TGTP - Thousands of Geometric problems for geometric Theorem Provers

Automated theorem provers, applications, and libraries of problems are often developed separately. In some cases, joint efforts of many of researchers led to standards such as DIMACS (for propositional logic) [6] and SMT (for satisfiability modulo theory) [1] and libraries of problems such as SAT-lib (for propositional logic) [11], TPTP (for predicate logic) [18], SMT-lib (for satisfiability modulo theory) [1] etc. Such efforts, standards, and libraries are fruitful for easier exchange of problems, ideas, and even program code. However, this is often very demanding and there are not many systems smoothly integrating libraries of problems, theorem provers, and real-world applications. The principal motivation in building TGTP (Thousands of Geometric problems for geometric Theorem Provers) is to support the testing and evaluation of geometric automated theorem proving (GATP) systems, to help ensure that performance results accurately reflect the capabilities of the GATP system being considered. TGTP is a library of problems, in geometry, for GATP systems. TGTP aims to supply the automated reasoning in geometry community with a comprehensive library of GATP test problems, in order to provide an overview and a simple, unambiguous reference mechanism. A common library of problems is necessary for meaningful system evaluations and comparisons, its size is important if the production of statistically significant results is intended. TGTP problems are stored in an xml-based format for constructive descriptions of geometrical figures and geometrical proofs. The conversion of this format to the DGSs/GATPs format is done via xslt files. A specific dtd document defines syntactical restrictions for constructing descriptions. This dtd document can then be used, in conjunction with the generic xml validation mechanism, for verifying whether a given description of a geometrical construction is legal [15]. The goal for building TGTP is, in a similar spirit of TPTP and other libraries, to provide the GATP community with a centralised problem collection with an easy access to all researchers. TGTP tries to address all relevant issues. In particular: