This paper describes the integration of the ATP support of the TPTPWorld into the Sigma Knowledge Engineering Environment. The result is an interactive knowledge based reasoning environment, with strong knowledge management features, and access to modern state of the art ATP systems for reasoning over knowledge bases.

Abstract. Many domains of reasoning include a set of distinct objects. For general-purpose automated theorem provers, this property has to be specified explicitly, by including distinctness axioms. Since their number grows quadratically with the number of distinct objects, this results in large and clumsy specifications, that may affect performance adversely. We show that object distinctness can be handled directly by a modified superposition-based inference system, including additional inference rules. The new calculus is shown to be sound and complete. A preliminary implementation shows promising results in the theory of arrays. 1

The standard input format for Satisfiability Modulo Theories (SMT) solvers has now reached its second version and integrates many of the features useful for users to interact with their favourite SMT solver. However, although many SMT solvers do output proofs, no standardised proof format exists. We, here, propose for discussion at the PxTP Workshop a generic proof format in the SMT-LIB philosophy that is flexible enough to be easily recast for any SMT solver. The format is configurable so that the proof can be provided by the solver at the desired level of detail. 1

Abstract. The event calculus is a powerful and highly usable formalism for reasoning about action and change. The discrete event calculus limits time to integers. This paper shows how discrete event calculus problems can be encoded in first-order logic, and solved using a first-order logic automated theorem proving system. The following techniques are discussed: reification is used to convert event and fluent atoms into first-order terms, uniqueness-of-names axioms are generated to ensure uniqueness of event and fluent terms, predicate completion is used to convert second-order circumscriptions into first-order formulae, and a limited first-order axiomatization of integer arithmetic is developed. The performance of first-order automated theorem proving is compared to that of satisfiability solving. 1

This paper describes a method for visualising proof search in automatic resolution-style first-order theorem provers. The method has been implemented in a simple tool called viz, which takes advantage of the widely-supported scalar vector graphics format to produce graphs which can be viewed interactively. This allows the user to zoom in and out, pan, and get more information by clicking on particular parts of the graph. We demonstrate how the graphs can be used to suggest improvements to the strategy and heuristics used in the proof attempt.

The first Workshop on Practical Aspects of Automated Reasoning was held on

Abstract. This paper describes the translation of proofs in the Thousands of Solutions from Theorem Provers (TSTP) solution library to the Proof Markup Language (PML), and the subsequent use of Inference Web (IW) tools to provide new presentations of the proofs. The translation enriches the TSTP proofs with proof provenance meta-data, and provides new possibilities for proof processing. 1

The idea of supporting interactive provers using automatic ones is an old one. An important early effort is the KIV system [1], which has been integrated with 3TAP. Hurd has integrated HOL4 with Gandalf [3], while Bezem et al. have integrated Coq with Bliksem [2]. None of these integrations appear to be used any more, and indeed none of their automatic theorem provers appear to be undergoing development. More successful have been integrations of interactive tools with speciallyconstructed automatic components. Hurd has written his own resolution prover, Metis, and integrated it with HOL4 [4]. Paulson wrote a tableau-style prover, blast, for integration with Isabelle [11]. Much of the prior work suffers from poor usability. Users have to collect relevant lemmas manually and often must transform problems into a suitable form for the automatic prover. Our project has aimed to eliminate the need for problem preparation, such as the removal of higher-order features; it has sought to use background processing, exploiting modern multi-core architectures; it has aimed

Abstract. Isabelle/HOL is a popular interactive theorem prover based on higherorder logic. It owes its success to its ease of use and powerful automation. Much of the automation is performed by external tools: The metaprover Sledgehammer relies on resolution provers and SMT solvers for its proof search, the counterexample generator Quickcheck uses the ML compiler as a fast evaluator for ground formulas, and its rival Nitpick is based on the model finder Kodkod, which performs a reduction to SAT. Together with the Isar structured proof format and a new asynchronous user interface, these tools have radically transformed the Isabelle user experience. This paper provides an overview of the main automatic proof and disproof tools. 1

Case splitting, with and without backtracking, is compared with straightforward ordered resolution. Both forms of splitting have been implemented for Meti-Tarski, an automatic theorem prover for real-valued special functions such as exp, ln, sin, cos and tan −1. The experimental findings confirm the superiority of true backtracking over the simulation of backtracking through the introduction of new