4,772 research outputs found
Defining the meaning of TPTP formatted proofs
International audienceThe TPTP library is one of the leading problem libraries in the automated theorem proving community. Over time, support was added for problems beyond those in first-order clausal form. TPTP has also been augmented with support for various proof formats output by theorem provers. Such proofs can also be maintained in the TSTP proof library. In this paper we propose an extension of this framework to support the semantic specification of the inference rules used in proofs
MaLeS: A Framework for Automatic Tuning of Automated Theorem Provers
MaLeS is an automatic tuning framework for automated theorem provers. It
provides solutions for both the strategy finding as well as the strategy
scheduling problem. This paper describes the tool and the methods used in it,
and evaluates its performance on three automated theorem provers: E, LEO-II and
Satallax. An evaluation on a subset of the TPTP library problems shows that on
average a MaLeS-tuned prover solves 8.67% more problems than the prover with
its default settings
A Formally Verified Checker for First-Order Proofs
The Verified TESC Verifier (VTV) is a formally verified checker for the new Theory-Extensible Sequent Calculus (TESC) proof format for first-order ATPs. VTV accepts a TPTP problem and a TESC proof as input, and uses the latter to verify the unsatisfiability of the former. VTV is written in Agda, and the soundness of its proof-checking kernel is verified in respect to a first-order semantics formalized in Agda. VTV shows robust performance in a comprehensive test using all eligible problems from the TPTP problem library, successfully verifying all but the largest 5 of 12296 proofs, with >97% of the proofs verified in less than 1 second
SAT-Inspired Higher-Order Eliminations
We generalize several propositional preprocessing techniques to higher-orderlogic, building on existing first-order generalizations. These techniqueseliminate literals, clauses, or predicate symbols from the problem, with theaim of making it more amenable to automatic proof search. We also introduce anew technique, which we call quasipure literal elimination, that strictlysubsumes pure literal elimination. The new techniques are implemented in theZipperposition theorem prover. Our evaluation shows that they sometimes helpprove problems originating from the TPTP library and Isabelle formalizations.<br
Automated Reasoning and Presentation Support for Formalizing Mathematics in Mizar
This paper presents a combination of several automated reasoning and proof
presentation tools with the Mizar system for formalization of mathematics. The
combination forms an online service called MizAR, similar to the SystemOnTPTP
service for first-order automated reasoning. The main differences to
SystemOnTPTP are the use of the Mizar language that is oriented towards human
mathematicians (rather than the pure first-order logic used in SystemOnTPTP),
and setting the service in the context of the large Mizar Mathematical Library
of previous theorems,definitions, and proofs (rather than the isolated problems
that are solved in SystemOnTPTP). These differences poses new challenges and
new opportunities for automated reasoning and for proof presentation tools.
This paper describes the overall structure of MizAR, and presents the automated
reasoning systems and proof presentation tools that are combined to make MizAR
a useful mathematical service.Comment: To appear in 10th International Conference on. Artificial
Intelligence and Symbolic Computation AISC 201
The Vampire and the FOOL
This paper presents new features recently implemented in the theorem prover
Vampire, namely support for first-order logic with a first class boolean sort
(FOOL) and polymorphic arrays. In addition to having a first class boolean
sort, FOOL also contains if-then-else and let-in expressions. We argue that
presented extensions facilitate reasoning-based program analysis, both by
increasing the expressivity of first-order reasoners and by gains in
efficiency
Initial Experiments with TPTP-style Automated Theorem Provers on ACL2 Problems
This paper reports our initial experiments with using external ATP on some
corpora built with the ACL2 system. This is intended to provide the first
estimate about the usefulness of such external reasoning and AI systems for
solving ACL2 problems.Comment: In Proceedings ACL2 2014, arXiv:1406.123
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