formulas(assumptions).
all x all y all z (x*(y*z)=(x*y)*z).
-all x (x*I=x).
-all x (x*inv(x)=I).
+all x (x*a=x).
+all x (x*inv(x)=a).
end_of_list.
formulas(goals).
-%I*x=x.
+%a*x=x.
%inv(inv(x))=x.
-%inv(x)*x=I.
+%inv(x)*x=a.
all x all y (x*y=y*x).
end_of_list.