% ********************************************************* % AIM: LC => aK1 % ********************************************************* assign(order,kbo). set(lex_order_vars). set(para_from_small). clear(back_demod). set(restrict_denials). assign(max_weight,5). formulas(assumptions). % loop axioms 1 * x = x. x * 1 = x. x \ (x * y) = y. x * (x \ y) = y. (x * y) / y = x. (x / y) * y = x. % cancellation laws x * y = u & x * z = u -> y = z. y * x = u & z * x = u -> y = z. % other form x * y = x * z -> y = z. y * x = z * x -> y = z. % useful in demodulation free runs x != y | z * x = z * y. x != y | x * z = y * z. % associator (right associated * a = left associated) (x * (y * z)) \ ((x * y) * z) = a(x,y,z) # label("associator"). % commutator ( (x * y) * K(y,x) = y * x ) (x * y) \ (y * x) = K(y,x) # label("commutator"). % inner mappings (y * x) \ (y * (x * u)) = L(u,x,y). ((u * x) * y) / (x * y) = R(u,x,y). x \ (u * x) = T(u,x). % obvious compatibility a(x,y,z) = 1 -> L(z,y,x) = z. L(x,y,z) = x -> a(z,y,x) = 1. T(x,y) = x -> T(y,x) = y. T(x,y) = x -> K(x,y) = 1. K(x,y) = 1 -> T(x,y) = x. % abelian inner mapping group T(T(u,x),y) = T(T(u,y),x). T(L(u,x,y),z) = L(T(u,z),x,y). T(R(u,x,y),z) = R(T(u,z),x,y). L(R(u,x,y),z,w) = R(L(u,z,w),x,y). L(L(u,x,y),z,w) = L(L(u,z,w),x,y). R(R(u,x,y),z,w) = R(R(u,z,w),x,y). % ------------ % Special Case % ------------ (x * (x * y)) * z = x * (x * (y * z)) # label("LC"). end_of_list. formulas(goals). a(K(x,y),z,u) = 1 # label("aK1"). 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 * u != z | u = y. x * y != z | u * y != z | u = x. x * y != x * z | y = z. x * y != z * y | x = z. x != y | z * x = z * y. x != y | x * z = y * z. (x * (y * z)) \ ((x * y) * z) = a(x,y,z). (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). 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. 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 \ (y * z))) = z. (x * (x \ 1)) * y = y. x * (y * (y \ 1)) = x. x * (y * (y \ (x \ z))) = z. x / x = 1. x / 1 = x. x * (((x \ y) * z) / z) = y. x / (y \ x) = y. (x / y) \ x = y. (x \ (x * (y / z))) * z = y. x != y | 1 * z != y | z = x. x != y | z * u != y | u = z \ x. x != y | z * u != y | z \ x = u. x != y | z * u != y | z = x / u. x != y | z * u != y | x / u = z. x != 1 * y | x = y. 1 * x != y | y = x. 1 * x != y | x = y. x != x * y | 1 = y. x * y != x | 1 = y. x != y * z | y \ x = z. x * y != z | x \ z = y. x * y != ((x * z) / u) * u | y = z. ((x * y) / z) * z != x * u | u = y. x * 1 != y | x = y. x * (y \ z) != z | x = y. x != y * z | x / z = y. x * y != z | z / y = x. x * y != ((z * y) / u) * u | x = z. ((x * y) / z) * z != u * y | u = x. x * (y * (y \ z)) = x * z. ((x / y) * y) * z = x * z. (x * (x \ y)) * z = y * z. (x * (y * z)) * a(x,y,z) = (x * y) * z. (x * ((x \ y) * z)) \ (y * z) = a(x,x \ y,z). (x * y) \ ((x * (y / z)) * z) = a(x,y / z,z). (x * y) * K(y,x) = y * x. x \ ((y \ x) * y) = K(y \ x,y). (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 * (y / z)) \ (x * y) = L(z,y / z,x). L(x,y / x,z) = (z * (y / x)) \ (z * y). (x * y) / ((z \ x) * y) = R(z,z \ x,y). R(x,x \ y,z) = (y * z) / ((x \ 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). ((x * (y / z)) * z) / y = R(x,y / z,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 * y != z | x = z / y. x * (x * y) = (x * (x * (y * z))) / z. (x * (x * (y * z))) / z = x * (x * y). x * y != z | y = x \ z. x = (y * (y * z)) \ (y * (y * (z * x))). (x * (x * y)) \ (x * (x * (y * z))) = 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 != y | z != y | z = x. x != y | x = (y / z) * z. (x * y) / y = (x / z) * z. x != y | x = z * (z \ y). x * 1 = y * (y \ x). x * (x \ y) = y * 1. (x * (x * y)) / z = x * (x * (y / z)). L(x \ 1,x,y) = (y * x) \ y. L((x \ y) \ z,x \ y,x) = y \ (x * z). L(x \ (y \ z),x,y) = (y * x) \ z. L(x \ y,x,z / x) = z \ ((z / x) * y). L(K(x,y),y * x,z) = (z * (y * x)) \ (z * (x * y)). (x * (y * z)) \ (x * (z * y)) = L(K(z,y),y * z,x). L(L(x,y,z),z * y,u) = (u * (z * y)) \ (u * (z * (y * x))). (x * (y * z)) \ (x * (y * (z * u))) = L(L(u,z,y),y * z,x). L(T(x,y),y,z) = (z * y) \ (z * (x * y)). (x * y) \ (x * (z * y)) = L(T(z,y),y,x). x \ ((x * y) * z) = x * ((x \ y) * z). ((x / y) \ x) * z = y * z. x * ((y / (x \ z)) \ y) = z. R(x,y,z) \ ((x * y) * z) = y * z. R(x,y,y \ z) * z = (x * y) * (y \ z). R(x,y / z,z) * y = (x * (y / z)) * z. (x * y) * z != u * (y * z) | R(x,y,z) = u. (((x * y) * z) * u) / ((y * z) * u) = R(R(x,y,z),y * z,u). L(R(x,y,z),u,w) * (y * z) = (L(x,u,w) * y) * z. R(R(x,y,z),u,w) * (y * z) = (R(x,u,w) * y) * z. R(x,R(y,z,u),z * u) * ((y * z) * u) = (x * R(y,z,u)) * (z * u). x * y != z | ((z / u) * u) / y = x. ((x / y) * y) / z = x / z. x * y != (z / u) \ z | u / y = x. x / 1 = (y / x) \ y. (x / y) \ x = y / 1. x * y != z * (z \ u) | u / y = x. x / 1 = y * (y \ x). x * (x \ y) = y / 1. x * y != 1 * z | z / y = x. x / 1 = 1 * x. x * (y * (y \ z)) = u * (u \ (x * z)). x * (x \ (y * z)) = y * (u * (u \ z)). x * y != z * 1 | z / y = x. x / (y * (y \ 1)) = x. x / 1 != y | y = x. (x / y) \ x != z | z = y. x \ (x * y) != z | z = y. (x * (x * y)) \ (x * (x * (y * z))) != u | u = z. L(L(x,y,z),z * y,z) = x. L(L(x,y,z),z * y,z) != u | u = x. L(L(x,y * z,y),z,y) = x. L(L(x,y * z,y),z,y) != u | u = x. x * y != z * (u * (u \ w)) | (z * w) / y = x. (x * y) / L(z \ y,z,x) = x * z. x * y != (z / u) * u | z / y = x. x / L(y,z,x / (z * y)) = (x / (z * y)) * z. (x * (y * z)) / L(z,y,x) = x * y. x * y != z * (u * w) | x \ ((z * u) * L(w,u,z)) = y. x \ ((x * y) * L(z,y,x)) = y * z. x * L(y,z \ x,z) = z * ((z \ x) * y). x * (y * z) != (x * y) * u | L(z,y,x) = u. (x * y) * z != x * (y * u) | L(u,y,x) = z. (x * y) * L(z,y,x) != x * u | y * z = u. (x * (y * z)) \ ((x * y) * (L(z,y,x) * u)) = L(u,L(z,y,x),x * y). ((x * (y * z)) * u) / (L(z,y,x) * u) = R(x * y,L(z,y,x),u). ((x * (y * z)) * L(u,z,y)) / (y * (z * u)) = R(x,y * z,L(u,z,y)). (x * y) * T(L(z,y,x),u) = x * (y * T(z,u)). (x * y) * R(L(z,y,x),u,w) = x * (y * R(z,u,w)). (x * y) * L(L(z,y,x),u,w) = x * (y * L(z,u,w)). L(L(x,y,z) \ u,L(x,y,z),z * y) = (z * (y * x)) \ ((z * y) * u). L(x \ L(y,z,u),x,u * z) = ((u * z) * x) \ (u * (z * y)). x * ((x \ 1) * y) = L(y,x \ 1,x). L(L(x,y \ z,y),z,y) = x. L(L(x,y,z / y),z,z / y) = x. L(x,y * z,y) = L(x,y \ z,y). L(x,y \ z,y) = L(x,y * z,y). x * L(y,z * x,z) = z * ((z \ x) * y). x * y != z * (u * (u \ w)) | x \ (z * w) = y. x \ (y * z) = L((y \ x) \ z,y * x,y). L((x \ y) \ z,x * y,x) = y \ (x * z). (x * y) \ (x * (y * z)) != u | u = L(z,y,x). (x * y) \ (x * (y * z)) != u | L(z,y,x) = u. x \ (y * ((y \ x) * z)) != u | u = L(z,y \ x,y). x \ (y * ((y \ x) * z)) != u | L(z,y \ x,y) = u. (x * y) \ (x * z) != u | L(y \ z,y,x) = u. (R(x,y,z) * y) \ ((x * y) * z) != u | L(z,y,R(x,y,z)) = u. (x * (y * z)) \ (x * (y * (z * u))) != w | L(L(u,z,y),y * z,x) = w. x != (y / z) * z | x = y. x * T(y / x,x) = y. x != y * (y \ z) | x = z. (x \ y) * T(x,x \ y) = y. x / T(y,y \ x) = y \ x. (x * y) / T(x,y) = y. x * y != z * u | (u * T(z,u)) / y = x. (x * T(y,x)) / x = y. 1 * x != y * 1 | x = y. T(x,1) = x. x * y != (x * z) * u | y = x * ((x \ z) * u). T(x * y,x) = x * ((x \ y) * x). x * ((x \ y) * x) = T(x * y,x). T((x * y) / x,x) = y. x * y != z | y * u != z | u = T(x,y). x * y != z | y * u != z | T(x,y) = u. x * y != y * z | T(x,y) = z. x * y != z * x | T(z,x) = y. (x * (y * z)) \ ((x * z) * T(y,z)) = a(x,z,T(y,z)). (x * (T(y,x) * z)) \ ((y * x) * z) = a(x,T(y,x),z). (x * (y * T(z,x * y))) \ (z * (x * y)) = a(x,y,T(z,x * y)). (x * y) \ (y * (T(x,y) * z)) = L(z,T(x,y),y). ((x * y) * z) / (T(x,y) * z) = R(y,T(x,y),z). ((x * y) * T(z,y)) / (z * y) = R(x,y,T(z,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. L(T(x,y) \ z,T(x,y),y) = (x * y) \ (y * z). R(x,y,T(z,y)) * (z * y) = (x * y) * T(z,y). (x * y) * L(z,T(x,y),y) = y * (T(x,y) * z). x \ (y * x) != z | z = T(y,x). x \ (y * x) != z | T(y,x) = z. (x * y) \ (x * (z * y)) != u | L(T(z,y),y,x) = u. x \ T(x * y,x) = (x \ y) * x. x * y != z * ((z \ u) * z) | x \ T(z * u,z) = y. x \ T(y * x,y) = L(y,y * x,y). L(x,x * y,x) = y \ T(x * y,x). x \ T(y,x) = (x \ (x \ y)) * x. (x \ (x \ y)) * x = x \ T(y,x). (x * (x * (y * z))) \ (x * (x * (y * (z * u)))) = L(u,z,x * (x * y)). (x * (x * y)) \ (x * (x * z)) = y \ z. x != (y * (y * (z * u))) \ (y * (y * (z * (u * w)))) | x = L(w,u,y * (y * z)). (x * y) \ (x * (y * z)) = L(z,y,u * (u * x)). L(x,y,z * (z * u)) = (u * y) \ (u * (y * x)). (x * y) \ (x * (x * z)) = (x \ y) \ z. x != (y * z) \ (y * (z * u)) | x = L(u,z,y). 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 \ 1) = L(x,y,z). x != (y * z) \ (y * u) | x = L(z \ u,z,y). (x \ y) \ z = L(y \ (x * z),y,x). L(x \ (y * z),x,y) = (y \ x) \ z. x != y \ (z * y) | x = T(z,y). (x \ y) \ y = T(x,x * y). T(x,x * y) = (x \ y) \ y. (x * y) \ (x * x) = (x \ y) \ 1. x \ (y * (y * z)) = (y \ (y \ x)) \ z. (x \ (x \ y)) \ z = y \ (x * (x * z)). (x * y) \ (x * z) = (x \ y) \ (x \ z). (x \ y) \ (x \ z) = (x * y) \ (x * z). (x * y) \ ((x * z) * u) = (x \ y) \ ((x \ z) * u). (x \ y) \ ((x \ z) * u) = (x * y) \ ((x * z) * u). (x \ y) * T(x,x * y) = y. (x \ y) * ((x \ y) * (T(x,x * y) * z)) = ((x \ y) * y) * z. ((x * y) * z) * a(R(x,y,z),y,z) = (R(x,y,z) * y) * z. (x * (y * z)) \ ((x * y) * z) != u | u = a(x,y,z). (x * (y * z)) \ ((x * y) * z) != u | a(x,y,z) = u. (x * (y * (z * u))) \ (x * ((y * z) * u)) != w | L(a(y,z,u),y * (z * u),x) = w. ((x / y) * (y * z)) \ (x * z) != u | a(x / y,y,z) = u. (x * y) / L(z,y / z,x) = x * (y / z). (x \ (y * z)) \ ((x \ y) * z) != u | a(x,y,z) = u. L(x \ y,x,y) = (y \ x) \ 1. L(x \ y,x,z) = (z \ x) \ (z \ y). L((x * y) \ z,x * y,x) = y \ (x \ z). L(x,y * z,y) = z \ (y \ ((y * z) * x)). x \ (y \ ((y * x) * z)) = L(z,y * x,y). L(x \ (y \ z),x,y) != u | u = (y * x) \ z. L(x \ (y \ z),x,y) != u | (y * x) \ z = u. T(x,y) = T(T(x,y),x). T(T(x,y),x) = T(x,y). T(L(x,y,z),x) = L(x,y,z). x != R(y,z,u) * (z * u) | x = (y * z) * u. (x * y) * R(T(z,x * y),x,y) = (z * x) * y. x * y != R(z,u,w) * (u * w) | x \ ((z * u) * w) = y. (x * y) \ ((z * x) * y) = R(T(z,x * y),x,y). R(x,y,z) * u != u * w | R(T(x,u),y,z) = w. 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). T(x,R(x,y,z)) = x. x != y | x = (y * z) / z. x / (y \ x) = (y * z) / z. (x * y) / y = z / (x \ z). x / T(y,y * x) = y \ x. (x \ y) / L(z \ y,z,x) = x \ z. x / (y / ((z \ x) \ y)) = z. (x * y) / z = x * (x * ((x \ y) / z)). x * (x * ((x \ y) / z)) = (x * y) / z. x * (x * y) = (x * z) / (y \ (x \ z)). (x * y) / (z \ (x \ y)) = x * (x * z). L(x,y,(z * (z * u)) * (z * w)) = L(x,y,u \ (z \ w)). L(x,y,z * (z * (u * (z * w)))) = L(x,y,u \ (z \ w)). x != L(y,z,u * (u * w)) | x = L(y,z,w). L(x,y,z \ (u \ w)) = L(x,y,z * (u * w)). x != L(y,z,u \ w) | x = L(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 \ 1)) = L(x,y,z * u). 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 * w) * v5)) = L(x,y,z * ((u \ w) * v5)). L(x,y,z * ((u \ w) * v5)) = L(x,y,z * ((u * w) * v5)). T((x \ y) \ 1,z) = L(T(y \ x,z),y,x). L(T(x \ y,z),x,y) = T((y \ x) \ 1,z). R(1 / x,x,y) = y / (x * y). R(x / y,y,x \ z) = z / (y * (x \ z)). R(x / y,y,y \ z) = (x * (y \ z)) / z. R((x / y) / z,z,y) = x / (z * y). R(x / (y / z),y / z,z) = (x * z) / y. T((x * y) / (z * y),u) = R(T(x / z,u),z,y). R(x / y,y,z) \ (x * z) = y * z. R(R(x,y,z) / u,u,y * z) = ((x * y) * z) / (u * (y * z)). R(x / R(y,z,u),R(y,z,u),z * u) = (x * (z * u)) / ((y * z) * u). R(R(x / y,y,z),y * z,u) = ((x * z) * u) / ((y * z) * u). T(x,y) = T(T((z * x) / z,y),z). T(T((x * y) / x,z),x) = T(y,z). x * R(y,z,u) = R((x * y) / x,z,u) * x. R((x * y) / x,z,u) * x = x * R(y,z,u). T(x \ y,z) = T(T(y / x,z),x). T(T(x / y,z),y) = T(y \ x,z). T(R(x / y,z,u),y) = R(y \ x,z,u). 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 * (x \ y) != z | z = y. (x * y) * L(z,y,x) != u | u = x * (y * z). (x * y) * L(z,y,x) != u | x * (y * z) = u. x * T(y,x) != z | z = y * x. x * T(y,x) != z | y * x = z. (x / y) * y != z | z = x. R(x,y,z) * (y * z) != u | u = (x * y) * z. R(x,y,z) * (y * z) != u | (x * y) * z = u. x * T(x,y) = T(x,y) * x. T(x,y) * x = x * T(x,y). x * T(y,z) = T((x * y) / x,z) * x. T((x * y) / x,z) * x = x * T(y,z). 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). T(x,y) * (x \ z) = (x \ z) * T((x \ z) \ z,y). (x \ y) * T((x \ y) \ y,z) = T(x,z) * (x \ y). T(T(x,y),x \ z) = T((x \ z) \ z,y). x != 1 \ y | x = y. K(x \ 1,x) = (x \ 1) * x. (x \ 1) * x = K(x \ 1,x). (x * y) \ ((x \ (x * y)) * x) = K(y,x). x * K(y \ x,y) = (y \ x) * y. x * K(x \ 1,x) = T(x * 1,x). x != y \ ((z \ y) * z) | x = K(z \ y,z). K(x,y) = K(y \ (y * x),y). K(x \ (x * y),x) = K(y,x). K(x,y) = K(z \ (z * x),y). K(x \ (x * y),z) = K(y,z). K((x / y) \ x,z) = K(y,z). (x * x) * y = x * (x * y). x != y * R(T(z,y),u,w) | x = R(z,u,w) * y. x * (x * R(T(y,x * x),z,u)) = R(y,z,u) * (x * x). x != y * T(z,y) | x = z * y. x * (x * T(y,x * x)) = y * (x * x). x * y != z * T(u,z) | x \ (u * z) = y. x \ (y * (x * x)) = x * T(y,x * x). x * (y * z) != (u * y) * z | x = R(u,y,z). x = R(x,x,y). R(x,x,y) = x. x != R(L(y,z,u),w,v5) | x = L(R(y,w,v5),z,u). 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). T(x,y) = R(T(x,y),x,z). R(T(x,y),x,z) = T(x,y). 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,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). R(x,y,z) * u != x * R(x,y,z) | u = x. (R(x,y,z) \ x) * R(x,y,z) = x. x / R(x,y,z) = R(x,y,z) \ x. x != L(y \ z,y,z) | x = (z \ y) \ 1. 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,K(z,y)) * (z * y) = (x * (y * z)) * K(z,y). (x * y) * L(z,K(x,y),y * x) = (y * x) * (K(x,y) * z). (x * (y * z)) * K(L(z,y,x),x * y) = L(z,y,x) * (x * y). (x * y) \ (y * x) != z | z = K(y,x). (x * y) \ (y * x) != z | K(y,x) = z. x * y != (x * z) * K(z,x) | T(z,x) = y. (x * y) * K(y,x) != x * z | T(y,x) = z. x * (y * T(z,x * y)) = L(z,y,x) * (x * y). (x * y) * T((x * y) \ (x * z),u) = x * (y * T(y \ z,u)). ((x / y) * y) * z != u | u = x * z. ((x / y) * y) * z != u | x * z = u. (x * y) / y != z | z = x. x / (y \ x) != z | z = y. ((x * y) * z) / (y * z) != u | u = R(x,y,z). ((x * y) * z) / (y * z) != u | R(x,y,z) = u. (x * T(y,x)) / x != z | z = y. L(T(x,y),y,x) = T(x,x * y). x \ (y * y) = (y \ (y \ x)) \ 1. (x \ (x \ y)) \ 1 = y \ (x * x). (x \ y) * z != y | T(x,x \ y) = z. T(x,x \ y) = T(x,x * y). ((x \ y) * (T(x,x * y) * z)) \ (y * z) = a(x \ y,T(x,x * y),z). T(x,y) * (x * z) = (T(x,y) * x) * z. (T(x,y) * x) * z = T(x,y) * (x * z). 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). L(x,y,T(y,z)) = x. L(x,(y * z) / y,z) = x. (x * T(y,z)) / x = T((x * y) / x,z). x * T(T(y,x),z) != u | T(y,z) * x = u. x * T(x \ (y * x),z) != u | T(y,z) * x = u. K(x,y) / T(y * x,x * y) = (y * x) \ K(x,y). x != (y * (y * z)) / u | x = y * (y * (z / u)). 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(L(x,y * z,z * y),K(y,z),z * y) = x. (x * (x * y)) \ z = y \ (x \ (x \ z)). L(x \ y,x,z) != u | (z * x) \ (z * y) = u. L(x,y,z) != u | (z * y) \ (z * (y * x)) = u. L(L(x,y,z),z * y,u) != w | (u * (z * y)) \ (u * (z * (y * x))) = w. R(x,x \ y,z) \ (y * z) = (x \ y) * z. R(x * y,L(z,y,x),u) \ ((x * (y * z)) * u) = L(z,y,x) * u. x != T(y / z,z) | x = z \ y. R(T(x / y,y * z),y,z) = (y * z) \ (x * z). T((x * y) / z,u) = R(T(x / (z / y),u),z / y,y). R(T(x / (y / z),u),y / z,z) = T((x * z) / y,u). T((x * y) / (z * y),u) * (z * y) = (T(x / z,u) * z) * y. T(((x * y) * z) / (x * z),x) = R(y,x,z). T((x * y) / (z * y),z) = R(z \ x,z,y). x != T((y * z) / y,u) * y | x = y * T(z,u). (T((x * y) / x,z) * x) * y = (x * y) * T(y,z). (x * y) * x = (y * x) * T(x,y). (x * y) * T(y,x) = (y * x) * y. (x * T(y,z)) * y = (x * y) * T(y,z). x * T(y,x / y) = (y * (x / y)) * y. (x * (y / x)) * x = y * T(x,y / x). (x * y) * z != (u * x) * y | T(R(u,x,y),x * y) = z. T(R(x,y,x),y * x) = T(x,y). x != (y * z) * u | x = R(y,z,u) * (z * u). (x * y) * T(y,x) = R(y,x,y) * (x * y). R(x,y,x) * (y * x) = (y * x) * T(x,y). x * y = ((x / T(y,z)) * y) * T(y,z). ((x / T(y,z)) * y) * T(y,z) = x * y. (x * T(y,z)) \ ((x * y) * T(y,z)) = y. x * T(y,z) = ((x / y) * T(y,z)) * y. ((x / y) * T(y,z)) * y = x * T(y,z). T(x,y) * z != (u * T(x,y)) * x | T(u * x,T(x,y)) = z. T(T(x,y) * x,T(x,y)) = T(x,y) * x. (x * (y \ z)) * (z / y) = (x * (z / y)) * T(z / y,y). (x * (y / z)) * T(y / z,z) = (x * (z \ y)) * (y / z). x * y != T(x * z,x) | y = (x \ z) * x. x = (T(x,y) \ x) * T(x,y). (T(x,y) \ x) * T(x,y) = x. R(x,y,x) * (y * x) = (x * T(y,x)) * T(x,y). (x * T(y,x)) * T(x,y) = R(x,y,x) * (y * x). x * K(x \ 1,x) = T(x,x). x != T(y,y) | x = y. x * K(x \ 1,x) = x. 1 = K(x \ 1,x). K(x \ 1,x) = 1. x != 1 | x = K(y \ 1,y). K(x \ 1,x) = K(y \ 1,y). x != K(y \ 1,y) | x = (y \ 1) * y. 1 = (x \ 1) * x. (x \ 1) * x = 1. x * y != K(z \ 1,z) | 1 / y = x. 1 / x = x \ 1. x * y != K(z \ 1,z) | x \ 1 = y. (x \ 1) \ 1 = x. T(x,x \ 1) = x. K((x \ 1) \ 1,y) = K(x,y). K(x \ 1,y) = K(1 / x,y). K(1 / x,y) = K(x \ 1,y). (x \ R(x,y,z)) \ 1 = R(x,y,z) \ x. T(x,y) = T(T(x,y),x \ 1). T(T(x,y),x \ 1) = T(x,y). x != y * L(z,u * y,u) | x = u * ((u \ y) * z). L(x,y * z,y) * z = y * ((y \ z) * T(x,z)). x * ((x \ y) * T(z,y)) = L(z,x * y,x) * y. x * L(x \ (y * x),z,u) = L(y,z,u) * x. x * L(R(T(y,x),z,u),w,v5) = L(R(y,z,u),w,v5) * x. x * L(x,y,z) = L(x,y,z) * x. L(x,y,z) * x = x * L(x,y,z). x * L(y,z,u) = L((x * y) / x,z,u) * x. L((x * y) / x,z,u) * x = x * L(y,z,u). x * L(x \ y,z,u) = L(y / x,z,u) * x. L(x / y,z,u) * y = y * L(y \ x,z,u). x * R(T(x,y),z,u) = R(T(x,y),z,u) * x. R(T(x,y),z,u) * x = x * R(T(x,y),z,u). x \ (y * z) = x * ((x \ (x \ y)) * z). x * ((x \ (x \ y)) * z) = x \ (y * z). x \ (x \ (y * z)) = (x \ (x \ y)) * z. 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). (x \ (x \ y)) \ (x \ (x \ z)) = y \ z. (x \ y) * ((x * y) \ z) = x \ (x \ z). (x \ (x \ y)) * z != x \ (x \ u) | z = y \ u. (x * (x \ y)) \ z = y \ z. 1 * x != (y * z) * L(u,z,y) | x = y * (z * u). L(x,y,1 / y) = (1 / y) * (y * x). (1 / x) * (x * y) = L(y,x,1 / x). x * y != z * y | x = (z / u) * u. x * y != z * y | (z / u) * u = x. x * y != (z * (z \ 1)) * u | u / y = x. T(x \ 1,y) / (x \ 1) = x * T(x \ 1,y). (x * ((y * z) / y)) * z = (x * (y \ (y * z))) * ((y * z) / y). (x * (y \ (y * z))) * ((y * z) / y) = (x * ((y * z) / y)) * z. (x * y) * ((z * y) / z) = (x * ((z * y) / z)) * y. (x * ((y * z) / y)) * z = (x * z) * ((y * z) / y). x * y != ((z / u) * u) * w | (z * w) / y = x. (x * y) / ((z * y) / z) = (x / ((z * y) / z)) * y. T(x / y,z) * y != u | u = y * T(y \ x,z). T(x / y,z) * y != u | y * T(y \ x,z) = u. T(x / y,y) != z | z = y \ x. T(x / y,y) != z | y \ x = z. T(x,x \ y) != z | (x \ y) \ y = z. x != (y / z) \ y | x = z. 1 / (1 / x) = x. x != y * (z * (z \ u)) | x = y * u. (L(x,y,z) * u) * (u \ w) = L(R(x,u,u \ w),y,z) * w. L(R(x,y,y \ z),u,w) * z = (L(x,u,w) * y) * (y \ z). x != L(T(y,z),u,w) | x = T(L(y,u,w),z). T(x,x * y) = T(L(x,y,x),y). T(L(x,y,x),y) = T(x,x * y). R(T(x,x * y),z,u) = L(R(T(x,y),z,u),y,x). L(R(T(x,y),z,u),y,x) = R(T(x,x * y),z,u). x * T(y,y * x) = L(y,x,y) * x. x * (y * (y \ z)) != u * w | u \ (x * z) = w. x * (y * (y \ z)) != u | u = x * z. x * (y * (y \ z)) != u | x * z = u. (x * x) / (y \ 1) = x * (x * y). L(x \ 1,x,y) != z | (y * x) \ y = z. x != ((y * z) * T(u,z)) / (u * z) | x = R(y,z,T(u,z)). T(((x * y) * x) / (x * y),y) = R(x,y,T(x,y)). (x * (y \ z)) / x = T((x * (z / y)) / x,y). T((x * (y / z)) / x,z) = (x * (z \ y)) / x. x * ((y * (x \ z)) / y) = ((y * (z / x)) / y) * x. ((x * (y / z)) / x) * z = z * ((x * (z \ y)) / x). ((x * (y / z)) / x) \ (z * ((x * (z \ y)) / x)) = z. ((x * y) / x) * (y \ z) = (y \ z) * ((x * ((y \ z) \ z)) / x). (x \ y) * ((z * ((x \ y) \ y)) / z) = ((z * x) / z) * (x \ y). ((x * R(y / z,z,u)) / x) * (z * u) = (z * u) * ((x * ((z * u) \ (y * u))) / x). ((x * (y / z)) / x) * z != u | u = z * ((x * (z \ y)) / x). ((x * (y / z)) / x) * z != u | z * ((x * (z \ y)) / x) = u. (x * x) / y = x * (x * (y \ 1)). x * (x * (y \ 1)) = (x * x) / y. L(x,y,(z * z) / u) = L(x,y,u \ 1). x != L(y,z,u \ 1) | x = L(y,z,u). 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)). (x * y) * R((x * y) \ (x * z),u,w) = x * (y * R(y \ z,u,w)). (x * y) \ (y * T(x,y / x)) = a(x,y / x,x). 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). x != L(L(y,z,u),u * z,u) | x = y. 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). 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. x != L(y \ z,y,u) | x = (u \ y) \ (u \ z). 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 = (x \ L(x,y,z)) \ 1. (x \ L(x,y,z)) \ 1 = L(x,y,z) \ x. x != L(y \ (z * u),y,z) | x = (z \ y) \ 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 = L(x,L(y \ 1,z,u),y). L(x,L(y \ 1,z,u),y) = x. L(x,y,L(y,z,u)) = x. (L(x,y,z) \ x) \ 1 = x \ L(x,y,z). L(x,y \ 1,y) = x. L(x \ L(y \ z,y,u),x,u * y) = ((u * y) * x) \ (u * z). L(x \ L(y \ z,y,u),x,u \ y) = ((u \ y) * x) \ (u \ z). (x * y) * T((x * y) \ z,u) = x * (y * T(y \ (x \ z),u)). (x * y) * R((x * y) \ z,u,w) = x * (y * R(y \ (x \ z),u,w)). (x * y) * R((x * y) \ x,z,u) = x * (y * R(y \ 1,z,u)). T(x,L(x,y,z)) = x. (x * L(x,y,z)) / x != u | u = L(x,y,z). (x * L(x,y,z)) / x != u | L(x,y,z) = u. L(R(x,x,y),z,u) * (x * y) = (x * L(x,z,u)) * y. 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 != L(y,L(z,u,w),z) | x = y. T(x,x * L(x,y,z)) = x. x != T(y,y * z) | x = (y \ z) \ z. x = (x \ L(x,y,z)) \ L(x,y,z). (x \ L(x,y,z)) \ 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 * y != L(x,z,u) | T(x \ L(x,z,u),x) = y. T(x \ L(x,y,z),x) = x \ L(x,y,z). L(x,y,z) / x != u | u = x \ L(x,y,z). L(x,y,z) / x != u | x \ L(x,y,z) = u. x != ((y / z) * z) / u | x = y / u. (x / y) * z = x / L(z \ y,z,x / y). x / L(y \ z,y,x / z) = (x / z) * y. (R(x,y,z) \ u) / (x \ u) = R(x,y,z) \ x. (x * y) / (z \ ((z * x) * y)) = R(z,x,y) \ z. (x * y) / (z * ((z \ x) * y)) = R(z,x,y) \ z. (x * y) / (z * ((z \ y) * T(x,y))) = R(z,y,T(x,y)) \ z. (x * y) / (L(x,z * y,z) * y) = R(z,y,T(x,y)) \ z. L((x \ y) \ 1,x \ y,x) = y \ x. L((x * y) \ x,z,u) = L(L(y \ 1,z,u),y,x). L(L(x \ 1,y,z),x,u) = L((u * x) \ u,y,z). (x * y) * T((x * y) \ x,z) = x * (y * T(y \ 1,z)). L(x,x \ 1,y) = (y * (x \ 1)) \ y. L(x,y \ z,z \ y) = x. T((x \ y) \ 1,y \ x) = (x \ y) \ 1. (x \ 1) / (y \ x) = x \ (x \ y). x = L(x,y \ z,z * y). L(x,y \ z,z * y) = x. L(x,y,y \ 1) = x. ((x \ 1) * x) \ ((x \ 1) * y) = x \ y. 1 \ ((x \ 1) * y) = x \ y. x \ y = (x \ 1) * y. (x \ 1) * y = x \ y. x * y != 1 \ ((z \ 1) * u) | (z \ u) / y = x. (x \ y) / y = x \ 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. T(x \ 1,y) = y \ (x \ y). (x \ 1) * y != z | z = x \ y. (x \ 1) * y != z | x \ y = z. (x * y) / ((z * x) * y) = R(z,x,y) \ 1. x \ T(T(y,x \ 1),z) = T(y,z) * (x \ 1). x \ T(y,x \ 1) = y * (x \ 1). x != y \ (y * z) | x = z. (x \ 1) * (x * y) = y. x * y != z \ (z * u) | x \ u = y. (x \ 1) \ y = x * 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 = (1 / x) \ y. (1 / x) \ y = x * y. (x \ y) * L(z,y,x \ 1) = (x \ 1) * (y * z). (x * (y \ z)) / L(z,y \ 1,x) = x * (y \ 1). (x \ (y * y)) * z = (y \ (y \ x)) \ z. (x \ (x \ y)) \ z = (y \ (x * x)) * z. (R(x,y,z) \ x) * u = (x \ R(x,y,z)) \ u. (x \ R(x,y,z)) \ u = (R(x,y,z) \ x) * u. (L(x,y,z) \ x) * u = (x \ L(x,y,z)) \ u. (x \ L(x,y,z)) \ u = (L(x,y,z) \ x) * u. x * y != (z * u) \ z | x \ L(u \ 1,u,z) = y. (x \ 1) \ L(y \ 1,y,z) = x * ((z * y) \ z). x != (y \ 1) * z | y * x = z. (x \ 1) * y != z | x * z = y. (x * y) / ((z * x) * y) = R(z \ 1,z * x,y). R(x \ 1,x * y,z) = (y * z) / ((x * y) * z). R((x \ 1) / y,y,x * z) = z / (y * (x * z)). (R(x,y,z) \ x) * ((x \ R(x,y,z)) * u) = u. (1 / x) * (x * y) = y. ((x \ y) / y) * (x * z) = 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 * (R(x,y,z) * u) = (x * R(x,y,z)) * u. (x * R(x,y,z)) * u = x * (R(x,y,z) * u). R(x,R(x,y,z),u) = x. x != (y * R(y,z,u)) * w | x = R(y,z,u) * (y * w). x * (R(x,y,z) * u) = R(x,y,z) * (x * u). R(x,y,z) * (x * u) = x * (R(x,y,z) * u). x * y != (z * R(z,u,w)) * v5 | x \ (z * (R(z,u,w) * v5)) = y. R(x,y,z) \ (x * (R(x,y,z) * u)) = x * 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) * w != R(x,y,z) * (x * u) | T(x,R(x,y,z) * u) = w. T(x,R(x,y,z) * (x \ u)) = (R(x,y,z) * (x \ u)) \ (R(x,y,z) * u). (R(x,y,z) * (x \ u)) \ (R(x,y,z) * u) = T(x,R(x,y,z) * (x \ u)). (R(x,y,z) * u) / (R(x,y,z) * (x \ u)) = x. x \ (R(x,y,z) * u) = R(x,y,z) * (x \ u). x * y != R(x,z,u) * w | y = (x \ R(x,z,u)) * w. 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)) * u = R(x,y,z) * (x \ u). (R(x,y,z) * u) / (x * u) = x \ R(x,y,z). x * y != R(z,u,w) * (u * w) | ((z * u) * w) / y = x. ((x * y) * z) / (x * (y * z)) = x \ R(x,y,z). x / (y * (R(y,z,u) \ x)) = y \ R(y,z,u). x * y != z * (z \ u) | x \ u = y. (x \ R(x,y,z)) \ u = x * (R(x,y,z) \ u). x * y != (z \ R(z,u,w)) * (z * v5) | (R(z,u,w) * v5) / y = x. (R(x,y,z) * (x \ u)) / u = x \ R(x,y,z). ((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). x * y != R(z,u,w) * (z \ x) | T(z \ R(z,u,w),x) = y. T(x \ R(x,y,z),u) = u \ (R(x,y,z) * (x \ u)). x \ (R(y,z,u) * (y \ x)) = T(y \ R(y,z,u),x). x \ R(x,y,z) = R(x,y,z) * (x \ 1). R(x,y,z) * (x \ 1) = x \ R(x,y,z). x \ (R(y,z,u) * (y \ x)) != w | T(y \ R(y,z,u),x) = w. T(x \ R(x,y,z),x * (y * z)) = (x * (y * z)) \ ((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(x,y,z)) * (x * u) != w | w = R(x,y,z) * u. (x \ R(x,y,z)) * (x * u) != w | R(x,y,z) * u = w. (x \ R(x,y,z)) * u != w | R(x,y,z) * (x \ u) = w. x != y \ (z \ ((z * y) * u)) | x = L(u,z * y,z). x * (y \ ((y * (x \ 1)) * z)) = L(z,y * (x \ 1),y). (x \ 1) \ 1 != y | x = y. x != (y \ (y \ z)) \ (y \ (y \ u)) | x = z \ u. (x \ (y * y)) * (y \ (y \ z)) = x \ z. x != (y \ (y \ z)) \ u | x = z \ (y * (y * u)). (x \ (y * y)) * z = x \ (y * (y * z)). x \ (y * (y * z)) = (x \ (y * y)) * z. (x \ y) * z != x \ (x \ u) | z = (x * y) \ u. x \ (x \ (y \ z)) = (y * (x * x)) \ z. (x * (y * y)) \ z = y \ (y \ (x \ z)). a(x,y,y) = y \ (y \ (x \ ((x * y) * y))). x \ (x \ (y \ ((y * x) * x))) = a(y,x,x). (x * (y * y)) \ x = y \ (y \ 1). 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). L(x,y,a(z,u,u)) = L(x,y,u * L(u,z * u,z)). L(x,y,z * L(z,u * z,u)) = L(x,y,a(u,z,z)). L(x,y,z * ((z \ u) * u)) = L(x,y,a(z,u,u)). x != L(y,z,u * ((w \ v5) * v6)) | x = L(y,z,u * ((w * v5) * v6)). L(x,y,a(z,u,u)) = L(x,y,z * ((z * u) * u)). L(x,y,z * ((z * u) * u)) = L(x,y,a(z,u,u)). (x \ (y * z)) \ ((x \ y) * z) = a(x \ 1,y,z). a(x,y,z) = a(x \ 1,y,z). a(x \ 1,y,z) = a(x,y,z). a(x \ 1,y,z) != u | a(x,y,z) = u. x \ 1 != y | 1 / x = y. x \ T(x,y) = T(x,y) * (x \ 1). T(x,y) * (x \ 1) = x \ T(x,y). (x / y) * (y / x) = 1. L(x,y,z / u) = L(x,y,u / z). (x \ L(x,y,z)) \ 1 = x / L(x,y,z). (x / y) * z != u | (y / x) \ z = u. (x / y) * z = (y / x) \ z. (x / y) \ z = (y / x) * z. (x / y) * ((y / x) * z) = z. a(x / y,z,u) != w | a(y / x,z,u) = w. x != (y / z) * u | (z / y) * x = u. (x / y) * z != u | (y / x) * u = z. (x / y) \ z != u | u = (y / x) * z. (x / y) \ z != u | (y / x) * z = u. x != (y \ L(y,z,u)) \ 1 | x = L(y,z,u) \ y. x / L(x,y,z) = L(x,y,z) \ x. (L(x,y,z) \ x) * L(x,y,z) = x. T(L(x,y,z),L(x,y,z) \ x) = L(x,y,z). x * (x * (R(x,y,z) \ 1)) = R(x,x * y,z). x != y * (y * (z \ 1)) | x = (y * 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 != (y \ R(y,z,u)) \ 1 | x = R(y,z,u) \ y. x * (R(x,y,z) \ 1) = R(x,y,z) \ x. (R(x,y,z) \ 1) * u != R(x,y,z) \ x | T(x,R(x,y,z) \ 1) = u. T(x,R(x,y,z) \ 1) = x. x * (R(x,y,z) \ x) = R(x,x * y,z). x \ R(x,x * y,z) = R(x,y,z) \ x. x \ R(x,x * y,z) != u | u = R(x,y,z) \ x. x \ R(x,x * y,z) != u | R(x,y,z) \ x = u. x * (R(x,x * y,z) \ x) = R(x,(x * x) * y,z). x != L(y,z,(u * u) / w) | x = L(y,z,w). 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). x / R(x,x * y,z) = x \ R(x,y,z). x != y / R(y,z,u) | x = R(y,z,u) \ y. x \ R(x,y,z) = R(x,x * y,z) \ x. R(x,x * y,z) \ x = x \ R(x,y,z). x * y != R(z,z * u,w) \ z | x \ (z \ R(z,u,w)) = y. x \ (x \ R(x,y,z)) = R(x,x * y,z) \ 1. R(x,x * y,z) \ 1 = x \ (x \ R(x,y,z)). L(x,y,z * (z / y)) = x. x != (y * z) / ((u * y) * z) | x = R(u,y,z) \ 1. 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 * ((x \ (y * y)) * z) = y * (y * z). (((x * y) * x) \ (x * x)) * y != z | K(x,x * y) = z. x * (y * (y * z)) = (x * (y * y)) * z. (x * (y * y)) * z = x * (y * (y * z)). x \ (y * (y * z)) != u | u = (x \ (y * y)) * z. x \ (y * (y * z)) != u | (x \ (y * y)) * z = u. (x * (y * (y * z))) \ ((x * (y * y)) * (z * u)) = L(u,z,x * (y * y)). (x * (y * y)) * z = x * ((y * y) * z). x != L(y,z,u * (w * w)) | x = L(y,z,u). (x * (y * (y * z))) \ ((x * (y * y)) * (z * u)) = L(u,z,x). (x * (y * (y * z))) \ (x * (y * (y * (z * u)))) = L(u,z,x). x != (y * (z * (z * u))) \ (y * (z * (z * (u * w)))) | x = L(w,z * (z * u),y). 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 * y) / z,u) = L(x,z \ 1,u). L(x,y * y,z) = x. R(x,y * y,z) = x. R(x,1,y) = x. R(x,y \ (y \ 1),z) = x. x != L(y,z \ u,u * z) | x = y. L(x,y * z,z * y) = x. L(x,y \ 1,z) = L(x,y,z). (x * (y \ z)) * L(u,y * z,x) = x * ((y \ z) * u). x != L(T(y,z),z,y) | x = T(y,y * 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. (x * y) * z = (y * x) * (K(x,y) * z). (x * y) * (K(y,x) * z) = (y * x) * z. (x * y) * z != (u * x) * L(y,x,u) | T(u,x * y) = z. T(x,y * x) = K(x,y) * L(x,y,x). K(x,y) * L(x,y,x) = T(x,y * x). (x * y) \ z = K(y,x) * ((y * x) \ z). K(x,y) * ((x * y) \ z) = (y * x) \ z. (x * y) * z != (y * x) * y | z = T(y,x). K(x,y) * x = T(x,y). (x * y) * z != (y * x) * (K(x,y) * u) | z = u. K(x,y) * (K(y,x) * z) = z. (x * y) * z != (y * x) * T(x,y) | z = x. K(x,y) * T(y,x) = y. x * y != (z * u) * (K(u,z) * w) | x \ ((u * z) * w) = y. x \ (((y \ x) * y) * z) = K(y \ x,y) * z. K(x,y) * z = K(y,x) \ z. K(x,y) \ z = K(y,x) * z. T(x,K(y,z)) = K(z,y) * (x * K(y,z)). K(x,y) * (z * K(y,x)) = T(z,K(y,x)). x / (K(y,z) * x) = K(z,y). 1 = K(x,y) * K(y,x). K(x,y) * K(y,x) = 1. x * (y * z) != z | x = y \ 1. K(x,y) = K(y,x) \ 1. K(x,y) \ 1 = K(y,x). x != K(y,z) * u | K(z,y) * x = u. K(x,y) * z != u | K(y,x) * u = z. x != y * (K(z,u) * x) | K(u,z) = y. x * (K(y,z) * u) != u | K(z,y) = x. L((K(x,y) * z) \ u,K(x,y) * z,K(y,x)) = z \ (K(y,x) * u). K(x,y) \ z != u | u = K(y,x) * z. K(x,y) \ z != u | K(y,x) * z = u. x / (K(y,z) * x) != u | u = K(z,y). x / (K(y,z) * x) != u | K(z,y) = u. L(x,y,K(z,u)) = L(x,y,K(u,z)). 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 != y \ 1 | x = 1 / y. K(x,y) = 1 / K(y,x). 1 / K(x,y) = K(y,x). 1 / K(x,y) != z | z = K(y,x). 1 / K(x,y) != z | K(y,x) = z. a(K(x,y),z,u) != w | a(K(y,x),z,u) = w. K(x,y) \ 1 != z | K(y,x) = z. 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). x != T(T(y,z),u) | x = T(T(y,u),z). K(T(x,y),z) * T(x,y) = T(T(x,z),y). x != T(L(y,z,u),w) | x = L(T(y,w),z,u). K(L(x,y,z),u) * L(x,y,z) = L(T(x,u),y,z). T(x,y) / x = K(x,y). (x * K(y,z)) \ (x * T(y,z)) = L(y,K(y,z),x). x * (K(y,x) * y) = y * x. T(x,y) * z != K(x,y) * (x * u) | L(u,x,K(x,y)) = z. T(x,y) / x != z | z = K(x,y). T(x,y) / x != z | K(x,y) = z. x * T(y,z) != y | x = T(y,z) \ y. K(x,y) = T(y,x) \ y. T(x,y) \ x = K(y,x). T(x,y) * K(y,x) = x. L(T(x,y),z,u) \ L(x,z,u) = K(y,L(x,z,u)). R(T(x,y),z,u) \ R(x,z,u) = K(y,R(x,z,u)). x / K(y,x) = T(x,y). ((K(x,y) * z) * u) / (K(x,y) * (z * u)) != w | K(y,x) * R(K(x,y),z,u) = w. x != T(x,y) * z | K(y,x) = z. T(x,y) * z != x | K(y,x) = z. T(x,y) \ x != z | z = K(y,x). T(x,y) \ x != z | K(y,x) = z. L(T(x,y),z,u) \ L(x,z,u) != w | K(y,L(x,z,u)) = w. R(T(x,y),z,u) \ R(x,z,u) != w | K(y,R(x,z,u)) = w. K(x,y) * (K(y,x) * z) != u | u = z. K(x,y) * x != z | z = T(x,y). K(x,y) * x != z | T(x,y) = z. x * y != K(z,u) * w | x \ (K(u,z) \ w) = y. x \ (K(y,z) \ x) = T(K(z,y),x). L(K(x,y) * (z \ u),K(y,x),z) != w | (z * K(y,x)) \ u = w. L(x,y / z,u) = L(x,z / y,u). (x * (y \ z)) / L(z,y,x) = x * (y \ 1). L(x,K(y,z),u) = L(x,K(z,y),u). (x * (y \ 1)) * L(z,y,x) = x * (y \ z). (T(x,y) * (x \ 1)) * z = T(x,y) * (x \ z). (x \ T(x,y)) * z = T(x,y) * (x \ z). x != L(y,K(z,u),u * z) | x = y. L(x,K(y,z),y * z) = x. x != K(y,z) \ u | x = K(z,y) * u. R(K(x,y),K(y,x) * z,u) \ K(x,y) = K(y,x) * R(K(x,y),z,u). (R(K(x,y),z,u) \ 1) \ K(y,x) = K(x,y) * R(K(y,x),z,u). x != (y \ 1) \ z | x = y * z. 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). K(x \ 1,y) = x * T(x \ 1,y). x * T(x \ 1,y) = K(x \ 1,y). x != (y \ 1) * z | x = y \ z. (x \ y) * L(z,y,x \ 1) = x \ (y * z). (x \ y) * L(z,y,x) = x \ (y * z). x * y != z \ (u * z) | x \ T(u,z) = y. (x \ y) \ T(y,x) = L(x,y,x). x \ (y * z) != (x \ y) * u | L(z,y,x) = u. (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. T(x,y) \ (x * z) = K(y,x) * z. T(x,y) * (K(y,x) * z) = x * z. T(x,y) \ z = K(y,x) * (x \ z). K(x,y) * (y \ z) = T(y,x) \ z. T(x,y) * (K(y,x) * z) != u | u = x * z. T(x,y) * (K(y,x) * z) != u | x * z = u. T(T(x,y),z) \ x = K(z,T(x,y)) * K(y,x). K(x,T(y,z)) * K(z,y) = T(T(y,z),x) \ y. T(x,y) * z = x * (K(x,y) * z). x * (K(x,y) * z) = T(x,y) * z. T(x,y) * T(y,x) = x * y. T(x,y) * z != x * y | T(y,T(x,y)) = z. T(x,T(y,x)) = T(x,y). (x * y) / T(y,x) = T(x,y). (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)). R(x,T(y,z),T(z,y)) * (y * z) = (x * T(y,z)) * T(z,y). T(x,y) * R(T(y,x),z,u) = R(y,z,u) * T(x,y). T(x,y) = T(x,(x * y) / x). T(x,(x * y) / x) = T(x,y). T(x,x \ y) = T(x,y / x). T(x,y / x) = T(x,x \ y). T(x,y) * T(T(y,x),z) = T(y,z) * T(x,y). (T(x,y) * z) / (K(x,y) * z) = x. x \ (T(x,y) * z) = K(x,y) * z. x \ y = K(x,z) * (T(x,z) \ y). K(x,y) * (T(x,y) \ z) = x \ z. (x * ((K(x,y) * z) * u)) \ ((T(x,y) * z) * u) = a(x,K(x,y) * z,u). x * (y * K(x,z)) = T(x,z) * T(y,K(x,z)). T(x,y) * T(z,K(x,y)) = x * (z * K(x,y)). x * (y * z) != (z * T(y,z)) * T(z,y) | x = R(z,y,z). R(x,T(y,x),T(x,y)) = R(x,y,x). (x * y) \ (y * T(x,x \ y)) = a(x,y / x,x). 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 \ L(y,z,u)) \ w | x = L(y,z,u) \ (y * w). (L(x,y,z) \ x) * u = L(x,y,z) \ (x * u). L(x,y,z) \ (x * u) = (L(x,y,z) \ x) * u. 1 != x * K(y,z) | K(z,y) = x. x * K(y,z) != 1 | K(z,y) = x. x != L(y,z \ 1,u) | x = L(y,z,u). (x * (y \ 1)) \ x = L(y,y,x). L(x,x,y) = (y * (x \ 1)) \ y. 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) \ 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(K(x,y),K(x,y) * z,u) = R(K(y,x),z,u) \ 1. x \ y != K(x,z) * u | T(x,z) \ y = u. K(x,y) * (y \ z) != u | u = T(y,x) \ z. K(x,y) * (y \ z) != u | T(y,x) \ z = u. K(x,y) \ ((x * y) * z) = ((x * y) \ K(x,y)) \ z. ((x * y) \ K(x,y)) \ z = K(x,y) \ ((x * y) * z). ((x * y) \ K(x,y)) \ z = K(y,x) * ((x * y) * z). R((x / y) \ z,x / y,y) = T((z * y) / x,x / y). (x * R(x \ y,z,u)) / x = R(y / x,z,u). R(x,y,z) * (x \ u) = (x \ u) * R((x \ u) \ u,y,z). (x \ y) * R((x \ y) \ y,z,u) = R(x,z,u) * (x \ y). R(x \ 1,y,z) * u = u * R(u \ (x \ u),y,z). x * R(x \ (y \ x),z,u) = R(y \ 1,z,u) * x. 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,1 / y,y) = (x * (1 / y)) * y. (x * (1 / y)) * y = R(x,1 / y,y). R(x,1 / y,y) / y = x * (1 / y). T((x * y) / z,u) * z = (T(x / (z / y),u) * (z / y)) * y. (T(x / (y / z),u) * (y / z)) * z = T((x * z) / y,u) * y. x != T(y / z,u) * z | x = z * T(z \ y,u). (T(x / (y / z),u) * (y / z)) * z = y * T(y \ (x * z),u). ((x / y) * T((x / y) \ z,u)) * y = x * T(x \ (z * y),u). x * y != z * T(u,z) | (u * z) / y = x. ((x \ (y * z)) * x) / z = (x / z) * T((x / z) \ y,x). (x / y) * T((x / y) \ z,x) = ((x \ (z * y)) * x) / y. ((x / y) * T((x / y) \ 1,z)) * y = x * T(x \ y,z). (x * T(((x * y) / y) \ z,u)) * y = (x * y) * T((x * y) \ (z * y),u). K((x / y) \ 1,z) * y = x * T(x \ y,z). K(x \ 1,y) * (x \ z) = z * T(z \ (x \ z),y). K(x / y,z) * x = y * T(y \ x,z). K(x,y / z) * (z * T(z \ y,x)) = y. (x * T(x \ y,z)) / y = K(y / x,z). K((x * y) / x,z) * (x * y) = x * T(y,z). K(x,y) * z = (x \ z) * T((x \ z) \ z,y). (x \ y) * T((x \ y) \ y,z) = K(x,z) * y. x / (y * T(y \ x,z)) = K(z,x / y). x != (y \ z) * T((y \ z) \ z,u) | x = T(y,u) * (y \ z). K(x,y) * z = T(x,y) * (x \ z). T(x,y) * (x \ z) = K(x,y) * z. x != y * 1 | x = y. T(x,y) * (x \ 1) = K(x,y). x * y != K(z,u) * K(u,z) | 1 / y = x. 1 / (x \ K(y,x)) = T(x,y). x * y != K(z,u) * (u \ w) | x \ (T(u,z) \ w) = y. T(x,y) \ (T(y,x) \ z) = x \ (y \ z). x * y != K(z,u) * T(u,z) | x \ u = y. T(x,y) \ y = x \ T(y,x). x * y != K(z,u) * (K(u,z) * w) | x \ w = y. T(x,y) \ z = x \ (K(y,x) * z). x \ (K(y,x) * z) = T(x,y) \ z. T(x,y) \ (z * K(x,y)) = x \ T(z,K(x,y)). x != T(y,z) * u | x = y * (K(y,z) * u). K(x,y) * z = x * (K(x,y) * (x \ z)). x * (K(x,y) * (x \ z)) = K(x,y) * z. x != T(y,z) * u | x = u * T(T(y,u),z). K(x,y) * z = (x \ z) * T(T(x,x \ z),y). (x \ y) * T(T(x,x \ y),z) = K(x,z) * y. x * y != T(z,u) * (z \ w) | x \ (K(z,u) * w) = y. x \ (K(x,y) * z) = K(x,y) * (x \ z). x * y != T(z,u) * (z \ y) | x = z \ T(z,u). K(x,y) = x \ T(x,y). x \ T(x,y) = K(x,y). T(x,y) * z = K(x,y) * (x * z). K(x,y) * (x * z) = T(x,y) * z. T(x,y) * T(z,x) = K(x,y) * (z * x). x * (T(x,y) * (x \ z)) = T(x,y) * z. K(x,y) * T(K(y,x),z) = K(K(y,x),z). x * K(x,y) = T(x,y). L(x,y,z) \ L(T(x,u),y,z) = K(L(x,y,z),u). R(x,y,z) \ R(T(x,u),y,z) = K(R(x,y,z),u). x \ ((x \ y) \ y) = K(x,x * y). x * K(x,y) != z | z = T(x,y). x * K(x,y) != z | T(x,y) = z. T(x,y) * K(x,z) = K(x,y) * T(x,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)). x != L(y,z,u * ((u \ w) * w)) | x = L(y,z,a(u,w,w)). L(x,y,K(z,z * u)) = L(x,y,a(z,u,u)). K(x,y) * (T(y,x) * z) = y * z. ((T(x,y) * z) * u) / ((x * z) * u) = R(K(x,y),x * z,u). K(R(x,y,z),u) * (R(x,y,z) * w) = R(T(x,u),y,z) * w. K(x,y) * (L(z,u,w) * x) = T(x,y) * L(T(z,x),u,w). T(x,y) * L(T(z,x),u,w) = K(x,y) * (L(z,u,w) * x). T(x,y) * (x \ z) != u | K(x,y) * z = u. T(x,y) * (T(y,x) * z) = x * (y * z). x * (T(x,y) * z) = T(x,y) * (x * z). T(x,y) * (x * z) = x * (T(x,y) * z). K(x,y) * z != T(x,y) | T(x,K(x,y)) = z. T(x,K(x,y)) = x. x * y != z * K(z,u) | T(z,u) / y = x. T(x,y) / (K(z,x) * K(x,y)) = T(x,z). T(x,y) != x * z | K(x,y) = z. (T(x,y) * z) / (K(x,y) * z) = R(x,K(x,y),z). x \ T(x,y) != z | z = K(x,y). x \ T(x,y) != z | K(x,y) = z. L(x,y,z) \ L(T(x,u),y,z) != w | K(L(x,y,z),u) = w. x \ L(T(x,y),y,x) != z | K(x,x * y) = z. K(x,y) * z = y * (T(y,x) \ z). x * (T(x,y) \ z) = K(y,x) * z. (x * y) \ (K(z,x) * (T(x,z) * (y * u))) = L(L(u,y,T(x,z)),T(x,z) * y,K(z,x)). L(L(x,y,T(z,u)),T(z,u) * y,K(u,z)) = (z * y) \ (K(u,z) * (T(z,u) * (y * x))). ((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). K(x,y) * y = y * K(x,y). K(x,y) * (x * z) != u | u = T(x,y) * z. K(x,y) * (x * z) != u | T(x,y) * z = u. K(x,y) * (y * z) = y * (K(x,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). K(x,y) * T(T(y,x),z) = y * K(T(y,x),z). 