% *********************************************************
% AIM:  left Bol => aa1
% *********************************************************

assign(order,kbo).
set(lex_order_vars).

set(para_from_small).

clear(back_demod).
set(restrict_denials).

assign(max_weight,5).

formulas(assumptions).

   % loop axioms
   1 * x = x.
   x * 1 = x.
   x \ (x * y) = y.
   x * (x \ y) = y.
   (x * y) / y = x.
   (x / y) * y = x.

   % cancellation laws
   x * y = u & x * z = u -> y = z.
   y * x = u & z * x = u -> y = z.

      % other form
      x * y = x * z -> y = z.
      y * x = z * x -> y = z.

   % useful in demodulation free runs
   x != y | z * x = z * y.
   x != y | x * z = y * z.

   % associator (right associated * a = left associated)
   (x * (y * z)) \ ((x * y) * z) = a(x,y,z) # label("associator").

   % commutator ( (x * y) * K(y,x) = y * x )
   (x * y) \ (y * x) = K(y,x) # label("commutator").

   % inner mappings
   (y * x) \ (y * (x * u)) = L(u,x,y).
   ((u * x) * y) / (x * y) = R(u,x,y).
   x \ (u * x) = T(u,x).

   % obvious compatibility
   a(x,y,z) = 1 -> L(z,y,x) = z.
   L(x,y,z) = x -> a(z,y,x) = 1.
   T(x,y) = x -> T(y,x) = y.
   T(x,y) = x -> K(x,y) = 1.
   K(x,y) = 1 -> T(x,y) = x.

   % abelian inner mapping group
   T(T(u,x),y) = T(T(u,y),x).
   T(L(u,x,y),z) = L(T(u,z),x,y).
   T(R(u,x,y),z) = R(T(u,z),x,y).
   L(R(u,x,y),z,w) = R(L(u,z,w),x,y).
   L(L(u,x,y),z,w) = L(L(u,z,w),x,y).
   R(R(u,x,y),z,w) = R(R(u,z,w),x,y).

   % ------------
   % Special Case
   % ------------

   (x * (y * x)) * z = x * (y * (x * z)) # label("left Bol").

end_of_list.

formulas(goals).

   a(a(x,y,z),u,w) = 1 # label("aa1").

end_of_list.

%
% Hints extracted from previously found proofs.
%

formulas(hints).

