% *********************************************************
% AIM:  T1-distributivity => aK1
% *********************************************************

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

set(para_from_small).

clear(back_demod).
set(restrict_denials).

assign(max_weight,5).

% **********
% AIM Axioms
% **********

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.

   % 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).

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

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

   T(x,y) * T(z,y) = T(x * z,y) # label("T1dist").

end_of_list.

formulas(goals).

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

end_of_list.

% *********************
% AIM: Auxiliary Lemmas
% *********************

formulas(assumptions).

   % cancellation laws (long form)

   x * y != u | x * z != u | y = z # label("*-Cancellation 1").
   y * x != u | z * x != u | y = z # label("*-Cancellation 2").

   x / y != u | x / z != u | y = z # label("/-Cancellation 1").
   y / x != u | z / x != u | y = z # label("/-Cancellation 2").

   x \ y != u | x \ z != u | y = z # label("\-Cancellation 1").
   y \ x != u | z \ x != u | y = z # label("\-Cancellation 2").

   T(x,y) != u | T(z,y) != u | x = z # label("T-Cancellation 1").
   L(z,x,y) != u | L(w,x,y) != u | z = w # label("L-Cancellation 1").
   R(z,x,y) != u | R(w,x,y) != u | z = w # label("R-Cancellation 1").

   % cancellation laws (short form)

   x * y != x * z | y = z # label("*-Cancellation 3").
   y * x != z * x | y = z # label("*-Cancellation 4").

   x / y != x / z | y = z # label("/-Cancellation 3").
   y / x != z / x | y = z # label("/-Cancellation 4").

   x \ y != x \ z | y = z # label("\-Cancellation 3").
   y \ x != z \ x | y = z # label("\-Cancellation 4").

   T(x,y) != T(z,y) | x = z # label("T-Cancellation 2").
   L(z,x,y) != L(w,x,y) | z = w # label("L-Cancellation 2").
   R(z,x,y) != R(w,x,y) | z = w # label("R-Cancellation 2").

   % compatibility

   a(x,y,z) != 1 | L(z,y,x) = z # label("Compat 1").
   L(x,y,z) != x | a(z,y,x) = 1 # label("Compat 2").
   T(x,y) != x | T(y,x) = y # label("Compat 3").
   T(x,y) != x | K(x,y) = 1 # label("Compat 4").
   K(x,y) != 1 | T(x,y) = x # label("Compat 5").

   % sometimes helpful for demodulation-free proofs

   x != y | x * z = y * z # label("Aux 1").
   x != y | z * x = z * y # label("Aux 2").
   x != y | x / z = y / z # label("Aux 3").
   x != y | z / x = z / y # label("Aux 4").
   x != y | x \ z = y \ z # label("Aux 5").
   x != y | z \ x = z \ y # label("Aux 6").

   x != y | y != z | x = z # label("Transitivity =").

end_of_list.

%
% Hints extracted from previously found proofs.
%

formulas(hints).