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). T(x,K(y,x)) = x. x * y != x * K(z,x) | T(K(z,x),x) = y. T(K(x,y),y) = K(x,y). x * y != K(z,u) * u | x \ (u * K(z,u)) = y. T(x,y) \ (y * K(x,y)) = x \ y. T(x,y) = T(T(x,y),K(z,x)). T(T(x,y),K(z,x)) = T(x,y). K(x,y) * R(y,z,u) = R(y,z,u) * K(x,y). R(x,y,z) * K(u,x) = K(u,x) * R(x,y,z). K(x,y) * T(y,z) = T(y,z) * K(x,y). T(x,y) * K(z,x) = K(z,x) * T(x,y). K(x,y) * T(y,z) != u | T(y,z) * K(x,y) = u. K(x,y) * R(T(y,z),u,w) = R(T(y,z),u,w) * K(x,y). R(T(x,y),z,u) * K(w,x) = K(w,x) * R(T(x,y),z,u). T(x,y) * z != x * u | T(x,y) * (x \ z) = u. x != K(y,z) * u | x = T(z,y) \ (z * u). x * (T(x,y) \ z) = T(x,y) \ (x * z). T(x,y) \ (x * z) = x * (T(x,y) \ z). x * (T(x,y) \ 1) = K(y,x). x * (T(x,y) \ z) = (T(x,y) \ x) * z. (T(x,y) \ x) * z = x * (T(x,y) \ z). T(x,y) \ x = x * (T(x,y) \ 1). x * (T(x,y) \ 1) = T(x,y) \ x. (x * y) / (x * (T(x,z) \ y)) = T(x,z). (x * x) / (x * K(y,x)) = T(x,y). R(T(x,y),z,u) * (x * (T(x,y) \ w)) = (x * (T(x,y) \ w)) * R((x * (T(x,y) \ w)) \ (x * w),z,u). (x * (T(x,y) \ z)) * R((x * (T(x,y) \ z)) \ (x * z),u,w) = R(T(x,y),u,w) * (x * (T(x,y) \ z)). (R(x,y,z) * u) / (R(T(x,w),y,z) * u) = K(w,R(x,y,z)). x != y * (K(z,y) * z) | x = z * y. K(x,y) * (y * x) = x * y. K(x,y) * (z * y) = y * (K(x,y) * T(z,y)). x * (K(y,x) * T(z,x)) = K(y,x) * (z * x). x * y != K(z,u) * (z * x) | T(T(z,u),x) = y. T(T(x,y),y) = K(x,y) * T(x,y). K(x,y) * T(x,y) = T(T(x,y),y). x * T(y,z) != T(T(y,u),z) | x = K(T(y,z),u). K(x,y) = K(T(x,y),y). K(T(x,y),y) = K(x,y). x * T(T(x,y),y) = T(x,y) * T(x,y). T(x,y) * T(x,y) = x * T(T(x,y),y). K(R(T(x,y),z,u),y) = K(R(x,z,u),y). K(x \ y,x) = K(y / x,x). K(x / y,y) = K(y \ x,y). K(T(x,y),y) \ 1 != z | K(y,x) = z. T(x,y) * K(x,y) = T(T(x,y),y). K(x,y) = K(x,T(y,x)). K(x,T(y,x)) = K(x,y). K(x,T(y,x)) != z | K(x,y) = z. K(x \ y,x) * y = (x \ y) * x. K(x,y) * z != x * y | T(y * x,K(x,y)) = z. T(x * y,K(y,x)) = x * y. K(x,x \ y) * ((x \ y) * x) = y. ((x * y) * z) / ((y * x) * z) = R(K(x,y),y * x,z). K(L(x,y,z),z * y) * (z * (y * x)) = L(x,y,z) * (z * y). L(x,K(y,z) * (y * z),u) = L(x,z * y,u). T(x,y) * (y * x) = x * (x * y). x != K(y,z) | x = K(z,y) \ 1. K(x / y,y) = K(y,y \ x) \ 1. K(x,x \ y) \ 1 = K(y / x,x). x != K(y,z) | x = y \ T(y,z). K(x \ y,x) = (y / x) \ T(y / x,x). (x / y) \ T(x / y,y) = K(y \ x,y). K(x,y) * (x \ y) = x \ (y * K(x,y)). x \ (y * K(x,y)) = K(x,y) * (x \ y). x != (T(y,z) * u) / (K(y,z) * u) | x = y. R(x,K(x,y),z) = x. T(x,y) = R(T(x,y),K(x,z),u). R(T(x,y),K(x,z),u) = T(x,y). L(x,y,z) * (K(x,u) * w) = (L(x,y,z) * K(x,u)) * w. (L(x,y,z) * K(x,u)) * w = L(x,y,z) * (K(x,u) * w). L(x,K(y,z),L(y,u,w)) = x. (L(x,y,z) * K(x,u)) \ w = K(u,x) * (L(x,y,z) \ w). L(x,K(y,z),y) = x. x != L(y,K(z,u),w) | x = L(y,K(u,z),w). x = L(x,K(y,z),z). L(x,K(y,z),z) = x. (x \ K(x,y)) * z = x \ (K(x,y) * z). x \ (K(x,y) * z) = (x \ K(x,y)) * z. (x * K(y,x)) \ z = K(x,y) * (x \ z). (x * K(y,x)) * z = x * (K(y,x) * z). x * y != z * (K(u,z) * x) | T(z * K(u,z),x) = y. T(x * K(y,x),y) = x. R(x,K(y,x),z) = x. (x * K(y,x)) * y = y * x. x * y != z * (K(u,z) * u) | (u * z) / y = x. (x * y) / x = y * K(x,y). ((x * y) * z) / R(x,y,z) = (y * z) * K(R(x,y,z),y * z). x / (x / y) = y * K(x / y,y). x / y = (y \ x) * K(y,y \ x). (x \ y) * K(x,x \ y) = y / x. (x * y) / x != z | z = y * K(x,y). (x * y) / x != z | y * K(x,y) = z. (x * K(y,x)) * ((y \ 1) \ 1) = ((y \ 1) \ 1) * x. ((x * y) * z) / (x * z) != u | R(y * K(x,y),x,z) = u. x != y * K(z,y) | x = K(z,y) * y. (x * y) / x = K(x,y) * y. x * y != z * K(u,z) | x \ ((u * z) / u) = y. x \ ((y * x) / y) = K(y,x). x * ((y * (x \ 1)) / y) = K(y,x \ 1). (x * y) / x != y * z | K(x,y) = z. (x * T(y,z)) / x = T(y * K(x,y),z). T(x * K(y,x),z) = (y * T(x,z)) / y. T(x,y * K(x,y)) = T(x,y). ((x * y) / x) * z = y * (K(x,y) * z). x != y * (K(z,y) * u) | x = K(z,y) * (y * u). ((x * y) / x) * z = K(x,y) * (y * z). K(x,y) * (y * z) = ((x * y) / x) * z. (x / y) * z = (y \ x) * (K(y,y \ x) * z). (x \ y) * (K(x,x \ y) * z) = (y / x) * z. x != K(y,z) * u | x = T(y,z) * (y \ u). (x * y) / x = T(x,y) * (x \ y). T(x,y) * (x \ y) = (x * y) / x. K(x,y) * ((y * x) / y) = x. x * ((x * y) / x) = T(x,y) * y. T(x,y) * y = x * ((x * y) / x). ((x * y) / x) \ (T(x,y) * ((x \ y) * z)) = L(z,x \ y,T(x,y)). L((x \ y) \ z,x \ y,T(x,y)) = ((x * y) / x) \ (T(x,y) * z). K(x \ y,x) * (y / x) = x \ y. K(a(x,y,z),x * (y * z)) * (((x * y) * z) / (x * (y * z))) = a(x,y,z). x * R(y,z,u) = R(y * K(x,y),z,u) * x. R(x * K(y,x),z,u) * y = y * R(x,z,u). (x * y) * (y * K(z,y)) = (x * (y * K(z,y))) * T(y * K(z,y),z). (x * (y * K(z,y))) * T(y * K(z,y),z) = (x * y) * (y * K(z,y)). x * L(y,z,u) = L(y * K(x,y),z,u) * x. L(x * K(y,x),z,u) * y = y * L(x,z,u). (x * y) / x = T((x * (y * K(z,y))) / x,z). T((x * (y * K(z,y))) / x,z) = (x * y) / x. T(x * K(y,x),T(y,x)) = x. x != (y * z) / y | x = z * K(y,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(y,x),z) != u | T(x,z) * K(y,T(x,z)) = u. x / (x / y) = y * K(y \ x,y). x != y * K(z,y) | x = (z * y) / z. x / (x / y) = ((y \ x) * y) / (y \ x). ((x \ y) * x) / (x \ y) = y / (y / x). (x / (x / y)) * z = y * (K(y \ x,y) * z). T(x / (x / y),y \ x) = y. (x / (x / y)) * x = y * ((y \ x) * y). x * y != z * ((z \ x) * z) | T(x / (x / z),x) = y. T(x / (x / y),x) = L(y,y \ x,y). x != y * ((y \ z) * y) | x = T(y * z,y). (x / (x / y)) * x = T(y * x,y). T(x * y,x) = (y / (y / x)) * y. T(x,((y / (y / x)) * y) / x) = T(x,(x \ y) * x). ((x / y) / x) * T(y * x,y) = x. x / T(y * x,y) = (x / y) / x. K(x,y) * z = ((x * y) / x) * (y \ z). ((x * y) / x) * (y \ z) = K(x,y) * z. x * y != (z / u) * (u / z) | x \ 1 = y. K(x,y) \ 1 = y * (x / (x * y)). x * (y / (y * x)) = K(y,x) \ 1. x * y != K(z,u) * z | T(z,u) / y = x. T(x * y,x) / y = ((x * y) * x) / (x * y). ((x * y) * x) / (x * y) = T(x * y,x) / y. T(T(x * y,x) / y,x * y) = x. T(T(x * y,x) / y,y) = R(x,y,T(x,y)). x * R(y,x,T(y,x)) = T(y * x,y). x != K(y,z) \ 1 | x = K(z,y). x * (y / (y * x)) = K(x,y). x * y != K(z,u) \ 1 | x \ K(u,z) = y. x \ K(x,y) = y / (y * x). x \ (K(x,y) * z) = (y / (y * x)) * z. x \ y = (y / (y * x)) * T(y,x). (x / (x * y)) * T(x,y) = y \ x. ((x * y) / x) * (y \ x) = T(x,y). (x \ y) * z != T(y,x) | T((y * x) / y,x \ y) = z. T((x * y) / x,y \ x) = (y \ x) \ T(x,y). T(x,y) / (y \ x) = (x * y) / x. ((x * (x / y)) / x) * y = T(x,x / y). x * ((y * (x \ y)) / y) = T(y,y / x). (x / y) * ((x * y) / x) = T(x,x / (x / y)). (x / T(y,x)) * y = T(x,x / (x / T(y,x))). T(x,x / (x / T(y,x))) = (x / T(y,x)) * y. T(x,x / (x / y)) * y = ((x / y) * y) * ((x * y) / x). ((x / y) * y) * ((x * y) / x) = T(x,x / (x / y)) * y. x * ((x * y) / x) = T(x,x / (x / y)) * y. T(x,x / (x / y)) * y = x * ((x * y) / x). T(x,x / (x / y)) * (x \ y) = (x * y) / x. x * (y \ z) != (y * z) / y | x = T(y,z). T(x,x / (x / y)) = T(x,y). x != T(y,y / (y / T(z,y))) | x = (y / T(z,y)) * z. T(x,T(y,x)) = (x / T(y,x)) * y. (x / T(y,x)) * y = T(x,T(y,x)). x * y != T(z,T(u,z)) | T(z,u) / y = x. T(x,y) / y = x / T(y,x). T(x,y) / T(y,x) = x / T(T(y,x),x). R(R(x,1 / y,y),z,u) / y = R(x,z,u) * (1 / y). R(x,y \ 1,y) / y = x * (1 / y). R(x,y \ 1,y) / y = x * (y \ 1). (x * (y \ 1)) * y = R(x,y \ 1,y). x * y = R(x / (y \ 1),y \ 1,y). R(x / (y \ 1),y \ 1,y) = x * y. (x \ (y \ 1)) * y = R(x \ 1,y \ 1,y). R(x \ 1,y \ 1,y) = (x \ (y \ 1)) * y. R(x / (1 / y),y \ 1,y) = x * y. T(x,y) * L(y,z,u) = L(y * K(x,y),z,u) * T(x,y). L(x * K(y,x),z,u) * T(y,x) = T(y,x) * L(x,z,u). (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. L(T(x,y),y * K(x,y),T(x,y)) = (x \ y) \ y. x * (1 / x) = K(x,x \ 1). x * (y / (y * x)) = (x \ ((y * x) / y)) \ 1. (x \ ((y * x) / y)) \ 1 = x * (y / (y * x)). (x * (y * K(z,y))) * y = (x * y) * (y * K(z,y)). ((x * y) * T((x * y) \ ((z * x) * y),u)) / ((z * x) * y) = K(R(z,x,y),u). ((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). x != ((T(y,z) * u) * w) / ((y * u) * w) | x = R(K(z,y),T(y,z) * u,w) \ 1. K(R(x,y,z),u) = R(K(u,x),T(x,u) * y,z) \ 1. R(K(x,y),T(y,x) * z,u) \ 1 = K(R(y,z,u),x). x != ((T(y,z) * u) * w) / ((y * u) * w) | x = R(K(y,z),y * u,w). 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). 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). K(R(x,x * y,z),u) = R(K(x,u),y,z). x != K(R(T(y,z),u,w),z) | x = K(R(y,u,w),z). 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). K(x,y) = R(K(x,y),x,z). R(K(x,y),x,z) = K(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). K(R(x,T(x,y) * z,u),y) = R(K(x,y),z,u). x != K(R(y,T(y,z) * u,w),v5) | x = R(K(y,v5),K(y,z) * u,w). R(K(x,y),z,u) = R(K(x,y),K(x,y) * z,u). R(K(x,y),K(x,y) * z,u) = R(K(x,y),z,u). x != R(K(y,z),K(y,z) * u,w) | x = R(K(z,y),u,w) \ 1. 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). R(K(x,y),z,u) \ 1 != w | R(K(y,x),z,u) = w. 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. 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(y,x) * z,u) = K(x,R(y,z,u)). R(K(x,y),T(y,x) * z,u) \ 1 != w | K(R(y,z,u),x) = w. 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),y * z,u) = K(x,R(y,z,u)). R(K(x,y),z,u) = K(x,R(y,y \ z,u)). K(x,R(y,y \ z,u)) = R(K(x,y),z,u). R(K(x,y),z * y,u) = K(x,R(y,T(z,y),u)). R(K(x,y),x * z,u) * K(y,x) = K(x,y) * K(y,R(x,z,u)). K(R(x,y,z),u) * K(u,x) = K(x,u) * K(u,R(x,y,z)). x != R(K(y,z),u,w) \ 1 | x = R(K(z,y),u,w). K(x,R(y,y * z,u)) = R(K(x,y),z,u). K(x,y) = R(K(x,y),y,z). R(K(x,y),y,z) = K(x,y). K(x,R(K(y,z),u,w)) = R(K(x,K(y,z)),u,w). R(K(x,K(y,z)),u,w) = K(x,R(K(y,z),u,w)). R(K(x,y),T(x,y) * z,u) != w | K(R(x,z,u),y) = w. T(x / (y * z),y) = R(y \ (x / z),y,z). R(x \ (y / z),x,z) = T(y / (x * z),x). 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 / (y * z),y) * (y * z) = ((y \ (x / z)) * y) * z. T(x / (y * (y \ z)),y) * z = ((y \ (x / (y \ z))) * y) * (y \ z). ((x \ (y / (x \ z))) * x) * (x \ z) = T(y / (x * (x \ z)),x) * z. (x * y) * T((x * y) \ z,x) = ((x \ (z / y)) * x) * y. x != y * T(y \ 1,z) | x = K(y \ 1,z). ((x \ (1 / y)) * x) * y = K((x * y) \ 1,x). x != T(R(y,z,u),w) | x = R(T(y,w),z,u). T(T((x * y) / (z * y),u),z) = R(T(z \ x,u),z,y). T((x * y) \ (z * y),x) = R(T(x \ z,x * y),x,y). R(T(x \ y,x * z),x,z) = T((x * z) \ (y * z),x). R(T(x,y * z),y,z) = T((y * z) \ ((y * x) * z),y). T((x * y) \ ((x * z) * y),x) = R(T(z,x * y),x,y). K(x,R(T(y,x * z),x,z)) != u | K(x,(x * z) \ ((x * y) * z)) = u. x != T(y,y \ z) | x = T(y,z / y). T(x,x * y) = T(x,y / x). T(x,y / x) = T(x,x * y). T(x * y,K(y,x)) = T(x * y,(x * y) * (y * x)). T(x * y,(x * y) * (y * x)) = T(x * y,K(y,x)). T(x,y) = T(x,x * (y * x)). T(x,x * (y * x)) = T(x,y). (x \ y) * (T(x,y / x) * z) = (y / x) * (x * z). (x \ y) * (T(x,x * y) * z) = (y / x) * (x * z). T(x,y) * K(x,z) != u | K(x,y) * T(x,z) = u. T(x,y) * (z / (z * x)) != u | K(x,y) * K(x,z) = u. T(x,y) * ((y * x) / ((x * y) * x)) = K(T(x,y),y * x). T(x,y) * (R(x,y,x) \ 1) = K(T(x,y),y * x). x != T(y,z) * (R(y,u,w) \ 1) | x = R(y,u,w) \ T(y,z). 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). x * y != y * T(z,u) | x = T((y * z) / y,u). L(x,y,x) = T((y * x) / y,x * y). T((x * y) / x,y * x) = L(y,x,y). (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 \ ((x * y) * z) = R(x,y,z) * (x \ (y * z)). R(x,y,z) * (x \ (y * z)) = x \ ((x * y) * z). (x / y) * y != z * u | z = x / u. (x / y) * y != z * u | x / u = z. ((x / y) * y) * z != u * w | (x * z) / w = u. (x * (y * z)) \ ((x * y) * z) = a(T(x,y),T(y,x),z). a(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(y,x),z) != u | a(x,y,z) = u. a(T(x,y),T(T(y,x),x),z) != u | a(x,T(y,x),z) = u. a(x,T(y,x),z) = a(T(x,y),T(T(y,x),x),z). a(T(x,y),T(T(y,x),x),z) = a(x,T(y,x),z). (x / y) \ x != z * u | y / u = z. T(x,y) \ (y \ z) = (y * (x * y)) \ (y * z). (x * (y * x)) \ (x * z) = T(y,x) \ (x \ z). K(x,y) \ ((y * x) \ z) = (x * y) \ z. K(x,y) * ((x * y) \ z) != u | u = (y * x) \ z. K(x,y) * ((x * y) \ z) != u | (y * x) \ z = u. L(x \ (y * z),x,y) != u | u = (y \ x) \ z. L(x \ (y * z),x,y) != u | (y \ x) \ z = u. L(x \ y,x,y) != z | (y \ x) \ 1 = z. L(x,y,z) \ (x * u) != w | (x \ L(x,y,z)) \ u = w. T(x,y * y) = T(x,x * (y * y)). T(x,x * (y * y)) = T(x,y * y). R(x / y,y,x \ z) \ z = y * (x \ z). R(x,T(y,x),(y * x) \ z) \ z = T(y,x) * ((y * x) \ z). K(x,(y * z) / ((u \ y) * z)) = R(K(x,u),y,z). K(x,(y * z) / (u * z)) = R(K(x,y / u),y,z). R(K(x,y / z),y,u) = K(x,(y * u) / (z * u)). R(x,y,y \ 1) = (x * y) * (y \ 1). (x * y) * (y \ 1) = R(x,y,y \ 1). R(x,y,y \ 1) / (y \ 1) = x * y. x * (y \ 1) = R(x / y,y,y \ 1). R(x / y,y,y \ 1) = x * (y \ 1). x != (y * (z * u)) \ ((y * z) * u) | x = a(y,z,u). 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). (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. 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). x * y != y * T(z,z * y) | x = L(z,y,z). R(x,y,x) = L(x,y * x,x). L(x,y * x,x) = R(x,y,x). x != L(y,z,y) | x = (y \ z) \ T(z,y). R(x,y,x) = (x \ (y * x)) \ T(y * x,x). (x \ (y * x)) \ T(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). L(x,y,x) * y = (x * (y / x)) * x. T(x,x \ y) * z = ((x \ y) \ y) * z. x * y != T(z,z \ u) | x \ ((z \ u) \ u) = y. (T(x,x \ y) / z) \ ((x \ y) \ y) = z. L(T(x,x \ y),x \ y,z) = (z * (x \ y)) \ (z * y). x * ((T(y,x) \ z) \ z) = T(y,T(y,x) \ z) * x. T(x,T(x,y) \ z) * y = y * ((T(x,y) \ z) \ z). ((x \ y) \ y) * K(x \ y,x) = x. K(x,x \ y) * (((x \ y) \ y) \ z) = x \ z. x * y != T(z,u) * (u * z) | x \ (z * (z * u)) = y. ((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)). (((x * y) * T(y,x)) \ (y * y)) * x = K(T(y,x),x * y). (((x * y) * x) \ (x * x)) * y = K(T(x,y),y * x). K(x,x * y) = K(T(x,y),y * x). K(T(x,y),y * x) = K(x,x * y). x != K(T(y,z),z * y) | x = R(y,z,y) \ T(y,z). K(x,x * y) = R(x,y,x) \ T(x,y). R(x,y,x) \ T(x,y) = K(x,x * y). x * y != T(z,u) * K(z,u) | x \ T(T(z,u),u) = y. x \ T(T(x,y),y) = K(x,y) * K(x,y). ((x / y) \ x) * (y \ z) = z. ((R(x,y,z) * u) * w) / ((x * u) * w) = R(x,u,w) \ R(R(x,u,w),y,z). x != ((R(y,z,u) * w) * v5) / ((y * w) * v5) | x = R(y \ R(y,z,u),y * w,v5). R(x,y,z) \ R(R(x,y,z),u,w) = R(x \ R(x,u,w),x * y,z). R(x \ R(x,y,z),x * u,w) = R(x,u,w) \ R(R(x,u,w),y,z). (x / T(y,y \ z)) * ((y \ z) \ z) = x. (x \ y) \ (x \ T(y,x)) = K(x \ (x \ y),x). x != (y \ z) \ (y \ u) | x = (y * z) \ (y * u). K(x \ (x \ y),x) = (x * y) \ (x * T(y,x)). (x * y) \ (x * T(y,x)) = K(x \ (x \ y),x). (x * y) \ (y * x) = K(x \ (x \ y),x). K(x \ (x \ y),x) = (x * y) \ (y * x). x != (y * z) \ (z * y) | x = K(z,y). K(x \ (x \ y),x) = K(y,x). K(x \ y,x) = K(x * y,x). (x \ y) * K(x * y,x) = T(x \ y,x). x / (x / y) = y * K(y * x,y). x != (R(y,z,u) \ y) * R(y,z,u) | x = y. (x \ R(x,y,z)) \ R(x,y,z) = x. x != (y \ R(y,z,u)) \ w | x = y * (R(y,z,u) \ w). (R(x,y,z) \ x) * u = x * (R(x,y,z) \ u). x != y * (R(y,z,u) \ y) | x = R(y,y * z,u). (R(x,y,z) \ x) * x = R(x,x * y,z). (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 != (y \ R(y,z,u)) * w | x = R(y,z,u) * (y \ w). x * (R(x,x * y,z) \ u) = R(x,y,z) * (x \ u). L(x,y,z) * (x * u) = (x * L(x,y,z)) * u. (x * L(x,y,z)) * u = L(x,y,z) * (x * u). x != (y * L(y,z,u)) * w | x = y * (L(y,z,u) * w). L(x,y,z) * (x * u) = x * (L(x,y,z) * u). x * y != (z * L(z,u,w)) * v5 | x \ (z * (L(z,u,w) * v5)) = y. L(x,y,z) \ (x * (L(x,y,z) * u)) = x * u. L(x,y,z) * (x * (L(x,y,z) \ u)) = x * u. (x * y) / (x * (L(x,z,u) \ y)) = L(x,z,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) != w | w = x * (L(x,y,z) \ u). L(x,y,z) \ (x * u) != w | x * (L(x,y,z) \ u) = w. 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 != w | x * (L(x,y,z) \ u) = w. (L(x,y,z) \ x) * (L(x,y,z) * u) = x * u. (x * y) / (L(x,z,u) * y) = L(x,z,u) \ x. x != (y * z) / (L(y,u * z,u) * z) | x = R(u,z,T(y,z)) \ u. L(x,y * z,y) \ x = R(y,z,T(x,z)) \ y. R(x,y,T(z,y)) \ x = L(z,x * y,x) \ z. x != R(y,y * z,u) \ y | x = y \ R(y,z,u). L(x,y * (y * z),y) \ x = y \ R(y,z,T(x,y * z)). (R(x,y,T(z,y)) \ x) \ 1 = z \ L(z,x * y,x). 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 \ R(x,y,T(z,x * y))) * L(z,y,x) = z. R(x,y,T(z,x * y)) * (x \ L(z,y,x)) = z. x != (R(y,z,u) \ y) \ 1 | x = y \ R(y,z,u). 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 * y != R(x,x * z,u) | y = R(x,z,u) \ 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. x != (y \ L(y,z,x)) * u | R(x,z,T(y,x * z)) = u. (x \ L(x,y,z)) * u != z | R(z,y,T(x,z * y)) = u. L(x,R(y,z,u),T(y,w)) * (T(y,w) \ T(y,w)) = x. L(x,R(y,z,u),T(y,w)) * 1 = x. L(x,R(y,z,u),T(y,w)) = x. x != L(y,y,z) | x = (z * (y \ 1)) \ z. R(x,y,z) = (T(x,u) * (R(x,y,z) \ 1)) \ T(x,u). (T(x,y) * (R(x,z,u) \ 1)) \ T(x,y) = R(x,z,u). L(x,R(y / z,u,w),z \ y) = x. x = L(x,R(y / z,u,w),z * y). L(x,R(y / z,u,w),z * y) = x. L(x,y / (z * (u * y)),z * (u \ 1)) = x. x != L(y,z,u * (w \ 1)) | x = L(y,z,u * w). x = L(x,y / (z * (u * 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 * z) * u) / (y * (z * u)) | x = y \ R(y,z,u). (x * y) * (z / (x * (y * z))) = x \ R(x,y,z). L(x,y \ R(y,z,u),y * z) = x. x != L(y,z \ u,w) | x = L(y,z * u,w). x = L(x,y * R(y,z,u),y * z). L(x,y * R(y,z,u),y * z) = x. (R(x,y,z) \ T(x,u)) \ T(x,u) = R(x,y,z). K(x,x * y) \ T(x,y) = R(x,y,x). K(x * y,x) * T(x,y) = R(x,y,x). T(x,y) * K(x * y,x) = R(x,y,x). x * y != T(z,u) * K(z * u,z) | x \ R(z,u,z) = y. x \ R(x,y,x) = K(x,y) * K(x * y,x). K(x,y) * K(x * y,x) = x \ R(x,y,x). (x * T(y,z)) \ (x * R(y,z,y)) = L(K(y * z,y),T(y,z),x). (x \ y) * T((x \ y) \ 1,z) = x \ (y * T(y \ x,z)). x \ (y * T(y \ x,z)) = K((x \ y) \ 1,z). (x \ y) * T((x \ y) \ 1,y) = x \ ((y \ x) * y). x * K((x \ y) \ 1,z) = y * T(y \ x,z). x * T(x \ y,z) = y * K((y \ x) \ 1,z). x * y != (z \ x) * T((z \ x) \ x,u) | T(K(z,u),x) = y. T(K(x,y),z) = K((z \ (x \ z)) \ 1,y). K((x \ (y \ x)) \ 1,z) = T(K(y,z),x). x != (y * z) * T((y * z) \ u,y) | x = ((y \ (u / z)) * y) * z. x * K((x \ (y * z)) \ 1,y) = ((y \ (x / z)) * y) * z. ((x \ (y / z)) * x) * z = y * K((y \ (x * z)) \ 1,x). (x * y) * T((x * y) \ x,z) = x * K(y \ 1,z). x * T(x \ y,z) != y * u | K((y \ x) \ 1,z) = u. x * T(x \ (x / y),z) = (x / y) * K(y \ 1,z). (x / y) * K(y \ 1,z) = x * T(x \ (x / y),z). (x \ ((y * x) / y)) \ 1 = ((y * x) / y) \ x. x != (y / z) \ u | x = (z / y) * u. (x \ ((y * x) / y)) \ 1 = (y / (y * x)) * x. (x / (x * y)) * z != (y \ ((x * y) / x)) \ 1 | T(y,x / (x * y)) = z. T(x,y / (y * x)) = x. T(x \ y,x / y) = x \ y. L(x,x \ y,x) = T(((x \ y) * x) / (x \ y),y). T(((x \ y) * x) / (x \ y),y) = L(x,x \ y,x). T(x * K(x \ y,x),y) = L(x,x \ y,x). T(x * K(x * y,x),y) = L(x,x \ y,x). T(x * K(x * y,x),y) = L(x,x * y,x). x = L(x,y * R(y,y * z,u),z). L(x,y * R(y,y * z,u),z) = x. x != R(y,y * z,u) \ 1 | x = R(y \ 1,z,u). 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 != y \ (R(y,z,u) * w) | x = R(y,z,u) * (y \ w). 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). x != y * (z * R(z \ (y \ u),w,v5)) | x = (y * z) * R((y * z) \ u,w,v5). R(x,y,z) * (x \ u) = (x * u) * R((x * u) \ u,y,z). (x * y) * R((x * y) \ y,z,u) = R(x,z,u) * (x \ y). R(x,x * y,z) \ (y * z) = (x \ y) * z. R(T(x,R(x,y,z) \ u),y,z) != w | (R(x,y,z) \ u) \ u = w. L(x,y,K(y,z)) = x. a(K(x,y),x,z) = 1. x != L(y,z,K(u,w)) | x = L(y,z,K(w,u)). x = L(x,y,K(z,y)). L(x,y,K(z,y)) = x. L(x,y,T(z,y) \ z) = x. (x / y) * ((z / y) \ z) = x. ((x / y) \ x) * z != u | T(u / y,(x / y) \ x) = z. T(x / y,(z / y) \ z) = y \ x. T(x,y) * K(x,y) != z | T(T(x,y),y) = z. (x * y) * R((x * y) \ x,z,u) = x * (y \ R(y,z,u)). T(x,y) * z = (x * z) * K(((x * z) \ z) \ 1,y). (x * y) * K(((x * y) \ y) \ 1,z) = T(x,z) * y. x * y != z * T(y,u) | (x / T(y,u)) * y = z. x * T(y,z) != u * y | (u / T(y,z)) * y = x. x * y != (z * (z \ 1)) * u | x \ u = y. x \ L(L(y,x \ 1,x),z,u) = (x \ 1) * L(y,z,u). (x * y) * L((x * y) \ z,u,w) = x * (y * L(y \ (x \ z),u,w)). x \ (x * y) != z * u | y / u = z. (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 \ 1) / y) \ 1 = (y / x) * (x * x). x != (y / z) \ 1 | x = z / y. (x / y) * (y * y) = x / (y \ 1). x * (y * y) = (x * y) / (y \ 1). (x * y) / (y \ 1) = x * (y * y). T(T(x,y),z) != u | T(T(x,z),y) = u. x * R(K(x,K(y,z)),u,w) != v5 | T(x,R(K(y,z),u,w)) = v5. T(x,R(T(x,y),z,u)) = x. R(T(x,x * y),y,T(x,y)) = T(x,y). T(x,y) * (x * y) = (T(x,x * y) * y) * T(x,y). (T(x,x * y) * y) * T(x,y) = T(x,y) * (x * y). T(x,y) * z != T(x,y) * (x * y) | T(T(x,x * y) * y,T(x,y)) = z. T(T(x,x * y) * y,T(x,y)) = x * y. T(x * K(y * x,x),y) = R(x,y,x). x != T(y * z,(y * z) * (z * y)) | x = T(y * z,K(z,y)). T(x * y,y * x) = T(x * y,K(y,x)). K(x,y) / T(y * x,K(x,y)) = (y * x) \ K(x,y). K(x,y) / (y * x) = (y * x) \ K(x,y). K(x,y) * ((K(x,y) \ 1) / (x * y)) = K(x,y) \ ((y * x) \ 1). K(x,y) * (K(y,x) / (x * y)) = K(x,y) \ ((y * x) \ 1). x != K(y,z) \ ((z * y) \ u) | x = (y * z) \ u. K(x,y) * (K(y,x) / (x * y)) = (x * y) \ 1. K(x,y) * ((x * y) \ K(y,x)) = (x * y) \ 1. (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. x * y != (z \ 1) \ u | (z * u) / y = x. ((x * y) * z) / ((y * x) * z) = K(x,y). x != ((y * z) * u) / ((z * y) * u) | x = R(K(y,z),z * y,u). K(x,y) = R(K(x,y),y * x,z). R(K(x,y),y * x,z) = K(x,y). x != R(K(y,z),z * u,w) | x = K(y,R(z,u,w)). K(x,y) = K(x,R(y,x,z)). K(x,R(y,x,z)) = K(x,y). K(x,R(y,x,z)) = x \ T(x,y). K(x,y) \ 1 = K(R(y,x,z),x). K(R(x,y,z),y) = K(y,x) \ 1. K(x,R(y,x,z)) != u | K(x,y) = u. 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)). x != (y * y) / (y * K(z,y)) | x = T(y,z). T(x,R(y,x,z)) = T(x,y). R(x,y,z) * T(y,x) = y * R(x,y,z). x * y != x * z | z = y. (x * (x * (y * (z * u)))) \ ((x * (x * (y * z))) * u) = a(x * (x * y),z,u). (x * (x * (y * (z * u)))) \ (x * (x * ((y * z) * u))) = a(x * (x * y),z,u). x != (y * (y * z)) \ (y * (y * u)) | x = z \ u. 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(T(y,x),z,u). a((x * x) / y,z,u) = a(y \ 1,z,u). x != a(y \ z,T(y,y * z),u) | x = ((y \ z) * (T(y,y * z) * u)) \ (z * u). a(x * y,T(x,x * y),z) = ((x \ y) * (T(x,x * y) * z)) \ (y * z). ((x \ y) * (T(x,x * y) * z)) \ (y * z) = a(x * y,T(x,x * y),z). ((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) != u | a(y / x,x,z) = u. x != a(y \ 1,z,u) | x = a(y,z,u). a((x * x) / y,z,u) = a(y,z,u). a(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(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). x != a(y,z,u) | x = (y * (z * u)) \ ((y * z) * u). a(x,y,z) = ((x * (u * u)) * (y * z)) \ (((x * (u * u)) * y) * 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). (x * (y * (y * (z * u)))) \ ((x * (y * (y * z))) * u) = a(x,z,u). x != (y * (z * (z * (u * w)))) \ ((y * (z * (z * u))) * w) | x = a(y,z * (z * u),w). 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,T(T(y,z),z),u) = a(x,y,u). a(T(x,y),y,z) != u | a(x,T(y,x),z) = u. T(x,y) = R(T(x,y * T(x,z)),y,T(x,z)). R(T(x,y * T(x,z)),y,T(x,z)) = T(x,y). (x * y) * R(z,x,y) = ((((x * y) * z) / (x * y)) * x) * y. ((((x * y) * z) / (x * y)) * x) * y = (x * y) * R(z,x,y). (x * (K(y * z,x) * y)) * z = (y * z) * R(x,y,z). K(x,(y * z) / (y * (u \ z))) * ((y * (u \ z)) * T(L(T(u,u \ z),u \ z,y),x)) = y * z. K(x,(y * z) / (y * (u \ z))) * (y * ((u \ z) * T(T(u,u \ z),x))) = y * z. K(x,(y * z) / (y * (u \ z))) * (y * (K(u,x) * z)) = y * z. K(x,y) * (R(y,z,u) * (K(y,x) * w)) = R(y,z,u) * w. K(x,y) * (R(y,z,u) * w) = R(y,z,u) * (K(x,y) * w). R(x,y,z) * (K(u,x) * w) = K(u,x) * (R(x,y,z) * w). L(x,(y * (y * z)) * (y * u),w) = L(x,z \ (y \ u),w). L(x,y * (y * (z * (y * u))),w) = L(x,z \ (y \ u),w). x != L(y,z * (z * u),w) | x = L(y,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),w). L(x,y * (z \ 1),u) = L(x,y * z,u). L(x,y * z,u) = L(x,y * (w * (w * z)),u). L(x,y * (z * (z * u)),w) = L(x,y * u,w). x != L(y,z * (u \ 1),z) | x = u * (z \ ((z * (u \ 1)) * y)). L(x,y * z,y) = z * (y \ ((y * (z \ 1)) * x)). x * (y \ ((y * (x \ 1)) * z)) = L(z,y * x,y). x * (y * ((y \ (x \ 1)) * z)) = L(z,y * x,y). x * (y * (R(y,y * (x \ 1),z) \ ((x \ 1) * z))) = L(z,y * x,y). 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). L(x,y * R(z,z * u,w),v5) = L(x,y * (R(z,u,w) \ 1),v5). x != L(y,z * (u \ 1),w) | x = L(y,z * u,w). L(x,y * R(z,z * u,w),v5) = L(x,y * R(z,u,w),v5). x != L(y,z * R(z,z * u,w),u) | x = y. L(x,y * R(y,z,u),z) = x. L(x,y * (z * R(z,y,u)),y) = x. L(x,y * (z * R(z,y,u)),y) != w | w = 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). (x * (y \ R(y,x,z))) * u = x * (R(y,x,z) * (y \ u)). x = L(x,y * R(y \ 1,z,u),z). L(x,y * R(y \ 1,z,u),z) = x. a(x,x * (y * R(y,x,z)),u) = 1. R(x / y,y,K(z,x)) \ ((z * x) / z) = y * K(z,x). R(x,y,z) * (K(u,x) * w) = (R(x,y,z) * K(u,x)) * w. (R(x,y,z) * K(u,x)) * w = R(x,y,z) * (K(u,x) * w). T((x \ K(y,z)) \ 1,K(z,y) * x) = (x \ K(y,z)) \ 1. (x * y) \ (x * K(z,y)) = L(T(y,z) \ 1,y,x). x \ (y * K(z,y \ x)) = L(T(y \ x,z) \ 1,y \ x,y). L(T(x \ y,z) \ 1,x \ y,x) = y \ (x * K(z,x \ y)). (R(x,y,z) * (K(x,u) * K(x,u))) / T(T(x,u),u) = x \ R(x,y,z). (x * (x * ((y * z) * u))) / (z * u) = R(x * (x * y),z,u). 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). x * (x * R(y,z,u)) = R(x * (x * y),z,u). x != y * (y * R(T(z,y * y),u,w)) | x = R(z,u,w) * (y * y). R(x * (x * T(y,x * x)),z,u) = R(y,z,u) * (x * x). x * (x * R(T(y,x),z,u)) = R(x * (y * x),z,u). L(x,y,R(z * (z * u),w,v5)) = L(x,y,R(u,w,v5)). R(x * (y * y),z,u) = R(x,z,u) * (y * y). R(x,y,z) * (u * u) = R(x * (u * u),y,z). R(x * (K(x,y) * K(x,y)),z,u) / T(T(x,y),y) = x \ R(x,z,u). 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(y,z,u) * x) = R(x * (y * x),z,u). 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 * (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). x \ R(x * y,z,u) = R(y / x,z,u) * x. x != R(y / z,u,w) * z | x = z * R(z \ y,u,w). 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). (x \ y) \ R(x \ z,u,w) = (x * y) \ R(x * z,u,w). (x * y) / x = (y / x) * T(x,y). (x / y) * T(y,x) = (y * x) / y. x / (y \ (y \ 1)) = x * (y * y). R((x / y) / (z \ (z \ 1)),z \ (z \ 1),y) = x / (z \ (z \ y)). R((x / y) * (z * z),z \ (z \ 1),y) = x / (z \ (z \ y)). x != R(y,z \ (z \ 1),u) | x = 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 != R(y,z,u) * (w * w) | x = R(y * (w * w),z,u). (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). x != ((y * (z \ 1)) * u) / (z \ u) | x = R(y,z \ 1,u). R(x,y,z) = R(x,y \ 1,z). R(x,y \ 1,z) = R(x,y,z). x != R(y,z \ 1,u) | x = R(y,z,u). R(x,(y \ 1) \ 1,z) = R(x,y,z). x != R(T(y,z),y,u) | x = T(y,z). R(T(x,y),x \ 1,z) = T(x,y). x != R(y,y,z) | x = y. R(x,x \ 1,y) = x. x != R(y / (z \ 1),z \ 1,z) | x = y * z. R(x / (y \ 1),y,y) = x * y. x * y != R(z,u \ 1,w) | R(z,u,w) / y = x. R(x,y,y) / y = x * (y \ 1). R(x,K(y,z),u) = R(x,K(z,y),u). x * (R(y,x,z) * (y \ (x \ z))) = L(z,y * x,y). T(x * y,z) = R(T(x / (y \ 1),z),y,y). R(T(x / (y \ 1),z),y,y) = T(x * y,z). R(T(x / (y \ 1),z),y,y) / y = (y \ 1) * T((y \ 1) \ x,z). 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. x \ T(x * y,z) = T(y * x,z) / x. T(x * y,z) / y = y \ T(y * x,z). T(x * y,z) / y != u | y \ T(y * x,z) = u. x != y \ T(y * z,y) | x = (y \ z) * y. T(x * y,y) / y = (y \ x) * y. x != T(y * z,u) / z | x = (z \ 1) * T((z \ 1) \ y,u). x \ T(x * y,z) = (x \ 1) * T((x \ 1) \ y,z). (x \ 1) * T((x \ 1) \ y,z) = x \ T(x * y,z). T(x,y) / (z \ x) = (z \ x) \ T((z \ x) * z,y). (x \ y) \ T((x \ y) * x,z) = T(y,z) / (x \ y). T((x \ y) * x,z) / x = x \ T(y,z). (x \ T(x * y,z)) * x = 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 * T(y,z),u) / x = x \ T(x * T((x * y) / x,z),u). x \ T(x * T((x * y) / x,z),u) = T(x * T(y,z),u) / x. ((x \ y) * x) * x = T(y * x,x). (x * y) * y = T((y * x) * y,y). T((x * y) * x,x) = (y * x) * x. T(L(x,y,x) * y,x) = ((y / x) * x) * x. R(x,y,z) = R(R(x,y,z),x \ 1,u). R(R(x,y,z),x \ 1,u) = R(x,y,z). x * y != R(R(z,u,w),z \ 1,v5) | R(z,u,w) / y = x. R(x,y,z) / x = R(x,y,z) * (x \ 1). R(x,y,z) * (x \ 1) = R(x,y,z) / x. x != R(y,z,u) * (y \ 1) | x = y \ R(y,z,u). R(x,y,z) / x = x \ R(x,y,z). x != R(T(T(y,z),z),u,w) / T(T(y,z),z) | x = y \ R(y,u,w). T(T(x,y),y) \ R(T(T(x,y),y),z,u) = x \ R(x,z,u). x != ((y / z) * z) * u | x = y * u. 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 * (y * x)) / x = L(x,y,x) * y. x * (y * z) != (L(u,w,v5) * y) * z | x = L(R(u,y,z),w,v5). x = L(R(x,y,x),y,x). L(R(x,y,x),y,x) = x. L(x,x * y,x) = R(x,y,x). x != L(y,y * z,y) | x = T(y * K(y * z,y),z). R(x,y,x) = T(x * K(x * y,x),y). T(x * K(x * y,x),y) = R(x,y,x). x != L(y,y * z,y) | x = z \ T(y * z,y). R(x,y,x) = y \ T(x * y,x). x \ T(y * x,y) = R(y,x,y). x * R(y,x,y) = T(y * x,y). (x \ y) \ T(y,x) = R(x,x \ y,x). R(x,x \ y,x) = (x \ y) \ T(y,x). x * y != T(z * x,z) | y = R(z,x,T(z,x)). R(x,y,x) = R(x,y,T(x,y)). R(x,y,T(x,y)) = R(x,y,x). (x / T(y * x,y)) * T(x,R(y,x,y)) = R(y,x,y) \ x. ((x / y) / x) * T(x,R(y,x,y)) = R(y,x,y) \ x. R(x,T(y,x),T(x,y)) = R(x,T(y,x),x). x != R(y,T(z,y),T(y,z)) | x = R(y,z,y). R(x,T(y,x),x) = R(x,y,x). T(x,y) * K(x * y,T(x,y)) = R(x,y,x). T(R(x,y,x),z) = T(T(x * K(x * y,x),z),y). T(T(x * K(x * y,x),z),y) = T(R(x,y,x),z). T(x,y) * K(y * T(x,y),T(x,y)) = R(x,y,x). (x \ T(y,z)) * x = T((x \ y) * x,z). R(x,y,z) * (((y \ 1) \ 1) * z) = (x * ((y \ 1) \ 1)) * z. (x * ((y \ 1) \ 1)) * z != u * (((y \ 1) \ 1) * z) | R(x,y,z) = u. (x \ 1) * T((x \ 1) \ y,z) != u | x \ T(x * y,z) = u. x \ T(x * y,z) = y * K((y \ (x \ 1)) \ 1,z). x * (y * K((y \ (x \ 1)) \ 1,z)) = T(x * y,z). x \ T(y,z) = (x \ y) * K(((x \ y) \ (x \ 1)) \ 1,z). (x \ y) * K(((x \ y) \ (x \ 1)) \ 1,z) = x \ T(y,z). K(x,y) * (z * K((z \ K(y,x)) \ 1,u)) = T(K(x,y) * z,u). K(x,y) * (K(y,x) * T(K(y,x) \ z,u)) = T(K(x,y) * z,u). K(x,y) \ T(K(x,y) * z,u) = K(y,x) * T(K(y,x) \ z,u). (K(x,y) * T(K(x,y) \ z,u)) * K(y,x) = T(z * K(y,x),u). (K(x,y) * T(z,u)) * K(y,x) = T((K(x,y) * z) * K(y,x),u). L(x,T(y,z) * z,u) = L(x,z * y,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)). R(K(x,(y / z) / u),y / z,z) = K(x,y / (u * z)). R(K(x,y / (z / u)),y,u) = K(x,(y * u) / z). R(x \ R(x,y,z),x,y * z) = ((x * y) * z) / (x * (y * z)). (x * R(y,z,u)) / x = R(y * K(x,y),z,u). R(x * K(y,x),z,u) = (y * R(x,z,u)) / y. x * y != y * z | x = z * K(y,z). R(x * K(y,x),z,u) = R(x,z,u) * K(y,R(x,z,u)). R(x,y,z) * K(u,R(x,y,z)) = R(x * K(u,x),y,z). R(x,y,z) \ R(x * K(u,x),y,z) = K(u,R(x,y,z)). K(x,y) * T(T(y,z),u) = T(T(y,z),u) * K(x,y). T(T(x,y),z) * K(u,x) = K(u,x) * T(T(x,y),z). K(x,y) * T(x,z) = T(x,z) * K(x,y). T(x,y) * K(x,z) = K(x,z) * T(x,y). x * y != T(z,u) * (z \ 1) | x \ K(z,u) = y. x \ K(x,y) = K(x,y) * (x \ 1). K(x,y) * (x \ 1) = x \ K(x,y). T(K(x,y),z) * K(y,x) = K(K(x,y),z). x * y != z * (u * (u \ 1)) | x \ z = y. x \ L(x,y,z) = L(x,y,z) * (x \ 1). L(x,y,z) * (x \ 1) = x \ L(x,y,z). x \ ((x * y) * (y \ 1)) = a(x,y,y \ 1). K(x,y) != z | z = K(y,x) \ 1. K(x,y) != z | K(y,x) \ 1 = z. R(K(x,y / z),y,z \ 1) = K(x,y * (z \ 1)). L(x,y,R(T(y,z),u,w)) = x. L(x,y,R((y \ z) \ z,u,w)) = x. x != L(y,z,R(u \ w,v5,v6)) | x = L(y,z,R(u * w,v5,v6)). x = L(x,y,R((y \ z) * z,u,w)). L(x,y,R((y \ z) * z,u,w)) = x. x != L(y,y \ z,y) * (y \ z) | x = (y \ z) * T(y,z). (x * ((x \ y) * x)) / x = (x \ y) * T(x,y). ((x / (x / y)) * x) / y = (y \ x) * T(y,x). x * (y * T(y \ (x \ z),x)) = ((x \ (z / y)) * x) * y. x * (y * T(y \ (x \ 1),z)) = K((x * y) \ 1,z). x * y != (z * u) * T((z * u) \ w,v5) | (z * (u * T(u \ (z \ w),v5))) / y = x. (x * (y * T(y \ (x \ (z * u)),w))) / u = ((x * y) / u) * T(((x * y) / u) \ z,w). (R(x,y,z) * z) \ ((x * y) * z) = L(T(y,z),z,R(x,y,z)). (K(x,y) * z) \ (y * (K(x,y) * z)) = L(T(y,z),z,K(x,y)). (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). ((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). (x * y) \ (x * (y * K(z \ 1,u))) = K(L(z,y,x) \ 1,u). L(K(x \ 1,y),z,u) = K(L(x,z,u) \ 1,y). L(K(x,y),z,u) = K(L(x \ 1,z,u) \ 1,y). K(L(x \ 1,y,z) \ 1,u) = L(K(x,u),y,z). L(K(K(x,y),z),u,w) = K(L(K(y,x),u,w) \ 1,z). K(L(K(x,y),z,u) \ 1,w) = L(K(K(y,x),w),z,u). L(K(x,y),z,u) \ 1 = K(y,L(x \ 1,z,u) \ 1). K(x,L(y \ 1,z,u) \ 1) = L(K(y,x),z,u) \ 1. L(K(x,y),z,u) \ w = K(y,L(x \ 1,z,u) \ 1) * w. K(x,L(y \ 1,z,u) \ 1) * w = L(K(y,x),z,u) \ w. T(x,L(K(y,x),z,u)) = x. T(x,y) * T((x / K(y,x)) \ z,x) = ((x \ (z * K(y,x))) * x) / K(y,x). ((x \ (y * K(z,x))) * x) / K(z,x) = T(x,z) * T((x / K(z,x)) \ y,x). ((x \ (y * K(z,x))) * x) / K(z,x) = T(x,z) * T(T(x,z) \ y,x). (x \ y) * ((y / x) * (x * z)) = ((x \ y) * y) * z. x * y != (x * z) * R((x * z) \ x,u,w) | y = z \ R(z,u,w). (x / y) * (y * R(((y \ x) * x) \ (y \ x),z,u)) = x \ R(x,z,u). x != y * K((y \ z) \ 1,u) | x = z * T(z \ y,u). x \ T(y,z) = (x \ 1) * T((x \ 1) \ (x \ y),z). (x \ 1) * T((x \ 1) \ (x \ y),z) = x \ T(y,z). (x \ R(y,z,u)) * K(((x \ R(y,z,u)) \ (x \ 1)) \ 1,w) = x \ R(T(y,w),z,u). K(x,y) * (z * (y * x)) = (x * y) * T(z,y * x). (x * y) * T(z,y * x) = K(x,y) * (z * (y * x)). (x * L(x \ y,z,u)) / x = L(y / x,z,u). ((x \ y) * z) \ (x \ u) = L(z \ L(y \ u,y,x),z,x * y). L(x \ L(y \ z,y,u),x,u * y) = ((u \ y) * x) \ (u \ z). x != L(y \ L(z \ u,z,w),y,w * z) | x = ((w * z) * y) \ (w * u). ((x \ y) * z) \ (x \ u) = ((x * y) * z) \ (x * u). (x / y) * (y * R(((y * x) * x) \ (y * x),z,u)) = x \ R(x,z,u). L(x \ y,x,1 / x) = (1 / x) * y. x != y | x = z \ (z * y). L(x,y \ 1,y) = z \ (z * x). L((x \ 1) \ y,z \ 1,z) = x * y. L(x,y,T(z,z * (u * u))) = L(x,y,z * (u * u)). 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 * R(y,z,u)) / x = R((x * y) / x,z,u). T(T(R(x,y,y \ 1),x * y) / (y \ 1),(x * y) * (y \ 1)) = x * y. T(T(R(x,y,y \ 1),x * y) / (y \ 1),R(x,y,y \ 1)) = x * y. T(R(T(x,x * y),y,y \ 1) / (y \ 1),R(x,y,y \ 1)) = x * y. T(T(x,x * y) * y,R(x,y,y \ 1)) = x * y. T(x * y,z) = T(T(T(x,x * y) * y,z),R(x,y,y \ 1)). T(T(T(x,x * y) * y,z),R(x,y,y \ 1)) = T(x * y,z). T(x * y,R(x,y,y \ 1)) = T(x * y,T(x,y)). T(x,R(x / y,y,y \ 1)) = T((x / y) * y,T(x / y,y)). T((x / y) * y,T(x / y,y)) = T(x,R(x / y,y,y \ 1)). T((x / y) * y,T(x / y,y)) = T(x,x * (y \ 1)). T(x,T(x / y,y)) = T(x,x * (y \ 1)). T(x,y \ x) = T(x,x * (y \ 1)). T(x,x * (y \ 1)) = T(x,y \ x). T(x,x * y) = T(x,(1 / y) \ x). T(x,(1 / y) \ x) = T(x,x * y). T(x,y * x) = T(x,x * y). x != T(y,z * y) | x = K(y,z) * L(y,z,y). T(x,x * y) = K(x,y) * L(x,y,x). K(x,y) * L(x,y,x) = T(x,x * y). T(x,(x \ y) * x) = T(x,y). T(T(x,x * y),z) = T(T(x,z),y * x). T(x,x * y) * K(y * x,x) = x. T(x,y * x) * (x \ 1) = K(x,x * y). K(x,y) * T(y,y * x) = L(y,x,y). T(x,x * y) * K(y,x) = L(x,y,x). K(x * y,x) = K(y * x,x). K(x * y,y) = K(y * x,y). K(x \ y,y) = K(y * (x \ 1),y). K(x * (y \ 1),x) = K(y \ x,x). K((1 / x) \ y,y) = K(y * x,y). x / (x / y) = y * K(x * y,y). K(x,y) * K(y * x,x) = x \ R(x,y,x). x != T(y,z) * K(z * T(y,z),T(y,z)) | x = R(y,z,y). x / (x / T(y,x)) = R(y,x,y). R(x,y,x) = y / (y / T(x,y)). T(x * y,x / (x / y)) = T(x * y,y). T(x / (x / y),x * y) = y. R(x,y,x) \ y = y / T(x,y). x != R(y,z,y) \ z | x = ((z / y) / z) * T(z,R(y,z,y)). x / T(y,x) = ((x / y) / x) * T(x,R(y,x,y)). ((x / y) / x) * T(x,R(y,x,y)) = x / T(y,x). ((x / y) / x) * T(x,y) = x / T(y,x). 