Fig. 5: AlphaGeometry discovers a more general theorem than the translated IMO 2004 P1.
From: Solving olympiad geometry without human demonstrations
Left, top to bottom, the IMO 2004 P1 stated in natural language, its translated statement and AlphaGeometry solution. Thanks to the traceback algorithm necessary to extract the minimal premises, AlphaGeometry identifies a premise unnecessary for the proof to work: O does not have to be the midpoint of BC for P, B, C to be collinear. Right, top, the original theorem diagram; bottom, the generalized theorem diagram, in which O is freed from its midpoint position and P still stays on line BC. Note that the original problem requires P to be between B and C, a condition where the generalized theorem and solution does not guarantee.
