% ****************
% AIM:  aa3 => aa1
% ****************

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

set(para_from_small).

clear(back_demod).
set(restrict_denials).

assign(max_weight,5).

formulas(assumptions).

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

   % cancellation laws
   x * y = u & x * z = u -> y = z.
   y * x = u & z * x = u -> y = z.

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

   % associator (right associated * a = left associated)
   (x * (y * z)) \ ((x * y) * z) = a(x,y,z) # label("associator").

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

   % inner mappings
   (y * x) \ (y * (x * u)) = L(u,x,y).
   ((u * x) * y) / (x * y) = R(u,x,y).
   x \ (u * x) = T(u,x).

   % obvious compatibility
   a(x,y,z) = 1 -> L(z,y,x) = z.
   L(x,y,z) = x -> a(z,y,x) = 1.
   T(x,y) = x -> T(y,x) = y.
   T(x,y) = x -> K(x,y) = 1.
   K(x,y) = 1 -> T(x,y) = x.

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

end_of_list.

formulas(assumptions).

   a(x,y,a(z,u,w)) = 1            # label("aa3").

end_of_list.

formulas(goals).

   a(a(x,y,z),u,w) = 1            # label("aa1").

end_of_list.

%
% Hints extracted from previously found proofs.
%

formulas(hints).

