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|
% These are Boolean Algebra identities in terms of the Sheffer stroke.
% Every such identity (or its mirror image), up through length 15,
% is captured by a member of this list.
f(f(x,x),f(x,y)) = x.
f(f(x,x),f(y,x)) = x.
f(f(y,f(y,y)),f(x,x)) = x.
f(f(f(y,y),y),f(x,x)) = x.
f(f(x,f(y,z)),f(x,z)) = x.
f(f(x,f(y,z)),f(z,x)) = x.
f(f(x,f(y,z)),f(x,y)) = x.
f(f(x,f(y,z)),f(y,x)) = x.
f(f(f(y,z),x),f(x,z)) = x.
f(f(f(y,z),x),f(z,x)) = x.
f(f(f(y,z),x),f(x,y)) = x.
f(f(f(y,z),x),f(y,x)) = x.
f(f(x,f(y,f(y,y))),f(x,z)) = x.
f(f(x,f(f(y,y),y)),f(x,z)) = x.
f(f(x,f(y,f(y,y))),f(z,x)) = x.
f(f(x,f(f(y,y),y)),f(z,x)) = x.
f(f(f(y,f(y,y)),x),f(x,z)) = x.
f(f(f(f(y,y),y),x),f(x,z)) = x.
f(f(f(y,f(y,y)),x),f(z,x)) = x.
f(f(f(f(y,y),y),x),f(z,x)) = x.
f(f(x,f(f(x,y),y)),f(x,z)) = x.
f(f(x,f(f(x,y),y)),f(z,x)) = x.
f(f(f(f(x,y),z),z),f(x,x)) = x.
f(f(x,f(y,f(x,y))),f(x,z)) = x.
f(f(x,f(f(y,x),y)),f(x,z)) = x.
f(f(x,f(y,f(x,y))),f(z,x)) = x.
f(f(x,f(f(y,x),y)),f(z,x)) = x.
f(f(x,f(y,f(y,x))),f(x,z)) = x.
f(f(f(f(x,y),y),x),f(x,z)) = x.
f(f(x,f(y,f(y,x))),f(z,x)) = x.
f(f(f(f(x,y),y),x),f(z,x)) = x.
f(f(f(f(y,x),z),z),f(x,x)) = x.
f(f(y,f(f(x,z),y)),f(x,x)) = x.
f(f(f(y,f(x,z)),y),f(x,x)) = x.
f(f(f(y,f(x,y)),x),f(x,z)) = x.
f(f(f(f(y,x),y),x),f(x,z)) = x.
f(f(f(y,f(x,y)),x),f(z,x)) = x.
f(f(f(f(y,x),y),x),f(z,x)) = x.
f(f(y,f(f(z,x),y)),f(x,x)) = x.
f(f(f(y,f(z,x)),y),f(x,x)) = x.
f(f(f(y,f(y,x)),x),f(x,z)) = x.
f(f(f(y,f(y,x)),x),f(z,x)) = x.
f(f(y,f(y,f(x,z))),f(x,x)) = x.
f(f(y,f(y,f(z,x))),f(x,x)) = x.
f(f(x,f(f(x,x),y)),f(x,z)) = x.
f(f(x,f(f(x,x),y)),f(z,x)) = x.
f(f(f(f(x,x),y),x),f(x,z)) = x.
f(f(f(f(x,x),y),x),f(z,x)) = x.
f(f(x,f(y,f(x,x))),f(x,z)) = x.
f(f(x,f(y,f(x,x))),f(z,x)) = x.
f(f(f(y,f(x,x)),x),f(x,z)) = x.
f(f(f(y,f(x,x)),x),f(z,x)) = x.
f(f(x,f(y,f(y,y))),f(z,f(z,z))) = x.
f(f(x,f(f(y,y),y)),f(z,f(z,z))) = x.
f(f(x,f(y,f(y,y))),f(f(z,z),z)) = x.
f(f(x,f(f(y,y),y)),f(f(z,z),z)) = x.
