% *********************************************************
% AIM:  Some properties of K
%
%    K(x,y) = x \ T(x,y)               # label("K_eq_T_a").
%    K(x,y) = y / T(y,x)               # label("K_eq_T_b").
%    K(T(x,y),T(z,y)) = K(x,z)         # label("K_eq_T_c").
% *********************************************************

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).

end_of_list.

formulas(goals).

   K(x,y) = x \ T(x,y)               # label("K_eq_T_a").
   K(x,y) = y / T(y,x)               # label("K_eq_T_b").
   K(T(x,y),T(z,y)) = K(x,z)         # label("K_eq_T_c").

end_of_list.

%
% Hints extracted from previously found proofs.
%

formulas(hints).

K(x,y) = y / T(y,x).
1 * x = x.
x * 1 = x.
x \ (x * y) = y.
x * (x \ y) = y.
(x * y) / y = x.
(x / y) * y = x.
x * y != z | x * u != z | u = y.
x * y != z | u * y != z | u = x.
x * y != x * z | y = z.
x * y != z * y | x = z.
x != y | z * x = z * y.
x != y | x * z = y * 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).
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).
K(c3,c4) != c4 / T(c4,c3).
c4 / T(c4,c3) != K(c3,c4).
1 \ x = x.
x \ x = 1.
x \ (x * (y \ (y * z))) = z.
(x * (x \ 1)) * y = y.
x * (x \ (1 * y)) = y.
x * (y * (y \ 1)) = x.
x \ (y * (y \ (x * z))) = z.
x * (y * (y \ (x \ z))) = z.
x / x = 1.
x / 1 = x.
x / (y \ x) = y.
((1 / x) * x) * y = y.
(x / y) \ x = y.
x \ (((x * y) / z) * z) = y.
(x \ (x * (y / z))) * z = y.
((x * (x \ y)) / z) * z = y.
(((x * y) / z) * z) / y = x.
(((x / y) / z) * z) * y = x.
x != y * z | y \ x = z.
x * y != z | x \ z = y.
x * 1 != y | x = y.
x * (y \ z) != z | x = y.
x != y * z | x / z = y.
x * y != z | z / y = x.
x * (y * (y \ z)) = x * z.
((x / y) * y) * z = x * z.
(x * (x \ y)) * z = y * z.
a(x,y / z,z) = (x * y) \ ((x * (y / z)) * z).
(x * y) \ ((x * (y / z)) * z) = a(x,y / z,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 / 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).
(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(1,x,y) = (x * y) / (x * y).
(x * y) / (x * y) = R(1,x,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).
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.
T(R(T(x,y),z,u),w) = T(T(R(x,z,u),w),y).
T(T(R(x,y,z),u),w) = T(R(T(x,w),y,z),u).
x * y != z | y = x \ z.
x = y \ (1 \ (y * x)).
x \ (1 \ (x * y)) = y.
(x * (x \ 1)) \ y = y.
((1 / x) * x) \ y = y.
x / (y * (y \ 1)) = x.
x / ((1 / y) * y) = x.
T(x,y) = T(T(x,y),x).
T(T(x,y),x) = T(x,y).
(x / (y \ x)) * z = y * z.
(x * y) / K(x,y) = y * x.
(x * (y * z)) / L(z,y,x) = x * y.
(x * y) / T(x,y) = y.
x / (y / ((z \ x) \ y)) = z.
((x / y) \ x) * z = y * z.
1 * x != y | x = y.
x = (y / (1 * x)) \ y.
(x / (1 * y)) \ x = y.
R(x,y,z) \ ((x * y) * z) = y * z.
T(1,x) = 1.
T(x,1) = x.
R(x,x \ 1,y) = y / ((x \ 1) * y).
L(x \ 1,x,y) = (y * x) \ y.
R(1 / x,x,y) = y / (x * y).
x * y != ((x * z) / u) * u | y = z.
T((x * y) / x,x) = y.
x * y != z | x = z / y.
x = (y * T(x,y)) / y.
(x * T(y,x)) / x = y.
x = y \ (x * T(y,x)).
x \ (y * T(x,y)) = y.
(x \ y) * T(x,x \ y) = y.
x * (y * (y \ T(z,x))) = z * x.
x * T(y / x,x) = y.
x * y != y * z | T(x,y) = z.
x * y != z * x | T(z,x) = y.
x * y != y * T(z,y) | x = z.
x * T(y,x) != z * x | z = y.
K(T(x,y),y) = (x * y) \ (T(x,y) * y).
(x * y) \ (T(x,y) * y) = K(T(x,y),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(x \ y,z) = T(T(y / x,z),x).
T(T(x / y,z),y) = T(y \ x,z).
L(x \ y,z,u) = T(L(y / x,z,u),x).
T(L(x / y,z,u),y) = L(y \ x,z,u).
R(x \ y,z,u) = T(R(y / x,z,u),x).
T(R(x / y,z,u),y) = R(y \ x,z,u).
T(x / (x / y),x / y) = y.
K(x \ 1,x) = (x \ 1) * x.
L(x,y \ 1,y) = y * ((y \ 1) * x).
x * ((x \ 1) * y) = L(y,x \ 1,x).
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).
R(x,y,y \ 1) = (x * y) * (y \ 1).
(x * y) * (y \ 1) = R(x,y,y \ 1).
R(x,1 / y,y) = (x * (1 / y)) * y.
(x * (1 / y)) * y = R(x,1 / y,y).
K(T(x,y),x) = 1.
T(T(x,y),z) = T(T(T(x,y),z),x).
T(T(T(x,y),z),x) = T(T(x,y),z).
x * T(x,y) = T(x,y) * x.
T(x,y) * x = x * T(x,y).
x / T(y,y \ x) = y \ x.
(T(x,y) * z) / T(T(x,z),y) = z.
(R(x,y,z) * u) / R(T(x,u),y,z) = u.
(x / (1 * y)) * y = x.
T(x,y) = T(T((z * x) / z,y),z).
T(T((x * y) / x,z),x) = T(y,z).
K(x,(y * x) / y) = 1.
(x * T(T(y,x),z)) / x = T(y,z).
T(x,(y * x) / y) = x.
x \ (y * (y \ x)) = 1.
x \ ((x * y) * L(z,y,x)) = y * z.
x * 1 = y * (y \ x).
x * (x \ y) = y * 1.
x * (x \ y) = y * (z * (z \ 1)).
L(x \ (y \ z),x,y) = (y * x) \ z.
x * (y * (y \ z)) = u * (u \ (x * z)).
x * (x \ (y * z)) = y * (u * (u \ z)).
((1 * x) / y) \ x = y.
((x * (x \ y)) / z) \ y = z.
(x / y) * y = 1 * x.
1 * x != y * z | x / z = y.
(x / y) * y != z * x | 1 = z.
(x / ((y / z) * z)) * y = x.
(((x / y) * y) / z) \ x = z.
((x / y) * y) / z = x / z.
(R(x,y,z) * (y * z)) / z = x * y.
R((x / y) / z,z,y) = x / (z * y).
((x / y) * y) * (x \ z) = z.
((x / y) * y) * z = ((x * z) / u) * u.
((x * y) / z) * z = ((x / u) * u) * y.
x \ (x * y) = z * (z \ y).
(x / (y * (y \ z))) * z = x.
(x * y) / y = (x / z) * z.
x * y != z * y | x = (z / u) * u.
x * y != z * y | (z / u) * u = x.
x * (x \ y) = (y / z) * z.
(x / y) * y = z * (z \ x).
x * K(y \ x,y) = (y \ x) * y.
x * y != (y * x) * z | K(x,y) = z.
(x * y) * z != y * x | K(y,x) = z.
L(K(x,y),y * x,z) = (z * (y * x)) \ (z * (x * y)).
(x * (y * z)) \ (x * (z * y)) = L(K(z,y),y * z,x).
R(x,y,K(y,x)) = (y * x) / (y * K(y,x)).
(x * y) / (x * K(x,y)) = R(y,x,K(x,y)).
(x * y) / T(y * x,K(x,y)) = K(x,y).
T(x,x \ y) * z = ((x \ y) \ y) * z.
x * T(y,y \ z) = x * ((y \ z) \ z).
T((x \ y) \ y,z) = T(T(x,z),x \ y).
T(T(x,y),x \ z) = T((x \ z) \ z,y).
T(x / y,(x / y) \ x) = y \ x.
x * y != z * (z \ (x * u)) | y = u.
x \ ((y / (x \ y)) * z) = z.
x / K(y,y \ x) = (y \ x) * y.
x * (((y / x) \ y) \ z) = z.
((x / y) \ x) * (y \ z) = z.
x != (y \ x) * z | T(y,y \ x) = z.
(x \ y) * z != y | T(x,x \ y) = z.
T(x \ y,T(x,x \ y)) = T(x,x \ y) \ y.
T(x / (x / y),(z / (x / y)) \ z) = y.
(x \ 1) \ K(x \ 1,x) = x.
a((x * y) \ 1,x,y) = K((x * y) \ 1,x * y) \ ((((x * y) \ 1) * x) * y).
K((x * y) \ 1,x * y) \ ((((x * y) \ 1) * x) * y) = a((x * y) \ 1,x,y).
R(x \ 1,x,y) = (K(x \ 1,x) * y) / (x * y).
(K(x \ 1,x) * y) / (x * y) = R(x \ 1,x,y).
T(x \ 1,x) = x \ K(x \ 1,x).
x \ K(x \ 1,x) = T(x \ 1,x).
x \ K(x,1 / x) = 1 / x.
L(x,1 / y,y) = K(y,1 / y) \ (y * ((1 / y) * x)).
K(x,1 / x) \ (x * ((1 / x) * y)) = L(y,1 / x,x).
R(x,y / z,z) * y = (x * (y / z)) * z.
x / (y \ ((x / z) * z)) = y.
R(x / y,y,x \ z) = z / (y * (x \ z)).
(x \ y) \ y = z * (z \ T(x,x \ y)).
R(x,y,y \ z) * z = (x * y) * (y \ z).
R(1,x,y) = 1.
x * L(y \ 1,y,z) = x * ((z * y) \ z).
(x * y) * L(y \ 1,y,x) = x.
L((x \ y) \ 1,x \ y,x) = y \ x.
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).
R((x * y) \ x,z,u) = L(R(y \ 1,z,u),y,x).
L((x * y) \ x,z,u) = L(L(y \ 1,z,u),y,x).
L(L(x \ 1,y,z),x,u) = L((u * x) \ u,y,z).
x / L(y \ 1,y,x) = x * y.
L(x,1 / x,y) = (y * (1 / x)) \ y.
L(x \ 1,x,1 / x) = 1 / x.
L(x \ 1,x,x \ 1) = K(x \ 1,x) \ (x \ 1).
K(x \ 1,x) \ (x \ 1) = L(x \ 1,x,x \ 1).
R(1 / x,x,x \ y) = (x \ y) / y.
R(1 / (x / y),x / y,y) = y / x.
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(x / (y * x),z,u) = R(R(1 / y,z,u),y,x).
R(R(1 / x,y,z),x,u) = R(u / (x * u),y,z).
R(1 / x,x,y) \ y = x * y.
R(1 / x,x,x \ 1) = x \ 1.
R(1 / x,x,1 / x) = (1 / x) / K(x,1 / x).
(1 / x) / K(x,1 / x) = R(1 / x,x,1 / x).
x * T(T(y,x),z) != u * x | u = T(y,z).
x * T(T(y,x),z) != u * x | T(y,z) = u.
((1 / x) * x) * y != z * u | y / u = z.
x / L(y,1 / y,x) = x * (1 / y).
L(x \ 1,x,y) * (((y * x) \ y) \ z) = z.
((x * y) \ x) * (L(y \ 1,y,x) \ z) = z.
L(T(x \ 1,y),x,1 / x) = T(1 / x,y).
R(x,x \ 1,y) \ y = (x \ 1) * y.
R(T(1 / x,y),x,x \ 1) = T(x \ 1,y).
(x * y) \ ((x \ (x * y)) * x) = K(y,x).
K(x,y) = (y * x) \ ((y \ (y * x)) * y).
x \ (y * T(y \ x,y)) = K(y \ x,y).
K(x \ 1,x) \ 1 = K(x,x \ 1).
K(x,1 / x) \ 1 = K(1 / x,x).
L(x \ T(y,z),x,z) = (z * x) \ (y * z).
x * T(x \ (y * x),z) = T(y,z) * x.
x * T(x \ y,z) = T(y / x,z) * x.
T(x / y,z) * y = y * T(y \ x,z).
x * T(y,z) = T((x * y) / x,z) * x.
T((x * y) / x,z) * x = x * T(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).
(x * T(x \ y,z)) / x = T(y / x,z).
T(x,T(T(x,y),z)) = x.
T((x * y) / x,T(y,z)) = (x * y) / x.
(x * T(y,z)) / x = T((x * y) / x,z).
((x / y) * T(y,z)) / (x / y) = T(x / (x / y),z).
(x \ y) * x != y * z | K(x \ y,x) = z.
L(K(x \ y,x),y,z) = (z * y) \ (z * ((x \ y) * x)).
(x * y) \ (x * ((z \ y) * z)) = L(K(z \ y,z),y,x).
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.
L(L(x,y,z),z * y,u) = (u * (z * y)) \ (u * (z * (y * x))).
(x * (y * z)) \ (x * (y * (z * u))) = L(L(u,z,y),y * z,x).
(x * y) * T(L(z,y,x),u) = x * (y * T(z,u)).
(x * y) * R(L(z,y,x),u,w) = x * (y * R(z,u,w)).
(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).
K(x \ 1,x) * L(y,x,x \ 1) = (x \ 1) * (x * y).
L((x \ y) \ z,x \ y,x) = 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(T(x \ y,z),x,u) = T((u * x) \ (u * y),z).
T((x * y) \ (x * z),u) = L(T(y \ z,u),y,x).
(x * y) / L(z \ y,z,x) = x * z.
L(T(x,y) \ z,T(x,y),y) = (x * y) \ (y * z).
L((x \ 1) \ y,x \ 1,x) = x * y.
L(x \ y,x,1 / x) = (1 / x) * y.
x / L(y \ z,y,x / z) = (x / z) * y.
(x * y) * z != u * (y * z) | R(x,y,z) = u.
T(R(x,y,z),u) * (y * z) = (T(x,u) * y) * z.
L(R(x,y,z),u,w) * (y * z) = (L(x,u,w) * y) * z.
R(R(x,y,z),u,w) * (y * z) = (R(x,u,w) * y) * z.
R(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,R(y,z,u),z * u) * ((y * z) * u) = (x * R(y,z,u)) * (z * u).
R(x / y,y,y \ z) = (x * (y \ z)) / z.
R(x / (y / z),y / z,z) = (x * z) / y.
T(R(x / y,y,z),y * z) = (y * z) \ (x * z).
R(x / y,y,y \ 1) = x * (y \ 1).
R(x / (1 / y),1 / y,y) = x * y.
R(x / T(y,z),T(y,z),y) = (x * y) / (y * T(y,z)).
R(x / y,y,x \ z) \ z = y * (x \ z).
(x * y) / L(z,y / z,x) = x * (y / z).
(x * (y * z)) / L(T(y,z),z,x) = x * z.
R(x,x \ y,z) \ (y * z) = (x \ y) * z.
R(x * y,K(y,x),z) \ ((y * x) * z) = K(y,x) * z.
R(x,x \ 1,x) = x / K(x \ 1,x).
x / K(x \ 1,x) = R(x,x \ 1,x).
L(x,y \ 1,y) / ((y \ 1) * x) = y.
x \ L(y,x \ 1,x) = (x \ 1) * y.
x * (y * (x \ 1)) = L(T(y,x \ 1),x \ 1,x).
L(T(x,y \ 1),y \ 1,y) = y * (x * (y \ 1)).
x * K(x \ 1,x) = L(x,x \ 1,x).
(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).
R(x,y,y \ 1) / (y \ 1) = x * y.
R(x,1 / y,y) / y = x * (1 / y).
K(x,1 / x) * x = R(x,1 / x,x).
R((x * y) \ z,u,w) = L(R(y \ (x \ z),u,w),y,x).
L(R(x \ (y \ z),u,w),x,y) = R((y * x) \ z,u,w).
L((x * y) \ z,u,w) = L(L(y \ (x \ z),u,w),y,x).
L(L(x \ (y \ z),u,w),x,y) = L((y * x) \ z,u,w).
L(T(x \ 1,y),x,z / x) = T(z \ (z / x),y).
T(x \ (x / y),z) = L(T(y \ 1,z),y,x / y).
L(x,1 / x,x) = K(x,1 / x) \ x.
K(x,1 / x) \ x = L(x,1 / x,x).
R(T(1 / x,y),x,x \ z) = T((x \ z) / z,y).
T((x \ y) / y,z) = R(T(1 / x,z),x,x \ y).
L(T(x,y),y,x) = T(x,x * y).
T(x,x * y) = T(L(x,y,x),y).
T(L(x,y,x),y) = 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 * T(y,y * x) = L(y,x,y) * x.
(x * T(y,y * x)) / x = L(y,x,y).
L(T((x \ 1) \ y,z),x \ 1,x) = T(x * y,z).
R(x * y,z,u) = L(R((x \ 1) \ y,z,u),x \ 1,x).
L(R((x \ 1) \ y,z,u),x \ 1,x) = R(x * y,z,u).
L(T(x \ y,z),x,1 / x) = T((1 / x) * y,z).
R((1 / x) * y,z,u) = L(R(x \ y,z,u),x,1 / x).
L(R(x \ y,z,u),x,1 / x) = R((1 / 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).
R(T(x / (1 / y),z),1 / y,y) = T(x * y,z).
x \ L(L(y,x \ 1,x),z,u) = (x \ 1) * L(y,z,u).
(1 / x) \ L(L(y,x,1 / x),z,u) = x * L(y,z,u).
L(R(x,y,y \ 1),z,u) / (y \ 1) = L(x,z,u) * y.
L(R(x,1 / y,y),z,u) / y = L(x,z,u) * (1 / y).
R(R(x,1 / y,y),z,u) / y = R(x,z,u) * (1 / y).
K(x,1 / x) * L(x,1 / x,x) = x.
x != K(x,1 / x) * y | L(x,1 / x,x) = y.
K(x,1 / x) * y != x | L(x,1 / x,x) = y.
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).
x * L(y,z,u) = L((x * y) / x,z,u) * x.
L((x * y) / x,z,u) * x = x * L(y,z,u).
(x \ y) * L((x \ y) \ y,z,u) = L(x,z,u) * (x \ y).
x * L(T(y \ 1,x),y,z) = ((z * y) \ z) * x.
((x * y) \ x) * z = z * L(T(y \ 1,z),y,x).
x * R(x,y,z) = R(x,y,z) * x.
R(x,y,z) * x = x * R(x,y,z).
x * R(x \ y,z,u) = R(y / x,z,u) * x.
R(x / y,z,u) * y = y * R(y \ x,z,u).
x * R(y,z,u) = R((x * y) / x,z,u) * x.
R((x * y) / x,z,u) * x = x * R(y,z,u).
(x \ y) * R((x \ y) \ y,z,u) = R(x,z,u) * (x \ y).
(x / y) * R(y,z,u) = R(x / (x / y),z,u) * (x / y).
R(x / (x / y),z,u) * (x / y) = (x / y) * R(y,z,u).
(x * y) * R(T(z,x * y),x,y) = (z * x) * y.
(x * y) * R(L(T(x,y),y,x),z,u) = R(x,z,u) * (x * y).
(x * L(x \ y,z,u)) / x = L(y / x,z,u).
(x * R(x \ y,z,u)) / x = R(y / x,z,u).
T(x / (y * x),y) = R(y \ 1,y,x).
T((x * y) / (z * y),z) = R(z \ x,z,y).
T(x / (y * z),y) = R(y \ (x / z),y,z).
R(x \ (y / z),x,z) = T(y / (x * z),x).
T((x \ y) / y,x) = R(x \ 1,x,x \ y).
T(x / y,y / x) = R((y / x) \ 1,y / x,x).
R((x / y) \ 1,x / y,y) = T(y / x,x / y).
x * R(x \ 1,x,y) = (y / (x * y)) * x.
(x / (y * x)) * y = y * R(y \ 1,y,x).
x * (y * (y \ z)) != u * w | u \ (x * z) = w.
((x / y) * y) * z != u * w | (x * z) / w = u.
K(x,(y \ z) \ z) = (T(y,y \ z) * x) \ (x * ((y \ z) \ z)).
(T(x,x \ y) * z) \ (z * ((x \ y) \ y)) = K(z,(x \ y) \ y).
L(x,y,(z \ u) \ u) = (T(z,z \ u) * y) \ (((z \ u) \ u) * (y * x)).
(T(x,x \ y) * z) \ (((x \ y) \ y) * (z * u)) = L(u,z,(x \ y) \ y).
x * y != ((z * y) / u) * u | x = z.
(x * T(y,y \ z)) / ((y \ z) \ z) = x.
x \ ((y \ z) \ z) = x \ T(y,y \ z).
x \ T(y,y \ z) = x \ ((y \ z) \ z).
K(x,y) = K(y \ (y * x),y).
K(x \ (x * y),x) = K(y,x).
K(x,y) = K(z \ (z * x),y).
K(x \ (x * y),z) = K(y,z).
K((x / y) \ x,z) = K(y,z).
x * y != y * T(z,z * y) | x = L(z,y,z).
T(x / y,(y \ x) * y) = L(y \ x,y,y \ x).
T((x * y) / x,y * x) = L(y,x,y).
T(((x \ y) * x) / (x \ y),y) = L(x,x \ y,x).
(x * y) * L(x,y,x) = ((y * x) / y) * (x * y).
((x * y) / x) * (y * x) = (y * x) * L(y,x,y).
x * ((y * T(z,x)) / y) = ((y * z) / y) * x.
(x * (y \ z)) / x = T((x * (z / y)) / x,y).
T((x * (y / z)) / x,z) = (x * (z \ y)) / x.
((x \ y) \ y) / T(z,z \ T(x,x \ y)) = z \ ((x \ y) \ y).
x \ ((x / y) * (z * y)) = L(T(z,y),y,x / y).
L(T(x,y),y,z / y) = z \ ((z / y) * (x * y)).
R(x,x \ (y / z),z) \ y = (x \ (y / z)) * z.
x * ((y * x) \ (y * (z * x))) = L(z,x,y) * x.
T(R(x,y,K(y,x)),z) * (y * K(y,x)) = (y * K(y,x)) * T((y * K(y,x)) \ (y * x),z).
(x * K(x,y)) * T((x * K(x,y)) \ (x * y),z) = T(R(y,x,K(x,y)),z) * (x * K(x,y)).
L(R(x,y / z,z),u,w) * y = (L(x,u,w) * (y / z)) * z.
L(R(x,y,y \ z),u,w) * z = (L(x,u,w) * y) * (y \ z).
1 = ((x * y) \ x) / L(y \ 1,y,x).
((x * y) \ x) / L(y \ 1,y,x) = 1.
(x * y) * T((x * y) \ x,z) = x * (y * T(y \ 1,z)).
T(x / (y * x),z) * (y * x) = (T(1 / y,z) * y) * x.
T(x,(y * z) \ y) = L(z \ 1,z,y) \ (x * ((y * z) \ y)).
L(x \ 1,x,y) \ (z * ((y * x) \ y)) = T(z,(y * x) \ y).
L(T(x \ 1,x),x,1 / x) = x \ 1.
(1 / x) \ T(1 / x,y) = x * T(x \ 1,y).
T(x \ 1,y) / (x \ 1) = T(1 / x,y) * x.
K(x,y) = L(x \ T(x,y),x,y).
L(T(x \ T(y,z),u),x,z) = T((z * x) \ (y * z),u).
x * ((x \ y) * z) != y * u | L(z,x \ y,x) = u.
x * L(L(y,z \ x,z),u,w) = z * ((z \ x) * L(y,u,w)).
x * ((x \ y) * T(z,y)) = L(z,x \ y,x) * y.
L(T((x \ y) \ z,u),x \ y,x) = T(y \ (x * z),u).
T(x / y,x) = L(y \ x,y,x / y).
L(x \ y,x,y / x) = T(y / x,y).
T(R(x / y,y,y \ z),z) = z \ (x * (y \ z)).
R(T(x / (y / z),u),y / z,z) = T((x * z) / y,u).
R((x * y) / z,u,w) = R(R(x / (z / y),u,w),z / y,y).
R(R(x / (y / z),u,w),y / z,z) = R((x * z) / y,u,w).
x * ((1 / x) * (y * x)) = L(y,x,1 / x) * x.
(1 / x) * ((x \ 1) * x) = x \ 1.
(1 / x) \ (x \ 1) = (x \ 1) * x.
(1 / (1 / x)) * (x * (1 / x)) = (1 / x) \ 1.
(1 / x) * K(x \ 1,x) = x \ 1.
K(x \ 1,x) = (1 / x) \ (x \ 1).
(1 / x) \ (x \ 1) = K(x \ 1,x).
L(x,K(y \ 1,y),1 / y) = (y \ 1) \ ((1 / y) * (K(y \ 1,y) * x)).
(x \ 1) \ ((1 / x) * (K(x \ 1,x) * y)) = L(y,K(x \ 1,x),1 / x).
x \ ((x \ 1) \ 1) = K((x \ 1) \ 1,x \ 1).
K((x \ 1) \ 1,x \ 1) = x \ ((x \ 1) \ 1).
(x \ 1) * L(y,K(x \ 1,x),1 / x) = (1 / x) * (K(x \ 1,x) * y).
(x * (y \ 1)) / L(K(y \ 1,y),1 / y,x) = x * (1 / y).
x / L(K(y \ 1,y),1 / y,x / (y \ 1)) = (x / (y \ 1)) * (1 / y).
(x * y) * T(T(x,x * y),z) = x * (y * T(T(x,y),z)).
T(((x * y) * z) / (x * z),x) = R(y,x,z).
R(x,y,z) = T(((y * x) * z) / (y * z),y).
T(x / (y * z),y) * (y * z) = ((y \ (x / z)) * y) * z.
T((x \ y) / y,x) * y = ((x \ 1) * x) * (x \ y).
(x / y) * (y / x) = (y / x) * R((y / x) \ 1,y / x,x).
(x / y) * R((x / y) \ 1,x / y,y) = (y / x) * (x / y).
K(x,y / (x * y)) = (x * R(x \ 1,x,y)) \ (x * (y / (x * y))).
(x * R(x \ 1,x,y)) \ (x * (y / (x * y))) = K(x,y / (x * y)).
T(x,R(x \ 1,x,y)) = R(x \ 1,x,y) \ ((y / (x * y)) * x).
R(x \ 1,x,y) \ ((y / (x * y)) * x) = T(x,R(x \ 1,x,y)).
x * R(y,x,z) = (((x * y) * z) / (x * z)) * x.
(((x * y) * z) / (x * z)) * x = x * R(y,x,z).
T(R(x,y,x),y * x) = T(x,y).
R(x,y,x) * (y * x) = (y * x) * T(x,y).
R(T(x,y * x),y,x) = T(x,y).
R(T(x,y),y / x,x) = T(x,y / x).
x * R(T(y,x * y),x,y) = y * x.
T(x,y) * (y * x) = (T(x,y * x) * y) * x.
(T(x,y * x) * y) * x = T(x,y) * (y * x).
R(x,1 / x,x) = T(x,1 / x).
R(T(x,1 / x),y,z) = R(R(x,y,z),1 / x,x).
R(R(x,y,z),1 / x,x) = R(T(x,1 / x),y,z).
T(x,1 / x) / x = x * (1 / x).
K(x,1 / x) = T(x,1 / x) / x.
T(x,1 / x) / x = K(x,1 / x).
(x * y) * T(y,x) = (y * x) * y.
(x * y) \ ((y * x) * y) = T(y,x).
T(x,y) = (y * x) \ ((x * y) * x).
T(x,x \ 1) = ((x \ 1) * x) \ x.
((x \ 1) * x) \ x = T(x,x \ 1).
K(x \ 1,x) \ x = T(x,x \ 1).
K(x \ 1,x) * T(x,x \ 1) = x.
K(x \ 1,x) \ x = (x \ 1) \ 1.
K(x \ 1,x) * ((x \ 1) \ 1) = x.
K(x,1 / x) \ (1 / x) = ((1 / x) \ 1) \ 1.
R(T(T(x,y),z),u,w) = T(T(R(x,u,w),z),y).
(x * (1 / y)) * K(y \ 1,y) != z * (y \ 1) | R(x,1 / y,K(y \ 1,y)) = z.
L(1 / x,x,y) * x = x * ((y * x) \ y).
L(1 / (x \ y),x \ y,x) * (x \ y) = (x \ y) * (y \ x).
(x * ((y * x) \ y)) / x = L(1 / x,x,y).
((x \ y) * (y \ x)) / (x \ y) = L(1 / (x \ y),x \ y,x).
(x * L(y,z,u)) / x = L((x * y) / x,z,u).
L((x * y) / x,z,u) = (x * L(y,z,u)) / x.
(x * R(x \ y,z,u)) * (x \ 1) = R(R(y / x,z,u),x,x \ 1).
R(R(x,y,K(y,x)),z,u) * (y * K(y,x)) = (y * K(y,x)) * R((y * K(y,x)) \ (y * x),z,u).
(x * K(x,y)) * R((x * K(x,y)) \ (x * y),z,u) = R(R(y,x,K(x,y)),z,u) * (x * K(x,y)).
(x * R(y,z,u)) / x = R((x * y) / x,z,u).
R((x * y) / x,z,u) = (x * R(y,z,u)) / x.
R((x * y) / x,z,u) \ (x * R(y,z,u)) = x.
((x * y) * R(z,x,y)) / y = (((x * y) * z) / (x * y)) * x.
x * R(y,z,z \ x) = (((x * y) / x) * z) * (z \ x).
(((x * y) / x) * z) * (z \ x) = x * R(y,z,z \ x).
(x * ((y * x) \ z)) / x = L((y \ z) / x,x,y).
L((x \ y) / z,z,x) = (z * ((x * z) \ y)) / z.
(x * K(x,y)) / x = L(T(x,y) / x,x,y).
L(T(x,y) / x,x,y) = (x * K(x,y)) / x.
((x / y) * R(y,z,u)) / (x / y) = R(x / (x / y),z,u).
x * ((y * (x \ z)) / y) = ((y * (z / x)) / y) * x.
((x * (y / z)) / x) * z = z * ((x * (z \ y)) / x).
(x \ y) * ((z * ((x \ y) \ y)) / z) = ((z * x) / z) * (x \ y).
((x * (y / z)) / x) \ (z * ((x * (z \ y)) / x)) = z.
T(x \ 1,y) / (x \ 1) = x * T(x \ 1,y).
(1 / (1 / x)) * (x * (1 / x)) = x.
(1 / (1 / x)) * K(x,1 / x) = x.
T(T(x,y * x) * y,x) = x \ (T(x,y) * (y * x)).
x \ (T(x,y) * (y * x)) = T(T(x,y * x) * y,x).
K(x,1 / x) \ (1 / x) = x \ 1.
K(x,1 / x) * (x \ 1) = 1 / x.
R(T(x \ y,z),u,w) = T(T(R(y / x,u,w),z),x).
T(T(R(x / y,z,u),w),y) = R(T(y \ x,w),z,u).
L((x * (y \ 1)) / x,y,z) = (x * ((z * y) \ z)) / x.
(x * y) * ((z * L(u,y,x)) / z) = x * (y * ((z * u) / z)).
L((x * (y \ 1)) / x,y,z / y) = (x * (z \ (z / y))) / x.
L((x * ((y \ 1) \ z)) / x,y \ 1,y) = (x * (y * z)) / x.
L((x * (y \ z)) / x,y,1 / y) = (x * ((1 / y) * z)) / x.
L((x * ((y \ z) \ u)) / x,y \ z,y) = (x * (z \ (y * u))) / x.
R((x * (1 / y)) / x,y,z) = (x * (z / (y * z))) / x.
((x * R(y,z,u)) / x) * (z * u) = (((x * y) / x) * z) * u.
R((x * ((y / z) / u)) / x,u,z) = (x * (y / (u * z))) / x.
R((x * (y / z)) / x,z,z \ 1) = (x * (y * (z \ 1))) / x.
R((x * (y / (1 / z))) / x,1 / z,z) = (x * (y * z)) / x.
x \ ((x * (1 / y)) * y) = a(x,1 / y,y).
x \ (K(x,1 / x) * x) = a(x,1 / x,x).
x \ R(x,1 / y,y) = a(x,1 / y,y).
T(K(x,1 / x),x) = a(x,1 / x,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).
(x * y) * R((x * y) \ x,z,u) = x * (y * R(y \ 1,z,u)).
L(1 / x,x,y) = L((y * x) \ y,x,1 / x).
L((x * y) \ x,y,1 / y) = L(1 / y,y,x).
(x * y) * L((x * y) \ x,z,u) = x * (y * L(y \ 1,z,u)).
L(x \ y,y \ x,1 / (y \ x)) = L(1 / (y \ x),y \ x,y).
R(x / (y * x),z,u) * (y * x) = (R(1 / y,z,u) * y) * x.
(x * y) * T((x * y) \ (x * z),u) = x * (y * T(y \ z,u)).
(x * y) * T((x * y) \ z,u) = x * (y * T(y \ (x \ z),u)).
(x * y) * L(L(z,T(x,y),y),u,w) = y * (T(x,y) * L(z,u,w)).
(x * y) * R((y * T(x,y)) \ y,z,u) = y * (T(x,y) * R(T(x,y) \ 1,z,u)).
(x * y) * L((y * T(x,y)) \ y,z,u) = y * (T(x,y) * L(T(x,y) \ 1,z,u)).
T((x * y) \ (y * z),u) = L(T(T(x,y) \ z,u),T(x,y),y).
L(T(T(x,y) \ z,u),T(x,y),y) = T((x * y) \ (y * z),u).
T((x * y) / (z * y),u) * (z * y) = (T(x / z,u) * z) * y.
T(x / (y * z),u) * (y * z) = (T((x / z) / y,u) * y) * z.
(T((x / y) / z,u) * z) * y = T(x / (z * y),u) * (z * y).
T(x,y) * (x * y) = (T(x,x * y) * y) * T(x,y).
(T(x,x * y) * y) * T(x,y) = T(x,y) * (x * y).
(x * y) * ((z * ((x * y) \ (u * y))) / z) = ((z * R(u / x,x,y)) / z) * (x * y).
((x * R(y / z,z,u)) / x) * (z * u) = (z * u) * ((x * ((z * u) \ (y * u))) / x).
R(T(T(x / y,z),y * u),y,u) = T((y * u) \ (x * u),z).
x * T(x \ (x / y),z) = (x / y) * (y * T(y \ 1,z)).
(x / y) * (y * T(y \ 1,z)) = x * T(x \ (x / y),z).
R(T(1 / x,y),x,x \ y) = y \ (x \ y).
T((x \ y) / y,z) * y = (T(1 / x,z) * x) * (x \ y).
(x * y) * L(T(x,x * y),z,u) = x * (y * L(T(x,y),z,u)).
x \ T(x * y,z) = (x \ 1) * T((x \ 1) \ y,z).
(x \ 1) * T((x \ 1) \ y,z) = x \ T(x * y,z).
T(x * y,x \ 1) = x * (((x \ 1) \ y) * (x \ 1)).
x * (((x \ 1) \ y) * (x \ 1)) = T(x * y,x \ 1).
T((1 / x) * y,x) = (1 / x) * ((x \ y) * x).
(1 / x) * ((x \ y) * x) = T((1 / x) * y,x).
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 * y) \ x) * (x * y) = x * (y * T(y \ 1,x * y)).
T(x / y,y / x) * y = (((y / x) \ 1) * (y / x)) * x.
T(1 / x,K(x \ 1,x)) = L(x \ 1,x,x \ 1).
L(x,x \ T(x,y),x) = ((x \ T(x,y)) * x) / (x \ T(x,y)).
((x \ T(x,y)) * x) / (x \ T(x,y)) = L(x,x \ T(x,y),x).
x * y != y * L(z,u,w) | x = L((y * z) / y,u,w).
(x * y) / x = L(((y * x) * y) / (y * x),x,y).
L(((x * y) * x) / (x * y),y,x) = (y * x) / y.
T(x \ (x / y),y) = x \ ((x / y) * ((y \ 1) * y)).
x \ ((x / y) * ((y \ 1) * y)) = T(x \ (x / y),y).
x \ (L(y,x \ z,x) * z) = (x \ z) * T(y,z).
x * y != y * R(T(z,y * z),y,z) | x = z.
((x * T(y,x * y)) * y) / (x * y) = y.
x * (y * x) = (y * T(x,y * x)) * x.
(x * T(y,x * y)) * y = y * (x * y).
(x * (y * x)) / x = y * T(x,y * x).
T(x * T(y,x * y),y) = x * y.
T((x / y) * T(y,(x / y) * y),y) = x.
x \ ((y * (x * y)) / y) = T(y,x * y).
T((x / y) * T(y,x),y) = x.
T(x * T(x \ y,y),x \ y) = y.
(x * y) / x = (y / x) * T(x,y).
(x / y) * T(y,x) = (y * x) / y.
((x \ y) * y) / (x \ y) = x * T(x \ y,y).
(x / (y / x)) * T(y / x,x) = y / (y / x).
T(x / y,T(y,x)) = T(y,x) \ ((y * x) / y).
T(x,y) \ ((x * y) / x) = T(y / x,T(x,y)).
(x * 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 * x) * T(L(x \ 1,x,y),y).
(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).
T(x,y * T(y \ x,x)) = x.
T(x,(x * y) * L(T(y \ 1,x),y,x)) = x.
T(x,x * (y * T(y \ 1,x))) = x.
(x / ((x * y) / x)) * y = (x * y) / ((x * y) / x).
(x * y) / ((x * y) / x) = (x / ((x * y) / x)) * y.
L(((x * y) * x) / (x * y),y,x) * y = y * x.
x \ ((y \ x) * y) = (x \ y) * T((x \ y) \ 1,y).
(x \ y) * T((x \ y) \ 1,y) = x \ ((y \ x) * y).
x * y != L(z,x,u) * x | y = (u * x) \ (u * (z * x)).
x = (x * y) \ (x * ((((x * y) * x) / (x * y)) * y)).
(x * y) \ (x * ((((x * y) * x) / (x * y)) * y)) = x.
((x / y) * ((y \ z) \ z)) / (x / y) = T(x / (x / y),y \ z).
((x \ 1) * x) * (x \ y) = y * T(y \ (x \ y),x).
R((x * (y / z)) / x,z,z \ 1) / (z \ 1) = z * ((x * (z \ y)) / x).
((x * (y / (y / z))) / x) \ ((y / z) * ((x * z) / x)) = y / z.
T(x \ (y * (z \ x)),z) = R(T(z \ y,x),z,z \ x).
R(T(x \ y,z),x,x \ z) = T(z \ (y * (x \ z)),x).
T(T(x,x * y) * y,T(x,y)) = x * y.
(x \ 1) * T((x \ 1) \ 1,y) = x \ T(x,y).
(x \ 1) * T((x \ 1) \ (x \ y),z) = x \ T(y,z).
T(1 / (x \ 1),y) * (x \ 1) = 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) \ T(y / x,x).
(x / y) \ T(x / y,y) = (y \ x) * ((x / y) \ 1).
T(x * (y \ 1),z) / (y \ 1) = y * T(y \ x,z).
T(1 / (1 / x),y) * (1 / x) = T(x,y) / x.
((1 / x) \ y) * (1 / x) = T(y * x,1 / x) / x.
T(x * y,1 / y) / y = ((1 / y) \ x) * (1 / y).
T(x * y,z) / y = (1 / y) * T((1 / y) \ x,z).
(1 / x) * T((1 / x) \ y,z) = T(y * x,z) / x.
T(((1 / x) * y) * x,z) / x = (1 / x) * T(y,z).
T(x,y) / x = (1 / x) * T((1 / x) \ 1,y).
(1 / x) * T((1 / x) \ 1,y) = T(x,y) / x.
T(x,y) / x = (1 / x) * T(x,y).
(1 / x) * T(x,y) = T(x,y) / x.
(T(x,y) / x) / T(x,y) = 1 / x.
(1 / x) \ (T(x,y) / x) = T(x,y).
T(1 / x,T(x,y)) = T(x,y) \ (T(x,y) / x).
T(x,y) \ (T(x,y) / x) = T(1 / x,T(x,y)).
(1 / (x / y)) * (y \ x) = T(x / y,y) / (x / y).
T(x / y,y) / (x / y) = (1 / (x / y)) * (y \ x).
(1 / x) * ((x \ y) \ y) = T(x,x \ y) / x.
T(x,x \ y) / x = (1 / x) * ((x \ y) \ y).
T((T(x,y) * (1 / x)) / T(x,y),T(x,y) / x) = L(1 / x,T(x,y),1 / x).
L(x \ 1,x,T(x,y) / x) = T(1 / x,T(x,y)).
((x \ y) \ y) / x = (1 / x) * ((x \ y) \ y).
(1 / x) * ((x \ y) \ y) = ((x \ y) \ y) / x.
x * T(x \ (x / y),y) = (x / y) * ((y \ 1) * y).
(x / y) * ((y \ 1) * y) = x * T(x \ (x / y),y).
K(x,y) = ((y * x) \ y) * T(((y * x) \ y) \ 1,y).
(x * y) * x = x * ((((x * y) * x) / (x * y)) * y).
x * ((((x * y) * x) / (x * y)) * y) = (x * y) * x.
K(x \ 1,x) * (x \ y) = y * T(y \ (x \ y),x).
(x \ T(y,x \ 1)) / (x \ 1) = (x \ 1) \ (x \ y).
(x \ T(y,z)) / (x \ 1) = T((x \ y) / (x \ 1),z).
(x / y) \ (y \ x) = (y \ x) * ((x / y) \ 1).
(x \ y) * ((y / x) \ 1) = (y / x) \ (x \ y).
x * (((y * x) / y) \ 1) = ((y * x) / y) \ (y \ (y * x)).
((x * y) / x) \ (x \ (x * y)) = y * (((x * y) / x) \ 1).
(x * T(x \ y,z)) * (x \ 1) = T(y * (x \ 1),z).
T(x * ((y \ 1) \ 1),z) / ((y \ 1) \ 1) = y \ T(y * x,z).
T(x,1 / y) / y = ((1 / y) \ (x / y)) * (1 / y).
((1 / x) \ (y / x)) * (1 / x) = T(y,1 / x) / x.
(1 / x) \ (T(y * x,z) / x) = T((1 / x) \ y,z).
((1 / x) * T(y,z)) * x = T(((1 / x) * y) * x,z).
T(((1 / x) * y) * x,z) = ((1 / x) * T(y,z)) * x.
(x \ y) / (y / x) = (1 / (y / x)) * (x \ y).
(1 / (x / y)) * (y \ x) = (y \ x) / (x / y).
T(1 / (x / y),y \ x) = (y \ x) \ ((y \ x) / (x / y)).
(x \ y) \ ((x \ y) / (y / x)) = T(1 / (y / x),x \ y).