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 / y)) \ T(x * y,x / (x / y)) = T(x,y). (x / (x / y)) \ T(x * y,y) = T(x,y). ((x / y) / x) * T(x * y,y) = T(x,y). L(x,y,z * (((u / w) / u) * T(u,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 * (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)). x != T(y,(y \ z) * y) | x = T(y,((z / (z / y)) * z) / y). T(x,y) = T(x,((y / (y / x)) * y) / x). T(x,((y / (y / x)) * y) / x) = T(x,y). T(x,(x \ y) * T(x,y)) = T(x,y). R(T(x,y),x \ y,T(x,y)) = T(x,x \ y). x != T(y,z) * (y \ 1) | x = K(y,z). K(x,x * y) = K(x,y * x). K(x,y * x) = K(x,x * y). K(x,y * (L(y,z,u) \ x)) = K(x,x * (L(y,z,u) \ y)). K(x,1) = 1. T(x,K(y \ 1,y)) = x. x * y != z * (u * (u \ (z \ w))) | x \ w = 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. (x \ R(x,y,z)) * K((R(x,y,z) \ 1) \ 1,u) = x \ R(T(x,u),y,z). (x \ R(x,y,z)) * K(R(x,y,z),u) = x \ R(T(x,u),y,z). (x * y) * K(z \ y,z) != u * ((z \ y) * z) | R(x,y,K(z \ y,z)) = u. x / y != z | (y / x) \ 1 = z. K(x,(y \ z) / (y \ 1)) * (y \ T(z,x)) = y \ z. x * ((y \ T(z,x)) * y) = ((y \ z) * y) * x. x * ((y \ (x \ z)) * y) = ((y \ (z / x)) * y) * x. ((x \ (y / z)) * x) * z = z * ((x \ (z \ y)) * x). K(x,y) = K(x,y * K(x,y)). K(x,y * K(x,y)) = K(x,y). K(x \ y,(x \ y) \ y) = K(x \ y,x). (x * L(y,z,u)) / x = L((x * y) / x,z,u). T(x * L(y,z,u),w) / x = x \ T(x * L((x * y) / x,z,u),w). x \ T(x * L((x * y) / x,z,u),w) = T(x * L(y,z,u),w) / x. (x * ((y * z) \ (y * u))) / x = L((x * (z \ u)) / x,z,y). L((x * (y \ z)) / x,y,u) = (x * ((u * y) \ (u * z))) / x. (x * L(y,z,u)) / x = L(y * K(x,y),z,u). L(x * K(y,x),z,u) = (y * L(x,z,u)) / y. L((x * ((y \ z) \ u)) / x,y \ z,y) = (x * (z \ (y * u))) / x. (x * y) * ((z * ((x * y) \ (x * u))) / z) = x * (y * ((z * (y \ u)) / z)). (x * y) * ((z * ((x * y) \ (x * u))) / z) != w | x * (y * ((z * (y \ u)) / z)) = w. (x * y) * ((z * ((x * y) \ x)) / z) = x * (y * ((z * (y \ 1)) / z)). (x * y) * ((z * ((x * y) \ u)) / z) = x * (y * ((z * (y \ (x \ u))) / z)). (x * (y * z)) * ((u * (((x * y) * L(z,y,x)) \ (x * y))) / u) = (x * y) * (L(z,y,x) * ((u * (L(z,y,x) \ 1)) / u)). (x * (y * z)) * ((u * ((x * (y * z)) \ (x * y))) / u) = (x * y) * (L(z,y,x) * ((u * (L(z,y,x) \ 1)) / u)). x * ((y * z) * ((u * ((y * z) \ y)) / u)) = (x * y) * (L(z,y,x) * ((u * (L(z,y,x) \ 1)) / u)). (x * y) * (L(z,y,x) * ((u * (L(z,y,x) \ 1)) / u)) = x * ((y * z) * ((u * ((y * z) \ y)) / u)). (x * y) * (L(z,y,x) * ((u * (L(z,y,x) \ 1)) / u)) = x * (y * (z * ((u * (z \ 1)) / u))). (x * y) \ (x * (y * (z * ((u * (z \ 1)) / u)))) = L(z,y,x) * ((u * (L(z,y,x) \ 1)) / u). L(x,y,z) * ((u * (L(x,y,z) \ 1)) / u) != w | L(x * ((u * (x \ 1)) / u),y,z) = w. L(x * ((y * (x \ 1)) / y),z,u) = K(y,L(x,z,u) \ 1). L(K(x,y \ 1),z,u) = K(x,L(y,z,u) \ 1). L(K(x,y),z,u) = K(x,L(y \ 1,z,u) \ 1). K(x,L(y \ 1,z,u) \ 1) = L(K(x,y),z,u). K(x,(y \ z) \ 1) = L(K(x,z \ y),z \ y,z). L(K(x,y \ z),y \ z,y) = K(x,(z \ y) \ 1). L(K(x,y),z,u) * w = L(K(y,x),z,u) \ w. L(K(x,y),z,u) \ w = L(K(y,x),z,u) * w. L(K(x,y),z,u) * (L(K(y,x),z,u) * w) = w. L(K(x,y),z,u) \ 1 = L(K(y,x),z,u). L(K(x,y),z,u) \ 1 != w | L(K(y,x),z,u) = w. x != L(K(y,z),u,w) * v5 | L(K(z,y),u,w) * x = v5. L(K(x,y),z,u) * w != v5 | L(K(y,x),z,u) * v5 = w. T(x \ (y * z),u) = L(T((y \ x) \ z,u),y \ x,y). L(T((x \ y) \ z,u),x \ y,x) = T(y \ (x * z),u). R(x \ (y * z),u,w) = L(R((y \ x) \ z,u,w),y \ x,y). L(R((x \ y) \ z,u,w),x \ y,x) = R(y \ (x * z),u,w). x * T(x \ (y * z),u) = y * ((y \ x) * T((y \ x) \ z,u)). x * ((x \ y) * T((x \ y) \ z,u)) = y * T(y \ (x * z),u). x \ (y * T(y \ (x * z),u)) = (x \ y) * T((x \ y) \ z,u). x \ ((y \ (x * z)) * y) = (x \ y) * T((x \ y) \ z,y). (x \ y) * T((x \ y) \ z,y) = x \ ((y \ (x * z)) * y). L(L(x,y,T(z,u)),T(z,u) * y,K(u,z)) = (z * y) \ (z * (y * x)). L(L(x,y,T(z,u)),T(z,u) * y,K(u,z)) != w | L(x,y,z) = w. T(R(x,y,z),(u * (y * z)) / ((x * y) * z)) = T(R(x,y,z),u / R(x,y,z)). T(R(x,y,z),u / R(x,y,z)) = R(T(x,(u * (y * z)) / ((x * y) * z)),y,z). R(T(x,(y * (z * u)) / ((x * z) * u)),z,u) = T(R(x,z,u),y / R(x,z,u)). x != T(y,z / y) | x = T(y,y \ z). R(T(x,(y * (z * u)) / ((x * z) * u)),z,u) = T(R(x,z,u),R(x,z,u) \ y). R(T(x,(y * (z * u)) / ((x * z) * u)),z,u) = R(T(x,R(x,z,u) \ y),z,u). K(x,R(x \ y,z,u)) = K(x,R(y / x,z,u)). K(x,R(y / x,z,u)) = K(x,R(x \ y,z,u)). x * (K(x,y) * T(z,x)) = K(x,y) * (z * x). x \ (y * 1) != z | z = x \ y. x \ (y * 1) != z | x \ y = z. L(x \ 1,x,y / x) != z | y \ (y / x) = z. x * y != x \ (z * u) | y = (x \ (x \ z)) * u. T(x,y * y) = (y \ (y \ x)) * (y * y). (x \ (x \ y)) * (x * x) = T(y,x * x). T(x,y * y) * z = (y \ (y \ x)) * (y * (y * z)). (x \ (x \ y)) * (x * (x * z)) = T(y,x * x) * z. ((x \ 1) / y) * (x * x) = T(x / y,x * x). (x * T(x \ y,z)) * u = (x * u) * T((x * u) \ (y * u),z). (x * y) * T((x * y) \ (z * y),u) = (x * T(x \ z,u)) * y. x * y != (z * x) * T((z * x) \ (u * x),w) | T(z * T(z \ u,w),x) = y. T(x * T(x \ y,z),x) = x * T(x \ (x \ (y * x)),z). x * T(x \ (x \ (y * x)),z) = T(x * T(x \ y,z),x). x != (y * z) * T((y * z) \ u,w) | x = y * (z * T(z \ (y \ u),w)). (x * T(x \ y,z)) * u = x * (u * T(u \ (x \ (y * u)),z)). x * (y * T(y \ (x \ (z * y)),u)) = (x * T(x \ z,u)) * y. (x * y) * T((x * y) \ (z * y),u) != y * w | T(x * T(x \ z,u),y) = w. (x / (y \ x)) * z != u | u = y * z. (x / (y \ x)) * z != u | y * z = u. (K(x,y) * z) \ T(x,y) != u | L(z \ x,z,K(x,y)) = u. T(x,y) * (z \ 1) = z \ T(z * (x * (z \ 1)),y). x \ T(x * (y * (x \ 1)),z) = T(y,z) * (x \ 1). K(x,y / (z \ 1)) * (z \ T(z * y,x)) = y. L(L(K(x,y),z,u),K(y,x),w) = L((w * K(y,x)) \ w,z,u). L(R(x / y,y,y \ z),u,w) * z = z * L(z \ (x * (y \ z)),u,w). x != L(R(y,z,z \ u),w,v5) * u | x = (L(y,w,v5) * z) * (z \ u). x * L(x \ (y * (z \ x)),u,w) = (L(y / z,u,w) * z) * (z \ x). (L(x / y,z,u) * y) * (y \ w) = w * L(w \ (x * (y \ w)),z,u). (x * L(x \ y,z,u)) * (x \ w) = w * L(w \ (y * (x \ w)),z,u). (x * L(x \ y,z,u)) * w = (x * w) * L((x * w) \ (y * (x \ (x * w))),z,u). (x * y) * L((x * y) \ (z * (x \ (x * y))),u,w) = (x * L(x \ z,u,w)) * y. (x * y) * L((x * y) \ (z * y),u,w) = (x * L(x \ z,u,w)) * y. x * L(((x / y) * y) \ (z * y),u,w) = ((x / y) * L((x / y) \ z,u,w)) * y. ((x / y) * L((x / y) \ z,u,w)) * y = x * L(((x / y) * y) \ (z * y),u,w). (x * y) * L((x * y) \ y,z,u) = (x * L(x \ 1,z,u)) * y. (x * T(y,z)) * L(y,u,w) = (x * L(x \ (x * y),u,w)) * T(y,z). (x * L(x \ (x * y),z,u)) * T(y,w) = (x * T(y,w)) * L(y,z,u). ((x / y) * L((x / y) \ z,u,w)) * y = x * L(x \ (z * y),u,w). (x * L(x \ (y * z),u,w)) / z = (x / z) * L((x / z) \ y,u,w). ((x / y) * L((x / y) \ x,z,u)) * y = x * L(y,z,u). ((x / y) * L(y,z,u)) * y = x * L(y,z,u). ((x / y) * L(y,z,u)) \ (x * L(y,z,u)) = y. (x * L(y,z,u)) * y = (x * y) * L(y,z,u). (x * y) / L(y,z,u) = (x / L(y,z,u)) * y. x * y != (z * L(u,w,v5)) * u | ((z * u) * L(u,w,v5)) / y = x. ((x * y) * L(y,z,u)) / (x * L(y,z,u)) = y * K(x * L(y,z,u),y). x * y != ((z / u) * u) * w | x \ (z * w) = y. ((x / L(y,z,u)) * y) \ (x * y) = L(y,z,u). (x * y) / L(y,z,u) != w | w = (x / L(y,z,u)) * y. (x * y) / L(y,z,u) != w | (x / L(y,z,u)) * y = w. R(x * K(y,x),y,L(x,z,u)) = x * K(y * L(x,z,u),x). T(x * K(y * L(x,z,u),x),y) = R(x,y,L(x,z,u)). T(x,y) * K(y * L(x,z,u),T(x,y)) = R(x,y,L(x,z,u)). a(x,(y * (y * z)) * (y * u),w) = a(x,z \ (y \ u),w). a(x,y * (y * (z * (y * u))),w) = a(x,z \ (y \ u),w). x != a(y,z * (z * u),w) | x = a(y,u,w). a(x,y \ (z \ u),w) = a(x,y * (z * u),w). x != a(y,z \ u,w) | x = a(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 * T(y \ (x \ y),z)) = (x * T(x \ 1,z)) * y. x * ((y \ z) * T((y \ z) \ (x \ z),u)) = (x * T(x \ y,u)) * (y \ z). x * (y * T(y \ (x \ z),u)) = (x * T(x \ (z / y),u)) * y. (x * T(x \ (y / z),u)) * z = x * (z * T(z \ (x \ y),u)). (x * y) * (z * T(z \ L(y \ z,y,x),u)) = ((x * y) * T((x * y) \ x,u)) * z. ((x * y) * T((x * y) \ x,z)) * u = (x * y) * (u * T(u \ L(y \ u,y,x),z)). x * ((y \ (x \ y)) * y) = (x * T(x \ 1,y)) * y. (x * T(x \ 1,y)) * y = x * ((y \ (x \ y)) * y). x * (y * T(y \ (x \ y),z)) = K(x \ 1,z) * y. ((x \ y) * T((x \ y) \ 1,y)) * y = (x \ y) * ((y \ T(x,x \ y)) * y). (x \ y) * ((y \ T(x,x \ y)) * y) = ((x \ y) * T((x \ y) \ 1,y)) * y. (x \ y) * ((y \ T(x,x \ y)) * y) = (x \ ((y \ x) * y)) * y. (x \ y) * ((y \ T(x,x \ y)) * y) = K(y \ x,y) * y. x != K(y,z) * z | x = z * K(y,z). (x \ y) * ((y \ T(x,x \ y)) * y) = y * K(y \ x,y). ((x * y) * T((x * y) \ x,z)) * z = (x * y) * ((z \ L(y \ z,y,x)) * z). ((x * (y \ z)) * T((x * (y \ z)) \ x,z)) * z = (x * (y \ z)) * ((z \ L(T(y,y \ z),y \ z,x)) * z). (x * ((y \ z) * T((y \ z) \ 1,z))) * z = (x * (y \ z)) * ((z \ L(T(y,y \ z),y \ z,x)) * z). (x * (y \ z)) * ((z \ L(T(y,y \ z),y \ z,x)) * z) = (x * ((y \ z) * T((y \ z) \ 1,z))) * z. (x * (y \ z)) * ((z \ L(T(y,y \ z),y \ z,x)) * z) = (x * (y \ ((z \ y) * z))) * z. (x * (y \ z)) * ((z \ L(T(y,y \ z),y \ z,x)) * z) = (x * K(z \ y,z)) * z. (x * ((y \ (x \ z)) * y)) / x = (y \ (z / x)) * y. ((x \ (y / z)) * x) * z != u | u = z * ((x \ (z \ y)) * x). ((x \ (y / z)) * x) * z != u | z * ((x \ (z \ y)) * x) = u. (x * (y * T(y \ T(z,x),u))) / x = ((x * y) / x) * T(((x * y) / x) \ z,u). ((x * y) / x) * T(((x * y) / x) \ z,u) = (x * (y * T(y \ T(z,x),u))) / x. x / (K(y,z) * (y \ x)) = y * K(z,y). (x / (x / y)) \ z = K(y,y \ x) * (y \ z). (x * K(y,x)) \ z != u | u = K(x,y) * (x \ z). (x * K(y,x)) \ z != u | K(x,y) * (x \ z) = u. x != (y \ z) \ z | x = T(y,y \ z). x = T(x,x \ R(x,y,z)). T(x,x \ R(x,y,z)) = x. R(x,y,z) \ R(x,y,z) = K(R(x,y,z),x \ R(x,u,w)). K(R(x,y,z),x \ R(x,u,w)) = R(x,y,z) \ R(x,y,z). x != y \ y | x = 1. K(R(x,y,z),x \ R(x,u,w)) = 1. x != K((y \ 1) \ 1,z) | x = K(y,z). K(x \ 1,x) = K(y,y \ 1). K(x \ 1,x) * T(y,y \ 1) = y. K(x \ 1,x) * y != z | K(u,u \ 1) * z = y. K(x \ 1,x) * (x * y) = x * (K(z \ 1,z) * y). L(x,y,K(z \ 1,z)) = x. K(x,x \ 1) * (y * (K(z \ 1,z) * u)) = y * u. K(x,x \ 1) * (y * z) = T(y,y \ 1) * z. T(x,x \ 1) * y = K(z,z \ 1) * (x * y). K(x,x \ 1) * y = T(y,y \ 1). T(x,x \ 1) = K(y,y \ 1) * x. K(x,x \ 1) * (y * z) = y * T(z,z \ 1). T(x,K(y,y \ 1)) = x. K(x,L(y \ 1,z,u) \ 1) != w | L(K(x,y),z,u) = w. R(T(x / y,y),(x / y) \ 1,z) = y \ x. 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. R(K(x,y),x * (z / (z * x)),u) = K(x,y). R(K(x,y),K(x,z),u) = K(x,y). x != R(y,K(z,u),w) | x = R(y,K(u,z),w). 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). 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) * K(y,z)) * u = K(x,y) * (K(y,z) * u). R(K(x,y),K(y,z),u) = K(x,y). x * y != (K(z,u) * K(u,w)) * v5 | (K(z,u) * (K(u,w) * v5)) / y = x. (K(x,y) * (K(y,z) * u)) / (K(x,y) * K(y,z)) = u * K(K(x,y) * K(y,z),u). 1 * x != (y * z) / u | x = R(y / (u / z),u / z,z). x * y = R(x / (1 / y),1 / y,y). R(x / (1 / y),1 / y,y) = x * y. R((x * y) / z,u,w) = R(R(x / (z / y),u,w),z / y,y). R(R(x / (y / z),u,w),y / z,z) = R((x * z) / y,u,w). (x \ ((x * y) * z)) / (x \ (y * z)) = R(x,y,z). x * L(L(x,y,z),u,w) = L(L(x,y,z),u,w) * x. L(L(x,y,z),u,w) * x = x * L(L(x,y,z),u,w). x * y != T((y * z) * y,y) | x = z * y. K(x \ 1,x) * y = y * K(x \ 1,x). K(x \ 1,x) * y != z | y * K(x \ 1,x) = z. (T(x,x \ y) * z) \ (z * ((x \ y) \ y)) = K(z,(x \ y) \ y). (T(x,x \ 1) * y) \ (y * ((x \ 1) \ 1)) = K(y,x). x != (T(y,y \ z) * u) \ (u * ((y \ z) \ z)) | x = K(u,(y \ z) \ z). K(x,y) = K(x,(y \ 1) \ 1). K(x,(y \ 1) \ 1) = K(x,y). K(x,(y / z) \ 1) = K(x,z / y). K(x,(y / z) \ 1) = K(z / y,x) \ 1. K(x / y,z) \ 1 = K(z,(y / x) \ 1). x * (y \ T(y * (x \ z),x)) = ((x \ (z / (y \ 1))) * x) * (y \ 1). ((x \ (y / (z \ 1))) * x) * (z \ 1) = x * (z \ T(z * (x \ y),x)). x * ((y \ (x \ z)) * y) = z * K((z \ (y * x)) \ 1,y). x * K((x \ (y * z)) \ 1,y) = z * ((y \ (z \ x)) * y). (x * (y \ z)) \ (x * (y \ (z * u))) = L(L(u,z,y),y * z,x). a(R(x,x * y,z),u,w) = a(R(x,y,z),u,w). x * y != (z * x) * L((z * x) \ (u * x),w,v5) | T(z * L(z \ u,w,v5),x) = y. T(x * L(x \ y,z,u),x) = x * L(x \ (x \ (y * x)),z,u). x * L(x \ (x \ (y * x)),z,u) = T(x * L(x \ y,z,u),x). x != (y * z) * L((y * z) \ (u * z),w,v5) | x = (y * L(y \ u,w,v5)) * z. x * (y * L(y \ (x \ (z * y)),u,w)) = (x * L(x \ z,u,w)) * y. K(x \ 1,x) * L(((x \ 1) * x) \ y,z,u) = (x \ 1) * (x * L(x \ ((x \ 1) \ y),z,u)). x * (y * L(y \ (x \ y),z,u)) = (x * L(x \ 1,z,u)) * y. K(x,y) * (z * L(T(K(y,x),z),u,w)) = (K(x,y) * L(K(x,y) \ 1,u,w)) * z. K(x,y) * (L(K(y,x),z,u) * w) = (K(x,y) * L(K(x,y) \ 1,z,u)) * w. (K(x,y) * L(K(x,y) \ 1,z,u)) * w = K(x,y) * (L(K(y,x),z,u) * w). (K(x,y) * L(K(y,x),z,u)) * w = K(x,y) * (L(K(y,x),z,u) * w). (x \ 1) / (x \ K(x,y)) = K(y,x). L(x * K(y,x),z,u) = L(x,z,u) * K(y,L(x,z,u)). L(x,y,z) * K(u,L(x,y,z)) = L(x * K(u,x),y,z). x * y != (z * L(u,w,v5)) / z | L(u * K(z,u),w,v5) / y = x. L(x * K(y,x),z,u) / L(x,z,u) = K(y,L(x,z,u)). L(x * K(y * z,x),z,y) = (y * (z * x)) / (y * z). (K(x \ 1,x) * y) / z = K(x \ 1,x) * (y / z). R((x * y) / z,u,w) * z = (R(x / (z / y),u,w) * (z / y)) * y. (R(x / (y / z),u,w) * (y / z)) * z = R((x * z) / y,u,w) * y. (R(x / (y / z),u,w) * (y / z)) * z = y * R(y \ (x * z),u,w). ((x / y) * R((x / y) \ z,u,w)) * y = x * R(x \ (z * y),u,w). ((x / y) * R((x / y) \ 1,z,u)) * y = x * R(x \ y,z,u). (x * R(((x * y) / y) \ z,u,w)) * y = (x * y) * R((x * y) \ (z * y),u,w). (x * R(x \ y,z,u)) * w = (x * w) * R((x * w) \ (y * w),z,u). (x * y) * R((x * y) \ (z * y),u,w) = (x * R(x \ z,u,w)) * y. (x * y) * R((x * y) \ y,z,u) = (x * R(x \ 1,z,u)) * y. (x * y) * R(y,z,u) = (x * R(x \ (x * y),z,u)) * y. (x * R(x \ (x * y),z,u)) * y = (x * y) * R(y,z,u). (x * R(y,z,u)) * y = (x * y) * R(y,z,u). (x * R(y,z,u)) / y = (x / y) * R(y,z,u). (x * y) / R(y,z,u) = (x / R(y,z,u)) * y. x * y != (z * R(u,w,v5)) * u | ((z * u) * R(u,w,v5)) / y = x. ((x * y) * R(y,z,u)) / (x * R(y,z,u)) = y * K(x * R(y,z,u),y). K(x,y) * ((y * R(x,z,u)) * x) = (x * y) * R(x,z,u). T(T(x * K(y * R(x,z,u),x),w),y) = R(T(y \ (y * x),w),y,R(x,z,u)). T(x * K(y * R(x,z,u),x),y) = R(x,y,R(x,z,u)). T(T(x * K(y * R(x,z,u),x),w),y) = R(T(x,w),y,R(x,z,u)). T(x,y) = R(T(x,y * R(x,z,u)),y,R(x,z,u)). R(T(x,y * R(x,z,u)),y,R(x,z,u)) = T(x,y). T(x,y) * K(y * R(x,z,u),T(x,y)) = R(x,y,R(x,z,u)). (x * R(y,z,u)) * T(y,x) = (y * x) * R(y,z,u). (x * (y * K(z * L(y,u,w),y))) / (y * K(z,y)) = (x / (y * K(z,y))) * R(y * K(z,y),z,L(y,u,w)). (x / (y * K(z,y))) * R(y * K(z,y),z,L(y,u,w)) = (x * (y * K(z * L(y,u,w),y))) / (y * K(z,y)). R(T(x,y),z,u) * (K(x,w) * v5) = (R(T(x,y),z,u) * K(x,w)) * v5. (R(T(x,y),z,u) * K(x,w)) * v5 = R(T(x,y),z,u) * (K(x,w) * v5). (K(x,y) * R(y,z,u)) * w = R(y,z,u) * (K(x,y) * w). R(x,y,z) * (K(u,x) * w) != v5 * (R(x,y,z) * w) | R(K(u,x),R(x,y,z),w) = v5. R(K(x,y),R(y,z,u),w) = K(x,y). T(L(L(x,y,x),z,u),y) = L(T(x,x * y),z,u). x * L(T(y,y * x),z,u) = L(L(y,x,y),z,u) * x. T(L(L(x,y,x),z,u),y) = T(L(x,z,u),x * y). K(x,x \ 1) * y != z | y * K(x,x \ 1) = z. (x * y) * K(z,z \ 1) = x * T(y,y \ 1). x * K(y,y \ 1) = (x / z) * T(z,z \ 1). (x / y) * T(y,y \ 1) = x * K(z,z \ 1). x * y != K(z \ 1,z) * T(u * y,(u * y) \ 1) | x = u. K(x \ 1,x) * (y * K(z,z \ 1)) = y. (x * K(y,y \ 1)) * z = x * T(z,z \ 1). (x * K(y,y \ 1)) * K(z \ 1,z) = x. K(x \ y,x) * z != x \ y | z = y / x. (x \ 1) * K(y,y \ 1) = 1 / x. x * K(y \ z,y) != z / (z / y) | x = y. (1 / (1 / x)) * K(y,y \ 1) = x. (R(x,y,z) * u) / (R(T(x,w),y,z) * u) != v5 | K(w,R(x,y,z)) = v5. (x \ 1) / (x \ K(x,y)) != z | K(y,x) = z. x * (y * z) != u | u = (x * y) * L(z,y,x). x * (y * z) != u | (x * y) * L(z,y,x) = u. x * y != K(z,u) * ((u * z) / u) | x \ z = y. ((x * y) / x) \ x = y \ ((y * x) / y). x * y != K(z,u) * (z * w) | x \ (T(z,u) * w) = y. ((x * y) / x) \ (T(x,y) * z) = y \ (x * z). R(x * K(y,x),z,u) \ y = R(x,z,u) \ ((R(x,z,u) * y) / R(x,z,u)). (x * R(x \ y,z,u)) / y = (x / y) * R((x / y) \ 1,z,u). (x / y) * R((x / y) \ 1,z,u) = (x * R(x \ y,z,u)) / y. R(x,y,z) * R((((x * y) * z) / (y * z)) \ 1,u,w) = (((x * y) * z) * R(((x * y) * z) \ (y * z),u,w)) / (y * z). (((x * y) * z) * R(((x * y) * z) \ (y * z),u,w)) / (y * z) = R(x,y,z) * R((((x * y) * z) / (y * z)) \ 1,u,w). (((x * y) * z) * R(((x * y) * z) \ (y * z),u,w)) / (y * z) = R(x,y,z) * R(R(x,y,z) \ 1,u,w). (((x * y) * R((x * y) \ y,z,u)) * w) / (y * w) = R(x,y,w) * R(R(x,y,w) \ 1,z,u). (((x * R(x \ 1,y,z)) * u) * w) / (u * w) = R(x,u,w) * R(R(x,u,w) \ 1,y,z). R(x * R(x \ 1,y,z),u,w) = R(x,u,w) * R(R(x,u,w) \ 1,y,z). R(x,y,z) * R(R(x,y,z) \ 1,u,w) = R(x * R(x \ 1,u,w),y,z). K(x,y) * R(R(K(x,y),K(y,z),u) \ 1,w,v5) = R(K(x,y) * R(K(x,y) \ 1,w,v5),K(y,z),u). K(x,y) * R(K(x,y) \ 1,z,u) = R(K(x,y) * R(K(x,y) \ 1,z,u),K(y,w),v5). R(K(x,y) * R(K(x,y) \ 1,z,u),K(y,w),v5) = K(x,y) * R(K(x,y) \ 1,z,u). R(K(x,y) * R(K(x,y) \ 1,z,u),K(y,w),v5) = K(x,y) * R(K(y,x),z,u). R(K(x,y) * R(K(y,x),z,u),K(y,w),v5) = K(x,y) * R(K(y,x),z,u). (1 / x) * ((y * x) / y) = K(y,x). L(T(x,y),y,K(z,x)) != u | T(x,K(z,x) * y) = u. (x \ 1) * R((x \ 1) \ 1,y,z) = x \ R(x,y,z). x * y != R(z,u,w) * x | y = R(T(z,x),u,w). R((x \ y) \ y,z,u) = R(T(x,x \ y),z,u). R(T(x,x \ y),z,u) = R((x \ y) \ y,z,u). x * y != R((z \ u) \ u,w,v5) | x \ R(T(z,z \ u),w,v5) = y. x \ R(T(y,y \ z),u,w) = x \ R((y \ z) \ z,u,w). K(x,x \ 1) * (y * K(z \ 1,z)) = y. (x * K(y \ 1,y)) * L(z,x,K(y \ 1,y)) = K(y \ 1,y) * (x * z). (1 / (1 / x)) * y = x * (y * K(x \ 1,x)). x * (y * K(x \ 1,x)) = (1 / (1 / x)) * y. (x * K(y \ 1,y)) * z = K(y \ 1,y) * (x * z). (x * (y * K(z \ 1,z))) \ (x * (K(z \ 1,z) * (y * u))) != w | L(u,y * K(z \ 1,z),x) = w. x * y != L(z,u * x,u) | y = u * ((u \ (x \ 1)) * z). a(x,y,y) = x * ((x \ (y \ 1)) * y). x * ((x \ (y \ 1)) * y) = a(x,y,y). T(x,y) * z != x * R(y,x,u) | T(R(y,x,u),T(x,y)) = z. 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)). x * y != z * R(u,z,u) | x \ T(u * z,u) = y. R(x,y,x) \ T(x * y,x) = 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). x * y != K(z,u) * R(z,u,w) | x \ R(T(z,u),u,w) = y. T(x,y) \ R(T(x,y),y,z) = x \ R(x,y,z). x != y \ (K(y,z) * u) | x = (y \ K(y,z)) * u. K(x,y) * (x \ z) = (x \ K(x,y)) * z. (x \ K(x,y)) * z = K(x,y) * (x \ z). (K(x,y) * (x \ z)) \ ((x \ K(x,y)) * (z * u)) = L(u,z,x \ K(x,y)). (K(x,y) * (x \ z)) \ (K(x,y) * (x \ (z * u))) = L(u,z,x \ K(x,y)). x != (y * (z \ u)) \ (y * (z \ (u * w))) | x = L(L(w,u,z),z * u,y). 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)). x != K(y,z) * (y \ u) | x = (y * K(z,y)) \ u. x \ (y * K(x,y)) = (x * K(y,x)) \ y. (x * K(y,x)) \ y = x \ (y * K(x,y)). x \ L(y * z,u,w) = (x \ 1) * L((y \ 1) \ z,u,w). (x \ 1) * L((y \ 1) \ z,u,w) = x \ L(y * z,u,w). (x \ 1) * L((y \ 1) \ 1,z,u) = x \ L(y,z,u). T(x,y * (y * z)) = z \ (y \ (y \ (x * (y * (y * z))))). x \ (y \ (y \ (z * (y * (y * x))))) = T(z,y * (y * x)). x \ ((y \ (y \ z)) * (y * (y * x))) = T(z,y * (y * x)). x \ (T(y,z * z) * x) = T(y,z * (z * x)). T(T(x,y * y),z) = T(x,y * (y * z)). T(T(x,y),z * z) = T(x,z * (z * y)). (L(x,y,z) * (z * y)) \ (x * (z * y)) = a(z,y,T(x,z * y)). (L(x,y \ z,y) * z) \ (x * (y * (y \ z))) = a(y,y \ z,T(x,y * (y \ z))). (L(x,y \ z,y) * z) \ (x * z) = a(y,y \ z,T(x,y * (y \ z))). a(x,x \ y,T(z,x * (x \ y))) = (L(z,x \ y,x) * y) \ (z * y). a(x,x \ y,T(z,y)) = (L(z,x \ y,x) * y) \ (z * y). (L(x,y \ z,y) * z) \ (x * z) = a(y,y \ z,T(x,z)). (x * L(y,z,u)) * T(y,w) = (x * T(y,w)) * L(y,z,u). (x * T(y,z)) * L(y,u,w) = (x * L(y,u,w)) * T(y,z). (x * y) * L(x,z,u) = (y * L(x,z,u)) * T(x,y). (x * L(y,z,u)) * T(y,x) = (y * x) * L(y,z,u). R(x / y,z,u) * y != w | w = y * R(y \ x,z,u). R(x / y,z,u) * y != w | y * R(y \ x,z,u) = w. (x * y) / ((z * y) / z) = (x / (y * K(z,y))) * y. (x \ y) \ z = K(x,x \ y) * ((y / x) \ z). K(x,x \ y) * ((y / x) \ z) = (x \ y) \ z. (x \ y) * z = (y / x) * (K(x \ y,x) * z). (x / y) * (K(y \ x,y) * z) = (y \ x) * z. (x / y) \ (z * (y \ x)) = K(y \ x,y) * T(z,y \ x). K(x \ y,x) * T(z,x \ y) = (y / x) \ (z * (x \ y)). K(x \ 1,x) * L(K(x \ 1,x) \ y,z,u) = (x \ 1) * (x * L(x \ ((x \ 1) \ y),z,u)). x != y * (z * L(z \ (y \ (u * z)),w,v5)) | x = (y * L(y \ u,w,v5)) * z. K(x \ 1,x) * L(K(x \ 1,x) \ (y * x),z,u) = ((x \ 1) * L((x \ 1) \ y,z,u)) * x. K(x \ 1,x) * L(K(x \ 1,x) \ (y * x),z,u) = (x \ L(x * y,z,u)) * x. K(x \ 1,x) * L(K(x,x \ 1) * (y * x),z,u) = (x \ L(x * y,z,u)) * x. K(x \ 1,x) * L(y * T(x,x \ 1),z,u) = (x \ L(x * y,z,u)) * x. K(x \ 1,x) * L(y * K(z,z \ 1),u,w) = (x \ L(x * (y / x),u,w)) * x. (L(x,y,z) \ u) / (x \ u) = L(x,y,z) \ x. R(L(x,y,z) \ x,x,u) = ((L(x,y,z) \ 1) * u) / (x \ u). R(L(x,y,z) \ x,x,u) = (L(x,y,z) \ u) / (x \ u). x != (L(y,z,u) \ w) / (y \ w) | x = L(y,z,u) \ y. R(L(x,y,z) \ x,x,u) = L(x,y,z) \ x. (x * y) * R(T(y,x),z,u) = R(R(y,x,y),z,u) * (x * y). R(R(x,y,x),z,u) * (y * x) = (y * x) * R(T(x,y),z,u). (x * y) * L(T(y,x),z,u) = L(R(y,x,y),z,u) * (x * y). L(R(x,y,x),z,u) * (y * x) = (y * x) * L(T(x,y),z,u). K(T(x,y),y * x) = K(R(x,y,x),y * x). K(R(x,y,x),y * x) = K(T(x,y),y * x). x != L(R(y,z,u),w,v5) * (z * u) | x = (L(y,w,v5) * z) * u. (x * y) * L(T(y,x),z,u) = (L(y,z,u) * x) * y. x \ ((L(y,z,u) * (y \ x)) * y) = K(y \ x,y) * L(T(y,y \ x),z,u). K(x \ y,x) * L(T(x,x \ y),z,u) = y \ ((L(x,z,u) * (x \ y)) * x). T(T(x * K(x * y,x),z),y) = R(T(x,z),y,x). T(T(x,y),z) = T(T(T(x,y),z),x). T(T(T(x,y),z),x) = T(T(x,y),z). x * L(T(x,y),z,u) = L(T(x,y),z,u) * x. L(T(x,y),z,u) * x = x * L(T(x,y),z,u). x != K(y,z) * u | x = K(z,y) \ u. T(T(x,y),z) * K(u,x) = K(x,u) \ T(T(x,y),z). K(x,y) \ T(T(x,z),u) = T(T(x,z),u) * K(y,x). x != K(y,z) * T(T(z,y),u) | x = z * K(T(z,y),u). T(T(x,y),z) * K(y,x) = x * K(T(x,y),z). T(x / y,x \ y) = x / y. (x / y) * (x \ y) != z | (x \ y) * (x / y) = z. (K(x,x \ 1) * y) * z = K(u,u \ 1) * (y * z). K(x,x \ 1) * (y * z) = (K(u,u \ 1) * y) * z. (K(x,x \ 1) * y) \ (K(z,z \ 1) * u) = y \ u. x \ (K(y,y \ 1) * z) = (x * K(u \ 1,u)) \ z. (x * K(y \ 1,y)) \ z = x \ (K(u,u \ 1) * z). T(K(x,y),T(x,z)) = K(x,y). x != T(y,z) * K(y,u) | x = K(y,z) * T(y,u). K(x,y) * T(x,z) = K(x,z) * T(x,y). x / (((y \ (x / z)) * y) * z) = K(y,x / (y * z)). x / (((y \ (x * z)) * y) / z) = K(y,x / (y / z)). x / (y * ((z \ (y \ x)) * z)) = K(z,x / (z * y)). ((x \ (y / (x \ z))) * x) * (x \ z) = T(y / z,x) * z. ((x \ (y / (x \ z))) * x) * (x \ z) = z * T(z \ y,x). ((x \ y) * x) * (x \ z) = z * T(z \ (y * (x \ z)),x). ((x \ y) * x) * K(z,x) = ((z * x) / z) * T(((z * x) / z) \ (y * (x \ ((z * x) / z))),x). ((x * y) / x) * T(((x * y) / x) \ (z * (y \ ((x * y) / x))),y) = ((y \ z) * y) * K(x,y). ((x * y) / x) * T(((x * y) / x) \ (z * K(x,y)),y) = ((y \ z) * y) * K(x,y). x != ((y * z) / y) * T(((y * z) / y) \ u,w) | x = (y * (z * T(z \ T(u,y),w))) / y. ((x \ y) * x) * K(z,x) = (z * (x * T(x \ T(y * K(z,x),z),x))) / z. (x * (y * T(y \ T(z * K(x,y),x),y))) / x = ((y \ z) * y) * K(x,y). (x * ((y \ T(z * K(x,y),x)) * y)) / x = ((y \ z) * y) * K(x,y). (((x \ (y * K(z,x))) * x) * z) / z = ((x \ y) * x) * K(z,x). ((x \ y) * x) * K(z,x) = (x \ (y * K(z,x))) * x. (x \ (y * K(z,x))) * x = ((x \ y) * x) * K(z,x). (((x \ y) * x) * K(z,x)) / K(z,x) = T(x,z) * T(T(x,z) \ y,x). T(x,y) * T(T(x,y) \ z,x) = (x \ z) * x. T(x,y) * T(y,z) = (y \ (x * T(y,z))) * y. (x \ (y * T(x,z))) * x = T(y,x) * T(x,z). x != (y * (y * z)) \ u | x = z \ (y \ (y \ u)). 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 \ (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). x * y != z \ z | x \ 1 = y. (L(x,y,z) \ 1) \ 1 = L((x \ 1) \ 1,y,z). (L(1 / x,y,z) \ 1) \ 1 = L(x \ 1,y,z). 1 / L(x \ 1,y,z) = L(1 / x,y,z) \ 1. 1 / L(x,y,z) = L(1 / (1 / x),y,z) \ 1. L(1 / (1 / x),y,z) \ 1 = 1 / L(x,y,z). 1 / (1 / L(x,y,z)) = L(1 / (1 / x),y,z). 1 / (1 / ((x * y) \ z)) = L(1 / (1 / (y \ (x \ z))),y,x). L(1 / (1 / (x \ (y \ z))),x,y) = 1 / (1 / ((y * x) \ z)). (x * y) * (1 / (1 / ((x * y) \ z))) = x * (y * (1 / (1 / (y \ (x \ z))))). ((x * R(y,z,u)) / x) * (z * u) != w | (((x * y) / x) * z) * u = w. (((x * (y / z)) / x) * z) * u = (z * u) * ((x * ((z * u) \ (y * u))) / x). (x * y) * ((z * ((x * y) \ (u * y))) / z) = (((z * (u / x)) / z) * x) * y. (x * y) * ((z * ((x * y) \ u)) / z) = (((z * ((u / y) / x)) / z) * x) * y. (((x * ((y / z) / u)) / x) * u) * z = (u * z) * ((x * ((u * z) \ y)) / x). (x * y) * ((z * ((x * y) \ (u * y))) / z) = (x * ((z * (x \ u)) / z)) * y. x * ((y * (((x / z) * z) \ (u * z))) / y) = ((x / z) * ((y * ((x / z) \ u)) / y)) * z. ((x / y) * ((z * ((x / y) \ u)) / z)) * y = x * ((z * (((x / y) * y) \ (u * y))) / z). (x * y) * ((z * ((x * y) \ y)) / z) = (x * ((z * (x \ 1)) / z)) * y. (x * y) * ((z * ((x * y) \ y)) / z) = K(z,x \ 1) * y. ((x / y) * ((z * ((x / y) \ u)) / z)) * y = x * ((z * (x \ (u * y))) / z). (x * ((y * (x \ (z * u))) / y)) / u = (x / u) * ((y * ((x / u) \ z)) / y). (x * ((y * (x \ z)) / y)) / z = (x / z) * ((y * ((x / z) \ 1)) / y). (x / y) * ((z * ((x / y) \ 1)) / z) = (x * ((z * (x \ y)) / z)) / y. x != y * ((z * (y \ 1)) / z) | x = K(z,y \ 1). (x * ((y * (x \ z)) / y)) / z = K(y,(x / z) \ 1). (x * (y * ((z * (y \ (x \ u))) / z))) / u = K(z,((x * y) / u) \ 1). (x * (y * ((x \ z) / y))) / z = K(y,((x * y) / z) \ 1). x != K(y,(z / u) \ 1) | x = K(y,u / z). (x * (y * ((x \ z) / y))) / z = K(y,z / (x * y)). R(K(x,(y / z) / (u * x)),y / z,z) = ((u * (x * ((u \ (y / z)) / x))) * z) / y. x != R(K(y,(z / u) / w),z / u,u) | x = K(y,z / (w * u)). ((x * (y * ((x \ (z / u)) / y))) * u) / z = K(y,z / ((x * y) * u)). K(x,y) * T(x,z) != u | K(x,z) * T(x,y) = u. x * R(x \ 1,y \ 1,y) = a(x,y,y). x * R(x \ 1,y,y) = a(x,y,y). x != y * R(y \ 1,z,u) | x = y \ R(y,z,u). a(x,y,y) = x \ R(x,y,y). x \ R(x,y,y) = a(x,y,y). L(x,a(y,z,z),z) = x. (x * a(y,x,x)) * z = x * (a(y,x,x) * z). a(x,y,y) \ z = (R(x,y,y) \ x) * z. (R(x,y,y) \ x) * z = a(x,y,y) \ z. a(x,y,y) \ R(x,y,y) = x. x != (R(y,z,u) \ y) * y | x = R(y,y * z,u). a(x,y,y) \ x = R(x,x * y,y). x * y != (z / u) * T(u,u \ 1) | (z * K(w,w \ 1)) / y = x. (x * K(y,y \ 1)) / z = (x / z) * K(u,u \ 1). (x * K(y,y \ 1)) * z = x * ((z \ 1) \ 1). T((x / y) * K(z,z \ 1),y) = y \ (x * K(u,u \ 1)). (x \ y) * K(x,x \ 1) = (1 / (1 / x)) \ y. ((1 / (1 / x)) \ y) * z = (x \ y) * ((z \ 1) \ 1). x \ K(y,y \ 1) = 1 / x. (R(T(x,y),z,u) * K(w,x)) * v5 = (K(w,x) * R(T(x,y),z,u)) * v5. (K(x,y) * R(T(y,z),u,w)) * v5 != R(T(y,z),u,w) * K(x,y) | 1 = v5. x * y != T(z / (z / u),z) | x \ L(u,u \ z,u) = y. (x / (x / y)) \ L(y,y \ x,y) = K(x / (x / y),x). T(T(x / (x / y),x),z) = L(T(y,z),y \ x,y). T(x,y) = T(x,(y \ x) \ x). T(x,(y \ x) \ x) = T(x,y). T(x,T(y,y * x)) = T(x,y). T(x \ y,T(x,y)) = T(x \ y,x). T(x,x * y) * L(T(y,x),z,u) = L(y,z,u) * T(x,x * y). T(x * y,T(y,x)) = T(x * y,y). T(x,y) * T(x \ y,x) = (x \ y) * T(x,y). R(T(x / (1 / y),z),1 / y,y) = T(x * y,z). x * y != R(T(z / (1 / u),w),1 / u,u) | T(z * u,w) / y = x. T(x * y,z) / y = T(x / (1 / y),z) * (1 / y). T(x / (1 / y),z) * (1 / y) = T(x * y,z) / y. (1 / x) * T((1 / x) \ y,z) = T(y * x,z) / x. (1 / x) * T((1 / x) \ (y / x),z) = T(y,z) / x. x * (T((x \ y) * z,x) / z) = ((x \ (y / (1 / z))) * x) * (1 / z). ((x \ (y / (1 / z))) * x) * (1 / z) = x * (T((x \ y) * z,x) / z). x != y * T(y \ z,u) | x = K((y / z) \ 1,u) * z. T(x,y) / z = K(((1 / z) / (x / z)) \ 1,y) * (x / z). K(((1 / x) / (y / x)) \ 1,z) * (y / x) = T(y,z) / x. x * y != (1 / z) * T((1 / z) \ (u / z),w) | (T(u,w) / z) / y = x. (T(x,y) / z) / (x / z) = K(((1 / z) / (x / z)) \ 1,y). K(((1 / x) / (y / x)) \ 1,z) = (T(y,z) / x) / (y / x). K(((x \ 1) / (y / x)) \ 1,z) = (T(y,z) / x) / (y / x). x * (T(y,z) / x) = T(x * (y / x),z). x * ((y \ z) / x) = T(x * ((z / y) / x),y). T(x * ((y / z) / x),z) = x * ((z \ y) / x). x * (y * ((x \ z) / y)) = (y * ((z / x) / y)) * x. (x * ((y / z) / x)) * z = z * (x * ((z \ y) / x)). (R(x,y,z) * z) * R(L(T(y,z),z,R(x,y,z)),u,w) = (R(x,y,z) * R(R(x,y,z) \ (x * y),u,w)) * z. (R(x,y,z) * R(R(x,y,z) \ (x * y),u,w)) * z = (R(x,y,z) * z) * R(L(T(y,z),z,R(x,y,z)),u,w). x != (y * z) * R(L(u,z,y),w,v5) | x = y * (z * R(u,w,v5)). (R(x,y,z) * R(R(x,y,z) \ (x * y),u,w)) * z = R(x,y,z) * (z * R(T(y,z),u,w)). (R(x,y,z) * R(R(x,y,z) \ (x * y),u,w)) * z = R(x,y,z) * (R(y,u,w) * z). (x / y) \ (y \ x) = K(y \ x,y). (x / y) * K(y \ x,y) = y \ x. (x / y) * K(y * x,y) = y \ x. (x / y) * (x \ y) = K(x * y,x). (x \ y) * (x / y) = K(x * y,x). L(x,y,(z \ u) * K(z * u,z)) = L(x,y,z / u). L(x,y,T(z \ u,z)) = L(x,y,z / u). ((x \ R(1 / y,y,z)) * x) * (y * z) = (y * z) * ((x \ ((y * z) \ z)) * x). (x * (y / (z * y))) / x = R((x * (1 / z)) / x,z,y). R((x * (1 / y)) / x,y,z) = (x * (z / (y * z))) / x. ((x * ((y * z) / (R(u,y,z) * (y * z)))) / x) * ((u * y) * z) = (((x * (1 / R(u,y,z))) / x) * R(u,y,z)) * (y * z). ((x * ((y * z) / ((u * y) * z))) / x) * ((u * y) * z) = (((x * (1 / R(u,y,z))) / x) * R(u,y,z)) * (y * z). (((x * (1 / R(y,z,u))) / x) * R(y,z,u)) * (z * u) = ((x * ((z * u) / ((y * z) * u))) / x) * ((y * z) * u). x != ((y * (z / u)) / y) * u | x = u * ((y * (u \ z)) / y). (((x * (1 / R(y,z,u))) / x) * R(y,z,u)) * (z * u) = ((y * z) * u) * ((x * (((y * z) * u) \ (z * u))) / x). x != (y * z) * ((u * ((y * z) \ (w * z))) / u) | x = (y * ((u * (y \ w)) / u)) * z. (((x * (1 / R(y,z,u))) / x) * R(y,z,u)) * (z * u) = ((y * z) * ((x * ((y * z) \ z)) / x)) * u. (R(x,y,z) * ((u * (R(x,y,z) \ 1)) / u)) * (y * z) = ((x * y) * ((u * ((x * y) \ y)) / u)) * z. K(x,R(y,z,u) \ 1) * (z * u) = ((y * z) * ((x * ((y * z) \ z)) / x)) * u. K(x,R(y,z,u) \ 1) * (z * u) = (K(x,y \ 1) * z) * u. K(x,R(y,z,u) \ 1) = R(K(x,y \ 1),z,u). R(K(x,y \ 1),z,u) = K(x,R(y,z,u) \ 1). x != R(K(y,z),y,u) | x = K(y,z). K(x,R(y,x,z) \ 1) = K(x,y \ 1). R(K(x,y / z),u,w) = K(x,R(z / y,u,w) \ 1). K(x,R(y / z,u,w) \ 1) = R(K(x,z / y),u,w). R(K(x,K(y,z \ 1)),u,w) = K(x,K(y,R(z,u,w) \ 1)). K(x,R(R(y,x,z),u,w) \ 1) = K(x,R(y,u,w) \ 1). K(x,(((y * z) * u) / ((x * z) * u)) \ 1) = K(x,R(y / x,x * z,u) \ 1). K(x,R(y / x,x * z,u) \ 1) = K(x,(((y * z) * u) / ((x * z) * u)) \ 1). K(x,R(y / x,x * z,u) \ 1) = K(x,((x * z) * u) / ((y * z) * u)). x != K(y,R(z / u,w,v5) \ 1) | x = R(K(y,u / z),w,v5). K(x,((x * y) * z) / ((u * y) * z)) = R(K(x,x / u),x * y,z). R(K(x,x / y),x * z,u) = K(x,((x * z) * u) / ((y * z) * u)). K((T(x,y) \ (T(y,x) \ x)) \ 1,z) = T(K(y,z),T(x,y)). 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,T(y \ 1,z),u) = L(x,z * (y \ z),u). K(T(x \ 1,y) \ 1,z) = T(K(x,z),y). K(T(1 / x,y) \ 1,z) = T(K(x,z),y). 1 / T(K(x,y),z) = K(y,T(x \ 1,z) \ 1). K(x,T(y \ 1,z) \ 1) = 1 / T(K(y,x),z). L(T(K(x,y),z),u,w) = K(L(T(1 / x,z),u,w) \ 1,y). K(L(T(1 / x,y),z,u) \ 1,w) = L(T(K(x,w),y),z,u). (x * ((y / z) / x)) * z = (x * z) * ((x * ((x * z) \ y)) / x). (x * y) * ((x * ((x * y) \ z)) / x) = (x * ((z / y) / x)) * y. x != (y * z) * ((u * ((y * z) \ w)) / u) | x = y * (z * ((u * (z \ (y \ w))) / u)). (x * ((y / z) / x)) * z = x * (z * ((x * (z \ (x \ y))) / x)). x * (y * ((x * (y \ (x \ z))) / x)) = (x * ((z / y) / x)) * y. x * ((y * (z \ u)) * ((x * ((y * (z \ u)) \ (x \ u))) / x)) = (x * (R(z / y,y,z \ u) / x)) * (y * (z \ u)). (x * (R(y / z,z,y \ u) / x)) * (z * (y \ u)) = x * ((z * (y \ u)) * ((x * ((z * (y \ u)) \ (x \ u))) / x)). x != y * (z * ((y * (z \ (y \ u))) / y)) | x = (y * ((u / z) / y)) * z. (x * (R(y / z,z,y \ u) / x)) * (z * (y \ u)) = (x * ((u / (z * (y \ u))) / x)) * (z * (y \ u)). (T(x,y) * ((x \ T(y,x)) * z)) \ (y * z) = a(T(x,y),T(x,y) \ y,z). (x * y) * L(R(T(x,y) \ z,u,w),T(x,y),y) = y * (R(z / T(x,y),u,w) * T(x,y)). x != ((y * z) * u) / R(y,z,u) | x = (z * u) * K(R(y,z,u),z * u). ((x * y) / R(x,y,x)) * x = (y * x) * K(R(x,y,x),y * x). (x * y) * K(R(y,x,y),x * y) = ((y * x) / R(y,x,y)) * y. (x * y) * K(T(y,x),x * y) = ((y * x) / R(y,x,y)) * y. ((x * y) / R(x,y,x)) * x = (y * x) * K(T(x,y),y * x). K(x,(y / z) \ 1) != u | K(x,z / y) = u. K(x,x \ 1) * y != z | y = z * K(u \ 1,u). ((x \ 1) \ 1) \ y = (x \ y) * K(z \ 1,z). (x \ y) * K(z \ 1,z) = ((x \ 1) \ 1) \ y. K(x \ y,x) * (x \ z) != u | u = ((x \ y) \ y) \ z. K(x \ y,x) * (x \ z) != u | ((x \ y) \ y) \ z = u. T(x,x \ y) \ z != u | ((x \ y) \ y) \ z = u. T(x,x \ y) \ R(T(z,z \ u),w,v5) != v6 | ((x \ y) \ y) \ R((z \ u) \ u,w,v5) = v6. x != L(y,z * (u * w),v5) | x = L(y,z * (u \ w),v5). L(x,T(y,z),u) = L(x,z * (y \ z),u). L(x,y * (z \ y),u) = L(x,T(z,y),u). x * y != K(z,z \ 1) * (u * x) | T(K(w,w \ 1) * u,x) = y. T(K(x,x \ 1) * y,z) = K(z,z \ 1) * T(y,z). T(x,y) = K(y,y \ 1) * T(K(z,z \ 1) \ x,y). K(x,x \ 1) * T(K(y,y \ 1) \ z,x) = T(z,x). T(x,y) * K(y,y \ 1) = T(x * K(y,y \ 1),y). (x \ y) * K(x,x \ 1) = T((y / x) * K(x,x \ 1),x). T((x / y) * K(y,y \ 1),y) = (y \ x) * K(y,y \ 1). x != T((y / z) * K(u,u \ 1),z) | x = z \ (y * K(w,w \ 1)). (x \ y) * K(x,x \ 1) = x \ (y * K(z,z \ 1)). x \ (y * K(z,z \ 1)) = (x \ y) * K(x,x \ 1). x * ((x \ y) * K(x,x \ 1)) = y * K(z,z \ 1). x * K(y,y \ 1) = z * ((z \ x) * K(z,z \ 1)). (x * y) * K(z,z \ 1) = x * (y * K(x,x \ 1)). R(x,y,K(x,x \ 1)) = x. (x * (y \ 1)) * K(z,z \ 1) = x * (1 / y). R(x,y,K(z \ 1,z)) = x. x * (y * K(z \ 1,z)) = (x * y) * K(z \ 1,z). (x * y) * K(z \ 1,z) = x * (y * K(z \ 1,z)). x \ (y * K(z \ 1,z)) = (x \ y) * K(z \ 1,z). (x * (y * K(z \ 1,z))) \ u = (x * y) \ (K(w,w \ 1) * u). L(x,y * K(z \ 1,z),u) = (u * y) \ (K(w,w \ 1) * (u * (K(z \ 1,z) * (y * x)))). (x * y) \ (K(z,z \ 1) * (x * (K(u \ 1,u) * (y * w)))) = L(w,y * K(u \ 1,u),x). (x * y) \ (x * (y * z)) = L(z,y * K(u \ 1,u),x). L(x,y * K(z \ 1,z),u) = (u * y) \ (u * (y * x)). L(x,y * K(z \ 1,z),u) = L(x,y,u). L(x,y,z) = L(x,T(y,y \ 1),z). L(x,T(y,y \ 1),z) = L(x,y,z). (x * T(y,y \ 1)) * L(z,y,x) = x * (T(y,y \ 1) * z). x * (T(y,y \ 1) * z) != (x * T(y,y \ 1)) * u | L(z,y,x) = u. (x * T(y,y \ 1)) * z != x * (T(y,y \ 1) * u) | L(u,y,x) = z. x != y * K(z \ 1,z) | x = K(z \ 1,z) * y. x \ (y * K(z \ 1,z)) = K(z \ 1,z) * (x \ y). (x * y) \ ((x * (y * z)) * K(u \ 1,u)) = K(u \ 1,u) * L(z,y,x). (x * y) \ (x * ((y * z) * K(u \ 1,u))) = K(u \ 1,u) * L(z,y,x). (x * y) \ (x * (y * (z * K(u \ 1,u)))) = K(u \ 1,u) * L(z,y,x). L(x * K(y \ 1,y),z,u) = K(y \ 1,y) * L(x,z,u). K(x \ 1,x) * L(y,z,u) = L(y * K(x \ 1,x),z,u). K(x \ 1,x) * L(y * K(z,z \ 1),u,w) = L(y,u,w). x != K(y \ 1,y) * L(z * K(u,u \ 1),w,v5) | x = (y \ L(y * (z / y),w,v5)) * y. L(x,y,z) = (u \ L(u * (x / u),y,z)) * u. (x \ L(x * (y / x),z,u)) * x = L(y,z,u). (x \ L(y,z,u)) * x = L((x \ y) * x,z,u). (x \ ((y * z) \ u)) * x = L((x \ (z \ (y \ u))) * x,z,y). L((x \ (y \ (z \ u))) * x,y,z) = (x \ ((z * y) \ u)) * x. (x * y) * ((z \ L(u,y,x)) * z) != w | x * (y * ((z \ u) * z)) = w. (x \ (y * z)) * x = L((x \ ((y \ 1) \ z)) * x,u \ 1,u). L((x \ ((y \ 1) \ z)) * x,u \ 1,u) = (x \ (y * z)) * x. x * ((y \ z) * ((z \ T(y,y \ z)) * z)) = (x * K(z \ y,z)) * z. x * (y * K(y \ z,y)) = (x * K(y \ z,y)) * y. (x * K(y \ z,y)) * y = x * (y * K(y \ z,y)). (x * K(y,z)) * z = x * (z * K(z \ (z * y),z)). x * (y * K(y \ (y * z),y)) = (x * K(z,y)) * y. x * (y * K(z,y)) = (x * K(z,y)) * y. (x * K(y,z)) * z = x * (z * K(y,z)). (x * (y * K(z,y))) / y = x * K(z,y). (x * K(y,z)) \ (x * (z * K(y,z))) = z. x * y != (z * y) * (y * K(u,y)) | x = z * (y * K(u,y)). (x * y) * K(z,y) = x * (y * K(z,y)). (x * (y * K(z,y))) / (x * K(z,y)) != y * u | K(x * K(z,y),y) = u. L(T(x,K(y,x)),K(y,x),z) = x. L(x,K(y,x),z) = x. x = L(x,K(x,y),z). L(x,K(x,y),z) = x. (x * K(y,z)) * T(z,u) = x * (K(y,z) * T(z,u)). R(x,K(y,z),T(z,u)) = x. (x * K(y,z)) * T(z,y) = x * z. (x / T(y,z)) * y = x * K(z,y). x / T(y,z) = (x / y) * K(z,y). (x / y) * K(z,y) = x / T(y,z). x * T(y,z) != (u * T(y,z)) * y | x = u * y. (x * T(y,z)) * K(z,y) = x * y. x != y / T(z,y) | x = T(y,z) / z. (x / y) * K(x,y) = T(x,y) / y. x * y != (z * u) / T(z,u) | x \ u = y. ((x * y) / x) \ y = K(y,x). x * y != (z / u) * K(w,u) | x \ (z / T(u,w)) = y. x \ (y / T(y / x,z)) = K(x \ y,x) * K(z,y / x). K(x \ y,x) * K(z,y / x) = x \ (y / T(y / x,z)). x / T(y \ x,z) != u | y * K(z,y \ x) = u. x != ((y * z) / y) * u | x = z * (K(y,z) * u). T(x * y,x) / x = y * (K(x,y) * K(x * y,x)). x * (K(y,x) * K(y * x,y)) = T(y * x,y) / y. (x * K(y,z)) / z = x / T(z,y). (x * T(x \ y,z)) \ y = K(z,x \ y). (x * T(y,z)) \ (x * y) != u | u = K(z,y). (x * T(y,z)) \ (x * y) != u | K(z,y) = u. (((x * y) * T(z,u)) * K(u,z)) / (y * z) = R(R(x,y,T(z,u)),y * T(z,u),K(u,z)). R(R(x,y,T(z,u)),y * T(z,u),K(u,z)) = (((x * y) * T(z,u)) * K(u,z)) / (y * z). (((x \ (y / z)) * x) * z) \ y = K(x,(x * z) \ y). (x * (y * T(y \ (x \ z),u))) \ z = K(u,(x * y) \ z). ((x * T(x \ y,z)) * u) \ (y * u) = K(z,(x * u) \ (y * u)). (T(x,y) / z) \ (x / z) = K(y,(1 / z) \ (x / z)). K(x,(1 / y) \ (z / y)) = (T(z,x) / y) \ (z / y). L(K(x,y),y,z) = K(x,y). R(x,y,K(z,y)) = x. (x * (y \ z)) * K(y,y \ z) = x * (z / y). a(x,y,K(z,y)) = 1. x != L(K(y,z \ u),z \ u,z) | x = K(y,(u \ z) \ 1). K(x,y \ z) = K(x,(z \ y) \ 1). K(x,(y \ z) \ 1) = K(x,z \ y). K(x,y) \ 1 = L(K(y,x),y,z). L(K(x,y),x,z) = K(y,x) \ 1. x != K(y,z \ u) | x = (z * T(z \ u,y)) \ u. K(x,(y \ z) \ 1) = (z * T(z \ y,x)) \ y. (x * T(x \ y,z)) \ y = K(z,(y \ x) \ 1). K(x,y \ 1) = K(x,(z * y) \ z). K(x,(y * z) \ y) = K(x,z \ 1). K(x,a(y,z,u) \ 1) = K(x,((y * z) * u) \ (y * (z * u))). K(x,((y * z) * u) \ (y * (z * u))) = K(x,a(y,z,u) \ 1). K(x,(K(y,z) * u) \ 1) = K(x,u \ K(z,y)). K(x,(y \ K(z,u)) \ 1) = K(x,K(u,z) * y). L(K(x,y \ z),u,w) = K(x,L(z \ y,u,w) \ 1). K(x,L(y \ z,u,w) \ 1) = L(K(x,z \ y),u,w). x != L(y,K(y,z),u) | x = (u * K(y,z)) \ (u * T(y,z)). x = (y * K(x,z)) \ (y * T(x,z)). (x * K(y,z)) \ (x * T(y,z)) = y. (x * K(y,z)) * L(y,u,w) = x * (K(y,z) * L(y,u,w)). (x * K(y,z)) * y = x * T(y,z). x * y != z * T(x,u) | T(z * K(x,u),x) = y. T(x * K(y,z),y) = y \ (x * T(y,z)). x \ (y * T(x,z)) = T(y * K(x,z),x). x * y != T(z,y) * T(y,u) | x = y \ (z * T(y,u)). T(x,y) * K(y,z) = y \ (x * T(y,z)). x \ (y * T(x,z)) = T(y,x) * K(x,z). x * y != z * T(y,u) | x = (z / y) * T(y,u). x * K(y,z) = (x / y) * T(y,z). (x / y) * T(y,z) = x * K(y,z). x * y != (z * y) * T(y,u) | x = z * T(y,u). (x * y) * K(y,z) = x * T(y,z). x * y != (z * K(u,y)) * T(y,u) | x = z. (x * K(y,z)) * K(z,y) = x. (x * (y * T(z,u))) \ ((x * (y * K(z,u))) * z) = a(x,y * K(z,u),z). x \ (y * T(x,z)) != u | T(y * K(x,z),x) = u. K(x,y * K(x,z)) * K(y * T(x,z),x) = x \ R(x,y * K(x,z),x). x != (y * (y \ z)) * u | x = z * u. x * T(x \ y,z) = y * K(x \ y,z). (x / y) \ (x * K(y,z)) = T(y,z). x * y != (z * u) * K(u,w) | x \ (z * T(u,w)) = y. (x * y) \ (y * T(x,z)) = K(y,x) * K(x,z). x \ (y * T(y \ x,z)) = K(y \ x,z). ((x * y) * T(z,u)) / ((y * z) * K(z,u)) = R(R(x,y,z),y * z,K(z,u)). x != (y * z) \ (z * T(y,y \ z)) | x = a(y,z / y,y). K(x,y) * K(y,y \ x) = a(y,x / y,y). (x * (y * R(x,z,u))) \ ((x * y) * R(x,z,u)) = K(y * R(x,z,u),x) * K(x,y). K((x \ y) \ 1,z) = K(y \ x,z). T(K(x,y),z) = K((x \ z) \ z,y). K((x \ y) \ y,z) = T(K(x,z),y). x != T(K(y,z),z) | x = K(y,z). K((x \ y) \ y,y) = K(x,y). K(T(x,x \ y),z) = T(K(x,z),y). ((x * y) * T(z,u)) / (y * T(z,u)) = R(R(x,y,z),y * z,K(z,u)). R(R(x,y,z),y * z,K(z,u)) = ((x * y) * T(z,u)) / (y * T(z,u)). R(R(x,y,z),y * z,K(z,u)) != w | R(x,y,T(z,u)) = w. (x * T(x \ y,z)) \ y != u | K(z,x \ y) = u. (x \ T(y,z)) \ (x \ y) != u | K(z,y) = u. (x * (y * T(y \ (x \ z),u))) \ z != w | K(u,(x * y) \ z) = w. K(x,(y \ z) \ 1) != u | K(x,z \ y) = u. K(x,L(y \ z,y,u) \ 1) != w | K(x,(u * z) \ (u * y)) = w. K(x,(y * z) \ (y * u)) = L(K(x,z \ u),u,y). L(K(x,y \ z),z,u) = K(x,(u * y) \ (u * z)). L(K(x,(y \ z) \ u),u,y) = K(x,z \ (y * u)). L(K(x,y \ (z \ u)),z \ u,z) = K(x,(z * y) \ u). L(K(x,y),z,u) = K(x,(u * (z / y)) \ (u * z)). K(x,(y * (z / u)) \ (y * z)) = L(K(x,u),z,y). T(x * K(y,z),y) = T(x,y) * K(y,z). T(x,y) * K(y,z) = T(x * K(y,z),y). x * K(y,z) != T((K(z,y) * u) * K(y,z),w) | x = K(z,y) * T(u,w). T(K(x,y) * z,y) = K(x,y) * T(z,y). K(x,y) * T(z,y) = T(K(x,y) * z,y). x * K(y,z) != T(u * K(y,z),w) | x = K(z,y) * T(K(z,y) \ u,w). T(x,y) = K(z,y) * T(K(z,y) \ x,y). K(x,y) * T(K(x,y) \ z,y) = T(z,y). x * y != T(z,u) * K(u,w) | x \ T(z * K(u,w),u) = y. x \ T(x * K(y,z),y) = K(x,y) * K(y,z). K(x,y) * T(z,x) = T(K(x,y) * z,x). x != K(y \ z,y) * T(u,y \ z) | x = (z / y) \ (u * (y \ z)). T(K(x \ y,x) * z,x \ y) = (y / x) \ (z * (x \ y)). x * y != K(z,u) * T(w,z) | T(K(z,u) * w,z) / y = x. T(K(x,y) * z,x) / z = K(x,y) * K(z,x). K(x,y) * L(T(z,x),u,w) = T(K(x,y) * L(z,u,w),x). K(x,y) * R(T(z,x),u,w) = T(K(x,y) * R(z,u,w),x). (T(x,y) / z) \ x = z * K(y,x). (x * K(y,z)) * K(z,u) = (x / T(z,y)) * T(z,u). (x / T(y,z)) * T(y,u) = (x * K(z,y)) * K(y,u). a(x,y,R(x,z,u)) = K(y * R(x,z,u),x) * K(x,y). K(x * R(y,z,u),y) * K(y,x) = a(y,x,R(y,z,u)). K(x * R(y,z,u),y) * K(y,x) != w | a(y,x,R(y,z,u)) = w. (x / y) * y = (x * K(z,u)) * K(u,z). x * K(y,z) = x / K(z,y). x / K(y,z) = x * K(z,y). (x * K(y,z)) \ x = K(z,y). x != y * K(z,u) | x * K(u,z) = y. x * K(y,z) != u | u * K(z,y) = x. (x * K(y,z)) \ x != u | u = K(z,y). (x * K(y,z)) \ x != u | K(z,y) = u. (x * y) \ ((x * (y * K(z,u))) * K(u,z)) != w | a(x,y * K(z,u),K(u,z)) = w. x / K(y,z) != u | x * K(z,y) = u. x * y = (x * K(y,z)) * (y * K(z,y)). (x * K(y,z)) * (y * K(z,y)) = x * y. (x * R(K(y,z),u,w)) \ x = K(z,R(y,y \ u,w)). K(x,R(y,y \ z,u)) = (w * R(K(y,x),z,u)) \ w. R(x * K(y,x),z,u) \ R(x,z,u) = K(R(x,z,u),y). (x * L(K(y,z),u,w)) \ x = K(z,L(y \ 1,u,w) \ 1). K(x,L(y \ 1,z,u) \ 1) = (w * L(K(y,x),z,u)) \ w. L(L(K(x,y),z,u),K(y,x),w) = L(K(x,y),z,u). K(T(x,y),z) = T(K(x,z),x * y). T(K(x,y),x * z) = K(T(x,z),y). (K(x,y) / z) \ 1 = z * K(y,x). R((x / y) * K(z,u),K(u,z),y) = x / (K(u,z) * y). x != R(y,K(z,u),T(u,w)) | x = y. x / (K(y,z) * T(z,u)) = (x / T(z,u)) * K(z,y). x / R(y,z,y) = (x / T(y,z)) * K(y,y * z). (x / T(y,z)) * K(y,y * z) = x / R(y,z,y). x / L(y,z,y) = (x / T(y,y * z)) * K(y,z). (x / T(y,y * z)) * K(y,z) = x / L(y,z,y). (x * y) * (1 / (1 / K(z \ (x * y),u))) = x * (y * (1 / (1 / (y \ (x \ (z * T(z \ (x * y),u))))))). x * (y * (1 / (1 / (y \ (x \ (z * T(z \ (x * y),u))))))) = (x * y) * (1 / (1 / K(z \ (x * y),u))). T(x,y) * z != u * K(x,y) | T(u / x,T(x,y)) = z. T(x / y,T(y,z)) = T(y,z) \ (x * K(y,z)). T(x,y) \ (z * K(x,y)) = T(z / x,T(x,y)). (x / y) \ ((y * x) / y) = T(y,x). x * y != (z / u) * T(u,w) | (z * K(u,w)) / y = x. (x * K(y,z)) / y = (x / y) * K(y,z). x * y != (z / u) * T(u,w) | x \ (z * K(u,w)) = y. ((x / y) * K(y,z)) \ (x * K(y,z)) = y. x * (K(y,x) * T(z,x)) = (K(y,x) * z) * x. x != y * (K(z,y) * T(u,y)) | x = K(z,y) * (u * y). (K(x,y) * z) * y = K(x,y) * (z * y). L(x,y,K(z,x)) = x. (K(x \ 1,x) * y) * z = K(z \ 1,z) * (y * z). K(x \ 1,x) * (y * x) = (K(z \ 1,z) * y) * x. x = L(x,y,K(x,z)). L(x,y,K(x,z)) = x. T(x,y) = L(T(x,y),z,K(u,x)). L(T(x,y),z,K(u,x)) = T(x,y). L(x,y,z) = L(L(x,y,z),u,K(w,x)). L(L(x,y,z),u,K(w,x)) = L(x,y,z). (K(x,y) * z) * x = K(x,y) * (z * x). (K(x,y) * z) * R(x,u,w) = K(x,y) * (z * R(x,u,w)). R(K(x,y),z,x) = K(x,y). K(R(x,y,x),z) = K(x,z). x != R(K(y,z / (u / w)),z,w) | x = K(y,(z * w) / u). K(x,y / (z / x)) = K(x,(y * x) / z). K(x,(y * x) / z) = K(x,y / (z / x)). K(x,y) = K(x,R(y,z,x)). K(x,R(y,z,x)) = K(x,y). K(x,y) != z | K(R(x,u,x),y) = z. K(x,y) * (R(x,z,x) * u) = R(T(x,y),z,x) * u. 1 / K(x,y) = K(y,R(x,z,x)). K(x,R(y,z,y)) = 1 / K(y,x). K(L(x,y,x),z) = K(x,z). K((x \ y) \ T(y,x),z) = K(x,z). x != K(L(y,z,u),w) | x = L(y,z,u) \ L(T(y,w),z,u). K(x,y) = L(x,z,x) \ L(T(x,y),z,x). L(x,y,x) \ L(T(x,z),y,x) = K(x,z). K((x \ y) \ y,z) = K(T(x,y),z). K(x,y) * L(x,z,x) = L(T(x,y),z,x). x != K((y \ z) \ z,u) | x = T(K(y,u),z). K(T(x,y),z) = T(K(x,z),y). T(K(x,y),z) = K(T(x,z),y). x * K(T(y,x),z) = K(y,z) * x. K(x,T(y,z)) * T(K(y,x),z) = 1. x * K(y,z) != u | x = u * K(z,y). x = (K(y,z) * x) * K(z,T(y,x)). (K(x,y) * z) * K(y,T(x,z)) = z. x * K(y,z) = K((x * y) / x,z) * x. K((x * y) / x,z) * x = x * K(y,z). K(x,y) * K(y,z) = K(y,z) * K(x,y). K(x,y) * K(z,x) = K(z,x) * K(x,y). L(K(x,y),z,u) * K(y,w) = K(y,w) * L(K(x,y),z,u). T(K(x,y),K(y,z)) = K(x,y). x != K(y,z) * K(z,u) | x = (z * y) \ (y * T(z,u)). K(x,y) * K(z,x) = (x * z) \ (z * T(x,y)). (x * y) \ (y * T(x,z)) = K(x,z) * K(y,x). x != K(y * R(z,u,w),z) * K(z,y) | x = a(z,y,R(z,u,w)). K(x,y) * K(y * R(x,z,u),x) = a(x,y,R(x,z,u)). x != K(R(y,z,u),w) * K(w,y) | x = K(y,w) * K(w,R(y,z,u)). K(x,y) * K(R(y,z,u),x) = K(y,x) * K(x,R(y,z,u)). x != K(y,z) * K(y * z,y) | x = y \ R(y,z,y). K(x * y,x) * K(x,y) = x \ R(x,y,x). x * (K(y,x) * K(x,z)) = T(x,z) * K(y,x). (K(x,y) * K(z,x)) * u = K(z,x) * (K(x,y) * u). K(x,y) * K(y,y \ x) = y \ R(y,y \ x,y). x \ R(x,x \ y,x) = K(y,x) * K(x,x \ y). x != K(y,z) * K(z,z \ y) | x = a(z,y / z,z). x \ R(x,x \ y,x) = a(x,y / x,x). x \ R(x,y,x) = a(x,(x * y) / x,x). a(x,(x * y) / x,x) = x \ R(x,y,x). a(x,y,x) = x \ R(x,T(y,x),x). x \ R(x,T(y,x),x) = a(x,y,x). x \ R(x,y,x) = a(x,y,x). x != y \ R(y,z,y) | x = K(y,z) * K(y * z,y). a(x,y,x) = K(x,y) * K(x * y,x). K(x,y) * K(x * y,x) = a(x,y,x). x != R(y,z,u) \ R(R(y,z,u),w,v5) | x = ((R(y,w,v5) * z) * u) / ((y * z) * u). a(R(x,y,z),u,R(x,y,z)) = ((R(x,u,R(x,y,z)) * y) * z) / ((x * y) * z). ((R(x,y,R(x,z,u)) * z) * u) / ((x * z) * u) = a(R(x,z,u),y,R(x,z,u)). x * a(x,y,x) = R(x,y,x). R(a(x,y,x),x * z,u) = ((R(x,y,x) * z) * u) / ((x * z) * u). ((R(x,y,x) * z) * u) / ((x * z) * u) = R(a(x,y,x),x * z,u). K(x,y) * a(y,x,y) = K(y * x,y). x * a(y,x,y) = T(y * x,y) / y. T(x * y,x) / x = y * a(x,y,x). a(x,y,x) * z = K(x * y,x) * (K(x,y) * z). K(x * y,x) * (K(x,y) * z) = a(x,y,x) * z. L(x,y,z * (T(u * z,u) / u)) = L(x,y,a(u,z,u)). T(x * a(y,x,y),y) = y \ T(y * x,y). (x * (y * z)) \ (x * (y * (T(u * z,u) / u))) != w | L(L(a(u,z,u),z,y),y * z,x) = w. x != L(y,z,u * (T(w,v5) / v5)) | x = L(y,z,u * T(w * v5,v5)). 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)). x != L(y,z,u * ((u * w) * w)) | x = L(y,z,a(u,w,w)). 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)). K(x,x * y) * (a(x,y,x) * z) = K(x,y) * z. x * y != K(y,z) * (u * y) | x = K(y,z) * u. K(x,y) = K(x,x * y) * a(x,y,x). K(x,x * y) * a(x,y,x) = K(x,y). K(x,y) * z != K(x,x * y) * u | a(x,y,x) * z = u. K(x,x * y) * z != K(x,y) * u | a(x,y,x) * u = z. L(x,y,x) * K(x,z) = L(T(x,z),y,x). L(T(x,y),z,x) \ u = K(y,x) * (L(x,z,x) \ u). K(x,y) * (L(y,z,y) \ u) = L(T(y,x),z,y) \ u. T(x,y) * (L(T(x,y),z,x) \ u) = x * (L(x,z,x) \ u). x != 1 / K(y,z) | x = K(z,y). K(x,R(y,z,y)) = K(x,y). K(x,R(y,z,y)) != u | K(x,y) = u. K(x,L(y,z,y)) = K(x,y). K(x,T(y,y \ z)) = K(x,T(y,z)). x * K(x,y) = T(x,L(y,z,y)). T(x,L(y,z,y)) = x * K(x,y). x != y * K(y,z) | x = T(y,z). T(x,L(y,z,y)) = T(x,y). L(x,y,x) \ z = T(z / L(x,y,x),x). T(x / L(y,z,y),y) = L(y,z,y) \ x. T(x,(y \ z) \ z) = T(x,T(y,z)). T(x,R(y,z,y)) = T(x,y). x * (L(x,y,x) \ z) = (z / L(x,y,x)) * x. (x / L(y,z,y)) * y = y * (L(y,z,y) \ x). K(x,T(y,z)) = K(x,T(y,y * z)). K(x,T(y,y * z)) = K(x,T(y,z)). K(x,y \ z) = K(x,T(z / y,z)). K(x,T(y / z,y)) = K(x,z \ y). K(x,x / y) = K(x,y \ x). K(x,y) = K(x,(y \ x) \ x). K(x,(y \ x) \ x) = K(x,y). R(K(x,(y / z) \ x),x,z) = K(x,(x * z) / y). R(K(x,y \ x),x * z,u) = K(x,((x * z) * u) / ((y * z) * u)). R(x,y,x) * T(z,x) = z * R(x,y,x). R(x,y,x) * (x \ z) = (z / x) * R(x,y,x). R(x,y,x) * (K(z,x) * (x \ u)) = K(z,x) * ((u / x) * R(x,y,x)). R(x,y,x) * (T(x,z) \ u) = K(z,x) * ((u / x) * R(x,y,x)). K(x,y) * ((z / y) * R(y,u,y)) = R(y,u,y) * (T(y,x) \ z). R(K(x,y),z,R(x,u,w)) = K(x,y). (x * (K(x,y) * (z * R(x,u,w)))) \ ((T(x,y) * z) * R(x,u,w)) = a(x,K(x,y) * z,R(x,u,w)). K(R(x,y,R(x,z,u)),w) = K(x,w). K(x,y / (z / R(x,u,w))) = K(x,(y * R(x,u,w)) / z). K(x,(y * R(x,z,u)) / w) = K(x,y / (w / R(x,z,u))). K(x,y) * ((y * R(x,z,R(x,u,w))) * v5) = (R(x,z,R(x,u,w)) * y) * v5. K(x,T(y,y \ z)) != u | K(x,T(y,z)) = u. K(x,y) * a(x,x \ y,x) = K(x,x \ y). K(x,(x * y) / z) = K(x,(z / y) \ x). K(x,(x / L(y,z,u)) * y) = K(x,(L(y,z,u) / y) \ x). K(x,(L(y,z,u) / y) \ x) = K(x,(x / L(y,z,u)) * y). x != R(K(y,z),y * u,w) | x = K(R(y,u,w),z). K(x,((x * y) * z) / ((u * y) * z)) = K(R(x,y,z),u \ x). K(x,(y * z) / ((u * (x \ y)) * z)) = K(R(x,x \ y,z),u \ x). K(R(x,x \ y,z),u \ x) = K(x,(y * z) / ((u * (x \ y)) * z)). K(x,((y * z) * R(x,y,z)) / ((u * (K(y * z,x) * y)) * z)) = K(R(x,K(y * z,x) * y,z),u \ x). x != K(R(y,y \ z,u),w) | x = R(K(y,w),z,u). K(x,(y * z) / ((u * (x \ y)) * z)) = R(K(x,u \ x),y,z). (K(x,y) / z) \ 1 = z * K(y,R(x,u,R(x,w,v5))). x * K(y,R(z,u,R(z,w,v5))) = (K(z,y) / x) \ 1. (x * (y * (z * T(z \ (y \ (x \ u)),w)))) \ u = K(w,(x * (y * z)) \ u). (x * (((y \ ((x \ z) * u)) * y) / u)) \ z = K(y,(x * (y / u)) \ z). (x * (y \ ((z \ (y * (x \ u))) * z))) \ u = K(z,(x * (y \ z)) \ u). (x * T(x \ y,z)) \ y = K(z,(x * K(u,z)) \ y). K(x,(y * K(z,x)) \ u) = (y * T(y \ u,x)) \ u. R(x * K(y,x),z,u) \ R(x,z,u) != w | K(R(x,z,u),y) = w. K(x,L(y,z / y,u)) = L(K(x,y),z,u). x != K(y,L(z,u,z)) | x = K(y,z). L(K(x,y),z,y) = K(x,y). K(x,L(y,z,u)) = L(K(x,y),z * y,u). L(K(x,y),z * y,u) = K(x,L(y,z,u)). (x * y) * K(z,L(u,y / u,x)) = x * (y * K(z,u)). K(x,y) = L(K(x,y),z,K(y,u)). L(K(x,y),z,K(y,u)) = K(x,y). L(x,y,x) = L(x,y,T(x,z)). L(x,y,T(x,z)) = L(x,y,x). x != L(L(y,z,u),u * z,K(u,w)) | x = L(y,z,T(u,w)). L(x,y,z) = L(x,y,T(z,x)). L(x,y,T(z,x)) = L(x,y,z). T(L(x,y,x),z) = L(T(x,z),y,T(x,u)). L(T(x,y),z,T(x,u)) = T(L(x,z,x),y). L(x * K(y,x),z,x) = L(x * K(y,x),z,x * K(y,x)). L(x * K(y,x),z,x * K(y,x)) = L(x * K(y,x),z,x). L(T(x,y),z,T(x,u)) = L(T(x,y),z,x). x * (y * (1 / (1 / (y \ (x \ (z * T(z \ (x * y),u))))))) = (x * y) * K(z \ (x * y),u). x * (y * (1 / (1 / (y \ ((x \ z) * T((x \ z) \ y,u)))))) = (x * y) * K(z \ (x * y),u). x * (y * (1 / (1 / K((x \ z) \ y,u)))) = (x * y) * K(z \ (x * y),u). x * (y * K((x \ z) \ y,u)) = (x * y) * K(z \ (x * y),u). (x * y) * K(z \ (x * y),u) = x * (y * K((x \ z) \ y,u)). L(K((x \ y) \ z,u),z,x) = K(y \ (x * z),u). (x * y) * z != x * (y * K(u,y)) | z = K(u,y). K(x \ (y * z),z) = K((y \ x) \ z,z). K((x \ y) \ z,z) = K(y \ (x * z),z). L(K(x \ y,z),y,u) = K((u * x) \ (u * y),z). L(K(((x * y) \ (x * (y * z))) \ z,u),z,x * y) = K(a(x,y,z),u). L(K((K(x,y) * z) \ u,w),u,K(y,x)) = K(z \ (K(y,x) * u),w). L(K(x \ (y \ z),u),y \ z,y) = K((y * x) \ z,u). L(K(x,y),z,u) = K((u * (z / x)) \ (u * z),y). K((x * (y / z)) \ (x * y),u) = L(K(z,u),y,x). K(L(x,y / x,z),u) = L(K(x,u),y,z). x != L(y,z,u) | x = (u * z) \ (u * (z * y)). K(L(x,y / x,z),u) = (z * y) \ (z * (y * K(x,u))). x != K(L(y,z,y),u) | x = K(y,u). L(K(x,y),z,x) = K(x,y). 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). 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). x != L(K(y,z),u * z,w) | x = K(y,L(z,u,w)). K(x,y) = K(x,L(y,z,x)). K(x,L(y,z,x)) = K(x,y). (x * y) * K(x,z) = x * (y * K(x,z)). L(K(x,y),z,x) != u | u = K(x,y). L(K(x,y),z,x) != u | K(x,y) = u. K(x,(x * y) \ z) != u | K(x,y \ (x \ z)) = u. K(x,y \ (x \ z)) = (((x \ (z / y)) * x) * y) \ z. (((x \ (y / z)) * x) * z) \ y = K(x,z \ (x \ y)). (((x \ y) * x) * z) \ (y * z) = K(x,z \ (x \ (y * z))). (x * ((y \ (x \ z)) * y)) \ z = K(y,x \ (y \ z)). ((x * y) * z) \ ((y * x) * z) = K(y,z \ (y \ ((y * x) * z))). K(x,y \ (x \ ((x * z) * y))) = ((z * x) * y) \ ((x * z) * y). R(x,y,K(x,z)) = x. x != y * (z * K(y,u)) | x = T(y,u) * T(z,K(y,u)). (x * y) * K(x,z) = T(x,z) * T(y,K(x,z)). T(x,y) * T(z,K(x,y)) = (x * z) * K(x,y). (x * (y * K(x,z))) * x = (x * y) * T(x,z). R(x,y,z) = R(R(x,y,z),u,K(x,w)). R(R(x,y,z),u,K(x,w)) = R(x,y,z). L(x,y,z) * (u * K(x,w)) = (L(x,y,z) * u) * K(x,w). (L(x,y,z) * u) * K(x,w) = L(x,y,z) * (u * K(x,w)). R(x,y,T(x,z)) = R(x,y,x). x * R(T(y,x),z,y) = R(y,z,T(y,u)) * x. R(x,y,T(x,z)) * u = u * R(T(x,u),y,x). R(T(x,y),z,T(x,u)) = R(T(x,y),z,x). R(T(x,y),z,x) \ T(T(x,y) * z,T(x,y)) = T(z,T(x,y)). L(K(L(x,y,z) \ x,u),x,z * y) = K(a(z,y,x),u). x * y != (K(z,u) / x) \ 1 | y = K(u,z). K(x,R(y,z,R(y,u,w))) = K(x,y). (((x / y) * T(y,z)) * u) \ (x * u) = K(z,((x / y) * u) \ (x * u)). ((x * K(y,z)) * u) \ (x * u) = K(z,((x / y) * u) \ (x * u)). ((x * K(y,z)) * u) * K(z,((x / y) * u) \ (x * u)) = x * u. ((x * K(y,z)) * K(y,u)) * K(z,y) = x * K(y,u). (x * K(y,z)) * K(u,y) = (x * K(u,y)) * K(y,z). x * y != (z * K(u,w)) * K(v5,u) | ((z * K(v5,u)) * K(u,w)) / y = x. ((x * K(y,z)) * K(z,u)) / z = (x * K(z,u)) / T(z,y). ((x * K(y,z)) * K(u,y)) * y = (x * K(u,y)) * T(y,z). x != K(y,z) | x = K((y \ 1) \ 1,z). L(K(x,y),z * x,u) = K((L(x,z,u) \ 1) \ 1,y). x != L(K(y,z),z * y,u) | x = (u * (z * y)) \ (u * (y * z)). K(L(x,y,z),y) = (z * (y * x)) \ (z * (x * y)). (x * (y * z)) \ (x * (z * y)) = K(L(z,y,x),y). K(L(x,y,x),z) != u | K(x,z) = u. K((x \ y) \ T(y,x),z) != u | K(x,z) = u. K((x \ y) \ y,z) != u | K(T(x,y),z) = u. K(x \ (x * y),z) != u | K(y,z) = u. K((x \ 1) \ 1,y) != z | K(x,y) = z. K((1 / x) \ y,z) != u | K(x * y,z) = u. (K(x,y) * z) * K(y,u) = K(x,y) * (z * K(y,u)). x != K(y,z) * (u * K(z,y)) | x = T(u,K(z,y)). (K(x,y) * z) * K(y,x) = T(z,K(y,x)). x != (K(y,z) * u) * K(z,T(y,u)) | x = u. K(x,y) * (z * K(y,T(x,z))) = z. T((K(x,y) * K(y,z)) \ (K(x,y) * (u * K(y,z))),K(x,y)) = R(T(u,K(x,y) * K(y,z)),K(x,y),K(y,z)). T(x,K(y,z)) * K(z,y) = K(z,y) * x. x != y * K(z,u) | x = y / K(u,z). T(x,K(y,z)) = (K(z,y) * x) / K(z,y). (K(x,y) * z) / K(x,y) = T(z,K(y,x)). (K(x,y) \ z) * K(x,y) = T(z,K(x,y)). x * K(K(y,z),x) = T(x,K(z,y)). T(T(x,K(y,z)),K(z,y)) != u | u = x. T(T(x,y),K(x,z)) != u | u = T(x,y). T(T(x,y),K(x,z)) != u | T(x,y) = u. x != L(K((K(y,z) * u) \ w,v5),w,K(z,y)) | x = K(u \ (K(z,y) * w),v5). K((K(x,y) * z) \ u,y) = K(z \ (K(y,x) * u),y). L(K(x,y),z,u) = L(L(K(x,y),z,u),w,K(y,v5)). L(L(K(x,y),z,u),w,K(y,v5)) = L(K(x,y),z,u). T(L(T(x,K(y,z)),K(y,z),K(u,y)),K(u,y)) = R(T(x,K(u,y) * K(y,z)),K(u,y),K(y,z)). T(T(x,K(y,z)),K(u,y)) = R(T(x,K(u,y) * K(y,z)),K(u,y),K(y,z)). R(T(x,K(y,z) * K(z,u)),K(y,z),K(z,u)) = T(T(x,K(z,u)),K(y,z)). x * y != T(x,z) | y = K(x,z). K(K(x,y),z) = K(z,K(y,x)). K(x,K(y,z)) \ 1 = K(x,K(z,y)). x != K(K(y,z),u) | x = K(z,y) * T(K(y,z),u). K(x,K(y,z)) = K(y,z) * T(K(z,y),x). K(x,y) * T(K(y,x),z) = K(z,K(x,y)). K(x,K(y,z)) * (K(z,y) * u) = T(K(z,y),x) * u. K(x,y) * K(z,K(y,x)) = T(K(x,y),z). K(x,K(y,z)) != u | K(K(z,y),x) = u. x * y != K(z,x) | y = T(x,z) \ 1. T(K(x,y),z) = T(K(y,x),z) \ 1. T(K(x,y),z) \ 1 = T(K(y,x),z). (x \ y) * K(z,K(x,x \ y)) = (y / x) * T(K(x \ y,x),z). (x / y) * T(K(y \ x,y),z) = (y \ x) * K(z,K(y,y \ x)). 1 / T(K(x,y),z) = T(K(y,x),z). x * T(K(y,z),u) != 1 | x = T(K(z,y),u). x * T(K(y,z),u) != 1 | T(K(z,y),u) = x. T(K(x,y),z) = K(x,T(y,z)). x != K(y,T(z,u)) | x = K(y,T(z,z \ u)). T(K(x,y),z) = K(x,T(y,y \ z)). K(x,T(y,y \ z)) = T(K(x,y),z). x != T(K(y,z),u) | x = K((y \ u) \ u,z). K(x,T(y,z)) = K((x \ z) \ z,y). K((x \ y) \ y,z) = K(x,T(z,y)). x != T(K(y,z),u) | x = K(T(y,u),z). K(x,T(y,z)) = K(T(x,z),y). K(T(x,y),z) = K(x,T(z,y)). x != T(K(y,z),y * u) | x = K(T(y,u),z). K(x,T(y,x * z)) = K(T(x,z),y). x * K(y,T(z,x)) = K(y,z) * x. x * T(K(x,y),z) != u | T(x,T(y,z)) = u. K(x,y) * K(y,T(x,z)) = K(z,K(x,y)). x != K(y,T(z / u,z)) | x = K(y,u \ z). K(T(x,y),y / z) = K(x,z \ y). K(R(T(x,y),z,u),w) = K(R(x,z,u),T(w,y)). K(x,y) = K((z * x) / z,T(y,z)). K((x * y) / x,T(z,x)) = K(y,z). K(x \ y,z) = K(y / x,T(z,x)). K(x / y,T(z,y)) = K(y \ x,z). K(T(x,y),z / y) = K(x,y \ z). K(x,T(y,z)) * T(x,z) = T(T(x,z),y). K(x,T(y,z)) \ u = K(y,T(x,z)) * u. K(x,y) = K(x,T(y,R(T(x,z),u,w))). K(x,T(y,R(T(x,z),u,w))) = K(x,y). K(x,y) = K(x,T(y,R(x,z,u))). K(x,T(y,R(x,z,u))) = K(x,y). x / K(y,T(z,u)) = x * K(z,T(y,u)). (K(x,y) * z) * K(T(y,z),x) = z. x != K(T(y,z),u) | x = K(y,T(u,z)). K(x,T(y,x * z)) = K(x,T(y,z)). K(x,T(y,z)) = K(x,T(y,x \ z)). K(x,T(y,x \ z)) = K(x,T(y,z)). K(x,R(T(y,x \ z),u,w)) = K(x,T(R(y,u,w),z)). x * K(x,T(y,z)) = T(x,T(y,x \ z)). R(K(x,T(y,z)),x * u,w) = K(R(x,u,w),T(y,x \ z)). K(x,R(T(y,x \ z),u,w)) = K(x,R(T(y,z),u,w)). K(x,R(T(y,z),u,w)) = K(x,R(T(y,x * z),u,w)). K(x,R(T(y,x * z),u,w)) = K(x,R(T(y,z),u,w)). K(x,(x * y) \ ((x * z) * y)) = K(x,R(T(z,y),x,y)). K(x,y \ (x \ ((x * z) * y))) = K(x,R(T(z,y),x,y)). x != K(y,z \ (y \ ((y * u) * z))) | x = ((u * y) * z) \ ((y * u) * z). K(x,R(T(y,z),x,z)) = ((y * x) * z) \ ((x * y) * z). ((x * y) * z) \ ((y * x) * z) = K(y,R(T(x,z),y,z)). ((x * y) * z) \ ((y * x) * z) != u | K(y,T(x,z)) = u. L(x,T(y,z),K(u,y)) = x. K(x,y) * (z * x) = z * T(x,T(y,z)). a(x,T(y,z),K(u,y)) = 1. L(x,T(T(y,z),u),K(w,y)) = x. (K(x,y) * T(T(y,z),u)) * w = K(x,y) * (T(T(y,z),u) * w). R(K(x,y),T(T(y,z),u),w) = K(x,y). K(x,y) \ z = T(T(y,u),K(x,y)) * ((T(y,u) * K(x,y)) \ z). T(T(x,y),K(z,x)) * ((T(x,y) * K(z,x)) \ u) = K(z,x) \ u. T(T(x,y),K(z,x)) * ((T(x,y) * K(z,x)) \ u) = K(x,z) * u. T(T(x,K(y,x)),z * x) * ((T(x,x * z) * K(y,x)) \ u) = K(x,y) * u. T(x,y * x) * ((T(x,x * y) * K(z,x)) \ u) = K(x,z) * u. T(x,y * x) * (L(x,y,x) \ z) = K(x,y) * z. T(x,x * y) * (L(x,y,x) \ z) = K(x,y) * z. x * K(y,x \ z) = K(y,z / x) * x. K(x,y / z) * z = z * K(x,z \ y). (x \ y) * K(z,T(x,y)) = K(z,x) * (x \ y). T(x / y,K(z,y \ x)) = x / y. K(x,R(T(x,y),z,u) / w) = K(x,w \ R(T(x,y),z,u)). K(x,R(x,y,z) / u) = K(x,u \ R(x,y,z)). L(K(x,y),T(y,z),u) = K(x,y). x != L(K(y * z,y),T(y,z),u) | x = (u * T(y,z)) \ (u * R(y,z,y)). K(x * y,x) = (z * T(x,y)) \ (z * R(x,y,x)). (x * T(y,z)) \ (x * R(y,z,y)) = K(y * z,y). (x * T(y,z)) * L(K(u,y),w,v5) = x * (T(y,z) * L(K(u,y),w,v5)). K(x,R(T(x,y),z,u) \ w) = K(x,w / R(T(x,y),z,u)). K(x,y / R(T(x,z),u,w)) = K(x,R(T(x,z),u,w) \ y). K(x,R(x,y,z) \ u) = K(x,u / R(x,y,z)). K(x,y / R(x,z,u)) = K(x,R(x,z,u) \ y). K(x,y) * T(K(y,x),z) != u | u = K(z,K(x,y)). K(x,y) * T(K(y,x),z) != u | K(z,K(x,y)) = u. K(K(x,y),z) != u | K(z,K(y,x)) = u. T(K(x,y),z) * K(y,x) != u | K(z,K(y,x)) = u. x != (y * K(z,u)) * u | x = y * (u * K(z,u)). (x * K(y,z)) * T(z,u) = (x * K(z,u)) * (z * K(y,z)). (x * K(y,z)) * (y * K(u,y)) = (x * K(u,y)) * T(y,z). x != (y * K(z,u)) * T(u,w) | x = y * (K(z,u) * T(u,w)). (x * K(y,z)) * (y * K(u,y)) = x * (K(u,y) * T(y,z)). (x * K(y,z)) * (y * K(u,y)) = x * (T(y,z) * K(u,y)). (x * (y / z)) / (z \ y) = x * K(z,z \ y). (x / (y / z)) * K(z,z \ y) = x / (z \ y). (x / (y \ z)) * K(y \ z,y) = x / (z / y). T(K(x,y),z) != u | K(T(x,z),y) = u. (x / (y / z)) * K(u,z \ y) = x / T(y / z,T(u,z)). K(x,T(y,y * z)) != u | K(x,T(y,z)) = u. T(K(x,y),z) != u | K(x,T(y,z)) = u. K(T(x,y),z) != u | K(x,T(z,y)) = u. K(x,T(y,x * z)) != u | K(x,T(y,z)) = u. x * y != K(z,u) * L(z,w,z) | x \ L(T(z,u),w,z) = y. x \ L(T(x,y),z,x) = K(x,y) * (x \ L(x,z,x)). K(x,y) * (x \ L(x,z,x)) = x \ L(T(x,y),z,x). T(x,y) \ L(T(x,y),z,x) = x \ L(x,z,x). x * y != L((z \ ((u \ 1) \ w)) * z,v5 \ 1,v5) | x \ ((z \ (u * w)) * z) = y. x \ ((y \ (z * u)) * y) = (x \ 1) * ((y \ ((z \ 1) \ u)) * y). (x \ 1) * ((y \ ((z \ 1) \ u)) * y) = x \ ((y \ (z * u)) * y). K(x,y) * (z * T(L(K(u,x),w,v5),K(x,y) * z)) = L(K(u,x),w,v5) * (K(x,y) * z). K(x,T(y,K(z,u))) * K(u,z) = K(u,z) * K(x,y). x \ R(x,y,x) != z | z = a(x,y,x). x \ R(x,y,x) != z | a(x,y,x) = z. x * y != (z * K(u,w)) * w | (z * (w * K(u,w))) / y = x. (x * (y * K(z,y))) / (y * K(u,y)) = (x * K(z,y)) * K(y,u). x * y != (z / u) * u | x \ z = y. ((x / y) * K(y,z)) \ x = y * K(z,y). (x / (y * K(z,y))) * u != w | ((x / y) * K(y,z)) * u = w. K(L(x,y / x,z),u) != w | L(K(x,u),y,z) = w. K(L(x \ y,x,z),u) != w | L(K(x \ y,u),y,z) = w. L(K(x,y),z,u) = (w * L(K(y,x),z,u)) \ w. (x * L(K(y,z),u,w)) \ x = L(K(z,y),u,w). (x * (y * K(z,u))) \ (x * y) = L(K(u,z),y,x). x / L(K(y,z),u,w) = x * L(K(z,y),u,w). x * L(K(y,z),u,w) != v5 | x = v5 * L(K(z,y),u,w). x * L(K(y,z),u,w) != v5 | v5 * L(K(z,y),u,w) = x. x != (y * (z * u)) / L(u,z,y) | x = y * z. (x * (y * K(z,u))) * L(K(u,z),y,x) = x * y. x / L(L(K(y,z),u,w),K(z,y),v5) = x * L(K(z,y),u,w). x != y / L(z,u,y / (u * z)) | x = (y / (u * z)) * u. x * L(K(y,z),u,w) = (x / (K(y,z) * L(K(z,y),u,w))) * K(y,z). (x / (K(y,z) * L(K(z,y),u,w))) * K(y,z) = x * L(K(y,z),u,w). K(x,L(L(y,z,x),u,w)) = K(x,L(y,u,w)). K(x,(x \ y) \ z) = K(x,y \ (x * z)). K(x,(x \ y) \ (x \ z)) = K(x,y \ z). K(x,T(y \ (x * z),u)) = K(x,T((x \ y) \ z,u)). K(x,T((x \ y) \ z,u)) = K(x,T(y \ (x * z),u)). L(K(x,y),z * x,u) = K(L(x,z,u),L(y,w,x)). K(L(x,y,z),L(u,w,x)) = L(K(x,u),y * x,z). x != K(y,R(z,z \ u,w)) | x = R(K(y,z),u,w). (x * R(K(y,z),u,w)) \ x = R(K(z,y),u,w). (x * R(K(y,z),u,w)) * R(K(z,y),u,w) = x. (x * K(y,z)) \ x = R(K(z,y),R(z,u,w),v5). R(K(x,y),R(x,z,u),w) = (v5 * K(y,x)) \ v5. x != (y * K(z,u)) \ y | x = K(u,z). R(K(x,y),R(x,z,u),w) = K(x,y). K(x,R(x,y,z) / (u / w)) = K(x,(R(x,y,z) * w) / u). K(x,(R(x,y,z) * u) / w) = K(x,R(x,y,z) / (w / u)). (x * y) * z != x * T(y,T(u,x)) | T(K(y,u),x * y) = z. T(K(x,y),z * x) = K(x,T(y,z)). K(x,T(y,z * x)) = K(x,T(y,z)). T(K(x,y),z) = K(x,T(y,z / x)). K(x,T(y,z / x)) = T(K(x,y),z). K(x,K(y,z)) = (z * y) \ (y * T(z,T(y,x))). (x * y) \ (y * T(x,T(y,z))) = K(z,K(y,x)). K(x,y) = K(x,L(y,z,K(x,u))). K(x,L(y,z,K(x,u))) = K(x,y). T(K(x,y),z) = L(T(K(x,y),z),u,K(x,w)). L(T(K(x,y),z),u,K(x,w)) = T(K(x,y),z). T(L(K(x,y),z,u),w) = T(L(K(x,y),z,u),K(x,y) * w). T(L(K(x,y),z,u),K(x,y) * w) = T(L(K(x,y),z,u),w). T(L(K(x,y),z,u),w) = T(L(K(x,y),z,u),K(y,x) * w). T(L(K(x,y),z,u),K(y,x) * w) = T(L(K(x,y),z,u),w). K(x,y) * (z * T(L(K(y,x),u,w),z)) = L(K(y,x),u,w) * (K(x,y) * z). K(x,y) * (L(K(y,x),z,u) * w) = L(K(y,x),z,u) * (K(x,y) * w). L(K(x,y),z,u) * (K(y,x) * w) = K(y,x) * (L(K(x,y),z,u) * w). R(R(x,y,T(z,u)),y * T(z,u),K(u,z)) = ((x * y) * z) / (y * z). x != ((y * z) * u) / (z * u) | x = R(y,z,u). R(R(x,y,T(z,u)),y * T(z,u),K(u,z)) = R(x,y,z). R(R(x,y \ z,T(y,y \ z)),z,K(y \ z,y)) = R(x,y \ z,y). x != (y * (z * K(u * L(z,w,v5),z))) / (z * K(u,z)) | x = (y / (z * K(u,z))) * R(z * K(u,z),u,L(z,w,v5)). (x * K(y * L(z,u,w),z)) * K(z,y) = (x / (z * K(y,z))) * R(z * K(y,z),y,L(z,u,w)). (x / (y * K(z,y))) * R(y * K(z,y),z,L(y,u,w)) = (x * K(z * L(y,u,w),y)) * K(y,z). (x * (y * T(x,z))) \ ((x * y) * T(x,z)) = a(x,y * K(x,z),x). a(x,y * K(x,z),x) != u | a(x,y,T(x,z)) = u. x * (y / x) = y * K(x,x \ y). x * K(y,y \ x) = y * (x / y). (x * (y / z)) * z = (x * (z \ y)) * T(z,z \ y). (x * (y \ z)) * T(y,y \ z) = (x * (z / y)) * y. x != (y * (z / u)) * u | x = R(y,z / u,u) * z. (x * (y \ z)) * T(y,y \ z) = R(x,z / y,y) * z. x != y * z | x = y * (u * (u \ z)). (x * (y \ z)) * T(y,y \ z) = R(x,z / y,y) * (u * (u \ z)). R(x,y / z,z) * (u * (u \ y)) = (x * (z \ y)) * T(z,z \ y). x * (y * z) != (u * z) * T(y,z) | x = R(u,z,T(y,z)). R(x,y / z,z) = R(x,z \ y,T(z,z \ y)). R(x,y \ z,T(y,y \ z)) = R(x,z / y,y). R(R(x,y / z,z),y,K(z \ y,z)) = R(x,z \ y,z). x * K((y * z) \ x,y) = z * ((y \ (z \ x)) * y). K(x,(y \ L(y,z,u)) \ x) = K(x,(x / L(y,z,u)) * y). K(x,L(y,z,u) \ (y * x)) = K(x,(x / L(y,z,u)) * y). K(x,y * (L(y,z,u) \ x)) = K(x,(x / L(y,z,u)) * y). K(x,(x / L(y,z,u)) * y) = K(x,y * (L(y,z,u) \ x)). K(x,y) * K(y,T(x,z)) = K(x * z,K(x,y)). x != K(y,z) * K(z,T(y,u)) | x = K(u,K(y,z)). K(x * y,K(x,z)) = K(y,K(x,z)). a(x,y,R(x,z,u)) * K(x,y * R(x,z,u)) = K(x,y). a(x,y / R(x,z,u),R(x,z,u)) * K(x,y) = K(x,y / R(x,z,u)). x != L(K(y,z),u * y,w) | x = K(L(y,u,w),z). K(x,y) = K(L(x,z,y),y). K(L(x,y,z),z) = K(x,z). x != L(K(y \ (z \ u),w),z \ u,z) | x = K((z * y) \ u,w). K(x \ (y \ z),y) = K((y * x) \ z,y). K((x * y) \ z,x) = K(y \ (x \ z),x). (x * y) * K(z,x) = x * (y * K(z,x)). L(K(x,y),z,y) != u | u = K(x,y). L(K(x,y),z,y) != u | K(x,y) = u. x != K((y * z) \ 1,y) | x = ((y \ (1 / z)) * y) * z. K(x \ (y \ 1),y) = ((y \ (1 / x)) * y) * x. ((x \ (1 / y)) * x) * y = K(y \ (x \ 1),x). K(x \ y,z) = K((z \ x) \ (z \ y),z). K((x \ y) \ (x \ z),x) = K(y \ z,x). x * K(y \ (z \ x),z) = y * ((z \ (y \ x)) * z). (x * K(y \ (z \ x),z)) * u = (y * ((z \ (y \ x)) * z)) * u. (x * y) * K(x \ (z \ (x * y)),z) = x * ((z \ y) * z). K(x,y) * R(K(z,x),u,w) = R(K(z,x),u,w) * K(x,y). R(K(x,y),z,u) * K(y,w) = K(y,w) * R(K(x,y),z,u). K(x * y,x) != z | K(y * x,x) = z. K(L(L(x,y,z),u,w),z) = K(L(x,u,w),z). x != K(y \ z,y) * L(T(y,y \ z),u,w) | x = z \ ((L(y,u,w) * (y \ z)) * y). T(K(x \ y,x) * L(x,z,u),x \ y) = y \ ((L(x,z,u) * (x \ y)) * x). x != T(K(y \ z,y) * u,y \ z) | x = (z / y) \ (u * (y \ z)). x \ ((L(y,z,u) * (y \ x)) * y) = (x / y) \ (L(y,z,u) * (y \ x)). (x / y) \ (L(y,z,u) * (y \ x)) = x \ ((L(y,z,u) * (y \ x)) * y). K((x * y) \ z,x) != u | K(y \ (x \ z),x) = u. T(x,K(y,x) * z) = T(x,z). T(x,y) = T(x,K(x,z) * y). T(x,K(x,y) * z) = T(x,z). T(x,T(x,y) \ z) = T(x,x \ z). T(x,y * T(z,x)) = T(x,y * z). x * y != T(z,K(z,u) * w) | x \ T(z,w) = y. x \ T(x,y) = K(x,K(x,z) * y). K(x,K(x,y) * z) = x \ T(x,z). T(x,y) * K(z,T(x,K(x,u) * y)) = T(x * K(z,x),K(x,u) * y). x != y \ T(y,z) | x = K(y,z). K(x,K(x,y) * z) = K(x,z). K(x,y) = K(x,K(z,x) * y). K(x,K(y,x) * z) = K(x,z). K(x,T(x,y) * z) = K(x,x * z). K(x,y \ z) = K(x,y \ T(z,x)). K(x,y \ T(z,x)) = K(x,y \ z). K(x,R(K(y,x),z,u) * w) = K(x,w). K(x,K(y,R(x,z,u)) * w) = K(x,w). K(x,y) = K(x,K(R(x,z,u),w) * y). K(x,K(R(x,y,z),u) * w) = K(x,w). K(x,T(R(x,y,z),u) \ w) = K(x,R(x,y,z) \ w). K(x,y * R(x,z,u)) = K(x,R(x,z,u) * y). K(x,R(x,y,z) * u) = K(x,u * R(x,y,z)). K(x,y * K(z,R(x,u,w))) = K(x,y). K(x,R(x,y,z) * (u \ 1)) = K(x,u \ R(x,y,z)). K(x,R(T(x,y),z,u) * w) = K(x,R(x,z,u) * w). K(x,y / (z / R(x,u,w))) = K(x,y / (R(x,u,w) \ z)). x != K(y,z / (u / R(y,w,v5))) | x = K(y,(z * R(y,w,v5)) / u). K(x,y / (R(x,z,u) \ w)) = K(x,(y * R(x,z,u)) / w). K(x,(y * R(x,z,u)) / w) = K(x,y / (R(x,z,u) \ w)). K(x,R(T(x,y),z,u) \ w) = K(x,R(x,z,u) \ w). x != K(y,R(T(y,z),u,w) \ v5) | x = K(y,v5 / R(T(y,z),u,w)). K(x,R(x,y,z) \ u) = K(x,u / R(T(x,w),y,z)). K(x,y / R(T(x,z),u,w)) = K(x,R(x,u,w) \ y). K(x,y / z) * K(z \ y,u) = K(z \ y,u) * K(x,y / z). K(x \ y,z) * K(u,y / x) = K(u,y / x) * K(x \ y,z). x != K(y \ z,y) * K(u,z / y) | x = y \ (z / T(z / y,u)). K(x,y / z) * K(z \ y,z) = z \ (y / T(y / z,x)). x * y != T(z,z * u) * K(u,z) | x \ L(z,u,z) = y. x \ L(x,y,x) = K(y,x) * K(x,x * y). K(x,y) * K(y,y * x) = y \ L(y,x,y). (T(x,y) * (z * R(x,u,w))) \ ((T(x,y) * z) * R(x,u,w)) = a(x,K(x,y) * z,R(x,u,w)). a(T(x,y),z,R(x,u,w)) = a(x,K(x,y) * z,R(x,u,w)). a(x,K(x,y) * z,R(x,u,w)) = a(T(x,y),z,R(x,u,w)). a(x,K(x,y) * z,R(x,u,w)) != v5 | a(T(x,y),z,R(x,u,w)) = v5. a(x,x \ y,R(x,z,u)) = a(T(x,w),T(x,w) \ y,R(x,z,u)). a(T(x,y),T(x,y) \ z,R(x,u,w)) = a(x,x \ z,R(x,u,w)). K(x \ y,y) = K(y / x,y). K(x / y,x) = K(y \ x,x). L(K(x,y),x,z) != u | K(x,y) = u. R(T(x,K(y,z)),K(z,y),x) \ T(K(z,y) * x,T(x,K(y,z))) = T(K(z,y),T(x,K(y,z))). x != T(y,z) \ (u * K(y,z)) | x = y \ T(u,K(y,z)). T(x / y,T(y,z)) = y \ T(x,K(y,z)). x \ T(y,K(x,z)) = T(y / x,T(x,z)). x * T(y / x,T(x,z)) = T(y,K(x,z)). x * T(y,T(x,z)) = T(y * x,K(x,z)). (x * y) \ T(x * y,K(y,z)) = K(z,K(y,x)). K(x * y,K(y,z)) = K(z,K(y,x)). (x * (y * z)) / K(L(y,z,x),z) = x * (z * y). x != y / K(z,u) | x = y * K(u,z). x * (y * z) = (x * (z * y)) * K(y,L(z,y,x)). (x * (y * z)) * K(z,L(y,z,x)) = x * (z * y). x * (y * z) != (x * (z * y)) * u | K(y,L(z,y,x)) = u. (x * (y * z)) * u != x * (z * y) | K(z,L(y,z,x)) = u. (x / R(y,z,y)) * y = (x / T(y,z)) * T(y,y * z). (x / T(y,z)) * T(y,y * z) = (x / R(y,z,y)) * y. x != (y / T(z,u)) * T(z,w) | x = (y * K(u,z)) * K(z,w). (x / R(y,z,y)) * y = (x * K(z,y)) * K(y,y * z). (x * K(y,z)) * K(z,z * y) = (x / R(z,y,z)) * z. x * K(y,z) != u * (z * K(y,z)) | x = u * z. x * K(y,z) = (x / (y * K(z,y))) * y. (x / (y * K(z,y))) * y = x * K(y,z). x != (y / (z * K(u,z))) * z | x = (y * z) / ((u * z) / u). x * K(y,z) = (x * y) / ((z * y) / z). (x * y) / ((z * y) / z) = x * K(y,z). K(T(x,y),z) = K(R(x,y,R(x,u,w)),T(z,y * R(x,u,w))). K(R(x,y,R(x,z,u)),T(w,y * R(x,z,u))) = K(T(x,y),w). K(R(x,y,R(x,z,u)),T(w,y * R(x,z,u))) = K(x,T(w,y)). x != K(R(y,z,R(y,u,w)),v5) | x = K(y,v5). K(x,T(y,z)) = K(x,T(y,z * R(x,u,w))). K(x,T(y,z * R(x,u,w))) = K(x,T(y,z)). K(x,T(y,z)) = K(x,T(y,z / R(x,u,w))). K(x,T(y,z / R(x,u,w))) = K(x,T(y,z)). x * T(K(x,y),z) = T(x,T(y,z / x)). T(x,T(y,z)) = T(x,T(y,z / x)). T(x,T(y,z / x)) = T(x,T(y,z)). T(x,T(y,z / x)) != u | T(x,T(y,z)) = u. T(x \ y,T(z,x)) = T(x \ y,T(z,y)). T(x \ y,T(z,y)) = T(x \ y,T(z,x)). T(x \ 1,y) = T(x \ 1,T(y,x)). T(x \ 1,T(y,x)) = T(x \ 1,y). L(K(x,y),z,L(x,u,w)) = K(x,y). K(x,y) = K(L(x,z,L(x,u,w)),y). K(L(x,y,L(x,z,u)),w) = K(x,w). x * K(L(x,y,L(x,z,u)),w) = T(x,w). ((x * y) * (1 / z)) / ((y * (z \ 1)) * K(u,u \ 1)) = R(R(x,y,z \ 1),y * (z \ 1),K(u,u \ 1)). ((x * y) * (1 / z)) / (y * (1 / z)) = R(R(x,y,z \ 1),y * (z \ 1),K(u,u \ 1)). R(R(x,y,z \ 1),y * (z \ 1),K(u,u \ 1)) = ((x * y) * (1 / z)) / (y * (1 / z)). R(R(x,y,z \ 1),y * (z \ 1),K(u,u \ 1)) = R(x,y,1 / z). R(R(x,y,(z \ 1) \ 1),y * T(z,z \ 1),K(u,u \ 1)) = R(x,y,1 / (z \ 1)). R(R(x,y,(z \ 1) \ 1),y * T(z,z \ 1),K(u \ 1,u)) = R(x,y,1 / (z \ 1)). R(R(x,y,(z \ 1) \ 1),y * T(z,z \ 1),K(u \ 1,u)) = R(x,y,z). x != R(y,z,K(u \ 1,u)) | x = y. R(x,y,z) = R(x,y,(z \ 1) \ 1). R(x,y,(z \ 1) \ 1) = R(x,y,z). R(x,y,z) * (y * ((z \ 1) \ 1)) = (x * y) * ((z \ 1) \ 1). (x * y) * ((z \ 1) \ 1) != u * (y * ((z \ 1) \ 1)) | R(x,y,z) = u. K(x \ 1,T(y,x)) = K(x \ 1,y). (x / y) * K(y \ x,z) = T(x / y,T(z,y)). K(x / y,L(y,z,u)) = K(y \ x,L(y,z,u)). (x / y) * K(y \ x,T(y,z)) = T(x / y,T(y,z)). x != K(y / (y / z),y) | x = (y / (y / z)) \ L(z,z \ y,z). K((x / y) \ x,x) = (x / (x / y)) \ L(y,y \ x,y). (x / (x / y)) \ L(y,y \ x,y) = K((x / y) \ x,x). x != K((y / z) \ y,u) | x = K(z,u). (x / (x / y)) \ L(y,y \ x,y) = K(y,x). K(x,y) * T(x,T(z,y)) = T(T(x,y),z). K(x,y) * T(T(y,x),z) = T(y,T(z,x)). K(x,y / z) * T(z \ y,x) = T(y / z,T(z,x)). x != K(y,z) * ((z * R(y,u,w)) * y) | x = (y * z) * R(y,u,w). (R(x,y,R(x,z,u)) * w) * x = (x * w) * R(x,y,R(x,z,u)). x != L(K((y \ z) \ u,w),u,y) | x = K(z \ (y * u),w). K((x \ y) \ z,u \ (x * z)) = K(y \ (x * z),(x \ u) \ z). T(K(x,y \ (z * u)),w) = L(T(K(x,(z \ y) \ u),w),u,z). L(T(K(x,(y \ z) \ u),w),u,y) = T(K(x,z \ (y * u)),w). K((R(x,y,z) \ (R(x,y,z) * (x \ u))) \ u,w \ (R(x,y,z) * u)) = K(T(x,R(x,y,z) * (x \ u)),(R(x,y,z) \ w) \ u). K((x \ y) \ y,z \ (R(x,u,w) * y)) = K(T(x,R(x,u,w) * (x \ y)),(R(x,u,w) \ z) \ y). K(T(x,R(x,y,z) * (x \ u)),(R(x,y,z) \ w) \ u) = K((x \ u) \ u,w \ (R(x,y,z) * u)). x != K((y \ z) \ z,u) | x = K(y,T(u,z)). K(T(x,R(x,y,z) * (x \ u)),(R(x,y,z) \ w) \ u) = K(x,T(w \ (R(x,y,z) * u),u)). x != T(K(y,z),u) | x = K(y,T(z,u)). L(T(K(x,(y \ z) \ u),w),u,y) = K(x,T(z \ (y * u),w)). L(K(x,T((y \ z) \ u,w)),u,y) = K(x,T(z \ (y * u),w)). K(x,T((y \ z) \ x,u)) = K(x,T(z \ (y * x),u)). L(K(x,y),z * x,u) != w | K(L(x,z,u),y) = w. L(K(x,y),z * T(x,u),w) != v5 | K(L(x,z * K(x,u),w),y) = v5. K(L(x,y,z),L(u,w,x)) != v5 | K(L(x,y,z),u) = v5. (x * (y * ((z \ (y \ (x \ u))) * z))) \ u = K(z,(x * (y * z)) \ u). x != 1 / T(K(y,z),u) | x = K(z,T(y \ 1,u) \ 1). T(K(x,y),z) = K(x,T(y \ 1,z) \ 1). K(x,T(y \ 1,z) \ 1) = T(K(x,y),z). K(x,T(y,z) \ 1) = T(K(x,y \ 1),z). T(K(x,y \ 1),z) = K(x,T(y,z) \ 1). K(x,T(1 / y,z) \ 1) = T(K(x,y),z). x != (y * T(y \ z,u)) \ z | x = K(u,y \ z). K(x,(y * K(z,x)) \ u) = K(x,y \ u). K(x,(y * L(K(z,x),u,w)) \ v5) = K(x,y \ v5). K(x,(K(y,x) * z) \ u) = K(x,z \ u). K(x,(y * (z * K(u,x))) \ w) = K(x,(y * z) \ w). T(K(x,y \ z),u) = K(x,T((y * L(K(w,x),v5,v6)) \ z,u)). K(x,T((y * L(K(z,x),u,w)) \ v5,v6)) = T(K(x,y \ v5),v6). K(x,T((y * L(K(z,x),u,w)) \ v5,v6)) = K(x,T(y \ v5,v6)). K(x,T((y * z) \ u,w)) = K(x,T((y * (z * K(x,v5))) \ u,w)). K(x,T((y * (z * K(x,u))) \ w,v5)) = K(x,T((y * z) \ w,v5)). K(x,(y * (x \ z)) \ u) = K(x,(y * (z / x)) \ u). K(x,(y * (z / x)) \ u) = K(x,(y * (x \ z)) \ u). K(x,(y * z) \ u) = K(x,(y * (K(x,w) * z)) \ u). K(x,(y * (K(x,z) * u)) \ w) = K(x,(y * u) \ w). (x \ 1) / (x \ K(x,(y * (x \ z)) \ u)) = K((y * (z / x)) \ u,x). L(K(x,(y * (x \ z)) \ (u \ w)),u \ w,u) = K(x,(u * (y * (z / x))) \ w). K((x * (y \ z)) \ u,y) = K((x * (z / y)) \ u,y). K((x * (y / z)) \ u,z) = K((x * (z \ y)) \ u,z). K(x,L(L(y,z,K(x,u)),w,v5)) = K(x,L(y,w,v5)). K(x,T(x * K(y,z),y)) = K(x,x * K(y,z)). (x * y) * ((z \ ((x * y) \ u)) * z) = x * (y * ((z \ (y \ (x \ u))) * z)). ((x * y) * ((z \ ((x * y) \ u)) * z)) \ u = K(z,(x * (y * z)) \ u). x != (y * ((z \ (y \ u)) * z)) \ u | x = K(z,y \ (z \ u)). K(x,(y * (z * x)) \ u) = K(x,(y * z) \ (x \ u)). K(x,(y * z) \ u) = K(x,(y * (z / x)) \ (x \ u)). K(x,(y * (z / x)) \ (x \ u)) = K(x,(y * z) \ u). (x * K(y,(z * u) \ (y \ w))) \ x = K((z * (u * y)) \ w,y). K((x * y) \ (z \ u),z) = K((x * (y * z)) \ u,z). K((x * (y * z)) \ u,z) = K((x * y) \ (z \ u),z). K((x * (y * z)) \ u,z) != w | K((x * y) \ (z \ u),z) = w. x != K(y,(z * (u / y)) \ w) | x = K(y,(z * (y \ u)) \ w). K(x,(y * z) \ u) = K(x,(y * (x \ z)) \ (x \ u)). K(x,(y * (x \ z)) \ (x \ u)) = K(x,(y * z) \ u). K(x,(y * ((x \ 1) * z)) \ (x \ u)) = K(x,(y * z) \ u). K(x,(y * ((x \ 1) * z)) \ T(u,x)) = K(x,(y * z) \ (u * x)). x != K(y,z \ T(u,y)) | x = K(y,z \ u). K(x,(y * z) \ (u * x)) = K(x,(y * ((x \ 1) * z)) \ u). K(x,(y * ((x \ 1) * z)) \ u) = K(x,(y * z) \ (u * x)). K(x,(y * (x \ z)) \ u) = K(x,(y * z) \ (u * x)). (x \ 1) / (x \ K(x,(y * z) \ (u * x))) = K((y * (z / x)) \ u,x). K((x * y) \ (z * u),u) = K((x * (y / u)) \ z,u). K((x * (y / z)) \ u,z) = K((x * y) \ (u * z),z). x != K((y * (z / u)) \ w,u) | x = K((y * (u \ z)) \ w,u). K((x * y) \ (z * u),u) = K((x * (u \ y)) \ z,u). K((x * (y \ z)) \ u,y) = K((x * z) \ (u * y),y). T((x * y) / x,T(x,z)) = T(y,K(x,z)). T(x,T(y,z)) = T(T(x,y),K(y,z)). T(T(x,y),K(y,z)) = T(x,T(y,z)). (x * K((y \ 1) \ (z \ x),z)) * u = (y \ ((z \ (y * x)) * z)) * u. (x \ ((y \ (x * z)) * y)) * u = (z * K((x \ 1) \ (y \ z),y)) * u. K(x,K(y,z)) * (K(z,y) * u) = K(z,T(y,x)) * u. (x * ((y \ (x \ z)) * y)) \ z != u | K(y,(x * y) \ z) = u. K(x,(y * x) \ z) = K(x,y \ (x \ z)). x != K(y,(z * u) \ (z * w)) | x = L(K(y,u \ w),w,z). K(x,y \ (x \ (y * z))) = L(K(x,x \ z),z,y). L(K(x,x \ y),y,z) = K(x,z \ (x \ (z * y))). x != K(y,(y \ z) \ (y \ u)) | x = K(y,z \ u). L(K(x,x \ y),y,x \ z) = K(x,z \ ((x \ z) * y)). (x * (K(y,z) * u)) \ (x * u) = L(K(z,T(y,u)),u,x). (x * (K(y,z) * L(y,u,w))) \ (x * L(y,u,w)) = K(z,((x / y) * L(y,u,w)) \ (x * L(y,u,w))). x != (y * (K(z,u) * w)) \ (y * w) | x = L(K(u,T(z,w)),w,y). K(x,((y / z) * L(z,u,w)) \ (y * L(z,u,w))) = L(K(x,T(z,L(z,u,w))),L(z,u,w),y). K(x,((y / z) * L(z,u,w)) \ (y * L(z,u,w))) = L(K(x,z),L(z,u,w),y). K(x,y) = L(K(x,y),L(y,z,u),w). L(K(x,y),L(y,z,u),w) = K(x,y). K((x \ y) \ L(z,u,w),z) = K(y \ (x * L(z,u,w)),z). R(x,y,K(z,x)) = x. x * y != z * K(u,x) | T(z / T(x,u),x) = y. T((x * y) / T(x,z),x) = y * K(z,x). x * y != z * K(z,u) | x \ T(z,u) = y. x \ T(x * y,x) = y * K(x * y,x). R(x,y,K(z,T(x,u))) = x. L(x,y,z) * (u * K(w,T(x,v5))) = (L(x,y,z) * u) * K(w,T(x,v5)). (L(x,y,z) * u) * K(w,T(x,v5)) = L(x,y,z) * (u * K(w,T(x,v5))). L(K(x,T(y,z)),u,L(y,w,v5)) = K(x,T(y,z)). L(K(x,T(y,z)),u,L(y,w,v5)) != v6 | v6 = K(x,T(y,z)). L(K(x,T(y,z)),u,L(y,w,v5)) != v6 | K(x,T(y,z)) = v6. x != T(y,y \ z) | x = (y \ z) \ z. T(x,T(x,y) \ z) = (x \ z) \ z. ((x \ y) \ y) * z = z * ((T(x,z) \ y) \ y). x * ((T(y,x) \ z) \ z) = ((y \ z) \ z) * x. T((x \ y) \ y,z) = (T(x,z) \ y) \ y. (T(x,y) \ z) \ z = T((x \ z) \ z,y). x / T((y \ x) \ x,z) = T(y,z) \ x. x / T(y \ x,z) = T(x / y,z) \ x. T(x,y) / T(R(x,z,u),w) = T(R(x,z,u),w) \ T(x,y). x * K(y,x \ z) = T(z / x,y) \ z. T(x / y,z) \ x = y * K(z,y \ x). x / (y * K(z,y \ x)) = T(x / y,z). K(x,y * K(z,y \ 1)) = T(K(x,y),z). (x * y) / (x * K(z,y)) = T((x * y) / x,z). x != T((y * (z * K(u,z))) / y,u) | x = (y * z) / y. (x * (y * K(z,y))) / (x * K(z,y * K(z,y))) = (x * y) / x. (x * (y * K(z,y))) / (x * K(z,y)) = (x * y) / x. (x * (y * K(z,y))) / (x * K(z,y)) = y * K(x,y). K(x * K(y,z),z) = K(x,z). K(x \ T(y,z),z) = K(x \ y,z). K(((x \ 1) \ 1) \ y,z) = K(x \ y,z). K(x * y,y) = K(x * T(y,z),y). K(x * T(y,z),y) = K(x * y,y). K(x,y) = K(x * K(y,z),y). K(x * K(y,z),y) = K(x,y). K(x * K(y,T(z,u)),z) = K(x,z). K(x,y) = K(K(y,z) * x,y). K(K(x,y) * z,x) = K(z,x). R(x * K(y,x),z,u) \ R(x,z,u) = K(R(x,z,u),y * K(x,w)). K(R(x,y,z),u * K(x,w)) = R(x * K(u,x),y,z) \ R(x,y,z). K(x * (y * K(z,u)),z) = K(x * y,z). x != R(y * K(z,y),u,w) \ R(y,u,w) | x = K(R(y,u,w),z). K(R(x,y,z),u * K(x,w)) = K(R(x,y,z),u). K(R(x,y,z),u) = K(R(x,y,z),u * K(w,x)). K(R(x,y,z),u * K(w,x)) = K(R(x,y,z),u). K(x,y) = K(K(y,z) \ x,y). K(K(x,y) \ z,x) = K(z,x). K(x \ y,x) = K(T(x,z) \ y,x). K(T(x,y) \ z,x) = K(x \ z,x). K(R(K(x,y),z,u) * w,x) = K(w,x). K((x * y) \ z,y) = K((y * x) \ z,y). K((K(x,y) * z) * u,x) = K(z * u,x). K(K(R(x,y,z),u) * w,x) = K(w,x). K(x * y,z) = K(T(x,R(z,u,w)) * y,z). K(T(x,R(y,z,u)) * w,y) = K(x * w,y). K(x * R(y,z,u),y) * K(y,T(x,R(y,w,v5))) = a(y,T(x,R(y,w,v5)),R(y,z,u)). K(x * R(y,z,u),y) * K(y,x) = a(y,T(x,R(y,w,v5)),R(y,z,u)). a(x,T(y,R(x,z,u)),R(x,w,v5)) = K(y * R(x,w,v5),x) * K(x,y). a(x,T(y,R(x,z,u)),R(x,w,v5)) = a(x,y,R(x,w,v5)). a(x,R(x,y,z) \ u,R(x,w,v5)) = a(x,u / R(x,y,z),R(x,w,v5)). a(x,y / R(x,z,u),R(x,w,v5)) = a(x,R(x,z,u) \ y,R(x,w,v5)). a(x,T(y,x),R(x,z,u)) = a(x,y,R(x,z,u)). a(x,R(x,y,z) \ u,R(x,y,z)) * K(x,u) = K(x,u / R(x,y,z)). x != K(y,z / R(y,u,w)) | x = K(y,R(y,u,w) \ z). a(x,R(x,y,z) \ u,R(x,y,z)) * K(x,u) = K(x,R(x,y,z) \ u). x != K((y * z) \ u,y) | x = K(z \ (y \ u),y). K((x * y) \ z,y) = K(x \ (y \ z),y). K((x * y) \ z,y) != u | K(x \ (y \ z),y) = u. L(K(x \ y,x),y,z) != u | K(z \ (x \ (z * y)),x) = u. K((x \ y) \ z,y) = K((x \ 1) \ (y \ z),y). K((x \ 1) \ (y \ z),y) = K((x \ y) \ z,y). L(x * K(y \ (x \ z),x),u,w) / L(x,u,w) = K((y * x) \ z,L(x,u,w)). K(x \ (y \ (z * y)),y) = K(x \ z,y). T(x,y) / (T(x,y) / y) = y * K(y \ x,y). x != K(y \ (z \ u),z) | x = K((y * z) \ u,z). K(x \ y,z) = K((x * z) \ (y * z),z). K((x * y) \ (z * y),y) = K(x \ z,y). K(x * (K(y,z) * u),y) = K(x * u,y). R(x,y,z) \ R(x * K(u * w,x),y,z) = K(u * (K(x,v5) * w),R(x,y,z)). K(x * (K(y,z) * u),R(y,w,v5)) = R(y,w,v5) \ R(y * K(x * u,y),w,v5). x != R(y,z,u) \ R(y * K(w,y),z,u) | x = K(w,R(y,z,u)). K(x * (K(y,z) * u),R(y,w,v5)) = K(x * u,R(y,w,v5)). K(x * y,R(x,z,u)) = K(y * x,R(x,z,u)). K(x * y,R(y,z,u)) = K(y * x,R(y,z,u)). K((x \ 1) * y,z) = K(x \ y,z). x != L(y * K(z,y),u,w) / L(y,u,w) | x = K(z,L(y,u,w)). K((x * y) \ z,L(y,u,w)) = K(x \ (y \ z),L(y,u,w)). K(L(x \ y,x,z),L(x,u,w)) = K(z \ (x \ (z * y)),L(x,u,w)). ((T(x,y) \ x) * z) / (T(x,y) \ z) = R(x,T(x,y) \ 1,z). (x * (T(x,y) \ z)) / (T(x,y) \ z) = R(x,T(x,y) \ 1,z). R(x,T(x,y) \ 1,z) = x. x = R(x,T(x,y),z). 