L(x,y,a(z,u,w)) = x.
L(x,y * z,a(u,w,y)) = x.
L(x,y * z,R(a(u,w,y),y,z)) = x.
L(x,y * z,R(a(u,w,y),y,z)) = (y * z) \ ((y * z) * x).
(x * y) \ ((x * y) * z) = L(z,x * y,R(a(u,w,x),x,y)).
(L(x,y,z) * (a(z,y,x) * u)) \ ((x * u) * w) = L(w,x * u,R(a(z,y,x),x,u)).
L(x,y * z,R(a(u,w,y),y,z)) = (L(y,w,u) * (a(u,w,y) * z)) \ ((y * z) * x).
(x * (a(y,z,x) * u)) \ (a(y,z,x) * ((x * u) * w)) = L(w,x * u,R(a(y,z,x),x,u)).
R(a(x,y,z),z,u) = a(x,y,z).
R(a(x,y,z),z,z \ u) = a(x,y,z).
R(a(x,y,z),z,z \ u) = L(a(x,y,z),w,v5).
R(a(x,y,z),z,z \ u) = L(u / (a(x,y,z) \ u),w,v5).
R(a(x,y,z),z,z \ u) = L(u / (u / a(x,y,T(z,u))),w,v5).
R(a(x,y,z),z,z \ u) = L((u * a(x,y,T(z,u))) / u,w,v5).
L((x * a(y,z,T(u,x))) / x,w,v5) = R(a(y,z,u),u,u \ x).
L(R(a(x,y,z),z,z \ u),w,v5) = L((u * a(x,y,T(z,u))) / u,w,v5).
R(a(x,y,z),L(z,y,x),u) = R(a(x,y,z),z,u).
R(a(x,y,z),L(z,y,x),u) = L(R(a(x,y,z),z,u),w,v5).
(x * y) / (L(x,z,u) * y) = R(a(u,z,x),x,y).
(L(x,y,z) * u) \ T(x * u,(x * u) / (L(x,y,z) * u)) = (x * u) / (L(x,y,z) * u).
(x * y) \ (a(z,u,x) * w) = (L(x,u,z) * y) \ w.
(x * (a(y,z,x) * u)) \ (R(a(y,z,x),x,u) * ((x * u) * w)) = L(w,x * u,R(a(y,z,x),x,u)).
L(x,y,z) * (a(z,y,x) * u) = x * u.
(x * a(y,z,x)) * u = x * (a(y,z,x) * u).
L(x,a(y,z,u),u) = x.
L(x \ (L(y,z,u) \ w),x,y) = (y * x) \ (a(u,z,y) * w).
a(x,y,z) * (a(x,y,z) \ u) = L(u,a(x,y,z),z).
L(x,y,z) * (x \ u) = a(z,y,x) \ u.
a(x,y,z) \ u = L(z,y,x) * (z \ u).
x / a(y,z,T(u,x)) = a(y,z,u) \ x.
(x \ y) * a(z,u,T(w,y)) = x \ (a(z,u,w) * y).
a(x,y,T(z,u)) = T(a(x,y,z),u).
T(a(x,y,z),u) = a(x,y,T(z,u)).
T(a(x,y,z),L(u,w,v5)) = T(a(x,y,z),u).
(x * (y * (a(z,u,w) \ v5))) \ (x * (y * v5)) = T(a(z,u,w),L(v5,y,x)).
((x * y) * L(a(z,u,w) \ v5,y,x)) \ (x * (y * v5)) = T(a(z,u,w),L(v5,y,x)).
((x * y) * (a(z,u,w) \ L(v5,y,x))) \ (x * (y * v5)) = T(a(z,u,w),L(v5,y,x)).
(x * (y * (a(z,u,w) \ v5))) \ (x * (y * v5)) = T(a(z,u,w),v5).
L(T(a(x,y,z),u),w * (a(x,y,z) \ u),v5) = (v5 * (w * (a(x,y,z) \ u))) \ (v5 * (w * u)).
a(x,y,z) * (L(z,y,x) * (z \ u)) = L(u,a(x,y,z),z).
a(x,y,z) * (L(z,y,x) * (z \ u)) = L(u,a(x,y,z),L(z,y,x)).
a(x,y,z) * (z \ (L(z,y,x) * u)) = L(u,a(x,y,z),L(z,y,x)).
L(L(T(a(x,y,z),u),a(x,y,z) \ u,w),w * (a(x,y,z) \ u),v5) = (v5 * (w * (a(x,y,z) \ u))) \ (v5 * (w * u)).
L(T(a(x,y,z),L(u,w,v5)),a(x,y,z) \ L(u,w,v5),v5 * w) = ((v5 * w) * (a(x,y,z) \ L(u,w,v5))) \ (v5 * (w * u)).
x / T(a(y,z,u),x) = a(y,z,u) \ x.
(a(x,y,z) \ u) \ u = T(a(x,y,z),u).
T(a(x,y,z),u / a(x,y,z)) = (a(x,y,z) \ u) \ u.
(a(x,y,z) \ u) \ u = T(a(x,y,z),u / a(x,y,z)).
(a(x,y,z) \ u) \ u = a(x,y,z) * K(a(x,y,z),u / a(x,y,z)).
a(x,y,z) * K(a(x,y,z),u / a(x,y,z)) = (a(x,y,z) \ u) \ u.
(a(x,y,z) \ u) \ (u / a(x,y,z)) = K(a(x,y,z),u / a(x,y,z)).
K(a(x,y,z),u / a(x,y,z)) = (a(x,y,z) \ u) \ (u / a(x,y,z)).
K(x,a(y,z,u)) \ 1 = K(a(y,z,u),x).
K(a(x,y,z) * u,a(x,y,z)) \ 1 = K(a(x,y,z),u).
K(a(x,y,z),u) = K(a(x,y,z) * u,a(x,y,z)) \ 1.
K(a(x,y,z) * u,a(x,y,z)) \ 1 = (u * a(x,y,z)) \ (a(x,y,z) * u).
(x * a(y,z,u)) \ (a(y,z,u) * x) = K(a(y,z,u) * x,a(y,z,u)) \ 1.
(x * (a(y,z,u) * 1)) \ (a(y,z,u) * x) = K(a(y,z,u) * x,a(y,z,u)) \ 1.
(a(x,y,z) \ 1) \ L((a(x,y,z) \ 1) * u,w,v5) = L(u,w,v5).
T(a(x,y,z),L(u,L(z,y,x) \ 1,z)) = a(x,y,T(z,u)).
T(x * (L(x,y,z) \ 1),L(u,L(x,y,z) \ 1,x)) = a(z,y,T(x,u)).
a(x,y,T(z,u)) = T(z * (L(z,y,x) \ 1),L(u,L(z,y,x) \ 1,z)).
L(x,L(y,z,u) \ 1,y) \ (y * ((L(y,z,u) \ 1) * x)) = a(u,z,T(y,x)).
L(x,L(y,z,u) \ 1,L(y,z,u)) \ (y * ((L(y,z,u) \ 1) * x)) = a(u,z,T(y,x)).
L(x,L(y,z,u) \ 1,L(y,z,u)) \ (y * ((L(y,z,u) \ 1) * x)) = a(u,z,T(y,1 * x)).
a(x,y,T(z,(L(z,u,w) \ v5) * v6)) = a(x,y,T(z,v5 * v6)).
a(x,y,T(z,(L(z,u,w) \ v5) * v6)) = a(x,y,T(z,v5 * (v6 * z))).
a(x,y,L(T(z,u * (w * z)),v5,v6)) = a(x,y,T(z,(L(z,v5,v6) \ u) * w)).
a(x,y,T(L(z,u,w),v5 * (v6 * z))) = a(x,y,T(z,(L(z,u,w) \ v5) * v6)).
a(x,y,T(z,(L(z,u,w) \ v5) * v6)) = a(x,y,T(L(z,u,w),v5 * (v6 * z))).
a(x,y,T((L(z,u,w) \ v5) \ v5,v6 * z)) = a(x,y,T(z,(L(z,u,w) \ v5) * v6)).
a(x,y,T(z,(L(z,u,w) \ v5) * v6)) = a(x,y,T((L(z,u,w) \ v5) \ v5,v6 * z)).
a(x,y,T(T((L(z,u,w) \ v5) \ v5,v6),z)) = a(x,y,T(z,(L(z,u,w) \ v5) * v6)).
a(x,y,T(T((L(z,u,w) \ v5) \ v5,v6),z)) = a(x,y,T(T(z,L(z,u,w) \ v5),v6)).
a(x,y,T(T((L(z,u,w) \ v5) \ v5,v6),z)) = a(x,y,L(T(T(z,L(z,u,w) \ v5),v6),u,w)).
a(x,y,T(T((L(z,u,w) \ v5) \ v5,v6),z)) = a(x,y,T(L(T(z,L(z,u,w) \ v5),u,w),v6)).
a(x,y,T(L(T(z,L(z,u,w) \ v5),u,w),v6)) = a(x,y,T(T((L(z,u,w) \ v5) \ v5,v6),z)).
L(x,y,z) * (a(z,y,x) * u) = x * L(u,a(z,y,x),x).
x * L(y,a(z,u,x),x) = L(x,u,z) * (a(z,u,x) * y).
L(x \ (L(y,z,u) \ w),x,y) = (L(y,z,u) * x) \ w.
L(x,y,L(z,u,w)) = L(x,y,z).
L(x,y,z) = L(x,y,L(z,u,w)).
L(x,y,L(z,u,w)) = x / a(z,y,x).
a(L(x,y,z),u,w) = a(x,u,w).
a(x,y,z) = a(L(x,u,w),y,z).
(x * (L(x,y,z) * (u * w))) \ (x * ((L(x,y,z) * u) * w)) = a(x,u,w).
L(x,y,z) * ((x * u) * w) = x * ((L(x,y,z) * u) * w).
x * ((L(x,y,z) * u) * w) = L(x,y,z) * ((x * u) * w).
L(x,y,z) * (u * (w * a(x,u,w))) = (L(x,y,z) * u) * w.
(x * y) * (z / a(u,w,T(x,y * z))) = L(x,w,u) * (y * (z * a(x,y,z))).
L(x,y,z) * (u * (w * a(x,u,w))) = (x * u) * (w / a(z,y,T(x,u * w))).
((x * y) * z) / a(u,w,T(x,y * z)) = L(x,w,u) * (y * (z * a(x,y,z))).
((x * y) * z) / a(u,w,T(x,x * (y * z))) = L(x,w,u) * (y * (z * a(x,y,z))).
a(x,y,T(z,(u * w) * v5)) = a(x,y,T(z,u * (w * v5))).
a(x,y,T(T(z,u),w * v5)) = a(x,y,T(z,(u * w) * v5)).
a(x,y,T(z,(u * w) * v5)) = a(x,y,T(T(z,u),w * v5)).
a(x,y,T(T(T(z,u),w),v5)) = a(x,y,T(z,(u * w) * v5)).
a(x,y,T(z,L(u,w,v5) * (v6 * v7))) = a(x,y,T(T(T(z,v6),v7),u)).
a(x,y,T(T(T(z,u),w),v5)) = a(x,y,T(z,L(v5,v6,v7) * (u * w))).