(1 / (x / (x / y))) * y = ((x / y) \ x) / (x / (x / y)).
((x / y) \ x) / (x / (x / y)) = (1 / (x / (x / y))) * y.
(x / y) * K(y \ 1,y) = x * T(x \ (x / y),y).
((x * y) \ x) \ K(y,x) = T(((x * y) \ x) \ 1,x).
T(((x * y) \ x) \ 1,x) = ((x * y) \ x) \ K(y,x).
T(x,x * K(y,x)) = x.
T(x * y,x) = (((x * y) * x) / (x * y)) * y.
(((x * y) * x) / (x * y)) * y = T(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,x * y) = x.
T(T(x * y,x) / y,y) = R(x,y,T(x,y)).
T(T(x,x / y) / y,(x / y) * y) = x / y.
T(T(R(x,y,y \ 1),x * y) / (y \ 1),(x * y) * (y \ 1)) = x * y.
x * R(y,x,T(y,x)) = T(y * x,y).
T(T(x,x / y) / y,x) = x / y.
(x * (x / y)) / x = T(x,x / y) / y.
T(x,x / y) / y = (x * (x / y)) / x.
T(x / y,y) = T(y \ T(x,x / y),x).
T(x \ T(y,y / x),y) = T(y / x,x).
((x * (x / y)) / x) * y = T(x,x / y).
T(x \ T(y,y / x),y) = x \ y.
T((x \ y) \ T(y,x),y) = (x \ y) \ y.
(x * (y \ x)) / x = y \ T(x,x / y).
x \ T(y,y / x) = (y * (x \ y)) / y.
T(x,x / y) = y * ((x * (y \ x)) / x).
x * ((y * (x \ y)) / y) = T(y,y / x).
(x / y) \ T(x,x / (x / y)) = (x * y) / x.
(x / y) * ((x * y) / x) = T(x,x / (x / y)).
(x * y) * L((x \ y) / y,y,x) = T(y,y / (x * y)).
(x / T(y,x)) * y = T(x,x / (x / T(y,x))).
T(x,x / (x / T(y,x))) = (x / T(y,x)) * y.
(1 / x) \ (T(y,z) / x) = T((1 / x) \ (y / x),z).
T(((1 / x) * y) * x,z) != u * x | (1 / x) * T(y,z) = u.
T(L(x \ 1,x,y) \ 1,y) = ((y * x) \ y) \ K(x,y).
(((x * y) \ x) \ K(y,x)) / (((x * y) \ x) \ 1) = ((x * y) \ x) * T(((x * y) \ x) \ 1,x).
K(x,1 / x) \ (x * (T(x,y) / x)) = L(T(x,y),1 / x,x).
(x * y) * R((x * y) \ (x * z),u,w) = x * (y * R(y \ z,u,w)).
(x * y) * R((x * y) \ z,u,w) = x * (y * R(y \ (x \ z),u,w)).
(x * y) * L((x * y) \ z,u,w) = x * (y * L(y \ (x \ z),u,w)).
K(x \ 1,x) * L(x \ y,x,x \ 1) = (x \ 1) * y.
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.
L(x / (y * z),u,w) * (y * z) = (L((x / z) / y,u,w) * y) * z.
(L((x / y) / z,u,w) * z) * y = L(x / (z * y),u,w) * (z * y).
R((x * y) / (z * y),u,w) * (z * y) = (R(x / z,u,w) * z) * y.
R(x \ T(x,y),K(x \ 1,T(x,y)),z) \ (((x \ 1) * T(x,y)) * z) = K(x \ 1,T(x,y)) * z.
K(x \ 1,x) * R(((x \ 1) * x) \ y,z,u) = (x \ 1) * (x * R(x \ ((x \ 1) \ y),z,u)).
K(x \ 1,x) * L(((x \ 1) * x) \ y,z,u) = (x \ 1) * (x * L(x \ ((x \ 1) \ y),z,u)).
x \ R(x * y,z,u) = (x \ 1) * R((x \ 1) \ y,z,u).
(x \ 1) * R((x \ 1) \ y,z,u) = x \ R(x * y,z,u).
(1 / x) * (x * R(x \ y,z,u)) = R((1 / x) * y,z,u).
x \ L(L(y,x \ 1,x),z,u) != (x \ 1) * w | L(y,z,u) = w.
x \ L(x * y,z,u) = (x \ 1) * L((x \ 1) \ y,z,u).
(x \ 1) * L((x \ 1) \ y,z,u) = x \ L(x * y,z,u).
(1 / x) \ L(1 / x,y,z) = x * L(x \ 1,y,z).
(1 / x) \ L(x \ 1,y,z) = x * L(T(x \ 1,x),y,z).
L(x \ 1,y,z) / (x \ 1) = L(1 / x,y,z) * x.
L(x \ 1,y,z) / (x \ 1) = x * L(x \ 1,y,z).
L(x \ 1,x,y) / (x \ 1) = x * ((y * x) \ y).
(x * ((y * x) \ y)) * (x \ 1) = L(x \ 1,x,y).
(x * ((y * x) \ y)) \ L(x \ 1,x,y) = x \ 1.
((x * y) \ x) / (y \ 1) = y * ((x * y) \ x).
(x * ((y * x) \ y)) * (x \ 1) = (y * x) \ y.
((x * y) \ x) * K(y \ 1,y * ((x * y) \ x)) = (y \ 1) * (y * ((x * y) \ x)).
K(x \ 1,x * ((y * x) \ y)) = L(x \ 1,x,y) \ ((x \ 1) * (x * ((y * x) \ y))).
L(x \ 1,x,y) \ ((x \ 1) * (x * ((y * x) \ y))) = K(x \ 1,x * ((y * x) \ y)).
((x \ y) * (y \ x)) \ L((x \ y) \ 1,x \ y,x) = (x \ y) \ 1.
L(T(x,1 / x),y,z) / x = L(x,y,z) * (1 / x).
T(L(x,y,z),1 / x) / x = L(x,y,z) * (1 / x).
x * (1 / y) != T(z,1 / y) / y | x = (1 / y) \ (z / y).
L(x,y,z) = (1 / x) \ (L(x,y,z) / x).
(1 / x) \ (L(x,y,z) / x) = L(x,y,z).
(1 / x) * L(x,y,z) = L(x,y,z) / x.
T(1 / x,L(x,y,z)) = L(x,y,z) \ (L(x,y,z) / x).
L(x,y,z) \ (L(x,y,z) / x) = T(1 / x,L(x,y,z)).
R(x / 1,y,z) / x = R(1 / (1 / x),y,z) * (1 / x).
R(1 / (1 / x),y,z) * (1 / x) = R(x / 1,y,z) / x.
x * T(x \ (y * z),u) = y * ((y \ x) * T((y \ x) \ z,u)).
x * ((x \ y) * T((x \ y) \ z,u)) = y * T(y \ (x * z),u).
T((x * y) / z,u) * z = (T(x / (z / y),u) * (z / y)) * y.
(T(x / (y / z),u) * (y / z)) * z = T((x * z) / y,u) * y.
(x * R(y,z,z \ x)) / (z \ x) = ((x * y) / x) * z.
(x * y) * ((z * ((x * y) \ x)) / z) = x * (y * ((z * (y \ 1)) / z)).
(x * y) * L((x * (y \ 1)) / x,y,x) = T(x,x / (x * y)).
((x * (y / (z * y))) / x) * (z * y) = (((x * (1 / z)) / x) * z) * y.
x \ T(y,y / (x * y)) = y * ((x \ y) / y).
L(x \ 1,x,y) * T(L(x \ 1,x,y) \ 1,y) = K(x,y).
K(x,y) = L(x \ 1,x,y) * T(L(x \ 1,x,y) \ 1,y).
(x \ 1) * y != K(x \ 1,x) * z | L(x \ y,x,x \ 1) = z.
K(x \ 1,x) * y != (x \ 1) * z | L(x \ z,x,x \ 1) = y.
(x * ((y \ x) / x)) / (y \ x) = ((x * (1 / y)) / x) * y.
x * R(T(y,y * x),z,u) = L(R(y,z,u),x,y) * x.
(T(1 / x,y) * x) * z = (x * z) * T((x * z) \ z,y).
(x * y) * T((x * y) \ y,z) = (T(1 / x,z) * x) * y.
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).
x \ (T(x,y) * z) = T(x,y) * (x \ z).
T(x,y) \ (x * (T(x,y) * z)) = x * z.
x * y != z * (u * (u \ w)) | y = x \ (z * w).
x * (T(x,y) \ z) = T(x,y) \ (x * z).
T(x,y) \ (x * z) = x * (T(x,y) \ z).
x * y != z * (u * (u \ 1)) | y = x \ z.
x * (T(x,y) \ 1) = T(x,y) \ x.
T(x,y) * z = x * (T(x,y) * (x \ z)).
x * (T(x,y) * (x \ z)) = T(x,y) * z.
T(x,y) * (x * (T(x,y) \ z)) = x * z.
T(x,y) * (z * x) = x * (T(x,y) * T(z,x)).
x * (T(x,y) * T(z,x)) = T(x,y) * (z * x).
(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) \ x) / (T(x,y) \ 1) = x.
x \ (T(x,y) \ x) = T(x,y) \ 1.
T(x,y) \ x != x * z | T(x,y) \ 1 = z.
(x / y) * ((y \ x) \ 1) = T(x / y,y) \ (x / y).
T(x / y,y) \ (x / y) = (x / y) * ((y \ x) \ 1).
(T(x,y) \ x) / T(x,T(x,y) \ 1) = T(x,y) \ 1.
(1 / x) * (T(x,y) \ x) = L(T(x,y) \ 1,x,1 / x).
L(T(x,y) \ 1,x,1 / x) = (1 / x) * (T(x,y) \ x).
(T(x,y) \ T(x,z)) / (T(x,y) \ 1) = T(x,z).
(1 / x) * ((T(x,y) \ 1) * x) = T((1 / x) * (T(x,y) \ x),x).
T((1 / x) * (T(x,y) \ x),x) = (1 / x) * ((T(x,y) \ 1) * x).
(T(x,y) * z) / (T(x,y) * (x \ z)) = x.
T(x,y) * (x \ (y * x)) = T(T(x,y * x) * y,x).
T(T(x,y * x) * y,x) = T(x,y) * (x \ (y * x)).
T(x,y) \ z = x * (T(x,y) \ (x \ z)).
x * (T(x,y) \ (x \ z)) = T(x,y) \ z.
x * (T(x,y) \ (T(x,y) / x)) = K(x,T(x,y) / x).
x * (T(x,y) \ y) = T(y,T(x,y)).
x * (T(x,y) \ ((x \ T(x,y)) * z)) = L(z,x \ T(x,y),x).
(x / y) * ((y \ x) \ y) = T(y,T(x / y,y)).
T(x,y) * z != x * u | T(x,y) * (x \ z) = u.
T(T(x,y),x * (T(x,y) \ z)) = (x * (T(x,y) \ z)) \ (x * z).
x * y != z * ((z \ x) * u) | y = L(u,z \ x,z).
T(x,y) * T(T(x,y) \ x,x) = L(x,T(x,y) \ x,T(x,y)).
T(x,y) * (T(x,z) \ 1) = T(x,z) \ T(x,y).
(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,y) = (x / (x / y)) * (y \ (x / y)).
(x / (x / y)) * (y \ (x / y)) = T(x / y,y).
T(x,R(1 / y,y,x)) = ((x * R(1 / y,y,x)) / x) * (y * x).
((x * R(1 / y,y,x)) / x) * (y * x) = T(x,R(1 / y,y,x)).
T(x,R(y,y \ 1,x)) = ((x * R(y,y \ 1,x)) / x) * ((y \ 1) * x).
((x * R(y,y \ 1,x)) / x) * ((y \ 1) * x) = T(x,R(y,y \ 1,x)).
(x / (x / y)) * (y \ (x / y)) = y \ x.
(x \ y) / (x \ (y / x)) = y / (y / x).
x / (y \ ((y * x) / y)) = (y * x) / ((y * x) / y).
(x * y) / ((x * y) / x) = y / (x \ ((x * y) / x)).
(x \ y) \ (y / x) = (y / x) * ((x \ y) \ 1).
(x / y) * ((y \ x) \ 1) = (y \ x) \ (x / y).
((x * y) / x) * (y \ 1) = (x \ (x * y)) \ ((x * y) / x).
(x \ (x * y)) \ ((x * y) / x) = ((x * y) / x) * (y \ 1).
(x / (x / y)) * (y \ 1) = ((x / y) \ x) \ (x / (x / y)).
((x / y) \ x) \ (x / (x / y)) = (x / (x / y)) * (y \ 1).
(x \ 1) \ (1 / x) = ((x \ 1) \ 1) / x.
((x \ 1) \ 1) / x = (x \ 1) \ (1 / x).
T(T(x,y * x) * y,x) = T(x,y) * T(y,x).
x * T(1 / x,T(x,y)) = K(x,T(x,y) / x).
x \ K(x,T(x,y) / x) = T(1 / x,T(x,y)).
((x \ (y / z)) * x) * z = (x * z) * T((x * z) \ y,x).
(x * y) * T((x * y) \ z,x) = ((x \ (z / y)) * x) * y.
(x / y) \ (x * T(x \ (x / y),z)) = y * T(y \ 1,z).
(T(1 / x,y) * x) * (x \ z) = z * T(z \ (x \ z),y).
K((x * y) \ x,x * y) = y * T(y \ 1,x * y).
K((x * y) \ x,x * y) / y = T(1 / y,x * y).
(((x / y) \ 1) * (x / y)) * y = x * T(x \ y,x / y).
((x * y) / x) \ y = y * (((x * y) / x) \ 1).
x * (((y * x) / y) \ 1) = ((y * x) / y) \ x.
T(x,y) * (T(z / (z / x),y) \ 1) = (((z / x) * T(x,y)) / (z / x)) \ T(x,y).
(((x / y) * T(y,z)) / (x / y)) \ T(y,z) = T(y,z) * (T(x / (x / y),z) \ 1).
x / (y / (y / x)) = (1 / (y / (y / x))) * x.
(1 / (x / (x / y))) * y = y / (x / (x / y)).
(x \ 1) * R((x \ 1) \ 1,y,z) = x \ R(x,y,z).
x \ R(x,y,z) = R(x,y,z) * (x \ 1).
R(x,y,z) * (x \ 1) = x \ R(x,y,z).
(x \ R(x,y,z)) / (x \ 1) = R(x,y,z).
R(x,y,z) \ (x \ R(x,y,z)) = x \ 1.
(x \ R(x,y,z)) / R(T(x,x \ 1),y,z) = x \ 1.
((x \ 1) / (x \ R(x,y,z))) * R(x,y,z) = R(x,y,z) * R(R(x,y,z) \ 1,R(x,y,z),x \ 1).
R(x,y,z) * R(R(x,y,z) \ 1,R(x,y,z),x \ 1) = ((x \ 1) / (x \ R(x,y,z))) * R(x,y,z).
T((R(x,y,z) * (1 / x)) / R(x,y,z),x) = (x \ R(x,y,z)) / R(x,y,z).
(1 / x) * (x * R(x \ 1,y,z)) = R(1 / x,y,z).
(1 / x) \ R(1 / x,y,z) = x * R(x \ 1,y,z).
(1 / x) * ((y / (x * y)) * x) = R(1 / x,x,y).
(1 / x) * ((y / (x * y)) * x) = y / (x * y).
T(1 / x,(y / (x * y)) * x) = ((y / (x * y)) * x) \ (y / (x * y)).
((x / (y * x)) * y) \ (x / (y * x)) = T(1 / y,(x / (y * x)) * y).
(1 / (x / y)) \ (y / x) = (x / y) * R((x / y) \ 1,x / y,y).
(x / y) * R((x / y) \ 1,x / y,y) = (1 / (x / y)) \ (y / x).
(x \ 1) * L((x \ 1) \ 1,y,z) = x \ L(x,y,z).
x \ L(x,y,z) = L(x,y,z) * (x \ 1).
L(x,y,z) * (x \ 1) = x \ L(x,y,z).
L(x,y,z) \ (x \ L(x,y,z)) = x \ 1.
(x \ y) \ (((y \ x) \ 1) \ L((y \ x) \ 1,y \ x,y)) = ((y \ x) \ 1) \ 1.
(1 / x) \ L(x \ 1,y,z) = L(x \ 1,y,z) * x.
(1 / (x \ y)) \ (y \ x) = L((x \ y) \ 1,x \ y,x) * (x \ y).
L((x \ y) \ 1,x \ y,x) * (x \ y) = (1 / (x \ y)) \ (y \ x).
R(1 / (1 / x),y,z) * (1 / x) = R(x,y,z) / x.
R(x,y,z) / x = (1 / x) * R((1 / x) \ 1,y,z).
(1 / x) * R((1 / x) \ 1,y,z) = R(x,y,z) / x.
R(x,y,z) / x = (1 / x) * R(x,y,z).
(1 / x) * R(x,y,z) = R(x,y,z) / x.
T(1 / x,R(x,y,z)) = R(x,y,z) \ (R(x,y,z) / x).
R(x,y,z) \ (R(x,y,z) / x) = T(1 / x,R(x,y,z)).
x * R(x \ 1,y,z) = R(x \ 1,y,z) / (x \ 1).
R(x \ 1,y,z) / (x \ 1) = x * R(x \ 1,y,z).
R(x,y,z) * u != R(x,y,z) / x | T(1 / x,R(x,y,z)) = u.
R(x,y,z) / x != R(x,y,z) * u | T(1 / x,R(x,y,z)) = u.
L(R(x,y,z) \ u,R(x,y,z),1 / x) = (R(x,y,z) / x) \ ((1 / x) * u).
R(R(x,y,z),T(1 / x,R(x,y,z)),x) \ R(x,y,z) = (R(x,y,z) \ (R(x,y,z) / x)) * x.
(x * ((y \ x) / x)) / (y \ x) = y * ((x * (y \ 1)) / x).
(x * y) * T((x * y) \ y,z) = (x * T(x \ 1,z)) * y.
(x / y) * ((y \ x) * z) = (y \ x) * ((x / y) * z).
((x * y) / x) * (y * z) = (x \ (x * y)) * (((x * y) / x) * z).
(x \ (x * y)) * (((x * y) / x) * z) = ((x * y) / x) * (y * z).
(x \ y) \ ((y / x) * z) = (y / x) * ((x \ y) \ z).
x \ ((y * x) / y) = ((y * x) / y) * (x \ 1).
((x * y) / x) * (y \ 1) = y \ ((x * y) / x).
x \ (y / (y / x)) = (y / (y / x)) * (x \ 1).
(x / (x / y)) * (y \ 1) = y \ (x / (x / y)).
x \ (1 / (1 / x)) = (x \ 1) / (1 / x).
(x \ 1) / (1 / x) = x \ (1 / (1 / x)).
((x \ (x / y)) * x) * y = x * (y * T(y \ 1,x)).
((x \ R(1 / y,y,x)) * x) * (y * x) = x * ((y * x) * T((y * x) \ 1,x)).
x * T(x \ 1,y) = K(y \ (y / x),y).
K(x \ (x / y),x) = y * T(y \ 1,x).
x \ K(y \ (y / x),y) = T(x \ 1,y).
K(x \ (x / y),x) / y = T(1 / y,x).
K(x \ (x / (y \ 1)),x) = y \ T(y,x).
K(x \ (x / (1 / y)),x) = T(y,x) / y.
K(T(1 / x,T(x,y)),T(x,y)) = x * T(x \ 1,T(x,y)).
(x \ y) \ K(T(y,x) \ ((y * x) / y),T(y,x)) = T((x \ y) \ 1,T(y,x)).
K(x \ (x / ((y / x) \ 1)),x) = (y / x) \ (x \ y).
K(x \ (x / (((x * y) / x) \ 1)),x) = ((x * y) / x) \ y.
K(R(x \ 1,y,z) \ (x * R(x \ 1,y,z)),R(x \ 1,y,z)) = x \ T(x,R(x \ 1,y,z)).
K(x \ (x / (1 / y)),x) * y = T(y,x).
T(x,y) = K(y \ (y / (1 / x)),y) * x.
K(x \ (x / (1 / (y / (x * y)))),x) = R(x \ 1,x,y) / (y / (x * y)).
K(T(1 / (1 / x),x \ 1),x \ 1) = T(x,x \ 1) / x.
K(R(x,y,z) \ (R(x,y,z) / (((x \ R(x,y,z)) / R(x,y,z)) \ 1)),R(x,y,z)) = ((x \ R(x,y,z)) / R(x,y,z)) \ (x \ 1).
(x * T(x \ 1,y)) * (x \ z) = z * T(z \ (x \ z),y).
(x \ T(x,y)) * ((x \ 1) \ z) = z * T(z \ ((x \ 1) \ z),y).
K((x / y) \ 1,x / y) * y = x * T(x \ y,x / y).
(x * T(x \ 1,y)) * x = x * (x * T(x \ 1,y)).
T(x,x * T(x \ 1,y)) = x.
T(x,(x \ 1) * x) = x.
R(x,(x * T(x \ 1,y)) / x,x) = T(x,(x * T(x \ 1,y)) / x).
T(x \ 1,T(x,y) * (x \ 1)) = x \ 1.
T(x \ 1,x \ T(x,y)) = x \ 1.
T(1 / x,T(x,y) / x) = 1 / x.
T(x,K(x \ 1,x)) = x.
R(x,x \ 1,x) = T(x,x \ 1).
K(x \ 1,x) * x = x * K(x \ 1,x).
R(x,x \ 1,x) = (x \ 1) \ 1.
T(x,x \ 1) \ x = (x \ 1) * x.
x / K(x \ 1,x) = T(x,x \ 1).
x / K(x \ 1,x) = (x \ 1) \ 1.
T(x \ T(x,y),x \ 1) = x \ T(x,y).
(x * (1 / y)) / x = T((x * (1 / y)) / x,T(y,z) / y).
T((x * (1 / y)) / x,T(y,z) / y) = (x * (1 / y)) / x.
x * T(x \ 1,x) = T(x,x \ 1) \ x.
T(x,x \ 1) \ x = x * T(x \ 1,x).
T(x,x \ 1) * K(x \ 1,x) = x.
((x \ 1) \ 1) * K(x \ 1,x) = x.
x * L(y,K(x \ 1,x),T(x,x \ 1)) = T(x,x \ 1) * (K(x \ 1,x) * y).
x * L(y,K(x \ 1,x),(x \ 1) \ 1) = ((x \ 1) \ 1) * (K(x \ 1,x) * y).
R(x \ 1,T(x,y),x \ 1) = T(x \ 1,T(x,y)).
(x * K(x \ 1,x)) / (x * x) = R(x \ 1,x,x).
L(x \ T(x,y),x,y) = T((y * x) \ (x * y),x \ 1).
T((x * y) \ (y * x),y \ 1) = L(y \ T(y,x),y,x).
T(x,x \ 1) \ 1 = T(x \ 1,x).
1 / T(x \ 1,x) = T(x,x \ 1).
((x \ 1) \ 1) \ 1 = T(x \ 1,x).
T(x \ 1,x) = ((x \ 1) \ 1) \ 1.
(x \ 1) \ 1 = T((1 / x) \ 1,1 / x).
T((1 / x) \ 1,1 / x) = (x \ 1) \ 1.
T(x \ 1,T(x,x \ 1)) = T(x \ 1,x).
T(x \ 1,(x \ 1) \ 1) = T(x \ 1,x).
T((x \ 1) \ 1,x \ 1) = T(x \ 1,x) \ 1.
T(x,1 / x) = (x \ 1) \ 1.
((1 / x) * ((x \ 1) \ 1)) / (1 / x) = x.
T(x,x \ 1) = T(x,1 / x).
T(x,1 / x) = T(x,x \ 1).
R(x,1 / x,x) = (x \ 1) \ 1.
((x \ 1) \ 1) / x = K(x,1 / x).
L((x \ 1) \ 1,y,z) / x = L(x,y,z) * (1 / x).
L(T(x,x \ 1),1 / x,x) = T(x,x * (1 / x)).
(x * T(y,y \ 1)) / x = T((x * y) / x,1 / y).
R(x,1 / x,x) = T(x,x \ 1).
T(x,x \ 1) / x = K(x,1 / x).
R(R(x,y,z),1 / x,x) = R(T(x,x \ 1),y,z).
K(x,1 / x) * x = (x \ 1) \ 1.
x \ ((x \ 1) \ 1) = a(x,1 / x,x).
a(x,1 / x,x) = x \ ((x \ 1) \ 1).
x \ T(x,x \ 1) = a(x,1 / x,x).
(x \ 1) / (1 / x) = K(1 / x,1 / (1 / x)).
K(1 / x,1 / (1 / x)) = (x \ 1) / (1 / x).
K(x,1 / x) = (x \ 1) \ (1 / x).
(x \ 1) \ (1 / x) = K(x,1 / x).
(x \ 1) * K(x,1 / x) = 1 / x.
(1 / x) / K(x,1 / x) = x \ 1.
x \ 1 = R(1 / x,x,1 / x).
R(1 / x,x,1 / x) = x \ 1.
R(x \ 1,x,y) = R(y / (x * y),x,1 / x).
R(x / (y * x),y,1 / y) = R(y \ 1,y,x).
R(x \ 1,x,y) \ (((y / (x * y)) * x) * (1 / x)) = x * (1 / x).
L(T(x,x \ 1),1 / x,x) = T(x,K(x,1 / x)).
R(x,y,z) \ R(T(x,x \ 1),y,z) = a(R(x,y,z),1 / x,x).
L(x \ 1,y,z) / (1 / x) = L(1 / x,y,z) * (1 / (1 / x)).
L(1 / x,y,z) * (1 / (1 / x)) = L(x \ 1,y,z) / (1 / x).
T((x * y) / x,1 / y) = T((x * y) / x,y \ 1).
T(x,1 / T(x,y)) = T((y * T(x,y)) / y,T(x,y) \ 1).
T((x * T(y,x)) / x,T(y,x) \ 1) = T(y,1 / T(y,x)).
K(x,y) = T((y * x) \ (x * y),x \ 1).
K(x,y) = T(K(x,y),x \ 1).
T(K(x,y),x \ 1) = K(x,y).
T(x \ 1,K(x,y)) = x \ 1.
(x \ 1) * ((x \ 1) \ 1) = T(x,K(x \ 1,y)) * (x \ 1).
T(x,K(x \ 1,y)) * (x \ 1) = (x \ 1) * ((x \ 1) \ 1).
T((x * y) / x,K(x \ (x / (((x * y) / x) \ 1)),x)) = (((x * y) / x) \ y) \ y.
K((x / y) \ ((x / y) / (T(x / (x / y),z) \ 1)),x / y) = (((x / y) * T(y,z)) / (x / y)) \ T(y,z).
(x * T(x \ (y \ x),z)) / (y \ x) = y * T(y \ 1,z).
K((x / (y * x)) \ 1,x / (y * x)) * (y * x) = T(y,x / (y * x)) * x.
T(x,T(x,y) \ 1) = T(x,1 / T(x,y)).
T(x,1 / T(x,y)) = T(x,T(x,y) \ 1).
T(x,K(x \ 1,y)) * (x \ 1) = 1.
T(x,K(x \ 1,y)) = x.
T(1 / x,K(x,y)) = 1 / x.
R(1 / (x / y),x / y,y) = T((1 * y) / x,K(x / y,z)).
T((1 * x) / y,K(y / x,z)) = R(1 / (y / x),y / x,x).
R(x,y,z) * (x * u) = x * (u * R(T(x,u),y,z)).
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).
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).
R(x,y,x) \ T(x * y,x) = T(y,x).
L((x * y) / z,u,w) * z = (L(x / (z / y),u,w) * (z / y)) * y.
(L(x / (y / z),u,w) * (y / z)) * z = L((x * z) / y,u,w) * y.
L((x \ y) / y,z,u) * y = (L(1 / x,z,u) * x) * (x \ y).
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).
R((x * y) / z,u,w) * z = (R(x / (z / y),u,w) * (z / y)) * y.
(R(x / (y / z),u,w) * (y / z)) * z = R((x * z) / y,u,w) * y.
(x * y) * ((z * ((x * y) \ (x * u))) / z) = x * (y * ((z * (y \ u)) / z)).
(x * y) * ((z * ((x * y) \ u)) / z) = x * (y * ((z * (y \ (x \ u))) / z)).
x * ((y * (x \ (x / z))) / y) = (x / z) * (z * ((y * (z \ 1)) / y)).
(x / y) * (y * ((z * (y \ 1)) / z)) = x * ((z * (x \ (x / y))) / z).
x \ ((y * (x * z)) / y) = (x \ 1) * ((y * ((x \ 1) \ z)) / y).
(x \ 1) * ((y * ((x \ 1) \ z)) / y) = x \ ((y * (x * z)) / y).
(1 / x) \ ((y * ((1 / x) * z)) / y) = x * ((y * (x \ z)) / y).
((x * (y * z)) / x) / z = ((x * (y / (1 / z))) / x) * (1 / z).
((x * (y / (1 / z))) / x) * (1 / z) = ((x * (y * z)) / x) / z.
(x * y) * T((x * y) \ (y * z),u) = y * (T(x,y) * T(T(x,y) \ z,u)).
(x * y) * T((x * y) \ (z * y),u) = (T(z / x,u) * x) * y.
T(x,x / (x * y)) = x * (y * ((x * (y \ 1)) / x)).
x * (y * ((x * (y \ 1)) / x)) = T(x,x / (x * y)).
x \ T(x,x / (x * y)) = y * ((x * (y \ 1)) / x).
T((1 * x) / y,K(y / x,z)) = x / y.
T(x / y,K(y / x,z)) = x / y.
T(x / y,y) = T(y \ x,K(y / x,z)).
T(x \ y,K(x / y,z)) = T(y / x,x).
T(x \ y,K(x / y,z)) = x \ y.
(x \ 1) * ((y * ((x \ 1) \ 1)) / y) = x \ ((y * x) / y).
L(1 / (x \ y),x \ y,x) * ((y \ x) \ 1) = (y \ x) \ L(y \ x,x \ y,1 / (x \ y)).
(x \ y) \ L(x \ y,y \ x,1 / (y \ x)) = L(1 / (y \ x),y \ x,y) * ((x \ y) \ 1).
(R(1 / x,y,z) * x) * u = (x * u) * R((x * u) \ u,y,z).
(x * y) * R((x * y) \ y,z,u) = (R(1 / x,z,u) * x) * y.
x * (y * T(y \ z,x)) = ((x \ ((x * z) / y)) * x) * y.
((x \ ((x * y) / z)) * x) * z = x * (z * T(z \ y,x)).
((x \ (y / z)) * x) * z = x * (z * T(z \ (x \ y),x)).
x * (y * T(y \ (x \ z),x)) = ((x \ (z / y)) * x) * y.
((x \ y) * x) * x = x * (x * T(x \ T(y,x),x)).
x * (x * T(x \ T(y,x),x)) = ((x \ y) * x) * x.
x * ((x \ T(y,x)) * x) = ((x \ y) * x) * x.
T((x \ y) * x,x) = (x \ T(y,x)) * x.
T((x \ y) * x,x) / x = x \ T(y,x).
T(x,y) \ T((y \ x) * y,y) = K(y \ T(x,y),y).
T(x * y,y) / y = y \ T(y * x,y).
x * (T((x \ y) * x,x) / x) = T(y,x).
T(x,y) / y = y \ T(y * (x / y),y).
x \ T(x * (y / x),x) = T(y,x) / x.
x * (T(y * x,x) / x) = T(x * y,x).
x * (T(y,x) / x) = T(x * (y / x),x).
T(x * (y / x),x) = x * (T(y,x) / x).
x * ((1 / x) * T(y,x)) = T(x * ((1 / x) * y),x).
T(x * ((1 / x) * y),x) = x * ((1 / x) * T(y,x)).
(x \ 1) * (T(x \ R(x,y,z),x \ 1) / (x \ 1)) = T((x \ 1) * R(x,y,z),x \ 1).
T(x * y,x) \ T(y * x,x) = K(x \ T(x * y,x),x).
x * (K(x \ 1,x) * (x \ y)) = ((x \ (y / y)) * x) * y.
((x \ (y / y)) * x) * y = x * (K(x \ 1,x) * (x \ y)).
((x \ 1) * x) * y = x * (K(x \ 1,x) * (x \ y)).
x * (K(x \ 1,x) * (x \ y)) = ((x \ 1) * x) * y.
x * (K(x \ 1,x) * (x \ y)) = K(x \ 1,x) * y.
x * (K(x \ 1,x) * y) = K(x \ 1,x) * (x * y).
K(x \ 1,x) * (x * y) = x * (K(x \ 1,x) * y).
x * (K(x \ 1,x) * T(y,x)) = K(x \ 1,x) * (y * x).
(K(x \ 1,x) * y) \ (x * (K(x \ 1,x) * y)) = L(T(x,y),y,K(x \ 1,x)).
x * (y * T(y \ (x \ y),z)) = (x * T(x \ 1,z)) * y.
x * ((y \ (x \ y)) * y) = (x * T(x \ 1,y)) * y.
(x * T(x \ 1,y)) * y = x * ((y \ (x \ y)) * y).
(x * ((y \ (x \ y)) * y)) / y = x * T(x \ 1,y).
(x * ((x \ 1) * R(x,y,z))) / R(x,y,z) = x * T(x \ 1,R(x,y,z)).
(T((x * y) / x,z) * x) * y = (x * y) * T(y,z).
(x * T(y,z)) * y = (x * y) * T(y,z).
(x * y) / T(y,z) = (x / T(y,z)) * y.
x / T(x,y) = (1 / T(x,y)) * x.
(1 / T(x,y)) * x = x / T(x,y).
x * y != ((z / u) * u) * w | x = (z * w) / y.
(x / y) * T(y,z) = (x * T(y,z)) / y.
(x * T(y,z)) / y = (x / y) * T(y,z).
x * y = ((x / T(y,z)) * y) * T(y,z).
((x / T(y,z)) * y) * T(y,z) = x * y.
(x * (y \ z)) * (z / y) = (x * (z / y)) * T(z / y,y).
(x * (y / z)) * T(y / z,z) = (x * (z \ y)) * (y / z).
(1 / T(x,y)) \ (x / T(x,y)) = x.
T(1 / T(x,y),x) = x \ (x / T(x,y)).
x * (1 / T(x,y)) = T(x,1 / T(x,y)) / T(x,y).
T(x,1 / T(x,y)) / T(x,y) = x * (1 / T(x,y)).
(1 / T(x,y)) \ (T(x,z) / T(x,y)) = T(x,z).
x / y = ((x / T(y,z)) / y) * T(y,z).
((x / T(y,z)) / y) * T(y,z) = x / y.
T(x,x / (x / T(y,x))) * T(y,x) = x * y.
(x \ (x / T(x,y))) * T(x,y) = T(x,y) * T(T(x,y) \ 1,x).
T(x,y) * T(T(x,y) \ 1,x) = (x \ (x / T(x,y))) * T(x,y).
x \ (x / T(x,y)) = K(x \ (x / (1 / (1 / T(x,y)))),x) * (1 / T(x,y)).
K(x \ (x / (1 / (1 / T(x,y)))),x) * (1 / T(x,y)) = x \ (x / T(x,y)).
(T(x,y) / T(x,z)) / T(x,y) = 1 / T(x,z).
(1 / T(x,y)) * T(T(x,z),u) = T((T(x,z) / T(x,y)) * T(x,y),u) / T(x,y).
T((T(x,y) / T(x,z)) * T(x,z),u) / T(x,z) = (1 / T(x,z)) * T(T(x,y),u).
x * (x * y) = T(x,x / (x / T(y,x))) * (y * x).
T(x,x / (x / T(y,x))) * (y * x) = x * (x * y).
T(x,T(x,y) \ 1) / T(x,y) = x * (1 / T(x,y)).
(x * (x * y)) / (y * x) = T(x,x / (x / T(y,x))).
T(x,x / (x / T(y,x))) = (x * (x * y)) / (y * x).
((x * (1 / T(x,y))) / x) * T(x,y) = T(x,T(x,y) \ 1) / x.
(x * (x * y)) / (y * x) = (x / T(y,x)) * y.
R(((x * (x * y)) / x) / y,y,x) = (x / T(y,x)) * y.
(x * (y / z)) * (z \ y) = (x * (z \ y)) * (y / z).
(x * ((y * z) / y)) * z = (x * (y \ (y * z))) * ((y * z) / y).
(x * (y \ (y * z))) * ((y * z) / y) = (x * ((y * z) / y)) * z.
(x * (y \ z)) / (z / y) = (x / (z / y)) * (y \ z).
(T((x / y) / z,u) * z) * y = (z * y) * T((z * y) \ x,u).
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).
x * (L(x,y,z) \ u) = L(x,y,z) \ (x * u).
L(x,y,z) \ (x * u) = x * (L(x,y,z) \ u).
x * (L(x,y,z) \ (L(x,y,z) / x)) = K(x,L(x,y,z) / x).
x * T(1 / x,L(x,y,z)) = K(x,L(x,y,z) / x).
(x \ 1) * T(x,L(x \ 1,y,z)) = K(x \ 1,L(x \ 1,y,z) / (x \ 1)).
K(x \ 1,L(x \ 1,y,z) / (x \ 1)) = (x \ 1) * T(x,L(x \ 1,y,z)).
T(1 / (1 / x),x \ 1) = x.
T(x,y) = T(T(1 / (1 / x),y),x \ 1).
T(T(1 / (1 / x),y),x \ 1) = T(x,y).
T(1 / (1 / (1 / x)),x) = 1 / x.
(x \ 1) * x = (1 / (1 / x)) * (x \ 1).
(1 / (1 / x)) * (x \ 1) = (x \ 1) * x.
(x * (1 / x)) * ((1 / x) \ y) = y * T(y \ ((1 / x) \ y),x \ 1).
K(x,x \ 1) = T(x,x \ 1) / x.
T(x,x \ 1) / x = K(x,x \ 1).
x * (1 / x) = (1 / (1 / (1 / x))) * x.
(1 / (1 / (1 / x))) * x = x * (1 / x).
K(x,x \ 1) * x = T(x,x \ 1).
((x \ 1) \ 1) / x = K(x,x \ 1).
K(x,x \ 1) = K(x,1 / x).
K(x,1 / x) = K(x,x \ 1).
K(x \ 1,x) = K(x \ 1,(x \ 1) \ 1).
K(x \ 1,(x \ 1) \ 1) = K(x \ 1,x).
K(x,x \ 1) = x * (1 / x).
x \ K(x,x \ 1) = 1 / x.
K(x,x \ 1) \ 1 = K(1 / x,x).
K((x / y) \ x,1 / y) = K(y,y \ 1).
(1 / (1 / x)) * K(x,x \ 1) = x.
K(x,x \ 1) * (x \ 1) = 1 / x.
K(x,x \ 1) * x = (x \ 1) \ 1.
(x \ 1) * K(x,x \ 1) = 1 / x.
K(x,x \ 1) * T((x * (1 / x)) \ y,z) = x * ((1 / x) * T((1 / x) \ (x \ y),z)).
L(x,y,z) * K(x,x \ 1) = x * (L(x,y,z) * (1 / x)).
R(T(1 / x,y),x,x \ y) = T(y \ (K(x,x \ 1) * (x \ y)),x).
T(x \ (K(y,y \ 1) * (y \ x)),y) = R(T(1 / y,x),y,y \ x).
T(x,x \ 1) * L(y,x,K(x,x \ 1)) = K(x,x \ 1) * (x * y).
L(x \ y,x,K(x,x \ 1)) = T(x,x \ 1) \ (K(x,x \ 1) * y).
T(x,x \ 1) \ (K(x,x \ 1) * y) = L(x \ y,x,K(x,x \ 1)).
T(x,x \ 1) * y != K(x,x \ 1) * (x * z) | L(z,x,K(x,x \ 1)) = y.
x * L(y,K(x,x \ 1),1 / (1 / x)) = (1 / (1 / x)) * (K(x,x \ 1) * y).
R(x,1 / (1 / y),K(y,y \ 1)) * y = (x * (1 / (1 / y))) * K(y,y \ 1).
R(x / (1 / (1 / y)),1 / (1 / y),K(y,y \ 1)) = (x * K(y,y \ 1)) / y.
(1 / x) / L(y,(x \ 1) / y,K(x,x \ 1)) = K(x,x \ 1) * ((x \ 1) / y).
((x \ 1) \ 1) / L(y \ x,y,K(x,x \ 1)) = K(x,x \ 1) * y.
L(x,K(y,y \ 1),y \ 1) = (1 / y) \ ((y \ 1) * (K(y,y \ 1) * x)).
(1 / x) \ ((x \ 1) * (K(x,x \ 1) * y)) = L(y,K(x,x \ 1),x \ 1).
(x \ 1) * x = (x \ 1) / (1 / x).
(x \ 1) / (1 / x) = (x \ 1) * x.
K(x \ 1,x) = (x \ 1) / (1 / x).
(x \ 1) / (1 / x) = K(x \ 1,x).
K(x \ 1,x) * (1 / x) = x \ 1.
K(x \ 1,x) \ (x \ 1) = 1 / x.
K(x \ 1,x) = x \ (1 / (1 / x)).
x \ (1 / (1 / x)) = K(x \ 1,x).
K(1 / x,1 / (1 / x)) = K(x \ 1,x).
(x \ 1) * L(y,1 / x,K(x \ 1,x)) = K(x \ 1,x) * ((1 / x) * y).
L((1 / x) \ y,1 / x,K(x \ 1,x)) = (x \ 1) \ (K(x \ 1,x) * y).
1 / x = L(x \ 1,x,x \ 1).
L(x \ 1,x,x \ 1) = 1 / x.
L(1 / x,y,z) = L(L(x \ 1,y,z),x,x \ 1).
L(L(x \ 1,y,z),x,x \ 1) = L(1 / x,y,z).
T(1 / x,K(x \ 1,x)) = 1 / x.
x * K(x \ 1,x) = 1 / (1 / x).
x * (T(x,y) \ K(x \ 1,x)) = T(x,y) \ (1 / (1 / x)).
K(x \ 1,x) * L(1 / x,y,z) = L(1 / x,y,z) * K(x \ 1,x).
L(1 / x,y,z) * K(x \ 1,x) = K(x \ 1,x) * L(1 / x,y,z).
1 / (1 / x) = L(x,x \ 1,x).
L(x,x \ 1,x) = 1 / (1 / x).
(1 / (1 / x)) / (x * x) = R(x \ 1,x,x).
L(T(x,y),x \ 1,x) = T(1 / (1 / x),y).
R(1 / (1 / x),y,z) = L(R(x,y,z),x \ 1,x).
L(R(x,y,z),x \ 1,x) = R(1 / (1 / x),y,z).
x * (1 / x) = x / (1 / (1 / x)).
x / (1 / (1 / x)) = x * (1 / x).
K(x,1 / x) = x / (1 / (1 / x)).
x / (1 / (1 / x)) = K(x,1 / x).
K(x,x \ 1) = x / (1 / (1 / x)).
x / (1 / (1 / x)) = K(x,x \ 1).
K(x,1 / x) * (1 / (1 / x)) = x.
