% *********************************************************
% AIM:  L1-distributivity => aK1
% *********************************************************

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
   % ------------

   L(x1,y,z) * L(x2,y,z) = L(x1 * x2,y,z) # label("L1dist").

end_of_list.

formulas(goals).

   a(K(x,y),z,u) = 1 # label("aK1").

end_of_list.

%
% Hints extracted from previously found proofs.
%

formulas(hints).

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

end_of_list.
