Implementing Reasoning Modules in Implicit Induction Theorem Provers

We detail the integration in SPIKE, an implicit induction theorem prover, of two reasoning modules operating over naturals combined with interpreted symbols. The first integration schema is à la Boyer-Moore, based on the combination of a congruence closure procedure with a decision procedure for linear arithmetic over rationals/reals. The second follows a 'black-box' approach and is based on external SMT solvers. It is shown that the two extensions significantly increase the power of SPIKE, their performances are compared when proving a non-trivial application.