% AIM result - Prove all 7 goals from {LC}

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

set(para_units_only).

clear(back_demod).
set(restrict_denials).
set(para_from_small).

assign(max_weight,5).

formulas(assumptions).

% loop axioms
1 * x = x.
x * 1 = x.
x \ (x * y) = y.
x * (x \ y) = y.
(x * y) / y = x.
(x / y) * y = x.

% cancellation laws
% (comment out if they clog the search)
x * y = u & x * z = u -> y = z.
y * x = u & z * x = u -> y = z.

   % other form
   x * y = x * z -> y = z.
   y * x = z * x -> y = z.

% associator
(x * (y * z)) \ ((x * y) * z) = a(x,y,z).

% commutator
(x * y) \ (y * x) = K(y,x).

% 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).

% obvious compatibility
% (comment out if they clog the search)
a(x,y,z) = 1 -> L(z,y,x) = z.
L(x,y,z) = x -> a(z,y,x) = 1.
T(x,y) = x -> T(y,x) = y.
T(x,y) = x -> K(x,y) = 1.
K(x,y) = 1 -> T(x,y) = x.

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

end_of_list.

formulas(goals).

   % Q/N(Q) is a group
   a(a(x,y,z),u,w) = 1            # label("aa1"). % old "aa"
   a(x,a(y,z,u),w) = 1            # label("aa2").
   a(x,y,a(z,u,w)) = 1            # label("aa3").

   % Q/C(Q) is a group
   K(a(x,y,z),u) = 1              # label("Ka").  % same as old "Ka"
 
   % Q/C(Q) is commutative
   % ***KEEP THIS ONE COMMENTED OUT EXCEPT IN VERY SPECIAL CASES***
%   K(K(x,y),z) = 1                # label("KK").
 
   % Q/N(Q) is commutative
   a(K(x,y),z,u) = 1              # label("aK1"). % old "aK"
   a(x,K(y,z),u) = 1              # label("aK2").
   a(x,y,K(z,u)) = 1              # label("aK3").

end_of_list.

formulas(sos).

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

end_of_list.

% Hints extracted from previously found proofs.

formulas(hints).