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). L(x,T(y,z),y) = x. (x * (T(x,y) * y)) \ ((x * T(x,y)) * (y * z)) = z. (x * (T(x,y) * y)) \ (x * (T(x,y) * (y * z))) = z. L(L(x,y,T(z,y)),T(z,y) * y,z) = x. x != L(y,T(z,u) * u,w) | x = L(y,u * z,w). 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(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). x \ (x / y) = L(y \ 1,y,x * y). L(x \ 1,x,y * x) = y \ (y / x). x != L(y,z,u / w) | x = L(y,z,w / u). L(x,y,z * y) = L(x,y,y / z). L(x,y,y / z) = L(x,y,z * y). ((x * y) * y) \ (x * y) = x \ (x / y). (x / y) * (y * R(y \ (y / x),z,u)) = x \ R(x,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 \ y) / y) * (y * R(y \ x,z,u)) = (x \ y) \ R(x \ y,z,u). (x \ 1) * (y * R(y \ x,z,u)) = (x \ y) \ R(x \ y,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)). x != y \ R(y,z,u) | x = y * R(y \ 1,z,u). x \ (y * R(y \ x,z,u)) = (x \ y) * R((x \ y) \ 1,z,u). (x \ y) * R((x \ y) \ 1,z,u) = x \ (y * R(y \ x,z,u)). x != (y \ z) \ R(y \ u,w,v5) | x = (y * z) \ R(y * u,w,v5). 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)). x != (y * (z * y)) \ R(y * (u * y),w,v5) | x = T(z,y) \ R(T(u,y),w,v5). x \ ((y * x) * R((y * x) \ x,z,u)) = T(y,x) \ R(T(y,x),z,u). 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)). x != y \ (R(z,u,w) * (z \ y)) | x = T(z \ R(z,u,w),y). T(x,y) \ R(T(x,y),z,u) = T(x \ R(x,z,u),y). T(x,y) \ R(T(x,y),z,u) != w | T(x \ R(x,z,u),y) = w. T(x \ R(x,y,z),y) = x \ R(x,y,z). T(T(x,y) \ R(T(x,y),z,u),y) = x \ R(x,z,u). 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 \ R(x,y,z),u),u) = x \ R(x,y,z). x != T(T(y \ R(y,z,u),w),y * (z * u)) | x = T(a(y,z,u),w). x \ R(x,y,z) = T(a(x,y,z),x * (y * z)). T(a(x,y,z),x * (y * z)) = x \ R(x,y,z). (x * (y \ R(y,z,u))) / x = T(y \ R(y,z,u),x). x != T(y,z) | x = y * K(y,z). (x * (y \ R(y,z,u))) / x = (y \ R(y,z,u)) * K(y \ R(y,z,u),x). T(T(x \ R(x,y,z),u),x * (y * z)) = (u * a(x,y,z)) / u. K(x,y \ R(y,z,u)) = K(y \ R(y,z,u),x). K(x \ R(x,y,z),u) = K(u,x \ R(x,y,z)). x != K(y,z) * R(T(u,y),w,v5) | x = T(K(y,z) * R(u,w,v5),y). x * T(x \ R(x,y,z),u) = T(K(u,x) * R(x,y,z),u). T(K(x,y) * R(y,z,u),x) = y * T(y \ R(y,z,u),x). x * y != z * T(z \ R(z,u,w),v5) | T(K(v5,z) * R(z,u,w),v5) / y = x. T(K(x,y) * R(y,z,u),x) / R(y,z,u) = K(R(y,z,u) / y,x). x != T(K(y,z) * u,y) / u | x = K(y,z) * K(u,y). 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). x != K(y \ R(y,z,u),w) | x = K(w,y \ R(y,z,u)). K(x,y) * K(R(y,z,u),x) = K(x,y \ R(y,z,u)). x \ R(x,y,z) = a(x,y,z) * K(a(x,y,z),x * (y * z)). a(x,y,z) * K(a(x,y,z),x * (y * z)) = x \ R(x,y,z). (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. K(a(x,y,z),u) * K(a(x,y,z),u) = 1. K(x,a(y,z,u)) = K(a(y,z,u),x). 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). ((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). (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) != v5 | L(x \ R(x,u,w),y,z) = v5. x != T(y \ R(y,z,u),w) | x = (w * (y \ R(y,z,u))) / w. x \ R(x,y,z) = (y * (x \ R(x,y,z))) / y. (x * (y \ R(y,x,z))) / x = y \ R(y,x,z). L(x,y * z,z) = L(x,y * z,T(z,y)). L(x,y * z,T(z,y)) = L(x,y * z,z). x * y != L(z,T(u,w) * w,T(u,w)) | x \ L(z,w * u,u) = y. x \ L(x,x * y,y) = a(T(y,x),x,x). x != L(y,z * u,T(u,z)) | x = L(y,u * z,u). L(x,y * z,z) = L(x,z * y,z). x * y != L(z,u * w,u) | x \ L(z,w * u,u) = y. x \ L(x,x * y,y) = a(y,x,x). x != L(y,z * (u * z),w) | x = L(y,T(u,z),w). L(x,(y * z) * z,y * z) = L(x,T(y,z),y * z). x != L(y,(z / u) * z,w) | x = L(y,u,w). L(x,y * (y / z),y) = L(x,z,y). x != y \ L(y,y * z,z) | x = a(T(z,y),y,y). a(x,y,y) = a(T(x,y),y,y). a(T(x,y),y,y) = a(x,y,y). x \ L(x,y,x * y) = a(x * y,x,x). x \ L(x,T(y,x),y * x) = a(y * x,x,x). x * L(x \ T(y,x),z,u) = T(x * L(x \ y,z,u),x). x \ T(x * L(x \ y,z,u),x) = L(x \ T(y,x),z,u). x \ T(x * L(y,z,u),x) = L(x \ T(x * y,x),z,u). x != K(y,z) | x = T(z,y) \ z. ((x * y) / x) \ y = T(x,y) \ x. T(x,y) * T(T(y,x),x * y) = (T(y,x) * (x * y)) / T(y,x). (T(x,y) * (y * x)) / T(x,y) = T(y,x) * T(T(x,y),y * x). x != T(y,z) * T(T(z,y),u) | x = T(z,u) * T(y,z). (T(x,y) * (y * x)) / T(x,y) = T(x,y * x) * T(y,x). (x * y) * K(T(y,x),x * y) = T(y,x * y) * T(x,y). x != (y * z) * K(T(z,y),y * z) | x = ((z * y) / R(z,y,z)) * z. T(x,y * x) * T(y,x) = ((x * y) / R(x,y,x)) * x. ((x * y) / R(x,y,x)) * x = T(x,y * x) * T(y,x). (x / R(y,y \ x,y)) * y = T(y,(y \ x) * y) * T(y \ x,y). T(x,(x \ y) * x) * T(x \ y,x) = (y / R(x,x \ y,x)) * x. T(x,y) * T(x \ y,x) = (y / R(x,x \ y,x)) * x. (x / R(y,y \ x,y)) * y = T(y,x) * T(y \ x,y). x != T(y,z) * T(y \ z,y) | x = (y \ z) * T(y,z). (x / R(y,y \ x,y)) * y = (y \ x) * T(y,x). K(x,y \ (K(x,z) * u)) = K(x,(K(z,x) * y) \ u). K(x,(K(y,x) * z) \ u) = K(x,z \ (K(x,y) * u)). x != K(y,(K(z,y) * u) \ w) | x = K(y,u \ w). K(x,y \ (K(x,z) * u)) = K(x,y \ u). K(x,y \ 1) = K(x,y \ K(z,x)). K(x,y \ K(z,x)) = K(x,y \ 1). K(x,y \ (x * z)) = K(x,y \ (z * x)). K(x,y \ (z * x)) = K(x,y \ (x * z)). x != K(y,z \ (y * u)) | x = K(y,(y \ z) \ u). K(x,y \ (z * x)) = K(x,(x \ y) \ z). K(x,(x \ y) \ z) = K(x,y \ (z * x)). K(x,y) = K(x,z \ (((x \ z) * y) * x)). K(x,y \ (((x \ y) * z) * x)) = K(x,z). L(K(x,y \ ((z \ u) * x)),z \ u,z) = K(x,(z * (x \ y)) \ u). T((x * y) \ (y * z),u) = L(T(T(x,y) \ z,u),T(x,y),y). L(T(T(x,y) \ z,u),T(x,y),y) = T((x * y) \ (y * z),u). R((x * y) \ (y * z),u,w) = L(R(T(x,y) \ z,u,w),T(x,y),y). L(R(T(x,y) \ z,u,w),T(x,y),y) = R((x * y) \ (y * z),u,w). L((x * y) \ (y * z),u,w) = L(L(T(x,y) \ z,u,w),T(x,y),y). L(L(T(x,y) \ z,u,w),T(x,y),y) = L((x * y) \ (y * z),u,w). (x * y) * L((x * y) \ (y * z),u,w) = y * (T(x,y) * L(T(x,y) \ z,u,w)). T(x * L(x \ y,z,u),y) = T(x,y) * L(T(x,y) \ y,z,u). T(x,y) * L(T(x,y) \ y,z,u) = T(x * L(x \ y,z,u),y). (x * y) * L((x * y) \ y,z,u) = y * (T(x,y) * L(T(x,y) \ 1,z,u)). x * (T(y,x) * L(T(y,x) \ 1,z,u)) = (y * x) * L((y * x) \ x,z,u). T(x,y) * L(x \ T(y,x),z,u) = T(x * L(x \ y,z,u),y). x * K(y,T(z,x) \ 1) = K(y,z \ 1) * x. x * K(y,(x \ z) \ 1) = K(y,(z / x) \ 1) * x. K(x,(y / z) \ 1) * z = z * K(x,(z \ y) \ 1). x * y != K(z,u) * x | y = K(z,T(u,x)). K(x,(y \ z) \ 1) = K(x,T((z / y) \ 1,y)). K(x,T((y / z) \ 1,z)) = K(x,(z \ y) \ 1). K(x \ 1,x) * (y * z) = (K(u \ 1,u) * y) * z. ((K(x \ 1,x) * (y * z)) * u) / (z * u) = R(K(w \ 1,w) * y,z,u). R(K(x \ 1,x) * y,z,u) = ((K(w \ 1,w) * (y * z)) * u) / (z * u). R(K(x \ 1,x) * y,z,u) = (K(w \ 1,w) * ((y * z) * u)) / (z * u). x != (K(y \ 1,y) * z) / u | x = K(y \ 1,y) * (z / u). R(K(x \ 1,x) * y,z,u) = K(w \ 1,w) * (((y * z) * u) / (z * u)). R(K(x \ 1,x) * y,z,u) = K(w \ 1,w) * R(y,z,u). K(x,x \ 1) * R(K(y \ 1,y) * z,u,w) = R(z,u,w). x * K(x,y) = T(x,R(y,z,x)). T(x,R(y,z,x)) = x * K(x,y). T(x,R(y,z,x)) = T(x,y). T(x,T((y * x) / z,z / x)) = T(x,(z / x) \ y). T(x,T((y * x) / z,z)) = T(x,(z / x) \ y). T(x,y \ (z * x)) = T(x,(y / x) \ z). T(x,(y / x) \ z) = T(x,y \ (z * x)). L(T(x,y \ (z * x)),u,w) \ L(x,u,w) = K((y / x) \ z,L(x,u,w)). K(x \ (y * z),L(z,u,w)) = K((x / z) \ y,L(z,u,w)). K((x / y) \ z,L(y,u,w)) = K(x \ (z * y),L(y,u,w)). R(x * y,z,u) / y = R(x / (1 / y),z,u) * (1 / y). R(x / (1 / y),z,u) * (1 / y) = R(x * y,z,u) / y. (1 / x) * R((1 / x) \ y,z,u) = R(y * x,z,u) / x. 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 * 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). x != K(y,z) * (u * y) | x = (K(y,z) * u) * y. T(x,y) * T(z,x) = (K(x,y) * z) * x. (K(x,y) * z) * x = T(x,y) * T(z,x). (T(x,y) * (x \ z)) * x = T(x,y) * T(z,x). x * y != T(x,z) * T(u,x) | T(T(x,z) * (x \ u),x) = y. T(T(x,y) * (x \ z),x) = T(x,y) * (x \ T(z,x)). T(x,y) * (x \ T(z,x)) = T(T(x,y) * (x \ z),x). T(x,y) * (x \ T(x * z,x)) = T(T(x,y) * z,x). T(x,y) * L(x \ T(z,x),u,w) = T(T(x,y) * L(x \ z,u,w),x). x != T(y,z) * L(y \ T(z,y),u,w) | x = T(y * L(y \ z,u,w),z). T(T(x,y) * L(x \ y,z,u),x) = T(x * L(x \ y,z,u),y). T(T(x,x * y) * L(y,z,u),x) = T(x * L(x \ (x * y),z,u),x * y). T(x * L(x \ (x * y),z,u),x * y) = T(T(x,x * y) * L(y,z,u),x). T(x * L(y,z,u),x * y) = T(T(x,x * y) * L(y,z,u),x). T(T(x,x * y) * L(y,z,u),x) = T(x * L(y,z,u),x * y). x != T(y,z) / (u \ y) | x = (u \ y) \ T((u \ y) * u,z). (x * y) / x = (y \ x) \ T((y \ x) * y,y). (x \ y) \ T((x \ y) * x,x) = (y * x) / y. 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). x != K((y \ (z \ y)) \ 1,u) | x = T(K(z,u),y). T(K(x,y),T(z,x)) = T(K(x,y),z). x * y != z * (1 / z) | x \ K(z,z \ 1) = y. L(x,y,z) \ K(x,x \ 1) = x * (L(x,y,z) \ (1 / x)). x * y != z \ K(u,u \ 1) | x \ (1 / z) = y. x \ (1 / L(x,y,z)) = L(x,y,z) \ (1 / x). L(x,y,z) \ (1 / x) = x \ (1 / L(x,y,z)). (x * ((y * x) \ z)) / x = L((y \ z) / x,x,y). L((x \ y) / z,z,x) = (z * ((x * z) \ y)) / z. L(((x / y) \ z) / y,y,x / y) = (y * (x \ z)) / y. L((x \ (y * (x * z))) / z,z,x) = (z * T(y,x * z)) / z. x != (y * T(z,u)) / y | x = T((y * z) / y,u). L((x \ (y * (x * z))) / z,z,x) = T((z * y) / z,x * z). L((x * y) / y,y,L(x,z,u)) = T((y * x) / y,L(x,z,u) * y). T((x * y) / x,L(y,z,u) * x) = L((y * x) / x,x,L(y,z,u)). T((x * y) / x,L(y,z,u) * x) = L(y,x,L(y,z,u)). L(x,y,L(x,z,u)) * y = y * T(x,L(x,z,u) * y). x * T(y,L(y,z,u) * x) = L(y,x,L(y,z,u)) * x. x * y != L(z,u,w) * x | y = L(T(z,x),u,w). T(x,L(x,y,z) * u) = L(T(x,u),u,L(x,y,z)). L(T(x,y),y,L(x,z,u)) = T(x,L(x,z,u) * y). (x * y) \ (y * (T(z * T(x,y),z) / z)) = L(a(z,T(x,y),z),T(x,y),y). (x / y) \ (x * K(y,z \ u)) = T(y,z \ (K(y,w) * u)). T(x,y \ (K(x,z) * u)) = (w / x) \ (w * K(x,y \ u)). K(T(x,y) \ z,x) = K(z / T(x,y),x). K(x / T(y,z),y) = K(T(y,z) \ x,y). K(T(x,T(y,z)) * u,y) = K(x * u,y). T(x * K(y * R(x,z,u),x),T(y,T(x,w))) = R(x,T(y,T(x,w)),R(x,z,u)). K(x,T(y,z * y)) != u | K(x,T(y,z)) = u. K(x / y,y) != z | K(y \ x,y) = z. K((x * (y * z)) \ ((x * y) * u),w) != v5 | L(K(L(z,y,x) \ u,w),u,x * y) = v5. x * R(x \ (y * z),u,w) = y * ((y \ x) * R((y \ x) \ z,u,w)). x * ((x \ y) * R((x \ y) \ z,u,w)) = y * R(y \ (x * z),u,w). x * y != (z * x) * R((z * x) \ (u * x),w,v5) | T(z * R(z \ u,w,v5),x) = y. T(x * R(x \ y,z,u),y) = (y \ (x * y)) * R((y \ (x * y)) \ y,z,u). (x \ (y * x)) * R((x \ (y * x)) \ x,z,u) = T(y * R(y \ x,z,u),x). x * ((1 / x) * R((x \ K(y,y \ 1)) \ z,u,w)) = K(y,y \ 1) * R(K(y,y \ 1) \ (x * z),u,w). K(x,x \ 1) * R(K(x,x \ 1) \ (y * z),u,w) = y * ((1 / y) * R((y \ K(x,x \ 1)) \ z,u,w)). K(x,x \ 1) * R(K(x,x \ 1) \ (y * z),u,w) = y * ((1 / y) * R((1 / y) \ z,u,w)). K(x,x \ 1) * R(K(x,x \ 1) \ (y * z),u,w) = y * (R(z * y,u,w) / y). K(x,x \ 1) * R(K(x \ 1,x) * (y * z),u,w) = y * (R(z * y,u,w) / y). K(x,x \ 1) * R(K(x \ 1,x) * y,z,u) = w * (R((w \ y) * w,z,u) / w). x * y != K(z,z \ 1) * R(K(u \ 1,u) * w,v5,v6) | x \ R(w,v5,v6) = y. x \ R(y,z,u) = R((x \ y) * x,z,u) / x. R((x \ y) * x,z,u) / x = x \ R(y,z,u). (x \ 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 * (z \ 1))) * x = R((x \ (y / z)) * x,z,z \ 1). R((x \ (y / z)) * x,z,z \ 1) = (x \ (y * (z \ 1))) * x. (x \ (y * z)) * x = R((x \ (y / (1 / z))) * x,z \ 1,z). R((x \ (y / (1 / z))) * x,z \ 1,z) = (x \ (y * z)) * x. R((x \ (1 / y)) * x,y,z) * (y * z) = (y * z) * ((x \ ((y * z) \ z)) * x). ((x \ (y * z)) * x) / z = ((x \ (y / (1 / z))) * x) * (1 / z). ((x \ (y / (1 / z))) * x) * (1 / z) = ((x \ (y * z)) * x) / z. x != ((y \ (z / (1 / u))) * y) * (1 / u) | x = y * (T((y \ z) * u,y) / u). ((x \ (y * z)) * x) / z = x * (T((x \ y) * z,x) / z). x * (T((x \ y) * z,x) / z) = ((x \ (y * z)) * x) / z. x * (y \ T(y * (x \ z),x)) = ((x \ (z * y)) * x) / y. x != y * (z \ T(z * (y \ u),y)) | x = ((y \ (u / (z \ 1))) * y) * (z \ 1). ((x \ (y * z)) * x) / z = ((x \ (y / (z \ 1))) * x) * (z \ 1). ((x \ (y / (z \ 1))) * x) * (z \ 1) = ((x \ (y * z)) * x) / z. (x \ 1) * ((y \ ((x \ 1) \ z)) * y) = ((y \ (z * x)) * y) / x. x != (y \ 1) * ((z \ ((u \ 1) \ w)) * z) | x = y \ ((z \ (u * w)) * z). ((x \ (y * z)) * x) / z = z \ ((x \ (z * y)) * x). (x \ ((y \ (x * z)) * y)) * x != u | u = (y \ (z * x)) * y. (x \ ((y \ (x * z)) * y)) * x != u | (y \ (z * x)) * y = u. (x * (y \ ((z \ (y * (x \ u))) * z))) \ u = K(z,(x * (z / y)) \ u). x != (y * (z \ ((u \ (z * (y \ w))) * u))) \ w | x = K(u,(y * (z \ u)) \ w). K(x,(y * (x / z)) \ u) = K(x,(y * (z \ x)) \ u). K(x,(y * z) \ u) = K(x,(y * ((z \ x) \ x)) \ u). K(x,(y * ((z \ x) \ x)) \ u) = K(x,(y * z) \ u). K(x,y \ z) = K(x,((y / T(u,u \ x)) * u) \ z). K(x,((y / T(z,z \ x)) * z) \ u) = K(x,y \ u). K(x,(y * K(z \ x,z)) \ u) = K(x,y \ u). K(x,y \ z) = K(x,((y \ x) \ x) \ z). K(x,((y \ x) \ x) \ z) = K(x,y \ z). (((x \ (1 / y)) * x) * y) * z = (y * z) * ((x \ ((y * z) \ z)) * x). (x * y) * ((z \ ((x * y) \ y)) * z) = (((z \ (1 / x)) * z) * x) * y. (x * y) * ((z \ ((x * y) \ y)) * z) = K(x \ (z \ 1),z) * y. x * y != R((z \ (u / w)) * z,w,w \ 1) | ((z \ (u * (w \ 1))) * z) / y = x. ((x \ (y * (z \ 1))) * x) / (z \ 1) = ((x \ (y / z)) * x) * z. x != ((y \ (z / u)) * y) * u | x = u * ((y \ (u \ z)) * y). ((x \ (y * (z \ 1))) * x) / (z \ 1) = z * ((x \ (z \ y)) * x). x / (y * ((z \ (y \ x)) * z)) = K(z,x / (z / (y \ 1))). x != y / (z * ((u \ (z \ y)) * u)) | x = K(u,y / (u * z)). K(x,y / (x / (z \ 1))) = K(x,y / (x * z)). x / (K(y \ (z \ 1),z) * x) = K(z,x / (z / ((y * x) \ 1))). K(x,y \ (x \ 1)) = K(x,z / (x / ((y * z) \ 1))). K(x,y / (x / ((z * y) \ 1))) = K(x,z \ (x \ 1)). x != K(y,z / (y / (u \ 1))) | x = K(y,z / (y * u)). K(x,y \ (x \ 1)) = K(x,z / (x * (y * z))). K(x,y / (x * (z * y))) = K(x,z \ (x \ 1)). (x \ (y * z)) * x = (y * K((z \ 1) \ (x \ y),x)) * z. (x * K((y \ 1) \ (z \ x),z)) * y = (z \ (x * y)) * z. (x * K((y \ z) \ x,z)) * y = (z \ (x * y)) * z. x * (R(y,z,u) / x) = R(x * (y / x),z,u). R(x * ((y / z) / x),z,y \ u) * (z * (y \ u)) = (x * ((u / (z * (y \ u))) / x)) * (z * (y \ u)). (x * ((y / (z * (u \ y))) / x)) * (z * (u \ y)) != w | ((x * ((u / z) / x)) * z) * (u \ y) = w. ((x * ((y / z) / x)) * z) * (y \ u) = (z * (y \ u)) * (x * (((z * (y \ u)) \ u) / x)). (x * (y \ z)) * (u * (((x * (y \ z)) \ z) / u)) = ((u * ((y / x) / u)) * x) * (y \ z). (x * (y \ z)) * (u * (((x * (y \ z)) \ z) / u)) = (x * (u * ((x \ y) / u))) * (y \ z). (x * y) * (z * (((x * ((u / y) \ u)) \ u) / z)) = (x * (z * ((x \ (u / y)) / z))) * ((u / y) \ u). (x * (y * ((x \ (z / u)) / y))) * ((z / u) \ z) = (x * u) * (y * (((x * ((z / u) \ z)) \ z) / y)). (x * (y * ((x \ (z / u)) / y))) * ((z / u) \ z) = (x * u) * (y * (((x * u) \ z) / y)). (x * (y * ((x \ (z / u)) / y))) * u = (x * u) * (y * (((x * u) \ z) / y)). ((x * y) * (z * (((x * y) \ u) / z))) / u = K(z,u / ((x * z) * y)). x != (y * (z * ((y \ u) / z))) / u | x = K(z,u / (y * z)). K(x,y / ((z * x) * u)) = K(x,y / ((z * u) * x)). K(x,y / ((z * u) * x)) = K(x,y / ((z * x) * u)). (x * y) * T((x * y) \ (y * z),u) = y * (T(x,y) * T(T(x,y) \ z,u)). T(x * T(x \ y,z),y) = T(x,y) * T(T(x,y) \ y,z). T(x,y) * T(T(x,y) \ y,z) = T(x * T(x \ y,z),y). T(x,y) * T(T(x,y) \ y,z) = T(y * K(x \ y,z),y). x * y != T(z,u) * T(T(z,u) \ u,w) | x \ T(u * K(z \ u,w),u) = y. x \ T(x * K(y \ x,z),x) = K(T(y,x) \ x,z). x \ T(x * K(y,z),x) = K(T(x / y,x) \ x,z). x != R(R(y,z,u),w,v5) * (z * u) | x = (R(y,w,v5) * z) * u. (x * y) * R(T(y,x),z,u) = (R(y,z,u) * x) * y. x \ ((R(y,z,u) * (y \ x)) * y) = K(y \ x,y) * R(T(y,y \ x),z,u). K(x \ y,x) * R(T(x,x \ y),z,u) = y \ ((R(x,z,u) * (x \ y)) * x). x * y != K(z \ u,z) * R(T(z,z \ u),w,v5) | x \ (u \ ((R(z,w,v5) * (z \ u)) * z)) = y. x \ (y \ ((R(x,z,u) * (x \ y)) * x)) = T(x,x \ y) \ R(T(x,x \ y),z,u). T(x,x \ y) \ R(T(x,x \ y),z,u) = x \ (y \ ((R(x,z,u) * (x \ y)) * x)). ((x \ y) \ y) \ R((x \ y) \ y,z,u) = x \ (y \ ((R(x,z,u) * (x \ y)) * x)). T(x / (x / (x / y)),y) = x / y. (x * (y / x)) / x = y / (y / (y / x)). R(x / y,x / (x / y),x / y) = T((x * (x / y)) / x,y). x != T((y * (z / u)) / y,u) | x = (y * (u \ z)) / y. R(x / y,x / (x / y),x / y) = (x * (y \ x)) / x. R(x / (x / y),(y * (x / y)) / y,x / (x / y)) = (x * ((x / y) \ x)) / x. R(x / (x / y),(y * (x / y)) / y,x / (x / y)) = (x * y) / x. T(x,(y * z) / y) = T(x,y / (y / z)). x != (y / z) \ (y * K(z,u)) | x = T(z,u). T(x,y \ (K(x,z) * u)) = T(x,y \ u). T(x,y \ ((x \ z) \ u)) = T(x,y \ ((z / x) \ u)). T(x,y \ ((z / x) \ u)) = T(x,y \ ((x \ z) \ u)). L(T(x,y \ ((x \ z) \ u)),w,v5) \ L(x,w,v5) = K(y \ ((z / x) \ u),L(x,w,v5)). K(x \ ((y / z) \ u),L(z,w,v5)) != v6 | K(x \ ((z \ y) \ u),L(z,w,v5)) = v6. T(x,y) * K(z,T(x,y)) = T(x * K(z,x),K(x,u) * y). T(x * K(y,x),K(x,z) * u) = T(x,u) * K(y,T(x,u)). x != T(y,z) * K(u,T(y,z)) | x = T(y * K(u,y),z). T(x * K(y,x),K(x,z) * u) = T(x * K(y,x),u). x != T(y * K(z * R(y,u,w),y),z) | x = R(y,z,R(y,u,w)). T(x * K((K(x,y) * z) * R(x,u,w),x),z) = R(x,K(x,y) * z,R(x,u,w)). T(x * K(y * R(x,z,u),x),y) = R(x,K(x,w) * y,R(x,z,u)). R(x,K(x,y) * z,R(x,u,w)) = R(x,z,R(x,u,w)). ((x \ y) \ y) \ R((x \ y) \ y,K(x,z) * u,R(x,w,v5)) = x \ (y \ ((R(x,u,R(x,w,v5)) * (x \ y)) * x)). L(x * K((y * z) \ (x \ u),x),w,v5) / L(x,w,v5) = K((y * (z * x)) \ u,L(x,w,v5)). K((x * (y * z)) \ u,L(z,w,v5)) = K((x * y) \ (z \ u),L(z,w,v5)). L(K(L(x,y,z) \ u,L(x,w,v5)),u,z * y) = K((z * y) \ (x \ ((z * y) * u)),L(x,w,v5)). K(x,(y / z) \ 1) * y = y * K(x,y \ z). K(x,y \ z) = K(x,T((y / z) \ 1,y)). K(x,T((y / z) \ 1,y)) = K(x,y \ z). K(x,T(y \ 1,z)) = K(x,z \ (y \ z)). L(K(x,(y * z) \ ((u \ w) * x)),u \ w,u) = K(x,(u * (y * (z / x))) \ w). x != K(y,(z * (y \ u)) \ w) | x = K(y,(z * u) \ (w * y)). L(K(x,y \ ((z \ u) * x)),z \ u,z) = K(x,(z * y) \ (u * x)). x != L(K(y,(z * u) \ ((w \ v5) * y)),w \ v5,w) | x = K(y,(w * (z * (u / y))) \ v5). K(x,(y * (z * u)) \ (w * x)) = K(x,(y * (z * (u / x))) \ w). K(x,(y * (z * (u / x))) \ w) = K(x,(y * (z * u)) \ (w * x)). L(x,(y * y) / z,u) = L(x,z,u). x != L(y,z / u,w) | x = L(y,u / z,w). 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 != L(y,(z * u) * u,z * u) | x = L(y,T(z,u),z * u). L(x,R(y,z,z),y * z) = L(x,T(y,z),y * z). L(x,(y \ z) \ z,y) = x. x = L(x,(y \ z) * z,y). L(x,(y \ z) * z,y) = x. (x * ((x \ y) * y)) \ z = ((x \ y) * y) \ (x \ z). x != ((y \ z) * u) \ (y \ w) | x = ((y * z) * u) \ (y * w). (x * ((x \ y) * y)) \ z = ((x * y) * y) \ (x * z). x != ((y * z) * z) \ (y * z) | x = y \ (y / z). (x * ((x \ y) * y)) \ y = x \ (x / y). x / (y \ (y / x)) = y * ((y \ x) * x). 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)). x != L(y,z,T(u \ w,u)) | x = L(y,z,u / w). L(x,y,T(z * u,z)) = L(x,y,z / u). (x * (R(x,y,z) * T(u,x))) \ ((u * x) * R(T(x,u),y,z)) = a(x,T(u,x),R(T(x,u),y,z)). (R(x,y,z) * (u * x)) \ ((u * x) * R(T(x,u),y,z)) = a(x,T(u,x),R(T(x,u),y,z)). (R(x,y,z) * (u * x)) \ ((R(x,y,z) * u) * x) = a(x,T(u,x),R(T(x,u),y,z)). a(R(x,y,z),u,x) = a(x,T(u,x),R(T(x,u),y,z)). a(x,T(y,x),R(T(x,y),z,u)) = a(R(x,z,u),y,x). x != a(y,T(z,y),u) | x = a(T(y,z),T(T(z,y),y),u). a(R(x,y,z),u,x) = a(T(x,u),T(T(u,x),x),R(T(x,u),y,z)). a(T(x,y),T(T(y,x),x),R(T(x,y),z,u)) = a(R(x,z,u),y,x). x != (y \ (y \ z)) * (y * y) | x = T(z,y * y). ((x \ (x \ y)) * x) / (x \ 1) = T(y,x * x). (x \ T(y,x)) / (x \ 1) = T(y,x * x). ((x \ 1) * T(y,x)) / (x \ 1) = T(y,x) * K(x \ 1,y). (x \ T(y,x)) / (x \ 1) = T(y,x) * K(x \ 1,y). x != (y \ T(z,y)) / (y \ 1) | x = T(z,y * y). T(x,y) * K(y \ 1,x) = T(x,y * y). x != T(y,y * z) * L(T(z,y),u,w) | x = L(z,u,w) * T(y,y * z). K(x,x * y) * (L(y,z,u) * x) = L(y,z,u) * T(x,x * y). K(R(x,L(y,z,u),x),R(x,L(y,z,u),x) * y) * T(x * L(y,z,u),x) = L(y,z,u) * T(R(x,L(y,z,u),x),R(x,L(y,z,u),x) * y). x != y * ((z \ u) * T((z \ u) \ (y \ u),w)) | x = (y * T(y \ z,w)) * (z \ u). K((x * (y \ 1)) \ 1,z) = (x * T(x \ y,z)) * (y \ 1). (x * T(x \ y,z)) * (y \ 1) = K((x * (y \ 1)) \ 1,z). (1 / x) * (y * T(y \ x,z)) = K(((1 / x) * y) \ 1,z). (1 / x) * (y \ T(y * x,z)) = K(((1 / x) * (y \ 1)) \ 1,z). K(((1 / x) * (y \ 1)) \ 1,z) = (1 / x) * (y \ T(y * x,z)). x != K((y * (z \ 1)) \ 1,u) | x = (y * T(y \ z,u)) * (z \ 1). (1 / x) * (y \ T(y * x,z)) = ((1 / x) * T((1 / x) \ y,z)) * (y \ 1). ((1 / x) * T((1 / x) \ y,z)) * (y \ 1) = (1 / x) * (y \ T(y * x,z)). (T(x * y,z) / y) * (x \ 1) = (1 / y) * (x \ T(x * y,z)). (x \ T(y,z)) * ((x \ y) \ 1) = (1 / x) * ((x \ y) \ T((x \ y) * x,z)). (1 / x) * ((x \ y) \ T((x \ y) * x,z)) = (x \ T(y,z)) * ((x \ y) \ 1). (1 / x) * ((y * x) / y) = (x \ T(y,x)) * ((x \ y) \ 1). (x \ T(y,x)) * ((x \ y) \ 1) = (1 / x) * ((y * x) / y). x != (1 / y) * ((z * y) / z) | x = K(z,y). (x \ T(y,x)) * ((x \ y) \ 1) = K(y,x). (x \ T(x * y,x)) * (y \ 1) = K(x * y,x). (x \ T(x * K(y,z),x)) * (K(z,y) * 1) = K(x * K(y,z),x). x * (K(x \ 1,y) * (x \ z)) = K(x \ 1,y) * z. (1 / x) * (K(x,y) * ((1 / x) \ z)) = K((1 / x) \ 1,y) * z. (1 / x) * (K(x,y) * ((1 / x) \ z)) = K(x,y) * z. (1 / x) * (K(x,y) * z) = K(x,y) * ((1 / x) * z). K(x,y) * ((1 / x) * z) = (1 / x) * (K(x,y) * z). x * y != (1 / z) * (K(z,u) * w) | x \ (K(z,u) * ((1 / z) * w)) = y. (K(x,y) * z) \ (K(x,y) * ((1 / x) * z)) = T(1 / x,K(x,y) * z). L(T(1 / x,y),y,K(x,z)) = T(1 / x,K(x,z) * y). K(T(1 / x,K(x,y) * z) \ 1,u) = L(T(K(x,u),z),z,K(x,y)). L(T(K(x,y),z),z,K(x,u)) = K(T(1 / x,K(x,u) * z) \ 1,y). x != K(T(1 / y,z) \ 1,u) | x = T(K(y,u),z). L(T(K(x,y),z),z,K(x,u)) = T(K(x,y),K(x,u) * z). x != L(T(K(y,z),u),w,K(y,v5)) | x = T(K(y,z),u). T(K(x,y),K(x,z) * u) = T(K(x,y),u). T(K(x,y),z) = T(K(x,y),K(u,x) * z). T(K(x,y),K(z,x) * u) = T(K(x,y),u). K(x,T(y,K(z,x) * u)) = T(K(x,y),u). K(x,T(y,K(z,x) * u)) = K(x,T(y,u)). K(x,T(y,z)) = K(x,T(y,K(x,u) * z)). K(x,T(y,K(x,z) * u)) = K(x,T(y,u)). K(x,T(y,T(z,x))) = K(x,T(y,z)). K(x,T(y \ x,T(z,y))) = K(x,T(y \ x,z)). K(x,T(y \ x,y \ z)) = K(x,T(y \ x,z / y)). K(x,T(y \ x,z / y)) = K(x,T(y \ x,y \ z)). 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 != L(y,(z * u) * u,w) | x = L(y,R(z,u,u),w). 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)). T(x,T(T(x,y),z)) = x. K(x,y) = K(x,T(y,T(T(x,z),u))). K(x,T(y,T(T(x,z),u))) = K(x,y). K(x,y) * x = T(x,T(y,T(T(x,z),u))). T(x,T(y,T(T(x,z),u))) = K(x,y) * x. x != K(y,z) * y | x = T(y,z). T(x,T(y,T(T(x,z),u))) = T(x,y). T(x,T(y,T(x,z))) = T(x,y). T(x * K(y,x),T(z,T(x,u))) = T(x * K(y,x),z). x != T(y * K(z * R(y,u,w),y),T(z,T(y,v5))) | x = R(y,T(z,T(y,v5)),R(y,u,w)). T(x * K(y * R(x,z,u),x),y) = R(x,T(y,T(x,w)),R(x,z,u)). R(x,T(y,T(x,z)),R(x,u,w)) = R(x,y,R(x,u,w)). T(x / (x / y),T(z,y)) = T(x / (x / y),z). T(T(T(x,y) / (T(x,y) / y),x),z) = L(T(y,z),y \ T(x,y),y). T(T(x * K(x \ y,x),y),z) = L(T(x,z),x \ T(y,x),x). T(L(x,x \ y,x),z) = L(T(x,z),x \ T(y,x),x). L(T(x,y),x \ T(z,x),x) = T(L(x,x \ z,x),y). L(T(x,y),x \ T(z,x),x) = L(T(x,y),x \ z,x). R(L(T(x,y),x \ z,x),u,w) = L(R(T(x,y),u,w),x \ T(z,x),x). L(R(T(x,y),z,u),x \ T(w,x),x) = R(L(T(x,y),x \ w,x),z,u). L(R(T(x,y),z,u),x \ T(w,x),x) = L(R(T(x,y),z,u),x \ w,x). T(x / y,y) = T(y \ x,x \ y). T(x \ y,y \ x) = T(y / x,x). x != T((y * z) / y,y) | x = z. T(x \ (x * y),(x * y) \ x) = y. T(x \ y,y \ x) = x \ y. T(x,(y * x) \ y) = x. T(x,y \ (y / x)) = 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 \ (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 != L(y,z,u * (u / z)) | x = y. ((x \ (x / y)) \ y) \ y = x \ (x / y). x / (y \ (y / x)) != z | z = (y \ (y / x)) \ x. x / (y \ (y / x)) != z | (y \ (y / x)) \ x = z. (x \ (x / y)) \ y = x * ((x \ y) * y). x != y * ((y \ z) * u) | x = z * L(u,y * z,y). (x \ (x / y)) \ y = y * L(y,x * y,x). x * L(x,y * x,y) = (y \ (y / x)) \ x. x * y != (z \ (z / u)) \ u | (u * L(u,z * u,z)) / y = x. (x * L(x,y * x,y)) / x = (y \ (y / x)) \ 1. L(x,y * x,y) = (y \ (y / x)) \ 1. x != L(y,z * y,z) | x = y * a(z,y,y). (x \ (x / y)) \ 1 = y * a(x,y,y). (x * a(y,x,x)) * z = (y \ (y / x)) \ z. (x \ (x / y)) \ z = (y * a(x,y,y)) * z. x != (y * a(z,y,y)) * u | x = y * (a(z,y,y) * u). (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 != L(y,z * (z / u),z) | x = L(y,u,z). (x / y) \ (x * z) = L(y * (a(x,y,y) * z),y,x). L(x * (a(y,x,x) * z),x,y) = (y / x) \ (y * z). L(x * (a(y,x,x) * z),x,y) = (x / y) * (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))) * (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 != L(y,z * (u \ w),v5) | x = L(y,z * (u * w),v5). (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)). R(x,y,z) * (x \ (y * u)) = y * (R(x,y,z) * (x \ u)). x != y * (R(z,y,u) * (z \ (y \ u))) | x = L(u,z * y,z). 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. x * y != R(z,u,w) * (z \ w) | L(w,z * u,z) / y = x. L(x,y * z,y) / x = y \ R(y,z,x). x \ L(x,y * z,y) = y \ R(y,z,x). x \ L(x,y,z) = z \ R(z,z * y,x). x \ R(x,x * y,z) = z \ L(z,y,x). R(x,y,z) \ x = z \ L(z,y,x). K(x,y) \ R(K(x,y),z,u) = u \ L(u,z,K(x,y)). x * y != R(z,u,w) \ z | x \ (w \ L(w,u,z)) = y. x \ (y \ L(y,z,x)) = R(x,z,y) \ 1. x * (R(y,z,x) \ y) = L(x,z,y). (x \ L(x,y,z)) * R(z,y,x) = z. 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. L(x,y,z) \ x = z \ R(z,y,x). R(x,y,z) * (x \ L(z,y,x)) = z. x * y != R(z,u,w) * (z \ L(w,u,z)) | x \ w = y. (x \ R(x,y,z)) \ z = L(z,y,x). a(x,y,x) \ x = L(x,y,x). x != y | x = y * 1. x \ R(x,y,z) = (L(z,y,x) \ z) * 1. (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 * (R(K(y,z),u,x) \ K(y,z)) = L(x,u,K(z,y)). x * (K(y,z) * K(z,R(y,u,x))) = L(x,y * u,K(y,z)). x \ R(x,y,z) != u * 1 | L(z,y,x) \ z = u. L(x,y,z) \ (x * z) = R(z,y,x). (L(x,y,z) * (R(z,y,x) * u)) \ ((x * z) * u) = a(L(x,y,z),R(z,y,x),u). x * (L(x,y,z) \ (z * u)) = R(z,y,x) * u. x != R(y,z,u) * T(z,y) | x = z * R(y,z,u). x * (L(x,y,z) \ (z * T(y,z))) = y * R(z,y,x). L(x,y,z) * (R(z,y,x) * u) = x * (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). x * (y \ L(z,u,y)) != z | x = R(y,u,z). R(x,y,L(z,y,x)) = R(x,y,z). x * (y * (L(y,z,x) \ u)) = R(x,z,y) * u. x * (L(x,y,z) \ u) != w | R(z,y,x) * (z \ u) = w. x * (L(x,y,z) \ (y * z)) = y * R(z,y,x). (x * (y * z)) / (y * R(z,y,x)) = L(x,y,z). x \ R(x,y,y \ 1) = a(x,y,y \ 1). K(x,y) * R(K(y,x),z,z \ 1) = a(K(y,x),z,z \ 1). x \ R(x,y \ 1,y) = a(x,y \ 1,(y \ 1) \ 1). a(x,y \ 1,(y \ 1) \ 1) = x \ R(x,y \ 1,y). a(x,y \ 1,y) = x \ R(x,y \ 1,y). x \ R(x,y \ 1,y) = a(x,y \ 1,y). K(x,y) * R(K(y,x),z \ 1,z) = a(K(y,x),z \ 1,z). x != ((y * z) / y) \ (T(y,z) * ((y \ z) * u)) | x = L(u,y \ z,T(y,z)). x \ (y * ((y \ x) * z)) = L(z,y \ x,T(y,x)). L(x,y \ z,y) = L(x,y \ z,T(y,z)). L(x,y \ z,T(y,z)) = L(x,y \ z,y). L(x,y \ (K(z,y) * u),T(y,u)) = L(x,y \ (K(z,y) * u),y). L(x,T(y,z) \ u,T(y,u)) = L(x,y \ (K(z,y) * u),y). L(x,T(y,z) \ u,T(y,u)) = L(x,T(y,z) \ u,y). x * L(y,T(z,x) \ x,z) = T(z,x) * ((T(z,x) \ x) * y). T(x,y) * ((T(x,y) \ y) * z) = y * L(z,T(x,y) \ y,x). T(x,y) * ((x \ T(y,x)) * z) = y * L(z,T(x,y) \ y,x). T(x,y) * ((x \ T(y,x)) * z) = y * L(z,x \ T(y,x),x). (x * L(y,z \ T(x,z),z)) \ (x * y) = a(T(z,x),T(z,x) \ x,y). R(x / (1 / (1 / y)),1 / (1 / y),K(z,z \ 1)) = (x * K(z,z \ 1)) / y. T(x,y) * R((y \ (x * y)) \ y,z,u) = T(x * R(x \ y,z,u),y). T(x,y) * R(T(x,y) \ y,z,u) = T(x * R(x \ y,z,u),y). x * ((y * (x \ (z * u))) / y) = z * ((z \ x) * ((y * ((z \ x) \ u)) / y)). x * ((x \ y) * ((z * ((x \ y) \ u)) / z)) = y * ((z * (y \ (x * u))) / z). x * y != (z * x) * ((u * ((z * x) \ (w * x))) / u) | T(z * ((u * (z \ w)) / u),x) = y. T(x * ((y * (x \ z)) / y),z) = (z \ (x * z)) * ((y * ((z \ (x * z)) \ z)) / y). (x \ (y * x)) * ((z * ((x \ (y * x)) \ x)) / z) = T(y * ((z * (y \ x)) / z),x). T(x,y) * ((z * ((y \ (x * y)) \ y)) / z) = T(x * ((z * (x \ y)) / z),y). T(x,y) * ((z * (T(x,y) \ y)) / z) = T(x * ((z * (x \ y)) / z),y). T(x * ((y * (x \ z)) / y),z) / z = K(y,(T(x,z) / z) \ 1). T(((x * y) / x) * (y \ z),z) / z = K(x,(T(y \ z,z) / z) \ 1). T(K(x,y) * z,z) / z = K(x,(T(y \ z,z) / z) \ 1). K(x,(T(y \ z,z) / z) \ 1) = T(K(x,y) * z,z) / z. x != T(y * z,u) / z | x = z \ T(z * y,u). K(x,(T(y \ z,z) / z) \ 1) = z \ T(z * K(x,y),z). K(x,y / T(z \ y,y)) = y \ T(y * K(x,z),y). x \ T(x * K(y,z),x) = K(y,x / T(z \ x,x)). x \ T(x * K(y,z),x) = K(y,T(x / z,x) \ x). x != y \ T(y * K(z,u),y) | x = K(T(y / z,y) \ y,u). K(x,T(y / z,y) \ y) = K(T(y / x,y) \ y,z). K(T(x / y,x) \ x,z) = K(y,T(x / z,x) \ x). K(x,T(y / z,y) \ y) * (K(z,x) * 1) = K(y * K(x,z),y). K(x,T(y / z,y) \ y) * K(z,x) = K(y * K(x,z),y). x != L(y,z * (u \ z),w) | x = L(y,T(u \ 1,z),w). L(x,T(y,z),u) = L(x,T(y \ 1,z),u). L(x,T(y \ 1,z),u) = L(x,T(y,z),u). R(T(x / y,z),y,y \ z) = (y * (y \ z)) \ (x * (y \ z)). (x * (x \ y)) \ (z * (x \ y)) = R(T(z / x,y),x,x \ y). x != (y * (y \ z)) \ u | x = z \ u. R(T(x / y,z),y,y \ z) = z \ (x * (y \ z)). (x \ (y * (z \ x))) * x = (T(y / z,x) * z) * (z \ x). (x \ (y * (z \ x))) * x = (z * T(z \ y,x)) * (z \ x). (x \ (y * (T(z,x) \ z))) * x = (((z * x) / z) * T(((z * x) / z) \ y,x)) * (((z * x) / z) \ x). (((x * y) / x) * T(((x * y) / x) \ z,y)) * (((x * y) / x) \ y) = (y \ (z * (T(x,y) \ x))) * y. ((x * (y * T(y \ T(z,x),y))) / x) * (((x * y) / x) \ y) = (y \ (z * (T(x,y) \ x))) * y. ((x * ((y \ T(z,x)) * y)) / x) * (((x * y) / x) \ y) = (y \ (z * (T(x,y) \ x))) * y. ((x * ((y \ T(z,x)) * y)) / x) * (T(x,y) \ x) = (y \ (z * (T(x,y) \ x))) * y. ((x * T((y \ z) * y,x)) / x) * (T(x,y) \ x) = (y \ (z * (T(x,y) \ x))) * y. ((x \ y) * x) * (T(z,x) \ z) = (x \ (y * (T(z,x) \ z))) * x. (x \ (y * (T(z,x) \ z))) * x = ((x \ y) * x) * (T(z,x) \ z). (x \ (y * K(x,z))) * x = ((x \ y) * x) * (T(z,x) \ z). ((x \ y) * x) * (T(z,x) \ z) = (x \ (y * K(x,z))) * x. ((x \ y) * x) * K(x,z) = (x \ (y * K(x,z))) * x. (x \ (y * K(x,z))) * x = ((x \ y) * x) * K(x,z). x != (y * z) * K(z,u) | x = y * T(z,u). (x \ (y * K(x,z))) * x = (x \ y) * T(x,z). x * y != (y \ z) * T(y,z) | x = z / R(y,y \ z,y). x \ (y * K(x,y)) = y / R(x,x \ y,x). x / R(y,y \ x,y) = y \ (x * K(y,x)). x != y \ (z * K(y,z)) | x = (y * K(z,y)) \ z. x / R(y,y \ x,y) = (y * K(x,y)) \ x. x / ((y \ x) \ T(x,y)) = (y * K(x,y)) \ x. ((x * K(y,x)) \ y) \ y = (x \ y) \ T(y,x). (x \ (y * K(x,y))) \ y = (x \ y) \ T(y,x). (x \ ((x * y) / x)) \ y = (x \ y) \ T(y,x). T(x,(y * z) \ z) = T(x,T(y \ 1,z)). T(x,T(y \ 1,z)) = T(x,(y * z) \ z). T(x,y \ (z \ y)) = T(x,(z * y) \ y). T(x,(y * z) \ z) = T(x,z \ (y \ z)). T(x,(y * z) \ z) = x * K(x,z \ (y \ z)). x * K(x,y \ (z \ y)) = T(x,(z * y) \ y). K(x,y \ (z \ y)) = K(x,(z * y) \ y). K(x,(y * z) \ z) = K(x,z \ (y \ z)). x * T(x \ T(y,x),z) = T(x * T(x \ y,z),x). x \ T(x * T(x \ y,z),x) = T(x \ T(y,x),z). x \ T(x * T(y,z),x) = T(x \ T(x * y,x),z). x \ T(x * T(y / x,z),x) = T(T(y,x) / x,z). x != y \ T(y * T((y * z) / y,u),w) | x = T(y * T(z,u),w) / y. T(T(x * y,x) / x,z) = T(x * T(y,z),x) / x. T(x * T(y,z),x) / x = T(T(x * y,x) / x,z). (x * y) \ (y * T(T(z * x,z) / z,y)) = L(a(z,T(x,y),z),T(x,y),y). (x * y) \ ((T(z * x,z) / z) * y) = L(a(z,T(x,y),z),T(x,y),y). L(a(x,T(y,z),x),T(y,z),z) = (y * z) \ ((T(x * y,x) / x) * z). (x \ T(x * y,x)) \ (y * K(z,K(x * y,x))) = L(T(K(x * y,x),z) \ 1,K(x * y,x),y). T(x \ a(y,x \ 1,y),y) = y \ T(y * (x \ 1),y). (x * y) \ (x * (y * z)) = L(z,T(y,x),T(x,y)). L(x,y,z) = L(x,T(y,z),T(z,y)). L(x,T(y,z),T(z,y)) = L(x,y,z). L(x,T(y \ 1,z),T(T(z,y),y \ 1)) = L(x,y \ 1,T(z,y)). x != L(y,T(z \ 1,u),w) | x = L(y,T(z,u),w). 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)). x != K(y,z) * (z \ u) | x = T(z,y) \ u. (x \ y) * K(z,T(x,y)) = T(x,z) \ y. (x * y) * R((x * y) \ (y * z),u,w) = y * (R(z / T(x,y),u,w) * T(x,y)). (x * y) * R((x * y) \ y,z,u) = y * (R(1 / T(x,y),z,u) * T(x,y)). x * (R(1 / T(y,x),z,u) * T(y,x)) = (y * x) * R((y * x) \ x,z,u). x * (T(y,x) * R(T(y,x) \ 1,z,u)) = (y * x) * R((y * x) \ x,z,u). x * y != (z * x) * R((z * x) \ x,u,w) | T(z * R(z \ 1,u,w),x) = y. T(x * R(x \ 1,y,z),u) = T(x,u) * R(T(x,u) \ 1,y,z). T(x,y) * R(T(x,y) \ 1,z,u) = T(x * R(x \ 1,z,u),y). T(K(x,y),z) * R(T(K(x,y),z) \ 1,u,w) = T(K(x,y) * R(K(y,x),u,w),z). (x \ T(x * (y \ 1),x)) * R(T(y \ a(x,y \ 1,x),x) \ 1,z,u) = T((y \ a(x,y \ 1,x)) * R((y \ a(x,y \ 1,x)) \ 1,z,u),x). T((x \ a(y,x \ 1,y)) * R((x \ a(y,x \ 1,y)) \ 1,z,u),y) = (y \ T(y * (x \ 1),y)) * R(T(x \ a(y,x \ 1,y),y) \ 1,z,u). T(K(x,y),z) * R(T(K(y,x),z),u,w) = T(K(x,y) * R(K(y,x),u,w),z). K(x,T(y,z)) * R(T(K(y,x),z),u,w) = T(K(x,y) * R(K(y,x),u,w),z). K(x,T(y,z)) * R(K(y,T(x,z)),u,w) = T(K(x,y) * R(K(y,x),u,w),z). T((x \ a(y,x \ 1,y)) * R((x \ a(y,x \ 1,y)) \ 1,z,u),y) = (y \ T(y * (x \ 1),y)) * R((y \ T(y * (x \ 1),y)) \ 1,z,u). x != (y \ z) * R((y \ z) \ 1,u,w) | x = y \ (z * R(z \ y,u,w)). T((x \ a(y,x \ 1,y)) * R((x \ a(y,x \ 1,y)) \ 1,z,u),y) = y \ (T(y * (x \ 1),y) * R(T(y * (x \ 1),y) \ y,z,u)). T((x \ a(y,x \ 1,y)) * R((x \ a(y,x \ 1,y)) \ 1,z,u),y) = y \ T((y * (x \ 1)) * R((y * (x \ 1)) \ y,z,u),y). T((x \ a(y,x \ 1,y)) * R((x \ a(y,x \ 1,y)) \ 1,z,u),y) = y \ T(y * ((x \ 1) * R((x \ 1) \ 1,z,u)),y). T((x \ a(y,x \ 1,y)) * R((x \ a(y,x \ 1,y)) \ 1,z,u),y) = y \ T(y * (x \ R(x,z,u)),y). T(x \ (a(y,x \ 1,y) * R(a(y,x \ 1,y) \ x,z,u)),y) = y \ T(y * (x \ R(x,z,u)),y). T(x,L(T(x,y),z,u)) = x. (x \ L(T(x,y),z,u)) * K(w,x) = T(x,w) \ L(T(x,y),z,u). x = R(x,y,K(z,y \ 1)). R(x,y,K(z,y \ 1)) = x. R(x,1 / y,K(z,y)) = x. R(x,y \ z,K(u,z \ y)) = x. R(x,1 / (y / z),K(u,z \ y)) = x. x != R(y / (1 / (1 / z)),1 / (1 / z),K(u,u \ 1)) | x = (y * K(u,u \ 1)) / z. x / (1 / (1 / y)) = (x * K(y,y \ 1)) / y. (x * K(y,y \ 1)) / y = x / (1 / (1 / y)). x != (y * K(z,z \ 1)) / u | x = (y / u) * K(w,w \ 1). x / (1 / (1 / y)) = (x / y) * K(z,z \ 1). (x / y) * K(z,z \ 1) = x / (1 / (1 / y)). (x / (1 / (1 / y))) * K(z \ 1,z) = x / y. x * (y / z) = (1 / (1 / x)) * (y / (1 / (1 / z))). (1 / (1 / x)) * (y / (1 / (1 / z))) = x * (y / z). T(x,T(y,z)) = T(x,T(y,x \ z)). T(x,T(y,x \ z)) = T(x,T(y,z)). T(x,T(y,x \ 1)) = T(x,y). L(x,T(y,z),T(T(z,y \ 1),y)) = L(x,y,T(z,y \ 1)). L(x,T(y,z),T(T(z,y),y \ 1)) = L(x,y,T(z,y \ 1)). x != L(y,T(z,u),T(T(u,z),z \ 1)) | x = L(y,z \ 1,T(u,z)). L(x,y,T(z,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)). x != L(y,z,T(z * u,z \ 1)) | x = L(y,R(z,u,u),z * u). L(x,y,T(y * z,y)) = L(x,R(y,z,z),y * z). L(x,R(y,z,z),y * z) = L(x,y,T(y * z,y)). x != L(y,z,T(u * w,u)) | x = L(y,z,u / w). L(x,R(y,z,z),y * z) = L(x,y,y / z). x != L(y,z,z / u) | x = L(y,z,u * z). L(x,R(y,z,z),y * z) = L(x,y,z * y). x != L(y,R(z,u,u),z * u) | x = L(y,T(z,u),z * u). L(x,y,z * y) = 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). x != y \ L(y,z,y * z) | x = a(y * z,y,y). a(x * y,y,y) = a(y * x,y,y). x != a((y * z) * z,u,w) | x = a(R(y,z,z),u,w). a(x * (y * x),x,x) = a(R(y,x,x),x,x). x != a(y * (z * y),u,w) | x = a(T(z,y),u,w). a(R(x,y,y),y,y) = a(T(x,y),y,y). x != a(T(y,z),z,z) | x = a(y,z,z). a(R(x,y,y),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). x != a(y,z,z) \ R(y,z,z) | x = y. R(R(x,y,y),R(x,y,y) * y,y) = x. x \ 1 = R(R(x,y,y) \ 1,y,y). 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. ((x \ 1) / y) * (x * x) = (((y * x) \ 1) * x) * x. (((x * y) \ 1) * y) * y = ((y \ 1) / x) * (y * y). x != ((y \ 1) / z) * (y * y) | x = T(y / z,y * y). (((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(y,z,R(T(u,w * w),v5,v6)) | x = L(y,z,R(u,v5,v6)). 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). x / L(x,y,z) = (x / (z * (y * x))) * (z * y). (x / (y * (z * x))) * (y * z) = x / L(x,z,y). x != y / L(y,z,u) | x = L(y,z,u) \ 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) * (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). R(x,y,z) * y = (x * y) * (L(z,y,x) \ z). (x * y) * (L(z,y,x) \ z) = R(x,y,z) * y. (x * y) * (x \ R(x,y,z)) = R(x,y,z) * y. L((x \ R(x,y,z)) \ u,x \ R(x,y,z),x * y) = (R(x,y,z) * y) \ ((x * y) * u). x != L(y,z \ R(z,u,w),z * u) | x = y. (R(x,y,z) * y) \ ((x * y) * u) = (x \ R(x,y,z)) \ u. L(x,y,R(z,y,x)) = (z \ R(z,y,x)) \ x. x != (y \ R(y,z,u)) \ u | x = L(u,z,y). L(x,y,R(z,y,x)) = L(x,y,z). T(x,L(L(x,y,z),u,w)) = x. K(x,L(L(x,y,z),u,w) / v5) = K(x,v5 \ L(L(x,y,z),u,w)). K(x,L(y \ L(y,z,u),y,u * z)) = K(x,a(u,z,y) \ 1). K(x,L(y * ((z * y) \ z),y \ 1,z * y)) = K(x,a(z,y,y \ 1) \ 1). T(x / T(y,z),y) = (y \ x) * K(z,y). (x \ y) * K(z,x) = T(y / T(x,z),x). K(x \ L(x,y,z),x) = 1. T(x,y) * (R(T(x,y),z,u) * (x * (T(x,y) \ w))) = R(T(x,y),z,u) * (x * w). (x * (y * z)) \ ((x * y) * (T(u * L(z,y,x),u) / u)) = L(a(u,L(z,y,x),u),L(z,y,x),x * y). ((x / y) * K(y \ 1,z)) * y = x * (y * T(y \ (x \ x),z)). ((x / y) * K(y \ 1,z)) * y = x * (y * T(y \ 1,z)). ((x / y) * K(y \ 1,z)) * y = x * K(y \ 1,z). x * y != T(z,u) * K(u,z) | z / y = x. x / y = (T(x,y \ 1) / y) * K(y \ 1,x). (T(x,y \ 1) / y) * K(y \ 1,x) = x / y. (T(x,y \ 1) / y) \ (x / y) = K(y \ 1,x). x != (T(y,z) / u) \ (y / u) | x = K(z,(1 / u) \ (y / u)). K(x \ 1,y) = K(x \ 1,(1 / x) \ (y / x)). K(x \ 1,(1 / x) \ (y / x)) = K(x \ 1,y). K(x \ 1,(1 / x) \ y) = K(x \ 1,y * x). x != K(y \ 1,z) | x = K(1 / y,z). K(x \ 1,y * x) = K(1 / x,(1 / x) \ y). K(1 / x,(1 / x) \ y) = K(x \ 1,y * x). x * K(y \ 1,x * y) = (1 / y) * (x / (1 / y)). (1 / x) * (y / (1 / x)) = y * K(x \ 1,y * x). x != (1 / (1 / y)) * (z / (1 / (1 / u))) | x = y * (z / u). x * K((1 / y) \ 1,x * (1 / y)) = y * (x / y). x * K(y,x * (1 / y)) = y * (x / y). x * y != z * (x / z) | y = K(z,z \ x). K(x,y * (1 / x)) = K(x,x \ y). 