K(x,x \ 1) * (1 / (1 / x)) = x.
K(x,x \ 1) \ x = 1 / (1 / x).
L(x,1 / x,x) = 1 / (1 / x).
L(T(x,y),1 / x,x) = T(1 / (1 / x),y).
T(L(x,1 / x,x),x \ 1) = x.
L(T(x,x \ 1),1 / x,x) = x.
x = T(x,K(x,1 / x)).
T(x,K(x,1 / x)) = x.
T(K(x,1 / x),x) = K(x,1 / x).
T(x,K(x,x \ 1)) = x.
K(x,x \ 1) * L(x,y,z) = L(x,y,z) * K(x,x \ 1).
L(x,y,z) * K(x,x \ 1) = K(x,x \ 1) * L(x,y,z).
x * L(y,1 / (1 / x),K(x,x \ 1)) = K(x,x \ 1) * ((1 / (1 / x)) * y).
L((1 / (1 / x)) \ y,1 / (1 / x),K(x,x \ 1)) = x \ (K(x,x \ 1) * y).
K(x,1 / x) = a(x,1 / x,x).
a(x,1 / x,x) = K(x,1 / x).
K(x,1 / x) = x \ ((x \ 1) \ 1).
x \ ((x \ 1) \ 1) = K(x,1 / x).
x \ T(x,x \ 1) = K(x,1 / x).
x * K(x,1 / x) = (x \ 1) \ 1.
K((x \ 1) \ 1,x \ 1) = K(x,1 / x).
x \ ((x \ 1) \ 1) = K(x,x \ 1).
x * K(x,1 / x) = T(x,x \ 1).
x \ T(x,x \ 1) = K(x,x \ 1).
x * K(x,x \ 1) = (x \ 1) \ 1.
K((x \ 1) \ 1,x \ 1) = K(x,x \ 1).
x * K(x,x \ 1) = T(x,x \ 1).
R(x,K(x,x \ 1),y) = (T(x,x \ 1) * y) / (K(x,x \ 1) * y).
(T(x,x \ 1) * y) / (K(x,x \ 1) * y) = R(x,K(x,x \ 1),y).
T(x,x \ 1) * L(y,K(x,x \ 1),x) = x * (K(x,x \ 1) * y).
K(x \ 1,x) = K(1 / x,(1 / x) \ 1).
K(1 / x,(1 / x) \ 1) = K(x \ 1,x).
K(T(x \ 1,x),(x \ 1) \ 1) = K(x \ 1,1 / (x \ 1)).
(x \ 1) * (K(x,x \ 1) * ((x \ 1) \ y)) = K((x \ 1) \ 1,x \ 1) * y.
K(1 / x,x) = K(x \ 1,x).
K(T(x,x \ 1),T(x \ 1,x)) = K(T(x \ 1,x) \ 1,T(x \ 1,x)).
K(T(x \ 1,x) \ 1,T(x \ 1,x)) = K(T(x,x \ 1),T(x \ 1,x)).
K(x,x \ 1) \ 1 = K(x \ 1,x).
K(1 / (1 / x),1 / x) = K(x,x \ 1).
L(R(x \ 1,x,x),y,z) * (x * x) = (x * x) * L((x * x) \ (1 / (1 / x)),y,z).
(x * x) * L((x * x) \ (1 / (1 / x)),y,z) = L(R(x \ 1,x,x),y,z) * (x * x).
T(1 / (1 / x),y) / ((x \ 1) * T(x,y)) = x.
K(x,1 / x) \ (x * (T(x,y) / x)) = T(1 / (1 / x),y).
K(x \ 1,x) * L(1 / x,y,z) = (x \ 1) * (x * L(x \ 1,y,z)).
K(x,x \ 1) * L(x,y,z) = x * (L(x,y,z) * (1 / x)).
K(T(x \ 1,x),(x \ 1) \ 1) = K(x \ 1,x).
K(T(x \ 1,x),T(x,x \ 1)) = K(x \ 1,x).
K(T((x \ 1) \ 1,x \ 1),T(x \ 1,(x \ 1) \ 1)) = K(x,x \ 1).
K(x,1 / x) * T(1 / (1 / x),y) = x * (T(x,y) / x).
K(x,x \ 1) * T(1 / (1 / x),y) = x * (T(x,y) / x).
K(x,x \ 1) * T(K(x,x \ 1) \ x,y) = x * (T(x,y) / x).
((x * (y / (y / T(z,x)))) / x) \ ((y / T(z,x)) * z) = y / T(z,x).
(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 * ((x \ y) * T((x \ y) \ 1,z)) = y * T(y \ x,z).
x \ (y * T(y \ x,z)) = (x \ y) * T((x \ y) \ 1,z).
(x \ y) * T((x \ y) \ 1,z) = x \ (y * T(y \ x,z)).
x * K(y \ (y / (x \ z)),y) = z * T(z \ x,y).
x * T(x \ y,z) = y * K(z \ (z / (y \ x)),z).
x \ (y * T(y \ x,z)) = K(z \ (z / (x \ y)),z).
K(x \ (x / (y \ z)),x) = y \ (z * T(z \ y,x)).
x * T(y,z) = (x * y) * K(z \ (z / ((x * y) \ x)),z).
(x * y) * K(z \ (z / ((x * y) \ x)),z) = x * T(y,z).
(x * (y * z)) * T((x * (y * z)) \ (x * y),u) = (x * y) * K(u \ (u / L(z,y,x)),u).
x * T(x \ y,y \ x) = y * K((y \ x) \ 1,y \ x).
K((x * (y \ z)) \ x,x * (y \ z)) = y \ (z * T(z \ y,x * (y \ z))).
K(x \ (x / T(y,z)),x) = z \ ((y * z) * T((y * z) \ z,x)).
K(x \ (x / (y \ (y / z))),x) = y \ ((y / z) * T(z,x)).
T(x,x * (y \ (z * T(z \ y,x)))) = x.
T(x,x * (T(x,y) \ ((y \ x) * ((y \ x) \ x)))) = x.
T(x,x * (T(x,y) \ x)) = x.
T(x,y) = T(T(x,y),x * (T(x,z) \ x)).
T(T(x,y),x * (T(x,z) \ x)) = T(x,y).
(x * y) * K(((x * y) \ x) \ 1,(x * y) \ x) = x * T(y,(x * y) \ x).
K(x \ (x / (x \ (x / y))),x) = x \ ((y * x) / y).
(T(1 / (x / y),z) * (x / y)) * y = T(y / x,z) * x.
(T(x / (y / z),u) * (y / z)) * z = y * T(y \ (x * z),u).
(T(1 / (x / y),z) * (x / y)) * y = x * T(x \ y,z).
((x / y) * T((x / y) \ 1,z)) * y = x * T(x \ y,z).
K(x \ (x / (y / z)),x) * z = y * T(y \ z,x).
(x * T(x \ y,z)) / y = K(z \ (z / (x / y)),z).
K(x \ (x / (y / z)),x) = (y * T(y \ z,x)) / z.
K((x * (y / z)) \ x,x * (y / z)) = (y * T(y \ z,x * (y / z))) / z.
K(x \ (x / R(y,z,u)),x) = (((y * z) * u) * T(((y * z) * u) \ (z * u),x)) / (z * u).
(x * (T(x,y) \ x)) \ (x * x) = T(x,y).
(x * x) / T(x,y) = x * (T(x,y) \ x).
T(((T(x,y) \ x) * x) / (T(x,y) \ x),(x * x) / T(x,y)) = L(x,T(x,y) \ x,x).
x * (T(x,y) \ x) = (x / T(x,y)) * x.
(x / T(x,y)) * x = x * (T(x,y) \ x).
T(x / T(x,y),x) = T(x,y) \ x.
(T(x,y) \ x) * T(x,y) = T(x,y) * T(T(x,y) \ x,x).
T(x,y) * T(T(x,y) \ x,x) = (T(x,y) \ x) * T(x,y).
T(x,R(1 / y,y,x)) = (((x * (1 / y)) / x) * y) * x.
(((x * (1 / y)) / x) * y) * x = T(x,R(1 / y,y,x)).
(x * ((y * (x \ 1)) / y)) * y = T(y,R(1 / x,x,y)).
(T(x,y) * ((T(x,y) \ x) / x)) * x = T(x,R(1 / T(x,y),T(x,y),x)).
(x \ T(x,x / (x * y))) * x = T(x,R(1 / y,y,x)).
T(x,R(1 / y,y,x)) = (x \ T(x,x / (x * y))) * x.
x * (((y * x) / y) * z) = ((y * x) / y) * (x * z).
((x * y) / x) * (y * z) = y * (((x * y) / x) * z).
x \ (((y * x) / y) * z) = ((y * x) / y) * (x \ z).
x * (((y * x) / y) \ z) = ((y * x) / y) \ (x * z).
((x * y) / x) \ (y * z) = y * (((x * y) / x) \ z).
((x * y) / x) * (y \ ((((x * y) / x) \ y) * z)) = L(z,((x * y) / x) \ y,(x * y) / x).
(L(1 / x,y,z) * x) * (x \ u) = u * L(u \ (x \ u),y,z).
x \ ((y * (x * y)) / y) = T(y,y / (x \ 1)).
T(x,x / (y \ 1)) = T(x,y * x).
((x * (1 / (1 / y))) / x) * (1 / y) = ((x * y) / x) / y.
((x * (x * y)) / x) / y = T(x,x / (1 / y)).
((x * y) / x) / (x \ y) = T(x,x / (1 / (x \ y))).
T(x,x / (1 / (x \ y))) = ((x * y) / x) / (x \ y).
R(T(x,x / (1 / y)),y,x) = (x / T(y,x)) * y.
((x * y) / x) / y = (1 / y) * ((x * ((1 / y) \ 1)) / x).
(1 / x) * ((y * ((1 / x) \ 1)) / y) = ((y * x) / y) / x.
(1 / x) * ((y * x) / y) = ((y * x) / y) / x.
x * ((y * (x \ 1)) / y) = ((y * (x \ 1)) / y) / (x \ 1).
((x * (y \ 1)) / x) / (y \ 1) = y * ((x * (y \ 1)) / x).
(x * y) * T((x * y) \ (z * y),u) = (x * T(x \ z,u)) * y.
(x * y) * R((x * y) \ y,z,u) = (x * R(x \ 1,z,u)) * y.
T(x,T(x,y) \ 1) / x = T(x,y) * ((x * (T(x,y) \ 1)) / x).
T(x,y) * ((x * (T(x,y) \ 1)) / x) = T(x,T(x,y) \ 1) / x.
(x * y) * ((z * y) / z) = (x * ((z * y) / z)) * y.
(x * ((y * z) / y)) * z = (x * z) * ((y * z) / y).
T(x,x / (x / y)) * y = ((x / y) * y) * ((x * y) / x).
((x / y) * y) * ((x * y) / x) = T(x,x / (x / y)) * y.
x * ((x * y) / x) = T(x,x / (x / y)) * y.
T(x,x / (x / y)) * y = x * ((x * y) / x).
T(x,x / (x / y)) * (x \ y) = (x * y) / x.
((x * y) / x) / (x \ y) = T(x,x / (x / y)).
T(x,x / (1 / (x \ y))) = T(x,x / (x / y)).
T(x,x / (1 / y)) = T(x,x / (x / (x * y))).
T(x,x / (x / (x * y))) = T(x,x / (1 / y)).
(T((x / y) / z,u) * z) * y = z * (y * T(y \ (z \ x),u)).
(x * (T(x,y) / x)) * (K(x,x \ 1) \ 1) = T(x * (K(x,x \ 1) \ 1),y).
(x * y) * L((x * y) \ y,z,u) = (x * L(x \ 1,z,u)) * y.
K(x \ (x / T(y,z)),x) = z \ ((y * T(y \ 1,x)) * z).
x * K(y \ (y / T(z,x)),y) = (z * T(z \ 1,y)) * x.
(x * T(x \ 1,y)) * z = z * K(y \ (y / T(x,z)),y).
T(x * T(x \ 1,y),z) = K(y \ (y / T(x,z)),y).
T(x * T(x \ 1,T(x,y)),y) = K(T(x,y) \ 1,T(x,y)).
T((x \ 1) * x,y) = K(x \ (x / T(x,y)),x).
K(x \ (x / T(x,y)),x) = T((x \ 1) * x,y).
T(x \ T(x,y),z) = K(y \ (y / T(x \ 1,z)),y).
T(x * T(x \ 1,y),z) = T(x,z) * T(T(x,z) \ 1,y).
T(x,y) * T(T(x,y) \ 1,z) = T(x * T(x \ 1,z),y).
T(K(x \ (x / y),x),z) = K(x \ (x / T(y,z)),x).
K(x \ (x / T(y,z)),x) = T(K(x \ (x / y),x),z).
T(x,y) \ T(x * T(x \ 1,z),y) = T(T(x,y) \ 1,z).
K(x \ (x / T(x,y)),x) = T(K(x \ 1,x),y).
T(x \ T(x,y),T(x,x \ 1)) = K(y \ (y / T(x \ 1,x)),y).
K(x \ (x / T(y \ x,z)),x) = T(K(x \ y,x),z).
K(x \ (x / (((y \ x) \ z) \ z)),x) = T(K(x \ y,x),(y \ x) \ z).
T(K(x \ y,x),(y \ x) \ z) = K(x \ (x / (((y \ x) \ z) \ z)),x).
T(x * T(x \ 1,T(x,y)),y) = (T(x,y) \ 1) * T(x,y).
T(x * T(x \ 1,x),y) = (x \ (x / T(x,y))) * T(x,y).
(x \ (x / T(x,y))) * T(x,y) = T(x * T(x \ 1,x),y).
T(x,y) \ T(x * (x \ 1),y) = T(T(x,y) \ 1,x \ T(x,z)).
T(T(x,y) \ 1,x \ T(x,z)) = T(x,y) \ T(x * (x \ 1),y).
(x \ (x / T(x,y))) * T(x,y) = T((x \ 1) * x,y).
(x \ (x / T(x,y))) * T(x,y) = T(K(x \ 1,x),y).
(x * T(x \ (y * z),u)) / z = T(y / (x / z),u) * (x / z).
(x * L(x \ 1,y,z)) * (x \ u) = u * L(u \ (x \ u),y,z).
(x * T(x \ y,z)) * u = x * (u * T(u \ (x \ (y * u)),z)).
x * (y * T(y \ (x \ (z * y)),u)) = (x * T(x \ z,u)) * y.
(x * R(x \ 1,y,z)) * x = x * (x * R(x \ 1,y,z)).
T(x,x * R(x \ 1,y,z)) = x.
T(x * R(x \ 1,y,z),x) = x * R(x \ 1,y,z).
T(1 / x,(1 / x) * R(x,y,z)) = 1 / x.
T(x,(y / (x * y)) * x) = x.
T(x \ 1,R(x,y,z) * (x \ 1)) = x \ 1.
T(x \ 1,x \ R(x,y,z)) = x \ 1.
T(x / y,(y / x) * (x / y)) = x / y.
T(x * (y / (x * y)),x) = T(x,y / (x * y)) * T(y / (x * y),x).
T(x,y / (x * y)) * T(y / (x * y),x) = T(x * (y / (x * y)),x).
T(x \ R(x,y,z),x \ 1) = x \ R(x,y,z).
T(x \ 1,y) = T(T(x \ 1,y),x \ R(x,z,u)).
T(T(x \ 1,y),x \ R(x,z,u)) = T(x \ 1,y).
T(x / (y * x),y * (x / (y * x))) = x / (y * x).
(R(x,y,z) * (1 / x)) / R(x,y,z) = L(1 / x,R(x,y,z),1 / x).
R(x \ 1,R(x,y,z),x \ 1) = T(x \ 1,R(x,y,z)).
T(x * ((x * R(x \ 1,y,z)) / x),x) = x * ((x * R(x \ 1,y,z)) / x).
R(x / (y * x),y,x / (y * x)) = T(x / (y * x),y).
T(x \ 1,R(x,y,z)) \ T((x \ 1) * R(x,y,z),x \ 1) = T(R(x,y,z),x \ 1).
R(x / (y * x),y,x / (y * x)) = R(y \ 1,y,x).
R(x \ 1,x,y) \ T((y / (x * y)) * x,y / (x * y)) = T(x,y / (x * y)).
T(x,y) * ((T(x,y) \ x) / x) = T(x,T(x,y) \ 1) / x.
x * (T(x,T(x,y) \ 1) / x) = T(x,x / (x * T(x,y))).
(x * T(x \ (y / z),u)) * z = x * (z * T(z \ (x \ y),u)).
(x * L(x \ 1,y,z)) * x = x * (x * L(x \ 1,y,z)).
T(x,x * L(x \ 1,y,z)) = x.
T(x,x * ((y * x) \ y)) = x.
T(x \ y,(x \ y) * (y \ x)) = x \ y.
(((x * y) \ x) * y) / ((x * y) \ x) = L(y,(x * y) \ x,y).
T(T(x,y),T(x,y) * ((T(x,y) / x) \ (1 / x))) = T(x,y).
T(x \ (x / y),(x \ (x / y)) * y) = x \ (x / y).
(x \ y) * (y \ x) = L(y \ x,x \ y,y \ x) * (x \ y).
L(x \ y,y \ x,x \ y) * (y \ x) = (y \ x) * (x \ y).
T((x \ (x / y)) * y,x \ (x / y)) = (x \ (x / y)) * y.
T(T(x,y) * ((T(x,y) / x) \ (1 / x)),T(x,y)) = T(x,y) * ((T(x,y) / x) \ (1 / x)).
x * (y \ z) != (y \ z) * (z \ y) | x = L(1 / (y \ z),y \ z,y).
L(x \ y,y \ x,x \ y) = L(1 / (y \ x),y \ x,y).
T(x \ T(x,y),x) = T(x \ T(x,y),T(x,x \ 1)).
T(x \ T(x,y),T(x,x \ 1)) = T(x \ T(x,y),x).
L(T(x \ T(x,y),x),x,y) = T((y * x) \ (x * y),T(x,x \ 1)).
T((x * y) \ (y * x),T(y,y \ 1)) = L(T(y \ T(y,x),y),y,x).
T(T(x,y) \ 1,x \ T(x,z)) = T(x,y) \ T(1,y).
T(T(x,y) \ 1,x \ T(x,z)) = T(x,y) \ 1.
(x * T(x \ (y * z),u)) / z = (x / z) * T((x / z) \ y,u).
(x * (1 / x)) * (x \ y) = y * L(y \ (x \ y),x,x \ 1).
x * L(x \ (y \ x),y,y \ 1) = (y * (1 / y)) * (y \ x).
x * L(x \ (y \ x),y,y \ 1) = K(y,y \ 1) * (y \ x).
T(x * T(x \ y,z),x) = x * T(x \ (x \ (y * x)),z).
x * T(x \ (x \ (y * x)),z) = T(x * T(x \ y,z),x).
T(x * ((1 / x) * ((1 / x) \ (x \ (y * (1 / x))))),x) = (x * T(x \ y,x)) * (1 / x).
x * T(x \ T(y,x),z) = T(x * T(x \ y,z),x).
T(x * T(x \ y,z),x) = x * T(x \ T(y,x),z).
x \ T(x * T(x \ y,z),x) = T(x \ T(y,x),z).
x \ T(x * T(y,z),x) = T(x \ T(x * y,x),z).
x \ T(x * T(y / x,z),x) = T(T(y,x) / x,z).
x * T(T(y,x) / x,z) = T(x * T(y / x,z),x).
T(x * T(y / x,z),x) = x * T(T(y,x) / x,z).
T(x * T(1 / x,y),x) = x * T(1 / x,y).
(x \ T(x * (y / z),u)) * z = (x \ 1) * (z * T(z \ ((x \ 1) \ y),u)).
(x \ 1) * (y * T(y \ ((x \ 1) \ z),u)) = (x \ T(x * (z / y),u)) * y.
((x / y) * K(y \ 1,y)) * y = x * (y * T(y \ (x \ x),y)).
(x * (y * T(y \ z,u))) / z = ((x * y) / z) * T(((x * y) / z) \ x,u).
((x * y) / z) * T(((x * y) / z) \ x,u) = (x * (y * T(y \ z,u))) / z.
((x / y) * K(y \ 1,y)) * y = x * (y * T(y \ 1,y)).
((x / y) * K(y \ 1,y)) * y = x * ((y \ 1) * y).
((x / y) * K(y \ 1,y)) * y = x * K(y \ 1,y).
(x * K(y \ 1,y)) * y = (x * y) * K(y \ 1,y).
(L(1 / x,x,y) * K(x \ 1,x)) * x = (x * ((y * x) \ y)) * K(x \ 1,x).
x * y = ((x / K(y \ 1,y)) * y) * K(y \ 1,y).
((x / K(y \ 1,y)) * y) * K(y \ 1,y) = x * y.
x * K(y \ 1,y) != (z * (y \ 1)) * y | x = R(z,y \ 1,y).
((x * (y \ 1)) / K(y \ 1,y)) * y = R(x,y \ 1,y).
(x * R(x \ y,z,u)) * (x \ 1) = R(y * (x \ 1),z,u).
R(x * (y \ 1),z,u) / (y \ 1) = y * R(y \ x,z,u).
R(x,y,z) / (u \ 1) = u * R(u \ (x / (u \ 1)),y,z).
x * R(x \ (y / (x \ 1)),z,u) = R(y,z,u) / (x \ 1).
R(1 / x,y,z) / (x \ 1) = x * R(x \ K(x,x \ 1),y,z).
x * R(x \ K(x,x \ 1),y,z) = R(1 / x,y,z) / (x \ 1).
x * R(1 / x,y,z) = R(1 / x,y,z) / (x \ 1).
R(1 / x,y,z) / (x \ 1) = x * R(1 / x,y,z).
R(1 / (x \ 1),y,z) / T(x,x \ 1) = (x \ 1) * R(1 / (x \ 1),y,z).
(x / y) / ((y / x) \ 1) = (y / x) * R(1 / (y / x),y / x,x).
(x / y) * R(1 / (x / y),x / y,y) = (y / x) / ((x / y) \ 1).
x * ((y * (x \ (z * u))) / y) = z * ((z \ x) * ((y * ((z \ x) \ u)) / y)).
x * ((x \ y) * ((z * ((x \ y) \ u)) / z)) = y * ((z * (y \ (x * u))) / z).
(x * y) * L((x * y) \ (y * z),u,w) = y * (T(x,y) * L(T(x,y) \ z,u,w)).
((x \ y) * (y \ x)) \ (y \ x) = (x \ y) \ 1.
(x \ y) / ((y \ x) \ 1) = (y \ x) * (x \ y).
(1 / (x / y)) \ (y / x) = (y / x) * (x / y).
(1 / ((x \ y) / y)) \ x = (y / (x \ y)) * ((x \ y) / y).
(x / (y \ x)) * ((y \ x) / x) = (1 / ((y \ x) / x)) \ y.
x * ((x \ y) / y) = (1 / ((x \ y) / y)) \ x.
(1 / ((x \ y) / y)) \ x = x * ((x \ y) / y).
(1 / ((x \ y) / y)) * (x * ((x \ y) / y)) = x.
T(1 / ((x \ y) / y),x * ((x \ y) / y)) = (x * ((x \ y) / y)) \ x.
(x \ y) * (y \ x) = (1 / (y \ x)) \ (x \ y).
(1 / (x \ y)) \ (y \ x) = (y \ x) * (x \ y).
(1 / (x \ y)) * ((y \ x) * (x \ y)) = y \ x.
T(1 / (x \ y),(y \ x) * (x \ y)) = ((y \ x) * (x \ y)) \ (y \ x).
R(x,T(1 / x,y),x) = T(x,(x * T(x \ 1,y)) / x).
T(x,(x * T(x \ 1,y)) / x) = R(x,T(1 / x,y),x).
T(x,T(1 / x,y)) = R(x,T(1 / x,y),x).
R(x,T(1 / x,y),x) = T(x,T(1 / x,y)).
R(T(x,T(1 / x,y)),z,u) = R(R(x,z,u),T(1 / x,y),x).
R(R(x,y,z),T(1 / x,u),x) = R(T(x,T(1 / x,u)),y,z).
T(x,T(1 / x,y)) * T(T(1 / x,y),x) = T(x * T(1 / x,y),x).
K(x,x \ 1) = R(x \ 1,x,y) \ (((y / (x * y)) * x) * (1 / x)).
R(x \ 1,x,y) \ (((y / (x * y)) * x) * (1 / x)) = K(x,x \ 1).
T(x \ (K(y,y \ 1) * (y \ x)),y) = x \ (y \ x).
T(x \ (K(y \ 1,y) * ((y \ 1) \ x)),y \ 1) = x \ ((y \ 1) \ x).
T((x * y) \ (y * x),T(y,y \ 1)) = T((x * y) \ (y * x),y).
T((x * y) \ (y * x),T(y,y \ 1)) = T(K(y,x),y).
T(K(x,y),T(x,x \ 1)) = T(K(x,y),x).
(x / y) * (y / x) = (y / x) / ((x / y) \ 1).
(x / y) / ((y / x) \ 1) = (y / x) * (x / y).
x / (((x \ y) / y) \ 1) = ((x \ y) / y) * (y / (x \ y)).
((x \ y) / y) * (y / (x \ y)) = x / (((x \ y) / y) \ 1).
((x \ y) / y) * x = x / (((x \ y) / y) \ 1).
x / (((x \ y) / y) \ 1) = ((x \ y) / y) * x.
((x \ y) / y) * R(((x \ y) / y) \ (((x \ y) / y) * x),z,u) = R(x,z,u) / (((x \ y) / y) \ 1).
x * (y * L(y \ (x \ y),z,u)) = (x * L(x \ 1,z,u)) * y.
x * (y * L(y \ (x \ y),x,x \ 1)) = (x * (1 / x)) * y.
x * (K(x,x \ 1) * (x \ y)) = (x * (1 / x)) * y.
x * y != (x * z) * L(u,z,x) | y = z * u.
K(x,x \ 1) * (x \ L(y,1 / x,x)) = (1 / x) * y.
x * (K(x,x \ 1) * (x \ y)) = K(x,x \ 1) * y.
x \ (K(x,x \ 1) * y) = K(x,x \ 1) * (x \ y).
x * y != K(x,x \ 1) * L(x,z,u) | y = L(x,z,u) * (1 / x).
K(x,x \ 1) * (x \ L(x,y,z)) = L(x,y,z) * (1 / x).
x * (K(x,x \ 1) * y) = K(x,x \ 1) * (x * y).
K(x,x \ 1) * (x * y) = x * (K(x,x \ 1) * y).
x * (K(x,x \ 1) * T(y,x)) = K(x,x \ 1) * (y * x).
(x \ 1) * (K(x \ 1,x) * ((x \ 1) \ y)) = K(x \ 1,(x \ 1) \ 1) * y.
(1 / x) * (K(x \ 1,x) * ((1 / x) \ y)) = K(1 / x,(1 / x) \ 1) * y.
T(x,x \ 1) * L(y,x,K(x,x \ 1)) = x * (K(x,x \ 1) * y).
(1 / x) * y != K(x,x \ 1) * z | x \ L(y,1 / x,x) = z.
K(x,x \ 1) * y != (1 / x) * z | x \ L(z,1 / x,x) = y.
K(1 / x,(1 / x) \ 1) * ((1 / x) \ L(1 / x,y,z)) = L(x \ 1,y,z) / (1 / x).
T(x,x \ 1) * y != x * (K(x,x \ 1) * z) | y = L(z,K(x,x \ 1),x).
L(x,y,K(y,y \ 1)) = L(x,K(y,y \ 1),y).
L(x,K(y,y \ 1),y) = L(x,y,K(y,y \ 1)).
L(x,K(1 / y,y),1 / y) = L(x,1 / y,K(1 / y,(1 / y) \ 1)).
L(x,1 / y,K(1 / y,(1 / y) \ 1)) = L(x,K(1 / y,y),1 / y).
L(x,K(y \ 1,y),1 / y) = L(x,1 / y,K(1 / y,(1 / y) \ 1)).
L(x,1 / y,K(1 / y,(1 / y) \ 1)) = L(x,K(y \ 1,y),1 / 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.
(L((x / y) / z,u,w) * z) * y = (z * y) * L((z * y) \ x,u,w).
(R(x / y,z,u) * y) * w = (y * w) * R((y * w) \ (x * w),z,u).
(x * y) * R((x * y) \ (z * y),u,w) = (R(z / x,u,w) * x) * y.
((x * ((y * z) / (R(u,y,z) * (y * z)))) / x) * ((u * y) * z) = (((x * (1 / R(u,y,z))) / x) * R(u,y,z)) * (y * z).
(((x * (1 / y)) / x) * y) * z = (y * z) * ((x * ((y * z) \ z)) / x).
(x * y) * ((z * ((x * y) \ y)) / z) = (((z * (1 / x)) / z) * x) * y.
T(x,R(y,y \ 1,x)) = (((x * y) / x) * (y \ 1)) * x.
(((x * y) / x) * (y \ 1)) * x = T(x,R(y,y \ 1,x)).
(x \ ((y * x) / y)) * y = T(y,R(x,x \ 1,y)).
T(x,R(y,y \ 1,x)) / x = y \ ((x * y) / x).
(T(x,y) \ x) * y = T(y,R(T(x,y),T(x,y) \ 1,y)).
T(x,R(T(y,x),T(y,x) \ 1,x)) = (T(y,x) \ y) * x.
L(x \ 1,x,y \ ((x * y) / x)) = T(1 / x,T(x,R(y,y \ 1,x))).
T(1 / x,T(x,R(y,y \ 1,x))) = L(x \ 1,x,y \ ((x * y) / x)).
(x * (((T(y,x) \ y) * x) \ x)) \ (x * x) = T(x,R(T(y,x),T(y,x) \ 1,x)).
L(x \ 1,x,y / (x * y)) = T(1 / x,(y / (x * y)) * x).
T(1 / x,(y / (x * y)) * x) = L(x \ 1,x,y / (x * y)).
(L(x / (y / z),u,w) * (y / z)) * z = y * L(y \ (x * z),u,w).
x \ (y * L(y \ (x * z),u,w)) = (x \ y) * L((x \ y) \ z,u,w).
(R(1 / (x / y),z,u) * (x / y)) * y = R(y / x,z,u) * x.
(R(1 / (x / y),z,u) * (x / y)) * y = x * R(x \ y,z,u).
((x / y) * R((x / y) \ 1,z,u)) * y = x * R(x \ y,z,u).
(x * R(x \ y,z,u)) / y = (x / y) * R((x / y) \ 1,z,u).
(x / y) * R((x / y) \ 1,z,u) = (x * R(x \ y,z,u)) / y.
R(x,y,z) * R((((x * y) * z) / (y * z)) \ 1,u,w) = (((x * y) * z) * R(((x * y) * z) \ (y * z),u,w)) / (y * z).
(((x * y) * z) * R(((x * y) * z) \ (y * z),u,w)) / (y * z) = R(x,y,z) * R((((x * y) * z) / (y * z)) \ 1,u,w).
(x / y) \ (x * ((z * (x \ (x / y))) / z)) = y * ((z * (y \ 1)) / z).
K(x,x \ 1) * ((1 / x) \ y) = y * T(y \ ((1 / x) \ y),x \ 1).
L(1 / x,y,z) * K(x \ 1,x) = (x \ 1) * (x * L(x \ 1,y,z)).
K(T(x \ 1,x) \ 1,T(x \ 1,(x \ 1) \ 1)) = K(x,x \ 1).
K(T(x \ 1,x) \ 1,T(x \ 1,x)) = K(x,x \ 1).
K(x,x \ 1) = K(T(x,x \ 1),T(x \ 1,x)).
K(T(x,x \ 1),T(x \ 1,x)) = K(x,x \ 1).
K(T(x,x \ 1),T(x,x \ 1) \ 1) = K(x,x \ 1).
T(x,x \ 1) \ (K(x,x \ 1) * y) = K(T(x,x \ 1),T(x,x \ 1) \ 1) * (T(x,x \ 1) \ y).
K(T(x,x \ 1),T(x,x \ 1) \ 1) * (T(x,x \ 1) \ y) = T(x,x \ 1) \ (K(x,x \ 1) * y).
((x * (1 / (1 / T(y,x)))) / x) \ (y / T(y,x)) = 1 / T(y,x).
T(x,y / (x * y)) * R(x \ 1,x,y) = T(x * (y / (x * y)),x).
T(x,T(1 / x,y)) * T(x \ 1,y) = T(x * T(1 / x,y),x).
T(x,T(1 / x,y)) * T(x \ 1,y) = x * T(1 / x,y).
L(x,1 / (1 / y),K(1 / (1 / y),(1 / (1 / y)) \ 1)) = L(x,K(y,y \ 1),1 / (1 / y)).
L(x,1 / y,K(y \ 1,y)) = L(x,K(y \ 1,y),1 / y).
L(x,K(y \ 1,y),1 / y) = L(x,1 / y,K(y \ 1,y)).
(x * y) * L((x * y) \ (z * y),u,w) = (x * L(x \ z,u,w)) * y.
(x * L(x \ (y / z),u,w)) * z = (x * z) * L((x * z) \ y,u,w).
(x * y) * R((x * y) \ (z * y),u,w) = (x * R(x \ z,u,w)) * y.
(x * y) * ((z * ((x * y) \ y)) / z) = (x * ((z * (x \ 1)) / z)) * y.
((x / y) * L((x / y) \ z,u,w)) * y = x * L(x \ (z * y),u,w).
x \ (y * L(y \ x,z,u)) = (x \ y) * L((x \ y) \ 1,z,u).
(x \ y) * L((x \ y) \ 1,z,u) = x \ (y * L(y \ x,z,u)).
(x / y) \ (x * ((x / y) / x)) = y * ((x * (y \ 1)) / x).
x * ((y * (x \ 1)) / y) = K(y,(y / x) / y).
K(x,(x / y) / x) = y * ((x * (y \ 1)) / x).
K(x,y / x) = (y \ x) * ((x * ((y \ x) \ 1)) / x).
(x \ y) * ((y * ((x \ y) \ 1)) / y) = K(y,x / y).
K(T(x,y),1 / x) = x * ((T(x,y) * (x \ 1)) / T(x,y)).
x * ((T(x,y) * (x \ 1)) / T(x,y)) = K(T(x,y),1 / x).
x * K(x,(x / y) / x) = T(x,x / (x * y)).
K(x,(x / (y \ 1)) / x) = y \ ((x * y) / x).
K(T(x,y),1 / T(x,z)) = T(x,z) * ((T(x,y) * (T(x,z) \ 1)) / T(x,y)).
T(x,y) * ((T(x,z) * (T(x,y) \ 1)) / T(x,z)) = K(T(x,z),1 / T(x,y)).
x * K(x,y / x) = T(x,x / (x * (y \ x))).
T(x,x / (x * (y \ x))) = x * K(x,y / x).
x * K(y,(y / (x \ 1)) / y) = (y * x) / y.
K(x,(x / ((T(x,y) \ 1) \ 1)) / x) = (T(x,y) \ 1) \ ((T(x,y) \ x) / x).
K(R(x,y,z),(R(x,y,z) / ((x \ 1) \ 1)) / R(x,y,z)) = (x \ 1) \ ((x \ R(x,y,z)) / R(x,y,z)).
T(x,R(y,x,(y * x) \ x)) = x * K(x,(y * x) / x).
T(x,R(y,x,(y * x) \ x)) = x * K(x,y).
x \ ((x * K(x,y)) * z) = T(x,R(y,x,(y * x) \ x)) * (x \ z).
T(x,R(y,x,(y * x) \ x)) * (x \ z) = x \ ((x * K(x,y)) * z).
x * (((x \ 1) * T((x \ 1) \ 1,y)) / T(x,y)) = K(T(x,y),1 / x).
(x * K(x,y)) * (x \ z) = x \ ((x * K(x,y)) * z).
x \ ((x * K(x,y)) * z) = (x * K(x,y)) * (x \ z).
x \ (x * K(x,y)) = (x * K(x,y)) * (x \ 1).
(x * K(x,y)) * (x \ 1) = x \ (x * K(x,y)).
(x * K(x,y)) * (x \ 1) = K(x,y).
K(x,y) / (x \ 1) = x * K(x,y).
(x * ((y * (x \ 1)) / y)) / (y \ 1) = y * K(y,(y / x) / y).
(x * ((y * (x \ 1)) / y)) / (y \ 1) = T(y,y / (y * x)).
(x * ((x \ R(x,y,z)) / R(x,y,z))) / (R(x,y,z) \ 1) = T(R(x,y,z),R(x,y,z) / (R(x,y,z) * x)).
((x * y) * L((x * y) \ x,z,u)) * y = (x * y) * (y * L(y \ 1,z,u)).
(x * L(x \ y,z,u)) * w = x * (w * L(w \ (x \ (y * w)),z,u)).
x * (y * L(y \ (x \ (z * y)),u,w)) = (x * L(x \ z,u,w)) * y.
(x * L(x \ (y / z),u,w)) * z = x * (z * L(z \ (x \ y),u,w)).
(x * R(x \ y,z,u)) * w = x * (w * R(w \ (x \ (y * w)),z,u)).
x * (y * R(y \ (x \ (z * y)),u,w)) = (x * R(x \ z,u,w)) * y.
(x * y) * (y / (x * y)) = (x * (((x * y) * (x \ 1)) / (x * y))) * y.
(x * (((x * y) * (x \ 1)) / (x * y))) * y = (x * y) * (y / (x * y)).
(x * ((y * (x \ 1)) / y)) * x = x * (x * ((y * (x \ 1)) / y)).
(((x * y) / x) / y) * (1 / y) = (1 / y) * ((1 / y) * ((x * ((1 / y) \ 1)) / x)).
(1 / x) * ((1 / x) * ((y * ((1 / x) \ 1)) / y)) = (((y * x) / y) / x) * (1 / x).
(x * L(x \ (y * z),u,w)) / z = (x / z) * L((x / z) \ y,u,w).
T(x * L(x \ (y / z),u,w),z) = z \ (x * (z * L(z \ (x \ y),u,w))).
x \ (y * (x * L(x \ (y \ z),u,w))) = T(y * L(y \ (z / x),u,w),x).
(x * L(x \ y,z,u)) / y = (x / y) * L((x / y) \ 1,z,u).
(x / y) * L((x / y) \ 1,z,u) = (x * L(x \ y,z,u)) / y.
R(x,y,z) * L((((x * y) * z) / (y * z)) \ 1,u,w) = (((x * y) * z) * L(((x * y) * z) \ (y * z),u,w)) / (y * z).
(((x * y) * z) * L(((x * y) * z) \ (y * z),u,w)) / (y * z) = R(x,y,z) * L((((x * y) * z) / (y * z)) \ 1,u,w).
L(x,K(y \ 1,y),1 / y) = (1 / y) * ((y \ 1) \ (K(y \ 1,y) * x)).
(1 / x) * ((x \ 1) \ (K(x \ 1,x) * y)) = L(y,K(x \ 1,x),1 / x).
((x * (y * (z \ 1))) / x) / (z \ 1) = z * ((x * (z \ y)) / x).
((x * y) / x) / ((y \ 1) \ 1) = (y \ 1) * ((x * ((y \ 1) \ K(y \ 1,y))) / x).
(x \ 1) * ((y * ((x \ 1) \ K(x \ 1,x))) / y) = ((y * x) / y) / ((x \ 1) \ 1).
T(T(R(x,y,y \ 1),x * y) / (y \ 1),R(x,y,y \ 1)) = x * y.
T(R(T(x,x * y),y,y \ 1) / (y \ 1),R(x,y,y \ 1)) = x * y.
T(T(x,x * y) * y,R(x,y,y \ 1)) = x * y.
T(x * y,z) = T(T(T(x,x * y) * y,z),R(x,y,y \ 1)).
T(T(T(x,x * y) * y,z),R(x,y,y \ 1)) = T(x * y,z).
T(x * y,R(x,y,y \ 1)) = T(x * y,T(x,y)).
T(x,R(x / y,y,y \ 1)) = T((x / y) * y,T(x / y,y)).
T((x / y) * y,T(x / y,y)) = T(x,R(x / y,y,y \ 1)).
T((x / y) * y,T(x / y,y)) = T(x,x * (y \ 1)).
T(x,T(x / y,y)) = T(x,x * (y \ 1)).
T(x,y \ x) = T(x,x * (y \ 1)).
T(x,x * (y \ 1)) = T(x,y \ x).
L(R(x,y,z),x \ 1,x) / R(x,y,z) = x * T(x \ 1,R(x,y,z)).
R(1 / (1 / x),y,z) / R(x,y,z) = x * T(x \ 1,R(x,y,z)).
L(x \ L(y,1 / x,K(x \ 1,x)),x,x \ 1) = (1 / x) * y.
(T(x,y) * ((T(x,y) \ x) / x)) * x = T(x,(1 * x) / (x * T(x,y))).
(T(x,y) * ((T(x,y) \ x) / x)) * x = T(x,x / (x * T(x,y))).
(T(x,T(x,y) \ 1) / x) * x = T(x,x / (x * T(x,y))).
T(x,x / (x * T(x,y))) = T(x,T(x,y) \ 1).
x * (T(x,T(x,y) \ 1) / x) = T(x,T(x,y) \ 1).
x * (T(x,y) * ((T(x,y) \ x) / x)) = T(x,T(x,y) \ 1).
(1 / x) * ((x \ 1) \ ((x \ 1) * (x * y))) = L(L(y,x,x \ 1),K(x \ 1,x),1 / x).
L(L(x,y,y \ 1),K(y \ 1,y),1 / y) = (1 / y) * ((y \ 1) \ ((y \ 1) * (y * x))).
T(L(1 / x,R(x,y,z),1 / x),x) = (x \ R(x,y,z)) / R(x,y,z).
(x \ R(x,y,z)) / R(x,y,z) = L(x \ 1,R(x,y,z),1 / x).
L(x \ 1,R(x,y,z),1 / x) = (x \ R(x,y,z)) / R(x,y,z).
(x \ y) \ K(T(x / y,T(y,x)),T(y,x)) = T((x \ y) \ 1,T(y,x)).
(x \ y) * T((x \ y) \ 1,T(y,x)) = K(T(x / y,T(y,x)),T(y,x)).
K(T(x / y,T(y,x)),T(y,x)) = x \ (y * T(y \ x,T(y,x))).
x * ((x * y) * ((z * ((x * y) \ y)) / z)) = (x * ((z * (x \ 1)) / z)) * (x * y).
(x * y) * T((x * y) \ (y * x),x) = y * L(x,T(x,y) \ x,T(x,y)).
(x * y) * T(K(y,x),x) = y * L(x,T(x,y) \ x,T(x,y)).
x * L(y,T(y,x) \ y,T(y,x)) = (y * x) * T(K(x,y),y).
K(x \ 1,x * L(x \ 1,y,z)) = (x \ 1) * T(x,L(x \ 1,y,z)).
K(x \ 1,x * L(x \ 1,x,y / x)) = (x \ 1) * T(x,y \ (y / x)).
K(x \ 1,x * (y \ (y / x))) = (x \ 1) * T(x,y \ (y / x)).