a(K(x,y),z,u) = 1.
T(x,y) * T(z,y) = T(x * z,y).
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 * 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(T(x,y),z) = T(T(x,z),y).
T(L(x,y,z),u) = L(T(x,u),y,z).
L(T(x,y),z,u) = T(L(x,z,u),y).
T(R(x,y,z),u) = R(T(x,u),y,z).
R(T(x,y),z,u) = T(R(x,z,u),y).
L(R(x,y,z),u,w) = R(L(x,u,w),y,z).
R(L(x,y,z),u,w) = L(R(x,u,w),y,z).
L(L(x,y,z),u,w) = L(L(x,u,w),y,z).
R(R(x,y,z),u,w) = R(R(x,u,w),y,z).
x * y != z | x * u != z | y = u.
x * y != z | u * y != z | x = u.
x / y != z | x / u != z | y = u.
x / y != z | u / y != z | x = u.
x \ y != z | x \ u != z | y = u.
x \ y != z | u \ y != z | x = u.
T(x,y) != z | T(u,y) != z | x = u.
L(x,y,z) != u | L(w,y,z) != u | x = w.
R(x,y,z) != u | R(w,y,z) != u | x = w.
x * y != x * z | y = z.
x * y != z * y | x = z.
x / y != x / z | y = z.
x / y != z / y | x = z.
x \ y != x \ z | y = z.
x \ y != z \ y | x = z.
T(x,y) != T(z,y) | x = z.
L(x,y,z) != L(u,y,z) | x = u.
R(x,y,z) != R(u,y,z) | x = u.
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.
x != y | x * z = y * z.
x != y | z * x = z * y.
x != y | y != z | x = z.
a(K(c1,c2),c3,c4) != 1.
1 \ x = x.
x \ x = 1.
x * (y * (y \ 1)) = x.
x * (y * (y \ (x \ z))) = z.
x / 1 = x.
x * (((x \ y) * z) / z) = y.
x / (y \ x) = y.
((1 / x) * x) * y = y.
(x / y) \ x = y.
(x \ (x * (y / z))) * z = y.
(x * y) \ ((x * y) * 1) = a(x,y,1).
(x * (y * z)) * a(x,y,z) = (x * y) * z.
(x * y) * K(y,x) = y * x.
x \ ((y \ x) * y) = K(y \ x,y).
((x \ y) * x) \ y = K(x,x \ y).
x \ (y * (x / y)) = K(y,x / y).
(x * 1) \ (x * y) = L(y,1,x).
(x * y) * L(z,y,x) = x * (y * z).
L(x \ y,x,z) = (z * x) \ (z * y).
L(x,y / x,z) = (z * (y / x)) \ (z * y).
((x * 1) * y) / y = R(x,1,y).
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(x,x) = x.
x * T(y,x) = y * x.
T(x,x \ y) = (x \ y) \ y.
T(x / y,y) = y \ x.
T(x,y) * T(T(z,y),u) = T(x * T(z,u),y).
T(T(T(x,y),z),u) = T(T(T(x,u),y),z).
T(R(T(x,y),z,u),w) = T(T(R(x,z,u),w),y).
1 * x != y | z != y | x = z.
x != y | x * z != y | 1 = z.
x != y | z * u != y | z \ x = u.
x != y | z * u != y | x / u = z.
x * y != z | x \ z = y.
((x * y) / z) * z != x * u | y = u.
x * 1 != y | y = x.
x * 1 != y | x = y.
x * (y \ z) != z | x = y.
x * y != z | z / y = x.
x / y != z | z * y = x.
x \ y != z | x * z = y.
x \ (y * (z * u)) != L(u,z,y) | y * z = x.
R(T(x,y),z,u) != T(w,y) | R(x,z,u) = w.
R(L(x,y,z),u,w) != L(v5,y,z) | R(x,u,w) = v5.
((x / y) * y) * z = x * z.
(x * (x \ y)) * z = y * z.
(x * y) / y = (x / z) * z.
(x / y) * y = x * 1.
x \ (x * y) = z * (z \ y).
x * (x \ y) = y * 1.
x / ((1 / y) * y) = x.
T(x,R(x,y,z)) = x.
T(x,L(x,y,z)) = x.
T(x * y,x) = x * T(y,x).
T(T(x,y),x) = T(x,y).
x / (y \ x) = (y / z) * z.
(x / (y \ x)) * z = y * z.
x / y != z | z \ x = y.
x / (y / ((z \ x) \ y)) = z.
x * ((y / (x \ z)) \ y) = z.
((x / (y / z)) \ x) \ y = z.
x \ y != z | y / z = x.
x * (y \ y) != z | x = z.
L(x \ 1,x,y) = (y * x) \ y.
R(1 / x,x,y) = y / (x * y).
(x \ y) * T(x,x \ y) = y.
T((x * y) / x,x) = y.
(x * T(y,x)) / x = y.
(x * y) \ (x * (z * y)) = L(T(z,y),y,x).
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.
x * y != z | y * u != z | T(x,y) = u.
x * y != z * x | T(z,x) = y.
T(T(x / y,z),y) = T(y \ x,z).
(x / y) * y != z | z = x.
x * (x \ y) != z | z = y.
(x * (1 / y)) * y = R(x,1 / y,y).
K(T(x,y),x) = 1.
(x * T(T(y,x),z)) / x = T(y,z).
T(x,y) != z | (y * z) / y = x.
K(x,(y * x) / y) = 1.
T(x,(y * x) / y) = x.
R(x,y,z) * (y * z) != u | (x * y) * z = u.
(x * y) * L(z,y,x) != u | x * (y * z) = u.
x * T(y,x) != z | y * x = z.
L(x \ (y \ z),x,y) = (y * x) \ z.
x * K(y \ x,y) = (y \ x) * y.
x * K(y,x / y) = y * (x / y).
K(x,y) \ (x * y) = T(y * x,K(x,y)).
T(x,1) = x.
x != y | z != y | x = z.
T(1,x) = 1.
T(x,1) != y | x = y.
K(x \ 1,x) = (x \ 1) * x.
((x / y) * y) * z != u | x * z = u.
(x * y) / y != z | z = x.
x / (y \ x) != z | z = y.
x \ (x * y) != z * u | z \ y = u.
x \ (x * y) != z | y = z.
x * (y * (y \ z)) != u | x * z = u.
x \ (x * y) != z | z = y.
x \ (y * T(x,y)) != z | y = z.
(x * y) \ (y * x) != z | K(y,x) = z.
T((x * y) / x,x) != z | z = y.
T(x * y,x) = y * x.
x \ T(x * y,x) = T(y,x).
T(x,y) = (y \ x) * y.
T(x,x / y) = y * (x / y).
T(x,y) != z * y | y * z = x.
(x \ T(x,y)) * x = T(x,y).
L(T(x,x \ y),x \ y,z) = (z * (x \ y)) \ (z * y).
T(x,y) / x = x \ T(x,y).
T(x,x \ T(x,y)) = x.
x \ (x * y) = L(y,1,x).
L(x,1,y) != z | z = x.
(x * y) / y = R(x,1,y).
R(x,1,y) = x.
L((x \ y) \ 1,x \ y,x) = y \ x.
L(x \ 1,x,y / x) = y \ (y / x).
R(1 / (x / y),x / y,y) = y / x.
x * L(T(y,x),z,u) != w | L(y,z,u) * x = w.
T(x * y,x) != z | y * x = z.
T(x,y) != z | (y \ x) * y = z.
K(x \ y,x) = y \ T(y,x).
T(x,K(y \ x,y)) = x.
T(x * y,K(y,x)) = x * y.
(x / y) \ (z * (z \ x)) = y.
1 / x = x \ 1.
(x \ 1) \ 1 = x.
(L(x,y,z) \ x) \ x = L(x,y,z).
1 / (1 / x) = x.
x * (x \ y) != z * u | y / u = z.
T(x / y,z) * y = y * T(y \ x,z).
T((x * y) / x,z) * x = x * T(y,z).
(x \ y) * T((x \ y) \ y,z) = T(x,z) * (x \ y).
(x * T(y,z)) / x = T((x * y) / x,z).
T(T(x,y),z) != u | T(T(x,z),y) = u.
(x \ y) * x != y * z | K(x \ y,x) = z.
x \ ((y \ x) * y) != z | K(y \ x,y) = z.
a(x,y,1) = 1.
x * L(y,z \ x,z) = z * ((z \ x) * y).
x * L(y,z,x / z) = (x / z) * (z * y).
x * ((x \ 1) * y) = L(y,x \ 1,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) * z != x * (y * u) | L(u,y,x) = z.
(x * y) \ (x * (y * z)) != u | L(z,y,x) = u.
(x * y) / L(z \ y,z,x) = x * z.
L((x \ y) \ z,x \ y,x) = y \ (x * z).
L(x \ T(y,z),x,z) = (z * x) \ (y * z).
L(L(x,y,z) \ u,L(x,y,z),z * y) = (z * (y * x)) \ ((z * y) * u).
R(x,x \ y,z) \ (y * z) = (x \ y) * z.
R(x,y / z,z) * y = (x * (y / z)) * z.
(((x * y) * z) * u) / ((y * z) * u) = R(R(x,y,z),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.
(x * y) * z != u * (y * z) | R(x,y,z) = u.
R(x,y * z,K(z,y)) * (z * y) = (x * (y * z)) * K(z,y).
((x * y) * z) / (y * z) != u | R(x,y,z) = u.
R(x / y,y,x \ z) = z / (y * (x \ z)).
R((x / y) / z,z,y) = x / (z * y).
R(x / (y / z),y / z,z) = (x * z) / y.
(x * (1 / y)) * y = R(x,y \ 1,y).
(x * (x \ y)) * z != u | y * z = u.
(x / (y \ x)) * z != u | y * z = u.
L(T(x \ 1,y),x,z / x) = T(z \ (z / x),y).
(x / y) \ (L(y \ 1,y,x / y) * x) = K(x \ (x / y),x).
(x / y) * y != z * u | x / u = z.
L((x \ 1) \ y,x \ 1,x) = x * y.
x \ L(L(y,x \ 1,x),z,u) = (x \ 1) * L(y,z,u).
(x * (y * z)) / L(K(y,z),z * y,x) = x * (z * y).
(x * y) / L(z,y / z,x) = x * (y / z).
R(x / (1 / y),y \ 1,y) = x * y.
x * ((1 / y) * y) != z * u | x / u = z.
((x / y) * y) * z != u * w | (x * z) / w = u.
L(T((x \ 1) \ y,z),x \ 1,x) = T(x * y,z).
L(R((x \ 1) \ y,z,u),x \ 1,x) = R(x * y,z,u).
x * (y * T(z,x * y)) = L(z,y,x) * (x * y).
x * L(R(T(y,x),z,u),w,v5) = L(R(y,z,u),w,v5) * x.
L(x / y,z,u) * y = y * L(y \ x,z,u).
L((x * y) / x,z,u) * x = x * L(y,z,u).
R(x / y,z,u) * y = y * R(y \ x,z,u).
K(x,y) \ (x * y) = y * x.
x / ((y \ x) * y) = K(y,y \ x).
x * (y * z) != z * y | K(z,y) = x.
K(x,x \ y) = y / T(y,x).
T((x * (y / z)) / x,z) = (x * (z \ y)) / x.
T((x * y) / x,z) * x != u | x * T(y,z) = u.
(x * (y * z)) * u != (x * y) * z | a(x,y,z) = u.
L(T(x,y),y,x) = T(x,x * y).
L(R(T(x,y),z,u),y,x) = R(T(x,x * y),z,u).
(x * y) * R(L(T(x,y),y,x),z,u) = R(x,z,u) * (x * y).
x \ (y * T(y \ x,y)) != z | K(y \ x,y) = z.
x \ T(x,y) != z | K(y \ x,y) = z.
x * ((x \ y) * z) != y * u | L(z,x \ y,x) = u.
(x / y) \ (L(z,y,x / y) * x) = y * T(z,x).
L(T((x \ y) \ z,u),x \ y,x) = T(y \ (x * z),u).
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).
R(T(x / (y / z),u),y / z,z) = T((x * z) / y,u).
R(T(T(x,y),z),u,w) = T(T(R(x,u,w),z),y).
(x * y) * T(L(z,y,x),u) != w | x * (y * T(z,u)) = w.
(x * (y \ 1)) * y != z * K(y \ 1,y) | R(x,y \ 1,y) = z.
(x * L(x \ y,z,u)) / x = L(y / x,z,u).
L((x * y) / x,z,u) = (x * L(y,z,u)) / x.
L(((x * y) * z) / (x * y),y,x) = (x * (y * z)) / (x * y).
(x * R(x \ y,z,u)) / x = R(y / x,z,u).
(x / (y * x)) * y = y * R(y \ 1,y,x).
((x * (y / z)) / x) * z = z * ((x * (z \ y)) / x).
T(T(R(x / y,z,u),w),y) = R(T(y \ x,w),z,u).
L(T(x,y) / x,x,y) = (x * K(x,y)) / x.
L((x * (y \ (z \ u))) / x,y,z) = (x * ((z * y) \ u)) / x.
L((x * (y \ 1)) / x,y,z / y) = (x * (z \ (z / y))) / x.
