% ********************************************************************
% AIM:  middle Bol + nil3 26 => nilpotency class 3
%
% From previous results, it suffices to prove nil3 24.
%
% Extra assumptions:
%
%    x * ((y * z) \ x) = (x / z) * (y \ x) # label("middle Bol").
%    a(a(x,y,a(z,u,w)),v5,v6) = 1   # label("nil3 26, aa3-Nl").
%
% This version includes the aK goals (lemmas of mbol) as assumptions.
% ********************************************************************

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

clear(back_demod).
set(restrict_denials).

set(para_from_small).
clear(cac_redundancy).

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.

   % 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
   
   % L(u,x,y) = u L(x) L(y) L(yx)^{-1}
   (y * x) \ (y * (x * u)) = L(u,x,y).

   % R(u,x,y) = u R(x) R(y) R(xy)^{-1}
   ((u * x) * y) / (x * y) = R(u,x,y).

   % T(u,x) = u R(x) L(x)^{-1}
   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).

   % extra assumptions for this special case
   x * ((y * z) \ x) = (x / z) * (y \ x) # label("middle Bol").
   a(a(x,y,a(z,u,w)),v5,v6) = 1   # label("nil3 26, aa3-Nl").

   % proved lemmas
   a(K(x,y),z,u) = 1              # label("aK1").
   a(x,K(y,z),u) = 1              # label("aK2").
   a(x,y,K(z,u)) = 1              # label("aK3").
   K(a(x,y,z),u) = 1              # label("Ka").

end_of_list.

formulas(goals).

   a(a(a(x,y,z),u,w),v5,v6) = 1 # label("nil3 24, aa1-Nl").

