Hilbert's programme and the search for automatic proof procedures

Hllbert's programme concerned the formalization, that Is mechanization of mathematical reasoning. It looked for formal languages (given by 'mechanical' rules as analysed by Turing) to represent mathematical assertions and for formal rules of inference to generate (representations of) mathematical proofs. As understood naively the search for automatic proof procedures, or more precisely, mechanical ones is the following 'practical' variant of Hilbert's programme.