The TPTP World is the well established infrastructure that supports research, development, and deployment of Automated Theorem Proving (ATP) systems. The TPTP World supports a range of classical logics, and since release v9.0.0 has supported non-classical logics. This paper provides a self-contained comprehensive overview of the TPTP World infrastructure for ATP in non-classical logics: the non-classical language extension, problems and solutions, and tool support. A detailed description of use of the infrastructure for quantified normal multi-modal logic is given.

This paper describes an evaluation of Automated Theorem Proving (ATP) systems on problems taken from the QMLTP library of first-order modal logic problems. Principally, the problems are translated to higher-order logic in the TPTP language using an embedding approach, and solved using higher-order logic ATP systems. Additionally, the results from native modal logic ATP systems are considered, and compared with those from the embedding approach. The findings are that the embedding process is reliable and successful, the choice of backend ATP system can significantly impact the performance of the embedding approach, native modal logic ATP systems outperform the embedding approach, and the embedding approach can cope with a wider range modal logics than the native modal systems considered.

LegalRuleML is a comprehensive XML-based representation framework for modeling and exchanging normative rules. The TPTP input and output formats, on the other hand, are general-purpose standards for the interaction with automated reasoning systems. In this paper we provide a bridge between the two communities by (i) defining a logic-pluralistic normative reasoning language based on the TPTP format, (ii) providing a translation scheme between relevant fragments of LegalRuleML and this language, and (iii) proposing a flexible architecture for automated normative reasoning based on this translation. We exemplarily instantiate and demonstrate the approach with three different normative logics.

Automated theorem proving in first-order logic is an active research area which is successfully supported by machine learning. While there have been various proposals for encoding logical formulas into numerical vectors -- from simple strings to much more involved graph-based embeddings --, little is known about how these different encodings compare. In this paper, we study and experimentally compare pattern-based embeddings that are applied in current systems with popular graph-based encodings, most of which have not been considered in the theorem proving context before. Our experiments show that some graph-based encodings help finding much shorter proofs and may yield better performance in terms of number of completed proofs. However, as expected, a detailed analysis shows the trade-offs in terms of runtime.

Leo-III is an automated theorem prover for extensional type theory with Henkin semantics and choice. Reasoning with primitive equality is enabled by adapting paramodulation-based proof search to higher-order logic. The prover may cooperate with multiple external specialist reasoning systems such as first-order provers and SMT solvers. Leo-III is compatible with the TPTP/TSTP framework for input formats, reporting results and proofs, and standardized communication between reasoning systems, enabling e.g. proof reconstruction from within proof assistants such as Isabelle/HOL. Leo-III supports reasoning in polymorphic first-order and higher-order logic, in all normal quantified modal logics, as well as in different deontic logics. Its development had initiated the ongoing extension of the TPTP infrastructure to reasoning within non-classical logics.

The automated theorem prover Leo-III for classical higher-order logic with Henkin semantics and choice is presented. Leo-III is based on extensional higher-order paramodulation and accepts every common TPTP dialect (FOF, TFF, THF), including their recent extensions to rank-1 polymorphism (TF1, TH1). In addition, the prover natively supports almost every normal higher-order modal logic. Leo-III cooperates with first-order reasoning tools using translations to many-sorted first-order logic and produces verifiable proof certificates. The prover is evaluated on heterogeneous benchmark sets.

The CADE ATP System Competition (CASC) is an annual evaluation of fully automatic automated theorem-proving (ATP) systems for classical logic -- the world championship for such systems. CASC provides a public evaluation of the relative capabilities of ATP systems, and aims to stimulate ATP research toward the development of more powerful ATP systems. Over the years CASC has been a catalyst for impressive improvements in ATP. CASC is held at the International Conference on Automated Deduction (CADE) or the International Joint Conference on Automated Reasoning (IJCAR, which replaces CADE on alternate years) each year. These conferences are the major forums for the presentation of new research in all aspects of automated deduction. The evaluation is in terms of the number of problems solved, the number of solutions output, and the average run time for problems solved in the context of a bounded number of eligible problems, chosen from the TPTP Problem Library (Sutcliffe 2009), and a CPU time limit for each solution attempt. One purpose of CASC is to provide a public evaluation of the relative capabilities of ATP systems.

ATP systems are used in a wide variety of domains: A mathematician might use the axioms of group theory to prove the conjecture that groups of order two are commutative; a management consultant might formulate axioms that describe how organizations grow and interact and, from these axioms, prove that organizational death rates decrease with age; or a frustrated teenager might formulate the jumbled faces of a Rubik's cube as a conjecture and prove, from axioms that describe legal changes to the cube's configuration, that the cube can be rearranged to the solution state. All these tasks can be performed by an ATP system, given an appropriate formulation of the problem as axioms, hypotheses, and a conjecture. Most commonly, ATP systems are embedded as components of larger, more complex software systems, and in this context, the ATP systems are required to autonomously solve subproblems that are generated by the overall system. To build a useful ATP system, several issues have to ...

There are however, a variety of different approaches that claim to capture the true nature of this concept. One reason for this diversity lies in the fact that abductive reasoning occurs in a multitude of contexts. It concerns cases that cover the simplest selection of already existing hypotheses to the generation of new concepts in science. It also concerns cases where the observation is puzzling because it is novel versus cases in which the surprise concerns an anomalous observation. For example, if we wake up, and the lawn is wet, we might explain this observation by assuming that it must have rained or that the sprinklers have been on.

One purpose of CASC is to provide a public evaluation of the relative capabilities of ATP systems. The TPTP version used for CASC is released beyond the ATP community. Fulfillment of these after the competition, so that new problems have not objectives provides insight and stimulus for the been seen by the entrants. In some divisions the systems development of more powerful ATP systems, leading are ranked according to the number of problems to increased and more effective use. The most recent CASC, accompanied by a proof or model (thus giving only held at CADE-25 in Berlin, Germany, in 2015, was an assurance of the existence of a proof/model).