Have there been any (interesting) computer-aided proofs that weren't proof-by-exhaustion?

In my opinion, most of the most famous "computer certifications" are done basically by forcing all cases, like the four color graph theorem. Is there a good example of computer certification that does not use this strategy? What strategies did they adopt?

EDIT: I think there is much evidence through the example / counter. Unless you have other reasons, you may not think that these are "interesting".

To date, most computer-assisted proofs have been implemented with large proofs exhausted by mathematical theorem. The idea is to use a computer program to perform long calculations and to provide proof that the results of these calculations imply a given theorem. In 1976, the four color theorem was the first major theorem verified using a computer program. In the field of artificial intelligence research, we also use mechanical inference techniques (like heuristic searches) to create smaller, more obvious proofs of the new mathematical theorem from bottom to top I will try. This automatic theorem prove proves many new results and finds new evidence for the known theorem. In addition, using the Interactive Certification Assistant, mathematicians can create human-readable evidence, but still can verify their validity officially.

There is controversy between what mathematicians constitute evidence. The four-color theorem is an example of this discussion because its "evidence" depends on detailed computer tests in many cases "can not be verified manually". Many mathematicians believe that certification by computers is effective, but puristists do not. Several computer systems for the proof of automation theorem including THOREM are currently being developed.

For the first time in the 20th century people believed that people could think that evidence was verified by leading mathematicians and its validity was confirmed. However, now the computer is used for both the proof theorem and the calculation time for examination by the human or human team, the first proof of the four color theorem is an example of a computer - assisted proof. Some mathematicians are concerned that the possibility of computer program errors and run-time errors in calculations could question the validity of such computer-assisted certificates. In fact, by incorporating redundancy and self-test into the calculation, and by developing multiple independent methods and procedures, we reduce the possibility of errors invalidating computer-assisted proofs. In the case of verification of evidence by human beings, natural languages ​​are included in particular evidence, and if detailed mathematical insight is required, it is not possible to completely eliminate the mistake.