SMTtoTPTP – A Converter for Theorem Proving Formats

Abstract

Abstract. SMTtoTPTP is a converter from proof problems written in the SMT-LIB format into the TPTP TFF format. The SMT-LIB format supports polymorphic sorts and frequently used theories like those of uninterpreted function symbols, arrays, and certain forms of arithmetics. The TPTP TFF format is an extension of the TPTP format widely used by automated theorem provers, adding a sort system and arithmetic theories. SMTtoTPTP is useful for, e.g., making SMT-LIB problems available to TPTP system developers, and for making TPTP systems available to users of SMT solvers. This paper describes how the conversion works, its functionality and limitations.

Beagle – A Hierarchic Superposition Theorem Prover

“…Beagle's internal formula representation follows TFF, so to support the SMT-LIB standard it must perform sort monomorphization and adding axioms for predefined theories like arrays. This is done with the help of the separately developed SMTtoTPTP library [5].…”

Solving quantified linear arithmetic by counterexample-guided instantiation

“…All benchmarks are in the SMT version 2 format. For comparisons with automated theorem provers, they were converted to the TPTP format by the SMTtoTPTP conversion tool [8]. We remark that all benchmarks consist purely of quantified formulas over linear arithmetic with very little, and in a majority of cases, no quantifier-free content.…”

The vampire and the FOOL

“…For example, after this translation (6) becomes g(2) + g (3), where g is a fresh function symbol of the type Z → Z defined by the following formula:…”

“…A recent work [3] presents SMTtoTPTP, a translator from SMT-LIB to TPTP. SMTtoTPTP does not fully support boolean sort, however one can use SMTtoTPTP with the --keepBool option to translate SMT-LIB problems to the extended TFF0 syntax, supported by Vampire.…”

“…One can use the polymorphic theory of arrays to express program properties. Recall the code snippet involving arrays mentioned in Section 2: array[3] := 5; array [2] + array [3]; Formula (6) used an interpreted function to represent the array in this code. We can alternatively use arrays to represent it as follows let array = store(array, 3, 5) in select(array, 2) + select(array, 3) (8)…”