============================== Prover9 =============================== Prover9 (64) version 2009-02A, February 2009. Process 3835 was started by veroff on proof, Mon Feb 20 13:26:15 2012 The command was "prover9 -f lc.in". ============================== end of head =========================== ============================== INPUT ================================= % Reading from file lc.in assign(order,kbo). set(lex_order_vars). set(para_units_only). % set(para_units_only) -> assign(para_lit_limit, 1). clear(back_demod). set(restrict_denials). set(para_from_small). assign(max_weight,5). formulas(assumptions). 1 * x = x. x * 1 = x. x \ (x * y) = y. x * (x \ y) = y. (x * y) / y = x. (x / y) * y = x. x * y = u & x * z = u -> y = z. y * x = u & z * x = u -> y = z. x * y = x * z -> y = z. y * x = z * x -> y = z. (x * (y * z)) \ ((x * y) * z) = a(x,y,z). (x * y) \ (y * x) = K(y,x). (y * x) \ (y * (x * u)) = L(u,x,y). ((u * x) * y) / (x * y) = R(u,x,y). x \ (u * x) = T(u,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(u,x),y) = T(T(u,y),x). T(L(u,x,y),z) = L(T(u,z),x,y). T(R(u,x,y),z) = R(T(u,z),x,y). L(R(u,x,y),z,w) = R(L(u,z,w),x,y). L(L(u,x,y),z,w) = L(L(u,z,w),x,y). R(R(u,x,y),z,w) = R(R(u,z,w),x,y). end_of_list. formulas(goals). a(a(x,y,z),u,w) = 1 # label("aa1"). a(x,a(y,z,u),w) = 1 # label("aa2"). a(x,y,a(z,u,w)) = 1 # label("aa3"). K(a(x,y,z),u) = 1 # label("Ka"). a(K(x,y),z,u) = 1 # label("aK1"). a(x,K(y,z),u) = 1 # label("aK2"). a(x,y,K(z,u)) = 1 # label("aK3"). end_of_list. formulas(sos). (x * (x * y)) * z = x * (x * (y * z)) # label("LC"). end_of_list. formulas(hints). a(K(x,y),z,u) = 1. 1 * x = x. x * 1 = x. x \ (x * y) = y. x * (x \ y) = y. (x * y) / y = x. (x / y) * y = x. (x * (y * z)) \ ((x * y) * z) = a(x,y,z). (x * y) \ (y * x) = K(y,x). (x * y) \ (x * (y * z)) = L(z,y,x). ((x * y) * z) / (y * z) = R(x,y,z). x \ (y * x) = T(y,x). T(T(x,y),z) = T(T(x,z),y). T(L(x,y,z),u) = L(T(x,u),y,z). T(R(x,y,z),u) = R(T(x,u),y,z). L(R(x,y,z),u,w) = R(L(x,u,w),y,z). R(L(x,y,z),u,w) = L(R(x,u,w),y,z). L(L(x,y,z),u,w) = L(L(x,u,w),y,z). R(R(x,y,z),u,w) = R(R(x,u,w),y,z). (x * (x * y)) * z = x * (x * (y * z)). a(K(c1,c2),c3,c4) != 1. 1 \ x = x. x \ x = 1. x \ ((x * y) * 1) = y. x \ (y * (y \ (x * z))) = z. x / 1 = x. x / (y \ x) = y. (x / y) \ x = y. (x * (y * z)) * a(x,y,z) = (x * y) * z. ((x / y) * (y * z)) \ (x * z) = a(x / y,y,z). (x * y) * K(y,x) = y * x. x \ ((y \ x) * y) = K(y \ x,y). ((x \ y) * x) \ y = K(x,x \ y). x \ (1 * (x * y)) = L(y,x,1). (x * 1) \ (x * y) = L(y,1,x). (x * y) * L(z,y,x) = x * (y * z). x \ (y * ((y \ x) * z)) = L(z,y \ x,y). (x * y) \ (x * z) = L(y \ z,y,x). L(x \ y,x,z) = (z * x) \ (z * y). x \ ((x / y) * (y * z)) = L(z,y,x / y). ((x * y) * (y \ z)) / z = R(x,y,y \ z). R(x,y,z) * (y * z) = (x * y) * z. (x * y) / (z * y) = R(x / z,z,y). R(x / y,y,z) = (x * z) / (y * z). T(x,x) = x. x * T(y,x) = y * x. (x \ y) \ y = T(x,x \ y). T(x,x \ y) = (x \ y) \ y. x \ y = T(y / x,x). T(x / y,y) = y \ x. x * (x * y) = (x * (x * (y * z))) / z. (x * (x * (y * z))) / z = x * (x * y). x = (y * (y * z)) \ (y * (y * (z * x))). (x * (x * y)) \ (x * (x * (y * z))) = z. x * (y * z) = x \ ((x * (x * y)) * z). x \ ((x * (x * y)) * z) = x * (y * z). (x * (x * 1)) * y = x * (x * y). (x * y) * z = x * (x * ((x \ y) * z)). x * (x * ((x \ y) * z)) = (x * y) * z. (x * (y * (y * (z * u)))) \ ((x * (y * (y * z))) * u) = a(x,y * (y * z),u). (x * (x * (y * (z * u)))) \ (((x * (x * y)) * z) * u) = a(x * (x * y),z,u). (x * (x * (y * z))) \ ((x * (x * y)) * (z * u)) = L(u,z,x * (x * y)). (x * (y * (y * z))) \ (x * (y * (y * (z * u)))) = L(u,y * (y * z),x). ((x * (x * (y * z))) * u) / (z * u) = R(x * (x * y),z,u). (x * (x * (y * z))) / ((x * y) * z) = R(x,x * y,z). x = ((x * y) / 1) / y. ((x * y) / 1) / y = x. T(x,y) = T(T(x,y),x). T(T(x,y),x) = T(x,y). (x * (y * z)) / L(z,y,x) = x * y. (x * y) / T(x,y) = y. R(x,y,z) \ ((x * y) * z) = y * z. x \ (y * 1) = x \ y. T(x * (x * y),x) = x * (y * x). T((x * y) / x,x) = y. x = (y * T(x,y)) / y. (x * T(y,x)) / x = y. (x * y) \ (x * (z * y)) = L(T(z,y),y,x). T(x,y) \ (x * y) = T(y,T(x,y)). x * T(T(y,x),z) = T(y,z) * x. x * L(T(y,x),z,u) = L(y,z,u) * x. x * R(T(y,x),z,u) = R(y,z,u) * x. T(R(x,y,z),y * z) = (y * z) \ ((x * y) * z). (x * y) \ ((z * x) * y) = T(R(z,x,y),x * y). T(x \ y,z) = T(T(y / x,z),x). T(T(x / y,z),y) = T(y \ x,z). ((x * y) / ((1 / z) * z)) / y = x. K(T(x,y),x) = 1. T(x,T(x,y)) = x. x * T(x,y) = T(x,y) * x. T(x,y) * x = x * T(x,y). (x * y) / T(y,T(x,y)) = T(x,y). x \ (y * (z * (z \ 1))) = x \ y. K(x,(y * x) / y) = 1. T(x,(y * x) / y) = x. K(x,y) \ (x * y) = T(y * x,K(x,y)). x \ (x * y) = L(y,x,1). L(x,y,1) = x. a(1,x,y) = 1. x \ (x * y) = L(y,1,x). L(x,1,y) = x. K(x \ 1,x) = (x \ 1) * x. (x \ 1) * x = K(x \ 1,x). x \ 1 = K(x \ 1,x) / x. K(x \ 1,x) / x = x \ 1. x = (x \ 1) \ K(x \ 1,x). (x \ 1) \ K(x \ 1,x) = x. (x * x) * y = x * (x * y). x * x = (x * (x * y)) / y. (x * (x * y)) / y = x * x. x = (y * y) \ (y * (y * x)). (x * x) \ (x * (x * y)) = y. ((x * (x * y)) * z) / (y * z) = R(x * x,y,z). x \ (y * (y * x)) = T(y * y,x). x * (x * T(y,x * x)) = y * (x * x). x = L(x,y,y). L(x,y,y) = x. T(x * y,x) = x * ((x \ y) * x). x * ((x \ y) * x) = T(x * y,x). x * T(x \ y,z) = T(y / x,z) * x. T(x / y,z) * y = y * T(y \ x,z). (x * T(x \ y,z)) / x = T(y / x,z). R(x,1 / y,y) / y = x * (1 / y). (x * y) \ x = L(y \ 1,y,x). L(x \ 1,x,y) = (y * x) \ y. L((x \ y) \ 1,x \ y,x) = y \ x. L(x \ 1,x,y / x) = y \ (y / x). x / L(y \ 1,y,x) = x * y. (x \ y) * x = x \ T(x * y,x). x \ T(x * y,x) = (x \ y) * x. x * K(x \ 1,x) = T(x * 1,x). x \ T(y,x) = (x \ (x \ y)) * x. (x \ (x \ y)) * x = x \ T(y,x). x * K(x \ 1,x) = T(x,x). x * K(x \ 1,x) = x. K(x \ 1,x) = 1. T(x \ 1,x) = x \ 1. (x \ 1) * x = 1. 1 / x = x \ 1. (x \ 1) \ 1 = x. x * (1 / x) = 1. T(x,x \ 1) = x. L(x,x \ 1,y) = (y * (x \ 1)) \ y. x / L(y,y \ 1,x) = x * (y \ 1). (x * 1) \ ((x * y) * (1 / y)) = a(x,y,1 / y). T(x,y) = T(T(x,y),x \ 1). T(T(x,y),x \ 1) = T(x,y). K(T(x,y),x \ 1) = 1. K(x \ y,(y / x) \ 1) = 1. K(x,((y * x) / y) \ 1) = 1. T(x \ y,(y / x) \ 1) = x \ y. T(x,((y * x) / y) \ 1) = x. (x \ y) \ (x \ T(y,x)) = K(x \ (x \ y),x). x * L(y,z \ x,z) = z * ((z \ x) * y). x * L(y,z,x / z) = (x / z) * (z * y). (x * (y * z)) \ (x * (y * (z * u))) = L(L(u,z,y),y * z,x). (x * y) * L(z,K(x,y),y * x) = (y * x) * (K(x,y) * z). L(x \ (y \ z),x,y) = (y * x) \ z. L(x \ (y * x),x,y) = T(y,y * x). (x * y) / L(z \ y,z,x) = x * z. L(x \ T(y,z),x,z) = (z * x) \ (y * z). L(x \ (y \ ((y * x) * z)),x,y) = z. R(x,x,y) = x. (R(x,y,z) * y) \ ((x * y) * z) = L(z,y,R(x,y,z)). L(R(x,y,z),u,w) * (y * z) = (L(x,u,w) * y) * z. R(R(x,y,z),u,w) * (y * z) = (R(x,u,w) * y) * z. T(x,y) = R(T(x,y),x,z). R(T(x,y),x,z) = T(x,y). L(x,y,z) = L(R(x,L(x,y,z),u),y,z). L(R(x,L(x,y,z),u),y,z) = L(x,y,z). R(x,y,z) = R(R(x,y,z),x,u). R(R(x,y,z),x,u) = R(x,y,z). R(T(x,y),z,u) = R(R(T(x,y),z,u),x,w). R(R(T(x,y),z,u),x,w) = R(T(x,y),z,u). T(x,y) * (x * z) = (T(x,y) * x) * z. (T(x,y) * x) * z = T(x,y) * (x * z). R(x,y,z) * (x * u) = (R(x,y,z) * x) * u. (R(x,y,z) * x) * u = R(x,y,z) * (x * u). R(1 / x,x,y) = y / (x * y). R((x / y) / z,z,y) = x / (z * y). T((x * y) / (z * y),u) = R(T(x / z,u),z,y). R(x,x \ 1,y) = y / ((x \ 1) * y). (x * y) / L(z,y / z,x) = x * (y / z). R(x,x \ y,z) \ (y * z) = (x \ y) * z. R(x,y \ 1,y) / y = x * (1 / y). L(K(x,y) \ ((y * x) \ z),K(x,y),y * x) = (x * y) \ z. (x * x) \ y = x \ (x \ y). L(x \ L(y \ z,y,u),x,u * y) = ((u * y) * x) \ (u * z). x \ (x \ (y * (x * x))) = T(y,x * x). L(T(x,y),y,x) = T(x,x * y). L(x,(y * x) / y,x) = T(x,x * ((y * x) / y)). T(x,x * ((y * x) / y)) = L(x,(y * x) / y,x). x / L(y \ z,y,x / z) = (x / z) * y. R(x,y \ 1,y) / y = x * (y \ 1). (x * (y \ 1)) * y = R(x,y \ 1,y). (x * (y \ 1)) \ R(x,y \ 1,y) = y. x * y = R(x / (y \ 1),y \ 1,y). R(x / (y \ 1),y \ 1,y) = x * y. (x * (x * y)) / z = x * (x * (y / z)). (x * (x * y)) \ (x * (x * z)) = y \ z. x \ ((x * y) * z) = x * ((x \ y) * z). x * L(x,y,z) = L(x,y,z) * x. L(x,y,z) * x = x * L(x,y,z). x * L(x \ 1,y,z) = L(x \ 1,y,z) * x. L(x \ 1,y,z) * x = x * L(x \ 1,y,z). x * T(y,y * x) = L(y,x,y) * x. L(x,y,z) = (x * L(x,y,z)) / x. (x * L(x,y,z)) / x = L(x,y,z). x = T(x,L(x,y,z)). T(x,L(x,y,z)) = x. L(x,L(x,y,z),x) = T(x,x * L(x,y,z)). T(x,x * L(x,y,z)) = L(x,L(x,y,z),x). (x \ y) * T(x,y) = L(x,x \ y,x) * (x \ y). L(x,x \ y,x) * (x \ y) = (x \ y) * T(x,y). x * R(T(T(y,x),z),u,w) = R(T(y,z),u,w) * x. x * R(x,y,z) = R(x,y,z) * x. R(x,y,z) * x = x * R(x,y,z). x * R(x \ y,z,u) = R(y / x,z,u) * x. R(x / y,z,u) * y = y * R(y \ x,z,u). (x \ y) * R((x \ y) \ y,z,u) = R(x,z,u) * (x \ y). R(x,y,z) * (u * u) = u * (u * R(T(x,u * u),y,z)). x * (x * R(T(y,x * x),z,u)) = R(y,z,u) * (x * x). x * R(x \ 1,y,z) = R(x \ 1,y,z) * x. R(x \ 1,y,z) * x = x * R(x \ 1,y,z). x = T(x,R(x,y,z)). T(x,R(x,y,z)) = x. T(x / y,y) = T(y \ x,R(x / y,z,u)). T(x \ y,R(y / x,z,u)) = T(y / x,x). x * T(y,x * x) = x \ (y * (x * x)). x \ (y * (x * x)) = x * T(y,x * x). T(x / (x * y),z) * (x * y) = (x * y) * T(L(y \ 1,y,x),z). T((x * y) / (x * z),u) * (x * z) = (x * z) * T(L(z \ y,z,x),u). (x * T(y,z)) / x = T((x * y) / x,z). x = L(x,y,T(y,z)). L(x,y,T(y,z)) = x. (x * T(x,y)) * z = T(x,y) * (x * z). L(x,(y * z) / y,z) = x. (x * y) / z = x * (x * ((x \ y) / z)). x * (x * ((x \ y) / z)) = (x * y) / z. (x * (x * y)) \ (x * x) = y \ 1. (x * y) \ (x * (x * z)) = (x \ y) \ z. x \ (y * x) = T(y,y * (y * x)). T(x,x * (x * y)) = y \ (x * y). (x * y) \ (x * x) = (x \ y) \ 1. (x * x) / (y \ 1) = x * (x * y). ((x * y) * z) \ (x * x) = ((x \ y) * z) \ 1. T(x,x * (x * y)) = T(x,y). T(x,x * y) = T(x,x \ y). T(x,x \ y) = T(x,x * y). T(x,x * (y * x)) = T(x,T(y,x)). T(x * y,(x * y) * (y * x)) = T(x * y,K(y,x)). T(x,x * y) = (x \ y) \ y. (x \ y) * T(x,x * y) = y. T(x / y,x) = ((x / y) \ y) \ y. x / T(y,y * x) = y \ x. (x \ y) * ((x \ y) * (T(x,x * y) * z)) = ((x \ y) * y) * z. (x \ (x \ y)) * T(x,y) = x \ y. ((x \ y) * (T(x,x * y) * z)) \ (y * z) = a(x \ y,T(x,x * y),z). K(x,y) / T(y * x,x * y) = (y * x) \ K(x,y). x \ (y * y) = (y \ (y \ x)) \ 1. (x \ (x \ y)) \ 1 = y \ (x * x). L(x \ y,x,y) = (y \ x) \ 1. L(K(x,y),y * x,x * y) = ((x * y) \ (y * x)) \ 1. T((x \ y) \ 1,z) = L(T(y \ x,z),y,x). L(T(x \ y,z),x,y) = T((y \ x) \ 1,z). (x \ ((y * x) / y)) \ 1 = ((y * x) / y) \ x. (x * x) / y = x * (x * (y \ 1)). x * (x * (y \ 1)) = (x * x) / y. x \ (y * z) = x * ((x \ (x \ y)) * z). x * ((x \ (x \ y)) * z) = x \ (y * z). L(x \ (y * ((y \ x) * z)),x,y) = z. L(x \ (y * z),x,y) = (y \ x) \ z. L(x \ y,x,z) = (z \ x) \ (z \ y). L(x \ (y * z),x,z) = (z \ x) \ T(y,z). L((x * y) \ z,x * y,x) = y \ (x \ z). (x \ y) / L(z \ y,z,x) = x \ z. L(x \ y,x,x / z) = z \ ((x / z) \ y). (x \ y) \ (x \ z) = (x * y) \ (x * z). L(x \ L(y \ z,y,u),x,u \ y) = ((u \ y) * x) \ (u \ z). (x \ 1) / (y \ x) = x \ (x \ y). (x \ 1) / y = x \ (x \ (x / y)). x \ (x \ (x / y)) = (x \ 1) / y. x * ((x \ 1) / y) = x \ (x / y). ((x \ 1) / y) \ 1 = (x / y) \ (x * x). x * T(x,y) = T(x * T(x,y),T(x,y)). T(x * T(x,y),T(x,y)) = x * T(x,y). (x * T(x,y)) * (x \ z) = T(x,y) * z. x * (x * y) = (x * z) / (y \ (x \ z)). (x * y) / (z \ (x \ y)) = x * (x * z). x \ (y * (y * z)) = (y \ (y \ x)) \ z. (x \ (x \ y)) \ z = y \ (x * (x * z)). (x * y) \ ((x * z) * u) = (x \ y) \ ((x \ z) * u). (x \ y) \ ((x \ z) * u) = (x * y) \ ((x * z) * u). (x \ (x \ y)) * z = x \ (x \ (y * z)). x \ (x \ (y * z)) = (x \ (x \ y)) * z. (x \ (x \ y)) * (x * x) = T(y,x * x). T(x,y) \ (y \ z) = (y * (x * y)) \ (y * z). (x * (y * x)) \ (x * z) = T(y,x) \ (x \ z). T(x,y) * x = T(x * T(x,y),T(x,y)). T(x * T(x,y),T(x,y)) = T(x,y) * x. x / (y \ (x \ 1)) = x * (x * y). (x \ (x \ y)) \ y = T(x * x,y). x \ (x \ y) = (x \ (x \ 1)) * y. (x \ (x \ 1)) * y = x \ (x \ y). x \ (x \ y) = (x \ (x \ z)) * (z \ y). (x \ (x \ y)) * (y \ z) = x \ (x \ z). R((x / y) / (z \ (z \ 1)),z \ (z \ 1),y) = x / (z \ (z \ y)). ((x \ 1) / y) * (x * x) = T(x / y,x * x). T(T(x,y) * x,T(x,y)) = T(x,y) * x. x \ y = (z \ (z \ x)) \ (z \ (z \ y)). (x \ (x \ y)) \ (x \ (x \ z)) = y \ z. (x \ y) * ((x * y) \ z) = x \ (x \ z). x = (T(x,y) \ x) * T(x,y). (T(x,y) \ x) * T(x,y) = x. T(x,y) \ x = x / T(x,y). x / T(x,y) = T(x,y) \ x. ((x * y) * z) / T(x * (y * z),a(x,y,z)) = a(x,y,z). x \ T(y * x,y) = L(y,y \ x,y). L(x,x \ y,x) = y \ T(x * y,x). L(L(x,y \ z,y),z,y) = x. L(L(x,y,z),z * y,z) = x. L(L(x,y,z / y),z,z / y) = x. x = L(x,y \ 1,y). L(x,y \ 1,y) = x. L(x,y,y \ 1) = x. x \ y = ((x \ 1) * x) \ ((x \ 1) * y). ((x \ 1) * x) \ ((x \ 1) * y) = x \ y. x = L(L(x,y * z,y),z,y). L(L(x,y * z,y),z,y) = x. L(x,y * z,y) = z \ (y \ ((y * z) * x)). x \ (y \ ((y * x) * z)) = L(z,y * x,y). L(L(x,y,z),z * y,z) = R(x,L(x,y,z),u). R(x,L(x,y,z),u) = L(L(x,y,z),z * y,z). L((x \ y) \ z,x * y,x) = y \ (x * z). L(x,y * z,y) = L(x,y \ z,y). L(x,y \ z,y) = L(x,y * z,y). L(x,y * (y * z),y) = L(x,z,y). L(L(x,y * z,z),T(y,z),z) = x. L(L(x,y * z,z * y),K(y,z),z * y) = x. x \ T(y * x,y) = L(y,y * x,y). L(x,x * y,x) = y \ T(x * y,x). 1 \ ((x \ 1) * y) = x \ y. x \ y = (x \ 1) * y. (x \ 1) * y = x \ y. x \ 1 = (x \ y) / y. (x \ y) / y = x \ 1. x * ((x \ 1) * y) = y. (x \ 1) * (x * y) = y. (x \ (y * z)) \ (((x \ 1) * y) * z) = a(x \ 1,y,z). ((x * (y \ 1)) * z) / (y \ z) = R(x,y \ 1,z). x \ (y \ x) = T(y \ 1,x). T(x \ 1,y) = y \ (x \ y). x \ T(y,x \ 1) = y * (x \ 1). x * T(y \ 1,x) = y \ x. (x \ y) * K(y,x \ 1) = y * (x \ 1). x \ T(T(y,x \ 1),z) = T(y,z) * (x \ 1). x * y = (x \ 1) \ y. (x \ 1) \ y = x * y. (x \ y) * L(z,y,x \ 1) = (x \ 1) * (y * z). R(x,y \ 1,z) * (y \ z) = (x * (y \ 1)) * z. (x * (y \ z)) / L(z,y \ 1,x) = x * (y \ 1). R(x,x \ 1,y) = y / (x \ y). (x \ (y \ 1)) * y = R(x \ 1,y \ 1,y). R(x \ 1,y \ 1,y) = (x \ (y \ 1)) * y. x * T(y \ 1,y \ x) = L(y \ 1,x,y \ 1) * x. L(x \ 1,y,x \ 1) * y = y * T(x \ 1,x \ y). T(x \ 1,(x \ 1) \ y) = T(x \ 1,x \ y). (x \ (y * y)) * z = (y \ (y \ x)) \ z. (x \ (x \ y)) \ z = (y \ (x * x)) * z. x / (y * x) = y \ 1. K(x,y) / (x * y) = (y * x) \ 1. L(x,y,z) / (z * (y * x)) = (z * y) \ 1. x / y = (y / x) \ 1. (x / y) \ 1 = y / x. (x * y) / ((z * x) * y) = R(z,x,y) \ 1. T(x * y,K(y,x)) / (y * x) = K(y,x) \ 1. T(x,x * y) / y = (x \ y) \ 1. x * (y * (x \ 1)) = T(y,x \ 1). (x * y) / ((z * x) * y) = R(z \ 1,z * x,y). R(x \ 1,x * y,z) = (y * z) / ((x * y) * z). (x * y) \ y = T(x \ 1,x * y). T(x \ 1,x * y) = (x * y) \ y. R((x \ 1) / y,y,x * z) = z / (y * (x * z)). L(x * y,x \ 1,y) = (y \ (x \ 1)) \ 1. L(x * (y * z),x \ 1,y) = (y \ (x \ 1)) \ z. (x / y) * (y / x) = 1. K(x \ y,x / y) = 1. T(x,y / (y * x)) = x. T(x \ y,x / y) = x \ y. (x / y) * z = (y / x) \ z. (x / y) \ z = (y / x) * z. (x / y) * ((y / x) * z) = z. x * ((y / z) * (z / y)) = x. K((x * y) \ y,x) = 1. (x / (x * y)) * y = y * (x / (x * y)). (x * (y / (y * x))) / x = y / (y * x). L(x,y / (y * x),x) = T(x,x * (y / (y * x))). T(x,x * (y / (y * x))) = L(x,y / (y * x),x). T((x * y) \ y,x) = (x * y) \ y. x * R(x \ (y \ x),z,u) = R(y \ 1,z,u) * x. T(x / y,x \ y) = x / y. (x / y) * (x \ y) = (x \ y) * (x / y). (x / y) * (z * (y / x)) = T(z,y / x). T(x / y,x) = ((y / x) * y) \ y. ((x \ 1) / y) \ 1 = (y / x) * (x * x). T(x / y,y) = T(y \ x,x \ y). T(x \ y,y \ x) = T(y / x,x). R(x,x \ 1,y) = x. T(x,y) = R(T(x,y),x \ 1,z). R(T(x,y),x \ 1,z) = T(x,y). R(x,y,z) = R(R(x,y,z),x \ 1,u). R(R(x,y,z),x \ 1,u) = R(x,y,z). R(T(x / y,y),(x / y) \ 1,z) = y \ x. x \ T(x,y) = T(x,y) * (x \ 1). T(x,y) * (x \ 1) = x \ T(x,y). (x \ (y * (x \ 1))) * x = x \ T(T(y,x \ 1),x). x \ T(T(y,x \ 1),x) = (x \ (y * (x \ 1))) * x. K(x,y) * ((K(x,y) \ 1) / (x * y)) = K(x,y) \ ((y * x) \ 1). (x \ (x \ (y * (x * x)))) \ 1 = T(y \ 1,y * (x * x)). T(x \ 1,x * (y * y)) = (y \ (y \ (x * (y * y)))) \ 1. x * ((x * y) \ y) = ((x * y) \ y) * x. ((x * y) \ y) * x = x * ((x * y) \ y). T(x \ y,y \ x) = x \ y. T(x \ (x * y),(x * y) \ x) = y. (x \ y) * (y \ x) = (y \ x) * (x \ y). ((x * y) \ y) * ((x \ 1) \ 1) = (x \ 1) \ T(x \ 1,x * y). (x \ 1) \ T(x \ 1,x * y) = ((x * y) \ y) * ((x \ 1) \ 1). T(x,(y * x) \ y) = x. T(x,y \ (y / x)) = x. ((x * y) \ x) * y = y * ((x * y) \ x). T(K(x,y),(x * y) \ (y * x)) = K(x,y). R(x,y,z) / x = R(x,y,z) * (x \ 1). R(x,y,z) * (x \ 1) = R(x,y,z) / x. (x \ (y * y)) * z = x \ (y * (y * z)). x \ (y * (y * z)) = (x \ (y * y)) * z. (x \ (y * y)) * x = T(y * y,x). (x \ (y * y)) * (y \ (y \ z)) = x \ z. T(x * x,y * z) \ ((((y * z) \ (x * x)) * y) * z) = a((y * z) \ (x * x),y,z). L(x \ 1,x,x \ (y * y)) = T(y * y,x) \ (x \ (y * y)). (x / y) * (y * y) = x / (y \ 1). x / y = (x / (y \ 1)) / (y * y). (x / (y \ 1)) / (y * y) = x / y. x * x = (x / y) * (y / (x \ 1)). (x / y) * (y / (x \ 1)) = x * x. x * (y * y) = (x * y) / (y \ 1). (x * y) / (y \ 1) = x * (y * y). x / (y * y) = (x * (y \ 1)) / y. (x * (y \ 1)) / y = x / (y * y). ((x \ (x \ y)) * x) / (x \ 1) = T(y,x * x). T(x / (y * y),y) = y \ (x * (y \ 1)). T(K(x,y),K(y,x)) = K(x,y). K(x,y) * T(K(y,x),z) = T(K(y,x),z) * K(x,y). T(K(x,y),z) * K(y,x) = K(y,x) * T(K(x,y),z). K(x,y) * R(K(y,x),z,u) = R(K(y,x),z,u) * K(x,y). R(K(x,y),z,u) * K(y,x) = K(y,x) * R(K(x,y),z,u). x * ((x \ (y * y)) * z) = y * (y * z). (((x * y) * x) \ (x * x)) * y = K(x,x * y). x \ (x \ (y \ z)) = (y * (x * x)) \ z. (x * (y * y)) \ z = y \ (y \ (x \ z)). (x * x) * y = z * ((z \ (x * x)) * y). x * ((x \ (y * y)) * z) = (y * y) * z. x * (y * (y * z)) = (x * (y * y)) * z. (x * (y * y)) * z = x * (y * (y * z)). x \ (x \ (y \ ((y * x) * x))) = a(y,x,x). (x * (y * y)) \ x = y \ (y \ 1). x \ (x / (y * y)) = y \ (y \ 1). x / (y \ (y \ 1)) = x * (y * y). x * (y \ (y \ 1)) = x / (y * y). x * ((y * y) * z) = (x * (y * y)) * z. (x * (y * y)) * z = x * ((y * y) * z). x * (y * y) = (x * (y * (y * z))) / z. (x * (y * (y * z))) / z = x * (y * y). (x * (y * (y * z))) \ ((x * (y * y)) * (z * u)) = L(u,z,x * (y * y)). T(x,y * y) * z = (y \ (y \ x)) * (y * (y * z)). (x \ (x \ y)) * (x * (x * z)) = T(y,x * x) * z. x = L(x,y * y,z). L(x,y * y,z) = x. x = R(x,y * y,z). R(x,y * y,z) = x. T(x,y * y) = T(x,x * (y * y)). T(x,x * (y * y)) = T(x,y * y). L(x,y,y / (z * z)) = x. L(x,y \ (y \ 1),z) = x. R(x,y \ (y \ 1),z) = x. L(x,y,y / (z \ (z \ 1))) = x. (x * (y \ (y \ 1))) * z = x * ((y \ (y \ 1)) * z). L(x,y,y * (z * z)) = x. T(x,x \ (y * y)) = T(x,y * y). T(x \ 1,x * (y * y)) = T(x \ 1,y * y). x \ (x / (y \ 1)) = L(y,y,x / y). L(x,x,y / x) = y \ (y / (x \ 1)). R(x,y,y \ 1) = (x * y) * (y \ 1). (x * y) * (y \ 1) = R(x,y,y \ 1). x * (y \ 1) = R(x / y,y,y \ 1). R(x / y,y,y \ 1) = x * (y \ 1). x * L(y,z * x,z) = z * ((z \ x) * y). R(T(x,y),z,u) * (x * w) = (R(T(x,y),z,u) * x) * w. (R(T(x,y),z,u) * x) * w = R(T(x,y),z,u) * (x * w). T(x \ y,R(y / x,z,u)) = x \ y. T((x \ 1) \ y,y * x) = (x \ 1) \ y. T(x * y,y * x) = (x \ 1) \ y. L(x,y,x) = (x \ y) \ T(y,x). (x \ y) \ T(y,x) = L(x,y,x). T(x,y) / L(y,x,y) = y \ x. ((x \ (x / y)) \ y) \ y = L(x \ (x / y),y,x \ (x / y)). L(x \ (x / y),y,x \ (x / y)) = ((x \ (x / y)) \ y) \ y. x \ (y \ (y \ z)) = (y * (y * x)) \ z. (x * (x * y)) \ z = y \ (x \ (x \ z)). x \ (y \ (y \ (z * (y * (y * x))))) = T(z,y * (y * x)). L(x \ 1,x,x / y) = y \ (y / x). L(x,y * (z \ 1),y) = z * (y \ ((y * (z \ 1)) * x)). x * (y \ ((y * (x \ 1)) * z)) = L(z,y * (x \ 1),y). R(x \ y,(y / x) \ 1,z) = x \ y. R(x \ y,x / y,z) = x \ y. R(x \ (x * y),x / (x * y),z) = y. R(x,y / (y * x),z) = x. x * ((y / (y * x)) * z) = (x * (y / (y * x))) * z. (x * (y / (y * x))) * z = x * ((y / (y * x)) * z). x \ L(x,y * x,y) = a(y,x,x). x * a(y,x,x) = L(x,y * x,y). L(x,y * x,y) = x * a(y,x,x). x * ((x \ y) * T(z,y)) = L(z,x * y,x) * y. K(x \ (x \ y),x) = (x * y) \ (x * T(y,x)). (x * y) \ (x * T(y,x)) = K(x \ (x \ y),x). x = L(x,y,R(y,z,u)). L(x,y,R(y,z,u)) = x. x * y = R(x,z,u) * ((R(x,z,u) \ x) * y). R(x,y,z) * ((R(x,y,z) \ x) * u) = x * u. (x * R(x,y,z)) * u = R(x,y,z) * (x * u). x \ R(x,y,z) = (R(x,y,z) \ x) \ 1. (R(x,y,z) \ x) \ 1 = x \ R(x,y,z). (R(x,y,z) \ u) / (x \ u) = R(x,y,z) \ x. (x \ R(x,y,z)) \ 1 = R(x,y,z) \ x. (x \ R(x,y,z)) * u = (R(x,y,z) \ x) \ u. (R(x,y,z) \ x) \ u = (x \ R(x,y,z)) * u. (R(x,y,z) \ x) * ((x \ R(x,y,z)) * u) = u. (x \ R(x,y,z)) \ u = (R(x,y,z) \ x) * u. x = T(x,L(x \ 1,y,z)). T(x,L(x \ 1,y,z)) = x. K(x,L(x \ 1,y,z)) = 1. K(x \ 1,L(x,y,z)) = 1. K(L(x,y,z) \ 1,x) = 1. T(L(x,y,z) \ 1,x) = L(x,y,z) \ 1. x * (L(x,y,z) \ 1) = L(x,y,z) \ x. R(x / (x * y),z,u) * (x * y) = (x * y) * R(L(y \ 1,y,x),z,u). R((x * y) / (x * z),u,w) * (x * z) = (x * z) * R(L(z \ y,z,x),u,w). x = T(x,R(x \ 1,y,z)). T(x,R(x \ 1,y,z)) = x. T(x \ 1,R(x,y,z)) = x \ 1. R(x,y,z) * (x \ 1) = x \ R(x,y,z). x \ R(x,y,z) = R(x,y,z) / x. R(x,y,z) / x = x \ R(x,y,z). (x \ R(x,y,z)) \ R(x,y,z) = x. (x * (y \ 1)) / (x / y) = (x / y) \ R(x / y,y,y \ 1). (x / y) \ R(x / y,y,y \ 1) = (x * (y \ 1)) / (x / y). (x \ ((y * x) / y)) \ 1 = (y / (y * x)) * x. R(x,L(x,y,z),u) = x. x * (L(x,y,z) * u) = (x * L(x,y,z)) * u. (x * L(x,y,z)) * u = x * (L(x,y,z) * u). T(x \ 1,x * y) = T(x \ 1,x \ y). T(x \ 1,x \ y) = T(x \ 1,x * y). (x \ T(y,x)) / (x \ 1) = T(y,x * x). (((x \ y) * x) \ 1) * y = K(x,x * y). K(x,x * y) = ((x \ y) * x) \ y. ((x \ y) * x) \ y = K(x,x * y). K(x,x * y) = K(x,x \ y). K(x,x \ y) = K(x,x * y). K(x,y) = K(x,x * (x * y)). K(x,x * (x * y)) = K(x,y). K(x,T(y,x)) = K(x,x * (y * x)). K(x,x * (y * x)) = K(x,T(y,x)). K(x,(x * x) / y) = K(x,y \ 1). (x * y) \ (y * x) = K(x \ (x \ y),x). K(x \ (x \ y),x) = (x * y) \ (y * x). K(x \ (x \ y),x) = K(y,x). K(x \ y,x) = K(x * y,x). (R(x,y,z) \ x) * R(x,y,z) = x. R(x,y,z) \ x = x / R(x,y,z). x / R(x,y,z) = R(x,y,z) \ x. T(R(x,y,z) \ 1,x) = x \ (x / R(x,y,z)). (x * y) / (z \ ((z * x) * y)) = R(z,x,y) \ z. R(x,y,z) * u = x * ((x \ R(x,y,z)) * u). x * ((x \ R(x,y,z)) * u) = R(x,y,z) * u. (x \ ((y * x) / y)) \ 1 = x * (y / (y * x)). x = L(x,L(y,z,u),y). L(x,L(y,z,u),y) = x. L(x,y,z) * u = x * ((x \ L(x,y,z)) * u). x * ((x \ L(x,y,z)) * u) = L(x,y,z) * u. L(x,(y * z) \ y,z \ 1) = x. L(x,y,z) \ x = (x \ L(x,y,z)) \ 1. (x \ L(x,y,z)) \ 1 = L(x,y,z) \ x. L(x,y,z) \ (x * u) = (x \ L(x,y,z)) \ u. (x \ L(x,y,z)) \ u = L(x,y,z) \ (x * u). L(x,y,L(y,z,u)) = x. T(x,x * L(x,y,z)) = x. x \ L(x,y,z) = (L(x,y,z) \ x) \ 1. (L(x,y,z) \ x) \ 1 = x \ L(x,y,z). (L(x,y,z) \ u) / (x \ u) = L(x,y,z) \ x. (x \ L(x,y,z)) * x = L(x,y,z). L(x,y,z) / x = x \ L(x,y,z). x / L(x,y,z) = (x \ L(x,y,z)) \ 1. (x \ L(x,y,z)) \ 1 = x / L(x,y,z). (L(x,y,z) \ x) * u = (x \ L(x,y,z)) \ u. (x \ L(x,y,z)) \ u = (L(x,y,z) \ x) * u. x / L(x,y,z) = L(x,y,z) \ x. (L(x,y,z) \ x) * L(x,y,z) = x. (L(x \ 1,x,x / y) \ (x \ 1)) * (y \ (y / x)) = x \ 1. x * (R(x,y,z) * u) = (x * R(x,y,z)) * u. (x * R(x,y,z)) * u = x * (R(x,y,z) * u). (L(x,y,z) \ x) * u = L(x,y,z) \ (x * u). L(x,y,z) \ (x * u) = (L(x,y,z) \ x) * u. x = R(x,R(x,y,z),u). R(x,R(x,y,z),u) = x. x * (R(x,y,z) * u) = R(x,y,z) * (x * u). R(x,y,z) * (x * u) = x * (R(x,y,z) * u). T(x,y) = R(T(x,y),R(x,z,u),w). R(T(x,y),R(x,z,u),w) = T(x,y). R(x,y,z) * u = (x \ R(x,y,z)) * (x * u). (x \ R(x,y,z)) * (x * u) = R(x,y,z) * u. R(x,y,z) * u = x * (R(x,y,z) * (x \ u)). x * (R(x,y,z) * (x \ u)) = R(x,y,z) * u. R(x,y,z) * (u * x) = x * (R(x,y,z) * T(u,x)). x * (R(x,y,z) * T(u,x)) = R(x,y,z) * (u * x). x \ R(x,y,z) = (R(x,y,z) * u) / (x * u). (R(x,y,z) * u) / (x * u) = x \ R(x,y,z). (x \ R(x,y,z)) * u = R(x,y,z) * (x \ u). ((R(x,y,z) * u) * w) / ((x * u) * w) = R(x \ R(x,y,z),x * u,w). R(x \ R(x,y,z),x * u,w) = ((R(x,y,z) * u) * w) / ((x * u) * w). R(x,y,z) * (x \ u) = x \ (R(x,y,z) * u). x \ (R(x,y,z) * u) = R(x,y,z) * (x \ u). x / (y * (R(y,z,u) \ x)) = y \ R(y,z,u). (R(x,y,z) * (x \ u)) / u = x \ R(x,y,z). ((x * y) * z) / (x * (y * z)) = x \ R(x,y,z). (R(R(x,y,z),u,w) * (y * z)) / ((x * y) * z) = R(x,y,z) \ R(R(x,y,z),u,w). x \ (R(y,z,u) * (y \ x)) = T(y \ R(y,z,u),x). (R(x,y,z) \ x) \ u = R(x,y,z) * (x \ u). (x \ R(x,y,z)) \ u = x * (R(x,y,z) \ u). x / (R(y,z,u) * (y \ x)) = R(y,z,u) \ y. x * (R(x,y,z) \ 1) = R(x,y,z) \ x. x * (R(x,y,z) \ u) = (R(x,y,z) \ x) * u. (R(x,y,z) \ x) * u = x * (R(x,y,z) \ u). R(x,y,z) \ 1 = T(R(x,y,z) \ 1,x). T(R(x,y,z) \ 1,x) = R(x,y,z) \ 1. T(x,R(x,y,z) \ 1) = x. R(x,y,z) \ 1 = x \ (x / R(x,y,z)). x \ (x / R(x,y,z)) = R(x,y,z) \ 1. R(x,y,z) \ T(x,u) = T(x,u) * (R(x,y,z) \ 1). T(x,y) * (R(x,z,u) \ 1) = R(x,z,u) \ T(x,y). (x * y) \ ((z * x) * y) = R(T(z,x * y),x,y). (x * (x * (y * z))) / (y * z) = R(x * x,y,z). x \ ((x * y) * (1 / y)) = a(x,y,1 / y). x \ ((x * y) * (y \ 1)) = a(x,y,1 / y). x \ ((x * y) * (y \ 1)) = a(x,y,y \ 1). (x / y) \ (x * (y \ 1)) = a(x / y,y,y \ 1). a(x / y,y,y \ 1) = (x / y) \ (x * (y \ 1)). T((x * y) / (z * y),z) = R(z \ x,z,y). T(R(x \ y,x,z),u) = T(T((y * z) / (x * z),u),x). T(T((x * y) / (z * y),u),z) = T(R(z \ x,z,y),u). T(x,x * ((y * x) / y)) = x. ((x * y) / x) / y = y \ ((x * y) / x). (x \ y) * L(z,y,x \ 1) = x \ (y * z). T(x,y) * (x \ z) = (T(x,y) * (x \ 1)) * z. (T(x,y) * (x \ 1)) * z = T(x,y) * (x \ z). (x \ T(x,y)) * z = T(x,y) * (x \ z). x \ T(x,y) = (T(x,y) * (x \ z)) / z. (T(x,y) * (x \ z)) / z = x \ T(x,y). x * (T(x,y) * (x \ x)) = T(x * T(x,y),x). (T(x,y) * z) / (x * z) = x \ T(x,y). (x \ T(x,y)) \ (T(x,y) * z) = x * z. (x \ T(x,y)) \ z = x * (T(x,y) \ z). x * (T(x,y) * 1) = T(x * T(x,y),x). T(x * T(x,y),x) = x * (T(x,y) * 1). T(x * T(x,y),x) = x * T(x,y). T(x,x * T(x,y)) = x. T(x,y) / x = x \ T(x,y). (x \ T(x,y)) \ z = (x / T(x,y)) * z. (x \ T(x,y)) \ z = (T(x,y) \ x) * z. (T(x,y) \ x) * (T(x,y) * z) = x * z. (T(x,y) \ x) * z = x * (T(x,y) \ z). T(x,y) \ x = (x * z) / (T(x,y) * z). (x * y) / (T(x,z) * y) = T(x,z) \ x. T(x,y) \ x = x * (T(x,y) \ 1). x * (T(x,y) \ 1) = T(x,y) \ x. 1 = K(x,T(x,y) \ 1). K(x,T(x,y) \ 1) = 1. T(x,T(x,y) \ 1) = x. T(x,y) \ T(x,z) = T(x,z) * (T(x,y) \ 1). T(x,y) * (T(x,z) \ 1) = T(x,z) \ T(x,y). T(x,y) \ 1 = x \ (T(x,y) \ x). x \ (T(x,y) \ x) = T(x,y) \ 1. ((T(x,y) \ x) * z) / (T(x,y) \ z) = R(x,T(x,y) \ 1,z). R(x \ 1,x * y,z) = R(x,y,z) \ 1. R(x \ 1,y,z) = R(x,x \ y,z) \ 1. R(x,x \ y,z) \ 1 = R(x \ 1,y,z). (x * y) / (z * ((z \ x) * y)) = R(z,x,y) \ z. T(x \ R(x,y,z),x * (y * z)) = (x * (y * z)) \ ((x * y) * z). R(x * x,y,z) = x * x. T(x * x,y) = R(T(x * x,y),z,u). R(T(x * x,y),z,u) = T(x * x,y). T(x * x,y) \ (z * u) = (T(x * x,y) \ z) * u. a(x / y,y,y \ 1) = (y / x) * (x * (y \ 1)). (x * y) / (z * ((z \ y) * T(x,y))) = R(z,y,T(x,y)) \ z. (x \ (y * z)) \ ((x \ y) * z) = a(x,y,z). (x \ (y * (x \ 1))) * x = T(y,x) * (x \ 1). x \ (y * (x \ 1)) = (T(y,x) * (x \ 1)) / x. (T(x,y) * (y \ 1)) / y = y \ (x * (y \ 1)). x \ (y * (x \ 1)) = T(y,x) / (x * x). x \ ((x * (x * y)) * (x \ 1)) = (x * (y * x)) / (x * x). T(x / (y * y),y) = T(x,y) / (y * y). T(x,y) / (y * y) = T(x / (y * y),y). (x / (y * y)) * z = x * ((y \ (y \ 1)) * z). x * ((y \ (y \ 1)) * z) = (x / (y * y)) * z. x * (y \ (y \ z)) = (x / (y * y)) * z. (x / (y * y)) * z = x * (y \ (y \ z)). x = L(x,y / (y * z),z). L(x,y / (y * z),z) = x. (x / (x * y)) \ (y \ z) = (y * (x / (x * y))) \ z. (x * (y / (y * x))) \ z = (y / (y * x)) \ (x \ z). T(x,x * (y / (y * x))) = x. (x * (y / (y * x))) \ z = ((y * x) / y) * (x \ z). R(x,x * y,z) = x * (x * ((y * z) / ((x * y) * z))). x * (x * ((y * z) / ((x * y) * z))) = R(x,x * y,z). L(R(x,x,y),z,u) * (x * y) = (x * L(x,z,u)) * y. L(K(x,y),y * x,x * y) = K(y,x) \ 1. (x \ (y * z)) \ ((x \ y) * z) = a(x \ 1,y,z). a(x \ 1,y,z) = a(x,y,z). a(x / y,z,u) = a(y / x,z,u). L(x \ 1,y,x \ 1) * y = y * T(x \ 1,x * y). T(T((x * y) / (z * y),u),z) = R(T(z \ x,u),z,y). x * (x * (R(x,y,z) \ 1)) = R(x,x * y,z). R(x,x * y,z) = (x * x) / R(x,y,z). (x * x) / R(x,y,z) = R(x,x * y,z). x * (R(x,y,z) \ x) = R(x,x * y,z). R(x,y,z) \ x = x \ R(x,x * y,z). x \ R(x,x * y,z) = R(x,y,z) \ x. x * (R(x,x * y,z) \ x) = R(x,(x * x) * y,z). x / R(x,x * y,z) = x \ R(x,y,z). (R(x,y,z) \ x) * x = R(x,x * y,z). x \ R(x,y,z) = R(x,x * y,z) \ x. R(x,x * y,z) \ x = x \ R(x,y,z). x \ (x \ R(x,y,z)) = R(x,x * y,z) \ 1. R(x,x * y,z) \ 1 = x \ (x \ R(x,y,z)). R(x,y,z) \ x = x \ R(x,x \ y,z). x \ R(x,x \ y,z) = R(x,y,z) \ x. (x \ R(x,y,z)) * u = x * (R(x,x * y,z) \ u). x * (R(x,x * y,z) \ u) = (x \ R(x,y,z)) * u. x * (x \ R(x,y,z)) = R(x,(x * x) * y,z). R(x,(x * x) * y,z) = R(x,y,z). R(x,x * (x * y),z) = R(x,y,z). R(x,x * y,z) = R(x,x \ y,z). R(x,x \ y,z) = R(x,x * y,z). R(x,x * y,z) \ (y * z) = (x \ y) * z. R(x,x * y,z) \ 1 = R(x \ 1,y,z). R(x \ 1,y,z) \ 1 = R(x,x * y,z). R(x,x * y,z) = R(x \ 1,y,z) \ 1. R(x \ 1,y,z) = x \ (x \ R(x,y,z)). x \ (x \ R(x,y,z)) = R(x \ 1,y,z). x * R(x \ 1,y,z) = x \ R(x,y,z). x * (R(x \ 1,y,z) * u) = x \ (R(x,y,z) * u). x * (R(x,x * y,z) \ u) = R(x,y,z) * (x \ u). x * (R(x \ 1,y,z) * u) = R(x,y,z) * (x \ u). x * (y * R(y \ (x \ y),z,u)) = R(x,z,u) * (x \ y). L(x,y,z) * (x * u) = (x * L(x,y,z)) * u. (x * L(x,y,z)) * u = L(x,y,z) * (x * u). x * y = L(x,z,u) \ ((x * L(x,z,u)) * y). L(x,y,z) \ ((x * L(x,y,z)) * u) = x * u. L(x,y,z) * (x * u) = x * (L(x,y,z) * u). L(x,y,z) \ (x * (L(x,y,z) * u)) = x * u. L(x,y,z) * u = x * (L(x,y,z) * (x \ u)). x * (L(x,y,z) * (x \ u)) = L(x,y,z) * u. L(x,y,z) * (x * (L(x,y,z) \ u)) = x * u. x * y = (L(x,z,u) \ x) * (L(x,z,u) * y). (L(x,y,z) \ x) * (L(x,y,z) * u) = x * u. L(x,y,z) * (x \ u) = (x \ L(x,y,z)) * u. (x \ L(x,y,z)) * u = L(x,y,z) * (x \ u). L(x,y,z) = (x * u) / (x * (L(x,y,z) \ u)). (x * y) / (x * (L(x,z,u) \ y)) = L(x,z,u). L(x,y,z) \ x = (x * u) / (L(x,y,z) * u). (x * y) / (L(x,z,u) * y) = L(x,z,u) \ x. (L(x,y,z) \ x) * u = x * (L(x,y,z) \ u). x = T(x,L(x,y,z) \ x). T(x,L(x,y,z) \ x) = x. K(x,L(x,y,z) \ x) = 1. T(x \ 1,x * (y * y)) = T(x,y * y) \ 1. T(x,y * y) \ 1 = T(x \ 1,y * y). x = L(x,y,R(T(y,z),u,w)). L(x,y,R(T(y,z),u,w)) = x. L(x,y,R((y \ z) \ z,u,w)) = x. x \ ((y \ (y \ z)) * (y * (y * x))) = T(z,y * (y * x)). x \ (x * (x * (y * (x \ 1)))) = (x * (y * x)) / (x * x). x \ (T(y,z * z) * x) = T(y,z * (z * x)). T(x,y * (y * z)) = T(T(x,y * y),z). T(T(x,y * y),z) = T(x,y * (y * z)). T(x,y * (y * z)) = T(T(x,z),y * y). T(T(x,y),z * z) = T(x,z * (z * y)). x \ (x * T(y,x \ 1)) = (x * (y * x)) / (x * x). (x * (y * x)) / (x * x) = T(y,x \ 1). T(x * y,x) / (x * x) = T(x \ y,x \ 1). T(x \ y,x \ 1) = T((x * y) / (x * x),x). T((x * y) / (x * x),x) = T(x \ y,x \ 1). (x * (x * ((y * z) * u))) / (z * u) = R(x * (x * y),z,u). (x / y) \ (x * (y \ 1)) = (x * (y \ 1)) / (x / y). (x * (y \ 1)) / (x / y) = (x / y) \ (x * (y \ 1)). (x * (y \ 1)) / (x / y) = (y / x) * (x * (y \ 1)). (x * (T(x,y) \ z)) / (T(x,y) \ z) = R(x,T(x,y) \ 1,z). (x * y) / (L(x,z * y,z) * y) = R(z,y,T(x,y)) \ z. R(x,y,T(z,y)) \ x = L(z,x * y,x) \ z. (R(x,y,T(z,y)) \ x) \ 1 = z \ L(z,x * y,x). L(x,y * (y * z),y) \ x = y \ R(y,z,T(x,y * z)). x \ L(x,y * z,y) = y \ R(y,z,T(x,z)). x \ R(x,y,T(z,y)) = z \ L(z,x * y,x). x * (y \ L(y,x * z,x)) = R(x,z,T(y,z)). R(x,y,T(z,y)) = x * (z \ L(z,x * y,x)). R(x,x * y,T(z,x * y)) = x * (z \ L(z,y,x)). x \ L(x,y,z) = R(z,y,T(x,z * y)) \ z. R(x,y,T(z,x * y)) \ x = z \ L(z,y,x). (x \ L(x,y,z)) * R(z,y,T(x,z * y)) = z. L(x,y,z) \ x = z \ R(z,y,T(x,z * y)). L(x,y,z) * (z \ R(z,y,T(x,z * y))) = x. x * (L(y,z,x) \ y) = R(x,z,T(y,x * z)). R(x,y,T(z,x * y)) = x * (L(z,y,x) \ z). (x \ R(x,y,T(z,x * y))) * L(z,y,x) = z. L(x,R(y,z,u),T(y,w)) * (T(y,w) \ T(y,w)) = x. x = R(y,z,T(x,y * z)) * (y \ L(x,z,y)). R(x,y,T(z,x * y)) * (x \ L(z,y,x)) = z. L(x,R(y,z,u),T(y,w)) * 1 = x. L(x,R(y,z,u),T(y,w)) = x. L(x,R(y / z,u,w),z \ y) = x. T(R(x,y,z),T(x,u)) / T(x,u) = T(x,u) \ R(x,y,z). R(T(x,T(x,y)),z,u) / T(x,y) = T(x,y) \ R(x,z,u). R(x,y,z) / T(x,u) = T(x,u) \ R(x,y,z). R(x * (x * y),z,u) = x * (x * (((y * z) * u) / (z * u))). x * (x * (((y * z) * u) / (z * u))) = R(x * (x * y),z,u). R(x,T(x,y) \ 1,z) = x. x * (x * R(y,z,u)) = R(x * (x * y),z,u). x * (x * R(T(y,x),z,u)) = R(x * (y * x),z,u). R(x * (x * T(y,x * x)),z,u) = R(y,z,u) * (x * x). x * (R(y,z,u) * x) = R(x * (y * x),z,u). R(x,y,z) * u = u \ R(u * (x * u),y,z). x \ R(x * (y * x),z,u) = R(y,z,u) * x. (x * (y * x)) \ R(x * (z * x),u,w) = T(y,x) \ (x \ (R(z,u,w) * x)). x \ R(x * y,z,u) = R(y / x,z,u) * x. x \ R(x * y,z,u) = x * R(x \ y,z,u). L(x \ (y * R(y \ z,u,w)),x,y) = (y * x) \ R(y * z,u,w). R(x * (y * y),z,u) = R(x,z,u) * (y * y). R(x,y,z) * (u * u) = R(x * (u * u),y,z). (x \ 1) \ T(x \ 1,x * y) = ((x * y) \ y) * x. (x \ 1) \ T(x \ 1,x * y) = x * ((x * y) \ y). (x * y) * T(L(y \ 1,y,x),z) = (x * y) * T((x * y) \ x,z). R((x / y) * (z * z),z \ (z \ 1),y) = x / (z \ (z \ y)). x / (y \ (y \ z)) = (x / z) * (y * y). x / (y \ z) = (x / (y * z)) * (y * y). (x / (y * z)) * (y * y) = x / (y \ z). R(x / y,y,z) * (y * y) = (x * z) / (y \ z). (x * y) / (z \ y) = R(x / z,z,y) * (z * z). (x * y) / (z \ y) = R((x / z) * (z * z),z,y). R((x / y) * (y * y),y,z) = (x * z) / (y \ z). R(x / (y \ 1),y,z) = (x * z) / (y \ z). R(x,y,z) = ((x * (y \ 1)) * z) / (y \ z). ((x * (y \ 1)) * z) / (y \ z) = R(x,y,z). R(L(x,y,z) \ x,x,u) = ((L(x,y,z) \ 1) * u) / (x \ u). R(x,y,z) = R(x,y \ 1,z). R(x,y \ 1,z) = R(x,y,z). R(x,y,y) / y = x * (y \ 1). (x * (y \ 1)) \ R(x,y,y) = y. R(x / (y \ 1),y,y) = x * y. R(x,T(x,y),z) = x. x * (T(x,y) * z) = (x * T(x,y)) * z. (x * T(x,y)) * z = x * (T(x,y) * z). R(T(x / (y \ 1),z),y,y) / y = (y \ 1) * T((y \ 1) \ x,z). (T(x,y) * (R(x,z,u) \ 1)) \ T(x,y) = R(x,z,u). T(x * y,z) = R(T(x / (y \ 1),z),y,y). R(T(x / (y \ 1),z),y,y) = T(x * y,z). x = L(x,T(y,z),y). L(x,T(y,z),y) = x. x * (T(x,y) * (x \ z)) = T(x,y) * z. L(x,y,(z * y) / z) = x. L(x,(y \ z) \ z,y) = x. T(x,y) * (x \ z) = x \ (T(x,y) * z). x \ (T(x,y) * z) = T(x,y) * (x \ z). (x \ T(x,y)) * z = x \ (T(x,y) * z). x \ (T(x,y) * z) = (x \ T(x,y)) * z. (R(x,y,z) \ T(x,u)) \ T(x,u) = R(x,y,z). R(L(x,y,z) \ x,x,u) = (L(x,y,z) \ u) / (x \ u). R(L(x,y,z) \ x,x,u) = L(x,y,z) \ x. T(x \ R(x,y,z),x * (y * z)) = a(x,y,z). T(a(x,y,z),u) = T(T(x \ R(x,y,z),u),x * (y * z)). T(T(x \ R(x,y,z),u),x * (y * z)) = T(a(x,y,z),u). T(T(R(x,y,z) / x,x * (y * z)),x) = a(x,y,z). (x * a(y,z,u)) / x = T((x * (y \ R(y,z,u))) / x,y * (z * u)). T((x * (y \ R(y,z,u))) / x,y * (z * u)) = (x * a(y,z,u)) / x. T(R(x,y,z) \ R(R(x,y,z),u,x),x * (R(x,y,z) * T(u,x))) = a(R(x,y,z),u,x). T(T((R(x,y,z) * u) / (x * u),x * (y * z)),x) = R(a(x,y,z),x,u). T(T(x \ R(x,y,z),x * (y * z)),x) = a(x,y,z). T(a(x,y,z),x) = a(x,y,z). x * a(x,y,z) = a(x,y,z) * x. a(x,y,z) * x = x * a(x,y,z). (x * a(x,y,z)) / x = a(x,y,z). ((x * (x * y)) * a(x * (x * y),z,u)) / y = a(x * (x * y),z,u) * (x * x). (x * y) \ R(x * z,u,w) = (x \ y) \ R(x \ z,u,w). (x \ y) \ R(x \ z,u,w) = (x * y) \ R(x * z,u,w). (x * y) * L(T(y \ 1,z),y,x) = (x * y) * T((x * y) \ x,z). (x * y) * T((x * y) \ x,z) = (x * y) * L(T(y \ 1,z),y,x). T(x * y,z) / y = (y \ 1) * T((y \ 1) \ x,z). (x \ 1) * T((x \ 1) \ y,z) = T(y * x,z) / x. (x \ 1) * T(x * y,z) = T(y * x,z) / x. T(x * y,z) / y = y \ T(y * x,z). T(x,y) / z = z \ T(z * (x / z),y). x \ T(x * (y / x),z) = T(y,z) / x. T(x * y,y) / y = (y \ x) * y. ((x \ y) * x) * x = T(y * x,x). (x * y) * y = T((y * x) * y,y). T((x * y) * x,x) = (y * x) * x. (x * y) * T((x * y) \ x,z) = x * (y * T(y \ 1,z)). (x * (x * (y * z))) \ (x * (x * (y * (z * u)))) = L(u,z,x * (x * y)). (x * y) * T(L(y \ z,y,x),u) = (x * y) * T((x * y) \ (x * z),u). (x * y) * R(L(y \ 1,y,x),z,u) = (x * y) * R((x * y) \ x,z,u). T(T(x \ R(x,y,z),x * (y * z)),x) = R(a(x,y,z),x,u). R(a(x,y,z),x,u) = a(x,y,z). a(x,y,z) * (x * u) = (a(x,y,z) * x) * u. (a(x,y,z) * x) * u = a(x,y,z) * (x * u). x = L(x,y,a(y,z,u)). L(x,y,a(y,z,u)) = x. (x * a(x,y,z)) * u = a(x,y,z) * (x * u). L(x,y,z * (z * u)) = (u * y) \ (u * (y * x)). L(x,y,z * (z * u)) = L(x,y,u). L(x,y,z * u) = L(x,y,z \ u). L(x,y,z \ u) = L(x,y,z * u). L(x,y,(z / u) * z) = L(x,y,u). L(x,y,z * (u * z)) = L(x,y,T(u,z)). L(x,y,(z * u) * (u * z)) = L(x,y,K(u,z)). L(x,y,z * ((z * u) * w)) = L(x,y,z * ((z \ u) * w)). L(x,y,z * ((z \ u) * w)) = L(x,y,z * ((z * u) * w)). L(x,y,(z * u) * w) = L(x,y,(z \ u) * w). L(x,y,(z \ u) * w) = L(x,y,(z * u) * w). L(x,y,(z \ (z \ u)) * (z \ u)) = L(x,y,T(z,u)). L(x,y,(z * z) / u) = L(x,y,u \ 1). L(x,y,z / u) = L(x,y,u / z). L(x,y,z * L(z,u * z,u)) = L(x,y,a(u,z,z)). L(x,y,R(z * (z * u),w,v5)) = L(x,y,R(u,w,v5)). L(x,y,z \ 1) = L(x,y,z). L(x,y,T(z / u,z)) = L(x,y,((u / z) * u) * u). L(x,y,y \ (z * z)) = x. L(x \ (x / y),y,x * (x / y)) = ((x \ (x / y)) \ y) \ y. L(x,R(y / z,u,w),z * y) = x. L(x \ L(y \ z,y,u),x,u * y) = ((u \ y) * x) \ (u \ z). x \ 1 = T(y * y,x) \ (x \ (y * y)). T(x * x,y) \ (y \ (x * x)) = y \ 1. L(x,L(y \ 1,z,u),y) = x. L(x,(y * z) \ y,z) = x. (x \ y) * L(z,y,x) = x \ (y * z). L(x \ 1,y,x) * y = y * T(x \ 1,x * y). x * T(y \ 1,y * x) = L(y \ 1,x,y) * x. L(x,y \ z,z \ y) = x. x = L(x,y \ z,z * y). L(x,y \ z,z * y) = x. L(x,y,z * (z / y)) = x. L(x \ 1,y,z) \ (x \ u) = (x * L(x \ 1,y,z)) \ u. (x * L(x \ 1,y,z)) \ u = L(x \ 1,y,z) \ (x \ u). L(x,y,(z * (z * u)) * (z * w)) = L(x,y,u \ (z \ w)). L(x,y,(z * (z * u)) * z) = L(x,y,u \ (z \ 1)). L(L(x,y,y / z),z,z / y) = x. L(x,x,x / y) = y \ (y / (x \ 1)). L(x,y,z / (z * y)) = x. x \ 1 = ((y / (y * x)) * x) \ (y / (y * x)). ((x / (x * y)) * y) \ (x / (x * y)) = y \ 1. ((x / (x * y)) * y) * z = (x / (x * y)) * (y * z). x \ ((y / (y * x)) \ z) = ((y / (y * x)) * x) \ z. ((x / (x * y)) * y) \ z = y \ ((x / (x * y)) \ z). L(x,y / (z * (u * y)),z * (u \ 1)) = x. (x * (y \ z)) \ (x * (y \ (z * u))) = L(L(u,z,y),y \ z,x). (T(x,y) \ x) * z = T(x,y) \ (x * z). T(x,y) \ (x * z) = (T(x,y) \ x) * z. (x \ ((y * x) / y)) * z = x \ (((y * x) / y) * z). x \ (((y * x) / y) * z) = (x \ ((y * x) / y)) * z. (x \ y) * T((x \ y) \ 1,z) = x \ (y * T(y \ x,z)). L(x,y,T(z * u,z)) = L(x,y,T(z \ u,z)). L(x,y,T(z \ u,z)) = L(x,y,T(z * u,z)). L(x,y,z * T(u * z,z)) = L(x,y,T((z \ u) * z,z)). L(x,y,(z * z) / u) = L(x,y,u). L(x,y,z \ (u * u)) = L(x,y,T(z,z * (u * u))). L(x,y,T(z,z * (u * u))) = L(x,y,z \ (u * u)). L(x,y,z) = L(x,y,z / (u * u)). L(x,y,z / (u * u)) = L(x,y,z). L(x,y,z) = L(x,y,z * (u * u)). L(x,y,z * (u * u)) = L(x,y,z). L(x,y,R(z,u,u)) = L(x,y,(z * u) * u). L(x,y,(z * u) * u) = L(x,y,R(z,u,u)). (x * (y * (y * z))) \ ((x * (y * y)) * (z * u)) = L(u,z,x). (T(x,y) \ x) * y = T(y,T(x,y)). T(x,y) \ (x * z) = x * (T(x,y) \ z). T(x,T(y,x)) = y * (T(y,x) \ x). x * (T(x,y) \ y) = T(y,T(x,y)). x = T(y,T(x,y)) / (T(x,y) \ y). T(x,T(y,x)) / (T(y,x) \ x) = y. T(x,y) \ y = x \ T(y,T(x,y)). x \ T(y,T(x,y)) = T(x,y) \ y. (x * y) / (x * (T(x,z) \ y)) = T(x,z). (((x * y) * (y * x)) * z) \ (((x * y) * (y * x)) * (z * u)) = L(u,z,K(y,x)). (x * (y / (y * x))) \ (y / (y * x)) = x \ 1. T(x \ 1,x * (y / (y * x))) = x \ 1. x * ((y * x) \ x) = L(y \ 1,x,y) * x. L(x \ 1,y,x) * y = y * ((x * y) \ y). L(x,y,T(z,u)) = L(x,y,(z * (z \ u)) * (z \ u)). L(x,y,(z * (z \ u)) * (z \ u)) = L(x,y,T(z,u)). L(x,y,z * ((z \ u) * u)) = L(x,y,a(z,u,u)). L(x,y,R(z * u,w,v5)) = L(x,y,R(z \ u,w,v5)). L(x,y,R(z \ u,w,v5)) = L(x,y,R(z * u,w,v5)). L(x,y,T(z / u,z)) = L(x,y,R(u / z,u,u)). L(x,y,z * (z * (u * z))) = L(x,y,u \ (z \ 1)). (x * (y / (y * x))) * z = (y / (y * x)) * (x * z). (x * (y / (y * x))) \ z = x \ ((y / (y * x)) \ z). L(x,y,T(z,z * (u * u))) = L(x,y,z * (u * u)). L(x,y,z * (u \ z)) = L(x,y,T(u,z)). L(x,y,z * u) = L(x,y,T(z / u,z)). L(x,y,T(z / u,z)) = L(x,y,z * u). L(x,y,z * u) = L(x,y,R(u / z,u,u)). L(x,y,R(z / u,z,z)) = L(x,y,u * z). L(x,y,R((y \ z) * z,u,w)) = x. L(x,y,z \ (u \ 1)) = L(x,y,z * u). L(x,y,z * u) = L(x,y,z * (u \ 1)). L(x,y,z * (u \ 1)) = L(x,y,z * u). L(x,y / (z * (u * y)),z * u) = x. L(x,(y * z) * (u / (y * (z * u))),y * z) = x. ((x * y) * z) / (x * (y * z)) = (x * y) * (z / (x * (y * z))). x \ ((y / (y * x)) \ z) = ((y * x) / y) * (x \ z). L(x,y,T(z,z * (u * u))) = L(x,y,z). L(x,y,T(z,u * u)) = L(x,y,z). L(x,y,R(T(z,u * u),w,v5)) = L(x,y,R(z,w,v5)). x \ (((y * x) / y) * z) = ((y * x) / y) * (x \ z). ((x * y) / x) * (y \ z) = (y \ ((x * y) / x)) * z. (x \ ((y * x) / y)) * z = ((y * x) / y) * (x \ z). L(x,y,z * ((z * u) * u)) = L(x,y,a(z,u,u)). L(x,y,z * (z * (u * (z * w)))) = L(x,y,u \ (z \ w)). L(x,y,(z * u) * u) = L(x,y,T((u \ z) * u,u)). L(x,y,T((z \ u) * z,z)) = L(x,y,(u * z) * z). L(x,y,T((z \ u) * z,z)) = L(x,y,R(u,z,z)). L(x,y,z \ (u \ w)) = L(x,y,z * (u * w)). L(x,y,z * (u * w)) = L(x,y,z * (u \ w)). L(x,y,z * (u \ w)) = L(x,y,z * (u * w)). L(x,y,z * u) = L(x,y,z * (w * (w * u))). L(x,y,z * (u * (u * w))) = L(x,y,z * w). L(x,y,(z \ u) * (u \ z)) = L(x,y,(u \ z) * (z * u)). ((x \ (x / y)) \ y) \ y = x \ (x / y). x / (y \ (y / x)) = (y \ (y / x)) \ x. (x * (y * (y * z))) \ (x * (y * (y * (z * u)))) = L(u,z,x). L(x,y,z) = L(x,u * (u * y),z). L(x,y * (y * z),u) = L(x,z,u). L(x,y * z,u) = L(x,y \ z,u). L(x,y \ z,u) = L(x,y * z,u). L(x,(y / z) * y,u) = L(x,z,u). L(x,y * (z * y),u) = L(x,T(z,y),u). L(x,(y * z) * (z * y),u) = L(x,K(z,y),u). L(x,(y * z) * u,w) = L(x,(y \ z) * u,w). L(x,(y \ z) * u,w) = L(x,(y * z) * u,w). L(x,(y \ z) * z,u) = L(x,T(y,y * z),u). L(x,T(y,y * z),u) = L(x,(y \ z) * z,u). L(x,(y * y) / z,u) = L(x,z \ 1,u). L(x,y * (z \ y),u) = L(x,T(z \ 1,y),u). L(x,T(y \ 1,z),u) = L(x,z * (y \ z),u). L(x,y / z,u) = L(x,z / y,u). L(x,y \ 1,z) = L(x,y,z). (x * (y \ z)) * L(u,y * z,x) = x * ((y \ z) * u). L(x,(y \ z) * z,y) = x. L(x,y * z,z * y) = x. ((x \ y) * y) \ (x \ z) = (x * ((x \ y) * y)) \ z. (x * ((x \ y) * y)) \ z = ((x \ y) * y) \ (x \ z). ((x * y) * (y * x)) * z = (x * y) * ((y * x) * z). T(x * y,y * x) = T(x * y,(x * y) * (y * x)). T(x * y,(x * y) * (y * x)) = T(x * y,y * x). L(x,K(y,z),z * y) = x. K(x,y) = K(y,x) \ 1. K(x,y) \ 1 = K(y,x). K(x,y) * K(y,x) = 1. 1 / K(x,y) = K(y,x). K(x,y) * z = K(y,x) \ z. K(x,y) \ z = K(y,x) * z. K(x,y) * (K(y,x) * z) = z. x / (K(y,z) * x) = K(z,y). T(x * y,K(y,x)) / (y * x) = K(x,y). R(K(x,y),K(y,x) * z,u) = R(K(y,x),z,u) \ 1. a(K(x,y),z,u) = a(K(y,x),z,u). R(K(x,y),K(x,y) * z,u) = R(K(y,x),z,u) \ 1. K(x,y) * (K(y,x) / (x * y)) = K(x,y) \ ((y * x) \ 1). R(x,K(y,z),u) = R(x,K(z,y),u). L(x,y,K(z,u)) = L(x,y,K(u,z)). L(K(x,y),z,K(y,x)) * z = z * ((K(y,x) * z) \ z). (x * y) * z = (y * x) * (K(x,y) * z). (x * y) * (K(y,x) * z) = (y * x) * z. K(x,y) \ ((y * x) \ z) = (x * y) \ z. L(x,x,y) = (y * (x \ 1)) \ y. x / L(y,y,x) = x * (y \ 1). L(L(x,y * (z \ 1),y),z,y) = x. L(x * y,x,y) = (y \ (x \ 1)) \ 1. L(x,y,L(y \ 1,z,u)) = x. (x * (y \ z)) / L(z,y,x) = x * (y \ 1). L(x * (y * z),x,y) = (y \ (x \ 1)) \ z. L(x,K(y,z),u) = L(x,K(z,y),u). K(x,y) * (y * x) = T(x * y,K(y,x)). K(x,y) \ R(K(x,y),z,u) = R(K(x,y),K(y,x) * z,u) \ K(x,y). R(K(x,y),K(y,x) * z,u) \ K(x,y) = K(x,y) \ R(K(x,y),z,u). x \ (L(x \ 1,y,z) \ u) = (L(x \ 1,y,z) * x) \ u. (L(x \ 1,y,z) * x) \ u = x \ (L(x \ 1,y,z) \ u). L(x / y,x / y,z) = (z * (y / x)) \ z. L(K(x,y),K(x,y),z) = (z * K(y,x)) \ z. L(x,(y * (y * z)) * (y * u),w) = L(x,z \ (y \ u),w). L(x,(y * (y * z)) * y,u) = L(x,z \ (y \ 1),u). K(x,y) / L(z,z,K(y,x)) = K(x,y) * (z \ 1). L(x,y * z,y) = L(x,y * (z \ 1),y). L(x,y * (z \ 1),y) = L(x,y * z,y). L(x,K(y,z),y * z) = x. K(x,y) \ ((x * y) * z) = ((x * y) \ K(x,y)) \ z. ((x * y) \ K(x,y)) \ z = K(x,y) \ ((x * y) * z). L(x * y,x,y) * z = (y \ (x \ 1)) \ z. L(x,(y * y) / z,u) = L(x,z,u). L(x,y,z) = L(x,y / (u * u),z). L(x,y / (z * z),u) = L(x,y,u). L(x,y,z) = L(x,y * (u * u),z). L(x,y * (z * z),u) = L(x,y,u). L(x,R(y,z,z),u) = L(x,(y * z) * z,u). L(x,(y * z) * z,u) = L(x,R(y,z,z),u). x * y = ((y * x) * z) / (K(y,x) * z). ((x * y) * z) / (K(x,y) * z) = y * x. K(x,y) * z = (y * x) \ ((x * y) * z). (x * y) \ ((y * x) * z) = K(y,x) * z. K(x,y) * ((x * y) \ z) = (y * x) \ z. x * (y \ ((y * (x \ 1)) * z)) = L(z,y * x,y). L(x,y * z,u) = L(x,K(z,y) * (z * y),u). L(x,K(y,z) * (y * z),u) = L(x,z * y,u). (x * y) \ (y * (x * z)) = K(y,x) * L(z,x,y). (x * (y \ 1)) * L(z,y,x) = x * (y \ z). (a(x,y,z) \ (x \ 1)) \ u = x * (a(x,y,z) * u). L(K(x,y),K(x,y),z) / z = (z * K(y,x)) \ 1. (x * a(x,y,z)) * u = (a(x,y,z) \ (x \ 1)) \ u. (a(x,y,z) \ (x \ 1)) \ u = (x * a(x,y,z)) * u. L(x,T(y,y * z),u) = L(x,(y * z) * z,u). L(x,T(y,z),u) = L(x,(y * (y \ z)) * (y \ z),u). L(x,(y * (y \ z)) * (y \ z),u) = L(x,T(y,z),u). x * (y * ((y \ (x \ 1)) * z)) = L(z,y * x,y). K(x,y) * L(x,y,x) = T(x,y * x). x * ((x \ (y \ 1)) * y) = a(x,y,y). x * (y * (R(y,y * (x \ 1),z) \ ((x \ 1) * z))) = L(z,y * x,y). x * R(x \ 1,y \ 1,y) = a(x,y,y). a(x,y,y) = x \ R(x,y \ 1,y). x \ R(x,y \ 1,y) = a(x,y,y). x * R(x \ 1,y,y) = a(x,y,y). T(x \ 1,R(x,y \ 1,y)) = R(x,y \ 1,y) \ a(x,y,y). R(x,y \ 1,y) \ a(x,y,y) = T(x \ 1,R(x,y \ 1,y)). x \ R(x,y,y) = a(x,y,y). x * a(x,y,y) = R(x,y,y). a(x,y,y) \ R(x,y,y) = x. a(x,y,y) \ z = (R(x,y,y) \ x) * z. (R(x,y,y) \ x) * z = a(x,y,y) \ z. x * (a(x,y,y) * z) = R(x,y,y) * z. x \ a(x,y,y) = R(x \ 1,y,y). R(x \ 1,y,y) = x \ a(x,y,y). a(x,y,y) \ x = R(x,x * y,y). T(x * y,y * x) = T(x * y,K(y,x)). T(x * y,K(y,x)) = (x \ 1) \ y. K(x,y) / T(y * x,K(x,y)) = (y * x) \ K(x,y). T(x * y,K(y,x)) = x * y. (x * y) / (y * x) = K(x,y). K(x,y) * (y * x) = x * y. (x * y) / (T(x,y) * y) = K(y,T(x,y)). (T(x,y) * y) / (x * y) = K(T(x,y),y). R(K(x,y),y * x,z) = ((x * y) * z) / ((y * x) * z). ((x * y) * z) / ((y * x) * z) = R(K(x,y),y * x,z). (x \ y) / (y * (x \ 1)) = K(x \ 1,y). ((K(x,y) * z) * K(y,x)) / z = K(K(x,y) * z,K(y,x)). K(x \ y,x) * y = (x \ y) * x. K(x * y,x) * y = (x \ y) * x. K(x,T(y,x)) = T(y,x) \ y. T(x,y) * K(y,T(x,y)) = x. K(x,T(y,x)) * T(y,x) = y. T(x,y) \ (x * z) = K(y,T(x,y)) * z. (x \ y) * K(x,T(y / x,x)) = y / x. T(x,y) = K(T(x,y),y) * x. K(T(x,y),y) * x = T(x,y). K(x,x \ y) * T(y / x,x) = y / x. K(T(x,y),y) = x \ T(x,y). x * K(T(x,y),y) = T(x,y). K(x \ y,x) = (y / x) \ T(y / x,x). (x / y) \ T(x / y,y) = K(y \ x,y). K(T(x \ 1,y),y) = x * T(x \ 1,y). (x / y) * K(T(x / y,y),y) = y \ x. T(x,y) * (K(y,T(x,y)) * z) = x * z. T(x,y) \ z = K(y,T(x,y)) * (x \ z). K(x,T(y,x)) * (y \ z) = T(y,x) \ z. (x \ y) * K(x,x \ y) = y / x. (x \ y) * K(x,x * y) = y / x. K(x,x * y) = (x \ y) \ (y / x). (x \ y) \ (y / x) = K(x,x * y). x \ ((y * x) / y) = K(y,y * (y * x)). K(x,x * (x * y)) = y \ ((x * y) / x). K(x,x * y) * T(y / x,x) = y / x. (x / y) \ T(x / y,y) = K(y * x,y). (x / y) * K(y \ x,y) = y \ x. (x / y) * K(y * x,y) = y \ x. K(x * y,x) = (x / y) * (x \ y). (x / y) * (x \ y) = K(x * y,x). K(x * y,x) = (x \ y) * (x / y). (x \ y) * (x / y) = K(x * y,x). L(x,y,(z \ u) * K(z * u,z)) = L(x,y,z / u). x \ ((y * x) / y) = K(y,x). x * K(y,x) = (y * x) / y. (x * y) / x = y * K(x,y). K(x,y) \ 1 = y * (x / (x * y)). x * (y / (y * x)) = K(y,x) \ 1. ((x * y) / x) / y = K(x,y). K(x,y) * z = ((x * y) / x) * (y \ z). ((x * y) / x) * (y \ z) = K(x,y) * z. (x * K(y,x)) * y = y * x. x / (x / y) = y * K(x / y,y). T(x * K(y,x),y) = x. L(x,y * K(z,y),y) = x. a(x * K(y,x),z,u) = a(y / (y * x),z,u). a(x / (x * y),z,u) = a(y * K(x,y),z,u). T(x,y) = T(T(x * K(z,x),y),z). T(T(x * K(y,x),z),y) = T(x,z). x * T(y,z) = T(y * K(x,y),z) * x. T(x * K(y,x),z) * y = y * T(x,z). x / L(y,x * K(y,x),y) = y \ (x * K(y,x)). L(x,K(y,z),z) = x. (x * K(y,x)) \ z = K(y,x) \ (x \ z). (x * K(y,x)) * z = x * (K(y,x) * z). x = L(x,K(y,z),y). L(x,K(y,z),y) = x. (x * K(x,y)) * z = x * (K(x,y) * z). (x \ K(x,y)) * z = x \ (K(x,y) * z). x \ (K(x,y) * z) = (x \ K(x,y)) * z. K(x,y) / x = (x * K(y,x)) \ 1. (x * K(y,x)) \ 1 = K(x,y) / x. K(x,y) * y = (x * y) / x. (x * y) / x = K(x,y) * y. (x * K(y,x)) / x = K(y,x). K(x,y) * y = y * K(x,y). T(K(x,y),y) = K(x,y). T(x,K(y,x)) = x. K(x,y) * T(y,z) = T(y,z) * K(x,y). T(x,y) * K(z,x) = K(z,x) * T(x,y). x * (y / (y * x)) = K(x,y). x / (x * y) = y \ K(y,x). x \ K(x,y) = y / (y * x). (x / (x * y)) * y = K(y,x). K(x,y) / x = y / (y * x). K(x,y) * z = x * ((y / (y * x)) * z). x * ((y / (y * x)) * z) = K(x,y) * z. T(x,K(x,y)) = x. K(x,y) \ z = ((y * x) / y) * (x \ z). ((x * y) / x) * (y \ z) = K(y,x) \ z. T(x \ 1,K(x,y)) = x \ 1. K(x,y) * z = (y / (y * x)) * (x * z). (x / (x * y)) * (y * z) = K(y,x) * z. K(x,y) * x = x * K(x,y). T(x,T(y,x) \ y) = x. (T(x,y) \ x) * y = y * (T(x,y) \ x). ((x * y) / x) \ y = K(y,x). x \ K(x,y) = K(x,y) / x. K(x,y) / x = x \ K(x,y). K(x,y) * (x \ 1) = x \ K(x,y). (x * K(y,x)) \ 1 = x \ K(x,y). (x \ 1) / (x \ K(x,y)) = K(y,x). (x \ K(x,y)) * z = (x * K(y,x)) \ z. (x * K(y,x)) \ z = (x \ K(x,y)) * z. ((x * y) / x) * z = K(x,y) * (y * z). K(x,y) * (y * z) = ((x * y) / x) * z. T(x * K(y,x),z) = T(x,z) * K(y,T(x,z)). T(x,y) * K(z,T(x,y)) = T(x * K(z,x),y). T(x * K(x \ y,x),y) = L(x,x \ y,x). (x * K(y,x)) \ z = K(x,y) * (x \ z). ((x * y) / x) * z = y * (K(x,y) * z). x \ (K(x,y) * z) = (y / (y * x)) * z. ((x * y) / x) * z = K(y,x) \ (y * z). K(x,y) \ (x * z) = ((y * x) / y) * z. (x / (x * y)) * z = K(y,x) * (y \ z). K(x,y) * (x \ z) = (y / (y * x)) * z. x * (K(x,y) * z) = K(x,y) * (x * z). K(x,y) * (x * z) = x * (K(x,y) * z). x * (T(y,x) \ y) = T(x,T(y,x)). x * K(x,T(y,x)) = T(x,T(y,x)). x / (K(y,z) * (y \ x)) = y * K(z,y). K(x,y) * (x \ z) = (x \ K(x,y)) * z. (x \ K(x,y)) * z = K(x,y) * (x \ z). K(x,y) * (y * z) = y * (K(x,y) * z). K(x,y) \ (x * z) = (K(y,x) * x) * z. K(x,y) * (x \ (y * x)) = y. x \ (K(x,y) * z) = K(x,y) * (x \ z). K(x,y) * T(y,x) = y. K(x,y / x) = K(x,x * y). K(x,y) = K(x,T(y,x)). K(x,T(y,x)) = K(x,y). K(x,y) = T(y,x) \ y. T(x,y) \ x = K(y,x). T(x,y) = K(x,y) * x. K(x,y) * x = T(x,y). K(x,T(y,z)) * T(T(y,x),z) = T(y,z). K(x,R(y,z,u)) * R(T(y,x),z,u) = R(y,z,u). L(x \ y,x,K(z,y)) = (K(z,y) \ x) \ T(y,z). L(x,y,K(z,u) * u) = L(x,y,T(u,z)). T(x,y) / x = K(x,y). (x * y) * x = (y * x) * T(x,y). (x * y) * T(y,x) = (y * x) * y. T(x,y) * T(x,y) = x * T(T(x,y),y). T(x,y) * K(y,x) = x. x \ y = (y / (y * x)) * T(y,x). (x / (x * y)) * T(x,y) = y \ x. K(x,T(T(y,x),z)) = K(x,T(y,z)). K(x,x * (y * x)) = K(x,y). T(x,y) \ (x * z) = K(y,x) * z. T(x,y) * (K(y,x) * z) = x * z. K(x,y) * (y \ z) = T(y,x) \ z. x * K(x,y) = T(x,T(y,x)). T(T(x,y),z) \ T(x,z) = K(y,T(x,z)). K(x,y) * (T(y,x) * z) = y * z. K(x,y) * z = y * (T(y,x) \ z). x * (T(x,y) \ z) = K(y,x) * z. x * (T(x,y) \ 1) = K(y,x). x \ K(y,x) = T(x,y) \ 1. T(x,y) \ 1 = x \ K(y,x). (x * y) / (T(x,z) * y) = K(z,x). ((x * y) * y) \ ((y * x) * y) = K(y,(y * x) * y). (x * x) / (x * K(y,x)) = T(x,y). K(x,y) = K(T(x,y),y). K(T(x,y),y) = K(x,y). (x * T(y,z)) / L(y,K(y,z),x) = x * K(y,z). T(x,y) = x * K(x,y). x * K(x,y) = T(x,y). K(x,y) = x \ T(x,y). x \ T(x,y) = K(x,y). K(R(T(x,y),z,u),y) = K(R(x,z,u),y). K(x \ 1,y) = x * T(x \ 1,y). x * T(x \ 1,y) = K(x \ 1,y). T(x * K(y,x),T(y,x)) = x. K(x,y) * T(x,y) = T(T(x,y),y). K(K(x,y),z) = K(y,x) * T(K(x,y),z). K(x,y) * T(K(y,x),z) = K(K(y,x),z). (x * y) \ (x * T(y,z)) = L(K(y,z),y,x). x * (y * K(y,x)) = y * x. (x * y) * L(K(y,z),y,x) = x * T(y,z). (x \ y) * K(x * y,x) = T(x \ y,x). L(x,y,z * T(z,u)) = L(x,y,K(z,u)). T(x,y) * z = x * (K(x,y) * z). x * (K(x,y) * z) = T(x,y) * z. T(x,y) * K(x,y) = T(T(x,y),y). T(x,y) \ T(T(x,z),y) = K(T(x,y),z). L(x,y,z) \ L(T(x,u),y,z) = K(L(x,y,z),u). x \ ((x \ y) \ y) = K(x,x * y). K(x,y) * z = T(x,y) * (x \ z). T(x,y) * (x \ z) = K(x,y) * z. K(x \ 1,x * y) = x * ((x * y) \ y). x \ (T(x,y) * z) = K(x,y) * z. K(x / y,y) = K(y * x,y). K(x,(y * (x \ 1)) / x) = K(x,T(y,x \ 1)). T(x,T(y,x)) = T(x,y). T(T(x,y),z) = T(T(x,z),T(y,x)). T(T(x,y),T(z,x)) = T(T(x,z),y). T(x,x \ y) = T(x,y / x). T(x,y / x) = T(x,x \ y). (x * y) / T(y,x) = T(x,y). L(T(x,y),T(y,x),x) = T(x,x * T(y,x)). T(x,x * (y * x)) = T(x,y). T(x,y) / (T(y,x) \ x) = y. x \ T(y,x) = T(x,y) \ y. T(x,y) \ y = x \ T(y,x). T(x,y) = T(x,y * K(x,y)). T(x,y * K(x,y)) = T(x,y). T(K(x,y),z) \ 1 = K(y,x) * K(z,K(x,y)). K(x,y) * K(z,K(y,x)) = T(K(y,x),z) \ 1. (T(x,y) \ (y * K(x,y))) \ y = L(T(x,y),y * K(x,y),T(x,y)). L(T(x,y),y * K(x,y),T(x,y)) = (T(x,y) \ (y * K(x,y))) \ y. K((x * (y \ 1)) / y,y) = K(T(x,y \ 1),y). x / (x / y) = y * K(y * x,y). T(x,y / x) = T(x,x * y). T(x,y) * T(y,x) = x * y. x / (y \ T(x,y)) = T(y,x). (T(x,y) \ y) * K(x,x * T(y,x)) = T(y,x) / x. T(x,(y * (x \ 1)) / x) = T(x,T(y,x \ 1)). (T(x,y) * (T(y,x) * z)) \ ((x * y) * z) = a(T(x,y),T(y,x),z). (x * y) \ (T(x,y) * (T(y,x) * z)) = L(z,T(y,x),T(x,y)). T(T(x,y),x \ T(y,x)) = (x \ T(y,x)) \ y. R(x,y,x) * (y * x) = (y * x) * T(x,y). T(x,y) * ((y * x) / ((x * y) * x)) = K(T(x,y),y * x). K(x,T(y,x)) = K(x,T(y,K(z,T(y,x)))). K(x,T(y,K(z,T(y,x)))) = K(x,T(y,x)). L(x,y * K(z,y),u) = L(x,T(y,z),u). T(x,y) * (y * x) = x * (x * y). x \ y = K(x,z) * (T(x,z) \ y). K(x,y) * (T(x,y) \ z) = x \ z. K(x,y) * (y \ x) = y \ T(x,y). T(x,y) * z = K(x,y) * (x * z). K(x,y) * (x * z) = T(x,y) * z. ((T(x,y) * z) * u) / ((x * z) * u) = R(K(y,x),T(x,y) * z,u) \ 1. R(K(x,y),T(y,x) * z,u) \ 1 = ((T(y,x) * z) * u) / ((y * z) * u). T(x,y) \ z = x \ (K(y,x) * z). x \ (K(y,x) * z) = T(x,y) \ z. (x * y) * T((x * y) \ x,z) = x * K(y \ 1,z). K((x \ y) \ 1,z) = x \ (y * T(y \ x,z)). x \ (y * T(y \ x,z)) = K((x \ y) \ 1,z). (x * ((K(x,y) * z) * u)) \ ((T(x,y) * z) * u) = a(x,K(x,y) * z,u). x * (y * z) = T(x,y) * (T(y,x) * z). T(x,y) * (T(y,x) * z) = x * (y * z). L(x,y,K(z,z * u)) = L(x,y,z * ((z \ u) * u)). L(x,y,z * ((z \ u) * u)) = L(x,y,K(z,z * u)). T(x,y) \ ((x \ T(y,x)) \ y) = K(T(x,y),T(x,y) * y). x \ y = T(x,z) \ (K(x,z) * y). T(x,y) \ (K(x,y) * z) = x \ z. T(x,y) * T(z,x) = K(x,y) * (z * x). T(x / y,z) * y = K(x / y,z) * x. T(x,y) * (z / (z * x)) = K(x,y) * K(x,z). T(x,y) * (T(x,z) \ 1) = K(x,y) * K(z,x). x \ T(T(x,y),y) = K(x,y) * K(x,y). T(T(x,x * y),T(z,x)) = T(T(x,z),x \ y). (x / (x / y)) * z = y * (K(y * x,y) * z). ((x * y) * T(y,x)) \ (y * (y * x)) = K(T(y,x),x * y). (x * (x * y)) \ (T(x,y) * ((y * x) * z)) = L(z,y * x,T(x,y)). K(x,y) * (T(x,y) \ T(x,z)) = K(x,z). K(T(x,y \ 1),y) * (x * (y \ 1)) = y \ T(T(x,y \ 1),y). ((T(x,y) * z) * u) / ((x * z) * u) = R(K(x,y),x * z,u). (x * y) \ (T(x,z) * y) = T(K(x,z),x * y). L(x,T(y,z) * z,u) = L(x,z * y,u). x \ (y \ z) = T(x,y) \ (T(y,x) \ z). T(x,y) \ (T(y,x) \ z) = x \ (y \ z). T(x,y) \ (y * K(x,y)) = x \ y. K(x,y) * (x \ y) = x \ (y * K(x,y)). x \ (y * K(x,y)) = K(x,y) * (x \ y). (K(x,y) * (x \ z)) \ ((x \ K(x,y)) * (z * u)) = L(u,z,x \ K(x,y)). (K(x,y) * z) \ (y * (K(x,y) * z)) = L(T(y,z),z,K(x,y)). K(x,y) \ (x * z) = (K(x,y) \ x) * z. L(x,y,(z * u) / z) = L(x,y,T(u,z)). T(x,y) * K(y,T(x,z)) = K(z,T(x,y)) * T(x,z). L(x,y,(z / (u * u)) * (u \ (z * (u \ 1)))) = L(x,y,K(z / (u * u),u)). L(K(T(x,y),z),T(x,y),y) = (y * T(x,y)) \ (T(x,z) * y). (x * T(y,x)) \ (T(y,z) * x) = L(K(T(y,x),z),T(y,x),x). K(x,T(y,K(z,T(y,x)))) = K(x,y). K(x,y) * T(T(y,x),K(z,T(y,x))) = T(y,K(z,T(y,x))). T(x,y) = (x * (y * z)) / (T(y,x) * z). (x * (y * z)) / (T(y,x) * z) = T(x,y). (x \ y) * (T(x,y / x) * z) = (y / x) * (x * z). K(x / y,z) = (T(x / y,z) * y) / x. (T(x / y,z) * y) / x = K(x / y,z). K(x / y,z) * x = y * T(y \ x,z). (R(x,y,z) * (K(x,u) * K(x,u))) / T(T(x,u),u) = x \ R(x,y,z). x = L(x,y,K(y,z)). L(x,y,K(y,z)) = x. L(x,y,T(z,y) \ z) = x. x = L(x,y,T(z,y) * z). L(x,y,T(z,y) * z) = x. L(x,y,z * T(z,y)) = x. ((x * T(x,y)) * y) \ ((x * T(x,y)) * (y * z)) = z. L(x,y,T(z * u,z) / z) = L(x,y,T((z \ u) * z,z)). (x * (R(y,z,u) * w)) / (R(T(y,x),z,u) * w) = T(x,R(y,z,u)). (x * (y * (a(T(y,x),z,z) * u))) / (R(T(y,x),z,z) * u) = T(x,y). (x * T(x \ y,z)) / y = K(y / x,z). K((x * y) / x,z) * (x * y) = x * T(y,z). x \ (y * T(y \ x,z)) = T(K(x / y,z),x). ((x * y) * T((x * y) \ ((z * x) * y),u)) / ((z * x) * y) = K(R(z,x,y),u). T(x * K(x * y,x),y) = L(x,x \ y,x). L(T(x,y),T(y,x),x) = T(x,y * x). R(x,y,x) * (y * x) = (y * x) * T(x,x * (y * x)). (x * y) * T(y,y * (x * y)) = R(y,x,y) * (x * y). T(x * K(x * y,x),y) = L(x,x * y,x). T(x / (x / y),x) = L(y,y * x,y). K(x,y / (x * x)) = K(x,T(y,x \ 1)). K(x,T(y,x \ 1)) = K(x,y / (x * x)). K(x / (y * y),y) = K(T(x,y \ 1),y). K(T(x,y \ 1),y) = K(x / (y * y),y). T(x,y / (x * x)) = T(x,T(y,x \ 1)). T(x,T(y,x \ 1)) = T(x,y / (x * x)). (x * y) \ (x * T(y,z)) = K(((x * y) \ x) \ 1,z). K(((x * y) \ x) \ 1,z) = (x * y) \ (x * T(y,z)). K(x,y) * K(z,x) = T(x,z) \ T(x,y). T(x,y) \ T(x,z) = K(x,z) * K(y,x). K(x,y) * (K(x,z) * K(y,x)) = K(x,z). K(x,y) * K(z,x) = K(z,x) * K(x,y). T(T(x,y),x \ z) = T(T(x,y),x * z). T(T(x,y),x * T(y,x)) = (x \ T(y,x)) \ y. (x / (x / y)) * x = y * ((y \ x) * y). (x / (x / y)) * x = T(y * x,y). T(x * y,x) = (y / (y / x)) * y. x / (x / y) = T(y * x,y) / x. T(x * y,x) / y = y / (y / x). x = ((x / y) / x) * T(y * x,y). ((x / y) / x) * T(y * x,y) = x. x / (x / y) = x \ T(x * y,y). x \ T(x * y,y) = x / (x / y). (x / y) / x = x / T(y * x,y). x / T(y * x,y) = (x / y) / x. x * (x / (x / y)) = T(x * y,y). T(x * y,y) = x * (x / (x / y)). T(x * (y \ x),y \ x) = x * (x / y). T(K(x / y,z),x) = K((x \ y) \ 1,z). T(K(x,y),z) = K((z \ (x \ z)) \ 1,y). K((x \ (y \ x)) \ 1,z) = T(K(y,z),x). T(K(x,y),T(z,x)) = K((T(z,x) \ (T(x,z) \ z)) \ 1,y). K((T(x,y) \ (T(y,x) \ x)) \ 1,z) = T(K(y,z),T(x,y)). K(T(x \ 1,y) \ 1,z) = T(K(x,z),y). K(T((x \ 1) \ 1,y * y),z) = T(K(x,z),y * y). T(T(x,y),y * x) = (x \ T(y,x)) \ y. (x \ T(y,x)) \ y = T(T(x,y),y * x). x / L(y,T(x,y),y) = y \ (x * K(y,x)). x / L(y,T(x,y),y) = K(y,x) * (y \ x). L(x \ y,x,K(z,y)) = (K(y,z) * x) \ T(y,z). R(K(x,y),y * z,u) = R(K(y,x),T(y,x) * z,u) \ 1. R(K(x,y),T(x,y) * z,u) \ 1 = R(K(y,x),x * z,u). L(x,y * (y * (z * y)),u) = L(x,z \ (y \ 1),u). ((x * y) \ K(x,y)) \ z = K(y,x) * ((x * y) * z). (x * a(x,y,z)) * u = x * (a(x,y,z) * u). x * (a(x,y,z) * u) = a(x,y,z) * (x * u). a(x,y,z) * (x * u) = x * (a(x,y,z) * u). a(x,y,z) * u = x * (a(x,y,z) * (x \ u)). x * (a(x,y,z) * (x \ u)) = a(x,y,z) * u. L(x,y * (z \ y),u) = L(x,T(z,y),u). L(x,T(y \ 1,z),u) = L(x,T(y,z),u). K(x,y) / (y * x) = (y * x) \ K(x,y). L(x,y,T(z \ u,z)) = L(x,y,z / u). L(x,y,z / u) = L(x,y,T(z * u,z)). L(x,y,T(z * u,z)) = L(x,y,z / u). (T(x,y) \ y) * K(x,y * x) = T(y,x) / x. L(x,y,K(z,z * u)) = L(x,y,a(z,u,u)). L(x,y,a(z,u,u)) = L(x,y,K(z * u,z)). L(x,y,K(z * u,z)) = L(x,y,a(z,u,u)). L(x,y,K(z,u)) = L(x,y,a(z,u * z,u * z)). L(x,y,a(z,u * z,u * z)) = L(x,y,K(z,u)). K(x,T(y,z)) * T(T(y,x),K(x,T(y,z))) = K(z,T(y,x)) * T(y,z). (x \ y) * (T(x,x * y) * z) = (y / x) * (x * z). (x * (T(x,y) * y)) \ ((x * T(x,y)) * (y * z)) = z. K(((x * y) \ x) \ 1,z) = L(K(y,z),y,x). L(K(x,y),x,z) = K(((z * x) \ z) \ 1,y). L(K(x,y),x,z) = K(L(x \ 1,x,z) \ 1,y). K(L(x \ 1,x,y) \ 1,z) = L(K(x,z),x,y). K(T(x,y * y),z) = T(K(x,z),y * y). T(K(x,y),z * z) = K(T(x,z * z),y). K(T(x,y * y),z) \ 1 = T(K(x,z) \ 1,y * y). L(x,y \ (z \ 1),u) = L(x,y * z,u). L(x,y * z,u) = L(x,y * (z \ 1),u). L(x,y * (z \ 1),u) = L(x,y * z,u). (x \ y) * ((y / x) * (x * z)) = ((x \ y) * y) * z. (x * (T(x,y) * y)) \ (x * (T(x,y) * (y * z))) = z. T(K(x,y) \ 1,z * z) = K(y,T(x,z * z)). T(K(x,y),z * z) = K(x,T(y,z * z)). K(x,T(y,z * z)) = K(T(x,z * z),y). K(T(x,y * y),z) = K(x,T(z,y * y)). x = L(L(x,y,T(z,y)),T(z,y) * y,z). L(L(x,y,T(z,y)),T(z,y) * y,z) = x. x = L(L(x,y,T(z,y)),y * z,z). L(L(x,y,T(z,y)),y * z,z) = x. L(L(x,y,T(y \ z,y)),z,y \ z) = x. L(x,y * (z * y),y) = L(x,z,T(y,z)). L(x,y * z,z) = L(x,T(z,y) * y,T(z,y)). L(x,T(y,z) * z,T(y,z)) = L(x,z * y,y). L(x,T(y,z),z) = L(x,y,T(z,y)). L(x,T(y,y * z),y * z) = L(x,y,y / z). L(L(x,y,y / z),z,y \ z) = x. x = L(L(x,y,y / z),z,y * z). L(L(x,y,y / z),z,y * z) = x. L(x,y,z * y) = L(x,y,z / y). L(x,y,z / y) = L(x,y,z * y). L(x \ (x / y),x,y * x) = y \ 1. L(x,y,z * y) = L(x,y,y / z). L(x,y,y / z) = L(x,y,z * y). L(x,y,z) = L(x,y,(z * y) * y). L(x,y,(z * y) * y) = L(x,y,z). L(x \ 1,x,y * x) = y \ (y / x). L(x,x,y * x) = y \ (y / (x \ 1)). x * L(y,z,x * z) = (x / z) * (z * y). (x \ 1) \ L(T(y \ (y / x),z),y,x * y) = K(L(y \ (y / x),y,x * y),z). x \ (x / y) = ((x * y) * y) \ (x * y). ((x * y) * y) \ (x * y) = x \ (x / y). L(x,(y * z) * z,y * z) = L(x,y \ 1,T(y * z,y \ 1)). L(x,y \ 1,T(y * z,y \ 1)) = L(x,(y * z) * z,y * z). x * K(L(y \ 1,y,x * y) \ 1,z) = (x / y) * (y * K(y,z)). x \ L(x,x * y,y) = a(T(y,x),x,x). L(x,y * z,z) = L(x,y * z,T(z,y)). L(x,y * z,T(z,y)) = L(x,y * z,z). (K(x,y) * z) \ z = T(L(K(y,x),z,K(x,y)),z). T(L(K(x,y),z,K(y,x)),z) = (K(y,x) * z) \ z. R(x,y,x) = L(x,y * x,x). L(x,y * x,x) = R(x,y,x). L(x,y,x) = R(x,y / x,x). R(x,y / x,x) = L(x,y,x). T(R(x,y,x),z) = L(T(x,z),y * x,x). L(T(x,y),z * x,x) = T(R(x,z,x),y). L(x,y,x) * ((y / x) * x) = (x * (y / x)) * x. L(T(x,y),z * x,x) = R(T(x,y),z,x). L(x,y,x) * y = (x * (y / x)) * x. T(L(x,y,x) * y,x) = ((y / x) * x) * x. T(L(x,y,x) * y,x) = y * x. x * (y * x) = (L(x,y,x) * y) * x. (L(x,y,x) * y) * x = x * (y * x). x = L(R(x,y,x),y,x). L(R(x,y,x),y,x) = x. x = R(L(x,y,x),y,x). R(L(x,y,x),y,x) = x. L(x,y,x) = R(x,x \ y,x). R(x,x \ y,x) = L(x,y,x). L(x,x * y,x) = R(x,y,x). L(x,y,x) = R(x,x * y,x). R(x,x * y,x) = L(x,y,x). R(x,y,x) = y \ T(x * y,x). x \ T(y * x,y) = R(y,x,y). T(x * K(x * y,x),y) = R(x,y,x). T(x / (x / y),x) = R(y,x,y). L(x,y,x) \ x = x \ R(x,y,x). x * R(y,x,y) = T(y * x,y). T(x,R(y,x,y)) = T(x,x / (x / y)). (x / T(y * x,y)) * T(x,R(y,x,y)) = R(y,x,y) \ x. T(x,y) * K(x * y,T(x,y)) = R(x,y,x). T(x,y) * K(y * T(x,y),T(x,y)) = R(x,y,x). K(x,y) * (K(y,x) / (x * y)) = (x * y) \ 1. K(x,y) * ((x * y) \ K(y,x)) = (x * y) \ 1. (x * y) \ 1 = (y * x) \ K(y,x). (x * y) \ K(x,y) = (y * x) \ 1. ((x * y) \ 1) \ z = K(x,y) * ((y * x) * z). K(x,y) * ((y * x) * z) = ((x * y) \ 1) \ z. K(x,y) * ((y * x) * z) = (x * y) * z. K(x,y) = ((x * y) * z) / ((y * x) * z). ((x * y) * z) / ((y * x) * z) = K(x,y). K(x,y) = R(K(x,y),y * x,z). R(K(x,y),y * x,z) = K(x,y). R(K(x,T(y,x)),T(y,x) * x,z) = K(x,y). R(K(x,y),T(y,x) * x,z) = K(x,y). ((T(x,y) * y) * z) / ((K(y,x) * (T(x,y) * y)) * z) = K(y,x) \ 1. (x * L(x \ 1,y,z)) \ u = x \ (L(x \ 1,y,z) \ u). L(x,y * (y * (z * (y * u))),w) = L(x,z \ (y \ u),w). T(x,y) * (R(x,y,x) \ 1) = K(T(x,y),y * x). K(T(x,y),y * x) = R(x,y,x) \ T(x,y). R(x,y,x) \ T(x,y) = K(T(x,y),y * x). T(x,y) \ T(T(x,y),y * x) = K(T(x,y),T(x,y) * y). K(T(x,y),y * x) = (((y * x) * T(x,y)) \ (x * x)) * y. (((x * y) * T(y,x)) \ (y * y)) * x = K(T(y,x),x * y). K(x,y) * T(y,x) = T(y,K(z,T(y,x))). T(x,K(y,T(x,z))) = K(z,x) * T(x,z). T(x,K(y,T(x,z))) = x. T(x,y) = T(T(x,y),K(z,T(x,u))). T(T(x,y),K(z,T(x,u))) = T(x,y). L(x,y,T(z * u,z) / z) = L(x,y,R(u,z,z)). K((x \ (y \ x)) \ 1,z) = T(K(y,z),T(x,y)). T(K(x,y),T(z,x)) = K((z \ (x \ z)) \ 1,y). T(K(x,y),T(z,x)) = T(K(x,y),z). T(x,y) * T(K(y,z),x) = K(y,z) * T(x,y). K(x,y) * T(z,x) = K(z,x) * (K(x,y) * z). K(x,y) * (K(y,z) * x) = K(y,z) * T(x,y). (K(x,y) * T(z,x)) / L(z,K(x,y),K(z,x)) = K(z,x) * K(x,y). ((x / y) / x) * T(x,R(y,x,y)) = R(y,x,y) \ x. x \ (L(x \ 1,y,z) \ u) = L(x \ 1,y,z) \ (x \ u). L(x \ 1,y,z) \ (x \ u) = x \ (L(x \ 1,y,z) \ u). L(x,y \ (z \ u),w) = L(x,y * (z * u),w). L(x,y * (z * u),w) = L(x,y * (z \ u),w). L(x,y * (z \ u),w) = L(x,y * (z * u),w). L(x,y * z,u) = L(x,y * (w * (w * z)),u). L(x,y * (z * (z * u)),w) = L(x,y * u,w). L(x,(y \ z) * (z \ y),u) = L(x,(z \ y) * (y * z),u). L(x,y * R(z,z * u,w),v5) = L(x,y * (R(z,u,w) \ 1),v5). K(T(x,y),T(x,y) * y) = K(T(x,y),y * x). (((x * y) * x) \ (x * x)) * y = K(T(x,y),y * x). K(T(x,y),y * x) = K(x,x * y). R(x,y,x) \ T(x,y) = K(x,x * y). K(x,x * y) \ T(x,y) = R(x,y,x). R(x,y,x) = K(x * y,x) * T(x,y). K(x * y,x) * T(x,y) = R(x,y,x). K(x * y,x) = R(x,y,x) / T(x,y). R(x,y,x) / T(x,y) = K(x * y,x). (x \ (L(x \ 1,x,x / y) \ 1)) * (y \ (y / x)) = x \ 1. R(x,y \ 1,y) \ a(x,y,y) = x \ 1. R(x,y,y) \ a(x,y,y) = x \ 1. (x * y) \ (x * (y * z)) = L(z,T(y,x),T(x,y)). L(x,T(y,z),T(z,y)) = L(x,y,z). L(T(x,y),y,K(z,x)) = T(x,K(z,x) * y). (x \ (L(x \ 1,x,y * x) \ 1)) * (y \ (y / x)) = x \ 1. ((x \ y) * z) \ (x \ u) = ((x * y) * z) \ (x * u). (x * ((x \ y) * y)) \ z = ((x * y) * y) \ (x * z). (x * ((x \ y) * y)) \ y = x \ (x / y). x / (y \ (y / x)) = y * ((y \ x) * x). x * ((x \ y) * y) = (x \ (x / y)) \ y. (x \ (x / y)) \ y = x * ((x \ y) * y). x * L(x,y * x,y) = (y \ (y / x)) \ x. (x * L(x,y * x,y)) / x = (y \ (y / x)) \ 1. (x \ (x / y)) \ 1 = L(y,x * y,x). L(x,y * x,y) = (y \ (y / x)) \ 1. x \ ((y \ (y / x)) \ 1) = a(y,x,x). (x \ (x / y)) \ 1 = y * a(x,y,y). (x \ 1) \ (L(x,x,y * x) \ 1) = a(y,x \ 1,x \ 1). (x * a(y,x,x)) * z = (y \ (y / x)) \ z. (x \ (x / y)) \ z = (y * a(x,y,y)) * z. K(x,(x * x) / (y \ (y / z))) = K(x,z * a(y,z,z)). L(x \ 1,x,y * x) \ 1 = x * a(y,x,x). (x \ (x * a(y,x,x))) * (y \ (y / x)) = x \ 1. a(x,y,y) * (x \ (x / y)) = y \ 1. a(K(x,y),z,z) * (K(y,x) \ (K(y,x) / z)) = z \ 1. x * (y \ 1) = a(x,y,y) * (x / y). a(x,y,y) * (x / y) = x * (y \ 1). a(x,y,y) = (x * (y \ 1)) / (x / y). (x * (y \ 1)) / (x / y) = a(x,y,y). a(x,y,y) = (y / x) * (x * (y \ 1)). (x / y) * (y * (x \ 1)) = a(y,x,x). a(x / y,y,y \ 1) = a(x,y,y). a(x * (y * y),y \ 1,(y \ 1) \ 1) = a(x * y,y \ 1,y \ 1). K(x,y * a(z,y,y)) = K(x,(z \ (z / y)) \ 1). K(x,(y \ (y / z)) \ 1) = K(x,z * a(y,z,z)). a(K(x,y),z,z) * (K(x,y) * (K(y,x) / z)) = z \ 1. x \ 1 = K(y,z) * (a(K(y,z),x,x) * (K(z,y) / x)). K(x,y) * (a(K(x,y),z,z) * (K(y,x) / z)) = z \ 1. x \ 1 = R(K(y,z),x,x) * (K(z,y) / x). R(K(x,y),z,z) * (K(y,x) / z) = z \ 1. a(x,y \ 1,y \ 1) = y * (L(y,y,x * y) \ 1). x * (L(x,x,y * x) \ 1) = a(y,x \ 1,x \ 1). a(x,y \ 1,y \ 1) = L(y,y,x * y) \ y. a(x * y,y \ 1,y \ 1) = L(y,y,x) \ y. (x * (y \ z)) \ (x * (y \ (z * u))) = L(L(u,z,y),y * z,x). (x * y) * (z / (x * (y * z))) = x \ R(x,y,z). L(x,y \ R(y,z,u),y * z) = x. x = L(x,y * R(y,z,u),y * z). L(x,y * R(y,z,u),y * z) = x. x = L(x,y * R(y,y * z,u),z). L(x,y * R(y,y * z,u),z) = x. K(T(x,y \ 1),y) * (x * (y \ 1)) = T(x,y) * (y \ 1). K(T(x,y \ 1),y) = K(x,y). (x * (y \ 1)) / (T(x,y) * (y \ 1)) = K(y,T(x,y \ 1)). K(x,y) = K(x / (y * y),y). K(x / (y * y),y) = K(x,y). K(x,T(y,x \ 1)) = K(x,y). K(x \ 1,T(y,x)) = K(x \ 1,y). x * K(x,y) = T(x,T(y,x \ 1)). T(x,T(y,x \ 1)) = x * K(x,y). K(x,y) = K(x,y / (x * x)). K(x,y / (x * x)) = K(x,y). K(x,R(y / x,x,x)) = K(x,y * x). ((x \ 1) * T(y,x)) / (x \ 1) = T(y,x) * K(x \ 1,y). T(x,T(y,x \ 1)) = T(x,y). T(x \ 1,T(y,x)) = T(x \ 1,y). T(x,y) = T(x,y / (x * x)). T(x,y / (x * x)) = T(x,y). L(x,T(y,z),T(T(z,y \ 1),y)) = L(x,y,T(z,y \ 1)). T(x,R(y,x,x)) = T(x,(y * x) * x). T(x,(y * x) * x) = T(x,R(y,x,x)). L(x,T(y \ 1,z),T(T(z,y),y \ 1)) = L(x,y \ 1,T(z,y)). (x \ T(y,x)) / (x \ 1) = T(y,x) * K(x \ 1,y). T(x,y) * K(y \ 1,x) = T(x,y * y). L(x,T(y,z),T(T(z,y),y \ 1)) = L(x,y,T(z,y \ 1)). L(x,y \ 1,T(y * z,y \ 1)) = L(x,R(y,z,z),y * z). L(x,R(y,z,z),y * z) = L(x,y \ 1,T(y * z,y \ 1)). L(x,R(y,z,z),y * z) = L(x,y,T(y * z,y \ 1)). L(x,y * R(z,z * u,w),v5) = L(x,y * R(z,u,w),v5). L(x,y * R(y,z,u),z) = x. L(x,y * (z * R(z,y,u)),y) = x. L(x,y \ R(y \ 1,z,u),z) = x. (x * (y \ R(y,x,z))) * u = x * ((y \ R(y,x,z)) * u). a(x,x * (y * R(y,x,z)),u) = 1. x = L(x,y * R(y \ 1,z,u),z). L(x,y * R(y \ 1,z,u),z) = x. L(x,a(y,z,z),z) = x. x / (a(y,x,x) \ 1) = x * a(y,x,x). (x * a(y,x,x)) * z = x * (a(y,x,x) * z). K(x,(y \ (y / z)) \ 1) = K(x,z / (a(y,z,z) \ 1)). (x \ (x / y)) \ z = y * (a(x,y,y) * z). L(x * (a(y,x,x) * z),y * (y / x),y) = (y / x) \ (y * z). (x * (y \ R(y,x,z))) * u = x * (R(y,x,z) * (y \ u)). L(x,y \ 1,T(z,y)) = L(x,T(y,z),T(T(z,y),y \ 1)). L(x,T(y,z),T(T(z,y),y \ 1)) = L(x,y \ 1,T(z,y)). L(x,y \ 1,T(z,y)) = L(x,y,T(z,y \ 1)). L(x,y,T(z,y \ 1)) = L(x,y,T(z,y)). L(x,R(y,z,z),y * z) = L(x,y,T(y * z,y)). L(x,R(y,z,z),y * z) = L(x,y,y / z). L(x,R(y,z,z),y * z) = L(x,y,z * y). L(T(x,y),y * K(x,y),T(x,y)) = (x \ y) \ y. (x * (y * z)) \ ((x * y) * z) = a(T(x,y),T(y,x),z). a(T(x,y),T(y,x),z) = a(x,y,z). a(T(x,y),T(T(y,x),x),z) = a(x,T(y,x),z). L(x,y * z,T(z,y)) = y \ (z \ (z \ (T(z,y) * ((y * z) * x)))). x \ (y \ (y \ (T(y,x) * ((x * y) * z)))) = L(z,x * y,T(y,x)). x * K(y * a(x,y,y),z) = (x / y) * (y * K(y,z)). x * K(y * a(x,y,y),z) = (x / y) * T(y,z). x \ (y \ (K(y,x) * ((x * y) * z))) = L(z,x * y,T(y,x)). x \ (y \ ((y * x) * z)) = L(z,x * y,T(y,x)). L(x,y * z,T(z,y)) = L(x,z * y,z). L(x,y * z,y) = L(x,z * y,y). L(x,y * z,z) = L(x,z * y,z). L(L(x,y,z),y * z,z) = x. x \ L(x,x * y,y) = a(y,x,x). L(x,y * (y / z),y) = L(x,z,y). L(x,(y * z) * z,y * z) = L(x,T(y,z),y * z). L(x,T(y,z),z) = L(x,y,z). L(T(x,y),y,x) = T(x,y * x). x / L(y,x,y) = K(y,x) * (y \ x). K(x,y) * (x \ y) = y / L(x,y,x). L(x,y,y * z) = L(x,y,y / z). L(x,y,y / z) = L(x,y,y * z). (x * T(y,x)) \ (T(y,z) * x) = L(K(T(y,x),z),y,x). T(x,y * x) = T(x,x * y). K(x,y) * L(x,y,x) = T(x,x * y). T(x,x * y) * K(y * x,x) = x. T(x,x * (y * x)) = T(x,R(y,x,x)). x \ L(x,y,x * y) = a(x * y,x,x). x \ L(x,T(y,x),y * x) = a(y * x,x,x). a(x,y,y) = a(T(x,y),y,y). a(T(x,y),y,y) = a(x,y,y). L(x * (a(y,x,x) * z),x,y) = (y / x) \ (y * z). L(x,x,x * y) = y \ (y / (x \ 1)). K(x * y,y) = K(y * x,y). T(x * K(x * y,x),y * x) = x. x / (x / y) = y * K(x * y,y). R(x,y,x) / T(x,y) = K(y * x,x). T(x / (x / y),x * y) = y. T(x * y,y) = T(x * y,x / (x / y)). T(x * y,x / (x / y)) = T(x * y,y). x \ (y * x) = (y / (y / x)) \ T(y * x,y / (y / x)). (x / (x / y)) \ T(x * y,x / (x / y)) = y \ (x * y). x / (x / T(y,x)) = R(y,x,y). R(x,y,x) = y / (y / T(x,y)). R(x,y,x) \ y = y / T(x,y). (T(x,y) \ y) * K(T(x,y),T(x,y) * y) = R(x,y,x) \ y. ((x / y) / x) * T(x,R(y,x,y)) = x / T(y,x). (x \ y) / (y / L(x,y,x)) = K(y,x). R(x,x * y,x) \ (x * y) = (x * y) / (K(x,y) * L(x,y,x)). (x * y) / (K(x,y) * L(x,y,x)) = R(x,x * y,x) \ (x * y). T(x,R(y,x,x)) = T(x,y). x \ T(x,y) = K(x,R(y,x,x)). K(x,R(y,x,x)) = x \ T(x,y). K(x,R(y,x,x)) = K(x,y). K(x,y / x) = K(x,y * x). K(x,y * x) = K(x,x * y). ((x * y) * y) \ ((y * x) * y) = K(y,y * (y * x)). (T(x,y) \ y) * K(x,x * y) = T(y,x) / x. K(T(x,y),y * T(x,y)) = K(T(x,y),y * x). K(x * y,y) = T(y,x) \ R(y,x,y). T(x,y) \ R(x,y,x) = K(y * x,x). K(x,y) * (y \ R(y,x,y)) = K(x * y,y). K(T(x,y),x * y) = K(T(x,y),y * x). K(T(x,y),y * x) = K(T(x,y),x * y). K(T(x,y),x * y) = K(x,x * y). L(x,T(y,z),y * z) = L(x,R(y,z,z),y * z). L(x,R(y,z,z),y * z) = L(x,T(y,z),y * z). L(x,T(y,z),y * z) = L(x,y,z * y). x \ L(x,y,x * y) = a(y * x,x,x). a(x * y,y,y) = a(y * x,y,y). L(x * (a(y,x,x) * z),x,y) = (x / y) * (y * z). ((x * y) * y) \ ((y * x) * y) = K(y,x). K(x * y,y) * K(y,x) = (y * (x * y)) \ ((y * x) * y). (x * (y * x)) \ ((x * y) * x) = K(y * x,x) * K(x,y). (x * y) \ (T(x,z) * y) = L(K(T(x,y),z),x,y). L(K(T(x,y),z),x,y) = T(K(x,z),x * y). (x / (x / y)) \ T(x * y,x / (x / y)) = T(x,y). (x / (x / y)) \ T(x * y,y) = T(x,y). T(x,y) = ((x / y) / x) * T(x * y,y). ((x / y) / x) * T(x * y,y) = T(x,y). (x / y) * T(y * (x \ y),x \ y) = T(y,x \ y). L(x,y,z * (((u / w) / u) * T(u,w))) = L(x,y,z * T(u * w,w)). (x / y) * (y * (y / x)) = T(y,x \ y). T(x,y \ x) = T(x,x / y). T(x,x / y) = T(x,y \ x). T(x,R(y,x,y)) = T(x,(x / y) \ x). T(x,R(y,x,y)) = T(x,y). ((x / y) / x) * T(x,y) = x / T(y,x). K(x * y,y) * K(y,x) = a(y,x,y). K(x,y) * K(y * x,x) = a(x,y,x). K(x * y,y) = K(x,y) * a(y,x,y). K(x,y) * a(y,x,y) = K(x * y,y). K(x,y) * K(x * y,x) = a(x,y,x). a(x,y,x) = x \ R(x,y,x). x \ R(x,y,x) = a(x,y,x). L(x,y,x) \ x = a(x,y,x). (T(x,y) \ y) * K(T(x,y),y * T(x,y)) = R(x,y,x) \ y. (T(x,y) \ y) * K(T(x,y),x * y) = R(x,y,x) \ y. (T(x,y) \ y) * K(x,x * y) = R(x,y,x) \ y. R(x,y,x) \ y = T(y,x) / x. T(x,y) / y = x / T(y,x). (x / T(y,x)) * y = T(x,y). (x / y) * (y * K(x,y)) = T(x,y * K(x,y)). (x / y) * (y * K(x,y)) = T(x,y). x * K(y,x) = (x / y) * T(y,x). (x / y) * T(y,x) = x * K(y,x). (x * (y \ 1)) * T(L(y,y,x),x) = x * K(L(y,y,x),x). (x * (y \ 1)) * L(T(y,x),y,x) = x * K(L(y,y,x),x). x * K(L(y,y,x),x) = x * (y \ T(y,x)). x * K(L(y,y,x),x) = x * K(y,x). T(x * K(y,x),L(y,y,x)) = x. T(x,y) = T(x,L(y,y,x)). T(x,L(y,y,x)) = T(x,y). (x * y) / (K(x,y) * L(x,y,x)) = L(x,y,x) \ (x * y). (x * y) / (K(x,y) * L(x,y,x)) = (L(x,y,x) \ x) * y. (x * y) / T(x,x * y) = (L(x,y,x) \ x) * y. T(x * y,x) / x = (L(x,y,x) \ x) * y. (L(x,y,x) \ x) * y = T(x * y,x) / x. a(x,y,x) * y = T(x * y,x) / x. T(x * y,x) / x = a(x,y,x) * y. R(K(x,y),K(y,x) * z,u) \ K(x,y) = K(y,x) * R(K(x,y),z,u). x * (y * (R(y,y * (x \ 1),z) \ (x \ z))) = L(z,y * x,y). x * (R(y,x \ 1,z) * (y \ (x \ z))) = L(z,y * x,y). x * (R(y,x,z) * (y \ (x \ z))) = L(z,y * x,y). R(x * (K(x,y) * K(x,y)),z,u) / T(T(x,y),y) = x \ R(x,z,u). K(x,T(y,z)) * T(y,x) = K(z,T(y,x)) * T(y,z). (K(x,T(y,z)) * T(y,x)) / L(y,K(y,z),K(z,T(y,x))) = K(z,T(y,x)) * K(y,z). ((T(x,y) * y) * z) / ((x * y) * z) = K(y,x) \ 1. a(x * (y * y),y \ 1,y) = a(x * y,y \ 1,y \ 1). L(x,y,z * (u / T(w,u))) = L(x,y,z * T(u * w,w)). L(x,y,z * T(u * w,w)) = L(x,y,z * (u / T(w,u))). L(x,y,z * T(u * w,w)) = L(x,y,z * (T(u,w) / w)). L(x,y,z * (T(u,w) / w)) = L(x,y,z * T(u * w,w)). (R(K(x,y),z,u) \ 1) \ K(y,x) = K(x,y) * R(K(y,x),z,u). K(x,y) * R(K(y,x),z,u) = R(K(x,y),z,u) * K(y,x). R(K(x,y),z,u) * K(y,x) = K(x,y) * R(K(y,x),z,u). R(K(x,y),y * z,u) \ K(x,y) = K(y,x) * R(K(x,y),T(y,x) * z,u). K(x,y) * R(K(y,x),T(x,y) * z,u) = R(K(y,x),x * z,u) \ K(y,x). R(T(x,y) * K(x,y),z,u) / T(T(x,y),y) = x \ R(x,z,u). R(T(T(x,y),y),z,u) / T(T(x,y),y) = x \ R(x,z,u). x \ R(x,y,z) = T(T(x,u),u) \ R(T(T(x,u),u),y,z). T(T(x,y),y) \ R(T(T(x,y),y),z,u) = x \ R(x,z,u). (x * y) * L(T(y \ z,u),y,x) = (x * y) * T((x * y) \ (x * z),u). (x * y) * T((x * y) \ (x * z),u) = (x * y) * L(T(y \ z,u),y,x). (x * y) * L(R(y \ 1,z,u),y,x) = (x * y) * R((x * y) \ x,z,u). (x * y) * R((x * y) \ x,z,u) = (x * y) * L(R(y \ 1,z,u),y,x). (K(x,y) * (x \ z)) \ (K(x,y) * (x \ (z * u))) = L(u,z,x \ K(x,y)). (x * y) * T((x * y) \ (x * z),u) = x * (y * T(y \ z,u)). (x * y) * R((x * y) \ x,z,u) = x * (y * R(y \ 1,z,u)). (x * y) * R((x * y) \ x,z,u) = x * (y \ R(y,z,u)). x \ R(x,y,z) = (x / u) * (u * R(((u \ x) * x) \ (u \ x),y,z)). (x / y) * (y * R(((y \ x) * x) \ (y \ x),z,u)) = x \ R(x,z,u). (x / y) * (y * R(((y * x) * x) \ (y * x),z,u)) = x \ R(x,z,u). (x / y) * (y * R(y \ (y / x),z,u)) = x \ R(x,z,u). ((x \ y) / y) * (y * R(y \ x,z,u)) = (x \ y) \ R(x \ y,z,u). (L(x,y,z) / (z * (y * x))) * ((z * (y * x)) * R((z * (y * x)) \ (z * y),u,w)) = L(x,y,z) \ R(L(x,y,z),u,w). (x \ 1) * (y * R(y \ x,z,u)) = (x \ y) \ R(x \ y,z,u). (x \ y) \ R(x \ y,z,u) = x \ (y * R(y \ x,z,u)). x \ (y * R(y \ x,z,u)) = (x * y) \ R(x * y,z,u). (x * y) \ R(x * y,z,u) = x \ (y * R(y \ x,z,u)). L(x,y,z \ K(z,u)) = L(L(x,y,z),z * y,K(z,u)). L(L(x,y,z),z * y,K(z,u)) = L(x,y,z \ K(z,u)). L(L(x,y,z),z * y,K(z,u)) = L(x,y,z * K(z,u)). L(L(x,y,z),z * y,K(z,u)) = L(x,y,T(z,u)). L(x,y * (y * z),K(y,u)) = L(L(x,z,y),y * z,T(y,u)). L(L(x,y,z),z * y,T(z,u)) = L(x,z * (z * y),K(z,u)). L(L(x,y,z),z * y,T(z,u)) = L(x,y,K(z,u)). (x * (y * x)) \ R(x * (z * x),u,w) = T(y,x) \ T(R(z,u,w),x). (x * (y * x)) \ R(x * (z * x),u,w) = T(y,x) \ R(T(z,x),u,w). T(x,y) \ R(T(x,y),z,u) = y \ ((x * y) * R((x * y) \ y,z,u)). x \ ((y * x) * R((y * x) \ x,z,u)) = T(y,x) \ R(T(y,x),z,u). L(x,y,z * (u \ (u \ (u \ (z * (u \ 1)))))) = L(x,y,K(z / (u * u),u)). L(x,y,z * (u \ ((u \ (u \ z)) * (u \ 1)))) = L(x,y,K(z / (u * u),u)). L(x,y,K(z / (u * u),u)) = L(x,y,z * (u * ((u \ (u \ z)) * (u \ 1)))). L(x,y,z * (u * ((u \ (u \ z)) * (u \ 1)))) = L(x,y,K(z / (u * u),u)). L(x,y,z * (u \ (z * (u \ 1)))) = L(x,y,K(z / (u * u),u)). L(x,y,K(z / (u * u),u)) = L(x,y,z * (u \ (z * (u \ 1)))). L(x,y,K(z / (u * u),u)) = L(x,y,z * (u * (z * (u \ 1)))). L(x,y,K(z / (u * u),u)) = L(x,y,z * T(z,u \ 1)). L(x,y,K(z / (u * u),u)) = L(x,y,K(z,u \ 1)). L(x,y,K(z,u)) = L(x,y,K(z,u \ 1)). L(x,y,K(z,u \ 1)) = L(x,y,K(z,u)). L(x,y,K(z,u \ 1)) = L(x,y,K(u,z)). (x * (x * (y * (z * u)))) \ ((x * (x * (y * z))) * u) = a(x * (x * y),z,u). (x * y) * R(L(y \ z,y,x),u,w) = (x * y) * R((x * y) \ (x * z),u,w). ((x * y) * ((y * x) * z)) \ (((x * y) * (y * x)) * (z * u)) = L(u,z,K(y,x)). ((x * y) * T(R(T(z,x * y),x,y),u)) / ((z * x) * y) = K(R(z,x,y),u). ((x * y) * R(T(T(z,x * y),u),x,y)) / ((z * x) * y) = K(R(z,x,y),u). (R(T(x,y),z,u) * (z * u)) / ((x * z) * u) = K(R(x,z,u),y). ((T(x,y) * z) * u) / ((x * z) * u) = K(R(x,z,u),y). K(R(x,y,z),u) = R(K(x,u),x * y,z). R(K(x,y),x * z,u) = K(R(x,z,u),y). K(R(x,y,z),y) = K(y,x) \ 1. R(K(x,y),T(y,x) * z,u) \ 1 = K(R(y,z,u),x). K(R(x,y,z),y) = K(x,y). (x * x) / (x * K(y,x)) = T(x,R(y,x,z)). T(x,R(y,x,z)) = (x * x) / (x * K(y,x)). R(K(x,y),z,u) = K(R(x,x \ z,u),y). K(R(x,x \ y,z),u) = R(K(x,u),y,z). R(K(x,y),x * (z / (z * x)),u) = K(x,y). R(K(x,y),T(x,y) * z,u) = K(R(T(x,y),z,u),y). K(R(x,x * y,z),u) = R(K(x,u),y,z). K(L(x,y,x),z) = R(K(x,z),y,x). R(K(x,y),z,x) = K(L(x,z,x),y). R(K(x,y),z,u) \ 1 = K(y,R(x,x * z,u)). K(x,R(y,y * z,u)) = R(K(y,x),z,u) \ 1. K(R(x,T(x,y) * z,u),w) = R(K(x,w),K(x,y) * z,u). R(K(x,y),K(x,z) * u,w) = K(R(x,T(x,z) * u,w),y). R(K(T(x,y),y),z,u) = K(R(x,T(x,y) * z,u),y). K(R(x,T(x,y) * z,u),y) = R(K(T(x,y),y),z,u). T(x,R(y,x,z)) = T(x,y). R(x,y,z) * T(y,x) = y * R(x,y,z). T(x,y) \ (x * R(y,x,z)) = T(R(y,x,z),T(x,y)). R(K(x,y),K(x,z),u) = K(x,y). K(x,y) = R(K(x,y),K(z,x),u). R(K(x,y),K(z,x),u) = K(x,y). K(x,y) * (K(z,x) * u) = (K(x,y) * K(z,x)) * u. (K(x,y) * K(z,x)) * u = K(x,y) * (K(z,x) * u). K(R(x,y,z),u) \ 1 = R(K(u,x),T(x,u) * y,z). R(K(x,y),T(y,x) * z,u) = K(R(y,z,u),x) \ 1. R(K(x,y),T(x,y) * z,u) = K(R(x,z,u),y). K(R(x,y,z),u) \ 1 = R(K(u,x),x * y,z). R(K(x,y),y * z,u) = K(R(y,z,u),x) \ 1. R(K(x,y),y * z,u) = K(x,R(y,z,u)). R(K(x,y),x * z,u) * K(y,x) = K(x,y) * K(y,R(x,z,u)). K(R(x,T(x,y) * z,u),y) = R(K(x,y),z,u). T(R(x,y,z),T(y,x)) = K(x,y) * R(x,y,z). K(x,y) * R(x,y,z) = T(R(x,y,z),T(y,x)). K(x,y) * R(x,y,z) = R(T(x,T(y,x)),y,z). K(x,y) * R(x,y,z) = R(T(x,y),y,z). T(x,y) \ R(T(x,y),y,z) = x \ R(x,y,z). (x \ y) \ R(T(y / x,x),x,z) = (y / x) \ R(y / x,x,z). x = L(x,K(y,z),K(z,u)). L(x,K(y,z),K(z,u)) = x. x = L(x,K(y,z),K(u,z)). L(x,K(y,z),K(u,z)) = x. x = L(x,K(y,z),K(u,y)). L(x,K(y,z),K(u,y)) = x. (K(x,y) * T(z,x)) / z = K(z,x) * K(x,y). R(K(x,y),T(y,x) * z,u) = K(x,R(y,z,u)). K(x,y) * K(y,R(x,z,u)) = R(K(y,x),x * z,u) \ K(y,x). R(K(x,y),y * z,u) \ K(x,y) = K(y,x) * K(x,R(y,z,u)). R(K(x,y),K(x,y) * z,u) = R(K(x,y),z,u). R(K(x,y),z,u) = R(K(y,x),z,u) \ 1. R(K(x,y),z,u) \ 1 = R(K(y,x),z,u). K(x,y) * R(K(y,x),z,u) = R(K(x,y),z,u) \ K(x,y). R(K(x,y),z,u) \ K(x,y) = K(x,y) * R(K(y,x),z,u). K(x,R(y,y * z,u)) = R(K(x,y),z,u). K(R(x,y,z),u) * K(u,x) = K(x,u) * K(u,R(x,y,z)). K(x,y) * K(R(y,z,u),x) = K(y,x) * K(x,R(y,z,u)). (x \ y) \ R(x \ y,x,z) = (y / x) \ R(y / x,x,z). (x / y) \ R(x / y,y,z) = (y \ x) \ R(y \ x,y,z). (x \ y) \ R(x \ y,x,z) = (x / y) * R(y / x,x,z). (x / y) * R(y / x,x,z) = x \ (y * R(y \ x,x,z)). x \ (y * R(y \ x,x,z)) = (x / y) * R(y / x,x,z). x \ ((y \ x) * R((y \ x) \ x,x,z)) = y * R((y \ x) / x,x,z). x \ (R(y,x,z) * (y \ x)) = y * R((y \ x) / x,x,z). x * R((x \ y) / y,y,z) = T(x \ R(x,y,z),y). x * R(x \ 1,y,z) = T(x \ R(x,y,z),y). T(x \ R(x,y,z),y) = x * R(x \ 1,y,z). T(x \ R(x,y,z),y) = x \ R(x,y,z). (x * (y \ R(y,x,z))) / x = y \ R(y,x,z). T(x \ R(x,y,z),x * (y * z)) = T(a(x,y,z),y). L((x * (y \ R(y,x,z))) * (a(x,x * (y \ R(y,x,z)),x * (y \ R(y,x,z))) * u),x * (y \ R(y,x,z)),x) = (y \ R(y,x,z)) * (x * u). T(a(x,y,z),y) = a(x,y,z). x * a(y,x,z) = a(y,x,z) * x. a(x,y,z) * y = y * a(x,y,z). x \ a(y,x \ 1,z) = a(y,x \ 1,z) * (x \ 1). a(x,y \ 1,z) * (y \ 1) = y \ a(x,y \ 1,z). T(x * y,x) / x = y * a(x,y,x). L(x,y,z * (T(u * z,u) / u)) = L(x,y,a(u,z,u)). L(x,y,z * a(u,z,u)) = L(x,y,R(z,u,u)). L(x,y,a(z,u,z)) = L(x,y,u * T((z * u) * z,z)). L(x,y,z * T((u * z) * u,u)) = L(x,y,a(u,z,u)). L(x,y,z * ((z * u) * u)) = L(x,y,a(u,z,u)). L(x,y,a(z,u,z)) = L(x,y,a(u,z,z)). L(x,y,a(z,u,u)) = L(x,y,a(u,z,u)). (x * (x * (y * (z * u)))) \ (x * (x * ((y * z) * u))) = a(x * (x * y),z,u). (x * y) * L(R(y \ z,u,w),y,x) = (x * y) * R((x * y) \ (x * z),u,w). (x * y) * R((x * y) \ (x * z),u,w) = (x * y) * L(R(y \ z,u,w),y,x). ((x * y) * ((y * x) * z)) \ ((x * y) * ((y * x) * (z * u))) = L(u,z,K(y,x)). a(x * (x * y),z,u) = (y * (z * u)) \ ((y * z) * u). a(x * (x * y),z,u) = a(y,z,u). a(x * y,z,u) = a(x \ y,z,u). a(x \ y,z,u) = a(x * y,z,u). a((x / y) * x,z,u) = a(y,z,u). a(x * (y * x),z,u) = a(T(y,x),z,u). a(x * ((x * y) * z),u,w) = a(x * ((x \ y) * z),u,w). a(x * ((x \ y) * z),u,w) = a(x * ((x * y) * z),u,w). a((x * y) * z,u,w) = a((x \ y) * z,u,w). a((x \ y) * z,u,w) = a((x * y) * z,u,w). a((x * x) / y,z,u) = a(y \ 1,z,u). a(x * L(x,y * x,y),z,u) = a(a(y,x,x),z,u). a(x * a(x,y,y),z,u) = a(R(x \ 1,y,y),z,u). a(R(x \ 1,y,y),z,u) = a(x * a(x,y,y),z,u). a(K(x,y) * y,z,u) = a(T(y,x),z,u). a(x * T(x,y),z,u) = a(K(x,y),z,u). ((x \ y) * (T(x,x * y) * z)) \ (y * z) = a(x * y,T(x,x * y),z). a(x \ ((x * y) \ y),z,u) = a(K(x \ 1,x * y),z,u). a(K(x \ 1,x * y),z,u) = a(x \ ((x * y) \ y),z,u). a((x * (x * y)) * (x * z),u,w) = a(y \ (x \ z),u,w). a((x * x) / y,z,u) = a(y,z,u). a(x,y,z) = a(x / (u * u),y,z). a(x / (y * y),z,u) = a(x,z,u). a(R(x,x * y,z),u,w) = a(R(x,y,z),u,w). a(T(x,y),z,u) = a(x * K(y,x),z,u). a(x * K(y,x),z,u) = a(T(x,y),z,u). a(x,y,z) = a(x * (u * u),y,z). a(x * (y * y),z,u) = a(x,z,u). a(R(x,y,y),z,u) = a((x * y) * y,z,u). a((x * y) * y,z,u) = a(R(x,y,y),z,u). a(x / y,z,u) = a(x / (y \ 1),z,u). a(x / (y \ 1),z,u) = a(x / y,z,u). ((x * (y * y)) * (z * u)) \ (((x * (y * y)) * z) * u) = a(x,z,u). a(x,y,z) = a(T(T(x,u),u),y,z). a(T(T(x,y),y),z,u) = a(x,z,u). a((x / (y * y)) * (y \ (x * (y \ 1))),z,u) = a(K(x / (y * y),y),z,u). a(x / (x * y),z,u) = a(T(y,x),z,u). a(x / y,z,u) = a((y \ 1) / x,z,u). a((x \ 1) / y,z,u) = a(y / x,z,u). a(x / T(y * x,y),z,u) = a(T(R(y,x,y),x),z,u). a(R(x,y,y),y,y) = a(y * (x * y),y,y). a(x * (y * x),x,x) = a(R(y,x,x),x,x). a(R(x,y,y),y,y) = a(T(x,y),y,y). a(R(x,y,y),y,y) = a(x,y,y). R(R(x,y,y) \ 1,y,y) = R(x,y,y) \ a(x,y,y). a(x,y,y) \ R(x,y,y) = R(R(x,y,y),R(x,y,y) * y,y). R(R(x,y,y),R(x,y,y) * y,y) = a(x,y,y) \ R(x,y,y). a(x * ((x \ y) * y),z,u) = a(a(x,y,y),z,u). a(R(x \ 1,y,y),z,u) = a(R(x,y,y),z,u). R(R(x,y,y) \ 1,y,y) = x \ 1. R((x * y) \ 1,y,y) = (x / (y \ 1)) \ 1. R((x * y) \ 1,y,y) = (y \ 1) / x. R(x \ 1,y,y) = (y \ 1) / (x / y). (x \ 1) / (y / x) = R(y \ 1,x,x). ((x \ 1) / y) * (x * x) = (((y * x) \ 1) * x) * x. (((x * y) \ 1) * y) * y = ((y \ 1) / x) * (y * y). R(x \ 1,y,y) \ 1 = (x / y) / (y \ 1). a((x \ 1) / ((y / x) \ 1),z,u) = a(R(y \ 1,x,x),z,u). R(x,x * y,y) = (x / y) / (y \ 1). K(R(x,x * y,y),z) * (x / y) = (y \ 1) * T((y \ 1) \ (x / y),z). (((x * y) \ 1) * y) * y = T(y / x,y * y). ((x * y) \ y) * y = T(y / x,y * y). L(x,y * z,R(T(z / y,z * z),u,w)) = x. x = L(x,y * z,R(z / y,u,w)). L(x,y * z,R(z / y,u,w)) = x. L(x,y * (z \ 1),u / (y * (z * u))) = x. x = L(x,y * z,u / (y * (z * u))). L(x,y * z,u / (y * (z * u))) = x. x / ((y * z) \ (y * (z * x))) = (x / (y * (z * x))) * (y * z). a((x / y) / x,z,u) = a(T(R(y,x,y),x),z,u). a(T(R(x,y,x),y),z,u) = a((y / x) / y,z,u). a(x * ((x * y) * y),z,u) = a(a(x,y,y),z,u). a(x * (x * (y * (x * z))),u,w) = a(y \ (x \ z),u,w). a(x \ (y \ z),u,w) = a(x * (y * z),u,w). a(x * (y * z),u,w) = a(x * (y \ z),u,w). a(x * (y \ z),u,w) = a(x * (y * z),u,w). a(K(x \ 1,x * y),z,u) = a(x * ((x * y) * y),z,u). R(R(x,y,y),R(x,y,y) * y,y) = x. K(x,y) = R(K(R(x,z,z),y),z,z). R(K(R(x,y,y),z),y,y) = K(x,z). K(x,y) / z = K(R(x,z,z),y) * (z \ 1). K(R(x,y,y),z) * (y \ 1) = K(x,z) / y. x \ 1 = K(y,R(z,x,x)) * (K(z,y) / x). K(x,R(y,z,z)) * (K(y,x) / z) = z \ 1. K(x,R(y,z,z)) = R(K(x,y),z,z). R(K(x,y),z,z) = K(x,R(y,z,z)). K(R(x,y,y),z) \ 1 = R(K(z,x),y,y). R(K(x,y),z,z) = K(x,R(y,z,z)) * 1. K(x,R(y,z,z)) * 1 = R(K(x,y),z,z). a((x \ 1) / (x / y),z,u) = a(R(y \ 1,x,x),z,u). a(R(x \ 1,y,y),z,u) = a((y / x) / y,z,u). a((x / y) / x,z,u) = a(R(y,x,x),z,u). a(T(R(x,y,x),y),z,u) = a(R(x,y,y),z,u). a(R(T(x,y),y,x),z,u) = a(R(x,y,y),z,u). x / L(x,y,z) = (x / (z * (y * x))) * (z * y). (x / (y * (z * x))) * (y * z) = x / L(x,z,y). (x / (y * (z * x))) * (y * z) = L(x,z,y) \ x. (L(x * y,z / (x * (y * z)),x * y) * (z / (x * (y * z)))) * (x * y) = (x * y) * (L(z,y,x) \ z). (x * (y * (y * (z * u)))) \ (((x * (y * y)) * z) * u) = a(x,z,u). (x * (y * (y * (z * u)))) \ ((x * (y * (y * z))) * u) = a(x,z,u). a(x,y,z) = a(x,u * (u * y),z). a(x,y * (y * z),u) = a(x,z,u). a(x,y * z,u) = a(x,y \ z,u). a(x,y \ z,u) = a(x,y * z,u). a(x,(y / z) * y,u) = a(x,z,u). a(x,K(y,z) * T(y,z),u) = a(x,y,u). a(x * (y * y),y * 1,y) = a(x * y,y \ 1,y \ 1). a(x,y \ 1,z) * (y \ 1) = y \ a(x,y * 1,z). a(x,(y * (y * z)) * (y * u),w) = a(x,z \ (y \ u),w). a(x,T(T(y,z),z),u) = a(x,y,u). a(T(x,y),y,z) = a(x,T(y,x),z). a(x,y \ 1,z) * (y \ 1) = y \ a(x,y,z). a(x,y * 1,z) * (y \ 1) = y \ a(x,y,z). a(x,y,z) * (y \ 1) = y \ a(x,y,z). a(x * (y * y),y,y) = a(x * y,y \ 1,y \ 1). a(x * y,y \ 1,y \ 1) = a(x,y,y). a(x,y,y) = L(y,y,x) \ y. L(x,x,y) \ x = a(y,x,x). a(x,y,y) * L(y,y,x) = y. x * y = R(x,y,y) * L(y,y,x). R(x,y,y) * L(y,y,x) = x * y. L(x,x,y) \ (y * x) = T(R(y,x,x),L(x,x,y)). T(R(x,y,y),L(y,y,x)) = L(y,y,x) \ (x * y). L(x,x,y) \ (y * x) = R(T(y,L(x,x,y)),x,x). R(T(x,L(y,y,x)),y,y) = L(y,y,x) \ (x * y). R(T(x,y),y,y) = L(y,y,x) \ (x * y). L(x,x,y) \ (y * x) = R(T(y,x),x,x). a(x,y * (y * (z * (y * u))),w) = a(x,z \ (y \ u),w). a(x,y \ (z \ u),w) = a(x,y * (z * u),w). a(x,y * (z * u),w) = a(x,y * (z \ u),w). a(x,y * (z \ u),w) = a(x,y * (z * u),w). ((x / y) * (y * z)) \ (x * z) = a(y * x,T(y,y * x),z). a(x * y,T(x,x * y),z) = ((y / x) * (x * z)) \ (y * z). a(x * y,T(x,x * y),z) = a(y / x,x,z). R(K(x,y),z,z) * (x / z) = (z \ 1) * T((z \ 1) \ (x / z),y). K(x,R(y,z,z)) * (x / z) = (z \ 1) * T((z \ 1) \ (x / z),y). K(x,R(y,z,z)) * (x / z) = (z \ 1) * T(z * (x / z),y). K(x,R(y,z,z)) * (x / z) = z \ T(z * (x / z),y). K(x,R(y,z,z)) * (x / z) = T(x,y) / z. a(x * (y \ (y \ (y \ (x * (y \ 1))))),z,u) = a(K(x / (y * y),y),z,u). a(x * (y \ ((y \ (y \ x)) * (y \ 1))),z,u) = a(K(x / (y * y),y),z,u). a(K(x / (y * y),y),z,u) = a(x * (y * ((y \ (y \ x)) * (y \ 1))),z,u). a(x * (y * ((y \ (y \ x)) * (y \ 1))),z,u) = a(K(x / (y * y),y),z,u). a(x * (y \ (x * (y \ 1))),z,u) = a(K(x / (y * y),y),z,u). a(K(x / (y * y),y),z,u) = a(x * (y \ (x * (y \ 1))),z,u). a(K(x / (y * y),y),z,u) = a(x * (y * (x * (y \ 1))),z,u). a(K(x / (y * y),y),z,u) = a(x * T(x,y \ 1),z,u). a(K(x / (y * y),y),z,u) = a(K(x,y \ 1),z,u). a(K(x,y),z,u) = a(K(x,y \ 1),z,u). a(K(x,y \ 1),z,u) = a(K(x,y),z,u). a(K(x,y),z,u) = a(K(y \ 1,x),z,u). a(K(x \ 1,y),z,u) = a(K(y,x),z,u). a(K(x * y,x),z,u) = a(x * ((x * y) * y),z,u). a(x * ((x * y) * y),z,u) = a(K(x * y,x),z,u). a(K(x * y,x),z,u) = a(a(x,y,y),z,u). (x * y) * R((x * y) \ (x * z),u,w) = x * (y * R(y \ z,u,w)). (x * y) * R((x * y) \ z,u,w) = x * (y * R(y \ (x \ z),u,w)). (x * y) * R((x * y) \ y,z,u) = R(x,z,u) * (x \ y). x \ (R(y,z,u) * (y \ x)) = T(y,x) \ R(T(y,x),z,u). T(x,y) \ R(T(x,y),z,u) = y \ (R(x,z,u) * (x \ y)). T(x,y) \ R(T(x,y),z,u) = T(x \ R(x,z,u),y). T(x \ R(x,y,z),u) \ w = (R(T(x,u),y,z) \ T(x,u)) * w. (R(T(x,y),z,u) \ T(x,y)) * w = T(x \ R(x,z,u),y) \ w. T(x \ R(x,y,y),z) = a(T(x,z),y,y). x * T(x \ R(x,y,z),u) = K(u,x) * R(T(x,u),y,z). K(x,y) * R(T(y,x),z,u) = y * T(y \ R(y,z,u),x). T(T(x,y) \ R(T(x,y),z,u),y) = x \ R(x,z,u). T(a(x,y,y),z) = a(T(x,z),y,y). T(T(x \ R(x,y,z),u),u) = x \ R(x,y,z). (x * (y \ R(y,z,u))) / x = T(y \ R(y,z,u),x). T(a(x,y,z),x * (y * z)) = x \ R(x,y,z). a(x,y,z) * K(a(x,y,z),x * (y * z)) = x \ R(x,y,z). T(T(x \ R(x,y,z),u),x * (y * z)) = (u * a(x,y,z)) / u. (x \ R(x,y,z)) * K(x \ R(x,y,z),u) = (u * (x \ R(x,y,z))) / u. (x * (y \ R(y,z,u))) / x = (y \ R(y,z,u)) * K(y \ R(y,z,u),x). (x * a(y,z,u)) / x = T(a(y,z,u),x). T(a(x,y,z),u) * (u / (u * a(x,y,z))) = 1. L(x,x,x * ((x \ 1) * a(y,z,u))) = ((x \ 1) * a(y,z,u)) \ T(a(y,z,u),x \ 1). 1 = K(a(x,y,z),u) * K(a(x,y,z),u). K(a(x,y,z),u) * K(a(x,y,z),u) = 1. K(a(x,y,z),u) = K(u,a(x,y,z)). a(x,y,z) * K(x * (y * z),a(x,y,z)) = x \ R(x,y,z). K(x \ R(x,y,z),u) = K(u,x \ R(x,y,z)). L(x,y,K(z,u)) = L(L(x,y,z * u),(z * u) * y,u * z). L(L(x,y,z * u),(z * u) * y,u * z) = L(x,y,K(z,u)). ((x * (x * y)) * a(y,z,u)) / y = a(x * (x * y),z,u) * (x * x). (x * (x * (y * a(y,z,u)))) / y = a(x * (x * y),z,u) * (x * x). a(x * (x * y),z,u) * (x * x) = x * (x * ((y * a(y,z,u)) / y)). a(x * (x * y),z,u) * (x * x) = x * (x * a(y,z,u)). a(x,y,z) * (u * u) = u * (u * a(x,y,z)). T((a(x,y,z) * (u * u)) / (u * u),u) = T(u \ (u * a(x,y,z)),u \ 1). T(a(x,y,z),u) = T(u \ (u * a(x,y,z)),u \ 1). T(x \ (x * a(y,z,u)),x \ 1) = T(a(y,z,u),x). T(a(x,y,z),u \ 1) = T(a(x,y,z),u). K(L(x \ (x / y),x,y * x),z) = y * L(T(x \ (x / y),z),x,y * x). x * L(T(y \ (y / x),z),y,x * y) = K(L(y \ (y / x),y,x * y),z). K(L(x \ (x / y),x,y * x),z) = (y / x) * (x * T(x \ (x / y),z)). (x / y) * (y * T(y \ (y / x),z)) = K(L(y \ (y / x),y,x * y),z). (x / y) * (y * T(y \ (y / x),z)) = K(x \ 1,z). (L(x,y,z) / (z * (y * x))) * ((z * (y * x)) * T((z * (y * x)) \ (z * y),u)) = K(L(x,y,z) \ 1,u). T(x * x,y * z) \ ((((y * z) \ (x * x)) * y) * z) = a((y * z) * (x * x),y,z). ((R(x,y,z) * u) * w) / ((x * u) * w) = R(x,u,w) \ R(R(x,u,w),y,z). R(x \ R(x,y,z),x * u,w) = R(x,u,w) \ R(R(x,u,w),y,z). R((x \ 1) \ R(x \ 1,y,z),(x \ 1) * (x * u),w) = (R(x,u,w) \ 1) \ R(R(x \ 1,x * u,w),y,z). (K(x,T(y,z)) * T(y,x)) / y = K(z,T(y,x)) * K(y,z). K(x,T(y,z)) * K(y,x) = K(y,z) * K(z,T(y,x)). T(x * x,y * z) \ ((((y * z) \ (x * x)) * y) * z) = a(y * z,y,z). a(x * y,x,y) = (T(z * z,x * y) \ (((x * y) \ (z * z)) * x)) * y. (T(x * x,y * z) \ (((y * z) \ (x * x)) * y)) * z = a(y * z,y,z). ((T(x * x,y * z) \ ((y * z) \ (x * x))) * y) * z = a(y * z,y,z). (((x * y) \ 1) * x) * y = a(x * y,x,y). ((x * y) \ x) * y = a(x * y,x,y). a(x * y,x,y) = y * ((x * y) \ x). x * ((y * x) \ y) = a(y * x,y,x). (x \ y) * (y \ x) = a(x * (x \ y),x,x \ y). a(x * (x \ y),x,x \ y) = (x \ y) * (y \ x). a(x,y,y \ x) = (y \ x) * (x \ y). (x \ y) * (y \ x) = a(y,x,x \ y). L(x,y,a(z,u,u \ z)) = L(x,y,(z \ u) * (u * z)). L(x,y,(z \ u) * (u * z)) = L(x,y,a(z,u,u \ z)). L(x,a(y,z,z \ y),u) = L(x,(y \ z) * (z * y),u). L(x,(y \ z) * (z * y),u) = L(x,a(y,z,z \ y),u). L(x,y,a(z,u,u \ z)) = L(x,y,(z * u) * (u * z)). L(x,y,(z * u) * (u * z)) = L(x,y,a(z,u,u \ z)). L(x,a(y,z,z \ y),u) = L(x,(y * z) * (z * y),u). L(x,(y * z) * (z * y),u) = L(x,a(y,z,z \ y),u). L(x,y,a(z,u,u \ z)) = L(x,y,K(u,z)). L(x,a(y,z,z \ y),u) = L(x,K(z,y),u). L(x,x,a(y,z,u)) = ((x \ 1) * a(y,z,u)) \ T(a(y,z,u),x \ 1). ((x \ 1) * a(y,z,u)) \ T(a(y,z,u),x \ 1) = L(x,x,a(y,z,u)). (x \ a(y,z,u)) \ T(a(y,z,u),x \ 1) = L(x,x,a(y,z,u)). (x \ a(y,z,u)) \ T(a(y,z,u),x) = L(x,x,a(y,z,u)). L(x,x,a(y,z,u)) = L(x,a(y,z,u),x). L(x,a(y,z,u),x) = L(x,x,a(y,z,u)). L(x,x,a(y,z,z \ y)) = L(x,K(z,y),x). L(x,K(y,z),x) = L(x,x,K(y,z)). L(x,K(y,z),x) = L(x,x,K(z,y)). (x \ K(y,z)) / (K(y,z) / L(x,x,K(z,y))) = K(K(y,z),x). (x \ K(y,z)) / (K(y,z) * (x \ 1)) = K(K(y,z),x). K(K(x,y),z) = K(z \ 1,K(x,y)). K(x \ 1,K(y,z)) = K(K(y,z),x). K(K(x,y),z) * (K(x,y) \ u) = T(K(x,y),z \ 1) \ u. T(K(x,y),z) * K(K(x,y),z) = T(K(x,y),z * z). T(K(x,y),z * z) = T(T(K(x,y),z),z). T(T(K(x,y),z),z) = T(K(x,y),z * z). T(T(K(x,y),z),T(z,x)) = T(K(x,y),T(z,x) * T(z,x)). T(K(x,y),T(z,x) * T(z,x)) = T(T(K(x,y),z),T(z,x)). x / (T(K(y,z),u \ 1) \ x) = K(y,z) * K(u,K(y,z)). T(K(x,y),z * T(T(z,x),x)) = T(T(K(x,y),z),T(z,x)). K(x,y) * K(z,K(x,y)) = T(K(x,y),z \ 1). T(K(x,y),z \ 1) * z = z * K(x,y). ((x * y) * (z / (x * (y * z)))) * (x * y) = (x * y) * (L(z,y,x) \ z). (x \ R(x,y,z)) * (x * y) = (x * y) * (L(z,y,x) \ z). (x * y) * (L(z,y,x) \ z) = R(x,y,z) * y. ((x * y) \ 1) * ((x * (y * z)) * T((x * (y * z)) \ (x * y),u)) = K(L(z,y,x) \ 1,u). ((x * y) \ 1) * (x * ((y * z) * T((y * z) \ y,u))) = K(L(z,y,x) \ 1,u). ((x * y) \ 1) * (x * (y * K(z \ 1,u))) = K(L(z,y,x) \ 1,u). K(L(x,y,z) \ 1,u) = (z * y) \ (z * (y * K(x \ 1,u))). (x * y) \ (x * (y * K(z \ 1,u))) = K(L(z,y,x) \ 1,u). K(L(x,y,z) \ 1,u) = L(K(x \ 1,u),y,z). L(K(x \ 1,y),z,u) = K(L(x,z,u) \ 1,y). L(K(x,y),z,u) = K(L(x \ 1,z,u) \ 1,y). K(L(x \ 1,y,z) \ 1,u) = L(K(x,u),y,z). R((x * 1) \ R(x * 1,y,z),(x \ 1) * (x * u),w) = (R(x,u,w) \ 1) \ R(R(x \ 1,x * u,w),y,z). R(x \ R(x * 1,y,z),(x \ 1) * (x * u),w) = (R(x,u,w) \ 1) \ R(R(x \ 1,x * u,w),y,z). R(x \ R(x,y,z),(x \ 1) * (x * u),w) = (R(x,u,w) \ 1) \ R(R(x \ 1,x * u,w),y,z). R(x \ R(x,y,z),u,w) = (R(x,u,w) \ 1) \ R(R(x \ 1,x * u,w),y,z). (R(x,y,z) \ 1) \ R(R(x \ 1,x * y,z),u,w) = R(x \ R(x,u,w),y,z). (R(x,y,z) \ 1) \ R(R(x,y,z) \ 1,u,w) = R(x \ R(x,u,w),y,z). R(x \ R(x,y,z),u,w) = (R(x,u,w) * 1) \ R(R(x,u,w) * 1,y,z). (R(x,y,z) * 1) \ R(R(x,y,z) * 1,u,w) = R(x \ R(x,u,w),y,z). R(x,y,z) \ R(R(x,y,z) * 1,u,w) = R(x \ R(x,u,w),y,z). R(x,y,z) \ R(R(x,y,z),u,w) = R(x \ R(x,u,w),y,z). R(x \ R(x,y,y),z,u) = a(R(x,z,u),y,y). T(R(x \ R(x,y,x),z,u),x * (R(x,z,u) * T(y,x))) = a(R(x,z,u),y,x). R(a(x,y,y),z,u) = a(R(x,z,u),y,y). T(R(a(x,y,x),z,u),x * (R(x,z,u) * T(y,x))) = a(R(x,z,u),y,x). T(R(a(x,y,x),z,u),R(x,z,u) * (y * x)) = a(R(x,z,u),y,x). a(R(x,y,z),u,x) = R(T(a(x,u,x),R(x,y,z) * (u * x)),y,z). R(T(a(x,y,x),R(x,z,u) * (y * x)),z,u) = a(R(x,z,u),y,x). ((x * y) \ 1) * ((x * (y * z)) * R((x * (y * z)) \ (x * y),u,w)) = L(z,y,x) \ R(L(z,y,x),u,w). ((x * y) \ 1) * (x * ((y * z) * R((y * z) \ y,u,w))) = L(z,y,x) \ R(L(z,y,x),u,w). ((x * y) \ 1) * (x * (y * (z \ R(z,u,w)))) = L(z,y,x) \ R(L(z,y,x),u,w). L(x,y,z) \ R(L(x,y,z),u,w) = (z * y) \ (z * (y * (x \ R(x,u,w)))). (x * y) \ (x * (y * (z \ R(z,u,w)))) = L(z,y,x) \ R(L(z,y,x),u,w). L(x,y,z) \ R(L(x,y,z),u,w) = L(x \ R(x,u,w),y,z). L((x * (y \ R(y,x,z))) * (a(x,x * (y * R(y,x,z)),x * (y \ R(y,x,z))) * u),x * (y \ R(y,x,z)),x) = (y \ R(y,x,z)) * (x * u). L((x * (y \ R(y,x,z))) * (1 * u),x * (y \ R(y,x,z)),x) = (y \ R(y,x,z)) * (x * u). L((x * (y \ R(y,x,z))) * u,x * (y \ R(y,x,z)),x) = (y \ R(y,x,z)) * (x * u). L(x * (R(y,x,z) * (y \ u)),x * (y \ R(y,x,z)),x) = (y \ R(y,x,z)) * (x * u). (x \ R(x,y,z)) * (y * u) = L(y * (R(x,y,z) * (x \ u)),y * (x * R(x,y,z)),y). L(x * (R(y,x,z) * (y \ u)),x * (y * R(y,x,z)),x) = (y \ R(y,x,z)) * (x * u). (x \ R(x,y,z)) * (y * u) = y * (R(x,y,z) * (x \ u)). x * (R(y,x,z) * (y \ u)) = R(y,x,z) * (y \ (x * u)). R(x,y,z) * (x \ (y * u)) = y * (R(x,y,z) * (x \ u)). R(x,y,z) * (x \ (y * (y \ z))) = L(z,x * y,x). R(x,y,z) * (x \ z) = L(z,x * y,x). R(x,y,L(z,y,x)) * (x \ L(z,y,x)) = z. L(x,y * z,y) / x = y \ R(y,z,x). x / L(x,y * z,y) = R(y,z,x) \ y. x \ R(x,y,z) = z \ L(z,x * y,x). x \ L(x,y * z,y) = y \ R(y,z,x). R(x,y,z) \ x = L(z,x * y,x) \ z. L(x,y * z,y) \ x = R(y,z,x) \ y. x \ L(x,y,z) = z \ R(z,z \ y,x). x \ R(x,x \ y,z) = z \ L(z,y,x). x \ L(x,y,z) = z \ R(z,z * y,x). x \ R(x,x * y,z) = z \ L(z,y,x). K(x,R(y,z,x) \ y) = 1. K(x,y \ R(y,z,x)) = 1. T(x,y \ R(y,z,x)) = x. K(x,T(y \ R(y,z,x),u)) = 1. T(x \ R(x,y,z),z) = x \ R(x,y,z). K(x,a(y,z,x)) = 1. T(x,a(y,z,x)) = x. a(x,y,z) * z = z * a(x,y,z). x \ L(x,y,z) = R(z,y,x) \ z. R(x,y,z) \ x = z \ L(z,y,x). x * (R(y,z,x) \ y) = L(x,z,y). x / (y \ L(y,z,x)) = R(x,z,y). (x \ L(x,y,z)) \ 1 = z \ R(z,y,x). (x \ L(x,y,z)) * R(z,y,x) = z. (R(x,y,z) \ x) * z = L(z,y,x). x * (R(K(y,z),u,x) \ K(y,z)) = L(x,u,K(z,y)). R(x,y,z) = R(x,y,T(z,x * y)). R(x,y,T(z,x * y)) = R(x,y,z). x * y = L(x,z,y) * R(y,z,x). L(x,y,z) * R(z,y,x) = x * z. x = L(y,z,x) * (y \ R(x,z,y)). L(x,y,z) * (x \ R(z,y,x)) = z. R(x,y,z) * L(z,y,x) = x * z. (x \ R(x,y,z)) \ z = L(z,y,x). L(x,y,T(z,u)) = T(z \ R(z,y,x),u) \ x. T(x \ R(x,y,z),u) \ z = L(z,y,T(x,u)). L(x,y,z) \ x = z \ R(z,y,x). R(x,y,z) = x * (L(z,y,x) \ z). x * (L(y,z,x) \ y) = R(x,z,y). R(x,y,z) * (x \ L(z,y,x)) = z. (L(x,y,z) * (R(z,y,x) * u)) \ ((x * z) * u) = a(L(x,y,z),R(z,y,x),u). (L(x,y,z) \ x) * (z * u) = R(z,y,x) * u. (x \ R(x,y,z)) * u = z * (L(z,y,x) \ u). R(x \ R(x,y,z),z,u) = L(z,y,x) \ z. (x * y) * (x \ R(x,y,z)) = R(x,y,z) * y. K(x,y) \ R(K(x,y),z,u) = u \ L(u,z,K(x,y)). x \ R(x,y,z) = (L(z,y,x) \ z) * 1. R(x,y,L(z,y,x)) = R(x,y,z). (x \ R(x,y,z)) \ z = L(z,y,T(x,z)). L(x,y,T(z,x)) = L(x,y,z). L(L(x,y,z),z * y,T(z,L(x,y,z))) = x. x = L(x,y,K(z,L(x,y,z))). L(x,y,K(z,L(x,y,z))) = x. R(x,y,z) * u = z * (L(z,y,x) \ (x * u)). x * (L(x,y,z) \ (z * u)) = R(z,y,x) * u. L((x \ R(x,y,z)) \ u,x \ R(x,y,z),x * y) = (R(x,y,z) * y) \ ((x * y) * u). L(x,y,z) * (R(z,y,x) * u) = x * (z * u). x * (L(x,y,z) \ (z * T(y,z))) = y * R(z,y,x). x * (L(x,y,z) \ (z * L(x,y,z))) = z * x. x * T(y,L(x,z,y)) = y * x. T(x,L(y,z,x)) = x * K(x,y). K(x,y) = K(x,L(y,z,x)). K(x,L(y,z,x)) = K(x,y). L(x,y,K(z,x)) = x. T(x,y) = L(T(x,y),z,K(u,x)). L(T(x,y),z,K(u,x)) = T(x,y). x = L(x,y,K(x,z)). L(x,y,K(x,z)) = x. x = L(x,y,a(x,z,z)). L(x,y,a(x,z,z)) = x. K((x \ 1) \ 1,y) = L(K(x,y),z,K(u,x \ 1)). L(K(x,y),z,K(u,x \ 1)) = K((x \ 1) \ 1,y). K(x,y) / (y \ y) = R(K(x,y),z,y). R(K(x,y),z,y) = K(x,y) / (y \ y). (K(x,y) * z) * x = K(x,y) * (z * x). x * (x \ R(a(x,y,y),z,x)) = a(x,y,y). T(x,y) = T(x,K(z,x) * y). T(x,K(y,x) * z) = T(x,z). T(x,y) \ x = K(K(z,x) * y,x). K(K(x,y) * z,y) = T(y,z) \ y. x \ T(x,y) = K(x,K(z,x) * y). K(x,K(y,x) * z) = x \ T(x,z). T(x,y * T(z,x)) = T(x,y * z). K(K(x,y) * z,y) = K(z,y). K(x,y) = K(K(y,z) * x,y). K(K(x,y) * z,x) = K(z,x). K(x * (K(x,y) * z),x) = K(x * z,x). K(x,K(y,x) * z) = K(x,z). K(x,y) = K(x,K(x,z) * y). K(x,K(x,y) * z) = K(x,z). K(x,y) * K(x * (K(x,z) * y),x) = a(x,K(x,z) * y,x). R(K(x,y),z,y) = K(x,y) / 1. R(K(x,y),z,y) = K(x,y). K(x,y) = K(x,R(y,z,y)). K(x,R(y,z,y)) = K(x,y). K(x,y) \ 1 = R(K(y,x),z,y). R(K(x,y),z,x) = K(y,x) \ 1. K(x,y) * R(T(y,x),z,y) = R(y,z,y). R(K(x,y),z,x) = K(x,y). K(x,y) = K(L(x,z,x),y). K(L(x,y,x),z) = K(x,z). K((x \ y) \ y,z) = K(T(x,y),z). K(T(x,x \ y),z) = K(T(x,y),z). x \ (K(x,y) * (z * x)) = T(K(x,y) * z,x). x * ((K(x,y) * z) * x) = T(x,y) * (z * x). x \ R(x,y,x) = T(x,z) \ R(T(x,z),y,x). T(x,y) \ R(T(x,y),z,x) = x \ R(x,z,x). x * (x \ a(R(x,y,x),z,z)) = a(x,z,z). x * (x \ a(L(x,y,x),z,z)) = a(x,z,z). a(x,y,y) = a(L(x,z,x),y,y). a(L(x,y,x),z,z) = a(x,z,z). a(L(T(x,y),y * x,x),z,z) = a(T(x,y),z,z). T(K(x,y) * z,x) = K(x,y) * (x \ (z * x)). K(x,y) * (x \ (z * x)) = T(K(x,y) * z,x). (T(x,y) * (z * x)) \ ((T(x,y) * z) * x) = a(x,K(x,y) * z,x). T(x,y) \ R(T(x,y),z,x) = a(x,z,x). a(x,y,x) = T(x \ R(x,y,x),z). T(x \ R(x,y,x),z) = a(x,y,x). T(a(x,y,x),z) = a(x,y,x). R(a(x,y,x),z,u) = a(R(x,z,u),y,x). a(x,y,x) \ a(R(x,z,z),y,x) = a(a(x,y,x),z,z). K(x,y) * T(z,x) = T(K(x,y) * z,x). K(x,y) * R(T(z,x),u,w) = T(K(x,y) * R(z,u,w),x). T(K(x,y) * z,x) / z = K(z,x) * K(x,y). K(x,y) * K(z,x) = T(K(x,y) * z,x) / z. T(K(x,y) * z,x) / z = K(x,y) * K(z,x). L(K(x,y),z,K(u,x \ 1)) = K(x,y). K(x,y) = L(K(x,y),z,K(u,x)). L(K(x,y),z,K(u,x)) = K(x,y). K(x,y) = L(K(x,y),z,K(x,u)). L(K(x,y),z,K(x,u)) = K(x,y). T(K(x,y),z) = (K(y,x) * z) \ z. (K(x,y) * z) \ z = T(K(y,x),z). T(K(x,y) * z,K(x,y)) = z * K(x,y). x / T(K(y,z),x) = K(z,y) * x. (K(x,y) * z) \ u = (T(K(y,x),z) / z) * u. (T(K(x,y),z) / z) * u = (K(y,x) * z) \ u. (K(x,y) * z) * K(y,x) = T(z,K(y,x)). T(x,K(y,z)) / x = K(K(z,y) * x,K(y,z)). K(K(x,y) * z,K(y,x)) = T(z,K(y,x)) / z. K(K(x,y) * z,K(y,x)) = K(z,K(y,x)). K(x,K(y,z)) = K(K(y,z) * x,K(y,z)). K(K(x,y) * z,K(x,y)) = K(z,K(x,y)). a(K(x,K(y,z)),u,w) = a(a(K(y,z),x,x),u,w). a(a(K(x,y),z,z),u,w) = a(K(z,K(x,y)),u,w). a(R(T(x,y),y,x),z,z) = a(T(x,y),z,z). a(T(x,y),z,z) = a(R(x,y,y),z,z). a(R(x,y,y),z,z) = a(T(x,y),z,z). x * (K(y,z) * R(K(z,y),u,x)) = L(x,u,K(z,y)). x * (K(y,z) * K(z,R(y,u,x))) = L(x,y * u,K(y,z)). x * (L(x,y,z) \ (y * z)) = y * R(z,y,x). (x * (y * z)) / (y * R(z,y,x)) = L(x,y,z). T(K(x,y) * R(y,z,u),x) = y * T(y \ R(y,z,u),x). T(K(x,y) * R(y,z,u),x) / R(y,z,u) = K(R(y,z,u) / y,x). K(x,y) * K(x * y,x) = a(x,K(x,z) * y,x). a(x,K(x,y) * z,x) = K(x,z) * K(x * z,x). a(x,K(x,y) * z,x) = a(x,z,x). a(x,K(x,y) * z,x) = a(T(x,y),z,x). a(T(x,y),z,x) = a(x,z,x). a((x \ y) \ y,z,x) = a(x,z,x). a(x,y,x) = a((x \ z) * z,y,x). a((x \ y) * y,z,x) = a(x,z,x). a(x,y,x) = a((x * z) * z,y,x). a((x * y) * y,z,x) = a(x,z,x). a(x,y,x) = a(R(x,z,z),y,x). a(R(x,y,y),z,x) = a(x,z,x). a(x,y,x) \ a(x,y,x) = a(a(x,y,x),z,z). a(a(x,y,x),z,z) = a(x,y,x) \ a(x,y,x). a(a(x,y,x),z,z) = 1. L(x,x,a(y,z,y)) = x. L(x,x,a(y,z,z)) = x. x = L(x,x,K(y,z)). L(x,x,K(y,z)) = x. x \ (a(y,z,z) * x) = R(T(a(y,z,z),x),x,x). R(T(a(x,y,y),z),z,z) = z \ (a(x,y,y) * z). a(K(x,y),z,z) = 1. x / y = (K(z,u) * (y / x)) \ K(z,u). (K(x,y) * (z / u)) \ K(x,y) = u / z. L(x,K(y,z),x) = x. K(x,y) * 1 = R(K(x,y),z,z). R(K(x,y),z,z) = K(x,y) * 1. a(1,x,y) = a(K(z,K(u,w)),x,y). a(K(x,K(y,z)),u,w) = a(1,u,w). T(K(x,y),z) / z = z \ K(x,y). K(x,y) = K(x,R(y,z,z)). K(x,R(y,z,z)) = K(x,y). K(x,y * z) = K(x,y / (z \ 1)). K(x,y / (z \ 1)) = K(x,y * z). K(x,y) * (x / z) = T(x,y) / z. a(K(x,K(y,z)),u,w) = 1. L(x,y,K(z,K(u,w))) = x. x * (x \ R(K(y,K(z,u)),w,x)) = K(y,K(z,u)). (x \ K(y,z)) * u = (K(z,y) * x) \ u. (K(x,y) * z) \ u = (z \ K(y,x)) * u. K(x,R(((y \ 1) * z) \ 1,z,z)) = K(x,(z \ 1) * y). K(x,y) * z = T(x,y) / (z \ x). T(x,y) / (z \ x) = K(x,y) * z. (K(x,y) * z) \ T(x,y) = z \ x. L(x \ y,x,K(z,y)) = x \ y. a(K(x,y),z,z \ y) = 1. a(K(x,y * z),y,z) = 1. ((x / y) \ K(z,u)) * K(u,z) = y / x. x * K(y,z) = x / K(z,y). x / K(y,z) = x * K(z,y). (K(x,y) * z) / K(x,y) = T(z,K(y,x)). T(x,K(y,z)) \ x = K(x,K(z,y)). K(x,K(y,z)) = K(K(z,y),x). K(K(x,y),z) = K(z,K(y,x)). K(x,K(y,z)) * K(x,K(z,y)) = 1. K(x,y) * K(z,K(y,x)) = T(K(x,y),z). K(x,y) * T(K(y,x),z) = K(z,K(x,y)). T(K(x,y),z) = T(K(y,x),z) \ 1. T(K(x,y),z) \ 1 = T(K(y,x),z). T(K(x,y),z) * T(K(y,x),z) = 1. T(K(x,y),z) * K(y,x) = K(z,K(y,x)). R(T(a(x,y,y),z),z,z) = T(a(x,y,y),z). R(T(a(x,y,y),z),z,z) = a(T(x,z),y,y). R(a(T(x,y),z,z),y,y) = a(T(x,y),z,z). a(T(x,y),z,z) = a(R(T(x,y),y,y),z,z). a(R(T(x,y),y,y),z,z) = a(T(x,y),z,z). a(T(x,y),z,z) = a(T(T(x,y),y),z,z). a(T(T(x,y),y),z,z) = a(T(x,y),z,z). a(T(x,y),z,z) = a(x,z,z). (x * (y * (a(y,z,z) * u))) / (R(T(y,x),z,z) * u) = T(x,y). K(x,K(y,z)) = R(K(x,K(y,z)),u,w). R(K(x,K(y,z)),u,w) = K(x,K(y,z)). K(x,K(y,z)) = K(x,R(K(y,z),u,w)). K(x,R(K(y,z),u,w)) = K(x,K(y,z)). K(x,K(y,R(z,u,w))) = K(x,K(y,z)). K(K(R(x,y,z),u),w) = K(w,K(u,x)). K(R(K(x,y),z,u),w) = K(w,K(y,x)). K(x,R((y \ z) \ 1,z,z)) = K(x,(z \ 1) * y). K(x,(y \ 1) * z) = K(x,(z \ y) \ 1). K(x,(y \ z) \ 1) = K(x,(z \ 1) * y). K(x,(y \ z) \ 1) = K(x,z \ y). K(x,(y / z) \ y) = K(x,z / (a(y,z,z) \ 1)). K(x,y) = K(x,y / (a(z,y,y) \ 1)). K(x,y / (a(z,y,y) \ 1)) = K(x,y). K(x,y * a(z,y,y)) = K(x,y). (x \ 1) / (x \ K(x,y)) = K(y * a(z,y,y),x). K(x * a(y,x,x),z) = (z \ 1) / (z \ K(z,x)). K(x * a(y,x,x),z) = K(x,z). x * K(y,z) = (x / y) * T(y,z). (x / y) * T(y,z) = x * K(y,z). x * T(y,z) = (x * y) * K(y,z). (x * y) * K(y,z) = x * T(y,z). K(x,y) = L(K(x,y),x,z). L(K(x,y),x,z) = K(x,y). K(T(x,y),z) = L(K(T(x,y),z),x,y). L(K(T(x,y),z),x,y) = K(T(x,y),z). K(T(x,y),z) = T(K(x,z),x * y). T(K(x,y),x * z) = K(T(x,z),y). T(K(x,y),z) = K(T(x,x \ z),y). K(T(x,x \ y),z) = T(K(x,z),y). T(K(x,y),z) = K(T(x,z),y). K(x,T(y,z)) * T(K(y,x),z) = 1. K(T(x,y * T(T(y,x),x)),z) = T(T(K(x,z),y),T(y,x)). K(x,T(y,z)) = T(K(x,y),z). T(K(x,y),z) = K(x,T(y,z)). K(x,y) * K(y,T(x,z)) = K(K(y,x),z). K(x,T(y,z \ 1)) * z = z * K(x,y). K(x,y) * K(y,T(x,z)) = K(z,K(x,y)). K(x,T(y,z)) * K(y,x) = K(z,K(y,x)). K(x,T(y,z)) = K(T(x,z),y). K(T(x,y),z) = K(x,T(z,y)). K(x,T(y,z)) * K(y,x) = K(K(x,y),z). K(x,T(y,z)) * K(y,x) = K(x,K(y,z)). K(x,y) * K(x,K(y,z)) = K(x,T(y,z)). K(x,K(y,z)) = K(z,K(y,x)). K(x,K(y,z)) = K(K(x,y),z). K(K(x,y),z) = K(x,K(y,z)). 1 / K(x,K(y,z)) = K(K(y,x),z). K(K(x,y),z) = K(K(x,z),y). K(K(x,y),z) = K(y,K(z,x)). K(x,K(y,z)) = K(z,K(x,y)). T(K(x,y) * K(x,K(y,z)),z) = K(x,y). T(K(x,T(y,z)),z) = K(x,y). x * K(y,z) = K(y,T(z,x)) * x. K(x,T(y,z)) * z = z * K(x,y). K(x,y) = K(x,T(T(y,z),z)). K(x,T(T(y,z),z)) = K(x,y). K(x,T(y,z)) = K(x,T(y,z \ 1)). K(x,T(y,z \ 1)) = K(x,T(y,z)). T(K(x,y) * z,K(x,y)) = K(x,T(y,z)) * z. K(x,T(y,z \ (z \ (u \ 1)))) = K(x,T(y,u * (z * z))). K(T(x,y * T(y,x)),z) = T(T(K(x,z),y),T(y,x)). T(T(K(x,y),z),T(z,x)) = K(T(x,z * T(z,x)),y). T(T(K(x,y),z),T(z,x)) = K(T(x,z * z),y). T(T(K(x,y),z),T(z,x)) = K(x,T(y,z * z)). T(K(x,T(y,z)),T(z,x)) = K(x,T(y,z * z)). K(x,T(y,z * z)) = K(T(x,T(z,x)),T(y,z)). K(T(x,T(y,x)),T(z,y)) = K(x,T(z,y * y)). K(T(x,y),T(z,y)) = K(x,T(z,y * y)). K(x,T(y,z * z)) = K(x,T(T(y,z),z)). K(x,T(T(y,z),z)) = K(x,T(y,z * z)). K(x,T(y,z * z)) = K(x,y). K(x,T(y,z * (z * u))) = K(x,T(y,u)). K(x,T(y,z * u)) = K(x,T(y,z \ u)). K(x,T(y,z \ u)) = K(x,T(y,z * u)). K(x,T(y,(z \ u) * u)) = K(x,T(y,T(z,z * u))). K(x,T(y,T(z,z * u))) = K(x,T(y,(z \ u) * u)). K(x,T(y,(z / u) * (z * z))) = K(x,T(y,u / (z \ 1))). K(x,T(y,z \ (z \ u))) = K(x,T(y,u)). K(x,T(y,z * (u * u))) = K(x,T(y,z \ 1)). K(x,T(y,z * (u * u))) = K(x,T(y,z)). K(x,T(y,z / (u \ 1))) = K(x,T(y,u / z)). (x * (R(y,z,z) * u)) / (R(T(y,x),z,z) * u) = T(x,y). T(x,y) = T(x,R(y,z,z)). T(x,R(y,z,z)) = T(x,y). T(x,y * z) = T(x,y / (z \ 1)). T(x,y / (z \ 1)) = T(x,y * z). K(x,T(y,z * u)) = K(x,T(y,u / z)). K(x,T(y,z / u)) = K(x,T(y,u * z)). K(x,T(y,z)) = K(x,T(y,(z \ u) * u)). K(x,T(y,(z \ u) * u)) = K(x,T(y,z)). K(x,T(y,T(z,z * u))) = K(x,T(y,z)). K(x,T(y,T(z,u))) = K(x,T(y,z)). K(x,T(y,z)) * K(y,x) = K(x,K(y,T(z,u))). K(x,K(y,T(z,u))) = K(x,T(y,z)) * K(y,x). K(x,K(y,T(z,u))) = K(x,K(y,z)). K(x,K(y,a(z,u,w))) = K(x,K(y,z \ R(z,u,w))). K(x,K(y,z \ R(z,u,w))) = K(x,K(y,a(z,u,w))). K(x,K(y \ R(y,z,u),w)) = K(x,K(w,a(y,z,u))). K(R(x,y,z) / x,u) = K(u,x) * K(R(x,y,z),u). K(x,y) * K(R(y,z,u),x) = K(R(y,z,u) / y,x). K(x,y) * K(R(y,z,u),x) = K(y \ R(y,z,u),x). K(x,y) * K(R(y,z,u),x) = K(x,y \ R(y,z,u)). K(x,K(y,z)) * K(x,K(z,y)) = K(x,K(y,z) \ R(K(y,z),u,w)). K(x,K(y,z) \ R(K(y,z),u,w)) = K(x,K(y,z)) * K(x,K(z,y)). K(x,K(y,z) \ R(K(y,z),u,w)) = 1. K(x,K(y,z) \ K(R(y,u,w),z)) = 1. K(x,K(y,z) * K(R(z,u,w),y)) = 1. K(x,K(y \ R(y,z,u),w)) = 1. 1 = K(x,K(y,a(z,u,w))). K(x,K(y,a(z,u,w))) = 1. T(x,K(y,a(z,u,w))) = x. K(x,a(y,z,u)) = K(x,T(a(y,z,u),w)). K(x,T(a(y,z,u),w)) = K(x,a(y,z,u)). K(x,y \ R(y,z,u)) = K(x,a(y,z,u)). K(a(x,y,z),u) = K(u,x \ R(x,y,z)). K(x,y \ R(y,z,u)) = K(a(y,z,u),x). K(x \ R(x,y,z),u) = K(u,a(x,y,z)). K(x,y \ R(y,z,u)) = K(x,a(y,z,L(u,z,y))). K(x,a(y,z,L(u,z,y))) = K(x,y \ R(y,z,u)). K(x,y) * K(R(y,z,u),x) = K(x,a(y,z,u)). K(x,a(K(y,z),u,w)) = 1. T(x,a(K(y,z),u,w)) = x. ((K(x,y) * z) * u) / (K(x,y) * (z * u)) = a(K(x,y),z,u). K(R(x,y,z) \ x,u) = K(u,a(x,x * y,z)). K(x,a(y,z,u)) = K(y,x) * K(x,R(y,z,u)). K(x,y) * K(y,R(x,z,u)) = K(y,a(x,z,u)). x * K(y,a(z,u,x)) = L(x,z * u,K(z,y)). L(x,y * z,K(y,u)) = x * K(u,a(y,z,x)). K(x,a(y,z,L(u,z,y))) = K(x,a(y,z,u)). a(K(x,y),z,u) = K(x,y) \ R(K(x,y),z,u). K(x,y) \ R(K(x,y),z,u) = a(K(x,y),z,u). a(K(x,y),z,u) = u \ L(u,z,K(x,y)). x \ L(x,y,K(z,u)) = a(K(z,u),y,x). x * a(K(y,z),u,x) = L(x,u,K(y,z)). a(K(x,y),x * z,u) = K(y,a(x,z,u)). x * a(K(y,z),u,x) = L(x,u,K(z,y)). K(x,a(y,y * z,u)) = a(K(y,x),z,u). K((x * y) * z,a(x,y,z)) = 1. K(x * (y * z),a(x,y,L(z,y,x))) = 1. K(x,a(y,y * z,u)) = a(K(x,y),z,u). 