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

The Higher-Order Prover Leo-II.

Leo-II is an automated theorem prover for classical higher-order logic. The prover has pioneered cooperative higher-order-first-order proof automation, it has influenced the development of the TPTP THF infrastructure for higher-order logic, and it has been applied in a wide array of problems. Leo-II may also be called in proof assistants as an external aid tool to save user effort. For this it is crucial that Leo-II returns proof information in a standardised syntax, so that these proofs can eventually be transformed and verified within proof assistants. Recent progress in this direction is reported for the Isabelle/HOL system.The Leo-II project has been supported by the following grants: EPSRC grant EP/D070511/1 and DFG grants BE/2501 6-1, 8-1 and 9-1.This is the final version of the article. It first appeared from Springer via http://dx.doi.org/10.1007/s10817-015-9348-y

Preserving User Proofs Across Specification Changes

International audienceIn the context of deductive program veri cation, both the speci fication and the code evolve as the veri fication process carries on. For instance, a loop invariant gets strengthened when additional properties are added to the specifi cation. This causes all the related proof obligations to change; thus previous user verifi cations become invalid. Yet it is often the case that most of previous proof attempts (goal trans- formations, calls to interactive or automated provers) are still directly applicable or are easy to adjust. In this paper, we describe a technique to maintain a proof session against modifi cation of verifi cation conditions. This technique is implemented in the Why3 platform. It was successfully used in developing more than a hundred verifi ed programs and in keeping them up to date along the evolution of Why3 and its standard library. It also helps out with changes in the environment, e.g. prover upgrades

Representation, Verification, and Visualization of Tarskian Interpretations for Typed First-order Logic

peer reviewedThis paper describes a new format for representing Tarskian-style interpretations for formulae in typed first-order logic, using the TPTP TF0 language. It further describes a technique and an implemented tool for verifying models using this representation, and a tool for visualizing interpretations. The research contributes to the advancement of automated reasoning technology for model finding, which has several applications, including verification

Leo-III Version 1.1 (System description)

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