1 / K(x,x \ y) = K(y * (1 / x),x). K(x \ y,x) = K(y * (1 / x),x). K(x * (1 / y),y) = K(y \ x,y). K(x * y,y \ 1) = K((y \ 1) \ x,y \ 1). K((x \ 1) \ y,x \ 1) = K(y * x,x \ 1). K(x * y,x \ 1) = K(y * x,x \ 1). K(x * y,y \ 1) = K(y * x,y \ 1). K(x,y * K(y * z,y \ 1)) = T(K(x,y),z * y). x != K(y,z * K(u,z \ 1)) | x = T(K(y,z),u). T(K(x,y),z * y) = T(K(x,y),y * z). T(K(x,y),z * y) * K(y,x) = K(K(x,y),y * z). K(x * y,K(y,z)) = K(K(z,y),y * x). K(K(x,y),y * z) = K(z * y,K(y,x)). K(x * y,K(x,z)) = K(y * x,K(x,z)). K(x * y,K(y,z)) = K(y * x,K(y,z)). x != K(y * z,K(y,u)) | x = K(z,K(y,u)). K(x * y,K(y,z)) = K(x,K(y,z)). x != K(y * z,K(z,u)) | x = K(u,K(z,y)). K(x,K(y,z)) = K(z,K(y,x)). K(K(x,y),z) = K(x,K(y,z)). K(x,K(y,z * y)) = K(x,K(y,z)). (K(x,y) * z) * K(y,K(x,z)) = z * K(x,y). K(x,K(y,z)) * z = T(z,K(y,x)). x * K(y,K(z,x)) = T(x,K(z,y)). K(x,K(y,z)) \ 1 = K(z,K(x,y)). K(x,y) * K(x,K(y,z)) = T(K(x,y),z). K(x,K(y,z)) * (K(x,y) * u) = T(K(x,y),z) * u. K(x,K(y,z)) * (K(x,y) * u) = K(x,T(y,z)) * u. K(x,y) * K(x,K(y,z)) != u | T(K(x,y),z) = u. K(x,K(y,z)) != u | K(z,K(y,x)) = u. K(K(x,y),z) = K(K(y,u) * x,K(y,z)). K(K(x,y) * z,K(x,u)) = K(K(z,x),u). K(L(K(x,y),z,u) \ 1,w) = L(K(y,K(x,w)),z,u). x != K(K(y,z),u) | x = K(y,K(z,u)). K(K(x,y) * z,K(x,u)) = K(z,K(x,u)). K(K(x,y),z) = K(y,K(z,x)). x != K(y,K(z,u)) \ 1 | x = K(y,K(u,z)). K(x,K(y,z)) = K(y,K(x,z)). K(x,K(y,z)) = K(y,K(z,x)). K(x,K(y,z)) = K(z,K(x,y)). x != K(y,K(z,u)) | x = K(K(y,z),u). K(x,K(y,z)) = K(K(y,x),z). K(K(x,y),z) = K(y,K(x,z)). K(x,K(y,z)) * y = T(y,K(x,z)). K(x,K(y,z)) * (y * u) != w | T(y,K(x,z)) * u = w. R(K(x,K(y,z)),u,w) = K(y,R(K(x,z),u,w)). K(x,K(y,z)) != u | K(z,K(x,y)) = u. K(x,K(y,z)) = K(x,K(z,y)). x != K(y,K(z,u)) | x = K(K(z,w) * y,K(z,u)). K(x,K(y,z)) = K(K(x,u) * z,K(x,y)). K(K(x,y) * z,K(x,u)) = K(x,K(u,z)). K(x,K(y,z)) = K(K(y,z),x). K(K(x,y),z) = K(z,K(x,y)). K(x,K(y,z)) * z = T(z,K(x,y)). x * (K(y,K(z,x)) * u) = T(x,K(y,z)) * u. x * K(y,K(z,x)) = T(x,K(y,z)). K(x,K(y,z)) * (z * u) != w | T(z,K(x,y)) * u = w. K(x,K(y,((1 / z) / (u / z)) \ 1)) * (u / z) = T(u,K(x,y)) / z. (x \ T(x * y,x)) \ (y * K(x,K(z,x * y))) = L(T(K(x * y,x),z) \ 1,K(x * y,x),y). K(x,K(y,z)) != u | K(x,K(z,y)) = u. K(x,K(y,z)) != u | K(y,K(x,z)) = u. K(x,K(y,z)) * K(x,K(y,z)) = 1. K(x,K(y,z)) * z = T(z,K(y,y * x)). T(x,K(y,y * z)) = K(z,K(y,x)) * x. K(x,T(y,T(z,K(u,x)))) = K(x,T(y,z)). K(x,K(y,z)) * x = T(x,K(z,y)). T(x,K(y,z)) = T(x,K(z,y)). T(x,K(y,z)) != u | T(x,K(z,y)) = u. R(K(x,K(y,z \ 1)),u,w) * x = T(x,K(R(z,u,w) \ 1,y)). x != T(y * z,K(z,u)) | x = z * T(y,T(z,u)). T(x * y,K(z,y)) = y * T(x,T(y,z)). x * T(y,T(x,z)) = T(y * x,K(z,x)). x != T(y,K(z,u)) | x = (K(u,z) * y) * K(z,u). T(x,K(y,z)) = (K(y,z) * x) * K(z,y). (K(x,y) * z) * K(y,x) = T(z,K(x,y)). x != T(y,K(z,u)) | x = K(u,z) * (y * K(z,u)). T(x,K(y,z)) = K(y,z) * (x * K(z,y)). K(x,y) * (z * K(y,x)) = T(z,K(x,y)). x != T(T(y,z),K(z,u)) | x = T(y,T(z,u)). T(T(x,y),K(z,y)) = T(x,T(y,z)). T(T(x,y),K(z,u)) != w | T(T(x,K(u,z)),y) = w. T(K(x,y) * z,T(z,K(y,x))) = T(K(x,y) * z,z). T(x,K(y,z)) * K(y,z) = K(y,z) * x. R(T(x,K(y,z) * K(z,u)),K(y,z),K(z,u)) != w | T(T(x,K(z,u)),K(z,y)) = w. K(x,K(y,z \ y)) = K(x,K(y,z \ 1)). K(x,K(y,z \ 1)) = K(x,K(y,z \ y)). K(x,K(y,y * z)) = K(x,K(y,z)). x != K(y,K(z,u)) | x = K(z,u) * K(u,T(z,y)). K(x,K(y,z)) = K(z,y) * K(y,T(z,x)). K(x,y) * K(y,T(x,z)) = K(z,K(y,x)). K(x,(T(y,z) / u) / (y / u)) = K(x,K(z,((1 / u) / (y / u)) \ 1)). K(x,K(y,((1 / z) / (u / z)) \ 1)) = K(x,(T(u,y) / z) / (u / z)). K(x,K(y,z)) != u | K(y,K(z,x)) = u. x * y != T(x,K(z,u)) * K(z,u) | T(K(z,u),x) = y. T(K(x,y),z) = (z * K(x,y)) / z. (x * K(y,z)) / x = T(K(y,z),x). T(x,T(y,z)) * K(y,z) = K(y,z) * T(x,y). T(T(K(x,y),z),z) = K(x,y). T(K(x,T(y,z)),z) = K(x,y). K(T(x,y),T(z,y)) = K(x,z). x * K(y,z) = K(y,T(z,x)) * x. K(x,T(y,z)) * z = z * K(x,y). T(K(x,y \ z),y) = K(x,z / y). T(K(x,y \ z),z) = K(x,z / y). x * y != y * K(z,y \ u) | x = K(z,u / y). K(x,T(y \ z,y)) = K(x,z / y). x * (y * K(x,z)) = T(x,T(z,y)) * y. T(x,T(y,z)) * z = x * (z * K(x,y)). K(x,y \ z) * z = z * K(x,z / y). T(x,y * K(x,z)) = T(x,y). K(x,y * K(x,z)) = K(x,y). K(x,T(y,z * K(x,u))) = K(x,T(y,z)). K(x * K(y,z),K(y,u)) = K(x,K(y,u)). K(T(x,y),T(T(z,y),u)) = K(x,T(z,u)). K(L(T(x,y),z,u),T(w,y)) = K(L(x,z,u),w). K(T(x,y),L(T(z,y),u,w)) = K(x,L(z,u,w)). K(R(T(x,y),z,u),T(w,y)) = K(R(x,z,u),w). K(T(x,y),R(T(z,y),u,w)) = K(x,R(z,u,w)). K(x \ y,T(z,x)) = K(y / x,z). K(x,y) * T(x,z) = T(T(x,z),T(y,z)). T(T(x,y),T(z,y)) = K(x,z) * T(x,y). x * K(T(x,y),T(z,y)) = T(x,z). K(T(x,y),z) = K(x,z * K(y,z)). K(x,y * K(z,y)) = K(T(x,z),y). R(K(x,y),T(y,z) * u,w) = K(T(x,z),R(T(y,z),u,w)). K(T(x,y),R(T(z,y * u),y,u)) = K(x,(y * u) \ ((y * z) * u)). K(x,y) * (R(T(y,z),u,w) * (K(T(y,z),T(x,z)) * v5)) = R(T(y,z),u,w) * v5. K(x,y) * K(z,y) = T(T(y,z),T(x,z)) \ y. T(T(x,y),T(z,y)) \ x = K(z,x) * K(y,x). L(K(x,T(y,z)),u,K(y,w)) = K(x,T(y,z)). K(x,T(y,z)) * (z * K(y,x)) = z. K(R(K(x,y),z,u) * w,T(x,v5)) = K(w,T(x,v5)). x != K(y,R(z,u,R(z,w,v5))) | x = K(y,z). K(x,R(y,z,R(T(y,u),w,v5))) = K(T(x,u),T(y,u)). K(T(x,y),T(z,y)) = K(x,R(z,u,R(T(z,y),w,v5))). x != K(T(y,z),T(u,z)) | x = K(y,u). K(x,R(y,z,R(T(y,u),w,v5))) = K(x,y). K(T(x,y),T(z,y)) != u | K(x,z) = u. K(x \ y,T(z,x)) != u | K(y / x,z) = u. K(x,T(y,R(T(x,z),u,w))) != v5 | K(x,y) = v5. K(x,T(T(y,z),z)) != u | K(x,y) = u. K(x,y \ R(T(x,z),u,w)) != v5 | K(x,R(T(x,z),u,w) / y) = v5. K(a(x,y,z),T(u,x * (y * z))) = K(((x * y) * z) / (x * (y * z)),u). K(((x * y) * z) / (x * (y * z)),u) = K(a(x,y,z),T(u,x * (y * z))). K(R(x \ R(x,y,z),x,y * z),u) = K(a(x,y,z),T(u,x * (y * z))). K(R(K(x,y) \ R(K(x,y),z,u),K(x,y),z * u),((z * u) \ K(y,x)) \ 1) = K(a(K(x,y),z,u),((z * u) \ K(y,x)) \ 1). K(R(K(x,y) * R(K(y,x),z,u),K(y,x),z * u),((z * u) \ K(x,y)) \ 1) = K(a(K(y,x),z,u),((z * u) \ K(x,y)) \ 1). K(K(x,y) * R(K(y,x),z,u),((z * u) \ K(x,y)) \ 1) = K(a(K(y,x),z,u),((z * u) \ K(x,y)) \ 1). x != K(y,(z \ K(u,w)) \ 1) | x = K(y,K(w,u) * z). K(a(K(x,y),z,u),((z * u) \ K(y,x)) \ 1) = K(K(y,x) * R(K(x,y),z,u),K(x,y) * (z * u)). K(K(x,y) * R(K(y,x),z,u),K(y,x) * (z * u)) = K(a(K(y,x),z,u),((z * u) \ K(x,y)) \ 1). T(x,K(y,x * K(y,z))) = x. K(x,y / (x \ z)) = K(x,y / (z / x)). K(x,y / (z / x)) = K(x,y / (x \ z)). K(x,y) * K(y * T(x,z),x) = x \ R(x,y * K(x,z),x). x \ R(x,y * K(x,z),x) = K(x,y) * K(y * T(x,z),x). x != K(y,z / (u / y)) | x = K(y,(z * y) / u). K(x,y / (x \ z)) = K(x,(y * x) / z). K(x,(y * x) / z) = K(x,y / (x \ z)). x != K(T(y,z),R(T(u,z),w,v5)) | x = K(y,R(u,w,v5)). R(K(x,y),T(y,z) * u,w) = K(x,R(y,u,w)). R(K(x,y),T(y,T(z,u)) * u,w) = K(x,R(y,u * K(y,z),w)). x != R(K(y,z),T(z,u) * w,v5) | x = K(y,R(z,w,v5)). K(x,R(y,z * K(y,u),w)) = K(x,R(y,z,w)). K(x,R(y,z,u)) = K(x,R(y,T(z,y),u)). K(x,R(y,T(z,y),u)) = K(x,R(y,z,u)). K(x,R(y,K(y,z) * u,w)) = K(x,R(y,u,w)). (x * K(y,R(z,u,w))) \ x = K(R(z,K(z,v5) * u,w),y). K(R(x,K(x,y) * z,u),w) = (v5 * K(w,R(x,z,u))) \ v5. K(R(x,K(x,y) * z,u),w) = K(R(x,z,u),w). K(R(x,y,z),u) = K(R(x,K(w,x) * y,z),u). K(R(x,K(y,x) * z,u),w) = K(R(x,z,u),w). K(x,T(y \ z,y)) != u | K(x,z / y) = u. K(x,T(y \ z,z)) = K(x,z / y). x != T(K(y,z),u * y) | x = K(y,T(z,u)). K(x,(y * x) / z) = K(x,T(z \ (y * x),y)). K(x,T(y \ (z * x),z)) = K(x,(z * x) / y). K(x,T(y \ (x * z),z)) = K(x,(x * z) / y). x != K(y,T((y \ z) \ u,w)) | x = K(y,T(z \ (y * u),w)). K(x,y / (x \ z)) = K(x,T(z \ (x * y),y)). K(x,T(y \ (x * z),z)) = K(x,z / (x \ y)). K(x,T(y,z)) = K(x,z / (z / y)). K(x,y / (y / z)) = K(x,T(z,y)). x != K(y,T(z \ (y * u),u)) | x = K(y,(y * u) / z). K(x,y / (x \ z)) = K(x,(x * y) / z). K(x,(x * y) / z) = K(x,y / (x \ z)). x != K(y,(y * z) / u) | x = K(y,(u / z) \ y). K(x,y / (x \ z)) = K(x,(z / y) \ x). K(x,y / z) = K(x,(x \ y) / (x \ z)). K(x,(x \ y) / (x \ z)) = K(x,y / z). x != K(y,z / (y \ u)) | x = K(y,z / (u / y)). K(x,y / z) = K(x,(x \ y) / (z / x)). K(x,(x \ y) / (z / x)) = K(x,y / z). K(x,(x \ y) / z) = K(x,y / (z * x)). x != K(y,z / (y \ u)) | x = K(y,(z * y) / u). K(x,(y / z) \ x) = K(x,(z * x) / y). K(x,(y * x) / z) = K(x,(z / y) \ x). K(x,y / z) = K(x,((x * z) / y) \ x). K(x,((x * y) / z) \ x) = K(x,z / y). R(K(x,(y / (z / u)) \ x),z / u,u) = K(x,z / ((x \ y) * u)). L(K(T(x,y),T(z,y)),u,w) = K(L(x,u / T(x,y),w),z). K(T(x,L(x,y,z) * u),T(w,u)) = K(L(x,u,L(x,y,z)),w). L(K(x,y),z,u) = K(L(x,z / T(x,w),u),y). K(L(x,y / T(x,z),u),w) = L(K(x,w),y,u). K(L(x,y,z),u) = L(K(x,u),y * T(x,w),z). L(K(x,y),z * T(x,u),w) = K(L(x,z,w),y). K(L(x,x \ y,z),u) = L(K(x,u),y,z). K(L(x,y,z),u) = L(K(x,u),x * y,z). L(K(x,y),x * z,u) = K(L(x,z,u),y). K(L(x,T(x,y) \ z,u),w) = L(K(x,w),K(y,x) * z,u). L(K(x,y),K(z,x) * u,w) = K(L(x,T(x,z) \ u,w),y). K(K(R(x,y,z),u) * w,T(x,v5)) = K(w,T(x,v5)). K(L(x,y,z) \ u,x) != w | K(u / L(x,y,z),x) = w. x != K(y,R(z,T(u,z),w)) | x = R(K(y,z),u * z,w). K(x,R(y,z,u)) = R(K(x,y),z * y,u). R(K(x,y),z * y,u) = K(x,R(y,z,u)). K(x,y) * (R(T(y,z),u,w) * (K(y,x) * v5)) = R(T(y,z),u,w) * v5. K(x,K(y,z)) * (z * K(y,x)) = K(y,x) * z. K(x,K(y,z)) * (z / K(x,y)) = K(y,x) * z. K(x,1) * ((y \ R(y,z,u)) / K(x,R(y,w,v5))) = K(R(y,w,v5),x) * (y \ R(y,z,u)). 1 * ((x \ R(x,y,z)) / K(u,R(x,w,v5))) = K(R(x,w,v5),u) * (x \ R(x,y,z)). 1 * ((x \ R(x,y,z)) * K(R(x,u,w),v5)) = K(R(x,u,w),v5) * (x \ R(x,y,z)). 1 * (x \ R(T(x,y),z,u)) = K(R(x,z,u),y) * (x \ R(x,z,u)). K(R(x,y,z),u) * (x \ R(x,y,z)) = 1 * (x \ R(T(x,u),y,z)). K(R(x,y,z),u) * (x \ R(x,y,z)) = x \ R(T(x,u),y,z). K(x,R(y,z,u)) * (y \ R(T(y,x),z,u)) = y \ R(y,z,u). K(x,y) * (x \ R(x,z,R(x,u,w))) = x \ R(T(x,y),z,R(x,u,w)). K(x,y) * (z * x) = T(z * T(x,y),K(x,y)). T(x * T(y,z),K(y,z)) = K(y,z) * (x * y). K(K(x,y) * (z * x),u) != w | K(z * T(x,y),T(u,K(x,y))) = w. K(x * T(R(y,z,u),w),T(T(y,v5),K(R(y,z,u),w))) = K(x * R(y,z,u),T(y,v5)). K(x * R(T(y,z),u,w),T(T(y,v5),K(R(y,u,w),z))) = K(x * R(y,u,w),T(y,v5)). K(x * R(T(y,z),u,w),T(T(y,v5),K(z,R(y,u,w)))) = K(x * R(y,u,w),T(y,v5)). K(L(x,y,z),y) = K(x,L(y,x,z)). x != L(K(y,(z \ u) \ w),w,z) | x = K(y,u \ (z * w)). K(L(x,y,z),(z \ u) \ (x * y)) = K(x,u \ (z * (x * y))). L(K(x,y),T(x,z) * u,w) = K(L(T(x,z),u,w),T(y,z)). x != K(L(T(y,z),u,w),T(v5,z)) | x = K(L(y,u,w),v5). L(K(x,y),T(x,z) * u,w) = K(L(x,u,w),y). L(K(x,y),z,u) = K(L(x,T(x,w) \ z,u),y). K(L(x,T(x,y) \ z,u),w) = L(K(x,w),z,u). x != K(L(y,T(y,z) \ u,w),v5) | x = L(K(y,v5),K(z,y) * u,w). L(K(x,y),z,u) = L(K(x,y),K(w,x) * z,u). L(K(x,y),K(z,x) * u,w) = L(K(x,y),u,w). x != L(y,z * z,u) | x = y. L(K(x,y),K(z,x),u) = K(x,y). L(K(x,y),z * K(u,x),w) = L(K(x,y),z,w). (x * K(y,z)) * R(K(z,u),w,v5) = x * (K(y,z) * R(K(z,u),w,v5)). (x * K(y,z)) * K(z,u) != w | x * (K(y,z) * K(z,u)) = w. L(K(x,y),L(K(z,x),u,w),v5) = K(x,y). (x * L(K(y,z),u,w)) * K(z,v5) = x * (L(K(y,z),u,w) * K(z,v5)). R(x,L(K(y,z),u,w),K(z,v5)) = x. (x * L(K(y,z),u,w)) * K(z,v5) = x * (K(z,v5) * L(K(y,z),u,w)). R(x,K(y,z),K(z,u)) = x. (x * y) \ ((x * (y * K(z,u))) * K(u,w)) = L(K(z,u),y,x) * K(u,w). T(T(x,K(y,z)),K(y,u)) = T(x,K(u,y) * K(y,z)). (x * R(R(x,K(y,z),K(z,u)) \ (x * K(y,z)),w,v5)) * K(z,u) = R(x,K(y,z),K(z,u)) * (R(K(y,z),w,v5) * K(z,u)). T(T(x,K(y,z)),K(z,u)) = T(x,K(y,z) * K(z,u)). T(T(x,K(y,z)),K(y,u)) = T(x,K(y,z) * K(u,y)). T(T(x,K(y,z)),K(z,u)) = T(x,K(z,u) * K(y,z)). T(T(x,K(y,z)),K(y,u)) = T(x,K(y,u) * K(z,y)). T(T(x,K(y,z)),K(y,u)) = x * K(x,K(y,z) * K(u,y)). x * K(x,K(y,z) * K(u,y)) = T(T(x,K(y,z)),K(y,u)). x != T(T(y,K(z,u)),K(z,w)) | x = T(y,K(z,u) * K(w,z)). T(x,K(y,z) * K(u,y)) = T(x,K(y,u) * K(z,y)). T(T(x,K(y,z)),K(y,u)) != w | T(x,K(y,z) * K(u,y)) = w. T(x,K(y,z) * K(u,y)) != w | T(x,K(y,u) * K(z,y)) = w. T(x,K(y,z) * K(u,y)) != x * w | K(x,K(y,u) * K(z,y)) = w. (x * (K(y,z) * L(K(u,y),w,v5))) * K(z,y) = x * L(K(u,y),w,v5). L(K(x,y),z,u) * K(y,x) != w | a(u,z * K(x,y),K(y,x)) = w. a(x,y * K(z,u),K(u,z)) = K(u,z) * L(K(z,u),y,x). K(x,y) * L(K(y,x),z,u) = a(u,z * K(y,x),K(x,y)). K(x,y) * L(K(y,x),z * K(x,y),u) = a(u,z,K(x,y)). K(x,y) * L(K(y,x),z,u) = a(u,z,K(x,y)). a(x,y,K(z,u)) * L(K(z,u),y,x) = K(z,u). x != K(y,z) * L(K(u,y),w,v5) | x = L(K(u,y),w,v5) * K(y,z). a(x,y,K(z,u)) = L(K(u,z),y,x) * K(z,u). L(K(x,y),z,u) * K(y,x) = a(u,z,K(y,x)). x * a(y,z,K(x,u)) = T(x,u) * L(K(u,x),z,y). T(x,y) * L(K(y,x),z,u) = x * a(u,z,K(x,y)). a(x,y,K(z,u)) * w = K(z,u) * (L(K(u,z),y,x) * w). K(x,y) * (L(K(y,x),z,u) * w) = a(u,z,K(x,y)) * w. K(x,y) * K(L(y,z,u),x) = a(u,z * y,K(x,y)). (x / a(y,z,K(u,w))) * K(u,w) = x * L(K(u,w),z,y). (x * a(y,z,K(u,w))) * K(w,u) = x * L(K(w,u),z,y). L(K(x,y),z,u) * a(u,z,K(x,y)) = K(x,y). K(x,L(y,z,u)) * K(y,x) = a(u,z * y,K(y,x)). K(a(x,y,z),u) * a(x * y,z,K(L(z,y,x) \ z,u)) = K(L(z,y,x) \ z,u). x * y != (z * y) * L(y,u,w) | x = z * L(y,u,w). (x * K(y,z)) * a(u,w,K(z,y)) = x * L(K(y,z),w,u). (x * y) * a(z,u,K(y,w)) = (x * T(y,w)) * L(K(w,y),u,z). (x * T(y,z)) * L(K(z,y),u,w) = (x * y) * a(w,u,K(y,z)). x != (y * T(z,u)) * L(K(w,z),v5,v6) | x = y * (T(z,u) * L(K(w,z),v5,v6)). (x * y) * a(z,u,K(y,w)) = x * (T(y,w) * L(K(w,y),u,z)). x * (T(y,z) * L(K(z,y),u,w)) = (x * y) * a(w,u,K(y,z)). x * (y * a(z,u,K(y,w))) = (x * y) * a(z,u,K(y,w)). (x * y) * a(z,u,K(y,w)) = x * (y * a(z,u,K(y,w))). L(a(x,y,K(z,u)),z,w) = a(x,y,K(z,u)). x * (y * a(z,u,K(y,w))) != v5 * a(z,u,K(y,w)) | x * y = v5. x * a(y,z,K(u,w)) != v5 * (u * a(y,z,K(u,w))) | v5 * u = x. a(x,y,a(z,u,K(y,w))) = 1. x * K(y,z) != u * L(K(y,z),w,v5) | x = u * a(v5,w,K(z,y)). x / a(y,z,K(u,w)) = x * a(y,z,K(w,u)). (T(x,x \ y) * a(z,u,K(w,v5))) \ ((x \ y) \ y) = a(z,u,K(v5,w)). x != K(y,z) * (L(K(z,y),u,w) * v5) | x = L(K(z,y),u,w) * (K(y,z) * v5). a(x,y,K(z,u)) * w = L(K(u,z),y,x) * (K(z,u) * w). L(K(x,y),z,u) * (K(y,x) * w) = a(u,z,K(y,x)) * w. K(x,y) * z = a(u,w,K(x,y)) * (L(K(x,y),w,u) * z). a(x,y,K(z,u)) * (L(K(z,u),y,x) * w) = K(z,u) * w. a(x,y,K(z,u)) \ w = L(K(z,u),y,x) * (K(u,z) * w). L(K(x,y),z,u) * (K(y,x) * w) = a(u,z,K(x,y)) \ w. x != L(K(y,z),u,w) * (K(z,y) * v5) | x = a(w,u,K(z,y)) * v5. a(x,y,K(z,u)) \ w = a(x,y,K(u,z)) * w. x / (a(y,z,K(u,w)) * x) = a(y,z,K(w,u)). x != K(y,K(z,u)) * u | x = T(u,K(z,y)). T(x,K(y,y * z)) = T(x,K(y,z)). x != T(y,K(z,u)) | x = T(y,K(u,z)). T(x,K(y,y * z)) = T(x,K(z,y)). T(x,K(y,z)) = T(x,K(y,y \ z)). T(x,K(y,y \ z)) = T(x,K(y,z)). x * R(K(y,z),u,w) = (x * K(y,v5)) * (K(v5,y) * R(K(y,z),u,w)). (x * K(y,z)) * (K(z,y) * R(K(y,u),w,v5)) = x * R(K(y,u),w,v5). x * y != (z * R(K(u,w),v5,v6)) * R(K(w,u),v5,v6) | z / y = x. x / (K(y,z) * R(K(z,u),w,v5)) = (x * R(K(u,z),w,v5)) * K(z,y). (x / (x / y)) * K(L(y,z,u),y \ x) = y * a(u,z * y,K(y \ x,y)). x * (K(y,z) * K(z,z * y)) = (x / R(z,y,z)) * z. x * (y \ L(y,z,y)) = (x / R(y,z,y)) * y. (x / R(y,z,y)) * y = x * (y \ L(y,z,y)). x != (y / (z / u)) * K(w,u \ z) | x = y / T(z / u,T(w,u)). x * a(y,z * x,K(x \ u,x)) = u / T(u / x,T(L(x,z,y),x)). x / T(x / y,T(L(y,z,u),y)) = y * a(u,z * y,K(y \ x,y)). x / T(x / y,L(y,z,u)) = y * a(u,z * y,K(y \ x,y)). x != K(y,(z * y) / u) | x = K(y,(u / z) \ y). K(x,T(y \ (z * x),z)) = K(x,(y / z) \ x). x != K(y,T(z \ (u * y),w)) | x = K(y,T((u \ z) \ y,w)). K(x,(y / z) \ x) = K(x,T((z \ y) \ x,z)). K(x,T((y \ z) \ x,y)) = K(x,(z / y) \ x). K(x,T(y \ x,z)) = K(x,((z * y) / z) \ x). K(x,((y * z) / y) \ x) = K(x,T(z \ x,y)). K(x,(y / (y / z)) \ x) = K(x,T(z \ x,z \ y)). K(x,T(y \ x,y \ z)) = K(x,(z / (z / y)) \ x). x != K(y,T(z,u)) | x = T(K(y,z),u). K(x,T(y,z)) = T(K(x,y),T(z,K(u,x))). T(K(x,y),T(z,K(u,x))) = K(x,T(y,z)). K(x,T(y,z * (u * K(x,w)))) = K(x,T(y,z * u)). K(x,T(y,z * (x * u))) = K(x,T(y,z * (u * x))). K(x,T(y,z * (u * x))) = K(x,T(y,z * (x * u))). K(x,y / (z * (u * K(x,w)))) = K(x,T((z * (u * K(x,w))) \ y,z * u)). K(x,T((y * (z * K(x,u))) \ w,y * z)) = K(x,w / (y * (z * K(x,u)))). x != K(y,T((z * (u * K(y,w))) \ v5,v6)) | x = K(y,T((z * u) \ v5,v6)). K(x,y / (z * (u * K(x,w)))) = K(x,T((z * u) \ y,z * u)). K(x,T((y * z) \ u,y * z)) = K(x,u / (y * (z * K(x,w)))). K(x,y / (z * u)) = K(x,y / (z * (u * K(x,w)))). K(x,y / (z * (u * K(x,w)))) = K(x,y / (z * u)). K(x,y / z) = K(x,y / (K(u,x) * z)). K(x,y / (K(z,x) * u)) = K(x,y / u). K(x,y / (z * x)) = K(x,y / (x * z)). K(x,y / ((z * x) * u)) = K(x,y / ((x * z) * u)). K(x,y / (z * K(u,x))) = K(x,y / z). K(x,y / (((x \ z) * x) * u)) = K(x,y / (z * u)). K(x,y / z) = K(x,y / (z * K(x,u))). K(x,y / (z * K(x,u))) = K(x,y / z). K(x,y / (z * u)) = K(x,y / ((z * K(w,x)) * u)). K(x,y / ((z * K(u,x)) * w)) = K(x,y / (z * w)). K(x,y / (z * u)) = K(x,y / ((K(x,w) * z) * u)). K(x,y / ((K(x,z) * u) * w)) = K(x,y / (u * w)). K(x,y / ((z * u) * w)) = K(x,y / ((z * (K(v5,x) * u)) * w)). K(x,y / ((z * (K(u,x) * w)) * v5)) = K(x,y / ((z * w) * v5)). x != K(y,((z * u) * R(y,z,u)) / ((w * (K(z * u,y) * z)) * u)) | x = K(R(y,K(z * u,y) * z,u),w \ y). K(x,((y * z) * R(x,y,z)) / ((u * y) * z)) = K(R(x,K(y * z,x) * y,z),u \ x). K(R(x,K(y * z,x) * y,z),u \ x) = K(x,((y * z) * R(x,y,z)) / ((u * y) * z)). x != K(y,z / (y * (u * z))) | x = K(y,u \ (y \ 1)). K(x,y / ((z * y) * x)) = K(x,z \ (x \ 1)). x != K(y,z / ((u * w) * y)) | x = K(y,z / ((u * y) * w)). K(x,y / (x * (z * u))) = K(x,y / ((z * x) * u)). K(x,y / ((z * x) * u)) = K(x,y / (x * (z * u))). K(x,(y * z) / (z * x)) = K(x,R(y / x,x,z)). K(x,R(y / x,x,z)) = K(x,(y * z) / (z * x)). x != K(y,R(z / y,u,w)) | x = K(y,R(y \ z,u,w)). K(x,(y * z) / (z * x)) = K(x,R(x \ y,x,z)). K(x,R(x \ y,x,z)) = K(x,(y * z) / (z * x)). x != K(y,z / ((u * y) * w)) | x = K(y,z / ((y * u) * w)). K(x,y / (x * (z * u))) = K(x,y / ((x * z) * u)). K(x,y / ((x * z) * u)) = K(x,y / (x * (z * u))). x * K(x,y / (x * (z * u))) = T(x,y / ((x * z) * u)). K(x,y / (z * x)) = K(x,(z / y) \ (x \ 1)). K(x,(y / z) \ (x \ 1)) = K(x,z / (y * x)). K(x,(y * z) / (z * x)) = K(x,((y \ u) / u) \ (x \ 1)). K(x,((y \ z) / z) \ (x \ 1)) = K(x,(y * u) / (u * x)). x != K(y,((z \ u) / u) \ (y \ 1)) | x = K(y,(z * w) / (w * y)). K(x,y / ((z \ y) * x)) = K(x,(z * u) / (u * x)). K(x,(y * z) / (z * x)) = K(x,u / ((y \ u) * x)). x != K(y,(z * u) / (u * y)) | x = K(y,R(y \ z,y,u)). K(x,y / ((z \ y) * x)) = K(x,R(x \ z,x,u)). K(x,R(x \ y,x,z)) = K(x,u / ((y \ u) * x)). K(x,R(x \ (y / z),x,u)) = K(x,y / (z * x)). K(x,x \ (y / z)) = K(x,y / (z * x)). K(x,y / (z * x)) = K(x,x \ (y / z)). x != K(y,z / (u * y)) | x = K(y,(y \ z) / u). K(x,x \ (y / z)) = K(x,(x \ y) / z). K(x,(x \ y) / z) = K(x,x \ (y / z)). x != K(y,z / (u * y)) | x = K(y,z / (y * u)). K(x,x \ (y / z)) = K(x,y / (x * z)). K(x,y / (x * z)) = K(x,x \ (y / z)). K(x,x \ (y / (z * u))) = K(x,y / ((z * x) * u)). K(x,y / ((z * x) * u)) = K(x,x \ (y / (z * u))). K(x,y / z) = K(x,x \ ((x * y) / z)). K(x,x \ ((x * y) / z)) = K(x,y / z). x != K(y,z / (((y \ u) * y) * w)) | x = K(y,z / (u * w)). K(x,x \ (y / ((x \ z) * u))) = K(x,y / (z * u)). x != K(y,y \ ((y * z) / u)) | x = K(y,z / u). K(x,(x * y) / (z * u)) = K(x,y / ((x \ z) * u)). K(x,y / ((x \ z) * u)) = K(x,((z * u) / y) \ x). x * K(x,x \ (y / (z * u))) = T(x,y / ((x * z) * u)). T(x,x \ (y / (z * u))) = T(x,y / ((x * z) * u)). T(x,y / ((x * z) * u)) = T(x,x \ (y / (z * u))). R(T(x,x \ ((y * (z * u)) / (z * u))),z,u) = R(T(x,R(x,z,u) \ y),z,u). R(T(x,x \ y),z,u) = R(T(x,R(x,z,u) \ y),z,u). R(T(x,R(x,y,z) \ u),y,z) = R(T(x,x \ u),y,z). (R(x,y,z) \ u) \ u = R(T(x,x \ u),y,z). R(T(x,x \ y),z,u) = (R(x,z,u) \ y) \ y. (R(x,y,z) * u) / (R(T(x,x \ w),y,z) * u) = K(R(x,y,z) \ w,R(x,y,z)). x != R(T(y,y \ z),u,w) | x = R((y \ z) \ z,u,w). (R(x,y,z) \ u) \ u = R((x \ u) \ u,y,z). R(T(x,y),z,u) = (R(x,z,u) \ (x * y)) \ (x * y). (R(x,y,z) \ (x * u)) \ (x * u) = R(T(x,u),y,z). R(x \ y,z,u) = (R(y / x,z,u) \ y) \ y. (R(x / y,z,u) \ x) \ x = R(y \ x,z,u). K(x,R(y \ x,z,u) \ w) = K(x,R(x / y,z,u) \ w). K(x,R(x / y,z,u) \ w) = K(x,R(y \ x,z,u) \ w). (R(x,y,z) \ ((R(x,y,z) * u) / R(x,y,z))) \ u = R(((x * K(u,x)) \ u) \ u,y,z). R(((x * K(y,x)) \ y) \ y,z,u) = (R(x,z,u) \ ((R(x,z,u) * y) / R(x,z,u))) \ y. x != (y \ ((y * z) / y)) \ z | x = (y \ z) \ T(z,y). R(((x * K(y,x)) \ y) \ y,z,u) = (R(x,z,u) \ y) \ T(y,R(x,z,u)). R((x \ y) \ T(y,x),z,u) = (R(x,z,u) \ y) \ T(y,R(x,z,u)). (R(x,y,z) \ u) \ T(u,R(x,y,z)) = R((x \ u) \ T(u,x),y,z). R(T(x,K(y,z)),K(z,y),x) \ T(K(z,y) * x,x) = T(K(z,y),T(x,K(y,z))). x != T(K(y,z),T(u,K(w,y))) | x = K(y,T(z,u)). R(T(x,K(y,z)),K(z,y),x) \ T(K(z,y) * x,x) = K(z,T(y,x)). x \ R(x,y * K(x,z),x) = K(x,y) * K(y * x,x). x != K(y,z) * K(z * y,y) | x = y \ R(y,z,y). x \ R(x,y * K(x,z),x) = x \ R(x,y,x). a(x,y * K(x,z),x) = x \ R(x,y,x). a(x,y,T(x,z)) = x \ R(x,y,x). a(x,y,T(x,z)) != u | a(x,y,x) = u. (x * R(x \ (x * K(y,z)),u,w)) * K(z,v5) = R(x,K(y,z),K(z,v5)) * (R(K(y,z),u,w) * K(z,v5)). R(x,K(y,z),K(z,u)) * (R(K(y,z),w,v5) * K(z,u)) = (x * R(x \ (x * K(y,z)),w,v5)) * K(z,u). R(x,K(y,z),K(z,u)) * (R(K(y,z),w,v5) * K(z,u)) = (x * R(K(y,z),w,v5)) * K(z,u). x * (R(K(y,z),u,w) * K(z,v5)) = (x * R(K(y,z),u,w)) * K(z,v5). (x * R(K(y,z),u,w)) * K(z,v5) = x * (R(K(y,z),u,w) * K(z,v5)). (x * R(K(y,z),u,w)) * K(z,v5) = x * (K(z,v5) * R(K(y,z),u,w)). x != (y * R(K(z,u),w,v5)) * K(u,v6) | x = y / (K(v6,u) * R(K(u,z),w,v5)). x * (K(y,z) * R(K(u,y),w,v5)) = x / (K(z,y) * R(K(y,u),w,v5)). x / (K(y,z) * R(K(z,u),w,v5)) = x * (K(z,y) * R(K(u,z),w,v5)). (x * (K(y,z) * R(K(z,u),w,v5))) * (K(z,y) * R(K(u,z),w,v5)) = x. x / a(K(y,z),u,u \ 1) = x * (K(y,z) * R(K(z,y),u,u \ 1)). x * (K(y,z) * R(K(z,y),u,u \ 1)) = x / a(K(y,z),u,u \ 1). K(x,y \ z) = K(x,y \ (z * K(u,x))). K(x,y \ (z * K(u,x))) = K(x,y \ z). x != K(y,z) * T(y,u) | x = K(y,u) * T(y,z). T(T(x,y),T(z,y)) = K(x,y) * T(x,z). K(x,y) * z != T(T(x,y),u) | z = T(x,T(u,y)). T(x,y) = T(x,T(T(y,z),z)). T(x,T(T(y,z),z)) = T(x,y). (T(T(x,y),T(z,y)) * u) / (T(K(x,y),T(x,z)) * u) = R(T(x,z),T(K(x,y),T(x,z)),u). (K(x,y) * T(x,z)) \ x = K(z,x) * K(y,x). (K(x,y) * T(x,K(z,u))) \ x = K(z,K(u,x)) * K(y,x). (K(x,K(y,z)) * T(x,K(u,w))) \ x = K(u,K(w,x)) * K(z,K(x,y)). (K(x,K(y,z)) * T(y,K(u,w))) \ y = K(u,K(w,y)) * K(x,K(y,z)). 1 = K(x,K(y,R(T(x,z),u,w))). K(x,K(y,R(T(x,z),u,w))) = 1. K(x,K(y,(z * u) \ ((z * x) * u))) = 1. K(x,K(y,K(x,z) * u)) = K(x,K(y,u)). K(x,K(y,z)) = K(x,K(y,z * K(u,x))). K(x,K(y,z * K(u,x))) = K(x,K(y,z)). K(x,K(y,z)) * (z * K(u,x)) = T(z * K(u,x),K(x,y)). T(x,K(y,z)) * K(u,y) = T(x * K(u,y),K(y,z)). T(K(x,y) * z,K(x,u)) = K(x,y) * T(z,K(x,u)). K(x,y) * T(z,K(x,u)) = T(K(x,y) * z,K(x,u)). T(x,K(y,z)) = K(y,u) * T(K(y,u) \ x,K(y,z)). K(x,y) * T(K(x,y) \ z,K(x,u)) = T(z,K(x,u)). T(x * K(y,z),K(z,u)) \ T(x,K(z,u)) = K(z,y). K(x,K(y,z)) * T(y,K(x,u)) = T(T(y,K(x,z)),K(x,u)). T(T(x,K(y,z)),K(y,u)) \ x = K(y,K(u,x)) * K(y,K(x,z)). T(T(x,K(y,z)),K(y,u)) \ x = K(x,K(y,u)) * K(y,K(x,z)). T(T(x,K(y,z)),K(y,u)) \ x = K(x,K(y,u)) * K(x,K(y,z)). T(x,K(y,z) * K(z,u)) \ x = K(x,K(z,y)) * K(x,K(z,u)). K(K(x,y) * K(y,z),u) = K(u,K(y,x)) * K(u,K(y,z)). K(x,K(y,z)) * K(x,K(y,u)) = K(K(z,y) * K(y,u),x). K(x,K(y,z)) * K(x,R(K(y,u),w,v5)) = K(K(z,y) * K(y,(w * v5) / ((u \ w) * v5)),x). K(K(x,y) * K(y,(z * u) / ((w \ z) * u)),v5) = K(v5,K(y,x)) * K(v5,R(K(y,w),z,u)). x != K(T(y,L(y,z,u) * w),T(v5,w)) | x = K(L(y,w,L(y,z,u)),v5). K(x,T(y,z)) = K(L(x,z,L(x,u,w)),T(y,L(x,u,w) * z)). K(L(x,y,L(x,z,u)),T(w,L(x,z,u) * y)) = K(x,T(w,y)). x != K(L(y,z,L(y,u,w)),v5) | x = K(y,v5). K(x,T(y,z)) = K(x,T(y,L(x,u,w) * z)). K(x,T(y,L(x,z,u) * w)) = K(x,T(y,w)). K(x,(T(y,z) / u) / (y / u)) * (y / u) = T(y,K(x,z)) / u. ((T(x,K(y,z)) / u) * u) / x = R(K(y,(T(x,z) / u) / (x / u)),x / u,u). R(K(x,(T(y,z) / u) / (y / u)),y / u,u) = ((T(y,K(x,z)) / u) * u) / y. R(K(x,(T(y,z) / u) / (y / u)),y / u,u) = T(y,K(x,z)) / y. x != T(y,z) / y | x = K(y,z). R(K(x,(T(y,z) / u) / (y / u)),y / u,u) = K(y,K(x,z)). x != K(y,K(z,u)) | x = K(z,K(y,u)). R(K(x,(T(y,z) / u) / (y / u)),y / u,u) = K(x,K(y,z)). K(x,y) * (y \ R(T(y,x),z,R(T(y,u),w,v5))) = y \ R(y,z,R(T(y,u),w,v5)). T(x,y) \ R(T(x,y),z,R(T(x,u),w,v5)) = x \ R(x,z,R(T(x,u),w,v5)). T(x,T(y,z)) = T(x,(z * y) / z). T(x,(y * z) / y) = T(x,T(z,y)). T(x,T(y \ z,y)) = T(x,z / y). T(x,T(y,z)) = T(x,y * K(z,y)). T(x,y * K(z,y)) = T(x,T(y,z)). R(T(x,y),T(z,x),R(T(x,y),u,w)) = R(T(x,y),z,R(T(x,y),u,w)). T(x,y / z) * K(z \ y,z) = K(z \ y,z) * T(x,z \ y). T(x,y / z) * K(z \ y,z) = (y / z) \ (x * (z \ y)). x * y != T(z,u / w) * K(w \ u,w) | x \ ((u / w) \ (z * (w \ u))) = y. x \ ((y / z) \ (x * (z \ y))) = K(x,y / z) * K(z \ y,z). x != K(y,z / u) * K(u \ z,u) | x = u \ (z / T(z / u,y)). x \ ((y / z) \ (x * (z \ y))) = z \ (y / T(y / z,x)). K(x,y) * z != K(x,u) * T(x,y) | z = T(x,u). K(x,y) * T(x,K(y,z)) = T(x,T(y,z)). K(x,K(y,z)) * T(x,y) = T(x,T(y,z)). K(x,K(y,z)) * T(z,y) = T(z,T(y,x)). K(x,T(y,T(z,R(x,u,w)))) = K(x,T(y,z)). K(x,T(y,R(x,z,u) \ w)) = K(x,T(y,w / R(x,z,u))). K(x,T(y,z / R(x,u,w))) = K(x,T(y,R(x,u,w) \ z)). x != K(y,T(z,u / R(y,w,v5))) | x = K(y,T(z,u)). K(x,T(y,R(x,z,u) \ w)) = K(x,T(y,w)). K(x,T(y,z)) = K(x,T(y,R(x,u,w) * z)). K(x,T(y,R(x,z,u) * w)) = K(x,T(y,w)). x != K(y,T(z \ u,u)) | x = K(y,u / z). K(x,T(y \ (R(x,z,u) * w),w)) = K(x,(R(x,z,u) * w) / y). x != K(y,T(z \ (R(y,u,w) * v5),v5)) | x = K(T(y,R(y,u,w) * (y \ v5)),(R(y,u,w) \ z) \ v5). K(x,(R(x,y,z) * u) / w) = K(T(x,R(x,y,z) * (x \ u)),(R(x,y,z) \ w) \ u). K(T(x,R(x,y,z) * (x \ u)),(R(x,y,z) \ w) \ u) = K(x,(R(x,y,z) * u) / w). K(x,T((R(x,y,z) \ u) \ w,R(x,y,z) * (x \ w))) = K(x,(R(x,y,z) * w) / u). K(x,K(y,z)) = K(x,K(y,y \ z)). K(x,K(y,y \ z)) = K(x,K(y,z)). (x / y) * T(K(y \ x,y),z) = (y \ x) * K(z,K(y,x)). (x / y) * K(y \ x,T(y,z)) = (y \ x) * K(z,K(y,x)). x != (y / z) * K(z \ y,T(z,u)) | x = T(y / z,T(z,u)). (x \ y) * K(z,K(x,y)) = T(y / x,T(x,z)). (x \ y) * K(x,K(y,z)) = T(y / x,T(x,z)). K(x,K(y,z)) * (y * u) = T(K(x,y),z) * (T(y,x) * u). T(K(x,y),z) * (T(y,x) * u) = K(x,K(y,z)) * (y * u). T(x,K(y,z)) * u = T(K(y,x),z) * (T(x,y) * u). T(K(x,y),z) * (T(y,x) * u) = T(y,K(x,z)) * u. T(K(x,y),z) * T(y,x) = T(y,K(x,z)). K(x,y / z) * T(z \ y,x) = T(z \ y,K(x,y)). x != K(y,z / u) * T(u \ z,y) | x = T(z / u,T(u,y)). T(x \ y,K(z,y)) = T(y / x,T(x,z)). x != T(y / z,T(z,u)) | x = (z \ y) * K(z,K(y,u)). T(x \ y,K(z,y)) = (x \ y) * K(x,K(y,z)). (x \ y) * K(x,K(y,z)) = T(x \ y,K(z,y)). (x \ y) * K(y,K(x,z)) = T(x \ y,K(z,y)). x * y != T(x,K(z,u)) | y = K(z,K(u,x)). K(x,K(y,z)) = K(z,K(x,y \ x)). K(x,K(y,z \ y)) = K(y,K(z,x)). x != K(y,K(z,u)) | x = K(u,K(y,z)). K(x,K(y,z \ y)) = K(x,K(y,z)). x != K(y,K(z,u \ z)) | x = K(y,K(z,u \ 1)). K(x,K(y,z)) = K(x,K(y,z \ 1)). K(x,K(y,z \ 1)) = K(x,K(y,z)). K(x,K(y \ 1,z)) = K(z,K(x,y)). K(x \ 1,K(y,z)) = K(y,K(z,x)). x != K(y,K(z,u)) | x = K(y,K(u,z)). K(x,K(y,z \ 1)) = K(x,K(z,y)). x != K(y,K(z,R(u,w,v5) \ 1)) | x = R(K(y,K(z,u \ 1)),w,v5). K(x,K(y,R(z,u,w))) = R(K(x,K(y,z \ 1)),u,w). R(K(x,K(y,z \ 1)),u,w) = K(x,K(y,R(z,u,w))). R(K(x,K(y,z)),u,w) = K(x,K(y,R(z,u,w))). x != R(K(y,K(z,u)),w,v5) | x = K(y,R(K(z,u),w,v5)). K(x,K(y,R(z,u,w))) = K(x,R(K(y,z),u,w)). K(x,R(K(y,z),u,w)) = K(x,K(y,R(z,u,w))). x * R(K(x,K(y,z)),u,w) = T(x,K(y,R(z,u,w))). R(K(x,K(y,z)),u,w) = K(y,K(z,R(x,u,w))). K(K(x,y) * K(y,(z * u) / ((w \ z) * u)),v5) = K(v5,K(y,x)) * K(v5,K(y,R(w,z,u))). x != K(y,K(z,u)) * K(y,K(z,w)) | x = K(K(u,z) * K(z,w),y). K(K(x,y) * K(y,(z * u) / ((w \ z) * u)),v5) = K(K(x,y) * K(y,R(w,z,u)),v5). K(K(x,y) * R(K(y,z),u,w),v5) = K(K(x,y) * K(y,R(z,u,w)),v5). x != K(K(y,z) * R(K(z,y),u,w),K(z,y) * (u * w)) | x = K(a(K(z,y),u,w),((u * w) \ K(y,z)) \ 1). K(K(x,y) * K(y,R(x,z,u)),K(y,x) * (z * u)) = K(a(K(y,x),z,u),((z * u) \ K(x,y)) \ 1). T(x,R(K(y,z),u,w)) = T(x,K(y,R(z,u,w))). R(K(x,K(y,z)),u,w) * x = T(x,K(R(y,u,w) \ 1,z)). T(x,K(R(y,z,u) \ 1,w)) = R(K(x,K(y,w)),z,u) * x. K(x,K(y,z \ 1)) != u | K(x,K(y,z)) = u. T(x,K(R(y,z,u) \ 1,w)) = K(x,R(K(y,w),z,u)) * x. T(x,K(R(y,z,u) \ 1,w)) = T(x,R(K(y,w),z,u)). K(x \ 1,K(y,z)) = K(K(y,z),x). K(x \ 1,K(y,z)) = K(x,K(y,z)). x * K(y,K(z,x)) = T(x,K(z,y \ 1)). T(x,K(y,z \ 1)) = x * K(z,K(y,x)). x != y * K(z,K(u,y)) | x = T(y,K(z,u)). T(x,K(y,z \ 1)) = T(x,K(z,y)). x != y * K(z,K(u,y)) | x = T(y,K(u,z)). T(x,K(y,z \ 1)) = T(x,K(y,z)). T(x,K(y \ 1,z)) = T(x,K(y,z)). T(x,K(y \ 1,z)) != u | T(x,K(z,y)) = u. T(x,K(y,R(z,u,w))) = T(x,R(K(z,y),u,w)). T(x,R(K(y,z),u,w)) = T(x,K(z,R(y,u,w))). x != T(y,R(K(z,u),w,v5)) | x = T(y,K(z,R(u,w,v5))). T(x,K(y,R(z,u,w))) = T(x,K(z,R(y,u,w))). T(x,K(y,z) * K(R(u,w,v5),y)) = T(T(x,K(y,z)),K(u,R(y,w,v5))). T(T(x,K(y,z)),K(u,R(y,w,v5))) = T(x,K(y,z) * K(R(u,w,v5),y)). T(x,y) = T(T(x,y),K(z,R(x,u,w))). T(T(x,y),K(z,R(x,u,w))) = T(x,y). x != T(T(y,K(z,u)),K(u,w)) | x = T(y,K(z,u) * K(u,w)). T(x,K(y,z) * K(R(z,u,w),y)) = T(x,K(y,z) * K(z,R(y,u,w))). T(x,K(y,R(z,u,w)) * K(z,y)) = T(x,K(y,z) * K(z,R(y,u,w))). T(x,K(y,R(z,u,w)) * K(z,y)) = x * K(x,K(y,z) * K(z,R(y,u,w))). x * K(x,K(y,z) * K(z,R(y,u,w))) = T(x,K(y,R(z,u,w)) * K(z,y)). K(x,K(y,z) * K(z,R(y,u,w))) = K(x,K(y,R(z,u,w)) * K(z,y)). K(x,K(y,R(z,u,w)) * K(z,y)) = K(x,K(y,z) * K(z,R(y,u,w))). K(x * R(T(y,z),u,w),T(y,v5)) = K(x * R(y,u,w),T(y,v5)). T(T(x,y) * K(z * R(x,u,w),T(x,y)),z) = R(T(x,y),z,R(T(x,y),u,w)). T(T(x * K(y * R(x,z,u),x),w),y) = R(T(x,w),y,R(T(x,w),z,u)). x != T(T(y * K(z * R(y,u,w),y),v5),z) | x = R(T(y,v5),z,R(y,u,w)). R(T(x,y),z,R(T(x,y),u,w)) = R(T(x,y),z,R(x,u,w)). K(x,y) * (y \ R(T(y,x),z,R(y,u,w))) = y \ R(y,z,R(T(y,x),u,w)). K(x,(T(y,z) / u) / (y / u)) = K(z,K(x,(u \ 1) / (y / u))). K(x,K(y,(z \ 1) / (u / z))) = K(y,(T(u,x) / z) / (u / z)). K(x,K(y,z / u)) != w | K(x,K(y,u / z)) = w. K(x \ y,R(x,z,u)) = K(R(x,z,u) \ y,R(x,z,u)). K(R(x,y,z) \ u,R(x,y,z)) = K(x \ u,R(x,y,z)). T(R(x,y,z) * K(x \ u,R(x,y,z)),u) = L(R(x,y,z),R(x,y,z) \ u,R(x,y,z)). T(R(x * K(x \ y,x),z,u),y) = L(R(x,z,u),R(x,z,u) \ y,R(x,z,u)). L(R(x,y,z),R(x,y,z) \ u,R(x,y,z)) = R(T(x * K(x \ u,x),u),y,z). R(T(x * K(x \ y,x),y),z,u) = L(R(x,z,u),R(x,z,u) \ y,R(x,z,u)). R(L(x,x \ y,x),z,u) = L(R(x,z,u),R(x,z,u) \ y,R(x,z,u)). L(R(x,y,z),R(x,y,z) \ u,R(x,y,z)) = R(L(x,x \ u,x),y,z). L(R(x,y,z),R(x,y,z) \ u,R(x,y,z)) = L(R(x,y,z),x \ u,x). (L(R(x,y,z),x \ u,x) * u) \ (R(x,y,z) * u) = a(R(x,y,z),R(x,y,z) \ u,T(R(x,y,z),u)). a(R(x,y,z),R(x,y,z) \ u,T(R(x,y,z),u)) = (L(R(x,y,z),x \ u,x) * u) \ (R(x,y,z) * u). x != (L(y,z \ u,z) * u) \ (y * u) | x = a(z,z \ u,T(y,u)). a(R(x,y,z),R(x,y,z) \ u,T(R(x,y,z),u)) = a(x,x \ u,T(R(x,y,z),u)). a(R(x,y,z),R(x,y,z) \ u,T(R(x,y,z),u)) = a(x,x \ u,R(T(x,u),y,z)). (x * y) \ (x * (R(x,z,u) * y)) = R(T(x,R(x,z,u) * y),z,u). R(T(x,R(x,y,z) * u),y,z) = (x * u) \ (x * (R(x,y,z) * u)). x != (y * z) \ (y * (u * z)) | x = L(T(u,z),z,y). R(T(x,R(x,y,z) * u),y,z) = L(T(R(x,y,z),u),u,x). R(T(x,R(x,y,z) * u),y,z) = L(R(T(x,u),y,z),u,x). x != L(R(T(y,z),u,w),z,y) | x = R(T(y,y * z),u,w). R(T(x,R(x,y,z) * u),y,z) = R(T(x,x * u),y,z). R(T(x,x * y),z,u) \ R(x,z,u) = K(R(x,z,u) * y,R(x,z,u)). K(x * y,R(x,z,u)) = K(R(x,z,u) * y,R(x,z,u)). K(R(x,y,z) * u,R(x,y,z)) = K(x * u,R(x,y,z)). K(x * R(y,z,u),R(y,z,u)) = K(y * x,R(y,z,u)). x != K(y * z,R(y,u,w)) | x = K(z * y,R(y,u,w)). K(x * R(y,z,u),R(y,z,u)) = K(x * y,R(y,z,u)). K(L(x,y * z,u),(u \ (u * (x * y))) \ (x * (y * z))) = K(x,L(L(z,y,x),x * y,u)). K(L(x,y * z,u),(x * y) \ (x * (y * z))) = K(x,L(L(z,y,x),x * y,u)). K(L(x,y * z,u),L(z,y,x)) = K(x,L(L(z,y,x),x * y,u)). K(L(x,y * z,u),z) = K(x,L(L(z,y,x),x * y,u)). x != K(y,L(L(z,u,y),w,v5)) | x = K(y,L(z,w,v5)). K(L(x,y * z,u),z) = K(x,L(z,x * y,u)). K(L(x,(x \ y) * z,u),z) = K(x,L(z,y,u)). K(L(x,y,z),u) = K(x,L(u,x * (y / u),z)). K(x,L(y,x * (z / y),u)) = K(L(x,z,u),y). K(L(x,T(y * (x \ z),y),u),R(y,x \ z,y)) = K(x,L(R(y,x \ z,y),z,u)). K(L(x,T(y * (x \ z),y),u),y) = K(x,L(R(y,x \ z,y),z,u)). K(x * K(L(y,z,u),w),y) = K(x,y). K(x,T(y,K(L(x,z,u),w) * v5)) = K(x,T(y,v5)). T(x,y * K(L(x,z,u),w)) = T(x,y). K(L(x,y,z) * u,x) = K(u * L(x,y,z),x). K(x,y) = K((L(y,z,u) \ x) * L(y,z,u),y). K((L(x,y,z) \ u) * L(x,y,z),x) = K(u,x). K(x,T(y,L(x,z,u) * (u * z))) = K(x,T(y,u * (z * x))). x != K(y,T(z,L(y,u,w) * v5)) | x = K(y,T(z,v5)). K(x,T(y,z * (u * x))) = K(x,T(y,z * u)). x != K(y,T(z,u * (w * y))) | x = K(y,T(z,u * (y * w))). K(x,T(y,z * u)) = K(x,T(y,z * (x * u))). K(x,T(y,z * (x * u))) = K(x,T(y,z * u)). K(x,T(y,z * u)) = K(x,T(y,z * (u / x))). K(x,T(y,z * (u / x))) = K(x,T(y,z * u)). K(x,T(y,z * u)) = K(x,T(y,z * (x \ u))). K(x,T(y,z * (x \ u))) = K(x,T(y,z * u)). K(x,y / (z * (x \ u))) = K(x,T((z * (x \ u)) \ y,z * u)). K(x,T((y * (x \ z)) \ u,y * z)) = K(x,u / (y * (x \ z))). x != K(y,T((R(y,z,u) \ w) \ v5,R(y,z,u) * (y \ v5))) | x = K(y,(R(y,z,u) * v5) / w). K(x,T((R(x,y,z) \ u) \ w,R(x,y,z) * w)) = K(x,(R(x,y,z) * w) / u). x != K(y,T(z,R(y,u,w) * v5)) | x = K(y,T(z,v5)). K(x,(R(x,y,z) * u) / w) = K(x,T((R(x,y,z) \ w) \ u,u)). K(x,T((R(x,y,z) \ u) \ w,w)) = K(x,(R(x,y,z) * w) / u). K(x,(R(x,y,z) * u) / w) = K(x,u / (R(x,y,z) \ w)). x != K(y,(R(y,z,u) * w) / v5) | x = K(y,R(y,z,u) / (v5 / w)). K(x,y / (R(x,z,u) \ w)) = K(x,R(x,z,u) / (w / y)). K(x,R(x,y,z) / (u / w)) = K(x,w / (R(x,y,z) \ u)). x != K(y,R(y,z,u) / w) | x = K(y,w \ R(y,z,u)). K(x,y / (R(x,z,u) \ w)) = K(x,(w / y) \ R(x,z,u)). x != K(y,z / (R(y,u,w) \ v5)) | x = K(y,(z * R(y,u,w)) / v5). K(x,(y / z) \ R(x,u,w)) = K(x,(z * R(x,u,w)) / y). K(x,(y * R(x,z,u)) / w) = K(x,(w / y) \ R(x,z,u)). x != K(y,((z * u) * R(y,z,u)) / ((w * z) * u)) | x = K(R(y,K(z * u,y) * z,u),w \ y). K(x,(((y * z) * u) / (z * u)) \ R(x,z,u)) = K(R(x,K(z * u,x) * z,u),y \ x). K(R(x,K(y * z,x) * y,z),u \ x) = K(x,(((u * y) * z) / (y * z)) \ R(x,y,z)). K(R(x,K(y * z,x) * y,z),u \ x) = K(x,R(u,y,z) \ R(x,y,z)). x != K(R(y,K(z,y) * u,w),v5) | x = K(R(y,u,w),v5). K(x,R(y,z,u) \ R(x,z,u)) = K(R(x,z,u),y \ x). T(x,L(x,y,z) * (z * y)) = T(x,z * (y * x)). L(T(x,y),z,u) \ L(x,z,u) = K(y * K(L(x,w,v5),v6),L(x,z,u)). K(x * K(L(y,z,u),w),L(y,v5,v6)) = L(T(y,x),v5,v6) \ L(y,v5,v6). x != T(y,(z * u) / z) | x = T(y,z / (z / u)). T(x,T(y,z)) = T(x,z / (z / y)). T(x,y / (y / z)) = T(x,T(z,y)). (T(T(x,y),T(z,y)) * u) / (K(x,y) * u) = R(T(x,z),T(K(x,y),T(x,z)),u). R(T(x,y),T(K(x,z),T(x,y)),u) = (T(T(x,z),T(y,z)) * u) / (K(x,z) * u). R(T(x,y),K(x,z),u) = (T(T(x,z),T(y,z)) * u) / (K(x,z) * u). (T(T(x,y),T(z,y)) * u) / (K(x,y) * u) = R(T(x,z),K(x,y),u). R(R(T(x,y),K(x,z),u),w,v5) * (K(x,z) * u) = (K(x,z) * u) * R((K(x,z) * u) \ (T(T(x,z),T(y,z)) * u),w,v5). (K(x,y) * z) * R((K(x,y) * z) \ (T(T(x,y),T(u,y)) * z),w,v5) = R(R(T(x,u),K(x,y),z),w,v5) * (K(x,y) * z). (K(x,y) * z) * R((K(x,y) * z) \ (T(T(x,y),T(u,y)) * z),w,v5) = (R(T(x,u),w,v5) * K(x,y)) * z. x != (y * z) * R((y * z) \ (u * z),w,v5) | x = (y * R(y \ u,w,v5)) * z. (R(T(x,y),z,u) * K(x,w)) * v5 = (K(x,w) * R(K(x,w) \ T(T(x,w),T(y,w)),z,u)) * v5. (K(x,y) * R(K(x,y) \ T(T(x,y),T(z,y)),u,w)) * v5 = (R(T(x,z),u,w) * K(x,y)) * v5. (K(x,y) * R(T(T(x,y),T(z,y)) * K(y,x),u,w)) * v5 = (R(T(x,z),u,w) * K(x,y)) * v5. (K(x,y) * R(x * K(T(x,y),T(z,y)),u,w)) * v5 = (R(T(x,z),u,w) * K(x,y)) * v5. (K(x,y) * R(T(x,z),u,w)) * v5 = (R(T(x,z),u,w) * K(x,y)) * v5. (R(T(x,y),z,u) * K(x,w)) * v5 = (K(x,w) * R(T(x,y),z,u)) * v5. x != (R(T(y,z),u,w) * K(y,v5)) * v6 | x = R(T(y,z),u,w) * (K(y,v5) * v6). (K(x,y) * R(T(x,z),u,w)) * v5 = R(T(x,z),u,w) * (K(x,y) * v5). (K(x,y) \ (R(T(x,z),u,w) * (K(x,y) * v5))) / (K(x,y) \ (R(T(x,z),u,w) * v5)) = R(K(x,y),R(T(x,z),u,w),v5). (K(x,y) * (R(T(y,z),u,w) * (K(y,x) * v5))) / (K(y,x) \ (R(T(y,z),u,w) * v5)) = R(K(y,x),R(T(y,z),u,w),v5). (R(T(x,y),z,u) * w) / (K(x,v5) \ (R(T(x,y),z,u) * w)) = R(K(x,v5),R(T(x,y),z,u),w). R(K(x,y),R(T(x,z),u,w),v5) = K(x,y). x != R(K(y,z / u),z,u \ 1) | x = K(y,z * (u \ 1)). K(x,R(T(x,y),z,u) / w) = K(x,R(T(x,y),z,u) * (w \ 1)). K(x,R(T(x,y),z,u) * (w \ 1)) = K(x,R(T(x,y),z,u) / w). x != K(y,R(T(y,z),u,w) / v5) | x = K(y,v5 \ R(T(y,z),u,w)). K(x,R(T(x,y),z,u) * (w \ 1)) = K(x,w \ R(T(x,y),z,u)). x != K(y,R(T(y,z),u,w) * v5) | x = K(y,R(y,u,w) * v5). K(x,y \ R(T(x,z),u,w)) = K(x,R(x,u,w) * (y \ 1)). x != K(y,R(y,z,u) * (w \ 1)) | x = K(y,w \ R(y,z,u)). K(x,y \ R(T(x,z),u,w)) = K(x,y \ R(x,u,w)). K(x,R(T(x,y),z,u) / w) = K(x,w \ R(x,z,u)). K(x,y \ (z * L(K(u,x),w,v5))) = K(x,y \ z). K(x,y \ (z * (u * K(w,x)))) = K(x,y \ (z * u)). K(x,y \ (z * (x \ u))) = K(x,y \ (z * (u / x))). K(x,y \ (z * (u / x))) = K(x,y \ (z * (x \ u))). K(x,y \ (z * u)) = K(x,y \ (z * (K(x,w) * u))). K(x,y \ (z * (K(x,u) * w))) = K(x,y \ (z * w)). K(x,L(L(y,z,K(x,u)),K(x,u) * z,w)) = K(x,(w * (K(x,u) * z)) \ (w * (z * y))). x != K(y,L(L(z,u,K(y,w)),v5,v6)) | x = K(y,L(z,v5,v6)). K(x,(y * (K(x,z) * u)) \ (y * (u * w))) = K(x,L(w,K(x,z) * u,y)). x != K(y,(z * (K(y,u) * w)) \ v5) | x = K(y,(z * w) \ v5). K(x,L(y,K(x,z) * u,w)) = K(x,(w * u) \ (w * (u * y))). K(x,L(y,K(x,z) * u,w)) = K(x,L(y,u,w)). (x \ 1) / (x \ K(x,L(y,z,u))) = K(L(y,K(x,w) * z,u),x). K(L(x,K(y,z) * u,w),y) = (y \ 1) / (y \ K(y,L(x,u,w))). x != (y \ 1) / (y \ K(y,z)) | x = K(z,y). K(L(x,K(y,z) * u,w),y) = K(L(x,u,w),y). K(L(x,y,z),u) = K(L(x,T(y,u),z),u). K(L(x,T(y,z),u),z) = K(L(x,y,u),z). K(x,y) = K(L(x,K(y,z),u),y). K(L(x,K(y,z),u),y) = K(x,y). x != K(L(y,T(z * (y \ u),z),w),z) | x = K(y,L(R(z,y \ u,z),u,w)). K(L(x,y * (x \ z),u),y) = K(x,L(R(y,x \ z,y),z,u)). K(x,L(R(y,x \ z,y),z,u)) = K(L(x,y * (x \ z),u),y). K((x * K(y,z)) \ u,y) = K(K(y,z) \ (x \ u),y). x != K(K(y,z) \ u,y) | x = K(u,y). K((x * K(y,z)) \ u,y) = K(x \ u,y). K(x \ y,z) = K((K(u,z) * x) \ y,z). K((K(x,y) * z) \ u,y) = K(z \ u,y). K((x * (y * z)) \ u,y) = K((x * (z * y)) \ u,y). K((x * (y * z)) \ u,z) = K((x * (z * y)) \ u,z). x != K((K(y,z) * u) \ w,z) | x = K(u \ (K(z,y) * w),z). K(x \ y,z) = K(x \ (K(z,u) * y),z). K(x \ (K(y,z) * u),y) = K(x \ u,y). K(x \ (y \ z),y \ z) = K(x \ (z / y),y \ z). K(x \ (y / z),z \ y) = K(x \ (z \ y),z \ y). K(x \ y,z) = K(x \ ((z \ y) * z),z). K(x \ ((y \ z) * y),y) = K(x \ z,y). K(K(x,y) \ z,x) != u | K(z,x) = u. K(x \ (y * K(z,u)),z) = K(x \ y,z). K(K(x,y) * z,y) != u | K(z,y) = u. K(x * K(y,z),z) != u | K(x,z) = u. R((x \ y) * K(z \ (x \ y),x \ y),u,w) \ R(x \ y,u,w) = K(R(x \ y,u,w),z \ (y / x)). K(R(x \ y,z,u),w \ (x \ y)) = K(R(x \ y,z,u),w \ (y / x)). K(R(x \ y,z,u),w \ (y / x)) = K(R(x \ y,z,u),w \ (x \ y)). K(R(x \ (x * y),z,u),w * K(x,y)) = K(R(x \ (x * y),z,u),R(y / w,w,K(x,y)) \ (x \ (x * y))). K(R(x \ (x * y),z,u),R(y / w,w,K(x,y)) \ (x \ (x * y))) = K(R(x \ (x * y),z,u),w * K(x,y)). K(R(x \ (x * y),z,u),R(y / w,w,K(x,y)) \ (x \ (x * y))) = K(R(y,z,u),w * K(x,y)). x != K(R(y,z,u),w * K(v5,y)) | x = K(R(y,z,u),w). K(R(x \ (x * y),z,u),R(y / w,w,K(x,y)) \ (x \ (x * y))) = K(R(y,z,u),w). K(R(x,y,z),R(x / u,u,K(w,x)) \ (w \ (w * x))) = K(R(x,y,z),u). K(R(x,y,z),R(x / u,u,K(w,x)) \ x) = K(R(x,y,z),u). K(R(x,y,z),R(x / u,u,L(K(w,x),v5,v6)) \ x) = K(R(x,y,z),u). K((x * (y * z)) \ u,y) != w | K((x * z) \ (y \ u),y) = w. K(x \ (y * z),u) = K(x \ (y * T(z,u)),u). K(x \ (y * T(z,u)),u) = K(x \ (y * z),u). K(x \ (y * (z * u)),z) = K(x \ (y * (u * z)),z). K(x \ (y * (z * u)),u) = K(x \ (y * (u * z)),u). K((x * (y * z)) \ (x * ((z * u) * y)),y) = K(L(L(u,z,y),y * z,x),y). x != K(L(L(y,z,u),w,v5),u) | x = K(L(y,w,v5),u). K((x * (y * z)) \ (x * ((z * u) * y)),y) = K(L(u,y * z,x),y). K((x * y) \ (z \ (x * ((y * u) * z))),z) = K(L(u,z * y,x),z). K(a(x,y,T(z,y)),y) = K((x * (z * y)) \ ((x * y) * z),y). K((x * (y * z)) \ ((x * z) * y),z) = K(a(x,z,T(y,z)),z). K(K(a(x,y,T(z,y)),y),u) = K((x * (z * y)) \ ((x * y) * z),K(y,u)). K((x * (y * z)) \ ((x * z) * y),K(z,u)) = K(K(a(x,z,T(y,z)),z),u). x != K(K(y,z),u) | x = K(z,K(u,y)). K((x * (y * z)) \ ((x * z) * y),K(z,u)) = K(z,K(u,a(x,z,T(y,z)))). K(x,K(y,(z * (u * x)) \ ((z * x) * u))) = K(x,K(y,a(z,x,T(u,x)))). K(L(K(x,y),z,u),w) = L(K(x,K(y,w)),z,u). L(K(x,K(y,z)),u,w) = K(L(K(x,y),u,w),z). K(x,K(y,x * K(y,z))) = 1. T(K(x,y),z) * K(K(x,y),z) = 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)). T(K(x,y),z * T(T(z,x),x)) = T(T(K(x,y),z),T(z,x)). K(T(x,y * T(T(y,x),x)),z) = T(T(K(x,z),y),T(y,x)). 