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(a(a(x,y,z),u,w),v5,v6) = 1.
1 * x = x.
x * 1 = x.
x \ (x * y) = y.
x * (x \ y) = y.
(x * y) / y = x.
(x / y) * y = x.
(x * (y * z)) \ ((x * 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) = (x / z) * (y \ x).
(x / y) * (z \ x) = x * ((z * y) \ x).
a(a(x,y,a(z,u,w)),v5,v6) = 1.
a(K(x,y),z,u) = 1.
a(x,K(y,z),u) = 1.
a(x,y,K(z,u)) = 1.
K(a(x,y,z),u) = 1.
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.
a(x,y,z) != 1 | L(z,y,x) = z.
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 | x / z = y / z.
x != y | x \ z = y \ z.
x != y | y != z | x = z.
a(a(a(c1,c2,c3),c4,c5),c6,c7) != 1.
1 \ x = x.
x \ x = 1.
x \ (x * (y \ (y * z))) = z.
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.
(x / y) \ x = y.
(x * (y * z)) * a(x,y,z) = (x * y) * z.
(x * y) \ ((x * z) * (z \ y)) = a(x,z,z \ y).
(x * (y * ((x * y) \ z))) \ z = a(x,y,(x * y) \ z).
x \ (((x / (y * z)) * y) * z) = a(x / (y * z),y,z).
(x * y) * K(y,x) = y * x.
(x * y) * L(z,y,x) = x * (y * z).
x \ (y * ((y \ x) * z)) = L(z,y \ x,y).
L(x \ y,x,z) = (z * x) \ (z * y).
x \ ((x / y) * (y * z)) = L(z,y,x / y).
L(x,y,z / (y * x)) = ((z / (y * x)) * y) \ z.
R(x,y,(x * y) \ z) = z / (y * ((x * y) \ z)).
((x * y) * (y \ z)) / z = R(x,y,y \ z).
R(x,y,z) * (y * z) = (x * y) * z.
R(x / y,y,z) = (x * z) / (y * z).
T(1,x) = x \ x.
T(x,x) = x.
x * T(y,x) = y * x.
T(x,x \ y) = (x \ y) \ y.
T(x / y,y) = y \ x.
x \ (T(y,z) * x) = T(T(y,x),z).
(x * ((y * z) \ x)) / (y \ x) = x / z.
a(1,x,y) = 1.
x != y | 1 * z != y | x = z.
x != y | z * u != y | z \ x = u.
x != y | z * u != y | x / u = z.
x != y | z \ u != y | z * x = u.
x * y != z | x \ z = y.
(x / y) * z != x | y = z.
x * 1 != y | x = y.
x * y != z | z / y = x.
x / y != z | z * y = x.
x \ y != z | x * z = y.
(x * y) \ z != K(y,x) | y * x = z.
x \ (y * z) != K(y,z) | z * y = x.
L(K(x,y),z,u) = K(x,y).
L(x,K(y,z),u) = x.
L(x,y,K(z,u)) = x.
T(a(x,y,z),u) = a(x,y,z).
(x * (x \ y)) * z = y * z.
x * (y * (y \ z)) = x * z.
((x / y) * y) / z = x / z.
(x * (x \ y)) \ z = y \ z.
(x * y) / y = (x / z) * z.
(x / y) * y = x * 1.
((1 / x) * x) \ y = y.
a(x,y,K(z,u)) = w \ w.
x * (y \ y) = x.
(x / x) * y = y.
T(x,R(x,y,z)) = x.
T(x,T(x,y)) = x.
T(T(x,y),x) = T(x,y).
L(x,y,1) = x.
L(x,y,1) = z \ (z * x).
(x / (y \ x)) * z = y * z.
(x * (y * z)) / L(z,y,x) = x * y.
x * ((y * (z \ x)) \ x) = z * (y \ x).
x / y != z | z \ x = y.
x * (((x / y) * z) \ x) = (x / z) * y.
x \ y != z | y / z = x.
T(1,x) = 1.
T(x,1) = x.
T(x,1) != y | x = y.
x * ((x * y) \ x) = x / y.
x * ((y * x) \ x) = y \ x.
L(x,K(y,z),u) = w \ (w * x).
L(x,K(y,z),u) != w | x = w.
L(x,y,K(z,u)) = w \ (w * x).
L(x,y,K(z,u)) != w | x = w.
L(x \ 1,x,y) = (y * x) \ y.
T((x * y) / x,x) = y.
(x * (y * z)) \ ((x * z) * T(y,z)) = a(x,z,T(y,z)).
(x * (y * T(z,x * y))) \ (z * (x * y)) = a(x,y,T(z,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(x,y) != y \ z | z / y = x.
(x / y) * y != z | x = z.
(1 / x) * (x * y) = L(y,x,1 / x).
K(T(x,y),x) = 1.
T(T((x * 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.
x * y != z | T(x,y) = y \ z.
(x * y) \ (x * (y * K(z,u))) = K(z,u).
(x * y) * K(z,u) = x * (y * K(z,u)).
x * (x \ y) != z | y = z.
(x * y) * L(z,y,x) != u | x * (y * z) = u.
x \ ((x * y) * L(z,y,x)) = y * z.
x * (x \ (y * z)) = y * (u * (u \ z)).
x * K(y \ x,y) = (y \ x) * y.
x * K(y,x / y) = y * (x / y).
x != y | z != y | x = z.
T(x,a(y,z,u)) = x.
a(x,y,z) * u = u * a(x,y,z).
(a(x,y,z) \ u) * a(x,y,z) = u.
(x / (y * (y \ z))) * z = x.
x / (y \ ((x / z) * z)) = y.
((x / y) * y) * z != u | x * z = u.
(x * y) / y != z | x = z.
x / (y \ x) != z | y = z.
(x * y) \ x = x \ (x / y).
(x * y) \ y = y \ (x \ y).
(x / y) \ y = y * (x \ y).
x \ (x * y) != z | y = z.
x \ (y * x) != z | T(y,x) = z.
T((x * y) / x,x) != z | y = z.
R(x,y,y \ z) * z = (x * y) * (y \ z).
x / L(y,z,x / (z * y)) = (x / (z * y)) * z.