a(a(x,y,z),u,w) = 1.
1 * x = x.
x * 1 = x.
x \ (x * y) = y.
x * (x \ y) = y.
(x * y) / y = x.
(x / y) * y = x.
x * y != z | x * u != z | u = y.
x * y != z | u * y != z | u = x.
x * y != x * z | y = z.
x * y != z * y | x = z.
x != y | z * x = z * y.
(x * (y * z)) \ ((x * y) * z) = a(x,y,z).
a(x,y,z) = (x * (y * z)) \ ((x * y) * z).
(x * y) \ (y * x) = K(y,x).
K(x,y) = (y * x) \ (x * y).
(x * y) \ (x * (y * z)) = L(z,y,x).
L(x,y,z) = (z * y) \ (z * (y * x)).
((x * y) * z) / (y * z) = R(x,y,z).
R(x,y,z) = ((x * y) * z) / (y * z).
x \ (y * x) = T(y,x).
T(x,y) = y \ (x * y).
a(x,y,z) != 1 | L(z,y,x) = z.
L(x,y,z) != x | a(z,y,x) = 1.
T(x,y) != x | T(y,x) = y.
T(x,y) != x | K(x,y) = 1.
K(x,y) != 1 | T(x,y) = x.
T(T(x,y),z) = T(T(x,z),y).
T(L(x,y,z),u) = L(T(x,u),y,z).
L(T(x,y),z,u) = T(L(x,z,u),y).
T(R(x,y,z),u) = R(T(x,u),y,z).
R(T(x,y),z,u) = T(R(x,z,u),y).
L(R(x,y,z),u,w) = R(L(x,u,w),y,z).
R(L(x,y,z),u,w) = L(R(x,u,w),y,z).
L(L(x,y,z),u,w) = L(L(x,u,w),y,z).
R(R(x,y,z),u,w) = R(R(x,u,w),y,z).
(x * (y * x)) * z = x * (y * (x * z)).
a(a(c1,c2,c3),c4,c5) != 1.
1 \ x = x.
x \ x = 1.
x / x = 1.
x / 1 = x.
x / (y \ x) = y.
(x / y) \ x = y.
1 * x != y | x = y.
x != y * z | y \ x = z.
x * y != z | x \ z = y.
x * y != z * (z \ (x * u)) | y = u.
x * (x \ (y * z)) != y * u | u = z.
x * 1 != y | x = y.
x * y != ((z * y) * u) / u | x = z.
((x * y) * z) / z != u * y | u = x.
x != y * z | x / z = y.
x * y != z | z / y = x.
(x * (y * z)) * a(x,y,z) = (x * y) * z.
a(x,y,y \ z) = (x * z) \ ((x * y) * (y \ z)).
(x * y) \ ((x * z) * (z \ y)) = a(x,z,z \ y).
a(x / y,y,z) = ((x / y) * (y * z)) \ (x * z).
((x / y) * (y * z)) \ (x * z) = a(x / y,y,z).
(x * y) * K(y,x) = y * x.
K(x \ y,x) = y \ ((x \ y) * x).
x \ ((y \ x) * y) = K(y \ x,y).
K(x,y / x) = y \ (x * (y / x)).
x \ (y * (x / y)) = K(y,x / y).
K(x / y,y) = (y * (x / y)) \ x.
(x * (y / x)) \ y = K(y / x,x).
L(1,x,y) = (y * x) \ (y * x).
(x * y) \ (x * y) = L(1,y,x).
(x * y) * L(z,y,x) = x * (y * z).
L(x,y \ z,y) = z \ (y * ((y \ z) * x)).
x \ (y * ((y \ x) * z)) = L(z,y \ x,y).
L(x \ y,x,z) = (z * x) \ (z * y).
L(x,y,z / y) = z \ ((z / y) * (y * x)).
x \ ((x / y) * (y * z)) = L(z,y,x / y).
L(x,y / x,z) = (z * (y / x)) \ (z * y).
R(x,x \ y,z) = (y * z) / ((x \ y) * z).
R(x,y,y \ z) = ((x * y) * (y \ z)) / z.
((x * y) * (y \ z)) / z = R(x,y,y \ z).
R(x,y,z) * (y * z) = (x * y) * z.
R(x / y,y,z) = (x * z) / (y * z).
R(x,y / z,z) = ((x * (y / z)) * z) / y.
((x * (y / z)) * z) / y = R(x,y / z,z).
T(1,x) = x \ x.
T(x,x) = x.
x * T(y,x) = y * x.
T(x,x \ y) = (x \ y) \ y.
T(x / y,y) = y \ x.
x * y != z | x = z / y.
x * (y * x) = (x * (y * (x * z))) / z.
(x * (y * (x * z))) / z = x * (y * x).
(x * x) * y = x * (1 * (x * y)).
x * (1 * (x * y)) = (x * x) * y.
(x * y) * z = x * ((y / x) * (x * z)).
x * ((y / x) * (x * z)) = (x * y) * z.
T(x,y) = T(T(x,y),x).
T(T(x,y),x) = T(x,y).
(x * y) / K(x,y) = y * x.
(x * (y * z)) / L(z,y,x) = x * y.
(x * y) / T(x,y) = y.
R(x,y,z) \ ((x * y) * z) = y * z.
T(1,x) = 1.
x * y != (x * (z * x)) * u | y = z * (x * u).
T(x * (y * x),x) = y * (x * x).
x * y != y * z | T(x,y) = z.
x * y != z * x | T(z,x) = y.
a(x,y,T(z,y)) = (x * (z * y)) \ ((x * y) * T(z,y)).
(x * (y * z)) \ ((x * z) * T(y,z)) = a(x,z,T(y,z)).
K(x,T(y,x)) = (T(y,x) * x) \ (y * x).
(T(x,y) * y) \ (x * y) = K(y,T(x,y)).
L(x,T(y,z),z) = (y * z) \ (z * (T(y,z) * x)).
(x * y) \ (y * (T(x,y) * z)) = L(z,T(x,y),y).
T(x,T(y,x)) = T(y,x) \ (y * x).
T(x,y) \ (x * y) = T(y,T(x,y)).
x * T(T(y,x),z) = T(y,z) * x.
x * L(T(y,x),z,u) = L(y,z,u) * x.
x * R(T(y,x),z,u) = R(y,z,u) * x.
T(R(x,y,z),y * z) = (y * z) \ ((x * y) * z).
(x * y) \ ((z * x) * y) = T(R(z,x,y),x * y).
K(T(x,y),x) = 1.
x * T(x,y) = T(x,y) * x.
T(x,y) * x = x * T(x,y).
K(x \ y,y / x) = 1.
x / T(y,y \ x) = y \ x.
x * K(y \ x,y) = (y \ x) * y.
L(x,K(y,z),z * y) = (y * z) \ ((z * y) * (K(y,z) * x)).
(x * y) \ ((y * x) * (K(x,y) * z)) = L(z,K(x,y),y * x).
((x / y) * (y \ x)) * 1 = (y \ x) * (x / y).
x * T(y,y \ z) = x * ((y \ z) \ z).
T((x \ y) \ y,z) = T(T(x,z),x \ y).
T(T(x,y),x \ z) = T((x \ z) \ z,y).
(x * y) / K(y,T(x,y)) = T(x,y) * y.
L(1,x,y) = 1.
K(x \ 1,x) = (x \ 1) * x.
a(x,y \ 1,y) = (x * K(y \ 1,y)) \ ((x * (y \ 1)) * y).
(x * K(y \ 1,y)) \ ((x * (y \ 1)) * y) = a(x,y \ 1,y).
R(x,y \ 1,y) = ((x * (y \ 1)) * y) / K(y \ 1,y).
((x * (y \ 1)) * y) / K(y \ 1,y) = R(x,y \ 1,y).
K(x,1 / x) = x * (1 / x).
x * (x * y) = (x * x) * y.
(x * x) * y = x * (x * y).
(x * (x * y)) / y = x * x.
x * ((x * x) \ (x * y)) = y.
L(x,y,z * z) = (z * (z * y)) \ ((z * z) * (y * x)).
(x * (x * y)) \ ((x * x) * (y * z)) = L(z,y,x * x).
(x * y) / (x \ y) = x * x.
(x * (y * x)) / T(y,x) = x * x.
x \ y = (x * x) \ (x * y).
(x * x) \ (x * y) = x \ y.
x / (x \ 1) = x * x.
x / ((x / y) \ y) = (x / y) * (x / y).
(1 / x) / x = (1 / x) * (1 / x).
(1 / x) * (1 / x) = (1 / x) / x.
(x * x) \ y = x \ (x \ y).
T(x * y,x) = (y / x) * (x * x).
(x / y) * (y * y) = T(y * x,y).
x * T(x \ y,z) = T(y / x,z) * x.
T(x / y,z) * y = y * T(y \ x,z).
T(x * y,x) / (x * x) = y / x.
T(x,x) / (x * x) = 1 / x.
T(x,y) / (y * y) = (y \ x) / y.
x / (x * x) = 1 / x.
(1 / x) \ x = x * x.
1 / (x * x) = (x \ 1) / x.
(x \ 1) / x = 1 / (x * x).
T(x,y) / (x * x) = (x \ T(x,y)) / x.
(x \ T(x,y)) / x = T(x,y) / (x * x).
(1 / (x * x)) * x = x \ 1.
(x * y) * L(z,y,x) != x * u | u = y * z.
(x * y) * L(z,y,x) != x * u | y * z = u.
x * L(y,z \ x,z) = z * ((z \ x) * y).
x * (y * z) != (x * y) * u | L(z,y,x) = u.
(x * y) * z != x * (y * u) | L(u,y,x) = z.
L(L(x,y,z),z * y,u) = (u * (z * y)) \ (u * (z * (y * x))).
(x * (y * z)) \ (x * (y * (z * u))) = L(L(u,z,y),y * z,x).
L(x \ 1,x,y) = (y * x) \ y.
L((x \ y) \ z,x \ y,x) = y \ (x * z).
L(x \ (y \ z),x,y) = (y * x) \ z.
L(x \ y,x,z / y) = ((z / y) * x) \ z.
T(x,x * y) = L(y \ (x * y),y,x).
L(x \ (y * x),x,y) = T(y,y * x).
(x * y) / L(z \ y,z,x) = x * z.
L(x \ T(y,z),x,z) = (z * x) \ (y * z).
x / L(y \ 1,y,x) = x * y.
x / L(y,1 / y,x) = x * (1 / y).
x * (y * z) != (y * y) * z | x = y.
R(x,x,y) = x.
L(R(x,y,z),u,w) * (y * z) = (L(x,u,w) * y) * z.
R(R(x,y,z),u,w) * (y * z) = (R(x,u,w) * y) * z.
R(T(x,y),x,z) = T(x,y).
R(x,y,z) = R(R(x,y,z),x,u).
R(R(x,y,z),x,u) = R(x,y,z).
R(T(x,y),z,u) = R(R(T(x,y),z,u),x,w).
R(R(T(x,y),z,u),x,w) = R(T(x,y),z,u).
T(x,y) * (x * z) = (T(x,y) * x) * z.
(T(x,y) * x) * z = T(x,y) * (x * z).
R(x,y,z) * (x * u) = (R(x,y,z) * x) * u.
(R(x,y,z) * x) * u = R(x,y,z) * (x * u).
R(1 / x,x,y) = y / (x * y).
R((x / y) / z,z,y) = x / (z * y).
R(x / (y / z),y / z,z) = (x * z) / y.
R(x / y,y,z) \ (x * z) = y * z.
T(R(x / y,y,z),y * z) = (y * z) \ (x * z).
(x * y) / L(z,y / z,x) = x * (y / z).
R(x,x \ y,z) \ (y * z) = (x \ y) * z.
R(x,T(y,x),z) \ ((y * x) * z) = T(y,x) * z.
L(x \ (y \ ((y * x) * z)),x,y) = z.
L(T(x,y),y,x) = T(x,x * y).
(x * (y * z)) / (x \ z) = x * (y * x).
x \ ((x * y) * z) = (y / x) * (x * z).
x * y != (x * z) * L(u,z,x) | y = z * u.
(x / y) * (y * L(z,x,y)) = x * z.
x * ((y / x) * z) = (x * y) * (x \ z).
(x * y) * (x \ z) = x * ((y / x) * z).
T(x,x / y) = y * L(x / y,x,y).
x * L(y / x,y,x) = T(y,y / x).
(x / y) \ (x * z) = y * L(z,x,y).
(x / y) \ z = y * L(x \ z,x,y).
x * L(y \ z,y,x) = (y / x) \ z.
x \ ((y / x) \ z) = L(y \ z,y,x).
L(x \ y,x,z) = z \ ((x / z) \ y).
x * ((x * y) \ z) = (y / x) \ (x \ z).
(x / y) \ (y \ z) = y * ((y * x) \ z).
L(x \ ((x / y) * z),x,y) = y \ z.
L((x * y) \ z,x * y,y) = y \ (x \ z).
L(x \ (x / y),x,y) = y \ 1.
L(x \ y,x,z \ x) = (z \ x) \ (z \ y).
L((x * y) \ z,x * y,K(x,y)) = K(x,y) \ ((y * x) \ z).
x \ ((y / x) \ z) = (x * y) \ (x * z).
(x * y) \ (x * z) = x \ ((y / x) \ z).
x \ 1 = (x * y) \ (x * (y / x)).
(x * y) \ (x * (y / x)) = x \ 1.
(x * y) * (x \ 1) = x * (y / x).
(x * (y * x)) \ (x * y) = x \ 1.
(x * y) * (x \ 1) != x * z | z = y / x.
(x * y) * (x \ 1) != x * z | y / x = z.
x * (y \ 1) = y * ((y \ x) / y).
x * ((x \ y) / x) = y * (x \ 1).
R(x,y,x \ 1) = (x * (y / x)) / (y * (x \ 1)).
(x * (y / x)) / (y * (x \ 1)) = R(x,y,x \ 1).
(x * y) * (y \ 1) = y * (T(x,y) / y).
(x * y) / (x \ 1) = x * (y * x).
x \ (y * (x \ 1)) = (x \ y) / x.
x * (y \ 1) != y * z | (y \ x) / y = z.
x / (y \ 1) = y * ((y \ x) * y).
x * ((x \ y) * x) = y / (x \ 1).
(x * y) / (y \ 1) = y * (T(x,y) * y).
x \ (y / (x \ 1)) = (x \ y) * x.
a(x,x \ y,x) = (y / (x \ 1)) \ ((x * (x \ y)) * x).
(x / (y \ 1)) \ ((y * (y \ x)) * y) = a(y,y \ x,y).
L(T(x / y,x),x,y) = y \ x.
x * L(x,y,z) = L(x,y,z) * x.
L(x,y,z) * x = x * L(x,y,z).
x * L(x \ y,z,u) = L(y / x,z,u) * x.
L(x / y,z,u) * y = y * L(y \ x,z,u).
L(x,y,z) * (z * y) = z * (y * T(x,z * y)).
x * (y * T(z,x * y)) = L(z,y,x) * (x * y).
x * T(y,y * x) = L(y,x,y) * x.
x * (y \ x) = L(x / y,x,y) * x.
L(x / y,x,y) * x = x * (y \ x).
(x \ y) * T(x,y) = L(x,x \ y,x) * (x \ y).
L(x,x \ y,x) * (x \ y) = (x \ y) * T(x,y).
(x * (y \ x)) / x = L(x / y,x,y).
L(x / y,x,y) = (x * (y \ x)) / x.
(x * (y \ x)) \ (x * L(x / y,x,y)) = K(x,(x * (y \ x)) / x).
x * R(x,y,z) = R(x,y,z) * x.
R(x,y,z) * x = x * R(x,y,z).
x * R(x \ y,z,u) = R(y / x,z,u) * x.
R(x / y,z,u) * y = y * R(y \ x,z,u).
a(x,R(y,z,u),y) = (x * (y * R(y,z,u))) \ ((x * R(y,z,u)) * y).
(x * (y * R(y,z,u))) \ ((x * R(y,z,u)) * y) = a(x,R(y,z,u),y).
R(x,R(y,z,u),y) * (y * R(y,z,u)) = (x * R(y,z,u)) * y.
1 / ((1 / x) \ x) = (1 / x) / x.
1 / (x * x) = (1 / x) / x.
(1 / x) / x = 1 / (x * x).
(1 / (x * x)) * x = 1 / x.
1 / x = x \ 1.
x * (1 / x) = 1.
(x \ 1) \ 1 = x.
1 / (1 / x) = x.
T(x \ 1,x) = x \ 1.
L(1 / x,x,y) = (y * x) \ y.
x / L(1 / y,y,x) = x * y.
R(x \ 1,x,y) = y / (x * y).
L(x \ (y \ 1),x,y) = 1 / (y * x).
R((1 / x) / y,y,x) = (y * x) \ 1.
x * ((x \ 1) * (x * y)) = (x * 1) * y.
(x * y) * (1 / x) = x * (y / x).
a(x,y,1 / y) = (x * 1) \ ((x * y) * (1 / y)).
(x * 1) \ ((x * y) * (1 / y)) = a(x,y,1 / y).
K(x,1 / x) = 1.
T(x,x \ 1) = x.
x / L(y,y \ 1,x) = x * (y \ 1).
T(T(x,y),x \ 1) = T(x,y).
T(x,1 / x) = x.
K(x \ 1,x) = 1.
(x \ 1) * L(x,y,z) = L(x,y,z) * (x \ 1).
L(x,y,z) * (x \ 1) = (x \ 1) * L(x,y,z).
T(x,y) = T(T(x,y),1 / x).
T(T(x,y),1 / x) = T(x,y).
(1 / x) * L(x,y,z) = L(x,y,z) * (1 / x).
L(x,y,z) * (1 / x) = (1 / x) * L(x,y,z).
x * L(x \ 1,y,z) = L(x \ 1,y,z) * x.
L(x \ 1,y,z) * x = x * L(x \ 1,y,z).
K(T(x,y),x \ 1) = 1.
T(x \ 1,T(x,y)) = x \ 1.
K(T(x,y),1 / x) = 1.
K(x \ y,1 / (y / x)) = 1.
T(1 / x,T(x,y)) = 1 / x.
T(x \ 1,(x \ y) \ y) = x \ 1.
K(x,1 / ((y * x) / y)) = 1.
T(1 / (x \ 1),T(x \ 1,y)) = x.
T(x,1 / ((y * x) / y)) = x.
L(1 / x,x,y / x) = y \ (y / x).
(x * y) * (1 / y) = y * (T(x,y) / y).
T((x \ y) \ y,x \ 1) = (x \ y) \ y.
T(x,T(x \ 1,y)) = x.
T(x,T(1 / x,y)) = x.
T(x,((1 / x) \ y) \ y) = x.
L(x \ (1 / y),x,y) = 1 / (y * x).
R((x \ 1) / y,y,x) = (y * x) \ 1.
(x * T(x \ y,z)) / x = T(y / x,z).
x * T(x \ y,z) != u * x | T(y / x,z) = u.
(x * y) * z != x * (y * u) | z = L(u,y,x).
x = L(x,y,T(y,z)).
L(x,y,T(y,z)) = x.
x * y != (x * z) * (x \ 1) | y = z / x.
x * (T(x,y) \ 1) = x / T(x,y).
(x * T(x,y)) * z = T(x,y) * (x * z).
L(x,y / z,z \ y) = x.
L(x,y,(y \ z) \ z) = x.
T(x,y) * (x \ z) = (x / T(x,y)) \ z.
(x / T(x,y)) \ z = T(x,y) * (x \ z).
x \ (x / T(x,y)) = T(x,y) \ 1.
(x * y) / (x \ z) = x * ((y / z) * x).
x \ (y * z) = ((x \ y) / x) * (x * z).
((x \ y) / x) * (x * z) = x \ (y * z).
T(x,y) * z != (T(x,y) * x) * u | z = x * u.
(x / T(x,y)) * z = x * (T(x,y) \ z).
x * (y \ z) = y * (((y \ x) / y) * z).
x * (((x \ y) / x) * z) = y * (x \ z).
(x / y) \ (y \ (x * y)) = y * K(x,y).
x \ (y * z) = y \ (((y \ x) / y) \ z).
x \ (((x \ y) / x) \ z) = y \ (x * z).
x * ((x \ 1) * (x * y)) = x * y.
(x \ 1) * (x * y) = y.
x / (y * x) = y \ 1.
(x \ 1) \ y = x * y.
(x \ 1) * y = x \ y.
x != (y \ 1) * z | y * x = z.
(x \ 1) * y != z | x * z = y.
R(x \ 1,x * y,z) = (y * z) / ((x * y) * z).
T(x \ 1,x * y) = (x * y) \ y.
(1 / x) * (x * y) = y.
(x \ y) / y = x \ 1.
x / y = (y / x) \ 1.
(x / y) \ 1 = y / x.
(x * y) / ((z * x) * y) = R(z,x,y) \ 1.
1 / x = y / (x * y).
x / (y * x) = 1 / y.
R(x \ 1,x,y) = x \ 1.
x \ y = (1 / x) * y.
(1 / x) * y = x \ y.
(1 / x) \ y = x * y.
a(x \ 1,y,z) = (x \ (y * z)) \ (((x \ 1) * y) * z).
(x \ (y * z)) \ (((x \ 1) * y) * z) = a(x \ 1,y,z).
T(x \ 1,y) = y \ (x \ y).
x \ T(y,x \ 1) = y * (x \ 1).
T(x,1 / y) = y * (x * (1 / y)).
x * (y * (1 / x)) = T(y,1 / x).
x != (1 / y) * z | y * x = z.
(1 / x) * y != z | x * z = y.
R(1 / x,x * y,z) = (y * z) / ((x * y) * z).
T(1 / x,x * y) = (x * y) \ y.
L(x \ (y * z),x,1 / y) = ((1 / y) * x) \ z.
L(x \ 1,x,y) / y = (y * x) \ 1.
(x * y) / (z * y) = R(z / x,x,y) \ 1.
R(x / y,y,z) \ 1 = (y * z) / (x * z).
1 / x = (x \ y) / y.
(x \ y) / y = 1 / x.
(x / y) * (y / x) = 1.
1 / (x / y) = y / x.
x / L(y / z,z / y,x) = x * (z / y).
x * L(y \ 1,y,x) = x / y.
L(x \ 1,x,y) = y \ (y / x).
(x / y) * ((y / x) * z) = z.
(x / y) \ z = (y / x) * z.
T(x,y) / (x * y) = 1 / y.
(x * y) / ((z * x) * y) = 1 / R(z,x,y).
R(1 / x,y,z) = ((x \ y) * z) / (y * z).
((x \ y) * z) / (y * z) = R(1 / x,y,z).
T(1 / x,y) = y \ (x \ y).
x \ T(y,1 / x) = y * (1 / x).
T(x,(x * y) \ y) = x.
T(x,x \ y) / y = 1 / (x \ y).
T(x,y / (y * x)) = x.
T(x / y,x \ y) = x / y.
((x * y) \ y) * x = x * ((x * y) \ y).
T(x / (x * y),y) = x / (x * y).
T(x \ 1,x / T(x,y)) = (x / T(x,y)) \ (T(x,y) \ 1).
(x / T(x,y)) \ (T(x,y) \ 1) = T(x \ 1,x / T(x,y)).
T(x / y,z) = z \ ((y / x) \ z).
x \ ((y / z) \ x) = T(z / y,x).
(x / y) * z != x * u | z = y * L(u,x,y).
(x / y) * (y * z) = x * L(z,y,x).
(x / y) * z != T(y * x,y) | z = y * y.
(x / y) * T(x * y,x) = x * x.
x != (y / z) * u | (z / y) * x = u.
(x / y) * z != u | (y / x) * u = z.
L(x \ y,x,z) = z \ ((z / x) * y).
(x / y) \ ((y / x) \ z) = z.
(x / y) \ T(z,y / x) = z * (y / x).
(x / y) \ (x * L(z,y,x)) = y * z.
x * L(y \ z,y,x) = (x / y) * z.
x \ ((x * y) * z) = (x / y) \ (x * z).
(x / y) \ (x * z) = x \ ((x * y) * z).
(x * y) * (x \ z) = x * ((x / y) \ z).
(x / y) * (x \ z) = x * ((x * y) \ z).
(x * y) \ (x * z) = x \ ((x / y) * z).
T(1 / (x * y),y * x) = (y * x) \ K(y,x).
T((x / y) / x,y) = (x / y) / x.
(x \ y) * (x / y) = (x / y) * (x \ y).
(x / y) * (x \ y) = (x \ y) * (x / y).
(x / y) / L(y \ 1,y,x) = x.
x * ((x * y) \ x) = x / y.
x * L(1 / y,y,x) = x / y.
x * L(y,y \ 1,x) = x / (y \ 1).
((x \ y) \ y) * (x \ 1) = ((x \ y) \ y) / x.
x * L(y / z,z / y,x) = x / (z / y).
x * ((1 / x) / y) = ((1 / x) * y) \ (1 / x).
((1 / x) * y) \ (1 / x) = x * ((1 / x) / y).
x \ (x / y) = (x * y) \ x.
(x * y) \ x = x \ (x / y).
x * (y \ x) = x / (x \ y).
x / (x \ y) = x * (y \ x).
x * ((y * x) \ x) = x / T(y,x).
x / (x \ (x / y)) = x * y.
(x * y) \ (y * x) = (y * x) \ ((y * x) / K(x,y)).
(x * y) \ ((x * y) / K(y,x)) = (y * x) \ (x * y).
(x \ (x / y)) / x = 1 / (x * y).
x / T(y \ 1,x) = x * ((y \ x) \ x).
(x * (y \ x)) \ z = ((x \ y) / x) * z.
L(T(x \ 1,y),x,z) = T(z \ (z / x),y).
T(x \ (x / y),z) = L(T(y \ 1,z),y,x).
T(x,y) * (1 / x) = T(x,y) / x.
x \ T(x,y) = T(x,y) * (x \ 1).
T(x,y) * (x \ 1) = x \ T(x,y).
T(x,1 / y) != y * z | x * (1 / y) = z.
x * (x * (y / x)) = T(x * y,1 / x).
T(x * y,1 / x) = x * (x * (y / x)).
x \ T(x,y) = T(x,y) * (1 / x).
T(x,y) * (1 / x) = x \ T(x,y).
L(x \ y,x,y) = T(y / x,y).
L(x,y,y * x) = T((y * x) / y,y * x).
T((x * y) / x,x * y) = L(y,x,x * y).
T(x * y,x) = y * L(x,x,y).
x * L(y,y,x) = T(y * x,y).
x \ T(y * x,y) = L(y,y,x).
(x \ y) \ T(y,x) = L(x,x,x \ y).
L(x,x,x \ y) = (x \ y) \ T(y,x).
x * ((y / x) / y) = ((y / x) / y) * x.
((x / y) / x) * y = y * ((x / y) / x).
(x \ (1 / y)) / x = 1 / (x * (y * x)).
x \ (x \ T(x,y)) = (x \ T(x,y)) / x.
(x \ T(x,y)) / x = x \ (x \ T(x,y)).
x \ T(x,y) = T(x,y) / x.
T(x,y) / x = x \ T(x,y).
x * (T(x,y) / x) = T(x,y).
T(T(x,y) / x,x) = T(x,y) / x.
T(x / y,y) / (x / y) = (x / y) \ (y \ x).
(T(x,y) / x) / x = T(x,y) / (x * x).
(x \ T(x,y)) \ z = (x / T(x,y)) * z.
T(x,y) != x * z | T(x,y) / x = z.
T(x,T(x,y) / x) = x.
((x / y) \ 1) / (y \ x) = ((y \ x) * (x / y)) \ 1.
x \ ((x / y) * (y * z)) = L(z,y,x).
L(x,y,z) = z \ ((z / y) * (y * x)).
x * y != (x / z) * (z * L(u,x,z)) | y = u.
L(L(x,y,z),z,y) = x.
x * (y * L(z,x,y)) = (x * y) * z.
x \ ((x * y) * z) = y * L(z,x,y).
L(x,y,z) = L(L(L(x,u,w),y,z),w,u).
L(L(L(x,y,z),u,w),z,y) = L(x,u,w).
L((x * y) \ z,x,y) = y \ (x \ z).
L(T(x,x * y),x,y) = T(x,y).
L(x,y,z) = z \ (y \ ((y * z) * x)).
L(1 / (x * y),x,y) = y \ (1 / x).
x = L(x,T(y,z),y).
L(x,T(y,z),y) = x.
x = L(x,y \ z,z / y).
L(x,y \ z,z / y) = x.
(x * T(x,y)) * z = x * (T(x,y) * z).
(T(x,y) / x) \ (T(x,y) * z) = x * z.
((x \ y) \ 1) / (y / x) = ((y / x) * (x \ y)) \ 1.
L(T(x,y),x,x \ y) = T(x,x \ y).
L((x \ y) \ z,x \ y,y) = y \ (x * z).
L(x,y / x,z) = z \ ((z / (y / x)) * y).
x \ (y * L(z,x \ y,y)) = (x \ y) * z.
T(x,y) / L(y,y,y \ x) = y \ x.
(x * y) * z != x * (y * L(u,x,y)) | z = u.
x * (L(y,x,z) * z) = (x * z) * T(y,z).
x \ (y * z) = (x \ y) * L(z,x,x \ y).
(x \ y) * L(z,x,x \ y) = x \ (y * z).
x \ ((x * y) * T(z,y)) = L(z,x,y) * y.
x * T(y,y \ x) = L(y,y,y \ x) * x.
L(x,x,x \ y) * y = y * T(x,x \ y).
x \ ((x \ y) \ y) = ((x \ y) \ y) * (x \ 1).
((x \ y) \ y) * (x \ 1) = x \ ((x \ y) \ y).
(x * T(y,z)) / x = T((x * y) / x,z).
(x * T(x,y)) * (x \ z) = T(x,y) * z.
x / (y \ z) = y * (((y \ x) / z) * y).
x * (((x \ y) / z) * x) = y / (x \ z).
((x \ 1) * y) / ((x \ 1) \ z) = x \ ((y / z) * (x \ 1)).
(x / y) \ T(x,y) = y * K(x,y).
x * (y \ (x * z)) = ((x \ y) / x) \ z.
((x \ y) / x) \ z = x * (y \ (x * z)).
((x * y) / x) \ y = y * (x / (x * y)).
(x * (y \ x)) \ (x * z) = x \ (y * z).
(x * y) \ (y * z) = y \ ((y / T(x,y)) * z).
x \ ((x / T(y,x)) * z) = (y * x) \ (x * z).
(x \ y) * (x / y) = x * ((x * y) \ y).
T(x * (y * x),1 / x) = x * (x * y).
T(x * y,1 / x) != x * z | x * (y / x) = z.
x \ (x \ T(x,y)) = T(x,y) / (x * x).
T(x,y) / (x * x) = x \ (x \ T(x,y)).
(x \ T(x,y)) \ z = x * (T(x,y) \ z).
x * (T(x,y) * z) = T(x,y) * (x * z).
T(x,y) * (x * z) = x * (T(x,y) * z).
(T(x,y) * z) / (x * z) = T(x,y) / x.
T(x,y) * z = x * ((T(x,y) / x) * z).
x * ((T(x,y) / x) * z) = T(x,y) * z.
T(x,y) * z = x * ((x / T(x,y)) \ z).
x * ((x / T(x,y)) \ z) = T(x,y) * z.
T(x,y) * z = x * (T(x,y) * (x \ z)).
x * (T(x,y) * (x \ z)) = T(x,y) * z.
(x / (y \ z)) * (y \ u) = y * (((((y \ x) / z) * y) / y) * u).
x * (((((x \ y) / z) * x) / x) * u) = (y / (x \ z)) * (x \ u).
((x \ (y * x)) / x) \ y = x * K(x,y).
T(x,y) / (x * x) = x \ (T(x,y) / x).
T(x,y) \ (x * (T(x,y) * z)) = x * z.
x * (T(x,y) * z) != T(x,y) * u | x * z = u.
T(x,y) * z != x * (T(x,y) * u) | x * u = z.
(T(x,y) * z) / (x * z) = x \ T(x,y).
x \ (T(x,y) * z) = (T(x,y) / x) * z.
x * ((x \ T(x,y)) * z) = T(x,y) * z.
x \ (T(x,y) * z) = T(x,y) * (x \ z).
x * y != z * (x \ u) | y = ((x \ z) / x) * u.
T(x,y) * (x \ (x \ z)) = ((x \ T(x,y)) / x) * z.
((x \ T(x,y)) / x) * z = T(x,y) * (x \ (x \ z)).
(T(x,y) / y) \ x = y * K(y,x).
T(x,y) \ (x * z) = x * (T(x,y) \ z).
(T(R(x,y,z),u) * (y * z)) / ((x * y) * z) = R(x,y,z) \ T(R(x,y,z),u).
R(x \ T(x,y),x * z,u) = ((T(x,y) * z) * u) / ((x * z) * u).
x * y != T(x,z) * u | y = T(x,z) * (x \ u).
(x \ T(x,y)) * z = T(x,y) * (x \ z).
T(x,y) * z != x * u | (x \ T(x,y)) * z = u.
x \ y = T(x,z) * (x \ (T(x,z) \ y)).
T(x,y) * (x \ (T(x,y) \ z)) = x \ z.
x \ (T(x,y) \ (x * z)) = T(x,y) \ z.
T(x,y) \ x = x * (T(x,y) \ 1).
x * (T(x,y) \ 1) = T(x,y) \ x.
