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An Infrastructure for Typed Higher-order Form Automated Theorem Proving

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Full-proof theorems

A new European research initiative is creating software that will help prove the validity of theorems in a quick, efficient and accurate way.

Digital Economy

Automated theorem proving, also known as automated deduction, is a key subfield of automated reasoning. It is concerned with proving formally represented theorems in a wide range of domains, through the use of computers. Since 1993 development of effective automated theorem proving systems has been supported by the Thousands of Problems for Theorem Provers (TPTP) problem library and the Thousands of Solutions from Theorem Provers (TSTP) solution library. The EU-funded project 'An Infrastructure for Typed Higher-order Form Automated Theorem Proving' (THFTPTP) was focused on research and development of automated theorem proving in classical higher-order logic. It designed a novel TPTP language to express problems and solutions in higher-order logic. The software involves a collection of higher-order test problems in TPTP and higher-order problem solutions in TSTP, as well as a result and output ontology for higher-order ATP. The project also provided tools for preparing, processing and analysing higher-order ATP problems and solutions. The results of the project were disseminated through several papers at conferences and workshops, as well as through conferences themselves and presentations. Three grant proposals were strongly influenced by the project, ascertaining the viability of its arguments and results. The new THFTPTP infrastructure has been integrated with the TPTP project, which is available at http://www.tptp.org. The THFTPTP project opened up several new research directions and initiatives that will facilitate the development of new principles. It has offered valuable transfer of knowledge and expertise to researchers and students at the project's host university and 11 other institutions across Europe. In short, THFTPTP successfully developed the software products it set out to create and helped develop five fully automated ATP systems for higher-order logic in the THF format.

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