a(x,y,T((z \ u) \ u,w)) = a(x,y,T(z,u * w)).
a(x,y,T(z,L(u,w,v5) * v6)) = a(x,y,T(z,v6 * u)).
a(x,y,T(T(z,L(u,w,v5)),v6 * v7)) = a(x,y,T(T(T(z,v6),v7),u)).
a(x,y,T(z,L(u,w,v5) * v6)) = a(x,y,T(T(z,v6),u)).
a(x,y,T((z \ u) \ u,w)) = a(x,y,T(z,(z \ u) * w)).
a(x,y,T(T(z,u),w)) = a(x,y,T(z,u * w)).
a(x,y,T(z,u * w)) = a(x,y,T(T(z,u),w)).
a(x,y,(z \ T(u,w)) * z) = a(x,y,T(u,w * z)).
a(x,y,(z \ (u \ (w * u))) * z) = a(x,y,T(w,u * z)).
a(x,y,T(z,u * w)) = a(x,y,(w \ (u \ (z * u))) * w).
a(x,y,((z * u) \ (w * z)) * u) = a(x,y,T(w,z * u)).
a(x,y,T(z,u * w)) = a(x,y,((u * w) \ (z * u)) * w).
a(x,y,(L(z * u,w,v5) \ (v6 * z)) * u) = a(x,y,T(v6,z * u)).
(a(x,y,z) \ 1) \ L((a(x,y,z) \ 1) * u,w,v5) = L(a(x,y,z) * (a(x,y,z) \ u),w,v5).
L(a(x,y,z) * u,w,v5) = a(x,y,z) * L(u,w,v5).
a(x,y,z) * L(u,w,v5) = L(a(x,y,z) * u,w,v5).
L(a(x,y,z) \ u,w,v5) = a(x,y,z) \ L(u,w,v5).
a(x,y,z) \ L(u,w,v5) = L(a(x,y,z) \ u,w,v5).
a(x,y,T(T(L(z,u,w),L(z,u,w) \ v5),v6)) = a(x,y,T(T((L(z,u,w) \ v5) \ v5,v6),z)).
a(x,y,T(T(T(z,L(u,w,v5)),v6),v7)) = a(x,y,T(T(T(z,v6),v7),u)).
a(x,y,T(T(z,L(u,w,v5)),v6)) = a(x,y,T(T(z,v6),u)).
a(x,y,T(z,L(u,w,v5))) = a(x,y,T(z,u)).
a(x,y,T(z,L(u,w,v5))) = a(x,y,(u \ z) * u).
a(x,y,(z \ u) * z) = a(x,y,T(u,L(z,w,v5))).
a(x,y,(L(z,u,w) \ v5) * v6) = a(x,y,(z \ v5) * v6).
a(x,y,(L(z * u,w,v5) \ (v6 * z)) * u) = a(x,y,R(T(v6,z * u),z,u)).
a(x,y,(L(z,u,w) \ v5) * v6) = a(x,y,z \ (v5 * v6)).
a(x,y,z \ (u * w)) = a(x,y,(L(z,v5,v6) \ u) * w).
a(x,y,L(z,u,w) \ v5) = a(x,y,z \ v5).
a(x,y,z \ u) = a(x,y,L(z,w,v5) \ u).
a(x,y,(a(z,u,w) / v5) * v6) = a(x,y,v5 \ v6).
a(x,y,z) * (u / a(w,v5,u)) = L(a(x,y,z) * u,v5,w).
a(x,y,z) \ (u / a(w,v5,u)) = L(a(x,y,z) \ u,v5,w).
a(x,y,a(z,u,w) * v5) = a(x,y,v5).
a(x,y,z) = a(x,y,a(u,w,v5) * z).
a(x,y,a(z,u,w) \ v5) = a(x,y,v5).
a(x,y,z / a(u,w,v5)) = a(x,y,a(u,w,v5) \ z).
a(x,y,a(z,u,w) \ v5) = a(x,y,v5 / a(z,u,w)).
a(x,y,T(z,a(u,w,v5))) = a(x,y,z).
L(T(x,a(y,z,u)),w,v5) \ T(x,a(y,z,u)) = a(v5,w,x).
L(T(x,a(y,z,u)),w,v5) \ (K(x,a(y,z,u)) * x) = a(v5,w,x).
K(L(x,y,z),a(u,w,v5)) = K(x,a(u,w,v5)).
L(K(x,a(y,z,u)),w * x,v5) = K(L(x,w,v5),a(y,z,u)).
L(L(K(x,a(y,z,u)),x,w),w * x,v5) = K(L(x,w,v5),a(y,z,u)).
(x * (y * z)) \ (x * (y * T(z,a(u,w,v5)))) = K(L(z,y,x),a(u,w,v5)).
L(K(L(x,y,z),a(u,w,v5)),L(x,y,z),z * y) = (z * (y * x)) \ (z * (y * T(x,a(u,w,v5)))).
(x * (y * z)) \ (x * (y * T(z,a(u,w,v5)))) = L(K(L(z,y,x),a(u,w,v5)),L(z,y,x),x * y).
L(R(a(x,y,z),L(z,y,x),z \ u),w,v5) = L((u * a(x,y,T(z,u))) / u,w,v5).
(x * y) * (z / a(u,w,T(x,y * z))) = (L(x,w,u) * y) * z.
(x * y) * (z / a(u,w,T(x,y * z))) = L(R(x,y,z),w,u) * (y * z).
(x * y) * L(R(T(z,x * y),x,y),u,w) = (z * x) * (y / a(w,u,T(z,x * y))).
(x * y) * L((x * y) \ ((z * x) * y),u,w) = (z * x) * (y / a(w,u,T(z,x * y))).
R(a(x,y,z),L(z,y,x),u) = L((z * u) / (L(z,y,x) * u),w,v5).
R(a(x,y,z),L(z,y,x),u) = L((z * u) / ((a(x,y,z) \ z) * u),w,v5).
L((x * y) / ((a(z,u,x) \ x) * y),w,v5) = R(a(z,u,x),L(x,u,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 / (u \ w)) = a(x,y,z * (w \ u)).
a(x,y,z * (u \ w)) = a(x,y,z / (w \ u)).
a(x,y,(L(z,u,w) \ v5) * z) = a(x,y,T(v5,L(z,u,w))).
a(x,y,z / ((1 / u) * w)) = a(x,y,z * (w \ u)).
a(x,y,z * (u \ w)) = a(x,y,z / ((1 / w) * u)).
a(x,y,z * L(u,w,v5)) = a(x,y,z * u).
a(x,y,z * u) = a(x,y,z * L(u,w,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 / ((1 / u) * w)) = a(x,y,z / (u \ w)).
a(x,y,z / L(u,w,v5)) = a(x,y,z / u).
a(x,y,z / u) = a(x,y,z / L(u,w,v5)).
a(x,y,(z \ u) * z) = a(x,y,T(u,z)).
a(x,y,T(z,u)) = a(x,y,(u \ z) * u).
a(x,y,((z * u) \ w) * v5) = a(x,y,(u \ (z \ w)) * v5).
a(x,y,L(z,u,w) * v5) = a(x,y,z * v5).
a(x,y,z * u) = a(x,y,L(z,w,v5) * u).
a(x,y,z * (L(z,u,w) \ v5)) = a(x,y,v5).
a(x,y,z \ (u * w)) = a(x,y,(z \ u) * w).
a(x,y,z * (u * a(w,v5,v6))) = a(x,y,z * u).
a(x,y,z * (u \ a(w,v5,v6))) = a(x,y,z / u).
a(x,y,z * a(u,w,v5)) = a(x,y,z).
a(x,y,z) = a(x,y,z * a(u,w,v5)).
a(x,y,z / a(u,w,v5)) = a(x,y,z).
a(x,y,z) = a(x,y,z / a(u,w,v5)).
a(x,y,z / a(u,w,v5)) = z / L(z,y,x).
x / L(x,y,z) = a(z,y,x / a(u,w,v5)).
x / L((x / a(y,z,u)) * a(y,z,u),w,v5) = a(v5,w,x / a(y,z,u)).
a(x,y,T(z,(z \ u) * w)) = a(x,y,T(z,u * w)).
a(x,y,T(z,(z \ u) * w)) = a(x,y,w \ ((z \ u) \ (u * w))).
a(x,y,z * L(u \ w,u,1 / w)) = a(x,y,z / ((1 / w) * u)).
((x * y) * z) / a(u,w,T(x,y * z)) = (y * z) * L((y * z) \ ((x * y) * z),w,u).
a(x,y,z \ ((u \ w) \ (w * z))) = a(x,y,T(u,w * z)).
a(x,y,T(z,u * w)) = a(x,y,w \ ((z \ u) \ (u * w))).
a(x,y,z * (u \ a(w,v5,u))) = a(x,y,z / L(u,v5,w)).
a(x,y,T(z,(z \ u) * w)) = a(x,y,((z \ u) * w) \ (u * w)).
a(x,y,((z \ u) * w) \ (u * w)) = a(x,y,T(z,(z \ u) * w)).
a(x,y,(z * (u \ w)) / w) = a(x,y,z / u).
a(x,y,z * (u \ 1)) = a(x,y,z / u).
a(x,y,R(z,u,w)) = a(x,y,z).
R(x,y,z) / L(R(x,y,z),u,w) = a(w,u,x).
R(x,y,z) / (R(x,y,z) / a(u,w,x)) = a(u,w,x).
((x * a(y,z,x)) * u) \ (R(a(y,z,x),x,u) * ((x * u) * w)) = L(w,x * u,R(a(y,z,x),x,u)).
T(x,a(y,z,x)) = x.
(L(x,y,z) * u) \ T(x * u,(x * u) / (L(x,y,z) * u)) = R(a(z,y,x),x,u).
L(R(a(x,y,z),L(z,y,x),L(z,y,x) \ u),w,v5) = L((u * a(x,y,T(z,u))) / u,w,v5).
a(x,y,z) * z = z * a(x,y,z).
x / (L(x / a(y,z,u),w,v5) * a(y,z,u)) = a(v5,w,x / a(y,z,u)).
a(x,y,z / a(u,w,v5)) = z / (L(z / a(u,w,v5),y,x) * a(u,w,v5)).
L(R(a(x,y,z),L(z,y,x),u),w,v5) = L((z * u) / ((a(x,y,z) \ z) * u),w,v5).
a(x,y,z) = z / L(z,y,x).
x / L(x,y,z) = a(z,y,x).
L(x,y,z) = a(z,y,x) \ x.
L(T(x,a(y,z,x)),z,y) = L(x,z,y).
L(T(x,x * (L(x,y,z) \ 1)),y,z) = L(x,y,z).
L(x,y,z) = L(T(x,x * (L(x,y,z) \ 1)),y,z).
