AVATAR: The Architecture for First-Order Theorem Provers

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 well-studied 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.