Fig. 4. Analysis of the generated synthetic data.
Of the generated synthetic proofs, 9% are with auxiliary constructions. Only roughly 0.05% of the synthetic training proofs are longer than the average AlphaGeometry proof for the test-set problems. The most complex synthetic proof has an impressive length of 247 with two auxiliary constructions. Most synthetic theorem premises tend not to be symmetrical like human-discovered theorems, as they are not biased towards any aesthetic standard.