L((L(x,y,z) \ 1) \ 1,L(x,y,z) \ 1,x) = L(x,y,z).
L(x,y,z) = L((L(x,y,z) \ 1) \ 1,L(x,y,z) \ 1,x).
L((L(x,y,z) \ 1) \ 1,L(x,y,z) \ 1,x) = L(x,y,z) * 1.
L(x,y,z) * 1 = L((L(x,y,z) \ 1) \ 1,L(x,y,z) \ 1,x).
(x * (y * z)) \ ((x * y) * L(T(z,a(u,w,v5)),y,x)) = L(K(L(z,y,x),a(u,w,v5)),L(z,y,x),x * y).
(L(x,y,z) * u) \ T(x * u,(x * u) / (L(x,y,z) * u)) = R(x / L(x,y,z),x,u).
(L(x,y,z) * u) \ T(x * u,(x * u) / (L(x,y,z) * u)) = ((x * a(z,y,x)) * u) / (x * u).
K(a(x,y,z) * u,a(x,y,z)) = K(u,a(x,y,z)).
K(x,a(y,z,u)) = K(a(y,z,u) * x,a(y,z,u)).
(a(x,y,z) * u) \ (u * a(x,y,z)) = K(a(x,y,z) * u,a(x,y,z)).
(a(x,y,z) * u) \ (u * (a(x,y,z) * 1)) = K(a(x,y,z) * u,a(x,y,z)).
(L(x,y,z) * u) \ T(x * u,(x * u) / (L(x,y,z) * u)) = (x * (u * a(z,y,T(x,u)))) / (x * u).
L(x,y,z) * ((L(x,y,z) \ 1) * ((L(x,y,z) \ 1) \ 1)) = L((L(x,y,z) \ 1) \ 1,L(x,y,z) \ 1,x).
L(x \ 1,x,L(y,z,u)) = L(x \ 1,x,y).
L(x \ 1,x,y) = L(x \ 1,x,L(y,z,u)).
L(x \ 1,x,L(y,z,u)) = (x \ 1) / a(y,x,x \ 1).
a(L(x,y,z),u,u \ 1) = a(x,u,u \ 1).
a(x,y,y \ 1) = a(L(x,z,u),y,y \ 1).
(x * (y * (z * u))) \ (x * (y * (z * R(u,w,w \ 1)))) = a(u,w,w \ 1).
(x * (y * (z * u))) \ (x * (y * (z * R(u,w,w \ 1)))) = a(L(u,z,y),w,w \ 1).
(a(x,y,z) \ 1) \ L((a(x,y,z) \ 1) * u,a(x,y,z),L(z,y,x)) = a(x,y,z) * (z \ (L(z,y,x) * u)).
(x * (y * (z * u))) \ (x * ((y * z) * L(R(u,w,w \ 1),z,y))) = a(L(u,z,y),w,w \ 1).
(a(x,y,z) \ 1) \ L((a(x,y,z) \ 1) * u,w,v5) = a(x,y,z) * L(a(x,y,z) \ u,w,v5).
(x * (a(y,z,u) * a(a(y,z,u),x,a(y,z,u)))) \ (a(y,z,u) * x) = K(a(y,z,u) * x,a(y,z,u)) \ 1.
K(x / a(y,z,u),a(y,z,u)) \ 1 = (a(y,z,u) \ x) \ (x / a(y,z,u)).
(a(x,y,z) \ u) \ (u / a(x,y,z)) = K(u / a(x,y,z),a(x,y,z)) \ 1.
T(x,a(y,z,u)) \ x = K(x,a(y,z,u)) \ 1.
T(x,a(y,z,u)) \ R(x,K(x,a(y,z,u)),K(a(y,z,u),x)) = K(x,a(y,z,u)) \ 1.
R(x,y,L(z,u,w) \ v5) = R(x,y,z \ v5).
R(x,y,z \ u) = R(x,y,L(z,w,v5) \ u).
R(x,y,z \ (L(z,u,w) * v5)) = R(x,y,v5).
R(x,y,z \ (u \ (u * (L(z,u,w) * v5)))) = R(x,y,v5).
R(x,y,z) = R(x,y,u \ (w \ (w * (L(u,w,v5) * z)))).
R(x,y,(z * u) \ (z * (L(u,z,w) * v5))) = R(x,y,v5).
R(x,y,z) = R(x,y,(u * w) \ (u * (L(w,u,v5) * z))).
R(x,y,(z * u) \ (w \ ((w * z) * (L(u,z,w) * v5)))) = R(x,y,v5).
L(T(x,a(y,z,u)),w,v5) \ (K(L(x,w,v5),a(y,z,u)) * x) = a(v5,w,x).
(x \ y) * T(a(z,u,w),y) = x \ (a(z,u,w) * y).
(x \ y) * (a(z,u,w) * K(a(z,u,w),y)) = x \ (a(z,u,w) * y).
x \ (a(y,z,u) * w) = (x \ w) * (a(y,z,u) * K(a(y,z,u),w)).
((x \ y) * a(z,u,w)) * K(a(z,u,w),y) = x \ (a(z,u,w) * y).
T(L(x,y,z),a(u,w,v5)) \ (K(L(x,y,z),a(u,w,v5)) * x) = a(z,y,x).
K(x,a(y,z,u)) * x = T(x,a(y,z,u)).
T(x,a(y,z,u)) / x = K(x,a(y,z,u)).
L(K(x,a(y,z,u)),x,1 / x) = T(x,a(y,z,u)) / x.
L(K(x,a(y,z,u)),w,v5) = K(x,a(y,z,u)).
(a(x,y,z) * u) \ (u * (a(x,y,z) * a(a(x,y,z),u,a(x,y,z)))) = K(a(x,y,z) * u,a(x,y,z)).
(x * (y * z)) \ ((x * y) * T(L(z,y,x),a(u,w,v5))) = L(K(L(z,y,x),a(u,w,v5)),L(z,y,x),x * y).
L(L(K(x,a(y,z,u)),x,w),w * x,v5) = (v5 * (w * x)) \ (v5 * (w * T(x,a(y,z,u)))).
(x * (y * z)) \ (x * (y * T(z,a(u,w,v5)))) = L(L(K(z,a(u,w,v5)),z,y),y * z,x).
T(x,a(y,z,u)) \ R(x,K(x,a(y,z,u)),K(x,a(y,z,u)) \ 1) = K(x,a(y,z,u)) \ 1.
L(K(x,a(y,z,u)),x,1 / x) = (1 / x) * T(x,a(y,z,u)).
(1 / x) * T(x,a(y,z,u)) = L(K(x,a(y,z,u)),x,1 / x).
x \ T(x,a(y,z,u)) = K(x,a(y,z,u)).
x * K(x,a(y,z,u)) = T(x,a(y,z,u)).
T(x,a(y,z,u)) = x * K(x,a(y,z,u)).
a(x,y,z) * K(a(x,y,z),u) = T(a(x,y,z),u).
T(a(x,y,z),u) = a(x,y,z) * K(a(x,y,z),u).
a(x,y,z) \ (u * a(x,y,z)) = u * K(u,a(x,y,z)).
(x * y) * K(z,a(u,w,v5)) = x * (y * K(z,a(u,w,v5))).
x * (y * K(z,a(u,w,v5))) = (x * y) * K(z,a(u,w,v5)).
R(x,y,K(z,a(u,w,v5))) = x.
x = R(x,y,K(z,a(u,w,v5))).
R(x,y,K(z,z \ a(u,w,v5))) = x.
x = R(x,y,K(z,z \ a(u,w,v5))).
R(x,y,T(z,z \ a(u,w,v5)) / z) = x.
x = R(x,y,T(z,z \ a(u,w,v5)) / z).
(x \ (y * a(z,u,w))) * K(a(z,u,w),y) = x \ (a(z,u,w) * y).
x \ (a(y,z,u) * w) = (x \ (w * a(y,z,u))) * K(a(y,z,u),w).
x \ (a(y,z,u) * x) = a(y,z,u) * K(a(y,z,u),x).
(x * y) * K(a(z,u,w),v5) = x * (y * K(a(z,u,w),v5)).
x * (y * K(a(z,u,w),v5)) = (x * y) * K(a(z,u,w),v5).
R(x,y,K(a(z,u,w),v5)) = x.
x = R(x,y,K(a(z,u,w),v5)).
R(x,y,T(z,z \ a(u,w,v5)) * (z \ a(u,w,v5))) = x.
R(x,y,(z \ a(u,w,v5)) * z) = x.
x = R(x,y,(z \ a(u,w,v5)) * z).
R(x,y,a(z,u,w) \ T(a(z,u,w),v5)) = x.
R(x,y,(a(z,u,w) \ v5) \ v5) = x.
R(x,y,T(a(z,u,w),v5)) = x.
R(x,y,L(T(a(z,u,w),v5),y,x)) = x.
x * (y * a(z,u,T(x,y))) = (x * a(z,u,x)) * y.
x * T(y * a(z,u,y),x) = y * (x * a(z,u,T(y,x))).
x * T(T(y * a(z,u,y),x),T(y,x)) = y * (x * a(z,u,T(y,x))).
x * T(T(y,x) * a(z,u,T(y,x)),T(y,x)) = y * (x * a(z,u,T(y,x))).
x * T(T(y,x) * a(z,u,T(y,x)),T(y,x)) = (y * x) * a(z,u,T(y,x)).
(x * (y * (z * u))) \ (x * (y * (z * R(u,w,w \ 1)))) = L(a(u,w,w \ 1),y * (z * u),x).
L(a(x,y,y \ 1),z * (u * x),w) = (w * (z * (u * x))) \ (w * (z * (u * R(x,y,y \ 1)))).
(x * (y * (z * u))) \ (x * ((y * z) * R(L(u,z,y),w,w \ 1))) = a(L(u,z,y),w,w \ 1).
(x * (y * z)) \ (x * (y * R(z,u,u \ 1))) = a(z,u,u \ 1).
(x * (y * z)) \ (x * (y * R(z,u,u \ 1))) = L(a(z,u,u \ 1),y * z,x).
L(a(x,y,y \ 1),z * x,u) = (u * (z * x)) \ (u * (z * R(x,y,y \ 1))).
a(x,y,R(T(z,u * w),z \ u,w)) = a(x,y,w \ ((z \ u) \ (u * w))).
a(x,y,R(T(z,u * w),z \ u,w)) = a(x,y,((z \ u) * w) \ (u * w)).
a(x,y,T(z,u * (w * z))) = a(x,y,T(z,u * w)).
a(x,y,T(z,u * (w * z))) = a(x,y,L(T(z,u * w),w,u)).
a(x,y,L(T(z,u * w),w,u)) = a(x,y,T(z,u * (w * z))).
a(x,y,T(L(z,u,w),w * u)) = a(x,y,T(z,w * (u * z))).
a(x,y,L(T(z,u * (w * z)),w,u)) = a(x,y,T(L(z,w,u),u * w)).
L(x \ (L(y,z,u) \ w),x,y) = ((y * x) \ w) * a(u,z,T(y,w)).
L(R(x / L(x,y,z),L(x,y,z),L(x,y,z) \ u),w,v5) = L((u * a(z,y,T(x,u))) / u,w,v5).