f(f(f(y,f(y,y)),x),f(z,f(z,z))) = x.
f(f(f(f(y,y),y),x),f(z,f(z,z))) = x.
f(f(f(y,f(y,y)),x),f(f(z,z),z)) = x.
f(f(f(f(y,y),y),x),f(f(z,z),z)) = x.
f(f(f(f(x,y),y),y),f(x,f(z,y))) = x.
f(f(f(f(x,y),y),y),f(x,f(y,z))) = x.
f(f(f(f(x,y),y),y),f(f(z,y),x)) = x.
f(f(f(f(x,y),y),y),f(f(y,z),x)) = x.
f(f(y,f(f(x,y),y)),f(x,f(z,y))) = x.
f(f(f(y,f(x,y)),y),f(x,f(z,y))) = x.
f(f(f(f(y,x),y),y),f(x,f(z,y))) = x.
f(f(y,f(f(x,y),y)),f(x,f(y,z))) = x.
f(f(f(y,f(x,y)),y),f(x,f(y,z))) = x.
f(f(f(f(y,x),y),y),f(x,f(y,z))) = x.
f(f(y,f(f(x,y),y)),f(f(z,y),x)) = x.
f(f(f(y,f(x,y)),y),f(f(z,y),x)) = x.
f(f(f(f(y,x),y),y),f(f(z,y),x)) = x.
f(f(y,f(f(x,y),y)),f(f(y,z),x)) = x.
f(f(f(y,f(x,y)),y),f(f(y,z),x)) = x.
f(f(f(f(y,x),y),y),f(f(y,z),x)) = x.
f(f(y,f(y,f(x,y))),f(x,f(z,y))) = x.
f(f(y,f(f(y,x),y)),f(x,f(z,y))) = x.
f(f(f(y,f(y,x)),y),f(x,f(z,y))) = x.
f(f(y,f(y,f(x,y))),f(x,f(y,z))) = x.
f(f(y,f(f(y,x),y)),f(x,f(y,z))) = x.
f(f(f(y,f(y,x)),y),f(x,f(y,z))) = x.
f(f(y,f(y,f(x,y))),f(f(z,y),x)) = x.
f(f(y,f(f(y,x),y)),f(f(z,y),x)) = x.
f(f(f(y,f(y,x)),y),f(f(z,y),x)) = x.
f(f(y,f(y,f(x,y))),f(f(y,z),x)) = x.
f(f(y,f(f(y,x),y)),f(f(y,z),x)) = x.
f(f(f(y,f(y,x)),y),f(f(y,z),x)) = x.
f(f(y,f(y,f(y,x))),f(x,f(z,y))) = x.
f(f(y,f(y,f(y,x))),f(x,f(y,z))) = x.
f(f(y,f(y,f(y,x))),f(f(z,y),x)) = x.
f(f(y,f(y,f(y,x))),f(f(y,z),x)) = x.
f(f(x,f(f(x,y),y)),f(z,f(z,z))) = x.
f(f(x,f(f(x,y),y)),f(f(z,z),z)) = x.
f(f(x,f(y,f(x,y))),f(z,f(z,z))) = x.
f(f(x,f(f(y,x),y)),f(z,f(z,z))) = x.
f(f(x,f(y,f(x,y))),f(f(z,z),z)) = x.
f(f(x,f(f(y,x),y)),f(f(z,z),z)) = x.
f(f(x,f(y,f(y,x))),f(z,f(z,z))) = x.
f(f(f(f(x,y),y),x),f(z,f(z,z))) = x.
f(f(x,f(y,f(y,x))),f(f(z,z),z)) = x.
f(f(f(f(x,y),y),x),f(f(z,z),z)) = x.
f(f(f(f(x,y),z),z),f(x,f(y,z))) = x.
f(f(f(f(x,y),z),z),f(x,f(z,y))) = x.
f(f(f(f(x,y),z),z),f(f(y,z),x)) = x.
f(f(f(f(x,y),z),z),f(f(z,y),x)) = x.
f(f(f(y,f(x,y)),x),f(z,f(z,z))) = x.