x * (T(x,y) \ y) = T(y,T(x,y)).
(x \ T(x,y)) \ z = T(x,y) \ (x * z).
x \ (T(x,y) \ x) = T(x,y) \ 1.
T(x,y) \ x = x / T(x,y).
x / T(x,y) = T(x,y) \ x.
x / (x / T(x,y)) = T(x,y).
(x / y) / (y \ x) = T(x / y,y) \ (x / y).
T(x / y,y) \ (x / y) = (x / y) / (y \ x).
(x / y) / T(x / y,y) = (y \ x) \ (x / y).
(T(x,y) \ x) \ z = T(x,y) * (x \ z).
(T(x,y) \ x) * z = x * (T(x,y) \ z).
(x / y) * ((y \ x) \ y) = T(y,T(x / y,y)).
T(T(x,y) \ 1,x) = T(x,y) \ 1.
T(x,T(x,y) \ 1) = x.
T(x / y,(y \ x) \ 1) = x / y.
(x \ y) \ (y / x) = (y / x) * ((x \ y) \ 1).
(x / y) * ((y \ x) \ 1) = (y \ x) \ (x / y).
(x \ ((x \ y) \ y)) * z = T(x,x \ y) * (x \ z).
T(x,x \ y) * (x \ z) = (x \ ((x \ y) \ y)) * z.
((x \ 1) \ T(x \ 1,x * y)) * z = ((x * y) \ y) * ((x \ 1) \ z).
(T(x,y) / x) \ z = T(x,y) \ (x * z).
T(x,T(x,y) \ x) = x.
T(x,x / T(x,y)) = x.
T(x * (y * z),a(x,y,z)) = a(x,y,z) \ ((x * y) * z).
a(x,y,z) \ ((x * y) * z) = T(x * (y * z),a(x,y,z)).
x \ (x / (y \ 1)) = L(y,y \ x,y).
L(x,x \ y,x) = y \ (y / (x \ 1)).
x / L(y,y \ x,y) = x * (y \ 1).
L(x,y,z) = L(x,y,z / y).
L(x,y,z / y) = L(x,y,z).
L(x,y,z) = L(x,y,z * y).
L(x,y,z * y) = L(x,y,z).
L(x,y \ z,y) = L(x,y \ z,z).
L(x,y \ z,z) = L(x,y \ z,y).
L(x,y,z \ 1) = L(x,y,z \ y).
L(x,y,1 / z) = L(x,y,z \ y).
L(x,y,z \ y) = L(x,y,1 / z).
L(L(x,y,z / y),z,y) = x.
L(L(x,y,z),z,y / z) = x.
L(x,T(y,z),y / T(y,z)) = x.
L((x * (y / x)) \ z,x,y) = (y / x) \ (x \ z).
L(x,y,(z / u) \ y) = L(x,y,u / z).
L(L(x,y,z),z * y,y) = x.
L(L(x,y,z \ 1),z \ y,y) = x.
L(L(x,y,1 / z),z \ y,y) = x.
L(x,y,z) = L(x,y / z,z).
L(x,y / z,z) = L(x,y,z).
L(T(x,y / x),y,x) = T(x,x * (y / x)).
L(L(x,y * z,K(y,z)),K(y,z),z * y) = x.
L(x,y * z,z) = L(x,y,z).
L(x,y,y \ z) = L(x,z,y \ z).
L(x,y,z \ y) = L(x,z,z \ y).
L(x,y \ 1,z) = L(x,y \ z,z).
L(x,1 / (y \ z),z) = L(x,T(y,y \ z),z).
L(x,T(y,y \ z),z) = L(x,1 / (y \ z),z).
L(x,T(y,z),T(y,z) \ y) = x.
x = L(L(x,y,z \ 1),z \ y,z).
L(L(x,y,z \ 1),z \ y,z) = x.
L(x,y,T(y,z) \ y) = x.
L(x,y,z \ 1) = L(x,z,z \ y).
L(x,y,y \ z) = L(x,z,1 / y).
L(x,y,y / T(y,z)) = x.
L(x,y,T(y,z) \ 1) = x.
L(x,T(y,z) \ 1,y) = x.
L(x,(y \ z) \ 1,z / y) = x.
((x \ y) \ 1) \ (((x \ y) \ 1) / (y / x)) = (y / x) \ 1.
((x \ y) \ 1) \ ((((x \ y) \ 1) / (y / x)) * z) = (y / x) \ z.
L(x,y \ 1,z) = L(x,y \ z,y).
L((x \ 1) \ y,x \ z,x) = z \ ((z / (x \ 1)) * y).
L(x,y * z,y \ 1) = L(x,y,z).
L(x,y \ 1,y * z) = L(x,z,y).
L(x,y \ 1,z * y) = L(x,T(z,y),y).
(x * (y \ 1)) * L(z,y \ x,y) = x * ((y \ 1) * z).
R(x,x \ y,y \ z) = z / ((x \ y) * (y \ z)).
R(x,y,y \ 1) = (x * y) * (y \ 1).
(x * y) * (y \ 1) = R(x,y,y \ 1).
R(x,y,y \ 1) / (y \ 1) = x * y.
(x * y) \ R(x,y,y \ 1) = y \ 1.
x * (y \ 1) = R(x / y,y,y \ 1).
R(x / y,y,y \ 1) = x * (y \ 1).
(x * L(x,y,z)) * (x \ 1) = R(L(x,y,z),x,x \ 1).
R(x,y,y \ 1) = y * (T(x,y) / y).
x * (T(y,x) / x) = R(y,x,x \ 1).
x \ R(y,x,x \ 1) = T(y,x) / x.
x * (T(R(x,y,z),x) / x) = R(x,y,z).
x * (T(y,x) / x) = R(y,x,1 / x).
x \ R(y,x,1 / x) = T(y,x) / x.
(x * y) * (1 / y) = R(x,y,1 / y).
(x * y) \ R(x,y,1 / y) = 1 / y.
x * (1 / y) = R(x / y,y,1 / y).
R(x / y,y,1 / y) = x * (1 / y).
(R(x,y,z) * x) \ R(x,y,z) = 1 / x.
R(T(x / y,z),y,1 / y) = T(x * (1 / y),z).
R(T((x * y) / x,z),x,1 / x) = (x * T(y,z)) * (1 / x).
x * (R(T(x,x),y,z) / x) = R(x,y,z).
1 / x = R(x,y,z) \ (R(x,y,z) / x).
R(x,y,z) \ (R(x,y,z) / x) = 1 / x.
x * (R(x,y,z) / x) = R(x,y,z).
x \ R(x,y,z) = R(x,y,z) / x.
R(x,y,z) / x = x \ R(x,y,z).
(x \ R(x,y,z)) * x = R(x,y,z).
T(x \ R(x,y,z),x) = x \ R(x,y,z).
(x \ R(x,y,z)) \ u = (x / R(x,y,z)) * u.
L(L(x,R(y,z,u),y),y,y \ R(y,z,u)) = x.
R(x,y,z) \ (R(x,y,z) / x) = x \ 1.
K(x \ R(x,y,z),x) = 1.
R(x,y,z) \ (x \ R(x,y,z)) = x \ 1.
R(x,y,z) * (x \ 1) = x \ R(x,y,z).
R(x,1 / y,y) = (x * (1 / y)) * y.
(x * (1 / y)) * y = R(x,1 / y,y).
R(x,1 / y,y) / y = x * (1 / y).
x * y = R(x / (1 / y),1 / y,y).
R(x / (1 / y),1 / y,y) = x * y.
T(x * (1 / y),y) = y \ R(x,1 / y,y).
x \ R(y,1 / x,x) = T(y * (1 / x),x).
R(T(x / (1 / y),z),1 / y,y) / y = (1 / y) * T((1 / y) \ x,z).
R(T(x / (1 / y),z),1 / y,y) = T(x * y,z).
T(x,y) * z != x * ((x \ T(x,y)) * u) | z = u.
L(x,y \ T(y,z),y) = x.
L(x,T(y,z),y \ 1) = x.
L(x,T(1 / y,z),y) = x.
L(x,y \ (z \ y),z) = x.
L(x,(y * z) \ z,y) = x.
L(x,y \ z,y / z) = x.
(x * ((x * y) \ y)) * z = x * (((x * y) \ y) * z).
((x * y) \ y) \ (x \ z) = (x * ((x * y) \ y)) \ z.
(x * ((x * y) \ y)) \ z = ((x * y) \ y) \ (x \ z).
x / (1 / ((x * y) \ y)) = x * ((x * y) \ y).
((x * y) \ y) * (x * z) = (((x * y) \ y) * x) * z.
(((x * y) \ y) * x) * z = ((x * y) \ y) * (x * z).
L(x,y,z / (z * y)) = x.
L(x,y,(z / y) / z) = x.
(x / y) * ((x \ y) \ z) = ((x / y) / (x \ y)) * z.
((x / y) / (x \ y)) * z = (x / y) * ((x \ y) \ z).
(x \ y) * ((x / y) * z) = ((x \ y) * (x / y)) * z.
((x \ y) * (x / y)) * z = (x \ y) * ((x / y) * z).
((x \ y) * (x / y)) \ z = (x / y) \ ((x \ y) \ z).
L(x,y / (y * z),z) = x.
x * (((y / x) / y) * z) = (x * ((y / x) / y)) * z.
(x * ((y / x) / y)) * z = x * (((y / x) / y) * z).
L(x \ (y * z),u,w) = L(L((y \ x) \ z,u,w),y \ x,y).
L(L((x \ y) \ z,u,w),x \ y,x) = L(y \ (x * z),u,w).
x \ (y \ (x \ z)) = (x * (y * x)) \ z.
(x * (y * x)) \ z = x \ (y \ (x \ z)).
a(x,y,x) = x \ (y \ (x \ ((x * y) * x))).
x \ (y \ (x \ ((x * y) * x))) = a(x,y,x).
K(x * y,y) = y \ (x \ (y \ ((x * y) * y))).
x \ (y \ (x \ ((y * x) * x))) = K(y * x,x).
T(x \ 1,x * (y * x)) = x \ (y \ (x \ (y * x))).
L(x \ y,x,z \ 1) = (z \ x) \ (z \ y).
R(x / y,y,z) = R(y / x,x,z) \ 1.
x / ((y * x) / y) = x * (y / (y * x)).
((x * y) / x) \ y = y / ((x * y) / x).
x / ((y * x) / y) = ((y * x) / y) \ x.
(x / (x * y)) \ (y / ((x * y) / x)) = y.
x \ (y * z) = (x \ y) * L(z,y,x \ 1).
(x \ y) * L(z,y,x \ 1) = x \ (y * z).
x \ (y * T(y \ (y / (x \ y)),z)) = (x \ y) * T((x \ y) \ 1,z).
x * T(y,y \ x) != z * x | L(y,y,y \ x) = z.
x \ L(x,x,y) = a(x,y,x).
x * a(x,y,x) = L(x,x,y).
x \ L(x,x,y) = a(x,y / x,x).
a(x,y / x,x) = x \ L(x,x,y).
a(x,y / x,x) = a(x,y,x).
L(x,y,z \ 1) = (z \ y) \ (z \ (y * x)).
(x \ y) \ (x \ (y * z)) = L(z,y,x \ 1).
(x / y) * (y \ x) = (y \ x) * (x / y).
(x * y) * L(L(z,y,x),u,w) != x * v5 | y * L(z,u,w) = v5.
x / R(x,y,z) = x * (R(x,y,z) \ 1).
x * (R(x,y,z) \ 1) = x / R(x,y,z).
L(x,y,R(y,z,u)) = x.
L(x,R(y,z,u),y) = x.
(x * R(x,y,z)) * u = R(x,y,z) * (x * u).
L(x,y / z,(y * u) / (z * u)) = x.
x * (R(x,y,z) * u) = (x * R(x,y,z)) * u.
(x * R(x,y,z)) * u = x * (R(x,y,z) * u).
L(x,R(y,z,u),y / R(y,z,u)) = x.
((x * y) / (z * y)) * z = z * R(z \ x,z,y).
L(x,y,z) * (x \ 1) = x \ L(x,y,z).
L(x,y,z) * (1 / x) = x \ L(x,y,z).
T(1 / x,L(x,y,z)) = 1 / x.
K(1 / x,L(x,y,z)) = 1.
K(x \ 1,L(x,y,z)) = 1.
K(L(x,y,z) \ 1,x) = 1.
(x * (L(x,y,z) \ 1)) * 1 = (L(x,y,z) \ 1) * x.
(x \ y) \ (1 / x) = x * ((1 / x) / y).
(x \ y) / (y / x) = (y / x) \ (x \ y).
x \ ((x \ y) \ y) = ((x \ y) \ y) / x.
((x \ y) \ y) / x = x \ ((x \ y) \ y).
(x \ y) \ (y / x) = (y / x) / (x \ y).
(x / y) / (y \ x) = (y \ x) \ (x / y).
(x / y) * ((y \ x) \ y) = T(y,y \ x).
L(x,y,y \ R(y,z,u)) = x.
L(x,y \ R(y,z,u),y) = x.
R(x,y,z) * u = x * ((x \ R(x,y,z)) * u).
x * ((x \ R(x,y,z)) * u) = R(x,y,z) * u.
(x \ R(x,y,z)) \ u = R(x,y,z) \ (x * u).
(x / y) \ (y \ x) = y / (1 / ((y * x) \ x)).
x / (1 / ((x * y) \ y)) = (y / x) \ (x \ y).
x \ (y \ T(y * x,x)) = K(y * x,x).
x * (R(x,y,z) * u) = R(x,y,z) * (x * u).
R(x,y,z) * (x * u) = x * (R(x,y,z) * u).
(x \ y) / (y / x) = x / (1 / ((x * y) \ y)).
x / (1 / ((x * y) \ y)) = (x \ y) / (y / x).
R(x,y,z) * u = x * (R(x,y,z) * (x \ u)).
x * (R(x,y,z) * (x \ u)) = R(x,y,z) * u.
1 / ((x \ y) / (y / x)) = (1 / ((x * y) \ y)) / x.
(1 / ((x * y) \ y)) / x = 1 / ((x \ y) / (y / x)).
x * y != R(x,z,u) * w | y = (x \ R(x,z,u)) * w.
R(x,y,z) * (x \ u) = (x \ R(x,y,z)) * u.
(x \ R(x,y,z)) * u = R(x,y,z) * (x \ u).
R(x,y,z) * u != x * w | R(x,y,z) * (x \ u) = w.
(R(x,y,z) * (x \ u)) / u = x \ R(x,y,z).
R(x \ R(x,y,z),u,w) = ((R(x,y,z) * (x \ u)) * w) / (u * w).
((R(x,y,z) * (x \ u)) * w) / (u * w) = R(x \ R(x,y,z),u,w).
(R(x,y,z) * u) / (x * u) = x \ R(x,y,z).
(R(R(x,x \ y,z),u,w) * ((x \ y) * z)) / (y * z) = R(x,x \ y,z) \ R(R(x,x \ y,z),u,w).
R(x,x \ y,z) \ R(R(x,x \ y,z),u,w) = (R(R(x,x \ y,z),u,w) * ((x \ y) * z)) / (y * z).
x / (y * (R(y,z,u) \ x)) = y \ R(y,z,u).
T(x \ R(x,y,z),x * u) = (x * u) \ (R(x,y,z) * u).
(x \ R(x,y,z)) \ u = x * (R(x,y,z) \ u).
(x * y) / ((x / z) * (z * y)) = (x / z) \ R(x / z,z,y).
(x / y) \ R(x / y,y,z) = (x * z) / ((x / y) * (y * z)).
1 / ((x / y) * ((y * z) / (x * z))) = (x / y) \ R(x / y,y,z).
(x / y) \ R(x / y,y,z) = 1 / ((x / y) * ((y * z) / (x * z))).
1 / ((x / y) * R(y / x,x,z)) = (x / y) \ R(x / y,y,z).
(x / y) \ R(x / y,y,z) = 1 / ((x / y) * R(y / x,x,z)).
x * (R(x,y,z) \ u) = R(x,y,z) \ (x * u).
R(x,y,z) \ (x * u) = x * (R(x,y,z) \ u).
R(x,y,z) \ x = x * (R(x,y,z) \ 1).
x * (R(x,y,z) \ 1) = R(x,y,z) \ x.
(x * y) / (x * (R(x,z,u) \ y)) = R(x,z,u).
R(x,y,z) \ x = x / R(x,y,z).
x / R(x,y,z) = R(x,y,z) \ x.
(R(x,y,z) \ x) * R(x,y,z) = x.
(R(x,y,z) \ x) \ x = R(x,y,z).
1 / (R(x,y,z) \ x) = R(x,y,z) / x.
(R(x,y,z) \ x) \ u = (R(x,y,z) / x) * u.
L(x,R(y,z,u),R(y,z,u) \ y) = x.
(x \ R(x,y,z)) \ u = (R(x,y,z) \ x) * u.
L(x,y,R(y,z,u) \ 1) = x.
x = L(x,y,1 / R(y,z,u)).
L(x,y,1 / R(y,z,u)) = x.
(R(x,y,z) \ x) * u = R(x,y,z) \ (x * u).
R(x,y,z) \ (x * u) = (R(x,y,z) \ x) * u.
((R(x,y,z) \ 1) * u) / (x \ u) = (R(x,y,z) \ 1) * x.
(R(x,y,z) \ x) \ u = (x \ R(x,y,z)) * u.
(R(x,y,z) \ x) * u = x * (R(x,y,z) \ u).
(x * y) / ((R(x,z,u) \ x) * y) = R(x,z,u).
(R(x,y,z) \ x) \ u = R(x,y,z) * (x \ u).
x \ ((x * y) * (y \ 1)) = a(x,y,y \ 1).
x \ R(x,y,y \ 1) = a(x,y,y \ 1).
x * a(x,y,y \ 1) = R(x,y,y \ 1).
(x * L(y,z,x)) \ (x * y) = a(x / z,z,y).
a(x / y,y,z) = (x * L(z,y,x)) \ (x * z).
(x \ (y * z)) \ ((x \ y) * z) = a((x \ y) / x,x,z).
a((x \ y) / x,x,z) = (x \ (y * z)) \ ((x \ y) * z).
a(x / y,y,z) = x \ ((x / L(z,y,x)) * z).
R(T(x,y * z),y,z) = (y * z) \ ((x * y) * z).
(x * y) \ ((z * x) * y) = R(T(z,x * y),x,y).
x \ ((x * y) * (1 / y)) = a(x,y,1 / y).
a(x,y,1 / y) = y * L(1 / y,x,y).
x * L(1 / x,y,x) = a(y,x,1 / x).
x \ R(x,y,1 / y) = a(x,y,1 / y).
x * L(1 / x,y,x) = a(y / x,x,1 / x).
a(x / y,y,1 / y) = y * L(1 / y,x,y).
R(x,y,1 / y) / x = a(x,y,1 / y).
a(x,y,1 / y) * x = R(x,y,1 / y).
a(x / y,y,1 / y) = a(x,y,1 / y).
a(x,y,1 / y) = a(x * y,y,1 / y).
a(x * y,y,1 / y) = a(x,y,1 / y).
R(x \ 1,x * y,z) = R(x,y,z) \ 1.
R(x \ 1,y,z) = R(x,x \ y,z) \ 1.
R(x,x \ y,z) \ 1 = R(x \ 1,y,z).
x * R(x \ 1,y,z) = R(x,x \ y,z) \ x.
R(x,x \ y,z) \ x = x * R(x \ 1,y,z).
R(1 / x,x * y,z) = 1 / R(x,y,z).
R(1 / x,y,z) = 1 / R(x,x \ y,z).
1 / R(x,x \ y,z) = R(1 / x,y,z).
1 / R(1 / x,y,z) = R(x,x \ y,z).
R(x,x \ y,z) = 1 / R(1 / x,y,z).
L(x \ (y * z),x,1 / y) = (y \ x) \ z.
(R(x,y,z) \ x) \ u = x \ (R(x,y,z) * u).
(x / R(x,y,z)) \ u = x \ (R(x,y,z) * u).
L((x * (y / x)) \ z,x,y) = x * ((x * y) \ z).
K(x,y) = (x * y) \ ((x * y) / K(y,x)).
(x * y) \ ((x * y) / K(y,x)) = K(x,y).
(x / y) / (x \ y) = ((x \ y) * (y / x)) \ 1.
((x \ y) * (y / x)) \ 1 = (x / y) / (x \ y).
(x * (T(x,y) \ x)) \ z = T(x,y) * (x \ (x \ z)).
(x \ (x \ T(x,y))) * z = T(x,y) * (x \ (x \ z)).
(x * ((x * y) \ y)) * z = ((x * y) \ y) * (x * z).
(x * ((x * y) \ y)) * z = (x \ y) * ((x / y) * z).
((x \ y) * (x / y)) \ z = (y / x) * ((x \ y) \ z).
T(x \ 1,x * (y * x)) = x \ (y \ T(y,x)).
x * (L(x,y,z) \ 1) = (L(x,y,z) \ 1) * x.
(L(x,y,z) \ 1) * x = x * (L(x,y,z) \ 1).
x * (L(x,y,z) \ 1) = L(x,y,z) \ x.
x * (1 / L(x,y,z)) = L(x,y,z) \ x.
(1 / ((x * y) \ y)) / x = (y / x) / (x \ y).
((x * y) \ y) * (x * z) = x * (((x * y) \ y) * z).
(x \ y) * ((x / y) * z) = x * (((x * y) \ y) * z).
(x * ((x * y) \ y)) \ z = (y / x) * ((x \ y) \ z).
(x / y) * ((y \ x) \ z) = ((y * x) \ x) \ (y \ z).
((x * y) \ y) \ (x \ z) = (y / x) * ((x \ y) \ z).
((x * y) \ y) \ 1 = (y / x) * ((x \ y) \ x).
(x / y) * ((y \ x) \ y) = ((y * x) \ x) \ 1.
((x * y) \ y) \ 1 = T(x,x \ y).
T(x,x \ y) = ((x * y) \ y) \ 1.
T(x / y,(x / y) \ y) = (x \ y) \ 1.
1 / T(x,x \ y) = (x * y) \ y.
(x * y) \ y = 1 / T(x,x \ y).
((x * y) \ y) \ 1 = (x \ y) \ y.
T(x,x \ y) \ 1 = (x * y) \ y.
(x * (x * y)) \ (x * y) = 1 / T(x,y).
1 / ((x * y) \ y) = (x \ y) \ y.
((x \ y) \ y) \ 1 = (x * y) \ y.
((x \ y) \ y) * z = ((x * y) \ y) \ z.
((x * y) \ y) \ z = ((x \ y) \ y) * z.
T(x,y) \ 1 = (x * (x * y)) \ (x * y).
(x * (x * y)) \ (x * y) = T(x,y) \ 1.
T(x \ 1,x * y) = T(x,x \ y) \ 1.
T(x,x \ y) \ 1 = T(x \ 1,x * y).
x * ((x * y) \ y) = T(x,x \ y) \ x.
T(x,x \ y) \ x = x * ((x * y) \ y).
1 / (x \ y) = ((x / y) \ y) \ y.
((x / y) \ y) \ y = 1 / (x \ y).
((x \ y) \ y) / x = (y / x) / (x \ y).
(x \ y) \ 1 = ((y / x) * y) \ y.
((x / y) * x) \ x = (y \ x) \ 1.
x / (1 / (y \ x)) = (y / x) \ x.
(((T(x,y) * y) / (x * y)) \ (x * y)) \ (x * y) = 1 / K(y,T(x,y)).
x / ((y \ x) \ 1) = (x / y) * x.
L(x \ y,x,x / y) = (y \ x) \ 1.
x / (1 / y) = ((x / y) / x) \ x.
((x / y) / x) \ x = x / (1 / y).
x / (y \ 1) = (x / (x / y)) * x.
(x / (x / y)) * x = x / (y \ 1).
(x * y) / ((K(x,y) \ (x * y)) \ 1) = (y * x) * (x * y).
x / (x / (1 / y)) = (x / y) / x.
(x / (y \ 1)) / x = x / (x / y).
(x / y) * ((y \ x) \ 1) = ((x / y) / x) * y.
(x * y) * (1 / T(x,y)) = (x * y) / T(x,x * y).
(x * y) / T(x,x * y) = (x * y) * (1 / T(x,y)).
((x \ y) \ y) * (x \ z) = (y / x) * ((x \ y) \ z).
(x * y) / (T(x,y) \ 1) = x * (x * y).
x * T(x \ 1,x * y) = T(x,x \ y) \ x.
(x / y) * (x \ y) = T(x,x \ y) \ x.
T(x,x \ y) \ x = (x / y) * (x \ y).
((x \ y) \ y) / x = (x \ y) \ (y / x).
(x / y) * (T(y,y \ x) \ y) = y \ x.
(x \ y) \ (y / x) = x \ ((x \ y) \ y).
(x / y) * ((y \ x) \ 1) = y \ ((y \ x) \ x).
(x / y) * ((y \ x) \ 1) = y * ((x / y) / x).
x * ((y / x) / y) = x \ ((x \ y) \ y).
x \ ((x \ y) \ y) = x * ((y / x) / y).
T(x,x \ y) * (x \ z) = (x * ((y / x) / y)) * z.
T(x / y,(y \ x) \ x) = y \ x.
T(x / (x / y),y \ x) = (x / y) \ x.
T(x / y,T(y,y \ x)) = y \ x.
T((x * y) / x,T(x,x \ (x * y))) = y.
T(x / (x / y),y \ x) = y.
T((x / y) / x,(1 / y) \ x) = 1 / y.
T((x * y) / x,T(x,y)) = y.
T(R((x * y) / x,x,y),T(x * y,y)) = y.
R(T((x * y) / x,T(x * y,y)),x,y) = y.
T(x,x \ y) * (x \ z) = x * (((y / x) / y) * z).
T(x,x \ y) * (x \ y) = x * (y / x).
T(x,y) * (x \ (x * y)) = x * ((x * y) / x).
T(x,y) * y = x * ((x * y) / x).
T(x,y) \ (x * ((x * y) / x)) = y.
x \ (T(x,y) * y) = (x * y) / x.
T(x / y,y) * y = (x / y) * (x / (x / y)).
(T(x,y) * y) \ (x * y) = K((x * y) / x,x).
K((x * y) / x,x) = (T(x,y) * y) \ (x * y).
x \ y = T(x,y) \ ((x * y) / x).
T(x,y) \ ((x * y) / x) = x \ y.
(x \ y) * x = (y / x) * (y / (y / x)).
(x / y) * (x / (x / y)) = (y \ x) * y.
((x \ y) * x) \ y = K(y / (y / x),y / x).
K(x / (x / y),x / y) = ((y \ x) * y) \ x.
K((x * y) / x,x) = K(y,T(x,y)).
K(x / y,y) = K(y \ x,T(y,y \ x)).
K(x \ y,T(x,x \ y)) = K(y / x,x).
((x * (y \ 1)) * y) / 1 = R(x,y \ 1,y).
R(x,y \ 1,y) = (x * (y \ 1)) * y.
(x * (y \ 1)) * y = R(x,y \ 1,y).
R(x,y \ 1,y) / y = x * (y \ 1).
x * y = R(x / (y \ 1),y \ 1,y).
R(x / (y \ 1),y \ 1,y) = x * y.
x * (((y \ 1) / x) * (x * y)) = R(x,y \ 1,y).
L(x,y / (z \ 1),y * z) = x.
(x * (x * y)) \ (x * (x * (y * z))) = L(z,y,x * x).
L(x \ 1,y,z) * (x * u) = (L(x \ 1,y,z) * x) * u.
(L(x \ 1,y,z) * x) * u = L(x \ 1,y,z) * (x * u).
(x / (y \ 1)) \ (x * y) = a(y,y \ x,y).
a(x,x \ y,x) = (y / (x \ 1)) \ (y * x).
a(x,x \ y,x) = (y / (1 / x)) \ (y * x).
a(x,x \ y,x) = ((x \ 1) / y) * (y * x).
a(x,x \ y,x) = y \ ((y * (1 / x)) * x).
a(x,x \ y,x) = y \ R(y,1 / x,x).
(x \ (y * z)) \ ((x \ y) * z) = a(x \ 1,y,z).
L(x * y,x \ z,x) = z \ ((z / (x \ 1)) * y).
(x * (y \ 1)) * L(z,y \ x,y) = x * (y \ z).
R(L(x,y,z),x,x \ 1) = x * (L(x,y,z) / x).
x * (L(x,y,z) / x) = L(R(x,x,x \ 1),y,z).
L(R(x,x,x \ 1),y,z) = x * (L(x,y,z) / x).
L(x,y,z) = x * (L(x,y,z) / x).
x * (L(x,y,z) / x) = L(x,y,z).
x \ L(x,y,z) = L(x,y,z) / x.
L(x,y,z) / x = x \ L(x,y,z).
x * y != L(x,x,z) | y = a(x,z,x).
L(x,x,y) / x = a(x,y,x).
a(x,y,x) * x = L(x,x,y).
(x \ L(x,y,z)) * x = L(x,y,z).
(x \ L(x,y,z)) \ u = (x / L(x,y,z)) * u.
L(x,y,z) * (1 / x) = L(x,y,z) / x.
L(x,y,z) != u * x | x \ L(x,y,z) = u.
a((x \ y) / x,x,z) = a(x \ 1,y,z).
a((x \ y) / x,x,z) = a(1 / x,y,z).
T(x \ 1,x / T(x,y)) = T(x,y) * (x \ (T(x,y) \ 1)).
T(x,y) * (x \ (T(x,y) \ 1)) = T(x \ 1,x / T(x,y)).
(x \ y) / ((x \ 1) \ z) = x \ ((y / z) * (x \ 1)).
(x \ y) / (x * z) = x \ ((y / z) * (x \ 1)).
x \ ((y / z) * (x \ 1)) = (x \ y) / (x * z).
(x \ y) / (x * z) = (x \ (y / z)) / x.
(x \ (y / z)) / x = (x \ y) / (x * z).
(x / y) \ 1 = (y \ x) * (((y \ x) \ 1) / (x / y)).
(x \ y) * (((x \ y) \ 1) / (y / x)) = (y / x) \ 1.
(x \ y) * (((x \ y) \ 1) / (y / x)) = x / y.
(x \ y) \ (x / y) = ((x \ y) \ 1) / (y / x).
((x \ y) \ 1) / (y / x) = (x \ y) \ (x / y).
(x \ y) \ (x / y) = ((y / x) * (x \ y)) \ 1.
((x / y) * (y \ x)) \ 1 = (y \ x) \ (y / x).
((x \ y) * (y / x)) \ 1 = (x \ y) \ (x / y).
(x \ y) \ (x / y) = (x / y) / (x \ y).
(x / y) / (x \ y) = (x \ y) \ (x / y).
((x \ y) \ (x / y)) * z = (x / y) * ((x \ y) \ z).
(R(x,y,z) \ u) / (x \ u) = (R(x,y,z) \ 1) * x.
(R(x,y,z) \ u) / (x \ u) = R(x,y,z) \ x.
(x * y) / (z \ ((z * x) * y)) = R(z,x,y) \ z.
(x * y) / ((x / z) * (z * y)) = R(z,x,y) \ z.
L(x,L(y \ 1,z,u),y) = x.
L(x,y,L(y \ 1,z,u)) = x.
L(x,L(y,z,u),y \ 1) = x.
L(x,1 / y,L(y,z,u)) = x.
(L(x,y,z) * (x \ 1)) \ u = (x \ 1) \ (L(x,y,z) \ u).
L(x,y \ L(y,z,u),y) = x.
x = L(x,y,y \ L(y,z,u)).
L(x,y,y \ L(y,z,u)) = x.
(x \ L(x,y,z)) * u = x \ (L(x,y,z) * u).
x \ (L(x,y,z) * u) = (x \ L(x,y,z)) * u.
(L(x,y,z) * u) / ((1 / x) \ u) = L(x,y,z) * (1 / x).
L(x,1 / L(y,z,u),y) = x.
(x * y) / ((x \ L(x,z,u)) \ y) = x * (x \ L(x,z,u)).
L(x,y,L(y,z,u) / y) = x.
(x * y) / ((1 / L(x,z,u)) \ y) = x * (1 / L(x,z,u)).
x / L(x,y,z) = x * (1 / L(x,y,z)).
x * (1 / L(x,y,z)) = x / L(x,y,z).
L(x,y,1 / L(y,z,u)) = x.
x = L(x,y,L(y,z,u)).
L(x,y,L(y,z,u)) = x.
L(x,y,z) * (x \ u) = (x / L(x,y,z)) \ u.
(x / L(x,y,z)) \ u = L(x,y,z) * (x \ u).
x / L(x,y,z) = L(x,y,z) \ x.
L(x,y,z) * (x / L(x,y,z)) = x.
(L(x,y,z) \ x) * L(x,y,z) = x.
x / (x / L(x,y,z)) = L(x,y,z).
L(L(x,y,1 / L(y,z,u)),y / L(y,z,u),y) = x.
(x \ L(x,y,z)) \ u = (L(x,y,z) \ x) * u.
x != y * L(x,z,u) | L(x,z,u) \ x = y.
x * L(y,z,u) != y | L(y,z,u) \ y = x.
L(x,y / L(y,z,u),y) = x.
T(x \ 1,x / T(x,y)) = x \ 1.
T(x \ 1,T(x,y) \ x) = x \ 1.
T((x \ 1) \ 1,((x * y) \ y) \ (x \ 1)) = (x \ 1) \ 1.
(L(x,y,z) * (x \ 1)) \ u = x * (L(x,y,z) \ u).
(x \ L(x,y,z)) \ u = x * (L(x,y,z) \ u).
x * (L(x,y,z) \ u) = (L(x,y,z) \ x) * u.
(L(x,y,z) \ x) * u = x * (L(x,y,z) \ u).
T(x,L(x,y,z) \ x) = x.
(L(x,y,z) * u) / (x * u) = L(x,y,z) * (1 / x).
(L(x,y,z) * u) / (x * u) = L(x,y,z) / x.
(x * y) / ((L(x,z,u) \ x) * y) = x * (x \ L(x,z,u)).
(x * y) / (L(x,z,u) * y) = x * (1 / L(x,z,u)).
(x * y) / (L(x,z,u) * y) = x / L(x,z,u).
x / (L(x / y,z,u) * y) = (x / y) / L(x / y,z,u).
(x / y) / L(x / y,z,u) = x / (L(x / y,z,u) * y).
T(x,((x * y) \ y) \ (x \ 1)) = (x \ 1) \ 1.
T(x,((x * y) \ y) \ (x \ 1)) = x.
T(x,(y / x) * ((x \ y) \ 1)) = x.
T(x,(x \ y) \ (y / x)) = x.
T(x,(x \ (y * x)) \ y) = x.
T(x,T(y,x) \ y) = x.
(T(x,y) \ x) * y = y * (T(x,y) \ x).
x * (T(y,x) \ y) = y * (T(y,x) \ x).
x * (T(y,x) \ y) = T(x,T(y,x)).
x \ T(x,T(y,x)) = T(y,x) \ y.
T(x,y) \ x = y \ T(y,T(x,y)).
x * y != T(x,z) | y = T(x,z) / x.
T(x,y) \ x = T(y,T(x,y)) / y.
T(x,y) * (y \ T(y,T(x,y))) = x.
L(x,T(y,z) \ y,z) = x.
((T(x,y) \ x) * y) \ z = y \ ((T(x,y) \ x) \ z).
L(x,y / T(y,z),z) = x.
x * (T(y,x) / y) = x / (y / T(y,x)).
x / (y / T(y,x)) = x * (T(y,x) / y).
x / (T(y,T(x,y)) / y) = T(x,y).
(T(x,y) \ x) \ 1 = y / T(y,T(x,y)).
x / T(x,y) = T(y,T(x,y)) / y.
T(x,T(y,x)) / x = y / T(y,x).
(T(x,T(y,x)) / x) \ y = T(y,x).
1 / (x / T(x,y)) = y / T(y,T(x,y)).
T(x,y) = T(y,T(x,y)) \ (y * x).
T(x,T(y,x)) \ (x * y) = T(y,x).
T(x,T(y,x)) * T(y,x) = x * y.
(x * T(y,x)) / (T(y,x) \ 1) = T(y,x) * (x * y).
(T(x,y) \ x) \ 1 = T(y,T(x,y)) \ y.
T(x,T(y,x)) \ x = (T(y,x) \ y) \ 1.
x / T(x,T(y,x)) = T(y,x) / y.
T(x,y) / x = y / T(y,T(x,y)).
x / (T(y,x) / y) = T(x,T(y,x)).
T(x,T(y,x) / y) = x.
L(x,y,T(z,y) / z) = x.
(T(x,y) / x) * y = y * (T(x,y) / x).
x / (x * (T(y,x) / y)) = 1 / (T(y,x) / y).
((T(x,y) / x) / y) \ ((T(x,y) / x) * z) = y * z.
((T(x,y) / x) / y) \ z = T(y,T(x,y)) * z.
T(x,T(y,x)) \ x = T(y,x) * (y \ 1).
x \ (T(x,y) * y) = y * (T(x,y) / x).
T(x,T(y,x)) \ x = y \ T(y,x).
x \ (y \ T(y,x)) = T(x,T(y,x)) \ 1.
T(x,T(y,x)) \ 1 = x \ (y \ T(y,x)).
x * (T(y,x) / y) = (y * x) / y.
x * (y \ T(y,x)) = (y * x) / y.
x / (y / T(y,x)) = (y * x) / y.
x / (x / (y / T(y,x))) = 1 / (T(y,x) / y).
x / (x / (y / T(y,x))) = y / T(y,x).
x / ((y * x) / y) = y / T(y,x).
(x / (x * y)) \ (x / T(x,y)) = y.
((T(x,y) \ x) * y) \ z = y \ (T(x,y) * (x \ z)).
(x * y) / (T(x,y) \ 1) = T(x,y) * (y * x).
T(x,y) * (y * x) = x * (x * y).
(x * (x * y)) / (y * x) = T(x,y).
T(x,y) = (x * (x * y)) / (y * x).
T(x,y) \ (x * (x * y)) = y * x.
a(T(x,y),y,x) = (x * (x * y)) \ ((T(x,y) * y) * x).
(x * (x * y)) \ ((T(x,y) * y) * x) = a(T(x,y),y,x).
K(T(x,y),y * x) = ((y * x) * T(x,y)) \ (x * (x * y)).
((x * y) * T(y,x)) \ (y * (y * x)) = K(T(y,x),x * y).
x * y = y * (T(y,x) \ (y * x)).
x * (T(x,y) \ (x * y)) = y * x.
T(x,y) = T(y,x) \ (y * x).
T(x,y) \ (x * y) = T(y,x).
T(x,y) * T(y,x) = x * y.
T(x,y) = T(x,T(y,x)).
T(x,T(y,x)) = T(x,y).
x \ T(y,x) = T(x,y) \ y.
T(x,y) \ y = x \ T(y,x).
T(T(x,y),z) = T(T(x,z),T(y,x)).
T(T(x,y),T(z,x)) = T(T(x,z),y).
T(x,x \ y) = T(x,y / x).
T(x,y / x) = T(x,x \ y).
T(x,y) * T(T(y,x),z) = T(y,z) * T(x,y).
(x * T(x \ y,z)) / x = T(y / x,T(z,x \ y)).
T(x / y,T(z,y \ x)) = (y * T(y \ x,z)) / y.
(x * T(y,z)) / x = T((x * y) / x,T(z,y)).
T((x * y) / x,T(z,y)) = (x * T(y,z)) / x.
T(x,y) \ x = y \ T(y,x).
T(x,y) * (y \ T(y,x)) = x.
x / (T(y,x) / y) = T(x,y).
T(x,y) / x = y / T(y,x).
T(x,y) \ 1 = x \ (y \ T(y,x)).
x \ (y \ T(y,x)) = T(x,y) \ 1.
(x \ T(x,y)) * T(y,x) = y.
a(T(x,y),T(y,x),z) = (T(x,y) * (T(y,x) * z)) \ ((x * y) * z).
(T(x,y) * (T(y,x) * z)) \ ((x * y) * z) = a(T(x,y),T(y,x),z).
L(x,T(y,z),T(z,y)) = (z * y) \ (T(z,y) * (T(y,z) * x)).
(x * y) \ (T(x,y) * (T(y,x) * z)) = L(z,T(y,x),T(x,y)).
T(x,y) * (x \ (x \ T(y,x))) = x \ y.
T(x,(x * y) / x) = T(x,y).
(x * (y / x)) / T(x,x \ y) = y / x.
T(x,y / x) = (x \ y) \ y.
x / T(y,x / y) = y \ x.
T(x,y / x) / y = 1 / (x \ y).
L(T(x,x \ y),y,x) = T(x,x * (y / x)).
L(x,T(y,z / y),z) = L(x,1 / (y \ z),z).
T(T(x,y),((x * y) / x) / T(x,y)) = T(T(x,y),x \ y).
x * (T(x,y) \ x) = (y * x) / y.
(x * y) / x = y * (T(y,x) \ y).
x / (T(x,y) / x) = (y * x) / y.
(x * y) / x = y / (T(y,x) / y).
(x / (x * y)) \ (T(y,x) / y) = y.
(x \ y) * T(x,y / x) = y.
T(T(x,y),((x * y) / x) / T(x,y)) = (x \ y) \ ((x * y) / x).
L(x,T(y,z / y),y \ z) = L(x,T(y,z / y),z).
L(x,y \ z,T(y,z / y)) = L(x,z,T(y,z / y)).
((x \ y) \ y) * T(x \ y,x) = y.
T(T(x,y),T(z,x)) = T(T(x,y),z).
T(x \ 1,x * (y * x)) = T(x,y) \ 1.
(1 / (x \ y)) \ T(T(x,y / x),y) = y * K(T(x,y / x),y).
x \ ((y * x) / y) = T(x,y) \ x.
T(x * (T(x,y) \ x),y) = y \ (y * x).
T(x / (T(x,y) / x),y) = y \ (y * x).
x * T(y / (y * z),z) = x * (((y / (y * z)) \ (T(z,y) / z)) \ (T(z,y) / z)).
x * (((y / (y * z)) \ (T(z,y) / z)) \ (T(z,y) / z)) = x * T(y / (y * z),z).
((x * y) \ y) \ T(x \ y,x) = y.
T(T(x,y),x \ z) = T(T(x,y),z / x).
T(T(x,y),z / x) = T(T(x,y),x \ z).
T(x \ y,x) / y = (x * y) \ y.
(x * (T(x,y) \ x)) \ T(y,x) = x \ y.
(x \ (x \ T(x,y))) * T(y,x) = x \ y.
T(x * (T(x,y) \ x),y) = x.
T(x / (T(x,y) / x),y) = x.
((x * y) / x) \ T(x,y) = y \ x.
T(x,y) / (y \ x) = (x * y) / x.
x \ y = (y / (y * x)) * T(y,x).
(x / (x * y)) * T(x,y) = y \ x.
T(x * y,x) / y = ((x * y) * x) / (x * y).
((x * y) * x) / (x * y) = T(x * y,x) / y.
x * T(y,z) != z \ y | x = y / (y * z).
x \ (x \ T(x,y)) = y / (y * x).
x * (y / (y * x)) = x \ T(x,y).
T((x * y) / x,T(z,y)) = T((x * y) / x,z).
R(T((x * y) / x,x * y),x,y) = y.
R(L(x,y,y * x),y,x) = x.
x = L(R(x,y,x),y,y * x).
L(R(x,y,x),y,y * x) = x.
L(x,y * x,y) = R(x,y,x).
((T(x,y) / x) / y) \ (x \ (T(x,y) * z)) = y * z.
(x * (T(x,y) \ y)) \ z = y \ (T(x,y) * (x \ z)).
T(x / y,T(z,y \ x)) = T(x / y,z).
T(x / (1 / y),1 / y) = T(x / (1 / y),(x / y) / x).
T(x / (1 / y),(x / y) / x) = T(x / (1 / y),1 / y).
x * y = T(x,T(z,x)) * (z \ (T(z,x) * y)).
T(x,T(y,x)) * (y \ (T(y,x) * z)) = x * z.
T(x,y) * (y \ (T(y,x) * z)) = x * z.
x * y = z \ (T(z,x) * (T(x,z) * y)).
x \ (T(x,y) * (T(y,x) * z)) = y * z.
T(x,y) * (y \ z) = x * (T(y,x) \ z).
x * (y * z) = T(x,y) * (T(y,x) * z).
T(x,y) * (T(y,x) * z) = x * (y * z).
T(x,y) \ (x * (T(y,x) \ z)) = y \ z.
T(x,y) * (1 / y) = x * (T(y,x) \ 1).
T(x,y) * (1 / y) = x * (1 / T(y,x)).
T(x,T(y,x)) \ z = x \ (T(y,x) * (y \ z)).
x \ (T(y,x) * (y \ z)) = T(x,T(y,x)) \ z.
x \ (T(y,x) * (y \ z)) = T(x,y) \ z.
x \ (y \ (T(y,x) * z)) = T(x,y) \ z.
(x * y) / ((L(x,z,u) \ x) * y) = L(x,z,u).
L(x,y,z) \ (x * u) = (L(x,y,z) \ x) * u.
(x * y) / (x * (L(x,z,u) \ y)) = L(x,z,u).
L(x,y,z) \ (x * u) = x * (L(x,y,z) \ u).
L(x,y,z) \ (u * x) = x * (L(x,y,z) \ T(u,x)).
x * (L(x,y,z) \ T(u,x)) = L(x,y,z) \ (u * x).
T(T(x,y),y / x) = T(T(x,y),((x * y) / x) / T(x,y)).
T(T(x,y),((x * y) / x) / T(x,y)) = T(T(x,y),y / x).
T(x / (1 / y),(x / y) / x) = (1 / y) \ x.
T(x / (1 / y),(x / y) / x) = y * x.
(x * 1) \ ((x * (y \ 1)) * y) = a(x,y \ 1,y).
x \ ((x * (y \ 1)) * y) = a(x,y \ 1,y).
x \ ((x * (1 / y)) * y) = a(x,y \ 1,y).
x \ R(x,1 / y,y) = a(x,y \ 1,y).
x \ R(x,1 / y,y) = a(x,1 / y,y).
a(x,1 / y,y) * x = R(x,1 / y,y).
a(x,x \ y,x) = a(y,1 / x,x).
((x * y) \ z) / L((y * x) \ z,y * x,K(y,x)) = K(y,x).
(x * T(y,z)) * (1 / x) = T((x * y) * (1 / x),z).
T((x * y) * (1 / x),z) = (x * T(y,z)) * (1 / x).
T(x * (y / x),z) = (x * T(y,z)) * (1 / x).
(x * T(y,z)) * (1 / x) = T(x * (y / x),z).
T(x * (y / x),z) = x * (T(y,z) / x).
x * ((y / x) / x) = T(y,1 / x) / x.
T(x,1 / y) / y = y * ((x / y) / y).
(x * (y / x)) * (1 / x) = T(y,1 / x) / x.
T(x * (y / x),x) = R(y,x,x \ 1).
T(x * (y / x),x) = R(y,x,1 / x).
T(x * ((y \ x) / x),y) = x * ((y * x) \ x).
T(x * y,x) = R(y * x,x,x \ 1).
R(x * y,y,y \ 1) = T(y * x,y).
T(T(x,y) * y,x) = R(x * y,x,1 / x).
T(x * y,x) / (x \ 1) = (y * x) * x.
T(x * y,1 / y) / y = y * (x / y).
T(x,y) / (y \ 1) = ((y \ x) * y) * y.
(x * (y / x)) * x = T(y * x,1 / x).
T(x * y,1 / y) = (y * (x / y)) * y.
T((x * y) * y,1 / y) = (y * x) * y.
T(x * y,y \ 1) = (y * (x / y)) * y.
T(x * ((y \ x) / x),y) = x / T(y,x).
T(x * (1 / y),y) = x / T(y,x).
T(x * (1 / y),y) \ x = T(y,x).
T((x * y) * (1 / x),x) = (x * y) * (1 / T(x,y)).
T(x * (y / x),x) = (x * y) * (1 / T(x,y)).
(x * y) * (1 / T(x,y)) = R(y,x,1 / x).
(x * y) / T(x,x * y) = R(y,x,1 / x).
(x * y) / T(x,x * y) = R(y,x,x \ 1).
(x / y) \ R(x / y,y,z) = R(y,x,z) \ y.
R(x,y,z) \ x = (x / y) * R(y / x,x,z).
(x / y) * R(y / x,x,z) = R(x,y,z) \ x.
(x * y) \ (x * (y * z)) = L(z,T(y,x),T(x,y)).
L(x,y,z) = L(x,T(y,z),T(z,y)).
L(x,T(y,z),T(z,y)) = L(x,y,z).
L(x,y \ z,T(y,z / y)) = L(x,z / y,y).
L(x,T(y,z / y),y \ z) = L(x,y,z / y).
L(T(x,y),T(y,x),T(x,y)) = T(x,x * y).
L(T(x,y),x,y) / T(x,y) = a(T(x,y),T(y,x),T(x,y)).
a(T(x,y),T(y,x),T(x,y)) = L(T(x,y),x,y) / T(x,y).
L(x,y / z,z) = L(x,y,T(z,y / z)).
L(x,y,T(z,y / z)) = L(x,y / z,z).
L(x,y,T(z,y / z)) = L(x,y,z).
L(x,y,(z \ y) \ y) = L(x,y,z).
L(x,y,z \ y) = L(x,y,y / z).
L(x,y,y / z) = L(x,y,z \ y).
L(x,y,y / z) = L(x,z,z \ y).
L(x,y,y \ z) = L(x,z,z / y).
L(x,T(y,z / y),y \ z) = L(x,y,z).
L(x,T(y,y \ z),y \ z) = L(x,y,z).
L(x,y,z) = L(x,T(y,z / y),z).
L(x,T(y,z / y),z) = L(x,y,z).
L(x,y,z) = L(x,1 / (y \ z),z).
L(x,1 / (y \ z),z) = L(x,y,z).
L(x,(y \ z) \ 1,z) = L(x,y,z).
L(x,y \ 1,z * y) = L(x,z,z * y).
L(x,((y \ z) \ 1) \ 1,z) = L(x,(z / y) * z,z).
L(x,y,y * z) = L(x,T(y,z),z).
L(x,T(y,z),z) = L(x,y,y * z).
L(L(x,y * z,y),T(y,z),z) = x.
L(x,y,T(z,y)) = L(x,z * y,z).
L(x,y * z,y) = L(x,z,T(y,z)).
T(x,y) * L(y,x * y,x) = T(y * T(x,y),y).
L(x,x,T(y,x)) = R(x,y,x).
R(x,y,x) / x = a(x,T(y,x),x).
a(x,T(y,x),x) = R(x,y,x) / x.
T(x,y) * L(y,x * y,x) = T(x * y,y).
T(x,y) * R(y,x,y) = T(x * y,y).
x \ (y \ T(y * x,x)) = T(x,y) \ R(x,y,x).
T(x,y) \ R(x,y,x) = K(y * x,x).
L(x,y \ z,z) = L(x,(z / y) * z,z).
L(x,(y / z) * y,y) = L(x,z \ y,y).
L(x,y \ z,z) = L(x,z / y,z).
L(x,y / z,y) = L(x,z \ y,y).
L(x,y / z,z * (y / z)) = L(x,T(z,z \ y) \ (z * (y / z)),z * (y / z)).
L(x,T(y,y \ z) \ (y * (z / y)),y * (z / y)) = L(x,z / y,y * (z / y)).
L(L(x,y,z),z * y,z) = L(x,y,z * z).
x * (((x \ y) / z) * u) = (y / (x \ z)) * (x \ u).
(x / (y \ z)) * (y \ u) = y * (((y \ x) / z) * u).
((x \ y) \ 1) \ ((((x \ y) \ 1) / (y / x)) * z) = (x / y) * z.
(x / y) \ R(x / y,y,z) = 1 / (R(x,y,z) \ x).
(x / y) \ R(x / y,y,z) = (R(x,y,z) \ x) \ 1.
(x / y) \ R(x / y,y,z) = R(x,y,z) * (x \ 1).
(x / y) \ R(x / y,y,z) = x \ R(x,y,z).
x \ R(x,y,z) = R(y,x,z) \ y.
R(x,y,z) \ x = y \ R(y,x,z).
x * (R(y,x,z) \ y) = R(x,y,z).
x / (y \ R(y,x,z)) = R(x,y,z).
(R(x,y,z) \ x) * y = R(y,x,z).
K(R(x,y,z) \ x,y) = 1.
(x \ R(x,y,z)) * u = y * (R(y,x,z) \ u).
x * (((y * z) / (x * z)) \ (y / x)) = R(x,y / x,z).
R(x,y,z) = y * (R(y,x,z) \ x).
x * (R(x,y,z) \ y) = R(y,x,z).
(x * y) / R(y,x,z) = R(x,y,z).
x * (R(x,y,z) \ u) = R(y,x,z) * (y \ u).
R(x,y,z) * (x \ u) = y * (R(y,x,z) \ u).
x * (((x * y) / (z * y)) * (z / x)) = R(x,z / x,y).
(x \ y) \ ((x * y) / x) = T(T(x,y),y / x).
(x \ y) * T(T(x,y),y / x) = (x * y) / x.
(1 / (x \ y)) \ T(T(x,y),y / x) = y * K(T(x,y / x),y).
(x / y) * z = (x \ y) * ((((x \ y) \ 1) / (y / x)) * z).
(x \ y) * ((((x \ y) \ 1) / (y / x)) * z) = (x / y) * z.
(x \ y) * (((x \ y) \ (x / y)) * z) = (x / y) * z.
(x \ y) * ((x / y) * ((x \ y) \ z)) = (x / y) * z.
(x / y) * z = x * (((x * y) \ y) * ((x \ y) \ z)).
x * (((x * y) \ y) * ((x \ y) \ z)) = (x / y) * z.
x * K(T(y,x / y),x) = (y \ x) * T(T(y,x),x / y).
(x \ y) * T(T(x,y),y / x) = y * K(T(x,y / x),y).
x * K(T(y,x / y),x) = (y * x) / y.
x * y != (z * x) / z | y = T(z,x) / z.
K(T(x,y / x),y) = T(x,y) / x.
K(x,(x * (y \ x)) / x) = x \ (y * L(x / y,x,y)).
K(x,(x * (y \ x)) / x) = x \ T(x,x / y).
(x / y) \ R(x / y,y,z) = ((x / y) * ((y * z) / (x * z))) \ 1.
(x * (y * z)) \ ((x * y) * z) = a(T(x,y),T(y,x),z).
a(x,y,z) = a(T(x,y),T(y,x),z).
a(T(x,y),T(y,x),z) = a(x,y,z).
a(T(x,y),T((x * y) / x,x),z) = a(x,(x * y) / x,z).
a(x,y,T(x,y)) = L(T(x,y),x,y) / T(x,y).
L(T(x,y),x,y) / T(x,y) = a(x,y,T(x,y)).
a(T(x,y),x \ (x * y),z) = a(x,(x * y) / x,z).
a(T(x,y),y,z) = a(x,(x * y) / x,z).
a(T(x,y),y,x) = a(x,x * y,x).
(x * T(x \ 1,x * y)) * z = ((x * y) \ y) * ((x \ 1) \ z).
((x * y) \ y) * ((x \ 1) \ z) = (x * T(x \ 1,x * y)) * z.
((x * y) \ y) * ((x \ 1) \ z) = (T(x,x \ y) \ x) * z.
(T(x,x \ y) \ x) * z = ((x * y) \ y) * ((x \ 1) \ z).
((x * y) \ y) * ((x \ 1) \ z) = x * (T(x,x \ y) \ z).
((x * y) \ y) * (x * z) = x * (T(x,x \ y) \ z).
x * (T(x,x \ y) \ z) = x * (((x * y) \ y) * z).
x \ (y * T(y \ x,z)) = (x \ y) * T((x \ y) \ 1,z).
(x \ y) * T((x \ y) \ 1,z) = x \ (y * T(y \ x,z)).
((T(x,y) / x) \ (x * y)) \ (x * y) = 1 / K(y,T(x,y)).
(T(x,y) \ (x * (x * y))) \ (x * y) = 1 / K(y,T(x,y)).
(x * y) \ (y * x) = 1 / K(x,T(y,x)).
K(x,y) = 1 / K(y,T(x,y)).
1 / K(x,T(y,x)) = K(y,x).
K(x,y) \ 1 = K(y,T(x,y)).
K(x,T(y,x)) = K(y,x) \ 1.
K(x,y) = K(y,T(x,y)) \ 1.
K(x,T(y,x)) \ 1 = K(y,x).
K(x,y) * z = K(y,T(x,y)) \ z.
K(x,T(y,x)) \ z = K(y,x) * z.
K(x,T(T(y,x),z)) = K(T(y,z),x) \ 1.
(x * y) / (K(x,y) \ 1) = T(x,y) * y.
K((x * y) / x,x) = K(x,y) \ 1.
(T(x,y) * y) / (x * y) = (x * y) / ((x * y) / K(x,y)).
(x * y) / ((x * y) / K(x,y)) = (T(x,y) * y) / (x * y).
(x * y) / (y * x) = (T(x,y) * y) / (x * y).
(T(x,y) * y) / (x * y) = (x * y) / (y * x).
(x * y) / (y * x) = T(x,y) / x.
T(x * y,z) / y = (1 / y) * T((1 / y) \ x,z).
(1 / x) * T((1 / x) \ y,z) = T(y * x,z) / x.
(1 / x) * T(x * y,z) = T(y * x,z) / x.
T(x * y,z) / y = y \ T(y * x,z).
T((x \ y) * x,z) / x = x \ T(y,z).
((x * y) * x) / (x * y) = y \ T(y * x,x).
T(x * (y * x),1 / x) / (y * x) = (y * x) \ ((x * y) * x).
(x \ T(y,z)) * x = T((x \ y) * x,z).
T((x \ y) * x,z) = (x \ T(y,z)) * x.
T((x \ y) * x,1 / y) = (x \ y) * x.
T(1 / x,(y \ x) * y) = 1 / x.
T(1 / (x * y),y * x) = 1 / (x * y).
1 / (x * y) = (y * x) \ K(y,x).
(x * y) \ K(x,y) = 1 / (y * x).
(x * y) * (1 / (y * x)) = K(x,y).
K(x,y) = (x * y) * (1 / (y * x)).
K(x,y) = (x * y) * ((y * x) \ 1).
((x * y) / ((y * x) \ 1)) * ((x * y) \ z) = (x * y) * (K(x,y) \ z).
x \ (y \ T(y * x,x)) = T(x,x * y) \ x.
T(x,x * y) \ x = K(y * x,x).
L(x,y,K(z * y,y)) = x.
L(x,y,K(z,y)) = x.
x \ (K(y,x) \ z) = (K(y,x) * x) \ z.
(K(x,y) * y) \ z = y \ (K(x,y) \ z).
L(x,K(y,z),z) = x.
x * (K(y,x) * z) = (x * K(y,x)) * z.
(x * K(y,x)) * z = x * (K(y,x) * z).
L(x,K(y,z) \ 1,y) = x.
x / K(x,y) = x * (K(x,y) \ 1).
x * (K(x,y) \ 1) = x / K(x,y).
x * ((K(x,y) \ 1) \ z) = (x / (K(x,y) \ 1)) * z.
(x / (K(x,y) \ 1)) * z = x * ((K(x,y) \ 1) \ z).
x * K(x,y) = x / (K(x,y) \ 1).
x / (K(x,y) \ 1) = x * K(x,y).
(x / (K(x,y) \ 1)) * z = x * (K(x,y) * z).
(x * K(x,y)) * z = x * (K(x,y) * z).
T(x * (y * x),1 / x) / (y * x) = R(T(x,y * x),y,x).
(x * (x * y)) / (y * x) = R(T(x,y * x),y,x).
T(x,y) = R(T(x,y * x),y,x).
R(T(x,y * x),y,x) = T(x,y).
(x * y) * T(y,x) = R(y,x,y) * (x * y).
R(x,y,x) * (y * x) = (y * x) * T(x,y).
(x * y) * T(y,x) = (y * x) * y.
x * T(y,x / y) = (y * (x / y)) * y.
(x * (y / x)) * x = y * T(x,y / x).
((x * y) * x) \ (x * (x * y)) = K(T(x,y),y * x).
(T(x,y) * y) * x = (x * y) * T(x,(x * y) / x).
(x * y) * T(x,(x * y) / x) = (T(x,y) * y) * x.
K(x,x * y) = K(T(x,y),y * x).
K(T(x,y),y * x) = K(x,x * y).
K(T(x,y / x),y) = K(x,x * (y / x)).
K(x,x * (y / x)) = T(x,y) / x.
K(x,x * y) = T(x,y * x) / x.
T(x,y * x) / x = K(x,x * y).
x * K(x,x * y) = T(x,y * x).
T(x,K(x,x * y)) = x.
T(x,K(x,y)) = x.
T(K(x,y),x) = K(x,y).
T(x,y * x) != x * z | K(x,x * y) = z.
(x * y) * T(x,y) = (T(x,y) * y) * x.
(T(x,y) * y) * x = (x * y) * T(x,y).
T(T(x,y) * y,x) = x \ ((x * y) * T(x,y)).
x \ ((x * y) * T(x,y)) = T(T(x,y) * y,x).
(x * (x * y)) \ ((x * y) * T(x,y)) = a(T(x,y),y,x).
T(T(x,y) * y,x) = L(x,x,y) * y.
L(x,x,y) * y = R(x * y,x,1 / x).
R(x * y,x,1 / x) = L(x,x,y) * y.
(L(x,x,y) * y) / (x * y) = a(x * y,x,1 / x).
a(x * y,x,1 / x) = L(x,x,y) / x.
a(x * y,x,1 / x) = a(x,y,x).
a(x * y,y,1 / y) = a(y,T(x,y),y).
a(x * (x \ y),x,1 / x) = a(y,1 / x,x).
a(x,T(y,x),x) = a(y,x,1 / x).
a(x,y,1 / y) = a(x,1 / y,y).
a(x,1 / y,y) = a(x,y,1 / y).
a(x,y,1 / y) * x = R(x,1 / y,y).
R(x,1 / y,y) = R(x,y,1 / y).
R(x,y,1 / y) / y = x * (1 / y).
x \ R(y,x,1 / x) = T(y * (1 / x),x).
T(x * (1 / y),y) = T(x,y) / y.
T(x * y,y \ 1) = T(x,y \ 1) / (y \ 1).
T(x,y \ 1) / (y \ 1) = T(x * y,y \ 1).
T(x * (y \ 1),y) = T(x,y) / y.
T(x,y) / y = x / T(y,x).
(T(x,y) / y) \ x = T(y,x).
(x / T(y,x)) * y = T(x,y).
T(x,y \ 1) / (y \ 1) = x * ((y \ x) \ x).
T(x,y) = x * K(x,y).
K(x,x * y) = K(x,y * x).
K(x,y * x) = K(x,x * y).
T(x,y) / x = K(x,y).
K(x,y) = T(x,y) / x.
x * T(x \ 1,y) = K(x \ 1,y).
T(x,y) / K(x,y) = x.
x \ T(x,y) = K(x,y).
K(x,y) = x \ T(x,y).
(x / y) * T(y,z) = x * L(K(y,z),y,x).
x * L(K(y,z),y,x) = (x / y) * T(y,z).
L(K(x,y),x,z) = z \ ((z / x) * T(x,y)).
x \ ((x / y) * T(y,z)) = L(K(y,z),y,x).
T(x,y) * z = x * (K(x,y) * z).
x * (K(x,y) * z) = T(x,y) * z.
T(x,x * y) = T(x,y * x).
T(x,y * x) = T(x,x * y).
K(x,y) * x = T(x,y).
T(x,y) = K(x,y) * x.
R(K(x,y) / z,z,x) = T(x,y) / (z * x).
K(x,y) \ 1 = x / T(x,y).
K(x,y) / x = T(x,y) / (x * x).
T(x,y) / (x * x) = K(x,y) / x.
K(x,y) \ (T(x,y) * z) = x * z.
K(x,y) \ z = T(x,y) \ (x * z).
T(x,y) \ (x * z) = K(x,y) \ z.
T(x,K(y,x)) = x.
x * K(y,x) = (y * x) / y.
(x * y) / x = y * K(x,y).
x / K(y,x) = T(x,y).
T(x,y) = x / K(y,x).
K(x,y) = y / T(y,x).
(x * y) / x = y / K(y,x).
T(x / K(x,y),y) = x.
(x * y) / (y * x) = K(x,y).
K(x,y) = (x * y) / (y * x).
K(x,y) * y = y * K(x,y).
K(T(x,y),z) = T(x,y) \ T(T(x,z),y).
T(x,y) \ T(T(x,z),y) = K(T(x,y),z).
K(R(x,y,z),u) = R(x,y,z) \ R(T(x,u),y,z).
R(x,y,z) \ R(T(x,u),y,z) = K(R(x,y,z),u).
K(x,y) \ z = x * (T(x,y) \ z).
x * (T(x,y) \ z) = K(x,y) \ z.
K(x,y) * z = T(x,y) * (x \ z).
T(x,y) * (x \ z) = K(x,y) * z.
T(x,y) \ x = K(y,x).
K(x,y) = T(y,x) \ y.
T(x,y) * K(y,x) = x.
K(x,y) * T(y,x) = y.
x \ K(y,x) = T(x,y) \ 1.
T(x,y) \ 1 = x \ K(y,x).
x * (y / (y * x)) = K(x,y).
K(x,y) = x * (y / (y * x)).
K(x,(x * (y \ x)) / x) = K(x,x / y).
R(x,K(y,z),y) * T(y,z) = (x * K(y,z)) * y.
R(x / K(y,z),K(y,z),y) = (x * y) / T(y,z).
K(x,y) \ y = T(y,x).
T(x,y) = K(y,x) \ x.
K(x,y) \ z = T(y,x) * (y \ z).
T(x,y) * (x \ z) = K(y,x) \ z.
K(x,y) * z = y * (T(y,x) \ z).
x * (T(x,y) \ z) = K(y,x) * z.
x * (K(y,x) \ z) = T(x,y) * z.
K(x,y / x) = (x \ y) \ (y / x).
(x \ y) \ (y / x) = K(x,y / x).
(x / y) * K(y \ x,y) = y \ x.
T(x * K(y,x),y) = x.
K(x * y,x) = K(y * x,x).
K(x * y,y) = K(y * x,y).
x * L(y,z,u) = L(y * K(x,y),z,u) * x.
L(x * K(y,x),z,u) * y = y * L(x,z,u).
R(x,y,y \ 1) * y = T(y * x,y).
K(x,(y / z) \ x) = K(x,x * (z / y)).
T(x,y) = T(x,x * (y / x)).
T(x,x * (y / x)) = T(x,y).
K(x,y) = K(y,x) \ 1.
K(x,y) \ 1 = K(y,x).
K(x,y) * K(y,x) = 1.
1 / K(x,y) = K(y,x).
K(x,y) \ (z / K(y,x)) = (K(x,y) \ z) * K(x,y).
K(x,y) * (K(y,x) * z) = z.
K(x,y) \ z = K(y,x) * z.
x * L(K(y,z),K(z,y),x) = x / K(z,y).
L(K(x,y),K(y,x),z) = z \ (z / K(y,x)).
(x / K(y,z)) / L(K(z,y),K(y,z),x) = x.
K(x,T(y,x)) = K(x,y).
K(T(x,y),y) = K(x,y).
K(x,T(T(y,x),z)) = K(x,T(y,z)).
x * K(y,x) = x / K(x,y).
x / K(x,y) = x * K(y,x).
R(x,K(y,z),K(z,y)) = ((x * K(y,z)) * K(z,y)) / 1.
((x * K(y,z)) * K(z,y)) / 1 = R(x,K(y,z),K(z,y)).
T(x,K(y,z)) * K(z,y) = x * (1 / T(K(y,z),x)).
K(x,x \ y) = K(x,y / x).
K(x,y / x) = K(x,x \ y).
K(x \ y,x) = K(y / x,x).
K(x / y,y) = K(y \ x,y).
R((x * y) / x,x,y) = y * K(x * y,y).
K(x,y) \ (x * y) = y * x.
(x \ K(y,x)) * z = T(x,y) \ z.
T(x,x \ K(y,x)) = x.
T(x,y) = T(T(x,y),x \ K(z,x)).
T(T(x,y),x \ K(z,x)) = T(x,y).
(x \ K(y,x)) * T(x,z) = T(x,z) * (x \ K(y,x)).
T(x,y) * (x \ K(z,x)) = (x \ K(z,x)) * T(x,y).
T(x,y * (x \ 1)) = T(x,x \ y).
L(T(x,x \ y),y,x) = T(x,y).
(x * (y / x)) / T(x,y) = R(y / x,x,x \ 1).
T(x,K(y,z)) = K(z,y) * (x * K(y,z)).
K(x,y) * (z * K(y,x)) = T(z,K(y,x)).
K(x,y) \ (K(y,x) \ z) = z.
K(x,K(y,z)) = (K(z,y) \ x) \ (x * K(y,z)).
(K(x,y) \ z) \ (z * K(y,x)) = K(z,K(y,x)).
K(x,y) \ T(z,K(y,x)) = z * K(y,x).
(K(x,y) \ z) / K(y,x) = z / K(z,K(y,x)).
K(x,y) * y = y / K(y,x).
x / K(x,y) = K(y,x) * x.
K(x / (x / y),x / y) = K(y,x / y).
K(1 / x,y) \ (x \ y) = y * (1 / x).
(x * y) / ((y * x) \ 1) = (y * x) * (x * y).
(x / K(x,y)) \ z = x \ (K(y,x) \ z).
(x \ y) * T(x,y) = L(x,y,x) * (x \ y).
L(x,y,x) * (x \ y) = (x \ y) * T(x,y).