L((x * ((y \ z) \ u)) / x,y \ z,y) = (x * (z \ (y * u))) / x.
R((x * y) / x,z,u) = (x * R(y,z,u)) / x.
(x * y) * T((x * y) \ x,z) = x * (y * T(y \ 1,z)).
(x * y) * T((x * y) \ z,u) = x * (y * T(y \ (x \ z),u)).
(x * y) * T(T(x,x * y),z) = x * (y * T(T(x,y),z)).
T((x * y) / (z * y),u) * (z * y) = (T(x / z,u) * z) * y.
(x / y) * (y * T(y \ 1,z)) = x * T(x \ (x / y),z).
(x \ 1) * T((x \ 1) \ y,z) = x \ T(x * y,z).
((x * y) \ x) * (x * y) = x * (y * T(y \ 1,x * y)).
T(x / y,z) * y != u | y * T(y \ x,z) = u.
((x * R(y / z,z,u)) / x) * (z * u) = (z * u) * ((x * ((z * u) \ (y * u))) / x).
T(T((x * y) / (z * y),u),z) = R(T(z \ x,u),z,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(x,y) * (x \ 1) = x \ T(x,y).
(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)).
(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.
(x \ 1) * L((x \ 1) \ y,z,u) = x \ L(x * y,z,u).
(x \ 1) * R((x \ 1) \ y,z,u) = x \ R(x * y,z,u).
x * ((x \ y) * T((x \ y) \ z,u)) = y * T(y \ (x * z),u).
R(T(x / (1 / y),z),1 / y,y) = T(x * y,z).
(T(x / (y / z),u) * (y / z)) * z = T((x * z) / y,u) * y.
T(x / (1 / y),z) * (1 / y) = T(x * y,z) / y.
(1 / x) * T((1 / x) \ y,z) = T(y * x,z) / x.
T(((1 / x) * y) * x,z) / x = (1 / x) * T(y,z).
(1 / x) * T((1 / x) \ 1,y) = T(x,y) / x.
(1 / x) * T(x,y) = T(x,y) / x.
(1 / x) * T(x,y) = x \ T(x,y).
(x \ 1) \ T(x \ 1,y) = x * T(x \ 1,y).
T(1 / x,T(x,y)) = x \ 1.
T((x * y) / (z * y),z) = R(z \ x,z,y).
R(T(x \ y,x * z),x,z) = T((x * z) \ (y * z),x).
R(x,y,z) = T(((y * x) * z) / (y * z),y).
R(x \ (y / z),x,z) = T(y / (x * z),x).
T(x / (y * z),y) * (y * z) = ((y \ (x / z)) * y) * z.
T((x * y) \ ((x * z) * y),x) = R(T(z,x * y),x,y).
R(T(x,y * x),y,x) = T(x,y).
x * R(T(y,y * x),z,u) = L(R(y,z,u),x,y) * x.
(x * y) * T((x * y) \ (x * z),u) != w | x * (y * T(y \ z,u)) = w.
x * (y * T(T(x,y),z)) = T(x,z) * (x * y).
T(x,y) * (x * z) = x * (T(x,y) * z).
x * (T(x,y) * (x \ z)) = T(x,y) * z.
x * (T(x,y) \ 1) = T(x,y) \ x.
T(x,y) * (x * (T(x,y) \ z)) = x * z.
(x / y) * (T(x / y,z) * y) = T(x / y,z) * x.
x * (T(x,y) * T(z,x)) = T(x,y) * (z * x).
x * (T(x,y) \ y) = T(y,T(x,y)).
T(x,y) * z != x * u | x * (T(x,y) \ u) = z.
(x / y) * ((y \ x) \ y) = T(y,T(x / y,y)).
(x / y) * ((y \ x) \ y) = T(y,y \ x).
((x * y) / x) * (y \ x) = T(x,x \ (x * y)).
T(x,y) = ((x * y) / x) * (y \ x).
T(x,y) / (y \ x) = (x * y) / x.
((x * (x / y)) / x) * y = T(x,x / y).
x * ((y * (x \ y)) / y) = T(y,y / x).
(x / y) * ((x * y) / x) = T(x,x / (x / y)).
(x * y) / x = x / (x / y).
T(x / (x / y),x) = y.
T(x / y,x) = y \ x.
T(x,y) = (x \ y) \ y.
T(x,y) != z \ y | y / z = x.
T(x,x \ y) = T(x,y).
(R(x,y,z) \ u) \ u = R(T(x,u),y,z).
x / T(y,x) = y \ x.
T(x,y) != z \ y | x \ y = z.
R(x,y,z) / x = x \ R(x,y,z).
x / T(x,y) = T(x,y) \ x.
((x * y) / x) / y = y \ ((x * y) / x).
(T(x,y) \ x) * T(x,y) = x.
(x \ R(x,y,z)) * x = R(x,y,z).
R(x,y,z) / x != u | x \ R(x,y,z) = u.
x * (((y * x) / y) / x) = (y * x) / y.
(x / y) * (y * T(y \ x,z)) = T(x / y,z) * x.
T(x / y,z) * u != (x / y) * (y * T(y \ x,z)) | u = x.
(x / y) * ((y \ 1) * y) = x * T(x \ (x / y),y).
(x / y) * K(y \ 1,y) = x * T(x \ (x / y),y).
K((x * y) \ x,x * y) = y * T(y \ 1,x * y).
(x * y) * T((x * y) \ z,x) = ((x \ (z / y)) * x) * y.
((x \ (x / y)) * x) * y = x * (y * T(y \ 1,x)).
K(x \ (x / y),x) = y * T(y \ 1,x).
x \ K(y \ (y / x),y) = T(x \ 1,y).
x * T(x \ 1,y) != z | K(y \ (y / x),y) = z.
(x \ y) \ K(T(y,x) \ ((y * x) / y),T(y,x)) = T((x \ y) \ 1,T(y,x)).
x * (y * R(T(x,y),z,u)) = R(x,z,u) * (x * y).
R(x,y,z) * (x * u) = x * (R(x,y,z) * u).
x * (R(x,y,z) * T(u,x)) = R(x,y,z) * (u * x).
R(x,y,x) * T(y,x) = T(x * y,x).
R(x,y,x) = x.
R(x,y,x) * (x \ (y * x)) = T(x * y,x).
R(x,y,x) = R(x,z,x).
R(T(x,y),z,T(x,y)) = T(x,x \ y).
R(x,y,x) = (x \ 1) \ 1.
R(T(x,y),z,x) = (x \ y) \ y.
R(T(x,y),z,x) = T(x,x \ y).
T(x,(x \ y) * x) = T(x,y).
R(T(x,x * y),z,x) = T(x,y).
T(x,y * x) = T(x,x * y).
T(x,T(y,x)) = T(x,y).
T(x,y) \ y = x \ T(y,x).
T(x,L(T(y,x),z,u)) = T(x,L(y,z,u)).
T(x,y) * T(T(y,x),z) = T(y,z) * T(x,y).
T(x,x / (x / y)) = T(x,y).
T(x,x / y) = T(x,y \ x).
T(x \ y,T(x,y)) = T(x \ y,x).
T(x,y) * (x \ T(y,x)) = y.
(x / y) \ T(x,y) = (x * y) / x.
T(x,y \ x) = y * (x / y).
T(x,y) * T(y,x) = x * y.
(x * y) / T(y,x) != z | T(x,y) = z.
R(T(x,x * y),z,x) = T(x,T(y,x)).
T(x,y * z) != T(y,z) | R(y,u,y) = x.
T(x / y,T(y,x)) = y \ x.
x \ (y * T(y \ x,T(y,x))) != z | K(y \ x,y) = z.
((x * y) * y) / (x * y) = x \ T(x * y,y).
R(T(x,x * y),z,T(x,x * y)) = T(x,y).
L(R(x,y,x),z,x) * z = z * T(x,T(z,x)).
R(x,y,x) * (x \ (z * x)) = T(x * z,x).
(x * y) / T(T(x,y),y) = T(y,x).
T(x \ T(x * y,y),x) = R(y,x,y).
(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)).
L(R(x,y,x),z,x) = T((z * x) / z,T(z,x)).
L(R(x,y,x),z * x,x) = T(z \ T(z * x,x),T(z * x,x)).
L(((x * y) * z) / (x * y),y,x) != u / (x * y) | x * (y * z) = u.
(x * y) * ((z * ((x * y) \ u)) / z) = x * (y * ((z * (y \ (x \ u))) / z)).
(x * y) * ((z * ((x * y) \ u)) / z) != w | x * (y * ((z * (y \ (x \ u))) / z)) = w.
(x / y) * (y * ((z * (y \ 1)) / z)) = x * ((z * (x \ (x / y))) / z).
x * (y * T(y \ (x \ z),x)) = ((x \ (z / y)) * x) * y.
((x \ ((x * y) / z)) * x) * z = x * (z * T(z \ y,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.
(x * y) * T((x * y) \ (z * y),u) = (T(z / x,u) * x) * y.
(T((x * y) / x,z) * x) * y = (x * y) * T(y,z).
(x * T(y,z)) * 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 * (y / z)) * T(y / z,z) = (x * (z \ y)) * (y / z).
(x / y) * T(y,x) = (y * x) / y.
T(x,y) \ ((x * y) / x) = T(y / x,T(x,y)).
(x * (y / z)) * (z \ y) = (x * (z \ y)) * (y / z).
(x * (y \ (y * z))) * ((y * z) / y) = (x * ((y * z) / y)) * z.
(x * (y \ z)) / (z / y) = (x / (z / y)) * (y \ z).
x * ((x \ y) * T((x \ y) \ 1,z)) = y * T(y \ x,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 \ y) * K(z \ (z / ((x \ y) \ (x \ 1))),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).
(T(1 / (x / y),z) * (x / y)) * y = T(y / x,z) * x.
(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).
(x / y) * T((x / y) \ 1,z) = (x * T(x \ y,z)) / y.
K(x \ (x / (y / z)),x) = (y * T(y \ z,x)) / z.
K(x \ (x / R(y,z,u)),x) = (((y * z) * u) * T(((y * z) * u) \ (z * u),x)) / (z * u).
(x * y) * T((x * y) \ (z * y),u) = (x * T(x \ z,u)) * y.
(x * ((y * z) / y)) * z = (x * z) * ((y * z) / y).
(1 / x) * ((y * x) / y) = ((y * x) / y) / x.
((x / y) * y) * ((x * y) / x) = T(x,x / (x / y)) * y.
((x * (y \ 1)) / x) / (y \ 1) = y * ((x * (y \ 1)) / x).
T(x,x / (x / y)) * y = x * ((x * y) / x).
T(x,x / (x / T(y,x))) * T(y,x) = x * y.
T(x,y) * y = x * ((x * y) / x).
T(x,x / (x / T(y,x))) * (y * x) = x * (x * y).
T(x,T(y,x)) * (y * x) = x * (x * y).
(x \ 1) * (x * ((y * (x \ 1)) / y)) = (y * (x \ 1)) / y.
x * (y * T(y \ (x \ (z * y)),u)) = (x * T(x \ z,u)) * y.
(x * y) * T((x * y) \ y,z) = (x * T(x \ 1,z)) * y.
x * (y * T(y \ (x \ y),z)) = (x * T(x \ 1,z)) * y.
T(x,x * T(x \ 1,y)) = x.
T(x \ 1,x \ T(x,y)) = x \ 1.
T(x \ T(x,y),x \ 1) = x \ T(x,y).
(x \ T(x,y)) * (x \ 1) = (x \ 1) * (x \ T(x,y)).
T((x * y) \ (y * x),y \ 1) = L(y \ T(y,x),y,x).
K(x,y) = T((y * x) \ (x * y),x \ 1).
T(K(x,y),x \ 1) = K(x,y).
(x \ 1) * K(x,y) != z | K(x,y) * (x \ 1) = z.
(x * T(x \ (y / z),u)) * z = x * (z * T(z \ (x \ y),u)).
((x * y) * T((x * y) \ x,z)) * u = (x * y) * (u * T(u \ L(y \ u,y,x),z)).
(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) * 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).
((x / K(y \ 1,y)) * y) * K(y \ 1,y) = x * y.
((x * (y \ 1)) / K(y \ 1,y)) * y = R(x,y \ 1,y).
(x * (y \ 1)) / K(y \ 1,y) = x * (1 / y).
(x / (1 / y)) * (y \ 1) = x * K(y \ 1,y).
(x * (y \ 1)) / (1 / y) = x * K(y \ 1,y).
x * K(x \ 1,x) = 1 / (1 / x).
R(x * K(y \ 1,y),y \ 1,y) = (x * (y \ 1)) * y.
K(x \ 1,x) = 1.
K(x \ 1,x) = K(y \ 1,y).
T(x,K(y \ 1,y)) = x.
R(x,K(y \ 1,y),z) = x.
K(x,x \ 1) = 1.
a(x,y,K(z \ 1,z)) = 1.
T(x,K(y,y \ 1)) = x.
R(x,K(y,y \ 1),z) = x.
x \ K(y,y \ 1) = 1 / x.
a(x,y,K(z,z \ 1)) = 1.
K(x \ 1,x) * y = y * K(x \ 1,x).
K(x,x \ 1) * y = y * K(x,x \ 1).
T(K(x,x \ 1),y) = K(x,x \ 1).
K(x,x \ 1) * y != z | y * K(x,x \ 1) = z.
