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Machine Learning Case Splits for Theorem Proving Ferdinand Hoermann (Imperial) Simon Colton (Imperial) Geoff Sutcliffe (Miami) Alison Pease (Edinburgh) PPP for First Order Provers PPP for First Order Provers Example from Abstract GRP119.1 (TPTP from Larry Wos) Otter = 74 seconds; with case split = 10 seconds Procedure #1 Given: A set of theorems from a domain (40 from GRP) A theorem prover (Otter) A descriptive learning system (HR) Aim: Produce an enhanced version of the prover Which is domain specific Which uses cases splitting Sensitive to time for each theorem and case ordering Procedure #2 Stage 1: Learn some specialisations of the domain using HR E.g., Abelian groups, self inverse groups, etc. Stage 2: Hold back 50% of the theorems Calculate average speed up for non-held-back theorems For specialisation as a positive and a negative case split Use these values and others from HR To hill climb a space of weighted sum Testing the ordering on the non-held-back theorems Results Of the 20 held back theorems: 4 considerably slower 12 roughly the same 4 faster GRP615: 7% speed up GRP414: 83% GRP120: 95% GRP122: 95% (from 22s to 1s) Bottom line: 20% chance of a speed up