a(K(x,y),z,u) = 1.
1 * x = x.
x * 1 = x.
x \ (x * y) = y.
x * (x \ y) = y.
(x * y) / y = x.
(x / y) * y = x.
(x * (y * z)) \ ((x * y) * z) = a(x,y,z).
(x * y) \ (y * x) = K(y,x).
(x * y) \ (x * (y * z)) = L(z,y,x).
((x * y) * z) / (y * z) = R(x,y,z).
x \ (y * x) = T(y,x).
T(T(x,y),z) = T(T(x,z),y).
T(L(x,y,z),u) = L(T(x,u),y,z).
T(R(x,y,z),u) = R(T(x,u),y,z).
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 * (x * y)) * z = x * (x * (y * z)).
a(K(c1,c2),c3,c4) != 1.
1 \ x = x.
x \ x = 1.
x \ ((x * y) * 1) = y.
x \ (y * (y \ (x * z))) = z.
x / 1 = x.
x / (y \ x) = y.
(x / y) \ x = y.
(x * (y * z)) * a(x,y,z) = (x * y) * z.
((x / y) * (y * z)) \ (x * z) = a(x / y,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 \ (1 * (x * y)) = L(y,x,1).
(x * 1) \ (x * y) = L(y,1,x).
(x * y) * L(z,y,x) = x * (y * z).
x \ (y * ((y \ x) * z)) = L(z,y \ x,y).
(x * y) \ (x * z) = L(y \ z,y,x).
L(x \ y,x,z) = (z * x) \ (z * y).
x \ ((x / y) * (y * z)) = L(z,y,x / y).
((x * y) * (y \ z)) / z = R(x,y,y \ z).
R(x,y,z) * (y * z) = (x * y) * z.
(x * y) / (z * y) = R(x / z,z,y).
R(x / y,y,z) = (x * z) / (y * z).
T(x,x) = x.
x * T(y,x) = y * x.
(x \ y) \ y = T(x,x \ y).
T(x,x \ y) = (x \ y) \ y.
x \ y = T(y / x,x).
T(x / y,y) = y \ x.
x * (x * y) = (x * (x * (y * z))) / z.
(x * (x * (y * z))) / z = x * (x * y).
x = (y * (y * z)) \ (y * (y * (z * x))).
(x * (x * y)) \ (x * (x * (y * z))) = z.
x * (y * z) = x \ ((x * (x * y)) * z).
x \ ((x * (x * y)) * z) = x * (y * z).
(x * (x * 1)) * y = x * (x * y).
(x * y) * z = x * (x * ((x \ y) * z)).
x * (x * ((x \ y) * z)) = (x * y) * z.
(x * (y * (y * (z * u)))) \ ((x * (y * (y * z))) * u) = a(x,y * (y * z),u).
(x * (x * (y * (z * u)))) \ (((x * (x * y)) * z) * u) = a(x * (x * y),z,u).
(x * (x * (y * z))) \ ((x * (x * y)) * (z * u)) = L(u,z,x * (x * y)).
(x * (y * (y * z))) \ (x * (y * (y * (z * u)))) = L(u,y * (y * z),x).
((x * (x * (y * z))) * u) / (z * u) = R(x * (x * y),z,u).
(x * (x * (y * z))) / ((x * y) * z) = R(x,x * y,z).
x = ((x * y) / 1) / y.
((x * y) / 1) / y = x.
T(x,y) = T(T(x,y),x).
T(T(x,y),x) = T(x,y).
(x * (y * z)) / L(z,y,x) = x * y.
(x * y) / T(x,y) = y.
R(x,y,z) \ ((x * y) * z) = y * z.
x \ (y * 1) = x \ y.
T(x * (x * y),x) = x * (y * x).
T((x * y) / x,x) = y.
x = (y * T(x,y)) / y.
(x * T(y,x)) / x = y.
(x * y) \ (x * (z * y)) = L(T(z,y),y,x).
T(x,y) \ (x * y) = T(y,T(x,y)).
x * T(T(y,x),z) = T(y,z) * x.
x * L(T(y,x),z,u) = L(y,z,u) * x.
x * R(T(y,x),z,u) = R(y,z,u) * x.
T(R(x,y,z),y * z) = (y * z) \ ((x * y) * z).
(x * y) \ ((z * x) * y) = T(R(z,x,y),x * y).
T(x \ y,z) = T(T(y / x,z),x).
T(T(x / y,z),y) = T(y \ x,z).
((x * y) / ((1 / z) * z)) / y = x.
K(T(x,y),x) = 1.
T(x,T(x,y)) = x.
x * T(x,y) = T(x,y) * x.
T(x,y) * x = x * T(x,y).
(x * y) / T(y,T(x,y)) = T(x,y).
x \ (y * (z * (z \ 1))) = x \ y.
K(x,(y * x) / y) = 1.
T(x,(y * x) / y) = x.
K(x,y) \ (x * y) = T(y * x,K(x,y)).
x \ (x * y) = L(y,x,1).
L(x,y,1) = x.
a(1,x,y) = 1.
x \ (x * y) = L(y,1,x).
L(x,1,y) = x.
K(x \ 1,x) = (x \ 1) * x.
(x \ 1) * x = K(x \ 1,x).
x \ 1 = K(x \ 1,x) / x.
K(x \ 1,x) / x = x \ 1.
x = (x \ 1) \ K(x \ 1,x).
(x \ 1) \ K(x \ 1,x) = x.
(x * x) * y = x * (x * y).
x * x = (x * (x * y)) / y.
(x * (x * y)) / y = x * x.
x = (y * y) \ (y * (y * x)).
(x * x) \ (x * (x * y)) = y.
((x * (x * y)) * z) / (y * z) = R(x * x,y,z).
x \ (y * (y * x)) = T(y * y,x).
x * (x * T(y,x * x)) = y * (x * x).
x = L(x,y,y).
L(x,y,y) = x.
T(x * y,x) = x * ((x \ y) * x).
x * ((x \ y) * x) = T(x * y,x).
x * T(x \ y,z) = T(y / x,z) * x.
T(x / y,z) * y = y * T(y \ x,z).
(x * T(x \ y,z)) / x = T(y / x,z).
R(x,1 / y,y) / y = x * (1 / y).
(x * y) \ x = L(y \ 1,y,x).
L(x \ 1,x,y) = (y * x) \ y.
L((x \ y) \ 1,x \ y,x) = y \ x.
L(x \ 1,x,y / x) = y \ (y / x).
x / L(y \ 1,y,x) = x * y.
(x \ y) * x = x \ T(x * y,x).
x \ T(x * y,x) = (x \ y) * x.
x * K(x \ 1,x) = T(x * 1,x).
x \ T(y,x) = (x \ (x \ y)) * x.
(x \ (x \ y)) * x = x \ T(y,x).
x * K(x \ 1,x) = T(x,x).
x * K(x \ 1,x) = x.
K(x \ 1,x) = 1.
T(x \ 1,x) = x \ 1.
(x \ 1) * x = 1.
1 / x = x \ 1.
(x \ 1) \ 1 = x.
x * (1 / x) = 1.
T(x,x \ 1) = x.
L(x,x \ 1,y) = (y * (x \ 1)) \ y.
x / L(y,y \ 1,x) = x * (y \ 1).
(x * 1) \ ((x * y) * (1 / y)) = a(x,y,1 / y).
T(x,y) = T(T(x,y),x \ 1).
T(T(x,y),x \ 1) = T(x,y).
K(T(x,y),x \ 1) = 1.
K(x \ y,(y / x) \ 1) = 1.
K(x,((y * x) / y) \ 1) = 1.
T(x \ y,(y / x) \ 1) = x \ y.
T(x,((y * x) / y) \ 1) = x.
(x \ y) \ (x \ T(y,x)) = K(x \ (x \ y),x).
x * L(y,z \ x,z) = z * ((z \ x) * y).
x * L(y,z,x / z) = (x / z) * (z * y).
(x * (y * z)) \ (x * (y * (z * u))) = L(L(u,z,y),y * z,x).
(x * y) * L(z,K(x,y),y * x) = (y * x) * (K(x,y) * z).
L(x \ (y \ z),x,y) = (y * x) \ z.
L(x \ (y * x),x,y) = T(y,y * x).
(x * y) / L(z \ y,z,x) = x * z.
L(x \ T(y,z),x,z) = (z * x) \ (y * z).
L(x \ (y \ ((y * x) * z)),x,y) = z.
R(x,x,y) = x.
(R(x,y,z) * y) \ ((x * y) * z) = L(z,y,R(x,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.
T(x,y) = R(T(x,y),x,z).
R(T(x,y),x,z) = T(x,y).
L(x,y,z) = L(R(x,L(x,y,z),u),y,z).
L(R(x,L(x,y,z),u),y,z) = L(x,y,z).
R(x,y,z) = R(R(x,y,z),x,u).
R(R(x,y,z),x,u) = R(x,y,z).
R(T(x,y),z,u) = R(R(T(x,y),z,u),x,w).
R(R(T(x,y),z,u),x,w) = R(T(x,y),z,u).
T(x,y) * (x * z) = (T(x,y) * x) * z.
(T(x,y) * x) * z = T(x,y) * (x * z).
R(x,y,z) * (x * u) = (R(x,y,z) * x) * u.
(R(x,y,z) * x) * u = R(x,y,z) * (x * u).
R(1 / x,x,y) = y / (x * y).
R((x / y) / z,z,y) = x / (z * y).
T((x * y) / (z * y),u) = R(T(x / z,u),z,y).
R(x,x \ 1,y) = y / ((x \ 1) * y).
(x * y) / L(z,y / z,x) = x * (y / z).
R(x,x \ y,z) \ (y * z) = (x \ y) * z.
R(x,y \ 1,y) / y = x * (1 / y).
L(K(x,y) \ ((y * x) \ z),K(x,y),y * x) = (x * y) \ z.
(x * x) \ y = x \ (x \ y).
L(x \ L(y \ z,y,u),x,u * y) = ((u * y) * x) \ (u * z).
x \ (x \ (y * (x * x))) = T(y,x * x).
L(T(x,y),y,x) = T(x,x * y).
L(x,(y * x) / y,x) = T(x,x * ((y * x) / y)).
T(x,x * ((y * x) / y)) = L(x,(y * x) / y,x).
x / L(y \ z,y,x / z) = (x / z) * y.
R(x,y \ 1,y) / y = x * (y \ 1).
(x * (y \ 1)) * y = R(x,y \ 1,y).
(x * (y \ 1)) \ R(x,y \ 1,y) = y.
x * y = R(x / (y \ 1),y \ 1,y).
R(x / (y \ 1),y \ 1,y) = x * y.
(x * (x * y)) / z = x * (x * (y / z)).
(x * (x * y)) \ (x * (x * z)) = y \ z.
x \ ((x * y) * z) = x * ((x \ y) * z).
x * L(x,y,z) = L(x,y,z) * x.
L(x,y,z) * x = x * L(x,y,z).
x * L(x \ 1,y,z) = L(x \ 1,y,z) * x.
L(x \ 1,y,z) * x = x * L(x \ 1,y,z).
x * T(y,y * x) = L(y,x,y) * x.
L(x,y,z) = (x * L(x,y,z)) / x.
(x * L(x,y,z)) / x = L(x,y,z).
x = T(x,L(x,y,z)).
T(x,L(x,y,z)) = x.
L(x,L(x,y,z),x) = T(x,x * L(x,y,z)).
T(x,x * L(x,y,z)) = L(x,L(x,y,z),x).
(x \ y) * T(x,y) = L(x,x \ y,x) * (x \ y).
L(x,x \ y,x) * (x \ y) = (x \ y) * T(x,y).
x * R(T(T(y,x),z),u,w) = R(T(y,z),u,w) * x.
x * R(x,y,z) = R(x,y,z) * x.
R(x,y,z) * x = x * R(x,y,z).
x * R(x \ y,z,u) = R(y / x,z,u) * x.
R(x / y,z,u) * y = y * R(y \ x,z,u).
(x \ y) * R((x \ y) \ y,z,u) = R(x,z,u) * (x \ y).
R(x,y,z) * (u * u) = u * (u * R(T(x,u * u),y,z)).
x * (x * R(T(y,x * x),z,u)) = R(y,z,u) * (x * x).
x * R(x \ 1,y,z) = R(x \ 1,y,z) * x.
R(x \ 1,y,z) * x = x * R(x \ 1,y,z).
x = T(x,R(x,y,z)).
T(x,R(x,y,z)) = x.
T(x / y,y) = T(y \ x,R(x / y,z,u)).
T(x \ y,R(y / x,z,u)) = T(y / x,x).
x * T(y,x * x) = x \ (y * (x * x)).
x \ (y * (x * x)) = x * T(y,x * x).
T(x / (x * y),z) * (x * y) = (x * y) * T(L(y \ 1,y,x),z).
T((x * y) / (x * z),u) * (x * z) = (x * z) * T(L(z \ y,z,x),u).
(x * T(y,z)) / x = T((x * y) / x,z).
x = L(x,y,T(y,z)).
L(x,y,T(y,z)) = x.
(x * T(x,y)) * z = T(x,y) * (x * z).
L(x,(y * z) / y,z) = x.
(x * y) / z = x * (x * ((x \ y) / z)).
x * (x * ((x \ y) / z)) = (x * y) / z.
(x * (x * y)) \ (x * x) = y \ 1.
(x * y) \ (x * (x * z)) = (x \ y) \ z.
x \ (y * x) = T(y,y * (y * x)).
T(x,x * (x * y)) = y \ (x * y).
(x * y) \ (x * x) = (x \ y) \ 1.
(x * x) / (y \ 1) = x * (x * y).
((x * y) * z) \ (x * x) = ((x \ y) * z) \ 1.
T(x,x * (x * y)) = T(x,y).
T(x,x * y) = T(x,x \ y).
T(x,x \ y) = T(x,x * y).
T(x,x * (y * x)) = T(x,T(y,x)).
T(x * y,(x * y) * (y * x)) = T(x * y,K(y,x)).
T(x,x * y) = (x \ y) \ y.
(x \ y) * T(x,x * y) = y.
T(x / y,x) = ((x / y) \ y) \ y.
x / T(y,y * x) = y \ x.
(x \ y) * ((x \ y) * (T(x,x * y) * z)) = ((x \ y) * y) * z.
(x \ (x \ y)) * T(x,y) = x \ y.
((x \ y) * (T(x,x * y) * z)) \ (y * z) = a(x \ y,T(x,x * y),z).
K(x,y) / T(y * x,x * y) = (y * x) \ K(x,y).
x \ (y * y) = (y \ (y \ x)) \ 1.
(x \ (x \ y)) \ 1 = y \ (x * x).
L(x \ y,x,y) = (y \ x) \ 1.
L(K(x,y),y * x,x * y) = ((x * y) \ (y * x)) \ 1.
T((x \ y) \ 1,z) = L(T(y \ x,z),y,x).
L(T(x \ y,z),x,y) = T((y \ x) \ 1,z).
(x \ ((y * x) / y)) \ 1 = ((y * x) / y) \ x.
(x * x) / y = x * (x * (y \ 1)).
x * (x * (y \ 1)) = (x * x) / y.
x \ (y * z) = x * ((x \ (x \ y)) * z).
x * ((x \ (x \ y)) * z) = x \ (y * z).
L(x \ (y * ((y \ x) * z)),x,y) = z.
L(x \ (y * z),x,y) = (y \ x) \ z.
L(x \ y,x,z) = (z \ x) \ (z \ y).
L(x \ (y * z),x,z) = (z \ x) \ T(y,z).
L((x * y) \ z,x * y,x) = y \ (x \ z).
(x \ y) / L(z \ y,z,x) = x \ z.
L(x \ y,x,x / z) = z \ ((x / z) \ y).
(x \ y) \ (x \ z) = (x * y) \ (x * z).
L(x \ L(y \ z,y,u),x,u \ y) = ((u \ y) * x) \ (u \ z).
(x \ 1) / (y \ x) = x \ (x \ y).
(x \ 1) / y = x \ (x \ (x / y)).
x \ (x \ (x / y)) = (x \ 1) / y.
x * ((x \ 1) / y) = x \ (x / y).
((x \ 1) / y) \ 1 = (x / y) \ (x * x).
x * T(x,y) = T(x * T(x,y),T(x,y)).
T(x * T(x,y),T(x,y)) = x * T(x,y).
(x * T(x,y)) * (x \ z) = T(x,y) * z.
x * (x * y) = (x * z) / (y \ (x \ z)).
(x * y) / (z \ (x \ y)) = x * (x * z).
x \ (y * (y * z)) = (y \ (y \ x)) \ z.
(x \ (x \ y)) \ z = y \ (x * (x * z)).
(x * y) \ ((x * z) * u) = (x \ y) \ ((x \ z) * u).
(x \ y) \ ((x \ z) * u) = (x * y) \ ((x * z) * u).
(x \ (x \ y)) * z = x \ (x \ (y * z)).
x \ (x \ (y * z)) = (x \ (x \ y)) * z.
(x \ (x \ y)) * (x * x) = T(y,x * x).
T(x,y) \ (y \ z) = (y * (x * y)) \ (y * z).
(x * (y * x)) \ (x * z) = T(y,x) \ (x \ z).
T(x,y) * x = T(x * T(x,y),T(x,y)).
T(x * T(x,y),T(x,y)) = T(x,y) * x.
x / (y \ (x \ 1)) = x * (x * y).
(x \ (x \ y)) \ y = T(x * x,y).
x \ (x \ y) = (x \ (x \ 1)) * y.
(x \ (x \ 1)) * y = x \ (x \ y).
x \ (x \ y) = (x \ (x \ z)) * (z \ y).
(x \ (x \ y)) * (y \ z) = x \ (x \ z).
R((x / y) / (z \ (z \ 1)),z \ (z \ 1),y) = x / (z \ (z \ y)).
((x \ 1) / y) * (x * x) = T(x / y,x * x).
T(T(x,y) * x,T(x,y)) = T(x,y) * x.
x \ y = (z \ (z \ x)) \ (z \ (z \ y)).
(x \ (x \ y)) \ (x \ (x \ z)) = y \ z.
(x \ y) * ((x * y) \ z) = x \ (x \ z).
x = (T(x,y) \ x) * T(x,y).
(T(x,y) \ x) * T(x,y) = x.
T(x,y) \ x = x / T(x,y).
x / T(x,y) = T(x,y) \ x.
((x * y) * z) / T(x * (y * z),a(x,y,z)) = a(x,y,z).
x \ T(y * x,y) = L(y,y \ x,y).
L(x,x \ y,x) = y \ T(x * y,x).
L(L(x,y \ z,y),z,y) = x.
L(L(x,y,z),z * y,z) = x.
L(L(x,y,z / y),z,z / y) = x.
x = L(x,y \ 1,y).
L(x,y \ 1,y) = x.
L(x,y,y \ 1) = x.
x \ y = ((x \ 1) * x) \ ((x \ 1) * y).
((x \ 1) * x) \ ((x \ 1) * y) = x \ y.
x = L(L(x,y * z,y),z,y).
L(L(x,y * z,y),z,y) = x.
L(x,y * z,y) = z \ (y \ ((y * z) * x)).
x \ (y \ ((y * x) * z)) = L(z,y * x,y).
L(L(x,y,z),z * y,z) = R(x,L(x,y,z),u).
R(x,L(x,y,z),u) = L(L(x,y,z),z * y,z).
L((x \ y) \ z,x * y,x) = y \ (x * z).
L(x,y * z,y) = L(x,y \ z,y).
L(x,y \ z,y) = L(x,y * z,y).
L(x,y * (y * z),y) = L(x,z,y).
L(L(x,y * z,z),T(y,z),z) = x.
L(L(x,y * z,z * y),K(y,z),z * y) = x.
x \ T(y * x,y) = L(y,y * x,y).
L(x,x * y,x) = y \ T(x * y,x).
1 \ ((x \ 1) * y) = x \ y.
x \ y = (x \ 1) * y.
(x \ 1) * y = x \ y.
x \ 1 = (x \ y) / y.
(x \ y) / y = x \ 1.
x * ((x \ 1) * y) = y.
(x \ 1) * (x * y) = y.
(x \ (y * z)) \ (((x \ 1) * y) * z) = a(x \ 1,y,z).
((x * (y \ 1)) * z) / (y \ z) = R(x,y \ 1,z).
x \ (y \ x) = T(y \ 1,x).
T(x \ 1,y) = y \ (x \ y).
x \ T(y,x \ 1) = y * (x \ 1).
x * T(y \ 1,x) = y \ x.
(x \ y) * K(y,x \ 1) = y * (x \ 1).
x \ T(T(y,x \ 1),z) = T(y,z) * (x \ 1).
x * y = (x \ 1) \ y.
(x \ 1) \ y = x * y.
(x \ y) * L(z,y,x \ 1) = (x \ 1) * (y * z).
R(x,y \ 1,z) * (y \ z) = (x * (y \ 1)) * z.
(x * (y \ z)) / L(z,y \ 1,x) = x * (y \ 1).
R(x,x \ 1,y) = y / (x \ y).
(x \ (y \ 1)) * y = R(x \ 1,y \ 1,y).
R(x \ 1,y \ 1,y) = (x \ (y \ 1)) * y.
x * T(y \ 1,y \ x) = L(y \ 1,x,y \ 1) * x.
L(x \ 1,y,x \ 1) * y = y * T(x \ 1,x \ y).
T(x \ 1,(x \ 1) \ y) = T(x \ 1,x \ y).
(x \ (y * y)) * z = (y \ (y \ x)) \ z.
(x \ (x \ y)) \ z = (y \ (x * x)) * z.
x / (y * x) = y \ 1.
K(x,y) / (x * y) = (y * x) \ 1.
L(x,y,z) / (z * (y * x)) = (z * y) \ 1.
x / y = (y / x) \ 1.
(x / y) \ 1 = y / x.
(x * y) / ((z * x) * y) = R(z,x,y) \ 1.
T(x * y,K(y,x)) / (y * x) = K(y,x) \ 1.
T(x,x * y) / y = (x \ y) \ 1.
x * (y * (x \ 1)) = T(y,x \ 1).
(x * y) / ((z * x) * y) = R(z \ 1,z * x,y).
R(x \ 1,x * y,z) = (y * z) / ((x * y) * z).
(x * y) \ y = T(x \ 1,x * y).
T(x \ 1,x * y) = (x * y) \ y.
R((x \ 1) / y,y,x * z) = z / (y * (x * z)).
L(x * y,x \ 1,y) = (y \ (x \ 1)) \ 1.
L(x * (y * z),x \ 1,y) = (y \ (x \ 1)) \ z.
(x / y) * (y / x) = 1.
K(x \ y,x / y) = 1.
T(x,y / (y * x)) = x.
T(x \ y,x / y) = x \ y.
(x / y) * z = (y / x) \ z.
(x / y) \ z = (y / x) * z.
(x / y) * ((y / x) * z) = z.
x * ((y / z) * (z / y)) = x.
K((x * y) \ y,x) = 1.
(x / (x * y)) * y = y * (x / (x * y)).
(x * (y / (y * x))) / x = y / (y * x).
L(x,y / (y * x),x) = T(x,x * (y / (y * x))).
T(x,x * (y / (y * x))) = L(x,y / (y * x),x).
T((x * y) \ y,x) = (x * y) \ y.
x * R(x \ (y \ x),z,u) = R(y \ 1,z,u) * x.
T(x / y,x \ y) = x / y.
(x / y) * (x \ y) = (x \ y) * (x / y).
(x / y) * (z * (y / x)) = T(z,y / x).
T(x / y,x) = ((y / x) * y) \ y.
((x \ 1) / y) \ 1 = (y / x) * (x * x).
T(x / y,y) = T(y \ x,x \ y).
T(x \ y,y \ x) = T(y / x,x).
R(x,x \ 1,y) = x.
T(x,y) = R(T(x,y),x \ 1,z).
R(T(x,y),x \ 1,z) = T(x,y).
R(x,y,z) = R(R(x,y,z),x \ 1,u).
R(R(x,y,z),x \ 1,u) = R(x,y,z).
R(T(x / y,y),(x / y) \ 1,z) = y \ x.
x \ T(x,y) = T(x,y) * (x \ 1).
T(x,y) * (x \ 1) = x \ T(x,y).
(x \ (y * (x \ 1))) * x = x \ T(T(y,x \ 1),x).
x \ T(T(y,x \ 1),x) = (x \ (y * (x \ 1))) * x.
K(x,y) * ((K(x,y) \ 1) / (x * y)) = K(x,y) \ ((y * x) \ 1).
(x \ (x \ (y * (x * x)))) \ 1 = T(y \ 1,y * (x * x)).
T(x \ 1,x * (y * y)) = (y \ (y \ (x * (y * y)))) \ 1.
x * ((x * y) \ y) = ((x * y) \ y) * x.
((x * y) \ y) * x = x * ((x * y) \ y).
T(x \ y,y \ x) = x \ y.
T(x \ (x * y),(x * y) \ x) = y.
(x \ y) * (y \ x) = (y \ x) * (x \ y).
((x * y) \ y) * ((x \ 1) \ 1) = (x \ 1) \ T(x \ 1,x * y).
(x \ 1) \ T(x \ 1,x * y) = ((x * y) \ y) * ((x \ 1) \ 1).
T(x,(y * x) \ y) = x.
T(x,y \ (y / x)) = x.
((x * y) \ x) * y = y * ((x * y) \ x).
T(K(x,y),(x * y) \ (y * x)) = K(x,y).
R(x,y,z) / x = R(x,y,z) * (x \ 1).
R(x,y,z) * (x \ 1) = R(x,y,z) / x.
(x \ (y * y)) * z = x \ (y * (y * z)).
x \ (y * (y * z)) = (x \ (y * y)) * z.
(x \ (y * y)) * x = T(y * y,x).
(x \ (y * y)) * (y \ (y \ z)) = x \ z.
T(x * x,y * z) \ ((((y * z) \ (x * x)) * y) * z) = a((y * z) \ (x * x),y,z).
L(x \ 1,x,x \ (y * y)) = T(y * y,x) \ (x \ (y * y)).
(x / y) * (y * y) = x / (y \ 1).
x / y = (x / (y \ 1)) / (y * y).
(x / (y \ 1)) / (y * y) = x / y.
x * x = (x / y) * (y / (x \ 1)).
(x / y) * (y / (x \ 1)) = x * x.
x * (y * y) = (x * y) / (y \ 1).
(x * y) / (y \ 1) = x * (y * y).
x / (y * y) = (x * (y \ 1)) / y.
(x * (y \ 1)) / y = x / (y * y).
((x \ (x \ y)) * x) / (x \ 1) = T(y,x * x).
T(x / (y * y),y) = y \ (x * (y \ 1)).
T(K(x,y),K(y,x)) = K(x,y).
K(x,y) * T(K(y,x),z) = T(K(y,x),z) * K(x,y).
T(K(x,y),z) * K(y,x) = K(y,x) * T(K(x,y),z).
K(x,y) * R(K(y,x),z,u) = R(K(y,x),z,u) * K(x,y).
R(K(x,y),z,u) * K(y,x) = K(y,x) * R(K(x,y),z,u).
x * ((x \ (y * y)) * z) = y * (y * z).
(((x * y) * x) \ (x * x)) * y = K(x,x * y).
x \ (x \ (y \ z)) = (y * (x * x)) \ z.
(x * (y * y)) \ z = y \ (y \ (x \ z)).
(x * x) * y = z * ((z \ (x * x)) * y).
x * ((x \ (y * y)) * z) = (y * y) * z.
x * (y * (y * z)) = (x * (y * y)) * z.
(x * (y * y)) * z = x * (y * (y * z)).
x \ (x \ (y \ ((y * x) * x))) = a(y,x,x).
(x * (y * y)) \ x = y \ (y \ 1).
x \ (x / (y * y)) = y \ (y \ 1).
x / (y \ (y \ 1)) = x * (y * y).
x * (y \ (y \ 1)) = x / (y * y).
x * ((y * y) * z) = (x * (y * y)) * z.
(x * (y * y)) * z = x * ((y * y) * z).
x * (y * y) = (x * (y * (y * z))) / z.
(x * (y * (y * z))) / z = x * (y * y).
(x * (y * (y * z))) \ ((x * (y * y)) * (z * u)) = L(u,z,x * (y * y)).
T(x,y * y) * z = (y \ (y \ x)) * (y * (y * z)).
(x \ (x \ y)) * (x * (x * z)) = T(y,x * x) * z.
x = L(x,y * y,z).
L(x,y * y,z) = x.
x = R(x,y * y,z).
R(x,y * y,z) = x.
T(x,y * y) = T(x,x * (y * y)).
T(x,x * (y * y)) = T(x,y * y).
L(x,y,y / (z * z)) = x.
L(x,y \ (y \ 1),z) = x.
R(x,y \ (y \ 1),z) = x.
L(x,y,y / (z \ (z \ 1))) = x.
(x * (y \ (y \ 1))) * z = x * ((y \ (y \ 1)) * z).
L(x,y,y * (z * z)) = x.
T(x,x \ (y * y)) = T(x,y * y).
T(x \ 1,x * (y * y)) = T(x \ 1,y * y).
x \ (x / (y \ 1)) = L(y,y,x / y).
L(x,x,y / x) = y \ (y / (x \ 1)).
R(x,y,y \ 1) = (x * y) * (y \ 1).
(x * y) * (y \ 1) = R(x,y,y \ 1).
x * (y \ 1) = R(x / y,y,y \ 1).
R(x / y,y,y \ 1) = x * (y \ 1).
x * L(y,z * x,z) = z * ((z \ x) * y).
R(T(x,y),z,u) * (x * w) = (R(T(x,y),z,u) * x) * w.
(R(T(x,y),z,u) * x) * w = R(T(x,y),z,u) * (x * w).
T(x \ y,R(y / x,z,u)) = x \ y.
T((x \ 1) \ y,y * x) = (x \ 1) \ y.
T(x * y,y * x) = (x \ 1) \ y.
L(x,y,x) = (x \ y) \ T(y,x).
(x \ y) \ T(y,x) = L(x,y,x).
T(x,y) / L(y,x,y) = y \ x.
((x \ (x / y)) \ y) \ y = L(x \ (x / y),y,x \ (x / y)).
L(x \ (x / y),y,x \ (x / y)) = ((x \ (x / y)) \ y) \ y.
x \ (y \ (y \ z)) = (y * (y * x)) \ z.
(x * (x * y)) \ z = y \ (x \ (x \ z)).
x \ (y \ (y \ (z * (y * (y * x))))) = T(z,y * (y * x)).
L(x \ 1,x,x / y) = y \ (y / x).
L(x,y * (z \ 1),y) = z * (y \ ((y * (z \ 1)) * x)).
x * (y \ ((y * (x \ 1)) * z)) = L(z,y * (x \ 1),y).
R(x \ y,(y / x) \ 1,z) = x \ y.
R(x \ y,x / y,z) = x \ y.
R(x \ (x * y),x / (x * y),z) = y.
R(x,y / (y * x),z) = x.
x * ((y / (y * x)) * z) = (x * (y / (y * x))) * z.
(x * (y / (y * x))) * z = x * ((y / (y * x)) * z).
x \ L(x,y * x,y) = a(y,x,x).
x * a(y,x,x) = L(x,y * x,y).
L(x,y * x,y) = x * a(y,x,x).
x * ((x \ y) * T(z,y)) = L(z,x * y,x) * y.
K(x \ (x \ y),x) = (x * y) \ (x * T(y,x)).
(x * y) \ (x * T(y,x)) = K(x \ (x \ y),x).
x = L(x,y,R(y,z,u)).
L(x,y,R(y,z,u)) = x.
x * y = R(x,z,u) * ((R(x,z,u) \ x) * y).
R(x,y,z) * ((R(x,y,z) \ x) * u) = x * u.
(x * R(x,y,z)) * u = R(x,y,z) * (x * u).
x \ R(x,y,z) = (R(x,y,z) \ x) \ 1.
(R(x,y,z) \ x) \ 1 = x \ R(x,y,z).
(R(x,y,z) \ u) / (x \ u) = R(x,y,z) \ x.
(x \ R(x,y,z)) \ 1 = R(x,y,z) \ x.
(x \ R(x,y,z)) * u = (R(x,y,z) \ x) \ u.
(R(x,y,z) \ x) \ u = (x \ R(x,y,z)) * u.
(R(x,y,z) \ x) * ((x \ R(x,y,z)) * u) = u.
(x \ R(x,y,z)) \ u = (R(x,y,z) \ x) * u.
x = T(x,L(x \ 1,y,z)).
T(x,L(x \ 1,y,z)) = x.
K(x,L(x \ 1,y,z)) = 1.
K(x \ 1,L(x,y,z)) = 1.
K(L(x,y,z) \ 1,x) = 1.
T(L(x,y,z) \ 1,x) = L(x,y,z) \ 1.
x * (L(x,y,z) \ 1) = L(x,y,z) \ x.
R(x / (x * y),z,u) * (x * y) = (x * y) * R(L(y \ 1,y,x),z,u).
R((x * y) / (x * z),u,w) * (x * z) = (x * z) * R(L(z \ y,z,x),u,w).
x = T(x,R(x \ 1,y,z)).
T(x,R(x \ 1,y,z)) = x.
T(x \ 1,R(x,y,z)) = x \ 1.
R(x,y,z) * (x \ 1) = x \ R(x,y,z).
x \ R(x,y,z) = R(x,y,z) / x.
R(x,y,z) / x = x \ R(x,y,z).
(x \ R(x,y,z)) \ R(x,y,z) = x.
(x * (y \ 1)) / (x / y) = (x / y) \ R(x / y,y,y \ 1).
(x / y) \ R(x / y,y,y \ 1) = (x * (y \ 1)) / (x / y).
(x \ ((y * x) / y)) \ 1 = (y / (y * x)) * x.
R(x,L(x,y,z),u) = x.
x * (L(x,y,z) * u) = (x * L(x,y,z)) * u.
(x * L(x,y,z)) * u = x * (L(x,y,z) * u).
T(x \ 1,x * y) = T(x \ 1,x \ y).
T(x \ 1,x \ y) = T(x \ 1,x * y).
(x \ T(y,x)) / (x \ 1) = T(y,x * x).
(((x \ y) * x) \ 1) * y = K(x,x * y).
K(x,x * y) = ((x \ y) * x) \ y.
((x \ y) * x) \ y = K(x,x * y).
K(x,x * y) = K(x,x \ y).
K(x,x \ y) = K(x,x * y).
K(x,y) = K(x,x * (x * y)).
K(x,x * (x * y)) = K(x,y).
K(x,T(y,x)) = K(x,x * (y * x)).
K(x,x * (y * x)) = K(x,T(y,x)).
K(x,(x * x) / y) = K(x,y \ 1).
(x * y) \ (y * x) = K(x \ (x \ y),x).
K(x \ (x \ y),x) = (x * y) \ (y * x).
K(x \ (x \ y),x) = K(y,x).
K(x \ y,x) = K(x * y,x).
(R(x,y,z) \ x) * R(x,y,z) = x.
R(x,y,z) \ x = x / R(x,y,z).
x / R(x,y,z) = R(x,y,z) \ x.
T(R(x,y,z) \ 1,x) = x \ (x / R(x,y,z)).
(x * y) / (z \ ((z * x) * y)) = R(z,x,y) \ z.
R(x,y,z) * u = x * ((x \ R(x,y,z)) * u).
x * ((x \ R(x,y,z)) * u) = R(x,y,z) * u.
(x \ ((y * x) / y)) \ 1 = x * (y / (y * x)).
x = L(x,L(y,z,u),y).
L(x,L(y,z,u),y) = x.
L(x,y,z) * u = x * ((x \ L(x,y,z)) * u).
x * ((x \ L(x,y,z)) * u) = L(x,y,z) * u.
L(x,(y * z) \ y,z \ 1) = x.
L(x,y,z) \ x = (x \ L(x,y,z)) \ 1.
(x \ L(x,y,z)) \ 1 = L(x,y,z) \ x.
L(x,y,z) \ (x * u) = (x \ L(x,y,z)) \ u.
(x \ L(x,y,z)) \ u = L(x,y,z) \ (x * u).
L(x,y,L(y,z,u)) = x.
T(x,x * L(x,y,z)) = x.
x \ L(x,y,z) = (L(x,y,z) \ x) \ 1.
(L(x,y,z) \ x) \ 1 = x \ L(x,y,z).
(L(x,y,z) \ u) / (x \ u) = L(x,y,z) \ x.
(x \ L(x,y,z)) * x = L(x,y,z).
L(x,y,z) / x = x \ L(x,y,z).
x / L(x,y,z) = (x \ L(x,y,z)) \ 1.
(x \ L(x,y,z)) \ 1 = x / L(x,y,z).
(L(x,y,z) \ x) * u = (x \ L(x,y,z)) \ u.
(x \ L(x,y,z)) \ u = (L(x,y,z) \ x) * u.
x / L(x,y,z) = L(x,y,z) \ x.
(L(x,y,z) \ x) * L(x,y,z) = x.
(L(x \ 1,x,x / y) \ (x \ 1)) * (y \ (y / x)) = x \ 1.
x * (R(x,y,z) * u) = (x * R(x,y,z)) * u.
(x * R(x,y,z)) * u = x * (R(x,y,z) * u).
(L(x,y,z) \ x) * u = L(x,y,z) \ (x * u).
L(x,y,z) \ (x * u) = (L(x,y,z) \ x) * u.
x = R(x,R(x,y,z),u).
R(x,R(x,y,z),u) = x.
x * (R(x,y,z) * u) = R(x,y,z) * (x * u).
R(x,y,z) * (x * u) = x * (R(x,y,z) * u).
T(x,y) = R(T(x,y),R(x,z,u),w).
R(T(x,y),R(x,z,u),w) = T(x,y).