L(T(x,y),x,y) = T(x,x \ y).
L(x \ y,y / x,x) = T(y / x,(y / x) \ x).
T(x / y,(x / y) \ y) = L(y \ x,x / y,y).
x * T(y,y \ x) = L(y,y,x) * x.
L(T(x,y),x,T(y,x)) = T(x,x \ T(y,x)).
T(x,y / x) = L(T(x,y),x,y).
L(T(x,y),x,y) = T(x,y / x).
L(T(x,y),T(x,y),T(y,x)) = T(x,x \ y).
T((x * (y * x)) * (x \ 1),x) = (y * (x * x)) / x.
x * y != T(x,z) * (T(z,x) * u) | y = z * u.
K(x,y) * (T(y,x) * z) = y * z.
x * y != T(x,z) * (x * u) | y = T(x,z) * u.
K(x,y) * (x * z) = T(x,y) * z.
x * y = T(x,z) * (K(z,x) * y).
T(x,y) * (K(y,x) * z) = x * z.
R(K(x,y),x * z,u) \ 1 = R(K(x,y) \ 1,T(x,y) * z,u).
R(K(x,y) \ 1,T(x,y) * z,u) = R(K(x,y),x * z,u) \ 1.
K(x,y) \ (y * z) = T(y,x) * z.
T(x,y) \ z = K(x,y) \ (x \ z).
K(x,y) \ (x \ z) = T(x,y) \ z.
K(x,y) \ (T(y,x) \ z) = y \ z.
T(x,y) \ (x * z) = K(y,x) * z.
T(x,y) \ (K(x,y) * z) = x \ z.
T(T(x,y),x \ z) = (x \ z) \ (K(x,y) * z).
(x \ y) \ (K(x,z) * y) = T(T(x,z),x \ y).
T(x / y,z) * y = K(x / y,z) * x.
x \ (K(y,x) * z) = T(x,y) \ z.
T(x,y) * T(z,x) = K(y,x) \ (z * x).
K(x,y) \ (z * y) = T(y,x) * T(z,y).
K(x \ y,x) * z = x * (((x * y) \ y) * z).
x * (((x * y) \ y) * z) = K(x \ y,x) * z.
T(x,y) * z != x * u | K(y,x) \ z = u.
K(x,T(y,x)) = K(x,T(y,K(T(y,x),z))).
K(x,T(y,K(T(y,x),z))) = K(x,T(y,x)).
R(K(x,y),T(y,x) * z,u) = ((y * z) * u) / ((T(y,x) * z) * u).
K(x,y) * (y * z) = y * (K(x,y) * z).
K(x,y / x) \ ((y / x) * z) = (x \ y) * z.
K(x,y) \ (T(z,u) * y) = T(y,x) * T(T(z,y),u).
T(x * y,x) != z * x | R(y,x,x \ 1) = z.
(x * (T(y,x) / x)) * x = T(x * y,x).
L(x,x,x \ y) = L(x,x,y).
x * ((y \ x) \ x) = L(y,y,x) * x.
L(x,x,y) * y = y * ((x \ y) \ y).
T(x,y) / L(y,y,x) = y \ x.
x \ L(x,x,y) = a(x,x \ y,x).
a(x,x \ y,x) = x \ L(x,x,y).
L(x,x,y) = L(x,y,y / x).
L(x,y,y / x) = L(x,x,y).
a(x,x \ y,x) = a(x,y,x).
a(x,y,x) = a(x,x * y,x).
a(x,x * y,x) = a(x,y,x).
a(x,y,x) = ((x \ 1) / y) * (y * x).
((x \ 1) / y) * (y * x) = a(x,y,x).
x * a(y,x,y) = R(x,y \ 1,y).
R(x,y \ 1,y) = x * a(y,x,y).
R(x,y \ 1,y) != x * z | a(y,x,y) = z.
K(x,x / y) = K(x,x \ (x * (y \ x))).
K(x,x \ (x * (y \ x))) = K(x,x / y).
K(x / y,z) * x = y * T(y \ x,z).
K(x,T(y,K(T(y,x),z))) = K(x,y).
T(T(x,K(T(x,y),z)),y) * K(y,x) = T(x,K(T(x,y),z)).
K(x,y \ x) = K(x,x / y).
K(x,x / y) = K(x,y \ x).
K(x,x / (x / y)) = K(x,y).
K(x,x / (y / z)) = K(x,x * (z / y)).
T(K(x / y,z),x) = x \ (y * T(y \ x,z)).
x \ (y * T(y \ x,z)) = T(K(x / y,z),x).
x / ((K(y,z) / x) \ (T(y,z) / (x * y))) = R(x,K(y,z) / x,y).
x * (y \ z) != (y \ z) * T(y,z) | x = L(y,y \ z,y).
L(x,y,x) = L(x,x \ y,x).
L(x,x \ y,x) = L(x,y,x).
L(x,y,x) = L(x,x * y,x).
L(x,x * y,x) = L(x,y,x).
x / L(y,x,y) = x * (y \ 1).
T(L(x,y,x),y * (x \ 1)) = T(L(x,y,x),L(x,y,x) \ y).
T(L(x,y,x),L(x,y,x) \ y) = T(L(x,y,x),y * (x \ 1)).
x * ((y \ x) \ x) = T(x * y,y \ 1).
T(x * y,y \ 1) = x * ((y \ x) \ x).
L(x,x,y) * y = T(y * x,x \ 1).
T(x * y,y \ 1) = L(y,y,x) * x.
L(x,x,y) * y = (x * (y / x)) * x.
L(x,x,y * x) * (y * x) = (x * y) * x.
L(x,x,y) * (y * x) = (x * y) * x.
x * (y * z) != (u * y) * z | x = R(u,y,z).
L(x,x,y) = R(x,y,x).
R(x,y,x) = L(x,x,y).
R(L(x,x,y),z,u) = R(R(x,z,u),y,x).
R(R(x,y,z),u,x) = R(L(x,x,u),y,z).
L(x \ 1,x \ 1,x * y) = R(x,y,x \ 1) \ 1.
L(x,x,T(y,x)) = L(x,x,y).
a(x,T(y,x),x) = L(x,x,y) / x.
T(x,y) \ L(x,x,y) = K(y * x,x).
L(T(x,y),x,T(z,x)) = T(L(x,x,z),y).
L(x,x,y) * T(y,x) = (x * (T(y,x) / x)) * x.
a(x,T(y,x),x) = a(x,y,x).
a(x,y,x) = a(y,x,1 / x).
a(x,y,1 / y) = a(y,x,y).
a(x,y \ 1,y) = a(y \ 1,x,y \ 1).
a(x \ 1,y,x \ 1) = a(y,x \ 1,x).
a(x,y,y \ 1) = a(y,x,y).
x * L(1 / x,y,x) = a(x,y,x).
x * a(y,x,y) = R(x,y,y \ 1).
R(x,y,y \ 1) = x * a(y,x,y).
x * L(x \ 1,y,x) = a(x,y,x).
R(x,y \ 1,y) = R(x,y,y \ 1).
R(x,y,y \ 1) / y = x * (y \ 1).
R(x / (y \ 1),y,y \ 1) = x * y.
K(x,y) \ K(x * y,y) = y \ L(y,y,x).
R(L(x / (y \ 1),z,u),y,y \ 1) / y = (y \ 1) * L((y \ 1) \ x,z,u).
R(R(x,y,z),u,x) = L(R(x,y,z),x,u).
L(T(x,y),x,z) = L(T(x,y),x,T(z,x)).
L(T(x,y),x,T(z,x)) = L(T(x,y),x,z).
(x * R(y,z,u)) / L(R(y,z,u),y,x) = R(x,R(y,z,u),y).
L(T(x,y),x,y) = T(x,x \ T(y,x)).
T(x,x \ T(y,x)) = L(T(x,y),x,y).
T(x,x \ T(y,x)) = T(x,x \ y).
K(x,y) \ K(x * y,y) = a(y,x,y).
K(x,y) \ K(y * x,y) = a(y,x,y).
L(R((x * y) / x,x,y),z,u) * (x * y) = (x * y) * L(y,z,u).
K(x \ y,x) * ((x \ y) \ z) = (x / y) * z.
K(x,y / x) \ ((x / y) \ z) = (x \ y) * z.
(x \ y) * T((x \ y) \ 1,z) = T(K(x / y,z),x).
(x * (y / x)) / T(x,y) = y * (x \ 1).
T(x / y,(x / y) \ y) = L(y \ x,x,y).
L(x \ y,y,x) = (y \ x) \ 1.
L((x / y) \ x,x,x / y) = L(y \ 1,y,x) \ 1.
L((x \ y) \ 1,y,x) = y \ x.
((x / y) \ ((x * z) / (y * z))) \ 1 = ((x * z) / (y * z)) \ (x / y).
(x / (y \ 1)) \ (x * y) = ((x * y) \ (x / (y \ 1))) \ 1.
((x * y) \ (x / (y \ 1))) \ 1 = (x / (y \ 1)) \ (x * y).
L(x,x,y) * T(y,x) = T(x * y,x).
x * L(y,y,x) = L(y,y,x) * T(x,y).
L(x,x,y) * T(y,x) = y * L(x,x,y).
T(x,L(y,y,x)) = T(x,y).
K(x / (x / K(y,z)),x / K(y,z)) = (K(y,z) \ (x / K(z,y))) \ x.
K(K(x,y),z) \ K(y,x) = 1 / T(K(x,y),z).
T(x,y) * (x \ K(z,x)) = T(x,z) \ T(x,y).
T(x,y) \ T(x,z) = K(x,z) * K(y,x).
T(x * (((y * x) / x) * 1),x) = (y * (x * x)) / x.
K(x,y) \ (T(x,z) * y) = T(x,z) * T(y,x).
K(x,y) \ (z * y) = K(y,z) \ (T(y,x) * z).
K(x,y) \ (T(x,z) * y) = K(z,x) \ (y * x).
R(x,y,x \ 1) \ 1 = L(x \ 1,y,x).
T(K(x / y,z),x) = K((x \ y) \ 1,z).
T(K(x,y),z) = K((z \ (x \ z)) \ 1,y).
K((x \ (y \ x)) \ 1,z) = T(K(y,z),x).
K((((x \ y) / y) * (x \ y)) \ (x \ y),z) = T(K(x,z),y).
L(x,y,y / x) = L(x \ 1,x,y) \ 1.
L(x \ 1,x,y) \ 1 = L(x,x,y).
(x \ (x / y)) \ 1 = L(y,y,x).
L(x,x,y) = (y \ (y / x)) \ 1.
L(x,x,y) \ z = (y \ (y / x)) * z.
x \ ((y \ (y / x)) \ 1) = a(x,y,x).
(x \ (x / y)) * T(L(y,y,x),z) = K((x \ (x / y)) \ 1,z).
T(x * (y * 1),x) = (y * (x * x)) / x.
T(x * y,x) = (y * (x * x)) / x.
(x * (y * y)) / y = T(y * x,y).
T(x * y,x) * x = y * (x * x).
x * y != R(z,u,y) * (u * y) | x = z * u.
T(x * R(y,x,x),x) = y * x.
R(R(x,y,y),y,y \ 1) = x.
x = R(R(x,y,y \ 1),y,y).
R(R(x,y,y \ 1),y,y) = x.
R(R(x,y,y),y,1 / y) = x.
x / (y \ 1) = R(x,y,y) * y.
R(x,y,y) * y = x / (y \ 1).
x / y = R(x,y,y) * (y \ 1).
R(x,y,y) * (y \ 1) = x / y.
R(R(x,y,1 / y),y,y) = x.
R(x * (y \ 1),y,y) = x / y.
R(T(x * y,x),x,x) = y * x.
R(x * y,y,y) = x / (y \ 1).
x / y = R(x,y,y) * (1 / y).
R(x,y,y) * (1 / y) = x / y.
R(x * (1 / y),y,y) = x / y.
(x / (y \ 1)) / y = R(x,y,y).
x * y != T(z,y) / (y \ 1) | x = (y \ z) * y.
R(T(x,y),y,y) = (y \ x) * y.
(x / y) / (y \ 1) = R(x,y,y).
R(x,y,y) \ (x / y) = y \ 1.
(x \ 1) / (y / x) = R(y,x,x) \ 1.
K(R(x,y,y),z) * (x / y) = T(R(x,y,y),z) * (y \ 1).
T(R(x,y,y),z) * (y \ 1) = K(R(x,y,y),z) * (x / y).
x * (1 / y) != T(z,1 / y) / y | x = y * (z / y).
R(T(x,1 / y),y,y) = y * (x / y).
R(x \ (1 / y),y,y) = (1 / x) / y.
(x * (y * x)) / x = R(x * y,x,x).
(x / y) / (y \ 1) = R(x,y \ 1,y \ 1).
R(x,y \ 1,y \ 1) = (x / y) / (y \ 1).
R(R(T(x,y),y,y),x,z) = (y \ x) * y.
(x / K(y,z)) / K(z,y) = R(x,K(y,z),K(y,z)).
R(L(T(x,1 / y),z,u),y,y) = y * (L(x,z,u) / y).
R(x * y,y * x,z) = (y \ (y * x)) * y.
R(x,y \ 1,y \ 1) = R(x,y,y).
R(x * y,y * x,z) = x * y.
(x * y) * ((y * x) * z) = ((x * y) * (y * x)) * z.
((x * y) * (y * x)) * z = (x * y) * ((y * x) * z).
a(T(x,y),y,x) = a(x,y,T(x,y)).
a(x,y,T(x,y)) = a(x,x * y,x).
a(x,x * y,x) = a(x,y,T(x,y)).
a(x,y,T(x,y)) = a(x,y,x).
L(T(x,y),x,y) / T(x,y) = a(x,y,x).
T(x,y / x) / T(x,y) = a(x,y,x).
R(x,K(y,z),K(z,y)) = (x * K(y,z)) * K(z,y).
(x * K(y,z)) * K(z,y) = R(x,K(y,z),K(z,y)).
x * (L(y,z,u) / x) = L(R(T(y,1 / x),x,x),z,u).
L(R(T(x,1 / y),y,y),z,u) = y * (L(x,z,u) / y).
L(x * (y / x),z,u) = x * (L(y,z,u) / x).
L(x,y,z) \ L(u * (x / u),y,z) = K(u,L(x,y,z) / u).
T(T(x,y),K(T(x,y),z)) * K(y,x) = T(x,K(T(x,y),z)).
((x * y) \ (x / (y \ 1))) \ 1 = ((y \ 1) / x) * (x * y).
K(((x \ 1) * (x \ y)) \ (x \ y),z) = T(K(x,z),y).
K((x \ (x \ y)) \ (x \ y),z) = T(K(x,z),y).
K(T(x,x \ (x \ y)),z) = T(K(x,z),y).
R(T(x,y),z,z) * (z \ 1) = K(R(x,z,z),y) * (x / z).
T(x,y) * K(y,x) = T(x,K(T(x,y),z)).
T(x,K(T(x,y),z)) = T(x,y) * K(y,x).
T(x,K(T(x,y),z)) = x.
K(T(x,y),z) * x = x * K(T(x,y),z).
K(x \ y,z) * (y / x) = (y / x) * K(T(y / x,x),z).
(x / y) * K(T(x / y,y),z) = K(y \ x,z) * (x / y).
((x * y) \ (x / (y \ 1))) \ 1 = a(y,x,y).
((x * (y * y)) \ (T(y * x,y) / (y \ 1))) \ 1 = a(y,T(y * x,y),y).
K(R(x,y,y),z) * (x / y) = T(x,z) / y.
(x / y) * K(y \ x,z) = K(y \ x,z) * (x / y).
K(x \ y,z) * (y / x) = (y / x) * K(x \ y,z).
L(T(x,y * (x \ 1)),y,x) = T(L(x,y,x),L(x,y,x) \ y).
T(L(x,y,x),L(x,y,x) \ y) = L(T(x,y * (x \ 1)),y,x).
(x \ (x / y)) * L(T(y,z),y,x) = K((x \ (x / y)) \ 1,z).
T(L(x,y,x),L(x,y,x) \ y) = L(T(x,x \ y),y,x).
T(L(x,y,x),L(x,y,x) \ y) = T(x,y).
x / T(y,x) = L(y,x,y) \ x.
L(x,y,x) \ y = y / T(x,y).
x / (x / T(y,x)) = L(y,x,y).
L(x,y,x) = y / (y / T(x,y)).
L(x,y,x) = y / (T(y,x) / x).
x / (T(x,y) / y) = L(y,x,y).
L(x,x * (y / x),x) = (x * (y / x)) / ((x * (y / x)) / T(x,y)).
(x * (y / x)) / ((x * (y / x)) / T(x,y)) = L(x,x * (y / x),x).
x / (T(x,y) / L(y,y,x)) = L(L(y,y,x),x,L(y,y,x)).
L(L(x,x,y),y,L(x,x,y)) = y / (T(y,x) / L(x,x,y)).
L(L(x,x,y),y,L(x,x,y)) = y / (x \ y).
L(L(x,x,y),y,L(x,x,y)) = x.
R(K(x,y),T(y,x) * z,u) = R(K(y,x),y * z,u) \ 1.
x / ((x / K(y,z)) * (T(y,z) / (x * y))) = R(x,K(y,z) / x,y).
(x * y) * L(y,z,u) = (L((x * y) / x,z,u) * x) * y.
(L((x * y) / x,z,u) * x) * y = (x * y) * L(y,z,u).
(x * L(x \ (x * y),z,u)) * y = (x * y) * L(y,z,u).
(x * L(y,z,u)) * y = (x * y) * L(y,z,u).
((x * y) * L(y,z,u)) / y = x * L(y,z,u).
x * y = ((x / L(y,z,u)) * y) * L(y,z,u).
((x / L(y,z,u)) * y) * L(y,z,u) = x * y.
(x * L(y,z,u)) / y = (x / y) * L(y,z,u).
(x * y) / L(y,z,u) = (x / L(y,z,u)) * y.
(x * (y / x)) / ((x * (y / x)) / T(x,y)) = L(x,y / x,x).
(x * (y / x)) / ((x * (y / x)) / T(x,y)) = L(x,y,x).
(x * (y / x)) / (y * (x \ 1)) = L(x,y,x).
L(x,y,x) = R(x,y,x \ 1).
R(x,y,x \ 1) = L(x,y,x).
L(x,y,x) \ 1 = L(x \ 1,y,x).
L(x \ 1,y,x) = L(x,y,x) \ 1.
x * (L(x,y,x) \ 1) = a(x,y,x).
a(x,y,x) = L(x,y,x) \ x.
L(x,y,x) \ x = a(x,y,x).
((x * y) * (y * x)) * ((y * x) \ z) = (y * x) * (K(y,x) \ z).
((x * y) * (y * x)) * ((y * x) \ z) = (y * x) * (K(x,y) * z).
(x * y) * (K(y,x) * z) = (y * x) * ((x * y) * ((x * y) \ z)).
(x * y) * ((y * x) * ((y * x) \ z)) = (y * x) * (K(x,y) * z).
(x * y) * z = (y * x) * (K(x,y) * z).
(x * y) * (K(y,x) * z) = (y * x) * z.
(x * y) \ ((x * y) * z) = L(z,K(x,y),y * x).
L(x,K(y,z),z * y) = x.
K(x,y) * ((y * x) * z) = (K(x,y) * (y * x)) * z.
(K(x,y) * (y * x)) * z = K(x,y) * ((y * x) * z).
L(x,y * z,K(y,z)) = x.
(x * y) \ z = K(x,y) \ ((y * x) \ z).
K(x,y) \ ((y * x) \ z) = (x * y) \ z.
((x * y) \ z) / ((y * x) \ z) = K(y,x).
K(x,y) * ((x * y) \ z) = (y * x) \ z.
x * ((y * x) \ z) = T(x,y) * ((x * y) \ z).
T(x,y) * ((x * y) \ z) = x * ((y * x) \ z).
T(x,y) * (y * ((x * y) \ z)) = x * (y * ((y * x) \ z)).
(x * (K(y,x) * y)) * z = K(y,x) * ((x * y) * z).
(x * T(y,x)) * z = K(y,x) * ((x * y) * z).
K(x,y) * ((y * x) * z) = (y * T(x,y)) * z.
K(x,y) * ((y * x) * z) = (x * y) * z.
((x * y) * z) / ((y * x) * z) = K(x,y).
K(x,y) * (y * (x * z)) = (x * y) * L(z,x,y).
((x * y) * z) / ((T(x,y) * y) * z) = K(y,T(x,y)).
(x * y) * L(z,x,y) = y * (K(x,y) * (x * z)).
x * (K(y,x) * (y * z)) = (y * x) * L(z,y,x).
x * (T(y,x) * z) = (y * x) * L(z,y,x).
(x * y) * L(z,x,y) = y * (T(x,y) * z).
(x * y) \ (y * (T(x,y) * z)) = L(z,x,y).
L(x,y,z) = (y * z) \ (z * (T(y,z) * x)).
L(T(x,y) \ z,x,y) = (x * y) \ (y * z).
L(x,y,z) = L(x,T(y,z),z).
L(x,T(y,z),z) = L(x,y,z).
L(x,T(y,z),T(z,y)) = L(x,y,T(z,y)).
L(x,y,y \ z) = L(x,y,z).
L(x,y,z \ y) = L(x,z,y).
L(x,y,z \ 1) = L(x,z,y).
L(x,y,z) = L(x,z,1 / y).
L(x,y,1 / z) = L(x,z,y).
(x \ y) * L(z,x,y) = x \ (y * z).
L(x,y,z) = L(x,z,z / y).
L(x,y,y / z) = L(x,z,y).
L(x,y / z,u) = L(x,u,z / y).
L(x,y \ z,z) = L(x,z,y).
L(x,y,z) = L(x,z \ 1,y).
L(x,y \ 1,z) = L(x,z,y).
L((x * (1 / y)) \ z,y,x) = (1 / y) \ (x \ z).
L(x,y,z) = L(x,z \ y,z).
L(x,y \ z,y) = L(x,z,y).
L((x \ y) \ z,y,x) = y \ (x * z).
x \ (y * L(z,y,x)) = (x \ y) * z.
x \ (y * ((y \ x) * z)) = L(z,x,y).
L(x,y,z) = y \ (z * ((z \ y) * x)).
x * L(y,x,z) = z * ((z \ x) * y).
L(x * y,z,x) = z \ ((z / (x \ 1)) * y).
(x * (y \ 1)) * L(z,x,y) = x * (y \ z).
L(L((x \ y) \ z,u,w),y,x) = L(y \ (x * z),u,w).
L(x,y,y / (y \ z)) = L(x,z,y).
L(x,y,y / z) = L(x,y * z,y).
L(x,y * z,y) = L(x,y,y / z).
L(L(x,y,z),z,z / y) = L(x,y,z * z).
(x \ y) * ((z / (x \ y)) * (x \ (y * u))) = ((x \ y) * z) * L(u,x,y).
(x \ (x / y)) * L(z,y,x) = x \ ((x / y) * z).
L((x \ y) \ 1,z,u) * (x \ y) = x \ (y * L(L((x \ y) \ 1,z,u),y,x)).
x \ (y * L(L((x \ y) \ 1,z,u),y,x)) = L((x \ y) \ 1,z,u) * (x \ y).
L(x,y,T(z,y)) = L(x,y,z).
L(x,y,z * z) = L(L(x,y,z),y,z).
L(L(x,y,z),y,z) = L(x,y,z * z).
L((x * (1 / y)) \ z,y,x) = y * (x \ z).
L(x,y,z) = y * (z \ ((z * (1 / y)) * x)).
x \ ((x / y) * T(y,z)) = K((x \ (x / y)) \ 1,z).
K((x \ (x / y)) \ 1,z) = x \ ((x / y) * T(y,z)).
K((x \ (x / y)) \ 1,z) = L(K(y,z),y,x).
L(K(x,y),x,z) = K((z \ (z / x)) \ 1,y).
(x * y) * K((x \ (x / y)) \ 1,z) = x * (y * K(y,z)).
L(K(x,y),x,z) = K(L(x,x,z),y).
x * K(L(y,y,x),z) = (x / y) * T(y,z).
K(L(x,x,y \ x),z) = L(K(x,z),y,x).
K(L(x,y,x),z) = L(K(x,z),y,x).
L(K(x,y),z,x) = K(L(x,z,x),y).
(x \ y) * K(L(y,x,y),z) = x \ (y * K(y,z)).
(x \ y) * K(L(y,x,y),z) = x \ T(y,z).
T(x / y,y) * (y * (((x / y) * y) \ z)) = x * L((y * (x / y)) \ z,y,x).
(x * y) * K((x \ (x / y)) \ 1,z) = x * T(y,z).
((x / y) * ((y * z) / (x * z))) \ 1 = ((y * z) / (x * z)) \ (y / x).
(K(x,y) \ (z / K(y,x))) \ z = K(K(x,y),z / K(x,y)).
((x / y) * ((y * z) / (x * z))) \ 1 = ((x * z) / (y * z)) * (y / x).
(x / y) \ R(x / y,y,z) = ((x * z) / (y * z)) * (y / x).
((x * y) / (z * y)) * (z / x) = R(z,x,y) \ z.
x * (R(y,x,z) \ y) = R(x,y / x,z).
R(x,y / x,z) = R(x,y,z).
R(x,y,z) = R(x,y * x,z).
R(x,y * x,z) = R(x,y,z).
x / ((x / K(y,z)) * (T(y,z) / (x * y))) = R(x,K(y,z),y).
R(T(x,y),z * x,u) = T(R(x,z,u),y).
R(T(x,y),z,u) = R(T(x,y),z * x,u).
R(T(x,y),z * x,u) = R(T(x,y),z,u).
((x * (y * y)) \ ((x * y) * y)) \ 1 = a(y,T(y * x,y),y).
a(x,y,y) \ 1 = a(y,T(y * x,y),y).
a(x,T(x * y,x),x) = a(y,x,x) \ 1.
a(x,y,y) \ 1 = a(y,y * x,y).
a(x,x * y,x) = a(y,x,x) \ 1.
a(x,y,y) \ 1 = a(y,x,y).
a(x,y,x) \ z = a(y,x,x) * z.
a(x,y,x) * z = a(y,x,x) \ z.
a(x,y,y) \ z = a(y,x,y) * z.
x / (a(y,z,z) * R(a(z,y,z),x,u)) = R(x,a(z,y,z),u).
(x \ y) * (x * (((x \ z) / y) * (y * u))) = ((x \ y) * z) * L(u,x,y).
(R(T(x,y),z,u) * (z * u)) / ((x * z) * u) = R(x,z,u) \ T(R(x,z,u),y).
L(R(x / (y \ 1),y,y \ 1),z,u) / y = (y \ 1) * L((y \ 1) \ x,z,u).
x \ (y * L(y \ (x * 1),z,u)) = L((x \ y) \ 1,z,u) * (x \ y).
x \ (y * L(y \ x,z,u)) = L((x \ y) \ 1,z,u) * (x \ y).
L((x \ y) \ 1,z,u) * (x \ y) = x \ (y * L(y \ x,z,u)).
x \ (y * L(y \ x,z,u)) = (x \ y) * L((x \ y) \ 1,z,u).
(x \ y) * L((x \ y) \ 1,z,u) = x \ (y * L(y \ x,z,u)).
(x \ y) * (x * (((y / x) * x) \ z)) = y * L((x * (y / x)) \ z,x,y).
(x \ y) * (x * (y \ z)) = y * L((x * (y / x)) \ z,x,y).
x * L((y * (x / y)) \ z,y,x) = (y \ x) * (y * (x \ z)).
x * (y * ((y * x) \ z)) = (y \ x) * (y * (x \ z)).
(x \ y) * (x * (y \ z)) = y * (x * ((x * y) \ z)).
(x \ y) * (x * (((x \ (x * (y \ z))) / y) * (y * u))) = (y * (x * ((x * y) \ z))) * L(u,x,y).
((T(x,y) * z) * u) / ((x * z) * u) = R(x,z,u) \ T(R(x,z,u),y).
((T(x,y) * z) * u) / ((x * z) * u) = R(x,z,u) \ R(T(x,y),z,u).
R(x \ T(x,y),x * z,u) = R(x,z,u) \ R(T(x,y),z,u).
R(K(x,y),x * z,u) = R(x,z,u) \ R(T(x,y),z,u).
R(x,y,z) \ R(T(x,u),y,z) = R(K(x,u),x * y,z).
R(K(x,y),x * z,u) = K(R(x,z,u),y).
R(K(x,y),z,u) = K(R(x,x \ z,u),y).
K(R(x,x \ y,z),u) = R(K(x,u),y,z).
R(K(x,y),T(y,x) * z,u) = K(R(y,z,u),x) \ 1.
R(K(x,y),T(y,x) * z,u) = K(x,R(y,z,u)).
K(x,R(y,z,u)) = ((y * z) * u) / ((T(y,x) * z) * u).
((x * y) * z) / ((T(x,u) * y) * z) = K(u,R(x,y,z)).
K(x,R(y,x,z)) = K(x,T(y,x)).
K(x,R(y,x,z)) = K(x,y).
K(x,y) * T(R(y,x,z),x) = R(y,x,z).
K(x,y) * R(T(y,x),x,z) = R(y,x,z).
x \ R(x,y,z) = T(x,y) \ R(T(x,y),y,z).
T(x,y) \ R(T(x,y),y,z) = x \ R(x,y,z).
x / (y \ R(y,x,z)) = R(x,T(y,x),z).
R(x,T(y,x),z) = R(x,y,z).
R(x,x \ y,z) = R(x,y / x,z).
R(x,y / x,z) = R(x,x \ y,z).
R(x,x \ y,z) = R(x,y,z).
R(x,y,z) = R(x,x * y,z).
R(x,x * y,z) = R(x,y,z).
R(x,y,z) \ (y * z) = (x \ y) * z.
R(x,y,z) \ 1 = R(x \ 1,y,z).
R(x \ 1,y,z) = R(x,y,z) \ 1.
R(x,y,z) \ x = x * R(x \ 1,y,z).
x * R(x \ 1,y,z) = R(x,y,z) \ x.
R(x,y,z) = 1 / R(1 / x,y,z).
1 / R(1 / x,y,z) = R(x,y,z).
R(x,y,y \ z) = z / ((x \ y) * (y \ z)).
x / ((y \ z) * (z \ x)) = R(y,z,z \ x).
K(R(x,y,z),u) = R(K(x,u),y,z).
R(K(x,y),z,u) = K(R(x,z,u),y).
R(T(x,y),x * z,u) = T(R(x,z,u),y).
x * (R(x,y,z) \ (x * y)) = R(x * y,x,z).
(x \ 1) / (y / x) = R(y \ 1,x,x).
L(x,y,R(z,u,w)) = L(x,R(1 / z,u,w),y).
L(x,R(1 / y,z,u),w) = L(x,w,R(y,z,u)).
K(R(x,y,y),z) \ (K(x,z) / y) = y \ 1.
R(K(x,y) \ 1,z,u) = K(R(x,z,u),y) \ 1.
R(x,y,z) * (x \ (x * z)) = y * ((y \ x) * z).
(x \ 1) / y = R((y * x) \ 1,x,x).
R((x * y) \ 1,y,y) = (y \ 1) / x.
R((x * (y \ 1)) \ 1,y \ 1,y \ 1) = T(y,y \ 1) / x.
R(T(x,y),z,u) = R(T(x,y),x * z,u).
R(T(x,y),x * z,u) = R(T(x,y),z,u).
R(x,(x * K(y,x)) * z,u) = R(T(x * K(y,x),y),z,u).
R(T(x * K(y,x),y),z,u) = R(x,(x * K(y,x)) * z,u).
T(x,y) / ((z \ x) * K(x,y)) = R(z,x,x \ T(x,y)).
x \ 1 = K(y,R(z,x,x)) * (K(z,y) / x).
K(x,R(y,z,z)) * (K(y,x) / z) = z \ 1.
x * (x * (R(x,y,z) \ y)) = R(x * y,x,z).
R(K(x,y) \ 1,z,u) = K(y,R(x,z,u)).
R(K(x,y),z,u) = K(x,R(y,z,u)).
K(x,R(y,z,u)) = K(R(x,z,u),y).
K(R(x,y,z),u) = K(x,R(u,y,z)).
K(L(x,x,y),z) = K(x,R(z,y,x)).
K((x \ (x / y)) \ 1,z) = K(y,R(z,x,y)).
x * K(y,R(z,x,y)) = (x / y) * T(y,z).
x * R(y,x,z) = R(x * y,x,z).
R(x * y,x,z) = x * R(y,x,z).
((x * y) / (z * y)) * z = R(z * (z \ x),z,y).
R(x * (x \ y),x,z) = ((y * z) / (x * z)) * x.
R(x,y,z) * z = y * ((y \ x) * z).
(x * ((x \ y) * z)) / z = R(y,x,z).
R(x,y,z) = (y * ((y \ x) * z)) / z.
R(x * y,x,z) * z = x * (y * z).
x * L(y,x,z) = R(x,z,y) * y.
R(x,y,z) * z = x * L(z,x,y).
R(x,y,z) * (x \ z) = L(z,x,y).
L(x,y,z) = R(y,z,x) * (y \ x).
T(x,L(y,x,z)) = L(y,x,z) \ (R(x,z,y) * y).
L(x,y,z) \ (R(y,z,x) * x) = T(y,L(x,y,z)).
L(x,y,z) = z * (R(z,y,x) \ x).
x \ L(y,z,x) = R(x,z,y) \ y.
R(x,y,z) \ z = x \ L(z,y,x).
(x * y) / L(y,z,x) = R(x,z,y).
R(x,y,z) = (x * z) / L(z,y,x).
L(x,y * z,T(z,u)) = T(z,u) * (R(T(z,u),y,x) \ x).
T(x,y) * (R(T(x,y),z,u) \ u) = L(u,z * x,T(x,y)).
R(x,y,z) * (x \ L(z,y,x)) = z.
R(x,y,z) * L(z,y,x) = x * z.
R(x,y,R(y,z,u)) = R(x,R(y,z,u),y).
R(x,R(y,z,u),y) = R(x,y,R(y,z,u)).
R(x,y,z) = (x / L(z,y,x)) * z.
x = y * (R(y,z,x) \ L(x,y,z)).
x * (R(x,y,z) \ L(z,x,y)) = z.
K(R(x,y,z),L(z,y,x)) = (L(z,y,x) * R(x,y,z)) \ (x * z).
(L(x,y,z) * R(z,y,x)) \ (z * x) = K(R(z,y,x),L(x,y,z)).
(L(x,y,z) / z) * R(z,y,x) = x.
a(x / y,y,z) = x \ R(x,y,z).
(R(x,y,z) \ x) * L(z,x,y) = z.
(x / y) * R(y,z,L(x,y,z)) = L(x,y,z).
a(x,y,z) = (x * y) \ R(x * y,y,z).
R(x,y,z) \ x = a(y / x,x,z).
a(x / y,y,z) = R(y,x,z) \ y.
L(x,y,z) \ x = R(y,z,x) \ y.
R(x,y,z) \ x = L(z,x,y) \ z.
a(x,y,z) = R(y,x * y,z) \ y.
T(x,R(y,z,x) \ y) = x.
R(x,y,y) \ x = a(y,x,y).
T(x,a(y / z,z,x)) = x.
T(x,a(y,z,x)) = x.
a(x,y,z) * z = z * a(x,y,z).
R(x,y,y) * a(y,x,y) = x.
a(x,y,z) = R(y,x,z) \ y.
x / a(y,x,z) = R(x,y,z).
R(x,y,z) = x / a(y,x,z).
x / R(x,y,z) = a(y,x,z).
a(x,y,z) = y / R(y,x,z).
a(x,y,z) * R(y,x,z) = y.
a(x,y,z) \ y = R(y,x,z).