1 = K(x * (y * z),a(x,y,z)). K(x * (y * z),a(x,y,z)) = 1. a(x,y,z) * 1 = x \ R(x,y,z). x \ R(x,y,z) = a(x,y,z) * 1. a(x,y,z) = x \ R(x,y,z). x \ R(x,y,z) = a(x,y,z). a(x,y,z) = L(z,y,x) \ z. L(x,y,z) \ x = a(z,y,x). a(x,y,z) \ 1 = R(x,y,z) \ x. R(x,y,z) \ x = a(x,y,z) \ 1. x * (a(x,y,z) * u) = R(x,y,z) * u. a(x,y,z) * (x * u) = R(x,y,z) * u. a(x,x * y,z) = R(x,y,z) \ x. R(x,y,z) \ x = a(x,x * y,z). x * R(x \ 1,y,z) = a(x,y,z). a(T(x,y),z,u) = T(x \ R(x,z,u),y). T(x \ R(x,y,z),u) = a(T(x,u),y,z). a(R(x,y,z),u,w) = R(x \ R(x,u,w),y,z). R(x \ R(x,y,z),u,w) = a(R(x,u,w),y,z). a(L(x,y,z),u,w) = L(x \ R(x,u,w),y,z). L(x \ R(x,y,z),u,w) = a(L(x,u,w),y,z). a(x,y,z) * u = z * (L(z,y,x) \ u). x * (L(x,y,z) \ u) = a(z,y,x) * u. L(x,y,z) \ (x * u) = a(z,y,x) * u. a(x,y,z) * (L(z,y,x) * u) = z * u. L(x,y,z) \ x = a(T(z,x),y,x). K(a(x,y,z) \ 1,u) = K(u,a(x,x * y,z)). a(x,x * y,z) = a(x,y,z) \ 1. L(x,a(y,z,u),z) = x. (x * a(y,x,z)) * u = x * (a(y,x,z) * u). a(x,y,z) \ y = (y \ a(x,y,z)) \ 1. (x \ a(y,x,z)) \ 1 = a(y,x,z) \ x. a(x,y,z) \ (y * u) = (y \ a(x,y,z)) \ u. (x \ a(y,x,z)) \ u = a(y,x,z) \ (x * u). a(T(x,y),z,y) = a(x,z,y). K(a(x,x * y,z),u) = a(K(u,x),y,z). x * (y * a(x,z,y)) = R(x,z,y) * y. T(a(x,y,z),u) = a(T(x,u),y,z). a(T(x,y),z,u) \ a(x,z,u) = K(y,a(x,z,u)). a(T(x,y),y,z) = a(x,y,z). a(x,y,z) = a(x,T(y,x),z). a(x,T(y,x),z) = a(x,y,z). a(x * y,x,z) = a(y / x,x,z). a(x / y,y,z) = a(y * x,y,z). a(x * y,x,z) = a(x / y,x,z). a(x / y,x,z) = a(x * y,x,z). x * (a(y,z,x) * u) = a(y,z,x) * (x * u). a(x,y,z) * (z * u) = z * (a(x,y,z) * u). a(x,y,z) * (z * x) = z * R(x,y,z). (a(x,y,z) \ y) * u = (y \ a(x,y,z)) \ u. (x \ a(y,x,z)) \ u = (a(y,x,z) \ x) * u. K(a(x,y,z) \ 1,u) = a(K(u,x),y,z). (x * y) * L(a(x,z,y),y,x) = R(x,z,y) * y. a(R(x,y,z),u,y) = L(y,u,x) \ y. R(a(x,y,z),u,w) = a(R(x,u,w),y,z). a(R(x,y,z),u,y) = a(x,u,y). a(x,y,z) = a(L(x,z,x),y,z). a(L(x,y,x),z,y) = a(x,z,y). R(a(x,y,z),x * u,w) = a(R(x,u,w),y,z). L(a(x,y,z),u,w) = a(L(x,u,w),y,z). K(a(x * y,x,z) \ 1,u) = K(u,a(y / x,(y / x) * x,z)). K(x,a(y / z,(y / z) * z,u)) = K(a(z * y,z,u) \ 1,x). (a(x,y,z) * y) * u = y * (a(x,y,z) * u). (a(x,y,z) \ y) * u = a(x,y,z) \ (y * u). a(x,y,z) \ (y * u) = (a(x,y,z) \ y) * u. x = L(x,y,a(z,y,u)). L(x,y,a(z,y,u)) = x. (a(x,y,z) * y) * u = a(x,y,z) * (y * u). (a(x,y,z) * (y \ 1)) * u = a(x,y,z) * (y \ u). a(x,y,z) * (y * u) = y * (a(x,y,z) * u). (x * y) \ (x * (a(z,x,u) * y)) = T(a(z,x,u),x * y). (x * y) * a(L(x,y,x),z,y) = R(x,z,y) * y. (x * y) * a(x,z,y) = R(x,z,y) * y. (x * (R(y,z,u) * u)) / ((y * u) * R(a(y,z,u),y * u,x)) = L(x,y * u,a(y,z,u)). (x \ a(y,x,z)) * u = a(y,x,z) * (x \ u). (a(x,y,z) * (y \ u)) \ ((y \ a(x,y,z)) * (u * w)) = L(w,u,y \ a(x,y,z)). T(a(x,y,z),y * u) = L(T(a(x,y,z),u),u,y). L(T(a(x,y,z),u),u,y) = T(a(x,y,z),y * u). L(a(T(x,y),z,u),y,z) = T(a(x,z,u),z * y). K(x,a(y / z,y,u)) = K(a(z * y,z,u) \ 1,x). K(a(x * y,x,z) \ 1,u) = K(u,a(y / x,y,z)). K(a(x * y,x,z) \ 1,u) = K(u,a(y * x,y,z)). K(x,a(y * z,y,u)) = a(K(x,z * y),z,u). (x * (y * z)) \ ((x * y) * z) = a(L(x,u,y),R(y,u,x),z). a(L(x,y,z),R(z,y,x),u) = (x * (z * u)) \ ((x * z) * u). a(L(x,y,z),R(z,y,x),u) = a(x,z,u). L(a(x,R(y,z,x),u),z,y) = a(x,y,u). (a(x,y,z) * (y \ u)) \ (a(x,y,z) * (y \ (u * w))) = L(w,u,y \ a(x,y,z)). L(x,y,z \ a(u,z,w)) = L(L(x,y,z),z * y,a(u,z,w)). L(L(x,y,z),z * y,a(u,z,w)) = L(x,y,z \ a(u,z,w)). L(L(x,y,z),z * y,a(u,z,w)) = L(x,y,z * a(u,z,w)). (R(x,y,z) * y) \ ((x * y) * u) = (x \ R(x,y,z)) \ u. (x \ R(x,y,z)) \ z = L(z,y,R(x,y,z)). L(x,y,R(z,y,x)) = (z \ R(z,y,x)) \ x. L(x,y,R(z,y,x)) = L(x,y,z). L(x,y * z,R(y,z,x) \ 1) = L(x,y * z,y \ 1). L(x,y * z,y \ 1) = L(x,y * z,R(y,z,x)). L(x,y * z,R(y,z,x)) = L(x,y * z,y \ 1). L(x,y * z,R(y,z,x)) = L(x,y * z,y). R(x,y,z) * (L(z,x * y,x) \ z) = R(R(x,y,z),x * y,z). R(x,y,z) * (R(x,y,z) \ x) = R(R(x,y,z),x * y,z). R(R(x,y,z),x * y,z) = x. x = R(R(x,x * y,z),y,z). R(R(x,x * y,z),y,z) = x. K(x,R(y,y * z,u)) * K(y,x) = K(x,R(y,y * z,u) \ R(R(y,y * z,u),z,u)). K(x,R(y,y * z,u) \ R(R(y,y * z,u),z,u)) = K(x,R(y,y * z,u)) * K(y,x). K(x,R(y,y * z,u) \ R(R(y,y * z,u),z,u)) = R(K(x,y),z,u) * K(y,x). K(x,R(y,y * z,u) \ R(R(y,y * z,u),z,u)) = K(y,x) * R(K(x,y),z,u). K(x,R(y,y * z,u) \ y) = K(y,x) * R(K(x,y),z,u). K(x,y \ R(y,z,u)) = K(y,x) * R(K(x,y),z,u). K(x,y) * R(K(y,x),z,u) = K(y,x \ R(x,z,u)). x * K(y,z \ R(z,u,x)) = L(x,u,K(y,z)). x * K(a(y,z,x),u) = L(x,z,K(u,y)). K(a(x,y,z),u) = a(K(x,u),y,z). K(a(x,y,z),u) = a(K(u,x),y,z). a(K(x,y),z,u) = K(y,a(x,z,u)). K(x,a(y,z,u)) = a(K(y,x),z,u). a(K(x,y),z,u) = K(x,a(y,z,u)). K(x,a(y,z,u)) = a(K(x,y),z,u). x * K(y,a(z,u,x)) = L(x,u,K(z,y)). K(x,a(y * z,y,u)) = K(z * y,a(x,z,u)). K(x * y,a(z,x,u)) = K(z,a(y * x,y,u)). K(x,a(y,z,u)) = K(y,a(x,z,u)). L(x,y * z,K(y,u)) = L(x,z,K(y,u)). (x * (R(y,z,u) * u)) / ((y * u) * a(R(y,u,x),z,u)) = L(x,y * u,a(y,z,u)). (x * (R(y,z,u) * u)) / ((y * u) * a(y,z,u)) = L(x,y * u,a(y,z,u)). (x * (R(y,z,u) * u)) / (R(y,z,u) * u) = L(x,y * u,a(y,z,u)). L(x,y * z,a(y,u,z)) = x. x = L(x,y * z,a(T(z,y),u,y)). L(x,y * z,a(T(z,y),u,y)) = x. L(x,y * z,a(z,u,y)) = x. (a(x,y,z) * (z * x)) \ (a(x,y,z) * (z * (x * u))) = L(u,x,z). (x * R(y,z,x)) \ (a(y,z,x) * (x * (y * u))) = L(u,y,x). (x * R(y,z,x)) \ (x * (a(y,z,x) * (y * u))) = L(u,y,x). (x * R(y,z,x)) \ (x * (R(y,z,x) * u)) = L(u,y,x). L(x,y,z) = L(x,R(y,u,z),z). L(x,R(y,z,u),u) = L(x,y,u). L(x,y,z) \ x = a(z,R(y,u,z),x). a(x,R(y,z,x),u) = L(u,y,x) \ u. a(x,R(y,z,x),u) = a(x,y,u). L(a(x,y,z),u,y) = a(x,y,z). a(T(x,y),z,u) = T(a(x,z,u),z * y). T(a(x,y,z),y * u) = a(T(x,u),y,z). a(T(x,y),z,u) \ a(x,z,u) = K(z * y,a(x,z,u)). K(x * y,a(z,x,u)) = K(y,a(z,x,u)). K(x,a(y,z,u)) = K(y,a(z * x,z,u)). K(x,a(y * z,y,u)) = K(z,a(x,y,u)). K(x,a(y,z,u)) = K(y,a(x * z,x,u)). K(x,a(y * z,y,u)) = K(y,a(x,z,u)). K(x,a(y,z,u)) = K(z,a(y,x,u)). x * K(y,a(z,u,x)) = L(x,y,K(z,u)). L(x,y,K(z,u)) = L(x,u,K(z,y)). L(x,y,K(z,z * u)) = L(x,u,K(z,y)). L(x,y,K(z,u)) = L(x,u,a(z,y,y)). L(x,y,a(z,u,u)) = L(x,u,K(z,y)). L(x,y,a(z,u,u)) = L(x,y,K(z,u)). L(x,y,K(z,u)) = L(x,y,a(u,z,u)). L(x,y,a(z,u,z)) = L(x,y,K(u,z)). L(L(x,y,z),z * y,K(z,u)) = L(x,y,z * a(u,z,u)). L(x,y,z * a(u,z,u)) = L(x,y,T(z,u)). L(x,y,T(z,u)) = L(x,y,R(z,u,u)). L(x,y,R(z,u,u)) = L(x,y,T(z,u)). L(x,y,T(z / u,z)) = L(x,y,u * z). L(x,y,z * u) = L(x,y,u * z). L(L(x,y,z * u),(z * u) * y,u * z) = x. x = L(x,y,K(z,u)). L(x,y,K(z,u)) = x. $F. K(a(x,y,z),u) = 1. K(a(c13,c14,c15),c16) != 1. a(x,K(y,z),u) = 1. a(c5,K(c6,c7),c8) != 1. K(x,y) / z = K(x,y) * (z \ 1). K(x,y) * (z \ 1) = K(x,y) / z. K(x,y) * z = K(x,y) / (z \ 1). K(x,y) / (z \ 1) = K(x,y) * z. (K(x,y) * z) \ K(x,y) = z \ 1. x \ K(y,z) = (K(y,z) \ x) \ 1. (K(x,y) \ z) \ 1 = z \ K(x,y). (x \ K(y,z)) * u = (K(y,z) \ x) \ u. (K(x,y) \ z) \ u = (z \ K(x,y)) * u. x \ (K(y,z) * u) = (K(y,z) \ x) \ u. (K(x,y) \ z) \ u = z \ (K(x,y) * u). x \ (K(y,z) * u) = (x \ K(y,z)) * u. x = L(x,K(y,z),u). L(x,K(y,z),u) = x. a(x,y,K(z,u)) = 1. a(c9,c10,K(c11,c12)) != 1. L(x,y / z,z \ y) = x. (x \ y) / T(x,y) = x \ (x \ y). (x \ (y * y)) \ 1 = y \ (y \ x). (x \ (x \ y)) * z = (y \ (x * x)) \ z. (x \ (y * y)) \ z = (y \ (y \ x)) * z. L(x,y,y * x) \ z = ((y * x) \ ((y * x) \ ((y * x) * y))) * z. ((x * y) \ ((x * y) \ ((x * y) * x))) * z = L(y,x,x * y) \ z. L(x * a(y,x,x),x,y) = x. L(x,x * y,x) * (x \ y) = (x \ y) * T(x,y). x * (T(x,y) * z) = T(x,y) * (x * z). T(x,y) * (x * z) = x * (T(x,y) * z). ((x * y) \ x) * z = L(y,x,x * y) \ z. L(x,y,y * x) \ z = ((y * x) \ y) * z. (x * T(y * x,x)) / (x * x) = T((x \ y) * x,x \ 1). ((x * y) * y) / (y * y) = T((y \ x) * y,y \ 1). T((x \ y) * x,x \ 1) = ((y * x) * x) / (x * x). T((x \ y) * x,x \ 1) = R(y,x,x). L(x,y / z,z * y) = x. (x \ y) * L(L(z,y,x),u,w) = x \ (y * L(z,u,w)). L(x,y * z,z / y) = x. (x * y) / (y / x) = (x * y) * ((y / x) \ 1). (x * y) * ((y / x) \ 1) = (x * y) / (y / x). (x * y) * (x / y) = (x * y) / (y / x). (x * y) / (y / x) = (x * y) * (x / y). K(x * y,x) = ((x \ y) * x) / y. ((x \ y) * x) / y = K(x * y,x). L(x,K(y,T(z,y)),u) = L(x,T(z,y) * z,u). T(x * K(y,x),x * y) = L(x,y,x). R(T(x,y),z,u) * K(y,R(x,z,u)) = R(x,z,u). L(x,T(y * z,y),u) = L(x,z / y,u). R(x,y,x) * (x \ y) = (x \ y) * T(x,y). L(L(x,y * z,z),y,z) = x. L(L(x,y,z * y),z,z * y) = x. L(x,y,y * x) = x * a(y * x,x,x). K(x * y,x) * K(x,y) = a(x,y,x). (((x \ y) * x) / y) * K(x,y) = a(x,y,x). a(x,y,x) * L(x,y,x) = x. (x * y) / L(L(y,z,y),a(y,z,y),x) = x * a(y,z,y). a(x,(y * z) * u,w) = a(x,(y \ z) * u,w). a(x,(y \ z) * u,w) = a(x,(y * z) * u,w). a(x,(y \ z) * z,u) = a(x,T(y,y * z),u). a(x,T(y,y * z),u) = a(x,(y \ z) * z,u). a(x,T(y * z,y),u) = a(x,z / y,u). a(x,T(y,y * z),u) = a(x,(y * z) * z,u). T(x,x * y) = T(x,T(x,z) * y). T(x,T(x,y) * z) = T(x,x * z). x * a(y,z,y) = a(y,z,y) * x. a(x,y,x) * z = z * a(x,y,x). (a(x,y,x) * z) * L(u,z,a(x,y,x)) = (z * u) * a(x,y,x). x \ T(y,z) = (K(z,y) * x) \ y. (K(x,y) * z) \ y = z \ T(y,x). (x \ K(y,z)) * y = x \ T(y,z). (x \ T(y,z)) \ ((x \ K(y,z)) * (y * u)) = L(u,y,x \ K(y,z)). (x * K(y,z)) \ x = K(z,y). K(x,y) = (z * x) \ (z * T(x,y)). (x * y) \ (x * T(y,z)) = K(y,z). (x * (y * z)) \ (x * (y * T(z,u))) = L(K(z,u),y * z,x). (x * T(y,z)) \ (x * y) = K(z,y). (x * (y * z)) \ ((x * y) * T(L(z,y,x),u)) = K(L(z,y,x),u). (x * (y * z)) \ ((x * y) * L(T(z,u),y,x)) = K(L(z,y,x),u). (x * (y * z)) \ (x * (y * T(z,u))) = K(L(z,y,x),u). K(L(x,y,z),u) = L(K(x,u),y * x,z). L(K(x,y),z * x,u) = K(L(x,z,u),y). L(K(x,y),z,u) = K(L(x,z / x,u),y). K(L(x,y / x,z),u) = L(K(x,u),y,z). L(x,y,z \ K(y,u)) = (z * T(y,u)) \ ((z * K(y,u)) * (y * x)). (x * T(y,z)) \ ((x * K(y,z)) * (y * u)) = L(u,y,x \ K(y,z)). R(x,x * y,z) \ x = a(x,y,z). a(T(x,y),z,u) = y \ (R(x,z,u) * (x \ y)). x \ (R(y,z,u) * (y \ x)) = a(T(y,x),z,u). x \ L(x,y * z,y) = a(y,z,x). a(x,x * y,z) = z \ L(z,y,x). a(x,y,z) \ 1 = z \ L(z,y,x). a(x,y,z) = a(x,x * y,z) \ 1. a(x,x * y,z) \ 1 = a(x,y,z). L(a(x,y,z),z,u) = (u * z) \ (u * L(z,x * y,x)). (x * y) \ (x * L(y,z * u,z)) = L(a(z,u,y),y,x). (x * L(y,z,u)) / L(a(u,u * z,y),y,x) = x * y. a(x,y,L(z,u,u * z)) \ 1 = ((u * z) \ u) * L(L(z,u,u * z),y,x). ((x * y) \ x) * L(L(y,x,x * y),z,u) = a(u,z,L(y,x,x * y)) \ 1. a(x,x * y,z) \ u = a(x,y,z) * u. x * T(y,L(x,z,u)) = a(u,z,x) * (y * L(x,z,u)). a(x,y,z) * (u * L(z,y,x)) = z * T(u,L(z,y,x)). x \ ((y \ x) * T(y,x)) = a(T(y,x),x,y). x \ ((y \ x) * T(y,x)) = a(y,x,y). (K(x,y) * z) * u = K(x,y) * (z * u). x \ y = (K(z,u) * x) \ (K(z,u) * y). (K(x,y) * z) \ (K(x,y) * u) = z \ u. (K(x,y) * z) / u = K(x,y) * (z / u). L(x,y,z) = L(x,y,T(z,u)). L(x,y,T(z,u)) = L(x,y,z). L(x,y,a(z,u,z)) = x. T(a(x,y,z),u) = a(x,y,z). (a(x,y,x) * z) * u = (z * u) * a(x,y,x). L(x,y,z * (u * z)) = L(x,y,u). x / a(y,z,u) = a(y,z,u) \ x. a(x,y,z) = a(T(x,u),y,z). a(T(x,y),z,u) = a(x,z,u). a(x * (y * x),z,u) = a(y,z,u). (x * (K(y,z) * (u * w))) \ ((x * (K(y,z) * u)) * w) = a(x,K(y,z) * u,w). (K(x,y) * (z * (u * w))) \ (((K(x,y) * z) * u) * w) = a(K(x,y) * z,u,w). (K(x,y) * (z * u)) \ ((K(x,y) * z) * (u * w)) = L(w,u,K(x,y) * z). ((K(x,y) * (z * u)) * w) / (u * w) = R(K(x,y) * z,u,w). (x * K(y,z)) * u = x * (K(y,z) * u). (x * (K(y,z) * u)) / u = x * K(y,z). x = L(x,T(y,z) * y,u). L(x,T(y,z) * y,u) = x. L(x,(y \ z) * (z / y),u) = x. x = L(x,(y * z) * (z / y),u). L(x,(y * z) * (z / y),u) = x. L(x,T(L(y / z,z * y,y / z) * (z * y),y / z),u) = x. (x * T(y,z)) \ (x * (K(y,z) * (y * u))) = L(u,y,x \ K(y,z)). (x * y) / T(y,z) = x * K(z,y). x / T(y,z) = (x / y) * K(z,y). (x / y) * K(z,y) = x / T(y,z). (x * (y * z)) / T(L(z,y,x),u) = (x * y) * K(u,L(z,y,x)). ((x \ y) * x) / T(y,x) = a(x,y,x). a(x,y,x) * T(y,x) = (x \ y) * x. (K(x,y) * ((z * u) * w)) / (u * w) = R(K(x,y) * z,u,w). R(K(x,y) * z,u,w) = K(x,y) * (((z * u) * w) / (u * w)). K(x,y) * (((z * u) * w) / (u * w)) = R(K(x,y) * z,u,w). K(x,y) * R(z,u,w) = R(K(x,y) * z,u,w). R(x * K(y,z),u,w) = R(x,u,w) * K(y,z). R(x,y,z) * K(u,w) = R(x * K(u,w),y,z). R(T(x,y),z,u) * K(y,x) = R(x,z,u). K(x,y) = K(x,R(y,z,u)). K(x,R(y,z,u)) = K(x,y). x * K(x,y) = T(x,R(y,z,u)). T(x,R(y,z,u)) = x * K(x,y). T(x,R(y,z,u)) = T(x,y). L(x,T((y / z) * (z * y),y / z),u) = x. x = L(x,(y * z) / (z / y),u). L(x,(y * z) / (z / y),u) = x. L(x,(y * z) * (y / z),u) = x. (x * (y * z)) / L(T(z,u),y,x) = (x * y) * K(u,L(z,y,x)). (x * T(y,z)) \ (x * (T(y,z) * u)) = L(u,y,x \ K(y,z)). L(x,y,z \ K(y,u)) = L(x,T(y,u),z). L(x,T(y,z),u) = L(x,y,u * K(y,z)). L(x,y,z * K(y,u)) = L(x,T(y,u),z). (K(x,y) * (z * u)) \ (K(x,y) * (z * (u * w))) = L(w,u,K(x,y) * z). L(x,y,K(z,u) * w) = (w * y) \ (w * (y * x)). L(x,y,K(z,u) * w) = L(x,y,w). ((x * K(y,z)) * u) \ ((x * K(y,z)) * (u * w)) = L(w,u,x). L(x,y,z * K(u,w)) = L(x,y,z). L(x,y,z) = L(x,T(y,u),z). L(x,T(y,z),u) = L(x,y,u). L(x,y,z) = L(x,(y * u) * u,z). L(x,(y * z) * z,u) = L(x,y,u). L(x,y * z,u) = L(x,z / y,u). L(x,y / z,u) = L(x,z * y,u). L(x,y * z,u) = L(x,y / z,u). L(x,y / z,u) = L(x,y * z,u). (x * y) / L(z,z * y,x) = x * (y / z). L(x,y * z,u) = L(x,z * y,u). L(x,(y / z) * (y * z),u) = x. L(x,(y \ (y \ z)) * ((y \ z) * T(y,z)),u) = x. (x * (y * z)) / L(T(z,u),T(z,u) * (y * z),x) = x * (y * K(u,z)). x = L(x,(y * (y \ z)) * ((y \ z) * T(y,z)),u). L(x,(y * (y \ z)) * ((y \ z) * T(y,z)),u) = x. L(x,y * ((z \ y) * T(z,y)),u) = x. L(x,y \ ((z \ y) * T(z,y)),u) = x. L(x,a(y,z,y),u) = x. (x * a(y,z,y)) * u = x * (a(y,z,y) * u). (x * y) / L(y,z,y) = x * a(y,z,y). (x * (y * (a(z,u,z) * w))) \ (((x * y) * a(z,u,z)) * w) = a(x,y,a(z,u,z) * w). (a(x,y,x) * z) * u = z * (a(x,y,x) * u). x * (a(y,z,y) * u) = (x * u) * a(y,z,y). (x * y) * a(z,u,z) = x * (a(z,u,z) * y). (x * (K(y,z) * u)) \ ((x * K(y,z)) * (u * w)) = L(w,u,x). (x * (K(y,z) * u)) \ (x * (K(y,z) * (u * w))) = L(w,u,x). L(x,y,z) = L(L(x,y,K(u,w)),K(u,w) * y,z). L(L(x,y,K(z,u)),K(z,u) * y,w) = L(x,y,w). L(x,K(y,z) * u,w) = L(x,u,w). L(x,y * z,u) = L(x,T(y,w) * z,u). L(x,T(y,z) * u,w) = L(x,y * u,w). L(x,T(y,z) * u,w) = L(x,u * y,w). (x * (y * z)) / L(T(z,u),(y * z) * z,x) = x * (y * K(u,z)). (x * (y * z)) / L(T(z,u),y,x) = x * (y * K(u,z)). x * (y * K(z,u)) = (x * y) * K(z,L(u,y,x)). (x * y) * K(z,L(u,y,x)) = x * (y * K(z,u)). (K(x,y) * (z * (u * w))) \ ((K(x,y) * (z * u)) * w) = a(K(x,y) * z,u,w). (K(x,y) * (z * (u * w))) \ (K(x,y) * ((z * u) * w)) = a(K(x,y) * z,u,w). a(K(x,y) * z,u,w) = (z * (u * w)) \ ((z * u) * w). ((x * K(y,z)) * (u * w)) \ (((x * K(y,z)) * u) * w) = a(x,u,w). (x * (K(y,z) * (u * w))) \ (((x * K(y,z)) * u) * w) = a(x,u,w). (x * (K(y,z) * (u * w))) \ ((x * (K(y,z) * u)) * w) = a(x,u,w). a(x,y,z) = a(x,K(u,w) * y,z). a(x,K(y,z) * u,w) = a(x,u,w). a(x,y * z,u) = a(x,z * y,u). a(x,y,z) = a(x,T(y,u),z). a(x,T(y,z),u) = a(x,y,u). a(x,y * T(z,u),w) = a(x,y * z,w). a(x,y * K(z,u),w) = a(x,y,w). a(x,y * z,u) = a(x,z / y,u). a(x,y / z,u) = a(x,z * y,u). a(x,y,z) = a(x,(y * u) * u,z). a(x,(y * z) * z,u) = a(x,y,u). a(x,y * (z * K(u,w)),v5) = a(x,y * z,v5). a(x,y * a(z,u,z),w) = a(x,L(z,u,z) * (y * z),w). a(x,L(y,z,y) * (u * y),w) = a(x,u * a(y,z,y),w). a(x,y * L(z,u,z),w) = a(x,y * (z * K(u,z)),w). a(x,y * (z * K(u,z)),w) = a(x,y * L(z,u,z),w). a(x,y * L(z,u,z),w) = a(x,y * z,w). a(x,y * z,u) = a(x,L(z,w,z) * y,u). a(x,L(y,z,y) * u,w) = a(x,u * y,w). a(x,y * a(z,u,z),w) = a(x,(y * z) * z,w). a(x,y * a(z,u,z),w) = a(x,y,w). a(x,a(y,z,y) * u,w) = a(x,u,w). (x * ((a(y,z,y) * u) * w)) \ ((x * (a(y,z,y) * u)) * w) = a(x,u,w). (x * (y * (a(z,u,z) * w))) \ ((x * (a(z,u,z) * y)) * w) = a(x,y,w). (x * (y * (a(z,u,z) * w))) \ ((x * (a(z,u,z) * y)) * w) = a(x,y,a(z,u,z) * w). a(x,y,a(z,u,z) * w) = a(x,y,w). a(x,y,z) = a(x,y,L(z,u,z)). a(x,y,L(z,u,z)) = a(x,y,z). a(x,y,(z \ u) * z) = a(x,y,T(u,z)). a(x,y,(T(z,u) * u) \ (T(z,u) * (z * u))) = a(x,y,T(z,u)). a(x,y,z * u) = a(x,y,T(u * z,u)). a(x,y,T(z * u,z)) = a(x,y,u * z). a(x,y,(T(z,u) * u) \ (z * (T(z,u) * u))) = a(x,y,T(z,u)). a(x,y,T(z,T(z,u) * u)) = a(x,y,T(z,u)). a(x,y,T(z,z * u)) = a(x,y,T(z,u)). a(x,y,T((z \ u) * z,((z \ u) * z) * (z \ 1))) = a(x,y,R(u,z,z)). a(x,y,T((z \ u) * z,R(z \ u,z,z \ 1))) = a(x,y,R(u,z,z)). a(x,y,T((z \ u) * z,z \ u)) = a(x,y,R(u,z,z)). a(x,y,R(z,u,u)) = a(x,y,u * (u \ z)). a(x,y,z * (z \ u)) = a(x,y,R(u,z,z)). a(x,y,z) = a(x,y,R(z,u,u)). a(x,y,R(z,u,u)) = a(x,y,z). a(x,y,z * u) = a(x,y,z / (u \ 1)). a(x,y,z / (u \ 1)) = a(x,y,z * u). a(x,y,R(((z \ 1) * u) \ 1,u,u)) = a(x,y,(u \ 1) * z). a(x,y,R((z \ u) \ 1,u,u)) = a(x,y,(u \ 1) * z). a(x,y,(z \ 1) * u) = a(x,y,(u \ z) \ 1). a(x,y,(z \ u) \ 1) = a(x,y,(u \ 1) * z). a(x,y,(z \ u) \ 1) = a(x,y,u \ z). a(x,y,z * a(u,z,z)) = a(x,y,(u / z) \ u). a(x,y,(z / u) \ z) = a(x,y,u * a(z,u,u)). a(x,y,z) = a(x,y,z * a(u,z,z)). a(x,y,z * a(u,z,z)) = a(x,y,z). a(x,y,L(z,u,u * z)) = a(x,y,z). ((x * y) \ x) * L(L(y,x,x * y),z,u) = a(u,z,y) \ 1. a(x,y,z) \ 1 = (u * z) \ (u * L(z,y,x)). (x * y) \ (x * L(y,z,u)) = a(u,z,y) \ 1. a(x,x * y,z) \ 1 = L(a(x,y,z),z,u). L(a(x,y,z),z,u) = a(x,x * y,z) \ 1. L(a(x,y,z),z,u) = a(x,y,z). (x * L(y,z,u)) / a(u,u * z,y) = x * y. x * y = a(z,z * u,y) \ (x * L(y,u,z)). a(x,x * y,z) \ (u * L(z,y,x)) = u * z. x * y = a(z,u,y) * (x * L(y,u,z)). a(x,y,z) * (u * L(z,y,x)) = u * z. x * y = y * T(x,L(y,z,u)). x * T(y,L(x,z,u)) = y * x. (x * y) \ (y * x) = K(L(y,z,u),x). K(L(x,y,z),u) = (u * x) \ (x * u). K(L(x,y,z),u) = K(x,u). K(x,y) = L(K(x,y),z,u). L(K(x,y),z,u) = K(x,y). a(x,y,a(z,u,w)) = 1. a(c27,c28,a(c29,c30,c31)) != 1. x * K(y,x / y) = y * (x / y). (x * y) * L(L(z,y,x),u,w) = x * (y * L(z,u,w)). R(x,x \ (y / z),z) = y / ((x \ (y / z)) * z). x * L(x \ y,z,u) = L(y / x,z,u) * x. L(x / y,z,u) * y = y * L(y \ x,z,u). L(((x * y) * z) \ u,(x * y) * z,x * (y * z)) = a(x,y,z) \ ((x * (y * z)) \ u). (x / (y * x)) * z = y \ z. R(R(x / y,y,z),u,w) * (y * z) = (y * z) * R((y * z) \ (x * z),u,w). (x \ R(x,y,z)) * x = R(x,y,z). (R(x,y,z) \ x) * u = R(x,y,z) \ (x * u). R(x,y,z) \ (x * u) = (R(x,y,z) \ x) * u. L(x,(y \ z) \ u,z \ (y * u)) = x. x \ (L(x,y,z) * u) = (L(x,y,z) \ x) \ u. (L(x,y,z) \ x) \ u = x \ (L(x,y,z) * u). (L(x,y,z) \ x) \ u = (x \ L(x,y,z)) * u. (x \ R(x,y,z)) \ u = R(x,y,z) \ (x * u). (x \ (y * z)) * a(x,y,z) = (x \ y) * z. R(x,x * (y / z),z) = y / ((x \ (y / z)) * z). (L(x,y,z) \ x) \ u = L(x,y,z) * (x \ u). R(L(x / (y \ 1),z,u),y,y) / y = (y \ 1) * L((y \ 1) \ x,z,u). L(R(x / (y \ 1),y,y),z,u) / y = (y \ 1) * L((y \ 1) \ x,z,u). L(x,(y \ z) \ u,z * (y * u)) = x. L(x,(y \ z) * u,z * (y * u)) = x. L(x,(y * z) * u,z * (y * u)) = x. L(x,(y * z) * u,T(y,z) * (z * u)) = x. x / y = K(x * y,x) / (x \ y). K(x * y,x) / (x \ y) = x / y. x / y = (x \ y) \ K(x * y,x). (x \ y) \ K(x * y,x) = x / y. x * K(y,y * x) = y * (x / y). K(x,y / x) * ((x \ y) * z) = (y / x) * z. ((T(x,y) * z) * u) / ((K(x,y) * z) * u) = R(x,K(x,y) * z,u). x * a(x,y,x) = R(x,y,x). L(x * y,z,u) / y = (y \ 1) * L((y \ 1) \ x,z,u). (x \ 1) * L((x \ 1) \ y,z,u) = L(y * x,z,u) / x. (x \ 1) * L(x * y,z,u) = L(y * x,z,u) / x. L(x * y,z,u) / y = y \ L(y * x,z,u). L(x,y,z) / (u \ x) = (u \ x) \ L((u \ x) * u,y,z). (x \ y) \ L((x \ y) * x,z,u) = L(y,z,u) / (x \ y). (x * y) * R((x * y) \ (z * y),u,w) = (R(z / x,u,w) * x) * y. (x * y) * R((x * y) \ (z * y),u,w) = (x * R(x \ z,u,w)) * y. a((x * y) * (x * (y * z)),u,w) = a(L(z,y,x),u,w). (T(x,y) * z) \ u = ((x * z) \ K(y,x)) * u. ((x * y) \ K(z,x)) * u = (T(x,z) * y) \ u. (x \ K(y,z)) * K(z,y) = x \ 1. (x / y) * K(x,x * y) = (x \ y) \ 1. (x * K(y,z)) \ u = (K(z,y) / x) * u. K(x,T(y,z)) / z = z \ K(x,y). x * a(x,y,z) = R(x,y,z). L(x,y,z) \ L(R(x,u,w),y,z) = a(L(x,y,z),u,w). a(x,y,z) * x = R(x,y,z). a(x,y,z) \ u = R(x,y,z) \ (x * u). R(x,y,z) \ (x * u) = a(x,y,z) \ u. a(x,y,z) * u = R(x,y,z) * (x \ u). R(x,y,z) * (x \ u) = a(x,y,z) * u. L(x,a(y,z,u),y * z) = x. (x * y) * R((x * y) \ x,z,u) = x * a(y,z,u). a(x,y,z) \ z = L(z,y,x). L(L(x,y,z),u,w) \ L(x,u,w) = a(z,y,L(x,u,w)). x / a(y,z,x) = L(x,z,y). (x \ (y \ z)) \ ((y * x) \ z) = a(y,y * x,(y * x) \ z). a(x,x * y,(x * y) \ z) = (y \ (x \ z)) \ ((x * y) \ z). x / L(x,y,z) = a(z,y,x). a(x,y,z) \ u = z \ (L(z,y,x) * u). x \ (L(x,y,z) * u) = a(z,y,x) \ u. (x * y) / (L(x,z,u) * y) = a(u,z,x). a(x,y,z) \ u = L(z,y,x) * (z \ u). L(x,y,z) * (x \ u) = a(z,y,x) \ u. x * a(x,y,z) = R(x,u * (u * y),z). R(x,y * (y * z),u) = x * a(x,z,u). ((x * y) * a(x,y,z)) * u = (x * y) * (a(x,y,z) * u). x * a(y,z,x) = L(x,y * z,y). L(x,y * z,y) = x * a(y,z,x). L(x,y,z) \ x = a(z,y,L(x,y,z)). a(x,y,L(z,y,x)) = L(z,y,x) \ z. a(x,x * y,z) * u = a(x,y,z) \ u. L(x,y,a(z,z * u,w)) = L(x,y,a(z,u,w)). L(x * a(y,z,x),z,y) = x. a(x,y,L(z,y,x)) = a(x,y,z). a(x,x * y,L(z,y,x)) = a(x,y,z) \ 1. R(a(x,y,z),u,w) \ R(x,y,z) = a(a(x,y,z),u,w) \ x. x * (a(y,z,x) \ u) = L(x,z,y) * u. ((L(x,y,z) * u) * w) \ ((x * u) * w) = R(T(a(z,y,x),(L(x,y,z) * u) * w),L(x,y,z) * u,w). R(T(a(x,y,z),(L(z,y,x) * u) * w),L(z,y,x) * u,w) = ((L(z,y,x) * u) * w) \ ((z * u) * w). L(a(x,y,z),u,w) * L(z,y,x) = a(w,u,a(x,y,z)) \ z. R(x,y * (y * z),u) = R(x,z,u). R(x,y * z,u) = R(x,y \ z,u). R(x,y \ z,u) = R(x,y * z,u). R(x,(y * z) / u,w) = R(x,(y \ z) / u,w). R(x,(y \ z) / u,w) = R(x,(y * z) / u,w). a(L(x,y,z),u,w) \ a(x,u,w) = a(z,y,a(x,u,w)). a(x,y,z) \ a(L(x,u * w,u),y,z) = a(u,w,a(x,y,z)). a(x,y,a(z,u,w)) \ 1 = a(z,u,w) \ a(L(z,y,x),u,w). a(x,y,z) \ a(L(x,u,w),y,z) = a(w,u,a(x,y,z)) \ 1. a(x,y,z) = R(a(x,y,z),y,u). R(a(x,y,z),y,u) = a(x,y,z). x * (y * (a(x,y,z) * u)) = R(x,y,z) * (y * u). a(L(x,y,z),u,w) * L(w,u,x) = a(z,y,a(x,u,w)) \ w. a(x,y,z) = a(L(x,u,y),y,z). a(L(x,y,z),z,u) = a(x,z,u). a((x * y) \ z,x,u) = a(y \ (x \ z),x,u). L(x,y,z) * a(x,z,u) = R(L(x,y,z),z,u). a(x \ (y \ z),y,u) = a((y * x) * z,y,u). L(x,y,z) * a(x,z,u) = L(R(x,z,u),y,z). a((x * y) * z,x,u) = a(y * (x * z),x,u). (x * a(x,y,z)) / L(R(x,y,z),u,y) = a(y,u,x). a((x * y) * z,y,u) = a(T(x,y) * (y * z),y,u). a(T(x,y) * (y * z),y,u) = a((x * y) * z,y,u). R(x,y,z) / L(R(x,y,z),u,y) = a(y,u,x). a(x,y,z) = a(x,y,R(z,x,u)). a(x,y,R(z,x,u)) = a(x,y,z). a(x,y,z / (x * u)) = a(x,y,(z / u) / x). a(x,y,(z / u) / x) = a(x,y,z / (x * u)). L(x,y,z \ u) = L(x,y,u * z). L(x,y,z * (u * (u * w))) = L(x,y,w * z). L(x,y,L(z,u,w)) = L(x,y,(w * (u * z)) * (w * u)). L(x,y,(z * (u * w)) * (z * u)) = L(x,y,L(w,u,z)). K(a(x,y,z) \ 1,u) = 1. T(a(x,y,z) \ 1,u) = a(x,y,z) \ 1. x * a(y,z,u) = a(y,z,u) * x. a(x,y,z) * u = u * a(x,y,z). a(x,y,z) = (a(x,y,z) \ u) \ u. (a(x,y,z) \ u) \ u = a(x,y,z). (a(x,y,z) \ u) * a(x,y,z) = u. x \ a(y,z,u) = a(y,z,u) * (x \ 1). a(x,y,z) * (u \ 1) = u \ a(x,y,z). a(x \ y,z,u) = a(y / x,z,u). a(x / y,z,u) = a(y \ x,z,u). a(x,y,z) * (u / a(x,y,z)) = u. (x * (a(y,z,u) * w)) \ ((x * w) * a(y,z,u)) = a(x,w,a(y,z,u)). (x * y) \ ((x * a(z,u,w)) * y) = R(T(a(z,u,w),x * y),x,y). x * (y * a(x,z,u)) = R(x,z,u) * y. (x * y) * a(x,z,u) = R(x,z,u) * y. x * (L(x,y,z) \ u) = u * a(z,y,x). (a(x,y,z) / u) * w = (a(x,y,z) \ u) \ w. (a(x,y,z) \ u) \ w = (a(x,y,z) / u) * w. a(x / y,z,u) = a(y * x,z,u). a(x * a(y,z,x),u,w) = a(L(x,z,y),u,w). (x * y) / a(z,u,x) = L(x,u,z) * y. a(x * y,z,u) = a(x / y,z,u). a(x / y,z,u) = a(x * y,z,u). a(x * y,z,u) = a(y * x,z,u). ((T(x,y) * z) * u) / (K(x,y) * (z * u)) = R(x,K(x,y) * z,u). (x * K(y,z)) * u = K(y,T(z,x)) * (x * u). K(x,T(y,z)) * (z * u) = (z * K(x,y)) * u. x \ y = (x \ K(z,u)) * (K(u,z) * y). (x \ K(y,z)) * (K(z,y) * u) = x \ u. x * (a(y,z,u) \ 1) = a(y,z,u) \ x. (x * y) \ (R(x,z,u) * y) = L(a(x,z,u),y,x). a(x,y,z) = (x * u) \ (R(x,y,z) * u). (x * y) \ (R(x,z,u) * y) = a(x,z,u). (R(x,y,z) * y) * u = (x * y) * (a(x,y,z) * u). (x * y) * (a(x,y,z) * u) = (R(x,y,z) * y) * u. L(x,y,z) * a(z,y,L(x,u,w)) = L(x,u,w) * a(w,u,L(x,y,z)). (L(x,y,z) * u) \ (x * u) = a(z,y,x). K(x,y) * (z \ u) = (z * K(y,x)) \ u. (x * K(y,z)) \ u = K(z,y) * (x \ u). x \ (R(x / y,z,u) * y) = a(x / y,z,u). (L(R(x,y,z),u,w) * (y * z)) \ ((x * y) * z) = a(w,u,R(x,y,z)). (x * (y / x)) \ z = K(x * y,x) * (y \ z). K(x * y,x) * (y \ z) = (x * (y / x)) \ z. K(x,y) * (z \ u) = (K(x,y) / z) * u. (K(x,y) / z) * u = K(x,y) * (z \ u). x = R(x,K(y,z),u). R(x,K(y,z),u) = x. (x / y) / K(z,u) = x / (K(z,u) * y). (x / y) * z = K(x * y,x) * ((x \ y) \ z). K(x * y,x) * ((x \ y) \ z) = (x / y) * z. (x \ K(y,z)) * u = K(y,T(z,x)) * (x \ u). K(x,T(y,z)) * (z \ u) = (z \ K(x,y)) * u. x / (K(y,z) * u) = (x / u) * K(z,y). a(L(x,y * z,y),u,w) = a(L(x,z,y),u,w). K(x,T(y,z)) * (z * u) = z * (K(x,y) * u). x \ (y * R(y \ x,z,u)) = a(x / y,z,u). L(x,y,z * (K(u * w,u) * ((u * (w / u)) \ v5))) = L(x,y,(w \ v5) * z). a(x,y,z) \ a(L(x,u,w),y,z) = a(w,u,a(x,y,z)). x \ (y * R(y \ x,z,u)) = a(y * x,z,u). (x * (y * z)) \ ((x * y) * R(L(z,y,x),u,w)) = a((x * y) * (x * (y * z)),u,w). L(a(x,y,z),u,x) = a(x,y,z). (x * (y * (a(x,y,z) * u))) \ ((R(x,y,z) * y) * u) = a(x,y,a(x,y,z) * u). x * a(y,z,a(u,w,x)) = L(x,w,u) * a(L(u,z,y),w,x). L(x,y,z) * a(L(z,u,w),y,x) = x * a(w,u,a(z,y,x)). a(x,y,a(z,u,w)) = a(x,y,a(z,u,w)) \ 1. a(x,y,a(z,u,w)) \ 1 = a(x,y,a(z,u,w)). a(x,y,a(z,u,w)) * a(x,y,a(z,u,w)) = 1. x * a(y,z,a(u,w,v5)) = a(y,z,a(u,w,v5)) \ x. a(x,y,a(z,u,w)) \ v5 = v5 * a(x,y,a(z,u,w)). a(L(x,y,z),u,w) * L(w,u,x) = w * a(z,y,a(x,u,w)). R(x,y,z) * T(u,x) = u * R(x,y,z). R(x,y,z) * (x \ u) = (u / x) * R(x,y,z). (x / y) * R(y,z,u) = a(y,z,u) * x. x * R(y,z,u) = a(y,z,u) * (x * y). a(x,y,z) * (u * x) = u * R(x,y,z). L(x,y,z) * R(a(z,y,x),u,w) = a(a(z,y,x),u,w) * x. x * R(y,z,u) = (x * y) * a(y,z,u). (x * y) * a(y,z,u) = x * R(y,z,u). (x * (y * z)) \ (x * (y * R(z,u,w))) = L(a(z,u,w),y * z,x). (x * y) \ ((x * a(z,u,w)) * y) = R(a(z,u,w),x,y). R(x,K(x,y) * z,u) = (((T(x,y) * z) * u) / (z * u)) * K(y,x). (((T(x,y) * z) * u) / (z * u)) * K(y,x) = R(x,K(x,y) * z,u). R(T(x,y),z,u) * K(y,x) = R(x,K(x,y) * z,u). R(x,K(x,y) * z,u) = R(x,z,u). R(x,x * y,z) = R(x,y * x,z). R(x,y * x,z) = R(x,x * y,z). x \ R(x,y * x,z) = R(x,y,z) \ x. R(x,y,z) \ x = a(x,y * x,z). a(x,y * x,z) = a(x,y,z) \ 1. a(x * y,x,z) \ 1 = a(x * y,y,z). a(x * y,y,z) = a(x * y,x,z) \ 1. a(x * y,y,a(z,u,w)) = a(x * y,x,a(z,u,w)). ((L(x,y,z) * u) * w) \ ((x * u) * w) = a(z,y,R(x,u,w)). L(x,y,z * u) = L(x,y,T(z,w) * u). L(x,y,T(z,u) * w) = L(x,y,z * w). L(x,y,(z / u) * w) = L(x,y,(u \ z) * w). L(x,y,z * T(u,w)) = L(x,y,z * u). L(x,y,z * (K(u,w) * v5)) = L(x,y,z * v5). L(x,(y * z) * u,y * (z * u)) = x. ((x * y) * z) \ u = a(x,y,z) \ ((x * (y * z)) \ u). a(x,y,z) \ ((x * (y * z)) \ u) = ((x * y) * z) \ u. L(x,y,z * (u \ w)) = L(x,y,z * (w / u)). L(x,y,z * (u / w)) = L(x,y,z * (w \ u)). L(x,y,(z / u) * w) = L(x,y,(u * z) * w). L(x,y,z * (u * w)) = L(x,y,z * (w * u)). L(x,y,z * (u / w)) = L(x,y,z * (w * u)). L(x,y,z * ((u * w) * u)) = L(x,y,w * z). a(x,y,z) \ 1 = ((x * y) * z) \ (x * (y * z)). ((x * y) * z) \ (x * (y * z)) = a(x,y,z) \ 1. a(x,a(y,z,u),w) \ a(x,w,a(y,z,u)) = ((x * a(y,z,u)) * w) \ ((x * w) * a(y,z,u)). ((x * a(y,z,u)) * w) \ ((x * w) * a(y,z,u)) = a(x,a(y,z,u),w) \ a(x,w,a(y,z,u)). L(x,y,(z \ u) * w) = L(x,y,w * ((v5 * (z / v5)) \ u)). L(x,y,z * ((u * (w / u)) \ v5)) = L(x,y,(w \ v5) * z). L(x,y,(z \ u) * w) = L(x,y,w * ((v5 * (z / v5)) * u)). L(x,y,z * ((u * (w / u)) * v5)) = L(x,y,(w \ v5) * z). L(x,y,z * ((u * (w / u)) * v5)) = L(x,y,(w * v5) * z). L(x,y,(z * u) * ((w * (z / w)) * (u * v5))) = L(x,y,L(v5,u,w * (z / w))). L(x,y,L(z,u,(u * z) * (w / (u * z)))) = L(x,y,(w / (u * z)) * (w * u)). L(x,y,L(z,u,(u * z) * (w / (u * z)))) = L(x,y,((u * z) * w) * (w * u)). a(K(x,y) * z,u,w) = a(z,u,w). a(x * y,z,u) = a(T(x,w) * y,z,u). a(T(x,y) * z,u,w) = a(x * z,u,w). a((x / y) * z,u,w) = a((y \ x) * z,u,w). a(x * T(y,z),u,w) = a(x * y,u,w). a(x * (y * z),y,u) = a((x * y) * z,y,u). a((x * y) * z,y,u) = a(x * (y * z),y,u). a((x / y) * z,u,w) = a((y * x) * z,u,w). a(x / (y / z),u,w) = a((z \ y) * x,u,w). a(x / (y * z),z,u) = a(y * (z * x),z,u). a(x / (y * z),u,w) = a((z / y) * x,u,w). a(x / (y \ z),u,w) = a(x / (z / y),u,w). a(x / (y / z),u,w) = a(x / (z \ y),u,w). a((x * y) / z,x,u) = a(y / (z * x),x,u). a(x / (y / z),u,w) = a(x / (z * y),u,w). a((x * y) / z,x,u) = a(y / (x / z),x,u). a(x,y,z) * x = R(x,K(u,w) * y,z). R(x,K(y,z) * u,w) = a(x,u,w) * x. a(x,y,z) * x = R(x,T(y,u),z). R(x,T(y,z),u) = a(x,y,u) * x. (x * ((y * K(z,u)) * w)) \ ((x * (y * K(z,u))) * w) = a(x,y,w). R(x,T(y,z),u) = R(x,y,u). R(x,y \ z,u) = R(x,z / y,u). R(x,y / z,u) = R(x,z \ y,u). R(x,y / z,u) = R(x,z * y,u). R(x,y * (z \ u),w) = R(x,(z * u) / y,w). R(x,(y * z) / u,w) = R(x,u * (y \ z),w). a(x,y * T(z,u),w) = a(x,z * y,w). R(x,K(y,z) * u,w) = R(x,u,w). R(x,y * K(z,u),w) = R(x,y,w). R(x,y * (z * K(u,w)),v5) = R(x,y * z,v5). x * a(x,y * z,u) = R(x,z * T(y,w),u). R(x,y * T(z,u),w) = x * a(x,z * y,w). R(x,y * (z \ u),w) = R(x,y * (z * u),w). R(x,y * ((z \ u) \ 1),w) = R(x,y * (z / u),w). R(x,y * T(z,u),w) = R(x,z * y,w). R(x,y * ((z \ u) \ u),w) = R(x,z * y,w). R(x,y * z,u) = R(x,z * ((y \ w) * w),u). R(x,y * ((z \ u) * u),w) = R(x,z * y,w). R(x,y * (z / u),w) = R(x,y * ((z \ u) * 1),w). R(x,y * ((z \ u) * 1),w) = R(x,y * (z / u),w). R(x,y * (z \ u),w) = R(x,y * (z / u),w). R(x,y * (z / u),w) = R(x,y * (z \ u),w). R(x,y * (z / u),w) = R(x,y * (z * u),w). R(x,x * (y * z),z) = y / ((x \ (y / z)) * z). R(x,x * ((y \ z) * z),z) = (y \ z) / ((x \ (y \ 1)) * z). (x \ y) / ((z \ (x \ 1)) * y) = R(z,x * z,y). R(x,y * x,z) = (y \ z) / ((x \ (y \ 1)) * z). (x * (y * (K(z,u) * w))) \ ((x * (y * K(z,u))) * w) = a(x,y,w). L(x,y,L(z,u,(u * z) * ((u * z) * w))) = L(x,y,((u * z) * w) * (w * u)). L(x,y,L(z,u,w)) = L(x,y,((u * z) * w) * (w * u)). L(x,y,((z * u) * w) * (w * z)) = L(x,y,L(u,z,w)). L(x,y,L(z,u,w)) = L(x,y,((u * z) * w) * (u * w)). L(x,y,((z * u) * w) * (z * w)) = L(x,y,L(u,z,w)). L(x,y,L(z,u,w)) \ x = a(((u * z) * w) * (u * w),y,x). a(((x * y) * z) * (x * z),u,w) = L(w,u,L(y,x,z)) \ w. a(((x * y) * z) * (x * z),u,w) = a(L(y,x,z),u,w). (x * y) \ (((x * z) * y) * R(((x * z) * y) \ (x * y),u,w)) = a(L(z,x,y),u,w). (R(x,y,z) * (y * u)) \ ((R(x,y,z) * y) * u) = a(x,y,a(x,y,z) * u). a(x,y,a(x,y,z) * u) = a(R(x,y,z),y,u). a(x,y,z * a(x,y,u)) = a(R(x,y,u),y,z). (x * (y * z)) \ ((x * y) * L(R(z,u,w),y,x)) = a((x * y) * (x * (y * z)),u,w). (x * y) \ (((x * z) * R((x * z) \ x,u,w)) * y) = a(L(z,x,y),u,w). (x * y) \ ((x * a(z,u,w)) * y) = a(L(z,x,y),u,w). a(L(x,y,z),u,w) = R(a(x,u,w),y,z). R(a(x,y,z),u,w) = a(L(x,u,w),y,z). a(L(x,y,z),u,w) = a(R(x,y,z),u,w). a(R(x,y,z),u,w) = a(L(x,y,z),u,w). a(L(x,y,z),y,u) = a(x,y,u). a(L(x,y,z),u,w) \ R(x,u,w) = a(a(x,u,w),y,z) \ x. L(x,y,z) * a(L(z,u,w),y,x) = a(a(z,y,x),u,w) * x. a((x * y) \ z,y,u) = a(y \ (x \ z),y,u). a((x \ y) \ z,y,u) = a(y \ (x * z),y,u). a((x \ y) \ T(z,x),y,u) = a(y \ (z * x),y,u). L(x,y,z) * a(x,y,u) = R(L(x,y,z),y,u). a(x,y,z * a(x,y,u)) = a(L(x,y,u),y,z). a(x \ (y \ z),x,u) = a((y * x) * z,x,u). a(x / (y \ z),z,u) = a(z \ (y * x),z,u). L(x,y,z) * a(x,y,u) = L(R(x,y,u),y,z). a(x,y,z * a(x,y,u)) = a(x,y,z). a(x \ (y \ z),x,u) = a(y * (x * z),x,u). a(x / (y / z),y,u) = a(y \ (z * x),y,u). L(R(x,y,z),y,u) \ (x * a(x,y,z)) = a(u,y,x). a(x * (y * z),y,u) = a(y * (x * z),y,u). a((x * y) / z,z,u) = a(y / (z / x),z,u). a(x \ (y * z),x,u) = a((z \ x) * T(y,z),x,u). a((x \ y) * T(z,x),y,u) = a(y \ (z * x),y,u). L(R(x,y,z),y,u) \ R(x,y,z) = a(u,y,x). a(x,y,z) = a(x,y,R(z,y,u)). a(x,y,R(z,y,u)) = a(x,y,z). a(x,y,z / (y * u)) = a(x,y,(z / u) / y). a(x,y,(z / u) / y) = a(x,y,z / (y * u)). a(x \ (y * z),x,u) = a((z \ x) * y,x,u). a(x \ (y * z),x,u) = a((z * x) * y,x,u). a(x \ (y * z),x,u) = a(z * (x * y),x,u). a(a(x,y,z),u,w) * z = z * a(w,u,a(x,y,z)). a(a(x,y,z),u,w) = a(w,u,a(x,y,z)). a(a(x,y,z),u,w) \ 1 = a(w,u,a(x,y,z)). a(a(x,y,z),u,w) \ v5 = v5 * a(w,u,a(x,y,z)). a(x,y,a(z,u,w)) = x \ L(x,y,a(z,u,w)). x \ L(x,y,a(z,u,w)) = a(x,y,a(z,u,w)). ((a(x,y,z) * u) * w) \ (a(x,y,z) * (u * w)) = a(w,u,a(x,y,z)). (x \ (a(y,z,u) * w)) \ ((a(y,z,u) \ x) \ w) = a(x \ (a(y,z,u) * w),x,a(y,z,u)). a(L(x,y,z),u,w) \ R(x,u,w) = x * a(z,y,a(x,u,w)). ((a(x,y,z) * u) * w) \ ((u * w) * a(x,y,z)) = a(w,u,a(x,y,z)). ((x * a(y,z,u)) * w) \ ((x * w) * a(y,z,u)) = a(w,x,a(y,z,u)). (x * (y * z)) \ (x * (y * R(z,u,w))) = a((x * y) * (x * (y * z)),u,w). a((x * y) * (x * (y * z)),u,w) = L(a(z,u,w),y * z,x). L(a(x,y,z),u * x,w) = a((w * u) * (w * (u * x)),y,z). L(a(x,y,z),u * x,w) = a(L(x,u,w),y,z). a(L(x,y,z),u,w) \ a(x,u,w) = a(z,y * x,a(x,u,w)). a(x,y * z,a(z,u,w)) = a(x,y,a(z,u,w)). a(x,y,a(z,u,w)) = a(x,z * y,a(z,u,w)). a(x,y * z,a(y,u,w)) = a(x,z,a(y,u,w)). a(x * y,z,a(u,w,v5)) = a(y * x,u * z,a(u,w,v5)). a(x * y,z * u,a(z,w,v5)) = a(y * x,u,a(z,w,v5)). a((x * y) * z,y,a(x,u,w)) = a(z * (x * y),z,a(x,u,w)). a(x * (y * z),x,a(y,u,w)) = a(y * (z * x),z,a(y,u,w)). a(x * (y * z),y,a(x,u,w)) = a(z * (x * y),z,a(x,u,w)). a(x * (y * z),y,a(x,u,w)) = a(x * (z * y),z,a(x,u,w)). x * L(y,z,u) = a(u,z,y) \ (x * y). a(x,y,z) \ (u * z) = u * L(z,y,x). L(x,y,z) * T(u,x) = u * L(x,y,z). (x * y) * K(z,u) = x * (y * K(z,u)). (x \ y) * K(z,u) = x \ (y * K(z,u)). x \ (y * K(z,u)) = (x \ y) * K(z,u). a(x,y,z) \ u = (u / z) * L(z,y,x). (x / y) * L(y,z,u) = a(u,z,y) \ x. (x * L(y,z,u)) \ (x * y) = a(u,z,y). (x * (y * K(z,u))) * w = (x * y) * (K(z,u) * w). x \ (y / z) = (x \ (z \ y)) * K(z,z * y). (x \ (y \ z)) * K(y,y * z) = x \ (z / y). a(x,y,z * u) \ u = z \ L(z * u,y,x). ((x * y) * L(L(z,y,x),u,w)) \ (x * (y * z)) = a(w,u,L(z,y,x)). L(a(x,y,z),u * L(z,y,x),w) = (w * (u * L(z,y,x))) \ (w * (u * z)). (x * (y * (K(z,u) * w))) \ ((x * (y * K(z,u))) * w) = a(x,y,K(z,u) * w). ((x * y) * (K(z,u) * w)) / ((y * K(z,u)) * w) = R(x,y * K(z,u),w). (x * (y * L(z,u,w))) \ (x * (y * z)) = a(w,u,L(z,y,x)). ((x * y) * (K(z,u) * w)) / (y * (K(z,u) * w)) = R(x,y * K(z,u),w). R(x,y * K(z,u),w) = R(x,y,K(z,u) * w). R(x,y,K(z,u) * w) = R(x,y,w). R(x,y,z) = R(x,y,T(z,u)). R(x,y,T(z,u)) = R(x,y,z). a(x,y,z) * x = R(x,y,T(z,u)). R(x,y,T(z,u)) = a(x,y,z) * x. a(x,y,z) = a(x,y,T(z,u)). a(x,y,T(z,u)) = a(x,y,z). a(x,y,z \ u) = a(x,y,u / z). a(x,y,z / u) = a(x,y,u \ z). a(x,y,(z \ u) * z) = a(x,y,u). a(x,y,(z / u) / x) = a(x,y,(x * u) \ z). a(x,y,(z / u) / y) = a(x,y,(y * u) \ z). a(x,y,((z / u) * w) * (u / z)) = a(x,y,w). a(x,y,z) \ u = (u \ z) \ L((u \ z) * u,y,x). (x \ y) \ L((x \ y) * x,z,u) = a(u,z,y) \ x. a(x,y,z) \ u = L(z,y,x) / (u \ z). L(x,y,z) / (u \ x) = a(z,y,x) \ u. x / (y \ L(x,z,u)) = a(u,u * z,L(x,z,u)) \ y. a(x,x * y,L(z,y,x)) \ u = z / (u \ L(z,y,x)). (a(x,y,z) \ 1) \ u = z / (u \ L(z,y,x)). x / (y \ L(x,z,u)) = a(u,z,x) * y. x / (y * L(x,z,u)) = a(u,z,x) * (y \ 1). R(x,y,z) / a(L(x,u,w),y,z) = a(w,u,R(x,y,z)) * L(x,u,w). x / (y * L(x,z,u)) = y \ a(u,z,x). a(x,y,R(z,u,w)) * L(z,y,x) = a(L(z,y,x),u,w) \ R(z,u,w). a(L(x,y,z),u,w) \ R(x,u,w) = a(z,y,R(x,u,w)) * L(x,y,z). a(x,y,R(z,u,w)) * L(z,y,x) = z * a(x,y,a(z,u,w)). L(a(x,y,z),u * L(z,y,x),w) = a(x,y,L(z,u,w)). a(x,y,L(z,u,w)) = a(L(x,u * L(z,y,x),w),y,z). a(L(x,y * L(z,u,x),w),u,z) = a(x,u,L(z,y,w)). a(x,y,L(z,u,x)) = a(x,y,z). a(x,y,L(L(z,u,x),w,v5)) = a(x,y,L(z,w,v5)). a(L(x,y * z,u),w,L(z,x * w,x)) = a(x,w,L(L(z,x * w,x),y,u)). a(L(x,L(y,z,x) * u,w),z,y) = a(x,z,L(y,T(u,v5),w)). a(x,y,K(z,u) * w) = a(x,y,w). a(x,y,(z / u) * w) = a(x,y,(u \ z) * w). a(x,y,z * T(u,w)) = a(x,y,z * u). a(x,y,a(z,u,z)) = a(x,y,K(z * u,z)). a(x,y,K(z * u,z)) = a(x,y,a(z,u,z)). a(x,y,T(z,u) / w) = a(x,y,z / w). a(x,y,(K(z,u) * w) * v5) = a(x,y,w * v5). a(x,y,(z * K(u,w)) * v5) = a(x,y,z * v5). a(x,y,(z / u) * w) = a(x,y,(z \ u) \ w). a(x,y,(z \ u) \ w) = a(x,y,(z / u) * w). a(x,y,(z \ K(u,w)) * v5) = a(x,y,z \ v5). a(x,y,z * (u \ w)) = a(x,y,z * (w / u)). a(x,y,z * (u / w)) = a(x,y,z * (w \ u)). a(x,y,z / u) = a(x,y,u \ T(z,w)). a(x,y,z \ T(u,w)) = a(x,y,u / z). a(x,y,z \ (u \ w)) = a(x,y,(w / u) / z). a(x,y,(z / u) / w) = a(x,y,w \ (u \ z)). a(x,y,a(z,u,z)) = 1. L(a(x,y,x),z,u) = a(x,y,x). a(x,y,x) = a(L(x,z,u),y,x). a(L(x,y,z),u,x) = a(x,u,x). L(x * a(x,y,x),y,L(x,z,u)) = x. L(R(x,y,x),y,L(x,z,u)) = x. (L(x,y,z) * u) * x = L(x,y,z) * (u * R(x,u,x)). L(x,y,z) * (u * R(x,u,x)) = (L(x,y,z) * u) * x. a(x,y,((z / u) * w) * v5) = a(x,y,((u \ z) * w) * v5). a(x,y,((z / u) * w) * v5) = a(x,y,((z \ u) \ w) * v5). a(x,y,((z \ u) \ w) * v5) = a(x,y,((z / u) * w) * v5). a(x,y,(z \ u) \ w) = a(x,y,(u \ z) * w). a(x,y,(T(z,u) * w) \ v5) = a(x,y,(z * w) \ v5). a(x,y,((z / u) * w) * (z \ u)) = a(x,y,w). a(x,y,x \ (z \ u)) = a(x,y,(x * z) \ u). a(x,y,(x * z) \ u) = a(x,y,x \ (z \ u)). a(x,y,y \ (z \ u)) = a(x,y,(y * z) \ u). a(x,y,(y * z) \ u) = a(x,y,y \ (z \ u)). a(x,y,((z / u) \ w) \ v5) = a(x,y,((w \ (u \ z)) * K(u,u * z)) * v5). a(x,y,((z \ (u \ w)) * K(u,u * w)) * v5) = a(x,y,((w / u) \ z) \ v5). a(x,x * y,x \ (y \ z)) = (y \ (x \ z)) \ ((x * y) \ z). a(x,y,K(z,y) * u) = a(x,y,y \ (z \ ((z * y) * u))). a(x,y,y \ (z \ ((z * y) * u))) = a(x,y,K(z,y) * u). a(x,y,((z \ u) * w) \ v5) = a(x,y,((u / z) * w) \ v5). a(x,y,((z / u) * w) \ v5) = a(x,y,((u \ z) * w) \ v5). L(x,y,z) * T(x * u,x) = (L(x,y,z) * u) * x. (L(x,y,z) * u) * x = (x * u) * L(x,y,z). x * y = (y * (L(y,z,u) \ x)) * L(y,z,u). (x * (L(x,y,z) \ u)) * L(x,y,z) = u * x. (x * a(y,z,u)) * L(u,z,y) = x * u. x * L(y,z,u) = (x / a(u,z,y)) * y. (x / a(y,z,u)) * u = x * L(u,z,y). (a(x,y,z) / u) \ z = u * L(z,y,x). x / (y * L(x,z,u)) = a(u,z,x) / y. a(x,y,z) / u = u \ a(x,y,z). (a(x,y,z) \ u) \ w = (u \ a(x,y,z)) * w. a(x,y,((z \ u) * w) * (u \ z)) = a(x,y,w). a(x,y,((z \ u) * w) * ((u * w) \ z)) = a(x,y,a(z,u,w)). a(x,y,(z \ (u * w)) * (u \ z)) = a(x,y,L(w,u,z)). a(x,y,((z \ u) \ w) * v5) = a(x,y,((u \ z) * w) * v5). a(x,y,y \ (z \ ((z * y) * u))) = a(x,y,u). a(x,y,L(z,u * y,u)) = a(x,y,z). a(L(x,y * z,u),w,z) = a(x,w,L(L(z,x * w,x),y,u)). x \ L(x,y,a(z,z * u,z \ (u \ w))) = a(x,y,(u \ (z \ w)) \ ((z * u) \ w)). a(x,y,(z \ (u \ w)) \ ((u * z) \ w)) = x \ L(x,y,a(u,u * z,u \ (z \ w))). a(L(x,y * z,u),w,z) = a(x,w,L(z,y,u)). a(L(x,y,z),u,w) = a(x,u,L(w,y * w,z)). a(x,y,L(z,u * z,w)) = a(L(x,u,w),y,z). a(x,y,((z \ (u \ w)) * K(u,u * w)) * v5) = a(x,y,((u / w) * z) \ v5). a(x,y,((z / u) * w) \ v5) = a(x,y,(w \ (z \ u)) * v5). a(x,y,(z \ (u \ w)) * v5) = a(x,y,((w \ u) * z) \ v5). a(x,y,((z \ u) * w) \ v5) = a(x,y,(w \ (u \ z)) * v5). a(x,y,z / ((u \ w) * v5)) = a(x,y,(v5 \ (w \ u)) * z). a(x,y,(z \ (u \ w)) \ ((u * z) \ w)) = x \ L(x,y,a(u,z,u \ (z \ w))). a(x,y,(z \ (u \ w)) \ ((u * z) \ w)) = a(x,y,a(u,z,u \ (z \ w))). (x \ (a(y,z,u) * w)) \ ((x \ a(y,z,u)) * w) = a(x \ (a(y,z,u) * w),x,a(y,z,u)). a(x \ (a(y,z,u) * w),x,a(y,z,u)) = a(x,a(y,z,u),w). a(x,a(y,z,u),w) = a(x * (a(y,z,u) * w),x,a(y,z,u)). a(x * (a(y,z,u) * w),x,a(y,z,u)) = a(x,a(y,z,u),w). a(x,a(y,z,u),w) = a(w * (x * a(y,z,u)),x,a(y,z,u)). a(x * (y * a(z,u,w)),y,a(z,u,w)) = a(y,a(z,u,w),x). a(a(x,y,z) * (u * w),u,a(x,y,z)) = a(u,a(x,y,z),w). a((x * a(y,z,u)) / w,x,a(y,z,u)) = a(x,a(y,z,u),w). a(x,x * a(y,z,u),w) * v5 = a(a(y,z,u) * (x * w),x,a(y,z,u)) \ v5. a(a(x,y,z) * (u * w),u,a(x,y,z)) \ v5 = a(u,u * a(x,y,z),w) * v5. a(x,a(y,z,u),w) = a(a(y,z,u) / (x / w),x,a(y,z,u)). a(a(x,y,z) / (u / w),u,a(x,y,z)) = a(u,a(x,y,z),w). a(x,x * a(y,z,u),w) = a(a(y,z,u) * (x * w),x,a(y,z,u)). a(a(x,y,z) * (u * w),u,a(x,y,z)) = a(u,u * a(x,y,z),w). a(x,x * a(y,z,u),w) = a(x,a(y,z,u),w). a(x,a(y,z,u),w) * v5 = a(x,a(y,z,u),w) \ v5. a(x,a(y,z,u),w) \ v5 = a(x,a(y,z,u),w) * v5. a(x,a(y,z,u),w) \ a(x,w,a(y,z,u)) = a(w,x,a(y,z,u)). a(x,y,a(z,u,w)) = a(y,a(z,u,w),x) * a(y,x,a(z,u,w)). a(x,a(y,z,u),w) * a(x,w,a(y,z,u)) = a(w,x,a(y,z,u)). R(T(a(x,y,z),(L(z,y,x) * u) * w),L(z,y,x) * u,w) = a(x,y,R(z,u,w)). R(a(x,y,z),L(z,y,x) * u,w) = a(x,y,R(z,u,w)). a(x,y,R(z,u,w)) = a(L(x,L(z,y,x) * u,w),y,z). a(L(x,L(y,z,x) * u,w),z,y) = a(x,z,R(y,u,w)). a(x,y,R(z,u,w)) = a(x,y,L(z,T(u,v5),w)). a(x,y,L(z,T(u,w),v5)) = a(x,y,R(z,u,v5)). a(x,y,L(z,u,w)) = a(x,y,R(z,u,w)). a(x,y,R(z,u,w)) = a(x,y,L(z,u,w)). a(x,y,(z \ u) / ((w \ (z \ 1)) * u)) = a(x,y,L(w,z * w,u)). a(x,y,L(z,u * z,w)) = a(x,y,(u \ w) / ((z \ (u \ 1)) * w)). a(x,y,L(z,u,w)) * L(z,y,x) = z * a(x,y,a(z,u,w)). a(x,y,L(z,u * z,w)) = a(x,y,(w \ ((u \ 1) \ z)) * (u \ w)). a(x,y,L(z,u * z,w)) = a(x,y,(w \ (u * z)) * (u \ w)). a(x,y,L(z,u * z,w)) = a(x,y,L(z,u,w)). a(x,y,L(z,u,w)) = a(L(x,u,w),y,z). a(L(x,y,z),u,w) = a(x,u,L(w,y,z)). L(x,y,z) * a(z,y,L(x,u,w)) = x * a(w,u,a(z,y,x)). a(x,y,L(z,u,w)) * L(z,y,x) = z * a(w,u,a(x,y,z)). x * a(y,z,a(u,w,x)) = L(x,z,y) * a(y,z,L(x,w,u)). L(x,y,z) * a(z,y,L(x,u,w)) = x * a(z,y,a(w,u,x)). a(x,y,a(z,u,w)) = a(z,u,a(w,y,x)). a(x,y,a(z,u,w)) = a(w,u,a(x,y,z)). a(x,y,a(z / u,w,v5)) = a(v5,w,a(x,y,u * z)). a(x,y,a(z,u,w * v5)) = a(v5 * w,u,a(x,y,z)). a(x * y,z,a(u,w,v5)) = a(u,w,a(v5,z,y * x)). a(x,y,a(z,u,w)) = a(z,y,a(w,u,x)). a(x,y,a(z,u,w)) = a(w,y,a(x,u,z)). a(x,y,a(z,u,w)) * a(z,y,a(w,u,x)) = 1. a(x,y,a(z,u,w * y)) = a(w * y,w,a(x,u,z)). a(x * y,x,a(z,u,w)) = a(z,y,a(w,u,x * y)). a(x,y * z,a(u,w,z)) = a(u,y,a(z,w,x)). a(x,y,a(a(x,y,z) / u,w,v5)) = a(v5,w,a(x,y,u)). a(x,y,a(z,u,w * v5)) = a(x,y,a(z,u,v5 / w)). a(x,y,a(z,u,w / v5)) = a(x,y,a(z,u,v5 * w)). a(x,y,a(z,u,w)) = a(z,u,a(x,y,w)). a(x,y,a(a(x,y,z) / (u / w),u,z)) = a(u,a(x,y,z),w). a(x,y,a(z,u,w)) = a(w,y,a(z,u,x)). a(x,y,a(z,u,w)) = a(x,y,a(w,u,z)). a(x,y,a(z,u,w)) = a(w,u,a(z,y,x)). a(x,a(y,z,u),w) * a(u,w,a(y,z,x)) = a(w,x,a(y,z,u)). a(x,y * z,a(u,w,z)) = a(x,y,a(z,w,u)). a(x,y,a(z / u,w,v5)) = a(x,y,a(v5,w,u / z)). a(x * y,z,a(u,w,v5)) = a(v5,w,a(u,z,y * x)). a(x,y,a(z,u,w / v5)) = a(v5 / w,u,a(z,y,x)). a(x / y,z,a(u,w,v5)) = a(v5,w,a(u,z,y / x)). a(x,y,a(z,u,z * (u * w))) = a(z * (w * u),w,a(z,y,x)). a(x * (y * z),y,a(x,u,w)) = a(w,u,a(x,z,x * (z * y))). a(x,y,(z \ (u \ w)) \ ((u * z) \ w)) = a(u \ (z \ w),z,a(u,y,x)). a(x,y,a(z,u,w * (u * v5))) = a(v5 * (u * w),u,a(z,y,x)). a(x * (y * z),y,a(u,w,v5)) = a(v5,w,a(u,y,z * (y * x))). a(x,a(y,z,u),w) = a(u,x,a(y,z,x / w)). a(x,y,a(z,u,y / w)) = a(y,a(z,u,x),w). a(x,a(y,z,u),w) = a(u,x,a(y,z,w * x)). a(x,y,a(z,u,w * y)) = a(y,a(z,u,x),w). a(x,a(y,z,u),w) = a(y,z,a(u,x,x / w)). a(x,y,a(z,u,u / w)) = a(u,a(x,y,z),w). a(x * y,x,a(z,u,w)) = a(y,a(w,u,z),x). a(x,y,a(z / u,u,w)) = a(u,a(x,y,w),z). a(x / y,y,a(z,u,w)) = a(y,a(w,u,z),x). a(x * (y * z),y,a(u,w,v5)) = a(x * z,a(v5,w,u),y). a(x,a(y,z,u),w) = a(y,z,a(u,x,w / x)). a(x,y,a(z,u,w / u)) = a(u,a(x,y,z),w). a(x,a(y,z,u),w * v5) = a(v5 / (x / w),x,a(u,z,y)). a(x / (y / z),y,a(u,w,v5)) = a(y,a(v5,w,u),z * x). a(x,a(y,z,u),w * v5) = a(v5 / (w * x),x,a(u,z,y)). a(x / (y * z),z,a(u,w,v5)) = a(z,a(v5,w,u),y * x). a(x,y,a(z,u,z * (u * w))) = a(z * u,a(x,y,z),w). a(x / (y * z),z,a(u,w,v5)) = a(v5,w,a(u,z,x * (z * y))). a(x,y,a(z,u,w * (u * v5))) = a(u,a(x,y,z),v5 * w). a(x,a(y,z,u),w * u) = a(u * x,a(y,z,u),w). a(x * y,a(z,u,x),w) = a(y,a(z,u,x),w * x). a(x,y,(z \ (u \ w)) \ ((u * z) \ w)) = a(u * (z * w),z,a(u,y,x)). a(x,y,(z \ (u \ w)) \ ((u * z) \ w)) = a(u * w,a(x,y,u),z). a(x,y,(z \ (u \ w)) \ ((u * z) \ w)) = a(w,a(x,y,u),z * u). a(x,a(y,z,u),w * u) = a(y,z,((u \ x) \ w) * ((u * w) \ x)). a(x,y,((z \ u) \ w) * ((z * w) \ u)) = a(u,a(x,y,z),w * z). a(x,a(y,z,u),w * u) = a(y,z,((x \ u) * w) * ((u * w) \ x)). a(x,y,((z \ u) * w) * ((u * w) \ z)) = a(z,a(x,y,u),w * u). a(x,a(y,z,u),w * u) = a(y,z,a(x,u,w)). a(x,a(y,z,u),w) = a(y,z,a(x,u,w / u)). a(x,y,a(z,u,w / u)) = a(z,a(x,y,u),w). a(x,a(y,z,u),w) = a(u,a(y,z,x),w). a(x,a(y,z,u),w) * a(u,w,a(y,z,x)) = a(w,u,a(y,z,x)). a(x,y,a(z,u,w)) = a(x,w,a(z,u,y)). a(x,y,a(z,u,w * y)) = a(x,w,a(y,u,z)). a(x,y,a(z,u,w)) = a(z,a(w,u,x),y). a(x,a(y,z,u),w) = a(u,w,a(x,z,y)). a(x,y,a(z,u,w)) * a(z,y,a(w,u,x)) = a(y,z,a(w,u,x)). a(a(x,y,z),u,w) = 1. a(a(c17,c18,c19),c20,c21) != 1. a(x,a(y,z,u),w) = 1. a(c22,a(c23,c24,c25),c26) != 1. 1 = a(x,a(y,z,u),w). end_of_list. ============================== end of input ========================== ============================== PROCESS NON-CLAUSAL FORMULAS ========== % Formulas that are not ordinary clauses: 1 x * y = u & x * z = u -> y = z # label(non_clause). [assumption]. 2 y * x = u & z * x = u -> y = z # label(non_clause). [assumption]. 3 x * y = x * z -> y = z # label(non_clause). [assumption]. 4 y * x = z * x -> y = z # label(non_clause). [assumption]. 5 a(x,y,z) = 1 -> L(z,y,x) = z # label(non_clause). [assumption]. 6 L(x,y,z) = x -> a(z,y,x) = 1 # label(non_clause). [assumption]. 7 T(x,y) = x -> T(y,x) = y # label(non_clause). [assumption]. 8 T(x,y) = x -> K(x,y) = 1 # label(non_clause). [assumption]. 9 K(x,y) = 1 -> T(x,y) = x # label(non_clause). [assumption]. 10 a(a(x,y,z),u,w) = 1 # label("aa1") # label(non_clause) # label(goal). [goal]. 11 a(x,a(y,z,u),w) = 1 # label("aa2") # label(non_clause) # label(goal). [goal]. 12 a(x,y,a(z,u,w)) = 1 # label("aa3") # label(non_clause) # label(goal). [goal]. 13 K(a(x,y,z),u) = 1 # label("Ka") # label(non_clause) # label(goal). [goal]. 14 a(K(x,y),z,u) = 1 # label("aK1") # label(non_clause) # label(goal). [goal]. 15 a(x,K(y,z),u) = 1 # label("aK2") # label(non_clause) # label(goal). [goal]. 16 a(x,y,K(z,u)) = 1 # label("aK3") # label(non_clause) # label(goal). [goal]. ============================== end of process non-clausal formulas === ============================== PROCESS INITIAL CLAUSES =============== % Clauses before input processing: formulas(usable). end_of_list. formulas(sos). 1 * x = x. [assumption]. x * 1 = x. [assumption]. x \ (x * y) = y. [assumption]. x * (x \ y) = y. [assumption]. (x * y) / y = x. [assumption]. (x / y) * y = x. [assumption]. x * y != z | x * u != z | u = y. [clausify(1)]. x * y != z | u * y != z | u = x. [clausify(2)]. x * y != x * z | y = z. [clausify(3)]. x * y != z * y | x = z. [clausify(4)]. (x * (y * z)) \ ((x * y) * z) = a(x,y,z). [assumption]. (x * y) \ (y * x) = K(y,x). [assumption]. (x * y) \ (x * (y * z)) = L(z,y,x). [assumption]. ((x * y) * z) / (y * z) = R(x,y,z). [assumption]. x \ (y * x) = T(y,x). [assumption]. a(x,y,z) != 1 | L(z,y,x) = z. [clausify(5)]. L(x,y,z) != x | a(z,y,x) = 1. [clausify(6)]. T(x,y) != x | T(y,x) = y. [clausify(7)]. T(x,y) != x | K(x,y) = 1. [clausify(8)]. K(x,y) != 1 | T(x,y) = x. [clausify(9)]. T(T(x,y),z) = T(T(x,z),y). [assumption]. T(L(x,y,z),u) = L(T(x,u),y,z). [assumption]. T(R(x,y,z),u) = R(T(x,u),y,z). [assumption]. L(R(x,y,z),u,w) = R(L(x,u,w),y,z). [assumption]. L(L(x,y,z),u,w) = L(L(x,u,w),y,z). [assumption]. R(R(x,y,z),u,w) = R(R(x,u,w),y,z). [assumption]. (x * (x * y)) * z = x * (x * (y * z)) # label("LC"). [assumption]. a(a(c1,c2,c3),c4,c5) != 1 # label("aa1"). [deny(10)]. a(c6,a(c7,c8,c9),c10) != 1 # label("aa2"). [deny(11)]. a(c11,c12,a(c13,c14,c15)) != 1 # label("aa3"). [deny(12)]. K(a(c16,c17,c18),c19) != 1 # label("Ka"). [deny(13)]. a(K(c20,c21),c22,c23) != 1 # label("aK1"). [deny(14)]. a(c24,K(c25,c26),c27) != 1 # label("aK2"). [deny(15)]. a(c28,c29,K(c30,c31)) != 1 # label("aK3"). [deny(16)]. end_of_list. formulas(demodulators). end_of_list. % 3753 hints input. ============================== PREDICATE ELIMINATION ================= No predicates eliminated. ============================== end predicate elimination =============  WARNING: denials share constants (see output). Auto_denials: % copying label "aa1" to answer in negative clause % copying label "aa2" to answer in negative clause % copying label "aa3" to answer in negative clause % copying label "Ka" to answer in negative clause % copying label "aK1" to answer in negative clause % copying label "aK2" to answer in negative clause % copying label "aK3" to answer in negative clause % assign(max_proofs, 7). % (Horn set with more than one neg. clause) WARNING, because some of the denials share constants, some of the denials or their descendents may be subsumed, preventing the target number of proofs from being found. The shared constants are: 1. Term ordering decisions: Function symbol KB weights: 1=1. c1=1. c2=1. c3=1. c4=1. c13=1. c14=1. c15=1. c16=1. c5=1. c6=1. c7=1. c8=1. c9=1. c10=1. c11=1. c12=1. c27=1. c28=1. c29=1. c30=1. c31=1. c17=1. c18=1. c19=1. c20=1. c21=1. c22=1. c23=1. c24=1. c25=1. c26=1. *=1. T=1. \=1. /=1. K=1. L=1. R=1. a=1. Predicate symbol precedence: predicate_order([ = ]). Function symbol precedence: function_order([ 1, c1, c2, c3, c4, c13, c14, c15, c16, c5, c6, c7, c8, c9, c10, c11, c12, c27, c28, c29, c30, c31, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, *, T, \, /, K, L, R, a ]). Skipping inverse_order, because term ordering is KBO. Unfolding symbols: K/2 T/2 L/3 R/3 a/3. Auto_inference settings: % set(paramodulation). % (positive equality literals) % set(hyper_resolution). % (nonunit Horn with equality) % set(hyper_resolution) -> set(pos_hyper_resolution). % set(neg_ur_resolution). % (nonunit Horn with equality) Auto_process settings: (no changes). kept: 17 1 * x = x. [assumption]. kept: 18 x * 1 = x. [assumption]. kept: 19 x \ (x * y) = y. [assumption]. kept: 20 x * (x \ y) = y. [assumption]. kept: 21 (x * y) / y = x. [assumption]. kept: 22 (x / y) * y = x. [assumption]. kept: 23 x * y != z | x * u != z | u = y. [clausify(1)]. kept: 24 x * y != z | u * y != z | u = x. [clausify(2)]. kept: 25 x * y != x * z | y = z. [clausify(3)]. kept: 26 x * y != z * y | x = z. [clausify(4)]. 27 (x * (y * z)) \ ((x * y) * z) = a(x,y,z). [assumption]. kept: 28 a(x,y,z) = (x * (y * z)) \ ((x * y) * z). [copy(27),flip(a)]. 29 (x * y) \ (y * x) = K(y,x). [assumption]. kept: 30 K(x,y) = (y * x) \ (x * y). [copy(29),flip(a)]. 31 (x * y) \ (x * (y * z)) = L(z,y,x). [assumption]. kept: 32 L(x,y,z) = (z * y) \ (z * (y * x)). [copy(31),flip(a)]. 33 ((x * y) * z) / (y * z) = R(x,y,z). [assumption]. kept: 34 R(x,y,z) = ((x * y) * z) / (y * z). [copy(33),flip(a)]. 35 x \ (y * x) = T(y,x). [assumption]. kept: 36 T(x,y) = y \ (x * y). [copy(35),flip(a)]. kept: 37 a(x,y,z) != 1 | L(z,y,x) = z. [clausify(5)]. kept: 38 L(x,y,z) != x | a(z,y,x) = 1. [clausify(6)]. kept: 39 T(x,y) != x | T(y,x) = y. [clausify(7)]. kept: 40 T(x,y) != x | K(x,y) = 1. [clausify(8)]. kept: 41 K(x,y) != 1 | T(x,y) = x. [clausify(9)]. kept: 42 T(T(x,y),z) = T(T(x,z),y). [assumption]. 43 T(L(x,y,z),u) = L(T(x,u),y,z). [assumption]. kept: 44 L(T(x,y),z,u) = T(L(x,z,u),y). [copy(43),flip(a)]. 45 T(R(x,y,z),u) = R(T(x,u),y,z). [assumption]. kept: 46 R(T(x,y),z,u) = T(R(x,z,u),y). [copy(45),flip(a)]. 47 L(R(x,y,z),u,w) = R(L(x,u,w),y,z). [assumption]. kept: 48 R(L(x,y,z),u,w) = L(R(x,u,w),y,z). [copy(47),flip(a)]. kept: 49 L(L(x,y,z),u,w) = L(L(x,u,w),y,z). [assumption]. kept: 50 R(R(x,y,z),u,w) = R(R(x,u,w),y,z). [assumption]. kept: 51 (x * (x * y)) * z = x * (x * (y * z)) # label("LC"). [assumption]. kept: 52 a(a(c1,c2,c3),c4,c5) != 1 # label("aa1") # answer("aa1"). [deny(10)]. kept: 53 a(c6,a(c7,c8,c9),c10) != 1 # label("aa2") # answer("aa2"). [deny(11)]. kept: 54 a(c11,c12,a(c13,c14,c15)) != 1 # label("aa3") # answer("aa3"). [deny(12)]. kept: 55 K(a(c16,c17,c18),c19) != 1 # label("Ka") # answer("Ka"). [deny(13)]. kept: 56 a(K(c20,c21),c22,c23) != 1 # label("aK1") # answer("aK1"). [deny(14)]. kept: 57 a(c24,K(c25,c26),c27) != 1 # label("aK2") # answer("aK2"). [deny(15)]. kept: 58 a(c28,c29,K(c30,c31)) != 1 # label("aK3") # answer("aK3"). [deny(16)]. ============================== end of process initial clauses ======== ============================== CLAUSES FOR SEARCH ==================== % Clauses after input processing: formulas(usable). 52 a(a(c1,c2,c3),c4,c5) != 1 # label("aa1") # answer("aa1"). [deny(10)]. 53 a(c6,a(c7,c8,c9),c10) != 1 # label("aa2") # answer("aa2"). [deny(11)]. 54 a(c11,c12,a(c13,c14,c15)) != 1 # label("aa3") # answer("aa3"). [deny(12)]. 55 K(a(c16,c17,c18),c19) != 1 # label("Ka") # answer("Ka"). [deny(13)]. 56 a(K(c20,c21),c22,c23) != 1 # label("aK1") # answer("aK1"). [deny(14)]. 57 a(c24,K(c25,c26),c27) != 1 # label("aK2") # answer("aK2"). [deny(15)]. 58 a(c28,c29,K(c30,c31)) != 1 # label("aK3") # answer("aK3"). [deny(16)]. end_of_list. formulas(sos). 17 1 * x = x. [assumption]. 18 x * 1 = x. [assumption]. 19 x \ (x * y) = y. [assumption]. 20 x * (x \ y) = y. [assumption]. 21 (x * y) / y = x. [assumption]. 22 (x / y) * y = x. [assumption]. 23 x * y != z | x * u != z | u = y. [clausify(1)]. 24 x * y != z | u * y != z | u = x. [clausify(2)]. 25 x * y != x * z | y = z. [clausify(3)]. 26 x * y != z * y | x = z. [clausify(4)]. 28 a(x,y,z) = (x * (y * z)) \ ((x * y) * z). [copy(27),flip(a)]. 30 K(x,y) = (y * x) \ (x * y). [copy(29),flip(a)]. 32 L(x,y,z) = (z * y) \ (z * (y * x)). [copy(31),flip(a)]. 34 R(x,y,z) = ((x * y) * z) / (y * z). [copy(33),flip(a)]. 36 T(x,y) = y \ (x * y). [copy(35),flip(a)]. 37 a(x,y,z) != 1 | L(z,y,x) = z. [clausify(5)]. 38 L(x,y,z) != x | a(z,y,x) = 1. [clausify(6)]. 39 T(x,y) != x | T(y,x) = y. [clausify(7)]. 40 T(x,y) != x | K(x,y) = 1. [clausify(8)]. 41 K(x,y) != 1 | T(x,y) = x. [clausify(9)]. 42 T(T(x,y),z) = T(T(x,z),y). [assumption]. 44 L(T(x,y),z,u) = T(L(x,z,u),y). [copy(43),flip(a)]. 46 R(T(x,y),z,u) = T(R(x,z,u),y). [copy(45),flip(a)]. 48 R(L(x,y,z),u,w) = L(R(x,u,w),y,z). [copy(47),flip(a)]. 49 L(L(x,y,z),u,w) = L(L(x,u,w),y,z). [assumption]. 50 R(R(x,y,z),u,w) = R(R(x,u,w),y,z). [assumption]. 51 (x * (x * y)) * z = x * (x * (y * z)) # label("LC"). [assumption]. end_of_list. formulas(demodulators). end_of_list. % 2827 hints (3753 processed, 926 redundant). ============================== end of clauses for search ============= ============================== SEARCH ================================ % Starting search at 0.10 seconds. given #1 (I,wt=5): 17 1 * x = x. [assumption]. given #2 (I,wt=5): 18 x * 1 = x. [assumption]. given #3 (I,wt=7): 19 x \ (x * y) = y. [assumption]. given #4 (I,wt=7): 20 x * (x \ y) = y. [assumption]. given #5 (I,wt=7): 21 (x * y) / y = x. [assumption]. given #6 (I,wt=7): 22 (x / y) * y = x. [assumption]. given #7 (I,wt=13): 23 x * y != z | x * u != z | u = y. [clausify(1)]. given #8 (I,wt=13): 24 x * y != z | u * y != z | u = x. [clausify(2)]. given #9 (I,wt=10): 25 x * y != x * z | y = z. [clausify(3)]. given #10 (I,wt=10): 26 x * y != z * y | x = z. [clausify(4)]. given #11 (I,wt=16): 28 a(x,y,z) = (x * (y * z)) \ ((x * y) * z). [copy(27),flip(a)]. given #12 (I,wt=11): 30 K(x,y) = (y * x) \ (x * y). [copy(29),flip(a)]. given #13 (I,wt=14): 32 L(x,y,z) = (z * y) \ (z * (y * x)). [copy(31),flip(a)]. given #14 (I,wt=14): 34 R(x,y,z) = ((x * y) * z) / (y * z). [copy(33),flip(a)]. given #15 (I,wt=9): 36 T(x,y) = y \ (x * y). [copy(35),flip(a)]. given #16 (I,wt=12): 37 a(x,y,z) != 1 | L(z,y,x) = z. [clausify(5)]. given #17 (I,wt=12): 38 L(x,y,z) != x | a(z,y,x) = 1. [clausify(6)]. given #18 (I,wt=10): 39 T(x,y) != x | T(y,x) = y. [clausify(7)]. given #19 (I,wt=10): 40 T(x,y) != x | K(x,y) = 1. [clausify(8)]. given #20 (I,wt=10): 41 K(x,y) != 1 | T(x,y) = x. [clausify(9)]. given #21 (I,wt=11): 42 T(T(x,y),z) = T(T(x,z),y). [assumption]. given #22 (I,wt=13): 44 L(T(x,y),z,u) = T(L(x,z,u),y). [copy(43),flip(a)]. given #23 (I,wt=13): 46 R(T(x,y),z,u) = T(R(x,z,u),y). [copy(45),flip(a)]. given #24 (I,wt=15): 48 R(L(x,y,z),u,w) = L(R(x,u,w),y,z). [copy(47),flip(a)]. given #25 (I,wt=15): 49 L(L(x,y,z),u,w) = L(L(x,u,w),y,z). [assumption]. given #26 (I,wt=15): 50 R(R(x,y,z),u,w) = R(R(x,u,w),y,z). [assumption]. given #27 (I,wt=15): 51 (x * (x * y)) * z = x * (x * (y * z)) # label("LC"). [assumption]. given #28 (H,wt=5): 59 1 \ x = x. [para(17(a,1),19(a,1,2))]. given #29 (H,wt=5): 60 x \ x = 1. [para(18(a,1),19(a,1,2))]. given #30 (H,wt=5): 64 x / 1 = x. [para(18(a,1),21(a,1,1))]. given #31 (H,wt=5): 81 T(x,x) = x. [para(36(a,2),19(a,1))]. given #32 (H,wt=7): 65 x / (y \ x) = y. [para(20(a,1),21(a,1,1))]. given #33 (H,wt=7): 66 (x / y) \ x = y. [para(22(a,1),19(a,1,2))]. given #34 (H,wt=9): 61 x \ ((x * y) * 1) = y. [para(18(a,2),19(a,1,2))]. given #35 (H,wt=9): 82 x * T(y,x) = y * x. [para(36(a,2),20(a,1,2))]. given #36 (H,wt=9): 84 T(x / y,y) = y \ x. [para(22(a,1),36(a,2,2))]. given #37 (H,wt=9): 97 ((x * y) / 1) / y = x. [hyper(24,a,22,a,b,64,a(flip)),flip(a)]. given #38 (H,wt=9): 98 T(T(x,y),x) = T(x,y). [para(81(a,1),42(a,1,1)),flip(a)]. given #39 (H,wt=7): 114 K(T(x,y),x) = 1. [hyper(40,a,98,a)]. given #40 (H,wt=7): 115 T(x,T(x,y)) = x. [hyper(39,a,98,a)]. given #41 (H,wt=9): 100 (x * y) / T(x,y) = y. [para(36(a,2),65(a,1,2))]. given #42 (H,wt=9): 102 x \ (y * 1) = x \ y. [para(20(a,1),61(a,1,2,1))]. given #43 (H,wt=9): 104 T((x * y) / x,x) = y. [hyper(23,a,22,a(flip),b,82,a)]. given #44 (H,wt=9): 105 (x * T(y,x)) / x = y. [hyper(24,a,22,a,b,82,a(flip)),flip(a)]. given #45 (H,wt=9): 119 K(x,(y * x) / y) = 1. [para(104(a,1),114(a,1,1))]. given #46 (H,wt=9): 120 T(x,(y * x) / y) = x. [hyper(41,a,119,a)]. given #47 (H,wt=11): 62 x \ (y * (y \ (x * z))) = z. [para(20(a,2),19(a,1,2))]. given #48 (H,wt=11): 69 (x * y) * K(y,x) = y * x. [para(30(a,2),20(a,1,2))]. given #49 (H,wt=11): 83 T(x,x \ y) = (x \ y) \ y. [para(20(a,1),36(a,2,2))]. given #50 (H,wt=11): 116 T(x,y) * x = x * T(x,y). [para(98(a,1),82(a,1,2)),flip(a)]. given #51 (H,wt=12): 72 x \ (1 * (x * y)) = L(y,x,1). [para(17(a,1),32(a,2,1)),flip(a)]. given #52 (H,wt=10): 123 x \ (x * y) = L(y,x,1). [para(17(a,1),72(a,1,2))]. given #53 (H,wt=6): 124 L(x,y,1) = x. [para(123(a,1),19(a,1))]. given #54 (H,wt=6): 125 a(1,x,y) = 1. [hyper(38,a,124,a)]. given #55 (H,wt=12): 73 (x * 1) \ (x * y) = L(y,1,x). [para(17(a,1),32(a,2,2,2)),flip(a)]. given #56 (H,wt=10): 126 x \ (x * y) = L(y,1,x). [para(18(a,1),73(a,1,1))]. given #57 (H,wt=6): 127 L(x,1,y) = x. [para(126(a,1),19(a,1))]. given #58 (H,wt=13): 70 x \ ((y \ x) * y) = K(y \ x,y). [para(20(a,1),30(a,2,1)),flip(a)]. given #59 (H,wt=11): 128 K(x \ 1,x) = (x \ 1) * x. [para(70(a,1),59(a,1))]. given #60 (H,wt=11): 129 K(x \ 1,x) / x = x \ 1. [hyper(24,a,22,a,b,128,a(flip)),flip(a)]. given #61 (H,wt=11): 130 (x \ 1) \ K(x \ 1,x) = x. [hyper(23,a,20,a,b,128,a(flip)),flip(a)]. given #62 (H,wt=13): 71 ((x \ y) * x) \ y = K(x,x \ y). [para(20(a,1),30(a,2,2)),flip(a)]. given #63 (H,wt=13): 88 (x * (x * 1)) * y = x * (x * y). [para(17(a,1),51(a,2,2,2))]. given #64 (H,wt=11): 131 (x * x) * y = x * (x * y). [para(18(a,1),88(a,1,1,2))]. given #65 (H,wt=11): 132 (x * (x * y)) / y = x * x. [hyper(24,a,22,a,b,131,a),flip(a)]. given #66 (H,wt=11): 133 (x * x) \ (x * (x * y)) = y. [hyper(23,a,20,a,b,131,a),flip(a)]. given #67 (H,wt=6): 137 L(x,y,y) = x. [para(133(a,1),32(a,2))]. given #68 (H,wt=13): 103 T(x * (x * y),x) = x * (y * x). [hyper(23,a,51,a(flip),b,82,a)]. given #69 (H,wt=13): 107 T(x,y) \ (x * y) = T(y,T(x,y)). [para(82(a,1),36(a,2,2)),flip(a)]. given #70 (H,wt=13): 108 x * T(T(y,x),z) = T(y,z) * x. [para(42(a,1),82(a,1,2))]. given #71 (H,wt=13): 112 T(T(x / y,z),y) = T(y \ x,z). [para(84(a,1),42(a,1,1)),flip(a)]. given #72 (H,wt=13): 113 ((x * y) / ((1 / z) * z)) / y = x. [para(22(a,2),97(a,1,1,2))]. given #73 (H,wt=13): 117 (x * y) / T(y,T(x,y)) = T(x,y). [para(82(a,1),100(a,1,1))]. given #74 (H,wt=13): 118 x \ (y * (z * (z \ 1))) = x \ y. [para(20(a,2),102(a,1,2,2))]. given #75 (H,wt=12): 142 L(x \ 1,x,y) = (y * x) \ y. [para(118(a,1),32(a,2))]. given #76 (H,wt=12): 145 x / L(y \ 1,y,x) = x * y. [para(142(a,2),65(a,1,2))]. given #77 (H,wt=13): 121 x * K(y,x / y) = y * (x / y). [para(22(a,1),69(a,1,1))]. given #78 (H,wt=13): 135 x \ (y * (y * x)) = T(y * y,x). [para(131(a,1),36(a,2,2)),flip(a)]. given #79 (H,wt=13): 138 x * ((x \ y) * x) = T(x * y,x). [para(20(a,1),103(a,1,1,2)),flip(a)]. given #80 (H,wt=13): 146 x \ T(x * y,x) = (x \ y) * x. [hyper(23,a,20,a,b,138,a),flip(a)]. given #81 (H,wt=13): 147 x * K(x \ 1,x) = T(x * 1,x). [para(128(a,2),138(a,1,2))]. given #82 (H,wt=11): 149 x * K(x \ 1,x) = T(x,x). [para(18(a,1),147(a,2,1))]. given #83 (H,wt=9): 150 x * K(x \ 1,x) = x. [para(149(a,2),81(a,1))]. given #84 (H,wt=7): 151 K(x \ 1,x) = 1. [hyper(23,a,18,a,b,150,a)]. given #85 (H,wt=7): 154 (x \ 1) * x = 1. [para(151(a,1),128(a,1)),flip(a)]. given #86 (H,wt=7): 155 1 / x = x \ 1. [para(151(a,1),129(a,1,1))]. given #87 (H,wt=7): 156 (x \ 1) \ 1 = x. [para(151(a,1),130(a,1,2))]. given #88 (H,wt=7): 157 x * (1 / x) = 1. [para(66(a,1),154(a,1,1))]. given #89 (H,wt=7): 160 T(x,x \ 1) = x. [para(156(a,1),83(a,2))]. given #90 (H,wt=9): 152 T(x \ 1,x) = x \ 1. [hyper(41,a,151,a)]. given #91 (H,wt=11): 165 T(T(x,y),x \ 1) = T(x,y). [para(160(a,1),42(a,1,1)),flip(a)]. given #92 (H,wt=9): 166 K(T(x,y),x \ 1) = 1. [hyper(40,a,165,a)]. given #93 (H,wt=11): 167 K(x \ y,(y / x) \ 1) = 1. [para(84(a,1),166(a,1,1))]. given #94 (H,wt=11): 168 K(x,((y * x) / y) \ 1) = 1. [para(104(a,1),166(a,1,1))]. given #95 (H,wt=11): 170 T(x,((y * x) / y) \ 1) = x. [hyper(41,a,168,a)]. given #96 (H,wt=13): 148 (x \ (x \ y)) * x = x \ T(y,x). [para(20(a,1),146(a,1,2,1)),flip(a)]. given #97 (H,wt=13): 169 T(x \ y,(y / x) \ 1) = x \ y. [hyper(41,a,167,a)]. given #98 (H,wt=14): 74 (x * y) * L(z,y,x) = x * (y * z). [para(32(a,2),20(a,1,2))]. given #99 (H,wt=14): 76 L(x \ y,x,z) = (z * x) \ (z * y). [para(20(a,1),32(a,2,2,2))]. given #100 (H,wt=14): 79 R(x,y,z) * (y * z) = (x * y) * z. [para(34(a,2),22(a,1,1))]. given #101 (H,wt=6): 182 R(x,x,y) = x. [hyper(24,a,131,a(flip),b,79,a)]. given #102 (H,wt=10): 186 R(T(x,y),x,z) = T(x,y). [para(182(a,1),46(a,2,1))]. given #103 (H,wt=12): 188 R(R(x,y,z),x,u) = R(x,y,z). [para(182(a,1),50(a,1,1)),flip(a)]. given #104 (H,wt=14): 80 R(x / y,y,z) = (x * z) / (y * z). [para(22(a,1),34(a,2,1,1))]. given #105 (H,wt=12): 192 R(1 / x,x,y) = y / (x * y). [para(17(a,1),80(a,2,1))]. given #106 (H,wt=14): 99 (x * (y * z)) / L(z,y,x) = x * y. [para(32(a,2),65(a,1,2))]. given #107 (H,wt=14): 101 R(x,y,z) \ ((x * y) * z) = y * z. [para(34(a,2),66(a,1,1))]. given #108 (H,wt=14): 141 R(x,1 / y,y) / y = x * (1 / y). [para(34(a,2),113(a,1,1))]. given #109 (H,wt=14): 143 L((x \ y) \ 1,x \ y,x) = y \ x. [para(20(a,1),142(a,2,1))]. given #110 (H,wt=14): 144 L(x \ 1,x,y / x) = y \ (y / x). [para(22(a,1),142(a,2,1))]. given #111 (H,wt=14): 161 L(x,x \ 1,y) = (y * (x \ 1)) \ y. [para(156(a,1),142(a,1,1))]. given #112 (H,wt=14): 162 x / L(y,y \ 1,x) = x * (y \ 1). [para(156(a,1),145(a,1,2,1))]. given #113 (H,wt=14): 177 L(x \ (y \ z),x,y) = (y * x) \ z. [para(20(a,1),76(a,2,2))]. given #114 (H,wt=11): 200 (x * x) \ y = x \ (x \ y). [para(177(a,1),137(a,1))]. given #115 (H,wt=14): 178 L(x \ (y * x),x,y) = T(y,y * x). [para(76(a,2),36(a,2)),flip(a)]. given #116 (H,wt=12): 203 L(T(x,y),y,x) = T(x,x * y). [para(36(a,2),178(a,1,1))]. given #117 (H,wt=14): 179 (x * y) / L(z \ y,z,x) = x * z. [para(76(a,2),65(a,1,2))]. given #118 (H,wt=14): 181 L(x \ (y \ ((y * x) * z)),x,y) = z. [para(76(a,2),62(a,1))]. given #119 (H,wt=14): 193 R((x / y) / z,z,y) = x / (z * y). [para(22(a,1),80(a,2,1))]. given #120 (H,wt=14): 195 R(x,x \ 1,y) = y / ((x \ 1) * y). [para(65(a,1),192(a,1,1))]. given #121 (H,wt=14): 198 R(x,y \ 1,y) / y = x * (1 / y). [para(155(a,1),141(a,1,1,2))]. given #122 (H,wt=14): 207 R(x,y \ 1,y) / y = x * (y \ 1). [para(155(a,1),198(a,2,2))]. given #123 (H,wt=14): 208 (x * (y \ 1)) * y = R(x,y \ 1,y). [para(207(a,1),22(a,1,1))]. given #124 (H,wt=14): 209 (x * (y \ 1)) \ R(x,y \ 1,y) = y. [para(207(a,1),66(a,1,1))]. given #125 (H,wt=14): 210 R(x / (y \ 1),y \ 1,y) = x * y. [para(22(a,1),208(a,1,1)),flip(a)]. given #126 (H,wt=15): 85 (x * (x * (y * z))) / z = x * (x * y). [hyper(24,a,22,a,b,51,a),flip(a)]. given #127 (H,wt=15): 86 (x * (x * y)) \ (x * (x * (y * z))) = z. [hyper(23,a,20,a,b,51,a),flip(a)]. given #128 (H,wt=15): 87 x \ ((x * (x * y)) * z) = x * (y * z). [hyper(23,a,20,a,b,51,a(flip)),flip(a)]. given #129 (H,wt=15): 89 x * (x * ((x \ y) * z)) = (x * y) * z. [para(20(a,1),51(a,1,1,2)),flip(a)]. given #130 (H,wt=15): 109 x * L(T(y,x),z,u) = L(y,z,u) * x. [para(44(a,2),82(a,1,2))]. given #131 (H,wt=13): 214 L(x,y,z) * x = x * L(x,y,z). [para(81(a,1),109(a,1,2,1)),flip(a)]. given #132 (H,wt=8): 219 T(x,L(x,y,z)) = x. [hyper(23,a,82,a,b,214,a),flip(a)]. given #133 (H,wt=13): 218 (x * L(x,y,z)) / x = L(x,y,z). [hyper(24,a,22,a,b,214,a),flip(a)]. given #134 (H,wt=14): 217 x * T(y,y * x) = L(y,x,y) * x. [para(203(a,1),109(a,1,2))]. given #135 (H,wt=15): 110 x * R(T(y,x),z,u) = R(y,z,u) * x. [para(46(a,2),82(a,1,2))]. given #136 (H,wt=13): 223 R(x,y,z) * x = x * R(x,y,z). [para(81(a,1),110(a,1,2,1)),flip(a)]. given #137 (H,wt=8): 228 T(x,R(x,y,z)) = x. [hyper(23,a,82,a,b,223,a),flip(a)]. given #138 (H,wt=15): 122 K(x,y) \ (x * y) = T(y * x,K(x,y)). [para(69(a,1),36(a,2,2)),flip(a)]. given #139 (H,wt=15): 136 x * (x * T(y,x * x)) = y * (x * x). [para(131(a,1),82(a,1))]. given #140 (H,wt=15): 139 T(x / y,z) * y = y * T(y \ x,z). [para(84(a,1),108(a,1,2,1)),flip(a)]. given #141 (H,wt=15): 140 (x * T(x \ y,z)) / x = T(y / x,z). [para(112(a,1),105(a,1,1,2))]. given #142 (H,wt=15): 187 L(R(x,L(x,y,z),u),y,z) = L(x,y,z). [para(182(a,1),48(a,1)),flip(a)]. given #143 (H,wt=15): 190 (T(x,y) * x) * z = T(x,y) * (x * z). [para(186(a,1),79(a,1,1)),flip(a)]. given #144 (H,wt=8): 234 L(x,y,T(y,z)) = x. [hyper(23,a,74,a,b,190,a),flip(a)]. given #145 (H,wt=10): 236 L(x,y / z,z \ y) = x. [para(84(a,1),234(a,1,3))]. given #146 (H,wt=10): 237 L(x,(y * z) / y,z) = x. [para(104(a,1),234(a,1,3))]. given #147 (H,wt=15): 202 x \ (x \ (y * (x * x))) = T(y,x * x). [para(200(a,1),36(a,2)),flip(a)]. given #148 (H,wt=15): 211 (x * (x * y)) / z = x * (x * (y / z)). [para(22(a,1),85(a,1,1,2,2))]. given #149 (H,wt=15): 212 (x * (x * y)) \ (x * (x * z)) = y \ z. [para(20(a,1),86(a,1,2,2,2))]. given #150 (H,wt=13): 239 (x * (x * y)) \ (x * x) = y \ 1. [para(18(a,1),212(a,1,2,2))]. given #151 (H,wt=13): 241 T(x,x * (x * y)) = y \ (x * y). [para(212(a,1),36(a,2))]. given #152 (H,wt=11): 245 T(x,x * (x * y)) = T(x,y). [para(241(a,2),36(a,2)),flip(a)]. given #153 (H,wt=11): 246 T(x,x \ y) = T(x,x * y). [para(20(a,1),245(a,1,2,2)),flip(a)]. given #154 (H,wt=11): 249 T(x,x * y) = (x \ y) \ y. [para(246(a,1),83(a,1))]. given #155 (H,wt=11): 250 (x \ y) * T(x,x * y) = y. [para(249(a,2),20(a,1,2))]. given #156 (H,wt=11): 252 x / T(y,y * x) = y \ x. [para(249(a,2),65(a,1,2))]. given #157 (H,wt=13): 242 (x * y) \ (x * x) = (x \ y) \ 1. [para(20(a,1),239(a,1,1,2))]. given #158 (H,wt=12): 259 L(x \ y,x,y) = (y \ x) \ 1. [para(242(a,1),76(a,2))]. given #159 (H,wt=13): 243 (x * x) / (y \ 1) = x * (x * y). [para(239(a,1),65(a,1,2))]. given #160 (H,wt=13): 247 T(x,x * (y * x)) = T(x,T(y,x)). [para(82(a,1),245(a,1,2,2))]. given #161 (H,wt=13): 251 T(x / y,x) = ((x / y) \ y) \ y. [para(22(a,1),249(a,1,2))]. given #162 (H,wt=13): 254 (x \ (x \ y)) * T(x,y) = x \ y. [para(20(a,1),250(a,1,2,2))]. given #163 (H,wt=13): 256 (x \ y) / T(x,y) = x \ (x \ y). [para(20(a,1),252(a,1,2,2))]. given #164 (H,wt=13): 258 (x \ (x \ y)) \ 1 = y \ (x * x). [para(20(a,1),242(a,1,1)),flip(a)]. given #165 (H,wt=13): 263 x * (x * (y \ 1)) = (x * x) / y. [para(156(a,1),243(a,1,2)),flip(a)]. given #166 (H,wt=13): 264 (x \ (y * y)) \ 1 = y \ (y \ x). [para(258(a,1),156(a,1,1))]. given #167 (H,wt=15): 213 x \ ((x * y) * z) = x * ((x \ y) * z). [para(20(a,1),87(a,1,2,1,2))]. given #168 (H,wt=14): 266 L(x \ (y * ((y \ x) * z)),x,y) = z. [para(213(a,1),181(a,1,1,2))]. given #169 (H,wt=14): 267 L(x \ (y * z),x,y) = (y \ x) \ z. [para(20(a,1),266(a,1,1,2,2))]. given #170 (H,wt=14): 268 L(x \ y,x,z) = (z \ x) \ (z \ y). [para(20(a,1),267(a,1,1,2))]. given #171 (H,wt=14): 272 (x \ y) / L(z \ y,z,x) = x \ z. [para(268(a,2),65(a,1,2))]. given #172 (H,wt=13): 276 (x \ 1) / (y \ x) = x \ (x \ y). [para(143(a,1),272(a,1,2))]. given #173 (H,wt=13): 277 x \ (x \ (x / y)) = (x \ 1) / y. [para(66(a,1),276(a,1,2)),flip(a)]. given #174 (H,wt=13): 278 x * ((x \ 1) / y) = x \ (x / y). [para(277(a,1),20(a,1,2))]. given #175 (H,wt=15): 230 x \ (y * (x * x)) = x * T(y,x * x). [hyper(23,a,20,a,b,136,a),flip(a)]. given #176 (H,wt=15): 233 (x * T(y,z)) / x = T((x * y) / x,z). [para(19(a,1),140(a,1,1,2,1))]. given #177 (H,wt=15): 235 (x * T(x,y)) * z = T(x,y) * (x * z). [para(116(a,1),190(a,1,1))]. given #178 (H,wt=15): 238 x * (x * ((x \ y) / z)) = (x * y) / z. [para(20(a,1),211(a,1,1,2)),flip(a)]. given #179 (H,wt=15): 240 (x * y) \ (x * (x * z)) = (x \ y) \ z. [para(20(a,1),212(a,1,1,2))]. given #180 (H,wt=15): 265 x * ((x \ (x \ y)) * z) = x \ (y * z). [para(20(a,1),213(a,1,2,1)),flip(a)]. given #181 (H,wt=15): 274 (x \ y) \ (x \ z) = (x * y) \ (x * z). [para(268(a,1),76(a,1))]. given #182 (H,wt=15): 279 ((x \ 1) / y) \ 1 = (x / y) \ (x * x). [para(277(a,1),258(a,1,1))]. given #183 (H,wt=15): 280 T(x * T(x,y),T(x,y)) = x * T(x,y). [hyper(23,a,82,a,b,235,a(flip)),flip(a)]. given #184 (H,wt=15): 281 (x * T(x,y)) * (x \ z) = T(x,y) * z. [para(20(a,1),235(a,2,2))]. given #185 (H,wt=15): 282 (x * y) / (z \ (x \ y)) = x * (x * z). [para(65(a,1),238(a,1,2,2)),flip(a)]. given #186 (H,wt=13): 289 x / (y \ (x \ 1)) = x * (x * y). [para(18(a,1),282(a,1,1))]. given #187 (H,wt=15): 283 (x \ (x \ y)) \ z = y \ (x * (x * z)). [para(20(a,1),240(a,1,1)),flip(a)]. given #188 (H,wt=13): 290 (x \ (x \ y)) \ y = T(x * x,y). [para(283(a,2),135(a,1))]. given #189 (H,wt=15): 285 x \ (x \ (y * z)) = (x \ (x \ y)) * z. [hyper(23,a,20,a,b,265,a),flip(a)]. given #190 (H,wt=13): 291 (x \ (x \ 1)) * y = x \ (x \ y). [para(17(a,1),285(a,1,2,2)),flip(a)]. given #191 (H,wt=15): 286 (x \ (x \ y)) * (x * x) = T(y,x * x). [hyper(23,a,230,a(flip),b,265,a)]. given #192 (H,wt=15): 288 T(x * T(x,y),T(x,y)) = T(x,y) * x. [para(280(a,2),116(a,2)),flip(a)]. given #193 (H,wt=15): 292 (x \ (x \ y)) * (y \ z) = x \ (x \ z). [para(20(a,1),285(a,1,2,2)),flip(a)]. given #194 (H,wt=15): 295 T(T(x,y) * x,T(x,y)) = T(x,y) * x. [para(116(a,2),288(a,1,1))]. given #195 (H,wt=11): 298 (T(x,y) \ x) * T(x,y) = x. [hyper(23,a,138,a,b,295,a(flip)),flip(a)]. given #196 (H,wt=11): 299 x / T(x,y) = T(x,y) \ x. [hyper(24,a,22,a,b,298,a),flip(a)]. given #197 (H,wt=15): 296 (x \ (x \ y)) \ (x \ (x \ z)) = y \ z. [hyper(23,a,20,a,b,292,a),flip(a)]. given #198 (H,wt=15): 297 (x \ y) * ((x * y) \ z) = x \ (x \ z). [para(19(a,1),292(a,1,1,2))]. given #199 (H,wt=16): 67 (x * (y * z)) * a(x,y,z) = (x * y) * z. [para(28(a,2),20(a,1,2))]. given #200 (H,wt=16): 75 x \ (y * ((y \ x) * z)) = L(z,y \ x,y). [para(20(a,1),32(a,2,1)),flip(a)]. given #201 (H,wt=11): 302 L(L(x,y \ z,y),z,y) = x. [para(75(a,1),266(a,1,1))]. given #202 (H,wt=8): 305 L(x,y \ 1,y) = x. [para(302(a,1),127(a,1)),flip(a)]. given #203 (H,wt=8): 306 L(x,y,y \ 1) = x. [para(156(a,1),305(a,1,2))]. given #204 (H,wt=11): 303 L(L(x,y,z),z * y,z) = x. [para(19(a,1),302(a,1,1,2))]. given #205 (H,wt=11): 308 L(L(x,y * z,y),z,y) = x. [para(303(a,1),49(a,1)),flip(a)]. given #206 (H,wt=13): 304 L(L(x,y,z / y),z,z / y) = x. [para(66(a,1),302(a,1,1,2))]. given #207 (H,wt=13): 312 L(x,y \ z,y) = L(x,y * z,y). [para(302(a,1),303(a,1,1)),flip(a)]. given #208 (H,wt=13): 313 L(x,y * (y * z),y) = L(x,z,y). [para(303(a,1),303(a,1,1))]. given #209 (H,wt=13): 314 L(L(x,y * z,z),T(y,z),z) = x. [para(82(a,1),308(a,1,1,2))]. given #210 (H,wt=14): 301 L(x,x \ y,x) = y \ T(x * y,x). [para(138(a,1),75(a,1,2)),flip(a)]. given #211 (H,wt=14): 316 L(x,x * y,x) = y \ T(x * y,x). [para(301(a,1),312(a,1)),flip(a)]. given #212 (H,wt=15): 307 ((x \ 1) * x) \ ((x \ 1) * y) = x \ y. [para(306(a,1),76(a,1)),flip(a)]. given #213 (H,wt=11): 317 1 \ ((x \ 1) * y) = x \ y. [para(154(a,1),307(a,1,1))]. given #214 (H,wt=9): 318 (x \ 1) * y = x \ y. [para(317(a,1),59(a,1)),flip(a)]. given #215 (H,wt=9): 320 (x \ y) / y = x \ 1. [hyper(24,a,22,a,b,318,a),flip(a)]. given #216 (H,wt=9): 321 x * ((x \ 1) * y) = y. [hyper(23,a,19,a(flip),b,318,a)]. given #217 (H,wt=9): 322 (x \ 1) * (x * y) = y. [para(318(a,2),19(a,1))]. given #218 (H,wt=9): 330 (x \ 1) \ y = x * y. [para(156(a,1),318(a,1,1)),flip(a)]. given #219 (H,wt=9): 340 x / (y * x) = y \ 1. [para(19(a,1),320(a,1,1))]. given #220 (H,wt=9): 343 (x / y) \ 1 = y / x. [para(66(a,1),320(a,1,1)),flip(a)]. given #221 (H,wt=9): 354 (x / y) * (y / x) = 1. [para(343(a,1),20(a,1,2))]. given #222 (H,wt=9): 355 K(x \ y,x / y) = 1. [para(343(a,1),167(a,1,2))]. given #223 (H,wt=9): 356 T(x,y / (y * x)) = x. [para(343(a,1),170(a,1,2))]. given #224 (H,wt=9): 361 K((x * y) \ y,x) = 1. [para(21(a,1),355(a,1,2))]. given #225 (H,wt=11): 325 T(x \ 1,y) = y \ (x \ y). [para(318(a,1),36(a,2,2))]. given #226 (H,wt=11): 327 x * T(y \ 1,x) = y \ x. [para(318(a,1),82(a,2))]. given #227 (H,wt=11): 353 (x / (y * x)) * z = y \ z. [para(340(a,2),318(a,1,1))]. given #228 (H,wt=11): 357 T(x \ y,x / y) = x \ y. [para(343(a,1),169(a,1,2))]. given #229 (H,wt=11): 358 (x / y) \ z = (y / x) * z. [para(343(a,1),318(a,1,1)),flip(a)]. given #230 (H,wt=11): 359 (x / y) * ((y / x) * z) = z. [para(343(a,1),321(a,1,2,1))]. given #231 (H,wt=11): 360 x * ((y / z) * (z / y)) = x. [para(354(a,2),18(a,1,2))]. given #232 (H,wt=11): 367 T(x / y,x \ y) = x / y. [hyper(39,a,357,a)]. given #233 (H,wt=12): 334 R(x,x \ 1,y) = y / (x \ y). [para(318(a,1),195(a,2,2))]. given #234 (H,wt=8): 373 R(x,x \ 1,y) = x. [para(334(a,2),65(a,1))]. given #235 (H,wt=12): 374 R(T(x,y),x \ 1,z) = T(x,y). [para(373(a,1),46(a,2,1))]. given #236 (H,wt=13): 326 x \ T(y,x \ 1) = y * (x \ 1). [para(318(a,1),82(a,1))]. given #237 (H,wt=13): 341 K(x,y) / (x * y) = (y * x) \ 1. [para(30(a,2),320(a,1,1))]. given #238 (H,wt=13): 346 T(x,x * y) / y = (x \ y) \ 1. [para(249(a,2),320(a,1,1))]. given #239 (H,wt=13): 347 x * (y * (x \ 1)) = T(y,x \ 1). [para(82(a,1),321(a,1,2))]. given #240 (H,wt=13): 349 T(x \ 1,x * y) = (x * y) \ y. [para(322(a,1),36(a,2,2))]. given #241 (H,wt=13): 365 T((x * y) \ y,x) = (x * y) \ y. [hyper(41,a,361,a)]. given #242 (H,wt=13): 370 T(x / y,x) = ((y / x) * y) \ y. [para(358(a,1),251(a,2,1))]. given #243 (H,wt=13): 372 T(x \ y,y \ x) = T(y / x,x). [para(367(a,1),112(a,1,1)),flip(a)]. given #244 (H,wt=11): 382 T(x \ y,y \ x) = x \ y. [para(372(a,2),84(a,1))]. given #245 (H,wt=13): 377 T(x,y) * (x \ 1) = x \ T(x,y). [para(165(a,1),326(a,1,2)),flip(a)]. given #246 (H,wt=13): 383 T(x \ (x * y),(x * y) \ x) = y. [para(372(a,2),104(a,1))]. given #247 (H,wt=9): 386 T(x,(y * x) \ y) = x. [para(19(a,1),383(a,1,1))]. given #248 (H,wt=9): 387 T(x,y \ (y / x)) = x. [para(22(a,1),386(a,1,2,1))]. given #249 (H,wt=14): 375 R(R(x,y,z),x \ 1,u) = R(x,y,z). [para(373(a,1),50(a,1,1)),flip(a)]. given #250 (H,wt=15): 328 (x \ y) * K(y,x \ 1) = y * (x \ 1). [para(318(a,1),69(a,1,1))]. given #251 (H,wt=15): 338 (x \ (x \ y)) \ z = (y \ (x * x)) * z. [para(258(a,1),318(a,1,1)),flip(a)]. given #252 (H,wt=13): 392 (x \ (y * y)) * x = T(y * y,x). [para(338(a,1),290(a,1))]. given #253 (H,wt=15): 339 (x \ (y * y)) \ z = (y \ (y \ x)) * z. [para(264(a,1),318(a,1,1)),flip(a)]. given #254 (H,wt=15): 362 (x / (x * y)) * y = y * (x / (x * y)). [para(356(a,1),82(a,1,2))]. given #255 (H,wt=15): 363 (x * (y / (y * x))) / x = y / (y * x). [para(356(a,1),100(a,1,2))]. given #256 (H,wt=15): 368 (x / y) * (x \ y) = (x \ y) * (x / y). [para(357(a,1),82(a,1,2))]. given #257 (H,wt=15): 369 (x / y) * (z * (y / x)) = T(z,y / x). [para(358(a,1),36(a,2)),flip(a)]. given #258 (H,wt=15): 371 ((x \ 1) / y) \ 1 = (y / x) * (x * x). [para(358(a,1),279(a,2))]. given #259 (H,wt=13): 397 (x / y) * (y * y) = x / (y \ 1). [para(371(a,1),343(a,1))]. given #260 (H,wt=13): 398 (x / (y \ 1)) / (y * y) = x / y. [hyper(24,a,22,a,b,397,a),flip(a)]. given #261 (H,wt=13): 399 (x / y) * (y / (x \ 1)) = x * x. [hyper(23,a,359,a,b,397,a),flip(a)]. given #262 (H,wt=13): 400 (x * y) / (y \ 1) = x * (y * y). [para(21(a,1),397(a,1,1)),flip(a)]. given #263 (H,wt=13): 401 (x * (y \ 1)) / y = x / (y * y). [para(21(a,1),398(a,1,1)),flip(a)]. given #264 (H,wt=15): 381 ((x * y) \ y) * x = x * ((x * y) \ y). [para(365(a,1),82(a,1,2)),flip(a)]. given #265 (H,wt=15): 384 (x \ y) * (y \ x) = (y \ x) * (x \ y). [para(382(a,1),82(a,1,2))]. given #266 (H,wt=15): 388 ((x * y) \ x) * y = y * ((x * y) \ x). [para(386(a,1),82(a,1,2))]. given #267 (H,wt=15): 389 T(K(x,y),(x * y) \ (y * x)) = K(x,y). [para(69(a,1),386(a,1,2,1))]. given #268 (H,wt=11): 404 T(K(x,y),K(y,x)) = K(x,y). [para(30(a,2),389(a,1,2))]. given #269 (H,wt=15): 390 R(x,y,z) * (x \ 1) = R(x,y,z) / x. [para(375(a,1),207(a,1,1)),flip(a)]. given #270 (H,wt=15): 391 x \ (y * (y * z)) = (x \ (y * y)) * z. [para(338(a,1),283(a,1)),flip(a)]. given #271 (H,wt=15): 393 (x \ (y * y)) * (y \ (y \ z)) = x \ z. [para(338(a,1),296(a,1))]. given #272 (H,wt=15): 403 T(x / (y * y),y) = y \ (x * (y \ 1)). [para(401(a,1),84(a,1,1))]. given #273 (H,wt=15): 407 x * ((x \ (y * y)) * z) = y * (y * z). [para(391(a,1),20(a,1,2))]. given #274 (H,wt=15): 409 (x * (y * y)) \ z = y \ (y \ (x \ z)). [hyper(23,a,297,a,b,393,a),flip(a)]. given #275 (H,wt=13): 413 (x * (y * y)) \ x = y \ (y \ 1). [para(60(a,1),409(a,2,2,2))]. given #276 (H,wt=13): 414 x \ (x / (y * y)) = y \ (y \ 1). [para(22(a,1),413(a,1,1))]. given #277 (H,wt=13): 415 x / (y \ (y \ 1)) = x * (y * y). [para(413(a,1),65(a,1,2))]. given #278 (H,wt=13): 416 x * (y \ (y \ 1)) = x / (y * y). [para(414(a,1),20(a,1,2))]. given #279 (H,wt=15): 410 x * ((x \ (y * y)) * z) = (y * y) * z. [para(407(a,2),131(a,2)),flip(a)]. given #280 (H,wt=15): 411 (x * (y * y)) * z = x * (y * (y * z)). [para(407(a,1),89(a,1,2)),flip(a)]. given #281 (H,wt=15): 417 (x * (y * y)) * z = x * ((y * y) * z). [para(410(a,1),89(a,1,2)),flip(a)]. given #282 (H,wt=8): 421 L(x,y * y,z) = x. [hyper(23,a,74,a,b,417,a),flip(a)]. given #283 (H,wt=8): 422 R(x,y * y,z) = x. [hyper(24,a,79,a,b,417,a(flip)),flip(a)]. given #284 (H,wt=10): 424 L(x,y,y / (z * z)) = x. [para(421(a,1),304(a,1,1))]. given #285 (H,wt=10): 425 L(x,y \ (y \ 1),z) = x. [para(318(a,1),421(a,1,2))]. given #286 (H,wt=10): 426 R(x,y \ (y \ 1),z) = x. [para(318(a,1),422(a,1,2))]. given #287 (H,wt=12): 427 L(x,y,y / (z \ (z \ 1))) = x. [para(318(a,1),424(a,1,3,2))]. given #288 (H,wt=10): 429 L(x,y,y * (z * z)) = x. [para(415(a,1),427(a,1,3))]. given #289 (H,wt=13): 423 T(x,x * (y * y)) = T(x,y * y). [para(421(a,1),203(a,1)),flip(a)]. given #290 (H,wt=13): 430 T(x,x \ (y * y)) = T(x,y * y). [para(423(a,1),246(a,2))]. given #291 (H,wt=15): 418 (x * (y * (y * z))) / z = x * (y * y). [hyper(24,a,22,a,b,411,a),flip(a)]. given #292 (H,wt=16): 77 x \ ((x / y) * (y * z)) = L(z,y,x / y). [para(22(a,1),32(a,2,1)),flip(a)]. given #293 (H,wt=14): 432 L(x,x,y / x) = y \ (y / (x \ 1)). [para(397(a,1),77(a,1,2)),flip(a)]. given #294 (H,wt=16): 78 ((x * y) * (y \ z)) / z = R(x,y,y \ z). [para(20(a,1),34(a,2,2)),flip(a)]. given #295 (H,wt=14): 433 (x * y) * (y \ 1) = R(x,y,y \ 1). [para(78(a,1),64(a,1)),flip(a)]. given #296 (H,wt=14): 434 R(x / y,y,y \ 1) = x * (y \ 1). [para(22(a,1),433(a,1,1)),flip(a)]. given #297 (H,wt=16): 106 (x * y) \ (x * (z * y)) = L(T(z,y),y,x). [para(82(a,1),32(a,2,2,2)),flip(a)]. given #298 (H,wt=16): 172 x * L(y,z \ x,z) = z * ((z \ x) * y). [para(20(a,1),74(a,1,1))]. given #299 (H,wt=16): 173 x * L(y,z,x / z) = (x / z) * (z * y). [para(22(a,1),74(a,1,1))]. given #300 (H,wt=16): 180 L(x \ T(y,z),x,z) = (z * x) \ (y * z). [para(82(a,1),76(a,2,2))]. given #301 (H,wt=16): 189 R(R(T(x,y),z,u),x,w) = R(T(x,y),z,u). [para(186(a,1),50(a,1,1)),flip(a)]. given #302 (H,wt=16): 196 (x * y) / L(z,y / z,x) = x * (y / z). [para(22(a,1),99(a,1,1,2))]. given #303 (H,wt=16): 197 R(x,x \ y,z) \ (y * z) = (x \ y) * z. [para(20(a,1),101(a,1,2,1))]. given #304 (H,wt=16): 205 x / L(y \ z,y,x / z) = (x / z) * y. [para(22(a,1),179(a,1,1))]. given #305 (H,wt=16): 220 T(x,x * L(x,y,z)) = L(x,L(x,y,z),x). [para(219(a,1),203(a,1,1)),flip(a)]. given #306 (H,wt=16): 229 T(x \ y,R(y / x,z,u)) = T(y / x,x). [para(228(a,1),112(a,1,1)),flip(a)]. given #307 (H,wt=14): 437 T(x \ y,R(y / x,z,u)) = x \ y. [para(229(a,2),84(a,1))]. given #308 (H,wt=15): 438 T((x \ 1) \ y,y * x) = (x \ 1) \ y. [para(210(a,1),437(a,1,2))]. given #309 (H,wt=13): 439 T(x * y,y * x) = (x \ 1) \ y. [para(330(a,1),438(a,1,1))]. given #310 (H,wt=16): 261 L(T(x \ y,z),x,y) = T((y \ x) \ 1,z). [para(259(a,1),44(a,2,1))]. given #311 (H,wt=16): 269 L(x \ (y * z),x,z) = (z \ x) \ T(y,z). [para(82(a,1),267(a,1,1,2))]. given #312 (H,wt=12): 440 (x \ y) \ T(y,x) = L(x,y,x). [para(19(a,1),269(a,1,1)),flip(a)]. given #313 (H,wt=12): 441 T(x,y) / L(y,x,y) = y \ x. [para(440(a,1),65(a,1,2))]. given #314 (H,wt=16): 270 L((x * y) \ z,x * y,x) = y \ (x \ z). [para(19(a,1),268(a,2,1))]. given #315 (H,wt=15): 443 (x * (x * y)) \ z = y \ (x \ (x \ z)). [para(270(a,1),177(a,1)),flip(a)]. given #316 (H,wt=16): 273 L(x \ y,x,x / z) = z \ ((x / z) \ y). [para(66(a,1),268(a,2,1))]. given #317 (H,wt=14): 445 L(x \ 1,x,x / y) = y \ (y / x). [para(343(a,1),273(a,2,2))]. given #318 (H,wt=16): 309 x \ (y \ ((y * x) * z)) = L(z,y * x,y). [para(181(a,1),303(a,1,1)),flip(a)]. given #319 (H,wt=16): 311 L((x \ y) \ z,x * y,x) = y \ (x * z). [para(267(a,1),303(a,1,1))]. given #320 (H,wt=16): 335 R(x \ 1,y \ 1,y) = (x \ (y \ 1)) * y. [para(318(a,1),208(a,1,1)),flip(a)]. given #321 (H,wt=16): 342 L(x,y,z) / (z * (y * x)) = (z * y) \ 1. [para(32(a,2),320(a,1,1))]. given #322 (H,wt=16): 344 (x * y) / ((z * x) * y) = R(z,x,y) \ 1. [para(101(a,1),320(a,1,1))]. given #323 (H,wt=16): 351 L(x * y,x \ 1,y) = (y \ (x \ 1)) \ 1. [para(330(a,1),259(a,1,1))]. given #324 (H,wt=16): 376 R(T(x / y,y),(x / y) \ 1,z) = y \ x. [para(374(a,2),84(a,1))]. given #325 (H,wt=14): 447 R(x \ y,(y / x) \ 1,z) = x \ y. [para(84(a,1),376(a,1,1))]. given #326 (H,wt=12): 448 R(x \ y,x / y,z) = x \ y. [para(343(a,1),447(a,1,2))]. given #327 (H,wt=14): 449 R(x \ (x * y),x / (x * y),z) = y. [para(448(a,2),19(a,1))]. given #328 (H,wt=10): 450 R(x,y / (y * x),z) = x. [para(19(a,1),449(a,1,1))]. given #329 (H,wt=16): 412 x \ (x \ (y \ ((y * x) * x))) = a(y,x,x). [para(409(a,1),28(a,2)),flip(a)]. given #330 (H,wt=13): 452 x \ L(x,y * x,y) = a(y,x,x). [para(309(a,1),412(a,1,2))]. given #331 (H,wt=13): 453 L(x,y * x,y) = x * a(y,x,x). [para(452(a,1),20(a,1,2)),flip(a)]. given #332 (H,wt=11): 454 L(x * a(y,x,x),x,y) = x. [para(453(a,1),308(a,1,1))]. given #333 (H,wt=16): 435 x * L(y,z * x,z) = z * ((z \ x) * y). [para(312(a,1),172(a,1,2))]. given #334 (H,wt=17): 171 (x \ y) \ (x \ T(y,x)) = K(x \ (x \ y),x). [para(148(a,1),70(a,1,2))]. given #335 (H,wt=17): 191 (R(x,y,z) * x) * u = R(x,y,z) * (x * u). [para(188(a,1),79(a,1,1)),flip(a)]. given #336 (H,wt=9): 457 L(x,y,R(y,z,u)) = x. [hyper(23,a,74,a,b,191,a),flip(a)]. given #337 (H,wt=15): 460 (R(x,y,z) \ x) \ 1 = x \ R(x,y,z). [para(457(a,1),259(a,1)),flip(a)]. given #338 (H,wt=15): 462 (x \ R(x,y,z)) \ 1 = R(x,y,z) \ x. [para(460(a,1),156(a,1,1))]. given #339 (H,wt=17): 215 L(x / y,z,u) * y = y * L(y \ x,z,u). [para(84(a,1),109(a,1,2,1)),flip(a)]. given #340 (H,wt=17): 216 L(x \ 1,y,z) * x = x * L(x \ 1,y,z). [para(152(a,1),109(a,1,2,1)),flip(a)]. given #341 (H,wt=10): 466 T(x,L(x \ 1,y,z)) = x. [hyper(23,a,82,a,b,216,a),flip(a)]. given #342 (H,wt=10): 467 K(x,L(x \ 1,y,z)) = 1. [hyper(40,a,466,a)]. given #343 (H,wt=10): 468 K(x \ 1,L(x,y,z)) = 1. [para(156(a,1),467(a,1,2,1))]. given #344 (H,wt=10): 469 K(L(x,y,z) \ 1,x) = 1. [para(303(a,1),468(a,1,2))]. given #345 (H,wt=15): 470 T(L(x,y,z) \ 1,x) = L(x,y,z) \ 1. [hyper(41,a,469,a)]. given #346 (H,wt=15): 471 x * (L(x,y,z) \ 1) = L(x,y,z) \ x. [para(470(a,1),327(a,1,2))]. given #347 (H,wt=17): 224 R(x / y,z,u) * y = y * R(y \ x,z,u). [para(84(a,1),110(a,1,2,1)),flip(a)]. given #348 (H,wt=17): 227 R(x \ 1,y,z) * x = x * R(x \ 1,y,z). [para(152(a,1),110(a,1,2,1)),flip(a)]. given #349 (H,wt=10): 475 T(x,R(x \ 1,y,z)) = x. [hyper(23,a,82,a,b,227,a),flip(a)]. given #350 (H,wt=12): 476 T(x \ 1,R(x,y,z)) = x \ 1. [para(156(a,1),475(a,1,2,1))]. given #351 (H,wt=15): 477 R(x,y,z) * (x \ 1) = x \ R(x,y,z). [para(476(a,1),327(a,1,2))]. given #352 (H,wt=13): 478 R(x,y,z) / x = x \ R(x,y,z). [para(477(a,1),390(a,1)),flip(a)]. given #353 (H,wt=13): 479 (x \ R(x,y,z)) * x = R(x,y,z). [para(478(a,1),22(a,1,1))]. given #354 (H,wt=13): 480 (x \ R(x,y,z)) \ R(x,y,z) = x. [para(478(a,1),66(a,1,1))]. given #355 (H,wt=17): 244 ((x * y) * z) \ (x * x) = ((x \ y) * z) \ 1. [para(89(a,1),239(a,1,1))]. given #356 (H,wt=17): 262 (x \ ((y * x) / y)) \ 1 = ((y * x) / y) \ x. [para(259(a,1),237(a,1))]. given #357 (H,wt=17): 287 (x * (y * x)) \ (x * z) = T(y,x) \ (x \ z). [para(36(a,2),274(a,1,1)),flip(a)]. given #358 (H,wt=17): 294 ((x \ 1) / y) * (x * x) = T(x / y,x * x). [para(277(a,1),286(a,1,1))]. given #359 (H,wt=17): 310 R(x,L(x,y,z),u) = L(L(x,y,z),z * y,z). [para(187(a,1),303(a,1,1)),flip(a)]. given #360 (H,wt=9): 483 R(x,L(x,y,z),u) = x. [para(310(a,2),303(a,1))]. given #361 (H,wt=17): 315 L(L(x,y * z,z * y),K(y,z),z * y) = x. [para(69(a,1),308(a,1,1,2))]. given #362 (H,wt=17): 329 x \ T(T(y,x \ 1),z) = T(y,z) * (x \ 1). [para(318(a,1),108(a,1))]. given #363 (H,wt=17): 337 T(x \ 1,(x \ 1) \ y) = T(x \ 1,x \ y). [para(318(a,1),246(a,2,2))]. given #364 (H,wt=15): 485 T(x \ 1,x \ y) = T(x \ 1,x * y). [para(330(a,1),337(a,1,2)),flip(a)]. given #365 (H,wt=17): 345 T(x * y,K(y,x)) / (y * x) = K(y,x) \ 1. [para(122(a,1),320(a,1,1))]. given #366 (H,wt=17): 402 ((x \ (x \ y)) * x) / (x \ 1) = T(y,x * x). [para(400(a,2),286(a,1))]. given #367 (H,wt=15): 486 (x \ T(y,x)) / (x \ 1) = T(y,x * x). [para(148(a,1),402(a,1,1))]. given #368 (H,wt=17): 408 (((x * y) * x) \ (x * x)) * y = K(x,x * y). [para(391(a,1),30(a,2)),flip(a)]. given #369 (H,wt=15): 487 (((x \ y) * x) \ 1) * y = K(x,x * y). [para(244(a,1),408(a,1,1))]. given #370 (H,wt=13): 488 ((x \ y) * x) \ y = K(x,x * y). [para(487(a,1),318(a,1)),flip(a)]. given #371 (H,wt=11): 489 K(x,x \ y) = K(x,x * y). [para(488(a,1),71(a,1)),flip(a)]. given #372 (H,wt=11): 490 K(x,x * (x * y)) = K(x,y). [para(19(a,1),489(a,1,2)),flip(a)]. given #373 (H,wt=13): 491 K(x,x * (y * x)) = K(x,T(y,x)). [para(36(a,2),489(a,1,2)),flip(a)]. given #374 (H,wt=13): 492 K(x,(x * x) / y) = K(x,y \ 1). [para(263(a,1),490(a,1,2))]. given #375 (H,wt=17): 431 T(x \ 1,x * (y * y)) = T(x \ 1,y * y). [para(330(a,1),430(a,1,2))]. given #376 (H,wt=17): 456 (x * y) \ (x * T(y,x)) = K(x \ (x \ y),x). [para(171(a,1),274(a,1)),flip(a)]. given #377 (H,wt=15): 493 K(x \ (x \ y),x) = (x * y) \ (y * x). [para(82(a,1),456(a,1,2)),flip(a)]. given #378 (H,wt=11): 494 K(x \ (x \ y),x) = K(y,x). [para(493(a,2),30(a,2)),flip(a)]. given #379 (H,wt=11): 495 K(x \ y,x) = K(x * y,x). [para(19(a,1),494(a,1,1,2))]. given #380 (H,wt=17): 458 R(x,y,z) * ((R(x,y,z) \ x) * u) = x * u. [hyper(23,a,89,a,b,191,a(flip)),flip(a)]. given #381 (H,wt=13): 496 (R(x,y,z) \ x) * R(x,y,z) = x. [hyper(23,a,223,a,b,458,a)]. given #382 (H,wt=13): 498 x / R(x,y,z) = R(x,y,z) \ x. [hyper(24,a,22,a,b,496,a),flip(a)]. given #383 (H,wt=17): 459 (x * R(x,y,z)) * u = R(x,y,z) * (x * u). [para(223(a,1),191(a,1,1))]. given #384 (H,wt=17): 461 (R(x,y,z) \ u) / (x \ u) = R(x,y,z) \ x. [para(457(a,1),272(a,1,2))]. given #385 (H,wt=17): 463 (R(x,y,z) \ x) \ u = (x \ R(x,y,z)) * u. [para(460(a,1),318(a,1,1)),flip(a)]. given #386 (H,wt=17): 464 (R(x,y,z) \ x) * ((x \ R(x,y,z)) * u) = u. [para(460(a,1),321(a,1,2,1))]. given #387 (H,wt=17): 465 (x \ R(x,y,z)) \ u = (R(x,y,z) \ x) * u. [para(460(a,1),330(a,1,1))]. given #388 (H,wt=17): 482 (x \ ((y * x) / y)) \ 1 = (y / (y * x)) * x. [para(262(a,2),358(a,1))]. given #389 (H,wt=17): 484 (x * L(x,y,z)) * u = x * (L(x,y,z) * u). [para(483(a,1),79(a,1,1)),flip(a)]. given #390 (H,wt=9): 503 L(x,L(y,z,u),y) = x. [hyper(23,a,74,a,b,484,a),flip(a)]. given #391 (H,wt=9): 509 L(x,y,L(y,z,u)) = x. [para(303(a,1),503(a,1,2))]. given #392 (H,wt=10): 510 T(x,x * L(x,y,z)) = x. [para(503(a,1),220(a,2))]. given #393 (H,wt=12): 505 L(x,(y * z) \ y,z \ 1) = x. [para(142(a,1),503(a,1,2))]. given #394 (H,wt=13): 514 (x \ L(x,y,z)) * x = L(x,y,z). [para(510(a,1),250(a,1,2))]. given #395 (H,wt=13): 515 L(x,y,z) / x = x \ L(x,y,z). [para(510(a,1),252(a,1,2))]. given #396 (H,wt=14): 508 L(x,(y \ z) \ u,z \ (y * u)) = x. [para(267(a,1),503(a,1,2))]. given #397 (H,wt=15): 506 (x \ L(x,y,z)) \ 1 = L(x,y,z) \ x. [para(503(a,1),259(a,1)),flip(a)]. given #398 (H,wt=15): 511 (L(x,y,z) \ x) \ 1 = x \ L(x,y,z). [para(509(a,1),259(a,1)),flip(a)]. given #399 (H,wt=15): 516 (x \ L(x,y,z)) \ 1 = x / L(x,y,z). [para(510(a,1),346(a,1,1)),flip(a)]. given #400 (H,wt=13): 519 x / L(x,y,z) = L(x,y,z) \ x. [para(516(a,1),506(a,1))]. given #401 (H,wt=13): 520 (L(x,y,z) \ x) * L(x,y,z) = x. [para(519(a,1),22(a,1,1))]. given #402 (H,wt=17): 497 R(x,y,z) \ (x * u) = (R(x,y,z) \ x) * u. [hyper(23,a,20,a,b,458,a),flip(a)]. given #403 (H,wt=17): 499 T(R(x,y,z) \ 1,x) = x \ (x / R(x,y,z)). [para(498(a,2),325(a,2,2))]. given #404 (H,wt=17): 501 x * ((x \ R(x,y,z)) * u) = R(x,y,z) * u. [para(464(a,1),458(a,1,2)),flip(a)]. given #405 (H,wt=17): 502 (x \ ((y * x) / y)) \ 1 = x * (y / (y * x)). [para(482(a,2),362(a,1))]. given #406 (H,wt=17): 504 x * ((x \ L(x,y,z)) * u) = L(x,y,z) * u. [hyper(23,a,89,a,b,484,a(flip)),flip(a)]. given #407 (H,wt=17): 507 (x \ L(x,y,z)) \ u = L(x,y,z) \ (x * u). [para(503(a,1),267(a,1)),flip(a)]. given #408 (H,wt=17): 512 (L(x,y,z) \ x) \ u = x \ (L(x,y,z) * u). [para(509(a,1),267(a,1)),flip(a)]. given #409 (H,wt=17): 513 (L(x,y,z) \ u) / (x \ u) = L(x,y,z) \ x. [para(509(a,1),272(a,1,2))]. given #410 (H,wt=17): 517 (x \ L(x,y,z)) \ u = (L(x,y,z) \ x) * u. [para(506(a,1),318(a,1,1)),flip(a)]. given #411 (H,wt=17): 518 (L(x,y,z) \ x) \ u = (x \ L(x,y,z)) * u. [para(506(a,1),330(a,1,1))]. given #412 (H,wt=17): 522 (x \ R(x,y,z)) \ u = R(x,y,z) \ (x * u). [para(497(a,2),465(a,2))]. given #413 (H,wt=17): 523 (x * R(x,y,z)) * u = x * (R(x,y,z) * u). [para(501(a,1),89(a,1,2)),flip(a)]. given #414 (H,wt=9): 525 R(x,R(x,y,z),u) = x. [hyper(24,a,79,a,b,523,a(flip)),flip(a)]. given #415 (H,wt=13): 527 R(T(x,y),R(x,z,u),w) = T(x,y). [para(525(a,1),46(a,2,1))]. given #416 (H,wt=17): 524 L(x,y,z) \ (x * u) = (L(x,y,z) \ x) * u. [para(517(a,1),507(a,1)),flip(a)]. given #417 (H,wt=17): 526 R(x,y,z) * (x * u) = x * (R(x,y,z) * u). [para(523(a,1),459(a,1)),flip(a)]. given #418 (H,wt=17): 528 (x \ R(x,y,z)) * (x * u) = R(x,y,z) * u. [hyper(23,a,501,a,b,526,a(flip)),flip(a)]. given #419 (H,wt=17): 529 x * (R(x,y,z) * (x \ u)) = R(x,y,z) * u. [para(20(a,1),526(a,1,2)),flip(a)]. given #420 (H,wt=17): 531 (R(x,y,z) * u) / (x * u) = x \ R(x,y,z). [hyper(24,a,22,a,b,528,a),flip(a)]. given #421 (H,wt=17): 532 (x \ R(x,y,z)) * u = R(x,y,z) * (x \ u). [para(20(a,1),528(a,1,2))]. given #422 (H,wt=17): 534 x \ (R(x,y,z) * u) = R(x,y,z) * (x \ u). [hyper(23,a,20,a,b,529,a),flip(a)]. given #423 (H,wt=17): 535 x / (y * (R(y,z,u) \ x)) = y \ R(y,z,u). [para(20(a,1),531(a,1,1))]. given #424 (H,wt=17): 536 (R(x,y,z) * (x \ u)) / u = x \ R(x,y,z). [para(20(a,1),531(a,1,2))]. given #425 (H,wt=17): 540 (R(x,y,z) \ x) \ u = R(x,y,z) * (x \ u). [para(532(a,1),463(a,2))]. given #426 (H,wt=17): 541 (x \ R(x,y,z)) \ u = x * (R(x,y,z) \ u). [para(535(a,1),66(a,1,1))]. given #427 (H,wt=15): 543 x * (R(x,y,z) \ 1) = R(x,y,z) \ x. [para(541(a,1),462(a,1))]. given #428 (H,wt=15): 545 T(R(x,y,z) \ 1,x) = R(x,y,z) \ 1. [hyper(23,a,327,a,b,543,a),flip(a)]. given #429 (H,wt=10): 546 T(x,R(x,y,z) \ 1) = x. [hyper(39,a,545,a)]. given #430 (H,wt=15): 547 x \ (x / R(x,y,z)) = R(x,y,z) \ 1. [para(545(a,1),499(a,1)),flip(a)]. given #431 (H,wt=17): 542 x / (R(y,z,u) * (y \ x)) = R(y,z,u) \ y. [para(540(a,1),65(a,1,2))]. given #432 (H,wt=17): 544 (R(x,y,z) \ x) * u = x * (R(x,y,z) \ u). [para(541(a,1),465(a,1)),flip(a)]. given #433 (H,wt=18): 68 ((x / y) * (y * z)) \ (x * z) = a(x / y,y,z). [para(22(a,1),28(a,2,2,1)),flip(a)]. given #434 (H,wt=18): 111 (x * y) \ ((z * x) * y) = T(R(z,x,y),x * y). [para(34(a,2),84(a,1,1)),flip(a)]. given #435 (H,wt=18): 134 ((x * (x * y)) * z) / (y * z) = R(x * x,y,z). [para(131(a,1),34(a,2,1,1)),flip(a)]. given #436 (H,wt=18): 164 (x * 1) \ ((x * y) * (1 / y)) = a(x,y,1 / y). [para(157(a,1),28(a,2,1,2)),flip(a)]. given #437 (H,wt=16): 551 x \ ((x * y) * (1 / y)) = a(x,y,1 / y). [para(18(a,1),164(a,1,1))]. given #438 (H,wt=16): 552 x \ ((x * y) * (y \ 1)) = a(x,y,1 / y). [para(155(a,1),551(a,1,2,2))]. given #439 (H,wt=16): 553 x \ ((x * y) * (y \ 1)) = a(x,y,y \ 1). [para(155(a,1),552(a,2,3))]. given #440 (H,wt=18): 194 T((x * y) / (z * y),u) = R(T(x / z,u),z,y). [para(80(a,1),46(a,2,1)),flip(a)]. given #441 (H,wt=16): 555 T((x * y) / (z * y),z) = R(z \ x,z,y). [para(84(a,1),194(a,2,1))]. given #442 (H,wt=18): 204 T(x,x * ((y * x) / y)) = L(x,(y * x) / y,x). [para(120(a,1),203(a,1,1)),flip(a)]. given #443 (H,wt=11): 557 T(x,x * ((y * x) / y)) = x. [para(204(a,2),237(a,1))]. given #444 (H,wt=15): 558 ((x * y) / x) / y = y \ ((x * y) / x). [para(557(a,1),252(a,1,2))]. given #445 (H,wt=18): 206 R(x,x \ (y / z),z) = y / ((x \ (y / z)) * z). [para(65(a,1),193(a,1,1))]. given #446 (H,wt=18): 221 L(x,x \ y,x) * (x \ y) = (x \ y) * T(x,y). [para(20(a,1),217(a,1,2,2)),flip(a)]. given #447 (H,wt=18): 324 ((x * (y \ 1)) * z) / (y \ z) = R(x,y \ 1,z). [para(318(a,1),34(a,2,2)),flip(a)]. given #448 (H,wt=18): 331 (x \ y) * L(z,y,x \ 1) = (x \ 1) * (y * z). [para(318(a,1),74(a,1,1))]. given #449 (H,wt=16): 560 (x \ y) * L(z,y,x \ 1) = x \ (y * z). [para(331(a,2),318(a,1))]. given #450 (H,wt=18): 332 R(x,y \ 1,z) * (y \ z) = (x * (y \ 1)) * z. [para(318(a,1),79(a,1,2))]. given #451 (H,wt=17): 561 (T(x,y) * (x \ 1)) * z = T(x,y) * (x \ z). [para(374(a,1),332(a,1,1)),flip(a)]. given #452 (H,wt=15): 562 (x \ T(x,y)) * z = T(x,y) * (x \ z). [para(377(a,1),561(a,1,1))]. given #453 (H,wt=15): 563 (T(x,y) * (x \ z)) / z = x \ T(x,y). [hyper(24,a,22,a,b,562,a),flip(a)]. given #454 (H,wt=15): 565 (T(x,y) * z) / (x * z) = x \ T(x,y). [para(19(a,1),563(a,1,1,2))]. given #455 (H,wt=15): 566 (x \ T(x,y)) \ (T(x,y) * z) = x * z. [para(565(a,1),66(a,1,1))]. given #456 (H,wt=15): 567 (x \ T(x,y)) \ z = x * (T(x,y) \ z). [para(20(a,1),566(a,1,2))]. given #457 (H,wt=17): 564 x * (T(x,y) * (x \ x)) = T(x * T(x,y),x). [para(562(a,1),138(a,1,2))]. given #458 (H,wt=15): 568 T(x * T(x,y),x) = x * (T(x,y) * 1). [para(60(a,1),564(a,1,2,2)),flip(a)]. given #459 (H,wt=13): 569 T(x * T(x,y),x) = x * T(x,y). [para(18(a,1),568(a,2,2))]. given #460 (H,wt=9): 571 T(x,x * T(x,y)) = x. [hyper(39,a,569,a)]. given #461 (H,wt=11): 572 T(x,y) / x = x \ T(x,y). [para(571(a,1),252(a,1,2))]. given #462 (H,wt=15): 573 (x \ T(x,y)) \ z = (x / T(x,y)) * z. [para(572(a,1),358(a,1,1))]. given #463 (H,wt=15): 574 (x \ T(x,y)) \ z = (T(x,y) \ x) * z. [para(299(a,1),573(a,2,1))]. given #464 (H,wt=15): 575 (T(x,y) \ x) * (T(x,y) * z) = x * z. [para(574(a,1),566(a,1))]. given #465 (H,wt=15): 576 (T(x,y) \ x) * z = x * (T(x,y) \ z). [para(574(a,1),567(a,1))]. given #466 (H,wt=9): 579 K(x,T(x,y) \ 1) = 1. [hyper(23,a,328,a,b,576,a),flip(a)]. given #467 (H,wt=9): 580 T(x,T(x,y) \ 1) = x. [hyper(41,a,579,a)]. given #468 (H,wt=13): 578 x * (T(x,y) \ 1) = T(x,y) \ x. [hyper(24,a,18,a,b,576,a),flip(a)]. given #469 (H,wt=13): 582 x \ (T(x,y) \ x) = T(x,y) \ 1. [hyper(23,a,20,a,b,578,a),flip(a)]. given #470 (H,wt=15): 577 (x * y) / (T(x,z) * y) = T(x,z) \ x. [hyper(24,a,22,a,b,575,a),flip(a)]. given #471 (H,wt=17): 581 T(x,y) * (T(x,z) \ 1) = T(x,z) \ T(x,y). [para(580(a,1),329(a,1,2,1)),flip(a)]. given #472 (H,wt=18): 333 (x * (y \ z)) / L(z,y \ 1,x) = x * (y \ 1). [para(318(a,1),99(a,1,1,2))]. given #473 (H,wt=18): 348 R(x \ 1,x * y,z) = (y * z) / ((x * y) * z). [para(322(a,1),34(a,2,1,1))]. given #474 (H,wt=15): 584 R(x \ 1,x * y,z) = R(x,y,z) \ 1. [para(348(a,2),344(a,1))]. given #475 (H,wt=15): 585 R(x,x \ y,z) \ 1 = R(x \ 1,y,z). [para(20(a,1),584(a,1,2)),flip(a)]. given #476 (H,wt=18): 350 R((x \ 1) / y,y,x * z) = z / (y * (x * z)). [para(322(a,1),80(a,2,1))]. given #477 (H,wt=18): 352 L(x * (y * z),x \ 1,y) = (y \ (x \ 1)) \ z. [para(330(a,1),267(a,1,1))]. given #478 (H,wt=18): 364 T(x,x * (y / (y * x))) = L(x,y / (y * x),x). [para(356(a,1),203(a,1,1)),flip(a)]. given #479 (H,wt=18): 455 x * ((x \ y) * T(z,y)) = L(z,x * y,x) * y. [para(435(a,1),109(a,1))]. given #480 (H,wt=18): 500 (x * y) / (z \ ((z * x) * y)) = R(z,x,y) \ z. [para(101(a,1),461(a,1,1))]. given #481 (H,wt=18): 537 ((x * y) * z) / (x * (y * z)) = x \ R(x,y,z). [para(79(a,1),531(a,1,1))]. given #482 (H,wt=18): 549 (x * y) \ ((z * x) * y) = R(T(z,x * y),x,y). [para(111(a,2),46(a,2)),flip(a)]. given #483 (H,wt=18): 550 (x * (x * (y * z))) / (y * z) = R(x * x,y,z). [para(51(a,1),134(a,1,1))]. given #484 (H,wt=10): 588 R(x * x,y,z) = x * x. [para(550(a,1),132(a,1))]. given #485 (H,wt=14): 589 R(T(x * x,y),z,u) = T(x * x,y). [para(588(a,1),46(a,2,1))]. given #486 (H,wt=18): 554 a(x / y,y,y \ 1) = (x / y) \ (x * (y \ 1)). [para(22(a,1),553(a,1,2,1)),flip(a)]. given #487 (H,wt=18): 559 L(x,x * y,x) * (x \ y) = (x \ y) * T(x,y). [para(312(a,1),221(a,1,1))]. given #488 (H,wt=18): 586 (x * y) / (z * ((z \ x) * y)) = R(z,x,y) \ z. [para(213(a,1),500(a,1,2))]. given #489 (H,wt=18): 592 a(x / y,y,y \ 1) = (y / x) * (x * (y \ 1)). [para(554(a,2),358(a,1))]. given #490 (H,wt=19): 222 x * R(T(T(y,x),z),u,w) = R(T(y,z),u,w) * x. [para(42(a,1),110(a,1,2,1))]. given #491 (H,wt=19): 248 T(x * y,(x * y) * (y * x)) = T(x * y,K(y,x)). [para(69(a,1),245(a,1,2,2))]. given #492 (H,wt=19): 257 K(x,y) / T(y * x,x * y) = (y * x) \ K(x,y). [para(69(a,1),252(a,1,2,2))]. given #493 (H,wt=19): 284 (x \ y) \ ((x \ z) * u) = (x * y) \ ((x * z) * u). [para(89(a,1),240(a,1,2)),flip(a)]. given #494 (H,wt=16): 594 a(x,y,z) = (x \ (y * z)) \ ((x \ y) * z). [para(284(a,2),28(a,2))]. given #495 (H,wt=16): 595 (x \ (y * z)) * a(x,y,z) = (x \ y) * z. [para(594(a,2),20(a,1,2))]. given #496 (H,wt=19): 366 x * R(x \ (y \ x),z,u) = R(y \ 1,z,u) * x. [para(325(a,1),110(a,1,2,1))]. given #497 (H,wt=19): 378 x \ T(T(y,x \ 1),x) = (x \ (y * (x \ 1))) * x. [para(326(a,1),148(a,1,1,2)),flip(a)]. given #498 (H,wt=17): 596 (x \ (y * (x \ 1))) * x = T(y,x) * (x \ 1). [para(378(a,1),329(a,1))]. given #499 (H,wt=17): 597 (T(x,y) * (y \ 1)) / y = y \ (x * (y \ 1)). [hyper(24,a,22,a,b,596,a),flip(a)]. NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 114 (0.00 of 2.71 sec). given #500 (H,wt=15): 598 x \ (y * (x \ 1)) = T(y,x) / (x * x). [para(597(a,1),401(a,1))]. given #501 (H,wt=15): 600 T(x,y) / (y * y) = T(x / (y * y),y). [para(598(a,1),403(a,2)),flip(a)]. given #502 (H,wt=19): 405 T(K(x,y),z) * K(y,x) = K(y,x) * T(K(x,y),z). [para(404(a,1),108(a,1,2,1)),flip(a)]. given #503 (H,wt=19): 420 (x \ (x \ y)) * (x * (x * z)) = T(y,x * x) * z. [para(286(a,1),411(a,1,1)),flip(a)]. given #504 (H,wt=19): 428 (x * (y \ (y \ 1))) * z = x * ((y \ (y \ 1)) * z). [para(425(a,1),74(a,1,2))]. given #505 (H,wt=17): 601 x * ((y \ (y \ 1)) * z) = (x / (y * y)) * z. [para(416(a,1),428(a,1,1)),flip(a)]. given #506 (H,wt=15): 602 (x / (y * y)) * z = x * (y \ (y \ z)). [para(291(a,1),601(a,1,2)),flip(a)]. given #507 (H,wt=19): 451 (x * (y / (y * x))) * z = x * ((y / (y * x)) * z). [para(450(a,1),79(a,1,1)),flip(a)]. given #508 (H,wt=10): 603 L(x,y / (y * z),z) = x. [hyper(23,a,74,a,b,451,a),flip(a)]. given #509 (H,wt=11): 605 T(x,x * (y / (y * x))) = x. [para(603(a,1),364(a,2))]. given #510 (H,wt=19): 530 x * (R(x,y,z) * T(u,x)) = R(x,y,z) * (u * x). [para(82(a,1),526(a,1,2)),flip(a)]. given #511 (H,wt=19): 539 x \ (R(y,z,u) * (y \ x)) = T(y \ R(y,z,u),x). [para(532(a,1),36(a,2,2)),flip(a)]. given #512 (H,wt=19): 548 T(x,y) * (R(x,z,u) \ 1) = R(x,z,u) \ T(x,y). [para(546(a,1),329(a,1,2,1)),flip(a)]. given #513 (H,wt=19): 591 T(x * x,y) \ (z * u) = (T(x * x,y) \ z) * u. [para(589(a,1),197(a,1,1))]. given #514 (H,wt=19): 604 (x * (y / (y * x))) \ z = (y / (y * x)) \ (x \ z). [para(603(a,1),177(a,1)),flip(a)]. given #515 (H,wt=19): 606 (x * (y / (y * x))) \ z = ((y * x) / y) * (x \ z). [para(604(a,2),358(a,1))]. given #516 (H,wt=20): 95 (x * (x * (y * z))) / ((x * y) * z) = R(x,x * y,z). [para(51(a,1),34(a,2,1)),flip(a)]. given #517 (H,wt=20): 175 (x * y) * L(L(z,y,x),u,w) = x * (y * L(z,u,w)). [para(49(a,1),74(a,1,2))]. given #518 (H,wt=20): 183 (R(x,y,z) * y) \ ((x * y) * z) = L(z,y,R(x,y,z)). [para(79(a,1),32(a,2,2)),flip(a)]. given #519 (H,wt=20): 184 L(R(x,y,z),u,w) * (y * z) = (L(x,u,w) * y) * z. [para(48(a,1),79(a,1,1))]. given #520 (H,wt=20): 185 R(R(x,y,z),u,w) * (y * z) = (R(x,u,w) * y) * z. [para(50(a,1),79(a,1,1))]. given #521 (H,wt=20): 260 L(K(x,y),y * x,x * y) = ((x * y) \ (y * x)) \ 1. [para(30(a,2),259(a,1,1))]. given #522 (H,wt=16): 609 L(K(x,y),y * x,x * y) = K(y,x) \ 1. [para(30(a,2),260(a,2,1))]. given #523 (H,wt=20): 323 (x \ (y * z)) \ (((x \ 1) * y) * z) = a(x \ 1,y,z). [para(318(a,1),28(a,2,1)),flip(a)]. given #524 (H,wt=18): 610 (x \ (y * z)) \ ((x \ y) * z) = a(x \ 1,y,z). [para(318(a,1),323(a,1,2,1))]. given #525 (H,wt=11): 611 a(x \ 1,y,z) = a(x,y,z). [para(610(a,1),594(a,2)),flip(a)]. given #526 (H,wt=13): 612 a(x / y,z,u) = a(y / x,z,u). [para(343(a,1),611(a,1,1))]. given #527 (H,wt=20): 336 L(x \ 1,y,x \ 1) * y = y * T(x \ 1,x \ y). [para(318(a,1),217(a,1,2,2)),flip(a)]. given #528 (H,wt=20): 446 x * (y \ ((y * (x \ 1)) * z)) = L(z,y * (x \ 1),y). [para(309(a,1),330(a,1)),flip(a)]. given #529 (H,wt=20): 556 T(T((x * y) / (z * y),u),z) = T(R(z \ x,z,y),u). [para(555(a,1),42(a,1,1)),flip(a)]. given #530 (H,wt=20): 607 x * (x * ((y * z) / ((x * y) * z))) = R(x,x * y,z). [para(95(a,1),211(a,1)),flip(a)]. given #531 (H,wt=17): 615 x * (x * (R(x,y,z) \ 1)) = R(x,x * y,z). [para(344(a,1),607(a,1,2,2))]. given #532 (H,wt=15): 616 (x * x) / R(x,y,z) = R(x,x * y,z). [para(615(a,1),263(a,1)),flip(a)]. given #533 (H,wt=15): 617 x * (R(x,y,z) \ x) = R(x,x * y,z). [para(543(a,1),615(a,1,2))]. given #534 (H,wt=15): 618 x \ R(x,x * y,z) = R(x,y,z) \ x. [hyper(23,a,20,a,b,617,a),flip(a)]. given #535 (H,wt=15): 620 x / R(x,x * y,z) = x \ R(x,y,z). [para(617(a,1),535(a,1,2))]. given #536 (H,wt=15): 621 (R(x,y,z) \ x) * x = R(x,x * y,z). [para(617(a,1),544(a,2))]. given #537 (H,wt=15): 622 R(x,x * y,z) \ x = x \ R(x,y,z). [para(620(a,1),498(a,1)),flip(a)]. given #538 (H,wt=15): 624 x \ R(x,x \ y,z) = R(x,y,z) \ x. [para(20(a,1),622(a,1,1,2)),flip(a)]. given #539 (H,wt=17): 623 R(x,x * y,z) \ 1 = x \ (x \ R(x,y,z)). [para(620(a,1),547(a,1,2)),flip(a)]. given #540 (H,wt=19): 619 x * (R(x,x * y,z) \ x) = R(x,(x * x) * y,z). [para(131(a,2),617(a,2,2))]. given #541 (H,wt=17): 626 R(x,(x * x) * y,z) = x * (x \ R(x,y,z)). [para(622(a,1),619(a,1,2)),flip(a)]. given #542 (H,wt=13): 627 R(x,(x * x) * y,z) = R(x,y,z). [para(626(a,2),20(a,1))]. given #543 (H,wt=13): 628 R(x,x * (x * y),z) = R(x,y,z). [para(131(a,1),627(a,1,2))]. given #544 (H,wt=13): 629 R(x,x \ y,z) = R(x,x * y,z). [para(20(a,1),628(a,1,2,2)),flip(a)]. given #545 (H,wt=15): 632 R(x,x * y,z) \ 1 = R(x \ 1,y,z). [para(629(a,1),585(a,1,1))]. given #546 (H,wt=15): 633 R(x,x * y,z) = R(x \ 1,y,z) \ 1. [para(632(a,1),156(a,1,1)),flip(a)]. given #547 (H,wt=15): 634 x \ (x \ R(x,y,z)) = R(x \ 1,y,z). [para(632(a,1),623(a,1)),flip(a)]. given #548 (H,wt=15): 635 x * R(x \ 1,y,z) = x \ R(x,y,z). [para(634(a,1),20(a,1,2))]. given #549 (H,wt=16): 630 R(x,x * y,z) \ (y * z) = (x \ y) * z. [para(629(a,1),197(a,1,1))]. given #550 (H,wt=18): 631 R(x,x * (y / z),z) = y / ((x \ (y / z)) * z). [para(629(a,1),206(a,1))]. given #551 (H,wt=19): 625 x * (R(x,x * y,z) \ u) = (x \ R(x,y,z)) * u. [para(622(a,1),544(a,1,1)),flip(a)]. given #552 (H,wt=19): 636 x * (R(x \ 1,y,z) * u) = x \ (R(x,y,z) * u). [para(634(a,1),265(a,1,2,1))]. given #553 (H,wt=19): 637 x * (R(x,x * y,z) \ u) = R(x,y,z) * (x \ u). [para(625(a,2),532(a,1))]. given #554 (H,wt=19): 638 x * (R(x \ 1,y,z) * u) = R(x,y,z) * (x \ u). [para(636(a,2),534(a,1))]. given #555 (H,wt=20): 608 L(R(x,x,y),z,u) * (x * y) = (x * L(x,z,u)) * y. [para(214(a,1),184(a,2,1))]. given #556 (H,wt=17): 640 (x * L(x,y,z)) * u = L(x,y,z) * (x * u). [para(182(a,1),608(a,1,1,1)),flip(a)]. given #557 (H,wt=17): 641 L(x,y,z) \ ((x * L(x,y,z)) * u) = x * u. [hyper(23,a,20,a,b,640,a(flip)),flip(a)]. given #558 (H,wt=17): 642 L(x,y,z) * (x * u) = x * (L(x,y,z) * u). [para(640(a,1),484(a,1))]. given #559 (H,wt=17): 643 L(x,y,z) \ (x * (L(x,y,z) * u)) = x * u. [para(484(a,1),641(a,1,2))]. given #560 (H,wt=17): 644 x * (L(x,y,z) * (x \ u)) = L(x,y,z) * u. [para(20(a,1),642(a,1,2)),flip(a)]. given #561 (H,wt=17): 645 L(x,y,z) * (x * (L(x,y,z) \ u)) = x * u. [para(20(a,1),642(a,2,2))]. given #562 (H,wt=17): 646 (L(x,y,z) \ x) * (L(x,y,z) * u) = x * u. [para(643(a,1),524(a,1)),flip(a)]. given #563 (H,wt=17): 647 (x \ L(x,y,z)) * u = L(x,y,z) * (x \ u). [hyper(23,a,504,a,b,644,a),flip(a)]. given #564 (H,wt=17): 648 (x * y) / (x * (L(x,z,u) \ y)) = L(x,z,u). [hyper(24,a,22,a,b,645,a),flip(a)]. given #565 (H,wt=17): 649 (x * y) / (L(x,z,u) * y) = L(x,z,u) \ x. [hyper(24,a,22,a,b,646,a),flip(a)]. given #566 (H,wt=17): 650 (L(x,y,z) \ x) * u = x * (L(x,y,z) \ u). [para(20(a,1),646(a,1,2))]. given #567 (H,wt=10): 652 T(x,L(x,y,z) \ x) = x. [hyper(23,a,82,a,b,650,a),flip(a)]. given #568 (H,wt=10): 653 K(x,L(x,y,z) \ x) = 1. [hyper(40,a,652,a)]. given #569 (H,wt=17): 651 (L(x,y,z) \ x) \ u = L(x,y,z) * (x \ u). [para(647(a,1),518(a,2))]. given #570 (H,wt=20): 613 L(x \ 1,y,x \ 1) * y = y * T(x \ 1,x * y). [para(485(a,1),336(a,2,2))]. given #571 (H,wt=20): 614 T(T((x * y) / (z * y),u),z) = R(T(z \ x,u),z,y). [para(556(a,2),46(a,2)),flip(a)]. given #572 (H,wt=21): 225 (x \ y) * R((x \ y) \ y,z,u) = R(x,z,u) * (x \ y). [para(83(a,1),110(a,1,2,1))]. given #573 (H,wt=21): 226 x * (x * R(T(y,x * x),z,u)) = R(y,z,u) * (x * x). [para(110(a,1),131(a,1)),flip(a)]. given #574 (H,wt=21): 300 ((x * y) * z) / T(x * (y * z),a(x,y,z)) = a(x,y,z). [para(67(a,1),100(a,1,1))]. given #575 (H,wt=21): 380 T(x \ 1,x * (y * y)) = (y \ (y \ (x * (y * y)))) \ 1. [para(349(a,2),258(a,2)),flip(a)]. given #576 (H,wt=17): 654 T(x \ 1,x * (y * y)) = T(x,y * y) \ 1. [para(202(a,1),380(a,2,1))]. given #577 (H,wt=15): 655 T(x,y * y) \ 1 = T(x \ 1,y * y). [para(654(a,1),431(a,1))]. given #578 (H,wt=21): 406 R(K(x,y),z,u) * K(y,x) = K(y,x) * R(K(x,y),z,u). [para(404(a,1),110(a,1,2,1)),flip(a)]. given #579 (H,wt=21): 436 (R(T(x,y),z,u) * x) * w = R(T(x,y),z,u) * (x * w). [para(189(a,1),79(a,1,1)),flip(a)]. given #580 (H,wt=11): 656 L(x,y,R(T(y,z),u,w)) = x. [hyper(23,a,74,a,b,436,a),flip(a)]. given #581 (H,wt=13): 657 L(x,y,R((y \ z) \ z,u,w)) = x. [para(83(a,1),656(a,1,3,1))]. given #582 (H,wt=21): 444 x \ (y \ (y \ (z * (y * (y * x))))) = T(z,y * (y * x)). [para(443(a,1),36(a,2)),flip(a)]. given #583 (H,wt=21): 599 x \ ((x * (x * y)) * (x \ 1)) = (x * (y * x)) / (x * x). [para(103(a,1),598(a,2,1))]. given #584 (H,wt=21): 639 x * (y * R(y \ (x \ y),z,u)) = R(x,z,u) * (x \ y). [para(366(a,2),638(a,1,2))]. given #585 (H,wt=21): 658 x \ ((y \ (y \ z)) * (y * (y * x))) = T(z,y * (y * x)). [para(285(a,1),444(a,1,2))]. given #586 (H,wt=17): 660 x \ (T(y,z * z) * x) = T(y,z * (z * x)). [para(420(a,1),658(a,1,2))]. given #587 (H,wt=15): 661 T(T(x,y * y),z) = T(x,y * (y * z)). [para(660(a,1),36(a,2))]. given #588 (H,wt=15): 662 T(T(x,y),z * z) = T(x,z * (z * y)). [para(661(a,1),42(a,1)),flip(a)]. given #589 (H,wt=21): 659 x \ (x * (x * (y * (x \ 1)))) = (x * (y * x)) / (x * x). [para(51(a,1),599(a,1,2))]. given #590 (H,wt=19): 663 x \ (x * T(y,x \ 1)) = (x * (y * x)) / (x * x). [para(347(a,1),659(a,1,2,2))]. given #591 (H,wt=15): 664 (x * (y * x)) / (x * x) = T(y,x \ 1). [para(663(a,1),19(a,1))]. given #592 (H,wt=17): 665 T(x * y,x) / (x * x) = T(x \ y,x \ 1). [para(138(a,1),664(a,1,1))]. given #593 (H,wt=17): 666 T((x * y) / (x * x),x) = T(x \ y,x \ 1). [para(665(a,1),600(a,1)),flip(a)]. given #594 (H,wt=22): 94 ((x * (x * (y * z))) * u) / (z * u) = R(x * (x * y),z,u). [para(51(a,1),34(a,2,1,1)),flip(a)]. given #595 (H,wt=22): 176 (x * y) * L(z,K(x,y),y * x) = (y * x) * (K(x,y) * z). [para(69(a,1),74(a,1,1))]. given #596 (H,wt=22): 199 L(K(x,y) \ ((y * x) \ z),K(x,y),y * x) = (x * y) \ z. [para(69(a,1),177(a,2,1))]. given #597 (H,wt=22): 395 L(x \ 1,x,x \ (y * y)) = T(y * y,x) \ (x \ (y * y)). [para(392(a,1),142(a,2,1))]. given #598 (H,wt=22): 442 L(x \ (x / y),y,x \ (x / y)) = ((x \ (x / y)) \ y) \ y. [para(387(a,1),440(a,1,2)),flip(a)]. given #599 (H,wt=22): 481 (x / y) \ R(x / y,y,y \ 1) = (x * (y \ 1)) / (x / y). [para(434(a,1),478(a,1,1)),flip(a)]. given #600 (H,wt=19): 668 (x * (y \ 1)) / (x / y) = (x / y) \ (x * (y \ 1)). [para(434(a,1),481(a,1,2)),flip(a)]. given #601 (H,wt=19): 669 (x * (y \ 1)) / (x / y) = (y / x) * (x * (y \ 1)). [para(668(a,2),358(a,1))]. given #602 (H,wt=22): 521 (L(x \ 1,x,x / y) \ (x \ 1)) * (y \ (y / x)) = x \ 1. [para(445(a,1),520(a,1,2))]. given #603 (H,wt=22): 583 ((T(x,y) \ x) * z) / (T(x,y) \ z) = R(x,T(x,y) \ 1,z). [para(578(a,1),324(a,1,1,1))]. given #604 (H,wt=22): 593 (x * y) / (z * ((z \ y) * T(x,y))) = R(z,y,T(x,y)) \ z. [para(82(a,1),586(a,1,1))]. given #605 (H,wt=21): 671 (x * y) / (L(x,z * y,z) * y) = R(z,y,T(x,y)) \ z. [para(455(a,1),593(a,1,2))]. given #606 (H,wt=17): 672 R(x,y,T(z,y)) \ x = L(z,x * y,x) \ z. [para(671(a,1),649(a,1))]. given #607 (H,wt=19): 673 (R(x,y,T(z,y)) \ x) \ 1 = z \ L(z,x * y,x). [para(672(a,2),511(a,1,1))]. given #608 (H,wt=17): 676 x \ R(x,y,T(z,y)) = z \ L(z,x * y,x). [para(673(a,1),460(a,1)),flip(a)]. given #609 (H,wt=17): 677 R(x,y,T(z,y)) = x * (z \ L(z,x * y,x)). [para(676(a,1),20(a,1,2)),flip(a)]. given #610 (H,wt=19): 678 R(x,x * y,T(z,x * y)) = x * (z \ L(z,y,x)). [para(313(a,1),677(a,2,2,2))]. given #611 (H,wt=17): 679 R(x,y,T(z,x * y)) \ x = z \ L(z,y,x). [hyper(23,a,617,a,b,678,a(flip)),flip(a)]. given #612 (H,wt=17): 680 (x \ L(x,y,z)) * R(z,y,T(x,z * y)) = z. [para(679(a,1),496(a,1,1))]. given #613 (H,wt=21): 674 L(x,y * (y * z),y) \ x = y \ R(y,z,T(x,y * z)). [para(672(a,1),622(a,1))]. given #614 (H,wt=17): 681 L(x,y,z) \ x = z \ R(z,y,T(x,z * y)). [para(313(a,1),674(a,1,1))]. given #615 (H,wt=17): 682 L(x,y,z) * (z \ R(z,y,T(x,z * y))) = x. [para(681(a,1),20(a,1,2))]. given #616 (H,wt=17): 683 R(x,y,T(z,x * y)) = x * (L(z,y,x) \ z). [para(681(a,2),20(a,1,2)),flip(a)]. given #617 (H,wt=17): 684 (x \ R(x,y,T(z,x * y))) * L(z,y,x) = z. [para(681(a,1),520(a,1,1))]. given #618 (H,wt=17): 686 R(x,y,T(z,x * y)) * (x \ L(z,y,x)) = z. [para(684(a,1),532(a,1)),flip(a)]. given #619 (H,wt=19): 685 L(x,R(y,z,u),T(y,w)) * (T(y,w) \ T(y,w)) = x. [para(527(a,1),682(a,1,2,2))]. given #620 (H,wt=13): 687 L(x,R(y,z,u),T(y,w)) * 1 = x. [para(60(a,1),685(a,1,2))]. given #621 (H,wt=11): 688 L(x,R(y,z,u),T(y,w)) = x. [hyper(24,a,18,a,b,687,a)]. given #622 (H,wt=13): 690 L(x,R(y / z,u,w),z \ y) = x. [para(84(a,1),688(a,1,3))]. given #623 (H,wt=21): 691 T(R(x,y,z),T(x,u)) / T(x,u) = T(x,u) \ R(x,y,z). [para(688(a,1),441(a,1,2))]. given #624 (H,wt=21): 692 R(T(x,T(x,y)),z,u) / T(x,y) = T(x,y) \ R(x,z,u). [para(46(a,2),691(a,1,1))]. given #625 (H,wt=17): 693 R(x,y,z) / T(x,u) = T(x,u) \ R(x,y,z). [para(115(a,1),692(a,1,1,1))]. given #626 (H,wt=22): 667 (x * (x * ((y * z) * u))) / (z * u) = R(x * (x * y),z,u). [para(51(a,1),94(a,1,1))]. given #627 (H,wt=22): 670 (x * (T(x,y) \ z)) / (T(x,y) \ z) = R(x,T(x,y) \ 1,z). [para(576(a,1),583(a,1,1))]. given #628 (H,wt=10): 695 R(x,T(x,y) \ 1,z) = x. [para(670(a,1),21(a,1))]. given #629 (H,wt=22): 694 x * (x * (((y * z) * u) / (z * u))) = R(x * (x * y),z,u). [para(667(a,1),211(a,1)),flip(a)]. given #630 (H,wt=17): 696 R(x * (x * y),z,u) = x * (x * R(y,z,u)). [para(34(a,2),694(a,1,2,2)),flip(a)]. given #631 (H,wt=19): 697 x * (x * R(T(y,x),z,u)) = R(x * (y * x),z,u). [para(82(a,1),696(a,1,1,2)),flip(a)]. given #632 (H,wt=17): 699 R(x * (y * x),z,u) = x * (R(y,z,u) * x). [para(110(a,1),697(a,1,2)),flip(a)]. given #633 (H,wt=17): 700 x \ R(x * (y * x),z,u) = R(y,z,u) * x. [hyper(23,a,20,a,b,699,a(flip)),flip(a)]. given #634 (H,wt=17): 702 x \ R(x * y,z,u) = R(y / x,z,u) * x. [para(22(a,1),700(a,1,2,1,2))]. given #635 (H,wt=17): 703 x \ R(x * y,z,u) = x * R(x \ y,z,u). [para(702(a,2),224(a,1))]. given #636 (H,wt=21): 698 R(x * (x * T(y,x * x)),z,u) = R(y,z,u) * (x * x). [para(696(a,2),226(a,1))]. given #637 (H,wt=17): 705 R(x * (y * y),z,u) = R(x,z,u) * (y * y). [para(136(a,1),698(a,1,1))]. given #638 (H,wt=23): 174 (x * (y * z)) \ (x * (y * (z * u))) = L(L(u,z,y),y * z,x). [para(74(a,1),32(a,2,2,2)),flip(a)]. given #639 (H,wt=23): 201 L(x \ L(y \ z,y,u),x,u * y) = ((u * y) * x) \ (u * z). [para(76(a,2),177(a,1,1,2))]. given #640 (H,wt=23): 253 (x \ y) * ((x \ y) * (T(x,x * y) * z)) = ((x \ y) * y) * z. [para(249(a,2),89(a,1,2,2,1))]. given #641 (H,wt=23): 275 L(x \ L(y \ z,y,u),x,u \ y) = ((u \ y) * x) \ (u \ z). [para(268(a,2),177(a,1,1,2))]. given #642 (H,wt=23): 379 K(x,y) * ((K(x,y) \ 1) / (x * y)) = K(x,y) \ ((y * x) \ 1). [para(341(a,1),278(a,2,2))]. given #643 (H,wt=23): 385 (x \ 1) \ T(x \ 1,x * y) = ((x * y) \ y) * ((x \ 1) \ 1). [para(349(a,1),377(a,1,1)),flip(a)]. given #644 (H,wt=19): 706 (x \ 1) \ T(x \ 1,x * y) = ((x * y) \ y) * x. [para(156(a,1),385(a,2,2))]. given #645 (H,wt=19): 707 (x \ 1) \ T(x \ 1,x * y) = x * ((x * y) \ y). [para(706(a,2),381(a,1))]. given #646 (H,wt=24): 231 T(x / (x * y),z) * (x * y) = (x * y) * T(L(y \ 1,y,x),z). [para(142(a,2),139(a,2,2,1))]. given #647 (H,wt=24): 293 R((x / y) / (z \ (z \ 1)),z \ (z \ 1),y) = x / (z \ (z \ y)). [para(291(a,1),193(a,2,2))]. given #648 (H,wt=22): 709 R((x / y) * (z * z),z \ (z \ 1),y) = x / (z \ (z \ y)). [para(415(a,1),293(a,1,1))]. given #649 (H,wt=15): 710 x / (y \ (y \ z)) = (x / z) * (y * y). [para(709(a,1),426(a,1))]. given #650 (H,wt=15): 711 (x / (y * z)) * (y * y) = x / (y \ z). [para(19(a,1),710(a,1,2,2)),flip(a)]. given #651 (H,wt=18): 712 (x * y) / (z \ y) = R(x / z,z,y) * (z * z). [para(80(a,2),711(a,1,1)),flip(a)]. given #652 (H,wt=18): 713 R((x / y) * (y * y),y,z) = (x * z) / (y \ z). [para(712(a,2),705(a,2))]. given #653 (H,wt=16): 714 R(x / (y \ 1),y,z) = (x * z) / (y \ z). [para(397(a,1),713(a,1,1))]. given #654 (H,wt=16): 715 R(x,y,z) = ((x * (y \ 1)) * z) / (y \ z). [para(21(a,1),714(a,1,1))]. given #655 (H,wt=11): 717 R(x,y \ 1,z) = R(x,y,z). [para(715(a,2),324(a,1)),flip(a)]. given #656 (H,wt=8): 721 R(x,T(x,y),z) = x. [para(717(a,1),695(a,1))]. given #657 (H,wt=12): 718 R(x,y,y) / y = x * (y \ 1). [para(717(a,1),207(a,1,1))]. given #658 (H,wt=12): 719 (x * (y \ 1)) \ R(x,y,y) = y. [para(717(a,1),209(a,1,2))]. given #659 (H,wt=12): 720 R(x / (y \ 1),y,y) = x * y. [para(717(a,1),210(a,1))]. given #660 (H,wt=15): 722 (x * T(x,y)) * z = x * (T(x,y) * z). [para(721(a,1),79(a,1,1)),flip(a)]. given #661 (H,wt=8): 727 L(x,T(y,z),y) = x. [hyper(23,a,74,a,b,722,a),flip(a)]. given #662 (H,wt=10): 730 L(x,y,(z * y) / z) = x. [para(104(a,1),727(a,1,2))]. given #663 (H,wt=10): 731 L(x,(y \ z) \ z,y) = x. [para(83(a,1),727(a,1,2))]. given #664 (H,wt=15): 728 T(x,y) * (x * z) = x * (T(x,y) * z). [para(722(a,1),235(a,1)),flip(a)]. given #665 (H,wt=15): 729 x * (T(x,y) * (x \ z)) = T(x,y) * z. [para(722(a,1),281(a,1))]. given #666 (H,wt=15): 732 x \ (T(x,y) * z) = T(x,y) * (x \ z). [hyper(23,a,20,a,b,729,a),flip(a)]. given #667 (H,wt=15): 733 x \ (T(x,y) * z) = (x \ T(x,y)) * z. [para(732(a,2),562(a,2)),flip(a)]. given #668 (H,wt=16): 726 R(T(x / (y \ 1),z),y,y) = T(x * y,z). [para(720(a,1),46(a,2,1))]. given #669 (H,wt=19): 725 (T(x,y) * (R(x,z,u) \ 1)) \ T(x,y) = R(x,z,u). [para(527(a,1),719(a,1,2))]. given #670 (H,wt=17): 734 (R(x,y,z) \ T(x,u)) \ T(x,u) = R(x,y,z). [para(548(a,1),725(a,1,1))]. given #671 (H,wt=22): 716 R(L(x,y,z) \ x,x,u) = ((L(x,y,z) \ 1) * u) / (x \ u). [para(513(a,1),714(a,1,1))]. given #672 (H,wt=20): 735 R(L(x,y,z) \ x,x,u) = (L(x,y,z) \ u) / (x \ u). [para(318(a,1),716(a,2,1))]. given #673 (H,wt=16): 736 R(L(x,y,z) \ x,x,u) = L(x,y,z) \ x. [para(735(a,2),513(a,1))]. given #674 (H,wt=24): 396 ((x * y) \ ((x * y) \ ((x * y) * x))) * z = L(y,x,x * y) \ z. [para(32(a,2),339(a,1,1)),flip(a)]. given #675 (H,wt=16): 738 L(x,y,y * x) \ z = ((y * x) \ y) * z. [para(19(a,1),396(a,1,1,2)),flip(a)]. given #676 (H,wt=24): 587 T(x \ R(x,y,z),x * (y * z)) = (x * (y * z)) \ ((x * y) * z). [para(537(a,1),84(a,1,1))]. given #677 (H,wt=17): 739 a(x,y,z) = T(x \ R(x,y,z),x * (y * z)). [para(587(a,2),28(a,2))]. given #678 (H,wt=19): 741 a(x,y,z) = T(T(R(x,y,z) / x,x * (y * z)),x). [para(739(a,2),112(a,2)),flip(a)]. given #679 (H,wt=19): 745 a(x,y,z) = T(T(x \ R(x,y,z),x * (y * z)),x). [para(478(a,1),741(a,2,1,1))]. given #680 (H,wt=11): 746 T(a(x,y,z),x) = a(x,y,z). [para(739(a,2),745(a,2,1)),flip(a)]. given #681 (H,wt=13): 747 a(x,y,z) * x = x * a(x,y,z). [para(746(a,1),82(a,1,2)),flip(a)]. given #682 (H,wt=13): 748 (x * a(x,y,z)) / x = a(x,y,z). [para(746(a,1),105(a,1,1,2))]. given #683 (H,wt=21): 740 T(T(x \ R(x,y,z),u),x * (y * z)) = T(a(x,y,z),u). [para(739(a,2),42(a,1,1)),flip(a)]. given #684 (H,wt=24): 704 L(x \ (y * R(y \ z,u,w)),x,y) = (y * x) \ R(y * z,u,w). [para(703(a,1),177(a,1,1,2))]. given #685 (H,wt=21): 750 (x \ y) \ R(x \ z,u,w) = (x * y) \ R(x * z,u,w). [para(704(a,1),267(a,1)),flip(a)]. given #686 (H,wt=24): 708 (x * y) * T(L(y \ 1,y,x),z) = (x * y) * T((x * y) \ x,z). [para(231(a,1),139(a,1))]. given #687 (H,wt=24): 723 R(T(x / (y \ 1),z),y,y) / y = (y \ 1) * T((y \ 1) \ x,z). [para(718(a,2),139(a,1))]. given #688 (H,wt=19): 752 (x \ 1) * T((x \ 1) \ y,z) = T(y * x,z) / x. [para(726(a,1),723(a,1,1)),flip(a)]. given #689 (H,wt=17): 753 (x \ 1) * T(x * y,z) = T(y * x,z) / x. [para(330(a,1),752(a,1,2,1))]. given #690 (H,wt=15): 754 T(x * y,z) / y = y \ T(y * x,z). [para(753(a,1),318(a,1))]. given #691 (H,wt=13): 756 T(x * y,y) / y = (y \ x) * y. [para(754(a,2),146(a,1))]. given #692 (H,wt=13): 757 ((x \ y) * x) * x = T(y * x,x). [para(756(a,1),22(a,1,1))]. given #693 (H,wt=13): 758 T((x * y) * x,x) = (y * x) * x. [para(19(a,1),757(a,1,1,1)),flip(a)]. given #694 (H,wt=15): 755 x \ T(x * (y / x),z) = T(y,z) / x. [para(22(a,1),754(a,1,1,1)),flip(a)]. given #695 (H,wt=21): 759 (x * T(y * x,x)) / (x * x) = T((x \ y) * x,x \ 1). [para(757(a,1),664(a,1,1,2))]. given #696 (H,wt=19): 760 T((x \ y) * x,x \ 1) = ((y * x) * x) / (x * x). [para(82(a,1),759(a,1,1)),flip(a)]. given #697 (H,wt=14): 761 T((x \ y) * x,x \ 1) = R(y,x,x). [para(760(a,2),34(a,2)),flip(a)]. given #698 (H,wt=24): 751 (x * y) * T((x * y) \ x,z) = (x * y) * L(T(y \ 1,z),y,x). [para(44(a,2),708(a,1,2)),flip(a)]. given #699 (H,wt=21): 762 (x * y) * T((x * y) \ x,z) = x * (y * T(y \ 1,z)). [para(751(a,2),74(a,1))]. given #700 (H,wt=25): 742 T((x * (y \ R(y,z,u))) / x,y * (z * u)) = (x * a(y,z,u)) / x. [para(739(a,2),233(a,1,1,2)),flip(a)]. given #701 (H,wt=26): 92 (x * (x * (y * z))) \ ((x * (x * y)) * (z * u)) = L(u,z,x * (x * y)). [para(51(a,1),32(a,2,1)),flip(a)]. given #702 (H,wt=26): 93 (x * (y * (y * z))) \ (x * (y * (y * (z * u)))) = L(u,y * (y * z),x). [para(51(a,1),32(a,2,2,2)),flip(a)]. given #703 (H,wt=26): 232 T((x * y) / (x * z),u) * (x * z) = (x * z) * T(L(z \ y,z,x),u). [para(76(a,2),139(a,2,2,1))]. given #704 (H,wt=26): 255 ((x \ y) * (T(x,x * y) * z)) \ (y * z) = a(x \ y,T(x,x * y),z). [para(250(a,1),28(a,2,2,1)),flip(a)]. given #705 (H,wt=26): 419 (x * (y * (y * z))) \ ((x * (y * y)) * (z * u)) = L(u,z,x * (y * y)). [para(411(a,1),32(a,2,1)),flip(a)]. given #706 (H,wt=26): 472 R(x / (x * y),z,u) * (x * y) = (x * y) * R(L(y \ 1,y,x),z,u). [para(142(a,2),224(a,2,2,1))]. given #707 (H,wt=26): 533 R(x \ R(x,y,z),x * u,w) = ((R(x,y,z) * u) * w) / ((x * u) * w). [para(528(a,1),34(a,2,1,1))]. given #708 (H,wt=26): 724 R(L(x / (y \ 1),z,u),y,y) / y = (y \ 1) * L((y \ 1) \ x,z,u). [para(718(a,2),215(a,1))]. given #709 (H,wt=26): 744 T(T((R(x,y,z) * u) / (x * u),x * (y * z)),x) = R(a(x,y,z),x,u). [para(739(a,2),614(a,2,1))]. given #710 (H,wt=22): 767 T(T(x \ R(x,y,z),x * (y * z)),x) = R(a(x,y,z),x,u). [para(531(a,1),744(a,1,1,1))]. given #711 (H,wt=12): 769 R(a(x,y,z),x,u) = a(x,y,z). [para(767(a,1),745(a,2)),flip(a)]. given #712 (H,wt=17): 770 (a(x,y,z) * x) * u = a(x,y,z) * (x * u). [para(769(a,1),79(a,1,1)),flip(a)]. given #713 (H,wt=9): 771 L(x,y,a(y,z,u)) = x. [hyper(23,a,74,a,b,770,a),flip(a)]. given #714 (H,wt=17): 772 (x * a(x,y,z)) * u = a(x,y,z) * (x * u). [para(747(a,1),770(a,1,1))]. given #715 (H,wt=26): 763 (x * (x * (y * z))) \ (x * (x * (y * (z * u)))) = L(u,z,x * (x * y)). [para(51(a,1),92(a,1,2))]. given #716 (H,wt=18): 773 L(x,y,z * (z * u)) = (u * y) \ (u * (y * x)). [para(763(a,1),212(a,1))]. given #717 (H,wt=13): 774 L(x,y,z * (z * u)) = L(x,y,u). [para(773(a,2),32(a,2)),flip(a)]. given #718 (H,wt=13): 776 L(x,y,z \ u) = L(x,y,z * u). [para(20(a,1),774(a,1,3,2)),flip(a)]. given #719 (H,wt=10): 788 L(x,y / z,z * y) = x. [para(776(a,1),236(a,1))]. given #720 (H,wt=10): 790 L(x,y,y \ (z * z)) = x. [para(776(a,2),429(a,1))]. given #721 (H,wt=11): 787 L(x,y,z \ 1) = L(x,y,z). [para(18(a,1),776(a,2,3))]. given #722 (H,wt=10): 797 L(x,(y * z) \ y,z) = x. [para(787(a,1),505(a,1))]. given #723 (H,wt=10): 800 L(x,y \ z,z \ y) = x. [para(20(a,1),797(a,1,2,1))]. given #724 (H,wt=10): 801 L(x,y \ z,z * y) = x. [para(800(a,1),776(a,1)),flip(a)]. given #725 (H,wt=10): 802 L(x,y,z * (z / y)) = x. [para(66(a,1),801(a,1,2))]. given #726 (H,wt=11): 796 L(x,L(y \ 1,z,u),y) = x. [para(787(a,1),503(a,1))]. given #727 (H,wt=13): 777 L(x,y,(z / u) * z) = L(x,y,u). [para(22(a,1),774(a,1,3,2))]. given #728 (H,wt=13): 784 L(x,y,z / u) = L(x,y,u / z). [para(360(a,1),774(a,1,3))]. given #729 (H,wt=10): 808 L(x,y,z / (z * y)) = x. [para(784(a,1),730(a,1))]. given #730 (H,wt=13): 793 L(x,R(y / z,u,w),z * y) = x. [para(776(a,1),690(a,1))]. given #731 (H,wt=13): 806 L(L(x,y,y / z),z,z / y) = x. [para(784(a,1),304(a,1,1))]. given #732 (H,wt=14): 791 L(x,(y \ z) \ u,z * (y * u)) = x. [para(776(a,1),508(a,1))]. given #733 (H,wt=14): 798 (x \ y) * L(z,y,x) = x \ (y * z). [para(787(a,1),560(a,1,2))]. given #734 (H,wt=14): 807 L(x,x,x / y) = y \ (y / (x \ 1)). [para(784(a,1),432(a,1))]. given #735 (H,wt=15): 778 L(x,y,z * (u * z)) = L(x,y,T(u,z)). [para(82(a,1),774(a,1,3,2))]. given #736 (H,wt=15): 783 L(x,y,(z * z) / u) = L(x,y,u \ 1). [para(263(a,1),774(a,1,3))]. given #737 (H,wt=13): 820 L(x,y,(z * z) / u) = L(x,y,u). [para(783(a,2),787(a,1))]. given #738 (H,wt=13): 822 L(x,y,z / (u * u)) = L(x,y,z). [para(820(a,1),784(a,1)),flip(a)]. given #739 (H,wt=13): 823 L(x,y,z * (u * u)) = L(x,y,z). [para(21(a,1),822(a,1,3)),flip(a)]. given #740 (H,wt=15): 795 T(x * x,y) \ (y \ (x * x)) = y \ 1. [para(790(a,1),395(a,1)),flip(a)]. given #741 (H,wt=15): 815 T(x,y) \ (x * z) = (T(x,y) \ x) * z. [para(234(a,1),798(a,1,2)),flip(a)]. given #742 (H,wt=13): 826 (T(x,y) \ x) * y = T(y,T(x,y)). [para(815(a,1),107(a,1))]. given #743 (H,wt=13): 828 x * (T(x,y) \ y) = T(y,T(x,y)). [para(826(a,1),576(a,1)),flip(a)]. given #744 (H,wt=13): 829 T(x,T(y,x)) / (T(y,x) \ x) = y. [hyper(24,a,22,a,b,828,a),flip(a)]. given #745 (H,wt=13): 830 x \ T(y,T(x,y)) = T(x,y) \ y. [hyper(23,a,20,a,b,828,a),flip(a)]. given #746 (H,wt=15): 827 T(x,y) \ (x * z) = x * (T(x,y) \ z). [para(815(a,2),576(a,1))]. given #747 (H,wt=15): 831 (x * y) / (x * (T(x,z) \ y)) = T(x,z). [para(827(a,1),65(a,1,2))]. given #748 (H,wt=16): 812 L(x,y / (z * (u * y)),z * (u \ 1)) = x. [para(350(a,1),793(a,1,2))]. given #749 (H,wt=16): 824 L(x,y,(z * u) * u) = L(x,y,R(z,u,u)). [para(34(a,2),822(a,1,3)),flip(a)]. given #750 (H,wt=17): 779 L(x,y,(z * u) * (u * z)) = L(x,y,K(u,z)). [para(69(a,1),774(a,1,3,2))]. given #751 (H,wt=17): 781 L(x,y,(z \ u) * w) = L(x,y,(z * u) * w). [para(89(a,1),774(a,1,3)),flip(a)]. given #752 (H,wt=17): 809 ((x / (x * y)) * y) \ (x / (x * y)) = y \ 1. [para(808(a,1),142(a,1)),flip(a)]. given #753 (H,wt=17): 818 L(x,y,T(z \ u,z)) = L(x,y,T(z * u,z)). [para(138(a,1),778(a,1,3)),flip(a)]. given #754 (H,wt=17): 833 (x * (y / (y * x))) \ (y / (y * x)) = x \ 1. [para(362(a,1),809(a,1,1))]. given #755 (H,wt=15): 834 T(x \ 1,x * (y / (y * x))) = x \ 1. [para(833(a,1),349(a,2))]. given #756 (H,wt=18): 799 x * T(y \ 1,y * x) = L(y \ 1,x,y) * x. [para(787(a,1),613(a,1,1)),flip(a)]. given #757 (H,wt=16): 835 L(x \ 1,y,x) * y = y * ((x * y) \ y). [para(349(a,1),799(a,1,2)),flip(a)]. given #758 (H,wt=19): 782 L(x,y,(z \ (z \ u)) * (z \ u)) = L(x,y,T(z,u)). [para(254(a,1),774(a,1,3,2))]. given #759 (H,wt=19): 785 L(x,y,z * L(z,u * z,u)) = L(x,y,a(u,z,z)). [para(453(a,2),774(a,1,3,2))]. given #760 (H,wt=18): 837 L(x,y,z * ((z \ u) * u)) = L(x,y,a(z,u,u)). [para(435(a,1),785(a,1,3))]. given #761 (H,wt=19): 786 L(x,y,R(z * (z * u),w,v5)) = L(x,y,R(u,w,v5)). [para(696(a,2),774(a,1,3))]. given #762 (H,wt=19): 789 L(x,y,T(z / u,z)) = L(x,y,((u / z) * u) * u). [para(370(a,2),776(a,1,3))]. given #763 (H,wt=18): 839 L(x,y,T(z / u,z)) = L(x,y,R(u / z,u,u)). [para(789(a,2),824(a,1))]. given #764 (H,wt=19): 805 L(x,y,(z * (z * u)) * z) = L(x,y,u \ (z \ 1)). [para(289(a,1),777(a,1,3,1))]. given #765 (H,wt=19): 810 ((x / (x * y)) * y) * z = (x / (x * y)) * (y * z). [para(808(a,1),74(a,1,2))]. given #766 (H,wt=19): 811 ((x / (x * y)) * y) \ z = y \ ((x / (x * y)) \ z). [para(808(a,1),177(a,1)),flip(a)]. given #767 (H,wt=19): 816 x \ (((y * x) / y) * z) = (x \ ((y * x) / y)) * z. [para(237(a,1),798(a,1,2)),flip(a)]. given #768 (H,wt=19): 821 L(x,y,T(z,z * (u * u))) = L(x,y,z \ (u * u)). [para(252(a,1),820(a,1,3)),flip(a)]. given #769 (H,wt=19): 836 L(x,y,(z * (z \ u)) * (z \ u)) = L(x,y,T(z,u)). [para(782(a,1),781(a,1)),flip(a)]. given #770 (H,wt=15): 844 L(x,y,z * (u \ z)) = L(x,y,T(u,z)). [para(20(a,1),836(a,1,3,1))]. given #771 (H,wt=15): 845 L(x,y,T(z / u,z)) = L(x,y,z * u). [para(66(a,1),844(a,1,3,2)),flip(a)]. given #772 (H,wt=16): 846 L(x,y,R(z / u,z,z)) = L(x,y,u * z). [para(845(a,1),839(a,1)),flip(a)]. given #773 (H,wt=19): 838 L(x,y,R(z \ u,w,v5)) = L(x,y,R(z * u,w,v5)). [para(20(a,1),786(a,1,3,1,2)),flip(a)]. given #774 (H,wt=13): 847 L(x,y,R((y \ z) * z,u,w)) = x. [para(838(a,1),657(a,1))]. given #775 (H,wt=19): 840 L(x,y,z * (z * (u * z))) = L(x,y,u \ (z \ 1)). [para(51(a,1),805(a,1,3))]. given #776 (H,wt=15): 848 L(x,y,z \ (u \ 1)) = L(x,y,z * u). [para(840(a,1),774(a,1))]. given #777 (H,wt=15): 850 L(x,y,z * (u \ 1)) = L(x,y,z * u). [para(848(a,1),776(a,1)),flip(a)]. given #778 (H,wt=14): 851 L(x,y / (z * (u * y)),z * u) = x. [para(850(a,1),812(a,1))]. given #779 (H,wt=18): 852 L(x,(y * z) * (u / (y * (z * u))),y * z) = x. [para(851(a,1),303(a,1,1))]. given #780 (H,wt=19): 841 (x * (y / (y * x))) * z = (y / (y * x)) * (x * z). [para(362(a,1),810(a,1,1))]. given #781 (H,wt=19): 842 (x * (y / (y * x))) \ z = x \ ((y / (y * x)) \ z). [para(362(a,1),811(a,1,1))]. given #782 (H,wt=19): 843 L(x,y,T(z,z * (u * u))) = L(x,y,z * (u * u)). [para(821(a,2),776(a,1))]. given #783 (H,wt=15): 855 L(x,y,T(z,z * (u * u))) = L(x,y,z). [para(843(a,2),823(a,1))]. given #784 (H,wt=13): 856 L(x,y,T(z,u * u)) = L(x,y,z). [para(423(a,1),855(a,1,3))]. given #785 (H,wt=19): 854 x \ ((y / (y * x)) \ z) = ((y * x) / y) * (x \ z). [para(842(a,1),606(a,1))]. given #786 (H,wt=19): 858 L(x,y,R(T(z,u * u),w,v5)) = L(x,y,R(z,w,v5)). [para(46(a,2),856(a,1,3))]. given #787 (H,wt=19): 859 x \ (((y * x) / y) * z) = ((y * x) / y) * (x \ z). [para(358(a,1),854(a,1,2))]. given #788 (H,wt=19): 860 (x \ ((y * x) / y)) * z = ((y * x) / y) * (x \ z). [para(859(a,1),816(a,1)),flip(a)]. given #789 (H,wt=20): 814 (x \ y) * L(L(z,y,x),u,w) = x \ (y * L(z,u,w)). [para(49(a,1),798(a,1,2))]. given #790 (H,wt=21): 780 L(x,y,z * ((z \ u) * w)) = L(x,y,z * ((z * u) * w)). [para(89(a,1),774(a,1,3,2)),flip(a)]. given #791 (H,wt=18): 861 L(x,y,z * ((z * u) * u)) = L(x,y,a(z,u,u)). [para(780(a,1),837(a,1))]. given #792 (H,wt=21): 803 (x * L(x \ 1,y,z)) \ u = L(x \ 1,y,z) \ (x \ u). [para(796(a,1),177(a,1)),flip(a)]. given #793 (H,wt=21): 804 L(x,y,(z * (z * u)) * (z * w)) = L(x,y,u \ (z \ w)). [para(282(a,1),777(a,1,3,1))]. given #794 (H,wt=21): 817 (x \ y) * T((x \ y) \ 1,z) = x \ (y * T(y \ x,z)). [para(261(a,1),798(a,1,2))]. given #795 (H,wt=21): 819 L(x,y,T((z \ u) * z,z)) = L(x,y,z * T(u * z,z)). [para(757(a,1),778(a,1,3,2)),flip(a)]. given #796 (H,wt=19): 863 L(x,y,T((z \ u) * z,z)) = L(x,y,(u * z) * z). [para(82(a,1),819(a,2,3))]. given #797 (H,wt=18): 864 L(x,y,T((z \ u) * z,z)) = L(x,y,R(u,z,z)). [para(863(a,2),824(a,1))]. given #798 (H,wt=21): 862 L(x,y,z * (z * (u * (z * w)))) = L(x,y,u \ (z \ w)). [para(51(a,1),804(a,1,3))]. given #799 (H,wt=17): 865 L(x,y,z \ (u \ w)) = L(x,y,z * (u * w)). [para(862(a,1),774(a,1))]. given #800 (H,wt=17): 867 L(x,y,z * (u \ w)) = L(x,y,z * (u * w)). [para(865(a,1),776(a,1)),flip(a)]. given #801 (H,wt=17): 868 L(x,y,z * (u * (u * w))) = L(x,y,z * w). [para(19(a,1),867(a,1,3,2)),flip(a)]. given #802 (H,wt=21): 869 L(x,y,(z \ u) * (u \ z)) = L(x,y,(u \ z) * (z * u)). [para(384(a,1),867(a,1,3))]. given #803 (H,wt=22): 792 L(x \ (x / y),y,x * (x / y)) = ((x \ (x / y)) \ y) \ y. [para(776(a,1),442(a,1))]. given #804 (H,wt=15): 871 ((x \ (x / y)) \ y) \ y = x \ (x / y). [para(792(a,1),802(a,1))]. given #805 (H,wt=15): 872 x / (y \ (y / x)) = (y \ (y / x)) \ x. [para(871(a,1),65(a,1,2))]. given #806 (H,wt=22): 825 (x * (y * (y * z))) \ ((x * (y * y)) * (z * u)) = L(u,z,x). [para(823(a,1),419(a,2))]. given #807 (H,wt=22): 873 (x * (y * (y * z))) \ (x * (y * (y * (z * u)))) = L(u,z,x). [para(411(a,1),825(a,1,2))]. given #808 (H,wt=13): 875 L(x,y * (y * z),u) = L(x,z,u). [para(873(a,1),93(a,1)),flip(a)]. given #809 (H,wt=13): 876 L(x,y \ z,u) = L(x,y * z,u). [para(20(a,1),875(a,1,2,2)),flip(a)]. given #810 (H,wt=10): 889 L(x,(y \ z) * z,y) = x. [para(876(a,1),731(a,1))]. given #811 (H,wt=10): 890 L(x,y * z,z * y) = x. [para(876(a,1),801(a,1))]. given #812 (H,wt=9): 897 K(x,y) \ 1 = K(y,x). [para(890(a,1),609(a,1)),flip(a)]. given #813 (H,wt=9): 898 K(x,y) * K(y,x) = 1. [para(897(a,1),20(a,1,2))]. given #814 (H,wt=9): 899 1 / K(x,y) = K(y,x). [para(897(a,1),65(a,1,2))]. given #815 (H,wt=10): 892 L(x,y * z,z / y) = x. [para(66(a,1),889(a,1,2,1))]. given #816 (H,wt=10): 896 L(x,K(y,z),z * y) = x. [para(890(a,1),315(a,1,1))]. given #817 (H,wt=11): 887 L(x,y \ 1,z) = L(x,y,z). [para(18(a,1),876(a,2,2))]. given #818 (H,wt=11): 900 K(x,y) \ z = K(y,x) * z. [para(897(a,1),318(a,1,1)),flip(a)]. given #819 (H,wt=11): 901 K(x,y) * (K(y,x) * z) = z. [para(897(a,1),321(a,1,2,1))]. given #820 (H,wt=11): 902 x / (K(y,z) * x) = K(z,y). [para(897(a,1),340(a,2))]. given #821 (H,wt=11): 918 L(x,y,L(y \ 1,z,u)) = x. [para(887(a,1),509(a,1))]. given #822 (H,wt=12): 914 L(x,x,y) = (y * (x \ 1)) \ y. [para(887(a,1),161(a,1))]. given #823 (H,wt=12): 915 x / L(y,y,x) = x * (y \ 1). [para(887(a,1),162(a,1,2))]. given #824 (H,wt=13): 877 L(x,(y / z) * y,u) = L(x,z,u). [para(22(a,1),875(a,1,2,2))]. given #825 (H,wt=13): 884 L(x,y / z,u) = L(x,z / y,u). [para(360(a,1),875(a,1,2))]. given #826 (H,wt=13): 905 a(K(x,y),z,u) = a(K(y,x),z,u). [para(897(a,1),611(a,1,1))]. given #827 (H,wt=13): 908 R(x,K(y,z),u) = R(x,K(z,y),u). [para(897(a,1),717(a,1,2))]. given #828 (H,wt=13): 909 L(x,y,K(z,u)) = L(x,y,K(u,z)). [para(897(a,1),787(a,1,3))]. given #829 (H,wt=13): 916 L(L(x,y * (z \ 1),y),z,y) = x. [para(887(a,1),308(a,1))]. given #830 (H,wt=13): 921 L(x,K(y,z),u) = L(x,K(z,y),u). [para(897(a,1),887(a,1,2))]. given #831 (H,wt=10): 932 L(x,K(y,z),y * z) = x. [para(921(a,1),896(a,1))]. given #832 (H,wt=14): 891 L(x,(y \ z) * u,z * (y * u)) = x. [para(876(a,1),791(a,1))]. given #833 (H,wt=14): 917 L(x * y,x,y) = (y \ (x \ 1)) \ 1. [para(887(a,1),351(a,1))]. given #834 (H,wt=15): 878 L(x,y * (z * y),u) = L(x,T(z,y),u). [para(82(a,1),875(a,1,2,2))]. given #835 (H,wt=15): 882 L(x,(y * y) / z,u) = L(x,z \ 1,u). [para(263(a,1),875(a,1,2))]. given #836 (H,wt=13): 935 L(x,(y * y) / z,u) = L(x,z,u). [para(882(a,2),887(a,1))]. given #837 (H,wt=13): 936 L(x,y / (z * z),u) = L(x,y,u). [para(935(a,1),884(a,1)),flip(a)]. given #838 (H,wt=13): 937 L(x,y * (z * z),u) = L(x,y,u). [para(21(a,1),936(a,1,2)),flip(a)]. given #839 (H,wt=15): 903 T(x * y,K(y,x)) / (y * x) = K(x,y). [para(897(a,1),345(a,2))]. given #840 (H,wt=15): 911 (x * y) * (K(y,x) * z) = (y * x) * z. [para(896(a,1),176(a,1,2)),flip(a)]. given #841 (H,wt=15): 912 K(x,y) \ ((y * x) \ z) = (x * y) \ z. [para(896(a,1),199(a,1))]. given #842 (H,wt=15): 922 T(x * y,K(y,x)) = K(x,y) * (y * x). [para(900(a,1),122(a,1)),flip(a)]. given #843 (H,wt=15): 931 L(x,y * (z \ 1),y) = L(x,y * z,y). [para(916(a,1),303(a,1,1)),flip(a)]. given #844 (H,wt=15): 939 ((x * y) * z) / (K(x,y) * z) = y * x. [hyper(24,a,22,a,b,911,a),flip(a)]. given #845 (H,wt=15): 940 (x * y) \ ((y * x) * z) = K(y,x) * z. [hyper(23,a,20,a,b,911,a),flip(a)]. given #846 (H,wt=15): 941 K(x,y) * ((x * y) \ z) = (y * x) \ z. [para(912(a,1),20(a,1,2))]. given #847 (H,wt=16): 919 (x * (y \ z)) / L(z,y,x) = x * (y \ 1). [para(887(a,1),333(a,1,2))]. given #848 (H,wt=16): 920 L(x * (y * z),x,y) = (y \ (x \ 1)) \ z. [para(887(a,1),352(a,1))]. given #849 (H,wt=16): 925 L(x / y,x / y,z) = (z * (y / x)) \ z. [para(343(a,1),914(a,2,1,2))]. given #850 (H,wt=16): 926 L(K(x,y),K(x,y),z) = (z * K(y,x)) \ z. [para(897(a,1),914(a,2,1,2))]. given #851 (H,wt=16): 934 L(x * y,x,y) * z = (y \ (x \ 1)) \ z. [para(917(a,2),318(a,1,1))]. given #852 (H,wt=16): 938 L(x,(y * z) * z,u) = L(x,R(y,z,z),u). [para(34(a,2),936(a,1,2)),flip(a)]. given #853 (H,wt=16): 945 (x * (y \ 1)) * L(z,y,x) = x * (y \ z). [para(919(a,1),22(a,1,1))]. given #854 (H,wt=17): 879 L(x,(y * z) * (z * y),u) = L(x,K(z,y),u). [para(69(a,1),875(a,1,2,2))]. given #855 (H,wt=17): 880 L(x,(y \ z) * u,w) = L(x,(y * z) * u,w). [para(89(a,1),875(a,1,2)),flip(a)]. given #856 (H,wt=14): 949 L(x,(y * z) * u,z * (y * u)) = x. [para(880(a,1),891(a,1))]. given #857 (H,wt=16): 950 L(x,(y * z) * u,T(y,z) * (z * u)) = x. [para(82(a,1),949(a,1,2,1))]. given #858 (H,wt=17): 881 L(x,T(y,y * z),u) = L(x,(y \ z) * z,u). [para(250(a,1),875(a,1,2,2)),flip(a)]. given #859 (H,wt=17): 883 L(x,T(y \ 1,z),u) = L(x,z * (y \ z),u). [para(327(a,1),875(a,1,2,2)),flip(a)]. given #860 (H,wt=17): 927 (x * y) * ((y / x) \ 1) = (x * y) / (y / x). [para(788(a,1),915(a,1,2)),flip(a)]. given #861 (H,wt=15): 952 (x * y) / (y / x) = (x * y) * (x / y). [para(343(a,1),927(a,1,2)),flip(a)]. given #862 (H,wt=17): 943 L(x,K(y,z) * (y * z),u) = L(x,z * y,u). [para(939(a,1),935(a,1,2)),flip(a)]. given #863 (H,wt=17): 951 L(x,T(y,y * z),u) = L(x,(y * z) * z,u). [para(881(a,2),880(a,1))]. given #864 (H,wt=18): 930 K(x,y) / L(z,z,K(y,x)) = K(x,y) * (z \ 1). [para(909(a,1),915(a,1,2))]. given #865 (H,wt=18): 942 x * (y \ ((y * (x \ 1)) * z)) = L(z,y * x,y). [para(931(a,1),446(a,2))]. given #866 (H,wt=18): 944 (x * y) \ (y * (x * z)) = K(y,x) * L(z,x,y). [para(74(a,1),940(a,1,2))]. given #867 (H,wt=14): 955 K(x,y) * L(x,y,x) = T(x,y * x). [para(944(a,1),36(a,2)),flip(a)]. given #868 (H,wt=18): 947 L(K(x,y),K(x,y),z) / z = (z * K(y,x)) \ 1. [para(926(a,2),320(a,1,1))]. given #869 (H,wt=18): 954 x * (y * ((y \ (x \ 1)) * z)) = L(z,y * x,y). [para(213(a,1),942(a,1,2))]. given #870 (H,wt=14): 956 x * ((x \ (y \ 1)) * y) = a(x,y,y). [hyper(23,a,453,a(flip),b,954,a)]. given #871 (H,wt=15): 958 x * R(x \ 1,y \ 1,y) = a(x,y,y). [para(335(a,2),956(a,1,2))]. given #872 (H,wt=13): 959 x \ R(x,y \ 1,y) = a(x,y,y). [para(958(a,1),635(a,1)),flip(a)]. given #873 (H,wt=11): 962 x \ R(x,y,y) = a(x,y,y). [para(717(a,1),959(a,1,2))]. given #874 (H,wt=11): 963 x * a(x,y,y) = R(x,y,y). [para(962(a,1),20(a,1,2))]. given #875 (H,wt=11): 964 a(x,y,y) \ R(x,y,y) = x. [para(962(a,1),480(a,1,1))]. given #876 (H,wt=13): 960 x * R(x \ 1,y,y) = a(x,y,y). [para(717(a,1),958(a,1,2))]. given #877 (H,wt=13): 967 R(x \ 1,y,y) = x \ a(x,y,y). [para(962(a,1),634(a,1,2)),flip(a)]. given #878 (H,wt=15): 965 (R(x,y,y) \ x) * z = a(x,y,y) \ z. [para(962(a,1),465(a,1,1)),flip(a)]. given #879 (H,wt=13): 968 R(x,x * y,y) = a(x,y,y) \ x. [para(965(a,1),621(a,1)),flip(a)]. given #880 (H,wt=15): 966 x * (a(x,y,y) * z) = R(x,y,y) * z. [para(962(a,1),501(a,1,2,1))]. given #881 (H,wt=19): 893 (x * ((x \ y) * y)) \ z = ((x \ y) * y) \ (x \ z). [para(889(a,1),177(a,1)),flip(a)]. given #882 (H,wt=19): 894 ((x * y) * (y * x)) * z = (x * y) * ((y * x) * z). [para(890(a,1),74(a,1,2))]. given #883 (H,wt=19): 895 T(x * y,(x * y) * (y * x)) = T(x * y,y * x). [para(890(a,1),203(a,1)),flip(a)]. given #884 (H,wt=15): 969 T(x * y,K(y,x)) = T(x * y,y * x). [para(895(a,1),248(a,1)),flip(a)]. given #885 (H,wt=13): 970 T(x * y,K(y,x)) = (x \ 1) \ y. [para(969(a,2),439(a,1))]. given #886 (H,wt=11): 972 T(x * y,K(y,x)) = x * y. [para(970(a,2),330(a,1))]. given #887 (H,wt=11): 973 K(x,y) = (x * y) / (y * x). [para(972(a,1),903(a,1,1)),flip(a)]. given #888 (H,wt=11): 974 K(x,y) * (y * x) = x * y. [para(972(a,1),922(a,1)),flip(a)]. given #889 (H,wt=13): 980 K(x \ y,x) * y = (x \ y) * x. [para(20(a,1),974(a,1,2))]. given #890 (H,wt=13): 981 K(x * y,x) * y = (x \ y) * x. [para(495(a,1),980(a,1,1))]. given #891 (H,wt=13): 982 ((x \ y) * x) / y = K(x * y,x). [hyper(24,a,22,a,b,981,a),flip(a)]. given #892 (H,wt=15): 975 (x * y) / (T(x,y) * y) = K(y,T(x,y)). [para(82(a,1),973(a,2,1)),flip(a)]. given #893 (H,wt=11): 983 K(x,T(y,x)) = T(y,x) \ y. [para(975(a,1),577(a,1))]. given #894 (H,wt=11): 984 T(x,y) * K(y,T(x,y)) = x. [para(983(a,2),20(a,1,2))]. given #895 (H,wt=11): 985 K(x,T(y,x)) * T(y,x) = y. [para(983(a,2),298(a,1,1))]. given #896 (H,wt=11): 990 K(T(x,y),y) * x = T(x,y). [hyper(23,a,901,a,b,985,a),flip(a)]. given #897 (H,wt=15): 976 (T(x,y) * y) / (x * y) = K(T(x,y),y). [para(82(a,1),973(a,2,2)),flip(a)]. given #898 (H,wt=11): 992 K(T(x,y),y) = x \ T(x,y). [para(976(a,1),565(a,1))]. given #899 (H,wt=11): 993 x * K(T(x,y),y) = T(x,y). [para(992(a,2),20(a,1,2))]. given #900 (H,wt=15): 978 (x \ y) / (y * (x \ 1)) = K(x \ 1,y). [para(318(a,1),973(a,2,1)),flip(a)]. given #901 (H,wt=15): 987 T(x,y) \ (x * z) = K(y,T(x,y)) * z. [para(983(a,2),815(a,2,1))]. given #902 (H,wt=15): 989 (x \ y) * K(x,T(y / x,x)) = y / x. [para(84(a,1),984(a,1,1))]. given #903 (H,wt=13): 1000 (x \ y) * K(x,x \ y) = y / x. [para(84(a,1),989(a,1,2,2))]. given #904 (H,wt=13): 1001 (x \ y) * K(x,x * y) = y / x. [para(489(a,1),1000(a,1,2))]. given #905 (H,wt=13): 1002 (x \ y) \ (y / x) = K(x,x * y). [hyper(23,a,20,a,b,1001,a),flip(a)]. given #906 (H,wt=15): 991 K(x,x \ y) * T(y / x,x) = y / x. [para(84(a,1),985(a,1,1,2))]. given #907 (H,wt=15): 994 (x / y) \ T(x / y,y) = K(y \ x,y). [para(84(a,1),992(a,1,1)),flip(a)]. given #908 (H,wt=15): 995 K(T(x \ 1,y),y) = x * T(x \ 1,y). [para(992(a,2),330(a,1))]. given #909 (H,wt=15): 997 (x / y) * K(T(x / y,y),y) = y \ x. [para(993(a,2),84(a,1))]. given #910 (H,wt=13): 1006 (x / y) * K(y \ x,y) = y \ x. [para(84(a,1),997(a,1,2,1))]. given #911 (H,wt=13): 1007 (x / y) * K(y * x,y) = y \ x. [para(495(a,1),1006(a,1,2))]. given #912 (H,wt=13): 1008 (x / y) * (x \ y) = K(x * y,x). [hyper(23,a,359,a,b,1007,a),flip(a)]. given #913 (H,wt=13): 1009 K(x * y,x) / (x \ y) = x / y. [hyper(24,a,22,a,b,1008,a),flip(a)]. given #914 (H,wt=13): 1010 (x \ y) * (x / y) = K(x * y,x). [para(1008(a,1),368(a,1)),flip(a)]. given #915 (H,wt=13): 1011 (x \ y) \ K(x * y,x) = x / y. [hyper(23,a,20,a,b,1010,a),flip(a)]. given #916 (H,wt=15): 998 T(x,y) * (K(y,T(x,y)) * z) = x * z. [para(987(a,1),20(a,1,2))]. given #917 (H,wt=15): 999 K(x,T(y,x)) * (y \ z) = T(y,x) \ z. [para(20(a,1),987(a,1,2)),flip(a)]. given #918 (H,wt=15): 1003 K(x,x * (x * y)) = y \ ((x * y) / x). [para(19(a,1),1002(a,1,1)),flip(a)]. given #919 (H,wt=11): 1013 K(x,y) = y \ ((x * y) / x). [para(1003(a,1),490(a,1)),flip(a)]. given #920 (H,wt=11): 1014 (x * y) / x = y * K(x,y). [para(1013(a,2),20(a,1,2)),flip(a)]. given #921 (H,wt=9): 1020 T(x * K(y,x),y) = x. [para(1014(a,1),104(a,1,1))]. given #922 (H,wt=10): 1021 L(x,y * K(z,y),y) = x. [para(1014(a,1),237(a,1,2))]. given #923 (H,wt=8): 1026 L(x,K(y,z),z) = x. [para(1021(a,1),303(a,1))]. given #924 (H,wt=8): 1029 L(x,K(y,z),y) = x. [para(1026(a,1),921(a,1)),flip(a)]. given #925 (H,wt=11): 1016 K(x,y) = ((x * y) / x) / y. [para(1013(a,2),558(a,2)),flip(a)]. given #926 (H,wt=11): 1018 (x * K(y,x)) * y = y * x. [para(1014(a,1),22(a,1,1))]. given #927 (H,wt=11): 1033 (x * y) / x = K(x,y) * y. [para(1016(a,2),22(a,1,1)),flip(a)]. given #928 (H,wt=11): 1035 (x * K(y,x)) / x = K(y,x). [para(1014(a,1),1016(a,2,1)),flip(a)]. given #929 (H,wt=9): 1037 T(K(x,y),y) = K(x,y). [para(1035(a,1),104(a,1,1))]. given #930 (H,wt=7): 1038 T(x,K(y,x)) = x. [hyper(39,a,1037,a)]. given #931 (H,wt=11): 1036 K(x,y) * y = y * K(x,y). [para(1033(a,1),1014(a,1))]. given #932 (H,wt=13): 1015 x * (y / (y * x)) = K(y,x) \ 1. [para(1013(a,2),502(a,1,1)),flip(a)]. given #933 (H,wt=11): 1041 K(x,y) = x * (y / (y * x)). [para(1015(a,2),897(a,1)),flip(a)]. given #934 (H,wt=7): 1046 T(x,K(x,y)) = x. [para(1041(a,2),605(a,1,2))]. given #935 (H,wt=9): 1051 T(x,T(y,x) \ y) = x. [para(983(a,1),1046(a,1,2))]. given #936 (H,wt=11): 1042 x \ K(x,y) = y / (y * x). [hyper(23,a,20,a,b,1041,a(flip)),flip(a)]. given #937 (H,wt=11): 1043 K(x,y) = (y / (y * x)) * x. [para(1041(a,2),362(a,2)),flip(a)]. given #938 (H,wt=11): 1044 K(x,y) / x = y / (y * x). [para(1041(a,2),363(a,1,1))]. given #939 (H,wt=11): 1048 T(x \ 1,K(x,y)) = x \ 1. [para(1041(a,2),834(a,1,2))]. given #940 (H,wt=11): 1050 K(x,y) * x = x * K(x,y). [para(1046(a,1),82(a,1,2))]. given #941 (H,wt=11): 1053 K(x,y) = ((y * x) / y) \ x. [para(1043(a,2),358(a,2)),flip(a)]. given #942 (H,wt=11): 1054 K(x,y) / x = x \ K(x,y). [para(1044(a,2),1042(a,2)),flip(a)]. given #943 (H,wt=13): 1019 x / (x / y) = y * K(x / y,y). [para(22(a,1),1014(a,1,1))]. given #944 (H,wt=13): 1023 T(T(x * K(y,x),z),y) = T(x,z). [para(1020(a,1),42(a,1,1)),flip(a)]. given #945 (H,wt=13): 1032 (x * K(y,x)) \ 1 = K(x,y) / x. [para(1029(a,1),947(a,1,1)),flip(a)]. given #946 (H,wt=13): 1055 K(x,y) * (x \ 1) = x \ K(x,y). [para(1048(a,1),327(a,1,2))]. given #947 (H,wt=13): 1056 (x * K(y,x)) \ 1 = x \ K(x,y). [para(1032(a,2),1054(a,1))]. given #948 (H,wt=13): 1057 (x \ 1) / (x \ K(x,y)) = K(y,x). [para(1055(a,1),902(a,1,2))]. given #949 (H,wt=15): 1004 K(x,x * y) * T(y / x,x) = y / x. [para(489(a,1),991(a,1,1))]. given #950 (H,wt=15): 1005 (x / y) \ T(x / y,y) = K(y * x,y). [para(994(a,2),495(a,1))]. given #951 (H,wt=15): 1017 ((x * y) / x) * (y \ z) = K(x,y) * z. [para(1013(a,2),860(a,1,1)),flip(a)]. given #952 (H,wt=15): 1024 T(x * K(y,x),z) * y = y * T(x,z). [para(1020(a,1),108(a,1,2,1)),flip(a)]. given #953 (H,wt=14): 1062 T(x * K(y,x),x * y) = L(x,y,x). [hyper(24,a,217,a(flip),b,1024,a)]. given #954 (H,wt=15): 1027 (x * K(y,x)) \ z = K(y,x) \ (x \ z). [para(1021(a,1),270(a,1))]. given #955 (H,wt=15): 1028 (x * K(y,x)) * z = x * (K(y,x) * z). [para(1026(a,1),74(a,1,2))]. given #956 (H,wt=15): 1030 (x * K(x,y)) * z = x * (K(x,y) * z). [para(1029(a,1),74(a,1,2))]. given #957 (H,wt=15): 1031 x \ (K(x,y) * z) = (x \ K(x,y)) * z. [para(1029(a,1),798(a,1,2)),flip(a)]. given #958 (H,wt=15): 1040 T(x,y) * K(z,x) = K(z,x) * T(x,y). [para(1038(a,1),108(a,1,2,1)),flip(a)]. given #959 (H,wt=15): 1045 x * ((y / (y * x)) * z) = K(x,y) * z. [para(1041(a,2),451(a,1,1)),flip(a)]. given #960 (H,wt=15): 1047 ((x * y) / x) * (y \ z) = K(y,x) \ z. [para(1041(a,2),606(a,1,1)),flip(a)]. given #961 (H,wt=15): 1049 (x / (x * y)) * (y * z) = K(y,x) * z. [para(1041(a,2),841(a,1,1)),flip(a)]. given #962 (H,wt=15): 1052 (T(x,y) \ x) * y = y * (T(x,y) \ x). [para(1051(a,1),82(a,1,2))]. given #963 (H,wt=13): 1069 x * (T(y,x) \ y) = T(x,T(y,x)). [para(1052(a,1),826(a,1))]. given #964 (H,wt=13): 1070 x * K(x,T(y,x)) = T(x,T(y,x)). [para(983(a,2),1069(a,1,2))]. given #965 (H,wt=15): 1058 (x * K(y,x)) \ z = (x \ K(x,y)) * z. [para(1056(a,1),318(a,1,1)),flip(a)]. given #966 (H,wt=15): 1059 K(x,y) * (y * z) = ((x * y) / x) * z. [para(19(a,1),1017(a,1,2)),flip(a)]. given #967 (H,wt=15): 1063 (x * K(y,x)) \ z = K(x,y) * (x \ z). [para(1027(a,2),900(a,1))]. given #968 (H,wt=15): 1064 ((x * y) / x) * z = y * (K(x,y) * z). [para(1014(a,2),1028(a,1,1))]. given #969 (H,wt=15): 1065 x \ (K(x,y) * z) = (y / (y * x)) * z. [para(1042(a,1),1031(a,2,1))]. given #970 (H,wt=15): 1066 K(x,y) \ (x * z) = ((y * x) / y) * z. [para(19(a,1),1047(a,1,2)),flip(a)]. given #971 (H,wt=15): 1067 K(x,y) * (x \ z) = (y / (y * x)) * z. [para(20(a,1),1049(a,1,2)),flip(a)]. given #972 (H,wt=11): 1075 K(x,y) * (x \ (y * x)) = y. [para(1067(a,2),22(a,1))]. given #973 (H,wt=9): 1077 K(x,y) * T(y,x) = y. [para(36(a,2),1075(a,1,2))]. given #974 (H,wt=9): 1079 K(x,T(y,x)) = K(x,y). [hyper(24,a,985,a,b,1077,a),flip(a)]. given #975 (H,wt=9): 1080 K(x,y) = T(y,x) \ y. [hyper(24,a,298,a,b,1077,a)]. given #976 (H,wt=9): 1081 T(x,y) = K(x,y) * x. [hyper(23,a,901,a,b,1077,a)]. given #977 (H,wt=9): 1086 K(x,y) = T(x,y) / x. [para(1077(a,1),902(a,1,2)),flip(a)]. given #978 (H,wt=9): 1089 T(x,y) * K(y,x) = x. [para(1077(a,1),1040(a,2))]. given #979 (H,wt=9): 1105 K(T(x,y),y) = K(x,y). [hyper(24,a,990,a,b,1081,a(flip)),flip(a)]. given #980 (H,wt=9): 1107 T(x,y) = x * K(x,y). [para(1081(a,2),1050(a,1))]. given #981 (H,wt=9): 1108 K(x,y) = x \ T(x,y). [para(1086(a,2),572(a,1))]. given #982 (H,wt=11): 1078 K(x,y / x) = K(x,x * y). [hyper(24,a,1004,a,b,1077,a)]. given #983 (H,wt=11): 1092 K(x,x * (y * x)) = K(x,y). [para(1079(a,1),491(a,2))]. given #984 (H,wt=11): 1096 T(x,T(y,x)) = x * K(x,y). [para(1079(a,1),1070(a,1,2)),flip(a)]. given #985 (H,wt=9): 1131 T(x,T(y,x)) = T(x,y). [para(1096(a,2),1107(a,2)),flip(a)]. given #986 (H,wt=11): 1100 K(x,y) = y * (T(y,x) \ 1). [para(1080(a,2),578(a,2)),flip(a)]. given #987 (H,wt=11): 1101 T(x,y) \ 1 = x \ K(y,x). [para(1080(a,2),582(a,1,2)),flip(a)]. given #988 (H,wt=11): 1112 T(x * K(y,x),T(y,x)) = x. [para(1105(a,1),1020(a,1,1,2))]. given #989 (H,wt=11): 1116 x * (y * K(y,x)) = y * x. [para(1107(a,1),82(a,1,2))]. given #990 (H,wt=11): 1128 K(x / y,y) = K(y * x,y). [para(1108(a,2),1005(a,1))]. given #991 (H,wt=11): 1133 T(x,y / x) = T(x,x \ y). [para(84(a,1),1131(a,1,2)),flip(a)]. given #992 (H,wt=11): 1134 (x * y) / T(y,x) = T(x,y). [para(1131(a,1),117(a,1,2))]. given #993 (H,wt=11): 1136 T(x,x * (y * x)) = T(x,y). [para(1131(a,1),247(a,2))]. given #994 (H,wt=11): 1137 T(x,y) / (T(y,x) \ x) = y. [para(1131(a,1),829(a,1,1))]. given #995 (H,wt=11): 1138 T(x,y) \ y = x \ T(y,x). [para(1131(a,1),830(a,1,2)),flip(a)]. given #996 (H,wt=11): 1139 T(x,y * K(x,y)) = T(x,y). [para(1020(a,1),1131(a,1,2)),flip(a)]. given #997 (H,wt=11): 1145 T(x,y / x) = T(x,x * y). [para(1133(a,2),246(a,1))]. given #998 (H,wt=11): 1146 T(x,y) * T(y,x) = x * y. [para(1134(a,1),22(a,1,1))]. given #999 (H,wt=11): 1147 x / (y \ T(x,y)) = T(y,x). [para(1138(a,1),65(a,1,2))]. given #1000 (H,wt=13): 1087 (x * y) * T(y,x) = (y * x) * y. [para(1077(a,1),911(a,1,2)),flip(a)]. given #1001 (H,wt=13): 1090 (x / (x * y)) * T(x,y) = y \ x. [para(1077(a,1),1065(a,1,2)),flip(a)]. given #1002 (H,wt=13): 1091 K(x,T(T(y,x),z)) = K(x,T(y,z)). [para(42(a,1),1079(a,1,2))]. given #1003 (H,wt=13): 1093 T(x,y) \ (x * z) = K(y,x) * z. [para(1079(a,1),987(a,2,1))]. given #1004 (H,wt=13): 1094 T(x,y) * (K(y,x) * z) = x * z. [para(1079(a,1),998(a,1,2,1))]. given #1005 (H,wt=13): 1095 K(x,y) * (y \ z) = T(y,x) \ z. [para(1079(a,1),999(a,1,1))]. given #1006 (H,wt=13): 1098 K(x,y) * (T(y,x) * z) = y * z. [para(1080(a,2),575(a,1,1))]. given #1007 (H,wt=13): 1099 x * (T(x,y) \ z) = K(y,x) * z. [para(1080(a,2),576(a,1,1)),flip(a)]. given #1008 (H,wt=13): 1102 (x * y) / (T(x,z) * y) = K(z,x). [para(1080(a,2),577(a,2))]. given #1009 (H,wt=13): 1104 T(x,y) = (x * x) / (x * K(y,x)). [para(1080(a,2),831(a,1,2,2)),flip(a)]. given #1010 (H,wt=13): 1111 x * T(x \ 1,y) = K(x \ 1,y). [para(1105(a,1),995(a,1)),flip(a)]. given #1011 (H,wt=13): 1113 K(x,y) * T(x,y) = T(T(x,y),y). [para(1105(a,1),1081(a,2,1)),flip(a)]. given #1012 (H,wt=13): 1120 x * (K(x,y) * z) = T(x,y) * z. [para(1107(a,2),1030(a,1,1)),flip(a)]. given #1013 (H,wt=13): 1121 T(x,y) * K(x,y) = T(T(x,y),y). [para(1105(a,1),1107(a,2,2)),flip(a)]. given #1014 (H,wt=13): 1124 x \ ((x \ y) \ y) = K(x,x * y). [para(249(a,1),1108(a,2,2)),flip(a)]. given #1015 (H,wt=13): 1125 T(x,y) * (x \ z) = K(x,y) * z. [para(1108(a,2),562(a,1,1)),flip(a)]. given #1016 (H,wt=13): 1127 x \ (T(x,y) * z) = K(x,y) * z. [para(1108(a,2),733(a,2,1))]. given #1017 (H,wt=13): 1129 x * K(y,y * x) = y * (x / y). [para(1078(a,1),121(a,1,2))]. given #1018 (H,wt=13): 1132 T(T(x,y),T(z,x)) = T(T(x,z),y). [para(1131(a,1),42(a,1,1)),flip(a)]. given #1019 (H,wt=13): 1144 x / (x / y) = y * K(y * x,y). [para(1128(a,1),1019(a,2,2))]. given #1020 (H,wt=13): 1157 T(x,y) * (y * x) = x * (x * y). [para(974(a,1),1094(a,1,2))]. given #1021 (H,wt=13): 1158 K(x,y) * (T(x,y) \ z) = x \ z. [hyper(23,a,901,a,b,1095,a),flip(a)]. given #1022 (H,wt=13): 1159 K(x,y) * (y \ x) = y \ T(x,y). [para(1095(a,2),1138(a,1))]. given #1023 (H,wt=13): 1160 K(x,y) * (x * z) = T(x,y) * z. [hyper(23,a,901,a,b,1098,a),flip(a)]. given #1024 (H,wt=13): 1163 x \ (K(y,x) * z) = T(x,y) \ z. [hyper(23,a,20,a,b,1099,a),flip(a)]. given #1025 (H,wt=13): 1171 T(x,y) \ (K(x,y) * z) = x \ z. [hyper(23,a,20,a,b,1125,a),flip(a)]. given #1026 (H,wt=13): 1187 T(x,y) \ (y * K(x,y)) = x \ y. [para(1036(a,1),1171(a,1,2))]. given #1027 (H,wt=15): 1068 K(x,y) * (x * z) = x * (K(x,y) * z). [para(1049(a,1),1045(a,1,2)),flip(a)]. given #1028 (H,wt=15): 1071 x / (K(y,z) * (y \ x)) = y * K(z,y). [para(1063(a,1),65(a,1,2))]. given #1029 (H,wt=15): 1072 (x \ K(x,y)) * z = K(x,y) * (x \ z). [para(1063(a,1),1058(a,1)),flip(a)]. given #1030 (H,wt=15): 1073 K(x,y) * (y * z) = y * (K(x,y) * z). [para(1064(a,1),1059(a,2))]. given #1031 (H,wt=15): 1074 K(x,y) \ (x * z) = (K(y,x) * x) * z. [para(1033(a,1),1066(a,2,1))]. given #1032 (H,wt=15): 1076 x \ (K(x,y) * z) = K(x,y) * (x \ z). [para(1067(a,2),1065(a,2))]. given #1033 (H,wt=15): 1082 K(x,T(y,z)) * T(T(y,x),z) = T(y,z). [para(42(a,1),1077(a,1,2))]. given #1034 (H,wt=15): 1085 L(x,y,K(z,u) * u) = L(x,y,T(u,z)). [para(1077(a,1),774(a,1,3,2))]. given #1035 (H,wt=15): 1088 T(x,y) * T(x,y) = x * T(T(x,y),y). [para(1077(a,1),998(a,1,2))]. given #1036 (H,wt=15): 1097 T(T(x,y),z) \ T(x,z) = K(y,T(x,z)). [para(42(a,1),1080(a,2,1)),flip(a)]. given #1037 (H,wt=15): 1110 K(R(T(x,y),z,u),y) = K(R(x,z,u),y). [para(46(a,2),1105(a,1,1))]. given #1038 (H,wt=15): 1114 K(x,y) * T(K(y,x),z) = K(K(y,x),z). [hyper(23,a,901,a,b,1107,a(flip)),flip(a)]. given #1039 (H,wt=15): 1118 (x \ y) * K(x * y,x) = T(x \ y,x). [para(495(a,1),1107(a,2,2)),flip(a)]. given #1040 (H,wt=15): 1119 L(x,y,z * T(z,u)) = L(x,y,K(z,u)). [para(1107(a,2),774(a,1,3,2))]. given #1041 (H,wt=15): 1122 T(x,y) \ T(T(x,z),y) = K(T(x,y),z). [para(42(a,1),1108(a,2,2)),flip(a)]. given #1042 (H,wt=15): 1126 K(x \ 1,x * y) = x * ((x * y) \ y). [para(1108(a,2),707(a,1))]. given #1043 (H,wt=15): 1155 K(x,T(y,K(z,T(y,x)))) = K(x,T(y,x)). [para(1038(a,1),1091(a,1,2)),flip(a)]. given #1044 (H,wt=13): 1196 K(x,T(y,K(z,T(y,x)))) = K(x,y). [para(1155(a,2),1079(a,1))]. given #1045 (H,wt=15): 1156 L(x,y * K(z,y),u) = L(x,T(y,z),u). [para(1094(a,1),937(a,1,2))]. given #1046 (H,wt=15): 1168 T(x,y) * (T(y,x) * z) = x * (y * z). [para(1098(a,1),1120(a,1,2)),flip(a)]. given #1047 (H,wt=15): 1172 K(x,y) * (z * x) = T(x,y) * T(z,x). [para(36(a,2),1125(a,1,2)),flip(a)]. given #1048 (H,wt=15): 1173 T(x / y,z) * y = K(x / y,z) * x. [para(66(a,1),1125(a,1,2))]. given #1049 (H,wt=15): 1176 x \ T(T(x,y),y) = K(x,y) * K(x,y). [para(1121(a,1),1127(a,1,2))]. given #1050 (H,wt=15): 1181 K(x,y) * (T(x,y) \ T(x,z)) = K(x,z). [para(1158(a,2),1108(a,2)),flip(a)]. given #1051 (H,wt=15): 1185 L(x,T(y,z) * z,u) = L(x,z * y,u). [para(1160(a,1),943(a,1,2))]. given #1052 (H,wt=15): 1186 T(x,y) \ (T(y,x) \ z) = x \ (y \ z). [para(1158(a,1),1163(a,1,2)),flip(a)]. given #1053 (H,wt=15): 1188 x \ (y * K(x,y)) = K(x,y) * (x \ y). [para(1187(a,1),1158(a,1,2)),flip(a)]. given #1054 (H,wt=15): 1191 K(x,y) \ (x * z) = (K(x,y) \ x) * z. [para(900(a,2),1074(a,2,1))]. given #1055 (H,wt=8): 1203 L(x,y,K(y,z)) = x. [hyper(23,a,798,a,b,1191,a(flip)),flip(a)]. given #1056 (H,wt=10): 1204 L(x,y,T(z,y) \ z) = x. [para(983(a,1),1203(a,1,3))]. given #1057 (H,wt=10): 1205 L(x,y,T(z,y) * z) = x. [para(1204(a,1),776(a,1)),flip(a)]. given #1058 (H,wt=10): 1206 L(x,y,z * T(z,y)) = x. [para(116(a,1),1205(a,1,3))]. given #1059 (H,wt=15): 1192 L(x,y,(z * u) / z) = L(x,y,T(u,z)). [para(1033(a,2),1085(a,1,3))]. given #1060 (H,wt=15): 1198 (x * (y * z)) / (T(y,x) * z) = T(x,y). [hyper(24,a,22,a,b,1168,a),flip(a)]. given #1061 (H,wt=15): 1200 (T(x / y,z) * y) / x = K(x / y,z). [hyper(24,a,22,a,b,1173,a(flip)),flip(a)]. given #1062 (H,wt=15): 1201 K(x / y,z) * x = y * T(y \ x,z). [para(1173(a,1),139(a,1))]. given #1063 (H,wt=15): 1211 (x * T(x \ y,z)) / y = K(y / x,z). [para(139(a,1),1200(a,1,1))]. given #1064 (H,wt=16): 1061 T(x * K(x \ y,x),y) = L(x,x \ y,x). [hyper(24,a,221,a,b,1024,a)]. given #1065 (H,wt=16): 1115 (x * y) \ (x * T(y,z)) = L(K(y,z),y,x). [para(1107(a,2),32(a,2,2,2)),flip(a)]. given #1066 (H,wt=16): 1117 (x * y) * L(K(y,z),y,x) = x * T(y,z). [para(1107(a,2),74(a,2,2))]. given #1067 (H,wt=16): 1135 L(T(x,y),T(y,x),x) = T(x,x * T(y,x)). [para(1131(a,1),203(a,1,1))]. given #1068 (H,wt=14): 1216 L(T(x,y),T(y,x),x) = T(x,y * x). [para(82(a,1),1135(a,2,2))]. given #1069 (H,wt=16): 1153 R(x,y,x) * (y * x) = (y * x) * T(x,y). [para(1087(a,2),79(a,2))]. given #1070 (H,wt=16): 1215 T(x * K(x * y,x),y) = L(x,x \ y,x). [para(495(a,1),1061(a,1,1,2))]. given #1071 (H,wt=16): 1218 T(x * K(x * y,x),y) = L(x,x * y,x). [para(1215(a,2),312(a,1))]. given #1072 (H,wt=14): 1219 T(x / (x / y),x) = L(y,y * x,y). [para(1144(a,2),1218(a,1,1))]. given #1073 (H,wt=17): 988 L(x,K(y,T(z,y)),u) = L(x,T(z,y) * z,u). [para(983(a,2),876(a,1,2))]. given #1074 (H,wt=17): 1022 a(x / (x * y),z,u) = a(y * K(x,y),z,u). [para(1014(a,1),612(a,1,1)),flip(a)]. given #1075 (H,wt=17): 1060 T(x,y) * K(z,T(x,y)) = T(x * K(z,x),y). [hyper(24,a,1018,a,b,1024,a),flip(a)]. given #1076 (H,wt=17): 1130 K(x,(y * (x \ 1)) / x) = K(x,T(y,x \ 1)). [para(347(a,1),1078(a,2,2))]. given #1077 (H,wt=15): 1220 K(x,T(y,x \ 1)) = K(x,y / (x * x)). [para(401(a,1),1130(a,1,2)),flip(a)]. given #1078 (H,wt=17): 1140 K(x,y) * K(z,K(y,x)) = T(K(y,x),z) \ 1. [hyper(23,a,901,a,b,1100,a(flip)),flip(a)]. given #1079 (H,wt=17): 1143 K((x * (y \ 1)) / y,y) = K(T(x,y \ 1),y). [para(347(a,1),1128(a,2,1))]. given #1080 (H,wt=15): 1221 K(T(x,y \ 1),y) = K(x / (y * y),y). [para(401(a,1),1143(a,1,1)),flip(a)]. given #1081 (H,wt=17): 1149 T(x,(y * (x \ 1)) / x) = T(x,T(y,x \ 1)). [para(347(a,1),1145(a,2,2))]. given #1082 (H,wt=15): 1222 T(x,T(y,x \ 1)) = T(x,y / (x * x)). [para(401(a,1),1149(a,1,2)),flip(a)]. given #1083 (H,wt=17): 1152 T(T(x,y),x \ T(y,x)) = (x \ T(y,x)) \ y. [para(1147(a,1),84(a,1,1))]. given #1084 (H,wt=17): 1161 K(x,y / x) * ((x \ y) * z) = (y / x) * z. [para(84(a,1),1098(a,1,2,1))]. given #1085 (H,wt=17): 1165 x \ (y * T(y \ x,z)) = K((x \ y) \ 1,z). [para(1111(a,1),817(a,1)),flip(a)]. given #1086 (H,wt=17): 1174 T(x,y) * (z / (z * x)) = K(x,y) * K(x,z). [para(1042(a,1),1125(a,1,2))]. given #1087 (H,wt=17): 1175 T(x,y) * (T(x,z) \ 1) = K(x,y) * K(z,x). [para(1101(a,2),1125(a,1,2))]. given #1088 (H,wt=15): 1224 T(x,y) \ T(x,z) = K(x,z) * K(y,x). [para(1175(a,1),581(a,1)),flip(a)]. given #1089 (H,wt=15): 1225 K(x,y) * (K(x,z) * K(y,x)) = K(x,z). [para(1224(a,1),1181(a,1,2))]. given #1090 (H,wt=15): 1226 K(x,y) * K(z,x) = K(z,x) * K(x,y). [hyper(23,a,901,a,b,1225,a)]. given #1091 (H,wt=17): 1177 T(T(x,x * y),T(z,x)) = T(T(x,z),x \ y). [para(246(a,1),1132(a,1,1))]. given #1092 (H,wt=15): 1229 T(T(x,y),x \ z) = T(T(x,y),x * z). [para(1177(a,1),1132(a,1))]. given #1093 (H,wt=17): 1178 (x / (x / y)) * z = y * (K(y * x,y) * z). [para(1144(a,2),1028(a,1,1))]. given #1094 (H,wt=15): 1231 (x / (x / y)) * x = y * ((y \ x) * y). [para(981(a,1),1178(a,2,2))]. given #1095 (H,wt=13): 1232 T(x * y,x) = (y / (y / x)) * y. [para(1231(a,2),138(a,1)),flip(a)]. given #1096 (H,wt=13): 1233 T(x * y,x) / y = y / (y / x). [hyper(24,a,22,a,b,1232,a(flip)),flip(a)]. given #1097 (H,wt=13): 1234 ((x / y) / x) * T(y * x,y) = x. [hyper(23,a,359,a,b,1232,a(flip)),flip(a)]. given #1098 (H,wt=13): 1236 x \ T(x * y,y) = x / (x / y). [para(1233(a,1),754(a,1)),flip(a)]. given #1099 (H,wt=13): 1237 x / T(y * x,y) = (x / y) / x. [hyper(24,a,22,a,b,1234,a),flip(a)]. given #1100 (H,wt=13): 1238 T(x * y,y) = x * (x / (x / y)). [para(1236(a,1),20(a,1,2)),flip(a)]. given #1101 (H,wt=15): 1235 L(x,T(y * z,y),u) = L(x,z / y,u). [para(1232(a,2),877(a,1,2))]. given #1102 (H,wt=15): 1239 T(x * (y \ x),y \ x) = x * (x / y). [para(65(a,1),1238(a,2,2,2))]. given #1103 (H,wt=17): 1184 (x * y) \ (T(x,z) * y) = T(K(x,z),x * y). [para(1160(a,1),36(a,2,2)),flip(a)]. given #1104 (H,wt=17): 1212 K((x * y) / x,z) * (x * y) = x * T(y,z). [para(19(a,1),1201(a,2,2,1))]. given #1105 (H,wt=17): 1213 x \ (y * T(y \ x,z)) = T(K(x / y,z),x). [para(1201(a,1),36(a,2,2)),flip(a)]. given #1106 (H,wt=15): 1240 T(K(x / y,z),x) = K((x \ y) \ 1,z). [para(1213(a,1),1165(a,1))]. given #1107 (H,wt=15): 1241 K((x \ (y \ x)) \ 1,z) = T(K(y,z),x). [para(65(a,1),1240(a,1,1,1)),flip(a)]. given #1108 (H,wt=15): 1243 K(T(x \ 1,y) \ 1,z) = T(K(x,z),y). [para(325(a,2),1241(a,1,1,1))]. given #1109 (H,wt=17): 1230 T(T(x,y),x * T(y,x)) = (x \ T(y,x)) \ y. [para(1229(a,1),1152(a,1))]. given #1110 (H,wt=15): 1245 (x \ T(y,x)) \ y = T(T(x,y),y * x). [para(82(a,1),1230(a,1,2)),flip(a)]. given #1111 (H,wt=18): 1025 x / L(y,x * K(y,x),y) = y \ (x * K(y,x)). [para(1020(a,1),441(a,1,1))]. given #1112 (H,wt=16): 1246 x / L(y,T(x,y),y) = y \ (x * K(y,x)). [para(1156(a,1),1025(a,1,2))]. given #1113 (H,wt=16): 1247 x / L(y,T(x,y),y) = K(y,x) * (y \ x). [para(1246(a,2),1188(a,1))]. given #1114 (H,wt=18): 1083 K(x,R(y,z,u)) * R(T(y,x),z,u) = R(y,z,u). [para(46(a,2),1077(a,1,2))]. given #1115 (H,wt=18): 1084 L(x \ y,x,K(z,y)) = (K(z,y) \ x) \ T(y,z). [para(1077(a,1),267(a,1,1,2))]. given #1116 (H,wt=18): 1106 (x * T(y,z)) / L(y,K(y,z),x) = x * K(y,z). [para(1081(a,2),99(a,1,1,2))]. given #1117 (H,wt=18): 1109 R(T(x,y),z,u) * K(y,R(x,z,u)) = R(x,z,u). [para(46(a,2),1089(a,1,1))]. given #1118 (H,wt=18): 1123 L(x,y,z) \ L(T(x,u),y,z) = K(L(x,y,z),u). [para(44(a,2),1108(a,2,2)),flip(a)]. given #1119 (H,wt=18): 1248 L(x \ y,x,K(z,y)) = (K(y,z) * x) \ T(y,z). [para(900(a,1),1084(a,2,1))]. given #1120 (H,wt=19): 904 R(K(x,y),K(y,x) * z,u) = R(K(y,x),z,u) \ 1. [para(897(a,1),584(a,1,1))]. given #1121 (H,wt=19): 906 R(K(x,y),K(x,y) * z,u) = R(K(y,x),z,u) \ 1. [para(897(a,1),633(a,2,1,1))]. given #1122 (H,wt=19): 929 L(x,(y * (y * z)) * y,u) = L(x,z \ (y \ 1),u). [para(289(a,1),877(a,1,2,1))]. given #1123 (H,wt=19): 933 ((x * y) \ K(x,y)) \ z = K(x,y) \ ((x * y) * z). [para(932(a,1),267(a,1)),flip(a)]. given #1124 (H,wt=19): 946 (a(x,y,z) \ (x \ 1)) \ u = x * (a(x,y,z) * u). [para(920(a,1),771(a,1))]. given #1125 (H,wt=19): 948 (a(x,y,z) \ (x \ 1)) \ u = (x * a(x,y,z)) * u. [para(771(a,1),934(a,1,1)),flip(a)]. given #1126 (H,wt=17): 1252 (x * a(x,y,z)) * u = x * (a(x,y,z) * u). [para(948(a,1),946(a,1))]. given #1127 (H,wt=17): 1253 a(x,y,z) * (x * u) = x * (a(x,y,z) * u). [para(1252(a,1),772(a,1)),flip(a)]. given #1128 (H,wt=17): 1254 x * (a(x,y,z) * (x \ u)) = a(x,y,z) * u. [para(20(a,1),1253(a,1,2)),flip(a)]. given #1129 (H,wt=19): 953 L(x,(y * (y \ z)) * (y \ z),u) = L(x,T(y,z),u). [para(20(a,1),951(a,1,2,2)),flip(a)]. given #1130 (H,wt=15): 1255 L(x,y * (z \ y),u) = L(x,T(z,y),u). [para(20(a,1),953(a,1,2,1))]. given #1131 (H,wt=15): 1256 L(x,T(y \ 1,z),u) = L(x,T(y,z),u). [para(1255(a,1),883(a,2))]. given #1132 (H,wt=19): 971 K(x,y) / T(y * x,K(x,y)) = (y * x) \ K(x,y). [para(969(a,2),257(a,1,2))]. given #1133 (H,wt=15): 1257 K(x,y) / (y * x) = (y * x) \ K(x,y). [para(972(a,1),971(a,1,2))]. given #1134 (H,wt=19): 1012 L(x,y,(z \ u) * K(z * u,z)) = L(x,y,z / u). [para(1010(a,1),774(a,1,3,2))]. given #1135 (H,wt=15): 1258 L(x,y,T(z \ u,z)) = L(x,y,z / u). [para(1118(a,1),1012(a,1,3))]. given #1136 (H,wt=15): 1259 L(x,y,T(z * u,z)) = L(x,y,z / u). [para(1258(a,1),818(a,1)),flip(a)]. given #1137 (H,wt=19): 1103 ((x * y) * y) \ ((y * x) * y) = K(y,(y * x) * y). [para(758(a,1),1080(a,2,1)),flip(a)]. given #1138 (H,wt=19): 1148 (T(x,y) \ y) * K(x,x * T(y,x)) = T(y,x) / x. [para(1138(a,2),1001(a,1,1))]. given #1139 (H,wt=17): 1260 (T(x,y) \ y) * K(x,y * x) = T(y,x) / x. [para(82(a,1),1148(a,1,2,2))]. given #1140 (H,wt=19): 1164 (x * y) * T((x * y) \ x,z) = x * K(y \ 1,z). [para(1111(a,1),762(a,2,2))]. given #1141 (H,wt=19): 1169 L(x,y,z * ((z \ u) * u)) = L(x,y,K(z,z * u)). [para(1124(a,1),865(a,1,3)),flip(a)]. given #1142 (H,wt=16): 1261 L(x,y,K(z,z * u)) = L(x,y,a(z,u,u)). [para(1169(a,1),837(a,1))]. given #1143 (H,wt=16): 1262 L(x,y,K(z * u,z)) = L(x,y,a(z,u,u)). [para(1261(a,1),909(a,1)),flip(a)]. given #1144 (H,wt=18): 1263 L(x,y,a(z,u * z,u * z)) = L(x,y,K(z,u)). [para(1092(a,1),1261(a,1,3)),flip(a)]. given #1145 (H,wt=19): 1193 T(x,y) * K(y,T(x,z)) = K(z,T(x,y)) * T(x,z). [para(1097(a,1),1099(a,1,2))]. given #1146 (H,wt=19): 1199 (x \ y) * (T(x,y / x) * z) = (y / x) * (x * z). [para(84(a,1),1168(a,1,1))]. given #1147 (H,wt=19): 1207 ((x * T(x,y)) * y) \ ((x * T(x,y)) * (y * z)) = z. [para(1206(a,1),32(a,1)),flip(a)]. given #1148 (H,wt=19): 1223 K(((x * y) \ x) \ 1,z) = (x * y) \ (x * T(y,z)). [para(19(a,1),1165(a,1,2,2,1)),flip(a)]. given #1149 (H,wt=16): 1267 L(K(x,y),x,z) = K(((z * x) \ z) \ 1,y). [para(1223(a,2),1115(a,1)),flip(a)]. given #1150 (H,wt=17): 1268 K(L(x \ 1,x,y) \ 1,z) = L(K(x,z),x,y). [para(142(a,2),1267(a,2,1,1)),flip(a)]. given #1151 (H,wt=19): 1244 K(T((x \ 1) \ 1,y * y),z) = T(K(x,z),y * y). [para(655(a,1),1243(a,1,1))]. given #1152 (H,wt=15): 1269 K(T(x,y * y),z) = T(K(x,z),y * y). [para(156(a,1),1244(a,1,1,1))]. given #1153 (H,wt=19): 1250 L(x,y * (y * (z * y)),u) = L(x,z \ (y \ 1),u). [para(51(a,1),929(a,1,2))]. given #1154 (H,wt=15): 1271 L(x,y \ (z \ 1),u) = L(x,y * z,u). [para(1250(a,1),875(a,1))]. given #1155 (H,wt=15): 1273 L(x,y * (z \ 1),u) = L(x,y * z,u). [para(1271(a,1),876(a,1)),flip(a)]. given #1156 (H,wt=19): 1251 ((x * y) \ K(x,y)) \ z = K(y,x) * ((x * y) * z). [para(933(a,2),900(a,1))]. given #1157 (H,wt=19): 1265 (x \ y) * (T(x,x * y) * z) = (y / x) * (x * z). [para(1145(a,1),1199(a,1,2,1))]. given #1158 (H,wt=19): 1266 (x * (T(x,y) * y)) \ ((x * T(x,y)) * (y * z)) = z. [para(722(a,1),1207(a,1,1))]. given #1159 (H,wt=19): 1270 K(T(x,y * y),z) \ 1 = T(K(x,z) \ 1,y * y). [para(1269(a,2),655(a,1,1))]. given #1160 (H,wt=17): 1276 T(K(x,y) \ 1,z * z) = K(y,T(x,z * z)). [para(1270(a,1),897(a,1))]. given #1161 (H,wt=15): 1277 K(x,T(y,z * z)) = T(K(x,y),z * z). [para(897(a,1),1276(a,1,1)),flip(a)]. given #1162 (H,wt=15): 1278 K(T(x,y * y),z) = K(x,T(z,y * y)). [para(1277(a,2),1269(a,2))]. given #1163 (H,wt=19): 1274 (x \ y) * ((y / x) * (x * z)) = ((x \ y) * y) * z. [para(1265(a,1),253(a,1,2))]. given #1164 (H,wt=19): 1275 (x * (T(x,y) * y)) \ (x * (T(x,y) * (y * z))) = z. [para(722(a,1),1266(a,1,2))]. given #1165 (H,wt=15): 1279 L(L(x,y,T(z,y)),T(z,y) * y,z) = x. [para(1275(a,1),174(a,1)),flip(a)]. given #1166 (H,wt=13): 1280 L(L(x,y,T(z,y)),y * z,z) = x. [para(1279(a,1),1185(a,1)),flip(a)]. given #1167 (H,wt=13): 1284 L(x,T(y,z),z) = L(x,y,T(z,y)). [para(1280(a,1),314(a,1,1))]. given #1168 (H,wt=15): 1281 L(L(x,y,T(y \ z,y)),z,y \ z) = x. [para(20(a,1),1280(a,1,2))]. given #1169 (H,wt=13): 1286 L(L(x,y,y / z),z,y \ z) = x. [para(1258(a,1),1281(a,1,1))]. given #1170 (H,wt=13): 1287 L(L(x,y,y / z),z,y * z) = x. [para(1286(a,1),776(a,1)),flip(a)]. given #1171 (H,wt=13): 1288 L(x,y,z / y) = L(x,y,z * y). [para(304(a,1),1287(a,1,1)),flip(a)]. given #1172 (H,wt=13): 1290 L(x,y,y / z) = L(x,y,z * y). [para(806(a,1),1287(a,1,1)),flip(a)]. given #1173 (H,wt=13): 1291 L(x,y,(z * y) * y) = L(x,y,z). [para(21(a,1),1288(a,1,3)),flip(a)]. given #1174 (H,wt=14): 1289 L(x \ (x / y),x,y * x) = y \ 1. [para(445(a,1),1287(a,1,1))]. given #1175 (H,wt=14): 1292 L(x \ 1,x,y * x) = y \ (y / x). [para(1288(a,1),144(a,1))]. given #1176 (H,wt=14): 1293 L(x,x,y * x) = y \ (y / (x \ 1)). [para(1288(a,1),432(a,1))]. given #1177 (H,wt=15): 1282 L(x,y * (z * y),y) = L(x,z,T(y,z)). [para(1280(a,1),303(a,1,1))]. given #1178 (H,wt=15): 1296 ((x * y) * y) \ (x * y) = x \ (x / y). [para(1292(a,1),142(a,1)),flip(a)]. given #1179 (H,wt=16): 1294 x * L(y,z,x * z) = (x / z) * (z * y). [para(1288(a,1),173(a,1,2))]. given #1180 (H,wt=17): 1283 L(x,T(y,z) * z,T(y,z)) = L(x,z * y,y). [para(308(a,1),1280(a,1,1)),flip(a)]. given #1181 (H,wt=15): 1299 x \ L(x,x * y,y) = a(T(y,x),x,x). [para(1283(a,1),452(a,1,2))]. given #1182 (H,wt=15): 1300 L(x,y * z,T(z,y)) = L(x,y * z,z). [para(1283(a,1),1185(a,1)),flip(a)]. given #1183 (H,wt=17): 1285 L(x,T(y,y * z),y * z) = L(x,y,y / z). [para(1284(a,2),1259(a,1))]. given #1184 (H,wt=20): 888 (x * (y \ z)) * L(u,y * z,x) = x * ((y \ z) * u). [para(876(a,1),74(a,1,2))]. given #1185 (H,wt=20): 910 L(K(x,y),z,K(y,x)) * z = z * ((K(y,x) * z) \ z). [para(897(a,1),835(a,1,1,1))]. given #1186 (H,wt=18): 1301 T(L(K(x,y),z,K(y,x)),z) = (K(y,x) * z) \ z. [hyper(23,a,82,a,b,910,a(flip)),flip(a)]. given #1187 (H,wt=20): 977 ((x * y) * z) / ((y * x) * z) = R(K(x,y),y * x,z). [para(973(a,2),80(a,1,1)),flip(a)]. given #1188 (H,wt=20): 1217 (x * y) * T(y,y * (x * y)) = R(y,x,y) * (x * y). [para(1136(a,2),1153(a,2,2)),flip(a)]. given #1189 (H,wt=11): 1302 L(x,y * x,x) = R(x,y,x). [hyper(24,a,217,a(flip),b,1217,a(flip)),flip(a)]. given #1190 (H,wt=11): 1303 R(x,y / x,x) = L(x,y,x). [para(22(a,1),1302(a,1,2)),flip(a)]. given #1191 (H,wt=15): 1304 L(T(x,y),z * x,x) = T(R(x,z,x),y). [para(1302(a,1),44(a,2,1))]. given #1192 (H,wt=15): 1306 L(T(x,y),z * x,x) = R(T(x,y),z,x). [para(1304(a,2),46(a,2)),flip(a)]. given #1193 (H,wt=18): 1305 L(x,y,x) * ((y / x) * x) = (x * (y / x)) * x. [para(1303(a,1),79(a,1,1))]. given #1194 (H,wt=14): 1307 L(x,y,x) * y = (x * (y / x)) * x. [para(22(a,1),1305(a,1,2))]. given #1195 (H,wt=16): 1308 T(L(x,y,x) * y,x) = ((y / x) * x) * x. [para(1307(a,2),758(a,1,1))]. given #1196 (H,wt=12): 1309 T(L(x,y,x) * y,x) = y * x. [para(22(a,1),1308(a,2,1))]. given #1197 (H,wt=14): 1310 (L(x,y,x) * y) * x = x * (y * x). [para(1309(a,1),82(a,1,2)),flip(a)]. given #1198 (H,wt=9): 1311 L(R(x,y,x),y,x) = x. [hyper(24,a,184,a,b,1310,a(flip)),flip(a)]. given #1199 (H,wt=9): 1312 R(L(x,y,x),y,x) = x. [hyper(24,a,79,a,b,1310,a(flip)),flip(a)]. given #1200 (H,wt=11): 1313 R(x,x \ y,x) = L(x,y,x). [para(1311(a,1),302(a,1,1)),flip(a)]. given #1201 (H,wt=11): 1314 L(x,x * y,x) = R(x,y,x). [para(1311(a,1),303(a,1,1))]. given #1202 (H,wt=11): 1315 R(x,x * y,x) = L(x,y,x). [para(1311(a,1),308(a,1,1)),flip(a)]. given #1203 (H,wt=12): 1316 x \ T(y * x,y) = R(y,x,y). [para(1314(a,1),316(a,1)),flip(a)]. given #1204 (H,wt=12): 1319 T(x / (x / y),x) = R(y,x,y). [para(1314(a,1),1219(a,2))]. given #1205 (H,wt=12): 1321 x * R(y,x,y) = T(y * x,y). [para(1316(a,1),20(a,1,2))]. given #1206 (H,wt=13): 1320 L(x,y,x) \ x = x \ R(x,y,x). [para(1315(a,1),622(a,1,1))]. given #1207 (H,wt=14): 1318 T(x * K(x * y,x),y) = R(x,y,x). [para(1314(a,1),1218(a,2))]. given #1208 (H,wt=14): 1322 T(x,R(y,x,y)) = T(x,x / (x / y)). [para(1319(a,1),1131(a,1,2))]. given #1209 (H,wt=16): 1317 R(x,y,x) * (x \ y) = (x \ y) * T(x,y). [para(1314(a,1),559(a,1,1))]. given #1210 (H,wt=16): 1324 T(x,y) * K(x * y,T(x,y)) = R(x,y,x). [para(1318(a,1),1060(a,2))]. given #1211 (H,wt=18): 1325 T(x,y) * K(y * T(x,y),T(x,y)) = R(x,y,x). [para(82(a,2),1324(a,1,2,1))]. given #1212 (H,wt=21): 907 K(x,y) * (K(y,x) / (x * y)) = K(x,y) \ ((y * x) \ 1). [para(897(a,1),379(a,1,2,1))]. given #1213 (H,wt=17): 1326 K(x,y) * (K(y,x) / (x * y)) = (x * y) \ 1. [para(907(a,2),912(a,1))]. given #1214 (H,wt=17): 1327 K(x,y) * ((x * y) \ K(y,x)) = (x * y) \ 1. [para(1257(a,1),1326(a,1,2))]. given #1215 (H,wt=13): 1328 (x * y) \ K(x,y) = (y * x) \ 1. [para(1327(a,1),941(a,1)),flip(a)]. given #1216 (H,wt=17): 1329 K(x,y) * ((y * x) * z) = ((x * y) \ 1) \ z. [para(1328(a,1),1251(a,1,1)),flip(a)]. given #1217 (H,wt=15): 1330 K(x,y) * ((y * x) * z) = (x * y) * z. [para(1329(a,2),330(a,1))]. given #1218 (H,wt=15): 1331 ((x * y) * z) / ((y * x) * z) = K(x,y). [hyper(24,a,22,a,b,1330,a),flip(a)]. given #1219 (H,wt=12): 1332 R(K(x,y),y * x,z) = K(x,y). [para(1331(a,1),977(a,1)),flip(a)]. given #1220 (H,wt=16): 1333 R(K(x,T(y,x)),T(y,x) * x,z) = K(x,y). [para(1332(a,2),1079(a,1))]. given #1221 (H,wt=14): 1335 R(K(x,y),T(y,x) * x,z) = K(x,y). [para(1079(a,1),1333(a,1,1))]. given #1222 (H,wt=21): 924 (L(x \ 1,y,z) * x) \ u = x \ (L(x \ 1,y,z) \ u). [para(918(a,1),177(a,1)),flip(a)]. given #1223 (H,wt=21): 928 L(x,(y * (y * z)) * (y * u),w) = L(x,z \ (y \ u),w). [para(282(a,1),877(a,1,2,1))]. given #1224 (H,wt=21): 979 ((K(x,y) * z) * K(y,x)) / z = K(K(x,y) * z,K(y,x)). [para(901(a,1),973(a,2,2)),flip(a)]. given #1225 (H,wt=21): 1154 T(x,y) * ((y * x) / ((x * y) * x)) = K(T(x,y),y * x). [para(1087(a,1),1041(a,2,2,2)),flip(a)]. given #1226 (H,wt=18): 1339 T(x,y) * (R(x,y,x) \ 1) = K(T(x,y),y * x). [para(344(a,1),1154(a,1,2))]. given #1227 (H,wt=16): 1340 R(x,y,x) \ T(x,y) = K(T(x,y),y * x). [para(1339(a,1),548(a,1)),flip(a)]. given #1228 (H,wt=21): 1170 T(x,y) \ ((x \ T(y,x)) \ y) = K(T(x,y),T(x,y) * y). [para(1138(a,1),1124(a,1,2,1))]. given #1229 (H,wt=21): 1179 ((x * y) * T(y,x)) \ (y * (y * x)) = K(T(y,x),x * y). [para(1157(a,1),30(a,2,2)),flip(a)]. given #1230 (H,wt=21): 1197 K(x,y) * T(T(y,x),K(z,T(y,x))) = T(y,K(z,T(y,x))). [para(1196(a,1),1082(a,1,1))]. given #1231 (H,wt=15): 1343 T(x,K(y,T(x,z))) = K(z,x) * T(x,z). [para(1038(a,1),1197(a,1,2)),flip(a)]. given #1232 (H,wt=9): 1345 T(x,K(y,T(x,z))) = x. [para(1343(a,2),1077(a,1))]. given #1233 (H,wt=13): 1346 T(T(x,y),K(z,T(x,u))) = T(x,y). [para(1345(a,1),42(a,1,1)),flip(a)]. given #1234 (H,wt=21): 1208 L(x,y,T(z * u,z) / z) = L(x,y,T((z \ u) * z,z)). [para(138(a,1),1192(a,1,3,1))]. given #1235 (H,wt=18): 1350 L(x,y,T(z * u,z) / z) = L(x,y,R(u,z,z)). [para(1208(a,2),864(a,1))]. given #1236 (H,wt=21): 1242 K((T(x,y) \ (T(y,x) \ x)) \ 1,z) = T(K(y,z),T(x,y)). [para(1137(a,1),1240(a,1,1,1)),flip(a)]. given #1237 (H,wt=17): 1351 T(K(x,y),T(z,x)) = K((z \ (x \ z)) \ 1,y). [para(1186(a,1),1242(a,1,1,1)),flip(a)]. given #1238 (H,wt=13): 1352 T(K(x,y),T(z,x)) = T(K(x,y),z). [para(1351(a,2),1241(a,1))]. given #1239 (H,wt=17): 1353 T(x,y) * T(K(y,z),x) = K(y,z) * T(x,y). [para(1352(a,1),82(a,1,2))]. given #1240 (H,wt=17): 1354 K(x,y) * (K(y,z) * x) = K(y,z) * T(x,y). [para(1353(a,1),1172(a,2))]. given #1241 (H,wt=21): 1249 R(K(x,y),T(x,y) * z,u) \ 1 = R(K(y,x),x * z,u). [para(1098(a,1),906(a,1,2)),flip(a)]. given #1242 (H,wt=21): 1323 (x / T(y * x,y)) * T(x,R(y,x,y)) = R(y,x,y) \ x. [para(1321(a,1),1090(a,1,1,2))]. given #1243 (H,wt=19): 1356 ((x / y) / x) * T(x,R(y,x,y)) = R(y,x,y) \ x. [para(1237(a,1),1323(a,1,1))]. given #1244 (H,wt=21): 1337 (x * L(x \ 1,y,z)) \ u = x \ (L(x \ 1,y,z) \ u). [para(216(a,1),924(a,1,1))]. given #1245 (H,wt=21): 1338 L(x,y * (y * (z * (y * u))),w) = L(x,z \ (y \ u),w). [para(51(a,1),928(a,1,2))]. given #1246 (H,wt=17): 1358 L(x,y \ (z \ u),w) = L(x,y * (z * u),w). [para(1338(a,1),875(a,1))]. given #1247 (H,wt=17): 1360 L(x,y * (z \ u),w) = L(x,y * (z * u),w). [para(1358(a,1),876(a,1)),flip(a)]. given #1248 (H,wt=17): 1361 L(x,y * (z * (z * u)),w) = L(x,y * u,w). [para(19(a,1),1360(a,1,2,2)),flip(a)]. given #1249 (H,wt=21): 1341 T(x,y) \ T(T(x,y),y * x) = K(T(x,y),T(x,y) * y). [para(1245(a,1),1170(a,1,2))]. given #1250 (H,wt=17): 1364 K(T(x,y),T(x,y) * y) = K(T(x,y),y * x). [para(1341(a,1),1108(a,2)),flip(a)]. given #1251 (H,wt=21): 1342 (((x * y) * T(y,x)) \ (y * y)) * x = K(T(y,x),x * y). [para(1179(a,1),391(a,1)),flip(a)]. given #1252 (H,wt=19): 1365 (((x * y) * x) \ (x * x)) * y = K(T(x,y),y * x). [para(1087(a,1),1342(a,1,1,1))]. given #1253 (H,wt=13): 1366 K(T(x,y),y * x) = K(x,x * y). [para(1365(a,1),408(a,1))]. given #1254 (H,wt=14): 1367 R(x,y,x) \ T(x,y) = K(x,x * y). [para(1366(a,1),1340(a,2))]. given #1255 (H,wt=14): 1368 K(x,x * y) \ T(x,y) = R(x,y,x). [para(1367(a,1),734(a,1,1))]. given #1256 (H,wt=14): 1369 K(x * y,x) * T(x,y) = R(x,y,x). [para(1368(a,1),900(a,1)),flip(a)]. given #1257 (H,wt=14): 1370 R(x,y,x) / T(x,y) = K(x * y,x). [hyper(24,a,22,a,b,1369,a),flip(a)]. given #1258 (H,wt=21): 1357 L(x \ 1,y,z) \ (x \ u) = x \ (L(x \ 1,y,z) \ u). [para(1337(a,1),803(a,1)),flip(a)]. given #1259 (H,wt=21): 1362 L(x,(y \ z) * (z \ y),u) = L(x,(z \ y) * (y * z),u). [para(384(a,1),1360(a,1,2))]. given #1260 (H,wt=22): 961 R(x,y \ 1,y) \ a(x,y,y) = T(x \ 1,R(x,y \ 1,y)). [para(959(a,1),325(a,2,2)),flip(a)]. given #1261 (H,wt=15): 1372 R(x,y \ 1,y) \ a(x,y,y) = x \ 1. [para(961(a,2),476(a,1))]. given #1262 (H,wt=13): 1374 R(x,y,y) \ a(x,y,y) = x \ 1. [para(717(a,1),1372(a,1,1))]. given #1263 (H,wt=22): 1151 (x * y) \ (T(x,y) * (T(y,x) * z)) = L(z,T(y,x),T(x,y)). [para(1146(a,1),32(a,2,1)),flip(a)]. given #1264 (H,wt=18): 1375 (x * y) \ (x * (y * z)) = L(z,T(y,x),T(x,y)). [para(1168(a,1),1151(a,1,2))]. given #1265 (H,wt=13): 1376 L(x,T(y,z),T(z,y)) = L(x,y,z). [para(1375(a,1),32(a,2)),flip(a)]. given #1266 (H,wt=22): 1183 ((T(x,y) * z) * u) / ((x * z) * u) = R(K(x,y),x * z,u). [para(1160(a,1),34(a,2,1,1)),flip(a)]. given #1267 (H,wt=22): 1190 (K(x,y) * z) \ (y * (K(x,y) * z)) = L(T(y,z),z,K(x,y)). [para(1073(a,1),106(a,1,2))]. given #1268 (H,wt=16): 1377 L(T(x,y),y,K(z,x)) = T(x,K(z,x) * y). [para(1190(a,1),36(a,2)),flip(a)]. given #1269 (H,wt=22): 1195 (x * T(y,x)) \ (T(y,z) * x) = L(K(T(y,x),z),T(y,x),x). [para(1122(a,1),180(a,1,1)),flip(a)]. given #1270 (H,wt=22): 1371 (x \ (L(x \ 1,x,x / y) \ 1)) * (y \ (y / x)) = x \ 1. [para(1357(a,1),521(a,1,1))]. given #1271 (H,wt=22): 1378 (x \ (L(x \ 1,x,y * x) \ 1)) * (y \ (y / x)) = x \ 1. [para(1290(a,1),1371(a,1,1,2,1))]. given #1272 (H,wt=23): 794 L(x \ L(y \ z,y,u),x,u * y) = ((u \ y) * x) \ (u \ z). [para(776(a,1),275(a,1))]. given #1273 (H,wt=19): 1379 ((x \ y) * z) \ (x \ u) = ((x * y) * z) \ (x * u). [para(794(a,1),201(a,1))]. given #1274 (H,wt=19): 1380 (x * ((x \ y) * y)) \ z = ((x * y) * y) \ (x * z). [para(1379(a,1),893(a,2))]. given #1275 (H,wt=15): 1381 (x * ((x \ y) * y)) \ y = x \ (x / y). [para(1380(a,2),1296(a,1))]. given #1276 (H,wt=15): 1382 x / (y \ (y / x)) = y * ((y \ x) * x). [para(1381(a,1),65(a,1,2))]. given #1277 (H,wt=15): 1383 (x \ (x / y)) \ y = x * ((x \ y) * y). [para(1382(a,1),872(a,1)),flip(a)]. given #1278 (H,wt=16): 1384 x * L(x,y * x,y) = (y \ (y / x)) \ x. [para(1383(a,2),435(a,2))]. given #1279 (H,wt=18): 1385 (x * L(x,y * x,y)) / x = (y \ (y / x)) \ 1. [para(1384(a,2),320(a,1,1))]. given #1280 (H,wt=14): 1386 L(x,y * x,y) = (y \ (y / x)) \ 1. [para(1385(a,1),218(a,1)),flip(a)]. given #1281 (H,wt=14): 1387 x \ ((y \ (y / x)) \ 1) = a(y,x,x). [para(1386(a,1),452(a,1,2))]. given #1282 (H,wt=14): 1388 (x \ (x / y)) \ 1 = y * a(x,y,y). [para(1386(a,1),453(a,1))]. given #1283 (H,wt=16): 1390 (x \ (x / y)) \ z = (y * a(x,y,y)) * z. [para(1388(a,1),318(a,1,1)),flip(a)]. given #1284 (H,wt=17): 1392 L(x \ 1,x,y * x) \ 1 = x * a(y,x,x). [para(1292(a,2),1388(a,1,1))]. given #1285 (H,wt=18): 1393 (x \ (x * a(y,x,x))) * (y \ (y / x)) = x \ 1. [para(1392(a,1),1378(a,1,1,2))]. given #1286 (H,wt=14): 1394 a(x,y,y) * (x \ (x / y)) = y \ 1. [para(19(a,1),1393(a,1,1))]. given #1287 (H,wt=14): 1397 a(x,y,y) * (x / y) = x * (y \ 1). [para(1394(a,1),1254(a,1,2)),flip(a)]. given #1288 (H,wt=14): 1398 (x * (y \ 1)) / (x / y) = a(x,y,y). [hyper(24,a,22,a,b,1397,a),flip(a)]. given #1289 (H,wt=14): 1399 (x / y) * (y * (x \ 1)) = a(y,x,x). [para(1398(a,1),669(a,1)),flip(a)]. given #1290 (H,wt=13): 1400 a(x / y,y,y \ 1) = a(x,y,y). [para(1399(a,1),592(a,2))]. given #1291 (H,wt=20): 1391 K(x,(x * x) / (y \ (y / z))) = K(x,z * a(y,z,z)). [para(1388(a,1),492(a,2,2))]. given #1292 (H,wt=18): 1402 K(x,(y \ (y / z)) \ 1) = K(x,z * a(y,z,z)). [para(1391(a,1),492(a,1)),flip(a)]. given #1293 (H,wt=20): 1396 a(K(x,y),z,z) * (K(y,x) \ (K(y,x) / z)) = z \ 1. [para(905(a,1),1394(a,1,1))]. given #1294 (H,wt=20): 1403 a(K(x,y),z,z) * (K(x,y) * (K(y,x) / z)) = z \ 1. [para(900(a,1),1396(a,1,2))]. given #1295 (H,wt=20): 1404 K(x,y) * (a(K(x,y),z,z) * (K(y,x) / z)) = z \ 1. [para(1403(a,1),1253(a,1)),flip(a)]. given #1296 (H,wt=16): 1405 R(K(x,y),z,z) * (K(y,x) / z) = z \ 1. [para(1404(a,1),966(a,1)),flip(a)]. given #1297 (H,wt=21): 1389 (x \ 1) \ (L(x,x,y * x) \ 1) = a(y,x \ 1,x \ 1). [para(1293(a,2),1387(a,1,2,1))]. given #1298 (H,wt=19): 1406 x * (L(x,x,y * x) \ 1) = a(y,x \ 1,x \ 1). [para(1389(a,1),330(a,1)),flip(a)]. given #1299 (H,wt=17): 1407 a(x,y \ 1,y \ 1) = L(y,y,x * y) \ y. [para(1406(a,1),471(a,1))]. given #1300 (H,wt=17): 1408 a(x * y,y \ 1,y \ 1) = L(y,y,x) \ y. [para(1291(a,1),1407(a,2,1))]. given #1301 (H,wt=23): 813 (x * (y \ z)) \ (x * (y \ (z * u))) = L(L(u,z,y),y \ z,x). [para(798(a,1),32(a,2,2,2)),flip(a)]. given #1302 (H,wt=23): 853 ((x * y) * z) / (x * (y * z)) = (x * y) * (z / (x * (y * z))). [para(851(a,1),196(a,1,2))]. given #1303 (H,wt=18): 1410 (x * y) * (z / (x * (y * z))) = x \ R(x,y,z). [para(853(a,1),537(a,1))]. given #1304 (H,wt=13): 1411 L(x,y \ R(y,z,u),y * z) = x. [para(1410(a,1),852(a,1,2))]. given #1305 (H,wt=13): 1412 L(x,y * R(y,z,u),y * z) = x. [para(1411(a,1),876(a,1)),flip(a)]. given #1306 (H,wt=13): 1413 L(x,y * R(y,y * z,u),z) = x. [para(1412(a,1),774(a,1)),flip(a)]. given #1307 (H,wt=23): 1182 K(T(x,y \ 1),y) * (x * (y \ 1)) = y \ T(T(x,y \ 1),y). [para(326(a,1),1159(a,1,2))]. given #1308 (H,wt=21): 1414 K(T(x,y \ 1),y) * (x * (y \ 1)) = T(x,y) * (y \ 1). [para(1182(a,2),329(a,1))]. given #1309 (H,wt=11): 1415 K(T(x,y \ 1),y) = K(x,y). [hyper(24,a,1160,a,b,1414,a)]. given #1310 (H,wt=11): 1418 K(x / (y * y),y) = K(x,y). [para(1415(a,1),1221(a,1)),flip(a)]. given #1311 (H,wt=21): 1416 (x * (y \ 1)) / (T(x,y) * (y \ 1)) = K(y,T(x,y \ 1)). [para(1414(a,1),902(a,1,2))]. given #1312 (H,wt=11): 1419 K(x,T(y,x \ 1)) = K(x,y). [para(1416(a,1),1102(a,1))]. given #1313 (H,wt=11): 1423 K(x,y / (x * x)) = K(x,y). [para(1419(a,1),1220(a,1)),flip(a)]. given #1314 (H,wt=13): 1420 K(x \ 1,T(y,x)) = K(x \ 1,y). [para(156(a,1),1419(a,1,2,2))]. given #1315 (H,wt=13): 1421 T(x,T(y,x \ 1)) = x * K(x,y). [para(1419(a,1),1107(a,2,2))]. given #1316 (H,wt=11): 1426 T(x,T(y,x \ 1)) = T(x,y). [para(1421(a,2),1107(a,2)),flip(a)]. given #1317 (H,wt=11): 1428 T(x,y / (x * x)) = T(x,y). [para(1426(a,1),1222(a,1)),flip(a)]. given #1318 (H,wt=13): 1427 T(x \ 1,T(y,x)) = T(x \ 1,y). [para(156(a,1),1426(a,1,2,2))]. given #1319 (H,wt=14): 1424 K(x,R(y / x,x,x)) = K(x,y * x). [para(80(a,2),1423(a,1,2))]. given #1320 (H,wt=14): 1430 T(x,(y * x) * x) = T(x,R(y,x,x)). [para(34(a,2),1428(a,1,2)),flip(a)]. given #1321 (H,wt=21): 1425 ((x \ 1) * T(y,x)) / (x \ 1) = T(y,x) * K(x \ 1,y). [para(1420(a,1),1014(a,2,2))]. given #1322 (H,wt=19): 1432 (x \ T(y,x)) / (x \ 1) = T(y,x) * K(x \ 1,y). [para(318(a,1),1425(a,1,1))]. given #1323 (H,wt=15): 1433 T(x,y) * K(y \ 1,x) = T(x,y * y). [para(1432(a,1),486(a,1))]. given #1324 (H,wt=21): 1429 L(x,T(y,z),T(T(z,y \ 1),y)) = L(x,y,T(z,y \ 1)). [para(1426(a,1),1376(a,1,2))]. given #1325 (H,wt=21): 1434 L(x,T(y,z),T(T(z,y),y \ 1)) = L(x,y,T(z,y \ 1)). [para(42(a,1),1429(a,1,3))]. given #1326 (H,wt=23): 1297 L(x,y \ 1,T(y * z,y \ 1)) = L(x,(y * z) * z,y * z). [para(322(a,1),1282(a,1,2,2)),flip(a)]. given #1327 (H,wt=22): 1435 L(x,R(y,z,z),y * z) = L(x,y \ 1,T(y * z,y \ 1)). [para(1297(a,2),938(a,1)),flip(a)]. given #1328 (H,wt=20): 1436 L(x,R(y,z,z),y * z) = L(x,y,T(y * z,y \ 1)). [para(1435(a,2),887(a,1))]. given #1329 (H,wt=23): 1363 L(x,y * R(z,z * u,w),v5) = L(x,y * (R(z,u,w) \ 1),v5). [para(615(a,1),1361(a,1,2,2))]. given #1330 (H,wt=21): 1437 L(x,y * R(z,z * u,w),v5) = L(x,y * R(z,u,w),v5). [para(1363(a,2),1273(a,1))]. given #1331 (H,wt=11): 1438 L(x,y * R(y,z,u),z) = x. [para(1437(a,1),1413(a,1))]. given #1332 (H,wt=13): 1439 L(x,y * (z * R(z,y,u)),y) = x. [para(1438(a,1),303(a,1,1))]. given #1333 (H,wt=13): 1440 L(x,y \ R(y \ 1,z,u),z) = x. [para(318(a,1),1438(a,1,2))]. given #1334 (H,wt=13): 1442 a(x,x * (y * R(y,x,z)),u) = 1. [hyper(38,a,1439,a)]. given #1335 (H,wt=13): 1443 L(x,y * R(y \ 1,z,u),z) = x. [para(1440(a,1),876(a,1)),flip(a)]. given #1336 (H,wt=9): 1444 L(x,a(y,z,z),z) = x. [para(960(a,1),1443(a,1,2))]. given #1337 (H,wt=15): 1445 x / (a(y,x,x) \ 1) = x * a(y,x,x). [para(1444(a,1),145(a,1,2))]. given #1338 (H,wt=17): 1446 (x * a(y,x,x)) * z = x * (a(y,x,x) * z). [para(1444(a,1),74(a,1,2))]. given #1339 (H,wt=16): 1448 (x \ (x / y)) \ z = y * (a(x,y,y) * z). [para(1446(a,1),1390(a,2))]. given #1340 (H,wt=20): 1447 K(x,(y \ (y / z)) \ 1) = K(x,z / (a(y,z,z) \ 1)). [para(1445(a,2),1402(a,2,2))]. given #1341 (H,wt=21): 1441 (x * (y \ R(y,x,z))) * u = x * ((y \ R(y,x,z)) * u). [para(1438(a,1),888(a,1,2))]. given #1342 (H,wt=21): 1450 (x * (y \ R(y,x,z))) * u = x * (R(y,x,z) * (y \ u)). [para(532(a,1),1441(a,2,2))]. given #1343 (H,wt=23): 1409 (x * (y \ z)) \ (x * (y \ (z * u))) = L(L(u,z,y),y * z,x). [para(813(a,2),876(a,1))]. given #1344 (H,wt=23): 1431 L(x,T(y \ 1,z),T(T(z,y),y \ 1)) = L(x,y \ 1,T(z,y)). [para(1427(a,1),1376(a,1,2))]. given #1345 (H,wt=21): 1451 L(x,T(y,z),T(T(z,y),y \ 1)) = L(x,y \ 1,T(z,y)). [para(1431(a,1),1256(a,1)),flip(a)]. given #1346 (H,wt=17): 1452 L(x,y \ 1,T(z,y)) = L(x,y,T(z,y \ 1)). [para(1451(a,1),1434(a,1))]. given #1347 (H,wt=15): 1453 L(x,y,T(z,y \ 1)) = L(x,y,T(z,y)). [para(1452(a,1),887(a,1))]. given #1348 (H,wt=18): 1454 L(x,R(y,z,z),y * z) = L(x,y,T(y * z,y)). [para(1453(a,1),1436(a,2))]. given #1349 (H,wt=16): 1455 L(x,R(y,z,z),y * z) = L(x,y,y / z). [para(1454(a,2),1259(a,1))]. given #1350 (H,wt=16): 1456 L(x,R(y,z,z),y * z) = L(x,y,z * y). [para(1455(a,2),1290(a,1))]. given #1351 (H,wt=23): 1449 L(x * (a(y,x,x) * z),y * (y / x),y) = (y / x) \ (y * z). [para(1448(a,1),311(a,1,1))]. given #1352 (H,wt=24): 1141 L(T(x,y),y * K(x,y),T(x,y)) = (T(x,y) \ (y * K(x,y))) \ y. [para(1112(a,1),440(a,1,2)),flip(a)]. given #1353 (H,wt=18): 1457 L(T(x,y),y * K(x,y),T(x,y)) = (x \ y) \ y. [para(1187(a,1),1141(a,2,1))]. given #1354 (H,wt=24): 1150 (T(x,y) * (T(y,x) * z)) \ ((x * y) * z) = a(T(x,y),T(y,x),z). [para(1146(a,1),28(a,2,2,1)),flip(a)]. given #1355 (H,wt=20): 1458 (x * (y * z)) \ ((x * y) * z) = a(T(x,y),T(y,x),z). [para(1168(a,1),1150(a,1,1))]. given #1356 (H,wt=13): 1459 a(T(x,y),T(y,x),z) = a(x,y,z). [para(1458(a,1),28(a,2)),flip(a)]. given #1357 (H,wt=17): 1460 a(T(x,y),T(T(y,x),x),z) = a(x,T(y,x),z). [para(1131(a,1),1459(a,1,1))]. given #1358 (H,wt=24): 1167 ((T(x,y) * z) * u) / ((K(x,y) * z) * u) = R(x,K(x,y) * z,u). [para(1120(a,1),34(a,2,1,1)),flip(a)]. given #1359 (H,wt=24): 1180 (x * (x * y)) \ (T(x,y) * ((y * x) * z)) = L(z,y * x,T(x,y)). [para(1157(a,1),32(a,2,1)),flip(a)]. given #1360 (H,wt=24): 1209 (x * (R(y,z,u) * w)) / (R(T(y,x),z,u) * w) = T(x,R(y,z,u)). [para(46(a,2),1198(a,1,2,1))]. given #1361 (H,wt=24): 1298 x * K(L(y \ 1,y,x * y) \ 1,z) = (x / y) * (y * K(y,z)). [para(1268(a,2),1294(a,1,2))]. given #1362 (H,wt=20): 1462 x * K(y * a(x,y,y),z) = (x / y) * (y * K(y,z)). [para(1392(a,1),1298(a,1,2,1))]. given #1363 (H,wt=18): 1463 x * K(y * a(x,y,y),z) = (x / y) * T(y,z). [para(1107(a,2),1462(a,2,2))]. given #1364 (H,wt=24): 1355 (K(x,y) * T(z,x)) / L(z,K(x,y),K(z,x)) = K(z,x) * K(x,y). [para(1354(a,1),99(a,1,1))]. given #1365 (H,wt=24): 1461 x \ (y \ (y \ (T(y,x) * ((x * y) * z)))) = L(z,x * y,T(y,x)). [para(1180(a,1),443(a,1)),flip(a)]. given #1366 (H,wt=22): 1464 x \ (y \ (K(y,x) * ((x * y) * z))) = L(z,x * y,T(y,x)). [para(1127(a,1),1461(a,1,2,2))]. given #1367 (H,wt=18): 1465 x \ (y \ ((y * x) * z)) = L(z,x * y,T(y,x)). [para(1330(a,1),1464(a,1,2,2))]. given #1368 (H,wt=15): 1466 L(x,y * z,T(z,y)) = L(x,z * y,z). [para(1465(a,1),309(a,1))]. given #1369 (H,wt=13): 1467 L(x,y * z,z) = L(x,z * y,z). [para(1466(a,1),1300(a,1)),flip(a)]. given #1370 (H,wt=11): 1468 L(L(x,y,z),y * z,z) = x. [para(1467(a,2),303(a,1))]. given #1371 (H,wt=11): 1469 L(L(x,y * z,z),y,z) = x. [para(1467(a,2),308(a,1,1))]. given #1372 (H,wt=11): 1473 L(x,T(y,z),z) = L(x,y,z). [para(1468(a,1),314(a,1,1))]. given #1373 (H,wt=12): 1475 L(T(x,y),y,x) = T(x,y * x). [para(1473(a,1),1216(a,1))]. given #1374 (H,wt=11): 1479 T(x,y * x) = T(x,x * y). [para(1475(a,1),203(a,1))]. given #1375 (H,wt=13): 1470 x \ L(x,x * y,y) = a(y,x,x). [para(1467(a,2),452(a,1,2))]. given #1376 (H,wt=11): 1485 a(T(x,y),y,y) = a(x,y,y). [para(1470(a,1),1299(a,1)),flip(a)]. given #1377 (H,wt=13): 1471 L(x,y * (y / z),y) = L(x,z,y). [para(1467(a,1),877(a,1))]. given #1378 (H,wt=13): 1474 L(L(x,y,z * y),z,z * y) = x. [para(875(a,1),1469(a,1,1))]. given #1379 (H,wt=13): 1477 L(x,y,y / z) = L(x,y,y * z). [para(1473(a,1),1285(a,1)),flip(a)]. given #1380 (H,wt=13): 1481 T(x,x * y) * K(y * x,x) = x. [para(1479(a,1),1089(a,1,1))]. given #1381 (H,wt=11): 1489 K(x * y,y) = K(y * x,y). [hyper(23,a,1089,a,b,1481,a)]. given #1382 (H,wt=13): 1490 T(x * K(x * y,x),y * x) = x. [para(1489(a,1),1020(a,1,1,2))]. given #1383 (H,wt=11): 1493 T(x / (x / y),x * y) = y. [para(1144(a,2),1490(a,1,1))]. given #1384 (H,wt=13): 1491 x / (x / y) = y * K(x * y,y). [para(1489(a,2),1144(a,2,2))]. given #1385 (H,wt=12): 1496 R(x,y,x) = y / (y / T(x,y)). [para(1491(a,2),1325(a,1)),flip(a)]. given #1386 (H,wt=12): 1497 R(x,y,x) \ y = y / T(x,y). [para(1496(a,2),66(a,1,1))]. given #1387 (H,wt=14): 1476 K(x,y) * (x \ y) = y / L(x,y,x). [para(1473(a,1),1247(a,1,2)),flip(a)]. given #1388 (H,wt=14): 1480 K(x,y) * L(x,y,x) = T(x,x * y). [para(1479(a,1),955(a,2))]. given #1389 (H,wt=14): 1482 T(x,x * (y * x)) = T(x,R(y,x,x)). [para(1479(a,1),1430(a,1))]. given #1390 (H,wt=10): 1502 T(x,R(y,x,x)) = T(x,y). [para(1482(a,1),1136(a,1))]. given #1391 (H,wt=12): 1503 K(x,R(y,x,x)) = x \ T(x,y). [para(1502(a,1),1108(a,2,2))]. given #1392 (H,wt=10): 1504 K(x,R(y,x,x)) = K(x,y). [para(1503(a,2),1108(a,2)),flip(a)]. given #1393 (H,wt=11): 1505 K(x,y / x) = K(x,y * x). [para(1504(a,1),1424(a,1))]. given #1394 (H,wt=11): 1506 K(x,y * x) = K(x,x * y). [para(1505(a,1),1078(a,1))]. given #1395 (H,wt=14): 1488 L(x,x,x * y) = y \ (y / (x \ 1)). [para(1477(a,1),807(a,1))]. given #1396 (H,wt=14): 1492 R(x,y,x) / T(x,y) = K(y * x,x). [para(1489(a,2),1370(a,2))]. given #1397 (H,wt=14): 1500 K(x,y) = (y \ x) / (x / L(y,x,y)). [para(1476(a,1),902(a,1,2)),flip(a)]. given #1398 (H,wt=14): 1510 T(x,y) \ R(x,y,x) = K(y * x,x). [para(1492(a,1),693(a,1)),flip(a)]. given #1399 (H,wt=15): 1483 x \ L(x,y,x * y) = a(x * y,x,x). [para(875(a,1),1470(a,1,2))]. given #1400 (H,wt=15): 1487 L(x,y,y * x) = x * a(y * x,x,x). [para(454(a,1),1474(a,1,1))]. given #1401 (H,wt=15): 1494 T(x * y,x / (x / y)) = T(x * y,y). [para(1493(a,1),1131(a,1,2)),flip(a)]. given #1402 (H,wt=16): 1511 K(x,y) * (y \ R(y,x,y)) = K(x * y,y). [para(1510(a,1),1095(a,2))]. given #1403 (H,wt=17): 1484 x \ L(x,T(y,x),y * x) = a(y * x,x,x). [para(878(a,1),1470(a,1,2))]. given #1404 (H,wt=17): 1508 (T(x,y) \ y) * K(x,x * y) = T(y,x) / x. [para(1506(a,1),1260(a,1,2))]. given #1405 (H,wt=17): 1509 K(T(x,y),y * T(x,y)) = K(T(x,y),y * x). [para(1506(a,2),1364(a,1))]. given #1406 (H,wt=15): 1512 K(T(x,y),y * x) = K(T(x,y),x * y). [para(82(a,1),1509(a,1,2)),flip(a)]. given #1407 (H,wt=13): 1513 K(T(x,y),x * y) = K(x,x * y). [para(1512(a,1),1366(a,1))]. given #1408 (H,wt=18): 1499 ((x / y) / x) * T(x,R(y,x,y)) = x / T(y,x). [para(1497(a,1),1356(a,2))]. given #1409 (H,wt=19): 1472 L(x,(y * z) * z,y * z) = L(x,T(y,z),y * z). [para(1467(a,1),878(a,1))]. given #1410 (H,wt=18): 1514 L(x,R(y,z,z),y * z) = L(x,T(y,z),y * z). [para(1472(a,1),938(a,1)),flip(a)]. given #1411 (H,wt=15): 1515 L(x,T(y,z),y * z) = L(x,y,z * y). [para(1514(a,1),1456(a,1))]. given #1412 (H,wt=15): 1516 x \ L(x,y,x * y) = a(y * x,x,x). [para(1515(a,1),1484(a,1,2))]. given #1413 (H,wt=13): 1517 a(x * y,y,y) = a(y * x,y,y). [para(1516(a,1),1483(a,1))]. given #1414 (H,wt=19): 1486 L(x * (a(y,x,x) * z),x,y) = (y / x) \ (y * z). [para(1471(a,1),1449(a,1))]. given #1415 (H,wt=19): 1507 ((x * y) * y) \ ((y * x) * y) = K(y,y * (y * x)). [para(1506(a,1),1103(a,2))]. given #1416 (H,wt=15): 1519 K(x,y) = ((y * x) * x) \ ((x * y) * x). [para(1507(a,2),490(a,1)),flip(a)]. given #1417 (H,wt=19): 1518 L(x * (a(y,x,x) * z),x,y) = (x / y) * (y * z). [para(1486(a,2),358(a,1))]. given #1418 (H,wt=20): 1478 (x * T(y,x)) \ (T(y,z) * x) = L(K(T(y,x),z),y,x). [para(1473(a,1),1195(a,2))]. given #1419 (H,wt=18): 1521 (x * y) \ (T(x,z) * y) = L(K(T(x,y),z),x,y). [para(82(a,1),1478(a,1,1))]. given #1420 (H,wt=16): 1522 L(K(T(x,y),z),x,y) = T(K(x,z),x * y). [para(1521(a,1),1184(a,1))]. given #1421 (H,wt=21): 1495 (x / (x / y)) \ T(x * y,x / (x / y)) = y \ (x * y). [para(1493(a,1),1138(a,1,1)),flip(a)]. given #1422 (H,wt=19): 1523 (x / (x / y)) \ T(x * y,x / (x / y)) = T(x,y). [para(1495(a,2),36(a,2)),flip(a)]. given #1423 (H,wt=15): 1524 (x / (x / y)) \ T(x * y,y) = T(x,y). [para(1494(a,1),1523(a,1,2))]. given #1424 (H,wt=15): 1525 ((x / y) / x) * T(x * y,y) = T(x,y). [para(1524(a,1),358(a,1)),flip(a)]. given #1425 (H,wt=19): 1526 (x / y) * T(y * (x \ y),x \ y) = T(y,x \ y). [para(65(a,1),1525(a,1,1,1))]. given #1426 (H,wt=15): 1528 (x / y) * (y * (y / x)) = T(y,x \ y). [para(1239(a,1),1526(a,1,2))]. given #1427 (H,wt=11): 1529 T(x,x / y) = T(x,y \ x). [para(1528(a,1),369(a,1)),flip(a)]. given #1428 (H,wt=14): 1530 T(x,R(y,x,y)) = T(x,(x / y) \ x). [para(1529(a,1),1322(a,2))]. given #1429 (H,wt=10): 1531 T(x,R(y,x,y)) = T(x,y). [para(66(a,1),1530(a,2,2))]. given #1430 (H,wt=15): 1532 ((x / y) / x) * T(x,y) = x / T(y,x). [para(1531(a,1),1499(a,1,2))]. given #1431 (H,wt=21): 1520 (x * (y * x)) \ ((x * y) * x) = K(y * x,x) * K(x,y). [para(1519(a,2),941(a,1,2)),flip(a)]. given #1432 (H,wt=14): 1533 K(x * y,y) * K(y,x) = a(y,x,y). [para(1520(a,1),28(a,2)),flip(a)]. given #1433 (H,wt=14): 1534 K(x,y) * K(y * x,x) = a(x,y,x). [para(1533(a,1),1226(a,2))]. given #1434 (H,wt=14): 1535 K(x * y,x) * K(x,y) = a(x,y,x). [para(1489(a,1),1533(a,1,1))]. given #1435 (H,wt=14): 1536 K(x,y) * a(y,x,y) = K(x * y,y). [hyper(23,a,901,a,b,1534,a),flip(a)]. given #1436 (H,wt=11): 1539 x \ R(x,y,x) = a(x,y,x). [hyper(23,a,1511,a,b,1536,a),flip(a)]. given #1437 (H,wt=11): 1540 x * a(x,y,x) = R(x,y,x). [para(1539(a,1),20(a,1,2))]. given #1438 (H,wt=11): 1541 L(x,y,x) \ x = a(x,y,x). [para(1539(a,1),1320(a,2))]. given #1439 (H,wt=11): 1542 a(x,y,x) * L(x,y,x) = x. [para(1541(a,1),520(a,1,1))]. given #1440 (H,wt=14): 1537 K(x,y) * K(x * y,x) = a(x,y,x). [para(1489(a,1),1534(a,1,2))]. given #1441 (H,wt=16): 1538 (((x \ y) * x) / y) * K(x,y) = a(x,y,x). [para(982(a,2),1535(a,1,1))]. given #1442 (H,wt=21): 1543 (x * y) / L(L(y,z,y),a(y,z,y),x) = x * a(y,z,y). [para(1542(a,1),99(a,1,1,2))]. given #1443 (H,wt=22): 1498 (T(x,y) \ y) * K(T(x,y),T(x,y) * y) = R(x,y,x) \ y. [para(1497(a,2),1001(a,2))]. given #1444 (H,wt=22): 1544 (T(x,y) \ y) * K(T(x,y),y * T(x,y)) = R(x,y,x) \ y. [para(1506(a,2),1498(a,1,2))]. given #1445 (H,wt=20): 1545 (T(x,y) \ y) * K(T(x,y),x * y) = R(x,y,x) \ y. [para(82(a,1),1544(a,1,2,2))]. given #1446 (H,wt=18): 1546 (T(x,y) \ y) * K(x,x * y) = R(x,y,x) \ y. [para(1513(a,1),1545(a,1,2))]. given #1447 (H,wt=12): 1547 R(x,y,x) \ y = T(y,x) / x. [para(1546(a,1),1508(a,1))]. given #1448 (H,wt=11): 1548 T(x,y) / y = x / T(y,x). [para(1547(a,1),1497(a,1))]. given #1449 (H,wt=11): 1549 (x / T(y,x)) * y = T(x,y). [para(1548(a,1),22(a,1,1))]. given #1450 (H,wt=17): 1550 (x / y) * (y * K(x,y)) = T(x,y * K(x,y)). [para(1020(a,1),1549(a,1,1,2))]. given #1451 (H,wt=13): 1551 T(x,y) = (x / y) * (y * K(x,y)). [para(1550(a,2),1139(a,1)),flip(a)]. given #1452 (H,wt=13): 1552 (x / y) * T(y,x) = x * K(y,x). [hyper(23,a,359,a,b,1551,a(flip)),flip(a)]. given #1453 (H,wt=21): 1553 (x * (y \ 1)) * T(L(y,y,x),x) = x * K(L(y,y,x),x). [para(915(a,1),1552(a,1,1))]. given #1454 (H,wt=21): 1554 (x * (y \ 1)) * L(T(y,x),y,x) = x * K(L(y,y,x),x). [para(44(a,2),1553(a,1,2))]. given #1455 (H,wt=16): 1555 x * K(L(y,y,x),x) = x * (y \ T(y,x)). [para(1554(a,1),945(a,1))]. given #1456 (H,wt=14): 1556 x * K(L(y,y,x),x) = x * K(y,x). [para(1108(a,2),1555(a,2,2))]. given #1457 (H,wt=12): 1557 T(x * K(y,x),L(y,y,x)) = x. [para(1556(a,1),1020(a,1,1))]. given #1458 (H,wt=10): 1558 T(x,L(y,y,x)) = T(x,y). [para(1557(a,1),1023(a,1,1)),flip(a)]. given #1459 (H,wt=23): 1501 (x * y) / (K(x,y) * L(x,y,x)) = R(x,x * y,x) \ (x * y). [para(1480(a,2),1497(a,2,2)),flip(a)]. given #1460 (H,wt=21): 1559 (x * y) / (K(x,y) * L(x,y,x)) = L(x,y,x) \ (x * y). [para(1315(a,1),1501(a,2,1))]. given #1461 (H,wt=21): 1560 (x * y) / (K(x,y) * L(x,y,x)) = (L(x,y,x) \ x) * y. [para(1559(a,2),524(a,1))]. given #1462 (H,wt=18): 1561 (x * y) / T(x,x * y) = (L(x,y,x) \ x) * y. [para(1480(a,1),1560(a,1,2))]. given #1463 (H,wt=16): 1562 (L(x,y,x) \ x) * y = T(x * y,x) / x. [para(1561(a,1),1548(a,2)),flip(a)]. given #1464 (H,wt=14): 1563 T(x * y,x) / x = a(x,y,x) * y. [para(1541(a,1),1562(a,1,1)),flip(a)]. given #1465 (H,wt=25): 923 R(K(x,y),K(y,x) * z,u) \ K(x,y) = K(x,y) \ R(K(x,y),z,u). [para(901(a,1),618(a,1,2,2)),flip(a)]. given #1466 (H,wt=25): 957 x * (y * (R(y,y * (x \ 1),z) \ ((x \ 1) * z))) = L(z,y * x,y). [para(630(a,2),954(a,1,2,2))]. given #1467 (H,wt=23): 1565 x * (y * (R(y,y * (x \ 1),z) \ (x \ z))) = L(z,y * x,y). [para(318(a,1),957(a,1,2,2,2))]. given #1468 (H,wt=21): 1566 x * (R(y,x \ 1,z) * (y \ (x \ z))) = L(z,y * x,y). [para(637(a,1),1565(a,1,2))]. given #1469 (H,wt=19): 1567 x * (R(y,x,z) * (y \ (x \ z))) = L(z,y * x,y). [para(717(a,1),1566(a,1,2,1))]. given #1470 (H,wt=25): 1202 (R(x,y,z) * (K(x,u) * K(x,u))) / T(T(x,u),u) = x \ R(x,y,z). [para(1176(a,1),536(a,1,1,2))]. given #1471 (H,wt=25): 1210 (x * (y * (a(T(y,x),z,z) * u))) / (R(T(y,x),z,z) * u) = T(x,y). [para(966(a,1),1198(a,1,2))]. given #1472 (H,wt=25): 1264 K(x,T(y,z)) * T(T(y,x),K(x,T(y,z))) = K(z,T(y,x)) * T(y,z). [para(1193(a,1),82(a,2))]. given #1473 (H,wt=19): 1569 K(x,T(y,z)) * T(y,x) = K(z,T(y,x)) * T(y,z). [para(1346(a,1),1264(a,1,2))]. given #1474 (H,wt=25): 1336 ((T(x,y) * y) * z) / ((K(y,x) * (T(x,y) * y)) * z) = K(y,x) \ 1. [para(1335(a,1),344(a,2,1))]. given #1475 (H,wt=19): 1572 ((T(x,y) * y) * z) / ((x * y) * z) = K(y,x) \ 1. [para(1098(a,1),1336(a,1,2,1))]. given #1476 (H,wt=25): 1401 a(x * (y * y),y \ 1,(y \ 1) \ 1) = a(x * y,y \ 1,y \ 1). [para(400(a,1),1400(a,1,1))]. given #1477 (H,wt=21): 1574 a(x * (y * y),y \ 1,y) = a(x * y,y \ 1,y \ 1). [para(156(a,1),1401(a,1,3))]. given #1478 (H,wt=25): 1527 L(x,y,z * (((u / w) / u) * T(u,w))) = L(x,y,z * T(u * w,w)). [para(1525(a,1),868(a,1,3,2,2))]. given #1479 (H,wt=21): 1575 L(x,y,z * T(u * w,w)) = L(x,y,z * (u / T(w,u))). [para(1532(a,1),1527(a,1,3,2)),flip(a)]. given #1480 (H,wt=21): 1576 L(x,y,z * (T(u,w) / w)) = L(x,y,z * T(u * w,w)). [para(1548(a,2),1575(a,2,3,2)),flip(a)]. given #1481 (H,wt=25): 1564 R(K(x,y),K(y,x) * z,u) \ K(x,y) = K(y,x) * R(K(x,y),z,u). [para(923(a,2),900(a,1))]. given #1482 (H,wt=23): 1577 (R(K(x,y),z,u) \ 1) \ K(y,x) = K(x,y) * R(K(y,x),z,u). [para(904(a,1),1564(a,1,1))]. given #1483 (H,wt=21): 1578 R(K(x,y),z,u) * K(y,x) = K(x,y) * R(K(y,x),z,u). [para(1577(a,1),330(a,1)),flip(a)]. given #1484 (H,wt=25): 1568 R(x * (K(x,y) * K(x,y)),z,u) / T(T(x,y),y) = x \ R(x,z,u). [para(705(a,2),1202(a,1,1))]. given #1485 (H,wt=23): 1580 R(T(x,y) * K(x,y),z,u) / T(T(x,y),y) = x \ R(x,z,u). [para(1120(a,1),1568(a,1,1,1))]. given #1486 (H,wt=21): 1581 R(T(T(x,y),y),z,u) / T(T(x,y),y) = x \ R(x,z,u). [para(1121(a,1),1580(a,1,1,1))]. given #1487 (H,wt=21): 1582 T(T(x,y),y) \ R(T(T(x,y),y),z,u) = x \ R(x,z,u). [para(1581(a,1),478(a,1)),flip(a)]. given #1488 (H,wt=26): 764 (x * y) * T(L(y \ z,y,x),u) = (x * y) * T((x * y) \ (x * z),u). [para(232(a,1),139(a,1))]. given #1489 (H,wt=26): 765 (x * y) * R(L(y \ 1,y,x),z,u) = (x * y) * R((x * y) \ x,z,u). [para(472(a,1),224(a,1))]. given #1490 (H,wt=26): 766 L(R(x / (y \ 1),y,y),z,u) / y = (y \ 1) * L((y \ 1) \ x,z,u). [para(48(a,1),724(a,1,1))]. given #1491 (H,wt=21): 1585 (x \ 1) * L((x \ 1) \ y,z,u) = L(y * x,z,u) / x. [para(720(a,1),766(a,1,1,1)),flip(a)]. given #1492 (H,wt=19): 1586 (x \ 1) * L(x * y,z,u) = L(y * x,z,u) / x. [para(330(a,1),1585(a,1,2,1))]. given #1493 (H,wt=17): 1587 L(x * y,z,u) / y = y \ L(y * x,z,u). [para(1586(a,1),318(a,1))]. given #1494 (H,wt=21): 1588 (x \ y) \ L((x \ y) * x,z,u) = L(y,z,u) / (x \ y). [para(20(a,1),1587(a,1,1,1)),flip(a)]. given #1495 (H,wt=26): 1162 R(K(x,y),T(y,x) * z,u) \ 1 = ((T(y,x) * z) * u) / ((y * z) * u). [para(1098(a,1),344(a,1,2,1)),flip(a)]. given #1496 (H,wt=26): 1166 (x * ((K(x,y) * z) * u)) \ ((T(x,y) * z) * u) = a(x,K(x,y) * z,u). [para(1120(a,1),28(a,2,2,1)),flip(a)]. given #1497 (H,wt=26): 1189 (K(x,y) * (x \ z)) \ ((x \ K(x,y)) * (z * u)) = L(u,z,x \ K(x,y)). [para(1072(a,1),32(a,2,1)),flip(a)]. given #1498 (H,wt=26): 1583 (x * y) * T((x * y) \ (x * z),u) = (x * y) * L(T(y \ z,u),y,x). [para(44(a,2),764(a,1,2)),flip(a)]. given #1499 (H,wt=23): 1590 (x * y) * T((x * y) \ (x * z),u) = x * (y * T(y \ z,u)). [para(1583(a,2),74(a,1))]. given #1500 (H,wt=26): 1584 (x * y) * R((x * y) \ x,z,u) = (x * y) * L(R(y \ 1,z,u),y,x). [para(48(a,1),765(a,1,2)),flip(a)]. given #1501 (H,wt=23): 1591 (x * y) * R((x * y) \ x,z,u) = x * (y * R(y \ 1,z,u)). [para(1584(a,2),74(a,1))]. given #1502 (H,wt=21): 1592 (x * y) * R((x * y) \ x,z,u) = x * (y \ R(y,z,u)). [para(635(a,1),1591(a,2,2))]. given #1503 (H,wt=25): 1593 (x / y) * (y * R(((y \ x) * x) \ (y \ x),z,u)) = x \ R(x,z,u). [hyper(23,a,1274,a,b,1592,a(flip)),flip(a)]. given #1504 (H,wt=25): 1594 (x / y) * (y * R(((y * x) * x) \ (y * x),z,u)) = x \ R(x,z,u). [para(1379(a,1),1593(a,1,2,2,1))]. given #1505 (H,wt=21): 1595 (x / y) * (y * R(y \ (y / x),z,u)) = x \ R(x,z,u). [para(1296(a,1),1594(a,1,2,2,1))]. given #1506 (H,wt=25): 1596 ((x \ y) / y) * (y * R(y \ x,z,u)) = (x \ y) \ R(x \ y,z,u). [para(65(a,1),1595(a,1,2,2,1,2))]. given #1507 (H,wt=23): 1598 (x \ 1) * (y * R(y \ x,z,u)) = (x \ y) \ R(x \ y,z,u). [para(320(a,1),1596(a,1,1))]. given #1508 (H,wt=21): 1599 (x \ y) \ R(x \ y,z,u) = x \ (y * R(y \ x,z,u)). [para(1598(a,1),318(a,1))]. given #1509 (H,wt=21): 1601 (x * y) \ R(x * y,z,u) = x \ (y * R(y \ x,z,u)). [para(1599(a,1),750(a,1)),flip(a)]. given #1510 (H,wt=26): 1589 (K(x,y) * (x \ z)) \ (K(x,y) * (x \ (z * u))) = L(u,z,x \ K(x,y)). [para(1072(a,1),1189(a,1,2))]. given #1511 (H,wt=20): 1602 L(L(x,y,z),z * y,K(z,u)) = L(x,y,z \ K(z,u)). [para(1589(a,1),1409(a,1)),flip(a)]. given #1512 (H,wt=20): 1603 L(L(x,y,z),z * y,K(z,u)) = L(x,y,z * K(z,u)). [para(1602(a,2),776(a,1))]. given #1513 (H,wt=18): 1604 L(L(x,y,z),z * y,K(z,u)) = L(x,y,T(z,u)). [para(1107(a,2),1603(a,2,3))]. given #1514 (H,wt=22): 1605 L(L(x,y,z),z * y,T(z,u)) = L(x,z * (z * y),K(z,u)). [para(303(a,1),1604(a,1,1)),flip(a)]. given #1515 (H,wt=18): 1606 L(L(x,y,z),z * y,T(z,u)) = L(x,y,K(z,u)). [para(1605(a,2),875(a,1))]. given #1516 (H,wt=27): 701 (x * (y * x)) \ R(x * (z * x),u,w) = T(y,x) \ (x \ (R(z,u,w) * x)). [para(699(a,2),287(a,1,2))]. given #1517 (H,wt=25): 1608 (x * (y * x)) \ R(x * (z * x),u,w) = T(y,x) \ T(R(z,u,w),x). [para(36(a,2),701(a,2,2))]. given #1518 (H,wt=25): 1609 (x * (y * x)) \ R(x * (z * x),u,w) = T(y,x) \ R(T(z,x),u,w). [para(46(a,2),1608(a,2,2))]. given #1519 (H,wt=25): 1610 x \ ((y * x) * R((y * x) \ x,z,u)) = T(y,x) \ R(T(y,x),z,u). [para(1609(a,1),1601(a,1)),flip(a)]. given #1520 (H,wt=27): 1194 L(x,y,(z / (u * u)) * (u \ (z * (u \ 1)))) = L(x,y,K(z / (u * u),u)). [para(403(a,1),1119(a,1,3,2))]. given #1521 (H,wt=27): 1579 K(x,y) * R(K(y,x),T(x,y) * z,u) = R(K(y,x),x * z,u) \ K(y,x). [para(1249(a,1),1577(a,1,1)),flip(a)]. given #1522 (H,wt=27): 1611 L(x,y,z * (u \ (u \ (u \ (z * (u \ 1)))))) = L(x,y,K(z / (u * u),u)). [para(602(a,1),1194(a,1,3))]. given #1523 (H,wt=27): 1612 L(x,y,z * (u \ ((u \ (u \ z)) * (u \ 1)))) = L(x,y,K(z / (u * u),u)). [para(285(a,1),1611(a,1,3,2,2))]. given #1524 (H,wt=27): 1613 L(x,y,z * (u * ((u \ (u \ z)) * (u \ 1)))) = L(x,y,K(z / (u * u),u)). [para(1612(a,1),867(a,1)),flip(a)]. given #1525 (H,wt=23): 1614 L(x,y,K(z / (u * u),u)) = L(x,y,z * (u \ (z * (u \ 1)))). [para(265(a,1),1613(a,1,3,2)),flip(a)]. given #1526 (H,wt=23): 1615 L(x,y,K(z / (u * u),u)) = L(x,y,z * (u * (z * (u \ 1)))). [para(1614(a,2),867(a,1))]. given #1527 (H,wt=21): 1616 L(x,y,K(z / (u * u),u)) = L(x,y,z * T(z,u \ 1)). [para(347(a,1),1615(a,2,3,2))]. given #1528 (H,wt=19): 1617 L(x,y,K(z / (u * u),u)) = L(x,y,K(z,u \ 1)). [para(1616(a,2),1119(a,1))]. given #1529 (H,wt=15): 1618 L(x,y,K(z,u \ 1)) = L(x,y,K(z,u)). [para(1418(a,1),1617(a,1,3)),flip(a)]. given #1530 (H,wt=15): 1619 L(x,y,K(z,u \ 1)) = L(x,y,K(u,z)). [para(1618(a,2),909(a,1))]. given #1531 (H,wt=28): 90 (x * (y * (y * (z * u)))) \ ((x * (y * (y * z))) * u) = a(x,y * (y * z),u). [para(51(a,1),28(a,2,1,2)),flip(a)]. given #1532 (H,wt=28): 91 (x * (x * (y * (z * u)))) \ (((x * (x * y)) * z) * u) = a(x * (x * y),z,u). [para(51(a,1),28(a,2,1)),flip(a)]. given #1533 (H,wt=28): 473 R((x * y) / (x * z),u,w) * (x * z) = (x * z) * R(L(z \ y,z,x),u,w). [para(76(a,2),224(a,2,2,1))]. given #1534 (H,wt=28): 474 R(R(x / y,y,z),u,w) * (y * z) = (y * z) * R((y * z) \ (x * z),u,w). [para(80(a,2),224(a,1,1,1))]. given #1535 (H,wt=25): 1622 (x * y) * R((x * y) \ (z * y),u,w) = (R(z / x,u,w) * x) * y. [para(474(a,1),185(a,1))]. given #1536 (H,wt=25): 1623 (x * y) * R((x * y) \ (z * y),u,w) = (x * R(x \ z,u,w)) * y. [para(224(a,1),1622(a,2,1))]. given #1537 (H,wt=28): 832 (((x * y) * (y * x)) * z) \ (((x * y) * (y * x)) * (z * u)) = L(u,z,K(y,x)). [para(779(a,1),32(a,1)),flip(a)]. given #1538 (H,wt=28): 1214 ((x * y) * T((x * y) \ ((z * x) * y),u)) / ((z * x) * y) = K(R(z,x,y),u). [para(34(a,2),1211(a,2,1))]. given #1539 (H,wt=27): 1625 ((x * y) * T(R(T(z,x * y),x,y),u)) / ((z * x) * y) = K(R(z,x,y),u). [para(549(a,1),1214(a,1,1,2,1))]. given #1540 (H,wt=27): 1626 ((x * y) * R(T(T(z,x * y),u),x,y)) / ((z * x) * y) = K(R(z,x,y),u). [para(46(a,2),1625(a,1,1,2))]. given #1541 (H,wt=23): 1627 (R(T(x,y),z,u) * (z * u)) / ((x * z) * u) = K(R(x,z,u),y). [para(222(a,1),1626(a,1,1))]. given #1542 (H,wt=20): 1628 ((T(x,y) * z) * u) / ((x * z) * u) = K(R(x,z,u),y). [para(79(a,1),1627(a,1,1))]. given #1543 (H,wt=12): 1630 K(R(x,y,z),y) = K(y,x) \ 1. [para(1628(a,1),1572(a,1))]. given #1544 (H,wt=10): 1632 K(R(x,y,z),y) = K(x,y). [para(1630(a,2),897(a,1))]. given #1545 (H,wt=15): 1629 R(K(x,y),x * z,u) = K(R(x,z,u),y). [para(1628(a,1),1183(a,1)),flip(a)]. given #1546 (H,wt=15): 1634 K(R(x,x \ y,z),u) = R(K(x,u),y,z). [para(20(a,1),1629(a,1,2)),flip(a)]. given #1547 (H,wt=13): 1638 R(K(x,y),z,x) = K(L(x,z,x),y). [para(1313(a,1),1634(a,1,1)),flip(a)]. given #1548 (H,wt=15): 1637 K(R(x,x * y,z),u) = R(K(x,u),y,z). [para(629(a,1),1634(a,1,1))]. given #1549 (H,wt=16): 1633 T(x,R(y,x,z)) = (x * x) / (x * K(y,x)). [para(1632(a,1),1104(a,2,2,2))]. given #1550 (H,wt=10): 1642 T(x,R(y,x,z)) = T(x,y). [para(1633(a,2),1104(a,2)),flip(a)]. given #1551 (H,wt=15): 1643 R(x,y,z) * T(y,x) = y * R(x,y,z). [para(1642(a,1),82(a,1,2))]. given #1552 (H,wt=16): 1635 R(K(x,y),x * (z / (z * x)),u) = K(x,y). [para(450(a,1),1629(a,2,1))]. given #1553 (H,wt=12): 1648 R(K(x,y),K(x,z),u) = K(x,y). [para(1041(a,2),1635(a,1,2))]. given #1554 (H,wt=12): 1649 R(K(x,y),K(z,x),u) = K(x,y). [para(1648(a,1),908(a,1)),flip(a)]. given #1555 (H,wt=17): 1639 K(x,R(y,y * z,u)) = R(K(y,x),z,u) \ 1. [para(1637(a,1),897(a,1,1)),flip(a)]. given #1556 (H,wt=19): 1631 R(K(x,y),T(y,x) * z,u) \ 1 = K(R(y,z,u),x). [para(1628(a,1),1162(a,2))]. given #1557 (H,wt=19): 1636 R(K(x,y),T(x,y) * z,u) = K(R(T(x,y),z,u),y). [para(1105(a,1),1629(a,1,1))]. given #1558 (H,wt=17): 1652 R(K(x,y),T(x,y) * z,u) = K(R(x,z,u),y). [para(1636(a,2),1110(a,1))]. given #1559 (H,wt=17): 1653 R(K(x,y),y * z,u) = K(R(y,z,u),x) \ 1. [para(1652(a,1),1249(a,1,1)),flip(a)]. given #1560 (H,wt=15): 1654 R(K(x,y),y * z,u) = K(x,R(y,z,u)). [para(1653(a,2),897(a,1))]. given #1561 (H,wt=19): 1641 K(R(x,T(x,y) * z,u),y) = R(K(T(x,y),y),z,u). [para(1637(a,1),1110(a,1)),flip(a)]. given #1562 (H,wt=17): 1657 K(R(x,T(x,y) * z,u),y) = R(K(x,y),z,u). [para(1105(a,1),1641(a,2,1))]. given #1563 (H,wt=19): 1647 T(x,y) \ (x * R(y,x,z)) = T(R(y,x,z),T(x,y)). [para(1643(a,1),36(a,2,2)),flip(a)]. given #1564 (H,wt=17): 1658 T(R(x,y,z),T(y,x)) = K(x,y) * R(x,y,z). [para(1647(a,1),1093(a,1))]. given #1565 (H,wt=17): 1659 R(T(x,T(y,x)),y,z) = K(x,y) * R(x,y,z). [para(1658(a,1),46(a,2))]. given #1566 (H,wt=15): 1660 K(x,y) * R(x,y,z) = R(T(x,y),y,z). [para(1131(a,1),1659(a,1,1)),flip(a)]. given #1567 (H,wt=17): 1661 T(x,y) \ R(T(x,y),y,z) = x \ R(x,y,z). [para(1660(a,1),1171(a,1,2))]. given #1568 (H,wt=19): 1650 (K(x,y) * K(z,x)) * u = K(x,y) * (K(z,x) * u). [para(1649(a,1),79(a,1,1)),flip(a)]. given #1569 (H,wt=10): 1663 L(x,K(y,z),K(z,u)) = x. [hyper(23,a,74,a,b,1650,a),flip(a)]. given #1570 (H,wt=10): 1664 L(x,K(y,z),K(u,z)) = x. [para(1663(a,1),909(a,1)),flip(a)]. given #1571 (H,wt=10): 1665 L(x,K(y,z),K(u,y)) = x. [para(1664(a,1),921(a,1)),flip(a)]. given #1572 (H,wt=17): 1666 (K(x,y) * T(z,x)) / z = K(z,x) * K(x,y). [para(1665(a,1),1355(a,1,2))]. given #1573 (H,wt=19): 1651 R(K(x,y),T(y,x) * z,u) = K(R(y,z,u),x) \ 1. [para(1631(a,1),156(a,1,1)),flip(a)]. given #1574 (H,wt=17): 1667 R(K(x,y),T(y,x) * z,u) = K(x,R(y,z,u)). [para(1651(a,2),897(a,1))]. given #1575 (H,wt=21): 1640 R(K(x,y),K(x,z) * u,w) = K(R(x,T(x,z) * u,w),y). [para(1120(a,1),1637(a,1,1,2)),flip(a)]. given #1576 (H,wt=17): 1669 R(K(x,y),K(x,y) * z,u) = R(K(x,y),z,u). [para(1640(a,2),1657(a,1))]. given #1577 (H,wt=15): 1670 R(K(x,y),z,u) \ 1 = R(K(y,x),z,u). [para(1669(a,1),906(a,1)),flip(a)]. given #1578 (H,wt=15): 1672 K(x,R(y,y * z,u)) = R(K(x,y),z,u). [para(1670(a,1),1639(a,2))]. given #1579 (H,wt=21): 1671 R(K(x,y),z,u) \ K(x,y) = K(x,y) * R(K(y,x),z,u). [para(1670(a,1),543(a,1,2)),flip(a)]. given #1580 (H,wt=23): 1656 R(K(x,y),x * z,u) * K(y,x) = K(x,y) * K(y,R(x,z,u)). [para(1654(a,1),1578(a,2,2))]. given #1581 (H,wt=21): 1673 K(R(x,y,z),u) * K(u,x) = K(x,u) * K(u,R(x,y,z)). [para(1629(a,1),1656(a,1,1))]. given #1582 (H,wt=21): 1674 K(x,y) * K(R(y,z,u),x) = K(y,x) * K(x,R(y,z,u)). [para(1673(a,1),1226(a,2))]. given #1583 (H,wt=23): 1662 (x \ y) \ R(T(y / x,x),x,z) = (y / x) \ R(y / x,x,z). [para(84(a,1),1661(a,1,1))]. given #1584 (H,wt=21): 1675 (x / y) \ R(x / y,y,z) = (y \ x) \ R(y \ x,y,z). [para(84(a,1),1662(a,1,2,1)),flip(a)]. given #1585 (H,wt=21): 1676 (x \ y) \ R(x \ y,x,z) = (x / y) * R(y / x,x,z). [para(1675(a,1),358(a,1))]. given #1586 (H,wt=21): 1677 x \ (y * R(y \ x,x,z)) = (x / y) * R(y / x,x,z). [para(1676(a,1),1599(a,1)),flip(a)]. given #1587 (H,wt=23): 1668 R(K(x,y),y * z,u) \ K(x,y) = K(y,x) * K(x,R(y,z,u)). [para(1667(a,1),1579(a,1,2)),flip(a)]. given #1588 (H,wt=25): 1678 x \ ((y \ x) * R((y \ x) \ x,x,z)) = y * R((y \ x) / x,x,z). [para(65(a,1),1677(a,2,1))]. given #1589 (H,wt=21): 1679 x \ (R(y,x,z) * (y \ x)) = y * R((y \ x) / x,x,z). [para(225(a,1),1678(a,1,2))]. given #1590 (H,wt=19): 1680 x * R((x \ y) / y,y,z) = T(x \ R(x,y,z),y). [para(1679(a,1),539(a,1))]. given #1591 (H,wt=17): 1681 T(x \ R(x,y,z),y) = x * R(x \ 1,y,z). [para(320(a,1),1680(a,1,2,1)),flip(a)]. given #1592 (H,wt=15): 1683 T(x \ R(x,y,z),y) = x \ R(x,y,z). [para(1681(a,2),635(a,1))]. given #1593 (H,wt=17): 1684 (x * (y \ R(y,x,z))) / x = y \ R(y,x,z). [para(1683(a,1),105(a,1,1,2))]. given #1594 (H,wt=19): 1685 T(x \ R(x,y,z),x * (y * z)) = T(a(x,y,z),y). [para(1683(a,1),740(a,1,1))]. given #1595 (H,wt=11): 1687 T(a(x,y,z),y) = a(x,y,z). [para(1685(a,1),739(a,2)),flip(a)]. given #1596 (H,wt=13): 1688 a(x,y,z) * y = y * a(x,y,z). [para(1687(a,1),82(a,1,2)),flip(a)]. given #1597 (H,wt=14): 1690 T(x * y,x) / x = y * a(x,y,x). [para(1688(a,1),1563(a,2))]. given #1598 (H,wt=17): 1692 L(x,y,z * a(u,z,u)) = L(x,y,R(z,u,u)). [para(1690(a,1),1350(a,1,3))]. given #1599 (H,wt=19): 1689 a(x,y \ 1,z) * (y \ 1) = y \ a(x,y \ 1,z). [para(1687(a,1),326(a,1,2)),flip(a)]. given #1600 (H,wt=20): 1691 L(x,y,z * (T(u * z,u) / u)) = L(x,y,a(u,z,u)). [para(1690(a,2),774(a,1,3,2))]. given #1601 (H,wt=20): 1693 L(x,y,z * T((u * z) * u,u)) = L(x,y,a(u,z,u)). [para(1691(a,1),1576(a,1)),flip(a)]. given #1602 (H,wt=18): 1694 L(x,y,z * ((z * u) * u)) = L(x,y,a(u,z,u)). [para(758(a,1),1693(a,1,3,2))]. given #1603 (H,wt=15): 1695 L(x,y,a(z,u,u)) = L(x,y,a(u,z,u)). [para(1694(a,1),861(a,1)),flip(a)]. given #1604 (H,wt=28): 1620 (x * (x * (y * (z * u)))) \ ((x * (x * (y * z))) * u) = a(x * (x * y),z,u). [para(51(a,1),91(a,1,2,1))]. given #1605 (H,wt=28): 1621 (x * y) * R(L(y \ z,y,x),u,w) = (x * y) * R((x * y) \ (x * z),u,w). [para(473(a,1),224(a,1))]. given #1606 (H,wt=28): 1624 ((x * y) * ((y * x) * z)) \ (((x * y) * (y * x)) * (z * u)) = L(u,z,K(y,x)). [para(894(a,1),832(a,1,1))]. given #1607 (H,wt=28): 1696 (x * (x * (y * (z * u)))) \ (x * (x * ((y * z) * u))) = a(x * (x * y),z,u). [para(51(a,1),1620(a,1,2))]. given #1608 (H,wt=20): 1699 a(x * (x * y),z,u) = (y * (z * u)) \ ((y * z) * u). [para(1696(a,1),212(a,1))]. given #1609 (H,wt=13): 1700 a(x * (x * y),z,u) = a(y,z,u). [para(1699(a,2),28(a,2)),flip(a)]. given #1610 (H,wt=13): 1702 a(x \ y,z,u) = a(x * y,z,u). [para(20(a,1),1700(a,1,1,2)),flip(a)]. given #1611 (H,wt=13): 1703 a((x / y) * x,z,u) = a(y,z,u). [para(22(a,1),1700(a,1,1,2))]. given #1612 (H,wt=15): 1704 a(x * (y * x),z,u) = a(T(y,x),z,u). [para(82(a,1),1700(a,1,1,2))]. given #1613 (H,wt=15): 1708 a((x * x) / y,z,u) = a(y \ 1,z,u). [para(263(a,1),1700(a,1,1))]. given #1614 (H,wt=13): 1716 a((x * x) / y,z,u) = a(y,z,u). [para(1708(a,2),611(a,1))]. given #1615 (H,wt=13): 1717 a(x / (y * y),z,u) = a(x,z,u). [para(1716(a,1),612(a,1)),flip(a)]. given #1616 (H,wt=13): 1720 a(x * (y * y),z,u) = a(x,z,u). [para(21(a,1),1717(a,1,1)),flip(a)]. given #1617 (H,wt=15): 1711 a(K(x,y) * y,z,u) = a(T(y,x),z,u). [para(1077(a,1),1700(a,1,1,2))]. given #1618 (H,wt=13): 1724 a(T(T(x,y),y),z,u) = a(x,z,u). [para(985(a,1),1711(a,1,1)),flip(a)]. given #1619 (H,wt=15): 1712 a(x * T(x,y),z,u) = a(K(x,y),z,u). [para(1107(a,2),1700(a,1,1,2))]. given #1620 (H,wt=15): 1719 a(x * K(y,x),z,u) = a(T(x,y),z,u). [para(1104(a,2),1716(a,1,1)),flip(a)]. given #1621 (H,wt=15): 1722 a(x / (y \ 1),z,u) = a(x / y,z,u). [para(398(a,1),1717(a,1,1)),flip(a)]. given #1622 (H,wt=15): 1726 a(x / (x * y),z,u) = a(T(y,x),z,u). [para(1719(a,1),1022(a,2))]. given #1623 (H,wt=15): 1727 a((x \ 1) / y,z,u) = a(y / x,z,u). [para(1722(a,1),612(a,1)),flip(a)]. given #1624 (H,wt=16): 1721 a((x * y) * y,z,u) = a(R(x,y,y),z,u). [para(34(a,2),1717(a,1,1)),flip(a)]. given #1625 (H,wt=16): 1729 a(x * (y * x),x,x) = a(R(y,x,x),x,x). [para(1721(a,1),1517(a,1)),flip(a)]. given #1626 (H,wt=14): 1730 a(R(x,y,y),y,y) = a(T(x,y),y,y). [para(1729(a,1),1704(a,1))]. given #1627 (H,wt=12): 1731 a(R(x,y,y),y,y) = a(x,y,y). [para(1730(a,2),1485(a,1))]. given #1628 (H,wt=17): 1707 a((x \ y) * z,u,w) = a((x * y) * z,u,w). [para(89(a,1),1700(a,1,1)),flip(a)]. given #1629 (H,wt=17): 1718 a(R(x,x * y,z),u,w) = a(R(x,y,z),u,w). [para(616(a,1),1716(a,1,1))]. given #1630 (H,wt=19): 1709 a(x * L(x,y * x,y),z,u) = a(a(y,x,x),z,u). [para(453(a,2),1700(a,1,1,2))]. given #1631 (H,wt=18): 1734 a(x * ((x \ y) * y),z,u) = a(a(x,y,y),z,u). [para(435(a,1),1709(a,1,1))]. given #1632 (H,wt=19): 1710 a(R(x \ 1,y,y),z,u) = a(x * a(x,y,y),z,u). [para(960(a,1),1700(a,1,1,2)),flip(a)]. given #1633 (H,wt=17): 1735 a(R(x \ 1,y,y),z,u) = a(R(x,y,y),z,u). [para(963(a,1),1710(a,2,1))]. given #1634 (H,wt=19): 1732 R(R(x,y,y) \ 1,y,y) = R(x,y,y) \ a(x,y,y). [para(1731(a,1),967(a,2,2))]. given #1635 (H,wt=13): 1736 R(R(x,y,y) \ 1,y,y) = x \ 1. [para(1732(a,2),1374(a,1))]. given #1636 (H,wt=16): 1737 R((x * y) \ 1,y,y) = (x / (y \ 1)) \ 1. [para(720(a,1),1736(a,1,1,1))]. given #1637 (H,wt=14): 1739 R((x * y) \ 1,y,y) = (y \ 1) / x. [para(1737(a,2),343(a,1))]. given #1638 (H,wt=14): 1740 (x \ 1) / (y / x) = R(y \ 1,x,x). [para(22(a,1),1739(a,1,1,1)),flip(a)]. given #1639 (H,wt=16): 1742 R(x \ 1,y,y) \ 1 = (x / y) / (y \ 1). [para(1740(a,1),343(a,1,1))]. given #1640 (H,wt=14): 1744 R(x,x * y,y) = (x / y) / (y \ 1). [para(1742(a,1),633(a,2))]. given #1641 (H,wt=19): 1741 (((x * y) \ 1) * y) * y = ((y \ 1) / x) * (y * y). [para(1739(a,1),79(a,1,1)),flip(a)]. given #1642 (H,wt=17): 1746 (((x * y) \ 1) * y) * y = T(y / x,y * y). [para(1741(a,2),294(a,1))]. given #1643 (H,wt=15): 1747 T(x / y,x * x) = ((y * x) \ x) * x. [para(318(a,1),1746(a,1,1)),flip(a)]. given #1644 (H,wt=17): 1748 L(x,y * z,R(T(z / y,z * z),u,w)) = x. [para(1747(a,2),847(a,1,3,1))]. given #1645 (H,wt=13): 1749 L(x,y * z,R(z / y,u,w)) = x. [para(1748(a,1),858(a,1)),flip(a)]. given #1646 (H,wt=16): 1750 L(x,y * (z \ 1),u / (y * (z * u))) = x. [para(350(a,1),1749(a,1,3))]. given #1647 (H,wt=14): 1752 L(x,y * z,u / (y * (z * u))) = x. [para(1750(a,1),1273(a,1)),flip(a)]. given #1648 (H,wt=20): 1705 a((x * y) * (x * (y * z)),u,w) = a(L(z,y,x),u,w). [para(74(a,1),1700(a,1,1,2))]. given #1649 (H,wt=20): 1728 a(x / T(y * x,y),z,u) = a(T(R(y,x,y),x),z,u). [para(1321(a,1),1726(a,1,1,2))]. given #1650 (H,wt=18): 1754 a(T(R(x,y,x),y),z,u) = a((y / x) / y,z,u). [para(1237(a,1),1728(a,1,1)),flip(a)]. given #1651 (H,wt=21): 1706 a(x * ((x \ y) * z),u,w) = a(x * ((x * y) * z),u,w). [para(89(a,1),1700(a,1,1,2)),flip(a)]. given #1652 (H,wt=18): 1755 a(x * ((x * y) * y),z,u) = a(a(x,y,y),z,u). [para(1706(a,1),1734(a,1))]. given #1653 (H,wt=21): 1714 a(K(x \ 1,x * y),z,u) = a(x \ ((x * y) \ y),z,u). [para(1126(a,2),1702(a,2,1)),flip(a)]. given #1654 (H,wt=21): 1715 a((x * (x * y)) * (x * z),u,w) = a(y \ (x \ z),u,w). [para(282(a,1),1703(a,1,1,1))]. given #1655 (H,wt=21): 1756 a(x * (x * (y * (x * z))),u,w) = a(y \ (x \ z),u,w). [para(51(a,1),1715(a,1,1))]. given #1656 (H,wt=17): 1757 a(x \ (y \ z),u,w) = a(x * (y * z),u,w). [para(1756(a,1),1700(a,1))]. given #1657 (H,wt=17): 1759 a(x * (y \ z),u,w) = a(x * (y * z),u,w). [para(1757(a,1),1702(a,1)),flip(a)]. given #1658 (H,wt=21): 1760 a(K(x \ 1,x * y),z,u) = a(x * ((x * y) * y),z,u). [para(1757(a,1),1714(a,2))]. given #1659 (H,wt=22): 1733 R(R(x,y,y),R(x,y,y) * y,y) = a(x,y,y) \ R(x,y,y). [para(1731(a,1),968(a,2,1))]. given #1660 (H,wt=14): 1761 R(R(x,y,y),R(x,y,y) * y,y) = x. [para(1733(a,2),964(a,1))]. given #1661 (H,wt=13): 1762 R(K(R(x,y,y),z),y,y) = K(x,z). [para(1761(a,1),1637(a,1,1)),flip(a)]. given #1662 (H,wt=16): 1763 K(R(x,y,y),z) * (y \ 1) = K(x,z) / y. [para(1762(a,1),718(a,1,1)),flip(a)]. given #1663 (H,wt=16): 1764 K(x,R(y,z,z)) * (K(y,x) / z) = z \ 1. [hyper(23,a,901,a,b,1763,a),flip(a)]. given #1664 (H,wt=13): 1765 R(K(x,y),z,z) = K(x,R(y,z,z)). [hyper(24,a,1405,a,b,1764,a),flip(a)]. given #1665 (H,wt=15): 1766 K(R(x,y,y),z) \ 1 = R(K(z,x),y,y). [para(1765(a,2),897(a,2))]. given #1666 (H,wt=15): 1767 K(x,R(y,z,z)) * 1 = R(K(x,y),z,z). [para(1766(a,1),900(a,1)),flip(a)]. given #1667 (H,wt=22): 1743 a((x \ 1) / ((y / x) \ 1),z,u) = a(R(y \ 1,x,x),z,u). [para(1740(a,1),1722(a,2,1))]. given #1668 (H,wt=20): 1768 a((x \ 1) / (x / y),z,u) = a(R(y \ 1,x,x),z,u). [para(343(a,1),1743(a,1,1,2))]. given #1669 (H,wt=18): 1769 a(R(x \ 1,y,y),z,u) = a((y / x) / y,z,u). [para(1768(a,1),1727(a,1))]. given #1670 (H,wt=16): 1770 a((x / y) / x,z,u) = a(R(y,x,x),z,u). [para(1769(a,1),1735(a,1))]. given #1671 (H,wt=17): 1771 a(T(R(x,y,x),y),z,u) = a(R(x,y,y),z,u). [para(1770(a,1),1754(a,2))]. given #1672 (H,wt=17): 1772 a(R(T(x,y),y,x),z,u) = a(R(x,y,y),z,u). [para(46(a,2),1771(a,1,1))]. given #1673 (H,wt=23): 1753 x / ((y * z) \ (y * (z * x))) = (x / (y * (z * x))) * (y * z). [para(1752(a,1),205(a,1,2))]. given #1674 (H,wt=18): 1773 (x / (y * (z * x))) * (y * z) = x / L(x,z,y). [para(32(a,2),1753(a,1,2)),flip(a)]. given #1675 (H,wt=18): 1774 (x / (y * (z * x))) * (y * z) = L(x,z,y) \ x. [para(1773(a,2),519(a,1))]. given #1676 (H,wt=24): 1723 ((x * (y * y)) * (z * u)) \ (((x * (y * y)) * z) * u) = a(x,z,u). [para(1720(a,1),28(a,1)),flip(a)]. given #1677 (H,wt=24): 1776 (x * (y * (y * (z * u)))) \ (((x * (y * y)) * z) * u) = a(x,z,u). [para(411(a,1),1723(a,1,1))]. given #1678 (H,wt=24): 1777 (x * (y * (y * (z * u)))) \ ((x * (y * (y * z))) * u) = a(x,z,u). [para(411(a,1),1776(a,1,2,1))]. given #1679 (H,wt=13): 1778 a(x,y * (y * z),u) = a(x,z,u). [para(1777(a,1),90(a,1)),flip(a)]. given #1680 (H,wt=13): 1779 a(x,y \ z,u) = a(x,y * z,u). [para(20(a,1),1778(a,1,2,2)),flip(a)]. given #1681 (H,wt=13): 1780 a(x,(y / z) * y,u) = a(x,z,u). [para(22(a,1),1778(a,1,2,2))]. given #1682 (H,wt=15): 1783 a(x,K(y,z) * T(y,z),u) = a(x,y,u). [para(1081(a,2),1778(a,1,2,2))]. given #1683 (H,wt=13): 1789 a(x,T(T(y,z),z),u) = a(x,y,u). [para(1113(a,1),1783(a,1,2))]. given #1684 (H,wt=13): 1790 a(T(x,y),y,z) = a(x,T(y,x),z). [para(1789(a,1),1460(a,1))]. given #1685 (H,wt=15): 1788 a(x,T(y * z,y),u) = a(x,z / y,u). [para(1232(a,2),1780(a,1,2))]. given #1686 (H,wt=17): 1781 a(x,(y \ z) * u,w) = a(x,(y * z) * u,w). [para(89(a,1),1778(a,1,2)),flip(a)]. given #1687 (H,wt=17): 1782 a(x,T(y,y * z),u) = a(x,(y \ z) * z,u). [para(250(a,1),1778(a,1,2,2)),flip(a)]. given #1688 (H,wt=17): 1792 a(x,T(y,y * z),u) = a(x,(y * z) * z,u). [para(1782(a,2),1781(a,1))]. given #1689 (H,wt=19): 1786 a(x,y \ 1,z) * (y \ 1) = y \ a(x,y * 1,z). [para(1779(a,1),1689(a,2,2))]. given #1690 (H,wt=17): 1793 a(x,y \ 1,z) * (y \ 1) = y \ a(x,y,z). [para(18(a,1),1786(a,2,2,2))]. given #1691 (H,wt=17): 1794 a(x,y * 1,z) * (y \ 1) = y \ a(x,y,z). [para(1779(a,1),1793(a,1,1))]. given #1692 (H,wt=15): 1795 a(x,y,z) * (y \ 1) = y \ a(x,y,z). [para(18(a,1),1794(a,1,1,2))]. given #1693 (H,wt=21): 1785 a(x * (y * y),y * 1,y) = a(x * y,y \ 1,y \ 1). [para(1779(a,1),1574(a,1))]. given #1694 (H,wt=19): 1796 a(x * (y * y),y,y) = a(x * y,y \ 1,y \ 1). [para(18(a,1),1785(a,1,2))]. given #1695 (H,wt=15): 1797 a(x * y,y \ 1,y \ 1) = a(x,y,y). [para(1796(a,1),1720(a,1))]. given #1696 (H,wt=11): 1798 L(x,x,y) \ x = a(y,x,x). [para(1797(a,1),1408(a,1)),flip(a)]. given #1697 (H,wt=11): 1800 a(x,y,y) * L(y,y,x) = y. [para(1798(a,1),520(a,1,1))]. given #1698 (H,wt=13): 1801 R(x,y,y) * L(y,y,x) = x * y. [para(1800(a,1),966(a,1,2)),flip(a)]. given #1699 (H,wt=18): 1802 T(R(x,y,y),L(y,y,x)) = L(y,y,x) \ (x * y). [para(1801(a,1),36(a,2,2))]. given #1700 (H,wt=18): 1803 R(T(x,L(y,y,x)),y,y) = L(y,y,x) \ (x * y). [para(1802(a,1),46(a,2))]. given #1701 (H,wt=15): 1804 L(x,x,y) \ (y * x) = R(T(y,x),x,x). [para(1558(a,1),1803(a,1,1)),flip(a)]. given #1702 (H,wt=21): 1787 a(x,(y * (y * z)) * (y * u),w) = a(x,z \ (y \ u),w). [para(282(a,1),1780(a,1,2,1))]. given #1703 (H,wt=21): 1805 a(x,y * (y * (z * (y * u))),w) = a(x,z \ (y \ u),w). [para(51(a,1),1787(a,1,2))]. given #1704 (H,wt=17): 1806 a(x,y \ (z \ u),w) = a(x,y * (z * u),w). [para(1805(a,1),1778(a,1))]. given #1705 (H,wt=17): 1808 a(x,y * (z \ u),w) = a(x,y * (z * u),w). [para(1806(a,1),1779(a,1)),flip(a)]. given #1706 (H,wt=26): 1713 ((x \ y) * (T(x,x * y) * z)) \ (y * z) = a(x * y,T(x,x * y),z). [para(1702(a,1),255(a,2))]. given #1707 (H,wt=22): 1809 a(x * y,T(x,x * y),z) = ((y / x) * (x * z)) \ (y * z). [para(1265(a,1),1713(a,1,1)),flip(a)]. given #1708 (H,wt=17): 1810 a(x * y,T(x,x * y),z) = a(y / x,x,z). [para(1809(a,2),68(a,1))]. given #1709 (H,wt=26): 1745 K(R(x,x * y,y),z) * (x / y) = (y \ 1) * T((y \ 1) \ (x / y),z). [para(1744(a,2),1201(a,1,1,1))]. given #1710 (H,wt=24): 1811 R(K(x,y),z,z) * (x / z) = (z \ 1) * T((z \ 1) \ (x / z),y). [para(1637(a,1),1745(a,1,1))]. given #1711 (H,wt=24): 1812 K(x,R(y,z,z)) * (x / z) = (z \ 1) * T((z \ 1) \ (x / z),y). [para(1765(a,1),1811(a,1,1))]. given #1712 (H,wt=22): 1813 K(x,R(y,z,z)) * (x / z) = (z \ 1) * T(z * (x / z),y). [para(330(a,1),1812(a,2,2,1))]. given #1713 (H,wt=20): 1814 K(x,R(y,z,z)) * (x / z) = z \ T(z * (x / z),y). [para(1813(a,2),318(a,1))]. given #1714 (H,wt=16): 1815 K(x,R(y,z,z)) * (x / z) = T(x,y) / z. [para(1814(a,2),755(a,1))]. given #1715 (H,wt=27): 1725 a((x / (y * y)) * (y \ (x * (y \ 1))),z,u) = a(K(x / (y * y),y),z,u). [para(403(a,1),1712(a,1,1,2))]. given #1716 (H,wt=27): 1816 a(x * (y \ (y \ (y \ (x * (y \ 1))))),z,u) = a(K(x / (y * y),y),z,u). [para(602(a,1),1725(a,1,1))]. given #1717 (H,wt=27): 1817 a(x * (y \ ((y \ (y \ x)) * (y \ 1))),z,u) = a(K(x / (y * y),y),z,u). [para(285(a,1),1816(a,1,1,2,2))]. given #1718 (H,wt=27): 1818 a(x * (y * ((y \ (y \ x)) * (y \ 1))),z,u) = a(K(x / (y * y),y),z,u). [para(1817(a,1),1759(a,1)),flip(a)]. given #1719 (H,wt=23): 1819 a(K(x / (y * y),y),z,u) = a(x * (y \ (x * (y \ 1))),z,u). [para(265(a,1),1818(a,1,1,2)),flip(a)]. given #1720 (H,wt=23): 1820 a(K(x / (y * y),y),z,u) = a(x * (y * (x * (y \ 1))),z,u). [para(1819(a,2),1759(a,1))]. given #1721 (H,wt=21): 1821 a(K(x / (y * y),y),z,u) = a(x * T(x,y \ 1),z,u). [para(347(a,1),1820(a,2,1,2))]. given #1722 (H,wt=19): 1822 a(K(x / (y * y),y),z,u) = a(K(x,y \ 1),z,u). [para(1821(a,2),1712(a,1))]. given #1723 (H,wt=15): 1823 a(K(x,y \ 1),z,u) = a(K(x,y),z,u). [para(1418(a,1),1822(a,1,1)),flip(a)]. given #1724 (H,wt=15): 1824 a(K(x \ 1,y),z,u) = a(K(y,x),z,u). [para(1823(a,1),905(a,1)),flip(a)]. given #1725 (H,wt=19): 1825 a(x * ((x * y) * y),z,u) = a(K(x * y,x),z,u). [para(1824(a,1),1760(a,1)),flip(a)]. given #1726 (H,wt=16): 1826 a(K(x * y,x),z,u) = a(a(x,y,y),z,u). [para(1825(a,1),1755(a,1))]. given #1727 (H,wt=28): 1697 (x * y) * R((x * y) \ (x * z),u,w) = (x * y) * L(R(y \ z,u,w),y,x). [para(48(a,1),1621(a,1,2)),flip(a)]. given #1728 (H,wt=25): 1827 (x * y) * R((x * y) \ (x * z),u,w) = x * (y * R(y \ z,u,w)). [para(1697(a,2),74(a,1))]. given #1729 (H,wt=25): 1828 (x * y) * R((x * y) \ z,u,w) = x * (y * R(y \ (x \ z),u,w)). [para(20(a,1),1827(a,1,2,1,2))]. given #1730 (H,wt=21): 1829 (x * y) * R((x * y) \ y,z,u) = R(x,z,u) * (x \ y). [para(1828(a,2),639(a,1))]. given #1731 (H,wt=21): 1830 T(x,y) \ R(T(x,y),z,u) = y \ (R(x,z,u) * (x \ y)). [para(1829(a,1),1610(a,1,2)),flip(a)]. given #1732 (H,wt=19): 1831 T(x,y) \ R(T(x,y),z,u) = T(x \ R(x,z,u),y). [para(1830(a,2),539(a,1))]. given #1733 (H,wt=15): 1833 T(x \ R(x,y,y),z) = a(T(x,z),y,y). [para(1831(a,1),962(a,1))]. given #1734 (H,wt=13): 1836 a(T(x,y),z,z) = T(a(x,z,z),y). [para(962(a,1),1833(a,1,1)),flip(a)]. given #1735 (H,wt=19): 1835 T(T(x,y) \ R(T(x,y),z,u),y) = x \ R(x,z,u). [para(1831(a,1),1582(a,1))]. given #1736 (H,wt=17): 1837 T(T(x \ R(x,y,z),u),u) = x \ R(x,y,z). [para(1831(a,1),1835(a,1,1))]. given #1737 (H,wt=17): 1839 T(a(x,y,z),x * (y * z)) = x \ R(x,y,z). [para(739(a,2),1837(a,1,1))]. given #1738 (H,wt=19): 1838 (x * (y \ R(y,z,u))) / x = T(y \ R(y,z,u),x). [para(1837(a,1),105(a,1,1,2))]. given #1739 (H,wt=21): 1834 K(x,y) * R(T(y,x),z,u) = y * T(y \ R(y,z,u),x). [para(1831(a,1),1099(a,1,2)),flip(a)]. given #1740 (H,wt=22): 1840 a(x,y,z) * K(a(x,y,z),x * (y * z)) = x \ R(x,y,z). [para(1839(a,1),1107(a,1)),flip(a)]. given #1741 (H,wt=23): 1832 (R(T(x,y),z,u) \ T(x,y)) * w = T(x \ R(x,z,u),y) \ w. [para(1831(a,1),465(a,1,1)),flip(a)]. given #1742 (H,wt=23): 1841 T(T(x \ R(x,y,z),u),x * (y * z)) = (u * a(x,y,z)) / u. [para(1838(a,1),742(a,1,1))]. given #1743 (H,wt=15): 1843 (x * a(y,z,u)) / x = T(a(y,z,u),x). [para(1841(a,1),740(a,1))]. given #1744 (H,wt=17): 1844 T(a(x,y,z),u) * (u / (u * a(x,y,z))) = 1. [para(1843(a,1),354(a,1,1))]. given #1745 (H,wt=15): 1846 K(a(x,y,z),u) * K(a(x,y,z),u) = 1. [para(1844(a,1),1174(a,1)),flip(a)]. given #1746 (H,wt=13): 1847 K(a(x,y,z),u) = K(u,a(x,y,z)). [hyper(24,a,898,a,b,1846,a)]. given #1747 (H,wt=22): 1848 a(x,y,z) * K(x * (y * z),a(x,y,z)) = x \ R(x,y,z). [para(1847(a,1),1840(a,1,2))]. given #1748 (H,wt=26): 1842 (x * (y \ R(y,z,u))) / x = (y \ R(y,z,u)) * K(y \ R(y,z,u),x). [para(1838(a,2),1107(a,1))]. given #1749 (H,wt=17): 1849 K(x \ R(x,y,z),u) = K(u,x \ R(x,y,z)). [hyper(23,a,1014,a(flip),b,1842,a(flip))]. given #1750 (H,wt=28): 1698 ((x * y) * ((y * x) * z)) \ ((x * y) * ((y * x) * (z * u))) = L(u,z,K(y,x)). [para(894(a,1),1624(a,1,2))]. given #1751 (H,wt=22): 1850 L(L(x,y,z * u),(z * u) * y,u * z) = L(x,y,K(z,u)). [para(1698(a,1),174(a,1)),flip(a)]. given #1752 (H,wt=29): 749 ((x * (x * y)) * a(x * (x * y),z,u)) / y = a(x * (x * y),z,u) * (x * x). [para(747(a,1),418(a,1,1))]. given #1753 (H,wt=25): 1851 ((x * (x * y)) * a(y,z,u)) / y = a(x * (x * y),z,u) * (x * x). [para(1700(a,1),749(a,1,1,2))]. given #1754 (H,wt=25): 1852 (x * (x * (y * a(y,z,u)))) / y = a(x * (x * y),z,u) * (x * x). [para(51(a,1),1851(a,1,1))]. given #1755 (H,wt=25): 1854 a(x * (x * y),z,u) * (x * x) = x * (x * ((y * a(y,z,u)) / y)). [para(1852(a,1),211(a,1))]. given #1756 (H,wt=21): 1855 a(x * (x * y),z,u) * (x * x) = x * (x * a(y,z,u)). [para(748(a,1),1854(a,2,2,2))]. given #1757 (H,wt=17): 1856 a(x,y,z) * (u * u) = u * (u * a(x,y,z)). [para(1700(a,1),1855(a,1,1))]. given #1758 (H,wt=27): 1857 T((a(x,y,z) * (u * u)) / (u * u),u) = T(u \ (u * a(x,y,z)),u \ 1). [para(1856(a,2),666(a,1,1,1))]. given #1759 (H,wt=19): 1859 T(x \ (x * a(y,z,u)),x \ 1) = T(a(y,z,u),x). [para(21(a,1),1857(a,1,1)),flip(a)]. given #1760 (H,wt=15): 1860 T(a(x,y,z),u \ 1) = T(a(x,y,z),u). [para(19(a,1),1859(a,1,1))]. given #1761 (H,wt=29): 1295 (x \ 1) \ L(T(y \ (y / x),z),y,x * y) = K(L(y \ (y / x),y,x * y),z). [para(1289(a,1),1123(a,1,1))]. given #1762 (H,wt=27): 1863 x * L(T(y \ (y / x),z),y,x * y) = K(L(y \ (y / x),y,x * y),z). [para(1295(a,1),330(a,1)),flip(a)]. given #1763 (H,wt=26): 1864 (x / y) * (y * T(y \ (y / x),z)) = K(L(y \ (y / x),y,x * y),z). [para(1863(a,1),1294(a,1)),flip(a)]. given #1764 (H,wt=19): 1865 (x / y) * (y * T(y \ (y / x),z)) = K(x \ 1,z). [para(1289(a,1),1864(a,2,1))]. given #1765 (H,wt=30): 394 T(x * x,y * z) \ ((((y * z) \ (x * x)) * y) * z) = a((y * z) \ (x * x),y,z). [para(392(a,1),28(a,2,1)),flip(a)]. given #1766 (H,wt=30): 538 (R(R(x,y,z),u,w) * (y * z)) / ((x * y) * z) = R(x,y,z) \ R(R(x,y,z),u,w). [para(79(a,1),531(a,1,2))]. given #1767 (H,wt=27): 1869 ((R(x,y,z) * u) * w) / ((x * u) * w) = R(x,u,w) \ R(R(x,u,w),y,z). [para(185(a,1),538(a,1,1))]. given #1768 (H,wt=24): 1870 R(x \ R(x,y,z),x * u,w) = R(x,u,w) \ R(R(x,u,w),y,z). [para(1869(a,1),533(a,2))]. given #1769 (H,wt=30): 1570 (K(x,T(y,z)) * T(y,x)) / L(y,K(y,z),K(z,T(y,x))) = K(z,T(y,x)) * K(y,z). [para(1569(a,1),1106(a,1,1))]. given #1770 (H,wt=21): 1872 (K(x,T(y,z)) * T(y,x)) / y = K(z,T(y,x)) * K(y,z). [para(1663(a,1),1570(a,1,2))]. given #1771 (H,wt=19): 1873 K(x,T(y,z)) * K(y,x) = K(y,z) * K(z,T(y,x)). [para(1872(a,1),1666(a,1))]. given #1772 (H,wt=30): 1868 T(x * x,y * z) \ ((((y * z) \ (x * x)) * y) * z) = a((y * z) * (x * x),y,z). [para(394(a,2),1702(a,1))]. given #1773 (H,wt=26): 1874 T(x * x,y * z) \ ((((y * z) \ (x * x)) * y) * z) = a(y * z,y,z). [para(1868(a,2),1720(a,1))]. given #1774 (H,wt=26): 1875 (T(x * x,y * z) \ (((y * z) \ (x * x)) * y)) * z = a(y * z,y,z). [para(1874(a,1),591(a,1)),flip(a)]. given #1775 (H,wt=26): 1877 ((T(x * x,y * z) \ ((y * z) \ (x * x))) * y) * z = a(y * z,y,z). [para(591(a,1),1875(a,1,1))]. given #1776 (H,wt=16): 1878 (((x * y) \ 1) * x) * y = a(x * y,x,y). [para(795(a,1),1877(a,1,1,1))]. given #1777 (H,wt=14): 1879 ((x * y) \ x) * y = a(x * y,x,y). [para(318(a,1),1878(a,1,1))]. given #1778 (H,wt=14): 1880 x * ((y * x) \ y) = a(y * x,y,x). [para(1879(a,1),388(a,1)),flip(a)]. given #1779 (H,wt=18): 1881 a(x * (x \ y),x,x \ y) = (x \ y) * (y \ x). [para(20(a,1),1880(a,1,2,1)),flip(a)]. given #1780 (H,wt=14): 1882 (x \ y) * (y \ x) = a(y,x,x \ y). [para(20(a,1),1881(a,1,1)),flip(a)]. given #1781 (H,wt=20): 1883 L(x,y,(z \ u) * (u * z)) = L(x,y,a(z,u,u \ z)). [para(1882(a,1),869(a,1,3)),flip(a)]. given #1782 (H,wt=20): 1884 L(x,(y \ z) * (z * y),u) = L(x,a(y,z,z \ y),u). [para(1882(a,1),1362(a,1,2)),flip(a)]. given #1783 (H,wt=20): 1885 L(x,y,(z * u) * (u * z)) = L(x,y,a(z,u,u \ z)). [para(1883(a,1),781(a,1)),flip(a)]. given #1784 (H,wt=16): 1887 L(x,y,a(z,u,u \ z)) = L(x,y,K(u,z)). [para(1885(a,1),779(a,1))]. given #1785 (H,wt=20): 1886 L(x,(y * z) * (z * y),u) = L(x,a(y,z,z \ y),u). [para(1884(a,1),880(a,1)),flip(a)]. given #1786 (H,wt=16): 1888 L(x,a(y,z,z \ y),u) = L(x,K(z,y),u). [para(1886(a,1),879(a,1))]. given #1787 (H,wt=31): 271 L(((x * y) * z) \ u,(x * y) * z,x * (y * z)) = a(x,y,z) \ ((x * (y * z)) \ u). [para(28(a,2),268(a,2,1))]. given #1788 (H,wt=31): 743 T(R(x,y,z) \ R(R(x,y,z),u,x),x * (R(x,y,z) * T(u,x))) = a(R(x,y,z),u,x). [para(530(a,2),739(a,2,2)),flip(a)]. given #1789 (H,wt=31): 1845 L(x,x,x * ((x \ 1) * a(y,z,u))) = ((x \ 1) * a(y,z,u)) \ T(a(y,z,u),x \ 1). [para(1843(a,1),1488(a,2,2))]. given #1790 (H,wt=25): 1889 ((x \ 1) * a(y,z,u)) \ T(a(y,z,u),x \ 1) = L(x,x,a(y,z,u)). [para(321(a,1),1845(a,1,3)),flip(a)]. given #1791 (H,wt=23): 1890 (x \ a(y,z,u)) \ T(a(y,z,u),x \ 1) = L(x,x,a(y,z,u)). [para(318(a,1),1889(a,1,1))]. given #1792 (H,wt=21): 1892 (x \ a(y,z,u)) \ T(a(y,z,u),x) = L(x,x,a(y,z,u)). [para(1860(a,1),1890(a,1,2))]. given #1793 (H,wt=15): 1893 L(x,a(y,z,u),x) = L(x,x,a(y,z,u)). [para(1892(a,1),440(a,1)),flip(a)]. given #1794 (H,wt=16): 1894 L(x,x,a(y,z,z \ y)) = L(x,K(z,y),x). [para(1893(a,1),1888(a,1))]. given #1795 (H,wt=13): 1895 L(x,K(y,z),x) = L(x,x,K(y,z)). [para(1894(a,1),1887(a,1))]. given #1796 (H,wt=13): 1896 L(x,K(y,z),x) = L(x,x,K(z,y)). [para(1895(a,2),909(a,1))]. given #1797 (H,wt=22): 1897 (x \ K(y,z)) / (K(y,z) / L(x,x,K(z,y))) = K(K(y,z),x). [para(1896(a,1),1500(a,2,2,2)),flip(a)]. given #1798 (H,wt=19): 1898 (x \ K(y,z)) / (K(y,z) * (x \ 1)) = K(K(y,z),x). [para(930(a,1),1897(a,1,2))]. given #1799 (H,wt=13): 1899 K(x \ 1,K(y,z)) = K(K(y,z),x). [para(1898(a,1),978(a,1)),flip(a)]. given #1800 (H,wt=19): 1901 T(K(x,y),z) * K(K(x,y),z) = T(K(x,y),z * z). [para(1899(a,1),1433(a,1,2))]. given #1801 (H,wt=15): 1902 T(T(K(x,y),z),z) = T(K(x,y),z * z). [para(1901(a,1),1121(a,1)),flip(a)]. given #1802 (H,wt=21): 1900 K(K(x,y),z) * (K(x,y) \ u) = T(K(x,y),z \ 1) \ u. [para(1899(a,1),1095(a,1,1))]. given #1803 (H,wt=21): 1903 T(K(x,y),T(z,x) * T(z,x)) = T(T(K(x,y),z),T(z,x)). [para(1352(a,1),1902(a,1,1)),flip(a)]. given #1804 (H,wt=21): 1904 x / (T(K(y,z),u \ 1) \ x) = K(y,z) * K(u,K(y,z)). [para(1900(a,1),1071(a,1,2))]. given #1805 (H,wt=17): 1906 K(x,y) * K(z,K(x,y)) = T(K(x,y),z \ 1). [para(1904(a,1),65(a,1))]. given #1806 (H,wt=15): 1907 T(K(x,y),z \ 1) * z = z * K(x,y). [para(1906(a,1),1018(a,1,1))]. given #1807 (H,wt=21): 1905 T(K(x,y),z * T(T(z,x),x)) = T(T(K(x,y),z),T(z,x)). [para(1088(a,1),1903(a,1,2))]. given #1808 (H,wt=37): 1775 (L(x * y,z / (x * (y * z)),x * y) * (z / (x * (y * z)))) * (x * y) = (x * y) * (L(z,y,x) \ z). [para(1774(a,1),1310(a,2,2))]. given #1809 (H,wt=26): 1908 ((x * y) * (z / (x * (y * z)))) * (x * y) = (x * y) * (L(z,y,x) \ z). [para(851(a,1),1775(a,1,1,1))]. given #1810 (H,wt=21): 1910 (x \ R(x,y,z)) * (x * y) = (x * y) * (L(z,y,x) \ z). [para(1410(a,1),1908(a,1,1))]. given #1811 (H,wt=17): 1911 (x * y) * (L(z,y,x) \ z) = R(x,y,z) * y. [para(1910(a,1),528(a,1))]. given #1812 (H,wt=37): 1866 (L(x,y,z) / (z * (y * x))) * ((z * (y * x)) * T((z * (y * x)) \ (z * y),u)) = K(L(x,y,z) \ 1,u). [para(99(a,1),1865(a,1,2,2,1,2))]. given #1813 (H,wt=32): 1912 ((x * y) \ 1) * ((x * (y * z)) * T((x * (y * z)) \ (x * y),u)) = K(L(z,y,x) \ 1,u). [para(342(a,1),1866(a,1,1))]. given #1814 (H,wt=28): 1914 ((x * y) \ 1) * (x * ((y * z) * T((y * z) \ y,u))) = K(L(z,y,x) \ 1,u). [para(1590(a,1),1912(a,1,2))]. given #1815 (H,wt=24): 1915 ((x * y) \ 1) * (x * (y * K(z \ 1,u))) = K(L(z,y,x) \ 1,u). [para(1164(a,1),1914(a,1,2,2))]. given #1816 (H,wt=22): 1916 (x * y) \ (x * (y * K(z \ 1,u))) = K(L(z,y,x) \ 1,u). [para(1915(a,1),318(a,1)),flip(a)]. given #1817 (H,wt=17): 1917 L(K(x \ 1,y),z,u) = K(L(x,z,u) \ 1,y). [para(1916(a,1),32(a,2))]. given #1818 (H,wt=17): 1918 K(L(x \ 1,y,z) \ 1,u) = L(K(x,u),y,z). [para(156(a,1),1917(a,1,1,1)),flip(a)]. given #1819 (H,wt=38): 1871 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). [para(584(a,1),1870(a,2,1))]. given #1820 (H,wt=38): 1920 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). [para(750(a,1),1871(a,1,1))]. given #1821 (H,wt=36): 1921 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). [para(18(a,1),1920(a,1,1,1))]. given #1822 (H,wt=34): 1922 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). [para(18(a,1),1921(a,1,1,2,1))]. given #1823 (H,wt=28): 1923 (R(x,y,z) \ 1) \ R(R(x \ 1,x * y,z),u,w) = R(x \ R(x,u,w),y,z). [para(322(a,1),1922(a,1,2)),flip(a)]. given #1824 (H,wt=26): 1924 (R(x,y,z) \ 1) \ R(R(x,y,z) \ 1,u,w) = R(x \ R(x,u,w),y,z). [para(584(a,1),1923(a,1,2,1))]. given #1825 (H,wt=26): 1925 (R(x,y,z) * 1) \ R(R(x,y,z) * 1,u,w) = R(x \ R(x,u,w),y,z). [para(1924(a,1),750(a,1)),flip(a)]. given #1826 (H,wt=24): 1926 R(x,y,z) \ R(R(x,y,z) * 1,u,w) = R(x \ R(x,u,w),y,z). [para(18(a,1),1925(a,1,1))]. given #1827 (H,wt=22): 1927 R(x,y,z) \ R(R(x,y,z),u,w) = R(x \ R(x,u,w),y,z). [para(18(a,1),1926(a,1,2,1))]. given #1828 (H,wt=17): 1928 R(x \ R(x,y,y),z,u) = a(R(x,z,u),y,y). [para(1927(a,1),962(a,1))]. given #1829 (H,wt=15): 1930 a(R(x,y,z),u,u) = R(a(x,u,u),y,z). [para(962(a,1),1928(a,1,1)),flip(a)]. given #1830 (H,wt=28): 1929 T(R(x \ R(x,y,x),z,u),x * (R(x,z,u) * T(y,x))) = a(R(x,z,u),y,x). [para(1927(a,1),743(a,1,1))]. given #1831 (H,wt=26): 1931 T(R(a(x,y,x),z,u),x * (R(x,z,u) * T(y,x))) = a(R(x,z,u),y,x). [para(1539(a,1),1929(a,1,1,1))]. given #1832 (H,wt=24): 1932 T(R(a(x,y,x),z,u),R(x,z,u) * (y * x)) = a(R(x,z,u),y,x). [para(530(a,1),1931(a,1,2))]. given #1833 (H,wt=24): 1933 R(T(a(x,y,x),R(x,z,u) * (y * x)),z,u) = a(R(x,z,u),y,x). [para(1932(a,1),46(a,2))]. given #1834 (H,wt=42): 1597 (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). [para(99(a,1),1595(a,1,2,2,1,2))]. given #1835 (H,wt=37): 1934 ((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). [para(342(a,1),1597(a,1,1))]. given #1836 (H,wt=33): 1936 ((x * y) \ 1) * (x * ((y * z) * R((y * z) \ y,u,w))) = L(z,y,x) \ R(L(z,y,x),u,w). [para(1827(a,1),1934(a,1,2))]. given #1837 (H,wt=29): 1937 ((x * y) \ 1) * (x * (y * (z \ R(z,u,w)))) = L(z,y,x) \ R(L(z,y,x),u,w). [para(1592(a,1),1936(a,1,2,2))]. given #1838 (H,wt=27): 1938 (x * y) \ (x * (y * (z \ R(z,u,w)))) = L(z,y,x) \ R(L(z,y,x),u,w). [para(1937(a,1),318(a,1)),flip(a)]. given #1839 (H,wt=22): 1939 L(x,y,z) \ R(L(x,y,z),u,w) = L(x \ R(x,u,w),y,z). [para(1938(a,1),32(a,2)),flip(a)]. given #1840 (H,wt=50): 1686 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). [para(1684(a,1),1518(a,2,1))]. given #1841 (H,wt=50): 1940 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). [para(1808(a,1),1686(a,1,1,2,1))]. given #1842 (H,wt=33): 1941 L((x * (y \ R(y,x,z))) * (1 * u),x * (y \ R(y,x,z)),x) = (y \ R(y,x,z)) * (x * u). [para(1442(a,1),1940(a,1,1,2,1))]. given #1843 (H,wt=31): 1942 L((x * (y \ R(y,x,z))) * u,x * (y \ R(y,x,z)),x) = (y \ R(y,x,z)) * (x * u). [para(17(a,1),1941(a,1,1,2))]. given #1844 (H,wt=31): 1944 L(x * (R(y,x,z) * (y \ u)),x * (y \ R(y,x,z)),x) = (y \ R(y,x,z)) * (x * u). [para(1450(a,1),1942(a,1,1))]. given #1845 (H,wt=31): 1945 L(x * (R(y,x,z) * (y \ u)),x * (y * R(y,x,z)),x) = (y \ R(y,x,z)) * (x * u). [para(1944(a,1),1360(a,1)),flip(a)]. given #1846 (H,wt=21): 1946 (x \ R(x,y,z)) * (y * u) = y * (R(x,y,z) * (x \ u)). [para(1945(a,1),1439(a,1))]. given #1847 (H,wt=21): 1947 R(x,y,z) * (x \ (y * u)) = y * (R(x,y,z) * (x \ u)). [para(1946(a,1),532(a,1)),flip(a)]. given #1848 (H,wt=19): 1948 R(x,y,z) * (x \ (y * (y \ z))) = L(z,x * y,x). [para(1947(a,2),1567(a,1))]. given #1849 (H,wt=15): 1949 R(x,y,z) * (x \ z) = L(z,x * y,x). [para(20(a,1),1948(a,1,2,2))]. given #1850 (H,wt=15): 1951 L(x,y * z,y) / x = y \ R(y,z,x). [para(1949(a,1),536(a,1,1))]. given #1851 (H,wt=15): 1952 x / L(x,y * z,y) = R(y,z,x) \ y. [para(1949(a,1),542(a,1,2))]. given #1852 (H,wt=15): 1953 x \ L(x,y * z,y) = y \ R(y,z,x). [para(1951(a,1),515(a,1)),flip(a)]. given #1853 (H,wt=15): 1954 L(x,y * z,y) \ x = R(y,z,x) \ y. [para(1952(a,1),519(a,1)),flip(a)]. given #1854 (H,wt=10): 1957 K(x,R(y,z,x) \ y) = 1. [para(1954(a,1),653(a,1,2))]. given #1855 (H,wt=10): 1958 K(x,y \ R(y,z,x)) = 1. [para(622(a,1),1957(a,1,2))]. given #1856 (H,wt=10): 1959 T(x,y \ R(y,z,x)) = x. [hyper(41,a,1958,a)]. given #1857 (H,wt=12): 1960 K(x,T(y \ R(y,z,x),u)) = 1. [para(1831(a,1),1958(a,1,2))]. given #1858 (H,wt=8): 1962 K(x,a(y,z,x)) = 1. [para(739(a,2),1960(a,1,2))]. given #1859 (H,wt=8): 1963 T(x,a(y,z,x)) = x. [hyper(41,a,1962,a)]. given #1860 (H,wt=13): 1964 a(x,y,z) * z = z * a(x,y,z). [para(1963(a,1),82(a,1,2))]. given #1861 (H,wt=15): 1955 x \ R(x,x \ y,z) = z \ L(z,y,x). [para(20(a,1),1953(a,1,2,2)),flip(a)]. given #1862 (H,wt=13): 1965 R(x,y,z) \ x = z \ L(z,y,x). [para(1955(a,1),624(a,1)),flip(a)]. given #1863 (H,wt=13): 1966 L(x,y,z) = x * (R(z,y,x) \ z). [para(1965(a,2),20(a,1,2)),flip(a)]. given #1864 (H,wt=13): 1967 R(x,y,z) = x / (z \ L(z,y,x)). [para(1965(a,1),65(a,1,2)),flip(a)]. given #1865 (H,wt=13): 1969 (x \ L(x,y,z)) * R(z,y,x) = z. [para(1965(a,1),496(a,1,1))]. given #1866 (H,wt=13): 1970 L(x,y,z) = (R(z,y,x) \ z) * x. [para(1965(a,2),514(a,1,1)),flip(a)]. given #1867 (H,wt=13): 1972 R(x,y,T(z,x * y)) = R(x,y,z). [hyper(23,a,680,a,b,1969,a),flip(a)]. given #1868 (H,wt=13): 1973 L(x,y,z) * R(z,y,x) = x * z. [para(1969(a,1),504(a,1,2)),flip(a)]. given #1869 (H,wt=13): 1974 L(x,y,z) * (x \ R(z,y,x)) = z. [para(1969(a,1),647(a,1)),flip(a)]. given #1870 (H,wt=13): 1975 R(x,y,z) * L(z,y,x) = x * z. [para(1970(a,2),458(a,1,2))]. given #1871 (H,wt=13): 1976 L(x,y,z) = (z \ R(z,y,x)) \ x. [para(1970(a,2),465(a,2)),flip(a)]. given #1872 (H,wt=13): 1978 L(x,y,z) \ x = z \ R(z,y,x). [para(1972(a,1),681(a,2,2))]. given #1873 (H,wt=13): 1979 R(x,y,z) = x * (L(z,y,x) \ z). [para(1972(a,1),683(a,1))]. given #1874 (H,wt=13): 1980 R(x,y,z) * (x \ L(z,y,x)) = z. [para(1972(a,1),686(a,1,1))]. given #1875 (H,wt=15): 1956 x \ R(x,x * y,z) = z \ L(z,y,x). [para(313(a,1),1953(a,1,2)),flip(a)]. given #1876 (H,wt=15): 1961 T(x \ R(x,y,z),z) = x \ R(x,y,z). [hyper(39,a,1959,a)]. given #1877 (H,wt=15): 1968 (x \ L(x,y,z)) \ 1 = z \ R(z,y,x). [para(1965(a,1),460(a,1,1))]. given #1878 (H,wt=15): 1989 x \ R(x,y,z) = (L(z,y,x) \ z) * 1. [para(1968(a,1),517(a,1))]. given #1879 (H,wt=16): 1950 R(x,y,L(z,y,x)) * (x \ L(z,y,x)) = z. [para(1949(a,2),303(a,1))]. given #1880 (H,wt=12): 1990 R(x,y,L(z,y,x)) = R(x,y,z). [hyper(24,a,1980,a,b,1950,a)]. given #1881 (H,wt=16): 1986 R(x \ R(x,y,z),z,u) = L(z,y,x) \ z. [para(1978(a,1),736(a,1,1))]. given #1882 (H,wt=17): 1977 T(x \ R(x,y,z),u) \ z = L(z,y,T(x,u)). [para(1970(a,2),1832(a,1)),flip(a)]. given #1883 (H,wt=15): 1991 (x \ R(x,y,z)) \ z = L(z,y,T(x,z)). [para(1961(a,1),1977(a,1,1))]. given #1884 (H,wt=11): 1992 L(x,y,T(z,x)) = L(x,y,z). [para(1991(a,1),1976(a,2)),flip(a)]. given #1885 (H,wt=16): 1993 L(L(x,y,z),z * y,T(z,L(x,y,z))) = x. [para(1992(a,2),303(a,1))]. given #1886 (H,wt=11): 1994 L(x,y,K(z,L(x,y,z))) = x. [para(1993(a,1),1606(a,1)),flip(a)]. given #1887 (H,wt=17): 1984 (L(x,y,z) \ x) * (z * u) = R(z,y,x) * u. [para(1978(a,2),528(a,1,1))]. given #1888 (H,wt=17): 1985 (x \ R(x,y,z)) * u = z * (L(z,y,x) \ u). [para(1978(a,1),650(a,1,1))]. given #1889 (H,wt=17): 1987 (x * y) * (x \ R(x,y,z)) = R(x,y,z) * y. [para(1978(a,1),1911(a,1,2))]. given #1890 (H,wt=17): 1995 x * (L(x,y,z) \ (z * u)) = R(z,y,x) * u. [para(1984(a,1),650(a,1)),flip(a)]. given #1891 (H,wt=17): 1998 L(x,y,z) * (R(z,y,x) * u) = x * (z * u). [para(1995(a,1),645(a,1,2))]. given #1892 (H,wt=17): 2000 x * (L(x,y,z) \ (z * L(x,y,z))) = z * x. [para(1995(a,2),1975(a,1))]. given #1893 (H,wt=12): 2001 x * T(y,L(x,z,y)) = y * x. [para(36(a,2),2000(a,1,2))]. given #1894 (H,wt=12): 2002 T(x,L(y,z,x)) = x * K(x,y). [hyper(23,a,1116,a,b,2001,a)]. given #1895 (H,wt=10): 2005 K(x,L(y,z,x)) = K(x,y). [hyper(23,a,1107,a(flip),b,2002,a(flip)),flip(a)]. given #1896 (H,wt=8): 2006 L(x,y,K(z,x)) = x. [para(2005(a,1),1994(a,1,3))]. given #1897 (H,wt=8): 2008 L(x,y,K(x,z)) = x. [para(2006(a,1),909(a,1)),flip(a)]. given #1898 (H,wt=9): 2009 L(x,y,a(x,z,z)) = x. [para(2006(a,1),1262(a,1)),flip(a)]. given #1899 (H,wt=12): 2007 L(T(x,y),z,K(u,x)) = T(x,y). [para(2006(a,1),44(a,2,1))]. given #1900 (H,wt=11): 2015 T(x,K(y,x) * z) = T(x,z). [para(2007(a,1),1377(a,1)),flip(a)]. given #1901 (H,wt=13): 2016 K(K(x,y) * z,y) = T(y,z) \ y. [para(2015(a,1),1080(a,2,1))]. given #1902 (H,wt=11): 2021 K(K(x,y) * z,y) = K(z,y). [para(2016(a,2),1080(a,2)),flip(a)]. given #1903 (H,wt=11): 2022 K(K(x,y) * z,x) = K(z,x). [para(901(a,1),2021(a,1,1)),flip(a)]. given #1904 (H,wt=13): 2017 K(x,K(y,x) * z) = x \ T(x,z). [para(2015(a,1),1108(a,2,2))]. given #1905 (H,wt=11): 2024 K(x,K(y,x) * z) = K(x,z). [para(2017(a,2),1108(a,2)),flip(a)]. given #1906 (H,wt=11): 2025 K(x,K(x,y) * z) = K(x,z). [para(901(a,1),2024(a,1,2)),flip(a)]. given #1907 (H,wt=13): 2018 T(x,T(x,y) * z) = T(x,x * z). [para(1098(a,1),2015(a,1,2)),flip(a)]. given #1908 (H,wt=13): 2019 T(x,y * T(z,x)) = T(x,y * z). [para(1212(a,1),2015(a,1,2))]. given #1909 (H,wt=14): 2011 R(K(x,y),z,y) = K(x,y) / (y \ y). [para(2006(a,1),1967(a,2,2,2))]. given #1910 (H,wt=12): 2027 R(K(x,y),z,y) = K(x,y) / 1. [para(60(a,1),2011(a,2,2))]. given #1911 (H,wt=10): 2029 R(K(x,y),z,y) = K(x,y). [para(2027(a,2),64(a,1))]. given #1912 (H,wt=10): 2030 K(x,R(y,z,y)) = K(x,y). [para(2029(a,1),1654(a,1)),flip(a)]. given #1913 (H,wt=12): 2031 R(K(x,y),z,x) = K(y,x) \ 1. [para(2029(a,1),1670(a,1,1)),flip(a)]. given #1914 (H,wt=10): 2033 R(K(x,y),z,x) = K(x,y). [para(2031(a,2),897(a,1))]. given #1915 (H,wt=10): 2034 K(L(x,y,x),z) = K(x,z). [para(2033(a,1),1638(a,1)),flip(a)]. given #1916 (H,wt=13): 2036 K((x \ y) \ y,z) = K(T(x,y),z). [para(1457(a,1),2034(a,1,1))]. given #1917 (H,wt=13): 2038 K(T(x,x \ y),z) = K(T(x,y),z). [para(83(a,2),2036(a,1,1))]. given #1918 (H,wt=15): 2013 (K(x,y) * z) * x = K(x,y) * (z * x). [para(2008(a,1),74(a,1,2))]. given #1919 (H,wt=15): 2023 K(x * (K(x,y) * z),x) = K(x * z,x). [para(1068(a,1),2022(a,1,1))]. given #1920 (H,wt=15): 2032 K(x,y) * R(T(y,x),z,y) = R(y,z,y). [para(2030(a,1),1083(a,1,1))]. given #1921 (H,wt=16): 2014 x * (x \ R(a(x,y,y),z,x)) = a(x,y,y). [para(2009(a,1),1974(a,1,1))]. given #1922 (H,wt=16): 2042 x * (x \ a(R(x,y,x),z,z)) = a(x,z,z). [para(1930(a,2),2014(a,1,2,2))]. given #1923 (H,wt=16): 2043 x * (x \ a(L(x,y,x),z,z)) = a(x,z,z). [para(1303(a,1),2042(a,1,2,2,1))]. given #1924 (H,wt=12): 2044 a(L(x,y,x),z,z) = a(x,z,z). [para(2043(a,1),20(a,1)),flip(a)]. given #1925 (H,wt=17): 2039 x \ (K(x,y) * (z * x)) = T(K(x,y) * z,x). [para(2013(a,1),36(a,2,2)),flip(a)]. given #1926 (H,wt=17): 2040 x * ((K(x,y) * z) * x) = T(x,y) * (z * x). [para(2013(a,2),1120(a,1,2))]. given #1927 (H,wt=17): 2041 T(x,y) \ R(T(x,y),z,x) = x \ R(x,z,x). [para(2032(a,1),1163(a,1,2)),flip(a)]. given #1928 (H,wt=15): 2048 T(x,y) \ R(T(x,y),z,x) = a(x,z,x). [para(2041(a,2),1539(a,1))]. given #1929 (H,wt=13): 2049 T(x \ R(x,y,x),z) = a(x,y,x). [para(2048(a,1),1831(a,1)),flip(a)]. given #1930 (H,wt=11): 2050 T(a(x,y,x),z) = a(x,y,x). [para(1539(a,1),2049(a,1,1))]. given #1931 (H,wt=13): 2051 a(x,y,x) * z = z * a(x,y,x). [para(2050(a,1),82(a,1,2)),flip(a)]. given #1932 (H,wt=15): 2052 a(R(x,y,z),u,x) = R(a(x,u,x),y,z). [para(2050(a,1),1933(a,1,1)),flip(a)]. given #1933 (H,wt=17): 2046 K(x,y) * (x \ (z * x)) = T(K(x,y) * z,x). [para(2039(a,1),1076(a,1)),flip(a)]. given #1934 (H,wt=15): 2056 T(K(x,y) * z,x) = K(x,y) * T(z,x). [para(36(a,2),2046(a,1,2)),flip(a)]. given #1935 (H,wt=17): 2058 T(K(x,y) * z,x) / z = K(z,x) * K(x,y). [para(2056(a,2),1666(a,1,1))]. given #1936 (H,wt=17): 2059 T(K(x,y) * z,x) / z = K(x,y) * K(z,x). [para(2058(a,2),1226(a,2)),flip(a)]. given #1937 (H,wt=18): 2010 L(K(x,y),z,K(u,x \ 1)) = K((x \ 1) \ 1,y). [para(2006(a,1),1918(a,1,1,1)),flip(a)]. given #1938 (H,wt=14): 2060 L(K(x,y),z,K(u,x \ 1)) = K(x,y). [para(156(a,1),2010(a,2,1))]. given #1939 (H,wt=12): 2061 L(K(x,y),z,K(u,x)) = K(x,y). [para(2060(a,1),1618(a,1)),flip(a)]. given #1940 (H,wt=12): 2062 L(K(x,y),z,K(x,u)) = K(x,y). [para(2060(a,1),1619(a,1)),flip(a)]. given #1941 (H,wt=13): 2063 (K(x,y) * z) \ z = T(K(y,x),z). [para(2061(a,1),1301(a,1,1)),flip(a)]. given #1942 (H,wt=13): 2065 x / T(K(y,z),x) = K(z,y) * x. [para(2063(a,1),65(a,1,2))]. given #1943 (H,wt=15): 2064 T(K(x,y) * z,K(x,y)) = z * K(x,y). [para(2062(a,1),1309(a,1,1,1))]. given #1944 (H,wt=15): 2068 (K(x,y) * z) * K(y,x) = T(z,K(y,x)). [para(2065(a,1),1549(a,1,1))]. given #1945 (H,wt=17): 2067 (T(K(x,y),z) / z) * u = (K(y,x) * z) \ u. [para(2065(a,1),358(a,1,1)),flip(a)]. given #1946 (H,wt=17): 2069 K(K(x,y) * z,K(y,x)) = T(z,K(y,x)) / z. [para(2068(a,1),979(a,1,1)),flip(a)]. given #1947 (H,wt=15): 2070 K(K(x,y) * z,K(y,x)) = K(z,K(y,x)). [para(2069(a,2),1086(a,2)),flip(a)]. given #1948 (H,wt=15): 2071 K(K(x,y) * z,K(x,y)) = K(z,K(x,y)). [para(901(a,1),2070(a,1,1)),flip(a)]. given #1949 (H,wt=18): 2045 a(L(T(x,y),y * x,x),z,z) = a(T(x,y),z,z). [para(1283(a,1),2044(a,1,1))]. given #1950 (H,wt=16): 2073 a(R(T(x,y),y,x),z,z) = a(T(x,y),z,z). [para(1306(a,1),2045(a,1,1))]. given #1951 (H,wt=14): 2074 a(R(x,y,y),z,z) = a(T(x,y),z,z). [para(2073(a,1),1772(a,1)),flip(a)]. given #1952 (H,wt=18): 2072 a(a(K(x,y),z,z),u,w) = a(K(z,K(x,y)),u,w). [para(2071(a,1),1826(a,1,1)),flip(a)]. given #1953 (H,wt=19): 1971 x * (R(K(y,z),u,x) \ K(y,z)) = L(x,u,K(z,y)). [para(1966(a,1),909(a,1))]. given #1954 (H,wt=19): 1988 K(x,y) \ R(K(x,y),z,u) = u \ L(u,z,K(x,y)). [para(1669(a,1),1956(a,1,2))]. given #1955 (H,wt=19): 1999 x * (L(x,y,z) \ (z * T(y,z))) = y * R(z,y,x). [para(1995(a,2),1643(a,1))]. given #1956 (H,wt=17): 2078 x * (L(x,y,z) \ (y * z)) = y * R(z,y,x). [para(82(a,1),1999(a,1,2,2))]. given #1957 (H,wt=17): 2079 L(x,y,z) = (x * (y * z)) / (y * R(z,y,x)). [para(2078(a,1),648(a,1,2)),flip(a)]. given #1958 (H,wt=19): 2076 x * (K(y,z) * R(K(z,y),u,x)) = L(x,u,K(z,y)). [para(1671(a,1),1971(a,1,2))]. given #1959 (H,wt=20): 2054 a(x,y,x) \ a(R(x,z,z),y,x) = a(a(x,y,x),z,z). [para(2052(a,2),962(a,1,2))]. given #1960 (H,wt=21): 2057 T(K(x,y) * R(z,u,w),x) = K(x,y) * R(T(z,x),u,w). [para(46(a,2),2056(a,2,2))]. given #1961 (H,wt=21): 2077 x * (K(y,z) * K(z,R(y,u,x))) = L(x,y * u,K(y,z)). [para(1668(a,1),1971(a,1,2))]. given #1962 (H,wt=21): 2080 T(K(x,y) * R(y,z,u),x) = y * T(y \ R(y,z,u),x). [para(2057(a,2),1834(a,1))]. given #1963 (H,wt=22): 2026 K(x,y) * K(x * (K(x,z) * y),x) = a(x,K(x,z) * y,x). [para(2025(a,1),1537(a,1,1))]. given #1964 (H,wt=18): 2082 a(x,K(x,y) * z,x) = K(x,z) * K(x * z,x). [para(2023(a,1),2026(a,1,2)),flip(a)]. given #1965 (H,wt=13): 2083 a(x,K(x,y) * z,x) = a(x,z,x). [para(2082(a,2),1537(a,1))]. given #1966 (H,wt=23): 2053 (a(x,y,x) * z) * L(u,z,a(x,y,x)) = (z * u) * a(x,y,x). [para(2051(a,1),74(a,2))]. given #1967 (H,wt=24): 2047 (T(x,y) * (z * x)) \ ((T(x,y) * z) * x) = a(x,K(x,y) * z,x). [para(2040(a,1),1166(a,1,1))]. given #1968 (H,wt=15): 2085 a(x,K(x,y) * z,x) = a(T(x,y),z,x). [para(2047(a,1),28(a,2)),flip(a)]. given #1969 (H,wt=11): 2086 a(T(x,y),z,x) = a(x,z,x). [para(2085(a,1),2083(a,1))]. given #1970 (H,wt=13): 2087 a((x \ y) \ y,z,x) = a(x,z,x). [para(83(a,1),2086(a,1,1))]. given #1971 (H,wt=13): 2089 a((x \ y) * y,z,x) = a(x,z,x). [para(2087(a,1),1702(a,1)),flip(a)]. given #1972 (H,wt=13): 2090 a((x * y) * y,z,x) = a(x,z,x). [para(2089(a,1),1707(a,1)),flip(a)]. given #1973 (H,wt=12): 2091 a(R(x,y,y),z,x) = a(x,z,x). [para(2090(a,1),1721(a,1)),flip(a)]. given #1974 (H,wt=17): 2092 a(a(x,y,x),z,z) = a(x,y,x) \ a(x,y,x). [para(2091(a,1),2054(a,1,2)),flip(a)]. given #1975 (H,wt=9): 2093 a(a(x,y,x),z,z) = 1. [para(2092(a,2),60(a,1))]. given #1976 (H,wt=9): 2095 L(x,x,a(y,z,y)) = x. [hyper(37,a,2093,a)]. given #1977 (H,wt=9): 2097 L(x,x,a(y,z,z)) = x. [para(2095(a,1),1695(a,2))]. given #1978 (H,wt=8): 2098 L(x,x,K(y,z)) = x. [para(2097(a,1),1263(a,1)),flip(a)]. given #1979 (H,wt=8): 2100 a(K(x,y),z,z) = 1. [hyper(38,a,2098,a)]. given #1980 (H,wt=8): 2103 L(x,K(y,z),x) = x. [para(2098(a,1),1895(a,2))]. given #1981 (H,wt=12): 2104 R(K(x,y),z,z) = K(x,y) * 1. [para(2100(a,1),963(a,1,2)),flip(a)]. given #1982 (H,wt=10): 2107 K(x,R(y,z,z)) = K(x,y). [hyper(24,a,1767,a,b,2104,a(flip)),flip(a)]. given #1983 (H,wt=13): 2101 K(x,y) * (z \ 1) = K(x,y) / z. [para(2098(a,1),915(a,1,2)),flip(a)]. given #1984 (H,wt=13): 2105 a(K(x,K(y,z)),u,w) = a(1,u,w). [para(2100(a,1),2072(a,1,1)),flip(a)]. given #1985 (H,wt=10): 2115 a(K(x,K(y,z)),u,w) = 1. [para(2105(a,2),125(a,1))]. given #1986 (H,wt=10): 2117 L(x,y,K(z,K(u,w))) = x. [hyper(37,a,2115,a)]. given #1987 (H,wt=13): 2106 T(K(x,y),z) / z = z \ K(x,y). [para(2103(a,1),441(a,1,2))]. given #1988 (H,wt=13): 2108 K(x,y / (z \ 1)) = K(x,y * z). [para(720(a,1),2107(a,1,2)),flip(a)]. given #1989 (H,wt=13): 2112 K(x,y) * (x / z) = T(x,y) / z. [para(2107(a,1),1815(a,1,1))]. given #1990 (H,wt=13): 2114 K(x,y) / (z \ 1) = K(x,y) * z. [para(156(a,1),2101(a,1,2)),flip(a)]. given #1991 (H,wt=13): 2123 T(x,y) / (z \ x) = K(x,y) * z. [para(65(a,1),2112(a,1,2)),flip(a)]. given #1992 (H,wt=13): 2125 (K(x,y) * z) \ K(x,y) = z \ 1. [para(2114(a,1),66(a,1,1))]. given #1993 (H,wt=13): 2126 (K(x,y) * z) \ T(x,y) = z \ x. [para(2123(a,1),66(a,1,1))]. given #1994 (H,wt=12): 2129 L(x \ y,x,K(z,y)) = x \ y. [para(2126(a,1),1248(a,2))]. given #1995 (H,wt=10): 2130 a(K(x,y),z,z \ y) = 1. [hyper(38,a,2129,a)]. given #1996 (H,wt=10): 2132 a(K(x,y * z),y,z) = 1. [para(19(a,1),2130(a,1,3))]. given #1997 (H,wt=13): 2127 (K(x,y) \ z) \ 1 = z \ K(x,y). [para(20(a,1),2125(a,1,1)),flip(a)]. given #1998 (H,wt=13): 2128 (K(x,y) * z) \ y = z \ T(y,x). [para(901(a,1),2126(a,1,1)),flip(a)]. given #1999 (H,wt=15): 2102 (K(x,y) * (z / u)) \ K(x,y) = u / z. [para(2098(a,1),925(a,1)),flip(a)]. given #2000 (H,wt=15): 2121 (K(x,y) * z) \ u = (z \ K(y,x)) * u. [para(2106(a,1),2067(a,1,1)),flip(a)]. given #2001 (H,wt=13): 2135 (x \ K(y,z)) * K(z,y) = x \ 1. [para(2121(a,1),2125(a,1))]. given #2002 (H,wt=13): 2136 (x \ K(y,z)) * y = x \ T(y,z). [para(2121(a,1),2128(a,1))]. given #2003 (H,wt=15): 2133 (K(x,y) \ z) \ u = (z \ K(x,y)) * u. [para(2127(a,1),318(a,1,1)),flip(a)]. given #2004 (H,wt=15): 2137 ((x / y) \ K(z,u)) * K(u,z) = y / x. [para(2121(a,1),2102(a,1))]. given #2005 (H,wt=11): 2140 x / K(y,z) = x * K(z,y). [para(66(a,1),2137(a,1,1)),flip(a)]. given #2006 (H,wt=11): 2141 (x * K(y,z)) \ x = K(z,y). [para(2140(a,1),66(a,1,1))]. given #2007 (H,wt=15): 2138 (x / y) * K(x,x * y) = (x \ y) \ 1. [para(1011(a,1),2135(a,1,1))]. given #2008 (H,wt=15): 2143 (x * K(y,z)) \ u = (K(z,y) / x) * u. [para(2140(a,1),358(a,1,1))]. given #2009 (H,wt=15): 2144 (K(x,y) * z) / K(x,y) = T(z,K(y,x)). [para(2140(a,2),2068(a,1))]. given #2010 (H,wt=13): 2145 T(x,K(y,z)) \ x = K(x,K(z,y)). [para(2144(a,1),1053(a,2,1)),flip(a)]. given #2011 (H,wt=11): 2146 K(K(x,y),z) = K(z,K(y,x)). [para(2145(a,1),1080(a,2))]. given #2012 (H,wt=13): 2147 K(x,K(y,z)) * K(x,K(z,y)) = 1. [para(2146(a,1),898(a,1,1))]. given #2013 (H,wt=15): 2148 K(x,y) * K(z,K(y,x)) = T(K(x,y),z). [para(2146(a,1),1107(a,2,2)),flip(a)]. given #2014 (H,wt=13): 2150 T(K(x,y),z) \ 1 = T(K(y,x),z). [para(2148(a,1),1140(a,1)),flip(a)]. given #2015 (H,wt=13): 2151 T(K(x,y),z) * T(K(y,x),z) = 1. [para(2150(a,1),20(a,1,2))]. given #2016 (H,wt=15): 2149 K(x,y) * T(K(y,x),z) = K(z,K(x,y)). [para(2146(a,1),1114(a,2))]. given #2017 (H,wt=15): 2152 T(K(x,y),z) * K(y,x) = K(z,K(y,x)). [para(2149(a,1),405(a,2))]. given #2018 (H,wt=17): 2134 ((x * y) \ K(z,x)) * u = (T(x,z) * y) \ u. [para(1160(a,1),2121(a,1,1)),flip(a)]. given #2019 (H,wt=18): 2099 R(T(a(x,y,y),z),z,z) = z \ (a(x,y,y) * z). [para(2097(a,1),1804(a,1,1)),flip(a)]. given #2020 (H,wt=16): 2153 R(T(a(x,y,y),z),z,z) = T(a(x,y,y),z). [para(2099(a,2),36(a,2)),flip(a)]. given #2021 (H,wt=16): 2154 R(T(a(x,y,y),z),z,z) = a(T(x,z),y,y). [para(2153(a,2),1836(a,2)),flip(a)]. given #2022 (H,wt=16): 2155 R(a(T(x,y),z,z),y,y) = a(T(x,y),z,z). [para(1836(a,2),2154(a,1,1))]. given #2023 (H,wt=16): 2156 a(R(T(x,y),y,y),z,z) = a(T(x,y),z,z). [para(2155(a,1),1930(a,2))]. given #2024 (H,wt=15): 2157 a(T(T(x,y),y),z,z) = a(T(x,y),z,z). [para(2156(a,1),2074(a,1)),flip(a)]. given #2025 (H,wt=11): 2158 a(T(x,y),z,z) = a(x,z,z). [para(2157(a,1),1724(a,1))]. given #2026 (H,wt=18): 2119 x * (x \ R(K(y,K(z,u)),w,x)) = K(y,K(z,u)). [para(2117(a,1),1974(a,1,1))]. given #2027 (H,wt=14): 2165 R(K(x,K(y,z)),u,w) = K(x,K(y,z)). [para(2119(a,1),20(a,1)),flip(a)]. given #2028 (H,wt=14): 2166 K(x,R(K(y,z),u,w)) = K(x,K(y,z)). [para(2165(a,1),1654(a,1)),flip(a)]. given #2029 (H,wt=14): 2167 K(x,K(y,R(z,u,w))) = K(x,K(y,z)). [para(1654(a,1),2166(a,1,2))]. given #2030 (H,wt=14): 2168 K(K(R(x,y,z),u),w) = K(w,K(u,x)). [para(2167(a,1),2146(a,2))]. given #2031 (H,wt=14): 2169 K(R(K(x,y),z,u),w) = K(w,K(y,x)). [para(1634(a,1),2168(a,1,1))]. given #2032 (H,wt=20): 2122 K(x,R(((y \ 1) * z) \ 1,z,z)) = K(x,(z \ 1) * y). [para(1739(a,2),2108(a,1,2))]. given #2033 (H,wt=18): 2170 K(x,R((y \ z) \ 1,z,z)) = K(x,(z \ 1) * y). [para(318(a,1),2122(a,1,2,1,1))]. given #2034 (H,wt=15): 2171 K(x,(y \ z) \ 1) = K(x,(z \ 1) * y). [para(2170(a,1),2107(a,1)),flip(a)]. given #2035 (H,wt=13): 2172 K(x,(y \ z) \ 1) = K(x,z \ y). [para(318(a,1),2171(a,2,2))]. given #2036 (H,wt=18): 2174 K(x,(y / z) \ y) = K(x,z / (a(y,z,z) \ 1)). [para(2172(a,1),1447(a,1))]. given #2037 (H,wt=14): 2175 K(x,y / (a(z,y,y) \ 1)) = K(x,y). [para(66(a,1),2174(a,1,2)),flip(a)]. given #2038 (H,wt=12): 2176 K(x,y * a(z,y,y)) = K(x,y). [para(1445(a,1),2175(a,1,2))]. given #2039 (H,wt=18): 2177 K(x * a(y,x,x),z) = (z \ 1) / (z \ K(z,x)). [para(2176(a,1),1057(a,1,2,2)),flip(a)]. given #2040 (H,wt=12): 2178 K(x * a(y,x,x),z) = K(x,z). [para(2177(a,2),1057(a,1))]. given #2041 (H,wt=13): 2179 (x / y) * T(y,z) = x * K(y,z). [para(2178(a,1),1463(a,1,2)),flip(a)]. given #2042 (H,wt=13): 2180 (x * y) * K(y,z) = x * T(y,z). [para(21(a,1),2179(a,1,1)),flip(a)]. given #2043 (H,wt=10): 2183 L(K(x,y),x,z) = K(x,y). [hyper(23,a,1117,a,b,2180,a),flip(a)]. given #2044 (H,wt=13): 2184 (x * y) \ (x * T(y,z)) = K(y,z). [hyper(23,a,20,a,b,2180,a),flip(a)]. given #2045 (H,wt=13): 2186 (x * T(y,z)) \ (x * y) = K(z,y). [para(2180(a,1),2141(a,1,1))]. given #2046 (H,wt=14): 2187 L(K(T(x,y),z),x,y) = K(T(x,y),z). [para(2183(a,1),1376(a,1)),flip(a)]. given #2047 (H,wt=13): 2192 T(K(x,y),x * z) = K(T(x,z),y). [para(2187(a,1),1522(a,1)),flip(a)]. given #2048 (H,wt=13): 2193 K(T(x,x \ y),z) = T(K(x,z),y). [para(20(a,1),2192(a,1,2)),flip(a)]. given #2049 (H,wt=11): 2194 K(T(x,y),z) = T(K(x,z),y). [para(2193(a,1),2038(a,1)),flip(a)]. given #2050 (H,wt=13): 2195 K(x,T(y,z)) * T(K(y,x),z) = 1. [para(2194(a,1),898(a,1,2))]. given #2051 (H,wt=11): 2197 K(x,T(y,z)) = T(K(x,y),z). [hyper(24,a,2151,a,b,2195,a)]. given #2052 (H,wt=11): 2204 K(T(x,y),z) = K(x,T(z,y)). [para(2197(a,2),2194(a,2))]. given #2053 (H,wt=13): 2201 K(x,T(y,z)) / z = z \ K(x,y). [para(2197(a,2),2106(a,1,1))]. given #2054 (H,wt=15): 2199 K(x,y) * K(y,T(x,z)) = K(K(y,x),z). [para(2197(a,2),1114(a,1,2))]. given #2055 (H,wt=15): 2200 K(x,T(y,z \ 1)) * z = z * K(x,y). [para(2197(a,2),1907(a,1,1))]. given #2056 (H,wt=15): 2202 K(x,y) * K(y,T(x,z)) = K(z,K(x,y)). [para(2197(a,2),2149(a,1,2))]. given #2057 (H,wt=15): 2203 K(x,T(y,z)) * K(y,x) = K(z,K(y,x)). [para(2197(a,2),2152(a,1,1))]. given #2058 (H,wt=15): 2205 K(x,T(y,z)) * K(y,x) = K(K(x,y),z). [para(2199(a,1),1226(a,2))]. given #2059 (H,wt=15): 2206 K(x,T(y,z)) * K(y,x) = K(x,K(y,z)). [para(2202(a,1),1873(a,2))]. given #2060 (H,wt=11): 2208 K(x,K(y,z)) = K(z,K(y,x)). [para(2206(a,1),2203(a,1))]. given #2061 (H,wt=11): 2209 K(K(x,y),z) = K(x,K(y,z)). [para(2206(a,1),2205(a,1)),flip(a)]. given #2062 (H,wt=13): 2210 1 / K(x,K(y,z)) = K(K(y,x),z). [para(2208(a,1),899(a,1,2))]. given #2063 (H,wt=11): 2211 K(K(x,y),z) = K(K(x,z),y). [para(2210(a,1),899(a,1))]. given #2064 (H,wt=11): 2212 K(K(x,y),z) = K(y,K(z,x)). [para(2211(a,1),2146(a,1))]. given #2065 (H,wt=11): 2213 K(x,K(y,z)) = K(z,K(x,y)). [para(2212(a,1),2209(a,1))]. given #2066 (H,wt=15): 2207 K(x,y) * K(x,K(y,z)) = K(x,T(y,z)). [para(2206(a,1),1225(a,1,2))]. given #2067 (H,wt=15): 2214 T(K(x,y) * K(x,K(y,z)),z) = K(x,y). [para(2213(a,2),1020(a,1,1,2))]. given #2068 (H,wt=11): 2215 T(K(x,T(y,z)),z) = K(x,y). [para(2207(a,1),2214(a,1,1))]. given #2069 (H,wt=11): 2217 K(x,T(T(y,z),z)) = K(x,y). [para(2215(a,1),2197(a,2))]. given #2070 (H,wt=13): 2216 K(x,T(y,z)) * z = z * K(x,y). [para(2215(a,1),82(a,1,2)),flip(a)]. given #2071 (H,wt=13): 2219 K(x,T(y,z \ 1)) = K(x,T(y,z)). [hyper(24,a,2200,a,b,2216,a),flip(a)]. given #2072 (H,wt=17): 2220 T(K(x,y) * z,K(x,y)) = K(x,T(y,z)) * z. [para(2216(a,2),2064(a,2))]. given #2073 (H,wt=21): 2196 K(T(x,y * T(T(y,x),x)),z) = T(T(K(x,z),y),T(y,x)). [para(2194(a,2),1905(a,1))]. given #2074 (H,wt=19): 2222 K(T(x,y * T(y,x)),z) = T(T(K(x,z),y),T(y,x)). [para(2019(a,1),2196(a,1,1))]. given #2075 (H,wt=17): 2223 T(T(K(x,y),z),T(z,x)) = K(T(x,z * z),y). [para(2019(a,1),2222(a,1,1)),flip(a)]. given #2076 (H,wt=17): 2224 T(T(K(x,y),z),T(z,x)) = K(x,T(y,z * z)). [para(2223(a,2),1278(a,1))]. given #2077 (H,wt=17): 2225 T(K(x,T(y,z)),T(z,x)) = K(x,T(y,z * z)). [para(2197(a,2),2224(a,1,1))]. given #2078 (H,wt=17): 2226 K(T(x,T(y,x)),T(z,y)) = K(x,T(z,y * y)). [para(2225(a,1),2194(a,2))]. given #2079 (H,wt=15): 2227 K(T(x,y),T(z,y)) = K(x,T(z,y * y)). [para(1131(a,1),2226(a,1,1))]. given #2080 (H,wt=15): 2228 K(x,T(T(y,z),z)) = K(x,T(y,z * z)). [para(2227(a,1),2204(a,1)),flip(a)]. given #2081 (H,wt=11): 2229 K(x,T(y,z * z)) = K(x,y). [para(2228(a,1),2217(a,1))]. given #2082 (H,wt=15): 2230 K(x,T(y,z * (z * u))) = K(x,T(y,u)). [para(662(a,1),2229(a,1,2))]. given #2083 (H,wt=15): 2232 K(x,T(y,z \ u)) = K(x,T(y,z * u)). [para(20(a,1),2230(a,1,2,2,2)),flip(a)]. given #2084 (H,wt=15): 2235 K(x,T(y,z \ (z \ u))) = K(x,T(y,u)). [para(20(a,1),2232(a,2,2,2))]. given #2085 (H,wt=19): 2233 K(x,T(y,T(z,z * u))) = K(x,T(y,(z \ u) * u)). [para(250(a,1),2230(a,1,2,2,2)),flip(a)]. given #2086 (H,wt=21): 2221 K(x,T(y,z \ (z \ (u \ 1)))) = K(x,T(y,u * (z * z))). [para(409(a,1),2219(a,1,2,2))]. given #2087 (H,wt=17): 2236 K(x,T(y,z * (u * u))) = K(x,T(y,z \ 1)). [para(2221(a,1),2235(a,1))]. given #2088 (H,wt=15): 2237 K(x,T(y,z * (u * u))) = K(x,T(y,z)). [para(2236(a,2),2219(a,1))]. given #2089 (H,wt=21): 2234 K(x,T(y,(z / u) * (z * z))) = K(x,T(y,u / (z \ 1))). [para(399(a,1),2230(a,1,2,2,2))]. given #2090 (H,wt=17): 2239 K(x,T(y,z / (u \ 1))) = K(x,T(y,u / z)). [para(2234(a,1),2237(a,1))]. given #2091 (H,wt=22): 2185 (x * (y * z)) \ (x * (y * T(z,u))) = L(K(z,u),y * z,x). [para(2180(a,1),32(a,2,2,2)),flip(a)]. given #2092 (H,wt=23): 2161 (x * (y * (a(y,z,z) * u))) / (R(T(y,x),z,z) * u) = T(x,y). [para(2158(a,1),1210(a,1,1,2,2,1))]. given #2093 (H,wt=21): 2241 (x * (R(y,z,z) * u)) / (R(T(y,x),z,z) * u) = T(x,y). [para(966(a,1),2161(a,1,1,2))]. given #2094 (H,wt=10): 2243 T(x,R(y,z,z)) = T(x,y). [para(2241(a,1),1209(a,1)),flip(a)]. given #2095 (H,wt=13): 2244 T(x,y / (z \ 1)) = T(x,y * z). [para(720(a,1),2243(a,1,2)),flip(a)]. given #2096 (H,wt=15): 2246 K(x,T(y,z / u)) = K(x,T(y,u * z)). [para(2244(a,1),2239(a,1,2)),flip(a)]. given #2097 (H,wt=15): 2247 K(x,T(y,(z \ u) * u)) = K(x,T(y,z)). [para(65(a,1),2246(a,1,2,2)),flip(a)]. given #2098 (H,wt=15): 2248 K(x,T(y,T(z,z * u))) = K(x,T(y,z)). [para(2247(a,1),2233(a,2))]. given #2099 (H,wt=13): 2249 K(x,T(y,T(z,u))) = K(x,T(y,z)). [para(20(a,1),2248(a,1,2,2,2))]. given #2100 (H,wt=17): 2251 K(x,K(y,T(z,u))) = K(x,T(y,z)) * K(y,x). [para(2249(a,1),2206(a,1,1)),flip(a)]. given #2101 (H,wt=13): 2253 K(x,K(y,T(z,u))) = K(x,K(y,z)). [para(2251(a,2),2206(a,1))]. given #2102 (H,wt=19): 2254 K(x,K(y,z \ R(z,u,w))) = K(x,K(y,a(z,u,w))). [para(739(a,2),2253(a,1,2,2)),flip(a)]. given #2103 (H,wt=19): 2255 K(x,K(y \ R(y,z,u),w)) = K(x,K(w,a(y,z,u))). [para(1849(a,2),2254(a,1,2))]. given #2104 (H,wt=23): 2189 (x * (y * z)) \ ((x * y) * T(L(z,y,x),u)) = K(L(z,y,x),u). [para(74(a,1),2184(a,1,1))]. given #2105 (H,wt=23): 2256 (x * (y * z)) \ ((x * y) * L(T(z,u),y,x)) = K(L(z,y,x),u). [para(44(a,2),2189(a,1,2,2))]. given #2106 (H,wt=20): 2257 (x * (y * z)) \ (x * (y * T(z,u))) = K(L(z,y,x),u). [para(74(a,1),2256(a,1,2))]. given #2107 (H,wt=15): 2258 L(K(x,y),z * x,u) = K(L(x,z,u),y). [para(2257(a,1),2185(a,1)),flip(a)]. given #2108 (H,wt=15): 2259 K(L(x,y / x,z),u) = L(K(x,u),y,z). [para(22(a,1),2258(a,1,2)),flip(a)]. given #2109 (H,wt=24): 2081 T(K(x,y) * R(y,z,u),x) / R(y,z,u) = K(R(y,z,u) / y,x). [para(2080(a,2),1211(a,1,1))]. given #2110 (H,wt=19): 2260 K(x,y) * K(R(y,z,u),x) = K(R(y,z,u) / y,x). [para(2081(a,1),2059(a,1)),flip(a)]. given #2111 (H,wt=19): 2261 K(x,y) * K(R(y,z,u),x) = K(y \ R(y,z,u),x). [para(478(a,1),2260(a,2,1))]. given #2112 (H,wt=19): 2262 K(x,y) * K(R(y,z,u),x) = K(x,y \ R(y,z,u)). [para(2261(a,2),1849(a,1))]. given #2113 (H,wt=24): 2139 (x \ T(y,z)) \ ((x \ K(y,z)) * (y * u)) = L(u,y,x \ K(y,z)). [para(2136(a,1),32(a,2,1)),flip(a)]. given #2114 (H,wt=24): 2263 K(x,K(y,z) \ R(K(y,z),u,w)) = K(x,K(y,z)) * K(x,K(z,y)). [para(2169(a,1),2262(a,1,2)),flip(a)]. given #2115 (H,wt=14): 2265 K(x,K(y,z) \ R(K(y,z),u,w)) = 1. [para(2263(a,2),2147(a,1))]. given #2116 (H,wt=14): 2266 K(x,K(y,z) \ K(R(y,u,w),z)) = 1. [para(1629(a,1),2265(a,1,2,2))]. given #2117 (H,wt=14): 2268 K(x,K(y,z) * K(R(z,u,w),y)) = 1. [para(900(a,1),2266(a,1,2))]. given #2118 (H,wt=12): 2269 K(x,K(y \ R(y,z,u),w)) = 1. [para(2261(a,1),2268(a,1,2))]. given #2119 (H,wt=10): 2270 K(x,K(y,a(z,u,w))) = 1. [para(2269(a,1),2255(a,1)),flip(a)]. given #2120 (H,wt=10): 2271 T(x,K(y,a(z,u,w))) = x. [hyper(41,a,2270,a)]. given #2121 (H,wt=15): 2273 K(x,T(a(y,z,u),w)) = K(x,a(y,z,u)). [hyper(24,a,2220,a(flip),b,2271,a(flip)),flip(a)]. given #2122 (H,wt=15): 2274 K(x,y \ R(y,z,u)) = K(x,a(y,z,u)). [para(1839(a,1),2273(a,1,2))]. given #2123 (H,wt=10): 2279 K(x,a(K(y,z),u,w)) = 1. [para(2274(a,1),2265(a,1))]. given #2124 (H,wt=10): 2280 T(x,a(K(y,z),u,w)) = x. [hyper(41,a,2279,a)]. given #2125 (H,wt=15): 2275 K(x,y \ R(y,z,u)) = K(a(y,z,u),x). [para(2274(a,2),1847(a,2)),flip(a)]. given #2126 (H,wt=15): 2276 K(x \ R(x,y,z),u) = K(u,a(x,y,z)). [para(2274(a,1),1849(a,2))]. given #2127 (H,wt=17): 2278 K(x,y) * K(R(y,z,u),x) = K(x,a(y,z,u)). [para(2274(a,1),2262(a,2))]. given #2128 (H,wt=17): 2282 K(R(x,y,z) \ x,u) = K(u,a(x,x * y,z)). [para(618(a,1),2276(a,1,1))]. given #2129 (H,wt=17): 2283 K(x,y) * K(y,R(x,z,u)) = K(y,a(x,z,u)). [para(2278(a,1),1674(a,1)),flip(a)]. given #2130 (H,wt=17): 2284 L(x,y * z,K(y,u)) = x * K(u,a(y,z,x)). [para(2283(a,1),2077(a,1,2)),flip(a)]. given #2131 (H,wt=18): 2277 K(x,a(y,z,L(u,z,y))) = K(x,y \ R(y,z,u)). [para(1990(a,1),2274(a,1,2,2)),flip(a)]. given #2132 (H,wt=16): 2285 K(x,a(y,z,L(u,z,y))) = K(x,a(y,z,u)). [para(2277(a,2),2274(a,1))]. given #2133 (H,wt=22): 2281 ((K(x,y) * z) * u) / (K(x,y) * (z * u)) = a(K(x,y),z,u). [para(2280(a,1),300(a,1,2))]. given #2134 (H,wt=17): 2286 K(x,y) \ R(K(x,y),z,u) = a(K(x,y),z,u). [para(2281(a,1),537(a,1)),flip(a)]. given #2135 (H,wt=15): 2287 x \ L(x,y,K(z,u)) = a(K(z,u),y,x). [para(2286(a,1),1988(a,1)),flip(a)]. given #2136 (H,wt=15): 2288 x * a(K(y,z),u,x) = L(x,u,K(y,z)). [para(2287(a,1),20(a,1,2))]. given #2137 (H,wt=15): 2289 a(K(x,y),x * z,u) = K(y,a(x,z,u)). [hyper(23,a,2284,a(flip),b,2288,a)]. given #2138 (H,wt=12): 2292 K((x * y) * z,a(x,y,z)) = 1. [para(2289(a,1),2132(a,1))]. given #2139 (H,wt=15): 2290 x * a(K(y,z),u,x) = L(x,u,K(z,y)). [para(905(a,1),2288(a,1,2))]. given #2140 (H,wt=15): 2291 K(x,a(y,y * z,u)) = a(K(y,x),z,u). [para(2289(a,1),1778(a,1))]. given #2141 (H,wt=15): 2293 K(x * (y * z),a(x,y,L(z,y,x))) = 1. [para(74(a,1),2292(a,1,1))]. given #2142 (H,wt=12): 2295 K(x * (y * z),a(x,y,z)) = 1. [para(2293(a,1),2285(a,1)),flip(a)]. given #2143 (H,wt=13): 2296 x \ R(x,y,z) = a(x,y,z) * 1. [para(2295(a,1),1848(a,1,2)),flip(a)]. given #2144 (H,wt=11): 2297 a(x,y,z) = x \ R(x,y,z). [hyper(24,a,18,a,b,2296,a(flip))]. given #2145 (H,wt=11): 2298 a(x,y,z) = L(z,y,x) \ z. [hyper(24,a,1989,a(flip),b,2296,a(flip))]. given #2146 (H,wt=11): 2300 R(x,y,z) = x * a(x,y,z). [para(2297(a,2),20(a,1,2)),flip(a)]. given #2147 (H,wt=11): 2303 R(x,y,z) = a(x,y,z) * x. [para(2297(a,2),479(a,1,1)),flip(a)]. given #2148 (H,wt=11): 2314 L(x,a(y,z,u),y * z) = x. [para(2297(a,2),1411(a,1,2))]. given #2149 (H,wt=11): 2321 L(x,y,z) = a(z,y,x) \ x. [para(2297(a,2),1976(a,2,1))]. given #2150 (H,wt=11): 2326 L(x,y,z) = x / a(z,y,x). [para(2298(a,2),65(a,1,2)),flip(a)]. given #2151 (H,wt=11): 2329 a(x,y,z) = z / L(z,y,x). [para(2298(a,2),519(a,2)),flip(a)]. given #2152 (H,wt=13): 2302 R(x,y,z) \ x = a(x,y,z) \ 1. [para(2297(a,2),462(a,1,1)),flip(a)]. given #2153 (H,wt=13): 2310 a(x,x * y,z) = R(x,y,z) \ x. [para(2297(a,2),618(a,1))]. given #2154 (H,wt=13): 2311 a(x,y,z) = R(x,x * y,z) \ x. [para(2297(a,2),622(a,2)),flip(a)]. given #2155 (H,wt=13): 2313 a(x,y,z) = x * R(x \ 1,y,z). [para(2297(a,2),635(a,2)),flip(a)]. given #2156 (H,wt=9): 2344 L(x,a(y,z,u),z) = x. [para(2313(a,2),1443(a,1,2))]. given #2157 (H,wt=13): 2320 a(x,y,z) = z \ L(z,x * y,x). [para(2297(a,2),1953(a,2)),flip(a)]. given #2158 (H,wt=13): 2322 a(x,x * y,z) = z \ L(z,y,x). [para(2297(a,2),1956(a,1))]. given #2159 (H,wt=13): 2328 a(x,y,z) \ 1 = z \ L(z,y,x). [para(2298(a,2),511(a,1,1))]. given #2160 (H,wt=13): 2336 a(T(x,y),z,y) = L(y,z,x) \ y. [para(1992(a,1),2298(a,2,1))]. given #2161 (H,wt=11): 2358 a(T(x,y),z,y) = a(x,z,y). [para(2336(a,2),2298(a,2)),flip(a)]. given #2162 (H,wt=13): 2341 a(x,x * y,z) = a(x,y,z) \ 1. [para(2310(a,2),2302(a,1))]. given #2163 (H,wt=13): 2342 L(x,y * z,y) = x * a(y,z,x). [para(2311(a,2),1966(a,2,2))]. given #2164 (H,wt=11): 2362 L(x * a(y,z,x),z,y) = x. [para(2342(a,1),308(a,1,1))]. given #2165 (H,wt=13): 2343 a(x,x * y,z) \ 1 = a(x,y,z). [para(2311(a,2),2302(a,1)),flip(a)]. given #2166 (H,wt=14): 2351 a(x,y,L(z,y,x)) = L(z,y,x) \ z. [para(303(a,1),2320(a,2,2))]. given #2167 (H,wt=12): 2364 a(x,y,L(z,y,x)) = a(x,y,z). [para(2351(a,2),2298(a,2)),flip(a)]. given #2168 (H,wt=15): 2294 K(x,a(y,y * z,u)) = a(K(x,y),z,u). [para(2291(a,2),905(a,1))]. given #2169 (H,wt=15): 2306 x * (a(x,y,z) * u) = R(x,y,z) * u. [para(2297(a,2),501(a,1,2,1))]. given #2170 (H,wt=15): 2307 R(x,y,z) \ (x * u) = a(x,y,z) \ u. [para(2297(a,2),522(a,1,1)),flip(a)]. given #2171 (H,wt=15): 2308 a(x,y,z) * (x * u) = R(x,y,z) * u. [para(2297(a,2),528(a,1,1))]. given #2172 (H,wt=15): 2309 R(x,y,z) * (x \ u) = a(x,y,z) * u. [para(2297(a,2),532(a,1,1)),flip(a)]. given #2173 (H,wt=15): 2317 T(x \ R(x,y,z),u) = a(T(x,u),y,z). [para(2297(a,2),1831(a,1)),flip(a)]. given #2174 (H,wt=13): 2370 a(T(x,y),z,u) = T(a(x,z,u),y). [para(2297(a,2),2317(a,1,1)),flip(a)]. given #2175 (H,wt=11): 2372 a(T(x,y),y,z) = a(x,y,z). [para(2370(a,2),1687(a,1))]. given #2176 (H,wt=11): 2373 a(x,T(y,x),z) = a(x,y,z). [para(2372(a,1),1790(a,1)),flip(a)]. given #2177 (H,wt=13): 2374 a(x / y,y,z) = a(y * x,y,z). [para(2373(a,1),1810(a,1)),flip(a)]. given #2178 (H,wt=13): 2375 a(x / y,x,z) = a(x * y,x,z). [para(2374(a,1),612(a,1)),flip(a)]. given #2179 (H,wt=15): 2323 x * (L(x,y,z) \ u) = a(z,y,x) * u. [para(2297(a,2),1985(a,1,1)),flip(a)]. given #2180 (H,wt=15): 2331 x \ (L(x,y,z) * u) = a(z,y,x) \ u. [para(2298(a,2),512(a,1,1)),flip(a)]. given #2181 (H,wt=15): 2332 L(x,y,z) \ (x * u) = a(z,y,x) * u. [para(2298(a,2),524(a,2,1))]. given #2182 (H,wt=15): 2333 a(x,y,z) * (L(z,y,x) * u) = z * u. [para(2298(a,2),646(a,1,1))]. given #2183 (H,wt=15): 2334 (x * y) / (L(x,z,u) * y) = a(u,z,x). [para(2298(a,2),649(a,2))]. given #2184 (H,wt=15): 2335 L(x,y,z) * (x \ u) = a(z,y,x) \ u. [para(2298(a,2),651(a,1,1)),flip(a)]. given #2185 (H,wt=15): 2337 R(x,y * (y * z),u) = x * a(x,z,u). [para(1778(a,1),2300(a,2,2))]. given #2186 (H,wt=13): 2382 R(x,y * (y * z),u) = R(x,z,u). [para(2337(a,2),2300(a,2)),flip(a)]. given #2187 (H,wt=13): 2383 R(x,y \ z,u) = R(x,y * z,u). [para(20(a,1),2382(a,1,2,2)),flip(a)]. given #2188 (H,wt=15): 2348 (x \ a(y,x,z)) \ 1 = a(y,x,z) \ x. [para(2344(a,1),259(a,1)),flip(a)]. given #2189 (H,wt=15): 2359 a(x,x * y,z) * u = a(x,y,z) \ u. [para(2341(a,2),318(a,1,1))]. given #2190 (H,wt=15): 2360 a(x,x * y,z) \ u = a(x,y,z) * u. [para(2341(a,2),330(a,1,1))]. given #2191 (H,wt=15): 2366 K(a(x,x * y,z),u) = a(K(u,x),y,z). [para(2294(a,1),1847(a,2))]. given #2192 (H,wt=15): 2368 x * (y * a(x,z,y)) = R(x,z,y) * y. [para(1964(a,1),2306(a,1,2))]. given #2193 (H,wt=15): 2377 x * (a(y,z,x) \ u) = L(x,z,y) * u. [para(2331(a,1),20(a,1,2))]. given #2194 (H,wt=15): 2380 a(x,y,z) * (z * x) = z * R(x,y,z). [para(1973(a,1),2333(a,1,2))]. given #2195 (H,wt=15): 2388 K(a(x,y,z) \ 1,u) = a(K(u,x),y,z). [para(2341(a,1),2366(a,1,1))]. given #2196 (H,wt=16): 2365 a(x,x * y,L(z,y,x)) = a(x,y,z) \ 1. [para(2364(a,1),2341(a,2,1))]. given #2197 (H,wt=17): 2316 x \ (R(y,z,u) * (y \ x)) = a(T(y,x),z,u). [para(2297(a,2),1830(a,1)),flip(a)]. given #2198 (H,wt=16): 2390 x \ ((y \ x) * T(y,x)) = a(T(y,x),x,y). [para(1317(a,1),2316(a,1,2))]. given #2199 (H,wt=14): 2391 x \ ((y \ x) * T(y,x)) = a(y,x,y). [para(2390(a,2),2086(a,1))]. given #2200 (H,wt=17): 2318 R(x \ R(x,y,z),u,w) = a(R(x,u,w),y,z). [para(2297(a,2),1927(a,1)),flip(a)]. given #2201 (H,wt=14): 2393 a(R(x,y,z),u,y) = L(y,u,x) \ y. [para(2318(a,1),1986(a,1))]. given #2202 (H,wt=12): 2396 a(R(x,y,z),u,y) = a(x,u,y). [para(2393(a,2),2298(a,2)),flip(a)]. given #2203 (H,wt=12): 2400 a(L(x,y,x),z,y) = a(x,z,y). [para(1312(a,1),2396(a,1,1)),flip(a)]. given #2204 (H,wt=15): 2394 a(R(x,y,z),u,w) = R(a(x,u,w),y,z). [para(2297(a,2),2318(a,1,1)),flip(a)]. given #2205 (H,wt=17): 2319 L(x \ R(x,y,z),u,w) = a(L(x,u,w),y,z). [para(2297(a,2),1939(a,1)),flip(a)]. given #2206 (H,wt=15): 2406 a(L(x,y,z),u,w) = L(a(x,u,w),y,z). [para(2297(a,2),2319(a,1,1)),flip(a)]. given #2207 (H,wt=17): 2340 K(a(x,y,z) \ 1,u) = K(u,a(x,x * y,z)). [para(2302(a,1),2282(a,1,1))]. given #2208 (H,wt=17): 2347 (x * a(y,x,z)) * u = x * (a(y,x,z) * u). [para(2344(a,1),74(a,1,2))]. given #2209 (H,wt=17): 2349 (x \ a(y,x,z)) \ u = a(y,x,z) \ (x * u). [para(2344(a,1),267(a,1)),flip(a)]. given #2210 (H,wt=17): 2361 L(x,y,a(z,z * u,w)) = L(x,y,a(z,u,w)). [para(2341(a,2),787(a,1,3))]. given #2211 (H,wt=17): 2378 a(x,y,z) * (z * u) = z * (a(x,y,z) * u). [para(2332(a,1),2323(a,1,2)),flip(a)]. given #2212 (H,wt=17): 2385 R(x,(y \ z) / u,w) = R(x,(y * z) / u,w). [para(238(a,1),2382(a,1,2)),flip(a)]. given #2213 (H,wt=17): 2386 (x \ a(y,x,z)) \ u = (a(y,x,z) \ x) * u. [para(2348(a,1),318(a,1,1)),flip(a)]. given #2214 (H,wt=17): 2404 R(a(x,y,z),x * u,w) = a(R(x,u,w),y,z). [para(2394(a,1),1718(a,1))]. given #2215 (H,wt=17): 2411 (a(x,y,z) * y) * u = y * (a(x,y,z) * u). [para(1688(a,2),2347(a,1,1))]. given #2216 (H,wt=17): 2412 a(x,y,z) \ (y * u) = (a(x,y,z) \ y) * u. [para(2386(a,1),2349(a,1)),flip(a)]. given #2217 (H,wt=9): 2413 L(x,y,a(z,y,u)) = x. [hyper(23,a,798,a,b,2412,a(flip)),flip(a)]. given #2218 (H,wt=17): 2414 (a(x,y,z) * y) * u = a(x,y,z) * (y * u). [para(2413(a,1),74(a,1,2))]. given #2219 (H,wt=12): 2416 R(a(x,y,z),y,u) = a(x,y,z). [hyper(24,a,79,a,b,2414,a(flip)),flip(a)]. given #2220 (H,wt=17): 2417 a(x,y,z) * (y * u) = y * (a(x,y,z) * u). [para(2414(a,1),2411(a,1))]. given #2221 (H,wt=18): 2371 a(T(x,y),z,u) \ a(x,z,u) = K(y,a(x,z,u)). [para(2370(a,2),1080(a,2,1)),flip(a)]. given #2222 (H,wt=18): 2389 (x * y) * L(a(x,z,y),y,x) = R(x,z,y) * y. [para(2368(a,1),74(a,2))]. given #2223 (H,wt=18): 2421 (x * y) * a(L(x,y,x),z,y) = R(x,z,y) * y. [para(2406(a,2),2389(a,1,2))]. given #2224 (H,wt=15): 2422 (x * y) * a(x,z,y) = R(x,z,y) * y. [para(2400(a,1),2421(a,1,2))]. given #2225 (H,wt=19): 2315 (x * y) * R((x * y) \ x,z,u) = x * a(y,z,u). [para(2297(a,2),1592(a,2,2))]. given #2226 (H,wt=19): 2415 (a(x,y,z) * (y \ 1)) * u = a(x,y,z) * (y \ u). [para(2413(a,1),945(a,1,2))]. given #2227 (H,wt=17): 2424 (x \ a(y,x,z)) * u = a(y,x,z) * (x \ u). [para(1795(a,1),2415(a,1,1))]. given #2228 (H,wt=19): 2420 x * (y * (a(x,y,z) * u)) = R(x,y,z) * (y * u). [para(2417(a,1),2306(a,1,2))]. given #2229 (H,wt=20): 2301 L(x,y,z) \ L(R(x,u,w),y,z) = a(L(x,y,z),u,w). [para(48(a,1),2297(a,2,2)),flip(a)]. given #2230 (H,wt=20): 2325 L(L(x,y,z),u,w) \ L(x,u,w) = a(z,y,L(x,u,w)). [para(49(a,1),2298(a,2,1)),flip(a)]. given #2231 (H,wt=20): 2350 (x * y) \ (x * L(y,z * u,z)) = L(a(z,u,y),y,x). [para(2320(a,2),76(a,1,1)),flip(a)]. given #2232 (H,wt=20): 2356 (x * L(y,z,u)) / L(a(u,u * z,y),y,x) = x * y. [para(2322(a,2),179(a,1,2,1))]. given #2233 (H,wt=20): 2376 a(x,y,z) * (u * L(z,y,x)) = z * T(u,L(z,y,x)). [para(36(a,2),2323(a,1,2)),flip(a)]. given #2234 (H,wt=20): 2407 a(L(x,y,z),u,w) \ a(x,u,w) = a(z,y,a(x,u,w)). [para(2406(a,2),2298(a,2,1)),flip(a)]. given #2235 (H,wt=21): 2338 ((x * y) * a(x,y,z)) * u = (x * y) * (a(x,y,z) * u). [para(2314(a,1),74(a,1,2))]. given #2236 (H,wt=21): 2419 (x * y) \ (x * (a(z,x,u) * y)) = T(a(z,x,u),x * y). [para(2417(a,1),36(a,2,2)),flip(a)]. given #2237 (H,wt=18): 2426 L(T(a(x,y,z),u),u,y) = T(a(x,y,z),y * u). [para(2419(a,1),106(a,1)),flip(a)]. given #2238 (H,wt=18): 2427 L(a(T(x,y),z,u),y,z) = T(a(x,z,u),z * y). [para(2370(a,2),2426(a,1,1))]. given #2239 (H,wt=22): 2327 a(x,x * y,(x * y) \ z) = (y \ (x \ z)) \ ((x * y) \ z). [para(270(a,1),2298(a,2,1))]. given #2240 (H,wt=22): 2369 R(a(x,y,z),u,w) \ R(x,y,z) = a(a(x,y,z),u,w) \ x. [para(2303(a,2),2307(a,1,2))]. given #2241 (H,wt=22): 2381 L(a(x,y,z),u,w) * L(z,y,x) = a(w,u,a(x,y,z)) \ z. [para(2321(a,2),2335(a,1,2))]. given #2242 (H,wt=22): 2408 a(x,y,z) \ a(L(x,u * w,u),y,z) = a(u,w,a(x,y,z)). [para(2406(a,2),2320(a,2,2)),flip(a)]. given #2243 (H,wt=22): 2409 a(x,y,z) \ a(L(x,u,w),y,z) = a(w,u,a(x,y,z)) \ 1. [para(2406(a,2),2328(a,2,2)),flip(a)]. given #2244 (H,wt=22): 2428 a(L(x,y,z),u,w) * L(w,u,x) = a(z,y,a(x,u,w)) \ w. [para(2406(a,2),2381(a,1,1))]. given #2245 (H,wt=23): 2410 K(x,a(y / z,(y / z) * z,u)) = K(a(z * y,z,u) \ 1,x). [para(2374(a,1),2340(a,1,1,1)),flip(a)]. given #2246 (H,wt=19): 2429 K(a(x * y,x,z) \ 1,u) = K(u,a(y / x,y,z)). [para(22(a,1),2410(a,1,2,2)),flip(a)]. given #2247 (H,wt=19): 2430 K(a(x * y,x,z) \ 1,u) = K(u,a(y * x,y,z)). [para(2375(a,1),2429(a,2,2))]. given #2248 (H,wt=17): 2431 K(x,a(y * z,y,u)) = a(K(x,z * y),z,u). [para(2430(a,1),2388(a,1))]. given #2249 (H,wt=24): 2264 (x * T(y,z)) \ ((x * K(y,z)) * (y * u)) = L(u,y,x \ K(y,z)). [para(2139(a,1),284(a,1)),flip(a)]. given #2250 (H,wt=27): 2357 ((x * y) \ x) * L(L(y,x,x * y),z,u) = a(u,z,L(y,x,x * y)) \ 1. [para(2328(a,2),738(a,1)),flip(a)]. given #2251 (H,wt=28): 1981 (L(x,y,z) * (R(z,y,x) * u)) \ ((x * z) * u) = a(L(x,y,z),R(z,y,x),u). [para(1973(a,1),28(a,2,2,1)),flip(a)]. given #2252 (H,wt=22): 2432 a(L(x,y,z),R(z,y,x),u) = (x * (z * u)) \ ((x * z) * u). [para(1998(a,1),1981(a,1,1)),flip(a)]. given #2253 (H,wt=15): 2433 a(L(x,y,z),R(z,y,x),u) = a(x,z,u). [para(2432(a,2),28(a,2)),flip(a)]. given #2254 (H,wt=15): 2435 L(a(x,R(y,z,x),u),z,y) = a(x,y,u). [para(2433(a,1),2406(a,1)),flip(a)]. given #2255 (H,wt=29): 2425 (a(x,y,z) * (y \ u)) \ ((y \ a(x,y,z)) * (u * w)) = L(w,u,y \ a(x,y,z)). [para(2424(a,1),32(a,2,1)),flip(a)]. given #2256 (H,wt=29): 2436 (a(x,y,z) * (y \ u)) \ (a(x,y,z) * (y \ (u * w))) = L(w,u,y \ a(x,y,z)). [para(2424(a,1),2425(a,1,2))]. given #2257 (H,wt=22): 2437 L(L(x,y,z),z * y,a(u,z,w)) = L(x,y,z \ a(u,z,w)). [para(2436(a,1),1409(a,1)),flip(a)]. given #2258 (H,wt=22): 2438 L(L(x,y,z),z * y,a(u,z,w)) = L(x,y,z * a(u,z,w)). [para(2437(a,2),776(a,1))]. given #2259 (H,wt=31): 1996 L((x \ R(x,y,z)) \ u,x \ R(x,y,z),x * y) = (R(x,y,z) * y) \ ((x * y) * u). [para(1987(a,1),76(a,2,1))]. given #2260 (H,wt=21): 2439 (R(x,y,z) * y) \ ((x * y) * u) = (x \ R(x,y,z)) \ u. [para(1996(a,1),1411(a,1))]. given #2261 (H,wt=16): 2440 L(x,y,R(z,y,x)) = (z \ R(z,y,x)) \ x. [para(2439(a,1),183(a,1)),flip(a)]. given #2262 (H,wt=12): 2441 L(x,y,R(z,y,x)) = L(x,y,z). [para(2440(a,2),1976(a,2)),flip(a)]. given #2263 (H,wt=20): 2442 L(x,y * z,R(y,z,x) \ 1) = L(x,y * z,y \ 1). [para(584(a,1),2441(a,1,3))]. given #2264 (H,wt=18): 2443 L(x,y * z,R(y,z,x)) = L(x,y * z,y \ 1). [para(2442(a,1),787(a,1)),flip(a)]. given #2265 (H,wt=16): 2444 L(x,y * z,R(y,z,x)) = L(x,y * z,y). [para(2443(a,2),787(a,1))]. given #2266 (H,wt=23): 2445 R(x,y,z) * (L(z,x * y,x) \ z) = R(R(x,y,z),x * y,z). [para(2444(a,1),1979(a,2,2,1)),flip(a)]. given #2267 (H,wt=21): 2446 R(x,y,z) * (R(x,y,z) \ x) = R(R(x,y,z),x * y,z). [para(1954(a,1),2445(a,1,2))]. given #2268 (H,wt=11): 2447 R(R(x,y,z),x * y,z) = x. [para(2446(a,1),20(a,1))]. given #2269 (H,wt=11): 2448 R(R(x,x * y,z),y,z) = x. [para(2447(a,1),50(a,1)),flip(a)]. given #2270 (H,wt=31): 2449 K(x,R(y,y * z,u) \ R(R(y,y * z,u),z,u)) = K(x,R(y,y * z,u)) * K(y,x). [para(2448(a,1),2262(a,1,2,1)),flip(a)]. given #2271 (H,wt=29): 2450 K(x,R(y,y * z,u) \ R(R(y,y * z,u),z,u)) = R(K(x,y),z,u) * K(y,x). [para(1672(a,1),2449(a,2,1))]. given #2272 (H,wt=29): 2451 K(x,R(y,y * z,u) \ R(R(y,y * z,u),z,u)) = K(y,x) * R(K(x,y),z,u). [para(2450(a,2),406(a,1))]. given #2273 (H,wt=21): 2452 K(x,R(y,y * z,u) \ y) = K(y,x) * R(K(x,y),z,u). [para(2448(a,1),2451(a,1,2,2))]. given #2274 (H,wt=19): 2453 K(x,y) * R(K(y,x),z,u) = K(y,x \ R(x,z,u)). [para(622(a,1),2452(a,1,2)),flip(a)]. given #2275 (H,wt=17): 2454 x * K(y,z \ R(z,u,x)) = L(x,u,K(y,z)). [para(2453(a,1),2076(a,1,2))]. given #2276 (H,wt=15): 2455 x * K(a(y,z,x),u) = L(x,z,K(u,y)). [para(2275(a,1),2454(a,1,2))]. given #2277 (H,wt=13): 2456 a(K(x,y),z,u) = K(a(x,z,u),y). [hyper(23,a,2290,a,b,2455,a),flip(a)]. given #2278 (H,wt=13): 2457 a(K(x,y),z,u) = K(a(y,z,u),x). [hyper(23,a,2288,a,b,2455,a),flip(a)]. given #2279 (H,wt=13): 2458 a(K(x,y),z,u) = K(y,a(x,z,u)). [para(2456(a,2),1847(a,1))]. given #2280 (H,wt=13): 2459 a(K(x,y),z,u) = K(x,a(y,z,u)). [para(2457(a,2),1847(a,1))]. given #2281 (H,wt=13): 2462 K(x,a(y,z,u)) = K(y,a(x,z,u)). [para(2459(a,1),2458(a,1))]. given #2282 (H,wt=15): 2460 x * K(y,a(z,u,x)) = L(x,u,K(z,y)). [para(2458(a,1),2288(a,1,2))]. given #2283 (H,wt=15): 2463 L(x,y * z,K(y,u)) = L(x,z,K(y,u)). [para(2460(a,1),2284(a,2))]. given #2284 (H,wt=17): 2461 K(x * y,a(z,x,u)) = K(z,a(y * x,y,u)). [para(2458(a,1),2431(a,2)),flip(a)]. given #2285 (H,wt=32): 2423 (x * (R(y,z,u) * u)) / ((y * u) * R(a(y,z,u),y * u,x)) = L(x,y * u,a(y,z,u)). [para(2422(a,1),2079(a,2,1,2)),flip(a)]. given #2286 (H,wt=30): 2464 (x * (R(y,z,u) * u)) / ((y * u) * a(R(y,u,x),z,u)) = L(x,y * u,a(y,z,u)). [para(2404(a,1),2423(a,1,2,2))]. given #2287 (H,wt=27): 2465 (x * (R(y,z,u) * u)) / ((y * u) * a(y,z,u)) = L(x,y * u,a(y,z,u)). [para(2396(a,1),2464(a,1,2,2))]. given #2288 (H,wt=25): 2467 (x * (R(y,z,u) * u)) / (R(y,z,u) * u) = L(x,y * u,a(y,z,u)). [para(2422(a,1),2465(a,1,2))]. given #2289 (H,wt=11): 2468 L(x,y * z,a(y,u,z)) = x. [para(2467(a,1),21(a,1))]. given #2290 (H,wt=13): 2469 L(x,y * z,a(T(z,y),u,y)) = x. [para(2468(a,1),1185(a,1)),flip(a)]. given #2291 (H,wt=11): 2470 L(x,y * z,a(z,u,y)) = x. [para(2358(a,1),2469(a,1,3))]. given #2292 (H,wt=24): 2471 (a(x,y,z) * (z * x)) \ (a(x,y,z) * (z * (x * u))) = L(u,x,z). [para(2470(a,1),174(a,2))]. given #2293 (H,wt=22): 2472 (x * R(y,z,x)) \ (a(y,z,x) * (x * (y * u))) = L(u,y,x). [para(2380(a,1),2471(a,1,1))]. given #2294 (H,wt=22): 2473 (x * R(y,z,x)) \ (x * (a(y,z,x) * (y * u))) = L(u,y,x). [para(2378(a,1),2472(a,1,2))]. given #2295 (H,wt=20): 2474 (x * R(y,z,x)) \ (x * (R(y,z,x) * u)) = L(u,y,x). [para(2308(a,1),2473(a,1,2,2))]. given #2296 (H,wt=12): 2475 L(x,R(y,z,u),u) = L(x,y,u). [para(2474(a,1),32(a,2))]. given #2297 (H,wt=14): 2476 a(x,R(y,z,x),u) = L(u,y,x) \ u. [para(2475(a,1),2298(a,2,1))]. given #2298 (H,wt=12): 2477 a(x,R(y,z,x),u) = a(x,y,u). [para(2476(a,2),2298(a,2)),flip(a)]. given #2299 (H,wt=12): 2478 L(a(x,y,z),u,y) = a(x,y,z). [para(2477(a,1),2435(a,1,1))]. given #2300 (H,wt=12): 2479 a(L(x,y,z),z,u) = a(x,z,u). [para(2478(a,1),2406(a,2))]. given #2301 (H,wt=15): 2480 T(a(x,y,z),y * u) = a(T(x,u),y,z). [para(2478(a,1),2427(a,1)),flip(a)]. given #2302 (H,wt=17): 2482 a((x * y) \ z,x,u) = a(y \ (x \ z),x,u). [para(177(a,1),2479(a,1,1))]. given #2303 (H,wt=17): 2483 L(x,y,z) * a(x,z,u) = R(L(x,y,z),z,u). [para(2479(a,1),2300(a,2,2)),flip(a)]. given #2304 (H,wt=17): 2486 a(x \ (y \ z),y,u) = a((y * x) * z,y,u). [para(2482(a,1),1702(a,1))]. given #2305 (H,wt=17): 2487 L(x,y,z) * a(x,z,u) = L(R(x,z,u),y,z). [para(2483(a,2),48(a,1))]. given #2306 (H,wt=17): 2488 a((x * y) * z,x,u) = a(y * (x * z),x,u). [para(2486(a,1),1757(a,1))]. given #2307 (H,wt=19): 2489 (x * a(x,y,z)) / L(R(x,y,z),u,y) = a(y,u,x). [para(2487(a,1),2334(a,1,2))]. given #2308 (H,wt=17): 2491 R(x,y,z) / L(R(x,y,z),u,y) = a(y,u,x). [para(2300(a,2),2489(a,1,1))]. given #2309 (H,wt=12): 2492 a(x,y,R(z,x,u)) = a(x,y,z). [para(2491(a,1),2329(a,2))]. given #2310 (H,wt=17): 2493 a(x,y,(z / u) / x) = a(x,y,z / (x * u)). [para(193(a,1),2492(a,1,3)),flip(a)]. given #2311 (H,wt=19): 2490 a(T(x,y) * (y * z),y,u) = a((x * y) * z,y,u). [para(82(a,1),2488(a,1,1,1)),flip(a)]. given #2312 (H,wt=20): 2484 a(T(x,y),z,u) \ a(x,z,u) = K(z * y,a(x,z,u)). [para(2480(a,1),1080(a,2,1)),flip(a)]. given #2313 (H,wt=15): 2494 K(x * y,a(z,x,u)) = K(y,a(z,x,u)). [para(2484(a,1),2371(a,1))]. given #2314 (H,wt=15): 2495 K(x,a(y * z,y,u)) = K(z,a(x,y,u)). [para(2494(a,1),2462(a,1)),flip(a)]. given #2315 (H,wt=15): 2496 K(x,a(y * z,y,u)) = K(y,a(x,z,u)). [para(2494(a,1),2461(a,1)),flip(a)]. given #2316 (H,wt=13): 2497 K(x,a(y,z,u)) = K(z,a(y,x,u)). [para(2496(a,1),2495(a,1))]. given #2317 (H,wt=15): 2498 x * K(y,a(z,u,x)) = L(x,y,K(z,u)). [para(2497(a,1),2460(a,1,2))]. given #2318 (H,wt=13): 2499 L(x,y,K(z,u)) = L(x,u,K(z,y)). [para(2498(a,1),2460(a,1))]. given #2319 (H,wt=15): 2501 L(x,y,K(z,z * u)) = L(x,u,K(z,y)). [para(2499(a,1),2463(a,1))]. given #2320 (H,wt=14): 2502 L(x,y,a(z,u,u)) = L(x,u,K(z,y)). [para(2501(a,1),1261(a,1)),flip(a)]. given #2321 (H,wt=14): 2503 L(x,y,a(z,u,u)) = L(x,y,K(z,u)). [para(2502(a,2),2499(a,1))]. given #2322 (H,wt=14): 2504 L(x,y,a(z,u,z)) = L(x,y,K(u,z)). [para(2503(a,1),1695(a,1)),flip(a)]. given #2323 (H,wt=21): 2505 L(L(x,y,z),z * y,K(z,u)) = L(x,y,z * a(u,z,u)). [para(2504(a,1),2438(a,1))]. given #2324 (H,wt=16): 2506 L(x,y,z * a(u,z,u)) = L(x,y,T(z,u)). [para(2505(a,1),1604(a,1))]. given #2325 (H,wt=14): 2507 L(x,y,R(z,u,u)) = L(x,y,T(z,u)). [para(2506(a,1),1692(a,1)),flip(a)]. given #2326 (H,wt=15): 2508 L(x,y,T(z / u,z)) = L(x,y,u * z). [para(2507(a,1),846(a,1))]. given #2327 (H,wt=13): 2509 L(x,y,z * u) = L(x,y,u * z). [para(2508(a,1),845(a,1))]. given #2328 (H,wt=13): 2511 L(x,y,z \ u) = L(x,y,u * z). [para(2509(a,1),776(a,2))]. given #2329 (H,wt=17): 2510 L(L(x,y,z * u),(z * u) * y,u * z) = x. [para(2509(a,1),303(a,1))]. given #2330 (H,wt=8): 2515 L(x,y,K(z,u)) = x. [para(2510(a,1),1850(a,1)),flip(a)]. -------- Proof 1 -------- "aK1". ============================== PROOF ================================= % Proof 1 at 55.14 (+ 0.89) seconds: "aK1". % Length of proof is 2191. % Level of proof is 221. % Maximum clause weight is 50. % Given clauses 2330. 1 x * y = u & x * z = u -> y = z # label(non_clause). [assumption]. 2 y * x = u & z * x = u -> y = z # label(non_clause). [assumption]. 5 a(x,y,z) = 1 -> L(z,y,x) = z # label(non_clause). [assumption]. 6 L(x,y,z) = x -> a(z,y,x) = 1 # label(non_clause). [assumption]. 7 T(x,y) = x -> T(y,x) = y # label(non_clause). [assumption]. 8 T(x,y) = x -> K(x,y) = 1 # label(non_clause). [assumption]. 9 K(x,y) = 1 -> T(x,y) = x # label(non_clause). [assumption]. 14 a(K(x,y),z,u) = 1 # label("aK1") # label(non_clause) # label(goal). [goal]. 17 1 * x = x. [assumption]. 18 x * 1 = x. [assumption]. 19 x \ (x * y) = y. [assumption]. 20 x * (x \ y) = y. [assumption]. 21 (x * y) / y = x. [assumption]. 22 (x / y) * y = x. [assumption]. 23 x * y != z | x * u != z | u = y. [clausify(1)]. 24 x * y != z | u * y != z | u = x. [clausify(2)]. 27 (x * (y * z)) \ ((x * y) * z) = a(x,y,z). [assumption]. 28 a(x,y,z) = (x * (y * z)) \ ((x * y) * z). [copy(27),flip(a)]. 29 (x * y) \ (y * x) = K(y,x). [assumption]. 30 K(x,y) = (y * x) \ (x * y). [copy(29),flip(a)]. 31 (x * y) \ (x * (y * z)) = L(z,y,x). [assumption]. 32 L(x,y,z) = (z * y) \ (z * (y * x)). [copy(31),flip(a)]. 33 ((x * y) * z) / (y * z) = R(x,y,z). [assumption]. 34 R(x,y,z) = ((x * y) * z) / (y * z). [copy(33),flip(a)]. 35 x \ (y * x) = T(y,x). [assumption]. 36 T(x,y) = y \ (x * y). [copy(35),flip(a)]. 37 a(x,y,z) != 1 | L(z,y,x) = z. [clausify(5)]. 38 L(x,y,z) != x | a(z,y,x) = 1. [clausify(6)]. 39 T(x,y) != x | T(y,x) = y. [clausify(7)]. 40 T(x,y) != x | K(x,y) = 1. [clausify(8)]. 41 K(x,y) != 1 | T(x,y) = x. [clausify(9)]. 42 T(T(x,y),z) = T(T(x,z),y). [assumption]. 43 T(L(x,y,z),u) = L(T(x,u),y,z). [assumption]. 44 L(T(x,y),z,u) = T(L(x,z,u),y). [copy(43),flip(a)]. 45 T(R(x,y,z),u) = R(T(x,u),y,z). [assumption]. 46 R(T(x,y),z,u) = T(R(x,z,u),y). [copy(45),flip(a)]. 47 L(R(x,y,z),u,w) = R(L(x,u,w),y,z). [assumption]. 48 R(L(x,y,z),u,w) = L(R(x,u,w),y,z). [copy(47),flip(a)]. 49 L(L(x,y,z),u,w) = L(L(x,u,w),y,z). [assumption]. 50 R(R(x,y,z),u,w) = R(R(x,u,w),y,z). [assumption]. 51 (x * (x * y)) * z = x * (x * (y * z)) # label("LC"). [assumption]. 56 a(K(c20,c21),c22,c23) != 1 # label("aK1") # answer("aK1"). [deny(14)]. 59 1 \ x = x. [para(17(a,1),19(a,1,2))]. 60 x \ x = 1. [para(18(a,1),19(a,1,2))]. 61 x \ ((x * y) * 1) = y. [para(18(a,2),19(a,1,2))]. 62 x \ (y * (y \ (x * z))) = z. [para(20(a,2),19(a,1,2))]. 64 x / 1 = x. [para(18(a,1),21(a,1,1))]. 65 x / (y \ x) = y. [para(20(a,1),21(a,1,1))]. 66 (x / y) \ x = y. [para(22(a,1),19(a,1,2))]. 67 (x * (y * z)) * a(x,y,z) = (x * y) * z. [para(28(a,2),20(a,1,2))]. 68 ((x / y) * (y * z)) \ (x * z) = a(x / y,y,z). [para(22(a,1),28(a,2,2,1)),flip(a)]. 69 (x * y) * K(y,x) = y * x. [para(30(a,2),20(a,1,2))]. 70 x \ ((y \ x) * y) = K(y \ x,y). [para(20(a,1),30(a,2,1)),flip(a)]. 71 ((x \ y) * x) \ y = K(x,x \ y). [para(20(a,1),30(a,2,2)),flip(a)]. 72 x \ (1 * (x * y)) = L(y,x,1). [para(17(a,1),32(a,2,1)),flip(a)]. 73 (x * 1) \ (x * y) = L(y,1,x). [para(17(a,1),32(a,2,2,2)),flip(a)]. 74 (x * y) * L(z,y,x) = x * (y * z). [para(32(a,2),20(a,1,2))]. 75 x \ (y * ((y \ x) * z)) = L(z,y \ x,y). [para(20(a,1),32(a,2,1)),flip(a)]. 76 L(x \ y,x,z) = (z * x) \ (z * y). [para(20(a,1),32(a,2,2,2))]. 77 x \ ((x / y) * (y * z)) = L(z,y,x / y). [para(22(a,1),32(a,2,1)),flip(a)]. 78 ((x * y) * (y \ z)) / z = R(x,y,y \ z). [para(20(a,1),34(a,2,2)),flip(a)]. 79 R(x,y,z) * (y * z) = (x * y) * z. [para(34(a,2),22(a,1,1))]. 80 R(x / y,y,z) = (x * z) / (y * z). [para(22(a,1),34(a,2,1,1))]. 81 T(x,x) = x. [para(36(a,2),19(a,1))]. 82 x * T(y,x) = y * x. [para(36(a,2),20(a,1,2))]. 83 T(x,x \ y) = (x \ y) \ y. [para(20(a,1),36(a,2,2))]. 84 T(x / y,y) = y \ x. [para(22(a,1),36(a,2,2))]. 85 (x * (x * (y * z))) / z = x * (x * y). [hyper(24,a,22,a,b,51,a),flip(a)]. 86 (x * (x * y)) \ (x * (x * (y * z))) = z. [hyper(23,a,20,a,b,51,a),flip(a)]. 87 x \ ((x * (x * y)) * z) = x * (y * z). [hyper(23,a,20,a,b,51,a(flip)),flip(a)]. 88 (x * (x * 1)) * y = x * (x * y). [para(17(a,1),51(a,2,2,2))]. 89 x * (x * ((x \ y) * z)) = (x * y) * z. [para(20(a,1),51(a,1,1,2)),flip(a)]. 90 (x * (y * (y * (z * u)))) \ ((x * (y * (y * z))) * u) = a(x,y * (y * z),u). [para(51(a,1),28(a,2,1,2)),flip(a)]. 91 (x * (x * (y * (z * u)))) \ (((x * (x * y)) * z) * u) = a(x * (x * y),z,u). [para(51(a,1),28(a,2,1)),flip(a)]. 92 (x * (x * (y * z))) \ ((x * (x * y)) * (z * u)) = L(u,z,x * (x * y)). [para(51(a,1),32(a,2,1)),flip(a)]. 93 (x * (y * (y * z))) \ (x * (y * (y * (z * u)))) = L(u,y * (y * z),x). [para(51(a,1),32(a,2,2,2)),flip(a)]. 94 ((x * (x * (y * z))) * u) / (z * u) = R(x * (x * y),z,u). [para(51(a,1),34(a,2,1,1)),flip(a)]. 95 (x * (x * (y * z))) / ((x * y) * z) = R(x,x * y,z). [para(51(a,1),34(a,2,1)),flip(a)]. 97 ((x * y) / 1) / y = x. [hyper(24,a,22,a,b,64,a(flip)),flip(a)]. 98 T(T(x,y),x) = T(x,y). [para(81(a,1),42(a,1,1)),flip(a)]. 99 (x * (y * z)) / L(z,y,x) = x * y. [para(32(a,2),65(a,1,2))]. 100 (x * y) / T(x,y) = y. [para(36(a,2),65(a,1,2))]. 101 R(x,y,z) \ ((x * y) * z) = y * z. [para(34(a,2),66(a,1,1))]. 102 x \ (y * 1) = x \ y. [para(20(a,1),61(a,1,2,1))]. 103 T(x * (x * y),x) = x * (y * x). [hyper(23,a,51,a(flip),b,82,a)]. 104 T((x * y) / x,x) = y. [hyper(23,a,22,a(flip),b,82,a)]. 105 (x * T(y,x)) / x = y. [hyper(24,a,22,a,b,82,a(flip)),flip(a)]. 106 (x * y) \ (x * (z * y)) = L(T(z,y),y,x). [para(82(a,1),32(a,2,2,2)),flip(a)]. 107 T(x,y) \ (x * y) = T(y,T(x,y)). [para(82(a,1),36(a,2,2)),flip(a)]. 108 x * T(T(y,x),z) = T(y,z) * x. [para(42(a,1),82(a,1,2))]. 109 x * L(T(y,x),z,u) = L(y,z,u) * x. [para(44(a,2),82(a,1,2))]. 110 x * R(T(y,x),z,u) = R(y,z,u) * x. [para(46(a,2),82(a,1,2))]. 111 (x * y) \ ((z * x) * y) = T(R(z,x,y),x * y). [para(34(a,2),84(a,1,1)),flip(a)]. 112 T(T(x / y,z),y) = T(y \ x,z). [para(84(a,1),42(a,1,1)),flip(a)]. 113 ((x * y) / ((1 / z) * z)) / y = x. [para(22(a,2),97(a,1,1,2))]. 114 K(T(x,y),x) = 1. [hyper(40,a,98,a)]. 115 T(x,T(x,y)) = x. [hyper(39,a,98,a)]. 116 T(x,y) * x = x * T(x,y). [para(98(a,1),82(a,1,2)),flip(a)]. 117 (x * y) / T(y,T(x,y)) = T(x,y). [para(82(a,1),100(a,1,1))]. 118 x \ (y * (z * (z \ 1))) = x \ y. [para(20(a,2),102(a,1,2,2))]. 119 K(x,(y * x) / y) = 1. [para(104(a,1),114(a,1,1))]. 120 T(x,(y * x) / y) = x. [hyper(41,a,119,a)]. 122 K(x,y) \ (x * y) = T(y * x,K(x,y)). [para(69(a,1),36(a,2,2)),flip(a)]. 123 x \ (x * y) = L(y,x,1). [para(17(a,1),72(a,1,2))]. 124 L(x,y,1) = x. [para(123(a,1),19(a,1))]. 125 a(1,x,y) = 1. [hyper(38,a,124,a)]. 126 x \ (x * y) = L(y,1,x). [para(18(a,1),73(a,1,1))]. 127 L(x,1,y) = x. [para(126(a,1),19(a,1))]. 128 K(x \ 1,x) = (x \ 1) * x. [para(70(a,1),59(a,1))]. 129 K(x \ 1,x) / x = x \ 1. [hyper(24,a,22,a,b,128,a(flip)),flip(a)]. 130 (x \ 1) \ K(x \ 1,x) = x. [hyper(23,a,20,a,b,128,a(flip)),flip(a)]. 131 (x * x) * y = x * (x * y). [para(18(a,1),88(a,1,1,2))]. 132 (x * (x * y)) / y = x * x. [hyper(24,a,22,a,b,131,a),flip(a)]. 133 (x * x) \ (x * (x * y)) = y. [hyper(23,a,20,a,b,131,a),flip(a)]. 134 ((x * (x * y)) * z) / (y * z) = R(x * x,y,z). [para(131(a,1),34(a,2,1,1)),flip(a)]. 135 x \ (y * (y * x)) = T(y * y,x). [para(131(a,1),36(a,2,2)),flip(a)]. 136 x * (x * T(y,x * x)) = y * (x * x). [para(131(a,1),82(a,1))]. 137 L(x,y,y) = x. [para(133(a,1),32(a,2))]. 138 x * ((x \ y) * x) = T(x * y,x). [para(20(a,1),103(a,1,1,2)),flip(a)]. 139 T(x / y,z) * y = y * T(y \ x,z). [para(84(a,1),108(a,1,2,1)),flip(a)]. 140 (x * T(x \ y,z)) / x = T(y / x,z). [para(112(a,1),105(a,1,1,2))]. 141 R(x,1 / y,y) / y = x * (1 / y). [para(34(a,2),113(a,1,1))]. 142 L(x \ 1,x,y) = (y * x) \ y. [para(118(a,1),32(a,2))]. 143 L((x \ y) \ 1,x \ y,x) = y \ x. [para(20(a,1),142(a,2,1))]. 144 L(x \ 1,x,y / x) = y \ (y / x). [para(22(a,1),142(a,2,1))]. 145 x / L(y \ 1,y,x) = x * y. [para(142(a,2),65(a,1,2))]. 146 x \ T(x * y,x) = (x \ y) * x. [hyper(23,a,20,a,b,138,a),flip(a)]. 147 x * K(x \ 1,x) = T(x * 1,x). [para(128(a,2),138(a,1,2))]. 148 (x \ (x \ y)) * x = x \ T(y,x). [para(20(a,1),146(a,1,2,1)),flip(a)]. 149 x * K(x \ 1,x) = T(x,x). [para(18(a,1),147(a,2,1))]. 150 x * K(x \ 1,x) = x. [para(149(a,2),81(a,1))]. 151 K(x \ 1,x) = 1. [hyper(23,a,18,a,b,150,a)]. 152 T(x \ 1,x) = x \ 1. [hyper(41,a,151,a)]. 154 (x \ 1) * x = 1. [para(151(a,1),128(a,1)),flip(a)]. 155 1 / x = x \ 1. [para(151(a,1),129(a,1,1))]. 156 (x \ 1) \ 1 = x. [para(151(a,1),130(a,1,2))]. 157 x * (1 / x) = 1. [para(66(a,1),154(a,1,1))]. 160 T(x,x \ 1) = x. [para(156(a,1),83(a,2))]. 161 L(x,x \ 1,y) = (y * (x \ 1)) \ y. [para(156(a,1),142(a,1,1))]. 162 x / L(y,y \ 1,x) = x * (y \ 1). [para(156(a,1),145(a,1,2,1))]. 164 (x * 1) \ ((x * y) * (1 / y)) = a(x,y,1 / y). [para(157(a,1),28(a,2,1,2)),flip(a)]. 165 T(T(x,y),x \ 1) = T(x,y). [para(160(a,1),42(a,1,1)),flip(a)]. 166 K(T(x,y),x \ 1) = 1. [hyper(40,a,165,a)]. 167 K(x \ y,(y / x) \ 1) = 1. [para(84(a,1),166(a,1,1))]. 168 K(x,((y * x) / y) \ 1) = 1. [para(104(a,1),166(a,1,1))]. 169 T(x \ y,(y / x) \ 1) = x \ y. [hyper(41,a,167,a)]. 170 T(x,((y * x) / y) \ 1) = x. [hyper(41,a,168,a)]. 171 (x \ y) \ (x \ T(y,x)) = K(x \ (x \ y),x). [para(148(a,1),70(a,1,2))]. 172 x * L(y,z \ x,z) = z * ((z \ x) * y). [para(20(a,1),74(a,1,1))]. 173 x * L(y,z,x / z) = (x / z) * (z * y). [para(22(a,1),74(a,1,1))]. 174 (x * (y * z)) \ (x * (y * (z * u))) = L(L(u,z,y),y * z,x). [para(74(a,1),32(a,2,2,2)),flip(a)]. 176 (x * y) * L(z,K(x,y),y * x) = (y * x) * (K(x,y) * z). [para(69(a,1),74(a,1,1))]. 177 L(x \ (y \ z),x,y) = (y * x) \ z. [para(20(a,1),76(a,2,2))]. 178 L(x \ (y * x),x,y) = T(y,y * x). [para(76(a,2),36(a,2)),flip(a)]. 179 (x * y) / L(z \ y,z,x) = x * z. [para(76(a,2),65(a,1,2))]. 180 L(x \ T(y,z),x,z) = (z * x) \ (y * z). [para(82(a,1),76(a,2,2))]. 181 L(x \ (y \ ((y * x) * z)),x,y) = z. [para(76(a,2),62(a,1))]. 182 R(x,x,y) = x. [hyper(24,a,131,a(flip),b,79,a)]. 183 (R(x,y,z) * y) \ ((x * y) * z) = L(z,y,R(x,y,z)). [para(79(a,1),32(a,2,2)),flip(a)]. 184 L(R(x,y,z),u,w) * (y * z) = (L(x,u,w) * y) * z. [para(48(a,1),79(a,1,1))]. 185 R(R(x,y,z),u,w) * (y * z) = (R(x,u,w) * y) * z. [para(50(a,1),79(a,1,1))]. 186 R(T(x,y),x,z) = T(x,y). [para(182(a,1),46(a,2,1))]. 187 L(R(x,L(x,y,z),u),y,z) = L(x,y,z). [para(182(a,1),48(a,1)),flip(a)]. 188 R(R(x,y,z),x,u) = R(x,y,z). [para(182(a,1),50(a,1,1)),flip(a)]. 189 R(R(T(x,y),z,u),x,w) = R(T(x,y),z,u). [para(186(a,1),50(a,1,1)),flip(a)]. 190 (T(x,y) * x) * z = T(x,y) * (x * z). [para(186(a,1),79(a,1,1)),flip(a)]. 191 (R(x,y,z) * x) * u = R(x,y,z) * (x * u). [para(188(a,1),79(a,1,1)),flip(a)]. 192 R(1 / x,x,y) = y / (x * y). [para(17(a,1),80(a,2,1))]. 193 R((x / y) / z,z,y) = x / (z * y). [para(22(a,1),80(a,2,1))]. 194 T((x * y) / (z * y),u) = R(T(x / z,u),z,y). [para(80(a,1),46(a,2,1)),flip(a)]. 195 R(x,x \ 1,y) = y / ((x \ 1) * y). [para(65(a,1),192(a,1,1))]. 196 (x * y) / L(z,y / z,x) = x * (y / z). [para(22(a,1),99(a,1,1,2))]. 197 R(x,x \ y,z) \ (y * z) = (x \ y) * z. [para(20(a,1),101(a,1,2,1))]. 198 R(x,y \ 1,y) / y = x * (1 / y). [para(155(a,1),141(a,1,1,2))]. 199 L(K(x,y) \ ((y * x) \ z),K(x,y),y * x) = (x * y) \ z. [para(69(a,1),177(a,2,1))]. 200 (x * x) \ y = x \ (x \ y). [para(177(a,1),137(a,1))]. 201 L(x \ L(y \ z,y,u),x,u * y) = ((u * y) * x) \ (u * z). [para(76(a,2),177(a,1,1,2))]. 202 x \ (x \ (y * (x * x))) = T(y,x * x). [para(200(a,1),36(a,2)),flip(a)]. 203 L(T(x,y),y,x) = T(x,x * y). [para(36(a,2),178(a,1,1))]. 204 T(x,x * ((y * x) / y)) = L(x,(y * x) / y,x). [para(120(a,1),203(a,1,1)),flip(a)]. 205 x / L(y \ z,y,x / z) = (x / z) * y. [para(22(a,1),179(a,1,1))]. 207 R(x,y \ 1,y) / y = x * (y \ 1). [para(155(a,1),198(a,2,2))]. 208 (x * (y \ 1)) * y = R(x,y \ 1,y). [para(207(a,1),22(a,1,1))]. 209 (x * (y \ 1)) \ R(x,y \ 1,y) = y. [para(207(a,1),66(a,1,1))]. 210 R(x / (y \ 1),y \ 1,y) = x * y. [para(22(a,1),208(a,1,1)),flip(a)]. 211 (x * (x * y)) / z = x * (x * (y / z)). [para(22(a,1),85(a,1,1,2,2))]. 212 (x * (x * y)) \ (x * (x * z)) = y \ z. [para(20(a,1),86(a,1,2,2,2))]. 213 x \ ((x * y) * z) = x * ((x \ y) * z). [para(20(a,1),87(a,1,2,1,2))]. 214 L(x,y,z) * x = x * L(x,y,z). [para(81(a,1),109(a,1,2,1)),flip(a)]. 216 L(x \ 1,y,z) * x = x * L(x \ 1,y,z). [para(152(a,1),109(a,1,2,1)),flip(a)]. 217 x * T(y,y * x) = L(y,x,y) * x. [para(203(a,1),109(a,1,2))]. 218 (x * L(x,y,z)) / x = L(x,y,z). [hyper(24,a,22,a,b,214,a),flip(a)]. 219 T(x,L(x,y,z)) = x. [hyper(23,a,82,a,b,214,a),flip(a)]. 220 T(x,x * L(x,y,z)) = L(x,L(x,y,z),x). [para(219(a,1),203(a,1,1)),flip(a)]. 221 L(x,x \ y,x) * (x \ y) = (x \ y) * T(x,y). [para(20(a,1),217(a,1,2,2)),flip(a)]. 222 x * R(T(T(y,x),z),u,w) = R(T(y,z),u,w) * x. [para(42(a,1),110(a,1,2,1))]. 223 R(x,y,z) * x = x * R(x,y,z). [para(81(a,1),110(a,1,2,1)),flip(a)]. 224 R(x / y,z,u) * y = y * R(y \ x,z,u). [para(84(a,1),110(a,1,2,1)),flip(a)]. 225 (x \ y) * R((x \ y) \ y,z,u) = R(x,z,u) * (x \ y). [para(83(a,1),110(a,1,2,1))]. 226 x * (x * R(T(y,x * x),z,u)) = R(y,z,u) * (x * x). [para(110(a,1),131(a,1)),flip(a)]. 227 R(x \ 1,y,z) * x = x * R(x \ 1,y,z). [para(152(a,1),110(a,1,2,1)),flip(a)]. 228 T(x,R(x,y,z)) = x. [hyper(23,a,82,a,b,223,a),flip(a)]. 229 T(x \ y,R(y / x,z,u)) = T(y / x,x). [para(228(a,1),112(a,1,1)),flip(a)]. 230 x \ (y * (x * x)) = x * T(y,x * x). [hyper(23,a,20,a,b,136,a),flip(a)]. 231 T(x / (x * y),z) * (x * y) = (x * y) * T(L(y \ 1,y,x),z). [para(142(a,2),139(a,2,2,1))]. 232 T((x * y) / (x * z),u) * (x * z) = (x * z) * T(L(z \ y,z,x),u). [para(76(a,2),139(a,2,2,1))]. 233 (x * T(y,z)) / x = T((x * y) / x,z). [para(19(a,1),140(a,1,1,2,1))]. 234 L(x,y,T(y,z)) = x. [hyper(23,a,74,a,b,190,a),flip(a)]. 235 (x * T(x,y)) * z = T(x,y) * (x * z). [para(116(a,1),190(a,1,1))]. 237 L(x,(y * z) / y,z) = x. [para(104(a,1),234(a,1,3))]. 238 x * (x * ((x \ y) / z)) = (x * y) / z. [para(20(a,1),211(a,1,1,2)),flip(a)]. 239 (x * (x * y)) \ (x * x) = y \ 1. [para(18(a,1),212(a,1,2,2))]. 240 (x * y) \ (x * (x * z)) = (x \ y) \ z. [para(20(a,1),212(a,1,1,2))]. 241 T(x,x * (x * y)) = y \ (x * y). [para(212(a,1),36(a,2))]. 242 (x * y) \ (x * x) = (x \ y) \ 1. [para(20(a,1),239(a,1,1,2))]. 243 (x * x) / (y \ 1) = x * (x * y). [para(239(a,1),65(a,1,2))]. 244 ((x * y) * z) \ (x * x) = ((x \ y) * z) \ 1. [para(89(a,1),239(a,1,1))]. 245 T(x,x * (x * y)) = T(x,y). [para(241(a,2),36(a,2)),flip(a)]. 246 T(x,x \ y) = T(x,x * y). [para(20(a,1),245(a,1,2,2)),flip(a)]. 247 T(x,x * (y * x)) = T(x,T(y,x)). [para(82(a,1),245(a,1,2,2))]. 248 T(x * y,(x * y) * (y * x)) = T(x * y,K(y,x)). [para(69(a,1),245(a,1,2,2))]. 249 T(x,x * y) = (x \ y) \ y. [para(246(a,1),83(a,1))]. 250 (x \ y) * T(x,x * y) = y. [para(249(a,2),20(a,1,2))]. 251 T(x / y,x) = ((x / y) \ y) \ y. [para(22(a,1),249(a,1,2))]. 252 x / T(y,y * x) = y \ x. [para(249(a,2),65(a,1,2))]. 253 (x \ y) * ((x \ y) * (T(x,x * y) * z)) = ((x \ y) * y) * z. [para(249(a,2),89(a,1,2,2,1))]. 254 (x \ (x \ y)) * T(x,y) = x \ y. [para(20(a,1),250(a,1,2,2))]. 255 ((x \ y) * (T(x,x * y) * z)) \ (y * z) = a(x \ y,T(x,x * y),z). [para(250(a,1),28(a,2,2,1)),flip(a)]. 257 K(x,y) / T(y * x,x * y) = (y * x) \ K(x,y). [para(69(a,1),252(a,1,2,2))]. 258 (x \ (x \ y)) \ 1 = y \ (x * x). [para(20(a,1),242(a,1,1)),flip(a)]. 259 L(x \ y,x,y) = (y \ x) \ 1. [para(242(a,1),76(a,2))]. 260 L(K(x,y),y * x,x * y) = ((x * y) \ (y * x)) \ 1. [para(30(a,2),259(a,1,1))]. 261 L(T(x \ y,z),x,y) = T((y \ x) \ 1,z). [para(259(a,1),44(a,2,1))]. 262 (x \ ((y * x) / y)) \ 1 = ((y * x) / y) \ x. [para(259(a,1),237(a,1))]. 263 x * (x * (y \ 1)) = (x * x) / y. [para(156(a,1),243(a,1,2)),flip(a)]. 265 x * ((x \ (x \ y)) * z) = x \ (y * z). [para(20(a,1),213(a,1,2,1)),flip(a)]. 266 L(x \ (y * ((y \ x) * z)),x,y) = z. [para(213(a,1),181(a,1,1,2))]. 267 L(x \ (y * z),x,y) = (y \ x) \ z. [para(20(a,1),266(a,1,1,2,2))]. 268 L(x \ y,x,z) = (z \ x) \ (z \ y). [para(20(a,1),267(a,1,1,2))]. 269 L(x \ (y * z),x,z) = (z \ x) \ T(y,z). [para(82(a,1),267(a,1,1,2))]. 270 L((x * y) \ z,x * y,x) = y \ (x \ z). [para(19(a,1),268(a,2,1))]. 272 (x \ y) / L(z \ y,z,x) = x \ z. [para(268(a,2),65(a,1,2))]. 273 L(x \ y,x,x / z) = z \ ((x / z) \ y). [para(66(a,1),268(a,2,1))]. 274 (x \ y) \ (x \ z) = (x * y) \ (x * z). [para(268(a,1),76(a,1))]. 275 L(x \ L(y \ z,y,u),x,u \ y) = ((u \ y) * x) \ (u \ z). [para(268(a,2),177(a,1,1,2))]. 276 (x \ 1) / (y \ x) = x \ (x \ y). [para(143(a,1),272(a,1,2))]. 277 x \ (x \ (x / y)) = (x \ 1) / y. [para(66(a,1),276(a,1,2)),flip(a)]. 278 x * ((x \ 1) / y) = x \ (x / y). [para(277(a,1),20(a,1,2))]. 279 ((x \ 1) / y) \ 1 = (x / y) \ (x * x). [para(277(a,1),258(a,1,1))]. 280 T(x * T(x,y),T(x,y)) = x * T(x,y). [hyper(23,a,82,a,b,235,a(flip)),flip(a)]. 281 (x * T(x,y)) * (x \ z) = T(x,y) * z. [para(20(a,1),235(a,2,2))]. 282 (x * y) / (z \ (x \ y)) = x * (x * z). [para(65(a,1),238(a,1,2,2)),flip(a)]. 283 (x \ (x \ y)) \ z = y \ (x * (x * z)). [para(20(a,1),240(a,1,1)),flip(a)]. 284 (x \ y) \ ((x \ z) * u) = (x * y) \ ((x * z) * u). [para(89(a,1),240(a,1,2)),flip(a)]. 285 x \ (x \ (y * z)) = (x \ (x \ y)) * z. [hyper(23,a,20,a,b,265,a),flip(a)]. 286 (x \ (x \ y)) * (x * x) = T(y,x * x). [hyper(23,a,230,a(flip),b,265,a)]. 287 (x * (y * x)) \ (x * z) = T(y,x) \ (x \ z). [para(36(a,2),274(a,1,1)),flip(a)]. 288 T(x * T(x,y),T(x,y)) = T(x,y) * x. [para(280(a,2),116(a,2)),flip(a)]. 289 x / (y \ (x \ 1)) = x * (x * y). [para(18(a,1),282(a,1,1))]. 290 (x \ (x \ y)) \ y = T(x * x,y). [para(283(a,2),135(a,1))]. 291 (x \ (x \ 1)) * y = x \ (x \ y). [para(17(a,1),285(a,1,2,2)),flip(a)]. 292 (x \ (x \ y)) * (y \ z) = x \ (x \ z). [para(20(a,1),285(a,1,2,2)),flip(a)]. 293 R((x / y) / (z \ (z \ 1)),z \ (z \ 1),y) = x / (z \ (z \ y)). [para(291(a,1),193(a,2,2))]. 294 ((x \ 1) / y) * (x * x) = T(x / y,x * x). [para(277(a,1),286(a,1,1))]. 295 T(T(x,y) * x,T(x,y)) = T(x,y) * x. [para(116(a,2),288(a,1,1))]. 296 (x \ (x \ y)) \ (x \ (x \ z)) = y \ z. [hyper(23,a,20,a,b,292,a),flip(a)]. 297 (x \ y) * ((x * y) \ z) = x \ (x \ z). [para(19(a,1),292(a,1,1,2))]. 298 (T(x,y) \ x) * T(x,y) = x. [hyper(23,a,138,a,b,295,a(flip)),flip(a)]. 299 x / T(x,y) = T(x,y) \ x. [hyper(24,a,22,a,b,298,a),flip(a)]. 300 ((x * y) * z) / T(x * (y * z),a(x,y,z)) = a(x,y,z). [para(67(a,1),100(a,1,1))]. 301 L(x,x \ y,x) = y \ T(x * y,x). [para(138(a,1),75(a,1,2)),flip(a)]. 302 L(L(x,y \ z,y),z,y) = x. [para(75(a,1),266(a,1,1))]. 303 L(L(x,y,z),z * y,z) = x. [para(19(a,1),302(a,1,1,2))]. 304 L(L(x,y,z / y),z,z / y) = x. [para(66(a,1),302(a,1,1,2))]. 305 L(x,y \ 1,y) = x. [para(302(a,1),127(a,1)),flip(a)]. 306 L(x,y,y \ 1) = x. [para(156(a,1),305(a,1,2))]. 307 ((x \ 1) * x) \ ((x \ 1) * y) = x \ y. [para(306(a,1),76(a,1)),flip(a)]. 308 L(L(x,y * z,y),z,y) = x. [para(303(a,1),49(a,1)),flip(a)]. 309 x \ (y \ ((y * x) * z)) = L(z,y * x,y). [para(181(a,1),303(a,1,1)),flip(a)]. 310 R(x,L(x,y,z),u) = L(L(x,y,z),z * y,z). [para(187(a,1),303(a,1,1)),flip(a)]. 311 L((x \ y) \ z,x * y,x) = y \ (x * z). [para(267(a,1),303(a,1,1))]. 312 L(x,y \ z,y) = L(x,y * z,y). [para(302(a,1),303(a,1,1)),flip(a)]. 313 L(x,y * (y * z),y) = L(x,z,y). [para(303(a,1),303(a,1,1))]. 314 L(L(x,y * z,z),T(y,z),z) = x. [para(82(a,1),308(a,1,1,2))]. 315 L(L(x,y * z,z * y),K(y,z),z * y) = x. [para(69(a,1),308(a,1,1,2))]. 316 L(x,x * y,x) = y \ T(x * y,x). [para(301(a,1),312(a,1)),flip(a)]. 317 1 \ ((x \ 1) * y) = x \ y. [para(154(a,1),307(a,1,1))]. 318 (x \ 1) * y = x \ y. [para(317(a,1),59(a,1)),flip(a)]. 320 (x \ y) / y = x \ 1. [hyper(24,a,22,a,b,318,a),flip(a)]. 321 x * ((x \ 1) * y) = y. [hyper(23,a,19,a(flip),b,318,a)]. 322 (x \ 1) * (x * y) = y. [para(318(a,2),19(a,1))]. 323 (x \ (y * z)) \ (((x \ 1) * y) * z) = a(x \ 1,y,z). [para(318(a,1),28(a,2,1)),flip(a)]. 324 ((x * (y \ 1)) * z) / (y \ z) = R(x,y \ 1,z). [para(318(a,1),34(a,2,2)),flip(a)]. 325 T(x \ 1,y) = y \ (x \ y). [para(318(a,1),36(a,2,2))]. 326 x \ T(y,x \ 1) = y * (x \ 1). [para(318(a,1),82(a,1))]. 327 x * T(y \ 1,x) = y \ x. [para(318(a,1),82(a,2))]. 328 (x \ y) * K(y,x \ 1) = y * (x \ 1). [para(318(a,1),69(a,1,1))]. 329 x \ T(T(y,x \ 1),z) = T(y,z) * (x \ 1). [para(318(a,1),108(a,1))]. 330 (x \ 1) \ y = x * y. [para(156(a,1),318(a,1,1)),flip(a)]. 331 (x \ y) * L(z,y,x \ 1) = (x \ 1) * (y * z). [para(318(a,1),74(a,1,1))]. 332 R(x,y \ 1,z) * (y \ z) = (x * (y \ 1)) * z. [para(318(a,1),79(a,1,2))]. 333 (x * (y \ z)) / L(z,y \ 1,x) = x * (y \ 1). [para(318(a,1),99(a,1,1,2))]. 334 R(x,x \ 1,y) = y / (x \ y). [para(318(a,1),195(a,2,2))]. 335 R(x \ 1,y \ 1,y) = (x \ (y \ 1)) * y. [para(318(a,1),208(a,1,1)),flip(a)]. 336 L(x \ 1,y,x \ 1) * y = y * T(x \ 1,x \ y). [para(318(a,1),217(a,1,2,2)),flip(a)]. 337 T(x \ 1,(x \ 1) \ y) = T(x \ 1,x \ y). [para(318(a,1),246(a,2,2))]. 338 (x \ (x \ y)) \ z = (y \ (x * x)) * z. [para(258(a,1),318(a,1,1)),flip(a)]. 340 x / (y * x) = y \ 1. [para(19(a,1),320(a,1,1))]. 341 K(x,y) / (x * y) = (y * x) \ 1. [para(30(a,2),320(a,1,1))]. 342 L(x,y,z) / (z * (y * x)) = (z * y) \ 1. [para(32(a,2),320(a,1,1))]. 343 (x / y) \ 1 = y / x. [para(66(a,1),320(a,1,1)),flip(a)]. 344 (x * y) / ((z * x) * y) = R(z,x,y) \ 1. [para(101(a,1),320(a,1,1))]. 345 T(x * y,K(y,x)) / (y * x) = K(y,x) \ 1. [para(122(a,1),320(a,1,1))]. 346 T(x,x * y) / y = (x \ y) \ 1. [para(249(a,2),320(a,1,1))]. 347 x * (y * (x \ 1)) = T(y,x \ 1). [para(82(a,1),321(a,1,2))]. 348 R(x \ 1,x * y,z) = (y * z) / ((x * y) * z). [para(322(a,1),34(a,2,1,1))]. 349 T(x \ 1,x * y) = (x * y) \ y. [para(322(a,1),36(a,2,2))]. 350 R((x \ 1) / y,y,x * z) = z / (y * (x * z)). [para(322(a,1),80(a,2,1))]. 351 L(x * y,x \ 1,y) = (y \ (x \ 1)) \ 1. [para(330(a,1),259(a,1,1))]. 352 L(x * (y * z),x \ 1,y) = (y \ (x \ 1)) \ z. [para(330(a,1),267(a,1,1))]. 354 (x / y) * (y / x) = 1. [para(343(a,1),20(a,1,2))]. 355 K(x \ y,x / y) = 1. [para(343(a,1),167(a,1,2))]. 356 T(x,y / (y * x)) = x. [para(343(a,1),170(a,1,2))]. 357 T(x \ y,x / y) = x \ y. [para(343(a,1),169(a,1,2))]. 358 (x / y) \ z = (y / x) * z. [para(343(a,1),318(a,1,1)),flip(a)]. 359 (x / y) * ((y / x) * z) = z. [para(343(a,1),321(a,1,2,1))]. 360 x * ((y / z) * (z / y)) = x. [para(354(a,2),18(a,1,2))]. 361 K((x * y) \ y,x) = 1. [para(21(a,1),355(a,1,2))]. 362 (x / (x * y)) * y = y * (x / (x * y)). [para(356(a,1),82(a,1,2))]. 363 (x * (y / (y * x))) / x = y / (y * x). [para(356(a,1),100(a,1,2))]. 364 T(x,x * (y / (y * x))) = L(x,y / (y * x),x). [para(356(a,1),203(a,1,1)),flip(a)]. 365 T((x * y) \ y,x) = (x * y) \ y. [hyper(41,a,361,a)]. 366 x * R(x \ (y \ x),z,u) = R(y \ 1,z,u) * x. [para(325(a,1),110(a,1,2,1))]. 367 T(x / y,x \ y) = x / y. [hyper(39,a,357,a)]. 368 (x / y) * (x \ y) = (x \ y) * (x / y). [para(357(a,1),82(a,1,2))]. 369 (x / y) * (z * (y / x)) = T(z,y / x). [para(358(a,1),36(a,2)),flip(a)]. 370 T(x / y,x) = ((y / x) * y) \ y. [para(358(a,1),251(a,2,1))]. 371 ((x \ 1) / y) \ 1 = (y / x) * (x * x). [para(358(a,1),279(a,2))]. 372 T(x \ y,y \ x) = T(y / x,x). [para(367(a,1),112(a,1,1)),flip(a)]. 373 R(x,x \ 1,y) = x. [para(334(a,2),65(a,1))]. 374 R(T(x,y),x \ 1,z) = T(x,y). [para(373(a,1),46(a,2,1))]. 375 R(R(x,y,z),x \ 1,u) = R(x,y,z). [para(373(a,1),50(a,1,1)),flip(a)]. 376 R(T(x / y,y),(x / y) \ 1,z) = y \ x. [para(374(a,2),84(a,1))]. 377 T(x,y) * (x \ 1) = x \ T(x,y). [para(165(a,1),326(a,1,2)),flip(a)]. 378 x \ T(T(y,x \ 1),x) = (x \ (y * (x \ 1))) * x. [para(326(a,1),148(a,1,1,2)),flip(a)]. 379 K(x,y) * ((K(x,y) \ 1) / (x * y)) = K(x,y) \ ((y * x) \ 1). [para(341(a,1),278(a,2,2))]. 380 T(x \ 1,x * (y * y)) = (y \ (y \ (x * (y * y)))) \ 1. [para(349(a,2),258(a,2)),flip(a)]. 381 ((x * y) \ y) * x = x * ((x * y) \ y). [para(365(a,1),82(a,1,2)),flip(a)]. 382 T(x \ y,y \ x) = x \ y. [para(372(a,2),84(a,1))]. 383 T(x \ (x * y),(x * y) \ x) = y. [para(372(a,2),104(a,1))]. 384 (x \ y) * (y \ x) = (y \ x) * (x \ y). [para(382(a,1),82(a,1,2))]. 385 (x \ 1) \ T(x \ 1,x * y) = ((x * y) \ y) * ((x \ 1) \ 1). [para(349(a,1),377(a,1,1)),flip(a)]. 386 T(x,(y * x) \ y) = x. [para(19(a,1),383(a,1,1))]. 387 T(x,y \ (y / x)) = x. [para(22(a,1),386(a,1,2,1))]. 388 ((x * y) \ x) * y = y * ((x * y) \ x). [para(386(a,1),82(a,1,2))]. 389 T(K(x,y),(x * y) \ (y * x)) = K(x,y). [para(69(a,1),386(a,1,2,1))]. 390 R(x,y,z) * (x \ 1) = R(x,y,z) / x. [para(375(a,1),207(a,1,1)),flip(a)]. 391 x \ (y * (y * z)) = (x \ (y * y)) * z. [para(338(a,1),283(a,1)),flip(a)]. 392 (x \ (y * y)) * x = T(y * y,x). [para(338(a,1),290(a,1))]. 393 (x \ (y * y)) * (y \ (y \ z)) = x \ z. [para(338(a,1),296(a,1))]. 394 T(x * x,y * z) \ ((((y * z) \ (x * x)) * y) * z) = a((y * z) \ (x * x),y,z). [para(392(a,1),28(a,2,1)),flip(a)]. 395 L(x \ 1,x,x \ (y * y)) = T(y * y,x) \ (x \ (y * y)). [para(392(a,1),142(a,2,1))]. 397 (x / y) * (y * y) = x / (y \ 1). [para(371(a,1),343(a,1))]. 398 (x / (y \ 1)) / (y * y) = x / y. [hyper(24,a,22,a,b,397,a),flip(a)]. 399 (x / y) * (y / (x \ 1)) = x * x. [hyper(23,a,359,a,b,397,a),flip(a)]. 400 (x * y) / (y \ 1) = x * (y * y). [para(21(a,1),397(a,1,1)),flip(a)]. 401 (x * (y \ 1)) / y = x / (y * y). [para(21(a,1),398(a,1,1)),flip(a)]. 402 ((x \ (x \ y)) * x) / (x \ 1) = T(y,x * x). [para(400(a,2),286(a,1))]. 403 T(x / (y * y),y) = y \ (x * (y \ 1)). [para(401(a,1),84(a,1,1))]. 404 T(K(x,y),K(y,x)) = K(x,y). [para(30(a,2),389(a,1,2))]. 405 T(K(x,y),z) * K(y,x) = K(y,x) * T(K(x,y),z). [para(404(a,1),108(a,1,2,1)),flip(a)]. 406 R(K(x,y),z,u) * K(y,x) = K(y,x) * R(K(x,y),z,u). [para(404(a,1),110(a,1,2,1)),flip(a)]. 407 x * ((x \ (y * y)) * z) = y * (y * z). [para(391(a,1),20(a,1,2))]. 408 (((x * y) * x) \ (x * x)) * y = K(x,x * y). [para(391(a,1),30(a,2)),flip(a)]. 409 (x * (y * y)) \ z = y \ (y \ (x \ z)). [hyper(23,a,297,a,b,393,a),flip(a)]. 410 x * ((x \ (y * y)) * z) = (y * y) * z. [para(407(a,2),131(a,2)),flip(a)]. 411 (x * (y * y)) * z = x * (y * (y * z)). [para(407(a,1),89(a,1,2)),flip(a)]. 412 x \ (x \ (y \ ((y * x) * x))) = a(y,x,x). [para(409(a,1),28(a,2)),flip(a)]. 413 (x * (y * y)) \ x = y \ (y \ 1). [para(60(a,1),409(a,2,2,2))]. 414 x \ (x / (y * y)) = y \ (y \ 1). [para(22(a,1),413(a,1,1))]. 415 x / (y \ (y \ 1)) = x * (y * y). [para(413(a,1),65(a,1,2))]. 416 x * (y \ (y \ 1)) = x / (y * y). [para(414(a,1),20(a,1,2))]. 417 (x * (y * y)) * z = x * ((y * y) * z). [para(410(a,1),89(a,1,2)),flip(a)]. 418 (x * (y * (y * z))) / z = x * (y * y). [hyper(24,a,22,a,b,411,a),flip(a)]. 419 (x * (y * (y * z))) \ ((x * (y * y)) * (z * u)) = L(u,z,x * (y * y)). [para(411(a,1),32(a,2,1)),flip(a)]. 420 (x \ (x \ y)) * (x * (x * z)) = T(y,x * x) * z. [para(286(a,1),411(a,1,1)),flip(a)]. 421 L(x,y * y,z) = x. [hyper(23,a,74,a,b,417,a),flip(a)]. 422 R(x,y * y,z) = x. [hyper(24,a,79,a,b,417,a(flip)),flip(a)]. 423 T(x,x * (y * y)) = T(x,y * y). [para(421(a,1),203(a,1)),flip(a)]. 424 L(x,y,y / (z * z)) = x. [para(421(a,1),304(a,1,1))]. 425 L(x,y \ (y \ 1),z) = x. [para(318(a,1),421(a,1,2))]. 426 R(x,y \ (y \ 1),z) = x. [para(318(a,1),422(a,1,2))]. 427 L(x,y,y / (z \ (z \ 1))) = x. [para(318(a,1),424(a,1,3,2))]. 428 (x * (y \ (y \ 1))) * z = x * ((y \ (y \ 1)) * z). [para(425(a,1),74(a,1,2))]. 429 L(x,y,y * (z * z)) = x. [para(415(a,1),427(a,1,3))]. 430 T(x,x \ (y * y)) = T(x,y * y). [para(423(a,1),246(a,2))]. 431 T(x \ 1,x * (y * y)) = T(x \ 1,y * y). [para(330(a,1),430(a,1,2))]. 432 L(x,x,y / x) = y \ (y / (x \ 1)). [para(397(a,1),77(a,1,2)),flip(a)]. 433 (x * y) * (y \ 1) = R(x,y,y \ 1). [para(78(a,1),64(a,1)),flip(a)]. 434 R(x / y,y,y \ 1) = x * (y \ 1). [para(22(a,1),433(a,1,1)),flip(a)]. 435 x * L(y,z * x,z) = z * ((z \ x) * y). [para(312(a,1),172(a,1,2))]. 436 (R(T(x,y),z,u) * x) * w = R(T(x,y),z,u) * (x * w). [para(189(a,1),79(a,1,1)),flip(a)]. 437 T(x \ y,R(y / x,z,u)) = x \ y. [para(229(a,2),84(a,1))]. 438 T((x \ 1) \ y,y * x) = (x \ 1) \ y. [para(210(a,1),437(a,1,2))]. 439 T(x * y,y * x) = (x \ 1) \ y. [para(330(a,1),438(a,1,1))]. 440 (x \ y) \ T(y,x) = L(x,y,x). [para(19(a,1),269(a,1,1)),flip(a)]. 441 T(x,y) / L(y,x,y) = y \ x. [para(440(a,1),65(a,1,2))]. 442 L(x \ (x / y),y,x \ (x / y)) = ((x \ (x / y)) \ y) \ y. [para(387(a,1),440(a,1,2)),flip(a)]. 443 (x * (x * y)) \ z = y \ (x \ (x \ z)). [para(270(a,1),177(a,1)),flip(a)]. 444 x \ (y \ (y \ (z * (y * (y * x))))) = T(z,y * (y * x)). [para(443(a,1),36(a,2)),flip(a)]. 445 L(x \ 1,x,x / y) = y \ (y / x). [para(343(a,1),273(a,2,2))]. 446 x * (y \ ((y * (x \ 1)) * z)) = L(z,y * (x \ 1),y). [para(309(a,1),330(a,1)),flip(a)]. 447 R(x \ y,(y / x) \ 1,z) = x \ y. [para(84(a,1),376(a,1,1))]. 448 R(x \ y,x / y,z) = x \ y. [para(343(a,1),447(a,1,2))]. 449 R(x \ (x * y),x / (x * y),z) = y. [para(448(a,2),19(a,1))]. 450 R(x,y / (y * x),z) = x. [para(19(a,1),449(a,1,1))]. 451 (x * (y / (y * x))) * z = x * ((y / (y * x)) * z). [para(450(a,1),79(a,1,1)),flip(a)]. 452 x \ L(x,y * x,y) = a(y,x,x). [para(309(a,1),412(a,1,2))]. 453 L(x,y * x,y) = x * a(y,x,x). [para(452(a,1),20(a,1,2)),flip(a)]. 455 x * ((x \ y) * T(z,y)) = L(z,x * y,x) * y. [para(435(a,1),109(a,1))]. 456 (x * y) \ (x * T(y,x)) = K(x \ (x \ y),x). [para(171(a,1),274(a,1)),flip(a)]. 457 L(x,y,R(y,z,u)) = x. [hyper(23,a,74,a,b,191,a),flip(a)]. 458 R(x,y,z) * ((R(x,y,z) \ x) * u) = x * u. [hyper(23,a,89,a,b,191,a(flip)),flip(a)]. 459 (x * R(x,y,z)) * u = R(x,y,z) * (x * u). [para(223(a,1),191(a,1,1))]. 460 (R(x,y,z) \ x) \ 1 = x \ R(x,y,z). [para(457(a,1),259(a,1)),flip(a)]. 461 (R(x,y,z) \ u) / (x \ u) = R(x,y,z) \ x. [para(457(a,1),272(a,1,2))]. 462 (x \ R(x,y,z)) \ 1 = R(x,y,z) \ x. [para(460(a,1),156(a,1,1))]. 463 (R(x,y,z) \ x) \ u = (x \ R(x,y,z)) * u. [para(460(a,1),318(a,1,1)),flip(a)]. 464 (R(x,y,z) \ x) * ((x \ R(x,y,z)) * u) = u. [para(460(a,1),321(a,1,2,1))]. 465 (x \ R(x,y,z)) \ u = (R(x,y,z) \ x) * u. [para(460(a,1),330(a,1,1))]. 466 T(x,L(x \ 1,y,z)) = x. [hyper(23,a,82,a,b,216,a),flip(a)]. 467 K(x,L(x \ 1,y,z)) = 1. [hyper(40,a,466,a)]. 468 K(x \ 1,L(x,y,z)) = 1. [para(156(a,1),467(a,1,2,1))]. 469 K(L(x,y,z) \ 1,x) = 1. [para(303(a,1),468(a,1,2))]. 470 T(L(x,y,z) \ 1,x) = L(x,y,z) \ 1. [hyper(41,a,469,a)]. 471 x * (L(x,y,z) \ 1) = L(x,y,z) \ x. [para(470(a,1),327(a,1,2))]. 472 R(x / (x * y),z,u) * (x * y) = (x * y) * R(L(y \ 1,y,x),z,u). [para(142(a,2),224(a,2,2,1))]. 473 R((x * y) / (x * z),u,w) * (x * z) = (x * z) * R(L(z \ y,z,x),u,w). [para(76(a,2),224(a,2,2,1))]. 475 T(x,R(x \ 1,y,z)) = x. [hyper(23,a,82,a,b,227,a),flip(a)]. 476 T(x \ 1,R(x,y,z)) = x \ 1. [para(156(a,1),475(a,1,2,1))]. 477 R(x,y,z) * (x \ 1) = x \ R(x,y,z). [para(476(a,1),327(a,1,2))]. 478 R(x,y,z) / x = x \ R(x,y,z). [para(477(a,1),390(a,1)),flip(a)]. 480 (x \ R(x,y,z)) \ R(x,y,z) = x. [para(478(a,1),66(a,1,1))]. 481 (x / y) \ R(x / y,y,y \ 1) = (x * (y \ 1)) / (x / y). [para(434(a,1),478(a,1,1)),flip(a)]. 482 (x \ ((y * x) / y)) \ 1 = (y / (y * x)) * x. [para(262(a,2),358(a,1))]. 483 R(x,L(x,y,z),u) = x. [para(310(a,2),303(a,1))]. 484 (x * L(x,y,z)) * u = x * (L(x,y,z) * u). [para(483(a,1),79(a,1,1)),flip(a)]. 485 T(x \ 1,x \ y) = T(x \ 1,x * y). [para(330(a,1),337(a,1,2)),flip(a)]. 486 (x \ T(y,x)) / (x \ 1) = T(y,x * x). [para(148(a,1),402(a,1,1))]. 487 (((x \ y) * x) \ 1) * y = K(x,x * y). [para(244(a,1),408(a,1,1))]. 488 ((x \ y) * x) \ y = K(x,x * y). [para(487(a,1),318(a,1)),flip(a)]. 489 K(x,x \ y) = K(x,x * y). [para(488(a,1),71(a,1)),flip(a)]. 490 K(x,x * (x * y)) = K(x,y). [para(19(a,1),489(a,1,2)),flip(a)]. 491 K(x,x * (y * x)) = K(x,T(y,x)). [para(36(a,2),489(a,1,2)),flip(a)]. 492 K(x,(x * x) / y) = K(x,y \ 1). [para(263(a,1),490(a,1,2))]. 493 K(x \ (x \ y),x) = (x * y) \ (y * x). [para(82(a,1),456(a,1,2)),flip(a)]. 494 K(x \ (x \ y),x) = K(y,x). [para(493(a,2),30(a,2)),flip(a)]. 495 K(x \ y,x) = K(x * y,x). [para(19(a,1),494(a,1,1,2))]. 496 (R(x,y,z) \ x) * R(x,y,z) = x. [hyper(23,a,223,a,b,458,a)]. 498 x / R(x,y,z) = R(x,y,z) \ x. [hyper(24,a,22,a,b,496,a),flip(a)]. 499 T(R(x,y,z) \ 1,x) = x \ (x / R(x,y,z)). [para(498(a,2),325(a,2,2))]. 500 (x * y) / (z \ ((z * x) * y)) = R(z,x,y) \ z. [para(101(a,1),461(a,1,1))]. 501 x * ((x \ R(x,y,z)) * u) = R(x,y,z) * u. [para(464(a,1),458(a,1,2)),flip(a)]. 502 (x \ ((y * x) / y)) \ 1 = x * (y / (y * x)). [para(482(a,2),362(a,1))]. 503 L(x,L(y,z,u),y) = x. [hyper(23,a,74,a,b,484,a),flip(a)]. 504 x * ((x \ L(x,y,z)) * u) = L(x,y,z) * u. [hyper(23,a,89,a,b,484,a(flip)),flip(a)]. 505 L(x,(y * z) \ y,z \ 1) = x. [para(142(a,1),503(a,1,2))]. 506 (x \ L(x,y,z)) \ 1 = L(x,y,z) \ x. [para(503(a,1),259(a,1)),flip(a)]. 507 (x \ L(x,y,z)) \ u = L(x,y,z) \ (x * u). [para(503(a,1),267(a,1)),flip(a)]. 509 L(x,y,L(y,z,u)) = x. [para(303(a,1),503(a,1,2))]. 510 T(x,x * L(x,y,z)) = x. [para(503(a,1),220(a,2))]. 511 (L(x,y,z) \ x) \ 1 = x \ L(x,y,z). [para(509(a,1),259(a,1)),flip(a)]. 513 (L(x,y,z) \ u) / (x \ u) = L(x,y,z) \ x. [para(509(a,1),272(a,1,2))]. 514 (x \ L(x,y,z)) * x = L(x,y,z). [para(510(a,1),250(a,1,2))]. 515 L(x,y,z) / x = x \ L(x,y,z). [para(510(a,1),252(a,1,2))]. 516 (x \ L(x,y,z)) \ 1 = x / L(x,y,z). [para(510(a,1),346(a,1,1)),flip(a)]. 517 (x \ L(x,y,z)) \ u = (L(x,y,z) \ x) * u. [para(506(a,1),318(a,1,1)),flip(a)]. 519 x / L(x,y,z) = L(x,y,z) \ x. [para(516(a,1),506(a,1))]. 520 (L(x,y,z) \ x) * L(x,y,z) = x. [para(519(a,1),22(a,1,1))]. 521 (L(x \ 1,x,x / y) \ (x \ 1)) * (y \ (y / x)) = x \ 1. [para(445(a,1),520(a,1,2))]. 523 (x * R(x,y,z)) * u = x * (R(x,y,z) * u). [para(501(a,1),89(a,1,2)),flip(a)]. 524 L(x,y,z) \ (x * u) = (L(x,y,z) \ x) * u. [para(517(a,1),507(a,1)),flip(a)]. 525 R(x,R(x,y,z),u) = x. [hyper(24,a,79,a,b,523,a(flip)),flip(a)]. 526 R(x,y,z) * (x * u) = x * (R(x,y,z) * u). [para(523(a,1),459(a,1)),flip(a)]. 527 R(T(x,y),R(x,z,u),w) = T(x,y). [para(525(a,1),46(a,2,1))]. 528 (x \ R(x,y,z)) * (x * u) = R(x,y,z) * u. [hyper(23,a,501,a,b,526,a(flip)),flip(a)]. 529 x * (R(x,y,z) * (x \ u)) = R(x,y,z) * u. [para(20(a,1),526(a,1,2)),flip(a)]. 530 x * (R(x,y,z) * T(u,x)) = R(x,y,z) * (u * x). [para(82(a,1),526(a,1,2)),flip(a)]. 531 (R(x,y,z) * u) / (x * u) = x \ R(x,y,z). [hyper(24,a,22,a,b,528,a),flip(a)]. 532 (x \ R(x,y,z)) * u = R(x,y,z) * (x \ u). [para(20(a,1),528(a,1,2))]. 533 R(x \ R(x,y,z),x * u,w) = ((R(x,y,z) * u) * w) / ((x * u) * w). [para(528(a,1),34(a,2,1,1))]. 534 x \ (R(x,y,z) * u) = R(x,y,z) * (x \ u). [hyper(23,a,20,a,b,529,a),flip(a)]. 535 x / (y * (R(y,z,u) \ x)) = y \ R(y,z,u). [para(20(a,1),531(a,1,1))]. 536 (R(x,y,z) * (x \ u)) / u = x \ R(x,y,z). [para(20(a,1),531(a,1,2))]. 537 ((x * y) * z) / (x * (y * z)) = x \ R(x,y,z). [para(79(a,1),531(a,1,1))]. 538 (R(R(x,y,z),u,w) * (y * z)) / ((x * y) * z) = R(x,y,z) \ R(R(x,y,z),u,w). [para(79(a,1),531(a,1,2))]. 539 x \ (R(y,z,u) * (y \ x)) = T(y \ R(y,z,u),x). [para(532(a,1),36(a,2,2)),flip(a)]. 540 (R(x,y,z) \ x) \ u = R(x,y,z) * (x \ u). [para(532(a,1),463(a,2))]. 541 (x \ R(x,y,z)) \ u = x * (R(x,y,z) \ u). [para(535(a,1),66(a,1,1))]. 542 x / (R(y,z,u) * (y \ x)) = R(y,z,u) \ y. [para(540(a,1),65(a,1,2))]. 543 x * (R(x,y,z) \ 1) = R(x,y,z) \ x. [para(541(a,1),462(a,1))]. 544 (R(x,y,z) \ x) * u = x * (R(x,y,z) \ u). [para(541(a,1),465(a,1)),flip(a)]. 545 T(R(x,y,z) \ 1,x) = R(x,y,z) \ 1. [hyper(23,a,327,a,b,543,a),flip(a)]. 546 T(x,R(x,y,z) \ 1) = x. [hyper(39,a,545,a)]. 547 x \ (x / R(x,y,z)) = R(x,y,z) \ 1. [para(545(a,1),499(a,1)),flip(a)]. 548 T(x,y) * (R(x,z,u) \ 1) = R(x,z,u) \ T(x,y). [para(546(a,1),329(a,1,2,1)),flip(a)]. 549 (x * y) \ ((z * x) * y) = R(T(z,x * y),x,y). [para(111(a,2),46(a,2)),flip(a)]. 550 (x * (x * (y * z))) / (y * z) = R(x * x,y,z). [para(51(a,1),134(a,1,1))]. 551 x \ ((x * y) * (1 / y)) = a(x,y,1 / y). [para(18(a,1),164(a,1,1))]. 552 x \ ((x * y) * (y \ 1)) = a(x,y,1 / y). [para(155(a,1),551(a,1,2,2))]. 553 x \ ((x * y) * (y \ 1)) = a(x,y,y \ 1). [para(155(a,1),552(a,2,3))]. 554 a(x / y,y,y \ 1) = (x / y) \ (x * (y \ 1)). [para(22(a,1),553(a,1,2,1)),flip(a)]. 555 T((x * y) / (z * y),z) = R(z \ x,z,y). [para(84(a,1),194(a,2,1))]. 556 T(T((x * y) / (z * y),u),z) = T(R(z \ x,z,y),u). [para(555(a,1),42(a,1,1)),flip(a)]. 557 T(x,x * ((y * x) / y)) = x. [para(204(a,2),237(a,1))]. 558 ((x * y) / x) / y = y \ ((x * y) / x). [para(557(a,1),252(a,1,2))]. 560 (x \ y) * L(z,y,x \ 1) = x \ (y * z). [para(331(a,2),318(a,1))]. 561 (T(x,y) * (x \ 1)) * z = T(x,y) * (x \ z). [para(374(a,1),332(a,1,1)),flip(a)]. 562 (x \ T(x,y)) * z = T(x,y) * (x \ z). [para(377(a,1),561(a,1,1))]. 563 (T(x,y) * (x \ z)) / z = x \ T(x,y). [hyper(24,a,22,a,b,562,a),flip(a)]. 564 x * (T(x,y) * (x \ x)) = T(x * T(x,y),x). [para(562(a,1),138(a,1,2))]. 565 (T(x,y) * z) / (x * z) = x \ T(x,y). [para(19(a,1),563(a,1,1,2))]. 566 (x \ T(x,y)) \ (T(x,y) * z) = x * z. [para(565(a,1),66(a,1,1))]. 567 (x \ T(x,y)) \ z = x * (T(x,y) \ z). [para(20(a,1),566(a,1,2))]. 568 T(x * T(x,y),x) = x * (T(x,y) * 1). [para(60(a,1),564(a,1,2,2)),flip(a)]. 569 T(x * T(x,y),x) = x * T(x,y). [para(18(a,1),568(a,2,2))]. 571 T(x,x * T(x,y)) = x. [hyper(39,a,569,a)]. 572 T(x,y) / x = x \ T(x,y). [para(571(a,1),252(a,1,2))]. 573 (x \ T(x,y)) \ z = (x / T(x,y)) * z. [para(572(a,1),358(a,1,1))]. 574 (x \ T(x,y)) \ z = (T(x,y) \ x) * z. [para(299(a,1),573(a,2,1))]. 575 (T(x,y) \ x) * (T(x,y) * z) = x * z. [para(574(a,1),566(a,1))]. 576 (T(x,y) \ x) * z = x * (T(x,y) \ z). [para(574(a,1),567(a,1))]. 577 (x * y) / (T(x,z) * y) = T(x,z) \ x. [hyper(24,a,22,a,b,575,a),flip(a)]. 578 x * (T(x,y) \ 1) = T(x,y) \ x. [hyper(24,a,18,a,b,576,a),flip(a)]. 579 K(x,T(x,y) \ 1) = 1. [hyper(23,a,328,a,b,576,a),flip(a)]. 580 T(x,T(x,y) \ 1) = x. [hyper(41,a,579,a)]. 581 T(x,y) * (T(x,z) \ 1) = T(x,z) \ T(x,y). [para(580(a,1),329(a,1,2,1)),flip(a)]. 582 x \ (T(x,y) \ x) = T(x,y) \ 1. [hyper(23,a,20,a,b,578,a),flip(a)]. 583 ((T(x,y) \ x) * z) / (T(x,y) \ z) = R(x,T(x,y) \ 1,z). [para(578(a,1),324(a,1,1,1))]. 584 R(x \ 1,x * y,z) = R(x,y,z) \ 1. [para(348(a,2),344(a,1))]. 585 R(x,x \ y,z) \ 1 = R(x \ 1,y,z). [para(20(a,1),584(a,1,2)),flip(a)]. 586 (x * y) / (z * ((z \ x) * y)) = R(z,x,y) \ z. [para(213(a,1),500(a,1,2))]. 587 T(x \ R(x,y,z),x * (y * z)) = (x * (y * z)) \ ((x * y) * z). [para(537(a,1),84(a,1,1))]. 588 R(x * x,y,z) = x * x. [para(550(a,1),132(a,1))]. 589 R(T(x * x,y),z,u) = T(x * x,y). [para(588(a,1),46(a,2,1))]. 591 T(x * x,y) \ (z * u) = (T(x * x,y) \ z) * u. [para(589(a,1),197(a,1,1))]. 592 a(x / y,y,y \ 1) = (y / x) * (x * (y \ 1)). [para(554(a,2),358(a,1))]. 593 (x * y) / (z * ((z \ y) * T(x,y))) = R(z,y,T(x,y)) \ z. [para(82(a,1),586(a,1,1))]. 594 a(x,y,z) = (x \ (y * z)) \ ((x \ y) * z). [para(284(a,2),28(a,2))]. 596 (x \ (y * (x \ 1))) * x = T(y,x) * (x \ 1). [para(378(a,1),329(a,1))]. 597 (T(x,y) * (y \ 1)) / y = y \ (x * (y \ 1)). [hyper(24,a,22,a,b,596,a),flip(a)]. 598 x \ (y * (x \ 1)) = T(y,x) / (x * x). [para(597(a,1),401(a,1))]. 599 x \ ((x * (x * y)) * (x \ 1)) = (x * (y * x)) / (x * x). [para(103(a,1),598(a,2,1))]. 600 T(x,y) / (y * y) = T(x / (y * y),y). [para(598(a,1),403(a,2)),flip(a)]. 601 x * ((y \ (y \ 1)) * z) = (x / (y * y)) * z. [para(416(a,1),428(a,1,1)),flip(a)]. 602 (x / (y * y)) * z = x * (y \ (y \ z)). [para(291(a,1),601(a,1,2)),flip(a)]. 603 L(x,y / (y * z),z) = x. [hyper(23,a,74,a,b,451,a),flip(a)]. 604 (x * (y / (y * x))) \ z = (y / (y * x)) \ (x \ z). [para(603(a,1),177(a,1)),flip(a)]. 605 T(x,x * (y / (y * x))) = x. [para(603(a,1),364(a,2))]. 606 (x * (y / (y * x))) \ z = ((y * x) / y) * (x \ z). [para(604(a,2),358(a,1))]. 607 x * (x * ((y * z) / ((x * y) * z))) = R(x,x * y,z). [para(95(a,1),211(a,1)),flip(a)]. 608 L(R(x,x,y),z,u) * (x * y) = (x * L(x,z,u)) * y. [para(214(a,1),184(a,2,1))]. 609 L(K(x,y),y * x,x * y) = K(y,x) \ 1. [para(30(a,2),260(a,2,1))]. 610 (x \ (y * z)) \ ((x \ y) * z) = a(x \ 1,y,z). [para(318(a,1),323(a,1,2,1))]. 611 a(x \ 1,y,z) = a(x,y,z). [para(610(a,1),594(a,2)),flip(a)]. 612 a(x / y,z,u) = a(y / x,z,u). [para(343(a,1),611(a,1,1))]. 613 L(x \ 1,y,x \ 1) * y = y * T(x \ 1,x * y). [para(485(a,1),336(a,2,2))]. 614 T(T((x * y) / (z * y),u),z) = R(T(z \ x,u),z,y). [para(556(a,2),46(a,2)),flip(a)]. 615 x * (x * (R(x,y,z) \ 1)) = R(x,x * y,z). [para(344(a,1),607(a,1,2,2))]. 616 (x * x) / R(x,y,z) = R(x,x * y,z). [para(615(a,1),263(a,1)),flip(a)]. 617 x * (R(x,y,z) \ x) = R(x,x * y,z). [para(543(a,1),615(a,1,2))]. 618 x \ R(x,x * y,z) = R(x,y,z) \ x. [hyper(23,a,20,a,b,617,a),flip(a)]. 619 x * (R(x,x * y,z) \ x) = R(x,(x * x) * y,z). [para(131(a,2),617(a,2,2))]. 620 x / R(x,x * y,z) = x \ R(x,y,z). [para(617(a,1),535(a,1,2))]. 621 (R(x,y,z) \ x) * x = R(x,x * y,z). [para(617(a,1),544(a,2))]. 622 R(x,x * y,z) \ x = x \ R(x,y,z). [para(620(a,1),498(a,1)),flip(a)]. 623 R(x,x * y,z) \ 1 = x \ (x \ R(x,y,z)). [para(620(a,1),547(a,1,2)),flip(a)]. 624 x \ R(x,x \ y,z) = R(x,y,z) \ x. [para(20(a,1),622(a,1,1,2)),flip(a)]. 625 x * (R(x,x * y,z) \ u) = (x \ R(x,y,z)) * u. [para(622(a,1),544(a,1,1)),flip(a)]. 626 R(x,(x * x) * y,z) = x * (x \ R(x,y,z)). [para(622(a,1),619(a,1,2)),flip(a)]. 627 R(x,(x * x) * y,z) = R(x,y,z). [para(626(a,2),20(a,1))]. 628 R(x,x * (x * y),z) = R(x,y,z). [para(131(a,1),627(a,1,2))]. 629 R(x,x \ y,z) = R(x,x * y,z). [para(20(a,1),628(a,1,2,2)),flip(a)]. 630 R(x,x * y,z) \ (y * z) = (x \ y) * z. [para(629(a,1),197(a,1,1))]. 632 R(x,x * y,z) \ 1 = R(x \ 1,y,z). [para(629(a,1),585(a,1,1))]. 633 R(x,x * y,z) = R(x \ 1,y,z) \ 1. [para(632(a,1),156(a,1,1)),flip(a)]. 634 x \ (x \ R(x,y,z)) = R(x \ 1,y,z). [para(632(a,1),623(a,1)),flip(a)]. 635 x * R(x \ 1,y,z) = x \ R(x,y,z). [para(634(a,1),20(a,1,2))]. 636 x * (R(x \ 1,y,z) * u) = x \ (R(x,y,z) * u). [para(634(a,1),265(a,1,2,1))]. 637 x * (R(x,x * y,z) \ u) = R(x,y,z) * (x \ u). [para(625(a,2),532(a,1))]. 638 x * (R(x \ 1,y,z) * u) = R(x,y,z) * (x \ u). [para(636(a,2),534(a,1))]. 639 x * (y * R(y \ (x \ y),z,u)) = R(x,z,u) * (x \ y). [para(366(a,2),638(a,1,2))]. 640 (x * L(x,y,z)) * u = L(x,y,z) * (x * u). [para(182(a,1),608(a,1,1,1)),flip(a)]. 641 L(x,y,z) \ ((x * L(x,y,z)) * u) = x * u. [hyper(23,a,20,a,b,640,a(flip)),flip(a)]. 642 L(x,y,z) * (x * u) = x * (L(x,y,z) * u). [para(640(a,1),484(a,1))]. 643 L(x,y,z) \ (x * (L(x,y,z) * u)) = x * u. [para(484(a,1),641(a,1,2))]. 644 x * (L(x,y,z) * (x \ u)) = L(x,y,z) * u. [para(20(a,1),642(a,1,2)),flip(a)]. 645 L(x,y,z) * (x * (L(x,y,z) \ u)) = x * u. [para(20(a,1),642(a,2,2))]. 646 (L(x,y,z) \ x) * (L(x,y,z) * u) = x * u. [para(643(a,1),524(a,1)),flip(a)]. 647 (x \ L(x,y,z)) * u = L(x,y,z) * (x \ u). [hyper(23,a,504,a,b,644,a),flip(a)]. 648 (x * y) / (x * (L(x,z,u) \ y)) = L(x,z,u). [hyper(24,a,22,a,b,645,a),flip(a)]. 649 (x * y) / (L(x,z,u) * y) = L(x,z,u) \ x. [hyper(24,a,22,a,b,646,a),flip(a)]. 650 (L(x,y,z) \ x) * u = x * (L(x,y,z) \ u). [para(20(a,1),646(a,1,2))]. 652 T(x,L(x,y,z) \ x) = x. [hyper(23,a,82,a,b,650,a),flip(a)]. 653 K(x,L(x,y,z) \ x) = 1. [hyper(40,a,652,a)]. 654 T(x \ 1,x * (y * y)) = T(x,y * y) \ 1. [para(202(a,1),380(a,2,1))]. 655 T(x,y * y) \ 1 = T(x \ 1,y * y). [para(654(a,1),431(a,1))]. 656 L(x,y,R(T(y,z),u,w)) = x. [hyper(23,a,74,a,b,436,a),flip(a)]. 657 L(x,y,R((y \ z) \ z,u,w)) = x. [para(83(a,1),656(a,1,3,1))]. 658 x \ ((y \ (y \ z)) * (y * (y * x))) = T(z,y * (y * x)). [para(285(a,1),444(a,1,2))]. 659 x \ (x * (x * (y * (x \ 1)))) = (x * (y * x)) / (x * x). [para(51(a,1),599(a,1,2))]. 660 x \ (T(y,z * z) * x) = T(y,z * (z * x)). [para(420(a,1),658(a,1,2))]. 661 T(T(x,y * y),z) = T(x,y * (y * z)). [para(660(a,1),36(a,2))]. 662 T(T(x,y),z * z) = T(x,z * (z * y)). [para(661(a,1),42(a,1)),flip(a)]. 663 x \ (x * T(y,x \ 1)) = (x * (y * x)) / (x * x). [para(347(a,1),659(a,1,2,2))]. 664 (x * (y * x)) / (x * x) = T(y,x \ 1). [para(663(a,1),19(a,1))]. 665 T(x * y,x) / (x * x) = T(x \ y,x \ 1). [para(138(a,1),664(a,1,1))]. 666 T((x * y) / (x * x),x) = T(x \ y,x \ 1). [para(665(a,1),600(a,1)),flip(a)]. 667 (x * (x * ((y * z) * u))) / (z * u) = R(x * (x * y),z,u). [para(51(a,1),94(a,1,1))]. 668 (x * (y \ 1)) / (x / y) = (x / y) \ (x * (y \ 1)). [para(434(a,1),481(a,1,2)),flip(a)]. 669 (x * (y \ 1)) / (x / y) = (y / x) * (x * (y \ 1)). [para(668(a,2),358(a,1))]. 670 (x * (T(x,y) \ z)) / (T(x,y) \ z) = R(x,T(x,y) \ 1,z). [para(576(a,1),583(a,1,1))]. 671 (x * y) / (L(x,z * y,z) * y) = R(z,y,T(x,y)) \ z. [para(455(a,1),593(a,1,2))]. 672 R(x,y,T(z,y)) \ x = L(z,x * y,x) \ z. [para(671(a,1),649(a,1))]. 673 (R(x,y,T(z,y)) \ x) \ 1 = z \ L(z,x * y,x). [para(672(a,2),511(a,1,1))]. 674 L(x,y * (y * z),y) \ x = y \ R(y,z,T(x,y * z)). [para(672(a,1),622(a,1))]. 676 x \ R(x,y,T(z,y)) = z \ L(z,x * y,x). [para(673(a,1),460(a,1)),flip(a)]. 677 R(x,y,T(z,y)) = x * (z \ L(z,x * y,x)). [para(676(a,1),20(a,1,2)),flip(a)]. 678 R(x,x * y,T(z,x * y)) = x * (z \ L(z,y,x)). [para(313(a,1),677(a,2,2,2))]. 679 R(x,y,T(z,x * y)) \ x = z \ L(z,y,x). [hyper(23,a,617,a,b,678,a(flip)),flip(a)]. 680 (x \ L(x,y,z)) * R(z,y,T(x,z * y)) = z. [para(679(a,1),496(a,1,1))]. 681 L(x,y,z) \ x = z \ R(z,y,T(x,z * y)). [para(313(a,1),674(a,1,1))]. 682 L(x,y,z) * (z \ R(z,y,T(x,z * y))) = x. [para(681(a,1),20(a,1,2))]. 683 R(x,y,T(z,x * y)) = x * (L(z,y,x) \ z). [para(681(a,2),20(a,1,2)),flip(a)]. 684 (x \ R(x,y,T(z,x * y))) * L(z,y,x) = z. [para(681(a,1),520(a,1,1))]. 685 L(x,R(y,z,u),T(y,w)) * (T(y,w) \ T(y,w)) = x. [para(527(a,1),682(a,1,2,2))]. 686 R(x,y,T(z,x * y)) * (x \ L(z,y,x)) = z. [para(684(a,1),532(a,1)),flip(a)]. 687 L(x,R(y,z,u),T(y,w)) * 1 = x. [para(60(a,1),685(a,1,2))]. 688 L(x,R(y,z,u),T(y,w)) = x. [hyper(24,a,18,a,b,687,a)]. 690 L(x,R(y / z,u,w),z \ y) = x. [para(84(a,1),688(a,1,3))]. 691 T(R(x,y,z),T(x,u)) / T(x,u) = T(x,u) \ R(x,y,z). [para(688(a,1),441(a,1,2))]. 692 R(T(x,T(x,y)),z,u) / T(x,y) = T(x,y) \ R(x,z,u). [para(46(a,2),691(a,1,1))]. 693 R(x,y,z) / T(x,u) = T(x,u) \ R(x,y,z). [para(115(a,1),692(a,1,1,1))]. 694 x * (x * (((y * z) * u) / (z * u))) = R(x * (x * y),z,u). [para(667(a,1),211(a,1)),flip(a)]. 695 R(x,T(x,y) \ 1,z) = x. [para(670(a,1),21(a,1))]. 696 R(x * (x * y),z,u) = x * (x * R(y,z,u)). [para(34(a,2),694(a,1,2,2)),flip(a)]. 697 x * (x * R(T(y,x),z,u)) = R(x * (y * x),z,u). [para(82(a,1),696(a,1,1,2)),flip(a)]. 698 R(x * (x * T(y,x * x)),z,u) = R(y,z,u) * (x * x). [para(696(a,2),226(a,1))]. 699 R(x * (y * x),z,u) = x * (R(y,z,u) * x). [para(110(a,1),697(a,1,2)),flip(a)]. 700 x \ R(x * (y * x),z,u) = R(y,z,u) * x. [hyper(23,a,20,a,b,699,a(flip)),flip(a)]. 701 (x * (y * x)) \ R(x * (z * x),u,w) = T(y,x) \ (x \ (R(z,u,w) * x)). [para(699(a,2),287(a,1,2))]. 702 x \ R(x * y,z,u) = R(y / x,z,u) * x. [para(22(a,1),700(a,1,2,1,2))]. 703 x \ R(x * y,z,u) = x * R(x \ y,z,u). [para(702(a,2),224(a,1))]. 704 L(x \ (y * R(y \ z,u,w)),x,y) = (y * x) \ R(y * z,u,w). [para(703(a,1),177(a,1,1,2))]. 705 R(x * (y * y),z,u) = R(x,z,u) * (y * y). [para(136(a,1),698(a,1,1))]. 706 (x \ 1) \ T(x \ 1,x * y) = ((x * y) \ y) * x. [para(156(a,1),385(a,2,2))]. 707 (x \ 1) \ T(x \ 1,x * y) = x * ((x * y) \ y). [para(706(a,2),381(a,1))]. 708 (x * y) * T(L(y \ 1,y,x),z) = (x * y) * T((x * y) \ x,z). [para(231(a,1),139(a,1))]. 709 R((x / y) * (z * z),z \ (z \ 1),y) = x / (z \ (z \ y)). [para(415(a,1),293(a,1,1))]. 710 x / (y \ (y \ z)) = (x / z) * (y * y). [para(709(a,1),426(a,1))]. 711 (x / (y * z)) * (y * y) = x / (y \ z). [para(19(a,1),710(a,1,2,2)),flip(a)]. 712 (x * y) / (z \ y) = R(x / z,z,y) * (z * z). [para(80(a,2),711(a,1,1)),flip(a)]. 713 R((x / y) * (y * y),y,z) = (x * z) / (y \ z). [para(712(a,2),705(a,2))]. 714 R(x / (y \ 1),y,z) = (x * z) / (y \ z). [para(397(a,1),713(a,1,1))]. 715 R(x,y,z) = ((x * (y \ 1)) * z) / (y \ z). [para(21(a,1),714(a,1,1))]. 716 R(L(x,y,z) \ x,x,u) = ((L(x,y,z) \ 1) * u) / (x \ u). [para(513(a,1),714(a,1,1))]. 717 R(x,y \ 1,z) = R(x,y,z). [para(715(a,2),324(a,1)),flip(a)]. 718 R(x,y,y) / y = x * (y \ 1). [para(717(a,1),207(a,1,1))]. 719 (x * (y \ 1)) \ R(x,y,y) = y. [para(717(a,1),209(a,1,2))]. 720 R(x / (y \ 1),y,y) = x * y. [para(717(a,1),210(a,1))]. 721 R(x,T(x,y),z) = x. [para(717(a,1),695(a,1))]. 722 (x * T(x,y)) * z = x * (T(x,y) * z). [para(721(a,1),79(a,1,1)),flip(a)]. 723 R(T(x / (y \ 1),z),y,y) / y = (y \ 1) * T((y \ 1) \ x,z). [para(718(a,2),139(a,1))]. 725 (T(x,y) * (R(x,z,u) \ 1)) \ T(x,y) = R(x,z,u). [para(527(a,1),719(a,1,2))]. 726 R(T(x / (y \ 1),z),y,y) = T(x * y,z). [para(720(a,1),46(a,2,1))]. 727 L(x,T(y,z),y) = x. [hyper(23,a,74,a,b,722,a),flip(a)]. 729 x * (T(x,y) * (x \ z)) = T(x,y) * z. [para(722(a,1),281(a,1))]. 730 L(x,y,(z * y) / z) = x. [para(104(a,1),727(a,1,2))]. 731 L(x,(y \ z) \ z,y) = x. [para(83(a,1),727(a,1,2))]. 732 x \ (T(x,y) * z) = T(x,y) * (x \ z). [hyper(23,a,20,a,b,729,a),flip(a)]. 733 x \ (T(x,y) * z) = (x \ T(x,y)) * z. [para(732(a,2),562(a,2)),flip(a)]. 734 (R(x,y,z) \ T(x,u)) \ T(x,u) = R(x,y,z). [para(548(a,1),725(a,1,1))]. 735 R(L(x,y,z) \ x,x,u) = (L(x,y,z) \ u) / (x \ u). [para(318(a,1),716(a,2,1))]. 736 R(L(x,y,z) \ x,x,u) = L(x,y,z) \ x. [para(735(a,2),513(a,1))]. 739 a(x,y,z) = T(x \ R(x,y,z),x * (y * z)). [para(587(a,2),28(a,2))]. 740 T(T(x \ R(x,y,z),u),x * (y * z)) = T(a(x,y,z),u). [para(739(a,2),42(a,1,1)),flip(a)]. 741 a(x,y,z) = T(T(R(x,y,z) / x,x * (y * z)),x). [para(739(a,2),112(a,2)),flip(a)]. 742 T((x * (y \ R(y,z,u))) / x,y * (z * u)) = (x * a(y,z,u)) / x. [para(739(a,2),233(a,1,1,2)),flip(a)]. 743 T(R(x,y,z) \ R(R(x,y,z),u,x),x * (R(x,y,z) * T(u,x))) = a(R(x,y,z),u,x). [para(530(a,2),739(a,2,2)),flip(a)]. 744 T(T((R(x,y,z) * u) / (x * u),x * (y * z)),x) = R(a(x,y,z),x,u). [para(739(a,2),614(a,2,1))]. 745 a(x,y,z) = T(T(x \ R(x,y,z),x * (y * z)),x). [para(478(a,1),741(a,2,1,1))]. 746 T(a(x,y,z),x) = a(x,y,z). [para(739(a,2),745(a,2,1)),flip(a)]. 747 a(x,y,z) * x = x * a(x,y,z). [para(746(a,1),82(a,1,2)),flip(a)]. 748 (x * a(x,y,z)) / x = a(x,y,z). [para(746(a,1),105(a,1,1,2))]. 749 ((x * (x * y)) * a(x * (x * y),z,u)) / y = a(x * (x * y),z,u) * (x * x). [para(747(a,1),418(a,1,1))]. 750 (x \ y) \ R(x \ z,u,w) = (x * y) \ R(x * z,u,w). [para(704(a,1),267(a,1)),flip(a)]. 751 (x * y) * T((x * y) \ x,z) = (x * y) * L(T(y \ 1,z),y,x). [para(44(a,2),708(a,1,2)),flip(a)]. 752 (x \ 1) * T((x \ 1) \ y,z) = T(y * x,z) / x. [para(726(a,1),723(a,1,1)),flip(a)]. 753 (x \ 1) * T(x * y,z) = T(y * x,z) / x. [para(330(a,1),752(a,1,2,1))]. 754 T(x * y,z) / y = y \ T(y * x,z). [para(753(a,1),318(a,1))]. 755 x \ T(x * (y / x),z) = T(y,z) / x. [para(22(a,1),754(a,1,1,1)),flip(a)]. 756 T(x * y,y) / y = (y \ x) * y. [para(754(a,2),146(a,1))]. 757 ((x \ y) * x) * x = T(y * x,x). [para(756(a,1),22(a,1,1))]. 758 T((x * y) * x,x) = (y * x) * x. [para(19(a,1),757(a,1,1,1)),flip(a)]. 762 (x * y) * T((x * y) \ x,z) = x * (y * T(y \ 1,z)). [para(751(a,2),74(a,1))]. 763 (x * (x * (y * z))) \ (x * (x * (y * (z * u)))) = L(u,z,x * (x * y)). [para(51(a,1),92(a,1,2))]. 764 (x * y) * T(L(y \ z,y,x),u) = (x * y) * T((x * y) \ (x * z),u). [para(232(a,1),139(a,1))]. 765 (x * y) * R(L(y \ 1,y,x),z,u) = (x * y) * R((x * y) \ x,z,u). [para(472(a,1),224(a,1))]. 767 T(T(x \ R(x,y,z),x * (y * z)),x) = R(a(x,y,z),x,u). [para(531(a,1),744(a,1,1,1))]. 769 R(a(x,y,z),x,u) = a(x,y,z). [para(767(a,1),745(a,2)),flip(a)]. 770 (a(x,y,z) * x) * u = a(x,y,z) * (x * u). [para(769(a,1),79(a,1,1)),flip(a)]. 771 L(x,y,a(y,z,u)) = x. [hyper(23,a,74,a,b,770,a),flip(a)]. 772 (x * a(x,y,z)) * u = a(x,y,z) * (x * u). [para(747(a,1),770(a,1,1))]. 773 L(x,y,z * (z * u)) = (u * y) \ (u * (y * x)). [para(763(a,1),212(a,1))]. 774 L(x,y,z * (z * u)) = L(x,y,u). [para(773(a,2),32(a,2)),flip(a)]. 776 L(x,y,z \ u) = L(x,y,z * u). [para(20(a,1),774(a,1,3,2)),flip(a)]. 777 L(x,y,(z / u) * z) = L(x,y,u). [para(22(a,1),774(a,1,3,2))]. 778 L(x,y,z * (u * z)) = L(x,y,T(u,z)). [para(82(a,1),774(a,1,3,2))]. 779 L(x,y,(z * u) * (u * z)) = L(x,y,K(u,z)). [para(69(a,1),774(a,1,3,2))]. 780 L(x,y,z * ((z \ u) * w)) = L(x,y,z * ((z * u) * w)). [para(89(a,1),774(a,1,3,2)),flip(a)]. 781 L(x,y,(z \ u) * w) = L(x,y,(z * u) * w). [para(89(a,1),774(a,1,3)),flip(a)]. 782 L(x,y,(z \ (z \ u)) * (z \ u)) = L(x,y,T(z,u)). [para(254(a,1),774(a,1,3,2))]. 783 L(x,y,(z * z) / u) = L(x,y,u \ 1). [para(263(a,1),774(a,1,3))]. 784 L(x,y,z / u) = L(x,y,u / z). [para(360(a,1),774(a,1,3))]. 785 L(x,y,z * L(z,u * z,u)) = L(x,y,a(u,z,z)). [para(453(a,2),774(a,1,3,2))]. 786 L(x,y,R(z * (z * u),w,v5)) = L(x,y,R(u,w,v5)). [para(696(a,2),774(a,1,3))]. 787 L(x,y,z \ 1) = L(x,y,z). [para(18(a,1),776(a,2,3))]. 789 L(x,y,T(z / u,z)) = L(x,y,((u / z) * u) * u). [para(370(a,2),776(a,1,3))]. 790 L(x,y,y \ (z * z)) = x. [para(776(a,2),429(a,1))]. 792 L(x \ (x / y),y,x * (x / y)) = ((x \ (x / y)) \ y) \ y. [para(776(a,1),442(a,1))]. 793 L(x,R(y / z,u,w),z * y) = x. [para(776(a,1),690(a,1))]. 794 L(x \ L(y \ z,y,u),x,u * y) = ((u \ y) * x) \ (u \ z). [para(776(a,1),275(a,1))]. 795 T(x * x,y) \ (y \ (x * x)) = y \ 1. [para(790(a,1),395(a,1)),flip(a)]. 796 L(x,L(y \ 1,z,u),y) = x. [para(787(a,1),503(a,1))]. 797 L(x,(y * z) \ y,z) = x. [para(787(a,1),505(a,1))]. 798 (x \ y) * L(z,y,x) = x \ (y * z). [para(787(a,1),560(a,1,2))]. 799 x * T(y \ 1,y * x) = L(y \ 1,x,y) * x. [para(787(a,1),613(a,1,1)),flip(a)]. 800 L(x,y \ z,z \ y) = x. [para(20(a,1),797(a,1,2,1))]. 801 L(x,y \ z,z * y) = x. [para(800(a,1),776(a,1)),flip(a)]. 802 L(x,y,z * (z / y)) = x. [para(66(a,1),801(a,1,2))]. 803 (x * L(x \ 1,y,z)) \ u = L(x \ 1,y,z) \ (x \ u). [para(796(a,1),177(a,1)),flip(a)]. 804 L(x,y,(z * (z * u)) * (z * w)) = L(x,y,u \ (z \ w)). [para(282(a,1),777(a,1,3,1))]. 805 L(x,y,(z * (z * u)) * z) = L(x,y,u \ (z \ 1)). [para(289(a,1),777(a,1,3,1))]. 806 L(L(x,y,y / z),z,z / y) = x. [para(784(a,1),304(a,1,1))]. 807 L(x,x,x / y) = y \ (y / (x \ 1)). [para(784(a,1),432(a,1))]. 808 L(x,y,z / (z * y)) = x. [para(784(a,1),730(a,1))]. 809 ((x / (x * y)) * y) \ (x / (x * y)) = y \ 1. [para(808(a,1),142(a,1)),flip(a)]. 810 ((x / (x * y)) * y) * z = (x / (x * y)) * (y * z). [para(808(a,1),74(a,1,2))]. 811 ((x / (x * y)) * y) \ z = y \ ((x / (x * y)) \ z). [para(808(a,1),177(a,1)),flip(a)]. 812 L(x,y / (z * (u * y)),z * (u \ 1)) = x. [para(350(a,1),793(a,1,2))]. 813 (x * (y \ z)) \ (x * (y \ (z * u))) = L(L(u,z,y),y \ z,x). [para(798(a,1),32(a,2,2,2)),flip(a)]. 815 T(x,y) \ (x * z) = (T(x,y) \ x) * z. [para(234(a,1),798(a,1,2)),flip(a)]. 816 x \ (((y * x) / y) * z) = (x \ ((y * x) / y)) * z. [para(237(a,1),798(a,1,2)),flip(a)]. 817 (x \ y) * T((x \ y) \ 1,z) = x \ (y * T(y \ x,z)). [para(261(a,1),798(a,1,2))]. 818 L(x,y,T(z \ u,z)) = L(x,y,T(z * u,z)). [para(138(a,1),778(a,1,3)),flip(a)]. 819 L(x,y,T((z \ u) * z,z)) = L(x,y,z * T(u * z,z)). [para(757(a,1),778(a,1,3,2)),flip(a)]. 820 L(x,y,(z * z) / u) = L(x,y,u). [para(783(a,2),787(a,1))]. 821 L(x,y,T(z,z * (u * u))) = L(x,y,z \ (u * u)). [para(252(a,1),820(a,1,3)),flip(a)]. 822 L(x,y,z / (u * u)) = L(x,y,z). [para(820(a,1),784(a,1)),flip(a)]. 823 L(x,y,z * (u * u)) = L(x,y,z). [para(21(a,1),822(a,1,3)),flip(a)]. 824 L(x,y,(z * u) * u) = L(x,y,R(z,u,u)). [para(34(a,2),822(a,1,3)),flip(a)]. 825 (x * (y * (y * z))) \ ((x * (y * y)) * (z * u)) = L(u,z,x). [para(823(a,1),419(a,2))]. 826 (T(x,y) \ x) * y = T(y,T(x,y)). [para(815(a,1),107(a,1))]. 827 T(x,y) \ (x * z) = x * (T(x,y) \ z). [para(815(a,2),576(a,1))]. 828 x * (T(x,y) \ y) = T(y,T(x,y)). [para(826(a,1),576(a,1)),flip(a)]. 829 T(x,T(y,x)) / (T(y,x) \ x) = y. [hyper(24,a,22,a,b,828,a),flip(a)]. 830 x \ T(y,T(x,y)) = T(x,y) \ y. [hyper(23,a,20,a,b,828,a),flip(a)]. 831 (x * y) / (x * (T(x,z) \ y)) = T(x,z). [para(827(a,1),65(a,1,2))]. 832 (((x * y) * (y * x)) * z) \ (((x * y) * (y * x)) * (z * u)) = L(u,z,K(y,x)). [para(779(a,1),32(a,1)),flip(a)]. 833 (x * (y / (y * x))) \ (y / (y * x)) = x \ 1. [para(362(a,1),809(a,1,1))]. 834 T(x \ 1,x * (y / (y * x))) = x \ 1. [para(833(a,1),349(a,2))]. 835 L(x \ 1,y,x) * y = y * ((x * y) \ y). [para(349(a,1),799(a,1,2)),flip(a)]. 836 L(x,y,(z * (z \ u)) * (z \ u)) = L(x,y,T(z,u)). [para(782(a,1),781(a,1)),flip(a)]. 837 L(x,y,z * ((z \ u) * u)) = L(x,y,a(z,u,u)). [para(435(a,1),785(a,1,3))]. 838 L(x,y,R(z \ u,w,v5)) = L(x,y,R(z * u,w,v5)). [para(20(a,1),786(a,1,3,1,2)),flip(a)]. 839 L(x,y,T(z / u,z)) = L(x,y,R(u / z,u,u)). [para(789(a,2),824(a,1))]. 840 L(x,y,z * (z * (u * z))) = L(x,y,u \ (z \ 1)). [para(51(a,1),805(a,1,3))]. 841 (x * (y / (y * x))) * z = (y / (y * x)) * (x * z). [para(362(a,1),810(a,1,1))]. 842 (x * (y / (y * x))) \ z = x \ ((y / (y * x)) \ z). [para(362(a,1),811(a,1,1))]. 843 L(x,y,T(z,z * (u * u))) = L(x,y,z * (u * u)). [para(821(a,2),776(a,1))]. 844 L(x,y,z * (u \ z)) = L(x,y,T(u,z)). [para(20(a,1),836(a,1,3,1))]. 845 L(x,y,T(z / u,z)) = L(x,y,z * u). [para(66(a,1),844(a,1,3,2)),flip(a)]. 846 L(x,y,R(z / u,z,z)) = L(x,y,u * z). [para(845(a,1),839(a,1)),flip(a)]. 847 L(x,y,R((y \ z) * z,u,w)) = x. [para(838(a,1),657(a,1))]. 848 L(x,y,z \ (u \ 1)) = L(x,y,z * u). [para(840(a,1),774(a,1))]. 850 L(x,y,z * (u \ 1)) = L(x,y,z * u). [para(848(a,1),776(a,1)),flip(a)]. 851 L(x,y / (z * (u * y)),z * u) = x. [para(850(a,1),812(a,1))]. 852 L(x,(y * z) * (u / (y * (z * u))),y * z) = x. [para(851(a,1),303(a,1,1))]. 853 ((x * y) * z) / (x * (y * z)) = (x * y) * (z / (x * (y * z))). [para(851(a,1),196(a,1,2))]. 854 x \ ((y / (y * x)) \ z) = ((y * x) / y) * (x \ z). [para(842(a,1),606(a,1))]. 855 L(x,y,T(z,z * (u * u))) = L(x,y,z). [para(843(a,2),823(a,1))]. 856 L(x,y,T(z,u * u)) = L(x,y,z). [para(423(a,1),855(a,1,3))]. 858 L(x,y,R(T(z,u * u),w,v5)) = L(x,y,R(z,w,v5)). [para(46(a,2),856(a,1,3))]. 859 x \ (((y * x) / y) * z) = ((y * x) / y) * (x \ z). [para(358(a,1),854(a,1,2))]. 860 (x \ ((y * x) / y)) * z = ((y * x) / y) * (x \ z). [para(859(a,1),816(a,1)),flip(a)]. 861 L(x,y,z * ((z * u) * u)) = L(x,y,a(z,u,u)). [para(780(a,1),837(a,1))]. 862 L(x,y,z * (z * (u * (z * w)))) = L(x,y,u \ (z \ w)). [para(51(a,1),804(a,1,3))]. 863 L(x,y,T((z \ u) * z,z)) = L(x,y,(u * z) * z). [para(82(a,1),819(a,2,3))]. 864 L(x,y,T((z \ u) * z,z)) = L(x,y,R(u,z,z)). [para(863(a,2),824(a,1))]. 865 L(x,y,z \ (u \ w)) = L(x,y,z * (u * w)). [para(862(a,1),774(a,1))]. 867 L(x,y,z * (u \ w)) = L(x,y,z * (u * w)). [para(865(a,1),776(a,1)),flip(a)]. 868 L(x,y,z * (u * (u * w))) = L(x,y,z * w). [para(19(a,1),867(a,1,3,2)),flip(a)]. 869 L(x,y,(z \ u) * (u \ z)) = L(x,y,(u \ z) * (z * u)). [para(384(a,1),867(a,1,3))]. 871 ((x \ (x / y)) \ y) \ y = x \ (x / y). [para(792(a,1),802(a,1))]. 872 x / (y \ (y / x)) = (y \ (y / x)) \ x. [para(871(a,1),65(a,1,2))]. 873 (x * (y * (y * z))) \ (x * (y * (y * (z * u)))) = L(u,z,x). [para(411(a,1),825(a,1,2))]. 875 L(x,y * (y * z),u) = L(x,z,u). [para(873(a,1),93(a,1)),flip(a)]. 876 L(x,y \ z,u) = L(x,y * z,u). [para(20(a,1),875(a,1,2,2)),flip(a)]. 877 L(x,(y / z) * y,u) = L(x,z,u). [para(22(a,1),875(a,1,2,2))]. 878 L(x,y * (z * y),u) = L(x,T(z,y),u). [para(82(a,1),875(a,1,2,2))]. 879 L(x,(y * z) * (z * y),u) = L(x,K(z,y),u). [para(69(a,1),875(a,1,2,2))]. 880 L(x,(y \ z) * u,w) = L(x,(y * z) * u,w). [para(89(a,1),875(a,1,2)),flip(a)]. 881 L(x,T(y,y * z),u) = L(x,(y \ z) * z,u). [para(250(a,1),875(a,1,2,2)),flip(a)]. 882 L(x,(y * y) / z,u) = L(x,z \ 1,u). [para(263(a,1),875(a,1,2))]. 883 L(x,T(y \ 1,z),u) = L(x,z * (y \ z),u). [para(327(a,1),875(a,1,2,2)),flip(a)]. 884 L(x,y / z,u) = L(x,z / y,u). [para(360(a,1),875(a,1,2))]. 887 L(x,y \ 1,z) = L(x,y,z). [para(18(a,1),876(a,2,2))]. 888 (x * (y \ z)) * L(u,y * z,x) = x * ((y \ z) * u). [para(876(a,1),74(a,1,2))]. 889 L(x,(y \ z) * z,y) = x. [para(876(a,1),731(a,1))]. 890 L(x,y * z,z * y) = x. [para(876(a,1),801(a,1))]. 893 (x * ((x \ y) * y)) \ z = ((x \ y) * y) \ (x \ z). [para(889(a,1),177(a,1)),flip(a)]. 894 ((x * y) * (y * x)) * z = (x * y) * ((y * x) * z). [para(890(a,1),74(a,1,2))]. 895 T(x * y,(x * y) * (y * x)) = T(x * y,y * x). [para(890(a,1),203(a,1)),flip(a)]. 896 L(x,K(y,z),z * y) = x. [para(890(a,1),315(a,1,1))]. 897 K(x,y) \ 1 = K(y,x). [para(890(a,1),609(a,1)),flip(a)]. 898 K(x,y) * K(y,x) = 1. [para(897(a,1),20(a,1,2))]. 899 1 / K(x,y) = K(y,x). [para(897(a,1),65(a,1,2))]. 900 K(x,y) \ z = K(y,x) * z. [para(897(a,1),318(a,1,1)),flip(a)]. 901 K(x,y) * (K(y,x) * z) = z. [para(897(a,1),321(a,1,2,1))]. 902 x / (K(y,z) * x) = K(z,y). [para(897(a,1),340(a,2))]. 903 T(x * y,K(y,x)) / (y * x) = K(x,y). [para(897(a,1),345(a,2))]. 904 R(K(x,y),K(y,x) * z,u) = R(K(y,x),z,u) \ 1. [para(897(a,1),584(a,1,1))]. 905 a(K(x,y),z,u) = a(K(y,x),z,u). [para(897(a,1),611(a,1,1))]. 906 R(K(x,y),K(x,y) * z,u) = R(K(y,x),z,u) \ 1. [para(897(a,1),633(a,2,1,1))]. 907 K(x,y) * (K(y,x) / (x * y)) = K(x,y) \ ((y * x) \ 1). [para(897(a,1),379(a,1,2,1))]. 908 R(x,K(y,z),u) = R(x,K(z,y),u). [para(897(a,1),717(a,1,2))]. 909 L(x,y,K(z,u)) = L(x,y,K(u,z)). [para(897(a,1),787(a,1,3))]. 910 L(K(x,y),z,K(y,x)) * z = z * ((K(y,x) * z) \ z). [para(897(a,1),835(a,1,1,1))]. 911 (x * y) * (K(y,x) * z) = (y * x) * z. [para(896(a,1),176(a,1,2)),flip(a)]. 912 K(x,y) \ ((y * x) \ z) = (x * y) \ z. [para(896(a,1),199(a,1))]. 914 L(x,x,y) = (y * (x \ 1)) \ y. [para(887(a,1),161(a,1))]. 915 x / L(y,y,x) = x * (y \ 1). [para(887(a,1),162(a,1,2))]. 916 L(L(x,y * (z \ 1),y),z,y) = x. [para(887(a,1),308(a,1))]. 917 L(x * y,x,y) = (y \ (x \ 1)) \ 1. [para(887(a,1),351(a,1))]. 918 L(x,y,L(y \ 1,z,u)) = x. [para(887(a,1),509(a,1))]. 919 (x * (y \ z)) / L(z,y,x) = x * (y \ 1). [para(887(a,1),333(a,1,2))]. 920 L(x * (y * z),x,y) = (y \ (x \ 1)) \ z. [para(887(a,1),352(a,1))]. 921 L(x,K(y,z),u) = L(x,K(z,y),u). [para(897(a,1),887(a,1,2))]. 922 T(x * y,K(y,x)) = K(x,y) * (y * x). [para(900(a,1),122(a,1)),flip(a)]. 923 R(K(x,y),K(y,x) * z,u) \ K(x,y) = K(x,y) \ R(K(x,y),z,u). [para(901(a,1),618(a,1,2,2)),flip(a)]. 924 (L(x \ 1,y,z) * x) \ u = x \ (L(x \ 1,y,z) \ u). [para(918(a,1),177(a,1)),flip(a)]. 925 L(x / y,x / y,z) = (z * (y / x)) \ z. [para(343(a,1),914(a,2,1,2))]. 926 L(K(x,y),K(x,y),z) = (z * K(y,x)) \ z. [para(897(a,1),914(a,2,1,2))]. 928 L(x,(y * (y * z)) * (y * u),w) = L(x,z \ (y \ u),w). [para(282(a,1),877(a,1,2,1))]. 929 L(x,(y * (y * z)) * y,u) = L(x,z \ (y \ 1),u). [para(289(a,1),877(a,1,2,1))]. 930 K(x,y) / L(z,z,K(y,x)) = K(x,y) * (z \ 1). [para(909(a,1),915(a,1,2))]. 931 L(x,y * (z \ 1),y) = L(x,y * z,y). [para(916(a,1),303(a,1,1)),flip(a)]. 932 L(x,K(y,z),y * z) = x. [para(921(a,1),896(a,1))]. 933 ((x * y) \ K(x,y)) \ z = K(x,y) \ ((x * y) * z). [para(932(a,1),267(a,1)),flip(a)]. 934 L(x * y,x,y) * z = (y \ (x \ 1)) \ z. [para(917(a,2),318(a,1,1))]. 935 L(x,(y * y) / z,u) = L(x,z,u). [para(882(a,2),887(a,1))]. 936 L(x,y / (z * z),u) = L(x,y,u). [para(935(a,1),884(a,1)),flip(a)]. 937 L(x,y * (z * z),u) = L(x,y,u). [para(21(a,1),936(a,1,2)),flip(a)]. 938 L(x,(y * z) * z,u) = L(x,R(y,z,z),u). [para(34(a,2),936(a,1,2)),flip(a)]. 939 ((x * y) * z) / (K(x,y) * z) = y * x. [hyper(24,a,22,a,b,911,a),flip(a)]. 940 (x * y) \ ((y * x) * z) = K(y,x) * z. [hyper(23,a,20,a,b,911,a),flip(a)]. 941 K(x,y) * ((x * y) \ z) = (y * x) \ z. [para(912(a,1),20(a,1,2))]. 942 x * (y \ ((y * (x \ 1)) * z)) = L(z,y * x,y). [para(931(a,1),446(a,2))]. 943 L(x,K(y,z) * (y * z),u) = L(x,z * y,u). [para(939(a,1),935(a,1,2)),flip(a)]. 944 (x * y) \ (y * (x * z)) = K(y,x) * L(z,x,y). [para(74(a,1),940(a,1,2))]. 945 (x * (y \ 1)) * L(z,y,x) = x * (y \ z). [para(919(a,1),22(a,1,1))]. 946 (a(x,y,z) \ (x \ 1)) \ u = x * (a(x,y,z) * u). [para(920(a,1),771(a,1))]. 947 L(K(x,y),K(x,y),z) / z = (z * K(y,x)) \ 1. [para(926(a,2),320(a,1,1))]. 948 (a(x,y,z) \ (x \ 1)) \ u = (x * a(x,y,z)) * u. [para(771(a,1),934(a,1,1)),flip(a)]. 951 L(x,T(y,y * z),u) = L(x,(y * z) * z,u). [para(881(a,2),880(a,1))]. 953 L(x,(y * (y \ z)) * (y \ z),u) = L(x,T(y,z),u). [para(20(a,1),951(a,1,2,2)),flip(a)]. 954 x * (y * ((y \ (x \ 1)) * z)) = L(z,y * x,y). [para(213(a,1),942(a,1,2))]. 955 K(x,y) * L(x,y,x) = T(x,y * x). [para(944(a,1),36(a,2)),flip(a)]. 956 x * ((x \ (y \ 1)) * y) = a(x,y,y). [hyper(23,a,453,a(flip),b,954,a)]. 957 x * (y * (R(y,y * (x \ 1),z) \ ((x \ 1) * z))) = L(z,y * x,y). [para(630(a,2),954(a,1,2,2))]. 958 x * R(x \ 1,y \ 1,y) = a(x,y,y). [para(335(a,2),956(a,1,2))]. 959 x \ R(x,y \ 1,y) = a(x,y,y). [para(958(a,1),635(a,1)),flip(a)]. 960 x * R(x \ 1,y,y) = a(x,y,y). [para(717(a,1),958(a,1,2))]. 961 R(x,y \ 1,y) \ a(x,y,y) = T(x \ 1,R(x,y \ 1,y)). [para(959(a,1),325(a,2,2)),flip(a)]. 962 x \ R(x,y,y) = a(x,y,y). [para(717(a,1),959(a,1,2))]. 963 x * a(x,y,y) = R(x,y,y). [para(962(a,1),20(a,1,2))]. 964 a(x,y,y) \ R(x,y,y) = x. [para(962(a,1),480(a,1,1))]. 965 (R(x,y,y) \ x) * z = a(x,y,y) \ z. [para(962(a,1),465(a,1,1)),flip(a)]. 966 x * (a(x,y,y) * z) = R(x,y,y) * z. [para(962(a,1),501(a,1,2,1))]. 967 R(x \ 1,y,y) = x \ a(x,y,y). [para(962(a,1),634(a,1,2)),flip(a)]. 968 R(x,x * y,y) = a(x,y,y) \ x. [para(965(a,1),621(a,1)),flip(a)]. 969 T(x * y,K(y,x)) = T(x * y,y * x). [para(895(a,1),248(a,1)),flip(a)]. 970 T(x * y,K(y,x)) = (x \ 1) \ y. [para(969(a,2),439(a,1))]. 971 K(x,y) / T(y * x,K(x,y)) = (y * x) \ K(x,y). [para(969(a,2),257(a,1,2))]. 972 T(x * y,K(y,x)) = x * y. [para(970(a,2),330(a,1))]. 973 K(x,y) = (x * y) / (y * x). [para(972(a,1),903(a,1,1)),flip(a)]. 974 K(x,y) * (y * x) = x * y. [para(972(a,1),922(a,1)),flip(a)]. 975 (x * y) / (T(x,y) * y) = K(y,T(x,y)). [para(82(a,1),973(a,2,1)),flip(a)]. 976 (T(x,y) * y) / (x * y) = K(T(x,y),y). [para(82(a,1),973(a,2,2)),flip(a)]. 977 ((x * y) * z) / ((y * x) * z) = R(K(x,y),y * x,z). [para(973(a,2),80(a,1,1)),flip(a)]. 978 (x \ y) / (y * (x \ 1)) = K(x \ 1,y). [para(318(a,1),973(a,2,1)),flip(a)]. 979 ((K(x,y) * z) * K(y,x)) / z = K(K(x,y) * z,K(y,x)). [para(901(a,1),973(a,2,2)),flip(a)]. 980 K(x \ y,x) * y = (x \ y) * x. [para(20(a,1),974(a,1,2))]. 981 K(x * y,x) * y = (x \ y) * x. [para(495(a,1),980(a,1,1))]. 983 K(x,T(y,x)) = T(y,x) \ y. [para(975(a,1),577(a,1))]. 984 T(x,y) * K(y,T(x,y)) = x. [para(983(a,2),20(a,1,2))]. 985 K(x,T(y,x)) * T(y,x) = y. [para(983(a,2),298(a,1,1))]. 987 T(x,y) \ (x * z) = K(y,T(x,y)) * z. [para(983(a,2),815(a,2,1))]. 989 (x \ y) * K(x,T(y / x,x)) = y / x. [para(84(a,1),984(a,1,1))]. 990 K(T(x,y),y) * x = T(x,y). [hyper(23,a,901,a,b,985,a),flip(a)]. 991 K(x,x \ y) * T(y / x,x) = y / x. [para(84(a,1),985(a,1,1,2))]. 992 K(T(x,y),y) = x \ T(x,y). [para(976(a,1),565(a,1))]. 993 x * K(T(x,y),y) = T(x,y). [para(992(a,2),20(a,1,2))]. 994 (x / y) \ T(x / y,y) = K(y \ x,y). [para(84(a,1),992(a,1,1)),flip(a)]. 995 K(T(x \ 1,y),y) = x * T(x \ 1,y). [para(992(a,2),330(a,1))]. 997 (x / y) * K(T(x / y,y),y) = y \ x. [para(993(a,2),84(a,1))]. 998 T(x,y) * (K(y,T(x,y)) * z) = x * z. [para(987(a,1),20(a,1,2))]. 999 K(x,T(y,x)) * (y \ z) = T(y,x) \ z. [para(20(a,1),987(a,1,2)),flip(a)]. 1000 (x \ y) * K(x,x \ y) = y / x. [para(84(a,1),989(a,1,2,2))]. 1001 (x \ y) * K(x,x * y) = y / x. [para(489(a,1),1000(a,1,2))]. 1002 (x \ y) \ (y / x) = K(x,x * y). [hyper(23,a,20,a,b,1001,a),flip(a)]. 1003 K(x,x * (x * y)) = y \ ((x * y) / x). [para(19(a,1),1002(a,1,1)),flip(a)]. 1004 K(x,x * y) * T(y / x,x) = y / x. [para(489(a,1),991(a,1,1))]. 1005 (x / y) \ T(x / y,y) = K(y * x,y). [para(994(a,2),495(a,1))]. 1006 (x / y) * K(y \ x,y) = y \ x. [para(84(a,1),997(a,1,2,1))]. 1007 (x / y) * K(y * x,y) = y \ x. [para(495(a,1),1006(a,1,2))]. 1008 (x / y) * (x \ y) = K(x * y,x). [hyper(23,a,359,a,b,1007,a),flip(a)]. 1010 (x \ y) * (x / y) = K(x * y,x). [para(1008(a,1),368(a,1)),flip(a)]. 1012 L(x,y,(z \ u) * K(z * u,z)) = L(x,y,z / u). [para(1010(a,1),774(a,1,3,2))]. 1013 K(x,y) = y \ ((x * y) / x). [para(1003(a,1),490(a,1)),flip(a)]. 1014 (x * y) / x = y * K(x,y). [para(1013(a,2),20(a,1,2)),flip(a)]. 1015 x * (y / (y * x)) = K(y,x) \ 1. [para(1013(a,2),502(a,1,1)),flip(a)]. 1016 K(x,y) = ((x * y) / x) / y. [para(1013(a,2),558(a,2)),flip(a)]. 1017 ((x * y) / x) * (y \ z) = K(x,y) * z. [para(1013(a,2),860(a,1,1)),flip(a)]. 1018 (x * K(y,x)) * y = y * x. [para(1014(a,1),22(a,1,1))]. 1019 x / (x / y) = y * K(x / y,y). [para(22(a,1),1014(a,1,1))]. 1020 T(x * K(y,x),y) = x. [para(1014(a,1),104(a,1,1))]. 1021 L(x,y * K(z,y),y) = x. [para(1014(a,1),237(a,1,2))]. 1022 a(x / (x * y),z,u) = a(y * K(x,y),z,u). [para(1014(a,1),612(a,1,1)),flip(a)]. 1023 T(T(x * K(y,x),z),y) = T(x,z). [para(1020(a,1),42(a,1,1)),flip(a)]. 1024 T(x * K(y,x),z) * y = y * T(x,z). [para(1020(a,1),108(a,1,2,1)),flip(a)]. 1025 x / L(y,x * K(y,x),y) = y \ (x * K(y,x)). [para(1020(a,1),441(a,1,1))]. 1026 L(x,K(y,z),z) = x. [para(1021(a,1),303(a,1))]. 1027 (x * K(y,x)) \ z = K(y,x) \ (x \ z). [para(1021(a,1),270(a,1))]. 1028 (x * K(y,x)) * z = x * (K(y,x) * z). [para(1026(a,1),74(a,1,2))]. 1029 L(x,K(y,z),y) = x. [para(1026(a,1),921(a,1)),flip(a)]. 1030 (x * K(x,y)) * z = x * (K(x,y) * z). [para(1029(a,1),74(a,1,2))]. 1031 x \ (K(x,y) * z) = (x \ K(x,y)) * z. [para(1029(a,1),798(a,1,2)),flip(a)]. 1032 (x * K(y,x)) \ 1 = K(x,y) / x. [para(1029(a,1),947(a,1,1)),flip(a)]. 1033 (x * y) / x = K(x,y) * y. [para(1016(a,2),22(a,1,1)),flip(a)]. 1035 (x * K(y,x)) / x = K(y,x). [para(1014(a,1),1016(a,2,1)),flip(a)]. 1036 K(x,y) * y = y * K(x,y). [para(1033(a,1),1014(a,1))]. 1037 T(K(x,y),y) = K(x,y). [para(1035(a,1),104(a,1,1))]. 1038 T(x,K(y,x)) = x. [hyper(39,a,1037,a)]. 1040 T(x,y) * K(z,x) = K(z,x) * T(x,y). [para(1038(a,1),108(a,1,2,1)),flip(a)]. 1041 K(x,y) = x * (y / (y * x)). [para(1015(a,2),897(a,1)),flip(a)]. 1042 x \ K(x,y) = y / (y * x). [hyper(23,a,20,a,b,1041,a(flip)),flip(a)]. 1043 K(x,y) = (y / (y * x)) * x. [para(1041(a,2),362(a,2)),flip(a)]. 1044 K(x,y) / x = y / (y * x). [para(1041(a,2),363(a,1,1))]. 1045 x * ((y / (y * x)) * z) = K(x,y) * z. [para(1041(a,2),451(a,1,1)),flip(a)]. 1046 T(x,K(x,y)) = x. [para(1041(a,2),605(a,1,2))]. 1047 ((x * y) / x) * (y \ z) = K(y,x) \ z. [para(1041(a,2),606(a,1,1)),flip(a)]. 1048 T(x \ 1,K(x,y)) = x \ 1. [para(1041(a,2),834(a,1,2))]. 1049 (x / (x * y)) * (y * z) = K(y,x) * z. [para(1041(a,2),841(a,1,1)),flip(a)]. 1050 K(x,y) * x = x * K(x,y). [para(1046(a,1),82(a,1,2))]. 1051 T(x,T(y,x) \ y) = x. [para(983(a,1),1046(a,1,2))]. 1052 (T(x,y) \ x) * y = y * (T(x,y) \ x). [para(1051(a,1),82(a,1,2))]. 1053 K(x,y) = ((y * x) / y) \ x. [para(1043(a,2),358(a,2)),flip(a)]. 1054 K(x,y) / x = x \ K(x,y). [para(1044(a,2),1042(a,2)),flip(a)]. 1055 K(x,y) * (x \ 1) = x \ K(x,y). [para(1048(a,1),327(a,1,2))]. 1056 (x * K(y,x)) \ 1 = x \ K(x,y). [para(1032(a,2),1054(a,1))]. 1057 (x \ 1) / (x \ K(x,y)) = K(y,x). [para(1055(a,1),902(a,1,2))]. 1058 (x * K(y,x)) \ z = (x \ K(x,y)) * z. [para(1056(a,1),318(a,1,1)),flip(a)]. 1059 K(x,y) * (y * z) = ((x * y) / x) * z. [para(19(a,1),1017(a,1,2)),flip(a)]. 1060 T(x,y) * K(z,T(x,y)) = T(x * K(z,x),y). [hyper(24,a,1018,a,b,1024,a),flip(a)]. 1061 T(x * K(x \ y,x),y) = L(x,x \ y,x). [hyper(24,a,221,a,b,1024,a)]. 1063 (x * K(y,x)) \ z = K(x,y) * (x \ z). [para(1027(a,2),900(a,1))]. 1064 ((x * y) / x) * z = y * (K(x,y) * z). [para(1014(a,2),1028(a,1,1))]. 1065 x \ (K(x,y) * z) = (y / (y * x)) * z. [para(1042(a,1),1031(a,2,1))]. 1066 K(x,y) \ (x * z) = ((y * x) / y) * z. [para(19(a,1),1047(a,1,2)),flip(a)]. 1067 K(x,y) * (x \ z) = (y / (y * x)) * z. [para(20(a,1),1049(a,1,2)),flip(a)]. 1068 K(x,y) * (x * z) = x * (K(x,y) * z). [para(1049(a,1),1045(a,1,2)),flip(a)]. 1069 x * (T(y,x) \ y) = T(x,T(y,x)). [para(1052(a,1),826(a,1))]. 1070 x * K(x,T(y,x)) = T(x,T(y,x)). [para(983(a,2),1069(a,1,2))]. 1071 x / (K(y,z) * (y \ x)) = y * K(z,y). [para(1063(a,1),65(a,1,2))]. 1072 (x \ K(x,y)) * z = K(x,y) * (x \ z). [para(1063(a,1),1058(a,1)),flip(a)]. 1073 K(x,y) * (y * z) = y * (K(x,y) * z). [para(1064(a,1),1059(a,2))]. 1074 K(x,y) \ (x * z) = (K(y,x) * x) * z. [para(1033(a,1),1066(a,2,1))]. 1075 K(x,y) * (x \ (y * x)) = y. [para(1067(a,2),22(a,1))]. 1076 x \ (K(x,y) * z) = K(x,y) * (x \ z). [para(1067(a,2),1065(a,2))]. 1077 K(x,y) * T(y,x) = y. [para(36(a,2),1075(a,1,2))]. 1078 K(x,y / x) = K(x,x * y). [hyper(24,a,1004,a,b,1077,a)]. 1079 K(x,T(y,x)) = K(x,y). [hyper(24,a,985,a,b,1077,a),flip(a)]. 1080 K(x,y) = T(y,x) \ y. [hyper(24,a,298,a,b,1077,a)]. 1081 T(x,y) = K(x,y) * x. [hyper(23,a,901,a,b,1077,a)]. 1082 K(x,T(y,z)) * T(T(y,x),z) = T(y,z). [para(42(a,1),1077(a,1,2))]. 1083 K(x,R(y,z,u)) * R(T(y,x),z,u) = R(y,z,u). [para(46(a,2),1077(a,1,2))]. 1084 L(x \ y,x,K(z,y)) = (K(z,y) \ x) \ T(y,z). [para(1077(a,1),267(a,1,1,2))]. 1085 L(x,y,K(z,u) * u) = L(x,y,T(u,z)). [para(1077(a,1),774(a,1,3,2))]. 1086 K(x,y) = T(x,y) / x. [para(1077(a,1),902(a,1,2)),flip(a)]. 1087 (x * y) * T(y,x) = (y * x) * y. [para(1077(a,1),911(a,1,2)),flip(a)]. 1088 T(x,y) * T(x,y) = x * T(T(x,y),y). [para(1077(a,1),998(a,1,2))]. 1089 T(x,y) * K(y,x) = x. [para(1077(a,1),1040(a,2))]. 1090 (x / (x * y)) * T(x,y) = y \ x. [para(1077(a,1),1065(a,1,2)),flip(a)]. 1091 K(x,T(T(y,x),z)) = K(x,T(y,z)). [para(42(a,1),1079(a,1,2))]. 1092 K(x,x * (y * x)) = K(x,y). [para(1079(a,1),491(a,2))]. 1093 T(x,y) \ (x * z) = K(y,x) * z. [para(1079(a,1),987(a,2,1))]. 1094 T(x,y) * (K(y,x) * z) = x * z. [para(1079(a,1),998(a,1,2,1))]. 1095 K(x,y) * (y \ z) = T(y,x) \ z. [para(1079(a,1),999(a,1,1))]. 1096 T(x,T(y,x)) = x * K(x,y). [para(1079(a,1),1070(a,1,2)),flip(a)]. 1097 T(T(x,y),z) \ T(x,z) = K(y,T(x,z)). [para(42(a,1),1080(a,2,1)),flip(a)]. 1098 K(x,y) * (T(y,x) * z) = y * z. [para(1080(a,2),575(a,1,1))]. 1099 x * (T(x,y) \ z) = K(y,x) * z. [para(1080(a,2),576(a,1,1)),flip(a)]. 1100 K(x,y) = y * (T(y,x) \ 1). [para(1080(a,2),578(a,2)),flip(a)]. 1101 T(x,y) \ 1 = x \ K(y,x). [para(1080(a,2),582(a,1,2)),flip(a)]. 1102 (x * y) / (T(x,z) * y) = K(z,x). [para(1080(a,2),577(a,2))]. 1103 ((x * y) * y) \ ((y * x) * y) = K(y,(y * x) * y). [para(758(a,1),1080(a,2,1)),flip(a)]. 1104 T(x,y) = (x * x) / (x * K(y,x)). [para(1080(a,2),831(a,1,2,2)),flip(a)]. 1105 K(T(x,y),y) = K(x,y). [hyper(24,a,990,a,b,1081,a(flip)),flip(a)]. 1106 (x * T(y,z)) / L(y,K(y,z),x) = x * K(y,z). [para(1081(a,2),99(a,1,1,2))]. 1107 T(x,y) = x * K(x,y). [para(1081(a,2),1050(a,1))]. 1108 K(x,y) = x \ T(x,y). [para(1086(a,2),572(a,1))]. 1110 K(R(T(x,y),z,u),y) = K(R(x,z,u),y). [para(46(a,2),1105(a,1,1))]. 1111 x * T(x \ 1,y) = K(x \ 1,y). [para(1105(a,1),995(a,1)),flip(a)]. 1112 T(x * K(y,x),T(y,x)) = x. [para(1105(a,1),1020(a,1,1,2))]. 1113 K(x,y) * T(x,y) = T(T(x,y),y). [para(1105(a,1),1081(a,2,1)),flip(a)]. 1114 K(x,y) * T(K(y,x),z) = K(K(y,x),z). [hyper(23,a,901,a,b,1107,a(flip)),flip(a)]. 1115 (x * y) \ (x * T(y,z)) = L(K(y,z),y,x). [para(1107(a,2),32(a,2,2,2)),flip(a)]. 1116 x * (y * K(y,x)) = y * x. [para(1107(a,1),82(a,1,2))]. 1117 (x * y) * L(K(y,z),y,x) = x * T(y,z). [para(1107(a,2),74(a,2,2))]. 1118 (x \ y) * K(x * y,x) = T(x \ y,x). [para(495(a,1),1107(a,2,2)),flip(a)]. 1119 L(x,y,z * T(z,u)) = L(x,y,K(z,u)). [para(1107(a,2),774(a,1,3,2))]. 1120 x * (K(x,y) * z) = T(x,y) * z. [para(1107(a,2),1030(a,1,1)),flip(a)]. 1121 T(x,y) * K(x,y) = T(T(x,y),y). [para(1105(a,1),1107(a,2,2)),flip(a)]. 1122 T(x,y) \ T(T(x,z),y) = K(T(x,y),z). [para(42(a,1),1108(a,2,2)),flip(a)]. 1123 L(x,y,z) \ L(T(x,u),y,z) = K(L(x,y,z),u). [para(44(a,2),1108(a,2,2)),flip(a)]. 1124 x \ ((x \ y) \ y) = K(x,x * y). [para(249(a,1),1108(a,2,2)),flip(a)]. 1125 T(x,y) * (x \ z) = K(x,y) * z. [para(1108(a,2),562(a,1,1)),flip(a)]. 1126 K(x \ 1,x * y) = x * ((x * y) \ y). [para(1108(a,2),707(a,1))]. 1127 x \ (T(x,y) * z) = K(x,y) * z. [para(1108(a,2),733(a,2,1))]. 1128 K(x / y,y) = K(y * x,y). [para(1108(a,2),1005(a,1))]. 1130 K(x,(y * (x \ 1)) / x) = K(x,T(y,x \ 1)). [para(347(a,1),1078(a,2,2))]. 1131 T(x,T(y,x)) = T(x,y). [para(1096(a,2),1107(a,2)),flip(a)]. 1132 T(T(x,y),T(z,x)) = T(T(x,z),y). [para(1131(a,1),42(a,1,1)),flip(a)]. 1133 T(x,y / x) = T(x,x \ y). [para(84(a,1),1131(a,1,2)),flip(a)]. 1134 (x * y) / T(y,x) = T(x,y). [para(1131(a,1),117(a,1,2))]. 1135 L(T(x,y),T(y,x),x) = T(x,x * T(y,x)). [para(1131(a,1),203(a,1,1))]. 1136 T(x,x * (y * x)) = T(x,y). [para(1131(a,1),247(a,2))]. 1137 T(x,y) / (T(y,x) \ x) = y. [para(1131(a,1),829(a,1,1))]. 1138 T(x,y) \ y = x \ T(y,x). [para(1131(a,1),830(a,1,2)),flip(a)]. 1139 T(x,y * K(x,y)) = T(x,y). [para(1020(a,1),1131(a,1,2)),flip(a)]. 1140 K(x,y) * K(z,K(y,x)) = T(K(y,x),z) \ 1. [hyper(23,a,901,a,b,1100,a(flip)),flip(a)]. 1141 L(T(x,y),y * K(x,y),T(x,y)) = (T(x,y) \ (y * K(x,y))) \ y. [para(1112(a,1),440(a,1,2)),flip(a)]. 1143 K((x * (y \ 1)) / y,y) = K(T(x,y \ 1),y). [para(347(a,1),1128(a,2,1))]. 1144 x / (x / y) = y * K(y * x,y). [para(1128(a,1),1019(a,2,2))]. 1145 T(x,y / x) = T(x,x * y). [para(1133(a,2),246(a,1))]. 1146 T(x,y) * T(y,x) = x * y. [para(1134(a,1),22(a,1,1))]. 1147 x / (y \ T(x,y)) = T(y,x). [para(1138(a,1),65(a,1,2))]. 1148 (T(x,y) \ y) * K(x,x * T(y,x)) = T(y,x) / x. [para(1138(a,2),1001(a,1,1))]. 1149 T(x,(y * (x \ 1)) / x) = T(x,T(y,x \ 1)). [para(347(a,1),1145(a,2,2))]. 1150 (T(x,y) * (T(y,x) * z)) \ ((x * y) * z) = a(T(x,y),T(y,x),z). [para(1146(a,1),28(a,2,2,1)),flip(a)]. 1151 (x * y) \ (T(x,y) * (T(y,x) * z)) = L(z,T(y,x),T(x,y)). [para(1146(a,1),32(a,2,1)),flip(a)]. 1152 T(T(x,y),x \ T(y,x)) = (x \ T(y,x)) \ y. [para(1147(a,1),84(a,1,1))]. 1153 R(x,y,x) * (y * x) = (y * x) * T(x,y). [para(1087(a,2),79(a,2))]. 1154 T(x,y) * ((y * x) / ((x * y) * x)) = K(T(x,y),y * x). [para(1087(a,1),1041(a,2,2,2)),flip(a)]. 1155 K(x,T(y,K(z,T(y,x)))) = K(x,T(y,x)). [para(1038(a,1),1091(a,1,2)),flip(a)]. 1156 L(x,y * K(z,y),u) = L(x,T(y,z),u). [para(1094(a,1),937(a,1,2))]. 1157 T(x,y) * (y * x) = x * (x * y). [para(974(a,1),1094(a,1,2))]. 1158 K(x,y) * (T(x,y) \ z) = x \ z. [hyper(23,a,901,a,b,1095,a),flip(a)]. 1159 K(x,y) * (y \ x) = y \ T(x,y). [para(1095(a,2),1138(a,1))]. 1160 K(x,y) * (x * z) = T(x,y) * z. [hyper(23,a,901,a,b,1098,a),flip(a)]. 1162 R(K(x,y),T(y,x) * z,u) \ 1 = ((T(y,x) * z) * u) / ((y * z) * u). [para(1098(a,1),344(a,1,2,1)),flip(a)]. 1163 x \ (K(y,x) * z) = T(x,y) \ z. [hyper(23,a,20,a,b,1099,a),flip(a)]. 1164 (x * y) * T((x * y) \ x,z) = x * K(y \ 1,z). [para(1111(a,1),762(a,2,2))]. 1165 x \ (y * T(y \ x,z)) = K((x \ y) \ 1,z). [para(1111(a,1),817(a,1)),flip(a)]. 1166 (x * ((K(x,y) * z) * u)) \ ((T(x,y) * z) * u) = a(x,K(x,y) * z,u). [para(1120(a,1),28(a,2,2,1)),flip(a)]. 1168 T(x,y) * (T(y,x) * z) = x * (y * z). [para(1098(a,1),1120(a,1,2)),flip(a)]. 1169 L(x,y,z * ((z \ u) * u)) = L(x,y,K(z,z * u)). [para(1124(a,1),865(a,1,3)),flip(a)]. 1170 T(x,y) \ ((x \ T(y,x)) \ y) = K(T(x,y),T(x,y) * y). [para(1138(a,1),1124(a,1,2,1))]. 1171 T(x,y) \ (K(x,y) * z) = x \ z. [hyper(23,a,20,a,b,1125,a),flip(a)]. 1172 K(x,y) * (z * x) = T(x,y) * T(z,x). [para(36(a,2),1125(a,1,2)),flip(a)]. 1173 T(x / y,z) * y = K(x / y,z) * x. [para(66(a,1),1125(a,1,2))]. 1174 T(x,y) * (z / (z * x)) = K(x,y) * K(x,z). [para(1042(a,1),1125(a,1,2))]. 1175 T(x,y) * (T(x,z) \ 1) = K(x,y) * K(z,x). [para(1101(a,2),1125(a,1,2))]. 1176 x \ T(T(x,y),y) = K(x,y) * K(x,y). [para(1121(a,1),1127(a,1,2))]. 1177 T(T(x,x * y),T(z,x)) = T(T(x,z),x \ y). [para(246(a,1),1132(a,1,1))]. 1178 (x / (x / y)) * z = y * (K(y * x,y) * z). [para(1144(a,2),1028(a,1,1))]. 1179 ((x * y) * T(y,x)) \ (y * (y * x)) = K(T(y,x),x * y). [para(1157(a,1),30(a,2,2)),flip(a)]. 1180 (x * (x * y)) \ (T(x,y) * ((y * x) * z)) = L(z,y * x,T(x,y)). [para(1157(a,1),32(a,2,1)),flip(a)]. 1181 K(x,y) * (T(x,y) \ T(x,z)) = K(x,z). [para(1158(a,2),1108(a,2)),flip(a)]. 1182 K(T(x,y \ 1),y) * (x * (y \ 1)) = y \ T(T(x,y \ 1),y). [para(326(a,1),1159(a,1,2))]. 1183 ((T(x,y) * z) * u) / ((x * z) * u) = R(K(x,y),x * z,u). [para(1160(a,1),34(a,2,1,1)),flip(a)]. 1184 (x * y) \ (T(x,z) * y) = T(K(x,z),x * y). [para(1160(a,1),36(a,2,2)),flip(a)]. 1185 L(x,T(y,z) * z,u) = L(x,z * y,u). [para(1160(a,1),943(a,1,2))]. 1186 T(x,y) \ (T(y,x) \ z) = x \ (y \ z). [para(1158(a,1),1163(a,1,2)),flip(a)]. 1187 T(x,y) \ (y * K(x,y)) = x \ y. [para(1036(a,1),1171(a,1,2))]. 1188 x \ (y * K(x,y)) = K(x,y) * (x \ y). [para(1187(a,1),1158(a,1,2)),flip(a)]. 1189 (K(x,y) * (x \ z)) \ ((x \ K(x,y)) * (z * u)) = L(u,z,x \ K(x,y)). [para(1072(a,1),32(a,2,1)),flip(a)]. 1190 (K(x,y) * z) \ (y * (K(x,y) * z)) = L(T(y,z),z,K(x,y)). [para(1073(a,1),106(a,1,2))]. 1191 K(x,y) \ (x * z) = (K(x,y) \ x) * z. [para(900(a,2),1074(a,2,1))]. 1192 L(x,y,(z * u) / z) = L(x,y,T(u,z)). [para(1033(a,2),1085(a,1,3))]. 1193 T(x,y) * K(y,T(x,z)) = K(z,T(x,y)) * T(x,z). [para(1097(a,1),1099(a,1,2))]. 1194 L(x,y,(z / (u * u)) * (u \ (z * (u \ 1)))) = L(x,y,K(z / (u * u),u)). [para(403(a,1),1119(a,1,3,2))]. 1195 (x * T(y,x)) \ (T(y,z) * x) = L(K(T(y,x),z),T(y,x),x). [para(1122(a,1),180(a,1,1)),flip(a)]. 1196 K(x,T(y,K(z,T(y,x)))) = K(x,y). [para(1155(a,2),1079(a,1))]. 1197 K(x,y) * T(T(y,x),K(z,T(y,x))) = T(y,K(z,T(y,x))). [para(1196(a,1),1082(a,1,1))]. 1198 (x * (y * z)) / (T(y,x) * z) = T(x,y). [hyper(24,a,22,a,b,1168,a),flip(a)]. 1199 (x \ y) * (T(x,y / x) * z) = (y / x) * (x * z). [para(84(a,1),1168(a,1,1))]. 1200 (T(x / y,z) * y) / x = K(x / y,z). [hyper(24,a,22,a,b,1173,a(flip)),flip(a)]. 1201 K(x / y,z) * x = y * T(y \ x,z). [para(1173(a,1),139(a,1))]. 1202 (R(x,y,z) * (K(x,u) * K(x,u))) / T(T(x,u),u) = x \ R(x,y,z). [para(1176(a,1),536(a,1,1,2))]. 1203 L(x,y,K(y,z)) = x. [hyper(23,a,798,a,b,1191,a(flip)),flip(a)]. 1204 L(x,y,T(z,y) \ z) = x. [para(983(a,1),1203(a,1,3))]. 1205 L(x,y,T(z,y) * z) = x. [para(1204(a,1),776(a,1)),flip(a)]. 1206 L(x,y,z * T(z,y)) = x. [para(116(a,1),1205(a,1,3))]. 1207 ((x * T(x,y)) * y) \ ((x * T(x,y)) * (y * z)) = z. [para(1206(a,1),32(a,1)),flip(a)]. 1208 L(x,y,T(z * u,z) / z) = L(x,y,T((z \ u) * z,z)). [para(138(a,1),1192(a,1,3,1))]. 1209 (x * (R(y,z,u) * w)) / (R(T(y,x),z,u) * w) = T(x,R(y,z,u)). [para(46(a,2),1198(a,1,2,1))]. 1210 (x * (y * (a(T(y,x),z,z) * u))) / (R(T(y,x),z,z) * u) = T(x,y). [para(966(a,1),1198(a,1,2))]. 1211 (x * T(x \ y,z)) / y = K(y / x,z). [para(139(a,1),1200(a,1,1))]. 1212 K((x * y) / x,z) * (x * y) = x * T(y,z). [para(19(a,1),1201(a,2,2,1))]. 1213 x \ (y * T(y \ x,z)) = T(K(x / y,z),x). [para(1201(a,1),36(a,2,2)),flip(a)]. 1214 ((x * y) * T((x * y) \ ((z * x) * y),u)) / ((z * x) * y) = K(R(z,x,y),u). [para(34(a,2),1211(a,2,1))]. 1215 T(x * K(x * y,x),y) = L(x,x \ y,x). [para(495(a,1),1061(a,1,1,2))]. 1216 L(T(x,y),T(y,x),x) = T(x,y * x). [para(82(a,1),1135(a,2,2))]. 1217 (x * y) * T(y,y * (x * y)) = R(y,x,y) * (x * y). [para(1136(a,2),1153(a,2,2)),flip(a)]. 1218 T(x * K(x * y,x),y) = L(x,x * y,x). [para(1215(a,2),312(a,1))]. 1219 T(x / (x / y),x) = L(y,y * x,y). [para(1144(a,2),1218(a,1,1))]. 1220 K(x,T(y,x \ 1)) = K(x,y / (x * x)). [para(401(a,1),1130(a,1,2)),flip(a)]. 1221 K(T(x,y \ 1),y) = K(x / (y * y),y). [para(401(a,1),1143(a,1,1)),flip(a)]. 1222 T(x,T(y,x \ 1)) = T(x,y / (x * x)). [para(401(a,1),1149(a,1,2)),flip(a)]. 1223 K(((x * y) \ x) \ 1,z) = (x * y) \ (x * T(y,z)). [para(19(a,1),1165(a,1,2,2,1)),flip(a)]. 1224 T(x,y) \ T(x,z) = K(x,z) * K(y,x). [para(1175(a,1),581(a,1)),flip(a)]. 1225 K(x,y) * (K(x,z) * K(y,x)) = K(x,z). [para(1224(a,1),1181(a,1,2))]. 1226 K(x,y) * K(z,x) = K(z,x) * K(x,y). [hyper(23,a,901,a,b,1225,a)]. 1229 T(T(x,y),x \ z) = T(T(x,y),x * z). [para(1177(a,1),1132(a,1))]. 1230 T(T(x,y),x * T(y,x)) = (x \ T(y,x)) \ y. [para(1229(a,1),1152(a,1))]. 1231 (x / (x / y)) * x = y * ((y \ x) * y). [para(981(a,1),1178(a,2,2))]. 1232 T(x * y,x) = (y / (y / x)) * y. [para(1231(a,2),138(a,1)),flip(a)]. 1233 T(x * y,x) / y = y / (y / x). [hyper(24,a,22,a,b,1232,a(flip)),flip(a)]. 1234 ((x / y) / x) * T(y * x,y) = x. [hyper(23,a,359,a,b,1232,a(flip)),flip(a)]. 1236 x \ T(x * y,y) = x / (x / y). [para(1233(a,1),754(a,1)),flip(a)]. 1237 x / T(y * x,y) = (x / y) / x. [hyper(24,a,22,a,b,1234,a),flip(a)]. 1238 T(x * y,y) = x * (x / (x / y)). [para(1236(a,1),20(a,1,2)),flip(a)]. 1239 T(x * (y \ x),y \ x) = x * (x / y). [para(65(a,1),1238(a,2,2,2))]. 1240 T(K(x / y,z),x) = K((x \ y) \ 1,z). [para(1213(a,1),1165(a,1))]. 1241 K((x \ (y \ x)) \ 1,z) = T(K(y,z),x). [para(65(a,1),1240(a,1,1,1)),flip(a)]. 1242 K((T(x,y) \ (T(y,x) \ x)) \ 1,z) = T(K(y,z),T(x,y)). [para(1137(a,1),1240(a,1,1,1)),flip(a)]. 1243 K(T(x \ 1,y) \ 1,z) = T(K(x,z),y). [para(325(a,2),1241(a,1,1,1))]. 1244 K(T((x \ 1) \ 1,y * y),z) = T(K(x,z),y * y). [para(655(a,1),1243(a,1,1))]. 1245 (x \ T(y,x)) \ y = T(T(x,y),y * x). [para(82(a,1),1230(a,1,2)),flip(a)]. 1246 x / L(y,T(x,y),y) = y \ (x * K(y,x)). [para(1156(a,1),1025(a,1,2))]. 1247 x / L(y,T(x,y),y) = K(y,x) * (y \ x). [para(1246(a,2),1188(a,1))]. 1248 L(x \ y,x,K(z,y)) = (K(y,z) * x) \ T(y,z). [para(900(a,1),1084(a,2,1))]. 1249 R(K(x,y),T(x,y) * z,u) \ 1 = R(K(y,x),x * z,u). [para(1098(a,1),906(a,1,2)),flip(a)]. 1250 L(x,y * (y * (z * y)),u) = L(x,z \ (y \ 1),u). [para(51(a,1),929(a,1,2))]. 1251 ((x * y) \ K(x,y)) \ z = K(y,x) * ((x * y) * z). [para(933(a,2),900(a,1))]. 1252 (x * a(x,y,z)) * u = x * (a(x,y,z) * u). [para(948(a,1),946(a,1))]. 1253 a(x,y,z) * (x * u) = x * (a(x,y,z) * u). [para(1252(a,1),772(a,1)),flip(a)]. 1254 x * (a(x,y,z) * (x \ u)) = a(x,y,z) * u. [para(20(a,1),1253(a,1,2)),flip(a)]. 1255 L(x,y * (z \ y),u) = L(x,T(z,y),u). [para(20(a,1),953(a,1,2,1))]. 1256 L(x,T(y \ 1,z),u) = L(x,T(y,z),u). [para(1255(a,1),883(a,2))]. 1257 K(x,y) / (y * x) = (y * x) \ K(x,y). [para(972(a,1),971(a,1,2))]. 1258 L(x,y,T(z \ u,z)) = L(x,y,z / u). [para(1118(a,1),1012(a,1,3))]. 1259 L(x,y,T(z * u,z)) = L(x,y,z / u). [para(1258(a,1),818(a,1)),flip(a)]. 1260 (T(x,y) \ y) * K(x,y * x) = T(y,x) / x. [para(82(a,1),1148(a,1,2,2))]. 1261 L(x,y,K(z,z * u)) = L(x,y,a(z,u,u)). [para(1169(a,1),837(a,1))]. 1262 L(x,y,K(z * u,z)) = L(x,y,a(z,u,u)). [para(1261(a,1),909(a,1)),flip(a)]. 1263 L(x,y,a(z,u * z,u * z)) = L(x,y,K(z,u)). [para(1092(a,1),1261(a,1,3)),flip(a)]. 1264 K(x,T(y,z)) * T(T(y,x),K(x,T(y,z))) = K(z,T(y,x)) * T(y,z). [para(1193(a,1),82(a,2))]. 1265 (x \ y) * (T(x,x * y) * z) = (y / x) * (x * z). [para(1145(a,1),1199(a,1,2,1))]. 1266 (x * (T(x,y) * y)) \ ((x * T(x,y)) * (y * z)) = z. [para(722(a,1),1207(a,1,1))]. 1267 L(K(x,y),x,z) = K(((z * x) \ z) \ 1,y). [para(1223(a,2),1115(a,1)),flip(a)]. 1268 K(L(x \ 1,x,y) \ 1,z) = L(K(x,z),x,y). [para(142(a,2),1267(a,2,1,1)),flip(a)]. 1269 K(T(x,y * y),z) = T(K(x,z),y * y). [para(156(a,1),1244(a,1,1,1))]. 1270 K(T(x,y * y),z) \ 1 = T(K(x,z) \ 1,y * y). [para(1269(a,2),655(a,1,1))]. 1271 L(x,y \ (z \ 1),u) = L(x,y * z,u). [para(1250(a,1),875(a,1))]. 1273 L(x,y * (z \ 1),u) = L(x,y * z,u). [para(1271(a,1),876(a,1)),flip(a)]. 1274 (x \ y) * ((y / x) * (x * z)) = ((x \ y) * y) * z. [para(1265(a,1),253(a,1,2))]. 1275 (x * (T(x,y) * y)) \ (x * (T(x,y) * (y * z))) = z. [para(722(a,1),1266(a,1,2))]. 1276 T(K(x,y) \ 1,z * z) = K(y,T(x,z * z)). [para(1270(a,1),897(a,1))]. 1277 K(x,T(y,z * z)) = T(K(x,y),z * z). [para(897(a,1),1276(a,1,1)),flip(a)]. 1278 K(T(x,y * y),z) = K(x,T(z,y * y)). [para(1277(a,2),1269(a,2))]. 1279 L(L(x,y,T(z,y)),T(z,y) * y,z) = x. [para(1275(a,1),174(a,1)),flip(a)]. 1280 L(L(x,y,T(z,y)),y * z,z) = x. [para(1279(a,1),1185(a,1)),flip(a)]. 1281 L(L(x,y,T(y \ z,y)),z,y \ z) = x. [para(20(a,1),1280(a,1,2))]. 1282 L(x,y * (z * y),y) = L(x,z,T(y,z)). [para(1280(a,1),303(a,1,1))]. 1283 L(x,T(y,z) * z,T(y,z)) = L(x,z * y,y). [para(308(a,1),1280(a,1,1)),flip(a)]. 1284 L(x,T(y,z),z) = L(x,y,T(z,y)). [para(1280(a,1),314(a,1,1))]. 