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There is a large area of contemporary mathematics which can be profitably
explored using an interactive first-order theorem prover.  This report
will describe #   applications of the the Stanford A.I. Project's theorem prover. 

The first application explores the field of Euclidean Geometry.  
The second example deals with abstract algebra, in particular, Implicative models.
Third, we used some of the programmable features of the prover to give a solution 
to a puzzle.