On a rewriting approach to satisfiability procedures: extension, combination of theories and an experimental appraisal

The rewriting approach to T-satisfiability is based on establishing termination of a rewrite-based inference system for first-order logic on the T-satisfiability problem. Extending previous such results, including the quantifier-free theory of equality and the theory of arrays with or without extensionality, we prove termination for the theories of records with or without extensionality, integer offsets and integer offsets modulo. A general theorem for termination on combinations of theories, that covers any combination of the theories above, is given next. For empirical evaluation, the rewrite-based theorem prover E is compared with the validity checkers CVC and CVC Lite, on both synthetic and real-world benchmarks, including both valid and invalid instances. Parametric synthetic benchmarks test scalability, while real-world benchmarks test ability to handle huge sets of literals. Contrary to the folklore that a general-purpose prover cannot compete with specialized reasoners, the experiments are overall favorable to the theorem prover, showing that the rewriting approach is both elegant and practical.