f(f(f(f(y,x),y),x),f(z,f(z,z))) = x.
f(f(f(y,f(x,y)),x),f(f(z,z),z)) = x.
f(f(f(f(y,x),y),x),f(f(z,z),z)) = x.
f(f(f(f(y,x),z),z),f(x,f(y,z))) = x.
f(f(f(f(y,x),z),z),f(x,f(z,y))) = x.
f(f(f(f(y,x),z),z),f(f(y,z),x)) = x.
f(f(f(f(y,x),z),z),f(f(z,y),x)) = x.
f(f(f(y,f(y,x)),x),f(z,f(z,z))) = x.
f(f(f(y,f(y,x)),x),f(f(z,z),z)) = x.
f(f(y,f(f(x,z),y)),f(x,f(z,y))) = x.
f(f(f(y,f(x,z)),y),f(x,f(z,y))) = x.
f(f(y,f(f(x,z),y)),f(x,f(y,z))) = x.
f(f(f(y,f(x,z)),y),f(x,f(y,z))) = x.
f(f(y,f(f(x,z),y)),f(f(z,y),x)) = x.
f(f(f(y,f(x,z)),y),f(f(z,y),x)) = x.
f(f(y,f(f(x,z),y)),f(f(y,z),x)) = x.
f(f(f(y,f(x,z)),y),f(f(y,z),x)) = x.
f(f(y,f(f(z,x),y)),f(x,f(z,y))) = x.
f(f(f(y,f(z,x)),y),f(x,f(z,y))) = x.
f(f(y,f(f(z,x),y)),f(x,f(y,z))) = x.
f(f(f(y,f(z,x)),y),f(x,f(y,z))) = x.
f(f(y,f(f(z,x),y)),f(f(z,y),x)) = x.
f(f(f(y,f(z,x)),y),f(f(z,y),x)) = x.
f(f(y,f(f(z,x),y)),f(f(y,z),x)) = x.
f(f(f(y,f(z,x)),y),f(f(y,z),x)) = x.
f(f(y,f(y,f(x,z))),f(x,f(z,y))) = x.
f(f(y,f(y,f(x,z))),f(x,f(y,z))) = x.
f(f(y,f(y,f(x,z))),f(f(z,y),x)) = x.
f(f(y,f(y,f(x,z))),f(f(y,z),x)) = x.
f(f(y,f(y,f(z,x))),f(x,f(z,y))) = x.
f(f(y,f(y,f(z,x))),f(x,f(y,z))) = x.
f(f(y,f(y,f(z,x))),f(f(z,y),x)) = x.
f(f(y,f(y,f(z,x))),f(f(y,z),x)) = x.
f(f(x,f(f(x,x),y)),f(z,f(z,z))) = x.
f(f(x,f(f(x,x),y)),f(f(z,z),z)) = x.
f(f(f(f(x,x),y),x),f(z,f(z,z))) = x.
f(f(f(f(x,x),y),x),f(f(z,z),z)) = x.
f(f(f(f(x,x),y),y),f(x,f(z,y))) = x.
f(f(f(f(x,x),y),y),f(x,f(y,z))) = x.
f(f(f(f(x,x),y),y),f(f(z,y),x)) = x.
f(f(f(f(x,x),y),y),f(f(y,z),x)) = x.
f(f(x,f(y,f(x,x))),f(z,f(z,z))) = x.
f(f(x,f(y,f(x,x))),f(f(z,z),z)) = x.
f(f(f(y,f(x,x)),x),f(z,f(z,z))) = x.
f(f(f(y,f(x,x)),x),f(f(z,z),z)) = x.
f(f(y,f(f(x,x),y)),f(x,f(z,y))) = x.
f(f(f(y,f(x,x)),y),f(x,f(z,y))) = x.
f(f(y,f(f(x,x),y)),f(x,f(y,z))) = x.
f(f(f(y,f(x,x)),y),f(x,f(y,z))) = x.
f(f(y,f(f(x,x),y)),f(f(z,y),x)) = x.
