Perhaps, the most significant (and first?!) example of such *automatically generated combinatorial conjectures* was *Graffiti* created by Siemion Fajtlowicz in 1982/3 or so. Later, he was joined by his student Ermelinda DeLaViña;

see https://en.wikipedia.org/wiki/Graffiti_(program).

Paul Erdos and other mathematicians enjoyed *Graffiti*.