Faster, Higher, Stronger: E 2.3

Abstract

E 2.3 is a theorem prover for many-sorted first-order logic with equality. We describe the basic logical and software architecture of the system, as well as core features of the implementation. We particularly discuss recently added features and extensions, including the extension to many-sorted logic, optional limited support for higher-order logic, and the integration of SAT techniques via PicoSAT. Minor additions include improved support for TPTP standard features, always-on internal proof objects, and lazy orphan removal. The paper also gives an overview of the performance of the system, and describes ongoing and future work.

Neural Precedence Recommender

“…In a refutation-based automated theorem prover (ATP), proving that the axioms entail the conjecture is reduced to proving that the axioms together with the negated conjecture entail a contradiction. The most popular first-order logic (FOL) automated theorem provers (ATPs), such as Vampire [21], E [34], or SPASS [40], start the proof search by converting the input FOL formulas to an equisatisfiable representation in clause normal form (CNF) [25,13]. We denote the problem in clause normal form (CNF) as P = (Σ, Cl ), where Σ is a list of all non-logical (predicate and function) symbols in the problem called the signature, and Cl is the set of clauses of the problem (including the negated conjecture).…”

“…Since the space of derivable clauses is typically very large, the efficacy of the prover depends on the order in which the inferences are applied. The standard saturation-based ATPs order the inferences by maintaining two classes of inferred clauses: processed and unprocessed [34]. In each iteration of the saturation loop, one clause (so-called given clause) is combined with all the processed clauses for inferences.…”

“…Modern saturation-based Automatic Theorem Provers (ATPs) such as E [34], SPASS [40], or Vampire [21] employ the superposition calculus [4,24] as their underlying inference system. Integrating the flavors of resolution [5], paramodulation [30], and the unfailing completion [3], superposition is a powerful calculus with native support for equational reasoning.…”

Subsumption Demodulation in First-Order Theorem Proving

“…When reasoning about properties of first-order logic with equality, one of the most common simplification rules is demodulation [10] for rewriting (and hence simplifying) formulas using unit equalities l r, where l, r are terms and denotes equality. As a special case of superposition, demodulation is implemented in first-order provers such as E [14], Spass [21] and Vampire [10]. Recent applications of superposition-based reasoning, for example to program analysis and verification [5], demand however new and efficient extensions of demodulation to reason about and simplify upon conditional equalities C → l r, where C is a first-order formula.…”

“…By properly adjusting clause indexing and multi-literal matching in first-order theorem provers, we provide an efficient implementation of subsumption demodulation in Vampire (Sect. 5) and evaluate our work against state-of-the-art reasoners, including E [14], Spass [21], CVC4 [3] and Z3 [7] (Sect. 6).…”