Machine Learning Case Splits for Theorem Proving

1
Machine Learning Case Splits for Theorem Proving

• Ferdinand Hoermann (Imperial)
• Simon Colton (Imperial)
• Geoff Sutcliffe (Miami)
• Alison Pease (Edinburgh)

2
PPP for First Order Provers
3
PPP for First Order Provers
4
Example from Abstract

• GRP119.1 (TPTP from Larry Wos)
• Otter 74 seconds with case split 10 seconds

5
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

6
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

7
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