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(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,y) = 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)). x != K(y,T(z,u * y)) | x = K(y,T(z,u)). K(x * y,T(z,y)) = K(x * y,T(z,x)). K(x,T(y * z,z)) != u | K(x,T(y * z,y)) = u. K(x * L(y,z,u),y) = K(x * L(y,z,u),T(y,x)). K(x * L(y,z,u),T(y,x)) = K(x * L(y,z,u),y). K(L(x,y,z) * u,T(x,u)) = K(L(x,y,z) * u,x). K(x * R(y,z,u),y) = K(x * R(y,z,u),T(y,x)). K(x * R(y,z,u),T(y,x)) = K(x * R(y,z,u),y). T(x,y) * K(y * L(x,z,u),x) = R(x,y,L(x,z,u)). x * y != T(z,u) * K(u * L(z,w,v5),z) | x \ R(z,u,L(z,w,v5)) = y. x \ R(x,y,L(x,z,u)) = K(x,y) * K(y * L(x,z,u),x). K(x,y) * K(y * L(x,z,u),x) = x \ R(x,y,L(x,z,u)). (x * T(y,z)) \ (x * R(y,z,L(y,u,w))) = L(K(z * L(y,u,w),y),T(y,z),x). T(x,y) * K(y * R(x,z,u),x) = R(x,y,R(x,z,u)). x * y != T(z,u) * K(u * R(z,w,v5),z) | x \ R(z,u,R(z,w,v5)) = y. x \ R(x,y,R(x,z,u)) = K(y * R(x,z,u),x) * K(x,y). K(x * R(y,z,u),y) * K(y,x) = y \ R(y,x,R(y,z,u)). a(x,y,R(x,z,u)) = x \ R(x,y,R(x,z,u)). x \ R(x,y,R(x,z,u)) = a(x,y,R(x,z,u)). x \ R(x,y,R(x,z,u)) != w | a(x,y,R(x,z,u)) = w. x * a(x,y,R(x,z,u)) = R(x,y,R(x,z,u)). a(x,y,R(x,z,u)) \ 1 = R(x,y,R(x,z,u)) \ x. R(x,y,R(x,z,u)) \ x = a(x,y,R(x,z,u)) \ 1. K(x,y) * a(x,z,R(x,u,w)) = x \ R(T(x,y),z,R(x,u,w)). x \ R(T(x,y),z,R(x,u,w)) = K(x,y) * a(x,z,R(x,u,w)). T(x,y) \ R(T(x,y),T(z,x),R(T(x,y),u,w)) = a(T(x,y),z,R(T(x,y),u,w)). T(x,y) \ R(T(x,y),z,R(x,u,w)) = a(x,z,R(x,u,w)). K(x,y) * (K(y,x) * a(y,z,R(y,u,w))) = y \ R(y,z,R(T(y,x),u,w)). ((x \ y) \ y) \ R((x \ y) \ y,z,R(x,u,w)) = a(x,z,R(x,u,w)). T(x,y) * a(x,z,R(x,u,w)) = R(T(x,y),z,R(x,u,w)). a(x,y,R(x,z,u)) * w = R(T(x,v5),y,R(x,z,u)) * (T(x,v5) \ w). R(T(x,y),z,R(x,u,w)) * (T(x,y) \ v5) = a(x,z,R(x,u,w)) * v5. x != K(y,z) * K(u,y) | x = (y * u) \ (u * T(y,z)). x \ R(x,y,L(x,z,u)) = (x * (y * L(x,z,u))) \ ((y * L(x,z,u)) * T(x,y)). (x * (y * L(x,z,u))) \ ((y * L(x,z,u)) * T(x,y)) = x \ R(x,y,L(x,z,u)). (x * (y * L(x,z,u))) \ ((x * y) * L(x,z,u)) = x \ R(x,y,L(x,z,u)). a(x,y,L(x,z,u)) = x \ R(x,y,L(x,z,u)). x \ R(x,y,L(x,z,u)) = a(x,y,L(x,z,u)). x != y \ R(y,z,L(y,u,w)) | x = K(y,z) * K(z * L(y,u,w),y). a(x,y,L(x,z,u)) = K(x,y) * K(y * L(x,z,u),x). K(x,y) * K(y * L(x,z,u),x) = a(x,y,L(x,z,u)). K(x,y) * a(y,x,L(y,z,u)) = K(x * L(y,z,u),y). x != K(y,z) * K(u,y) | x = K(u,y) * K(y,z). a(x,y,L(x,z,u)) = K(y * L(x,z,u),x) * K(x,y). K(x * L(y,z,u),y) * K(y,x) = a(y,x,L(y,z,u)). x \ R(x,y,R(T(x,z),u,w)) = a(x,y,R(x,u,w)). x \ R(x,y,R(T(x,z),u,w)) != v5 | a(T(x,z),y,R(T(x,z),u,w)) = v5. a(T(x,y),z,R(T(x,y),u,w)) = a(x,z,R(x,u,w)). x != L(K(y,z),T(z,u),w) | x = K(y,z). (x * T(y,z)) \ (x * R(y,z,L(y,u,w))) = K(z * L(y,u,w),y). R(T(x,y),T(y,x),R(T(x,y),z,u)) \ T(x,y) = a(x,y,R(T(x,y),z,u)) \ 1. x != ((y \ z) \ z) \ R((y \ z) \ z,K(y,u) * w,R(y,v5,v6)) | x = y \ (z \ ((R(y,w,R(y,v5,v6)) * (y \ z)) * y)). a(x,K(x,y) * z,R(x,u,w)) = x \ (v5 \ ((R(x,z,R(x,u,w)) * (x \ v5)) * x)). a(T(x,y),z,R(x,u,w)) = x \ (v5 \ ((R(x,z,R(x,u,w)) * (x \ v5)) * x)). a(T(x,y),z,R(x,u,w)) = x \ (v5 \ ((x * (x \ v5)) * R(x,z,R(x,u,w)))). a(T(x,y),z,R(x,u,w)) = x \ (v5 \ (v5 * R(x,z,R(x,u,w)))). a(T(x,y),z,R(x,u,w)) = x \ R(x,z,R(x,u,w)). x != y \ R(y,z,R(y,u,w)) | x = a(y,z,R(y,u,w)). a(T(x,y),z,R(x,u,w)) = a(x,z,R(x,u,w)). x != a(T(y,z),T(y,z) \ u,R(y,w,v5)) | x = a(y,y \ u,R(y,w,v5)). a(x,T(x,y) \ z,R(x,u,w)) = a(x,x \ z,R(x,u,w)). R(T(x,y),y,R(T(x,y),z,u)) \ T(x,y) = a(x,y,R(T(x,y),z,u)) \ 1. K(x * L(y,z,u),y) != K(x,y) * w | a(y,x,L(y,z,u)) = w. a(T(x,y),T(z,x),R(T(x,y),u,w)) = a(T(x,y),z,R(T(x,y),u,w)). x != a(T(y,z),T(T(z,y),y),R(T(y,z),u,w)) | x = a(R(y,u,w),z,y). a(T(x,y),T(y,x),R(T(x,y),z,u)) = a(R(x,z,u),y,x). a(x,y,R(T(x,y),z,u)) = a(R(x,z,u),y,x). R(T(x,y),y,R(T(x,y),z,u)) \ T(x,y) = a(R(x,z,u),y,x) \ 1. x != R(y,z,R(y,u,w)) \ y | x = a(y,z,R(y,u,w)) \ 1. a(R(x,y,z),u,x) \ 1 = a(T(x,u),u,R(T(x,u),y,z)) \ 1. a(T(x,y),y,R(T(x,y),z,u)) \ 1 = a(R(x,z,u),y,x) \ 1. a(x,y,R(x,z,u)) \ 1 = a(R(x,z,u),y,x) \ 1. a(R(x,y,z),u,x) \ 1 = a(x,u,R(x,y,z)) \ 1. (a(x,y,R(x,z,u)) \ 1) \ 1 = a(R(x,z,u),y,x). a(x,y,R(x,z,u)) = a(R(x,z,u),y,x). a(R(x,y,z),u,x) = a(x,u,R(x,y,z)). a(R(x,y,z),u,x) != w | a(x,u,R(x,y,z)) = w. x != a(T(y,z),T(y,z) \ z,u) | x = (z * L(u,y \ T(z,y),y)) \ (z * u). a(R(T(x,y),z,u),T(x,y) \ y,T(x,y)) = (y * L(R(T(x,y),z,u),x \ T(y,x),x)) \ (y * R(T(x,y),z,u)). (x * L(R(T(y,x),z,u),y \ T(x,y),y)) \ (x * R(T(y,x),z,u)) = a(R(T(y,x),z,u),T(y,x) \ x,T(y,x)). (x * L(R(T(y,x),z,u),y \ x,y)) \ (x * R(T(y,x),z,u)) = a(R(T(y,x),z,u),T(y,x) \ x,T(y,x)). (L(R(x,y,z),x \ u,x) * u) \ (u * R(T(x,u),y,z)) = a(R(T(x,u),y,z),T(x,u) \ u,T(x,u)). (L(R(x,y,z),x \ u,x) * u) \ (R(x,y,z) * u) = a(R(T(x,u),y,z),T(x,u) \ u,T(x,u)). a(R(T(x,y),z,u),T(x,y) \ y,T(x,y)) = (L(R(x,z,u),x \ y,x) * y) \ (R(x,z,u) * y). a(R(T(x,y),z,u),T(x,y) \ y,T(x,y)) = a(x,x \ y,T(R(x,z,u),y)). a(R(T(x,y),z,u),T(x,y) \ y,T(x,y)) = a(x,x \ y,R(T(x,y),z,u)). a(T(x,y),T(x,y) \ y,R(T(x,y),z,u)) = a(x,x \ y,R(T(x,y),z,u)). x != a(T(y,z),u,R(T(y,z),w,v5)) | x = a(y,u,R(y,w,v5)). a(x,x \ y,R(T(x,y),z,u)) = a(x,T(x,y) \ y,R(x,z,u)). a(x,T(x,y) \ y,R(x,z,u)) = a(x,x \ y,R(T(x,y),z,u)). x != a(y,T(y,z) \ u,R(y,w,v5)) | x = a(y,y \ u,R(y,w,v5)). a(x,x \ y,R(T(x,y),z,u)) = a(x,x \ y,R(x,z,u)). x != a(y,y \ z,R(T(y,z),u,w)) | x = a(R(y,u,w),R(y,u,w) \ z,T(R(y,u,w),z)). a(x,x \ y,R(x,z,u)) = a(R(x,z,u),R(x,z,u) \ y,T(R(x,z,u),y)). a(R(x,y,z),R(x,y,z) \ u,T(R(x,y,z),u)) = a(x,x \ u,R(x,y,z)). a(R(x,y,z),R(x,y,z) \ u,R(x,y,z)) = a(x,x \ u,R(x,y,z)). x != L(T(y,z),u,w) \ L(y,u,w) | x = K(z,L(y,u,w)). K(x * K(L(y,z,u),w),L(y,v5,v6)) = K(x,L(y,v5,v6)). K(K(L(x,y,z),u) * w,L(x,v5,v6)) = K(w,L(x,v5,v6)). K(K(x,y) * z,L(x,u,w)) = K(z,L(x,u,w)). K(x \ y,L(z,u,w)) = K(x \ T(y,z),L(z,u,w)). K(x \ T(y,z),L(z,u,w)) = K(x \ y,L(z,u,w)). K(x \ (y \ z),L(y,u,w)) = K(x \ (z / y),L(y,u,w)). K(x \ (y / z),L(z,u,w)) = K(x \ (z \ y),L(z,u,w)). x != K(y,(z * u) \ u) | x = K(y,u \ (z \ u)). K(x,(y * (z * (u / x))) \ (z * (x \ u))) = K(x,(z * (u / x)) \ (y \ (z * (u / x)))). x != K(y,(z * (u * (w / y))) \ v5) | x = K(y,(z * (u * w)) \ (v5 * y)). K(x,(y * (z / x)) \ (u \ (y * (z / x)))) = K(x,(u * (y * z)) \ ((y * (x \ z)) * x)). x != K(y,z \ (u \ z)) | x = K(y,T(u \ 1,z)). K(x,(y * (z * u)) \ ((z * (x \ u)) * x)) = K(x,T(y \ 1,z * (u / x))). x != K(y,T(z,u * (w / y))) | x = K(y,T(z,u * w)). K(x,(y * (z * u)) \ ((z * (x \ u)) * x)) = K(x,T(y \ 1,z * u)). K(x,y \ ((z * (x \ u)) * x)) = K(x,T((y / (z * u)) \ 1,z * u)). K(x,T((y / (z * u)) \ 1,z * u)) = K(x,y \ ((z * (x \ u)) * x)). x != K(y,T((z / u) \ 1,u)) | x = K(y,(u \ z) \ 1). K(x,y \ ((z * (x \ u)) * x)) = K(x,((z * u) \ y) \ 1). x != K(y,(z \ u) \ 1) | x = K(y,u \ z). K(x,y \ ((z * (x \ u)) * x)) = K(x,y \ (z * u)). x != K(y,z \ (((y \ z) * u) * y)) | x = K(y,u). K(x,y \ ((x \ y) * z)) = K(x,x \ z). x != K(y,z \ ((y \ z) * u)) | x = L(K(y,y \ u),u,y \ z). K(x,x \ y) = L(K(x,x \ y),y,x \ z). L(K(x,x \ y),y,x \ z) = K(x,x \ y). L(K(x,x \ y),y,z) = K(x,x \ y). a(x,y,K(z,z \ y)) = 1. a(x,y,K(z \ y,z)) = 1. L(K(x \ y,x),y,z) = K(x \ y,x). K(x \ (y \ (x * z)),y) = K(y \ z,y). x != K(y \ z,y) | x = K(z / y,y). L(K(x \ y,x),y,z) = K(y / x,x). K(x \ (y \ z),y) = K(y \ (x \ z),y). (x * y) * K(z \ y,z) = x * ((z \ y) * z). R(x,y,K(z \ y,z)) = x. x != R(R(y,z / u,u),z,K(u \ z,u)) | x = R(y,u \ z,u). R(x,y / z,z) = R(x,z \ y,z). R(x,y * z,K(z,y)) = x. x != R(K(y,(z / (u / w)) \ y),u / w,w) | x = K(y,u / ((y \ z) * w)). R(K(x,(y / (z / u)) \ x),u \ z,u) = K(x,z / ((x \ y) * u)). R(K(x,(y / z) / u),z \ y,z) = K(x,y / (u * z)). x != K((y \ z) \ (y \ u),y) | x = K(z \ u,y). K(x \ ((x \ y) \ z),x) = K(y \ z,x). K(L(x,y,z) \ ((x \ (1 / L(x,y,z))) \ u),L(x,y,z)) = K((1 / x) \ u,L(x,y,z)). 1 / (x \ K(y \ z,x)) = T(x,x \ ((x \ y) \ z)). T(x,x \ ((x \ y) \ z)) = 1 / (x \ K(y \ z,x)). L(K(x \ y,x),y,z) != u | K(x \ y,x) = u. K((x * y) \ (z \ ((x * y) * u)),L(z,y,x)) != w | K(L(z,y,x) \ u,L(z,y,x)) = w. x != R(K(y,K(z,u)),w,v5) | x = K(z,K(u,R(y,w,v5))). K(x,R(K(y,z),u,w)) = K(x,K(z,R(y,u,w))). K(x,K(y,R(z,u,w))) * (K(z,y) \ R(T(K(z,y),x),u,w)) = K(z,y) \ R(K(z,y),u,w). K(x,K(y,R(z,u,w))) * (K(z,y) \ R(K(z,T(y,x)),u,w)) = K(z,y) \ R(K(z,y),u,w). K(x,K(y,R(z,u,w))) * (K(y,z) * R(K(z,T(y,x)),u,w)) = K(z,y) \ R(K(z,y),u,w). K(x,y) \ R(K(x,y),z,u) != w * (K(y,x) * R(K(x,T(y,v5)),z,u)) | K(v5,K(y,R(x,z,u))) = w. x * (K(y,z) * R(K(z,T(y,u)),w,v5)) != K(z,y) \ R(K(z,y),w,v5) | K(u,K(y,R(z,w,v5))) = x. (x \ T(x * y,x)) \ (y * K(x,K(z,x * y))) = L(K(x * y,T(x,z)) \ 1,K(x * y,x),y). (x \ T(x * y,x)) \ (y * K(x,K(z,x * y))) = L(K(x,T(x * y,z)) * 1,K(x * y,x),y). (x \ T(x * y,x)) \ (y * K(x,K(z,x * y))) = L(K(x,T(x * y,z)),K(x * y,x),y). x != L(K(y,z),K(u,y),w) | x = K(y,z). (x \ T(x * y,x)) \ (y * K(x,K(z,x * y))) = K(x,T(x * y,z)). K(x,T(y / z,y) \ y) \ (K(x,z) * K(y,K(u,y * K(x,z)))) = K(y,T(y * K(x,z),u)). K(x,T(y / z,y) \ y) \ (K(x,z) * 1) = K(y,T(y * K(x,z),x)). K(x,T(y / z,y) \ y) \ K(x,z) = K(y,T(y * K(x,z),x)). K(T(x / y,x) \ x,z) * K(z,y) = K(x,T(x * K(z,y),z)). K(x,T(y / z,y) \ y) * K(z,x) = K(y,T(y * K(z,x),z)). x != K(y,T(y * K(z,u),z)) | x = K(y,y * K(z,u)). K(x,T(y / z,y) \ y) * K(z,x) = K(y,y * K(z,x)). x != K(y,T(z / u,z) \ z) * K(u,y) | x = K(z * K(y,u),z). K(x,x * K(y,z)) = K(x * K(z,y),x). K(x * K(y,z),x) = K(x,x * K(z,y)). T(T(x * K(x,x * K(y,z)),u),K(z,y)) = R(T(x,u),K(z,y),x). T(T(T(x,x * K(y,z)),u),K(z,y)) = R(T(x,u),K(z,y),x). R(T(x,K(y,z)),K(z,y),x) = T(x,x * K(y,z)). T(x,x * K(y,z)) \ T(K(z,y) * x,x) = K(z,T(y,x)). T(x,x * K((y * z) \ (u * w),w)) \ T(K(w,(y * (w \ z)) \ u) * x,x) = K(w,T((y * (w \ z)) \ u,x)). T(x,x * K((y * z) \ (u * w),w)) \ T(K(w,(y * z) \ (u * w)) * x,x) = K(w,T((y * (w \ z)) \ u,x)). x != T(y,y * K(z,u)) \ T(K(u,z) * y,y) | x = K(u,T(z,y)). K(x,T((y * (x \ z)) \ u,w)) = K(x,T((y * z) \ (u * x),w)). x != K(y,T((z * (y \ u)) \ w,z * u)) | x = K(y,w / (z * (y \ u))). K(x,T((y * z) \ (u * x),y * z)) = K(x,u / (y * (x \ z))). K(x,(y * x) / (z * u)) = K(x,y / (z * (x \ u))). K(x,y / (z * (x \ u))) = K(x,((z * u) / y) \ x). R(K(x,((y * z) / (u / w)) \ x),w \ u,w) = K(x,u / ((y * (x \ z)) * w)). x != R(K(y,(z / (u / w)) \ y),w \ u,w) | x = K(y,u / ((y \ z) * w)). K(x,y / ((z * (x \ u)) * w)) = K(x,y / ((x \ (z * u)) * w)). K(x,y / ((x \ (z * u)) * w)) = K(x,y / ((z * (x \ u)) * w)). x != K(y,z / ((y \ u) * w)) | x = K(y,((u * w) / z) \ y). K(x,y / ((z * (x \ u)) * w)) = K(x,(((z * u) * w) / y) \ x). x != K(y,(z * u) / ((w * (y \ z)) * u)) | x = R(K(y,w \ y),z,u). K(x,(((y * z) * u) / (z * u)) \ x) = R(K(x,y \ x),z,u). K(x,R(y,z,u) \ x) = R(K(x,y \ x),z,u). R(K(x,y \ x),z,u) = K(x,R(y,z,u) \ x). R(K(x,y),z,u) = K(x,R(y \ x,z,u) \ x). K(x,R(y \ x,z,u) \ x) = R(K(x,y),z,u). R(K(x,R(y \ x,z,u) \ x),w,v5) = K(x,R(R(x / y,z,u),w,v5) \ x). R(R(K(x,y),z,u),w,v5) = K(x,R(R(x / y,z,u),w,v5) \ x). K(x,R(R(x / y,z,u),w,v5) \ x) = R(R(K(x,y),z,u),w,v5). K(x,y) * K(x,K(y,z)) = K(x,T(y,z)). K(x,y) * K(x,K(y,z)) = T(K(x,y),z \ 1). T(K(x,y),z) = T(K(x,y),z \ 1). T(K(x,y),z \ 1) = T(K(x,y),z). x * (y * z) = (x * (z * y)) * K(y,z). (x * (y * z)) * K(z,y) = x * (z * y). K(x,L(y,x,z)) = K(x,y). K(x,y) * (z * (y * x)) = T(z * (x * y),K(x,y)). x * y != K(z,u) * (w * (u * z)) | x \ T(w * (z * u),K(z,u)) = y. (x * y) \ T(z * (x * y),K(x,y)) = T(z,y * x). x != K(y,L(z,u / z,w)) | x = L(K(y,z),u,w). K(x,L(y,z / T(y,u),w)) = L(K(T(x,u),T(y,u)),z,w). L(K(T(x,y),T(z,y)),u,w) = K(x,L(z,u / T(z,y),w)). L(K(x,y),z,u) = K(x,L(y,z / T(y,w),u)). K(x,L(y,z / T(y,u),w)) = L(K(x,y),z,w). K(x,L(y,z,u)) = L(K(x,y),y * z,u). L(K(x,y),y * z,u) = K(x,L(y,z,u)). L(K(x,y),T(y,z) * u,w) = K(x,L(y,K(y,z) * u,w)). K(L(x,y * K(x,z),u),w) = K(L(x,y,u),w). T(x * K(L(y,z,u),w),K(w,v5)) \ T(x,K(w,v5)) = K(w,L(y,z * K(y,v6),u)). K(x,L(y,z * K(y,u),w)) = T(v5 * K(L(y,z,w),x),K(x,v6)) \ T(v5,K(x,v6)). x != T(y * K(z,u),K(u,w)) \ T(y,K(u,w)) | x = K(u,z). K(x,L(y,z * K(y,u),w)) = K(x,L(y,z,w)). K(x,L(y,K(y,z) * u,w)) = K(x,L(y,u,w)). x != K(y,L(z,K(z,u) * w,v5)) | x = L(K(y,z),T(z,u) * w,v5). K(x,L(y,z,u)) = L(K(x,y),T(y,w) * z,u). L(K(x,y),T(y,z) * u,w) = K(x,L(y,u,w)). L(K(x,L(y,x,z)),T(y,u) * w,v5) = K(L(x,y,z),L(y,w,v5)). L(K(x,y),T(y,z) * u,w) = K(L(x,y,v5),L(y,u,w)). x != L(K(y,z),T(z,u) * w,v5) | x = K(y,L(z,w,v5)). K(L(x,y,z),L(y,u,w)) = K(x,L(y,u,w)). x != K(L(y \ z,y,u),L(y,w,v5)) | x = K(u \ (y \ (u * z)),L(y,w,v5)). K(x \ y,L(x,z,u)) = K(w \ (x \ (w * y)),L(x,z,u)). K(x \ (y \ (x * z)),L(y,u,w)) = K(y \ z,L(y,u,w)). K((x * (y \ z)) / x,L(x,u,w)) = K(((y / x) \ z) / x,L(x,u,w)). K(((x / y) \ z) / y,L(y,u,w)) = K((y * (x \ z)) / y,L(y,u,w)). K(L(x,y,z) \ u,L(x,y,z)) = K(x \ u,L(x,y,z)). x != K(L(y,z,u) \ ((y \ (1 / L(y,z,u))) \ w),L(y,z,u)) | x = K((1 / y) \ w,L(y,z,u)). K(x \ ((x \ (1 / L(x,y,z))) \ u),L(x,y,z)) = K((1 / x) \ u,L(x,y,z)). x != K(y / z,L(z,u,w)) | x = K(z \ y,L(z,u,w)). K(((x / y) \ z) / y,L(y,u,w)) = K(y \ (y * (x \ z)),L(y,u,w)). x != K(y \ (y * z),u) | x = K(z,u). K(((x / y) \ z) / y,L(y,u,w)) = K(x \ z,L(y,u,w)). K(x \ y,L(z,u,w)) = K(z \ ((x / z) \ y),L(z,u,w)). K(x \ ((y / x) \ z),L(x,u,w)) = K(y \ z,L(x,u,w)). K(x \ ((x \ y) \ z),L(x,u,w)) = K(y \ z,L(x,u,w)). x != K(y \ ((y \ (1 / L(y,z,u))) \ w),L(y,z,u)) | x = K((1 / y) \ w,L(y,z,u)). K((1 / L(x,y,z)) \ u,L(x,y,z)) = K((1 / x) \ u,L(x,y,z)). K(L(x,y,z) * u,L(x,y,z)) = K((1 / x) \ u,L(x,y,z)). K(x * L(y,z,u),L(y,z,u)) = K((1 / y) \ x,L(y,z,u)). x != K((y / z) \ u,L(z,w,v5)) | x = K(y \ (u * z),L(z,w,v5)). K(x * L(y,z,u),L(y,z,u)) = K(1 \ (x * y),L(y,z,u)). K(x * L(y,z,u),L(y,z,u)) = K(x * y,L(y,z,u)). T(L(x,y,z) * K(u * x,L(x,y,z)),u) = R(L(x,y,z),u,L(x,y,z)). T(L(x * K(y * x,x),z,u),y) = R(L(x,z,u),y,L(x,z,u)). T(L(x * K(x * y,x),z,u),y) = R(L(x,z,u),y,L(x,z,u)). R(L(x,y,z),u,L(x,y,z)) = L(T(x * K(x * u,x),u),y,z). R(L(x,y,z),u,L(x,y,z)) = L(R(x,u,x),y,z). (x * y) * L(R(z,u,z),y,x) = x * (y * R(z,u,L(z,y,x))). K(x,L(R(y,z,y),u,w)) != v5 | K(x,L(y,u,w)) = v5. x * R(y,z,y) = x * R(y,z,L(y,x,u)). x * R(y,z,L(y,x,u)) = x * R(y,z,y). R(x,y,x) = R(x,y,L(x,z,u)). R(x,y,L(x,z,u)) = R(x,y,x). x != R(y,z,y) | x = T(y * K(z * y,y),z). R(x,y,L(x,z,u)) = T(x * K(y * x,x),y). T(x * K(y * x,x),y) = R(x,y,L(x,z,u)). (x * T(y,z)) \ (x * R(y,z,y)) = K(z * L(y,u,w),y). K(x * L(y,z,u),y) = (w * T(y,x)) \ (w * R(y,x,y)). K(L(x,y * (x \ z),u),y) != w | K(x,L(y,z,u)) = w. T(R(x,y,z) * K(u * x,R(x,y,z)),u) = R(R(x,y,z),u,L(R(x,y,z),w,v5)). T(R(x * K(y * x,x),z,u),y) = R(R(x,z,u),y,L(R(x,z,u),w,v5)). T(R(x * K(x * y,x),z,u),y) = R(R(x,z,u),y,L(R(x,z,u),w,v5)). R(R(x,y,z),u,L(R(x,y,z),w,v5)) = R(T(x * K(x * u,x),u),y,z). R(T(x * K(x * y,x),y),z,u) = R(R(x,z,u),y,L(R(x,z,u),w,v5)). R(R(x,y,x),z,u) = R(R(x,z,u),y,L(R(x,z,u),w,v5)). R(R(x,y,z),u,L(R(x,y,z),w,v5)) = R(R(x,u,x),y,z). x != R(y,z,L(y,u,w)) | x = R(y,z,y). R(R(x,y,x),z,u) = R(R(x,z,u),y,R(x,z,u)). R(R(x,y,z),u,R(x,y,z)) = R(R(x,u,x),y,z). R(R(x,y,x),z,u) * (z * u) = (R(x,y,R(x,z,u)) * z) * u. (R(x,y,R(x,z,u)) * z) * u = R(R(x,y,x),z,u) * (z * u). (R(x,y,R(x,z,u)) * z) * u = (R(x,y,x) * z) * u. ((R(x,y,x) * z) * u) / ((x * z) * u) = a(R(x,z,u),y,R(x,z,u)). (R(T(x,y),z,R(x,u,w)) * u) * w = (R(T(x,y),z,T(x,y)) * u) * w. (R(T(x,y),z,T(x,y)) * u) * w = (R(T(x,y),z,R(x,u,w)) * u) * w. x != ((R(y,z,y) * u) * w) / ((y * u) * w) | x = R(a(y,z,y),y * u,w). a(R(x,y,z),u,R(x,y,z)) = R(a(x,u,x),x * y,z). R(a(x,y,x),x * z,u) = a(R(x,z,u),y,R(x,z,u)). x != (y * T(z,u)) \ (y * R(z,u,z)) | x = K(z * u,z). K(x * L(y,z,u),y) = K(y * x,y). x != K(y * z,y) | x = K(z,y) * a(y,z,y). K(x * L(y,z,u),y) = K(x,y) * a(y,x,y). x != K((L(y,z,u) \ w) * L(y,z,u),y) | x = K(w,y). K(x * (L(x,y,z) \ u),x) = K(u,x). x != K((y \ 1) * z,u) | x = K(y \ z,u). K(x * (y \ 1),x) = K(y \ L(x,z,u),x). K(x \ L(y,z,u),y) = K(y * (x \ 1),y). K(x \ (y * z),z) = K(z * (x \ y),z). K(x * R(y,z,y),y) = K(y * x,y). x != K(y \ (z * u),u) | x = K((z \ y) \ u,u). K(x * (y \ z),x) = K((z \ y) \ x,x). K((x \ y) \ z,z) = K(z * (y \ x),z). x != K(y \ ((z \ u) * z),z) | x = K(y \ u,z). K(x * (y \ (x \ z)),x) = K(y \ z,x). x != K((y * z) \ (u * z),z) | x = K(y \ u,z). K(x * ((y * x) \ z),x) = K(y \ z,x). x != K(y * (L(y,z,u) \ w),y) | x = K(w,y). K(L(x,y,z) \ u,x) = K(x \ u,x). K(x / L(y,z,u),y) = K(y \ x,y). x != K(y * (z \ 1),y) | x = K(z \ y,y). K(x \ L(y,z,u),y) = K(x \ y,y). x != K((y \ z) \ L(u,w,v5),u) | x = K(z \ (y * L(u,w,v5)),u). K((x \ y) \ z,z) = K(y \ (x * L(z,u,w)),z). K(x \ (y * L(z,u,w)),z) = K((y \ x) \ z,z). (L(x,y,z) * K((u \ x) \ x,x)) * u = (x \ (L(x,y,z) * u)) * x. (L(x,y,z) * K(u,x)) * u = (x \ (L(x,y,z) * u)) * x. (x \ (L(x,y,z) * u)) * x = (L(x,y,z) * K(u,x)) * u. x != (y * K(z,u)) * z | x = y * T(z,u). (x \ (L(x,y,z) * u)) * x = L(x,y,z) * T(u,x). (L(x,y,z) * (x \ u)) * x = L(x,y,z) * T(u,x). (x / y) \ (L(y,z,u) * (y \ x)) = x \ (L(y,z,u) * T(x,y)). x != y \ (z * T(y,u)) | x = T(z * K(y,u),y). (x / y) \ (L(y,z,u) * (y \ x)) = T(L(y,z,u) * K(x,y),x). x != K((y \ z) \ u,u) | x = K(u * (z \ y),u). K(x \ (y * L(z,u,w)),z) = K(z * (x \ y),z). K(x \ (y * (z * u)),u) = K(u * (x \ (y * z)),u). K(x \ (y \ (z * (u * y))),y) = K(y * ((x * y) \ (z * u)),y). x != K(y * ((z * y) \ u),y) | x = K(z \ u,y). K(x \ (y \ (z * (u * y))),y) = K(x \ (z * u),y). x != K((y * z) \ (u \ (y * ((z * w) * u))),u) | x = K(L(w,u * z,y),u). K((x * y) \ (x * (y * z)),u) = K(L(z,u * y,x),u). K(L(x,y * z,u),y) = K((u * z) \ (u * (z * x)),y). K(L(x,y * z,u),y) = K(L(x,z,u),y). K(x,L(y,z,u)) = K(L(x,x \ z,u),y). K(L(x,x \ y,z),u) = K(x,L(u,y,z)). x != K(L(y,y \ z,u),w) | x = L(K(y,w),z,u). K(x,L(y,z,u)) = L(K(x,y),z,u). L(K(x,y),z,u) = K(x,L(y,z,u)). L(K(x,y),K(y,z),u) = K(x,y). L(K(x,T(y,z)),z,L(y,u,w)) = K(x,T(y,L(y,u,w) * z)). L(K(x,K(y,z)),u,w) = K(x,L(K(z,y),u,w)). K(x,L(y,z,u)) * K(y,x) = a(u,z,K(y,x)). K(x,L(y,z,u)) * a(u,z,K(x,y)) = K(x,y). a(x,y,K(z,u)) * K(z,L(u,y,x)) = K(z,u). K(L(x,y,z),u) * a(z,y,K(x,u)) = K(x,u). x != K(y,L(z,u,w)) * K(z,y) | x = a(w,u * z,K(z,y)). a(x,y,K(z,u)) = a(x,y * z,K(z,u)). a(x,y * z,K(z,u)) = a(x,y,K(z,u)). x * a(y,z,K(u,w)) != K(u,w) | K(L(u,z,y),w) = x. x != a(y,z,K(u,z)) | x = 1. a(x,y,K(z,y * z)) = 1. (x * K(y,z)) * K(u,y) = x * (K(y,z) * K(u,y)). (x * K(y,z)) * K(u,y) != w | x * (K(y,z) * K(u,y)) = w. x != (y * K(z,u)) * K(w,z) | x = (y * K(w,z)) * K(z,u). x * (K(y,z) * K(u,y)) = (x * K(u,y)) * K(y,z). (x * K(y,z)) * K(z,u) = x * (K(z,u) * K(y,z)). ((x \ y) * ((K(z,u) \ 1) \ 1)) * K(w,z) = ((1 / (1 / x)) \ y) * (K(z,u) * K(w,z)). (x * (K(y,z) * K(u,y))) * K(z,y) = x * K(u,y). K(x,y) * z != u * (K(x,y) * K(w,x)) | T(u * K(w,x),K(x,y)) = z. T(L(x,K(y,z),K(z,u)) * K(y,z),K(z,u)) = K(y,z) * T(x,K(z,u) * K(y,z)). x != (y * K(z * L(u,w,v5),u)) * K(u,z) | x = (y / (u * K(z,u))) * R(u * K(z,u),z,L(u,w,v5)). x * (K(y,z) * K(z * L(y,u,w),y)) = (x / (y * K(z,y))) * R(y * K(z,y),z,L(y,u,w)). (x / (y * K(z,y))) * R(y * K(z,y),z,L(y,u,w)) = x * (K(y,z) * K(z * L(y,u,w),y)). (x / T(y,z)) * K(y,u) = (x / y) * (K(y,u) * K(z,y)). (x / y) * (K(y,z) * K(u,y)) = (x / T(y,u)) * K(y,z). x != (y / T(z,z * u)) * K(z,u) | x = y / L(z,u,z). (x / y) * (K(y,z) * K(y * z,y)) = x / L(y,z,y). (x / y) * a(y,z,y) = x / L(y,z,y). x * a(y,z,y) = (x * y) / L(y,z,y). (x * y) / L(y,z,y) = x * a(y,z,y). (x / L(y,z,y)) * y = x * a(y,z,y). x != (y / L(z,u,z)) * z | x = z * (L(z,u,z) \ y). x * a(y,z,y) = y * (L(y,z,y) \ x). x * (L(x,y,x) \ z) = z * a(x,y,x). R(x,y,x) * (x \ z) = z * a(x,y,x). x * y != 1 * z | x \ z = y. x \ a(x,y,x) = L(x,y,x) \ 1. L(x,y,x) \ 1 = x \ a(x,y,x). x != y * (L(y,z,y) \ u) | x = T(y,w) * (L(T(y,w),z,y) \ u). x * a(y,z,y) = T(y,u) * (L(T(y,u),z,y) \ x). T(x,y) * (L(T(x,y),z,x) \ u) = u * a(x,z,x). x != y * (L(y,z,u) \ w) | x = L(y,z,u) \ (y * w). x * a(y,z,y) = L(y,z,y) \ (y * x). L(x,y,x) \ (x * z) = z * a(x,y,x). K(x,y) * (z * a(x,u,x)) = T(x,y) * (L(x,u,x) \ z). T(x,y) * (L(x,z,x) \ u) = K(x,y) * (u * a(x,z,x)). T(x,y) * (L(T(x,y),z,x) \ u) = u * a(T(x,y),z,T(x,y)). K(x,y) * (z * a(y,u,y)) = y * (L(T(y,x),u,y) \ z). x != T(y,y * z) * (L(y,z,y) \ u) | x = K(y,z) * u. K(x,x * y) * (z * a(x,y,x)) = K(x,y) * z. a(x,y,x) * z = z * a(x,y,x). x * y != x * a(z,u,z) | T(a(z,u,z),x) = y. T(a(x,y,x),z) = a(x,y,x). x * ((y \ 1) \ 1) != ((y \ 1) \ 1) * z | x = z * K(y,z). a(x,y,x) = a(x,y,x) * K(z,a(x,y,x)). a(x,y,x) * K(z,a(x,y,x)) = a(x,y,x). a(x,y,x) * z != z * u | a(x,y,x) = u. (x * y) \ ((x * a(z,u,z)) * y) = R(T(a(z,u,z),x * y),x,y). 1 = K(x,a(y,z,y)). K(x,a(y,z,y)) = 1. L(a(x,y,x),z,u) = (u * (z * a(x,y,x))) / (u * z). (x * (y * a(z,u,z))) / (x * y) = L(a(z,u,z),y,x). x != R(y,z,y) * (y \ u) | x = (u / y) * R(y,z,y). x * a(y,z,y) = (x / y) * R(y,z,y). (x / y) * R(y,z,y) = x * a(y,z,y). x * R(y,z,y) = (x * y) * a(y,z,y). (x * y) * a(y,z,y) = x * R(y,z,y). (x / y) * ((y \ z) \ T(z,y)) = x * a(y,y \ z,y). K(x,y) * ((z / y) * R(y,u,y)) = y * (L(T(y,x),u,y) \ z). x != K(y,z) * ((u / z) * R(z,w,z)) | x = R(z,w,z) * (T(z,y) \ u). x * (L(T(x,y),z,x) \ u) = R(x,z,x) * (T(x,y) \ u). R(x,y,x) * (T(x,z) \ u) = x * (L(T(x,z),y,x) \ u). K(x,y) * (x * (L(T(x,z),u,x) \ w)) = R(T(x,y),u,x) * (T(x,z) \ w). T(x,y) * (L(T(x,z),u,x) \ w) = R(T(x,y),u,x) * (T(x,z) \ w). R(T(x,y),z,x) * (T(x,u) \ w) = T(x,y) * (L(T(x,u),z,x) \ w). x * y != T(z,u) * (L(T(z,u),w,z) \ x) | y = a(z,w,z). T(x,y) \ R(T(x,y),z,x) = a(x,z,x). a(T(x,y),z,T(x,y)) = a(x,z,x). K(L(x,y,z),u) = K(x,L(u,y,z)). K(x,K(y,L(z,u,w))) = K(z,K(x,L(y,u,w))). (x / R(y,z,u)) * R((y \ w) \ T(w,y),z,u) = x * a(R(y,z,u),R(y,z,u) \ w,R(y,z,u)). (x / R(y,z,u)) * R(R(y,w,y),z,u) = x * a(R(y,z,u),R(y,z,u) \ (w * y),R(y,z,u)). x * a(R(y,z,u),R(y,z,u) \ (w * y),R(y,z,u)) = (x / R(y,z,u)) * R(R(y,w,y),z,u). x * a(y,y \ (z * y),R(y,u,w)) = (x / R(y,u,w)) * R(R(y,z,y),u,w). (x / R(y,z,u)) * R(R(y,w,y),z,u) = x * a(y,y \ (w * y),R(y,z,u)). (x / R(y,z,u)) * R(R(y,w,y),z,u) = x * a(y,T(w,y),R(y,z,u)). (x / R(y,z,u)) * R(R(y,w,y),z,u) = x * a(y,w,R(y,z,u)). T(x * K(y,z),K(z,u)) = K(y,z) * T(x,K(z,u) * K(y,z)). K(x,y) * T(z,K(y,u) * K(x,y)) = T(z * K(x,y),K(y,u)). K(x,y) * T(z,K(x,y) * K(y,u)) = T(z * K(x,y),K(y,u)). T((K(x,y) \ z) * K(x,y),K(y,u)) \ z = K(K(x,y) * K(y,u),K(x,y) \ z). T(T(x,K(y,z)),K(z,u)) \ x = K(K(y,z) * K(z,u),K(y,z) \ x). K(K(x,y) * K(y,z),K(x,y) \ u) = T(T(u,K(x,y)),K(y,z)) \ u. K(K(x,y) * K(y,z),K(x,y) \ u) = T(u,K(y,z) * K(x,y)) \ u. x != T(y,z) \ y | x = K(z,y). K(K(x,y) * K(y,z),K(x,y) \ u) = K(K(y,z) * K(x,y),u). K(K(x,y) * K(y,z),K(y,x) * u) = K(K(y,z) * K(x,y),u). (x / (y * K(z,y))) * R(y * K(z,y),z,L(y,u,w)) = x * a(y,z,L(y,u,w)). ((x / y) * K(y,z)) * R(y * K(z,y),z,L(y,u,w)) = x * a(y,z,L(y,u,w)). ((x / y) * K(y,z)) * (y * K(z * L(y,u,w),y)) = x * a(y,z,L(y,u,w)). x != (y * K(z,u)) * (z * K(w,z)) | x = y * (T(z,u) * K(w,z)). x * a(y,z,L(y,u,w)) = (x / y) * (T(y,z) * K(z * L(y,u,w),y)). (x / y) * (T(y,z) * K(z * L(y,u,w),y)) = x * a(y,z,L(y,u,w)). (x / y) * R(y,z,L(y,u,w)) = x * a(y,z,L(y,u,w)). (x / R(y,z,u)) * R(R(y,w,y),z,u) = x * a(R(y,z,u),w,L(R(y,z,u),v5,v6)). x != (y / R(z,u,w)) * R(R(z,v5,z),u,w) | x = y * a(z,v5,R(z,u,w)). x * a(R(y,z,u),w,L(R(y,z,u),v5,v6)) = x * a(y,w,R(y,z,u)). x * a(R(y,z,u),w,R(y,z,u)) = x * a(y,w,R(y,z,u)). a(R(x,y,z),u,R(x,y,z)) = a(x,u,R(x,y,z)). x != a(R(y,z,u),w,R(y,z,u)) | x = R(a(y,w,y),y * z,u). a(x,y,R(x,z,u)) = R(a(x,y,x),x * z,u). R(a(x,y,x),x * z,u) = a(x,y,R(x,z,u)). x != a(R(y,z,u),R(y,z,u) \ w,R(y,z,u)) | x = a(y,y \ w,R(y,z,u)). a(x,R(x,y,z) \ u,R(x,y,z)) = a(x,x \ u,R(x,y,z)). R(a(x,y,x),z,u) = a(x,y,R(x,x \ z,u)). a(x,y,R(x,x \ z,u)) = R(a(x,y,x),z,u). T(x,y) * R(a(x,z,x),u,w) = R(T(x,y),z,R(x,x \ u,w)). x * R(a(x,y,x),z,u) = R(x,y,R(x,x \ z,u)). x != R(T(y,z),u,R(T(y,z),w,v5)) | x = R(T(y,z),u,R(y,w,v5)). T(x,y) * R(a(T(x,y),z,T(x,y)),u,w) = R(T(x,y),z,R(x,T(x,y) \ u,w)). T(x,y) * R(a(x,z,x),u,w) = R(T(x,y),z,R(x,T(x,y) \ u,w)). R(T(x,y),z,R(x,T(x,y) \ u,w)) = T(x,y) * R(a(x,z,x),u,w). x != T(y,z) * R(a(y,u,y),w,v5) | x = R(T(y,z),u,R(y,y \ w,v5)). R(T(x,y),z,R(x,T(x,y) \ u,w)) = R(T(x,y),z,R(x,x \ u,w)). (R(T(x,y),z,T(x,y)) * (T(x,y) \ u)) * w = (R(T(x,y),z,R(x,x \ u,w)) * (T(x,y) \ u)) * w. (R(T(x,y),z,T(x,y)) * (T(x,y) \ u)) * w = (a(x,z,R(x,x \ u,w)) * u) * w. (R(T(x,y),z,T(x,y)) * (T(x,y) \ u)) * w = (R(a(x,z,x),u,w) * u) * w. (R(T(x,y),z,x) * (T(x,y) \ u)) * w = (R(a(x,z,x),u,w) * u) * w. (T(x,y) * (L(T(x,y),z,x) \ u)) * w = (R(a(x,z,x),u,w) * u) * w. (x * a(y,z,y)) * u = (R(a(y,z,y),x,u) * x) * u. (R(a(x,y,x),z,u) * z) * u = (z * a(x,y,x)) * u. x * y != (R(a(z,u,z),w,v5) * w) * v5 | x \ ((w * a(z,u,z)) * v5) = y. ((a(x,y,x) * z) * u) \ ((z * a(x,y,x)) * u) = a(R(a(x,y,x),z,u),z,u). K(x,T(a(y,z,y),u)) = a(R(a(y,z,y),x,u),x,u). a(R(a(x,y,x),z,u),z,u) = K(z,T(a(x,y,x),u)). a(R(a(x,y,x),z,u),z,u) = K(z,a(x,y,x)). x != K(y,a(z,u,z)) | x = 1. a(R(a(x,y,x),z,u),z,u) = 1. L(x,y,R(a(z,u,z),y,x)) = x. x != L(y,z,R(u,z,y)) | x = L(y,z,u). x = L(x,y,a(z,u,z)). L(x,y,a(z,u,z)) = x. L(x,y,a(z,u,z)) != w | w = x. (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,x) * (z * u)) * w) / (u * w) = R(a(x,y,x) * z,L(u,z,a(x,y,x)),w). R(a(x,y,x) * z,L(u,z,a(x,y,x)),w) = ((a(x,y,x) * (z * u)) * w) / (u * w). R(a(x,y,x),z,u) = a(x,y,x). (a(x,y,x) * (z * (u * w))) \ (((a(x,y,x) * z) * u) * w) = a(a(x,y,x) * z,u,w). x != R(y,z * u,L(w,u,z)) | x = ((y * (z * u)) * L(w,u,z)) / (z * (u * w)). a(x,y,x) = ((a(x,y,x) * (z * u)) * L(w,u,z)) / (z * (u * w)). ((a(x,y,x) * (z * u)) * L(w,u,z)) / (z * (u * w)) = a(x,y,x). x != R(a(y,z,y),y * u,w) | x = a(y,z,R(y,u,w)). a(x,y,x) = a(x,y,R(x,z,u)). a(x,y,R(x,z,u)) = a(x,y,x). a(x,x \ y,R(x,z,u)) * K(x,y) = K(x,R(x,z,u) \ y). (x * (K(y,z) * K(z,u))) * K(u,z) = x * K(y,z). x * K(y,z) != (u * (K(z,w) * K(y,z))) * K(w,z) | x = u. (x * (K(y,z) * K(u,y))) * (K(z,y) * K(y,u)) = x. x * (K(y,z) * K(z,u)) = x / (K(z,y) * K(u,z)). x / (K(y,z) * K(u,y)) = x * (K(z,y) * K(y,u)). x / (K(y,z) * K(z,u)) != w | w = x * (K(z,y) * K(u,z)). x / (K(y,z) * K(z,u)) != w | x * (K(z,y) * K(u,z)) = w. (K(x,y) * (K(y,z) * u)) * (K(y,x) * K(z,y)) = u * K(K(x,y) * K(y,z),u). x != y * a(z,u,z) | x = a(z,u,z) * y. x * R(y,z,y) = a(y,z,y) * (x * y). a(x,y,x) * (z * x) = z * R(x,y,x). a(x,y,x) \ z = (z / R(x,y,x)) * x. (x / R(y,z,y)) * y = a(y,z,y) \ x. a(x,y,x) * z != (a(x,y,x) * u) * w | z = u * w. (a(x,y,x) * z) * x = z * R(x,y,x). x != (y / R(z,u,z)) * z | x = y * (z \ L(z,u,z)). a(x,y,x) \ z = z * (x \ L(x,y,x)). x * (y \ L(y,z,y)) = a(y,z,y) \ x. x != K(y,z) * (y \ L(y,u,y)) | x = y \ L(T(y,z),u,y). a(x,y,x) \ K(x,z) = x \ L(T(x,z),y,x). K(x,y) * K(L(y,z,u),x) = a(u,z,K(x,y)). x != K(y,z) * K(L(z,u,w),y) | x = a(w,u * z,K(y,z)). a(x,y,K(z,u)) = a(x,y * u,K(z,u)). a(x,y * z,K(u,z)) = a(x,y,K(u,z)). x != a(y,z,K(u,w)) | x = K(w,L(u,z,y)) * K(u,w). a(x,y * z,K(u,z)) = K(z,L(u,y,x)) * K(u,z). K(x,L(y,z,u)) * K(y,x) = a(u,z * x,K(y,x)). x / T(x / y,L(y,z,u)) = y * a(u,z,K(y \ x,y)). L(x,y,z) \ ((u / x) \ (L(x,y,z) * (x \ u))) = x \ (x * a(z,y,K(x \ u,x))). L(x,y,z) \ T(L(x,y,z) * K(u,x),u) = x \ (x * a(z,y,K(x \ u,x))). x != y \ T(y * K(z,u),z) | x = K(y,z) * K(z,u). x \ (x * a(y,z,K(x \ u,x))) = K(L(x,z,y),u) * K(u,x). x \ (x * a(y,z,K(x \ u,x))) = K(x,L(u,z,y)) * K(u,x). x != K(y,L(z,u,w)) * K(z,y) | x = a(w,u,K(z,y)). x \ (x * a(y,z,K(x \ u,x))) = a(y,z,K(u,x)). a(x,y,K(z,u)) = a(x,y,K(u \ z,u)). a(x,y,K(z \ u,z)) = a(x,y,K(u,z)). a(x,y,K(z,u)) = a(x,y,K(u * z,u)). a(x,y,K(z * u,z)) = a(x,y,K(u,z)). ((K(x,y) * z) * ((K(u,w) \ 1) \ 1)) * K(v5,u) = ((1 / (1 / K(y,x))) \ z) * (K(u,w) * K(v5,u)). ((K(x,y) * z) * K(u,w)) * K(v5,u) = ((1 / (1 / K(y,x))) \ z) * (K(u,w) * K(v5,u)). ((1 / (1 / K(x,y))) \ z) * (K(u,w) * K(v5,u)) = ((K(y,x) * z) * K(u,w)) * K(v5,u). ((1 / (1 / K(x,y))) \ z) * (K(x,y) * K(u,x)) = T(z,K(x,y)) * K(u,x). x != T(y,K(z,u)) * K(w,z) | x = T(y * K(w,z),K(z,u)). ((1 / (1 / K(x,y))) \ z) * (K(x,y) * K(u,x)) = T(z * K(u,x),K(x,y)). (K(x,y) \ z) * (K(x,y) * K(u,x)) = T(z * K(u,x),K(x,y)). (K(x,y) * z) * (K(y,x) * K(u,y)) = T(z * K(u,y),K(y,x)). x != (K(y,z) * (K(z,u) * w)) * (K(z,y) * K(u,z)) | x = w * K(K(y,z) * K(z,u),w). T((K(x,y) * z) * K(y,x),K(x,u)) = z * K(K(u,x) * K(x,y),z). T(T(x,K(y,z)),K(y,u)) = x * K(K(u,y) * K(y,z),x). x * K(K(y,z) * K(z,u),x) = T(T(x,K(z,u)),K(z,y)). x * K(K(y,z) * K(z,u),x) = T(x,K(z,u) * K(y,z)). K(x,K(y,z) * K(u,y)) = K(K(z,y) * K(y,u),x). K(K(x,y) * K(y,z),u) = K(u,K(y,x) * K(z,y)). x * K(K(y,z) * K(u,y),x) = T(x,K(y,z) * K(u,y)). x != K(K(y,z) * K(z,u),w) | x = K(w,K(z,y)) * K(w,K(z,u)). K(x,K(y,z) * K(u,y)) = K(x,K(y,z)) * K(x,K(y,u)). K(x,K(y,z)) * K(x,K(y,u)) = K(x,K(y,z) * K(u,y)). K(x,K(y,z)) * K(x * K(y,u),K(y,w)) = K(x * K(y,u),K(y,z) * K(w,y)). K(x,K(y,z)) * K(x,K(y,u)) = K(x * K(y,w),K(y,z) * K(u,y)). K(x * K(y,z),K(y,u) * K(w,y)) = K(x,K(y,u)) * K(x,K(y,w)). K(x,K(y,z)) * K(x,K(y,u)) != w | K(x,K(y,z) * K(u,y)) = w. K(K(x,y) * K(z,x),u) = K(u,K(x,y) * K(z,x)). x != K(y,K(z,u) * K(w,z)) | x = K(y,K(z,u)) * K(y,K(z,w)). K(K(x,y) * K(z,x),u) = K(u,K(x,y)) * K(u,K(x,z)). K(x,K(y,z)) * K(x,K(y,u)) = K(K(y,z) * K(u,y),x). K(K(x,y) * K(z,x),u) != w | K(u,K(x,y) * K(z,x)) = w. K(K(x,y) * K(y,z),K(y,x) * u) != w | K(u,K(y,z) * K(x,y)) = w. K(x * y,K(z,R(u,x,y)) * K(u,z)) = K(a(K(z,u),x,y),((x * y) \ K(u,z)) \ 1). K(a(K(x,y),z,u),((z * u) \ K(y,x)) \ 1) = K(z * u,K(x,R(y,z,u)) * K(y,x)). x != K(y,K(z,R(u,w,v5)) * K(u,z)) | x = K(y,K(z,u) * K(u,R(z,w,v5))). K(a(K(x,y),z,u),((z * u) \ K(y,x)) \ 1) = K(z * u,K(x,y) * K(y,R(x,z,u))). K(x,L(y,z,u)) * K(y,x) != w | w = a(u,z,K(y,x)). K(x,L(y,z,u)) * K(y,x) != w | a(u,z,K(y,x)) = w. a(x,y * z,K(u,z)) != w | a(x,y,K(u,z)) = w. K(x,y) * K(L(y,z,u),x) != w | a(u,z,K(x,y)) = w. K(x,T(y,z)) = K(x,T(y,L(y,u,w) * z)). K(x,T(y,L(y,z,u) * w)) = K(x,T(y,w)). K(x,T(y,z * (u * y))) = K(x,T(y,z * u)). K(x,T(y \ z,u * z)) = K(x,T(y \ z,u * y)). K(x,T(y \ x,z * y)) = K(x,T(y \ x,z)). K(x,T(y \ x,z)) = K(x,T(y \ x,z / y)). K(x,T(y \ x,z / y)) = K(x,T(y \ x,z)). x != K(y,T(z \ y,u / z)) | x = K(y,T(z \ y,z \ u)). K(x,T(y \ x,z)) = K(x,T(y \ x,y \ z)). K(x,T(y \ x,y \ z)) = K(x,T(y \ x,z)). x != K(y,T(z \ y,z \ u)) | x = K(y,(u / (u / z)) \ y). K(x,T(y \ x,z)) = K(x,(z / (z / y)) \ x). K(x,(y / (y / z)) \ x) = K(x,T(z \ x,y)). x != K(y,((y * z) / u) \ y) | x = K(y,u / z). K(x,T(y \ x,x * z)) = K(x,((x * z) / y) / z). K(x,T(y \ x,z)) = K(x,((x * z) / y) / z). K(x,((x * y) / z) / y) = K(x,T(z \ x,y)). x != K(y,z / R(T(y,u),w,v5)) | x = K(y,R(y,w,v5) \ z). K(x,T(y \ x,R(T(x,z),u,w))) = K(x,R(x,u,w) \ ((x * R(T(x,z),u,w)) / y)). K(x,R(x,y,z) \ ((x * R(T(x,u),y,z)) / w)) = K(x,T(w \ x,R(T(x,u),y,z))). K(x,R(x,y,z) \ ((x * R(T(x,u),y,z)) / w)) != v5 | K(x,w \ x) = v5. (a(x,y,x) * (z * (u * w))) \ ((a(x,y,x) * (z * u)) * w) = a(a(x,y,x) * z,u,w). (a(x,y,x) * (z * (u * w))) \ (a(x,y,x) * ((z * u) * w)) = a(a(x,y,x) * z,u,w). L(a(x,y,z),x * (y * z),a(u,w,u)) = a(a(u,w,u) * x,y,z). a(a(x,y,x) * z,u,w) = a(z,u,w). x != a(y * z,u,w) | x = a(y \ z,u,w). a(x,y,z) = a(a(u,w,u) \ x,y,z). a(a(x,y,x) \ z,u,w) = a(z,u,w). a(L(x,y,x),z,u) = a(x,z,u). K(x,K(y,L(z,u,w))) = K(z,K(y,L(x,u,w))). K(x,K(y \ (z \ u),L(w,y,z))) = K(w,K(x,(z * y) \ u)). a(x,y,L(x,z,u)) = a(x,y,x). (x * (y * R(z,u,z))) / (x * (y * z)) = L(a(z,u,z),y * z,x). ((x * y) * R(L(z,y,x),u,L(z,y,x))) / (x * (y * z)) = a(L(z,y,x),u,L(z,y,x)). (x * (y * R(z,u,L(z,y,x)))) / (x * (y * z)) = a(L(z,y,x),u,L(z,y,x)). (x * (y * R(z,u,z))) / (x * (y * z)) = a(L(z,y,x),u,L(z,y,x)). x != (y * (z * R(u,w,u))) / (y * (z * u)) | x = L(a(u,w,u),z * u,y). a(L(x,y,z),u,L(x,y,z)) = L(a(x,u,x),y * x,z). L(a(x,y,x),z * x,u) = a(L(x,z,u),y,L(x,z,u)). L(a(x,y,x),z,u) = a(L(x,z / x,u),y,L(x,z / x,u)). a(L(x,y / x,z),u,L(x,y / x,z)) = L(a(x,u,x),y,z). (x * y) \ ((x * a(z,u,z)) * y) = R(a(z,u,z),x,y). (x * y) \ ((T(z * x,z) / z) * y) = R(a(z,x,z),x,y). x != (y * z) \ ((T(u * y,u) / u) * z) | x = L(a(u,T(y,z),u),T(y,z),z). R(a(x,y,x),y,z) = L(a(x,T(y,z),x),T(y,z),z). L(a(x,T(y,z),x),T(y,z),z) = R(a(x,y,x),y,z). L(a(x,y,x),T(y * K(z,y),z),z) = R(a(x,y * K(z,y),x),y * K(z,y),z). R(a(x,y * K(z,y),x),y * K(z,y),z) = L(a(x,y,x),T(y * K(z,y),z),z). R(a(x,y * K(z,y),x),y * K(z,y),z) = L(a(x,y,x),y,z). x != R(a(y,z,y),u,w) | x = a(y,z,y). L(a(x,y,x),y,z) = a(x,y * K(z,y),x). a(x,y * K(z,y),x) = L(a(x,y,x),y,z). a(x,L(y * K(z,y),u,w),x) = L(a(x,L(y,u,w),x),L(y,u,w),z). L(a(x,L(y,z,u),x),L(y,z,u),w) = a(x,L(y * K(w,y),z,u),x). L(K(x,K(y,z)),u,w) = K(x,K(z,L(y,u,w))). x != K(y,K(z,L(u,w,v5))) | x = K(u,K(z,L(y,w,v5))). L(K(x,K(y,z)),u,w) = K(y,K(z,L(x,u,w))). x != L(K(y,K(z,u)),w,v5) | x = K(y,L(K(u,z),w,v5)). K(x,K(y,L(z,u,w))) = K(x,L(K(y,z),u,w)). K(x,L(K(y,z),u,w)) = K(x,K(y,L(z,u,w))). x != L(K(y,K(z,u)),w,v5) | x = K(L(K(y,z),w,v5),u). K(x,K(y,L(z,u,w))) = K(L(K(z,x),u,w),y). K(L(K(x,y),z,u),w) = K(y,K(w,L(x,z,u))). K(x,K(y,L(z,u,w))) = K(x,K(y,L(z,u * z,w))). K(x,K(y,L(z,u * z,w))) = K(x,K(y,L(z,u,w))). K(x,K(y,L(z,u,w))) = K(z,K(y,L(x,u * z,w))). K(x,K(y,L(z,u * x,w))) = K(z,K(y,L(x,u,w))). x != K(y,K(z \ (u \ w),L(v5,z,u))) | x = K(v5,K(y,(u * z) \ w)). K(x,K((y * z) \ (u \ w),L(z,y,u))) = K(x,K(z,(u * (y * z)) \ w)). K(x,K(y \ (z \ (u \ w)),L(z,y,u))) = K(x,K(z,(u * (y * z)) \ w)). (x \ L(x,y,x)) \ z = z * a(x,y,x). x / a(y,z,L(y,u,w)) = x * (K(z,y) * K(y,z * L(y,u,w))). x * (K(y,z) * K(z,y * L(z,u,w))) = x / a(z,y,L(z,u,w)). x * y != z / z | x \ 1 = y. a(x,y,L(x,z,u)) \ 1 = K(y,x) * K(x,y * L(x,z,u)). K(x,y) * K(y,x * L(y,z,u)) = a(y,x,L(y,z,u)) \ 1. R(a(x,y,x) * z,L(u,z,a(x,y,x)),w) = (a(x,y,x) * ((z * u) * w)) / (u * w). x != (a(y,z,y) * u) / w | x = a(y,z,y) * (u / w). R(a(x,y,x) * z,L(u,z,a(x,y,x)),w) = a(x,y,x) * (((z * u) * w) / (u * w)). R(a(x,y,x) * z,L(u,z,a(x,y,x)),w) = a(x,y,x) * R(z,u,w). R(a(x,y,x) * z,u,w) = a(x,y,x) * R(z,u,w). a(x,y,x) * R(z,u,w) = R(a(x,y,x) * z,u,w). T(x \ R(a(y,x \ 1,y) * (a(y,x \ 1,y) \ x),z,u),y) = y \ T(y * (x \ R(x,z,u)),y). T(x \ R(x,y,z),u) = u \ T(u * (x \ R(x,y,z)),u). x \ T(x * (y \ R(y,z,u)),x) = T(y \ R(y,z,u),x). T(x,K(y,z * y)) = T(x,K(z,y)). x * y != T(z,K(u,w * u)) | x \ T(z,K(w,u)) = y. (x * y) \ T(z * (x * y),K(x,y)) = T(z,T(x * y,y)). x != (y * z) \ T(u * (y * z),K(y,z)) | x = T(u,z * y). T(x,T(y * z,z)) = T(x,z * y). K(x,y) * T(x,y * z) = T(T(x,y),z * y). K(x,y * z) * T(x,y) = T(T(x,y),z * y). x * T(y,z) != T(T(y,z),u) | x = K(y,T(u,z)). K(x,y * z) = K(x,T(z * y,y)). K(x,T(y * z,z)) = K(x,z * y). K(x,T(y * z,y)) = K(x,z * y). x != K(y,T(z,u)) | x = K(y,u / (u / z)). K(x,y * z) = K(x,z / (z / (z * y))). K(x,y / (y / (y * z))) = K(x,z * y). x * K(x,y * z) = T(x,z / (z / (z * y))). T(x,y / (y / (y * z))) = x * K(x,z * y). T(x,y / (y / (y * z))) = T(x,z * y). x != T(y,z / (z / u)) | x = T(y,T(u,z)). T(x,y * z) = T(x,T(z * y,z)). T(x,T(y * z,y)) = T(x,z * y). T(x,y) * (a(x,z,x) * u) = R(T(x,y),z,x) * u. K(x,y) * a(x,z,x) = x \ R(T(x,y),z,x). x \ R(T(x,y),z,x) = K(x,y) * a(x,z,x). x * a(K(y,z),u,u \ 1) = x / a(K(z,y),u,u \ 1). x / a(K(y,z),u,u \ 1) = x * a(K(z,y),u,u \ 1). a(K(x,y),z,z \ 1) \ 1 = a(K(y,x),z,z \ 1). 