f(f(f(y,f(x,x)),y),f(f(z,y),x)) = x.
f(f(y,f(f(x,x),y)),f(f(y,z),x)) = x.
f(f(f(y,f(x,x)),y),f(f(y,z),x)) = x.
f(f(y,f(y,f(x,x))),f(x,f(z,y))) = x.
f(f(y,f(y,f(x,x))),f(x,f(y,z))) = x.
f(f(y,f(y,f(x,x))),f(f(z,y),x)) = x.
f(f(y,f(y,f(x,x))),f(f(y,z),x)) = x.
f(f(x,f(y,f(z,z))),f(x,f(u,z))) = x.
f(f(x,f(y,f(z,z))),f(x,f(z,u))) = x.
f(f(x,f(y,f(z,z))),f(f(u,z),x)) = x.
f(f(x,f(y,f(z,z))),f(f(z,u),x)) = x.
f(f(x,f(f(y,y),z)),f(x,f(u,y))) = x.
f(f(x,f(f(y,y),z)),f(x,f(y,u))) = x.
f(f(x,f(f(y,y),z)),f(f(u,y),x)) = x.
f(f(x,f(f(y,y),z)),f(f(y,u),x)) = x.
f(f(f(y,f(z,z)),x),f(x,f(u,z))) = x.
f(f(f(y,f(z,z)),x),f(x,f(z,u))) = x.
f(f(f(y,f(z,z)),x),f(f(u,z),x)) = x.
f(f(f(y,f(z,z)),x),f(f(z,u),x)) = x.
f(f(f(f(y,y),z),x),f(x,f(u,y))) = x.
f(f(f(f(y,y),z),x),f(x,f(y,u))) = x.
f(f(f(f(y,y),z),x),f(f(u,y),x)) = x.
f(f(f(f(y,y),z),x),f(f(y,u),x)) = x.
f(f(x,f(y,f(z,u))),f(x,f(u,z))) = x.
f(f(x,f(y,f(z,u))),f(f(u,z),x)) = x.
f(f(x,f(y,f(y,z))),f(x,f(u,z))) = x.
f(f(x,f(y,f(y,z))),f(x,f(z,u))) = x.
f(f(x,f(y,f(y,z))),f(f(u,z),x)) = x.
f(f(x,f(y,f(y,z))),f(f(z,u),x)) = x.
f(f(x,f(f(y,z),u)),f(x,f(z,y))) = x.
f(f(x,f(f(y,z),u)),f(f(z,y),x)) = x.
f(f(x,f(y,f(z,y))),f(x,f(u,z))) = x.
f(f(x,f(f(y,z),y)),f(x,f(u,z))) = x.
f(f(x,f(y,f(z,y))),f(x,f(z,u))) = x.
f(f(x,f(f(y,z),y)),f(x,f(z,u))) = x.
f(f(x,f(y,f(z,y))),f(f(u,z),x)) = x.
f(f(x,f(f(y,z),y)),f(f(u,z),x)) = x.
f(f(x,f(y,f(z,y))),f(f(z,u),x)) = x.
f(f(x,f(f(y,z),y)),f(f(z,u),x)) = x.
f(f(x,f(f(y,z),z)),f(x,f(u,y))) = x.
f(f(x,f(f(y,z),z)),f(x,f(y,u))) = x.
f(f(x,f(f(y,z),z)),f(f(u,y),x)) = x.
f(f(x,f(f(y,z),z)),f(f(y,u),x)) = x.
f(f(f(y,f(z,u)),x),f(x,f(u,z))) = x.
f(f(f(y,f(z,u)),x),f(f(u,z),x)) = x.
f(f(f(y,f(y,z)),x),f(x,f(u,z))) = x.
f(f(f(y,f(y,z)),x),f(x,f(z,u))) = x.
f(f(f(y,f(y,z)),x),f(f(u,z),x)) = x.
f(f(f(y,f(y,z)),x),f(f(z,u),x)) = x.
f(f(f(f(y,z),u),x),f(x,f(z,y))) = x.