x * (K(y \ 1,y) * z) != u | (x * K(y \ 1,y)) * z = u.
L(K(x \ 1,x),y,z) = K(x \ 1,x).
(x * K(y,y \ 1)) * z = x * (K(y,y \ 1) * z).
L(K(x,x \ 1),y,z) = K(x,x \ 1).
K(x \ 1,x) = (y \ 1) * y.
K(x,x \ 1) = y * (1 / y).
K(x \ 1,x) / y != z | y \ 1 = z.
K(x,x \ 1) * T((y * (1 / y)) \ z,u) = y * ((1 / y) * T((1 / y) \ (y \ z),u)).
T(K(x,x \ 1) * y,z) = K(x,x \ 1) * T(y,z).
(x * y) * K(z \ 1,z) = x * (y * K(z \ 1,z)).
(x \ 1) * K(y,y \ 1) = x \ K(y,y \ 1).
(x * y) * K(z,z \ 1) = x * (y * K(z,z \ 1)).
K(x \ 1,x) * y = y * K(z \ 1,z).
x * (K(y \ 1,y) * z) = x * (z * K(u \ 1,u)).
(x \ 1) * K(y,y \ 1) = 1 / x.
x * K(y,y \ 1) = 1 / (1 / x).
(x \ 1) * (K(y,y \ 1) * z) = (1 / x) * z.
K(x,x \ 1) * ((1 / y) \ z) = (y \ 1) \ z.
(x \ 1) * y != (1 / x) * z | K(u,u \ 1) * z = y.
((1 / x) \ y) * K(z,z \ 1) = (x \ 1) \ y.
(x \ y) * K(z,z \ 1) = ((x \ 1) \ 1) \ y.
(x \ y) * K(z \ 1,z) = ((x \ 1) \ 1) \ y.
K(x \ 1,x) * (y \ z) = ((y \ 1) \ 1) \ z.
K(x,x \ 1) * T(K(x,x \ 1) \ y,z) = T(y,z).
R(x,y,K(z \ 1,z)) = x.
K(x \ 1,x) * (y * z) = y * (z * K(u \ 1,u)).
(x * y) * K(z \ 1,z) = x * (K(u \ 1,u) * y).
R(x,y,K(z \ 1,z)) != u | x = u.
R(x,y,K(z,z \ 1)) = x.
R(x,y,1) = x.
R(x,y,(z \ 1) * z) = x.
x \ (y * K(z,z \ 1)) = (x \ y) * K(z,z \ 1).
R(x,y,(z \ 1) * z) != u | u = x.
(x * (y \ 1)) * K(z,z \ 1) = x * (1 / y).
x * K(y,y \ 1) = z * (1 / (1 / (z \ x))).
((x * y) * (1 / z)) / ((y * (z \ 1)) * K(u,u \ 1)) = R(R(x,y,z \ 1),y * (z \ 1),K(u,u \ 1)).
K(x \ 1,x) * (y * z) = y * (K(u \ 1,u) * z).
x \ (K(y,y \ 1) * z) = (x \ z) * K(y,y \ 1).
(x * y) \ (x * (K(z \ 1,z) * (y * u))) != w | L(K(v5 \ 1,v5) * u,y,x) = w.
x \ (K(y,y \ 1) * z) = ((x \ 1) \ 1) \ z.
x \ (K(y \ 1,y) * z) = ((x \ 1) \ 1) \ z.
x \ (K(y \ 1,y) * z) = (x \ z) * K(u \ 1,u).
K(x \ 1,x) * y = z * (((z \ 1) \ 1) \ y).
x * K(y \ 1,y) = z * (((z \ 1) \ 1) \ x).
K(x \ 1,x) * (((y \ 1) \ 1) * z) = y * z.
K(x \ 1,x) * y = (1 / (1 / z)) * (z \ y).
((x \ 1) \ 1) * K(y \ 1,y) = x.
T(x,x \ 1) * K(y \ 1,y) = x.
K(x \ 1,x) * (y * T(z,z \ 1)) = y * z.
((x \ 1) \ 1) * (K(y \ 1,y) * z) = x * z.
(x * y) \ ((K(z \ 1,z) * y) * ((x \ 1) \ 1)) = K(K(z \ 1,z) * y,(x \ 1) \ 1).
x * (K(y \ 1,y) * z) = (1 / (1 / x)) * z.
(x * y) * K(z \ 1,z) = (1 / (1 / x)) * y.
x \ (y * (K(z \ 1,z) * u)) = (x \ (y * u)) * K(w \ 1,w).
R(((x \ (x / (y \ 1))) * x) * K(y \ 1,y),y \ 1,y) = (x * ((y \ 1) * T((y \ 1) \ 1,x))) * y.
K(x \ 1,x) * (y * z) = (y * K(u \ 1,u)) * z.
(x * K(y \ 1,y)) * z = (x * z) * K(u \ 1,u).
K(x \ 1,x) / y = (1 / y) * K(z \ 1,z).
(x * (y * K(z \ 1,z))) \ (x * (K(u \ 1,u) * (y * w))) != v5 | L(w,y * K(z \ 1,z),x) = v5.
K(x \ 1,x) * (y * z) = (K(u \ 1,u) * y) * z.
K(x \ 1,x) * ((y * z) * u) = (y * (z * K(w \ 1,w))) * u.
(1 / x) * K(y \ 1,y) = x \ 1.
(x * K(y \ 1,y)) \ (z * K(u \ 1,u)) = x \ z.
((1 / x) * y) * K(z \ 1,z) = (x \ 1) * y.
(1 / x) * (K(y \ 1,y) * z) = (x \ 1) * z.
K(x,x \ 1) * (K(y \ 1,y) * z) = z.
(K(x \ 1,x) * y) * K(z,z \ 1) = y.
K(x \ 1,x) \ y = K(z,z \ 1) * y.
(K(x,x \ 1) * y) * K(z \ 1,z) = y.
K(x \ 1,x) * (y * K(z,z \ 1)) = y.
K(x,x \ 1) * (y * (K(z \ 1,z) * u)) = y * u.
K(x,x \ 1) * (y * z) = y * T(z,z \ 1).
R((K(x,x \ 1) * y) / z,z,K(u \ 1,u)) = y / (z * K(u \ 1,u)).
R(x,K(y \ 1,y),z) = K(u \ 1,u) * (x * K(w,w \ 1)).
K(x \ 1,x) * y != z | z * K(u,u \ 1) = y.
K(x,x \ 1) * (y * z) = y * ((z \ 1) \ 1).
(x * y) * K(z,z \ 1) = x * ((y \ 1) \ 1).
(x * (1 / (1 / y))) * K(z,z \ 1) = x * y.
K(x \ 1,x) * (y * z) = y * (1 / (1 / z)).
(1 / (1 / x)) * (x \ (y * z)) = y * (1 / (1 / z)).
L(x,y,K(z \ 1,z)) = x.
R(K(x \ 1,x) * y,z,u) = ((K(w \ 1,w) * (y * z)) * u) / (z * u).
K(x,x \ 1) * ((K(y \ 1,y) * z) * u) = z * u.
L(x,y,K(z,z \ 1)) = x.
(K(x \ 1,x) * y) / z = K(x \ 1,x) * (y / z).
L(x,y,1) = x.
(K(x,x \ 1) * y) / z = K(x,x \ 1) * (y / z).
(x * K(y \ 1,y)) \ z = x \ (K(u,u \ 1) * z).
(1 / (1 / x)) * T(y,x) = y * (1 / (1 / x)).
T(x,1 / (1 / y)) = T(x,y).
T(x,(y \ 1) \ 1) = T(x,y).
x * T(y,(x \ 1) \ 1) = y * x.
K(x \ 1,y) * x = x * K(x \ 1,y).
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)).
(K(x \ 1,x) * y) * ((z \ 1) \ 1) = y * z.
(x * K(y,y \ 1)) * z = x * ((z \ 1) \ 1).
(x / ((y \ 1) \ 1)) * K(z,z \ 1) = x / y.
(x / y) * K(z,z \ 1) = x / (1 / (1 / y)).
x * (1 / (1 / (x \ (y / z)))) = y / (1 / (1 / z)).
1 / (1 / (x \ (y / z))) = x \ (y / (1 / (1 / z))).
(x * (y * K(z \ 1,z))) \ u = (x * y) \ (K(w,w \ 1) * u).
x / (1 / (1 / (y \ x))) = z * (1 / (1 / (z \ y))).
(x \ (y / (1 / (1 / z)))) \ 1 = 1 / (x \ (y / z)).
x / (1 / (1 / ((y * z) \ x))) = y * (1 / (1 / z)).
1 / (x \ (y / (z \ 1))) = (x \ (y / (1 / z))) \ 1.
((x \ (y / (z \ 1))) * u) * K(w \ 1,w) = (1 / ((x \ (y / (1 / z))) \ 1)) * u.
K(x \ 1,x) * (y * K(z,z \ 1)) != u | u = y.
T((1 * x) / y,K(y / x,z)) = x / y.
T(x / y,K(y / x,z)) = x / y.
T(x \ y,K(x / y,z)) = T(y / x,x).
T(x \ y,K(x / y,z)) = x \ y.
(x * y) \ (x * (K(z \ 1,z) * (y * u))) = L(u,y,x) * K(w \ 1,w).
(K(x \ 1,x) * ((y * z) * u)) / ((z * K(w \ 1,w)) * u) = R(y,z * K(w \ 1,w),u).
x * ((x \ y) * ((z * ((x \ y) \ u)) / z)) = y * ((z * (y \ (x * u))) / z).
K(x \ 1,x) * R(((y \ 1) * y) \ z,u,w) = (y \ 1) * (y * R(y \ ((y \ 1) \ z),u,w)).
K(x \ 1,x) * L(((y \ 1) * y) \ z,u,w) = (y \ 1) * (y * L(y \ ((y \ 1) \ z),u,w)).
(L((x / y) / z,u,w) * z) * y = (z * y) * L((z * y) \ x,u,w).
(x * y) * R((x * y) \ (z * y),u,w) = (R(z / x,u,w) * x) * y.
(x / y) \ (x * ((z * (x \ (x / y))) / z)) = y * ((z * (y \ 1)) / z).
(x * y) * L((x * y) \ (z * y),u,w) = (L(z / x,u,w) * x) * y.
(x * y) * R((x * y) \ (z * y),u,w) = (x * R(x \ z,u,w)) * y.
(x / y) \ (x * ((x / y) / x)) = y * ((x * (y \ 1)) / x).
K(x,(x / y) / x) = y * ((x * (y \ 1)) / x).
(x \ y) * ((y * ((x \ y) \ 1)) / y) = K(y,x / y).
(L((x * y) / x,z,u) * x) * y = (x * y) * L(y,z,u).
(x * y) * L((x * y) \ (z * y),u,w) = (x * L(x \ z,u,w)) * y.
(x * L(y,z,u)) * y = (x * y) * L(y,z,u).
((x / y) * L(y,z,u)) \ (x * L(y,z,u)) = y.
x * (y * R(y \ (x \ (z * y)),u,w)) = (x * R(x \ z,u,w)) * y.
x * (y * L(y \ (x \ (z * y)),u,w)) = (x * L(x \ z,u,w)) * y.
x * L(x \ (x \ (y * x)),z,u) = T(x * L(x \ y,z,u),x).
(x * y) * L((x * y) \ y,z,u) = (x * L(x \ 1,z,u)) * y.
T(x * L(x \ y,z,u),x) = x * L(x \ T(y,x),z,u).
x \ T(x * L(x \ y,z,u),x) = L(x \ T(y,x),z,u).
L(x \ T(x * y,x),z,u) = x \ T(x * L(y,z,u),x).
x * (y * L(y \ (x \ y),z,u)) = (x * L(x \ 1,z,u)) * y.
a(x,y,z) = L(L(z,y,x) \ z,L(z,y,x),x * y).
L(x,L(y,z,u),u * z) != a(u,z,y) | L(y,z,u) \ y = x.
R(K(x,x \ 1) * (y / z),z,K(u \ 1,u)) = y / (z * K(u \ 1,u)).
R(K(x \ 1,x) * y,z,u) = (K(w \ 1,w) * ((y * z) * u)) / (z * u).
x / (y * K(z \ 1,z)) = K(u,u \ 1) * (x / y).
x / (K(y \ 1,y) * z) = K(u,u \ 1) * (x / z).
R(K(x \ 1,x) * y,z,u) = K(w \ 1,w) * (((y * z) * u) / (z * u)).
R(K(x \ 1,x) * y,z,u) = K(w \ 1,w) * R(y,z,u).
K(x,x \ 1) * R(K(y \ 1,y) * z,u,w) = R(z,u,w).
(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 \ (y * T(y \ x,T(y,x))) = K(y \ x,T(y,x)).
K(x \ y,T(x,y)) = K(x \ y,x).
K(x \ (x * y),x) = K(y,T(x,x * y)).
K(x,T(y,y * x)) = K(x,y).
K(x,T(y,x * y)) = K(x,y).
K(x,T(x \ y,y)) = K(x,x \ y).
(x * y) * ((z * ((x * y) \ (x * u))) / z) = x * (y * ((z * (y \ u)) / z)).
(x * y) * ((z * ((x * y) \ x)) / z) = x * (y * ((z * (y \ 1)) / z)).
x * (y * ((x * (y \ 1)) / x)) = T(x,x / (x * y)).
x \ T(x,x / (x * y)) = y * ((x * (y \ 1)) / x).
(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)).
T(x,x / (x * (y \ x))) = x * K(x,y / x).
T(x,R(y,x,(y * x) \ x)) = x * K(x,(y * x) / x).
x \ y != z * ((x * (z \ 1)) / x) | T(x,x / (x * z)) = y.
T(x,R(y,x,(y * x) \ x)) = x * K(x,y).
(x \ T(x * (y / z),z)) * z = (x \ 1) * ((z \ ((x \ 1) \ y)) * z).
T((x \ (x * (y / x))) * x,x) = (x \ 1) * ((x \ ((x \ 1) \ y)) * x).
T(x,y) = (y \ 1) * ((y \ ((y \ 1) \ x)) * y).
x \ T(x * (y / x),x) = T(y,x) / x.
T(x * (y / x),x) = x * (T(y,x) / x).
x * (T(y * x,x) / x) = T(x * y,x).
T(x * ((1 / x) * y),x) = x * ((1 / x) * T(y,x)).
T(x * ((1 / x) * ((1 / x) \ (x \ (y * (1 / x))))),x) = (x * T(x \ y,x)) * (1 / x).
x * ((x \ y) * ((z * ((x \ y) \ 1)) / z)) = y * ((z * (y \ x)) / z).
x * K(y,(y / (x \ z)) / y) = z * ((y * (z \ x)) / y).
(x * y) * ((z * ((x * y) \ y)) / z) = y * K(z,(z / T(x,y)) / z).