x / (x * (y \ x)) = y / x.
(x * y) / x = x / (x / y).
1 / (1 / x) = x.
(x * (y \ x)) / x = x / y.
1 / x = x \ 1.
(x \ 1) \ 1 = x.
(x / y) * x = x * (y \ x).
T(x / y,x) = y \ x.
T(x,y) != z \ y | y / z = x.
T(x,y) = (x \ y) \ y.
T(x,x \ y) = T(x,y).
x / T(y,x) = y \ x.
(x \ y) * T(x,y) = y.
T(x,x \ T(x,y)) = x.
T(x,x * y) = T(x,y).
R(x,y,z) / x = x \ R(x,y,z).
x / T(x,y) = T(x,y) \ x.
(x \ y) * z != y | T(x,y) = z.
(x \ T(x,y)) * x = T(x,y).
(T(x,y) \ x) * T(x,y) = x.
(x \ ((y * x) / y)) * x = (y * x) / y.
(x * K(y,z)) * u = x * (K(y,z) * u).
(K(x,y) * z) * u = K(x,y) * (z * u).
L(x \ 1,x,y) = y \ (y / x).
(K(x,y) * z) \ K(x,y) = z \ 1.
L(T(x,y) \ 1,T(x,y),y) = (x * y) \ y.
x * L(y \ 1,y,x) = x / y.
T(x / y,y) != z | y \ x = z.
K(x,y) * (z \ 1) = K(x,y) / z.
T(x,y) != z | y \ (x * y) = z.
T(T(x,y),z) != u | T(T(x,z),y) = u.
(x * (y \ z)) \ z = z \ (y * (x \ z)).
x != y | z * u != y | T(z,u) = u \ x.
(x * y) * T(L(z,y,x),u) = x * (y * T(z,u)).
T(x / y,z) * y = y * T(y \ x,z).
(x * T(y,z)) / x = T((x * y) / x,z).
K(x,y) * (1 / z) = K(x,y) / z.
x \ (y * L(z,x \ y,x)) = (x \ y) * z.
(x * y) * z != x * (y * u) | L(u,y,x) = z.
(x * y) * L(z,T(x,y),y) = y * (T(x,y) * z).
(x * y) \ (x * (y * z)) != u | L(z,y,x) = u.
L((x \ y) \ z,x \ y,x) = y \ (x * z).
(K(x,y) * z) \ (K(x,y) * u) = z \ u.
(K(x,y) * z) * (z \ u) = K(x,y) * u.
R(x,y,T(z,y)) * (z * y) = (x * y) * T(z,y).
R((x / y) / z,z,y) = x / (z * y).
R(x / (y / z),y / z,z) = (x * z) / y.
(K(x,y) * (z * u)) / u = K(x,y) * z.
(1 / x) \ K(y,z) = x * K(y,z).
(x \ 1) * K(y,z) = x \ K(y,z).
(x * (y \ x)) / (z \ x) = x / (z \ y).
(x * (y \ z)) / z = z / (y * (x \ z)).
((x / y) * z) \ x = x \ ((x / z) * y).
x * (y * T(z,x * y)) = L(z,y,x) * (x * y).
(x * y) * L(T(x,y),z,u) = L(x,z,u) * (x * y).
R((x * y) / x,z,u) * x = x * R(y,z,u).
x * (y * K(y,x)) = y * x.
x * ((x \ y) * K(z,u)) = y * K(z,u).
T(x,y) = x * K(x,y).
x \ K(x \ 1,y) = T(x \ 1,y).
x * T(x \ 1,y) = K(x \ 1,y).
K(x,y) = x \ T(x,y).
T(x,y) \ (K(x,y) * x) = K(K(x,y),x).
T(x,y) != x * z | K(x,y) = z.
x \ T(x,y) != z | K(x,y) = z.
(x * y) \ (x * T(y,z)) = K(y,z).
K(x,y) != x \ z | T(x,y) = z.
T(x,K(x,y)) = x.
T(x,y) = K(x,y) * x.
T(K(x,y),x) = K(x,y).
K(1 / x,y) / x = T(1 / x,y).
K(R(x,y,z),u) * R(x,y,z) = R(T(x,u),y,z).
x * (K(y,x) * y) = y * x.
T(x \ 1,y) != x \ z | K(x \ 1,y) = z.
(x * y) * K(y,z) = x * T(y,z).
x \ (y * T(y \ x,z)) = K(y \ x,z).
x * T(x \ y,z) = y * K(x \ y,z).
K(x \ 1,y) / x = T(1 / x,y).
K(x,y) \ (z * T(x,y)) = T(z * x,K(x,y)).
K(1 / x,y) = K(x \ 1,y).
x * (T(y,x) * K(z,u)) = (y * x) * K(z,u).
(x * (y * z)) * K(z,y) = x * (z * y).
x * (y * (y \ z)) != u | x * z = u.
(x * K(y,x)) * y = y * x.
T(x * K(y,x),y) = x.
(x * y) / x = y * K(x,y).
R(x,K(y,z),u) = x.
(x * y) * (K(y,x) * z) = (y * x) * z.
x * (K(x,y) * z) = T(x,y) * z.
(x * K(y,z)) * y = x * T(y,z).
R(x,K(y,z),u) = L(x,K(w,v5),v6).
(x \ y) * K(y,x \ y) = y / x.
(x \ y) * K(x,x \ y) = y / x.
T(x,y) * K(y,T(x,y)) = x.
T(x,y) != z | z * K(y,z) = x.
((x * K(y,x)) * (y * z)) \ ((y * x) * z) = a(x * K(y,x),y,z).
K(x,y) = y \ ((x * y) / x).
x / (x / y) = y * K(x,y).
(x * y) / x = K(x,y) * y.
x / y != K(y,z) * z | y * z = x.
T(x,y) * T(z,K(x,y)) = x * (z * K(x,y)).
x \ (T(x,y) * z) != u | K(x,y) * z = u.
(x * T(y,z)) / y = x * K(y,z).
(x \ y) * K(x,y) = y / x.
(x / T(y,z)) * K(y,z) = x / y.
(x \ y) * (K(x,y) * z) = (y / x) * z.
K(x,y \ x) = K(y,x).
(x * y) * K(z,y) = x * T(y,z \ y).
T(x,y \ x) = x * K(y,x).
(x * K(y,z)) * z = x * T(z,y \ z).
T(x,y \ x) = (y * x) / y.
T(T(x,y \ x),y) = x.
T(T(x,y),y \ x) = x.
T(x,y) = x * K(y \ x,x).
T(x,(y \ x) \ x) = T(x,y).
K(x \ y,y) = K(y,x).
x * K(y \ z,z) = x * K(z,y).
T(x,T(y,x)) = T(x,y).
T(T(x,y),T(z,x)) = T(T(x,z),y).
T(x,y / x) = T(x,x \ y).
T(x,y) * T(T(y,x),z) = T(y,z) * T(x,y).
x * K(x,x \ y) = T(x,y / x).
K(x,x \ y) = K(x,y).
(x \ y) * (K(x,x \ y) * z) = (y / x) * z.
(x / T(y,z)) \ (x / y) = K(y,z).