(x \ 1) * (K(x,x \ 1) * ((x \ 1) \ y)) = K(x,x \ 1) * y.
(x \ 1) \ (K(x,x \ 1) * y) = K(x,x \ 1) * ((x \ 1) \ y).
K(((x \ y) * (y \ x)) \ (x \ y),(x \ y) * (y \ x)) = y \ (x * (x \ y)).
(x * (T(x,y) / x)) * K(x \ 1,x) = T(x * (K(x,x \ 1) \ 1),y).
(x * (T(x,y) / x)) * K(x \ 1,x) = T(x * K(x \ 1,x),y).
(x * (T(x,y) / x)) * K(x \ 1,x) = T(1 / (1 / x),y).
T(x * ((x * R(x \ 1,y,z)) / x),x) = x * R(1 / x,y,z).
T(x * R(1 / x,y,z),x) = x * R(1 / x,y,z).
T(x * (y / (x * y)),x) = x * R(1 / x,x,y).
T(x * (y / (x * y)),x) = x * (y / (x * y)).
T(x,x * (y / (x * y))) = x.
T(x,y / (x * y)) * R(x \ 1,x,y) = x * (y / (x * y)).
T(x,x * ((x \ y) / y)) = x.
T(x / y,(x / y) * (y / x)) = x / y.
T(x,x \ y) = T((x \ y) \ y,x * ((x \ z) / z)).
T((x \ y) \ y,x * ((x \ z) / z)) = T(x,x \ y).
T(x / (y * x),(x / (y * x)) * y) = x / (y * x).
T(x / y,y) = T(y \ x,(x / y) * (y / x)).
T(x \ y,(y / x) * (x / y)) = T(y / x,x).
T(x \ y,(y / x) * (x / y)) = x \ y.
K(((x / y) * (y / x)) \ (x / y),(x / y) * (y / x)) = (y * (y \ x)) / x.
K((x * ((x \ y) / y)) \ x,x * ((x \ y) / y)) = ((x \ y) * T(x,x \ y)) / y.
T((x / (y * x)) * y,x / (y * x)) = (x / (y * x)) * y.
(x \ 1) * ((y \ ((x \ 1) \ z)) * y) = (x \ T(x * (z / y),y)) * y.
(x \ T(x * (y / z),z)) * z = (x \ 1) * ((z \ ((x \ 1) \ y)) * z).
(x \ 1) * ((x \ T(x,y)) * ((x \ 1) \ z)) = (x \ T(x * (z / z),y)) * z.
(x \ T(x * (y / y),z)) * y = (x \ 1) * ((x \ T(x,z)) * ((x \ 1) \ y)).
T((x \ (x * (y / x))) * x,x) = (x \ 1) * ((x \ ((x \ 1) \ y)) * x).
T(x,y) = (y \ 1) * ((y \ ((y \ 1) \ x)) * y).
T((x \ 1) * y,x) = (x \ 1) * ((x \ y) * x).
(x \ 1) * ((x \ y) * x) = T((x \ 1) * y,x).
((x \ 1) * y) \ T((x \ 1) * y,x) = L(K(x \ y,x),y,x \ 1).
R(x,y,z) / T(x,x \ 1) = (x \ 1) * R(1 / (x \ 1),y,z).
R(x,y,z) / T(x,x \ 1) = (x \ 1) * R(x,y,z).
R(x,y,z) / ((x \ 1) \ 1) = (x \ 1) * R(x,y,z).
x * K(y,(y / (x \ z)) / y) = z * ((y * (z \ (x * 1))) / y).
x * K(y,(y / (x \ z)) / y) = z * ((y * (z \ x)) / y).
x * K(y,(y / T(z,x)) / y) = (z * x) * ((y * ((z * x) \ x)) / y).
(x * y) * ((z * ((x * y) \ y)) / z) = y * K(z,(z / T(x,y)) / z).
x * K(y,(y / T(z,x)) / y) = (z * ((y * (z \ 1)) / y)) * x.
(x * ((y * (x \ 1)) / y)) * z = z * K(y,(y / T(x,z)) / y).
T(x * ((y * (x \ 1)) / y),z) = K(y,(y / T(x,z)) / y).
T(x * (1 / x),y) = K(x,(x / T(x,y)) / x).
K(x,(x / T(x,y)) / x) = T(x * (1 / x),y).
T(x \ T(x,x / (x * y)),z) = K(x,(x / T(y,z)) / x).
T(x * ((y * (x \ 1)) / y),z) = T(x,z) * ((y * (T(x,z) \ 1)) / y).
T(x,y) * ((z * (T(x,y) \ 1)) / z) = T(x * ((z * (x \ 1)) / z),y).
T(K(x,y / x),z) = K(x,(x / T(y \ x,z)) / x).
K(x,(x / T(y \ x,z)) / x) = T(K(x,y / x),z).
T(x * (1 / x),y) = T(x,y) * ((x * (T(x,y) \ 1)) / x).
T(x,y) * ((x * (T(x,y) \ 1)) / x) = T(x * (1 / x),y).
K(x,(x / (y \ x)) / x) = T(K(x,y / x),K(y / x,z)).
T(K(x,y / x),K(y / x,z)) = K(x,(x / (y \ x)) / x).
T(x,y) * ((T(x,y) \ x) / x) = T(x * (1 / x),y).
T(x,y) * ((T(x,y) \ x) / x) = T(K(x,x \ 1),y).
x * T(K(x,x \ 1),y) = T(x,T(x,y) \ 1).
T(K(x,y / x),K(y / x,z)) = K(x,y / x).
T(K(x,y),K((y * x) / x,z)) = K(x,(y * x) / x).
T(K(x,y),K(y,z)) = K(x,(y * x) / x).
T(K(x,y),K(y,z)) = K(x,y).
T(x,y) * (1 / T(x,y)) = T(x * ((T(x,y) * (x \ 1)) / T(x,y)),y).
T(x * ((T(x,y) * (x \ 1)) / T(x,y)),y) = T(x,y) * (1 / T(x,y)).
T(x,y) * ((T(x,z) * (T(x,y) \ 1)) / T(x,z)) = T(x * (((x \ 1) * T((x \ 1) \ 1,z)) / T(x,z)),y).
T(x * (((x \ 1) * T((x \ 1) \ 1,y)) / T(x,y)),z) = T(x,z) * ((T(x,y) * (T(x,z) \ 1)) / T(x,y)).
K(T(x,y),T(x,y) \ 1) = T(x * ((T(x,y) * (x \ 1)) / T(x,y)),y).
T(x * ((T(x,y) * (x \ 1)) / T(x,y)),y) = K(T(x,y),T(x,y) \ 1).
T(K(T(x,y),1 / x),y) = K(T(x,y),T(x,y) \ 1).
K(T(x,y),T(x,y) \ 1) = T(K(T(x,y),1 / x),y).
(x \ 1) * (K(x \ 1,x) * ((x \ 1) \ y)) = K(x \ 1,x) * y.
(x \ 1) \ (K(x \ 1,x) * y) = K(x \ 1,x) * ((x \ 1) \ y).
L((1 / x) \ y,1 / x,K(x \ 1,x)) = K(x \ 1,x) * ((x \ 1) \ y).
(1 / x) * (K(x \ 1,x) * (x * y)) = K(1 / x,(1 / x) \ 1) * L(y,x,1 / x).
K(1 / x,(1 / x) \ 1) * L(y,x,1 / x) = (1 / x) * (K(x \ 1,x) * (x * y)).
T(x,y) * ((T(x,y) \ T(x,z)) / T(x,z)) = K(T(x,z),1 / T(x,y)).
(x * (y * L(y \ 1,z,u))) * y = (x * y) * (y * L(y \ 1,z,u)).
(x * (y * (1 / y))) * y = (x * y) * (y * L(y \ 1,y,1 / y)).
(x * y) * (y * L(y \ 1,y,1 / y)) = (x * (y * (1 / y))) * y.
(x * y) * (y * (1 / y)) = (x * (y * (1 / y))) * y.
(x * (y * (1 / y))) * y = (x * y) * (y * (1 / y)).
(x * K(y,y \ 1)) * y = (x * y) * (y * (1 / y)).
(x * K(y,y \ 1)) * y = (x * y) * K(y,y \ 1).
(x / y) * K(y,y \ 1) = (x * K(y,y \ 1)) / y.
(x * K(y,y \ 1)) / y = (x / y) * K(y,y \ 1).
T((x / y) * K(y,y \ 1),y) = y \ (x * K(y,y \ 1)).
K(((x \ y) * (y \ x)) \ (x \ y),(x \ y) * (y \ x)) = 1.
1 / (x \ y) = T(1 / (x \ y),(y \ x) * (x \ y)).
T(1 / (x \ y),(y \ x) * (x \ y)) = 1 / (x \ y).
1 / (x \ y) = ((y \ x) * (x \ y)) \ (y \ x).
((x \ y) * (y \ x)) \ (x \ y) = 1 / (y \ x).
(((x * y) \ x) * y) \ ((x * y) \ x) = 1 / (x \ (x * y)).
L((x \ y) \ 1,x \ y,y \ x) = 1 / (x \ y).
(x \ y) * (1 / (x \ y)) = x \ (y * L(y \ x,x \ y,y \ x)).
x \ (y * L(y \ x,x \ y,y \ x)) = (x \ y) * (1 / (x \ y)).
(((x * y) \ x) * y) \ ((x * y) \ x) = 1 / y.
(((x * y) \ x) * y) * (1 / y) = (x * y) \ x.
((x * y) \ x) / (1 / y) = ((x * y) \ x) * y.
L(x \ 1,x,(y * x) \ y) = 1 / x.
L(x \ 1,x,y \ (y / x)) = 1 / x.
L(1 / x,x,y) = L((y * x) \ y,x,(z * x) \ z).
L((x * y) \ x,y,(z * y) \ z) = L(1 / y,y,x).
(x \ (x / y)) / (1 / y) = (x \ (x / y)) * y.
(L(x \ 1,x,y) * x) * (1 / x) = (y * x) \ y.
(x * y) \ x = (L(y \ 1,y,x) * y) * (1 / y).
T(x,(y * x) \ y) = K(((y * x) \ y) \ (((y * x) \ y) * x),(y * x) \ y) * x.
K(((x * y) \ x) \ (((x * y) \ x) * y),(x * y) \ x) * y = T(y,(x * y) \ x).
T(1 / T(x,y),x) / (1 / T(x,y)) = (x \ (x / T(x,y))) * T(x,y).
L(x \ 1,x,y) = (L(x \ 1,x,y) * x) * (1 / x).
(L(x \ 1,x,y) * x) * (1 / x) = L(x \ 1,x,y).
L(x \ 1,x,y) / (1 / x) = L(x \ 1,x,y) * x.
K(x \ y,(x \ y) \ 1) = x \ (y * L(y \ x,x \ y,y \ x)).
x \ (y * L(y \ x,x \ y,y \ x)) = K(x \ y,(x \ y) \ 1).
x * K(x \ y,(x \ y) \ 1) = y * L(y \ x,x \ y,y \ x).
x * L(x \ y,y \ x,x \ y) = y * K(y \ x,(y \ x) \ 1).
T(1 / T(x,y),x) / (1 / T(x,y)) = T(K(x \ 1,x),y).
K(x \ (x / (1 / (1 / T(x,y)))),x) = T(K(x \ 1,x),y).
T(K(x \ 1,x),y) * (1 / T(x,y)) = x \ (x / T(x,y)).
K(((x / y) * (y / x)) \ (x / y),(x / y) * (y / x)) = x / x.
K(((x / y) * (y / x)) \ (x / y),(x / y) * (y / x)) = 1.
(x \ T(x * 1,y)) * z = (x \ 1) * ((x \ T(x,y)) * ((x \ 1) \ z)).
(x \ 1) * ((x \ T(x,y)) * ((x \ 1) \ z)) = (x \ T(x * 1,y)) * z.
(x \ 1) * ((x \ T(x,y)) * ((x \ 1) \ z)) = (x \ T(x,y)) * z.
x * y != z * (z \ x) | y = 1.
(x \ T(x,y)) * ((x \ 1) \ ((x \ T(x,y)) \ (x \ 1))) = 1.
(L(x \ 1,x,y) * y) / L(x \ 1,x,y) = y * (x * T(x \ 1,y)).
(x * (y * T(y \ 1,x))) * (x \ 1) = x \ ((L(y \ 1,y,x) * x) / L(y \ 1,y,x)).
x \ ((L(y \ 1,y,x) * x) / L(y \ 1,y,x)) = (x * (y * T(y \ 1,x))) * (x \ 1).
(1 / x) * (x * (y * T(y \ 1,x))) = ((L(y \ 1,y,x) * x) / L(y \ 1,y,x)) / x.
((L(x \ 1,x,y) * y) / L(x \ 1,x,y)) / y = (1 / y) * (y * (x * T(x \ 1,y))).
L(1 / x,T(x,y),1 / x) = (T(x,y) * (1 / x)) / T(x,y).
(T(x,y) * (1 / x)) / T(x,y) = L(1 / x,T(x,y),1 / x).
T(L(1 / x,T(x,y),1 / x),x) = (T(x,y) * (x \ 1)) / T(x,y).
(T(x,y) * (x \ 1)) / T(x,y) = L(x \ 1,T(x,y),1 / x).
x * L(x \ 1,T(x,y),1 / x) = K(T(x,y),1 / x).
(x \ y) \ (((y \ x) \ 1) \ (x \ y)) = ((y \ x) \ 1) \ 1.
(x \ y) * (((y \ x) \ 1) \ 1) = ((y \ x) \ 1) \ (x \ y).
((x \ y) \ 1) * ((((x \ y) \ 1) \ (y \ x)) / (y \ x)) = (((y \ x) * (x \ y)) / (y \ x)) * ((x \ y) \ 1).
K(x \ y,((x \ y) / ((y \ x) \ 1)) / (x \ y)) = ((y \ x) \ 1) * ((((y \ x) \ 1) \ (x \ y)) / (x \ y)).
((x \ y) \ 1) * ((((x \ y) \ 1) \ (y \ x)) / (y \ x)) = K(y \ x,((y \ x) / ((x \ y) \ 1)) / (y \ x)).
T(x,K(x \ 1,x) * y) = L(T(x,y),y,K(x \ 1,x)).
L(T(x,y),y,K(x \ 1,x)) = T(x,K(x \ 1,x) * y).
R(x \ 1,x,y) \ ((y / (x * y)) * x) = T(x,y / (x * y)).
T(x,y / (x * y)) = T(x,R(x \ 1,x,y)).
T(x,R(x \ 1,x,y)) = T(x,y / (x * y)).
(x * R(x \ 1,x,y)) \ (T(x,y / (x * y)) * R(x \ 1,x,y)) = K(T(x,R(x \ 1,x,y)),R(x \ 1,x,y)).
((x \ 1) * (x * L(x \ 1,x,y))) * x = (x * ((y * x) \ y)) * K(x \ 1,x).
(x * (((T(y,x) \ y) * x) \ x)) \ (x * x) = (T(y,x) \ y) * x.
(x * ((y * x) \ y)) * K(x \ 1,x) = ((x \ 1) * x) * (x * L(x \ 1,x,y)).
((x \ 1) * x) * (x * L(x \ 1,x,y)) = (x * ((y * x) \ y)) * K(x \ 1,x).
K(x \ 1,x) * (x * L(x \ 1,x,y)) = (x * ((y * x) \ y)) * K(x \ 1,x).
(x * y) * R((x * y) \ y,z,u) = y * (T(x,y) * R(T(x,y) \ 1,z,u)).
x * (T(y,x) * R(T(y,x) \ 1,z,u)) = (y * x) * R((y * x) \ x,z,u).
x * (T(y,x) * R(T(y,x) \ 1,z,u)) = (y * R(y \ 1,z,u)) * x.
T(x * R(x \ 1,y,z),u) = T(x,u) * R(T(x,u) \ 1,y,z).
T(x,y) * R(T(x,y) \ 1,z,u) = T(x * R(x \ 1,z,u),y).
(x / (T(y,z) * x)) * T(y,z) = T(y * R(y \ 1,T(y,z),x),z).
T(x * R(x \ 1,T(x,y),z),y) = (z / (T(x,y) * z)) * T(x,y).
T(x * R(x \ 1,T(x,y),x \ 1),y) = ((x \ 1) / (x \ T(x,y))) * T(x,y).
T(x * T(x \ 1,T(x,y)),y) = ((x \ 1) / (x \ T(x,y))) * T(x,y).
((x \ 1) / (x \ T(x,y))) * T(x,y) = T(x * T(x \ 1,T(x,y)),y).
x * T(y,z) != T(y * T(y \ 1,T(y,z)),z) | x = T(y,z) \ 1.
(x \ 1) / (x \ T(x,y)) = T(x,y) \ 1.
T(T(x,y) \ 1,x \ T(x,y)) = (x \ T(x,y)) \ (x \ 1).
(x \ T(x,y)) \ (x \ 1) = T(x,y) \ 1.
(x * T(x \ 1,y)) \ ((1 / x) \ 1) = T(1 / x,y) \ 1.
(x \ T(x,y)) * ((x \ 1) \ (T(x,y) \ 1)) = 1.
(x \ T(x,y)) \ 1 = (x \ 1) \ (T(x,y) \ 1).
(x \ 1) \ (T(x,y) \ 1) = (x \ T(x,y)) \ 1.
(x * T(x \ 1,y)) \ x = T(1 / x,y) \ 1.
x / (T(1 / x,y) \ 1) = x * T(x \ 1,y).
K(x \ (x / y),x) \ y = T(1 / y,x) \ 1.
(x * y) * L((x * y) \ y,z,u) = y * (T(x,y) * L(T(x,y) \ 1,z,u)).
x * (T(y,x) * L(T(y,x) \ 1,z,u)) = (y * x) * L((y * x) \ x,z,u).
x * (T(y,x) * L(T(y,x) \ 1,z,u)) = (y * L(y \ 1,z,u)) * x.
T(x * L(x \ 1,y,z),u) = T(x,u) * L(T(x,u) \ 1,y,z).
T(x,y) * L(T(x,y) \ 1,z,u) = T(x * L(x \ 1,z,u),y).
T(x,y) * ((z * T(x,y)) \ z) = T(x * L(x \ 1,T(x,y),z),y).
T(x * L(x \ 1,T(x,y),z),y) = T(x,y) * ((z * T(x,y)) \ z).
T(x,y) * L(T(x,y) \ 1,x,1 / x) = T(x * T(1 / x,1),y).
T(x * L(x \ 1,T(x,y),1 / x),y) = T(x,y) * ((T(x,y) / x) \ (1 / x)).
T(x,y) * ((1 / x) * (T(x,y) \ x)) = T(x * T(1 / x,1),y).
T(x,y) * ((1 / x) * (T(x,y) \ x)) = T(x * (1 / x),y).
T(x,y) * z != T(x * (1 / x),y) | z = (T(x,y) \ x) / x.
(1 / x) * (T(x,y) \ x) = (T(x,y) \ x) / x.
T(x,y) * ((1 / x) * (T(x,y) \ x)) = T(K(x,x \ 1),y).
T(1 / x,T(x,y) \ x) = (T(x,y) \ x) \ ((T(x,y) \ x) / x).
(T(x,y) \ x) \ ((T(x,y) \ x) / x) = T(1 / x,T(x,y) \ x).
T((T(x,y) \ x) / x,x) = (1 / x) * ((T(x,y) \ 1) * x).
T(x,y) \ T(K(x,x \ 1),y) = (1 / x) * (T(x,y) \ x).
(1 / x) * ((T(x,y) \ 1) * x) = x \ (T(x,y) \ x).
(1 / x) * ((T(x,y) \ 1) * x) = T(x,y) \ 1.
((T(x,y) \ x) / x) * K(x \ 1,x) = (T(x,y) \ x) * T(T(1 / x,T(x,y) \ x),x).
(T(x,y) \ x) * T(T(1 / x,T(x,y) \ x),x) = ((T(x,y) \ x) / x) * K(x \ 1,x).
T(K(T(x,y),1 / x),y) = T(x,y) * ((T(x,y) / x) \ (1 / x)).
T(x,y) * ((T(x,y) / x) \ (1 / x)) = T(K(T(x,y),1 / x),y).
K(T(x,y),T(x,y) \ 1) = T(x,y) * ((T(x,y) / x) \ (1 / x)).
T(x,y) * ((T(x,y) / x) \ (1 / x)) = K(T(x,y),T(x,y) \ 1).
x * y != K(x,x \ 1) | y = 1 / x.
(T(x,y) / x) \ (1 / x) = 1 / T(x,y).
(T(T(x,x \ 1),y) / T(x,x \ 1)) \ (x \ 1) = 1 / T(T(x,x \ 1),y).
T(x / (x / y),z) \ T(y,z) = T(y,z) * (T(x / (x / y),z) \ 1).
T(x,y) * (T(z / (z / x),y) \ 1) = T(z / (z / x),y) \ T(x,y).
T(T(x,y),z) / T(x,u) = (1 / T(x,u)) * T(T(x,y),z).
(1 / T(x,y)) * T(T(x,z),u) = T(T(x,z),u) / T(x,y).
(x \ 1) * T(T(x,y),z) = T(T(x,y),z) / T(x,x \ 1).
T(T(x,y),z) / T(x,x \ 1) = (x \ 1) * T(T(x,y),z).
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 \ T(x,y)) \ (x \ 1) = 1 / T(T(x,x \ 1),y).
1 / T(T(x,x \ 1),y) = T(x,y) \ 1.
(T(x,y) \ 1) \ 1 = T(T(x,x \ 1),y).
T(T(x,x \ 1),y) = (T(x,y) \ 1) \ 1.
1 / T(x,y) = T(1 / (1 / x),y) \ 1.
T(1 / (1 / x),y) \ 1 = 1 / T(x,y).
T((x \ 1) \ 1,y) = (T(x,y) \ 1) \ 1.
(T(x,y) \ 1) \ 1 = T((x \ 1) \ 1,y).
1 / (1 / T(x,y)) = T(1 / (1 / x),y).
((x \ y) \ 1) \ 1 = T(((y / x) \ 1) \ 1,x).
T(((x / y) \ 1) \ 1,y) = ((y \ x) \ 1) \ 1.
T(x,y) * K(T(x,y) \ 1,T(x,y)) = T(1 / (1 / x),y).
((x * T(1 / (1 / y),x)) / x) \ (y / T(y,x)) = 1 / T(y,x).
x * (((x \ y) \ 1) \ 1) = (((y / x) \ 1) \ 1) * x.
(((x / y) \ 1) \ 1) * y = y * (((y \ x) \ 1) \ 1).
(x * (((x \ y) \ 1) \ 1)) / x = ((y / x) \ 1) \ 1.
((R(x / y,y,z) \ 1) \ 1) * (y * z) = (y * z) * ((((y * z) \ (x * z)) \ 1) \ 1).
(1 / (1 / x)) \ (x / T(x,y)) = 1 / T(x,y).
x * (T(y,x) * L(T(y,x) \ z,u,w)) = y * (x * L(x \ (y \ (x * z)),u,w)).
(1 / x) * (((y * x) / y) / x) = (((y * x) / y) / x) * (1 / x).
(((x * y) / x) / y) * (1 / y) = (1 / y) * (((x * y) / x) / y).
((1 / x) * (((y * x) / y) / x)) / (1 / x) = ((y * x) / y) / x.
R(((x * y) / x) / y,y,x) = ((1 / y) * ((x * y) / (y * x))) / (1 / y).
((1 / x) * ((y * x) / (x * y))) / (1 / x) = (y * x) / (x * y).
T((x * y) / (y * x),y * x) = ((1 / y) * ((y * x) \ (x * y))) / (1 / y).
((1 / x) * ((x * y) \ (y * x))) / (1 / x) = (x * y) \ (y * x).
K(x,y) = ((1 / y) * ((y * x) \ (x * y))) / (1 / y).
K(x,y) = ((1 / y) * K(x,y)) / (1 / y).
((1 / x) * K(y,x)) / (1 / x) = K(y,x).
(K(x,y) * (1 / y)) / K(x,y) = 1 / y.
R(1 / x,y,z) \ (K(u,x) * R(1 / x,y,z)) = K(u,x).
T(K(x,y),R(1 / y,z,u)) = K(x,y).
T(K(x,y),z / (y * z)) = K(x,y).
(x / (y * x)) * K(z,y) = K(z,y) * (x / (y * x)).
K(x,y) * (z / (y * z)) = (z / (y * z)) * K(x,y).
(x \ 1) * ((y * x) / y) = ((y * x) / y) / ((x \ 1) \ 1).
((x * y) / x) / ((y \ 1) \ 1) = (y \ 1) * ((x * y) / x).
x / ((T(x,y) \ 1) \ 1) = (T(x,y) \ 1) * ((y * T(x,y)) / y).
(T(x,y) \ 1) * ((y * T(x,y)) / y) = x / ((T(x,y) \ 1) \ 1).
(T(x,y) \ 1) * x = x / ((T(x,y) \ 1) \ 1).
x / ((T(x,y) \ 1) \ 1) = (T(x,y) \ 1) * x.
K(x,((T(x,y) \ 1) * x) / x) = (T(x,y) \ 1) \ ((T(x,y) \ x) / x).
(T(x,y) \ 1) \ ((T(x,y) \ x) / x) = K(x,((T(x,y) \ 1) * x) / x).
(T(x,y) \ 1) \ ((T(x,y) \ x) / x) = K(x,T(x,y) \ 1).
(T(x,y) \ 1) * K(x,T(x,y) \ 1) = (T(x,y) \ x) / x.
x * ((x * ((y * (x \ 1)) / y)) * z) = (x * ((y * (x \ 1)) / y)) * (x * z).
(x * ((y * (x \ 1)) / y)) * (x * z) = x * ((x * ((y * (x \ 1)) / y)) * z).
K(x,(x / y) / x) * (y * z) = y * ((y * ((x * (y \ 1)) / x)) * z).
K((x * ((x \ y) / y)) \ x,x * ((x \ y) / y)) = y / y.
K((x * ((x \ y) / y)) \ x,x * ((x \ y) / y)) = 1.
1 / ((x \ y) / y) = T(1 / ((x \ y) / y),x * ((x \ y) / y)).
T(1 / ((x \ y) / y),x * ((x \ y) / y)) = 1 / ((x \ y) / y).
1 / ((x \ y) / y) = (x * ((x \ y) / y)) \ x.
(x * ((x \ y) / y)) \ x = 1 / ((x \ y) / y).
((x / y) * (y / x)) \ (x / y) = 1 / (((x / y) \ x) / x).
((x / y) * (y / x)) \ (x / y) = 1 / (y / x).
((x / y) * (y / x)) * (1 / (y / x)) = x / y.
K(1 / (x / y),(y / x) * (x / y)) = 1.
K(1 / x,(y / (x * y)) * ((x * y) / y)) = 1.
x * y != (z * u) / u | x = z / y.
((x * y) / y) * (y / (x * y)) = x / (1 / (y / (x * y))).
K(1 / x,(y / (x * y)) * x) = 1.
T(1 / x,(y / (x * y)) * x) = 1 / x.
1 / x = L(x \ 1,x,y / (x * y)).
L(x \ 1,x,y / (x * y)) = 1 / x.
L(x \ 1,x,R(1 / x,x,y)) = 1 / x.
((x / (y * x)) * y) * (1 / y) = x / (y * x).
R(1 / x,x,y) / (1 / x) = R(1 / x,x,y) * x.
R(x \ 1,x,y) \ (y / (x * y)) = K(x,x \ 1).
R(x \ 1,x,y) * K(x,x \ 1) = y / (x * y).
x / (y * x) = R(y \ 1,y,x) * K(y,y \ 1).
T(1 / (1 / x),R(1 / x,x,y)) = x.
T(1 / (1 / x),y / (x * y)) = x.
T(x,x \ 1) = T(x,y / (x * y)).
T(x,y / (x * y)) = T(x,x \ 1).
T(x,y / (x * y)) = (x \ 1) \ 1.
x \ T(x,y / (x * y)) = K(x,x \ 1).
K((x / (y * x)) \ 1,x / (y * x)) * (y * x) = T(y,y \ 1) * x.
x * (y / (x * y)) = x / (1 / (y / (x * y))).
x / (1 / (y / (x * y))) = x * (y / (x * y)).
K(x \ (x * (y / (x * y))),x) = R(x \ 1,x,y) / (y / (x * y)).
K(x / (y * x),y) = R(y \ 1,y,x) / (x / (y * x)).
R(x \ 1,x,y) / (y / (x * y)) = K(y / (x * y),x).
K(x / (y * x),y) * (x / (y * x)) = R(y \ 1,y,x).
R(x \ 1,x,y) = (y / (x * y)) * K(y / (x * y),x).
(x / (y * x)) * K(x / (y * x),y) = R(y \ 1,y,x).
K(x,(y * x) \ y) * x = T(x,(y * x) \ y).
T(x,(y * x) \ y) / x = K(x,(y * x) \ y).
T(K(x,(y * x) \ y),x) = x \ T(x,(y * x) \ y).
x \ T(x,(y * x) \ y) = T(K(x,(y * x) \ y),x).
x \ T(x,L(x \ 1,x,y)) = T(K(x,(y * x) \ y),x).
T(K(x,(y * x) \ y),x) = x \ T(x,L(x \ 1,x,y)).
x \ (y * (x * L(x \ (y \ (x * z)),u,w))) = T(y,x) * L(T(y,x) \ z,u,w).
T(x,y) * L(T(x,y) \ z,u,w) = T(x * L(x \ ((y * z) / y),u,w),y).
T(x * L(x \ ((y * z) / y),u,w),y) = T(x,y) * L(T(x,y) \ z,u,w).
(x * y) * ((z * ((x * y) \ (u * y))) / z) = (((z * (u / x)) / z) * x) * y.
(x * y) * ((z * ((x * y) \ u)) / z) = (((z * ((u / y) / x)) / z) * x) * y.
(((x * ((y / z) / u)) / x) * u) * z = (u * z) * ((x * ((u * z) \ y)) / x).
(x * y) * ((z * ((x * y) \ (u * y))) / z) = (x * ((z * (x \ u)) / z)) * y.
(x * ((y / z) / x)) * z = (x * z) * ((x * ((x * z) \ y)) / x).
(x * y) * ((x * ((x * y) \ z)) / x) = (x * ((z / y) / x)) * y.
(x * ((x / y) / x)) * y = T(x,x / (x * y)).
(x * ((y / z) / x)) * z = x * (z * ((x * (z \ (x \ y))) / x)).
x * (y * ((x * (y \ (x \ z))) / x)) = (x * ((z / y) / x)) * y.
T(x * ((x / y) / x),y) = y \ T(x,x / (x * y)).
x \ T(y,y / (y * x)) = T(y * ((y / x) / y),x).
x * ((y * (z \ u)) * ((x * ((y * (z \ u)) \ (x \ u))) / x)) = (x * (R(z / y,y,z \ u) / x)) * (y * (z \ u)).
(x * (R(y / z,z,y \ u) / x)) * (z * (y \ u)) = x * ((z * (y \ u)) * ((x * ((z * (y \ u)) \ (x \ u))) / x)).
x * ((y * ((x * (y \ 1)) / x)) * (x \ z)) = (x * ((z / (y * (x \ z))) / x)) * (y * (x \ z)).
(x * ((y / (z * (x \ y))) / x)) * (z * (x \ y)) = x * ((z * ((x * (z \ 1)) / x)) * (x \ y)).
(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)) \ (x * z) = x * (((L(y,1 / y,x) * x) / L(y,1 / y,x)) \ z).
x * (((L(y,1 / y,x) * x) / L(y,1 / y,x)) \ z) = (x * (T(y,x) / y)) \ (x * z).
K(x \ 1,x * ((y * x) \ y)) = (x \ 1) * (L(x \ 1,x,y) \ (x * ((y * x) \ y))).
(x \ 1) * (L(x \ 1,x,y) \ (x * ((y * x) \ y))) = K(x \ 1,x * ((y * x) \ y)).
(x * x) * L((x * x) \ (1 / (1 / x)),y,z) = (L(x \ 1,y,z) * x) * x.
(L(x \ 1,y,z) * x) * x = x * (x * L(x \ (x \ (1 / (1 / x))),y,z)).
x * (x * L(x \ (x \ (1 / (1 / x))),y,z)) = (L(x \ 1,y,z) * x) * x.
x * (x * L(x \ K(x \ 1,x),y,z)) = (L(x \ 1,y,z) * x) * x.
x * (x * L(T(x \ 1,x),y,z)) = (L(x \ 1,y,z) * x) * x.
x * (L(x \ 1,y,z) * x) = (L(x \ 1,y,z) * x) * x.
(L(x \ 1,y,z) * x) * x = x * (L(x \ 1,y,z) * x).
T(x,L(x \ 1,y,z) * x) = x.
T(x \ y,(y \ x) * (x \ y)) = x \ y.
T(x \ (x / y),y * (x \ (x / y))) = x \ (x / y).
R(x \ (x / y),y,x \ (x / y)) = T(x \ (x / y),y).
T(x \ (x / y),y) \ T((x \ (x / y)) * y,x \ (x / y)) = T(y,x \ (x / y)).
T(x \ (x / y),y) \ ((x \ (x / y)) * y) = T(y,x \ (x / y)).
T(x,y \ (y / x)) = T(x,T(y \ (y / x),x)).
T(x,T(y \ (y / x),x)) = T(x,y \ (y / x)).
T(x,T(T(1 / x,R(x,y,z)),x)) = T(x,R(x,y,z) \ (R(x,y,z) / x)).
T(x,R(x,y,z) \ (R(x,y,z) / x)) = T(x,T(T(1 / x,R(x,y,z)),x)).
T(x,R(x,y,z) \ (R(x,y,z) / x)) = T(x,T(x \ 1,R(x,y,z))).
T(x,T(1 / x,R(x,y,z))) = T(x,T(x \ 1,R(x,y,z))).
T(T(x,y) * T(T(x,y) \ x,x),(x * x) / T(x,y)) = L(x,T(x,y) \ x,x).
T(L(x,T(x,y) \ x,T(x,y)),(x * x) / T(x,y)) = L(x,T(x,y) \ x,x).
T(L(x,T(x,y) \ x,T(x,y)),x * (T(x,y) \ x)) = L(x,T(x,y) \ x,x).
L(T(x,x * (T(x,y) \ x)),T(x,y) \ x,T(x,y)) = L(x,T(x,y) \ x,x).
L(x,T(x,y) \ x,T(x,y)) = L(x,T(x,y) \ x,x).
T(x,y) * T(T(x,y) \ x,x) = L(x,T(x,y) \ x,x).
x * L(y,T(y,x) \ y,y) = (y * x) * T(K(x,y),y).
L(x,T(x,y) \ x,x) = (T(x,y) \ x) * T(x,y).
K(1 / x,(1 / x) \ 1) * L(y,x,1 / x) = (1 / x) * (x * (K(x \ 1,x) * y)).
(x \ 1) * T(x,(y * x) \ y) = K(x \ 1,x * ((y * x) \ y)).
K(x \ 1,x * ((y * x) \ y)) = (x \ 1) * T(x,(y * x) \ y).
T(1 / (1 / x),(y * x) \ y) / K(x \ 1,x * ((y * x) \ y)) = x.
K(1 / x,(1 / x) \ 1) * L(y,x,1 / x) = L(K(x \ 1,x) * y,x,1 / x).
K(x \ 1,x) * L(y,x,1 / x) = L(K(x \ 1,x) * y,x,1 / x).
L(K(x \ 1,x) * y,x,1 / x) = K(x \ 1,x) * L(y,x,1 / x).
L(x * K(y \ 1,y),y,1 / y) = K(y \ 1,y) * L(T(x,K(y \ 1,y)),y,1 / y).
K(x \ 1,x) * L(T(y,K(x \ 1,x)),x,1 / x) = L(y * K(x \ 1,x),x,1 / x).
(x \ 1) * ((x \ R(x,y,z)) / (x \ 1)) = T((x \ 1) * R(x,y,z),x \ 1).
(x \ 1) * R(x,y,z) = T((x \ 1) * R(x,y,z),x \ 1).
T((x \ 1) * R(x,y,z),x \ 1) = (x \ 1) * R(x,y,z).
T(x \ 1,R(x,y,z)) \ ((x \ 1) * R(x,y,z)) = T(R(x,y,z),x \ 1).
T(R(x,y,z),x \ 1) = T(R(x,y,z),T(x \ 1,R(x,y,z))).
T(R(x,y,z),T(x \ 1,R(x,y,z))) = T(R(x,y,z),x \ 1).
R(T(x,T(x \ 1,R(x,y,z))),y,z) = T(R(x,y,z),x \ 1).
R(T(x,x \ 1),y,z) = R(T(x,T(x \ 1,R(x,y,z))),y,z).
R(T(x,T(x \ 1,R(x,y,z))),y,z) = R(T(x,x \ 1),y,z).
R(T(x,T(1 / x,R(x,y,z))),y,z) = R(T(x,x \ 1),y,z).
K(x,x \ 1) * T(K(x,x \ 1) \ y,z) = x * ((1 / x) * T((1 / x) \ (x \ y),z)).
T(T(x,y) * ((T(x,y) / x) \ (1 / x)),T(x,y)) = T(x,y) * (K(y \ (y / (1 / x)),y) \ (1 / x)).
T(x * (1 / y),y) = (y * T(y \ x,y)) * (1 / y).
(x * T(x \ y,x)) * (1 / x) = T(y * (1 / x),x).
((x \ y) * x) * (1 / x) = T(y * (1 / x),x).
(x * y) * (1 / y) = T((y * x) * (1 / y),y).
T((x * y) * (1 / x),x) = (y * x) * (1 / x).
T((x * y) * (1 / x),x) != z * (1 / x) | y * x = z.
K(x \ 1,x) * ((1 / x) \ L(1 / x,y,z)) = L(x \ 1,y,z) / (1 / x).
K(x \ 1,x) * (x * L(x \ 1,y,z)) = L(x \ 1,y,z) / (1 / x).
L(x \ 1,x,y) / (1 / x) = (x * ((y * x) \ y)) * K(x \ 1,x).
(x * ((y * x) \ y)) * K(x \ 1,x) = L(x \ 1,x,y) / (1 / x).
(x * ((y * x) \ y)) * K(x \ 1,x) = L(x \ 1,x,y) * x.
x * y != (y * ((z * y) \ z)) * K(y \ 1,y) | x = (y \ 1) * (y * L(y \ 1,y,z)).
L(x \ 1,x,y) = (x \ 1) * (x * L(x \ 1,x,y)).
(x \ 1) * (x * L(x \ 1,x,y)) = L(x \ 1,x,y).
(x \ 1) * (x * L(x \ 1,x,y)) = (y * x) \ y.
(x * y) \ x = (y \ 1) * (y * L(y \ 1,y,x)).
(x * y) \ x = (y \ 1) * (y * ((x * y) \ x)).
(x \ 1) * (x * ((y * x) \ y)) = (y * x) \ y.
(x \ 1) \ ((y * x) \ y) = x * ((y * x) \ y).
(x \ 1) * (x * ((y * x) \ y)) = ((y * x) \ y) * 1.
((x * y) \ x) * z != (y \ 1) * (y * ((x * y) \ x)) | z = K(y \ 1,y * ((x * y) \ x)).
1 = K(x \ 1,x * ((y * x) \ y)).
K(x \ 1,x * ((y * x) \ y)) = 1.
K(x \ 1,x * (y \ (y / x))) = 1.
T(1 / (1 / x),(y * x) \ y) / 1 = x.
1 = (x \ 1) * T(x,y \ (y / x)).
(x \ 1) * T(x,y \ (y / x)) = 1.
T(x,x \ 1) = T(x,y \ (y / x)).
T(x,y \ (y / x)) = T(x,x \ 1).
(x \ 1) \ 1 = T(x,y \ (y / x)).
T(x,y \ (y / x)) = (x \ 1) \ 1.
T(x,(y * x) \ y) = T(x,x \ 1).
T(K(x,y),(x * y) \ (y * x)) = T(K(x,y),K(x,y) \ 1).
T(x,(y * x) \ y) = (x \ 1) \ 1.
T(x \ y,y \ x) = ((x \ y) \ 1) \ 1.
T(x,L(x \ 1,x,y)) = T(x,x \ 1).
((x \ 1) \ 1) / x = K(x,(y * x) \ y).
K(x,(y * x) \ y) = ((x \ 1) \ 1) / x.
x \ T(x,L(x \ 1,x,y)) = K(x,x \ 1).
x = T(1 / (1 / x),(y * x) \ y).
T(1 / (1 / x),(y * x) \ y) = x.
T(1 / (1 / (x \ y)),y \ x) = x \ y.
(((x * y) \ x) * y) / ((x * y) \ x) = 1 / (1 / y).
T(x \ (x / y),y) = ((x \ (x / y)) \ 1) \ 1.
T(K(x \ (x / (y \ 1)),x),T(y,x) \ y) = ((y \ T(y,x)) \ 1) \ 1.
x * (((x \ y) \ 1) \ 1) = y * K((y \ x) \ 1,y \ x).
x * K((x \ y) \ 1,x \ y) = y * (((y \ x) \ 1) \ 1).
T(K(x \ y,x),(y \ x) \ 1) = K(x \ (x / T(y \ x,x \ y)),x).
K(x \ (x / T(y \ x,x \ y)),x) = T(K(x \ y,x),(y \ x) \ 1).
(x * T(x \ y,y \ x)) / x = ((y / x) \ 1) \ 1.
K(x,(y * x) \ y) = K(x,x \ 1).
K(x \ y,y \ x) = K(x \ y,(x \ y) \ 1).
K(x \ y,(x \ y) \ 1) = K(x \ y,y \ x).
K(x,y \ (y / x)) = K(x,x \ 1).
K(x,(y * x) \ y) \ 1 = K(x \ 1,x).
K((x / y) \ x,z \ (z / y)) = K(y,y \ 1).
T(1 / (1 / K(x \ (x / (y \ 1)),x)),T(y,x) \ y) = y \ T(y,x).
T(K(x,(y * x) \ y),x) = K(x,x \ 1).
K((x * y) \ x,((x * y) \ x) \ 1) = K((x * y) \ x,y).
1 / (1 / x) = L(x,(y * x) \ y,x).
L(x,(y * x) \ y,x) = 1 / (1 / x).
L(x \ y,y \ x,x \ y) = 1 / (1 / (x \ y)).
L((x * y) \ x,y,(x * y) \ x) = 1 / (1 / ((x * y) \ x)).
1 / (1 / (x \ y)) = L(1 / (y \ x),y \ x,y).
L(1 / (x \ y),x \ y,x) = 1 / (1 / (y \ x)).
x * (1 / (1 / (x \ y))) = y * K(y \ x,(y \ x) \ 1).
x * K(x \ y,(x \ y) \ 1) = y * (1 / (1 / (y \ x))).
((x / y) \ 1) \ 1 = T(x / y,x \ y).
T(x / y,x \ y) = ((x / y) \ 1) \ 1.
T(K(x,y),K(y,x)) = T(K(x,y),K(x,y) \ 1).
T(K(x,y),K(x,y) \ 1) = T(K(x,y),K(y,x)).
