AVATAR: The Architecture for First-Order Theorem Provers

Abstract

This paper describes a new architecture for first-order resolution and superposition theorem provers called AVATAR (Advanced Vampire Architecture for Theories and Resolution). Its original motivation comes from a problem wellstudied in the past -dealing with problems having clauses containing propositional variables and other clauses that can be split into components with disjoint sets of variables. Such clauses are common for problems coming from applications, for example in program verification and program analysis, where many ground literals occur in the problems and even more are generated during the proof-search.This problem was previously studied by adding various versions of splitting. The addition of splitting resulted in some improvements in performance of theorem provers. However, even with various versions of splitting, the performance of superposition theorem provers is nowhere near SMT solvers on variable-free problems or SAT solvers on propositional problems.This paper describes a new architecture for superposition theorem provers, where a superposition theorem prover is tightly integrated with a SAT or an SMT solver. Its implementation in our theorem prover Vampire resulted in drastic improvements over all previous implementations of splitting. Over four hundred TPTP problems previously unsolvable by any modern prover, including Vampire itself, have been proved, most of them with short runtimes. Nearly all problems solved with one of 481 variants of splitting previously implemented in Vampire can also be solved with AVATAR.We also believe that AVATAR is an important step towards efficient reasoning with both quantifiers and theories, which is one of the key areas in modern applications of theorem provers in program analysis and verification. Definitions of Avatar (from various dictionaries):(Hindu Mythology) the descent of a deity to the earth in an incarnate form or some manifest shape; the incarnation of a god (Science Fiction) a hybrid creature, composed of human and alien DNA and remotely controlled by the mind of a genetically matched human being (Automated Reasoning) a first-order theorem prover, which embodies a SAT solver controlling the prover's behaviour

The CADE-26 automated theorem proving system competition – CASC-26

“…It benefits from being "built on the shoulders of giants", the well known Vampire [6] and Z3 [5] systems. VampireZ3 leveraged the new AVATAR architecture in Vampire [16], using Z3 to guide splitting decisions so that the first-order solver deals with sets of clauses whose ground part is consistent with the theories of equality and arithmetic. This approach seems to have great potential.…”

“…VampireZ3 1.0 is a combination of Vampire 4.0 [6] and Z3 4.3.1 [5]. A key to the recent success of Vampire 4.0 is its usage of AVATAR [16], which uses a SAT solver to make splitting decisions. VampireZ3 leverages this architecture.…”

The Challenges of Evaluating a New Feature in Vampire

“…These results were partially extended for AVATAR in [9] but some questions remained unanswered. The aim of the project was to extend the experimental analysis of splitting in AVATAR.…”

Revisiting Question Answering in Vampire

“…AVATAR [6,11] is a very useful component of VAMPIRE but it is not immediately compatible with question answering. This is because if we ever split the answer literal it becomes non-obvious when we have found an answer as a unit clause does not mean that the rest of the clause has been discharged.…”