Aiming for the Goal with SInE

The Sumo Inference Engine (SInE) is a well-established premise selection algorithm for 

first-order theorem provers, routinely used, especially on large theory problems.

The main idea of SInE is to start from the goal formula and to iteratively

add other formulas to those already added that are related by sharing signature symbols. 

This implicitly defines a certain heuristical distance 

of the individual formulas and symbols from the goal.

In this paper, we show how this distance can be successfully used for other purposes than

just premise selection. In particular, biasing clause selection to postpone introduction

of input clauses further from the goal helps to solve more problems. 

Moreover, a precedence which respects such goal distance of symbols

gives rise to a goal sensitive simplification ordering. 

We implemented both ideas in the automatic theorem prover Vampire

and present their experimental evaluation on the TPTP benchmark.