T(K(x,y),K(y,x)) = (K(x,y) \ 1) \ 1.
(K(x,y) \ 1) \ 1 = K(x,y).
1 / (1 / K(x,y)) = K(x,y).
x * K(x \ y,y \ x) = y * (1 / (1 / (y \ x))).
x \ (y * K(y \ x,x \ y)) = 1 / (1 / (x \ y)).
(x / y) * K(y,y \ 1) = x * (1 / (1 / (x \ (x / y)))).
x \ ((x / y) * K(y,y \ 1)) = 1 / (1 / (x \ (x / y))).
1 / (1 / ((x * y) \ x)) = L(1 / y,y,x).
L(1 / x,x,y) = 1 / (1 / ((y * x) \ y)).
L(x,x \ 1,y) = 1 / (1 / ((y * (x \ 1)) \ y)).
T(K(x \ y,x),(y \ x) \ 1) = T(K(x \ y,x),x \ y).
T(K(x,y),((y * x) \ y) \ 1) = T(K(y \ (y * x),y),y \ (y * x)).
T(K(x \ (x * y),x),x \ (x * y)) = T(K(y,x),((x * y) \ x) \ 1).
T(K(x \ (x / (y \ 1)),x),T(y,x) \ y) = y \ T(y,x).
x \ T(x,y) = ((x \ T(x,y)) \ 1) \ 1.
((x \ T(x,y)) \ 1) \ 1 = x \ T(x,y).
1 / (x \ T(x,y)) = (x \ T(x,y)) \ 1.
(x \ 1) \ (T(x,y) \ 1) = 1 / (x \ T(x,y)).
T(K(x,y),y \ (y * x)) = T(K(x,y),((y * x) \ y) \ 1).
T(K(x,y),((y * x) \ y) \ 1) = T(K(x,y),y \ (y * x)).
T(K(x,y),((y * x) \ y) \ 1) = T(K(x,y),x).
L(L(x,y,y \ 1),K(y \ 1,y),1 / y) = (1 / y) * (y * x).
L(L(x,y,y \ 1),K(y \ 1,y),1 / y) = L(x,y,1 / y).
L(x,y,1 / y) = L(L(x,y,y \ 1),1 / y,K(y \ 1,y)).
L(L(x,y,y \ 1),1 / y,K(y \ 1,y)) = L(x,y,1 / y).
x \ (x * (y * T(y \ 1,x))) = (x * (y * T(y \ 1,x))) * (x \ 1).
(x * (y * T(y \ 1,x))) * (x \ 1) = x \ (x * (y * T(y \ 1,x))).
(x * (y * T(y \ 1,x))) * (x \ 1) = y * T(y \ 1,x).
(x * (y \ T(y,x))) * (x \ 1) = (y \ 1) * T((y \ 1) \ 1,x).
(x \ 1) * T((x \ 1) \ 1,y) = (y * (x \ T(x,y))) * (y \ 1).
(x * (y \ T(y,x))) * (x \ 1) = y \ T(y,x).
((L(x \ 1,x,y) * y) / L(x \ 1,x,y)) / y = L(x * T(x \ 1,y),y,1 / y).
(x * (y * T(y \ 1,x))) / x = L(y * T(y \ 1,x),x,1 / x).
L(x * T(x \ 1,y),y,1 / y) = (y * (x * T(x \ 1,y))) / y.
L(K(x,y),y,1 / y) = (y * (((y * x) \ y) * T(((y * x) \ y) \ 1,y))) / y.
(x * (((x * y) \ x) * T(((x * y) \ x) \ 1,x))) / x = L(K(y,x),x,1 / x).
(x * K(y,x)) / x = L(K(y,x),x,1 / x).
L(K(x,y),y,1 / y) = (y * K(x,y)) / y.
(T(x,y) \ x) * T(x \ 1,T(x,y) \ x) = ((T(x,y) \ x) / x) * K(x \ 1,x).
((T(x,y) \ x) / x) * K(x \ 1,x) = (x \ 1) * (T(x,y) \ x).
x * ((x * (T(y,x) / y)) \ z) = (x * (T(y,x) / y)) \ (x * z).
(x * (T(y,x) / y)) \ (x * z) = x * ((x * (T(y,x) / y)) \ z).
L(x * K(y \ 1,y),y,1 / y) = L(x,y,1 / y) * K(y \ 1,y).
K(x,x \ 1) * T(K(x,x \ 1) \ y,z) = x * (T((x \ y) * x,z) / x).
K(x,x \ 1) * T(K(x,x \ 1) \ y,x) = T(y,x).
K(x,x \ 1) * T(y,x) = T(K(x,x \ 1) * y,x).
T(K(x,x \ 1) * y,x) = K(x,x \ 1) * T(y,x).
T(x * K(y,y \ 1),y) = T(x,y) * K(y,y \ 1).
x * T(K(x,x \ 1) * y,x) = K(x,x \ 1) * (y * x).
(1 / K(x,x \ 1)) * T(y,x) = T((1 / K(x,x \ 1)) * y,x).
T((1 / K(x,x \ 1)) * y,x) = (1 / K(x,x \ 1)) * T(y,x).
T((x / y) * K(y,y \ 1),y) = (y \ x) * K(y,y \ 1).
K(x,x \ 1) * (y * x) = (K(x,x \ 1) * y) * x.
(K(x,x \ 1) * y) * x = K(x,x \ 1) * (y * x).
L(x,y,K(x,x \ 1)) = x.
L(1 / x,y,K(x \ 1,x)) = 1 / x.
L(T(1 / x,y),z,K(x \ 1,x)) = T(1 / x,y).
(x \ y) * K(x,x \ 1) = x \ (y * K(x,x \ 1)).
x \ (y * K(x,x \ 1)) = (x \ y) * K(x,x \ 1).
x * ((x \ y) * K(x,x \ 1)) = y * K(x,x \ 1).
(1 / x) \ (y * K(1 / x,x)) = ((1 / x) \ y) * K(1 / x,(1 / x) \ 1).
((1 / x) \ y) * K(1 / x,(1 / x) \ 1) = (1 / x) \ (y * K(1 / x,x)).
x * (y * K(x,x \ 1)) = (x * y) * K(x,x \ 1).
(x * y) * K(x,x \ 1) = x * (y * K(x,x \ 1)).
((1 / x) * y) * K(x \ 1,x) = (1 / x) * (y * K(1 / x,(1 / x) \ 1)).
(1 / x) * (y * K(1 / x,(1 / x) \ 1)) = ((1 / x) * y) * K(x \ 1,x).
T(((x \ 1) * x) * y,x) = (1 / K(x,x \ 1)) * T(y,x).
(1 / K(x,x \ 1)) * T(y,x) = T(((x \ 1) * x) * y,x).
(1 / K(x,x \ 1)) * T(y,x) = T(K(x \ 1,x) * y,x).
((x \ 1) * x) * T(y,x) = T(K(x \ 1,x) * y,x).
T(K(x \ 1,x) * y,x) = ((x \ 1) * x) * T(y,x).
T(K(x \ 1,x) * y,x) = K(x \ 1,x) * T(y,x).
x * T(K(x \ 1,x) * y,x) = K(x \ 1,x) * (y * x).
K(x \ 1,x) * (y * x) = (K(x \ 1,x) * y) * x.
(K(x \ 1,x) * y) * x = K(x \ 1,x) * (y * x).
L(x,y,K(x \ 1,x)) = x.
L(T(x,y),z,K(x \ 1,x)) = T(x,y).
T(x,y) = T(x,K(x \ 1,x) * y).
T(x,K(x \ 1,x) * y) = T(x,y).
T(x,y) = T(x,K(x \ 1,x) \ y).
T(x,K(x \ 1,x) \ y) = T(x,y).
T(x,(x \ 1) * y) = T(x,L(x \ y,x,x \ 1)).
T(x,L(x \ y,x,x \ 1)) = T(x,(x \ 1) * y).
K(x \ (x / T(x,y)),x) = T(K(x \ 1,x),K(x \ 1,x) \ y).
T(K(x \ 1,x),K(x \ 1,x) \ y) = K(x \ (x / T(x,y)),x).
T(K(x \ 1,x),K(x \ 1,x) \ y) = T(K(x \ 1,x),y).
(K(x \ 1,x) \ y) * T(K(x \ 1,x),y) = y.
(x * y) * K(1 / x,(1 / x) \ 1) = (1 / x) \ (L(y,x,1 / x) * K(1 / x,x)).
(1 / x) \ (L(y,x,1 / x) * K(1 / x,x)) = (x * y) * K(1 / x,(1 / x) \ 1).
(1 / x) * ((T(x,y) \ x) * K(1 / x,(1 / x) \ 1)) = ((T(x,y) \ x) / x) * K(x \ 1,x).
(1 / x) \ (L(y,x,1 / x) * K(x \ 1,x)) = (x * y) * K(1 / x,(1 / x) \ 1).
(1 / x) \ L(y * K(x \ 1,x),x,1 / x) = (x * y) * K(1 / x,(1 / x) \ 1).
(x * y) * K(1 / x,(1 / x) \ 1) = x * (y * K(x \ 1,x)).
(x * y) * K(x \ 1,x) = x * (y * K(x \ 1,x)).
R(x,y,K(x \ 1,x)) = x.
(T(x,y) \ x) * K(x \ 1,x) = x * ((T(x,y) \ 1) * K(x \ 1,x)).
x * ((T(x,y) \ 1) * K(x \ 1,x)) = (T(x,y) \ x) * K(x \ 1,x).
R(T(x,y),z,K(x \ 1,x)) = T(x,y).
T(x,y) \ K(x \ 1,x) = (T(x,y) \ 1) * K(x \ 1,x).
(T(x,y) \ 1) * K(x \ 1,x) = T(x,y) \ K(x \ 1,x).
x * (T(x,y) \ K(x \ 1,x)) = (T(x,y) \ x) * K(x \ 1,x).
(T(x,y) \ x) * K(x \ 1,x) = x * (T(x,y) \ K(x \ 1,x)).
(T(x,y) \ x) * K(x \ 1,x) = T(x,y) \ (1 / (1 / x)).
(x * K(x,y)) * T((x * K(x,y)) \ (x * y),z) = (T(y,z) * x) * K(x,y).
(T(x,y) * z) * K(z,x) = z * (K(z,x) * T(K(z,x) \ x,y)).
x * (K(x,y) * T(K(x,y) \ y,z)) = (T(y,z) * x) * K(x,y).
x * ((K(x,y) \ y) * K(x,y)) = (T(y,K(x,y)) * x) * K(x,y).
(T(x,K(y,x)) * y) * K(y,x) = y * ((K(y,x) \ x) * K(y,x)).
(x * y) * K(z \ (z / L(u,y,x)),z) = x * ((y * u) * T((y * u) \ y,z)).
(x * y) * K(z \ (z / L(u,y,x)),z) = x * (y * (u * T(u \ 1,z))).
L(x * T(x \ 1,y),z,u) = K(y \ (y / L(x,z,u)),y).
L(x \ T(x,y),z,u) = K(y \ (y / L(x \ 1,z,u)),y).
L(x \ T(x,(y * x) \ y),x,y) = K(((y * x) \ y) \ 1,(y * x) \ y).
L(T(K(x,(y * x) \ y),x),x,y) = K(((y * x) \ y) \ 1,(y * x) \ y).
L(K(x,x \ 1),x,y) = K(((y * x) \ y) \ 1,(y * x) \ y).
L(K(x,x \ 1),x,y) \ 1 = K((y * x) \ y,((y * x) \ y) \ 1).
K((x * y) \ x,((x * y) \ x) \ 1) = L(K(y,y \ 1),y,x) \ 1.
L(K(x,x \ 1),x,y) \ 1 = K((y * x) \ y,x).
K((x * y) \ x,y) = L(K(y,y \ 1),y,x) \ 1.
K(x \ (x / R(y,z,u)),x) = (((y * z) * T((y * z) \ z,x)) * u) / (z * u).
K(x \ (x / R(y,z,u)),x) = (((y * T(y \ 1,x)) * z) * u) / (z * u).
R(x * T(x \ 1,y),z,u) = K(y \ (y / R(x,z,u)),y).
R(x * T(x \ 1,R(x,y,z)),y,z) = K(R(x,y,z) \ 1,R(x,y,z)).
R(T(x,x \ 1) * T(T(x,x \ 1) \ 1,x \ R(x,y,z)),y,z) = K((x \ R(x,y,z)) \ (x \ 1),x \ R(x,y,z)).
R(x * T(x \ 1,y),z,u) = R(x,z,u) * T(R(x,z,u) \ 1,y).
R(x,y,z) * T(R(x,y,z) \ 1,u) = R(x * T(x \ 1,u),y,z).
R(x * T(x \ 1,R(x,y,z)),y,z) = (R(x,y,z) \ 1) * R(x,y,z).
K(x,y) = (((y * x) \ y) \ K(x,y)) / (((y * x) \ y) \ 1).
(((x * y) \ x) \ K(y,x)) / (((x * y) \ x) \ 1) = K(y,x).
T(K(x,y),((y * x) \ y) \ 1) = (((y * x) \ y) \ 1) \ (((y * x) \ y) \ K(x,y)).
(((x * y) \ x) \ 1) \ (((x * y) \ x) \ K(y,x)) = T(K(y,x),((x * y) \ x) \ 1).
(((x * y) \ x) \ 1) \ (((x * y) \ x) \ K(y,x)) = T(K(y,x),y).
K(x \ 1,x) * R(K(x \ 1,x) \ y,z,u) = (x \ 1) * (x * R(x \ ((x \ 1) \ y),z,u)).
K(x \ 1,x) * L(K(x \ 1,x) \ y,z,u) = (x \ 1) * (x * L(x \ ((x \ 1) \ y),z,u)).
R(T(x,T(1 / x,R(x,y,z))),y,z) \ R(x,y,z) = (R(x,y,z) \ (R(x,y,z) / x)) * x.
R(T(x,x \ 1),y,z) \ R(x,y,z) = (R(x,y,z) \ (R(x,y,z) / x)) * x.
R(T(x,x \ 1),y,z) \ R(x,y,z) = T(1 / x,R(x,y,z)) * x.
R(T(x,x \ 1),y,z) \ R(x,y,z) = x * T(x \ 1,R(x,y,z)).
K(T(x,R(x \ 1,y,z)),R(x \ 1,y,z)) = x \ T(x,R(x \ 1,y,z)).
K(T(x,R(x \ 1,x,y)),R(x \ 1,x,y)) = x \ T(x,y / (x * y)).
(x \ y) \ L(1 / (y \ x),y \ x,y) = L(1 / (y \ x),y \ x,y) * ((x \ y) \ 1).
L(1 / (x \ y),x \ y,x) * ((y \ x) \ 1) = (y \ x) \ L(1 / (x \ y),x \ y,x).
(1 / x) * ((T(x,y) \ x) * K(1 / x,(1 / x) \ 1)) = (x \ 1) * (T(x,y) \ x).
(1 / x) * ((T(x,y) \ x) * K(x \ 1,x)) = (x \ 1) * (T(x,y) \ x).
(1 / x) * (T(x,y) \ (1 / (1 / x))) = (x \ 1) * (T(x,y) \ x).
K(x \ 1,x) * R(K(x \ 1,x) \ (y * x),z,u) = ((x \ 1) * R((x \ 1) \ y,z,u)) * x.
K(x \ 1,x) * L(K(x \ 1,x) \ (y * x),z,u) = ((x \ 1) * L((x \ 1) \ y,z,u)) * x.
K(x \ 1,x) * R(K(x \ 1,x) \ (y * x),z,u) = (x \ R(x * y,z,u)) * x.
K(x \ 1,x) * L(K(x \ 1,x) \ (y * x),z,u) = (x \ L(x * y,z,u)) * x.
(x * K(x,y)) * R((x * K(x,y)) \ (x * y),z,u) = (R(y,z,u) * x) * K(x,y).
(R(x,y,z) * u) * K(u,x) = u * (K(u,x) * R(K(u,x) \ x,y,z)).
x * (K(x,y) * R(K(x,y) \ y,z,u)) = (R(y,z,u) * x) * K(x,y).
x * (K(x,y) * R(K(x,y) \ y,y \ 1,y)) = (T(y,y \ 1) * x) * K(x,y).
((x \ y) / y) * R(x,z,u) = R(x,z,u) / (((x \ y) / y) \ 1).
R(x,y,z) / (((x \ u) / u) \ 1) = ((x \ u) / u) * R(x,y,z).
K(T(x,x \ 1),T(x,x \ 1) \ 1) * (T(x,x \ 1) \ y) = L(x \ y,x,K(x,x \ 1)).
K(x,x \ 1) * (T(x,x \ 1) \ y) = L(x \ y,x,K(x,x \ 1)).
K(x,x \ 1) * (((x \ 1) \ 1) \ y) = L(x \ y,x,K(x,x \ 1)).
L(x \ y,x,K(x,x \ 1)) = K(x,x \ 1) * (((x \ 1) \ 1) \ y).
T(x,y) * (K(y \ (y / (1 / x)),y) \ (1 / x)) = T(x,y) * ((T(x,y) / x) \ (1 / x)).
T(x,y) * (T(1 / (1 / x),y) \ 1) = T(x,y) * ((T(x,y) / x) \ (1 / x)).
T(x,y) * ((T(x,y) / x) \ (1 / x)) = T(1 / (1 / x),y) \ T(x,y).
T(1 / (1 / x),y) \ T(x,y) = K(T(x,y),T(x,y) \ 1).
K(R(x,y,z),((x \ 1) * R(x,y,z)) / R(x,y,z)) = (x \ 1) \ ((x \ R(x,y,z)) / R(x,y,z)).
K(R(x,y,z),x \ 1) = (x \ 1) \ ((x \ R(x,y,z)) / R(x,y,z)).
(x \ 1) \ ((x \ R(x,y,z)) / R(x,y,z)) = K(R(x,y,z),x \ 1).
(x \ 1) * K(R(x,y,z),x \ 1) = (x \ R(x,y,z)) / R(x,y,z).
(x \ R(x,y,z)) / R(x,y,z) = (x \ 1) * K(R(x,y,z),x \ 1).
K((1 / x) \ ((1 / x) * T((1 / x) \ 1,y)),1 / x) = (((1 / x) * T(x,y)) / (1 / x)) \ T(x,y).
K((1 / x) \ (T(x,y) / x),1 / x) = (((1 / x) * T(x,y)) / (1 / x)) \ T(x,y).
(((1 / x) * T(x,y)) / (1 / x)) \ T(x,y) = K((1 / x) \ (T(x,y) / x),1 / x).
(((1 / x) * T(x,y)) / (1 / x)) \ T(x,y) = K(T(x,y),1 / x).
T(1 / (1 / x),y) \ T(x,y) = K(T(x,y),1 / x).
K(T(x,y),1 / x) = K(T(x,y),T(x,y) \ 1).
K(T(x,y),T(x,y) \ 1) = K(T(x,y),1 / x).
T(x * (((x \ 1) * T((x \ 1) \ 1,y)) / T(x,y)),z) = T(x,z) * ((T(x,z) \ T(x,y)) / T(x,y)).
T(K(T(x,y),1 / x),z) = T(x,z) * ((T(x,z) \ T(x,y)) / T(x,y)).
T(x,y) * ((T(x,y) \ T(x,z)) / T(x,z)) = T(K(T(x,z),1 / x),y).
T(K(T(x,y),1 / x),z) = K(T(x,y),1 / T(x,z)).
K(T(x,y),1 / T(x,z)) = T(K(T(x,y),1 / x),z).
((x \ y) \ 1) * ((((x \ y) \ 1) \ (y \ x)) / (y \ x)) = L(1 / (y \ x),y \ x,y) * ((x \ y) \ 1).
((x \ y) \ 1) * ((((x \ y) \ 1) \ (y \ x)) / (y \ x)) = (x \ y) \ L(1 / (y \ x),y \ x,y).
((x \ y) \ 1) * ((((x \ y) \ 1) \ (y \ x)) / (y \ x)) = K(y \ x,((x \ y) * (y \ x)) / (y \ x)).
((x \ y) \ 1) * ((((x \ y) \ 1) \ (y \ x)) / (y \ x)) = K(y \ x,x \ y).
K(x \ y,y \ x) = (y \ x) \ L(1 / (x \ y),x \ y,x).
(x \ y) \ L(1 / (y \ x),y \ x,y) = K(y \ x,x \ y).
(x \ y) * K(y \ x,x \ y) = L(1 / (y \ x),y \ x,y).
(x \ y) * K(y \ x,x \ y) = 1 / (1 / (x \ y)).
x * y != 1 / (1 / x) | y = K(x \ 1,x).
K(x \ y,y \ x) = K((y \ x) \ 1,y \ x).
K((x \ y) \ 1,x \ y) = K(y \ x,x \ y).
K(((x * y) \ x) \ 1,(x * y) \ x) = K(y,(x * y) \ x).
x * K(y \ x,x \ y) = y * (((y \ x) \ 1) \ 1).
(x * y) * K(y,(x * y) \ x) = x * T(y,(x * y) \ x).
L(K(x,x \ 1),x,y) = K(x,(y * x) \ y).
L(K(x,x \ 1),x,y) = K(x,x \ 1).
K((x * y) \ x,y) = K(y,(x * y) \ x) \ 1.
K(x,(y * x) \ y) \ 1 = K((y * x) \ y,x).
L(K(x \ 1,x),1 / x,y) = K(1 / x,(1 / x) \ 1).
K((x * y) \ x,y) = K(y \ 1,y).
K((x * y) \ y,T(x,y)) = K(T(x,y) \ 1,T(x,y)).
K(T(x,y) \ 1,T(x,y)) = K((x * y) \ y,T(x,y)).
K(T(x,y) \ 1,T(x,y)) = K((x * y) \ y,y \ (x * y)).
K((x * y) \ y,y \ (x * y)) = K(T(x,y) \ 1,T(x,y)).
L(K(x \ 1,x),1 / x,y) = K(x \ 1,x).
(x * (y \ 1)) / K(y \ 1,y) = x * (1 / y).
x / K(y \ 1,y) = (x / (y \ 1)) * (1 / y).
(x / (y \ 1)) * (1 / y) = x / K(y \ 1,y).
(x * (1 / y)) * K(y \ 1,y) = x * (y \ 1).
(x * (1 / y)) * y = R(x,y \ 1,y).
x * y = R(x / (1 / y),y \ 1,y).
R(x / (1 / y),y \ 1,y) = x * y.
R(x,y \ 1,y) = R(x,1 / y,y).
R(x,1 / y,y) = R(x,y \ 1,y).
(x * K(y \ 1,y)) / (y \ 1) = x / (1 / y).
R(x,1 / y,K(y \ 1,y)) = x.
x * K(y \ 1,y) = (x / (1 / y)) * (y \ 1).
(x / (1 / y)) * (y \ 1) = x * K(y \ 1,y).
R(x,1 / (1 / y),K(y,y \ 1)) = x.
x * y = (x * (1 / (1 / y))) * K(y,y \ 1).
(x * (1 / (1 / y))) * K(y,y \ 1) = x * y.
x / (1 / (1 / y)) = (x * K(y,y \ 1)) / y.
(x * K(y,y \ 1)) / y = x / (1 / (1 / y)).
(x * (y \ 1)) / (1 / y) = x * K(y \ 1,y).
x * y != z * K(y,y \ 1) | x * (1 / (1 / y)) = z.
x * K(y,y \ 1) != z * y | z * (1 / (1 / y)) = x.
x / (1 / (1 / y)) = (x / y) * K(y,y \ 1).
(x / y) * K(y,y \ 1) = x / (1 / (1 / y)).
(x * K(y \ 1,y)) * (1 / y) = x * (y \ 1).
R(x * K(y \ 1,y),y \ 1,y) = (x * (y \ 1)) * y.
x / (1 / (1 / y)) = x * (1 / (1 / (x \ (x / y)))).
x * (1 / (1 / (x \ (x / y)))) = x / (1 / (1 / y)).
x \ (x / (1 / (1 / y))) = 1 / (1 / (x \ (x / y))).
1 / (1 / (x \ (x / y))) = x \ (x / (1 / (1 / y))).
x * (1 / (1 / (x \ y))) = x / (1 / (1 / (y \ x))).
x / (1 / (1 / (y \ x))) = x * (1 / (1 / (x \ y))).
(x \ (x / (1 / (1 / y)))) \ 1 = 1 / (x \ (x / y)).
x / (1 / (1 / ((x * y) \ x))) = x * (1 / (1 / y)).
(x * (1 / (1 / (x \ y)))) \ x = 1 / (1 / (y \ x)).
(x \ (x / (1 / y))) \ 1 = 1 / (x \ (x / (y \ 1))).
1 / (x \ (x / (y \ 1))) = (x \ (x / (1 / y))) \ 1.
(x \ (x / y)) \ 1 = 1 / (x \ (x / ((y \ 1) \ 1))).
1 / (x \ (x / ((y \ 1) \ 1))) = (x \ (x / y)) \ 1.
x / L(y,y \ 1,x) = x * (1 / (1 / (y \ 1))).
x / L(y,y \ 1,x) = x * (1 / y).
K(x \ (x / L(y,y \ 1,x)),z) = K(1 / y,z).
L(x * T(x \ 1,y),x \ 1,y) = K(1 / x,y).
L((1 / x) * T((1 / x) \ 1,y),x,y) = K(1 / (1 / x),y).
(x * K(x \ y,y \ x)) \ y = 1 / (1 / (x \ y)).
((x \ (x / y)) \ 1) \ 1 = x \ (x / ((y \ 1) \ 1)).
T(x \ (x / y),y) = x \ (x / ((y \ 1) \ 1)).
x * T(x \ (x / y),y) = x / ((y \ 1) \ 1).
(x / ((y \ 1) \ 1)) / x = T((x / y) / x,y).
T((x / y) / x,y) = (x / ((y \ 1) \ 1)) / x.
(x / y) * K(y \ 1,y) = x / ((y \ 1) \ 1).
x * K(y \ 1,y) = (x * y) / ((y \ 1) \ 1).
(x * y) / ((y \ 1) \ 1) = x * K(y \ 1,y).
(x / ((y \ 1) \ 1)) * y = x * K(y \ 1,y).
(x * K(y \ 1,y)) * ((y \ 1) \ 1) = x * y.
x * y = (x * ((y \ 1) \ 1)) * K(y \ 1,y).
(x * ((y \ 1) \ 1)) * K(y \ 1,y) = x * y.
x * y = (x * T(y,y \ 1)) * K(y \ 1,y).
(x * T(y,y \ 1)) * K(y \ 1,y) = x * y.
(x \ T(x * y,z)) * x = T(y * ((x \ 1) \ 1),z) * K(x \ 1,x).
T(x * ((y \ 1) \ 1),z) * K(y \ 1,y) = (y \ T(y * x,z)) * y.
x * y != z * ((y \ 1) \ 1) | x * K(y \ 1,y) = z.
x * ((y \ 1) \ 1) != z * y | z * K(y \ 1,y) = x.
(x * (y \ 1)) * ((y \ 1) \ 1) = R(x,y \ 1,y).
x * y != z * K(y \ 1,y) | x * T(y,y \ 1) = z.
x * K(y \ 1,y) != z * y | z * T(y,y \ 1) = x.
R(((x \ (x / (y \ 1))) * x) * K(y \ 1,y),y \ 1,y) = (x * ((y \ 1) * T((y \ 1) \ 1,x))) * y.
(x * y) * K(y,y \ 1) = x * T(y,(x * y) \ x).
(x * y) * K(y,y \ 1) = x * T(y,y \ 1).
(x * y) * K(y,y \ 1) = x * ((y \ 1) \ 1).
x * K(y,y \ 1) = (x / y) * T(y,y \ 1).
(x / y) * T(y,y \ 1) = x * K(y,y \ 1).
x * K(y,y \ 1) = (x / y) * ((y \ 1) \ 1).
(x / y) * ((y \ 1) \ 1) = x * K(y,y \ 1).
(x * y) * K(T(x,y),T(x,y) \ 1) = y * ((T(x,y) \ 1) \ 1).
(x * K(y,y \ 1)) * y = x * ((y \ 1) \ 1).
(x / T(y,z)) * T((y \ 1) \ 1,z) = x * K(T(y,z),T(y,z) \ 1).
x * y != (z * K(y \ 1,y)) * ((y \ 1) \ 1) | x = z.
(x * K(y \ 1,y)) * K(y,y \ 1) = x.
(x * K(y,y \ 1)) * K(y \ 1,y) = x.
x * (1 / (1 / y)) = (x * y) * K(y \ 1,y).
(x * y) * K(y \ 1,y) = x * (1 / (1 / y)).
(x / y) * y = (x * K(z,z \ 1)) * K(z \ 1,z).
x * K(y,y \ 1) != z / (y * z) | x = R(y \ 1,y,z).
(x / (y * x)) * K(y \ 1,y) = R(y \ 1,y,x).
(x / ((y \ 1) \ 1)) * K(y,y \ 1) = x / y.
T((K(x \ 1,x) * y) * K(x,x \ 1),K(x \ 1,x)) = y.
x != y * K(z \ 1,z) | x * K(z,z \ 1) = y.
x * K(y \ 1,y) != z | z * K(y,y \ 1) = x.
(x / (y * x)) * z != R(y \ 1,y,x) | z = K(x / (y * x),y).
K(x \ 1,x) = K(y / (x * y),x).
K(x / (y * x),y) = K(y \ 1,y).
K(x \ 1,x) * (y / (x * y)) = R(x \ 1,x,y).
K(x / y,y / x) = K((y / x) \ 1,y / x).
K((x / y) \ 1,x / y) = K(y / x,x / y).
K((x / (y * x)) \ 1,x / (y * x)) = K(y,x / (y * x)).
x * K(T(y,x) \ 1,T(y,x)) = (y * x) * ((((y * x) \ x) \ 1) \ 1).
(x * y) * ((((x * y) \ y) \ 1) \ 1) = y * K(T(x,y) \ 1,T(x,y)).
x * y != T((K(z \ 1,z) * (u * y)) * K(z,z \ 1),K(z \ 1,z)) | x = u.
T((K(x \ 1,x) * (y * z)) * K(x,x \ 1),K(x \ 1,x)) != u * z | u = y.
L(T(x,y) / x,x,y) = K(1 / (1 / x),y).
K(1 / (1 / x),y) = (x * K(x,y)) / x.
T(K(1 / (1 / x),y),x) = K(x,y).
T(K(1 / (x \ 1),y),T(x,x \ 1)) = K(T(x,x \ 1),y).
T(K(x,y),T(x,x \ 1)) = K(T(x,x \ 1),y).
K(T(x,x \ 1),y) = T(K(x,y),x).
K((x \ 1) \ 1,y) = T(K(x,y),x).
T(K(x,y),x) = K((x \ 1) \ 1,y).
(((x * y) \ x) \ 1) \ (((x * y) \ x) \ K(y,x)) = K((y \ 1) \ 1,x).
(x * y) * K(T(x,y),1 / x) = y * ((T(x,y) \ 1) \ 1).
(x * y) * K(T(x,y),1 / x) = y * T((x \ 1) \ 1,y).
(x * y) * K(T(x,y),1 / x) = ((x \ 1) \ 1) * y.
x * T((T(y,x) \ 1) \ 1,z) = (T(y,z) * x) * K(T(T(y,x),z),T(T(y,x),z) \ 1).
(T(x,y) * z) * K(T(T(x,z),y),T(T(x,z),y) \ 1) = z * T((T(x,z) \ 1) \ 1,y).
(T(x,y) * z) * K(T(T(x,z),y),T(T(x,z),y) \ 1) = z * T(T((x \ 1) \ 1,z),y).
(T(x,y) * z) * K(T(T(x,z),y),T(T(x,z),y) \ 1) = T((x \ 1) \ 1,y) * z.
(x * R(x \ 1,x,y)) \ (x * (y / (x * y))) = K(T(x,R(x \ 1,x,y)),R(x \ 1,x,y)).
K(T(x,R(x \ 1,x,y)),R(x \ 1,x,y)) = K(x,y / (x * y)).
K(x,y / (x * y)) = x \ T(x,y / (x * y)).
x \ T(x,y / (x * y)) = K(x,y / (x * y)).
K(x,y / (x * y)) = K(x,x \ 1).
K(x / y,y / x) = K(x / y,(x / y) \ 1).
K(x / y,(x / y) \ 1) = K(x / y,y / x).
K((x / (y * x)) \ 1,x / (y * x)) = K(y,y \ 1).
K(x / (y * x),(x / (y * x)) \ 1) = K(x / (y * x),y).
K(x,x \ 1) * (x * y) = T(x,x \ 1) * y.
T(x,x \ 1) \ (K(x,x \ 1) * y) = x \ y.
L(x,y,K(y,y \ 1)) = x.
K(x,x \ 1) * y = T(x,x \ 1) * (x \ y).
T(x,x \ 1) * (x \ y) = K(x,x \ 1) * y.
K(x,x \ 1) * (x * y) = ((x \ 1) \ 1) * y.
L(x,1 / y,K(1 / y,y)) = x.
L(x,1 / y,K(y \ 1,y)) = x.
x = L(x,K(y \ 1,y),1 / y).
L(x,K(y \ 1,y),1 / y) = x.
x = L(x,K(y,y \ 1),1 / (1 / y)).
L(x,K(y,y \ 1),1 / (1 / y)) = x.
x \ y = K(x,x \ 1) * (((x \ 1) \ 1) \ y).
K(x,x \ 1) * (((x \ 1) \ 1) \ y) = x \ y.
L(x,1 / (1 / y),K(y,y \ 1)) = x.
(x \ 1) * y = K(x \ 1,x) * ((1 / x) * y).
K(x \ 1,x) * ((1 / x) * y) = (x \ 1) * y.
L(x \ y,x,x \ 1) = (1 / x) * y.
(1 / x) \ y = K(x \ 1,x) * ((x \ 1) \ y).
K(x \ 1,x) * ((x \ 1) \ y) = (1 / x) \ y.
L(x,y,y \ 1) = L(x,y,1 / y).
L(x,y,1 / y) = L(x,y,y \ 1).
(x \ 1) * y = (1 / x) * (K(x \ 1,x) * y).
(1 / x) * (K(x \ 1,x) * y) = (x \ 1) * y.
L(x,y,y \ 1) = (1 / y) * (y * x).
(1 / x) * (x * y) = L(y,x,x \ 1).
x * ((1 / x) * (y * x)) = L(y,x,x \ 1) * x.
x * y = (1 / (1 / x)) * (K(x,x \ 1) * y).
(1 / (1 / x)) * (K(x,x \ 1) * y) = x * y.
x * y = K(x,x \ 1) * ((1 / (1 / x)) * y).
K(x,x \ 1) * ((1 / (1 / x)) * y) = x * y.
(1 / (1 / x)) \ y = x \ (K(x,x \ 1) * y).
x \ (K(x,x \ 1) * y) = (1 / (1 / x)) \ y.
L((x \ 1) * y,x,x \ 1) = (1 / x) * L(y,x \ 1,x).
T(x,(1 / x) * y) = T(x,(x \ 1) * y).
L(x,y,y \ 1) \ ((1 / y) * (x * y)) = L(K(x,y),y * x,1 / y).
((x \ 1) \ 1) \ (K(x,x \ 1) * y) = x \ y.
(T(x,x \ 1) * y) / (K(x,x \ 1) * y) = x.
x * y != z \ (z * u) | y = x \ u.
((x \ 1) \ 1) \ (x * y) = K(x,x \ 1) \ y.
K(x \ 1,x) * y = (x \ 1) * ((1 / x) \ y).
(x \ 1) * ((1 / x) \ y) = K(x \ 1,x) * y.
R(x,K(y \ 1,y),(1 / y) * z) = ((x * K(y \ 1,y)) * ((1 / y) * z)) / ((y \ 1) * z).
((x * K(y \ 1,y)) * ((1 / y) * z)) / ((y \ 1) * z) = R(x,K(y \ 1,y),(1 / y) * z).
((x \ 1) * y) / L(T(1 / x,y),y,K(x \ 1,x)) = K(x \ 1,x) * y.
((x \ 1) * y) \ (K(x \ 1,x) * ((1 / x) * (y * z))) = L(L(z,y,1 / x),(1 / x) * y,K(x \ 1,x)).
K(x \ 1,x) * y = (1 / x) \ ((x \ 1) * y).
(1 / x) \ ((x \ 1) * y) = K(x \ 1,x) * y.
T(x \ ((1 / y) \ x),y \ 1) = x \ ((y \ 1) \ x).
K(x,x \ 1) * ((y \ (1 / (1 / x))) * y) = x * K(y \ (1 / (1 / x)),y).
(1 / (1 / x)) \ y = K(x,x \ 1) * (x \ y).
K(x,x \ 1) * (x \ y) = (1 / (1 / x)) \ y.
x = R(x,K(x,x \ 1),y).
R(x,K(x,x \ 1),y) = x.
R(1 / x,K(x \ 1,x),y) = 1 / x.
(1 / x) * T(R(1 / x,K(x \ 1,x),y) \ 1,z) = R((1 / x) * T((1 / x) \ 1,z),K(x \ 1,x),y).
R((1 / x) * T((1 / x) \ 1,y),K(x \ 1,x),z) = (1 / x) * T(R(1 / x,K(x \ 1,x),z) \ 1,y).
(x \ 1) * (x * ((y * (x \ z)) / y)) = K(x \ 1,x) * ((y * ((1 / x) * z)) / y).
K(x \ 1,x) * ((y * ((1 / x) * z)) / y) = (x \ 1) * (x * ((y * (x \ z)) / y)).
x * T(x \ ((1 / y) \ x),y \ 1) = (y \ 1) \ x.
K(x,x \ 1) * ((1 / x) \ y) = (x \ 1) \ y.
x * y != z \ (z * (x * u)) | y = u.
(1 / x) \ ((x \ 1) * (K(x,x \ 1) * y)) = y.
K(x,x \ 1) * y = (x \ 1) \ ((1 / x) * y).
(x \ 1) \ ((1 / x) * y) = K(x,x \ 1) * y.
K(x \ 1,x) * y != (1 / x) \ ((x \ 1) * z) | y = z.
x = K(y,y \ 1) * (K(y \ 1,y) * x).
K(x,x \ 1) * (K(x \ 1,x) * y) = y.
(1 / x) * y = (x \ 1) * (K(x,x \ 1) * y).
(x \ 1) * (K(x,x \ 1) * y) = (1 / x) * y.
x = L(x,K(y,y \ 1),y \ 1).
L(x,K(y,y \ 1),y \ 1) = x.
x = K(y \ 1,y) * (K(y,y \ 1) * x).
K(x \ 1,x) * (K(x,x \ 1) * y) = y.
L(x,K(y \ 1,y),(y \ 1) \ 1) = x.
L(x,K(y \ 1,y),T(y,y \ 1)) = x.
x * y = ((x \ 1) \ 1) * (K(x \ 1,x) * y).
((x \ 1) \ 1) * (K(x \ 1,x) * y) = x * y.
x * y = T(x,x \ 1) * (K(x \ 1,x) * y).
T(x,x \ 1) * (K(x \ 1,x) * y) = x * y.
K(x,x \ 1) \ y = K(x \ 1,x) * y.
K(x,x \ 1) * y != (1 / (1 / x)) \ z | y = x \ z.
K(x \ 1,x) * ((1 / (1 / x)) \ y) = x \ y.
K(x,x \ 1) * y != x * z | y = (1 / (1 / x)) * z.
K(x \ 1,x) * (x * y) = (1 / (1 / x)) * y.
K(x,x \ 1) * y != x \ z | y = ((x \ 1) \ 1) \ z.
K(x \ 1,x) * (x \ y) = ((x \ 1) \ 1) \ y.
K(x,x \ 1) * y != ((x \ 1) \ 1) * z | y = x * z.
K(x \ 1,x) * (((x \ 1) \ 1) * y) = x * y.
K(x,x \ 1) * y = K(x \ 1,x) \ y.
K(x \ 1,x) \ y = K(x,x \ 1) * y.
x != K(y,y \ 1) * z | K(y \ 1,y) * x = z.
K(x,x \ 1) * y != z | K(x \ 1,x) * z = y.
T(x,x \ 1) \ y = x \ (K(x \ 1,x) * y).
x \ (K(x \ 1,x) * y) = T(x,x \ 1) \ y.
K(x,x \ 1) * ((x \ 1) * y) = (1 / x) * y.
(1 / (1 / x)) * y = x * (K(x \ 1,x) * y).
x * (K(x \ 1,x) * y) = (1 / (1 / x)) * y.
((x \ 1) \ 1) \ y = x \ (K(x \ 1,x) * y).
x \ (K(x \ 1,x) * y) = ((x \ 1) \ 1) \ y.
x != K(y \ 1,y) * z | K(y,y \ 1) * x = z.
K(x \ 1,x) * y != z | K(x,x \ 1) * z = y.
((x \ 1) \ 1) \ (x * y) = K(x \ 1,x) * y.
K(x * y,(x * y) \ 1) * ((((x * y) \ 1) * x) * y) = a((x * y) \ 1,x,y).
(K(x,x \ 1) * y) * T(K(x \ 1,x),y) = y.
K(x \ 1,x) * R(K(x,x \ 1) * (y * x),z,u) = (x \ R(x * y,z,u)) * x.
K(x \ 1,x) * L(K(x,x \ 1) * (y * x),z,u) = (x \ L(x * y,z,u)) * x.
L(K(x,x \ 1) * y,x \ 1,x) = x * ((1 / x) * y).
K(x \ 1,x) * (1 / T(x,y)) = x \ (x / T(x,y)).
K(x \ 1,x) * y = (1 / (1 / x)) * (x \ y).
(1 / (1 / x)) * (x \ y) = K(x \ 1,x) * y.
x \ L(y,1 / x,x) = (x \ 1) * y.
L((x \ 1) * y,K(x,x \ 1),z) = (z * K(x,x \ 1)) \ (z * ((1 / x) * y)).
(x * K(y,y \ 1)) \ (x * ((1 / y) * z)) = L((y \ 1) * z,K(y,y \ 1),x).
(x * ((1 / y) * z)) / L((y \ 1) * z,K(y,y \ 1),x) = x * K(y,y \ 1).
L(x,1 / y,y) = L(x,y \ 1,y).
L(x,y,y \ 1) = L(x,(y \ 1) \ 1,y \ 1).
L(x,(y \ 1) \ 1,y \ 1) = L(x,y,y \ 1).
(x \ 1) \ (K(x,x \ 1) * y) = (((x \ 1) \ 1) \ 1) \ y.
L(((x \ 1) \ 1) \ y,x,x \ 1) = (x \ 1) * y.
x * (1 / T(y,z)) != y \ (y / T(y,z)) | x = T(K(y \ 1,y),z).
K(x \ 1,x) = T(K(x \ 1,x),y).
T(K(x \ 1,x),y) = K(x \ 1,x).
K(K(x \ 1,x),y) = 1.
T(x,K(y \ 1,y)) = x.
x * K(y \ 1,y) = K(y \ 1,y) * x.
K(x \ 1,x) * y = y * K(x \ 1,x).
K(x \ (x / T(x,y)),x) = K(x \ 1,x).