R(x,y,z) * u = (x \ R(x,y,z)) * (x * u).
(x \ R(x,y,z)) * (x * u) = R(x,y,z) * u.
R(x,y,z) * u = x * (R(x,y,z) * (x \ u)).
x * (R(x,y,z) * (x \ u)) = R(x,y,z) * u.
R(x,y,z) * (u * x) = x * (R(x,y,z) * T(u,x)).
x * (R(x,y,z) * T(u,x)) = R(x,y,z) * (u * x).
x \ R(x,y,z) = (R(x,y,z) * u) / (x * u).
(R(x,y,z) * u) / (x * u) = x \ R(x,y,z).
(x \ R(x,y,z)) * u = R(x,y,z) * (x \ u).
((R(x,y,z) * u) * w) / ((x * u) * w) = R(x \ R(x,y,z),x * u,w).
R(x \ R(x,y,z),x * u,w) = ((R(x,y,z) * u) * w) / ((x * u) * w).
R(x,y,z) * (x \ u) = x \ (R(x,y,z) * u).
x \ (R(x,y,z) * u) = R(x,y,z) * (x \ u).
x / (y * (R(y,z,u) \ x)) = y \ R(y,z,u).
(R(x,y,z) * (x \ u)) / u = x \ R(x,y,z).
((x * y) * z) / (x * (y * z)) = x \ R(x,y,z).
(R(R(x,y,z),u,w) * (y * z)) / ((x * y) * z) = R(x,y,z) \ R(R(x,y,z),u,w).
x \ (R(y,z,u) * (y \ x)) = T(y \ R(y,z,u),x).
(R(x,y,z) \ x) \ u = R(x,y,z) * (x \ u).
(x \ R(x,y,z)) \ u = x * (R(x,y,z) \ u).
x / (R(y,z,u) * (y \ x)) = R(y,z,u) \ y.
x * (R(x,y,z) \ 1) = R(x,y,z) \ x.
x * (R(x,y,z) \ u) = (R(x,y,z) \ x) * u.
(R(x,y,z) \ x) * u = x * (R(x,y,z) \ u).
R(x,y,z) \ 1 = T(R(x,y,z) \ 1,x).
T(R(x,y,z) \ 1,x) = R(x,y,z) \ 1.
T(x,R(x,y,z) \ 1) = x.
R(x,y,z) \ 1 = x \ (x / R(x,y,z)).
x \ (x / R(x,y,z)) = R(x,y,z) \ 1.
R(x,y,z) \ T(x,u) = T(x,u) * (R(x,y,z) \ 1).
T(x,y) * (R(x,z,u) \ 1) = R(x,z,u) \ T(x,y).
(x * y) \ ((z * x) * y) = R(T(z,x * y),x,y).
(x * (x * (y * z))) / (y * z) = R(x * x,y,z).
x \ ((x * y) * (1 / y)) = a(x,y,1 / y).
x \ ((x * y) * (y \ 1)) = a(x,y,1 / y).
x \ ((x * y) * (y \ 1)) = a(x,y,y \ 1).
(x / y) \ (x * (y \ 1)) = a(x / y,y,y \ 1).
a(x / y,y,y \ 1) = (x / y) \ (x * (y \ 1)).
T((x * y) / (z * y),z) = R(z \ x,z,y).
T(R(x \ y,x,z),u) = T(T((y * z) / (x * z),u),x).
T(T((x * y) / (z * y),u),z) = T(R(z \ x,z,y),u).
T(x,x * ((y * x) / y)) = x.
((x * y) / x) / y = y \ ((x * y) / x).
(x \ y) * L(z,y,x \ 1) = x \ (y * z).
T(x,y) * (x \ z) = (T(x,y) * (x \ 1)) * z.
(T(x,y) * (x \ 1)) * z = T(x,y) * (x \ z).
(x \ T(x,y)) * z = T(x,y) * (x \ z).
x \ T(x,y) = (T(x,y) * (x \ z)) / z.
(T(x,y) * (x \ z)) / z = x \ T(x,y).
x * (T(x,y) * (x \ x)) = T(x * T(x,y),x).
(T(x,y) * z) / (x * z) = x \ T(x,y).
(x \ T(x,y)) \ (T(x,y) * z) = x * z.
(x \ T(x,y)) \ z = x * (T(x,y) \ z).
x * (T(x,y) * 1) = T(x * T(x,y),x).
T(x * T(x,y),x) = x * (T(x,y) * 1).
T(x * T(x,y),x) = x * T(x,y).
T(x,x * T(x,y)) = x.
T(x,y) / x = x \ T(x,y).
(x \ T(x,y)) \ z = (x / T(x,y)) * z.
(x \ T(x,y)) \ z = (T(x,y) \ x) * z.
(T(x,y) \ x) * (T(x,y) * z) = x * z.
(T(x,y) \ x) * z = x * (T(x,y) \ z).
T(x,y) \ x = (x * z) / (T(x,y) * z).
(x * y) / (T(x,z) * y) = T(x,z) \ x.
T(x,y) \ x = x * (T(x,y) \ 1).
x * (T(x,y) \ 1) = T(x,y) \ x.
1 = K(x,T(x,y) \ 1).
K(x,T(x,y) \ 1) = 1.
T(x,T(x,y) \ 1) = x.
T(x,y) \ T(x,z) = T(x,z) * (T(x,y) \ 1).
T(x,y) * (T(x,z) \ 1) = T(x,z) \ T(x,y).
T(x,y) \ 1 = x \ (T(x,y) \ x).
x \ (T(x,y) \ x) = T(x,y) \ 1.
((T(x,y) \ x) * z) / (T(x,y) \ z) = R(x,T(x,y) \ 1,z).
R(x \ 1,x * y,z) = R(x,y,z) \ 1.
R(x \ 1,y,z) = R(x,x \ y,z) \ 1.
R(x,x \ y,z) \ 1 = R(x \ 1,y,z).
(x * y) / (z * ((z \ x) * y)) = R(z,x,y) \ z.
T(x \ R(x,y,z),x * (y * z)) = (x * (y * z)) \ ((x * y) * z).
R(x * x,y,z) = x * x.
T(x * x,y) = R(T(x * x,y),z,u).
R(T(x * x,y),z,u) = T(x * x,y).
T(x * x,y) \ (z * u) = (T(x * x,y) \ z) * u.
a(x / y,y,y \ 1) = (y / x) * (x * (y \ 1)).
(x * y) / (z * ((z \ y) * T(x,y))) = R(z,y,T(x,y)) \ z.
(x \ (y * z)) \ ((x \ y) * z) = a(x,y,z).
(x \ (y * (x \ 1))) * x = T(y,x) * (x \ 1).
x \ (y * (x \ 1)) = (T(y,x) * (x \ 1)) / x.
(T(x,y) * (y \ 1)) / y = y \ (x * (y \ 1)).
x \ (y * (x \ 1)) = T(y,x) / (x * x).
x \ ((x * (x * y)) * (x \ 1)) = (x * (y * x)) / (x * x).
T(x / (y * y),y) = T(x,y) / (y * y).
T(x,y) / (y * y) = T(x / (y * y),y).
(x / (y * y)) * z = x * ((y \ (y \ 1)) * z).
x * ((y \ (y \ 1)) * z) = (x / (y * y)) * z.
x * (y \ (y \ z)) = (x / (y * y)) * z.
(x / (y * y)) * z = x * (y \ (y \ z)).
x = L(x,y / (y * z),z).
L(x,y / (y * z),z) = x.
(x / (x * y)) \ (y \ z) = (y * (x / (x * y))) \ z.
(x * (y / (y * x))) \ z = (y / (y * x)) \ (x \ z).
T(x,x * (y / (y * x))) = x.
(x * (y / (y * x))) \ z = ((y * x) / y) * (x \ z).
R(x,x * y,z) = x * (x * ((y * z) / ((x * y) * z))).
x * (x * ((y * z) / ((x * y) * z))) = R(x,x * y,z).
L(R(x,x,y),z,u) * (x * y) = (x * L(x,z,u)) * y.
L(K(x,y),y * x,x * y) = K(y,x) \ 1.
(x \ (y * z)) \ ((x \ y) * z) = a(x \ 1,y,z).
a(x \ 1,y,z) = a(x,y,z).
a(x / y,z,u) = a(y / x,z,u).
L(x \ 1,y,x \ 1) * y = y * T(x \ 1,x * y).
T(T((x * y) / (z * y),u),z) = R(T(z \ x,u),z,y).
x * (x * (R(x,y,z) \ 1)) = R(x,x * y,z).
R(x,x * y,z) = (x * x) / R(x,y,z).
(x * x) / R(x,y,z) = R(x,x * y,z).
x * (R(x,y,z) \ x) = R(x,x * y,z).
R(x,y,z) \ x = x \ R(x,x * y,z).
x \ R(x,x * y,z) = R(x,y,z) \ x.
x * (R(x,x * y,z) \ x) = R(x,(x * x) * y,z).
x / R(x,x * y,z) = x \ R(x,y,z).
(R(x,y,z) \ x) * x = R(x,x * y,z).
x \ R(x,y,z) = R(x,x * y,z) \ x.
R(x,x * y,z) \ x = x \ R(x,y,z).
x \ (x \ R(x,y,z)) = R(x,x * y,z) \ 1.
R(x,x * y,z) \ 1 = x \ (x \ R(x,y,z)).
R(x,y,z) \ x = x \ R(x,x \ y,z).
x \ R(x,x \ y,z) = R(x,y,z) \ x.
(x \ R(x,y,z)) * u = x * (R(x,x * y,z) \ u).
x * (R(x,x * y,z) \ u) = (x \ R(x,y,z)) * u.
x * (x \ R(x,y,z)) = R(x,(x * x) * y,z).
R(x,(x * x) * y,z) = R(x,y,z).
R(x,x * (x * y),z) = R(x,y,z).
R(x,x * y,z) = R(x,x \ y,z).
R(x,x \ y,z) = R(x,x * y,z).
R(x,x * y,z) \ (y * z) = (x \ y) * z.
R(x,x * y,z) \ 1 = R(x \ 1,y,z).
R(x \ 1,y,z) \ 1 = R(x,x * y,z).
R(x,x * y,z) = R(x \ 1,y,z) \ 1.
R(x \ 1,y,z) = x \ (x \ R(x,y,z)).
x \ (x \ R(x,y,z)) = R(x \ 1,y,z).
x * R(x \ 1,y,z) = x \ R(x,y,z).
x * (R(x \ 1,y,z) * u) = x \ (R(x,y,z) * u).
x * (R(x,x * y,z) \ u) = R(x,y,z) * (x \ u).
x * (R(x \ 1,y,z) * u) = R(x,y,z) * (x \ u).
x * (y * R(y \ (x \ y),z,u)) = R(x,z,u) * (x \ y).
L(x,y,z) * (x * u) = (x * L(x,y,z)) * u.
(x * L(x,y,z)) * u = L(x,y,z) * (x * u).
x * y = L(x,z,u) \ ((x * L(x,z,u)) * y).
L(x,y,z) \ ((x * L(x,y,z)) * u) = x * u.
L(x,y,z) * (x * u) = x * (L(x,y,z) * u).
L(x,y,z) \ (x * (L(x,y,z) * u)) = x * u.
L(x,y,z) * u = x * (L(x,y,z) * (x \ u)).
x * (L(x,y,z) * (x \ u)) = L(x,y,z) * u.
L(x,y,z) * (x * (L(x,y,z) \ u)) = x * u.
x * y = (L(x,z,u) \ x) * (L(x,z,u) * y).
(L(x,y,z) \ x) * (L(x,y,z) * u) = x * u.
L(x,y,z) * (x \ u) = (x \ L(x,y,z)) * u.
(x \ L(x,y,z)) * u = L(x,y,z) * (x \ u).
L(x,y,z) = (x * u) / (x * (L(x,y,z) \ u)).
(x * y) / (x * (L(x,z,u) \ y)) = L(x,z,u).
L(x,y,z) \ x = (x * u) / (L(x,y,z) * u).
(x * y) / (L(x,z,u) * y) = L(x,z,u) \ x.
(L(x,y,z) \ x) * u = x * (L(x,y,z) \ u).
x = T(x,L(x,y,z) \ x).
T(x,L(x,y,z) \ x) = x.
K(x,L(x,y,z) \ x) = 1.
T(x \ 1,x * (y * y)) = T(x,y * y) \ 1.
T(x,y * y) \ 1 = T(x \ 1,y * y).
x = L(x,y,R(T(y,z),u,w)).
L(x,y,R(T(y,z),u,w)) = x.
L(x,y,R((y \ z) \ z,u,w)) = x.
x \ ((y \ (y \ z)) * (y * (y * x))) = T(z,y * (y * x)).
x \ (x * (x * (y * (x \ 1)))) = (x * (y * x)) / (x * x).
x \ (T(y,z * z) * x) = T(y,z * (z * x)).
T(x,y * (y * z)) = T(T(x,y * y),z).
T(T(x,y * y),z) = T(x,y * (y * z)).
T(x,y * (y * z)) = T(T(x,z),y * y).
T(T(x,y),z * z) = T(x,z * (z * y)).
x \ (x * T(y,x \ 1)) = (x * (y * x)) / (x * x).
(x * (y * x)) / (x * x) = T(y,x \ 1).
T(x * y,x) / (x * x) = T(x \ y,x \ 1).
T(x \ y,x \ 1) = T((x * y) / (x * x),x).
T((x * y) / (x * x),x) = T(x \ y,x \ 1).
(x * (x * ((y * z) * u))) / (z * u) = R(x * (x * y),z,u).
(x / y) \ (x * (y \ 1)) = (x * (y \ 1)) / (x / y).
(x * (y \ 1)) / (x / y) = (x / y) \ (x * (y \ 1)).
(x * (y \ 1)) / (x / y) = (y / x) * (x * (y \ 1)).
(x * (T(x,y) \ z)) / (T(x,y) \ z) = R(x,T(x,y) \ 1,z).
(x * y) / (L(x,z * y,z) * y) = R(z,y,T(x,y)) \ z.
R(x,y,T(z,y)) \ x = L(z,x * y,x) \ z.
(R(x,y,T(z,y)) \ x) \ 1 = z \ L(z,x * y,x).
L(x,y * (y * z),y) \ x = y \ R(y,z,T(x,y * z)).
x \ L(x,y * z,y) = y \ R(y,z,T(x,z)).
x \ R(x,y,T(z,y)) = z \ L(z,x * y,x).
x * (y \ L(y,x * z,x)) = R(x,z,T(y,z)).
R(x,y,T(z,y)) = x * (z \ L(z,x * y,x)).
R(x,x * y,T(z,x * y)) = x * (z \ L(z,y,x)).
x \ L(x,y,z) = R(z,y,T(x,z * y)) \ z.
R(x,y,T(z,x * y)) \ x = z \ L(z,y,x).
(x \ L(x,y,z)) * R(z,y,T(x,z * y)) = z.
L(x,y,z) \ x = z \ R(z,y,T(x,z * y)).
L(x,y,z) * (z \ R(z,y,T(x,z * y))) = x.
x * (L(y,z,x) \ y) = R(x,z,T(y,x * z)).
R(x,y,T(z,x * y)) = x * (L(z,y,x) \ z).
(x \ R(x,y,T(z,x * y))) * L(z,y,x) = z.
L(x,R(y,z,u),T(y,w)) * (T(y,w) \ T(y,w)) = x.
x = R(y,z,T(x,y * z)) * (y \ L(x,z,y)).
R(x,y,T(z,x * y)) * (x \ L(z,y,x)) = z.
L(x,R(y,z,u),T(y,w)) * 1 = x.
L(x,R(y,z,u),T(y,w)) = x.
L(x,R(y / z,u,w),z \ y) = x.
T(R(x,y,z),T(x,u)) / T(x,u) = T(x,u) \ R(x,y,z).
R(T(x,T(x,y)),z,u) / T(x,y) = T(x,y) \ R(x,z,u).
R(x,y,z) / T(x,u) = T(x,u) \ R(x,y,z).
R(x * (x * y),z,u) = x * (x * (((y * z) * u) / (z * u))).
x * (x * (((y * z) * u) / (z * u))) = R(x * (x * y),z,u).
R(x,T(x,y) \ 1,z) = x.
x * (x * R(y,z,u)) = R(x * (x * y),z,u).
x * (x * R(T(y,x),z,u)) = R(x * (y * x),z,u).
R(x * (x * T(y,x * x)),z,u) = R(y,z,u) * (x * x).
x * (R(y,z,u) * x) = R(x * (y * x),z,u).
R(x,y,z) * u = u \ R(u * (x * u),y,z).
x \ R(x * (y * x),z,u) = R(y,z,u) * x.
(x * (y * x)) \ R(x * (z * x),u,w) = T(y,x) \ (x \ (R(z,u,w) * x)).
x \ R(x * y,z,u) = R(y / x,z,u) * x.
x \ R(x * y,z,u) = x * R(x \ y,z,u).
L(x \ (y * R(y \ z,u,w)),x,y) = (y * x) \ R(y * z,u,w).
R(x * (y * y),z,u) = R(x,z,u) * (y * y).
R(x,y,z) * (u * u) = R(x * (u * u),y,z).
(x \ 1) \ T(x \ 1,x * y) = ((x * y) \ y) * x.
(x \ 1) \ T(x \ 1,x * y) = x * ((x * y) \ y).
(x * y) * T(L(y \ 1,y,x),z) = (x * y) * T((x * y) \ x,z).
R((x / y) * (z * z),z \ (z \ 1),y) = x / (z \ (z \ y)).
x / (y \ (y \ z)) = (x / z) * (y * y).
x / (y \ z) = (x / (y * z)) * (y * y).
(x / (y * z)) * (y * y) = x / (y \ z).
R(x / y,y,z) * (y * y) = (x * z) / (y \ z).
(x * y) / (z \ y) = R(x / z,z,y) * (z * z).
(x * y) / (z \ y) = R((x / z) * (z * z),z,y).
R((x / y) * (y * y),y,z) = (x * z) / (y \ z).
R(x / (y \ 1),y,z) = (x * z) / (y \ z).
R(x,y,z) = ((x * (y \ 1)) * z) / (y \ z).
((x * (y \ 1)) * z) / (y \ z) = R(x,y,z).
R(L(x,y,z) \ x,x,u) = ((L(x,y,z) \ 1) * u) / (x \ u).
R(x,y,z) = R(x,y \ 1,z).
R(x,y \ 1,z) = R(x,y,z).
R(x,y,y) / y = x * (y \ 1).
(x * (y \ 1)) \ R(x,y,y) = y.
R(x / (y \ 1),y,y) = x * y.
R(x,T(x,y),z) = x.
x * (T(x,y) * z) = (x * T(x,y)) * z.
(x * T(x,y)) * z = x * (T(x,y) * z).
R(T(x / (y \ 1),z),y,y) / y = (y \ 1) * T((y \ 1) \ x,z).
(T(x,y) * (R(x,z,u) \ 1)) \ T(x,y) = R(x,z,u).
T(x * y,z) = R(T(x / (y \ 1),z),y,y).
R(T(x / (y \ 1),z),y,y) = T(x * y,z).
x = L(x,T(y,z),y).
L(x,T(y,z),y) = x.
x * (T(x,y) * (x \ z)) = T(x,y) * z.
L(x,y,(z * y) / z) = x.
L(x,(y \ z) \ z,y) = x.
T(x,y) * (x \ z) = x \ (T(x,y) * z).
x \ (T(x,y) * z) = T(x,y) * (x \ z).
(x \ T(x,y)) * z = x \ (T(x,y) * z).
x \ (T(x,y) * z) = (x \ T(x,y)) * z.
(R(x,y,z) \ T(x,u)) \ T(x,u) = R(x,y,z).
R(L(x,y,z) \ x,x,u) = (L(x,y,z) \ u) / (x \ u).
R(L(x,y,z) \ x,x,u) = L(x,y,z) \ x.
T(x \ R(x,y,z),x * (y * z)) = a(x,y,z).
T(a(x,y,z),u) = T(T(x \ R(x,y,z),u),x * (y * z)).
T(T(x \ R(x,y,z),u),x * (y * z)) = T(a(x,y,z),u).
T(T(R(x,y,z) / x,x * (y * z)),x) = a(x,y,z).
(x * a(y,z,u)) / x = T((x * (y \ R(y,z,u))) / x,y * (z * u)).
T((x * (y \ R(y,z,u))) / x,y * (z * u)) = (x * a(y,z,u)) / x.
T(R(x,y,z) \ R(R(x,y,z),u,x),x * (R(x,y,z) * T(u,x))) = a(R(x,y,z),u,x).
T(T((R(x,y,z) * u) / (x * u),x * (y * z)),x) = R(a(x,y,z),x,u).
T(T(x \ R(x,y,z),x * (y * z)),x) = a(x,y,z).
T(a(x,y,z),x) = a(x,y,z).
x * a(x,y,z) = a(x,y,z) * x.
a(x,y,z) * x = x * a(x,y,z).
(x * a(x,y,z)) / x = a(x,y,z).
((x * (x * y)) * a(x * (x * y),z,u)) / y = a(x * (x * y),z,u) * (x * x).
(x * y) \ R(x * z,u,w) = (x \ y) \ R(x \ z,u,w).
(x \ y) \ R(x \ z,u,w) = (x * y) \ R(x * z,u,w).
(x * y) * L(T(y \ 1,z),y,x) = (x * y) * T((x * y) \ x,z).
(x * y) * T((x * y) \ x,z) = (x * y) * L(T(y \ 1,z),y,x).
T(x * y,z) / y = (y \ 1) * T((y \ 1) \ x,z).
(x \ 1) * T((x \ 1) \ y,z) = T(y * x,z) / x.
(x \ 1) * T(x * y,z) = T(y * x,z) / x.
T(x * y,z) / y = y \ T(y * x,z).
T(x,y) / z = z \ T(z * (x / z),y).
x \ T(x * (y / x),z) = T(y,z) / x.
T(x * y,y) / y = (y \ x) * y.
((x \ y) * x) * x = T(y * x,x).
(x * y) * y = T((y * x) * y,y).
T((x * y) * x,x) = (y * x) * x.
(x * y) * T((x * y) \ x,z) = x * (y * T(y \ 1,z)).
(x * (x * (y * z))) \ (x * (x * (y * (z * u)))) = L(u,z,x * (x * y)).
(x * y) * T(L(y \ z,y,x),u) = (x * y) * T((x * y) \ (x * z),u).
(x * y) * R(L(y \ 1,y,x),z,u) = (x * y) * R((x * y) \ x,z,u).
T(T(x \ R(x,y,z),x * (y * z)),x) = R(a(x,y,z),x,u).
R(a(x,y,z),x,u) = a(x,y,z).
a(x,y,z) * (x * u) = (a(x,y,z) * x) * u.
(a(x,y,z) * x) * u = a(x,y,z) * (x * u).
x = L(x,y,a(y,z,u)).
L(x,y,a(y,z,u)) = x.
(x * a(x,y,z)) * u = a(x,y,z) * (x * u).
L(x,y,z * (z * u)) = (u * y) \ (u * (y * x)).
L(x,y,z * (z * u)) = L(x,y,u).
L(x,y,z * u) = L(x,y,z \ u).
L(x,y,z \ u) = L(x,y,z * u).
L(x,y,(z / u) * z) = L(x,y,u).
L(x,y,z * (u * z)) = L(x,y,T(u,z)).
L(x,y,(z * u) * (u * z)) = L(x,y,K(u,z)).
L(x,y,z * ((z * u) * w)) = L(x,y,z * ((z \ u) * w)).
L(x,y,z * ((z \ u) * w)) = L(x,y,z * ((z * u) * w)).
L(x,y,(z * u) * w) = L(x,y,(z \ u) * w).
L(x,y,(z \ u) * w) = L(x,y,(z * u) * w).
L(x,y,(z \ (z \ u)) * (z \ u)) = L(x,y,T(z,u)).
L(x,y,(z * z) / u) = L(x,y,u \ 1).
L(x,y,z / u) = L(x,y,u / z).
L(x,y,z * L(z,u * z,u)) = L(x,y,a(u,z,z)).
L(x,y,R(z * (z * u),w,v5)) = L(x,y,R(u,w,v5)).
L(x,y,z \ 1) = L(x,y,z).
L(x,y,T(z / u,z)) = L(x,y,((u / z) * u) * u).
L(x,y,y \ (z * z)) = x.
L(x \ (x / y),y,x * (x / y)) = ((x \ (x / y)) \ y) \ y.
L(x,R(y / z,u,w),z * y) = x.
L(x \ L(y \ z,y,u),x,u * y) = ((u \ y) * x) \ (u \ z).
x \ 1 = T(y * y,x) \ (x \ (y * y)).
T(x * x,y) \ (y \ (x * x)) = y \ 1.
L(x,L(y \ 1,z,u),y) = x.
L(x,(y * z) \ y,z) = x.
(x \ y) * L(z,y,x) = x \ (y * z).
L(x \ 1,y,x) * y = y * T(x \ 1,x * y).
x * T(y \ 1,y * x) = L(y \ 1,x,y) * x.
L(x,y \ z,z \ y) = x.
x = L(x,y \ z,z * y).
L(x,y \ z,z * y) = x.
L(x,y,z * (z / y)) = x.
L(x \ 1,y,z) \ (x \ u) = (x * L(x \ 1,y,z)) \ u.
(x * L(x \ 1,y,z)) \ u = L(x \ 1,y,z) \ (x \ u).
L(x,y,(z * (z * u)) * (z * w)) = L(x,y,u \ (z \ w)).
L(x,y,(z * (z * u)) * z) = L(x,y,u \ (z \ 1)).
L(L(x,y,y / z),z,z / y) = x.
L(x,x,x / y) = y \ (y / (x \ 1)).
L(x,y,z / (z * y)) = x.
x \ 1 = ((y / (y * x)) * x) \ (y / (y * x)).
((x / (x * y)) * y) \ (x / (x * y)) = y \ 1.
((x / (x * y)) * y) * z = (x / (x * y)) * (y * z).
x \ ((y / (y * x)) \ z) = ((y / (y * x)) * x) \ z.
((x / (x * y)) * y) \ z = y \ ((x / (x * y)) \ z).
L(x,y / (z * (u * y)),z * (u \ 1)) = x.
(x * (y \ z)) \ (x * (y \ (z * u))) = L(L(u,z,y),y \ z,x).
(T(x,y) \ x) * z = T(x,y) \ (x * z).
T(x,y) \ (x * z) = (T(x,y) \ x) * z.
(x \ ((y * x) / y)) * z = x \ (((y * x) / y) * z).
x \ (((y * x) / y) * z) = (x \ ((y * x) / y)) * z.
(x \ y) * T((x \ y) \ 1,z) = x \ (y * T(y \ x,z)).
L(x,y,T(z * u,z)) = L(x,y,T(z \ u,z)).
L(x,y,T(z \ u,z)) = L(x,y,T(z * u,z)).
L(x,y,z * T(u * z,z)) = L(x,y,T((z \ u) * z,z)).
L(x,y,(z * z) / u) = L(x,y,u).
L(x,y,z \ (u * u)) = L(x,y,T(z,z * (u * u))).
L(x,y,T(z,z * (u * u))) = L(x,y,z \ (u * u)).
L(x,y,z) = L(x,y,z / (u * u)).
L(x,y,z / (u * u)) = L(x,y,z).
L(x,y,z) = L(x,y,z * (u * u)).
L(x,y,z * (u * u)) = L(x,y,z).
L(x,y,R(z,u,u)) = L(x,y,(z * u) * u).
L(x,y,(z * u) * u) = L(x,y,R(z,u,u)).
(x * (y * (y * z))) \ ((x * (y * y)) * (z * u)) = L(u,z,x).
(T(x,y) \ x) * y = T(y,T(x,y)).
T(x,y) \ (x * z) = x * (T(x,y) \ z).
T(x,T(y,x)) = y * (T(y,x) \ x).
x * (T(x,y) \ y) = T(y,T(x,y)).
x = T(y,T(x,y)) / (T(x,y) \ y).
T(x,T(y,x)) / (T(y,x) \ x) = y.
T(x,y) \ y = x \ T(y,T(x,y)).
x \ T(y,T(x,y)) = T(x,y) \ y.
(x * y) / (x * (T(x,z) \ y)) = T(x,z).
(((x * y) * (y * x)) * z) \ (((x * y) * (y * x)) * (z * u)) = L(u,z,K(y,x)).
(x * (y / (y * x))) \ (y / (y * x)) = x \ 1.
T(x \ 1,x * (y / (y * x))) = x \ 1.
x * ((y * x) \ x) = L(y \ 1,x,y) * x.
L(x \ 1,y,x) * y = y * ((x * y) \ y).
L(x,y,T(z,u)) = L(x,y,(z * (z \ u)) * (z \ u)).
L(x,y,(z * (z \ u)) * (z \ u)) = L(x,y,T(z,u)).
L(x,y,z * ((z \ u) * u)) = L(x,y,a(z,u,u)).
L(x,y,R(z * u,w,v5)) = L(x,y,R(z \ u,w,v5)).
L(x,y,R(z \ u,w,v5)) = L(x,y,R(z * u,w,v5)).
L(x,y,T(z / u,z)) = L(x,y,R(u / z,u,u)).
L(x,y,z * (z * (u * z))) = L(x,y,u \ (z \ 1)).
(x * (y / (y * x))) * z = (y / (y * x)) * (x * z).
(x * (y / (y * x))) \ z = x \ ((y / (y * x)) \ z).
L(x,y,T(z,z * (u * u))) = L(x,y,z * (u * u)).
L(x,y,z * (u \ z)) = L(x,y,T(u,z)).
L(x,y,z * u) = L(x,y,T(z / u,z)).
L(x,y,T(z / u,z)) = L(x,y,z * u).
L(x,y,z * u) = L(x,y,R(u / z,u,u)).
L(x,y,R(z / u,z,z)) = L(x,y,u * z).
L(x,y,R((y \ z) * z,u,w)) = x.
L(x,y,z \ (u \ 1)) = L(x,y,z * u).
L(x,y,z * u) = L(x,y,z * (u \ 1)).
L(x,y,z * (u \ 1)) = L(x,y,z * u).
L(x,y / (z * (u * y)),z * u) = x.
L(x,(y * z) * (u / (y * (z * u))),y * z) = x.
((x * y) * z) / (x * (y * z)) = (x * y) * (z / (x * (y * z))).
x \ ((y / (y * x)) \ z) = ((y * x) / y) * (x \ z).
L(x,y,T(z,z * (u * u))) = L(x,y,z).
L(x,y,T(z,u * u)) = L(x,y,z).
L(x,y,R(T(z,u * u),w,v5)) = L(x,y,R(z,w,v5)).
x \ (((y * x) / y) * z) = ((y * x) / y) * (x \ z).
((x * y) / x) * (y \ z) = (y \ ((x * y) / x)) * z.
(x \ ((y * x) / y)) * z = ((y * x) / y) * (x \ z).
L(x,y,z * ((z * u) * u)) = L(x,y,a(z,u,u)).
L(x,y,z * (z * (u * (z * w)))) = L(x,y,u \ (z \ w)).
L(x,y,(z * u) * u) = L(x,y,T((u \ z) * u,u)).
L(x,y,T((z \ u) * z,z)) = L(x,y,(u * z) * z).
L(x,y,T((z \ u) * z,z)) = L(x,y,R(u,z,z)).
L(x,y,z \ (u \ w)) = L(x,y,z * (u * w)).
L(x,y,z * (u * w)) = L(x,y,z * (u \ w)).
L(x,y,z * (u \ w)) = L(x,y,z * (u * w)).
L(x,y,z * u) = L(x,y,z * (w * (w * u))).
L(x,y,z * (u * (u * w))) = L(x,y,z * w).
L(x,y,(z \ u) * (u \ z)) = L(x,y,(u \ z) * (z * u)).
((x \ (x / y)) \ y) \ y = x \ (x / y).
x / (y \ (y / x)) = (y \ (y / x)) \ x.
(x * (y * (y * z))) \ (x * (y * (y * (z * u)))) = L(u,z,x).
L(x,y,z) = L(x,u * (u * y),z).
L(x,y * (y * z),u) = L(x,z,u).
L(x,y * z,u) = L(x,y \ z,u).
L(x,y \ z,u) = L(x,y * z,u).
L(x,(y / z) * y,u) = L(x,z,u).
L(x,y * (z * y),u) = L(x,T(z,y),u).
L(x,(y * z) * (z * y),u) = L(x,K(z,y),u).
L(x,(y * z) * u,w) = L(x,(y \ z) * u,w).
L(x,(y \ z) * u,w) = L(x,(y * z) * u,w).
L(x,(y \ z) * z,u) = L(x,T(y,y * z),u).
L(x,T(y,y * z),u) = L(x,(y \ z) * z,u).
L(x,(y * y) / z,u) = L(x,z \ 1,u).
L(x,y * (z \ y),u) = L(x,T(z \ 1,y),u).
L(x,T(y \ 1,z),u) = L(x,z * (y \ z),u).
L(x,y / z,u) = L(x,z / y,u).
L(x,y \ 1,z) = L(x,y,z).
(x * (y \ z)) * L(u,y * z,x) = x * ((y \ z) * u).
L(x,(y \ z) * z,y) = x.
L(x,y * z,z * y) = x.
((x \ y) * y) \ (x \ z) = (x * ((x \ y) * y)) \ z.
(x * ((x \ y) * y)) \ z = ((x \ y) * y) \ (x \ z).
((x * y) * (y * x)) * z = (x * y) * ((y * x) * z).
T(x * y,y * x) = T(x * y,(x * y) * (y * x)).
T(x * y,(x * y) * (y * x)) = T(x * y,y * x).
L(x,K(y,z),z * y) = x.
K(x,y) = K(y,x) \ 1.
K(x,y) \ 1 = K(y,x).
K(x,y) * K(y,x) = 1.
1 / K(x,y) = K(y,x).
K(x,y) * z = K(y,x) \ z.
K(x,y) \ z = K(y,x) * z.
K(x,y) * (K(y,x) * z) = z.
x / (K(y,z) * x) = K(z,y).
T(x * y,K(y,x)) / (y * x) = K(x,y).
R(K(x,y),K(y,x) * z,u) = R(K(y,x),z,u) \ 1.
a(K(x,y),z,u) = a(K(y,x),z,u).
R(K(x,y),K(x,y) * z,u) = R(K(y,x),z,u) \ 1.
K(x,y) * (K(y,x) / (x * y)) = K(x,y) \ ((y * x) \ 1).
R(x,K(y,z),u) = R(x,K(z,y),u).
L(x,y,K(z,u)) = L(x,y,K(u,z)).
L(K(x,y),z,K(y,x)) * z = z * ((K(y,x) * z) \ z).
(x * y) * z = (y * x) * (K(x,y) * z).
(x * y) * (K(y,x) * z) = (y * x) * z.
K(x,y) \ ((y * x) \ z) = (x * y) \ z.
L(x,x,y) = (y * (x \ 1)) \ y.
x / L(y,y,x) = x * (y \ 1).
L(L(x,y * (z \ 1),y),z,y) = x.
L(x * y,x,y) = (y \ (x \ 1)) \ 1.
L(x,y,L(y \ 1,z,u)) = x.
(x * (y \ z)) / L(z,y,x) = x * (y \ 1).
L(x * (y * z),x,y) = (y \ (x \ 1)) \ z.
L(x,K(y,z),u) = L(x,K(z,y),u).
K(x,y) * (y * x) = T(x * y,K(y,x)).
K(x,y) \ R(K(x,y),z,u) = R(K(x,y),K(y,x) * z,u) \ K(x,y).
R(K(x,y),K(y,x) * z,u) \ K(x,y) = K(x,y) \ R(K(x,y),z,u).
x \ (L(x \ 1,y,z) \ u) = (L(x \ 1,y,z) * x) \ u.
(L(x \ 1,y,z) * x) \ u = x \ (L(x \ 1,y,z) \ u).
L(x / y,x / y,z) = (z * (y / x)) \ z.
L(K(x,y),K(x,y),z) = (z * K(y,x)) \ z.
L(x,(y * (y * z)) * (y * u),w) = L(x,z \ (y \ u),w).
L(x,(y * (y * z)) * y,u) = L(x,z \ (y \ 1),u).
K(x,y) / L(z,z,K(y,x)) = K(x,y) * (z \ 1).
L(x,y * z,y) = L(x,y * (z \ 1),y).
L(x,y * (z \ 1),y) = L(x,y * z,y).
L(x,K(y,z),y * z) = x.
K(x,y) \ ((x * y) * z) = ((x * y) \ K(x,y)) \ z.
((x * y) \ K(x,y)) \ z = K(x,y) \ ((x * y) * z).
L(x * y,x,y) * z = (y \ (x \ 1)) \ z.
L(x,(y * y) / z,u) = L(x,z,u).
L(x,y,z) = L(x,y / (u * u),z).
L(x,y / (z * z),u) = L(x,y,u).
L(x,y,z) = L(x,y * (u * u),z).
L(x,y * (z * z),u) = L(x,y,u).
L(x,R(y,z,z),u) = L(x,(y * z) * z,u).
L(x,(y * z) * z,u) = L(x,R(y,z,z),u).
x * y = ((y * x) * z) / (K(y,x) * z).
((x * y) * z) / (K(x,y) * z) = y * x.
K(x,y) * z = (y * x) \ ((x * y) * z).
(x * y) \ ((y * x) * z) = K(y,x) * z.
K(x,y) * ((x * y) \ z) = (y * x) \ z.
x * (y \ ((y * (x \ 1)) * z)) = L(z,y * x,y).
L(x,y * z,u) = L(x,K(z,y) * (z * y),u).
L(x,K(y,z) * (y * z),u) = L(x,z * y,u).
(x * y) \ (y * (x * z)) = K(y,x) * L(z,x,y).
(x * (y \ 1)) * L(z,y,x) = x * (y \ z).
(a(x,y,z) \ (x \ 1)) \ u = x * (a(x,y,z) * u).
L(K(x,y),K(x,y),z) / z = (z * K(y,x)) \ 1.
(x * a(x,y,z)) * u = (a(x,y,z) \ (x \ 1)) \ u.
(a(x,y,z) \ (x \ 1)) \ u = (x * a(x,y,z)) * u.
L(x,T(y,y * z),u) = L(x,(y * z) * z,u).
L(x,T(y,z),u) = L(x,(y * (y \ z)) * (y \ z),u).
L(x,(y * (y \ z)) * (y \ z),u) = L(x,T(y,z),u).
x * (y * ((y \ (x \ 1)) * z)) = L(z,y * x,y).
K(x,y) * L(x,y,x) = T(x,y * x).
x * ((x \ (y \ 1)) * y) = a(x,y,y).