x \ (y * (L(y,z,u) \ w)) = (x \ w) * a(u,z,T(y,w)).
x * a(y,z,T(u,x)) = u * (L(u,z,y) \ x).
a(x,y,T(z,L(z,u,w) \ v5)) = a(x,y,T(z,v5)).
a(x,y,T(z,L(z,u,w) \ v5)) = a(x,y,L(T(z,v5),u,w)).
a(x,y,T(z,L(z,u,w) \ v5)) = a(x,y,T(L(z,u,w),v5)).
a(x,y,T(z,L(z,u,w) \ v5)) = a(x,y,v5 \ (L(z,u,w) * v5)).
R(x,y,z) / a(u,w,x) = L(R(x,y,z),w,u).
L(R(x,y,z),u,w) = R(x,y,z) / a(w,u,x).
L(x * (x \ R(x,y,z)),u,w) = R(x,y,z) / a(w,u,x).
((x * y) * z) / a(u,w,T(x,(x * y) * z)) = L(x,w,u) * (y * (z * a(x,y,z))).
L(x,y,z) * (x \ R(x,u,w)) = R(x,u,w) / a(z,y,x).
R(x,y,z) / a(u,w,x) = L(x,w,u) * (x \ R(x,y,z)).
x / a(y,z,T(u,x)) = L(u,z,y) * (u \ x).
a(x,y,T(L(z,u,w),w * (u * z))) = a(x,y,T(L(z,u,w),w * u)).
a(x,y,T(R(z,z \ u,w),u * w)) = a(x,y,((z \ u) * w) \ (u * w)).
a(x,y,(a(z,u,w) / w) * v5) = a(x,y,L(w,u,z) \ v5).
a(x,y,T(z,z \ u)) = a(x,y,T(z,u)).
a(x,y,T(z,u)) = a(x,y,T(z,z \ u)).
a(x,y,T(z,u * z)) = a(x,y,T(z,u)).
a(x,y,T(z,L(z,u,w) \ v5)) = a(x,y,(L(z,u,w) \ v5) \ v5).
a(x,y,(L(z,u,w) \ v5) \ v5) = a(x,y,T(z,L(z,u,w) \ v5)).
a(x,y,T(z / u,z)) = a(x,y,u \ z).
a(x,y,(z \ u) \ w) = a(x,y,u \ (z * w)).
a(x,y,z \ (u * w)) = a(x,y,(u \ z) \ w).
a(x,y,(1 / z) * u) = a(x,y,z \ u).
a(x,y,T(z,z * u)) = a(x,y,T(z,u)).
a(x,y,(z * u) \ w) = a(x,y,u \ (z \ w)).
a(x,y,L(z,u,w)) = a(x,y,z).
a(x,y,z) = a(x,y,L(z,u,w)).
(x * (y * L(z,u,w))) \ (x * (y * z)) = a(w,u,z).
a(x,y,L(z,y,x)) = (u * (w * L(z,y,x))) \ (u * (w * z)).
(x * (y * L(z,u,w))) \ (x * (y * z)) = a(w,u,L(z,u,w)).
L(a(x,y,z) \ u,a(x,y,z),L(z,y,x)) = z \ (L(z,y,x) * u).
L(a(x,y,z) \ u,a(x,y,L(z,y,x)),L(z,y,x)) = z \ (L(z,y,x) * u).
x * L(y,a(z,u,x),L(x,u,z)) = L(x,u,z) * (a(z,u,x) * y).
L(x,y,z) * (a(z,y,x) * u) = x * L(u,a(z,y,x),L(x,y,z)).
L(x,y,z) * (a(z,y,L(x,y,z)) * u) = x * L(u,a(z,y,x),L(x,y,z)).
x * L(y,a(z,u,x),L(x,u,z)) = L(x,u,z) * (a(z,u,L(x,u,z)) * y).
x * a(y,z,T(u,L(u,z,y) \ x)) = u * (L(u,z,y) \ x).
a(x,y,z) * ((a(x,y,z) \ u) \ (u / a(x,y,z))) = (a(x,y,z) \ u) \ u.
(x \ y) / a(z,u,w) = x \ (y / a(z,u,w)).
x \ (y / a(z,u,w)) = (x \ y) / a(z,u,w).
x \ (y * (a(z,u,w) \ 1)) = (x \ y) / a(z,u,w).
(L(x,y,z) \ u) * T(x,L(x,y,z) \ u) = u * a(z,y,T(x,L(x,y,z) \ u)).
((x * a(y,z,u)) * w) / (u * w) = R(x / L(u,z,y),u,w).
R(x / L(y,z,u),y,w) = ((x * a(u,z,y)) * w) / (y * w).
(x / L(y,z,u)) * y = x * a(u,z,y).
x / (a(y,z,u) \ 1) = (x / L(u,z,y)) * u.
L(a(x,y,z) \ 1,u,w) = a(x,y,z) \ 1.
a(x,y,a(z,u,w) \ 1) = 1.
(x * (y / a(z,u,w))) \ (x * (y / a(z,u,w))) = a(x,y,a(z,u,w) \ 1).
(x * (y / a(z,u,w))) \ ((x * y) / a(z,u,w)) = a(x,y,a(z,u,w) \ 1).
L(x * (y \ R(y,z,u)),w,v5) = L(x,w,v5) * (y \ R(y,z,u)).
(x * y) \ (x * (y * (z * (u \ R(u,w,v5))))) = L(z,y,x) * (u \ R(u,w,v5)).
(x * y) \ (x * ((y * z) * (u \ R(u,w,v5)))) = L(z,y,x) * (u \ R(u,w,v5)).
(x * (y * L(z,u,w))) \ (x * (y * z)) = a(w,u,L(z,y,x)).
a(x,y,L(L(z,u,w),y,x)) = (w * (u * L(z,y,x))) \ (w * (u * z)).
R(x / L(y,z,u),L(y,z,u),y \ 1) = x * (y \ a(u,z,y)).
R(x / L(y,z,u),L(y,z,u),y \ 1) = x * ((y \ 1) * a(u,z,y)).
x / a(y,z,T(u,u \ x)) = L(u,z,y) * (u \ x).
(x * y) \ ((x * (y * z)) * (u \ R(u,w,v5))) = L(z,y,x) * (u \ R(u,w,v5)).
(x * y) * (z \ R(z,u,w)) = x * (y * (z \ R(z,u,w))).
x * (y * (z \ R(z,u,w))) = (x * y) * (z \ R(z,u,w)).
R(x,y,z \ R(z,u,w)) = x.
R(x,y,z * (z \ (u \ R(u,z,w)))) = x.
x = R(x,y,z * (z \ (u \ R(u,z,w)))).
R(x,y,z * ((u * z) \ R(u,z,w))) = x.
R(x,y,z * (u * (u \ ((w * z) \ R(w,z,u))))) = x.
x = R(x,y,z * (u * (u \ ((w * z) \ R(w,z,u))))).
R(x,y,(z * u) * (u \ ((w * z) \ R(w,z,u)))) = x.
L(T(x,a(y,z,x)),z,y) = a(y,z,x) \ x.
((x * y) * z) / a(u,w,R(T(x,y * z),y,z)) = (y * z) * L((y * z) \ ((x * y) * z),w,u).
x \ (y / a(z,u,x \ y)) = L(x \ y,u,z).
(L(x,y,z) * u) \ T(x * u,(x * u) / (L(x,y,z) * u)) = ((x * u) * a(z,y,T(x,u))) / (x * u).
R((x * y) / (L(x,z,u) * y),L(x,z,u) * y,a(u,z,T(x,y))) = (L(x,z,u) * y) \ T(x * y,(x * y) / (L(x,z,u) * y)).
L(x,L(y,z,u) \ 1,L(y,z,u)) \ (y * ((L(y,z,u) \ 1) * x)) = a(u,z,T(y,(L(y,z,u) \ 1) * x)).
R(x,y,z * ((u * w) \ v5)) = R(x,y,z * (w \ (u \ v5))).
(x \ y) * L(T(x,x \ y),z,u) = y / a(u,z,T(x,x \ y)).
x / a(y,z,u \ x) = u * L(u \ x,z,y).
x * L(x \ y,z,u) = y / a(u,z,x \ y).
R(x / L(y,z,u),L(y,z,u),y \ 1) = (x * (y \ 1)) * a(u,z,y).
(x / y) * L(y,z,u) = x / a(u,z,y).
x / a(y,z,u) = (x / u) * L(u,z,y).
(L(x,y,z) * u) \ (x * u) = a(z,y,T(x,u)).
a(x,y,T(z,u)) = (L(z,y,x) * u) \ (z * u).
(x * L(y,z,u)) \ (x * y) = a(u,z,y).
a(x,y,z) = (u * L(z,y,x)) \ (u * z).
L(T(x,a(y,z,x)),z,y) = a(y,z,L(x,z,y)) \ x.
a(x,y,z) = z * (L(z,y,x) \ 1).
x * (L(x,y,z) \ 1) = a(z,y,x).
a(x,y,L(z,y,x)) = a(x,y,z).
R(x,y,z * L(u,w,v5)) = R(x,y,z * u).
x * (y / a(z,u,x * y)) = L(x * y,u,z).
L(x * y,z,u) = x * (y / a(u,z,x * y)).
a(x,y,z) / z = 1 / L(z,y,x).
1 / L(x,y,z) = a(z,y,x) / x.
a(x,y,z) = L(z,y,x) \ z.
L(x,y,z) \ x = a(z,y,x).
L(x,y,z) = x / a(z,y,x).
x / (y \ L(y,z,u)) = x * a(u,z,y).
x / L(a(y,z,u) \ 1,u,x / L(u,z,y)) = (x / L(u,z,y)) * u.
L(x,y,z) = x * (a(z,y,x) \ 1).
x * (a(y,z,x) \ 1) = L(x,z,y).
a(x,y,z) \ 1 = z \ L(z,y,x).
x \ L(x,y,z) = a(z,y,x) \ 1.
L(x \ L(x,y,z),u,w) = x \ L(x,y,z).
R(x,y,(z * u) * (((w * z) * u) \ R(w,z,u))) = x.
R(x,y,z * (u \ (u / z))) = x.
R(x,y,1 \ (z * (u \ (u / z)))) = x.
x = R(x,y,1 \ (z * (u \ (u / z)))).
R(x,y,(z \ 1) \ (u \ (u / z))) = x.
(x * y) * (z \ L(z,u,w)) = x * (y * (z \ L(z,u,w))).
x * (y * (z \ L(z,u,w))) = (x * y) * (z \ L(z,u,w)).
R(x,y,z \ L(z,u,w)) = x.
R(x,y,z \ (L(z,u,w) * 1)) = x.
x = R(x,y,z \ (L(z,u,w) * 1)).
R(x,y,(L(z,u,w) \ z) \ 1) = x.
R(x,y,a(z,u,w) \ 1) = x.
