From: Don Smith
April 29: Progress Report/Plan 

I found two formulas ('30b' and 31) which are provable quickly using
focussing alone but which are unprovable using focussing+Dyckhoff's
technique (even with the maximum depth of iterative deepening set to a
high value -- it reaches the maximum depth quickly).  I don't know if
this is because of a bug in my code, or if Dyckhoff's method is
inherently incomplete when combined with focussing.  If I copy
assumptions (exists(_,_)=>B) into SynchronousLeft, Dyckhoff's method
succeeds on one of the examples ('30b').

Even if it turns out that Dyckhoff's method IS incomplete, it is still
faster on most theorems (significantly faster on some). So if a formula
is unprovable with Dykhoff's method, the theorem prover could try with
focussing alone.

I combined prover.pl and proverD.pl into a single, new module
prover.pl. The user can choose between using and not using Dyckhoff by
the predicates d/0 and d/1.

I wrote a procedure in Scheme to convert Gandalf examples to Prolog syntax.


I also wrote a procedure in Prolog to convert Prolog examples to Gandalf
syntax.

I've been comparing Gandalf with my prover(s).  Generally, Gandalf is
much faster (often orders of magnitude faster). There are formulas that
Gandalf solves quickly but my prover couldn't solve in an hour. But
there are some examples on which my prover is faster (e.g., 7.3 seconds
for Gandalf, <1 mls for mine; 47 mls for Gandalf, <1 mls for mine).

Disturbingly, I found formulas (sics1.6 and sics1.6-2) listed among
Gandalf's examples for which Gandalf terminates saying that they are not
theorems, but my prover proved them immediately (in less than 1 mls).
There are also formulas that cause Gandalf to crash, and there are
formulas that cause SWI-Prolog (or gprolog) to crash (and it's not from
stack overflow, apparently -- I think it's from a bug in SWI-Prolog).