x * (y * (R(y,y * (x \ 1),z) \ ((x \ 1) * z))) = L(z,y * x,y).
x * R(x \ 1,y \ 1,y) = a(x,y,y).
a(x,y,y) = x \ R(x,y \ 1,y).
x \ R(x,y \ 1,y) = a(x,y,y).
x * R(x \ 1,y,y) = a(x,y,y).
T(x \ 1,R(x,y \ 1,y)) = R(x,y \ 1,y) \ a(x,y,y).
R(x,y \ 1,y) \ a(x,y,y) = T(x \ 1,R(x,y \ 1,y)).
x \ R(x,y,y) = a(x,y,y).
x * a(x,y,y) = R(x,y,y).
a(x,y,y) \ R(x,y,y) = x.
a(x,y,y) \ z = (R(x,y,y) \ x) * z.
(R(x,y,y) \ x) * z = a(x,y,y) \ z.
x * (a(x,y,y) * z) = R(x,y,y) * z.
x \ a(x,y,y) = R(x \ 1,y,y).
R(x \ 1,y,y) = x \ a(x,y,y).
a(x,y,y) \ x = R(x,x * y,y).
T(x * y,y * x) = T(x * y,K(y,x)).
T(x * y,K(y,x)) = (x \ 1) \ y.
K(x,y) / T(y * x,K(x,y)) = (y * x) \ K(x,y).
T(x * y,K(y,x)) = x * y.
(x * y) / (y * x) = K(x,y).
K(x,y) * (y * x) = x * y.
(x * y) / (T(x,y) * y) = K(y,T(x,y)).
(T(x,y) * y) / (x * y) = K(T(x,y),y).
R(K(x,y),y * x,z) = ((x * y) * z) / ((y * x) * z).
((x * y) * z) / ((y * x) * z) = R(K(x,y),y * x,z).
(x \ y) / (y * (x \ 1)) = K(x \ 1,y).
((K(x,y) * z) * K(y,x)) / z = K(K(x,y) * z,K(y,x)).
K(x \ y,x) * y = (x \ y) * x.
K(x * y,x) * y = (x \ y) * x.
K(x,T(y,x)) = T(y,x) \ y.
T(x,y) * K(y,T(x,y)) = x.
K(x,T(y,x)) * T(y,x) = y.
T(x,y) \ (x * z) = K(y,T(x,y)) * z.
(x \ y) * K(x,T(y / x,x)) = y / x.
T(x,y) = K(T(x,y),y) * x.
K(T(x,y),y) * x = T(x,y).
K(x,x \ y) * T(y / x,x) = y / x.
K(T(x,y),y) = x \ T(x,y).
x * K(T(x,y),y) = T(x,y).
K(x \ y,x) = (y / x) \ T(y / x,x).
(x / y) \ T(x / y,y) = K(y \ x,y).
K(T(x \ 1,y),y) = x * T(x \ 1,y).
(x / y) * K(T(x / y,y),y) = y \ x.
T(x,y) * (K(y,T(x,y)) * z) = x * z.
T(x,y) \ z = K(y,T(x,y)) * (x \ z).
K(x,T(y,x)) * (y \ z) = T(y,x) \ z.
(x \ y) * K(x,x \ y) = y / x.
(x \ y) * K(x,x * y) = y / x.
K(x,x * y) = (x \ y) \ (y / x).
(x \ y) \ (y / x) = K(x,x * y).
x \ ((y * x) / y) = K(y,y * (y * x)).
K(x,x * (x * y)) = y \ ((x * y) / x).
K(x,x * y) * T(y / x,x) = y / x.
(x / y) \ T(x / y,y) = K(y * x,y).
(x / y) * K(y \ x,y) = y \ x.
(x / y) * K(y * x,y) = y \ x.
K(x * y,x) = (x / y) * (x \ y).
(x / y) * (x \ y) = K(x * y,x).
K(x * y,x) = (x \ y) * (x / y).
(x \ y) * (x / y) = K(x * y,x).
L(x,y,(z \ u) * K(z * u,z)) = L(x,y,z / u).
x \ ((y * x) / y) = K(y,x).
x * K(y,x) = (y * x) / y.
(x * y) / x = y * K(x,y).
K(x,y) \ 1 = y * (x / (x * y)).
x * (y / (y * x)) = K(y,x) \ 1.
((x * y) / x) / y = K(x,y).
K(x,y) * z = ((x * y) / x) * (y \ z).
((x * y) / x) * (y \ z) = K(x,y) * z.
(x * K(y,x)) * y = y * x.
x / (x / y) = y * K(x / y,y).
T(x * K(y,x),y) = x.
L(x,y * K(z,y),y) = x.
a(x * K(y,x),z,u) = a(y / (y * x),z,u).
a(x / (x * y),z,u) = a(y * K(x,y),z,u).
T(x,y) = T(T(x * K(z,x),y),z).
T(T(x * K(y,x),z),y) = T(x,z).
x * T(y,z) = T(y * K(x,y),z) * x.
T(x * K(y,x),z) * y = y * T(x,z).
x / L(y,x * K(y,x),y) = y \ (x * K(y,x)).
L(x,K(y,z),z) = x.
(x * K(y,x)) \ z = K(y,x) \ (x \ z).
(x * K(y,x)) * z = x * (K(y,x) * z).
x = L(x,K(y,z),y).
L(x,K(y,z),y) = x.
(x * K(x,y)) * z = x * (K(x,y) * z).
(x \ K(x,y)) * z = x \ (K(x,y) * z).
x \ (K(x,y) * z) = (x \ K(x,y)) * z.
K(x,y) / x = (x * K(y,x)) \ 1.
(x * K(y,x)) \ 1 = K(x,y) / x.
K(x,y) * y = (x * y) / x.
(x * y) / x = K(x,y) * y.
(x * K(y,x)) / x = K(y,x).
K(x,y) * y = y * K(x,y).
T(K(x,y),y) = K(x,y).
T(x,K(y,x)) = x.
K(x,y) * T(y,z) = T(y,z) * K(x,y).
T(x,y) * K(z,x) = K(z,x) * T(x,y).
x * (y / (y * x)) = K(x,y).
x / (x * y) = y \ K(y,x).
x \ K(x,y) = y / (y * x).
(x / (x * y)) * y = K(y,x).
K(x,y) / x = y / (y * x).
K(x,y) * z = x * ((y / (y * x)) * z).
x * ((y / (y * x)) * z) = K(x,y) * z.
T(x,K(x,y)) = x.
K(x,y) \ z = ((y * x) / y) * (x \ z).
((x * y) / x) * (y \ z) = K(y,x) \ z.
T(x \ 1,K(x,y)) = x \ 1.
K(x,y) * z = (y / (y * x)) * (x * z).
(x / (x * y)) * (y * z) = K(y,x) * z.
K(x,y) * x = x * K(x,y).
T(x,T(y,x) \ y) = x.
(T(x,y) \ x) * y = y * (T(x,y) \ x).
((x * y) / x) \ y = K(y,x).
x \ K(x,y) = K(x,y) / x.
K(x,y) / x = x \ K(x,y).
K(x,y) * (x \ 1) = x \ K(x,y).
(x * K(y,x)) \ 1 = x \ K(x,y).
(x \ 1) / (x \ K(x,y)) = K(y,x).
(x \ K(x,y)) * z = (x * K(y,x)) \ z.
(x * K(y,x)) \ z = (x \ K(x,y)) * z.
((x * y) / x) * z = K(x,y) * (y * z).
K(x,y) * (y * z) = ((x * y) / x) * z.
T(x * K(y,x),z) = T(x,z) * K(y,T(x,z)).
T(x,y) * K(z,T(x,y)) = T(x * K(z,x),y).
T(x * K(x \ y,x),y) = L(x,x \ y,x).
(x * K(y,x)) \ z = K(x,y) * (x \ z).
((x * y) / x) * z = y * (K(x,y) * z).
x \ (K(x,y) * z) = (y / (y * x)) * z.
((x * y) / x) * z = K(y,x) \ (y * z).
K(x,y) \ (x * z) = ((y * x) / y) * z.
(x / (x * y)) * z = K(y,x) * (y \ z).
K(x,y) * (x \ z) = (y / (y * x)) * z.
x * (K(x,y) * z) = K(x,y) * (x * z).
K(x,y) * (x * z) = x * (K(x,y) * z).
x * (T(y,x) \ y) = T(x,T(y,x)).
x * K(x,T(y,x)) = T(x,T(y,x)).
x / (K(y,z) * (y \ x)) = y * K(z,y).
K(x,y) * (x \ z) = (x \ K(x,y)) * z.
(x \ K(x,y)) * z = K(x,y) * (x \ z).
K(x,y) * (y * z) = y * (K(x,y) * z).
K(x,y) \ (x * z) = (K(y,x) * x) * z.
K(x,y) * (x \ (y * x)) = y.
x \ (K(x,y) * z) = K(x,y) * (x \ z).
K(x,y) * T(y,x) = y.
K(x,y / x) = K(x,x * y).
K(x,y) = K(x,T(y,x)).
K(x,T(y,x)) = K(x,y).
K(x,y) = T(y,x) \ y.
T(x,y) \ x = K(y,x).
T(x,y) = K(x,y) * x.
K(x,y) * x = T(x,y).
K(x,T(y,z)) * T(T(y,x),z) = T(y,z).
K(x,R(y,z,u)) * R(T(y,x),z,u) = R(y,z,u).
L(x \ y,x,K(z,y)) = (K(z,y) \ x) \ T(y,z).
L(x,y,K(z,u) * u) = L(x,y,T(u,z)).
T(x,y) / x = K(x,y).
(x * y) * x = (y * x) * T(x,y).
(x * y) * T(y,x) = (y * x) * y.
T(x,y) * T(x,y) = x * T(T(x,y),y).
T(x,y) * K(y,x) = x.
x \ y = (y / (y * x)) * T(y,x).
(x / (x * y)) * T(x,y) = y \ x.
K(x,T(T(y,x),z)) = K(x,T(y,z)).
K(x,x * (y * x)) = K(x,y).
T(x,y) \ (x * z) = K(y,x) * z.
T(x,y) * (K(y,x) * z) = x * z.
K(x,y) * (y \ z) = T(y,x) \ z.
x * K(x,y) = T(x,T(y,x)).
T(T(x,y),z) \ T(x,z) = K(y,T(x,z)).
K(x,y) * (T(y,x) * z) = y * z.
K(x,y) * z = y * (T(y,x) \ z).
x * (T(x,y) \ z) = K(y,x) * z.
x * (T(x,y) \ 1) = K(y,x).
x \ K(y,x) = T(x,y) \ 1.
T(x,y) \ 1 = x \ K(y,x).
(x * y) / (T(x,z) * y) = K(z,x).
((x * y) * y) \ ((y * x) * y) = K(y,(y * x) * y).
(x * x) / (x * K(y,x)) = T(x,y).
K(x,y) = K(T(x,y),y).
K(T(x,y),y) = K(x,y).
(x * T(y,z)) / L(y,K(y,z),x) = x * K(y,z).
T(x,y) = x * K(x,y).
x * K(x,y) = T(x,y).
K(x,y) = x \ T(x,y).
x \ T(x,y) = K(x,y).
K(R(T(x,y),z,u),y) = K(R(x,z,u),y).
K(x \ 1,y) = x * T(x \ 1,y).
x * T(x \ 1,y) = K(x \ 1,y).
T(x * K(y,x),T(y,x)) = x.
K(x,y) * T(x,y) = T(T(x,y),y).
K(K(x,y),z) = K(y,x) * T(K(x,y),z).
K(x,y) * T(K(y,x),z) = K(K(y,x),z).
(x * y) \ (x * T(y,z)) = L(K(y,z),y,x).
x * (y * K(y,x)) = y * x.
(x * y) * L(K(y,z),y,x) = x * T(y,z).
(x \ y) * K(x * y,x) = T(x \ y,x).
L(x,y,z * T(z,u)) = L(x,y,K(z,u)).
T(x,y) * z = x * (K(x,y) * z).
x * (K(x,y) * z) = T(x,y) * z.
T(x,y) * K(x,y) = T(T(x,y),y).
T(x,y) \ T(T(x,z),y) = K(T(x,y),z).
L(x,y,z) \ L(T(x,u),y,z) = K(L(x,y,z),u).
x \ ((x \ y) \ y) = K(x,x * y).
K(x,y) * z = T(x,y) * (x \ z).
T(x,y) * (x \ z) = K(x,y) * z.
K(x \ 1,x * y) = x * ((x * y) \ y).
x \ (T(x,y) * z) = K(x,y) * z.
K(x / y,y) = K(y * x,y).
K(x,(y * (x \ 1)) / x) = K(x,T(y,x \ 1)).
T(x,T(y,x)) = T(x,y).
T(T(x,y),z) = T(T(x,z),T(y,x)).
T(T(x,y),T(z,x)) = T(T(x,z),y).
T(x,x \ y) = T(x,y / x).
T(x,y / x) = T(x,x \ y).
(x * y) / T(y,x) = T(x,y).
L(T(x,y),T(y,x),x) = T(x,x * T(y,x)).
T(x,x * (y * x)) = T(x,y).
T(x,y) / (T(y,x) \ x) = y.
x \ T(y,x) = T(x,y) \ y.
T(x,y) \ y = x \ T(y,x).
T(x,y) = T(x,y * K(x,y)).
T(x,y * K(x,y)) = T(x,y).
T(K(x,y),z) \ 1 = K(y,x) * K(z,K(x,y)).
K(x,y) * K(z,K(y,x)) = T(K(y,x),z) \ 1.
(T(x,y) \ (y * K(x,y))) \ y = L(T(x,y),y * K(x,y),T(x,y)).
L(T(x,y),y * K(x,y),T(x,y)) = (T(x,y) \ (y * K(x,y))) \ y.
K((x * (y \ 1)) / y,y) = K(T(x,y \ 1),y).
x / (x / y) = y * K(y * x,y).
T(x,y / x) = T(x,x * y).
T(x,y) * T(y,x) = x * y.
x / (y \ T(x,y)) = T(y,x).
(T(x,y) \ y) * K(x,x * T(y,x)) = T(y,x) / x.
T(x,(y * (x \ 1)) / x) = T(x,T(y,x \ 1)).
(T(x,y) * (T(y,x) * z)) \ ((x * y) * z) = a(T(x,y),T(y,x),z).
(x * y) \ (T(x,y) * (T(y,x) * z)) = L(z,T(y,x),T(x,y)).
T(T(x,y),x \ T(y,x)) = (x \ T(y,x)) \ y.
R(x,y,x) * (y * x) = (y * x) * T(x,y).
T(x,y) * ((y * x) / ((x * y) * x)) = K(T(x,y),y * x).
K(x,T(y,x)) = K(x,T(y,K(z,T(y,x)))).
K(x,T(y,K(z,T(y,x)))) = K(x,T(y,x)).
L(x,y * K(z,y),u) = L(x,T(y,z),u).
T(x,y) * (y * x) = x * (x * y).
x \ y = K(x,z) * (T(x,z) \ y).
K(x,y) * (T(x,y) \ z) = x \ z.
K(x,y) * (y \ x) = y \ T(x,y).
T(x,y) * z = K(x,y) * (x * z).
K(x,y) * (x * z) = T(x,y) * z.
((T(x,y) * z) * u) / ((x * z) * u) = R(K(y,x),T(x,y) * z,u) \ 1.
R(K(x,y),T(y,x) * z,u) \ 1 = ((T(y,x) * z) * u) / ((y * z) * u).
T(x,y) \ z = x \ (K(y,x) * z).
x \ (K(y,x) * z) = T(x,y) \ z.
(x * y) * T((x * y) \ x,z) = x * K(y \ 1,z).
K((x \ y) \ 1,z) = x \ (y * T(y \ x,z)).
x \ (y * T(y \ x,z)) = K((x \ y) \ 1,z).
(x * ((K(x,y) * z) * u)) \ ((T(x,y) * z) * u) = a(x,K(x,y) * z,u).
x * (y * z) = T(x,y) * (T(y,x) * z).
T(x,y) * (T(y,x) * z) = x * (y * z).
L(x,y,K(z,z * u)) = L(x,y,z * ((z \ u) * u)).
L(x,y,z * ((z \ u) * u)) = L(x,y,K(z,z * u)).
T(x,y) \ ((x \ T(y,x)) \ y) = K(T(x,y),T(x,y) * y).
x \ y = T(x,z) \ (K(x,z) * y).
T(x,y) \ (K(x,y) * z) = x \ z.
T(x,y) * T(z,x) = K(x,y) * (z * x).
T(x / y,z) * y = K(x / y,z) * x.
T(x,y) * (z / (z * x)) = K(x,y) * K(x,z).
T(x,y) * (T(x,z) \ 1) = K(x,y) * K(z,x).
x \ T(T(x,y),y) = K(x,y) * K(x,y).
T(T(x,x * y),T(z,x)) = T(T(x,z),x \ y).
(x / (x / y)) * z = y * (K(y * x,y) * z).
((x * y) * T(y,x)) \ (y * (y * x)) = K(T(y,x),x * y).
(x * (x * y)) \ (T(x,y) * ((y * x) * z)) = L(z,y * x,T(x,y)).
K(x,y) * (T(x,y) \ T(x,z)) = K(x,z).
K(T(x,y \ 1),y) * (x * (y \ 1)) = y \ T(T(x,y \ 1),y).
((T(x,y) * z) * u) / ((x * z) * u) = R(K(x,y),x * z,u).
(x * y) \ (T(x,z) * y) = T(K(x,z),x * y).
L(x,T(y,z) * z,u) = L(x,z * y,u).
x \ (y \ z) = T(x,y) \ (T(y,x) \ z).
T(x,y) \ (T(y,x) \ z) = x \ (y \ z).
T(x,y) \ (y * K(x,y)) = x \ y.
K(x,y) * (x \ y) = x \ (y * K(x,y)).
x \ (y * K(x,y)) = K(x,y) * (x \ y).
(K(x,y) * (x \ z)) \ ((x \ K(x,y)) * (z * u)) = L(u,z,x \ K(x,y)).
(K(x,y) * z) \ (y * (K(x,y) * z)) = L(T(y,z),z,K(x,y)).
K(x,y) \ (x * z) = (K(x,y) \ x) * z.
L(x,y,(z * u) / z) = L(x,y,T(u,z)).
T(x,y) * K(y,T(x,z)) = K(z,T(x,y)) * T(x,z).
L(x,y,(z / (u * u)) * (u \ (z * (u \ 1)))) = L(x,y,K(z / (u * u),u)).
L(K(T(x,y),z),T(x,y),y) = (y * T(x,y)) \ (T(x,z) * y).
(x * T(y,x)) \ (T(y,z) * x) = L(K(T(y,x),z),T(y,x),x).
K(x,T(y,K(z,T(y,x)))) = K(x,y).
K(x,y) * T(T(y,x),K(z,T(y,x))) = T(y,K(z,T(y,x))).
T(x,y) = (x * (y * z)) / (T(y,x) * z).
(x * (y * z)) / (T(y,x) * z) = T(x,y).
(x \ y) * (T(x,y / x) * z) = (y / x) * (x * z).
K(x / y,z) = (T(x / y,z) * y) / x.
(T(x / y,z) * y) / x = K(x / y,z).
K(x / y,z) * x = y * T(y \ x,z).
(R(x,y,z) * (K(x,u) * K(x,u))) / T(T(x,u),u) = x \ R(x,y,z).
x = L(x,y,K(y,z)).
L(x,y,K(y,z)) = x.
L(x,y,T(z,y) \ z) = x.
x = L(x,y,T(z,y) * z).
L(x,y,T(z,y) * z) = x.
L(x,y,z * T(z,y)) = x.
((x * T(x,y)) * y) \ ((x * T(x,y)) * (y * z)) = z.
L(x,y,T(z * u,z) / z) = L(x,y,T((z \ u) * z,z)).
(x * (R(y,z,u) * w)) / (R(T(y,x),z,u) * w) = T(x,R(y,z,u)).
(x * (y * (a(T(y,x),z,z) * u))) / (R(T(y,x),z,z) * u) = T(x,y).
(x * T(x \ y,z)) / y = K(y / x,z).
K((x * y) / x,z) * (x * y) = x * T(y,z).
x \ (y * T(y \ x,z)) = T(K(x / y,z),x).
((x * y) * T((x * y) \ ((z * x) * y),u)) / ((z * x) * y) = K(R(z,x,y),u).
T(x * K(x * y,x),y) = L(x,x \ y,x).
L(T(x,y),T(y,x),x) = T(x,y * x).
R(x,y,x) * (y * x) = (y * x) * T(x,x * (y * x)).
(x * y) * T(y,y * (x * y)) = R(y,x,y) * (x * y).
T(x * K(x * y,x),y) = L(x,x * y,x).
T(x / (x / y),x) = L(y,y * x,y).
K(x,y / (x * x)) = K(x,T(y,x \ 1)).
K(x,T(y,x \ 1)) = K(x,y / (x * x)).
K(x / (y * y),y) = K(T(x,y \ 1),y).
K(T(x,y \ 1),y) = K(x / (y * y),y).
T(x,y / (x * x)) = T(x,T(y,x \ 1)).
T(x,T(y,x \ 1)) = T(x,y / (x * x)).
(x * y) \ (x * T(y,z)) = K(((x * y) \ x) \ 1,z).
K(((x * y) \ x) \ 1,z) = (x * y) \ (x * T(y,z)).
K(x,y) * K(z,x) = T(x,z) \ T(x,y).
T(x,y) \ T(x,z) = K(x,z) * K(y,x).
K(x,y) * (K(x,z) * K(y,x)) = K(x,z).
K(x,y) * K(z,x) = K(z,x) * K(x,y).
T(T(x,y),x \ z) = T(T(x,y),x * z).
T(T(x,y),x * T(y,x)) = (x \ T(y,x)) \ y.
(x / (x / y)) * x = y * ((y \ x) * y).
(x / (x / y)) * x = T(y * x,y).
T(x * y,x) = (y / (y / x)) * y.
x / (x / y) = T(y * x,y) / x.
T(x * y,x) / y = y / (y / x).
x = ((x / y) / x) * T(y * x,y).
((x / y) / x) * T(y * x,y) = x.
x / (x / y) = x \ T(x * y,y).
x \ T(x * y,y) = x / (x / y).
(x / y) / x = x / T(y * x,y).
x / T(y * x,y) = (x / y) / x.
x * (x / (x / y)) = T(x * y,y).
T(x * y,y) = x * (x / (x / y)).
T(x * (y \ x),y \ x) = x * (x / y).
T(K(x / y,z),x) = K((x \ y) \ 1,z).
T(K(x,y),z) = K((z \ (x \ z)) \ 1,y).
K((x \ (y \ x)) \ 1,z) = T(K(y,z),x).
T(K(x,y),T(z,x)) = K((T(z,x) \ (T(x,z) \ z)) \ 1,y).
K((T(x,y) \ (T(y,x) \ x)) \ 1,z) = T(K(y,z),T(x,y)).
K(T(x \ 1,y) \ 1,z) = T(K(x,z),y).
K(T((x \ 1) \ 1,y * y),z) = T(K(x,z),y * y).
T(T(x,y),y * x) = (x \ T(y,x)) \ y.
(x \ T(y,x)) \ y = T(T(x,y),y * x).
x / L(y,T(x,y),y) = y \ (x * K(y,x)).
x / L(y,T(x,y),y) = K(y,x) * (y \ x).
L(x \ y,x,K(z,y)) = (K(y,z) * x) \ T(y,z).
R(K(x,y),y * z,u) = R(K(y,x),T(y,x) * z,u) \ 1.
R(K(x,y),T(x,y) * z,u) \ 1 = R(K(y,x),x * z,u).
L(x,y * (y * (z * y)),u) = L(x,z \ (y \ 1),u).
((x * y) \ K(x,y)) \ z = K(y,x) * ((x * y) * z).
(x * a(x,y,z)) * u = x * (a(x,y,z) * u).
x * (a(x,y,z) * u) = a(x,y,z) * (x * u).
a(x,y,z) * (x * u) = x * (a(x,y,z) * u).
a(x,y,z) * u = x * (a(x,y,z) * (x \ u)).
x * (a(x,y,z) * (x \ u)) = a(x,y,z) * u.
L(x,y * (z \ y),u) = L(x,T(z,y),u).
L(x,T(y \ 1,z),u) = L(x,T(y,z),u).
K(x,y) / (y * x) = (y * x) \ K(x,y).
L(x,y,T(z \ u,z)) = L(x,y,z / u).
L(x,y,z / u) = L(x,y,T(z * u,z)).
L(x,y,T(z * u,z)) = L(x,y,z / u).
(T(x,y) \ y) * K(x,y * x) = T(y,x) / x.
L(x,y,K(z,z * u)) = L(x,y,a(z,u,u)).
L(x,y,a(z,u,u)) = L(x,y,K(z * u,z)).
L(x,y,K(z * u,z)) = L(x,y,a(z,u,u)).
L(x,y,K(z,u)) = L(x,y,a(z,u * z,u * z)).
L(x,y,a(z,u * z,u * z)) = L(x,y,K(z,u)).
K(x,T(y,z)) * T(T(y,x),K(x,T(y,z))) = K(z,T(y,x)) * T(y,z).
(x \ y) * (T(x,x * y) * z) = (y / x) * (x * z).
(x * (T(x,y) * y)) \ ((x * T(x,y)) * (y * z)) = z.
K(((x * y) \ x) \ 1,z) = L(K(y,z),y,x).
L(K(x,y),x,z) = K(((z * x) \ z) \ 1,y).
L(K(x,y),x,z) = K(L(x \ 1,x,z) \ 1,y).
K(L(x \ 1,x,y) \ 1,z) = L(K(x,z),x,y).
K(T(x,y * y),z) = T(K(x,z),y * y).
T(K(x,y),z * z) = K(T(x,z * z),y).
K(T(x,y * y),z) \ 1 = T(K(x,z) \ 1,y * y).
L(x,y \ (z \ 1),u) = L(x,y * z,u).
L(x,y * z,u) = L(x,y * (z \ 1),u).
L(x,y * (z \ 1),u) = L(x,y * z,u).
(x \ y) * ((y / x) * (x * z)) = ((x \ y) * y) * z.
(x * (T(x,y) * y)) \ (x * (T(x,y) * (y * z))) = z.
T(K(x,y) \ 1,z * z) = K(y,T(x,z * z)).
T(K(x,y),z * z) = K(x,T(y,z * z)).
K(x,T(y,z * z)) = K(T(x,z * z),y).
K(T(x,y * y),z) = K(x,T(z,y * y)).
x = L(L(x,y,T(z,y)),T(z,y) * y,z).
L(L(x,y,T(z,y)),T(z,y) * y,z) = x.
x = L(L(x,y,T(z,y)),y * z,z).
L(L(x,y,T(z,y)),y * z,z) = x.
L(L(x,y,T(y \ z,y)),z,y \ z) = x.
L(x,y * (z * y),y) = L(x,z,T(y,z)).
L(x,y * z,z) = L(x,T(z,y) * y,T(z,y)).
L(x,T(y,z) * z,T(y,z)) = L(x,z * y,y).
L(x,T(y,z),z) = L(x,y,T(z,y)).
L(x,T(y,y * z),y * z) = L(x,y,y / z).
L(L(x,y,y / z),z,y \ z) = x.
x = L(L(x,y,y / z),z,y * z).
L(L(x,y,y / z),z,y * z) = x.
L(x,y,z * y) = L(x,y,z / y).
L(x,y,z / y) = L(x,y,z * y).
L(x \ (x / y),x,y * x) = y \ 1.
L(x,y,z * y) = L(x,y,y / z).
L(x,y,y / z) = L(x,y,z * y).
L(x,y,z) = L(x,y,(z * y) * y).
L(x,y,(z * y) * y) = L(x,y,z).
L(x \ 1,x,y * x) = y \ (y / x).
L(x,x,y * x) = y \ (y / (x \ 1)).
x * L(y,z,x * z) = (x / z) * (z * y).
(x \ 1) \ L(T(y \ (y / x),z),y,x * y) = K(L(y \ (y / x),y,x * y),z).
x \ (x / y) = ((x * y) * y) \ (x * y).
((x * y) * y) \ (x * y) = x \ (x / y).
L(x,(y * z) * z,y * z) = L(x,y \ 1,T(y * z,y \ 1)).
L(x,y \ 1,T(y * z,y \ 1)) = L(x,(y * z) * z,y * z).
x * K(L(y \ 1,y,x * y) \ 1,z) = (x / y) * (y * K(y,z)).
x \ L(x,x * y,y) = a(T(y,x),x,x).
L(x,y * z,z) = L(x,y * z,T(z,y)).
L(x,y * z,T(z,y)) = L(x,y * z,z).
(K(x,y) * z) \ z = T(L(K(y,x),z,K(x,y)),z).
T(L(K(x,y),z,K(y,x)),z) = (K(y,x) * z) \ z.
R(x,y,x) = L(x,y * x,x).
L(x,y * x,x) = R(x,y,x).
L(x,y,x) = R(x,y / x,x).
R(x,y / x,x) = L(x,y,x).
T(R(x,y,x),z) = L(T(x,z),y * x,x).
L(T(x,y),z * x,x) = T(R(x,z,x),y).
L(x,y,x) * ((y / x) * x) = (x * (y / x)) * x.
L(T(x,y),z * x,x) = R(T(x,y),z,x).
L(x,y,x) * y = (x * (y / x)) * x.
T(L(x,y,x) * y,x) = ((y / x) * x) * x.
T(L(x,y,x) * y,x) = y * x.
x * (y * x) = (L(x,y,x) * y) * x.
(L(x,y,x) * y) * x = x * (y * x).
x = L(R(x,y,x),y,x).
L(R(x,y,x),y,x) = x.
x = R(L(x,y,x),y,x).
R(L(x,y,x),y,x) = x.
L(x,y,x) = R(x,x \ y,x).
R(x,x \ y,x) = L(x,y,x).
L(x,x * y,x) = R(x,y,x).
L(x,y,x) = R(x,x * y,x).
R(x,x * y,x) = L(x,y,x).
R(x,y,x) = y \ T(x * y,x).
x \ T(y * x,y) = R(y,x,y).
T(x * K(x * y,x),y) = R(x,y,x).
T(x / (x / y),x) = R(y,x,y).
L(x,y,x) \ x = x \ R(x,y,x).
x * R(y,x,y) = T(y * x,y).
T(x,R(y,x,y)) = T(x,x / (x / y)).
(x / T(y * x,y)) * T(x,R(y,x,y)) = R(y,x,y) \ x.
T(x,y) * K(x * y,T(x,y)) = R(x,y,x).
T(x,y) * K(y * T(x,y),T(x,y)) = R(x,y,x).
K(x,y) * (K(y,x) / (x * y)) = (x * y) \ 1.
K(x,y) * ((x * y) \ K(y,x)) = (x * y) \ 1.
(x * y) \ 1 = (y * x) \ K(y,x).
(x * y) \ K(x,y) = (y * x) \ 1.
((x * y) \ 1) \ z = K(x,y) * ((y * x) * z).
K(x,y) * ((y * x) * z) = ((x * y) \ 1) \ z.
K(x,y) * ((y * x) * z) = (x * y) * z.
K(x,y) = ((x * y) * z) / ((y * x) * z).
((x * y) * z) / ((y * x) * z) = K(x,y).
K(x,y) = R(K(x,y),y * x,z).
R(K(x,y),y * x,z) = K(x,y).
R(K(x,T(y,x)),T(y,x) * x,z) = K(x,y).
R(K(x,y),T(y,x) * x,z) = K(x,y).
((T(x,y) * y) * z) / ((K(y,x) * (T(x,y) * y)) * z) = K(y,x) \ 1.
(x * L(x \ 1,y,z)) \ u = x \ (L(x \ 1,y,z) \ u).
L(x,y * (y * (z * (y * u))),w) = L(x,z \ (y \ u),w).
T(x,y) * (R(x,y,x) \ 1) = K(T(x,y),y * x).
K(T(x,y),y * x) = R(x,y,x) \ T(x,y).
R(x,y,x) \ T(x,y) = K(T(x,y),y * x).
T(x,y) \ T(T(x,y),y * x) = K(T(x,y),T(x,y) * y).
K(T(x,y),y * x) = (((y * x) * T(x,y)) \ (x * x)) * y.
(((x * y) * T(y,x)) \ (y * y)) * x = K(T(y,x),x * y).
K(x,y) * T(y,x) = T(y,K(z,T(y,x))).
T(x,K(y,T(x,z))) = K(z,x) * T(x,z).
T(x,K(y,T(x,z))) = x.
T(x,y) = T(T(x,y),K(z,T(x,u))).
T(T(x,y),K(z,T(x,u))) = T(x,y).
L(x,y,T(z * u,z) / z) = L(x,y,R(u,z,z)).
K((x \ (y \ x)) \ 1,z) = T(K(y,z),T(x,y)).
T(K(x,y),T(z,x)) = K((z \ (x \ z)) \ 1,y).
T(K(x,y),T(z,x)) = T(K(x,y),z).
T(x,y) * T(K(y,z),x) = K(y,z) * T(x,y).
K(x,y) * T(z,x) = K(z,x) * (K(x,y) * z).
K(x,y) * (K(y,z) * x) = K(y,z) * T(x,y).
(K(x,y) * T(z,x)) / L(z,K(x,y),K(z,x)) = K(z,x) * K(x,y).
((x / y) / x) * T(x,R(y,x,y)) = R(y,x,y) \ x.
x \ (L(x \ 1,y,z) \ u) = L(x \ 1,y,z) \ (x \ u).
L(x \ 1,y,z) \ (x \ u) = x \ (L(x \ 1,y,z) \ u).
L(x,y \ (z \ u),w) = L(x,y * (z * u),w).
L(x,y * (z * u),w) = L(x,y * (z \ u),w).
L(x,y * (z \ u),w) = L(x,y * (z * u),w).
L(x,y * z,u) = L(x,y * (w * (w * z)),u).
L(x,y * (z * (z * u)),w) = L(x,y * u,w).
L(x,(y \ z) * (z \ y),u) = L(x,(z \ y) * (y * z),u).
L(x,y * R(z,z * u,w),v5) = L(x,y * (R(z,u,w) \ 1),v5).
K(T(x,y),T(x,y) * y) = K(T(x,y),y * x).
(((x * y) * x) \ (x * x)) * y = K(T(x,y),y * x).
K(T(x,y),y * x) = K(x,x * y).
R(x,y,x) \ T(x,y) = K(x,x * y).
K(x,x * y) \ T(x,y) = R(x,y,x).
R(x,y,x) = K(x * y,x) * T(x,y).
K(x * y,x) * T(x,y) = R(x,y,x).
K(x * y,x) = R(x,y,x) / T(x,y).
R(x,y,x) / T(x,y) = K(x * y,x).
(x \ (L(x \ 1,x,x / y) \ 1)) * (y \ (y / x)) = x \ 1.
R(x,y \ 1,y) \ a(x,y,y) = x \ 1.
R(x,y,y) \ a(x,y,y) = x \ 1.
(x * y) \ (x * (y * z)) = L(z,T(y,x),T(x,y)).
L(x,T(y,z),T(z,y)) = L(x,y,z).
L(T(x,y),y,K(z,x)) = T(x,K(z,x) * y).
(x \ (L(x \ 1,x,y * x) \ 1)) * (y \ (y / x)) = x \ 1.
((x \ y) * z) \ (x \ u) = ((x * y) * z) \ (x * u).
(x * ((x \ y) * y)) \ z = ((x * y) * y) \ (x * z).
(x * ((x \ y) * y)) \ y = x \ (x / y).
x / (y \ (y / x)) = y * ((y \ x) * x).
x * ((x \ y) * y) = (x \ (x / y)) \ y.
(x \ (x / y)) \ y = x * ((x \ y) * y).
x * L(x,y * x,y) = (y \ (y / x)) \ x.
(x * L(x,y * x,y)) / x = (y \ (y / x)) \ 1.
(x \ (x / y)) \ 1 = L(y,x * y,x).
L(x,y * x,y) = (y \ (y / x)) \ 1.
x \ ((y \ (y / x)) \ 1) = a(y,x,x).
(x \ (x / y)) \ 1 = y * a(x,y,y).
(x \ 1) \ (L(x,x,y * x) \ 1) = a(y,x \ 1,x \ 1).
(x * a(y,x,x)) * z = (y \ (y / x)) \ z.
(x \ (x / y)) \ z = (y * a(x,y,y)) * z.
K(x,(x * x) / (y \ (y / z))) = K(x,z * a(y,z,z)).
L(x \ 1,x,y * x) \ 1 = x * a(y,x,x).
(x \ (x * a(y,x,x))) * (y \ (y / x)) = x \ 1.
a(x,y,y) * (x \ (x / y)) = y \ 1.
a(K(x,y),z,z) * (K(y,x) \ (K(y,x) / z)) = z \ 1.
x * (y \ 1) = a(x,y,y) * (x / y).
a(x,y,y) * (x / y) = x * (y \ 1).
a(x,y,y) = (x * (y \ 1)) / (x / y).
(x * (y \ 1)) / (x / y) = a(x,y,y).
a(x,y,y) = (y / x) * (x * (y \ 1)).
(x / y) * (y * (x \ 1)) = a(y,x,x).
a(x / y,y,y \ 1) = a(x,y,y).
a(x * (y * y),y \ 1,(y \ 1) \ 1) = a(x * y,y \ 1,y \ 1).
K(x,y * a(z,y,y)) = K(x,(z \ (z / y)) \ 1).
K(x,(y \ (y / z)) \ 1) = K(x,z * a(y,z,z)).
a(K(x,y),z,z) * (K(x,y) * (K(y,x) / z)) = z \ 1.
x \ 1 = K(y,z) * (a(K(y,z),x,x) * (K(z,y) / x)).
K(x,y) * (a(K(x,y),z,z) * (K(y,x) / z)) = z \ 1.
x \ 1 = R(K(y,z),x,x) * (K(z,y) / x).
R(K(x,y),z,z) * (K(y,x) / z) = z \ 1.
a(x,y \ 1,y \ 1) = y * (L(y,y,x * y) \ 1).
x * (L(x,x,y * x) \ 1) = a(y,x \ 1,x \ 1).
a(x,y \ 1,y \ 1) = L(y,y,x * y) \ y.
a(x * y,y \ 1,y \ 1) = L(y,y,x) \ y.
(x * (y \ z)) \ (x * (y \ (z * u))) = L(L(u,z,y),y * z,x).
(x * y) * (z / (x * (y * z))) = x \ R(x,y,z).
L(x,y \ R(y,z,u),y * z) = x.
x = L(x,y * R(y,z,u),y * z).
L(x,y * R(y,z,u),y * z) = x.
x = L(x,y * R(y,y * z,u),z).
L(x,y * R(y,y * z,u),z) = x.
K(T(x,y \ 1),y) * (x * (y \ 1)) = T(x,y) * (y \ 1).
K(T(x,y \ 1),y) = K(x,y).