(x * (y / a(z,u,w))) / (y / a(z,u,w)) = R(x,y,a(z,u,w) \ 1).
T(x,y) * a(z,u,T(x,y)) = T(x * a(z,u,x),y).
(a(x,y,z) \ 1) \ L((1 / a(x,y,z)) * u,w,v5) = a(x,y,z) * L(a(x,y,z) \ u,w,v5).
(1 / x) \ L((1 / x) * y,z,u) = x * L(x \ y,z,u).
(1 / x) \ L(1 \ ((1 / x) * y),z,u) = x * L(x \ y,z,u).
(x * (y / a(z,u,w))) / (y * (a(z,u,w) \ 1)) = R(x,y,a(z,u,w) \ 1).
(x * (L(x,y,z) * (u * w))) \ (L(x,y,z) * ((x * u) * w)) = a(x,u,w).
(x * (y * (z * u))) \ (x * ((y * z) * u)) = a(y,z,u).
R(x,y,z \ (u \ ((u * w) * v5))) = R(x,y,z \ (w * v5)).
R(x,y,z \ (u \ ((u * w) * v5))) = R(x,y,(z \ (w * v5)) * a(u,w,v5)).
R(x,y,z \ (u \ ((u * w) * v5))) = R(x,y,z \ (w * (v5 * a(u,w,v5)))).
R(x,y,z \ (u * (w * a(v5,u,w)))) = R(x,y,z \ (v5 \ ((v5 * u) * w))).
x / a(y,z,L(u,z,y)) = (x / u) * L(u,z,y).
L(x \ L(x,y,z),x,z * y) = a(z,y,x) \ 1.
((x * y) * z) \ (x * (y * z)) = a(x,y,z) \ 1.
(x * a(y,z,u)) \ x = a(y,z,u) \ 1.
x / (a(y,z,u) \ 1) = x * a(y,z,u).
R(x,a(y,z,u),a(y,z,u) \ 1) = x.
R(x,a(y,z,u),a(y,z,u) \ 1) = x / 1.
x / 1 = R(x,a(y,z,u),a(y,z,u) \ 1).
R(x,y,(z * u) \ (w \ ((w * z) * (L(u,z,w) * v5)))) = R(x,y,L(v5,L(u,z,w),w * z)).
R(x,y,L(z,L(u,w,v5),v5 * w)) = R(x,y,(w * u) \ (v5 \ ((v5 * w) * (L(u,w,v5) * z)))).
R(x,y,K(z,z \ u)) = R(x,y,K(z,u)).
R(x,y,z \ (u \ (z * u))) = R(x,y,K(z,z \ u)).
R(x,y,z * (u \ a(w,v5,v6))) = R(x,y,z / u).
R(x,y,z * ((u \ 1) * a(w,v5,v6))) = R(x,y,z / u).
R(x,y,K(z,u) \ 1) = R(x,y,K(u,z)).
R(x,y,K(z,u)) = R(x,y,K(u,z) \ 1).
R(x,y,T(z,u) / z) = R(x,y,K(z,u)).
R(x,y,z \ T(z,u)) = R(x,y,K(z,u)).
R(x,y,a(z,u,w) \ T(a(z,u,w),v5)) = R(x,y,T(a(z,u,w),v5)).
R(x,y,(z \ u) \ w) = R(x,y,(u \ z) * w).
R(x,y,(z * u) \ ((z * w) * v5)) = R(x,y,u \ (w * (v5 * a(z,w,v5)))).
R(x,y,z \ ((z \ u) \ u)) = R(x,y,K(z,z \ u)).
R(x,y,K(z,z \ u)) = R(x,y,z \ ((z \ u) \ u)).
R(x,y,z \ (u \ (z * u))) = R(x,y,K(z,u)).
R(x,y,K(z,u)) = R(x,y,z \ (u \ (z * u))).
R(x,y,z \ ((u \ w) \ v5)) = R(x,y,z \ (w \ (u * v5))).
R(x,y,z \ (u \ (w * v5))) = R(x,y,z \ ((w \ u) \ v5)).
R(x,y,(z * (u \ 1)) * a(w,v5,v6)) = R(x,y,z / u).
R(x,y,T(z,u) / z) = R(x,y,z \ T(z,u)).
R(x,y,(z * u) \ (u * z)) = R(x,y,K(z,u) \ 1).
R(x,y,z * (u \ 1)) = R(x,y,z / u).
R(x,y,z * (u / a(w,v5,v6))) = R(x,y,z * u).
R(x,y,(z \ u) \ w) = R(x,y,u \ (z * w)).
R(x,y,z \ (u * w)) = R(x,y,(u \ z) \ w).
R(x,y,(1 / z) * u) = R(x,y,z \ u).
R(x,y,z \ (z / u)) = R(x,y,u \ 1).
R(x,y,(z * u) \ w) = R(x,y,u \ (z \ w)).
R(x,y,z \ L(u,w,v5)) = R(x,y,z \ u).
R(x,y,z \ u) = R(x,y,z \ L(u,w,v5)).
R(x,y,L(z,u,w)) = R(x,y,z).
R(x,y,z) = R(x,y,L(z,u,w)).
R(x,y,z \ (u * w)) = R(x,y,(z \ u) * w).
R(x,y,R(z,u,u \ 1)) = R(x,y,z).
R(x,y,(z * u) * w) = R(x,y,z * (u * w)).
R(x,y,z / a(u,w,v5)) = R(x,y,z).
R(x,y,z) = R(x,y,z / a(u,w,v5)).
R(x,y,z * a(u,w,v5)) = R(x,y,z).
R(x,y,z) = R(x,y,z * a(u,w,v5)).
L(x * a(y,z,u),w,v5) = L(x,w,v5) * a(y,z,u).
R(x,y,z) * (y * (z * a(u,w,v5))) = (x * y) * (z * a(u,w,v5)).
a(x,y,L(T(z,u),y,x)) = (L(z,y,x) * u) \ (z * u).
L(a(x,y,L(z,y,x)),u * L(z,y,x),w) = (w * (u * L(z,y,x))) \ (w * (u * z)).
a(x,y,L(L(z,u,w),y,x)) = ((w * u) * L(L(z,u,w),y,x)) \ (w * (u * z)).
a(x,y,L(T(z,u),y,x)) = (u * L(T(z,u),y,x)) \ (z * u).
a(x,y,L(z,y,x)) = (u * L(z,y,x)) \ (u * z).
(x * L(y,z,u)) \ (x * y) = a(u,z,L(y,z,u)).
(x * y) \ (x * (y * (z * a(u,w,v5)))) = L(z,y,x) * a(u,w,v5).
L(T(x,y),y,(y * x) / y) = T(x,y * x).
T(x,y * x) = L(T(x,y),y,(y * x) / y).
L(T(x,y),y,(y * x) / y) = (y * x) \ (x * (y * x)).
(x * y) \ (y * (x * y)) = L(T(y,x),x,(x * y) / x).
R(x,y,z) * ((y * z) * a(u,w,v5)) = (x * y) * (z * a(u,w,v5)).
R(x / L(y,z,u),L(y,z,u),y \ 1) = (x * (y \ 1)) / (y \ L(y,z,u)).
L(x,y,z) * (x \ 1) = x \ L(x,y,z).
x \ L(x,y,z) = L(x,y,z) * (x \ 1).
x * (L(x,y,z) \ 1) = L(x,y,z) \ x.
L(x,y,z) \ x = x * (L(x,y,z) \ 1).
x \ (L(x,y,z) * u) = L(x,y,z) * (x \ u).
L(x,y,z) \ (x * u) = x * (L(x,y,z) \ u).
x * (L(x,y,z) * (u * (w * a(x,u,w)))) = L(x,y,z) * ((x * u) * w).
L(x,y,z) * ((x * u) * w) = x * (L(x,y,z) * (u * (w * a(x,u,w)))).
x * (L(x,y,z) * (x \ u)) = L(x,y,z) * u.
L(x,y,z) * u = x * (L(x,y,z) * (x \ u)).
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).
x * (y * L(T(x,y),z,u)) = L(x,z,u) * (x * y).
(1 / x) * T(x,y) = T(x,y) / x.
(1 / x) * T((1 / x) \ 1,y) = T(x,y) / x.
T(x,y) / x = (1 / x) * T((1 / x) \ 1,y).
T(1 / (1 / x),y) * (1 / x) = T(x,y) / x.
T(1 / (1 / x),y) * (1 / x) = T(x / 1,y) / x.
T(x / 1,y) / x = T(1 / (1 / x),y) * (1 / x).
L(L(a(x,y,y \ 1),x,z),z * x,u) = (u * (z * x)) \ (u * (z * R(x,y,y \ 1))).
(x * (y * z)) \ (x * (y * R(z,u,u \ 1))) = L(L(a(z,u,u \ 1),z,y),y * z,x).
L(T(x,a(y,z,L(x,z,y))),z,y) = a(y,z,L(x,z,y)) \ x.
T(a(x,y,z),u / a(x,y,z)) = T(a(x,y,z),u).
x / L(a(y,z,L(u,z,y)),L(u,z,y),x / u) = (x / u) * L(u,z,y).
(x \ L(y,z,u)) * a(u,z,L(y,z,u)) = x \ y.
x \ y = (x \ L(y,z,u)) * a(u,z,L(y,z,u)).
T(x,y) * a(z,u,L(T(x * a(z,u,x),y),u,z)) = T(x * a(z,u,x),y).
L(a(x,y,L(z,y,x)) \ u,a(x,y,L(z,y,x)),L(z,y,x)) = z \ (L(z,y,x) * u).
x * L(y,a(z,u,L(x,u,z)),L(x,u,z)) = L(x,u,z) * (a(z,u,L(x,u,z)) * y).
T(L(x,y,z),a(z,y,L(x,y,z))) = a(z,y,L(x,y,z)) \ x.
L(a(x,y,L(z,y,x)),L(z,y,x),u) = (u * L(z,y,x)) \ (u * z).
a(x,y,L(z,y,x)) = L(z,y,x) \ z.
L(x,y,z) \ x = a(z,y,L(x,y,z)).
L(x,y,z) * a(z,y,L(x,y,z)) = x.
L(x,y,z) * a(z,y,L(x,y,z)) = y \ (y * x).
L(R(x / y,y,y \ z),u,w) = L((x * (y \ z)) / z,u,w).
L((x * (y \ z)) / z,u,w) = L(R(x / y,y,y \ z),u,w).
L(R(x,x \ y,z),u,w) = L((y * z) / ((x \ y) * z),u,w).
L((x * y) / ((z \ x) * y),u,w) = L(R(z,z \ x,y),u,w).
x \ T(y,y / x) = (y * (x \ y)) / y.
R(x / y,y,y \ x) = y \ T(x,x / y).