K(x,y / x) = K(x,x \ y).
K(x,y / x) = K(x,y).
K(x,x \ (y * x)) = K(x,y).
x * K(y,x) = y * (x / y).
K(x,T(y,x)) = K(x,y).
K(x,T(T(y,x),z)) = K(x,T(y,z)).
T(x,y) * K(y,x) = x.
K(x,y) = T(y,x) \ y.
(x * T(y,z)) * K(z,y) = x * y.
T(x,y) * (K(y,x) * z) = x * z.
T(x,y) * T(y,x) = x * y.
K(x,y) = y / T(y,x).
K(x,y) * T(y,x) = y.
T(x,y) = K(y,x) \ x.
K(x,y) \ y != z | T(y,x) = z.
T(x,y) \ 1 = x \ K(y,x).
K(1 / x,y) \ y = T(y,x \ 1).
T(x,y \ x) = y * (x / y).
(x * y) / x = x * (y / x).
x * ((y \ x) / x) = x / y.
x \ (x / (x / y)) = y / x.
T(x,y) / y = y \ x.
(x \ y) / y = y \ (y / x).
(x * (y / x)) * z = y * (K(x,y) * z).
T(x * (y / x),x) = y.
(x \ y) \ T(y,x) = x.
T(x,y) = (y \ x) * y.
L(T(x,y),z,u) / y = y \ L(x,z,u).
T(x * y,x) = y * x.
(x * (y / x)) \ x = x / y.
x \ T(y,z) != z | z \ y = x.
T(x,y) = x * K(y \ x,y).
(x * (y * x)) / x = x * y.
((x * y) \ x) * (y * x) = x.
(x * y) * x = x * (y * x).
T(T(x * y,z),x) = T(y * x,z).
(x * (y * z)) \ ((x * T(y,z)) * T(z,y)) = a(x,T(y,z),T(z,y)).
L(x \ 1,x,y) = (x \ y) / y.
K(x \ y,x) = K(y,x).
K(x * y,x) = K(y,x).
K(x \ (x * y),x) = K(y,x).
L(x,y,x) = x.
T(x * y,x) != z | y * x = z.
L(x,y,L(x,z,u)) = x.
L(T(x,y),z,x) = T(x,y).
L(R(x,y,z),u,x) = R(x,y,z).
L(L(x,y,z),u,x) = L(x,y,z).
(L(x,y,z) * u) * x = L(x,y,z) * (u * x).
L(T(x,y),z,x) = T(x,x * y).
L(L(T(x,y),z,u),w,x) = L(T(x,y),z,u).
R(x,y,x) = x.
R(x,y,x) = (x \ 1) \ 1.
R(x,y,R(x,z,u)) = x.
R(x,y,T(x,z)) = x.
R(x,y,R(T(x,z),u,w)) = x.
K(x \ (x * y),z) = K(y,z).
K((x / y) \ x,z) = K(y,z).
L(K(x,y),z,u) = K((w / x) \ w,y).
L(x \ 1,x,y) * y = x \ y.
L(T(x \ 1,y),x,y) = y \ (x \ y).
(x / T(y,z)) * y = x * K(z,y).
(x * T(y,z)) * T(z,y) = (x * y) * z.
T(x,y) \ (x * z) = K(y,x) * z.
K(x,y) * (K(y,x) * z) = z.
K(x,y) \ z = K(y,x) * z.
T(x / T(y,z),K(y,z)) = K(z,y) * (x / y).
(x * K(y,z)) \ x = K(z,y).
K(x,y) * z != u | K(y,x) * u = z.
(x * K(y,z)) * (K(z,y) * u) = x * u.
(K(x,y) * z) * K(y,x) = T(z,K(y,x)).
(K(x,y) * z) * u != z | T(K(y,x),z) = u.
T(x,K(y,z)) * K(z,y) = K(y,z) \ x.
(x / y) * K(z,y) = x / T(y,z).
(x * K(y,z)) * K(z,y) != u | x = u.
T(x,1 / y) = T(x,y \ 1).
T(x,(y \ 1) \ 1) = T(x,y).
T(x,R(y,z,y)) = T(x,y).
T(x,L(y,K(z,u),w)) = T(x,y).
T(x,L(y,K(z,u),w)) = x * K(x,y).
(x * (y * K(z,u))) / u = (x * y) / T(u,z).
x / T(y,z \ y) = (x / y) * K(y,z).
K((x / y) \ x,z) != u | K(y,z) = u.
L(T(x \ 1,y),x,y) = (x * y) \ y.
x * K(y,z) != u | x / K(z,y) = u.
(x / y) * K(z,y) != u | x / T(y,z) = u.
K(x,L(y,K(z,u),w)) = K(x,y).
K(x,T(y,y * z)) = K(x,T(y,z)).
K(x \ 1,y) != z | K(1 / x,y) = z.
K((x \ y) \ y,z) != u | K(T(x,y),z) = u.
x \ (K(y,z) * (u * x)) = T(K(y,z) * u,x).
K(x,y) * ((K(y,x) * z) * u) = z * u.
((K(x,y) * (z * u)) * w) / (u * w) = R(K(x,y) * z,u,w).
K(x,y) * (x * z) = T(x,y) * z.
K(x,y) * (T(y,x) * z) = y * z.
T(x,y) * (x \ z) = K(x,y) * z.
K(x,y) \ (z * T(x,y)) = x * T(z,T(x,y)).
T(x,y) * (T(y,x) * z) = x * (y * z).
K(x,y) * (z * x) = T(x,y) * T(z,x).
K(x,y) * ((x * z) * u) = (T(x,y) * z) * u.
x * (T(x,y) \ z) = K(y,x) * z.
(x * T(y,z)) \ (x * (K(y,z) * u)) = L(y \ u,T(y,z),x).
T(x,y) \ (y * x) = T(T(y,x),x).
x \ ((y / z) * x) = T(y / z,x).
K(x / y,z) * ((x / y) * y) = y * T(y \ x,z).
T(T((x * y) / x,z),x) != u | T(y,z) = u.
(K(x,y) * z) \ u = z \ (K(y,x) * u).
x / (y \ T(x,z)) = K(z,x) * y.
K(x,y) * (x \ y) = y / x.
K(x,y) * (y * x) = x * y.
(K(x,y) * z) / u = K(x,y) * (z / u).
(K(x,y) * z) * u != w | K(x,y) * (z * u) = w.
K(x,y) * ((y * x) * z) = (x * y) * z.
((x * y) * (z \ (x * y))) / T(x,y) = (x * y) / (y \ z).
((x / y) * z) / (u \ x) = x / (u \ ((x / z) * y)).
x \ (y * (z * K(u,w))) = (x \ (y * z)) * K(u,w).
x * K(x,y) = T(x,y).
x * T(x \ y,z) != y * u | K(x \ y,z) = u.
(x * (y * z)) / T(y,z) = (x * (z * y)) / y.
(x * y) \ (y * T(x,z)) = K(y,x) * K(x,z).
(x \ y) \ ((y / x) * z) = K(x,y) * z.
x \ L(x * (y / x),z,u) = L(y,z,u) / x.
(x * y) / (K(z,u) * y) = x * K(u,z).
(K(x,y) * z) / K(x,y) = T(z,K(y,x)).