(x * (y \ 1)) / (T(x,y) * (y \ 1)) = K(y,T(x,y \ 1)).
K(x,y) = K(x / (y * y),y).
K(x / (y * y),y) = K(x,y).
K(x,T(y,x \ 1)) = K(x,y).
K(x \ 1,T(y,x)) = K(x \ 1,y).
x * K(x,y) = T(x,T(y,x \ 1)).
T(x,T(y,x \ 1)) = x * K(x,y).
K(x,y) = K(x,y / (x * x)).
K(x,y / (x * x)) = K(x,y).
K(x,R(y / x,x,x)) = K(x,y * x).
((x \ 1) * T(y,x)) / (x \ 1) = T(y,x) * K(x \ 1,y).
T(x,T(y,x \ 1)) = T(x,y).
T(x \ 1,T(y,x)) = T(x \ 1,y).
T(x,y) = T(x,y / (x * x)).
T(x,y / (x * x)) = T(x,y).
L(x,T(y,z),T(T(z,y \ 1),y)) = L(x,y,T(z,y \ 1)).
T(x,R(y,x,x)) = T(x,(y * x) * x).
T(x,(y * x) * x) = T(x,R(y,x,x)).
L(x,T(y \ 1,z),T(T(z,y),y \ 1)) = L(x,y \ 1,T(z,y)).
(x \ T(y,x)) / (x \ 1) = T(y,x) * K(x \ 1,y).
T(x,y) * K(y \ 1,x) = T(x,y * y).
L(x,T(y,z),T(T(z,y),y \ 1)) = L(x,y,T(z,y \ 1)).
L(x,y \ 1,T(y * z,y \ 1)) = L(x,R(y,z,z),y * z).
L(x,R(y,z,z),y * z) = L(x,y \ 1,T(y * z,y \ 1)).
L(x,R(y,z,z),y * z) = L(x,y,T(y * z,y \ 1)).
L(x,y * R(z,z * u,w),v5) = L(x,y * R(z,u,w),v5).
L(x,y * R(y,z,u),z) = x.
L(x,y * (z * R(z,y,u)),y) = x.
L(x,y \ R(y \ 1,z,u),z) = x.
(x * (y \ R(y,x,z))) * u = x * ((y \ R(y,x,z)) * u).
a(x,x * (y * R(y,x,z)),u) = 1.
x = L(x,y * R(y \ 1,z,u),z).
L(x,y * R(y \ 1,z,u),z) = x.
L(x,a(y,z,z),z) = x.
x / (a(y,x,x) \ 1) = x * a(y,x,x).
(x * a(y,x,x)) * z = x * (a(y,x,x) * z).
K(x,(y \ (y / z)) \ 1) = K(x,z / (a(y,z,z) \ 1)).
(x \ (x / y)) \ z = y * (a(x,y,y) * z).
L(x * (a(y,x,x) * z),y * (y / x),y) = (y / x) \ (y * z).
(x * (y \ R(y,x,z))) * u = x * (R(y,x,z) * (y \ u)).
L(x,y \ 1,T(z,y)) = L(x,T(y,z),T(T(z,y),y \ 1)).
L(x,T(y,z),T(T(z,y),y \ 1)) = L(x,y \ 1,T(z,y)).
L(x,y \ 1,T(z,y)) = L(x,y,T(z,y \ 1)).
L(x,y,T(z,y \ 1)) = L(x,y,T(z,y)).
L(x,R(y,z,z),y * z) = L(x,y,T(y * z,y)).
L(x,R(y,z,z),y * z) = L(x,y,y / z).
L(x,R(y,z,z),y * z) = L(x,y,z * y).
L(T(x,y),y * K(x,y),T(x,y)) = (x \ y) \ y.
(x * (y * z)) \ ((x * y) * z) = a(T(x,y),T(y,x),z).
a(T(x,y),T(y,x),z) = a(x,y,z).
a(T(x,y),T(T(y,x),x),z) = a(x,T(y,x),z).
L(x,y * z,T(z,y)) = y \ (z \ (z \ (T(z,y) * ((y * z) * x)))).
x \ (y \ (y \ (T(y,x) * ((x * y) * z)))) = L(z,x * y,T(y,x)).
x * K(y * a(x,y,y),z) = (x / y) * (y * K(y,z)).
x * K(y * a(x,y,y),z) = (x / y) * T(y,z).
x \ (y \ (K(y,x) * ((x * y) * z))) = L(z,x * y,T(y,x)).
x \ (y \ ((y * x) * z)) = L(z,x * y,T(y,x)).
L(x,y * z,T(z,y)) = L(x,z * y,z).
L(x,y * z,y) = L(x,z * y,y).
L(x,y * z,z) = L(x,z * y,z).
L(L(x,y,z),y * z,z) = x.
x \ L(x,x * y,y) = a(y,x,x).
L(x,y * (y / z),y) = L(x,z,y).
L(x,(y * z) * z,y * z) = L(x,T(y,z),y * z).
L(x,T(y,z),z) = L(x,y,z).
L(T(x,y),y,x) = T(x,y * x).
x / L(y,x,y) = K(y,x) * (y \ x).
K(x,y) * (x \ y) = y / L(x,y,x).
L(x,y,y * z) = L(x,y,y / z).
L(x,y,y / z) = L(x,y,y * z).
(x * T(y,x)) \ (T(y,z) * x) = L(K(T(y,x),z),y,x).
T(x,y * x) = T(x,x * y).
K(x,y) * L(x,y,x) = T(x,x * y).
T(x,x * y) * K(y * x,x) = x.
T(x,x * (y * x)) = T(x,R(y,x,x)).
x \ L(x,y,x * y) = a(x * y,x,x).
x \ L(x,T(y,x),y * x) = a(y * x,x,x).
a(x,y,y) = a(T(x,y),y,y).
a(T(x,y),y,y) = a(x,y,y).
L(x * (a(y,x,x) * z),x,y) = (y / x) \ (y * z).
L(x,x,x * y) = y \ (y / (x \ 1)).
K(x * y,y) = K(y * x,y).
T(x * K(x * y,x),y * x) = x.
x / (x / y) = y * K(x * y,y).
R(x,y,x) / T(x,y) = K(y * x,x).
T(x / (x / y),x * y) = y.
T(x * y,y) = T(x * y,x / (x / y)).
T(x * y,x / (x / y)) = T(x * y,y).
x \ (y * x) = (y / (y / x)) \ T(y * x,y / (y / x)).
(x / (x / y)) \ T(x * y,x / (x / y)) = y \ (x * y).
x / (x / T(y,x)) = R(y,x,y).
R(x,y,x) = y / (y / T(x,y)).
R(x,y,x) \ y = y / T(x,y).
(T(x,y) \ y) * K(T(x,y),T(x,y) * y) = R(x,y,x) \ y.
((x / y) / x) * T(x,R(y,x,y)) = x / T(y,x).
(x \ y) / (y / L(x,y,x)) = K(y,x).
R(x,x * y,x) \ (x * y) = (x * y) / (K(x,y) * L(x,y,x)).
(x * y) / (K(x,y) * L(x,y,x)) = R(x,x * y,x) \ (x * y).
T(x,R(y,x,x)) = T(x,y).
x \ T(x,y) = K(x,R(y,x,x)).
K(x,R(y,x,x)) = x \ T(x,y).
K(x,R(y,x,x)) = K(x,y).
K(x,y / x) = K(x,y * x).
K(x,y * x) = K(x,x * y).
((x * y) * y) \ ((y * x) * y) = K(y,y * (y * x)).
(T(x,y) \ y) * K(x,x * y) = T(y,x) / x.
K(T(x,y),y * T(x,y)) = K(T(x,y),y * x).
K(x * y,y) = T(y,x) \ R(y,x,y).
T(x,y) \ R(x,y,x) = K(y * x,x).
K(x,y) * (y \ R(y,x,y)) = K(x * y,y).
K(T(x,y),x * y) = K(T(x,y),y * x).
K(T(x,y),y * x) = K(T(x,y),x * y).
K(T(x,y),x * y) = K(x,x * y).
L(x,T(y,z),y * z) = L(x,R(y,z,z),y * z).
L(x,R(y,z,z),y * z) = L(x,T(y,z),y * z).
L(x,T(y,z),y * z) = L(x,y,z * y).
x \ L(x,y,x * y) = a(y * x,x,x).
a(x * y,y,y) = a(y * x,y,y).
L(x * (a(y,x,x) * z),x,y) = (x / y) * (y * z).
((x * y) * y) \ ((y * x) * y) = K(y,x).
K(x * y,y) * K(y,x) = (y * (x * y)) \ ((y * x) * y).
(x * (y * x)) \ ((x * y) * x) = K(y * x,x) * K(x,y).
(x * y) \ (T(x,z) * y) = L(K(T(x,y),z),x,y).
L(K(T(x,y),z),x,y) = T(K(x,z),x * y).
(x / (x / y)) \ T(x * y,x / (x / y)) = T(x,y).
(x / (x / y)) \ T(x * y,y) = T(x,y).
T(x,y) = ((x / y) / x) * T(x * y,y).
((x / y) / x) * T(x * y,y) = T(x,y).
(x / y) * T(y * (x \ y),x \ y) = T(y,x \ y).
L(x,y,z * (((u / w) / u) * T(u,w))) = L(x,y,z * T(u * w,w)).
(x / y) * (y * (y / x)) = T(y,x \ y).
T(x,y \ x) = T(x,x / y).
T(x,x / y) = T(x,y \ x).
T(x,R(y,x,y)) = T(x,(x / y) \ x).
T(x,R(y,x,y)) = T(x,y).
((x / y) / x) * T(x,y) = x / T(y,x).
K(x * y,y) * K(y,x) = a(y,x,y).
K(x,y) * K(y * x,x) = a(x,y,x).
K(x * y,y) = K(x,y) * a(y,x,y).
K(x,y) * a(y,x,y) = K(x * y,y).
K(x,y) * K(x * y,x) = a(x,y,x).
a(x,y,x) = x \ R(x,y,x).
x \ R(x,y,x) = a(x,y,x).
L(x,y,x) \ x = a(x,y,x).
(T(x,y) \ y) * K(T(x,y),y * T(x,y)) = R(x,y,x) \ y.
(T(x,y) \ y) * K(T(x,y),x * y) = R(x,y,x) \ y.
(T(x,y) \ y) * K(x,x * y) = R(x,y,x) \ y.
R(x,y,x) \ y = T(y,x) / x.
T(x,y) / y = x / T(y,x).
(x / T(y,x)) * y = T(x,y).
(x / y) * (y * K(x,y)) = T(x,y * K(x,y)).
(x / y) * (y * K(x,y)) = T(x,y).
x * K(y,x) = (x / y) * T(y,x).
(x / y) * T(y,x) = x * K(y,x).
(x * (y \ 1)) * T(L(y,y,x),x) = x * K(L(y,y,x),x).
(x * (y \ 1)) * L(T(y,x),y,x) = x * K(L(y,y,x),x).
x * K(L(y,y,x),x) = x * (y \ T(y,x)).
x * K(L(y,y,x),x) = x * K(y,x).
T(x * K(y,x),L(y,y,x)) = x.
T(x,y) = T(x,L(y,y,x)).
T(x,L(y,y,x)) = T(x,y).
(x * y) / (K(x,y) * L(x,y,x)) = L(x,y,x) \ (x * y).
(x * y) / (K(x,y) * L(x,y,x)) = (L(x,y,x) \ x) * y.
(x * y) / T(x,x * y) = (L(x,y,x) \ x) * y.
T(x * y,x) / x = (L(x,y,x) \ x) * y.
(L(x,y,x) \ x) * y = T(x * y,x) / x.
a(x,y,x) * y = T(x * y,x) / x.
T(x * y,x) / x = a(x,y,x) * y.
R(K(x,y),K(y,x) * z,u) \ K(x,y) = K(y,x) * R(K(x,y),z,u).
x * (y * (R(y,y * (x \ 1),z) \ (x \ z))) = L(z,y * x,y).
x * (R(y,x \ 1,z) * (y \ (x \ z))) = L(z,y * x,y).
x * (R(y,x,z) * (y \ (x \ z))) = L(z,y * x,y).
R(x * (K(x,y) * K(x,y)),z,u) / T(T(x,y),y) = x \ R(x,z,u).
K(x,T(y,z)) * T(y,x) = K(z,T(y,x)) * T(y,z).
(K(x,T(y,z)) * T(y,x)) / L(y,K(y,z),K(z,T(y,x))) = K(z,T(y,x)) * K(y,z).
((T(x,y) * y) * z) / ((x * y) * z) = K(y,x) \ 1.
a(x * (y * y),y \ 1,y) = a(x * y,y \ 1,y \ 1).
L(x,y,z * (u / T(w,u))) = L(x,y,z * T(u * w,w)).
L(x,y,z * T(u * w,w)) = L(x,y,z * (u / T(w,u))).
L(x,y,z * T(u * w,w)) = L(x,y,z * (T(u,w) / w)).
L(x,y,z * (T(u,w) / w)) = L(x,y,z * T(u * w,w)).
(R(K(x,y),z,u) \ 1) \ K(y,x) = K(x,y) * R(K(y,x),z,u).
K(x,y) * R(K(y,x),z,u) = R(K(x,y),z,u) * K(y,x).
R(K(x,y),z,u) * K(y,x) = K(x,y) * R(K(y,x),z,u).
R(K(x,y),y * z,u) \ K(x,y) = K(y,x) * R(K(x,y),T(y,x) * z,u).
K(x,y) * R(K(y,x),T(x,y) * z,u) = R(K(y,x),x * z,u) \ K(y,x).
R(T(x,y) * K(x,y),z,u) / T(T(x,y),y) = x \ R(x,z,u).
R(T(T(x,y),y),z,u) / T(T(x,y),y) = x \ R(x,z,u).
x \ R(x,y,z) = T(T(x,u),u) \ R(T(T(x,u),u),y,z).
T(T(x,y),y) \ R(T(T(x,y),y),z,u) = x \ R(x,z,u).
(x * y) * L(T(y \ z,u),y,x) = (x * y) * T((x * y) \ (x * z),u).
(x * y) * T((x * y) \ (x * z),u) = (x * y) * L(T(y \ z,u),y,x).
(x * y) * L(R(y \ 1,z,u),y,x) = (x * y) * R((x * y) \ x,z,u).
(x * y) * R((x * y) \ x,z,u) = (x * y) * L(R(y \ 1,z,u),y,x).
(K(x,y) * (x \ z)) \ (K(x,y) * (x \ (z * u))) = L(u,z,x \ K(x,y)).
(x * y) * T((x * y) \ (x * z),u) = x * (y * T(y \ z,u)).
(x * y) * R((x * y) \ x,z,u) = x * (y * R(y \ 1,z,u)).
(x * y) * R((x * y) \ x,z,u) = x * (y \ R(y,z,u)).
x \ R(x,y,z) = (x / u) * (u * R(((u \ x) * x) \ (u \ x),y,z)).
(x / y) * (y * R(((y \ x) * x) \ (y \ x),z,u)) = x \ R(x,z,u).
(x / y) * (y * R(((y * x) * x) \ (y * x),z,u)) = x \ R(x,z,u).
(x / y) * (y * R(y \ (y / x),z,u)) = x \ R(x,z,u).
((x \ y) / y) * (y * R(y \ x,z,u)) = (x \ y) \ R(x \ y,z,u).
(L(x,y,z) / (z * (y * x))) * ((z * (y * x)) * R((z * (y * x)) \ (z * y),u,w)) = L(x,y,z) \ R(L(x,y,z),u,w).
(x \ 1) * (y * R(y \ x,z,u)) = (x \ y) \ R(x \ y,z,u).
(x \ y) \ R(x \ y,z,u) = x \ (y * R(y \ x,z,u)).
x \ (y * R(y \ x,z,u)) = (x * y) \ R(x * y,z,u).
(x * y) \ R(x * y,z,u) = x \ (y * R(y \ x,z,u)).
L(x,y,z \ K(z,u)) = L(L(x,y,z),z * y,K(z,u)).
L(L(x,y,z),z * y,K(z,u)) = L(x,y,z \ K(z,u)).
L(L(x,y,z),z * y,K(z,u)) = L(x,y,z * K(z,u)).
L(L(x,y,z),z * y,K(z,u)) = L(x,y,T(z,u)).
L(x,y * (y * z),K(y,u)) = L(L(x,z,y),y * z,T(y,u)).
L(L(x,y,z),z * y,T(z,u)) = L(x,z * (z * y),K(z,u)).
L(L(x,y,z),z * y,T(z,u)) = L(x,y,K(z,u)).
(x * (y * x)) \ R(x * (z * x),u,w) = T(y,x) \ T(R(z,u,w),x).
(x * (y * x)) \ R(x * (z * x),u,w) = T(y,x) \ R(T(z,x),u,w).
T(x,y) \ R(T(x,y),z,u) = y \ ((x * y) * R((x * y) \ y,z,u)).
x \ ((y * x) * R((y * x) \ x,z,u)) = T(y,x) \ R(T(y,x),z,u).
L(x,y,z * (u \ (u \ (u \ (z * (u \ 1)))))) = L(x,y,K(z / (u * u),u)).
L(x,y,z * (u \ ((u \ (u \ z)) * (u \ 1)))) = L(x,y,K(z / (u * u),u)).
L(x,y,K(z / (u * u),u)) = L(x,y,z * (u * ((u \ (u \ z)) * (u \ 1)))).
L(x,y,z * (u * ((u \ (u \ z)) * (u \ 1)))) = L(x,y,K(z / (u * u),u)).
L(x,y,z * (u \ (z * (u \ 1)))) = L(x,y,K(z / (u * u),u)).
L(x,y,K(z / (u * u),u)) = L(x,y,z * (u \ (z * (u \ 1)))).
L(x,y,K(z / (u * u),u)) = L(x,y,z * (u * (z * (u \ 1)))).
L(x,y,K(z / (u * u),u)) = L(x,y,z * T(z,u \ 1)).
L(x,y,K(z / (u * u),u)) = L(x,y,K(z,u \ 1)).
L(x,y,K(z,u)) = L(x,y,K(z,u \ 1)).
L(x,y,K(z,u \ 1)) = L(x,y,K(z,u)).
L(x,y,K(z,u \ 1)) = L(x,y,K(u,z)).
(x * (x * (y * (z * u)))) \ ((x * (x * (y * z))) * u) = a(x * (x * y),z,u).
(x * y) * R(L(y \ z,y,x),u,w) = (x * y) * R((x * y) \ (x * z),u,w).
((x * y) * ((y * x) * z)) \ (((x * y) * (y * x)) * (z * u)) = L(u,z,K(y,x)).
((x * y) * T(R(T(z,x * y),x,y),u)) / ((z * x) * y) = K(R(z,x,y),u).
((x * y) * R(T(T(z,x * y),u),x,y)) / ((z * x) * y) = K(R(z,x,y),u).
(R(T(x,y),z,u) * (z * u)) / ((x * z) * u) = K(R(x,z,u),y).
((T(x,y) * z) * u) / ((x * z) * u) = K(R(x,z,u),y).
K(R(x,y,z),u) = R(K(x,u),x * y,z).
R(K(x,y),x * z,u) = K(R(x,z,u),y).
K(R(x,y,z),y) = K(y,x) \ 1.
R(K(x,y),T(y,x) * z,u) \ 1 = K(R(y,z,u),x).
K(R(x,y,z),y) = K(x,y).
(x * x) / (x * K(y,x)) = T(x,R(y,x,z)).
T(x,R(y,x,z)) = (x * x) / (x * K(y,x)).
R(K(x,y),z,u) = K(R(x,x \ z,u),y).
K(R(x,x \ y,z),u) = R(K(x,u),y,z).
R(K(x,y),x * (z / (z * x)),u) = K(x,y).
R(K(x,y),T(x,y) * z,u) = K(R(T(x,y),z,u),y).
K(R(x,x * y,z),u) = R(K(x,u),y,z).
K(L(x,y,x),z) = R(K(x,z),y,x).
R(K(x,y),z,x) = K(L(x,z,x),y).
R(K(x,y),z,u) \ 1 = K(y,R(x,x * z,u)).
K(x,R(y,y * z,u)) = R(K(y,x),z,u) \ 1.
K(R(x,T(x,y) * z,u),w) = R(K(x,w),K(x,y) * z,u).
R(K(x,y),K(x,z) * u,w) = K(R(x,T(x,z) * u,w),y).
R(K(T(x,y),y),z,u) = K(R(x,T(x,y) * z,u),y).
K(R(x,T(x,y) * z,u),y) = R(K(T(x,y),y),z,u).
T(x,R(y,x,z)) = T(x,y).
R(x,y,z) * T(y,x) = y * R(x,y,z).
T(x,y) \ (x * R(y,x,z)) = T(R(y,x,z),T(x,y)).
R(K(x,y),K(x,z),u) = K(x,y).
K(x,y) = R(K(x,y),K(z,x),u).
R(K(x,y),K(z,x),u) = K(x,y).
K(x,y) * (K(z,x) * u) = (K(x,y) * K(z,x)) * u.
(K(x,y) * K(z,x)) * u = K(x,y) * (K(z,x) * u).
K(R(x,y,z),u) \ 1 = R(K(u,x),T(x,u) * y,z).
R(K(x,y),T(y,x) * z,u) = K(R(y,z,u),x) \ 1.
R(K(x,y),T(x,y) * z,u) = K(R(x,z,u),y).
K(R(x,y,z),u) \ 1 = R(K(u,x),x * y,z).
R(K(x,y),y * z,u) = K(R(y,z,u),x) \ 1.
R(K(x,y),y * z,u) = K(x,R(y,z,u)).
R(K(x,y),x * z,u) * K(y,x) = K(x,y) * K(y,R(x,z,u)).
K(R(x,T(x,y) * z,u),y) = R(K(x,y),z,u).
T(R(x,y,z),T(y,x)) = K(x,y) * R(x,y,z).
K(x,y) * R(x,y,z) = T(R(x,y,z),T(y,x)).
K(x,y) * R(x,y,z) = R(T(x,T(y,x)),y,z).
K(x,y) * R(x,y,z) = R(T(x,y),y,z).
T(x,y) \ R(T(x,y),y,z) = x \ R(x,y,z).
(x \ y) \ R(T(y / x,x),x,z) = (y / x) \ R(y / x,x,z).
x = L(x,K(y,z),K(z,u)).
L(x,K(y,z),K(z,u)) = x.
x = L(x,K(y,z),K(u,z)).
L(x,K(y,z),K(u,z)) = x.
x = L(x,K(y,z),K(u,y)).
L(x,K(y,z),K(u,y)) = x.
(K(x,y) * T(z,x)) / z = K(z,x) * K(x,y).
R(K(x,y),T(y,x) * z,u) = K(x,R(y,z,u)).
K(x,y) * K(y,R(x,z,u)) = R(K(y,x),x * z,u) \ K(y,x).
R(K(x,y),y * z,u) \ K(x,y) = K(y,x) * K(x,R(y,z,u)).
R(K(x,y),K(x,y) * z,u) = R(K(x,y),z,u).
R(K(x,y),z,u) = R(K(y,x),z,u) \ 1.
R(K(x,y),z,u) \ 1 = R(K(y,x),z,u).
K(x,y) * R(K(y,x),z,u) = R(K(x,y),z,u) \ K(x,y).
R(K(x,y),z,u) \ K(x,y) = K(x,y) * R(K(y,x),z,u).
K(x,R(y,y * z,u)) = R(K(x,y),z,u).
K(R(x,y,z),u) * K(u,x) = K(x,u) * K(u,R(x,y,z)).
K(x,y) * K(R(y,z,u),x) = K(y,x) * K(x,R(y,z,u)).
(x \ y) \ R(x \ y,x,z) = (y / x) \ R(y / x,x,z).
(x / y) \ R(x / y,y,z) = (y \ x) \ R(y \ x,y,z).
(x \ y) \ R(x \ y,x,z) = (x / y) * R(y / x,x,z).
(x / y) * R(y / x,x,z) = x \ (y * R(y \ x,x,z)).
x \ (y * R(y \ x,x,z)) = (x / y) * R(y / x,x,z).
x \ ((y \ x) * R((y \ x) \ x,x,z)) = y * R((y \ x) / x,x,z).
x \ (R(y,x,z) * (y \ x)) = y * R((y \ x) / x,x,z).
x * R((x \ y) / y,y,z) = T(x \ R(x,y,z),y).
x * R(x \ 1,y,z) = T(x \ R(x,y,z),y).
T(x \ R(x,y,z),y) = x * R(x \ 1,y,z).
T(x \ R(x,y,z),y) = x \ R(x,y,z).
(x * (y \ R(y,x,z))) / x = y \ R(y,x,z).
T(x \ R(x,y,z),x * (y * z)) = T(a(x,y,z),y).
L((x * (y \ R(y,x,z))) * (a(x,x * (y \ R(y,x,z)),x * (y \ R(y,x,z))) * u),x * (y \ R(y,x,z)),x) = (y \ R(y,x,z)) * (x * u).
T(a(x,y,z),y) = a(x,y,z).
x * a(y,x,z) = a(y,x,z) * x.
a(x,y,z) * y = y * a(x,y,z).
x \ a(y,x \ 1,z) = a(y,x \ 1,z) * (x \ 1).
a(x,y \ 1,z) * (y \ 1) = y \ a(x,y \ 1,z).
T(x * y,x) / x = y * a(x,y,x).
L(x,y,z * (T(u * z,u) / u)) = L(x,y,a(u,z,u)).
L(x,y,z * a(u,z,u)) = L(x,y,R(z,u,u)).
L(x,y,a(z,u,z)) = L(x,y,u * T((z * u) * z,z)).
L(x,y,z * T((u * z) * u,u)) = L(x,y,a(u,z,u)).
L(x,y,z * ((z * u) * u)) = L(x,y,a(u,z,u)).
L(x,y,a(z,u,z)) = L(x,y,a(u,z,z)).
L(x,y,a(z,u,u)) = L(x,y,a(u,z,u)).
(x * (x * (y * (z * u)))) \ (x * (x * ((y * z) * u))) = a(x * (x * y),z,u).
(x * y) * L(R(y \ z,u,w),y,x) = (x * y) * R((x * y) \ (x * z),u,w).
(x * y) * R((x * y) \ (x * z),u,w) = (x * y) * L(R(y \ z,u,w),y,x).
((x * y) * ((y * x) * z)) \ ((x * y) * ((y * x) * (z * u))) = L(u,z,K(y,x)).
a(x * (x * y),z,u) = (y * (z * u)) \ ((y * z) * u).
a(x * (x * y),z,u) = a(y,z,u).
a(x * y,z,u) = a(x \ y,z,u).
a(x \ y,z,u) = a(x * y,z,u).
a((x / y) * x,z,u) = a(y,z,u).
a(x * (y * x),z,u) = a(T(y,x),z,u).
a(x * ((x * y) * z),u,w) = a(x * ((x \ y) * z),u,w).
a(x * ((x \ y) * z),u,w) = a(x * ((x * y) * z),u,w).
a((x * y) * z,u,w) = a((x \ y) * z,u,w).
a((x \ y) * z,u,w) = a((x * y) * z,u,w).
a((x * x) / y,z,u) = a(y \ 1,z,u).
a(x * L(x,y * x,y),z,u) = a(a(y,x,x),z,u).
a(x * a(x,y,y),z,u) = a(R(x \ 1,y,y),z,u).
a(R(x \ 1,y,y),z,u) = a(x * a(x,y,y),z,u).
a(K(x,y) * y,z,u) = a(T(y,x),z,u).
a(x * T(x,y),z,u) = a(K(x,y),z,u).
((x \ y) * (T(x,x * y) * z)) \ (y * z) = a(x * y,T(x,x * y),z).
a(x \ ((x * y) \ y),z,u) = a(K(x \ 1,x * y),z,u).
a(K(x \ 1,x * y),z,u) = a(x \ ((x * y) \ y),z,u).
a((x * (x * y)) * (x * z),u,w) = a(y \ (x \ z),u,w).
a((x * x) / y,z,u) = a(y,z,u).
a(x,y,z) = a(x / (u * u),y,z).
a(x / (y * y),z,u) = a(x,z,u).
a(R(x,x * y,z),u,w) = a(R(x,y,z),u,w).
a(T(x,y),z,u) = a(x * K(y,x),z,u).
a(x * K(y,x),z,u) = a(T(x,y),z,u).
a(x,y,z) = a(x * (u * u),y,z).
a(x * (y * y),z,u) = a(x,z,u).
a(R(x,y,y),z,u) = a((x * y) * y,z,u).
a((x * y) * y,z,u) = a(R(x,y,y),z,u).
a(x / y,z,u) = a(x / (y \ 1),z,u).
a(x / (y \ 1),z,u) = a(x / y,z,u).
((x * (y * y)) * (z * u)) \ (((x * (y * y)) * z) * u) = a(x,z,u).
a(x,y,z) = a(T(T(x,u),u),y,z).
a(T(T(x,y),y),z,u) = a(x,z,u).
a((x / (y * y)) * (y \ (x * (y \ 1))),z,u) = a(K(x / (y * y),y),z,u).
a(x / (x * y),z,u) = a(T(y,x),z,u).
a(x / y,z,u) = a((y \ 1) / x,z,u).
a((x \ 1) / y,z,u) = a(y / x,z,u).
a(x / T(y * x,y),z,u) = a(T(R(y,x,y),x),z,u).
a(R(x,y,y),y,y) = a(y * (x * y),y,y).
a(x * (y * x),x,x) = a(R(y,x,x),x,x).
a(R(x,y,y),y,y) = a(T(x,y),y,y).
a(R(x,y,y),y,y) = a(x,y,y).
R(R(x,y,y) \ 1,y,y) = R(x,y,y) \ a(x,y,y).
a(x,y,y) \ R(x,y,y) = R(R(x,y,y),R(x,y,y) * y,y).
R(R(x,y,y),R(x,y,y) * y,y) = a(x,y,y) \ R(x,y,y).
a(x * ((x \ y) * y),z,u) = a(a(x,y,y),z,u).
a(R(x \ 1,y,y),z,u) = a(R(x,y,y),z,u).
R(R(x,y,y) \ 1,y,y) = x \ 1.
R((x * y) \ 1,y,y) = (x / (y \ 1)) \ 1.
R((x * y) \ 1,y,y) = (y \ 1) / x.
R(x \ 1,y,y) = (y \ 1) / (x / y).
(x \ 1) / (y / x) = R(y \ 1,x,x).
((x \ 1) / y) * (x * x) = (((y * x) \ 1) * x) * x.
(((x * y) \ 1) * y) * y = ((y \ 1) / x) * (y * y).
R(x \ 1,y,y) \ 1 = (x / y) / (y \ 1).
a((x \ 1) / ((y / x) \ 1),z,u) = a(R(y \ 1,x,x),z,u).
R(x,x * y,y) = (x / y) / (y \ 1).
K(R(x,x * y,y),z) * (x / y) = (y \ 1) * T((y \ 1) \ (x / y),z).
(((x * y) \ 1) * y) * y = T(y / x,y * y).
((x * y) \ y) * y = T(y / x,y * y).
L(x,y * z,R(T(z / y,z * z),u,w)) = x.
x = L(x,y * z,R(z / y,u,w)).
L(x,y * z,R(z / y,u,w)) = x.
L(x,y * (z \ 1),u / (y * (z * u))) = x.
x = L(x,y * z,u / (y * (z * u))).
L(x,y * z,u / (y * (z * u))) = x.
x / ((y * z) \ (y * (z * x))) = (x / (y * (z * x))) * (y * z).
a((x / y) / x,z,u) = a(T(R(y,x,y),x),z,u).
a(T(R(x,y,x),y),z,u) = a((y / x) / y,z,u).
a(x * ((x * y) * y),z,u) = a(a(x,y,y),z,u).
a(x * (x * (y * (x * z))),u,w) = a(y \ (x \ z),u,w).
a(x \ (y \ z),u,w) = a(x * (y * z),u,w).
a(x * (y * z),u,w) = a(x * (y \ z),u,w).
a(x * (y \ z),u,w) = a(x * (y * z),u,w).
a(K(x \ 1,x * y),z,u) = a(x * ((x * y) * y),z,u).
R(R(x,y,y),R(x,y,y) * y,y) = x.
K(x,y) = R(K(R(x,z,z),y),z,z).
R(K(R(x,y,y),z),y,y) = K(x,z).
K(x,y) / z = K(R(x,z,z),y) * (z \ 1).
K(R(x,y,y),z) * (y \ 1) = K(x,z) / y.
x \ 1 = K(y,R(z,x,x)) * (K(z,y) / x).
K(x,R(y,z,z)) * (K(y,x) / z) = z \ 1.
K(x,R(y,z,z)) = R(K(x,y),z,z).
R(K(x,y),z,z) = K(x,R(y,z,z)).
K(R(x,y,y),z) \ 1 = R(K(z,x),y,y).
R(K(x,y),z,z) = K(x,R(y,z,z)) * 1.
K(x,R(y,z,z)) * 1 = R(K(x,y),z,z).
a((x \ 1) / (x / y),z,u) = a(R(y \ 1,x,x),z,u).
a(R(x \ 1,y,y),z,u) = a((y / x) / y,z,u).
a((x / y) / x,z,u) = a(R(y,x,x),z,u).
a(T(R(x,y,x),y),z,u) = a(R(x,y,y),z,u).
a(R(T(x,y),y,x),z,u) = a(R(x,y,y),z,u).
x / L(x,y,z) = (x / (z * (y * x))) * (z * y).
(x / (y * (z * x))) * (y * z) = x / L(x,z,y).
(x / (y * (z * x))) * (y * z) = L(x,z,y) \ x.
(L(x * y,z / (x * (y * z)),x * y) * (z / (x * (y * z)))) * (x * y) = (x * y) * (L(z,y,x) \ z).
(x * (y * (y * (z * u)))) \ (((x * (y * y)) * z) * u) = a(x,z,u).
(x * (y * (y * (z * u)))) \ ((x * (y * (y * z))) * u) = a(x,z,u).
a(x,y,z) = a(x,u * (u * y),z).
a(x,y * (y * z),u) = a(x,z,u).
a(x,y * z,u) = a(x,y \ z,u).
a(x,y \ z,u) = a(x,y * z,u).
a(x,(y / z) * y,u) = a(x,z,u).
a(x,K(y,z) * T(y,z),u) = a(x,y,u).
a(x * (y * y),y * 1,y) = a(x * y,y \ 1,y \ 1).
a(x,y \ 1,z) * (y \ 1) = y \ a(x,y * 1,z).
a(x,(y * (y * z)) * (y * u),w) = a(x,z \ (y \ u),w).
a(x,T(T(y,z),z),u) = a(x,y,u).
a(T(x,y),y,z) = a(x,T(y,x),z).
a(x,y \ 1,z) * (y \ 1) = y \ a(x,y,z).
a(x,y * 1,z) * (y \ 1) = y \ a(x,y,z).
a(x,y,z) * (y \ 1) = y \ a(x,y,z).
a(x * (y * y),y,y) = a(x * y,y \ 1,y \ 1).
a(x * y,y \ 1,y \ 1) = a(x,y,y).
a(x,y,y) = L(y,y,x) \ y.
L(x,x,y) \ x = a(y,x,x).
a(x,y,y) * L(y,y,x) = y.
x * y = R(x,y,y) * L(y,y,x).
R(x,y,y) * L(y,y,x) = x * y.
L(x,x,y) \ (y * x) = T(R(y,x,x),L(x,x,y)).
T(R(x,y,y),L(y,y,x)) = L(y,y,x) \ (x * y).
L(x,x,y) \ (y * x) = R(T(y,L(x,x,y)),x,x).
R(T(x,L(y,y,x)),y,y) = L(y,y,x) \ (x * y).
R(T(x,y),y,y) = L(y,y,x) \ (x * y).
L(x,x,y) \ (y * x) = R(T(y,x),x,x).
a(x,y * (y * (z * (y * u))),w) = a(x,z \ (y \ u),w).
a(x,y \ (z \ u),w) = a(x,y * (z * u),w).
a(x,y * (z * u),w) = a(x,y * (z \ u),w).
a(x,y * (z \ u),w) = a(x,y * (z * u),w).
((x / y) * (y * z)) \ (x * z) = a(y * x,T(y,y * x),z).
a(x * y,T(x,x * y),z) = ((y / x) * (x * z)) \ (y * z).
a(x * y,T(x,x * y),z) = a(y / x,x,z).
R(K(x,y),z,z) * (x / z) = (z \ 1) * T((z \ 1) \ (x / z),y).
K(x,R(y,z,z)) * (x / z) = (z \ 1) * T((z \ 1) \ (x / z),y).
K(x,R(y,z,z)) * (x / z) = (z \ 1) * T(z * (x / z),y).
K(x,R(y,z,z)) * (x / z) = z \ T(z * (x / z),y).
K(x,R(y,z,z)) * (x / z) = T(x,y) / z.
a(x * (y \ (y \ (y \ (x * (y \ 1))))),z,u) = a(K(x / (y * y),y),z,u).
a(x * (y \ ((y \ (y \ x)) * (y \ 1))),z,u) = a(K(x / (y * y),y),z,u).
a(K(x / (y * y),y),z,u) = a(x * (y * ((y \ (y \ x)) * (y \ 1))),z,u).
a(x * (y * ((y \ (y \ x)) * (y \ 1))),z,u) = a(K(x / (y * y),y),z,u).
a(x * (y \ (x * (y \ 1))),z,u) = a(K(x / (y * y),y),z,u).
a(K(x / (y * y),y),z,u) = a(x * (y \ (x * (y \ 1))),z,u).
a(K(x / (y * y),y),z,u) = a(x * (y * (x * (y \ 1))),z,u).
a(K(x / (y * y),y),z,u) = a(x * T(x,y \ 1),z,u).
a(K(x / (y * y),y),z,u) = a(K(x,y \ 1),z,u).
a(K(x,y),z,u) = a(K(x,y \ 1),z,u).
a(K(x,y \ 1),z,u) = a(K(x,y),z,u).
a(K(x,y),z,u) = a(K(y \ 1,x),z,u).
a(K(x \ 1,y),z,u) = a(K(y,x),z,u).
a(K(x * y,x),z,u) = a(x * ((x * y) * y),z,u).
a(x * ((x * y) * y),z,u) = a(K(x * y,x),z,u).
a(K(x * y,x),z,u) = a(a(x,y,y),z,u).
(x * y) * R((x * y) \ (x * z),u,w) = x * (y * R(y \ z,u,w)).
(x * y) * R((x * y) \ z,u,w) = x * (y * R(y \ (x \ z),u,w)).
(x * y) * R((x * y) \ y,z,u) = R(x,z,u) * (x \ y).
x \ (R(y,z,u) * (y \ x)) = T(y,x) \ R(T(y,x),z,u).
T(x,y) \ R(T(x,y),z,u) = y \ (R(x,z,u) * (x \ y)).
T(x,y) \ R(T(x,y),z,u) = T(x \ R(x,z,u),y).
T(x \ R(x,y,z),u) \ w = (R(T(x,u),y,z) \ T(x,u)) * w.
(R(T(x,y),z,u) \ T(x,y)) * w = T(x \ R(x,z,u),y) \ w.
T(x \ R(x,y,y),z) = a(T(x,z),y,y).