(K(x,x \ 1) * y) * K(x \ 1,x) = y.
K(K(x,x \ 1),y) = 1.
K(x \ 1,x) * (y * K(x,x \ 1)) = y.
T(x,K(y,y \ 1)) = x.
(K(x \ 1,x) * y) * K(x,x \ 1) = y.
T(K(x,x \ 1),y) = K(x,x \ 1).
x * K(y,y \ 1) = K(y,y \ 1) * x.
K(x,x \ 1) * y = y * K(x,x \ 1).
x * K(x,x \ 1) = T(x,T(x,y) \ 1).
T(x,T(x,y) \ 1) = x * K(x,x \ 1).
T(x,y) \ K(x,x \ 1) = (1 / x) * (T(x,y) \ x).
(x * K(y \ 1,y)) * L(z,x,K(y \ 1,y)) = K(y \ 1,y) * (x * z).
R(x,x \ y,K(z \ 1,z)) \ (K(z \ 1,z) * y) = (x \ y) * K(z \ 1,z).
(K(x \ 1,x) * y) * ((x \ 1) \ 1) = y * x.
K(x \ 1,x) * (y * T(x,x \ 1)) = y * x.
K(x \ 1,x) * (y * x) = y * (1 / (1 / x)).
K(x \ 1,x) * y != z | z * K(x,x \ 1) = y.
((1 / x) * y) * K(x \ 1,x) = (x \ 1) * y.
(x \ 1) * ((1 / x) \ y) = y * K(x \ 1,x).
(x * y) * K(x \ 1,x) = (1 / (1 / x)) * y.
x \ (y * K(x \ 1,x)) = T(x,x \ 1) \ y.
((x \ 1) \ 1) \ (x * y) = y * K(x \ 1,x).
x * K(y \ 1,y) != z | K(y,y \ 1) * z = x.
T(x,y) \ K(x \ 1,x) = T(T(x,y) \ 1,x).
K(x \ 1,x) / T(x,y) = T(1 / T(x,y),x).
x * T(y,y \ 1) = K(y,y \ 1) * (x * y).
K(x,x \ 1) * (y * x) = y * T(x,x \ 1).
K(x \ 1,x) * y != x * z | y = ((x \ 1) \ 1) * z.
(x * y) * K(x,x \ 1) = ((x \ 1) \ 1) * y.
K(x \ 1,x) * y != (x \ 1) * z | y = (1 / x) * z.
((x \ 1) * y) * K(x,x \ 1) = (1 / x) * y.
L((x * K(y,y \ 1)) \ z,x * K(y,y \ 1),K(y \ 1,y)) = x \ (K(y \ 1,y) * z).
T(x,x \ 1) * y = x * (y * K(x,x \ 1)).
x * (y * K(x,x \ 1)) = T(x,x \ 1) * y.
R(x,y,K(z,z \ 1)) = ((x * y) * K(z,z \ 1)) / (K(z,z \ 1) * y).
((x * y) * K(z,z \ 1)) / (K(z,z \ 1) * y) = R(x,y,K(z,z \ 1)).
T(x,T(x,y) \ 1) = (x \ 1) \ 1.
(T(x,y) \ x) / ((x \ 1) \ 1) = T(x,y) \ 1.
(((x \ 1) \ 1) \ y) * ((x \ 1) \ 1) = (x \ y) * x.
(1 / (1 / x)) * (x \ (y * x)) = y * (1 / (1 / x)).
((x \ 1) * y) / (x \ 1) = ((1 / x) * y) / (1 / x).
((1 / x) * y) / (1 / x) = ((x \ 1) * y) / (x \ 1).
((x \ y) * z) * K(y \ x,x \ y) = (1 / (1 / (x \ y))) * z.
((1 / (1 / x)) * y) * (1 / x) = (x * y) * (x \ 1).
L(x * K(y \ 1,y),y,y \ 1) = (y \ 1) * (y * x).
x * (T(x,y) \ K(x \ 1,x)) = (T(x,y) \ 1) * x.
(T(x,y) \ 1) * K(x,x \ 1) = (T(x,y) \ x) / x.
T(x,y) \ K(x,x \ 1) = (T(x,y) \ x) / x.
(1 / (1 / x)) * T(y,x) = y * (1 / (1 / x)).
T(x,y) = T(x,1 / (1 / y)).
T(x,1 / (1 / y)) = T(x,y).
T(x,y) = T(x,(y \ 1) \ 1).
T(x,(y \ 1) \ 1) = T(x,y).
T(x,T(y,y \ 1)) = T(x,y).
T(x,x \ 1) * T(y,x) = y * T(x,x \ 1).
((x \ (1 / (1 / y))) * x) * (1 / y) = (y * K(x \ (1 / (1 / y)),x)) * (y \ 1).
(x * K(y \ (1 / (1 / x)),y)) * (x \ 1) = ((y \ (1 / (1 / x))) * y) * (1 / x).
(T(x,y) \ 1) * x = T(x,y) \ (1 / (1 / x)).
T(x,y) \ (1 / (1 / x)) = (T(x,y) \ 1) * x.
(1 / x) * ((T(x,y) \ 1) * x) = (x \ 1) * (T(x,y) \ x).
(T(x,y) \ 1) * z != (T(x,y) \ x) / x | z = K(x,T(x,y) \ 1).
K(x,x \ 1) = K(x,T(x,y) \ 1).
K(x,T(x,y) \ 1) = K(x,x \ 1).
T(K(x,x \ 1),y) = K(x,T(x,z) \ 1).
T(K(T(x,y),1 / x),z) = K(T(x,y),T(T(x,y),u) \ 1).
L((x \ 1) * ((1 / x) \ y),x,x \ 1) = (x \ 1) * (x * y).
K(x / (y * x),(x / (y * x)) \ 1) = K(y \ 1,y).
K(x \ 1,x) * (y / (x * y)) = ((y / (x * y)) \ 1) \ 1.
T(L((x \ 1) * ((1 / x) \ ((y * z) / y)),x,x \ 1),y) = T(1 / x,y) * L(T(1 / x,y) \ z,x \ 1,x).
(x \ 1) * (T(x,y) \ x) = T(x,y) \ 1.
(x \ 1) \ (T(x,y) \ 1) = T(x,y) \ x.
T(x,y) \ x = (x \ T(x,y)) \ 1.
(x \ T(x,y)) \ 1 = T(x,y) \ x.
T(x,y) \ x = 1 / (x \ T(x,y)).
1 / (x \ T(x,y)) = T(x,y) \ x.
(R(x,y,z) \ R(T(x,u),y,z)) \ 1 = T(R(x,y,z),u) \ R(x,y,z).
((x / y) \ (y \ x)) \ 1 = T(x / y,y) \ (x / y).
T(x / y,y) \ (x / y) = ((x / y) \ (y \ x)) \ 1.
(x \ (x * K(x,y))) \ 1 = T(x,R(y,x,(y * x) \ x)) \ x.
T(x,R(y,x,(y * x) \ x)) \ x = (x \ (x * K(x,y))) \ 1.
(T(x,y) \ x) \ 1 = x \ T(x,y).
x * ((T(x,y) \ x) \ 1) = T(x,y).
(x \ y) \ (y / x) = ((y / x) \ (x \ y)) \ 1.
((x / y) \ (y \ x)) \ 1 = (y \ x) \ (x / y).
(((x * y) / x) \ y) \ 1 = (x \ (x * y)) \ ((x * y) / x).
(x \ (x * y)) \ ((x * y) / x) = (((x * y) / x) \ y) \ 1.
K(T(x,y),1 / T(x,z)) = K(T(x,y),T(T(x,y),u) \ 1).
K(T(x,y),T(T(x,y),z) \ 1) = K(T(x,y),1 / T(x,u)).
((x / (y * x)) \ 1) \ 1 = R(y \ 1,y,x).
R(x \ 1,x,y) = ((y / (x * y)) \ 1) \ 1.
R(R(x,y,z) \ 1,R(x,y,z),y * z) = (((y * z) / ((x * y) * z)) \ 1) \ 1.
T(x,R(y \ 1,y,z)) = T(x,z / (y * z)).
T(x,R(y \ 1,y,z)) = T(x,R(1 / y,y,z)).
T(x,R(1 / y,y,z)) = T(x,R(y \ 1,y,z)).
(x * ((y * (x \ 1)) / y)) * y = T(y,R(x \ 1,x,y)).
T(x * y,R(x \ 1,x,x * y)) = x * ((x * (((x * y) * (x \ 1)) / (x * y))) * y).
x * ((x * (((x * y) * (x \ 1)) / (x * y))) * y) = T(x * y,R(x \ 1,x,x * y)).
x \ ((y * x) / y) = (((y * x) / y) \ x) \ 1.
(((x * y) / x) \ y) \ 1 = y \ ((x * y) / x).
1 / (x \ ((y * x) / y)) = ((y * x) / y) \ x.
K(T(x,y),T(x,y) \ 1) = K(T(x,y),1 / T(x,z)).
K(T(x,y),T(x,y) \ 1) = K(T(x,y),x \ 1).
K(T(x,y),x \ 1) = K(T(x,y),1 / x).
K(T(x,y),1 / x) = K(T(x,y),x \ 1).
(x * y) * K(T(x,y),x \ 1) = ((x \ 1) \ 1) * y.
(x * y) * z != ((x \ 1) \ 1) * y | z = K(x,x \ 1).
K(T(x,y),x \ 1) = K(x,x \ 1).
K(T(x,y),T(x,y) \ 1) = K(x,x \ 1).
T(x,y) \ K(x,x \ 1) = 1 / T(x,y).
(T(x,y) * z) * K(T(x,z),T(x,z) \ 1) = T((x \ 1) \ 1,y) * z.
1 / T(x,y) = (T(x,y) \ x) / x.
(T(x,y) \ x) / x = 1 / T(x,y).
(1 / T(x,y)) * x = T(x,y) \ x.
T(x,y) \ x = x / T(x,y).
x / T(x,y) = T(x,y) \ x.
(T(x,y) \ x) * T(x,y) = x.
(T(x,y) \ x) \ x = T(x,y).
x \ (x / T(x,y)) = T(x,y) \ 1.
L(x,T(x,y) \ x,x) = x.
x * y = (y * x) * T(K(x,y),y).
(x * y) * T(K(y,x),x) = y * x.
T(1 / T(x,y),x) = T(x,y) \ 1.
K(x,y) = T(K(x,y),y).
T(K(x,y),y) = K(x,y).
T(x,K(y,x)) = x.
(x * K(y,x)) / x = K(y,x).
T(x,y) = T(T(x,y),K(z,x)).
T(T(x,y),K(z,x)) = T(x,y).
T(x,y \ T(y,x)) = x.
T(x,x \ ((y * x) / y)) = x.
(x * y) * K(y,x) = y * ((K(y,x) \ x) * K(y,x)).
x * ((K(x,y) \ y) * K(x,y)) = (y * x) * K(x,y).
(x \ T(x,y)) * y = y * (x \ T(x,y)).
(x \ T(x,y)) * T(y,z) = T(y,z) * (x \ T(x,y)).
T(x,y) * (z \ T(z,x)) = (z \ T(z,x)) * T(x,y).
L(K(x,y),y,1 / y) = K(x,y).
T(K(x,y),T(y,z)) = K(x,y).
((x * y) / x) / y = y \ ((x * y) / x).
K(K(x,y),T(y,z)) = 1.
K(x \ T(x,y),T(y,z)) = 1.
T(x \ T(x,y),T(y,z)) = x \ T(x,y).
(1 / x) * (x * K(y,x)) = K(y,x).
K(x \ 1,x) / T(x,y) = T(x,y) \ 1.
x \ K(y,x \ 1) = (x \ 1) * K(y,x \ 1).
(x \ 1) * K(y,x \ 1) = x \ K(y,x \ 1).
x * (T(x,y) \ (y * (x \ T(x,y)))) = L(y,x \ T(x,y),x).
x * (((y * x) / y) / x) = (y * x) / y.
R(x / (x / y),z,u) / R(y,z,u) = R(y,z,u) \ (((x / y) * R(y,z,u)) / (x / y)).
R(x,y,z) \ (((u / x) * R(x,y,z)) / (u / x)) = R(u / (u / x),y,z) / R(x,y,z).
(T(x,y) \ 1) * T(x,y) = K(x \ 1,x).
(x \ 1) * (x * ((y * (x \ 1)) / y)) = (y * (x \ 1)) / y.
K(T(x,y) \ 1,T(x,y)) = K(x \ 1,x).
T(x,y) * K(x \ 1,x) = T(1 / (1 / x),y).
K((x * y) \ y,y \ (x * y)) = K(x \ 1,x).
(x * y) * ((((x * y) \ y) \ 1) \ 1) = y * K(x \ 1,x).
T(x,y) * (K(x \ 1,x) * z) = (1 / (1 / T(x,y))) * z.
(x \ R(x,y,z)) / R(x,y,z) = x \ K(R(x,y,z),x \ 1).
x * K(y \ 1,y) != T(1 / (1 / y),z) | x = y * (T(y,z) / y).
T(x,y) = x * (T(x,y) / x).
x * (T(x,y) / x) = T(x,y).
x \ T(x,y) = T(x,y) / x.
T(x,y) / x = x \ T(x,y).
(x \ T(x,y)) * x = T(x,y).
R(x \ T(x,y),x,z) = (T(x,y) * z) / (x * z).
R((x / y) \ T(x / y,z),x / y,y) = (T(x / y,z) * y) / x.
(x \ 1) \ T(x \ 1,y) = x * T(x \ 1,y).
(1 / x) * T((1 / x) \ 1,y) = x \ T(x,y).
x \ T(x,R(y,y \ 1,x)) = y \ ((x * y) / x).
(x * (y \ T(y,x))) \ (x * z) = x * ((x * (T(y,x) / y)) \ z).
T(x,x \ T(x,y)) = x.
L(x,y,y \ T(y,z)) = T(y,z) \ ((y \ T(y,z)) * (y * x)).
T(x,y) \ ((x \ T(x,y)) * (x * z)) = L(z,x,x \ T(x,y)).
(x \ ((x \ y) \ y)) * x = T(x,x \ y).
T(x,y) * L(z,x,x \ T(x,y)) = (x \ T(x,y)) * (x * z).
T(x,y) / (x \ T(x,y)) = L(x,x \ T(x,y),x).
L(x,x \ T(x,y),x) = T(x,y) / (x \ T(x,y)).
T(x,R(1 / y,y,x)) = T(x,x / (x * y)).
K(x,x \ T(x,y)) = 1.
T(x,K(y \ (y / (x \ 1)),y)) = x.
K(x,T(x,y) / x) = 1.
x \ 1 = T(1 / x,T(x,y)).
T(1 / x,T(x,y)) = x \ 1.
T(1 / (1 / x),T(1 / x,y)) = x.
T(x \ 1,x) = T(x \ 1,T(x,y)).
T(x \ 1,T(x,y)) = T(x \ 1,x).
T(x / (y * x),T(y,z)) = R(y \ 1,y,x).
K(x \ 1,T(x,y)) = x * T(x \ 1,T(x,y)).
x * T(x \ 1,T(x,y)) = K(x \ 1,T(x,y)).
x \ 1 = L(x \ 1,x,y \ ((x * y) / x)).
L(x \ 1,x,y \ ((x * y) / x)) = x \ 1.
(x * y) / x = (((x * y) / x) \ y) \ y.
(((x * y) / x) \ y) \ y = (x * y) / x.
T(x,x \ 1) = T(x,T(1 / x,y)).
T(x,T(1 / x,y)) = T(x,x \ 1).
T(x,x \ 1) * T(x \ 1,y) = x * T(1 / x,y).
(((x * y) / x) \ y) * ((x * y) / x) = y.
(((x \ R(x,y,z)) / R(x,y,z)) \ (x \ 1)) \ (x \ 1) = (R(x,y,z) * (x \ 1)) / R(x,y,z).
(((L(x,y,y \ 1) * y) / y) \ ((1 / y) * (x * y))) * ((y * ((1 / y) * (x * y))) / y) = (1 / y) * (x * y).
T(x,x / (y * x)) = T(x,x / (x * y)).
T(x,x / (x * y)) = T(x,R(y \ 1,y,x)).
T(x,R(y \ 1,y,x)) = T(x,x / (x * y)).
L(x \ 1,x,T(y,x) \ y) = x \ 1.
((x * y) * K(x \ 1,x)) \ y = 1 / (1 / ((x * y) \ y)).
K(x \ 1,y) = L(x * T(x \ 1,y),x \ 1,y).
L(x * T(x \ 1,y),x \ 1,y) = K(x \ 1,y).
(x * T(x \ 1,y)) \ 1 = T(x \ 1,y) \ (x \ 1).
x * T(x \ 1,x) = K(x \ 1,T(x,y)).
K(x \ 1,T(x,y)) = x * T(x \ 1,x).
K(x \ 1,T(x,y)) = (x \ 1) * x.
K(x \ 1,x) = K(x \ 1,T(x,y)).
K(x \ 1,T(x,y)) = K(x \ 1,x).
R(x \ T(x,y),K(x \ 1,x),z) \ (((x \ 1) * T(x,y)) * z) = K(x \ 1,T(x,y)) * z.
1 / (x \ ((y * x) / y)) = T(y,R(x,x \ 1,y)) \ y.
T(x,R(y,y \ 1,x)) \ x = 1 / (y \ ((x * y) / x)).
T(x,y \ ((x * y) / x)) = x.
T(x,T(y,x) \ y) = x.
(T(x,y) \ x) * y = y * (T(x,y) \ x).
T(x,R(T(y,x),T(y,x) \ 1,x)) = x * (T(y,x) \ y).
(x * ((x * (T(y,x) \ y)) \ x)) \ (x * x) = (T(y,x) \ y) * x.
L(x,x \ T(x,y),x) = x.
K(x \ 1,y) = K(1 / x,y).
K(1 / x,y) = K(x \ 1,y).
K(x,y) = K((x \ 1) \ 1,y).
K((x \ 1) \ 1,y) = K(x,y).
(((x * y) \ x) \ 1) \ (((x * y) \ x) \ K(y,x)) = K(y,x).
x * y != (z * x) * K(x,z) | y = z.
(K(x,y) \ y) * K(x,y) = y.
x / K(y,x) = K(y,x) \ x.
((x \ 1) \ 1) * T(x \ 1,y) = x * T(1 / x,y).
(x * T(1 / x,y)) \ (((x \ 1) \ 1) * (T(x \ 1,y) * z)) = L(z,T(x \ 1,y),(x \ 1) \ 1).
K(x,y) \ 1 = T(L(x \ 1,x,y) \ 1,y) \ (L(x \ 1,x,y) \ 1).
T(L(x \ 1,x,y) \ 1,y) \ (L(x \ 1,x,y) \ 1) = K(x,y) \ 1.
(x \ (y * T(y \ x,z))) \ 1 = T((x \ y) \ 1,z) \ ((x \ y) \ 1).
T((x \ y) \ 1,z) \ ((x \ y) \ 1) = (x \ (y * T(y \ x,z))) \ 1.
T(x,R(y,y \ 1,x)) \ x = ((x * y) / x) \ y.
T(x,R(T(y,x),T(y,x) \ 1,x)) \ x = y \ T(y,x).
(x * (T(y,x) \ y)) \ x = y \ T(y,x).
x / (y \ T(y,x)) = x * (T(y,x) \ y).
x / ((((x * y) \ x) \ 1) \ (((x * y) \ x) \ K(y,x))) = x * (T(((x * y) \ x) \ 1,x) \ (((x * y) \ x) \ 1)).
T(x,y) * (K(x \ 1,x) * z) = T(1 / (1 / x),y) * z.
((1 / (1 / x)) * y) \ y = 1 / (1 / ((x * y) \ y)).
1 / (1 / ((x * y) \ y)) = ((1 / (1 / x)) * y) \ y.
(((1 / (1 / x)) * y) \ y) \ 1 = 1 / ((x * y) \ y).
(((1 / x) * y) \ y) \ 1 = 1 / (((x \ 1) * y) \ y).
1 / (((x \ 1) * y) \ y) = (((1 / x) * y) \ y) \ 1.
((((1 / x) * y) \ y) \ 1) \ 1 = ((x \ 1) * y) \ y.
K(((x \ 1) * y) \ y,z) = K(((1 / x) * y) \ y,z).
K(((1 / x) * y) \ y,z) = K(((x \ 1) * y) \ y,z).
(T(1 / (1 / x),y) * z) / (K(x \ 1,x) * z) = T(x,y).
T(x,y) \ z = K(x \ 1,x) * (T(1 / (1 / x),y) \ z).
K(x \ 1,x) * (T(1 / (1 / x),y) \ z) = T(x,y) \ z.
(T(x,y) \ z) * K(x,x \ 1) = T(1 / (1 / x),y) \ z.
(T(x \ 1,y) \ z) * K(x \ 1,x) = T(1 / (1 / (x \ 1)),y) \ z.
T(x,R(y,x,(y * x) \ x)) \ x = K(x,y) \ 1.
x * ((x \ R(x,y,z)) / R(x,y,z)) = K(R(x,y,z),x \ 1).
x * L(y,x,x \ T(x,z)) = L(x * y,x \ T(x,z),x).
L(x * y,x \ T(x,z),x) = x * L(y,x,x \ T(x,z)).
L(x,y \ T(y,z),y) = y * L(y \ x,y,y \ T(y,z)).
x * L(x \ y,x,x \ T(x,z)) = L(y,x \ T(x,z),x).
T(x * L(x \ ((y * z) / y),x,x \ T(x,y)),y) = (x \ T(x,y)) * (x * (T(x,y) \ z)).
K(R(x,y,z),x \ 1) / (R(x,y,z) \ 1) = T(R(x,y,z),R(x,y,z) / (R(x,y,z) * x)).
T(R(x,y,z),R(x,y,z) / (R(x,y,z) * x)) = K(R(x,y,z),x \ 1) / (R(x,y,z) \ 1).
((x \ (x / y)) * z) * K(y,y \ 1) = (1 / (1 / (x \ (x / y)))) * z.
(x * (y \ T(y,x))) \ (x * z) = x * ((x * (y \ T(y,x))) \ z).
(x * ((x * (T(y,x) \ y)) \ x)) \ (x * x) = x * (T(y,x) \ y).
(x * (y \ T(y,x))) \ (x * x) = x * (T(y,x) \ y).
x * y != (x * (z \ T(z,x))) \ (x * u) | y = (x * (z \ T(z,x))) \ u.
T(x,y) \ x = (y * (x \ T(x,y))) \ y.
(x * (y \ T(y,x))) \ x = T(y,x) \ y.
R((x / y) \ T(x / y,z),x / y,y) = (y * T(y \ x,z)) / x.
(R(x,y,z) \ R(T(x,u),y,z)) \ 1 = R(T(x,u),y,z) \ R(x,y,z).
(T(x,y) * z) * K(x,x \ 1) = T((x \ 1) \ 1,y) * z.
x * (T((x \ 1) \ 1,y) * z) = T(x,x \ 1) * (T(x,y) * z).
T(x,x \ 1) * (T(x,y) * z) = x * (T((x \ 1) \ 1,y) * z).
(x \ 1) * (T(1 / x,y) * z) = (1 / x) * (T(((1 / x) \ 1) \ 1,y) * z).
(1 / x) * (T(((1 / x) \ 1) \ 1,y) * z) = (x \ 1) * (T(1 / x,y) * z).
L(x \ 1,x,K(y,x) \ 1) = x \ 1.
T(x,K(y,x) \ 1) = x.
(K(x,y) \ 1) * y = y * (K(x,y) \ 1).
(K(x,y) \ y) / (K(x,y) \ 1) = (K(x,y) \ 1) \ (K(x,y) \ y).
L(x \ 1,x,K(y,x) \ 1) = (x * (K(y,x) \ 1)) \ (K(y,x) \ 1).
(x * (K(y,x) \ 1)) \ (K(y,x) \ 1) = L(x \ 1,x,K(y,x) \ 1).
(x * (K(y,x) \ 1)) \ (K(y,x) \ 1) = x \ 1.
(T(x \ 1,y) \ z) * K(x \ 1,x) = T(1 / x,y) \ z.
K(x,x \ 1) * (T(1 / x,y) \ z) = T(x \ 1,y) \ z.
K(x,x \ 1) * y = T(x \ 1,z) \ (T(1 / x,z) * y).
T(x \ 1,y) \ (T(1 / x,y) * z) = K(x,x \ 1) * z.
T(x \ 1,y) * (K(x,x \ 1) * z) = T(1 / x,y) * z.
T(x \ 1,y) * ((x \ 1) \ (K(x,x \ 1) * z)) = T(1 / x,y) * ((x \ 1) \ z).
T(x \ 1,y) * ((x \ 1) \ z) = T(1 / x,y) * ((1 / x) \ z).
T(1 / x,y) * ((1 / x) \ z) = T(x \ 1,y) * ((x \ 1) \ z).
(1 / x) * (T(x \ 1,y) * ((x \ 1) \ z)) = T(1 / x,y) * z.
((x \ (x / (y \ 1))) * z) * K(y \ 1,y) = (1 / (1 / (x \ (x / (y \ 1))))) * z.
((x \ 1) * y) / T(1 / x,y) = K(x \ 1,x) * y.
((1 / x) * T((1 / x) \ 1,(x \ 1) * y)) * y = y * K(((x \ 1) * y) \ (K(x \ 1,x) * y),(x \ 1) * y).
x * K(((y \ 1) * x) \ (K(y \ 1,y) * x),(y \ 1) * x) = ((1 / y) * T((1 / y) \ 1,(y \ 1) * x)) * x.
(K(x,x \ 1) * (y * z)) / (K(x,x \ 1) * z) = R(y,z,K(x,x \ 1)).
(1 / x) * (T(x \ 1,y) * z) = (x \ 1) * (T(1 / x,y) * z).
(1 / x) * y != (x \ 1) * z | y = K(x \ 1,x) * z.
T(x \ 1,y) * z = K(x \ 1,x) * (T(1 / x,y) * z).
K(x \ 1,x) * (T(1 / x,y) * z) = T(x \ 1,y) * z.
(x \ 1) * (T(1 / x,y) * ((x \ 1) \ z)) = T(1 / x,y) * z.
((x \ 1) \ 1) * (T(x \ 1,y) * z) = x * (T(1 / x,y) * z).
(T(1 / x,y) * z) / (T(1 / x,y) * ((x \ 1) \ z)) = x \ 1.
((((x * y) / ((z * x) * y)) \ 1) \ 1) * ((z * x) * y) = ((R(z,x,y) \ 1) * R(z,x,y)) * (x * y).
K(x \ 1,x) * R(y * T(x,x \ 1),z,u) = (x \ R(x * y,z,u)) * x.
K(x \ 1,x) * L(y * T(x,x \ 1),z,u) = (x \ L(x * y,z,u)) * x.
K(x \ 1,x) * L(y * K(x,x \ 1),z,u) = (x \ L(x * (y / x),z,u)) * x.
R((x \ (1 / (1 / y))) * x,1 / y,(1 / y) \ 1) / ((1 / y) \ 1) = (y * K(x \ (1 / (1 / y)),x)) * (y \ 1).
T(x \ 1,y) * ((((x \ 1) \ 1) \ 1) \ z) = T(1 / x,y) * ((x \ 1) \ z).
T(x \ 1,y) * (T(x \ 1,(x \ 1) \ 1) \ z) = T(1 / x,y) * ((x \ 1) \ z).
((x \ (x / (y \ 1))) * z) * K(y \ 1,y) = (1 / ((x \ (x / (1 / y))) \ 1)) * z.
((x \ (x / (y \ 1))) * z) * K(y \ 1,y) = (x \ (x / (1 / y))) * z.
R((x \ (x / (1 / y))) * x,y \ 1,y) = (x * ((y \ 1) * T((y \ 1) \ 1,x))) * y.
x * ((x * y) * (y / (x * y))) = T(x * y,R(x \ 1,x,x * y)).
T(x * y,R(x \ 1,x,x * y)) = x * ((x * y) * (y / (x * y))).
R((x \ (x / (1 / y))) * x,y \ 1,y) = (x * (y \ T(y,x))) * y.
R(x,y,z) \ R(u / (u / x),y,z) = R(u / (u / x),y,z) / R(x,y,z).
R(x / (x / y),z,u) / R(y,z,u) = R(y,z,u) \ R(x / (x / y),z,u).
R(x,y,z) \ R(1 / (1 / x),y,z) = x * T(x \ 1,R(x,y,z)).
T(L((x * y) / x,z \ T(z,x),z),x) = (z \ T(z,x)) * (z * (T(z,x) \ y)).
(x \ T(x,y)) * (x * (T(x,y) \ z)) = L(y \ (y * z),x \ T(x,y),x).
L(x \ (x * y),z \ T(z,x),z) = (z \ T(z,x)) * (z * (T(z,x) \ y)).
L(x,y \ T(y,z),y) = (y \ T(y,z)) * (y * (T(y,z) \ x)).
(x \ T(x,y)) * (x * (T(x,y) \ z)) = L(z,x \ T(x,y),x).
(x \ T(x,y)) \ L(z,x \ T(x,y),x) = x * (T(x,y) \ z).
(x \ T(x,y)) * T(y,T(x,y)) = L(y,x \ T(x,y),x).
(x \ T(x,y)) * (x * (T(x,y) \ x)) = x.
(x \ T(x,y)) \ x = x * (T(x,y) \ x).
(x \ (x * K(x,y))) \ x = x * (T(x,R(y,x,(y * x) \ x)) \ x).
x * (T(x,R(y,x,(y * x) \ x)) \ x) = (x \ (x * K(x,y))) \ x.
(x \ ((y * x) / y)) \ y = y * (T(y,R(x,x \ 1,y)) \ y).
x * (T(x,R(y,y \ 1,x)) \ x) = (y \ ((x * y) / x)) \ x.
T(x,T(y,x)) * (y \ T(y,x)) = L(x,y \ T(y,x),y).
x * (((x * y) / x) \ y) = (y \ ((x * y) / x)) \ x.
(x \ ((y * x) / y)) \ y = y * (((y * x) / y) \ x).
(T(x,y) \ x) \ y = y * (((y * T(x,y)) / y) \ T(x,y)).
x * (((x * T(y,x)) / x) \ T(y,x)) = (T(y,x) \ y) \ x.
x * (y \ T(y,x)) = (T(y,x) \ y) \ x.
(T(x,y) \ x) \ y = y * (x \ T(x,y)).
(T(x,y) \ x) * (y * (x \ T(x,y))) = y.
x * (T(x,R(y,x,(y * x) \ x)) \ x) = K(x,y) \ x.
x * (K(x,y) \ 1) = K(x,y) \ x.
x \ (K(x,y) \ x) = K(x,y) \ 1.
T(R(x,y,z),R(x,y,z) / (R(x,y,z) * x)) = R(x,y,z) * K(R(x,y,z),x \ 1).
T(R(x,y,z),R(x,y,z) / (x * R(x,y,z))) = R(x,y,z) * K(R(x,y,z),x \ 1).
R(T(x,R(x,y,z) / (x * R(x,y,z))),y,z) = R(x,y,z) * K(R(x,y,z),x \ 1).
R((x \ 1) \ 1,y,z) = R(x,y,z) * K(R(x,y,z),x \ 1).
R(x,y,z) * K(R(x,y,z),x \ 1) = R((x \ 1) \ 1,y,z).
R(x,y,z) \ R((x \ 1) \ 1,y,z) = K(R(x,y,z),x \ 1).
R(x,y,z) \ R(T(x,x \ 1),y,z) = K(R(x,y,z),x \ 1).
K(R(x,y,z),x \ 1) = a(R(x,y,z),1 / x,x).
a(R(x,y,z),1 / x,x) = K(R(x,y,z),x \ 1).
K(R(x,y,z),x \ 1) \ 1 = R(T(x,x \ 1),y,z) \ R(x,y,z).
R(T(x,x \ 1),y,z) \ R(x,y,z) = K(R(x,y,z),x \ 1) \ 1.
x * ((x \ R(x,y,z)) / R(x,y,z)) = a(R(x,y,z),1 / x,x).
x * L(x \ 1,R(x,y,z),1 / x) = a(R(x,y,z),1 / x,x).
K(R(x,y,z),x \ 1) \ 1 = x * T(x \ 1,R(x,y,z)).
(((x \ R(x,y,z)) / R(x,y,z)) \ (x \ 1)) \ (x \ 1) = (x \ R(x,y,z)) / R(x,y,z).
(x * T(1 / x,y)) \ (x * (T(1 / x,y) * z)) = L(z,T(x \ 1,y),(x \ 1) \ 1).
L(x,T(1 / y,z),y) = L(x,T(y \ 1,z),(y \ 1) \ 1).
L(x,T(y \ 1,z),(y \ 1) \ 1) = L(x,T(1 / y,z),y).
((R(x,y,z) \ 1) * R(x,y,z)) * (y * z) = ((x * y) * z) * (((((x * y) * z) \ (y * z)) \ 1) \ 1).
((x * y) * z) * (((((x * y) * z) \ (y * z)) \ 1) \ 1) = ((R(x,y,z) \ 1) * R(x,y,z)) * (y * z).
((x \ 1) * y) \ ((x \ 1) * (y * z)) = L(L(z,y,1 / x),(1 / x) * y,K(x \ 1,x)).
L(L(x,y,1 / z),(1 / z) * y,K(z \ 1,z)) = ((z \ 1) * y) \ ((z \ 1) * (y * x)).
L(x,y,z \ 1) = L(L(x,y,1 / z),(1 / z) * y,K(z \ 1,z)).
L(L(x,y,1 / z),(1 / z) * y,K(z \ 1,z)) = L(x,y,z \ 1).
R((1 / x) * T((1 / x) \ 1,y),K(x \ 1,x),z) = (1 / x) * T((1 / x) \ 1,y).
R((1 / x) * T((1 / x) \ 1,y),K(x \ 1,x),z) = x \ T(x,y).
R(x \ T(x,y),K(x \ 1,x),z) = x \ T(x,y).
(x \ T(x,y)) \ (((x \ 1) * T(x,y)) * z) = K(x \ 1,T(x,y)) * z.
(x \ T(x,y)) \ (((x \ 1) * T(x,y)) * z) = K(x \ 1,x) * z.
(x \ T(x,y)) * (K(x \ 1,x) * z) = ((x \ 1) * T(x,y)) * z.
(x \ T(x,y)) * (z * K(x \ 1,x)) = ((x \ 1) * T(x,y)) * z.
(L(x,y,y \ 1) \ ((1 / y) * (x * y))) * ((y * ((1 / y) * (x * y))) / y) = (1 / y) * (x * y).
(1 / x) * (y * x) != z * ((x * ((1 / x) * (y * x))) / x) | L(y,x,x \ 1) \ ((1 / x) * (y * x)) = z.
x * ((y * ((1 / y) * (z * y))) / y) != (1 / y) * (z * y) | L(z,y,y \ 1) \ ((1 / y) * (z * y)) = x.
T((x \ 1) * (x * ((y * z) / y)),y) = T(1 / x,y) * L(T(1 / x,y) \ z,x \ 1,x).
x / K(y,x) = x * (T(((x * y) \ x) \ 1,x) \ (((x * y) \ x) \ 1)).
x * (T(((x * y) \ x) \ 1,x) \ (((x * y) \ x) \ 1)) = x / K(y,x).
x * (((x * y) \ (x * T(x \ (x * y),x))) \ 1) = x / K(y,x).
x * (((x * y) \ (x * T(y,x))) \ 1) = x / K(y,x).
x * (((x * y) \ (y * x)) \ 1) = x / K(y,x).
x * (K(y,x) \ 1) = x / K(y,x).
x * (K(y,x) \ 1) = K(y,x) \ x.
(K(x,y) \ y) / (K(x,y) \ 1) = y.
(K(x,y) \ y) \ (K(x,y) \ 1) = y \ 1.
x = (K(y,x) \ 1) \ (K(y,x) \ x).
(K(x,y) \ 1) \ (K(x,y) \ y) = y.
(K(x,y) \ 1) * T(y,z) = K(x,y) \ T(y,z).
(K(x,y) \ y) * (y \ 1) = K(x,y) \ 1.
(K(x,y) \ 1) * ((y \ 1) \ 1) = R(K(x,y) \ y,y \ 1,y).
R(K(x,y) \ y,y \ 1,y) = (K(x,y) \ 1) * ((y \ 1) \ 1).
(K(x,y) \ 1) * ((y \ z) \ z) = K(x,y) \ T(y,y \ z).
K(x,y) \ T(y,y \ z) = (K(x,y) \ 1) * ((y \ z) \ z).
K(x,y) \ ((y \ z) \ z) = (K(x,y) \ 1) * ((y \ z) \ z).
(K(x,y) \ 1) * ((y \ z) \ z) = K(x,y) \ ((y \ z) \ z).
R(K(x,y) \ y,y \ 1,y) = K(x,y) \ ((y \ 1) \ 1).
x * (K(x,y) * (K(x,y) \ ((y \ 1) \ 1))) = (T(y,y \ 1) * x) * K(x,y).
(T(x,x \ 1) * y) \ (y * ((x \ 1) \ 1)) = K(y,x).
K(x,y) = (T(y,y \ 1) * x) \ (x * ((y \ 1) \ 1)).
K(x,y) = K(x,(y \ 1) \ 1).
K(x,(y \ 1) \ 1) = K(x,y).
K(x,T(y / z,y \ z)) = K(x,y / z).
K(x,T((y / z) / y,z)) = K(x,(y / z) / y).
K(x,(y / ((z \ 1) \ 1)) / y) = K(x,(y / z) / y).
x * K(((y \ 1) * x) \ (K(y \ 1,y) * x),(y \ 1) * x) = (y \ T(y,(y \ 1) * x)) * x.
(x * (R(y / z,z,y \ u) / x)) * (z * (y \ u)) = (x * ((u / (z * (y \ u))) / x)) * (z * (y \ u)).
R((x \ (1 / (1 / y))) * x,1 / y,y) / ((1 / y) \ 1) = (y * K(x \ (1 / (1 / y)),x)) * (y \ 1).
R((x \ (1 / (1 / y))) * x,y \ 1,y) / ((1 / y) \ 1) = (y * K(x \ (1 / (1 / y)),x)) * (y \ 1).
R(T(x,x \ 1) * T(T(x \ 1,x),x \ R(x,y,z)),y,z) = K((x \ R(x,y,z)) \ (x \ 1),x \ R(x,y,z)).
R(T(x,x \ 1) * T(x \ 1,x),y,z) = K((x \ R(x,y,z)) \ (x \ 1),x \ R(x,y,z)).
K((x \ R(x,y,z)) \ (x \ 1),x \ R(x,y,z)) = R(T(x,x \ 1) * T(x \ 1,x),y,z).
K((x \ R(x,y,z)) \ (x \ 1),x \ R(x,y,z)) = R((x \ 1) * T(x,x \ 1),y,z).
K((x \ R(x,y,z)) \ (x \ 1),x \ R(x,y,z)) = R(1,y,z).
K((x \ R(x,y,z)) \ (x \ 1),x \ R(x,y,z)) = 1.
(x \ 1) * 1 = ((x \ R(x,y,z)) \ (x \ 1)) * (x \ R(x,y,z)).
((x \ R(x,y,z)) \ (x \ 1)) * (x \ R(x,y,z)) = (x \ 1) * 1.
x \ 1 = ((x \ R(x,y,z)) \ (x \ 1)) * (x \ R(x,y,z)).
((x \ R(x,y,z)) \ (x \ 1)) * (x \ R(x,y,z)) = x \ 1.
(x \ 1) / (x \ R(x,y,z)) = (x \ R(x,y,z)) \ (x \ 1).
((x * ((y * z) / ((u * y) * z))) / x) * ((u * y) * z) = (((x * (1 / R(u,y,z))) / x) * R(u,y,z)) * (y * z).
(((x * (1 / R(y,z,u))) / x) * R(y,z,u)) * (z * u) = ((x * ((z * u) / ((y * z) * u))) / x) * ((y * z) * u).
(((x * (1 / R(y,z,u))) / x) * R(y,z,u)) * (z * u) = ((y * z) * u) * ((x * (((y * z) * u) \ (z * u))) / x).
(((x * (1 / R(y,z,u))) / x) * R(y,z,u)) * (z * u) = ((y * z) * ((x * ((y * z) \ z)) / x)) * u.
(R(x,y,z) * ((u * (R(x,y,z) \ 1)) / u)) * (y * z) = ((x * y) * ((u * ((x * y) \ y)) / u)) * z.
(R(x,y,z) * ((u * (R(x,y,z) \ 1)) / u)) * (y * z) = ((x * ((u * (x \ 1)) / u)) * y) * z.
x * (y * z) != (u * y) * z | x = R(u,y,z).
R(x,y,z) * ((u * (R(x,y,z) \ 1)) / u) = R(x * ((u * (x \ 1)) / u),y,z).
R(x,y,z) * (1 / R(x,y,z)) = R(x * ((R(x,y,z) * (x \ 1)) / R(x,y,z)),y,z).
R(x * ((R(x,y,z) * (x \ 1)) / R(x,y,z)),y,z) = R(x,y,z) * (1 / R(x,y,z)).
K(x,(x / R(y,z,u)) / x) = R(y * ((x * (y \ 1)) / x),z,u).
R(x * ((y * (x \ 1)) / y),z,u) = K(y,(y / R(x,z,u)) / y).
R(K(x,(x / y) / x),z,u) = K(x,(x / R(y,z,u)) / x).
K(R(x,y,z),R(x,y,z) \ 1) = R(x * ((R(x,y,z) * (x \ 1)) / R(x,y,z)),y,z).
R(x * ((R(x,y,z) * (x \ 1)) / R(x,y,z)),y,z) = K(R(x,y,z),R(x,y,z) \ 1).
R(x * ((x \ R(x,y,z)) / R(x,y,z)),y,z) = K(R(x,y,z),R(x,y,z) \ 1).
R(K(R(x,y,z),x \ 1),y,z) = K(R(x,y,z),R(x,y,z) \ 1).
(((x * y) * z) * R(((x * y) * z) \ (y * z),u,w)) / (y * z) = R(x,y,z) * R(R(x,y,z) \ 1,u,w).
(((x * y) * R((x * y) \ y,z,u)) * w) / (y * w) = R(x,y,w) * R(R(x,y,w) \ 1,z,u).
(((x * R(x \ 1,y,z)) * u) * w) / (u * w) = R(x,u,w) * R(R(x,u,w) \ 1,y,z).
R(x * R(x \ 1,y,z),u,w) = R(x,u,w) * R(R(x,u,w) \ 1,y,z).
R(x,y,z) * R(R(x,y,z) \ 1,u,w) = R(x * R(x \ 1,u,w),y,z).
R(x * R(x \ 1,R(x,y,z),x \ 1),y,z) = ((x \ 1) / (x \ R(x,y,z))) * R(x,y,z).
R(x * T(x \ 1,R(x,y,z)),y,z) = ((x \ 1) / (x \ R(x,y,z))) * R(x,y,z).
((x \ 1) / (x \ R(x,y,z))) * R(x,y,z) = R(x * T(x \ 1,R(x,y,z)),y,z).
x * R(y,z,u) != R(y * T(y \ 1,R(y,z,u)),z,u) | x = R(y,z,u) \ 1.
