Over the last decade several environments and formalisms for the combination and integration of mathematical software systems have been proposed. Many of these systems aim at a traditional automated theorem proving approach, in which a given conjecture is to be proved or refuted by the cooperation of different reasoning engines. However, they offer little support for experimental mathematics in which new conjectures are constructed by an interleaved process of model computation, model inspection, property conjecture and verification. In particular, despite some previous research in that direction, there are currently no systems available that provide, in an easy to use environment, the flexible combination of diverse reasoning system in a plug-and-play fashion via a high level specification of experiments.[2, 3] presents an integration of more than a dozen different reasoning systems -first order theorem provers, SAT solvers, SMT solvers, model generators, computer algebra, and machine learning systems -in a general bootstrapping algorithm to generate novel theorems in the specialised algebraic domain of quasigroups and loops. While the integration leads to provably correct results, the integration itself was achieved in an ad-hoc manner, i.e., systems where combined and recombined in an experimental fashion with a set of purpose built bridges that not only perform syntax translations but also semantic filtering.In recent work we have started a rational reconstruction of the system, in order to expose the general principles behind the combination and communications of the single systems. We use the framework for trustable communication between mathematics systems that was put forth in [1]. It employs the concept of biform theories that enable the combined formalisation of the axiomatic and algorithmic theory behind the generation process. These should ultimately be used in the design of a flexible environment for experimental mathematics that enables a user to specify complex experiments on a high level without the need of detailed knowledge of the underlying logical relations and the particularities of the integrated systems.In a first stage we concentrate on an interesting sub-process of the bootstrapping algorithm, namely the generation of isotopy invariants for loops. A loop is a simple algebraic structure with a single operation -generally non-associative -and isotopy is an equivalence relation, which is a generalisation of isomor-
