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 Making Automatic Theorem Provers more Versatile

10.29007/n6j7 ◽  
2018 ◽  
Author(s):  
Simon Cruanes
Keyword(s):  
Higher Order ◽  
Order Logic ◽  
Higher Order Logic ◽  
Research Directions ◽  
First Order ◽  
Theorem Provers ◽  
Smt Solvers ◽  
Automatic Theorem Provers ◽  
Automatic Theorem

We argue that automatic theorem provers should become more versatile and should be able to tackle problems expressed in richer input formats. Salient research directions include (i) developing tight combinations of SMT solvers and first-order provers; (ii) adding better handling of theories in first-order provers; (iii) adding support for inductive proving; (iv) adding support for user-defined theories and functions; and (v) bringing to the provers some basic abilities to deal with logics beyond first-order, such as higher-order logic.

scholarly journals Improving ENIGMA-style Clause Selection while Learning From History

2021 ◽  
pp. 543-561
Author(s):  
Martin Suda
Keyword(s):  
Neural Network ◽  
Real Time ◽  
Theorem Prover ◽  
Central Idea ◽  
Theorem Provers ◽  
Recursive Neural Network ◽  
Time Evaluation ◽  
Automatic Theorem ◽  
Learning From History

AbstractWe re-examine the topic of machine-learned clause selection guidance in saturation-based theorem provers. The central idea, recently popularized by the ENIGMA system, is to learn a classifier for recognizing clauses that appeared in previously discovered proofs. In subsequent runs, clauses classified positively are prioritized for selection. We propose several improvements to this approach and experimentally confirm their viability. For the demonstration, we use a recursive neural network to classify clauses based on their derivation history and the presence or absence of automatically supplied theory axioms therein. The automatic theorem prover Vampire guided by the network achieves a 41 % improvement on a relevant subset of SMT-LIB in a real time evaluation.

scholarly journals AN EMPIRICAL EVALUATION OF AUTOMATED THEOREM PROVERS IN SOFTWARE CERTIFICATION

2006 ◽  
Vol 15 (01) ◽  
pp. 81-107 ◽  
Author(s):  
EWEN DENNEY ◽  
BERND FISCHER ◽  
JOHANN SCHUMANN
Keyword(s):  
System Architecture ◽  
High Performance ◽  
Program Verification ◽  
Source Code ◽  
Empirical Evaluation ◽  
Theorem Prover ◽  
Safety Properties ◽  
Proof Checking ◽  
First Order ◽  
The Individual

We describe a system for the automated certification of safety properties of NASA software. The system uses Hoare-style program verification technology to generate proof obligations which are then processed by an automated first-order theorem prover (ATP). We discuss the unique requirements this application places on the ATPs, focusing on automation, proof checking, traceability, and usability, and describe the resulting system architecture, including a certification browser that maintains and displays links between obligations and source code locations. For full automation, the obligations must be aggressively preprocessed and simplified, and we demonstrate how the individual simplification stages, which are implemented by rewriting, influence the ability of the ATPs to solve the proof tasks. Our results are based on 13 comprehensive certification experiments that lead to 366 top-level safety obligations and ultimately to more than 25,000 proof tasks which have been used to determine the suitability of the high-performance provers DCTP, E-Setheo, E, Gandalf, Otter, Setheo, Spass, and Vampire, and our associated infrastructure. The proofs found by Otter have been checked by Ivy.