x * T(x \ R(x,y,z),u) = K(u,x) * R(T(x,u),y,z).
K(x,y) * R(T(y,x),z,u) = y * T(y \ R(y,z,u),x).
T(T(x,y) \ R(T(x,y),z,u),y) = x \ R(x,z,u).
T(a(x,y,y),z) = a(T(x,z),y,y).
T(T(x \ R(x,y,z),u),u) = x \ R(x,y,z).
(x * (y \ R(y,z,u))) / x = T(y \ R(y,z,u),x).
T(a(x,y,z),x * (y * z)) = x \ R(x,y,z).
a(x,y,z) * K(a(x,y,z),x * (y * z)) = x \ R(x,y,z).
T(T(x \ R(x,y,z),u),x * (y * z)) = (u * a(x,y,z)) / u.
(x \ R(x,y,z)) * K(x \ R(x,y,z),u) = (u * (x \ R(x,y,z))) / u.
(x * (y \ R(y,z,u))) / x = (y \ R(y,z,u)) * K(y \ R(y,z,u),x).
(x * a(y,z,u)) / x = T(a(y,z,u),x).
T(a(x,y,z),u) * (u / (u * a(x,y,z))) = 1.
L(x,x,x * ((x \ 1) * a(y,z,u))) = ((x \ 1) * a(y,z,u)) \ T(a(y,z,u),x \ 1).
1 = K(a(x,y,z),u) * K(a(x,y,z),u).
K(a(x,y,z),u) * K(a(x,y,z),u) = 1.
K(a(x,y,z),u) = K(u,a(x,y,z)).
a(x,y,z) * K(x * (y * z),a(x,y,z)) = x \ R(x,y,z).
K(x \ R(x,y,z),u) = K(u,x \ R(x,y,z)).
L(x,y,K(z,u)) = L(L(x,y,z * u),(z * u) * y,u * z).
L(L(x,y,z * u),(z * u) * y,u * z) = L(x,y,K(z,u)).
((x * (x * y)) * a(y,z,u)) / y = a(x * (x * y),z,u) * (x * x).
(x * (x * (y * a(y,z,u)))) / y = a(x * (x * y),z,u) * (x * x).
a(x * (x * y),z,u) * (x * x) = x * (x * ((y * a(y,z,u)) / y)).
a(x * (x * y),z,u) * (x * x) = x * (x * a(y,z,u)).
a(x,y,z) * (u * u) = u * (u * a(x,y,z)).
T((a(x,y,z) * (u * u)) / (u * u),u) = T(u \ (u * a(x,y,z)),u \ 1).
T(a(x,y,z),u) = T(u \ (u * a(x,y,z)),u \ 1).
T(x \ (x * a(y,z,u)),x \ 1) = T(a(y,z,u),x).
T(a(x,y,z),u \ 1) = T(a(x,y,z),u).
K(L(x \ (x / y),x,y * x),z) = y * L(T(x \ (x / y),z),x,y * x).
x * L(T(y \ (y / x),z),y,x * y) = K(L(y \ (y / x),y,x * y),z).
K(L(x \ (x / y),x,y * x),z) = (y / x) * (x * T(x \ (x / y),z)).
(x / y) * (y * T(y \ (y / x),z)) = K(L(y \ (y / x),y,x * y),z).
(x / y) * (y * T(y \ (y / x),z)) = K(x \ 1,z).
(L(x,y,z) / (z * (y * x))) * ((z * (y * x)) * T((z * (y * x)) \ (z * y),u)) = K(L(x,y,z) \ 1,u).
T(x * x,y * z) \ ((((y * z) \ (x * x)) * y) * z) = a((y * z) * (x * x),y,z).
((R(x,y,z) * u) * w) / ((x * u) * w) = R(x,u,w) \ R(R(x,u,w),y,z).
R(x \ R(x,y,z),x * u,w) = R(x,u,w) \ R(R(x,u,w),y,z).
R((x \ 1) \ R(x \ 1,y,z),(x \ 1) * (x * u),w) = (R(x,u,w) \ 1) \ R(R(x \ 1,x * u,w),y,z).
(K(x,T(y,z)) * T(y,x)) / y = K(z,T(y,x)) * K(y,z).
K(x,T(y,z)) * K(y,x) = K(y,z) * K(z,T(y,x)).
T(x * x,y * z) \ ((((y * z) \ (x * x)) * y) * z) = a(y * z,y,z).
a(x * y,x,y) = (T(z * z,x * y) \ (((x * y) \ (z * z)) * x)) * y.
(T(x * x,y * z) \ (((y * z) \ (x * x)) * y)) * z = a(y * z,y,z).
((T(x * x,y * z) \ ((y * z) \ (x * x))) * y) * z = a(y * z,y,z).
(((x * y) \ 1) * x) * y = a(x * y,x,y).
((x * y) \ x) * y = a(x * y,x,y).
a(x * y,x,y) = y * ((x * y) \ x).
x * ((y * x) \ y) = a(y * x,y,x).
(x \ y) * (y \ x) = a(x * (x \ y),x,x \ y).
a(x * (x \ y),x,x \ y) = (x \ y) * (y \ x).
a(x,y,y \ x) = (y \ x) * (x \ y).
(x \ y) * (y \ x) = a(y,x,x \ y).
L(x,y,a(z,u,u \ z)) = L(x,y,(z \ u) * (u * z)).
L(x,y,(z \ u) * (u * z)) = L(x,y,a(z,u,u \ z)).
L(x,a(y,z,z \ y),u) = L(x,(y \ z) * (z * y),u).
L(x,(y \ z) * (z * y),u) = L(x,a(y,z,z \ y),u).
L(x,y,a(z,u,u \ z)) = L(x,y,(z * u) * (u * z)).
L(x,y,(z * u) * (u * z)) = L(x,y,a(z,u,u \ z)).
L(x,a(y,z,z \ y),u) = L(x,(y * z) * (z * y),u).
L(x,(y * z) * (z * y),u) = L(x,a(y,z,z \ y),u).
L(x,y,a(z,u,u \ z)) = L(x,y,K(u,z)).
L(x,a(y,z,z \ y),u) = L(x,K(z,y),u).
L(x,x,a(y,z,u)) = ((x \ 1) * a(y,z,u)) \ T(a(y,z,u),x \ 1).
((x \ 1) * a(y,z,u)) \ T(a(y,z,u),x \ 1) = L(x,x,a(y,z,u)).
(x \ a(y,z,u)) \ T(a(y,z,u),x \ 1) = L(x,x,a(y,z,u)).
(x \ a(y,z,u)) \ T(a(y,z,u),x) = L(x,x,a(y,z,u)).
L(x,x,a(y,z,u)) = L(x,a(y,z,u),x).
L(x,a(y,z,u),x) = L(x,x,a(y,z,u)).
L(x,x,a(y,z,z \ y)) = L(x,K(z,y),x).
L(x,K(y,z),x) = L(x,x,K(y,z)).
L(x,K(y,z),x) = L(x,x,K(z,y)).
(x \ K(y,z)) / (K(y,z) / L(x,x,K(z,y))) = K(K(y,z),x).
(x \ K(y,z)) / (K(y,z) * (x \ 1)) = K(K(y,z),x).
K(K(x,y),z) = K(z \ 1,K(x,y)).
K(x \ 1,K(y,z)) = K(K(y,z),x).
K(K(x,y),z) * (K(x,y) \ u) = T(K(x,y),z \ 1) \ u.
T(K(x,y),z) * K(K(x,y),z) = T(K(x,y),z * z).
T(K(x,y),z * z) = T(T(K(x,y),z),z).
T(T(K(x,y),z),z) = T(K(x,y),z * z).
T(T(K(x,y),z),T(z,x)) = T(K(x,y),T(z,x) * T(z,x)).
T(K(x,y),T(z,x) * T(z,x)) = T(T(K(x,y),z),T(z,x)).
x / (T(K(y,z),u \ 1) \ x) = K(y,z) * K(u,K(y,z)).
T(K(x,y),z * T(T(z,x),x)) = T(T(K(x,y),z),T(z,x)).
K(x,y) * K(z,K(x,y)) = T(K(x,y),z \ 1).
T(K(x,y),z \ 1) * z = z * K(x,y).
((x * y) * (z / (x * (y * z)))) * (x * y) = (x * y) * (L(z,y,x) \ z).
(x \ R(x,y,z)) * (x * y) = (x * y) * (L(z,y,x) \ z).
(x * y) * (L(z,y,x) \ z) = R(x,y,z) * y.
((x * y) \ 1) * ((x * (y * z)) * T((x * (y * z)) \ (x * y),u)) = K(L(z,y,x) \ 1,u).
((x * y) \ 1) * (x * ((y * z) * T((y * z) \ y,u))) = K(L(z,y,x) \ 1,u).
((x * y) \ 1) * (x * (y * K(z \ 1,u))) = K(L(z,y,x) \ 1,u).
K(L(x,y,z) \ 1,u) = (z * y) \ (z * (y * K(x \ 1,u))).
(x * y) \ (x * (y * K(z \ 1,u))) = K(L(z,y,x) \ 1,u).
K(L(x,y,z) \ 1,u) = L(K(x \ 1,u),y,z).
L(K(x \ 1,y),z,u) = K(L(x,z,u) \ 1,y).
L(K(x,y),z,u) = K(L(x \ 1,z,u) \ 1,y).
K(L(x \ 1,y,z) \ 1,u) = L(K(x,u),y,z).
R((x * 1) \ R(x * 1,y,z),(x \ 1) * (x * u),w) = (R(x,u,w) \ 1) \ R(R(x \ 1,x * u,w),y,z).
R(x \ R(x * 1,y,z),(x \ 1) * (x * u),w) = (R(x,u,w) \ 1) \ R(R(x \ 1,x * u,w),y,z).
R(x \ R(x,y,z),(x \ 1) * (x * u),w) = (R(x,u,w) \ 1) \ R(R(x \ 1,x * u,w),y,z).
R(x \ R(x,y,z),u,w) = (R(x,u,w) \ 1) \ R(R(x \ 1,x * u,w),y,z).
(R(x,y,z) \ 1) \ R(R(x \ 1,x * y,z),u,w) = R(x \ R(x,u,w),y,z).
(R(x,y,z) \ 1) \ R(R(x,y,z) \ 1,u,w) = R(x \ R(x,u,w),y,z).
R(x \ R(x,y,z),u,w) = (R(x,u,w) * 1) \ R(R(x,u,w) * 1,y,z).
(R(x,y,z) * 1) \ R(R(x,y,z) * 1,u,w) = R(x \ R(x,u,w),y,z).
R(x,y,z) \ R(R(x,y,z) * 1,u,w) = R(x \ R(x,u,w),y,z).
R(x,y,z) \ R(R(x,y,z),u,w) = R(x \ R(x,u,w),y,z).
R(x \ R(x,y,y),z,u) = a(R(x,z,u),y,y).
T(R(x \ R(x,y,x),z,u),x * (R(x,z,u) * T(y,x))) = a(R(x,z,u),y,x).
R(a(x,y,y),z,u) = a(R(x,z,u),y,y).
T(R(a(x,y,x),z,u),x * (R(x,z,u) * T(y,x))) = a(R(x,z,u),y,x).
T(R(a(x,y,x),z,u),R(x,z,u) * (y * x)) = a(R(x,z,u),y,x).
a(R(x,y,z),u,x) = R(T(a(x,u,x),R(x,y,z) * (u * x)),y,z).
R(T(a(x,y,x),R(x,z,u) * (y * x)),z,u) = a(R(x,z,u),y,x).
((x * y) \ 1) * ((x * (y * z)) * R((x * (y * z)) \ (x * y),u,w)) = L(z,y,x) \ R(L(z,y,x),u,w).
((x * y) \ 1) * (x * ((y * z) * R((y * z) \ y,u,w))) = L(z,y,x) \ R(L(z,y,x),u,w).
((x * y) \ 1) * (x * (y * (z \ R(z,u,w)))) = L(z,y,x) \ R(L(z,y,x),u,w).
L(x,y,z) \ R(L(x,y,z),u,w) = (z * y) \ (z * (y * (x \ R(x,u,w)))).
(x * y) \ (x * (y * (z \ R(z,u,w)))) = L(z,y,x) \ R(L(z,y,x),u,w).
L(x,y,z) \ R(L(x,y,z),u,w) = L(x \ R(x,u,w),y,z).
L((x * (y \ R(y,x,z))) * (a(x,x * (y * R(y,x,z)),x * (y \ R(y,x,z))) * u),x * (y \ R(y,x,z)),x) = (y \ R(y,x,z)) * (x * u).
L((x * (y \ R(y,x,z))) * (1 * u),x * (y \ R(y,x,z)),x) = (y \ R(y,x,z)) * (x * u).
L((x * (y \ R(y,x,z))) * u,x * (y \ R(y,x,z)),x) = (y \ R(y,x,z)) * (x * u).
L(x * (R(y,x,z) * (y \ u)),x * (y \ R(y,x,z)),x) = (y \ R(y,x,z)) * (x * u).
(x \ R(x,y,z)) * (y * u) = L(y * (R(x,y,z) * (x \ u)),y * (x * R(x,y,z)),y).
L(x * (R(y,x,z) * (y \ u)),x * (y * R(y,x,z)),x) = (y \ R(y,x,z)) * (x * u).
(x \ R(x,y,z)) * (y * u) = y * (R(x,y,z) * (x \ u)).
x * (R(y,x,z) * (y \ u)) = R(y,x,z) * (y \ (x * u)).
R(x,y,z) * (x \ (y * u)) = y * (R(x,y,z) * (x \ u)).
R(x,y,z) * (x \ (y * (y \ z))) = L(z,x * y,x).
R(x,y,z) * (x \ z) = L(z,x * y,x).
R(x,y,L(z,y,x)) * (x \ L(z,y,x)) = z.
L(x,y * z,y) / x = y \ R(y,z,x).
x / L(x,y * z,y) = R(y,z,x) \ y.
x \ R(x,y,z) = z \ L(z,x * y,x).
x \ L(x,y * z,y) = y \ R(y,z,x).
R(x,y,z) \ x = L(z,x * y,x) \ z.
L(x,y * z,y) \ x = R(y,z,x) \ y.
x \ L(x,y,z) = z \ R(z,z \ y,x).
x \ R(x,x \ y,z) = z \ L(z,y,x).
x \ L(x,y,z) = z \ R(z,z * y,x).
x \ R(x,x * y,z) = z \ L(z,y,x).
K(x,R(y,z,x) \ y) = 1.
K(x,y \ R(y,z,x)) = 1.
T(x,y \ R(y,z,x)) = x.
K(x,T(y \ R(y,z,x),u)) = 1.
T(x \ R(x,y,z),z) = x \ R(x,y,z).
K(x,a(y,z,x)) = 1.
T(x,a(y,z,x)) = x.
a(x,y,z) * z = z * a(x,y,z).
x \ L(x,y,z) = R(z,y,x) \ z.
R(x,y,z) \ x = z \ L(z,y,x).
x * (R(y,z,x) \ y) = L(x,z,y).
x / (y \ L(y,z,x)) = R(x,z,y).
(x \ L(x,y,z)) \ 1 = z \ R(z,y,x).
(x \ L(x,y,z)) * R(z,y,x) = z.
(R(x,y,z) \ x) * z = L(z,y,x).
x * (R(K(y,z),u,x) \ K(y,z)) = L(x,u,K(z,y)).
R(x,y,z) = R(x,y,T(z,x * y)).
R(x,y,T(z,x * y)) = R(x,y,z).
x * y = L(x,z,y) * R(y,z,x).
L(x,y,z) * R(z,y,x) = x * z.
x = L(y,z,x) * (y \ R(x,z,y)).
L(x,y,z) * (x \ R(z,y,x)) = z.
R(x,y,z) * L(z,y,x) = x * z.
(x \ R(x,y,z)) \ z = L(z,y,x).
L(x,y,T(z,u)) = T(z \ R(z,y,x),u) \ x.
T(x \ R(x,y,z),u) \ z = L(z,y,T(x,u)).
L(x,y,z) \ x = z \ R(z,y,x).
R(x,y,z) = x * (L(z,y,x) \ z).
x * (L(y,z,x) \ y) = R(x,z,y).
R(x,y,z) * (x \ L(z,y,x)) = z.
(L(x,y,z) * (R(z,y,x) * u)) \ ((x * z) * u) = a(L(x,y,z),R(z,y,x),u).
(L(x,y,z) \ x) * (z * u) = R(z,y,x) * u.
(x \ R(x,y,z)) * u = z * (L(z,y,x) \ u).
R(x \ R(x,y,z),z,u) = L(z,y,x) \ z.
(x * y) * (x \ R(x,y,z)) = R(x,y,z) * y.
K(x,y) \ R(K(x,y),z,u) = u \ L(u,z,K(x,y)).
x \ R(x,y,z) = (L(z,y,x) \ z) * 1.
R(x,y,L(z,y,x)) = R(x,y,z).
(x \ R(x,y,z)) \ z = L(z,y,T(x,z)).
L(x,y,T(z,x)) = L(x,y,z).
L(L(x,y,z),z * y,T(z,L(x,y,z))) = x.
x = L(x,y,K(z,L(x,y,z))).
L(x,y,K(z,L(x,y,z))) = x.
R(x,y,z) * u = z * (L(z,y,x) \ (x * u)).
x * (L(x,y,z) \ (z * u)) = R(z,y,x) * u.
L((x \ R(x,y,z)) \ u,x \ R(x,y,z),x * y) = (R(x,y,z) * y) \ ((x * y) * u).
L(x,y,z) * (R(z,y,x) * u) = x * (z * u).
x * (L(x,y,z) \ (z * T(y,z))) = y * R(z,y,x).
x * (L(x,y,z) \ (z * L(x,y,z))) = z * x.
x * T(y,L(x,z,y)) = y * x.
T(x,L(y,z,x)) = x * K(x,y).
K(x,y) = K(x,L(y,z,x)).
K(x,L(y,z,x)) = K(x,y).
L(x,y,K(z,x)) = x.
T(x,y) = L(T(x,y),z,K(u,x)).
L(T(x,y),z,K(u,x)) = T(x,y).
x = L(x,y,K(x,z)).
L(x,y,K(x,z)) = x.
x = L(x,y,a(x,z,z)).
L(x,y,a(x,z,z)) = x.
K((x \ 1) \ 1,y) = L(K(x,y),z,K(u,x \ 1)).
L(K(x,y),z,K(u,x \ 1)) = K((x \ 1) \ 1,y).
K(x,y) / (y \ y) = R(K(x,y),z,y).
R(K(x,y),z,y) = K(x,y) / (y \ y).
(K(x,y) * z) * x = K(x,y) * (z * x).
x * (x \ R(a(x,y,y),z,x)) = a(x,y,y).
T(x,y) = T(x,K(z,x) * y).
T(x,K(y,x) * z) = T(x,z).
T(x,y) \ x = K(K(z,x) * y,x).
K(K(x,y) * z,y) = T(y,z) \ y.
x \ T(x,y) = K(x,K(z,x) * y).
K(x,K(y,x) * z) = x \ T(x,z).
T(x,y * T(z,x)) = T(x,y * z).
K(K(x,y) * z,y) = K(z,y).
K(x,y) = K(K(y,z) * x,y).
K(K(x,y) * z,x) = K(z,x).
K(x * (K(x,y) * z),x) = K(x * z,x).
K(x,K(y,x) * z) = K(x,z).
K(x,y) = K(x,K(x,z) * y).
K(x,K(x,y) * z) = K(x,z).
K(x,y) * K(x * (K(x,z) * y),x) = a(x,K(x,z) * y,x).
R(K(x,y),z,y) = K(x,y) / 1.
R(K(x,y),z,y) = K(x,y).
K(x,y) = K(x,R(y,z,y)).
K(x,R(y,z,y)) = K(x,y).
K(x,y) \ 1 = R(K(y,x),z,y).
R(K(x,y),z,x) = K(y,x) \ 1.
K(x,y) * R(T(y,x),z,y) = R(y,z,y).
R(K(x,y),z,x) = K(x,y).
K(x,y) = K(L(x,z,x),y).
K(L(x,y,x),z) = K(x,z).
K((x \ y) \ y,z) = K(T(x,y),z).
K(T(x,x \ y),z) = K(T(x,y),z).
x \ (K(x,y) * (z * x)) = T(K(x,y) * z,x).
x * ((K(x,y) * z) * x) = T(x,y) * (z * x).
x \ R(x,y,x) = T(x,z) \ R(T(x,z),y,x).
T(x,y) \ R(T(x,y),z,x) = x \ R(x,z,x).
x * (x \ a(R(x,y,x),z,z)) = a(x,z,z).
x * (x \ a(L(x,y,x),z,z)) = a(x,z,z).
a(x,y,y) = a(L(x,z,x),y,y).
a(L(x,y,x),z,z) = a(x,z,z).
a(L(T(x,y),y * x,x),z,z) = a(T(x,y),z,z).
T(K(x,y) * z,x) = K(x,y) * (x \ (z * x)).
K(x,y) * (x \ (z * x)) = T(K(x,y) * z,x).
(T(x,y) * (z * x)) \ ((T(x,y) * z) * x) = a(x,K(x,y) * z,x).
T(x,y) \ R(T(x,y),z,x) = a(x,z,x).
a(x,y,x) = T(x \ R(x,y,x),z).
T(x \ R(x,y,x),z) = a(x,y,x).
T(a(x,y,x),z) = a(x,y,x).
R(a(x,y,x),z,u) = a(R(x,z,u),y,x).
a(x,y,x) \ a(R(x,z,z),y,x) = a(a(x,y,x),z,z).
K(x,y) * T(z,x) = T(K(x,y) * z,x).
K(x,y) * R(T(z,x),u,w) = T(K(x,y) * R(z,u,w),x).
T(K(x,y) * z,x) / z = K(z,x) * K(x,y).
K(x,y) * K(z,x) = T(K(x,y) * z,x) / z.
T(K(x,y) * z,x) / z = K(x,y) * K(z,x).
L(K(x,y),z,K(u,x \ 1)) = K(x,y).
K(x,y) = L(K(x,y),z,K(u,x)).
L(K(x,y),z,K(u,x)) = K(x,y).
K(x,y) = L(K(x,y),z,K(x,u)).
L(K(x,y),z,K(x,u)) = K(x,y).
T(K(x,y),z) = (K(y,x) * z) \ z.
(K(x,y) * z) \ z = T(K(y,x),z).
T(K(x,y) * z,K(x,y)) = z * K(x,y).
x / T(K(y,z),x) = K(z,y) * x.
(K(x,y) * z) \ u = (T(K(y,x),z) / z) * u.
(T(K(x,y),z) / z) * u = (K(y,x) * z) \ u.
(K(x,y) * z) * K(y,x) = T(z,K(y,x)).
T(x,K(y,z)) / x = K(K(z,y) * x,K(y,z)).
K(K(x,y) * z,K(y,x)) = T(z,K(y,x)) / z.
K(K(x,y) * z,K(y,x)) = K(z,K(y,x)).
K(x,K(y,z)) = K(K(y,z) * x,K(y,z)).
K(K(x,y) * z,K(x,y)) = K(z,K(x,y)).
a(K(x,K(y,z)),u,w) = a(a(K(y,z),x,x),u,w).
a(a(K(x,y),z,z),u,w) = a(K(z,K(x,y)),u,w).
a(R(T(x,y),y,x),z,z) = a(T(x,y),z,z).
a(T(x,y),z,z) = a(R(x,y,y),z,z).
a(R(x,y,y),z,z) = a(T(x,y),z,z).
x * (K(y,z) * R(K(z,y),u,x)) = L(x,u,K(z,y)).
x * (K(y,z) * K(z,R(y,u,x))) = L(x,y * u,K(y,z)).
x * (L(x,y,z) \ (y * z)) = y * R(z,y,x).
(x * (y * z)) / (y * R(z,y,x)) = L(x,y,z).
T(K(x,y) * R(y,z,u),x) = y * T(y \ R(y,z,u),x).
T(K(x,y) * R(y,z,u),x) / R(y,z,u) = K(R(y,z,u) / y,x).
K(x,y) * K(x * y,x) = a(x,K(x,z) * y,x).
a(x,K(x,y) * z,x) = K(x,z) * K(x * z,x).
a(x,K(x,y) * z,x) = a(x,z,x).
a(x,K(x,y) * z,x) = a(T(x,y),z,x).
a(T(x,y),z,x) = a(x,z,x).
a((x \ y) \ y,z,x) = a(x,z,x).
a(x,y,x) = a((x \ z) * z,y,x).
a((x \ y) * y,z,x) = a(x,z,x).
a(x,y,x) = a((x * z) * z,y,x).
a((x * y) * y,z,x) = a(x,z,x).
a(x,y,x) = a(R(x,z,z),y,x).
a(R(x,y,y),z,x) = a(x,z,x).
a(x,y,x) \ a(x,y,x) = a(a(x,y,x),z,z).
a(a(x,y,x),z,z) = a(x,y,x) \ a(x,y,x).
a(a(x,y,x),z,z) = 1.
L(x,x,a(y,z,y)) = x.
L(x,x,a(y,z,z)) = x.
x = L(x,x,K(y,z)).
L(x,x,K(y,z)) = x.
x \ (a(y,z,z) * x) = R(T(a(y,z,z),x),x,x).
R(T(a(x,y,y),z),z,z) = z \ (a(x,y,y) * z).
a(K(x,y),z,z) = 1.
x / y = (K(z,u) * (y / x)) \ K(z,u).
(K(x,y) * (z / u)) \ K(x,y) = u / z.
L(x,K(y,z),x) = x.
K(x,y) * 1 = R(K(x,y),z,z).
R(K(x,y),z,z) = K(x,y) * 1.
a(1,x,y) = a(K(z,K(u,w)),x,y).
a(K(x,K(y,z)),u,w) = a(1,u,w).
T(K(x,y),z) / z = z \ K(x,y).
K(x,y) = K(x,R(y,z,z)).
K(x,R(y,z,z)) = K(x,y).
K(x,y * z) = K(x,y / (z \ 1)).
K(x,y / (z \ 1)) = K(x,y * z).
K(x,y) * (x / z) = T(x,y) / z.
a(K(x,K(y,z)),u,w) = 1.
L(x,y,K(z,K(u,w))) = x.
x * (x \ R(K(y,K(z,u)),w,x)) = K(y,K(z,u)).
(x \ K(y,z)) * u = (K(z,y) * x) \ u.
(K(x,y) * z) \ u = (z \ K(y,x)) * u.
K(x,R(((y \ 1) * z) \ 1,z,z)) = K(x,(z \ 1) * y).
K(x,y) * z = T(x,y) / (z \ x).
T(x,y) / (z \ x) = K(x,y) * z.
(K(x,y) * z) \ T(x,y) = z \ x.
L(x \ y,x,K(z,y)) = x \ y.
a(K(x,y),z,z \ y) = 1.
a(K(x,y * z),y,z) = 1.
((x / y) \ K(z,u)) * K(u,z) = y / x.
x * K(y,z) = x / K(z,y).
x / K(y,z) = x * K(z,y).
(K(x,y) * z) / K(x,y) = T(z,K(y,x)).
T(x,K(y,z)) \ x = K(x,K(z,y)).
K(x,K(y,z)) = K(K(z,y),x).
K(K(x,y),z) = K(z,K(y,x)).
K(x,K(y,z)) * K(x,K(z,y)) = 1.
K(x,y) * K(z,K(y,x)) = T(K(x,y),z).
K(x,y) * T(K(y,x),z) = K(z,K(x,y)).
T(K(x,y),z) = T(K(y,x),z) \ 1.
T(K(x,y),z) \ 1 = T(K(y,x),z).
T(K(x,y),z) * T(K(y,x),z) = 1.
T(K(x,y),z) * K(y,x) = K(z,K(y,x)).
R(T(a(x,y,y),z),z,z) = T(a(x,y,y),z).
R(T(a(x,y,y),z),z,z) = a(T(x,z),y,y).
R(a(T(x,y),z,z),y,y) = a(T(x,y),z,z).
a(T(x,y),z,z) = a(R(T(x,y),y,y),z,z).
a(R(T(x,y),y,y),z,z) = a(T(x,y),z,z).
a(T(x,y),z,z) = a(T(T(x,y),y),z,z).
a(T(T(x,y),y),z,z) = a(T(x,y),z,z).
a(T(x,y),z,z) = a(x,z,z).
(x * (y * (a(y,z,z) * u))) / (R(T(y,x),z,z) * u) = T(x,y).
K(x,K(y,z)) = R(K(x,K(y,z)),u,w).
R(K(x,K(y,z)),u,w) = K(x,K(y,z)).
K(x,K(y,z)) = K(x,R(K(y,z),u,w)).
K(x,R(K(y,z),u,w)) = K(x,K(y,z)).
K(x,K(y,R(z,u,w))) = K(x,K(y,z)).
K(K(R(x,y,z),u),w) = K(w,K(u,x)).
K(R(K(x,y),z,u),w) = K(w,K(y,x)).
K(x,R((y \ z) \ 1,z,z)) = K(x,(z \ 1) * y).
K(x,(y \ 1) * z) = K(x,(z \ y) \ 1).
K(x,(y \ z) \ 1) = K(x,(z \ 1) * y).
K(x,(y \ z) \ 1) = K(x,z \ y).
K(x,(y / z) \ y) = K(x,z / (a(y,z,z) \ 1)).
K(x,y) = K(x,y / (a(z,y,y) \ 1)).
K(x,y / (a(z,y,y) \ 1)) = K(x,y).
K(x,y * a(z,y,y)) = K(x,y).
(x \ 1) / (x \ K(x,y)) = K(y * a(z,y,y),x).
K(x * a(y,x,x),z) = (z \ 1) / (z \ K(z,x)).
K(x * a(y,x,x),z) = K(x,z).
x * K(y,z) = (x / y) * T(y,z).
(x / y) * T(y,z) = x * K(y,z).
x * T(y,z) = (x * y) * K(y,z).
(x * y) * K(y,z) = x * T(y,z).
K(x,y) = L(K(x,y),x,z).
L(K(x,y),x,z) = K(x,y).
K(T(x,y),z) = L(K(T(x,y),z),x,y).
L(K(T(x,y),z),x,y) = K(T(x,y),z).
K(T(x,y),z) = T(K(x,z),x * y).
T(K(x,y),x * z) = K(T(x,z),y).
T(K(x,y),z) = K(T(x,x \ z),y).
K(T(x,x \ y),z) = T(K(x,z),y).
T(K(x,y),z) = K(T(x,z),y).
K(x,T(y,z)) * T(K(y,x),z) = 1.
K(T(x,y * T(T(y,x),x)),z) = T(T(K(x,z),y),T(y,x)).
K(x,T(y,z)) = T(K(x,y),z).
T(K(x,y),z) = K(x,T(y,z)).
K(x,y) * K(y,T(x,z)) = K(K(y,x),z).
K(x,T(y,z \ 1)) * z = z * K(x,y).
K(x,y) * K(y,T(x,z)) = K(z,K(x,y)).
K(x,T(y,z)) * K(y,x) = K(z,K(y,x)).
K(x,T(y,z)) = K(T(x,z),y).
K(T(x,y),z) = K(x,T(z,y)).
K(x,T(y,z)) * K(y,x) = K(K(x,y),z).
K(x,T(y,z)) * K(y,x) = K(x,K(y,z)).
K(x,y) * K(x,K(y,z)) = K(x,T(y,z)).
K(x,K(y,z)) = K(z,K(y,x)).
K(x,K(y,z)) = K(K(x,y),z).
K(K(x,y),z) = K(x,K(y,z)).
1 / K(x,K(y,z)) = K(K(y,x),z).
K(K(x,y),z) = K(K(x,z),y).
K(K(x,y),z) = K(y,K(z,x)).
K(x,K(y,z)) = K(z,K(x,y)).
T(K(x,y) * K(x,K(y,z)),z) = K(x,y).
T(K(x,T(y,z)),z) = K(x,y).
x * K(y,z) = K(y,T(z,x)) * x.
K(x,T(y,z)) * z = z * K(x,y).
K(x,y) = K(x,T(T(y,z),z)).
K(x,T(T(y,z),z)) = K(x,y).
K(x,T(y,z)) = K(x,T(y,z \ 1)).
K(x,T(y,z \ 1)) = K(x,T(y,z)).
T(K(x,y) * z,K(x,y)) = K(x,T(y,z)) * z.
K(x,T(y,z \ (z \ (u \ 1)))) = K(x,T(y,u * (z * z))).
K(T(x,y * T(y,x)),z) = T(T(K(x,z),y),T(y,x)).
T(T(K(x,y),z),T(z,x)) = K(T(x,z * T(z,x)),y).
T(T(K(x,y),z),T(z,x)) = K(T(x,z * z),y).
T(T(K(x,y),z),T(z,x)) = K(x,T(y,z * z)).
T(K(x,T(y,z)),T(z,x)) = K(x,T(y,z * z)).
K(x,T(y,z * z)) = K(T(x,T(z,x)),T(y,z)).
K(T(x,T(y,x)),T(z,y)) = K(x,T(z,y * y)).
K(T(x,y),T(z,y)) = K(x,T(z,y * y)).
K(x,T(y,z * z)) = K(x,T(T(y,z),z)).
K(x,T(T(y,z),z)) = K(x,T(y,z * z)).
K(x,T(y,z * z)) = K(x,y).
K(x,T(y,z * (z * u))) = K(x,T(y,u)).
K(x,T(y,z * u)) = K(x,T(y,z \ u)).
K(x,T(y,z \ u)) = K(x,T(y,z * u)).
K(x,T(y,(z \ u) * u)) = K(x,T(y,T(z,z * u))).
K(x,T(y,T(z,z * u))) = K(x,T(y,(z \ u) * u)).
K(x,T(y,(z / u) * (z * z))) = K(x,T(y,u / (z \ 1))).
K(x,T(y,z \ (z \ u))) = K(x,T(y,u)).
K(x,T(y,z * (u * u))) = K(x,T(y,z \ 1)).
K(x,T(y,z * (u * u))) = K(x,T(y,z)).
K(x,T(y,z / (u \ 1))) = K(x,T(y,u / z)).
(x * (R(y,z,z) * u)) / (R(T(y,x),z,z) * u) = T(x,y).
T(x,y) = T(x,R(y,z,z)).
T(x,R(y,z,z)) = T(x,y).
T(x,y * z) = T(x,y / (z \ 1)).
T(x,y / (z \ 1)) = T(x,y * z).
K(x,T(y,z * u)) = K(x,T(y,u / z)).
K(x,T(y,z / u)) = K(x,T(y,u * z)).
K(x,T(y,z)) = K(x,T(y,(z \ u) * u)).
K(x,T(y,(z \ u) * u)) = K(x,T(y,z)).
K(x,T(y,T(z,z * u))) = K(x,T(y,z)).
K(x,T(y,T(z,u))) = K(x,T(y,z)).
K(x,T(y,z)) * K(y,x) = K(x,K(y,T(z,u))).
K(x,K(y,T(z,u))) = K(x,T(y,z)) * K(y,x).
K(x,K(y,T(z,u))) = K(x,K(y,z)).
K(x,K(y,a(z,u,w))) = K(x,K(y,z \ R(z,u,w))).
K(x,K(y,z \ R(z,u,w))) = K(x,K(y,a(z,u,w))).
K(x,K(y \ R(y,z,u),w)) = K(x,K(w,a(y,z,u))).
K(R(x,y,z) / x,u) = K(u,x) * K(R(x,y,z),u).
K(x,y) * K(R(y,z,u),x) = K(R(y,z,u) / y,x).
K(x,y) * K(R(y,z,u),x) = K(y \ R(y,z,u),x).
K(x,y) * K(R(y,z,u),x) = K(x,y \ R(y,z,u)).
K(x,K(y,z)) * K(x,K(z,y)) = K(x,K(y,z) \ R(K(y,z),u,w)).
K(x,K(y,z) \ R(K(y,z),u,w)) = K(x,K(y,z)) * K(x,K(z,y)).
K(x,K(y,z) \ R(K(y,z),u,w)) = 1.
K(x,K(y,z) \ K(R(y,u,w),z)) = 1.
K(x,K(y,z) * K(R(z,u,w),y)) = 1.
K(x,K(y \ R(y,z,u),w)) = 1.
1 = K(x,K(y,a(z,u,w))).
K(x,K(y,a(z,u,w))) = 1.
T(x,K(y,a(z,u,w))) = x.
K(x,a(y,z,u)) = K(x,T(a(y,z,u),w)).
K(x,T(a(y,z,u),w)) = K(x,a(y,z,u)).
K(x,y \ R(y,z,u)) = K(x,a(y,z,u)).
K(a(x,y,z),u) = K(u,x \ R(x,y,z)).
K(x,y \ R(y,z,u)) = K(a(y,z,u),x).
K(x \ R(x,y,z),u) = K(u,a(x,y,z)).
K(x,y \ R(y,z,u)) = K(x,a(y,z,L(u,z,y))).
K(x,a(y,z,L(u,z,y))) = K(x,y \ R(y,z,u)).
K(x,y) * K(R(y,z,u),x) = K(x,a(y,z,u)).
K(x,a(K(y,z),u,w)) = 1.
T(x,a(K(y,z),u,w)) = x.
((K(x,y) * z) * u) / (K(x,y) * (z * u)) = a(K(x,y),z,u).
K(R(x,y,z) \ x,u) = K(u,a(x,x * y,z)).
K(x,a(y,z,u)) = K(y,x) * K(x,R(y,z,u)).
K(x,y) * K(y,R(x,z,u)) = K(y,a(x,z,u)).
x * K(y,a(z,u,x)) = L(x,z * u,K(z,y)).
L(x,y * z,K(y,u)) = x * K(u,a(y,z,x)).
K(x,a(y,z,L(u,z,y))) = K(x,a(y,z,u)).
a(K(x,y),z,u) = K(x,y) \ R(K(x,y),z,u).
K(x,y) \ R(K(x,y),z,u) = a(K(x,y),z,u).
a(K(x,y),z,u) = u \ L(u,z,K(x,y)).
x \ L(x,y,K(z,u)) = a(K(z,u),y,x).
x * a(K(y,z),u,x) = L(x,u,K(y,z)).
a(K(x,y),x * z,u) = K(y,a(x,z,u)).
x * a(K(y,z),u,x) = L(x,u,K(z,y)).
K(x,a(y,y * z,u)) = a(K(y,x),z,u).
K((x * y) * z,a(x,y,z)) = 1.
K(x * (y * z),a(x,y,L(z,y,x))) = 1.
K(x,a(y,y * z,u)) = a(K(x,y),z,u).
1 = K(x * (y * z),a(x,y,z)).
K(x * (y * z),a(x,y,z)) = 1.
a(x,y,z) * 1 = x \ R(x,y,z).
x \ R(x,y,z) = a(x,y,z) * 1.
a(x,y,z) = x \ R(x,y,z).
x \ R(x,y,z) = a(x,y,z).
a(x,y,z) = L(z,y,x) \ z.
L(x,y,z) \ x = a(z,y,x).
a(x,y,z) \ 1 = R(x,y,z) \ x.
R(x,y,z) \ x = a(x,y,z) \ 1.
x * (a(x,y,z) * u) = R(x,y,z) * u.
a(x,y,z) * (x * u) = R(x,y,z) * u.
a(x,x * y,z) = R(x,y,z) \ x.
R(x,y,z) \ x = a(x,x * y,z).
x * R(x \ 1,y,z) = a(x,y,z).
a(T(x,y),z,u) = T(x \ R(x,z,u),y).
T(x \ R(x,y,z),u) = a(T(x,u),y,z).
a(R(x,y,z),u,w) = R(x \ R(x,u,w),y,z).
R(x \ R(x,y,z),u,w) = a(R(x,u,w),y,z).
a(L(x,y,z),u,w) = L(x \ R(x,u,w),y,z).
L(x \ R(x,y,z),u,w) = a(L(x,u,w),y,z).
a(x,y,z) * u = z * (L(z,y,x) \ u).
x * (L(x,y,z) \ u) = a(z,y,x) * u.
L(x,y,z) \ (x * u) = a(z,y,x) * u.
a(x,y,z) * (L(z,y,x) * u) = z * u.
L(x,y,z) \ x = a(T(z,x),y,x).
K(a(x,y,z) \ 1,u) = K(u,a(x,x * y,z)).
a(x,x * y,z) = a(x,y,z) \ 1.
L(x,a(y,z,u),z) = x.
(x * a(y,x,z)) * u = x * (a(y,x,z) * u).
a(x,y,z) \ y = (y \ a(x,y,z)) \ 1.
(x \ a(y,x,z)) \ 1 = a(y,x,z) \ x.
a(x,y,z) \ (y * u) = (y \ a(x,y,z)) \ u.
(x \ a(y,x,z)) \ u = a(y,x,z) \ (x * u).
a(T(x,y),z,y) = a(x,z,y).
K(a(x,x * y,z),u) = a(K(u,x),y,z).
x * (y * a(x,z,y)) = R(x,z,y) * y.
T(a(x,y,z),u) = a(T(x,u),y,z).
