We introduce a notion of modular redundancy for theorem proving. It can be used to exploit redundancy elimination techniques (like tautology elimination, subsumption, demodulation or other more reened methods) in combination with arbitrary existing theorem provers, in a refutation complete way, even if these provers are not (or not known to be) complete in combination with the redundancy techni...

We present in expository style the main ideas in SGGS, which stands for Semantically-Guided GoalSensitive theorem proving. SGGS uses sequences of constrained clauses to represent models, instance generation to go from a candidate model to the next, and resolution as well as other inferences to repair the model. SGGS is refutationally complete for first-order logic, DPLL-style model based, seman...

This article is concerned with interactive support for \declarative theorem prov-ing". After introducing declarative theorem proving, both in general and as implemented in the Declare system, we outline the requirements of an interactive system in this context. We describe Ideclare, the interactive environment for Declare, and in particular its support for visualisation, logical navigation and ...

The power and automation offered by modern satisfiability-modulotheories (SMT) solvers is changing the landscape for mechanized formal theorem proving. For instance, the SMT-based program verifier Dafny supports a number of proof features traditionally found only in interactive proof assistants, like inductive, co-inductive, and declarative proofs. To show that proof tools rooted in SMT are gro...

The area of commonsense reasoning aims at the creation of systems able to simulate the human way of rational thinking. This paper describes the use of automated reasoning methods for tackling commonsense reasoning benchmarks. For this we use a benchmark suite introduced in literature. Our goal is to use general purpose background knowledge without domain specific hand coding of axioms, such tha...

In this paper we show that distributing the theorem proving task to several experts is a promising idea. We describe the team work method which allows the experts to compete for a while and then to cooperate. In the cooperation phase the best results derived in the competition phase are collected and the less important results are forgotten. We describe some useful experts and explain in detail...

In this chapter, the authors first provide the overall methodology for the theorem proving formal probabilistic analysis followed by a brief introduction to the HOL4 theorem prover. The main focus of this book is to provide a comprehensive framework for formal probabilistic analysis as an alternative to less accurate techniques like simulation and paper-and-pencil methods and to other less scal...

Peers is a prototype for parallel theorem proving in a distributed environment. It implements a number of strategies for refutational, contraction-based theorem proving in equational theories, whose signatures may include associative-commutative (AC) function symbols. “Contraction-based” strategies is a more general term for “simplification-based”, “rewriting-based” or “(Knuth-Bendix) completio...

Formal methods for program verification, optimization, and synthesis rely on complex mathematical proofs, which often involve reasoning about computations. Because of that there is no single automated proof procedure that can handle all the reasoning problems occurring during a program derivation or verification. Instead, one usually relies on proof assistants like NuPRL (Constable et al., 1986...

Motivated by the problem of query answering over multiple structured commonsense theories, we exploit graph-based techniques to improve the efficiency of theorem proving for structured theories. Theories are organized into subtheories that are minimally connected by the literals they share. We present message-passing algorithms that reason over these theories using consequence finding, speciali...