(x * y) \ (x * ((y * z) * a(u,w,v5))) = L(z,y,x) * a(u,w,v5).
(x / y) * a(x / y,y,x / y) = R(x / y,y,y \ x).
R(x / y,y,y \ x) = (x / y) * a(x / y,y,x / y).
R(x,y,T(x,y)) = x * a(x,y,x).
x \ T(y * x,y) = R(y,x,T(y,x)).
R(x,y,T(x,y)) = y \ T(x * y,x).
T(T(x * y,x) / y,y) = R(x,y,T(x,y)).
((x * y) * x) / (x * y) = T(x * y,x) / y.
T(x * y,x) / y = ((x * y) * x) / (x * y).
T(x,y) / (y \ x) = (x * y) / x.
T(x,y) = ((x * y) / x) * (y \ x).
((x * y) / x) * (y \ x) = T(x,y).
((x * y) / x) * (y \ x) = T(x,x \ (x * y)).
(x / y) * ((y \ x) \ y) = T(y,y \ x).
(x / y) * ((y \ x) \ y) = T(y,T(x / y,y)).
x * (T(x,y) \ y) = T(y,T(x,y)).
T(x,y) \ (x * z) = x * (T(x,y) \ z).
T(x,y) \ (x * (T(x,y) * z)) = x * z.
T(x,y) * (x * z) = x * (T(x,y) * z).
x * (T(x,y) * z) = T(x,y) * (x * z).
x * (y * T(T(x,y),z)) = T(x,z) * (x * y).
(1 / x) \ L(((1 / x) * x) \ ((1 / x) * y),z,u) = x * L(x \ y,z,u).
R(x,y,L(T(a(z,u,w),v5),y,x)) = (x * (y * T(a(z,u,w),v5))) / (y * T(a(z,u,w),v5)).
(x * (y * T(a(z,u,w),v5))) / (y * T(a(z,u,w),v5)) = R(x,y,L(T(a(z,u,w),v5),y,x)).
L((L(x,y,z) \ u) \ u,L(x,y,z) \ u,x) = L(T(x,x * (L(x,y,z) \ u)),y,z).
(((x * y) / x) * x) \ (y * (x * y)) = L(T(y,x),x,(x * y) / x).
((x * y) / x) * (y * x) = y * (x * y).
R(T(x,(x \ y) * z),x \ y,z) = ((x \ y) * z) \ (y * z).
((x \ y) * z) \ (y * z) = R(T(x,(x \ y) * z),x \ y,z).
((x \ y) * z) * a(x,x \ y,z) = x \ (y * z).
T(a(x,y,z),u / a(x,y,z)) = T((u / a(x,y,z)) \ u,u).
T(x / (x / a(y,z,u)),x) = a(y,z,u).
((x * y) / x) * (y * x) = (y * x) * L(y,x,y).
(x * y) * L(x,y,x) = ((y * x) / y) * (x * y).
T((x * y) / x,y * x) = L(y,x,y).
(x * y) * L(T(x,x * y),z,u) = x * (y * L(T(x,y),z,u)).
x * T(T(y,x) * a(z,u,T(y,x)),T(y,x)) = (y * x) * L(a(z,u,T(y,x)),T(y,x),x).
(x * y) * L(a(z,u,T(x,y)),T(x,y),y) = y * T(T(x,y) * a(z,u,T(x,y)),T(x,y)).
(x * y) \ ((z * x) * y) = R(T(z,x * y),x,y).
R(T(x,y * z),y,z) = (y * z) \ ((x * y) * z).
T(((x * y) * x) / (x * y),y) = R(x,y,T(x,y)).
R(x,y,T(x,y)) = T(((x * y) * x) / (x * y),y).
x * a(x,y,y \ 1) = R(x,y,y \ 1).
x \ R(x,y,y \ 1) = a(x,y,y \ 1).
x \ ((x * y) * (y \ 1)) = a(x,y,y \ 1).
x \ (y * (z * a(u,w,v5))) = (x \ (y * z)) * a(u,w,v5).
R(x,y,z) / (R(T(x,a(u,w,v5)),y,z) / a(u,w,v5)) = a(u,w,v5).
a(x,y,z) * (((a(x,y,z) \ u) \ u) / a(x,y,z)) = (a(x,y,z) \ u) \ u.
L(x,y,z) * a(z,y,L(x,y,z)) = y \ (z \ (z * (y * x))).
x \ (y \ (y * (x * z))) = L(z,x,y) * a(y,x,L(z,x,y)).
(x \ y) * (z * a(x,x \ y,z)) = x \ (y * z).
x \ (y * z) = (x \ y) * (z * a(x,x \ y,z)).
x \ (y \ ((y * x) * z)) = z * a(y,x,z).
T(T(x * a(y,z,x),u),T(x,u)) = T(x * a(y,z,x),u).
(x / y) * a(x / y,y,x / y) = y \ T(x,x / y).
x \ T(y,y / x) = (y / x) * a(y / x,x,y / x).
x \ T(y * x,y) = y * a(y,x,y).
T(x * a(y,z,x),x) = x * a(y,z,x).
L(T(x * a(y,z,x),u),z,y) = T(x,u).
L(x * a(y,z,x),z,y) = x.
x \ ((x * y) * z) = y * (z * a(x,y,z)).
x * (y * a(y,x,y)) = T(y * x,y).
T(x * y,x) = y * (x * a(x,y,x)).
x * (y * (z * a(x,y,z))) = (x * y) * z.
x \ (y * a(z,u,w)) = (x \ y) * a(z,u,w).
(x * a(y,z,u)) / w = x / (w / a(y,z,u)).
x / (y / a(z,u,w)) = (x * a(z,u,w)) / y.
(x / a(y,z,u)) / w = x / (w * a(y,z,u)).
x * ((y * z) * a(x,y,z)) = (x * y) * z.
R(x,y,z) * ((y * z) * a(u,w,v5)) = ((x * y) * z) * a(u,w,v5).
((x * y) * z) * a(u,w,v5) = R(x,y,z) * ((y * z) * a(u,w,v5)).
R(x,y,a(z,u,w)) = x.
x = R(x,y,a(z,u,w)).
x * (y * z) != (u * y) * z | x = R(u,y,z).
(x * y) / a(z,u,w) = x * (y / a(z,u,w)).
(x * y) * T(T(x,x * y),z) = x * (y * T(T(x,y),z)).
R(x,x \ y,a(z,u,w) \ 1) \ (y * (a(z,u,w) \ 1)) = (x \ y) / a(z,u,w).
R(x,x \ (y * z),K(z,y)) \ (z * y) = (x \ (y * z)) * K(z,y).
T(x / ((1 / x) * x),y) / x = T(1 / (1 / x),y) * (1 / x).
R(L(x / y,z,u),y,y \ w) = L((x * (y \ w)) / w,z,u).
L(x,y / x,y / (y / x)) = T(y / (y / x),y).
L(x \ y,x,y / x) = T(y / x,y).
T(x / y,x) = L(y \ x,y,x / y).
R(x,1 / y,y) / y = x * (1 / y).
(x * (1 / y)) * y = R(x,1 / y,y).
R(x,1 / y,y) = (x * (1 / y)) * y.
R(x / y,y,y \ 1) = x * (y \ 1).
x * (y \ 1) = R(x / y,y,y \ 1).
(x * y) \ R(x,y,y \ 1) = y \ 1.
R(x,y,y \ 1) / (y \ 1) = x * y.
((x * a(y,z,u)) / a(y,z,u)) / 1 = R(x,a(y,z,u),a(y,z,u) \ 1).
(x * y) * (y \ 1) = R(x,y,y \ 1).
R(x,y,y \ 1) = (x * y) * (y \ 1).
R(L(x,y,z),x \ u,w) = L((u * w) / ((x \ u) * w),y,z).
L(x \ y,x,1 / x) = (1 / x) * y.
(1 / x) * y = L(x \ y,x,1 / x).
(1 / x) \ L(y,x,1 / x) = x * y.
(1 / x) * (x * y) = L(y,x,1 / x).
L(x,y,1 / y) = (1 / y) * (y * x).
((x * y) / a(z,u,w)) / (y * (a(z,u,w) \ 1)) = R(x,y,a(z,u,w) \ 1).
R(x,y,a(z,u,w) \ 1) = ((x * y) / a(z,u,w)) / (y * (a(z,u,w) \ 1)).
(x * (y / a(z,u,w))) \ ((x * y) * (a(z,u,w) \ 1)) = a(x,y,a(z,u,w) \ 1).
a(x,y,a(z,u,w) \ 1) = (x * (y / a(z,u,w))) \ ((x * y) * (a(z,u,w) \ 1)).
x * (a(y,z,u) \ 1) = x / a(y,z,u).
1 / a(x,y,z) = a(x,y,z) \ 1.
a(x,y,z) \ 1 = 1 / a(x,y,z).
(a(x,y,z) / u) \ 1 = u / a(x,y,z).
1 / (x / a(y,z,u)) = a(y,z,u) / x.
a(x,y,z) / u = 1 / (u / a(x,y,z)).
a(x,y,z) / (u * a(x,y,z)) = 1 / u.
(1 / x) \ a(y,z,u) = x * a(y,z,u).
x * a(y,z,u) = (1 / x) \ a(y,z,u).
(x \ 1) * a(y,z,u) = x \ a(y,z,u).
x \ a(y,z,u) = (x \ 1) * a(y,z,u).
x \ L(y,x \ 1,x) = (x \ 1) * y.
x * ((x \ 1) * y) = L(y,x \ 1,x).
L(x,y \ 1,y) = y * ((y \ 1) * x).
T((x * y) / x,y * x) = (L(y,x,y) * x) / x.
(L(x,y,x) * y) / y = T((y * x) / y,x * y).
(x * T(y,z)) / x = T((x * y) / x,z).
(x * T(x \ y,z)) / x = T(y / x,z).
T(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(x,L(x,y,z)) = x.
x * T(y,y * x) = L(y,x,y) * x.
L(x,y,z) * x = x * L(x,y,z).
x * L(x,y,z) = L(x,y,z) * x.
x * L(R(T(y,x),z,u),w,v5) = L(R(y,z,u),w,v5) * x.
x * (1 / a(y,z,u)) = x / a(y,z,u).