(x \ 1) / (x \ R(x,y,z)) = R(x,y,z) \ 1.
R(x,y,z) \ 1 = (x \ R(x,y,z)) \ (x \ 1).
(x \ R(x,y,z)) \ (x \ 1) = R(x,y,z) \ 1.
((1 / x) \ R(1 / x,y,z)) \ x = R(1 / x,y,z) \ 1.
(x * R(x \ 1,y,z)) \ x = R(1 / x,y,z) \ 1.
(R(x,y,z) / x) \ (1 / x) = R(1 / (1 / x),y,z) \ 1.
R(1 / (1 / x),y,z) \ 1 = (R(x,y,z) / x) \ (1 / x).
(((x * y) * z) * L(((x * y) * z) \ (y * z),u,w)) / (y * z) = R(x,y,z) * L(R(x,y,z) \ 1,u,w).
(((x * y) * L((x * y) \ y,z,u)) * w) / (y * w) = R(x,y,w) * L(R(x,y,w) \ 1,z,u).
(((x * L(x \ 1,y,z)) * u) * w) / (u * w) = R(x,u,w) * L(R(x,u,w) \ 1,y,z).
R(x * L(x \ 1,y,z),u,w) = R(x,u,w) * L(R(x,u,w) \ 1,y,z).
R(x,y,z) * L(R(x,y,z) \ 1,u,w) = R(x * L(x \ 1,u,w),y,z).
R(x,y,z) * ((R(x,y,z) / x) \ ((1 / x) * 1)) = R(x * L(x \ 1,R(x,y,z),1 / x),y,z).
R(x,y,z) * ((R(x,y,z) / x) \ (1 / x)) = R(x * L(x \ 1,R(x,y,z),1 / x),y,z).
R(x * L(x \ 1,R(x,y,z),1 / x),y,z) = R(x,y,z) * ((R(x,y,z) / x) \ (1 / x)).
R(a(R(x,y,z),1 / x,x),y,z) = R(x,y,z) * ((R(x,y,z) / x) \ (1 / x)).
R(x,y,z) * ((R(x,y,z) / x) \ (1 / x)) = R(a(R(x,y,z),1 / x,x),y,z).
R(x,y,z) * ((R(x,y,z) / x) \ (1 / x)) = R(K(R(x,y,z),x \ 1),y,z).
R(x,y,z) * ((R(x,y,z) / x) \ (1 / x)) = K(R(x,y,z),R(x,y,z) \ 1).
(R(x,y,z) / x) \ (1 / x) = 1 / R(x,y,z).
R(1 / (1 / x),y,z) \ 1 = 1 / R(x,y,z).
1 / (1 / R(x,y,z)) = R(1 / (1 / x),y,z).
R(1 / (1 / x),y,z) = 1 / (1 / R(x,y,z)).
R(x,y,z) \ 1 = 1 / R((x \ 1) \ 1,y,z).
1 / R((x \ 1) \ 1,y,z) = R(x,y,z) \ 1.
(R(x,y,z) \ 1) \ 1 = R((x \ 1) \ 1,y,z).
R((x \ 1) \ 1,y,z) = (R(x,y,z) \ 1) \ 1.
R(((x / y) \ 1) \ 1,y,z) * (y * z) = (y * z) * ((((y * z) \ (x * z)) \ 1) \ 1).
(x * y) * ((((x * y) \ (z * y)) \ 1) \ 1) = ((((z / x) \ 1) \ 1) * x) * y.
(x * y) * ((((x * y) \ (z * y)) \ 1) \ 1) = (x * (((x \ z) \ 1) \ 1)) * y.
((x * y) * ((((x * y) \ y) \ 1) \ 1)) * z = ((R(x,y,z) \ 1) * R(x,y,z)) * (y * z).
((R(x,y,z) \ 1) * R(x,y,z)) * (y * z) = ((x * y) * ((((x * y) \ y) \ 1) \ 1)) * z.
((R(x,y,z) \ 1) * R(x,y,z)) * (y * z) = (y * K(x \ 1,x)) * z.
K(R(x,y,z) \ (((x \ R(x,y,z)) / R(x,y,z)) * R(x,y,z)),R(x,y,z)) = ((x \ R(x,y,z)) / R(x,y,z)) \ (x \ 1).
K(R(x,y,z) \ (x \ R(x,y,z)),R(x,y,z)) = ((x \ R(x,y,z)) / R(x,y,z)) \ (x \ 1).
K(x \ 1,R(x,y,z)) = ((x \ R(x,y,z)) / R(x,y,z)) \ (x \ 1).
((x \ R(x,y,z)) / R(x,y,z)) \ (x \ 1) = K(x \ 1,R(x,y,z)).
K(x \ 1,R(x,y,z)) \ (x \ 1) = (x \ R(x,y,z)) / R(x,y,z).
(x \ 1) \ ((x \ R(x,y,z)) / R(x,y,z)) = K(x \ 1,R(x,y,z)) \ 1.
K(x \ 1,R(x,y,z)) \ 1 = K(R(x,y,z),x \ 1).
K(R(x,y,z),x \ 1) \ 1 = K(x \ 1,R(x,y,z)).
K(x \ 1,R(x,y,z)) = x * T(x \ 1,R(x,y,z)).
x * T(x \ 1,R(x,y,z)) = K(x \ 1,R(x,y,z)).
R(K(x \ 1,R(x,y,z)),y,z) = K(R(x,y,z) \ 1,R(x,y,z)).
R(x,y,z) \ R(1 / (1 / x),y,z) = K(x \ 1,R(x,y,z)).
R(x,y,z) * K(x \ 1,R(x,y,z)) = R(1 / (1 / x),y,z).
R(x,y,z) * K(x \ 1,R(x,y,z)) = 1 / (1 / R(x,y,z)).
K(x \ 1,R(x,y,z)) = K(R(x,y,z) \ 1,R(x,y,z)).
K(R(x,y,z) \ 1,R(x,y,z)) = K(x \ 1,R(x,y,z)).
K(x \ 1,R(x,y,z)) = (R(x,y,z) \ 1) * R(x,y,z).
(R(x,y,z) \ 1) * R(x,y,z) = K(x \ 1,R(x,y,z)).
K(x \ 1,R(x,y,z)) * (y * z) = (y * K(x \ 1,x)) * z.
K(x,R(x \ 1,y,z)) * (y * z) = (y * K((x \ 1) \ 1,x \ 1)) * z.
R(K(x,R(x \ 1,y,z)),y,z) = K(R(x \ 1,y,z) \ 1,R(x \ 1,y,z)).
K(R(x \ 1,y,z) \ 1,R(x \ 1,y,z)) = R(K(x,R(x \ 1,y,z)),y,z).
K(x,R(x \ 1,y,z)) * (y * z) = (y * K(x,x \ 1)) * z.
R(K(x,R(x \ 1,y,z)),y,z) = K((x \ 1) \ 1,R(x \ 1,y,z)).
R(K(x,R(x \ 1,y,z)),y,z) = K(x,R(x \ 1,y,z)).
K(x,R(x \ 1,y,z)) * (y * z) = (K(x,R(x \ 1,y,z)) * y) * z.
(K(x,R(x \ 1,y,z)) * y) * z = K(x,R(x \ 1,y,z)) * (y * z).
L(x,y,K(z,R(z \ 1,y,x))) = x.
x * y != K(z,R(z \ 1,u,y)) * (u * y) | x = u * K(z,z \ 1).
K(x,R(x \ 1,y,z)) * y = y * K(x,x \ 1).
x * y != y * K(z,z \ 1) | x = K(z,z \ 1).
K(x,R(x \ 1,y,z)) = K(x,x \ 1).
K(x,x \ 1) * (y * z) = (y * K(x,x \ 1)) * z.
(x * K(y,y \ 1)) * z = K(y,y \ 1) * (x * z).
L(x,y,K(z,z \ 1)) = x.
(K(x,x \ 1) * y) / z = K(x,x \ 1) * (y / z).
L(x,y,K(z \ 1,z)) = x.
((x \ 1) \ 1) / (y \ x) = K(x,x \ 1) * y.
(1 / x) / y = K(x,x \ 1) * ((x \ 1) / y).
K(x,x \ 1) * ((x \ 1) / y) = (1 / x) / y.
(K(x \ 1,x) * y) * z = K(x \ 1,x) * (y * z).
x \ y = (K(z \ 1,z) * x) \ (K(z \ 1,z) * y).
(K(x \ 1,x) * y) \ (K(x \ 1,x) * z) = y \ z.
(K(x \ 1,x) * y) / z = K(x \ 1,x) * (y / z).
(x * K(y \ 1,y)) * z = K(y \ 1,y) * (x * z).
(x * K(y,y \ 1)) \ z = x \ (K(y \ 1,y) * z).
L(x,y,1 / z) = L(x,y,z \ 1).
L(x,y,z) = L(x,y,(z \ 1) \ 1).
L(x,y,(z \ 1) \ 1) = L(x,y,z).
L(x,y,y \ 1) \ ((1 / y) * (x * y)) = L(K(x,y),y * x,y \ 1).
L(x,T(y \ 1,z),y) = L(x,T(1 / y,z),y).
L(x,T(1 / y,z),y) = L(x,T(y \ 1,z),y).
((x \ 1) \ 1) / y = K(x,x \ 1) * (x / y).
K(x,x \ 1) * (x / y) = ((x \ 1) \ 1) / y.
(1 / x) / y = ((x \ 1) / y) * K(x,x \ 1).
((x \ 1) / y) * K(x,x \ 1) = (1 / x) / y.
L(T(1 / x,y) \ z,T(x \ 1,y),x) = (x * T(1 / x,y)) \ (x * z).
((x \ 1) \ 1) / y = (x / y) * K(x,x \ 1).
(x / y) * K(x,x \ 1) = ((x \ 1) \ 1) / y.
(x \ ((y \ 1) \ 1)) * K(y \ 1,(y \ 1) \ 1) = (1 / (y \ 1)) / T(x,x \ T(y,y \ 1)).
(1 / (x \ 1)) / T(y,y \ T(x,x \ 1)) = (y \ ((x \ 1) \ 1)) * K(x \ 1,(x \ 1) \ 1).
R(x,K(y,y \ 1),z) = (K(y,y \ 1) * (x * z)) / (K(y,y \ 1) * z).
(K(x,x \ 1) * (y * z)) / (K(x,x \ 1) * z) = R(y,K(x,x \ 1),z).
x * y = K(z,z \ 1) * ((K(z \ 1,z) * x) * y).
K(x,x \ 1) * ((K(x \ 1,x) * y) * z) = y * z.
((1 / x) * y) * z = K(x,x \ 1) * (((x \ 1) * y) * z).
K(x,x \ 1) * (((x \ 1) * y) * z) = ((1 / x) * y) * z.
x / y = K(x,x \ 1) * ((1 / (1 / x)) / y).
K(x,x \ 1) * ((1 / (1 / x)) / y) = x / y.
K(x \ 1,x) * (x / y) = (1 / (1 / x)) / y.
K(x \ 1,x) * (y \ x) = (1 / (1 / x)) / T(y,y \ x).
(1 / (1 / x)) / T(y,y \ x) = K(x \ 1,x) * (y \ x).
R(K(x \ 1,x) * y,z,u) = ((K(x \ 1,x) * (y * z)) * u) / (z * u).
((K(x \ 1,x) * (y * z)) * u) / (z * u) = R(K(x \ 1,x) * y,z,u).
((x \ 1) * y) \ (K(x \ 1,x) * z) = ((1 / x) * y) \ z.
T(K(x \ 1,x) * (y / z),z) = z \ (K(x \ 1,x) * y).
(K(x \ 1,x) * (y * ((1 / x) * z))) / ((x \ 1) * z) = R(y,K(x \ 1,x),(1 / x) * z).
x \ (K(y \ 1,y) * (x * ((1 / y) * z))) = L((y \ 1) * z,K(y,y \ 1),x).
((1 / (x * y)) * x) * y = a((x * y) \ 1,x,y).
a((x * y) \ 1,x,y) / y = (1 / (x * y)) * x.
x * K(((1 / y) * x) \ x,(y \ 1) * x) = (y \ T(y,(y \ 1) * x)) * x.
(x \ T(x,(x \ 1) * y)) * y = y * K(((1 / x) * y) \ y,(x \ 1) * y).
T((x \ 1) * (x * ((y * (x \ z)) / y)),y) = y \ (K(x \ 1,x) * (y * ((1 / x) * z))).
R(x,K(y,y \ 1),z) = R(x,z,K(y,y \ 1)).
R(x,K(y \ 1,y),z) = R(x,z,K(y \ 1,(y \ 1) \ 1)).
R(x,y,K(z \ 1,(z \ 1) \ 1)) = R(x,K(z \ 1,z),y).
R(x,y,K(z \ 1,z)) = R(x,K(z \ 1,z),y).
R(x,K(y \ 1,y),z) = R(x,z,K(y \ 1,y)).
(K(x \ 1,x) * ((y * z) * u)) / (z * u) = R(K(x \ 1,x) * y,z,u).
R(K(x \ 1,x) * y,z,u) = K(x \ 1,x) * (((y * z) * u) / (z * u)).
K(x \ 1,x) * (((y * z) * u) / (z * u)) = R(K(x \ 1,x) * y,z,u).
K(x \ 1,x) * R(y,z,u) = R(K(x \ 1,x) * y,z,u).
R(K(x \ 1,x) * y,z,u) = K(x \ 1,x) * R(y,z,u).
R(K(x \ 1,x) * (y * T(x,x \ 1)),z,u) = (x \ R(x * y,z,u)) * x.
(x \ T(x,(x \ 1) * y)) * y = y * K(((x \ 1) * y) \ y,(x \ 1) * y).
R(x * y,z,u) = (y \ R(y * x,z,u)) * y.
(x \ R(x * y,z,u)) * x = R(y * x,z,u).
R(x * y,z,u) / y = y \ R(y * x,z,u).
(x \ R(y,z,u)) * x = R((x \ y) * x,z,u).
R((x \ y) * x,z,u) = (x \ R(y,z,u)) * x.
R(x,y,z) / u = u \ R(u * (x / u),y,z).
x \ R(x * (y / x),z,u) = R(y,z,u) / x.
R((x \ (1 / y)) * x,y,x) * (y * x) = x * ((y * x) * T((y * x) \ 1,x)).
R((x \ (y / (1 / z))) * x,z \ 1,z) = (x \ (y * z)) * x.
x * (R(y,z,u) / x) = R(x * (y / x),z,u).
R(x * (y / x),z,u) = x * (R(y,z,u) / x).
R(x * ((y / z) / x),z,y \ u) * (z * (y \ u)) = (x * ((u / (z * (y \ u))) / x)) * (z * (y \ u)).
(x \ (x * y)) * x = (x * (y \ T(y,x))) * y.
((x \ (1 * y)) * x) / ((1 / y) \ 1) = (y * K(x \ (1 / (1 / y)),x)) * (y \ 1).
(x * K(y \ (1 / (1 / x)),y)) * (x \ 1) = ((y \ (1 * x)) * y) / ((1 / x) \ 1).
x * y = (y * (x \ T(x,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.
x * y != z * (z \ u) | x = u / y.
(x \ y) * (x \ T(x,x \ y)) = y / x.
T(x,y) * (y \ T(y,T(x,y))) = x.
x \ ((y * x) / y) = y \ T(y,x).
(x \ 1) * y != (z * (x \ 1)) / z | y = x * ((z * (x \ 1)) / z).
x \ T(x,y \ 1) = y * ((x * (y \ 1)) / x).
x * ((y * (x \ 1)) / y) = y \ T(y,x \ 1).
x * y != (z * x) / z | y = ((z * x) / z) / x.
x \ T(x,y) = ((x * y) / x) / y.
((x * y) / x) / y = x \ T(x,y).
x * y != (z * x) / z | y = K(z,(z / (x \ 1)) / z).
x \ T(x,y) = K(x,(x / (y \ 1)) / x).
K(x,(x / (y \ 1)) / x) = x \ T(x,y).
((x * y) / x) * (y \ 1) = x \ T(x,y).
(x \ T(x,y)) * y = (x * y) / x.
x * (y * T(y \ 1,x)) = ((y \ 1) * x) / (y \ 1).
((x \ 1) * y) / (x \ 1) = y * (x * T(x \ 1,y)).
((x * y) / x) \ y = T(x,y) \ x.
(T(x,y) \ x) * ((x * y) / x) = y.
T(x,y) \ x = y \ T(y,T(x,y)).
x \ T(x,y) = T(y,T(x,y)) \ y.
T(x,T(y,x)) \ x = y \ T(y,x).
x \ (y / (y / x)) = (y / x) \ T(y / x,x).
(x / y) \ T(x / y,y) = y \ (x / (x / y)).
R(x \ T(x,y),y,((x * y) / x) \ z) \ z = y * (((x * y) / x) \ z).
((1 / (x * y)) \ T(1 / (x * y),x)) * x = (a((x * y) \ 1,x,y) / y) / (1 / (x * y)).
(a((x * y) \ 1,x,y) / y) / (1 / (x * y)) = ((1 / (x * y)) \ T(1 / (x * y),x)) * x.
(x / y) \ (y \ x) = T(y,y \ x) \ y.
T(x,x \ y) \ x = (y / x) \ (x \ y).
((x * y) / x) * (y \ ((T(x,y) \ x) * z)) = L(z,((x * y) / x) \ y,(x * y) / x).
L(x,y,y \ 1) \ ((1 / y) * (x * y)) = T(y,(1 / y) * (x * y)) \ y.
T(x,T(y,x)) * (y \ T(y,x)) = x.
x * (y \ T(y,z)) != z | x = T(z,T(y,z)).
x * (y \ T(y,z)) != z | T(z,T(y,z)) = x.
(x \ T(x,y)) \ y = T(y,T(x,y)).
(x * (T(x,T(y,x)) \ x)) * y = y * x.
x * (T(x,T(y,x)) \ x) = (y * x) / y.
(x * y) / x = y * (T(y,T(x,y)) \ y).
x = L(x,y \ T(y,x),y).
L(x,y \ T(y,x),y) = x.
x * (T(x,y) \ (y * (x \ T(x,y)))) = y.
(x * T(x \ 1,y)) \ y = T(y,T(x \ 1,y)).
(x \ y) * (x \ ((x \ y) \ y)) = y / x.
x \ T(x,y \ 1) = K(x,(x / y) / x).
K(x,(x / y) / x) = x \ T(x,y \ 1).
T(x * (T(x,T(y,x)) \ x),y) = x.
x \ y = T(x,y) \ (y * (x \ T(x,y))).
T(x,y) \ (y * (x \ T(x,y))) = x \ y.
(x \ y) \ (y / x) = x \ ((x \ y) \ y).
x * K(x,(x / y) / x) = T(x,y \ 1).
R(x \ T(x,y \ 1),z,u) = K(x,(x / R(y,z,u)) / x).
T(x,y) \ ((x * y) / x) = x \ y.
T(x,y) * (x \ y) = (x * y) / x.
x \ y = T(y / x,T(x,y)).
T(x / y,T(y,x)) = y \ x.
T(x / ((x * y) / x),y) = ((x * y) / x) \ x.
T(x \ y,x) = T(x \ y,T(x,y)).
T(x \ y,T(x,y)) = T(x \ y,x).
K(x \ y,T(x,y)) = y \ (x * T(x \ y,T(x,y))).
x \ (y * T(y \ x,T(y,x))) = K(y \ x,T(y,x)).
x * (y \ z) != (y * z) / y | x = T(y,y / (y / z)).
T(x,y) = T(x,x / (x / y)).
T(x,x / (x / y)) = T(x,y).
T(x,(y \ x) * y) * K(y \ x,y) = (x * ((y \ x) * y)) / x.
x * ((x * y) / x) = T(x,y) * y.
T(x,y) * y = x * ((x * y) / x).
T(x,x / y) = T(x,y \ x).
(x / y) \ T(x,y) = (x * y) / x.
T(x,T(y,x)) = (x / T(y,x)) * y.
(x / T(y,x)) * y = T(x,T(y,x)).
T(x,T(y,x)) * (y * x) = x * (x * y).
T(x,x * y) = T(x,x / (1 / y)).
T(x,x / (1 / y)) = T(x,x * y).
T(x,(y \ 1) \ x) = T(x,y * x).
x \ (y * T(y \ x,T(y,x))) = K(y \ x,y).
T(x,x \ y) * (x \ y) = x * (y / x).
x \ T(x * y,y) = ((x * y) * y) / (x * y).
((x * y) * y) / (x * y) = x \ T(x * y,y).
R(T(x,x * y),y,x) = (x / T(y,x)) * y.
T(x,y \ 1) = T(x,x / (x * y)).
T(x,x / (x * y)) = T(x,y \ 1).
T(x \ T(x,y \ 1),z) = K(x,(x / T(y,z)) / x).
(x * ((x / y) / x)) * y = T(x,y \ 1).
x \ T(y,x \ 1) = T(y * ((y / x) / y),x).
T(x * ((x / y) / x),y) = y \ T(x,y \ 1).
T(x,x / (y * x)) = T(x,y \ 1).
T(x,R(y \ 1,y,x)) = T(x,y \ 1).
x \ T(y,x \ 1) = y * ((x \ y) / y).
T(x * y,x \ 1) = x * ((x * y) * (y / (x * y))).
x * ((x * y) * (y / (x * y))) = T(x * y,x \ 1).
x * (x * (y / x)) = T(x,x \ y) * y.
T(x,x \ y) * y = x * (x * (y / x)).
x \ (y \ T(x,y \ 1)) = (y \ x) / x.
R(T(x,x * y),y,x) = T(x,T(y,x)).
(x * y) * T(x,T(y,x)) = R(x,y,x) * (x * y).
x * T(y,T(x,y)) = L(R(y,x,y),x,y) * x.
L(R(x,y,x),y,x) * y = y * T(x,T(y,x)).
(x * ((y \ x) / x)) / (y \ x) = x \ T(x,y \ 1).
K(x,(x / y) / x) * (y * z) = y * ((x \ T(x,y \ 1)) * z).
(x * ((y / (z * (x \ y))) / x)) * (z * (x \ y)) = x * ((x \ T(x,z \ 1)) * (x \ y)).
(x / y) \ (y \ x) = y \ (x / (x / y)).
x * ((y / x) \ (x \ y)) = y / (y / x).
T(x,x \ y) \ x = x \ (y / (y / x)).
x * (T(x,x \ y) \ x) = y / (y / x).
x / (x / y) = y * (T(y,y \ x) \ y).
(x * y) / ((x * y) / x) = x * (T(x,y) \ x).
(x \ T(x * y,y)) * x = x * R(y,x,y).
(x * R(y,x,y)) \ T(x * y,y) = K(x,x \ T(x * y,y)).
T(((x / y) / x) * ((x \ 1) \ 1),y) * K(x \ 1,x) = (x \ (y \ T(x,y \ 1))) * x.
x * y != y * T(z,u) | x = T((y * z) / y,u).
L(R(x,y,x),y,x) = T((y * x) / y,T(y,x)).
T((x * y) / x,T(x,y)) = L(R(y,x,y),x,y).
x * (T(x,y) \ x) = (x / ((x * y) / x)) * y.
(x / ((x * y) / x)) * y = x * (T(x,y) \ x).
x * (T(x,y) \ x) = y / (x \ ((x * y) / x)).
x / (y \ ((y * x) / y)) = y * (T(y,x) \ y).
T(x * (T(x,T(y,x)) \ x),T(y,x)) = L(R(x,y,x),y,x).
T(x \ T(x * y,y),T(x * y,y)) = L(R(y,x * y,y),x * y,y).
T(x / ((x * y) / x),y) = y \ (x * (T(x,y) \ x)).
x \ (y * (T(y,x) \ y)) = T(y / ((y * x) / y),x).
(x * (T(x,y) \ x)) \ y = x \ ((x * y) / x).
((x * y) / x) * T(((x * y) / x) \ x,y) = x * K(y \ (x * (T(x,y) \ x)),y).
(((x * y) \ 1) * x) / ((x * y) \ 1) = x * (((x \ (1 / y)) * x) * y).
K(x \ y,T(x,y)) = K(x \ y,x).
K(x,T(y,y * x)) = K(y \ (y * x),y).
K(x \ (x * y),x) = K(y,T(x,x * y)).
K(x,y) = K(x,T(y,y * x)).
K(x,T(y,y * x)) = K(x,y).
K(x \ 1,T(y,x \ y)) = K(x \ 1,y).
K((x \ 1) \ 1,T(y,x * y)) = K((x \ 1) \ 1,y).
T(x \ T(x,y \ 1),z) = x \ T(x,T(y,z) \ 1).
x \ T(x,T(y,z) \ 1) = T(x \ T(x,y \ 1),z).
x * y != T(x * z,x \ 1) | y = ((x \ 1) \ z) * (x \ 1).
(x * y) * (y / (x * y)) = ((x \ 1) \ y) * (x \ 1).
((x \ 1) \ y) * (x \ 1) = (x * y) * (y / (x * y)).
x \ (y * (T(y,x) \ y)) = ((y * x) / y) \ y.
K((x \ 1) \ 1,y) = K(x,T(y,x * y)).
K(x,T(y,x * y)) = K(x,y).
K(x,T(x \ y,y)) = K(x,x \ y).
x \ T(x,R(y \ 1,y,z) \ 1) = T(x \ T(x,(z / (y * z)) \ 1),T(y,u)).
T(x \ T(x,(y / (z * y)) \ 1),T(z,u)) = x \ T(x,R(z \ 1,z,y) \ 1).
((x \ 1) * y) * (y / ((x \ 1) * y)) = (x \ y) * x.
((x \ 1) * y) * R(x,x \ 1,y) = (x \ y) * x.
((x \ y) * x) / y = ((((x \ 1) * y) * x) / ((x \ 1) * y)) * (x \ 1).
((((x \ 1) * y) * x) / ((x \ 1) * y)) * (x \ 1) = ((x \ y) * x) / y.
R(x \ T(x,y \ 1),z,u) = x \ T(x,R(y,z,u) \ 1).
(x * ((y \ x) * y)) / x != z * K(y \ x,y) | T(x,(y \ x) * y) = z.
(x \ T(x,y \ 1)) * (y * z) = y * ((x \ T(x,y \ 1)) * z).
((1 / (x * y)) * x) / (1 / (x * y)) = x * (((x \ (1 / y)) * x) * y).
((x \ y) * x) / y = ((x \ 1) * y) \ T((x \ 1) * y,x).
((x \ 1) * y) \ T((x \ 1) * y,x) = ((x \ y) * x) / y.
((x \ y) * x) / y = L(K(x \ y,x),y,x \ 1).
L(K(x \ y,x),y,x \ 1) = ((x \ y) * x) / y.
L(K(x,y),y * x,y \ 1) = ((y \ (y * x)) * y) / (y * x).
((x \ (x * y)) * x) / (x * y) = L(K(y,x),x * y,x \ 1).
(x * y) / (y * x) = L(K(x,y),y * x,y \ 1).
L(K(x,y),y * x,y \ 1) = (x * y) / (y * x).
(a((x * y) \ 1,x,y) / y) / (1 / (x * y)) = x * (((x \ (1 / y)) * x) * y).
T(x,(1 / x) * (y * x)) \ x = L(K(y,x),x * y,x \ 1).
L(K(x,y),y * x,y \ 1) = T(y,(1 / y) * (x * y)) \ y.
L(K(x,y),y * x,y \ 1) = T(y,(y \ 1) * (x * y)) \ y.
T(x,(x \ 1) * (y * x)) \ x = (y * x) / (x * y).
x * (((y * x) / (x * y)) \ 1) = T(x,(x \ 1) * (y * x)).
(x \ T(x,(x \ 1) * y)) * y = (((x \ 1) * y) \ y) * ((x \ 1) * y).
(((x \ 1) * y) \ y) * ((x \ 1) * y) = (x \ T(x,(x \ 1) * y)) * y.
x * ((y * x) * T((y * x) \ 1,x)) = (((x \ (1 / y)) * x) * y) * x.
x * (y * (x * T(x \ (y \ 1),x))) = (((x \ (1 / y)) * x) * y) * x.
x * (y * ((x \ (y \ 1)) * x)) = (((x \ (1 / y)) * x) * y) * x.
(((x \ (1 / y)) * x) * y) * x = x * (y * ((x \ (y \ 1)) * x)).
R(x \ T(x,(y \ 1) \ 1),y,z) = T(x \ T(x,(z / (y * z)) \ 1),T(y,u)).
T(x \ T(x,(y / (z * y)) \ 1),T(z,u)) = R(x \ T(x,(z \ 1) \ 1),z,y).
(a((x * y) \ 1,x,y) / y) / (1 / (x * y)) != x * z | ((x \ (1 / y)) * x) * y = z.
T(x \ T(x,(y / (z * y)) \ 1),T(z,u)) = R(x \ T(x,z),z,y).
(x * K(y \ (1 / (1 / x)),y)) * (x \ 1) = ((y \ x) * y) / ((1 / x) \ 1).
(x * K(y \ (1 / (1 / x)),y)) * (x \ 1) = ((y \ x) * y) / x.
x * K(y \ (x * (T(x,y) \ x)),y) = (x * (y * T(y \ x,y))) / x.
x * K(y \ (x * (T(x,y) \ x)),y) = (x * ((y \ x) * y)) / x.
x * K(((x * y) / x) \ x,y) = (x * ((y \ x) * y)) / x.
((x * y) / x) * (y \ ((T(x,y) \ x) * z)) = L(z,T(x,y) \ x,(x * y) / x).
((x * y) / x) \ L(z,T(x,y) \ x,(x * y) / x) = y \ ((T(x,y) \ x) * z).
T((x \ 1) * (x * ((y * (x \ z)) / y)),y) = L((x \ 1) * z,K(x,x \ 1),y).
T((x / y) * K(x,x \ 1),y) * K(x \ 1,x) = (x \ (y \ T(x,y \ 1))) * x.
T(((x \ 1) \ 1) / y,y) * K(x \ 1,x) = (x \ (y \ T(x,y \ 1))) * x.
(x \ ((y \ 1) \ 1)) * K(y \ 1,y) = (y \ (x \ T(y,x \ 1))) * y.
(x \ ((y \ 1) \ 1)) * K(y \ 1,y) = ((x \ y) / y) * y.
x * K(y \ 1,y) != (z / u) * u | x = z * K(y,y \ 1).
x \ ((y \ 1) \ 1) = (x \ y) * K(y,y \ 1).
(x \ y) * K(y,y \ 1) = x \ ((y \ 1) \ 1).
(x \ ((y \ 1) \ 1)) * K(y \ 1,y) = x \ y.
(x \ ((y \ 1) \ 1)) * z = K(y,y \ 1) * ((x \ y) * z).
K(x,x \ 1) * ((y \ x) * z) = (y \ ((x \ 1) \ 1)) * z.
(x \ 1) * ((y \ ((x \ 1) \ 1)) * z) = (1 / x) * ((y \ x) * z).
L((x \ ((y \ 1) \ 1)) * z,y \ 1,y) = y * ((1 / y) * ((x \ y) * z)).
R(x,K(y \ 1,y),(1 / y) * z) = K(y \ 1,y) * ((x * ((1 / y) * z)) / ((y \ 1) * z)).
K(x \ 1,x) * ((y * ((1 / x) * z)) / ((x \ 1) * z)) = R(y,K(x \ 1,x),(1 / x) * z).
(a((x * y) \ 1,x,y) / y) / (1 / (x * y)) = ((x * y) * T((x * y) \ 1,x)) * x.
(a((x * y) \ 1,x,y) / y) / (1 / (x * y)) = (((x \ (1 / y)) * x) * y) * x.
(a((x * y) \ 1,x,y) / y) / (1 / (x * y)) = x * (y * ((x \ (y \ 1)) * x)).
((x \ (1 / y)) * x) * y = y * ((x \ (y \ 1)) * x).
((x \ y) * x) * (y \ 1) = (y \ 1) * ((x \ ((y \ 1) \ 1)) * x).
(x \ 1) * ((y \ ((x \ 1) \ 1)) * y) = ((y \ x) * y) * (x \ 1).
((x \ y) * x) * (y \ 1) = (1 / y) * ((x \ y) * x).
(1 / (x \ 1)) / T(y,y \ T(x,x \ 1)) = (y \ ((x \ 1) \ 1)) * K(x \ 1,x).
x / T(y,y \ T(x,x \ 1)) = (y \ ((x \ 1) \ 1)) * K(x \ 1,x).
x / T(y,y \ T(x,x \ 1)) = y \ x.
(1 / (1 / x)) / T(y,y \ x) = y \ (1 / (1 / x)).
x \ (1 / (1 / y)) = K(y \ 1,y) * (x \ y).
K(x \ 1,x) * (y \ x) = y \ (1 / (1 / x)).
K(x,x \ 1) * ((y \ (1 / (1 / x))) * z) = (y \ x) * z.
(x \ y) * x = y * K(x \ (1 / (1 / y)),x).
x * K(y \ (1 / (1 / x)),y) = (y \ x) * y.
((x \ y) * x) * (y \ 1) = ((x \ y) * x) / y.
((x \ y) * x) / y = (1 / y) * ((x \ y) * x).
(1 / x) * ((y \ x) * y) = ((y \ x) * y) / x.
(x * ((y / (z * (u \ y))) / x)) * (z * (u \ y)) = ((x * ((u / z) / x)) * z) * (u \ y).
((x * ((x / y) / x)) * y) * (x \ z) = x * ((x \ T(x,y \ 1)) * (x \ z)).
T(x,y \ 1) * (x \ z) = x * ((x \ T(x,y \ 1)) * (x \ z)).
x * ((x \ T(x,y \ 1)) * (x \ z)) = T(x,y \ 1) * (x \ z).
x * ((x \ T(x,y)) * (x \ z)) = T(x,(y \ 1) \ 1) * (x \ z).
T(x,(y \ 1) \ 1) * (x \ z) = x * ((x \ T(x,y)) * (x \ z)).
T(x,y) * (x \ z) = x * ((x \ T(x,y)) * (x \ z)).
x * ((x \ T(x,y)) * (x \ z)) = T(x,y) * (x \ z).
x * ((x \ T(x,y)) * z) = T(x,y) * (x \ (x * z)).
T(x,y) * (x \ (x * z)) = x * ((x \ T(x,y)) * z).
T(x,y) * z = x * ((x \ T(x,y)) * z).
x * ((x \ T(x,y)) * z) = T(x,y) * z.
L(x,y \ T(y,z),y) = x.
x * y != T(x,z) * u | y = T(x,z) * (x \ u).
(x \ T(x,y)) * z = T(x,y) * (x \ z).
x * y != T(x,x \ z) * z | y = x * (z / x).
(x \ T(x,x \ y)) * y = x * (y / x).
x * y != T(x,z) * (x * u) | y = T(x,z) * u.
(x \ T(x,y)) * (x * z) = T(x,y) * z.
x * ((T(y,x) \ y) * z) = T(x,T(y,x)) * z.
(x \ T(x,y)) \ z = x * (T(x,y) \ z).
L(x,T(y,T(z,y)) \ y,z) = x.
L(x,T(y,z) \ y,(y * z) / y) = x.
((x * y) / x) \ z = y \ ((T(x,y) \ x) * z).
x \ ((T(y,x) \ y) * z) = ((y * x) / y) \ z.
T(x,y) * (x \ (z * K(x \ 1,x))) = ((x \ 1) * T(x,y)) * z.
T(x,y \ 1) * (x \ (y * z)) = y * ((x \ T(x,y \ 1)) * z).
(T(x,y) * z) / (x * z) = x \ T(x,y).
(x \ T(x,y)) \ (T(x,y) * z) = x * z.
R(x \ T(x,y),x,z) = x \ T(x,y).
(x / y) \ T(x / y,z) = (y * T(y \ x,z)) / x.
(x * T(x \ y,z)) / y = (y / x) \ T(y / x,z).
x * y != T(x,T(z,x)) * (z * x) | y = x * z.
(T(x,y) \ x) * (x * y) = y * x.
(x * y) / (y * x) = T(y,x) \ y.
T(T(x,y) \ x,x * y) = (x * y) \ (y * x).
x / (y * (x / y)) = T(y,x / y) \ y.
T(x,y / x) \ x = y / (x * (y / x)).
(x * (y / x)) / y = T(y / x,x) \ (y / x).
T(x / y,y) \ (x / y) = (y * (x / y)) / x.
x * (((y * x) / (x * y)) \ 1) = T(x,y).
T(x,y) = x * (((y * x) / (x * y)) \ 1).
T(x,y) = T(x,(x \ 1) * (y * x)).
T(x,(x \ 1) * (y * x)) = T(x,y).
T(x,T((x \ 1) * y,x)) = T(x,x \ y).
x * (((y * x) / y) \ z) = (T(y,x) \ y) * z.
K(x,y) = T(T(y,x) \ y,y * x).
K(x \ y,x) = T(T(x,x \ y) \ x,y).
T(T(x,x \ y) \ x,y) = K(x \ y,x).
T(x \ (y / (y / x)),y) = K(x \ y,x).
(x \ y) \ (y / x) = (x * (y / x)) / y.
(x * (y / x)) / y = (x \ y) \ (y / x).
(x * (y / x)) / y = x \ ((x \ y) \ y).
x \ ((x \ (y \ x)) \ (y \ x)) = x \ T(x,y \ 1).
R(x \ T(x,y),y,((x * y) / x) \ z) \ z = (T(x,y) \ x) * z.
((x \ y) / y) \ T((x \ y) / y,z) = x * T(x \ 1,z).
(x \ T(x,y \ 1)) * x = T(x,x \ (y \ x)).
T(x,x \ (y \ x)) = T(x,y \ 1).
T(x,y \ 1) \ x = x \ ((y \ x) / ((y \ x) / x)).
x \ ((y \ x) / ((y \ x) / x)) = T(x,y \ 1) \ x.
(x * T(x \ 1,y)) \ y = T(y,T((x \ z) / z,y)).
T(x,T((y \ z) / z,x)) = (y * T(y \ 1,x)) \ x.
x * T(x \ 1,y) = y \ ((x \ y) / ((x \ y) / y)).
x \ ((y \ x) / ((y \ x) / x)) = y * T(y \ 1,x).
T(x,T((y \ z) / z,x)) = T(x,T(y \ 1,x)).
x * T(x \ 1,y) = T(y,x \ 1) \ y.
T(x,y \ 1) \ x = y * T(y \ 1,x).
L(x,T(y \ 1,z),y) = (T(z,y \ 1) \ z) \ (y * (T(y \ 1,z) * x)).
(T(x,y \ 1) \ x) \ (y * (T(y \ 1,x) * z)) = L(z,T(y \ 1,x),y).
T(x,(y \ 1) \ 1) \ x = y \ T(y,x).
T(x,y) \ x = y \ T(y,x).
T(x,y) * (y \ T(y,x)) = x.
x * (T(x,y) \ x) = (y * x) / y.
(x * y) / x = y * (T(y,x) \ y).
T(x,y / x) \ x = x \ (y / (y / x)).
(T(x,y) \ x) * z = T(y,x) * (y \ z).
T(x,y) * (x \ z) = (T(y,x) \ y) * z.
T(x,T(y,x)) = T(x,y).
T(x \ y,x) = T(x,x \ y) \ y.
T(x,x \ y) \ y = T(x \ y,x).
T(x * (T(x,y) \ x),y) = x.
(x * y) * T(x,y) = R(x,y,x) * (x * y).
R(x,y,x) * (x * y) = (x * y) * T(x,y).
T(x,(x \ 1) * y) = T(x,x \ y).
T(x,(y \ z) / z) = T(x,T(y \ 1,x)).
T(x,T(y \ 1,x)) = T(x,(y \ z) / z).
x = L(R(x,y,x),y,x).
L(R(x,y,x),y,x) = x.
T(x \ T(x * y,y),T(x * y,y)) = y.
((x * y) / x) \ x = y \ ((y * x) / y).
(x \ T(x,x \ y)) \ y = x * T(x \ y,x).
(((x \ 1) * y) \ y) * ((x \ 1) * y) = (x \ T(x,x \ y)) * y.
x \ (y / (y / x)) = y / (x * (y / x)).
x / (y * (x / y)) = y \ (x / (x / y)).
T(x,(y \ z) / z) = T(x,y \ 1).
T(x,y / z) = T(x,(z / y) \ 1).
T(x,(y / z) \ 1) = T(x,z / y).
T(x \ T(x,(y * z) / z),T(y,u)) = R(x \ T(x,y),y,z).
K(x,y) = K(x,x \ T(x * y,y)).
K(x,x \ T(x * y,y)) = K(x,y).
(x * R(y,x,y)) \ T(x * y,y) = K(x,y).
K(x,y) = (x * R(y,x,y)) \ T(x * y,y).
x * (y * z) != (u * z) * T(y,z) | x = R(u,z,T(y,z)).
R(x,y,x) = R(x,y,T(x,y)).
R(x,y,T(x,y)) = R(x,y,x).
x * R(y,x,y) = T(y * x,y).
K(x,y) = T(y * x,y) \ T(x * y,y).
K(x,y) = K(y \ T(y * x,y),y).
K(x \ T(x * y,x),x) = K(y,x).
K(x \ T(y,x),x) = K(x \ y,x).
K(x \ y,x) = K(x \ ((x * y) / x),x).
K(x \ ((x * y) / x),x) = K(x \ y,x).
K(((x * y) / x) \ x,y) = K(y \ x,y).
x * K(y \ x,y) = (x * ((y \ x) * y)) / x.
(x * ((y \ x) * y)) / x = x * K(y \ x,y).
(x \ T(x,x \ y)) \ y = (x \ y) * x.
(x \ ((x \ y) \ y)) \ y = (x \ y) * x.
x / ((y \ x) * y) = y \ ((y \ x) \ x).
(x * (y / x)) / y = y / ((x \ y) * x).
T(x,(y \ x) * y) = x.
T((x \ y) * x,y) = (x \ y) * x.
T(x * (y / x),y) = x * (y / x).
T(x * (y / x),y) / y = y / ((x \ y) * x).
T((x \ y) * x,y) / y = y / ((((x \ 1) * y) \ y) * ((x \ 1) * y)).
x / ((((y \ 1) * x) \ x) * ((y \ 1) * x)) = T((y \ x) * y,x) / x.
T(x \ T(x,y),T(y,z)) = R(x \ T(x,y),y,u).
R(x \ T(x,y),y,z) = x \ T(x,y).
T(x,y) * (T(x,x \ 1) \ z) = ((x \ 1) * T(x,y)) * z.
(((x \ 1) \ 1) * T(x \ 1,y)) * z = T(1 / x,y) * ((x \ 1) \ z).
T(x,y \ 1) * (x \ (y * z)) = y * (T(x,y \ 1) * (x \ z)).
(((x \ 1) * y) \ y) * ((x \ 1) * y) = x * (y / x).
(x \ T(x,y)) \ z = (T(x,y) \ x) * z.
(T(x,y) \ x) * (T(x,y) * z) = x * z.
T(x,y) * (x \ z) = (y \ T(y,x)) \ z.
