% *********************************************************
% AIM:  Moufang => 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
   % ------------

   ((x * y) * x) * z = x * (y * (x * z)) # label("Moufang").

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

end_of_list.