f(f(f(f(y,z),u),x),f(f(z,y),x)) = x.
f(f(f(y,f(z,y)),x),f(x,f(u,z))) = x.
f(f(f(f(y,z),y),x),f(x,f(u,z))) = x.
f(f(f(y,f(z,y)),x),f(x,f(z,u))) = x.
f(f(f(f(y,z),y),x),f(x,f(z,u))) = x.
f(f(f(y,f(z,y)),x),f(f(u,z),x)) = x.
f(f(f(f(y,z),y),x),f(f(u,z),x)) = x.
f(f(f(y,f(z,y)),x),f(f(z,u),x)) = x.
f(f(f(f(y,z),y),x),f(f(z,u),x)) = x.
f(f(f(f(y,z),z),x),f(x,f(u,y))) = x.
f(f(f(f(y,z),z),x),f(x,f(y,u))) = x.
f(f(f(f(y,z),z),x),f(f(u,y),x)) = x.
f(f(f(f(y,z),z),x),f(f(y,u),x)) = x.
f(f(x,f(f(x,y),z)),f(x,f(u,y))) = x.
f(f(x,f(f(x,y),z)),f(x,f(y,u))) = x.
f(f(x,f(f(x,y),z)),f(f(u,y),x)) = x.
f(f(x,f(f(x,y),z)),f(f(y,u),x)) = x.
f(f(x,f(y,f(x,z))),f(x,f(u,z))) = x.
f(f(x,f(y,f(x,z))),f(x,f(z,u))) = x.
f(f(x,f(y,f(x,z))),f(f(u,z),x)) = x.
f(f(x,f(y,f(x,z))),f(f(z,u),x)) = x.
f(f(x,f(y,f(z,x))),f(x,f(u,z))) = x.
f(f(x,f(y,f(z,x))),f(x,f(z,u))) = x.
f(f(x,f(y,f(z,x))),f(f(u,z),x)) = x.
f(f(x,f(y,f(z,x))),f(f(z,u),x)) = x.
f(f(x,f(f(y,x),z)),f(x,f(u,y))) = x.
f(f(x,f(f(y,x),z)),f(x,f(y,u))) = x.
f(f(x,f(f(y,x),z)),f(f(u,y),x)) = x.
f(f(x,f(f(y,x),z)),f(f(y,u),x)) = x.
f(f(f(f(x,y),z),x),f(x,f(u,y))) = x.
f(f(f(f(x,y),z),x),f(x,f(y,u))) = x.
f(f(f(f(x,y),z),x),f(f(u,y),x)) = x.
f(f(f(f(x,y),z),x),f(f(y,u),x)) = x.
f(f(f(y,f(x,z)),x),f(x,f(u,z))) = x.
f(f(f(y,f(x,z)),x),f(x,f(z,u))) = x.
f(f(f(y,f(x,z)),x),f(f(u,z),x)) = x.
f(f(f(y,f(x,z)),x),f(f(z,u),x)) = x.
f(f(f(y,f(z,x)),x),f(x,f(u,z))) = x.
f(f(f(y,f(z,x)),x),f(x,f(z,u))) = x.
f(f(f(y,f(z,x)),x),f(f(u,z),x)) = x.
f(f(f(y,f(z,x)),x),f(f(z,u),x)) = x.
f(f(f(f(y,x),z),x),f(x,f(u,y))) = x.
f(f(f(f(y,x),z),x),f(x,f(y,u))) = x.
f(f(f(f(y,x),z),x),f(f(u,y),x)) = x.
f(f(f(f(y,x),z),x),f(f(y,u),x)) = x.
f(f(f(f(y,f(z,z)),z),z),f(x,x)) = x.
f(f(y,f(f(z,f(y,y)),y)),f(x,x)) = x.
f(f(f(y,f(z,f(y,y))),y),f(x,x)) = x.
f(f(y,f(y,f(z,f(y,y)))),f(x,x)) = x.
f(f(f(f(f(y,y),z),y),y),f(x,x)) = x.