x / a(y,z,u) = x * (1 / a(y,z,u)).
(x * y) / L(z,y / z,x) = x * (y / z).
x / L(y \ z,y,x / z) = (x / z) * y.
L(L(T(x,y),z,u),y,x) = L(T(x,x * y),z,u).
L(T(x,x * y),z,u) = L(L(T(x,y),z,u),y,x).
L(T(T(x,y),z),y,x) = T(T(x,x * y),z).
L(T(x,y),y,x) = T(x,x * y).
R(x * y,L(z,y,x),u) \ ((x * (y * z)) * u) = L(z,y,x) * u.
R(x,y,K(y,x)) \ (y * x) = y * K(y,x).
R(x,x \ y,z) \ (y * z) = (x \ y) * z.
T(x / (y * x),z) = R(T(1 / y,z),y,x).
R(T(1 / x,y),x,z) = T(z / (x * z),y).
R(x / (y / z),y / z,z) = (x * z) / y.
R((x / y) / z,z,y) = x / (z * y).
R(x / y,y,y \ z) = (x * (y \ z)) / z.
R(1 / x,x,y) = y / (x * y).
L(R(x,y,z),u,w) * (y * z) = (L(x,u,w) * y) * z.
((x * y) * z) \ (R(x,y,z) * ((y * z) * u)) = L(u,y * z,R(x,y,z)).
L(x,y * z,R(u,y,z)) = ((u * y) * z) \ (R(u,y,z) * ((y * z) * x)).
x / L(y,1 / y,x) = x * (1 / y).
x / L(y \ 1,y,x) = x * y.
L(x \ 1,x,y / x) = y \ (y / x).
L(L(x \ y,x,z),z * x,u) = (u * (z * x)) \ (u * (z * y)).
L(x \ L(y,z,u),x,u * z) = ((u * z) * x) \ (u * (z * y)).
(x * y) / L(z \ y,z,x) = x * z.
L(L(x \ y,z,u),x,w) = L((w * x) \ (w * y),z,u).
L((x * y) \ (x * z),u,w) = L(L(y \ z,u,w),y,x).
L(x \ (y * x),x,y) = T(y,y * x).
T(x,x * y) = L(y \ (x * y),y,x).
(x * (y * (z * u))) \ (x * ((y * z) * u)) = L(a(y,z,u),y * (z * u),x).
L(a(x,y,z),x * (y * z),u) = (u * (x * (y * z))) \ (u * ((x * y) * z)).
L(x \ y,x,z / y) = ((z / y) * x) \ z.
L(x \ y,x,z / x) = z \ ((z / x) * y).
L(x \ (y \ z),x,y) = (y * x) \ z.
L((x \ y) \ z,x \ y,x) = y \ (x * z).
L(x \ 1,x,y) = (y * x) \ y.
(x * y) * a(z,u,w) = x * (y * a(z,u,w)).
(x * y) * L(z,T(x,y),y) = y * (T(x,y) * z).
(x * y) * L(L(z,y,x),u,w) = x * (y * L(z,u,w)).
L(x,y,z) \ (z * (y * x)) = T(z * y,L(x,y,z)).
T(x * y,L(z,y,x)) = L(z,y,x) \ (x * (y * z)).
(x * (y * z)) / (y * L(z,y,x)) = R(x,y,L(z,y,x)).
R(x,y,L(z,y,x)) = (x * (y * z)) / (y * L(z,y,x)).
(x * (y * z)) \ (x * (y * (z * u))) = L(L(u,z,y),y * z,x).
L(L(x,y,z),z * y,u) = (u * (z * y)) \ (u * (z * (y * x))).
(x * (y * z)) \ ((x * y) * (L(z,y,x) * u)) = L(u,L(z,y,x),x * y).
L(x,L(y,z,u),u * z) = (u * (z * y)) \ ((u * z) * (L(y,z,u) * x)).
(x * y) * z != x * (y * u) | L(u,y,x) = z.
x * (y * z) != (x * y) * u | L(z,y,x) = u.
T(T((x \ y) \ y,z),x) = T(T(x,x \ y),z).
T(x / y,z) * y = y * T(y \ x,z).
x * T(x \ y,z) = T(y / x,z) * x.
L(R(a(x,y,z),u,w),v5,v6) = R(a(x,y,z),u,w).
R(a(x,y,z),u,w) = L(R(a(x,y,z),u,w),v5,v6).
L(T(a(x,y,z),u),w,v5) = T(a(x,y,z),u).
x / L(T(y,L(y,z,u) \ x),z,u) = L(y,z,u) \ x.
L(T(x,L(x,y,z) \ u),y,z) = (L(x,y,z) \ u) \ u.
(x * ((x \ y) \ y)) / x = (x \ y) \ y.
T(x,(x \ y) \ y) = x.
K(x,(x \ y) \ y) = 1.
(R(x,y,z) * u) / R(T(x,u),y,z) = u.
x / T(y,y \ x) = y \ x.
K(x / y,y \ x) = 1.
K(x,T(x,y)) = 1.
T(T(T(x,y),z),x) = T(T(x,y),z).
T(T(x,y),z) = T(T(T(x,y),z),x).
T(x,T(x,y)) = x.
T(T(x / y,z),y) = T(y \ x,z).
T(x \ y,z) = T(T(y / x,z),x).
(x * y) \ ((z * x) * y) = T(R(z,x,y),x * y).
T(R(x,y,z),y * z) = (y * z) \ ((x * y) * z).
x * R(T(y,x),z,u) = R(y,z,u) * x.
x * L(T(y,x),z,u) = L(y,z,u) * x.
x * T(T(y,x),z) = T(y,z) * x.
T(x,y) \ (x * y) = T(y,T(x,y)).
T(x,T(y,x)) = T(y,x) \ (y * x).
((x * y) * T(z,y)) / (z * y) = R(x,y,T(z,y)).
R(x,y,T(z,y)) = ((x * y) * T(z,y)) / (z * y).
(x * y) \ (x * (z * y)) = L(T(z,y),y,x).
L(T(x,y),y,z) = (z * y) \ (z * (x * y)).
x * y != z * x | T(z,x) = y.
x * y != y * z | T(x,y) = z.
R(x,y,z) \ ((x * y) * z) = y * z.
(x * y) / T(x,y) = y.
(x * y) / K(x,y) = y * x.
T(T(x,y),x) = T(x,y).
T(x,y) = T(T(x,y),x).
L(a(x,y,z),u,w) = a(x,y,z).
T(T(T(x,y),z),u) = T(T(T(x,u),y),z).
T(T(T(x,y),z),u) = T(T(T(x,z),u),y).
T(x / y,y) = y \ x.
T(x,x \ y) = (x \ y) \ y.
x * T(y,x) = y * x.
T(x,x) = x.
((x * (y / z)) * z) / y = R(x,y / z,z).
R(x,y / z,z) = ((x * (y / z)) * z) / y.
R(x / y,y,z) = (x * z) / (y * z).
R(x,y,z) * (y * z) = (x * y) * z.
((x * y) * (y \ z)) / z = R(x,y,y \ z).
R(x,y,y \ z) = ((x * y) * (y \ z)) / z.
R(x,x \ y,z) = (y * z) / ((x \ y) * z).
x \ ((x / y) * (y * z)) = L(z,y,x / y).
L(x,y,z / y) = z \ ((z / y) * (y * x)).
L(x \ y,x,z) = (z * x) \ (z * y).
x \ (y * ((y \ x) * z)) = L(z,y \ x,y).
L(x,y \ z,y) = z \ (y * ((y \ z) * x)).
(x * y) * L(z,y,x) = x * (y * z).
((x \ y) * x) \ y = K(x,x \ y).
K(x,x \ y) = ((x \ y) * x) \ y.
(x * y) * K(y,x) = y * x.
(x * y) \ ((x * z) * (z \ y)) = a(x,z,z \ y).
a(x,y,y \ z) = (x * z) \ ((x * y) * (y \ z)).
(x * (y * z)) * a(x,y,z) = (x * y) * z.
x * y != z | z / y = x.
x != y * z | x / z = y.
x * 1 != y | x = y.
x * y != z | x \ z = y.
x != y * z | y \ x = z.
(x / y) \ x = y.
x / (y \ x) = y.
x / 1 = x.
x \ x = 1.
1 \ x = x.
a(a(c1,c2,c3),c4,c5) != 1.
a(x,y,a(z,u,w)) = 1.
L(L(x,y,z),u,w) = L(L(x,u,w),y,z).
R(L(x,y,z),u,w) = L(R(x,u,w),y,z).
L(R(x,y,z),u,w) = R(L(x,u,w),y,z).
R(T(x,y),z,u) = T(R(x,z,u),y).
T(R(x,y,z),u) = R(T(x,u),y,z).
L(T(x,y),z,u) = T(L(x,z,u),y).
T(L(x,y,z),u) = L(T(x,u),y,z).
T(T(x,y),z) = T(T(x,z),y).
K(x,y) != 1 | T(x,y) = x.
T(x,y) != x | K(x,y) = 1.
T(x,y) != x | T(y,x) = y.
L(x,y,z) != x | a(z,y,x) = 1.
a(x,y,z) != 1 | L(z,y,x) = z.
T(x,y) = y \ (x * y).
x \ (y * x) = T(y,x).
R(x,y,z) = ((x * y) * z) / (y * z).
((x * y) * z) / (y * z) = R(x,y,z).
L(x,y,z) = (z * y) \ (z * (y * x)).
(x * y) \ (x * (y * z)) = L(z,y,x).
K(x,y) = (y * x) \ (x * y).
(x * y) \ (y * x) = K(y,x).
a(x,y,z) = (x * (y * z)) \ ((x * y) * z).
(x * (y * z)) \ ((x * y) * z) = a(x,y,z).
x * y != z * y | x = z.
x * y != x * z | y = z.
x * y != z | u * y != z | u = x.
(x / y) * y = x.
(x * y) / y = x.
x * (x \ y) = y.
x \ (x * y) = y.
x * 1 = x.
1 * x = x.
a(a(x,y,z),u,w) = 1.

end_of_list.