1285 L(x,T(y,y * z),y * z) = L(x,y,y / z). [para(1284(a,2),1259(a,1))]. 1286 L(L(x,y,y / z),z,y \ z) = x. [para(1258(a,1),1281(a,1,1))]. 1287 L(L(x,y,y / z),z,y * z) = x. [para(1286(a,1),776(a,1)),flip(a)]. 1288 L(x,y,z / y) = L(x,y,z * y). [para(304(a,1),1287(a,1,1)),flip(a)]. 1289 L(x \ (x / y),x,y * x) = y \ 1. [para(445(a,1),1287(a,1,1))]. 1290 L(x,y,y / z) = L(x,y,z * y). [para(806(a,1),1287(a,1,1)),flip(a)]. 1291 L(x,y,(z * y) * y) = L(x,y,z). [para(21(a,1),1288(a,1,3)),flip(a)]. 1292 L(x \ 1,x,y * x) = y \ (y / x). [para(1288(a,1),144(a,1))]. 1293 L(x,x,y * x) = y \ (y / (x \ 1)). [para(1288(a,1),432(a,1))]. 1294 x * L(y,z,x * z) = (x / z) * (z * y). [para(1288(a,1),173(a,1,2))]. 1295 (x \ 1) \ L(T(y \ (y / x),z),y,x * y) = K(L(y \ (y / x),y,x * y),z). [para(1289(a,1),1123(a,1,1))]. 1296 ((x * y) * y) \ (x * y) = x \ (x / y). [para(1292(a,1),142(a,1)),flip(a)]. 1297 L(x,y \ 1,T(y * z,y \ 1)) = L(x,(y * z) * z,y * z). [para(322(a,1),1282(a,1,2,2)),flip(a)]. 1298 x * K(L(y \ 1,y,x * y) \ 1,z) = (x / y) * (y * K(y,z)). [para(1268(a,2),1294(a,1,2))]. 1299 x \ L(x,x * y,y) = a(T(y,x),x,x). [para(1283(a,1),452(a,1,2))]. 1300 L(x,y * z,T(z,y)) = L(x,y * z,z). [para(1283(a,1),1185(a,1)),flip(a)]. 1301 T(L(K(x,y),z,K(y,x)),z) = (K(y,x) * z) \ z. [hyper(23,a,82,a,b,910,a(flip)),flip(a)]. 1302 L(x,y * x,x) = R(x,y,x). [hyper(24,a,217,a(flip),b,1217,a(flip)),flip(a)]. 1303 R(x,y / x,x) = L(x,y,x). [para(22(a,1),1302(a,1,2)),flip(a)]. 1304 L(T(x,y),z * x,x) = T(R(x,z,x),y). [para(1302(a,1),44(a,2,1))]. 1305 L(x,y,x) * ((y / x) * x) = (x * (y / x)) * x. [para(1303(a,1),79(a,1,1))]. 1306 L(T(x,y),z * x,x) = R(T(x,y),z,x). [para(1304(a,2),46(a,2)),flip(a)]. 1307 L(x,y,x) * y = (x * (y / x)) * x. [para(22(a,1),1305(a,1,2))]. 1308 T(L(x,y,x) * y,x) = ((y / x) * x) * x. [para(1307(a,2),758(a,1,1))]. 1309 T(L(x,y,x) * y,x) = y * x. [para(22(a,1),1308(a,2,1))]. 1310 (L(x,y,x) * y) * x = x * (y * x). [para(1309(a,1),82(a,1,2)),flip(a)]. 1311 L(R(x,y,x),y,x) = x. [hyper(24,a,184,a,b,1310,a(flip)),flip(a)]. 1312 R(L(x,y,x),y,x) = x. [hyper(24,a,79,a,b,1310,a(flip)),flip(a)]. 1313 R(x,x \ y,x) = L(x,y,x). [para(1311(a,1),302(a,1,1)),flip(a)]. 1314 L(x,x * y,x) = R(x,y,x). [para(1311(a,1),303(a,1,1))]. 1315 R(x,x * y,x) = L(x,y,x). [para(1311(a,1),308(a,1,1)),flip(a)]. 1316 x \ T(y * x,y) = R(y,x,y). [para(1314(a,1),316(a,1)),flip(a)]. 1318 T(x * K(x * y,x),y) = R(x,y,x). [para(1314(a,1),1218(a,2))]. 1319 T(x / (x / y),x) = R(y,x,y). [para(1314(a,1),1219(a,2))]. 1320 L(x,y,x) \ x = x \ R(x,y,x). [para(1315(a,1),622(a,1,1))]. 1321 x * R(y,x,y) = T(y * x,y). [para(1316(a,1),20(a,1,2))]. 1322 T(x,R(y,x,y)) = T(x,x / (x / y)). [para(1319(a,1),1131(a,1,2))]. 1323 (x / T(y * x,y)) * T(x,R(y,x,y)) = R(y,x,y) \ x. [para(1321(a,1),1090(a,1,1,2))]. 1324 T(x,y) * K(x * y,T(x,y)) = R(x,y,x). [para(1318(a,1),1060(a,2))]. 1325 T(x,y) * K(y * T(x,y),T(x,y)) = R(x,y,x). [para(82(a,2),1324(a,1,2,1))]. 1326 K(x,y) * (K(y,x) / (x * y)) = (x * y) \ 1. [para(907(a,2),912(a,1))]. 1327 K(x,y) * ((x * y) \ K(y,x)) = (x * y) \ 1. [para(1257(a,1),1326(a,1,2))]. 1328 (x * y) \ K(x,y) = (y * x) \ 1. [para(1327(a,1),941(a,1)),flip(a)]. 1329 K(x,y) * ((y * x) * z) = ((x * y) \ 1) \ z. [para(1328(a,1),1251(a,1,1)),flip(a)]. 1330 K(x,y) * ((y * x) * z) = (x * y) * z. [para(1329(a,2),330(a,1))]. 1331 ((x * y) * z) / ((y * x) * z) = K(x,y). [hyper(24,a,22,a,b,1330,a),flip(a)]. 1332 R(K(x,y),y * x,z) = K(x,y). [para(1331(a,1),977(a,1)),flip(a)]. 1333 R(K(x,T(y,x)),T(y,x) * x,z) = K(x,y). [para(1332(a,2),1079(a,1))]. 1335 R(K(x,y),T(y,x) * x,z) = K(x,y). [para(1079(a,1),1333(a,1,1))]. 1336 ((T(x,y) * y) * z) / ((K(y,x) * (T(x,y) * y)) * z) = K(y,x) \ 1. [para(1335(a,1),344(a,2,1))]. 1337 (x * L(x \ 1,y,z)) \ u = x \ (L(x \ 1,y,z) \ u). [para(216(a,1),924(a,1,1))]. 1338 L(x,y * (y * (z * (y * u))),w) = L(x,z \ (y \ u),w). [para(51(a,1),928(a,1,2))]. 1339 T(x,y) * (R(x,y,x) \ 1) = K(T(x,y),y * x). [para(344(a,1),1154(a,1,2))]. 1340 R(x,y,x) \ T(x,y) = K(T(x,y),y * x). [para(1339(a,1),548(a,1)),flip(a)]. 1341 T(x,y) \ T(T(x,y),y * x) = K(T(x,y),T(x,y) * y). [para(1245(a,1),1170(a,1,2))]. 1342 (((x * y) * T(y,x)) \ (y * y)) * x = K(T(y,x),x * y). [para(1179(a,1),391(a,1)),flip(a)]. 1343 T(x,K(y,T(x,z))) = K(z,x) * T(x,z). [para(1038(a,1),1197(a,1,2)),flip(a)]. 1345 T(x,K(y,T(x,z))) = x. [para(1343(a,2),1077(a,1))]. 1346 T(T(x,y),K(z,T(x,u))) = T(x,y). [para(1345(a,1),42(a,1,1)),flip(a)]. 1350 L(x,y,T(z * u,z) / z) = L(x,y,R(u,z,z)). [para(1208(a,2),864(a,1))]. 1351 T(K(x,y),T(z,x)) = K((z \ (x \ z)) \ 1,y). [para(1186(a,1),1242(a,1,1,1)),flip(a)]. 1352 T(K(x,y),T(z,x)) = T(K(x,y),z). [para(1351(a,2),1241(a,1))]. 1353 T(x,y) * T(K(y,z),x) = K(y,z) * T(x,y). [para(1352(a,1),82(a,1,2))]. 1354 K(x,y) * (K(y,z) * x) = K(y,z) * T(x,y). [para(1353(a,1),1172(a,2))]. 1355 (K(x,y) * T(z,x)) / L(z,K(x,y),K(z,x)) = K(z,x) * K(x,y). [para(1354(a,1),99(a,1,1))]. 1356 ((x / y) / x) * T(x,R(y,x,y)) = R(y,x,y) \ x. [para(1237(a,1),1323(a,1,1))]. 1357 L(x \ 1,y,z) \ (x \ u) = x \ (L(x \ 1,y,z) \ u). [para(1337(a,1),803(a,1)),flip(a)]. 1358 L(x,y \ (z \ u),w) = L(x,y * (z * u),w). [para(1338(a,1),875(a,1))]. 1360 L(x,y * (z \ u),w) = L(x,y * (z * u),w). [para(1358(a,1),876(a,1)),flip(a)]. 1361 L(x,y * (z * (z * u)),w) = L(x,y * u,w). [para(19(a,1),1360(a,1,2,2)),flip(a)]. 1362 L(x,(y \ z) * (z \ y),u) = L(x,(z \ y) * (y * z),u). [para(384(a,1),1360(a,1,2))]. 1363 L(x,y * R(z,z * u,w),v5) = L(x,y * (R(z,u,w) \ 1),v5). [para(615(a,1),1361(a,1,2,2))]. 1364 K(T(x,y),T(x,y) * y) = K(T(x,y),y * x). [para(1341(a,1),1108(a,2)),flip(a)]. 1365 (((x * y) * x) \ (x * x)) * y = K(T(x,y),y * x). [para(1087(a,1),1342(a,1,1,1))]. 1366 K(T(x,y),y * x) = K(x,x * y). [para(1365(a,1),408(a,1))]. 1367 R(x,y,x) \ T(x,y) = K(x,x * y). [para(1366(a,1),1340(a,2))]. 1368 K(x,x * y) \ T(x,y) = R(x,y,x). [para(1367(a,1),734(a,1,1))]. 1369 K(x * y,x) * T(x,y) = R(x,y,x). [para(1368(a,1),900(a,1)),flip(a)]. 1370 R(x,y,x) / T(x,y) = K(x * y,x). [hyper(24,a,22,a,b,1369,a),flip(a)]. 1371 (x \ (L(x \ 1,x,x / y) \ 1)) * (y \ (y / x)) = x \ 1. [para(1357(a,1),521(a,1,1))]. 1372 R(x,y \ 1,y) \ a(x,y,y) = x \ 1. [para(961(a,2),476(a,1))]. 1374 R(x,y,y) \ a(x,y,y) = x \ 1. [para(717(a,1),1372(a,1,1))]. 1375 (x * y) \ (x * (y * z)) = L(z,T(y,x),T(x,y)). [para(1168(a,1),1151(a,1,2))]. 1376 L(x,T(y,z),T(z,y)) = L(x,y,z). [para(1375(a,1),32(a,2)),flip(a)]. 1377 L(T(x,y),y,K(z,x)) = T(x,K(z,x) * y). [para(1190(a,1),36(a,2)),flip(a)]. 1378 (x \ (L(x \ 1,x,y * x) \ 1)) * (y \ (y / x)) = x \ 1. [para(1290(a,1),1371(a,1,1,2,1))]. 1379 ((x \ y) * z) \ (x \ u) = ((x * y) * z) \ (x * u). [para(794(a,1),201(a,1))]. 1380 (x * ((x \ y) * y)) \ z = ((x * y) * y) \ (x * z). [para(1379(a,1),893(a,2))]. 1381 (x * ((x \ y) * y)) \ y = x \ (x / y). [para(1380(a,2),1296(a,1))]. 1382 x / (y \ (y / x)) = y * ((y \ x) * x). [para(1381(a,1),65(a,1,2))]. 1383 (x \ (x / y)) \ y = x * ((x \ y) * y). [para(1382(a,1),872(a,1)),flip(a)]. 1384 x * L(x,y * x,y) = (y \ (y / x)) \ x. [para(1383(a,2),435(a,2))]. 1385 (x * L(x,y * x,y)) / x = (y \ (y / x)) \ 1. [para(1384(a,2),320(a,1,1))]. 1386 L(x,y * x,y) = (y \ (y / x)) \ 1. [para(1385(a,1),218(a,1)),flip(a)]. 1387 x \ ((y \ (y / x)) \ 1) = a(y,x,x). [para(1386(a,1),452(a,1,2))]. 1388 (x \ (x / y)) \ 1 = y * a(x,y,y). [para(1386(a,1),453(a,1))]. 1389 (x \ 1) \ (L(x,x,y * x) \ 1) = a(y,x \ 1,x \ 1). [para(1293(a,2),1387(a,1,2,1))]. 1390 (x \ (x / y)) \ z = (y * a(x,y,y)) * z. [para(1388(a,1),318(a,1,1)),flip(a)]. 1391 K(x,(x * x) / (y \ (y / z))) = K(x,z * a(y,z,z)). [para(1388(a,1),492(a,2,2))]. 1392 L(x \ 1,x,y * x) \ 1 = x * a(y,x,x). [para(1292(a,2),1388(a,1,1))]. 1393 (x \ (x * a(y,x,x))) * (y \ (y / x)) = x \ 1. [para(1392(a,1),1378(a,1,1,2))]. 1394 a(x,y,y) * (x \ (x / y)) = y \ 1. [para(19(a,1),1393(a,1,1))]. 1396 a(K(x,y),z,z) * (K(y,x) \ (K(y,x) / z)) = z \ 1. [para(905(a,1),1394(a,1,1))]. 1397 a(x,y,y) * (x / y) = x * (y \ 1). [para(1394(a,1),1254(a,1,2)),flip(a)]. 1398 (x * (y \ 1)) / (x / y) = a(x,y,y). [hyper(24,a,22,a,b,1397,a),flip(a)]. 1399 (x / y) * (y * (x \ 1)) = a(y,x,x). [para(1398(a,1),669(a,1)),flip(a)]. 1400 a(x / y,y,y \ 1) = a(x,y,y). [para(1399(a,1),592(a,2))]. 1401 a(x * (y * y),y \ 1,(y \ 1) \ 1) = a(x * y,y \ 1,y \ 1). [para(400(a,1),1400(a,1,1))]. 1402 K(x,(y \ (y / z)) \ 1) = K(x,z * a(y,z,z)). [para(1391(a,1),492(a,1)),flip(a)]. 1403 a(K(x,y),z,z) * (K(x,y) * (K(y,x) / z)) = z \ 1. [para(900(a,1),1396(a,1,2))]. 1404 K(x,y) * (a(K(x,y),z,z) * (K(y,x) / z)) = z \ 1. [para(1403(a,1),1253(a,1)),flip(a)]. 1405 R(K(x,y),z,z) * (K(y,x) / z) = z \ 1. [para(1404(a,1),966(a,1)),flip(a)]. 1406 x * (L(x,x,y * x) \ 1) = a(y,x \ 1,x \ 1). [para(1389(a,1),330(a,1)),flip(a)]. 1407 a(x,y \ 1,y \ 1) = L(y,y,x * y) \ y. [para(1406(a,1),471(a,1))]. 1408 a(x * y,y \ 1,y \ 1) = L(y,y,x) \ y. [para(1291(a,1),1407(a,2,1))]. 1409 (x * (y \ z)) \ (x * (y \ (z * u))) = L(L(u,z,y),y * z,x). [para(813(a,2),876(a,1))]. 1410 (x * y) * (z / (x * (y * z))) = x \ R(x,y,z). [para(853(a,1),537(a,1))]. 1411 L(x,y \ R(y,z,u),y * z) = x. [para(1410(a,1),852(a,1,2))]. 1412 L(x,y * R(y,z,u),y * z) = x. [para(1411(a,1),876(a,1)),flip(a)]. 1413 L(x,y * R(y,y * z,u),z) = x. [para(1412(a,1),774(a,1)),flip(a)]. 1414 K(T(x,y \ 1),y) * (x * (y \ 1)) = T(x,y) * (y \ 1). [para(1182(a,2),329(a,1))]. 1415 K(T(x,y \ 1),y) = K(x,y). [hyper(24,a,1160,a,b,1414,a)]. 1416 (x * (y \ 1)) / (T(x,y) * (y \ 1)) = K(y,T(x,y \ 1)). [para(1414(a,1),902(a,1,2))]. 1418 K(x / (y * y),y) = K(x,y). [para(1415(a,1),1221(a,1)),flip(a)]. 1419 K(x,T(y,x \ 1)) = K(x,y). [para(1416(a,1),1102(a,1))]. 1420 K(x \ 1,T(y,x)) = K(x \ 1,y). [para(156(a,1),1419(a,1,2,2))]. 1421 T(x,T(y,x \ 1)) = x * K(x,y). [para(1419(a,1),1107(a,2,2))]. 1423 K(x,y / (x * x)) = K(x,y). [para(1419(a,1),1220(a,1)),flip(a)]. 1424 K(x,R(y / x,x,x)) = K(x,y * x). [para(80(a,2),1423(a,1,2))]. 1425 ((x \ 1) * T(y,x)) / (x \ 1) = T(y,x) * K(x \ 1,y). [para(1420(a,1),1014(a,2,2))]. 1426 T(x,T(y,x \ 1)) = T(x,y). [para(1421(a,2),1107(a,2)),flip(a)]. 1427 T(x \ 1,T(y,x)) = T(x \ 1,y). [para(156(a,1),1426(a,1,2,2))]. 1428 T(x,y / (x * x)) = T(x,y). [para(1426(a,1),1222(a,1)),flip(a)]. 1429 L(x,T(y,z),T(T(z,y \ 1),y)) = L(x,y,T(z,y \ 1)). [para(1426(a,1),1376(a,1,2))]. 1430 T(x,(y * x) * x) = T(x,R(y,x,x)). [para(34(a,2),1428(a,1,2)),flip(a)]. 1431 L(x,T(y \ 1,z),T(T(z,y),y \ 1)) = L(x,y \ 1,T(z,y)). [para(1427(a,1),1376(a,1,2))]. 1432 (x \ T(y,x)) / (x \ 1) = T(y,x) * K(x \ 1,y). [para(318(a,1),1425(a,1,1))]. 1433 T(x,y) * K(y \ 1,x) = T(x,y * y). [para(1432(a,1),486(a,1))]. 1434 L(x,T(y,z),T(T(z,y),y \ 1)) = L(x,y,T(z,y \ 1)). [para(42(a,1),1429(a,1,3))]. 1435 L(x,R(y,z,z),y * z) = L(x,y \ 1,T(y * z,y \ 1)). [para(1297(a,2),938(a,1)),flip(a)]. 1436 L(x,R(y,z,z),y * z) = L(x,y,T(y * z,y \ 1)). [para(1435(a,2),887(a,1))]. 1437 L(x,y * R(z,z * u,w),v5) = L(x,y * R(z,u,w),v5). [para(1363(a,2),1273(a,1))]. 1438 L(x,y * R(y,z,u),z) = x. [para(1437(a,1),1413(a,1))]. 1439 L(x,y * (z * R(z,y,u)),y) = x. [para(1438(a,1),303(a,1,1))]. 1440 L(x,y \ R(y \ 1,z,u),z) = x. [para(318(a,1),1438(a,1,2))]. 1441 (x * (y \ R(y,x,z))) * u = x * ((y \ R(y,x,z)) * u). [para(1438(a,1),888(a,1,2))]. 1442 a(x,x * (y * R(y,x,z)),u) = 1. [hyper(38,a,1439,a)]. 1443 L(x,y * R(y \ 1,z,u),z) = x. [para(1440(a,1),876(a,1)),flip(a)]. 1444 L(x,a(y,z,z),z) = x. [para(960(a,1),1443(a,1,2))]. 1445 x / (a(y,x,x) \ 1) = x * a(y,x,x). [para(1444(a,1),145(a,1,2))]. 1446 (x * a(y,x,x)) * z = x * (a(y,x,x) * z). [para(1444(a,1),74(a,1,2))]. 1447 K(x,(y \ (y / z)) \ 1) = K(x,z / (a(y,z,z) \ 1)). [para(1445(a,2),1402(a,2,2))]. 1448 (x \ (x / y)) \ z = y * (a(x,y,y) * z). [para(1446(a,1),1390(a,2))]. 1449 L(x * (a(y,x,x) * z),y * (y / x),y) = (y / x) \ (y * z). [para(1448(a,1),311(a,1,1))]. 1450 (x * (y \ R(y,x,z))) * u = x * (R(y,x,z) * (y \ u)). [para(532(a,1),1441(a,2,2))]. 1451 L(x,T(y,z),T(T(z,y),y \ 1)) = L(x,y \ 1,T(z,y)). [para(1431(a,1),1256(a,1)),flip(a)]. 1452 L(x,y \ 1,T(z,y)) = L(x,y,T(z,y \ 1)). [para(1451(a,1),1434(a,1))]. 1453 L(x,y,T(z,y \ 1)) = L(x,y,T(z,y)). [para(1452(a,1),887(a,1))]. 1454 L(x,R(y,z,z),y * z) = L(x,y,T(y * z,y)). [para(1453(a,1),1436(a,2))]. 1455 L(x,R(y,z,z),y * z) = L(x,y,y / z). [para(1454(a,2),1259(a,1))]. 1456 L(x,R(y,z,z),y * z) = L(x,y,z * y). [para(1455(a,2),1290(a,1))]. 1457 L(T(x,y),y * K(x,y),T(x,y)) = (x \ y) \ y. [para(1187(a,1),1141(a,2,1))]. 1458 (x * (y * z)) \ ((x * y) * z) = a(T(x,y),T(y,x),z). [para(1168(a,1),1150(a,1,1))]. 1459 a(T(x,y),T(y,x),z) = a(x,y,z). [para(1458(a,1),28(a,2)),flip(a)]. 1460 a(T(x,y),T(T(y,x),x),z) = a(x,T(y,x),z). [para(1131(a,1),1459(a,1,1))]. 1461 x \ (y \ (y \ (T(y,x) * ((x * y) * z)))) = L(z,x * y,T(y,x)). [para(1180(a,1),443(a,1)),flip(a)]. 1462 x * K(y * a(x,y,y),z) = (x / y) * (y * K(y,z)). [para(1392(a,1),1298(a,1,2,1))]. 1463 x * K(y * a(x,y,y),z) = (x / y) * T(y,z). [para(1107(a,2),1462(a,2,2))]. 1464 x \ (y \ (K(y,x) * ((x * y) * z))) = L(z,x * y,T(y,x)). [para(1127(a,1),1461(a,1,2,2))]. 1465 x \ (y \ ((y * x) * z)) = L(z,x * y,T(y,x)). [para(1330(a,1),1464(a,1,2,2))]. 1466 L(x,y * z,T(z,y)) = L(x,z * y,z). [para(1465(a,1),309(a,1))]. 1467 L(x,y * z,z) = L(x,z * y,z). [para(1466(a,1),1300(a,1)),flip(a)]. 1468 L(L(x,y,z),y * z,z) = x. [para(1467(a,2),303(a,1))]. 1470 x \ L(x,x * y,y) = a(y,x,x). [para(1467(a,2),452(a,1,2))]. 1471 L(x,y * (y / z),y) = L(x,z,y). [para(1467(a,1),877(a,1))]. 1472 L(x,(y * z) * z,y * z) = L(x,T(y,z),y * z). [para(1467(a,1),878(a,1))]. 1473 L(x,T(y,z),z) = L(x,y,z). [para(1468(a,1),314(a,1,1))]. 1475 L(T(x,y),y,x) = T(x,y * x). [para(1473(a,1),1216(a,1))]. 1476 K(x,y) * (x \ y) = y / L(x,y,x). [para(1473(a,1),1247(a,1,2)),flip(a)]. 1477 L(x,y,y / z) = L(x,y,y * z). [para(1473(a,1),1285(a,1)),flip(a)]. 1478 (x * T(y,x)) \ (T(y,z) * x) = L(K(T(y,x),z),y,x). [para(1473(a,1),1195(a,2))]. 1479 T(x,y * x) = T(x,x * y). [para(1475(a,1),203(a,1))]. 1480 K(x,y) * L(x,y,x) = T(x,x * y). [para(1479(a,1),955(a,2))]. 1481 T(x,x * y) * K(y * x,x) = x. [para(1479(a,1),1089(a,1,1))]. 1482 T(x,x * (y * x)) = T(x,R(y,x,x)). [para(1479(a,1),1430(a,1))]. 1483 x \ L(x,y,x * y) = a(x * y,x,x). [para(875(a,1),1470(a,1,2))]. 1484 x \ L(x,T(y,x),y * x) = a(y * x,x,x). [para(878(a,1),1470(a,1,2))]. 1485 a(T(x,y),y,y) = a(x,y,y). [para(1470(a,1),1299(a,1)),flip(a)]. 1486 L(x * (a(y,x,x) * z),x,y) = (y / x) \ (y * z). [para(1471(a,1),1449(a,1))]. 1488 L(x,x,x * y) = y \ (y / (x \ 1)). [para(1477(a,1),807(a,1))]. 1489 K(x * y,y) = K(y * x,y). [hyper(23,a,1089,a,b,1481,a)]. 1490 T(x * K(x * y,x),y * x) = x. [para(1489(a,1),1020(a,1,1,2))]. 1491 x / (x / y) = y * K(x * y,y). [para(1489(a,2),1144(a,2,2))]. 1492 R(x,y,x) / T(x,y) = K(y * x,x). [para(1489(a,2),1370(a,2))]. 1493 T(x / (x / y),x * y) = y. [para(1144(a,2),1490(a,1,1))]. 1494 T(x * y,x / (x / y)) = T(x * y,y). [para(1493(a,1),1131(a,1,2)),flip(a)]. 1495 (x / (x / y)) \ T(x * y,x / (x / y)) = y \ (x * y). [para(1493(a,1),1138(a,1,1)),flip(a)]. 1496 R(x,y,x) = y / (y / T(x,y)). [para(1491(a,2),1325(a,1)),flip(a)]. 1497 R(x,y,x) \ y = y / T(x,y). [para(1496(a,2),66(a,1,1))]. 1498 (T(x,y) \ y) * K(T(x,y),T(x,y) * y) = R(x,y,x) \ y. [para(1497(a,2),1001(a,2))]. 1499 ((x / y) / x) * T(x,R(y,x,y)) = x / T(y,x). [para(1497(a,1),1356(a,2))]. 1500 K(x,y) = (y \ x) / (x / L(y,x,y)). [para(1476(a,1),902(a,1,2)),flip(a)]. 1501 (x * y) / (K(x,y) * L(x,y,x)) = R(x,x * y,x) \ (x * y). [para(1480(a,2),1497(a,2,2)),flip(a)]. 1502 T(x,R(y,x,x)) = T(x,y). [para(1482(a,1),1136(a,1))]. 1503 K(x,R(y,x,x)) = x \ T(x,y). [para(1502(a,1),1108(a,2,2))]. 1504 K(x,R(y,x,x)) = K(x,y). [para(1503(a,2),1108(a,2)),flip(a)]. 1505 K(x,y / x) = K(x,y * x). [para(1504(a,1),1424(a,1))]. 1506 K(x,y * x) = K(x,x * y). [para(1505(a,1),1078(a,1))]. 1507 ((x * y) * y) \ ((y * x) * y) = K(y,y * (y * x)). [para(1506(a,1),1103(a,2))]. 1508 (T(x,y) \ y) * K(x,x * y) = T(y,x) / x. [para(1506(a,1),1260(a,1,2))]. 1509 K(T(x,y),y * T(x,y)) = K(T(x,y),y * x). [para(1506(a,2),1364(a,1))]. 1510 T(x,y) \ R(x,y,x) = K(y * x,x). [para(1492(a,1),693(a,1)),flip(a)]. 1511 K(x,y) * (y \ R(y,x,y)) = K(x * y,y). [para(1510(a,1),1095(a,2))]. 1512 K(T(x,y),y * x) = K(T(x,y),x * y). [para(82(a,1),1509(a,1,2)),flip(a)]. 1513 K(T(x,y),x * y) = K(x,x * y). [para(1512(a,1),1366(a,1))]. 1514 L(x,R(y,z,z),y * z) = L(x,T(y,z),y * z). [para(1472(a,1),938(a,1)),flip(a)]. 1515 L(x,T(y,z),y * z) = L(x,y,z * y). [para(1514(a,1),1456(a,1))]. 1516 x \ L(x,y,x * y) = a(y * x,x,x). [para(1515(a,1),1484(a,1,2))]. 1517 a(x * y,y,y) = a(y * x,y,y). [para(1516(a,1),1483(a,1))]. 1518 L(x * (a(y,x,x) * z),x,y) = (x / y) * (y * z). [para(1486(a,2),358(a,1))]. 1519 K(x,y) = ((y * x) * x) \ ((x * y) * x). [para(1507(a,2),490(a,1)),flip(a)]. 1520 (x * (y * x)) \ ((x * y) * x) = K(y * x,x) * K(x,y). [para(1519(a,2),941(a,1,2)),flip(a)]. 1521 (x * y) \ (T(x,z) * y) = L(K(T(x,y),z),x,y). [para(82(a,1),1478(a,1,1))]. 1522 L(K(T(x,y),z),x,y) = T(K(x,z),x * y). [para(1521(a,1),1184(a,1))]. 1523 (x / (x / y)) \ T(x * y,x / (x / y)) = T(x,y). [para(1495(a,2),36(a,2)),flip(a)]. 1524 (x / (x / y)) \ T(x * y,y) = T(x,y). [para(1494(a,1),1523(a,1,2))]. 1525 ((x / y) / x) * T(x * y,y) = T(x,y). [para(1524(a,1),358(a,1)),flip(a)]. 1526 (x / y) * T(y * (x \ y),x \ y) = T(y,x \ y). [para(65(a,1),1525(a,1,1,1))]. 1527 L(x,y,z * (((u / w) / u) * T(u,w))) = L(x,y,z * T(u * w,w)). [para(1525(a,1),868(a,1,3,2,2))]. 1528 (x / y) * (y * (y / x)) = T(y,x \ y). [para(1239(a,1),1526(a,1,2))]. 1529 T(x,x / y) = T(x,y \ x). [para(1528(a,1),369(a,1)),flip(a)]. 1530 T(x,R(y,x,y)) = T(x,(x / y) \ x). [para(1529(a,1),1322(a,2))]. 1531 T(x,R(y,x,y)) = T(x,y). [para(66(a,1),1530(a,2,2))]. 1532 ((x / y) / x) * T(x,y) = x / T(y,x). [para(1531(a,1),1499(a,1,2))]. 1533 K(x * y,y) * K(y,x) = a(y,x,y). [para(1520(a,1),28(a,2)),flip(a)]. 1534 K(x,y) * K(y * x,x) = a(x,y,x). [para(1533(a,1),1226(a,2))]. 1536 K(x,y) * a(y,x,y) = K(x * y,y). [hyper(23,a,901,a,b,1534,a),flip(a)]. 1537 K(x,y) * K(x * y,x) = a(x,y,x). [para(1489(a,1),1534(a,1,2))]. 1539 x \ R(x,y,x) = a(x,y,x). [hyper(23,a,1511,a,b,1536,a),flip(a)]. 1541 L(x,y,x) \ x = a(x,y,x). [para(1539(a,1),1320(a,2))]. 1544 (T(x,y) \ y) * K(T(x,y),y * T(x,y)) = R(x,y,x) \ y. [para(1506(a,2),1498(a,1,2))]. 1545 (T(x,y) \ y) * K(T(x,y),x * y) = R(x,y,x) \ y. [para(82(a,1),1544(a,1,2,2))]. 1546 (T(x,y) \ y) * K(x,x * y) = R(x,y,x) \ y. [para(1513(a,1),1545(a,1,2))]. 1547 R(x,y,x) \ y = T(y,x) / x. [para(1546(a,1),1508(a,1))]. 1548 T(x,y) / y = x / T(y,x). [para(1547(a,1),1497(a,1))]. 1549 (x / T(y,x)) * y = T(x,y). [para(1548(a,1),22(a,1,1))]. 1550 (x / y) * (y * K(x,y)) = T(x,y * K(x,y)). [para(1020(a,1),1549(a,1,1,2))]. 1551 T(x,y) = (x / y) * (y * K(x,y)). [para(1550(a,2),1139(a,1)),flip(a)]. 1552 (x / y) * T(y,x) = x * K(y,x). [hyper(23,a,359,a,b,1551,a(flip)),flip(a)]. 1553 (x * (y \ 1)) * T(L(y,y,x),x) = x * K(L(y,y,x),x). [para(915(a,1),1552(a,1,1))]. 1554 (x * (y \ 1)) * L(T(y,x),y,x) = x * K(L(y,y,x),x). [para(44(a,2),1553(a,1,2))]. 1555 x * K(L(y,y,x),x) = x * (y \ T(y,x)). [para(1554(a,1),945(a,1))]. 1556 x * K(L(y,y,x),x) = x * K(y,x). [para(1108(a,2),1555(a,2,2))]. 1557 T(x * K(y,x),L(y,y,x)) = x. [para(1556(a,1),1020(a,1,1))]. 1558 T(x,L(y,y,x)) = T(x,y). [para(1557(a,1),1023(a,1,1)),flip(a)]. 1559 (x * y) / (K(x,y) * L(x,y,x)) = L(x,y,x) \ (x * y). [para(1315(a,1),1501(a,2,1))]. 1560 (x * y) / (K(x,y) * L(x,y,x)) = (L(x,y,x) \ x) * y. [para(1559(a,2),524(a,1))]. 1561 (x * y) / T(x,x * y) = (L(x,y,x) \ x) * y. [para(1480(a,1),1560(a,1,2))]. 1562 (L(x,y,x) \ x) * y = T(x * y,x) / x. [para(1561(a,1),1548(a,2)),flip(a)]. 1563 T(x * y,x) / x = a(x,y,x) * y. [para(1541(a,1),1562(a,1,1)),flip(a)]. 1564 R(K(x,y),K(y,x) * z,u) \ K(x,y) = K(y,x) * R(K(x,y),z,u). [para(923(a,2),900(a,1))]. 1565 x * (y * (R(y,y * (x \ 1),z) \ (x \ z))) = L(z,y * x,y). [para(318(a,1),957(a,1,2,2,2))]. 1566 x * (R(y,x \ 1,z) * (y \ (x \ z))) = L(z,y * x,y). [para(637(a,1),1565(a,1,2))]. 1567 x * (R(y,x,z) * (y \ (x \ z))) = L(z,y * x,y). [para(717(a,1),1566(a,1,2,1))]. 1568 R(x * (K(x,y) * K(x,y)),z,u) / T(T(x,y),y) = x \ R(x,z,u). [para(705(a,2),1202(a,1,1))]. 1569 K(x,T(y,z)) * T(y,x) = K(z,T(y,x)) * T(y,z). [para(1346(a,1),1264(a,1,2))]. 1570 (K(x,T(y,z)) * T(y,x)) / L(y,K(y,z),K(z,T(y,x))) = K(z,T(y,x)) * K(y,z). [para(1569(a,1),1106(a,1,1))]. 1572 ((T(x,y) * y) * z) / ((x * y) * z) = K(y,x) \ 1. [para(1098(a,1),1336(a,1,2,1))]. 1574 a(x * (y * y),y \ 1,y) = a(x * y,y \ 1,y \ 1). [para(156(a,1),1401(a,1,3))]. 1575 L(x,y,z * T(u * w,w)) = L(x,y,z * (u / T(w,u))). [para(1532(a,1),1527(a,1,3,2)),flip(a)]. 1576 L(x,y,z * (T(u,w) / w)) = L(x,y,z * T(u * w,w)). [para(1548(a,2),1575(a,2,3,2)),flip(a)]. 1577 (R(K(x,y),z,u) \ 1) \ K(y,x) = K(x,y) * R(K(y,x),z,u). [para(904(a,1),1564(a,1,1))]. 1578 R(K(x,y),z,u) * K(y,x) = K(x,y) * R(K(y,x),z,u). [para(1577(a,1),330(a,1)),flip(a)]. 1579 K(x,y) * R(K(y,x),T(x,y) * z,u) = R(K(y,x),x * z,u) \ K(y,x). [para(1249(a,1),1577(a,1,1)),flip(a)]. 1580 R(T(x,y) * K(x,y),z,u) / T(T(x,y),y) = x \ R(x,z,u). [para(1120(a,1),1568(a,1,1,1))]. 1581 R(T(T(x,y),y),z,u) / T(T(x,y),y) = x \ R(x,z,u). [para(1121(a,1),1580(a,1,1,1))]. 1582 T(T(x,y),y) \ R(T(T(x,y),y),z,u) = x \ R(x,z,u). [para(1581(a,1),478(a,1)),flip(a)]. 1583 (x * y) * T((x * y) \ (x * z),u) = (x * y) * L(T(y \ z,u),y,x). [para(44(a,2),764(a,1,2)),flip(a)]. 1584 (x * y) * R((x * y) \ x,z,u) = (x * y) * L(R(y \ 1,z,u),y,x). [para(48(a,1),765(a,1,2)),flip(a)]. 1589 (K(x,y) * (x \ z)) \ (K(x,y) * (x \ (z * u))) = L(u,z,x \ K(x,y)). [para(1072(a,1),1189(a,1,2))]. 1590 (x * y) * T((x * y) \ (x * z),u) = x * (y * T(y \ z,u)). [para(1583(a,2),74(a,1))]. 1591 (x * y) * R((x * y) \ x,z,u) = x * (y * R(y \ 1,z,u)). [para(1584(a,2),74(a,1))]. 1592 (x * y) * R((x * y) \ x,z,u) = x * (y \ R(y,z,u)). [para(635(a,1),1591(a,2,2))]. 1593 (x / y) * (y * R(((y \ x) * x) \ (y \ x),z,u)) = x \ R(x,z,u). [hyper(23,a,1274,a,b,1592,a(flip)),flip(a)]. 1594 (x / y) * (y * R(((y * x) * x) \ (y * x),z,u)) = x \ R(x,z,u). [para(1379(a,1),1593(a,1,2,2,1))]. 1595 (x / y) * (y * R(y \ (y / x),z,u)) = x \ R(x,z,u). [para(1296(a,1),1594(a,1,2,2,1))]. 1596 ((x \ y) / y) * (y * R(y \ x,z,u)) = (x \ y) \ R(x \ y,z,u). [para(65(a,1),1595(a,1,2,2,1,2))]. 1597 (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). [para(99(a,1),1595(a,1,2,2,1,2))]. 1598 (x \ 1) * (y * R(y \ x,z,u)) = (x \ y) \ R(x \ y,z,u). [para(320(a,1),1596(a,1,1))]. 1599 (x \ y) \ R(x \ y,z,u) = x \ (y * R(y \ x,z,u)). [para(1598(a,1),318(a,1))]. 1601 (x * y) \ R(x * y,z,u) = x \ (y * R(y \ x,z,u)). [para(1599(a,1),750(a,1)),flip(a)]. 1602 L(L(x,y,z),z * y,K(z,u)) = L(x,y,z \ K(z,u)). [para(1589(a,1),1409(a,1)),flip(a)]. 1603 L(L(x,y,z),z * y,K(z,u)) = L(x,y,z * K(z,u)). [para(1602(a,2),776(a,1))]. 1604 L(L(x,y,z),z * y,K(z,u)) = L(x,y,T(z,u)). [para(1107(a,2),1603(a,2,3))]. 1605 L(L(x,y,z),z * y,T(z,u)) = L(x,z * (z * y),K(z,u)). [para(303(a,1),1604(a,1,1)),flip(a)]. 1606 L(L(x,y,z),z * y,T(z,u)) = L(x,y,K(z,u)). [para(1605(a,2),875(a,1))]. 1608 (x * (y * x)) \ R(x * (z * x),u,w) = T(y,x) \ T(R(z,u,w),x). [para(36(a,2),701(a,2,2))]. 1609 (x * (y * x)) \ R(x * (z * x),u,w) = T(y,x) \ R(T(z,x),u,w). [para(46(a,2),1608(a,2,2))]. 1610 x \ ((y * x) * R((y * x) \ x,z,u)) = T(y,x) \ R(T(y,x),z,u). [para(1609(a,1),1601(a,1)),flip(a)]. 1611 L(x,y,z * (u \ (u \ (u \ (z * (u \ 1)))))) = L(x,y,K(z / (u * u),u)). [para(602(a,1),1194(a,1,3))]. 1612 L(x,y,z * (u \ ((u \ (u \ z)) * (u \ 1)))) = L(x,y,K(z / (u * u),u)). [para(285(a,1),1611(a,1,3,2,2))]. 1613 L(x,y,z * (u * ((u \ (u \ z)) * (u \ 1)))) = L(x,y,K(z / (u * u),u)). [para(1612(a,1),867(a,1)),flip(a)]. 1614 L(x,y,K(z / (u * u),u)) = L(x,y,z * (u \ (z * (u \ 1)))). [para(265(a,1),1613(a,1,3,2)),flip(a)]. 1615 L(x,y,K(z / (u * u),u)) = L(x,y,z * (u * (z * (u \ 1)))). [para(1614(a,2),867(a,1))]. 1616 L(x,y,K(z / (u * u),u)) = L(x,y,z * T(z,u \ 1)). [para(347(a,1),1615(a,2,3,2))]. 1617 L(x,y,K(z / (u * u),u)) = L(x,y,K(z,u \ 1)). [para(1616(a,2),1119(a,1))]. 1618 L(x,y,K(z,u \ 1)) = L(x,y,K(z,u)). [para(1418(a,1),1617(a,1,3)),flip(a)]. 1619 L(x,y,K(z,u \ 1)) = L(x,y,K(u,z)). [para(1618(a,2),909(a,1))]. 1620 (x * (x * (y * (z * u)))) \ ((x * (x * (y * z))) * u) = a(x * (x * y),z,u). [para(51(a,1),91(a,1,2,1))]. 1621 (x * y) * R(L(y \ z,y,x),u,w) = (x * y) * R((x * y) \ (x * z),u,w). [para(473(a,1),224(a,1))]. 1624 ((x * y) * ((y * x) * z)) \ (((x * y) * (y * x)) * (z * u)) = L(u,z,K(y,x)). [para(894(a,1),832(a,1,1))]. 1625 ((x * y) * T(R(T(z,x * y),x,y),u)) / ((z * x) * y) = K(R(z,x,y),u). [para(549(a,1),1214(a,1,1,2,1))]. 1626 ((x * y) * R(T(T(z,x * y),u),x,y)) / ((z * x) * y) = K(R(z,x,y),u). [para(46(a,2),1625(a,1,1,2))]. 1627 (R(T(x,y),z,u) * (z * u)) / ((x * z) * u) = K(R(x,z,u),y). [para(222(a,1),1626(a,1,1))]. 1628 ((T(x,y) * z) * u) / ((x * z) * u) = K(R(x,z,u),y). [para(79(a,1),1627(a,1,1))]. 1629 R(K(x,y),x * z,u) = K(R(x,z,u),y). [para(1628(a,1),1183(a,1)),flip(a)]. 1630 K(R(x,y,z),y) = K(y,x) \ 1. [para(1628(a,1),1572(a,1))]. 1631 R(K(x,y),T(y,x) * z,u) \ 1 = K(R(y,z,u),x). [para(1628(a,1),1162(a,2))]. 1632 K(R(x,y,z),y) = K(x,y). [para(1630(a,2),897(a,1))]. 1633 T(x,R(y,x,z)) = (x * x) / (x * K(y,x)). [para(1632(a,1),1104(a,2,2,2))]. 1634 K(R(x,x \ y,z),u) = R(K(x,u),y,z). [para(20(a,1),1629(a,1,2)),flip(a)]. 1635 R(K(x,y),x * (z / (z * x)),u) = K(x,y). [para(450(a,1),1629(a,2,1))]. 1636 R(K(x,y),T(x,y) * z,u) = K(R(T(x,y),z,u),y). [para(1105(a,1),1629(a,1,1))]. 1637 K(R(x,x * y,z),u) = R(K(x,u),y,z). [para(629(a,1),1634(a,1,1))]. 1638 R(K(x,y),z,x) = K(L(x,z,x),y). [para(1313(a,1),1634(a,1,1)),flip(a)]. 1639 K(x,R(y,y * z,u)) = R(K(y,x),z,u) \ 1. [para(1637(a,1),897(a,1,1)),flip(a)]. 1640 R(K(x,y),K(x,z) * u,w) = K(R(x,T(x,z) * u,w),y). [para(1120(a,1),1637(a,1,1,2)),flip(a)]. 1641 K(R(x,T(x,y) * z,u),y) = R(K(T(x,y),y),z,u). [para(1637(a,1),1110(a,1)),flip(a)]. 1642 T(x,R(y,x,z)) = T(x,y). [para(1633(a,2),1104(a,2)),flip(a)]. 1643 R(x,y,z) * T(y,x) = y * R(x,y,z). [para(1642(a,1),82(a,1,2))]. 1647 T(x,y) \ (x * R(y,x,z)) = T(R(y,x,z),T(x,y)). [para(1643(a,1),36(a,2,2)),flip(a)]. 1648 R(K(x,y),K(x,z),u) = K(x,y). [para(1041(a,2),1635(a,1,2))]. 1649 R(K(x,y),K(z,x),u) = K(x,y). [para(1648(a,1),908(a,1)),flip(a)]. 1650 (K(x,y) * K(z,x)) * u = K(x,y) * (K(z,x) * u). [para(1649(a,1),79(a,1,1)),flip(a)]. 1651 R(K(x,y),T(y,x) * z,u) = K(R(y,z,u),x) \ 1. [para(1631(a,1),156(a,1,1)),flip(a)]. 1652 R(K(x,y),T(x,y) * z,u) = K(R(x,z,u),y). [para(1636(a,2),1110(a,1))]. 1653 R(K(x,y),y * z,u) = K(R(y,z,u),x) \ 1. [para(1652(a,1),1249(a,1,1)),flip(a)]. 1654 R(K(x,y),y * z,u) = K(x,R(y,z,u)). [para(1653(a,2),897(a,1))]. 1656 R(K(x,y),x * z,u) * K(y,x) = K(x,y) * K(y,R(x,z,u)). [para(1654(a,1),1578(a,2,2))]. 1657 K(R(x,T(x,y) * z,u),y) = R(K(x,y),z,u). [para(1105(a,1),1641(a,2,1))]. 1658 T(R(x,y,z),T(y,x)) = K(x,y) * R(x,y,z). [para(1647(a,1),1093(a,1))]. 1659 R(T(x,T(y,x)),y,z) = K(x,y) * R(x,y,z). [para(1658(a,1),46(a,2))]. 1660 K(x,y) * R(x,y,z) = R(T(x,y),y,z). [para(1131(a,1),1659(a,1,1)),flip(a)]. 1661 T(x,y) \ R(T(x,y),y,z) = x \ R(x,y,z). [para(1660(a,1),1171(a,1,2))]. 1662 (x \ y) \ R(T(y / x,x),x,z) = (y / x) \ R(y / x,x,z). [para(84(a,1),1661(a,1,1))]. 1663 L(x,K(y,z),K(z,u)) = x. [hyper(23,a,74,a,b,1650,a),flip(a)]. 1664 L(x,K(y,z),K(u,z)) = x. [para(1663(a,1),909(a,1)),flip(a)]. 1665 L(x,K(y,z),K(u,y)) = x. [para(1664(a,1),921(a,1)),flip(a)]. 1666 (K(x,y) * T(z,x)) / z = K(z,x) * K(x,y). [para(1665(a,1),1355(a,1,2))]. 1667 R(K(x,y),T(y,x) * z,u) = K(x,R(y,z,u)). [para(1651(a,2),897(a,1))]. 1668 R(K(x,y),y * z,u) \ K(x,y) = K(y,x) * K(x,R(y,z,u)). [para(1667(a,1),1579(a,1,2)),flip(a)]. 1669 R(K(x,y),K(x,y) * z,u) = R(K(x,y),z,u). [para(1640(a,2),1657(a,1))]. 1670 R(K(x,y),z,u) \ 1 = R(K(y,x),z,u). [para(1669(a,1),906(a,1)),flip(a)]. 1671 R(K(x,y),z,u) \ K(x,y) = K(x,y) * R(K(y,x),z,u). [para(1670(a,1),543(a,1,2)),flip(a)]. 1672 K(x,R(y,y * z,u)) = R(K(x,y),z,u). [para(1670(a,1),1639(a,2))]. 1673 K(R(x,y,z),u) * K(u,x) = K(x,u) * K(u,R(x,y,z)). [para(1629(a,1),1656(a,1,1))]. 1674 K(x,y) * K(R(y,z,u),x) = K(y,x) * K(x,R(y,z,u)). [para(1673(a,1),1226(a,2))]. 1675 (x / y) \ R(x / y,y,z) = (y \ x) \ R(y \ x,y,z). [para(84(a,1),1662(a,1,2,1)),flip(a)]. 1676 (x \ y) \ R(x \ y,x,z) = (x / y) * R(y / x,x,z). [para(1675(a,1),358(a,1))]. 1677 x \ (y * R(y \ x,x,z)) = (x / y) * R(y / x,x,z). [para(1676(a,1),1599(a,1)),flip(a)]. 1678 x \ ((y \ x) * R((y \ x) \ x,x,z)) = y * R((y \ x) / x,x,z). [para(65(a,1),1677(a,2,1))]. 1679 x \ (R(y,x,z) * (y \ x)) = y * R((y \ x) / x,x,z). [para(225(a,1),1678(a,1,2))]. 1680 x * R((x \ y) / y,y,z) = T(x \ R(x,y,z),y). [para(1679(a,1),539(a,1))]. 1681 T(x \ R(x,y,z),y) = x * R(x \ 1,y,z). [para(320(a,1),1680(a,1,2,1)),flip(a)]. 1683 T(x \ R(x,y,z),y) = x \ R(x,y,z). [para(1681(a,2),635(a,1))]. 1684 (x * (y \ R(y,x,z))) / x = y \ R(y,x,z). [para(1683(a,1),105(a,1,1,2))]. 1685 T(x \ R(x,y,z),x * (y * z)) = T(a(x,y,z),y). [para(1683(a,1),740(a,1,1))]. 1686 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). [para(1684(a,1),1518(a,2,1))]. 1687 T(a(x,y,z),y) = a(x,y,z). [para(1685(a,1),739(a,2)),flip(a)]. 1688 a(x,y,z) * y = y * a(x,y,z). [para(1687(a,1),82(a,1,2)),flip(a)]. 1689 a(x,y \ 1,z) * (y \ 1) = y \ a(x,y \ 1,z). [para(1687(a,1),326(a,1,2)),flip(a)]. 1690 T(x * y,x) / x = y * a(x,y,x). [para(1688(a,1),1563(a,2))]. 1691 L(x,y,z * (T(u * z,u) / u)) = L(x,y,a(u,z,u)). [para(1690(a,2),774(a,1,3,2))]. 1692 L(x,y,z * a(u,z,u)) = L(x,y,R(z,u,u)). [para(1690(a,1),1350(a,1,3))]. 1693 L(x,y,z * T((u * z) * u,u)) = L(x,y,a(u,z,u)). [para(1691(a,1),1576(a,1)),flip(a)]. 1694 L(x,y,z * ((z * u) * u)) = L(x,y,a(u,z,u)). [para(758(a,1),1693(a,1,3,2))]. 1695 L(x,y,a(z,u,u)) = L(x,y,a(u,z,u)). [para(1694(a,1),861(a,1)),flip(a)]. 1696 (x * (x * (y * (z * u)))) \ (x * (x * ((y * z) * u))) = a(x * (x * y),z,u). [para(51(a,1),1620(a,1,2))]. 1697 (x * y) * R((x * y) \ (x * z),u,w) = (x * y) * L(R(y \ z,u,w),y,x). [para(48(a,1),1621(a,1,2)),flip(a)]. 1698 ((x * y) * ((y * x) * z)) \ ((x * y) * ((y * x) * (z * u))) = L(u,z,K(y,x)). [para(894(a,1),1624(a,1,2))]. 1699 a(x * (x * y),z,u) = (y * (z * u)) \ ((y * z) * u). [para(1696(a,1),212(a,1))]. 1700 a(x * (x * y),z,u) = a(y,z,u). [para(1699(a,2),28(a,2)),flip(a)]. 1702 a(x \ y,z,u) = a(x * y,z,u). [para(20(a,1),1700(a,1,1,2)),flip(a)]. 1703 a((x / y) * x,z,u) = a(y,z,u). [para(22(a,1),1700(a,1,1,2))]. 1704 a(x * (y * x),z,u) = a(T(y,x),z,u). [para(82(a,1),1700(a,1,1,2))]. 1706 a(x * ((x \ y) * z),u,w) = a(x * ((x * y) * z),u,w). [para(89(a,1),1700(a,1,1,2)),flip(a)]. 1707 a((x \ y) * z,u,w) = a((x * y) * z,u,w). [para(89(a,1),1700(a,1,1)),flip(a)]. 1708 a((x * x) / y,z,u) = a(y \ 1,z,u). [para(263(a,1),1700(a,1,1))]. 1709 a(x * L(x,y * x,y),z,u) = a(a(y,x,x),z,u). [para(453(a,2),1700(a,1,1,2))]. 1710 a(R(x \ 1,y,y),z,u) = a(x * a(x,y,y),z,u). [para(960(a,1),1700(a,1,1,2)),flip(a)]. 1711 a(K(x,y) * y,z,u) = a(T(y,x),z,u). [para(1077(a,1),1700(a,1,1,2))]. 1712 a(x * T(x,y),z,u) = a(K(x,y),z,u). [para(1107(a,2),1700(a,1,1,2))]. 1713 ((x \ y) * (T(x,x * y) * z)) \ (y * z) = a(x * y,T(x,x * y),z). [para(1702(a,1),255(a,2))]. 1714 a(K(x \ 1,x * y),z,u) = a(x \ ((x * y) \ y),z,u). [para(1126(a,2),1702(a,2,1)),flip(a)]. 1715 a((x * (x * y)) * (x * z),u,w) = a(y \ (x \ z),u,w). [para(282(a,1),1703(a,1,1,1))]. 1716 a((x * x) / y,z,u) = a(y,z,u). [para(1708(a,2),611(a,1))]. 1717 a(x / (y * y),z,u) = a(x,z,u). [para(1716(a,1),612(a,1)),flip(a)]. 1718 a(R(x,x * y,z),u,w) = a(R(x,y,z),u,w). [para(616(a,1),1716(a,1,1))]. 1719 a(x * K(y,x),z,u) = a(T(x,y),z,u). [para(1104(a,2),1716(a,1,1)),flip(a)]. 1720 a(x * (y * y),z,u) = a(x,z,u). [para(21(a,1),1717(a,1,1)),flip(a)]. 1721 a((x * y) * y,z,u) = a(R(x,y,y),z,u). [para(34(a,2),1717(a,1,1)),flip(a)]. 1722 a(x / (y \ 1),z,u) = a(x / y,z,u). [para(398(a,1),1717(a,1,1)),flip(a)]. 1723 ((x * (y * y)) * (z * u)) \ (((x * (y * y)) * z) * u) = a(x,z,u). [para(1720(a,1),28(a,1)),flip(a)]. 1724 a(T(T(x,y),y),z,u) = a(x,z,u). [para(985(a,1),1711(a,1,1)),flip(a)]. 1725 a((x / (y * y)) * (y \ (x * (y \ 1))),z,u) = a(K(x / (y * y),y),z,u). [para(403(a,1),1712(a,1,1,2))]. 1726 a(x / (x * y),z,u) = a(T(y,x),z,u). [para(1719(a,1),1022(a,2))]. 1727 a((x \ 1) / y,z,u) = a(y / x,z,u). [para(1722(a,1),612(a,1)),flip(a)]. 1728 a(x / T(y * x,y),z,u) = a(T(R(y,x,y),x),z,u). [para(1321(a,1),1726(a,1,1,2))]. 1729 a(x * (y * x),x,x) = a(R(y,x,x),x,x). [para(1721(a,1),1517(a,1)),flip(a)]. 1730 a(R(x,y,y),y,y) = a(T(x,y),y,y). [para(1729(a,1),1704(a,1))]. 1731 a(R(x,y,y),y,y) = a(x,y,y). [para(1730(a,2),1485(a,1))]. 1732 R(R(x,y,y) \ 1,y,y) = R(x,y,y) \ a(x,y,y). [para(1731(a,1),967(a,2,2))]. 1733 R(R(x,y,y),R(x,y,y) * y,y) = a(x,y,y) \ R(x,y,y). [para(1731(a,1),968(a,2,1))]. 1734 a(x * ((x \ y) * y),z,u) = a(a(x,y,y),z,u). [para(435(a,1),1709(a,1,1))]. 1735 a(R(x \ 1,y,y),z,u) = a(R(x,y,y),z,u). [para(963(a,1),1710(a,2,1))]. 1736 R(R(x,y,y) \ 1,y,y) = x \ 1. [para(1732(a,2),1374(a,1))]. 1737 R((x * y) \ 1,y,y) = (x / (y \ 1)) \ 1. [para(720(a,1),1736(a,1,1,1))]. 1739 R((x * y) \ 1,y,y) = (y \ 1) / x. [para(1737(a,2),343(a,1))]. 1740 (x \ 1) / (y / x) = R(y \ 1,x,x). [para(22(a,1),1739(a,1,1,1)),flip(a)]. 1741 (((x * y) \ 1) * y) * y = ((y \ 1) / x) * (y * y). [para(1739(a,1),79(a,1,1)),flip(a)]. 1742 R(x \ 1,y,y) \ 1 = (x / y) / (y \ 1). [para(1740(a,1),343(a,1,1))]. 1743 a((x \ 1) / ((y / x) \ 1),z,u) = a(R(y \ 1,x,x),z,u). [para(1740(a,1),1722(a,2,1))]. 1744 R(x,x * y,y) = (x / y) / (y \ 1). [para(1742(a,1),633(a,2))]. 1745 K(R(x,x * y,y),z) * (x / y) = (y \ 1) * T((y \ 1) \ (x / y),z). [para(1744(a,2),1201(a,1,1,1))]. 1746 (((x * y) \ 1) * y) * y = T(y / x,y * y). [para(1741(a,2),294(a,1))]. 1747 T(x / y,x * x) = ((y * x) \ x) * x. [para(318(a,1),1746(a,1,1)),flip(a)]. 1748 L(x,y * z,R(T(z / y,z * z),u,w)) = x. [para(1747(a,2),847(a,1,3,1))]. 1749 L(x,y * z,R(z / y,u,w)) = x. [para(1748(a,1),858(a,1)),flip(a)]. 1750 L(x,y * (z \ 1),u / (y * (z * u))) = x. [para(350(a,1),1749(a,1,3))]. 1752 L(x,y * z,u / (y * (z * u))) = x. [para(1750(a,1),1273(a,1)),flip(a)]. 1753 x / ((y * z) \ (y * (z * x))) = (x / (y * (z * x))) * (y * z). [para(1752(a,1),205(a,1,2))]. 1754 a(T(R(x,y,x),y),z,u) = a((y / x) / y,z,u). [para(1237(a,1),1728(a,1,1)),flip(a)]. 1755 a(x * ((x * y) * y),z,u) = a(a(x,y,y),z,u). [para(1706(a,1),1734(a,1))]. 1756 a(x * (x * (y * (x * z))),u,w) = a(y \ (x \ z),u,w). [para(51(a,1),1715(a,1,1))]. 1757 a(x \ (y \ z),u,w) = a(x * (y * z),u,w). [para(1756(a,1),1700(a,1))]. 1759 a(x * (y \ z),u,w) = a(x * (y * z),u,w). [para(1757(a,1),1702(a,1)),flip(a)]. 1760 a(K(x \ 1,x * y),z,u) = a(x * ((x * y) * y),z,u). [para(1757(a,1),1714(a,2))]. 1761 R(R(x,y,y),R(x,y,y) * y,y) = x. [para(1733(a,2),964(a,1))]. 1762 R(K(R(x,y,y),z),y,y) = K(x,z). [para(1761(a,1),1637(a,1,1)),flip(a)]. 1763 K(R(x,y,y),z) * (y \ 1) = K(x,z) / y. [para(1762(a,1),718(a,1,1)),flip(a)]. 1764 K(x,R(y,z,z)) * (K(y,x) / z) = z \ 1. [hyper(23,a,901,a,b,1763,a),flip(a)]. 1765 R(K(x,y),z,z) = K(x,R(y,z,z)). [hyper(24,a,1405,a,b,1764,a),flip(a)]. 1766 K(R(x,y,y),z) \ 1 = R(K(z,x),y,y). [para(1765(a,2),897(a,2))]. 1767 K(x,R(y,z,z)) * 1 = R(K(x,y),z,z). [para(1766(a,1),900(a,1)),flip(a)]. 1768 a((x \ 1) / (x / y),z,u) = a(R(y \ 1,x,x),z,u). [para(343(a,1),1743(a,1,1,2))]. 1769 a(R(x \ 1,y,y),z,u) = a((y / x) / y,z,u). [para(1768(a,1),1727(a,1))]. 1770 a((x / y) / x,z,u) = a(R(y,x,x),z,u). [para(1769(a,1),1735(a,1))]. 1771 a(T(R(x,y,x),y),z,u) = a(R(x,y,y),z,u). [para(1770(a,1),1754(a,2))]. 1772 a(R(T(x,y),y,x),z,u) = a(R(x,y,y),z,u). [para(46(a,2),1771(a,1,1))]. 1773 (x / (y * (z * x))) * (y * z) = x / L(x,z,y). [para(32(a,2),1753(a,1,2)),flip(a)]. 1774 (x / (y * (z * x))) * (y * z) = L(x,z,y) \ x. [para(1773(a,2),519(a,1))]. 1775 (L(x * y,z / (x * (y * z)),x * y) * (z / (x * (y * z)))) * (x * y) = (x * y) * (L(z,y,x) \ z). [para(1774(a,1),1310(a,2,2))]. 1776 (x * (y * (y * (z * u)))) \ (((x * (y * y)) * z) * u) = a(x,z,u). [para(411(a,1),1723(a,1,1))]. 1777 (x * (y * (y * (z * u)))) \ ((x * (y * (y * z))) * u) = a(x,z,u). [para(411(a,1),1776(a,1,2,1))]. 1778 a(x,y * (y * z),u) = a(x,z,u). [para(1777(a,1),90(a,1)),flip(a)]. 1779 a(x,y \ z,u) = a(x,y * z,u). [para(20(a,1),1778(a,1,2,2)),flip(a)]. 1780 a(x,(y / z) * y,u) = a(x,z,u). [para(22(a,1),1778(a,1,2,2))]. 1783 a(x,K(y,z) * T(y,z),u) = a(x,y,u). [para(1081(a,2),1778(a,1,2,2))]. 1785 a(x * (y * y),y * 1,y) = a(x * y,y \ 1,y \ 1). [para(1779(a,1),1574(a,1))]. 1786 a(x,y \ 1,z) * (y \ 1) = y \ a(x,y * 1,z). [para(1779(a,1),1689(a,2,2))]. 1787 a(x,(y * (y * z)) * (y * u),w) = a(x,z \ (y \ u),w). [para(282(a,1),1780(a,1,2,1))]. 1789 a(x,T(T(y,z),z),u) = a(x,y,u). [para(1113(a,1),1783(a,1,2))]. 1790 a(T(x,y),y,z) = a(x,T(y,x),z). [para(1789(a,1),1460(a,1))]. 1793 a(x,y \ 1,z) * (y \ 1) = y \ a(x,y,z). [para(18(a,1),1786(a,2,2,2))]. 1794 a(x,y * 1,z) * (y \ 1) = y \ a(x,y,z). [para(1779(a,1),1793(a,1,1))]. 1795 a(x,y,z) * (y \ 1) = y \ a(x,y,z). [para(18(a,1),1794(a,1,1,2))]. 1796 a(x * (y * y),y,y) = a(x * y,y \ 1,y \ 1). [para(18(a,1),1785(a,1,2))]. 1797 a(x * y,y \ 1,y \ 1) = a(x,y,y). [para(1796(a,1),1720(a,1))]. 1798 L(x,x,y) \ x = a(y,x,x). [para(1797(a,1),1408(a,1)),flip(a)]. 1800 a(x,y,y) * L(y,y,x) = y. [para(1798(a,1),520(a,1,1))]. 1801 R(x,y,y) * L(y,y,x) = x * y. [para(1800(a,1),966(a,1,2)),flip(a)]. 1802 T(R(x,y,y),L(y,y,x)) = L(y,y,x) \ (x * y). [para(1801(a,1),36(a,2,2))]. 1803 R(T(x,L(y,y,x)),y,y) = L(y,y,x) \ (x * y). [para(1802(a,1),46(a,2))]. 1804 L(x,x,y) \ (y * x) = R(T(y,x),x,x). [para(1558(a,1),1803(a,1,1)),flip(a)]. 1805 a(x,y * (y * (z * (y * u))),w) = a(x,z \ (y \ u),w). [para(51(a,1),1787(a,1,2))]. 1806 a(x,y \ (z \ u),w) = a(x,y * (z * u),w). [para(1805(a,1),1778(a,1))]. 1808 a(x,y * (z \ u),w) = a(x,y * (z * u),w). [para(1806(a,1),1779(a,1)),flip(a)]. 1809 a(x * y,T(x,x * y),z) = ((y / x) * (x * z)) \ (y * z). [para(1265(a,1),1713(a,1,1)),flip(a)]. 1810 a(x * y,T(x,x * y),z) = a(y / x,x,z). [para(1809(a,2),68(a,1))]. 1811 R(K(x,y),z,z) * (x / z) = (z \ 1) * T((z \ 1) \ (x / z),y). [para(1637(a,1),1745(a,1,1))]. 1812 K(x,R(y,z,z)) * (x / z) = (z \ 1) * T((z \ 1) \ (x / z),y). [para(1765(a,1),1811(a,1,1))]. 1813 K(x,R(y,z,z)) * (x / z) = (z \ 1) * T(z * (x / z),y). [para(330(a,1),1812(a,2,2,1))]. 1814 K(x,R(y,z,z)) * (x / z) = z \ T(z * (x / z),y). [para(1813(a,2),318(a,1))]. 1815 K(x,R(y,z,z)) * (x / z) = T(x,y) / z. [para(1814(a,2),755(a,1))]. 1816 a(x * (y \ (y \ (y \ (x * (y \ 1))))),z,u) = a(K(x / (y * y),y),z,u). [para(602(a,1),1725(a,1,1))]. 1817 a(x * (y \ ((y \ (y \ x)) * (y \ 1))),z,u) = a(K(x / (y * y),y),z,u). [para(285(a,1),1816(a,1,1,2,2))]. 1818 a(x * (y * ((y \ (y \ x)) * (y \ 1))),z,u) = a(K(x / (y * y),y),z,u). [para(1817(a,1),1759(a,1)),flip(a)]. 1819 a(K(x / (y * y),y),z,u) = a(x * (y \ (x * (y \ 1))),z,u). [para(265(a,1),1818(a,1,1,2)),flip(a)]. 1820 a(K(x / (y * y),y),z,u) = a(x * (y * (x * (y \ 1))),z,u). [para(1819(a,2),1759(a,1))]. 1821 a(K(x / (y * y),y),z,u) = a(x * T(x,y \ 1),z,u). [para(347(a,1),1820(a,2,1,2))]. 1822 a(K(x / (y * y),y),z,u) = a(K(x,y \ 1),z,u). [para(1821(a,2),1712(a,1))]. 1823 a(K(x,y \ 1),z,u) = a(K(x,y),z,u). [para(1418(a,1),1822(a,1,1)),flip(a)]. 1824 a(K(x \ 1,y),z,u) = a(K(y,x),z,u). [para(1823(a,1),905(a,1)),flip(a)]. 1825 a(x * ((x * y) * y),z,u) = a(K(x * y,x),z,u). [para(1824(a,1),1760(a,1)),flip(a)]. 1826 a(K(x * y,x),z,u) = a(a(x,y,y),z,u). [para(1825(a,1),1755(a,1))]. 1827 (x * y) * R((x * y) \ (x * z),u,w) = x * (y * R(y \ z,u,w)). [para(1697(a,2),74(a,1))]. 1828 (x * y) * R((x * y) \ z,u,w) = x * (y * R(y \ (x \ z),u,w)). [para(20(a,1),1827(a,1,2,1,2))]. 1829 (x * y) * R((x * y) \ y,z,u) = R(x,z,u) * (x \ y). [para(1828(a,2),639(a,1))]. 1830 T(x,y) \ R(T(x,y),z,u) = y \ (R(x,z,u) * (x \ y)). [para(1829(a,1),1610(a,1,2)),flip(a)]. 1831 T(x,y) \ R(T(x,y),z,u) = T(x \ R(x,z,u),y). [para(1830(a,2),539(a,1))]. 1832 (R(T(x,y),z,u) \ T(x,y)) * w = T(x \ R(x,z,u),y) \ w. [para(1831(a,1),465(a,1,1)),flip(a)]. 1833 T(x \ R(x,y,y),z) = a(T(x,z),y,y). [para(1831(a,1),962(a,1))]. 1834 K(x,y) * R(T(y,x),z,u) = y * T(y \ R(y,z,u),x). [para(1831(a,1),1099(a,1,2)),flip(a)]. 1835 T(T(x,y) \ R(T(x,y),z,u),y) = x \ R(x,z,u). [para(1831(a,1),1582(a,1))]. 1836 a(T(x,y),z,z) = T(a(x,z,z),y). [para(962(a,1),1833(a,1,1)),flip(a)]. 1837 T(T(x \ R(x,y,z),u),u) = x \ R(x,y,z). [para(1831(a,1),1835(a,1,1))]. 1838 (x * (y \ R(y,z,u))) / x = T(y \ R(y,z,u),x). [para(1837(a,1),105(a,1,1,2))]. 1839 T(a(x,y,z),x * (y * z)) = x \ R(x,y,z). [para(739(a,2),1837(a,1,1))]. 1840 a(x,y,z) * K(a(x,y,z),x * (y * z)) = x \ R(x,y,z). [para(1839(a,1),1107(a,1)),flip(a)]. 1841 T(T(x \ R(x,y,z),u),x * (y * z)) = (u * a(x,y,z)) / u. [para(1838(a,1),742(a,1,1))]. 1842 (x * (y \ R(y,z,u))) / x = (y \ R(y,z,u)) * K(y \ R(y,z,u),x). [para(1838(a,2),1107(a,1))]. 1843 (x * a(y,z,u)) / x = T(a(y,z,u),x). [para(1841(a,1),740(a,1))]. 1844 T(a(x,y,z),u) * (u / (u * a(x,y,z))) = 1. [para(1843(a,1),354(a,1,1))]. 1845 L(x,x,x * ((x \ 1) * a(y,z,u))) = ((x \ 1) * a(y,z,u)) \ T(a(y,z,u),x \ 1). [para(1843(a,1),1488(a,2,2))]. 1846 K(a(x,y,z),u) * K(a(x,y,z),u) = 1. [para(1844(a,1),1174(a,1)),flip(a)]. 1847 K(a(x,y,z),u) = K(u,a(x,y,z)). [hyper(24,a,898,a,b,1846,a)]. 1848 a(x,y,z) * K(x * (y * z),a(x,y,z)) = x \ R(x,y,z). [para(1847(a,1),1840(a,1,2))]. 1849 K(x \ R(x,y,z),u) = K(u,x \ R(x,y,z)). [hyper(23,a,1014,a(flip),b,1842,a(flip))]. 1850 L(L(x,y,z * u),(z * u) * y,u * z) = L(x,y,K(z,u)). [para(1698(a,1),174(a,1)),flip(a)]. 1851 ((x * (x * y)) * a(y,z,u)) / y = a(x * (x * y),z,u) * (x * x). [para(1700(a,1),749(a,1,1,2))]. 1852 (x * (x * (y * a(y,z,u)))) / y = a(x * (x * y),z,u) * (x * x). [para(51(a,1),1851(a,1,1))]. 1854 a(x * (x * y),z,u) * (x * x) = x * (x * ((y * a(y,z,u)) / y)). [para(1852(a,1),211(a,1))]. 1855 a(x * (x * y),z,u) * (x * x) = x * (x * a(y,z,u)). [para(748(a,1),1854(a,2,2,2))]. 1856 a(x,y,z) * (u * u) = u * (u * a(x,y,z)). [para(1700(a,1),1855(a,1,1))]. 1857 T((a(x,y,z) * (u * u)) / (u * u),u) = T(u \ (u * a(x,y,z)),u \ 1). [para(1856(a,2),666(a,1,1,1))]. 1859 T(x \ (x * a(y,z,u)),x \ 1) = T(a(y,z,u),x). [para(21(a,1),1857(a,1,1)),flip(a)]. 1860 T(a(x,y,z),u \ 1) = T(a(x,y,z),u). [para(19(a,1),1859(a,1,1))]. 1863 x * L(T(y \ (y / x),z),y,x * y) = K(L(y \ (y / x),y,x * y),z). [para(1295(a,1),330(a,1)),flip(a)]. 1864 (x / y) * (y * T(y \ (y / x),z)) = K(L(y \ (y / x),y,x * y),z). [para(1863(a,1),1294(a,1)),flip(a)]. 1865 (x / y) * (y * T(y \ (y / x),z)) = K(x \ 1,z). [para(1289(a,1),1864(a,2,1))]. 1866 (L(x,y,z) / (z * (y * x))) * ((z * (y * x)) * T((z * (y * x)) \ (z * y),u)) = K(L(x,y,z) \ 1,u). [para(99(a,1),1865(a,1,2,2,1,2))]. 1868 T(x * x,y * z) \ ((((y * z) \ (x * x)) * y) * z) = a((y * z) * (x * x),y,z). [para(394(a,2),1702(a,1))]. 1869 ((R(x,y,z) * u) * w) / ((x * u) * w) = R(x,u,w) \ R(R(x,u,w),y,z). [para(185(a,1),538(a,1,1))]. 1870 R(x \ R(x,y,z),x * u,w) = R(x,u,w) \ R(R(x,u,w),y,z). [para(1869(a,1),533(a,2))]. 1871 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). [para(584(a,1),1870(a,2,1))]. 1872 (K(x,T(y,z)) * T(y,x)) / y = K(z,T(y,x)) * K(y,z). [para(1663(a,1),1570(a,1,2))]. 1873 K(x,T(y,z)) * K(y,x) = K(y,z) * K(z,T(y,x)). [para(1872(a,1),1666(a,1))]. 1874 T(x * x,y * z) \ ((((y * z) \ (x * x)) * y) * z) = a(y * z,y,z). [para(1868(a,2),1720(a,1))]. 1875 (T(x * x,y * z) \ (((y * z) \ (x * x)) * y)) * z = a(y * z,y,z). [para(1874(a,1),591(a,1)),flip(a)]. 1877 ((T(x * x,y * z) \ ((y * z) \ (x * x))) * y) * z = a(y * z,y,z). [para(591(a,1),1875(a,1,1))]. 1878 (((x * y) \ 1) * x) * y = a(x * y,x,y). [para(795(a,1),1877(a,1,1,1))]. 1879 ((x * y) \ x) * y = a(x * y,x,y). [para(318(a,1),1878(a,1,1))]. 1880 x * ((y * x) \ y) = a(y * x,y,x). [para(1879(a,1),388(a,1)),flip(a)]. 1881 a(x * (x \ y),x,x \ y) = (x \ y) * (y \ x). [para(20(a,1),1880(a,1,2,1)),flip(a)]. 1882 (x \ y) * (y \ x) = a(y,x,x \ y). [para(20(a,1),1881(a,1,1)),flip(a)]. 1883 L(x,y,(z \ u) * (u * z)) = L(x,y,a(z,u,u \ z)). [para(1882(a,1),869(a,1,3)),flip(a)]. 1884 L(x,(y \ z) * (z * y),u) = L(x,a(y,z,z \ y),u). [para(1882(a,1),1362(a,1,2)),flip(a)]. 1885 L(x,y,(z * u) * (u * z)) = L(x,y,a(z,u,u \ z)). [para(1883(a,1),781(a,1)),flip(a)]. 1886 L(x,(y * z) * (z * y),u) = L(x,a(y,z,z \ y),u). [para(1884(a,1),880(a,1)),flip(a)]. 1887 L(x,y,a(z,u,u \ z)) = L(x,y,K(u,z)). [para(1885(a,1),779(a,1))]. 1888 L(x,a(y,z,z \ y),u) = L(x,K(z,y),u). [para(1886(a,1),879(a,1))]. 1889 ((x \ 1) * a(y,z,u)) \ T(a(y,z,u),x \ 1) = L(x,x,a(y,z,u)). [para(321(a,1),1845(a,1,3)),flip(a)]. 1890 (x \ a(y,z,u)) \ T(a(y,z,u),x \ 1) = L(x,x,a(y,z,u)). [para(318(a,1),1889(a,1,1))]. 1892 (x \ a(y,z,u)) \ T(a(y,z,u),x) = L(x,x,a(y,z,u)). [para(1860(a,1),1890(a,1,2))]. 1893 L(x,a(y,z,u),x) = L(x,x,a(y,z,u)). [para(1892(a,1),440(a,1)),flip(a)]. 1894 L(x,x,a(y,z,z \ y)) = L(x,K(z,y),x). [para(1893(a,1),1888(a,1))]. 1895 L(x,K(y,z),x) = L(x,x,K(y,z)). [para(1894(a,1),1887(a,1))]. 1896 L(x,K(y,z),x) = L(x,x,K(z,y)). [para(1895(a,2),909(a,1))]. 1897 (x \ K(y,z)) / (K(y,z) / L(x,x,K(z,y))) = K(K(y,z),x). [para(1896(a,1),1500(a,2,2,2)),flip(a)]. 1898 (x \ K(y,z)) / (K(y,z) * (x \ 1)) = K(K(y,z),x). [para(930(a,1),1897(a,1,2))]. 1899 K(x \ 1,K(y,z)) = K(K(y,z),x). [para(1898(a,1),978(a,1)),flip(a)]. 1900 K(K(x,y),z) * (K(x,y) \ u) = T(K(x,y),z \ 1) \ u. [para(1899(a,1),1095(a,1,1))]. 1901 T(K(x,y),z) * K(K(x,y),z) = T(K(x,y),z * z). [para(1899(a,1),1433(a,1,2))]. 1902 T(T(K(x,y),z),z) = T(K(x,y),z * z). [para(1901(a,1),1121(a,1)),flip(a)]. 1903 T(K(x,y),T(z,x) * T(z,x)) = T(T(K(x,y),z),T(z,x)). [para(1352(a,1),1902(a,1,1)),flip(a)]. 1904 x / (T(K(y,z),u \ 1) \ x) = K(y,z) * K(u,K(y,z)). [para(1900(a,1),1071(a,1,2))]. 1905 T(K(x,y),z * T(T(z,x),x)) = T(T(K(x,y),z),T(z,x)). [para(1088(a,1),1903(a,1,2))]. 1906 K(x,y) * K(z,K(x,y)) = T(K(x,y),z \ 1). [para(1904(a,1),65(a,1))]. 1907 T(K(x,y),z \ 1) * z = z * K(x,y). [para(1906(a,1),1018(a,1,1))]. 1908 ((x * y) * (z / (x * (y * z)))) * (x * y) = (x * y) * (L(z,y,x) \ z). [para(851(a,1),1775(a,1,1,1))]. 1910 (x \ R(x,y,z)) * (x * y) = (x * y) * (L(z,y,x) \ z). [para(1410(a,1),1908(a,1,1))]. 1911 (x * y) * (L(z,y,x) \ z) = R(x,y,z) * y. [para(1910(a,1),528(a,1))]. 1912 ((x * y) \ 1) * ((x * (y * z)) * T((x * (y * z)) \ (x * y),u)) = K(L(z,y,x) \ 1,u). [para(342(a,1),1866(a,1,1))]. 1914 ((x * y) \ 1) * (x * ((y * z) * T((y * z) \ y,u))) = K(L(z,y,x) \ 1,u). [para(1590(a,1),1912(a,1,2))]. 1915 ((x * y) \ 1) * (x * (y * K(z \ 1,u))) = K(L(z,y,x) \ 1,u). [para(1164(a,1),1914(a,1,2,2))]. 1916 (x * y) \ (x * (y * K(z \ 1,u))) = K(L(z,y,x) \ 1,u). [para(1915(a,1),318(a,1)),flip(a)]. 1917 L(K(x \ 1,y),z,u) = K(L(x,z,u) \ 1,y). [para(1916(a,1),32(a,2))]. 1918 K(L(x \ 1,y,z) \ 1,u) = L(K(x,u),y,z). [para(156(a,1),1917(a,1,1,1)),flip(a)]. 1920 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). [para(750(a,1),1871(a,1,1))]. 1921 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). [para(18(a,1),1920(a,1,1,1))]. 1922 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). [para(18(a,1),1921(a,1,1,2,1))]. 1923 (R(x,y,z) \ 1) \ R(R(x \ 1,x * y,z),u,w) = R(x \ R(x,u,w),y,z). [para(322(a,1),1922(a,1,2)),flip(a)]. 1924 (R(x,y,z) \ 1) \ R(R(x,y,z) \ 1,u,w) = R(x \ R(x,u,w),y,z). [para(584(a,1),1923(a,1,2,1))]. 1925 (R(x,y,z) * 1) \ R(R(x,y,z) * 1,u,w) = R(x \ R(x,u,w),y,z). [para(1924(a,1),750(a,1)),flip(a)]. 1926 R(x,y,z) \ R(R(x,y,z) * 1,u,w) = R(x \ R(x,u,w),y,z). [para(18(a,1),1925(a,1,1))]. 1927 R(x,y,z) \ R(R(x,y,z),u,w) = R(x \ R(x,u,w),y,z). [para(18(a,1),1926(a,1,2,1))]. 1928 R(x \ R(x,y,y),z,u) = a(R(x,z,u),y,y). [para(1927(a,1),962(a,1))]. 1929 T(R(x \ R(x,y,x),z,u),x * (R(x,z,u) * T(y,x))) = a(R(x,z,u),y,x). [para(1927(a,1),743(a,1,1))]. 1930 a(R(x,y,z),u,u) = R(a(x,u,u),y,z). [para(962(a,1),1928(a,1,1)),flip(a)]. 1931 T(R(a(x,y,x),z,u),x * (R(x,z,u) * T(y,x))) = a(R(x,z,u),y,x). [para(1539(a,1),1929(a,1,1,1))]. 1932 T(R(a(x,y,x),z,u),R(x,z,u) * (y * x)) = a(R(x,z,u),y,x). [para(530(a,1),1931(a,1,2))]. 1933 R(T(a(x,y,x),R(x,z,u) * (y * x)),z,u) = a(R(x,z,u),y,x). [para(1932(a,1),46(a,2))]. 1934 ((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). [para(342(a,1),1597(a,1,1))]. 1936 ((x * y) \ 1) * (x * ((y * z) * R((y * z) \ y,u,w))) = L(z,y,x) \ R(L(z,y,x),u,w). [para(1827(a,1),1934(a,1,2))]. 1937 ((x * y) \ 1) * (x * (y * (z \ R(z,u,w)))) = L(z,y,x) \ R(L(z,y,x),u,w). [para(1592(a,1),1936(a,1,2,2))]. 1938 (x * y) \ (x * (y * (z \ R(z,u,w)))) = L(z,y,x) \ R(L(z,y,x),u,w). [para(1937(a,1),318(a,1)),flip(a)]. 1939 L(x,y,z) \ R(L(x,y,z),u,w) = L(x \ R(x,u,w),y,z). [para(1938(a,1),32(a,2)),flip(a)]. 1940 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). [para(1808(a,1),1686(a,1,1,2,1))]. 1941 L((x * (y \ R(y,x,z))) * (1 * u),x * (y \ R(y,x,z)),x) = (y \ R(y,x,z)) * (x * u). [para(1442(a,1),1940(a,1,1,2,1))]. 1942 L((x * (y \ R(y,x,z))) * u,x * (y \ R(y,x,z)),x) = (y \ R(y,x,z)) * (x * u). [para(17(a,1),1941(a,1,1,2))]. 1944 L(x * (R(y,x,z) * (y \ u)),x * (y \ R(y,x,z)),x) = (y \ R(y,x,z)) * (x * u). [para(1450(a,1),1942(a,1,1))]. 1945 L(x * (R(y,x,z) * (y \ u)),x * (y * R(y,x,z)),x) = (y \ R(y,x,z)) * (x * u). [para(1944(a,1),1360(a,1)),flip(a)]. 1946 (x \ R(x,y,z)) * (y * u) = y * (R(x,y,z) * (x \ u)). [para(1945(a,1),1439(a,1))]. 1947 R(x,y,z) * (x \ (y * u)) = y * (R(x,y,z) * (x \ u)). [para(1946(a,1),532(a,1)),flip(a)]. 1948 R(x,y,z) * (x \ (y * (y \ z))) = L(z,x * y,x). [para(1947(a,2),1567(a,1))]. 1949 R(x,y,z) * (x \ z) = L(z,x * y,x). [para(20(a,1),1948(a,1,2,2))]. 1950 R(x,y,L(z,y,x)) * (x \ L(z,y,x)) = z. [para(1949(a,2),303(a,1))]. 1951 L(x,y * z,y) / x = y \ R(y,z,x). [para(1949(a,1),536(a,1,1))]. 1952 x / L(x,y * z,y) = R(y,z,x) \ y. [para(1949(a,1),542(a,1,2))]. 1953 x \ L(x,y * z,y) = y \ R(y,z,x). [para(1951(a,1),515(a,1)),flip(a)]. 1954 L(x,y * z,y) \ x = R(y,z,x) \ y. [para(1952(a,1),519(a,1)),flip(a)]. 1955 x \ R(x,x \ y,z) = z \ L(z,y,x). [para(20(a,1),1953(a,1,2,2)),flip(a)]. 1956 x \ R(x,x * y,z) = z \ L(z,y,x). [para(313(a,1),1953(a,1,2)),flip(a)]. 1957 K(x,R(y,z,x) \ y) = 1. [para(1954(a,1),653(a,1,2))]. 1958 K(x,y \ R(y,z,x)) = 1. [para(622(a,1),1957(a,1,2))]. 1959 T(x,y \ R(y,z,x)) = x. [hyper(41,a,1958,a)]. 1960 K(x,T(y \ R(y,z,x),u)) = 1. [para(1831(a,1),1958(a,1,2))]. 1961 T(x \ R(x,y,z),z) = x \ R(x,y,z). [hyper(39,a,1959,a)]. 1962 K(x,a(y,z,x)) = 1. [para(739(a,2),1960(a,1,2))]. 1963 T(x,a(y,z,x)) = x. [hyper(41,a,1962,a)]. 1964 a(x,y,z) * z = z * a(x,y,z). [para(1963(a,1),82(a,1,2))]. 1965 R(x,y,z) \ x = z \ L(z,y,x). [para(1955(a,1),624(a,1)),flip(a)]. 1966 L(x,y,z) = x * (R(z,y,x) \ z). [para(1965(a,2),20(a,1,2)),flip(a)]. 1967 R(x,y,z) = x / (z \ L(z,y,x)). [para(1965(a,1),65(a,1,2)),flip(a)]. 1968 (x \ L(x,y,z)) \ 1 = z \ R(z,y,x). [para(1965(a,1),460(a,1,1))]. 1969 (x \ L(x,y,z)) * R(z,y,x) = z. [para(1965(a,1),496(a,1,1))]. 1970 L(x,y,z) = (R(z,y,x) \ z) * x. [para(1965(a,2),514(a,1,1)),flip(a)]. 1971 x * (R(K(y,z),u,x) \ K(y,z)) = L(x,u,K(z,y)). [para(1966(a,1),909(a,1))]. 1972 R(x,y,T(z,x * y)) = R(x,y,z). [hyper(23,a,680,a,b,1969,a),flip(a)]. 1973 L(x,y,z) * R(z,y,x) = x * z. [para(1969(a,1),504(a,1,2)),flip(a)]. 1974 L(x,y,z) * (x \ R(z,y,x)) = z. [para(1969(a,1),647(a,1)),flip(a)]. 1975 R(x,y,z) * L(z,y,x) = x * z. [para(1970(a,2),458(a,1,2))]. 1976 L(x,y,z) = (z \ R(z,y,x)) \ x. [para(1970(a,2),465(a,2)),flip(a)]. 1977 T(x \ R(x,y,z),u) \ z = L(z,y,T(x,u)). [para(1970(a,2),1832(a,1)),flip(a)]. 1978 L(x,y,z) \ x = z \ R(z,y,x). [para(1972(a,1),681(a,2,2))]. 1979 R(x,y,z) = x * (L(z,y,x) \ z). [para(1972(a,1),683(a,1))]. 1980 R(x,y,z) * (x \ L(z,y,x)) = z. [para(1972(a,1),686(a,1,1))]. 1981 (L(x,y,z) * (R(z,y,x) * u)) \ ((x * z) * u) = a(L(x,y,z),R(z,y,x),u). [para(1973(a,1),28(a,2,2,1)),flip(a)]. 1984 (L(x,y,z) \ x) * (z * u) = R(z,y,x) * u. [para(1978(a,2),528(a,1,1))]. 1985 (x \ R(x,y,z)) * u = z * (L(z,y,x) \ u). [para(1978(a,1),650(a,1,1))]. 1986 R(x \ R(x,y,z),z,u) = L(z,y,x) \ z. [para(1978(a,1),736(a,1,1))]. 1987 (x * y) * (x \ R(x,y,z)) = R(x,y,z) * y. [para(1978(a,1),1911(a,1,2))]. 1988 K(x,y) \ R(K(x,y),z,u) = u \ L(u,z,K(x,y)). [para(1669(a,1),1956(a,1,2))]. 1989 x \ R(x,y,z) = (L(z,y,x) \ z) * 1. [para(1968(a,1),517(a,1))]. 1990 R(x,y,L(z,y,x)) = R(x,y,z). [hyper(24,a,1980,a,b,1950,a)]. 1991 (x \ R(x,y,z)) \ z = L(z,y,T(x,z)). [para(1961(a,1),1977(a,1,1))]. 1992 L(x,y,T(z,x)) = L(x,y,z). [para(1991(a,1),1976(a,2)),flip(a)]. 1993 L(L(x,y,z),z * y,T(z,L(x,y,z))) = x. [para(1992(a,2),303(a,1))]. 1994 L(x,y,K(z,L(x,y,z))) = x. [para(1993(a,1),1606(a,1)),flip(a)]. 1995 x * (L(x,y,z) \ (z * u)) = R(z,y,x) * u. [para(1984(a,1),650(a,1)),flip(a)]. 1996 L((x \ R(x,y,z)) \ u,x \ R(x,y,z),x * y) = (R(x,y,z) * y) \ ((x * y) * u). [para(1987(a,1),76(a,2,1))]. 1998 L(x,y,z) * (R(z,y,x) * u) = x * (z * u). [para(1995(a,1),645(a,1,2))]. 1999 x * (L(x,y,z) \ (z * T(y,z))) = y * R(z,y,x). [para(1995(a,2),1643(a,1))]. 2000 x * (L(x,y,z) \ (z * L(x,y,z))) = z * x. [para(1995(a,2),1975(a,1))]. 2001 x * T(y,L(x,z,y)) = y * x. [para(36(a,2),2000(a,1,2))]. 2002 T(x,L(y,z,x)) = x * K(x,y). [hyper(23,a,1116,a,b,2001,a)]. 2005 K(x,L(y,z,x)) = K(x,y). [hyper(23,a,1107,a(flip),b,2002,a(flip)),flip(a)]. 2006 L(x,y,K(z,x)) = x. [para(2005(a,1),1994(a,1,3))]. 2007 L(T(x,y),z,K(u,x)) = T(x,y). [para(2006(a,1),44(a,2,1))]. 2008 L(x,y,K(x,z)) = x. [para(2006(a,1),909(a,1)),flip(a)]. 2009 L(x,y,a(x,z,z)) = x. [para(2006(a,1),1262(a,1)),flip(a)]. 2010 L(K(x,y),z,K(u,x \ 1)) = K((x \ 1) \ 1,y). [para(2006(a,1),1918(a,1,1,1)),flip(a)]. 2011 R(K(x,y),z,y) = K(x,y) / (y \ y). [para(2006(a,1),1967(a,2,2,2))]. 2013 (K(x,y) * z) * x = K(x,y) * (z * x). [para(2008(a,1),74(a,1,2))]. 2014 x * (x \ R(a(x,y,y),z,x)) = a(x,y,y). [para(2009(a,1),1974(a,1,1))]. 2015 T(x,K(y,x) * z) = T(x,z). [para(2007(a,1),1377(a,1)),flip(a)]. 2016 K(K(x,y) * z,y) = T(y,z) \ y. [para(2015(a,1),1080(a,2,1))]. 2017 K(x,K(y,x) * z) = x \ T(x,z). [para(2015(a,1),1108(a,2,2))]. 2019 T(x,y * T(z,x)) = T(x,y * z). [para(1212(a,1),2015(a,1,2))]. 2021 K(K(x,y) * z,y) = K(z,y). [para(2016(a,2),1080(a,2)),flip(a)]. 2022 K(K(x,y) * z,x) = K(z,x). [para(901(a,1),2021(a,1,1)),flip(a)]. 2023 K(x * (K(x,y) * z),x) = K(x * z,x). [para(1068(a,1),2022(a,1,1))]. 2024 K(x,K(y,x) * z) = K(x,z). [para(2017(a,2),1108(a,2)),flip(a)]. 2025 K(x,K(x,y) * z) = K(x,z). [para(901(a,1),2024(a,1,2)),flip(a)]. 2026 K(x,y) * K(x * (K(x,z) * y),x) = a(x,K(x,z) * y,x). [para(2025(a,1),1537(a,1,1))]. 2027 R(K(x,y),z,y) = K(x,y) / 1. [para(60(a,1),2011(a,2,2))]. 2029 R(K(x,y),z,y) = K(x,y). [para(2027(a,2),64(a,1))]. 2030 K(x,R(y,z,y)) = K(x,y). [para(2029(a,1),1654(a,1)),flip(a)]. 2031 R(K(x,y),z,x) = K(y,x) \ 1. [para(2029(a,1),1670(a,1,1)),flip(a)]. 2032 K(x,y) * R(T(y,x),z,y) = R(y,z,y). [para(2030(a,1),1083(a,1,1))]. 2033 R(K(x,y),z,x) = K(x,y). [para(2031(a,2),897(a,1))]. 2034 K(L(x,y,x),z) = K(x,z). [para(2033(a,1),1638(a,1)),flip(a)]. 2036 K((x \ y) \ y,z) = K(T(x,y),z). [para(1457(a,1),2034(a,1,1))]. 2038 K(T(x,x \ y),z) = K(T(x,y),z). [para(83(a,2),2036(a,1,1))]. 2039 x \ (K(x,y) * (z * x)) = T(K(x,y) * z,x). [para(2013(a,1),36(a,2,2)),flip(a)]. 2040 x * ((K(x,y) * z) * x) = T(x,y) * (z * x). [para(2013(a,2),1120(a,1,2))]. 2041 T(x,y) \ R(T(x,y),z,x) = x \ R(x,z,x). [para(2032(a,1),1163(a,1,2)),flip(a)]. 2042 x * (x \ a(R(x,y,x),z,z)) = a(x,z,z). [para(1930(a,2),2014(a,1,2,2))]. 2043 x * (x \ a(L(x,y,x),z,z)) = a(x,z,z). [para(1303(a,1),2042(a,1,2,2,1))]. 2044 a(L(x,y,x),z,z) = a(x,z,z). [para(2043(a,1),20(a,1)),flip(a)]. 2045 a(L(T(x,y),y * x,x),z,z) = a(T(x,y),z,z). [para(1283(a,1),2044(a,1,1))]. 2046 K(x,y) * (x \ (z * x)) = T(K(x,y) * z,x). [para(2039(a,1),1076(a,1)),flip(a)]. 2047 (T(x,y) * (z * x)) \ ((T(x,y) * z) * x) = a(x,K(x,y) * z,x). [para(2040(a,1),1166(a,1,1))]. 2048 T(x,y) \ R(T(x,y),z,x) = a(x,z,x). [para(2041(a,2),1539(a,1))]. 2049 T(x \ R(x,y,x),z) = a(x,y,x). [para(2048(a,1),1831(a,1)),flip(a)]. 2050 T(a(x,y,x),z) = a(x,y,x). [para(1539(a,1),2049(a,1,1))]. 2052 a(R(x,y,z),u,x) = R(a(x,u,x),y,z). [para(2050(a,1),1933(a,1,1)),flip(a)]. 2054 a(x,y,x) \ a(R(x,z,z),y,x) = a(a(x,y,x),z,z). [para(2052(a,2),962(a,1,2))]. 2056 T(K(x,y) * z,x) = K(x,y) * T(z,x). [para(36(a,2),2046(a,1,2)),flip(a)]. 2057 T(K(x,y) * R(z,u,w),x) = K(x,y) * R(T(z,x),u,w). [para(46(a,2),2056(a,2,2))]. 2058 T(K(x,y) * z,x) / z = K(z,x) * K(x,y). [para(2056(a,2),1666(a,1,1))]. 2059 T(K(x,y) * z,x) / z = K(x,y) * K(z,x). [para(2058(a,2),1226(a,2)),flip(a)]. 2060 L(K(x,y),z,K(u,x \ 1)) = K(x,y). [para(156(a,1),2010(a,2,1))]. 2061 L(K(x,y),z,K(u,x)) = K(x,y). [para(2060(a,1),1618(a,1)),flip(a)]. 2062 L(K(x,y),z,K(x,u)) = K(x,y). [para(2060(a,1),1619(a,1)),flip(a)]. 2063 (K(x,y) * z) \ z = T(K(y,x),z). [para(2061(a,1),1301(a,1,1)),flip(a)]. 2064 T(K(x,y) * z,K(x,y)) = z * K(x,y). [para(2062(a,1),1309(a,1,1,1))]. 2065 x / T(K(y,z),x) = K(z,y) * x. [para(2063(a,1),65(a,1,2))]. 2067 (T(K(x,y),z) / z) * u = (K(y,x) * z) \ u. [para(2065(a,1),358(a,1,1)),flip(a)]. 2068 (K(x,y) * z) * K(y,x) = T(z,K(y,x)). [para(2065(a,1),1549(a,1,1))]. 2069 K(K(x,y) * z,K(y,x)) = T(z,K(y,x)) / z. [para(2068(a,1),979(a,1,1)),flip(a)]. 2070 K(K(x,y) * z,K(y,x)) = K(z,K(y,x)). [para(2069(a,2),1086(a,2)),flip(a)]. 2071 K(K(x,y) * z,K(x,y)) = K(z,K(x,y)). [para(901(a,1),2070(a,1,1)),flip(a)]. 2072 a(a(K(x,y),z,z),u,w) = a(K(z,K(x,y)),u,w). [para(2071(a,1),1826(a,1,1)),flip(a)]. 2073 a(R(T(x,y),y,x),z,z) = a(T(x,y),z,z). [para(1306(a,1),2045(a,1,1))]. 2074 a(R(x,y,y),z,z) = a(T(x,y),z,z). [para(2073(a,1),1772(a,1)),flip(a)]. 2076 x * (K(y,z) * R(K(z,y),u,x)) = L(x,u,K(z,y)). [para(1671(a,1),1971(a,1,2))]. 2077 x * (K(y,z) * K(z,R(y,u,x))) = L(x,y * u,K(y,z)). [para(1668(a,1),1971(a,1,2))]. 2078 x * (L(x,y,z) \ (y * z)) = y * R(z,y,x). [para(82(a,1),1999(a,1,2,2))]. 2079 L(x,y,z) = (x * (y * z)) / (y * R(z,y,x)). [para(2078(a,1),648(a,1,2)),flip(a)]. 2080 T(K(x,y) * R(y,z,u),x) = y * T(y \ R(y,z,u),x). [para(2057(a,2),1834(a,1))]. 2081 T(K(x,y) * R(y,z,u),x) / R(y,z,u) = K(R(y,z,u) / y,x). [para(2080(a,2),1211(a,1,1))]. 2082 a(x,K(x,y) * z,x) = K(x,z) * K(x * z,x). [para(2023(a,1),2026(a,1,2)),flip(a)]. 2083 a(x,K(x,y) * z,x) = a(x,z,x). [para(2082(a,2),1537(a,1))]. 2085 a(x,K(x,y) * z,x) = a(T(x,y),z,x). [para(2047(a,1),28(a,2)),flip(a)]. 2086 a(T(x,y),z,x) = a(x,z,x). [para(2085(a,1),2083(a,1))]. 2087 a((x \ y) \ y,z,x) = a(x,z,x). [para(83(a,1),2086(a,1,1))]. 2089 a((x \ y) * y,z,x) = a(x,z,x). [para(2087(a,1),1702(a,1)),flip(a)]. 2090 a((x * y) * y,z,x) = a(x,z,x). [para(2089(a,1),1707(a,1)),flip(a)]. 2091 a(R(x,y,y),z,x) = a(x,z,x). [para(2090(a,1),1721(a,1)),flip(a)]. 2092 a(a(x,y,x),z,z) = a(x,y,x) \ a(x,y,x). [para(2091(a,1),2054(a,1,2)),flip(a)]. 2093 a(a(x,y,x),z,z) = 1. [para(2092(a,2),60(a,1))]. 2095 L(x,x,a(y,z,y)) = x. [hyper(37,a,2093,a)]. 2097 L(x,x,a(y,z,z)) = x. [para(2095(a,1),1695(a,2))]. 2098 L(x,x,K(y,z)) = x. [para(2097(a,1),1263(a,1)),flip(a)]. 2099 R(T(a(x,y,y),z),z,z) = z \ (a(x,y,y) * z). [para(2097(a,1),1804(a,1,1)),flip(a)]. 2100 a(K(x,y),z,z) = 1. [hyper(38,a,2098,a)]. 2102 (K(x,y) * (z / u)) \ K(x,y) = u / z. [para(2098(a,1),925(a,1)),flip(a)]. 2103 L(x,K(y,z),x) = x. [para(2098(a,1),1895(a,2))]. 2104 R(K(x,y),z,z) = K(x,y) * 1. [para(2100(a,1),963(a,1,2)),flip(a)]. 2105 a(K(x,K(y,z)),u,w) = a(1,u,w). [para(2100(a,1),2072(a,1,1)),flip(a)]. 2106 T(K(x,y),z) / z = z \ K(x,y). [para(2103(a,1),441(a,1,2))]. 2107 K(x,R(y,z,z)) = K(x,y). [hyper(24,a,1767,a,b,2104,a(flip)),flip(a)]. 2108 K(x,y / (z \ 1)) = K(x,y * z). [para(720(a,1),2107(a,1,2)),flip(a)]. 2112 K(x,y) * (x / z) = T(x,y) / z. [para(2107(a,1),1815(a,1,1))]. 2115 a(K(x,K(y,z)),u,w) = 1. [para(2105(a,2),125(a,1))]. 2117 L(x,y,K(z,K(u,w))) = x. [hyper(37,a,2115,a)]. 2119 x * (x \ R(K(y,K(z,u)),w,x)) = K(y,K(z,u)). [para(2117(a,1),1974(a,1,1))]. 2121 (K(x,y) * z) \ u = (z \ K(y,x)) * u. [para(2106(a,1),2067(a,1,1)),flip(a)]. 2122 K(x,R(((y \ 1) * z) \ 1,z,z)) = K(x,(z \ 1) * y). [para(1739(a,2),2108(a,1,2))]. 2123 T(x,y) / (z \ x) = K(x,y) * z. [para(65(a,1),2112(a,1,2)),flip(a)]. 2126 (K(x,y) * z) \ T(x,y) = z \ x. [para(2123(a,1),66(a,1,1))]. 2129 L(x \ y,x,K(z,y)) = x \ y. [para(2126(a,1),1248(a,2))]. 2130 a(K(x,y),z,z \ y) = 1. [hyper(38,a,2129,a)]. 2132 a(K(x,y * z),y,z) = 1. [para(19(a,1),2130(a,1,3))]. 2137 ((x / y) \ K(z,u)) * K(u,z) = y / x. [para(2121(a,1),2102(a,1))]. 2140 x / K(y,z) = x * K(z,y). [para(66(a,1),2137(a,1,1)),flip(a)]. 2144 (K(x,y) * z) / K(x,y) = T(z,K(y,x)). [para(2140(a,2),2068(a,1))]. 2145 T(x,K(y,z)) \ x = K(x,K(z,y)). [para(2144(a,1),1053(a,2,1)),flip(a)]. 2146 K(K(x,y),z) = K(z,K(y,x)). [para(2145(a,1),1080(a,2))]. 2147 K(x,K(y,z)) * K(x,K(z,y)) = 1. [para(2146(a,1),898(a,1,1))]. 2148 K(x,y) * K(z,K(y,x)) = T(K(x,y),z). [para(2146(a,1),1107(a,2,2)),flip(a)]. 2149 K(x,y) * T(K(y,x),z) = K(z,K(x,y)). [para(2146(a,1),1114(a,2))]. 2150 T(K(x,y),z) \ 1 = T(K(y,x),z). [para(2148(a,1),1140(a,1)),flip(a)]. 2151 T(K(x,y),z) * T(K(y,x),z) = 1. [para(2150(a,1),20(a,1,2))]. 2152 T(K(x,y),z) * K(y,x) = K(z,K(y,x)). [para(2149(a,1),405(a,2))]. 2153 R(T(a(x,y,y),z),z,z) = T(a(x,y,y),z). [para(2099(a,2),36(a,2)),flip(a)]. 2154 R(T(a(x,y,y),z),z,z) = a(T(x,z),y,y). [para(2153(a,2),1836(a,2)),flip(a)]. 2155 R(a(T(x,y),z,z),y,y) = a(T(x,y),z,z). [para(1836(a,2),2154(a,1,1))]. 2156 a(R(T(x,y),y,y),z,z) = a(T(x,y),z,z). [para(2155(a,1),1930(a,2))]. 2157 a(T(T(x,y),y),z,z) = a(T(x,y),z,z). [para(2156(a,1),2074(a,1)),flip(a)]. 2158 a(T(x,y),z,z) = a(x,z,z). [para(2157(a,1),1724(a,1))]. 2161 (x * (y * (a(y,z,z) * u))) / (R(T(y,x),z,z) * u) = T(x,y). [para(2158(a,1),1210(a,1,1,2,2,1))]. 2165 R(K(x,K(y,z)),u,w) = K(x,K(y,z)). [para(2119(a,1),20(a,1)),flip(a)]. 2166 K(x,R(K(y,z),u,w)) = K(x,K(y,z)). [para(2165(a,1),1654(a,1)),flip(a)]. 2167 K(x,K(y,R(z,u,w))) = K(x,K(y,z)). [para(1654(a,1),2166(a,1,2))]. 2168 K(K(R(x,y,z),u),w) = K(w,K(u,x)). [para(2167(a,1),2146(a,2))]. 2169 K(R(K(x,y),z,u),w) = K(w,K(y,x)). [para(1634(a,1),2168(a,1,1))]. 2170 K(x,R((y \ z) \ 1,z,z)) = K(x,(z \ 1) * y). [para(318(a,1),2122(a,1,2,1,1))]. 2171 K(x,(y \ z) \ 1) = K(x,(z \ 1) * y). [para(2170(a,1),2107(a,1)),flip(a)]. 2172 K(x,(y \ z) \ 1) = K(x,z \ y). [para(318(a,1),2171(a,2,2))]. 2174 K(x,(y / z) \ y) = K(x,z / (a(y,z,z) \ 1)). [para(2172(a,1),1447(a,1))]. 2175 K(x,y / (a(z,y,y) \ 1)) = K(x,y). [para(66(a,1),2174(a,1,2)),flip(a)]. 2176 K(x,y * a(z,y,y)) = K(x,y). [para(1445(a,1),2175(a,1,2))]. 2177 K(x * a(y,x,x),z) = (z \ 1) / (z \ K(z,x)). [para(2176(a,1),1057(a,1,2,2)),flip(a)]. 2178 K(x * a(y,x,x),z) = K(x,z). [para(2177(a,2),1057(a,1))]. 2179 (x / y) * T(y,z) = x * K(y,z). [para(2178(a,1),1463(a,1,2)),flip(a)]. 2180 (x * y) * K(y,z) = x * T(y,z). [para(21(a,1),2179(a,1,1)),flip(a)]. 2183 L(K(x,y),x,z) = K(x,y). [hyper(23,a,1117,a,b,2180,a),flip(a)]. 2187 L(K(T(x,y),z),x,y) = K(T(x,y),z). [para(2183(a,1),1376(a,1)),flip(a)]. 2192 T(K(x,y),x * z) = K(T(x,z),y). [para(2187(a,1),1522(a,1)),flip(a)]. 2193 K(T(x,x \ y),z) = T(K(x,z),y). [para(20(a,1),2192(a,1,2)),flip(a)]. 2194 K(T(x,y),z) = T(K(x,z),y). [para(2193(a,1),2038(a,1)),flip(a)]. 2195 K(x,T(y,z)) * T(K(y,x),z) = 1. [para(2194(a,1),898(a,1,2))]. 2196 K(T(x,y * T(T(y,x),x)),z) = T(T(K(x,z),y),T(y,x)). [para(2194(a,2),1905(a,1))]. 2197 K(x,T(y,z)) = T(K(x,y),z). [hyper(24,a,2151,a,b,2195,a)]. 2199 K(x,y) * K(y,T(x,z)) = K(K(y,x),z). [para(2197(a,2),1114(a,1,2))]. 2200 K(x,T(y,z \ 1)) * z = z * K(x,y). [para(2197(a,2),1907(a,1,1))]. 2202 K(x,y) * K(y,T(x,z)) = K(z,K(x,y)). [para(2197(a,2),2149(a,1,2))]. 2203 K(x,T(y,z)) * K(y,x) = K(z,K(y,x)). [para(2197(a,2),2152(a,1,1))]. 2204 K(T(x,y),z) = K(x,T(z,y)). [para(2197(a,2),2194(a,2))]. 2205 K(x,T(y,z)) * K(y,x) = K(K(x,y),z). [para(2199(a,1),1226(a,2))]. 2206 K(x,T(y,z)) * K(y,x) = K(x,K(y,z)). [para(2202(a,1),1873(a,2))]. 2207 K(x,y) * K(x,K(y,z)) = K(x,T(y,z)). [para(2206(a,1),1225(a,1,2))]. 2208 K(x,K(y,z)) = K(z,K(y,x)). [para(2206(a,1),2203(a,1))]. 2209 K(K(x,y),z) = K(x,K(y,z)). [para(2206(a,1),2205(a,1)),flip(a)]. 2210 1 / K(x,K(y,z)) = K(K(y,x),z). [para(2208(a,1),899(a,1,2))]. 2211 K(K(x,y),z) = K(K(x,z),y). [para(2210(a,1),899(a,1))]. 2212 K(K(x,y),z) = K(y,K(z,x)). [para(2211(a,1),2146(a,1))]. 2213 K(x,K(y,z)) = K(z,K(x,y)). [para(2212(a,1),2209(a,1))]. 2214 T(K(x,y) * K(x,K(y,z)),z) = K(x,y). [para(2213(a,2),1020(a,1,1,2))]. 2215 T(K(x,T(y,z)),z) = K(x,y). [para(2207(a,1),2214(a,1,1))]. 2216 K(x,T(y,z)) * z = z * K(x,y). [para(2215(a,1),82(a,1,2)),flip(a)]. 2217 K(x,T(T(y,z),z)) = K(x,y). [para(2215(a,1),2197(a,2))]. 2219 K(x,T(y,z \ 1)) = K(x,T(y,z)). [hyper(24,a,2200,a,b,2216,a),flip(a)]. 2220 T(K(x,y) * z,K(x,y)) = K(x,T(y,z)) * z. [para(2216(a,2),2064(a,2))]. 2221 K(x,T(y,z \ (z \ (u \ 1)))) = K(x,T(y,u * (z * z))). [para(409(a,1),2219(a,1,2,2))]. 2222 K(T(x,y * T(y,x)),z) = T(T(K(x,z),y),T(y,x)). [para(2019(a,1),2196(a,1,1))]. 2223 T(T(K(x,y),z),T(z,x)) = K(T(x,z * z),y). [para(2019(a,1),2222(a,1,1)),flip(a)]. 2224 T(T(K(x,y),z),T(z,x)) = K(x,T(y,z * z)). [para(2223(a,2),1278(a,1))]. 2225 T(K(x,T(y,z)),T(z,x)) = K(x,T(y,z * z)). [para(2197(a,2),2224(a,1,1))]. 2226 K(T(x,T(y,x)),T(z,y)) = K(x,T(z,y * y)). [para(2225(a,1),2194(a,2))]. 2227 K(T(x,y),T(z,y)) = K(x,T(z,y * y)). [para(1131(a,1),2226(a,1,1))]. 2228 K(x,T(T(y,z),z)) = K(x,T(y,z * z)). [para(2227(a,1),2204(a,1)),flip(a)]. 2229 K(x,T(y,z * z)) = K(x,y). [para(2228(a,1),2217(a,1))]. 2230 K(x,T(y,z * (z * u))) = K(x,T(y,u)). [para(662(a,1),2229(a,1,2))]. 2232 K(x,T(y,z \ u)) = K(x,T(y,z * u)). [para(20(a,1),2230(a,1,2,2,2)),flip(a)]. 2233 K(x,T(y,T(z,z * u))) = K(x,T(y,(z \ u) * u)). [para(250(a,1),2230(a,1,2,2,2)),flip(a)]. 2234 K(x,T(y,(z / u) * (z * z))) = K(x,T(y,u / (z \ 1))). [para(399(a,1),2230(a,1,2,2,2))]. 2235 K(x,T(y,z \ (z \ u))) = K(x,T(y,u)). [para(20(a,1),2232(a,2,2,2))]. 2236 K(x,T(y,z * (u * u))) = K(x,T(y,z \ 1)). [para(2221(a,1),2235(a,1))]. 2237 K(x,T(y,z * (u * u))) = K(x,T(y,z)). [para(2236(a,2),2219(a,1))]. 2239 K(x,T(y,z / (u \ 1))) = K(x,T(y,u / z)). [para(2234(a,1),2237(a,1))]. 2241 (x * (R(y,z,z) * u)) / (R(T(y,x),z,z) * u) = T(x,y). [para(966(a,1),2161(a,1,1,2))]. 2243 T(x,R(y,z,z)) = T(x,y). [para(2241(a,1),1209(a,1)),flip(a)]. 2244 T(x,y / (z \ 1)) = T(x,y * z). [para(720(a,1),2243(a,1,2)),flip(a)]. 2246 K(x,T(y,z / u)) = K(x,T(y,u * z)). [para(2244(a,1),2239(a,1,2)),flip(a)]. 2247 K(x,T(y,(z \ u) * u)) = K(x,T(y,z)). [para(65(a,1),2246(a,1,2,2)),flip(a)]. 2248 K(x,T(y,T(z,z * u))) = K(x,T(y,z)). [para(2247(a,1),2233(a,2))]. 2249 K(x,T(y,T(z,u))) = K(x,T(y,z)). [para(20(a,1),2248(a,1,2,2,2))]. 2251 K(x,K(y,T(z,u))) = K(x,T(y,z)) * K(y,x). [para(2249(a,1),2206(a,1,1)),flip(a)]. 2253 K(x,K(y,T(z,u))) = K(x,K(y,z)). [para(2251(a,2),2206(a,1))]. 2254 K(x,K(y,z \ R(z,u,w))) = K(x,K(y,a(z,u,w))). [para(739(a,2),2253(a,1,2,2)),flip(a)]. 2255 K(x,K(y \ R(y,z,u),w)) = K(x,K(w,a(y,z,u))). [para(1849(a,2),2254(a,1,2))]. 2260 K(x,y) * K(R(y,z,u),x) = K(R(y,z,u) / y,x). [para(2081(a,1),2059(a,1)),flip(a)]. 2261 K(x,y) * K(R(y,z,u),x) = K(y \ R(y,z,u),x). [para(478(a,1),2260(a,2,1))]. 2262 K(x,y) * K(R(y,z,u),x) = K(x,y \ R(y,z,u)). [para(2261(a,2),1849(a,1))]. 2263 K(x,K(y,z) \ R(K(y,z),u,w)) = K(x,K(y,z)) * K(x,K(z,y)). [para(2169(a,1),2262(a,1,2)),flip(a)]. 2265 K(x,K(y,z) \ R(K(y,z),u,w)) = 1. [para(2263(a,2),2147(a,1))]. 2266 K(x,K(y,z) \ K(R(y,u,w),z)) = 1. [para(1629(a,1),2265(a,1,2,2))]. 2268 K(x,K(y,z) * K(R(z,u,w),y)) = 1. [para(900(a,1),2266(a,1,2))]. 2269 K(x,K(y \ R(y,z,u),w)) = 1. [para(2261(a,1),2268(a,1,2))]. 2270 K(x,K(y,a(z,u,w))) = 1. [para(2269(a,1),2255(a,1)),flip(a)]. 2271 T(x,K(y,a(z,u,w))) = x. [hyper(41,a,2270,a)]. 2273 K(x,T(a(y,z,u),w)) = K(x,a(y,z,u)). [hyper(24,a,2220,a(flip),b,2271,a(flip)),flip(a)]. 2274 K(x,y \ R(y,z,u)) = K(x,a(y,z,u)). [para(1839(a,1),2273(a,1,2))]. 2275 K(x,y \ R(y,z,u)) = K(a(y,z,u),x). [para(2274(a,2),1847(a,2)),flip(a)]. 2276 K(x \ R(x,y,z),u) = K(u,a(x,y,z)). [para(2274(a,1),1849(a,2))]. 2277 K(x,a(y,z,L(u,z,y))) = K(x,y \ R(y,z,u)). [para(1990(a,1),2274(a,1,2,2)),flip(a)]. 2278 K(x,y) * K(R(y,z,u),x) = K(x,a(y,z,u)). [para(2274(a,1),2262(a,2))]. 2279 K(x,a(K(y,z),u,w)) = 1. [para(2274(a,1),2265(a,1))]. 2280 T(x,a(K(y,z),u,w)) = x. [hyper(41,a,2279,a)]. 2281 ((K(x,y) * z) * u) / (K(x,y) * (z * u)) = a(K(x,y),z,u). [para(2280(a,1),300(a,1,2))]. 2282 K(R(x,y,z) \ x,u) = K(u,a(x,x * y,z)). [para(618(a,1),2276(a,1,1))]. 2283 K(x,y) * K(y,R(x,z,u)) = K(y,a(x,z,u)). [para(2278(a,1),1674(a,1)),flip(a)]. 2284 L(x,y * z,K(y,u)) = x * K(u,a(y,z,x)). [para(2283(a,1),2077(a,1,2)),flip(a)]. 2285 K(x,a(y,z,L(u,z,y))) = K(x,a(y,z,u)). [para(2277(a,2),2274(a,1))]. 2286 K(x,y) \ R(K(x,y),z,u) = a(K(x,y),z,u). [para(2281(a,1),537(a,1)),flip(a)]. 2287 x \ L(x,y,K(z,u)) = a(K(z,u),y,x). [para(2286(a,1),1988(a,1)),flip(a)]. 2288 x * a(K(y,z),u,x) = L(x,u,K(y,z)). [para(2287(a,1),20(a,1,2))]. 2289 a(K(x,y),x * z,u) = K(y,a(x,z,u)). [hyper(23,a,2284,a(flip),b,2288,a)]. 2290 x * a(K(y,z),u,x) = L(x,u,K(z,y)). [para(905(a,1),2288(a,1,2))]. 2291 K(x,a(y,y * z,u)) = a(K(y,x),z,u). [para(2289(a,1),1778(a,1))]. 2292 K((x * y) * z,a(x,y,z)) = 1. [para(2289(a,1),2132(a,1))]. 2293 K(x * (y * z),a(x,y,L(z,y,x))) = 1. [para(74(a,1),2292(a,1,1))]. 2294 K(x,a(y,y * z,u)) = a(K(x,y),z,u). [para(2291(a,2),905(a,1))]. 2295 K(x * (y * z),a(x,y,z)) = 1. [para(2293(a,1),2285(a,1)),flip(a)]. 2296 x \ R(x,y,z) = a(x,y,z) * 1. [para(2295(a,1),1848(a,1,2)),flip(a)]. 2297 a(x,y,z) = x \ R(x,y,z). [hyper(24,a,18,a,b,2296,a(flip))]. 2298 a(x,y,z) = L(z,y,x) \ z. [hyper(24,a,1989,a(flip),b,2296,a(flip))]. 2302 R(x,y,z) \ x = a(x,y,z) \ 1. [para(2297(a,2),462(a,1,1)),flip(a)]. 2306 x * (a(x,y,z) * u) = R(x,y,z) * u. [para(2297(a,2),501(a,1,2,1))]. 2308 a(x,y,z) * (x * u) = R(x,y,z) * u. [para(2297(a,2),528(a,1,1))]. 2310 a(x,x * y,z) = R(x,y,z) \ x. [para(2297(a,2),618(a,1))]. 2313 a(x,y,z) = x * R(x \ 1,y,z). [para(2297(a,2),635(a,2)),flip(a)]. 2317 T(x \ R(x,y,z),u) = a(T(x,u),y,z). [para(2297(a,2),1831(a,1)),flip(a)]. 2318 R(x \ R(x,y,z),u,w) = a(R(x,u,w),y,z). [para(2297(a,2),1927(a,1)),flip(a)]. 2319 L(x \ R(x,y,z),u,w) = a(L(x,u,w),y,z). [para(2297(a,2),1939(a,1)),flip(a)]. 2323 x * (L(x,y,z) \ u) = a(z,y,x) * u. [para(2297(a,2),1985(a,1,1)),flip(a)]. 2332 L(x,y,z) \ (x * u) = a(z,y,x) * u. [para(2298(a,2),524(a,2,1))]. 2333 a(x,y,z) * (L(z,y,x) * u) = z * u. [para(2298(a,2),646(a,1,1))]. 2336 a(T(x,y),z,y) = L(y,z,x) \ y. [para(1992(a,1),2298(a,2,1))]. 2340 K(a(x,y,z) \ 1,u) = K(u,a(x,x * y,z)). [para(2302(a,1),2282(a,1,1))]. 2341 a(x,x * y,z) = a(x,y,z) \ 1. [para(2310(a,2),2302(a,1))]. 2344 L(x,a(y,z,u),z) = x. [para(2313(a,2),1443(a,1,2))]. 2347 (x * a(y,x,z)) * u = x * (a(y,x,z) * u). [para(2344(a,1),74(a,1,2))]. 2348 (x \ a(y,x,z)) \ 1 = a(y,x,z) \ x. [para(2344(a,1),259(a,1)),flip(a)]. 2349 (x \ a(y,x,z)) \ u = a(y,x,z) \ (x * u). [para(2344(a,1),267(a,1)),flip(a)]. 2358 a(T(x,y),z,y) = a(x,z,y). [para(2336(a,2),2298(a,2)),flip(a)]. 2366 K(a(x,x * y,z),u) = a(K(u,x),y,z). [para(2294(a,1),1847(a,2))]. 2368 x * (y * a(x,z,y)) = R(x,z,y) * y. [para(1964(a,1),2306(a,1,2))]. 2370 a(T(x,y),z,u) = T(a(x,z,u),y). [para(2297(a,2),2317(a,1,1)),flip(a)]. 2371 a(T(x,y),z,u) \ a(x,z,u) = K(y,a(x,z,u)). [para(2370(a,2),1080(a,2,1)),flip(a)]. 2372 a(T(x,y),y,z) = a(x,y,z). [para(2370(a,2),1687(a,1))]. 2373 a(x,T(y,x),z) = a(x,y,z). [para(2372(a,1),1790(a,1)),flip(a)]. 2374 a(x / y,y,z) = a(y * x,y,z). [para(2373(a,1),1810(a,1)),flip(a)]. 2375 a(x / y,x,z) = a(x * y,x,z). [para(2374(a,1),612(a,1)),flip(a)]. 2378 a(x,y,z) * (z * u) = z * (a(x,y,z) * u). [para(2332(a,1),2323(a,1,2)),flip(a)]. 2380 a(x,y,z) * (z * x) = z * R(x,y,z). [para(1973(a,1),2333(a,1,2))]. 2386 (x \ a(y,x,z)) \ u = (a(y,x,z) \ x) * u. [para(2348(a,1),318(a,1,1)),flip(a)]. 2388 K(a(x,y,z) \ 1,u) = a(K(u,x),y,z). [para(2341(a,1),2366(a,1,1))]. 2389 (x * y) * L(a(x,z,y),y,x) = R(x,z,y) * y. [para(2368(a,1),74(a,2))]. 2393 a(R(x,y,z),u,y) = L(y,u,x) \ y. [para(2318(a,1),1986(a,1))]. 2394 a(R(x,y,z),u,w) = R(a(x,u,w),y,z). [para(2297(a,2),2318(a,1,1)),flip(a)]. 2396 a(R(x,y,z),u,y) = a(x,u,y). [para(2393(a,2),2298(a,2)),flip(a)]. 2400 a(L(x,y,x),z,y) = a(x,z,y). [para(1312(a,1),2396(a,1,1)),flip(a)]. 2404 R(a(x,y,z),x * u,w) = a(R(x,u,w),y,z). [para(2394(a,1),1718(a,1))]. 2406 a(L(x,y,z),u,w) = L(a(x,u,w),y,z). [para(2297(a,2),2319(a,1,1)),flip(a)]. 2410 K(x,a(y / z,(y / z) * z,u)) = K(a(z * y,z,u) \ 1,x). [para(2374(a,1),2340(a,1,1,1)),flip(a)]. 2411 (a(x,y,z) * y) * u = y * (a(x,y,z) * u). [para(1688(a,2),2347(a,1,1))]. 2412 a(x,y,z) \ (y * u) = (a(x,y,z) \ y) * u. [para(2386(a,1),2349(a,1)),flip(a)]. 2413 L(x,y,a(z,y,u)) = x. [hyper(23,a,798,a,b,2412,a(flip)),flip(a)]. 2414 (a(x,y,z) * y) * u = a(x,y,z) * (y * u). [para(2413(a,1),74(a,1,2))]. 2415 (a(x,y,z) * (y \ 1)) * u = a(x,y,z) * (y \ u). [para(2413(a,1),945(a,1,2))]. 2417 a(x,y,z) * (y * u) = y * (a(x,y,z) * u). [para(2414(a,1),2411(a,1))]. 2419 (x * y) \ (x * (a(z,x,u) * y)) = T(a(z,x,u),x * y). [para(2417(a,1),36(a,2,2)),flip(a)]. 2421 (x * y) * a(L(x,y,x),z,y) = R(x,z,y) * y. [para(2406(a,2),2389(a,1,2))]. 2422 (x * y) * a(x,z,y) = R(x,z,y) * y. [para(2400(a,1),2421(a,1,2))]. 2423 (x * (R(y,z,u) * u)) / ((y * u) * R(a(y,z,u),y * u,x)) = L(x,y * u,a(y,z,u)). [para(2422(a,1),2079(a,2,1,2)),flip(a)]. 2424 (x \ a(y,x,z)) * u = a(y,x,z) * (x \ u). [para(1795(a,1),2415(a,1,1))]. 2425 (a(x,y,z) * (y \ u)) \ ((y \ a(x,y,z)) * (u * w)) = L(w,u,y \ a(x,y,z)). [para(2424(a,1),32(a,2,1)),flip(a)]. 2426 L(T(a(x,y,z),u),u,y) = T(a(x,y,z),y * u). [para(2419(a,1),106(a,1)),flip(a)]. 2427 L(a(T(x,y),z,u),y,z) = T(a(x,z,u),z * y). [para(2370(a,2),2426(a,1,1))]. 2429 K(a(x * y,x,z) \ 1,u) = K(u,a(y / x,y,z)). [para(22(a,1),2410(a,1,2,2)),flip(a)]. 2430 K(a(x * y,x,z) \ 1,u) = K(u,a(y * x,y,z)). [para(2375(a,1),2429(a,2,2))]. 2431 K(x,a(y * z,y,u)) = a(K(x,z * y),z,u). [para(2430(a,1),2388(a,1))]. 2432 a(L(x,y,z),R(z,y,x),u) = (x * (z * u)) \ ((x * z) * u). [para(1998(a,1),1981(a,1,1)),flip(a)]. 2433 a(L(x,y,z),R(z,y,x),u) = a(x,z,u). [para(2432(a,2),28(a,2)),flip(a)]. 2435 L(a(x,R(y,z,x),u),z,y) = a(x,y,u). [para(2433(a,1),2406(a,1)),flip(a)]. 2436 (a(x,y,z) * (y \ u)) \ (a(x,y,z) * (y \ (u * w))) = L(w,u,y \ a(x,y,z)). [para(2424(a,1),2425(a,1,2))]. 2437 L(L(x,y,z),z * y,a(u,z,w)) = L(x,y,z \ a(u,z,w)). [para(2436(a,1),1409(a,1)),flip(a)]. 2438 L(L(x,y,z),z * y,a(u,z,w)) = L(x,y,z * a(u,z,w)). [para(2437(a,2),776(a,1))]. 2439 (R(x,y,z) * y) \ ((x * y) * u) = (x \ R(x,y,z)) \ u. [para(1996(a,1),1411(a,1))]. 2440 L(x,y,R(z,y,x)) = (z \ R(z,y,x)) \ x. [para(2439(a,1),183(a,1)),flip(a)]. 2441 L(x,y,R(z,y,x)) = L(x,y,z). [para(2440(a,2),1976(a,2)),flip(a)]. 2442 L(x,y * z,R(y,z,x) \ 1) = L(x,y * z,y \ 1). [para(584(a,1),2441(a,1,3))]. 2443 L(x,y * z,R(y,z,x)) = L(x,y * z,y \ 1). [para(2442(a,1),787(a,1)),flip(a)]. 2444 L(x,y * z,R(y,z,x)) = L(x,y * z,y). [para(2443(a,2),787(a,1))]. 2445 R(x,y,z) * (L(z,x * y,x) \ z) = R(R(x,y,z),x * y,z). [para(2444(a,1),1979(a,2,2,1)),flip(a)]. 2446 R(x,y,z) * (R(x,y,z) \ x) = R(R(x,y,z),x * y,z). [para(1954(a,1),2445(a,1,2))]. 2447 R(R(x,y,z),x * y,z) = x. [para(2446(a,1),20(a,1))]. 2448 R(R(x,x * y,z),y,z) = x. [para(2447(a,1),50(a,1)),flip(a)]. 2449 K(x,R(y,y * z,u) \ R(R(y,y * z,u),z,u)) = K(x,R(y,y * z,u)) * K(y,x). [para(2448(a,1),2262(a,1,2,1)),flip(a)]. 2450 K(x,R(y,y * z,u) \ R(R(y,y * z,u),z,u)) = R(K(x,y),z,u) * K(y,x). [para(1672(a,1),2449(a,2,1))]. 2451 K(x,R(y,y * z,u) \ R(R(y,y * z,u),z,u)) = K(y,x) * R(K(x,y),z,u). [para(2450(a,2),406(a,1))]. 2452 K(x,R(y,y * z,u) \ y) = K(y,x) * R(K(x,y),z,u). [para(2448(a,1),2451(a,1,2,2))]. 2453 K(x,y) * R(K(y,x),z,u) = K(y,x \ R(x,z,u)). [para(622(a,1),2452(a,1,2)),flip(a)]. 2454 x * K(y,z \ R(z,u,x)) = L(x,u,K(y,z)). [para(2453(a,1),2076(a,1,2))]. 2455 x * K(a(y,z,x),u) = L(x,z,K(u,y)). [para(2275(a,1),2454(a,1,2))]. 2456 a(K(x,y),z,u) = K(a(x,z,u),y). [hyper(23,a,2290,a,b,2455,a),flip(a)]. 2457 a(K(x,y),z,u) = K(a(y,z,u),x). [hyper(23,a,2288,a,b,2455,a),flip(a)]. 2458 a(K(x,y),z,u) = K(y,a(x,z,u)). [para(2456(a,2),1847(a,1))]. 2459 a(K(x,y),z,u) = K(x,a(y,z,u)). [para(2457(a,2),1847(a,1))]. 2460 x * K(y,a(z,u,x)) = L(x,u,K(z,y)). [para(2458(a,1),2288(a,1,2))]. 2461 K(x * y,a(z,x,u)) = K(z,a(y * x,y,u)). [para(2458(a,1),2431(a,2)),flip(a)]. 2462 K(x,a(y,z,u)) = K(y,a(x,z,u)). [para(2459(a,1),2458(a,1))]. 2463 L(x,y * z,K(y,u)) = L(x,z,K(y,u)). [para(2460(a,1),2284(a,2))]. 2464 (x * (R(y,z,u) * u)) / ((y * u) * a(R(y,u,x),z,u)) = L(x,y * u,a(y,z,u)). [para(2404(a,1),2423(a,1,2,2))]. 2465 (x * (R(y,z,u) * u)) / ((y * u) * a(y,z,u)) = L(x,y * u,a(y,z,u)). [para(2396(a,1),2464(a,1,2,2))]. 2467 (x * (R(y,z,u) * u)) / (R(y,z,u) * u) = L(x,y * u,a(y,z,u)). [para(2422(a,1),2465(a,1,2))]. 2468 L(x,y * z,a(y,u,z)) = x. [para(2467(a,1),21(a,1))]. 2469 L(x,y * z,a(T(z,y),u,y)) = x. [para(2468(a,1),1185(a,1)),flip(a)]. 2470 L(x,y * z,a(z,u,y)) = x. [para(2358(a,1),2469(a,1,3))]. 2471 (a(x,y,z) * (z * x)) \ (a(x,y,z) * (z * (x * u))) = L(u,x,z). [para(2470(a,1),174(a,2))]. 2472 (x * R(y,z,x)) \ (a(y,z,x) * (x * (y * u))) = L(u,y,x). [para(2380(a,1),2471(a,1,1))]. 2473 (x * R(y,z,x)) \ (x * (a(y,z,x) * (y * u))) = L(u,y,x). [para(2378(a,1),2472(a,1,2))]. 2474 (x * R(y,z,x)) \ (x * (R(y,z,x) * u)) = L(u,y,x). [para(2308(a,1),2473(a,1,2,2))]. 2475 L(x,R(y,z,u),u) = L(x,y,u). [para(2474(a,1),32(a,2))]. 2476 a(x,R(y,z,x),u) = L(u,y,x) \ u. [para(2475(a,1),2298(a,2,1))]. 2477 a(x,R(y,z,x),u) = a(x,y,u). [para(2476(a,2),2298(a,2)),flip(a)]. 2478 L(a(x,y,z),u,y) = a(x,y,z). [para(2477(a,1),2435(a,1,1))]. 2480 T(a(x,y,z),y * u) = a(T(x,u),y,z). [para(2478(a,1),2427(a,1)),flip(a)]. 2484 a(T(x,y),z,u) \ a(x,z,u) = K(z * y,a(x,z,u)). [para(2480(a,1),1080(a,2,1)),flip(a)]. 2494 K(x * y,a(z,x,u)) = K(y,a(z,x,u)). [para(2484(a,1),2371(a,1))]. 2495 K(x,a(y * z,y,u)) = K(z,a(x,y,u)). [para(2494(a,1),2462(a,1)),flip(a)]. 2496 K(x,a(y * z,y,u)) = K(y,a(x,z,u)). [para(2494(a,1),2461(a,1)),flip(a)]. 2497 K(x,a(y,z,u)) = K(z,a(y,x,u)). [para(2496(a,1),2495(a,1))]. 2498 x * K(y,a(z,u,x)) = L(x,y,K(z,u)). [para(2497(a,1),2460(a,1,2))]. 2499 L(x,y,K(z,u)) = L(x,u,K(z,y)). [para(2498(a,1),2460(a,1))]. 2501 L(x,y,K(z,z * u)) = L(x,u,K(z,y)). [para(2499(a,1),2463(a,1))]. 2502 L(x,y,a(z,u,u)) = L(x,u,K(z,y)). [para(2501(a,1),1261(a,1)),flip(a)]. 2503 L(x,y,a(z,u,u)) = L(x,y,K(z,u)). [para(2502(a,2),2499(a,1))]. 2504 L(x,y,a(z,u,z)) = L(x,y,K(u,z)). [para(2503(a,1),1695(a,1)),flip(a)]. 2505 L(L(x,y,z),z * y,K(z,u)) = L(x,y,z * a(u,z,u)). [para(2504(a,1),2438(a,1))]. 2506 L(x,y,z * a(u,z,u)) = L(x,y,T(z,u)). [para(2505(a,1),1604(a,1))]. 2507 L(x,y,R(z,u,u)) = L(x,y,T(z,u)). [para(2506(a,1),1692(a,1)),flip(a)]. 2508 L(x,y,T(z / u,z)) = L(x,y,u * z). [para(2507(a,1),846(a,1))]. 2509 L(x,y,z * u) = L(x,y,u * z). [para(2508(a,1),845(a,1))]. 2510 L(L(x,y,z * u),(z * u) * y,u * z) = x. [para(2509(a,1),303(a,1))]. 2515 L(x,y,K(z,u)) = x. [para(2510(a,1),1850(a,1)),flip(a)]. 2516 a(K(x,y),z,u) = 1. [hyper(38,a,2515,a)]. 2517 $F # answer("aK1"). [resolve(2516,a,56,a)]. ============================== end of proof ========================== % Disable descendants (x means already disabled): 56 given #2331 (H,wt=8): 2516 a(K(x,y),z,u) = 1. [hyper(38,a,2515,a)]. -------- Proof 2 -------- "Ka". ============================== PROOF ================================= % Proof 2 at 55.30 (+ 0.90) seconds: "Ka". % Length of proof is 2192. % Level of proof is 222. % Maximum clause weight is 50. % Given clauses 2331. 1 x * y = u & x * z = u -> y = z # label(non_clause). [assumption]. 2 y * x = u & z * x = u -> y = z # label(non_clause). [assumption]. 5 a(x,y,z) = 1 -> L(z,y,x) = z # label(non_clause). [assumption]. 6 L(x,y,z) = x -> a(z,y,x) = 1 # label(non_clause). [assumption]. 7 T(x,y) = x -> T(y,x) = y # label(non_clause). [assumption]. 8 T(x,y) = x -> K(x,y) = 1 # label(non_clause). [assumption]. 9 K(x,y) = 1 -> T(x,y) = x # label(non_clause). [assumption]. 13 K(a(x,y,z),u) = 1 # label("Ka") # label(non_clause) # label(goal). [goal]. 17 1 * x = x. [assumption]. 18 x * 1 = x. [assumption]. 19 x \ (x * y) = y. [assumption]. 20 x * (x \ y) = y. [assumption]. 21 (x * y) / y = x. [assumption]. 22 (x / y) * y = x. [assumption]. 23 x * y != z | x * u != z | u = y. [clausify(1)]. 24 x * y != z | u * y != z | u = x. [clausify(2)]. 27 (x * (y * z)) \ ((x * y) * z) = a(x,y,z). [assumption]. 28 a(x,y,z) = (x * (y * z)) \ ((x * y) * z). [copy(27),flip(a)]. 29 (x * y) \ (y * x) = K(y,x). [assumption]. 30 K(x,y) = (y * x) \ (x * y). [copy(29),flip(a)]. 31 (x * y) \ (x * (y * z)) = L(z,y,x). [assumption]. 32 L(x,y,z) = (z * y) \ (z * (y * x)). [copy(31),flip(a)]. 33 ((x * y) * z) / (y * z) = R(x,y,z). [assumption]. 34 R(x,y,z) = ((x * y) * z) / (y * z). [copy(33),flip(a)]. 35 x \ (y * x) = T(y,x). [assumption]. 36 T(x,y) = y \ (x * y). [copy(35),flip(a)]. 37 a(x,y,z) != 1 | L(z,y,x) = z. [clausify(5)]. 38 L(x,y,z) != x | a(z,y,x) = 1. [clausify(6)]. 39 T(x,y) != x | T(y,x) = y. [clausify(7)]. 40 T(x,y) != x | K(x,y) = 1. [clausify(8)]. 41 K(x,y) != 1 | T(x,y) = x. [clausify(9)]. 42 T(T(x,y),z) = T(T(x,z),y). [assumption]. 43 T(L(x,y,z),u) = L(T(x,u),y,z). [assumption]. 44 L(T(x,y),z,u) = T(L(x,z,u),y). [copy(43),flip(a)]. 45 T(R(x,y,z),u) = R(T(x,u),y,z). [assumption]. 46 R(T(x,y),z,u) = T(R(x,z,u),y). [copy(45),flip(a)]. 47 L(R(x,y,z),u,w) = R(L(x,u,w),y,z). [assumption]. 48 R(L(x,y,z),u,w) = L(R(x,u,w),y,z). [copy(47),flip(a)]. 49 L(L(x,y,z),u,w) = L(L(x,u,w),y,z). [assumption]. 50 R(R(x,y,z),u,w) = R(R(x,u,w),y,z). [assumption]. 51 (x * (x * y)) * z = x * (x * (y * z)) # label("LC"). [assumption]. 55 K(a(c16,c17,c18),c19) != 1 # label("Ka") # answer("Ka"). [deny(13)]. 59 1 \ x = x. [para(17(a,1),19(a,1,2))]. 60 x \ x = 1. [para(18(a,1),19(a,1,2))]. 61 x \ ((x * y) * 1) = y. [para(18(a,2),19(a,1,2))]. 62 x \ (y * (y \ (x * z))) = z. [para(20(a,2),19(a,1,2))]. 64 x / 1 = x. [para(18(a,1),21(a,1,1))]. 65 x / (y \ x) = y. [para(20(a,1),21(a,1,1))]. 66 (x / y) \ x = y. [para(22(a,1),19(a,1,2))]. 67 (x * (y * z)) * a(x,y,z) = (x * y) * z. [para(28(a,2),20(a,1,2))]. 68 ((x / y) * (y * z)) \ (x * z) = a(x / y,y,z). [para(22(a,1),28(a,2,2,1)),flip(a)]. 69 (x * y) * K(y,x) = y * x. [para(30(a,2),20(a,1,2))]. 70 x \ ((y \ x) * y) = K(y \ x,y). [para(20(a,1),30(a,2,1)),flip(a)]. 71 ((x \ y) * x) \ y = K(x,x \ y). [para(20(a,1),30(a,2,2)),flip(a)]. 72 x \ (1 * (x * y)) = L(y,x,1). [para(17(a,1),32(a,2,1)),flip(a)]. 73 (x * 1) \ (x * y) = L(y,1,x). [para(17(a,1),32(a,2,2,2)),flip(a)]. 74 (x * y) * L(z,y,x) = x * (y * z). [para(32(a,2),20(a,1,2))]. 75 x \ (y * ((y \ x) * z)) = L(z,y \ x,y). [para(20(a,1),32(a,2,1)),flip(a)]. 76 L(x \ y,x,z) = (z * x) \ (z * y). [para(20(a,1),32(a,2,2,2))]. 77 x \ ((x / y) * (y * z)) = L(z,y,x / y). [para(22(a,1),32(a,2,1)),flip(a)]. 78 ((x * y) * (y \ z)) / z = R(x,y,y \ z). [para(20(a,1),34(a,2,2)),flip(a)]. 79 R(x,y,z) * (y * z) = (x * y) * z. [para(34(a,2),22(a,1,1))]. 80 R(x / y,y,z) = (x * z) / (y * z). [para(22(a,1),34(a,2,1,1))]. 81 T(x,x) = x. [para(36(a,2),19(a,1))]. 82 x * T(y,x) = y * x. [para(36(a,2),20(a,1,2))]. 83 T(x,x \ y) = (x \ y) \ y. [para(20(a,1),36(a,2,2))]. 84 T(x / y,y) = y \ x. [para(22(a,1),36(a,2,2))]. 85 (x * (x * (y * z))) / z = x * (x * y). [hyper(24,a,22,a,b,51,a),flip(a)]. 86 (x * (x * y)) \ (x * (x * (y * z))) = z. [hyper(23,a,20,a,b,51,a),flip(a)]. 87 x \ ((x * (x * y)) * z) = x * (y * z). [hyper(23,a,20,a,b,51,a(flip)),flip(a)]. 88 (x * (x * 1)) * y = x * (x * y). [para(17(a,1),51(a,2,2,2))]. 89 x * (x * ((x \ y) * z)) = (x * y) * z. [para(20(a,1),51(a,1,1,2)),flip(a)]. 90 (x * (y * (y * (z * u)))) \ ((x * (y * (y * z))) * u) = a(x,y * (y * z),u). [para(51(a,1),28(a,2,1,2)),flip(a)]. 91 (x * (x * (y * (z * u)))) \ (((x * (x * y)) * z) * u) = a(x * (x * y),z,u). [para(51(a,1),28(a,2,1)),flip(a)]. 92 (x * (x * (y * z))) \ ((x * (x * y)) * (z * u)) = L(u,z,x * (x * y)). [para(51(a,1),32(a,2,1)),flip(a)]. 93 (x * (y * (y * z))) \ (x * (y * (y * (z * u)))) = L(u,y * (y * z),x). [para(51(a,1),32(a,2,2,2)),flip(a)]. 94 ((x * (x * (y * z))) * u) / (z * u) = R(x * (x * y),z,u). [para(51(a,1),34(a,2,1,1)),flip(a)]. 95 (x * (x * (y * z))) / ((x * y) * z) = R(x,x * y,z). [para(51(a,1),34(a,2,1)),flip(a)]. 97 ((x * y) / 1) / y = x. [hyper(24,a,22,a,b,64,a(flip)),flip(a)]. 98 T(T(x,y),x) = T(x,y). [para(81(a,1),42(a,1,1)),flip(a)]. 99 (x * (y * z)) / L(z,y,x) = x * y. [para(32(a,2),65(a,1,2))]. 100 (x * y) / T(x,y) = y. [para(36(a,2),65(a,1,2))]. 101 R(x,y,z) \ ((x * y) * z) = y * z. [para(34(a,2),66(a,1,1))]. 102 x \ (y * 1) = x \ y. [para(20(a,1),61(a,1,2,1))]. 103 T(x * (x * y),x) = x * (y * x). [hyper(23,a,51,a(flip),b,82,a)]. 104 T((x * y) / x,x) = y. [hyper(23,a,22,a(flip),b,82,a)]. 105 (x * T(y,x)) / x = y. [hyper(24,a,22,a,b,82,a(flip)),flip(a)]. 106 (x * y) \ (x * (z * y)) = L(T(z,y),y,x). [para(82(a,1),32(a,2,2,2)),flip(a)]. 107 T(x,y) \ (x * y) = T(y,T(x,y)). [para(82(a,1),36(a,2,2)),flip(a)]. 108 x * T(T(y,x),z) = T(y,z) * x. [para(42(a,1),82(a,1,2))]. 109 x * L(T(y,x),z,u) = L(y,z,u) * x. [para(44(a,2),82(a,1,2))]. 110 x * R(T(y,x),z,u) = R(y,z,u) * x. [para(46(a,2),82(a,1,2))]. 111 (x * y) \ ((z * x) * y) = T(R(z,x,y),x * y). [para(34(a,2),84(a,1,1)),flip(a)]. 112 T(T(x / y,z),y) = T(y \ x,z). [para(84(a,1),42(a,1,1)),flip(a)]. 113 ((x * y) / ((1 / z) * z)) / y = x. [para(22(a,2),97(a,1,1,2))]. 114 K(T(x,y),x) = 1. [hyper(40,a,98,a)]. 115 T(x,T(x,y)) = x. [hyper(39,a,98,a)]. 116 T(x,y) * x = x * T(x,y). [para(98(a,1),82(a,1,2)),flip(a)]. 117 (x * y) / T(y,T(x,y)) = T(x,y). [para(82(a,1),100(a,1,1))]. 118 x \ (y * (z * (z \ 1))) = x \ y. [para(20(a,2),102(a,1,2,2))]. 119 K(x,(y * x) / y) = 1. [para(104(a,1),114(a,1,1))]. 120 T(x,(y * x) / y) = x. [hyper(41,a,119,a)]. 122 K(x,y) \ (x * y) = T(y * x,K(x,y)). [para(69(a,1),36(a,2,2)),flip(a)]. 123 x \ (x * y) = L(y,x,1). [para(17(a,1),72(a,1,2))]. 124 L(x,y,1) = x. [para(123(a,1),19(a,1))]. 125 a(1,x,y) = 1. [hyper(38,a,124,a)]. 126 x \ (x * y) = L(y,1,x). [para(18(a,1),73(a,1,1))]. 127 L(x,1,y) = x. [para(126(a,1),19(a,1))]. 128 K(x \ 1,x) = (x \ 1) * x. [para(70(a,1),59(a,1))]. 129 K(x \ 1,x) / x = x \ 1. [hyper(24,a,22,a,b,128,a(flip)),flip(a)]. 130 (x \ 1) \ K(x \ 1,x) = x. [hyper(23,a,20,a,b,128,a(flip)),flip(a)]. 131 (x * x) * y = x * (x * y). [para(18(a,1),88(a,1,1,2))]. 132 (x * (x * y)) / y = x * x. [hyper(24,a,22,a,b,131,a),flip(a)]. 133 (x * x) \ (x * (x * y)) = y. [hyper(23,a,20,a,b,131,a),flip(a)]. 134 ((x * (x * y)) * z) / (y * z) = R(x * x,y,z). [para(131(a,1),34(a,2,1,1)),flip(a)]. 135 x \ (y * (y * x)) = T(y * y,x). [para(131(a,1),36(a,2,2)),flip(a)]. 136 x * (x * T(y,x * x)) = y * (x * x). [para(131(a,1),82(a,1))]. 137 L(x,y,y) = x. [para(133(a,1),32(a,2))]. 138 x * ((x \ y) * x) = T(x * y,x). [para(20(a,1),103(a,1,1,2)),flip(a)]. 139 T(x / y,z) * y = y * T(y \ x,z). [para(84(a,1),108(a,1,2,1)),flip(a)]. 140 (x * T(x \ y,z)) / x = T(y / x,z). [para(112(a,1),105(a,1,1,2))]. 141 R(x,1 / y,y) / y = x * (1 / y). [para(34(a,2),113(a,1,1))]. 142 L(x \ 1,x,y) = (y * x) \ y. [para(118(a,1),32(a,2))]. 143 L((x \ y) \ 1,x \ y,x) = y \ x. [para(20(a,1),142(a,2,1))]. 144 L(x \ 1,x,y / x) = y \ (y / x). [para(22(a,1),142(a,2,1))]. 145 x / L(y \ 1,y,x) = x * y. [para(142(a,2),65(a,1,2))]. 146 x \ T(x * y,x) = (x \ y) * x. [hyper(23,a,20,a,b,138,a),flip(a)]. 147 x * K(x \ 1,x) = T(x * 1,x). [para(128(a,2),138(a,1,2))]. 148 (x \ (x \ y)) * x = x \ T(y,x). [para(20(a,1),146(a,1,2,1)),flip(a)]. 149 x * K(x \ 1,x) = T(x,x). [para(18(a,1),147(a,2,1))]. 150 x * K(x \ 1,x) = x. [para(149(a,2),81(a,1))]. 151 K(x \ 1,x) = 1. [hyper(23,a,18,a,b,150,a)]. 152 T(x \ 1,x) = x \ 1. [hyper(41,a,151,a)]. 154 (x \ 1) * x = 1. [para(151(a,1),128(a,1)),flip(a)]. 155 1 / x = x \ 1. [para(151(a,1),129(a,1,1))]. 156 (x \ 1) \ 1 = x. [para(151(a,1),130(a,1,2))]. 157 x * (1 / x) = 1. [para(66(a,1),154(a,1,1))]. 160 T(x,x \ 1) = x. [para(156(a,1),83(a,2))]. 161 L(x,x \ 1,y) = (y * (x \ 1)) \ y. [para(156(a,1),142(a,1,1))]. 162 x / L(y,y \ 1,x) = x * (y \ 1). [para(156(a,1),145(a,1,2,1))]. 164 (x * 1) \ ((x * y) * (1 / y)) = a(x,y,1 / y). [para(157(a,1),28(a,2,1,2)),flip(a)]. 165 T(T(x,y),x \ 1) = T(x,y). [para(160(a,1),42(a,1,1)),flip(a)]. 166 K(T(x,y),x \ 1) = 1. [hyper(40,a,165,a)]. 167 K(x \ y,(y / x) \ 1) = 1. [para(84(a,1),166(a,1,1))]. 168 K(x,((y * x) / y) \ 1) = 1. [para(104(a,1),166(a,1,1))]. 169 T(x \ y,(y / x) \ 1) = x \ y. [hyper(41,a,167,a)]. 170 T(x,((y * x) / y) \ 1) = x. [hyper(41,a,168,a)]. 171 (x \ y) \ (x \ T(y,x)) = K(x \ (x \ y),x). [para(148(a,1),70(a,1,2))]. 172 x * L(y,z \ x,z) = z * ((z \ x) * y). [para(20(a,1),74(a,1,1))]. 173 x * L(y,z,x / z) = (x / z) * (z * y). [para(22(a,1),74(a,1,1))]. 174 (x * (y * z)) \ (x * (y * (z * u))) = L(L(u,z,y),y * z,x). [para(74(a,1),32(a,2,2,2)),flip(a)]. 176 (x * y) * L(z,K(x,y),y * x) = (y * x) * (K(x,y) * z). [para(69(a,1),74(a,1,1))]. 177 L(x \ (y \ z),x,y) = (y * x) \ z. [para(20(a,1),76(a,2,2))]. 178 L(x \ (y * x),x,y) = T(y,y * x). [para(76(a,2),36(a,2)),flip(a)]. 179 (x * y) / L(z \ y,z,x) = x * z. [para(76(a,2),65(a,1,2))]. 180 L(x \ T(y,z),x,z) = (z * x) \ (y * z). [para(82(a,1),76(a,2,2))]. 181 L(x \ (y \ ((y * x) * z)),x,y) = z. [para(76(a,2),62(a,1))]. 182 R(x,x,y) = x. [hyper(24,a,131,a(flip),b,79,a)]. 183 (R(x,y,z) * y) \ ((x * y) * z) = L(z,y,R(x,y,z)). [para(79(a,1),32(a,2,2)),flip(a)]. 184 L(R(x,y,z),u,w) * (y * z) = (L(x,u,w) * y) * z. [para(48(a,1),79(a,1,1))]. 185 R(R(x,y,z),u,w) * (y * z) = (R(x,u,w) * y) * z. [para(50(a,1),79(a,1,1))]. 186 R(T(x,y),x,z) = T(x,y). [para(182(a,1),46(a,2,1))]. 187 L(R(x,L(x,y,z),u),y,z) = L(x,y,z). [para(182(a,1),48(a,1)),flip(a)]. 188 R(R(x,y,z),x,u) = R(x,y,z). [para(182(a,1),50(a,1,1)),flip(a)]. 189 R(R(T(x,y),z,u),x,w) = R(T(x,y),z,u). [para(186(a,1),50(a,1,1)),flip(a)]. 190 (T(x,y) * x) * z = T(x,y) * (x * z). [para(186(a,1),79(a,1,1)),flip(a)]. 191 (R(x,y,z) * x) * u = R(x,y,z) * (x * u). [para(188(a,1),79(a,1,1)),flip(a)]. 192 R(1 / x,x,y) = y / (x * y). [para(17(a,1),80(a,2,1))]. 193 R((x / y) / z,z,y) = x / (z * y). [para(22(a,1),80(a,2,1))]. 194 T((x * y) / (z * y),u) = R(T(x / z,u),z,y). [para(80(a,1),46(a,2,1)),flip(a)]. 195 R(x,x \ 1,y) = y / ((x \ 1) * y). [para(65(a,1),192(a,1,1))]. 196 (x * y) / L(z,y / z,x) = x * (y / z). [para(22(a,1),99(a,1,1,2))]. 197 R(x,x \ y,z) \ (y * z) = (x \ y) * z. [para(20(a,1),101(a,1,2,1))]. 198 R(x,y \ 1,y) / y = x * (1 / y). [para(155(a,1),141(a,1,1,2))]. 199 L(K(x,y) \ ((y * x) \ z),K(x,y),y * x) = (x * y) \ z. [para(69(a,1),177(a,2,1))]. 200 (x * x) \ y = x \ (x \ y). [para(177(a,1),137(a,1))]. 201 L(x \ L(y \ z,y,u),x,u * y) = ((u * y) * x) \ (u * z). [para(76(a,2),177(a,1,1,2))]. 202 x \ (x \ (y * (x * x))) = T(y,x * x). [para(200(a,1),36(a,2)),flip(a)]. 203 L(T(x,y),y,x) = T(x,x * y). [para(36(a,2),178(a,1,1))]. 204 T(x,x * ((y * x) / y)) = L(x,(y * x) / y,x). [para(120(a,1),203(a,1,1)),flip(a)]. 205 x / L(y \ z,y,x / z) = (x / z) * y. [para(22(a,1),179(a,1,1))]. 207 R(x,y \ 1,y) / y = x * (y \ 1). [para(155(a,1),198(a,2,2))]. 208 (x * (y \ 1)) * y = R(x,y \ 1,y). [para(207(a,1),22(a,1,1))]. 209 (x * (y \ 1)) \ R(x,y \ 1,y) = y. [para(207(a,1),66(a,1,1))]. 210 R(x / (y \ 1),y \ 1,y) = x * y. [para(22(a,1),208(a,1,1)),flip(a)]. 211 (x * (x * y)) / z = x * (x * (y / z)). [para(22(a,1),85(a,1,1,2,2))]. 212 (x * (x * y)) \ (x * (x * z)) = y \ z. [para(20(a,1),86(a,1,2,2,2))]. 213 x \ ((x * y) * z) = x * ((x \ y) * z). [para(20(a,1),87(a,1,2,1,2))]. 214 L(x,y,z) * x = x * L(x,y,z). [para(81(a,1),109(a,1,2,1)),flip(a)]. 216 L(x \ 1,y,z) * x = x * L(x \ 1,y,z). [para(152(a,1),109(a,1,2,1)),flip(a)]. 217 x * T(y,y * x) = L(y,x,y) * x. [para(203(a,1),109(a,1,2))]. 218 (x * L(x,y,z)) / x = L(x,y,z). [hyper(24,a,22,a,b,214,a),flip(a)]. 219 T(x,L(x,y,z)) = x. [hyper(23,a,82,a,b,214,a),flip(a)]. 220 T(x,x * L(x,y,z)) = L(x,L(x,y,z),x). [para(219(a,1),203(a,1,1)),flip(a)]. 221 L(x,x \ y,x) * (x \ y) = (x \ y) * T(x,y). [para(20(a,1),217(a,1,2,2)),flip(a)]. 222 x * R(T(T(y,x),z),u,w) = R(T(y,z),u,w) * x. [para(42(a,1),110(a,1,2,1))]. 223 R(x,y,z) * x = x * R(x,y,z). [para(81(a,1),110(a,1,2,1)),flip(a)]. 224 R(x / y,z,u) * y = y * R(y \ x,z,u). [para(84(a,1),110(a,1,2,1)),flip(a)]. 225 (x \ y) * R((x \ y) \ y,z,u) = R(x,z,u) * (x \ y). [para(83(a,1),110(a,1,2,1))]. 226 x * (x * R(T(y,x * x),z,u)) = R(y,z,u) * (x * x). [para(110(a,1),131(a,1)),flip(a)]. 227 R(x \ 1,y,z) * x = x * R(x \ 1,y,z). [para(152(a,1),110(a,1,2,1)),flip(a)]. 228 T(x,R(x,y,z)) = x. [hyper(23,a,82,a,b,223,a),flip(a)]. 229 T(x \ y,R(y / x,z,u)) = T(y / x,x). [para(228(a,1),112(a,1,1)),flip(a)]. 230 x \ (y * (x * x)) = x * T(y,x * x). [hyper(23,a,20,a,b,136,a),flip(a)]. 231 T(x / (x * y),z) * (x * y) = (x * y) * T(L(y \ 1,y,x),z). [para(142(a,2),139(a,2,2,1))]. 232 T((x * y) / (x * z),u) * (x * z) = (x * z) * T(L(z \ y,z,x),u). [para(76(a,2),139(a,2,2,1))]. 233 (x * T(y,z)) / x = T((x * y) / x,z). [para(19(a,1),140(a,1,1,2,1))]. 234 L(x,y,T(y,z)) = x. [hyper(23,a,74,a,b,190,a),flip(a)]. 235 (x * T(x,y)) * z = T(x,y) * (x * z). [para(116(a,1),190(a,1,1))]. 237 L(x,(y * z) / y,z) = x. [para(104(a,1),234(a,1,3))]. 238 x * (x * ((x \ y) / z)) = (x * y) / z. [para(20(a,1),211(a,1,1,2)),flip(a)]. 239 (x * (x * y)) \ (x * x) = y \ 1. [para(18(a,1),212(a,1,2,2))]. 240 (x * y) \ (x * (x * z)) = (x \ y) \ z. [para(20(a,1),212(a,1,1,2))]. 241 T(x,x * (x * y)) = y \ (x * y). [para(212(a,1),36(a,2))]. 242 (x * y) \ (x * x) = (x \ y) \ 1. [para(20(a,1),239(a,1,1,2))]. 243 (x * x) / (y \ 1) = x * (x * y). [para(239(a,1),65(a,1,2))]. 244 ((x * y) * z) \ (x * x) = ((x \ y) * z) \ 1. [para(89(a,1),239(a,1,1))]. 245 T(x,x * (x * y)) = T(x,y). [para(241(a,2),36(a,2)),flip(a)]. 246 T(x,x \ y) = T(x,x * y). [para(20(a,1),245(a,1,2,2)),flip(a)]. 247 T(x,x * (y * x)) = T(x,T(y,x)). [para(82(a,1),245(a,1,2,2))]. 248 T(x * y,(x * y) * (y * x)) = T(x * y,K(y,x)). [para(69(a,1),245(a,1,2,2))]. 249 T(x,x * y) = (x \ y) \ y. [para(246(a,1),83(a,1))]. 250 (x \ y) * T(x,x * y) = y. [para(249(a,2),20(a,1,2))]. 251 T(x / y,x) = ((x / y) \ y) \ y. [para(22(a,1),249(a,1,2))]. 252 x / T(y,y * x) = y \ x. [para(249(a,2),65(a,1,2))]. 253 (x \ y) * ((x \ y) * (T(x,x * y) * z)) = ((x \ y) * y) * z. [para(249(a,2),89(a,1,2,2,1))]. 254 (x \ (x \ y)) * T(x,y) = x \ y. [para(20(a,1),250(a,1,2,2))]. 255 ((x \ y) * (T(x,x * y) * z)) \ (y * z) = a(x \ y,T(x,x * y),z). [para(250(a,1),28(a,2,2,1)),flip(a)]. 257 K(x,y) / T(y * x,x * y) = (y * x) \ K(x,y). [para(69(a,1),252(a,1,2,2))]. 258 (x \ (x \ y)) \ 1 = y \ (x * x). [para(20(a,1),242(a,1,1)),flip(a)]. 259 L(x \ y,x,y) = (y \ x) \ 1. [para(242(a,1),76(a,2))]. 260 L(K(x,y),y * x,x * y) = ((x * y) \ (y * x)) \ 1. [para(30(a,2),259(a,1,1))]. 261 L(T(x \ y,z),x,y) = T((y \ x) \ 1,z). [para(259(a,1),44(a,2,1))]. 262 (x \ ((y * x) / y)) \ 1 = ((y * x) / y) \ x. [para(259(a,1),237(a,1))]. 263 x * (x * (y \ 1)) = (x * x) / y. [para(156(a,1),243(a,1,2)),flip(a)]. 265 x * ((x \ (x \ y)) * z) = x \ (y * z). [para(20(a,1),213(a,1,2,1)),flip(a)]. 266 L(x \ (y * ((y \ x) * z)),x,y) = z. [para(213(a,1),181(a,1,1,2))]. 267 L(x \ (y * z),x,y) = (y \ x) \ z. [para(20(a,1),266(a,1,1,2,2))]. 268 L(x \ y,x,z) = (z \ x) \ (z \ y). [para(20(a,1),267(a,1,1,2))]. 269 L(x \ (y * z),x,z) = (z \ x) \ T(y,z). [para(82(a,1),267(a,1,1,2))]. 270 L((x * y) \ z,x * y,x) = y \ (x \ z). [para(19(a,1),268(a,2,1))]. 272 (x \ y) / L(z \ y,z,x) = x \ z. [para(268(a,2),65(a,1,2))]. 273 L(x \ y,x,x / z) = z \ ((x / z) \ y). [para(66(a,1),268(a,2,1))]. 274 (x \ y) \ (x \ z) = (x * y) \ (x * z). [para(268(a,1),76(a,1))]. 275 L(x \ L(y \ z,y,u),x,u \ y) = ((u \ y) * x) \ (u \ z). [para(268(a,2),177(a,1,1,2))]. 276 (x \ 1) / (y \ x) = x \ (x \ y). [para(143(a,1),272(a,1,2))]. 277 x \ (x \ (x / y)) = (x \ 1) / y. [para(66(a,1),276(a,1,2)),flip(a)]. 278 x * ((x \ 1) / y) = x \ (x / y). [para(277(a,1),20(a,1,2))]. 279 ((x \ 1) / y) \ 1 = (x / y) \ (x * x). [para(277(a,1),258(a,1,1))]. 280 T(x * T(x,y),T(x,y)) = x * T(x,y). [hyper(23,a,82,a,b,235,a(flip)),flip(a)]. 281 (x * T(x,y)) * (x \ z) = T(x,y) * z. [para(20(a,1),235(a,2,2))]. 282 (x * y) / (z \ (x \ y)) = x * (x * z). [para(65(a,1),238(a,1,2,2)),flip(a)]. 283 (x \ (x \ y)) \ z = y \ (x * (x * z)). [para(20(a,1),240(a,1,1)),flip(a)]. 284 (x \ y) \ ((x \ z) * u) = (x * y) \ ((x * z) * u). [para(89(a,1),240(a,1,2)),flip(a)]. 285 x \ (x \ (y * z)) = (x \ (x \ y)) * z. [hyper(23,a,20,a,b,265,a),flip(a)]. 286 (x \ (x \ y)) * (x * x) = T(y,x * x). [hyper(23,a,230,a(flip),b,265,a)]. 287 (x * (y * x)) \ (x * z) = T(y,x) \ (x \ z). [para(36(a,2),274(a,1,1)),flip(a)]. 288 T(x * T(x,y),T(x,y)) = T(x,y) * x. [para(280(a,2),116(a,2)),flip(a)]. 289 x / (y \ (x \ 1)) = x * (x * y). [para(18(a,1),282(a,1,1))]. 290 (x \ (x \ y)) \ y = T(x * x,y). [para(283(a,2),135(a,1))]. 291 (x \ (x \ 1)) * y = x \ (x \ y). [para(17(a,1),285(a,1,2,2)),flip(a)]. 292 (x \ (x \ y)) * (y \ z) = x \ (x \ z). [para(20(a,1),285(a,1,2,2)),flip(a)]. 293 R((x / y) / (z \ (z \ 1)),z \ (z \ 1),y) = x / (z \ (z \ y)). [para(291(a,1),193(a,2,2))]. 294 ((x \ 1) / y) * (x * x) = T(x / y,x * x). [para(277(a,1),286(a,1,1))]. 295 T(T(x,y) * x,T(x,y)) = T(x,y) * x. [para(116(a,2),288(a,1,1))]. 296 (x \ (x \ y)) \ (x \ (x \ z)) = y \ z. [hyper(23,a,20,a,b,292,a),flip(a)]. 297 (x \ y) * ((x * y) \ z) = x \ (x \ z). [para(19(a,1),292(a,1,1,2))]. 298 (T(x,y) \ x) * T(x,y) = x. [hyper(23,a,138,a,b,295,a(flip)),flip(a)]. 299 x / T(x,y) = T(x,y) \ x. [hyper(24,a,22,a,b,298,a),flip(a)]. 300 ((x * y) * z) / T(x * (y * z),a(x,y,z)) = a(x,y,z). [para(67(a,1),100(a,1,1))]. 301 L(x,x \ y,x) = y \ T(x * y,x). [para(138(a,1),75(a,1,2)),flip(a)]. 302 L(L(x,y \ z,y),z,y) = x. [para(75(a,1),266(a,1,1))]. 303 L(L(x,y,z),z * y,z) = x. [para(19(a,1),302(a,1,1,2))]. 304 L(L(x,y,z / y),z,z / y) = x. [para(66(a,1),302(a,1,1,2))]. 305 L(x,y \ 1,y) = x. [para(302(a,1),127(a,1)),flip(a)]. 306 L(x,y,y \ 1) = x. [para(156(a,1),305(a,1,2))]. 307 ((x \ 1) * x) \ ((x \ 1) * y) = x \ y. [para(306(a,1),76(a,1)),flip(a)]. 308 L(L(x,y * z,y),z,y) = x. [para(303(a,1),49(a,1)),flip(a)]. 309 x \ (y \ ((y * x) * z)) = L(z,y * x,y). [para(181(a,1),303(a,1,1)),flip(a)]. 310 R(x,L(x,y,z),u) = L(L(x,y,z),z * y,z). [para(187(a,1),303(a,1,1)),flip(a)]. 311 L((x \ y) \ z,x * y,x) = y \ (x * z). [para(267(a,1),303(a,1,1))]. 312 L(x,y \ z,y) = L(x,y * z,y). [para(302(a,1),303(a,1,1)),flip(a)]. 313 L(x,y * (y * z),y) = L(x,z,y). [para(303(a,1),303(a,1,1))]. 314 L(L(x,y * z,z),T(y,z),z) = x. [para(82(a,1),308(a,1,1,2))]. 315 L(L(x,y * z,z * y),K(y,z),z * y) = x. [para(69(a,1),308(a,1,1,2))]. 316 L(x,x * y,x) = y \ T(x * y,x). [para(301(a,1),312(a,1)),flip(a)]. 317 1 \ ((x \ 1) * y) = x \ y. [para(154(a,1),307(a,1,1))]. 318 (x \ 1) * y = x \ y. [para(317(a,1),59(a,1)),flip(a)]. 320 (x \ y) / y = x \ 1. [hyper(24,a,22,a,b,318,a),flip(a)]. 321 x * ((x \ 1) * y) = y. [hyper(23,a,19,a(flip),b,318,a)]. 322 (x \ 1) * (x * y) = y. [para(318(a,2),19(a,1))]. 323 (x \ (y * z)) \ (((x \ 1) * y) * z) = a(x \ 1,y,z). [para(318(a,1),28(a,2,1)),flip(a)]. 324 ((x * (y \ 1)) * z) / (y \ z) = R(x,y \ 1,z). [para(318(a,1),34(a,2,2)),flip(a)]. 325 T(x \ 1,y) = y \ (x \ y). [para(318(a,1),36(a,2,2))]. 326 x \ T(y,x \ 1) = y * (x \ 1). [para(318(a,1),82(a,1))]. 327 x * T(y \ 1,x) = y \ x. [para(318(a,1),82(a,2))]. 328 (x \ y) * K(y,x \ 1) = y * (x \ 1). [para(318(a,1),69(a,1,1))]. 329 x \ T(T(y,x \ 1),z) = T(y,z) * (x \ 1). [para(318(a,1),108(a,1))]. 330 (x \ 1) \ y = x * y. [para(156(a,1),318(a,1,1)),flip(a)]. 331 (x \ y) * L(z,y,x \ 1) = (x \ 1) * (y * z). [para(318(a,1),74(a,1,1))]. 332 R(x,y \ 1,z) * (y \ z) = (x * (y \ 1)) * z. [para(318(a,1),79(a,1,2))]. 333 (x * (y \ z)) / L(z,y \ 1,x) = x * (y \ 1). [para(318(a,1),99(a,1,1,2))]. 334 R(x,x \ 1,y) = y / (x \ y). [para(318(a,1),195(a,2,2))]. 335 R(x \ 1,y \ 1,y) = (x \ (y \ 1)) * y. [para(318(a,1),208(a,1,1)),flip(a)]. 336 L(x \ 1,y,x \ 1) * y = y * T(x \ 1,x \ y). [para(318(a,1),217(a,1,2,2)),flip(a)]. 337 T(x \ 1,(x \ 1) \ y) = T(x \ 1,x \ y). [para(318(a,1),246(a,2,2))]. 338 (x \ (x \ y)) \ z = (y \ (x * x)) * z. [para(258(a,1),318(a,1,1)),flip(a)]. 340 x / (y * x) = y \ 1. [para(19(a,1),320(a,1,1))]. 341 K(x,y) / (x * y) = (y * x) \ 1. [para(30(a,2),320(a,1,1))]. 342 L(x,y,z) / (z * (y * x)) = (z * y) \ 1. [para(32(a,2),320(a,1,1))]. 343 (x / y) \ 1 = y / x. [para(66(a,1),320(a,1,1)),flip(a)]. 344 (x * y) / ((z * x) * y) = R(z,x,y) \ 1. [para(101(a,1),320(a,1,1))]. 345 T(x * y,K(y,x)) / (y * x) = K(y,x) \ 1. [para(122(a,1),320(a,1,1))]. 346 T(x,x * y) / y = (x \ y) \ 1. [para(249(a,2),320(a,1,1))]. 347 x * (y * (x \ 1)) = T(y,x \ 1). [para(82(a,1),321(a,1,2))]. 348 R(x \ 1,x * y,z) = (y * z) / ((x * y) * z). [para(322(a,1),34(a,2,1,1))]. 349 T(x \ 1,x * y) = (x * y) \ y. [para(322(a,1),36(a,2,2))]. 350 R((x \ 1) / y,y,x * z) = z / (y * (x * z)). [para(322(a,1),80(a,2,1))]. 351 L(x * y,x \ 1,y) = (y \ (x \ 1)) \ 1. [para(330(a,1),259(a,1,1))]. 352 L(x * (y * z),x \ 1,y) = (y \ (x \ 1)) \ z. [para(330(a,1),267(a,1,1))]. 354 (x / y) * (y / x) = 1. [para(343(a,1),20(a,1,2))]. 355 K(x \ y,x / y) = 1. [para(343(a,1),167(a,1,2))]. 356 T(x,y / (y * x)) = x. [para(343(a,1),170(a,1,2))]. 357 T(x \ y,x / y) = x \ y. [para(343(a,1),169(a,1,2))]. 358 (x / y) \ z = (y / x) * z. [para(343(a,1),318(a,1,1)),flip(a)]. 359 (x / y) * ((y / x) * z) = z. [para(343(a,1),321(a,1,2,1))]. 360 x * ((y / z) * (z / y)) = x. [para(354(a,2),18(a,1,2))]. 361 K((x * y) \ y,x) = 1. [para(21(a,1),355(a,1,2))]. 362 (x / (x * y)) * y = y * (x / (x * y)). [para(356(a,1),82(a,1,2))]. 363 (x * (y / (y * x))) / x = y / (y * x). [para(356(a,1),100(a,1,2))]. 364 T(x,x * (y / (y * x))) = L(x,y / (y * x),x). [para(356(a,1),203(a,1,1)),flip(a)]. 365 T((x * y) \ y,x) = (x * y) \ y. [hyper(41,a,361,a)]. 366 x * R(x \ (y \ x),z,u) = R(y \ 1,z,u) * x. [para(325(a,1),110(a,1,2,1))]. 367 T(x / y,x \ y) = x / y. [hyper(39,a,357,a)]. 368 (x / y) * (x \ y) = (x \ y) * (x / y). [para(357(a,1),82(a,1,2))]. 369 (x / y) * (z * (y / x)) = T(z,y / x). [para(358(a,1),36(a,2)),flip(a)]. 370 T(x / y,x) = ((y / x) * y) \ y. [para(358(a,1),251(a,2,1))]. 371 ((x \ 1) / y) \ 1 = (y / x) * (x * x). [para(358(a,1),279(a,2))]. 372 T(x \ y,y \ x) = T(y / x,x). [para(367(a,1),112(a,1,1)),flip(a)]. 373 R(x,x \ 1,y) = x. [para(334(a,2),65(a,1))]. 374 R(T(x,y),x \ 1,z) = T(x,y). [para(373(a,1),46(a,2,1))]. 375 R(R(x,y,z),x \ 1,u) = R(x,y,z). [para(373(a,1),50(a,1,1)),flip(a)]. 376 R(T(x / y,y),(x / y) \ 1,z) = y \ x. [para(374(a,2),84(a,1))]. 377 T(x,y) * (x \ 1) = x \ T(x,y). [para(165(a,1),326(a,1,2)),flip(a)]. 378 x \ T(T(y,x \ 1),x) = (x \ (y * (x \ 1))) * x. [para(326(a,1),148(a,1,1,2)),flip(a)]. 379 K(x,y) * ((K(x,y) \ 1) / (x * y)) = K(x,y) \ ((y * x) \ 1). [para(341(a,1),278(a,2,2))]. 380 T(x \ 1,x * (y * y)) = (y \ (y \ (x * (y * y)))) \ 1. [para(349(a,2),258(a,2)),flip(a)]. 381 ((x * y) \ y) * x = x * ((x * y) \ y). [para(365(a,1),82(a,1,2)),flip(a)]. 382 T(x \ y,y \ x) = x \ y. [para(372(a,2),84(a,1))]. 383 T(x \ (x * y),(x * y) \ x) = y. [para(372(a,2),104(a,1))]. 384 (x \ y) * (y \ x) = (y \ x) * (x \ y). [para(382(a,1),82(a,1,2))]. 385 (x \ 1) \ T(x \ 1,x * y) = ((x * y) \ y) * ((x \ 1) \ 1). [para(349(a,1),377(a,1,1)),flip(a)]. 386 T(x,(y * x) \ y) = x. [para(19(a,1),383(a,1,1))]. 387 T(x,y \ (y / x)) = x. [para(22(a,1),386(a,1,2,1))]. 388 ((x * y) \ x) * y = y * ((x * y) \ x). [para(386(a,1),82(a,1,2))]. 389 T(K(x,y),(x * y) \ (y * x)) = K(x,y). [para(69(a,1),386(a,1,2,1))]. 390 R(x,y,z) * (x \ 1) = R(x,y,z) / x. [para(375(a,1),207(a,1,1)),flip(a)]. 391 x \ (y * (y * z)) = (x \ (y * y)) * z. [para(338(a,1),283(a,1)),flip(a)]. 392 (x \ (y * y)) * x = T(y * y,x). [para(338(a,1),290(a,1))]. 393 (x \ (y * y)) * (y \ (y \ z)) = x \ z. [para(338(a,1),296(a,1))]. 394 T(x * x,y * z) \ ((((y * z) \ (x * x)) * y) * z) = a((y * z) \ (x * x),y,z). [para(392(a,1),28(a,2,1)),flip(a)]. 395 L(x \ 1,x,x \ (y * y)) = T(y * y,x) \ (x \ (y * y)). [para(392(a,1),142(a,2,1))]. 397 (x / y) * (y * y) = x / (y \ 1). [para(371(a,1),343(a,1))]. 398 (x / (y \ 1)) / (y * y) = x / y. [hyper(24,a,22,a,b,397,a),flip(a)]. 399 (x / y) * (y / (x \ 1)) = x * x. [hyper(23,a,359,a,b,397,a),flip(a)]. 400 (x * y) / (y \ 1) = x * (y * y). [para(21(a,1),397(a,1,1)),flip(a)]. 401 (x * (y \ 1)) / y = x / (y * y). [para(21(a,1),398(a,1,1)),flip(a)]. 402 ((x \ (x \ y)) * x) / (x \ 1) = T(y,x * x). [para(400(a,2),286(a,1))]. 403 T(x / (y * y),y) = y \ (x * (y \ 1)). [para(401(a,1),84(a,1,1))]. 404 T(K(x,y),K(y,x)) = K(x,y). [para(30(a,2),389(a,1,2))]. 405 T(K(x,y),z) * K(y,x) = K(y,x) * T(K(x,y),z). [para(404(a,1),108(a,1,2,1)),flip(a)]. 406 R(K(x,y),z,u) * K(y,x) = K(y,x) * R(K(x,y),z,u). [para(404(a,1),110(a,1,2,1)),flip(a)]. 407 x * ((x \ (y * y)) * z) = y * (y * z). [para(391(a,1),20(a,1,2))]. 408 (((x * y) * x) \ (x * x)) * y = K(x,x * y). [para(391(a,1),30(a,2)),flip(a)]. 409 (x * (y * y)) \ z = y \ (y \ (x \ z)). [hyper(23,a,297,a,b,393,a),flip(a)]. 410 x * ((x \ (y * y)) * z) = (y * y) * z. [para(407(a,2),131(a,2)),flip(a)]. 411 (x * (y * y)) * z = x * (y * (y * z)). [para(407(a,1),89(a,1,2)),flip(a)]. 412 x \ (x \ (y \ ((y * x) * x))) = a(y,x,x). [para(409(a,1),28(a,2)),flip(a)]. 413 (x * (y * y)) \ x = y \ (y \ 1). [para(60(a,1),409(a,2,2,2))]. 414 x \ (x / (y * y)) = y \ (y \ 1). [para(22(a,1),413(a,1,1))]. 415 x / (y \ (y \ 1)) = x * (y * y). [para(413(a,1),65(a,1,2))]. 416 x * (y \ (y \ 1)) = x / (y * y). [para(414(a,1),20(a,1,2))]. 417 (x * (y * y)) * z = x * ((y * y) * z). [para(410(a,1),89(a,1,2)),flip(a)]. 418 (x * (y * (y * z))) / z = x * (y * y). [hyper(24,a,22,a,b,411,a),flip(a)]. 419 (x * (y * (y * z))) \ ((x * (y * y)) * (z * u)) = L(u,z,x * (y * y)). [para(411(a,1),32(a,2,1)),flip(a)]. 420 (x \ (x \ y)) * (x * (x * z)) = T(y,x * x) * z. [para(286(a,1),411(a,1,1)),flip(a)]. 421 L(x,y * y,z) = x. [hyper(23,a,74,a,b,417,a),flip(a)]. 422 R(x,y * y,z) = x. [hyper(24,a,79,a,b,417,a(flip)),flip(a)]. 423 T(x,x * (y * y)) = T(x,y * y). [para(421(a,1),203(a,1)),flip(a)]. 424 L(x,y,y / (z * z)) = x. [para(421(a,1),304(a,1,1))]. 425 L(x,y \ (y \ 1),z) = x. [para(318(a,1),421(a,1,2))]. 426 R(x,y \ (y \ 1),z) = x. [para(318(a,1),422(a,1,2))]. 427 L(x,y,y / (z \ (z \ 1))) = x. [para(318(a,1),424(a,1,3,2))]. 428 (x * (y \ (y \ 1))) * z = x * ((y \ (y \ 1)) * z). [para(425(a,1),74(a,1,2))]. 429 L(x,y,y * (z * z)) = x. [para(415(a,1),427(a,1,3))]. 430 T(x,x \ (y * y)) = T(x,y * y). [para(423(a,1),246(a,2))]. 431 T(x \ 1,x * (y * y)) = T(x \ 1,y * y). [para(330(a,1),430(a,1,2))]. 432 L(x,x,y / x) = y \ (y / (x \ 1)). [para(397(a,1),77(a,1,2)),flip(a)]. 433 (x * y) * (y \ 1) = R(x,y,y \ 1). [para(78(a,1),64(a,1)),flip(a)]. 434 R(x / y,y,y \ 1) = x * (y \ 1). [para(22(a,1),433(a,1,1)),flip(a)]. 435 x * L(y,z * x,z) = z * ((z \ x) * y). [para(312(a,1),172(a,1,2))]. 436 (R(T(x,y),z,u) * x) * w = R(T(x,y),z,u) * (x * w). [para(189(a,1),79(a,1,1)),flip(a)]. 437 T(x \ y,R(y / x,z,u)) = x \ y. [para(229(a,2),84(a,1))]. 438 T((x \ 1) \ y,y * x) = (x \ 1) \ y. [para(210(a,1),437(a,1,2))]. 439 T(x * y,y * x) = (x \ 1) \ y. [para(330(a,1),438(a,1,1))]. 440 (x \ y) \ T(y,x) = L(x,y,x). [para(19(a,1),269(a,1,1)),flip(a)]. 441 T(x,y) / L(y,x,y) = y \ x. [para(440(a,1),65(a,1,2))]. 442 L(x \ (x / y),y,x \ (x / y)) = ((x \ (x / y)) \ y) \ y. [para(387(a,1),440(a,1,2)),flip(a)]. 443 (x * (x * y)) \ z = y \ (x \ (x \ z)). [para(270(a,1),177(a,1)),flip(a)]. 444 x \ (y \ (y \ (z * (y * (y * x))))) = T(z,y * (y * x)). [para(443(a,1),36(a,2)),flip(a)]. 445 L(x \ 1,x,x / y) = y \ (y / x). [para(343(a,1),273(a,2,2))]. 446 x * (y \ ((y * (x \ 1)) * z)) = L(z,y * (x \ 1),y). [para(309(a,1),330(a,1)),flip(a)]. 447 R(x \ y,(y / x) \ 1,z) = x \ y. [para(84(a,1),376(a,1,1))]. 448 R(x \ y,x / y,z) = x \ y. [para(343(a,1),447(a,1,2))]. 449 R(x \ (x * y),x / (x * y),z) = y. [para(448(a,2),19(a,1))]. 450 R(x,y / (y * x),z) = x. [para(19(a,1),449(a,1,1))]. 451 (x * (y / (y * x))) * z = x * ((y / (y * x)) * z). [para(450(a,1),79(a,1,1)),flip(a)]. 452 x \ L(x,y * x,y) = a(y,x,x). [para(309(a,1),412(a,1,2))]. 453 L(x,y * x,y) = x * a(y,x,x). [para(452(a,1),20(a,1,2)),flip(a)]. 455 x * ((x \ y) * T(z,y)) = L(z,x * y,x) * y. [para(435(a,1),109(a,1))]. 456 (x * y) \ (x * T(y,x)) = K(x \ (x \ y),x). [para(171(a,1),274(a,1)),flip(a)]. 457 L(x,y,R(y,z,u)) = x. [hyper(23,a,74,a,b,191,a),flip(a)]. 458 R(x,y,z) * ((R(x,y,z) \ x) * u) = x * u. [hyper(23,a,89,a,b,191,a(flip)),flip(a)]. 459 (x * R(x,y,z)) * u = R(x,y,z) * (x * u). [para(223(a,1),191(a,1,1))]. 460 (R(x,y,z) \ x) \ 1 = x \ R(x,y,z). [para(457(a,1),259(a,1)),flip(a)]. 461 (R(x,y,z) \ u) / (x \ u) = R(x,y,z) \ x. [para(457(a,1),272(a,1,2))]. 462 (x \ R(x,y,z)) \ 1 = R(x,y,z) \ x. [para(460(a,1),156(a,1,1))]. 463 (R(x,y,z) \ x) \ u = (x \ R(x,y,z)) * u. [para(460(a,1),318(a,1,1)),flip(a)]. 464 (R(x,y,z) \ x) * ((x \ R(x,y,z)) * u) = u. [para(460(a,1),321(a,1,2,1))]. 465 (x \ R(x,y,z)) \ u = (R(x,y,z) \ x) * u. [para(460(a,1),330(a,1,1))]. 466 T(x,L(x \ 1,y,z)) = x. [hyper(23,a,82,a,b,216,a),flip(a)]. 467 K(x,L(x \ 1,y,z)) = 1. [hyper(40,a,466,a)]. 468 K(x \ 1,L(x,y,z)) = 1. [para(156(a,1),467(a,1,2,1))]. 469 K(L(x,y,z) \ 1,x) = 1. [para(303(a,1),468(a,1,2))]. 470 T(L(x,y,z) \ 1,x) = L(x,y,z) \ 1. [hyper(41,a,469,a)]. 471 x * (L(x,y,z) \ 1) = L(x,y,z) \ x. [para(470(a,1),327(a,1,2))]. 472 R(x / (x * y),z,u) * (x * y) = (x * y) * R(L(y \ 1,y,x),z,u). [para(142(a,2),224(a,2,2,1))]. 473 R((x * y) / (x * z),u,w) * (x * z) = (x * z) * R(L(z \ y,z,x),u,w). [para(76(a,2),224(a,2,2,1))]. 475 T(x,R(x \ 1,y,z)) = x. [hyper(23,a,82,a,b,227,a),flip(a)]. 476 T(x \ 1,R(x,y,z)) = x \ 1. [para(156(a,1),475(a,1,2,1))]. 477 R(x,y,z) * (x \ 1) = x \ R(x,y,z). [para(476(a,1),327(a,1,2))]. 478 R(x,y,z) / x = x \ R(x,y,z). [para(477(a,1),390(a,1)),flip(a)]. 480 (x \ R(x,y,z)) \ R(x,y,z) = x. [para(478(a,1),66(a,1,1))]. 481 (x / y) \ R(x / y,y,y \ 1) = (x * (y \ 1)) / (x / y). [para(434(a,1),478(a,1,1)),flip(a)]. 482 (x \ ((y * x) / y)) \ 1 = (y / (y * x)) * x. [para(262(a,2),358(a,1))]. 483 R(x,L(x,y,z),u) = x. [para(310(a,2),303(a,1))]. 484 (x * L(x,y,z)) * u = x * (L(x,y,z) * u). [para(483(a,1),79(a,1,1)),flip(a)]. 485 T(x \ 1,x \ y) = T(x \ 1,x * y). [para(330(a,1),337(a,1,2)),flip(a)]. 486 (x \ T(y,x)) / (x \ 1) = T(y,x * x). [para(148(a,1),402(a,1,1))]. 487 (((x \ y) * x) \ 1) * y = K(x,x * y). [para(244(a,1),408(a,1,1))]. 488 ((x \ y) * x) \ y = K(x,x * y). [para(487(a,1),318(a,1)),flip(a)]. 489 K(x,x \ y) = K(x,x * y). [para(488(a,1),71(a,1)),flip(a)]. 490 K(x,x * (x * y)) = K(x,y). [para(19(a,1),489(a,1,2)),flip(a)]. 491 K(x,x * (y * x)) = K(x,T(y,x)). [para(36(a,2),489(a,1,2)),flip(a)]. 492 K(x,(x * x) / y) = K(x,y \ 1). [para(263(a,1),490(a,1,2))]. 493 K(x \ (x \ y),x) = (x * y) \ (y * x). [para(82(a,1),456(a,1,2)),flip(a)]. 494 K(x \ (x \ y),x) = K(y,x). [para(493(a,2),30(a,2)),flip(a)]. 495 K(x \ y,x) = K(x * y,x). [para(19(a,1),494(a,1,1,2))]. 496 (R(x,y,z) \ x) * R(x,y,z) = x. [hyper(23,a,223,a,b,458,a)]. 498 x / R(x,y,z) = R(x,y,z) \ x. [hyper(24,a,22,a,b,496,a),flip(a)]. 499 T(R(x,y,z) \ 1,x) = x \ (x / R(x,y,z)). [para(498(a,2),325(a,2,2))]. 500 (x * y) / (z \ ((z * x) * y)) = R(z,x,y) \ z. [para(101(a,1),461(a,1,1))]. 501 x * ((x \ R(x,y,z)) * u) = R(x,y,z) * u. [para(464(a,1),458(a,1,2)),flip(a)]. 502 (x \ ((y * x) / y)) \ 1 = x * (y / (y * x)). [para(482(a,2),362(a,1))]. 503 L(x,L(y,z,u),y) = x. [hyper(23,a,74,a,b,484,a),flip(a)]. 504 x * ((x \ L(x,y,z)) * u) = L(x,y,z) * u. [hyper(23,a,89,a,b,484,a(flip)),flip(a)]. 505 L(x,(y * z) \ y,z \ 1) = x. [para(142(a,1),503(a,1,2))]. 506 (x \ L(x,y,z)) \ 1 = L(x,y,z) \ x. [para(503(a,1),259(a,1)),flip(a)]. 507 (x \ L(x,y,z)) \ u = L(x,y,z) \ (x * u). [para(503(a,1),267(a,1)),flip(a)]. 509 L(x,y,L(y,z,u)) = x. [para(303(a,1),503(a,1,2))]. 510 T(x,x * L(x,y,z)) = x. [para(503(a,1),220(a,2))]. 511 (L(x,y,z) \ x) \ 1 = x \ L(x,y,z). [para(509(a,1),259(a,1)),flip(a)]. 513 (L(x,y,z) \ u) / (x \ u) = L(x,y,z) \ x. [para(509(a,1),272(a,1,2))]. 514 (x \ L(x,y,z)) * x = L(x,y,z). [para(510(a,1),250(a,1,2))]. 515 L(x,y,z) / x = x \ L(x,y,z). [para(510(a,1),252(a,1,2))]. 516 (x \ L(x,y,z)) \ 1 = x / L(x,y,z). [para(510(a,1),346(a,1,1)),flip(a)]. 517 (x \ L(x,y,z)) \ u = (L(x,y,z) \ x) * u. [para(506(a,1),318(a,1,1)),flip(a)]. 519 x / L(x,y,z) = L(x,y,z) \ x. [para(516(a,1),506(a,1))]. 520 (L(x,y,z) \ x) * L(x,y,z) = x. [para(519(a,1),22(a,1,1))]. 521 (L(x \ 1,x,x / y) \ (x \ 1)) * (y \ (y / x)) = x \ 1. [para(445(a,1),520(a,1,2))]. 523 (x * R(x,y,z)) * u = x * (R(x,y,z) * u). [para(501(a,1),89(a,1,2)),flip(a)]. 524 L(x,y,z) \ (x * u) = (L(x,y,z) \ x) * u. [para(517(a,1),507(a,1)),flip(a)]. 525 R(x,R(x,y,z),u) = x. [hyper(24,a,79,a,b,523,a(flip)),flip(a)]. 526 R(x,y,z) * (x * u) = x * (R(x,y,z) * u). [para(523(a,1),459(a,1)),flip(a)]. 527 R(T(x,y),R(x,z,u),w) = T(x,y). [para(525(a,1),46(a,2,1))]. 528 (x \ R(x,y,z)) * (x * u) = R(x,y,z) * u. [hyper(23,a,501,a,b,526,a(flip)),flip(a)]. 529 x * (R(x,y,z) * (x \ u)) = R(x,y,z) * u. [para(20(a,1),526(a,1,2)),flip(a)]. 530 x * (R(x,y,z) * T(u,x)) = R(x,y,z) * (u * x). [para(82(a,1),526(a,1,2)),flip(a)]. 531 (R(x,y,z) * u) / (x * u) = x \ R(x,y,z). [hyper(24,a,22,a,b,528,a),flip(a)]. 532 (x \ R(x,y,z)) * u = R(x,y,z) * (x \ u). [para(20(a,1),528(a,1,2))]. 533 R(x \ R(x,y,z),x * u,w) = ((R(x,y,z) * u) * w) / ((x * u) * w). [para(528(a,1),34(a,2,1,1))]. 534 x \ (R(x,y,z) * u) = R(x,y,z) * (x \ u). [hyper(23,a,20,a,b,529,a),flip(a)]. 535 x / (y * (R(y,z,u) \ x)) = y \ R(y,z,u). [para(20(a,1),531(a,1,1))]. 536 (R(x,y,z) * (x \ u)) / u = x \ R(x,y,z). [para(20(a,1),531(a,1,2))]. 537 ((x * y) * z) / (x * (y * z)) = x \ R(x,y,z). [para(79(a,1),531(a,1,1))]. 538 (R(R(x,y,z),u,w) * (y * z)) / ((x * y) * z) = R(x,y,z) \ R(R(x,y,z),u,w). [para(79(a,1),531(a,1,2))]. 539 x \ (R(y,z,u) * (y \ x)) = T(y \ R(y,z,u),x). [para(532(a,1),36(a,2,2)),flip(a)]. 540 (R(x,y,z) \ x) \ u = R(x,y,z) * (x \ u). [para(532(a,1),463(a,2))]. 541 (x \ R(x,y,z)) \ u = x * (R(x,y,z) \ u). [para(535(a,1),66(a,1,1))]. 542 x / (R(y,z,u) * (y \ x)) = R(y,z,u) \ y. [para(540(a,1),65(a,1,2))]. 543 x * (R(x,y,z) \ 1) = R(x,y,z) \ x. [para(541(a,1),462(a,1))]. 544 (R(x,y,z) \ x) * u = x * (R(x,y,z) \ u). [para(541(a,1),465(a,1)),flip(a)]. 545 T(R(x,y,z) \ 1,x) = R(x,y,z) \ 1. [hyper(23,a,327,a,b,543,a),flip(a)]. 546 T(x,R(x,y,z) \ 1) = x. [hyper(39,a,545,a)]. 547 x \ (x / R(x,y,z)) = R(x,y,z) \ 1. [para(545(a,1),499(a,1)),flip(a)]. 548 T(x,y) * (R(x,z,u) \ 1) = R(x,z,u) \ T(x,y). [para(546(a,1),329(a,1,2,1)),flip(a)]. 549 (x * y) \ ((z * x) * y) = R(T(z,x * y),x,y). [para(111(a,2),46(a,2)),flip(a)]. 550 (x * (x * (y * z))) / (y * z) = R(x * x,y,z). [para(51(a,1),134(a,1,1))]. 551 x \ ((x * y) * (1 / y)) = a(x,y,1 / y). [para(18(a,1),164(a,1,1))]. 552 x \ ((x * y) * (y \ 1)) = a(x,y,1 / y). [para(155(a,1),551(a,1,2,2))]. 553 x \ ((x * y) * (y \ 1)) = a(x,y,y \ 1). [para(155(a,1),552(a,2,3))]. 554 a(x / y,y,y \ 1) = (x / y) \ (x * (y \ 1)). [para(22(a,1),553(a,1,2,1)),flip(a)]. 555 T((x * y) / (z * y),z) = R(z \ x,z,y). [para(84(a,1),194(a,2,1))]. 556 T(T((x * y) / (z * y),u),z) = T(R(z \ x,z,y),u). [para(555(a,1),42(a,1,1)),flip(a)]. 557 T(x,x * ((y * x) / y)) = x. [para(204(a,2),237(a,1))]. 558 ((x * y) / x) / y = y \ ((x * y) / x). [para(557(a,1),252(a,1,2))]. 560 (x \ y) * L(z,y,x \ 1) = x \ (y * z). [para(331(a,2),318(a,1))]. 561 (T(x,y) * (x \ 1)) * z = T(x,y) * (x \ z). [para(374(a,1),332(a,1,1)),flip(a)]. 562 (x \ T(x,y)) * z = T(x,y) * (x \ z). [para(377(a,1),561(a,1,1))]. 563 (T(x,y) * (x \ z)) / z = x \ T(x,y). [hyper(24,a,22,a,b,562,a),flip(a)]. 564 x * (T(x,y) * (x \ x)) = T(x * T(x,y),x). [para(562(a,1),138(a,1,2))]. 565 (T(x,y) * z) / (x * z) = x \ T(x,y). [para(19(a,1),563(a,1,1,2))]. 566 (x \ T(x,y)) \ (T(x,y) * z) = x * z. [para(565(a,1),66(a,1,1))]. 567 (x \ T(x,y)) \ z = x * (T(x,y) \ z). [para(20(a,1),566(a,1,2))]. 568 T(x * T(x,y),x) = x * (T(x,y) * 1). [para(60(a,1),564(a,1,2,2)),flip(a)]. 569 T(x * T(x,y),x) = x * T(x,y). [para(18(a,1),568(a,2,2))]. 571 T(x,x * T(x,y)) = x. [hyper(39,a,569,a)]. 572 T(x,y) / x = x \ T(x,y). [para(571(a,1),252(a,1,2))]. 573 (x \ T(x,y)) \ z = (x / T(x,y)) * z. [para(572(a,1),358(a,1,1))]. 574 (x \ T(x,y)) \ z = (T(x,y) \ x) * z. [para(299(a,1),573(a,2,1))]. 575 (T(x,y) \ x) * (T(x,y) * z) = x * z. [para(574(a,1),566(a,1))]. 576 (T(x,y) \ x) * z = x * (T(x,y) \ z). [para(574(a,1),567(a,1))]. 577 (x * y) / (T(x,z) * y) = T(x,z) \ x. [hyper(24,a,22,a,b,575,a),flip(a)]. 578 x * (T(x,y) \ 1) = T(x,y) \ x. [hyper(24,a,18,a,b,576,a),flip(a)]. 579 K(x,T(x,y) \ 1) = 1. [hyper(23,a,328,a,b,576,a),flip(a)]. 580 T(x,T(x,y) \ 1) = x. [hyper(41,a,579,a)]. 581 T(x,y) * (T(x,z) \ 1) = T(x,z) \ T(x,y). [para(580(a,1),329(a,1,2,1)),flip(a)]. 582 x \ (T(x,y) \ x) = T(x,y) \ 1. [hyper(23,a,20,a,b,578,a),flip(a)]. 583 ((T(x,y) \ x) * z) / (T(x,y) \ z) = R(x,T(x,y) \ 1,z). [para(578(a,1),324(a,1,1,1))]. 584 R(x \ 1,x * y,z) = R(x,y,z) \ 1. [para(348(a,2),344(a,1))]. 585 R(x,x \ y,z) \ 1 = R(x \ 1,y,z). [para(20(a,1),584(a,1,2)),flip(a)]. 586 (x * y) / (z * ((z \ x) * y)) = R(z,x,y) \ z. [para(213(a,1),500(a,1,2))]. 587 T(x \ R(x,y,z),x * (y * z)) = (x * (y * z)) \ ((x * y) * z). [para(537(a,1),84(a,1,1))]. 588 R(x * x,y,z) = x * x. [para(550(a,1),132(a,1))]. 589 R(T(x * x,y),z,u) = T(x * x,y). [para(588(a,1),46(a,2,1))]. 591 T(x * x,y) \ (z * u) = (T(x * x,y) \ z) * u. [para(589(a,1),197(a,1,1))]. 592 a(x / y,y,y \ 1) = (y / x) * (x * (y \ 1)). [para(554(a,2),358(a,1))]. 593 (x * y) / (z * ((z \ y) * T(x,y))) = R(z,y,T(x,y)) \ z. [para(82(a,1),586(a,1,1))]. 594 a(x,y,z) = (x \ (y * z)) \ ((x \ y) * z). [para(284(a,2),28(a,2))]. 596 (x \ (y * (x \ 1))) * x = T(y,x) * (x \ 1). [para(378(a,1),329(a,1))]. 597 (T(x,y) * (y \ 1)) / y = y \ (x * (y \ 1)). [hyper(24,a,22,a,b,596,a),flip(a)]. 598 x \ (y * (x \ 1)) = T(y,x) / (x * x). [para(597(a,1),401(a,1))]. 599 x \ ((x * (x * y)) * (x \ 1)) = (x * (y * x)) / (x * x). [para(103(a,1),598(a,2,1))]. 600 T(x,y) / (y * y) = T(x / (y * y),y). [para(598(a,1),403(a,2)),flip(a)]. 601 x * ((y \ (y \ 1)) * z) = (x / (y * y)) * z. [para(416(a,1),428(a,1,1)),flip(a)]. 602 (x / (y * y)) * z = x * (y \ (y \ z)). [para(291(a,1),601(a,1,2)),flip(a)]. 603 L(x,y / (y * z),z) = x. [hyper(23,a,74,a,b,451,a),flip(a)]. 604 (x * (y / (y * x))) \ z = (y / (y * x)) \ (x \ z). [para(603(a,1),177(a,1)),flip(a)]. 605 T(x,x * (y / (y * x))) = x. [para(603(a,1),364(a,2))]. 606 (x * (y / (y * x))) \ z = ((y * x) / y) * (x \ z). [para(604(a,2),358(a,1))]. 607 x * (x * ((y * z) / ((x * y) * z))) = R(x,x * y,z). [para(95(a,1),211(a,1)),flip(a)]. 608 L(R(x,x,y),z,u) * (x * y) = (x * L(x,z,u)) * y. [para(214(a,1),184(a,2,1))]. 609 L(K(x,y),y * x,x * y) = K(y,x) \ 1. [para(30(a,2),260(a,2,1))]. 