L(K(x \ 1,x) * y,z,u) = L(y,z,u) * K(w \ 1,w).
L(K(x \ 1,x) * y,z,u) = K(w \ 1,w) * L(y,z,u).
K(x \ 1,x) * L(y * K(z,z \ 1),u,w) = L(y,u,w).
L(x * K(y,y \ 1),z,u) = L(x,z,u) * K(w,w \ 1).
L(x \ 1,y,z) * K(u,u \ 1) = L(1 / x,y,z).
K(x \ 1,x) * L(y * K(z,z \ 1),u,w) != v5 | L(y,u,w) = v5.
1 / (1 / L(x \ 1,y,z)) = L(1 / x,y,z).
L(1 / x,x,y) = 1 / (1 / ((y * x) \ y)).
L(x,x \ 1,y) = 1 / (1 / ((y * (x \ 1)) \ y)).
x / L(y,y \ 1,x) = x * (1 / (1 / (y \ 1))).
x / L(y,y \ 1,x) = x * (1 / y).
((x \ (y / (z \ 1))) * u) * K(w \ 1,w) = (x \ (y / (1 / z))) * u.
R((x * (y / z)) / x,z,u) * (z * u) = (z * u) * ((x * ((z * u) \ (y * u))) / x).
(x * y) * (z * T(z \ L(y \ z,y,x),u)) = (x * (y * T(y \ 1,u))) * z.
(x * y) * ((z * ((x * y) \ (u * y))) / z) = (((z * (u / 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) * ((x * ((x * y) \ z)) / x) = (x * ((z / y) / x)) * y.
(x * y) * ((x * ((x * y) \ z)) / x) != u | (x * ((z / y) / x)) * y = u.
x * (y * ((x * (y \ (x \ z))) / x)) = (x * ((z / y) / x)) * y.
(x * (R(y / z,z,y \ u) / x)) * (z * (y \ u)) = x * ((z * (y \ u)) * ((x * ((z * (y \ u)) \ (x \ u))) / x)).
T(x,x / (x * y)) != z | (x * ((x / y) / x)) * y = z.
(x * y) * ((z * ((x * y) \ y)) / z) = (x * ((z * (x \ 1)) / z)) * y.
K(x,(x / T(y,z)) / x) = T(y * ((x * (y \ 1)) / x),z).
(x * ((y / (z * (x \ y))) / x)) * (z * (x \ y)) = x * ((z * ((x * (z \ 1)) / x)) * (x \ y)).
K(x,(x / T(y \ x,z)) / x) = T(K(x,y / x),z).
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,y / x).
T(K(x,y),K((y * x) / x,z)) = K(x,(y * x) / x).
K(x,(y * x) / x) = T(K(x,y),K(y,z)).
T(K(x,y),K(y,z)) = K(x,y).
T(x * K(y,z),K(z,u)) = T(x,K(z,u)) * K(y,z).
T(x * K(y,z),K(z,u)) != K(y,z) * w | T(T(x,K(z,u)),K(y,z)) = w.
K(x,x \ 1) * T(K(y,y \ 1) \ z,u) = w * ((1 / w) * T((1 / w) \ (w \ z),u)).
K(K(x \ 1,x) * y,(z \ 1) \ 1) = (z * y) \ (y * z).
K(K(x \ 1,x) * y,(z \ 1) \ 1) = K(y,z).
K(K(x \ 1,x) * y,(z \ 1) \ 1) != u | K(y,z) = u.
K(K(x \ 1,x) * y,z) = K(y,z).
K(x,(y \ 1) \ 1) = K(x,y).
K(x * K(y,y \ 1),z) = K(x,z).
K(x,R(y,z,y)) = K(x,y).
K(x,T(y,y * z)) = K(x,T(y,z)).
K(1 / x,y) = K(x \ 1,y).
K(1 / (1 / x),y) = K(x,y).
K(x,T(y,x)) = K(x,y).
K(x,y / x) = K(x,x \ y).
x * K(y,y \ x) = y * (x / y).
x * K(y,y \ x) = T(x,y \ x).
K(((x \ 1) \ 1) \ y,(z \ 1) \ 1) != u | K(x \ y,z) = u.
K(x,(y \ 1) \ 1) != z | K(x,y) = z.
K(x,R(y,z,y)) != u | K(x,y) = u.
K(((x \ 1) \ 1) \ y,z) != u | K(x \ y,z) = u.
(x * T(x \ y,x)) * (1 / x) = T(y * (1 / x),x).
((x \ y) * x) * (1 / x) = T(y * (1 / x),x).
T((x * y) * (1 / x),x) = (y * x) * (1 / x).
T((x * y) * (1 / x),x) != z * (1 / x) | y * x = z.
K(x,x \ 1) * T(K(y,y \ 1) \ z,u) = w * (T((w \ z) * w,u) / w).
T((x \ y) * x,z) / x = x \ T(y,z).
T((x \ y) * x,z) = (x \ T(y,z)) * x.
(x \ T(x * y,z)) * x = T(y * x,z).
T((x \ (y / z)) * x,z) = (x \ (z \ y)) * x.
T(x \ T(x * y,z),x) = x \ T(y * x,z).
T(x * y,z) \ T(y * x,z) != u | K(x \ T(x * y,z),x) = u.
(x * ((y \ (x \ z)) * y)) / x = (y \ (z / x)) * y.
x \ T(y * x,y) = R(y,x,y).
x * R(y,x,y) = T(y * x,y).
(x * y) \ (x * T(z * y,z)) = L(R(z,y,z),y,x).
((x \ (y / z)) * x) * z != u | z * ((x \ (z \ y)) * x) = u.
L(R(x,y,x),y,x) = x.
T(x \ T(x * y,y),T(x * y,y)) = y.
L(x,y,x) = x.
L(x,y,x) = L(x,z,x).
L(x,y,x) = T(z / (z / x),z).
L(x,y,x) = 1 / (1 / x).
L(R(x,y,x),z,R(x,y,x)) = x.
a(x,y,x) = 1.
a(x,y,x) \ z = z.
T(x,a(y,z,y)) = x.
R(x,y,a(z,u,z)) = x.
L(x,y,a(z,u,z)) = x.
L(x,y,x) = a(z,u,z) \ x.
a(x,y,x) * z = z * a(x,y,x).
L(x,y,x) != z | z = x.
(x * y) * a(z,u,z) = x * (y * a(z,u,z)).
x \ (y * a(z,u,z)) = (x \ y) * a(z,u,z).
(a(x,y,x) * z) * u = a(x,y,x) * (z * u).
L(x,y,x) \ 1 = 1 / x.
K(L(x,y,x),z) = K(x,z).
K(L(x,y,x) \ 1,z) = K(x \ 1,z).
a(x,y,x) = L(z,u,z) \ z.
K(T(x / (x / y),x),z) = K(y,z).
a(x,y,x) = z \ R(z,u,z).
a(x,y,x) = R(z,u,z) / z.
R(x,y,x) = x * a(z,u,z).
R(x,y,x) = a(z,u,z) * x.
a(x,y,x) != z | u \ R(u,w,u) = z.
K((x / y) \ x,z) = K(y,z).
K(x \ (x * y),z) = K(y,z).
K(x \ (x / L(y,y \ 1,x)),z) = K(1 / y,z).
K(x,x \ T(x * y,y)) = K(x,y).
K(x,y) = (x * R(y,x,y)) \ T(x * y,y).
K(x,y) = T(y * x,y) \ T(x * y,y).
x \ (y * (z * a(u,w,u))) = (x \ (y * z)) * a(u,w,u).
R(x,y,x) * z = a(u,w,u) * (x * z).
R(x,y,x) * z = (x * z) * a(u,w,u).
R(x,y,x) * (x \ z) = z * a(u,w,u).
T(x * y,x) = (y * x) * a(z,u,z).
(x * y) \ (x * ((y * z) * a(u,w,u))) = L(z,y,x) * a(u,w,u).
K(x \ T(x * y,x),x) = K(y,x).
K(T(x,y),y) = K(x,y).
(x * y) \ (x * (y * (z * a(u,w,u)))) = L(z,y,x) * a(u,w,u).
L(x * a(y,z,y),u,w) = L(x,u,w) * a(y,z,y).
L(R(x,y,x),z,u) = L(x,z,u) * a(w,v5,w).
R(L(x,y,z),u,L(x,y,z)) = L(R(x,w,x),y,z).
R(x,y,L(x,z,u)) = R(x,w,x).
K(x,L(R(y,z,y),u,w)) != v5 | K(x,L(y,u,w)) = v5.
(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 \ 1,y),x \ 1,y) = K(1 / x,y).
L(x,y,z) * T(L(x,y,z) \ 1,u) = L(x * T(x \ 1,u),y,z).
L((1 / x) * T((1 / x) \ 1,y),x,y) = K(1 / (1 / x),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(x,y),x) = K(x,y).
T(K(x,y) * z,x) = K(x,y) * T(z,x).
T(x * K(y,z),y) = T(x,y) * K(y,z).
K(x,y) * T(K(x,y) \ z,x) = T(z,x).
T(x,y) != T(z,y) * K(y,u) | z * K(y,u) = x.
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,y,z) * T(R(x,y,z) \ 1,u) = R(x * T(x \ 1,u),y,z).
R(x,y * K(z \ 1,z),u) = (K(w \ 1,w) * ((x * y) * u)) / (K(v5 \ 1,v5) * (y * u)).
R(x,y * K(z \ 1,z),u) = K(w,w \ 1) * ((K(v5 \ 1,v5) * ((x * y) * u)) / (y * u)).
R(x,y * K(z \ 1,z),u) = K(w,w \ 1) * R(K(v5 \ 1,v5) * x,y,u).
R(x,y * K(z \ 1,z),u) = R(x,y,u).
R(x,(y \ 1) \ 1,z) = R(x,y,z).
R(x,y,z) * (((y \ 1) \ 1) * z) = (x * ((y \ 1) \ 1)) * z.
(x * ((y \ 1) \ 1)) * z != u * (((y \ 1) \ 1) * z) | R(x,y,z) = u.
K(x \ 1,x) * R(K(y \ 1,y) \ z,u,w) = (v5 \ 1) * (v5 * R(v5 \ ((v5 \ 1) \ z),u,w)).
K(x \ 1,x) * L(K(y \ 1,y) \ z,u,w) = (v5 \ 1) * (v5 * L(v5 \ ((v5 \ 1) \ z),u,w)).
K(x \ 1,x) * R(K(y \ 1,y) \ (z * u),w,v5) = ((u \ 1) * R((u \ 1) \ z,w,v5)) * u.
K(x \ 1,x) * L(K(y \ 1,y) \ (z * u),w,v5) = ((u \ 1) * L((u \ 1) \ z,w,v5)) * u.
K(x \ 1,x) * R(K(y \ 1,y) \ (z * u),w,v5) = (u \ R(u * z,w,v5)) * u.
K(x \ 1,x) * R(K(y,y \ 1) * (z * u),w,v5) = (u \ R(u * z,w,v5)) * u.
K(x \ 1,x) * R(y * T(z,z \ 1),u,w) = (z \ R(z * y,u,w)) * z.
R(K(x \ 1,x) * (y * T(z,z \ 1)),u,w) = (z \ R(z * y,u,w)) * z.
(x \ R(x * y,z,u)) * x = R(y * x,z,u).
R(x * y,z,u) / y = y \ R(y * x,z,u).
R((x \ y) * x,z,u) = (x \ R(y,z,u)) * x.
x \ R(x * (y / x),z,u) = R(y,z,u) / x.
R((x \ (y / (1 / z))) * x,z \ 1,z) = (x \ (y * z)) * x.
R(x * (y / x),z,u) = x * (R(y,z,u) / x).
K(x \ 1,x) * L(K(y \ 1,y) \ (z * u),w,v5) = (u \ L(u * z,w,v5)) * u.
K(x \ 1,x) * L(K(y,y \ 1) * (z * u),w,v5) = (u \ L(u * z,w,v5)) * u.
K(x \ 1,x) * L(K(y,y \ 1) * z,u,w) = (v5 \ L(v5 * (z / v5),u,w)) * v5.
K(x \ 1,x) * L(y * K(z,z \ 1),u,w) = (v5 \ L(v5 * (y / v5),u,w)) * v5.
(x \ L(x * (y / x),z,u)) * x = L(y,z,u).
L((x \ y) * x,z,u) = (x \ L(y,z,u)) * x.
(x * y) * ((z \ L(u,y,x)) * z) = x * (y * ((z \ u) * z)).
(x * y) * ((z \ ((x * y) \ u)) * z) = x * (y * ((z \ (y \ (x \ u))) * z)).
L(x,y * K(z \ 1,z),u) = (u * y) \ (K(w,w \ 1) * (u * (K(v5 \ 1,v5) * (y * x)))).
L(x,y * K(z \ 1,z),u) = (u * y) \ (u * (y * x)).
L(x,y * K(z \ 1,z),u) = L(x,y,u).
L(x,T(y,y \ 1),z) = L(x,y,z).
(x * T(y,y \ 1)) * L(z,y,x) = x * (T(y,y \ 1) * z).
(x * T(y,y \ 1)) * z != x * (T(y,y \ 1) * u) | L(u,y,x) = z.
R((x \ (x / (1 / y))) * x,y \ 1,y) = (x * ((y \ 1) * T((y \ 1) \ 1,x))) * y.
R((x \ (x / (1 / y))) * x,y \ 1,y) = (x * (y \ T(y,x))) * y.
(x \ (x * y)) * x = (x * (y \ T(y,x))) * y.
(x * (y \ T(y,x))) * y = y * x.
x * (y \ T(y,x)) = (y * x) / y.
T(x,y) \ x = y \ T(y,T(x,y)).
x * ((y * (x \ 1)) / y) = y \ T(y,x \ 1).
(x * y) / x != y * z | x \ T(x,y) = z.
((x \ 1) * y) / (x \ 1) = y * (x * T(x \ 1,y)).
T(x,x / (x * y)) = T(x,y \ 1).
(x * ((y / (z * (x \ y))) / x)) * (z * (x \ y)) = x * ((x \ T(x,z \ 1)) * (x \ y)).
(x * ((x / y) / x)) * y = T(x,y \ 1).
((x \ 1) * y) / (x \ 1) != y * z | x * T(x \ 1,y) = z.
R(R(x,y,z \ 1),y * (z \ 1),K(u,u \ 1)) = ((x * y) * (1 / z)) / (y * (1 / z)).
R(R(x,y,z \ 1),y * (z \ 1),K(u,u \ 1)) != w | R(x,y,1 / z) = w.
R(x,y,1 / z) = R(x,y,z \ 1).
R(x,y,(z \ 1) \ 1) = R(x,y,z).
R(x,y,z) * (y * ((z \ 1) \ 1)) = (x * y) * ((z \ 1) \ 1).
