Abstract

. "prove((E,F),A,B,C,D) :- !, prove(E,[F---A],B,C,D). prove((E;F),A,B,C,D) :- !, prove(E,A,B,C,D), prove(F,A,B,C,D). prove(all(H,I),A,B,C,D) :- !, "+length(C,D), copyterm((H,I,C),(G,F,C)), append(A,[all(H,I)],E), prove(F,E,B,[G---C],D). prove(A,,[C---D],,) :- ((A= -(B); -(A)=B)) -? (unify(B,C); prove(A,[],D,,)). prove(A,[E---F],B,C,D) :- prove(E,F,[A---B],C,D)." implements a first-order theorem prover based on free-variable semantic tableaux. It is complete, sound, and efficient. 1 Introduction The Prolog program listed in the abstract implements a complete and sound theorem prover for first-order logic; it is based on free-variable semantic tableaux (Fitting, 1990). We call this lean deduction: the idea is to achieve maximal efficiency from minimal means. We will see that the above program is indeed very efficient---not although but because it is extremely short and compact. Our approach surely does not lead to a deduction system which is superior to highly sophisticated systems li...

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