Patching Proofs for Reuse

1 We investigate the application of machine learning paradigms in automated reasoning in order to improve a theorem prover by reusing previously computed proofs. Our reuse procedure generalizes a previously computed proof of a conjecture yielding a schematic proof which can be instantiated subsequently if a new, similar conjecture is given. We show that for exploiting the full exibility of second-order instantiations the instantiated schematic proof has to be patched such that a proof of the new conjecture is obtained. We develop an algorithm which computes patched proofs showing thereby that proof patching is always possible in a uniform way. This enables a further processing of the obtained proof, justiies the soundness of our proposal for reusing proofs, and provides a key for comparing our method with other reuse paradigms.