(x * y) * ((z \ 1) \ 1) != u * (y * ((z \ 1) \ 1)) | R(x,y,z) = u.
(x * (R(y / z,z,y \ u) / x)) * (z * (y \ u)) = (x * ((u / (z * (y \ u))) / x)) * (z * (y \ u)).
R(x * ((y / z) / x),z,y \ u) * (z * (y \ u)) = (x * ((u / (z * (y \ u))) / x)) * (z * (y \ u)).
(x * ((y / (z * (u \ y))) / x)) * (z * (u \ y)) != w | ((x * ((u / z) / x)) * z) * (u \ y) = w.
((x * ((x / y) / x)) * y) * (x \ z) = x * ((x \ T(x,y \ 1)) * (x \ z)).
x * ((x \ T(x,y \ 1)) * (x \ z)) = T(x,y \ 1) * (x \ z).
T(x,(y \ 1) \ 1) * (x \ z) = x * ((x \ T(x,y)) * (x \ z)).
x * ((x \ T(x,y)) * (x \ z)) = T(x,y) * (x \ z).
T(x,y) * (x \ (x * 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 * ((T(y,x) \ y) * z) = T(x,T(y,x)) * z.
x * ((x \ T(x,y)) * T(z,x * (x \ T(x,y)))) = z * (x * (x \ T(x,y))).
(T(x,y) \ x) * (x * y) = y * x.
K(x,y) = T(y,x) \ y.
K(x,y) = y / T(y,x).
T(x,y) \ 1 = x \ K(y,x).
T(x,y) * K(y,x) = x.
K(x,y) * T(y,x) = y.
K(x,x \ y) = K(x,y).
T(x * K(y,x),y) = x.
T(x,y) != z | z * K(y,z) = x.
K(x,x * y) = K(x,y).
T(x,y \ x) = x * K(y,x).
(x * y) / x = y * K(x,y).
T(T(x * K(y,x),z),y) = T(x,z).
T(x,L(y * K(x,y),z,u)) = T(x,L(y,z,u)).
K(x * K(y,x),y) = K(x,y).
x * T(x \ 1,y) = K(x \ 1,y).
K(x,y) = x \ T(x,y).
T(x * K(y * x,x),y) = R(x,y,x).
x * (y * K(x,y)) = T(x,y) * y.
((x * y) * L(y,z,u)) / (x * L(y,z,u)) = y * K(x * L(y,z,u),y).
T(x,y) = x * K(x,y).
x * K(x,y) != z | T(x,y) = z.
(x * y) \ (y * x) = K(x * y,x).
T(x,y) = K(x,y) * x.
K(x,y) != z | K(y \ x,y) = z.
x * (K(x,y) * z) = T(x,y) * z.
L(x,K(y,z),y) = x.
K(x,y \ x) = K(y,x).
x \ T(x,y) != z | K(x,y) = z.
K(T(x,y),z) * T(x,y) = T(T(x,z),y).
(x * K(y,z)) \ (x * T(y,z)) = L(y,K(y,z),x).
L(x,K(y,z),z) = x.
K((x * y) \ x,x * y) = K(x,y).
x * T(x \ 1,y) != z | K(x \ 1,y) = z.
T(x,y) * K(z,T(x,y)) = T(x * K(z,x),y).
R(x,y,x) = T(x * K(x * z,x),z).
K((x * y) \ x,x * y) = K(y \ 1,x * y).
R(x * T(x \ 1,y),z,u) = K(R(x,z,u) \ 1,y).
(x / y) * K(y \ 1,z) = x * T(x \ (x / y),z).
x * K((x \ y) \ 1,z) = y * T(y \ x,z).
K((x / y) \ 1,z) * y = x * T(x \ y,z).
x * (y * T(y \ (x \ y),z)) = K(x \ 1,z) * y.
(x * y) * (z * T(z \ L(y \ z,y,x),u)) = (x * K(y \ 1,u)) * z.
K(x * y,x) = K(y,x).
K(x * y,x) != z | K(y,x) = z.
x \ T(x * K(y,z),y) = K(x,y) * K(y,z).
K(x,y) * (T(x,y) \ z) = x \ z.
K(x,y) * K(y,x) = 1.
T(x,y) * (x \ z) = K(x,y) * z.
K(x,y) * (x * z) = T(x,y) * z.
(x * y) * (K(x * y,x) * z) = (y * x) * z.
1 / K(x,y) = K(y,x).
K(x,y) \ 1 = K(y,x).
1 / K(x,y) != z | K(y,x) = z.
K(x,y) * K(y,x) != z | 1 = z.
K(x,y) \ (z * T(x,y)) = x * T(z,T(x,y)).
K(x * y,x) * ((x * y) * z) = (y * x) * z.
x \ T(x * y,y) = y * K(y * x,y).
L(x * T(x \ 1,y),z,u) != w | K(L(x,z,u) \ 1,y) = w.
K(x,T(y,z)) = T(K(x,y),z).
T(K(x,y),y * z) = K(x,T(y,z)).
K(x,T(y,z)) * T(u,z) = T(K(x,y) * u,z).
T(x,y) * K(z,T(u,y)) = T(x * K(z,u),y).
x * K(y,T(z,x)) = K(y,z) * x.
K(x \ 1,y * x) = K(y,x).
((x \ (y / z)) * x) * z = y * K((y \ (x * z)) \ 1,x).
(x * y) * K(((x * y) \ x) \ 1,z) = x * T(y,z).
K((x / (x * y)) \ 1,z) * (x * y) = x * T(y,z).
(x * y) * (K(y,x) * z) = (y * x) * z.
(x * y) * (K(y,x) * K(y * x,z)) = T(y * x,z).
K(x,y) * ((x * y) \ z) = (y * x) \ z.
K(x,y) * (K(y,x) * z) = z.
K(x,y) \ z = K(y,x) * z.
x / (K(y,z) * x) = K(z,y).
K(x,y) * (y \ z) = T(y,x) \ z.
K(x,y) * T(K(y,x),z) = K(K(y,x),z).
K(x,y) \ z != u | K(y,x) * z = u.
L(x \ (K(y,z) * u),x,K(z,y)) = (K(z,y) * x) \ u.
T(x,y) * (K(y,x) * z) = x * z.
T(x * K(y,z),x) = K(z,y) \ x.
K(x,y) \ (y * z) = T(y,x) * z.
x \ (K(y,z) \ x) = T(K(z,y),x).
L(K(x,y) * (z \ u),K(y,x),z) = (z * K(y,x)) \ u.
T(x,y) \ (x * z) = K(y,x) * z.
K(x,y / z) * (z * T(z \ y,x)) = y.
x * (T(x,y) \ z) = K(y,x) * z.
T(x,y) * (T(y,x) * z) = x * (y * z).
(x * K(y,z)) \ x = K(z,y).
x / K(y,z) = x * K(z,y).
(x * K(y,z)) * K(z,y) = x.
x * K(y,z) != u | u * K(z,y) = x.
x / K(y,z) != u | x * K(z,y) = u.
T(x * K(y,z),K(z,y)) = K(z,y) \ x.
R((x / y) * K(z,u),K(u,z),y) = x / (K(u,z) * y).
T(x * K(y,z),K(z,y)) = K(y,z) * x.
(K(x,y) * z) * K(T(y,z),x) = z.
(x * K(y,z)) \ x != u | K(z,y) = u.
K(x,y) * (z * L(T(K(y,x),z),u,w)) = (K(x,y) * L(K(x,y) \ 1,u,w)) * z.
((x * y) * (K(y,x) * (T(y * x,z) \ u))) / u = K(z,y * x).
K(x,y) * (y * z) = y * (K(x,y) * z).
K(T(x,y),T(z,y)) * (T(x * z,y) \ u) = (T(z,y) * T(x,y)) \ u.
K(x,(y * z) / (y * (u \ z))) * ((y * (u \ z)) * T(L(T(u,u \ z),u \ z,y),x)) = y * z.
T(x * K(y,z),K(z,y)) != u | K(y,z) * x = u.
T(T(x,K(y,z)),K(z,y)) = x.
x * K(K(y,z),x) = T(x,K(z,y)).
K(K(x,y),z) = K(z,K(y,x)).
K(x,K(y,z)) * K(x,K(z,y)) = 1.
K(x,y) * T(K(y,x),z) = K(z,K(x,y)).
K(x,K(y,z)) * u != 1 | K(x,K(z,y)) = u.
K(x,K(y,z)) \ 1 != u | K(x,K(z,y)) = u.
K(x,y) * K(y,T(x,z)) = K(z,K(x,y)).
K(x,y) * K(y,T(x,z)) = K(x * z,K(x,y)).
K(K(x,y),z) != u | K(z,K(y,x)) = u.
K(x,y) * T(K(y,x),z) != u | K(z,K(x,y)) = u.
K(x,y) * ((y * x) * z) = (x * y) * z.
K(x,y) * (y * (x * z)) = (x * y) * L(z,x,y).
K(x,T(y,z)) * T(x,z) = T(T(x,y),z).
K(T(x,y),z) = K(x,T(z,y)).
K((x * y) / x,T(z,x)) = K(y,z).
K(x * y,T(z,x)) = K(y * x,z).
x * K(T(y,x),z) = K(y,z) * x.
(K(x,y) * z) * K(y,T(x,z)) = z.
K((x * y) / x,z) * x = x * K(y,z).
K(L(x,y,z) * u,x) = K(u * L(x,y,z),x).
K(x * y,K(y,z)) = K(y * x,K(y,z)).
x * K(T(y,x),z) = K(z,y) \ x.
T(x * K(y * z,u),y) = T(x,y) * K(z * y,u).
K(x * L(y,z,u),T(y,x)) = K(x * L(y,z,u),y).
K(x,y) * K(y,T(x,z)) != u | K(z,K(x,y)) = u.
x * (K(y,x) * (y * z)) = (y * x) * L(z,y,x).
K(x * y,K(x,z)) != u | K(y,K(x,z)) = u.
K(x * y,K(y,z)) != u | K(x,K(y,z)) = u.
(x * y) * L(z,x,y) = y * (T(x,y) * z).
x * (T(y,x) * T(z,y * x)) = L(z,y,x) * (y * x).
R(K(x \ 1,y),z,u) = K(R(x,z,u) \ 1,y).
K(R(x,y,z) \ 1,u) * (y * z) = (K(x \ 1,u) * y) * z.
((x / y) * K(y \ 1,z)) * y = x * (y * T(y \ (x \ x),z)).
x * (y \ T(y * (x \ (y \ 1)),z)) = K(x \ 1,z) * (y \ 1).
a(x,y,x) = K(z,u) * K(z * u,z).
x \ R(x,y,x) = K(z,u) * K(z * u,z).
T(x,y) * K(x * y,x) = R(x,y,x).
(x * T(y,z)) \ (x * R(y,z,y)) = L(K(y * z,y),T(y,z),x).
(x * K(y,x)) \ z = K(x,y) * (x \ z).
x * K((x \ (y * z)) \ 1,y) = z * ((y \ (z \ x)) * y).
L(K(x \ 1,y),z,u) != w | K(L(x,z,u) \ 1,y) = w.
L(K(x \ 1,y),z,u) = K(L(x,z,u) \ 1,y).
L(K(x \ 1,y),z,x) = K(x \ 1,y).
K(L(x \ 1,y,z) \ 1,u) = L(K(x,u),y,z).
(x * y) * K(x \ 1,z) = x * (y * K(x \ 1,z)).
K(x,L(y \ 1,z,u) \ 1) * w = L(K(y,x),z,u) \ w.
R(x,y,K(x \ 1,z)) = x.
R(T(x,y),z,K(x \ 1,u)) = T(x,y).
R(x,y,K(z,x \ 1)) = x.
R(x,y,K(z,x)) = x.
(R(x,y,z) * u) * K(w,x) = R(x,y,z) * (u * K(w,x)).
L(K(x,y),z,R(y,u,w)) = K(x,y).
L(K(x,y),z,y) = K(x,y).
(K(x \ 1,y) * z) * x = K(x \ 1,y) * (z * x).
L(x,y,K(x \ 1,z)) = x.
L(x,y,K(z,x \ 1)) = x.
L(x,y,K(z,x)) = x.
((x / y) * K(y \ 1,z)) * y = x * (y * T(y \ 1,z)).
((x / y) * K(y \ 1,z)) * y = x * K(y \ 1,z).
(x * K(y \ 1,z)) * y = (x * y) * K(y \ 1,z).
(x * K(y \ 1,z)) \ ((x * y) * K(y \ 1,z)) = y.
((x * y) * K(y \ 1,z)) / (K(y \ 1,z) * y) = R(x,K(y \ 1,z),y).
R(T(x,y * K(x \ 1,z)),y,K(x \ 1,z)) = T(x,y).
T(x,y * K(x \ 1,z)) = T(x,y).
T(x,K(y,x \ 1) * z) = T(x,z).
T(x,K(y,1 / x) * z) = T(x,z).
K(K(x,1 / y) * z,y) = y / T(y,z).
K(K(x,1 / y) * z,y) = K(z,y).
K(K(x,y \ 1) * z,y) = K(z,y).
K(x * K(y,z \ 1),z) = K(x,z).
K(x * K(y \ 1,z),y) = K(x,y).
K(x * K(y,z),z) = K(x,z).
K(x * K(y,z),z) = 1 / K(z,x).
K(K(x,y) * z,x) = K(z,x).
K(K(x,y) \ z,x) = K(z,x).
K((x * y) \ z,y) = K((y * x) \ z,y).
K(x * K(y,z),z) != u | K(x,z) = u.
K(x \ T(y,z),z) != u | K(x \ y,z) = u.
K(x \ (y \ (z * y)),y) != u | K(x \ z,y) = u.
K(x \ ((y \ z) * y),y) != u | K(x \ z,y) = u.
K(x \ ((y \ z) * y),y) = K(x \ z,y).
T(x * K(y * L(x,z,u),x),y) = R(x,y,L(x,z,u)).
T(x,y) * K(y * L(x,z,u),T(x,y)) = R(x,y,L(x,z,u)).
T(x,y) * K(y * L(x,z,u),x) = R(x,y,L(x,z,u)).
(x * T(y,z)) \ (x * R(y,z,L(y,u,w))) = L(K(z * L(y,u,w),y),T(y,z),x).
(x * y) * (z \ T(z * L(y \ (z \ 1),y,x),u)) = (x * K(y \ 1,u)) * (z \ 1).
((x * y) * K(y \ 1,z)) / (y * K(y \ 1,z)) = R(x,K(y \ 1,z),y).
R(x,K(y \ 1,z),y) != u | R(x,y,K(y \ 1,z)) = u.
x * ((x \ T(x,y)) * T(z,T(x,y))) = z * (x * (x \ T(x,y))).
(1 / x) * (x * (x \ T(x,y))) = x * ((x \ T(x,y)) * (x \ 1)).
(1 / x) * (x * (x \ T(x,y))) = x * ((x \ 1) * (x \ T(x,y))).
(1 / x) * (x * (x \ T(x,y))) = L(x \ T(x,y),x \ 1,x).
L(x \ T(x,y),x \ 1,x) = (1 / x) * T(x,y).