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,y) * K(z,K(y,x)) = T(K(x,y),z).
K(x,K(y,z)) * (K(x,K(z,y)) * u) = u.
K(x,y) * (y * (x * z)) = y * (T(x,y) * z).
x \ (T(x,y) * T(z,x)) = T(K(x,y) * z,x).
(x \ y) \ (K(y,x) * z) = (y / x) \ z.
K(x,y) * (y * (x * z)) = (x * y) * L(z,x,y).
(x * (y \ z)) / (z / y) = x * K(z,y).
T(T(x,K(y,z)),K(z,y)) != u | x = u.
K(x,y) * T(K(y,x),z) = K(z,K(x,y)).
x * (K(y,K(z,u)) * w) != w | K(y,K(u,z)) = x.
T(x * K(y,z),y / z) = (y / z) \ (x * (z \ y)).
a(x,y,z) \ ((x * y) * z) = x * (y * z).
a(x,y,z) = ((x * y) * z) / (x * (y * z)).
(x * y) * a(x,z,z \ y) = (x * z) * (z \ y).
(x * (y * z)) \ ((x * y) * z) != u | a(x,y,z) = u.
x * ((x \ y) * L(x,z,u)) = y * L(x,z,u).
x / (y * ((z * y) \ x)) = R(z,y,y \ x).
x \ ((y * z) * (z \ x)) = R(T(y,x),z,z \ x).
L(R((x \ y) \ z,u,w),x \ y,x) = R(y \ (x * z),u,w).
L(L((x \ y) \ z,u,w),x \ y,x) = L(y \ (x * z),u,w).
L(T(L(x,y,z),u),w,x) = L(T(x,u),y,z).
T(T(T(x,y \ x),z),y) != u | T(x,z) = u.
a(x,y,z) = R((((x * y) * z) / (y * z)) / x,x,y * z).
R(x,y,y \ z) \ z = y * ((x * y) \ z).
(x * y) * L(T(x,y),z,u) = x * (L(x,z,u) * y).
R(x,y,z) \ (y * z) = y * ((x * y) \ (y * z)).
(x * y) * R(x,z,u) != w | x * (y * R(x,z,u)) = w.
(x * (y * (z * u))) \ (x * ((y * z) * u)) != w | L(a(y,z,u),y * (z * u),x) = w.
x * (T(y,x) * K(x,z)) = y * T(x,z).
T(x * K(y,z),y) = T(x,y) * K(y,z).
T(T(x,y),K(y,z)) = T(x,T(y,z)).
T(T(x,K(y,z)),y) = T(x,T(y,z)).
(T(x,y) * (T(T(y,x),z) * u)) \ ((T(y,z) * T(x,y)) * u) = a(T(x,y),T(T(y,x),z),u).
(L(x,y,z) * (x \ u)) * x = L(x,y,z) * T(u,x).
(x * (y * T(z,u))) / T(z,u) = (x * (y * z)) / z.
T(K(x,y) * z,y \ x) = (x / y) \ (z * (y \ x)).
T(x * y,K(y,z)) = y * T(x,T(y,z)).
T(x,y) \ ((T(x,y) * z) * u) = x \ ((x * z) * u).
((x * y) * (z \ (x * y))) / T(x,y) = (((x * y) / z) * (y * x)) / x.
L(x * (y / x),z,u) = x * (L(y,z,u) / x).
T(K(x,y) * z,x) = K(x,y) * T(z,x).
T(K(x,y) * z,x) * u = K(x,y) * (T(z,x) * u).
L(T(x,y \ x),z,u) = y * (L(x,z,u) / y).
L(T(x,y \ x),z,u) = (y * L(x,z,u)) / y.
L(x * K(y,x),z,u) = (y * L(x,z,u)) / y.
L(x,y,z) * K(u,L(x,y,z)) = L(x * K(u,x),y,z).
L(x,y,z / (y * x)) = z \ ((z / y) * (y * x)).
R(x,y,(x * y) \ z) = R(x,y,y \ z).
R(x,y,y \ ((x * z) * (z \ y))) = R(x,y,a(x,z,z \ y)).
(x * y) * T((x * y) \ x,z) = x * (y * T(y \ 1,z)).
((((x * y) * z) / (x * y)) * y) * T(x,y) = (x * y) * R(z,y,T(x,y)).
(x * y) * L(z,x,y) = y * (T(x,y) * z).
L(x,T(y,z),z) = L(x,y,z).
(T(x,y) * T(z,x)) * L(u,T(x,y),T(z,x)) = T(z,x) * (T(T(x,z),y) * u).
L(T(x \ 1,y),T(x,y),y) = (x * y) \ y.
T(x \ 1,y) = T(x,y) \ 1.
T(x \ 1,y) = x \ K(y,x).
K(x \ 1,y) = K(y,x).
K(x,y \ 1) = K(y,x).
T(x,y \ 1) = x * K(y,x).
T(x,y \ 1) = (y * x) / y.
T(T(x,y),y \ 1) = x.
T(x \ y,x \ 1) = y / x.
T(x,y \ 1) * y = y * x.
T(x,a(y,z,u) \ 1) = x.
T(x,a(y,z,u) \ 1) != w | x = w.
T(T(x,y \ 1),y) != z | x = z.
T(T(x,y),y \ 1) != z | x = z.
T(x * y,y \ 1) != z | y * x = z.
R(x,y,a(x,z,z \ y)) \ ((x * z) * (z \ y)) = y * a(x,z,z \ y).
x \ (y * z) != y * ((u * y) \ (y * z)) | R(u,y,z) = x.
L(x,y,z / (y * x)) = L(x,y,z / y).
x / L(y,z,x / z) = (x / (z * y)) * z.
K(x / y,z) * x = y * T(y \ x,z).
T(K(x / y,z),x) = K(y \ x,z).
K((x * y) / x,z) * (x * y) = x * T(y,z).
K((x \ y) \ y,z) = T(K(x,z),y).
K(T(x,y),z) = T(K(x,z),y).
T(K(x,y),z) != u | K(T(x,z),y) = u.
x \ (K(y,z) * x) = K(T(y,x),z).
(K(x,y) * z) * K(y,T(x,z)) = z.
K(x,T(y,z)) = T(K(x,y),z).
x * K(y,T(z,x)) = K(y,z) * x.
K(T(x,y),z) = K(x,T(z,y)).
T(K(x,y),y * z) = K(x,T(y,z)).
K(x,y) * K(y,T(x,z)) = K(z,K(x,y)).
T(x,T(y,z) \ x) = x * K(y,T(x,z)).
K(x * y,T(z,x)) = K(y * x,z).
x * (K(y,T(z,x)) * u) = (K(y,z) * x) * u.
K(x,y) * K(y,T(x,z)) = K(x * z,K(x,y)).
K(x * y,K(y,z)) = K(y * x,K(y,z)).
(x * y) \ (y * T(x,T(y,z))) = K(z,K(y,x)).
x * (K(y,T(z,x)) * u) = K(y,z) * (x * u).
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)).
K(x,K(y,z)) * z = T(z,K(y,x)).
K(x,K(y,z)) * (K(y,K(z,x)) * u) = u.