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 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 Leo-III Version 1.1 (System description)

10.29007/grmx ◽  
2018 ◽  
Author(s):  
Christoph Benzmüller ◽  
Alexander Steen ◽  
Max Wisniewski
Keyword(s):  
Higher Order ◽  
Order Logic ◽  
Theorem Prover ◽  
Higher Order Logic ◽  
System Description ◽  
Agent Based ◽  
First Order ◽  
Theorem Provers ◽  
Automated Theorem Prover ◽  
Ordering Constraints

Leo-III is an automated theorem prover for (polymorphic) higher-order logic which supports all common TPTP dialects, including THF, TFF and FOF as well as their rank-1 polymorphic derivatives. It is based on a paramodulation calculus with ordering constraints and, in tradition of its predecessor LEO-II, heavily relies on cooperation with external first-order theorem provers.Unlike LEO-II, asynchronous cooperation with typed first-order provers and an agent-based internal cooperation scheme is supported. In this paper, we sketch Leo-III's underlying calculus, survey implementation details and give examples of use.

scholarly journals Implementing Polymorphism in Zenon

10.29007/87vl ◽  
2018 ◽  
Author(s):  
Guillaume Bury ◽  
Raphaël Cauderlier ◽  
Pierre Halmagrand
Keyword(s):  
Search Algorithm ◽  
Order Logic ◽  
Theorem Prover ◽  
First Order Logic ◽  
First Order ◽  
Proof Search ◽  
Theorem Provers ◽  
Automated Theorem Prover

Extending first-order logic with ML-style polymorphism allows to definegeneric axioms dealing with several sorts. Until recently, mostautomated theorem provers relied on preprocess encodings intomono/many-sorted logic to reason within such theories. In this paper, wediscuss the implementation of polymorphism into thefirst-order tableau-based automated theorem prover Zenon. Thisimplementation leads to slightly modify some basic parts of the code,from the representation of expressions to the proof-search algorithm.

scholarly journals An Inference Rule for the Acyclicity Property of Term Algebras

10.29007/tlw4 ◽  
2018 ◽  
Author(s):  
Simon Robillard
Keyword(s):  
Computer Science ◽  
Inference Rule ◽  
Theorem Prover ◽  
Science Reasoning ◽  
First Order ◽  
Theorem Provers ◽  
Smt Solvers ◽  
Indexing Technique ◽  
Superposition Calculus

Term algebras are important structures in many areas of mathematics and computer science. Reasoning about their theories in superposition-based first-order theorem provers is made difficult by the acyclicity property of terms, which is not finitely axiomatizable. We present an inference rule that extends the superposition calculus and allows reasoning about term algebras without axioms to describe the acyclicity property. We detail an indexing technique to efficiently apply this rule in problems containing a large number of clauses. Finally we experimentally evaluate an implementation of this extended calculus in the first-order theorem prover Vampire. The results show that this technique is able to find proofs for difficult problems that existing SMT solvers and first-order theorem provers are unable to solve.

Tableaux Versus Resolution a Comparison

1993 ◽  
Vol 18 (2-4) ◽  
pp. 109-127
Author(s):  
W.M.J. Ophelders ◽  
H.C.M. De Swart
Keyword(s):  
Theorem Prover ◽  
Full Description ◽  
Test Results ◽  
Theorem Provers ◽  
Automatic Theorem Provers ◽  
Automated Theorem Prover ◽  
Main Ideas ◽  
Automatic Theorem

In [13] we have presented the ideas underlying an automated theorem prover based on tableaux extended with unification under restrictions. In [6] a full description of an implementation of this theorem prover in PROLOG is given. In this paper we first shortly repeat the main ideas, referring to [13] for more details. Next we present the test results of our theorem prover mainly with respect to Pelletier’s 75 problems for testing automatic theorem provers ([7]). We also give a comparison of our results with the results obtained by the resolution-based theorem provers PCPROVE and OTTER and by the tableau-based theorem provers of M. Fitting and S. Reeves. Short discussions of these theorem provers accompany the test results. For more elaborate discussions the reader is referred to [6].

scholarly journals Local proofs and AVATAR

10.29007/qgdk ◽  
2018 ◽  
Author(s):  
Giles Reger ◽  
Martin Suda
Keyword(s):  
Experimental Results ◽  
Theorem Prover ◽  
First Order ◽  
Theorem Provers

With first-order interpolation as the application in mind, we study the problem of gen- erating local proofs in theorem provers employing the AVATAR architecture. The theory is complemented by experimental results based on our implementation of the techniques in theorem prover Vampire.

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