L(x \ T(x,y),x \ 1,x) = x \ T(x,y).
L(x \ (x * K(x,y)),x \ 1,x) = x \ T(x,R(y,x,(y * x) \ x)).
x \ T(x,R(y,x,(y * x) \ x)) = L(K(x,y),x \ 1,x).
L(K(x,y),x \ 1,x) = x \ (x * K(x,y)).
L(K(x,y),x \ 1,x) != z * u | z \ K(x,y) = u.
(x \ 1) * K(x,y) = x \ K(x,y).
K(x,y) * (x \ 1) = x \ K(x,y).
(x \ 1) / (x \ K(x,y)) = K(y,x).
(K(x,y) * L(K(x,y) \ 1,z,u)) * w = K(x,y) * (L(K(y,x),z,u) * w).
(K(x,y) * L(K(y,x),z,u)) * w = K(x,y) * (L(K(y,x),z,u) * w).
(x * y) * L(z \ T(z * (y \ (z \ 1)),z),y,x) = (x * K(y \ 1,z)) * (z \ 1).
x * (y * (z \ T(z * (y \ (z \ 1)),z))) = (x * K(y \ 1,z)) * (z \ 1).
(x * K(y \ 1,z)) * (z \ 1) = x * (K(y \ 1,z) * (z \ 1)).
(x * K(y \ 1,z)) * (z \ 1) = x * (T(z,y \ 1) \ 1).
(x * K(y,z)) * (z \ 1) = x * (T(z,(1 / y) \ 1) \ 1).
(x * K(y,z)) * (z \ 1) = x * (T(z,y) \ 1).
(x * K(y,z)) * (T(y,z) \ 1) = x * (y \ 1).
(x * K(y * K(z,y),z)) * (y \ 1) = x * ((y * K(z,y)) \ 1).
(x * K(y,z)) * (y \ 1) = x * ((y * K(z,y)) \ 1).
(x * K(y,z)) * (y \ 1) = x * (K(y,z) * (y \ 1)).
R(x,K(y \ 1,z),y) = x.
R(x,y,K(y \ 1,z)) = x.
R(x,y,K(z,y \ 1)) = x.
R(x,y,K(z,y)) = x.
(x * y) * K(z,y) = x * (y * K(z,y)).
R(x,y \ 1,K(z,y)) = x.
R(x,y \ 1,K(z,y)) = (x * u) / u.
(x * y) / y != z | x = z.
L(K(x,y),y,z) = K(x,y).
a(x,y,K(z,y)) = 1.
a(x,T(y,z),K(u,y)) = 1.
L(K(x,y),y,z) = L(K(x,y),y,u).
L(K(x,y),y,z) \ (y * u) = T(y,x) * u.
L(K(x,y),T(y,z),u) = K(x,y).
(x * T(y,z)) \ (x * R(y,z,L(y,u,w))) = K(z * L(y,u,w),y).
(x * T(y,z)) \ (x * R(y,z,y)) = K(y * z,y).
L(K(x,y),y,z) != u | K(x,y) = u.
K(x * L(y,z,u),y) = (w * T(y,x)) \ (w * R(y,v5,y)).
K(x * L(y,z,u),y) = K(y * x,y).
K(x,(y * z) / (y * (u \ z))) * (y * ((u \ z) * T(T(u,u \ z),x))) = y * z.
K(x,(y * z) / (y * (u \ z))) * (y * (T(u,x) * (u \ z))) = y * z.
K(x,(y * z) / (y * (u \ z))) * (y * (K(u,x) * z)) = y * z.
(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,z) * ((u * (L(x,y,z) \ 1)) / u) = L(x * ((u * (x \ 1)) / u),y,z).
L(x * ((y * (x \ 1)) / y),z,u) = y \ T(y,L(x,z,u) \ 1).
L(x \ T(x,y \ 1),z,u) = x \ T(x,L(y,z,u) \ 1).
L(x \ T(x,y \ 1),z,u) = K(x,L(y,z,u) \ 1).
L(K(x,y \ 1),z,u) = K(x,L(y,z,u) \ 1).
K(x,L(y \ 1,z,u) \ 1) = L(K(x,y),z,u).
(x * K(L(y \ 1,z,u) \ 1,w)) \ x = L(K(w,y),z,u).
L(K(x,y \ z),y \ z,y) = K(x,(z \ y) \ 1).
L(K(x,y),z,u) \ w = L(K(y,x),z,u) * w.
L(K(x,y),z,u) * (L(K(y,x),z,u) * w) = w.
L(K(x,y),z,u) \ 1 = L(K(y,x),z,u).
L(K(x,y),x,z) = (T(x,y) * u) / (x * u).
L(K(x,y),x,z) = (T(x,y) * R(x \ 1,x,u)) / ((u / (x * u)) * x).
L(K(x,y),z,u) \ w != v5 | L(K(y,x),z,u) * w = v5.
K(x,(y \ z) \ 1) = K(x,z \ y).
K(x,(y \ z) \ 1) != u | K(x,z \ y) = u.
K(x,(y \ z) \ 1) = K(z \ y,x) \ 1.
K(x,(y * z) \ y) = K(x,z \ 1).
x \ R(x,y,x) = K(z,u \ w) * K(z * ((w \ u) \ 1),z).
K(x,L(y \ z,u,w) \ 1) = L(K(x,z \ y),u,w).
K(x * y,x) = K(x,y \ 1).
K(x,y \ 1) = K(y,x).
K(x \ y,z) = K(z,y \ x).
R(x,y,K(x,z)) = x.
L(x,y,K(x,z)) = x.
R(x,y,K(y,z)) = x.
(x * y) * K(x,z) = x * (y * K(x,z)).
R(x,y * z,K(z,y)) = x.
(x * (y * z)) * K(z,y) = x * (z * y).
K((x \ y) \ 1,z) = K(y \ x,z).
K(((x * y) \ x) \ 1,z) = K(y,z).
K(L(x \ y,x,z) \ 1,u) = K((z * y) \ (z * x),u).
x * K(y \ x,z) = y * T(y \ x,z).
x * K((y * z) \ x,y) = z * ((y \ (z \ x)) * y).
K(L(x \ y,z,u) \ 1,w) = L(K(y \ x,w),z,u).
(x * y) * K(y,z) = x * T(y,z).
(x * T(y,z)) * K(z,y) = x * y.
(x / y) * T(y,z) = x * K(y,z).
K(x,y) \ (z * T(x,y)) = T(z * x,K(x,y)).
(x * y) \ (x * T(y,z)) = K(y,z).
(x * y) \ (y * T(x,z)) = K(y,x) * K(x,z).
(x * T(x \ y,z)) \ y = K(z,x \ y).
(x * T(y,z)) / y = x * K(y,z).
(x * K(y,z)) \ (x * T(y,z)) = y.
(x \ y) \ (K(x,z) * T(T(x,z) \ y,u)) = K(T(x,z) \ y,u).
L(x,K(x,y),z) = x.
((x / y) * K(y,z)) \ (x * K(y,z)) = y.
(x * K(y,z)) * L(y,u,w) = x * (K(y,z) * L(y,u,w)).
L(x,K(y,x),z) = x.
(x * K(y,z)) * T(z,u) = x * (K(y,z) * T(z,u)).
L(K(x,y),z,x) = K(x,y).
L(K(x,y),z,x) = u \ (u * K(x,y)).
L(K(x,y),z,x) != u | K(x,y) = u.
(x * (y * z)) * u != x * (z * y) | K(z,y) = u.
x \ T(x * y,z) = y * K((x \ 1) \ y,z).
x \ T(y * (T(y,z) \ x),z) = K(T(y,z) \ x,z).
x * K(y,x \ z) = z * T(z \ x,y).
(x * (y * T(y \ (x \ z),u))) \ z = K(u,(x * y) \ z).
((x * T(x \ y,z)) * u) \ (y * u) = K(z,(x * u) \ (y * u)).
(x * K(y,z)) * T((x * K(y,z)) \ ((x / y) * K(y,z)),u) = ((x / y) * K(y,z)) * K(u,y).
K(x,L(y \ z,y,u) \ 1) != w | K(x,(u * z) \ (u * y)) = w.
T(x * y,K(y,z)) = y * T(x,T(y,z)).
(x * y) \ (y * T(x,T(y,z))) = K(z,K(y,x)).
K((x \ 1) \ y,y) = K(y * x,y).
K(x * (y \ 1),x) = K(y \ x,x).
(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)).
K(x,K(y,z)) * K(z,K(x,y)) = 1.
K(x,K(y,z)) = K(y,K(x,z)).
K(x,K(y,z)) = K(z,K(x,y)).
K(x,K(y,z)) = K(x,K(z,y)).
K(x,y) * K(y,T(x,z)) = K(x,K(y,z)).
x * K(x,K(y,z)) = T(x,K(z,y)).
T(x,K(y,z)) != u | T(x,K(z,y)) = u.
T(T(x,K(y,z)),K(y,z)) = x.
(x * K(y,z)) / x = T(K(y,z),x).
(x * K(y,z)) / x = K(y,T(z,x)).
K(x,T(y,z)) * z != z * u | K(x,y) = u.
K(x * y,z) * K(z,y * x) = K(x * y,K(z,x)).
K(T(x,y),T(z,y)) = K(x,z).
K(L(T(x,y),z,u),T(w,y)) = K(L(x,z,u),w).
(T(x,y) * T(z,y)) \ u = K(z,x) * (T(z * x,y) \ u).
R(x,K(y,z),T(z,u)) = x.
(x * K(y,z)) * T(z,y) = x * z.
x / (K(y,z) * T(z,u)) = (x / T(z,u)) * K(z,y).
T(x,y) / T(x,z) = K(x,y) * K(z,x).
(x / y) * K(z,y) = x / T(y,z).
x / T(y \ x,z) = y * K(z,y \ x).
(x * T(y,z)) * T(z,y) = (x * y) * z.
(x / y) * K(y,z \ u) = x / T(y,u \ z).
(x / y) * K(z,(x / y) \ x) = x / T(y,z).
(x * T(y,L(z,y,x))) \ (x * (y * z)) = T(L(z,y,x),y).
x * T(x \ (x / y),z) = x / T(y,z).
x \ T(K(y,z) * x,y) = K(T(z,y) \ x,y).
K(x * y,z) * K(z,y * x) = K(z,K(x * y,x)).
K(x * y,z) * K(z,y * x) = K(z,K(y,x)).
K(x * y,z) * K(z,y * x) = K(x,K(y,z)).
L(K(x \ y,z),y,u) = K((u * x) \ (u * y),z).
L(K((x \ y) \ z,u),z,x) = K(y \ (x * z),u).
K((x * (y / z)) \ (x * y),u) = L(K(z,u),y,x).
L(K((K(x,y) * z) \ u,w),u,K(y,x)) = K(z \ (K(y,x) * u),w).
K((x \ y) \ z,z) = K(y \ (x * z),z).
K(L(x,y / x,z),u) = L(K(x,u),y,z).
K(L(x,y / x,z),u) = (z * y) \ (z * (y * K(x,u))).
L(K(x,y),z * x,u) = K(L(x,z,u),y).
K(x,L(y,z / y,u)) = L(K(y,x),z,u) \ 1.
L(K(x,y),z,K(u,x)) = K(x,y).
K(L(x,y,z),z) = K(x,z).
(x * (y * z)) / K(L(y,z,x),z) = x * (z * y).
K(L(L(x,y,z),u,w),z) = K(L(x,u,w),z).
K((x * y) \ z,x) = K(y \ (x \ z),x).
K((x * y) \ z,y) = K(x \ (y \ z),y).
x * K(y \ (z \ x),z) = y * ((z \ (y \ x)) * z).
K((x * y) \ (z * y),y) != u | K(x \ z,y) = u.
K(x,L(y,z / y,u)) = L(K(x,y),z,u).
L(K(x,y),z * y,u) = K(x,L(y,z,u)).
L(K(x,y),z,K(y,u)) = K(x,y).
K(x,L(y,z,x)) = K(x,y).
K(x,L(y,z,K(u,x))) = K(x,y).
K(x,L(L(y,z,x),u,w)) = K(x,L(y,u,w)).
K(L(x,y,z),L(u,w,x)) = L(K(x,u),y * x,z).
K(x,L(L(y,z,K(u,x)),w,v5)) = K(x,L(y,w,v5)).
K(x,(K(y,x) * z) \ u) = K(x,z \ (K(x,y) * u)).
(x * (y * z)) * K(z,L(y,z,x)) = x * (z * y).
K((x * y) \ z,y) != u | K(x \ (y \ z),y) = u.
K(L(x,y,z),L(u,w,x)) = K(L(x,y,z),u).
K(x,L(y,x,z)) = K(x,y).
T(x,L(y,x,z)) = x * K(x,y).
T(x,L(y,x,z)) = T(x,y).
(x * ((y \ (x \ z)) * y)) \ z = K(y,x \ (y \ z)).
K(L(x,y / x,z),u) != w | L(K(x,u),y,z) = w.
(x * L(K(y,z),u,w)) \ x = L(K(z,y),u,w).
(x * (y * K(z,u))) * L(K(u,z),y,x) = x * y.
(x * (K(y,z) * u)) * L(K(z,T(y,u)),u,x) = x * u.
(x * (K(y,z) * u)) \ (x * u) != w | L(K(z,T(y,u)),u,x) = w.
(x * (y * (z * T(z \ (y \ (x \ u)),w)))) \ u = K(w,(x * (y * z)) \ u).
K(x,(y * K(x,z)) \ u) = (y * T(y \ u,x)) \ u.
K(x,(y * K(x,z)) \ u) = K(x,y \ u).
K(x,(y * K(z,x)) \ u) = K(x,y \ u).
K(x,(K(y,x) * z) \ u) = K(x,z \ u).
K(x,(y * L(K(z,x),u,w)) \ v5) = K(x,y \ v5).
K(x,y \ (K(x,z) * u)) = K(x,y \ u).
K(x,y \ (z * (K(u,x) * w))) = K(x,y \ (z * w)).
K(x,(y * (z * K(u,x))) \ w) = K(x,(y * z) \ w).
K(x,L(L(y,z,K(u,x)),K(u,x) * z,w)) = K(x,(w * (K(u,x) * z)) \ (w * (z * y))).
K(x,(y * (K(z,x) * u)) \ w) = K(x,(y * u) \ w).
K(x,y) * (T(x * y,z) \ u) = T(y * x,z) \ u.
((x * y) * (T(x * y,z) \ u)) / u = K(z,y * x).
(K(x,y * z) * u) / u = K(x,z * y).
K(x,y * z) = K(x,z * y).
K(x * y,z) * K(z,x * y) = K(x,K(y,z)).
K(x,K(y,z)) = 1.
T(x,K(y,z)) = x.
K(x,y) * z = z * K(x,y).
T(K(x,y),z) = K(x,y).
T(x,T(y,z)) = T(x,y).
x * K(y,z) != u | K(y,z) * x = u.
T(K(x,y),z) = T(K(x,y),u).
K(x,T(y,z)) = K(x,y).
T(K(x,y) * z,u) = K(x,y) * T(z,u).
T(x,y * z) = T(x,z * y).
K(T(x,y),z) = K(x,z).
K(x,y) * T(x,z) = T(T(x,y),z).