1 / (x \ K(x * y,x)) = T(x,y * R(x,z,x)). T(x,y * R(x,z,x)) = 1 / (x \ K(x * y,x)). x != 1 / (y \ K(z,y)) | x = T(y,z). T(x,y * R(x,z,x)) = T(x,x * y). T(x,y * R(x,z,x)) = x * K(x,x * y). K(x,y * R(x,z,x)) = K(x,x * y). x != K(y,z * R(y,u,w)) | x = K(y,R(y,u,w) * z). K(x,x * y) = K(x,R(x,z,x) * y). K(x,R(x,y,x) * z) = K(x,x * z). K(R(x,y,x),R(x,z,x) * u) = K(x,x * u). K(x,x * y) * T(x * L(y,z,u),x) = L(y,z,u) * T(R(x,L(y,z,u),x),R(x,L(y,z,u),x) * y). L(x,y,z) * T(R(u,L(x,y,z),u),R(u,L(x,y,z),u) * x) = K(u,u * x) * T(u * L(x,y,z),u). x != K(y,z) * T(u,y) | x = T(K(y,z) * u,y). L(x,y,z) * T(R(u,L(x,y,z),u),R(u,L(x,y,z),u) * x) = T(K(u,u * x) * (u * L(x,y,z)),u). L(x,y,z) * T(R(u,L(x,y,z),u),R(u,L(x,y,z),u) * x) = T(T(u,u * x) * L(x,y,z),u). K(x,y) * K(x,K(y,z \ (u * y))) = K(x,T(y,(y \ z) \ u)). (K(x,y) * z) * K(u,T(x,w)) = K(x,y) * (z * K(u,T(x,w))). (x \ y) * L(T((x \ y) \ y,z),u,w) = L(T(x,z),u,w) * (x \ y). T(x,y) / T(R(x,z,u),w) = R(T(x,w),z,u) \ T(x,y). R(T(x,y),z,x) \ (x * ((K(x,y) * a(x,z,x)) * u)) = L(u,x \ R(T(x,y),z,x),x). (x \ L(x,y,z)) * T(x,u) = T(x,u) * (x \ L(x,y,z)). T(x,y) * (x \ L(x,z,u)) = (x \ L(x,z,u)) * T(x,y). (x \ L(x,y,z)) * T(x,u) = K(x,u) * L(x,y,z). T((x \ y) \ T(y,x),y) = T(x,x \ y). T(x,x \ ((x \ y) \ z)) = T(x,y \ z). K(x,T(y,z \ u)) = K(x,T(y,(y \ z) \ u)). K(x,T(y,(y \ z) \ u)) = K(x,T(y,z \ u)). x != K(y,T(z,u)) | x = K(y,z) * K(y,K(z,u)). K(x,T(y,(y \ z) \ u)) = K(x,y) * K(x,K(y,z \ u)). K(x,y) * K(x,K(y,z \ u)) = K(x,T(y,(y \ z) \ u)). K(x,y) * z != K(x,T(y,(y \ u) \ w)) | z = K(x,K(y,u \ (w * y))). K(x,K(y,z \ u)) = K(x,K(y,z \ (u * y))). K(x,K(y,z \ (u * y))) = K(x,K(y,z \ u)). K(x,K(y,z \ (u * y))) = K(y,K(x,z \ u)). K(x,K(y,z \ (u * x))) = K(x,K(y,z \ u)). K(x,y) * K(x,K(y,z \ u)) = T(K(x,y),(z \ (u * x)) \ 1). T(K(x,y),(z \ (u * x)) \ 1) = K(x,y) * K(x,K(y,z \ u)). x != K(y,z) * K(y,K(z,u)) | x = T(K(y,z),u). T(K(x,y),(z \ (u * x)) \ 1) = T(K(x,y),z \ u). x != T(K(y,z),u \ 1) | x = T(K(y,z),u). T(K(x,y),z \ u) = T(K(x,y),z \ (u * x)). T(K(x,y),z \ (u * x)) = T(K(x,y),z \ u). T(K(x,y),z \ u) = T(K(x,y),z \ (u / x)). T(K(x,y),z \ (u / x)) = T(K(x,y),z \ u). L(K(x,y),z,u) \ L(T(K(x,y),w \ v5),z,u) = K(L(K(x,y),z,u),w \ (v5 / x)). K(L(K(x,y),z,u),w \ v5) = K(L(K(x,y),z,u),w \ (v5 / x)). K(L(K(x,y),z,u),w \ (v5 / x)) = K(L(K(x,y),z,u),w \ v5). x != K(L(K(y,z),u,w),v5) | x = K(z,K(v5,L(y,u,w))). K(L(K(x,y),z,u),w \ (v5 / x)) = K(y,K(w \ v5,L(x,z,u))). K(x,K(y \ z,L(u,w,v5))) = K(x,K(y \ (z / u),L(u,w,v5))). K(x,K(y \ (z / u),L(u,w,v5))) = K(x,K(y \ z,L(u,w,v5))). K(x,K(y \ (z \ u),L(z,w,v5))) = K(x,K(y \ u,L(z,w,v5))). x != K(y,K(z \ (u \ (w \ v5)),L(u,z,w))) | x = K(y,K(u,(w * (z * u)) \ v5)). K(x,K(y \ (z \ u),L(w,y,z))) = K(x,K(w,(z * (y * w)) \ u)). K(x,K(y,(z * (u * y)) \ w)) = K(y,K(x,(z * u) \ w)). K(x,K(y,(z * (u * x)) \ w)) = K(x,K(y,(z * u) \ w)). x != K(y,K(z,(u * (w * y)) \ ((u * y) * w))) | x = K(y,K(z,a(u,y,T(w,y)))). K(x,K(y,(z * u) \ ((z * x) * u))) = K(x,K(y,a(z,x,T(u,x)))). K(x,K(y,a(z,x,T(u,x)))) = K(x,K(y,(z * u) \ ((z * x) * u))). x != K(y,K(z,(u * w) \ ((u * y) * w))) | x = 1. K(x,K(y,a(z,x,T(u,x)))) = 1. K(x,K(y,a(z,x,u))) = 1. a(x,y,z) * 1 = T(a(x,y,z),K(u,y)). T(a(x,y,z),K(u,y)) = a(x,y,z) * 1. T(a(x,y,z),K(u,y)) = a(x,y,z). x != T(y,K(z,z \ u)) | x = T(y,K(z,u)). a(x,y \ z,u) = T(a(x,y \ z,u),K(y,z)). T(a(x,y \ z,u),K(y,z)) = a(x,y \ z,u). K(x,y) * a(z,x \ y,u) = a(z,x \ y,u) * K(x,y). a(x,y \ z,u) * K(y,z) = K(y,z) * a(x,y \ z,u). x != a(y,y \ z,R(y,u,w)) * K(y,z) | x = K(y,R(y,u,w) \ z). K(x,y) * a(x,x \ y,R(x,z,u)) = K(x,R(x,z,u) \ y). K(x,y) * a(x,x \ y,x) = K(x,R(x,z,u) \ y). K(x,R(x,y,z) \ u) = K(x,u) * a(x,x \ u,x). x != K(y,z) * a(y,y \ z,y) | x = K(y,y \ z). K(x,R(x,y,z) \ u) = K(x,x \ u). K(x,y \ x) = K(x,x \ ((x * R(T(x,z),u,w)) / y)). K(x,x \ ((x * R(T(x,y),z,u)) / w)) = K(x,w \ x). K(x,y \ x) = K(x,R(T(x,z),u,w) / y). K(x,R(T(x,y),z,u) / w) = K(x,w \ x). x != K(y,R(T(y,z),u,w) / v5) | x = K(y,v5 \ R(y,u,w)). K(x,y \ x) = K(x,y \ R(x,z,u)). K(x,y \ R(x,z,u)) = K(x,y \ x). x != K(y,R(z,u,w) \ R(y,u,w)) | x = K(R(y,u,w),z \ y). K(x,R(y,z,u) \ x) = K(R(x,z,u),y \ x). K(R(x,y,z),u \ x) = K(x,R(u,y,z) \ x). x != K(R(y,z,u),R(y / w,w,L(K(v5,y),v6,v7)) \ y) | x = K(R(y,z,u),w). K(x,R(R(x / y,y,L(K(z,x),u,w)),v5,v6) \ x) = K(R(x,v5,v6),y). x != K(y,R(R(y / z,u,w),v5,v6) \ y) | x = R(R(K(y,z),u,w),v5,v6). K(R(x,y,z),u) = R(R(K(x,u),u,L(K(w,x),v5,v6)),y,z). R(R(K(x,y),y,L(K(z,x),u,w)),v5,v6) = K(R(x,v5,v6),y). R(K(x,y),z,u) = K(R(x,z,u),y). R(K(x,y),z,u) \ 1 = K(y,R(x,z,u)). R(K(x,y),z,u) = K(x,R(y,z,u)). x \ T(x * L(y / x,z,u),x) = L(T(y,x) / x,z,u). x != y \ T(y * L((y * z) / y,u,w),v5) | x = T(y * L(z,u,w),v5) / y. L(T(x * y,x) / x,z,u) = T(x * L(y,z,u),x) / x. T(x * L(y,z,u),x) / x = L(T(x * y,x) / x,z,u). (x * (y * z)) \ ((x * y) * L(T(u * z,u) / u,y,x)) = L(a(u,L(z,y,x),u),L(z,y,x),x * y). (x * (y * z)) \ (x * (y * (T(u * z,u) / u))) = L(a(u,L(z,y,x),u),L(z,y,x),x * y). L(a(x,L(y,z,u),x),L(y,z,u),u * z) = (u * (z * y)) \ (u * (z * (T(x * y,x) / x))). x != L(a(y,L(z,u,w),y),L(z,u,w),v5) | x = a(y,L(z * K(v5,z),u,w),y). (x * (y * z)) \ (x * (y * (T(u * z,u) / u))) = a(u,L(z * K(x * y,z),y,x),u). (x * (y * z)) \ (x * (y * (T(u * z,u) / u))) = a(u,(x * (y * z)) / (x * y),u). L(L(a(x,y,x),y,z),z * y,u) = a(x,(u * (z * y)) / (u * z),x). K(L(x,y,z) * u,x) * K(x,u) = a(x,u,L(x,y,z)). x != K(T(y,z) \ u,y) | x = K(y \ u,y). K(x / T(y,z),y) = K(y \ x,y). (x / T(y,z)) * K(y \ x,y) = T(x / T(y,z),y). K(x,y \ K(z,L(x,u,w))) = K(x,y \ 1). K(x,y \ K(z,L(L(x,u,w),v5,v6))) = K(x,y \ 1). L((K(x,y) * a(x,z,x)) \ u,x \ R(T(x,y),z,x),T(x,R(T(x,y),z,x))) = ((x * R(T(x,y),z,x)) / x) \ (T(x,R(T(x,y),z,x)) * u). L((K(x,y) * a(x,z,x)) \ u,K(x,y) * a(x,z,x),T(x,R(T(x,y),z,x))) = ((x * R(T(x,y),z,x)) / x) \ (T(x,R(T(x,y),z,x)) * u). L((K(x,y) * a(x,z,x)) \ u,K(x,y) * a(x,z,x),x) = ((x * R(T(x,y),z,x)) / x) \ (T(x,R(T(x,y),z,x)) * u). ((x * R(T(x,y),z,x)) / x) \ (T(x,R(T(x,y),z,x)) * u) = L((K(x,y) * a(x,z,x)) \ u,K(x,y) * a(x,z,x),x). x != (y * z) * R((y * z) \ (y * u),w,v5) | x = y * (z * R(z \ u,w,v5)). R(T(x,y),z,u) * (x * (T(x,y) \ w)) = x * ((T(x,y) \ w) * R((T(x,y) \ w) \ w,z,u)). x * ((T(x,y) \ z) * R((T(x,y) \ z) \ z,u,w)) = R(T(x,y),u,w) * (x * (T(x,y) \ z)). x * (R(T(x,y),z,u) * (T(x,y) \ w)) = R(T(x,y),z,u) * (x * (T(x,y) \ w)). R(T(x,y),z,u) * (x * (T(x,y) \ w)) = x * (R(T(x,y),z,u) * (T(x,y) \ w)). T(x,y) * (x * (R(T(x,y),z,u) * (T(x,y) \ w))) = R(T(x,y),z,u) * (x * w). x != T(y,z) * (y * u) | x = y * (T(y,z) * u). R(T(x,y),z,u) * (x * w) = x * (T(x,y) * (R(T(x,y),z,u) * (T(x,y) \ w))). x * (T(x,y) * (R(T(x,y),z,u) * (T(x,y) \ w))) = R(T(x,y),z,u) * (x * w). x * (R(T(x,y),z,u) * w) = R(T(x,y),z,u) * (x * w). R(T(x,y),z,u) * (x * w) = x * (R(T(x,y),z,u) * w). R(T(x,y),z,u) \ (x * w) = x * (R(T(x,y),z,u) \ w). T(L(x,y,x),z) = T(T((y * x) / y,z),x * y). T(T((x * y) / x,z),y * x) = T(L(y,x,y),z). K(R(L(x,y,x),z,u),w) = K(R((y * x) / y,z,u),T(w,x * y)). K(R((x * y) / x,z,u),T(w,y * x)) = K(R(L(y,x,y),z,u),w). T(T((x * y) / x,z),y * x) = L(T(y,z),x,y). T((x \ y) \ T(y,x),x * y) = L(T(x,x \ y),y,x). T(T(x,y),K(y,z)) = T(x,T(y,z \ 1)). T(x,T(y,z \ 1)) = T(x,T(y,z)). x * y != T(z,u) * (z \ L(z,w,v5)) | x \ ((z \ L(z,w,v5)) * T(z,u)) = y. x \ ((x \ L(x,y,z)) * T(x,u)) = T(x,u) * (x \ (x \ L(x,y,z))). x \ ((x \ L(x,y,x)) * T(x,z)) = T(x,z) * (R(x,y,x) \ 1). x \ ((x \ L(x,y,x)) * T(x,z)) = R(x,y,x) \ T(x,z). x \ (K(x,y) * L(x,z,x)) = R(x,z,x) \ T(x,y). x \ L(T(x,y),z,x) = R(x,z,x) \ T(x,y). R(x,y,x) \ T(x,z) = x \ L(T(x,z),y,x). (x \ L(T(x,y),z,x)) * K(u,R(x,z,x)) = T(T(x,y) / T(R(x,z,x),u),R(x,z,x)). (T(x,y) / T(R(x,z,x),u)) * K(x \ L(T(x,y),z,x),R(x,z,x)) = T(T(x,y) / T(R(x,z,x),u),R(x,z,x)). (x \ L(T(x,y),z,x)) * K(u,x) = T(T(x,y) / T(R(x,z,x),u),R(x,z,x)). T(T(x,y) / T(R(x,z,x),u),R(x,z,x)) = (x \ L(T(x,y),z,x)) * K(u,x). x != (y \ L(T(y,z),u,w)) * K(v5,y) | x = T(y,v5) \ L(T(y,z),u,w). T(T(x,y) / T(R(x,z,x),u),R(x,z,x)) = T(x,u) \ L(T(x,y),z,x). (R(T(x,y),z,x) \ T(x,u)) * K(x \ L(T(x,u),z,x),R(x,z,x)) = T(T(x,u) / T(R(x,z,x),y),R(x,z,x)). (R(T(x,y),z,x) \ T(x,u)) * K(x \ L(T(x,u),z,x),x) = T(T(x,u) / T(R(x,z,x),y),R(x,z,x)). x != ((y * K(z,u)) * K(u,w)) / u | x = (y * K(u,w)) / T(u,z). ((x * K(y,z)) / z) * K(z,u) = (x * K(z,u)) / T(z,y). (x / T(y,z)) * K(y,u) = (x * K(y,u)) / T(y,z). (x * K(y,z)) / T(y,u) = (x / T(y,u)) * K(y,z). ((x / T(y,z)) * K(y,u)) \ (x * K(y,u)) = T(y,z). ((x \ y) * K(x,z)) \ (y * K(x,z)) = T(x,x \ y). x != K(y,T(z,u)) | x = K(T(y,u),z). K(L(x,y,z) * u,x) = K(T(L(x,y,z) * u,u),x). K(T(L(x,y,z) * u,u),x) = K(L(x,y,z) * u,x). K(x,(T(y,z) * (y \ u)) \ 1) = K(x,u \ K(z,y)). K(x,(T(y,z) * u) \ y) = K(x,(T(y,z) * (y \ u)) \ 1). K(x,(T(y,z) * (y \ u)) \ 1) = K(x,(T(y,z) * u) \ y). (((x * y) \ x) * z) * K(z,y \ 1) != ((x * y) \ x) * u | T(z,(x * y) \ x) = u. ((x * y) \ x) * z != (((x * y) \ x) * u) * K(u,y \ 1) | T(u,(x * y) \ x) = z. T(x,(y * z) \ y) = T(x,z \ 1). T(x * y,T(z,y \ 1)) = T(x * y,T(z,x)). x != T(y,T(z,u \ 1)) | x = T(y,T(z,u)). T(x * y,T(z,x)) = T(x * y,T(z,y)). T(x * y,T(z,y)) = T(x * y,T(z,x)). T(x * L(L(y,z,u),w,v5),y) = T(x * L(L(y,z,u),w,v5),T(y,x)). T(x * L(L(y,z,u),w,v5),T(y,x)) = T(x * L(L(y,z,u),w,v5),y). x != K(y,(T(z,u) * (z \ w)) \ 1) | x = K(y,w \ K(u,z)). K(x,(T(y,z) * u) \ y) = K(x,u \ K(z,y)). K(x,y \ z) = K(x,(T(z,u) \ y) \ K(u,z)). K(x,(T(y,z) \ u) \ K(z,y)) = K(x,u \ y). x != K(y,z \ K(u,L(y,w,v5))) | x = K(y,z \ 1). K(x,y \ L(x,z,u)) = K(x,(T(L(x,z,u),w) \ y) \ 1). K(x,(T(L(x,y,z),u) \ w) \ 1) = K(x,w \ L(x,y,z)). K(x,(L(T(x,y),z,u) \ w) \ 1) = K(x,w \ L(x,z,u)). K(x,y \ L(T(x,z),u,w)) = K(x,y \ L(x,u,w)). K((x \ y) \ T(y,x),z \ L(T(x,x \ y),u,w)) = K((x \ y) \ T(y,x),z \ L((x \ y) \ T(y,x),u,w)). K((x \ y) \ T(y,x),z \ L((x \ y) \ T(y,x),u,w)) = K((x \ y) \ T(y,x),z \ L(T(x,x \ y),u,w)). K((x \ y) \ T(y,x),z \ L(L(T(x,x \ y),y,x),u,w)) = K((x \ y) \ T(y,x),z \ L((x \ y) \ T(y,x),u,w)). x != K((y \ z) \ T(z,y),u) | x = K(y,u). K((x \ y) \ T(y,x),z \ L((x \ y) \ T(y,x),u,w)) = K(x,z \ L(T(x,x \ y),u,w)). x != K(y,z \ L(T(y,u),w,v5)) | x = K(y,z \ L(y,w,v5)). K((x \ y) \ T(y,x),z \ L((x \ y) \ T(y,x),u,w)) = K(x,z \ L(x,u,w)). K(x,y \ L(L(T(x,x \ z),z,x),u,w)) = K((x \ z) \ T(z,x),y \ L((x \ z) \ T(z,x),u,w)). K((x \ y) \ T(y,x),z \ L((x \ y) \ T(y,x),u,w)) = K(x,z \ L(L(T(x,x \ y),y,x),u,w)). T(x,K(y,z)) * K(y,u) = T(x * K(y,u),K(y,z)). x \ (y * K(z,y \ x)) = (x \ y) * K(z,y \ x). (x \ y) * K(z,y \ x) = K(z,y \ x) * (x \ y). K(x,y \ z) * (z \ y) = (z \ y) * K(x,y \ z). T(x \ y,z) * ((y \ x) * K(z,x \ y)) != u | (x \ y) * (y \ x) = u. L(L(x,y,z) * K(u,L(x,y,z)),w,v5) * u = u * L(L(x,w,v5),y,z). L(L(x * K(y,x),z,u),w,v5) * y = y * L(L(x,w,v5),z,u). x \ T(x * (x \ L(x,y,z)),u) = T(L(x,y,z),u) * (x \ 1). x \ T(L(x,y,z),u) = T(L(x,y,z),u) * (x \ 1). T(L(x,y,z),u) * (x \ 1) = x \ T(L(x,y,z),u). T(L(x,y,z),u) * (x \ 1) = x \ L(T(x,u),y,z). L(T(x,y),z,u) * (x \ 1) = x \ L(T(x,y),z,u). x != y * z | x = (1 / y) \ z. (T(x,y) / z) \ x = (1 / z) \ K(y,x). x \ y = (1 / (x \ T(y,z))) \ K(z,y). (1 / (x \ T(y,z))) \ K(z,y) = x \ y. K(x,L(L(x,y,z),u,w) / v5) = K(x,(1 / (v5 \ T(L(L(x,y,z),u,w),v6))) \ K(v6,L(L(x,y,z),u,w))). K(x,(1 / (y \ T(L(L(x,z,u),w,v5),v6))) \ K(v6,L(L(x,z,u),w,v5))) = K(x,L(L(x,z,u),w,v5) / y). x != K(y,L(L(y,z,u),w,v5) / v6) | x = K(y,v6 \ L(L(y,z,u),w,v5)). K(x,(1 / (y \ T(L(L(x,z,u),w,v5),v6))) \ K(v6,L(L(x,z,u),w,v5))) = K(x,y \ L(L(x,z,u),w,v5)). K(x,(1 / (y \ L(T(L(x,z,u),w),v5,v6))) \ K(w,L(L(x,z,u),v5,v6))) = K(x,y \ L(L(x,z,u),v5,v6)). K(x,(1 / (y \ L(L(T(x,z),u,w),v5,v6))) \ K(z,L(L(x,u,w),v5,v6))) = K(x,y \ L(L(x,u,w),v5,v6)). x != K(y,z \ K(u,L(L(y,w,v5),v6,v7))) | x = K(y,z \ 1). K(x,y \ L(L(x,z,u),w,v5)) = K(x,(1 / (y \ L(L(T(x,v6),z,u),w,v5))) \ 1). K(x,(1 / (y \ L(L(T(x,z),u,w),v5,v6))) \ 1) = K(x,y \ L(L(x,u,w),v5,v6)). K(x,y \ L(L(T(x,z),u,w),v5,v6)) = K(x,y \ L(L(x,u,w),v5,v6)). x != K(y,z \ L(L(T(y,y \ u),u,y),w,v5)) | x = K((y \ u) \ T(u,y),z \ L((y \ u) \ T(u,y),w,v5)). K(x,y \ L(L(x,z,x),u,w)) = K((x \ z) \ T(z,x),y \ L((x \ z) \ T(z,x),u,w)). K((x \ y) \ T(y,x),z \ L((x \ y) \ T(y,x),u,w)) = K(x,z \ L(L(x,y,x),u,w)). x != K((y \ z) \ T(z,y),u \ L((y \ z) \ T(z,y),w,v5)) | x = K(y,u \ L(y,w,v5)). K(x,y \ L(L(x,z,x),u,w)) = K(x,y \ L(x,u,w)). (x \ y) * T((x \ y) \ (x \ L(x,z,u)),w) = (x \ L(x,z,u)) * K((L(x,z,u) \ y) \ 1,w). (x \ L(x,y,z)) * K((L(x,y,z) \ u) \ 1,w) = (x \ u) * T((x \ u) \ (x \ L(x,y,z)),w). T(x,K(y,z / x)) = T(x,K(y,x \ z)). x * L(T(y,x * y),z,u) = L(L(y,x,y),z,u) * x. T(x,K(y,z \ u)) = T(x,K(y,u \ z)). x * y != (z * x) * L((z * x) \ x,u,w) | T(z * L(z \ 1,u,w),x) = y. T(x * L(x \ 1,y,z),u) = T(x,u) * L(T(x,u) \ 1,y,z). T(x,y) * L(T(x,y) \ 1,z,u) = T(x * L(x \ 1,z,u),y). T(x,y) \ T(x * L(x \ 1,z,u),y) = L(T(x,y) \ 1,z,u). T(x \ y,z) \ T((x \ y) * (y \ x),z) = L(T(x \ y,z) \ 1,x \ y,x). x != L(T(y \ z,u) \ 1,y \ z,y) | x = z \ (y * K(u,y \ z)). T(x \ y,z) \ T((x \ y) * (y \ x),z) = y \ (x * K(z,x \ y)). T(x \ y,z) * (y \ (x * K(z,x \ y))) = T((x \ y) * (y \ x),z). T(x \ y,z) * ((y \ x) * K(z,x \ y)) = T((x \ y) * (y \ x),z). (x \ y) * (y \ x) = T((x \ y) * (y \ x),z). T((x \ y) * (y \ x),z) = (x \ y) * (y \ x). T(x,(y \ z) * (z \ y)) = x. T(x,y * ((z * y) \ z)) = x. K(x,y * ((z * y) \ z)) = 1. K(x,L(y * ((z * y) \ z),u,w)) = 1. x != K(y,L(z * ((u * z) \ u),z \ 1,u * z)) | x = K(y,a(u,z,z \ 1) \ 1). 1 = K(x,a(y,z,z \ 1) \ 1). K(x,a(y,z,z \ 1) \ 1) = 1. T(x,a(y,z,z \ 1) \ 1) = x. T(x,a(K(y,z),u,u \ 1)) = x. T(x,a(K(y,z),u \ 1,u)) = x. T(a(K(x,y),z \ 1,z),u) = a(K(x,y),z \ 1,z). x != a(y,z \ 1,z) | x = y \ R(y,z \ 1,z). T(a(K(x,y),z \ 1,z),u) = K(x,y) \ R(K(x,y),z \ 1,z). T(K(x,y) * R(K(y,x),z \ 1,z),u) = K(y,x) \ R(K(y,x),z \ 1,z). x != T(K(y,z) * R(K(z,y),u,w),v5) | x = K(y,T(z,v5)) * R(K(z,T(y,v5)),u,w). K(x,y) \ R(K(x,y),z \ 1,z) = K(y,T(x,u)) * R(K(x,T(y,u)),z \ 1,z). K(x,T(y,z)) * R(K(y,T(x,z)),u \ 1,u) = K(y,x) \ R(K(y,x),u \ 1,u). x != K(y,T(z,u)) * w | x = K(u,K(z,y)) * (K(y,z) * w). K(x,y) \ R(K(x,y),z \ 1,z) = K(u,K(x,y)) * (K(y,x) * R(K(x,T(y,u)),z \ 1,z)). K(x,K(y,z)) * (K(z,y) * R(K(y,T(z,x)),u \ 1,u)) = K(y,z) \ R(K(y,z),u \ 1,u). K(x,K(y,R(z,u \ 1,u))) = K(x,K(z,y)). K(x,K(y,R(z,u,u \ 1))) = K(x,K(z,y)). K(x,K(y,R(z,u,u \ 1))) = K(x,K(y,z)). K(x,K(y,z * (u \ 1))) = K(x,K(y,z / u)). K(x,K(y,z * u)) = K(x,K(y,z / (u \ 1))). K(x,K(y,z / (u \ 1))) = K(x,K(y,z * u)). K(x,K(y,(z \ 1) / u)) = K(x,K(y,u * z)). K(x,K(y,(z \ 1) / (u / z))) = K(x,K(y,u)). K(x,K(y,(z \ 1) / (u / z))) = K(y,K(x,u)). x != K(y,K(z,(u \ 1) / (w / u))) | x = K(z,(T(w,y) / u) / (w / u)). K(x,K(y,z)) = K(x,(T(z,y) / u) / (z / u)). K(x,(T(y,z) / u) / (y / u)) = K(x,K(z,y)). K(x,K(y,z)) * (z / u) = T(z,K(x,y)) / u. R(K(x,K(y,z)),z / u,u) = K(x,K(z,y)). R(K(x,K(y,z)),y / u,u) = K(x,K(y,z)). K(x,K(y,z)) = K(y,K(z,R(x,y / u,u))). K(x,K(y,R(z,x / u,u))) = K(z,K(x,y)). K(x,K(y,R(z,u,u \ x))) = K(z,K(x,y)). K(x,K(y,z)) * u = T(z,K(x,y)) / (u \ z). T(x,K(y,z)) / (u \ x) = K(y,K(z,x)) * u. T(x,K(y,z)) / (u \ x) = K(x,K(y,z)) * u. (K(x,K(y,z)) * u) \ T(x,K(y,z)) = u \ x. L(x \ y,x,K(y,K(z,u))) = x \ y. a(K(x,K(y,z)),u,u \ x) = 1. a(K(K(x,y),z),u,u \ z) = 1. x != 1 | x = K(y,K(z,u)) * K(y,K(z,u)). a(K(K(x,y),z),u,u \ z) = K(w,K(v5,v6)) * K(w,K(v5,v6)). a(K(K(x,y),z),u,u \ z) = K(w,K(v5,R(v6,v7,v7 \ w))) * K(v6,K(w,v5)). a(K(K(x,y),z),u,u \ z) = K(w,K(v5,R(v6,v7,v7 \ w))) * K(w,K(v5,v6)). a(K(x,K(y,z)),u,u \ x) = K(w,K(v5,R(v6,v7,v7 \ w))) * K(w,K(v5,v6)). x != K(y,K(z,u)) * K(y,K(z,w)) | x = K(y,K(z,u) * K(w,z)). a(K(x,K(y,z)),u,u \ x) = K(w,K(v5,R(v6,v7,v7 \ w)) * K(v6,v5)). K(x,K(y,R(z,u,u \ x)) * K(z,y)) = a(K(w,K(v5,v6)),v7,v7 \ w). x != a(K(K(y,z),u),w,w \ u) | x = 1. K(x,K(y,R(z,u,u \ x)) * K(z,y)) = 1. 1 = K(x,K(y,z) * K(z,R(y,u,u \ x))). K(x,K(y,z) * K(z,R(y,u,u \ x))) = 1. K(x * y,K(z,u) * K(u,R(z,x,y))) = 1. x != K(y * z,K(u,w) * K(w,R(u,y,z))) | x = K(a(K(u,w),y,z),((y * z) \ K(w,u)) \ 1). 1 = K(a(K(x,y),z,u),((z * u) \ K(y,x)) \ 1). K(a(K(x,y),z,u),((z * u) \ K(y,x)) \ 1) = 1. 1 = K(a(K(x,y),z,u),K(x,y) * (z * u)). K(a(K(x,y),z,u),K(x,y) * (z * u)) = 1. 1 * (((K(x,y) * z) * u) / (K(x,y) * (z * u))) = a(K(x,y),z,u). ((K(x,y) * z) * u) / (K(x,y) * (z * u)) = a(K(x,y),z,u). K(x,y) * R(K(y,x),z,u) = a(K(y,x),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). x != K(y,z) \ R(K(y,z),u,w) | x = w \ L(w,u,K(y,z)). 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)). L(x,y,K(z,u)) != x * w | a(K(z,u),y,x) = w. K(x,y) * K(y,R(x,z,u)) = a(K(y,x),z * x,u). (x * a(K(y,z),u,w)) * (K(y,z) * R(K(z,y),u,w)) = x. K(x,y) * K(y,R(x,z,u)) = a(K(y,x),z,u). (x * a(K(y,z),u,w)) * a(K(z,y),u,w) = x. (T(x,x \ y) * a(K(z,u),w,v5)) \ ((x \ y) \ y) = a(K(u,z),w,v5). x != K(y,z) * K(z,R(y,u,w)) | x = a(K(z,y),u,w). a(K(x,y),z * y,u) = a(K(x,y),z,u). x != R(K(y,z),u,w) | x = K(R(y,y \ u,w),z). K(x,y) = K(R(x,x \ 1,z),y). K(R(x,x \ 1,y),z) = K(x,z). K(R(L(x,y,x),x \ a(x,y,x),z),u) = K(L(x,y,x),u). x / (K(y,x * K(z,x)) * K(x * K(z,x),z)) = T(x * K(z,x),y). x / (K(T(y,z),x) * K(x * K(z,x),z)) = T(x * K(z,x),y). x / (K(T(y,z),x) * K(x,z)) = T(x * K(z,x),y). T(x * K(y,x),z) \ x = K(T(z,y),x) * K(x,y). T((x * y) / x,z) \ y = K(T(z,x),y) * K(y,x). x != K(y,z) * K(z,u) | x = K(z,u) * K(y,z). T((x * y) / x,z) \ y = K(y,x) * K(T(z,x),y). L(x,y,L(x,z,u)) \ x = K(x,y) * K(T(L(x,z,u) * y,y),x). K(x,y) * K(T(L(x,z,u) * y,y),x) = L(x,y,L(x,z,u)) \ x. K(x,y) * K(L(x,z,u) * y,x) = L(x,y,L(x,z,u)) \ x. L(x,y,L(x,z,u)) \ x = K(L(x,z,u) * y,x) * K(x,y). K(L(x,y,z) * u,x) * K(x,u) = L(x,u,L(x,y,z)) \ x. x != K(L(y,z,u) * w,y) * K(y,w) | x = a(y,w,L(y,z,u)). L(x,y,L(x,z,u)) \ x = a(x,y,L(x,z,u)). (a(x,y,L(x,z,u)) * K(L(x,y,L(x,z,u)),w)) \ (x * K(L(x,y,L(x,z,u)),w)) = T(L(x,y,L(x,z,u)),L(x,y,L(x,z,u)) \ x). (a(x,y,L(x,z,u)) * K(x,w)) \ (x * K(L(x,y,L(x,z,u)),w)) = T(L(x,y,L(x,z,u)),L(x,y,L(x,z,u)) \ x). (a(x,y,L(x,z,u)) * K(x,w)) \ T(x,w) = T(L(x,y,L(x,z,u)),L(x,y,L(x,z,u)) \ x). T(L(x,y,L(x,z,u)),L(x,y,L(x,z,u)) \ x) = (a(x,y,L(x,z,u)) * K(x,w)) \ T(x,w). x != T(L(y,z,u),L(y,z,u) \ y) | x = L(y,z,u). (a(x,y,L(x,z,u)) * K(x,w)) \ T(x,w) = L(x,y,L(x,z,u)). (a(x,y,x) * K(x,z)) \ T(x,z) = L(x,y,L(x,u,w)). L(x,y,L(x,z,u)) = (a(x,y,x) * K(x,w)) \ T(x,w). L((1 / x) * y,z,u) = L(L(x \ y,z,u),x,1 / x). L(L(x \ y,z,u),x,1 / x) = L((1 / x) * y,z,u). x * y != L(L(z \ u,w,v5),z,1 / z) | x \ L((1 / z) * u,w,v5) = y. (1 / x) \ L((1 / x) * y,z,u) = x * L(x \ y,z,u). (1 / x) \ L(y,z,u) = x * L(x \ ((1 / x) \ y),z,u). x * L(x \ ((1 / x) \ y),z,u) = (1 / x) \ L(y,z,u). x \ ((1 / x) \ L(y,z,u)) = L(x \ ((1 / x) \ y),z,u). (x \ 1) \ (x \ L(y,z,u)) = L((x \ 1) \ ((1 / (x \ 1)) \ y),z,u). L((x \ 1) \ ((1 / (x \ 1)) \ y),z,u) = (x \ 1) \ (x \ L(y,z,u)). L((x \ 1) \ (x \ y),z,u) = (x \ 1) \ (x \ L(y,z,u)). (x \ 1) \ (x \ L(y,z,u)) = L((x \ 1) \ (x \ y),z,u). (x \ L(x,y,z)) * K((L(x,y,z) \ 1) \ 1,u) = (x \ 1) * T(L((x \ 1) \ (x \ x),y,z),u). (x \ L(x,y,z)) * K((L(x,y,z) \ 1) \ 1,u) = (x \ 1) * T(L((x \ 1) \ 1,y,z),u). (x \ L(x,y,z)) * K((L(x,y,z) \ 1) \ 1,u) = (x \ 1) * L(T((x \ 1) \ 1,u),y,z). x != (y \ z) * L(T((y \ z) \ z,u),w,v5) | x = L(T(y,u),w,v5) * (y \ z). (x \ L(x,y,z)) * K((L(x,y,z) \ 1) \ 1,u) = L(T(x,u),y,z) * (x \ 1). x != L(T(y,z),u,w) * (y \ 1) | x = y \ L(T(y,z),u,w). (x \ L(x,y,z)) * K((L(x,y,z) \ 1) \ 1,u) = x \ L(T(x,u),y,z). (x \ L(x,y,z)) * K(L(x,y,z),u) = x \ L(T(x,u),y,z). K(x \ L(T(x,y),z,u),x) = K(x \ L(x,z,u),x). x != K(y \ L(y,z,u),y) | x = 1. K(x \ L(T(x,y),z,u),x) = 1. (R(T(x,y),z,x) \ T(x,u)) * 1 = T(T(x,u) / T(R(x,z,x),y),R(x,z,x)). T(T(x,y) / T(R(x,z,x),u),R(x,z,x)) = (R(T(x,u),z,x) \ T(x,y)) * 1. T(T(x,y) / T(R(x,z,x),u),R(x,z,x)) = R(T(x,u),z,x) \ T(x,y). x != T(T(y,z) / T(R(y,u,y),w),R(y,u,y)) | x = T(y,w) \ L(T(y,z),u,y). R(T(x,y),z,x) \ T(x,u) = T(x,y) \ L(T(x,u),z,x). (x * L(x \ y,z,u)) / w = (x / w) * L((x / w) \ (y / w),z,u). (x / y) * L((x / y) \ (z / y),u,w) = (x * L(x \ z,u,w)) / y. (x / y) * L(T(y,x),z,u) = (x * L(x \ (y * x),z,u)) / y. (x * L(x \ (y * x),z,u)) / y = (x / y) * L(T(y,x),z,u). (L(x,y,z) * u) / x = (u / x) * L(T(x,u),y,z). (x / y) * L(T(y,x),z,u) = (L(y,z,u) * x) / y. x * L(T(y,x * y),z,u) = (L(y,z,u) * (x * y)) / y. (L(x,y,z) * (u * x)) / x = u * L(T(x,u * x),y,z). T(x * L(T(y,x * y),z,u),y) = y \ (L(y,z,u) * (x * y)). x != y \ (L(y,z,u) * w) | x = L(y,z,u) * (y \ w). T(x * L(T(y,x * y),z,u),y) = L(y,z,u) * (y \ (x * y)). T(x * L(T(y,x * y),z,u),y) = L(y,z,u) * T(x,y). T(L(L(x,y,x),z,u) * y,x) = L(x,z,u) * T(y,x). T(L(L(x * K(y,x),y,x * K(y,x)),z,u) * y,x * K(y,x)) = L(x * K(y,x),z,u) * T(y,x). T(L(L(x * K(y,x),y,x),z,u) * y,x * K(y,x)) = L(x * K(y,x),z,u) * T(y,x). T(x * L(L(y,z,u),x,y),y * K(x,y)) = L(y * K(x,y),z,u) * T(x,y). x != L(y * K(z,y),u,w) * T(z,y) | x = T(z,y) * L(y,u,w). T(x * L(L(y,z,u),x,y),y * K(x,y)) = T(x,y) * L(y,z,u). T(x * L(L(y,x,y),z,u),y * K(x,y)) = T(x,y) * L(y,z,u). x != T(y,z * K(u,z)) | x = T(y,T(z,u)). T(x,y) * L(y,z,u) = T(x * L(L(y,x,y),z,u),T(y,x)). T(x * L(L(y,x,y),z,u),T(y,x)) = T(x,y) * L(y,z,u). x != T(y * L(L(z,u,w),v5,v6),T(z,y)) | x = T(y * L(L(z,u,w),v5,v6),z). T(x,y) * L(y,z,u) = T(x * L(L(y,x,y),z,u),y). T(x * L(L(y,x,y),z,u),y) = T(x,y) * L(y,z,u). K(x,L(L(x,y,x),z,u) / (y \ 1)) * (y \ (T(y,x) * L(x,z,u))) = L(L(x,y,x),z,u). K(x,(y \ 1) \ L(L(x,y,x),z,u)) * (y \ (T(y,x) * L(x,z,u))) = L(L(x,y,x),z,u). K(x,(y \ 1) \ L(x,z,u)) * (y \ (T(y,x) * L(x,z,u))) = L(L(x,y,x),z,u). K(x,y * L(x,z,u)) * (y \ (T(y,x) * L(x,z,u))) = L(L(x,y,x),z,u). K(x,y * L(x,z,u)) * (K(y,x) * L(x,z,u)) = L(L(x,y,x),z,u). K(R(x,y,z),T(u,x \ w)) = K(R(x,y,z),T(u,w)). K(R(x,y,z),T(u,w)) = K(R(x,y,z),T(u,x * w)). K(R(x,y,z),T(u,x * w)) = K(R(x,y,z),T(u,w)). K(R((x * y) / x,z,u),T(w,y * x)) = K(L(R(y,z,u),x,y),w). K(R(x,y,z),T(u,w)) = K(R((w * x) / w,y,z),u). K(R((x * y) / x,z,u),w) = K(R(y,z,u),T(w,x)). x != K(R((y * z) / y,u,w),T(v5,z * y)) | x = K(L(R(z,u,w),y,z),v5). K(R(x,y,z),T(T(u,x * w),w)) = K(L(R(x,y,z),w,x),u). K(R(x,y,z),T(T(u,w),x * w)) = K(L(R(x,y,z),w,x),u). x != K(R(y,z,u),T(w,y * v5)) | x = K(R(y,z,u),T(w,v5)). K(L(R(x,y,z),u,x),w) = K(R(x,y,z),T(T(w,u),u)). K(R(x,y,z),T(T(u,w),w)) = K(L(R(x,y,z),w,x),u). K(R(x,y,z),u) = K(L(R(x,y,z),w,x),u). K(L(R(x,y,z),u,x),w) = K(R(x,y,z),w). K(R(L(x,y,x),z,u),w) = K(R(x,z,u),w). x != K(R(L(y,z,y),y \ a(y,z,y),u),w) | x = K(L(y,z,y),w). K(R(x,x \ a(x,y,x),z),u) = K(L(x,y,x),u). K(R(x,x \ a(x,y,x),z),u) = K(x,u). K(x,y) = R(K(x,y),a(x,z,x),u). R(K(x,y),a(x,z,x),u) = K(x,y). K(x,y) * (a(x,z,x) * u) = (K(x,y) * a(x,z,x)) * u. (K(x,y) * a(x,z,x)) * u = K(x,y) * (a(x,z,x) * u). R(T(x,y),z,x) \ (x * (K(x,y) * (a(x,z,x) * u))) = L(u,x \ R(T(x,y),z,x),x). R(T(x,y),z,x) \ (T(x,y) * (a(x,z,x) * u)) = L(u,x \ R(T(x,y),z,x),x). R(T(x,y),z,x) \ (R(T(x,y),z,x) * u) = L(u,x \ R(T(x,y),z,x),x). L(x,y \ R(T(y,z),u,y),y) = x. L(x,K(y,z) * a(y,u,y),y) = x. x != L((K(y,z) * a(y,u,y)) \ w,K(y,z) * a(y,u,y),y) | x = ((y * R(T(y,z),u,y)) / y) \ (T(y,R(T(y,z),u,y)) * w). (K(x,y) * a(x,z,x)) \ u = ((x * R(T(x,y),z,x)) / x) \ (T(x,R(T(x,y),z,x)) * u). ((x * R(T(x,y),z,x)) / x) \ (T(x,R(T(x,y),z,x)) * u) = (K(x,y) * a(x,z,x)) \ u. x != ((y * z) / y) \ (T(y,z) * u) | x = z \ (y * u). (K(x,y) * a(x,z,x)) \ u = R(T(x,y),z,x) \ (x * u). x != R(T(y,z),u,w) \ (y * v5) | x = y * (R(T(y,z),u,w) \ v5). (K(x,y) * a(x,z,x)) \ u = x * (R(T(x,y),z,x) \ u). (a(x,y,x) * K(x,z)) \ u = x * (R(T(x,z),y,x) \ u). x != (a(y,z,y) * K(y,u)) \ T(y,u) | x = L(y,z,L(y,w,v5)). x * (R(T(x,y),z,x) \ T(x,y)) = L(x,z,L(x,u,w)). L(x,y,L(x,z,u)) = x * (R(T(x,w),y,x) \ T(x,w)). L(x,y,L(x,z,u)) = x * (T(x,w) \ L(T(x,w),y,x)). L(x,y,L(x,z,u)) = x * (x \ L(x,y,x)). L(x,y,L(x,z,u)) = L(x,y,x). L(L(x,y,x),z,u) = L(L(x,z,u),y,L(x,w,v5)). L(L(x,y,z),u,L(x,w,v5)) = L(L(x,u,x),y,z). (L(x,y,z) \ L(L(x,u,x),y,z)) \ w = w * a(L(x,y,z),u,L(x,y,z)). K(x \ y,z) * K(z,y / x) = K(x,K(z,x \ y)). K(x \ y,z) * K(z,y / x) = K(z,K(x,x \ y)). K(x,K(y,y \ z)) = K(x,z / y) * K(y \ z,x). K(x,y / z) * K(z \ y,x) = K(x,K(z,z \ y)). x != K(y,K(z,z \ u)) | x = K(y,K(z,u)). K(x,y / z) * K(z \ y,x) = K(x,K(z,y)). K(x,K(y,z)) * K(x,y \ z) = K(x,z / y). x * K(y,x / z) = T(x,K(y,z)) * K(y,z \ x). T(x,K(y,z)) * K(y,z \ x) = x * K(y,x / z). x != y * K(z,y / u) | x = K(z,u \ y) * y. T(x,K(y,z)) * K(y,z \ x) = K(y,z \ x) * x. x * K(y,z) != K(y,z) * u | x = T(u,K(y,z)). T(x,K(y,z)) = T(x,K(y,z \ x)). T(x,K(y,z \ x)) = T(x,K(y,z)). x != T(y,K(z,u \ w)) | x = T(y,K(z,w \ u)). T(x,K(y,z)) = T(x,K(y,x \ z)). T(x,K(y,x \ z)) = T(x,K(y,z)). x != T(y,K(z,y \ u)) | x = T(y,K(z,u / y)). T(x,K(y,z)) = T(x,K(y,z / x)). T(x,K(y,z / x)) = T(x,K(y,z)). T(x,K(y,z)) = T(x,K(y,z * x)). T(x,K(y,z * x)) = T(x,K(y,z)). T(x,K(y,z)) * K(y,z * x) = K(y,z * x) * x. x != T(y,K(z,u)) * K(z,w) | x = T(y * K(z,w),K(z,u)). K(x,y * z) * z = T(z * K(x,y * z),K(x,y)). T(x * K(y,z * x),K(y,z)) = K(y,z * x) * x. (K(x,y * z) * z) / T(K(x,y),z * K(x,y * z)) = (z * K(x,y * z)) / T(T(K(x,y),z * K(x,y * z)),z * K(x,y * z)). (x * K(y,z * x)) / T(T(K(y,z),x * K(y,z * x)),x * K(y,z * x)) = (K(y,z * x) * x) / T(K(y,z),x * K(y,z * x)). (x * K(y,z * x)) / T(T(K(y,z),x * K(y,z * x)),x * K(y,z * x)) = (K(y,z * x) * x) / K(y,T(z,x * K(y,z * x))). (x * K(y,z * x)) / T(T(K(y,z),x * K(y,z * x)),x * K(y,z * x)) = (K(y,z * x) * x) / K(y,T(z,x)). x != y / K(z,T(u,w)) | x = y * K(u,T(z,w)). (x * K(y,z * x)) / T(T(K(y,z),x * K(y,z * x)),x * K(y,z * x)) = (K(y,z * x) * x) * K(z,T(y,x)). x != (K(y,z) * u) * K(w,T(y,v5)) | x = K(y,z) * (u * K(w,T(y,v5))). (x * K(y,z * x)) / T(T(K(y,z),x * K(y,z * x)),x * K(y,z * x)) = K(y,z * x) * (x * K(z,T(y,x))). (x * K(y,z * x)) / T(T(K(y,z),x * K(y,z * x)),x * K(y,z * x)) = K(y,z * x) * (K(z,y) * x). (x * K(y,z * x)) / K(y,z) = K(y,z * x) * (K(z,y) * x). (x * K(y,z * x)) * K(z,y) = K(y,z * x) * (K(z,y) * x). x * (K(y,z * x) * K(z,y)) = K(y,z * x) * (K(z,y) * x). K(x,y * z) * (K(y,x) * z) = z * (K(x,y * z) * K(y,x)). x != K(y,z * L(y,u,w)) * (K(z,y) * L(y,u,w)) | x = L(L(y,z,y),u,w). L(x,y,z) * (K(x,u * L(x,y,z)) * K(u,x)) = L(L(x,u,x),y,z). L(x,y,z) * (K(u,x) * K(x,u * L(x,y,z))) = L(L(x,u,x),y,z). L(x,y,z) * (a(x,u,L(x,y,z)) \ 1) = L(L(x,u,x),y,z). L(x,y,z) \ L(L(x,u,x),y,z) = a(x,u,L(x,y,z)) \ 1. (a(x,y,L(x,z,u)) \ 1) \ w = w * a(L(x,z,u),y,L(x,z,u)). x * a(L(y,z,u),w,L(y,z,u)) = (a(y,w,L(y,z,u)) \ 1) \ x. 1 * x != (y \ 1) \ 1 | x = y. a(L(x,y,z),u,L(x,y,z)) = a(x,u,L(x,y,z)). x != a(y,z,L(y,u,w)) | x = a(y,z,y). a(L(x,y,z),u,L(x,y,z)) = a(x,u,x). x != a(L(y,z / y,u),w,L(y,z / y,u)) | x = L(a(y,w,y),z,u). a(x,y,x) = L(a(x,y,x),z,u). L(a(x,y,x),z,u) = a(x,y,x). x != L(a(y,z,y),z,u) | x = a(y,z * K(u,z),y). a(x,y,x) = a(x,y * K(z,y),x). a(x,y * K(z,y),x) = a(x,y,x). L(a(x,y,x),z,u) != w | w = a(x,y,x). L(a(x,y,x),z,u) != w | a(x,y,x) = w. L(a(x,y,x),z * y,u) = a(x,(u * (z * y)) / (u * z),x). a(x,y / z,x) = a(x,z \ y,x). a(x,y \ R(y,z,u),x) = a(x,a(y,z,u),x). a(x,L(y,z,u) \ y,x) = a(x,a(u,z,y),x). a(x,a(y,z,u),x) \ x = L(x,L(u,z,y) \ u,x). L(x,L(y,z,u) \ y,x) = a(x,a(u,z,y),x) \ x. x != a(y,z,y) \ y | x = L(y,z,y). L(x,L(y,z,u) \ y,x) = L(x,a(u,z,y),x). L(x,y \ R(y,z,u),x) = L(x,a(y,z,u),x). x != a(y,(z * (u * w)) / (z * u),y) | x = L(a(y,w,y),u * w,z). a(x,(y * z) \ (y * (z * u)),x) = L(a(x,u,x),z * u,y). L(a(x,y,x),z * y,u) = a(x,(u * z) \ (u * (z * y)),x). L(a(x,y,x),z * y,u) = a(x,L(y,z,u),x). a(x,y,x) = a(x,L(y,z,u),x). a(x,L(y,z,u),x) = a(x,y,x). x * a(x,y,x) = R(x,L(y,z,u),x). R(x,L(y,z,u),x) = x * a(x,y,x). x != y * a(y,z,y) | x = R(y,z,y). R(x,L(y,z,u),x) = R(x,y,x). L(x,y,z) * T(R(u,x,u),R(u,L(x,y,z),u) * x) = T(T(u,u * x) * L(x,y,z),u). L(x,y,z) * T(R(u,x,u),R(u,x,u) * x) = T(T(u,u * x) * L(x,y,z),u). L(x,y,z) * T(R(u,x,u),x * R(u,x,u)) = T(T(u,u * x) * L(x,y,z),u). L(x,y,z) * T(R(u,x,u),T(u * x,u)) = T(T(u,u * x) * L(x,y,z),u). L(x,y,z) * T(R(u,x,u),x * u) = T(T(u,u * x) * L(x,y,z),u). L(x,y,z) * T(u,x) = T(T(u,u * x) * L(x,y,z),u). T(T(x,x * y) * L(y,z,u),x) = L(y,z,u) * T(x,y). x != T(T(y,y * z) * L(z,u,w),y) | x = T(y * L(z,u,w),y * z). L(x,y,z) * T(u,x) = T(u * L(x,y,z),u * x). T(x * L(y,z,u),x * y) = L(y,z,u) * T(x,y). x * y != T(z * L(u,w,v5),z * u) | x \ (L(u,w,v5) * T(z,u)) = y. (x * L(y,z,u)) \ (L(y,z,u) * T(x,y)) = K(x * L(y,z,u),x * y). x != (y * z) \ (z * T(y,u)) | x = K(y,u) * K(z,y). K(x * L(y,z,u),x * y) = K(x,y) * K(L(y,z,u),x). K(x,y) * K(L(y,z,u),x) = K(x * L(y,z,u),x * y). a(x,y,K(z,u)) = K(z * L(u,y,x),z * u). K(x * L(y,z,u),x * y) = a(u,z,K(x,y)). K(x,(x / L(y,z,u)) * y) = a(u,z,K(x / L(y,z,u),y)). x != K(y,(y / L(z,u,w)) * z) | x = K(y,z * (L(z,u,w) \ y)). a(x,y,K(z / L(u,y,x),u)) = K(z,u * (L(u,y,x) \ z)). K(x,y * (L(y,z,u) \ x)) = a(u,z,K(x / L(y,z,u),y)). K(x,y * (L(y,z,u) \ x)) = a(u,z,K(y \ x,y)). x != a(y,z,K(u \ w,u)) | x = a(y,z,K(w,u)). K(x,y * (L(y,z,u) \ x)) = a(u,z,K(x,y)). x != K(y,z * (L(z,u,w) \ y)) | x = K(y,y * (L(z,u,w) \ z)). a(x,y,K(z,u)) = K(z,z * (L(u,y,x) \ u)). K(x,x * (L(y,z,u) \ y)) = a(u,z,K(x,y)). x != K(y,z) | x = (z / (z / y)) \ L(y,y \ z,y). a(x,y,K(z,u)) = ((z * (L(u,y,x) \ u)) / ((z * (L(u,y,x) \ u)) / z)) \ L(z,z \ (z * (L(u,y,x) \ u)),z). ((x * (L(y,z,u) \ y)) / ((x * (L(y,z,u) \ y)) / x)) \ L(x,x \ (x * (L(y,z,u) \ y)),x) = a(u,z,K(x,y)). x / (a(y,z,K(u,w)) * x) = K(u * (L(w,z,y) \ w),u). K(x * (L(y,z,u) \ y),x) = w / (a(u,z,K(x,y)) * w). x != y / (a(z,u,K(w,v5)) * y) | x = a(z,u,K(v5,w)). K(x * (L(y,z,u) \ y),x) = a(u,z,K(y,x)). a(x,y,a(z,u,K(w,v5))) = a(x,y,K(L(w,u,z) \ w,v5)). a(x,y,K(L(z,u,w) \ z,v5)) = a(x,y,a(w,u,K(z,v5))). K(a(x,y,z),u) * a(x * y,z,a(x,y,K(z,u))) = K(L(z,y,x) \ z,u). K(a(x,y,z),u) * 1 = K(L(z,y,x) \ z,u). K(L(x,y,z) \ x,u) = K(a(z,y,x),u) * 1. K(L(x,y,z) \ x,u) = K(a(z,y,x),u). x / (K(a(y,z,u),w) * x) = K(w,L(u,z,y) \ u). K(x,L(y,z,u) \ y) = w / (K(a(u,z,y),x) * w). x != y / (K(z,u) * y) | x = K(u,z). K(x,L(y,z,u) \ y) = K(x,a(u,z,y)). x * K(x,a(y,z,u)) = T(x,L(u,z,y) \ u). T(x,L(y,z,u) \ y) = x * K(x,a(u,z,y)). K(x,y \ R(y,z,u)) = K(x,a(y,z,u)). x != K(y,z \ R(z,u,w)) | x = K(y,z) * K(R(z,u,w),y). K(x,a(y,z,u)) = K(x,y) * K(R(y,z,u),x). K(x,y) * K(R(y,z,u),x) = K(x,a(y,z,u)). x != K(y,z \ R(z,u,w)) | x = K(z \ R(z,u,w),y). K(x,a(y,z,u)) = K(y \ R(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)). x != K(y,z) * K(R(z,u,w),y) | x = K(z,y) * K(y,R(z,u,w)). 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)). K(x,a(y,z,u)) = a(K(x,y),z,u). x != K(y,z) * K(z,R(y,u,w)) | x = a(K(z,y),u * y,w). K(x,a(y,z,u)) = a(K(x,y),z * y,u). a(K(x,y),z * y,u) = K(x,a(y,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)). x != a(K(y,z),u,w) | x = a(K(z,y),u,w). K(x,a(y,z,u)) = a(K(y,x),z,u). x != K(y,a(z,u,w)) | x = K(a(z,u,w),y). a(K(x,y),z,u) = K(a(y,z,u),x). K(a(x,y,z),u) = a(K(u,x),y,z). x != a(K(y,z),u,w) | x = K(y,a(z,u,w)). K(x,a(y,z,u)) = K(y,a(x,z,u)). x * K(y,a(z,u,x)) = L(x,u,K(z,y)). a(K(x,y),x * z,u) = K(y,a(x,z,u)). x != y * K(z,a(u,w,y)) | x = L(y,w,K(u,z)). L(x,y * z,K(y,u)) = L(x,z,K(y,u)). K(R(x,y,z) \ x,u) = K(u,a(x,x * y,z)). K(x,a(y,y * z,u)) = a(K(y,x),z,u). K(x,a(y,y * z,u)) != w | a(K(x,y),z,u) = w. x != K(y,z \ R(z,u,w)) | x = K(y,a(z,u,w)). K(x,a(y,z,L(u,z,y))) = K(x,a(y,z,u)). x != a(K(y,z),y,u) | x = 1. K(a(x,y,z),y) = 1. 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). T(x,L(y,z,u) \ y) = T(x,a(u,z,y)). x != K(y,a(z,u,w)) | x = K(y,z \ R(z,u,w)). a(K(x,y),z * y,u) = K(x,y \ R(y,z,u)). K(x,y \ R(y,z,u)) = a(K(x,y),z * y,u). a(K(x,y),z * y,u) = T(y \ R(y,z,u),x) \ (y \ R(y,z,u)). T(x \ R(x,y,z),u) \ (x \ R(x,y,z)) = a(K(u,x),y * x,z). (x * K(L(y,z,u) \ y,x)) \ L(x,x \ (x * (L(y,z,u) \ y)),x) = a(u,z,K(x,y)). (x * K(L(y,z,u) \ y,x)) \ L(x,L(y,z,u) \ y,x) = a(u,z,K(x,y)). (x * K(L(y,z,u) \ y,x)) \ L(x,a(u,z,y),x) = a(u,z,K(x,y)). K(x,L(y,z,u) \ y) * (x \ L(x,a(u,z,y),x)) = a(u,z,K(x,y)). a(x,y,K(z,u)) = z \ L(T(z,L(u,y,x) \ u),a(x,y,u),z). x \ L(T(x,L(y,z,u) \ y),a(u,z,y),x) = a(u,z,K(x,y)). x \ L(T(x,a(y,z,u)),a(y,z,u),x) = a(y,z,K(x,u)). K(x,x * a(y,z,u)) = a(y,z,K(x,u)). T(x \ R(x,y,z),u) \ (w \ (w * (x \ R(x,y,z)))) = a(K(u,x),y * x,z). (x \ T(x * (y \ R(y,z,u)),x)) \ (w \ (w * (y \ R(y,z,u)))) = a(K(x,y),z * y,u). K(x,x * (y \ R(y,z,u))) = a(K(x,y),z * y,u). a(K(x,y),z * y,u) = ((x * (y \ R(y,z,u))) / ((x * (y \ R(y,z,u))) / x)) \ L(x,x \ (x * (y \ R(y,z,u))),x). ((x * (y \ R(y,z,u))) / ((x * (y \ R(y,z,u))) / x)) \ L(x,x \ (x * (y \ R(y,z,u))),x) = a(K(x,y),z * y,u). (x * K(y \ R(y,z,u),x)) \ L(x,x \ (x * (y \ R(y,z,u))),x) = a(K(x,y),z * y,u). (x * K(y \ R(y,z,u),x)) \ L(x,y \ R(y,z,u),x) = a(K(x,y),z * y,u). (x * K(y \ R(y,z,u),x)) \ L(x,a(y,z,u),x) = a(K(x,y),z * y,u). K(x,y \ R(y,z,u)) * (x \ L(x,a(y,z,u),x)) = a(K(x,y),z * y,u). a(K(x,y),z * y,u) * (x \ L(x,a(y,z,u),x)) = a(K(x,y),z * y,u). x != y * (z \ L(z,u,z)) | x = a(z,u,z) \ y. a(K(x,y),z * y,u) = a(x,a(y,z,u),x) \ a(K(x,y),z * y,u). a(x,a(y,z,u),x) \ a(K(x,y),z * y,u) = a(K(x,y),z * y,u). a(x,a(y,z,u),x) \ K(x,a(y,z,u)) = a(K(x,y),z * y,u). x != a(y,z,y) \ K(y,u) | x = y \ L(T(y,u),z,y). a(K(x,y),z * y,u) = x \ L(T(x,a(y,z,u)),a(y,z,u),x). x \ L(T(x,a(y,z,u)),a(y,z,u),x) = a(K(x,y),z * y,u). K(x,x * a(y,z,u)) = a(K(x,y),z * y,u). x != a(K(y,z),u * z,w) | x = a(K(y,z),u,w). K(x,x * a(y,z,u)) = a(K(x,y),z,u). x != K(y,y * a(z,u,w)) | x = a(z,u,K(y,w)). a(K(x,y),z,u) = a(y,z,K(x,u)). (T(x,x \ y) * a(z,u,K(w,v5))) \ ((x \ y) \ y) = a(K(z,w),u,v5). x != (T(y,y \ z) * a(u,w,K(v5,v6))) \ ((y \ z) \ z) | x = a(u,w,K(v6,v5)). a(K(x,y),z,u) = a(x,z,K(u,y)). x != a(y,z,K(u,z * u)) | x = 1. a(K(x,y * z),y,z) = 1. x != a(K(y,z),y * u,w) | x = K(z,a(y,u,w)). 1 = K((x * y) * z,a(x,y,z)). K((x * y) * z,a(x,y,z)) = 1. K(x * (y * z),a(x,y,L(z,y,x))) = 1. x != K(y,a(z,u,L(w,u,z))) | x = K(y,a(z,u,w)). 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. L(x,y,z) \ x = a(z,y,x). x \ R(x,y,z) = a(x,y,z). L(x \ R(x,y,z),u,w) = a(L(x,u,w),y,z). T(x \ R(x,y,z),u) = a(T(x,u),y,z). a(x,y,z) = x * R(x \ 1,y,z). x * R(x \ 1,y,z) = a(x,y,z). x != R(y,z,u) \ R(R(y,z,u),w,v5) | x = R(y \ R(y,w,v5),z,u). 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(x,y,z) \ 1 = R(x,y,z) \ x. R(x,y,z) \ x = a(x,y,z) \ 1. a(x,y,z) * (x * u) = R(x,y,z) * u. a(x,y,z) * u = z * (L(z,y,x) \ u). x * (L(x,y,z) \ u) = a(z,y,x) * u. T(a(x,y,z),u) = a(T(x,u),y,z). x != T(a(y,z,u),z) | x = a(y,z,u). a(T(x,y),y,z) = a(x,y,z). a(T(x,y),z,u) \ a(x,z,u) != w | K(y,a(x,z,u)) = w. K(a(x,y,z) \ 1,u) = K(u,a(x,x * y,z)). K(a(x,y,z) \ 1,u) != w | a(K(u,x),y,z) = w. L(x,y,z) \ (x * u) = a(z,y,x) * u. L(x,y,z) \ x = a(T(z,x),y,x). x * (y * a(x,z,y)) = R(x,z,y) * y. L(a(x,y,z),u,w) = a(L(x,u,w),y,z). x != a(L(y,z,u),R(u,z,y),w) | x = a(y,u,w). L(a(x,R(y,z,x),u),z,y) = a(x,y,u). a(x,T(y,x),z) = a(x,y,z). a(x / y,y,z) = a(y * x,y,z). a(x / y,x,z) = a(x * y,x,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). 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)). a(K(x,y * z),y,u) = K(x,a(z * y,z,u)). K(x,a(y * z,y,u)) = a(K(x,z * y),z,u). x != a(K(y,z),u,w) | x = K(z,a(y,u,w)). 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)). x * R(y,z,x) = a(y,z,x) * (x * y). a(x,y,z) * (z * x) = z * R(x,y,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). L(x,a(y,z,u),z) = x. (x \ a(y,x,z)) \ 1 = a(y,x,z) \ x. (x \ a(y,x,z)) \ u = a(y,x,z) \ (x * u). (x * a(y,x,z)) * u = x * (a(y,x,z) * u). (a(x,y,z) * y) * u = y * (a(x,y,z) * u). (a(x,y,z) \ y) * u = (y \ a(x,y,z)) \ u. (x \ a(y,x,z)) \ u = (a(y,x,z) \ x) * u. x != (y \ a(z,y,u)) \ w | x = a(z,y,u) \ (y * 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. L(x,y,a(z,y,u)) = x. (a(x,y,z) * y) * u = a(x,y,z) * (y * u). x != (a(y,z,u) * z) * w | x = z * (a(y,z,u) * w). a(x,y,z) * (y * u) = y * (a(x,y,z) * u). (x * y) * z != x * (a(u,x,w) * y) | T(a(u,x,w),x * y) = z. T(a(x,y,z),y * u) = (y * u) \ (y * (a(x,y,z) * u)). (x * y) \ (x * (a(z,x,u) * y)) = T(a(z,x,u),x * 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). x != L(y,z,u) \ y | x = a(u,z,y). a(T(x,y),z,y) = a(x,z,y). x != R(y \ R(y,z,u),u,w) | x = L(u,z,y) \ u. 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). x != a(R(y,y * z,u),w,v5) | x = a(R(y,z,u),w,v5). R(a(x,y,z),x * u,w) = a(R(x,u,w),y,z). (x * y) * L(a(x,z,y),y,x) = R(x,z,y) * 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 * (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,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). x != L(a(T(y,z),u,w),z,u) | x = T(a(y,u,w),u * 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,a(y,z,u)) = K(z * x,a(y,z,u)). K(x * y,a(z,x,u)) = K(y,a(z,x,u)). x != K(y,a(z,u,w)) | x = K(z,a(y,u,w)). 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)). x != K(y * z,a(u,y,w)) | x = K(u,a(z * y,z,w)). 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)). x != K(y,a(z * u,z,w)) | x = K(z,a(y,u,w)). 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)). x != L(y,z * u,K(z,w)) | x = L(y,u,K(z,w)). L(x,y,K(z,z * u)) = L(x,u,K(z,y)). x != L(y,z,K(u,u * w)) | x = L(y,z,a(u,w,w)). 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)). x != L(y,z,K(u,w)) | x = L(y,w,K(u,z)). L(x,y,a(z,u,u)) = L(x,y,K(z,u)). x != L(y,z,a(u,w,w)) | x = L(y,z,a(w,u,w)). 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(x,y,K(z,u)) = x. end_of_list.