K(x,K(y,z)) = K(y,K(x,z)).
K(x,K(y,z)) * z = T(z,K(x,y)).
T(x,K(y,z)) = T(x,K(z,y)).
T(T(x,K(y,z)),K(y,z)) = x.
T(K(x,y),z) * z = z * K(x,y).
T(T(x,K(y,z)),T(y,z)) = T(x,y).
T(K(x,T(y,z)),z) = K(x,y).
K(T(x,y),T(z,y)) = K(x,z).
(x * K(y,z)) / x = K(y,T(z,x)).
K(x,T(T(y,z),z)) = K(x,y).
K((x * y) / x,z) = K(y,T(z,x)).
K(x,T(T(y,z),z)) = K(y \ 1,x).
K(x,T(y,z)) * (z * u) = z * (K(x,y) * u).
T(T(x,T(y,z) \ x),y) = T(x,K(y,z)).
T(K(x,T(y,z)),z) != u | K(x,y) = u.
K((x * y) / x,z) = K(T(y,x),z).
K(T(x,y),z) * (y * x) = y * T(x,z).
K(x,T(T(y,z),z)) != u | K(x,y) = u.
K(x \ 1,y) != z | K(y,x) = z.
T(x * K(y,T(x,z)),y) = T(x,K(y,z)).
(x * T(y,z)) * ((x * y) \ u) = K(T(y,x),z) * u.
T(x,y) * K(y,T(x,z)) = T(x,K(y,z)).
x * (K(y,z) * (x \ u)) = K(y,T(z,x)) * u.
(x * y) \ (x * ((y * z) * K(u,w))) = L(z,y,x) * K(u,w).
(x * (T(y,x) * z)) \ ((y * x) * z) != u | a(x,T(y,x),z) = u.
L(x,y,z) * (x * u) = x * (L(x,y,z) * u).
L(x,y,z) \ (x * u) = x * (L(x,y,z) \ u).
T(K(x,y) * z,y \ x) = T(z * K(x,y),x / y).
(T(x,y) * z) * L(u,z,x) = T(x,y) * (z * u).
L(x,y,T(z,u)) = L(x,y,z).
L(L(x,y,z),u,K(w,v5)) = L(x,y,T(z,v6)).
L(x,y,z / u) = L(x,y,u \ z).
x * L(y,z,z \ x) = (x / z) * (z * y).
x / L(y,z,z \ x) = (x / (z * y)) * z.
L(x,y,T(z,u)) != w | L(x,y,z) = w.
(x \ y) * L(x,z,z \ y) = x \ ((y / z) * (z * x)).
(K(x,y) * (T(z,x) * (u * w))) \ ((T(K(x,y) * z,x) * u) * w) = a(T(K(x,y) * z,x),u,w).
(x * T(y,z)) * ((x * y) \ u) = K(y,T(z,x)) * u.
T(K(x,y) * (z * y),y \ x) = T(z * T(y,x \ y),x / y).
(x * T(y,z)) \ (x * (K(y,z) * (x \ u))) = (x * y) \ u.
(x / (y * ((z * y) \ x))) * (z \ x) = x * a(z,y,(z * y) \ x).
((x * y) * z) \ ((T(z,(x * y) \ 1) * y) * T(x,y)) = a(T(z,(x * y) \ 1),y,T(x,y)).
T(((x / y) * (y * z)) / z,z) = (z \ x) * L(z,y,y \ x).
a(x,y,z) = R(R(x,y,z) / x,x,y * z).
a(x,y,z) = R(x \ R(x,y,z),x,y * z).
R(T(x \ R(x,y,z),u),x,y * z) = T(a(x,y,z),u).
K((x * y) \ x,z) = y * T(y \ 1,z).
K((x * y) \ x,z) = K(y \ 1,z).
K((x \ y) \ 1,z) = K(y \ x,z).
K((x / y) \ 1,z) = K(y / x,z).
K(x \ y,z) = K(z,y \ x).
K(x \ (x / y),z) = K(z,y).
(x / y) * K(z,y) = x * T(x \ (x / y),z).
K(1 / (x / y),z) = K(y / x,z).
K((x \ y) / y,z) = K(1 / x,z).
T(x,(y \ z) / z) = K(1 / y,x) \ x.
T(x,(y \ z) / z) = T(x,y \ 1).
T(x,(y / z) \ 1) = T(x,z / y).
T(x,y \ (y / z)) = T(x,z \ 1).
T(x,(y * (z * u)) / ((y * z) * u)) = T(x,a(y,z,u) \ 1).
T(x,(y \ R(y,z,u)) \ 1) = T(x,y / R(y,z,u)).
T(x \ y,z \ (z / x)) = y / x.
T(x,(y \ z) \ 1) = T(x,z \ y).
T((x \ y) \ z,y \ x) = z / (x \ y).
T(x * (y \ z),z \ y) = (y \ z) * x.
T(T(x,y \ z),z \ y) = x.
T(x,(y \ z) \ 1) != u | T(x,z \ y) = u.
((x / y) * z) / (y \ x) = T(K(y,x) * z,x \ y).
T(x * (y \ z),z \ y) != x * u | T(y \ z,x) = u.
x * T(x \ (x / y),z) = x / T(y,z).
x / T(x / y,z) = x * T(y / x,z).
T(x,y / R(y,z,u)) != w | T(x,R(y,z,u) \ y) = w.
x / (y \ ((x / z) * y)) = T(K(y,x) * z,x \ y).
T(K(x,y) * z,y \ x) = y / T(y / z,x).
T(K(x,y) * z,y \ x) = y * T(z / y,x).
(K(x,y) * ((z * u) * w)) / (u * w) = R(K(x,y) * z,u,w).
L(x \ (y \ z),T(x,u),y) = (y * x) \ z.
L(x \ (y \ (y * (x * z))),T(x,u),y) = L(z,x,y).
L(x \ (x * y),T(x,z),u) = L(y,x,u).
L(x,T(y,z),u) = L(x,y,u).
x \ (y * R(y \ (x * z),u,w)) = (x \ y) * R((x \ y) \ z,u,w).
x \ (y * L(y \ (x * z),u,w)) = (x \ y) * L((x \ y) \ z,u,w).
R(x,y,R(T(x,y),z,z \ y)) = R(x,y,a(x,z,z \ y)).
R(x,y,a(x,z,z \ y)) = x.
(x * y) \ (x * (y * (z * K(u,w)))) = L(z,y,x) * K(u,w).
T(x,(y * (z * u)) / ((y * z) * u)) != w | x = w.
K(x,y) * (((z * u) * w) / (u * w)) = R(K(x,y) * z,u,w).
L(x * K(y,z),u,w) = L(x,u,w) * K(y,z).
K(x,L(y,z,u)) = K(x,y).
K(x,L(y,z,u)) = x \ T(x,y).
T(x,L(y,z,u)) = T(x,y).
T(L(x,y,z) * u,x) = u * L(x,y,z).
L(x,y,z) \ (u * L(x,y,z)) = T(u,x).
T(x / L(y,z,u),y) = L(y,z,u) \ x.
L(x,y,z) * T(u,x) = u * L(x,y,z).
L(x,y,y \ z) * (x \ z) = ((z / y) * (y * x)) / x.
L(x,y,z) * (x \ u) = (u / x) * L(x,y,z).
(x / L(y,z,u)) * y = y * (L(y,z,u) \ x).