R(x,y,z) = a(y,x,z) \ x.
1 / a(x,y,z) = R(y,x,z) / y.
R(x,y,z) / x = 1 / a(y,x,z).
R(x,y,z) \ (x * u) = a(y,x,z) * u.
a(x,y,z) * u = y * (R(y,x,z) \ u).
x * (R(x,y,z) \ u) = a(y,x,z) * u.
a(x,y,z) = x \ R(x,y,z).
K(a(x,y,z),x) = 1.
x * a(x,y,z) = R(x,y,z).
R(x,y,z) = x * a(x,y,z).
a(x,y,z) * x = R(x,y,z).
R(x,y,z) = a(x,y,z) * x.
x * R(x \ 1,y,z) = a(y,x,z).
a(x,y,z) = y * R(y \ 1,x,z).
a(x,K(y,z),u) = K(y,R(z,x,u)) \ K(y,z).
K(x,R(y,z,u)) \ K(x,y) = a(z,K(x,y),u).
a(x,y,z) * L(z,y,x) = z.
a(x / y,y,z) = a(x,y,z).
a(x,y,z) = a(x * y,y,z).
a(x * y,y,z) = a(x,y,z).
T(a(x,y,z),x) = a(x,y,z).
a(x,L(y,z,u),w) = L(y,z,u) / L(R(y,x,w),z,u).
L(x,y,z) / L(R(x,u,w),y,z) = a(u,L(x,y,z),w).
L(a(x,y,z),x,u) = u \ ((u / x) * R(x,y,z)).
x \ ((x / y) * R(y,z,u)) = L(a(y,z,u),y,x).
R(x,y,z) / x = a(x,y,z).
a(x,y,z) = R(x,y,z) / x.
R(x,y,z) \ a(x,y,z) = x \ 1.
L(x,y,a(y,z,u)) = x.
x * (a(x,y,z) * u) = R(x,y,z) * u.
a(x,y,z) * u = R(x,y,z) * (x \ u).
R(x,y,z) * (x \ u) = a(x,y,z) * u.
a(x,y,z) \ u = x * (R(x,y,z) \ u).
x * (R(x,y,z) \ u) = a(x,y,z) \ u.
T(a(x,y,z),x * u) = (x * u) \ (R(x,y,z) * u).
(x * y) \ (R(x,z,u) * y) = T(a(x,z,u),x * y).
a(L(x,x,y),z,u) = (y \ (y / x)) * R(L(x,x,y),z,u).
(x \ (x / y)) * R(L(y,y,x),z,u) = a(L(y,y,x),z,u).
L(a(T(x,y),z,u),x,y) = (x * y) \ (y * R(T(x,y),z,u)).
(x * y) \ (y * R(T(x,y),z,u)) = L(a(T(x,y),z,u),x,y).
x \ T(y,a(x,z,u)) = (a(x,z,u) * x) \ (y * a(x,z,u)).
(a(x,y,z) * x) \ (u * a(x,y,z)) = x \ T(u,a(x,y,z)).
a(x,y,x) = a(y,x \ 1,x).
a(x,y \ 1,y) = a(y,x,y).
R(x,y,a(y,z,u)) * R(y,z,u) = (x * y) * a(y,z,u).
L(x,a(x,y,z),u) = u \ ((u / a(x,y,z)) * R(x,y,z)).
x \ ((x / a(y,z,u)) * R(y,z,u)) = L(y,a(y,z,u),x).
x / L(x,y,z) = a(z,y,x).
a(x,y,z) = z / L(z,y,x).
R(x,a(y,z,u),L(u,z,y)) = ((x * a(y,z,u)) * L(u,z,y)) / u.
((x * a(y,z,u)) * L(u,z,y)) / u = R(x,a(y,z,u),L(u,z,y)).
K(a(x,y,z),u) * z = T(a(x,y,z),u) * L(z,y,x).
T(a(x,y,z),u) * L(z,y,x) = K(a(x,y,z),u) * z.
a(L(x,y,z),u,w) = L(R(x,u,w),y,z) / L(x,y,z).
L(R(x,y,z),u,w) / L(x,u,w) = a(L(x,u,w),y,z).
a(x \ 1,y,x \ 1) = a(x,y,x).
R(x / a(y,z,u),u / L(u,z,y),L(u,z,y)) = (x * L(u,z,y)) / u.
L(x,y,z) * a(z,y,x) = x.
x / a(y,z,x) = L(x,z,y).
L(x,y,z) = x / a(z,y,x).
a(x,y,z) \ u = L(z,y,x) * (z \ u).
L(x,y,z) * (x \ u) = a(z,y,x) \ u.
L(x,a(y,z,u),u) = x.
a(1 / x,y,z) = z / L(z,x,y).
a(x,y,z) * (u * z) = (a(x,y,z) * z) * T(u,z).
(a(x,y,z) * z) * T(u,z) = a(x,y,z) * (u * z).
a(x,y,z) = 1 / a(y,x,z).
1 / a(x,y,z) = a(y,x,z).
a(x,y,z) * a(y,x,z) = 1.
a(x,y,z) \ 1 = a(y,x,z).
a(x,y,z) * (a(y,x,z) * u) = u.
a(x,y,z) * u = a(y,x,z) \ u.
a(x,y,z) \ u = a(y,x,z) * u.
K(a(x,y,z),u) * 1 = T(a(x,y,z),u) * a(y,x,z).
T(a(x,y,z),u) * a(y,x,z) = K(a(x,y,z),u) * 1.
a(x,y,z) = a(1 / y,x,z).
a(1 / x,y,z) = a(y,x,z).
a(x,y,z) = a(y,x \ 1,z).
a(x,y \ 1,z) = a(y,x,z).
a(x \ 1,y,z) = a(y,x,z).
a((x \ y) / x,x,z) = a(y,x,z).
a(x,y \ 1,y \ 1) = a(y,x \ 1,y).
T(x,a(y,z,u)) = a(z,y,u) * (x * a(y,z,u)).
a(x,y,z) * (u * a(y,x,z)) = T(u,a(y,x,z)).
a(x,y,z) * u != z | u = L(z,y,x).
a(x,y,z) * z = L(z,x,y).
L(x,y,z) = a(y,z,x) * x.
K(a(x,y,z) * u,a(y,x,z)) = u \ ((a(x,y,z) * u) * a(y,x,z)).
x \ ((a(y,z,u) * x) * a(z,y,u)) = K(a(y,z,u) * x,a(z,y,u)).
x \ L(x,y,z) = a(y,z,x).
a(x,y,z) = z \ L(z,x,y).
L(x,y,z) / x = a(y,z,x).
a(x,y,z) = L(z,x,y) / z.
L(x,y,z) = x * a(y,z,x).
a(x,y,z \ 1) = z * L(z \ 1,x,y).
x * L(x \ 1,y,z) = a(y,z,x \ 1).
a(x,y,x \ z) = (x \ z) \ (y \ ((y / x) * z)).
(x \ y) \ (z \ ((z / x) * y)) = a(x,z,x \ y).
x * L(a(y,z,u),u,x) = (x / u) * L(u,y,z).
((L(x,y,z) / x) * L(x,y,z)) \ L(x,y,z) = a(y,z,x) \ 1.
x \ (L(x,y,z) * u) = a(y,z,x) * u.
a(x,y,z) \ u = z * (L(z,x,y) \ u).
x * (L(x,y,z) \ u) = a(y,z,x) \ u.
a(x,y,K(z,u)) = K(u,z) * L(K(z,u),x,y).
K(x,y) * L(K(y,x),z,u) = a(z,u,K(y,x)).
L(a(x,y,z \ u),u,z) = u \ (z * L(z \ u,x,y)).
x \ (y * L(y \ x,z,u)) = L(a(z,u,y \ x),x,y).
R(a(x,y,z) * 1,u,w) = R(a(y,x,z),u,w) \ 1.
a(x,y,z) = a(y \ x,y,z).
a(x \ y,x,z) = a(y,x,z).
a(x,y,z) = a(y * x,y,z).
a(x * y,x,z) = a(y,x,z).
R(x,y,R(y,z,u)) * (y * R(y,z,u)) = (x * R(y,z,u)) * y.
a(R(x,y,z) / u,u,x) = R(u,x,R(x,y,z)) \ u.
a(x,y,y) = (x * y) \ (x / (y \ 1)).
(x * y) \ (x / (y \ 1)) = a(x,y,y).
(x * (y \ 1)) \ (x / y) = a(x,y \ 1,y \ 1).
x * y = a(z,x,u) * (R(x,z,u) * y).
a(x,y,z) * (R(y,x,z) * u) = y * u.
x * (y * z) = a(y,x,z) * ((x * y) * z).
a(x,y,z) * ((y * x) * z) = y * (x * z).
x * (a(y,x,z) * u) = a(y,x,z) * (x * u).
a(x,y,z) * (y * u) = y * (a(x,y,z) * u).
(R(x,y,z) * u) / (a(x,y,z) * u) = x.
x * y != R(x,z,u) * (x * w) | y = R(x,z,u) * w.
a(x,y,z) * (x * u) = R(x,y,z) * u.
R(x,a(x,y,z) * u,w) = ((R(x,y,z) * u) * w) / ((a(x,y,z) * u) * w).
((R(x,y,z) * u) * w) / ((a(x,y,z) * u) * w) = R(x,a(x,y,z) * u,w).
x * (y * z) = a(x,y,z) \ ((x * y) * z).
a(x,y,z) \ ((x * y) * z) = x * (y * z).
a(x,y \ 1,y \ 1) = a(x,y,y).
a(x,y,y) = a(y,x,y \ 1).
a(x,y,x \ 1) = a(y,x,x).
a(x,y,(z \ u) \ 1) = z \ (u * L(u \ z,x,y)).
x \ (y * L(y \ x,z,u)) = a(z,u,(x \ y) \ 1).
x * (a(y,z,x) * u) = L(x,y,z) * u.
R(x,y,z) = z * (L(z,y,x) \ x).
x * (L(x,y,z) \ u) = a(z,y,x) * u.
(x * y) / R(y,z,x) = L(x,z,y).
L(x,y,z) = (x * z) / R(z,y,x).
L(x,y,z) * R(z,y,x) = x * z.
a(L(x,y,z),R(z,y,x),u) = (L(x,y,z) * (R(z,y,x) * u)) \ ((x * z) * u).
(L(x,y,z) * (R(z,y,x) * u)) \ ((x * z) * u) = a(L(x,y,z),R(z,y,x),u).
x * R(y,z,L(x,y,z)) = L(x,y,z) * y.
((R(x,y,z) * u) * w) / (a(R(x,u,w),y,z) * (u * w)) = R(x,u,w).
x * R(y,z,x) = L(x,y,z) * y.
L(x,y,z) * y = x * R(y,z,x).
x * (y * z) = L(x,u,y) * (R(y,u,x) * z).
L(x,y,z) * (R(z,y,x) * u) = x * (z * u).
x * y = a(z,u,x) * (L(x,u,z) * y).
a(x,y,z) * (L(z,y,x) * u) = z * u.
x * T(y,L(x,z,u)) = a(u,z,x) * (y * L(x,z,u)).
a(x,y,z) * (u * L(z,y,x)) = z * T(u,L(z,y,x)).
(x * y) / (a(z,u,x) * y) = L(x,u,z).
a(x,y,z) * T(u,z) = L(z,y,x) \ (u * z).
L(x,y,z) \ (u * x) = a(z,y,x) * T(u,x).
R(a(x,y,z),L(z,y,x) * u,w) = ((z * u) * w) / ((L(z,y,x) * u) * w).
x * (y * z) = T(x * (y * z),a(x,y,z)).
T(x * (y * z),a(x,y,z)) = x * (y * z).
x * y != L(x,z,u) * z | y = R(z,u,x).
R(x,y,L(z,x,y)) = R(x,y,z).
R(x * y,y,L(z,x,y)) = R(x * y,y,z).
(x / y) * R(y,z,x) = L(x,y,z).
L(x,y,z) = (x / y) * R(y,z,x).
x \ L(x,T(y,x),z) = (y * x) \ (x * R(T(y,x),z,x)).
(x * y) \ (y * R(T(x,y),z,y)) = y \ L(y,T(x,y),z).
L(x * R(x \ 1,y,z),z,x) = z \ L(z,x \ 1,y).
K(x * (y * z),a(x,y,z)) = 1.
K(x * y,a(x / z,z,L(y,x,z))) = 1.
K(x * y,a(x,z,L(y,x,z))) = 1.
a(x,y,L(z,x,y)) = (x * y) \ R(x * y,y,z).
(x * y) \ R(x * y,y,z) = a(x,y,L(z,x,y)).
a(x,K(y,z),u) = K(R(z,x,u),y) * K(y,z).
K(R(x,y,z),u) * K(u,x) = a(y,K(u,x),z).
(x * (a(y,x,z) * u)) / a(y,x,z) = (x * u) * K(a(y,x,z),x * u).
K(x,R(y,z,u)) * K(y,x) = a(z,K(y,x),u).
R(x,y,z) = ((x * z) / (y * z)) * y.
R(x,y,z) / y = (x * z) / (y * z).
R(x / y,z,y) = (x / (z * y)) * z.
R(K(x,y),z,x) / z = T(x,y) / (z * x).
(x / (y * z)) * y = ((x / z) * z) / L(z,y,x / z).
((x / y) * y) / L(y,z,x / y) = (x / (z * y)) * z.
K(x,R(y,z,x)) / z = T(x,y) / (z * x).
T(x,L(y,x,z)) = a(z,x,y) * T(R(x,z,y),y).
a(x,y,z) * T(R(y,x,z),z) = T(y,L(z,y,x)).
T(x,a(y,z,u)) != a(z,y,u) * w | x * a(y,z,u) = w.
L(a(x,y,x \ z),x \ z,y) = (y * (x \ z)) \ ((y / x) * z).
(x * (y \ 1)) \ (x / y) = a(x,y,y).
a(x,y,z) = a(x,y,L(z,x,y)).
a(x,y,L(z,x,y)) = a(x,y,z).
K(x * y,a(x,z,y)) = 1.
T(a(x,y,z),x * z) * 1 = a(x,y,z).
K((x * y) * z,a(y,x,z)) = 1.
T(a(x,y,z),(y * x) * z) * 1 = a(x,y,z).
T(a(x,y,z),x * z) = a(x,y,z).
T(a(x,y,z),(y * x) * z) = a(x,y,z).
a(x,y,z) = ((y * x) * z) \ (a(x,y,z) * ((y * x) * z)).
((x * y) * z) \ (a(y,x,z) * ((x * y) * z)) = a(y,x,z).
a(x,y,z) * R(T(y,z),x,z) = T(y,L(z,y,x)).
L(x,y,z) * T(u,x) = a(y,z,x) * (u * x).
a(x,y,z) * (u * z) = L(z,x,y) * T(u,z).
a(x,y,R(x,z,u)) = a(R(x,z,u) / y,y,x).
a(R(x,y,z) / u,u,x) = a(x,u,R(x,y,z)).
a(x,y,R(x,z,u)) = a(R(x,z,u),y,x).
a(R(x,y,z),u,x) = a(x,u,R(x,y,z)).
T(x,y) / ((z \ x) * K(x,y)) = R(z,x,K(x,y)).
K(a(x,y,z),u) = T(a(x,y,z),u) * a(y,x,z).
T(a(x,y,z),u) * a(y,x,z) = K(a(x,y,z),u).
L(a(x,y,z \ u),u,z) = a(x,y,(u \ z) \ 1).
L(a(x,y,(z / u) \ z),z,z / u) = a(x,y,L(u \ 1,u,z) \ 1).
L(a(x,y,z),z,y) = z \ L(z,y \ 1,x).
L(a(x,y,z),z,y) = z \ L(z,x,y).
a(x,y,z) = L(a(x,y,z),z,y).
L(a(x,y,z),z,y) = a(x,y,z).
x / L(y,z,x / y) = (x / (z * y)) * z.
R(T(x * K(y,x),y),z,u) = R(x,x * (K(y,x) * z),u).
L(x,y,T(z,u)) = L(x,y * z,T(z,u)).
L(x,y * z,T(z,u)) = L(x,y,T(z,u)).
(x \ (x / y)) * L(R(y,z,u),y,x) = a(L(y,y,x),z,u).
a(T(x,y),z,y) = (x * y) \ (y * R(T(x,y),z,y)).
(x * y) \ (y * R(T(x,y),z,y)) = a(T(x,y),z,y).
(x * y) \ (R(x,z,y) * y) = a(T(x,y),z,y).
a(T(x,y),z,y) = T(a(x,z,y),x * y).
T(a(x,y,z),x * z) = a(T(x,z),y,z).
a(T(x,y),z,y) = a(x,z,y).
a(x,y \ 1,z) = a(y,T(x,z),z).
a(x,T(y,z),z) = a(y,x \ 1,z).
L(x,T(y,x),z) = x * a(y,z,x).
a(x,T(y,z),z) = a(x,y,z).
a(x,y,z) * R(T(y,z),x,z) = T(y,z).
L(x,y,z) = L(x,T(y,x),z).
L(x,T(y,x),z) = L(x,y,z).
L(x,T(y / x,x),z) = z \ ((z / (y / x)) * y).
T(x,y) = T(x,L(y,x,z)).
T(x,L(y,x,z)) = T(x,y).
K(L(x,y,z),y) = T(y,x) \ y.
K(x,y) = K(L(x,y,z),y).
K(L(x,y,z),y) = K(x,y).
L(x,x \ y,z) = z \ ((z / (y / x)) * y).
((x * y) * z) \ (x * (y * z)) = a(y,x,z).
a(x,y,z) = ((y * x) * z) \ (y * (x * z)).
a(x \ y,x,z) = (y * z) \ (x * ((x \ y) * z)).
(x * y) \ (z * ((z \ x) * y)) = a(z \ x,z,y).
(x * y) \ (z * ((z \ x) * y)) = a(x,z,y).
a(x,y,z) = (x * z) \ (y * ((y \ x) * z)).
R(T(x * K(y,x),y),z,u) = R(x,K(y,x) * z,u).
R(x,y,z) = R(x,K(u,x) * y,z).
R(x,K(y,x) * z,u) = R(x,z,u).
R(x,y,z) = R(x,K(x,u) * y,z).
R(x,K(x,y) * z,u) = R(x,z,u).
L(x,y,K(z,y) * u) = R(y,u,x) * (y \ x).
L(x,K(y,z) * u,y) = y * (R(y,u,x) \ x).
L(x,y,z) = L(x,y,K(u,y) * z).
L(x,y,K(z,y) * u) = L(x,y,u).
L(x,y,z) = L(x,y,K(y,u) * z).
L(x,y,K(y,z) * u) = L(x,y,u).
L(x,y,(y * z) \ u) = L(x,y,(z * y) \ u).
L(x,y,(z * y) \ u) = L(x,y,(y * z) \ u).
L(x,y,z \ 1) = L(x,y,K(u,y) / z).
L(x,y,K(z,y) / u) = L(x,y,u \ 1).
L(x,y,K(z,y) / u) = L(x,u,y).
L(x,y,K(z,y) * (u \ K(z,y))) = L(x,K(z,y) \ u,y).
L(x,y,z) = L(x,K(z,u) * y,z).
L(x,K(y,z) * u,y) = L(x,u,y).
a(L(x,x,y),z,u) = y \ ((y / x) * R(x,z,u)).
x \ ((x / y) * R(y,z,u)) = a(L(y,y,x),z,u).
a(L(x,x,y),z,u) = L(a(x,z,u),x,y).
a(L(T(x,y),T(x,y),T(y,x)),z,u) = L(a(T(x,y),z,u),x,y).
L(x,K(y,z) \ u,z) = L(x,z,u \ K(y,z)).
L(x,K(y,z) * u,y) = L(x,y,u \ K(z,y)).
L(x,y,z \ K(u,y)) = L(x,z,y).
a(x,y \ K(z,x),u) = u \ L(u,y,x).
a(x,y,z) = a(y,x \ K(u,y),z).
a(x,y \ K(z,x),u) = a(y,x,u).
T(x,x \ 1) / y = R((y * (x \ 1)) \ 1,x,x).
R((x * (y \ 1)) \ 1,y,y) = T(y,y \ 1) / x.
R((x * (y \ 1)) \ 1,y,y) = y / x.
(x * y) \ (R(x,z,u) * y) = L(a(T(x,y),z,u),x,y).
L(a(T(x,y),z,u),x,y) = T(a(x,z,u),x * y).
R(x,y,z) \ (u * a(x,y,z)) = x \ T(u,a(x,y,z)).
(L(x,y,z) * R(z,y,x)) \ (z * x) = K(z,R(L(x,y,z),y,x)).
(a(x,y,z) * L(z,x,y)) \ L(z,x,y) = a(x,y,z) \ 1.
(a(x,y,z) * L(z,x,y)) \ L(z,x,y) = a(y,x,z).
(x * R(y,z,u)) * y = (x * y) * R(y,z,u).
x * y = ((x / R(y,z,u)) * y) * R(y,z,u).
((x / R(y,z,u)) * y) * R(y,z,u) = x * y.
(x * (y * R(y,z,u))) \ ((x * y) * R(y,z,u)) = a(x,R(y,z,u),y).
(x * (y \ z)) \ ((x / y) * z) = a(y,x,y \ z).
(x * (y \ 1)) \ ((x / R(y,z,u)) * a(y,z,u)) = a(R(y,z,u),x,R(y,z,u) \ a(y,z,u)).
a(R(x,y,z),u,R(x,y,z) \ a(x,y,z)) = (u * (x \ 1)) \ ((u / R(x,y,z)) * a(x,y,z)).
a(T(x,x \ y),z,u) = L(a(T(x,y),z,u),x,y).
L(a(T(x,y),z,u),x,y) = a(T(x,x \ y),z,u).
a(T(x,x \ y),z,u) = T(a(x,z,u),x * y).
a(T(x,x \ T(y,x)),z,u) = T(a(x,z,u),y * x).
a(T(x,x \ y),z,u) = T(a(x,z,u),y * x).
a(T(x \ 1,(x \ 1) \ (y * x)),z,u) = T(a(x \ 1,z,u),R(y,x,x \ 1)).
(L(x,y,z) * R(z,y,x)) \ (z * x) = K(z,L(R(x,y,x),y,z)).
(L(x,y,z) * R(z,y,x)) \ (z * x) = K(z,L(L(x,x,y),y,z)).
(x * y) \ (y * x) = K(y,L(L(x,x,z),z,y)).
K(x,L(L(y,y,z),z,x)) = (y * x) \ (x * y).
K(x,y) = K(x,L(L(y,y,z),z,x)).
K(x,L(L(y,y,z),z,x)) = K(x,y).
T(x,L(L(y,y,z),z,x)) = x * K(x,y).
K(x,y) \ 1 = K(L(L(y,y,z),z,x),x).
K(L(L(x,x,y),y,z),z) = K(z,x) \ 1.
T(x,y) = T(x,L(L(y,y,z),z,x)).
T(x,L(L(y,y,z),z,x)) = T(x,y).
T(x,L(L(y,y,z \ 1),x,z)) = T(x,y).
K(L(L(x,x,y),y,z),z) = K(x,z).
K(L(L(x,x,y \ 1),z,y),z) = K(x,z).
T(x,L(L(y,z,y),x,z)) = T(x,y).
T(x,y) = T(x,L(y,z,y)).
T(x,L(y,z,y)) = T(x,y).
L(x,y,x) * T(z,x) = z * L(x,y,x).
K(L(L(x,y,x),z,y),z) = K(x,z).
K(L(x,y,z),y) = K(L(x,x,z),y).
K(x,y) = K(L(x,z,x),y).
K(L(x,y,x),z) = K(x,z).
K(T(x,x * y),z) = K(T(x,y),z).
(x \ y) * K(y,z) = x \ T(y,z).
K(L(x,y,z),y) = K(x,R(y,z,x)).
K(T(x,y),z) = K(T(x,x \ y),z).
K(T(x,x \ y),z) = K(T(x,y),z).
L(K(x,y),z \ x,u) = u \ ((u / (z \ x)) * (z \ T(x,y))).
x \ ((x / (y \ z)) * (y \ T(z,u))) = L(K(z,u),y \ z,x).
T(x,y) / (z \ T(x,y)) = R(z,x,K(x,y)).
K(x,R(y,z,x)) = K(x,y).
K((x \ (x / y)) \ 1,z) = K(y,z).
x * K(y,z) = (x / y) * T(y,z).
(x / y) * T(y,z) = x * K(y,z).
K(x,y) / z = T(x,y) / (z * x).
T(x,y) / (z * x) = K(x,y) / z.
K(T(x,x \ y),z) = T(K(x,z),y).
(x * y) * K(y,z) = x * T(y,z).
(x * y) * T(L(z,y,x),u) = (x * (y * z)) * K(L(z,y,x),u).
(x * (y * z)) * K(L(z,y,x),u) = (x * y) * T(L(z,y,x),u).
T(x,y) / T(x,z) = K(x,y) / K(x,z).
K(x,y) / K(x,z) = T(x,y) / T(x,z).
x / ((x / K(y,z)) * (K(y,z) / x)) = R(x,K(y,z),y).
T(K(x,y),z) = K(T(x,z),y).
K(T(x,y),z) = T(K(x,z),y).
1 / T(K(x,y),z) = K(y,T(x,z)).
L(K(x,y),z * x,u) = u \ ((u / (z * x)) * (z * T(x,y))).
x \ ((x / (y * z)) * (y * T(z,u))) = L(K(z,u),y * z,x).
a(x,y,y) * (z * y) = z * L(y,x,y).
K(x,y / x) / K(x,y) = a(x,y,x).
x * y != ((x * z) / u) * u | y = z.
((a(x,y,y) * z) / L(y,x,y)) * y = z.
(x \ ((a(y,x \ 1,x \ 1) * (x * z)) / L(x \ 1,y,x \ 1))) / x = z.
R(x,y,K(y,z)) = x.
(x * y) / y = R(x,y,K(x,z)).
R(x,y,K(x,z)) = (x * y) / y.
R(x,y,K(x,z)) = x.
x \ ((y * x) * K(x,z)) = T(y,x) * K(x,z).
x \ (y * T(x,z)) = T(y,x) * K(x,z).
x / 1 = R(x,K(y,z),y).
R(x,K(y,z),y) = x / 1.
R(x,K(y,z),y) = x.
x * T(y,z) = (x * K(y,z)) * y.
(x * K(y,z)) * y = x * T(y,z).
x / K(y,z) = (x * y) / T(y,z).
(x * y) / T(y,z) = x / K(y,z).
L(x,K(x,y),z) = (x * z) / z.
L(x,K(x,y),z) = x.
L(x,y,K(x,z)) = x.
L(x,y,K(x,z) \ y) = x.
(x \ K(y,z)) \ (x \ (K(y,z) * y)) = y.
L(x,y,K(z,x) * y) = x.
x = L(x,y,K(z,x)).
L(x,y,K(z,x)) = x.
T(x * K(y,z),y) = y \ (x * T(y,z)).
x \ (y * T(x,z)) = T(y * K(x,z),x).
x / T(y,z) = (x / y) / K(y,z).
(x / y) / K(y,z) = x / T(y,z).
(x \ K(y,z)) \ (x \ T(y,z)) = y.
T(x * K(y,z),y) = T(x,y) * K(y,z).
x \ (y * (((y \ x) / z) * T(z,u))) = L(K(z,u),y \ z,x).
x \ (y * ((y \ x) * K(z,u))) = L(K(z,u),y \ z,x).
L(K(x,y),z \ x,u) = u \ (z * ((z \ u) * K(x,y))).
L(K(x,y),z,u) = L(K(x,y),u \ x,z).
L(K(x,y),z \ x,u) = L(K(x,y),u,z).
(x * (y * z)) * K(L(z,y,x),u) = (x * y) * L(T(z,u),y,x).
(x * (y * z)) * K(L(z,y,x),u) = x * (y * T(z,u)).
(x * (y * z)) \ (x * (y * T(z,u))) = K(L(z,y,x),u).
K(L(x,y,z),u) = z \ ((z / (y * x)) * (y * T(x,u))).
x \ ((x / (y * z)) * (y * T(z,u))) = K(L(z,y,x),u).
K(L(x,y,z),u) = L(K(x,u),y * x,z).
L(K(x,y),z * x,u) = K(L(x,z,u),y).
L(K(x,y),z \ x,u) = K(L(x,z \ 1,u),y).
K(L(x,y \ 1,z),u) = L(K(x,u),z,y).
K(L(x,y,z),u) = L(K(x,u),y,z).
L(K(x,y),z,u) = K(L(x,z,u),y).
K(x,y) = L(K(x,y),K(z,x),u).
L(K(x,y),K(z,x),u) = K(x,y).
x * K(y,z) = x / K(z,y).
x / K(y,z) = x * K(z,y).
K(x,y) = z \ (z / K(y,x)).
x \ (x / K(y,z)) = K(z,y).
(x / K(y,z)) / K(z,y) = x.
T(x,K(y,z)) = K(y,z) \ (x / K(z,y)).
K(x,y) \ (z / K(y,x)) = T(z,K(x,y)).
(x / y) \ (x / K(z,u)) = y * L(K(u,z),x,y).
(x \ K(y,z)) * K(z,y) = x \ 1.
K(x,y) \ K(z,u) = K(y,x) / K(u,z).
K(x,y) / K(z,u) = K(y,x) \ K(u,z).
K(x,y) \ T(z,K(y,x)) = z / K(x,y).
(K(x,y) \ z) \ (z / K(x,y)) = K(z,K(y,x)).
(x * K(y,z)) / K(y,z) = R(x,K(z,y),K(z,y)).
(x \ y) / K(z,y) = x \ T(y,z).
(x * y) / K(z,y) = x * T(y,z).
(x * y) / T(y,z) = x * K(z,y).
x = R(x,K(y,z),K(y,z)).
R(x,K(y,z),K(y,z)) = x.
(x / T(y,z)) / K(z,y) = x / y.
(x * y) * K(L(z,y,x),u) = x * (y * K(z,u)).
(x / y) * (y * K(z,u)) = x * K(L(z,y,x),u).
K(x,y) * K(L(y,z,u),x) = a(z,u,K(y,x)).
K(L(x,K(x,y) \ z,u),y) = u \ ((u / (z / K(x,y))) * z).
a(x \ 1,K(y,z),u) = a(x \ K(z,y),K(y,z),u).
a(x \ K(y,z),K(z,y),u) = a(x \ 1,K(z,y),u).
x / K(y,z) = (z / x) \ T(z,y).
(x / y) \ T(x,z) = y / K(z,x).
(x * K(y,z)) * T(z,y) = x * z.
L(x,y,z) / T(a(y,z,x),u) = x * K(u,a(y,z,x)).
x / K(y,z) = (x * T(z,y)) / z.
(x * T(y,z)) / y = x / K(z,y).
(x / (y \ z)) / K(y,z / y) = x / (z / y).
T(x,y) \ (z / K(y,x)) = T(z / x,T(x,y)).
(x / K(y,z)) \ (x * T(z,y)) = z.
(K(x,y) / z) \ y = z * T(y,x).
x / (y * T(x,z)) = K(z,x) / y.
x \ y = (x \ K(z,y)) * T(y,z).
(x \ K(y,z)) * T(z,y) = x \ z.
x / y = K(z,x) / (y / T(x,z)).
K(x,y) / (z / T(y,x)) = y / z.
T(x,y) / (z \ x) = 1 / (z \ K(y,x)).
(x / y) \ K(z,x) = y / T(x,z).
T(x,K(y,z)) \ x = K(K(y,z),x / K(y,z)).
K(K(x,y),z / K(x,y)) = T(z,K(x,y)) \ z.
K(x,y) / K(x,x * y) = a(x,y,x).
K(x,K(y,z)) = K(K(z,y),x / K(z,y)).
K(K(x,y),z / K(x,y)) = K(z,K(y,x)).
K(K(x,y),z) = K(K(x,y),z / K(x,y)).
K(K(x,y),z / K(x,y)) = K(K(x,y),z).
K(K(x,y),z / K(x,y)) = T(K(x,y),z) / K(x,y).
T(K(x,y),z) / K(K(x,y),z / K(x,y)) = K(x,y).
K(K(x,y),z) = K(z,K(y,x)).
T(x,K(y,z)) = x / K(x,K(z,y)).
x / K(x,K(y,z)) = T(x,K(z,y)).
K(x,K(y,z)) \ K(y,z) = 1 / T(K(z,y),x).
T(T(x,K(y,z)),K(z,y)) = x.
(K(x,y) \ z) / K(y,x) = T(z,K(x,y)).
K(x,y) \ z = T(z,K(x,y)) / K(x,y).
T(x,K(y,z)) / K(y,z) = K(y,z) \ x.
(T(x,y) \ z) / K(y,x) = T(x \ z,K(x,y)).
K(x,y) \ z = z / T(K(x,y),z).
x / T(K(y,z),x) = K(y,z) \ x.
(K(x,y) \ z) \ z = T(K(x,y),z).
(T(x,y) * z) \ (x * z) = T(K(y,x),x * z).
T(K(x,y),z) = 1 / T(K(y,x),z).
1 / T(K(x,y),z) = T(K(y,x),z).
T(K(x,y),z) = K(x,T(y,z)).
K(x,T(y,z)) = T(K(x,y),z).
x * K(y,T(z,x)) = K(y,z) * x.
K(x,K(y,z)) = K(y,z) / K(y,T(z,x)).
K(x,y) / K(x,T(y,z)) = K(z,K(x,y)).
K(x,K(y,T(z,x))) = K(x,K(y,z)).
K(T(x,y),z) = K(x,T(z,y)).
x / K(y,T(z,x)) = K(y,z) \ x.
K(K(x,y),z) = K(K(x,y),T(z,x)).
K(K(x,y),T(z,x)) = K(K(x,y),z).
K(x,y) * z != z * u | K(x,T(y,z)) = u.
T(K(x,T(y,z)),z) = K(x,T(y,z)) / K(z,K(x,y)).
K(x,T(y,z)) / K(z,K(x,y)) = T(K(x,T(y,z)),z).
K(K(x,y),T(z,x)) = K(z,K(y,x)).
K(K(x,y),y * z) = ((T(y,x) * z) \ (y * z)) / K(x,y).
((T(x,y) * z) \ (x * z)) / K(y,x) = K(K(y,x),x * z).
K(x,T(y,y * z)) = (T(y,x) * z) \ (y * z).
(T(x,y) * z) \ (x * z) = K(y,T(x,x * z)).
R(x,K(y,z),K(y,z)) = (x * K(z,y)) * K(y,z).
(x * K(y,z)) * K(z,y) = R(x,K(z,y),K(z,y)).
(x * (y * K(z,u))) \ R(x * y,K(L(z,y,x),u),K(L(z,y,x),u) \ 1) = K(L(z,y,x),u) \ 1.
R(x,K(y,z),K(y,z)) = R(x,K(z,y),K(y,z)).
R(x,K(y,z),K(z,y)) = R(x,K(z,y),K(z,y)).
R(x,K(y,z),K(z,y)) = x.
a(x \ K(y,z),K(z,y),u) = a(K(z,y),x,u).
K(K(x,y),z / K(x,y)) = K(x,T(y,z)) / K(x,y).
K(x,T(y,z)) / K(K(x,y),z / K(x,y)) = K(x,y).
K(x,T(T(y,z),z)) = K(x,T(y,z)) / K(z,K(x,y)).
K(x,T(y,z)) / K(z,K(x,y)) = K(x,T(T(y,z),z)).
K(x,T(y,z)) / K(x,y) = K(z,K(y,x)).
K(x,T(y,z)) / K(z,K(y,x)) = K(x,y).
K(L(x,K(y,x) * z,u),y) = u \ ((u / (z / K(x,y))) * z).
R(x,a(y,z,u),L(u,z,y)) = ((x * a(y,z,u)) / u) * L(u,z,y).
((x * a(y,z,u)) / u) * L(u,z,y) = R(x,a(y,z,u),L(u,z,y)).
L(a(x,y,z),u,u / z) = a(x,y,L(z \ 1,z,u) \ 1).
a(x,y,L(z \ 1,z,u) \ 1) = L(a(x,y,z),z,u).
a(x,y,L(z,z,u)) = L(a(x,y,z),z,u).
x * a(y,z,L(u,u,x)) = (x / u) * L(u,y,z).
a(x,y,R(y,z,u)) = a(x,R(y,z,u),y).
a(x,R(y,z,u),y) = a(x,y,R(y,z,u)).
(x \ ((a(y,x,x) * (x * z)) / L(x \ 1,y,x \ 1))) / x = z.
(x \ ((x * (a(y,x,x) * z)) / L(x \ 1,y,x \ 1))) / x = z.
(x \ ((L(x,y,x) * z) / L(x \ 1,y,x \ 1))) / x = z.
(x \ ((L(x,y,x) * z) / L(x \ 1,x,y))) / x = z.
x = (y \ (L(y,z,y) * x)) / (y * L(y \ 1,y,z)).