f(f(y,f(f(f(y,y),z),y)),f(x,x)) = x.
f(f(f(y,f(f(y,y),z)),y),f(x,x)) = x.
f(f(y,f(y,f(f(y,y),z))),f(x,x)) = x.
f(f(y,f(y,f(z,f(z,z)))),f(x,x)) = x.
f(f(y,f(y,f(f(z,z),z))),f(x,x)) = x.
f(f(f(f(y,f(y,z)),z),z),f(x,x)) = x.
f(f(f(f(y,f(z,y)),z),z),f(x,x)) = x.
f(f(f(f(f(y,z),y),z),z),f(x,x)) = x.
f(f(y,f(f(z,f(z,z)),y)),f(x,x)) = x.
f(f(y,f(f(f(z,z),z),y)),f(x,x)) = x.
f(f(f(y,f(z,f(z,z))),y),f(x,x)) = x.
f(f(f(y,f(f(z,z),z)),y),f(x,x)) = x.
f(f(y,f(f(z,f(z,y)),y)),f(x,x)) = x.
f(f(f(y,f(z,f(z,y))),y),f(x,x)) = x.
f(f(f(f(f(y,z),z),y),y),f(x,x)) = x.
f(f(y,f(f(z,f(y,z)),y)),f(x,x)) = x.
f(f(y,f(f(f(z,y),z),y)),f(x,x)) = x.
f(f(f(y,f(z,f(y,z))),y),f(x,x)) = x.
f(f(f(y,f(f(z,y),z)),y),f(x,x)) = x.
f(f(y,f(y,f(z,f(z,y)))),f(x,x)) = x.
f(f(y,f(f(f(y,z),z),y)),f(x,x)) = x.
f(f(f(y,f(f(y,z),z)),y),f(x,x)) = x.
f(f(y,f(y,f(z,f(y,z)))),f(x,x)) = x.
f(f(y,f(y,f(f(z,y),z))),f(x,x)) = x.
f(f(y,f(y,f(f(y,z),z))),f(x,x)) = x.
f(f(f(f(y,f(y,y)),z),z),f(x,x)) = x.
f(f(f(f(f(y,y),y),z),z),f(x,x)) = x.
f(f(x,f(f(f(y,z),u),u)),f(x,z)) = x.
f(f(x,f(f(f(y,z),u),u)),f(z,x)) = x.
f(f(x,f(y,f(f(z,u),y))),f(x,u)) = x.
f(f(x,f(f(y,f(z,u)),y)),f(x,u)) = x.
f(f(x,f(y,f(f(z,u),y))),f(u,x)) = x.
f(f(x,f(f(y,f(z,u)),y)),f(u,x)) = x.
f(f(x,f(f(f(y,z),u),u)),f(x,y)) = x.
f(f(x,f(f(f(y,z),u),u)),f(y,x)) = x.
f(f(x,f(y,f(y,f(z,u)))),f(x,u)) = x.
f(f(x,f(y,f(y,f(z,u)))),f(u,x)) = x.
f(f(x,f(y,f(y,f(z,u)))),f(x,z)) = x.
f(f(x,f(y,f(y,f(z,u)))),f(z,x)) = x.
f(f(x,f(y,f(f(z,u),y))),f(x,z)) = x.
f(f(x,f(f(y,f(z,u)),y)),f(x,z)) = x.
f(f(x,f(y,f(f(z,u),y))),f(z,x)) = x.
f(f(x,f(f(y,f(z,u)),y)),f(z,x)) = x.
f(f(f(f(f(y,z),u),u),x),f(x,z)) = x.
f(f(f(f(f(y,z),u),u),x),f(z,x)) = x.
f(f(f(y,f(f(z,u),y)),x),f(x,u)) = x.
f(f(f(f(y,f(z,u)),y),x),f(x,u)) = x.
f(f(f(y,f(f(z,u),y)),x),f(u,x)) = x.
f(f(f(f(y,f(z,u)),y),x),f(u,x)) = x.