a(T(x,y),z,u) \ a(x,z,u) = K(y,a(x,z,u)).
a(T(x,y),y,z) = a(x,y,z).
a(x,y,z) = a(x,T(y,x),z).
a(x,T(y,x),z) = a(x,y,z).
a(x * y,x,z) = a(y / x,x,z).
a(x / y,y,z) = a(y * x,y,z).
a(x * y,x,z) = a(x / y,x,z).
a(x / y,x,z) = a(x * y,x,z).
x * (a(y,z,x) * u) = a(y,z,x) * (x * u).
a(x,y,z) * (z * u) = z * (a(x,y,z) * u).
a(x,y,z) * (z * x) = z * R(x,y,z).
(a(x,y,z) \ y) * u = (y \ a(x,y,z)) \ u.
(x \ a(y,x,z)) \ u = (a(y,x,z) \ x) * u.
K(a(x,y,z) \ 1,u) = a(K(u,x),y,z).
(x * y) * L(a(x,z,y),y,x) = R(x,z,y) * y.
a(R(x,y,z),u,y) = L(y,u,x) \ y.
R(a(x,y,z),u,w) = a(R(x,u,w),y,z).
a(R(x,y,z),u,y) = a(x,u,y).
a(x,y,z) = a(L(x,z,x),y,z).
a(L(x,y,x),z,y) = a(x,z,y).
R(a(x,y,z),x * u,w) = a(R(x,u,w),y,z).
L(a(x,y,z),u,w) = a(L(x,u,w),y,z).
K(a(x * y,x,z) \ 1,u) = K(u,a(y / x,(y / x) * x,z)).
K(x,a(y / z,(y / z) * z,u)) = K(a(z * y,z,u) \ 1,x).
(a(x,y,z) * y) * u = y * (a(x,y,z) * u).
(a(x,y,z) \ y) * u = a(x,y,z) \ (y * u).
a(x,y,z) \ (y * u) = (a(x,y,z) \ y) * u.
x = L(x,y,a(z,y,u)).
L(x,y,a(z,y,u)) = x.
(a(x,y,z) * y) * u = a(x,y,z) * (y * u).
(a(x,y,z) * (y \ 1)) * u = a(x,y,z) * (y \ u).
a(x,y,z) * (y * u) = y * (a(x,y,z) * u).
(x * y) \ (x * (a(z,x,u) * y)) = T(a(z,x,u),x * y).
(x * y) * a(L(x,y,x),z,y) = R(x,z,y) * y.
(x * y) * a(x,z,y) = R(x,z,y) * y.
(x * (R(y,z,u) * u)) / ((y * u) * R(a(y,z,u),y * u,x)) = L(x,y * u,a(y,z,u)).
(x \ a(y,x,z)) * u = a(y,x,z) * (x \ u).
(a(x,y,z) * (y \ u)) \ ((y \ a(x,y,z)) * (u * w)) = L(w,u,y \ a(x,y,z)).
T(a(x,y,z),y * u) = L(T(a(x,y,z),u),u,y).
L(T(a(x,y,z),u),u,y) = T(a(x,y,z),y * u).
L(a(T(x,y),z,u),y,z) = T(a(x,z,u),z * y).
K(x,a(y / z,y,u)) = K(a(z * y,z,u) \ 1,x).
K(a(x * y,x,z) \ 1,u) = K(u,a(y / x,y,z)).
K(a(x * y,x,z) \ 1,u) = K(u,a(y * x,y,z)).
K(x,a(y * z,y,u)) = a(K(x,z * y),z,u).
(x * (y * z)) \ ((x * y) * z) = a(L(x,u,y),R(y,u,x),z).
a(L(x,y,z),R(z,y,x),u) = (x * (z * u)) \ ((x * z) * u).
a(L(x,y,z),R(z,y,x),u) = a(x,z,u).
L(a(x,R(y,z,x),u),z,y) = a(x,y,u).
(a(x,y,z) * (y \ u)) \ (a(x,y,z) * (y \ (u * w))) = L(w,u,y \ a(x,y,z)).
L(x,y,z \ a(u,z,w)) = L(L(x,y,z),z * y,a(u,z,w)).
L(L(x,y,z),z * y,a(u,z,w)) = L(x,y,z \ a(u,z,w)).
L(L(x,y,z),z * y,a(u,z,w)) = L(x,y,z * a(u,z,w)).
(R(x,y,z) * y) \ ((x * y) * u) = (x \ R(x,y,z)) \ u.
(x \ R(x,y,z)) \ z = L(z,y,R(x,y,z)).
L(x,y,R(z,y,x)) = (z \ R(z,y,x)) \ x.
L(x,y,R(z,y,x)) = L(x,y,z).
L(x,y * z,R(y,z,x) \ 1) = L(x,y * z,y \ 1).
L(x,y * z,y \ 1) = L(x,y * z,R(y,z,x)).
L(x,y * z,R(y,z,x)) = L(x,y * z,y \ 1).
L(x,y * z,R(y,z,x)) = L(x,y * z,y).
R(x,y,z) * (L(z,x * y,x) \ z) = R(R(x,y,z),x * y,z).
R(x,y,z) * (R(x,y,z) \ x) = R(R(x,y,z),x * y,z).
R(R(x,y,z),x * y,z) = x.
x = R(R(x,x * y,z),y,z).
R(R(x,x * y,z),y,z) = x.
K(x,R(y,y * z,u)) * K(y,x) = K(x,R(y,y * z,u) \ R(R(y,y * z,u),z,u)).
K(x,R(y,y * z,u) \ R(R(y,y * z,u),z,u)) = K(x,R(y,y * z,u)) * K(y,x).
K(x,R(y,y * z,u) \ R(R(y,y * z,u),z,u)) = R(K(x,y),z,u) * K(y,x).
K(x,R(y,y * z,u) \ R(R(y,y * z,u),z,u)) = K(y,x) * R(K(x,y),z,u).
K(x,R(y,y * z,u) \ y) = K(y,x) * R(K(x,y),z,u).
K(x,y \ R(y,z,u)) = K(y,x) * R(K(x,y),z,u).
K(x,y) * R(K(y,x),z,u) = K(y,x \ R(x,z,u)).
x * K(y,z \ R(z,u,x)) = L(x,u,K(y,z)).
x * K(a(y,z,x),u) = L(x,z,K(u,y)).
K(a(x,y,z),u) = a(K(x,u),y,z).
K(a(x,y,z),u) = a(K(u,x),y,z).
a(K(x,y),z,u) = K(y,a(x,z,u)).
K(x,a(y,z,u)) = a(K(y,x),z,u).
a(K(x,y),z,u) = K(x,a(y,z,u)).
K(x,a(y,z,u)) = a(K(x,y),z,u).
x * K(y,a(z,u,x)) = L(x,u,K(z,y)).
K(x,a(y * z,y,u)) = K(z * y,a(x,z,u)).
K(x * y,a(z,x,u)) = K(z,a(y * x,y,u)).
K(x,a(y,z,u)) = K(y,a(x,z,u)).
L(x,y * z,K(y,u)) = L(x,z,K(y,u)).
(x * (R(y,z,u) * u)) / ((y * u) * a(R(y,u,x),z,u)) = L(x,y * u,a(y,z,u)).
(x * (R(y,z,u) * u)) / ((y * u) * a(y,z,u)) = L(x,y * u,a(y,z,u)).
(x * (R(y,z,u) * u)) / (R(y,z,u) * u) = L(x,y * u,a(y,z,u)).
L(x,y * z,a(y,u,z)) = x.
x = L(x,y * z,a(T(z,y),u,y)).
L(x,y * z,a(T(z,y),u,y)) = x.
L(x,y * z,a(z,u,y)) = x.
(a(x,y,z) * (z * x)) \ (a(x,y,z) * (z * (x * u))) = L(u,x,z).
(x * R(y,z,x)) \ (a(y,z,x) * (x * (y * u))) = L(u,y,x).
(x * R(y,z,x)) \ (x * (a(y,z,x) * (y * u))) = L(u,y,x).
(x * R(y,z,x)) \ (x * (R(y,z,x) * u)) = L(u,y,x).
L(x,y,z) = L(x,R(y,u,z),z).
L(x,R(y,z,u),u) = L(x,y,u).
L(x,y,z) \ x = a(z,R(y,u,z),x).
a(x,R(y,z,x),u) = L(u,y,x) \ u.
a(x,R(y,z,x),u) = a(x,y,u).
L(a(x,y,z),u,y) = a(x,y,z).
a(T(x,y),z,u) = T(a(x,z,u),z * y).
T(a(x,y,z),y * u) = a(T(x,u),y,z).
a(T(x,y),z,u) \ a(x,z,u) = K(z * y,a(x,z,u)).
K(x * y,a(z,x,u)) = K(y,a(z,x,u)).
K(x,a(y,z,u)) = K(y,a(z * x,z,u)).
K(x,a(y * z,y,u)) = K(z,a(x,y,u)).
K(x,a(y,z,u)) = K(y,a(x * z,x,u)).
K(x,a(y * z,y,u)) = K(y,a(x,z,u)).
K(x,a(y,z,u)) = K(z,a(y,x,u)).
x * K(y,a(z,u,x)) = L(x,y,K(z,u)).
L(x,y,K(z,u)) = L(x,u,K(z,y)).
L(x,y,K(z,z * u)) = L(x,u,K(z,y)).
L(x,y,K(z,u)) = L(x,u,a(z,y,y)).
L(x,y,a(z,u,u)) = L(x,u,K(z,y)).
L(x,y,a(z,u,u)) = L(x,y,K(z,u)).
L(x,y,K(z,u)) = L(x,y,a(u,z,u)).
L(x,y,a(z,u,z)) = L(x,y,K(u,z)).
L(L(x,y,z),z * y,K(z,u)) = L(x,y,z * a(u,z,u)).
L(x,y,z * a(u,z,u)) = L(x,y,T(z,u)).
L(x,y,T(z,u)) = L(x,y,R(z,u,u)).
L(x,y,R(z,u,u)) = L(x,y,T(z,u)).
L(x,y,T(z / u,z)) = L(x,y,u * z).
L(x,y,z * u) = L(x,y,u * z).
L(L(x,y,z * u),(z * u) * y,u * z) = x.
x = L(x,y,K(z,u)).
L(x,y,K(z,u)) = x.
$F.
K(a(x,y,z),u) = 1.
K(a(c13,c14,c15),c16) != 1.
a(x,K(y,z),u) = 1.
a(c5,K(c6,c7),c8) != 1.
K(x,y) / z = K(x,y) * (z \ 1).
K(x,y) * (z \ 1) = K(x,y) / z.
K(x,y) * z = K(x,y) / (z \ 1).
K(x,y) / (z \ 1) = K(x,y) * z.
(K(x,y) * z) \ K(x,y) = z \ 1.
x \ K(y,z) = (K(y,z) \ x) \ 1.
(K(x,y) \ z) \ 1 = z \ K(x,y).
(x \ K(y,z)) * u = (K(y,z) \ x) \ u.
(K(x,y) \ z) \ u = (z \ K(x,y)) * u.
x \ (K(y,z) * u) = (K(y,z) \ x) \ u.
(K(x,y) \ z) \ u = z \ (K(x,y) * u).
x \ (K(y,z) * u) = (x \ K(y,z)) * u.
x = L(x,K(y,z),u).
L(x,K(y,z),u) = x.
a(x,y,K(z,u)) = 1.
a(c9,c10,K(c11,c12)) != 1.
L(x,y / z,z \ y) = x.
(x \ y) / T(x,y) = x \ (x \ y).
(x \ (y * y)) \ 1 = y \ (y \ x).
(x \ (x \ y)) * z = (y \ (x * x)) \ z.
(x \ (y * y)) \ z = (y \ (y \ x)) * z.
L(x,y,y * x) \ z = ((y * x) \ ((y * x) \ ((y * x) * y))) * z.
((x * y) \ ((x * y) \ ((x * y) * x))) * z = L(y,x,x * y) \ z.
L(x * a(y,x,x),x,y) = x.
L(x,x * y,x) * (x \ y) = (x \ y) * T(x,y).
x * (T(x,y) * z) = T(x,y) * (x * z).
T(x,y) * (x * z) = x * (T(x,y) * z).
((x * y) \ x) * z = L(y,x,x * y) \ z.
L(x,y,y * x) \ z = ((y * x) \ y) * z.
(x * T(y * x,x)) / (x * x) = T((x \ y) * x,x \ 1).
((x * y) * y) / (y * y) = T((y \ x) * y,y \ 1).
T((x \ y) * x,x \ 1) = ((y * x) * x) / (x * x).
T((x \ y) * x,x \ 1) = R(y,x,x).
L(x,y / z,z * y) = x.
(x \ y) * L(L(z,y,x),u,w) = x \ (y * L(z,u,w)).
L(x,y * z,z / y) = x.
(x * y) / (y / x) = (x * y) * ((y / x) \ 1).
(x * y) * ((y / x) \ 1) = (x * y) / (y / x).
(x * y) * (x / y) = (x * y) / (y / x).
(x * y) / (y / x) = (x * y) * (x / y).
K(x * y,x) = ((x \ y) * x) / y.
((x \ y) * x) / y = K(x * y,x).
L(x,K(y,T(z,y)),u) = L(x,T(z,y) * z,u).
T(x * K(y,x),x * y) = L(x,y,x).
R(T(x,y),z,u) * K(y,R(x,z,u)) = R(x,z,u).
L(x,T(y * z,y),u) = L(x,z / y,u).
R(x,y,x) * (x \ y) = (x \ y) * T(x,y).
L(L(x,y * z,z),y,z) = x.
L(L(x,y,z * y),z,z * y) = x.
L(x,y,y * x) = x * a(y * x,x,x).
K(x * y,x) * K(x,y) = a(x,y,x).
(((x \ y) * x) / y) * K(x,y) = a(x,y,x).
a(x,y,x) * L(x,y,x) = x.
(x * y) / L(L(y,z,y),a(y,z,y),x) = x * a(y,z,y).
a(x,(y * z) * u,w) = a(x,(y \ z) * u,w).
a(x,(y \ z) * u,w) = a(x,(y * z) * u,w).
a(x,(y \ z) * z,u) = a(x,T(y,y * z),u).
a(x,T(y,y * z),u) = a(x,(y \ z) * z,u).
a(x,T(y * z,y),u) = a(x,z / y,u).
a(x,T(y,y * z),u) = a(x,(y * z) * z,u).
T(x,x * y) = T(x,T(x,z) * y).
T(x,T(x,y) * z) = T(x,x * z).
x * a(y,z,y) = a(y,z,y) * x.
a(x,y,x) * z = z * a(x,y,x).
(a(x,y,x) * z) * L(u,z,a(x,y,x)) = (z * u) * a(x,y,x).
x \ T(y,z) = (K(z,y) * x) \ y.
(K(x,y) * z) \ y = z \ T(y,x).
(x \ K(y,z)) * y = x \ T(y,z).
(x \ T(y,z)) \ ((x \ K(y,z)) * (y * u)) = L(u,y,x \ K(y,z)).
(x * K(y,z)) \ x = K(z,y).
K(x,y) = (z * x) \ (z * T(x,y)).
(x * y) \ (x * T(y,z)) = K(y,z).
(x * (y * z)) \ (x * (y * T(z,u))) = L(K(z,u),y * z,x).
(x * T(y,z)) \ (x * y) = K(z,y).
(x * (y * z)) \ ((x * y) * T(L(z,y,x),u)) = K(L(z,y,x),u).
(x * (y * z)) \ ((x * y) * L(T(z,u),y,x)) = K(L(z,y,x),u).
(x * (y * z)) \ (x * (y * T(z,u))) = K(L(z,y,x),u).
K(L(x,y,z),u) = L(K(x,u),y * x,z).
L(K(x,y),z * x,u) = K(L(x,z,u),y).
L(K(x,y),z,u) = K(L(x,z / x,u),y).
K(L(x,y / x,z),u) = L(K(x,u),y,z).
L(x,y,z \ K(y,u)) = (z * T(y,u)) \ ((z * K(y,u)) * (y * x)).
(x * T(y,z)) \ ((x * K(y,z)) * (y * u)) = L(u,y,x \ K(y,z)).
R(x,x * y,z) \ x = a(x,y,z).
a(T(x,y),z,u) = y \ (R(x,z,u) * (x \ y)).
x \ (R(y,z,u) * (y \ x)) = a(T(y,x),z,u).
x \ L(x,y * z,y) = a(y,z,x).
a(x,x * y,z) = z \ L(z,y,x).
a(x,y,z) \ 1 = z \ L(z,y,x).
a(x,y,z) = a(x,x * y,z) \ 1.
a(x,x * y,z) \ 1 = a(x,y,z).
L(a(x,y,z),z,u) = (u * z) \ (u * L(z,x * y,x)).
(x * y) \ (x * L(y,z * u,z)) = L(a(z,u,y),y,x).
(x * L(y,z,u)) / L(a(u,u * z,y),y,x) = x * y.
a(x,y,L(z,u,u * z)) \ 1 = ((u * z) \ u) * L(L(z,u,u * z),y,x).
((x * y) \ x) * L(L(y,x,x * y),z,u) = a(u,z,L(y,x,x * y)) \ 1.
a(x,x * y,z) \ u = a(x,y,z) * u.
x * T(y,L(x,z,u)) = a(u,z,x) * (y * L(x,z,u)).
a(x,y,z) * (u * L(z,y,x)) = z * T(u,L(z,y,x)).
x \ ((y \ x) * T(y,x)) = a(T(y,x),x,y).
x \ ((y \ x) * T(y,x)) = a(y,x,y).
(K(x,y) * z) * u = K(x,y) * (z * u).
x \ y = (K(z,u) * x) \ (K(z,u) * y).
(K(x,y) * z) \ (K(x,y) * u) = z \ u.
(K(x,y) * z) / u = K(x,y) * (z / u).
L(x,y,z) = L(x,y,T(z,u)).
L(x,y,T(z,u)) = L(x,y,z).
L(x,y,a(z,u,z)) = x.
T(a(x,y,z),u) = a(x,y,z).
(a(x,y,x) * z) * u = (z * u) * a(x,y,x).
L(x,y,z * (u * z)) = L(x,y,u).
x / a(y,z,u) = a(y,z,u) \ x.
a(x,y,z) = a(T(x,u),y,z).
a(T(x,y),z,u) = a(x,z,u).
a(x * (y * x),z,u) = a(y,z,u).
(x * (K(y,z) * (u * w))) \ ((x * (K(y,z) * u)) * w) = a(x,K(y,z) * u,w).
(K(x,y) * (z * (u * w))) \ (((K(x,y) * z) * u) * w) = a(K(x,y) * z,u,w).
(K(x,y) * (z * u)) \ ((K(x,y) * z) * (u * w)) = L(w,u,K(x,y) * z).
((K(x,y) * (z * u)) * w) / (u * w) = R(K(x,y) * z,u,w).
(x * K(y,z)) * u = x * (K(y,z) * u).
(x * (K(y,z) * u)) / u = x * K(y,z).
x = L(x,T(y,z) * y,u).
L(x,T(y,z) * y,u) = x.
L(x,(y \ z) * (z / y),u) = x.
x = L(x,(y * z) * (z / y),u).
L(x,(y * z) * (z / y),u) = x.
L(x,T(L(y / z,z * y,y / z) * (z * y),y / z),u) = x.
(x * T(y,z)) \ (x * (K(y,z) * (y * u))) = L(u,y,x \ K(y,z)).
(x * y) / T(y,z) = x * K(z,y).
x / T(y,z) = (x / y) * K(z,y).
(x / y) * K(z,y) = x / T(y,z).
(x * (y * z)) / T(L(z,y,x),u) = (x * y) * K(u,L(z,y,x)).
((x \ y) * x) / T(y,x) = a(x,y,x).
a(x,y,x) * T(y,x) = (x \ y) * x.
(K(x,y) * ((z * u) * w)) / (u * w) = R(K(x,y) * z,u,w).
R(K(x,y) * z,u,w) = K(x,y) * (((z * u) * w) / (u * w)).
K(x,y) * (((z * u) * w) / (u * w)) = R(K(x,y) * z,u,w).
K(x,y) * R(z,u,w) = R(K(x,y) * z,u,w).
R(x * K(y,z),u,w) = R(x,u,w) * K(y,z).
R(x,y,z) * K(u,w) = R(x * K(u,w),y,z).
R(T(x,y),z,u) * K(y,x) = R(x,z,u).
K(x,y) = K(x,R(y,z,u)).
K(x,R(y,z,u)) = K(x,y).
x * K(x,y) = T(x,R(y,z,u)).
T(x,R(y,z,u)) = x * K(x,y).
T(x,R(y,z,u)) = T(x,y).
L(x,T((y / z) * (z * y),y / z),u) = x.
x = L(x,(y * z) / (z / y),u).
L(x,(y * z) / (z / y),u) = x.
L(x,(y * z) * (y / z),u) = x.
(x * (y * z)) / L(T(z,u),y,x) = (x * y) * K(u,L(z,y,x)).
(x * T(y,z)) \ (x * (T(y,z) * u)) = L(u,y,x \ K(y,z)).
L(x,y,z \ K(y,u)) = L(x,T(y,u),z).
L(x,T(y,z),u) = L(x,y,u * K(y,z)).
L(x,y,z * K(y,u)) = L(x,T(y,u),z).
(K(x,y) * (z * u)) \ (K(x,y) * (z * (u * w))) = L(w,u,K(x,y) * z).
L(x,y,K(z,u) * w) = (w * y) \ (w * (y * x)).
L(x,y,K(z,u) * w) = L(x,y,w).
((x * K(y,z)) * u) \ ((x * K(y,z)) * (u * w)) = L(w,u,x).
L(x,y,z * K(u,w)) = L(x,y,z).
L(x,y,z) = L(x,T(y,u),z).
L(x,T(y,z),u) = L(x,y,u).
L(x,y,z) = L(x,(y * u) * u,z).
L(x,(y * z) * z,u) = L(x,y,u).
L(x,y * z,u) = L(x,z / y,u).
L(x,y / z,u) = L(x,z * y,u).
L(x,y * z,u) = L(x,y / z,u).
L(x,y / z,u) = L(x,y * z,u).
(x * y) / L(z,z * y,x) = x * (y / z).
L(x,y * z,u) = L(x,z * y,u).
L(x,(y / z) * (y * z),u) = x.
L(x,(y \ (y \ z)) * ((y \ z) * T(y,z)),u) = x.
(x * (y * z)) / L(T(z,u),T(z,u) * (y * z),x) = x * (y * K(u,z)).
x = L(x,(y * (y \ z)) * ((y \ z) * T(y,z)),u).
L(x,(y * (y \ z)) * ((y \ z) * T(y,z)),u) = x.
L(x,y * ((z \ y) * T(z,y)),u) = x.
L(x,y \ ((z \ y) * T(z,y)),u) = x.
L(x,a(y,z,y),u) = x.
(x * a(y,z,y)) * u = x * (a(y,z,y) * u).
(x * y) / L(y,z,y) = x * a(y,z,y).
(x * (y * (a(z,u,z) * w))) \ (((x * y) * a(z,u,z)) * w) = a(x,y,a(z,u,z) * w).
(a(x,y,x) * z) * u = z * (a(x,y,x) * u).
x * (a(y,z,y) * u) = (x * u) * a(y,z,y).
(x * y) * a(z,u,z) = x * (a(z,u,z) * y).
(x * (K(y,z) * u)) \ ((x * K(y,z)) * (u * w)) = L(w,u,x).
(x * (K(y,z) * u)) \ (x * (K(y,z) * (u * w))) = L(w,u,x).
L(x,y,z) = L(L(x,y,K(u,w)),K(u,w) * y,z).
L(L(x,y,K(z,u)),K(z,u) * y,w) = L(x,y,w).
L(x,K(y,z) * u,w) = L(x,u,w).
L(x,y * z,u) = L(x,T(y,w) * z,u).
L(x,T(y,z) * u,w) = L(x,y * u,w).
L(x,T(y,z) * u,w) = L(x,u * y,w).
(x * (y * z)) / L(T(z,u),(y * z) * z,x) = x * (y * K(u,z)).
(x * (y * z)) / L(T(z,u),y,x) = x * (y * K(u,z)).
x * (y * K(z,u)) = (x * y) * K(z,L(u,y,x)).
(x * y) * K(z,L(u,y,x)) = x * (y * K(z,u)).
(K(x,y) * (z * (u * w))) \ ((K(x,y) * (z * u)) * w) = a(K(x,y) * z,u,w).
(K(x,y) * (z * (u * w))) \ (K(x,y) * ((z * u) * w)) = a(K(x,y) * z,u,w).
a(K(x,y) * z,u,w) = (z * (u * w)) \ ((z * u) * w).
((x * K(y,z)) * (u * w)) \ (((x * K(y,z)) * u) * w) = a(x,u,w).
(x * (K(y,z) * (u * w))) \ (((x * K(y,z)) * u) * w) = a(x,u,w).
(x * (K(y,z) * (u * w))) \ ((x * (K(y,z) * u)) * w) = a(x,u,w).
a(x,y,z) = a(x,K(u,w) * y,z).
a(x,K(y,z) * u,w) = a(x,u,w).
a(x,y * z,u) = a(x,z * y,u).
a(x,y,z) = a(x,T(y,u),z).
a(x,T(y,z),u) = a(x,y,u).
a(x,y * T(z,u),w) = a(x,y * z,w).
a(x,y * K(z,u),w) = a(x,y,w).
a(x,y * z,u) = a(x,z / y,u).
a(x,y / z,u) = a(x,z * y,u).
a(x,y,z) = a(x,(y * u) * u,z).
a(x,(y * z) * z,u) = a(x,y,u).
a(x,y * (z * K(u,w)),v5) = a(x,y * z,v5).
a(x,y * a(z,u,z),w) = a(x,L(z,u,z) * (y * z),w).
a(x,L(y,z,y) * (u * y),w) = a(x,u * a(y,z,y),w).
a(x,y * L(z,u,z),w) = a(x,y * (z * K(u,z)),w).
a(x,y * (z * K(u,z)),w) = a(x,y * L(z,u,z),w).
a(x,y * L(z,u,z),w) = a(x,y * z,w).
a(x,y * z,u) = a(x,L(z,w,z) * y,u).
a(x,L(y,z,y) * u,w) = a(x,u * y,w).
a(x,y * a(z,u,z),w) = a(x,(y * z) * z,w).
a(x,y * a(z,u,z),w) = a(x,y,w).
a(x,a(y,z,y) * u,w) = a(x,u,w).
(x * ((a(y,z,y) * u) * w)) \ ((x * (a(y,z,y) * u)) * w) = a(x,u,w).
(x * (y * (a(z,u,z) * w))) \ ((x * (a(z,u,z) * y)) * w) = a(x,y,w).
(x * (y * (a(z,u,z) * w))) \ ((x * (a(z,u,z) * y)) * w) = a(x,y,a(z,u,z) * w).
a(x,y,a(z,u,z) * w) = a(x,y,w).
a(x,y,z) = a(x,y,L(z,u,z)).
a(x,y,L(z,u,z)) = a(x,y,z).
a(x,y,(z \ u) * z) = a(x,y,T(u,z)).
a(x,y,(T(z,u) * u) \ (T(z,u) * (z * u))) = a(x,y,T(z,u)).
a(x,y,z * u) = a(x,y,T(u * z,u)).
a(x,y,T(z * u,z)) = a(x,y,u * z).
a(x,y,(T(z,u) * u) \ (z * (T(z,u) * u))) = a(x,y,T(z,u)).
a(x,y,T(z,T(z,u) * u)) = a(x,y,T(z,u)).
a(x,y,T(z,z * u)) = a(x,y,T(z,u)).
a(x,y,T((z \ u) * z,((z \ u) * z) * (z \ 1))) = a(x,y,R(u,z,z)).
a(x,y,T((z \ u) * z,R(z \ u,z,z \ 1))) = a(x,y,R(u,z,z)).
a(x,y,T((z \ u) * z,z \ u)) = a(x,y,R(u,z,z)).
a(x,y,R(z,u,u)) = a(x,y,u * (u \ z)).
a(x,y,z * (z \ u)) = a(x,y,R(u,z,z)).
a(x,y,z) = a(x,y,R(z,u,u)).
a(x,y,R(z,u,u)) = a(x,y,z).
a(x,y,z * u) = a(x,y,z / (u \ 1)).
a(x,y,z / (u \ 1)) = a(x,y,z * u).
a(x,y,R(((z \ 1) * u) \ 1,u,u)) = a(x,y,(u \ 1) * z).
a(x,y,R((z \ u) \ 1,u,u)) = a(x,y,(u \ 1) * z).
a(x,y,(z \ 1) * u) = a(x,y,(u \ z) \ 1).
a(x,y,(z \ u) \ 1) = a(x,y,(u \ 1) * z).
a(x,y,(z \ u) \ 1) = a(x,y,u \ z).
a(x,y,z * a(u,z,z)) = a(x,y,(u / z) \ u).
a(x,y,(z / u) \ z) = a(x,y,u * a(z,u,u)).
a(x,y,z) = a(x,y,z * a(u,z,z)).
a(x,y,z * a(u,z,z)) = a(x,y,z).
a(x,y,L(z,u,u * z)) = a(x,y,z).
((x * y) \ x) * L(L(y,x,x * y),z,u) = a(u,z,y) \ 1.
a(x,y,z) \ 1 = (u * z) \ (u * L(z,y,x)).
(x * y) \ (x * L(y,z,u)) = a(u,z,y) \ 1.
a(x,x * y,z) \ 1 = L(a(x,y,z),z,u).
L(a(x,y,z),z,u) = a(x,x * y,z) \ 1.
L(a(x,y,z),z,u) = a(x,y,z).
(x * L(y,z,u)) / a(u,u * z,y) = x * y.
x * y = a(z,z * u,y) \ (x * L(y,u,z)).
a(x,x * y,z) \ (u * L(z,y,x)) = u * z.
x * y = a(z,u,y) * (x * L(y,u,z)).
a(x,y,z) * (u * L(z,y,x)) = u * z.
x * y = y * T(x,L(y,z,u)).
x * T(y,L(x,z,u)) = y * x.
(x * y) \ (y * x) = K(L(y,z,u),x).
K(L(x,y,z),u) = (u * x) \ (x * u).
K(L(x,y,z),u) = K(x,u).
K(x,y) = L(K(x,y),z,u).
L(K(x,y),z,u) = K(x,y).
a(x,y,a(z,u,w)) = 1.
a(c27,c28,a(c29,c30,c31)) != 1.
x * K(y,x / y) = y * (x / y).
(x * y) * L(L(z,y,x),u,w) = x * (y * L(z,u,w)).
R(x,x \ (y / z),z) = y / ((x \ (y / z)) * z).
x * L(x \ y,z,u) = L(y / x,z,u) * x.
L(x / y,z,u) * y = y * L(y \ x,z,u).
L(((x * y) * z) \ u,(x * y) * z,x * (y * z)) = a(x,y,z) \ ((x * (y * z)) \ u).
(x / (y * x)) * z = y \ z.
R(R(x / y,y,z),u,w) * (y * z) = (y * z) * R((y * z) \ (x * z),u,w).
(x \ R(x,y,z)) * x = R(x,y,z).
(R(x,y,z) \ x) * u = R(x,y,z) \ (x * u).
R(x,y,z) \ (x * u) = (R(x,y,z) \ x) * u.
L(x,(y \ z) \ u,z \ (y * u)) = x.
x \ (L(x,y,z) * u) = (L(x,y,z) \ x) \ u.
(L(x,y,z) \ x) \ u = x \ (L(x,y,z) * u).
(L(x,y,z) \ x) \ u = (x \ L(x,y,z)) * u.
(x \ R(x,y,z)) \ u = R(x,y,z) \ (x * u).
(x \ (y * z)) * a(x,y,z) = (x \ y) * z.
R(x,x * (y / z),z) = y / ((x \ (y / z)) * z).
(L(x,y,z) \ x) \ u = L(x,y,z) * (x \ u).
R(L(x / (y \ 1),z,u),y,y) / y = (y \ 1) * L((y \ 1) \ x,z,u).
L(R(x / (y \ 1),y,y),z,u) / y = (y \ 1) * L((y \ 1) \ x,z,u).
L(x,(y \ z) \ u,z * (y * u)) = x.
L(x,(y \ z) * u,z * (y * u)) = x.
L(x,(y * z) * u,z * (y * u)) = x.
L(x,(y * z) * u,T(y,z) * (z * u)) = x.
x / y = K(x * y,x) / (x \ y).
K(x * y,x) / (x \ y) = x / y.
x / y = (x \ y) \ K(x * y,x).
(x \ y) \ K(x * y,x) = x / y.
x * K(y,y * x) = y * (x / y).
K(x,y / x) * ((x \ y) * z) = (y / x) * z.
((T(x,y) * z) * u) / ((K(x,y) * z) * u) = R(x,K(x,y) * z,u).
x * a(x,y,x) = R(x,y,x).
L(x * y,z,u) / y = (y \ 1) * L((y \ 1) \ x,z,u).
(x \ 1) * L((x \ 1) \ y,z,u) = L(y * x,z,u) / x.
(x \ 1) * L(x * y,z,u) = L(y * x,z,u) / x.
L(x * y,z,u) / y = y \ L(y * x,z,u).
L(x,y,z) / (u \ x) = (u \ x) \ L((u \ x) * u,y,z).
(x \ y) \ L((x \ y) * x,z,u) = L(y,z,u) / (x \ y).
(x * y) * R((x * y) \ (z * y),u,w) = (R(z / x,u,w) * x) * y.
(x * y) * R((x * y) \ (z * y),u,w) = (x * R(x \ z,u,w)) * y.
a((x * y) * (x * (y * z)),u,w) = a(L(z,y,x),u,w).
(T(x,y) * z) \ u = ((x * z) \ K(y,x)) * u.
((x * y) \ K(z,x)) * u = (T(x,z) * y) \ u.
(x \ K(y,z)) * K(z,y) = x \ 1.
(x / y) * K(x,x * y) = (x \ y) \ 1.
(x * K(y,z)) \ u = (K(z,y) / x) * u.
K(x,T(y,z)) / z = z \ K(x,y).
x * a(x,y,z) = R(x,y,z).
L(x,y,z) \ L(R(x,u,w),y,z) = a(L(x,y,z),u,w).
a(x,y,z) * x = R(x,y,z).
a(x,y,z) \ u = R(x,y,z) \ (x * u).
R(x,y,z) \ (x * u) = a(x,y,z) \ u.
a(x,y,z) * u = R(x,y,z) * (x \ u).
R(x,y,z) * (x \ u) = a(x,y,z) * u.
L(x,a(y,z,u),y * z) = x.
(x * y) * R((x * y) \ x,z,u) = x * a(y,z,u).
a(x,y,z) \ z = L(z,y,x).
L(L(x,y,z),u,w) \ L(x,u,w) = a(z,y,L(x,u,w)).
x / a(y,z,x) = L(x,z,y).
(x \ (y \ z)) \ ((y * x) \ z) = a(y,y * x,(y * x) \ z).
a(x,x * y,(x * y) \ z) = (y \ (x \ z)) \ ((x * y) \ z).
x / L(x,y,z) = a(z,y,x).
a(x,y,z) \ u = z \ (L(z,y,x) * u).
x \ (L(x,y,z) * u) = a(z,y,x) \ u.
(x * y) / (L(x,z,u) * y) = a(u,z,x).
a(x,y,z) \ u = L(z,y,x) * (z \ u).
L(x,y,z) * (x \ u) = a(z,y,x) \ u.
x * a(x,y,z) = R(x,u * (u * y),z).
R(x,y * (y * z),u) = x * a(x,z,u).
((x * y) * a(x,y,z)) * u = (x * y) * (a(x,y,z) * u).
x * a(y,z,x) = L(x,y * z,y).
L(x,y * z,y) = x * a(y,z,x).
L(x,y,z) \ x = a(z,y,L(x,y,z)).
a(x,y,L(z,y,x)) = L(z,y,x) \ z.
a(x,x * y,z) * u = a(x,y,z) \ u.
L(x,y,a(z,z * u,w)) = L(x,y,a(z,u,w)).
L(x * a(y,z,x),z,y) = x.
a(x,y,L(z,y,x)) = a(x,y,z).
a(x,x * y,L(z,y,x)) = a(x,y,z) \ 1.
R(a(x,y,z),u,w) \ R(x,y,z) = a(a(x,y,z),u,w) \ x.
x * (a(y,z,x) \ u) = L(x,z,y) * u.
((L(x,y,z) * u) * w) \ ((x * u) * w) = R(T(a(z,y,x),(L(x,y,z) * u) * w),L(x,y,z) * u,w).
R(T(a(x,y,z),(L(z,y,x) * u) * w),L(z,y,x) * u,w) = ((L(z,y,x) * u) * w) \ ((z * u) * w).
L(a(x,y,z),u,w) * L(z,y,x) = a(w,u,a(x,y,z)) \ z.
R(x,y * (y * z),u) = R(x,z,u).
R(x,y * z,u) = R(x,y \ z,u).
R(x,y \ z,u) = R(x,y * z,u).
R(x,(y * z) / u,w) = R(x,(y \ z) / u,w).
R(x,(y \ z) / u,w) = R(x,(y * z) / u,w).
a(L(x,y,z),u,w) \ a(x,u,w) = a(z,y,a(x,u,w)).
a(x,y,z) \ a(L(x,u * w,u),y,z) = a(u,w,a(x,y,z)).
a(x,y,a(z,u,w)) \ 1 = a(z,u,w) \ a(L(z,y,x),u,w).
a(x,y,z) \ a(L(x,u,w),y,z) = a(w,u,a(x,y,z)) \ 1.
a(x,y,z) = R(a(x,y,z),y,u).
R(a(x,y,z),y,u) = a(x,y,z).
x * (y * (a(x,y,z) * u)) = R(x,y,z) * (y * u).
a(L(x,y,z),u,w) * L(w,u,x) = a(z,y,a(x,u,w)) \ w.
a(x,y,z) = a(L(x,u,y),y,z).
a(L(x,y,z),z,u) = a(x,z,u).
a((x * y) \ z,x,u) = a(y \ (x \ z),x,u).
L(x,y,z) * a(x,z,u) = R(L(x,y,z),z,u).
a(x \ (y \ z),y,u) = a((y * x) * z,y,u).
L(x,y,z) * a(x,z,u) = L(R(x,z,u),y,z).
a((x * y) * z,x,u) = a(y * (x * z),x,u).
(x * a(x,y,z)) / L(R(x,y,z),u,y) = a(y,u,x).
a((x * y) * z,y,u) = a(T(x,y) * (y * z),y,u).
a(T(x,y) * (y * z),y,u) = a((x * y) * z,y,u).
R(x,y,z) / L(R(x,y,z),u,y) = a(y,u,x).
a(x,y,z) = a(x,y,R(z,x,u)).
a(x,y,R(z,x,u)) = a(x,y,z).
a(x,y,z / (x * u)) = a(x,y,(z / u) / x).
a(x,y,(z / u) / x) = a(x,y,z / (x * u)).
L(x,y,z \ u) = L(x,y,u * z).
L(x,y,z * (u * (u * w))) = L(x,y,w * z).
L(x,y,L(z,u,w)) = L(x,y,(w * (u * z)) * (w * u)).
L(x,y,(z * (u * w)) * (z * u)) = L(x,y,L(w,u,z)).
K(a(x,y,z) \ 1,u) = 1.
T(a(x,y,z) \ 1,u) = a(x,y,z) \ 1.
x * a(y,z,u) = a(y,z,u) * x.
a(x,y,z) * u = u * a(x,y,z).
a(x,y,z) = (a(x,y,z) \ u) \ u.
(a(x,y,z) \ u) \ u = a(x,y,z).
(a(x,y,z) \ u) * a(x,y,z) = u.
x \ a(y,z,u) = a(y,z,u) * (x \ 1).