T((x / (y * z)) * y,z) = L(z,y,y \ x) \ x.
(x * L(y,z,u)) / y = L(y,z,u) * (y \ x).
x * (L(x,y,y \ z) \ z) = ((z / (y * x)) * y) * x.
(x * L(y,z,u)) / y = (x / y) * L(y,z,u).
L(x,y,z) * (x \ (z * y)) = (z * (y * x)) / x.
((x * y) / z) * L(z,y,x) = (x * (y * z)) / z.
T((x / T(y,z \ y)) * z,y / z) = L(y / z,z,z \ x) \ x.
(x * y) * (((x * (y * z)) / z) \ (x * y)) = z * (L(z,y,x) \ (x * y)).
x \ (y * (L(y,z,z \ x) \ x)) = (((x / z) * (z * y)) / y) \ x.
R(K(x,y) * z,u,w) = K(x,y) * R(z,u,w).
K(x,y) * R(x,z,u) = R(T(x,y),z,u).
K(R(x,y,z),u) = K(x,u).
T(x,y) \ R(T(x,y),z,u) = x \ R(x,z,u).
x * (K(y,x) * R(y,z,u)) = R(y,z,u) * x.
(x * K(y,x)) * R(y,z,u) = R(y,z,u) * x.
(x * (y / x)) * R(x,z,u) = R(x,z,u) * y.
R(x,y,z) * (x \ u) = (u / x) * R(x,y,z).
R(x,y,z) * T(u,x) = u * R(x,y,z).
T(x,R(y,z,u)) = T(x,y).
T(x,(y * z) / u) = T(x,y / (u / z)).
T(x,y / (((y * z) * u) / (z * u))) = x.
T(x,y / R(y,z,u)) = x.
T(x,R(y,z,u) \ y) = x.
T(x \ R(x,y,z),u) = x \ R(x,y,z).
T(x,R(y,z,u) \ y) != w | x = w.
T(x \ R(x,y,z),u) = T(x,w) \ R(T(x,w),y,z).
x * ((y / x) * R(x,z,u)) = R(x,z,u) * y.
((x * y) / z) * R(z,x,y) = z \ ((z * x) * y).
R(x,y,z) = (x \ ((x * y) * z)) / (x \ (y * z)).
R(x,y,z) * (x \ (y * z)) != u | x \ ((x * y) * z) = u.
R(T(x \ R(x,y,z),u),T(x,w),y * z) = a(T(x,w),y,z).
R(x,y,y \ z) * (x \ z) != u | x \ ((x * y) * (y \ z)) = u.
T(x * T(y,z \ y),z / y) = y * T((x * y) / y,z).
T(x * T(y,z \ y),z / y) = y * T(x,z).
(L(x,y,z) * (z * y)) \ (x * (z * y)) = a(z,y,T(x,z * y)).
R(L(x,y,z),z * y,(z * y) \ (x * (z * y))) \ (x * (z * y)) = (z * y) * a(z,y,T(x,z * y)).
(x * (K(y,x) * (y * z))) \ ((y * x) * z) = a(x * K(y,x),y,z).
(x * (y * z)) \ ((x * y) * z) = a(x,T(y,z),T(z,y)).
a(x,T(y,z),T(z,y)) != u | a(x,y,z) = u.
R(x,y,y \ z) * (x \ z) = z * a(x,y,(x * y) \ z).
x * a(y,z,(y * z) \ x) = y \ ((y * z) * (z \ x)).
x \ ((x * y) * (y \ z)) != z * u | a(x,y,(x * y) \ z) = u.
T(((x / y) * K(y,z)) * z,y / z) = L(y / z,z,z \ x) \ x.
(((x / y) * (y * z)) / z) \ x = x \ (((x / (y * z)) * y) * z).
(((x / y) * (y * z)) / z) \ x = a(x / (y * z),y,z).
(x * (T(y,x) * z)) \ ((y * x) * z) = a(x * K(y,x),y,z).
a(x * K(y,x),y,z) = a(x,T(y,x),z).
a(T(x,y) * K(T(y,z),T(x,y)),T(y,z),u) = a(T(x,y),T(T(y,x),z),u).
T((x / y) * T(z,y \ z),y / z) = L(y / z,z,z \ x) \ x.
L(x / y,y,y \ z) \ z = y * T(z / x,x).
L(x / y,y,y \ z) \ z = y * (x \ z).
L(x,y,y \ z) \ z = y * ((x * y) \ z).
L(x,y,z) \ (y * z) = y * ((x * y) \ (y * z)).
R(x,y,z) = L(x,y,z).
L(x,y,T(z,u)) = R(x,y,z).
R(x,y,T(z,u)) = L(x,y,z).
R(T(x \ L(x,y,z),u),x,y * z) = T(a(x,y,z),u).
R(T(x \ L(x,y,z),u),T(x,w),y * z) = a(T(x,w),y,z).
R(x,y,T(z,u)) = R(x,y,z).
R(x,y,z) != u | L(x,y,z) = u.
L(x,y,z) * (z * y) = (x * y) * T(z,y).
L(T(x \ L(x,y,z),u),x,y * z) = T(a(x,y,z),u).
L(T(x \ L(x,y,z),u),T(x,w),y * z) = a(T(x,w),y,z).
L(T(x \ L(x,y,z),u),x,y * z) = a(T(x,w),y,z).
T(a(x,y,z),u) = a(T(x,w),y,z).
a(T(x,y),z,u) = a(x,z,u).
a(T(x,y),z,u) != w | a(x,z,u) = w.
a(x / y,z,u) = a(y \ x,z,u).
(((x / y) * (y * z)) / z) \ x = a((y * z) \ x,y,z).
a(K(x,y) * (z / y),u,w) != v5 | a(z / T(y,x),u,w) = v5.
a(x / y,z,u) != w | a(y \ x,z,u) = w.
(((x / y) * (y * z)) / z) \ x != u | a((y * z) \ x,y,z) = u.
(((x / y) * (y * (y \ z))) / (y \ z)) \ x = a(z \ x,y,y \ z).
(((x / y) * z) / (y \ z)) \ x = a(z \ x,y,y \ z).
a(x \ (y * z),z,z \ x) = ((y * x) / (z \ x)) \ (y * z).
(((x * y) / z) * (y * x)) / x = (x * y) / (y \ z).
(x \ y) * R((x \ y) \ 1,z,u) = x \ (y * R(y \ x,z,u)).
((x * y) \ x) * R(((x * y) \ x) \ 1,z,u) = (x * y) \ (x * R(y,z,u)).
(x \ y) * L((x \ y) \ 1,z,u) = x \ (y * L(y \ x,z,u)).
((x * y) \ x) * L(((x * y) \ x) \ 1,z,u) = (x * y) \ (x * L(y,z,u)).
(T(x,(y * z) \ 1) * z) * T(y,z) = (y * z) * R(x,z,T(y,z)).
x \ ((x * y) * (y \ z)) = z * a(x,y,y \ z).
a(x,y,(x * y) \ z) = a(x,y,y \ z).
a(x,y,y \ (z * (x * y))) = a(x,y,T(z,x * y)).
(x * y) * z != u * (L(u,y,x) \ (x * y)) | ((x * (y * u)) / u) \ (x * y) = z.