610 (x \ (y * z)) \ ((x \ y) * z) = a(x \ 1,y,z). [para(318(a,1),323(a,1,2,1))]. 611 a(x \ 1,y,z) = a(x,y,z). [para(610(a,1),594(a,2)),flip(a)]. 612 a(x / y,z,u) = a(y / x,z,u). [para(343(a,1),611(a,1,1))]. 613 L(x \ 1,y,x \ 1) * y = y * T(x \ 1,x * y). [para(485(a,1),336(a,2,2))]. 614 T(T((x * y) / (z * y),u),z) = R(T(z \ x,u),z,y). [para(556(a,2),46(a,2)),flip(a)]. 615 x * (x * (R(x,y,z) \ 1)) = R(x,x * y,z). [para(344(a,1),607(a,1,2,2))]. 616 (x * x) / R(x,y,z) = R(x,x * y,z). [para(615(a,1),263(a,1)),flip(a)]. 617 x * (R(x,y,z) \ x) = R(x,x * y,z). [para(543(a,1),615(a,1,2))]. 618 x \ R(x,x * y,z) = R(x,y,z) \ x. [hyper(23,a,20,a,b,617,a),flip(a)]. 619 x * (R(x,x * y,z) \ x) = R(x,(x * x) * y,z). [para(131(a,2),617(a,2,2))]. 620 x / R(x,x * y,z) = x \ R(x,y,z). [para(617(a,1),535(a,1,2))]. 621 (R(x,y,z) \ x) * x = R(x,x * y,z). [para(617(a,1),544(a,2))]. 622 R(x,x * y,z) \ x = x \ R(x,y,z). [para(620(a,1),498(a,1)),flip(a)]. 623 R(x,x * y,z) \ 1 = x \ (x \ R(x,y,z)). [para(620(a,1),547(a,1,2)),flip(a)]. 624 x \ R(x,x \ y,z) = R(x,y,z) \ x. [para(20(a,1),622(a,1,1,2)),flip(a)]. 625 x * (R(x,x * y,z) \ u) = (x \ R(x,y,z)) * u. [para(622(a,1),544(a,1,1)),flip(a)]. 626 R(x,(x * x) * y,z) = x * (x \ R(x,y,z)). [para(622(a,1),619(a,1,2)),flip(a)]. 627 R(x,(x * x) * y,z) = R(x,y,z). [para(626(a,2),20(a,1))]. 628 R(x,x * (x * y),z) = R(x,y,z). [para(131(a,1),627(a,1,2))]. 629 R(x,x \ y,z) = R(x,x * y,z). [para(20(a,1),628(a,1,2,2)),flip(a)]. 630 R(x,x * y,z) \ (y * z) = (x \ y) * z. [para(629(a,1),197(a,1,1))]. 632 R(x,x * y,z) \ 1 = R(x \ 1,y,z). [para(629(a,1),585(a,1,1))]. 633 R(x,x * y,z) = R(x \ 1,y,z) \ 1. [para(632(a,1),156(a,1,1)),flip(a)]. 634 x \ (x \ R(x,y,z)) = R(x \ 1,y,z). [para(632(a,1),623(a,1)),flip(a)]. 635 x * R(x \ 1,y,z) = x \ R(x,y,z). [para(634(a,1),20(a,1,2))]. 636 x * (R(x \ 1,y,z) * u) = x \ (R(x,y,z) * u). [para(634(a,1),265(a,1,2,1))]. 637 x * (R(x,x * y,z) \ u) = R(x,y,z) * (x \ u). [para(625(a,2),532(a,1))]. 638 x * (R(x \ 1,y,z) * u) = R(x,y,z) * (x \ u). [para(636(a,2),534(a,1))]. 639 x * (y * R(y \ (x \ y),z,u)) = R(x,z,u) * (x \ y). [para(366(a,2),638(a,1,2))]. 640 (x * L(x,y,z)) * u = L(x,y,z) * (x * u). [para(182(a,1),608(a,1,1,1)),flip(a)]. 641 L(x,y,z) \ ((x * L(x,y,z)) * u) = x * u. [hyper(23,a,20,a,b,640,a(flip)),flip(a)]. 642 L(x,y,z) * (x * u) = x * (L(x,y,z) * u). [para(640(a,1),484(a,1))]. 643 L(x,y,z) \ (x * (L(x,y,z) * u)) = x * u. [para(484(a,1),641(a,1,2))]. 644 x * (L(x,y,z) * (x \ u)) = L(x,y,z) * u. [para(20(a,1),642(a,1,2)),flip(a)]. 645 L(x,y,z) * (x * (L(x,y,z) \ u)) = x * u. [para(20(a,1),642(a,2,2))]. 646 (L(x,y,z) \ x) * (L(x,y,z) * u) = x * u. [para(643(a,1),524(a,1)),flip(a)]. 647 (x \ L(x,y,z)) * u = L(x,y,z) * (x \ u). [hyper(23,a,504,a,b,644,a),flip(a)]. 648 (x * y) / (x * (L(x,z,u) \ y)) = L(x,z,u). [hyper(24,a,22,a,b,645,a),flip(a)]. 649 (x * y) / (L(x,z,u) * y) = L(x,z,u) \ x. [hyper(24,a,22,a,b,646,a),flip(a)]. 650 (L(x,y,z) \ x) * u = x * (L(x,y,z) \ u). [para(20(a,1),646(a,1,2))]. 652 T(x,L(x,y,z) \ x) = x. [hyper(23,a,82,a,b,650,a),flip(a)]. 653 K(x,L(x,y,z) \ x) = 1. [hyper(40,a,652,a)]. 654 T(x \ 1,x * (y * y)) = T(x,y * y) \ 1. [para(202(a,1),380(a,2,1))]. 655 T(x,y * y) \ 1 = T(x \ 1,y * y). [para(654(a,1),431(a,1))]. 656 L(x,y,R(T(y,z),u,w)) = x. [hyper(23,a,74,a,b,436,a),flip(a)]. 657 L(x,y,R((y \ z) \ z,u,w)) = x. [para(83(a,1),656(a,1,3,1))]. 658 x \ ((y \ (y \ z)) * (y * (y * x))) = T(z,y * (y * x)). [para(285(a,1),444(a,1,2))]. 659 x \ (x * (x * (y * (x \ 1)))) = (x * (y * x)) / (x * x). [para(51(a,1),599(a,1,2))]. 660 x \ (T(y,z * z) * x) = T(y,z * (z * x)). [para(420(a,1),658(a,1,2))]. 661 T(T(x,y * y),z) = T(x,y * (y * z)). [para(660(a,1),36(a,2))]. 662 T(T(x,y),z * z) = T(x,z * (z * y)). [para(661(a,1),42(a,1)),flip(a)]. 663 x \ (x * T(y,x \ 1)) = (x * (y * x)) / (x * x). [para(347(a,1),659(a,1,2,2))]. 664 (x * (y * x)) / (x * x) = T(y,x \ 1). [para(663(a,1),19(a,1))]. 665 T(x * y,x) / (x * x) = T(x \ y,x \ 1). [para(138(a,1),664(a,1,1))]. 666 T((x * y) / (x * x),x) = T(x \ y,x \ 1). [para(665(a,1),600(a,1)),flip(a)]. 667 (x * (x * ((y * z) * u))) / (z * u) = R(x * (x * y),z,u). [para(51(a,1),94(a,1,1))]. 668 (x * (y \ 1)) / (x / y) = (x / y) \ (x * (y \ 1)). [para(434(a,1),481(a,1,2)),flip(a)]. 669 (x * (y \ 1)) / (x / y) = (y / x) * (x * (y \ 1)). [para(668(a,2),358(a,1))]. 670 (x * (T(x,y) \ z)) / (T(x,y) \ z) = R(x,T(x,y) \ 1,z). [para(576(a,1),583(a,1,1))]. 671 (x * y) / (L(x,z * y,z) * y) = R(z,y,T(x,y)) \ z. [para(455(a,1),593(a,1,2))]. 672 R(x,y,T(z,y)) \ x = L(z,x * y,x) \ z. [para(671(a,1),649(a,1))]. 673 (R(x,y,T(z,y)) \ x) \ 1 = z \ L(z,x * y,x). [para(672(a,2),511(a,1,1))]. 674 L(x,y * (y * z),y) \ x = y \ R(y,z,T(x,y * z)). [para(672(a,1),622(a,1))]. 676 x \ R(x,y,T(z,y)) = z \ L(z,x * y,x). [para(673(a,1),460(a,1)),flip(a)]. 677 R(x,y,T(z,y)) = x * (z \ L(z,x * y,x)). [para(676(a,1),20(a,1,2)),flip(a)]. 678 R(x,x * y,T(z,x * y)) = x * (z \ L(z,y,x)). [para(313(a,1),677(a,2,2,2))]. 679 R(x,y,T(z,x * y)) \ x = z \ L(z,y,x). [hyper(23,a,617,a,b,678,a(flip)),flip(a)]. 680 (x \ L(x,y,z)) * R(z,y,T(x,z * y)) = z. [para(679(a,1),496(a,1,1))]. 681 L(x,y,z) \ x = z \ R(z,y,T(x,z * y)). [para(313(a,1),674(a,1,1))]. 682 L(x,y,z) * (z \ R(z,y,T(x,z * y))) = x. [para(681(a,1),20(a,1,2))]. 683 R(x,y,T(z,x * y)) = x * (L(z,y,x) \ z). [para(681(a,2),20(a,1,2)),flip(a)]. 684 (x \ R(x,y,T(z,x * y))) * L(z,y,x) = z. [para(681(a,1),520(a,1,1))]. 685 L(x,R(y,z,u),T(y,w)) * (T(y,w) \ T(y,w)) = x. [para(527(a,1),682(a,1,2,2))]. 686 R(x,y,T(z,x * y)) * (x \ L(z,y,x)) = z. [para(684(a,1),532(a,1)),flip(a)]. 687 L(x,R(y,z,u),T(y,w)) * 1 = x. [para(60(a,1),685(a,1,2))]. 688 L(x,R(y,z,u),T(y,w)) = x. [hyper(24,a,18,a,b,687,a)]. 690 L(x,R(y / z,u,w),z \ y) = x. [para(84(a,1),688(a,1,3))]. 691 T(R(x,y,z),T(x,u)) / T(x,u) = T(x,u) \ R(x,y,z). [para(688(a,1),441(a,1,2))]. 692 R(T(x,T(x,y)),z,u) / T(x,y) = T(x,y) \ R(x,z,u). [para(46(a,2),691(a,1,1))]. 693 R(x,y,z) / T(x,u) = T(x,u) \ R(x,y,z). [para(115(a,1),692(a,1,1,1))]. 694 x * (x * (((y * z) * u) / (z * u))) = R(x * (x * y),z,u). [para(667(a,1),211(a,1)),flip(a)]. 695 R(x,T(x,y) \ 1,z) = x. [para(670(a,1),21(a,1))]. 696 R(x * (x * y),z,u) = x * (x * R(y,z,u)). [para(34(a,2),694(a,1,2,2)),flip(a)]. 697 x * (x * R(T(y,x),z,u)) = R(x * (y * x),z,u). [para(82(a,1),696(a,1,1,2)),flip(a)]. 698 R(x * (x * T(y,x * x)),z,u) = R(y,z,u) * (x * x). [para(696(a,2),226(a,1))]. 699 R(x * (y * x),z,u) = x * (R(y,z,u) * x). [para(110(a,1),697(a,1,2)),flip(a)]. 700 x \ R(x * (y * x),z,u) = R(y,z,u) * x. [hyper(23,a,20,a,b,699,a(flip)),flip(a)]. 701 (x * (y * x)) \ R(x * (z * x),u,w) = T(y,x) \ (x \ (R(z,u,w) * x)). [para(699(a,2),287(a,1,2))]. 702 x \ R(x * y,z,u) = R(y / x,z,u) * x. [para(22(a,1),700(a,1,2,1,2))]. 703 x \ R(x * y,z,u) = x * R(x \ y,z,u). [para(702(a,2),224(a,1))]. 704 L(x \ (y * R(y \ z,u,w)),x,y) = (y * x) \ R(y * z,u,w). [para(703(a,1),177(a,1,1,2))]. 705 R(x * (y * y),z,u) = R(x,z,u) * (y * y). [para(136(a,1),698(a,1,1))]. 706 (x \ 1) \ T(x \ 1,x * y) = ((x * y) \ y) * x. [para(156(a,1),385(a,2,2))]. 707 (x \ 1) \ T(x \ 1,x * y) = x * ((x * y) \ y). [para(706(a,2),381(a,1))]. 708 (x * y) * T(L(y \ 1,y,x),z) = (x * y) * T((x * y) \ x,z). [para(231(a,1),139(a,1))]. 709 R((x / y) * (z * z),z \ (z \ 1),y) = x / (z \ (z \ y)). [para(415(a,1),293(a,1,1))]. 710 x / (y \ (y \ z)) = (x / z) * (y * y). [para(709(a,1),426(a,1))]. 711 (x / (y * z)) * (y * y) = x / (y \ z). [para(19(a,1),710(a,1,2,2)),flip(a)]. 712 (x * y) / (z \ y) = R(x / z,z,y) * (z * z). [para(80(a,2),711(a,1,1)),flip(a)]. 713 R((x / y) * (y * y),y,z) = (x * z) / (y \ z). [para(712(a,2),705(a,2))]. 714 R(x / (y \ 1),y,z) = (x * z) / (y \ z). [para(397(a,1),713(a,1,1))]. 715 R(x,y,z) = ((x * (y \ 1)) * z) / (y \ z). [para(21(a,1),714(a,1,1))]. 716 R(L(x,y,z) \ x,x,u) = ((L(x,y,z) \ 1) * u) / (x \ u). [para(513(a,1),714(a,1,1))]. 717 R(x,y \ 1,z) = R(x,y,z). [para(715(a,2),324(a,1)),flip(a)]. 718 R(x,y,y) / y = x * (y \ 1). [para(717(a,1),207(a,1,1))]. 719 (x * (y \ 1)) \ R(x,y,y) = y. [para(717(a,1),209(a,1,2))]. 720 R(x / (y \ 1),y,y) = x * y. [para(717(a,1),210(a,1))]. 721 R(x,T(x,y),z) = x. [para(717(a,1),695(a,1))]. 722 (x * T(x,y)) * z = x * (T(x,y) * z). [para(721(a,1),79(a,1,1)),flip(a)]. 723 R(T(x / (y \ 1),z),y,y) / y = (y \ 1) * T((y \ 1) \ x,z). [para(718(a,2),139(a,1))]. 725 (T(x,y) * (R(x,z,u) \ 1)) \ T(x,y) = R(x,z,u). [para(527(a,1),719(a,1,2))]. 726 R(T(x / (y \ 1),z),y,y) = T(x * y,z). [para(720(a,1),46(a,2,1))]. 727 L(x,T(y,z),y) = x. [hyper(23,a,74,a,b,722,a),flip(a)]. 729 x * (T(x,y) * (x \ z)) = T(x,y) * z. [para(722(a,1),281(a,1))]. 730 L(x,y,(z * y) / z) = x. [para(104(a,1),727(a,1,2))]. 731 L(x,(y \ z) \ z,y) = x. [para(83(a,1),727(a,1,2))]. 732 x \ (T(x,y) * z) = T(x,y) * (x \ z). [hyper(23,a,20,a,b,729,a),flip(a)]. 733 x \ (T(x,y) * z) = (x \ T(x,y)) * z. [para(732(a,2),562(a,2)),flip(a)]. 734 (R(x,y,z) \ T(x,u)) \ T(x,u) = R(x,y,z). [para(548(a,1),725(a,1,1))]. 735 R(L(x,y,z) \ x,x,u) = (L(x,y,z) \ u) / (x \ u). [para(318(a,1),716(a,2,1))]. 736 R(L(x,y,z) \ x,x,u) = L(x,y,z) \ x. [para(735(a,2),513(a,1))]. 739 a(x,y,z) = T(x \ R(x,y,z),x * (y * z)). [para(587(a,2),28(a,2))]. 740 T(T(x \ R(x,y,z),u),x * (y * z)) = T(a(x,y,z),u). [para(739(a,2),42(a,1,1)),flip(a)]. 741 a(x,y,z) = T(T(R(x,y,z) / x,x * (y * z)),x). [para(739(a,2),112(a,2)),flip(a)]. 742 T((x * (y \ R(y,z,u))) / x,y * (z * u)) = (x * a(y,z,u)) / x. [para(739(a,2),233(a,1,1,2)),flip(a)]. 743 T(R(x,y,z) \ R(R(x,y,z),u,x),x * (R(x,y,z) * T(u,x))) = a(R(x,y,z),u,x). [para(530(a,2),739(a,2,2)),flip(a)]. 744 T(T((R(x,y,z) * u) / (x * u),x * (y * z)),x) = R(a(x,y,z),x,u). [para(739(a,2),614(a,2,1))]. 745 a(x,y,z) = T(T(x \ R(x,y,z),x * (y * z)),x). [para(478(a,1),741(a,2,1,1))]. 746 T(a(x,y,z),x) = a(x,y,z). [para(739(a,2),745(a,2,1)),flip(a)]. 747 a(x,y,z) * x = x * a(x,y,z). [para(746(a,1),82(a,1,2)),flip(a)]. 748 (x * a(x,y,z)) / x = a(x,y,z). [para(746(a,1),105(a,1,1,2))]. 749 ((x * (x * y)) * a(x * (x * y),z,u)) / y = a(x * (x * y),z,u) * (x * x). [para(747(a,1),418(a,1,1))]. 750 (x \ y) \ R(x \ z,u,w) = (x * y) \ R(x * z,u,w). [para(704(a,1),267(a,1)),flip(a)]. 751 (x * y) * T((x * y) \ x,z) = (x * y) * L(T(y \ 1,z),y,x). [para(44(a,2),708(a,1,2)),flip(a)]. 752 (x \ 1) * T((x \ 1) \ y,z) = T(y * x,z) / x. [para(726(a,1),723(a,1,1)),flip(a)]. 753 (x \ 1) * T(x * y,z) = T(y * x,z) / x. [para(330(a,1),752(a,1,2,1))]. 754 T(x * y,z) / y = y \ T(y * x,z). [para(753(a,1),318(a,1))]. 755 x \ T(x * (y / x),z) = T(y,z) / x. [para(22(a,1),754(a,1,1,1)),flip(a)]. 756 T(x * y,y) / y = (y \ x) * y. [para(754(a,2),146(a,1))]. 757 ((x \ y) * x) * x = T(y * x,x). [para(756(a,1),22(a,1,1))]. 758 T((x * y) * x,x) = (y * x) * x. [para(19(a,1),757(a,1,1,1)),flip(a)]. 762 (x * y) * T((x * y) \ x,z) = x * (y * T(y \ 1,z)). [para(751(a,2),74(a,1))]. 763 (x * (x * (y * z))) \ (x * (x * (y * (z * u)))) = L(u,z,x * (x * y)). [para(51(a,1),92(a,1,2))]. 764 (x * y) * T(L(y \ z,y,x),u) = (x * y) * T((x * y) \ (x * z),u). [para(232(a,1),139(a,1))]. 765 (x * y) * R(L(y \ 1,y,x),z,u) = (x * y) * R((x * y) \ x,z,u). [para(472(a,1),224(a,1))]. 767 T(T(x \ R(x,y,z),x * (y * z)),x) = R(a(x,y,z),x,u). [para(531(a,1),744(a,1,1,1))]. 769 R(a(x,y,z),x,u) = a(x,y,z). [para(767(a,1),745(a,2)),flip(a)]. 770 (a(x,y,z) * x) * u = a(x,y,z) * (x * u). [para(769(a,1),79(a,1,1)),flip(a)]. 771 L(x,y,a(y,z,u)) = x. [hyper(23,a,74,a,b,770,a),flip(a)]. 772 (x * a(x,y,z)) * u = a(x,y,z) * (x * u). [para(747(a,1),770(a,1,1))]. 773 L(x,y,z * (z * u)) = (u * y) \ (u * (y * x)). [para(763(a,1),212(a,1))]. 774 L(x,y,z * (z * u)) = L(x,y,u). [para(773(a,2),32(a,2)),flip(a)]. 776 L(x,y,z \ u) = L(x,y,z * u). [para(20(a,1),774(a,1,3,2)),flip(a)]. 777 L(x,y,(z / u) * z) = L(x,y,u). [para(22(a,1),774(a,1,3,2))]. 778 L(x,y,z * (u * z)) = L(x,y,T(u,z)). [para(82(a,1),774(a,1,3,2))]. 779 L(x,y,(z * u) * (u * z)) = L(x,y,K(u,z)). [para(69(a,1),774(a,1,3,2))]. 780 L(x,y,z * ((z \ u) * w)) = L(x,y,z * ((z * u) * w)). [para(89(a,1),774(a,1,3,2)),flip(a)]. 781 L(x,y,(z \ u) * w) = L(x,y,(z * u) * w). [para(89(a,1),774(a,1,3)),flip(a)]. 782 L(x,y,(z \ (z \ u)) * (z \ u)) = L(x,y,T(z,u)). [para(254(a,1),774(a,1,3,2))]. 783 L(x,y,(z * z) / u) = L(x,y,u \ 1). [para(263(a,1),774(a,1,3))]. 784 L(x,y,z / u) = L(x,y,u / z). [para(360(a,1),774(a,1,3))]. 785 L(x,y,z * L(z,u * z,u)) = L(x,y,a(u,z,z)). [para(453(a,2),774(a,1,3,2))]. 786 L(x,y,R(z * (z * u),w,v5)) = L(x,y,R(u,w,v5)). [para(696(a,2),774(a,1,3))]. 787 L(x,y,z \ 1) = L(x,y,z). [para(18(a,1),776(a,2,3))]. 789 L(x,y,T(z / u,z)) = L(x,y,((u / z) * u) * u). [para(370(a,2),776(a,1,3))]. 790 L(x,y,y \ (z * z)) = x. [para(776(a,2),429(a,1))]. 792 L(x \ (x / y),y,x * (x / y)) = ((x \ (x / y)) \ y) \ y. [para(776(a,1),442(a,1))]. 793 L(x,R(y / z,u,w),z * y) = x. [para(776(a,1),690(a,1))]. 794 L(x \ L(y \ z,y,u),x,u * y) = ((u \ y) * x) \ (u \ z). [para(776(a,1),275(a,1))]. 795 T(x * x,y) \ (y \ (x * x)) = y \ 1. [para(790(a,1),395(a,1)),flip(a)]. 796 L(x,L(y \ 1,z,u),y) = x. [para(787(a,1),503(a,1))]. 797 L(x,(y * z) \ y,z) = x. [para(787(a,1),505(a,1))]. 798 (x \ y) * L(z,y,x) = x \ (y * z). [para(787(a,1),560(a,1,2))]. 799 x * T(y \ 1,y * x) = L(y \ 1,x,y) * x. [para(787(a,1),613(a,1,1)),flip(a)]. 800 L(x,y \ z,z \ y) = x. [para(20(a,1),797(a,1,2,1))]. 801 L(x,y \ z,z * y) = x. [para(800(a,1),776(a,1)),flip(a)]. 802 L(x,y,z * (z / y)) = x. [para(66(a,1),801(a,1,2))]. 803 (x * L(x \ 1,y,z)) \ u = L(x \ 1,y,z) \ (x \ u). [para(796(a,1),177(a,1)),flip(a)]. 804 L(x,y,(z * (z * u)) * (z * w)) = L(x,y,u \ (z \ w)). [para(282(a,1),777(a,1,3,1))]. 805 L(x,y,(z * (z * u)) * z) = L(x,y,u \ (z \ 1)). [para(289(a,1),777(a,1,3,1))]. 806 L(L(x,y,y / z),z,z / y) = x. [para(784(a,1),304(a,1,1))]. 807 L(x,x,x / y) = y \ (y / (x \ 1)). [para(784(a,1),432(a,1))]. 808 L(x,y,z / (z * y)) = x. [para(784(a,1),730(a,1))]. 809 ((x / (x * y)) * y) \ (x / (x * y)) = y \ 1. [para(808(a,1),142(a,1)),flip(a)]. 810 ((x / (x * y)) * y) * z = (x / (x * y)) * (y * z). [para(808(a,1),74(a,1,2))]. 811 ((x / (x * y)) * y) \ z = y \ ((x / (x * y)) \ z). [para(808(a,1),177(a,1)),flip(a)]. 812 L(x,y / (z * (u * y)),z * (u \ 1)) = x. [para(350(a,1),793(a,1,2))]. 813 (x * (y \ z)) \ (x * (y \ (z * u))) = L(L(u,z,y),y \ z,x). [para(798(a,1),32(a,2,2,2)),flip(a)]. 815 T(x,y) \ (x * z) = (T(x,y) \ x) * z. [para(234(a,1),798(a,1,2)),flip(a)]. 816 x \ (((y * x) / y) * z) = (x \ ((y * x) / y)) * z. [para(237(a,1),798(a,1,2)),flip(a)]. 817 (x \ y) * T((x \ y) \ 1,z) = x \ (y * T(y \ x,z)). [para(261(a,1),798(a,1,2))]. 818 L(x,y,T(z \ u,z)) = L(x,y,T(z * u,z)). [para(138(a,1),778(a,1,3)),flip(a)]. 819 L(x,y,T((z \ u) * z,z)) = L(x,y,z * T(u * z,z)). [para(757(a,1),778(a,1,3,2)),flip(a)]. 820 L(x,y,(z * z) / u) = L(x,y,u). [para(783(a,2),787(a,1))]. 821 L(x,y,T(z,z * (u * u))) = L(x,y,z \ (u * u)). [para(252(a,1),820(a,1,3)),flip(a)]. 822 L(x,y,z / (u * u)) = L(x,y,z). [para(820(a,1),784(a,1)),flip(a)]. 823 L(x,y,z * (u * u)) = L(x,y,z). [para(21(a,1),822(a,1,3)),flip(a)]. 824 L(x,y,(z * u) * u) = L(x,y,R(z,u,u)). [para(34(a,2),822(a,1,3)),flip(a)]. 825 (x * (y * (y * z))) \ ((x * (y * y)) * (z * u)) = L(u,z,x). [para(823(a,1),419(a,2))]. 826 (T(x,y) \ x) * y = T(y,T(x,y)). [para(815(a,1),107(a,1))]. 827 T(x,y) \ (x * z) = x * (T(x,y) \ z). [para(815(a,2),576(a,1))]. 828 x * (T(x,y) \ y) = T(y,T(x,y)). [para(826(a,1),576(a,1)),flip(a)]. 829 T(x,T(y,x)) / (T(y,x) \ x) = y. [hyper(24,a,22,a,b,828,a),flip(a)]. 830 x \ T(y,T(x,y)) = T(x,y) \ y. [hyper(23,a,20,a,b,828,a),flip(a)]. 831 (x * y) / (x * (T(x,z) \ y)) = T(x,z). [para(827(a,1),65(a,1,2))]. 832 (((x * y) * (y * x)) * z) \ (((x * y) * (y * x)) * (z * u)) = L(u,z,K(y,x)). [para(779(a,1),32(a,1)),flip(a)]. 833 (x * (y / (y * x))) \ (y / (y * x)) = x \ 1. [para(362(a,1),809(a,1,1))]. 834 T(x \ 1,x * (y / (y * x))) = x \ 1. [para(833(a,1),349(a,2))]. 835 L(x \ 1,y,x) * y = y * ((x * y) \ y). [para(349(a,1),799(a,1,2)),flip(a)]. 836 L(x,y,(z * (z \ u)) * (z \ u)) = L(x,y,T(z,u)). [para(782(a,1),781(a,1)),flip(a)]. 837 L(x,y,z * ((z \ u) * u)) = L(x,y,a(z,u,u)). [para(435(a,1),785(a,1,3))]. 838 L(x,y,R(z \ u,w,v5)) = L(x,y,R(z * u,w,v5)). [para(20(a,1),786(a,1,3,1,2)),flip(a)]. 839 L(x,y,T(z / u,z)) = L(x,y,R(u / z,u,u)). [para(789(a,2),824(a,1))]. 840 L(x,y,z * (z * (u * z))) = L(x,y,u \ (z \ 1)). [para(51(a,1),805(a,1,3))]. 841 (x * (y / (y * x))) * z = (y / (y * x)) * (x * z). [para(362(a,1),810(a,1,1))]. 842 (x * (y / (y * x))) \ z = x \ ((y / (y * x)) \ z). [para(362(a,1),811(a,1,1))]. 843 L(x,y,T(z,z * (u * u))) = L(x,y,z * (u * u)). [para(821(a,2),776(a,1))]. 844 L(x,y,z * (u \ z)) = L(x,y,T(u,z)). [para(20(a,1),836(a,1,3,1))]. 845 L(x,y,T(z / u,z)) = L(x,y,z * u). [para(66(a,1),844(a,1,3,2)),flip(a)]. 846 L(x,y,R(z / u,z,z)) = L(x,y,u * z). [para(845(a,1),839(a,1)),flip(a)]. 847 L(x,y,R((y \ z) * z,u,w)) = x. [para(838(a,1),657(a,1))]. 848 L(x,y,z \ (u \ 1)) = L(x,y,z * u). [para(840(a,1),774(a,1))]. 850 L(x,y,z * (u \ 1)) = L(x,y,z * u). [para(848(a,1),776(a,1)),flip(a)]. 851 L(x,y / (z * (u * y)),z * u) = x. [para(850(a,1),812(a,1))]. 852 L(x,(y * z) * (u / (y * (z * u))),y * z) = x. [para(851(a,1),303(a,1,1))]. 853 ((x * y) * z) / (x * (y * z)) = (x * y) * (z / (x * (y * z))). [para(851(a,1),196(a,1,2))]. 854 x \ ((y / (y * x)) \ z) = ((y * x) / y) * (x \ z). [para(842(a,1),606(a,1))]. 855 L(x,y,T(z,z * (u * u))) = L(x,y,z). [para(843(a,2),823(a,1))]. 856 L(x,y,T(z,u * u)) = L(x,y,z). [para(423(a,1),855(a,1,3))]. 858 L(x,y,R(T(z,u * u),w,v5)) = L(x,y,R(z,w,v5)). [para(46(a,2),856(a,1,3))]. 859 x \ (((y * x) / y) * z) = ((y * x) / y) * (x \ z). [para(358(a,1),854(a,1,2))]. 860 (x \ ((y * x) / y)) * z = ((y * x) / y) * (x \ z). [para(859(a,1),816(a,1)),flip(a)]. 861 L(x,y,z * ((z * u) * u)) = L(x,y,a(z,u,u)). [para(780(a,1),837(a,1))]. 862 L(x,y,z * (z * (u * (z * w)))) = L(x,y,u \ (z \ w)). [para(51(a,1),804(a,1,3))]. 863 L(x,y,T((z \ u) * z,z)) = L(x,y,(u * z) * z). [para(82(a,1),819(a,2,3))]. 864 L(x,y,T((z \ u) * z,z)) = L(x,y,R(u,z,z)). [para(863(a,2),824(a,1))]. 865 L(x,y,z \ (u \ w)) = L(x,y,z * (u * w)). [para(862(a,1),774(a,1))]. 867 L(x,y,z * (u \ w)) = L(x,y,z * (u * w)). [para(865(a,1),776(a,1)),flip(a)]. 868 L(x,y,z * (u * (u * w))) = L(x,y,z * w). [para(19(a,1),867(a,1,3,2)),flip(a)]. 869 L(x,y,(z \ u) * (u \ z)) = L(x,y,(u \ z) * (z * u)). [para(384(a,1),867(a,1,3))]. 871 ((x \ (x / y)) \ y) \ y = x \ (x / y). [para(792(a,1),802(a,1))]. 872 x / (y \ (y / x)) = (y \ (y / x)) \ x. [para(871(a,1),65(a,1,2))]. 873 (x * (y * (y * z))) \ (x * (y * (y * (z * u)))) = L(u,z,x). [para(411(a,1),825(a,1,2))]. 875 L(x,y * (y * z),u) = L(x,z,u). [para(873(a,1),93(a,1)),flip(a)]. 876 L(x,y \ z,u) = L(x,y * z,u). [para(20(a,1),875(a,1,2,2)),flip(a)]. 877 L(x,(y / z) * y,u) = L(x,z,u). [para(22(a,1),875(a,1,2,2))]. 878 L(x,y * (z * y),u) = L(x,T(z,y),u). [para(82(a,1),875(a,1,2,2))]. 879 L(x,(y * z) * (z * y),u) = L(x,K(z,y),u). [para(69(a,1),875(a,1,2,2))]. 880 L(x,(y \ z) * u,w) = L(x,(y * z) * u,w). [para(89(a,1),875(a,1,2)),flip(a)]. 881 L(x,T(y,y * z),u) = L(x,(y \ z) * z,u). [para(250(a,1),875(a,1,2,2)),flip(a)]. 882 L(x,(y * y) / z,u) = L(x,z \ 1,u). [para(263(a,1),875(a,1,2))]. 883 L(x,T(y \ 1,z),u) = L(x,z * (y \ z),u). [para(327(a,1),875(a,1,2,2)),flip(a)]. 884 L(x,y / z,u) = L(x,z / y,u). [para(360(a,1),875(a,1,2))]. 887 L(x,y \ 1,z) = L(x,y,z). [para(18(a,1),876(a,2,2))]. 888 (x * (y \ z)) * L(u,y * z,x) = x * ((y \ z) * u). [para(876(a,1),74(a,1,2))]. 889 L(x,(y \ z) * z,y) = x. [para(876(a,1),731(a,1))]. 890 L(x,y * z,z * y) = x. [para(876(a,1),801(a,1))]. 893 (x * ((x \ y) * y)) \ z = ((x \ y) * y) \ (x \ z). [para(889(a,1),177(a,1)),flip(a)]. 894 ((x * y) * (y * x)) * z = (x * y) * ((y * x) * z). [para(890(a,1),74(a,1,2))]. 895 T(x * y,(x * y) * (y * x)) = T(x * y,y * x). [para(890(a,1),203(a,1)),flip(a)]. 896 L(x,K(y,z),z * y) = x. [para(890(a,1),315(a,1,1))]. 897 K(x,y) \ 1 = K(y,x). [para(890(a,1),609(a,1)),flip(a)]. 898 K(x,y) * K(y,x) = 1. [para(897(a,1),20(a,1,2))]. 899 1 / K(x,y) = K(y,x). [para(897(a,1),65(a,1,2))]. 900 K(x,y) \ z = K(y,x) * z. [para(897(a,1),318(a,1,1)),flip(a)]. 901 K(x,y) * (K(y,x) * z) = z. [para(897(a,1),321(a,1,2,1))]. 902 x / (K(y,z) * x) = K(z,y). [para(897(a,1),340(a,2))]. 903 T(x * y,K(y,x)) / (y * x) = K(x,y). [para(897(a,1),345(a,2))]. 904 R(K(x,y),K(y,x) * z,u) = R(K(y,x),z,u) \ 1. [para(897(a,1),584(a,1,1))]. 905 a(K(x,y),z,u) = a(K(y,x),z,u). [para(897(a,1),611(a,1,1))]. 906 R(K(x,y),K(x,y) * z,u) = R(K(y,x),z,u) \ 1. [para(897(a,1),633(a,2,1,1))]. 907 K(x,y) * (K(y,x) / (x * y)) = K(x,y) \ ((y * x) \ 1). [para(897(a,1),379(a,1,2,1))]. 908 R(x,K(y,z),u) = R(x,K(z,y),u). [para(897(a,1),717(a,1,2))]. 909 L(x,y,K(z,u)) = L(x,y,K(u,z)). [para(897(a,1),787(a,1,3))]. 910 L(K(x,y),z,K(y,x)) * z = z * ((K(y,x) * z) \ z). [para(897(a,1),835(a,1,1,1))]. 911 (x * y) * (K(y,x) * z) = (y * x) * z. [para(896(a,1),176(a,1,2)),flip(a)]. 912 K(x,y) \ ((y * x) \ z) = (x * y) \ z. [para(896(a,1),199(a,1))]. 914 L(x,x,y) = (y * (x \ 1)) \ y. [para(887(a,1),161(a,1))]. 915 x / L(y,y,x) = x * (y \ 1). [para(887(a,1),162(a,1,2))]. 916 L(L(x,y * (z \ 1),y),z,y) = x. [para(887(a,1),308(a,1))]. 917 L(x * y,x,y) = (y \ (x \ 1)) \ 1. [para(887(a,1),351(a,1))]. 918 L(x,y,L(y \ 1,z,u)) = x. [para(887(a,1),509(a,1))]. 919 (x * (y \ z)) / L(z,y,x) = x * (y \ 1). [para(887(a,1),333(a,1,2))]. 920 L(x * (y * z),x,y) = (y \ (x \ 1)) \ z. [para(887(a,1),352(a,1))]. 921 L(x,K(y,z),u) = L(x,K(z,y),u). [para(897(a,1),887(a,1,2))]. 922 T(x * y,K(y,x)) = K(x,y) * (y * x). [para(900(a,1),122(a,1)),flip(a)]. 923 R(K(x,y),K(y,x) * z,u) \ K(x,y) = K(x,y) \ R(K(x,y),z,u). [para(901(a,1),618(a,1,2,2)),flip(a)]. 924 (L(x \ 1,y,z) * x) \ u = x \ (L(x \ 1,y,z) \ u). [para(918(a,1),177(a,1)),flip(a)]. 925 L(x / y,x / y,z) = (z * (y / x)) \ z. [para(343(a,1),914(a,2,1,2))]. 926 L(K(x,y),K(x,y),z) = (z * K(y,x)) \ z. [para(897(a,1),914(a,2,1,2))]. 928 L(x,(y * (y * z)) * (y * u),w) = L(x,z \ (y \ u),w). [para(282(a,1),877(a,1,2,1))]. 929 L(x,(y * (y * z)) * y,u) = L(x,z \ (y \ 1),u). [para(289(a,1),877(a,1,2,1))]. 930 K(x,y) / L(z,z,K(y,x)) = K(x,y) * (z \ 1). [para(909(a,1),915(a,1,2))]. 931 L(x,y * (z \ 1),y) = L(x,y * z,y). [para(916(a,1),303(a,1,1)),flip(a)]. 932 L(x,K(y,z),y * z) = x. [para(921(a,1),896(a,1))]. 933 ((x * y) \ K(x,y)) \ z = K(x,y) \ ((x * y) * z). [para(932(a,1),267(a,1)),flip(a)]. 934 L(x * y,x,y) * z = (y \ (x \ 1)) \ z. [para(917(a,2),318(a,1,1))]. 935 L(x,(y * y) / z,u) = L(x,z,u). [para(882(a,2),887(a,1))]. 936 L(x,y / (z * z),u) = L(x,y,u). [para(935(a,1),884(a,1)),flip(a)]. 937 L(x,y * (z * z),u) = L(x,y,u). [para(21(a,1),936(a,1,2)),flip(a)]. 938 L(x,(y * z) * z,u) = L(x,R(y,z,z),u). [para(34(a,2),936(a,1,2)),flip(a)]. 939 ((x * y) * z) / (K(x,y) * z) = y * x. [hyper(24,a,22,a,b,911,a),flip(a)]. 940 (x * y) \ ((y * x) * z) = K(y,x) * z. [hyper(23,a,20,a,b,911,a),flip(a)]. 941 K(x,y) * ((x * y) \ z) = (y * x) \ z. [para(912(a,1),20(a,1,2))]. 942 x * (y \ ((y * (x \ 1)) * z)) = L(z,y * x,y). [para(931(a,1),446(a,2))]. 943 L(x,K(y,z) * (y * z),u) = L(x,z * y,u). [para(939(a,1),935(a,1,2)),flip(a)]. 944 (x * y) \ (y * (x * z)) = K(y,x) * L(z,x,y). [para(74(a,1),940(a,1,2))]. 945 (x * (y \ 1)) * L(z,y,x) = x * (y \ z). [para(919(a,1),22(a,1,1))]. 946 (a(x,y,z) \ (x \ 1)) \ u = x * (a(x,y,z) * u). [para(920(a,1),771(a,1))]. 947 L(K(x,y),K(x,y),z) / z = (z * K(y,x)) \ 1. [para(926(a,2),320(a,1,1))]. 948 (a(x,y,z) \ (x \ 1)) \ u = (x * a(x,y,z)) * u. [para(771(a,1),934(a,1,1)),flip(a)]. 951 L(x,T(y,y * z),u) = L(x,(y * z) * z,u). [para(881(a,2),880(a,1))]. 953 L(x,(y * (y \ z)) * (y \ z),u) = L(x,T(y,z),u). [para(20(a,1),951(a,1,2,2)),flip(a)]. 954 x * (y * ((y \ (x \ 1)) * z)) = L(z,y * x,y). [para(213(a,1),942(a,1,2))]. 955 K(x,y) * L(x,y,x) = T(x,y * x). [para(944(a,1),36(a,2)),flip(a)]. 956 x * ((x \ (y \ 1)) * y) = a(x,y,y). [hyper(23,a,453,a(flip),b,954,a)]. 957 x * (y * (R(y,y * (x \ 1),z) \ ((x \ 1) * z))) = L(z,y * x,y). [para(630(a,2),954(a,1,2,2))]. 958 x * R(x \ 1,y \ 1,y) = a(x,y,y). [para(335(a,2),956(a,1,2))]. 959 x \ R(x,y \ 1,y) = a(x,y,y). [para(958(a,1),635(a,1)),flip(a)]. 960 x * R(x \ 1,y,y) = a(x,y,y). [para(717(a,1),958(a,1,2))]. 961 R(x,y \ 1,y) \ a(x,y,y) = T(x \ 1,R(x,y \ 1,y)). [para(959(a,1),325(a,2,2)),flip(a)]. 962 x \ R(x,y,y) = a(x,y,y). [para(717(a,1),959(a,1,2))]. 963 x * a(x,y,y) = R(x,y,y). [para(962(a,1),20(a,1,2))]. 964 a(x,y,y) \ R(x,y,y) = x. [para(962(a,1),480(a,1,1))]. 965 (R(x,y,y) \ x) * z = a(x,y,y) \ z. [para(962(a,1),465(a,1,1)),flip(a)]. 966 x * (a(x,y,y) * z) = R(x,y,y) * z. [para(962(a,1),501(a,1,2,1))]. 967 R(x \ 1,y,y) = x \ a(x,y,y). [para(962(a,1),634(a,1,2)),flip(a)]. 968 R(x,x * y,y) = a(x,y,y) \ x. [para(965(a,1),621(a,1)),flip(a)]. 969 T(x * y,K(y,x)) = T(x * y,y * x). [para(895(a,1),248(a,1)),flip(a)]. 970 T(x * y,K(y,x)) = (x \ 1) \ y. [para(969(a,2),439(a,1))]. 971 K(x,y) / T(y * x,K(x,y)) = (y * x) \ K(x,y). [para(969(a,2),257(a,1,2))]. 972 T(x * y,K(y,x)) = x * y. [para(970(a,2),330(a,1))]. 973 K(x,y) = (x * y) / (y * x). [para(972(a,1),903(a,1,1)),flip(a)]. 974 K(x,y) * (y * x) = x * y. [para(972(a,1),922(a,1)),flip(a)]. 975 (x * y) / (T(x,y) * y) = K(y,T(x,y)). [para(82(a,1),973(a,2,1)),flip(a)]. 976 (T(x,y) * y) / (x * y) = K(T(x,y),y). [para(82(a,1),973(a,2,2)),flip(a)]. 977 ((x * y) * z) / ((y * x) * z) = R(K(x,y),y * x,z). [para(973(a,2),80(a,1,1)),flip(a)]. 978 (x \ y) / (y * (x \ 1)) = K(x \ 1,y). [para(318(a,1),973(a,2,1)),flip(a)]. 979 ((K(x,y) * z) * K(y,x)) / z = K(K(x,y) * z,K(y,x)). [para(901(a,1),973(a,2,2)),flip(a)]. 980 K(x \ y,x) * y = (x \ y) * x. [para(20(a,1),974(a,1,2))]. 981 K(x * y,x) * y = (x \ y) * x. [para(495(a,1),980(a,1,1))]. 983 K(x,T(y,x)) = T(y,x) \ y. [para(975(a,1),577(a,1))]. 984 T(x,y) * K(y,T(x,y)) = x. [para(983(a,2),20(a,1,2))]. 985 K(x,T(y,x)) * T(y,x) = y. [para(983(a,2),298(a,1,1))]. 987 T(x,y) \ (x * z) = K(y,T(x,y)) * z. [para(983(a,2),815(a,2,1))]. 989 (x \ y) * K(x,T(y / x,x)) = y / x. [para(84(a,1),984(a,1,1))]. 990 K(T(x,y),y) * x = T(x,y). [hyper(23,a,901,a,b,985,a),flip(a)]. 991 K(x,x \ y) * T(y / x,x) = y / x. [para(84(a,1),985(a,1,1,2))]. 992 K(T(x,y),y) = x \ T(x,y). [para(976(a,1),565(a,1))]. 993 x * K(T(x,y),y) = T(x,y). [para(992(a,2),20(a,1,2))]. 994 (x / y) \ T(x / y,y) = K(y \ x,y). [para(84(a,1),992(a,1,1)),flip(a)]. 995 K(T(x \ 1,y),y) = x * T(x \ 1,y). [para(992(a,2),330(a,1))]. 997 (x / y) * K(T(x / y,y),y) = y \ x. [para(993(a,2),84(a,1))]. 998 T(x,y) * (K(y,T(x,y)) * z) = x * z. [para(987(a,1),20(a,1,2))]. 999 K(x,T(y,x)) * (y \ z) = T(y,x) \ z. [para(20(a,1),987(a,1,2)),flip(a)]. 1000 (x \ y) * K(x,x \ y) = y / x. [para(84(a,1),989(a,1,2,2))]. 1001 (x \ y) * K(x,x * y) = y / x. [para(489(a,1),1000(a,1,2))]. 1002 (x \ y) \ (y / x) = K(x,x * y). [hyper(23,a,20,a,b,1001,a),flip(a)]. 1003 K(x,x * (x * y)) = y \ ((x * y) / x). [para(19(a,1),1002(a,1,1)),flip(a)]. 1004 K(x,x * y) * T(y / x,x) = y / x. [para(489(a,1),991(a,1,1))]. 1005 (x / y) \ T(x / y,y) = K(y * x,y). [para(994(a,2),495(a,1))]. 1006 (x / y) * K(y \ x,y) = y \ x. [para(84(a,1),997(a,1,2,1))]. 1007 (x / y) * K(y * x,y) = y \ x. [para(495(a,1),1006(a,1,2))]. 1008 (x / y) * (x \ y) = K(x * y,x). [hyper(23,a,359,a,b,1007,a),flip(a)]. 1010 (x \ y) * (x / y) = K(x * y,x). [para(1008(a,1),368(a,1)),flip(a)]. 1012 L(x,y,(z \ u) * K(z * u,z)) = L(x,y,z / u). [para(1010(a,1),774(a,1,3,2))]. 1013 K(x,y) = y \ ((x * y) / x). [para(1003(a,1),490(a,1)),flip(a)]. 1014 (x * y) / x = y * K(x,y). [para(1013(a,2),20(a,1,2)),flip(a)]. 1015 x * (y / (y * x)) = K(y,x) \ 1. [para(1013(a,2),502(a,1,1)),flip(a)]. 1016 K(x,y) = ((x * y) / x) / y. [para(1013(a,2),558(a,2)),flip(a)]. 1017 ((x * y) / x) * (y \ z) = K(x,y) * z. [para(1013(a,2),860(a,1,1)),flip(a)]. 1018 (x * K(y,x)) * y = y * x. [para(1014(a,1),22(a,1,1))]. 1019 x / (x / y) = y * K(x / y,y). [para(22(a,1),1014(a,1,1))]. 1020 T(x * K(y,x),y) = x. [para(1014(a,1),104(a,1,1))]. 1021 L(x,y * K(z,y),y) = x. [para(1014(a,1),237(a,1,2))]. 1022 a(x / (x * y),z,u) = a(y * K(x,y),z,u). [para(1014(a,1),612(a,1,1)),flip(a)]. 1023 T(T(x * K(y,x),z),y) = T(x,z). [para(1020(a,1),42(a,1,1)),flip(a)]. 1024 T(x * K(y,x),z) * y = y * T(x,z). [para(1020(a,1),108(a,1,2,1)),flip(a)]. 1025 x / L(y,x * K(y,x),y) = y \ (x * K(y,x)). [para(1020(a,1),441(a,1,1))]. 1026 L(x,K(y,z),z) = x. [para(1021(a,1),303(a,1))]. 1027 (x * K(y,x)) \ z = K(y,x) \ (x \ z). [para(1021(a,1),270(a,1))]. 1028 (x * K(y,x)) * z = x * (K(y,x) * z). [para(1026(a,1),74(a,1,2))]. 1029 L(x,K(y,z),y) = x. [para(1026(a,1),921(a,1)),flip(a)]. 1030 (x * K(x,y)) * z = x * (K(x,y) * z). [para(1029(a,1),74(a,1,2))]. 1031 x \ (K(x,y) * z) = (x \ K(x,y)) * z. [para(1029(a,1),798(a,1,2)),flip(a)]. 1032 (x * K(y,x)) \ 1 = K(x,y) / x. [para(1029(a,1),947(a,1,1)),flip(a)]. 1033 (x * y) / x = K(x,y) * y. [para(1016(a,2),22(a,1,1)),flip(a)]. 1035 (x * K(y,x)) / x = K(y,x). [para(1014(a,1),1016(a,2,1)),flip(a)]. 1036 K(x,y) * y = y * K(x,y). [para(1033(a,1),1014(a,1))]. 1037 T(K(x,y),y) = K(x,y). [para(1035(a,1),104(a,1,1))]. 1038 T(x,K(y,x)) = x. [hyper(39,a,1037,a)]. 1040 T(x,y) * K(z,x) = K(z,x) * T(x,y). [para(1038(a,1),108(a,1,2,1)),flip(a)]. 1041 K(x,y) = x * (y / (y * x)). [para(1015(a,2),897(a,1)),flip(a)]. 1042 x \ K(x,y) = y / (y * x). [hyper(23,a,20,a,b,1041,a(flip)),flip(a)]. 1043 K(x,y) = (y / (y * x)) * x. [para(1041(a,2),362(a,2)),flip(a)]. 1044 K(x,y) / x = y / (y * x). [para(1041(a,2),363(a,1,1))]. 1045 x * ((y / (y * x)) * z) = K(x,y) * z. [para(1041(a,2),451(a,1,1)),flip(a)]. 1046 T(x,K(x,y)) = x. [para(1041(a,2),605(a,1,2))]. 1047 ((x * y) / x) * (y \ z) = K(y,x) \ z. [para(1041(a,2),606(a,1,1)),flip(a)]. 1048 T(x \ 1,K(x,y)) = x \ 1. [para(1041(a,2),834(a,1,2))]. 1049 (x / (x * y)) * (y * z) = K(y,x) * z. [para(1041(a,2),841(a,1,1)),flip(a)]. 1050 K(x,y) * x = x * K(x,y). [para(1046(a,1),82(a,1,2))]. 1051 T(x,T(y,x) \ y) = x. [para(983(a,1),1046(a,1,2))]. 1052 (T(x,y) \ x) * y = y * (T(x,y) \ x). [para(1051(a,1),82(a,1,2))]. 1053 K(x,y) = ((y * x) / y) \ x. [para(1043(a,2),358(a,2)),flip(a)]. 1054 K(x,y) / x = x \ K(x,y). [para(1044(a,2),1042(a,2)),flip(a)]. 1055 K(x,y) * (x \ 1) = x \ K(x,y). [para(1048(a,1),327(a,1,2))]. 1056 (x * K(y,x)) \ 1 = x \ K(x,y). [para(1032(a,2),1054(a,1))]. 1057 (x \ 1) / (x \ K(x,y)) = K(y,x). [para(1055(a,1),902(a,1,2))]. 1058 (x * K(y,x)) \ z = (x \ K(x,y)) * z. [para(1056(a,1),318(a,1,1)),flip(a)]. 1059 K(x,y) * (y * z) = ((x * y) / x) * z. [para(19(a,1),1017(a,1,2)),flip(a)]. 1060 T(x,y) * K(z,T(x,y)) = T(x * K(z,x),y). [hyper(24,a,1018,a,b,1024,a),flip(a)]. 1061 T(x * K(x \ y,x),y) = L(x,x \ y,x). [hyper(24,a,221,a,b,1024,a)]. 1063 (x * K(y,x)) \ z = K(x,y) * (x \ z). [para(1027(a,2),900(a,1))]. 1064 ((x * y) / x) * z = y * (K(x,y) * z). [para(1014(a,2),1028(a,1,1))]. 1065 x \ (K(x,y) * z) = (y / (y * x)) * z. [para(1042(a,1),1031(a,2,1))]. 1066 K(x,y) \ (x * z) = ((y * x) / y) * z. [para(19(a,1),1047(a,1,2)),flip(a)]. 1067 K(x,y) * (x \ z) = (y / (y * x)) * z. [para(20(a,1),1049(a,1,2)),flip(a)]. 1068 K(x,y) * (x * z) = x * (K(x,y) * z). [para(1049(a,1),1045(a,1,2)),flip(a)]. 1069 x * (T(y,x) \ y) = T(x,T(y,x)). [para(1052(a,1),826(a,1))]. 1070 x * K(x,T(y,x)) = T(x,T(y,x)). [para(983(a,2),1069(a,1,2))]. 1071 x / (K(y,z) * (y \ x)) = y * K(z,y). [para(1063(a,1),65(a,1,2))]. 1072 (x \ K(x,y)) * z = K(x,y) * (x \ z). [para(1063(a,1),1058(a,1)),flip(a)]. 1073 K(x,y) * (y * z) = y * (K(x,y) * z). [para(1064(a,1),1059(a,2))]. 1074 K(x,y) \ (x * z) = (K(y,x) * x) * z. [para(1033(a,1),1066(a,2,1))]. 1075 K(x,y) * (x \ (y * x)) = y. [para(1067(a,2),22(a,1))]. 1076 x \ (K(x,y) * z) = K(x,y) * (x \ z). [para(1067(a,2),1065(a,2))]. 1077 K(x,y) * T(y,x) = y. [para(36(a,2),1075(a,1,2))]. 1078 K(x,y / x) = K(x,x * y). [hyper(24,a,1004,a,b,1077,a)]. 1079 K(x,T(y,x)) = K(x,y). [hyper(24,a,985,a,b,1077,a),flip(a)]. 1080 K(x,y) = T(y,x) \ y. [hyper(24,a,298,a,b,1077,a)]. 1081 T(x,y) = K(x,y) * x. [hyper(23,a,901,a,b,1077,a)]. 1082 K(x,T(y,z)) * T(T(y,x),z) = T(y,z). [para(42(a,1),1077(a,1,2))]. 1083 K(x,R(y,z,u)) * R(T(y,x),z,u) = R(y,z,u). [para(46(a,2),1077(a,1,2))]. 1084 L(x \ y,x,K(z,y)) = (K(z,y) \ x) \ T(y,z). [para(1077(a,1),267(a,1,1,2))]. 1085 L(x,y,K(z,u) * u) = L(x,y,T(u,z)). [para(1077(a,1),774(a,1,3,2))]. 1086 K(x,y) = T(x,y) / x. [para(1077(a,1),902(a,1,2)),flip(a)]. 1087 (x * y) * T(y,x) = (y * x) * y. [para(1077(a,1),911(a,1,2)),flip(a)]. 1088 T(x,y) * T(x,y) = x * T(T(x,y),y). [para(1077(a,1),998(a,1,2))]. 1089 T(x,y) * K(y,x) = x. [para(1077(a,1),1040(a,2))]. 1090 (x / (x * y)) * T(x,y) = y \ x. [para(1077(a,1),1065(a,1,2)),flip(a)]. 1091 K(x,T(T(y,x),z)) = K(x,T(y,z)). [para(42(a,1),1079(a,1,2))]. 1092 K(x,x * (y * x)) = K(x,y). [para(1079(a,1),491(a,2))]. 1093 T(x,y) \ (x * z) = K(y,x) * z. [para(1079(a,1),987(a,2,1))]. 1094 T(x,y) * (K(y,x) * z) = x * z. [para(1079(a,1),998(a,1,2,1))]. 1095 K(x,y) * (y \ z) = T(y,x) \ z. [para(1079(a,1),999(a,1,1))]. 1096 T(x,T(y,x)) = x * K(x,y). [para(1079(a,1),1070(a,1,2)),flip(a)]. 1097 T(T(x,y),z) \ T(x,z) = K(y,T(x,z)). [para(42(a,1),1080(a,2,1)),flip(a)]. 1098 K(x,y) * (T(y,x) * z) = y * z. [para(1080(a,2),575(a,1,1))]. 1099 x * (T(x,y) \ z) = K(y,x) * z. [para(1080(a,2),576(a,1,1)),flip(a)]. 1100 K(x,y) = y * (T(y,x) \ 1). [para(1080(a,2),578(a,2)),flip(a)]. 1101 T(x,y) \ 1 = x \ K(y,x). [para(1080(a,2),582(a,1,2)),flip(a)]. 1102 (x * y) / (T(x,z) * y) = K(z,x). [para(1080(a,2),577(a,2))]. 1103 ((x * y) * y) \ ((y * x) * y) = K(y,(y * x) * y). [para(758(a,1),1080(a,2,1)),flip(a)]. 1104 T(x,y) = (x * x) / (x * K(y,x)). [para(1080(a,2),831(a,1,2,2)),flip(a)]. 1105 K(T(x,y),y) = K(x,y). [hyper(24,a,990,a,b,1081,a(flip)),flip(a)]. 1106 (x * T(y,z)) / L(y,K(y,z),x) = x * K(y,z). [para(1081(a,2),99(a,1,1,2))]. 1107 T(x,y) = x * K(x,y). [para(1081(a,2),1050(a,1))]. 1108 K(x,y) = x \ T(x,y). [para(1086(a,2),572(a,1))]. 1110 K(R(T(x,y),z,u),y) = K(R(x,z,u),y). [para(46(a,2),1105(a,1,1))]. 1111 x * T(x \ 1,y) = K(x \ 1,y). [para(1105(a,1),995(a,1)),flip(a)]. 1112 T(x * K(y,x),T(y,x)) = x. [para(1105(a,1),1020(a,1,1,2))]. 1113 K(x,y) * T(x,y) = T(T(x,y),y). [para(1105(a,1),1081(a,2,1)),flip(a)]. 1114 K(x,y) * T(K(y,x),z) = K(K(y,x),z). [hyper(23,a,901,a,b,1107,a(flip)),flip(a)]. 1115 (x * y) \ (x * T(y,z)) = L(K(y,z),y,x). [para(1107(a,2),32(a,2,2,2)),flip(a)]. 1116 x * (y * K(y,x)) = y * x. [para(1107(a,1),82(a,1,2))]. 1117 (x * y) * L(K(y,z),y,x) = x * T(y,z). [para(1107(a,2),74(a,2,2))]. 1118 (x \ y) * K(x * y,x) = T(x \ y,x). [para(495(a,1),1107(a,2,2)),flip(a)]. 1119 L(x,y,z * T(z,u)) = L(x,y,K(z,u)). [para(1107(a,2),774(a,1,3,2))]. 1120 x * (K(x,y) * z) = T(x,y) * z. [para(1107(a,2),1030(a,1,1)),flip(a)]. 1121 T(x,y) * K(x,y) = T(T(x,y),y). [para(1105(a,1),1107(a,2,2)),flip(a)]. 1122 T(x,y) \ T(T(x,z),y) = K(T(x,y),z). [para(42(a,1),1108(a,2,2)),flip(a)]. 1123 L(x,y,z) \ L(T(x,u),y,z) = K(L(x,y,z),u). [para(44(a,2),1108(a,2,2)),flip(a)]. 1124 x \ ((x \ y) \ y) = K(x,x * y). [para(249(a,1),1108(a,2,2)),flip(a)]. 1125 T(x,y) * (x \ z) = K(x,y) * z. [para(1108(a,2),562(a,1,1)),flip(a)]. 1126 K(x \ 1,x * y) = x * ((x * y) \ y). [para(1108(a,2),707(a,1))]. 1127 x \ (T(x,y) * z) = K(x,y) * z. [para(1108(a,2),733(a,2,1))]. 1128 K(x / y,y) = K(y * x,y). [para(1108(a,2),1005(a,1))]. 1130 K(x,(y * (x \ 1)) / x) = K(x,T(y,x \ 1)). [para(347(a,1),1078(a,2,2))]. 1131 T(x,T(y,x)) = T(x,y). [para(1096(a,2),1107(a,2)),flip(a)]. 1132 T(T(x,y),T(z,x)) = T(T(x,z),y). [para(1131(a,1),42(a,1,1)),flip(a)]. 1133 T(x,y / x) = T(x,x \ y). [para(84(a,1),1131(a,1,2)),flip(a)]. 1134 (x * y) / T(y,x) = T(x,y). [para(1131(a,1),117(a,1,2))]. 1135 L(T(x,y),T(y,x),x) = T(x,x * T(y,x)). [para(1131(a,1),203(a,1,1))]. 1136 T(x,x * (y * x)) = T(x,y). [para(1131(a,1),247(a,2))]. 1137 T(x,y) / (T(y,x) \ x) = y. [para(1131(a,1),829(a,1,1))]. 1138 T(x,y) \ y = x \ T(y,x). [para(1131(a,1),830(a,1,2)),flip(a)]. 1139 T(x,y * K(x,y)) = T(x,y). [para(1020(a,1),1131(a,1,2)),flip(a)]. 1140 K(x,y) * K(z,K(y,x)) = T(K(y,x),z) \ 1. [hyper(23,a,901,a,b,1100,a(flip)),flip(a)]. 1141 L(T(x,y),y * K(x,y),T(x,y)) = (T(x,y) \ (y * K(x,y))) \ y. [para(1112(a,1),440(a,1,2)),flip(a)]. 1143 K((x * (y \ 1)) / y,y) = K(T(x,y \ 1),y). [para(347(a,1),1128(a,2,1))]. 1144 x / (x / y) = y * K(y * x,y). [para(1128(a,1),1019(a,2,2))]. 1145 T(x,y / x) = T(x,x * y). [para(1133(a,2),246(a,1))]. 1146 T(x,y) * T(y,x) = x * y. [para(1134(a,1),22(a,1,1))]. 1147 x / (y \ T(x,y)) = T(y,x). [para(1138(a,1),65(a,1,2))]. 1148 (T(x,y) \ y) * K(x,x * T(y,x)) = T(y,x) / x. [para(1138(a,2),1001(a,1,1))]. 1149 T(x,(y * (x \ 1)) / x) = T(x,T(y,x \ 1)). [para(347(a,1),1145(a,2,2))]. 1150 (T(x,y) * (T(y,x) * z)) \ ((x * y) * z) = a(T(x,y),T(y,x),z). [para(1146(a,1),28(a,2,2,1)),flip(a)]. 1151 (x * y) \ (T(x,y) * (T(y,x) * z)) = L(z,T(y,x),T(x,y)). [para(1146(a,1),32(a,2,1)),flip(a)]. 1152 T(T(x,y),x \ T(y,x)) = (x \ T(y,x)) \ y. [para(1147(a,1),84(a,1,1))]. 1153 R(x,y,x) * (y * x) = (y * x) * T(x,y). [para(1087(a,2),79(a,2))]. 1154 T(x,y) * ((y * x) / ((x * y) * x)) = K(T(x,y),y * x). [para(1087(a,1),1041(a,2,2,2)),flip(a)]. 1155 K(x,T(y,K(z,T(y,x)))) = K(x,T(y,x)). [para(1038(a,1),1091(a,1,2)),flip(a)]. 1156 L(x,y * K(z,y),u) = L(x,T(y,z),u). [para(1094(a,1),937(a,1,2))]. 1157 T(x,y) * (y * x) = x * (x * y). [para(974(a,1),1094(a,1,2))]. 1158 K(x,y) * (T(x,y) \ z) = x \ z. [hyper(23,a,901,a,b,1095,a),flip(a)]. 1159 K(x,y) * (y \ x) = y \ T(x,y). [para(1095(a,2),1138(a,1))]. 1160 K(x,y) * (x * z) = T(x,y) * z. [hyper(23,a,901,a,b,1098,a),flip(a)]. 1162 R(K(x,y),T(y,x) * z,u) \ 1 = ((T(y,x) * z) * u) / ((y * z) * u). [para(1098(a,1),344(a,1,2,1)),flip(a)]. 1163 x \ (K(y,x) * z) = T(x,y) \ z. [hyper(23,a,20,a,b,1099,a),flip(a)]. 1164 (x * y) * T((x * y) \ x,z) = x * K(y \ 1,z). [para(1111(a,1),762(a,2,2))]. 1165 x \ (y * T(y \ x,z)) = K((x \ y) \ 1,z). [para(1111(a,1),817(a,1)),flip(a)]. 1166 (x * ((K(x,y) * z) * u)) \ ((T(x,y) * z) * u) = a(x,K(x,y) * z,u). [para(1120(a,1),28(a,2,2,1)),flip(a)]. 1168 T(x,y) * (T(y,x) * z) = x * (y * z). [para(1098(a,1),1120(a,1,2)),flip(a)]. 1169 L(x,y,z * ((z \ u) * u)) = L(x,y,K(z,z * u)). [para(1124(a,1),865(a,1,3)),flip(a)]. 1170 T(x,y) \ ((x \ T(y,x)) \ y) = K(T(x,y),T(x,y) * y). [para(1138(a,1),1124(a,1,2,1))]. 1171 T(x,y) \ (K(x,y) * z) = x \ z. [hyper(23,a,20,a,b,1125,a),flip(a)]. 1172 K(x,y) * (z * x) = T(x,y) * T(z,x). [para(36(a,2),1125(a,1,2)),flip(a)]. 1173 T(x / y,z) * y = K(x / y,z) * x. [para(66(a,1),1125(a,1,2))]. 1174 T(x,y) * (z / (z * x)) = K(x,y) * K(x,z). [para(1042(a,1),1125(a,1,2))]. 1175 T(x,y) * (T(x,z) \ 1) = K(x,y) * K(z,x). [para(1101(a,2),1125(a,1,2))]. 1176 x \ T(T(x,y),y) = K(x,y) * K(x,y). [para(1121(a,1),1127(a,1,2))]. 1177 T(T(x,x * y),T(z,x)) = T(T(x,z),x \ y). [para(246(a,1),1132(a,1,1))]. 1178 (x / (x / y)) * z = y * (K(y * x,y) * z). [para(1144(a,2),1028(a,1,1))]. 1179 ((x * y) * T(y,x)) \ (y * (y * x)) = K(T(y,x),x * y). [para(1157(a,1),30(a,2,2)),flip(a)]. 1180 (x * (x * y)) \ (T(x,y) * ((y * x) * z)) = L(z,y * x,T(x,y)). [para(1157(a,1),32(a,2,1)),flip(a)]. 1181 K(x,y) * (T(x,y) \ T(x,z)) = K(x,z). [para(1158(a,2),1108(a,2)),flip(a)]. 1182 K(T(x,y \ 1),y) * (x * (y \ 1)) = y \ T(T(x,y \ 1),y). [para(326(a,1),1159(a,1,2))]. 1183 ((T(x,y) * z) * u) / ((x * z) * u) = R(K(x,y),x * z,u). [para(1160(a,1),34(a,2,1,1)),flip(a)]. 1184 (x * y) \ (T(x,z) * y) = T(K(x,z),x * y). [para(1160(a,1),36(a,2,2)),flip(a)]. 1185 L(x,T(y,z) * z,u) = L(x,z * y,u). [para(1160(a,1),943(a,1,2))]. 1186 T(x,y) \ (T(y,x) \ z) = x \ (y \ z). [para(1158(a,1),1163(a,1,2)),flip(a)]. 1187 T(x,y) \ (y * K(x,y)) = x \ y. [para(1036(a,1),1171(a,1,2))]. 1188 x \ (y * K(x,y)) = K(x,y) * (x \ y). [para(1187(a,1),1158(a,1,2)),flip(a)]. 1189 (K(x,y) * (x \ z)) \ ((x \ K(x,y)) * (z * u)) = L(u,z,x \ K(x,y)). [para(1072(a,1),32(a,2,1)),flip(a)]. 1190 (K(x,y) * z) \ (y * (K(x,y) * z)) = L(T(y,z),z,K(x,y)). [para(1073(a,1),106(a,1,2))]. 1191 K(x,y) \ (x * z) = (K(x,y) \ x) * z. [para(900(a,2),1074(a,2,1))]. 1192 L(x,y,(z * u) / z) = L(x,y,T(u,z)). [para(1033(a,2),1085(a,1,3))]. 1193 T(x,y) * K(y,T(x,z)) = K(z,T(x,y)) * T(x,z). [para(1097(a,1),1099(a,1,2))]. 1194 L(x,y,(z / (u * u)) * (u \ (z * (u \ 1)))) = L(x,y,K(z / (u * u),u)). [para(403(a,1),1119(a,1,3,2))]. 1195 (x * T(y,x)) \ (T(y,z) * x) = L(K(T(y,x),z),T(y,x),x). [para(1122(a,1),180(a,1,1)),flip(a)]. 1196 K(x,T(y,K(z,T(y,x)))) = K(x,y). [para(1155(a,2),1079(a,1))]. 1197 K(x,y) * T(T(y,x),K(z,T(y,x))) = T(y,K(z,T(y,x))). [para(1196(a,1),1082(a,1,1))]. 1198 (x * (y * z)) / (T(y,x) * z) = T(x,y). [hyper(24,a,22,a,b,1168,a),flip(a)]. 1199 (x \ y) * (T(x,y / x) * z) = (y / x) * (x * z). [para(84(a,1),1168(a,1,1))]. 1200 (T(x / y,z) * y) / x = K(x / y,z). [hyper(24,a,22,a,b,1173,a(flip)),flip(a)]. 1201 K(x / y,z) * x = y * T(y \ x,z). [para(1173(a,1),139(a,1))]. 1202 (R(x,y,z) * (K(x,u) * K(x,u))) / T(T(x,u),u) = x \ R(x,y,z). [para(1176(a,1),536(a,1,1,2))]. 1203 L(x,y,K(y,z)) = x. [hyper(23,a,798,a,b,1191,a(flip)),flip(a)]. 1204 L(x,y,T(z,y) \ z) = x. [para(983(a,1),1203(a,1,3))]. 1205 L(x,y,T(z,y) * z) = x. [para(1204(a,1),776(a,1)),flip(a)]. 1206 L(x,y,z * T(z,y)) = x. [para(116(a,1),1205(a,1,3))]. 1207 ((x * T(x,y)) * y) \ ((x * T(x,y)) * (y * z)) = z. [para(1206(a,1),32(a,1)),flip(a)]. 1208 L(x,y,T(z * u,z) / z) = L(x,y,T((z \ u) * z,z)). [para(138(a,1),1192(a,1,3,1))]. 1209 (x * (R(y,z,u) * w)) / (R(T(y,x),z,u) * w) = T(x,R(y,z,u)). [para(46(a,2),1198(a,1,2,1))]. 1210 (x * (y * (a(T(y,x),z,z) * u))) / (R(T(y,x),z,z) * u) = T(x,y). [para(966(a,1),1198(a,1,2))]. 1211 (x * T(x \ y,z)) / y = K(y / x,z). [para(139(a,1),1200(a,1,1))]. 1212 K((x * y) / x,z) * (x * y) = x * T(y,z). [para(19(a,1),1201(a,2,2,1))]. 1213 x \ (y * T(y \ x,z)) = T(K(x / y,z),x). [para(1201(a,1),36(a,2,2)),flip(a)]. 1214 ((x * y) * T((x * y) \ ((z * x) * y),u)) / ((z * x) * y) = K(R(z,x,y),u). [para(34(a,2),1211(a,2,1))]. 1215 T(x * K(x * y,x),y) = L(x,x \ y,x). [para(495(a,1),1061(a,1,1,2))]. 1216 L(T(x,y),T(y,x),x) = T(x,y * x). [para(82(a,1),1135(a,2,2))]. 1217 (x * y) * T(y,y * (x * y)) = R(y,x,y) * (x * y). [para(1136(a,2),1153(a,2,2)),flip(a)]. 1218 T(x * K(x * y,x),y) = L(x,x * y,x). [para(1215(a,2),312(a,1))]. 1219 T(x / (x / y),x) = L(y,y * x,y). [para(1144(a,2),1218(a,1,1))]. 1220 K(x,T(y,x \ 1)) = K(x,y / (x * x)). [para(401(a,1),1130(a,1,2)),flip(a)]. 1221 K(T(x,y \ 1),y) = K(x / (y * y),y). [para(401(a,1),1143(a,1,1)),flip(a)]. 1222 T(x,T(y,x \ 1)) = T(x,y / (x * x)). [para(401(a,1),1149(a,1,2)),flip(a)]. 1223 K(((x * y) \ x) \ 1,z) = (x * y) \ (x * T(y,z)). [para(19(a,1),1165(a,1,2,2,1)),flip(a)]. 1224 T(x,y) \ T(x,z) = K(x,z) * K(y,x). [para(1175(a,1),581(a,1)),flip(a)]. 1225 K(x,y) * (K(x,z) * K(y,x)) = K(x,z). [para(1224(a,1),1181(a,1,2))]. 1226 K(x,y) * K(z,x) = K(z,x) * K(x,y). [hyper(23,a,901,a,b,1225,a)]. 1229 T(T(x,y),x \ z) = T(T(x,y),x * z). [para(1177(a,1),1132(a,1))]. 1230 T(T(x,y),x * T(y,x)) = (x \ T(y,x)) \ y. [para(1229(a,1),1152(a,1))]. 1231 (x / (x / y)) * x = y * ((y \ x) * y). [para(981(a,1),1178(a,2,2))]. 1232 T(x * y,x) = (y / (y / x)) * y. [para(1231(a,2),138(a,1)),flip(a)]. 1233 T(x * y,x) / y = y / (y / x). [hyper(24,a,22,a,b,1232,a(flip)),flip(a)]. 1234 ((x / y) / x) * T(y * x,y) = x. [hyper(23,a,359,a,b,1232,a(flip)),flip(a)]. 1236 x \ T(x * y,y) = x / (x / y). [para(1233(a,1),754(a,1)),flip(a)]. 1237 x / T(y * x,y) = (x / y) / x. [hyper(24,a,22,a,b,1234,a),flip(a)]. 1238 T(x * y,y) = x * (x / (x / y)). [para(1236(a,1),20(a,1,2)),flip(a)]. 1239 T(x * (y \ x),y \ x) = x * (x / y). [para(65(a,1),1238(a,2,2,2))]. 1240 T(K(x / y,z),x) = K((x \ y) \ 1,z). [para(1213(a,1),1165(a,1))]. 1241 K((x \ (y \ x)) \ 1,z) = T(K(y,z),x). [para(65(a,1),1240(a,1,1,1)),flip(a)]. 1242 K((T(x,y) \ (T(y,x) \ x)) \ 1,z) = T(K(y,z),T(x,y)). [para(1137(a,1),1240(a,1,1,1)),flip(a)]. 1243 K(T(x \ 1,y) \ 1,z) = T(K(x,z),y). [para(325(a,2),1241(a,1,1,1))]. 1244 K(T((x \ 1) \ 1,y * y),z) = T(K(x,z),y * y). [para(655(a,1),1243(a,1,1))]. 1245 (x \ T(y,x)) \ y = T(T(x,y),y * x). [para(82(a,1),1230(a,1,2)),flip(a)]. 1246 x / L(y,T(x,y),y) = y \ (x * K(y,x)). [para(1156(a,1),1025(a,1,2))]. 1247 x / L(y,T(x,y),y) = K(y,x) * (y \ x). [para(1246(a,2),1188(a,1))]. 1248 L(x \ y,x,K(z,y)) = (K(y,z) * x) \ T(y,z). [para(900(a,1),1084(a,2,1))]. 1249 R(K(x,y),T(x,y) * z,u) \ 1 = R(K(y,x),x * z,u). [para(1098(a,1),906(a,1,2)),flip(a)]. 1250 L(x,y * (y * (z * y)),u) = L(x,z \ (y \ 1),u). [para(51(a,1),929(a,1,2))]. 1251 ((x * y) \ K(x,y)) \ z = K(y,x) * ((x * y) * z). [para(933(a,2),900(a,1))]. 1252 (x * a(x,y,z)) * u = x * (a(x,y,z) * u). [para(948(a,1),946(a,1))]. 1253 a(x,y,z) * (x * u) = x * (a(x,y,z) * u). [para(1252(a,1),772(a,1)),flip(a)]. 1254 x * (a(x,y,z) * (x \ u)) = a(x,y,z) * u. [para(20(a,1),1253(a,1,2)),flip(a)]. 1255 L(x,y * (z \ y),u) = L(x,T(z,y),u). [para(20(a,1),953(a,1,2,1))]. 1256 L(x,T(y \ 1,z),u) = L(x,T(y,z),u). [para(1255(a,1),883(a,2))]. 1257 K(x,y) / (y * x) = (y * x) \ K(x,y). [para(972(a,1),971(a,1,2))]. 1258 L(x,y,T(z \ u,z)) = L(x,y,z / u). [para(1118(a,1),1012(a,1,3))]. 1259 L(x,y,T(z * u,z)) = L(x,y,z / u). [para(1258(a,1),818(a,1)),flip(a)]. 1260 (T(x,y) \ y) * K(x,y * x) = T(y,x) / x. [para(82(a,1),1148(a,1,2,2))]. 1261 L(x,y,K(z,z * u)) = L(x,y,a(z,u,u)). [para(1169(a,1),837(a,1))]. 1262 L(x,y,K(z * u,z)) = L(x,y,a(z,u,u)). [para(1261(a,1),909(a,1)),flip(a)]. 1263 L(x,y,a(z,u * z,u * z)) = L(x,y,K(z,u)). [para(1092(a,1),1261(a,1,3)),flip(a)]. 1264 K(x,T(y,z)) * T(T(y,x),K(x,T(y,z))) = K(z,T(y,x)) * T(y,z). [para(1193(a,1),82(a,2))]. 1265 (x \ y) * (T(x,x * y) * z) = (y / x) * (x * z). [para(1145(a,1),1199(a,1,2,1))]. 1266 (x * (T(x,y) * y)) \ ((x * T(x,y)) * (y * z)) = z. [para(722(a,1),1207(a,1,1))]. 1267 L(K(x,y),x,z) = K(((z * x) \ z) \ 1,y). [para(1223(a,2),1115(a,1)),flip(a)]. 1268 K(L(x \ 1,x,y) \ 1,z) = L(K(x,z),x,y). [para(142(a,2),1267(a,2,1,1)),flip(a)]. 1269 K(T(x,y * y),z) = T(K(x,z),y * y). [para(156(a,1),1244(a,1,1,1))]. 1270 K(T(x,y * y),z) \ 1 = T(K(x,z) \ 1,y * y). [para(1269(a,2),655(a,1,1))]. 1271 L(x,y \ (z \ 1),u) = L(x,y * z,u). [para(1250(a,1),875(a,1))]. 1273 L(x,y * (z \ 1),u) = L(x,y * z,u). [para(1271(a,1),876(a,1)),flip(a)]. 1274 (x \ y) * ((y / x) * (x * z)) = ((x \ y) * y) * z. [para(1265(a,1),253(a,1,2))]. 1275 (x * (T(x,y) * y)) \ (x * (T(x,y) * (y * z))) = z. [para(722(a,1),1266(a,1,2))]. 1276 T(K(x,y) \ 1,z * z) = K(y,T(x,z * z)). [para(1270(a,1),897(a,1))]. 1277 K(x,T(y,z * z)) = T(K(x,y),z * z). [para(897(a,1),1276(a,1,1)),flip(a)]. 1278 K(T(x,y * y),z) = K(x,T(z,y * y)). [para(1277(a,2),1269(a,2))]. 1279 L(L(x,y,T(z,y)),T(z,y) * y,z) = x. [para(1275(a,1),174(a,1)),flip(a)]. 1280 L(L(x,y,T(z,y)),y * z,z) = x. [para(1279(a,1),1185(a,1)),flip(a)]. 1281 L(L(x,y,T(y \ z,y)),z,y \ z) = x. [para(20(a,1),1280(a,1,2))]. 1282 L(x,y * (z * y),y) = L(x,z,T(y,z)). [para(1280(a,1),303(a,1,1))]. 1283 L(x,T(y,z) * z,T(y,z)) = L(x,z * y,y). [para(308(a,1),1280(a,1,1)),flip(a)]. 1284 L(x,T(y,z),z) = L(x,y,T(z,y)). [para(1280(a,1),314(a,1,1))]. 1285 L(x,T(y,y * z),y * z) = L(x,y,y / z). [para(1284(a,2),1259(a,1))]. 1286 L(L(x,y,y / z),z,y \ z) = x. [para(1258(a,1),1281(a,1,1))]. 1287 L(L(x,y,y / z),z,y * z) = x. [para(1286(a,1),776(a,1)),flip(a)]. 1288 L(x,y,z / y) = L(x,y,z * y). [para(304(a,1),1287(a,1,1)),flip(a)]. 1289 L(x \ (x / y),x,y * x) = y \ 1. [para(445(a,1),1287(a,1,1))]. 1290 L(x,y,y / z) = L(x,y,z * y). [para(806(a,1),1287(a,1,1)),flip(a)]. 1291 L(x,y,(z * y) * y) = L(x,y,z). [para(21(a,1),1288(a,1,3)),flip(a)]. 1292 L(x \ 1,x,y * x) = y \ (y / x). [para(1288(a,1),144(a,1))]. 1293 L(x,x,y * x) = y \ (y / (x \ 1)). [para(1288(a,1),432(a,1))]. 1294 x * L(y,z,x * z) = (x / z) * (z * y). [para(1288(a,1),173(a,1,2))]. 1295 (x \ 1) \ L(T(y \ (y / x),z),y,x * y) = K(L(y \ (y / x),y,x * y),z). [para(1289(a,1),1123(a,1,1))]. 1296 ((x * y) * y) \ (x * y) = x \ (x / y). [para(1292(a,1),142(a,1)),flip(a)]. 1297 L(x,y \ 1,T(y * z,y \ 1)) = L(x,(y * z) * z,y * z). [para(322(a,1),1282(a,1,2,2)),flip(a)]. 1298 x * K(L(y \ 1,y,x * y) \ 1,z) = (x / y) * (y * K(y,z)). [para(1268(a,2),1294(a,1,2))]. 1299 x \ L(x,x * y,y) = a(T(y,x),x,x). [para(1283(a,1),452(a,1,2))]. 1300 L(x,y * z,T(z,y)) = L(x,y * z,z). [para(1283(a,1),1185(a,1)),flip(a)]. 1301 T(L(K(x,y),z,K(y,x)),z) = (K(y,x) * z) \ z. [hyper(23,a,82,a,b,910,a(flip)),flip(a)]. 1302 L(x,y * x,x) = R(x,y,x). [hyper(24,a,217,a(flip),b,1217,a(flip)),flip(a)]. 1303 R(x,y / x,x) = L(x,y,x). [para(22(a,1),1302(a,1,2)),flip(a)]. 1304 L(T(x,y),z * x,x) = T(R(x,z,x),y). [para(1302(a,1),44(a,2,1))]. 1305 L(x,y,x) * ((y / x) * x) = (x * (y / x)) * x. [para(1303(a,1),79(a,1,1))]. 1306 L(T(x,y),z * x,x) = R(T(x,y),z,x). [para(1304(a,2),46(a,2)),flip(a)]. 1307 L(x,y,x) * y = (x * (y / x)) * x. [para(22(a,1),1305(a,1,2))]. 1308 T(L(x,y,x) * y,x) = ((y / x) * x) * x. [para(1307(a,2),758(a,1,1))]. 1309 T(L(x,y,x) * y,x) = y * x. [para(22(a,1),1308(a,2,1))]. 1310 (L(x,y,x) * y) * x = x * (y * x). [para(1309(a,1),82(a,1,2)),flip(a)]. 1311 L(R(x,y,x),y,x) = x. [hyper(24,a,184,a,b,1310,a(flip)),flip(a)]. 1312 R(L(x,y,x),y,x) = x. [hyper(24,a,79,a,b,1310,a(flip)),flip(a)]. 1313 R(x,x \ y,x) = L(x,y,x). [para(1311(a,1),302(a,1,1)),flip(a)]. 1314 L(x,x * y,x) = R(x,y,x). [para(1311(a,1),303(a,1,1))]. 1315 R(x,x * y,x) = L(x,y,x). [para(1311(a,1),308(a,1,1)),flip(a)]. 1316 x \ T(y * x,y) = R(y,x,y). [para(1314(a,1),316(a,1)),flip(a)]. 1318 T(x * K(x * y,x),y) = R(x,y,x). [para(1314(a,1),1218(a,2))]. 1319 T(x / (x / y),x) = R(y,x,y). [para(1314(a,1),1219(a,2))]. 1320 L(x,y,x) \ x = x \ R(x,y,x). [para(1315(a,1),622(a,1,1))]. 1321 x * R(y,x,y) = T(y * x,y). [para(1316(a,1),20(a,1,2))]. 1322 T(x,R(y,x,y)) = T(x,x / (x / y)). [para(1319(a,1),1131(a,1,2))]. 1323 (x / T(y * x,y)) * T(x,R(y,x,y)) = R(y,x,y) \ x. [para(1321(a,1),1090(a,1,1,2))]. 1324 T(x,y) * K(x * y,T(x,y)) = R(x,y,x). [para(1318(a,1),1060(a,2))]. 1325 T(x,y) * K(y * T(x,y),T(x,y)) = R(x,y,x). [para(82(a,2),1324(a,1,2,1))]. 1326 K(x,y) * (K(y,x) / (x * y)) = (x * y) \ 1. [para(907(a,2),912(a,1))]. 1327 K(x,y) * ((x * y) \ K(y,x)) = (x * y) \ 1. [para(1257(a,1),1326(a,1,2))]. 1328 (x * y) \ K(x,y) = (y * x) \ 1. [para(1327(a,1),941(a,1)),flip(a)]. 1329 K(x,y) * ((y * x) * z) = ((x * y) \ 1) \ z. [para(1328(a,1),1251(a,1,1)),flip(a)]. 1330 K(x,y) * ((y * x) * z) = (x * y) * z. [para(1329(a,2),330(a,1))]. 1331 ((x * y) * z) / ((y * x) * z) = K(x,y). [hyper(24,a,22,a,b,1330,a),flip(a)]. 1332 R(K(x,y),y * x,z) = K(x,y). [para(1331(a,1),977(a,1)),flip(a)]. 1333 R(K(x,T(y,x)),T(y,x) * x,z) = K(x,y). [para(1332(a,2),1079(a,1))]. 1335 R(K(x,y),T(y,x) * x,z) = K(x,y). [para(1079(a,1),1333(a,1,1))]. 1336 ((T(x,y) * y) * z) / ((K(y,x) * (T(x,y) * y)) * z) = K(y,x) \ 1. [para(1335(a,1),344(a,2,1))]. 1337 (x * L(x \ 1,y,z)) \ u = x \ (L(x \ 1,y,z) \ u). [para(216(a,1),924(a,1,1))]. 1338 L(x,y * (y * (z * (y * u))),w) = L(x,z \ (y \ u),w). [para(51(a,1),928(a,1,2))]. 1339 T(x,y) * (R(x,y,x) \ 1) = K(T(x,y),y * x). [para(344(a,1),1154(a,1,2))]. 1340 R(x,y,x) \ T(x,y) = K(T(x,y),y * x). [para(1339(a,1),548(a,1)),flip(a)]. 1341 T(x,y) \ T(T(x,y),y * x) = K(T(x,y),T(x,y) * y). [para(1245(a,1),1170(a,1,2))]. 1342 (((x * y) * T(y,x)) \ (y * y)) * x = K(T(y,x),x * y). [para(1179(a,1),391(a,1)),flip(a)]. 1343 T(x,K(y,T(x,z))) = K(z,x) * T(x,z). [para(1038(a,1),1197(a,1,2)),flip(a)]. 1345 T(x,K(y,T(x,z))) = x. [para(1343(a,2),1077(a,1))]. 1346 T(T(x,y),K(z,T(x,u))) = T(x,y). [para(1345(a,1),42(a,1,1)),flip(a)]. 1350 L(x,y,T(z * u,z) / z) = L(x,y,R(u,z,z)). [para(1208(a,2),864(a,1))]. 1351 T(K(x,y),T(z,x)) = K((z \ (x \ z)) \ 1,y). [para(1186(a,1),1242(a,1,1,1)),flip(a)]. 1352 T(K(x,y),T(z,x)) = T(K(x,y),z). [para(1351(a,2),1241(a,1))]. 1353 T(x,y) * T(K(y,z),x) = K(y,z) * T(x,y). [para(1352(a,1),82(a,1,2))]. 1354 K(x,y) * (K(y,z) * x) = K(y,z) * T(x,y). [para(1353(a,1),1172(a,2))]. 1355 (K(x,y) * T(z,x)) / L(z,K(x,y),K(z,x)) = K(z,x) * K(x,y). [para(1354(a,1),99(a,1,1))]. 1356 ((x / y) / x) * T(x,R(y,x,y)) = R(y,x,y) \ x. [para(1237(a,1),1323(a,1,1))]. 1357 L(x \ 1,y,z) \ (x \ u) = x \ (L(x \ 1,y,z) \ u). [para(1337(a,1),803(a,1)),flip(a)]. 1358 L(x,y \ (z \ u),w) = L(x,y * (z * u),w). [para(1338(a,1),875(a,1))]. 1360 L(x,y * (z \ u),w) = L(x,y * (z * u),w). [para(1358(a,1),876(a,1)),flip(a)]. 1361 L(x,y * (z * (z * u)),w) = L(x,y * u,w). [para(19(a,1),1360(a,1,2,2)),flip(a)]. 1362 L(x,(y \ z) * (z \ y),u) = L(x,(z \ y) * (y * z),u). [para(384(a,1),1360(a,1,2))]. 1363 L(x,y * R(z,z * u,w),v5) = L(x,y * (R(z,u,w) \ 1),v5). [para(615(a,1),1361(a,1,2,2))]. 1364 K(T(x,y),T(x,y) * y) = K(T(x,y),y * x). [para(1341(a,1),1108(a,2)),flip(a)]. 1365 (((x * y) * x) \ (x * x)) * y = K(T(x,y),y * x). [para(1087(a,1),1342(a,1,1,1))]. 1366 K(T(x,y),y * x) = K(x,x * y). [para(1365(a,1),408(a,1))]. 1367 R(x,y,x) \ T(x,y) = K(x,x * y). [para(1366(a,1),1340(a,2))]. 1368 K(x,x * y) \ T(x,y) = R(x,y,x). [para(1367(a,1),734(a,1,1))]. 1369 K(x * y,x) * T(x,y) = R(x,y,x). [para(1368(a,1),900(a,1)),flip(a)]. 1370 R(x,y,x) / T(x,y) = K(x * y,x). [hyper(24,a,22,a,b,1369,a),flip(a)]. 1371 (x \ (L(x \ 1,x,x / y) \ 1)) * (y \ (y / x)) = x \ 1. [para(1357(a,1),521(a,1,1))]. 1372 R(x,y \ 1,y) \ a(x,y,y) = x \ 1. [para(961(a,2),476(a,1))]. 1374 R(x,y,y) \ a(x,y,y) = x \ 1. [para(717(a,1),1372(a,1,1))]. 1375 (x * y) \ (x * (y * z)) = L(z,T(y,x),T(x,y)). [para(1168(a,1),1151(a,1,2))]. 1376 L(x,T(y,z),T(z,y)) = L(x,y,z). [para(1375(a,1),32(a,2)),flip(a)]. 1377 L(T(x,y),y,K(z,x)) = T(x,K(z,x) * y). [para(1190(a,1),36(a,2)),flip(a)]. 1378 (x \ (L(x \ 1,x,y * x) \ 1)) * (y \ (y / x)) = x \ 1. [para(1290(a,1),1371(a,1,1,2,1))]. 1379 ((x \ y) * z) \ (x \ u) = ((x * y) * z) \ (x * u). [para(794(a,1),201(a,1))]. 1380 (x * ((x \ y) * y)) \ z = ((x * y) * y) \ (x * z). [para(1379(a,1),893(a,2))]. 1381 (x * ((x \ y) * y)) \ y = x \ (x / y). [para(1380(a,2),1296(a,1))]. 1382 x / (y \ (y / x)) = y * ((y \ x) * x). [para(1381(a,1),65(a,1,2))]. 1383 (x \ (x / y)) \ y = x * ((x \ y) * y). [para(1382(a,1),872(a,1)),flip(a)]. 1384 x * L(x,y * x,y) = (y \ (y / x)) \ x. [para(1383(a,2),435(a,2))]. 1385 (x * L(x,y * x,y)) / x = (y \ (y / x)) \ 1. [para(1384(a,2),320(a,1,1))]. 1386 L(x,y * x,y) = (y \ (y / x)) \ 1. [para(1385(a,1),218(a,1)),flip(a)]. 1387 x \ ((y \ (y / x)) \ 1) = a(y,x,x). [para(1386(a,1),452(a,1,2))]. 1388 (x \ (x / y)) \ 1 = y * a(x,y,y). [para(1386(a,1),453(a,1))]. 1389 (x \ 1) \ (L(x,x,y * x) \ 1) = a(y,x \ 1,x \ 1). [para(1293(a,2),1387(a,1,2,1))]. 1390 (x \ (x / y)) \ z = (y * a(x,y,y)) * z. [para(1388(a,1),318(a,1,1)),flip(a)]. 1391 K(x,(x * x) / (y \ (y / z))) = K(x,z * a(y,z,z)). [para(1388(a,1),492(a,2,2))]. 1392 L(x \ 1,x,y * x) \ 1 = x * a(y,x,x). [para(1292(a,2),1388(a,1,1))]. 1393 (x \ (x * a(y,x,x))) * (y \ (y / x)) = x \ 1. [para(1392(a,1),1378(a,1,1,2))]. 1394 a(x,y,y) * (x \ (x / y)) = y \ 1. [para(19(a,1),1393(a,1,1))]. 1396 a(K(x,y),z,z) * (K(y,x) \ (K(y,x) / z)) = z \ 1. [para(905(a,1),1394(a,1,1))]. 1397 a(x,y,y) * (x / y) = x * (y \ 1). [para(1394(a,1),1254(a,1,2)),flip(a)]. 1398 (x * (y \ 1)) / (x / y) = a(x,y,y). [hyper(24,a,22,a,b,1397,a),flip(a)]. 1399 (x / y) * (y * (x \ 1)) = a(y,x,x). [para(1398(a,1),669(a,1)),flip(a)]. 1400 a(x / y,y,y \ 1) = a(x,y,y). [para(1399(a,1),592(a,2))]. 1401 a(x * (y * y),y \ 1,(y \ 1) \ 1) = a(x * y,y \ 1,y \ 1). [para(400(a,1),1400(a,1,1))]. 1402 K(x,(y \ (y / z)) \ 1) = K(x,z * a(y,z,z)). [para(1391(a,1),492(a,1)),flip(a)]. 1403 a(K(x,y),z,z) * (K(x,y) * (K(y,x) / z)) = z \ 1. [para(900(a,1),1396(a,1,2))]. 1404 K(x,y) * (a(K(x,y),z,z) * (K(y,x) / z)) = z \ 1. [para(1403(a,1),1253(a,1)),flip(a)]. 1405 R(K(x,y),z,z) * (K(y,x) / z) = z \ 1. [para(1404(a,1),966(a,1)),flip(a)]. 1406 x * (L(x,x,y * x) \ 1) = a(y,x \ 1,x \ 1). [para(1389(a,1),330(a,1)),flip(a)]. 1407 a(x,y \ 1,y \ 1) = L(y,y,x * y) \ y. [para(1406(a,1),471(a,1))]. 1408 a(x * y,y \ 1,y \ 1) = L(y,y,x) \ y. [para(1291(a,1),1407(a,2,1))]. 1409 (x * (y \ z)) \ (x * (y \ (z * u))) = L(L(u,z,y),y * z,x). [para(813(a,2),876(a,1))]. 1410 (x * y) * (z / (x * (y * z))) = x \ R(x,y,z). [para(853(a,1),537(a,1))]. 1411 L(x,y \ R(y,z,u),y * z) = x. [para(1410(a,1),852(a,1,2))]. 1412 L(x,y * R(y,z,u),y * z) = x. [para(1411(a,1),876(a,1)),flip(a)]. 1413 L(x,y * R(y,y * z,u),z) = x. [para(1412(a,1),774(a,1)),flip(a)]. 1414 K(T(x,y \ 1),y) * (x * (y \ 1)) = T(x,y) * (y \ 1). [para(1182(a,2),329(a,1))]. 1415 K(T(x,y \ 1),y) = K(x,y). [hyper(24,a,1160,a,b,1414,a)]. 1416 (x * (y \ 1)) / (T(x,y) * (y \ 1)) = K(y,T(x,y \ 1)). [para(1414(a,1),902(a,1,2))]. 1418 K(x / (y * y),y) = K(x,y). [para(1415(a,1),1221(a,1)),flip(a)]. 1419 K(x,T(y,x \ 1)) = K(x,y). [para(1416(a,1),1102(a,1))]. 1420 K(x \ 1,T(y,x)) = K(x \ 1,y). [para(156(a,1),1419(a,1,2,2))]. 1421 T(x,T(y,x \ 1)) = x * K(x,y). [para(1419(a,1),1107(a,2,2))]. 1423 K(x,y / (x * x)) = K(x,y). [para(1419(a,1),1220(a,1)),flip(a)]. 1424 K(x,R(y / x,x,x)) = K(x,y * x). [para(80(a,2),1423(a,1,2))]. 1425 ((x \ 1) * T(y,x)) / (x \ 1) = T(y,x) * K(x \ 1,y). [para(1420(a,1),1014(a,2,2))]. 1426 T(x,T(y,x \ 1)) = T(x,y). [para(1421(a,2),1107(a,2)),flip(a)]. 1427 T(x \ 1,T(y,x)) = T(x \ 1,y). [para(156(a,1),1426(a,1,2,2))]. 1428 T(x,y / (x * x)) = T(x,y). [para(1426(a,1),1222(a,1)),flip(a)]. 1429 L(x,T(y,z),T(T(z,y \ 1),y)) = L(x,y,T(z,y \ 1)). [para(1426(a,1),1376(a,1,2))]. 1430 T(x,(y * x) * x) = T(x,R(y,x,x)). [para(34(a,2),1428(a,1,2)),flip(a)]. 1431 L(x,T(y \ 1,z),T(T(z,y),y \ 1)) = L(x,y \ 1,T(z,y)). [para(1427(a,1),1376(a,1,2))]. 1432 (x \ T(y,x)) / (x \ 1) = T(y,x) * K(x \ 1,y). [para(318(a,1),1425(a,1,1))]. 1433 T(x,y) * K(y \ 1,x) = T(x,y * y). [para(1432(a,1),486(a,1))]. 1434 L(x,T(y,z),T(T(z,y),y \ 1)) = L(x,y,T(z,y \ 1)). [para(42(a,1),1429(a,1,3))]. 1435 L(x,R(y,z,z),y * z) = L(x,y \ 1,T(y * z,y \ 1)). [para(1297(a,2),938(a,1)),flip(a)]. 1436 L(x,R(y,z,z),y * z) = L(x,y,T(y * z,y \ 1)). [para(1435(a,2),887(a,1))]. 1437 L(x,y * R(z,z * u,w),v5) = L(x,y * R(z,u,w),v5). [para(1363(a,2),1273(a,1))]. 1438 L(x,y * R(y,z,u),z) = x. [para(1437(a,1),1413(a,1))]. 1439 L(x,y * (z * R(z,y,u)),y) = x. [para(1438(a,1),303(a,1,1))]. 1440 L(x,y \ R(y \ 1,z,u),z) = x. [para(318(a,1),1438(a,1,2))]. 1441 (x * (y \ R(y,x,z))) * u = x * ((y \ R(y,x,z)) * u). [para(1438(a,1),888(a,1,2))]. 1442 a(x,x * (y * R(y,x,z)),u) = 1. [hyper(38,a,1439,a)]. 1443 L(x,y * R(y \ 1,z,u),z) = x. [para(1440(a,1),876(a,1)),flip(a)]. 1444 L(x,a(y,z,z),z) = x. [para(960(a,1),1443(a,1,2))]. 1445 x / (a(y,x,x) \ 1) = x * a(y,x,x). [para(1444(a,1),145(a,1,2))]. 1446 (x * a(y,x,x)) * z = x * (a(y,x,x) * z). [para(1444(a,1),74(a,1,2))]. 1447 K(x,(y \ (y / z)) \ 1) = K(x,z / (a(y,z,z) \ 1)). [para(1445(a,2),1402(a,2,2))]. 1448 (x \ (x / y)) \ z = y * (a(x,y,y) * z). [para(1446(a,1),1390(a,2))]. 1449 L(x * (a(y,x,x) * z),y * (y / x),y) = (y / x) \ (y * z). [para(1448(a,1),311(a,1,1))]. 1450 (x * (y \ R(y,x,z))) * u = x * (R(y,x,z) * (y \ u)). [para(532(a,1),1441(a,2,2))]. 1451 L(x,T(y,z),T(T(z,y),y \ 1)) = L(x,y \ 1,T(z,y)). [para(1431(a,1),1256(a,1)),flip(a)]. 1452 L(x,y \ 1,T(z,y)) = L(x,y,T(z,y \ 1)). [para(1451(a,1),1434(a,1))]. 1453 L(x,y,T(z,y \ 1)) = L(x,y,T(z,y)). [para(1452(a,1),887(a,1))]. 1454 L(x,R(y,z,z),y * z) = L(x,y,T(y * z,y)). [para(1453(a,1),1436(a,2))]. 1455 L(x,R(y,z,z),y * z) = L(x,y,y / z). [para(1454(a,2),1259(a,1))]. 1456 L(x,R(y,z,z),y * z) = L(x,y,z * y). [para(1455(a,2),1290(a,1))]. 1457 L(T(x,y),y * K(x,y),T(x,y)) = (x \ y) \ y. [para(1187(a,1),1141(a,2,1))]. 1458 (x * (y * z)) \ ((x * y) * z) = a(T(x,y),T(y,x),z). [para(1168(a,1),1150(a,1,1))]. 1459 a(T(x,y),T(y,x),z) = a(x,y,z). [para(1458(a,1),28(a,2)),flip(a)]. 1460 a(T(x,y),T(T(y,x),x),z) = a(x,T(y,x),z). [para(1131(a,1),1459(a,1,1))]. 1461 x \ (y \ (y \ (T(y,x) * ((x * y) * z)))) = L(z,x * y,T(y,x)). [para(1180(a,1),443(a,1)),flip(a)]. 1462 x * K(y * a(x,y,y),z) = (x / y) * (y * K(y,z)). [para(1392(a,1),1298(a,1,2,1))]. 1463 x * K(y * a(x,y,y),z) = (x / y) * T(y,z). [para(1107(a,2),1462(a,2,2))]. 1464 x \ (y \ (K(y,x) * ((x * y) * z))) = L(z,x * y,T(y,x)). [para(1127(a,1),1461(a,1,2,2))]. 1465 x \ (y \ ((y * x) * z)) = L(z,x * y,T(y,x)). [para(1330(a,1),1464(a,1,2,2))]. 1466 L(x,y * z,T(z,y)) = L(x,z * y,z). [para(1465(a,1),309(a,1))]. 1467 L(x,y * z,z) = L(x,z * y,z). [para(1466(a,1),1300(a,1)),flip(a)]. 1468 L(L(x,y,z),y * z,z) = x. [para(1467(a,2),303(a,1))]. 1470 x \ L(x,x * y,y) = a(y,x,x). [para(1467(a,2),452(a,1,2))]. 1471 L(x,y * (y / z),y) = L(x,z,y). [para(1467(a,1),877(a,1))]. 1472 L(x,(y * z) * z,y * z) = L(x,T(y,z),y * z). [para(1467(a,1),878(a,1))]. 1473 L(x,T(y,z),z) = L(x,y,z). [para(1468(a,1),314(a,1,1))]. 1475 L(T(x,y),y,x) = T(x,y * x). [para(1473(a,1),1216(a,1))]. 1476 K(x,y) * (x \ y) = y / L(x,y,x). [para(1473(a,1),1247(a,1,2)),flip(a)]. 1477 L(x,y,y / z) = L(x,y,y * z). [para(1473(a,1),1285(a,1)),flip(a)]. 1478 (x * T(y,x)) \ (T(y,z) * x) = L(K(T(y,x),z),y,x). [para(1473(a,1),1195(a,2))]. 1479 T(x,y * x) = T(x,x * y). [para(1475(a,1),203(a,1))]. 1480 K(x,y) * L(x,y,x) = T(x,x * y). [para(1479(a,1),955(a,2))]. 1481 T(x,x * y) * K(y * x,x) = x. [para(1479(a,1),1089(a,1,1))]. 1482 T(x,x * (y * x)) = T(x,R(y,x,x)). [para(1479(a,1),1430(a,1))]. 1483 x \ L(x,y,x * y) = a(x * y,x,x). [para(875(a,1),1470(a,1,2))]. 1484 x \ L(x,T(y,x),y * x) = a(y * x,x,x). [para(878(a,1),1470(a,1,2))]. 1485 a(T(x,y),y,y) = a(x,y,y). [para(1470(a,1),1299(a,1)),flip(a)]. 1486 L(x * (a(y,x,x) * z),x,y) = (y / x) \ (y * z). [para(1471(a,1),1449(a,1))]. 1488 L(x,x,x * y) = y \ (y / (x \ 1)). [para(1477(a,1),807(a,1))]. 1489 K(x * y,y) = K(y * x,y). [hyper(23,a,1089,a,b,1481,a)]. 1490 T(x * K(x * y,x),y * x) = x. [para(1489(a,1),1020(a,1,1,2))]. 1491 x / (x / y) = y * K(x * y,y). [para(1489(a,2),1144(a,2,2))]. 1492 R(x,y,x) / T(x,y) = K(y * x,x). [para(1489(a,2),1370(a,2))]. 1493 T(x / (x / y),x * y) = y. [para(1144(a,2),1490(a,1,1))]. 1494 T(x * y,x / (x / y)) = T(x * y,y). [para(1493(a,1),1131(a,1,2)),flip(a)]. 1495 (x / (x / y)) \ T(x * y,x / (x / y)) = y \ (x * y). [para(1493(a,1),1138(a,1,1)),flip(a)]. 1496 R(x,y,x) = y / (y / T(x,y)). [para(1491(a,2),1325(a,1)),flip(a)]. 1497 R(x,y,x) \ y = y / T(x,y). [para(1496(a,2),66(a,1,1))]. 1498 (T(x,y) \ y) * K(T(x,y),T(x,y) * y) = R(x,y,x) \ y. [para(1497(a,2),1001(a,2))]. 1499 ((x / y) / x) * T(x,R(y,x,y)) = x / T(y,x). [para(1497(a,1),1356(a,2))]. 1500 K(x,y) = (y \ x) / (x / L(y,x,y)). [para(1476(a,1),902(a,1,2)),flip(a)]. 1501 (x * y) / (K(x,y) * L(x,y,x)) = R(x,x * y,x) \ (x * y). [para(1480(a,2),1497(a,2,2)),flip(a)]. 1502 T(x,R(y,x,x)) = T(x,y). [para(1482(a,1),1136(a,1))]. 1503 K(x,R(y,x,x)) = x \ T(x,y). [para(1502(a,1),1108(a,2,2))]. 1504 K(x,R(y,x,x)) = K(x,y). [para(1503(a,2),1108(a,2)),flip(a)]. 1505 K(x,y / x) = K(x,y * x). [para(1504(a,1),1424(a,1))]. 1506 K(x,y * x) = K(x,x * y). [para(1505(a,1),1078(a,1))]. 1507 ((x * y) * y) \ ((y * x) * y) = K(y,y * (y * x)). [para(1506(a,1),1103(a,2))]. 1508 (T(x,y) \ y) * K(x,x * y) = T(y,x) / x. [para(1506(a,1),1260(a,1,2))]. 1509 K(T(x,y),y * T(x,y)) = K(T(x,y),y * x). [para(1506(a,2),1364(a,1))]. 1510 T(x,y) \ R(x,y,x) = K(y * x,x). [para(1492(a,1),693(a,1)),flip(a)]. 1511 K(x,y) * (y \ R(y,x,y)) = K(x * y,y). [para(1510(a,1),1095(a,2))]. 1512 K(T(x,y),y * x) = K(T(x,y),x * y). [para(82(a,1),1509(a,1,2)),flip(a)]. 1513 K(T(x,y),x * y) = K(x,x * y). [para(1512(a,1),1366(a,1))]. 1514 L(x,R(y,z,z),y * z) = L(x,T(y,z),y * z). [para(1472(a,1),938(a,1)),flip(a)]. 1515 L(x,T(y,z),y * z) = L(x,y,z * y). [para(1514(a,1),1456(a,1))]. 1516 x \ L(x,y,x * y) = a(y * x,x,x). [para(1515(a,1),1484(a,1,2))]. 1517 a(x * y,y,y) = a(y * x,y,y). [para(1516(a,1),1483(a,1))]. 1518 L(x * (a(y,x,x) * z),x,y) = (x / y) * (y * z). [para(1486(a,2),358(a,1))]. 1519 K(x,y) = ((y * x) * x) \ ((x * y) * x). [para(1507(a,2),490(a,1)),flip(a)]. 1520 (x * (y * x)) \ ((x * y) * x) = K(y * x,x) * K(x,y). [para(1519(a,2),941(a,1,2)),flip(a)]. 1521 (x * y) \ (T(x,z) * y) = L(K(T(x,y),z),x,y). [para(82(a,1),1478(a,1,1))]. 1522 L(K(T(x,y),z),x,y) = T(K(x,z),x * y). [para(1521(a,1),1184(a,1))]. 1523 (x / (x / y)) \ T(x * y,x / (x / y)) = T(x,y). [para(1495(a,2),36(a,2)),flip(a)]. 1524 (x / (x / y)) \ T(x * y,y) = T(x,y). [para(1494(a,1),1523(a,1,2))]. 1525 ((x / y) / x) * T(x * y,y) = T(x,y). [para(1524(a,1),358(a,1)),flip(a)]. 1526 (x / y) * T(y * (x \ y),x \ y) = T(y,x \ y). [para(65(a,1),1525(a,1,1,1))]. 1527 L(x,y,z * (((u / w) / u) * T(u,w))) = L(x,y,z * T(u * w,w)). [para(1525(a,1),868(a,1,3,2,2))]. 1528 (x / y) * (y * (y / x)) = T(y,x \ y). [para(1239(a,1),1526(a,1,2))]. 1529 T(x,x / y) = T(x,y \ x). [para(1528(a,1),369(a,1)),flip(a)]. 1530 T(x,R(y,x,y)) = T(x,(x / y) \ x). [para(1529(a,1),1322(a,2))]. 1531 T(x,R(y,x,y)) = T(x,y). [para(66(a,1),1530(a,2,2))]. 1532 ((x / y) / x) * T(x,y) = x / T(y,x). [para(1531(a,1),1499(a,1,2))]. 1533 K(x * y,y) * K(y,x) = a(y,x,y). [para(1520(a,1),28(a,2)),flip(a)]. 1534 K(x,y) * K(y * x,x) = a(x,y,x). [para(1533(a,1),1226(a,2))]. 1536 K(x,y) * a(y,x,y) = K(x * y,y). [hyper(23,a,901,a,b,1534,a),flip(a)]. 1537 K(x,y) * K(x * y,x) = a(x,y,x). [para(1489(a,1),1534(a,1,2))]. 1539 x \ R(x,y,x) = a(x,y,x). [hyper(23,a,1511,a,b,1536,a),flip(a)]. 1541 L(x,y,x) \ x = a(x,y,x). [para(1539(a,1),1320(a,2))]. 1544 (T(x,y) \ y) * K(T(x,y),y * T(x,y)) = R(x,y,x) \ y. [para(1506(a,2),1498(a,1,2))]. 1545 (T(x,y) \ y) * K(T(x,y),x * y) = R(x,y,x) \ y. [para(82(a,1),1544(a,1,2,2))]. 1546 (T(x,y) \ y) * K(x,x * y) = R(x,y,x) \ y. [para(1513(a,1),1545(a,1,2))]. 1547 R(x,y,x) \ y = T(y,x) / x. [para(1546(a,1),1508(a,1))]. 1548 T(x,y) / y = x / T(y,x). [para(1547(a,1),1497(a,1))]. 1549 (x / T(y,x)) * y = T(x,y). [para(1548(a,1),22(a,1,1))]. 1550 (x / y) * (y * K(x,y)) = T(x,y * K(x,y)). [para(1020(a,1),1549(a,1,1,2))]. 1551 T(x,y) = (x / y) * (y * K(x,y)). [para(1550(a,2),1139(a,1)),flip(a)]. 1552 (x / y) * T(y,x) = x * K(y,x). [hyper(23,a,359,a,b,1551,a(flip)),flip(a)]. 1553 (x * (y \ 1)) * T(L(y,y,x),x) = x * K(L(y,y,x),x). [para(915(a,1),1552(a,1,1))]. 1554 (x * (y \ 1)) * L(T(y,x),y,x) = x * K(L(y,y,x),x). [para(44(a,2),1553(a,1,2))]. 1555 x * K(L(y,y,x),x) = x * (y \ T(y,x)). [para(1554(a,1),945(a,1))]. 1556 x * K(L(y,y,x),x) = x * K(y,x). [para(1108(a,2),1555(a,2,2))]. 1557 T(x * K(y,x),L(y,y,x)) = x. [para(1556(a,1),1020(a,1,1))]. 1558 T(x,L(y,y,x)) = T(x,y). [para(1557(a,1),1023(a,1,1)),flip(a)]. 1559 (x * y) / (K(x,y) * L(x,y,x)) = L(x,y,x) \ (x * y). [para(1315(a,1),1501(a,2,1))]. 1560 (x * y) / (K(x,y) * L(x,y,x)) = (L(x,y,x) \ x) * y. [para(1559(a,2),524(a,1))]. 1561 (x * y) / T(x,x * y) = (L(x,y,x) \ x) * y. [para(1480(a,1),1560(a,1,2))]. 1562 (L(x,y,x) \ x) * y = T(x * y,x) / x. [para(1561(a,1),1548(a,2)),flip(a)]. 1563 T(x * y,x) / x = a(x,y,x) * y. [para(1541(a,1),1562(a,1,1)),flip(a)]. 1564 R(K(x,y),K(y,x) * z,u) \ K(x,y) = K(y,x) * R(K(x,y),z,u). [para(923(a,2),900(a,1))]. 1565 x * (y * (R(y,y * (x \ 1),z) \ (x \ z))) = L(z,y * x,y). [para(318(a,1),957(a,1,2,2,2))]. 1566 x * (R(y,x \ 1,z) * (y \ (x \ z))) = L(z,y * x,y). [para(637(a,1),1565(a,1,2))]. 1567 x * (R(y,x,z) * (y \ (x \ z))) = L(z,y * x,y). [para(717(a,1),1566(a,1,2,1))]. 1568 R(x * (K(x,y) * K(x,y)),z,u) / T(T(x,y),y) = x \ R(x,z,u). [para(705(a,2),1202(a,1,1))]. 1569 K(x,T(y,z)) * T(y,x) = K(z,T(y,x)) * T(y,z). [para(1346(a,1),1264(a,1,2))]. 1570 (K(x,T(y,z)) * T(y,x)) / L(y,K(y,z),K(z,T(y,x))) = K(z,T(y,x)) * K(y,z). [para(1569(a,1),1106(a,1,1))]. 1572 ((T(x,y) * y) * z) / ((x * y) * z) = K(y,x) \ 1. [para(1098(a,1),1336(a,1,2,1))]. 1574 a(x * (y * y),y \ 1,y) = a(x * y,y \ 1,y \ 1). [para(156(a,1),1401(a,1,3))]. 1575 L(x,y,z * T(u * w,w)) = L(x,y,z * (u / T(w,u))). [para(1532(a,1),1527(a,1,3,2)),flip(a)]. 1576 L(x,y,z * (T(u,w) / w)) = L(x,y,z * T(u * w,w)). [para(1548(a,2),1575(a,2,3,2)),flip(a)]. 1577 (R(K(x,y),z,u) \ 1) \ K(y,x) = K(x,y) * R(K(y,x),z,u). [para(904(a,1),1564(a,1,1))]. 1578 R(K(x,y),z,u) * K(y,x) = K(x,y) * R(K(y,x),z,u). [para(1577(a,1),330(a,1)),flip(a)]. 1579 K(x,y) * R(K(y,x),T(x,y) * z,u) = R(K(y,x),x * z,u) \ K(y,x). [para(1249(a,1),1577(a,1,1)),flip(a)]. 1580 R(T(x,y) * K(x,y),z,u) / T(T(x,y),y) = x \ R(x,z,u). [para(1120(a,1),1568(a,1,1,1))]. 1581 R(T(T(x,y),y),z,u) / T(T(x,y),y) = x \ R(x,z,u). [para(1121(a,1),1580(a,1,1,1))]. 1582 T(T(x,y),y) \ R(T(T(x,y),y),z,u) = x \ R(x,z,u). [para(1581(a,1),478(a,1)),flip(a)]. 1583 (x * y) * T((x * y) \ (x * z),u) = (x * y) * L(T(y \ z,u),y,x). [para(44(a,2),764(a,1,2)),flip(a)]. 1584 (x * y) * R((x * y) \ x,z,u) = (x * y) * L(R(y \ 1,z,u),y,x). [para(48(a,1),765(a,1,2)),flip(a)]. 1589 (K(x,y) * (x \ z)) \ (K(x,y) * (x \ (z * u))) = L(u,z,x \ K(x,y)). [para(1072(a,1),1189(a,1,2))]. 1590 (x * y) * T((x * y) \ (x * z),u) = x * (y * T(y \ z,u)). [para(1583(a,2),74(a,1))]. 1591 (x * y) * R((x * y) \ x,z,u) = x * (y * R(y \ 1,z,u)). [para(1584(a,2),74(a,1))]. 1592 (x * y) * R((x * y) \ x,z,u) = x * (y \ R(y,z,u)). [para(635(a,1),1591(a,2,2))]. 1593 (x / y) * (y * R(((y \ x) * x) \ (y \ x),z,u)) = x \ R(x,z,u). [hyper(23,a,1274,a,b,1592,a(flip)),flip(a)]. 1594 (x / y) * (y * R(((y * x) * x) \ (y * x),z,u)) = x \ R(x,z,u). [para(1379(a,1),1593(a,1,2,2,1))]. 1595 (x / y) * (y * R(y \ (y / x),z,u)) = x \ R(x,z,u). [para(1296(a,1),1594(a,1,2,2,1))]. 1596 ((x \ y) / y) * (y * R(y \ x,z,u)) = (x \ y) \ R(x \ y,z,u). [para(65(a,1),1595(a,1,2,2,1,2))]. 1597 (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). [para(99(a,1),1595(a,1,2,2,1,2))]. 1598 (x \ 1) * (y * R(y \ x,z,u)) = (x \ y) \ R(x \ y,z,u). [para(320(a,1),1596(a,1,1))]. 1599 (x \ y) \ R(x \ y,z,u) = x \ (y * R(y \ x,z,u)). [para(1598(a,1),318(a,1))]. 1601 (x * y) \ R(x * y,z,u) = x \ (y * R(y \ x,z,u)). [para(1599(a,1),750(a,1)),flip(a)]. 1602 L(L(x,y,z),z * y,K(z,u)) = L(x,y,z \ K(z,u)). [para(1589(a,1),1409(a,1)),flip(a)]. 1603 L(L(x,y,z),z * y,K(z,u)) = L(x,y,z * K(z,u)). [para(1602(a,2),776(a,1))]. 1604 L(L(x,y,z),z * y,K(z,u)) = L(x,y,T(z,u)). [para(1107(a,2),1603(a,2,3))]. 1605 L(L(x,y,z),z * y,T(z,u)) = L(x,z * (z * y),K(z,u)). [para(303(a,1),1604(a,1,1)),flip(a)]. 1606 L(L(x,y,z),z * y,T(z,u)) = L(x,y,K(z,u)). [para(1605(a,2),875(a,1))]. 1608 (x * (y * x)) \ R(x * (z * x),u,w) = T(y,x) \ T(R(z,u,w),x). [para(36(a,2),701(a,2,2))]. 1609 (x * (y * x)) \ R(x * (z * x),u,w) = T(y,x) \ R(T(z,x),u,w). [para(46(a,2),1608(a,2,2))]. 1610 x \ ((y * x) * R((y * x) \ x,z,u)) = T(y,x) \ R(T(y,x),z,u). [para(1609(a,1),1601(a,1)),flip(a)]. 1611 L(x,y,z * (u \ (u \ (u \ (z * (u \ 1)))))) = L(x,y,K(z / (u * u),u)). [para(602(a,1),1194(a,1,3))]. 1612 L(x,y,z * (u \ ((u \ (u \ z)) * (u \ 1)))) = L(x,y,K(z / (u * u),u)). [para(285(a,1),1611(a,1,3,2,2))]. 1613 L(x,y,z * (u * ((u \ (u \ z)) * (u \ 1)))) = L(x,y,K(z / (u * u),u)). [para(1612(a,1),867(a,1)),flip(a)]. 1614 L(x,y,K(z / (u * u),u)) = L(x,y,z * (u \ (z * (u \ 1)))). [para(265(a,1),1613(a,1,3,2)),flip(a)]. 1615 L(x,y,K(z / (u * u),u)) = L(x,y,z * (u * (z * (u \ 1)))). [para(1614(a,2),867(a,1))]. 1616 L(x,y,K(z / (u * u),u)) = L(x,y,z * T(z,u \ 1)). [para(347(a,1),1615(a,2,3,2))]. 1617 L(x,y,K(z / (u * u),u)) = L(x,y,K(z,u \ 1)). [para(1616(a,2),1119(a,1))]. 1618 L(x,y,K(z,u \ 1)) = L(x,y,K(z,u)). [para(1418(a,1),1617(a,1,3)),flip(a)]. 1619 L(x,y,K(z,u \ 1)) = L(x,y,K(u,z)). [para(1618(a,2),909(a,1))]. 1620 (x * (x * (y * (z * u)))) \ ((x * (x * (y * z))) * u) = a(x * (x * y),z,u). [para(51(a,1),91(a,1,2,1))]. 1621 (x * y) * R(L(y \ z,y,x),u,w) = (x * y) * R((x * y) \ (x * z),u,w). [para(473(a,1),224(a,1))]. 1624 ((x * y) * ((y * x) * z)) \ (((x * y) * (y * x)) * (z * u)) = L(u,z,K(y,x)). [para(894(a,1),832(a,1,1))]. 1625 ((x * y) * T(R(T(z,x * y),x,y),u)) / ((z * x) * y) = K(R(z,x,y),u). [para(549(a,1),1214(a,1,1,2,1))]. 1626 ((x * y) * R(T(T(z,x * y),u),x,y)) / ((z * x) * y) = K(R(z,x,y),u). [para(46(a,2),1625(a,1,1,2))]. 1627 (R(T(x,y),z,u) * (z * u)) / ((x * z) * u) = K(R(x,z,u),y). [para(222(a,1),1626(a,1,1))]. 1628 ((T(x,y) * z) * u) / ((x * z) * u) = K(R(x,z,u),y). [para(79(a,1),1627(a,1,1))]. 1629 R(K(x,y),x * z,u) = K(R(x,z,u),y). [para(1628(a,1),1183(a,1)),flip(a)]. 1630 K(R(x,y,z),y) = K(y,x) \ 1. [para(1628(a,1),1572(a,1))]. 1631 R(K(x,y),T(y,x) * z,u) \ 1 = K(R(y,z,u),x). [para(1628(a,1),1162(a,2))]. 1632 K(R(x,y,z),y) = K(x,y). [para(1630(a,2),897(a,1))]. 1633 T(x,R(y,x,z)) = (x * x) / (x * K(y,x)). [para(1632(a,1),1104(a,2,2,2))]. 1634 K(R(x,x \ y,z),u) = R(K(x,u),y,z). [para(20(a,1),1629(a,1,2)),flip(a)]. 1635 R(K(x,y),x * (z / (z * x)),u) = K(x,y). [para(450(a,1),1629(a,2,1))]. 1636 R(K(x,y),T(x,y) * z,u) = K(R(T(x,y),z,u),y). [para(1105(a,1),1629(a,1,1))]. 1637 K(R(x,x * y,z),u) = R(K(x,u),y,z). [para(629(a,1),1634(a,1,1))]. 1638 R(K(x,y),z,x) = K(L(x,z,x),y). [para(1313(a,1),1634(a,1,1)),flip(a)]. 1639 K(x,R(y,y * z,u)) = R(K(y,x),z,u) \ 1. [para(1637(a,1),897(a,1,1)),flip(a)]. 1640 R(K(x,y),K(x,z) * u,w) = K(R(x,T(x,z) * u,w),y). [para(1120(a,1),1637(a,1,1,2)),flip(a)]. 1641 K(R(x,T(x,y) * z,u),y) = R(K(T(x,y),y),z,u). [para(1637(a,1),1110(a,1)),flip(a)]. 1642 T(x,R(y,x,z)) = T(x,y). [para(1633(a,2),1104(a,2)),flip(a)]. 1643 R(x,y,z) * T(y,x) = y * R(x,y,z). [para(1642(a,1),82(a,1,2))]. 1647 T(x,y) \ (x * R(y,x,z)) = T(R(y,x,z),T(x,y)). [para(1643(a,1),36(a,2,2)),flip(a)]. 1648 R(K(x,y),K(x,z),u) = K(x,y). [para(1041(a,2),1635(a,1,2))]. 1649 R(K(x,y),K(z,x),u) = K(x,y). [para(1648(a,1),908(a,1)),flip(a)]. 1650 (K(x,y) * K(z,x)) * u = K(x,y) * (K(z,x) * u). [para(1649(a,1),79(a,1,1)),flip(a)]. 1651 R(K(x,y),T(y,x) * z,u) = K(R(y,z,u),x) \ 1. [para(1631(a,1),156(a,1,1)),flip(a)]. 1652 R(K(x,y),T(x,y) * z,u) = K(R(x,z,u),y). [para(1636(a,2),1110(a,1))]. 1653 R(K(x,y),y * z,u) = K(R(y,z,u),x) \ 1. [para(1652(a,1),1249(a,1,1)),flip(a)]. 1654 R(K(x,y),y * z,u) = K(x,R(y,z,u)). [para(1653(a,2),897(a,1))]. 1656 R(K(x,y),x * z,u) * K(y,x) = K(x,y) * K(y,R(x,z,u)). [para(1654(a,1),1578(a,2,2))]. 1657 K(R(x,T(x,y) * z,u),y) = R(K(x,y),z,u). [para(1105(a,1),1641(a,2,1))]. 1658 T(R(x,y,z),T(y,x)) = K(x,y) * R(x,y,z). [para(1647(a,1),1093(a,1))]. 1659 R(T(x,T(y,x)),y,z) = K(x,y) * R(x,y,z). [para(1658(a,1),46(a,2))]. 1660 K(x,y) * R(x,y,z) = R(T(x,y),y,z). [para(1131(a,1),1659(a,1,1)),flip(a)]. 1661 T(x,y) \ R(T(x,y),y,z) = x \ R(x,y,z). [para(1660(a,1),1171(a,1,2))]. 1662 (x \ y) \ R(T(y / x,x),x,z) = (y / x) \ R(y / x,x,z). [para(84(a,1),1661(a,1,1))]. 1663 L(x,K(y,z),K(z,u)) = x. [hyper(23,a,74,a,b,1650,a),flip(a)]. 1664 L(x,K(y,z),K(u,z)) = x. [para(1663(a,1),909(a,1)),flip(a)]. 1665 L(x,K(y,z),K(u,y)) = x. [para(1664(a,1),921(a,1)),flip(a)]. 1666 (K(x,y) * T(z,x)) / z = K(z,x) * K(x,y). [para(1665(a,1),1355(a,1,2))]. 1667 R(K(x,y),T(y,x) * z,u) = K(x,R(y,z,u)). [para(1651(a,2),897(a,1))]. 1668 R(K(x,y),y * z,u) \ K(x,y) = K(y,x) * K(x,R(y,z,u)). [para(1667(a,1),1579(a,1,2)),flip(a)]. 1669 R(K(x,y),K(x,y) * z,u) = R(K(x,y),z,u). [para(1640(a,2),1657(a,1))]. 1670 R(K(x,y),z,u) \ 1 = R(K(y,x),z,u). [para(1669(a,1),906(a,1)),flip(a)]. 1671 R(K(x,y),z,u) \ K(x,y) = K(x,y) * R(K(y,x),z,u). [para(1670(a,1),543(a,1,2)),flip(a)]. 1672 K(x,R(y,y * z,u)) = R(K(x,y),z,u). [para(1670(a,1),1639(a,2))]. 1673 K(R(x,y,z),u) * K(u,x) = K(x,u) * K(u,R(x,y,z)). [para(1629(a,1),1656(a,1,1))]. 1674 K(x,y) * K(R(y,z,u),x) = K(y,x) * K(x,R(y,z,u)). [para(1673(a,1),1226(a,2))]. 1675 (x / y) \ R(x / y,y,z) = (y \ x) \ R(y \ x,y,z). [para(84(a,1),1662(a,1,2,1)),flip(a)]. 1676 (x \ y) \ R(x \ y,x,z) = (x / y) * R(y / x,x,z). [para(1675(a,1),358(a,1))]. 1677 x \ (y * R(y \ x,x,z)) = (x / y) * R(y / x,x,z). [para(1676(a,1),1599(a,1)),flip(a)]. 1678 x \ ((y \ x) * R((y \ x) \ x,x,z)) = y * R((y \ x) / x,x,z). [para(65(a,1),1677(a,2,1))]. 1679 x \ (R(y,x,z) * (y \ x)) = y * R((y \ x) / x,x,z). [para(225(a,1),1678(a,1,2))]. 1680 x * R((x \ y) / y,y,z) = T(x \ R(x,y,z),y). [para(1679(a,1),539(a,1))]. 1681 T(x \ R(x,y,z),y) = x * R(x \ 1,y,z). [para(320(a,1),1680(a,1,2,1)),flip(a)]. 1683 T(x \ R(x,y,z),y) = x \ R(x,y,z). [para(1681(a,2),635(a,1))]. 1684 (x * (y \ R(y,x,z))) / x = y \ R(y,x,z). [para(1683(a,1),105(a,1,1,2))]. 1685 T(x \ R(x,y,z),x * (y * z)) = T(a(x,y,z),y). [para(1683(a,1),740(a,1,1))]. 1686 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). [para(1684(a,1),1518(a,2,1))]. 1687 T(a(x,y,z),y) = a(x,y,z). [para(1685(a,1),739(a,2)),flip(a)]. 1688 a(x,y,z) * y = y * a(x,y,z). [para(1687(a,1),82(a,1,2)),flip(a)]. 1689 a(x,y \ 1,z) * (y \ 1) = y \ a(x,y \ 1,z). [para(1687(a,1),326(a,1,2)),flip(a)]. 1690 T(x * y,x) / x = y * a(x,y,x). [para(1688(a,1),1563(a,2))]. 1691 L(x,y,z * (T(u * z,u) / u)) = L(x,y,a(u,z,u)). [para(1690(a,2),774(a,1,3,2))]. 1692 L(x,y,z * a(u,z,u)) = L(x,y,R(z,u,u)). [para(1690(a,1),1350(a,1,3))]. 1693 L(x,y,z * T((u * z) * u,u)) = L(x,y,a(u,z,u)). [para(1691(a,1),1576(a,1)),flip(a)]. 1694 L(x,y,z * ((z * u) * u)) = L(x,y,a(u,z,u)). [para(758(a,1),1693(a,1,3,2))]. 1695 L(x,y,a(z,u,u)) = L(x,y,a(u,z,u)). [para(1694(a,1),861(a,1)),flip(a)]. 1696 (x * (x * (y * (z * u)))) \ (x * (x * ((y * z) * u))) = a(x * (x * y),z,u). [para(51(a,1),1620(a,1,2))]. 1697 (x * y) * R((x * y) \ (x * z),u,w) = (x * y) * L(R(y \ z,u,w),y,x). [para(48(a,1),1621(a,1,2)),flip(a)]. 1698 ((x * y) * ((y * x) * z)) \ ((x * y) * ((y * x) * (z * u))) = L(u,z,K(y,x)). [para(894(a,1),1624(a,1,2))]. 1699 a(x * (x * y),z,u) = (y * (z * u)) \ ((y * z) * u). [para(1696(a,1),212(a,1))]. 1700 a(x * (x * y),z,u) = a(y,z,u). [para(1699(a,2),28(a,2)),flip(a)]. 1702 a(x \ y,z,u) = a(x * y,z,u). [para(20(a,1),1700(a,1,1,2)),flip(a)]. 1703 a((x / y) * x,z,u) = a(y,z,u). [para(22(a,1),1700(a,1,1,2))]. 1704 a(x * (y * x),z,u) = a(T(y,x),z,u). [para(82(a,1),1700(a,1,1,2))]. 1706 a(x * ((x \ y) * z),u,w) = a(x * ((x * y) * z),u,w). [para(89(a,1),1700(a,1,1,2)),flip(a)]. 1707 a((x \ y) * z,u,w) = a((x * y) * z,u,w). [para(89(a,1),1700(a,1,1)),flip(a)]. 1708 a((x * x) / y,z,u) = a(y \ 1,z,u). [para(263(a,1),1700(a,1,1))]. 1709 a(x * L(x,y * x,y),z,u) = a(a(y,x,x),z,u). [para(453(a,2),1700(a,1,1,2))]. 1710 a(R(x \ 1,y,y),z,u) = a(x * a(x,y,y),z,u). [para(960(a,1),1700(a,1,1,2)),flip(a)]. 1711 a(K(x,y) * y,z,u) = a(T(y,x),z,u). [para(1077(a,1),1700(a,1,1,2))]. 1712 a(x * T(x,y),z,u) = a(K(x,y),z,u). [para(1107(a,2),1700(a,1,1,2))]. 1713 ((x \ y) * (T(x,x * y) * z)) \ (y * z) = a(x * y,T(x,x * y),z). [para(1702(a,1),255(a,2))]. 1714 a(K(x \ 1,x * y),z,u) = a(x \ ((x * y) \ y),z,u). [para(1126(a,2),1702(a,2,1)),flip(a)]. 1715 a((x * (x * y)) * (x * z),u,w) = a(y \ (x \ z),u,w). [para(282(a,1),1703(a,1,1,1))]. 1716 a((x * x) / y,z,u) = a(y,z,u). [para(1708(a,2),611(a,1))]. 1717 a(x / (y * y),z,u) = a(x,z,u). [para(1716(a,1),612(a,1)),flip(a)]. 1718 a(R(x,x * y,z),u,w) = a(R(x,y,z),u,w). [para(616(a,1),1716(a,1,1))]. 1719 a(x * K(y,x),z,u) = a(T(x,y),z,u). [para(1104(a,2),1716(a,1,1)),flip(a)]. 1720 a(x * (y * y),z,u) = a(x,z,u). [para(21(a,1),1717(a,1,1)),flip(a)]. 1721 a((x * y) * y,z,u) = a(R(x,y,y),z,u). [para(34(a,2),1717(a,1,1)),flip(a)]. 1722 a(x / (y \ 1),z,u) = a(x / y,z,u). [para(398(a,1),1717(a,1,1)),flip(a)]. 1723 ((x * (y * y)) * (z * u)) \ (((x * (y * y)) * z) * u) = a(x,z,u). [para(1720(a,1),28(a,1)),flip(a)]. 1724 a(T(T(x,y),y),z,u) = a(x,z,u). [para(985(a,1),1711(a,1,1)),flip(a)]. 1725 a((x / (y * y)) * (y \ (x * (y \ 1))),z,u) = a(K(x / (y * y),y),z,u). [para(403(a,1),1712(a,1,1,2))]. 1726 a(x / (x * y),z,u) = a(T(y,x),z,u). [para(1719(a,1),1022(a,2))]. 1727 a((x \ 1) / y,z,u) = a(y / x,z,u). [para(1722(a,1),612(a,1)),flip(a)]. 1728 a(x / T(y * x,y),z,u) = a(T(R(y,x,y),x),z,u). [para(1321(a,1),1726(a,1,1,2))]. 1729 a(x * (y * x),x,x) = a(R(y,x,x),x,x). [para(1721(a,1),1517(a,1)),flip(a)]. 1730 a(R(x,y,y),y,y) = a(T(x,y),y,y). [para(1729(a,1),1704(a,1))]. 1731 a(R(x,y,y),y,y) = a(x,y,y). [para(1730(a,2),1485(a,1))]. 1732 R(R(x,y,y) \ 1,y,y) = R(x,y,y) \ a(x,y,y). [para(1731(a,1),967(a,2,2))]. 1733 R(R(x,y,y),R(x,y,y) * y,y) = a(x,y,y) \ R(x,y,y). [para(1731(a,1),968(a,2,1))]. 1734 a(x * ((x \ y) * y),z,u) = a(a(x,y,y),z,u). [para(435(a,1),1709(a,1,1))]. 1735 a(R(x \ 1,y,y),z,u) = a(R(x,y,y),z,u). [para(963(a,1),1710(a,2,1))]. 1736 R(R(x,y,y) \ 1,y,y) = x \ 1. [para(1732(a,2),1374(a,1))]. 1737 R((x * y) \ 1,y,y) = (x / (y \ 1)) \ 1. [para(720(a,1),1736(a,1,1,1))]. 1739 R((x * y) \ 1,y,y) = (y \ 1) / x. [para(1737(a,2),343(a,1))]. 1740 (x \ 1) / (y / x) = R(y \ 1,x,x). [para(22(a,1),1739(a,1,1,1)),flip(a)]. 1741 (((x * y) \ 1) * y) * y = ((y \ 1) / x) * (y * y). [para(1739(a,1),79(a,1,1)),flip(a)]. 1742 R(x \ 1,y,y) \ 1 = (x / y) / (y \ 1). [para(1740(a,1),343(a,1,1))]. 1743 a((x \ 1) / ((y / x) \ 1),z,u) = a(R(y \ 1,x,x),z,u). [para(1740(a,1),1722(a,2,1))]. 1744 R(x,x * y,y) = (x / y) / (y \ 1). [para(1742(a,1),633(a,2))]. 1745 K(R(x,x * y,y),z) * (x / y) = (y \ 1) * T((y \ 1) \ (x / y),z). [para(1744(a,2),1201(a,1,1,1))]. 1746 (((x * y) \ 1) * y) * y = T(y / x,y * y). [para(1741(a,2),294(a,1))]. 1747 T(x / y,x * x) = ((y * x) \ x) * x. [para(318(a,1),1746(a,1,1)),flip(a)]. 1748 L(x,y * z,R(T(z / y,z * z),u,w)) = x. [para(1747(a,2),847(a,1,3,1))]. 1749 L(x,y * z,R(z / y,u,w)) = x. [para(1748(a,1),858(a,1)),flip(a)]. 1750 L(x,y * (z \ 1),u / (y * (z * u))) = x. [para(350(a,1),1749(a,1,3))]. 1752 L(x,y * z,u / (y * (z * u))) = x. [para(1750(a,1),1273(a,1)),flip(a)]. 1753 x / ((y * z) \ (y * (z * x))) = (x / (y * (z * x))) * (y * z). [para(1752(a,1),205(a,1,2))]. 1754 a(T(R(x,y,x),y),z,u) = a((y / x) / y,z,u). [para(1237(a,1),1728(a,1,1)),flip(a)]. 1755 a(x * ((x * y) * y),z,u) = a(a(x,y,y),z,u). [para(1706(a,1),1734(a,1))]. 1756 a(x * (x * (y * (x * z))),u,w) = a(y \ (x \ z),u,w). [para(51(a,1),1715(a,1,1))]. 1757 a(x \ (y \ z),u,w) = a(x * (y * z),u,w). [para(1756(a,1),1700(a,1))]. 1759 a(x * (y \ z),u,w) = a(x * (y * z),u,w). [para(1757(a,1),1702(a,1)),flip(a)]. 1760 a(K(x \ 1,x * y),z,u) = a(x * ((x * y) * y),z,u). [para(1757(a,1),1714(a,2))]. 1761 R(R(x,y,y),R(x,y,y) * y,y) = x. [para(1733(a,2),964(a,1))]. 1762 R(K(R(x,y,y),z),y,y) = K(x,z). [para(1761(a,1),1637(a,1,1)),flip(a)]. 1763 K(R(x,y,y),z) * (y \ 1) = K(x,z) / y. [para(1762(a,1),718(a,1,1)),flip(a)]. 1764 K(x,R(y,z,z)) * (K(y,x) / z) = z \ 1. [hyper(23,a,901,a,b,1763,a),flip(a)]. 1765 R(K(x,y),z,z) = K(x,R(y,z,z)). [hyper(24,a,1405,a,b,1764,a),flip(a)]. 1766 K(R(x,y,y),z) \ 1 = R(K(z,x),y,y). [para(1765(a,2),897(a,2))]. 1767 K(x,R(y,z,z)) * 1 = R(K(x,y),z,z). [para(1766(a,1),900(a,1)),flip(a)]. 1768 a((x \ 1) / (x / y),z,u) = a(R(y \ 1,x,x),z,u). [para(343(a,1),1743(a,1,1,2))]. 1769 a(R(x \ 1,y,y),z,u) = a((y / x) / y,z,u). [para(1768(a,1),1727(a,1))]. 1770 a((x / y) / x,z,u) = a(R(y,x,x),z,u). [para(1769(a,1),1735(a,1))]. 1771 a(T(R(x,y,x),y),z,u) = a(R(x,y,y),z,u). [para(1770(a,1),1754(a,2))]. 1772 a(R(T(x,y),y,x),z,u) = a(R(x,y,y),z,u). [para(46(a,2),1771(a,1,1))]. 1773 (x / (y * (z * x))) * (y * z) = x / L(x,z,y). [para(32(a,2),1753(a,1,2)),flip(a)]. 1774 (x / (y * (z * x))) * (y * z) = L(x,z,y) \ x. [para(1773(a,2),519(a,1))]. 1775 (L(x * y,z / (x * (y * z)),x * y) * (z / (x * (y * z)))) * (x * y) = (x * y) * (L(z,y,x) \ z). [para(1774(a,1),1310(a,2,2))]. 1776 (x * (y * (y * (z * u)))) \ (((x * (y * y)) * z) * u) = a(x,z,u). [para(411(a,1),1723(a,1,1))]. 1777 (x * (y * (y * (z * u)))) \ ((x * (y * (y * z))) * u) = a(x,z,u). [para(411(a,1),1776(a,1,2,1))]. 1778 a(x,y * (y * z),u) = a(x,z,u). [para(1777(a,1),90(a,1)),flip(a)]. 1779 a(x,y \ z,u) = a(x,y * z,u). [para(20(a,1),1778(a,1,2,2)),flip(a)]. 1780 a(x,(y / z) * y,u) = a(x,z,u). [para(22(a,1),1778(a,1,2,2))]. 1783 a(x,K(y,z) * T(y,z),u) = a(x,y,u). [para(1081(a,2),1778(a,1,2,2))]. 1785 a(x * (y * y),y * 1,y) = a(x * y,y \ 1,y \ 1). [para(1779(a,1),1574(a,1))]. 1786 a(x,y \ 1,z) * (y \ 1) = y \ a(x,y * 1,z). [para(1779(a,1),1689(a,2,2))]. 1787 a(x,(y * (y * z)) * (y * u),w) = a(x,z \ (y \ u),w). [para(282(a,1),1780(a,1,2,1))]. 1789 a(x,T(T(y,z),z),u) = a(x,y,u). [para(1113(a,1),1783(a,1,2))]. 1790 a(T(x,y),y,z) = a(x,T(y,x),z). [para(1789(a,1),1460(a,1))]. 1793 a(x,y \ 1,z) * (y \ 1) = y \ a(x,y,z). [para(18(a,1),1786(a,2,2,2))]. 1794 a(x,y * 1,z) * (y \ 1) = y \ a(x,y,z). [para(1779(a,1),1793(a,1,1))]. 1795 a(x,y,z) * (y \ 1) = y \ a(x,y,z). [para(18(a,1),1794(a,1,1,2))]. 1796 a(x * (y * y),y,y) = a(x * y,y \ 1,y \ 1). [para(18(a,1),1785(a,1,2))]. 1797 a(x * y,y \ 1,y \ 1) = a(x,y,y). [para(1796(a,1),1720(a,1))]. 1798 L(x,x,y) \ x = a(y,x,x). [para(1797(a,1),1408(a,1)),flip(a)]. 1800 a(x,y,y) * L(y,y,x) = y. [para(1798(a,1),520(a,1,1))]. 1801 R(x,y,y) * L(y,y,x) = x * y. [para(1800(a,1),966(a,1,2)),flip(a)]. 1802 T(R(x,y,y),L(y,y,x)) = L(y,y,x) \ (x * y). [para(1801(a,1),36(a,2,2))]. 1803 R(T(x,L(y,y,x)),y,y) = L(y,y,x) \ (x * y). [para(1802(a,1),46(a,2))]. 1804 L(x,x,y) \ (y * x) = R(T(y,x),x,x). [para(1558(a,1),1803(a,1,1)),flip(a)]. 1805 a(x,y * (y * (z * (y * u))),w) = a(x,z \ (y \ u),w). [para(51(a,1),1787(a,1,2))]. 1806 a(x,y \ (z \ u),w) = a(x,y * (z * u),w). [para(1805(a,1),1778(a,1))]. 1808 a(x,y * (z \ u),w) = a(x,y * (z * u),w). [para(1806(a,1),1779(a,1)),flip(a)]. 1809 a(x * y,T(x,x * y),z) = ((y / x) * (x * z)) \ (y * z). [para(1265(a,1),1713(a,1,1)),flip(a)]. 1810 a(x * y,T(x,x * y),z) = a(y / x,x,z). [para(1809(a,2),68(a,1))]. 1811 R(K(x,y),z,z) * (x / z) = (z \ 1) * T((z \ 1) \ (x / z),y). [para(1637(a,1),1745(a,1,1))]. 1812 K(x,R(y,z,z)) * (x / z) = (z \ 1) * T((z \ 1) \ (x / z),y). [para(1765(a,1),1811(a,1,1))]. 1813 K(x,R(y,z,z)) * (x / z) = (z \ 1) * T(z * (x / z),y). [para(330(a,1),1812(a,2,2,1))]. 1814 K(x,R(y,z,z)) * (x / z) = z \ T(z * (x / z),y). [para(1813(a,2),318(a,1))]. 1815 K(x,R(y,z,z)) * (x / z) = T(x,y) / z. [para(1814(a,2),755(a,1))]. 1816 a(x * (y \ (y \ (y \ (x * (y \ 1))))),z,u) = a(K(x / (y * y),y),z,u). [para(602(a,1),1725(a,1,1))]. 1817 a(x * (y \ ((y \ (y \ x)) * (y \ 1))),z,u) = a(K(x / (y * y),y),z,u). [para(285(a,1),1816(a,1,1,2,2))]. 1818 a(x * (y * ((y \ (y \ x)) * (y \ 1))),z,u) = a(K(x / (y * y),y),z,u). [para(1817(a,1),1759(a,1)),flip(a)]. 1819 a(K(x / (y * y),y),z,u) = a(x * (y \ (x * (y \ 1))),z,u). [para(265(a,1),1818(a,1,1,2)),flip(a)]. 1820 a(K(x / (y * y),y),z,u) = a(x * (y * (x * (y \ 1))),z,u). [para(1819(a,2),1759(a,1))]. 1821 a(K(x / (y * y),y),z,u) = a(x * T(x,y \ 1),z,u). [para(347(a,1),1820(a,2,1,2))]. 1822 a(K(x / (y * y),y),z,u) = a(K(x,y \ 1),z,u). [para(1821(a,2),1712(a,1))]. 1823 a(K(x,y \ 1),z,u) = a(K(x,y),z,u). [para(1418(a,1),1822(a,1,1)),flip(a)]. 1824 a(K(x \ 1,y),z,u) = a(K(y,x),z,u). [para(1823(a,1),905(a,1)),flip(a)]. 1825 a(x * ((x * y) * y),z,u) = a(K(x * y,x),z,u). [para(1824(a,1),1760(a,1)),flip(a)]. 1826 a(K(x * y,x),z,u) = a(a(x,y,y),z,u). [para(1825(a,1),1755(a,1))]. 1827 (x * y) * R((x * y) \ (x * z),u,w) = x * (y * R(y \ z,u,w)). [para(1697(a,2),74(a,1))]. 1828 (x * y) * R((x * y) \ z,u,w) = x * (y * R(y \ (x \ z),u,w)). [para(20(a,1),1827(a,1,2,1,2))]. 1829 (x * y) * R((x * y) \ y,z,u) = R(x,z,u) * (x \ y). [para(1828(a,2),639(a,1))]. 1830 T(x,y) \ R(T(x,y),z,u) = y \ (R(x,z,u) * (x \ y)). [para(1829(a,1),1610(a,1,2)),flip(a)]. 1831 T(x,y) \ R(T(x,y),z,u) = T(x \ R(x,z,u),y). [para(1830(a,2),539(a,1))]. 1832 (R(T(x,y),z,u) \ T(x,y)) * w = T(x \ R(x,z,u),y) \ w. [para(1831(a,1),465(a,1,1)),flip(a)]. 1833 T(x \ R(x,y,y),z) = a(T(x,z),y,y). [para(1831(a,1),962(a,1))]. 1834 K(x,y) * R(T(y,x),z,u) = y * T(y \ R(y,z,u),x). [para(1831(a,1),1099(a,1,2)),flip(a)]. 1835 T(T(x,y) \ R(T(x,y),z,u),y) = x \ R(x,z,u). [para(1831(a,1),1582(a,1))]. 1836 a(T(x,y),z,z) = T(a(x,z,z),y). [para(962(a,1),1833(a,1,1)),flip(a)]. 1837 T(T(x \ R(x,y,z),u),u) = x \ R(x,y,z). [para(1831(a,1),1835(a,1,1))]. 1838 (x * (y \ R(y,z,u))) / x = T(y \ R(y,z,u),x). [para(1837(a,1),105(a,1,1,2))]. 1839 T(a(x,y,z),x * (y * z)) = x \ R(x,y,z). [para(739(a,2),1837(a,1,1))]. 1840 a(x,y,z) * K(a(x,y,z),x * (y * z)) = x \ R(x,y,z). [para(1839(a,1),1107(a,1)),flip(a)]. 1841 T(T(x \ R(x,y,z),u),x * (y * z)) = (u * a(x,y,z)) / u. [para(1838(a,1),742(a,1,1))]. 1842 (x * (y \ R(y,z,u))) / x = (y \ R(y,z,u)) * K(y \ R(y,z,u),x). [para(1838(a,2),1107(a,1))]. 1843 (x * a(y,z,u)) / x = T(a(y,z,u),x). [para(1841(a,1),740(a,1))]. 1844 T(a(x,y,z),u) * (u / (u * a(x,y,z))) = 1. [para(1843(a,1),354(a,1,1))]. 1845 L(x,x,x * ((x \ 1) * a(y,z,u))) = ((x \ 1) * a(y,z,u)) \ T(a(y,z,u),x \ 1). [para(1843(a,1),1488(a,2,2))]. 1846 K(a(x,y,z),u) * K(a(x,y,z),u) = 1. [para(1844(a,1),1174(a,1)),flip(a)]. 1847 K(a(x,y,z),u) = K(u,a(x,y,z)). [hyper(24,a,898,a,b,1846,a)]. 1848 a(x,y,z) * K(x * (y * z),a(x,y,z)) = x \ R(x,y,z). [para(1847(a,1),1840(a,1,2))]. 1849 K(x \ R(x,y,z),u) = K(u,x \ R(x,y,z)). [hyper(23,a,1014,a(flip),b,1842,a(flip))]. 1850 L(L(x,y,z * u),(z * u) * y,u * z) = L(x,y,K(z,u)). [para(1698(a,1),174(a,1)),flip(a)]. 1851 ((x * (x * y)) * a(y,z,u)) / y = a(x * (x * y),z,u) * (x * x). [para(1700(a,1),749(a,1,1,2))]. 1852 (x * (x * (y * a(y,z,u)))) / y = a(x * (x * y),z,u) * (x * x). [para(51(a,1),1851(a,1,1))]. 1854 a(x * (x * y),z,u) * (x * x) = x * (x * ((y * a(y,z,u)) / y)). [para(1852(a,1),211(a,1))]. 1855 a(x * (x * y),z,u) * (x * x) = x * (x * a(y,z,u)). [para(748(a,1),1854(a,2,2,2))]. 1856 a(x,y,z) * (u * u) = u * (u * a(x,y,z)). [para(1700(a,1),1855(a,1,1))]. 1857 T((a(x,y,z) * (u * u)) / (u * u),u) = T(u \ (u * a(x,y,z)),u \ 1). [para(1856(a,2),666(a,1,1,1))]. 1859 T(x \ (x * a(y,z,u)),x \ 1) = T(a(y,z,u),x). [para(21(a,1),1857(a,1,1)),flip(a)]. 1860 T(a(x,y,z),u \ 1) = T(a(x,y,z),u). [para(19(a,1),1859(a,1,1))]. 1863 x * L(T(y \ (y / x),z),y,x * y) = K(L(y \ (y / x),y,x * y),z). [para(1295(a,1),330(a,1)),flip(a)]. 1864 (x / y) * (y * T(y \ (y / x),z)) = K(L(y \ (y / x),y,x * y),z). [para(1863(a,1),1294(a,1)),flip(a)]. 1865 (x / y) * (y * T(y \ (y / x),z)) = K(x \ 1,z). [para(1289(a,1),1864(a,2,1))]. 1866 (L(x,y,z) / (z * (y * x))) * ((z * (y * x)) * T((z * (y * x)) \ (z * y),u)) = K(L(x,y,z) \ 1,u). [para(99(a,1),1865(a,1,2,2,1,2))]. 1868 T(x * x,y * z) \ ((((y * z) \ (x * x)) * y) * z) = a((y * z) * (x * x),y,z). [para(394(a,2),1702(a,1))]. 1869 ((R(x,y,z) * u) * w) / ((x * u) * w) = R(x,u,w) \ R(R(x,u,w),y,z). [para(185(a,1),538(a,1,1))]. 1870 R(x \ R(x,y,z),x * u,w) = R(x,u,w) \ R(R(x,u,w),y,z). [para(1869(a,1),533(a,2))]. 1871 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). [para(584(a,1),1870(a,2,1))]. 1872 (K(x,T(y,z)) * T(y,x)) / y = K(z,T(y,x)) * K(y,z). [para(1663(a,1),1570(a,1,2))]. 1873 K(x,T(y,z)) * K(y,x) = K(y,z) * K(z,T(y,x)). [para(1872(a,1),1666(a,1))]. 1874 T(x * x,y * z) \ ((((y * z) \ (x * x)) * y) * z) = a(y * z,y,z). [para(1868(a,2),1720(a,1))]. 1875 (T(x * x,y * z) \ (((y * z) \ (x * x)) * y)) * z = a(y * z,y,z). [para(1874(a,1),591(a,1)),flip(a)]. 1877 ((T(x * x,y * z) \ ((y * z) \ (x * x))) * y) * z = a(y * z,y,z). [para(591(a,1),1875(a,1,1))]. 1878 (((x * y) \ 1) * x) * y = a(x * y,x,y). [para(795(a,1),1877(a,1,1,1))]. 1879 ((x * y) \ x) * y = a(x * y,x,y). [para(318(a,1),1878(a,1,1))]. 1880 x * ((y * x) \ y) = a(y * x,y,x). [para(1879(a,1),388(a,1)),flip(a)]. 1881 a(x * (x \ y),x,x \ y) = (x \ y) * (y \ x). [para(20(a,1),1880(a,1,2,1)),flip(a)]. 1882 (x \ y) * (y \ x) = a(y,x,x \ y). [para(20(a,1),1881(a,1,1)),flip(a)]. 1883 L(x,y,(z \ u) * (u * z)) = L(x,y,a(z,u,u \ z)). [para(1882(a,1),869(a,1,3)),flip(a)]. 1884 L(x,(y \ z) * (z * y),u) = L(x,a(y,z,z \ y),u). [para(1882(a,1),1362(a,1,2)),flip(a)]. 1885 L(x,y,(z * u) * (u * z)) = L(x,y,a(z,u,u \ z)). [para(1883(a,1),781(a,1)),flip(a)]. 1886 L(x,(y * z) * (z * y),u) = L(x,a(y,z,z \ y),u). [para(1884(a,1),880(a,1)),flip(a)]. 1887 L(x,y,a(z,u,u \ z)) = L(x,y,K(u,z)). [para(1885(a,1),779(a,1))]. 1888 L(x,a(y,z,z \ y),u) = L(x,K(z,y),u). [para(1886(a,1),879(a,1))]. 1889 ((x \ 1) * a(y,z,u)) \ T(a(y,z,u),x \ 1) = L(x,x,a(y,z,u)). [para(321(a,1),1845(a,1,3)),flip(a)]. 1890 (x \ a(y,z,u)) \ T(a(y,z,u),x \ 1) = L(x,x,a(y,z,u)). [para(318(a,1),1889(a,1,1))]. 1892 (x \ a(y,z,u)) \ T(a(y,z,u),x) = L(x,x,a(y,z,u)). [para(1860(a,1),1890(a,1,2))]. 1893 L(x,a(y,z,u),x) = L(x,x,a(y,z,u)). [para(1892(a,1),440(a,1)),flip(a)]. 1894 L(x,x,a(y,z,z \ y)) = L(x,K(z,y),x). [para(1893(a,1),1888(a,1))]. 1895 L(x,K(y,z),x) = L(x,x,K(y,z)). [para(1894(a,1),1887(a,1))]. 1896 L(x,K(y,z),x) = L(x,x,K(z,y)). [para(1895(a,2),909(a,1))]. 1897 (x \ K(y,z)) / (K(y,z) / L(x,x,K(z,y))) = K(K(y,z),x). [para(1896(a,1),1500(a,2,2,2)),flip(a)]. 1898 (x \ K(y,z)) / (K(y,z) * (x \ 1)) = K(K(y,z),x). [para(930(a,1),1897(a,1,2))]. 1899 K(x \ 1,K(y,z)) = K(K(y,z),x). [para(1898(a,1),978(a,1)),flip(a)]. 1900 K(K(x,y),z) * (K(x,y) \ u) = T(K(x,y),z \ 1) \ u. [para(1899(a,1),1095(a,1,1))]. 1901 T(K(x,y),z) * K(K(x,y),z) = T(K(x,y),z * z). [para(1899(a,1),1433(a,1,2))]. 1902 T(T(K(x,y),z),z) = T(K(x,y),z * z). [para(1901(a,1),1121(a,1)),flip(a)]. 1903 T(K(x,y),T(z,x) * T(z,x)) = T(T(K(x,y),z),T(z,x)). [para(1352(a,1),1902(a,1,1)),flip(a)]. 1904 x / (T(K(y,z),u \ 1) \ x) = K(y,z) * K(u,K(y,z)). [para(1900(a,1),1071(a,1,2))]. 1905 T(K(x,y),z * T(T(z,x),x)) = T(T(K(x,y),z),T(z,x)). [para(1088(a,1),1903(a,1,2))]. 1906 K(x,y) * K(z,K(x,y)) = T(K(x,y),z \ 1). [para(1904(a,1),65(a,1))]. 1907 T(K(x,y),z \ 1) * z = z * K(x,y). [para(1906(a,1),1018(a,1,1))]. 1908 ((x * y) * (z / (x * (y * z)))) * (x * y) = (x * y) * (L(z,y,x) \ z). [para(851(a,1),1775(a,1,1,1))]. 1910 (x \ R(x,y,z)) * (x * y) = (x * y) * (L(z,y,x) \ z). [para(1410(a,1),1908(a,1,1))]. 1911 (x * y) * (L(z,y,x) \ z) = R(x,y,z) * y. [para(1910(a,1),528(a,1))]. 1912 ((x * y) \ 1) * ((x * (y * z)) * T((x * (y * z)) \ (x * y),u)) = K(L(z,y,x) \ 1,u). [para(342(a,1),1866(a,1,1))]. 1914 ((x * y) \ 1) * (x * ((y * z) * T((y * z) \ y,u))) = K(L(z,y,x) \ 1,u). [para(1590(a,1),1912(a,1,2))]. 1915 ((x * y) \ 1) * (x * (y * K(z \ 1,u))) = K(L(z,y,x) \ 1,u). [para(1164(a,1),1914(a,1,2,2))]. 1916 (x * y) \ (x * (y * K(z \ 1,u))) = K(L(z,y,x) \ 1,u). [para(1915(a,1),318(a,1)),flip(a)]. 1917 L(K(x \ 1,y),z,u) = K(L(x,z,u) \ 1,y). [para(1916(a,1),32(a,2))]. 1918 K(L(x \ 1,y,z) \ 1,u) = L(K(x,u),y,z). [para(156(a,1),1917(a,1,1,1)),flip(a)]. 1920 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). [para(750(a,1),1871(a,1,1))]. 1921 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). [para(18(a,1),1920(a,1,1,1))]. 1922 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). [para(18(a,1),1921(a,1,1,2,1))]. 1923 (R(x,y,z) \ 1) \ R(R(x \ 1,x * y,z),u,w) = R(x \ R(x,u,w),y,z). [para(322(a,1),1922(a,1,2)),flip(a)]. 1924 (R(x,y,z) \ 1) \ R(R(x,y,z) \ 1,u,w) = R(x \ R(x,u,w),y,z). [para(584(a,1),1923(a,1,2,1))]. 1925 (R(x,y,z) * 1) \ R(R(x,y,z) * 1,u,w) = R(x \ R(x,u,w),y,z). [para(1924(a,1),750(a,1)),flip(a)]. 1926 R(x,y,z) \ R(R(x,y,z) * 1,u,w) = R(x \ R(x,u,w),y,z). [para(18(a,1),1925(a,1,1))]. 1927 R(x,y,z) \ R(R(x,y,z),u,w) = R(x \ R(x,u,w),y,z). [para(18(a,1),1926(a,1,2,1))]. 1928 R(x \ R(x,y,y),z,u) = a(R(x,z,u),y,y). [para(1927(a,1),962(a,1))]. 1929 T(R(x \ R(x,y,x),z,u),x * (R(x,z,u) * T(y,x))) = a(R(x,z,u),y,x). [para(1927(a,1),743(a,1,1))]. 1930 a(R(x,y,z),u,u) = R(a(x,u,u),y,z). [para(962(a,1),1928(a,1,1)),flip(a)]. 1931 T(R(a(x,y,x),z,u),x * (R(x,z,u) * T(y,x))) = a(R(x,z,u),y,x). [para(1539(a,1),1929(a,1,1,1))]. 1932 T(R(a(x,y,x),z,u),R(x,z,u) * (y * x)) = a(R(x,z,u),y,x). [para(530(a,1),1931(a,1,2))]. 1933 R(T(a(x,y,x),R(x,z,u) * (y * x)),z,u) = a(R(x,z,u),y,x). [para(1932(a,1),46(a,2))]. 1934 ((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). [para(342(a,1),1597(a,1,1))]. 1936 ((x * y) \ 1) * (x * ((y * z) * R((y * z) \ y,u,w))) = L(z,y,x) \ R(L(z,y,x),u,w). [para(1827(a,1),1934(a,1,2))]. 1937 ((x * y) \ 1) * (x * (y * (z \ R(z,u,w)))) = L(z,y,x) \ R(L(z,y,x),u,w). [para(1592(a,1),1936(a,1,2,2))]. 1938 (x * y) \ (x * (y * (z \ R(z,u,w)))) = L(z,y,x) \ R(L(z,y,x),u,w). [para(1937(a,1),318(a,1)),flip(a)]. 1939 L(x,y,z) \ R(L(x,y,z),u,w) = L(x \ R(x,u,w),y,z). [para(1938(a,1),32(a,2)),flip(a)]. 1940 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). [para(1808(a,1),1686(a,1,1,2,1))]. 1941 L((x * (y \ R(y,x,z))) * (1 * u),x * (y \ R(y,x,z)),x) = (y \ R(y,x,z)) * (x * u). [para(1442(a,1),1940(a,1,1,2,1))]. 1942 L((x * (y \ R(y,x,z))) * u,x * (y \ R(y,x,z)),x) = (y \ R(y,x,z)) * (x * u). [para(17(a,1),1941(a,1,1,2))]. 1944 L(x * (R(y,x,z) * (y \ u)),x * (y \ R(y,x,z)),x) = (y \ R(y,x,z)) * (x * u). [para(1450(a,1),1942(a,1,1))]. 1945 L(x * (R(y,x,z) * (y \ u)),x * (y * R(y,x,z)),x) = (y \ R(y,x,z)) * (x * u). [para(1944(a,1),1360(a,1)),flip(a)]. 1946 (x \ R(x,y,z)) * (y * u) = y * (R(x,y,z) * (x \ u)). [para(1945(a,1),1439(a,1))]. 1947 R(x,y,z) * (x \ (y * u)) = y * (R(x,y,z) * (x \ u)). [para(1946(a,1),532(a,1)),flip(a)]. 1948 R(x,y,z) * (x \ (y * (y \ z))) = L(z,x * y,x). [para(1947(a,2),1567(a,1))]. 1949 R(x,y,z) * (x \ z) = L(z,x * y,x). [para(20(a,1),1948(a,1,2,2))]. 1950 R(x,y,L(z,y,x)) * (x \ L(z,y,x)) = z. [para(1949(a,2),303(a,1))]. 1951 L(x,y * z,y) / x = y \ R(y,z,x). [para(1949(a,1),536(a,1,1))]. 1952 x / L(x,y * z,y) = R(y,z,x) \ y. [para(1949(a,1),542(a,1,2))]. 1953 x \ L(x,y * z,y) = y \ R(y,z,x). [para(1951(a,1),515(a,1)),flip(a)]. 1954 L(x,y * z,y) \ x = R(y,z,x) \ y. [para(1952(a,1),519(a,1)),flip(a)]. 1955 x \ R(x,x \ y,z) = z \ L(z,y,x). [para(20(a,1),1953(a,1,2,2)),flip(a)]. 1956 x \ R(x,x * y,z) = z \ L(z,y,x). [para(313(a,1),1953(a,1,2)),flip(a)]. 1957 K(x,R(y,z,x) \ y) = 1. [para(1954(a,1),653(a,1,2))]. 1958 K(x,y \ R(y,z,x)) = 1. [para(622(a,1),1957(a,1,2))]. 1959 T(x,y \ R(y,z,x)) = x. [hyper(41,a,1958,a)]. 1960 K(x,T(y \ R(y,z,x),u)) = 1. [para(1831(a,1),1958(a,1,2))]. 1961 T(x \ R(x,y,z),z) = x \ R(x,y,z). [hyper(39,a,1959,a)]. 1962 K(x,a(y,z,x)) = 1. [para(739(a,2),1960(a,1,2))]. 1963 T(x,a(y,z,x)) = x. [hyper(41,a,1962,a)]. 1964 a(x,y,z) * z = z * a(x,y,z). [para(1963(a,1),82(a,1,2))]. 1965 R(x,y,z) \ x = z \ L(z,y,x). [para(1955(a,1),624(a,1)),flip(a)]. 1966 L(x,y,z) = x * (R(z,y,x) \ z). [para(1965(a,2),20(a,1,2)),flip(a)]. 1967 R(x,y,z) = x / (z \ L(z,y,x)). [para(1965(a,1),65(a,1,2)),flip(a)]. 1968 (x \ L(x,y,z)) \ 1 = z \ R(z,y,x). [para(1965(a,1),460(a,1,1))]. 1969 (x \ L(x,y,z)) * R(z,y,x) = z. [para(1965(a,1),496(a,1,1))]. 1970 L(x,y,z) = (R(z,y,x) \ z) * x. [para(1965(a,2),514(a,1,1)),flip(a)]. 1971 x * (R(K(y,z),u,x) \ K(y,z)) = L(x,u,K(z,y)). [para(1966(a,1),909(a,1))]. 1972 R(x,y,T(z,x * y)) = R(x,y,z). [hyper(23,a,680,a,b,1969,a),flip(a)]. 1973 L(x,y,z) * R(z,y,x) = x * z. [para(1969(a,1),504(a,1,2)),flip(a)]. 1974 L(x,y,z) * (x \ R(z,y,x)) = z. [para(1969(a,1),647(a,1)),flip(a)]. 1975 R(x,y,z) * L(z,y,x) = x * z. [para(1970(a,2),458(a,1,2))]. 1976 L(x,y,z) = (z \ R(z,y,x)) \ x. [para(1970(a,2),465(a,2)),flip(a)]. 1977 T(x \ R(x,y,z),u) \ z = L(z,y,T(x,u)). [para(1970(a,2),1832(a,1)),flip(a)]. 1978 L(x,y,z) \ x = z \ R(z,y,x). [para(1972(a,1),681(a,2,2))]. 1979 R(x,y,z) = x * (L(z,y,x) \ z). [para(1972(a,1),683(a,1))]. 1980 R(x,y,z) * (x \ L(z,y,x)) = z. [para(1972(a,1),686(a,1,1))]. 1981 (L(x,y,z) * (R(z,y,x) * u)) \ ((x * z) * u) = a(L(x,y,z),R(z,y,x),u). [para(1973(a,1),28(a,2,2,1)),flip(a)]. 1984 (L(x,y,z) \ x) * (z * u) = R(z,y,x) * u. [para(1978(a,2),528(a,1,1))]. 1985 (x \ R(x,y,z)) * u = z * (L(z,y,x) \ u). [para(1978(a,1),650(a,1,1))]. 1986 R(x \ R(x,y,z),z,u) = L(z,y,x) \ z. [para(1978(a,1),736(a,1,1))]. 1987 (x * y) * (x \ R(x,y,z)) = R(x,y,z) * y. [para(1978(a,1),1911(a,1,2))]. 1988 K(x,y) \ R(K(x,y),z,u) = u \ L(u,z,K(x,y)). [para(1669(a,1),1956(a,1,2))]. 1989 x \ R(x,y,z) = (L(z,y,x) \ z) * 1. [para(1968(a,1),517(a,1))]. 1990 R(x,y,L(z,y,x)) = R(x,y,z). [hyper(24,a,1980,a,b,1950,a)]. 1991 (x \ R(x,y,z)) \ z = L(z,y,T(x,z)). [para(1961(a,1),1977(a,1,1))]. 1992 L(x,y,T(z,x)) = L(x,y,z). [para(1991(a,1),1976(a,2)),flip(a)]. 1993 L(L(x,y,z),z * y,T(z,L(x,y,z))) = x. [para(1992(a,2),303(a,1))]. 1994 L(x,y,K(z,L(x,y,z))) = x. [para(1993(a,1),1606(a,1)),flip(a)]. 1995 x * (L(x,y,z) \ (z * u)) = R(z,y,x) * u. [para(1984(a,1),650(a,1)),flip(a)]. 1996 L((x \ R(x,y,z)) \ u,x \ R(x,y,z),x * y) = (R(x,y,z) * y) \ ((x * y) * u). [para(1987(a,1),76(a,2,1))]. 1998 L(x,y,z) * (R(z,y,x) * u) = x * (z * u). [para(1995(a,1),645(a,1,2))]. 1999 x * (L(x,y,z) \ (z * T(y,z))) = y * R(z,y,x). [para(1995(a,2),1643(a,1))]. 2000 x * (L(x,y,z) \ (z * L(x,y,z))) = z * x. [para(1995(a,2),1975(a,1))]. 2001 x * T(y,L(x,z,y)) = y * x. [para(36(a,2),2000(a,1,2))]. 2002 T(x,L(y,z,x)) = x * K(x,y). [hyper(23,a,1116,a,b,2001,a)]. 2005 K(x,L(y,z,x)) = K(x,y). [hyper(23,a,1107,a(flip),b,2002,a(flip)),flip(a)]. 2006 L(x,y,K(z,x)) = x. [para(2005(a,1),1994(a,1,3))]. 2007 L(T(x,y),z,K(u,x)) = T(x,y). [para(2006(a,1),44(a,2,1))]. 2008 L(x,y,K(x,z)) = x. [para(2006(a,1),909(a,1)),flip(a)]. 2009 L(x,y,a(x,z,z)) = x. [para(2006(a,1),1262(a,1)),flip(a)]. 2010 L(K(x,y),z,K(u,x \ 1)) = K((x \ 1) \ 1,y). [para(2006(a,1),1918(a,1,1,1)),flip(a)]. 2011 R(K(x,y),z,y) = K(x,y) / (y \ y). [para(2006(a,1),1967(a,2,2,2))]. 2013 (K(x,y) * z) * x = K(x,y) * (z * x). [para(2008(a,1),74(a,1,2))]. 2014 x * (x \ R(a(x,y,y),z,x)) = a(x,y,y). [para(2009(a,1),1974(a,1,1))]. 2015 T(x,K(y,x) * z) = T(x,z). [para(2007(a,1),1377(a,1)),flip(a)]. 2016 K(K(x,y) * z,y) = T(y,z) \ y. [para(2015(a,1),1080(a,2,1))]. 2017 K(x,K(y,x) * z) = x \ T(x,z). [para(2015(a,1),1108(a,2,2))]. 2019 T(x,y * T(z,x)) = T(x,y * z). [para(1212(a,1),2015(a,1,2))]. 2021 K(K(x,y) * z,y) = K(z,y). [para(2016(a,2),1080(a,2)),flip(a)]. 2022 K(K(x,y) * z,x) = K(z,x). [para(901(a,1),2021(a,1,1)),flip(a)]. 2023 K(x * (K(x,y) * z),x) = K(x * z,x). [para(1068(a,1),2022(a,1,1))]. 2024 K(x,K(y,x) * z) = K(x,z). [para(2017(a,2),1108(a,2)),flip(a)]. 2025 K(x,K(x,y) * z) = K(x,z). [para(901(a,1),2024(a,1,2)),flip(a)]. 2026 K(x,y) * K(x * (K(x,z) * y),x) = a(x,K(x,z) * y,x). [para(2025(a,1),1537(a,1,1))]. 2027 R(K(x,y),z,y) = K(x,y) / 1. [para(60(a,1),2011(a,2,2))]. 2029 R(K(x,y),z,y) = K(x,y). [para(2027(a,2),64(a,1))]. 2030 K(x,R(y,z,y)) = K(x,y). [para(2029(a,1),1654(a,1)),flip(a)]. 2031 R(K(x,y),z,x) = K(y,x) \ 1. [para(2029(a,1),1670(a,1,1)),flip(a)]. 2032 K(x,y) * R(T(y,x),z,y) = R(y,z,y). [para(2030(a,1),1083(a,1,1))]. 2033 R(K(x,y),z,x) = K(x,y). [para(2031(a,2),897(a,1))]. 2034 K(L(x,y,x),z) = K(x,z). [para(2033(a,1),1638(a,1)),flip(a)]. 2036 K((x \ y) \ y,z) = K(T(x,y),z). [para(1457(a,1),2034(a,1,1))]. 2038 K(T(x,x \ y),z) = K(T(x,y),z). [para(83(a,2),2036(a,1,1))]. 2039 x \ (K(x,y) * (z * x)) = T(K(x,y) * z,x). [para(2013(a,1),36(a,2,2)),flip(a)]. 2040 x * ((K(x,y) * z) * x) = T(x,y) * (z * x). [para(2013(a,2),1120(a,1,2))]. 2041 T(x,y) \ R(T(x,y),z,x) = x \ R(x,z,x). [para(2032(a,1),1163(a,1,2)),flip(a)]. 2042 x * (x \ a(R(x,y,x),z,z)) = a(x,z,z). [para(1930(a,2),2014(a,1,2,2))]. 2043 x * (x \ a(L(x,y,x),z,z)) = a(x,z,z). [para(1303(a,1),2042(a,1,2,2,1))]. 2044 a(L(x,y,x),z,z) = a(x,z,z). [para(2043(a,1),20(a,1)),flip(a)]. 2045 a(L(T(x,y),y * x,x),z,z) = a(T(x,y),z,z). [para(1283(a,1),2044(a,1,1))]. 2046 K(x,y) * (x \ (z * x)) = T(K(x,y) * z,x). [para(2039(a,1),1076(a,1)),flip(a)]. 2047 (T(x,y) * (z * x)) \ ((T(x,y) * z) * x) = a(x,K(x,y) * z,x). [para(2040(a,1),1166(a,1,1))]. 2048 T(x,y) \ R(T(x,y),z,x) = a(x,z,x). [para(2041(a,2),1539(a,1))]. 2049 T(x \ R(x,y,x),z) = a(x,y,x). [para(2048(a,1),1831(a,1)),flip(a)]. 2050 T(a(x,y,x),z) = a(x,y,x). [para(1539(a,1),2049(a,1,1))]. 2052 a(R(x,y,z),u,x) = R(a(x,u,x),y,z). [para(2050(a,1),1933(a,1,1)),flip(a)]. 2054 a(x,y,x) \ a(R(x,z,z),y,x) = a(a(x,y,x),z,z). [para(2052(a,2),962(a,1,2))]. 2056 T(K(x,y) * z,x) = K(x,y) * T(z,x). [para(36(a,2),2046(a,1,2)),flip(a)]. 2057 T(K(x,y) * R(z,u,w),x) = K(x,y) * R(T(z,x),u,w). [para(46(a,2),2056(a,2,2))]. 2058 T(K(x,y) * z,x) / z = K(z,x) * K(x,y). [para(2056(a,2),1666(a,1,1))]. 2059 T(K(x,y) * z,x) / z = K(x,y) * K(z,x). [para(2058(a,2),1226(a,2)),flip(a)]. 2060 L(K(x,y),z,K(u,x \ 1)) = K(x,y). [para(156(a,1),2010(a,2,1))]. 2061 L(K(x,y),z,K(u,x)) = K(x,y). [para(2060(a,1),1618(a,1)),flip(a)]. 2062 L(K(x,y),z,K(x,u)) = K(x,y). [para(2060(a,1),1619(a,1)),flip(a)]. 2063 (K(x,y) * z) \ z = T(K(y,x),z). [para(2061(a,1),1301(a,1,1)),flip(a)]. 2064 T(K(x,y) * z,K(x,y)) = z * K(x,y). [para(2062(a,1),1309(a,1,1,1))]. 2065 x / T(K(y,z),x) = K(z,y) * x. [para(2063(a,1),65(a,1,2))]. 2067 (T(K(x,y),z) / z) * u = (K(y,x) * z) \ u. [para(2065(a,1),358(a,1,1)),flip(a)]. 2068 (K(x,y) * z) * K(y,x) = T(z,K(y,x)). [para(2065(a,1),1549(a,1,1))]. 2069 K(K(x,y) * z,K(y,x)) = T(z,K(y,x)) / z. [para(2068(a,1),979(a,1,1)),flip(a)]. 2070 K(K(x,y) * z,K(y,x)) = K(z,K(y,x)). [para(2069(a,2),1086(a,2)),flip(a)]. 2071 K(K(x,y) * z,K(x,y)) = K(z,K(x,y)). [para(901(a,1),2070(a,1,1)),flip(a)]. 2072 a(a(K(x,y),z,z),u,w) = a(K(z,K(x,y)),u,w). [para(2071(a,1),1826(a,1,1)),flip(a)]. 2073 a(R(T(x,y),y,x),z,z) = a(T(x,y),z,z). [para(1306(a,1),2045(a,1,1))]. 2074 a(R(x,y,y),z,z) = a(T(x,y),z,z). [para(2073(a,1),1772(a,1)),flip(a)]. 2076 x * (K(y,z) * R(K(z,y),u,x)) = L(x,u,K(z,y)). [para(1671(a,1),1971(a,1,2))]. 2077 x * (K(y,z) * K(z,R(y,u,x))) = L(x,y * u,K(y,z)). [para(1668(a,1),1971(a,1,2))]. 2078 x * (L(x,y,z) \ (y * z)) = y * R(z,y,x). [para(82(a,1),1999(a,1,2,2))]. 2079 L(x,y,z) = (x * (y * z)) / (y * R(z,y,x)). [para(2078(a,1),648(a,1,2)),flip(a)]. 2080 T(K(x,y) * R(y,z,u),x) = y * T(y \ R(y,z,u),x). [para(2057(a,2),1834(a,1))]. 2081 T(K(x,y) * R(y,z,u),x) / R(y,z,u) = K(R(y,z,u) / y,x). [para(2080(a,2),1211(a,1,1))]. 2082 a(x,K(x,y) * z,x) = K(x,z) * K(x * z,x). [para(2023(a,1),2026(a,1,2)),flip(a)]. 2083 a(x,K(x,y) * z,x) = a(x,z,x). [para(2082(a,2),1537(a,1))]. 2085 a(x,K(x,y) * z,x) = a(T(x,y),z,x). [para(2047(a,1),28(a,2)),flip(a)]. 2086 a(T(x,y),z,x) = a(x,z,x). [para(2085(a,1),2083(a,1))]. 2087 a((x \ y) \ y,z,x) = a(x,z,x). [para(83(a,1),2086(a,1,1))]. 2089 a((x \ y) * y,z,x) = a(x,z,x). [para(2087(a,1),1702(a,1)),flip(a)]. 2090 a((x * y) * y,z,x) = a(x,z,x). [para(2089(a,1),1707(a,1)),flip(a)]. 2091 a(R(x,y,y),z,x) = a(x,z,x). [para(2090(a,1),1721(a,1)),flip(a)]. 2092 a(a(x,y,x),z,z) = a(x,y,x) \ a(x,y,x). [para(2091(a,1),2054(a,1,2)),flip(a)]. 2093 a(a(x,y,x),z,z) = 1. [para(2092(a,2),60(a,1))]. 2095 L(x,x,a(y,z,y)) = x. [hyper(37,a,2093,a)]. 2097 L(x,x,a(y,z,z)) = x. [para(2095(a,1),1695(a,2))]. 2098 L(x,x,K(y,z)) = x. [para(2097(a,1),1263(a,1)),flip(a)]. 2099 R(T(a(x,y,y),z),z,z) = z \ (a(x,y,y) * z). [para(2097(a,1),1804(a,1,1)),flip(a)]. 2100 a(K(x,y),z,z) = 1. [hyper(38,a,2098,a)]. 2102 (K(x,y) * (z / u)) \ K(x,y) = u / z. [para(2098(a,1),925(a,1)),flip(a)]. 2103 L(x,K(y,z),x) = x. [para(2098(a,1),1895(a,2))]. 2104 R(K(x,y),z,z) = K(x,y) * 1. [para(2100(a,1),963(a,1,2)),flip(a)]. 2105 a(K(x,K(y,z)),u,w) = a(1,u,w). [para(2100(a,1),2072(a,1,1)),flip(a)]. 2106 T(K(x,y),z) / z = z \ K(x,y). [para(2103(a,1),441(a,1,2))]. 2107 K(x,R(y,z,z)) = K(x,y). [hyper(24,a,1767,a,b,2104,a(flip)),flip(a)]. 2108 K(x,y / (z \ 1)) = K(x,y * z). [para(720(a,1),2107(a,1,2)),flip(a)]. 2112 K(x,y) * (x / z) = T(x,y) / z. [para(2107(a,1),1815(a,1,1))]. 2115 a(K(x,K(y,z)),u,w) = 1. [para(2105(a,2),125(a,1))]. 2117 L(x,y,K(z,K(u,w))) = x. [hyper(37,a,2115,a)]. 2119 x * (x \ R(K(y,K(z,u)),w,x)) = K(y,K(z,u)). [para(2117(a,1),1974(a,1,1))]. 2121 (K(x,y) * z) \ u = (z \ K(y,x)) * u. [para(2106(a,1),2067(a,1,1)),flip(a)]. 2122 K(x,R(((y \ 1) * z) \ 1,z,z)) = K(x,(z \ 1) * y). [para(1739(a,2),2108(a,1,2))]. 2123 T(x,y) / (z \ x) = K(x,y) * z. [para(65(a,1),2112(a,1,2)),flip(a)]. 2126 (K(x,y) * z) \ T(x,y) = z \ x. [para(2123(a,1),66(a,1,1))]. 2129 L(x \ y,x,K(z,y)) = x \ y. [para(2126(a,1),1248(a,2))]. 2130 a(K(x,y),z,z \ y) = 1. [hyper(38,a,2129,a)]. 2132 a(K(x,y * z),y,z) = 1. [para(19(a,1),2130(a,1,3))]. 2137 ((x / y) \ K(z,u)) * K(u,z) = y / x. [para(2121(a,1),2102(a,1))]. 2140 x / K(y,z) = x * K(z,y). [para(66(a,1),2137(a,1,1)),flip(a)]. 2144 (K(x,y) * z) / K(x,y) = T(z,K(y,x)). [para(2140(a,2),2068(a,1))]. 2145 T(x,K(y,z)) \ x = K(x,K(z,y)). [para(2144(a,1),1053(a,2,1)),flip(a)]. 2146 K(K(x,y),z) = K(z,K(y,x)). [para(2145(a,1),1080(a,2))]. 2147 K(x,K(y,z)) * K(x,K(z,y)) = 1. [para(2146(a,1),898(a,1,1))]. 2148 K(x,y) * K(z,K(y,x)) = T(K(x,y),z). [para(2146(a,1),1107(a,2,2)),flip(a)]. 2149 K(x,y) * T(K(y,x),z) = K(z,K(x,y)). [para(2146(a,1),1114(a,2))]. 2150 T(K(x,y),z) \ 1 = T(K(y,x),z). [para(2148(a,1),1140(a,1)),flip(a)]. 2151 T(K(x,y),z) * T(K(y,x),z) = 1. [para(2150(a,1),20(a,1,2))]. 2152 T(K(x,y),z) * K(y,x) = K(z,K(y,x)). [para(2149(a,1),405(a,2))]. 2153 R(T(a(x,y,y),z),z,z) = T(a(x,y,y),z). [para(2099(a,2),36(a,2)),flip(a)]. 2154 R(T(a(x,y,y),z),z,z) = a(T(x,z),y,y). [para(2153(a,2),1836(a,2)),flip(a)]. 2155 R(a(T(x,y),z,z),y,y) = a(T(x,y),z,z). [para(1836(a,2),2154(a,1,1))]. 2156 a(R(T(x,y),y,y),z,z) = a(T(x,y),z,z). [para(2155(a,1),1930(a,2))]. 2157 a(T(T(x,y),y),z,z) = a(T(x,y),z,z). [para(2156(a,1),2074(a,1)),flip(a)]. 2158 a(T(x,y),z,z) = a(x,z,z). [para(2157(a,1),1724(a,1))]. 2161 (x * (y * (a(y,z,z) * u))) / (R(T(y,x),z,z) * u) = T(x,y). [para(2158(a,1),1210(a,1,1,2,2,1))]. 2165 R(K(x,K(y,z)),u,w) = K(x,K(y,z)). [para(2119(a,1),20(a,1)),flip(a)]. 2166 K(x,R(K(y,z),u,w)) = K(x,K(y,z)). [para(2165(a,1),1654(a,1)),flip(a)]. 2167 K(x,K(y,R(z,u,w))) = K(x,K(y,z)). [para(1654(a,1),2166(a,1,2))]. 2168 K(K(R(x,y,z),u),w) = K(w,K(u,x)). [para(2167(a,1),2146(a,2))]. 2169 K(R(K(x,y),z,u),w) = K(w,K(y,x)). [para(1634(a,1),2168(a,1,1))]. 2170 K(x,R((y \ z) \ 1,z,z)) = K(x,(z \ 1) * y). [para(318(a,1),2122(a,1,2,1,1))]. 2171 K(x,(y \ z) \ 1) = K(x,(z \ 1) * y). [para(2170(a,1),2107(a,1)),flip(a)]. 2172 K(x,(y \ z) \ 1) = K(x,z \ y). [para(318(a,1),2171(a,2,2))]. 2174 K(x,(y / z) \ y) = K(x,z / (a(y,z,z) \ 1)). [para(2172(a,1),1447(a,1))]. 2175 K(x,y / (a(z,y,y) \ 1)) = K(x,y). [para(66(a,1),2174(a,1,2)),flip(a)]. 2176 K(x,y * a(z,y,y)) = K(x,y). [para(1445(a,1),2175(a,1,2))]. 2177 K(x * a(y,x,x),z) = (z \ 1) / (z \ K(z,x)). [para(2176(a,1),1057(a,1,2,2)),flip(a)]. 2178 K(x * a(y,x,x),z) = K(x,z). [para(2177(a,2),1057(a,1))]. 2179 (x / y) * T(y,z) = x * K(y,z). [para(2178(a,1),1463(a,1,2)),flip(a)]. 2180 (x * y) * K(y,z) = x * T(y,z). [para(21(a,1),2179(a,1,1)),flip(a)]. 2183 L(K(x,y),x,z) = K(x,y). [hyper(23,a,1117,a,b,2180,a),flip(a)]. 2187 L(K(T(x,y),z),x,y) = K(T(x,y),z). [para(2183(a,1),1376(a,1)),flip(a)]. 2192 T(K(x,y),x * z) = K(T(x,z),y). [para(2187(a,1),1522(a,1)),flip(a)]. 2193 K(T(x,x \ y),z) = T(K(x,z),y). [para(20(a,1),2192(a,1,2)),flip(a)]. 2194 K(T(x,y),z) = T(K(x,z),y). [para(2193(a,1),2038(a,1)),flip(a)]. 2195 K(x,T(y,z)) * T(K(y,x),z) = 1. [para(2194(a,1),898(a,1,2))]. 2196 K(T(x,y * T(T(y,x),x)),z) = T(T(K(x,z),y),T(y,x)). [para(2194(a,2),1905(a,1))]. 2197 K(x,T(y,z)) = T(K(x,y),z). [hyper(24,a,2151,a,b,2195,a)]. 2199 K(x,y) * K(y,T(x,z)) = K(K(y,x),z). [para(2197(a,2),1114(a,1,2))]. 2200 K(x,T(y,z \ 1)) * z = z * K(x,y). [para(2197(a,2),1907(a,1,1))]. 2202 K(x,y) * K(y,T(x,z)) = K(z,K(x,y)). [para(2197(a,2),2149(a,1,2))]. 2203 K(x,T(y,z)) * K(y,x) = K(z,K(y,x)). [para(2197(a,2),2152(a,1,1))]. 2204 K(T(x,y),z) = K(x,T(z,y)). [para(2197(a,2),2194(a,2))]. 2205 K(x,T(y,z)) * K(y,x) = K(K(x,y),z). [para(2199(a,1),1226(a,2))]. 2206 K(x,T(y,z)) * K(y,x) = K(x,K(y,z)). [para(2202(a,1),1873(a,2))]. 2207 K(x,y) * K(x,K(y,z)) = K(x,T(y,z)). [para(2206(a,1),1225(a,1,2))]. 2208 K(x,K(y,z)) = K(z,K(y,x)). [para(2206(a,1),2203(a,1))]. 2209 K(K(x,y),z) = K(x,K(y,z)). [para(2206(a,1),2205(a,1)),flip(a)]. 2210 1 / K(x,K(y,z)) = K(K(y,x),z). [para(2208(a,1),899(a,1,2))]. 2211 K(K(x,y),z) = K(K(x,z),y). [para(2210(a,1),899(a,1))]. 2212 K(K(x,y),z) = K(y,K(z,x)). [para(2211(a,1),2146(a,1))]. 2213 K(x,K(y,z)) = K(z,K(x,y)). [para(2212(a,1),2209(a,1))]. 2214 T(K(x,y) * K(x,K(y,z)),z) = K(x,y). [para(2213(a,2),1020(a,1,1,2))]. 2215 T(K(x,T(y,z)),z) = K(x,y). [para(2207(a,1),2214(a,1,1))]. 2216 K(x,T(y,z)) * z = z * K(x,y). [para(2215(a,1),82(a,1,2)),flip(a)]. 2217 K(x,T(T(y,z),z)) = K(x,y). [para(2215(a,1),2197(a,2))]. 2219 K(x,T(y,z \ 1)) = K(x,T(y,z)). [hyper(24,a,2200,a,b,2216,a),flip(a)]. 2220 T(K(x,y) * z,K(x,y)) = K(x,T(y,z)) * z. [para(2216(a,2),2064(a,2))]. 2221 K(x,T(y,z \ (z \ (u \ 1)))) = K(x,T(y,u * (z * z))). [para(409(a,1),2219(a,1,2,2))]. 2222 K(T(x,y * T(y,x)),z) = T(T(K(x,z),y),T(y,x)). [para(2019(a,1),2196(a,1,1))]. 2223 T(T(K(x,y),z),T(z,x)) = K(T(x,z * z),y). [para(2019(a,1),2222(a,1,1)),flip(a)]. 2224 T(T(K(x,y),z),T(z,x)) = K(x,T(y,z * z)). [para(2223(a,2),1278(a,1))]. 2225 T(K(x,T(y,z)),T(z,x)) = K(x,T(y,z * z)). [para(2197(a,2),2224(a,1,1))]. 2226 K(T(x,T(y,x)),T(z,y)) = K(x,T(z,y * y)). [para(2225(a,1),2194(a,2))]. 2227 K(T(x,y),T(z,y)) = K(x,T(z,y * y)). [para(1131(a,1),2226(a,1,1))]. 2228 K(x,T(T(y,z),z)) = K(x,T(y,z * z)). [para(2227(a,1),2204(a,1)),flip(a)]. 2229 K(x,T(y,z * z)) = K(x,y). [para(2228(a,1),2217(a,1))]. 2230 K(x,T(y,z * (z * u))) = K(x,T(y,u)). [para(662(a,1),2229(a,1,2))]. 2232 K(x,T(y,z \ u)) = K(x,T(y,z * u)). [para(20(a,1),2230(a,1,2,2,2)),flip(a)]. 2233 K(x,T(y,T(z,z * u))) = K(x,T(y,(z \ u) * u)). [para(250(a,1),2230(a,1,2,2,2)),flip(a)]. 2234 K(x,T(y,(z / u) * (z * z))) = K(x,T(y,u / (z \ 1))). [para(399(a,1),2230(a,1,2,2,2))]. 2235 K(x,T(y,z \ (z \ u))) = K(x,T(y,u)). [para(20(a,1),2232(a,2,2,2))]. 2236 K(x,T(y,z * (u * u))) = K(x,T(y,z \ 1)). [para(2221(a,1),2235(a,1))]. 2237 K(x,T(y,z * (u * u))) = K(x,T(y,z)). [para(2236(a,2),2219(a,1))]. 2239 K(x,T(y,z / (u \ 1))) = K(x,T(y,u / z)). [para(2234(a,1),2237(a,1))]. 2241 (x * (R(y,z,z) * u)) / (R(T(y,x),z,z) * u) = T(x,y). [para(966(a,1),2161(a,1,1,2))]. 2243 T(x,R(y,z,z)) = T(x,y). [para(2241(a,1),1209(a,1)),flip(a)]. 2244 T(x,y / (z \ 1)) = T(x,y * z). [para(720(a,1),2243(a,1,2)),flip(a)]. 2246 K(x,T(y,z / u)) = K(x,T(y,u * z)). [para(2244(a,1),2239(a,1,2)),flip(a)]. 2247 K(x,T(y,(z \ u) * u)) = K(x,T(y,z)). [para(65(a,1),2246(a,1,2,2)),flip(a)]. 2248 K(x,T(y,T(z,z * u))) = K(x,T(y,z)). [para(2247(a,1),2233(a,2))]. 2249 K(x,T(y,T(z,u))) = K(x,T(y,z)). [para(20(a,1),2248(a,1,2,2,2))]. 2251 K(x,K(y,T(z,u))) = K(x,T(y,z)) * K(y,x). [para(2249(a,1),2206(a,1,1)),flip(a)]. 2253 K(x,K(y,T(z,u))) = K(x,K(y,z)). [para(2251(a,2),2206(a,1))]. 2254 K(x,K(y,z \ R(z,u,w))) = K(x,K(y,a(z,u,w))). [para(739(a,2),2253(a,1,2,2)),flip(a)]. 2255 K(x,K(y \ R(y,z,u),w)) = K(x,K(w,a(y,z,u))). [para(1849(a,2),2254(a,1,2))]. 2260 K(x,y) * K(R(y,z,u),x) = K(R(y,z,u) / y,x). [para(2081(a,1),2059(a,1)),flip(a)]. 2261 K(x,y) * K(R(y,z,u),x) = K(y \ R(y,z,u),x). [para(478(a,1),2260(a,2,1))]. 2262 K(x,y) * K(R(y,z,u),x) = K(x,y \ R(y,z,u)). [para(2261(a,2),1849(a,1))]. 2263 K(x,K(y,z) \ R(K(y,z),u,w)) = K(x,K(y,z)) * K(x,K(z,y)). [para(2169(a,1),2262(a,1,2)),flip(a)]. 2265 K(x,K(y,z) \ R(K(y,z),u,w)) = 1. [para(2263(a,2),2147(a,1))]. 2266 K(x,K(y,z) \ K(R(y,u,w),z)) = 1. [para(1629(a,1),2265(a,1,2,2))]. 2268 K(x,K(y,z) * K(R(z,u,w),y)) = 1. [para(900(a,1),2266(a,1,2))]. 2269 K(x,K(y \ R(y,z,u),w)) = 1. [para(2261(a,1),2268(a,1,2))]. 2270 K(x,K(y,a(z,u,w))) = 1. [para(2269(a,1),2255(a,1)),flip(a)]. 2271 T(x,K(y,a(z,u,w))) = x. [hyper(41,a,2270,a)]. 2273 K(x,T(a(y,z,u),w)) = K(x,a(y,z,u)). [hyper(24,a,2220,a(flip),b,2271,a(flip)),flip(a)]. 2274 K(x,y \ R(y,z,u)) = K(x,a(y,z,u)). [para(1839(a,1),2273(a,1,2))]. 2275 K(x,y \ R(y,z,u)) = K(a(y,z,u),x). [para(2274(a,2),1847(a,2)),flip(a)]. 2276 K(x \ R(x,y,z),u) = K(u,a(x,y,z)). [para(2274(a,1),1849(a,2))]. 2277 K(x,a(y,z,L(u,z,y))) = K(x,y \ R(y,z,u)). [para(1990(a,1),2274(a,1,2,2)),flip(a)]. 2278 K(x,y) * K(R(y,z,u),x) = K(x,a(y,z,u)). [para(2274(a,1),2262(a,2))]. 2279 K(x,a(K(y,z),u,w)) = 1. [para(2274(a,1),2265(a,1))]. 2280 T(x,a(K(y,z),u,w)) = x. [hyper(41,a,2279,a)]. 2281 ((K(x,y) * z) * u) / (K(x,y) * (z * u)) = a(K(x,y),z,u). [para(2280(a,1),300(a,1,2))]. 2282 K(R(x,y,z) \ x,u) = K(u,a(x,x * y,z)). [para(618(a,1),2276(a,1,1))]. 2283 K(x,y) * K(y,R(x,z,u)) = K(y,a(x,z,u)). [para(2278(a,1),1674(a,1)),flip(a)]. 2284 L(x,y * z,K(y,u)) = x * K(u,a(y,z,x)). [para(2283(a,1),2077(a,1,2)),flip(a)]. 2285 K(x,a(y,z,L(u,z,y))) = K(x,a(y,z,u)). [para(2277(a,2),2274(a,1))]. 2286 K(x,y) \ R(K(x,y),z,u) = a(K(x,y),z,u). [para(2281(a,1),537(a,1)),flip(a)]. 2287 x \ L(x,y,K(z,u)) = a(K(z,u),y,x). [para(2286(a,1),1988(a,1)),flip(a)]. 2288 x * a(K(y,z),u,x) = L(x,u,K(y,z)). [para(2287(a,1),20(a,1,2))]. 2289 a(K(x,y),x * z,u) = K(y,a(x,z,u)). [hyper(23,a,2284,a(flip),b,2288,a)]. 2290 x * a(K(y,z),u,x) = L(x,u,K(z,y)). [para(905(a,1),2288(a,1,2))]. 2291 K(x,a(y,y * z,u)) = a(K(y,x),z,u). [para(2289(a,1),1778(a,1))]. 2292 K((x * y) * z,a(x,y,z)) = 1. [para(2289(a,1),2132(a,1))]. 2293 K(x * (y * z),a(x,y,L(z,y,x))) = 1. [para(74(a,1),2292(a,1,1))]. 2294 K(x,a(y,y * z,u)) = a(K(x,y),z,u). [para(2291(a,2),905(a,1))]. 2295 K(x * (y * z),a(x,y,z)) = 1. [para(2293(a,1),2285(a,1)),flip(a)]. 2296 x \ R(x,y,z) = a(x,y,z) * 1. [para(2295(a,1),1848(a,1,2)),flip(a)]. 2297 a(x,y,z) = x \ R(x,y,z). [hyper(24,a,18,a,b,2296,a(flip))]. 2298 a(x,y,z) = L(z,y,x) \ z. [hyper(24,a,1989,a(flip),b,2296,a(flip))]. 2302 R(x,y,z) \ x = a(x,y,z) \ 1. [para(2297(a,2),462(a,1,1)),flip(a)]. 2306 x * (a(x,y,z) * u) = R(x,y,z) * u. [para(2297(a,2),501(a,1,2,1))]. 2308 a(x,y,z) * (x * u) = R(x,y,z) * u. [para(2297(a,2),528(a,1,1))]. 2310 a(x,x * y,z) = R(x,y,z) \ x. [para(2297(a,2),618(a,1))]. 2313 a(x,y,z) = x * R(x \ 1,y,z). [para(2297(a,2),635(a,2)),flip(a)]. 2317 T(x \ R(x,y,z),u) = a(T(x,u),y,z). [para(2297(a,2),1831(a,1)),flip(a)]. 2318 R(x \ R(x,y,z),u,w) = a(R(x,u,w),y,z). [para(2297(a,2),1927(a,1)),flip(a)]. 2319 L(x \ R(x,y,z),u,w) = a(L(x,u,w),y,z). [para(2297(a,2),1939(a,1)),flip(a)]. 2323 x * (L(x,y,z) \ u) = a(z,y,x) * u. [para(2297(a,2),1985(a,1,1)),flip(a)]. 2332 L(x,y,z) \ (x * u) = a(z,y,x) * u. [para(2298(a,2),524(a,2,1))]. 2333 a(x,y,z) * (L(z,y,x) * u) = z * u. [para(2298(a,2),646(a,1,1))]. 2336 a(T(x,y),z,y) = L(y,z,x) \ y. [para(1992(a,1),2298(a,2,1))]. 2340 K(a(x,y,z) \ 1,u) = K(u,a(x,x * y,z)). [para(2302(a,1),2282(a,1,1))]. 2341 a(x,x * y,z) = a(x,y,z) \ 1. [para(2310(a,2),2302(a,1))]. 2344 L(x,a(y,z,u),z) = x. [para(2313(a,2),1443(a,1,2))]. 2347 (x * a(y,x,z)) * u = x * (a(y,x,z) * u). [para(2344(a,1),74(a,1,2))]. 2348 (x \ a(y,x,z)) \ 1 = a(y,x,z) \ x. [para(2344(a,1),259(a,1)),flip(a)]. 2349 (x \ a(y,x,z)) \ u = a(y,x,z) \ (x * u). [para(2344(a,1),267(a,1)),flip(a)]. 2358 a(T(x,y),z,y) = a(x,z,y). [para(2336(a,2),2298(a,2)),flip(a)]. 2366 K(a(x,x * y,z),u) = a(K(u,x),y,z). [para(2294(a,1),1847(a,2))]. 2368 x * (y * a(x,z,y)) = R(x,z,y) * y. [para(1964(a,1),2306(a,1,2))]. 2370 a(T(x,y),z,u) = T(a(x,z,u),y). [para(2297(a,2),2317(a,1,1)),flip(a)]. 2371 a(T(x,y),z,u) \ a(x,z,u) = K(y,a(x,z,u)). [para(2370(a,2),1080(a,2,1)),flip(a)]. 2372 a(T(x,y),y,z) = a(x,y,z). [para(2370(a,2),1687(a,1))]. 2373 a(x,T(y,x),z) = a(x,y,z). [para(2372(a,1),1790(a,1)),flip(a)]. 2374 a(x / y,y,z) = a(y * x,y,z). [para(2373(a,1),1810(a,1)),flip(a)]. 2375 a(x / y,x,z) = a(x * y,x,z). [para(2374(a,1),612(a,1)),flip(a)]. 2378 a(x,y,z) * (z * u) = z * (a(x,y,z) * u). [para(2332(a,1),2323(a,1,2)),flip(a)]. 2380 a(x,y,z) * (z * x) = z * R(x,y,z). [para(1973(a,1),2333(a,1,2))]. 2386 (x \ a(y,x,z)) \ u = (a(y,x,z) \ x) * u. [para(2348(a,1),318(a,1,1)),flip(a)]. 