We describe the superposition-based theorem prover E. E is a sound and complete...

Lava is a tool to assist circuit designers in specifying, designing, verifying and implementing hardware. It is a collection of Haskell modules. The system design exploits functional programming language features, such as monads and type classes, to provide multiple interpretations of circuit descriptions. These interpretations implement standard circuit analyses such as simulation, formal veri#cation and the generation of code for the production of real circuits.

Abstract. Matita is a new, document-centric, tactic-based interactive theorem prover. This paper focuses on some of the distinctive features of the user interaction with Matita, mostly characterized by the organization of the library as a searchable knowledge base, the emphasis on a high-quality notational rendering, and the complex interplay between syntax, presentation, and semantics.

This case study shows how non-ACL2 programs can be combined with ACL2 functions in such a way that useful properties can be proved about the composite programs. Nothing is proved about the non-ACL2 programs. Instead, the results of the non-ACL2 programs are checked at run time by ACL2 functions, and properties of these checker functions are proved. The application is resolution/paramodulation automated theorem proving for first-order logic. The top ACL2 function takes a conjecture, preprocesses the conjecture, and calls a non-ACL2 program to search for a proof or countermodel. If the non-ACL2 program succeeds, ACL2 functions check the proof or countermodel. The top ACL2 function is proved sound with respect to finite interpretations. Introduction Our ACL2 project arose from a different kind of automated theorem proving. We work with fully automatic resolution/paramodulation theo- This work was supported by the Mathematical, Information, and Computational Sciences Division subprogram...

This note answers questions on whether three identities known to hold for orthomodular lattices are true also for ortholattices. One identity is shown to fail by MACE, a program that searches for counterexamples, an the other two are proved to hold by EQP, an equational theorem prover. The problems, from work in quantum logic, were given to us by Norman Megill. Keywords: Automatic theorem proving, ortholattice, quantum logic, theory of computation. 1 Introduction An ortholattice is an algebra with a binary operation (join) and a unary operation 0 (complement) satisfying the following (independent) set of identities. x y = (x 0 y 0 ) 0 (definition of meet) x y = y x (x y) z = x (y z) x (x y) = x x 00 = x x (y y 0 ) = y y 0 Supported by the Mathematical, Information, and Computational Sciences Division subprogram of the Office of Computational and Technology Research, U.S. Department of Energy, under Contract W-31-109-Eng-38. From these identities one can...

Real-world applications of automated theorem proving require modern software environments that enable modularisation, networked inter-operability, robustness, and scalability. These requirements are met by the Agent-Oriented Programming paradigm of Distributed Artificial Intelligence. We argue that a reasonable framework for automated theorem proving in the large regards typical mathematical services as autonomous agents that provide internal functionality to the outside and that, in turn, are able to access a variety of existing external services. This article describes...

One of the major problems in clausal theorem proving is the control of the proof search. In the presence of equality, this problem is particularly hard, since nearly all state-of-the-art systems perform the proof search by saturating a mostly unstructured set of clauses. We describe an approach that enables a superposition-based prover to pick good clauses for generating inferences based on experiences from previous successful proof searches for other problems. Information about good and bad search decisions (useful and superfluous clauses) is automatically collected from search protocols and represented in the form of annotated clause patterns. At run time, new clauses are compared with stored patterns and evaluated according to the associated information found. We describe our implementation of the system. Experimental results demonstrate that a learned heuristic significantly outperforms the conventional base strategy, especially in domains where enough training examples are available.

We introduce a resource adaptive agent mechanism which supports the user of an interactive theorem proving system. The mechanism, an extension of [4], uses a two layered architecture of agent societies to suggest applicable commands together with appropriate command argument instantiations. Experiments with this approach show that its effectiveness can be further improved by introducing a resource concept. In this paper we provide an abstract view on the overall mechanism, motivate the necessity of an appropriate resource concept and discuss its realization within the agent architecture.

Abstract Many theorems involving special functions such as ln, exp and sin can be proved automatically by MetiTarski: a resolution theorem prover modified to call a decision procedure for the theory of real closed fields. Special functions are approximated by upper and lower bounds, which are typically rational functions derived from Taylor or continued fraction expansions. The decision procedure simplifies clauses by deleting literals that are inconsistent with other algebraic facts. MetiTarski simplifies arithmetic expressions by conversion to a recursive representation, followed by flattening of nested quotients. Applications include verifying hybrid and control systems.

. The model elimination theorem prover SETHEO (version V3.3) and its equational extension E-SETHEO are presented. SETHEO employs sophisticated mechanisms of subgoal selection, elaborate iterative deepening techniques, and local failure caching methods. Its equational counterpart E-SETHEO transforms formulae containing equality (using a variant of Brand's modification method) and processes the output with the standard SETHEO system. The paper gives an overview of the theoretical background, the system architecture, and the performance of both systems. Key words: Automated theorem proving, competition, SETHEO, E-SETHEO, first-order logic, model elimination, equality. 1. Introduction In this paper we describe the theorem provers SETHEO and E-SETHEO. SETHEO is based on the model elimination calculus [13] and performs proof search using iterative deepening. The proof procedure is implemented as an extension of the Warren Abstract Machine. The system is being continuously extended and enh...