a(T(x,y) * K(y,T(T(x,y),z)),T(y,z),u) = a(T(x,y),T(T(y,x),z),u).
(x \ (x / y)) * R(((x * y) \ x) \ 1,z,u) = (x * y) \ (x * R(y,z,u)).
(x \ (x / y)) * L(((x * y) \ x) \ 1,z,u) = (x * y) \ (x * L(y,z,u)).
a(T(x,y) * K(y,T(x,z)),T(y,z),u) = a(T(x,y),T(T(y,x),z),u).
a(T(x,K(y,z)),T(y,z),u) = a(T(x,y),T(T(y,x),z),u).
(x \ (x / y)) * R((x \ (x / y)) \ 1,z,u) = (x * y) \ (x * R(y,z,u)).
(x \ (x / y)) * L((x \ (x / y)) \ 1,z,u) = (x * y) \ (x * L(y,z,u)).
x \ ((x / y) * R((x / y) \ x,z,u)) = (x * y) \ (x * R(y,z,u)).
(x * y) \ (x * R(y,z,u)) = x \ ((x / y) * R(y,z,u)).
x \ ((x / y) * L((x / y) \ x,z,u)) = (x * y) \ (x * L(y,z,u)).
(x * y) \ (x * L(y,z,u)) = x \ ((x / y) * L(y,z,u)).
(x * y) \ (((x * y) / z) * L(z,y,x)) = ((x * y) * z) \ (x * (y * z)).
((x * y) * z) \ (x * (y * z)) = (x * y) \ ((x * (y * z)) / z).
(x * y) \ ((x * (y * T(z,y))) / T(z,y)) = ((x * y) * T(z,y)) \ (x * (z * y)).
(K(x,y) * (z * x)) * L(u,T(x,y),T(z,x)) = T(z,x) * (T(T(x,z),y) * u).
(K(x,y) * (z * x)) * L(u,T(x,y),z) = T(z,x) * (T(T(x,z),y) * u).
K(x,y) * ((z * x) * L(u,T(x,y),z)) = T(z,x) * (T(T(x,z),y) * u).
K(x,y) * ((z * x) * L(u,x,z)) = T(z,x) * (T(T(x,z),y) * u).
T(x,y) * (T(T(y,x),z) * u) = K(y,z) * (x * (y * u)).
((x * y) * T(z,y)) \ (x * (z * y)) = (x * y) \ ((x * (y * z)) / z).
(T(x,y) * (T(T(y,x),z) * u)) \ ((K(y,z) * (x * y)) * u) = a(T(x,y),T(T(y,x),z),u).
((x * y) * z) \ ((x * y) * R(z,y,T(x,y))) = a(T(z,(x * y) \ 1),y,T(x,y)).
(x * y) \ (((x * y) / z) * R(z,y,T(x,y))) = a(T(z,(x * y) \ 1),y,T(x,y)).
(x * y) \ (((x * y) / z) * R(z,y,x)) = a(T(z,(x * y) \ 1),y,T(x,y)).
(x * y) \ (((x * y) / z) * R(z,y,x)) = a(z,y,T(x,y)).
(x * y) \ (((x * y) / z) * L(z,y,x)) = a(z,y,T(x,y)).
(x * y) \ ((x * (y * z)) / z) = a(z,y,T(x,y)).
(T(x,y) * (T(T(y,x),z) * u)) \ (K(y,z) * ((x * y) * u)) = a(T(x,y),T(T(y,x),z),u).
(K(x,y) * (z * (x * u))) \ (K(x,y) * ((z * x) * u)) = a(T(z,x),T(T(x,z),y),u).
L(a(x,y,z),x * (y * z),K(y,u)) = a(T(x,y),T(T(y,x),u),z).
a(T(x,y),T(T(y,x),z),u) = a(x,y,u).
a(T(x,K(y,z)),T(y,z),u) = a(x,y,u).
a(x,T(y,z),u) = a(x,y,u).
a(x,y,T(z,y)) = a(x,y,z).
a(x,y,z) = (z * y) \ ((z * (y * x)) / x).
a(x,y,z) = ((z * y) * T(x,y)) \ (z * (x * y)).
a(x,y,z) = (L(z,y,x) * (x * y)) \ (z * (x * y)).
a(x,y,T(z,x * y)) = a(x,y,z).
a(x,y,y \ (z * (x * y))) = a(x,y,z).
(K(x,y) * (T(z,x) * (u * w))) \ ((K(x,y) * (T(z,x) * u)) * w) = a(T(K(x,y) * z,x),u,w).
(K(x,y) * (T(z,x) * (u * w))) \ (K(x,y) * ((T(z,x) * u) * w)) = a(T(K(x,y) * z,x),u,w).
L(a(T(x,y),z,u),T(x,y) * (z * u),K(y,w)) = a(T(K(y,w) * x,y),z,u).
L(a(x,y,z),T(x,u) * (y * z),K(u,w)) = a(T(K(u,w) * x,u),y,z).
a(T(K(x,y) * z,x),u,w) = a(z,u,w).
a(K(x,y) * z,u,w) = a(z,u,w).
a(x / T(y,z),u,w) = a(x / y,u,w).
a(x / T(y,z),u,w) = a(y \ x,u,w).
a(x / (y * z),u,w) = a((z * y) \ x,u,w).
a((x * y) \ z,u,w) != v5 | a((y * x) \ z,u,w) = v5.
R(L(x,y,z),z * y,T(x,z * y)) \ (x * (z * y)) = (z * y) * a(z,y,T(x,z * y)).
L(R(x,y * z,T(x,y * z)),z,y) \ (x * (y * z)) = (y * z) * a(y,z,T(x,y * z)).
L(x,y,z) \ (x * (z * y)) = (z * y) * a(z,y,T(x,z * y)).
L(x,y,z) \ (x * (z * y)) = (z * y) * a(z,y,x).
x * (L(x,y,z) \ (z * y)) = (z * y) * a(z,y,x).
a(x,y,z) = ((x * (y * z)) / z) \ (x * y).
(((x / y) * (z * u)) / u) \ ((x / y) * z) = a(y \ x,z,u).
((x * y) / (z \ y)) \ (x * z) = a(x,z,z \ y).
(((x / y) * (y * z)) / z) \ x = a(x / y,y,z).
(((x / y) * z) / (u \ z)) \ ((x / y) * u) = a(y \ x,u,u \ z).
a(x \ (y * z),z,z \ x) = a(y,z,z \ x).
a((x * y) \ z,x,y) = a(z / x,x,y).
a((x * y) \ z,x,y) = a(x \ z,x,y).
a((x * y) \ z,y,x) = a(y \ z,y,x).
((x * y) / (y \ z)) \ (((x * y) / z) * y) = a(z \ (x * y),y,x).
(x / (y \ z)) \ ((x / z) * y) = a(z \ x,y,y \ z).
a(x \ (y * z),z,z \ x) = a(x \ (y * z),z,y).
a(x \ (y * z),z,y) = a(y,z,z \ x).
a((x * y) \ (z \ (x * y)),y,x) = a(x,y,y \ (z * (x * y))).
a(x \ (y \ (z * x)),x,z) = a(z,x,x \ (y * (z * x))).
a(x \ (y \ (z * x)),x,z) = a(z,x,y).

end_of_list.