f(f(f(f(f(y,z),u),u),x),f(x,y)) = x.
f(f(f(f(f(y,z),u),u),x),f(y,x)) = x.
f(f(f(y,f(y,f(z,u))),x),f(x,u)) = x.
f(f(f(y,f(y,f(z,u))),x),f(u,x)) = x.
f(f(f(y,f(y,f(z,u))),x),f(x,z)) = x.
f(f(f(y,f(y,f(z,u))),x),f(z,x)) = x.
f(f(f(y,f(f(z,u),y)),x),f(x,z)) = x.
f(f(f(f(y,f(z,u)),y),x),f(x,z)) = x.
f(f(f(y,f(f(z,u),y)),x),f(z,x)) = x.
f(f(f(f(y,f(z,u)),y),x),f(z,x)) = x.
f(f(x,f(f(x,f(y,z)),u)),f(x,z)) = x.
f(f(x,f(f(x,f(y,z)),u)),f(z,x)) = x.
f(f(x,f(f(x,f(y,z)),u)),f(x,y)) = x.
f(f(x,f(f(x,f(y,z)),u)),f(y,x)) = x.
f(f(x,f(y,f(x,f(z,u)))),f(x,u)) = x.
f(f(x,f(y,f(x,f(z,u)))),f(u,x)) = x.
f(f(x,f(y,f(x,f(z,u)))),f(x,z)) = x.
f(f(x,f(y,f(x,f(z,u)))),f(z,x)) = x.
f(f(x,f(y,f(f(z,u),x))),f(x,u)) = x.
f(f(x,f(y,f(f(z,u),x))),f(u,x)) = x.
f(f(x,f(f(f(y,z),x),u)),f(x,z)) = x.
f(f(x,f(f(f(y,z),x),u)),f(z,x)) = x.
f(f(x,f(y,f(f(z,u),x))),f(x,z)) = x.
f(f(f(f(x,f(y,z)),u),x),f(x,z)) = x.
f(f(x,f(y,f(f(z,u),x))),f(z,x)) = x.
f(f(f(f(x,f(y,z)),u),x),f(z,x)) = x.
f(f(x,f(f(f(y,z),x),u)),f(x,y)) = x.
f(f(x,f(f(f(y,z),x),u)),f(y,x)) = x.
f(f(f(f(x,f(y,z)),u),x),f(x,y)) = x.
f(f(f(f(x,f(y,z)),u),x),f(y,x)) = x.
f(f(f(y,f(x,f(z,u))),x),f(x,u)) = x.
f(f(f(y,f(x,f(z,u))),x),f(u,x)) = x.
f(f(f(y,f(x,f(z,u))),x),f(x,z)) = x.
f(f(f(y,f(x,f(z,u))),x),f(z,x)) = x.
f(f(f(y,f(f(z,u),x)),x),f(x,u)) = x.
f(f(f(y,f(f(z,u),x)),x),f(u,x)) = x.
f(f(f(f(f(y,z),x),u),x),f(x,z)) = x.
f(f(f(f(f(y,z),x),u),x),f(z,x)) = x.
f(f(f(y,f(f(z,u),x)),x),f(x,z)) = x.
f(f(f(y,f(f(z,u),x)),x),f(z,x)) = x.
f(f(f(f(f(y,z),x),u),x),f(x,y)) = x.
f(f(f(f(f(y,z),x),u),x),f(y,x)) = x.
f(f(f(f(x,y),f(x,z)),u),f(x,x)) = x.
f(f(f(f(x,y),f(z,x)),u),f(x,x)) = x.
f(f(f(f(y,x),f(x,z)),u),f(x,x)) = x.
f(f(y,f(f(x,z),f(x,u))),f(x,x)) = x.
f(f(f(f(y,x),f(z,x)),u),f(x,x)) = x.
f(f(y,f(f(x,z),f(u,x))),f(x,x)) = x.
f(f(y,f(f(z,x),f(x,u))),f(x,x)) = x.
f(f(y,f(f(z,x),f(u,x))),f(x,x)) = x.
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