a(x,y,z) * (u \ 1) = u \ a(x,y,z).
a(x \ y,z,u) = a(y / x,z,u).
a(x / y,z,u) = a(y \ x,z,u).
a(x,y,z) * (u / a(x,y,z)) = u.
(x * (a(y,z,u) * w)) \ ((x * w) * a(y,z,u)) = a(x,w,a(y,z,u)).
(x * y) \ ((x * a(z,u,w)) * y) = R(T(a(z,u,w),x * y),x,y).
x * (y * a(x,z,u)) = R(x,z,u) * y.
(x * y) * a(x,z,u) = R(x,z,u) * y.
x * (L(x,y,z) \ u) = u * a(z,y,x).
(a(x,y,z) / u) * w = (a(x,y,z) \ u) \ w.
(a(x,y,z) \ u) \ w = (a(x,y,z) / u) * w.
a(x / y,z,u) = a(y * x,z,u).
a(x * a(y,z,x),u,w) = a(L(x,z,y),u,w).
(x * y) / a(z,u,x) = L(x,u,z) * y.
a(x * y,z,u) = a(x / y,z,u).
a(x / y,z,u) = a(x * y,z,u).
a(x * y,z,u) = a(y * x,z,u).
((T(x,y) * z) * u) / (K(x,y) * (z * u)) = R(x,K(x,y) * z,u).
(x * K(y,z)) * u = K(y,T(z,x)) * (x * u).
K(x,T(y,z)) * (z * u) = (z * K(x,y)) * u.
x \ y = (x \ K(z,u)) * (K(u,z) * y).
(x \ K(y,z)) * (K(z,y) * u) = x \ u.
x * (a(y,z,u) \ 1) = a(y,z,u) \ x.
(x * y) \ (R(x,z,u) * y) = L(a(x,z,u),y,x).
a(x,y,z) = (x * u) \ (R(x,y,z) * u).
(x * y) \ (R(x,z,u) * y) = a(x,z,u).
(R(x,y,z) * y) * u = (x * y) * (a(x,y,z) * u).
(x * y) * (a(x,y,z) * u) = (R(x,y,z) * y) * u.
L(x,y,z) * a(z,y,L(x,u,w)) = L(x,u,w) * a(w,u,L(x,y,z)).
(L(x,y,z) * u) \ (x * u) = a(z,y,x).
K(x,y) * (z \ u) = (z * K(y,x)) \ u.
(x * K(y,z)) \ u = K(z,y) * (x \ u).
x \ (R(x / y,z,u) * y) = a(x / y,z,u).
(L(R(x,y,z),u,w) * (y * z)) \ ((x * y) * z) = a(w,u,R(x,y,z)).
(x * (y / x)) \ z = K(x * y,x) * (y \ z).
K(x * y,x) * (y \ z) = (x * (y / x)) \ z.
K(x,y) * (z \ u) = (K(x,y) / z) * u.
(K(x,y) / z) * u = K(x,y) * (z \ u).
x = R(x,K(y,z),u).
R(x,K(y,z),u) = x.
(x / y) / K(z,u) = x / (K(z,u) * y).
(x / y) * z = K(x * y,x) * ((x \ y) \ z).
K(x * y,x) * ((x \ y) \ z) = (x / y) * z.
(x \ K(y,z)) * u = K(y,T(z,x)) * (x \ u).
K(x,T(y,z)) * (z \ u) = (z \ K(x,y)) * u.
x / (K(y,z) * u) = (x / u) * K(z,y).
a(L(x,y * z,y),u,w) = a(L(x,z,y),u,w).
K(x,T(y,z)) * (z * u) = z * (K(x,y) * u).
x \ (y * R(y \ x,z,u)) = a(x / y,z,u).
L(x,y,z * (K(u * w,u) * ((u * (w / u)) \ v5))) = L(x,y,(w \ v5) * z).
a(x,y,z) \ a(L(x,u,w),y,z) = a(w,u,a(x,y,z)).
x \ (y * R(y \ x,z,u)) = a(y * x,z,u).
(x * (y * z)) \ ((x * y) * R(L(z,y,x),u,w)) = a((x * y) * (x * (y * z)),u,w).
L(a(x,y,z),u,x) = a(x,y,z).
(x * (y * (a(x,y,z) * u))) \ ((R(x,y,z) * y) * u) = a(x,y,a(x,y,z) * u).
x * a(y,z,a(u,w,x)) = L(x,w,u) * a(L(u,z,y),w,x).
L(x,y,z) * a(L(z,u,w),y,x) = x * a(w,u,a(z,y,x)).
a(x,y,a(z,u,w)) = a(x,y,a(z,u,w)) \ 1.
a(x,y,a(z,u,w)) \ 1 = a(x,y,a(z,u,w)).
a(x,y,a(z,u,w)) * a(x,y,a(z,u,w)) = 1.
x * a(y,z,a(u,w,v5)) = a(y,z,a(u,w,v5)) \ x.
a(x,y,a(z,u,w)) \ v5 = v5 * a(x,y,a(z,u,w)).
a(L(x,y,z),u,w) * L(w,u,x) = w * a(z,y,a(x,u,w)).
R(x,y,z) * T(u,x) = u * R(x,y,z).
R(x,y,z) * (x \ u) = (u / x) * R(x,y,z).
(x / y) * R(y,z,u) = a(y,z,u) * x.
x * R(y,z,u) = a(y,z,u) * (x * y).
a(x,y,z) * (u * x) = u * R(x,y,z).
L(x,y,z) * R(a(z,y,x),u,w) = a(a(z,y,x),u,w) * x.
x * R(y,z,u) = (x * y) * a(y,z,u).
(x * y) * a(y,z,u) = x * R(y,z,u).
(x * (y * z)) \ (x * (y * R(z,u,w))) = L(a(z,u,w),y * z,x).
(x * y) \ ((x * a(z,u,w)) * y) = R(a(z,u,w),x,y).
R(x,K(x,y) * z,u) = (((T(x,y) * z) * u) / (z * u)) * K(y,x).
(((T(x,y) * z) * u) / (z * u)) * K(y,x) = R(x,K(x,y) * z,u).
R(T(x,y),z,u) * K(y,x) = R(x,K(x,y) * z,u).
R(x,K(x,y) * z,u) = R(x,z,u).
R(x,x * y,z) = R(x,y * x,z).
R(x,y * x,z) = R(x,x * y,z).
x \ R(x,y * x,z) = R(x,y,z) \ x.
R(x,y,z) \ x = a(x,y * x,z).
a(x,y * x,z) = a(x,y,z) \ 1.
a(x * y,x,z) \ 1 = a(x * y,y,z).
a(x * y,y,z) = a(x * y,x,z) \ 1.
a(x * y,y,a(z,u,w)) = a(x * y,x,a(z,u,w)).
((L(x,y,z) * u) * w) \ ((x * u) * w) = a(z,y,R(x,u,w)).
L(x,y,z * u) = L(x,y,T(z,w) * u).
L(x,y,T(z,u) * w) = L(x,y,z * w).
L(x,y,(z / u) * w) = L(x,y,(u \ z) * w).
L(x,y,z * T(u,w)) = L(x,y,z * u).
L(x,y,z * (K(u,w) * v5)) = L(x,y,z * v5).
L(x,(y * z) * u,y * (z * u)) = x.
((x * y) * z) \ u = a(x,y,z) \ ((x * (y * z)) \ u).
a(x,y,z) \ ((x * (y * z)) \ u) = ((x * y) * z) \ u.
L(x,y,z * (u \ w)) = L(x,y,z * (w / u)).
L(x,y,z * (u / w)) = L(x,y,z * (w \ u)).
L(x,y,(z / u) * w) = L(x,y,(u * z) * w).
L(x,y,z * (u * w)) = L(x,y,z * (w * u)).
L(x,y,z * (u / w)) = L(x,y,z * (w * u)).
L(x,y,z * ((u * w) * u)) = L(x,y,w * z).
a(x,y,z) \ 1 = ((x * y) * z) \ (x * (y * z)).
((x * y) * z) \ (x * (y * z)) = a(x,y,z) \ 1.
a(x,a(y,z,u),w) \ a(x,w,a(y,z,u)) = ((x * a(y,z,u)) * w) \ ((x * w) * a(y,z,u)).
((x * a(y,z,u)) * w) \ ((x * w) * a(y,z,u)) = a(x,a(y,z,u),w) \ a(x,w,a(y,z,u)).
L(x,y,(z \ u) * w) = L(x,y,w * ((v5 * (z / v5)) \ u)).
L(x,y,z * ((u * (w / u)) \ v5)) = L(x,y,(w \ v5) * z).
L(x,y,(z \ u) * w) = L(x,y,w * ((v5 * (z / v5)) * u)).
L(x,y,z * ((u * (w / u)) * v5)) = L(x,y,(w \ v5) * z).
L(x,y,z * ((u * (w / u)) * v5)) = L(x,y,(w * v5) * z).
L(x,y,(z * u) * ((w * (z / w)) * (u * v5))) = L(x,y,L(v5,u,w * (z / w))).
L(x,y,L(z,u,(u * z) * (w / (u * z)))) = L(x,y,(w / (u * z)) * (w * u)).
L(x,y,L(z,u,(u * z) * (w / (u * z)))) = L(x,y,((u * z) * w) * (w * u)).
a(K(x,y) * z,u,w) = a(z,u,w).
a(x * y,z,u) = a(T(x,w) * y,z,u).
a(T(x,y) * z,u,w) = a(x * z,u,w).
a((x / y) * z,u,w) = a((y \ x) * z,u,w).
a(x * T(y,z),u,w) = a(x * y,u,w).
a(x * (y * z),y,u) = a((x * y) * z,y,u).
a((x * y) * z,y,u) = a(x * (y * z),y,u).
a((x / y) * z,u,w) = a((y * x) * z,u,w).
a(x / (y / z),u,w) = a((z \ y) * x,u,w).
a(x / (y * z),z,u) = a(y * (z * x),z,u).
a(x / (y * z),u,w) = a((z / y) * x,u,w).
a(x / (y \ z),u,w) = a(x / (z / y),u,w).
a(x / (y / z),u,w) = a(x / (z \ y),u,w).
a((x * y) / z,x,u) = a(y / (z * x),x,u).
a(x / (y / z),u,w) = a(x / (z * y),u,w).
a((x * y) / z,x,u) = a(y / (x / z),x,u).
a(x,y,z) * x = R(x,K(u,w) * y,z).
R(x,K(y,z) * u,w) = a(x,u,w) * x.
a(x,y,z) * x = R(x,T(y,u),z).
R(x,T(y,z),u) = a(x,y,u) * x.
(x * ((y * K(z,u)) * w)) \ ((x * (y * K(z,u))) * w) = a(x,y,w).
R(x,T(y,z),u) = R(x,y,u).
R(x,y \ z,u) = R(x,z / y,u).
R(x,y / z,u) = R(x,z \ y,u).
R(x,y / z,u) = R(x,z * y,u).
R(x,y * (z \ u),w) = R(x,(z * u) / y,w).
R(x,(y * z) / u,w) = R(x,u * (y \ z),w).
a(x,y * T(z,u),w) = a(x,z * y,w).
R(x,K(y,z) * u,w) = R(x,u,w).
R(x,y * K(z,u),w) = R(x,y,w).
R(x,y * (z * K(u,w)),v5) = R(x,y * z,v5).
x * a(x,y * z,u) = R(x,z * T(y,w),u).
R(x,y * T(z,u),w) = x * a(x,z * y,w).
R(x,y * (z \ u),w) = R(x,y * (z * u),w).
R(x,y * ((z \ u) \ 1),w) = R(x,y * (z / u),w).
R(x,y * T(z,u),w) = R(x,z * y,w).
R(x,y * ((z \ u) \ u),w) = R(x,z * y,w).
R(x,y * z,u) = R(x,z * ((y \ w) * w),u).
R(x,y * ((z \ u) * u),w) = R(x,z * y,w).
R(x,y * (z / u),w) = R(x,y * ((z \ u) * 1),w).
R(x,y * ((z \ u) * 1),w) = R(x,y * (z / u),w).
R(x,y * (z \ u),w) = R(x,y * (z / u),w).
R(x,y * (z / u),w) = R(x,y * (z \ u),w).
R(x,y * (z / u),w) = R(x,y * (z * u),w).
R(x,x * (y * z),z) = y / ((x \ (y / z)) * z).
R(x,x * ((y \ z) * z),z) = (y \ z) / ((x \ (y \ 1)) * z).
(x \ y) / ((z \ (x \ 1)) * y) = R(z,x * z,y).
R(x,y * x,z) = (y \ z) / ((x \ (y \ 1)) * z).
(x * (y * (K(z,u) * w))) \ ((x * (y * K(z,u))) * w) = a(x,y,w).
L(x,y,L(z,u,(u * z) * ((u * z) * w))) = L(x,y,((u * z) * w) * (w * u)).
L(x,y,L(z,u,w)) = L(x,y,((u * z) * w) * (w * u)).
L(x,y,((z * u) * w) * (w * z)) = L(x,y,L(u,z,w)).
L(x,y,L(z,u,w)) = L(x,y,((u * z) * w) * (u * w)).
L(x,y,((z * u) * w) * (z * w)) = L(x,y,L(u,z,w)).
L(x,y,L(z,u,w)) \ x = a(((u * z) * w) * (u * w),y,x).
a(((x * y) * z) * (x * z),u,w) = L(w,u,L(y,x,z)) \ w.
a(((x * y) * z) * (x * z),u,w) = a(L(y,x,z),u,w).
(x * y) \ (((x * z) * y) * R(((x * z) * y) \ (x * y),u,w)) = a(L(z,x,y),u,w).
(R(x,y,z) * (y * u)) \ ((R(x,y,z) * y) * u) = a(x,y,a(x,y,z) * u).
a(x,y,a(x,y,z) * u) = a(R(x,y,z),y,u).
a(x,y,z * a(x,y,u)) = a(R(x,y,u),y,z).
(x * (y * z)) \ ((x * y) * L(R(z,u,w),y,x)) = a((x * y) * (x * (y * z)),u,w).
(x * y) \ (((x * z) * R((x * z) \ x,u,w)) * y) = a(L(z,x,y),u,w).
(x * y) \ ((x * a(z,u,w)) * y) = a(L(z,x,y),u,w).
a(L(x,y,z),u,w) = R(a(x,u,w),y,z).
R(a(x,y,z),u,w) = a(L(x,u,w),y,z).
a(L(x,y,z),u,w) = a(R(x,y,z),u,w).
a(R(x,y,z),u,w) = a(L(x,y,z),u,w).
a(L(x,y,z),y,u) = a(x,y,u).
a(L(x,y,z),u,w) \ R(x,u,w) = a(a(x,u,w),y,z) \ x.
L(x,y,z) * a(L(z,u,w),y,x) = a(a(z,y,x),u,w) * x.
a((x * y) \ z,y,u) = a(y \ (x \ z),y,u).
a((x \ y) \ z,y,u) = a(y \ (x * z),y,u).
a((x \ y) \ T(z,x),y,u) = a(y \ (z * x),y,u).
L(x,y,z) * a(x,y,u) = R(L(x,y,z),y,u).
a(x,y,z * a(x,y,u)) = a(L(x,y,u),y,z).
a(x \ (y \ z),x,u) = a((y * x) * z,x,u).
a(x / (y \ z),z,u) = a(z \ (y * x),z,u).
L(x,y,z) * a(x,y,u) = L(R(x,y,u),y,z).
a(x,y,z * a(x,y,u)) = a(x,y,z).
a(x \ (y \ z),x,u) = a(y * (x * z),x,u).
a(x / (y / z),y,u) = a(y \ (z * x),y,u).
L(R(x,y,z),y,u) \ (x * a(x,y,z)) = a(u,y,x).
a(x * (y * z),y,u) = a(y * (x * z),y,u).
a((x * y) / z,z,u) = a(y / (z / x),z,u).
a(x \ (y * z),x,u) = a((z \ x) * T(y,z),x,u).
a((x \ y) * T(z,x),y,u) = a(y \ (z * x),y,u).
L(R(x,y,z),y,u) \ R(x,y,z) = a(u,y,x).
a(x,y,z) = a(x,y,R(z,y,u)).
a(x,y,R(z,y,u)) = a(x,y,z).
a(x,y,z / (y * u)) = a(x,y,(z / u) / y).
a(x,y,(z / u) / y) = a(x,y,z / (y * u)).
a(x \ (y * z),x,u) = a((z \ x) * y,x,u).
a(x \ (y * z),x,u) = a((z * x) * y,x,u).
a(x \ (y * z),x,u) = a(z * (x * y),x,u).
a(a(x,y,z),u,w) * z = z * a(w,u,a(x,y,z)).
a(a(x,y,z),u,w) = a(w,u,a(x,y,z)).
a(a(x,y,z),u,w) \ 1 = a(w,u,a(x,y,z)).
a(a(x,y,z),u,w) \ v5 = v5 * a(w,u,a(x,y,z)).
a(x,y,a(z,u,w)) = x \ L(x,y,a(z,u,w)).
x \ L(x,y,a(z,u,w)) = a(x,y,a(z,u,w)).
((a(x,y,z) * u) * w) \ (a(x,y,z) * (u * w)) = a(w,u,a(x,y,z)).
(x \ (a(y,z,u) * w)) \ ((a(y,z,u) \ x) \ w) = a(x \ (a(y,z,u) * w),x,a(y,z,u)).
a(L(x,y,z),u,w) \ R(x,u,w) = x * a(z,y,a(x,u,w)).
((a(x,y,z) * u) * w) \ ((u * w) * a(x,y,z)) = a(w,u,a(x,y,z)).
((x * a(y,z,u)) * w) \ ((x * w) * a(y,z,u)) = a(w,x,a(y,z,u)).
(x * (y * z)) \ (x * (y * R(z,u,w))) = a((x * y) * (x * (y * z)),u,w).
a((x * y) * (x * (y * z)),u,w) = L(a(z,u,w),y * z,x).
L(a(x,y,z),u * x,w) = a((w * u) * (w * (u * x)),y,z).
L(a(x,y,z),u * x,w) = a(L(x,u,w),y,z).
a(L(x,y,z),u,w) \ a(x,u,w) = a(z,y * x,a(x,u,w)).
a(x,y * z,a(z,u,w)) = a(x,y,a(z,u,w)).
a(x,y,a(z,u,w)) = a(x,z * y,a(z,u,w)).
a(x,y * z,a(y,u,w)) = a(x,z,a(y,u,w)).
a(x * y,z,a(u,w,v5)) = a(y * x,u * z,a(u,w,v5)).
a(x * y,z * u,a(z,w,v5)) = a(y * x,u,a(z,w,v5)).
a((x * y) * z,y,a(x,u,w)) = a(z * (x * y),z,a(x,u,w)).
a(x * (y * z),x,a(y,u,w)) = a(y * (z * x),z,a(y,u,w)).
a(x * (y * z),y,a(x,u,w)) = a(z * (x * y),z,a(x,u,w)).
a(x * (y * z),y,a(x,u,w)) = a(x * (z * y),z,a(x,u,w)).
x * L(y,z,u) = a(u,z,y) \ (x * y).
a(x,y,z) \ (u * z) = u * L(z,y,x).
L(x,y,z) * T(u,x) = u * L(x,y,z).
(x * y) * K(z,u) = x * (y * K(z,u)).
(x \ y) * K(z,u) = x \ (y * K(z,u)).
x \ (y * K(z,u)) = (x \ y) * K(z,u).
a(x,y,z) \ u = (u / z) * L(z,y,x).
(x / y) * L(y,z,u) = a(u,z,y) \ x.
(x * L(y,z,u)) \ (x * y) = a(u,z,y).
(x * (y * K(z,u))) * w = (x * y) * (K(z,u) * w).
x \ (y / z) = (x \ (z \ y)) * K(z,z * y).
(x \ (y \ z)) * K(y,y * z) = x \ (z / y).
a(x,y,z * u) \ u = z \ L(z * u,y,x).
((x * y) * L(L(z,y,x),u,w)) \ (x * (y * z)) = a(w,u,L(z,y,x)).
L(a(x,y,z),u * L(z,y,x),w) = (w * (u * L(z,y,x))) \ (w * (u * z)).
(x * (y * (K(z,u) * w))) \ ((x * (y * K(z,u))) * w) = a(x,y,K(z,u) * w).
((x * y) * (K(z,u) * w)) / ((y * K(z,u)) * w) = R(x,y * K(z,u),w).
(x * (y * L(z,u,w))) \ (x * (y * z)) = a(w,u,L(z,y,x)).
((x * y) * (K(z,u) * w)) / (y * (K(z,u) * w)) = R(x,y * K(z,u),w).
R(x,y * K(z,u),w) = R(x,y,K(z,u) * w).
R(x,y,K(z,u) * w) = R(x,y,w).
R(x,y,z) = R(x,y,T(z,u)).
R(x,y,T(z,u)) = R(x,y,z).
a(x,y,z) * x = R(x,y,T(z,u)).
R(x,y,T(z,u)) = a(x,y,z) * x.
a(x,y,z) = a(x,y,T(z,u)).
a(x,y,T(z,u)) = a(x,y,z).
a(x,y,z \ u) = a(x,y,u / z).
a(x,y,z / u) = a(x,y,u \ z).
a(x,y,(z \ u) * z) = a(x,y,u).
a(x,y,(z / u) / x) = a(x,y,(x * u) \ z).
a(x,y,(z / u) / y) = a(x,y,(y * u) \ z).
a(x,y,((z / u) * w) * (u / z)) = a(x,y,w).
a(x,y,z) \ u = (u \ z) \ L((u \ z) * u,y,x).
(x \ y) \ L((x \ y) * x,z,u) = a(u,z,y) \ x.
a(x,y,z) \ u = L(z,y,x) / (u \ z).
L(x,y,z) / (u \ x) = a(z,y,x) \ u.
x / (y \ L(x,z,u)) = a(u,u * z,L(x,z,u)) \ y.
a(x,x * y,L(z,y,x)) \ u = z / (u \ L(z,y,x)).
(a(x,y,z) \ 1) \ u = z / (u \ L(z,y,x)).
x / (y \ L(x,z,u)) = a(u,z,x) * y.
x / (y * L(x,z,u)) = a(u,z,x) * (y \ 1).
R(x,y,z) / a(L(x,u,w),y,z) = a(w,u,R(x,y,z)) * L(x,u,w).
x / (y * L(x,z,u)) = y \ a(u,z,x).
a(x,y,R(z,u,w)) * L(z,y,x) = a(L(z,y,x),u,w) \ R(z,u,w).
a(L(x,y,z),u,w) \ R(x,u,w) = a(z,y,R(x,u,w)) * L(x,y,z).
a(x,y,R(z,u,w)) * L(z,y,x) = z * a(x,y,a(z,u,w)).
L(a(x,y,z),u * L(z,y,x),w) = a(x,y,L(z,u,w)).
a(x,y,L(z,u,w)) = a(L(x,u * L(z,y,x),w),y,z).
a(L(x,y * L(z,u,x),w),u,z) = a(x,u,L(z,y,w)).
a(x,y,L(z,u,x)) = a(x,y,z).
a(x,y,L(L(z,u,x),w,v5)) = a(x,y,L(z,w,v5)).
a(L(x,y * z,u),w,L(z,x * w,x)) = a(x,w,L(L(z,x * w,x),y,u)).
a(L(x,L(y,z,x) * u,w),z,y) = a(x,z,L(y,T(u,v5),w)).
a(x,y,K(z,u) * w) = a(x,y,w).
a(x,y,(z / u) * w) = a(x,y,(u \ z) * w).
a(x,y,z * T(u,w)) = a(x,y,z * u).
a(x,y,a(z,u,z)) = a(x,y,K(z * u,z)).
a(x,y,K(z * u,z)) = a(x,y,a(z,u,z)).
a(x,y,T(z,u) / w) = a(x,y,z / w).
a(x,y,(K(z,u) * w) * v5) = a(x,y,w * v5).
a(x,y,(z * K(u,w)) * v5) = a(x,y,z * v5).
a(x,y,(z / u) * w) = a(x,y,(z \ u) \ w).
a(x,y,(z \ u) \ w) = a(x,y,(z / u) * w).
a(x,y,(z \ K(u,w)) * v5) = a(x,y,z \ v5).
a(x,y,z * (u \ w)) = a(x,y,z * (w / u)).
a(x,y,z * (u / w)) = a(x,y,z * (w \ u)).
a(x,y,z / u) = a(x,y,u \ T(z,w)).
a(x,y,z \ T(u,w)) = a(x,y,u / z).
a(x,y,z \ (u \ w)) = a(x,y,(w / u) / z).
a(x,y,(z / u) / w) = a(x,y,w \ (u \ z)).
a(x,y,a(z,u,z)) = 1.
L(a(x,y,x),z,u) = a(x,y,x).
a(x,y,x) = a(L(x,z,u),y,x).
a(L(x,y,z),u,x) = a(x,u,x).
L(x * a(x,y,x),y,L(x,z,u)) = x.
L(R(x,y,x),y,L(x,z,u)) = x.
(L(x,y,z) * u) * x = L(x,y,z) * (u * R(x,u,x)).
L(x,y,z) * (u * R(x,u,x)) = (L(x,y,z) * u) * x.
a(x,y,((z / u) * w) * v5) = a(x,y,((u \ z) * w) * v5).
a(x,y,((z / u) * w) * v5) = a(x,y,((z \ u) \ w) * v5).
a(x,y,((z \ u) \ w) * v5) = a(x,y,((z / u) * w) * v5).
a(x,y,(z \ u) \ w) = a(x,y,(u \ z) * w).
a(x,y,(T(z,u) * w) \ v5) = a(x,y,(z * w) \ v5).
a(x,y,((z / u) * w) * (z \ u)) = a(x,y,w).
a(x,y,x \ (z \ u)) = a(x,y,(x * z) \ u).
a(x,y,(x * z) \ u) = a(x,y,x \ (z \ u)).
a(x,y,y \ (z \ u)) = a(x,y,(y * z) \ u).
a(x,y,(y * z) \ u) = a(x,y,y \ (z \ u)).
a(x,y,((z / u) \ w) \ v5) = a(x,y,((w \ (u \ z)) * K(u,u * z)) * v5).
a(x,y,((z \ (u \ w)) * K(u,u * w)) * v5) = a(x,y,((w / u) \ z) \ v5).
a(x,x * y,x \ (y \ z)) = (y \ (x \ z)) \ ((x * y) \ z).
a(x,y,K(z,y) * u) = a(x,y,y \ (z \ ((z * y) * u))).
a(x,y,y \ (z \ ((z * y) * u))) = a(x,y,K(z,y) * u).
a(x,y,((z \ u) * w) \ v5) = a(x,y,((u / z) * w) \ v5).
a(x,y,((z / u) * w) \ v5) = a(x,y,((u \ z) * w) \ v5).
L(x,y,z) * T(x * u,x) = (L(x,y,z) * u) * x.
(L(x,y,z) * u) * x = (x * u) * L(x,y,z).
x * y = (y * (L(y,z,u) \ x)) * L(y,z,u).
(x * (L(x,y,z) \ u)) * L(x,y,z) = u * x.
(x * a(y,z,u)) * L(u,z,y) = x * u.
x * L(y,z,u) = (x / a(u,z,y)) * y.
(x / a(y,z,u)) * u = x * L(u,z,y).
(a(x,y,z) / u) \ z = u * L(z,y,x).
x / (y * L(x,z,u)) = a(u,z,x) / y.
a(x,y,z) / u = u \ a(x,y,z).
(a(x,y,z) \ u) \ w = (u \ a(x,y,z)) * w.
a(x,y,((z \ u) * w) * (u \ z)) = a(x,y,w).
a(x,y,((z \ u) * w) * ((u * w) \ z)) = a(x,y,a(z,u,w)).
a(x,y,(z \ (u * w)) * (u \ z)) = a(x,y,L(w,u,z)).
a(x,y,((z \ u) \ w) * v5) = a(x,y,((u \ z) * w) * v5).
a(x,y,y \ (z \ ((z * y) * u))) = a(x,y,u).
a(x,y,L(z,u * y,u)) = a(x,y,z).
a(L(x,y * z,u),w,z) = a(x,w,L(L(z,x * w,x),y,u)).
x \ L(x,y,a(z,z * u,z \ (u \ w))) = a(x,y,(u \ (z \ w)) \ ((z * u) \ w)).
a(x,y,(z \ (u \ w)) \ ((u * z) \ w)) = x \ L(x,y,a(u,u * z,u \ (z \ w))).
a(L(x,y * z,u),w,z) = a(x,w,L(z,y,u)).
a(L(x,y,z),u,w) = a(x,u,L(w,y * w,z)).
a(x,y,L(z,u * z,w)) = a(L(x,u,w),y,z).
a(x,y,((z \ (u \ w)) * K(u,u * w)) * v5) = a(x,y,((u / w) * z) \ v5).
a(x,y,((z / u) * w) \ v5) = a(x,y,(w \ (z \ u)) * v5).
a(x,y,(z \ (u \ w)) * v5) = a(x,y,((w \ u) * z) \ v5).
a(x,y,((z \ u) * w) \ v5) = a(x,y,(w \ (u \ z)) * v5).
a(x,y,z / ((u \ w) * v5)) = a(x,y,(v5 \ (w \ u)) * z).
a(x,y,(z \ (u \ w)) \ ((u * z) \ w)) = x \ L(x,y,a(u,z,u \ (z \ w))).
a(x,y,(z \ (u \ w)) \ ((u * z) \ w)) = a(x,y,a(u,z,u \ (z \ w))).
(x \ (a(y,z,u) * w)) \ ((x \ a(y,z,u)) * w) = a(x \ (a(y,z,u) * w),x,a(y,z,u)).
a(x \ (a(y,z,u) * w),x,a(y,z,u)) = a(x,a(y,z,u),w).
a(x,a(y,z,u),w) = a(x * (a(y,z,u) * w),x,a(y,z,u)).
a(x * (a(y,z,u) * w),x,a(y,z,u)) = a(x,a(y,z,u),w).
a(x,a(y,z,u),w) = a(w * (x * a(y,z,u)),x,a(y,z,u)).
a(x * (y * a(z,u,w)),y,a(z,u,w)) = a(y,a(z,u,w),x).
a(a(x,y,z) * (u * w),u,a(x,y,z)) = a(u,a(x,y,z),w).
a((x * a(y,z,u)) / w,x,a(y,z,u)) = a(x,a(y,z,u),w).
a(x,x * a(y,z,u),w) * v5 = a(a(y,z,u) * (x * w),x,a(y,z,u)) \ v5.
a(a(x,y,z) * (u * w),u,a(x,y,z)) \ v5 = a(u,u * a(x,y,z),w) * v5.
a(x,a(y,z,u),w) = a(a(y,z,u) / (x / w),x,a(y,z,u)).
a(a(x,y,z) / (u / w),u,a(x,y,z)) = a(u,a(x,y,z),w).
a(x,x * a(y,z,u),w) = a(a(y,z,u) * (x * w),x,a(y,z,u)).
a(a(x,y,z) * (u * w),u,a(x,y,z)) = a(u,u * a(x,y,z),w).
a(x,x * a(y,z,u),w) = a(x,a(y,z,u),w).
a(x,a(y,z,u),w) * v5 = a(x,a(y,z,u),w) \ v5.
a(x,a(y,z,u),w) \ v5 = a(x,a(y,z,u),w) * v5.
a(x,a(y,z,u),w) \ a(x,w,a(y,z,u)) = a(w,x,a(y,z,u)).
a(x,y,a(z,u,w)) = a(y,a(z,u,w),x) * a(y,x,a(z,u,w)).
a(x,a(y,z,u),w) * a(x,w,a(y,z,u)) = a(w,x,a(y,z,u)).
R(T(a(x,y,z),(L(z,y,x) * u) * w),L(z,y,x) * u,w) = a(x,y,R(z,u,w)).
R(a(x,y,z),L(z,y,x) * u,w) = a(x,y,R(z,u,w)).
a(x,y,R(z,u,w)) = a(L(x,L(z,y,x) * u,w),y,z).
a(L(x,L(y,z,x) * u,w),z,y) = a(x,z,R(y,u,w)).
a(x,y,R(z,u,w)) = a(x,y,L(z,T(u,v5),w)).
a(x,y,L(z,T(u,w),v5)) = a(x,y,R(z,u,v5)).
a(x,y,L(z,u,w)) = a(x,y,R(z,u,w)).
a(x,y,R(z,u,w)) = a(x,y,L(z,u,w)).
a(x,y,(z \ u) / ((w \ (z \ 1)) * u)) = a(x,y,L(w,z * w,u)).
a(x,y,L(z,u * z,w)) = a(x,y,(u \ w) / ((z \ (u \ 1)) * w)).
a(x,y,L(z,u,w)) * L(z,y,x) = z * a(x,y,a(z,u,w)).
a(x,y,L(z,u * z,w)) = a(x,y,(w \ ((u \ 1) \ z)) * (u \ w)).
a(x,y,L(z,u * z,w)) = a(x,y,(w \ (u * z)) * (u \ w)).
a(x,y,L(z,u * z,w)) = a(x,y,L(z,u,w)).
a(x,y,L(z,u,w)) = a(L(x,u,w),y,z).
a(L(x,y,z),u,w) = a(x,u,L(w,y,z)).
L(x,y,z) * a(z,y,L(x,u,w)) = x * a(w,u,a(z,y,x)).
a(x,y,L(z,u,w)) * L(z,y,x) = z * a(w,u,a(x,y,z)).
x * a(y,z,a(u,w,x)) = L(x,z,y) * a(y,z,L(x,w,u)).
L(x,y,z) * a(z,y,L(x,u,w)) = x * a(z,y,a(w,u,x)).
a(x,y,a(z,u,w)) = a(z,u,a(w,y,x)).
a(x,y,a(z,u,w)) = a(w,u,a(x,y,z)).
a(x,y,a(z / u,w,v5)) = a(v5,w,a(x,y,u * z)).
a(x,y,a(z,u,w * v5)) = a(v5 * w,u,a(x,y,z)).
a(x * y,z,a(u,w,v5)) = a(u,w,a(v5,z,y * x)).
a(x,y,a(z,u,w)) = a(z,y,a(w,u,x)).
a(x,y,a(z,u,w)) = a(w,y,a(x,u,z)).
a(x,y,a(z,u,w)) * a(z,y,a(w,u,x)) = 1.
a(x,y,a(z,u,w * y)) = a(w * y,w,a(x,u,z)).
a(x * y,x,a(z,u,w)) = a(z,y,a(w,u,x * y)).
a(x,y * z,a(u,w,z)) = a(u,y,a(z,w,x)).
a(x,y,a(a(x,y,z) / u,w,v5)) = a(v5,w,a(x,y,u)).
a(x,y,a(z,u,w * v5)) = a(x,y,a(z,u,v5 / w)).
a(x,y,a(z,u,w / v5)) = a(x,y,a(z,u,v5 * w)).
a(x,y,a(z,u,w)) = a(z,u,a(x,y,w)).
a(x,y,a(a(x,y,z) / (u / w),u,z)) = a(u,a(x,y,z),w).
a(x,y,a(z,u,w)) = a(w,y,a(z,u,x)).
a(x,y,a(z,u,w)) = a(x,y,a(w,u,z)).
a(x,y,a(z,u,w)) = a(w,u,a(z,y,x)).
a(x,a(y,z,u),w) * a(u,w,a(y,z,x)) = a(w,x,a(y,z,u)).
a(x,y * z,a(u,w,z)) = a(x,y,a(z,w,u)).
a(x,y,a(z / u,w,v5)) = a(x,y,a(v5,w,u / z)).
a(x * y,z,a(u,w,v5)) = a(v5,w,a(u,z,y * x)).
a(x,y,a(z,u,w / v5)) = a(v5 / w,u,a(z,y,x)).
a(x / y,z,a(u,w,v5)) = a(v5,w,a(u,z,y / x)).
a(x,y,a(z,u,z * (u * w))) = a(z * (w * u),w,a(z,y,x)).
a(x * (y * z),y,a(x,u,w)) = a(w,u,a(x,z,x * (z * y))).
a(x,y,(z \ (u \ w)) \ ((u * z) \ w)) = a(u \ (z \ w),z,a(u,y,x)).
a(x,y,a(z,u,w * (u * v5))) = a(v5 * (u * w),u,a(z,y,x)).
a(x * (y * z),y,a(u,w,v5)) = a(v5,w,a(u,y,z * (y * x))).
a(x,a(y,z,u),w) = a(u,x,a(y,z,x / w)).
a(x,y,a(z,u,y / w)) = a(y,a(z,u,x),w).
a(x,a(y,z,u),w) = a(u,x,a(y,z,w * x)).
a(x,y,a(z,u,w * y)) = a(y,a(z,u,x),w).
a(x,a(y,z,u),w) = a(y,z,a(u,x,x / w)).
a(x,y,a(z,u,u / w)) = a(u,a(x,y,z),w).
a(x * y,x,a(z,u,w)) = a(y,a(w,u,z),x).
a(x,y,a(z / u,u,w)) = a(u,a(x,y,w),z).
a(x / y,y,a(z,u,w)) = a(y,a(w,u,z),x).
a(x * (y * z),y,a(u,w,v5)) = a(x * z,a(v5,w,u),y).
a(x,a(y,z,u),w) = a(y,z,a(u,x,w / x)).
a(x,y,a(z,u,w / u)) = a(u,a(x,y,z),w).
a(x,a(y,z,u),w * v5) = a(v5 / (x / w),x,a(u,z,y)).
a(x / (y / z),y,a(u,w,v5)) = a(y,a(v5,w,u),z * x).
a(x,a(y,z,u),w * v5) = a(v5 / (w * x),x,a(u,z,y)).
a(x / (y * z),z,a(u,w,v5)) = a(z,a(v5,w,u),y * x).
a(x,y,a(z,u,z * (u * w))) = a(z * u,a(x,y,z),w).
a(x / (y * z),z,a(u,w,v5)) = a(v5,w,a(u,z,x * (z * y))).
a(x,y,a(z,u,w * (u * v5))) = a(u,a(x,y,z),v5 * w).
a(x,a(y,z,u),w * u) = a(u * x,a(y,z,u),w).
a(x * y,a(z,u,x),w) = a(y,a(z,u,x),w * x).
a(x,y,(z \ (u \ w)) \ ((u * z) \ w)) = a(u * (z * w),z,a(u,y,x)).
a(x,y,(z \ (u \ w)) \ ((u * z) \ w)) = a(u * w,a(x,y,u),z).
a(x,y,(z \ (u \ w)) \ ((u * z) \ w)) = a(w,a(x,y,u),z * u).
a(x,a(y,z,u),w * u) = a(y,z,((u \ x) \ w) * ((u * w) \ x)).
a(x,y,((z \ u) \ w) * ((z * w) \ u)) = a(u,a(x,y,z),w * z).
a(x,a(y,z,u),w * u) = a(y,z,((x \ u) * w) * ((u * w) \ x)).
a(x,y,((z \ u) * w) * ((u * w) \ z)) = a(z,a(x,y,u),w * u).
a(x,a(y,z,u),w * u) = a(y,z,a(x,u,w)).
a(x,a(y,z,u),w) = a(y,z,a(x,u,w / u)).
a(x,y,a(z,u,w / u)) = a(z,a(x,y,u),w).
a(x,a(y,z,u),w) = a(u,a(y,z,x),w).
a(x,a(y,z,u),w) * a(u,w,a(y,z,x)) = a(w,u,a(y,z,x)).
a(x,y,a(z,u,w)) = a(x,w,a(z,u,y)).
a(x,y,a(z,u,w * y)) = a(x,w,a(y,u,z)).
a(x,y,a(z,u,w)) = a(z,a(w,u,x),y).
a(x,a(y,z,u),w) = a(u,w,a(x,z,y)).
a(x,y,a(z,u,w)) * a(z,y,a(w,u,x)) = a(y,z,a(w,u,x)).
a(a(x,y,z),u,w) = 1.
a(a(c17,c18,c19),c20,c21) != 1.
a(x,a(y,z,u),w) = 1.
a(c22,a(c23,c24,c25),c26) != 1.
1 = a(x,a(y,z,u),w).

end_of_list.