(x \ (L(x,y,x) * z)) / (x * L(x \ 1,x,y)) = z.
(a(x,y,y) * z) / (y * L(y \ 1,y,x)) = z.
(a(x,y,y) * z) / a(y,x,y \ 1) = z.
(a(x,y,y) * z) / a(x,y,y) = z.
x * a(y,z,z) = a(y,z,z) * x.
a(x,y,y) * z = z * a(x,y,y).
T(x,a(y,z,z)) = x.
a(x,y,y) * (z \ 1) = z \ a(x,y,y).
x * (y * a(x,z,z)) = R(x,z,z) * y.
(x * y) * a(x,z,z) = R(x,z,z) * y.
K(x,a(y,z,z)) = 1.
T(x,a(y,z,y)) = x.
1 * ((a(x,y,y) \ z) \ u) = (a(x,y,y) / z) * u.
(a(x,y,y) * z) * a(y,x,y) = z.
x / a(y,z,y) = a(z,y,y) * x.
R(x,y,a(y,z,z)) = (R(y,z,z) * (y \ x)) / a(y,z,z).
(R(x,y,y) * (x \ z)) / a(x,y,y) = R(z,x,a(x,y,y)).
(R(x,y,y) * z) / ((z * x) * a(x,y,y)) = K(x,z).
1 * ((a(x,y,x) * z) \ u) = (a(y,x,x) / z) * u.
(a(x,y,x) * z) \ u = (a(y,x,x) / z) * u.
(a(x,y,y) * z) / a(x,y,y) = R(z,x,a(x,y,y)).
R(x,y,a(y,z,z)) = x.
x * R(y,z,z) = (x * y) * a(y,z,z).
(x * y) * a(y,z,z) = x * R(y,z,z).
(R(x,y,y) * z) / (z * R(x,y,y)) = K(x,z).
K(R(x,y,y),z) = K(x,z).
K(x,y) * (x / z) = T(x,y) / z.
K(x,y) \ (K(x,y) / z) = z \ 1.
K(x,y) = K(x,R(y,z,z)).
K(x,R(y,z,z)) = K(x,y).
T(x,R(y,z,z)) = x * K(x,y).
T(x,y) = T(x,R(y,z,z)).
T(x,R(y,z,z)) = T(x,y).
T(x,y) = T(x,R(y,z,z \ 1)).
T(x,R(y,z,z \ 1)) = T(x,y).
T(x,y) \ (T(x,y) / z) = x \ (x / z).
1 / x = K(y,z) \ (K(y,z) / x).
K(x,y) \ (K(x,y) / z) = 1 / z.
(K(x,y) * z) \ K(x,y) = z \ 1.
K(x,y) \ z = 1 / (z \ K(x,y)).
1 / (x \ K(y,z)) = K(y,z) \ x.
K(x,y) / (1 / z) = K(x,y) * z.
K(x,y) \ (1 / z) = K(y,x) / z.
x \ K(y,z) = (K(z,y) * x) \ 1.
(K(x,y) * z) \ 1 = z \ K(y,x).
T(x,y) / (z \ x) = K(y,x) \ z.
K(x,y) / (z / u) = K(x,y) * (u / z).
(x \ K(y,z)) \ u = (K(z,y) * x) * u.
(x \ y) * L(T(y,z) \ u,T(y,z),x \ y) = (K(z,y) \ x) \ u.
x \ ((y \ (y / x)) \ 1) = a(x,T(y,z),x).
a(x,T(y,z),x) = x \ ((y \ (y / x)) \ 1).
(K(x,y) * z) * (z \ T(y,x)) = y.
L(x,y,K(z,x) * u) = y \ ((y / ((K(z,x) * u) \ 1)) * (u \ T(x,z))).
x \ ((x / ((K(y,z) * u) \ 1)) * (u \ T(z,y))) = L(z,x,K(y,z) * u).
a(x,T(y,z),x) = a(x,y,x).
x \ ((x / (y \ K(z,u))) * (y \ T(z,u))) = L(z,x,K(u,z) * y).
x \ (y * (((y \ x) / K(z,u)) * T(z,u))) = L(z,x,K(u,z) * y).
x \ (y * (((y \ x) * K(z,u)) * T(u,z))) = L(u,x,K(z,u) * y).
x \ (y * ((y \ x) * z)) = L(z,x,K(u,z) * y).
L(x,y,K(z,x) * u) = y \ (u * ((u \ y) * x)).
L(x,y,z) = L(x,y,K(u,x) * z).
L(x,y,K(z,x) * u) = L(x,y,u).
L(x,y \ 1,z) = L(x,K(u,x) * z,y).
L(x,K(y,x) * z,u) = L(x,u \ 1,z).
L(x,K(y,x) * z,u) = L(x,z,u).
K(L(x,y,z),u) = z \ ((z / (y / K(x,u))) * y).
x \ ((x / (y / K(z,u))) * y) = K(L(z,y,x),u).
x \ ((x / (y * K(z,u))) * y) = K(L(u,y,x),z).
L(x * y,z,u) / y = (y \ 1) * L((y \ 1) \ x,z,u).
(x \ 1) * L((x \ 1) \ y,z,u) = L(y * x,z,u) / x.
(x \ 1) * L(x * y,z,u) = L(y * x,z,u) / x.
L(x * y,z,u) / y = y \ L(y * x,z,u).
L(x,y,z) / a(u,w,x) = a(u,w,x) \ L(a(u,w,x) * L(x,w,u),y,z).
a(x,y,z) \ L(a(x,y,z) * L(z,y,x),u,w) = L(z,u,w) / a(x,y,z).
a(x,y,z) \ L(z,u,w) = L(z,u,w) / a(x,y,z).
L(x,y,z) / a(u,w,x) = a(u,w,x) \ L(x,y,z).
L(x,y,z) / a(u,w,x) = a(w,u,x) * L(x,y,z).
(x * (y * z)) \ ((x * y) * z) = a(L(x,u,y),R(y,u,x),z).
a(L(x,y,z),R(z,y,x),u) = (x * (z * u)) \ ((x * z) * u).
a(x,y,z) = a(L(x,u,y),R(y,u,x),z).
a(L(x,y,z),R(z,y,x),u) = a(x,z,u).
a(x,R(y,z,L(x,y,z)),u) = a(L(x,y,z),y,u).
L(x,R(y,z,u),L(u,z,y)) = x / a(u,y,x).
L(x,y,z) = L(x,R(y,u,z),L(z,u,y)).
L(x,R(y,z,u),L(u,z,y)) = L(x,y,u).
a(x,R(y,z,x),u) = a(L(x,y,z),y,u).
a(L(x,y,z),y,u) = a(x,R(y,z,x),u).
a(T(x \ 1,(x \ 1) \ (y * x)),z,u) = T(a(z,x,u),R(y,x,x \ 1)).
a(T(x \ 1,(x \ 1) \ (y * x)),z,u) = T(a(z,x,u),y).
a(T(x \ 1,x * (y * x)),z,u) = T(a(z,x,u),y).
a(T(x,y) \ 1,z,u) = T(a(z,x,u),y).
T(a(x,y,z),u) = a(x,T(y,u),z).
a(x,T(y,z),u) = T(a(x,y,u),z).
x * a(y,T(z,x),u) = a(y,z,u) * x.
K(x,a(y,z,u)) = a(y,T(z,x),u) \ a(y,z,u).
a(x,T(y,z),u) \ a(x,y,u) = K(z,a(x,y,u)).
T(a(x \ 1,y,z),u) = a(T(y,u),x,z).
a(x,T(y,z),u) * L(u,y,x) = K(a(x,y,u),z) * u.
a(x,T(y,z),u) * a(y,x,u) = K(a(x,y,u),z).
L(x,y,z) / a(y,T(z,u),x) = x * K(u,a(y,z,x)).
T(a(x,y,z),u) = a(T(x,u),y,z).
a(T(x,y),z,u) = T(a(x,z,u),y).
a(x,T(y,z),u) = a(T(x,z),y,u).
a(T(x,y),z,u) = a(x,T(z,y),u).
K(x,a(y,z,u)) = a(T(z,x),y,u) * a(y,z,u).
a(T(x,y),z,u) * a(z,x,u) = K(y,a(z,x,u)).
a(x,T(y,z),u) * a(y,x,u) = K(z,a(y,x,u)).
K(x,a(y,z,u)) = K(a(z,y,u),x).
K(a(x,y,z),u) = K(u,a(y,x,z)).
T(x,a(y,z,u)) = x * K(a(z,y,u),x).
x * K(a(y,z,u),x) = T(x,a(z,y,u)).
(x * (a(y,x,z) * u)) / a(y,x,z) = T(x * u,a(x,y,z)).
x * K(y,a(z,u,x)) = a(T(u,y),z,x) * L(x,z,u).
a(T(x,y),z,u) * L(u,z,x) = u * K(y,a(z,x,u)).
a(x,T(y,z),u) * L(u,y,x) = u * K(z,a(y,x,u)).
x * K(y,a(z,u,x)) = K(a(u,z,x),y) * x.
K(a(x,y,z),u) * z = z * K(u,a(y,x,z)).
K(a(x,y,z),T(u,z)) = K(u,a(y,x,z)).
x * (((y / (y * z)) \ (T(z,y) / z)) \ (T(z,y) / z)) = x * (y / (y * z)).
x * (y \ (T(y,z) / y)) = x * (z / (z * y)).
x * (T(y,z) / (y * y)) = x * (z / (z * y)).
x * (K(y,z) / y) = x * (z / (z * y)).
L(x,T(y,y \ z) \ (y * (z / y)),y * (z / y)) = L(x,z / y,y).
L(x,T(y,y \ z) \ (y * (z / y)),y * (z / y)) = L(x,z,y).
L(x,K(y \ z,y) * (z / y),y * (z / y)) = L(x,z,y).
L(x,(y / z) * K(z \ y,z),z * (y / z)) = L(x,y,z).
L(x,y \ z,y * (z / y)) = L(x,z,y).
a(R(x,y,z),u,x \ 1) = (u * (x \ 1)) \ ((u / R(x,y,z)) * a(x,y,z)).
(x * (y \ 1)) \ ((x / R(y,z,u)) * a(y,z,u)) = a(R(y,z,u),x,y \ 1).
(x \ y) * (x * (((y \ z) / y) * (y * u))) = (y * (x * ((x * y) \ z))) * L(u,x,y).
(x \ y) * (x * (y \ (z * u))) = (y * (x * ((x * y) \ z))) * L(u,x,y).
(x * (y * ((y * x) \ z))) * L(u,y,x) = (y \ x) * (y * (x \ (z * u))).
(x * (y * ((y * x) \ z))) * L(u,y,x) = x * (y * ((y * x) \ (z * u))).
(x * (y * ((y * x) \ 1))) * L(z,y,x) = x * (y * ((y * x) \ z)).
(x * (y * ((y * x) \ z))) * L(u,y,x) = (x * (y * ((y * x) \ 1))) * L(z * u,y,x).
(x * (y * ((y * x) \ 1))) * L(z * u,y,x) = (x * (y * ((y * x) \ z))) * L(u,y,x).
(x * (y * ((y * x) \ 1))) * L(z * u,y,x) = ((x * (y * ((y * x) \ 1))) * L(z,y,x)) * L(u,y,x).
((x * (y * ((y * x) \ 1))) * L(z,y,x)) * L(u,y,x) = (x * (y * ((y * x) \ 1))) * L(z * u,y,x).
(x * (y * K(z,u))) \ R(x * y,K(L(z,y,x),u),K(u,L(z,y,x))) = K(L(z,y,x),u) \ 1.
(x * (y * K(z,u))) \ (x * y) = K(L(z,y,x),u) \ 1.
K(L(x,y,z),u) \ 1 = z \ ((z / (y * K(x,u))) * y).
x \ ((x / (y * K(z,u))) * y) = K(L(z,y,x),u) \ 1.
K(L(x,y,z),u) \ 1 = K(L(u,y,z),x).
K(L(x,y,z),u) = K(x,L(u,y,z)).
L(K(x,y),z,u) = K(x,L(y,z,u)).
(x / y) * (y * K(z,u)) = x * K(z,L(u,y,x)).
R(x,x \ y,z) \ R(R(x,x \ y,z),u,w) = ((R(x,u,w) * (x \ y)) * z) / (y * z).
R(x,x \ y,z) \ R(R(x,x \ y,z),u,w) = R(x \ R(x,u,w),y,z).
R(x,y,z) \ R(R(x,x \ y,z),u,w) = R(x \ R(x,u,w),y,z).
R(x,y,z) \ R(R(x,y,z),u,w) = R(x \ R(x,u,w),y,z).
a(R(x,y,z),u,w) = R(x \ R(x,u,w),y,z).
R(x \ R(x,y,z),u,w) = a(R(x,u,w),y,z).
R(a(x,y,z),u,w) = a(R(x,u,w),y,z).
a(R(x,y,z),u,w) = R(a(x,u,w),y,z).
a(R(x,y,z),u,w) * (y * z) = (a(x,u,w) * y) * z.
x / (a(y,z,z) * a(R(z,x,u),y,z)) = R(x,a(z,y,z),u).
R(a(x,y,z) * 1,u,w) = a(R(y,u,w),x,z) \ 1.
R(a(x,y,z) * 1,u,w) = a(x,R(y,u,w),z).
R(a(x,y,z),u,w) = a(x,R(y,u,w),z).
a(x,R(y,z,u),w) = R(a(x,y,w),z,u).
a(R(x,y,z),u,w) = a(x,R(u,y,z),w).
(x * y) / (a(z,R(u,w,v5),x) * y) = L(x,u,R(z,w,v5)).
(x * (y \ 1)) \ ((x / R(y,z,u)) * a(y,z,u)) = a(y,R(x,z,u),y \ 1).
((R(x,y,z) * u) * w) / ((a(x,y,z) * u) * w) = R(x,u,w).
L(x,y,R(z,u,w)) = L(x,R(y,u,w),z).
L(x,R(y,z,u),w) = L(x,y,R(w,z,u)).
L(x,y,R(L(z,u,y),u,z)) = L(x,y,z).
L(x,y,L(R(z,u,z),u,y)) = L(x,y,z).
L(x,y,L(L(z,z,u),u,y)) = L(x,y,z).
x / (a(y,z,z) * a(z,y,R(z,x,u))) = R(x,a(z,y,z),u).
R(x,y,z) = R(x,a(x,u,w) * y,z).
R(x,a(x,y,z) * u,w) = R(x,u,w).
R(x,y,z) = R(x,L(y,u,x),z).
R(x,L(y,z,x),u) = R(x,y,u).
a(x,L(y,z,x),u) = x \ R(x,y,u).
L(x,y,L(z,u,y)) = (x / y) * R(y,z,x).
a(x,y,z) = a(x,L(y,u,x),z).
a(x,L(y,z,x),u) = a(x,y,u).
a(x \ 1,L(y,x,z),u) = a(x \ 1,y,u).
L(x,y,z) = L(x,y,L(z,u,y)).
L(x,y,L(z,u,y)) = L(x,y,z).
L(x,y,z) = L(x,y,L(z,y,u)).
L(x,y,L(z,y,u)) = L(x,y,z).
L(x,y,y \ (z \ u)) = L(x,y,(z * y) \ u).
L(x,y,(z * y) \ u) = L(x,y,y \ (z \ u)).
L(x,y,L(z,z,u)) = L(x,y,z).
L(x,y,L(z,u,z)) = L(x,y,z).
(a(x,L(y,z,y),u) * L(u,x,y)) \ L(u,x,L(y,z,y)) = a(L(y,z,y),x,u).
a(x \ 1,y,z) = a(L(y,x,u),x,z).
a(L(x,y,z),y,u) = a(y \ 1,x,u).
a(L(x,y,z),y,u) = a(x,y,u).
a(x,y,z) = a(x,R(y,u,x),z).
a(x,R(y,z,x),u) = a(x,y,u).
a(x \ 1,y,z) = a(R(y,u,x \ 1),x,z).
a(R(x,y,z \ 1),z,u) = a(z \ 1,x,u).
a(R(x,y,z \ 1),z,u) = a(x,z,u).
a(x,y,z) = a(x,R(y,u,y \ 1),z).
a(x,R(y,z,y \ 1),u) = a(x,y,u).
a(x,L(y,z,y),u) = a(x,y,u).
L(x,y,(z * y) \ u) = L(x,y,z \ u).
(x * (y \ 1)) \ ((x / R(y,z,u)) * a(y,z,u)) = a(R(x,z,u),y,y).
(x * (y \ 1)) \ ((x / R(y,z,u)) * a(y,z,u)) = a(x,R(y,z,u),y).
(x * (y \ 1)) \ ((x / R(y,z,u)) * a(y,z,u)) = a(x,y,R(y,z,u)).
(a(x,y,z) * L(z,x,y)) \ L(z,x,L(y,u,y)) = a(L(y,u,y),x,z).
(a(x,y,z) * L(z,x,y)) \ L(z,x,y) = a(L(y,u,y),x,z).
a(L(x,y,x),z,u) = (a(z,x,u) * L(u,z,x)) \ L(u,z,x).
a(L(x,y,x),z,u) = a(x,z,u).
a(T(x,x * y),z,u) = a(T(x,y),z,u).
a(T(x,y),z,u) = a(x,T(z,x * y),u).
a(x,T(y,x * z),u) = a(T(x,z),y,u).
a(x,T(y,x * z),u) = a(x,T(y,z),u).
(x * y) * a(x,T(z,y),u) = a(x,z,u) * (x * y).
(x * y) * a(x,T(z,y),u) = R(x,z,u) * y.
a(x,y,a(x,T(z,y),u)) = (x * (y * a(x,T(z,y),u))) \ (R(x,z,u) * y).
(x * (y * a(x,T(z,y),u))) \ (R(x,z,u) * y) = a(x,y,a(x,T(z,y),u)).
(x * (a(x,y,z) * u)) \ (R(x,y,z) * u) = a(x,u,a(x,T(y,u),z)).
(R(x,y,z) * u) \ (R(x,y,z) * u) = a(x,u,a(x,T(y,u),z)).
a(x,y,a(x,T(z,y),u)) = 1.
a(x,y,a(x,z,u)) = 1.
R(x,y,a(y,z,u)) = x / 1.
a(x,y,a(z,x,u)) = 1.
1 = a(x,y,a(z,y,u)).
a(x,y,a(z,y,u)) = 1.
L(a(x,y,z),y,u) = a(x,y,z).
R(x,y,a(y,z,u)) = x.
T(x / y,y * a(y,z,u)) = (y * a(y,z,u)) \ (x * a(y,z,u)).
(x * a(x,y,z)) \ (u * a(x,y,z)) = T(u / x,x * a(x,y,z)).
(x * y) * a(x,z,u) = x * (y * a(x,z,u)).
x / a(y,z,u) = (x / (y * a(y,z,u))) * y.
(x / (y * a(y,z,u))) * y = x / a(y,z,u).
(x / R(y,z,u)) * y = x / a(y,z,u).
x * L(R(y,z,u) \ y,R(y,z,u),x) = x / a(y,z,u).
(x / a(y,z,u)) * R(y,z,u) = x * y.
x \ (x * y) = L(y,a(y,z,u),x).
L(x,a(x,y,z),u) = u \ (u * x).
L(x,a(x,y,z),u) = x.
x / y = (x / (a(y,z,u) * y)) * a(y,z,u).
(x / (a(y,z,u) * y)) * a(y,z,u) = x / y.
(x / R(y,z,u)) * a(y,z,u) = x / y.
(x * (y \ 1)) \ (x / y) = a(x,y,R(y,z,u)).
a(x,y,R(y,z,u)) = (x * (y \ 1)) \ (x / y).
a(x,y,R(y,z,u)) = a(x,y,y).
a(x \ 1,y,y) = a(y,x,R(y,z,u)).
a(x,y,R(x,z,u)) = a(y \ 1,x,x).
a(x,y,R(x,z,u)) = a(x,y,x).
x / (a(y,z,z) * a(z,y,z)) = R(x,a(z,y,z),u).
R(x,a(y,z,y),u) = x / (a(z,y,y) * a(y,z,y)).
R(x,a(y,z,y),u) = x / 1.
R(x,a(y,z,y),u) = x.
x * (a(y,z,y) * u) = (x * a(y,z,y)) * u.
(x * a(y,z,y)) * u = x * (a(y,z,y) * u).
(x \ 1) / a(y,z,y) = (a(y,z,y) * x) \ 1.
R(x,a(y,z,z),u) = x.
(a(x,y,x) * z) * u = a(x,y,x) * (z * u).
a(x,a(y,z,z),u) = x \ x.
(a(x,y,y) * z) * u = a(x,y,y) * (z * u).
a(x,a(y,z,z),u) = 1.
L(x,a(y,z,z),u) = x.
(a(x,y,y) * (z \ 1)) * u = a(x,y,y) * (z \ u).
a(x,y * a(z,u,z),w) = (x * w) \ (y * (a(z,u,z) * (((y * a(z,u,z)) \ x) * w))).
(x * y) \ (z * (a(u,w,u) * (((z * a(u,w,u)) \ x) * y))) = a(x,z * a(u,w,u),y).
(a(x,y,x) * z) * u = z * (a(x,T(y,z),x) * u).
x * (a(y,T(z,x),y) * u) = (a(y,z,y) * x) * u.
(a(x,y,x) * z) \ 1 = a(y,x,x) * (z \ 1).
(a(x,y,x) * z) \ 1 = z \ a(y,x,x).
x \ a(y,z,z) = (a(y,z,z) / x) * 1.
(a(x,y,y) / z) * 1 = z \ a(x,y,y).
a(x,y,y) / z = z \ a(x,y,y).
(x \ a(y,z,z)) * u = a(y,z,z) * (x \ u).
x * (a(y,z,y) * u) = (a(y,z,y) * x) * u.
(a(x,y,x) * z) * u = z * (a(x,y,x) * u).
x * (a(y,z,y) * u) = a(y,z,y) * (x * u).
a(x,y,x) * (z * u) = z * (a(x,y,x) * u).
a(x,a(y,z,y) * u,w) = (x * ((a(y,z,y) * u) * w)) \ ((a(y,z,y) * (x * u)) * w).
(x * ((a(y,z,y) * u) * w)) \ ((a(y,z,y) * (x * u)) * w) = a(x,a(y,z,y) * u,w).
x * L(a(y,z,u),R(z,y,u),x) = x / a(z,y,u).
x * L(a(y,z,u),z,R(x,y,u)) = x / a(z,y,u).
x * a(y,z,u) = x / a(z,y,u).
x / a(y,z,u) = x * a(z,y,u).
(x * a(y,z,u)) * a(z,y,u) = x.
(x * a(y,z,u)) \ w = (a(z,y,u) / x) * w.
(a(x,y,z) * u) * a(y,x,z) = u * K(a(x,y,z),u).
x / a(y,z,u) = x * (R(z,y,u) / z).
x * (R(y,z,u) / y) = x / a(z,y,u).
(x * (a(y,x,z) * u)) * a(x,y,z) = T(x * u,a(x,y,z)).
(a(x,y,z) * u) * a(y,x,z) = T(u,a(y,x,z)).
x \ T(x,a(y,z,u)) = K(a(z,y,u) * x,a(y,z,u)).
K(a(x,y,z) * u,a(y,x,z)) = u \ T(u,a(y,x,z)).
K(x,a(y,z,u)) = K(a(z,y,u) * x,a(y,z,u)).
K(a(x,y,z) * u,a(y,x,z)) = K(u,a(y,x,z)).
T(x * y,a(x,z,u)) = x * ((a(z,x,u) * y) * a(x,z,u)).
x * ((a(y,x,z) * u) * a(x,y,z)) = T(x * u,a(x,y,z)).
x * T(y,a(x,z,u)) = T(x * y,a(x,z,u)).
T(x * y,a(x,z,u)) = x * T(y,a(x,z,u)).
T(x * T(y,x),a(x,z,u)) = T(y,a(x,z,u)) * x.
T(x * y,a(y,z,u)) = T(x,a(y,z,u)) * y.
T(T(x,a(y,z,u)),y) = y \ T(x * y,a(y,z,u)).
x \ T(y * x,a(x,z,u)) = T(T(y,a(x,z,u)),x).
(x * a(x,y,z)) \ (u * a(x,y,z)) = T(u / x,R(x,y,z)).
R(x,y,z) \ (u * a(x,y,z)) = T(u / x,R(x,y,z)).
T(x / y,R(y,z,u)) = y \ T(x,a(y,z,u)).
x \ T(y,a(x,z,u)) = T(y / x,R(x,z,u)).
T((x * y) / y,R(y,z,u)) = T(T(x,a(y,z,u)),y).
T(x,R(y,z,u)) = T(T(x,a(y,z,u)),y).
T(T(x,a(y,z,u)),y) = T(x,R(y,z,u)).
T(x,y) \ T(x,R(y,z,u)) = K(T(x,y),a(y,z,u)).
K(T(x,y),a(y,z,u)) = K(x,R(y,z,u)) * K(y,x).
K(x,R(y,z,u)) * K(y,x) = K(T(x,y),a(y,z,u)).
K(T(x,y),a(y,z,u)) = a(z,K(y,x),u).
a(x,K(y,z),u) = K(z,T(a(y,x,u),y)).
K(x,T(a(y,z,u),y)) = a(z,K(y,x),u).
K(x,a(y,z,u)) = a(z,K(y,x),u).
a(x,K(y,z),u) = K(z,a(y,x,u)).
L(x,y,K(z,u)) = x * K(u,a(z,y,x)).
x * K(y,a(z,u,x)) = L(x,u,K(z,y)).
K(x,a(y,z \ K(x,y),u)) = a(K(y,x),z,u).
K(x,a(y,z,u)) = a(K(z,x),y,u).
a(K(x,y),z,u) = K(y,a(z,x,u)).
L(x,K(y,z),u) = x * K(z,a(u,y,x)).
x * K(y,a(z,u,x)) = L(x,K(u,y),z).
L(x,K(y,z),u) = L(x,y,K(u,z)).
(x * y) \ (z * (a(u,w,u) * (((a(w,u,u) / z) * x) * y))) = a(x,z * a(u,w,u),y).
(x * (y * (a(z,u,z) * w))) \ ((a(z,u,z) * (x * y)) * w) = a(x,a(z,u,z) * y,w).
(x * y) \ (z * (a(u,w,u) * (((z \ a(w,u,u)) * x) * y))) = a(x,z * a(u,w,u),y).
(x * (y * (a(z,u,z) * w))) \ ((x * y) * (a(z,u,z) * w)) = a(x,a(z,u,z) * y,w).
(x * y) \ (z * (a(u,w,u) * ((a(w,u,u) * (z \ x)) * y))) = a(x,z * a(u,w,u),y).
a(x,y,a(z,u,z) * w) = a(x,a(z,u,z) * y,w).
a(x,a(y,z,y) * u,w) = a(x,u,a(y,z,y) * w).
(x * y) \ (z * (a(u,w,u) * (a(w,u,u) * ((z \ x) * y)))) = a(x,z * a(u,w,u),y).
(x * y) \ (z * ((z \ x) * y)) = a(x,z * a(u,w,u),y).
a(x,y * a(z,u,z),w) = (x * w) \ (y * ((y \ x) * w)).
a(x,y,z) = a(x,y * a(u,w,u),z).
a(x,y * a(z,u,z),w) = a(x,y,w).
a(x,y,z) = a(x,R(y,u,u),z).
a(x,R(y,z,z),u) = a(x,y,u).
L(x,y,z * a(u,w,u)) = x * a(y,z,x).
a(x,a(y,z,y) * u,w) = a(x,u,w).
L(x,y,R(z,u,u)) = x * a(y,z,x).
a(x,y,z) = a(x,y,a(u,w,u) * z).
a(x,y,a(z,u,z) * w) = a(x,y,w).
L(x,y,z) = L(x,y,R(z,u,u)).
L(x,y,R(z,u,u)) = L(x,y,z).
L(x,y,z / u) = L(x,y,z * (u \ 1)).
L(x,y,z * (u \ 1)) = L(x,y,z / u).
L(x,y,z / (u \ 1)) = L(x,y,z * u).
L(x,y,(1 / z) / u) = L(x,y,z \ (1 / u)).
a(x,y,L(z,z,u)) = a(x,y,z).
x * a(y,z,u) = (x / u) * L(u,y,z).
(x / y) * L(y,z,u) = x * a(z,u,y).
L(x,y,z * u) = L(x,y,z / (1 / u)).
L(x,y,z / (1 / u)) = L(x,y,z * u).
L(x,y,z * (u / w)) = L(x,y,z / (w / u)).
L(x,y,z / (u / w)) = L(x,y,z * (w / u)).
L(x,y,(z / R(u \ 1,w,v5)) * a(u \ 1,w,v5)) = L(x,y,z * u).
(x * a(y,z,u)) * a(z,y,u) = R(x,a(y,z,u),L(u,z,y)).
L(x,y,z) = L(x,y,z * a(u,w,u)).
L(x,y,z * a(u,w,u)) = L(x,y,z).
L(x,y,z) = L(x,y,z / a(u,w,u)).
L(x,y,z / a(u,w,u)) = L(x,y,z).
L(x,y * (z / a(u,w,u)),z) = L(x,y,z / a(u,w,u)).
R(x,a(y,z,u),L(u,z,y)) = x.
T(x / a(y,z,u),a(y,z,u) * L(u,z,y)) = (a(y,z,u) * L(u,z,y)) \ (x * L(u,z,y)).
(a(x,y,z) * L(z,y,x)) \ (u * L(z,y,x)) = T(u / a(x,y,z),a(x,y,z) * L(z,y,x)).
R(x,y / L(y,z,u),L(y,z,u)) = x.
(a(x,y,z) * u) * L(z,y,x) = a(x,y,z) * (u * L(z,y,x)).
x / a(y,z,u) = (x * L(u,z,y)) / u.
(x * L(y,z,u)) / y = x / a(u,z,y).
x / y = (x / L(y,z,u)) / a(u,z,y).
(x / L(y,z,u)) / a(u,z,y) = x / y.
(x / y) \ (x / L(y,z,u)) = a(u,z,y).
a(x,y,z) = (z / u) * (u / L(z,y,x)).
(x / y) * (y / L(x,z,u)) = a(u,z,x).
(L(x,y,z) / u) * (u / x) = a(y,z,L(x,y,z)).
a(x,y,L(z,x,y)) = (L(z,x,y) / u) * (u / z).
(L(x,y,z) / u) * (u / x) = a(y,z,x).
(L(x \ y,z,u) / y) * x = a(z,u,x \ y).
a(x,y,(z * K(u,w)) \ z) = L((z * K(u,w)) \ z,x,y) * K(u,L(w,z,L((z * K(u,w)) \ z,x,y))).
L((x * K(y,z)) \ x,u,w) * K(y,L(z,x,L((x * K(y,z)) \ x,u,w))) = a(u,w,(x * K(y,z)) \ x).
(a(x,y,z) * u) * L(z,y,x) = z * T(u,L(z,y,x)).
L(x,y,(z / R(u \ 1,w,v5)) * a(w,u,v5)) = L(x,y,z * u).
L(x,y,(z / (u / w)) * a(u,w * (u \ 1),u)) = L(x,y,z * (w * (u \ 1))).
L(x,y,z * (u * (w \ 1))) = L(x,y,z / (w / u)).
L(x,y,z * (u * (w \ 1))) = L(x,y,z * (u / w)).
(a(x,y,z) * L(z,y,x)) \ (u * L(z,y,x)) = T(u * a(y,x,z),a(x,y,z) * L(z,y,x)).
(a(x,y,z) * L(z,y,x)) \ (u * L(z,y,x)) = T(u * a(y,x,z),z).
x \ (y * L(x,z,u)) = T(y * a(z,u,x),x).
x \ ((a(y,z,x) \ u) * L(x,y,z)) = T(u * K(a(y,z,x) \ u,a(y,z,x)),x).
T(x * K(a(y,z,u) \ x,a(y,z,u)),u) = u \ ((a(y,z,u) \ x) * L(u,y,z)).
T(x * K(a(y,z,u) \ x,a(y,z,u)),u) = u \ ((a(z,y,u) * x) * L(u,y,z)).
T(x * K(a(y,z,u) \ x,a(y,z,u)),u) = u \ (u * T(x,L(u,y,z))).
T(x * K(a(y,z,u) \ x,a(y,z,u)),u) = T(x,L(u,y,z)).
T(x * K(a(y,z,u) * x,a(z,y,u)),u) = T(x,L(u,z,y)).
T(x * K(x,a(y,z,u)),u) = T(x,L(u,y,z)).
T(T(x,a(y,z,u)),u) = T(x,L(u,y,z)).
T(x,L(y,z,u)) = T(T(x,y),a(z,u,y)).
T(T(x,y),a(z,u,y)) = T(x,L(y,z,u)).
K(a(x,y,z),T(u,z)) = T(u,L(z,x,y)) \ T(u,z).
T(x,L(y,z,u)) \ T(x,y) = K(a(z,u,y),T(x,y)).
K(a(x,y,z),T(u,z)) = K(u,z) * K(L(z,x,y),u).
K(x,y) * K(L(y,z,u),x) = K(a(z,u,y),T(x,y)).
K(x,y) * K(L(y,z,u),x) = K(x,a(u,z,y)).
K(x,a(y,z,u)) = a(z,y,K(u,x)).
a(x,y,K(z,u)) = K(u,a(y,x,z)).
L(x,y,z) * L(u,y,z) = L(x * L(u,L(x,y,z),z * (y * ((y * z) \ 1))),y,z).
L(x * L(y,L(x,z,u),u * (z * ((z * u) \ 1))),z,u) = L(x,z,u) * L(y,z,u).
L(x * L(y,L(x,z,u),u * (z / (z * u))),z,u) = L(x,z,u) * L(y,z,u).
L(x * L(y,L(x,z,u),K(u,z)),z,u) = L(x,z,u) * L(y,z,u).
L(x * L(T(y,L(x,z,u)),L(x,z,u),K(u,z)),z,u) = L(y,z,u) * L(x,z,u).
L(x \ (x / K(y,z)),u,w) * K(y,L(z,x,L((x * K(y,z)) \ x,u,w))) = a(u,w,(x * K(y,z)) \ x).
L(K(x,y),z,u) * K(y,L(x,w,L((w * K(y,x)) \ w,z,u))) = a(z,u,(w * K(y,x)) \ w).
K(x,L(y,z,u)) * K(y,L(x,w,L((w * K(y,x)) \ w,z,u))) = a(z,u,(w * K(y,x)) \ w).
K(x,L(y,z,u)) * K(y,L(x,w,L(w \ (w / K(y,x)),z,u))) = a(z,u,(w * K(y,x)) \ w).
K(x,L(y,z,u)) * K(y,L(x,w,L(K(x,y),z,u))) = a(z,u,(w * K(y,x)) \ w).
a(x,y,(z * K(u,w)) \ z) = K(w,L(u,x,y)) * K(u,L(w,z,L(K(w,u),x,y))).
a(x,y,(z * K(u,w)) \ z) = K(w,L(u,x,y)) * K(u,L(w,z,K(w,L(u,x,y)))).
a(x,y,(z * K(u,w)) \ z) = K(w,L(u,x,y)) * K(u,w).
a(x,y,z \ (z / K(u,w))) = K(w,L(u,x,y)) * K(u,w).
a(x,y,K(z,u)) = K(z,L(u,x,y)) * K(u,z).
K(x,L(y,z,u)) * K(y,x) = a(z,u,K(x,y)).
K(x,L(y,z,u)) * K(y,x) = K(y,a(u,z,x)).
(x \ K(y,x)) \ K(y,a(z,u,x)) = T(T(x,L(y,u,z)),x \ K(y,x)).
T(T(x,L(y,z,u)),x \ K(y,x)) = (K(x,y) * x) * K(y,a(u,z,x)).
T(T(x,L(y,z,u)),x \ K(y,x)) = T(x,y) * K(y,a(u,z,x)).
T(x * K(y,a(z,u,x)),y) = T(T(x,L(y,u,z)),x \ K(y,x)).
T(T(x,L(y,z,u)),x \ K(y,x)) = T(x * K(y,a(u,z,x)),y).
T(T(x,L(y,z,u)),x \ K(y,x)) = T(L(x,z,K(u,y)),y).
L(T(x,y),z,K(u,y)) = T(T(x,L(y,z,u)),x \ K(y,x)).
T(T(x,L(y,z,u)),x \ K(y,x)) = L(T(x,y),z,K(u,y)).
L(T(x,y),z,K(u,y)) = T(x,L(y,z,u)).
L(T(x,y),K(z,y) \ u,K(z,y) * (u / K(z,y))) = T(x,L(y,u,z)).
L(T(x,y),K(y,z) * u,K(z,y) * (u / K(z,y))) = T(x,L(y,u,z)).
L(T(x,y),K(y,z) * u,K(z,y) * (u * K(y,z))) = T(x,L(y,u,z)).
L(T(x,y),K(y,z) * u,T(u,K(y,z))) = T(x,L(y,u,z)).
T(x,L(y,z,u)) = L(T(x,y),K(y,u),T(z,K(y,u))).
L(T(x,y),K(y,z),T(u,K(y,z))) = T(x,L(y,u,z)).
T(x,L(y,z,u)) = L(T(x,y),K(y,u),z).
L(T(x,y),K(y,z),u) = T(x,L(y,u,z)).
T(x,L(y,z,u)) = L(T(x,y),y,K(z,u)).
L(T(x,y),y,K(z,u)) = T(x,L(y,z,u)).