(x \ T(x,y)) \ z = T(y,x) * (y \ z).
T(x,y) * (x \ (T(y,x) * z)) = y * z.
(T(x,y) \ x) \ z = T(x,y) * (x \ z).
x / (y * (x / y)) = T((y \ x) * y,x) / x.
T((x \ y) * x,y) / y = y / (x * (y / x)).
((x \ y) * x) / y = y / (x * (y / x)).
((x \ y) * x) / y = x \ (y / (y / x)).
(1 / x) * ((y \ x) * y) = y \ (x / (x / y)).
L((x \ ((y \ 1) \ 1)) * x,y \ 1,y) = y * (x \ (y / (y / x))).
(x * T(1 / x,y)) * z = T(1 / x,y) * ((x \ 1) \ z).
T(1 / x,y) * ((x \ 1) \ z) = (x * T(1 / x,y)) * z.
(T(1 / x,y) * z) / ((x * T(1 / x,y)) * z) = x \ 1.
(x \ 1) * y = T(1 / x,z) * ((x * T(1 / x,z)) \ y).
T(1 / x,y) * ((x * T(1 / x,y)) \ z) = (x \ 1) * z.
L(x,T(y \ 1,z),y) = T(z,y \ 1) * (z \ (y * (T(y \ 1,z) * x))).
T(x,y \ 1) * (x \ (y * (T(y \ 1,x) * z))) = L(z,T(y \ 1,x),y).
L(x,T(y \ 1,z),y) = y * (T(z,y \ 1) * (z \ (T(y \ 1,z) * x))).
x * (T(y,x \ 1) * (y \ (T(x \ 1,y) * z))) = L(z,T(x \ 1,y),x).
x * ((x \ 1) * y) = L(y,T(x \ 1,z),x).
L(x,T(y \ 1,z),y) = y * ((y \ 1) * x).
L(x,T(y \ 1,z),y) = L(x,y \ 1,y).
L(T(1 / x,y) \ z,x \ 1,x) = (x * T(1 / x,y)) \ (x * z).
T((x \ 1) * (x * ((y * z) / y)),y) = T(1 / x,y) * ((x * T(1 / x,y)) \ (x * z)).
T((x \ 1) * (x * ((y * z) / y)),y) = (x \ 1) * (x * z).
(x \ 1) * (x * (x \ y)) = L((x \ 1) * y,K(x,x \ 1),z).
L((x \ 1) * y,K(x,x \ 1),z) = (x \ 1) * (x * (x \ y)).
L((x \ 1) * y,K(x,x \ 1),z) = (x \ 1) * y.
(x * ((1 / y) * z)) / ((y \ 1) * z) = x * K(y,y \ 1).
K(x \ 1,x) * (y * K(x,x \ 1)) = R(y,K(x \ 1,x),(1 / x) * z).
R(x,K(y \ 1,y),(1 / y) * z) = K(y \ 1,y) * (x * K(y,y \ 1)).
R(x,K(y \ 1,y),(1 / y) * z) = x.
R(x,K(y \ 1,y),z) = x.
x * (K(y \ 1,y) * z) = (x * K(y \ 1,y)) * z.
(x * K(y \ 1,y)) * z = x * (K(y \ 1,y) * z).
x = R(x,y,K(z \ 1,z)).
R(x,y,K(z \ 1,z)) = x.
x \ (K(y \ 1,y) * z) = (x \ z) * K(y \ 1,y).
x * (K(y \ 1,y) * z) = K(y \ 1,y) * (x * z).
K(x \ 1,x) * (y * z) = y * (K(x \ 1,x) * z).
L(K(x \ 1,x) * y,z,u) = (u * z) \ (u * (K(x \ 1,x) * (z * y))).
(x * y) \ (x * (K(z \ 1,z) * (y * u))) = L(K(z \ 1,z) * u,y,x).
x \ (y * (K(z \ 1,z) * u)) = (x \ (y * u)) * K(z \ 1,z).
(x * y) \ (x * (K(z \ 1,z) * (y * u))) = L(u,y,x) * K(z \ 1,z).
L(x,y,z) * K(u \ 1,u) = L(K(u \ 1,u) * x,y,z).
L(K(x \ 1,x) * y,z,u) = L(y,z,u) * K(x \ 1,x).
K(x \ 1,x) * L(y,z,u) = L(K(x \ 1,x) * y,z,u).
L(K(x \ 1,x) * y,z,u) = K(x \ 1,x) * L(y,z,u).
L(x,y,z) = K(u \ 1,u) * L(x * K(u,u \ 1),y,z).
K(x \ 1,x) * L(y * K(x,x \ 1),z,u) = L(y,z,u).
L(x,y,z) = (u \ L(u * (x / u),y,z)) * u.
(x \ L(x * (y / x),z,u)) * x = L(y,z,u).
(x \ L(x * y,z,u)) * x = L(y * x,z,u).
(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) \ u)) * x,y \ z,y) = (x \ (z \ (y * u))) * x.
(x \ (1 \ (y * 1))) * x = y * (x \ (y / (y / x))).
(x \ (1 \ y)) * x = y * (x \ (y / (y / x))).
x * (y \ (x / (x / y))) = (y \ (1 \ x)) * y.
x * (y \ (x / (x / y))) = (y \ x) * y.
x * y != (z \ x) * z | y = K(z \ x,z).
x \ (y / (y / x)) = K(x \ y,x).
T(K(x \ y,x),y) = K(x \ y,x).
T(x,K(y \ x,y)) = x.
T(x * y,K(y,x)) = x * y.
(x * y) / (y * x) = K(x,y).
K(x,y) = (x * y) / (y * x).
K(x,y) = T(y,x) \ y.
x / T(x,y) = K(y,x).
K(x,y) = x \ T(x,y).
K(c1,c2) != c1 \ T(c1,c2).
c1 \ T(c1,c2) != K(c1,c2).
K(T(x,y),T(z,y)) = K(x,z).
K(T(c5,c6),T(c7,c6)) != K(c5,c7).
L(x,y / x,z) = (z * (y / x)) \ (z * y).
T(R(x,y,z),y * z) = (y * z) \ ((x * y) * z).
(x * y) \ ((z * x) * y) = T(R(z,x,y),x * y).
x * K(y,x / y) = y * (x / y).
x * y != z * y | x = u * (u \ z).
(x / y) \ x = z * (z \ y).
((x / y) \ x) * z != u | y \ u = z.
L(x \ ((y * x) / y),x,y) = K(y,(y * x) / y).
x \ (L(y,z,x) * (x * z)) = z * T(y,x * z).
R(T(x,y * z),y,z) = (y * z) \ ((x * y) * z).
(x * y) \ ((z * x) * y) = R(T(z,x * y),x,y).
(x * y) * T(K(y,x),z) = x * (y * T(y \ T(y,x),z)).
x * (y * T(y \ T(y,x),z)) = (x * y) * T(K(y,x),z).
(1 / x) \ T((1 / x) * y,z) = x * T(x \ y,z).
R(T(x / y,z),y,y \ z) = z \ (x * (y \ z)).
L((x \ (T(x,y) * y)) / y,y,x) = (y * K(T(x,y),y)) / y.
(x \ (y * (z \ x))) * x = (T(y / z,x) * z) * (z \ x).
(1 / x) \ T(y,z) = x * T(x \ ((1 / x) \ y),z).
x * T(x \ ((1 / x) \ y),z) = (1 / x) \ T(y,z).
((1 / x) \ y) \ ((1 / x) \ T(y,x)) = K(x \ ((1 / x) \ y),x).
(T(x,1 / y) / y) \ (x / y) = K(1 / y,(1 / y) \ (x / y)).
K(1 / x,(1 / x) \ (y / x)) = (T(y,1 / x) / x) \ (y / x).
T(x / y,z) * x = (x / y) * (T(x / y,z) * y).
(x / y) * (T(x / y,z) * y) = T(x / y,z) * x.
(x / y) * (y * T(y \ x,z)) = T(x / y,z) * x.
(x \ (y * (z \ x))) * x = (z * T(z \ y,x)) * (z \ x).
L((T(x,y) * (x \ y)) / y,y,x) = (y * K(T(x,y),y)) / y.
x * T(y * T(y \ 1,x),x) = y * ((x \ (y \ x)) * x).
((x / y) * T(y,z)) * y = x * T(y,z).
x / (y / z) = ((x / (z \ y)) / (y / z)) * (z \ y).
((x / (y \ z)) / (z / y)) * (y \ z) = x / (z / y).
(x * y) * T((x * y) \ (y * x),z) = (y * x) * K(z \ (z / K(x,y)),z).
x * K(y \ (y / (x \ (1 / z))),y) = T(x * z,y) / z.
T(x * y,z) / y = x * K(z \ (z / (x \ (1 / y))),z).
K(x \ (x / (y \ (z \ y))),x) = y \ (T(z,x) * (z \ y)).
T(x,y) / z = (x / z) * K(y \ (y / ((x / z) \ (1 / z))),y).
(x / y) * K(z \ (z / ((x / y) \ (1 / y))),z) = T(x,z) / y.
(x * y) / ((z * y) / z) = (x / ((z * y) / z)) * y.
((x * y) * T((x * y) \ x,z)) * y = (x * y) * (y * T(y \ 1,z)).
(x * y) * (z * T(z \ L(y \ z,y,x),u)) = ((x * y) * T((x * y) \ x,u)) * z.
((x * y) * T((x * y) \ x,z)) * u = (x * y) * (u * T(u \ L(y \ u,y,x),z)).
(x * (y * T(y \ (x \ (z * u)),w))) / u = ((x * y) / u) * T(((x * y) / u) \ z,w).
(x * (y * z)) * ((u * (((x * y) * L(z,y,x)) \ (x * y))) / u) = (x * y) * (L(z,y,x) * ((u * (L(z,y,x) \ 1)) / u)).
(x * (y * T(y \ 1,z))) * y = (x * y) * (y * T(y \ 1,z)).
(x * y) * T(K(y,x),z) = (y * x) * K(z \ (z / K(x,y)),z).
(x * y) * K(z \ (z / K(y,x)),z) = (y * x) * T(K(x,y),z).
(x * y) * (K(y,x) * T(K(y,x) \ 1,z)) = (y * x) * T(K(x,y),z).
(x * y) \ ((y * x) * T(K(x,y),z)) = K(y,x) * T(K(y,x) \ 1,z).
T(x / y,y / x) = ((x / y) \ 1) \ 1.
(x * (y * T(y \ 1,z))) * u = (x * y) * (u * T(u \ L(y \ u,y,x),z)).
(x * y) * (z * T(z \ L(y \ z,y,x),u)) = (x * (y * T(y \ 1,u))) * z.
(x * y) * ((z \ L(y \ z,y,x)) * z) = (x * (y * T(y \ 1,z))) * z.
(x * (y * T(y \ T(z,x),u))) / x = ((x * y) / x) * T(((x * y) / x) \ z,u).
((x * y) / x) * T(((x * y) / x) \ z,u) = (x * (y * T(y \ T(z,x),u))) / x.
T(x / y,y / x) = T(x / y,x \ y).
T(T(x / y,x \ y),y) = T(y \ x,y / x).
T(x \ y,x / y) = T(x \ y,y \ x).
T(x \ (y \ x),y) = T(x \ (y \ x),(y \ x) \ x).
T(x \ (y \ x),(y \ x) \ x) = T(x \ (y \ x),y).
T(x \ (y \ x),y) = ((x \ (y \ x)) \ 1) \ 1.
L(x * T(x \ 1,y),z,u) = L(x,z,u) * T(L(x,z,u) \ 1,y).
L(x,y,z) * T(L(x,y,z) \ 1,u) = L(x * T(x \ 1,u),y,z).
(x / (y \ 1)) * K(y \ 1,y) = x / (1 / y).
x * K(y,y \ 1) != z / (1 / (1 / y)) | x = z / y.
(x / (1 / (1 / y))) * K(y \ 1,y) = x / y.
x * y != (z / u) \ z | y = x \ u.
(((x / y) \ 1) \ 1) \ x = K(x / y,(x / y) \ 1) \ y.
K(x / y,(x / y) \ 1) \ y = (((x / y) \ 1) \ 1) \ x.
((x \ 1) \ 1) \ ((x \ 1) \ y) = x \ ((1 / x) \ y).
K(x \ 1,x) \ (x * y) = ((x \ 1) \ 1) * y.
K(K(x \ 1,x) * y,(x \ 1) \ 1) = (x * y) \ ((K(x \ 1,x) * y) * ((x \ 1) \ 1)).
(x * y) \ ((K(x \ 1,x) * y) * ((x \ 1) \ 1)) = K(K(x \ 1,x) * y,(x \ 1) \ 1).
((x \ 1) \ 1) \ y = y * T(y \ (x \ y),x).
x * T(x \ (y \ x),y) = ((y \ 1) \ 1) \ x.
x * (((x \ (y \ x)) \ 1) \ 1) = ((y \ 1) \ 1) \ x.
(K(x \ 1,x) * y) \ ((z * y) * K(x \ 1,x)) = L(T(z,y),y,K(x \ 1,x)).
(K(x \ 1,x) * y) \ ((z * y) * K(x \ 1,x)) = R(T(z,y * K(x \ 1,x)),y,K(x \ 1,x)).
x * (y * K(x \ 1,x)) = (1 / (1 / x)) * y.
x * (y / x) = (1 / (1 / x)) * (y / (1 / (1 / x))).
(1 / (1 / x)) * (y / (1 / (1 / x))) = x * (y / x).
(((x \ 1) \ 1) \ y) / y = (((x \ y) / y) \ 1) \ 1.
(((x \ 1) \ 1) \ y) * ((x \ 1) \ 1) != y * z | K(x \ y,x) = z.
T(x,1 / y) = T(x,y \ 1).
((x \ 1) \ y) / y = ((((1 / x) \ y) / y) \ 1) \ 1.
((((1 / x) \ y) / y) \ 1) \ 1 = ((x \ 1) \ y) / y.
K(x \ 1,x) \ (x * y) = (((y / (x * y)) \ 1) \ 1) \ y.
x \ (T(1 / x,y) \ 1) = T(1 / x,y) \ (1 / x).
T(1 / x,y) \ (1 / x) = x \ (T(1 / x,y) \ 1).
(x * T(x \ 1,y)) \ 1 = T(1 / x,y) \ (1 / x).
(x * T(x \ 1,y)) \ 1 = x \ (T(1 / x,y) \ 1).
K(x \ 1,x) \ (x * y) = R(x \ 1,x,y) \ y.
R(x \ 1,x,y) \ y = K(x \ 1,x) \ (x * y).
R(x \ 1,x,y) \ y = ((x \ 1) \ 1) * y.
R(x,1 / x,y) \ y = (((1 / x) \ 1) \ 1) * y.
R(x,1 / x,y) \ y = (x \ 1) * y.
x / ((y \ 1) * x) = R(y,1 / y,x).
R(x,1 / x,y) = y / ((x \ 1) * y).
R(x,x \ 1,y) = R(x,1 / x,y).
R(x,1 / x,y) = R(x,x \ 1,y).
L(R(x,x \ 1,y),x \ 1,x) = R(1 / (1 / x),1 / x,y).
x * K(y,x) = K(y,x) * x.
K(x,y) * y = y * K(x,y).
T(x,y * T(y \ 1,x)) = x.
R(x,K(y,z),z) = ((x * K(y,z)) * z) / (z * K(y,z)).
((x * K(y,z)) * z) / (z * K(y,z)) = R(x,K(y,z),z).
(x * K(y,z)) * z != u * (z * K(y,z)) | R(x,K(y,z),z) = u.
L((T(x,y) * (x \ y)) / y,y,x) = K(T(x,y),y).
T(x * T(x \ 1,y),y) = x * T(x \ 1,y).
x * (y * T(y \ 1,x)) = y * ((x \ (y \ x)) * x).
x * ((y \ (x \ y)) * y) = y * (x * T(x \ 1,y)).
R(x,y \ T(y,z),y) * T(y,z) = (x * (y \ T(y,z))) * y.
K(x \ (x / (y \ 1)),x) * y = T(y,x).
T(x,y) = K(y \ (y / (x \ 1)),y) * x.
K(x \ (x / (y \ 1)),x) \ (L(z,y,K(x \ (x / (y \ 1)),x)) * T(y,x)) = y * T(z,K(x \ (x / (y \ 1)),x) * y).
K(x \ 1,(1 / x) \ (y / x)) = (T(y,1 / x) / x) \ (y / x).
T(x \ 1,y) \ (x \ 1) = x \ (T(1 / x,y) \ 1).
R(1 / (1 / x),1 / x,y) = R(1 / (1 / x),x \ 1,y).
R(1 / (1 / x),x \ 1,(1 / x) \ y) = ((1 / x) \ y) / y.
L(x * y,x \ T(x,z),x) != x * u | L(y,x,x \ T(x,z)) = u.
((1 / x) \ y) \ (y * R(1 / (1 / x),x \ 1,(1 / x) \ y)) = K(y,((1 / x) \ y) / y).
K(x \ 1,(1 / x) \ (y / x)) = (T(y,x \ 1) / x) \ (y / x).
K(x \ y,x) = K(((x \ 1) \ 1) \ y,(x \ 1) \ 1).
K(((x \ 1) \ 1) \ y,(x \ 1) \ 1) = K(x \ y,x).
(x * y) \ (y * x) = K(K(x \ 1,x) * y,(x \ 1) \ 1).
K(K(x \ 1,x) * y,(x \ 1) \ 1) = (x * y) \ (y * x).
K(x,y) = K(K(y \ 1,y) * x,(y \ 1) \ 1).
K(K(x \ 1,x) * y,(x \ 1) \ 1) = K(y,x).
R(T(x,y * K(z \ 1,z)),y,K(z \ 1,z)) = L(T(x,y),y,K(z \ 1,z)).
K(x,y) \ y != y * z | K(x,y) \ 1 = z.
K(x,((y \ 1) \ z) / z) = K(x,((1 / y) \ z) / z).
K(x,((1 / y) \ z) / z) = K(x,((y \ 1) \ z) / z).
K(((x \ 1) \ 1) \ y,x) = K(x \ y,x).
K(K(x \ 1,x) * y,x) = K(y,x).
K((x \ 1) * y,x) = K((1 / x) * y,x).
K((1 / x) * y,x) = K((x \ 1) * y,x).
K(x \ ((1 / x) \ y),x) = K(x \ ((x \ 1) \ y),x).
((1 / x) \ y) \ (y * R(1 / (1 / x),x \ 1,(1 / x) \ y)) = K(y,((x \ 1) \ y) / y).
((1 / x) \ y) \ ((1 / x) \ T(y,x)) = K(x \ ((x \ 1) \ y),x).
(x * (y * z)) * ((u * ((x * (y * z)) \ (x * y))) / u) = (x * y) * (L(z,y,x) * ((u * (L(z,y,x) \ 1)) / u)).
(x * y) * (L(z,y,x) * ((u * (L(z,y,x) \ 1)) / u)) = x * ((y * z) * ((u * ((y * z) \ y)) / u)).
(x * y) * (L(z,y,x) * ((u * (L(z,y,x) \ 1)) / u)) = x * (y * (z * ((u * (z \ 1)) / u))).
L(x * ((y * (x \ 1)) / y),z,u) = L(x,z,u) * ((y * (L(x,z,u) \ 1)) / y).
L(x,y,z) * ((u * (L(x,y,z) \ 1)) / u) = L(x * ((u * (x \ 1)) / u),y,z).
K(x \ (x / (y \ 1)),x) \ (L(z,y,K(x \ (x / (y \ 1)),x)) * T(y,x)) = y * T(z,T(y,x)).
R(T(x,y * K(z \ 1,z)),y,K(z \ 1,z)) = T(x,y).
R(T(x,y / (1 / z)),y / (z \ 1),K(z \ 1,z)) = T(x,y / (z \ 1)).
R(x,y \ T(y,x),y) = (y * x) / ((y \ T(y,x)) * y).
(x * y) / ((x \ T(x,y)) * x) = R(y,x \ T(x,y),x).
L(x \ T(x,y),y,x) = K(x,(x * y) / x).
(x \ (y * (T(z,x) \ z))) * x = (((z * x) / z) * T(((z * x) / z) \ y,x)) * (((z * x) / z) \ x).
(((x * y) / x) * T(((x * y) / x) \ z,y)) * (((x * y) / x) \ y) = (y \ (z * (T(x,y) \ x))) * y.
K(x \ (x / (y \ 1)),x) = T(x,T(y,x)) \ x.
L(((x * y) / x) / y,y,x) = K(T(x,y),y).
x * K(x,y / x) = T(x,(y \ x) \ 1).
T(x,(y \ x) \ 1) = x * K(x,y / x).
x * K(x,(y \ x) / x) = T(x,T(y,y \ x) \ 1).
T(x,T(y,y \ x) \ 1) = x * K(x,(y \ x) / x).
x \ T(y,x \ 1) = y * R(1 / x,x,x \ y).
x * R(1 / y,y,y \ x) = y \ T(x,y \ 1).
L(x \ T(x,y),y,x) = K(T(x,y),y).
K(T(x,y),y) = K(x,(x * y) / x).
K(T(x,x \ y),x \ y) = K(x,y / x).
x \ T(x,L(y,z,u) \ 1) = L(y * ((x * (y \ 1)) / x),z,u).
L(x * ((y * (x \ 1)) / y),z,u) = y \ T(y,L(x,z,u) \ 1).
(T(x,T(y,x)) \ x) \ (L(z,y,K(x \ (x / (y \ 1)),x)) * T(y,x)) = y * T(z,T(y,x)).
x * R(1 / (1 / y),1 / y,(1 / y) \ x) = (1 / y) \ T(x,y).
T(x,T(y,y \ x) \ 1) != x * z | K(x,(y \ x) / x) = z.
(x * y) / T(x,y) = R(y,x \ T(x,y),x).
R(x,y \ T(y,x),y) = (y * x) / T(y,x).
R(x,y \ T(y,x),y) = x.
R(T(x,y),z \ T(z,x),z) = T(x,y).
T(x,y) * T(z,x) = (T(x,y) * (z \ T(z,x))) * z.
(T(x,y) * (z \ T(z,x))) * z = T(x,y) * T(z,x).
L(x \ T(x,y \ 1),z,u) = x \ T(x,L(y,z,u) \ 1).
x * R(1 / (1 / y),y \ 1,(1 / y) \ x) = (1 / y) \ T(x,y).
((1 / x) \ y) \ ((1 / x) \ T(y,x)) = K(y,((x \ 1) \ y) / y).
K(x,((y \ 1) \ x) / x) = ((1 / y) \ x) \ ((1 / y) \ T(x,y)).
K(x,((y \ 1) \ x) / x) = K(y \ ((y \ 1) \ x),y).
K(x \ ((x \ 1) \ y),x) = K(y,((x \ 1) \ y) / y).
(T(x,T(y,x)) \ x) \ (L(z,y,T(x,T(y,x)) \ x) * T(y,x)) = y * T(z,T(y,x)).
((x * (y * T(y \ T(z,x),y))) / x) * (((x * y) / x) \ y) = (y \ (z * (T(x,y) \ x))) * y.
((x * ((y \ T(z,x)) * y)) / x) * (((x * y) / x) \ y) = (y \ (z * (T(x,y) \ x))) * y.
((x * ((y \ T(z,x)) * y)) / x) * (T(x,y) \ x) = (y \ (z * (T(x,y) \ x))) * y.
L(x,y,y \ T(y,z)) = x.
L(x,y,T(z,T(y,z)) \ z) = x.
(T(x,T(y,x)) \ x) \ (z * T(y,x)) = y * T(z,T(y,x)).
K(x \ (x / y),x) = T(x,y \ 1) \ x.
T(T(x,y \ 1) \ x,z) = K(x \ (x / T(y,z)),x).
x * ((y \ (x \ y)) * y) = y * (T(y,x \ 1) \ y).
x * (T(x,y \ 1) \ x) = y * ((x \ (y \ x)) * x).
x * ((T(y,x) \ y) * z) = T(x,y) * z.
K(x,y) = T(x \ T(x,y),y * x).
x * y = T(x,y) * T(y,x).
T(x,y) * T(y,x) = x * y.
T(T(x,y),z) = T(T(x,z),T(y,x)).
T(T(x,y),T(z,x)) = T(T(x,z),y).
T(T(x,y),T(y,x)) = T(y,x) \ (x * y).
T(x,y) \ (y * x) = T(T(y,x),T(x,y)).
T(x / (x / y),y \ x) = y.
((x \ y) * x) / (x \ y) = y / (y / x).
x \ T(x,T(y,(y \ 1) * x) \ 1) = K(x,y \ 1).
K(x \ (x / y),x) \ x = T(x,y \ 1).
(x / y) * z != T(x / y,u) * x | z = y * T(y \ x,u).
(T(x,y / z) \ x) * y = z * T(z \ y,x).
T(x,y) \ (y * x) = T(T(y,x),x).
(x * y) / T(T(x,y),y) = T(y,x).
T(x / (x / y),x) = L(y,y \ x,y).
K(x \ y,x) \ x = T(x,(y \ x) \ 1).
T(x,(y \ x) \ 1) = K(x \ y,x) \ x.
K(x \ y,x) \ x = x * K(x,y / x).
K(x \ y,x) \ 1 = K(x,y / x).
K(x,y) \ 1 = K(y,(y * x) / y).
K(x,(x * y) / x) = K(y,x) \ 1.
K(x,y) = K(T(y,x),x) \ 1.
K(T(x,y),y) \ 1 = K(y,x).
K(T(x,y),y) * K(y,x) = 1.
(T(x,y / z) \ x) * y = y * K(x \ (x / (y \ z)),x).
x * K(y \ (y / (x \ z)),y) = (T(y,x / z) \ y) * x.
x \ T(x,T(y,y \ x) \ 1) = K(x,y \ 1).
x * K(x,y \ 1) = T(x,T(y,y \ x) \ 1).
T(x,T(y,y \ x) \ 1) = x * K(x,y \ 1).
K(x,(y \ x) / x) = K(x,y \ 1).
K(x \ ((x \ 1) \ y),x) = K(y,(x \ 1) \ 1).
K(x \ ((x \ 1) \ y),x) = K(y,x).
K(x \ y,x) = K((x \ 1) * y,x).
K((x \ 1) * y,x) = K(x \ y,x).
K((1 / x) * y,x) = K(x \ y,x).
K(x * y,x \ 1) = K((x \ 1) \ y,x \ 1).
K((x \ 1) \ y,x \ 1) = K(x * y,x \ 1).
(T(x,(y / z) / (1 / z)) \ x) * (y / z) = T(y,x) / z.
(T(x,y) \ x) * z = x * (T(x,y) \ z).
T(T(x,y) \ x,z) = z \ (x * (T(x,y) \ z)).
x \ (y * (T(y,z) \ x)) = T(T(y,z) \ y,x).
T(x,y) * (x \ z) = y * (T(y,x) \ z).
x * (T(x,y / z) \ y) = z * T(z \ y,x).
x * T(x \ y,z) = z * (T(z,y / x) \ y).
x * (T(x,(y / z) / (1 / z)) \ (y / z)) = T(y,x) / z.
K(x \ (x / (y \ (z \ y))),x) = y \ (x * (T(x,z) \ y)).
x * (T(x,y / (z \ 1)) \ y) = z \ T(z * y,x).
x \ T(x * y,z) = z * (T(z,y / (x \ 1)) \ y).
K(x \ (x / (y \ (z \ y))),x) = T(T(x,z) \ x,y).
T(T(x,y) \ x,z) = T(x,(z \ (y \ z)) \ 1) \ x.
T(x,(y \ (z \ y)) \ 1) \ x = T(T(x,z) \ x,y).
T(x,y / (1 / z)) = T(x,y / (z \ 1)).
x * (T(x,(y / z) / (z \ 1)) \ (y / z)) = T(y,x) / z.
x \ T(x * (y / x),z) = T(y,z) / x.
x \ T(x * y,z) = T(y * x,z) / x.
T(x * y,z) / y = y \ T(y * x,z).
T((x \ y) * x,z) / x = x \ T(y,z).
(x \ T(y,z)) * x = T((x \ y) * x,z).
T((x \ y) * x,z) = (x \ T(y,z)) * x.
((x * T((y \ z) * y,x)) / x) * (T(x,y) \ x) = (y \ (z * (T(x,y) \ x))) * y.
T(x,y) * K(y,x) = x.
x * (T(x,y) \ 1) = K(y,x).
K(x,y) = y * (T(y,x) \ 1).
(1 / T(x,y)) * x = K(y,x).
K(x,y) = (1 / T(y,x)) * y.
K(x,y \ 1) = y \ (T(1 / y,x) \ 1).
x \ (T(1 / x,y) \ 1) = K(y,x \ 1).
K(T(x,y),y) = x \ T(x,y).
K(x \ 1,y) = x * T(x \ 1,y).
x * T(x \ 1,y) = K(x \ 1,y).
K(x,y) = T(y,T(x,y)) \ y.
T(x * K(y,x),y) = x.
(x * y) / x = y * K(x,y).
K(x \ (x / y),x) = K(y \ 1,x).
T(K(x \ 1,y),z) = K(y \ (y / T(x,z)),y).
K(x \ (x / T(y,z)),x) = T(K(y \ 1,x),z).
x * K(y \ 1,x) = y * ((x \ (y \ x)) * x).
x * ((y \ (x \ y)) * y) = y * K(x \ 1,y).
K((x \ (y \ x)) \ 1,z) = T(T(z,y) \ z,x).
T(T(x,y) \ x,z) = K((z \ (y \ z)) \ 1,x).
x * K(x,y) = T(x,y).
T(x,y) = x * K(x,y).
L(K(x,y),x,z) = (z * x) \ (z * T(x,y)).
(x * y) \ (x * T(y,z)) = L(K(y,z),y,x).
L(K(x,y),x,z / x) = z \ ((z / x) * T(x,y)).
T(x,y) * (x \ 1) = K(x,y).
K(x,y) = T(x,y) * (x \ 1).
x * (y * T(K(y,x),z)) = (x * y) * T(K(y,x),z).
(x * y) * T(K(y,x),z) = x * (y * T(K(y,x),z)).
K(x,T(y,z) \ 1) = T(x \ T(x,y \ 1),z).
T(x \ T(x,y \ 1),z) = K(x,T(y,z) \ 1).
L(x \ T(x,y \ 1),z,u) = K(x,L(y,z,u) \ 1).
K(x,y) = K(T(x,y),y).
K(T(x,y),y) = K(x,y).
K(x,x \ y) = K(x,y / x).
K(x,y / x) = K(x,x \ y).
K(x,y) \ 1 = K(y,x).
K(x,y) * K(y,x) = 1.
1 / K(x,y) = K(y,x).
(x * y) \ ((y * x) * T(K(x,y),z)) = K(y,x) * T(K(x,y),z).
K(x,y) \ (z * T(x,y)) = x * T(z,T(x,y)).
(x * y) / ((z * y) / z) = (x / (y * K(z,y))) * y.
K(K(x,y),z) = T(K(x,y),z) * K(y,x).
T(K(x,y),z) * K(y,x) = K(K(x,y),z).
x * K(y,y \ x) = y * (x / y).
(x * (y * T(y \ 1,z))) * y = (x * y) * K(y \ 1,z).
(x * y) * ((z \ L(y \ z,y,x)) * z) = (x * K(y \ 1,z)) * z.
K(L(x,y,z) \ 1,u) = L(x * T(x \ 1,u),y,z).
L(x * T(x \ 1,y),z,u) = K(L(x,z,u) \ 1,y).
(x * y) * K(((x * y) \ x) \ 1,z) = x * T(y,z).
x * K(y,x \ 1) = T(1 / x,y) \ 1.
T(1 / x,y) \ 1 = x * K(y,x \ 1).
T(K(x \ 1,y),z) = K(T(x,z) \ 1,y).
K(T(x,y) \ 1,z) = T(K(x \ 1,z),y).
K(T(x \ 1,y) \ 1,z) = T(K(x,z),y).
1 / T(K(x,y),z) = K(y,T(x \ 1,z) \ 1).
K(x,T(y \ 1,z) \ 1) = 1 / T(K(y,x),z).
T(K(x,y),z) = K((z \ (x \ z)) \ 1,y).
K((x \ (y \ x)) \ 1,z) = T(K(y,z),x).
K((x \ y) \ 1,z) = T(K(x / y,z),x).
T(K(x / y,z),x) = K((x \ y) \ 1,z).
T(K(x / y,z),x) \ 1 = K(z,(x \ y) \ 1).
T(K(x,y \ 1),z) = K(x,T(y,z) \ 1).
K(x,T(y,z) \ 1) = T(K(x,y \ 1),z).
K(x,T(1 / y,z) \ 1) = T(K(x,y),z).
K(x,T(y \ 1,z) \ 1) = T(K(x,y),z).
K(x,y * K(z,y \ 1)) = T(K(x,y),z).
1 / T(K(x,y),z) = T(K(y,x),z).
T(K(x,y),z) * T(K(y,x),z) = 1.
T(K(x,y),z) \ 1 = T(K(y,x),z).
K(x,K(y,z)) = T(K(z,y),x) * K(y,z).
T(K(x,y),z) * K(y,x) = K(z,K(y,x)).
1 != x * T(K(y,z),u) | T(K(z,y),u) = x.
x * T(K(y,z),u) != 1 | T(K(z,y),u) = x.
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,K(y,z)) = K(K(z,y),x).
K(K(x,y),z) = K(z,K(y,x)).
T(x,K(y,z)) = x * K(K(z,y),x).
x * K(K(y,z),x) = T(x,K(z,y)).
K(x,K(y,z)) \ 1 = K(x,K(z,y)).
T(T(x,K(y,z)),K(z,y)) = x.
K(x,(y \ z) \ 1) = T(K(x,y / z),y).
T(K(x,y / z),y) = K(x,(y \ z) \ 1).
T(K(x,y),y * z) = K(x,((y * z) \ z) \ 1).
K(x,y) * K(y,((x * z) \ z) \ 1) = K(x * z,K(x,y)).
L(K(x,y \ 1),z,u) = K(x,L(y,z,u) \ 1).
L(K(x,y),z,u) = K(x,L(y \ 1,z,u) \ 1).
K(x,L(y \ 1,z,u) \ 1) = L(K(x,y),z,u).
K(x,(y \ z) \ 1) = L(K(x,z \ y),z \ y,z).
L(K(x,y \ z),y \ z,y) = K(x,(z \ y) \ 1).
(x * y) / (y * K(z,y)) = (x / (y * K(z,y))) * y.
L(K(x \ 1,y),z,u) = K(L(x,z,u) \ 1,y).
L(K(x,y),z,u) = K(L(x \ 1,z,u) \ 1,y).
K(L(x \ 1,y,z) \ 1,u) = L(K(x,u),y,z).
L(K(x,y),z,u) \ 1 = K(y,L(x \ 1,z,u) \ 1).
K(x,L(y \ 1,z,u) \ 1) = L(K(y,x),z,u) \ 1.
x * T(y,z) != (x * y) * u | K(((x * y) \ x) \ 1,z) = u.
(x * y) * z != x * T(y,u) | K(((x * y) \ x) \ 1,u) = z.
((x * K(y,z)) / (z * K(y,z))) * z = R(x,K(y,z),z).
L(K(x,y),z,u) \ 1 = L(K(y,x),z,u).
R(x,y,K(z,y)) * y = R(x * y,K(z,y),y).
R(x * y,K(z,y),y) = R(x,y,K(z,y)) * y.
R(x * y,K(z,y),y) != u * y | R(x,y,K(z,y)) = u.
(x * K(y \ 1,z)) * y = (x * y) * K(y \ 1,z).
(x / y) * K(y \ 1,z) = (x * K(y \ 1,z)) / y.
(x * K(y \ 1,z)) / y = (x / y) * K(y \ 1,z).
x / y = (T(x,y \ 1) / y) * K(y \ 1,x).
(T(x,y \ 1) / y) * K(y \ 1,x) = x / y.
(T(x,y \ 1) / y) \ (x / y) = K(y \ 1,x).
K(x \ 1,(1 / x) \ (y / x)) = K(x \ 1,y).
K(x \ 1,(1 / x) \ y) = K(x \ 1,y * x).
K(1 / x,(1 / x) \ y) = K(x \ 1,y * x).
x * K(y \ 1,x * y) = (1 / y) * (x / (1 / y)).
(1 / x) * (y / (1 / x)) = y * K(x \ 1,y * x).
x * K((1 / y) \ 1,x * (1 / y)) = y * (x / y).
x * K(y,x * (1 / y)) = y * (x / y).
x * y != z * (x / z) | y = K(z,z \ x).
K(x,y * (1 / x)) = K(x,x \ y).
1 / K(x,x \ y) = K(y * (1 / x),x).
K(x * (1 / y),y) = 1 / K(y,y \ x).
K(x * (1 / y),y) = K(y \ x,y).
K(x * y,y \ 1) = K((y \ 1) \ x,y \ 1).
K((x \ 1) \ y,x \ 1) = K(y * x,x \ 1).
K(x * y,y \ 1) = K(y * x,y \ 1).
K(x,y * K(y * z,y \ 1)) = T(K(x,y),z * y).
T(K(x,y),z * y) = T(K(x,y),y * z).
T(K(x,y),z * y) * K(y,x) = K(K(x,y),y * z).
K(K(x,y),y * z) = K(z * y,K(y,x)).
K(x * y,K(y,z)) = K(y * x,K(y,z)).
(x * y) \ (y * (x * T(K(x,y),z))) = K(y,x) * T(K(x,y),z).
(x * y) \ (y * (x * T(K(x,y),z))) = K(z,K(y,x)).
(x * y) * L((z \ (y \ z)) * z,y,x) = (x * K(y \ 1,z)) * z.
(x * K(y \ 1,z)) * z = x * (y * ((z \ (y \ z)) * z)).
x * (y * ((z \ (y \ z)) * z)) = (x * K(y \ 1,z)) * z.
x * (y * K(z \ 1,y)) = (x * K(z \ 1,y)) * y.
(x * K(y \ 1,z)) * z = x * (z * K(y \ 1,z)).
R(x,K(y \ 1,z),z) = x.
R(x,K(y,z),z) = x.
R(x,y,K(z,y)) = x.
x * (y * K(z,y)) = (x * y) * K(z,y).
(x * y) * K(z,y) = x * (y * K(z,y)).
L(K(x,y),y,z) = K(x,y).
K(x,y \ z) = K(x,(z \ y) \ 1).
K(x,(y \ z) \ 1) = K(x,z \ y).
K(x,y) \ 1 = L(K(y,x),y,z).
L(K(x,y),x,z) = K(y,x) \ 1.
L(K(x,y),x,z) = K(x,y).
(x * y) \ (x * T(y,z)) = K(y,z).
K(x,y) = z \ ((z / x) * T(x,y)).
x \ ((x / y) * T(y,z)) = K(y,z).
K(x,y) * K(y,z \ (x * z)) = K(x * z,K(x,y)).
(x * y) * K(y,z) = x * T(y,z).
x * K(y,z) = (x / y) * T(y,z).
(x / y) * T(y,z) = x * K(y,z).
K(((x * y) \ x) \ 1,z) = K(y,z).
T(x * y,K(y,z)) = K(y,z) \ (x * T(y,z)).
K(x,y) \ (z * T(x,y)) = T(z * x,K(x,y)).
(x * K(y,z)) * y = x * T(y,z).
K((x \ y) \ 1,z) = K(y \ x,z).
(x * y) * K(y,z) = (x * K(y,z)) * y.
(x * K(y,z)) * y = (x * y) * K(y,z).
K(L(x \ y,x,z) \ 1,u) = K((z * y) \ (z * x),u).
K((x \ y) \ y,z) = T(K(x,z),y).
L(K(x \ y,z),u,w) = K(L(y \ x,u,w) \ 1,z).
K(L(x \ y,z,u) \ 1,w) = L(K(y \ x,w),z,u).
T(x * y,K(y,z)) = y * T(x,T(y,z)).
K(x,y) * K(y,T(x,z)) = K(x * z,K(x,y)).
K((x * y) \ (x * z),u) = L(K(y \ z,u),z,x).
L(K(x \ y,z),y,u) = K((u * x) \ (u * y),z).
L(K(x,y),z,u) = K((u * (z / x)) \ (u * z),y).
K((x * (y / z)) \ (x * y),u) = L(K(z,u),y,x).
K(L(x,y / x,z),u) = L(K(x,u),y,z).
K(L(x,y,z),u) = L(K(x,u),y * x,z).
L(K(x,y),z * x,u) = K(L(x,z,u),y).
((x \ y) * x) * (T(z,x) \ z) = (x \ (y * (T(z,x) \ z))) * x.
(x \ (y * (T(z,x) \ z))) * x = ((x \ y) * x) * (T(z,x) \ z).
(x \ (y * K(x,z))) * x = ((x \ y) * x) * (T(z,x) \ z).
((x \ y) * x) * (T(z,x) \ z) = (x \ (y * K(x,z))) * x.
((x \ y) * x) * K(x,z) = (x \ (y * K(x,z))) * x.
(x \ (y * K(x,z))) * x = ((x \ y) * x) * K(x,z).
x * y != (z * y) * K(y,u) | x = z * K(y,u).
x \ (y * K(x,z)) = (x \ y) * K(x,z).
x * ((x \ y) * K(x,z)) = y * K(x,z).
x * (y * K(x,z)) = (x * y) * K(x,z).
(x * y) * K(x,z) = x * (y * K(x,z)).
L(K(x,y),z,x) = K(x,y).
K(x,y) = K(L(x,z,x),y).
K(L(x,y,x),z) = K(x,z).
K(T(x / (x / y),x),z) = K(y,z).
K(T(x,y),z) = K((x \ y) \ y,z).
K((x \ y) \ y,z) = K(T(x,y),z).
K(T(x,y),z) = T(K(x,z),y).
K(x,T(y,z)) * T(K(y,x),z) = 1.
T(K(x,y),z) = K(x,T(y,z)).
K(x,T(y,z)) = T(K(x,y),z).
T(x,T(y,z)) = x * T(K(x,y),z).
x * T(K(x,y),z) = T(x,T(y,z)).
K(x,y) * K(y,T(x,z)) = K(z,K(x,y)).
(x * y) \ (y * T(x,T(y,z))) = K(z,K(y,x)).
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)).
(x * y) \ T(x * y,K(y,z)) = K(z,K(y,x)).
K(x * y,K(y,z)) = K(z,K(y,x)).
K(x,K(y,z)) = K(z,K(y,x)).
T(x,K(y,z)) = x * K(z,K(y,x)).
x * K(y,K(z,x)) = T(x,K(z,y)).
K(x,K(y,z)) \ 1 = K(z,K(x,y)).
K(x,K(y,z)) = K(y,K(x,z)).
x * K(y,K(z,x)) = T(x,K(y,z)).
T(x,K(y,z)) = T(x,K(z,y)).
T(T(x,K(y,z)),K(y,z)) = x.
(x * K(y,z)) / x = T(K(y,z),x).
T(T(K(x,y),z),z) = K(x,y).
T(K(x,T(y,z)),z) = K(x,y).

end_of_list.