(K(x,y) * z) * u = (z * K(x,y)) * u.
x * (y * K(x,z)) = T(x,z) * y.
x \ T(x * K(y,z),y) = K(T(z,y) \ x,y).
T(K(x,y),z) != u | K(x,y) = u.
x * (T(y,x) * T(z,x * y)) = L(z,y,x) * (y * x).
K(x,T(y,z)) != u | K(x,y) = u.
K(x * y,z) != u | K(y * x,z) = u.
T(x,y) * (z * T(y,x)) = x * (z * y).
T(x * K(y,z),u) = K(y,z) * T(x,u).
(x * (y * z)) / (T(y,x) * T(z,T(x,y))) = T(T(x,y),z).
K(T(x,y) \ z,y) = K(z,y) * K(y,x).
(x * T(y,L(z,y,x))) \ (x * (y * z)) = L(T(z,y),y,x).
(x * (y * z)) / (T(y,x) * T(z,x)) = T(T(x,y),z).
(x * (y * z)) / T(y * z,x) = T(T(x,y),z).
T(T(x,y),z) = T(x,y * z).
T(T(x,y),z) != u | T(x,y * z) = u.
T(T(x,y),z) = T(x,z * y).
T(x,y) * T(z,y * u) = T(x * T(z,u),y).
T(T(x,y),z) != u | T(x,z * y) = u.
x * T(y * T(z,y),x) = L(z,y,x) * (y * x).
L(x,y,z) * (y * z) = z * T(x * y,z).
L(x,y,z) * (y * z) = (x * y) * z.
(x * T(y,L(z * K(y,z),y,x))) \ (x * (y * (z * K(y,z)))) = L(z,y,x).
x \ R(x,y,x) = K(z,u \ w) * K((w \ u) \ z,z).
K((x \ y) \ z,z) = K(z * (y \ x),z).
K(x \ (y * z),z) = K(z * (x \ y),z).
K(x * ((y * x) \ z),x) = K(y \ z,x).
(x \ y) \ T(K(x,z) * (T(x,z) \ y),u) = K(T(x,z) \ y,u).
(((x / y) * T(y,z)) * u) \ (x * u) = K(z,((x / y) * u) \ (x * u)).
L(K(x,y \ z),z,u) = K(x,(u * y) \ (u * z)).
L(K(x,(y \ z) \ u),u,y) = K(x,z \ (y * u)).
K(T(x,y) \ z,u) = (x \ z) \ T(x \ z,u).
K(T(x,y) \ z,u) = K(x \ z,u).
K(T(x,y) \ z,u) = K(u,z \ x).
K(x,y) * K(y,z) = K(y,x \ z).
K(x,y) * K(z,x) = K(x,z \ y).
T(x,y) / T(x,z) = K(x,z \ y).
K((K(x,y) * z) \ u,y) = K(z \ (K(y,x) * u),y).
(T(x,y) * R(x \ 1,x,z)) / ((z / (x * z)) * x) != u | K(x,y) = u.
K(x,((y / z) * u) \ (y * u)) = ((y * K(z,x)) * u) \ (y * u).
((x * K(y,z)) * u) * K(z,((x / y) * u) \ (x * u)) = x * u.
K(x,((y / z) * L(z,u,w)) \ (y * L(z,u,w))) = (y * (K(z,x) * L(z,u,w))) \ (y * L(z,u,w)).
((x * K(y,z)) * K(y,u)) * K(z,y) = x * K(y,u).
(x * K(y,z)) * K(u,y) = (x * K(u,y)) * K(y,z).
L(K(x,y),x,z) = K(x,y).
L(K(x,y),K(y,z) * x,u) = K(K(y,z) * x,y).
K(L(x,K(y,z),u),y) = K(K(y,z) * x,y).
K(L(x,K(y,z),u),y) = K(x,y).
K((x * K(y,z)) \ u,y) = K(K(y,z) \ (x \ u),y).
K((x * K(y,z)) \ u,y) = K(x \ u,y).
K((K(x,y) * z) \ u,y) = K(z \ u,y).
K((x * (y * z)) \ u,z) = K((x * (z * y)) \ u,z).
K(x \ (K(y,z) * u),y) = K(x \ u,y).
K(x \ (K(y,z) * u),z) = K(x \ u,z).
K(x \ (y * T(z,u)),u) = K(x \ (y * z),u).
K(x \ (y * (z * u)),u) = K(x \ (y * (u * z)),u).
K((x * (y * z)) \ (x * ((z * u) * y)),y) = K(L(L(u,z,y),y * z,x),y).
(x * (y * ((z \ (y \ (x \ u))) * z))) \ u = K(z,(x * (y * z)) \ u).
((x * y) * ((z \ ((x * y) \ u)) * z)) \ u = K(z,(x * (y * z)) \ u).
K(x,(y * (z * x)) \ u) = K(x,(y * z) \ (x \ u)).
(x * K(y,(z * u) \ (y \ w))) \ x = K((z * (u * y)) \ w,y).
K((x * (y * z)) \ u,z) = K((x * y) \ (z \ u),z).
K((x * (y * z)) \ u,y) = K((x * z) \ (y \ u),y).
(x * T(y,L(z,y,x))) \ (x * (y * (z * K(y,z)))) = L(z,y,x).
(x * T(y,L(z,y,x))) \ (x * (T(y,z) * z)) = L(z,y,x).
L(x,y,z) = (z * T(y,x)) \ (z * (T(y,x) * x)).
L(x,T(y,x),z) = L(x,y,z).
L(x,y / x,z) = L(x,x \ y,z).
K(L(x,x \ y,z),u) = L(K(x,u),y,z).
K(L(x,x \ y,z),u) != w | L(K(x,u),y,z) = w.
L(K(x,y),x * z,u) = K(L(x,z,u),y).
K(L(x,T(x,y) \ 1,z),u) = L(K(x,u),K(y,x),z).
K(L(x,y,z),(z \ u) \ (x * y)) = K(x,u \ (z * (x * y))).
L(K(x,y),T(x,z) * u,w) = K(L(T(x,z),u,w),T(y,z)).
L(K(x,y),T(x,z) * u,w) = K(L(x,u,w),y).
K(L(x,T(x,y) \ z,u),w) = L(K(x,w),z,u).
K(L(x,T(x,y) \ 1,z),u) != w | K(x,u) = w.
L(K(x,y),K(z,x),u) = K(x,y).
(x * K(y,z)) * K(z,u) = x * (K(y,z) * K(z,u)).
(K(x,y) * K(z,x)) * u = K(x,y) * (K(z,x) * u).
(x * K(y,z)) * K(u,y) = x * (K(u,y) * K(y,z)).
K(L(x,y * z,u),(u \ (u * (x * y))) \ (x * (y * z))) = K(x,L(L(z,y,x),x * y,u)).
K((x * (y * z)) \ (x * ((z * u) * y)),y) = K(L(u,y * z,x),y).
K((x * y) \ (z \ (x * ((y * u) * z))),z) = K(L(u,z * y,x),z).
K(x,(y * (K(z,x) * u)) \ (y * (u * w))) = K(x,L(w,K(z,x) * u,y)).
K(x,L(y,K(z,x) * u,w)) = K(x,(w * u) \ (w * (u * y))).
K(x,L(y,K(z,x) * u,w)) = K(x,L(y,u,w)).
K(x,L(y,K(x,z) * u,w)) = K(x,L(y,u,w)).
K(L(x,K(y,z) * u,w),y) = (y \ 1) / (y \ K(y,L(x,u,w))).
K(L(x,K(y,z) * u,w),y) = K(L(x,u,w),y).
K(L(x,T(y,z),u),z) = K(L(x,y,u),z).
K(L(x,y * z,u),(x * y) \ (x * (y * z))) = K(x,L(L(z,y,x),x * y,u)).
K(L(x,y * z,u),L(z,y,x)) = K(x,L(L(z,y,x),x * y,u)).
K(L(x,y * z,u),z) = K(x,L(L(z,y,x),x * y,u)).
K(L(x,y * z,u),z) = K(x,L(z,x * y,u)).
K(L(x,(x \ y) * z,u),z) = K(x,L(z,y,u)).
K(L(x,T(y * (x \ z),y),u),R(y,x \ z,y)) = K(x,L(R(y,x \ z,y),z,u)).
K(L(x,T(y * (x \ z),y),u),y) = K(x,L(R(y,x \ z,y),z,u)).
K(x,L(R(y,x \ z,y),z,u)) = K(L(x,y * (x \ z),u),y).
K(L(x,y * (x \ z),u),y) != w | K(x,L(y,z,u)) = w.
(x * K(y,z)) * T((x * K(y,z)) \ ((x / y) * K(y,z)),u) = (x / y) * (K(u,y) * K(y,z)).
(x * K(y,z)) * T((x * K(y,z)) \ ((x / y) * K(y,z)),u) = (x / y) * K(y,u \ z).
(x * K(y,z)) * T((x * K(y,z)) \ ((x / y) * K(y,z)),u) = x / T(y,z \ u).
(x * T(x \ (x / y),z)) * K(y,u) = x / T(y,u \ z).
(x / T(y,z)) * K(y,u) = x / T(y,u \ z).
T((K(x,y) * T(T(x,y \ z),u)) / T(x,z),K(x,y)) = K(T(x,y \ z),u).
K(x,y) * T(y,z) = T(y,x \ z).
T(x * K(y,x),z) = T(x,y \ z).
T(T(x,y \ x),z) = T(x,y \ z).
T(x,y * (z \ x)) = T(x,z \ y).
T(T(T(x,y),z),u \ x) = T(T(x,u \ y),z).
T(T(x,y * z),u \ x) = T(T(x,u \ y),z).
T(x,(y * z) * (u \ x)) = T(T(x,u \ y),z).
T(T(x,y \ z),u) = T(x,y \ (z * u)).
T(x,y \ (z * u)) = T(x,u * (y \ z)).
T(x,y * (z \ 1)) = T(x,z \ y).
T(x,(1 / y) \ z) = T(x,z * y).
K((1 / x) \ y,z) = T(z,y * x) \ z.
K((1 / x) \ y,z) = K(y * x,z).
K(x * (y \ 1),z) = K(y \ x,z).
K((x \ 1) * y,z) = K(x \ y,z).
K(x \ L(y,z,u),y) = K(y * (x \ 1),y).
K(x \ L(y,z,u),y) = K(x \ y,y).
T((K(x,y) * T(x,z * (y \ u))) / T(x,u),K(x,y)) = K(T(x,y \ u),z).
T(T(T(x,y),z * (y \ u)) / T(x,u),K(x,y)) = K(T(x,y \ u),z).
T(T(x,y * (z * (y \ u))) / T(x,u),K(x,y)) = K(T(x,y \ u),z).
T(K(x,y \ (z * (u * (z \ y)))),K(x,z)) = K(T(x,z \ y),u).
K(x,y \ (z * (u * (z \ y)))) = K(T(x,z \ y),u).
K(x,y \ (z * (u * (z \ y)))) = K(x,u).
K(x,((y / z) * L(z,u,w)) \ (y * L(z,u,w))) = L(K(x,T(z,L(z,u,w))),L(z,u,w),y).
K(x,((y / z) * L(z,u,w)) \ (y * L(z,u,w))) = L(K(x,z),L(z,u,w),y).
L(K(x,y),L(y,z,u),w) = K(x,y).
K((x \ y) \ L(z,u,w),z) = K(y \ (x * L(z,u,w)),z).
K(x \ (y * L(z,u,w)),z) = K((y \ x) \ z,z).
K(x \ (y * L(z,u,w)),z) = K(z * (x \ y),z).
K(x \ (y * (z * u)),u) = K(u * (x \ (y * z)),u).
K(x \ (y \ (z * (u * y))),y) = K(y * ((x * y) \ (z * u)),y).
K(x \ (y \ (z * (u * y))),y) = K(x \ (z * u),y).
K(L(x,y * z,u),y) = K((u * z) \ (u * (z * x)),y).
K(L(x,y * z,u),y) = K(L(x,z,u),y).
K(L(x,x \ y,z),u) = K(x,L(u,y,z)).
L(K(x,y),z,u) = K(x,L(y,z,u)).
(x * y) * K(z,L(u,y,x)) = x * (y * K(z,u)).
L(K(x,y),K(y,z),u) = K(x,y).
(K(x,y) * K(y,z)) * u = K(x,y) * (K(y,z) * u).
(x * (x \ y)) * K(z,y \ (x * u)) = x * ((x \ y) * K(z,(x \ y) \ u)).
(K(x,y) * K(z,x)) * u = K(z,x) * (K(x,y) * u).
K(x,y) * (K(z,x) * u) = K(z,x) * (K(x,y) * u).
K(L(x,y / x,z),u) * (K(u,w) * v5) = K(u,w) * (L(K(x,u),y,z) * v5).
x * ((x \ y) * K(z,(x \ y) \ u)) = y * K(z,y \ (x * u)).
x * K(y,x \ (z * (u * (z \ x)))) = z * ((z \ x) * K(y,T(u,z \ x))).
L(K(x,y),z,u) * (K(y,w) * v5) = K(y,w) * (L(K(x,y),z,u) * v5).
x * K(y,x \ (z * (u * (z \ x)))) = z * ((z \ x) * K(y,u)).
x * ((x \ y) * K(z,u)) = y * K(z,u).
(x * y) * K(z,u) = x * (y * K(z,u)).
a(x,y,K(z,u)) = 1.
a(x,y,K(z,u)) = a(w,v5,K(v6,v7)).
T(x,a(y,z,K(u,w))) = x.
a(x,y,a(z,u,K(w,v5))) = 1.
(a(x,y,K(z,u)) \ w) * a(x,y,K(z,u)) = w.
L(a(x,y,K(z,u)),w,v5) = a(x,y,K(z,u)).
L(K(x,y),z,u) \ K(x,y) = a(u,z,K(x,y)).
L(K(x,y),z,u) * K(y,x) = a(u,z,K(y,x)).
a(x,y,K(z,u)) != w | K(z,u) * L(K(u,z),y,x) = w.
a(x,y,K(z,u)) = K(w,v5) * L(K(v5,w),v6,v7).
L(K(x,y),z,u) = L(K(x,y),w,v5).
a(x,y,K(z,u)) * w = K(v5,v6) * (L(K(v6,v5),v7,v8) * w).
L(K(x,y),z,u) * (w * v5) = (K(x,y) * w) * v5.
a(x,y,K(z,u)) * (L(K(w,v5),v6,v7) * v8) = K(w,v5) * v8.
a(x,y,K(z,u)) \ w = L(K(v5,v6),v7,v8) * (K(v6,v5) * w).
a(x,y,K(z,u)) \ w = K(v5,v6) * (L(K(v6,v5),v7,v8) * w).
a(x,y,K(z,u)) \ w = a(v5,v6,K(v7,v8)) * w.
(a(x,y,K(z,u)) * w) * a(v5,v6,K(v7,v8)) = w.
L(K(x,y),z,u) * w = (K(x,y) * w) * a(v5,v6,K(v7,v8)).
(K(x,y) * (z * u)) * a(w,v5,K(v6,v7)) = (K(x,y) * z) * u.
a(K(x,y),z,u) = a(w,v5,K(v6,v7)).

end_of_list.
