanced techniques implemented in Herky made it a high-performance theorem prover for equational reasoning. Herky is...
A logic for specification and verification is derived from the axioms of Zermelo-Fraenkel set theory. The proofs are performed using the proof assistant Isabelle. Isabelle is generic, supporting several different logics. Isabelle has the flexibility to adapt to variants of set theory. Its...
In this paper we describe a new inference rule, called −-match, which is used for finding set instantiations within an automated reasoning program. We have implemented −-match within a theorem prover called & and have used the system to prove some non-trivial theorems in mathematics, including...
This article is the thirtieth of a series of articles discussing various open research problems in automated reasoning. The problem proposed for research asks for criteria for accurately determining when an induction argument is the appropriate form of argument for an automated reasoning program...
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