2388 K(a(x,y,z) \ 1,u) = a(K(u,x),y,z). [para(2341(a,1),2366(a,1,1))]. 2389 (x * y) * L(a(x,z,y),y,x) = R(x,z,y) * y. [para(2368(a,1),74(a,2))]. 2393 a(R(x,y,z),u,y) = L(y,u,x) \ y. [para(2318(a,1),1986(a,1))]. 2394 a(R(x,y,z),u,w) = R(a(x,u,w),y,z). [para(2297(a,2),2318(a,1,1)),flip(a)]. 2396 a(R(x,y,z),u,y) = a(x,u,y). [para(2393(a,2),2298(a,2)),flip(a)]. 2400 a(L(x,y,x),z,y) = a(x,z,y). [para(1312(a,1),2396(a,1,1)),flip(a)]. 2404 R(a(x,y,z),x * u,w) = a(R(x,u,w),y,z). [para(2394(a,1),1718(a,1))]. 2406 a(L(x,y,z),u,w) = L(a(x,u,w),y,z). [para(2297(a,2),2319(a,1,1)),flip(a)]. 2410 K(x,a(y / z,(y / z) * z,u)) = K(a(z * y,z,u) \ 1,x). [para(2374(a,1),2340(a,1,1,1)),flip(a)]. 2411 (a(x,y,z) * y) * u = y * (a(x,y,z) * u). [para(1688(a,2),2347(a,1,1))]. 2412 a(x,y,z) \ (y * u) = (a(x,y,z) \ y) * u. [para(2386(a,1),2349(a,1)),flip(a)]. 2413 L(x,y,a(z,y,u)) = x. [hyper(23,a,798,a,b,2412,a(flip)),flip(a)]. 2414 (a(x,y,z) * y) * u = a(x,y,z) * (y * u). [para(2413(a,1),74(a,1,2))]. 2415 (a(x,y,z) * (y \ 1)) * u = a(x,y,z) * (y \ u). [para(2413(a,1),945(a,1,2))]. 2417 a(x,y,z) * (y * u) = y * (a(x,y,z) * u). [para(2414(a,1),2411(a,1))]. 2419 (x * y) \ (x * (a(z,x,u) * y)) = T(a(z,x,u),x * y). [para(2417(a,1),36(a,2,2)),flip(a)]. 2421 (x * y) * a(L(x,y,x),z,y) = R(x,z,y) * y. [para(2406(a,2),2389(a,1,2))]. 2422 (x * y) * a(x,z,y) = R(x,z,y) * y. [para(2400(a,1),2421(a,1,2))]. 2423 (x * (R(y,z,u) * u)) / ((y * u) * R(a(y,z,u),y * u,x)) = L(x,y * u,a(y,z,u)). [para(2422(a,1),2079(a,2,1,2)),flip(a)]. 2424 (x \ a(y,x,z)) * u = a(y,x,z) * (x \ u). [para(1795(a,1),2415(a,1,1))]. 2425 (a(x,y,z) * (y \ u)) \ ((y \ a(x,y,z)) * (u * w)) = L(w,u,y \ a(x,y,z)). [para(2424(a,1),32(a,2,1)),flip(a)]. 2426 L(T(a(x,y,z),u),u,y) = T(a(x,y,z),y * u). [para(2419(a,1),106(a,1)),flip(a)]. 2427 L(a(T(x,y),z,u),y,z) = T(a(x,z,u),z * y). [para(2370(a,2),2426(a,1,1))]. 2429 K(a(x * y,x,z) \ 1,u) = K(u,a(y / x,y,z)). [para(22(a,1),2410(a,1,2,2)),flip(a)]. 2430 K(a(x * y,x,z) \ 1,u) = K(u,a(y * x,y,z)). [para(2375(a,1),2429(a,2,2))]. 2431 K(x,a(y * z,y,u)) = a(K(x,z * y),z,u). [para(2430(a,1),2388(a,1))]. 2432 a(L(x,y,z),R(z,y,x),u) = (x * (z * u)) \ ((x * z) * u). [para(1998(a,1),1981(a,1,1)),flip(a)]. 2433 a(L(x,y,z),R(z,y,x),u) = a(x,z,u). [para(2432(a,2),28(a,2)),flip(a)]. 2435 L(a(x,R(y,z,x),u),z,y) = a(x,y,u). [para(2433(a,1),2406(a,1)),flip(a)]. 2436 (a(x,y,z) * (y \ u)) \ (a(x,y,z) * (y \ (u * w))) = L(w,u,y \ a(x,y,z)). [para(2424(a,1),2425(a,1,2))]. 2437 L(L(x,y,z),z * y,a(u,z,w)) = L(x,y,z \ a(u,z,w)). [para(2436(a,1),1409(a,1)),flip(a)]. 2438 L(L(x,y,z),z * y,a(u,z,w)) = L(x,y,z * a(u,z,w)). [para(2437(a,2),776(a,1))]. 2439 (R(x,y,z) * y) \ ((x * y) * u) = (x \ R(x,y,z)) \ u. [para(1996(a,1),1411(a,1))]. 2440 L(x,y,R(z,y,x)) = (z \ R(z,y,x)) \ x. [para(2439(a,1),183(a,1)),flip(a)]. 2441 L(x,y,R(z,y,x)) = L(x,y,z). [para(2440(a,2),1976(a,2)),flip(a)]. 2442 L(x,y * z,R(y,z,x) \ 1) = L(x,y * z,y \ 1). [para(584(a,1),2441(a,1,3))]. 2443 L(x,y * z,R(y,z,x)) = L(x,y * z,y \ 1). [para(2442(a,1),787(a,1)),flip(a)]. 2444 L(x,y * z,R(y,z,x)) = L(x,y * z,y). [para(2443(a,2),787(a,1))]. 2445 R(x,y,z) * (L(z,x * y,x) \ z) = R(R(x,y,z),x * y,z). [para(2444(a,1),1979(a,2,2,1)),flip(a)]. 2446 R(x,y,z) * (R(x,y,z) \ x) = R(R(x,y,z),x * y,z). [para(1954(a,1),2445(a,1,2))]. 2447 R(R(x,y,z),x * y,z) = x. [para(2446(a,1),20(a,1))]. 2448 R(R(x,x * y,z),y,z) = x. [para(2447(a,1),50(a,1)),flip(a)]. 2449 K(x,R(y,y * z,u) \ R(R(y,y * z,u),z,u)) = K(x,R(y,y * z,u)) * K(y,x). [para(2448(a,1),2262(a,1,2,1)),flip(a)]. 2450 K(x,R(y,y * z,u) \ R(R(y,y * z,u),z,u)) = R(K(x,y),z,u) * K(y,x). [para(1672(a,1),2449(a,2,1))]. 2451 K(x,R(y,y * z,u) \ R(R(y,y * z,u),z,u)) = K(y,x) * R(K(x,y),z,u). [para(2450(a,2),406(a,1))]. 2452 K(x,R(y,y * z,u) \ y) = K(y,x) * R(K(x,y),z,u). [para(2448(a,1),2451(a,1,2,2))]. 2453 K(x,y) * R(K(y,x),z,u) = K(y,x \ R(x,z,u)). [para(622(a,1),2452(a,1,2)),flip(a)]. 2454 x * K(y,z \ R(z,u,x)) = L(x,u,K(y,z)). [para(2453(a,1),2076(a,1,2))]. 2455 x * K(a(y,z,x),u) = L(x,z,K(u,y)). [para(2275(a,1),2454(a,1,2))]. 2456 a(K(x,y),z,u) = K(a(x,z,u),y). [hyper(23,a,2290,a,b,2455,a),flip(a)]. 2457 a(K(x,y),z,u) = K(a(y,z,u),x). [hyper(23,a,2288,a,b,2455,a),flip(a)]. 2458 a(K(x,y),z,u) = K(y,a(x,z,u)). [para(2456(a,2),1847(a,1))]. 2459 a(K(x,y),z,u) = K(x,a(y,z,u)). [para(2457(a,2),1847(a,1))]. 2460 x * K(y,a(z,u,x)) = L(x,u,K(z,y)). [para(2458(a,1),2288(a,1,2))]. 2461 K(x * y,a(z,x,u)) = K(z,a(y * x,y,u)). [para(2458(a,1),2431(a,2)),flip(a)]. 2462 K(x,a(y,z,u)) = K(y,a(x,z,u)). [para(2459(a,1),2458(a,1))]. 2463 L(x,y * z,K(y,u)) = L(x,z,K(y,u)). [para(2460(a,1),2284(a,2))]. 2464 (x * (R(y,z,u) * u)) / ((y * u) * a(R(y,u,x),z,u)) = L(x,y * u,a(y,z,u)). [para(2404(a,1),2423(a,1,2,2))]. 2465 (x * (R(y,z,u) * u)) / ((y * u) * a(y,z,u)) = L(x,y * u,a(y,z,u)). [para(2396(a,1),2464(a,1,2,2))]. 2467 (x * (R(y,z,u) * u)) / (R(y,z,u) * u) = L(x,y * u,a(y,z,u)). [para(2422(a,1),2465(a,1,2))]. 2468 L(x,y * z,a(y,u,z)) = x. [para(2467(a,1),21(a,1))]. 2469 L(x,y * z,a(T(z,y),u,y)) = x. [para(2468(a,1),1185(a,1)),flip(a)]. 2470 L(x,y * z,a(z,u,y)) = x. [para(2358(a,1),2469(a,1,3))]. 2471 (a(x,y,z) * (z * x)) \ (a(x,y,z) * (z * (x * u))) = L(u,x,z). [para(2470(a,1),174(a,2))]. 2472 (x * R(y,z,x)) \ (a(y,z,x) * (x * (y * u))) = L(u,y,x). [para(2380(a,1),2471(a,1,1))]. 2473 (x * R(y,z,x)) \ (x * (a(y,z,x) * (y * u))) = L(u,y,x). [para(2378(a,1),2472(a,1,2))]. 2474 (x * R(y,z,x)) \ (x * (R(y,z,x) * u)) = L(u,y,x). [para(2308(a,1),2473(a,1,2,2))]. 2475 L(x,R(y,z,u),u) = L(x,y,u). [para(2474(a,1),32(a,2))]. 2476 a(x,R(y,z,x),u) = L(u,y,x) \ u. [para(2475(a,1),2298(a,2,1))]. 2477 a(x,R(y,z,x),u) = a(x,y,u). [para(2476(a,2),2298(a,2)),flip(a)]. 2478 L(a(x,y,z),u,y) = a(x,y,z). [para(2477(a,1),2435(a,1,1))]. 2480 T(a(x,y,z),y * u) = a(T(x,u),y,z). [para(2478(a,1),2427(a,1)),flip(a)]. 2484 a(T(x,y),z,u) \ a(x,z,u) = K(z * y,a(x,z,u)). [para(2480(a,1),1080(a,2,1)),flip(a)]. 2494 K(x * y,a(z,x,u)) = K(y,a(z,x,u)). [para(2484(a,1),2371(a,1))]. 2495 K(x,a(y * z,y,u)) = K(z,a(x,y,u)). [para(2494(a,1),2462(a,1)),flip(a)]. 2496 K(x,a(y * z,y,u)) = K(y,a(x,z,u)). [para(2494(a,1),2461(a,1)),flip(a)]. 2497 K(x,a(y,z,u)) = K(z,a(y,x,u)). [para(2496(a,1),2495(a,1))]. 2498 x * K(y,a(z,u,x)) = L(x,y,K(z,u)). [para(2497(a,1),2460(a,1,2))]. 2499 L(x,y,K(z,u)) = L(x,u,K(z,y)). [para(2498(a,1),2460(a,1))]. 2501 L(x,y,K(z,z * u)) = L(x,u,K(z,y)). [para(2499(a,1),2463(a,1))]. 2502 L(x,y,a(z,u,u)) = L(x,u,K(z,y)). [para(2501(a,1),1261(a,1)),flip(a)]. 2503 L(x,y,a(z,u,u)) = L(x,y,K(z,u)). [para(2502(a,2),2499(a,1))]. 2504 L(x,y,a(z,u,z)) = L(x,y,K(u,z)). [para(2503(a,1),1695(a,1)),flip(a)]. 2505 L(L(x,y,z),z * y,K(z,u)) = L(x,y,z * a(u,z,u)). [para(2504(a,1),2438(a,1))]. 2506 L(x,y,z * a(u,z,u)) = L(x,y,T(z,u)). [para(2505(a,1),1604(a,1))]. 2507 L(x,y,R(z,u,u)) = L(x,y,T(z,u)). [para(2506(a,1),1692(a,1)),flip(a)]. 2508 L(x,y,T(z / u,z)) = L(x,y,u * z). [para(2507(a,1),846(a,1))]. 2509 L(x,y,z * u) = L(x,y,u * z). [para(2508(a,1),845(a,1))]. 2510 L(L(x,y,z * u),(z * u) * y,u * z) = x. [para(2509(a,1),303(a,1))]. 2515 L(x,y,K(z,u)) = x. [para(2510(a,1),1850(a,1)),flip(a)]. 2516 a(K(x,y),z,u) = 1. [hyper(38,a,2515,a)]. 2540 K(a(x,y,z),u) = 1. [para(2516(a,1),2456(a,1)),flip(a)]. 2541 $F # answer("Ka"). [resolve(2540,a,55,a)]. ============================== end of proof ========================== % Disable descendants (x means already disabled): 55 given #2332 (H,wt=8): 2540 K(a(x,y,z),u) = 1. [para(2516(a,1),2456(a,1)),flip(a)]. given #2333 (H,wt=9): 2534 L(x,y,a(z,u,z)) = x. [para(2515(a,1),2504(a,2))]. given #2334 (H,wt=10): 2539 K(a(x,y,z) \ 1,u) = 1. [para(2516(a,1),2388(a,2))]. given #2335 (H,wt=11): 2526 L(x,y,T(z,u)) = L(x,y,z). [para(2515(a,1),1604(a,1)),flip(a)]. given #2336 (H,wt=11): 2543 T(a(x,y,z),u) = a(x,y,z). [hyper(41,a,2540,a)]. given #2337 (H,wt=11): 2578 a(T(x,y),z,u) = a(x,z,u). [para(2543(a,1),2370(a,2))]. given #2338 (H,wt=13): 2553 L(x,y,z * (u * z)) = L(x,y,u). [para(2526(a,1),778(a,2))]. given #2339 (H,wt=13): 2567 a(x,y,z) * u = u * a(x,y,z). [para(2543(a,1),82(a,1,2)),flip(a)]. given #2340 (H,wt=13): 2569 (a(x,y,z) \ u) \ u = a(x,y,z). [para(2543(a,1),83(a,1)),flip(a)]. given #2341 (H,wt=13): 2570 (a(x,y,z) \ u) * a(x,y,z) = u. [para(2543(a,1),250(a,1,2))]. given #2342 (H,wt=13): 2571 x / a(y,z,u) = a(y,z,u) \ x. [para(2543(a,1),252(a,1,2))]. given #2343 (H,wt=13): 2584 a(x / y,z,u) = a(y \ x,z,u). [para(84(a,1),2578(a,1,1)),flip(a)]. given #2344 (H,wt=13): 2586 a(x * (y * x),z,u) = a(y,z,u). [para(2578(a,1),1704(a,2))]. given #2345 (H,wt=13): 2597 a(x,y,z) * (u / a(x,y,z)) = u. [para(2567(a,2),22(a,1))]. given #2346 (H,wt=13): 2606 a(x / y,z,u) = a(y * x,z,u). [para(2584(a,2),1702(a,1))]. given #2347 (H,wt=13): 2613 a(x / y,z,u) = a(x * y,z,u). [para(2606(a,1),612(a,1)),flip(a)]. given #2348 (H,wt=13): 2618 a(x * y,z,u) = a(y * x,z,u). [para(2613(a,1),2606(a,1))]. given #2349 (H,wt=15): 2518 (K(x,y) * z) * u = K(x,y) * (z * u). [para(2515(a,1),74(a,1,2))]. given #2350 (H,wt=15): 2519 (K(x,y) * z) \ (K(x,y) * u) = z \ u. [para(2515(a,1),76(a,1)),flip(a)]. given #2351 (H,wt=15): 2520 (K(x,y) \ z) \ u = z \ (K(x,y) * u). [para(2515(a,1),267(a,1)),flip(a)]. given #2352 (H,wt=15): 2521 (K(x,y) * z) / u = K(x,y) * (z / u). [para(2515(a,1),196(a,1,2))]. given #2353 (H,wt=15): 2549 T(a(x,y,z) \ 1,u) = a(x,y,z) \ 1. [hyper(41,a,2539,a)]. given #2354 (H,wt=15): 2572 a(x,y,z) * (u \ 1) = u \ a(x,y,z). [para(2543(a,1),326(a,1,2)),flip(a)]. given #2355 (H,wt=15): 2602 x * (y * a(x,z,u)) = R(x,z,u) * y. [para(2567(a,1),2306(a,1,2))]. given #2356 (H,wt=15): 2603 (x * y) * a(x,z,u) = R(x,z,u) * y. [para(2567(a,1),2308(a,1))]. given #2357 (H,wt=15): 2604 x * (L(x,y,z) \ u) = u * a(z,y,x). [para(2567(a,1),2323(a,2))]. given #2358 (H,wt=15): 2612 (x * y) / a(z,u,x) = L(x,u,z) * y. [hyper(23,a,2333,a,b,2597,a)]. given #2359 (H,wt=15): 2631 (x \ K(y,z)) * (K(z,y) * u) = x \ u. [para(2519(a,1),2121(a,1)),flip(a)]. given #2360 (H,wt=15): 2632 x \ (K(y,z) * u) = (x \ K(y,z)) * u. [para(2520(a,1),2133(a,1))]. given #2361 (H,wt=8): 2646 L(x,K(y,z),u) = x. [hyper(23,a,798,a,b,2632,a(flip)),flip(a)]. -------- Proof 3 -------- "aK2". ============================== PROOF ================================= % Proof 3 at 56.64 (+ 0.93) seconds: "aK2". % Length of proof is 2199. % Level of proof is 224. % Maximum clause weight is 50. % Given clauses 2361. 1 x * y = u & x * z = u -> y = z # label(non_clause). [assumption]. 2 y * x = u & z * x = u -> y = z # label(non_clause). [assumption]. 5 a(x,y,z) = 1 -> L(z,y,x) = z # label(non_clause). [assumption]. 6 L(x,y,z) = x -> a(z,y,x) = 1 # label(non_clause). [assumption]. 7 T(x,y) = x -> T(y,x) = y # label(non_clause). [assumption]. 8 T(x,y) = x -> K(x,y) = 1 # label(non_clause). [assumption]. 9 K(x,y) = 1 -> T(x,y) = x # label(non_clause). [assumption]. 15 a(x,K(y,z),u) = 1 # label("aK2") # label(non_clause) # label(goal). [goal]. 17 1 * x = x. [assumption]. 18 x * 1 = x. [assumption]. 19 x \ (x * y) = y. [assumption]. 20 x * (x \ y) = y. [assumption]. 21 (x * y) / y = x. [assumption]. 22 (x / y) * y = x. [assumption]. 23 x * y != z | x * u != z | u = y. [clausify(1)]. 24 x * y != z | u * y != z | u = x. [clausify(2)]. 27 (x * (y * z)) \ ((x * y) * z) = a(x,y,z). [assumption]. 28 a(x,y,z) = (x * (y * z)) \ ((x * y) * z). [copy(27),flip(a)]. 29 (x * y) \ (y * x) = K(y,x). [assumption]. 30 K(x,y) = (y * x) \ (x * y). [copy(29),flip(a)]. 31 (x * y) \ (x * (y * z)) = L(z,y,x). [assumption]. 32 L(x,y,z) = (z * y) \ (z * (y * x)). [copy(31),flip(a)]. 33 ((x * y) * z) / (y * z) = R(x,y,z). [assumption]. 34 R(x,y,z) = ((x * y) * z) / (y * z). [copy(33),flip(a)]. 35 x \ (y * x) = T(y,x). [assumption]. 36 T(x,y) = y \ (x * y). [copy(35),flip(a)]. 37 a(x,y,z) != 1 | L(z,y,x) = z. [clausify(5)]. 38 L(x,y,z) != x | a(z,y,x) = 1. [clausify(6)]. 39 T(x,y) != x | T(y,x) = y. [clausify(7)]. 40 T(x,y) != x | K(x,y) = 1. [clausify(8)]. 41 K(x,y) != 1 | T(x,y) = x. [clausify(9)]. 42 T(T(x,y),z) = T(T(x,z),y). [assumption]. 43 T(L(x,y,z),u) = L(T(x,u),y,z). [assumption]. 44 L(T(x,y),z,u) = T(L(x,z,u),y). [copy(43),flip(a)]. 45 T(R(x,y,z),u) = R(T(x,u),y,z). [assumption]. 46 R(T(x,y),z,u) = T(R(x,z,u),y). [copy(45),flip(a)]. 47 L(R(x,y,z),u,w) = R(L(x,u,w),y,z). [assumption]. 48 R(L(x,y,z),u,w) = L(R(x,u,w),y,z). [copy(47),flip(a)]. 49 L(L(x,y,z),u,w) = L(L(x,u,w),y,z). [assumption]. 50 R(R(x,y,z),u,w) = R(R(x,u,w),y,z). [assumption]. 51 (x * (x * y)) * z = x * (x * (y * z)) # label("LC"). [assumption]. 57 a(c24,K(c25,c26),c27) != 1 # label("aK2") # answer("aK2"). [deny(15)]. 59 1 \ x = x. [para(17(a,1),19(a,1,2))]. 60 x \ x = 1. [para(18(a,1),19(a,1,2))]. 61 x \ ((x * y) * 1) = y. [para(18(a,2),19(a,1,2))]. 62 x \ (y * (y \ (x * z))) = z. [para(20(a,2),19(a,1,2))]. 64 x / 1 = x. [para(18(a,1),21(a,1,1))]. 65 x / (y \ x) = y. [para(20(a,1),21(a,1,1))]. 66 (x / y) \ x = y. [para(22(a,1),19(a,1,2))]. 67 (x * (y * z)) * a(x,y,z) = (x * y) * z. [para(28(a,2),20(a,1,2))]. 68 ((x / y) * (y * z)) \ (x * z) = a(x / y,y,z). [para(22(a,1),28(a,2,2,1)),flip(a)]. 69 (x * y) * K(y,x) = y * x. [para(30(a,2),20(a,1,2))]. 70 x \ ((y \ x) * y) = K(y \ x,y). [para(20(a,1),30(a,2,1)),flip(a)]. 71 ((x \ y) * x) \ y = K(x,x \ y). [para(20(a,1),30(a,2,2)),flip(a)]. 72 x \ (1 * (x * y)) = L(y,x,1). [para(17(a,1),32(a,2,1)),flip(a)]. 73 (x * 1) \ (x * y) = L(y,1,x). [para(17(a,1),32(a,2,2,2)),flip(a)]. 74 (x * y) * L(z,y,x) = x * (y * z). [para(32(a,2),20(a,1,2))]. 75 x \ (y * ((y \ x) * z)) = L(z,y \ x,y). [para(20(a,1),32(a,2,1)),flip(a)]. 76 L(x \ y,x,z) = (z * x) \ (z * y). [para(20(a,1),32(a,2,2,2))]. 77 x \ ((x / y) * (y * z)) = L(z,y,x / y). [para(22(a,1),32(a,2,1)),flip(a)]. 78 ((x * y) * (y \ z)) / z = R(x,y,y \ z). [para(20(a,1),34(a,2,2)),flip(a)]. 79 R(x,y,z) * (y * z) = (x * y) * z. [para(34(a,2),22(a,1,1))]. 80 R(x / y,y,z) = (x * z) / (y * z). [para(22(a,1),34(a,2,1,1))]. 81 T(x,x) = x. [para(36(a,2),19(a,1))]. 82 x * T(y,x) = y * x. [para(36(a,2),20(a,1,2))]. 83 T(x,x \ y) = (x \ y) \ y. [para(20(a,1),36(a,2,2))]. 84 T(x / y,y) = y \ x. [para(22(a,1),36(a,2,2))]. 85 (x * (x * (y * z))) / z = x * (x * y). [hyper(24,a,22,a,b,51,a),flip(a)]. 86 (x * (x * y)) \ (x * (x * (y * z))) = z. [hyper(23,a,20,a,b,51,a),flip(a)]. 87 x \ ((x * (x * y)) * z) = x * (y * z). [hyper(23,a,20,a,b,51,a(flip)),flip(a)]. 88 (x * (x * 1)) * y = x * (x * y). [para(17(a,1),51(a,2,2,2))]. 89 x * (x * ((x \ y) * z)) = (x * y) * z. [para(20(a,1),51(a,1,1,2)),flip(a)]. 90 (x * (y * (y * (z * u)))) \ ((x * (y * (y * z))) * u) = a(x,y * (y * z),u). [para(51(a,1),28(a,2,1,2)),flip(a)]. 91 (x * (x * (y * (z * u)))) \ (((x * (x * y)) * z) * u) = a(x * (x * y),z,u). [para(51(a,1),28(a,2,1)),flip(a)]. 92 (x * (x * (y * z))) \ ((x * (x * y)) * (z * u)) = L(u,z,x * (x * y)). [para(51(a,1),32(a,2,1)),flip(a)]. 93 (x * (y * (y * z))) \ (x * (y * (y * (z * u)))) = L(u,y * (y * z),x). [para(51(a,1),32(a,2,2,2)),flip(a)]. 94 ((x * (x * (y * z))) * u) / (z * u) = R(x * (x * y),z,u). [para(51(a,1),34(a,2,1,1)),flip(a)]. 95 (x * (x * (y * z))) / ((x * y) * z) = R(x,x * y,z). [para(51(a,1),34(a,2,1)),flip(a)]. 97 ((x * y) / 1) / y = x. [hyper(24,a,22,a,b,64,a(flip)),flip(a)]. 98 T(T(x,y),x) = T(x,y). [para(81(a,1),42(a,1,1)),flip(a)]. 99 (x * (y * z)) / L(z,y,x) = x * y. [para(32(a,2),65(a,1,2))]. 100 (x * y) / T(x,y) = y. [para(36(a,2),65(a,1,2))]. 101 R(x,y,z) \ ((x * y) * z) = y * z. [para(34(a,2),66(a,1,1))]. 102 x \ (y * 1) = x \ y. [para(20(a,1),61(a,1,2,1))]. 103 T(x * (x * y),x) = x * (y * x). [hyper(23,a,51,a(flip),b,82,a)]. 104 T((x * y) / x,x) = y. [hyper(23,a,22,a(flip),b,82,a)]. 105 (x * T(y,x)) / x = y. [hyper(24,a,22,a,b,82,a(flip)),flip(a)]. 106 (x * y) \ (x * (z * y)) = L(T(z,y),y,x). [para(82(a,1),32(a,2,2,2)),flip(a)]. 107 T(x,y) \ (x * y) = T(y,T(x,y)). [para(82(a,1),36(a,2,2)),flip(a)]. 108 x * T(T(y,x),z) = T(y,z) * x. [para(42(a,1),82(a,1,2))]. 109 x * L(T(y,x),z,u) = L(y,z,u) * x. [para(44(a,2),82(a,1,2))]. 110 x * R(T(y,x),z,u) = R(y,z,u) * x. [para(46(a,2),82(a,1,2))]. 111 (x * y) \ ((z * x) * y) = T(R(z,x,y),x * y). [para(34(a,2),84(a,1,1)),flip(a)]. 112 T(T(x / y,z),y) = T(y \ x,z). [para(84(a,1),42(a,1,1)),flip(a)]. 113 ((x * y) / ((1 / z) * z)) / y = x. [para(22(a,2),97(a,1,1,2))]. 114 K(T(x,y),x) = 1. [hyper(40,a,98,a)]. 115 T(x,T(x,y)) = x. [hyper(39,a,98,a)]. 116 T(x,y) * x = x * T(x,y). [para(98(a,1),82(a,1,2)),flip(a)]. 117 (x * y) / T(y,T(x,y)) = T(x,y). [para(82(a,1),100(a,1,1))]. 118 x \ (y * (z * (z \ 1))) = x \ y. [para(20(a,2),102(a,1,2,2))]. 119 K(x,(y * x) / y) = 1. [para(104(a,1),114(a,1,1))]. 120 T(x,(y * x) / y) = x. [hyper(41,a,119,a)]. 122 K(x,y) \ (x * y) = T(y * x,K(x,y)). [para(69(a,1),36(a,2,2)),flip(a)]. 123 x \ (x * y) = L(y,x,1). [para(17(a,1),72(a,1,2))]. 124 L(x,y,1) = x. [para(123(a,1),19(a,1))]. 125 a(1,x,y) = 1. [hyper(38,a,124,a)]. 126 x \ (x * y) = L(y,1,x). [para(18(a,1),73(a,1,1))]. 127 L(x,1,y) = x. [para(126(a,1),19(a,1))]. 128 K(x \ 1,x) = (x \ 1) * x. [para(70(a,1),59(a,1))]. 129 K(x \ 1,x) / x = x \ 1. [hyper(24,a,22,a,b,128,a(flip)),flip(a)]. 130 (x \ 1) \ K(x \ 1,x) = x. [hyper(23,a,20,a,b,128,a(flip)),flip(a)]. 131 (x * x) * y = x * (x * y). [para(18(a,1),88(a,1,1,2))]. 132 (x * (x * y)) / y = x * x. [hyper(24,a,22,a,b,131,a),flip(a)]. 133 (x * x) \ (x * (x * y)) = y. [hyper(23,a,20,a,b,131,a),flip(a)]. 134 ((x * (x * y)) * z) / (y * z) = R(x * x,y,z). [para(131(a,1),34(a,2,1,1)),flip(a)]. 135 x \ (y * (y * x)) = T(y * y,x). [para(131(a,1),36(a,2,2)),flip(a)]. 136 x * (x * T(y,x * x)) = y * (x * x). [para(131(a,1),82(a,1))]. 137 L(x,y,y) = x. [para(133(a,1),32(a,2))]. 138 x * ((x \ y) * x) = T(x * y,x). [para(20(a,1),103(a,1,1,2)),flip(a)]. 139 T(x / y,z) * y = y * T(y \ x,z). [para(84(a,1),108(a,1,2,1)),flip(a)]. 140 (x * T(x \ y,z)) / x = T(y / x,z). [para(112(a,1),105(a,1,1,2))]. 141 R(x,1 / y,y) / y = x * (1 / y). [para(34(a,2),113(a,1,1))]. 142 L(x \ 1,x,y) = (y * x) \ y. [para(118(a,1),32(a,2))]. 143 L((x \ y) \ 1,x \ y,x) = y \ x. [para(20(a,1),142(a,2,1))]. 144 L(x \ 1,x,y / x) = y \ (y / x). [para(22(a,1),142(a,2,1))]. 145 x / L(y \ 1,y,x) = x * y. [para(142(a,2),65(a,1,2))]. 146 x \ T(x * y,x) = (x \ y) * x. [hyper(23,a,20,a,b,138,a),flip(a)]. 147 x * K(x \ 1,x) = T(x * 1,x). [para(128(a,2),138(a,1,2))]. 148 (x \ (x \ y)) * x = x \ T(y,x). [para(20(a,1),146(a,1,2,1)),flip(a)]. 149 x * K(x \ 1,x) = T(x,x). [para(18(a,1),147(a,2,1))]. 150 x * K(x \ 1,x) = x. [para(149(a,2),81(a,1))]. 151 K(x \ 1,x) = 1. [hyper(23,a,18,a,b,150,a)]. 152 T(x \ 1,x) = x \ 1. [hyper(41,a,151,a)]. 154 (x \ 1) * x = 1. [para(151(a,1),128(a,1)),flip(a)]. 155 1 / x = x \ 1. [para(151(a,1),129(a,1,1))]. 156 (x \ 1) \ 1 = x. [para(151(a,1),130(a,1,2))]. 157 x * (1 / x) = 1. [para(66(a,1),154(a,1,1))]. 160 T(x,x \ 1) = x. [para(156(a,1),83(a,2))]. 161 L(x,x \ 1,y) = (y * (x \ 1)) \ y. [para(156(a,1),142(a,1,1))]. 162 x / L(y,y \ 1,x) = x * (y \ 1). [para(156(a,1),145(a,1,2,1))]. 164 (x * 1) \ ((x * y) * (1 / y)) = a(x,y,1 / y). [para(157(a,1),28(a,2,1,2)),flip(a)]. 165 T(T(x,y),x \ 1) = T(x,y). [para(160(a,1),42(a,1,1)),flip(a)]. 166 K(T(x,y),x \ 1) = 1. [hyper(40,a,165,a)]. 167 K(x \ y,(y / x) \ 1) = 1. [para(84(a,1),166(a,1,1))]. 168 K(x,((y * x) / y) \ 1) = 1. [para(104(a,1),166(a,1,1))]. 169 T(x \ y,(y / x) \ 1) = x \ y. [hyper(41,a,167,a)]. 170 T(x,((y * x) / y) \ 1) = x. [hyper(41,a,168,a)]. 171 (x \ y) \ (x \ T(y,x)) = K(x \ (x \ y),x). [para(148(a,1),70(a,1,2))]. 172 x * L(y,z \ x,z) = z * ((z \ x) * y). [para(20(a,1),74(a,1,1))]. 173 x * L(y,z,x / z) = (x / z) * (z * y). [para(22(a,1),74(a,1,1))]. 174 (x * (y * z)) \ (x * (y * (z * u))) = L(L(u,z,y),y * z,x). [para(74(a,1),32(a,2,2,2)),flip(a)]. 176 (x * y) * L(z,K(x,y),y * x) = (y * x) * (K(x,y) * z). [para(69(a,1),74(a,1,1))]. 177 L(x \ (y \ z),x,y) = (y * x) \ z. [para(20(a,1),76(a,2,2))]. 178 L(x \ (y * x),x,y) = T(y,y * x). [para(76(a,2),36(a,2)),flip(a)]. 179 (x * y) / L(z \ y,z,x) = x * z. [para(76(a,2),65(a,1,2))]. 180 L(x \ T(y,z),x,z) = (z * x) \ (y * z). [para(82(a,1),76(a,2,2))]. 181 L(x \ (y \ ((y * x) * z)),x,y) = z. [para(76(a,2),62(a,1))]. 182 R(x,x,y) = x. [hyper(24,a,131,a(flip),b,79,a)]. 183 (R(x,y,z) * y) \ ((x * y) * z) = L(z,y,R(x,y,z)). [para(79(a,1),32(a,2,2)),flip(a)]. 184 L(R(x,y,z),u,w) * (y * z) = (L(x,u,w) * y) * z. [para(48(a,1),79(a,1,1))]. 185 R(R(x,y,z),u,w) * (y * z) = (R(x,u,w) * y) * z. [para(50(a,1),79(a,1,1))]. 186 R(T(x,y),x,z) = T(x,y). [para(182(a,1),46(a,2,1))]. 187 L(R(x,L(x,y,z),u),y,z) = L(x,y,z). [para(182(a,1),48(a,1)),flip(a)]. 188 R(R(x,y,z),x,u) = R(x,y,z). [para(182(a,1),50(a,1,1)),flip(a)]. 189 R(R(T(x,y),z,u),x,w) = R(T(x,y),z,u). [para(186(a,1),50(a,1,1)),flip(a)]. 190 (T(x,y) * x) * z = T(x,y) * (x * z). [para(186(a,1),79(a,1,1)),flip(a)]. 191 (R(x,y,z) * x) * u = R(x,y,z) * (x * u). [para(188(a,1),79(a,1,1)),flip(a)]. 192 R(1 / x,x,y) = y / (x * y). [para(17(a,1),80(a,2,1))]. 193 R((x / y) / z,z,y) = x / (z * y). [para(22(a,1),80(a,2,1))]. 194 T((x * y) / (z * y),u) = R(T(x / z,u),z,y). [para(80(a,1),46(a,2,1)),flip(a)]. 195 R(x,x \ 1,y) = y / ((x \ 1) * y). [para(65(a,1),192(a,1,1))]. 196 (x * y) / L(z,y / z,x) = x * (y / z). [para(22(a,1),99(a,1,1,2))]. 197 R(x,x \ y,z) \ (y * z) = (x \ y) * z. [para(20(a,1),101(a,1,2,1))]. 198 R(x,y \ 1,y) / y = x * (1 / y). [para(155(a,1),141(a,1,1,2))]. 199 L(K(x,y) \ ((y * x) \ z),K(x,y),y * x) = (x * y) \ z. [para(69(a,1),177(a,2,1))]. 200 (x * x) \ y = x \ (x \ y). [para(177(a,1),137(a,1))]. 201 L(x \ L(y \ z,y,u),x,u * y) = ((u * y) * x) \ (u * z). [para(76(a,2),177(a,1,1,2))]. 202 x \ (x \ (y * (x * x))) = T(y,x * x). [para(200(a,1),36(a,2)),flip(a)]. 203 L(T(x,y),y,x) = T(x,x * y). [para(36(a,2),178(a,1,1))]. 204 T(x,x * ((y * x) / y)) = L(x,(y * x) / y,x). [para(120(a,1),203(a,1,1)),flip(a)]. 205 x / L(y \ z,y,x / z) = (x / z) * y. [para(22(a,1),179(a,1,1))]. 207 R(x,y \ 1,y) / y = x * (y \ 1). [para(155(a,1),198(a,2,2))]. 208 (x * (y \ 1)) * y = R(x,y \ 1,y). [para(207(a,1),22(a,1,1))]. 209 (x * (y \ 1)) \ R(x,y \ 1,y) = y. [para(207(a,1),66(a,1,1))]. 210 R(x / (y \ 1),y \ 1,y) = x * y. [para(22(a,1),208(a,1,1)),flip(a)]. 211 (x * (x * y)) / z = x * (x * (y / z)). [para(22(a,1),85(a,1,1,2,2))]. 212 (x * (x * y)) \ (x * (x * z)) = y \ z. [para(20(a,1),86(a,1,2,2,2))]. 213 x \ ((x * y) * z) = x * ((x \ y) * z). [para(20(a,1),87(a,1,2,1,2))]. 214 L(x,y,z) * x = x * L(x,y,z). [para(81(a,1),109(a,1,2,1)),flip(a)]. 216 L(x \ 1,y,z) * x = x * L(x \ 1,y,z). [para(152(a,1),109(a,1,2,1)),flip(a)]. 217 x * T(y,y * x) = L(y,x,y) * x. [para(203(a,1),109(a,1,2))]. 218 (x * L(x,y,z)) / x = L(x,y,z). [hyper(24,a,22,a,b,214,a),flip(a)]. 219 T(x,L(x,y,z)) = x. [hyper(23,a,82,a,b,214,a),flip(a)]. 220 T(x,x * L(x,y,z)) = L(x,L(x,y,z),x). [para(219(a,1),203(a,1,1)),flip(a)]. 221 L(x,x \ y,x) * (x \ y) = (x \ y) * T(x,y). [para(20(a,1),217(a,1,2,2)),flip(a)]. 222 x * R(T(T(y,x),z),u,w) = R(T(y,z),u,w) * x. [para(42(a,1),110(a,1,2,1))]. 223 R(x,y,z) * x = x * R(x,y,z). [para(81(a,1),110(a,1,2,1)),flip(a)]. 224 R(x / y,z,u) * y = y * R(y \ x,z,u). [para(84(a,1),110(a,1,2,1)),flip(a)]. 225 (x \ y) * R((x \ y) \ y,z,u) = R(x,z,u) * (x \ y). [para(83(a,1),110(a,1,2,1))]. 226 x * (x * R(T(y,x * x),z,u)) = R(y,z,u) * (x * x). [para(110(a,1),131(a,1)),flip(a)]. 227 R(x \ 1,y,z) * x = x * R(x \ 1,y,z). [para(152(a,1),110(a,1,2,1)),flip(a)]. 228 T(x,R(x,y,z)) = x. [hyper(23,a,82,a,b,223,a),flip(a)]. 229 T(x \ y,R(y / x,z,u)) = T(y / x,x). [para(228(a,1),112(a,1,1)),flip(a)]. 230 x \ (y * (x * x)) = x * T(y,x * x). [hyper(23,a,20,a,b,136,a),flip(a)]. 231 T(x / (x * y),z) * (x * y) = (x * y) * T(L(y \ 1,y,x),z). [para(142(a,2),139(a,2,2,1))]. 232 T((x * y) / (x * z),u) * (x * z) = (x * z) * T(L(z \ y,z,x),u). [para(76(a,2),139(a,2,2,1))]. 233 (x * T(y,z)) / x = T((x * y) / x,z). [para(19(a,1),140(a,1,1,2,1))]. 234 L(x,y,T(y,z)) = x. [hyper(23,a,74,a,b,190,a),flip(a)]. 235 (x * T(x,y)) * z = T(x,y) * (x * z). [para(116(a,1),190(a,1,1))]. 237 L(x,(y * z) / y,z) = x. [para(104(a,1),234(a,1,3))]. 238 x * (x * ((x \ y) / z)) = (x * y) / z. [para(20(a,1),211(a,1,1,2)),flip(a)]. 239 (x * (x * y)) \ (x * x) = y \ 1. [para(18(a,1),212(a,1,2,2))]. 240 (x * y) \ (x * (x * z)) = (x \ y) \ z. [para(20(a,1),212(a,1,1,2))]. 241 T(x,x * (x * y)) = y \ (x * y). [para(212(a,1),36(a,2))]. 242 (x * y) \ (x * x) = (x \ y) \ 1. [para(20(a,1),239(a,1,1,2))]. 243 (x * x) / (y \ 1) = x * (x * y). [para(239(a,1),65(a,1,2))]. 244 ((x * y) * z) \ (x * x) = ((x \ y) * z) \ 1. [para(89(a,1),239(a,1,1))]. 245 T(x,x * (x * y)) = T(x,y). [para(241(a,2),36(a,2)),flip(a)]. 246 T(x,x \ y) = T(x,x * y). [para(20(a,1),245(a,1,2,2)),flip(a)]. 247 T(x,x * (y * x)) = T(x,T(y,x)). [para(82(a,1),245(a,1,2,2))]. 248 T(x * y,(x * y) * (y * x)) = T(x * y,K(y,x)). [para(69(a,1),245(a,1,2,2))]. 249 T(x,x * y) = (x \ y) \ y. [para(246(a,1),83(a,1))]. 250 (x \ y) * T(x,x * y) = y. [para(249(a,2),20(a,1,2))]. 251 T(x / y,x) = ((x / y) \ y) \ y. [para(22(a,1),249(a,1,2))]. 252 x / T(y,y * x) = y \ x. [para(249(a,2),65(a,1,2))]. 253 (x \ y) * ((x \ y) * (T(x,x * y) * z)) = ((x \ y) * y) * z. [para(249(a,2),89(a,1,2,2,1))]. 254 (x \ (x \ y)) * T(x,y) = x \ y. [para(20(a,1),250(a,1,2,2))]. 255 ((x \ y) * (T(x,x * y) * z)) \ (y * z) = a(x \ y,T(x,x * y),z). [para(250(a,1),28(a,2,2,1)),flip(a)]. 257 K(x,y) / T(y * x,x * y) = (y * x) \ K(x,y). [para(69(a,1),252(a,1,2,2))]. 258 (x \ (x \ y)) \ 1 = y \ (x * x). [para(20(a,1),242(a,1,1)),flip(a)]. 259 L(x \ y,x,y) = (y \ x) \ 1. [para(242(a,1),76(a,2))]. 260 L(K(x,y),y * x,x * y) = ((x * y) \ (y * x)) \ 1. [para(30(a,2),259(a,1,1))]. 261 L(T(x \ y,z),x,y) = T((y \ x) \ 1,z). [para(259(a,1),44(a,2,1))]. 262 (x \ ((y * x) / y)) \ 1 = ((y * x) / y) \ x. [para(259(a,1),237(a,1))]. 263 x * (x * (y \ 1)) = (x * x) / y. [para(156(a,1),243(a,1,2)),flip(a)]. 265 x * ((x \ (x \ y)) * z) = x \ (y * z). [para(20(a,1),213(a,1,2,1)),flip(a)]. 266 L(x \ (y * ((y \ x) * z)),x,y) = z. [para(213(a,1),181(a,1,1,2))]. 267 L(x \ (y * z),x,y) = (y \ x) \ z. [para(20(a,1),266(a,1,1,2,2))]. 268 L(x \ y,x,z) = (z \ x) \ (z \ y). [para(20(a,1),267(a,1,1,2))]. 269 L(x \ (y * z),x,z) = (z \ x) \ T(y,z). [para(82(a,1),267(a,1,1,2))]. 270 L((x * y) \ z,x * y,x) = y \ (x \ z). [para(19(a,1),268(a,2,1))]. 272 (x \ y) / L(z \ y,z,x) = x \ z. [para(268(a,2),65(a,1,2))]. 273 L(x \ y,x,x / z) = z \ ((x / z) \ y). [para(66(a,1),268(a,2,1))]. 274 (x \ y) \ (x \ z) = (x * y) \ (x * z). [para(268(a,1),76(a,1))]. 275 L(x \ L(y \ z,y,u),x,u \ y) = ((u \ y) * x) \ (u \ z). [para(268(a,2),177(a,1,1,2))]. 276 (x \ 1) / (y \ x) = x \ (x \ y). [para(143(a,1),272(a,1,2))]. 277 x \ (x \ (x / y)) = (x \ 1) / y. [para(66(a,1),276(a,1,2)),flip(a)]. 278 x * ((x \ 1) / y) = x \ (x / y). [para(277(a,1),20(a,1,2))]. 279 ((x \ 1) / y) \ 1 = (x / y) \ (x * x). [para(277(a,1),258(a,1,1))]. 280 T(x * T(x,y),T(x,y)) = x * T(x,y). [hyper(23,a,82,a,b,235,a(flip)),flip(a)]. 281 (x * T(x,y)) * (x \ z) = T(x,y) * z. [para(20(a,1),235(a,2,2))]. 282 (x * y) / (z \ (x \ y)) = x * (x * z). [para(65(a,1),238(a,1,2,2)),flip(a)]. 283 (x \ (x \ y)) \ z = y \ (x * (x * z)). [para(20(a,1),240(a,1,1)),flip(a)]. 284 (x \ y) \ ((x \ z) * u) = (x * y) \ ((x * z) * u). [para(89(a,1),240(a,1,2)),flip(a)]. 285 x \ (x \ (y * z)) = (x \ (x \ y)) * z. [hyper(23,a,20,a,b,265,a),flip(a)]. 286 (x \ (x \ y)) * (x * x) = T(y,x * x). [hyper(23,a,230,a(flip),b,265,a)]. 287 (x * (y * x)) \ (x * z) = T(y,x) \ (x \ z). [para(36(a,2),274(a,1,1)),flip(a)]. 288 T(x * T(x,y),T(x,y)) = T(x,y) * x. [para(280(a,2),116(a,2)),flip(a)]. 289 x / (y \ (x \ 1)) = x * (x * y). [para(18(a,1),282(a,1,1))]. 290 (x \ (x \ y)) \ y = T(x * x,y). [para(283(a,2),135(a,1))]. 291 (x \ (x \ 1)) * y = x \ (x \ y). [para(17(a,1),285(a,1,2,2)),flip(a)]. 292 (x \ (x \ y)) * (y \ z) = x \ (x \ z). [para(20(a,1),285(a,1,2,2)),flip(a)]. 293 R((x / y) / (z \ (z \ 1)),z \ (z \ 1),y) = x / (z \ (z \ y)). [para(291(a,1),193(a,2,2))]. 294 ((x \ 1) / y) * (x * x) = T(x / y,x * x). [para(277(a,1),286(a,1,1))]. 295 T(T(x,y) * x,T(x,y)) = T(x,y) * x. [para(116(a,2),288(a,1,1))]. 296 (x \ (x \ y)) \ (x \ (x \ z)) = y \ z. [hyper(23,a,20,a,b,292,a),flip(a)]. 297 (x \ y) * ((x * y) \ z) = x \ (x \ z). [para(19(a,1),292(a,1,1,2))]. 298 (T(x,y) \ x) * T(x,y) = x. [hyper(23,a,138,a,b,295,a(flip)),flip(a)]. 299 x / T(x,y) = T(x,y) \ x. [hyper(24,a,22,a,b,298,a),flip(a)]. 300 ((x * y) * z) / T(x * (y * z),a(x,y,z)) = a(x,y,z). [para(67(a,1),100(a,1,1))]. 301 L(x,x \ y,x) = y \ T(x * y,x). [para(138(a,1),75(a,1,2)),flip(a)]. 302 L(L(x,y \ z,y),z,y) = x. [para(75(a,1),266(a,1,1))]. 303 L(L(x,y,z),z * y,z) = x. [para(19(a,1),302(a,1,1,2))]. 304 L(L(x,y,z / y),z,z / y) = x. [para(66(a,1),302(a,1,1,2))]. 305 L(x,y \ 1,y) = x. [para(302(a,1),127(a,1)),flip(a)]. 306 L(x,y,y \ 1) = x. [para(156(a,1),305(a,1,2))]. 307 ((x \ 1) * x) \ ((x \ 1) * y) = x \ y. [para(306(a,1),76(a,1)),flip(a)]. 308 L(L(x,y * z,y),z,y) = x. [para(303(a,1),49(a,1)),flip(a)]. 309 x \ (y \ ((y * x) * z)) = L(z,y * x,y). [para(181(a,1),303(a,1,1)),flip(a)]. 310 R(x,L(x,y,z),u) = L(L(x,y,z),z * y,z). [para(187(a,1),303(a,1,1)),flip(a)]. 311 L((x \ y) \ z,x * y,x) = y \ (x * z). [para(267(a,1),303(a,1,1))]. 312 L(x,y \ z,y) = L(x,y * z,y). [para(302(a,1),303(a,1,1)),flip(a)]. 313 L(x,y * (y * z),y) = L(x,z,y). [para(303(a,1),303(a,1,1))]. 314 L(L(x,y * z,z),T(y,z),z) = x. [para(82(a,1),308(a,1,1,2))]. 315 L(L(x,y * z,z * y),K(y,z),z * y) = x. [para(69(a,1),308(a,1,1,2))]. 316 L(x,x * y,x) = y \ T(x * y,x). [para(301(a,1),312(a,1)),flip(a)]. 317 1 \ ((x \ 1) * y) = x \ y. [para(154(a,1),307(a,1,1))]. 318 (x \ 1) * y = x \ y. [para(317(a,1),59(a,1)),flip(a)]. 320 (x \ y) / y = x \ 1. [hyper(24,a,22,a,b,318,a),flip(a)]. 321 x * ((x \ 1) * y) = y. [hyper(23,a,19,a(flip),b,318,a)]. 322 (x \ 1) * (x * y) = y. [para(318(a,2),19(a,1))]. 323 (x \ (y * z)) \ (((x \ 1) * y) * z) = a(x \ 1,y,z). [para(318(a,1),28(a,2,1)),flip(a)]. 324 ((x * (y \ 1)) * z) / (y \ z) = R(x,y \ 1,z). [para(318(a,1),34(a,2,2)),flip(a)]. 325 T(x \ 1,y) = y \ (x \ y). [para(318(a,1),36(a,2,2))]. 326 x \ T(y,x \ 1) = y * (x \ 1). [para(318(a,1),82(a,1))]. 327 x * T(y \ 1,x) = y \ x. [para(318(a,1),82(a,2))]. 328 (x \ y) * K(y,x \ 1) = y * (x \ 1). [para(318(a,1),69(a,1,1))]. 329 x \ T(T(y,x \ 1),z) = T(y,z) * (x \ 1). [para(318(a,1),108(a,1))]. 330 (x \ 1) \ y = x * y. [para(156(a,1),318(a,1,1)),flip(a)]. 331 (x \ y) * L(z,y,x \ 1) = (x \ 1) * (y * z). [para(318(a,1),74(a,1,1))]. 332 R(x,y \ 1,z) * (y \ z) = (x * (y \ 1)) * z. [para(318(a,1),79(a,1,2))]. 333 (x * (y \ z)) / L(z,y \ 1,x) = x * (y \ 1). [para(318(a,1),99(a,1,1,2))]. 334 R(x,x \ 1,y) = y / (x \ y). [para(318(a,1),195(a,2,2))]. 335 R(x \ 1,y \ 1,y) = (x \ (y \ 1)) * y. [para(318(a,1),208(a,1,1)),flip(a)]. 336 L(x \ 1,y,x \ 1) * y = y * T(x \ 1,x \ y). [para(318(a,1),217(a,1,2,2)),flip(a)]. 337 T(x \ 1,(x \ 1) \ y) = T(x \ 1,x \ y). [para(318(a,1),246(a,2,2))]. 338 (x \ (x \ y)) \ z = (y \ (x * x)) * z. [para(258(a,1),318(a,1,1)),flip(a)]. 340 x / (y * x) = y \ 1. [para(19(a,1),320(a,1,1))]. 341 K(x,y) / (x * y) = (y * x) \ 1. [para(30(a,2),320(a,1,1))]. 342 L(x,y,z) / (z * (y * x)) = (z * y) \ 1. [para(32(a,2),320(a,1,1))]. 343 (x / y) \ 1 = y / x. [para(66(a,1),320(a,1,1)),flip(a)]. 344 (x * y) / ((z * x) * y) = R(z,x,y) \ 1. [para(101(a,1),320(a,1,1))]. 345 T(x * y,K(y,x)) / (y * x) = K(y,x) \ 1. [para(122(a,1),320(a,1,1))]. 346 T(x,x * y) / y = (x \ y) \ 1. [para(249(a,2),320(a,1,1))]. 347 x * (y * (x \ 1)) = T(y,x \ 1). [para(82(a,1),321(a,1,2))]. 348 R(x \ 1,x * y,z) = (y * z) / ((x * y) * z). [para(322(a,1),34(a,2,1,1))]. 349 T(x \ 1,x * y) = (x * y) \ y. [para(322(a,1),36(a,2,2))]. 350 R((x \ 1) / y,y,x * z) = z / (y * (x * z)). [para(322(a,1),80(a,2,1))]. 351 L(x * y,x \ 1,y) = (y \ (x \ 1)) \ 1. [para(330(a,1),259(a,1,1))]. 352 L(x * (y * z),x \ 1,y) = (y \ (x \ 1)) \ z. [para(330(a,1),267(a,1,1))]. 354 (x / y) * (y / x) = 1. [para(343(a,1),20(a,1,2))]. 355 K(x \ y,x / y) = 1. [para(343(a,1),167(a,1,2))]. 356 T(x,y / (y * x)) = x. [para(343(a,1),170(a,1,2))]. 357 T(x \ y,x / y) = x \ y. [para(343(a,1),169(a,1,2))]. 358 (x / y) \ z = (y / x) * z. [para(343(a,1),318(a,1,1)),flip(a)]. 359 (x / y) * ((y / x) * z) = z. [para(343(a,1),321(a,1,2,1))]. 360 x * ((y / z) * (z / y)) = x. [para(354(a,2),18(a,1,2))]. 361 K((x * y) \ y,x) = 1. [para(21(a,1),355(a,1,2))]. 362 (x / (x * y)) * y = y * (x / (x * y)). [para(356(a,1),82(a,1,2))]. 363 (x * (y / (y * x))) / x = y / (y * x). [para(356(a,1),100(a,1,2))]. 364 T(x,x * (y / (y * x))) = L(x,y / (y * x),x). [para(356(a,1),203(a,1,1)),flip(a)]. 365 T((x * y) \ y,x) = (x * y) \ y. [hyper(41,a,361,a)]. 366 x * R(x \ (y \ x),z,u) = R(y \ 1,z,u) * x. [para(325(a,1),110(a,1,2,1))]. 367 T(x / y,x \ y) = x / y. [hyper(39,a,357,a)]. 368 (x / y) * (x \ y) = (x \ y) * (x / y). [para(357(a,1),82(a,1,2))]. 369 (x / y) * (z * (y / x)) = T(z,y / x). [para(358(a,1),36(a,2)),flip(a)]. 370 T(x / y,x) = ((y / x) * y) \ y. [para(358(a,1),251(a,2,1))]. 371 ((x \ 1) / y) \ 1 = (y / x) * (x * x). [para(358(a,1),279(a,2))]. 372 T(x \ y,y \ x) = T(y / x,x). [para(367(a,1),112(a,1,1)),flip(a)]. 373 R(x,x \ 1,y) = x. [para(334(a,2),65(a,1))]. 374 R(T(x,y),x \ 1,z) = T(x,y). [para(373(a,1),46(a,2,1))]. 375 R(R(x,y,z),x \ 1,u) = R(x,y,z). [para(373(a,1),50(a,1,1)),flip(a)]. 376 R(T(x / y,y),(x / y) \ 1,z) = y \ x. [para(374(a,2),84(a,1))]. 377 T(x,y) * (x \ 1) = x \ T(x,y). [para(165(a,1),326(a,1,2)),flip(a)]. 378 x \ T(T(y,x \ 1),x) = (x \ (y * (x \ 1))) * x. [para(326(a,1),148(a,1,1,2)),flip(a)]. 379 K(x,y) * ((K(x,y) \ 1) / (x * y)) = K(x,y) \ ((y * x) \ 1). [para(341(a,1),278(a,2,2))]. 380 T(x \ 1,x * (y * y)) = (y \ (y \ (x * (y * y)))) \ 1. [para(349(a,2),258(a,2)),flip(a)]. 381 ((x * y) \ y) * x = x * ((x * y) \ y). [para(365(a,1),82(a,1,2)),flip(a)]. 382 T(x \ y,y \ x) = x \ y. [para(372(a,2),84(a,1))]. 383 T(x \ (x * y),(x * y) \ x) = y. [para(372(a,2),104(a,1))]. 384 (x \ y) * (y \ x) = (y \ x) * (x \ y). [para(382(a,1),82(a,1,2))]. 385 (x \ 1) \ T(x \ 1,x * y) = ((x * y) \ y) * ((x \ 1) \ 1). [para(349(a,1),377(a,1,1)),flip(a)]. 386 T(x,(y * x) \ y) = x. [para(19(a,1),383(a,1,1))]. 387 T(x,y \ (y / x)) = x. [para(22(a,1),386(a,1,2,1))]. 388 ((x * y) \ x) * y = y * ((x * y) \ x). [para(386(a,1),82(a,1,2))]. 389 T(K(x,y),(x * y) \ (y * x)) = K(x,y). [para(69(a,1),386(a,1,2,1))]. 390 R(x,y,z) * (x \ 1) = R(x,y,z) / x. [para(375(a,1),207(a,1,1)),flip(a)]. 391 x \ (y * (y * z)) = (x \ (y * y)) * z. [para(338(a,1),283(a,1)),flip(a)]. 392 (x \ (y * y)) * x = T(y * y,x). [para(338(a,1),290(a,1))]. 393 (x \ (y * y)) * (y \ (y \ z)) = x \ z. [para(338(a,1),296(a,1))]. 394 T(x * x,y * z) \ ((((y * z) \ (x * x)) * y) * z) = a((y * z) \ (x * x),y,z). [para(392(a,1),28(a,2,1)),flip(a)]. 395 L(x \ 1,x,x \ (y * y)) = T(y * y,x) \ (x \ (y * y)). [para(392(a,1),142(a,2,1))]. 397 (x / y) * (y * y) = x / (y \ 1). [para(371(a,1),343(a,1))]. 398 (x / (y \ 1)) / (y * y) = x / y. [hyper(24,a,22,a,b,397,a),flip(a)]. 399 (x / y) * (y / (x \ 1)) = x * x. [hyper(23,a,359,a,b,397,a),flip(a)]. 400 (x * y) / (y \ 1) = x * (y * y). [para(21(a,1),397(a,1,1)),flip(a)]. 401 (x * (y \ 1)) / y = x / (y * y). [para(21(a,1),398(a,1,1)),flip(a)]. 402 ((x \ (x \ y)) * x) / (x \ 1) = T(y,x * x). [para(400(a,2),286(a,1))]. 403 T(x / (y * y),y) = y \ (x * (y \ 1)). [para(401(a,1),84(a,1,1))]. 404 T(K(x,y),K(y,x)) = K(x,y). [para(30(a,2),389(a,1,2))]. 405 T(K(x,y),z) * K(y,x) = K(y,x) * T(K(x,y),z). [para(404(a,1),108(a,1,2,1)),flip(a)]. 406 R(K(x,y),z,u) * K(y,x) = K(y,x) * R(K(x,y),z,u). [para(404(a,1),110(a,1,2,1)),flip(a)]. 407 x * ((x \ (y * y)) * z) = y * (y * z). [para(391(a,1),20(a,1,2))]. 408 (((x * y) * x) \ (x * x)) * y = K(x,x * y). [para(391(a,1),30(a,2)),flip(a)]. 409 (x * (y * y)) \ z = y \ (y \ (x \ z)). [hyper(23,a,297,a,b,393,a),flip(a)]. 410 x * ((x \ (y * y)) * z) = (y * y) * z. [para(407(a,2),131(a,2)),flip(a)]. 411 (x * (y * y)) * z = x * (y * (y * z)). [para(407(a,1),89(a,1,2)),flip(a)]. 412 x \ (x \ (y \ ((y * x) * x))) = a(y,x,x). [para(409(a,1),28(a,2)),flip(a)]. 413 (x * (y * y)) \ x = y \ (y \ 1). [para(60(a,1),409(a,2,2,2))]. 414 x \ (x / (y * y)) = y \ (y \ 1). [para(22(a,1),413(a,1,1))]. 415 x / (y \ (y \ 1)) = x * (y * y). [para(413(a,1),65(a,1,2))]. 416 x * (y \ (y \ 1)) = x / (y * y). [para(414(a,1),20(a,1,2))]. 417 (x * (y * y)) * z = x * ((y * y) * z). [para(410(a,1),89(a,1,2)),flip(a)]. 418 (x * (y * (y * z))) / z = x * (y * y). [hyper(24,a,22,a,b,411,a),flip(a)]. 419 (x * (y * (y * z))) \ ((x * (y * y)) * (z * u)) = L(u,z,x * (y * y)). [para(411(a,1),32(a,2,1)),flip(a)]. 420 (x \ (x \ y)) * (x * (x * z)) = T(y,x * x) * z. [para(286(a,1),411(a,1,1)),flip(a)]. 421 L(x,y * y,z) = x. [hyper(23,a,74,a,b,417,a),flip(a)]. 422 R(x,y * y,z) = x. [hyper(24,a,79,a,b,417,a(flip)),flip(a)]. 423 T(x,x * (y * y)) = T(x,y * y). [para(421(a,1),203(a,1)),flip(a)]. 424 L(x,y,y / (z * z)) = x. [para(421(a,1),304(a,1,1))]. 425 L(x,y \ (y \ 1),z) = x. [para(318(a,1),421(a,1,2))]. 426 R(x,y \ (y \ 1),z) = x. [para(318(a,1),422(a,1,2))]. 427 L(x,y,y / (z \ (z \ 1))) = x. [para(318(a,1),424(a,1,3,2))]. 428 (x * (y \ (y \ 1))) * z = x * ((y \ (y \ 1)) * z). [para(425(a,1),74(a,1,2))]. 429 L(x,y,y * (z * z)) = x. [para(415(a,1),427(a,1,3))]. 430 T(x,x \ (y * y)) = T(x,y * y). [para(423(a,1),246(a,2))]. 431 T(x \ 1,x * (y * y)) = T(x \ 1,y * y). [para(330(a,1),430(a,1,2))]. 432 L(x,x,y / x) = y \ (y / (x \ 1)). [para(397(a,1),77(a,1,2)),flip(a)]. 433 (x * y) * (y \ 1) = R(x,y,y \ 1). [para(78(a,1),64(a,1)),flip(a)]. 434 R(x / y,y,y \ 1) = x * (y \ 1). [para(22(a,1),433(a,1,1)),flip(a)]. 435 x * L(y,z * x,z) = z * ((z \ x) * y). [para(312(a,1),172(a,1,2))]. 436 (R(T(x,y),z,u) * x) * w = R(T(x,y),z,u) * (x * w). [para(189(a,1),79(a,1,1)),flip(a)]. 437 T(x \ y,R(y / x,z,u)) = x \ y. [para(229(a,2),84(a,1))]. 438 T((x \ 1) \ y,y * x) = (x \ 1) \ y. [para(210(a,1),437(a,1,2))]. 439 T(x * y,y * x) = (x \ 1) \ y. [para(330(a,1),438(a,1,1))]. 440 (x \ y) \ T(y,x) = L(x,y,x). [para(19(a,1),269(a,1,1)),flip(a)]. 441 T(x,y) / L(y,x,y) = y \ x. [para(440(a,1),65(a,1,2))]. 442 L(x \ (x / y),y,x \ (x / y)) = ((x \ (x / y)) \ y) \ y. [para(387(a,1),440(a,1,2)),flip(a)]. 443 (x * (x * y)) \ z = y \ (x \ (x \ z)). [para(270(a,1),177(a,1)),flip(a)]. 444 x \ (y \ (y \ (z * (y * (y * x))))) = T(z,y * (y * x)). [para(443(a,1),36(a,2)),flip(a)]. 445 L(x \ 1,x,x / y) = y \ (y / x). [para(343(a,1),273(a,2,2))]. 446 x * (y \ ((y * (x \ 1)) * z)) = L(z,y * (x \ 1),y). [para(309(a,1),330(a,1)),flip(a)]. 447 R(x \ y,(y / x) \ 1,z) = x \ y. [para(84(a,1),376(a,1,1))]. 448 R(x \ y,x / y,z) = x \ y. [para(343(a,1),447(a,1,2))]. 449 R(x \ (x * y),x / (x * y),z) = y. [para(448(a,2),19(a,1))]. 450 R(x,y / (y * x),z) = x. [para(19(a,1),449(a,1,1))]. 451 (x * (y / (y * x))) * z = x * ((y / (y * x)) * z). [para(450(a,1),79(a,1,1)),flip(a)]. 452 x \ L(x,y * x,y) = a(y,x,x). [para(309(a,1),412(a,1,2))]. 453 L(x,y * x,y) = x * a(y,x,x). [para(452(a,1),20(a,1,2)),flip(a)]. 455 x * ((x \ y) * T(z,y)) = L(z,x * y,x) * y. [para(435(a,1),109(a,1))]. 456 (x * y) \ (x * T(y,x)) = K(x \ (x \ y),x). [para(171(a,1),274(a,1)),flip(a)]. 457 L(x,y,R(y,z,u)) = x. [hyper(23,a,74,a,b,191,a),flip(a)]. 458 R(x,y,z) * ((R(x,y,z) \ x) * u) = x * u. [hyper(23,a,89,a,b,191,a(flip)),flip(a)]. 459 (x * R(x,y,z)) * u = R(x,y,z) * (x * u). [para(223(a,1),191(a,1,1))]. 460 (R(x,y,z) \ x) \ 1 = x \ R(x,y,z). [para(457(a,1),259(a,1)),flip(a)]. 461 (R(x,y,z) \ u) / (x \ u) = R(x,y,z) \ x. [para(457(a,1),272(a,1,2))]. 462 (x \ R(x,y,z)) \ 1 = R(x,y,z) \ x. [para(460(a,1),156(a,1,1))]. 463 (R(x,y,z) \ x) \ u = (x \ R(x,y,z)) * u. [para(460(a,1),318(a,1,1)),flip(a)]. 464 (R(x,y,z) \ x) * ((x \ R(x,y,z)) * u) = u. [para(460(a,1),321(a,1,2,1))]. 465 (x \ R(x,y,z)) \ u = (R(x,y,z) \ x) * u. [para(460(a,1),330(a,1,1))]. 466 T(x,L(x \ 1,y,z)) = x. [hyper(23,a,82,a,b,216,a),flip(a)]. 467 K(x,L(x \ 1,y,z)) = 1. [hyper(40,a,466,a)]. 468 K(x \ 1,L(x,y,z)) = 1. [para(156(a,1),467(a,1,2,1))]. 469 K(L(x,y,z) \ 1,x) = 1. [para(303(a,1),468(a,1,2))]. 470 T(L(x,y,z) \ 1,x) = L(x,y,z) \ 1. [hyper(41,a,469,a)]. 471 x * (L(x,y,z) \ 1) = L(x,y,z) \ x. [para(470(a,1),327(a,1,2))]. 472 R(x / (x * y),z,u) * (x * y) = (x * y) * R(L(y \ 1,y,x),z,u). [para(142(a,2),224(a,2,2,1))]. 473 R((x * y) / (x * z),u,w) * (x * z) = (x * z) * R(L(z \ y,z,x),u,w). [para(76(a,2),224(a,2,2,1))]. 475 T(x,R(x \ 1,y,z)) = x. [hyper(23,a,82,a,b,227,a),flip(a)]. 476 T(x \ 1,R(x,y,z)) = x \ 1. [para(156(a,1),475(a,1,2,1))]. 477 R(x,y,z) * (x \ 1) = x \ R(x,y,z). [para(476(a,1),327(a,1,2))]. 478 R(x,y,z) / x = x \ R(x,y,z). [para(477(a,1),390(a,1)),flip(a)]. 480 (x \ R(x,y,z)) \ R(x,y,z) = x. [para(478(a,1),66(a,1,1))]. 481 (x / y) \ R(x / y,y,y \ 1) = (x * (y \ 1)) / (x / y). [para(434(a,1),478(a,1,1)),flip(a)]. 482 (x \ ((y * x) / y)) \ 1 = (y / (y * x)) * x. [para(262(a,2),358(a,1))]. 483 R(x,L(x,y,z),u) = x. [para(310(a,2),303(a,1))]. 484 (x * L(x,y,z)) * u = x * (L(x,y,z) * u). [para(483(a,1),79(a,1,1)),flip(a)]. 485 T(x \ 1,x \ y) = T(x \ 1,x * y). [para(330(a,1),337(a,1,2)),flip(a)]. 486 (x \ T(y,x)) / (x \ 1) = T(y,x * x). [para(148(a,1),402(a,1,1))]. 487 (((x \ y) * x) \ 1) * y = K(x,x * y). [para(244(a,1),408(a,1,1))]. 488 ((x \ y) * x) \ y = K(x,x * y). [para(487(a,1),318(a,1)),flip(a)]. 489 K(x,x \ y) = K(x,x * y). [para(488(a,1),71(a,1)),flip(a)]. 490 K(x,x * (x * y)) = K(x,y). [para(19(a,1),489(a,1,2)),flip(a)]. 491 K(x,x * (y * x)) = K(x,T(y,x)). [para(36(a,2),489(a,1,2)),flip(a)]. 492 K(x,(x * x) / y) = K(x,y \ 1). [para(263(a,1),490(a,1,2))]. 493 K(x \ (x \ y),x) = (x * y) \ (y * x). [para(82(a,1),456(a,1,2)),flip(a)]. 494 K(x \ (x \ y),x) = K(y,x). [para(493(a,2),30(a,2)),flip(a)]. 495 K(x \ y,x) = K(x * y,x). [para(19(a,1),494(a,1,1,2))]. 496 (R(x,y,z) \ x) * R(x,y,z) = x. [hyper(23,a,223,a,b,458,a)]. 498 x / R(x,y,z) = R(x,y,z) \ x. [hyper(24,a,22,a,b,496,a),flip(a)]. 499 T(R(x,y,z) \ 1,x) = x \ (x / R(x,y,z)). [para(498(a,2),325(a,2,2))]. 500 (x * y) / (z \ ((z * x) * y)) = R(z,x,y) \ z. [para(101(a,1),461(a,1,1))]. 501 x * ((x \ R(x,y,z)) * u) = R(x,y,z) * u. [para(464(a,1),458(a,1,2)),flip(a)]. 502 (x \ ((y * x) / y)) \ 1 = x * (y / (y * x)). [para(482(a,2),362(a,1))]. 503 L(x,L(y,z,u),y) = x. [hyper(23,a,74,a,b,484,a),flip(a)]. 504 x * ((x \ L(x,y,z)) * u) = L(x,y,z) * u. [hyper(23,a,89,a,b,484,a(flip)),flip(a)]. 505 L(x,(y * z) \ y,z \ 1) = x. [para(142(a,1),503(a,1,2))]. 506 (x \ L(x,y,z)) \ 1 = L(x,y,z) \ x. [para(503(a,1),259(a,1)),flip(a)]. 507 (x \ L(x,y,z)) \ u = L(x,y,z) \ (x * u). [para(503(a,1),267(a,1)),flip(a)]. 509 L(x,y,L(y,z,u)) = x. [para(303(a,1),503(a,1,2))]. 510 T(x,x * L(x,y,z)) = x. [para(503(a,1),220(a,2))]. 511 (L(x,y,z) \ x) \ 1 = x \ L(x,y,z). [para(509(a,1),259(a,1)),flip(a)]. 513 (L(x,y,z) \ u) / (x \ u) = L(x,y,z) \ x. [para(509(a,1),272(a,1,2))]. 514 (x \ L(x,y,z)) * x = L(x,y,z). [para(510(a,1),250(a,1,2))]. 515 L(x,y,z) / x = x \ L(x,y,z). [para(510(a,1),252(a,1,2))]. 516 (x \ L(x,y,z)) \ 1 = x / L(x,y,z). [para(510(a,1),346(a,1,1)),flip(a)]. 517 (x \ L(x,y,z)) \ u = (L(x,y,z) \ x) * u. [para(506(a,1),318(a,1,1)),flip(a)]. 519 x / L(x,y,z) = L(x,y,z) \ x. [para(516(a,1),506(a,1))]. 520 (L(x,y,z) \ x) * L(x,y,z) = x. [para(519(a,1),22(a,1,1))]. 521 (L(x \ 1,x,x / y) \ (x \ 1)) * (y \ (y / x)) = x \ 1. [para(445(a,1),520(a,1,2))]. 523 (x * R(x,y,z)) * u = x * (R(x,y,z) * u). [para(501(a,1),89(a,1,2)),flip(a)]. 524 L(x,y,z) \ (x * u) = (L(x,y,z) \ x) * u. [para(517(a,1),507(a,1)),flip(a)]. 525 R(x,R(x,y,z),u) = x. [hyper(24,a,79,a,b,523,a(flip)),flip(a)]. 526 R(x,y,z) * (x * u) = x * (R(x,y,z) * u). [para(523(a,1),459(a,1)),flip(a)]. 527 R(T(x,y),R(x,z,u),w) = T(x,y). [para(525(a,1),46(a,2,1))]. 528 (x \ R(x,y,z)) * (x * u) = R(x,y,z) * u. [hyper(23,a,501,a,b,526,a(flip)),flip(a)]. 529 x * (R(x,y,z) * (x \ u)) = R(x,y,z) * u. [para(20(a,1),526(a,1,2)),flip(a)]. 530 x * (R(x,y,z) * T(u,x)) = R(x,y,z) * (u * x). [para(82(a,1),526(a,1,2)),flip(a)]. 531 (R(x,y,z) * u) / (x * u) = x \ R(x,y,z). [hyper(24,a,22,a,b,528,a),flip(a)]. 532 (x \ R(x,y,z)) * u = R(x,y,z) * (x \ u). [para(20(a,1),528(a,1,2))]. 533 R(x \ R(x,y,z),x * u,w) = ((R(x,y,z) * u) * w) / ((x * u) * w). [para(528(a,1),34(a,2,1,1))]. 534 x \ (R(x,y,z) * u) = R(x,y,z) * (x \ u). [hyper(23,a,20,a,b,529,a),flip(a)]. 535 x / (y * (R(y,z,u) \ x)) = y \ R(y,z,u). [para(20(a,1),531(a,1,1))]. 536 (R(x,y,z) * (x \ u)) / u = x \ R(x,y,z). [para(20(a,1),531(a,1,2))]. 537 ((x * y) * z) / (x * (y * z)) = x \ R(x,y,z). [para(79(a,1),531(a,1,1))]. 538 (R(R(x,y,z),u,w) * (y * z)) / ((x * y) * z) = R(x,y,z) \ R(R(x,y,z),u,w). [para(79(a,1),531(a,1,2))]. 539 x \ (R(y,z,u) * (y \ x)) = T(y \ R(y,z,u),x). [para(532(a,1),36(a,2,2)),flip(a)]. 540 (R(x,y,z) \ x) \ u = R(x,y,z) * (x \ u). [para(532(a,1),463(a,2))]. 541 (x \ R(x,y,z)) \ u = x * (R(x,y,z) \ u). [para(535(a,1),66(a,1,1))]. 542 x / (R(y,z,u) * (y \ x)) = R(y,z,u) \ y. [para(540(a,1),65(a,1,2))]. 543 x * (R(x,y,z) \ 1) = R(x,y,z) \ x. [para(541(a,1),462(a,1))]. 544 (R(x,y,z) \ x) * u = x * (R(x,y,z) \ u). [para(541(a,1),465(a,1)),flip(a)]. 545 T(R(x,y,z) \ 1,x) = R(x,y,z) \ 1. [hyper(23,a,327,a,b,543,a),flip(a)]. 546 T(x,R(x,y,z) \ 1) = x. [hyper(39,a,545,a)]. 547 x \ (x / R(x,y,z)) = R(x,y,z) \ 1. [para(545(a,1),499(a,1)),flip(a)]. 548 T(x,y) * (R(x,z,u) \ 1) = R(x,z,u) \ T(x,y). [para(546(a,1),329(a,1,2,1)),flip(a)]. 549 (x * y) \ ((z * x) * y) = R(T(z,x * y),x,y). [para(111(a,2),46(a,2)),flip(a)]. 550 (x * (x * (y * z))) / (y * z) = R(x * x,y,z). [para(51(a,1),134(a,1,1))]. 551 x \ ((x * y) * (1 / y)) = a(x,y,1 / y). [para(18(a,1),164(a,1,1))]. 552 x \ ((x * y) * (y \ 1)) = a(x,y,1 / y). [para(155(a,1),551(a,1,2,2))]. 553 x \ ((x * y) * (y \ 1)) = a(x,y,y \ 1). [para(155(a,1),552(a,2,3))]. 554 a(x / y,y,y \ 1) = (x / y) \ (x * (y \ 1)). [para(22(a,1),553(a,1,2,1)),flip(a)]. 555 T((x * y) / (z * y),z) = R(z \ x,z,y). [para(84(a,1),194(a,2,1))]. 556 T(T((x * y) / (z * y),u),z) = T(R(z \ x,z,y),u). [para(555(a,1),42(a,1,1)),flip(a)]. 557 T(x,x * ((y * x) / y)) = x. [para(204(a,2),237(a,1))]. 558 ((x * y) / x) / y = y \ ((x * y) / x). [para(557(a,1),252(a,1,2))]. 560 (x \ y) * L(z,y,x \ 1) = x \ (y * z). [para(331(a,2),318(a,1))]. 561 (T(x,y) * (x \ 1)) * z = T(x,y) * (x \ z). [para(374(a,1),332(a,1,1)),flip(a)]. 562 (x \ T(x,y)) * z = T(x,y) * (x \ z). [para(377(a,1),561(a,1,1))]. 563 (T(x,y) * (x \ z)) / z = x \ T(x,y). [hyper(24,a,22,a,b,562,a),flip(a)]. 564 x * (T(x,y) * (x \ x)) = T(x * T(x,y),x). [para(562(a,1),138(a,1,2))]. 565 (T(x,y) * z) / (x * z) = x \ T(x,y). [para(19(a,1),563(a,1,1,2))]. 566 (x \ T(x,y)) \ (T(x,y) * z) = x * z. [para(565(a,1),66(a,1,1))]. 567 (x \ T(x,y)) \ z = x * (T(x,y) \ z). [para(20(a,1),566(a,1,2))]. 568 T(x * T(x,y),x) = x * (T(x,y) * 1). [para(60(a,1),564(a,1,2,2)),flip(a)]. 569 T(x * T(x,y),x) = x * T(x,y). [para(18(a,1),568(a,2,2))]. 571 T(x,x * T(x,y)) = x. [hyper(39,a,569,a)]. 572 T(x,y) / x = x \ T(x,y). [para(571(a,1),252(a,1,2))]. 573 (x \ T(x,y)) \ z = (x / T(x,y)) * z. [para(572(a,1),358(a,1,1))]. 574 (x \ T(x,y)) \ z = (T(x,y) \ x) * z. [para(299(a,1),573(a,2,1))]. 575 (T(x,y) \ x) * (T(x,y) * z) = x * z. [para(574(a,1),566(a,1))]. 576 (T(x,y) \ x) * z = x * (T(x,y) \ z). [para(574(a,1),567(a,1))]. 577 (x * y) / (T(x,z) * y) = T(x,z) \ x. [hyper(24,a,22,a,b,575,a),flip(a)]. 578 x * (T(x,y) \ 1) = T(x,y) \ x. [hyper(24,a,18,a,b,576,a),flip(a)]. 579 K(x,T(x,y) \ 1) = 1. [hyper(23,a,328,a,b,576,a),flip(a)]. 580 T(x,T(x,y) \ 1) = x. [hyper(41,a,579,a)]. 581 T(x,y) * (T(x,z) \ 1) = T(x,z) \ T(x,y). [para(580(a,1),329(a,1,2,1)),flip(a)]. 582 x \ (T(x,y) \ x) = T(x,y) \ 1. [hyper(23,a,20,a,b,578,a),flip(a)]. 583 ((T(x,y) \ x) * z) / (T(x,y) \ z) = R(x,T(x,y) \ 1,z). [para(578(a,1),324(a,1,1,1))]. 584 R(x \ 1,x * y,z) = R(x,y,z) \ 1. [para(348(a,2),344(a,1))]. 585 R(x,x \ y,z) \ 1 = R(x \ 1,y,z). [para(20(a,1),584(a,1,2)),flip(a)]. 586 (x * y) / (z * ((z \ x) * y)) = R(z,x,y) \ z. [para(213(a,1),500(a,1,2))]. 587 T(x \ R(x,y,z),x * (y * z)) = (x * (y * z)) \ ((x * y) * z). [para(537(a,1),84(a,1,1))]. 588 R(x * x,y,z) = x * x. [para(550(a,1),132(a,1))]. 589 R(T(x * x,y),z,u) = T(x * x,y). [para(588(a,1),46(a,2,1))]. 591 T(x * x,y) \ (z * u) = (T(x * x,y) \ z) * u. [para(589(a,1),197(a,1,1))]. 592 a(x / y,y,y \ 1) = (y / x) * (x * (y \ 1)). [para(554(a,2),358(a,1))]. 593 (x * y) / (z * ((z \ y) * T(x,y))) = R(z,y,T(x,y)) \ z. [para(82(a,1),586(a,1,1))]. 594 a(x,y,z) = (x \ (y * z)) \ ((x \ y) * z). [para(284(a,2),28(a,2))]. 596 (x \ (y * (x \ 1))) * x = T(y,x) * (x \ 1). [para(378(a,1),329(a,1))]. 597 (T(x,y) * (y \ 1)) / y = y \ (x * (y \ 1)). [hyper(24,a,22,a,b,596,a),flip(a)]. 598 x \ (y * (x \ 1)) = T(y,x) / (x * x). [para(597(a,1),401(a,1))]. 599 x \ ((x * (x * y)) * (x \ 1)) = (x * (y * x)) / (x * x). [para(103(a,1),598(a,2,1))]. 600 T(x,y) / (y * y) = T(x / (y * y),y). [para(598(a,1),403(a,2)),flip(a)]. 601 x * ((y \ (y \ 1)) * z) = (x / (y * y)) * z. [para(416(a,1),428(a,1,1)),flip(a)]. 602 (x / (y * y)) * z = x * (y \ (y \ z)). [para(291(a,1),601(a,1,2)),flip(a)]. 603 L(x,y / (y * z),z) = x. [hyper(23,a,74,a,b,451,a),flip(a)]. 604 (x * (y / (y * x))) \ z = (y / (y * x)) \ (x \ z). [para(603(a,1),177(a,1)),flip(a)]. 605 T(x,x * (y / (y * x))) = x. [para(603(a,1),364(a,2))]. 606 (x * (y / (y * x))) \ z = ((y * x) / y) * (x \ z). [para(604(a,2),358(a,1))]. 607 x * (x * ((y * z) / ((x * y) * z))) = R(x,x * y,z). [para(95(a,1),211(a,1)),flip(a)]. 608 L(R(x,x,y),z,u) * (x * y) = (x * L(x,z,u)) * y. [para(214(a,1),184(a,2,1))]. 609 L(K(x,y),y * x,x * y) = K(y,x) \ 1. [para(30(a,2),260(a,2,1))]. 610 (x \ (y * z)) \ ((x \ y) * z) = a(x \ 1,y,z). [para(318(a,1),323(a,1,2,1))]. 611 a(x \ 1,y,z) = a(x,y,z). [para(610(a,1),594(a,2)),flip(a)]. 612 a(x / y,z,u) = a(y / x,z,u). [para(343(a,1),611(a,1,1))]. 613 L(x \ 1,y,x \ 1) * y = y * T(x \ 1,x * y). [para(485(a,1),336(a,2,2))]. 614 T(T((x * y) / (z * y),u),z) = R(T(z \ x,u),z,y). [para(556(a,2),46(a,2)),flip(a)]. 615 x * (x * (R(x,y,z) \ 1)) = R(x,x * y,z). [para(344(a,1),607(a,1,2,2))]. 616 (x * x) / R(x,y,z) = R(x,x * y,z). [para(615(a,1),263(a,1)),flip(a)]. 617 x * (R(x,y,z) \ x) = R(x,x * y,z). [para(543(a,1),615(a,1,2))]. 618 x \ R(x,x * y,z) = R(x,y,z) \ x. [hyper(23,a,20,a,b,617,a),flip(a)]. 619 x * (R(x,x * y,z) \ x) = R(x,(x * x) * y,z). [para(131(a,2),617(a,2,2))]. 620 x / R(x,x * y,z) = x \ R(x,y,z). [para(617(a,1),535(a,1,2))]. 621 (R(x,y,z) \ x) * x = R(x,x * y,z). [para(617(a,1),544(a,2))]. 622 R(x,x * y,z) \ x = x \ R(x,y,z). [para(620(a,1),498(a,1)),flip(a)]. 623 R(x,x * y,z) \ 1 = x \ (x \ R(x,y,z)). [para(620(a,1),547(a,1,2)),flip(a)]. 624 x \ R(x,x \ y,z) = R(x,y,z) \ x. [para(20(a,1),622(a,1,1,2)),flip(a)]. 625 x * (R(x,x * y,z) \ u) = (x \ R(x,y,z)) * u. [para(622(a,1),544(a,1,1)),flip(a)]. 626 R(x,(x * x) * y,z) = x * (x \ R(x,y,z)). [para(622(a,1),619(a,1,2)),flip(a)]. 627 R(x,(x * x) * y,z) = R(x,y,z). [para(626(a,2),20(a,1))]. 628 R(x,x * (x * y),z) = R(x,y,z). [para(131(a,1),627(a,1,2))]. 629 R(x,x \ y,z) = R(x,x * y,z). [para(20(a,1),628(a,1,2,2)),flip(a)]. 630 R(x,x * y,z) \ (y * z) = (x \ y) * z. [para(629(a,1),197(a,1,1))]. 632 R(x,x * y,z) \ 1 = R(x \ 1,y,z). [para(629(a,1),585(a,1,1))]. 633 R(x,x * y,z) = R(x \ 1,y,z) \ 1. [para(632(a,1),156(a,1,1)),flip(a)]. 634 x \ (x \ R(x,y,z)) = R(x \ 1,y,z). [para(632(a,1),623(a,1)),flip(a)]. 635 x * R(x \ 1,y,z) = x \ R(x,y,z). [para(634(a,1),20(a,1,2))]. 636 x * (R(x \ 1,y,z) * u) = x \ (R(x,y,z) * u). [para(634(a,1),265(a,1,2,1))]. 637 x * (R(x,x * y,z) \ u) = R(x,y,z) * (x \ u). [para(625(a,2),532(a,1))]. 638 x * (R(x \ 1,y,z) * u) = R(x,y,z) * (x \ u). [para(636(a,2),534(a,1))]. 639 x * (y * R(y \ (x \ y),z,u)) = R(x,z,u) * (x \ y). [para(366(a,2),638(a,1,2))]. 640 (x * L(x,y,z)) * u = L(x,y,z) * (x * u). [para(182(a,1),608(a,1,1,1)),flip(a)]. 641 L(x,y,z) \ ((x * L(x,y,z)) * u) = x * u. [hyper(23,a,20,a,b,640,a(flip)),flip(a)]. 642 L(x,y,z) * (x * u) = x * (L(x,y,z) * u). [para(640(a,1),484(a,1))]. 643 L(x,y,z) \ (x * (L(x,y,z) * u)) = x * u. [para(484(a,1),641(a,1,2))]. 644 x * (L(x,y,z) * (x \ u)) = L(x,y,z) * u. [para(20(a,1),642(a,1,2)),flip(a)]. 645 L(x,y,z) * (x * (L(x,y,z) \ u)) = x * u. [para(20(a,1),642(a,2,2))]. 646 (L(x,y,z) \ x) * (L(x,y,z) * u) = x * u. [para(643(a,1),524(a,1)),flip(a)]. 647 (x \ L(x,y,z)) * u = L(x,y,z) * (x \ u). [hyper(23,a,504,a,b,644,a),flip(a)]. 648 (x * y) / (x * (L(x,z,u) \ y)) = L(x,z,u). [hyper(24,a,22,a,b,645,a),flip(a)]. 649 (x * y) / (L(x,z,u) * y) = L(x,z,u) \ x. [hyper(24,a,22,a,b,646,a),flip(a)]. 650 (L(x,y,z) \ x) * u = x * (L(x,y,z) \ u). [para(20(a,1),646(a,1,2))]. 652 T(x,L(x,y,z) \ x) = x. [hyper(23,a,82,a,b,650,a),flip(a)]. 653 K(x,L(x,y,z) \ x) = 1. [hyper(40,a,652,a)]. 654 T(x \ 1,x * (y * y)) = T(x,y * y) \ 1. [para(202(a,1),380(a,2,1))]. 655 T(x,y * y) \ 1 = T(x \ 1,y * y). [para(654(a,1),431(a,1))]. 656 L(x,y,R(T(y,z),u,w)) = x. [hyper(23,a,74,a,b,436,a),flip(a)]. 657 L(x,y,R((y \ z) \ z,u,w)) = x. [para(83(a,1),656(a,1,3,1))]. 658 x \ ((y \ (y \ z)) * (y * (y * x))) = T(z,y * (y * x)). [para(285(a,1),444(a,1,2))]. 659 x \ (x * (x * (y * (x \ 1)))) = (x * (y * x)) / (x * x). [para(51(a,1),599(a,1,2))]. 660 x \ (T(y,z * z) * x) = T(y,z * (z * x)). [para(420(a,1),658(a,1,2))]. 661 T(T(x,y * y),z) = T(x,y * (y * z)). [para(660(a,1),36(a,2))]. 662 T(T(x,y),z * z) = T(x,z * (z * y)). [para(661(a,1),42(a,1)),flip(a)]. 663 x \ (x * T(y,x \ 1)) = (x * (y * x)) / (x * x). [para(347(a,1),659(a,1,2,2))]. 664 (x * (y * x)) / (x * x) = T(y,x \ 1). [para(663(a,1),19(a,1))]. 665 T(x * y,x) / (x * x) = T(x \ y,x \ 1). [para(138(a,1),664(a,1,1))]. 666 T((x * y) / (x * x),x) = T(x \ y,x \ 1). [para(665(a,1),600(a,1)),flip(a)]. 667 (x * (x * ((y * z) * u))) / (z * u) = R(x * (x * y),z,u). [para(51(a,1),94(a,1,1))]. 668 (x * (y \ 1)) / (x / y) = (x / y) \ (x * (y \ 1)). [para(434(a,1),481(a,1,2)),flip(a)]. 669 (x * (y \ 1)) / (x / y) = (y / x) * (x * (y \ 1)). [para(668(a,2),358(a,1))]. 670 (x * (T(x,y) \ z)) / (T(x,y) \ z) = R(x,T(x,y) \ 1,z). [para(576(a,1),583(a,1,1))]. 671 (x * y) / (L(x,z * y,z) * y) = R(z,y,T(x,y)) \ z. [para(455(a,1),593(a,1,2))]. 672 R(x,y,T(z,y)) \ x = L(z,x * y,x) \ z. [para(671(a,1),649(a,1))]. 673 (R(x,y,T(z,y)) \ x) \ 1 = z \ L(z,x * y,x). [para(672(a,2),511(a,1,1))]. 674 L(x,y * (y * z),y) \ x = y \ R(y,z,T(x,y * z)). [para(672(a,1),622(a,1))]. 676 x \ R(x,y,T(z,y)) = z \ L(z,x * y,x). [para(673(a,1),460(a,1)),flip(a)]. 677 R(x,y,T(z,y)) = x * (z \ L(z,x * y,x)). [para(676(a,1),20(a,1,2)),flip(a)]. 678 R(x,x * y,T(z,x * y)) = x * (z \ L(z,y,x)). [para(313(a,1),677(a,2,2,2))]. 679 R(x,y,T(z,x * y)) \ x = z \ L(z,y,x). [hyper(23,a,617,a,b,678,a(flip)),flip(a)]. 680 (x \ L(x,y,z)) * R(z,y,T(x,z * y)) = z. [para(679(a,1),496(a,1,1))]. 681 L(x,y,z) \ x = z \ R(z,y,T(x,z * y)). [para(313(a,1),674(a,1,1))]. 682 L(x,y,z) * (z \ R(z,y,T(x,z * y))) = x. [para(681(a,1),20(a,1,2))]. 683 R(x,y,T(z,x * y)) = x * (L(z,y,x) \ z). [para(681(a,2),20(a,1,2)),flip(a)]. 684 (x \ R(x,y,T(z,x * y))) * L(z,y,x) = z. [para(681(a,1),520(a,1,1))]. 685 L(x,R(y,z,u),T(y,w)) * (T(y,w) \ T(y,w)) = x. [para(527(a,1),682(a,1,2,2))]. 686 R(x,y,T(z,x * y)) * (x \ L(z,y,x)) = z. [para(684(a,1),532(a,1)),flip(a)]. 687 L(x,R(y,z,u),T(y,w)) * 1 = x. [para(60(a,1),685(a,1,2))]. 688 L(x,R(y,z,u),T(y,w)) = x. [hyper(24,a,18,a,b,687,a)]. 690 L(x,R(y / z,u,w),z \ y) = x. [para(84(a,1),688(a,1,3))]. 691 T(R(x,y,z),T(x,u)) / T(x,u) = T(x,u) \ R(x,y,z). [para(688(a,1),441(a,1,2))]. 692 R(T(x,T(x,y)),z,u) / T(x,y) = T(x,y) \ R(x,z,u). [para(46(a,2),691(a,1,1))]. 693 R(x,y,z) / T(x,u) = T(x,u) \ R(x,y,z). [para(115(a,1),692(a,1,1,1))]. 694 x * (x * (((y * z) * u) / (z * u))) = R(x * (x * y),z,u). [para(667(a,1),211(a,1)),flip(a)]. 695 R(x,T(x,y) \ 1,z) = x. [para(670(a,1),21(a,1))]. 696 R(x * (x * y),z,u) = x * (x * R(y,z,u)). [para(34(a,2),694(a,1,2,2)),flip(a)]. 697 x * (x * R(T(y,x),z,u)) = R(x * (y * x),z,u). [para(82(a,1),696(a,1,1,2)),flip(a)]. 698 R(x * (x * T(y,x * x)),z,u) = R(y,z,u) * (x * x). [para(696(a,2),226(a,1))]. 699 R(x * (y * x),z,u) = x * (R(y,z,u) * x). [para(110(a,1),697(a,1,2)),flip(a)]. 700 x \ R(x * (y * x),z,u) = R(y,z,u) * x. [hyper(23,a,20,a,b,699,a(flip)),flip(a)]. 701 (x * (y * x)) \ R(x * (z * x),u,w) = T(y,x) \ (x \ (R(z,u,w) * x)). [para(699(a,2),287(a,1,2))]. 702 x \ R(x * y,z,u) = R(y / x,z,u) * x. [para(22(a,1),700(a,1,2,1,2))]. 703 x \ R(x * y,z,u) = x * R(x \ y,z,u). [para(702(a,2),224(a,1))]. 704 L(x \ (y * R(y \ z,u,w)),x,y) = (y * x) \ R(y * z,u,w). [para(703(a,1),177(a,1,1,2))]. 705 R(x * (y * y),z,u) = R(x,z,u) * (y * y). [para(136(a,1),698(a,1,1))]. 706 (x \ 1) \ T(x \ 1,x * y) = ((x * y) \ y) * x. [para(156(a,1),385(a,2,2))]. 707 (x \ 1) \ T(x \ 1,x * y) = x * ((x * y) \ y). [para(706(a,2),381(a,1))]. 708 (x * y) * T(L(y \ 1,y,x),z) = (x * y) * T((x * y) \ x,z). [para(231(a,1),139(a,1))]. 709 R((x / y) * (z * z),z \ (z \ 1),y) = x / (z \ (z \ y)). [para(415(a,1),293(a,1,1))]. 710 x / (y \ (y \ z)) = (x / z) * (y * y). [para(709(a,1),426(a,1))]. 711 (x / (y * z)) * (y * y) = x / (y \ z). [para(19(a,1),710(a,1,2,2)),flip(a)]. 712 (x * y) / (z \ y) = R(x / z,z,y) * (z * z). [para(80(a,2),711(a,1,1)),flip(a)]. 713 R((x / y) * (y * y),y,z) = (x * z) / (y \ z). [para(712(a,2),705(a,2))]. 714 R(x / (y \ 1),y,z) = (x * z) / (y \ z). [para(397(a,1),713(a,1,1))]. 715 R(x,y,z) = ((x * (y \ 1)) * z) / (y \ z). [para(21(a,1),714(a,1,1))]. 716 R(L(x,y,z) \ x,x,u) = ((L(x,y,z) \ 1) * u) / (x \ u). [para(513(a,1),714(a,1,1))]. 717 R(x,y \ 1,z) = R(x,y,z). [para(715(a,2),324(a,1)),flip(a)]. 718 R(x,y,y) / y = x * (y \ 1). [para(717(a,1),207(a,1,1))]. 719 (x * (y \ 1)) \ R(x,y,y) = y. [para(717(a,1),209(a,1,2))]. 720 R(x / (y \ 1),y,y) = x * y. [para(717(a,1),210(a,1))]. 721 R(x,T(x,y),z) = x. [para(717(a,1),695(a,1))]. 722 (x * T(x,y)) * z = x * (T(x,y) * z). [para(721(a,1),79(a,1,1)),flip(a)]. 723 R(T(x / (y \ 1),z),y,y) / y = (y \ 1) * T((y \ 1) \ x,z). [para(718(a,2),139(a,1))]. 725 (T(x,y) * (R(x,z,u) \ 1)) \ T(x,y) = R(x,z,u). [para(527(a,1),719(a,1,2))]. 726 R(T(x / (y \ 1),z),y,y) = T(x * y,z). [para(720(a,1),46(a,2,1))]. 727 L(x,T(y,z),y) = x. [hyper(23,a,74,a,b,722,a),flip(a)]. 729 x * (T(x,y) * (x \ z)) = T(x,y) * z. [para(722(a,1),281(a,1))]. 730 L(x,y,(z * y) / z) = x. [para(104(a,1),727(a,1,2))]. 731 L(x,(y \ z) \ z,y) = x. [para(83(a,1),727(a,1,2))]. 732 x \ (T(x,y) * z) = T(x,y) * (x \ z). [hyper(23,a,20,a,b,729,a),flip(a)]. 733 x \ (T(x,y) * z) = (x \ T(x,y)) * z. [para(732(a,2),562(a,2)),flip(a)]. 734 (R(x,y,z) \ T(x,u)) \ T(x,u) = R(x,y,z). [para(548(a,1),725(a,1,1))]. 735 R(L(x,y,z) \ x,x,u) = (L(x,y,z) \ u) / (x \ u). [para(318(a,1),716(a,2,1))]. 736 R(L(x,y,z) \ x,x,u) = L(x,y,z) \ x. [para(735(a,2),513(a,1))]. 739 a(x,y,z) = T(x \ R(x,y,z),x * (y * z)). [para(587(a,2),28(a,2))]. 740 T(T(x \ R(x,y,z),u),x * (y * z)) = T(a(x,y,z),u). [para(739(a,2),42(a,1,1)),flip(a)]. 741 a(x,y,z) = T(T(R(x,y,z) / x,x * (y * z)),x). [para(739(a,2),112(a,2)),flip(a)]. 742 T((x * (y \ R(y,z,u))) / x,y * (z * u)) = (x * a(y,z,u)) / x. [para(739(a,2),233(a,1,1,2)),flip(a)]. 743 T(R(x,y,z) \ R(R(x,y,z),u,x),x * (R(x,y,z) * T(u,x))) = a(R(x,y,z),u,x). [para(530(a,2),739(a,2,2)),flip(a)]. 744 T(T((R(x,y,z) * u) / (x * u),x * (y * z)),x) = R(a(x,y,z),x,u). [para(739(a,2),614(a,2,1))]. 745 a(x,y,z) = T(T(x \ R(x,y,z),x * (y * z)),x). [para(478(a,1),741(a,2,1,1))]. 746 T(a(x,y,z),x) = a(x,y,z). [para(739(a,2),745(a,2,1)),flip(a)]. 747 a(x,y,z) * x = x * a(x,y,z). [para(746(a,1),82(a,1,2)),flip(a)]. 748 (x * a(x,y,z)) / x = a(x,y,z). [para(746(a,1),105(a,1,1,2))]. 749 ((x * (x * y)) * a(x * (x * y),z,u)) / y = a(x * (x * y),z,u) * (x * x). [para(747(a,1),418(a,1,1))]. 750 (x \ y) \ R(x \ z,u,w) = (x * y) \ R(x * z,u,w). [para(704(a,1),267(a,1)),flip(a)]. 751 (x * y) * T((x * y) \ x,z) = (x * y) * L(T(y \ 1,z),y,x). [para(44(a,2),708(a,1,2)),flip(a)]. 752 (x \ 1) * T((x \ 1) \ y,z) = T(y * x,z) / x. [para(726(a,1),723(a,1,1)),flip(a)]. 753 (x \ 1) * T(x * y,z) = T(y * x,z) / x. [para(330(a,1),752(a,1,2,1))]. 754 T(x * y,z) / y = y \ T(y * x,z). [para(753(a,1),318(a,1))]. 755 x \ T(x * (y / x),z) = T(y,z) / x. [para(22(a,1),754(a,1,1,1)),flip(a)]. 756 T(x * y,y) / y = (y \ x) * y. [para(754(a,2),146(a,1))]. 757 ((x \ y) * x) * x = T(y * x,x). [para(756(a,1),22(a,1,1))]. 758 T((x * y) * x,x) = (y * x) * x. [para(19(a,1),757(a,1,1,1)),flip(a)]. 762 (x * y) * T((x * y) \ x,z) = x * (y * T(y \ 1,z)). [para(751(a,2),74(a,1))]. 763 (x * (x * (y * z))) \ (x * (x * (y * (z * u)))) = L(u,z,x * (x * y)). [para(51(a,1),92(a,1,2))]. 764 (x * y) * T(L(y \ z,y,x),u) = (x * y) * T((x * y) \ (x * z),u). [para(232(a,1),139(a,1))]. 765 (x * y) * R(L(y \ 1,y,x),z,u) = (x * y) * R((x * y) \ x,z,u). [para(472(a,1),224(a,1))]. 767 T(T(x \ R(x,y,z),x * (y * z)),x) = R(a(x,y,z),x,u). [para(531(a,1),744(a,1,1,1))]. 769 R(a(x,y,z),x,u) = a(x,y,z). [para(767(a,1),745(a,2)),flip(a)]. 770 (a(x,y,z) * x) * u = a(x,y,z) * (x * u). [para(769(a,1),79(a,1,1)),flip(a)]. 771 L(x,y,a(y,z,u)) = x. [hyper(23,a,74,a,b,770,a),flip(a)]. 772 (x * a(x,y,z)) * u = a(x,y,z) * (x * u). [para(747(a,1),770(a,1,1))]. 773 L(x,y,z * (z * u)) = (u * y) \ (u * (y * x)). [para(763(a,1),212(a,1))]. 774 L(x,y,z * (z * u)) = L(x,y,u). [para(773(a,2),32(a,2)),flip(a)]. 776 L(x,y,z \ u) = L(x,y,z * u). [para(20(a,1),774(a,1,3,2)),flip(a)]. 777 L(x,y,(z / u) * z) = L(x,y,u). [para(22(a,1),774(a,1,3,2))]. 778 L(x,y,z * (u * z)) = L(x,y,T(u,z)). [para(82(a,1),774(a,1,3,2))]. 779 L(x,y,(z * u) * (u * z)) = L(x,y,K(u,z)). [para(69(a,1),774(a,1,3,2))]. 780 L(x,y,z * ((z \ u) * w)) = L(x,y,z * ((z * u) * w)). [para(89(a,1),774(a,1,3,2)),flip(a)]. 781 L(x,y,(z \ u) * w) = L(x,y,(z * u) * w). [para(89(a,1),774(a,1,3)),flip(a)]. 782 L(x,y,(z \ (z \ u)) * (z \ u)) = L(x,y,T(z,u)). [para(254(a,1),774(a,1,3,2))]. 783 L(x,y,(z * z) / u) = L(x,y,u \ 1). [para(263(a,1),774(a,1,3))]. 784 L(x,y,z / u) = L(x,y,u / z). [para(360(a,1),774(a,1,3))]. 785 L(x,y,z * L(z,u * z,u)) = L(x,y,a(u,z,z)). [para(453(a,2),774(a,1,3,2))]. 786 L(x,y,R(z * (z * u),w,v5)) = L(x,y,R(u,w,v5)). [para(696(a,2),774(a,1,3))]. 787 L(x,y,z \ 1) = L(x,y,z). [para(18(a,1),776(a,2,3))]. 789 L(x,y,T(z / u,z)) = L(x,y,((u / z) * u) * u). [para(370(a,2),776(a,1,3))]. 790 L(x,y,y \ (z * z)) = x. [para(776(a,2),429(a,1))]. 792 L(x \ (x / y),y,x * (x / y)) = ((x \ (x / y)) \ y) \ y. [para(776(a,1),442(a,1))]. 793 L(x,R(y / z,u,w),z * y) = x. [para(776(a,1),690(a,1))]. 794 L(x \ L(y \ z,y,u),x,u * y) = ((u \ y) * x) \ (u \ z). [para(776(a,1),275(a,1))]. 795 T(x * x,y) \ (y \ (x * x)) = y \ 1. [para(790(a,1),395(a,1)),flip(a)]. 796 L(x,L(y \ 1,z,u),y) = x. [para(787(a,1),503(a,1))]. 797 L(x,(y * z) \ y,z) = x. [para(787(a,1),505(a,1))]. 798 (x \ y) * L(z,y,x) = x \ (y * z). [para(787(a,1),560(a,1,2))]. 799 x * T(y \ 1,y * x) = L(y \ 1,x,y) * x. [para(787(a,1),613(a,1,1)),flip(a)]. 800 L(x,y \ z,z \ y) = x. [para(20(a,1),797(a,1,2,1))]. 801 L(x,y \ z,z * y) = x. [para(800(a,1),776(a,1)),flip(a)]. 802 L(x,y,z * (z / y)) = x. [para(66(a,1),801(a,1,2))]. 803 (x * L(x \ 1,y,z)) \ u = L(x \ 1,y,z) \ (x \ u). [para(796(a,1),177(a,1)),flip(a)]. 804 L(x,y,(z * (z * u)) * (z * w)) = L(x,y,u \ (z \ w)). [para(282(a,1),777(a,1,3,1))]. 805 L(x,y,(z * (z * u)) * z) = L(x,y,u \ (z \ 1)). [para(289(a,1),777(a,1,3,1))]. 806 L(L(x,y,y / z),z,z / y) = x. [para(784(a,1),304(a,1,1))]. 807 L(x,x,x / y) = y \ (y / (x \ 1)). [para(784(a,1),432(a,1))]. 808 L(x,y,z / (z * y)) = x. [para(784(a,1),730(a,1))]. 809 ((x / (x * y)) * y) \ (x / (x * y)) = y \ 1. [para(808(a,1),142(a,1)),flip(a)]. 810 ((x / (x * y)) * y) * z = (x / (x * y)) * (y * z). [para(808(a,1),74(a,1,2))]. 811 ((x / (x * y)) * y) \ z = y \ ((x / (x * y)) \ z). [para(808(a,1),177(a,1)),flip(a)]. 812 L(x,y / (z * (u * y)),z * (u \ 1)) = x. [para(350(a,1),793(a,1,2))]. 813 (x * (y \ z)) \ (x * (y \ (z * u))) = L(L(u,z,y),y \ z,x). [para(798(a,1),32(a,2,2,2)),flip(a)]. 815 T(x,y) \ (x * z) = (T(x,y) \ x) * z. [para(234(a,1),798(a,1,2)),flip(a)]. 816 x \ (((y * x) / y) * z) = (x \ ((y * x) / y)) * z. [para(237(a,1),798(a,1,2)),flip(a)]. 817 (x \ y) * T((x \ y) \ 1,z) = x \ (y * T(y \ x,z)). [para(261(a,1),798(a,1,2))]. 818 L(x,y,T(z \ u,z)) = L(x,y,T(z * u,z)). [para(138(a,1),778(a,1,3)),flip(a)]. 819 L(x,y,T((z \ u) * z,z)) = L(x,y,z * T(u * z,z)). [para(757(a,1),778(a,1,3,2)),flip(a)]. 820 L(x,y,(z * z) / u) = L(x,y,u). [para(783(a,2),787(a,1))]. 821 L(x,y,T(z,z * (u * u))) = L(x,y,z \ (u * u)). [para(252(a,1),820(a,1,3)),flip(a)]. 822 L(x,y,z / (u * u)) = L(x,y,z). [para(820(a,1),784(a,1)),flip(a)]. 823 L(x,y,z * (u * u)) = L(x,y,z). [para(21(a,1),822(a,1,3)),flip(a)]. 824 L(x,y,(z * u) * u) = L(x,y,R(z,u,u)). [para(34(a,2),822(a,1,3)),flip(a)]. 825 (x * (y * (y * z))) \ ((x * (y * y)) * (z * u)) = L(u,z,x). [para(823(a,1),419(a,2))]. 826 (T(x,y) \ x) * y = T(y,T(x,y)). [para(815(a,1),107(a,1))]. 827 T(x,y) \ (x * z) = x * (T(x,y) \ z). [para(815(a,2),576(a,1))]. 828 x * (T(x,y) \ y) = T(y,T(x,y)). [para(826(a,1),576(a,1)),flip(a)]. 829 T(x,T(y,x)) / (T(y,x) \ x) = y. [hyper(24,a,22,a,b,828,a),flip(a)]. 830 x \ T(y,T(x,y)) = T(x,y) \ y. [hyper(23,a,20,a,b,828,a),flip(a)]. 831 (x * y) / (x * (T(x,z) \ y)) = T(x,z). [para(827(a,1),65(a,1,2))]. 832 (((x * y) * (y * x)) * z) \ (((x * y) * (y * x)) * (z * u)) = L(u,z,K(y,x)). [para(779(a,1),32(a,1)),flip(a)]. 833 (x * (y / (y * x))) \ (y / (y * x)) = x \ 1. [para(362(a,1),809(a,1,1))]. 834 T(x \ 1,x * (y / (y * x))) = x \ 1. [para(833(a,1),349(a,2))]. 835 L(x \ 1,y,x) * y = y * ((x * y) \ y). [para(349(a,1),799(a,1,2)),flip(a)]. 836 L(x,y,(z * (z \ u)) * (z \ u)) = L(x,y,T(z,u)). [para(782(a,1),781(a,1)),flip(a)]. 837 L(x,y,z * ((z \ u) * u)) = L(x,y,a(z,u,u)). [para(435(a,1),785(a,1,3))]. 838 L(x,y,R(z \ u,w,v5)) = L(x,y,R(z * u,w,v5)). [para(20(a,1),786(a,1,3,1,2)),flip(a)]. 839 L(x,y,T(z / u,z)) = L(x,y,R(u / z,u,u)). [para(789(a,2),824(a,1))]. 840 L(x,y,z * (z * (u * z))) = L(x,y,u \ (z \ 1)). [para(51(a,1),805(a,1,3))]. 841 (x * (y / (y * x))) * z = (y / (y * x)) * (x * z). [para(362(a,1),810(a,1,1))]. 842 (x * (y / (y * x))) \ z = x \ ((y / (y * x)) \ z). [para(362(a,1),811(a,1,1))]. 843 L(x,y,T(z,z * (u * u))) = L(x,y,z * (u * u)). [para(821(a,2),776(a,1))]. 844 L(x,y,z * (u \ z)) = L(x,y,T(u,z)). [para(20(a,1),836(a,1,3,1))]. 845 L(x,y,T(z / u,z)) = L(x,y,z * u). [para(66(a,1),844(a,1,3,2)),flip(a)]. 846 L(x,y,R(z / u,z,z)) = L(x,y,u * z). [para(845(a,1),839(a,1)),flip(a)]. 847 L(x,y,R((y \ z) * z,u,w)) = x. [para(838(a,1),657(a,1))]. 848 L(x,y,z \ (u \ 1)) = L(x,y,z * u). [para(840(a,1),774(a,1))]. 850 L(x,y,z * (u \ 1)) = L(x,y,z * u). [para(848(a,1),776(a,1)),flip(a)]. 851 L(x,y / (z * (u * y)),z * u) = x. [para(850(a,1),812(a,1))]. 852 L(x,(y * z) * (u / (y * (z * u))),y * z) = x. [para(851(a,1),303(a,1,1))]. 853 ((x * y) * z) / (x * (y * z)) = (x * y) * (z / (x * (y * z))). [para(851(a,1),196(a,1,2))]. 854 x \ ((y / (y * x)) \ z) = ((y * x) / y) * (x \ z). [para(842(a,1),606(a,1))]. 855 L(x,y,T(z,z * (u * u))) = L(x,y,z). [para(843(a,2),823(a,1))]. 856 L(x,y,T(z,u * u)) = L(x,y,z). [para(423(a,1),855(a,1,3))]. 858 L(x,y,R(T(z,u * u),w,v5)) = L(x,y,R(z,w,v5)). [para(46(a,2),856(a,1,3))]. 859 x \ (((y * x) / y) * z) = ((y * x) / y) * (x \ z). [para(358(a,1),854(a,1,2))]. 860 (x \ ((y * x) / y)) * z = ((y * x) / y) * (x \ z). [para(859(a,1),816(a,1)),flip(a)]. 861 L(x,y,z * ((z * u) * u)) = L(x,y,a(z,u,u)). [para(780(a,1),837(a,1))]. 862 L(x,y,z * (z * (u * (z * w)))) = L(x,y,u \ (z \ w)). [para(51(a,1),804(a,1,3))]. 863 L(x,y,T((z \ u) * z,z)) = L(x,y,(u * z) * z). [para(82(a,1),819(a,2,3))]. 864 L(x,y,T((z \ u) * z,z)) = L(x,y,R(u,z,z)). [para(863(a,2),824(a,1))]. 865 L(x,y,z \ (u \ w)) = L(x,y,z * (u * w)). [para(862(a,1),774(a,1))]. 867 L(x,y,z * (u \ w)) = L(x,y,z * (u * w)). [para(865(a,1),776(a,1)),flip(a)]. 868 L(x,y,z * (u * (u * w))) = L(x,y,z * w). [para(19(a,1),867(a,1,3,2)),flip(a)]. 869 L(x,y,(z \ u) * (u \ z)) = L(x,y,(u \ z) * (z * u)). [para(384(a,1),867(a,1,3))]. 871 ((x \ (x / y)) \ y) \ y = x \ (x / y). [para(792(a,1),802(a,1))]. 872 x / (y \ (y / x)) = (y \ (y / x)) \ x. [para(871(a,1),65(a,1,2))]. 873 (x * (y * (y * z))) \ (x * (y * (y * (z * u)))) = L(u,z,x). [para(411(a,1),825(a,1,2))]. 875 L(x,y * (y * z),u) = L(x,z,u). [para(873(a,1),93(a,1)),flip(a)]. 876 L(x,y \ z,u) = L(x,y * z,u). [para(20(a,1),875(a,1,2,2)),flip(a)]. 877 L(x,(y / z) * y,u) = L(x,z,u). [para(22(a,1),875(a,1,2,2))]. 878 L(x,y * (z * y),u) = L(x,T(z,y),u). [para(82(a,1),875(a,1,2,2))]. 879 L(x,(y * z) * (z * y),u) = L(x,K(z,y),u). [para(69(a,1),875(a,1,2,2))]. 880 L(x,(y \ z) * u,w) = L(x,(y * z) * u,w). [para(89(a,1),875(a,1,2)),flip(a)]. 881 L(x,T(y,y * z),u) = L(x,(y \ z) * z,u). [para(250(a,1),875(a,1,2,2)),flip(a)]. 882 L(x,(y * y) / z,u) = L(x,z \ 1,u). [para(263(a,1),875(a,1,2))]. 883 L(x,T(y \ 1,z),u) = L(x,z * (y \ z),u). [para(327(a,1),875(a,1,2,2)),flip(a)]. 884 L(x,y / z,u) = L(x,z / y,u). [para(360(a,1),875(a,1,2))]. 887 L(x,y \ 1,z) = L(x,y,z). [para(18(a,1),876(a,2,2))]. 888 (x * (y \ z)) * L(u,y * z,x) = x * ((y \ z) * u). [para(876(a,1),74(a,1,2))]. 889 L(x,(y \ z) * z,y) = x. [para(876(a,1),731(a,1))]. 890 L(x,y * z,z * y) = x. [para(876(a,1),801(a,1))]. 893 (x * ((x \ y) * y)) \ z = ((x \ y) * y) \ (x \ z). [para(889(a,1),177(a,1)),flip(a)]. 894 ((x * y) * (y * x)) * z = (x * y) * ((y * x) * z). [para(890(a,1),74(a,1,2))]. 895 T(x * y,(x * y) * (y * x)) = T(x * y,y * x). [para(890(a,1),203(a,1)),flip(a)]. 896 L(x,K(y,z),z * y) = x. [para(890(a,1),315(a,1,1))]. 897 K(x,y) \ 1 = K(y,x). [para(890(a,1),609(a,1)),flip(a)]. 898 K(x,y) * K(y,x) = 1. [para(897(a,1),20(a,1,2))]. 899 1 / K(x,y) = K(y,x). [para(897(a,1),65(a,1,2))]. 900 K(x,y) \ z = K(y,x) * z. [para(897(a,1),318(a,1,1)),flip(a)]. 901 K(x,y) * (K(y,x) * z) = z. [para(897(a,1),321(a,1,2,1))]. 902 x / (K(y,z) * x) = K(z,y). [para(897(a,1),340(a,2))]. 903 T(x * y,K(y,x)) / (y * x) = K(x,y). [para(897(a,1),345(a,2))]. 904 R(K(x,y),K(y,x) * z,u) = R(K(y,x),z,u) \ 1. [para(897(a,1),584(a,1,1))]. 905 a(K(x,y),z,u) = a(K(y,x),z,u). [para(897(a,1),611(a,1,1))]. 906 R(K(x,y),K(x,y) * z,u) = R(K(y,x),z,u) \ 1. [para(897(a,1),633(a,2,1,1))]. 907 K(x,y) * (K(y,x) / (x * y)) = K(x,y) \ ((y * x) \ 1). [para(897(a,1),379(a,1,2,1))]. 908 R(x,K(y,z),u) = R(x,K(z,y),u). [para(897(a,1),717(a,1,2))]. 909 L(x,y,K(z,u)) = L(x,y,K(u,z)). [para(897(a,1),787(a,1,3))]. 910 L(K(x,y),z,K(y,x)) * z = z * ((K(y,x) * z) \ z). [para(897(a,1),835(a,1,1,1))]. 911 (x * y) * (K(y,x) * z) = (y * x) * z. [para(896(a,1),176(a,1,2)),flip(a)]. 912 K(x,y) \ ((y * x) \ z) = (x * y) \ z. [para(896(a,1),199(a,1))]. 914 L(x,x,y) = (y * (x \ 1)) \ y. [para(887(a,1),161(a,1))]. 915 x / L(y,y,x) = x * (y \ 1). [para(887(a,1),162(a,1,2))]. 916 L(L(x,y * (z \ 1),y),z,y) = x. [para(887(a,1),308(a,1))]. 917 L(x * y,x,y) = (y \ (x \ 1)) \ 1. [para(887(a,1),351(a,1))]. 918 L(x,y,L(y \ 1,z,u)) = x. [para(887(a,1),509(a,1))]. 919 (x * (y \ z)) / L(z,y,x) = x * (y \ 1). [para(887(a,1),333(a,1,2))]. 920 L(x * (y * z),x,y) = (y \ (x \ 1)) \ z. [para(887(a,1),352(a,1))]. 921 L(x,K(y,z),u) = L(x,K(z,y),u). [para(897(a,1),887(a,1,2))]. 922 T(x * y,K(y,x)) = K(x,y) * (y * x). [para(900(a,1),122(a,1)),flip(a)]. 923 R(K(x,y),K(y,x) * z,u) \ K(x,y) = K(x,y) \ R(K(x,y),z,u). [para(901(a,1),618(a,1,2,2)),flip(a)]. 924 (L(x \ 1,y,z) * x) \ u = x \ (L(x \ 1,y,z) \ u). [para(918(a,1),177(a,1)),flip(a)]. 925 L(x / y,x / y,z) = (z * (y / x)) \ z. [para(343(a,1),914(a,2,1,2))]. 926 L(K(x,y),K(x,y),z) = (z * K(y,x)) \ z. [para(897(a,1),914(a,2,1,2))]. 928 L(x,(y * (y * z)) * (y * u),w) = L(x,z \ (y \ u),w). [para(282(a,1),877(a,1,2,1))]. 929 L(x,(y * (y * z)) * y,u) = L(x,z \ (y \ 1),u). [para(289(a,1),877(a,1,2,1))]. 930 K(x,y) / L(z,z,K(y,x)) = K(x,y) * (z \ 1). [para(909(a,1),915(a,1,2))]. 931 L(x,y * (z \ 1),y) = L(x,y * z,y). [para(916(a,1),303(a,1,1)),flip(a)]. 932 L(x,K(y,z),y * z) = x. [para(921(a,1),896(a,1))]. 933 ((x * y) \ K(x,y)) \ z = K(x,y) \ ((x * y) * z). [para(932(a,1),267(a,1)),flip(a)]. 934 L(x * y,x,y) * z = (y \ (x \ 1)) \ z. [para(917(a,2),318(a,1,1))]. 935 L(x,(y * y) / z,u) = L(x,z,u). [para(882(a,2),887(a,1))]. 936 L(x,y / (z * z),u) = L(x,y,u). [para(935(a,1),884(a,1)),flip(a)]. 937 L(x,y * (z * z),u) = L(x,y,u). [para(21(a,1),936(a,1,2)),flip(a)]. 938 L(x,(y * z) * z,u) = L(x,R(y,z,z),u). [para(34(a,2),936(a,1,2)),flip(a)]. 939 ((x * y) * z) / (K(x,y) * z) = y * x. [hyper(24,a,22,a,b,911,a),flip(a)]. 940 (x * y) \ ((y * x) * z) = K(y,x) * z. [hyper(23,a,20,a,b,911,a),flip(a)]. 941 K(x,y) * ((x * y) \ z) = (y * x) \ z. [para(912(a,1),20(a,1,2))]. 942 x * (y \ ((y * (x \ 1)) * z)) = L(z,y * x,y). [para(931(a,1),446(a,2))]. 943 L(x,K(y,z) * (y * z),u) = L(x,z * y,u). [para(939(a,1),935(a,1,2)),flip(a)]. 944 (x * y) \ (y * (x * z)) = K(y,x) * L(z,x,y). [para(74(a,1),940(a,1,2))]. 945 (x * (y \ 1)) * L(z,y,x) = x * (y \ z). [para(919(a,1),22(a,1,1))]. 946 (a(x,y,z) \ (x \ 1)) \ u = x * (a(x,y,z) * u). [para(920(a,1),771(a,1))]. 947 L(K(x,y),K(x,y),z) / z = (z * K(y,x)) \ 1. [para(926(a,2),320(a,1,1))]. 948 (a(x,y,z) \ (x \ 1)) \ u = (x * a(x,y,z)) * u. [para(771(a,1),934(a,1,1)),flip(a)]. 951 L(x,T(y,y * z),u) = L(x,(y * z) * z,u). [para(881(a,2),880(a,1))]. 953 L(x,(y * (y \ z)) * (y \ z),u) = L(x,T(y,z),u). [para(20(a,1),951(a,1,2,2)),flip(a)]. 954 x * (y * ((y \ (x \ 1)) * z)) = L(z,y * x,y). [para(213(a,1),942(a,1,2))]. 955 K(x,y) * L(x,y,x) = T(x,y * x). [para(944(a,1),36(a,2)),flip(a)]. 956 x * ((x \ (y \ 1)) * y) = a(x,y,y). [hyper(23,a,453,a(flip),b,954,a)]. 957 x * (y * (R(y,y * (x \ 1),z) \ ((x \ 1) * z))) = L(z,y * x,y). [para(630(a,2),954(a,1,2,2))]. 958 x * R(x \ 1,y \ 1,y) = a(x,y,y). [para(335(a,2),956(a,1,2))]. 959 x \ R(x,y \ 1,y) = a(x,y,y). [para(958(a,1),635(a,1)),flip(a)]. 960 x * R(x \ 1,y,y) = a(x,y,y). [para(717(a,1),958(a,1,2))]. 961 R(x,y \ 1,y) \ a(x,y,y) = T(x \ 1,R(x,y \ 1,y)). [para(959(a,1),325(a,2,2)),flip(a)]. 962 x \ R(x,y,y) = a(x,y,y). [para(717(a,1),959(a,1,2))]. 963 x * a(x,y,y) = R(x,y,y). [para(962(a,1),20(a,1,2))]. 964 a(x,y,y) \ R(x,y,y) = x. [para(962(a,1),480(a,1,1))]. 965 (R(x,y,y) \ x) * z = a(x,y,y) \ z. [para(962(a,1),465(a,1,1)),flip(a)]. 966 x * (a(x,y,y) * z) = R(x,y,y) * z. [para(962(a,1),501(a,1,2,1))]. 967 R(x \ 1,y,y) = x \ a(x,y,y). [para(962(a,1),634(a,1,2)),flip(a)]. 968 R(x,x * y,y) = a(x,y,y) \ x. [para(965(a,1),621(a,1)),flip(a)]. 969 T(x * y,K(y,x)) = T(x * y,y * x). [para(895(a,1),248(a,1)),flip(a)]. 970 T(x * y,K(y,x)) = (x \ 1) \ y. [para(969(a,2),439(a,1))]. 971 K(x,y) / T(y * x,K(x,y)) = (y * x) \ K(x,y). [para(969(a,2),257(a,1,2))]. 972 T(x * y,K(y,x)) = x * y. [para(970(a,2),330(a,1))]. 973 K(x,y) = (x * y) / (y * x). [para(972(a,1),903(a,1,1)),flip(a)]. 974 K(x,y) * (y * x) = x * y. [para(972(a,1),922(a,1)),flip(a)]. 975 (x * y) / (T(x,y) * y) = K(y,T(x,y)). [para(82(a,1),973(a,2,1)),flip(a)]. 976 (T(x,y) * y) / (x * y) = K(T(x,y),y). [para(82(a,1),973(a,2,2)),flip(a)]. 977 ((x * y) * z) / ((y * x) * z) = R(K(x,y),y * x,z). [para(973(a,2),80(a,1,1)),flip(a)]. 978 (x \ y) / (y * (x \ 1)) = K(x \ 1,y). [para(318(a,1),973(a,2,1)),flip(a)]. 979 ((K(x,y) * z) * K(y,x)) / z = K(K(x,y) * z,K(y,x)). [para(901(a,1),973(a,2,2)),flip(a)]. 980 K(x \ y,x) * y = (x \ y) * x. [para(20(a,1),974(a,1,2))]. 981 K(x * y,x) * y = (x \ y) * x. [para(495(a,1),980(a,1,1))]. 983 K(x,T(y,x)) = T(y,x) \ y. [para(975(a,1),577(a,1))]. 984 T(x,y) * K(y,T(x,y)) = x. [para(983(a,2),20(a,1,2))]. 985 K(x,T(y,x)) * T(y,x) = y. [para(983(a,2),298(a,1,1))]. 987 T(x,y) \ (x * z) = K(y,T(x,y)) * z. [para(983(a,2),815(a,2,1))]. 989 (x \ y) * K(x,T(y / x,x)) = y / x. [para(84(a,1),984(a,1,1))]. 990 K(T(x,y),y) * x = T(x,y). [hyper(23,a,901,a,b,985,a),flip(a)]. 991 K(x,x \ y) * T(y / x,x) = y / x. [para(84(a,1),985(a,1,1,2))]. 992 K(T(x,y),y) = x \ T(x,y). [para(976(a,1),565(a,1))]. 993 x * K(T(x,y),y) = T(x,y). [para(992(a,2),20(a,1,2))]. 994 (x / y) \ T(x / y,y) = K(y \ x,y). [para(84(a,1),992(a,1,1)),flip(a)]. 995 K(T(x \ 1,y),y) = x * T(x \ 1,y). [para(992(a,2),330(a,1))]. 997 (x / y) * K(T(x / y,y),y) = y \ x. [para(993(a,2),84(a,1))]. 998 T(x,y) * (K(y,T(x,y)) * z) = x * z. [para(987(a,1),20(a,1,2))]. 999 K(x,T(y,x)) * (y \ z) = T(y,x) \ z. [para(20(a,1),987(a,1,2)),flip(a)]. 1000 (x \ y) * K(x,x \ y) = y / x. [para(84(a,1),989(a,1,2,2))]. 1001 (x \ y) * K(x,x * y) = y / x. [para(489(a,1),1000(a,1,2))]. 1002 (x \ y) \ (y / x) = K(x,x * y). [hyper(23,a,20,a,b,1001,a),flip(a)]. 1003 K(x,x * (x * y)) = y \ ((x * y) / x). [para(19(a,1),1002(a,1,1)),flip(a)]. 1004 K(x,x * y) * T(y / x,x) = y / x. [para(489(a,1),991(a,1,1))]. 1005 (x / y) \ T(x / y,y) = K(y * x,y). [para(994(a,2),495(a,1))]. 1006 (x / y) * K(y \ x,y) = y \ x. [para(84(a,1),997(a,1,2,1))]. 1007 (x / y) * K(y * x,y) = y \ x. [para(495(a,1),1006(a,1,2))]. 1008 (x / y) * (x \ y) = K(x * y,x). [hyper(23,a,359,a,b,1007,a),flip(a)]. 1010 (x \ y) * (x / y) = K(x * y,x). [para(1008(a,1),368(a,1)),flip(a)]. 1012 L(x,y,(z \ u) * K(z * u,z)) = L(x,y,z / u). [para(1010(a,1),774(a,1,3,2))]. 1013 K(x,y) = y \ ((x * y) / x). [para(1003(a,1),490(a,1)),flip(a)]. 1014 (x * y) / x = y * K(x,y). [para(1013(a,2),20(a,1,2)),flip(a)]. 1015 x * (y / (y * x)) = K(y,x) \ 1. [para(1013(a,2),502(a,1,1)),flip(a)]. 1016 K(x,y) = ((x * y) / x) / y. [para(1013(a,2),558(a,2)),flip(a)]. 1017 ((x * y) / x) * (y \ z) = K(x,y) * z. [para(1013(a,2),860(a,1,1)),flip(a)]. 1018 (x * K(y,x)) * y = y * x. [para(1014(a,1),22(a,1,1))]. 1019 x / (x / y) = y * K(x / y,y). [para(22(a,1),1014(a,1,1))]. 1020 T(x * K(y,x),y) = x. [para(1014(a,1),104(a,1,1))]. 1021 L(x,y * K(z,y),y) = x. [para(1014(a,1),237(a,1,2))]. 1022 a(x / (x * y),z,u) = a(y * K(x,y),z,u). [para(1014(a,1),612(a,1,1)),flip(a)]. 1023 T(T(x * K(y,x),z),y) = T(x,z). [para(1020(a,1),42(a,1,1)),flip(a)]. 1024 T(x * K(y,x),z) * y = y * T(x,z). [para(1020(a,1),108(a,1,2,1)),flip(a)]. 1025 x / L(y,x * K(y,x),y) = y \ (x * K(y,x)). [para(1020(a,1),441(a,1,1))]. 1026 L(x,K(y,z),z) = x. [para(1021(a,1),303(a,1))]. 1027 (x * K(y,x)) \ z = K(y,x) \ (x \ z). [para(1021(a,1),270(a,1))]. 1028 (x * K(y,x)) * z = x * (K(y,x) * z). [para(1026(a,1),74(a,1,2))]. 1029 L(x,K(y,z),y) = x. [para(1026(a,1),921(a,1)),flip(a)]. 1030 (x * K(x,y)) * z = x * (K(x,y) * z). [para(1029(a,1),74(a,1,2))]. 1031 x \ (K(x,y) * z) = (x \ K(x,y)) * z. [para(1029(a,1),798(a,1,2)),flip(a)]. 1032 (x * K(y,x)) \ 1 = K(x,y) / x. [para(1029(a,1),947(a,1,1)),flip(a)]. 1033 (x * y) / x = K(x,y) * y. [para(1016(a,2),22(a,1,1)),flip(a)]. 1035 (x * K(y,x)) / x = K(y,x). [para(1014(a,1),1016(a,2,1)),flip(a)]. 1036 K(x,y) * y = y * K(x,y). [para(1033(a,1),1014(a,1))]. 1037 T(K(x,y),y) = K(x,y). [para(1035(a,1),104(a,1,1))]. 1038 T(x,K(y,x)) = x. [hyper(39,a,1037,a)]. 1040 T(x,y) * K(z,x) = K(z,x) * T(x,y). [para(1038(a,1),108(a,1,2,1)),flip(a)]. 1041 K(x,y) = x * (y / (y * x)). [para(1015(a,2),897(a,1)),flip(a)]. 1042 x \ K(x,y) = y / (y * x). [hyper(23,a,20,a,b,1041,a(flip)),flip(a)]. 1043 K(x,y) = (y / (y * x)) * x. [para(1041(a,2),362(a,2)),flip(a)]. 1044 K(x,y) / x = y / (y * x). [para(1041(a,2),363(a,1,1))]. 1045 x * ((y / (y * x)) * z) = K(x,y) * z. [para(1041(a,2),451(a,1,1)),flip(a)]. 1046 T(x,K(x,y)) = x. [para(1041(a,2),605(a,1,2))]. 1047 ((x * y) / x) * (y \ z) = K(y,x) \ z. [para(1041(a,2),606(a,1,1)),flip(a)]. 1048 T(x \ 1,K(x,y)) = x \ 1. [para(1041(a,2),834(a,1,2))]. 1049 (x / (x * y)) * (y * z) = K(y,x) * z. [para(1041(a,2),841(a,1,1)),flip(a)]. 1050 K(x,y) * x = x * K(x,y). [para(1046(a,1),82(a,1,2))]. 1051 T(x,T(y,x) \ y) = x. [para(983(a,1),1046(a,1,2))]. 1052 (T(x,y) \ x) * y = y * (T(x,y) \ x). [para(1051(a,1),82(a,1,2))]. 1053 K(x,y) = ((y * x) / y) \ x. [para(1043(a,2),358(a,2)),flip(a)]. 1054 K(x,y) / x = x \ K(x,y). [para(1044(a,2),1042(a,2)),flip(a)]. 1055 K(x,y) * (x \ 1) = x \ K(x,y). [para(1048(a,1),327(a,1,2))]. 1056 (x * K(y,x)) \ 1 = x \ K(x,y). [para(1032(a,2),1054(a,1))]. 1057 (x \ 1) / (x \ K(x,y)) = K(y,x). [para(1055(a,1),902(a,1,2))]. 1058 (x * K(y,x)) \ z = (x \ K(x,y)) * z. [para(1056(a,1),318(a,1,1)),flip(a)]. 1059 K(x,y) * (y * z) = ((x * y) / x) * z. [para(19(a,1),1017(a,1,2)),flip(a)]. 1060 T(x,y) * K(z,T(x,y)) = T(x * K(z,x),y). [hyper(24,a,1018,a,b,1024,a),flip(a)]. 1061 T(x * K(x \ y,x),y) = L(x,x \ y,x). [hyper(24,a,221,a,b,1024,a)]. 1063 (x * K(y,x)) \ z = K(x,y) * (x \ z). [para(1027(a,2),900(a,1))]. 1064 ((x * y) / x) * z = y * (K(x,y) * z). [para(1014(a,2),1028(a,1,1))]. 1065 x \ (K(x,y) * z) = (y / (y * x)) * z. [para(1042(a,1),1031(a,2,1))]. 1066 K(x,y) \ (x * z) = ((y * x) / y) * z. [para(19(a,1),1047(a,1,2)),flip(a)]. 1067 K(x,y) * (x \ z) = (y / (y * x)) * z. [para(20(a,1),1049(a,1,2)),flip(a)]. 1068 K(x,y) * (x * z) = x * (K(x,y) * z). [para(1049(a,1),1045(a,1,2)),flip(a)]. 1069 x * (T(y,x) \ y) = T(x,T(y,x)). [para(1052(a,1),826(a,1))]. 1070 x * K(x,T(y,x)) = T(x,T(y,x)). [para(983(a,2),1069(a,1,2))]. 1071 x / (K(y,z) * (y \ x)) = y * K(z,y). [para(1063(a,1),65(a,1,2))]. 1072 (x \ K(x,y)) * z = K(x,y) * (x \ z). [para(1063(a,1),1058(a,1)),flip(a)]. 1073 K(x,y) * (y * z) = y * (K(x,y) * z). [para(1064(a,1),1059(a,2))]. 1074 K(x,y) \ (x * z) = (K(y,x) * x) * z. [para(1033(a,1),1066(a,2,1))]. 1075 K(x,y) * (x \ (y * x)) = y. [para(1067(a,2),22(a,1))]. 1076 x \ (K(x,y) * z) = K(x,y) * (x \ z). [para(1067(a,2),1065(a,2))]. 1077 K(x,y) * T(y,x) = y. [para(36(a,2),1075(a,1,2))]. 1078 K(x,y / x) = K(x,x * y). [hyper(24,a,1004,a,b,1077,a)]. 1079 K(x,T(y,x)) = K(x,y). [hyper(24,a,985,a,b,1077,a),flip(a)]. 1080 K(x,y) = T(y,x) \ y. [hyper(24,a,298,a,b,1077,a)]. 1081 T(x,y) = K(x,y) * x. [hyper(23,a,901,a,b,1077,a)]. 1082 K(x,T(y,z)) * T(T(y,x),z) = T(y,z). [para(42(a,1),1077(a,1,2))]. 1083 K(x,R(y,z,u)) * R(T(y,x),z,u) = R(y,z,u). [para(46(a,2),1077(a,1,2))]. 1084 L(x \ y,x,K(z,y)) = (K(z,y) \ x) \ T(y,z). [para(1077(a,1),267(a,1,1,2))]. 1085 L(x,y,K(z,u) * u) = L(x,y,T(u,z)). [para(1077(a,1),774(a,1,3,2))]. 1086 K(x,y) = T(x,y) / x. [para(1077(a,1),902(a,1,2)),flip(a)]. 1087 (x * y) * T(y,x) = (y * x) * y. [para(1077(a,1),911(a,1,2)),flip(a)]. 1088 T(x,y) * T(x,y) = x * T(T(x,y),y). [para(1077(a,1),998(a,1,2))]. 1089 T(x,y) * K(y,x) = x. [para(1077(a,1),1040(a,2))]. 1090 (x / (x * y)) * T(x,y) = y \ x. [para(1077(a,1),1065(a,1,2)),flip(a)]. 1091 K(x,T(T(y,x),z)) = K(x,T(y,z)). [para(42(a,1),1079(a,1,2))]. 1092 K(x,x * (y * x)) = K(x,y). [para(1079(a,1),491(a,2))]. 1093 T(x,y) \ (x * z) = K(y,x) * z. [para(1079(a,1),987(a,2,1))]. 1094 T(x,y) * (K(y,x) * z) = x * z. [para(1079(a,1),998(a,1,2,1))]. 1095 K(x,y) * (y \ z) = T(y,x) \ z. [para(1079(a,1),999(a,1,1))]. 1096 T(x,T(y,x)) = x * K(x,y). [para(1079(a,1),1070(a,1,2)),flip(a)]. 1097 T(T(x,y),z) \ T(x,z) = K(y,T(x,z)). [para(42(a,1),1080(a,2,1)),flip(a)]. 1098 K(x,y) * (T(y,x) * z) = y * z. [para(1080(a,2),575(a,1,1))]. 1099 x * (T(x,y) \ z) = K(y,x) * z. [para(1080(a,2),576(a,1,1)),flip(a)]. 1100 K(x,y) = y * (T(y,x) \ 1). [para(1080(a,2),578(a,2)),flip(a)]. 1101 T(x,y) \ 1 = x \ K(y,x). [para(1080(a,2),582(a,1,2)),flip(a)]. 1102 (x * y) / (T(x,z) * y) = K(z,x). [para(1080(a,2),577(a,2))]. 1103 ((x * y) * y) \ ((y * x) * y) = K(y,(y * x) * y). [para(758(a,1),1080(a,2,1)),flip(a)]. 1104 T(x,y) = (x * x) / (x * K(y,x)). [para(1080(a,2),831(a,1,2,2)),flip(a)]. 1105 K(T(x,y),y) = K(x,y). [hyper(24,a,990,a,b,1081,a(flip)),flip(a)]. 1106 (x * T(y,z)) / L(y,K(y,z),x) = x * K(y,z). [para(1081(a,2),99(a,1,1,2))]. 1107 T(x,y) = x * K(x,y). [para(1081(a,2),1050(a,1))]. 1108 K(x,y) = x \ T(x,y). [para(1086(a,2),572(a,1))]. 1110 K(R(T(x,y),z,u),y) = K(R(x,z,u),y). [para(46(a,2),1105(a,1,1))]. 1111 x * T(x \ 1,y) = K(x \ 1,y). [para(1105(a,1),995(a,1)),flip(a)]. 1112 T(x * K(y,x),T(y,x)) = x. [para(1105(a,1),1020(a,1,1,2))]. 1113 K(x,y) * T(x,y) = T(T(x,y),y). [para(1105(a,1),1081(a,2,1)),flip(a)]. 1114 K(x,y) * T(K(y,x),z) = K(K(y,x),z). [hyper(23,a,901,a,b,1107,a(flip)),flip(a)]. 1115 (x * y) \ (x * T(y,z)) = L(K(y,z),y,x). [para(1107(a,2),32(a,2,2,2)),flip(a)]. 1116 x * (y * K(y,x)) = y * x. [para(1107(a,1),82(a,1,2))]. 1117 (x * y) * L(K(y,z),y,x) = x * T(y,z). [para(1107(a,2),74(a,2,2))]. 1118 (x \ y) * K(x * y,x) = T(x \ y,x). [para(495(a,1),1107(a,2,2)),flip(a)]. 1119 L(x,y,z * T(z,u)) = L(x,y,K(z,u)). [para(1107(a,2),774(a,1,3,2))]. 1120 x * (K(x,y) * z) = T(x,y) * z. [para(1107(a,2),1030(a,1,1)),flip(a)]. 1121 T(x,y) * K(x,y) = T(T(x,y),y). [para(1105(a,1),1107(a,2,2)),flip(a)]. 1122 T(x,y) \ T(T(x,z),y) = K(T(x,y),z). [para(42(a,1),1108(a,2,2)),flip(a)]. 1123 L(x,y,z) \ L(T(x,u),y,z) = K(L(x,y,z),u). [para(44(a,2),1108(a,2,2)),flip(a)]. 1124 x \ ((x \ y) \ y) = K(x,x * y). [para(249(a,1),1108(a,2,2)),flip(a)]. 1125 T(x,y) * (x \ z) = K(x,y) * z. [para(1108(a,2),562(a,1,1)),flip(a)]. 1126 K(x \ 1,x * y) = x * ((x * y) \ y). [para(1108(a,2),707(a,1))]. 1127 x \ (T(x,y) * z) = K(x,y) * z. [para(1108(a,2),733(a,2,1))]. 1128 K(x / y,y) = K(y * x,y). [para(1108(a,2),1005(a,1))]. 1130 K(x,(y * (x \ 1)) / x) = K(x,T(y,x \ 1)). [para(347(a,1),1078(a,2,2))]. 1131 T(x,T(y,x)) = T(x,y). [para(1096(a,2),1107(a,2)),flip(a)]. 1132 T(T(x,y),T(z,x)) = T(T(x,z),y). [para(1131(a,1),42(a,1,1)),flip(a)]. 1133 T(x,y / x) = T(x,x \ y). [para(84(a,1),1131(a,1,2)),flip(a)]. 1134 (x * y) / T(y,x) = T(x,y). [para(1131(a,1),117(a,1,2))]. 1135 L(T(x,y),T(y,x),x) = T(x,x * T(y,x)). [para(1131(a,1),203(a,1,1))]. 1136 T(x,x * (y * x)) = T(x,y). [para(1131(a,1),247(a,2))]. 1137 T(x,y) / (T(y,x) \ x) = y. [para(1131(a,1),829(a,1,1))]. 1138 T(x,y) \ y = x \ T(y,x). [para(1131(a,1),830(a,1,2)),flip(a)]. 1139 T(x,y * K(x,y)) = T(x,y). [para(1020(a,1),1131(a,1,2)),flip(a)]. 1140 K(x,y) * K(z,K(y,x)) = T(K(y,x),z) \ 1. [hyper(23,a,901,a,b,1100,a(flip)),flip(a)]. 1141 L(T(x,y),y * K(x,y),T(x,y)) = (T(x,y) \ (y * K(x,y))) \ y. [para(1112(a,1),440(a,1,2)),flip(a)]. 1143 K((x * (y \ 1)) / y,y) = K(T(x,y \ 1),y). [para(347(a,1),1128(a,2,1))]. 1144 x / (x / y) = y * K(y * x,y). [para(1128(a,1),1019(a,2,2))]. 1145 T(x,y / x) = T(x,x * y). [para(1133(a,2),246(a,1))]. 1146 T(x,y) * T(y,x) = x * y. [para(1134(a,1),22(a,1,1))]. 1147 x / (y \ T(x,y)) = T(y,x). [para(1138(a,1),65(a,1,2))]. 1148 (T(x,y) \ y) * K(x,x * T(y,x)) = T(y,x) / x. [para(1138(a,2),1001(a,1,1))]. 1149 T(x,(y * (x \ 1)) / x) = T(x,T(y,x \ 1)). [para(347(a,1),1145(a,2,2))]. 1150 (T(x,y) * (T(y,x) * z)) \ ((x * y) * z) = a(T(x,y),T(y,x),z). [para(1146(a,1),28(a,2,2,1)),flip(a)]. 1151 (x * y) \ (T(x,y) * (T(y,x) * z)) = L(z,T(y,x),T(x,y)). [para(1146(a,1),32(a,2,1)),flip(a)]. 1152 T(T(x,y),x \ T(y,x)) = (x \ T(y,x)) \ y. [para(1147(a,1),84(a,1,1))]. 1153 R(x,y,x) * (y * x) = (y * x) * T(x,y). [para(1087(a,2),79(a,2))]. 1154 T(x,y) * ((y * x) / ((x * y) * x)) = K(T(x,y),y * x). [para(1087(a,1),1041(a,2,2,2)),flip(a)]. 1155 K(x,T(y,K(z,T(y,x)))) = K(x,T(y,x)). [para(1038(a,1),1091(a,1,2)),flip(a)]. 1156 L(x,y * K(z,y),u) = L(x,T(y,z),u). [para(1094(a,1),937(a,1,2))]. 1157 T(x,y) * (y * x) = x * (x * y). [para(974(a,1),1094(a,1,2))]. 1158 K(x,y) * (T(x,y) \ z) = x \ z. [hyper(23,a,901,a,b,1095,a),flip(a)]. 1159 K(x,y) * (y \ x) = y \ T(x,y). [para(1095(a,2),1138(a,1))]. 1160 K(x,y) * (x * z) = T(x,y) * z. [hyper(23,a,901,a,b,1098,a),flip(a)]. 1162 R(K(x,y),T(y,x) * z,u) \ 1 = ((T(y,x) * z) * u) / ((y * z) * u). [para(1098(a,1),344(a,1,2,1)),flip(a)]. 1163 x \ (K(y,x) * z) = T(x,y) \ z. [hyper(23,a,20,a,b,1099,a),flip(a)]. 1164 (x * y) * T((x * y) \ x,z) = x * K(y \ 1,z). [para(1111(a,1),762(a,2,2))]. 1165 x \ (y * T(y \ x,z)) = K((x \ y) \ 1,z). [para(1111(a,1),817(a,1)),flip(a)]. 1166 (x * ((K(x,y) * z) * u)) \ ((T(x,y) * z) * u) = a(x,K(x,y) * z,u). [para(1120(a,1),28(a,2,2,1)),flip(a)]. 1168 T(x,y) * (T(y,x) * z) = x * (y * z). [para(1098(a,1),1120(a,1,2)),flip(a)]. 1169 L(x,y,z * ((z \ u) * u)) = L(x,y,K(z,z * u)). [para(1124(a,1),865(a,1,3)),flip(a)]. 1170 T(x,y) \ ((x \ T(y,x)) \ y) = K(T(x,y),T(x,y) * y). [para(1138(a,1),1124(a,1,2,1))]. 1171 T(x,y) \ (K(x,y) * z) = x \ z. [hyper(23,a,20,a,b,1125,a),flip(a)]. 1172 K(x,y) * (z * x) = T(x,y) * T(z,x). [para(36(a,2),1125(a,1,2)),flip(a)]. 1173 T(x / y,z) * y = K(x / y,z) * x. [para(66(a,1),1125(a,1,2))]. 1174 T(x,y) * (z / (z * x)) = K(x,y) * K(x,z). [para(1042(a,1),1125(a,1,2))]. 1175 T(x,y) * (T(x,z) \ 1) = K(x,y) * K(z,x). [para(1101(a,2),1125(a,1,2))]. 1176 x \ T(T(x,y),y) = K(x,y) * K(x,y). [para(1121(a,1),1127(a,1,2))]. 1177 T(T(x,x * y),T(z,x)) = T(T(x,z),x \ y). [para(246(a,1),1132(a,1,1))]. 1178 (x / (x / y)) * z = y * (K(y * x,y) * z). [para(1144(a,2),1028(a,1,1))]. 1179 ((x * y) * T(y,x)) \ (y * (y * x)) = K(T(y,x),x * y). [para(1157(a,1),30(a,2,2)),flip(a)]. 1180 (x * (x * y)) \ (T(x,y) * ((y * x) * z)) = L(z,y * x,T(x,y)). [para(1157(a,1),32(a,2,1)),flip(a)]. 1181 K(x,y) * (T(x,y) \ T(x,z)) = K(x,z). [para(1158(a,2),1108(a,2)),flip(a)]. 1182 K(T(x,y \ 1),y) * (x * (y \ 1)) = y \ T(T(x,y \ 1),y). [para(326(a,1),1159(a,1,2))]. 1183 ((T(x,y) * z) * u) / ((x * z) * u) = R(K(x,y),x * z,u). [para(1160(a,1),34(a,2,1,1)),flip(a)]. 1184 (x * y) \ (T(x,z) * y) = T(K(x,z),x * y). [para(1160(a,1),36(a,2,2)),flip(a)]. 1185 L(x,T(y,z) * z,u) = L(x,z * y,u). [para(1160(a,1),943(a,1,2))]. 1186 T(x,y) \ (T(y,x) \ z) = x \ (y \ z). [para(1158(a,1),1163(a,1,2)),flip(a)]. 1187 T(x,y) \ (y * K(x,y)) = x \ y. [para(1036(a,1),1171(a,1,2))]. 1188 x \ (y * K(x,y)) = K(x,y) * (x \ y). [para(1187(a,1),1158(a,1,2)),flip(a)]. 1189 (K(x,y) * (x \ z)) \ ((x \ K(x,y)) * (z * u)) = L(u,z,x \ K(x,y)). [para(1072(a,1),32(a,2,1)),flip(a)]. 1190 (K(x,y) * z) \ (y * (K(x,y) * z)) = L(T(y,z),z,K(x,y)). [para(1073(a,1),106(a,1,2))]. 1191 K(x,y) \ (x * z) = (K(x,y) \ x) * z. [para(900(a,2),1074(a,2,1))]. 1192 L(x,y,(z * u) / z) = L(x,y,T(u,z)). [para(1033(a,2),1085(a,1,3))]. 1193 T(x,y) * K(y,T(x,z)) = K(z,T(x,y)) * T(x,z). [para(1097(a,1),1099(a,1,2))]. 1194 L(x,y,(z / (u * u)) * (u \ (z * (u \ 1)))) = L(x,y,K(z / (u * u),u)). [para(403(a,1),1119(a,1,3,2))]. 1195 (x * T(y,x)) \ (T(y,z) * x) = L(K(T(y,x),z),T(y,x),x). [para(1122(a,1),180(a,1,1)),flip(a)]. 1196 K(x,T(y,K(z,T(y,x)))) = K(x,y). [para(1155(a,2),1079(a,1))]. 1197 K(x,y) * T(T(y,x),K(z,T(y,x))) = T(y,K(z,T(y,x))). [para(1196(a,1),1082(a,1,1))]. 1198 (x * (y * z)) / (T(y,x) * z) = T(x,y). [hyper(24,a,22,a,b,1168,a),flip(a)]. 1199 (x \ y) * (T(x,y / x) * z) = (y / x) * (x * z). [para(84(a,1),1168(a,1,1))]. 1200 (T(x / y,z) * y) / x = K(x / y,z). [hyper(24,a,22,a,b,1173,a(flip)),flip(a)]. 1201 K(x / y,z) * x = y * T(y \ x,z). [para(1173(a,1),139(a,1))]. 1202 (R(x,y,z) * (K(x,u) * K(x,u))) / T(T(x,u),u) = x \ R(x,y,z). [para(1176(a,1),536(a,1,1,2))]. 1203 L(x,y,K(y,z)) = x. [hyper(23,a,798,a,b,1191,a(flip)),flip(a)]. 1204 L(x,y,T(z,y) \ z) = x. [para(983(a,1),1203(a,1,3))]. 1205 L(x,y,T(z,y) * z) = x. [para(1204(a,1),776(a,1)),flip(a)]. 1206 L(x,y,z * T(z,y)) = x. [para(116(a,1),1205(a,1,3))]. 1207 ((x * T(x,y)) * y) \ ((x * T(x,y)) * (y * z)) = z. [para(1206(a,1),32(a,1)),flip(a)]. 1208 L(x,y,T(z * u,z) / z) = L(x,y,T((z \ u) * z,z)). [para(138(a,1),1192(a,1,3,1))]. 1209 (x * (R(y,z,u) * w)) / (R(T(y,x),z,u) * w) = T(x,R(y,z,u)). [para(46(a,2),1198(a,1,2,1))]. 1210 (x * (y * (a(T(y,x),z,z) * u))) / (R(T(y,x),z,z) * u) = T(x,y). [para(966(a,1),1198(a,1,2))]. 1211 (x * T(x \ y,z)) / y = K(y / x,z). [para(139(a,1),1200(a,1,1))]. 1212 K((x * y) / x,z) * (x * y) = x * T(y,z). [para(19(a,1),1201(a,2,2,1))]. 1213 x \ (y * T(y \ x,z)) = T(K(x / y,z),x). [para(1201(a,1),36(a,2,2)),flip(a)]. 1214 ((x * y) * T((x * y) \ ((z * x) * y),u)) / ((z * x) * y) = K(R(z,x,y),u). [para(34(a,2),1211(a,2,1))]. 1215 T(x * K(x * y,x),y) = L(x,x \ y,x). [para(495(a,1),1061(a,1,1,2))]. 1216 L(T(x,y),T(y,x),x) = T(x,y * x). [para(82(a,1),1135(a,2,2))]. 1217 (x * y) * T(y,y * (x * y)) = R(y,x,y) * (x * y). [para(1136(a,2),1153(a,2,2)),flip(a)]. 1218 T(x * K(x * y,x),y) = L(x,x * y,x). [para(1215(a,2),312(a,1))]. 1219 T(x / (x / y),x) = L(y,y * x,y). [para(1144(a,2),1218(a,1,1))]. 1220 K(x,T(y,x \ 1)) = K(x,y / (x * x)). [para(401(a,1),1130(a,1,2)),flip(a)]. 1221 K(T(x,y \ 1),y) = K(x / (y * y),y). [para(401(a,1),1143(a,1,1)),flip(a)]. 1222 T(x,T(y,x \ 1)) = T(x,y / (x * x)). [para(401(a,1),1149(a,1,2)),flip(a)]. 1223 K(((x * y) \ x) \ 1,z) = (x * y) \ (x * T(y,z)). [para(19(a,1),1165(a,1,2,2,1)),flip(a)]. 1224 T(x,y) \ T(x,z) = K(x,z) * K(y,x). [para(1175(a,1),581(a,1)),flip(a)]. 1225 K(x,y) * (K(x,z) * K(y,x)) = K(x,z). [para(1224(a,1),1181(a,1,2))]. 1226 K(x,y) * K(z,x) = K(z,x) * K(x,y). [hyper(23,a,901,a,b,1225,a)]. 1229 T(T(x,y),x \ z) = T(T(x,y),x * z). [para(1177(a,1),1132(a,1))]. 1230 T(T(x,y),x * T(y,x)) = (x \ T(y,x)) \ y. [para(1229(a,1),1152(a,1))]. 1231 (x / (x / y)) * x = y * ((y \ x) * y). [para(981(a,1),1178(a,2,2))]. 1232 T(x * y,x) = (y / (y / x)) * y. [para(1231(a,2),138(a,1)),flip(a)]. 1233 T(x * y,x) / y = y / (y / x). [hyper(24,a,22,a,b,1232,a(flip)),flip(a)]. 1234 ((x / y) / x) * T(y * x,y) = x. [hyper(23,a,359,a,b,1232,a(flip)),flip(a)]. 1236 x \ T(x * y,y) = x / (x / y). [para(1233(a,1),754(a,1)),flip(a)]. 1237 x / T(y * x,y) = (x / y) / x. [hyper(24,a,22,a,b,1234,a),flip(a)]. 1238 T(x * y,y) = x * (x / (x / y)). [para(1236(a,1),20(a,1,2)),flip(a)]. 1239 T(x * (y \ x),y \ x) = x * (x / y). [para(65(a,1),1238(a,2,2,2))]. 1240 T(K(x / y,z),x) = K((x \ y) \ 1,z). [para(1213(a,1),1165(a,1))]. 1241 K((x \ (y \ x)) \ 1,z) = T(K(y,z),x). [para(65(a,1),1240(a,1,1,1)),flip(a)]. 1242 K((T(x,y) \ (T(y,x) \ x)) \ 1,z) = T(K(y,z),T(x,y)). [para(1137(a,1),1240(a,1,1,1)),flip(a)]. 1243 K(T(x \ 1,y) \ 1,z) = T(K(x,z),y). [para(325(a,2),1241(a,1,1,1))]. 1244 K(T((x \ 1) \ 1,y * y),z) = T(K(x,z),y * y). [para(655(a,1),1243(a,1,1))]. 1245 (x \ T(y,x)) \ y = T(T(x,y),y * x). [para(82(a,1),1230(a,1,2)),flip(a)]. 1246 x / L(y,T(x,y),y) = y \ (x * K(y,x)). [para(1156(a,1),1025(a,1,2))]. 1247 x / L(y,T(x,y),y) = K(y,x) * (y \ x). [para(1246(a,2),1188(a,1))]. 1248 L(x \ y,x,K(z,y)) = (K(y,z) * x) \ T(y,z). [para(900(a,1),1084(a,2,1))]. 1249 R(K(x,y),T(x,y) * z,u) \ 1 = R(K(y,x),x * z,u). [para(1098(a,1),906(a,1,2)),flip(a)]. 1250 L(x,y * (y * (z * y)),u) = L(x,z \ (y \ 1),u). [para(51(a,1),929(a,1,2))]. 1251 ((x * y) \ K(x,y)) \ z = K(y,x) * ((x * y) * z). [para(933(a,2),900(a,1))]. 1252 (x * a(x,y,z)) * u = x * (a(x,y,z) * u). [para(948(a,1),946(a,1))]. 1253 a(x,y,z) * (x * u) = x * (a(x,y,z) * u). [para(1252(a,1),772(a,1)),flip(a)]. 1254 x * (a(x,y,z) * (x \ u)) = a(x,y,z) * u. [para(20(a,1),1253(a,1,2)),flip(a)]. 1255 L(x,y * (z \ y),u) = L(x,T(z,y),u). [para(20(a,1),953(a,1,2,1))]. 1256 L(x,T(y \ 1,z),u) = L(x,T(y,z),u). [para(1255(a,1),883(a,2))]. 1257 K(x,y) / (y * x) = (y * x) \ K(x,y). [para(972(a,1),971(a,1,2))]. 1258 L(x,y,T(z \ u,z)) = L(x,y,z / u). [para(1118(a,1),1012(a,1,3))]. 1259 L(x,y,T(z * u,z)) = L(x,y,z / u). [para(1258(a,1),818(a,1)),flip(a)]. 1260 (T(x,y) \ y) * K(x,y * x) = T(y,x) / x. [para(82(a,1),1148(a,1,2,2))]. 1261 L(x,y,K(z,z * u)) = L(x,y,a(z,u,u)). [para(1169(a,1),837(a,1))]. 1262 L(x,y,K(z * u,z)) = L(x,y,a(z,u,u)). [para(1261(a,1),909(a,1)),flip(a)]. 1263 L(x,y,a(z,u * z,u * z)) = L(x,y,K(z,u)). [para(1092(a,1),1261(a,1,3)),flip(a)]. 1264 K(x,T(y,z)) * T(T(y,x),K(x,T(y,z))) = K(z,T(y,x)) * T(y,z). [para(1193(a,1),82(a,2))]. 1265 (x \ y) * (T(x,x * y) * z) = (y / x) * (x * z). [para(1145(a,1),1199(a,1,2,1))]. 1266 (x * (T(x,y) * y)) \ ((x * T(x,y)) * (y * z)) = z. [para(722(a,1),1207(a,1,1))]. 1267 L(K(x,y),x,z) = K(((z * x) \ z) \ 1,y). [para(1223(a,2),1115(a,1)),flip(a)]. 1268 K(L(x \ 1,x,y) \ 1,z) = L(K(x,z),x,y). [para(142(a,2),1267(a,2,1,1)),flip(a)]. 1269 K(T(x,y * y),z) = T(K(x,z),y * y). [para(156(a,1),1244(a,1,1,1))]. 1270 K(T(x,y * y),z) \ 1 = T(K(x,z) \ 1,y * y). [para(1269(a,2),655(a,1,1))]. 1271 L(x,y \ (z \ 1),u) = L(x,y * z,u). [para(1250(a,1),875(a,1))]. 1273 L(x,y * (z \ 1),u) = L(x,y * z,u). [para(1271(a,1),876(a,1)),flip(a)]. 1274 (x \ y) * ((y / x) * (x * z)) = ((x \ y) * y) * z. [para(1265(a,1),253(a,1,2))]. 1275 (x * (T(x,y) * y)) \ (x * (T(x,y) * (y * z))) = z. [para(722(a,1),1266(a,1,2))]. 1276 T(K(x,y) \ 1,z * z) = K(y,T(x,z * z)). [para(1270(a,1),897(a,1))]. 1277 K(x,T(y,z * z)) = T(K(x,y),z * z). [para(897(a,1),1276(a,1,1)),flip(a)]. 1278 K(T(x,y * y),z) = K(x,T(z,y * y)). [para(1277(a,2),1269(a,2))]. 1279 L(L(x,y,T(z,y)),T(z,y) * y,z) = x. [para(1275(a,1),174(a,1)),flip(a)]. 1280 L(L(x,y,T(z,y)),y * z,z) = x. [para(1279(a,1),1185(a,1)),flip(a)]. 1281 L(L(x,y,T(y \ z,y)),z,y \ z) = x. [para(20(a,1),1280(a,1,2))]. 1282 L(x,y * (z * y),y) = L(x,z,T(y,z)). [para(1280(a,1),303(a,1,1))]. 1283 L(x,T(y,z) * z,T(y,z)) = L(x,z * y,y). [para(308(a,1),1280(a,1,1)),flip(a)]. 1284 L(x,T(y,z),z) = L(x,y,T(z,y)). [para(1280(a,1),314(a,1,1))]. 1285 L(x,T(y,y * z),y * z) = L(x,y,y / z). [para(1284(a,2),1259(a,1))]. 1286 L(L(x,y,y / z),z,y \ z) = x. [para(1258(a,1),1281(a,1,1))]. 1287 L(L(x,y,y / z),z,y * z) = x. [para(1286(a,1),776(a,1)),flip(a)]. 1288 L(x,y,z / y) = L(x,y,z * y). [para(304(a,1),1287(a,1,1)),flip(a)]. 1289 L(x \ (x / y),x,y * x) = y \ 1. [para(445(a,1),1287(a,1,1))]. 1290 L(x,y,y / z) = L(x,y,z * y). [para(806(a,1),1287(a,1,1)),flip(a)]. 1291 L(x,y,(z * y) * y) = L(x,y,z). [para(21(a,1),1288(a,1,3)),flip(a)]. 1292 L(x \ 1,x,y * x) = y \ (y / x). [para(1288(a,1),144(a,1))]. 1293 L(x,x,y * x) = y \ (y / (x \ 1)). [para(1288(a,1),432(a,1))]. 1294 x * L(y,z,x * z) = (x / z) * (z * y). [para(1288(a,1),173(a,1,2))]. 1295 (x \ 1) \ L(T(y \ (y / x),z),y,x * y) = K(L(y \ (y / x),y,x * y),z). [para(1289(a,1),1123(a,1,1))]. 1296 ((x * y) * y) \ (x * y) = x \ (x / y). [para(1292(a,1),142(a,1)),flip(a)]. 1297 L(x,y \ 1,T(y * z,y \ 1)) = L(x,(y * z) * z,y * z). [para(322(a,1),1282(a,1,2,2)),flip(a)]. 1298 x * K(L(y \ 1,y,x * y) \ 1,z) = (x / y) * (y * K(y,z)). [para(1268(a,2),1294(a,1,2))]. 1299 x \ L(x,x * y,y) = a(T(y,x),x,x). [para(1283(a,1),452(a,1,2))]. 1300 L(x,y * z,T(z,y)) = L(x,y * z,z). [para(1283(a,1),1185(a,1)),flip(a)]. 1301 T(L(K(x,y),z,K(y,x)),z) = (K(y,x) * z) \ z. [hyper(23,a,82,a,b,910,a(flip)),flip(a)]. 1302 L(x,y * x,x) = R(x,y,x). [hyper(24,a,217,a(flip),b,1217,a(flip)),flip(a)]. 1303 R(x,y / x,x) = L(x,y,x). [para(22(a,1),1302(a,1,2)),flip(a)]. 1304 L(T(x,y),z * x,x) = T(R(x,z,x),y). [para(1302(a,1),44(a,2,1))]. 1305 L(x,y,x) * ((y / x) * x) = (x * (y / x)) * x. [para(1303(a,1),79(a,1,1))]. 1306 L(T(x,y),z * x,x) = R(T(x,y),z,x). [para(1304(a,2),46(a,2)),flip(a)]. 1307 L(x,y,x) * y = (x * (y / x)) * x. [para(22(a,1),1305(a,1,2))]. 1308 T(L(x,y,x) * y,x) = ((y / x) * x) * x. [para(1307(a,2),758(a,1,1))]. 1309 T(L(x,y,x) * y,x) = y * x. [para(22(a,1),1308(a,2,1))]. 1310 (L(x,y,x) * y) * x = x * (y * x). [para(1309(a,1),82(a,1,2)),flip(a)]. 1311 L(R(x,y,x),y,x) = x. [hyper(24,a,184,a,b,1310,a(flip)),flip(a)]. 1312 R(L(x,y,x),y,x) = x. [hyper(24,a,79,a,b,1310,a(flip)),flip(a)]. 1313 R(x,x \ y,x) = L(x,y,x). [para(1311(a,1),302(a,1,1)),flip(a)]. 1314 L(x,x * y,x) = R(x,y,x). [para(1311(a,1),303(a,1,1))]. 1315 R(x,x * y,x) = L(x,y,x). [para(1311(a,1),308(a,1,1)),flip(a)]. 1316 x \ T(y * x,y) = R(y,x,y). [para(1314(a,1),316(a,1)),flip(a)]. 1318 T(x * K(x * y,x),y) = R(x,y,x). [para(1314(a,1),1218(a,2))]. 1319 T(x / (x / y),x) = R(y,x,y). [para(1314(a,1),1219(a,2))]. 1320 L(x,y,x) \ x = x \ R(x,y,x). [para(1315(a,1),622(a,1,1))]. 1321 x * R(y,x,y) = T(y * x,y). [para(1316(a,1),20(a,1,2))]. 1322 T(x,R(y,x,y)) = T(x,x / (x / y)). [para(1319(a,1),1131(a,1,2))]. 1323 (x / T(y * x,y)) * T(x,R(y,x,y)) = R(y,x,y) \ x. [para(1321(a,1),1090(a,1,1,2))]. 1324 T(x,y) * K(x * y,T(x,y)) = R(x,y,x). [para(1318(a,1),1060(a,2))]. 1325 T(x,y) * K(y * T(x,y),T(x,y)) = R(x,y,x). [para(82(a,2),1324(a,1,2,1))]. 1326 K(x,y) * (K(y,x) / (x * y)) = (x * y) \ 1. [para(907(a,2),912(a,1))]. 1327 K(x,y) * ((x * y) \ K(y,x)) = (x * y) \ 1. [para(1257(a,1),1326(a,1,2))]. 1328 (x * y) \ K(x,y) = (y * x) \ 1. [para(1327(a,1),941(a,1)),flip(a)]. 1329 K(x,y) * ((y * x) * z) = ((x * y) \ 1) \ z. [para(1328(a,1),1251(a,1,1)),flip(a)]. 1330 K(x,y) * ((y * x) * z) = (x * y) * z. [para(1329(a,2),330(a,1))]. 1331 ((x * y) * z) / ((y * x) * z) = K(x,y). [hyper(24,a,22,a,b,1330,a),flip(a)]. 1332 R(K(x,y),y * x,z) = K(x,y). [para(1331(a,1),977(a,1)),flip(a)]. 1333 R(K(x,T(y,x)),T(y,x) * x,z) = K(x,y). [para(1332(a,2),1079(a,1))]. 1335 R(K(x,y),T(y,x) * x,z) = K(x,y). [para(1079(a,1),1333(a,1,1))]. 1336 ((T(x,y) * y) * z) / ((K(y,x) * (T(x,y) * y)) * z) = K(y,x) \ 1. [para(1335(a,1),344(a,2,1))]. 1337 (x * L(x \ 1,y,z)) \ u = x \ (L(x \ 1,y,z) \ u). [para(216(a,1),924(a,1,1))]. 1338 L(x,y * (y * (z * (y * u))),w) = L(x,z \ (y \ u),w). [para(51(a,1),928(a,1,2))]. 1339 T(x,y) * (R(x,y,x) \ 1) = K(T(x,y),y * x). [para(344(a,1),1154(a,1,2))]. 1340 R(x,y,x) \ T(x,y) = K(T(x,y),y * x). [para(1339(a,1),548(a,1)),flip(a)]. 1341 T(x,y) \ T(T(x,y),y * x) = K(T(x,y),T(x,y) * y). [para(1245(a,1),1170(a,1,2))]. 1342 (((x * y) * T(y,x)) \ (y * y)) * x = K(T(y,x),x * y). [para(1179(a,1),391(a,1)),flip(a)]. 1343 T(x,K(y,T(x,z))) = K(z,x) * T(x,z). [para(1038(a,1),1197(a,1,2)),flip(a)]. 1345 T(x,K(y,T(x,z))) = x. [para(1343(a,2),1077(a,1))]. 1346 T(T(x,y),K(z,T(x,u))) = T(x,y). [para(1345(a,1),42(a,1,1)),flip(a)]. 1350 L(x,y,T(z * u,z) / z) = L(x,y,R(u,z,z)). [para(1208(a,2),864(a,1))]. 1351 T(K(x,y),T(z,x)) = K((z \ (x \ z)) \ 1,y). [para(1186(a,1),1242(a,1,1,1)),flip(a)]. 1352 T(K(x,y),T(z,x)) = T(K(x,y),z). [para(1351(a,2),1241(a,1))]. 1353 T(x,y) * T(K(y,z),x) = K(y,z) * T(x,y). [para(1352(a,1),82(a,1,2))]. 1354 K(x,y) * (K(y,z) * x) = K(y,z) * T(x,y). [para(1353(a,1),1172(a,2))]. 1355 (K(x,y) * T(z,x)) / L(z,K(x,y),K(z,x)) = K(z,x) * K(x,y). [para(1354(a,1),99(a,1,1))]. 1356 ((x / y) / x) * T(x,R(y,x,y)) = R(y,x,y) \ x. [para(1237(a,1),1323(a,1,1))]. 1357 L(x \ 1,y,z) \ (x \ u) = x \ (L(x \ 1,y,z) \ u). [para(1337(a,1),803(a,1)),flip(a)]. 1358 L(x,y \ (z \ u),w) = L(x,y * (z * u),w). [para(1338(a,1),875(a,1))]. 1360 L(x,y * (z \ u),w) = L(x,y * (z * u),w). [para(1358(a,1),876(a,1)),flip(a)]. 1361 L(x,y * (z * (z * u)),w) = L(x,y * u,w). [para(19(a,1),1360(a,1,2,2)),flip(a)]. 1362 L(x,(y \ z) * (z \ y),u) = L(x,(z \ y) * (y * z),u). [para(384(a,1),1360(a,1,2))]. 1363 L(x,y * R(z,z * u,w),v5) = L(x,y * (R(z,u,w) \ 1),v5). [para(615(a,1),1361(a,1,2,2))]. 1364 K(T(x,y),T(x,y) * y) = K(T(x,y),y * x). [para(1341(a,1),1108(a,2)),flip(a)]. 1365 (((x * y) * x) \ (x * x)) * y = K(T(x,y),y * x). [para(1087(a,1),1342(a,1,1,1))]. 1366 K(T(x,y),y * x) = K(x,x * y). [para(1365(a,1),408(a,1))]. 1367 R(x,y,x) \ T(x,y) = K(x,x * y). [para(1366(a,1),1340(a,2))]. 1368 K(x,x * y) \ T(x,y) = R(x,y,x). [para(1367(a,1),734(a,1,1))]. 1369 K(x * y,x) * T(x,y) = R(x,y,x). [para(1368(a,1),900(a,1)),flip(a)]. 1370 R(x,y,x) / T(x,y) = K(x * y,x). [hyper(24,a,22,a,b,1369,a),flip(a)]. 1371 (x \ (L(x \ 1,x,x / y) \ 1)) * (y \ (y / x)) = x \ 1. [para(1357(a,1),521(a,1,1))]. 1372 R(x,y \ 1,y) \ a(x,y,y) = x \ 1. [para(961(a,2),476(a,1))]. 1374 R(x,y,y) \ a(x,y,y) = x \ 1. [para(717(a,1),1372(a,1,1))]. 1375 (x * y) \ (x * (y * z)) = L(z,T(y,x),T(x,y)). [para(1168(a,1),1151(a,1,2))]. 1376 L(x,T(y,z),T(z,y)) = L(x,y,z). [para(1375(a,1),32(a,2)),flip(a)]. 1377 L(T(x,y),y,K(z,x)) = T(x,K(z,x) * y). [para(1190(a,1),36(a,2)),flip(a)]. 1378 (x \ (L(x \ 1,x,y * x) \ 1)) * (y \ (y / x)) = x \ 1. [para(1290(a,1),1371(a,1,1,2,1))]. 1379 ((x \ y) * z) \ (x \ u) = ((x * y) * z) \ (x * u). [para(794(a,1),201(a,1))]. 1380 (x * ((x \ y) * y)) \ z = ((x * y) * y) \ (x * z). [para(1379(a,1),893(a,2))]. 1381 (x * ((x \ y) * y)) \ y = x \ (x / y). [para(1380(a,2),1296(a,1))]. 1382 x / (y \ (y / x)) = y * ((y \ x) * x). [para(1381(a,1),65(a,1,2))]. 1383 (x \ (x / y)) \ y = x * ((x \ y) * y). [para(1382(a,1),872(a,1)),flip(a)]. 1384 x * L(x,y * x,y) = (y \ (y / x)) \ x. [para(1383(a,2),435(a,2))]. 1385 (x * L(x,y * x,y)) / x = (y \ (y / x)) \ 1. [para(1384(a,2),320(a,1,1))]. 1386 L(x,y * x,y) = (y \ (y / x)) \ 1. [para(1385(a,1),218(a,1)),flip(a)]. 1387 x \ ((y \ (y / x)) \ 1) = a(y,x,x). [para(1386(a,1),452(a,1,2))]. 1388 (x \ (x / y)) \ 1 = y * a(x,y,y). [para(1386(a,1),453(a,1))]. 1389 (x \ 1) \ (L(x,x,y * x) \ 1) = a(y,x \ 1,x \ 1). [para(1293(a,2),1387(a,1,2,1))]. 1390 (x \ (x / y)) \ z = (y * a(x,y,y)) * z. [para(1388(a,1),318(a,1,1)),flip(a)]. 1391 K(x,(x * x) / (y \ (y / z))) = K(x,z * a(y,z,z)). [para(1388(a,1),492(a,2,2))]. 1392 L(x \ 1,x,y * x) \ 1 = x * a(y,x,x). [para(1292(a,2),1388(a,1,1))]. 1393 (x \ (x * a(y,x,x))) * (y \ (y / x)) = x \ 1. [para(1392(a,1),1378(a,1,1,2))]. 1394 a(x,y,y) * (x \ (x / y)) = y \ 1. [para(19(a,1),1393(a,1,1))]. 1396 a(K(x,y),z,z) * (K(y,x) \ (K(y,x) / z)) = z \ 1. [para(905(a,1),1394(a,1,1))]. 1397 a(x,y,y) * (x / y) = x * (y \ 1). [para(1394(a,1),1254(a,1,2)),flip(a)]. 1398 (x * (y \ 1)) / (x / y) = a(x,y,y). [hyper(24,a,22,a,b,1397,a),flip(a)]. 1399 (x / y) * (y * (x \ 1)) = a(y,x,x). [para(1398(a,1),669(a,1)),flip(a)]. 1400 a(x / y,y,y \ 1) = a(x,y,y). [para(1399(a,1),592(a,2))]. 1401 a(x * (y * y),y \ 1,(y \ 1) \ 1) = a(x * y,y \ 1,y \ 1). [para(400(a,1),1400(a,1,1))]. 1402 K(x,(y \ (y / z)) \ 1) = K(x,z * a(y,z,z)). [para(1391(a,1),492(a,1)),flip(a)]. 1403 a(K(x,y),z,z) * (K(x,y) * (K(y,x) / z)) = z \ 1. [para(900(a,1),1396(a,1,2))]. 1404 K(x,y) * (a(K(x,y),z,z) * (K(y,x) / z)) = z \ 1. [para(1403(a,1),1253(a,1)),flip(a)]. 1405 R(K(x,y),z,z) * (K(y,x) / z) = z \ 1. [para(1404(a,1),966(a,1)),flip(a)]. 1406 x * (L(x,x,y * x) \ 1) = a(y,x \ 1,x \ 1). [para(1389(a,1),330(a,1)),flip(a)]. 1407 a(x,y \ 1,y \ 1) = L(y,y,x * y) \ y. [para(1406(a,1),471(a,1))]. 1408 a(x * y,y \ 1,y \ 1) = L(y,y,x) \ y. [para(1291(a,1),1407(a,2,1))]. 1409 (x * (y \ z)) \ (x * (y \ (z * u))) = L(L(u,z,y),y * z,x). [para(813(a,2),876(a,1))]. 1410 (x * y) * (z / (x * (y * z))) = x \ R(x,y,z). [para(853(a,1),537(a,1))]. 1411 L(x,y \ R(y,z,u),y * z) = x. [para(1410(a,1),852(a,1,2))]. 1412 L(x,y * R(y,z,u),y * z) = x. [para(1411(a,1),876(a,1)),flip(a)]. 1413 L(x,y * R(y,y * z,u),z) = x. [para(1412(a,1),774(a,1)),flip(a)]. 1414 K(T(x,y \ 1),y) * (x * (y \ 1)) = T(x,y) * (y \ 1). [para(1182(a,2),329(a,1))]. 1415 K(T(x,y \ 1),y) = K(x,y). [hyper(24,a,1160,a,b,1414,a)]. 1416 (x * (y \ 1)) / (T(x,y) * (y \ 1)) = K(y,T(x,y \ 1)). [para(1414(a,1),902(a,1,2))]. 1418 K(x / (y * y),y) = K(x,y). [para(1415(a,1),1221(a,1)),flip(a)]. 1419 K(x,T(y,x \ 1)) = K(x,y). [para(1416(a,1),1102(a,1))]. 1420 K(x \ 1,T(y,x)) = K(x \ 1,y). [para(156(a,1),1419(a,1,2,2))]. 1421 T(x,T(y,x \ 1)) = x * K(x,y). [para(1419(a,1),1107(a,2,2))]. 1423 K(x,y / (x * x)) = K(x,y). [para(1419(a,1),1220(a,1)),flip(a)]. 1424 K(x,R(y / x,x,x)) = K(x,y * x). [para(80(a,2),1423(a,1,2))]. 1425 ((x \ 1) * T(y,x)) / (x \ 1) = T(y,x) * K(x \ 1,y). [para(1420(a,1),1014(a,2,2))]. 1426 T(x,T(y,x \ 1)) = T(x,y). [para(1421(a,2),1107(a,2)),flip(a)]. 1427 T(x \ 1,T(y,x)) = T(x \ 1,y). [para(156(a,1),1426(a,1,2,2))]. 1428 T(x,y / (x * x)) = T(x,y). [para(1426(a,1),1222(a,1)),flip(a)]. 1429 L(x,T(y,z),T(T(z,y \ 1),y)) = L(x,y,T(z,y \ 1)). [para(1426(a,1),1376(a,1,2))]. 1430 T(x,(y * x) * x) = T(x,R(y,x,x)). [para(34(a,2),1428(a,1,2)),flip(a)]. 1431 L(x,T(y \ 1,z),T(T(z,y),y \ 1)) = L(x,y \ 1,T(z,y)). [para(1427(a,1),1376(a,1,2))]. 1432 (x \ T(y,x)) / (x \ 1) = T(y,x) * K(x \ 1,y). [para(318(a,1),1425(a,1,1))]. 1433 T(x,y) * K(y \ 1,x) = T(x,y * y). [para(1432(a,1),486(a,1))]. 1434 L(x,T(y,z),T(T(z,y),y \ 1)) = L(x,y,T(z,y \ 1)). [para(42(a,1),1429(a,1,3))]. 1435 L(x,R(y,z,z),y * z) = L(x,y \ 1,T(y * z,y \ 1)). [para(1297(a,2),938(a,1)),flip(a)]. 1436 L(x,R(y,z,z),y * z) = L(x,y,T(y * z,y \ 1)). [para(1435(a,2),887(a,1))]. 1437 L(x,y * R(z,z * u,w),v5) = L(x,y * R(z,u,w),v5). [para(1363(a,2),1273(a,1))]. 1438 L(x,y * R(y,z,u),z) = x. [para(1437(a,1),1413(a,1))]. 1439 L(x,y * (z * R(z,y,u)),y) = x. [para(1438(a,1),303(a,1,1))]. 1440 L(x,y \ R(y \ 1,z,u),z) = x. [para(318(a,1),1438(a,1,2))]. 1441 (x * (y \ R(y,x,z))) * u = x * ((y \ R(y,x,z)) * u). [para(1438(a,1),888(a,1,2))]. 1442 a(x,x * (y * R(y,x,z)),u) = 1. [hyper(38,a,1439,a)]. 1443 L(x,y * R(y \ 1,z,u),z) = x. [para(1440(a,1),876(a,1)),flip(a)]. 1444 L(x,a(y,z,z),z) = x. [para(960(a,1),1443(a,1,2))]. 1445 x / (a(y,x,x) \ 1) = x * a(y,x,x). [para(1444(a,1),145(a,1,2))]. 1446 (x * a(y,x,x)) * z = x * (a(y,x,x) * z). [para(1444(a,1),74(a,1,2))]. 1447 K(x,(y \ (y / z)) \ 1) = K(x,z / (a(y,z,z) \ 1)). [para(1445(a,2),1402(a,2,2))]. 1448 (x \ (x / y)) \ z = y * (a(x,y,y) * z). [para(1446(a,1),1390(a,2))]. 1449 L(x * (a(y,x,x) * z),y * (y / x),y) = (y / x) \ (y * z). [para(1448(a,1),311(a,1,1))]. 1450 (x * (y \ R(y,x,z))) * u = x * (R(y,x,z) * (y \ u)). [para(532(a,1),1441(a,2,2))]. 1451 L(x,T(y,z),T(T(z,y),y \ 1)) = L(x,y \ 1,T(z,y)). [para(1431(a,1),1256(a,1)),flip(a)]. 1452 L(x,y \ 1,T(z,y)) = L(x,y,T(z,y \ 1)). [para(1451(a,1),1434(a,1))]. 1453 L(x,y,T(z,y \ 1)) = L(x,y,T(z,y)). [para(1452(a,1),887(a,1))]. 1454 L(x,R(y,z,z),y * z) = L(x,y,T(y * z,y)). [para(1453(a,1),1436(a,2))]. 1455 L(x,R(y,z,z),y * z) = L(x,y,y / z). [para(1454(a,2),1259(a,1))]. 1456 L(x,R(y,z,z),y * z) = L(x,y,z * y). [para(1455(a,2),1290(a,1))]. 1457 L(T(x,y),y * K(x,y),T(x,y)) = (x \ y) \ y. [para(1187(a,1),1141(a,2,1))]. 1458 (x * (y * z)) \ ((x * y) * z) = a(T(x,y),T(y,x),z). [para(1168(a,1),1150(a,1,1))]. 1459 a(T(x,y),T(y,x),z) = a(x,y,z). [para(1458(a,1),28(a,2)),flip(a)]. 1460 a(T(x,y),T(T(y,x),x),z) = a(x,T(y,x),z). [para(1131(a,1),1459(a,1,1))]. 1461 x \ (y \ (y \ (T(y,x) * ((x * y) * z)))) = L(z,x * y,T(y,x)). [para(1180(a,1),443(a,1)),flip(a)]. 1462 x * K(y * a(x,y,y),z) = (x / y) * (y * K(y,z)). [para(1392(a,1),1298(a,1,2,1))]. 1463 x * K(y * a(x,y,y),z) = (x / y) * T(y,z). [para(1107(a,2),1462(a,2,2))]. 1464 x \ (y \ (K(y,x) * ((x * y) * z))) = L(z,x * y,T(y,x)). [para(1127(a,1),1461(a,1,2,2))]. 1465 x \ (y \ ((y * x) * z)) = L(z,x * y,T(y,x)). [para(1330(a,1),1464(a,1,2,2))]. 1466 L(x,y * z,T(z,y)) = L(x,z * y,z). [para(1465(a,1),309(a,1))]. 1467 L(x,y * z,z) = L(x,z * y,z). [para(1466(a,1),1300(a,1)),flip(a)]. 1468 L(L(x,y,z),y * z,z) = x. [para(1467(a,2),303(a,1))]. 1470 x \ L(x,x * y,y) = a(y,x,x). [para(1467(a,2),452(a,1,2))]. 1471 L(x,y * (y / z),y) = L(x,z,y). [para(1467(a,1),877(a,1))]. 1472 L(x,(y * z) * z,y * z) = L(x,T(y,z),y * z). [para(1467(a,1),878(a,1))]. 1473 L(x,T(y,z),z) = L(x,y,z). [para(1468(a,1),314(a,1,1))]. 1475 L(T(x,y),y,x) = T(x,y * x). [para(1473(a,1),1216(a,1))]. 1476 K(x,y) * (x \ y) = y / L(x,y,x). [para(1473(a,1),1247(a,1,2)),flip(a)]. 1477 L(x,y,y / z) = L(x,y,y * z). [para(1473(a,1),1285(a,1)),flip(a)]. 1478 (x * T(y,x)) \ (T(y,z) * x) = L(K(T(y,x),z),y,x). [para(1473(a,1),1195(a,2))]. 1479 T(x,y * x) = T(x,x * y). [para(1475(a,1),203(a,1))]. 1480 K(x,y) * L(x,y,x) = T(x,x * y). [para(1479(a,1),955(a,2))]. 1481 T(x,x * y) * K(y * x,x) = x. [para(1479(a,1),1089(a,1,1))]. 1482 T(x,x * (y * x)) = T(x,R(y,x,x)). [para(1479(a,1),1430(a,1))]. 1483 x \ L(x,y,x * y) = a(x * y,x,x). [para(875(a,1),1470(a,1,2))]. 1484 x \ L(x,T(y,x),y * x) = a(y * x,x,x). [para(878(a,1),1470(a,1,2))]. 1485 a(T(x,y),y,y) = a(x,y,y). [para(1470(a,1),1299(a,1)),flip(a)]. 1486 L(x * (a(y,x,x) * z),x,y) = (y / x) \ (y * z). [para(1471(a,1),1449(a,1))]. 1488 L(x,x,x * y) = y \ (y / (x \ 1)). [para(1477(a,1),807(a,1))]. 1489 K(x * y,y) = K(y * x,y). [hyper(23,a,1089,a,b,1481,a)]. 1490 T(x * K(x * y,x),y * x) = x. [para(1489(a,1),1020(a,1,1,2))]. 1491 x / (x / y) = y * K(x * y,y). [para(1489(a,2),1144(a,2,2))]. 1492 R(x,y,x) / T(x,y) = K(y * x,x). [para(1489(a,2),1370(a,2))]. 1493 T(x / (x / y),x * y) = y. [para(1144(a,2),1490(a,1,1))]. 1494 T(x * y,x / (x / y)) = T(x * y,y). [para(1493(a,1),1131(a,1,2)),flip(a)]. 1495 (x / (x / y)) \ T(x * y,x / (x / y)) = y \ (x * y). [para(1493(a,1),1138(a,1,1)),flip(a)]. 1496 R(x,y,x) = y / (y / T(x,y)). [para(1491(a,2),1325(a,1)),flip(a)]. 1497 R(x,y,x) \ y = y / T(x,y). [para(1496(a,2),66(a,1,1))]. 1498 (T(x,y) \ y) * K(T(x,y),T(x,y) * y) = R(x,y,x) \ y. [para(1497(a,2),1001(a,2))]. 1499 ((x / y) / x) * T(x,R(y,x,y)) = x / T(y,x). [para(1497(a,1),1356(a,2))]. 1500 K(x,y) = (y \ x) / (x / L(y,x,y)). [para(1476(a,1),902(a,1,2)),flip(a)]. 1501 (x * y) / (K(x,y) * L(x,y,x)) = R(x,x * y,x) \ (x * y). [para(1480(a,2),1497(a,2,2)),flip(a)]. 1502 T(x,R(y,x,x)) = T(x,y). [para(1482(a,1),1136(a,1))]. 1503 K(x,R(y,x,x)) = x \ T(x,y). [para(1502(a,1),1108(a,2,2))]. 1504 K(x,R(y,x,x)) = K(x,y). [para(1503(a,2),1108(a,2)),flip(a)]. 1505 K(x,y / x) = K(x,y * x). [para(1504(a,1),1424(a,1))]. 1506 K(x,y * x) = K(x,x * y). [para(1505(a,1),1078(a,1))]. 1507 ((x * y) * y) \ ((y * x) * y) = K(y,y * (y * x)). [para(1506(a,1),1103(a,2))]. 1508 (T(x,y) \ y) * K(x,x * y) = T(y,x) / x. [para(1506(a,1),1260(a,1,2))]. 1509 K(T(x,y),y * T(x,y)) = K(T(x,y),y * x). [para(1506(a,2),1364(a,1))]. 1510 T(x,y) \ R(x,y,x) = K(y * x,x). [para(1492(a,1),693(a,1)),flip(a)]. 1511 K(x,y) * (y \ R(y,x,y)) = K(x * y,y). [para(1510(a,1),1095(a,2))]. 1512 K(T(x,y),y * x) = K(T(x,y),x * y). [para(82(a,1),1509(a,1,2)),flip(a)]. 1513 K(T(x,y),x * y) = K(x,x * y). [para(1512(a,1),1366(a,1))]. 1514 L(x,R(y,z,z),y * z) = L(x,T(y,z),y * z). [para(1472(a,1),938(a,1)),flip(a)]. 1515 L(x,T(y,z),y * z) = L(x,y,z * y). [para(1514(a,1),1456(a,1))]. 1516 x \ L(x,y,x * y) = a(y * x,x,x). [para(1515(a,1),1484(a,1,2))]. 1517 a(x * y,y,y) = a(y * x,y,y). [para(1516(a,1),1483(a,1))]. 1518 L(x * (a(y,x,x) * z),x,y) = (x / y) * (y * z). [para(1486(a,2),358(a,1))]. 1519 K(x,y) = ((y * x) * x) \ ((x * y) * x). [para(1507(a,2),490(a,1)),flip(a)]. 1520 (x * (y * x)) \ ((x * y) * x) = K(y * x,x) * K(x,y). [para(1519(a,2),941(a,1,2)),flip(a)]. 1521 (x * y) \ (T(x,z) * y) = L(K(T(x,y),z),x,y). [para(82(a,1),1478(a,1,1))]. 1522 L(K(T(x,y),z),x,y) = T(K(x,z),x * y). [para(1521(a,1),1184(a,1))]. 1523 (x / (x / y)) \ T(x * y,x / (x / y)) = T(x,y). [para(1495(a,2),36(a,2)),flip(a)]. 1524 (x / (x / y)) \ T(x * y,y) = T(x,y). [para(1494(a,1),1523(a,1,2))]. 1525 ((x / y) / x) * T(x * y,y) = T(x,y). [para(1524(a,1),358(a,1)),flip(a)]. 1526 (x / y) * T(y * (x \ y),x \ y) = T(y,x \ y). [para(65(a,1),1525(a,1,1,1))]. 1527 L(x,y,z * (((u / w) / u) * T(u,w))) = L(x,y,z * T(u * w,w)). [para(1525(a,1),868(a,1,3,2,2))]. 1528 (x / y) * (y * (y / x)) = T(y,x \ y). [para(1239(a,1),1526(a,1,2))]. 1529 T(x,x / y) = T(x,y \ x). [para(1528(a,1),369(a,1)),flip(a)]. 1530 T(x,R(y,x,y)) = T(x,(x / y) \ x). [para(1529(a,1),1322(a,2))]. 1531 T(x,R(y,x,y)) = T(x,y). [para(66(a,1),1530(a,2,2))]. 1532 ((x / y) / x) * T(x,y) = x / T(y,x). [para(1531(a,1),1499(a,1,2))]. 1533 K(x * y,y) * K(y,x) = a(y,x,y). [para(1520(a,1),28(a,2)),flip(a)]. 1534 K(x,y) * K(y * x,x) = a(x,y,x). [para(1533(a,1),1226(a,2))]. 1536 K(x,y) * a(y,x,y) = K(x * y,y). [hyper(23,a,901,a,b,1534,a),flip(a)]. 1537 K(x,y) * K(x * y,x) = a(x,y,x). [para(1489(a,1),1534(a,1,2))]. 1539 x \ R(x,y,x) = a(x,y,x). [hyper(23,a,1511,a,b,1536,a),flip(a)]. 1541 L(x,y,x) \ x = a(x,y,x). [para(1539(a,1),1320(a,2))]. 1544 (T(x,y) \ y) * K(T(x,y),y * T(x,y)) = R(x,y,x) \ y. [para(1506(a,2),1498(a,1,2))]. 1545 (T(x,y) \ y) * K(T(x,y),x * y) = R(x,y,x) \ y. [para(82(a,1),1544(a,1,2,2))]. 1546 (T(x,y) \ y) * K(x,x * y) = R(x,y,x) \ y. [para(1513(a,1),1545(a,1,2))]. 1547 R(x,y,x) \ y = T(y,x) / x. [para(1546(a,1),1508(a,1))]. 1548 T(x,y) / y = x / T(y,x). [para(1547(a,1),1497(a,1))]. 1549 (x / T(y,x)) * y = T(x,y). [para(1548(a,1),22(a,1,1))]. 1550 (x / y) * (y * K(x,y)) = T(x,y * K(x,y)). [para(1020(a,1),1549(a,1,1,2))]. 1551 T(x,y) = (x / y) * (y * K(x,y)). [para(1550(a,2),1139(a,1)),flip(a)]. 1552 (x / y) * T(y,x) = x * K(y,x). [hyper(23,a,359,a,b,1551,a(flip)),flip(a)]. 1553 (x * (y \ 1)) * T(L(y,y,x),x) = x * K(L(y,y,x),x). [para(915(a,1),1552(a,1,1))]. 1554 (x * (y \ 1)) * L(T(y,x),y,x) = x * K(L(y,y,x),x). [para(44(a,2),1553(a,1,2))]. 1555 x * K(L(y,y,x),x) = x * (y \ T(y,x)). [para(1554(a,1),945(a,1))]. 1556 x * K(L(y,y,x),x) = x * K(y,x). [para(1108(a,2),1555(a,2,2))]. 1557 T(x * K(y,x),L(y,y,x)) = x. [para(1556(a,1),1020(a,1,1))]. 1558 T(x,L(y,y,x)) = T(x,y). [para(1557(a,1),1023(a,1,1)),flip(a)]. 1559 (x * y) / (K(x,y) * L(x,y,x)) = L(x,y,x) \ (x * y). [para(1315(a,1),1501(a,2,1))]. 1560 (x * y) / (K(x,y) * L(x,y,x)) = (L(x,y,x) \ x) * y. [para(1559(a,2),524(a,1))]. 1561 (x * y) / T(x,x * y) = (L(x,y,x) \ x) * y. [para(1480(a,1),1560(a,1,2))]. 1562 (L(x,y,x) \ x) * y = T(x * y,x) / x. [para(1561(a,1),1548(a,2)),flip(a)]. 1563 T(x * y,x) / x = a(x,y,x) * y. [para(1541(a,1),1562(a,1,1)),flip(a)]. 1564 R(K(x,y),K(y,x) * z,u) \ K(x,y) = K(y,x) * R(K(x,y),z,u). [para(923(a,2),900(a,1))]. 1565 x * (y * (R(y,y * (x \ 1),z) \ (x \ z))) = L(z,y * x,y). [para(318(a,1),957(a,1,2,2,2))]. 1566 x * (R(y,x \ 1,z) * (y \ (x \ z))) = L(z,y * x,y). [para(637(a,1),1565(a,1,2))]. 1567 x * (R(y,x,z) * (y \ (x \ z))) = L(z,y * x,y). [para(717(a,1),1566(a,1,2,1))]. 1568 R(x * (K(x,y) * K(x,y)),z,u) / T(T(x,y),y) = x \ R(x,z,u). [para(705(a,2),1202(a,1,1))]. 1569 K(x,T(y,z)) * T(y,x) = K(z,T(y,x)) * T(y,z). [para(1346(a,1),1264(a,1,2))]. 1570 (K(x,T(y,z)) * T(y,x)) / L(y,K(y,z),K(z,T(y,x))) = K(z,T(y,x)) * K(y,z). [para(1569(a,1),1106(a,1,1))]. 1572 ((T(x,y) * y) * z) / ((x * y) * z) = K(y,x) \ 1. [para(1098(a,1),1336(a,1,2,1))]. 1574 a(x * (y * y),y \ 1,y) = a(x * y,y \ 1,y \ 1). [para(156(a,1),1401(a,1,3))]. 1575 L(x,y,z * T(u * w,w)) = L(x,y,z * (u / T(w,u))). [para(1532(a,1),1527(a,1,3,2)),flip(a)]. 1576 L(x,y,z * (T(u,w) / w)) = L(x,y,z * T(u * w,w)). [para(1548(a,2),1575(a,2,3,2)),flip(a)]. 1577 (R(K(x,y),z,u) \ 1) \ K(y,x) = K(x,y) * R(K(y,x),z,u). [para(904(a,1),1564(a,1,1))]. 1578 R(K(x,y),z,u) * K(y,x) = K(x,y) * R(K(y,x),z,u). [para(1577(a,1),330(a,1)),flip(a)]. 1579 K(x,y) * R(K(y,x),T(x,y) * z,u) = R(K(y,x),x * z,u) \ K(y,x). [para(1249(a,1),1577(a,1,1)),flip(a)]. 1580 R(T(x,y) * K(x,y),z,u) / T(T(x,y),y) = x \ R(x,z,u). [para(1120(a,1),1568(a,1,1,1))]. 1581 R(T(T(x,y),y),z,u) / T(T(x,y),y) = x \ R(x,z,u). [para(1121(a,1),1580(a,1,1,1))]. 1582 T(T(x,y),y) \ R(T(T(x,y),y),z,u) = x \ R(x,z,u). [para(1581(a,1),478(a,1)),flip(a)]. 1583 (x * y) * T((x * y) \ (x * z),u) = (x * y) * L(T(y \ z,u),y,x). [para(44(a,2),764(a,1,2)),flip(a)]. 1584 (x * y) * R((x * y) \ x,z,u) = (x * y) * L(R(y \ 1,z,u),y,x). [para(48(a,1),765(a,1,2)),flip(a)]. 1589 (K(x,y) * (x \ z)) \ (K(x,y) * (x \ (z * u))) = L(u,z,x \ K(x,y)). [para(1072(a,1),1189(a,1,2))]. 1590 (x * y) * T((x * y) \ (x * z),u) = x * (y * T(y \ z,u)). [para(1583(a,2),74(a,1))]. 1591 (x * y) * R((x * y) \ x,z,u) = x * (y * R(y \ 1,z,u)). [para(1584(a,2),74(a,1))]. 1592 (x * y) * R((x * y) \ x,z,u) = x * (y \ R(y,z,u)). [para(635(a,1),1591(a,2,2))]. 