# Machine Learning Case Splits for Theorem Proving Ferdinand Hoermann (Imperial) Simon Colton (Imperial)

```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
```