Deep Network Guided Proof Search
This work addresses the challenge of enhancing efficiency and coverage in automated theorem proving for formal verification and mathematical reasoning, representing an incremental improvement.
The paper tackled the problem of improving automated theorem proving by using deep learning to guide proof search in the E theorem prover, resulting in a 7.36% increase in proved theorems from the Mizar Mathematical Library and raising the proof ratio from 56% to 59%.
Deep learning techniques lie at the heart of several significant AI advances in recent years including object recognition and detection, image captioning, machine translation, speech recognition and synthesis, and playing the game of Go. Automated first-order theorem provers can aid in the formalization and verification of mathematical theorems and play a crucial role in program analysis, theory reasoning, security, interpolation, and system verification. Here we suggest deep learning based guidance in the proof search of the theorem prover E. We train and compare several deep neural network models on the traces of existing ATP proofs of Mizar statements and use them to select processed clauses during proof search. We give experimental evidence that with a hybrid, two-phase approach, deep learning based guidance can significantly reduce the average number of proof search steps while increasing the number of theorems proved. Using a few proof guidance strategies that leverage deep neural networks, we have found first-order proofs of 7.36% of the first-order logic translations of the Mizar Mathematical Library theorems that did not previously have ATP generated proofs. This increases the ratio of statements in the corpus with ATP generated proofs from 56% to 59%.