STRATEGY PARALLELISM IN AUTOMATED THEOREM PROVING

1999 ◽  
Vol 13 (02) ◽  
pp. 219-245 ◽  
Author(s):  
ANDREAS WOLF ◽  
REINHOLD LETZ
Keyword(s):  
Theorem Proving ◽  
Experimental Evaluation ◽  
Automated Theorem Proving ◽  
Search Strategies ◽  
Theorem Prover ◽  
Strategy Selection ◽  
Theorem Provers ◽  
Initial Strategy ◽  
Basic Concepts ◽  
Run Time

Automated theorem provers use search strategies. Unfortunately, there is no unique strategy which is uniformly successful on all problems. This motivates us to apply different strategies in parallel, in a competitive manner. In this paper, we discuss properties, problems, and perspectives of strategy parallelism in theorem proving. We develop basic concepts like the complementarity and the overlap value of strategy sets. Some of the problems such as initial strategy selection and run-time strategy exchange are discussed in more detail. The paper also contains the description of an implementation of a strategy parallel theorem prover (p-SETHEO) and an experimental evaluation.

scholarly journals Understanding LEO-II’s proofs

10.29007/x9c9 ◽  
2018 ◽  
Author(s):  
Nik Sultana ◽  
Christoph Benzmüller
Keyword(s):  
Theorem Proving ◽  
Automated Theorem Proving ◽  
Higher Order ◽  
Target Audience ◽  
Theorem Prover ◽  
First Order

The LEO and LEO-II provers have pioneered the integration of higher-order and first-order automated theorem proving. To date, the LEO-II system is, to our knowledge, the only automated higher-order theorem prover which is capable of generating joint higher-order–first-order proof objects in TPTP format. This paper discusses LEO-II’s proof objects. The target audience are practitioners with an interest in using LEO-II proofs within other systems.

scholarly journals The Thousands of Models for Theorem Provers (TMTP) Model Library - First Steps

10.29007/7dg5 ◽  
2018 ◽  
Author(s):  
Geoff Sutcliffe ◽  
Stephan Schulz
Keyword(s):  
Theorem Proving ◽  
Automated Theorem Proving ◽  
Theorem Provers ◽  
Model Library ◽  
Problems And Solutions ◽  
Model Finding ◽  
Problem Library

The TPTP World is a well established infrastructure that supports research,development, and deployment of Automated Theorem Proving (ATP) systems forclassical logics.The TPTP world includes the TPTP problem library, the TSTP solution library,standards for writing ATP problems and reporting ATP solutions, and itprovides tools and services for processing ATP problems and solutions.This work describes a new component of the TPTP world - the Thousands ofModels for Theorem Provers (TMTP) Model Library.This is a library of models for identified axiomatizations built fromaxiom sets in the TPTP problem library, along with functions for efficientlyevaluating formulae wrt models, and tools for examining and processingthe models.The TMTP supports the development of semantically guided theorem provingATP systems, provide examples for developers of model finding ATP systems,and provides insights into the semantics of axiomatizations.

scholarly journals Integer Induction in Saturation

2021 ◽  
pp. 361-377
Author(s):  
Petra Hozzová ◽  
Laura Kovács ◽  
Andrei Voronkov
Keyword(s):  
Theorem Proving ◽  
Program Analysis ◽  
State Of The Art ◽  
Inductive Reasoning ◽  
Theorem Prover ◽  
Inference Rules ◽  
First Order ◽  
Theorem Provers ◽  
Mathematical Properties

AbstractIntegers are ubiquitous in programming and therefore also in applications of program analysis and verification. Such applications often require some sort of inductive reasoning. In this paper we analyze the challenge of automating inductive reasoning with integers. We introduce inference rules for integer induction within the saturation framework of first-order theorem proving. We implemented these rules in the theorem prover Vampire and evaluated our work against other state-of-the-art theorem provers. Our results demonstrate the strength of our approach by solving new problems coming from program analysis and mathematical properties of integers.

scholarly journals Aiming for the Goal with SInE

10.29007/q4pt ◽  
2020 ◽  
Author(s):  
Martin Suda
Keyword(s):  
Experimental Evaluation ◽  
Main Idea ◽  
Inference Engine ◽  
Theorem Prover ◽  
Selection Algorithm ◽  
First Order ◽  
Theorem Provers ◽  
The Individual ◽  
Goal Distance ◽  
Automatic Theorem

The Sumo INference Engine (SInE) is a well-established premise selection algorithm for first-order theorem provers, routinely used, especially on large theory problems. The main idea of SInE is to start from the goal formula and to iteratively add other formulas to those already added that are related by sharing signature symbols. This implicitly defines a certain heuristical distance of the individual formulas and symbols from the goal.In this paper, we show how this distance can be successfully used for other purposes than just premise selection. In particular, biasing clause selection to postpone introduction of input clauses further from the goal helps to solve more problems. Moreover, a precedence which respects such goal distance of symbols gives rise to a goal sensitive simplification ordering. We implemented both ideas in the automatic theorem prover Vampire and present their experimental evaluation on the TPTP benchmark.

