The BCSK Axioms

P(i(x,i(y,x)))                     % A1
P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))) % A2
P(i(i(i(x,y),x),x))                % A3
P(i(x,j(y,x)))                     % A4
P(i(j(x,j(y,z)),j(j(x,y),j(x,z)))) % A5
P(i(j(x,j(y,z)),j(y,j(x,z))))      % A6
P(i(j(j(x,y),x),x))                % A7
P(i(j(i(x,y),y),j(i(y,x),x)))      % A8
P(j(i(x,y),j(x,y)))                % A9