Extending a brainiac prover to lambda-free higher-order logic

Abstract Decades of work have gone into developing efficient proof calculi, data structures, algorithms, and heuristics for first-order automatic theorem proving. Higher-order provers lag behind in terms efficiency. Instead a new higher-order prover from the ground up, we propose to start with state-of-the-art superposition E gradually enrich it features. We explain how extend prover’s $$\lambda $$ λ -free logic, formalism that supports partial application applied variables. Our extension outperforms traditional encoding appears promising as stepping stone toward full logic.