L(x * T(y,L(L(x,z,u),u,z)),z,u) = L(y,z,u) * L(x,z,u).
L(x * T(y,x),z,u) = L(y,z,u) * L(x,z,u).
L(x * y,z,u) = L(x,z,u) * L(y,z,u).
L(x,y,z) * L(u,y,z) = L(x * u,y,z).
L(x * y,z,u) / L(y,z,u) = L(x,z,u).
x * L(y,z,u) = L(L(x,u,z) * y,z,u).
L(L(x,y,z) * u,z,y) = x * L(u,z,y).
L(x,y,z) * u = L(x * L(u,z,y),y,z).
L(x * L(y,z,u),u,z) = L(x,u,z) * y.
L(x,y,z) / L(u,y,z) = L(x / u,y,z).
L(L(x,y,z) * u,z,y) = L(u,z,y) * T(x,u).
L(x \ L(y,z,u),u,z) = L(1 / x,u,z) * y.
L(x,y,z) / L(L(u,y,z),w,v5) = L(x / L(u,w,v5),y,z).
1 / L(x,y,z) = L(1 / x,y,z).
L(1 / x,y,z) = 1 / L(x,y,z).
L(x / R(x,y,z),u,w) = a(y,L(x,u,w),z).
L(R(x,y,z) / x,u,w) = a(L(x,u,w),y,z).
L(1 / x,y,z) * u = L(x,y,z) \ u.
L(1 / x,y,z) \ u = L(x,y,z) * u.
L(x,y,L(1 / z,u,w)) = L(x,L(z,u,w),y).
L(x / y,z,u) * w = L(y / x,z,u) \ w.
L(x / y,z,u) \ w = L(y / x,z,u) * w.
L(a(x,y,z),u,w) = a(x,L(y,u,w),z).
a(x,L(y,z,u),w) = L(a(x,y,w),z,u).
L(a(x,y,z),u,w) = a(L(x,u,w),y,z).
a(L(x,y,z),u,w) = L(a(x,u,w),y,z).
(x / y) / L(x / y,z,u) = x / (L(y / x,z,u) \ y).
L(x,y,z) * T(u,x) = u * L(x,y,z).
T(x / L(y,z,u),y) = L(y,z,u) \ x.
T(x,L(y,z,u)) = T(x,y).
K(x,L(y,z,u)) = T(x,y) / x.
K(x,y) = K(x,L(y,z,u)).
K(x,L(y,z,u)) = K(x,y).
K(x,T(y,y * z)) = K(x,T(y,z)).
K(L(x,y,z),u) = K(x,u).
L(K(x,y),z,u) = K(x,y).
K(x \ y,z) = K(T(y / x,y),z).
K(T(x / y,x),z) = K(y \ x,z).
a(x,y,K(z,u)) = 1.
(x * y) / K(z,u) = x * (y / K(z,u)).
(x / y) \ (x / K(z,u)) = y * K(u,z).
1 = K(x,a(y,z,u)).
K(x,a(y,z,u)) = 1.
T(x,a(y,z,u)) = x.
1 = a(x,K(y,z),u).
a(x,K(y,z),u) = 1.
1 = a(K(x,y),z,u).
a(K(x,y),z,u) = 1.
T(a(x,y,z),u) = a(x,y,z).
x / a(y,z,u) = a(y,z,u) \ x.
T(x,R(y,z,u) / y) = x.
L(x,K(y,z),u) = x.
L(x,y,K(z,u)) = x.
x * (K(y,z) \ u) = (K(y,z) / x) \ u.
(K(x,y) / z) \ u = z * (K(x,y) \ u).
(K(x,y) \ z) * u = K(x,y) \ (z * u).
K(x,y) \ (z * u) = (K(x,y) \ z) * u.
(K(x,y) * z) / u = K(x,y) * (z / u).
(x / R(x,y,z)) \ u = u * (R(x,y,z) / x).
T(x / L(x,y,z),u) = a(z,y,x).
a(T(x,y),z,u) = a(x,z,u).
L(x,y,T(z,u)) = x / a(z,y,x).
K(x,T(y,z * y)) = K(x,T(y,z)).
(T(x,y) * z) \ (x * z) = K(y,T(x,z)).
K(x \ y,y) = K(y / x,y).
K(x / y,x) = K(y \ x,x).
K(x / (x / y),x) = K(y,x).
K((x / y) / x,x) = K(1 / y,x).
x / a(y,z,u) = a(z,y,u) * x.
L(x,y,z) * (x \ u) = u / a(z,y,x).
L(x,y,z) = L(x,y,T(z,u)).
L(x,y,T(z,u)) = L(x,y,z).
L(x,y,z \ u) = L(x,y,u / z).
L(x,y,z / u) = L(x,y,u \ z).
L(x,y,z) = L(x,y,u / (u / z)).
L(x,y,z / (z / u)) = L(x,y,u).
L(x,y,z * u) = L(x,y,u / (1 / z)).
L(x,y,z / (1 / u)) = L(x,y,u * z).
L(x,y,(z * u) / (z * (u / w))) = L(x,y,L(w,u / w,z)).
L(x,y,L(z,u / z,w)) = L(x,y,(w * u) / (w * (u / z))).
L(x,y,(z * y) \ u) = L(x,y,u / (y * z)).
L(x,y,z / (y * u)) = L(x,y,(u * y) \ z).
L(x,y,K(z,u) / (u / w)) = L(x,y,w / T(u,z)).
(x \ y) * L(T(y,z) \ u,T(y,z),y / x) = (K(z,y) \ x) \ u.
L(x,y,z / (u * y)) = L(x,y,u \ z).
L(x,(y / z) / y,u) = L(x,u,z).
L(x,K(y,z) / ((z * y) \ u),w) = L(x,w,(y * z) \ u).
T(x * y,y \ z) = L(y \ z,y,x) \ (x * z).
L(x \ y,x,z) \ (z * y) = T(z * x,x \ y).
(x * y) / K(z,T(u,y)) = x * (K(z,u) \ y).
(x / K(y,z)) / (u * K(z,y)) = x / u.
x / K(y,z) = (u / x) \ (u / K(y,z)).
(x / y) \ (x / K(z,u)) = y / K(z,u).
(K(x,y) \ z) / u = K(y,x) * (z / u).
K(x,T(y,z)) / K(x,y) = K(K(x,y),y * z).
L(x,y,z * u) = L(x,y,u * z).
L(x,y,z / u) = L(x,y,z / (u * y)).
L(x,y,z / (u * y)) = L(x,y,z / u).
(x / K(y,z)) / u = x / (u / K(z,y)).
x \ (y / K(z,u)) = (x \ y) / K(z,u).
(x \ y) / K(z,u) = x \ (y / K(z,u)).
K(x,y) / (z / u) = (K(y,x) \ u) / z.
(K(x,y) \ z) / u = K(y,x) / (u / z).
T((x / K(y,z)) / u,u) = (u \ x) / K(y,z).
(T(x,y) \ z) / K(y,x) = T(z / x,T(x,y)).
x * (R(y,z,u) / y) = y \ (R(y,z,u) * x).
x \ (R(x,y,z) * u) = u * (R(x,y,z) / x).
L(x,y,z / (u * y)) = L(x,y,z / (y * u)).
(K(x,y) / z) \ u = (z * u) / K(x,T(y,u)).
(x * y) / K(z,T(u,y)) = (K(z,u) / x) \ y.
K(K(x,y),y * z) = K(z,K(y,x)).
K(K(x,y),z * y) = K(T(z,y),K(y,x)).
K(T(x,y),K(y,z)) = K(K(z,y),x * y).
1 / K(x,K(y,z)) = K(y * x,K(z,y)).
K(x * y,K(z,x)) = 1 / K(y,K(x,z)).
K(K(x,y),z * y) = K(z,T(K(y,x),y)).
K(x * y,K(z,x)) = K(K(x,z),y).
K(x * y,K(z,x)) = K(y,K(z,x)).
K(x,K(y,x / z)) = K(z,K(y,x / z)).
K(x,K(y,z / x)) = K(z,K(y,z / x)).
K(K(x,y),z * y) = K(z,K(y,x)).
K(x,K(y,z)) = K(x * y,K(y,z)).
K(x * y,K(y,z)) = K(x,K(y,z)).
K(x,K(y,z)) = K(x / y,K(y,z)).
K(x / y,K(y,z)) = K(x,K(y,z)).
T(x / (y / K(z,u)),y) = (y \ x) / K(u,z).
T(x / y,T(y,z)) = T(y \ x,K(y,z)).
T(x,T(y,z)) = T(y \ (x * y),K(y,z)).
T(x \ (y * x),K(x,z)) = T(y,T(x,z)).
T(T(x,y),K(y,z)) = T(x,T(y,z)).
K(T(x,y),K(y,z)) = T(x,T(y,z)) / T(x,y).
T(x,T(y,z)) / T(x,y) = K(T(x,y),K(y,z)).
K(K(x,y),T(z,x)) = T(z,x) / T(z,T(x,y)).
T(x,y) / T(x,T(y,z)) = K(K(y,z),T(x,y)).
x \ (R(x,y,z) * u) = u / a(y,x,z).
x \ y = (R(x,z,u) \ y) / a(z,x,u).
(R(x,y,z) \ u) / a(y,x,z) = x \ u.
L(x,y,z / (y * u)) = L(x,y,z / u).
L(x,(y * z) / u,y) = L(x,y,u / z).
L(x,(y * z) / u,z) = L(x,z,u / T(y,z)).
L(x,y,(z \ u) / K(w,v5)) = L(x,y,u / (z / K(v5,w))).
K(x,T(y,z)) / K(x,y) = K(T(x,y),K(y,z)).
K(x,y) / K(x,T(y,z)) = K(K(y,z),T(x,y)).
K(T(x,y),K(y,z)) = K(z,K(y,x)).
K(x,K(y,z)) = K(z,T(K(y,x),y)).
K(x,T(K(y,z),y)) = K(z,K(y,x)).
K(x,K(y,z)) = K(z,K(y,x)).
K(x,K(y,1 / z)) \ (z \ K(y,x)) = K(y,x) * (1 / z).
K(x,T(y,z)) / K(x,K(y,z)) = K(x,y).
K(x,K(y,z / y)) = K(z,K(y,x)).
K(K(x,y),T(z,x)) = K(y,K(z,x)).
K(K(x,y),T(z,x)) = K(x,K(z,y)).
K(x,K(y,z)) = K(y,K(z,x)).
K(x,K(y,z)) = K(z,K(x,y)).
K(x,T(y,z)) / K(x,K(y,z)) = K(x,T(T(y,z),z)).
K(x,K(y,z)) = K(x,K(z,y)).
K(x,K(y / x,z)) = K(y,K(x,z)).
K(x,K(y / x,z)) = K(y,K(z,x)).
K(x,K(y,z)) = K(y,K(x / z,z)).
K(x,K(y / z,z)) = K(y,K(x,z)).
K(x,K(y,z)) = K(z,K(y,x / z)).
K(x,K(y,z / x)) = K(z,K(y,x)).
K(x,K(1 / y,z)) = K(z / y,K(x,z)).
K(x / y,K(z,x)) = K(z,K(1 / y,x)).
K(x,K(y,z)) = K(x,K(y,x / z)).
K(x,K(y,x / z)) = K(x,K(y,z)).
K(x,K(y,x / z)) = K(z,K(y,x)).
K(x,K(y / z,y)) = K(z,K(x,y)).
K(x,K(1 / y,z)) = K(z,K(x,z / y)).
K(x,K(y / z,y)) = K(x,K(1 / z,y)).
K(x,K(1 / y,z)) = K(x,K(z / y,z)).
K(x,K(y / z,y)) = K(x,K(y,1 / z)).
K(x,K(y,1 / z)) = K(z,K(x,y)).
L((x * y) \ L(z,y,x),x,y) = (y \ (1 / x)) * z.
L(x \ L(y,z,u),u,z) = L(x,u,z) \ y.
L(x \ y,z,u) = L(x,z,u) \ L(y,z,u).
L(x,y,z) \ L(u,y,z) = L(x \ u,y,z).
L(x,y,z) * (L(u,y,z) \ w) = L(x * (u \ L(w,z,y)),y,z).
L(x * (y \ L(z,u,w)),w,u) = L(x,w,u) * (L(y,w,u) \ z).
L(x \ (y * (x / y)),z,u) = K(y,L(x,z,u) / y).
L(K(x,y),y * x,z) \ (z * (x * y)) = T(z * (y * x),(y * x) \ (x * y)).
K(x,T(T(y,z),z)) = K(x,y).
x / K(y,z) = K(y,T(z,x)) \ x.
K(x,T(y,z)) \ z = z / K(x,y).
K(x,T(y,z)) \ (z * y) = (z * y) / K(x,y).
K(x,T(y,z)) \ (z * y) = z * T(y,x).
(x \ (1 / y)) * z = x \ (y \ L(z,x,y)).
x \ (y \ L(z,x,y)) = (x \ (1 / y)) * z.
x \ (y \ z) = (x \ (1 / y)) * L(z,y,x).
(x \ (1 / y)) * L(z,y,x) = x \ (y \ z).
(x \ (1 / y)) \ (x \ (y \ z)) = L(z,y,x).
L(x,y,z) = (z \ (1 / y)) \ (z \ (y \ x)).
L(x * y,x,z) = (z \ (1 / x)) \ (z \ y).
L(K(x,y / x),z,u) = K(x,L(y,z,u) / x).
K(x,L(y,z,u) / x) = K(x,y / x).
K(x,y / x) / K(x,x * (L(y,z,u) / x)) = a(x,L(y,z,u) / x,x).
a(x,y,z / u) = z / (L(u / z,y,x) \ u).
x / (L(y / x,z,u) \ y) = a(u,z,x / y).
((x * y) * z) / (L((y * z) / ((x * y) * z),u,w) \ (y * z)) = a(w,u,R(x,y,z)).
L(x,y,z / (u * w)) = L(x,K(u,w) / ((w * u) \ z),y).
L(x,K(y,z) / ((z * y) \ u),w) = L(x,w,u / (y * z)).
K(x,K(y,z)) \ (x \ K(z,y)) = K(z,y) * (1 / x).
K(x,y) * (1 / z) = T(z,K(y,x)) \ K(x,y).
T(x,K(y,z)) \ K(z,y) = K(z,y) * (1 / x).
K(x,y) \ (1 / z) = T(z,K(x,y)) \ K(y,x).
T(x,K(y,z)) \ K(z,y) = K(y,z) \ (1 / x).
T(x,K(y,z)) \ K(z,y) = K(z,y) / x.
T(L(x / L(x,y,z),u,w),v5) = a(z,y,L(x,u,w)).
L(T(x / L(x,y,z),u),w,v5) = a(z,y,L(x,w,v5)).
L(a(x,y,z),u,w) = a(x,y,L(z,u,w)).
a(x,y,L(z,u,w)) = L(a(x,y,z),u,w).
x * (y * T(a(z,u,w),x * y)) = a(z,u,L(w,y,x)) * (x * y).
a(x,y,a(z,u,w)) = a(z,u,w) / a(z,u,L(w,y,x)).
a(x,y,z) / a(x,y,L(z,u,w)) = a(w,u,a(x,y,z)).
a(x,L(y,z,u),w) = a(x,y,L(w,z,u)).
a(L(x,y,z),u,w) = a(x,u,L(w,y,z)).
L(x,L(y,z,u),w) = x / a(w,y,L(x,z,u)).
x / a(y,z,L(x,u,w)) = L(x,L(z,u,w),y).
L(x,y,L(z,u,w)) = x / a(z,y,L(x,u,w)).
x / a(y,z,L(x,u,w)) = L(x,z,L(y,u,w)).
L(x,y,L(z,u,w)) = L(x,L(y,u,w),z).
L(x,L(y,z,u),w) = L(x,y,L(w,z,u)).
L(x,L(y,y,z),u) = L(x,y,u).
L(x,y,L(1 / z,z,u)) = L(x,z,y).
L(x,y,z \ (z / u)) = L(x,u,y).
L(x,y,(z * (u * z)) \ (z * z)) = L(x,T(u,z),y).
L(x,y,z \ (1 / u)) = L(x,u * z,y).
L(x,y,(1 / z) / u) = L(x,u * z,y).
L(x,y,(1 / z) / u) = L(x,z * u,y).
L(x,y * z,u) = L(x,z * y,u).
L(x,(y / z) \ u,w) = L(x,u * (z / y),w).
L(x,y * (z / (z * u)),w) = L(x,(K(u,z) / u) * y,w).
L(x,(K(y,z) / y) * u,w) = L(x,u * (z / (z * y)),w).
L(x,y,z \ (((u * z) / z) \ z)) = L(x,T(u,z),y).
L(x,y,z \ (u \ z)) = L(x,T(u,z),y).
L(x,y,T(1 / z,u)) = L(x,T(z,u),y).
L(x,T(y,z),u) = L(x,u,1 / y).
L(x,T(y,z),u) = L(x,y,u).
L(x,y \ z,u) = L(x,z / y,u).
L(x,y / z,u) = L(x,z \ y,u).
L(x,y / (z / u),w) = L(x,y * (u / z),w).
L(x,y / ((z * u) / z),w) = L(x,(K(u,z) / u) * y,w).
L(x,y / ((z * u) / z),w) = L(x,(u / K(u,z)) \ y,w).
L(x,(y / K(y,z)) \ u,w) = L(x,u / ((z * y) / z),w).
L(x,y \ (K(z,y) \ u),w) = L(x,u / ((z * y) / z),w).
L(x,(K(y,z) \ u) / z,w) = L(x,u / ((y * z) / y),w).
L(x,K(y,z) / (y / u),w) = L(x,u / ((z * y) / z),w).
L(x,L(y,z,u),L(w,z,u)) = L(y * (w \ L((L(w,z,u) * (1 / L(y,z,u))) * x,u,z)),z,u).
L(x * (y \ L((L(y,z,u) * (1 / L(x,z,u))) * w,u,z)),z,u) = L(w,L(x,z,u),L(y,z,u)).
(x \ y) * L(T(y,z) \ u,y,y / x) = (K(z,y) \ x) \ u.
(x \ y) * L(T(y,z) \ u,x,y) = (K(z,y) \ x) \ u.
(K(x,y) \ z) \ u = z \ (y * (T(y,x) \ u)).
x \ (y * (T(y,z) \ u)) = (K(z,y) \ x) \ u.
x \ (K(y,z) \ u) = (K(z,y) \ x) \ u.
(K(x,y) \ z) \ u = z \ (K(y,x) \ u).
L(x,y,K(z,u) \ w) = y * (w \ (K(u,z) \ (((K(z,u) \ w) * (1 / y)) * x))).
x * (y \ (K(z,u) \ (((K(u,z) \ y) * (1 / x)) * w))) = L(w,x,K(u,z) \ y).
x * (y * a(z,u,w)) = a(z,u,L(w,y,x)) * (x * y).
a(x,y,L(z,u,w)) * (w * u) = w * (u * a(x,y,z)).
(x * y) / a(z,u,L(w,y,x)) = x * (y * a(u,z,w)).
(x * y) / a(z,u,L(w,y,x)) = x * (y / a(z,u,w)).
K(x,y / x) / K(x,L(x * (y / x),z,u)) = a(x,L(y,z,u) / x,x).
K(x,y / x) / K(x,x * (y / x)) = a(x,L(y,z,u) / x,x).
a(x,L(y,z,u) / x,x) = K(x,y / x) / K(x,x * (y / x)).
a(x,L(y,z,u) / x,x) = K(x,y / x) / K(x,x / (x / y)).
a(x,L(y,z,u) / x,x) = K(x,y / x) / K(x,y).
a(x,L(y,z,u) / x,x) = a(x,y,x).
a(x,y,x) = a(x,L(y,z,u),x).
a(x,L(y,z,u),x) = a(x,y,x).
a(x,y,x) = L(a(x,y,x),z,u).
L(a(x,y,x),z,u) = a(x,y,x).
(x * y) / a(z,u,z) = x * (y / a(z,u,z)).
L(x,(y * z) / a(u,w,u),z) = L(x,y,z / a(u,w,u)).
K(x,y) \ (z * (x * y)) = T(z * (y * x),(y * x) \ (x * y)).
T(x * (y * z),(y * z) \ (z * y)) = K(z,y) \ (x * (z * y)).
T(x * (y * z),K(z,y)) = K(z,y) \ (x * (z * y)).
K(x,y) \ (z * (x * y)) = T(z * (y * x),K(x,y)).
T(x * (y * z),K(z,y)) \ (1 / K(z,y)) = K(z,y) * ((1 / K(z,y)) / (x * (z * y))).
x * (y \ (K(z,u) \ ((K(u,z) \ (y * (1 / x))) * w))) = L(w,x,K(u,z) \ y).
x * (y \ (K(z,u) \ (K(u,z) \ ((y * (1 / x)) * w)))) = L(w,x,K(u,z) \ y).
x * (y \ ((y * (1 / x)) * z)) = L(z,x,K(u,w) \ y).
L(x,y,K(z,u) \ w) = y * (w \ ((w * (1 / y)) * x)).
L(x,y,z) = L(x,y,K(u,w) \ z).
L(x,y,K(z,u) \ w) = L(x,y,w).
L(x,y,z * u) = L(x,y,T(z,w) * u).
L(x,y,T(z,u) * w) = L(x,y,z * w).
L(x,y,z / K(u,w)) = L(x,y,z).
L(x,y,z * T(u,w)) = L(x,y,z * u).
L(x,y,K(z,u) / w) = L(x,w,y).
L(x,K(y,z) / u,w) = L(x,w,u).
L(x,y,z / (u / w)) = L(x,y,z / (w \ u)).
L(x,y,z \ u) = L(x,y,u / (z / K(w,v5))).
L(x,y,z / (u / K(w,v5))) = L(x,y,u \ z).
L(x,y / z,u) = L(x,u,z / T(y,w)).
L(x,y,z / T(u,w)) = L(x,u / z,y).
L(x,y,(z * u) \ w) = L(x,y,w / (u * z)).
L(x,y,z / (u * w)) = L(x,y,(w * u) \ z).
L(x,y,z / u) = L(x,u / ((w * z) / w),y).
L(x,y / ((z * u) / z),w) = L(x,w,u / y).
L(x,y,T(R(z,u,w),v5) * (u * w)) = L(x,y,(z * u) * w).
L(x,y,z * (u \ w)) = L(x,y,z * (w / u)).
L(x,y,z * (u / w)) = L(x,y,z * (w \ u)).
L(x,y,(z * u) / K(w,v5)) = L(x,y,z * T(u,v6)).
L(x,(y * z) / u,z) = L(x,y / u,z).
L(x,y / a(z,u,z),w) = L(x,y,w / a(z,u,z)).
L(x,y,z / (((u / w) \ v5) / K(u,w / u))) = L(x,y,z / ((u \ w) * v5)).
L(x,y,z / u) = L(x,y,z / (u / K(w,v5))).
L(x,y,z / (u / K(w,v5))) = L(x,y,z / u).
L(x,y,z / (u * w)) = L(x,y,z / (w * u)).
L(x,y / R(z * u,z,z),w) = L(x,w,(u * z) / y).
L(x,y,z / (u / w)) = L(x,y,z * (u \ w)).
L(x,y,z / ((u / w) \ v5)) = L(x,y,z / (v5 * (w / u))).
L(x,y,(z * u) / (z / w)) = L(x,y,z * ((z / u) \ w)).
L(x,y,z / (K(u,w) / (T(u,v5) * w))) = L(x,y,z * (K(v5,u) \ (w * u))).
L(x,y,z / (u / w)) = L(x,y,(u \ w) * z).
L(x,y,(K(z,u) / w) \ v5) = L(x,y,w * T(v5,v6)).
L(x,y / a(z,u,z),w) = L(x,y,w).
L(x,y \ z,u) = L(x,R(y,w,w) \ z,u).
L(x,R(y,z,z) \ u,w) = L(x,y \ u,w).
L(x,y / z,u) = L(x,R(z,w,w) \ y,u).
L(x,R(y,z,z) \ u,w) = L(x,u / y,w).
L(x,y / R(z,u,u),w) = L(x,y / z,w).
L(x,y,z / (K(u,w) / v5)) = L(x,y,v5 * T(z,v6)).
L(x,y,z / (K(u,w) / v5)) = L(x,y,v5 * z).
L(x,y,(z * u) / w) = L(x,w / (u * z),y).
L(x,y / (z * u),w) = L(x,w,(u * z) / y).
L(x,R(1 / y,z,u),w) = L(x,w,(u * z) / ((y \ z) * u)).
L(x,y,(z * u) / ((w \ u) * z)) = L(x,R(1 / w,u,z),y).
L(x,y,z / (u / (w / v5))) = L(x,y,z / (u * (v5 / w))).
L(x,y,z / ((z / u) / w)) = L(x,y,(z * u) / (z / w)).
L(x,y,(z * u) / (z / w)) = L(x,y,z / ((z / u) / w)).
L(x,y,L(z,u / z,w)) = L(x,y,(w * u) / (w / (z / u))).
L(x,y,(z * L(1 / u,u,z)) / (z / w)) = L(x,y,z / ((z * u) / w)).
L(x,y,R(T(z,u),w,v5) * (w * v5)) = L(x,y,(z * w) * v5).
L(x,y,(z * u) / ((w \ u) * z)) = L(x,y,R(w,u,z)).
L(x,y,(T(z,u) * w) * v5) = L(x,y,(z * w) * v5).
L(x,y,(z * u) * w) = L(x,y,((v5 / (v5 / z)) * u) * w).
L(x,y,((z / (z / u)) * w) * v5) = L(x,y,(u * w) * v5).
L(x,y,(((z / u) / z) \ w) * v5) = L(x,y,(u * w) * v5).
L(x,y,z / (((u / w) / u) / v5)) = L(x,y,(w * v5) * z).
L(x,y,z / ((u / w) / v5)) = L(x,y,((u \ w) * v5) * z).
L(x,y,(z / u) / (z / w)) = L(x,y,z / ((z * u) / w)).
L(x,y,z / ((u \ w) * v5)) = L(x,y,z / ((u / w) \ v5)).
L(x,y,z / ((u / w) \ v5)) = L(x,y,z / ((u \ w) * v5)).
L(x,y,z / (u / (w / v5))) = L(x,y,z / ((w \ v5) * u)).
L(x,y,(z * u) / (z / (w / u))) = L(x,y,R(w,u,z)).
L(x,y,L(z,u / z,w)) = L(x,y,R(z,u,w)).
L(x,y,L(z,u,w)) = L(x,y,R(z,u * z,w)).
L(x,y,R(z,u * z,w)) = L(x,y,L(z,u,w)).
L(x,y,R(z,u,w)) = L(x,y,L(z,u,w)).
L(x,y,z / (K(u,w) / (T(u,v5) * w))) = L(x,y,(K(v5,u) / z) \ (w * u)).
L(x,y,(z * u) / (K(w,u) / v5)) = L(x,y,v5 / (K(u,z) / (T(u,w) * z))).
L(x,y,z / (K(u,w) / (T(u,v5) * w))) = L(x,y,(w * u) / (K(v5,u) / z)).
L(x,y,z / (K(u,w) / (T(u,v5) * w))) = L(x,y,z * (w * u)).
L(x,y,z * (u * w)) = L(x,y,(T(w,v5) * u) * z).
L(x,y,(T(z,u) * w) * v5) = L(x,y,v5 * (w * z)).
L(x,y,(z * u) * w) = L(x,y,w * (u * z)).
L(x,y,z / ((u / w) / v5)) = L(x,y,z * (v5 * (u \ w))).
((x * y) * z) / (L(1 / R(x,y,z),u,w) \ (y * z)) = a(w,u,R(x,y,z)).
((x * y) * z) / (L(R(x,y,z),u,w) * (y * z)) = a(w,u,R(x,y,z)).
((x * y) * z) / ((L(x,u,w) * y) * z) = a(w,u,R(x,y,z)).
R(a(x,y,z),L(z,y,x) * u,w) = a(x,y,R(z,u,w)).
R(a(x,y,z),u / a(x,y,z),w) = a(x,y,R(z,z \ u,w)).
a(x,y,R(z,z \ u,w)) = R(a(x,y,z),u,w).
a(x,y,R(z,u,w)) = R(a(x,y,z),u,w).
a(x,a(y,z,u),w) = a(y,z,u) / a(y,z,R(u,x,w)).
a(x,y,z) / a(x,y,R(z,u,w)) = a(u,a(x,y,z),w).
T(x * (y * z),K(z,y)) \ (1 / K(z,y)) = K(z,y) * (K(y,z) / (x * (z * y))).
K(x,y) \ (K(x,y) / (z * (y * x))) = T(z * (x * y),K(y,x)) \ (1 / K(y,x)).
T(x * (y * z),K(z,y)) \ (1 / K(z,y)) = K(y,z) \ (K(y,z) / (x * (z * y))).
T(x * (y * z),K(z,y)) \ (1 / K(z,y)) = 1 / (x * (z * y)).
T(x * (y * z),K(z,y)) \ K(y,z) = 1 / (x * (z * y)).
1 / (x * (y * z)) = K(z,y) / (x * (z * y)).
K(x,y) / (z * (x * y)) = 1 / (z * (y * x)).
L(x,y,(K(z,u) / w) / (1 / (v5 * (u * z)))) = L(x,y,K(z,u) / ((K(z,u) * w) / (v5 * (z * u)))).
L(x,y,K(z,u) / ((K(z,u) * w) / (v5 * (z * u)))) = L(x,y,(K(z,u) / w) / (1 / (v5 * (u * z)))).
L(x * (y \ L((L(y,z,u) * L(1 / x,z,u)) * w,u,z)),z,u) = L(w,L(x,z,u),L(y,z,u)).
L(x * (y \ L(L(y * (1 / x),z,u) * w,u,z)),z,u) = L(w,L(x,z,u),L(y,z,u)).
L(x * (y \ ((y * (1 / x)) * L(z,u,w))),w,u) = L(z,L(x,w,u),L(y,w,u)).
L(L(L(x,y,z),u,w),z,y) = L(x,L(u,z,y),L(w,z,y)).
L(x,L(y,z,u),L(w,z,u)) = L(x,y,w).
L(x,y,z) = L(x,y,L(L(z,u,w),u,w)).
L(x,y,L(L(z,u,w),u,w)) = L(x,y,z).
L(x,y,L(z,u,w * w)) = L(x,y,z).
L(x,y,((z * z) \ (1 / u)) \ ((z * z) \ w)) = L(x,y,u * w).
L(x,y,(z \ (z \ (1 / u))) \ ((z * z) \ w)) = L(x,y,u * w).
L(x,y,(z \ (z \ (1 / u))) \ (z \ (z \ w))) = L(x,y,u * w).
L(x,y,(z \ (z \ u)) / (z \ (z \ (1 / w)))) = L(x,y,w * u).
L(x,y,(z \ (z \ u)) / ((z \ (1 / w)) / z)) = L(x,y,w * u).
L(x,y,(z \ (z \ u)) / (1 / (z * (w * z)))) = L(x,y,w * u).
L(x,y,z * u) = L(x,y,(w * (z * w)) * (w \ (w \ u))).
L(x,y,(z * (u * z)) * (z \ (z \ w))) = L(x,y,u * w).
L(x,y,z * ((z / (u * z)) \ (z \ w))) = L(x,y,u * w).
L(x,y,z * ((1 / u) \ (z \ w))) = L(x,y,u * w).
L(x,y,z * (u * (z \ w))) = L(x,y,u * w).
L(x,y,z / ((z / u) / w)) = L(x,y,w * u).
L(x,y,z * u) = L(x,y,(w * z) * (u / w)).
L(x,y,(z * u) * (w / z)) = L(x,y,u * w).
L(x,y,(z * u) / (z / w)) = L(x,y,u * w).
L(x,y,(z * u) / w) = L(x,y,u * (w \ z)).
L(x,y,z / (u / w)) = L(x,y,(w * z) / u).
L(x,y,(z * u) / w) = L(x,y,u / (w / z)).
L(x,y,K(z,u) / ((K(z,u) * w) / (v5 * (z * u)))) = L(x,y,(v5 * (u * z)) * (K(z,u) / w)).
L(x,y,(z * (u * w)) / (v5 / K(w,u))) = L(x,y,K(w,u) / ((K(w,u) * v5) / (z * (w * u)))).
L(x,y,K(z,u) / ((K(z,u) * w) / (v5 * (z * u)))) = L(x,y,(v5 * (u * z)) / (w / K(z,u))).
L(x,y,K(z,u) / ((K(z,u) * w) / (v5 * (z * u)))) = L(x,y,(v5 * (u * z)) / w).
L(x,y,K(z,u) / ((K(u,z) \ w) / (v5 * (z * u)))) = L(x,y,(v5 * (u * z)) / w).
L(x,y,K(z,u) / (K(z,u) / ((w * (z * u)) / v5))) = L(x,y,(w * (u * z)) / v5).
L(x,y,(z * (u * w)) / v5) = L(x,y,(z * (w * u)) / v5).
L(x,y,R(z,u,w)) = L(x,y,(u * (w * (u \ z))) / w).
L(x,y,(z * (u * (z \ w))) / u) = L(x,y,R(w,z,u)).
L(x,y,(z * (u * (z \ w))) / u) = L(x,y,L(w,z,u)).
L(x,y,L(z,u,w)) = L(x,y,(w * (u \ z)) / (w / u)).
L(x,y,(z * (u \ w)) / (z / u)) = L(x,y,L(w,u,z)).
L(x,y,L(z,u,w)) = L(x,y,(u \ z) * u).
L(x,y,z / (z / u)) = L(x,y,L(u,z,w)).
L(x,y,L(z,u,w)) = L(x,y,u / (u / z)).
L(x,y,L(z,u,w)) = L(x,y,z).
a(L(x,y,z),u,w) = w / L(w,u,x).
a(x,y,z) = a(L(x,u,w),y,z).
a(L(x,y,z),u,w) = a(x,u,w).
a(x,y,z) = a(x,y,L(z,u,w)).
a(x,y,L(z,u,w)) = a(x,y,z).
a(x,y,z) / a(x,y,z) = a(u,w,a(x,y,z)).
a(x,y,a(z,u,w)) = a(z,u,w) / a(z,u,w).
(x * y) / a(z,u,w) = x * (y / a(z,u,w)).
a(x,y,a(z,u,w)) = 1.
R(x,y,a(z,u,w)) = x / 1.
R(x,y,a(z,u,w)) = x.
(x / a(y,z,u)) / w = x / (w * a(y,z,u)).
R(x,y,z / a(u,w,v5)) = (((x * y) * z) / a(u,w,v5)) / (y * (z / a(u,w,v5))).
(((x * y) * z) / a(u,w,v5)) / (y * (z / a(u,w,v5))) = R(x,y,z / a(u,w,v5)).
(x / a(y,z,u)) / w = x / (w / a(z,y,u)).
(((x * y) * z) / a(u,w,v5)) / ((y * z) / a(u,w,v5)) = R(x,y,z / a(u,w,v5)).
R(x,y,z / a(u,w,v5)) = ((x * y) * z) / (((y * z) / a(u,w,v5)) / a(w,u,v5)).
((x * y) * z) / (((y * z) / a(u,w,v5)) / a(w,u,v5)) = R(x,y,z / a(u,w,v5)).
((x * y) * z) / ((y * z) / (a(u,w,v5) / a(u,w,v5))) = R(x,y,z / a(w,u,v5)).
((x * y) * z) / ((y * z) / 1) = R(x,y,z / a(u,w,v5)).
R(x,y,z / a(u,w,v5)) = ((x * y) * z) / ((y * z) / 1).
R(x,y,z / a(u,w,v5)) = ((x * y) * z) / (y * z).
R(x,y,z) = R(x,y,z / a(u,w,v5)).
R(x,y,z / a(u,w,v5)) = R(x,y,z).
R(x,y,R(z,u,w)) = R(x,y,z).
a(x,y,R(z,u,w)) = y / R(y,x,z).
a(x,y,z) = a(x,y,R(z,u,w)).
a(x,y,R(z,u,w)) = a(x,y,z).
a(x,y,z) / a(x,y,z) = a(u,a(x,y,z),w).
a(x,a(y,z,u),w) = a(y,z,u) / a(y,z,u).
a(x,a(y,z,u),w) = 1.
1 = a(a(x,y,z),u,w).

end_of_list.