scholarly journals The Efficiency of Automated Theorem Proving by Translation to Less Expressive Logics

10.29007/kvb1 ◽  
2018 ◽  
Author(s):  
Negin Arhami ◽  
Geoff Sutcliffe
Keyword(s):  
Theorem Proving ◽  
Automated Theorem Proving ◽  
The Other ◽  
Theorem Prover ◽  
Trade Off ◽  
Other Hand ◽  
Automated Theorem Prover

Many Automated Theorem Prover (ATP) systems for different logics, andtranslators for translating different logics from one to another, havebeen developed and are now available.Some logics are more expressive than others, and it is easier to expressproblems in those logics.On the other hand, the ATP systems for less expressive logics have beenunder development for many years, and are more powerful and reliable.There is a trade-off between expressivity of a logic, and the power andreliability of the available ATP systems.Translators and ATP systems can be combined to try to solvea problem.In this research, an experiment has been carried out to compare theperformance of difference combinations of translators and ATP systems.

scholarly journals Automated Theorem Proving using the TPTP Process Instruction Language

10.29007/f997 ◽  
2018 ◽  
Author(s):  
Muhammad Nassar ◽  
Geoff Sutcliffe
Keyword(s):  
Theorem Proving ◽  
Automated Theorem Proving ◽  
Input Output ◽  
Theorem Provers ◽  
And Control

The TPTP (Thousands of Problems for Theorem Provers) World is a well established infrastructure for Automated Theorem Proving (ATP). In the context of the TPTP World, the TPTP Process Instruction (TPI) language provides capabilities to input, output and organize logical formulae, and control the execution of ATP systems. This paper reviews the TPI language, describes a shell interpreter for the language, and demonstrates their use in theorem proving.

scholarly journals Proof simplification and automated theorem proving

2019 ◽  
Vol 377 (2140) ◽  
pp. 20180034 ◽  
Author(s):  
Michael Kinyon
Keyword(s):  
Theorem Proving ◽  
Simple Proof ◽  
Automated Theorem Proving ◽  
Theme Issue ◽  
Theorem Provers ◽  
Open Question

The proofs first generated by automated theorem provers are far from optimal by any measure of simplicity. In this paper, I describe a technique for simplifying automated proofs. Hopefully, this discussion will stimulate interest in the larger, still open, question of what reasonable measures of proof simplicity might be. This article is part of the theme issue ‘The notion of ‘simple proof’ - Hilbert's 24th problem’.

scholarly journals Automated Reasoning in the Simulation of Evolvable Systems

10.29007/jj86 ◽  
2018 ◽  
Author(s):  
Djihed Afifi ◽  
David Rydeheard ◽  
Howard Barringer
Keyword(s):  
Theorem Proving ◽  
Automated Theorem Proving ◽  
Rapid Assessment ◽  
Theorem Prover ◽  
System Description ◽  
Large Sets ◽  
Simulation Engine ◽  
Meta Level ◽  
Almost All ◽  
Computational Systems

We present a novel application of automated theorem proving for the simulation of computational systems. The computational systems we consider are evolvable, i.e. may reconfigure their structure and programs at run-time. In [1], a logical framework for describing such systems is introduced. The underlying logic of this framework allows us to build a simulation engine for executing system specifications. This engine makes intensive use of automated theorem proving – when running a simulation, almost all computational steps are those of a theorem prover. In this paper, we present this novel combination of a logical setting involving meta-level logics and large sets of formulae for system description, together with theorem proving requirements which involve often slowly changing specifications with the need for rapid assessment of deducibility and consistency. We will evaluate the suitability of several theorem provers for this application.

scholarly journals Rewriting and Well-Definedness within a Proof System

10.29007/b7wc ◽  
2018 ◽  
Author(s):  
Issam Maamria ◽  
Michael Butler
Keyword(s):  
Theorem Proving ◽  
Automated Theorem Proving ◽  
Term Rewriting ◽  
Proof System ◽  
Proof Technique ◽  
Partial Functions ◽  
Deductive Proof ◽  
Theorem Provers ◽  
Theoretical Foundations

Term rewriting has a significant presence in various areas, not least in automated theorem proving where it is used as a proof technique. Many theorem provers employ specialised proof tactics for rewriting. This results in an interleaving between deduction and computation (i.e., rewriting) steps. If the logic of reasoning supports partial functions, it is necessary that rewriting copes with potentially ill-defined terms. In this paper, we provide a basis for integrating rewriting with a deductive proof system that deals with well-definedness. The definitions and theorems presented in this paper are the theoretical foundations for an extensible rewriting-based prover that has been implemented for the set theoretical formalism Event-B.

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