scholarly journals Generation and Verification of Finite Models and Counterexamples Using an Automated Theorem Prover Answering Two Open Questions

1982 ◽  
Vol 29 (2) ◽  
pp. 273-284 ◽  
Author(s):  
Steve Winker
Keyword(s):  
Theorem Prover ◽  
Finite Models ◽  
Open Questions ◽  
Automated Theorem Prover

scholarly journals CSE_E 1.0: An Integrated Automated Theorem Prover for First-Order Logic

Symmetry ◽  
2019 ◽  
Vol 11 (9) ◽  
pp. 1142
Author(s):  
Feng Cao ◽  
Yang Xu ◽  
Jun Liu ◽  
Shuwei Chen ◽  
Xinran Ning
Keyword(s):  
Order Logic ◽  
Theorem Prover ◽  
First Order Logic ◽  
Inference Mechanism ◽  
First Order ◽  
Proof Search ◽  
Interdisciplinary Field ◽  
Heuristic Strategies ◽  
Automated Theorem Prover ◽  
Hard Problems

First-order logic is an important part of mathematical logic, and automated theorem proving is an interdisciplinary field of mathematics and computer science. The paper presents an automated theorem prover for first-order logic, called C S E _ E 1.0, which is a combination of two provers contradiction separation extension (CSE) and E, where CSE is based on the recently-introduced multi-clause standard contradiction separation (S-CS) calculus for first-order logic and E is the well-known equational theorem prover for first-order logic based on superposition and rewriting. The motivation of the combined prover C S E _ E 1.0 is to (1) evaluate the capability, applicability and generality of C S E _ E , and (2) take advantage of novel multi-clause S-CS dynamic deduction of CSE and mature equality handling of E to solve more and harder problems. In contrast to other improvements of E, C S E _ E 1.0 optimizes E mainly from the inference mechanism aspect. The focus of the present work is given to the description of C S E _ E including its S-CS rule, heuristic strategies, and the S-CS dynamic deduction algorithm for implementation. In terms of combination, in order not to lose the capability of E and use C S E _ E to solve some hard problems which are unsolved by E, C S E _ E 1.0 schedules the running of the two provers in time. It runs plain E first, and if E does not find a proof, it runs plain CSE, then if it does not find a proof, some clauses inferred in the CSE run as lemmas are added to the original clause set and the combined clause set handed back to E for further proof search. C S E _ E 1.0 is evaluated through benchmarks, e.g., CASC-26 (2017) and CASC-J9 (2018) competition problems (FOFdivision). Experimental results show that C S E _ E 1.0 indeed enhances the performance of E to a certain extent.

scholarly journals Engineering Software Correctness

2007 ◽  
Vol 17 (6) ◽  
pp. 675-686 ◽  
Author(s):  
REX PAGE
Keyword(s):  
Software Engineering ◽  
Functional Programming ◽  
Central Element ◽  
Theorem Prover ◽  
Good Design ◽  
Engineering Software ◽  
Automated Theorem Prover ◽  
New Perspective ◽  
Mechanical Logic ◽  
Software Correctness

AbstractDesign and quality are fundamental themes in engineering education. Functional programming builds software from small components, a central element of good design, and facilitates reasoning about correctness, an important aspect of quality. Software engineering courses that employ functional programming provide a platform for educating students in the design of quality software. This pearl describes experiments in the use of ACL2, a purely functional subset of Common Lisp with an embedded mechanical logic, to focus on design and correctness in software engineering courses. Students find the courses challenging and interesting. A few acquire enough skill to use an automated theorem prover on the job without additional training. Many students, but not quite a majority, find enough success to suggest that additional experience would make them effective users of mechanized logic in commercial software development. Nearly all gain a new perspective on what it means for software to be correct and acquire a good understanding of functional programming.

scholarly journals Automated Theorem Prover for Pointer Logic

2009 ◽  
Vol 20 (8) ◽  
pp. 2037-2050
Author(s):  
Zhen-Ming WANG ◽  
Yi-Yun CHEN ◽  
Zhi-Fang WANG
Keyword(s):  
Theorem Prover ◽  
Automated Theorem Prover ◽  
Pointer Logic

scholarly journals SAT solving experiments in Vampire

10.29007/5l47 ◽  
2018 ◽  
Author(s):  
Armin Biere ◽  
Ioan Dragan ◽  
Laura Kovács ◽  
Andrei Voronkov
Keyword(s):  
State Of The Art ◽  
Theorem Prover ◽  
Sat Solving ◽  
First Order ◽  
Automated Theorem Prover ◽  
Sat Solver ◽  
Overall Performance

In order to better understand how well a state of the art SAT solver would behave in the framework of a first-order automated theorem prover we have decided to integrate Lingeling, best performing SAT solver, inside Vampire’s AVATAR framework. In this paper we propose two ways of integrating a SAT solver inside of Vampire and evaluate overall performance of this combination. Our experiments show that by using a state of the art SAT solver in Vampire we manage to solve more problems. Surprisingly though, there are cases where combination of the two solvers does not always prove to generate best results.

A Tableau Based Automated Theorem Prover Using High Performance Computing

2012 ◽  
Vol 7 (3) ◽  
Author(s):  
Md Zahidul Islam ◽  
Ahmed Shah Mashiyat ◽  
Kashif Nizam Khan ◽  
S.M. Masud Karim
Keyword(s):  
High Performance Computing ◽  
High Performance ◽  
Theorem Prover ◽  
Automated Theorem Prover ◽  
Performance Computing

scholarly journals Automated Deduction in the B Set Theory using Typed Proof Search and Deduction Modulo

10.29007/14v7 ◽  
2018 ◽  
Author(s):  
Guillaume Bury ◽  
David Delahaye ◽  
Damien Doligez ◽  
Pierre Halmagrand ◽  
Olivier Hermant
Keyword(s):  
Set Theory ◽  
Automated Deduction ◽  
Theorem Prover ◽  
Automated Verification ◽  
Proof Obligation ◽  
Proof Search ◽  
Automated Theorem Prover ◽  
Proof Checker ◽  
Rewrite Rules ◽  
Deduction Modulo

We introduce an encoding of the set theory of the B method using polymorphic types and deduction modulo, which is used for the automated verification of proof obligations in the framework of the BWare project. Deduction modulo is an extension of predicate calculus with rewriting both on terms and propositions. It is well suited for proof search in theories because it turns many axioms into rewrite rules. We also present the associated automated theorem prover Zenon Modulo, an extension of Zenon to polymorphic types and deduction modulo, along with its backend to the Dedukti universal proof checker, which also relies on types and deduction modulo, and which allows us to verify the proofs produced by Zenon Modulo. Finally, we assess our approach over the proof obligation benchmark provided by the BWare project.

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