Importing SMT and Connection proofs as expansion trees

Different automated theorem provers reason in various deductive systems and, thus, produce proof objects which are in general not compatible. To understand and analyze these objects, one needs to study the corresponding proof theory, and then study the language used to represent proofs, on a prover by prover basis. In this work we present an implementation that takes SMT and Connection proof objects from two different provers and imports them both as expansion trees. By representing the proofs in the same framework, all the algorithms and tools available for expansion trees (compression, visualization, sequent calculus proof construction, proof checking, etc.) can be employed uniformly. The expansion proofs can also be used as a validation tool for the proof objects produced.Comment: In Proceedings PxTP 2015, arXiv:1507.0837

The Pocket Reasoner -- Automatic Reasoning on Small Devices

Automated reasoning in classical first-order logic is a core research field in Artificial Intelligence. Most of the fully automated reasoning tools are large and complex systems implementing proof search methods that have significant memory requirements. This paper presents an automated reasoning tool implemented on an iPod Nano. It is based on leanCoP, a very compact Prolog implementation of the connection calculus, which operates on the structure of the given formula without generating new subformula instances. Hence, the memory requirements are significantly lower, allowing leanCoP to run on devices with only little (random-access) memory. The paper presents details of the proof search calculus, its implementation, and a practical evaluation of the presented reasoning tool

Efficient Instantiation Techniques in SMT (Work In Progress)

International audienceIn SMT solving one generally applies heuristic instantiation to handle quantified formulas. This has the side effect of producing many spurious instances and may lead to loss of performance. Therefore deriving both fewer and more meaningful instances as well as eliminating or dismissing , i.e., keeping but ignoring, those not significant for the solving are desirable features for dealing with first-order problems. This paper presents preliminary work on two approaches: the implementation of an efficient instantiation framework with an incomplete goal-oriented search; and the introduction of dismissing criteria for heuristic instances. Our experiments show that while the former improves performance in general the latter is highly dependent on the problem structure, but its combination with the classic strategy leads to competitive results w.r.t. state-of-the-art SMT solvers in several benchmark libraries

Lemmas: Generation, Selection, Application

Noting that lemmas are a key feature of mathematics, we engage in an investigation of the role of lemmas in automated theorem proving. The paper describes experiments with a combined system involving learning technology that generates useful lemmas for automated theorem provers, demonstrating improvement for several representative systems and solving a hard problem not solved by any system for twenty years. By focusing on condensed detachment problems we simplify the setting considerably, allowing us to get at the essence of lemmas and their role in proof search

The PIE Environment for First-Order-Based Proving, Interpolating and Eliminating

Abstract The PIE system aims at providing an environment for creating complex applications of automated first-order theorem proving techniques. It is embedded in Prolog. Beyond actual proving tasks, also interpolation and second-order quantifier elimination are supported. A macro feature and a L A T E X formula pretty-printer facilitate the construction of elaborate formalizations from small, understandable and documented units. For use with interpolation and elimination, preprocessing operations allow to preserve the semantics of chosen predicates. The system comes with a built-in default prover that can compute interpolants

Range-Restricted Interpolation through Clausal Tableaux

We show how variations of range-restriction and also the Horn property can be passed from inputs to outputs of Craig interpolation in first-order logic. The proof system is clausal tableaux, which stems from first-order ATP. Our results are induced by a restriction of the clausal tableau structure, which can be achieved in general by a proof transformation, also if the source proof is by resolution/paramodulation. Primarily addressed applications are query synthesis and reformulation with interpolation. Our methodical approach combines operations on proof structures with the immediate perspective of feasible implementation through incorporating highly optimized first-order provers