1593 (x / y) * (y * R(((y \ x) * x) \ (y \ x),z,u)) = x \ R(x,z,u). [hyper(23,a,1274,a,b,1592,a(flip)),flip(a)]. 1594 (x / y) * (y * R(((y * x) * x) \ (y * x),z,u)) = x \ R(x,z,u). [para(1379(a,1),1593(a,1,2,2,1))]. 1595 (x / y) * (y * R(y \ (y / x),z,u)) = x \ R(x,z,u). [para(1296(a,1),1594(a,1,2,2,1))]. 1596 ((x \ y) / y) * (y * R(y \ x,z,u)) = (x \ y) \ R(x \ y,z,u). [para(65(a,1),1595(a,1,2,2,1,2))]. 1597 (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). [para(99(a,1),1595(a,1,2,2,1,2))]. 1598 (x \ 1) * (y * R(y \ x,z,u)) = (x \ y) \ R(x \ y,z,u). [para(320(a,1),1596(a,1,1))]. 1599 (x \ y) \ R(x \ y,z,u) = x \ (y * R(y \ x,z,u)). [para(1598(a,1),318(a,1))]. 1601 (x * y) \ R(x * y,z,u) = x \ (y * R(y \ x,z,u)). [para(1599(a,1),750(a,1)),flip(a)]. 1602 L(L(x,y,z),z * y,K(z,u)) = L(x,y,z \ K(z,u)). [para(1589(a,1),1409(a,1)),flip(a)]. 1603 L(L(x,y,z),z * y,K(z,u)) = L(x,y,z * K(z,u)). [para(1602(a,2),776(a,1))]. 1604 L(L(x,y,z),z * y,K(z,u)) = L(x,y,T(z,u)). [para(1107(a,2),1603(a,2,3))]. 1605 L(L(x,y,z),z * y,T(z,u)) = L(x,z * (z * y),K(z,u)). [para(303(a,1),1604(a,1,1)),flip(a)]. 1606 L(L(x,y,z),z * y,T(z,u)) = L(x,y,K(z,u)). [para(1605(a,2),875(a,1))]. 1608 (x * (y * x)) \ R(x * (z * x),u,w) = T(y,x) \ T(R(z,u,w),x). [para(36(a,2),701(a,2,2))]. 1609 (x * (y * x)) \ R(x * (z * x),u,w) = T(y,x) \ R(T(z,x),u,w). [para(46(a,2),1608(a,2,2))]. 1610 x \ ((y * x) * R((y * x) \ x,z,u)) = T(y,x) \ R(T(y,x),z,u). [para(1609(a,1),1601(a,1)),flip(a)]. 1611 L(x,y,z * (u \ (u \ (u \ (z * (u \ 1)))))) = L(x,y,K(z / (u * u),u)). [para(602(a,1),1194(a,1,3))]. 1612 L(x,y,z * (u \ ((u \ (u \ z)) * (u \ 1)))) = L(x,y,K(z / (u * u),u)). [para(285(a,1),1611(a,1,3,2,2))]. 1613 L(x,y,z * (u * ((u \ (u \ z)) * (u \ 1)))) = L(x,y,K(z / (u * u),u)). [para(1612(a,1),867(a,1)),flip(a)]. 1614 L(x,y,K(z / (u * u),u)) = L(x,y,z * (u \ (z * (u \ 1)))). [para(265(a,1),1613(a,1,3,2)),flip(a)]. 1615 L(x,y,K(z / (u * u),u)) = L(x,y,z * (u * (z * (u \ 1)))). [para(1614(a,2),867(a,1))]. 1616 L(x,y,K(z / (u * u),u)) = L(x,y,z * T(z,u \ 1)). [para(347(a,1),1615(a,2,3,2))]. 1617 L(x,y,K(z / (u * u),u)) = L(x,y,K(z,u \ 1)). [para(1616(a,2),1119(a,1))]. 1618 L(x,y,K(z,u \ 1)) = L(x,y,K(z,u)). [para(1418(a,1),1617(a,1,3)),flip(a)]. 1619 L(x,y,K(z,u \ 1)) = L(x,y,K(u,z)). [para(1618(a,2),909(a,1))]. 1620 (x * (x * (y * (z * u)))) \ ((x * (x * (y * z))) * u) = a(x * (x * y),z,u). [para(51(a,1),91(a,1,2,1))]. 1621 (x * y) * R(L(y \ z,y,x),u,w) = (x * y) * R((x * y) \ (x * z),u,w). [para(473(a,1),224(a,1))]. 1624 ((x * y) * ((y * x) * z)) \ (((x * y) * (y * x)) * (z * u)) = L(u,z,K(y,x)). [para(894(a,1),832(a,1,1))]. 1625 ((x * y) * T(R(T(z,x * y),x,y),u)) / ((z * x) * y) = K(R(z,x,y),u). [para(549(a,1),1214(a,1,1,2,1))]. 1626 ((x * y) * R(T(T(z,x * y),u),x,y)) / ((z * x) * y) = K(R(z,x,y),u). [para(46(a,2),1625(a,1,1,2))]. 1627 (R(T(x,y),z,u) * (z * u)) / ((x * z) * u) = K(R(x,z,u),y). [para(222(a,1),1626(a,1,1))]. 1628 ((T(x,y) * z) * u) / ((x * z) * u) = K(R(x,z,u),y). [para(79(a,1),1627(a,1,1))]. 1629 R(K(x,y),x * z,u) = K(R(x,z,u),y). [para(1628(a,1),1183(a,1)),flip(a)]. 1630 K(R(x,y,z),y) = K(y,x) \ 1. [para(1628(a,1),1572(a,1))]. 1631 R(K(x,y),T(y,x) * z,u) \ 1 = K(R(y,z,u),x). [para(1628(a,1),1162(a,2))]. 1632 K(R(x,y,z),y) = K(x,y). [para(1630(a,2),897(a,1))]. 1633 T(x,R(y,x,z)) = (x * x) / (x * K(y,x)). [para(1632(a,1),1104(a,2,2,2))]. 1634 K(R(x,x \ y,z),u) = R(K(x,u),y,z). [para(20(a,1),1629(a,1,2)),flip(a)]. 1635 R(K(x,y),x * (z / (z * x)),u) = K(x,y). [para(450(a,1),1629(a,2,1))]. 1636 R(K(x,y),T(x,y) * z,u) = K(R(T(x,y),z,u),y). [para(1105(a,1),1629(a,1,1))]. 1637 K(R(x,x * y,z),u) = R(K(x,u),y,z). [para(629(a,1),1634(a,1,1))]. 1638 R(K(x,y),z,x) = K(L(x,z,x),y). [para(1313(a,1),1634(a,1,1)),flip(a)]. 1639 K(x,R(y,y * z,u)) = R(K(y,x),z,u) \ 1. [para(1637(a,1),897(a,1,1)),flip(a)]. 1640 R(K(x,y),K(x,z) * u,w) = K(R(x,T(x,z) * u,w),y). [para(1120(a,1),1637(a,1,1,2)),flip(a)]. 1641 K(R(x,T(x,y) * z,u),y) = R(K(T(x,y),y),z,u). [para(1637(a,1),1110(a,1)),flip(a)]. 1642 T(x,R(y,x,z)) = T(x,y). [para(1633(a,2),1104(a,2)),flip(a)]. 1643 R(x,y,z) * T(y,x) = y * R(x,y,z). [para(1642(a,1),82(a,1,2))]. 1647 T(x,y) \ (x * R(y,x,z)) = T(R(y,x,z),T(x,y)). [para(1643(a,1),36(a,2,2)),flip(a)]. 1648 R(K(x,y),K(x,z),u) = K(x,y). [para(1041(a,2),1635(a,1,2))]. 1649 R(K(x,y),K(z,x),u) = K(x,y). [para(1648(a,1),908(a,1)),flip(a)]. 1650 (K(x,y) * K(z,x)) * u = K(x,y) * (K(z,x) * u). [para(1649(a,1),79(a,1,1)),flip(a)]. 1651 R(K(x,y),T(y,x) * z,u) = K(R(y,z,u),x) \ 1. [para(1631(a,1),156(a,1,1)),flip(a)]. 1652 R(K(x,y),T(x,y) * z,u) = K(R(x,z,u),y). [para(1636(a,2),1110(a,1))]. 1653 R(K(x,y),y * z,u) = K(R(y,z,u),x) \ 1. [para(1652(a,1),1249(a,1,1)),flip(a)]. 1654 R(K(x,y),y * z,u) = K(x,R(y,z,u)). [para(1653(a,2),897(a,1))]. 1656 R(K(x,y),x * z,u) * K(y,x) = K(x,y) * K(y,R(x,z,u)). [para(1654(a,1),1578(a,2,2))]. 1657 K(R(x,T(x,y) * z,u),y) = R(K(x,y),z,u). [para(1105(a,1),1641(a,2,1))]. 1658 T(R(x,y,z),T(y,x)) = K(x,y) * R(x,y,z). [para(1647(a,1),1093(a,1))]. 1659 R(T(x,T(y,x)),y,z) = K(x,y) * R(x,y,z). [para(1658(a,1),46(a,2))]. 1660 K(x,y) * R(x,y,z) = R(T(x,y),y,z). [para(1131(a,1),1659(a,1,1)),flip(a)]. 1661 T(x,y) \ R(T(x,y),y,z) = x \ R(x,y,z). [para(1660(a,1),1171(a,1,2))]. 1662 (x \ y) \ R(T(y / x,x),x,z) = (y / x) \ R(y / x,x,z). [para(84(a,1),1661(a,1,1))]. 1663 L(x,K(y,z),K(z,u)) = x. [hyper(23,a,74,a,b,1650,a),flip(a)]. 1664 L(x,K(y,z),K(u,z)) = x. [para(1663(a,1),909(a,1)),flip(a)]. 1665 L(x,K(y,z),K(u,y)) = x. [para(1664(a,1),921(a,1)),flip(a)]. 1666 (K(x,y) * T(z,x)) / z = K(z,x) * K(x,y). [para(1665(a,1),1355(a,1,2))]. 1667 R(K(x,y),T(y,x) * z,u) = K(x,R(y,z,u)). [para(1651(a,2),897(a,1))]. 1668 R(K(x,y),y * z,u) \ K(x,y) = K(y,x) * K(x,R(y,z,u)). [para(1667(a,1),1579(a,1,2)),flip(a)]. 1669 R(K(x,y),K(x,y) * z,u) = R(K(x,y),z,u). [para(1640(a,2),1657(a,1))]. 1670 R(K(x,y),z,u) \ 1 = R(K(y,x),z,u). [para(1669(a,1),906(a,1)),flip(a)]. 1671 R(K(x,y),z,u) \ K(x,y) = K(x,y) * R(K(y,x),z,u). [para(1670(a,1),543(a,1,2)),flip(a)]. 1672 K(x,R(y,y * z,u)) = R(K(x,y),z,u). [para(1670(a,1),1639(a,2))]. 1673 K(R(x,y,z),u) * K(u,x) = K(x,u) * K(u,R(x,y,z)). [para(1629(a,1),1656(a,1,1))]. 1674 K(x,y) * K(R(y,z,u),x) = K(y,x) * K(x,R(y,z,u)). [para(1673(a,1),1226(a,2))]. 1675 (x / y) \ R(x / y,y,z) = (y \ x) \ R(y \ x,y,z). [para(84(a,1),1662(a,1,2,1)),flip(a)]. 1676 (x \ y) \ R(x \ y,x,z) = (x / y) * R(y / x,x,z). [para(1675(a,1),358(a,1))]. 1677 x \ (y * R(y \ x,x,z)) = (x / y) * R(y / x,x,z). [para(1676(a,1),1599(a,1)),flip(a)]. 1678 x \ ((y \ x) * R((y \ x) \ x,x,z)) = y * R((y \ x) / x,x,z). [para(65(a,1),1677(a,2,1))]. 1679 x \ (R(y,x,z) * (y \ x)) = y * R((y \ x) / x,x,z). [para(225(a,1),1678(a,1,2))]. 1680 x * R((x \ y) / y,y,z) = T(x \ R(x,y,z),y). [para(1679(a,1),539(a,1))]. 1681 T(x \ R(x,y,z),y) = x * R(x \ 1,y,z). [para(320(a,1),1680(a,1,2,1)),flip(a)]. 1683 T(x \ R(x,y,z),y) = x \ R(x,y,z). [para(1681(a,2),635(a,1))]. 1684 (x * (y \ R(y,x,z))) / x = y \ R(y,x,z). [para(1683(a,1),105(a,1,1,2))]. 1685 T(x \ R(x,y,z),x * (y * z)) = T(a(x,y,z),y). [para(1683(a,1),740(a,1,1))]. 1686 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). [para(1684(a,1),1518(a,2,1))]. 1687 T(a(x,y,z),y) = a(x,y,z). [para(1685(a,1),739(a,2)),flip(a)]. 1688 a(x,y,z) * y = y * a(x,y,z). [para(1687(a,1),82(a,1,2)),flip(a)]. 1689 a(x,y \ 1,z) * (y \ 1) = y \ a(x,y \ 1,z). [para(1687(a,1),326(a,1,2)),flip(a)]. 1690 T(x * y,x) / x = y * a(x,y,x). [para(1688(a,1),1563(a,2))]. 1691 L(x,y,z * (T(u * z,u) / u)) = L(x,y,a(u,z,u)). [para(1690(a,2),774(a,1,3,2))]. 1692 L(x,y,z * a(u,z,u)) = L(x,y,R(z,u,u)). [para(1690(a,1),1350(a,1,3))]. 1693 L(x,y,z * T((u * z) * u,u)) = L(x,y,a(u,z,u)). [para(1691(a,1),1576(a,1)),flip(a)]. 1694 L(x,y,z * ((z * u) * u)) = L(x,y,a(u,z,u)). [para(758(a,1),1693(a,1,3,2))]. 1695 L(x,y,a(z,u,u)) = L(x,y,a(u,z,u)). [para(1694(a,1),861(a,1)),flip(a)]. 1696 (x * (x * (y * (z * u)))) \ (x * (x * ((y * z) * u))) = a(x * (x * y),z,u). [para(51(a,1),1620(a,1,2))]. 1697 (x * y) * R((x * y) \ (x * z),u,w) = (x * y) * L(R(y \ z,u,w),y,x). [para(48(a,1),1621(a,1,2)),flip(a)]. 1698 ((x * y) * ((y * x) * z)) \ ((x * y) * ((y * x) * (z * u))) = L(u,z,K(y,x)). [para(894(a,1),1624(a,1,2))]. 1699 a(x * (x * y),z,u) = (y * (z * u)) \ ((y * z) * u). [para(1696(a,1),212(a,1))]. 1700 a(x * (x * y),z,u) = a(y,z,u). [para(1699(a,2),28(a,2)),flip(a)]. 1702 a(x \ y,z,u) = a(x * y,z,u). [para(20(a,1),1700(a,1,1,2)),flip(a)]. 1703 a((x / y) * x,z,u) = a(y,z,u). [para(22(a,1),1700(a,1,1,2))]. 1704 a(x * (y * x),z,u) = a(T(y,x),z,u). [para(82(a,1),1700(a,1,1,2))]. 1706 a(x * ((x \ y) * z),u,w) = a(x * ((x * y) * z),u,w). [para(89(a,1),1700(a,1,1,2)),flip(a)]. 1707 a((x \ y) * z,u,w) = a((x * y) * z,u,w). [para(89(a,1),1700(a,1,1)),flip(a)]. 1708 a((x * x) / y,z,u) = a(y \ 1,z,u). [para(263(a,1),1700(a,1,1))]. 1709 a(x * L(x,y * x,y),z,u) = a(a(y,x,x),z,u). [para(453(a,2),1700(a,1,1,2))]. 1710 a(R(x \ 1,y,y),z,u) = a(x * a(x,y,y),z,u). [para(960(a,1),1700(a,1,1,2)),flip(a)]. 1711 a(K(x,y) * y,z,u) = a(T(y,x),z,u). [para(1077(a,1),1700(a,1,1,2))]. 1712 a(x * T(x,y),z,u) = a(K(x,y),z,u). [para(1107(a,2),1700(a,1,1,2))]. 1713 ((x \ y) * (T(x,x * y) * z)) \ (y * z) = a(x * y,T(x,x * y),z). [para(1702(a,1),255(a,2))]. 1714 a(K(x \ 1,x * y),z,u) = a(x \ ((x * y) \ y),z,u). [para(1126(a,2),1702(a,2,1)),flip(a)]. 1715 a((x * (x * y)) * (x * z),u,w) = a(y \ (x \ z),u,w). [para(282(a,1),1703(a,1,1,1))]. 1716 a((x * x) / y,z,u) = a(y,z,u). [para(1708(a,2),611(a,1))]. 1717 a(x / (y * y),z,u) = a(x,z,u). [para(1716(a,1),612(a,1)),flip(a)]. 1718 a(R(x,x * y,z),u,w) = a(R(x,y,z),u,w). [para(616(a,1),1716(a,1,1))]. 1719 a(x * K(y,x),z,u) = a(T(x,y),z,u). [para(1104(a,2),1716(a,1,1)),flip(a)]. 1720 a(x * (y * y),z,u) = a(x,z,u). [para(21(a,1),1717(a,1,1)),flip(a)]. 1721 a((x * y) * y,z,u) = a(R(x,y,y),z,u). [para(34(a,2),1717(a,1,1)),flip(a)]. 1722 a(x / (y \ 1),z,u) = a(x / y,z,u). [para(398(a,1),1717(a,1,1)),flip(a)]. 1723 ((x * (y * y)) * (z * u)) \ (((x * (y * y)) * z) * u) = a(x,z,u). [para(1720(a,1),28(a,1)),flip(a)]. 1724 a(T(T(x,y),y),z,u) = a(x,z,u). [para(985(a,1),1711(a,1,1)),flip(a)]. 1725 a((x / (y * y)) * (y \ (x * (y \ 1))),z,u) = a(K(x / (y * y),y),z,u). [para(403(a,1),1712(a,1,1,2))]. 1726 a(x / (x * y),z,u) = a(T(y,x),z,u). [para(1719(a,1),1022(a,2))]. 1727 a((x \ 1) / y,z,u) = a(y / x,z,u). [para(1722(a,1),612(a,1)),flip(a)]. 1728 a(x / T(y * x,y),z,u) = a(T(R(y,x,y),x),z,u). [para(1321(a,1),1726(a,1,1,2))]. 1729 a(x * (y * x),x,x) = a(R(y,x,x),x,x). [para(1721(a,1),1517(a,1)),flip(a)]. 1730 a(R(x,y,y),y,y) = a(T(x,y),y,y). [para(1729(a,1),1704(a,1))]. 1731 a(R(x,y,y),y,y) = a(x,y,y). [para(1730(a,2),1485(a,1))]. 1732 R(R(x,y,y) \ 1,y,y) = R(x,y,y) \ a(x,y,y). [para(1731(a,1),967(a,2,2))]. 1733 R(R(x,y,y),R(x,y,y) * y,y) = a(x,y,y) \ R(x,y,y). [para(1731(a,1),968(a,2,1))]. 1734 a(x * ((x \ y) * y),z,u) = a(a(x,y,y),z,u). [para(435(a,1),1709(a,1,1))]. 1735 a(R(x \ 1,y,y),z,u) = a(R(x,y,y),z,u). [para(963(a,1),1710(a,2,1))]. 1736 R(R(x,y,y) \ 1,y,y) = x \ 1. [para(1732(a,2),1374(a,1))]. 1737 R((x * y) \ 1,y,y) = (x / (y \ 1)) \ 1. [para(720(a,1),1736(a,1,1,1))]. 1739 R((x * y) \ 1,y,y) = (y \ 1) / x. [para(1737(a,2),343(a,1))]. 1740 (x \ 1) / (y / x) = R(y \ 1,x,x). [para(22(a,1),1739(a,1,1,1)),flip(a)]. 1741 (((x * y) \ 1) * y) * y = ((y \ 1) / x) * (y * y). [para(1739(a,1),79(a,1,1)),flip(a)]. 1742 R(x \ 1,y,y) \ 1 = (x / y) / (y \ 1). [para(1740(a,1),343(a,1,1))]. 1743 a((x \ 1) / ((y / x) \ 1),z,u) = a(R(y \ 1,x,x),z,u). [para(1740(a,1),1722(a,2,1))]. 1744 R(x,x * y,y) = (x / y) / (y \ 1). [para(1742(a,1),633(a,2))]. 1745 K(R(x,x * y,y),z) * (x / y) = (y \ 1) * T((y \ 1) \ (x / y),z). [para(1744(a,2),1201(a,1,1,1))]. 1746 (((x * y) \ 1) * y) * y = T(y / x,y * y). [para(1741(a,2),294(a,1))]. 1747 T(x / y,x * x) = ((y * x) \ x) * x. [para(318(a,1),1746(a,1,1)),flip(a)]. 1748 L(x,y * z,R(T(z / y,z * z),u,w)) = x. [para(1747(a,2),847(a,1,3,1))]. 1749 L(x,y * z,R(z / y,u,w)) = x. [para(1748(a,1),858(a,1)),flip(a)]. 1750 L(x,y * (z \ 1),u / (y * (z * u))) = x. [para(350(a,1),1749(a,1,3))]. 1752 L(x,y * z,u / (y * (z * u))) = x. [para(1750(a,1),1273(a,1)),flip(a)]. 1753 x / ((y * z) \ (y * (z * x))) = (x / (y * (z * x))) * (y * z). [para(1752(a,1),205(a,1,2))]. 1754 a(T(R(x,y,x),y),z,u) = a((y / x) / y,z,u). [para(1237(a,1),1728(a,1,1)),flip(a)]. 1755 a(x * ((x * y) * y),z,u) = a(a(x,y,y),z,u). [para(1706(a,1),1734(a,1))]. 1756 a(x * (x * (y * (x * z))),u,w) = a(y \ (x \ z),u,w). [para(51(a,1),1715(a,1,1))]. 1757 a(x \ (y \ z),u,w) = a(x * (y * z),u,w). [para(1756(a,1),1700(a,1))]. 1759 a(x * (y \ z),u,w) = a(x * (y * z),u,w). [para(1757(a,1),1702(a,1)),flip(a)]. 1760 a(K(x \ 1,x * y),z,u) = a(x * ((x * y) * y),z,u). [para(1757(a,1),1714(a,2))]. 1761 R(R(x,y,y),R(x,y,y) * y,y) = x. [para(1733(a,2),964(a,1))]. 1762 R(K(R(x,y,y),z),y,y) = K(x,z). [para(1761(a,1),1637(a,1,1)),flip(a)]. 1763 K(R(x,y,y),z) * (y \ 1) = K(x,z) / y. [para(1762(a,1),718(a,1,1)),flip(a)]. 1764 K(x,R(y,z,z)) * (K(y,x) / z) = z \ 1. [hyper(23,a,901,a,b,1763,a),flip(a)]. 1765 R(K(x,y),z,z) = K(x,R(y,z,z)). [hyper(24,a,1405,a,b,1764,a),flip(a)]. 1766 K(R(x,y,y),z) \ 1 = R(K(z,x),y,y). [para(1765(a,2),897(a,2))]. 1767 K(x,R(y,z,z)) * 1 = R(K(x,y),z,z). [para(1766(a,1),900(a,1)),flip(a)]. 1768 a((x \ 1) / (x / y),z,u) = a(R(y \ 1,x,x),z,u). [para(343(a,1),1743(a,1,1,2))]. 1769 a(R(x \ 1,y,y),z,u) = a((y / x) / y,z,u). [para(1768(a,1),1727(a,1))]. 1770 a((x / y) / x,z,u) = a(R(y,x,x),z,u). [para(1769(a,1),1735(a,1))]. 1771 a(T(R(x,y,x),y),z,u) = a(R(x,y,y),z,u). [para(1770(a,1),1754(a,2))]. 1772 a(R(T(x,y),y,x),z,u) = a(R(x,y,y),z,u). [para(46(a,2),1771(a,1,1))]. 1773 (x / (y * (z * x))) * (y * z) = x / L(x,z,y). [para(32(a,2),1753(a,1,2)),flip(a)]. 1774 (x / (y * (z * x))) * (y * z) = L(x,z,y) \ x. [para(1773(a,2),519(a,1))]. 1775 (L(x * y,z / (x * (y * z)),x * y) * (z / (x * (y * z)))) * (x * y) = (x * y) * (L(z,y,x) \ z). [para(1774(a,1),1310(a,2,2))]. 1776 (x * (y * (y * (z * u)))) \ (((x * (y * y)) * z) * u) = a(x,z,u). [para(411(a,1),1723(a,1,1))]. 1777 (x * (y * (y * (z * u)))) \ ((x * (y * (y * z))) * u) = a(x,z,u). [para(411(a,1),1776(a,1,2,1))]. 1778 a(x,y * (y * z),u) = a(x,z,u). [para(1777(a,1),90(a,1)),flip(a)]. 1779 a(x,y \ z,u) = a(x,y * z,u). [para(20(a,1),1778(a,1,2,2)),flip(a)]. 1780 a(x,(y / z) * y,u) = a(x,z,u). [para(22(a,1),1778(a,1,2,2))]. 1783 a(x,K(y,z) * T(y,z),u) = a(x,y,u). [para(1081(a,2),1778(a,1,2,2))]. 1785 a(x * (y * y),y * 1,y) = a(x * y,y \ 1,y \ 1). [para(1779(a,1),1574(a,1))]. 1786 a(x,y \ 1,z) * (y \ 1) = y \ a(x,y * 1,z). [para(1779(a,1),1689(a,2,2))]. 1787 a(x,(y * (y * z)) * (y * u),w) = a(x,z \ (y \ u),w). [para(282(a,1),1780(a,1,2,1))]. 1789 a(x,T(T(y,z),z),u) = a(x,y,u). [para(1113(a,1),1783(a,1,2))]. 1790 a(T(x,y),y,z) = a(x,T(y,x),z). [para(1789(a,1),1460(a,1))]. 1793 a(x,y \ 1,z) * (y \ 1) = y \ a(x,y,z). [para(18(a,1),1786(a,2,2,2))]. 1794 a(x,y * 1,z) * (y \ 1) = y \ a(x,y,z). [para(1779(a,1),1793(a,1,1))]. 1795 a(x,y,z) * (y \ 1) = y \ a(x,y,z). [para(18(a,1),1794(a,1,1,2))]. 1796 a(x * (y * y),y,y) = a(x * y,y \ 1,y \ 1). [para(18(a,1),1785(a,1,2))]. 1797 a(x * y,y \ 1,y \ 1) = a(x,y,y). [para(1796(a,1),1720(a,1))]. 1798 L(x,x,y) \ x = a(y,x,x). [para(1797(a,1),1408(a,1)),flip(a)]. 1800 a(x,y,y) * L(y,y,x) = y. [para(1798(a,1),520(a,1,1))]. 1801 R(x,y,y) * L(y,y,x) = x * y. [para(1800(a,1),966(a,1,2)),flip(a)]. 1802 T(R(x,y,y),L(y,y,x)) = L(y,y,x) \ (x * y). [para(1801(a,1),36(a,2,2))]. 1803 R(T(x,L(y,y,x)),y,y) = L(y,y,x) \ (x * y). [para(1802(a,1),46(a,2))]. 1804 L(x,x,y) \ (y * x) = R(T(y,x),x,x). [para(1558(a,1),1803(a,1,1)),flip(a)]. 1805 a(x,y * (y * (z * (y * u))),w) = a(x,z \ (y \ u),w). [para(51(a,1),1787(a,1,2))]. 1806 a(x,y \ (z \ u),w) = a(x,y * (z * u),w). [para(1805(a,1),1778(a,1))]. 1808 a(x,y * (z \ u),w) = a(x,y * (z * u),w). [para(1806(a,1),1779(a,1)),flip(a)]. 1809 a(x * y,T(x,x * y),z) = ((y / x) * (x * z)) \ (y * z). [para(1265(a,1),1713(a,1,1)),flip(a)]. 1810 a(x * y,T(x,x * y),z) = a(y / x,x,z). [para(1809(a,2),68(a,1))]. 1811 R(K(x,y),z,z) * (x / z) = (z \ 1) * T((z \ 1) \ (x / z),y). [para(1637(a,1),1745(a,1,1))]. 1812 K(x,R(y,z,z)) * (x / z) = (z \ 1) * T((z \ 1) \ (x / z),y). [para(1765(a,1),1811(a,1,1))]. 1813 K(x,R(y,z,z)) * (x / z) = (z \ 1) * T(z * (x / z),y). [para(330(a,1),1812(a,2,2,1))]. 1814 K(x,R(y,z,z)) * (x / z) = z \ T(z * (x / z),y). [para(1813(a,2),318(a,1))]. 1815 K(x,R(y,z,z)) * (x / z) = T(x,y) / z. [para(1814(a,2),755(a,1))]. 1816 a(x * (y \ (y \ (y \ (x * (y \ 1))))),z,u) = a(K(x / (y * y),y),z,u). [para(602(a,1),1725(a,1,1))]. 1817 a(x * (y \ ((y \ (y \ x)) * (y \ 1))),z,u) = a(K(x / (y * y),y),z,u). [para(285(a,1),1816(a,1,1,2,2))]. 1818 a(x * (y * ((y \ (y \ x)) * (y \ 1))),z,u) = a(K(x / (y * y),y),z,u). [para(1817(a,1),1759(a,1)),flip(a)]. 1819 a(K(x / (y * y),y),z,u) = a(x * (y \ (x * (y \ 1))),z,u). [para(265(a,1),1818(a,1,1,2)),flip(a)]. 1820 a(K(x / (y * y),y),z,u) = a(x * (y * (x * (y \ 1))),z,u). [para(1819(a,2),1759(a,1))]. 1821 a(K(x / (y * y),y),z,u) = a(x * T(x,y \ 1),z,u). [para(347(a,1),1820(a,2,1,2))]. 1822 a(K(x / (y * y),y),z,u) = a(K(x,y \ 1),z,u). [para(1821(a,2),1712(a,1))]. 1823 a(K(x,y \ 1),z,u) = a(K(x,y),z,u). [para(1418(a,1),1822(a,1,1)),flip(a)]. 1824 a(K(x \ 1,y),z,u) = a(K(y,x),z,u). [para(1823(a,1),905(a,1)),flip(a)]. 1825 a(x * ((x * y) * y),z,u) = a(K(x * y,x),z,u). [para(1824(a,1),1760(a,1)),flip(a)]. 1826 a(K(x * y,x),z,u) = a(a(x,y,y),z,u). [para(1825(a,1),1755(a,1))]. 1827 (x * y) * R((x * y) \ (x * z),u,w) = x * (y * R(y \ z,u,w)). [para(1697(a,2),74(a,1))]. 1828 (x * y) * R((x * y) \ z,u,w) = x * (y * R(y \ (x \ z),u,w)). [para(20(a,1),1827(a,1,2,1,2))]. 1829 (x * y) * R((x * y) \ y,z,u) = R(x,z,u) * (x \ y). [para(1828(a,2),639(a,1))]. 1830 T(x,y) \ R(T(x,y),z,u) = y \ (R(x,z,u) * (x \ y)). [para(1829(a,1),1610(a,1,2)),flip(a)]. 1831 T(x,y) \ R(T(x,y),z,u) = T(x \ R(x,z,u),y). [para(1830(a,2),539(a,1))]. 1832 (R(T(x,y),z,u) \ T(x,y)) * w = T(x \ R(x,z,u),y) \ w. [para(1831(a,1),465(a,1,1)),flip(a)]. 1833 T(x \ R(x,y,y),z) = a(T(x,z),y,y). [para(1831(a,1),962(a,1))]. 1834 K(x,y) * R(T(y,x),z,u) = y * T(y \ R(y,z,u),x). [para(1831(a,1),1099(a,1,2)),flip(a)]. 1835 T(T(x,y) \ R(T(x,y),z,u),y) = x \ R(x,z,u). [para(1831(a,1),1582(a,1))]. 1836 a(T(x,y),z,z) = T(a(x,z,z),y). [para(962(a,1),1833(a,1,1)),flip(a)]. 1837 T(T(x \ R(x,y,z),u),u) = x \ R(x,y,z). [para(1831(a,1),1835(a,1,1))]. 1838 (x * (y \ R(y,z,u))) / x = T(y \ R(y,z,u),x). [para(1837(a,1),105(a,1,1,2))]. 1839 T(a(x,y,z),x * (y * z)) = x \ R(x,y,z). [para(739(a,2),1837(a,1,1))]. 1840 a(x,y,z) * K(a(x,y,z),x * (y * z)) = x \ R(x,y,z). [para(1839(a,1),1107(a,1)),flip(a)]. 1841 T(T(x \ R(x,y,z),u),x * (y * z)) = (u * a(x,y,z)) / u. [para(1838(a,1),742(a,1,1))]. 1842 (x * (y \ R(y,z,u))) / x = (y \ R(y,z,u)) * K(y \ R(y,z,u),x). [para(1838(a,2),1107(a,1))]. 1843 (x * a(y,z,u)) / x = T(a(y,z,u),x). [para(1841(a,1),740(a,1))]. 1844 T(a(x,y,z),u) * (u / (u * a(x,y,z))) = 1. [para(1843(a,1),354(a,1,1))]. 1845 L(x,x,x * ((x \ 1) * a(y,z,u))) = ((x \ 1) * a(y,z,u)) \ T(a(y,z,u),x \ 1). [para(1843(a,1),1488(a,2,2))]. 1846 K(a(x,y,z),u) * K(a(x,y,z),u) = 1. [para(1844(a,1),1174(a,1)),flip(a)]. 1847 K(a(x,y,z),u) = K(u,a(x,y,z)). [hyper(24,a,898,a,b,1846,a)]. 1848 a(x,y,z) * K(x * (y * z),a(x,y,z)) = x \ R(x,y,z). [para(1847(a,1),1840(a,1,2))]. 1849 K(x \ R(x,y,z),u) = K(u,x \ R(x,y,z)). [hyper(23,a,1014,a(flip),b,1842,a(flip))]. 1850 L(L(x,y,z * u),(z * u) * y,u * z) = L(x,y,K(z,u)). [para(1698(a,1),174(a,1)),flip(a)]. 1851 ((x * (x * y)) * a(y,z,u)) / y = a(x * (x * y),z,u) * (x * x). [para(1700(a,1),749(a,1,1,2))]. 1852 (x * (x * (y * a(y,z,u)))) / y = a(x * (x * y),z,u) * (x * x). [para(51(a,1),1851(a,1,1))]. 1854 a(x * (x * y),z,u) * (x * x) = x * (x * ((y * a(y,z,u)) / y)). [para(1852(a,1),211(a,1))]. 1855 a(x * (x * y),z,u) * (x * x) = x * (x * a(y,z,u)). [para(748(a,1),1854(a,2,2,2))]. 1856 a(x,y,z) * (u * u) = u * (u * a(x,y,z)). [para(1700(a,1),1855(a,1,1))]. 1857 T((a(x,y,z) * (u * u)) / (u * u),u) = T(u \ (u * a(x,y,z)),u \ 1). [para(1856(a,2),666(a,1,1,1))]. 1859 T(x \ (x * a(y,z,u)),x \ 1) = T(a(y,z,u),x). [para(21(a,1),1857(a,1,1)),flip(a)]. 1860 T(a(x,y,z),u \ 1) = T(a(x,y,z),u). [para(19(a,1),1859(a,1,1))]. 1863 x * L(T(y \ (y / x),z),y,x * y) = K(L(y \ (y / x),y,x * y),z). [para(1295(a,1),330(a,1)),flip(a)]. 1864 (x / y) * (y * T(y \ (y / x),z)) = K(L(y \ (y / x),y,x * y),z). [para(1863(a,1),1294(a,1)),flip(a)]. 1865 (x / y) * (y * T(y \ (y / x),z)) = K(x \ 1,z). [para(1289(a,1),1864(a,2,1))]. 1866 (L(x,y,z) / (z * (y * x))) * ((z * (y * x)) * T((z * (y * x)) \ (z * y),u)) = K(L(x,y,z) \ 1,u). [para(99(a,1),1865(a,1,2,2,1,2))]. 1868 T(x * x,y * z) \ ((((y * z) \ (x * x)) * y) * z) = a((y * z) * (x * x),y,z). [para(394(a,2),1702(a,1))]. 1869 ((R(x,y,z) * u) * w) / ((x * u) * w) = R(x,u,w) \ R(R(x,u,w),y,z). [para(185(a,1),538(a,1,1))]. 1870 R(x \ R(x,y,z),x * u,w) = R(x,u,w) \ R(R(x,u,w),y,z). [para(1869(a,1),533(a,2))]. 1871 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). [para(584(a,1),1870(a,2,1))]. 1872 (K(x,T(y,z)) * T(y,x)) / y = K(z,T(y,x)) * K(y,z). [para(1663(a,1),1570(a,1,2))]. 1873 K(x,T(y,z)) * K(y,x) = K(y,z) * K(z,T(y,x)). [para(1872(a,1),1666(a,1))]. 1874 T(x * x,y * z) \ ((((y * z) \ (x * x)) * y) * z) = a(y * z,y,z). [para(1868(a,2),1720(a,1))]. 1875 (T(x * x,y * z) \ (((y * z) \ (x * x)) * y)) * z = a(y * z,y,z). [para(1874(a,1),591(a,1)),flip(a)]. 1877 ((T(x * x,y * z) \ ((y * z) \ (x * x))) * y) * z = a(y * z,y,z). [para(591(a,1),1875(a,1,1))]. 1878 (((x * y) \ 1) * x) * y = a(x * y,x,y). [para(795(a,1),1877(a,1,1,1))]. 1879 ((x * y) \ x) * y = a(x * y,x,y). [para(318(a,1),1878(a,1,1))]. 1880 x * ((y * x) \ y) = a(y * x,y,x). [para(1879(a,1),388(a,1)),flip(a)]. 1881 a(x * (x \ y),x,x \ y) = (x \ y) * (y \ x). [para(20(a,1),1880(a,1,2,1)),flip(a)]. 1882 (x \ y) * (y \ x) = a(y,x,x \ y). [para(20(a,1),1881(a,1,1)),flip(a)]. 1883 L(x,y,(z \ u) * (u * z)) = L(x,y,a(z,u,u \ z)). [para(1882(a,1),869(a,1,3)),flip(a)]. 1884 L(x,(y \ z) * (z * y),u) = L(x,a(y,z,z \ y),u). [para(1882(a,1),1362(a,1,2)),flip(a)]. 1885 L(x,y,(z * u) * (u * z)) = L(x,y,a(z,u,u \ z)). [para(1883(a,1),781(a,1)),flip(a)]. 1886 L(x,(y * z) * (z * y),u) = L(x,a(y,z,z \ y),u). [para(1884(a,1),880(a,1)),flip(a)]. 1887 L(x,y,a(z,u,u \ z)) = L(x,y,K(u,z)). [para(1885(a,1),779(a,1))]. 1888 L(x,a(y,z,z \ y),u) = L(x,K(z,y),u). [para(1886(a,1),879(a,1))]. 1889 ((x \ 1) * a(y,z,u)) \ T(a(y,z,u),x \ 1) = L(x,x,a(y,z,u)). [para(321(a,1),1845(a,1,3)),flip(a)]. 1890 (x \ a(y,z,u)) \ T(a(y,z,u),x \ 1) = L(x,x,a(y,z,u)). [para(318(a,1),1889(a,1,1))]. 1892 (x \ a(y,z,u)) \ T(a(y,z,u),x) = L(x,x,a(y,z,u)). [para(1860(a,1),1890(a,1,2))]. 1893 L(x,a(y,z,u),x) = L(x,x,a(y,z,u)). [para(1892(a,1),440(a,1)),flip(a)]. 1894 L(x,x,a(y,z,z \ y)) = L(x,K(z,y),x). [para(1893(a,1),1888(a,1))]. 1895 L(x,K(y,z),x) = L(x,x,K(y,z)). [para(1894(a,1),1887(a,1))]. 1896 L(x,K(y,z),x) = L(x,x,K(z,y)). [para(1895(a,2),909(a,1))]. 1897 (x \ K(y,z)) / (K(y,z) / L(x,x,K(z,y))) = K(K(y,z),x). [para(1896(a,1),1500(a,2,2,2)),flip(a)]. 1898 (x \ K(y,z)) / (K(y,z) * (x \ 1)) = K(K(y,z),x). [para(930(a,1),1897(a,1,2))]. 1899 K(x \ 1,K(y,z)) = K(K(y,z),x). [para(1898(a,1),978(a,1)),flip(a)]. 1900 K(K(x,y),z) * (K(x,y) \ u) = T(K(x,y),z \ 1) \ u. [para(1899(a,1),1095(a,1,1))]. 1901 T(K(x,y),z) * K(K(x,y),z) = T(K(x,y),z * z). [para(1899(a,1),1433(a,1,2))]. 1902 T(T(K(x,y),z),z) = T(K(x,y),z * z). [para(1901(a,1),1121(a,1)),flip(a)]. 1903 T(K(x,y),T(z,x) * T(z,x)) = T(T(K(x,y),z),T(z,x)). [para(1352(a,1),1902(a,1,1)),flip(a)]. 1904 x / (T(K(y,z),u \ 1) \ x) = K(y,z) * K(u,K(y,z)). [para(1900(a,1),1071(a,1,2))]. 1905 T(K(x,y),z * T(T(z,x),x)) = T(T(K(x,y),z),T(z,x)). [para(1088(a,1),1903(a,1,2))]. 1906 K(x,y) * K(z,K(x,y)) = T(K(x,y),z \ 1). [para(1904(a,1),65(a,1))]. 1907 T(K(x,y),z \ 1) * z = z * K(x,y). [para(1906(a,1),1018(a,1,1))]. 1908 ((x * y) * (z / (x * (y * z)))) * (x * y) = (x * y) * (L(z,y,x) \ z). [para(851(a,1),1775(a,1,1,1))]. 1910 (x \ R(x,y,z)) * (x * y) = (x * y) * (L(z,y,x) \ z). [para(1410(a,1),1908(a,1,1))]. 1911 (x * y) * (L(z,y,x) \ z) = R(x,y,z) * y. [para(1910(a,1),528(a,1))]. 1912 ((x * y) \ 1) * ((x * (y * z)) * T((x * (y * z)) \ (x * y),u)) = K(L(z,y,x) \ 1,u). [para(342(a,1),1866(a,1,1))]. 1914 ((x * y) \ 1) * (x * ((y * z) * T((y * z) \ y,u))) = K(L(z,y,x) \ 1,u). [para(1590(a,1),1912(a,1,2))]. 1915 ((x * y) \ 1) * (x * (y * K(z \ 1,u))) = K(L(z,y,x) \ 1,u). [para(1164(a,1),1914(a,1,2,2))]. 1916 (x * y) \ (x * (y * K(z \ 1,u))) = K(L(z,y,x) \ 1,u). [para(1915(a,1),318(a,1)),flip(a)]. 1917 L(K(x \ 1,y),z,u) = K(L(x,z,u) \ 1,y). [para(1916(a,1),32(a,2))]. 1918 K(L(x \ 1,y,z) \ 1,u) = L(K(x,u),y,z). [para(156(a,1),1917(a,1,1,1)),flip(a)]. 1920 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). [para(750(a,1),1871(a,1,1))]. 1921 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). [para(18(a,1),1920(a,1,1,1))]. 1922 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). [para(18(a,1),1921(a,1,1,2,1))]. 1923 (R(x,y,z) \ 1) \ R(R(x \ 1,x * y,z),u,w) = R(x \ R(x,u,w),y,z). [para(322(a,1),1922(a,1,2)),flip(a)]. 1924 (R(x,y,z) \ 1) \ R(R(x,y,z) \ 1,u,w) = R(x \ R(x,u,w),y,z). [para(584(a,1),1923(a,1,2,1))]. 1925 (R(x,y,z) * 1) \ R(R(x,y,z) * 1,u,w) = R(x \ R(x,u,w),y,z). [para(1924(a,1),750(a,1)),flip(a)]. 1926 R(x,y,z) \ R(R(x,y,z) * 1,u,w) = R(x \ R(x,u,w),y,z). [para(18(a,1),1925(a,1,1))]. 1927 R(x,y,z) \ R(R(x,y,z),u,w) = R(x \ R(x,u,w),y,z). [para(18(a,1),1926(a,1,2,1))]. 1928 R(x \ R(x,y,y),z,u) = a(R(x,z,u),y,y). [para(1927(a,1),962(a,1))]. 1929 T(R(x \ R(x,y,x),z,u),x * (R(x,z,u) * T(y,x))) = a(R(x,z,u),y,x). [para(1927(a,1),743(a,1,1))]. 1930 a(R(x,y,z),u,u) = R(a(x,u,u),y,z). [para(962(a,1),1928(a,1,1)),flip(a)]. 1931 T(R(a(x,y,x),z,u),x * (R(x,z,u) * T(y,x))) = a(R(x,z,u),y,x). [para(1539(a,1),1929(a,1,1,1))]. 1932 T(R(a(x,y,x),z,u),R(x,z,u) * (y * x)) = a(R(x,z,u),y,x). [para(530(a,1),1931(a,1,2))]. 1933 R(T(a(x,y,x),R(x,z,u) * (y * x)),z,u) = a(R(x,z,u),y,x). [para(1932(a,1),46(a,2))]. 1934 ((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). [para(342(a,1),1597(a,1,1))]. 1936 ((x * y) \ 1) * (x * ((y * z) * R((y * z) \ y,u,w))) = L(z,y,x) \ R(L(z,y,x),u,w). [para(1827(a,1),1934(a,1,2))]. 1937 ((x * y) \ 1) * (x * (y * (z \ R(z,u,w)))) = L(z,y,x) \ R(L(z,y,x),u,w). [para(1592(a,1),1936(a,1,2,2))]. 1938 (x * y) \ (x * (y * (z \ R(z,u,w)))) = L(z,y,x) \ R(L(z,y,x),u,w). [para(1937(a,1),318(a,1)),flip(a)]. 1939 L(x,y,z) \ R(L(x,y,z),u,w) = L(x \ R(x,u,w),y,z). [para(1938(a,1),32(a,2)),flip(a)]. 1940 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). [para(1808(a,1),1686(a,1,1,2,1))]. 1941 L((x * (y \ R(y,x,z))) * (1 * u),x * (y \ R(y,x,z)),x) = (y \ R(y,x,z)) * (x * u). [para(1442(a,1),1940(a,1,1,2,1))]. 1942 L((x * (y \ R(y,x,z))) * u,x * (y \ R(y,x,z)),x) = (y \ R(y,x,z)) * (x * u). [para(17(a,1),1941(a,1,1,2))]. 1944 L(x * (R(y,x,z) * (y \ u)),x * (y \ R(y,x,z)),x) = (y \ R(y,x,z)) * (x * u). [para(1450(a,1),1942(a,1,1))]. 1945 L(x * (R(y,x,z) * (y \ u)),x * (y * R(y,x,z)),x) = (y \ R(y,x,z)) * (x * u). [para(1944(a,1),1360(a,1)),flip(a)]. 1946 (x \ R(x,y,z)) * (y * u) = y * (R(x,y,z) * (x \ u)). [para(1945(a,1),1439(a,1))]. 1947 R(x,y,z) * (x \ (y * u)) = y * (R(x,y,z) * (x \ u)). [para(1946(a,1),532(a,1)),flip(a)]. 1948 R(x,y,z) * (x \ (y * (y \ z))) = L(z,x * y,x). [para(1947(a,2),1567(a,1))]. 1949 R(x,y,z) * (x \ z) = L(z,x * y,x). [para(20(a,1),1948(a,1,2,2))]. 1950 R(x,y,L(z,y,x)) * (x \ L(z,y,x)) = z. [para(1949(a,2),303(a,1))]. 1951 L(x,y * z,y) / x = y \ R(y,z,x). [para(1949(a,1),536(a,1,1))]. 1952 x / L(x,y * z,y) = R(y,z,x) \ y. [para(1949(a,1),542(a,1,2))]. 1953 x \ L(x,y * z,y) = y \ R(y,z,x). [para(1951(a,1),515(a,1)),flip(a)]. 1954 L(x,y * z,y) \ x = R(y,z,x) \ y. [para(1952(a,1),519(a,1)),flip(a)]. 1955 x \ R(x,x \ y,z) = z \ L(z,y,x). [para(20(a,1),1953(a,1,2,2)),flip(a)]. 1956 x \ R(x,x * y,z) = z \ L(z,y,x). [para(313(a,1),1953(a,1,2)),flip(a)]. 1957 K(x,R(y,z,x) \ y) = 1. [para(1954(a,1),653(a,1,2))]. 1958 K(x,y \ R(y,z,x)) = 1. [para(622(a,1),1957(a,1,2))]. 1959 T(x,y \ R(y,z,x)) = x. [hyper(41,a,1958,a)]. 1960 K(x,T(y \ R(y,z,x),u)) = 1. [para(1831(a,1),1958(a,1,2))]. 1961 T(x \ R(x,y,z),z) = x \ R(x,y,z). [hyper(39,a,1959,a)]. 1962 K(x,a(y,z,x)) = 1. [para(739(a,2),1960(a,1,2))]. 1963 T(x,a(y,z,x)) = x. [hyper(41,a,1962,a)]. 1964 a(x,y,z) * z = z * a(x,y,z). [para(1963(a,1),82(a,1,2))]. 1965 R(x,y,z) \ x = z \ L(z,y,x). [para(1955(a,1),624(a,1)),flip(a)]. 1966 L(x,y,z) = x * (R(z,y,x) \ z). [para(1965(a,2),20(a,1,2)),flip(a)]. 1967 R(x,y,z) = x / (z \ L(z,y,x)). [para(1965(a,1),65(a,1,2)),flip(a)]. 1968 (x \ L(x,y,z)) \ 1 = z \ R(z,y,x). [para(1965(a,1),460(a,1,1))]. 1969 (x \ L(x,y,z)) * R(z,y,x) = z. [para(1965(a,1),496(a,1,1))]. 1970 L(x,y,z) = (R(z,y,x) \ z) * x. [para(1965(a,2),514(a,1,1)),flip(a)]. 1971 x * (R(K(y,z),u,x) \ K(y,z)) = L(x,u,K(z,y)). [para(1966(a,1),909(a,1))]. 1972 R(x,y,T(z,x * y)) = R(x,y,z). [hyper(23,a,680,a,b,1969,a),flip(a)]. 1973 L(x,y,z) * R(z,y,x) = x * z. [para(1969(a,1),504(a,1,2)),flip(a)]. 1974 L(x,y,z) * (x \ R(z,y,x)) = z. [para(1969(a,1),647(a,1)),flip(a)]. 1975 R(x,y,z) * L(z,y,x) = x * z. [para(1970(a,2),458(a,1,2))]. 1976 L(x,y,z) = (z \ R(z,y,x)) \ x. [para(1970(a,2),465(a,2)),flip(a)]. 1977 T(x \ R(x,y,z),u) \ z = L(z,y,T(x,u)). [para(1970(a,2),1832(a,1)),flip(a)]. 1978 L(x,y,z) \ x = z \ R(z,y,x). [para(1972(a,1),681(a,2,2))]. 1979 R(x,y,z) = x * (L(z,y,x) \ z). [para(1972(a,1),683(a,1))]. 1980 R(x,y,z) * (x \ L(z,y,x)) = z. [para(1972(a,1),686(a,1,1))]. 1981 (L(x,y,z) * (R(z,y,x) * u)) \ ((x * z) * u) = a(L(x,y,z),R(z,y,x),u). [para(1973(a,1),28(a,2,2,1)),flip(a)]. 1984 (L(x,y,z) \ x) * (z * u) = R(z,y,x) * u. [para(1978(a,2),528(a,1,1))]. 1985 (x \ R(x,y,z)) * u = z * (L(z,y,x) \ u). [para(1978(a,1),650(a,1,1))]. 1986 R(x \ R(x,y,z),z,u) = L(z,y,x) \ z. [para(1978(a,1),736(a,1,1))]. 1987 (x * y) * (x \ R(x,y,z)) = R(x,y,z) * y. [para(1978(a,1),1911(a,1,2))]. 1988 K(x,y) \ R(K(x,y),z,u) = u \ L(u,z,K(x,y)). [para(1669(a,1),1956(a,1,2))]. 1989 x \ R(x,y,z) = (L(z,y,x) \ z) * 1. [para(1968(a,1),517(a,1))]. 1990 R(x,y,L(z,y,x)) = R(x,y,z). [hyper(24,a,1980,a,b,1950,a)]. 1991 (x \ R(x,y,z)) \ z = L(z,y,T(x,z)). [para(1961(a,1),1977(a,1,1))]. 1992 L(x,y,T(z,x)) = L(x,y,z). [para(1991(a,1),1976(a,2)),flip(a)]. 1993 L(L(x,y,z),z * y,T(z,L(x,y,z))) = x. [para(1992(a,2),303(a,1))]. 1994 L(x,y,K(z,L(x,y,z))) = x. [para(1993(a,1),1606(a,1)),flip(a)]. 1995 x * (L(x,y,z) \ (z * u)) = R(z,y,x) * u. [para(1984(a,1),650(a,1)),flip(a)]. 1996 L((x \ R(x,y,z)) \ u,x \ R(x,y,z),x * y) = (R(x,y,z) * y) \ ((x * y) * u). [para(1987(a,1),76(a,2,1))]. 1998 L(x,y,z) * (R(z,y,x) * u) = x * (z * u). [para(1995(a,1),645(a,1,2))]. 1999 x * (L(x,y,z) \ (z * T(y,z))) = y * R(z,y,x). [para(1995(a,2),1643(a,1))]. 2000 x * (L(x,y,z) \ (z * L(x,y,z))) = z * x. [para(1995(a,2),1975(a,1))]. 2001 x * T(y,L(x,z,y)) = y * x. [para(36(a,2),2000(a,1,2))]. 2002 T(x,L(y,z,x)) = x * K(x,y). [hyper(23,a,1116,a,b,2001,a)]. 2005 K(x,L(y,z,x)) = K(x,y). [hyper(23,a,1107,a(flip),b,2002,a(flip)),flip(a)]. 2006 L(x,y,K(z,x)) = x. [para(2005(a,1),1994(a,1,3))]. 2007 L(T(x,y),z,K(u,x)) = T(x,y). [para(2006(a,1),44(a,2,1))]. 2008 L(x,y,K(x,z)) = x. [para(2006(a,1),909(a,1)),flip(a)]. 2009 L(x,y,a(x,z,z)) = x. [para(2006(a,1),1262(a,1)),flip(a)]. 2010 L(K(x,y),z,K(u,x \ 1)) = K((x \ 1) \ 1,y). [para(2006(a,1),1918(a,1,1,1)),flip(a)]. 2011 R(K(x,y),z,y) = K(x,y) / (y \ y). [para(2006(a,1),1967(a,2,2,2))]. 2013 (K(x,y) * z) * x = K(x,y) * (z * x). [para(2008(a,1),74(a,1,2))]. 2014 x * (x \ R(a(x,y,y),z,x)) = a(x,y,y). [para(2009(a,1),1974(a,1,1))]. 2015 T(x,K(y,x) * z) = T(x,z). [para(2007(a,1),1377(a,1)),flip(a)]. 2016 K(K(x,y) * z,y) = T(y,z) \ y. [para(2015(a,1),1080(a,2,1))]. 2017 K(x,K(y,x) * z) = x \ T(x,z). [para(2015(a,1),1108(a,2,2))]. 2019 T(x,y * T(z,x)) = T(x,y * z). [para(1212(a,1),2015(a,1,2))]. 2021 K(K(x,y) * z,y) = K(z,y). [para(2016(a,2),1080(a,2)),flip(a)]. 2022 K(K(x,y) * z,x) = K(z,x). [para(901(a,1),2021(a,1,1)),flip(a)]. 2023 K(x * (K(x,y) * z),x) = K(x * z,x). [para(1068(a,1),2022(a,1,1))]. 2024 K(x,K(y,x) * z) = K(x,z). [para(2017(a,2),1108(a,2)),flip(a)]. 2025 K(x,K(x,y) * z) = K(x,z). [para(901(a,1),2024(a,1,2)),flip(a)]. 2026 K(x,y) * K(x * (K(x,z) * y),x) = a(x,K(x,z) * y,x). [para(2025(a,1),1537(a,1,1))]. 2027 R(K(x,y),z,y) = K(x,y) / 1. [para(60(a,1),2011(a,2,2))]. 2029 R(K(x,y),z,y) = K(x,y). [para(2027(a,2),64(a,1))]. 2030 K(x,R(y,z,y)) = K(x,y). [para(2029(a,1),1654(a,1)),flip(a)]. 2031 R(K(x,y),z,x) = K(y,x) \ 1. [para(2029(a,1),1670(a,1,1)),flip(a)]. 2032 K(x,y) * R(T(y,x),z,y) = R(y,z,y). [para(2030(a,1),1083(a,1,1))]. 2033 R(K(x,y),z,x) = K(x,y). [para(2031(a,2),897(a,1))]. 2034 K(L(x,y,x),z) = K(x,z). [para(2033(a,1),1638(a,1)),flip(a)]. 2036 K((x \ y) \ y,z) = K(T(x,y),z). [para(1457(a,1),2034(a,1,1))]. 2038 K(T(x,x \ y),z) = K(T(x,y),z). [para(83(a,2),2036(a,1,1))]. 2039 x \ (K(x,y) * (z * x)) = T(K(x,y) * z,x). [para(2013(a,1),36(a,2,2)),flip(a)]. 2040 x * ((K(x,y) * z) * x) = T(x,y) * (z * x). [para(2013(a,2),1120(a,1,2))]. 2041 T(x,y) \ R(T(x,y),z,x) = x \ R(x,z,x). [para(2032(a,1),1163(a,1,2)),flip(a)]. 2042 x * (x \ a(R(x,y,x),z,z)) = a(x,z,z). [para(1930(a,2),2014(a,1,2,2))]. 2043 x * (x \ a(L(x,y,x),z,z)) = a(x,z,z). [para(1303(a,1),2042(a,1,2,2,1))]. 2044 a(L(x,y,x),z,z) = a(x,z,z). [para(2043(a,1),20(a,1)),flip(a)]. 2045 a(L(T(x,y),y * x,x),z,z) = a(T(x,y),z,z). [para(1283(a,1),2044(a,1,1))]. 2046 K(x,y) * (x \ (z * x)) = T(K(x,y) * z,x). [para(2039(a,1),1076(a,1)),flip(a)]. 2047 (T(x,y) * (z * x)) \ ((T(x,y) * z) * x) = a(x,K(x,y) * z,x). [para(2040(a,1),1166(a,1,1))]. 2048 T(x,y) \ R(T(x,y),z,x) = a(x,z,x). [para(2041(a,2),1539(a,1))]. 2049 T(x \ R(x,y,x),z) = a(x,y,x). [para(2048(a,1),1831(a,1)),flip(a)]. 2050 T(a(x,y,x),z) = a(x,y,x). [para(1539(a,1),2049(a,1,1))]. 2052 a(R(x,y,z),u,x) = R(a(x,u,x),y,z). [para(2050(a,1),1933(a,1,1)),flip(a)]. 2054 a(x,y,x) \ a(R(x,z,z),y,x) = a(a(x,y,x),z,z). [para(2052(a,2),962(a,1,2))]. 2056 T(K(x,y) * z,x) = K(x,y) * T(z,x). [para(36(a,2),2046(a,1,2)),flip(a)]. 2057 T(K(x,y) * R(z,u,w),x) = K(x,y) * R(T(z,x),u,w). [para(46(a,2),2056(a,2,2))]. 2058 T(K(x,y) * z,x) / z = K(z,x) * K(x,y). [para(2056(a,2),1666(a,1,1))]. 2059 T(K(x,y) * z,x) / z = K(x,y) * K(z,x). [para(2058(a,2),1226(a,2)),flip(a)]. 2060 L(K(x,y),z,K(u,x \ 1)) = K(x,y). [para(156(a,1),2010(a,2,1))]. 2061 L(K(x,y),z,K(u,x)) = K(x,y). [para(2060(a,1),1618(a,1)),flip(a)]. 2062 L(K(x,y),z,K(x,u)) = K(x,y). [para(2060(a,1),1619(a,1)),flip(a)]. 2063 (K(x,y) * z) \ z = T(K(y,x),z). [para(2061(a,1),1301(a,1,1)),flip(a)]. 2064 T(K(x,y) * z,K(x,y)) = z * K(x,y). [para(2062(a,1),1309(a,1,1,1))]. 2065 x / T(K(y,z),x) = K(z,y) * x. [para(2063(a,1),65(a,1,2))]. 2067 (T(K(x,y),z) / z) * u = (K(y,x) * z) \ u. [para(2065(a,1),358(a,1,1)),flip(a)]. 2068 (K(x,y) * z) * K(y,x) = T(z,K(y,x)). [para(2065(a,1),1549(a,1,1))]. 2069 K(K(x,y) * z,K(y,x)) = T(z,K(y,x)) / z. [para(2068(a,1),979(a,1,1)),flip(a)]. 2070 K(K(x,y) * z,K(y,x)) = K(z,K(y,x)). [para(2069(a,2),1086(a,2)),flip(a)]. 2071 K(K(x,y) * z,K(x,y)) = K(z,K(x,y)). [para(901(a,1),2070(a,1,1)),flip(a)]. 2072 a(a(K(x,y),z,z),u,w) = a(K(z,K(x,y)),u,w). [para(2071(a,1),1826(a,1,1)),flip(a)]. 2073 a(R(T(x,y),y,x),z,z) = a(T(x,y),z,z). [para(1306(a,1),2045(a,1,1))]. 2074 a(R(x,y,y),z,z) = a(T(x,y),z,z). [para(2073(a,1),1772(a,1)),flip(a)]. 2076 x * (K(y,z) * R(K(z,y),u,x)) = L(x,u,K(z,y)). [para(1671(a,1),1971(a,1,2))]. 2077 x * (K(y,z) * K(z,R(y,u,x))) = L(x,y * u,K(y,z)). [para(1668(a,1),1971(a,1,2))]. 2078 x * (L(x,y,z) \ (y * z)) = y * R(z,y,x). [para(82(a,1),1999(a,1,2,2))]. 2079 L(x,y,z) = (x * (y * z)) / (y * R(z,y,x)). [para(2078(a,1),648(a,1,2)),flip(a)]. 2080 T(K(x,y) * R(y,z,u),x) = y * T(y \ R(y,z,u),x). [para(2057(a,2),1834(a,1))]. 2081 T(K(x,y) * R(y,z,u),x) / R(y,z,u) = K(R(y,z,u) / y,x). [para(2080(a,2),1211(a,1,1))]. 2082 a(x,K(x,y) * z,x) = K(x,z) * K(x * z,x). [para(2023(a,1),2026(a,1,2)),flip(a)]. 2083 a(x,K(x,y) * z,x) = a(x,z,x). [para(2082(a,2),1537(a,1))]. 2085 a(x,K(x,y) * z,x) = a(T(x,y),z,x). [para(2047(a,1),28(a,2)),flip(a)]. 2086 a(T(x,y),z,x) = a(x,z,x). [para(2085(a,1),2083(a,1))]. 2087 a((x \ y) \ y,z,x) = a(x,z,x). [para(83(a,1),2086(a,1,1))]. 2089 a((x \ y) * y,z,x) = a(x,z,x). [para(2087(a,1),1702(a,1)),flip(a)]. 2090 a((x * y) * y,z,x) = a(x,z,x). [para(2089(a,1),1707(a,1)),flip(a)]. 2091 a(R(x,y,y),z,x) = a(x,z,x). [para(2090(a,1),1721(a,1)),flip(a)]. 2092 a(a(x,y,x),z,z) = a(x,y,x) \ a(x,y,x). [para(2091(a,1),2054(a,1,2)),flip(a)]. 2093 a(a(x,y,x),z,z) = 1. [para(2092(a,2),60(a,1))]. 2095 L(x,x,a(y,z,y)) = x. [hyper(37,a,2093,a)]. 2097 L(x,x,a(y,z,z)) = x. [para(2095(a,1),1695(a,2))]. 2098 L(x,x,K(y,z)) = x. [para(2097(a,1),1263(a,1)),flip(a)]. 2099 R(T(a(x,y,y),z),z,z) = z \ (a(x,y,y) * z). [para(2097(a,1),1804(a,1,1)),flip(a)]. 2100 a(K(x,y),z,z) = 1. [hyper(38,a,2098,a)]. 2101 K(x,y) * (z \ 1) = K(x,y) / z. [para(2098(a,1),915(a,1,2)),flip(a)]. 2102 (K(x,y) * (z / u)) \ K(x,y) = u / z. [para(2098(a,1),925(a,1)),flip(a)]. 2103 L(x,K(y,z),x) = x. [para(2098(a,1),1895(a,2))]. 2104 R(K(x,y),z,z) = K(x,y) * 1. [para(2100(a,1),963(a,1,2)),flip(a)]. 2105 a(K(x,K(y,z)),u,w) = a(1,u,w). [para(2100(a,1),2072(a,1,1)),flip(a)]. 2106 T(K(x,y),z) / z = z \ K(x,y). [para(2103(a,1),441(a,1,2))]. 2107 K(x,R(y,z,z)) = K(x,y). [hyper(24,a,1767,a,b,2104,a(flip)),flip(a)]. 2108 K(x,y / (z \ 1)) = K(x,y * z). [para(720(a,1),2107(a,1,2)),flip(a)]. 2112 K(x,y) * (x / z) = T(x,y) / z. [para(2107(a,1),1815(a,1,1))]. 2114 K(x,y) / (z \ 1) = K(x,y) * z. [para(156(a,1),2101(a,1,2)),flip(a)]. 2115 a(K(x,K(y,z)),u,w) = 1. [para(2105(a,2),125(a,1))]. 2117 L(x,y,K(z,K(u,w))) = x. [hyper(37,a,2115,a)]. 2119 x * (x \ R(K(y,K(z,u)),w,x)) = K(y,K(z,u)). [para(2117(a,1),1974(a,1,1))]. 2121 (K(x,y) * z) \ u = (z \ K(y,x)) * u. [para(2106(a,1),2067(a,1,1)),flip(a)]. 2122 K(x,R(((y \ 1) * z) \ 1,z,z)) = K(x,(z \ 1) * y). [para(1739(a,2),2108(a,1,2))]. 2123 T(x,y) / (z \ x) = K(x,y) * z. [para(65(a,1),2112(a,1,2)),flip(a)]. 2125 (K(x,y) * z) \ K(x,y) = z \ 1. [para(2114(a,1),66(a,1,1))]. 2126 (K(x,y) * z) \ T(x,y) = z \ x. [para(2123(a,1),66(a,1,1))]. 2127 (K(x,y) \ z) \ 1 = z \ K(x,y). [para(20(a,1),2125(a,1,1)),flip(a)]. 2129 L(x \ y,x,K(z,y)) = x \ y. [para(2126(a,1),1248(a,2))]. 2130 a(K(x,y),z,z \ y) = 1. [hyper(38,a,2129,a)]. 2132 a(K(x,y * z),y,z) = 1. [para(19(a,1),2130(a,1,3))]. 2133 (K(x,y) \ z) \ u = (z \ K(x,y)) * u. [para(2127(a,1),318(a,1,1)),flip(a)]. 2137 ((x / y) \ K(z,u)) * K(u,z) = y / x. [para(2121(a,1),2102(a,1))]. 2140 x / K(y,z) = x * K(z,y). [para(66(a,1),2137(a,1,1)),flip(a)]. 2144 (K(x,y) * z) / K(x,y) = T(z,K(y,x)). [para(2140(a,2),2068(a,1))]. 2145 T(x,K(y,z)) \ x = K(x,K(z,y)). [para(2144(a,1),1053(a,2,1)),flip(a)]. 2146 K(K(x,y),z) = K(z,K(y,x)). [para(2145(a,1),1080(a,2))]. 2147 K(x,K(y,z)) * K(x,K(z,y)) = 1. [para(2146(a,1),898(a,1,1))]. 2148 K(x,y) * K(z,K(y,x)) = T(K(x,y),z). [para(2146(a,1),1107(a,2,2)),flip(a)]. 2149 K(x,y) * T(K(y,x),z) = K(z,K(x,y)). [para(2146(a,1),1114(a,2))]. 2150 T(K(x,y),z) \ 1 = T(K(y,x),z). [para(2148(a,1),1140(a,1)),flip(a)]. 2151 T(K(x,y),z) * T(K(y,x),z) = 1. [para(2150(a,1),20(a,1,2))]. 2152 T(K(x,y),z) * K(y,x) = K(z,K(y,x)). [para(2149(a,1),405(a,2))]. 2153 R(T(a(x,y,y),z),z,z) = T(a(x,y,y),z). [para(2099(a,2),36(a,2)),flip(a)]. 2154 R(T(a(x,y,y),z),z,z) = a(T(x,z),y,y). [para(2153(a,2),1836(a,2)),flip(a)]. 2155 R(a(T(x,y),z,z),y,y) = a(T(x,y),z,z). [para(1836(a,2),2154(a,1,1))]. 2156 a(R(T(x,y),y,y),z,z) = a(T(x,y),z,z). [para(2155(a,1),1930(a,2))]. 2157 a(T(T(x,y),y),z,z) = a(T(x,y),z,z). [para(2156(a,1),2074(a,1)),flip(a)]. 2158 a(T(x,y),z,z) = a(x,z,z). [para(2157(a,1),1724(a,1))]. 2161 (x * (y * (a(y,z,z) * u))) / (R(T(y,x),z,z) * u) = T(x,y). [para(2158(a,1),1210(a,1,1,2,2,1))]. 2165 R(K(x,K(y,z)),u,w) = K(x,K(y,z)). [para(2119(a,1),20(a,1)),flip(a)]. 2166 K(x,R(K(y,z),u,w)) = K(x,K(y,z)). [para(2165(a,1),1654(a,1)),flip(a)]. 2167 K(x,K(y,R(z,u,w))) = K(x,K(y,z)). [para(1654(a,1),2166(a,1,2))]. 2168 K(K(R(x,y,z),u),w) = K(w,K(u,x)). [para(2167(a,1),2146(a,2))]. 2169 K(R(K(x,y),z,u),w) = K(w,K(y,x)). [para(1634(a,1),2168(a,1,1))]. 2170 K(x,R((y \ z) \ 1,z,z)) = K(x,(z \ 1) * y). [para(318(a,1),2122(a,1,2,1,1))]. 2171 K(x,(y \ z) \ 1) = K(x,(z \ 1) * y). [para(2170(a,1),2107(a,1)),flip(a)]. 2172 K(x,(y \ z) \ 1) = K(x,z \ y). [para(318(a,1),2171(a,2,2))]. 2174 K(x,(y / z) \ y) = K(x,z / (a(y,z,z) \ 1)). [para(2172(a,1),1447(a,1))]. 2175 K(x,y / (a(z,y,y) \ 1)) = K(x,y). [para(66(a,1),2174(a,1,2)),flip(a)]. 2176 K(x,y * a(z,y,y)) = K(x,y). [para(1445(a,1),2175(a,1,2))]. 2177 K(x * a(y,x,x),z) = (z \ 1) / (z \ K(z,x)). [para(2176(a,1),1057(a,1,2,2)),flip(a)]. 2178 K(x * a(y,x,x),z) = K(x,z). [para(2177(a,2),1057(a,1))]. 2179 (x / y) * T(y,z) = x * K(y,z). [para(2178(a,1),1463(a,1,2)),flip(a)]. 2180 (x * y) * K(y,z) = x * T(y,z). [para(21(a,1),2179(a,1,1)),flip(a)]. 2183 L(K(x,y),x,z) = K(x,y). [hyper(23,a,1117,a,b,2180,a),flip(a)]. 2187 L(K(T(x,y),z),x,y) = K(T(x,y),z). [para(2183(a,1),1376(a,1)),flip(a)]. 2192 T(K(x,y),x * z) = K(T(x,z),y). [para(2187(a,1),1522(a,1)),flip(a)]. 2193 K(T(x,x \ y),z) = T(K(x,z),y). [para(20(a,1),2192(a,1,2)),flip(a)]. 2194 K(T(x,y),z) = T(K(x,z),y). [para(2193(a,1),2038(a,1)),flip(a)]. 2195 K(x,T(y,z)) * T(K(y,x),z) = 1. [para(2194(a,1),898(a,1,2))]. 2196 K(T(x,y * T(T(y,x),x)),z) = T(T(K(x,z),y),T(y,x)). [para(2194(a,2),1905(a,1))]. 2197 K(x,T(y,z)) = T(K(x,y),z). [hyper(24,a,2151,a,b,2195,a)]. 2199 K(x,y) * K(y,T(x,z)) = K(K(y,x),z). [para(2197(a,2),1114(a,1,2))]. 2200 K(x,T(y,z \ 1)) * z = z * K(x,y). [para(2197(a,2),1907(a,1,1))]. 2202 K(x,y) * K(y,T(x,z)) = K(z,K(x,y)). [para(2197(a,2),2149(a,1,2))]. 2203 K(x,T(y,z)) * K(y,x) = K(z,K(y,x)). [para(2197(a,2),2152(a,1,1))]. 2204 K(T(x,y),z) = K(x,T(z,y)). [para(2197(a,2),2194(a,2))]. 2205 K(x,T(y,z)) * K(y,x) = K(K(x,y),z). [para(2199(a,1),1226(a,2))]. 2206 K(x,T(y,z)) * K(y,x) = K(x,K(y,z)). [para(2202(a,1),1873(a,2))]. 2207 K(x,y) * K(x,K(y,z)) = K(x,T(y,z)). [para(2206(a,1),1225(a,1,2))]. 2208 K(x,K(y,z)) = K(z,K(y,x)). [para(2206(a,1),2203(a,1))]. 2209 K(K(x,y),z) = K(x,K(y,z)). [para(2206(a,1),2205(a,1)),flip(a)]. 2210 1 / K(x,K(y,z)) = K(K(y,x),z). [para(2208(a,1),899(a,1,2))]. 2211 K(K(x,y),z) = K(K(x,z),y). [para(2210(a,1),899(a,1))]. 2212 K(K(x,y),z) = K(y,K(z,x)). [para(2211(a,1),2146(a,1))]. 2213 K(x,K(y,z)) = K(z,K(x,y)). [para(2212(a,1),2209(a,1))]. 2214 T(K(x,y) * K(x,K(y,z)),z) = K(x,y). [para(2213(a,2),1020(a,1,1,2))]. 2215 T(K(x,T(y,z)),z) = K(x,y). [para(2207(a,1),2214(a,1,1))]. 2216 K(x,T(y,z)) * z = z * K(x,y). [para(2215(a,1),82(a,1,2)),flip(a)]. 2217 K(x,T(T(y,z),z)) = K(x,y). [para(2215(a,1),2197(a,2))]. 2219 K(x,T(y,z \ 1)) = K(x,T(y,z)). [hyper(24,a,2200,a,b,2216,a),flip(a)]. 2220 T(K(x,y) * z,K(x,y)) = K(x,T(y,z)) * z. [para(2216(a,2),2064(a,2))]. 2221 K(x,T(y,z \ (z \ (u \ 1)))) = K(x,T(y,u * (z * z))). [para(409(a,1),2219(a,1,2,2))]. 2222 K(T(x,y * T(y,x)),z) = T(T(K(x,z),y),T(y,x)). [para(2019(a,1),2196(a,1,1))]. 2223 T(T(K(x,y),z),T(z,x)) = K(T(x,z * z),y). [para(2019(a,1),2222(a,1,1)),flip(a)]. 2224 T(T(K(x,y),z),T(z,x)) = K(x,T(y,z * z)). [para(2223(a,2),1278(a,1))]. 2225 T(K(x,T(y,z)),T(z,x)) = K(x,T(y,z * z)). [para(2197(a,2),2224(a,1,1))]. 2226 K(T(x,T(y,x)),T(z,y)) = K(x,T(z,y * y)). [para(2225(a,1),2194(a,2))]. 2227 K(T(x,y),T(z,y)) = K(x,T(z,y * y)). [para(1131(a,1),2226(a,1,1))]. 2228 K(x,T(T(y,z),z)) = K(x,T(y,z * z)). [para(2227(a,1),2204(a,1)),flip(a)]. 2229 K(x,T(y,z * z)) = K(x,y). [para(2228(a,1),2217(a,1))]. 2230 K(x,T(y,z * (z * u))) = K(x,T(y,u)). [para(662(a,1),2229(a,1,2))]. 2232 K(x,T(y,z \ u)) = K(x,T(y,z * u)). [para(20(a,1),2230(a,1,2,2,2)),flip(a)]. 2233 K(x,T(y,T(z,z * u))) = K(x,T(y,(z \ u) * u)). [para(250(a,1),2230(a,1,2,2,2)),flip(a)]. 2234 K(x,T(y,(z / u) * (z * z))) = K(x,T(y,u / (z \ 1))). [para(399(a,1),2230(a,1,2,2,2))]. 2235 K(x,T(y,z \ (z \ u))) = K(x,T(y,u)). [para(20(a,1),2232(a,2,2,2))]. 2236 K(x,T(y,z * (u * u))) = K(x,T(y,z \ 1)). [para(2221(a,1),2235(a,1))]. 2237 K(x,T(y,z * (u * u))) = K(x,T(y,z)). [para(2236(a,2),2219(a,1))]. 2239 K(x,T(y,z / (u \ 1))) = K(x,T(y,u / z)). [para(2234(a,1),2237(a,1))]. 2241 (x * (R(y,z,z) * u)) / (R(T(y,x),z,z) * u) = T(x,y). [para(966(a,1),2161(a,1,1,2))]. 2243 T(x,R(y,z,z)) = T(x,y). [para(2241(a,1),1209(a,1)),flip(a)]. 2244 T(x,y / (z \ 1)) = T(x,y * z). [para(720(a,1),2243(a,1,2)),flip(a)]. 2246 K(x,T(y,z / u)) = K(x,T(y,u * z)). [para(2244(a,1),2239(a,1,2)),flip(a)]. 2247 K(x,T(y,(z \ u) * u)) = K(x,T(y,z)). [para(65(a,1),2246(a,1,2,2)),flip(a)]. 2248 K(x,T(y,T(z,z * u))) = K(x,T(y,z)). [para(2247(a,1),2233(a,2))]. 2249 K(x,T(y,T(z,u))) = K(x,T(y,z)). [para(20(a,1),2248(a,1,2,2,2))]. 2251 K(x,K(y,T(z,u))) = K(x,T(y,z)) * K(y,x). [para(2249(a,1),2206(a,1,1)),flip(a)]. 2253 K(x,K(y,T(z,u))) = K(x,K(y,z)). [para(2251(a,2),2206(a,1))]. 2254 K(x,K(y,z \ R(z,u,w))) = K(x,K(y,a(z,u,w))). [para(739(a,2),2253(a,1,2,2)),flip(a)]. 2255 K(x,K(y \ R(y,z,u),w)) = K(x,K(w,a(y,z,u))). [para(1849(a,2),2254(a,1,2))]. 2260 K(x,y) * K(R(y,z,u),x) = K(R(y,z,u) / y,x). [para(2081(a,1),2059(a,1)),flip(a)]. 2261 K(x,y) * K(R(y,z,u),x) = K(y \ R(y,z,u),x). [para(478(a,1),2260(a,2,1))]. 2262 K(x,y) * K(R(y,z,u),x) = K(x,y \ R(y,z,u)). [para(2261(a,2),1849(a,1))]. 2263 K(x,K(y,z) \ R(K(y,z),u,w)) = K(x,K(y,z)) * K(x,K(z,y)). [para(2169(a,1),2262(a,1,2)),flip(a)]. 2265 K(x,K(y,z) \ R(K(y,z),u,w)) = 1. [para(2263(a,2),2147(a,1))]. 2266 K(x,K(y,z) \ K(R(y,u,w),z)) = 1. [para(1629(a,1),2265(a,1,2,2))]. 2268 K(x,K(y,z) * K(R(z,u,w),y)) = 1. [para(900(a,1),2266(a,1,2))]. 2269 K(x,K(y \ R(y,z,u),w)) = 1. [para(2261(a,1),2268(a,1,2))]. 2270 K(x,K(y,a(z,u,w))) = 1. [para(2269(a,1),2255(a,1)),flip(a)]. 2271 T(x,K(y,a(z,u,w))) = x. [hyper(41,a,2270,a)]. 2273 K(x,T(a(y,z,u),w)) = K(x,a(y,z,u)). [hyper(24,a,2220,a(flip),b,2271,a(flip)),flip(a)]. 2274 K(x,y \ R(y,z,u)) = K(x,a(y,z,u)). [para(1839(a,1),2273(a,1,2))]. 2275 K(x,y \ R(y,z,u)) = K(a(y,z,u),x). [para(2274(a,2),1847(a,2)),flip(a)]. 2276 K(x \ R(x,y,z),u) = K(u,a(x,y,z)). [para(2274(a,1),1849(a,2))]. 2277 K(x,a(y,z,L(u,z,y))) = K(x,y \ R(y,z,u)). [para(1990(a,1),2274(a,1,2,2)),flip(a)]. 2278 K(x,y) * K(R(y,z,u),x) = K(x,a(y,z,u)). [para(2274(a,1),2262(a,2))]. 2279 K(x,a(K(y,z),u,w)) = 1. [para(2274(a,1),2265(a,1))]. 2280 T(x,a(K(y,z),u,w)) = x. [hyper(41,a,2279,a)]. 2281 ((K(x,y) * z) * u) / (K(x,y) * (z * u)) = a(K(x,y),z,u). [para(2280(a,1),300(a,1,2))]. 2282 K(R(x,y,z) \ x,u) = K(u,a(x,x * y,z)). [para(618(a,1),2276(a,1,1))]. 2283 K(x,y) * K(y,R(x,z,u)) = K(y,a(x,z,u)). [para(2278(a,1),1674(a,1)),flip(a)]. 2284 L(x,y * z,K(y,u)) = x * K(u,a(y,z,x)). [para(2283(a,1),2077(a,1,2)),flip(a)]. 2285 K(x,a(y,z,L(u,z,y))) = K(x,a(y,z,u)). [para(2277(a,2),2274(a,1))]. 2286 K(x,y) \ R(K(x,y),z,u) = a(K(x,y),z,u). [para(2281(a,1),537(a,1)),flip(a)]. 2287 x \ L(x,y,K(z,u)) = a(K(z,u),y,x). [para(2286(a,1),1988(a,1)),flip(a)]. 2288 x * a(K(y,z),u,x) = L(x,u,K(y,z)). [para(2287(a,1),20(a,1,2))]. 2289 a(K(x,y),x * z,u) = K(y,a(x,z,u)). [hyper(23,a,2284,a(flip),b,2288,a)]. 2290 x * a(K(y,z),u,x) = L(x,u,K(z,y)). [para(905(a,1),2288(a,1,2))]. 2291 K(x,a(y,y * z,u)) = a(K(y,x),z,u). [para(2289(a,1),1778(a,1))]. 2292 K((x * y) * z,a(x,y,z)) = 1. [para(2289(a,1),2132(a,1))]. 2293 K(x * (y * z),a(x,y,L(z,y,x))) = 1. [para(74(a,1),2292(a,1,1))]. 2294 K(x,a(y,y * z,u)) = a(K(x,y),z,u). [para(2291(a,2),905(a,1))]. 2295 K(x * (y * z),a(x,y,z)) = 1. [para(2293(a,1),2285(a,1)),flip(a)]. 2296 x \ R(x,y,z) = a(x,y,z) * 1. [para(2295(a,1),1848(a,1,2)),flip(a)]. 2297 a(x,y,z) = x \ R(x,y,z). [hyper(24,a,18,a,b,2296,a(flip))]. 2298 a(x,y,z) = L(z,y,x) \ z. [hyper(24,a,1989,a(flip),b,2296,a(flip))]. 2302 R(x,y,z) \ x = a(x,y,z) \ 1. [para(2297(a,2),462(a,1,1)),flip(a)]. 2306 x * (a(x,y,z) * u) = R(x,y,z) * u. [para(2297(a,2),501(a,1,2,1))]. 2308 a(x,y,z) * (x * u) = R(x,y,z) * u. [para(2297(a,2),528(a,1,1))]. 2310 a(x,x * y,z) = R(x,y,z) \ x. [para(2297(a,2),618(a,1))]. 2313 a(x,y,z) = x * R(x \ 1,y,z). [para(2297(a,2),635(a,2)),flip(a)]. 2317 T(x \ R(x,y,z),u) = a(T(x,u),y,z). [para(2297(a,2),1831(a,1)),flip(a)]. 2318 R(x \ R(x,y,z),u,w) = a(R(x,u,w),y,z). [para(2297(a,2),1927(a,1)),flip(a)]. 2319 L(x \ R(x,y,z),u,w) = a(L(x,u,w),y,z). [para(2297(a,2),1939(a,1)),flip(a)]. 2323 x * (L(x,y,z) \ u) = a(z,y,x) * u. [para(2297(a,2),1985(a,1,1)),flip(a)]. 2332 L(x,y,z) \ (x * u) = a(z,y,x) * u. [para(2298(a,2),524(a,2,1))]. 2333 a(x,y,z) * (L(z,y,x) * u) = z * u. [para(2298(a,2),646(a,1,1))]. 2336 a(T(x,y),z,y) = L(y,z,x) \ y. [para(1992(a,1),2298(a,2,1))]. 2340 K(a(x,y,z) \ 1,u) = K(u,a(x,x * y,z)). [para(2302(a,1),2282(a,1,1))]. 2341 a(x,x * y,z) = a(x,y,z) \ 1. [para(2310(a,2),2302(a,1))]. 2344 L(x,a(y,z,u),z) = x. [para(2313(a,2),1443(a,1,2))]. 2347 (x * a(y,x,z)) * u = x * (a(y,x,z) * u). [para(2344(a,1),74(a,1,2))]. 2348 (x \ a(y,x,z)) \ 1 = a(y,x,z) \ x. [para(2344(a,1),259(a,1)),flip(a)]. 2349 (x \ a(y,x,z)) \ u = a(y,x,z) \ (x * u). [para(2344(a,1),267(a,1)),flip(a)]. 2358 a(T(x,y),z,y) = a(x,z,y). [para(2336(a,2),2298(a,2)),flip(a)]. 2366 K(a(x,x * y,z),u) = a(K(u,x),y,z). [para(2294(a,1),1847(a,2))]. 2368 x * (y * a(x,z,y)) = R(x,z,y) * y. [para(1964(a,1),2306(a,1,2))]. 2370 a(T(x,y),z,u) = T(a(x,z,u),y). [para(2297(a,2),2317(a,1,1)),flip(a)]. 2371 a(T(x,y),z,u) \ a(x,z,u) = K(y,a(x,z,u)). [para(2370(a,2),1080(a,2,1)),flip(a)]. 2372 a(T(x,y),y,z) = a(x,y,z). [para(2370(a,2),1687(a,1))]. 2373 a(x,T(y,x),z) = a(x,y,z). [para(2372(a,1),1790(a,1)),flip(a)]. 2374 a(x / y,y,z) = a(y * x,y,z). [para(2373(a,1),1810(a,1)),flip(a)]. 2375 a(x / y,x,z) = a(x * y,x,z). [para(2374(a,1),612(a,1)),flip(a)]. 2378 a(x,y,z) * (z * u) = z * (a(x,y,z) * u). [para(2332(a,1),2323(a,1,2)),flip(a)]. 2380 a(x,y,z) * (z * x) = z * R(x,y,z). [para(1973(a,1),2333(a,1,2))]. 2386 (x \ a(y,x,z)) \ u = (a(y,x,z) \ x) * u. [para(2348(a,1),318(a,1,1)),flip(a)]. 2388 K(a(x,y,z) \ 1,u) = a(K(u,x),y,z). [para(2341(a,1),2366(a,1,1))]. 2389 (x * y) * L(a(x,z,y),y,x) = R(x,z,y) * y. [para(2368(a,1),74(a,2))]. 2393 a(R(x,y,z),u,y) = L(y,u,x) \ y. [para(2318(a,1),1986(a,1))]. 2394 a(R(x,y,z),u,w) = R(a(x,u,w),y,z). [para(2297(a,2),2318(a,1,1)),flip(a)]. 2396 a(R(x,y,z),u,y) = a(x,u,y). [para(2393(a,2),2298(a,2)),flip(a)]. 2400 a(L(x,y,x),z,y) = a(x,z,y). [para(1312(a,1),2396(a,1,1)),flip(a)]. 2404 R(a(x,y,z),x * u,w) = a(R(x,u,w),y,z). [para(2394(a,1),1718(a,1))]. 2406 a(L(x,y,z),u,w) = L(a(x,u,w),y,z). [para(2297(a,2),2319(a,1,1)),flip(a)]. 2410 K(x,a(y / z,(y / z) * z,u)) = K(a(z * y,z,u) \ 1,x). [para(2374(a,1),2340(a,1,1,1)),flip(a)]. 2411 (a(x,y,z) * y) * u = y * (a(x,y,z) * u). [para(1688(a,2),2347(a,1,1))]. 2412 a(x,y,z) \ (y * u) = (a(x,y,z) \ y) * u. [para(2386(a,1),2349(a,1)),flip(a)]. 2413 L(x,y,a(z,y,u)) = x. [hyper(23,a,798,a,b,2412,a(flip)),flip(a)]. 2414 (a(x,y,z) * y) * u = a(x,y,z) * (y * u). [para(2413(a,1),74(a,1,2))]. 2415 (a(x,y,z) * (y \ 1)) * u = a(x,y,z) * (y \ u). [para(2413(a,1),945(a,1,2))]. 2417 a(x,y,z) * (y * u) = y * (a(x,y,z) * u). [para(2414(a,1),2411(a,1))]. 2419 (x * y) \ (x * (a(z,x,u) * y)) = T(a(z,x,u),x * y). [para(2417(a,1),36(a,2,2)),flip(a)]. 2421 (x * y) * a(L(x,y,x),z,y) = R(x,z,y) * y. [para(2406(a,2),2389(a,1,2))]. 2422 (x * y) * a(x,z,y) = R(x,z,y) * y. [para(2400(a,1),2421(a,1,2))]. 2423 (x * (R(y,z,u) * u)) / ((y * u) * R(a(y,z,u),y * u,x)) = L(x,y * u,a(y,z,u)). [para(2422(a,1),2079(a,2,1,2)),flip(a)]. 2424 (x \ a(y,x,z)) * u = a(y,x,z) * (x \ u). [para(1795(a,1),2415(a,1,1))]. 2425 (a(x,y,z) * (y \ u)) \ ((y \ a(x,y,z)) * (u * w)) = L(w,u,y \ a(x,y,z)). [para(2424(a,1),32(a,2,1)),flip(a)]. 2426 L(T(a(x,y,z),u),u,y) = T(a(x,y,z),y * u). [para(2419(a,1),106(a,1)),flip(a)]. 2427 L(a(T(x,y),z,u),y,z) = T(a(x,z,u),z * y). [para(2370(a,2),2426(a,1,1))]. 2429 K(a(x * y,x,z) \ 1,u) = K(u,a(y / x,y,z)). [para(22(a,1),2410(a,1,2,2)),flip(a)]. 2430 K(a(x * y,x,z) \ 1,u) = K(u,a(y * x,y,z)). [para(2375(a,1),2429(a,2,2))]. 2431 K(x,a(y * z,y,u)) = a(K(x,z * y),z,u). [para(2430(a,1),2388(a,1))]. 2432 a(L(x,y,z),R(z,y,x),u) = (x * (z * u)) \ ((x * z) * u). [para(1998(a,1),1981(a,1,1)),flip(a)]. 2433 a(L(x,y,z),R(z,y,x),u) = a(x,z,u). [para(2432(a,2),28(a,2)),flip(a)]. 2435 L(a(x,R(y,z,x),u),z,y) = a(x,y,u). [para(2433(a,1),2406(a,1)),flip(a)]. 2436 (a(x,y,z) * (y \ u)) \ (a(x,y,z) * (y \ (u * w))) = L(w,u,y \ a(x,y,z)). [para(2424(a,1),2425(a,1,2))]. 2437 L(L(x,y,z),z * y,a(u,z,w)) = L(x,y,z \ a(u,z,w)). [para(2436(a,1),1409(a,1)),flip(a)]. 2438 L(L(x,y,z),z * y,a(u,z,w)) = L(x,y,z * a(u,z,w)). [para(2437(a,2),776(a,1))]. 2439 (R(x,y,z) * y) \ ((x * y) * u) = (x \ R(x,y,z)) \ u. [para(1996(a,1),1411(a,1))]. 2440 L(x,y,R(z,y,x)) = (z \ R(z,y,x)) \ x. [para(2439(a,1),183(a,1)),flip(a)]. 2441 L(x,y,R(z,y,x)) = L(x,y,z). [para(2440(a,2),1976(a,2)),flip(a)]. 2442 L(x,y * z,R(y,z,x) \ 1) = L(x,y * z,y \ 1). [para(584(a,1),2441(a,1,3))]. 2443 L(x,y * z,R(y,z,x)) = L(x,y * z,y \ 1). [para(2442(a,1),787(a,1)),flip(a)]. 2444 L(x,y * z,R(y,z,x)) = L(x,y * z,y). [para(2443(a,2),787(a,1))]. 2445 R(x,y,z) * (L(z,x * y,x) \ z) = R(R(x,y,z),x * y,z). [para(2444(a,1),1979(a,2,2,1)),flip(a)]. 2446 R(x,y,z) * (R(x,y,z) \ x) = R(R(x,y,z),x * y,z). [para(1954(a,1),2445(a,1,2))]. 2447 R(R(x,y,z),x * y,z) = x. [para(2446(a,1),20(a,1))]. 2448 R(R(x,x * y,z),y,z) = x. [para(2447(a,1),50(a,1)),flip(a)]. 2449 K(x,R(y,y * z,u) \ R(R(y,y * z,u),z,u)) = K(x,R(y,y * z,u)) * K(y,x). [para(2448(a,1),2262(a,1,2,1)),flip(a)]. 2450 K(x,R(y,y * z,u) \ R(R(y,y * z,u),z,u)) = R(K(x,y),z,u) * K(y,x). [para(1672(a,1),2449(a,2,1))]. 2451 K(x,R(y,y * z,u) \ R(R(y,y * z,u),z,u)) = K(y,x) * R(K(x,y),z,u). [para(2450(a,2),406(a,1))]. 2452 K(x,R(y,y * z,u) \ y) = K(y,x) * R(K(x,y),z,u). [para(2448(a,1),2451(a,1,2,2))]. 2453 K(x,y) * R(K(y,x),z,u) = K(y,x \ R(x,z,u)). [para(622(a,1),2452(a,1,2)),flip(a)]. 2454 x * K(y,z \ R(z,u,x)) = L(x,u,K(y,z)). [para(2453(a,1),2076(a,1,2))]. 2455 x * K(a(y,z,x),u) = L(x,z,K(u,y)). [para(2275(a,1),2454(a,1,2))]. 2456 a(K(x,y),z,u) = K(a(x,z,u),y). [hyper(23,a,2290,a,b,2455,a),flip(a)]. 2457 a(K(x,y),z,u) = K(a(y,z,u),x). [hyper(23,a,2288,a,b,2455,a),flip(a)]. 2458 a(K(x,y),z,u) = K(y,a(x,z,u)). [para(2456(a,2),1847(a,1))]. 2459 a(K(x,y),z,u) = K(x,a(y,z,u)). [para(2457(a,2),1847(a,1))]. 2460 x * K(y,a(z,u,x)) = L(x,u,K(z,y)). [para(2458(a,1),2288(a,1,2))]. 2461 K(x * y,a(z,x,u)) = K(z,a(y * x,y,u)). [para(2458(a,1),2431(a,2)),flip(a)]. 2462 K(x,a(y,z,u)) = K(y,a(x,z,u)). [para(2459(a,1),2458(a,1))]. 2463 L(x,y * z,K(y,u)) = L(x,z,K(y,u)). [para(2460(a,1),2284(a,2))]. 2464 (x * (R(y,z,u) * u)) / ((y * u) * a(R(y,u,x),z,u)) = L(x,y * u,a(y,z,u)). [para(2404(a,1),2423(a,1,2,2))]. 2465 (x * (R(y,z,u) * u)) / ((y * u) * a(y,z,u)) = L(x,y * u,a(y,z,u)). [para(2396(a,1),2464(a,1,2,2))]. 2467 (x * (R(y,z,u) * u)) / (R(y,z,u) * u) = L(x,y * u,a(y,z,u)). [para(2422(a,1),2465(a,1,2))]. 2468 L(x,y * z,a(y,u,z)) = x. [para(2467(a,1),21(a,1))]. 2469 L(x,y * z,a(T(z,y),u,y)) = x. [para(2468(a,1),1185(a,1)),flip(a)]. 2470 L(x,y * z,a(z,u,y)) = x. [para(2358(a,1),2469(a,1,3))]. 2471 (a(x,y,z) * (z * x)) \ (a(x,y,z) * (z * (x * u))) = L(u,x,z). [para(2470(a,1),174(a,2))]. 2472 (x * R(y,z,x)) \ (a(y,z,x) * (x * (y * u))) = L(u,y,x). [para(2380(a,1),2471(a,1,1))]. 2473 (x * R(y,z,x)) \ (x * (a(y,z,x) * (y * u))) = L(u,y,x). [para(2378(a,1),2472(a,1,2))]. 2474 (x * R(y,z,x)) \ (x * (R(y,z,x) * u)) = L(u,y,x). [para(2308(a,1),2473(a,1,2,2))]. 2475 L(x,R(y,z,u),u) = L(x,y,u). [para(2474(a,1),32(a,2))]. 2476 a(x,R(y,z,x),u) = L(u,y,x) \ u. [para(2475(a,1),2298(a,2,1))]. 2477 a(x,R(y,z,x),u) = a(x,y,u). [para(2476(a,2),2298(a,2)),flip(a)]. 2478 L(a(x,y,z),u,y) = a(x,y,z). [para(2477(a,1),2435(a,1,1))]. 2480 T(a(x,y,z),y * u) = a(T(x,u),y,z). [para(2478(a,1),2427(a,1)),flip(a)]. 2484 a(T(x,y),z,u) \ a(x,z,u) = K(z * y,a(x,z,u)). [para(2480(a,1),1080(a,2,1)),flip(a)]. 2494 K(x * y,a(z,x,u)) = K(y,a(z,x,u)). [para(2484(a,1),2371(a,1))]. 2495 K(x,a(y * z,y,u)) = K(z,a(x,y,u)). [para(2494(a,1),2462(a,1)),flip(a)]. 2496 K(x,a(y * z,y,u)) = K(y,a(x,z,u)). [para(2494(a,1),2461(a,1)),flip(a)]. 2497 K(x,a(y,z,u)) = K(z,a(y,x,u)). [para(2496(a,1),2495(a,1))]. 2498 x * K(y,a(z,u,x)) = L(x,y,K(z,u)). [para(2497(a,1),2460(a,1,2))]. 2499 L(x,y,K(z,u)) = L(x,u,K(z,y)). [para(2498(a,1),2460(a,1))]. 2501 L(x,y,K(z,z * u)) = L(x,u,K(z,y)). [para(2499(a,1),2463(a,1))]. 2502 L(x,y,a(z,u,u)) = L(x,u,K(z,y)). [para(2501(a,1),1261(a,1)),flip(a)]. 2503 L(x,y,a(z,u,u)) = L(x,y,K(z,u)). [para(2502(a,2),2499(a,1))]. 2504 L(x,y,a(z,u,z)) = L(x,y,K(u,z)). [para(2503(a,1),1695(a,1)),flip(a)]. 2505 L(L(x,y,z),z * y,K(z,u)) = L(x,y,z * a(u,z,u)). [para(2504(a,1),2438(a,1))]. 2506 L(x,y,z * a(u,z,u)) = L(x,y,T(z,u)). [para(2505(a,1),1604(a,1))]. 2507 L(x,y,R(z,u,u)) = L(x,y,T(z,u)). [para(2506(a,1),1692(a,1)),flip(a)]. 2508 L(x,y,T(z / u,z)) = L(x,y,u * z). [para(2507(a,1),846(a,1))]. 2509 L(x,y,z * u) = L(x,y,u * z). [para(2508(a,1),845(a,1))]. 2510 L(L(x,y,z * u),(z * u) * y,u * z) = x. [para(2509(a,1),303(a,1))]. 2515 L(x,y,K(z,u)) = x. [para(2510(a,1),1850(a,1)),flip(a)]. 2520 (K(x,y) \ z) \ u = z \ (K(x,y) * u). [para(2515(a,1),267(a,1)),flip(a)]. 2632 x \ (K(y,z) * u) = (x \ K(y,z)) * u. [para(2520(a,1),2133(a,1))]. 2646 L(x,K(y,z),u) = x. [hyper(23,a,798,a,b,2632,a(flip)),flip(a)]. 2647 a(x,K(y,z),u) = 1. [hyper(38,a,2646,a)]. 2648 $F # answer("aK2"). [resolve(2647,a,57,a)]. ============================== end of proof ========================== % Disable descendants (x means already disabled): 57 given #2362 (H,wt=8): 2647 a(x,K(y,z),u) = 1. [hyper(38,a,2646,a)]. given #2363 (H,wt=10): 2656 L(x,T(y,z) * y,u) = x. [para(2646(a,1),988(a,1)),flip(a)]. given #2364 (H,wt=12): 2658 L(x,(y \ z) * (z / y),u) = x. [para(84(a,1),2656(a,1,2,1))]. given #2365 (H,wt=12): 2659 L(x,(y * z) * (z / y),u) = x. [para(2658(a,1),880(a,1)),flip(a)]. given #2366 (H,wt=15): 2633 x * (a(y,z,u) \ 1) = a(y,z,u) \ x. [para(2549(a,1),327(a,1,2))]. given #2367 (H,wt=15): 2637 (x * y) \ (R(x,z,u) * y) = a(x,z,u). [hyper(23,a,20,a,b,2603,a),flip(a)]. given #2368 (H,wt=15): 2644 (L(x,y,z) * u) \ (x * u) = a(z,y,x). [para(2612(a,1),66(a,1,1))]. given #2369 (H,wt=15): 2645 (x * K(y,z)) \ u = K(z,y) * (x \ u). [hyper(23,a,297,a,b,2631,a),flip(a)]. given #2370 (H,wt=15): 2649 (x * K(y,z)) * u = x * (K(y,z) * u). [para(2646(a,1),74(a,1,2))]. given #2371 (H,wt=8): 2666 R(x,K(y,z),u) = x. [hyper(24,a,79,a,b,2649,a(flip)),flip(a)]. given #2372 (H,wt=15): 2650 (x * (K(y,z) * u)) / u = x * K(y,z). [para(2646(a,1),99(a,1,2))]. given #2373 (H,wt=13): 2670 (x * y) / T(y,z) = x * K(z,y). [para(1077(a,1),2650(a,1,1,2))]. given #2374 (H,wt=13): 2671 (x / y) * K(z,y) = x / T(y,z). [para(22(a,1),2670(a,1,1)),flip(a)]. given #2375 (H,wt=14): 2673 ((x \ y) * x) / T(y,x) = a(x,y,x). [para(2671(a,1),1538(a,1))]. given #2376 (H,wt=14): 2675 a(x,y,x) * T(y,x) = (x \ y) * x. [para(2673(a,1),22(a,1,1))]. given #2377 (H,wt=15): 2665 (K(x,y) / z) * u = K(x,y) * (z \ u). [para(2645(a,1),2143(a,1)),flip(a)]. given #2378 (H,wt=15): 2668 (x / y) / K(z,u) = x / (K(z,u) * y). [para(2666(a,1),193(a,1))]. given #2379 (H,wt=15): 2678 x / (K(y,z) * u) = (x / u) * K(z,y). [para(2668(a,1),2140(a,1))]. given #2380 (H,wt=17): 2513 L(x,y,z * (u * (u * w))) = L(x,y,w * z). [para(2509(a,1),868(a,2))]. given #2381 (H,wt=17): 2548 (a(x,y,x) * z) * u = (z * u) * a(x,y,x). [para(2534(a,1),2053(a,1,2))]. given #2382 (H,wt=17): 2605 (a(x,y,z) \ u) \ w = (a(x,y,z) / u) * w. [para(2570(a,1),353(a,1,1,2)),flip(a)]. given #2383 (H,wt=17): 2609 a(x * a(y,z,x),u,w) = a(L(x,z,y),u,w). [para(2333(a,1),2586(a,1,1))]. given #2384 (H,wt=17): 2630 K(x,T(y,z)) * (z * u) = (z * K(x,y)) * u. [para(2216(a,1),2518(a,1,1)),flip(a)]. given #2385 (H,wt=17): 2661 x \ (R(x / y,z,u) * y) = a(x / y,z,u). [para(22(a,1),2637(a,1,1))]. given #2386 (H,wt=17): 2664 K(x * y,x) * (y \ z) = (x * (y / x)) \ z. [para(1129(a,1),2645(a,1,1)),flip(a)]. given #2387 (H,wt=17): 2676 K(x * y,x) * ((x \ y) \ z) = (x / y) * z. [para(1009(a,1),2665(a,1,1)),flip(a)]. given #2388 (H,wt=17): 2677 K(x,T(y,z)) * (z \ u) = (z \ K(x,y)) * u. [para(2201(a,1),2665(a,1,1)),flip(a)]. given #2389 (H,wt=17): 2679 a(L(x,y * z,y),u,w) = a(L(x,z,y),u,w). [para(2342(a,2),2609(a,1,1))]. given #2390 (H,wt=17): 2680 K(x,T(y,z)) * (z * u) = z * (K(x,y) * u). [para(2630(a,2),2649(a,1))]. given #2391 (H,wt=17): 2681 x \ (y * R(y \ x,z,u)) = a(x / y,z,u). [para(224(a,1),2661(a,1,2))]. given #2392 (H,wt=17): 2685 x \ (y * R(y \ x,z,u)) = a(y * x,z,u). [para(2681(a,2),2606(a,1))]. given #2393 (H,wt=18): 2635 (x * y) \ (R(x,z,u) * y) = L(a(x,z,u),y,x). [para(2602(a,1),32(a,2,2)),flip(a)]. given #2394 (H,wt=12): 2687 L(a(x,y,z),u,x) = a(x,y,z). [para(2635(a,1),2637(a,1))]. given #2395 (H,wt=19): 2642 (x * y) * (a(x,y,z) * u) = (R(x,y,z) * y) * u. [para(2603(a,1),2338(a,1,1)),flip(a)]. given #2396 (H,wt=20): 2514 L(x,y,(z * (u * w)) * (z * u)) = L(x,y,L(w,u,z)). [para(32(a,2),2511(a,1,3)),flip(a)]. given #2397 (H,wt=20): 2683 a(x,y,z) \ a(L(x,u,w),y,z) = a(w,u,a(x,y,z)). [para(2679(a,1),2408(a,1,2))]. given #2398 (H,wt=17): 2694 a(x,y,a(z,u,w)) \ 1 = a(x,y,a(z,u,w)). [para(2683(a,1),2409(a,1)),flip(a)]. given #2399 (H,wt=17): 2695 a(x,y,a(z,u,w)) * a(x,y,a(z,u,w)) = 1. [para(2694(a,1),20(a,1,2))]. given #2400 (H,wt=19): 2696 a(x,y,a(z,u,w)) \ v5 = v5 * a(x,y,a(z,u,w)). [para(2694(a,1),2633(a,1,2)),flip(a)]. given #2401 (H,wt=22): 2624 ((K(x,y) * (z * u)) * w) / (u * w) = R(K(x,y) * z,u,w). [para(2518(a,1),34(a,2,1,1)),flip(a)]. given #2402 (H,wt=22): 2693 L(x,y,z) * a(L(z,u,w),y,x) = x * a(w,u,a(z,y,x)). [para(2683(a,1),2377(a,1,2)),flip(a)]. given #2403 (H,wt=22): 2697 a(L(x,y,z),u,w) * L(w,u,x) = w * a(z,y,a(x,u,w)). [para(2696(a,1),2428(a,2))]. given #2404 (H,wt=22): 2698 (K(x,y) * ((z * u) * w)) / (u * w) = R(K(x,y) * z,u,w). [para(2518(a,1),2624(a,1,1))]. given #2405 (H,wt=22): 2699 K(x,y) * (((z * u) * w) / (u * w)) = R(K(x,y) * z,u,w). [para(2698(a,1),2521(a,1)),flip(a)]. given #2406 (H,wt=17): 2700 R(K(x,y) * z,u,w) = K(x,y) * R(z,u,w). [para(34(a,2),2699(a,1,2)),flip(a)]. given #2407 (H,wt=17): 2701 R(x * K(y,z),u,w) = R(x,u,w) * K(y,z). [hyper(23,a,699,a(flip),b,2700,a(flip))]. given #2408 (H,wt=15): 2704 R(T(x,y),z,u) * K(y,x) = R(x,z,u). [para(1089(a,1),2701(a,1,1)),flip(a)]. given #2409 (H,wt=10): 2706 K(x,R(y,z,u)) = K(x,y). [hyper(23,a,1109,a,b,2704,a),flip(a)]. given #2410 (H,wt=12): 2708 T(x,R(y,z,u)) = x * K(x,y). [para(2706(a,1),1107(a,2,2))]. given #2411 (H,wt=10): 2716 T(x,R(y,z,u)) = T(x,y). [para(2708(a,2),1107(a,2)),flip(a)]. given #2412 (H,wt=15): 2717 R(x,y,z) * T(u,x) = u * R(x,y,z). [para(2716(a,1),82(a,1,2))]. given #2413 (H,wt=17): 2723 R(x,y,z) * (x \ u) = (u / x) * R(x,y,z). [para(84(a,1),2717(a,1,2))]. given #2414 (H,wt=15): 2725 (x / y) * R(y,z,u) = a(y,z,u) * x. [para(2723(a,1),2309(a,1))]. given #2415 (H,wt=15): 2726 a(x,y,z) * (u * x) = u * R(x,y,z). [para(21(a,1),2725(a,1,1)),flip(a)]. given #2416 (H,wt=15): 2729 (x * y) * a(y,z,u) = x * R(y,z,u). [para(2726(a,1),2567(a,1)),flip(a)]. given #2417 (H,wt=22): 2727 L(x,y,z) * R(a(z,y,x),u,w) = a(a(z,y,x),u,w) * x. [para(2326(a,2),2725(a,1,1))]. given #2418 (H,wt=23): 2660 L(x,T(L(y / z,z * y,y / z) * (z * y),y / z),u) = x. [para(1309(a,2),2659(a,1,2))]. given #2419 (H,wt=16): 2731 L(x,T((y / z) * (z * y),y / z),u) = x. [para(892(a,1),2660(a,1,2,1,1))]. given #2420 (H,wt=12): 2733 L(x,(y * z) / (z / y),u) = x. [para(2731(a,1),1235(a,1)),flip(a)]. given #2421 (H,wt=12): 2734 L(x,(y * z) * (y / z),u) = x. [para(952(a,1),2733(a,1,2))]. given #2422 (H,wt=23): 2672 (x * (y * z)) / T(L(z,y,x),u) = (x * y) * K(u,L(z,y,x)). [para(74(a,1),2670(a,1,1))]. given #2423 (H,wt=23): 2735 (x * (y * z)) / L(T(z,u),y,x) = (x * y) * K(u,L(z,y,x)). [para(44(a,2),2672(a,1,2))]. given #2424 (H,wt=24): 2601 (x * y) \ ((x * a(z,u,w)) * y) = R(T(a(z,u,w),x * y),x,y). [para(2567(a,1),549(a,1,2,1))]. given #2425 (H,wt=20): 2736 (x * y) \ ((x * a(z,u,w)) * y) = R(a(z,u,w),x,y). [para(2543(a,1),2601(a,2,1))]. given #2426 (H,wt=24): 2629 ((T(x,y) * z) * u) / (K(x,y) * (z * u)) = R(x,K(x,y) * z,u). [para(2518(a,1),1167(a,1,2))]. given #2427 (H,wt=24): 2667 (x * T(y,z)) \ (x * (K(y,z) * (y * u))) = L(u,y,x \ K(y,z)). [para(2649(a,1),2264(a,1,2))]. given #2428 (H,wt=22): 2739 (x * T(y,z)) \ (x * (T(y,z) * u)) = L(u,y,x \ K(y,z)). [para(1160(a,1),2667(a,1,2,2))]. given #2429 (H,wt=15): 2740 L(x,y,z \ K(y,u)) = L(x,T(y,u),z). [para(2739(a,1),32(a,2)),flip(a)]. given #2430 (H,wt=15): 2741 L(x,y,z * K(y,u)) = L(x,T(y,u),z). [para(2740(a,1),776(a,1)),flip(a)]. given #2431 (H,wt=24): 2730 (x * (y * z)) \ (x * (y * R(z,u,w))) = L(a(z,u,w),y * z,x). [para(2729(a,1),32(a,2,2,2)),flip(a)]. given #2432 (H,wt=24): 2738 (((T(x,y) * z) * u) / (z * u)) * K(y,x) = R(x,K(x,y) * z,u). [para(2629(a,1),2678(a,1)),flip(a)]. given #2433 (H,wt=19): 2742 R(T(x,y),z,u) * K(y,x) = R(x,K(x,y) * z,u). [para(34(a,2),2738(a,1,1))]. given #2434 (H,wt=13): 2743 R(x,K(x,y) * z,u) = R(x,z,u). [para(2742(a,1),2704(a,1))]. given #2435 (H,wt=13): 2744 R(x,y * x,z) = R(x,x * y,z). [para(974(a,1),2743(a,1,2)),flip(a)]. given #2436 (H,wt=15): 2746 x \ R(x,y * x,z) = R(x,y,z) \ x. [para(2744(a,2),618(a,1,2))]. given #2437 (H,wt=13): 2747 a(x,y * x,z) = R(x,y,z) \ x. [para(2746(a,1),2297(a,2))]. given #2438 (H,wt=13): 2748 a(x,y * x,z) = a(x,y,z) \ 1. [para(2747(a,2),2302(a,1))]. given #2439 (H,wt=15): 2749 a(x * y,y,z) = a(x * y,x,z) \ 1. [para(2748(a,1),1778(a,1)),flip(a)]. given #2440 (H,wt=19): 2750 a(x * y,y,a(z,u,w)) = a(x * y,x,a(z,u,w)). [para(2749(a,2),2694(a,1))]. given #2441 (H,wt=25): 2598 (x * (a(y,z,u) * w)) \ ((x * w) * a(y,z,u)) = a(x,w,a(y,z,u)). [para(2567(a,2),28(a,2,1,2)),flip(a)]. given #2442 (H,wt=25): 2643 L(x,y,z) * a(z,y,L(x,u,w)) = L(x,u,w) * a(w,u,L(x,y,z)). [para(2325(a,1),2604(a,1,2))]. given #2443 (H,wt=25): 2662 (L(R(x,y,z),u,w) * (y * z)) \ ((x * y) * z) = a(w,u,R(x,y,z)). [para(79(a,1),2644(a,1,2))]. given #2444 (H,wt=22): 2751 ((L(x,y,z) * u) * w) \ ((x * u) * w) = a(z,y,R(x,u,w)). [para(184(a,1),2662(a,1,1))]. given #2445 (H,wt=26): 2623 (K(x,y) * (z * u)) \ ((K(x,y) * z) * (u * w)) = L(w,u,K(x,y) * z). [para(2518(a,1),32(a,2,1)),flip(a)]. given #2446 (H,wt=26): 2752 (K(x,y) * (z * u)) \ (K(x,y) * (z * (u * w))) = L(w,u,K(x,y) * z). [para(2518(a,1),2623(a,1,2))]. given #2447 (H,wt=18): 2753 L(x,y,K(z,u) * w) = (w * y) \ (w * (y * x)). [para(2752(a,1),2519(a,1))]. given #2448 (H,wt=13): 2754 L(x,y,K(z,u) * w) = L(x,y,w). [para(2753(a,2),32(a,2)),flip(a)]. given #2449 (H,wt=13): 2760 L(x,y,z * K(u,w)) = L(x,y,z). [para(2200(a,1),2754(a,1,3))]. given #2450 (H,wt=11): 2763 L(x,T(y,z),u) = L(x,y,u). [para(2760(a,1),2741(a,1)),flip(a)]. given #2451 (H,wt=13): 2765 L(x,(y * z) * z,u) = L(x,y,u). [para(2763(a,1),951(a,1)),flip(a)]. given #2452 (H,wt=13): 2766 L(x,y / z,u) = L(x,z * y,u). [para(2763(a,1),1235(a,1)),flip(a)]. given #2453 (H,wt=13): 2777 L(x,y / z,u) = L(x,y * z,u). [para(22(a,1),2765(a,1,2,1)),flip(a)]. given #2454 (H,wt=13): 2782 L(x,y * z,u) = L(x,z * y,u). [para(2777(a,1),2766(a,1))]. given #2455 (H,wt=12): 2787 L(x,(y / z) * (y * z),u) = x. [para(2782(a,1),2734(a,1))]. given #2456 (H,wt=15): 2757 L(x,y,T(z,u) * w) = L(x,y,z * w). [para(1098(a,1),2754(a,1,3)),flip(a)]. given #2457 (H,wt=14): 2789 L(x,(y * z) * u,y * (z * u)) = x. [para(2757(a,1),950(a,1))]. given #2458 (H,wt=15): 2759 L(x,y,z * T(u,w)) = L(x,y,z * u). [para(1212(a,1),2754(a,1,3))]. given #2459 (H,wt=16): 2779 (x * y) / L(z,z * y,x) = x * (y / z). [para(2766(a,1),196(a,1,2))]. given #2460 (H,wt=17): 2758 L(x,y,(z / u) * w) = L(x,y,(u \ z) * w). [para(1161(a,1),2754(a,1,3))]. given #2461 (H,wt=17): 2762 L(x,y,z * (K(u,w) * v5)) = L(x,y,z * v5). [para(2680(a,1),2754(a,1,3))]. given #2462 (H,wt=17): 2792 L(x,y,z * (u / w)) = L(x,y,z * (w \ u)). [para(84(a,1),2759(a,1,3,2)),flip(a)]. given #2463 (H,wt=17): 2794 L(x,y,(z / u) * w) = L(x,y,(u * z) * w). [para(2758(a,2),781(a,1))]. given #2464 (H,wt=17): 2795 L(x,y,z * (u * w)) = L(x,y,z * (w * u)). [para(974(a,1),2762(a,1,3,2))]. given #2465 (H,wt=17): 2796 L(x,y,z * (u / w)) = L(x,y,z * (w * u)). [para(2792(a,2),867(a,1))]. given #2466 (H,wt=17): 2797 L(x,y,z * ((u * w) * u)) = L(x,y,w * z). [para(2795(a,1),2513(a,1))]. given #2467 (H,wt=18): 2788 L(x,(y \ (y \ z)) * ((y \ z) * T(y,z)),u) = x. [para(256(a,1),2787(a,1,2,1))]. given #2468 (H,wt=18): 2798 L(x,(y * (y \ z)) * ((y \ z) * T(y,z)),u) = x. [para(2788(a,1),880(a,1)),flip(a)]. given #2469 (H,wt=14): 2799 L(x,y * ((z \ y) * T(z,y)),u) = x. [para(20(a,1),2798(a,1,2,1))]. given #2470 (H,wt=14): 2800 L(x,y \ ((z \ y) * T(z,y)),u) = x. [para(2799(a,1),876(a,2))]. given #2471 (H,wt=9): 2801 L(x,a(y,z,y),u) = x. [para(2391(a,1),2800(a,1,2))]. given #2472 (H,wt=15): 2803 (x * y) / L(y,z,y) = x * a(y,z,y). [para(2801(a,1),1543(a,1,2))]. given #2473 (H,wt=17): 2802 (x * a(y,z,y)) * u = x * (a(y,z,y) * u). [para(2801(a,1),74(a,1,2))]. given #2474 (H,wt=17): 2806 (a(x,y,x) * z) * u = z * (a(x,y,x) * u). [para(2051(a,2),2802(a,1,1))]. given #2475 (H,wt=17): 2807 (x * y) * a(z,u,z) = x * (a(z,u,z) * y). [para(2806(a,1),2548(a,1)),flip(a)]. given #2476 (H,wt=20): 2790 a(x,y,z) \ ((x * (y * z)) \ u) = ((x * y) * z) \ u. [para(2789(a,1),271(a,1)),flip(a)]. given #2477 (H,wt=18): 2808 ((x * y) * z) \ (x * (y * z)) = a(x,y,z) \ 1. [para(60(a,1),2790(a,1,2)),flip(a)]. given #2478 (H,wt=22): 2755 ((x * K(y,z)) * u) \ ((x * K(y,z)) * (u * w)) = L(w,u,x). [para(2753(a,1),2553(a,1))]. given #2479 (H,wt=22): 2810 (x * (K(y,z) * u)) \ ((x * K(y,z)) * (u * w)) = L(w,u,x). [para(2649(a,1),2755(a,1,1))]. given #2480 (H,wt=22): 2811 (x * (K(y,z) * u)) \ (x * (K(y,z) * (u * w))) = L(w,u,x). [para(2649(a,1),2810(a,1,2))]. given #2481 (H,wt=18): 2812 L(L(x,y,K(z,u)),K(z,u) * y,w) = L(x,y,w). [para(2811(a,1),174(a,1)),flip(a)]. given #2482 (H,wt=13): 2813 L(x,K(y,z) * u,w) = L(x,u,w). [para(2515(a,1),2812(a,1,1))]. given #2483 (H,wt=15): 2815 L(x,T(y,z) * u,w) = L(x,y * u,w). [para(1098(a,1),2813(a,1,2)),flip(a)]. given #2484 (H,wt=15): 2817 L(x,T(y,z) * u,w) = L(x,u * y,w). [para(2815(a,2),2782(a,1))]. given #2485 (H,wt=26): 2793 (x * (y * z)) / L(T(z,u),T(z,u) * (y * z),x) = x * (y * K(u,z)). [para(2670(a,1),2779(a,2,2))]. given #2486 (H,wt=24): 2821 (x * (y * z)) / L(T(z,u),(y * z) * z,x) = x * (y * K(u,z)). [para(2817(a,1),2793(a,1,2))]. given #2487 (H,wt=20): 2822 (x * (y * z)) / L(T(z,u),y,x) = x * (y * K(u,z)). [para(2765(a,1),2821(a,1,2))]. given #2488 (H,wt=18): 2824 (x * y) * K(z,L(u,y,x)) = x * (y * K(z,u)). [para(2822(a,1),2735(a,1)),flip(a)]. given #2489 (H,wt=27): 2682 L(x,y,z * (K(u * w,u) * ((u * (w / u)) \ v5))) = L(x,y,(w \ v5) * z). [para(2664(a,1),2513(a,1,3,2,2))]. given #2490 (H,wt=21): 2826 L(x,y,z * ((u * (w / u)) \ v5)) = L(x,y,(w \ v5) * z). [para(2682(a,1),2762(a,1)),flip(a)]. given #2491 (H,wt=21): 2827 L(x,y,z * ((u * (w / u)) * v5)) = L(x,y,(w \ v5) * z). [para(2826(a,1),867(a,1)),flip(a)]. given #2492 (H,wt=21): 2829 L(x,y,z * ((u * (w / u)) * v5)) = L(x,y,(w * v5) * z). [para(2827(a,2),781(a,1))]. given #2493 (H,wt=28): 2621 (x * (K(y,z) * (u * w))) \ ((x * (K(y,z) * u)) * w) = a(x,K(y,z) * u,w). [para(2518(a,1),28(a,2,1,2)),flip(a)]. given #2494 (H,wt=28): 2622 (K(x,y) * (z * (u * w))) \ (((K(x,y) * z) * u) * w) = a(K(x,y) * z,u,w). [para(2518(a,1),28(a,2,1)),flip(a)]. given #2495 (H,wt=28): 2830 L(x,y,(z * u) * ((w * (z / w)) * (u * v5))) = L(x,y,L(v5,u,w * (z / w))). [para(2829(a,1),2514(a,1))]. given #2496 (H,wt=28): 2831 (K(x,y) * (z * (u * w))) \ ((K(x,y) * (z * u)) * w) = a(K(x,y) * z,u,w). [para(2518(a,1),2622(a,1,2,1))]. given #2497 (H,wt=28): 2832 L(x,y,L(z,u,(u * z) * (w / (u * z)))) = L(x,y,(w / (u * z)) * (w * u)). [para(2830(a,1),2797(a,1))]. given #2498 (H,wt=28): 2833 (K(x,y) * (z * (u * w))) \ (K(x,y) * ((z * u) * w)) = a(K(x,y) * z,u,w). [para(2518(a,1),2831(a,1,2))]. given #2499 (H,wt=20): 2835 a(K(x,y) * z,u,w) = (z * (u * w)) \ ((z * u) * w). [para(2833(a,1),2519(a,1))]. given #2500 (H,wt=13): 2836 a(K(x,y) * z,u,w) = a(z,u,w). [para(2835(a,2),28(a,2)),flip(a)]. given #2501 (H,wt=15): 2839 a(T(x,y) * z,u,w) = a(x * z,u,w). [para(1098(a,1),2836(a,1,1)),flip(a)]. given #2502 (H,wt=15): 2841 a(x * T(y,z),u,w) = a(x * y,u,w). [para(1212(a,1),2836(a,1,1))]. given #2503 (H,wt=17): 2840 a((x / y) * z,u,w) = a((y \ x) * z,u,w). [para(1161(a,1),2836(a,1,1))]. given #2504 (H,wt=17): 2843 a((x * y) * z,y,u) = a(x * (y * z),y,u). [para(2839(a,1),2490(a,1)),flip(a)]. given #2505 (H,wt=17): 2844 a((x / y) * z,u,w) = a((y * x) * z,u,w). [para(2840(a,2),1707(a,1))]. given #2506 (H,wt=17): 2845 a(x / (y / z),u,w) = a((z \ y) * x,u,w). [para(2840(a,1),2606(a,2))]. given #2507 (H,wt=17): 2846 a(x / (y * z),z,u) = a(y * (z * x),z,u). [para(2843(a,1),2606(a,2))]. given #2508 (H,wt=17): 2848 a(x / (y * z),u,w) = a((z / y) * x,u,w). [para(2844(a,2),2606(a,2))]. given #2509 (H,wt=17): 2849 a(x / (y / z),u,w) = a(x / (z \ y),u,w). [para(2845(a,2),2606(a,2)),flip(a)]. given #2510 (H,wt=17): 2850 a((x * y) / z,x,u) = a(y / (z * x),x,u). [para(2846(a,2),2606(a,2))]. given #2511 (H,wt=17): 2851 a(x / (y / z),u,w) = a(x / (z * y),u,w). [para(2848(a,2),2606(a,2))]. given #2512 (H,wt=17): 2852 a((x * y) / z,x,u) = a(y / (x / z),x,u). [para(2851(a,2),2850(a,2))]. given #2513 (H,wt=24): 2837 ((x * K(y,z)) * (u * w)) \ (((x * K(y,z)) * u) * w) = a(x,u,w). [para(2835(a,1),2586(a,1))]. given #2514 (H,wt=24): 2853 (x * (K(y,z) * (u * w))) \ (((x * K(y,z)) * u) * w) = a(x,u,w). [para(2649(a,1),2837(a,1,1))]. given #2515 (H,wt=24): 2854 (x * (K(y,z) * (u * w))) \ ((x * (K(y,z) * u)) * w) = a(x,u,w). [para(2649(a,1),2853(a,1,2,1))]. given #2516 (H,wt=13): 2855 a(x,K(y,z) * u,w) = a(x,u,w). [para(2854(a,1),2621(a,1)),flip(a)]. given #2517 (H,wt=11): 2857 a(x,T(y,z),u) = a(x,y,u). [para(985(a,1),2855(a,1,2)),flip(a)]. given #2518 (H,wt=13): 2856 a(x,y * z,u) = a(x,z * y,u). [para(974(a,1),2855(a,1,2))]. given #2519 (H,wt=13): 2861 a(x,y * K(z,u),w) = a(x,y,w). [para(2200(a,1),2855(a,1,2))]. given #2520 (H,wt=13): 2865 a(x,y / z,u) = a(x,z * y,u). [para(2857(a,1),1788(a,1)),flip(a)]. given #2521 (H,wt=13): 2866 a(x,(y * z) * z,u) = a(x,y,u). [para(2857(a,1),1792(a,1)),flip(a)]. given #2522 (H,wt=13): 2867 R(x,T(y,z),u) = a(x,y,u) * x. [para(2857(a,1),2303(a,2,1))]. given #2523 (H,wt=11): 2882 R(x,T(y,z),u) = R(x,y,u). [para(2867(a,2),2303(a,2)),flip(a)]. given #2524 (H,wt=13): 2883 R(x,y / z,u) = R(x,z \ y,u). [para(84(a,1),2882(a,1,2)),flip(a)]. given #2525 (H,wt=13): 2884 R(x,y / z,u) = R(x,z * y,u). [para(2883(a,2),2383(a,1))]. given #2526 (H,wt=15): 2858 a(x,y * T(z,u),w) = a(x,y * z,w). [para(1212(a,1),2855(a,1,2))]. given #2527 (H,wt=15): 2862 R(x,K(y,z) * u,w) = a(x,u,w) * x. [para(2855(a,1),2303(a,2,1))]. given #2528 (H,wt=13): 2888 R(x,K(y,z) * u,w) = R(x,u,w). [para(2862(a,2),2303(a,2)),flip(a)]. given #2529 (H,wt=13): 2892 R(x,y * K(z,u),w) = R(x,y,w). [para(2200(a,1),2888(a,1,2))]. given #2530 (H,wt=15): 2887 a(x,y * T(z,u),w) = a(x,z * y,w). [para(2858(a,2),2856(a,1))]. given #2531 (H,wt=17): 2877 a(x,y * (z * K(u,w)),v5) = a(x,y * z,v5). [para(2824(a,1),2861(a,1,2))]. given #2532 (H,wt=17): 2885 R(x,(y * z) / u,w) = R(x,u * (y \ z),w). [para(2884(a,1),2385(a,1)),flip(a)]. given #2533 (H,wt=17): 2894 R(x,y * (z * K(u,w)),v5) = R(x,y * z,v5). [para(2824(a,1),2892(a,1,2))]. given #2534 (H,wt=17): 2896 R(x,y * T(z,u),w) = x * a(x,z * y,w). [para(2887(a,1),2300(a,2,2))]. given #2535 (H,wt=15): 2899 R(x,y * T(z,u),w) = R(x,z * y,w). [para(2896(a,2),2300(a,2)),flip(a)]. given #2536 (H,wt=17): 2897 R(x,y * (z \ u),w) = R(x,y * (z * u),w). [para(2885(a,1),2884(a,1))]. given #2537 (H,wt=17): 2900 R(x,y * ((z \ u) \ u),w) = R(x,z * y,w). [para(83(a,1),2899(a,1,2,2))]. given #2538 (H,wt=17): 2901 R(x,y * ((z \ u) * u),w) = R(x,z * y,w). [para(2900(a,1),2897(a,1)),flip(a)]. given #2539 (H,wt=19): 2898 R(x,y * ((z \ u) \ 1),w) = R(x,y * (z / u),w). [para(2138(a,1),2894(a,1,2,2))]. given #2540 (H,wt=19): 2902 R(x,y * ((z \ u) * 1),w) = R(x,y * (z / u),w). [para(2898(a,1),2897(a,1)),flip(a)]. given #2541 (H,wt=17): 2903 R(x,y * (z / u),w) = R(x,y * (z \ u),w). [para(18(a,1),2902(a,1,2,2)),flip(a)]. given #2542 (H,wt=17): 2904 R(x,y * (z / u),w) = R(x,y * (z * u),w). [para(2903(a,2),2897(a,1))]. given #2543 (H,wt=18): 2905 R(x,x * (y * z),z) = y / ((x \ (y / z)) * z). [para(2904(a,1),631(a,1))]. given #2544 (H,wt=20): 2886 a(x,y * (z * K(u,z)),w) = a(x,y * L(z,u,z),w). [para(1062(a,1),2858(a,1,2,2)),flip(a)]. given #2545 (H,wt=16): 2907 a(x,y * L(z,u,z),w) = a(x,y * z,w). [para(2886(a,1),2877(a,1))]. given #2546 (H,wt=16): 2908 a(x,L(y,z,y) * u,w) = a(x,u * y,w). [para(2907(a,1),2856(a,1)),flip(a)]. given #2547 (H,wt=21): 2878 a(x,L(y,z,y) * (u * y),w) = a(x,u * a(y,z,y),w). [para(2803(a,1),2865(a,1,2)),flip(a)]. given #2548 (H,wt=18): 2910 a(x,y * a(z,u,z),w) = a(x,(y * z) * z,w). [para(2878(a,1),2908(a,1))]. given #2549 (H,wt=14): 2911 a(x,y * a(z,u,z),w) = a(x,y,w). [para(2910(a,2),2866(a,1))]. given #2550 (H,wt=14): 2913 a(x,a(y,z,y) * u,w) = a(x,u,w). [para(2051(a,2),2911(a,1,2))]. given #2551 (H,wt=22): 2906 R(x,x * ((y \ z) * z),z) = (y \ z) / ((x \ (y \ 1)) * z). [para(320(a,1),2905(a,2,2,1,2))]. given #2552 (H,wt=18): 2916 R(x,y * x,z) = (y \ z) / ((x \ (y \ 1)) * z). [para(2906(a,1),2901(a,1)),flip(a)]. given #2553 (H,wt=24): 2876 (x * ((y * K(z,u)) * w)) \ ((x * (y * K(z,u))) * w) = a(x,y,w). [para(2861(a,1),28(a,1)),flip(a)]. given #2554 (H,wt=24): 2918 (x * (y * (K(z,u) * w))) \ ((x * (y * K(z,u))) * w) = a(x,y,w). [para(2649(a,1),2876(a,1,1,2))]. given #2555 (H,wt=26): 2915 (x * ((a(y,z,y) * u) * w)) \ ((x * (a(y,z,y) * u)) * w) = a(x,u,w). [para(2913(a,1),28(a,1)),flip(a)]. given #2556 (H,wt=26): 2919 (x * (y * (a(z,u,z) * w))) \ ((x * (a(z,u,z) * y)) * w) = a(x,y,w). [para(2806(a,1),2915(a,1,1,2))]. given #2557 (H,wt=28): 2834 L(x,y,L(z,u,(u * z) * (w / (u * z)))) = L(x,y,((u * z) * w) * (w * u)). [para(2832(a,2),2794(a,1))]. given #2558 (H,wt=28): 2920 L(x,y,L(z,u,(u * z) * ((u * z) * w))) = L(x,y,((u * z) * w) * (w * u)). [para(2796(a,1),2834(a,1,3))]. given #2559 (H,wt=20): 2921 L(x,y,((z * u) * w) * (w * z)) = L(x,y,L(u,z,w)). [para(774(a,1),2920(a,1,3)),flip(a)]. given #2560 (H,wt=20): 2923 L(x,y,((z * u) * w) * (z * w)) = L(x,y,L(u,z,w)). [para(2921(a,1),2795(a,1)),flip(a)]. given #2561 (H,wt=22): 2924 a(((x * y) * z) * (x * z),u,w) = L(w,u,L(y,x,z)) \ w. [para(2923(a,1),2298(a,2,1))]. given #2562 (H,wt=20): 2925 a(((x * y) * z) * (x * z),u,w) = a(L(y,x,z),u,w). [para(2924(a,2),2298(a,2)),flip(a)]. given #2563 (H,wt=29): 2692 (x * (y * (a(x,y,z) * u))) \ ((R(x,y,z) * y) * u) = a(x,y,a(x,y,z) * u). [para(2642(a,1),28(a,2,2)),flip(a)]. given #2564 (H,wt=27): 2927 (R(x,y,z) * (y * u)) \ ((R(x,y,z) * y) * u) = a(x,y,a(x,y,z) * u). [para(2420(a,1),2692(a,1,1))]. given #2565 (H,wt=17): 2928 a(x,y,a(x,y,z) * u) = a(R(x,y,z),y,u). [para(2927(a,1),28(a,2)),flip(a)]. given #2566 (H,wt=17): 2929 a(x,y,z * a(x,y,u)) = a(R(x,y,u),y,z). [para(2567(a,1),2928(a,1,3))]. given #2567 (H,wt=30): 2686 (x * (y * z)) \ ((x * y) * R(L(z,y,x),u,w)) = a((x * y) * (x * (y * z)),u,w). [para(32(a,2),2685(a,1,2,2,1))]. given #2568 (H,wt=30): 2926 (x * y) \ (((x * z) * y) * R(((x * z) * y) \ (x * y),u,w)) = a(L(z,x,y),u,w). [para(2925(a,1),2685(a,2))]. given #2569 (H,wt=26): 2931 (x * y) \ (((x * z) * R((x * z) \ x,u,w)) * y) = a(L(z,x,y),u,w). [para(1623(a,1),2926(a,1,2))]. given #2570 (H,wt=20): 2932 (x * y) \ ((x * a(z,u,w)) * y) = a(L(z,x,y),u,w). [para(2315(a,1),2931(a,1,2,1))]. given #2571 (H,wt=15): 2933 a(L(x,y,z),u,w) = R(a(x,u,w),y,z). [para(2932(a,1),2736(a,1))]. given #2572 (H,wt=12): 2936 a(L(x,y,z),y,u) = a(x,y,u). [para(2933(a,2),2416(a,1))]. given #2573 (H,wt=15): 2935 a(R(x,y,z),u,w) = a(L(x,y,z),u,w). [para(2933(a,2),2394(a,2))]. given #2574 (H,wt=17): 2939 a((x * y) \ z,y,u) = a(y \ (x \ z),y,u). [para(177(a,1),2936(a,1,1))]. given #2575 (H,wt=17): 2940 a((x \ y) \ z,y,u) = a(y \ (x * z),y,u). [para(267(a,1),2936(a,1,1))]. given #2576 (H,wt=17): 2942 L(x,y,z) * a(x,y,u) = R(L(x,y,z),y,u). [para(2936(a,1),2300(a,2,2)),flip(a)]. given #2577 (H,wt=17): 2946 a(x,y,z * a(x,y,u)) = a(L(x,y,u),y,z). [para(2935(a,1),2929(a,2))]. given #2578 (H,wt=14): 2950 a(x,y,z * a(x,y,u)) = a(x,y,z). [para(2946(a,2),2936(a,1))]. given #2579 (H,wt=17): 2947 a(x \ (y \ z),x,u) = a((y * x) * z,x,u). [para(2939(a,1),1702(a,1))]. given #2580 (H,wt=17): 2948 a(x / (y \ z),z,u) = a(z \ (y * x),z,u). [para(2940(a,1),2584(a,2))]. given #2581 (H,wt=17): 2949 L(x,y,z) * a(x,y,u) = L(R(x,y,u),y,z). [para(2942(a,2),48(a,1))]. given #2582 (H,wt=17): 2952 a(x \ (y \ z),x,u) = a(y * (x * z),x,u). [para(2947(a,2),2843(a,1))]. given #2583 (H,wt=17): 2953 a(x / (y / z),y,u) = a(y \ (z * x),y,u). [para(2948(a,1),2849(a,2))]. given #2584 (H,wt=17): 2955 a(x * (y * z),y,u) = a(y * (x * z),y,u). [para(2952(a,1),1757(a,1))]. given #2585 (H,wt=17): 2956 a((x * y) / z,z,u) = a(y / (z / x),z,u). [para(2953(a,2),2584(a,2))]. given #2586 (H,wt=19): 2941 a((x \ y) \ T(z,x),y,u) = a(y \ (z * x),y,u). [para(269(a,1),2936(a,1,1))]. given #2587 (H,wt=19): 2954 L(R(x,y,z),y,u) \ (x * a(x,y,z)) = a(u,y,x). [para(2949(a,1),2644(a,1,1))]. given #2588 (H,wt=17): 2958 L(R(x,y,z),y,u) \ R(x,y,z) = a(u,y,x). [para(2300(a,2),2954(a,1,2))]. given #2589 (H,wt=12): 2959 a(x,y,R(z,y,u)) = a(x,y,z). [para(2958(a,1),2298(a,2))]. given #2590 (H,wt=17): 2960 a(x,y,(z / u) / y) = a(x,y,z / (y * u)). [para(193(a,1),2959(a,1,3)),flip(a)]. given #2591 (H,wt=19): 2957 a((x \ y) * T(z,x),y,u) = a(y \ (z * x),y,u). [para(2941(a,1),1702(a,1)),flip(a)]. given #2592 (H,wt=17): 2961 a(x \ (y * z),x,u) = a((z \ x) * y,x,u). [para(2957(a,1),2841(a,1))]. given #2593 (H,wt=17): 2962 a(x \ (y * z),x,u) = a((z * x) * y,x,u). [para(2961(a,2),1707(a,1))]. given #2594 (H,wt=17): 2964 a(x \ (y * z),x,u) = a(z * (x * y),x,u). [para(2962(a,2),2843(a,1))]. given #2595 (H,wt=22): 2937 a(L(x,y,z),u,w) \ R(x,u,w) = a(a(x,u,w),y,z) \ x. [para(2933(a,2),2369(a,1,1))]. given #2596 (H,wt=22): 2938 L(x,y,z) * a(L(z,u,w),y,x) = a(a(z,y,x),u,w) * x. [para(2933(a,2),2727(a,1,2))]. given #2597 (H,wt=19): 2965 a(a(x,y,z),u,w) * z = z * a(w,u,a(x,y,z)). [para(2938(a,1),2693(a,1))]. given #2598 (H,wt=15): 2966 a(a(x,y,z),u,w) = a(w,u,a(x,y,z)). [hyper(24,a,2567,a,b,2965,a)]. given #2599 (H,wt=17): 2968 a(a(x,y,z),u,w) \ 1 = a(w,u,a(x,y,z)). [para(2966(a,2),2694(a,1,1))]. given #2600 (H,wt=17): 2970 x \ L(x,y,a(z,u,w)) = a(x,y,a(z,u,w)). [para(2968(a,1),2328(a,1)),flip(a)]. given #2601 (H,wt=19): 2969 a(a(x,y,z),u,w) \ v5 = v5 * a(w,u,a(x,y,z)). [para(2966(a,2),2696(a,1,1))]. given #2602 (H,wt=22): 2973 a(L(x,y,z),u,w) \ R(x,u,w) = x * a(z,y,a(x,u,w)). [para(2969(a,1),2937(a,2))]. given #2603 (H,wt=25): 2971 ((a(x,y,z) * u) * w) \ (a(x,y,z) * (u * w)) = a(w,u,a(x,y,z)). [para(2968(a,1),2808(a,2))]. given #2604 (H,wt=25): 2974 ((a(x,y,z) * u) * w) \ ((u * w) * a(x,y,z)) = a(w,u,a(x,y,z)). [para(2567(a,1),2971(a,1,2))]. given #2605 (H,wt=25): 2975 ((x * a(y,z,u)) * w) \ ((x * w) * a(y,z,u)) = a(w,x,a(y,z,u)). [para(2567(a,1),2974(a,1,1,1))]. given #2606 (H,wt=30): 2930 (x * (y * z)) \ ((x * y) * L(R(z,u,w),y,x)) = a((x * y) * (x * (y * z)),u,w). [para(48(a,1),2686(a,1,2,2))]. given #2607 (H,wt=27): 2976 (x * (y * z)) \ (x * (y * R(z,u,w))) = a((x * y) * (x * (y * z)),u,w). [para(74(a,1),2930(a,1,2))]. given #2608 (H,wt=22): 2977 L(a(x,y,z),u * x,w) = a((w * u) * (w * (u * x)),y,z). [para(2976(a,1),2730(a,1)),flip(a)]. given #2609 (H,wt=17): 2978 L(a(x,y,z),u * x,w) = a(L(x,u,w),y,z). [para(2977(a,2),1705(a,1))]. given #2610 (H,wt=22): 2979 a(L(x,y,z),u,w) \ a(x,u,w) = a(z,y * x,a(x,u,w)). [para(2978(a,1),2298(a,2,1)),flip(a)]. given #2611 (H,wt=17): 2980 a(x,y * z,a(z,u,w)) = a(x,y,a(z,u,w)). [para(2979(a,1),2407(a,1))]. given #2612 (H,wt=17): 2981 a(x,y * z,a(y,u,w)) = a(x,z,a(y,u,w)). [para(2980(a,1),2856(a,1)),flip(a)]. given #2613 (H,wt=21): 2982 a(x * y,z * u,a(z,w,v5)) = a(y * x,u,a(z,w,v5)). [para(2981(a,1),2618(a,1)),flip(a)]. given #2614 (H,wt=23): 2983 a((x * y) * z,y,a(x,u,w)) = a(z * (x * y),z,a(x,u,w)). [para(2982(a,1),2750(a,1))]. given #2615 (H,wt=23): 2984 a(x * (y * z),y,a(x,u,w)) = a(z * (x * y),z,a(x,u,w)). [para(2983(a,1),2843(a,1)),flip(a)]. given #2616 (H,wt=23): 2985 a(x * (y * z),y,a(x,u,w)) = a(x * (z * y),z,a(x,u,w)). [para(2984(a,2),2955(a,2))]. given #2617 (H,wt=31): 2805 (x * (y * (a(z,u,z) * w))) \ (((x * y) * a(z,u,z)) * w) = a(x,y,a(z,u,z) * w). [para(2802(a,2),28(a,2,2)),flip(a)]. given #2618 (H,wt=31): 2986 (x * (y * (a(z,u,z) * w))) \ ((x * (a(z,u,z) * y)) * w) = a(x,y,a(z,u,z) * w). [para(2807(a,1),2805(a,1,2,1))]. given #2619 (H,wt=14): 2987 a(x,y,a(z,u,z) * w) = a(x,y,w). [para(2986(a,1),2919(a,1))]. given #2620 (H,wt=12): 2988 a(x,y,L(z,u,z)) = a(x,y,z). [para(1542(a,1),2987(a,1,3)),flip(a)]. given #2621 (H,wt=15): 2989 a(x,y,(z \ u) * z) = a(x,y,T(u,z)). [para(2675(a,1),2987(a,1,3))]. given #2622 (H,wt=15): 2992 a(x,y,T(z * u,z)) = a(x,y,u * z). [para(19(a,1),2989(a,1,3,1)),flip(a)]. given #2623 (H,wt=23): 2991 a(x,y,(T(z,u) * u) \ (T(z,u) * (z * u))) = a(x,y,T(z,u)). [para(106(a,2),2988(a,1,3))]. given #2624 (H,wt=23): 2993 a(x,y,(T(z,u) * u) \ (z * (T(z,u) * u))) = a(x,y,T(z,u)). [para(728(a,1),2991(a,1,3,2))]. given #2625 (H,wt=17): 2994 a(x,y,T(z,T(z,u) * u)) = a(x,y,T(z,u)). [para(36(a,2),2993(a,1,3))]. given #2626 (H,wt=15): 2995 a(x,y,T(z,z * u)) = a(x,y,T(z,u)). [para(2018(a,1),2994(a,1,3))]. given #2627 (H,wt=26): 2996 a(x,y,T((z \ u) * z,((z \ u) * z) * (z \ 1))) = a(x,y,R(u,z,z)). [para(761(a,1),2995(a,2,3))]. given #2628 (H,wt=25): 2998 a(x,y,T((z \ u) * z,R(z \ u,z,z \ 1))) = a(x,y,R(u,z,z)). [para(433(a,1),2996(a,1,3,2))]. given #2629 (H,wt=20): 2999 a(x,y,T((z \ u) * z,z \ u)) = a(x,y,R(u,z,z)). [para(2716(a,1),2998(a,1,3))]. given #2630 (H,wt=16): 3001 a(x,y,z * (z \ u)) = a(x,y,R(u,z,z)). [para(2999(a,1),2992(a,1)),flip(a)]. given #2631 (H,wt=12): 3002 a(x,y,R(z,u,u)) = a(x,y,z). [para(20(a,1),3001(a,1,3)),flip(a)]. given #2632 (H,wt=15): 3003 a(x,y,z / (u \ 1)) = a(x,y,z * u). [para(720(a,1),3002(a,1,3)),flip(a)]. given #2633 (H,wt=22): 3004 a(x,y,R(((z \ 1) * u) \ 1,u,u)) = a(x,y,(u \ 1) * z). [para(1739(a,2),3003(a,1,3))]. given #2634 (H,wt=20): 3005 a(x,y,R((z \ u) \ 1,u,u)) = a(x,y,(u \ 1) * z). [para(318(a,1),3004(a,1,3,1,1))]. given #2635 (H,wt=17): 3006 a(x,y,(z \ u) \ 1) = a(x,y,(u \ 1) * z). [para(3005(a,1),3002(a,1)),flip(a)]. given #2636 (H,wt=15): 3007 a(x,y,(z \ u) \ 1) = a(x,y,u \ z). [para(318(a,1),3006(a,2,3))]. given #2637 (H,wt=18): 3009 a(x,y,(z / u) \ z) = a(x,y,u * a(z,u,u)). [para(1388(a,1),3007(a,1,3)),flip(a)]. given #2638 (H,wt=14): 3010 a(x,y,z * a(u,z,z)) = a(x,y,z). [para(66(a,1),3009(a,1,3)),flip(a)]. given #2639 (H,wt=14): 3011 a(x,y,L(z,u,u * z)) = a(x,y,z). [para(1487(a,2),3010(a,1,3))]. given #2640 (H,wt=22): 3012 ((x * y) \ x) * L(L(y,x,x * y),z,u) = a(u,z,y) \ 1. [para(3011(a,1),2357(a,2,1))]. given #2641 (H,wt=17): 3013 (x * y) \ (x * L(y,z,u)) = a(u,z,y) \ 1. [para(3012(a,1),814(a,1)),flip(a)]. given #2642 (H,wt=16): 3015 L(a(x,y,z),z,u) = a(x,x * y,z) \ 1. [para(3013(a,1),2350(a,1)),flip(a)]. given #2643 (H,wt=12): 3016 L(a(x,y,z),z,u) = a(x,y,z). [para(3015(a,2),2343(a,1))]. given #2644 (H,wt=17): 3019 (x * L(y,z,u)) / a(u,u * z,y) = x * y. [para(3016(a,1),2356(a,1,2))]. given #2645 (H,wt=17): 3021 a(x,x * y,z) \ (u * L(z,y,x)) = u * z. [para(3019(a,1),2571(a,1)),flip(a)]. given #2646 (H,wt=15): 3023 a(x,y,z) * (u * L(z,y,x)) = u * z. [para(3021(a,1),2360(a,1)),flip(a)]. given #2647 (H,wt=12): 3026 x * T(y,L(x,z,u)) = y * x. [para(3023(a,1),2376(a,1)),flip(a)]. given #2648 (H,wt=14): 3032 K(L(x,y,z),u) = (u * x) \ (x * u). [para(3026(a,1),2186(a,1,1)),flip(a)]. given #2649 (H,wt=10): 3034 K(L(x,y,z),u) = K(x,u). [para(3032(a,2),30(a,2)),flip(a)]. given #2650 (H,wt=10): 3036 L(K(x,y),z,u) = K(x,y). [para(3034(a,1),2259(a,1)),flip(a)]. -------- Proof 4 -------- "aK3". ============================== PROOF ================================= % Proof 4 at 71.96 (+ 1.17) seconds: "aK3". % Length of proof is 2394. % Level of proof is 276. % Maximum clause weight is 50. % Given clauses 2650. 1 x * y = u & x * z = u -> y = z # label(non_clause). [assumption]. 2 y * x = u & z * x = u -> y = z # label(non_clause). [assumption]. 5 a(x,y,z) = 1 -> L(z,y,x) = z # label(non_clause). [assumption]. 6 L(x,y,z) = x -> a(z,y,x) = 1 # label(non_clause). [assumption]. 7 T(x,y) = x -> T(y,x) = y # label(non_clause). [assumption]. 8 T(x,y) = x -> K(x,y) = 1 # label(non_clause). [assumption]. 9 K(x,y) = 1 -> T(x,y) = x # label(non_clause). [assumption]. 16 a(x,y,K(z,u)) = 1 # label("aK3") # label(non_clause) # label(goal). [goal]. 17 1 * x = x. [assumption]. 18 x * 1 = x. [assumption]. 19 x \ (x * y) = y. [assumption]. 20 x * (x \ y) = y. [assumption]. 21 (x * y) / y = x. [assumption]. 22 (x / y) * y = x. [assumption]. 23 x * y != z | x * u != z | u = y. [clausify(1)]. 24 x * y != z | u * y != z | u = x. [clausify(2)]. 27 (x * (y * z)) \ ((x * y) * z) = a(x,y,z). [assumption]. 28 a(x,y,z) = (x * (y * z)) \ ((x * y) * z). [copy(27),flip(a)]. 29 (x * y) \ (y * x) = K(y,x). [assumption]. 30 K(x,y) = (y * x) \ (x * y). [copy(29),flip(a)]. 31 (x * y) \ (x * (y * z)) = L(z,y,x). [assumption]. 32 L(x,y,z) = (z * y) \ (z * (y * x)). [copy(31),flip(a)]. 33 ((x * y) * z) / (y * z) = R(x,y,z). [assumption]. 34 R(x,y,z) = ((x * y) * z) / (y * z). [copy(33),flip(a)]. 35 x \ (y * x) = T(y,x). [assumption]. 36 T(x,y) = y \ (x * y). [copy(35),flip(a)]. 37 a(x,y,z) != 1 | L(z,y,x) = z. [clausify(5)]. 38 L(x,y,z) != x | a(z,y,x) = 1. [clausify(6)]. 39 T(x,y) != x | T(y,x) = y. [clausify(7)]. 40 T(x,y) != x | K(x,y) = 1. [clausify(8)]. 41 K(x,y) != 1 | T(x,y) = x. [clausify(9)]. 42 T(T(x,y),z) = T(T(x,z),y). [assumption]. 43 T(L(x,y,z),u) = L(T(x,u),y,z). [assumption]. 44 L(T(x,y),z,u) = T(L(x,z,u),y). [copy(43),flip(a)]. 45 T(R(x,y,z),u) = R(T(x,u),y,z). [assumption]. 46 R(T(x,y),z,u) = T(R(x,z,u),y). [copy(45),flip(a)]. 47 L(R(x,y,z),u,w) = R(L(x,u,w),y,z). [assumption]. 48 R(L(x,y,z),u,w) = L(R(x,u,w),y,z). [copy(47),flip(a)]. 49 L(L(x,y,z),u,w) = L(L(x,u,w),y,z). [assumption]. 50 R(R(x,y,z),u,w) = R(R(x,u,w),y,z). [assumption]. 51 (x * (x * y)) * z = x * (x * (y * z)) # label("LC"). [assumption]. 58 a(c28,c29,K(c30,c31)) != 1 # label("aK3") # answer("aK3"). [deny(16)]. 59 1 \ x = x. [para(17(a,1),19(a,1,2))]. 60 x \ x = 1. [para(18(a,1),19(a,1,2))]. 61 x \ ((x * y) * 1) = y. [para(18(a,2),19(a,1,2))]. 62 x \ (y * (y \ (x * z))) = z. [para(20(a,2),19(a,1,2))]. 64 x / 1 = x. [para(18(a,1),21(a,1,1))]. 65 x / (y \ x) = y. [para(20(a,1),21(a,1,1))]. 66 (x / y) \ x = y. [para(22(a,1),19(a,1,2))]. 67 (x * (y * z)) * a(x,y,z) = (x * y) * z. [para(28(a,2),20(a,1,2))]. 68 ((x / y) * (y * z)) \ (x * z) = a(x / y,y,z). [para(22(a,1),28(a,2,2,1)),flip(a)]. 69 (x * y) * K(y,x) = y * x. [para(30(a,2),20(a,1,2))]. 70 x \ ((y \ x) * y) = K(y \ x,y). [para(20(a,1),30(a,2,1)),flip(a)]. 71 ((x \ y) * x) \ y = K(x,x \ y). [para(20(a,1),30(a,2,2)),flip(a)]. 72 x \ (1 * (x * y)) = L(y,x,1). [para(17(a,1),32(a,2,1)),flip(a)]. 73 (x * 1) \ (x * y) = L(y,1,x). [para(17(a,1),32(a,2,2,2)),flip(a)]. 74 (x * y) * L(z,y,x) = x * (y * z). [para(32(a,2),20(a,1,2))]. 75 x \ (y * ((y \ x) * z)) = L(z,y \ x,y). [para(20(a,1),32(a,2,1)),flip(a)]. 76 L(x \ y,x,z) = (z * x) \ (z * y). [para(20(a,1),32(a,2,2,2))]. 77 x \ ((x / y) * (y * z)) = L(z,y,x / y). [para(22(a,1),32(a,2,1)),flip(a)]. 78 ((x * y) * (y \ z)) / z = R(x,y,y \ z). [para(20(a,1),34(a,2,2)),flip(a)]. 79 R(x,y,z) * (y * z) = (x * y) * z. [para(34(a,2),22(a,1,1))]. 80 R(x / y,y,z) = (x * z) / (y * z). [para(22(a,1),34(a,2,1,1))]. 81 T(x,x) = x. [para(36(a,2),19(a,1))]. 82 x * T(y,x) = y * x. [para(36(a,2),20(a,1,2))]. 83 T(x,x \ y) = (x \ y) \ y. [para(20(a,1),36(a,2,2))]. 84 T(x / y,y) = y \ x. [para(22(a,1),36(a,2,2))]. 85 (x * (x * (y * z))) / z = x * (x * y). [hyper(24,a,22,a,b,51,a),flip(a)]. 86 (x * (x * y)) \ (x * (x * (y * z))) = z. [hyper(23,a,20,a,b,51,a),flip(a)]. 87 x \ ((x * (x * y)) * z) = x * (y * z). [hyper(23,a,20,a,b,51,a(flip)),flip(a)]. 88 (x * (x * 1)) * y = x * (x * y). [para(17(a,1),51(a,2,2,2))]. 89 x * (x * ((x \ y) * z)) = (x * y) * z. [para(20(a,1),51(a,1,1,2)),flip(a)]. 90 (x * (y * (y * (z * u)))) \ ((x * (y * (y * z))) * u) = a(x,y * (y * z),u). [para(51(a,1),28(a,2,1,2)),flip(a)]. 91 (x * (x * (y * (z * u)))) \ (((x * (x * y)) * z) * u) = a(x * (x * y),z,u). [para(51(a,1),28(a,2,1)),flip(a)]. 92 (x * (x * (y * z))) \ ((x * (x * y)) * (z * u)) = L(u,z,x * (x * y)). [para(51(a,1),32(a,2,1)),flip(a)]. 93 (x * (y * (y * z))) \ (x * (y * (y * (z * u)))) = L(u,y * (y * z),x). [para(51(a,1),32(a,2,2,2)),flip(a)]. 94 ((x * (x * (y * z))) * u) / (z * u) = R(x * (x * y),z,u). [para(51(a,1),34(a,2,1,1)),flip(a)]. 95 (x * (x * (y * z))) / ((x * y) * z) = R(x,x * y,z). [para(51(a,1),34(a,2,1)),flip(a)]. 97 ((x * y) / 1) / y = x. [hyper(24,a,22,a,b,64,a(flip)),flip(a)]. 98 T(T(x,y),x) = T(x,y). [para(81(a,1),42(a,1,1)),flip(a)]. 99 (x * (y * z)) / L(z,y,x) = x * y. [para(32(a,2),65(a,1,2))]. 100 (x * y) / T(x,y) = y. [para(36(a,2),65(a,1,2))]. 101 R(x,y,z) \ ((x * y) * z) = y * z. [para(34(a,2),66(a,1,1))]. 102 x \ (y * 1) = x \ y. [para(20(a,1),61(a,1,2,1))]. 103 T(x * (x * y),x) = x * (y * x). [hyper(23,a,51,a(flip),b,82,a)]. 104 T((x * y) / x,x) = y. [hyper(23,a,22,a(flip),b,82,a)]. 105 (x * T(y,x)) / x = y. [hyper(24,a,22,a,b,82,a(flip)),flip(a)]. 106 (x * y) \ (x * (z * y)) = L(T(z,y),y,x). [para(82(a,1),32(a,2,2,2)),flip(a)]. 107 T(x,y) \ (x * y) = T(y,T(x,y)). [para(82(a,1),36(a,2,2)),flip(a)]. 108 x * T(T(y,x),z) = T(y,z) * x. [para(42(a,1),82(a,1,2))]. 109 x * L(T(y,x),z,u) = L(y,z,u) * x. [para(44(a,2),82(a,1,2))]. 110 x * R(T(y,x),z,u) = R(y,z,u) * x. [para(46(a,2),82(a,1,2))]. 111 (x * y) \ ((z * x) * y) = T(R(z,x,y),x * y). [para(34(a,2),84(a,1,1)),flip(a)]. 112 T(T(x / y,z),y) = T(y \ x,z). [para(84(a,1),42(a,1,1)),flip(a)]. 113 ((x * y) / ((1 / z) * z)) / y = x. [para(22(a,2),97(a,1,1,2))]. 114 K(T(x,y),x) = 1. [hyper(40,a,98,a)]. 115 T(x,T(x,y)) = x. [hyper(39,a,98,a)]. 116 T(x,y) * x = x * T(x,y). [para(98(a,1),82(a,1,2)),flip(a)]. 117 (x * y) / T(y,T(x,y)) = T(x,y). [para(82(a,1),100(a,1,1))]. 118 x \ (y * (z * (z \ 1))) = x \ y. [para(20(a,2),102(a,1,2,2))]. 119 K(x,(y * x) / y) = 1. [para(104(a,1),114(a,1,1))]. 120 T(x,(y * x) / y) = x. [hyper(41,a,119,a)]. 122 K(x,y) \ (x * y) = T(y * x,K(x,y)). [para(69(a,1),36(a,2,2)),flip(a)]. 123 x \ (x * y) = L(y,x,1). [para(17(a,1),72(a,1,2))]. 124 L(x,y,1) = x. [para(123(a,1),19(a,1))]. 125 a(1,x,y) = 1. [hyper(38,a,124,a)]. 126 x \ (x * y) = L(y,1,x). [para(18(a,1),73(a,1,1))]. 127 L(x,1,y) = x. [para(126(a,1),19(a,1))]. 128 K(x \ 1,x) = (x \ 1) * x. [para(70(a,1),59(a,1))]. 129 K(x \ 1,x) / x = x \ 1. [hyper(24,a,22,a,b,128,a(flip)),flip(a)]. 130 (x \ 1) \ K(x \ 1,x) = x. [hyper(23,a,20,a,b,128,a(flip)),flip(a)]. 131 (x * x) * y = x * (x * y). [para(18(a,1),88(a,1,1,2))]. 132 (x * (x * y)) / y = x * x. [hyper(24,a,22,a,b,131,a),flip(a)]. 133 (x * x) \ (x * (x * y)) = y. [hyper(23,a,20,a,b,131,a),flip(a)]. 134 ((x * (x * y)) * z) / (y * z) = R(x * x,y,z). [para(131(a,1),34(a,2,1,1)),flip(a)]. 135 x \ (y * (y * x)) = T(y * y,x). [para(131(a,1),36(a,2,2)),flip(a)]. 136 x * (x * T(y,x * x)) = y * (x * x). [para(131(a,1),82(a,1))]. 137 L(x,y,y) = x. [para(133(a,1),32(a,2))]. 138 x * ((x \ y) * x) = T(x * y,x). [para(20(a,1),103(a,1,1,2)),flip(a)]. 139 T(x / y,z) * y = y * T(y \ x,z). [para(84(a,1),108(a,1,2,1)),flip(a)]. 140 (x * T(x \ y,z)) / x = T(y / x,z). [para(112(a,1),105(a,1,1,2))]. 141 R(x,1 / y,y) / y = x * (1 / y). [para(34(a,2),113(a,1,1))]. 142 L(x \ 1,x,y) = (y * x) \ y. [para(118(a,1),32(a,2))]. 143 L((x \ y) \ 1,x \ y,x) = y \ x. [para(20(a,1),142(a,2,1))]. 144 L(x \ 1,x,y / x) = y \ (y / x). [para(22(a,1),142(a,2,1))]. 145 x / L(y \ 1,y,x) = x * y. [para(142(a,2),65(a,1,2))]. 146 x \ T(x * y,x) = (x \ y) * x. [hyper(23,a,20,a,b,138,a),flip(a)]. 147 x * K(x \ 1,x) = T(x * 1,x). [para(128(a,2),138(a,1,2))]. 148 (x \ (x \ y)) * x = x \ T(y,x). [para(20(a,1),146(a,1,2,1)),flip(a)]. 149 x * K(x \ 1,x) = T(x,x). [para(18(a,1),147(a,2,1))]. 150 x * K(x \ 1,x) = x. [para(149(a,2),81(a,1))]. 151 K(x \ 1,x) = 1. [hyper(23,a,18,a,b,150,a)]. 152 T(x \ 1,x) = x \ 1. [hyper(41,a,151,a)]. 154 (x \ 1) * x = 1. [para(151(a,1),128(a,1)),flip(a)]. 155 1 / x = x \ 1. [para(151(a,1),129(a,1,1))]. 156 (x \ 1) \ 1 = x. [para(151(a,1),130(a,1,2))]. 157 x * (1 / x) = 1. [para(66(a,1),154(a,1,1))]. 160 T(x,x \ 1) = x. [para(156(a,1),83(a,2))]. 161 L(x,x \ 1,y) = (y * (x \ 1)) \ y. [para(156(a,1),142(a,1,1))]. 162 x / L(y,y \ 1,x) = x * (y \ 1). [para(156(a,1),145(a,1,2,1))]. 164 (x * 1) \ ((x * y) * (1 / y)) = a(x,y,1 / y). [para(157(a,1),28(a,2,1,2)),flip(a)]. 165 T(T(x,y),x \ 1) = T(x,y). [para(160(a,1),42(a,1,1)),flip(a)]. 166 K(T(x,y),x \ 1) = 1. [hyper(40,a,165,a)]. 167 K(x \ y,(y / x) \ 1) = 1. [para(84(a,1),166(a,1,1))]. 168 K(x,((y * x) / y) \ 1) = 1. [para(104(a,1),166(a,1,1))]. 169 T(x \ y,(y / x) \ 1) = x \ y. [hyper(41,a,167,a)]. 170 T(x,((y * x) / y) \ 1) = x. [hyper(41,a,168,a)]. 171 (x \ y) \ (x \ T(y,x)) = K(x \ (x \ y),x). [para(148(a,1),70(a,1,2))]. 172 x * L(y,z \ x,z) = z * ((z \ x) * y). [para(20(a,1),74(a,1,1))]. 173 x * L(y,z,x / z) = (x / z) * (z * y). [para(22(a,1),74(a,1,1))]. 174 (x * (y * z)) \ (x * (y * (z * u))) = L(L(u,z,y),y * z,x). [para(74(a,1),32(a,2,2,2)),flip(a)]. 176 (x * y) * L(z,K(x,y),y * x) = (y * x) * (K(x,y) * z). [para(69(a,1),74(a,1,1))]. 177 L(x \ (y \ z),x,y) = (y * x) \ z. [para(20(a,1),76(a,2,2))]. 178 L(x \ (y * x),x,y) = T(y,y * x). [para(76(a,2),36(a,2)),flip(a)]. 179 (x * y) / L(z \ y,z,x) = x * z. [para(76(a,2),65(a,1,2))]. 180 L(x \ T(y,z),x,z) = (z * x) \ (y * z). [para(82(a,1),76(a,2,2))]. 181 L(x \ (y \ ((y * x) * z)),x,y) = z. [para(76(a,2),62(a,1))]. 182 R(x,x,y) = x. [hyper(24,a,131,a(flip),b,79,a)]. 183 (R(x,y,z) * y) \ ((x * y) * z) = L(z,y,R(x,y,z)). [para(79(a,1),32(a,2,2)),flip(a)]. 184 L(R(x,y,z),u,w) * (y * z) = (L(x,u,w) * y) * z. [para(48(a,1),79(a,1,1))]. 185 R(R(x,y,z),u,w) * (y * z) = (R(x,u,w) * y) * z. [para(50(a,1),79(a,1,1))]. 186 R(T(x,y),x,z) = T(x,y). [para(182(a,1),46(a,2,1))]. 187 L(R(x,L(x,y,z),u),y,z) = L(x,y,z). [para(182(a,1),48(a,1)),flip(a)]. 188 R(R(x,y,z),x,u) = R(x,y,z). [para(182(a,1),50(a,1,1)),flip(a)]. 189 R(R(T(x,y),z,u),x,w) = R(T(x,y),z,u). [para(186(a,1),50(a,1,1)),flip(a)]. 190 (T(x,y) * x) * z = T(x,y) * (x * z). [para(186(a,1),79(a,1,1)),flip(a)]. 191 (R(x,y,z) * x) * u = R(x,y,z) * (x * u). [para(188(a,1),79(a,1,1)),flip(a)]. 192 R(1 / x,x,y) = y / (x * y). [para(17(a,1),80(a,2,1))]. 193 R((x / y) / z,z,y) = x / (z * y). [para(22(a,1),80(a,2,1))]. 194 T((x * y) / (z * y),u) = R(T(x / z,u),z,y). [para(80(a,1),46(a,2,1)),flip(a)]. 195 R(x,x \ 1,y) = y / ((x \ 1) * y). [para(65(a,1),192(a,1,1))]. 196 (x * y) / L(z,y / z,x) = x * (y / z). [para(22(a,1),99(a,1,1,2))]. 197 R(x,x \ y,z) \ (y * z) = (x \ y) * z. [para(20(a,1),101(a,1,2,1))]. 198 R(x,y \ 1,y) / y = x * (1 / y). [para(155(a,1),141(a,1,1,2))]. 199 L(K(x,y) \ ((y * x) \ z),K(x,y),y * x) = (x * y) \ z. [para(69(a,1),177(a,2,1))]. 200 (x * x) \ y = x \ (x \ y). [para(177(a,1),137(a,1))]. 201 L(x \ L(y \ z,y,u),x,u * y) = ((u * y) * x) \ (u * z). [para(76(a,2),177(a,1,1,2))]. 202 x \ (x \ (y * (x * x))) = T(y,x * x). [para(200(a,1),36(a,2)),flip(a)]. 203 L(T(x,y),y,x) = T(x,x * y). [para(36(a,2),178(a,1,1))]. 204 T(x,x * ((y * x) / y)) = L(x,(y * x) / y,x). [para(120(a,1),203(a,1,1)),flip(a)]. 205 x / L(y \ z,y,x / z) = (x / z) * y. [para(22(a,1),179(a,1,1))]. 207 R(x,y \ 1,y) / y = x * (y \ 1). [para(155(a,1),198(a,2,2))]. 208 (x * (y \ 1)) * y = R(x,y \ 1,y). [para(207(a,1),22(a,1,1))]. 209 (x * (y \ 1)) \ R(x,y \ 1,y) = y. [para(207(a,1),66(a,1,1))]. 210 R(x / (y \ 1),y \ 1,y) = x * y. [para(22(a,1),208(a,1,1)),flip(a)]. 211 (x * (x * y)) / z = x * (x * (y / z)). [para(22(a,1),85(a,1,1,2,2))]. 212 (x * (x * y)) \ (x * (x * z)) = y \ z. [para(20(a,1),86(a,1,2,2,2))]. 213 x \ ((x * y) * z) = x * ((x \ y) * z). [para(20(a,1),87(a,1,2,1,2))]. 214 L(x,y,z) * x = x * L(x,y,z). [para(81(a,1),109(a,1,2,1)),flip(a)]. 216 L(x \ 1,y,z) * x = x * L(x \ 1,y,z). [para(152(a,1),109(a,1,2,1)),flip(a)]. 217 x * T(y,y * x) = L(y,x,y) * x. [para(203(a,1),109(a,1,2))]. 218 (x * L(x,y,z)) / x = L(x,y,z). [hyper(24,a,22,a,b,214,a),flip(a)]. 219 T(x,L(x,y,z)) = x. [hyper(23,a,82,a,b,214,a),flip(a)]. 220 T(x,x * L(x,y,z)) = L(x,L(x,y,z),x). [para(219(a,1),203(a,1,1)),flip(a)]. 221 L(x,x \ y,x) * (x \ y) = (x \ y) * T(x,y). [para(20(a,1),217(a,1,2,2)),flip(a)]. 222 x * R(T(T(y,x),z),u,w) = R(T(y,z),u,w) * x. [para(42(a,1),110(a,1,2,1))]. 223 R(x,y,z) * x = x * R(x,y,z). [para(81(a,1),110(a,1,2,1)),flip(a)]. 224 R(x / y,z,u) * y = y * R(y \ x,z,u). [para(84(a,1),110(a,1,2,1)),flip(a)]. 225 (x \ y) * R((x \ y) \ y,z,u) = R(x,z,u) * (x \ y). [para(83(a,1),110(a,1,2,1))]. 226 x * (x * R(T(y,x * x),z,u)) = R(y,z,u) * (x * x). [para(110(a,1),131(a,1)),flip(a)]. 227 R(x \ 1,y,z) * x = x * R(x \ 1,y,z). [para(152(a,1),110(a,1,2,1)),flip(a)]. 228 T(x,R(x,y,z)) = x. [hyper(23,a,82,a,b,223,a),flip(a)]. 229 T(x \ y,R(y / x,z,u)) = T(y / x,x). [para(228(a,1),112(a,1,1)),flip(a)]. 230 x \ (y * (x * x)) = x * T(y,x * x). [hyper(23,a,20,a,b,136,a),flip(a)]. 231 T(x / (x * y),z) * (x * y) = (x * y) * T(L(y \ 1,y,x),z). [para(142(a,2),139(a,2,2,1))]. 232 T((x * y) / (x * z),u) * (x * z) = (x * z) * T(L(z \ y,z,x),u). [para(76(a,2),139(a,2,2,1))]. 233 (x * T(y,z)) / x = T((x * y) / x,z). [para(19(a,1),140(a,1,1,2,1))]. 234 L(x,y,T(y,z)) = x. [hyper(23,a,74,a,b,190,a),flip(a)]. 235 (x * T(x,y)) * z = T(x,y) * (x * z). [para(116(a,1),190(a,1,1))]. 236 L(x,y / z,z \ y) = x. [para(84(a,1),234(a,1,3))]. 237 L(x,(y * z) / y,z) = x. [para(104(a,1),234(a,1,3))]. 238 x * (x * ((x \ y) / z)) = (x * y) / z. [para(20(a,1),211(a,1,1,2)),flip(a)]. 239 (x * (x * y)) \ (x * x) = y \ 1. [para(18(a,1),212(a,1,2,2))]. 240 (x * y) \ (x * (x * z)) = (x \ y) \ z. [para(20(a,1),212(a,1,1,2))]. 241 T(x,x * (x * y)) = y \ (x * y). [para(212(a,1),36(a,2))]. 242 (x * y) \ (x * x) = (x \ y) \ 1. [para(20(a,1),239(a,1,1,2))]. 243 (x * x) / (y \ 1) = x * (x * y). [para(239(a,1),65(a,1,2))]. 244 ((x * y) * z) \ (x * x) = ((x \ y) * z) \ 1. [para(89(a,1),239(a,1,1))]. 245 T(x,x * (x * y)) = T(x,y). [para(241(a,2),36(a,2)),flip(a)]. 246 T(x,x \ y) = T(x,x * y). [para(20(a,1),245(a,1,2,2)),flip(a)]. 247 T(x,x * (y * x)) = T(x,T(y,x)). [para(82(a,1),245(a,1,2,2))]. 248 T(x * y,(x * y) * (y * x)) = T(x * y,K(y,x)). [para(69(a,1),245(a,1,2,2))]. 249 T(x,x * y) = (x \ y) \ y. [para(246(a,1),83(a,1))]. 250 (x \ y) * T(x,x * y) = y. [para(249(a,2),20(a,1,2))]. 251 T(x / y,x) = ((x / y) \ y) \ y. [para(22(a,1),249(a,1,2))]. 252 x / T(y,y * x) = y \ x. [para(249(a,2),65(a,1,2))]. 253 (x \ y) * ((x \ y) * (T(x,x * y) * z)) = ((x \ y) * y) * z. [para(249(a,2),89(a,1,2,2,1))]. 254 (x \ (x \ y)) * T(x,y) = x \ y. [para(20(a,1),250(a,1,2,2))]. 255 ((x \ y) * (T(x,x * y) * z)) \ (y * z) = a(x \ y,T(x,x * y),z). [para(250(a,1),28(a,2,2,1)),flip(a)]. 256 (x \ y) / T(x,y) = x \ (x \ y). [para(20(a,1),252(a,1,2,2))]. 257 K(x,y) / T(y * x,x * y) = (y * x) \ K(x,y). [para(69(a,1),252(a,1,2,2))]. 258 (x \ (x \ y)) \ 1 = y \ (x * x). [para(20(a,1),242(a,1,1)),flip(a)]. 259 L(x \ y,x,y) = (y \ x) \ 1. [para(242(a,1),76(a,2))]. 260 L(K(x,y),y * x,x * y) = ((x * y) \ (y * x)) \ 1. [para(30(a,2),259(a,1,1))]. 261 L(T(x \ y,z),x,y) = T((y \ x) \ 1,z). [para(259(a,1),44(a,2,1))]. 262 (x \ ((y * x) / y)) \ 1 = ((y * x) / y) \ x. [para(259(a,1),237(a,1))]. 263 x * (x * (y \ 1)) = (x * x) / y. [para(156(a,1),243(a,1,2)),flip(a)]. 264 (x \ (y * y)) \ 1 = y \ (y \ x). [para(258(a,1),156(a,1,1))]. 265 x * ((x \ (x \ y)) * z) = x \ (y * z). [para(20(a,1),213(a,1,2,1)),flip(a)]. 266 L(x \ (y * ((y \ x) * z)),x,y) = z. [para(213(a,1),181(a,1,1,2))]. 267 L(x \ (y * z),x,y) = (y \ x) \ z. [para(20(a,1),266(a,1,1,2,2))]. 268 L(x \ y,x,z) = (z \ x) \ (z \ y). [para(20(a,1),267(a,1,1,2))]. 269 L(x \ (y * z),x,z) = (z \ x) \ T(y,z). [para(82(a,1),267(a,1,1,2))]. 270 L((x * y) \ z,x * y,x) = y \ (x \ z). [para(19(a,1),268(a,2,1))]. 272 (x \ y) / L(z \ y,z,x) = x \ z. [para(268(a,2),65(a,1,2))]. 273 L(x \ y,x,x / z) = z \ ((x / z) \ y). [para(66(a,1),268(a,2,1))]. 274 (x \ y) \ (x \ z) = (x * y) \ (x * z). [para(268(a,1),76(a,1))]. 275 L(x \ L(y \ z,y,u),x,u \ y) = ((u \ y) * x) \ (u \ z). [para(268(a,2),177(a,1,1,2))]. 276 (x \ 1) / (y \ x) = x \ (x \ y). [para(143(a,1),272(a,1,2))]. 277 x \ (x \ (x / y)) = (x \ 1) / y. [para(66(a,1),276(a,1,2)),flip(a)]. 278 x * ((x \ 1) / y) = x \ (x / y). [para(277(a,1),20(a,1,2))]. 279 ((x \ 1) / y) \ 1 = (x / y) \ (x * x). [para(277(a,1),258(a,1,1))]. 280 T(x * T(x,y),T(x,y)) = x * T(x,y). [hyper(23,a,82,a,b,235,a(flip)),flip(a)]. 281 (x * T(x,y)) * (x \ z) = T(x,y) * z. [para(20(a,1),235(a,2,2))]. 282 (x * y) / (z \ (x \ y)) = x * (x * z). [para(65(a,1),238(a,1,2,2)),flip(a)]. 283 (x \ (x \ y)) \ z = y \ (x * (x * z)). [para(20(a,1),240(a,1,1)),flip(a)]. 284 (x \ y) \ ((x \ z) * u) = (x * y) \ ((x * z) * u). [para(89(a,1),240(a,1,2)),flip(a)]. 285 x \ (x \ (y * z)) = (x \ (x \ y)) * z. [hyper(23,a,20,a,b,265,a),flip(a)]. 286 (x \ (x \ y)) * (x * x) = T(y,x * x). [hyper(23,a,230,a(flip),b,265,a)]. 287 (x * (y * x)) \ (x * z) = T(y,x) \ (x \ z). [para(36(a,2),274(a,1,1)),flip(a)]. 288 T(x * T(x,y),T(x,y)) = T(x,y) * x. [para(280(a,2),116(a,2)),flip(a)]. 289 x / (y \ (x \ 1)) = x * (x * y). [para(18(a,1),282(a,1,1))]. 290 (x \ (x \ y)) \ y = T(x * x,y). [para(283(a,2),135(a,1))]. 291 (x \ (x \ 1)) * y = x \ (x \ y). [para(17(a,1),285(a,1,2,2)),flip(a)]. 292 (x \ (x \ y)) * (y \ z) = x \ (x \ z). [para(20(a,1),285(a,1,2,2)),flip(a)]. 293 R((x / y) / (z \ (z \ 1)),z \ (z \ 1),y) = x / (z \ (z \ y)). [para(291(a,1),193(a,2,2))]. 294 ((x \ 1) / y) * (x * x) = T(x / y,x * x). [para(277(a,1),286(a,1,1))]. 295 T(T(x,y) * x,T(x,y)) = T(x,y) * x. [para(116(a,2),288(a,1,1))]. 296 (x \ (x \ y)) \ (x \ (x \ z)) = y \ z. [hyper(23,a,20,a,b,292,a),flip(a)]. 297 (x \ y) * ((x * y) \ z) = x \ (x \ z). [para(19(a,1),292(a,1,1,2))]. 298 (T(x,y) \ x) * T(x,y) = x. [hyper(23,a,138,a,b,295,a(flip)),flip(a)]. 299 x / T(x,y) = T(x,y) \ x. [hyper(24,a,22,a,b,298,a),flip(a)]. 300 ((x * y) * z) / T(x * (y * z),a(x,y,z)) = a(x,y,z). [para(67(a,1),100(a,1,1))]. 301 L(x,x \ y,x) = y \ T(x * y,x). [para(138(a,1),75(a,1,2)),flip(a)]. 302 L(L(x,y \ z,y),z,y) = x. [para(75(a,1),266(a,1,1))]. 303 L(L(x,y,z),z * y,z) = x. [para(19(a,1),302(a,1,1,2))]. 304 L(L(x,y,z / y),z,z / y) = x. [para(66(a,1),302(a,1,1,2))]. 305 L(x,y \ 1,y) = x. [para(302(a,1),127(a,1)),flip(a)]. 306 L(x,y,y \ 1) = x. [para(156(a,1),305(a,1,2))]. 307 ((x \ 1) * x) \ ((x \ 1) * y) = x \ y. [para(306(a,1),76(a,1)),flip(a)]. 308 L(L(x,y * z,y),z,y) = x. [para(303(a,1),49(a,1)),flip(a)]. 309 x \ (y \ ((y * x) * z)) = L(z,y * x,y). [para(181(a,1),303(a,1,1)),flip(a)]. 310 R(x,L(x,y,z),u) = L(L(x,y,z),z * y,z). [para(187(a,1),303(a,1,1)),flip(a)]. 311 L((x \ y) \ z,x * y,x) = y \ (x * z). [para(267(a,1),303(a,1,1))]. 312 L(x,y \ z,y) = L(x,y * z,y). [para(302(a,1),303(a,1,1)),flip(a)]. 313 L(x,y * (y * z),y) = L(x,z,y). [para(303(a,1),303(a,1,1))]. 314 L(L(x,y * z,z),T(y,z),z) = x. [para(82(a,1),308(a,1,1,2))]. 315 L(L(x,y * z,z * y),K(y,z),z * y) = x. [para(69(a,1),308(a,1,1,2))]. 316 L(x,x * y,x) = y \ T(x * y,x). [para(301(a,1),312(a,1)),flip(a)]. 317 1 \ ((x \ 1) * y) = x \ y. [para(154(a,1),307(a,1,1))]. 318 (x \ 1) * y = x \ y. [para(317(a,1),59(a,1)),flip(a)]. 320 (x \ y) / y = x \ 1. [hyper(24,a,22,a,b,318,a),flip(a)]. 321 x * ((x \ 1) * y) = y. [hyper(23,a,19,a(flip),b,318,a)]. 322 (x \ 1) * (x * y) = y. [para(318(a,2),19(a,1))]. 323 (x \ (y * z)) \ (((x \ 1) * y) * z) = a(x \ 1,y,z). [para(318(a,1),28(a,2,1)),flip(a)]. 324 ((x * (y \ 1)) * z) / (y \ z) = R(x,y \ 1,z). [para(318(a,1),34(a,2,2)),flip(a)]. 325 T(x \ 1,y) = y \ (x \ y). [para(318(a,1),36(a,2,2))]. 326 x \ T(y,x \ 1) = y * (x \ 1). [para(318(a,1),82(a,1))]. 327 x * T(y \ 1,x) = y \ x. [para(318(a,1),82(a,2))]. 328 (x \ y) * K(y,x \ 1) = y * (x \ 1). [para(318(a,1),69(a,1,1))]. 329 x \ T(T(y,x \ 1),z) = T(y,z) * (x \ 1). [para(318(a,1),108(a,1))]. 330 (x \ 1) \ y = x * y. [para(156(a,1),318(a,1,1)),flip(a)]. 331 (x \ y) * L(z,y,x \ 1) = (x \ 1) * (y * z). [para(318(a,1),74(a,1,1))]. 332 R(x,y \ 1,z) * (y \ z) = (x * (y \ 1)) * z. [para(318(a,1),79(a,1,2))]. 333 (x * (y \ z)) / L(z,y \ 1,x) = x * (y \ 1). [para(318(a,1),99(a,1,1,2))]. 334 R(x,x \ 1,y) = y / (x \ y). [para(318(a,1),195(a,2,2))]. 335 R(x \ 1,y \ 1,y) = (x \ (y \ 1)) * y. [para(318(a,1),208(a,1,1)),flip(a)]. 336 L(x \ 1,y,x \ 1) * y = y * T(x \ 1,x \ y). [para(318(a,1),217(a,1,2,2)),flip(a)]. 337 T(x \ 1,(x \ 1) \ y) = T(x \ 1,x \ y). [para(318(a,1),246(a,2,2))]. 338 (x \ (x \ y)) \ z = (y \ (x * x)) * z. [para(258(a,1),318(a,1,1)),flip(a)]. 339 (x \ (y * y)) \ z = (y \ (y \ x)) * z. [para(264(a,1),318(a,1,1)),flip(a)]. 340 x / (y * x) = y \ 1. [para(19(a,1),320(a,1,1))]. 341 K(x,y) / (x * y) = (y * x) \ 1. [para(30(a,2),320(a,1,1))]. 342 L(x,y,z) / (z * (y * x)) = (z * y) \ 1. [para(32(a,2),320(a,1,1))]. 343 (x / y) \ 1 = y / x. [para(66(a,1),320(a,1,1)),flip(a)]. 344 (x * y) / ((z * x) * y) = R(z,x,y) \ 1. [para(101(a,1),320(a,1,1))]. 345 T(x * y,K(y,x)) / (y * x) = K(y,x) \ 1. [para(122(a,1),320(a,1,1))]. 346 T(x,x * y) / y = (x \ y) \ 1. [para(249(a,2),320(a,1,1))]. 347 x * (y * (x \ 1)) = T(y,x \ 1). [para(82(a,1),321(a,1,2))]. 348 R(x \ 1,x * y,z) = (y * z) / ((x * y) * z). [para(322(a,1),34(a,2,1,1))]. 349 T(x \ 1,x * y) = (x * y) \ y. [para(322(a,1),36(a,2,2))]. 350 R((x \ 1) / y,y,x * z) = z / (y * (x * z)). [para(322(a,1),80(a,2,1))]. 351 L(x * y,x \ 1,y) = (y \ (x \ 1)) \ 1. [para(330(a,1),259(a,1,1))]. 352 L(x * (y * z),x \ 1,y) = (y \ (x \ 1)) \ z. [para(330(a,1),267(a,1,1))]. 354 (x / y) * (y / x) = 1. [para(343(a,1),20(a,1,2))]. 355 K(x \ y,x / y) = 1. [para(343(a,1),167(a,1,2))]. 356 T(x,y / (y * x)) = x. [para(343(a,1),170(a,1,2))]. 357 T(x \ y,x / y) = x \ y. [para(343(a,1),169(a,1,2))]. 358 (x / y) \ z = (y / x) * z. [para(343(a,1),318(a,1,1)),flip(a)]. 359 (x / y) * ((y / x) * z) = z. [para(343(a,1),321(a,1,2,1))]. 360 x * ((y / z) * (z / y)) = x. [para(354(a,2),18(a,1,2))]. 361 K((x * y) \ y,x) = 1. [para(21(a,1),355(a,1,2))]. 362 (x / (x * y)) * y = y * (x / (x * y)). [para(356(a,1),82(a,1,2))]. 363 (x * (y / (y * x))) / x = y / (y * x). [para(356(a,1),100(a,1,2))]. 364 T(x,x * (y / (y * x))) = L(x,y / (y * x),x). [para(356(a,1),203(a,1,1)),flip(a)]. 365 T((x * y) \ y,x) = (x * y) \ y. [hyper(41,a,361,a)]. 366 x * R(x \ (y \ x),z,u) = R(y \ 1,z,u) * x. [para(325(a,1),110(a,1,2,1))]. 367 T(x / y,x \ y) = x / y. [hyper(39,a,357,a)]. 368 (x / y) * (x \ y) = (x \ y) * (x / y). [para(357(a,1),82(a,1,2))]. 369 (x / y) * (z * (y / x)) = T(z,y / x). [para(358(a,1),36(a,2)),flip(a)]. 370 T(x / y,x) = ((y / x) * y) \ y. [para(358(a,1),251(a,2,1))]. 371 ((x \ 1) / y) \ 1 = (y / x) * (x * x). [para(358(a,1),279(a,2))]. 372 T(x \ y,y \ x) = T(y / x,x). [para(367(a,1),112(a,1,1)),flip(a)]. 373 R(x,x \ 1,y) = x. [para(334(a,2),65(a,1))]. 374 R(T(x,y),x \ 1,z) = T(x,y). [para(373(a,1),46(a,2,1))]. 375 R(R(x,y,z),x \ 1,u) = R(x,y,z). [para(373(a,1),50(a,1,1)),flip(a)]. 376 R(T(x / y,y),(x / y) \ 1,z) = y \ x. [para(374(a,2),84(a,1))]. 377 T(x,y) * (x \ 1) = x \ T(x,y). [para(165(a,1),326(a,1,2)),flip(a)]. 378 x \ T(T(y,x \ 1),x) = (x \ (y * (x \ 1))) * x. [para(326(a,1),148(a,1,1,2)),flip(a)]. 379 K(x,y) * ((K(x,y) \ 1) / (x * y)) = K(x,y) \ ((y * x) \ 1). [para(341(a,1),278(a,2,2))]. 380 T(x \ 1,x * (y * y)) = (y \ (y \ (x * (y * y)))) \ 1. [para(349(a,2),258(a,2)),flip(a)]. 381 ((x * y) \ y) * x = x * ((x * y) \ y). [para(365(a,1),82(a,1,2)),flip(a)]. 382 T(x \ y,y \ x) = x \ y. [para(372(a,2),84(a,1))]. 383 T(x \ (x * y),(x * y) \ x) = y. [para(372(a,2),104(a,1))]. 384 (x \ y) * (y \ x) = (y \ x) * (x \ y). [para(382(a,1),82(a,1,2))]. 385 (x \ 1) \ T(x \ 1,x * y) = ((x * y) \ y) * ((x \ 1) \ 1). [para(349(a,1),377(a,1,1)),flip(a)]. 386 T(x,(y * x) \ y) = x. [para(19(a,1),383(a,1,1))]. 387 T(x,y \ (y / x)) = x. [para(22(a,1),386(a,1,2,1))]. 388 ((x * y) \ x) * y = y * ((x * y) \ x). [para(386(a,1),82(a,1,2))]. 389 T(K(x,y),(x * y) \ (y * x)) = K(x,y). [para(69(a,1),386(a,1,2,1))]. 390 R(x,y,z) * (x \ 1) = R(x,y,z) / x. [para(375(a,1),207(a,1,1)),flip(a)]. 391 x \ (y * (y * z)) = (x \ (y * y)) * z. [para(338(a,1),283(a,1)),flip(a)]. 392 (x \ (y * y)) * x = T(y * y,x). [para(338(a,1),290(a,1))]. 393 (x \ (y * y)) * (y \ (y \ z)) = x \ z. [para(338(a,1),296(a,1))]. 394 T(x * x,y * z) \ ((((y * z) \ (x * x)) * y) * z) = a((y * z) \ (x * x),y,z). [para(392(a,1),28(a,2,1)),flip(a)]. 395 L(x \ 1,x,x \ (y * y)) = T(y * y,x) \ (x \ (y * y)). [para(392(a,1),142(a,2,1))]. 396 ((x * y) \ ((x * y) \ ((x * y) * x))) * z = L(y,x,x * y) \ z. [para(32(a,2),339(a,1,1)),flip(a)]. 397 (x / y) * (y * y) = x / (y \ 1). [para(371(a,1),343(a,1))]. 398 (x / (y \ 1)) / (y * y) = x / y. [hyper(24,a,22,a,b,397,a),flip(a)]. 399 (x / y) * (y / (x \ 1)) = x * x. [hyper(23,a,359,a,b,397,a),flip(a)]. 400 (x * y) / (y \ 1) = x * (y * y). [para(21(a,1),397(a,1,1)),flip(a)]. 401 (x * (y \ 1)) / y = x / (y * y). [para(21(a,1),398(a,1,1)),flip(a)]. 402 ((x \ (x \ y)) * x) / (x \ 1) = T(y,x * x). [para(400(a,2),286(a,1))]. 403 T(x / (y * y),y) = y \ (x * (y \ 1)). [para(401(a,1),84(a,1,1))]. 404 T(K(x,y),K(y,x)) = K(x,y). [para(30(a,2),389(a,1,2))]. 405 T(K(x,y),z) * K(y,x) = K(y,x) * T(K(x,y),z). [para(404(a,1),108(a,1,2,1)),flip(a)]. 406 R(K(x,y),z,u) * K(y,x) = K(y,x) * R(K(x,y),z,u). [para(404(a,1),110(a,1,2,1)),flip(a)]. 407 x * ((x \ (y * y)) * z) = y * (y * z). [para(391(a,1),20(a,1,2))]. 408 (((x * y) * x) \ (x * x)) * y = K(x,x * y). [para(391(a,1),30(a,2)),flip(a)]. 409 (x * (y * y)) \ z = y \ (y \ (x \ z)). [hyper(23,a,297,a,b,393,a),flip(a)]. 410 x * ((x \ (y * y)) * z) = (y * y) * z. [para(407(a,2),131(a,2)),flip(a)]. 411 (x * (y * y)) * z = x * (y * (y * z)). [para(407(a,1),89(a,1,2)),flip(a)]. 412 x \ (x \ (y \ ((y * x) * x))) = a(y,x,x). [para(409(a,1),28(a,2)),flip(a)]. 413 (x * (y * y)) \ x = y \ (y \ 1). [para(60(a,1),409(a,2,2,2))]. 414 x \ (x / (y * y)) = y \ (y \ 1). [para(22(a,1),413(a,1,1))]. 415 x / (y \ (y \ 1)) = x * (y * y). [para(413(a,1),65(a,1,2))]. 416 x * (y \ (y \ 1)) = x / (y * y). [para(414(a,1),20(a,1,2))]. 417 (x * (y * y)) * z = x * ((y * y) * z). [para(410(a,1),89(a,1,2)),flip(a)]. 418 (x * (y * (y * z))) / z = x * (y * y). [hyper(24,a,22,a,b,411,a),flip(a)]. 419 (x * (y * (y * z))) \ ((x * (y * y)) * (z * u)) = L(u,z,x * (y * y)). [para(411(a,1),32(a,2,1)),flip(a)]. 420 (x \ (x \ y)) * (x * (x * z)) = T(y,x * x) * z. [para(286(a,1),411(a,1,1)),flip(a)]. 421 L(x,y * y,z) = x. [hyper(23,a,74,a,b,417,a),flip(a)]. 422 R(x,y * y,z) = x. [hyper(24,a,79,a,b,417,a(flip)),flip(a)]. 423 T(x,x * (y * y)) = T(x,y * y). [para(421(a,1),203(a,1)),flip(a)]. 424 L(x,y,y / (z * z)) = x. [para(421(a,1),304(a,1,1))]. 425 L(x,y \ (y \ 1),z) = x. [para(318(a,1),421(a,1,2))]. 426 R(x,y \ (y \ 1),z) = x. [para(318(a,1),422(a,1,2))]. 427 L(x,y,y / (z \ (z \ 1))) = x. [para(318(a,1),424(a,1,3,2))]. 428 (x * (y \ (y \ 1))) * z = x * ((y \ (y \ 1)) * z). [para(425(a,1),74(a,1,2))]. 429 L(x,y,y * (z * z)) = x. [para(415(a,1),427(a,1,3))]. 430 T(x,x \ (y * y)) = T(x,y * y). [para(423(a,1),246(a,2))]. 431 T(x \ 1,x * (y * y)) = T(x \ 1,y * y). [para(330(a,1),430(a,1,2))]. 432 L(x,x,y / x) = y \ (y / (x \ 1)). [para(397(a,1),77(a,1,2)),flip(a)]. 433 (x * y) * (y \ 1) = R(x,y,y \ 1). [para(78(a,1),64(a,1)),flip(a)]. 434 R(x / y,y,y \ 1) = x * (y \ 1). [para(22(a,1),433(a,1,1)),flip(a)]. 435 x * L(y,z * x,z) = z * ((z \ x) * y). [para(312(a,1),172(a,1,2))]. 436 (R(T(x,y),z,u) * x) * w = R(T(x,y),z,u) * (x * w). [para(189(a,1),79(a,1,1)),flip(a)]. 437 T(x \ y,R(y / x,z,u)) = x \ y. [para(229(a,2),84(a,1))]. 438 T((x \ 1) \ y,y * x) = (x \ 1) \ y. [para(210(a,1),437(a,1,2))]. 439 T(x * y,y * x) = (x \ 1) \ y. [para(330(a,1),438(a,1,1))]. 440 (x \ y) \ T(y,x) = L(x,y,x). [para(19(a,1),269(a,1,1)),flip(a)]. 441 T(x,y) / L(y,x,y) = y \ x. [para(440(a,1),65(a,1,2))]. 442 L(x \ (x / y),y,x \ (x / y)) = ((x \ (x / y)) \ y) \ y. [para(387(a,1),440(a,1,2)),flip(a)]. 443 (x * (x * y)) \ z = y \ (x \ (x \ z)). [para(270(a,1),177(a,1)),flip(a)]. 444 x \ (y \ (y \ (z * (y * (y * x))))) = T(z,y * (y * x)). [para(443(a,1),36(a,2)),flip(a)]. 445 L(x \ 1,x,x / y) = y \ (y / x). [para(343(a,1),273(a,2,2))]. 446 x * (y \ ((y * (x \ 1)) * z)) = L(z,y * (x \ 1),y). [para(309(a,1),330(a,1)),flip(a)]. 447 R(x \ y,(y / x) \ 1,z) = x \ y. [para(84(a,1),376(a,1,1))]. 448 R(x \ y,x / y,z) = x \ y. [para(343(a,1),447(a,1,2))]. 449 R(x \ (x * y),x / (x * y),z) = y. [para(448(a,2),19(a,1))]. 450 R(x,y / (y * x),z) = x. [para(19(a,1),449(a,1,1))]. 451 (x * (y / (y * x))) * z = x * ((y / (y * x)) * z). [para(450(a,1),79(a,1,1)),flip(a)]. 452 x \ L(x,y * x,y) = a(y,x,x). [para(309(a,1),412(a,1,2))]. 453 L(x,y * x,y) = x * a(y,x,x). [para(452(a,1),20(a,1,2)),flip(a)]. 454 L(x * a(y,x,x),x,y) = x. [para(453(a,1),308(a,1,1))]. 455 x * ((x \ y) * T(z,y)) = L(z,x * y,x) * y. [para(435(a,1),109(a,1))]. 456 (x * y) \ (x * T(y,x)) = K(x \ (x \ y),x). [para(171(a,1),274(a,1)),flip(a)]. 457 L(x,y,R(y,z,u)) = x. [hyper(23,a,74,a,b,191,a),flip(a)]. 458 R(x,y,z) * ((R(x,y,z) \ x) * u) = x * u. [hyper(23,a,89,a,b,191,a(flip)),flip(a)]. 459 (x * R(x,y,z)) * u = R(x,y,z) * (x * u). [para(223(a,1),191(a,1,1))]. 460 (R(x,y,z) \ x) \ 1 = x \ R(x,y,z). [para(457(a,1),259(a,1)),flip(a)]. 461 (R(x,y,z) \ u) / (x \ u) = R(x,y,z) \ x. [para(457(a,1),272(a,1,2))]. 462 (x \ R(x,y,z)) \ 1 = R(x,y,z) \ x. [para(460(a,1),156(a,1,1))]. 463 (R(x,y,z) \ x) \ u = (x \ R(x,y,z)) * u. [para(460(a,1),318(a,1,1)),flip(a)]. 464 (R(x,y,z) \ x) * ((x \ R(x,y,z)) * u) = u. [para(460(a,1),321(a,1,2,1))]. 465 (x \ R(x,y,z)) \ u = (R(x,y,z) \ x) * u. [para(460(a,1),330(a,1,1))]. 466 T(x,L(x \ 1,y,z)) = x. [hyper(23,a,82,a,b,216,a),flip(a)]. 467 K(x,L(x \ 1,y,z)) = 1. [hyper(40,a,466,a)]. 468 K(x \ 1,L(x,y,z)) = 1. [para(156(a,1),467(a,1,2,1))]. 469 K(L(x,y,z) \ 1,x) = 1. [para(303(a,1),468(a,1,2))]. 470 T(L(x,y,z) \ 1,x) = L(x,y,z) \ 1. [hyper(41,a,469,a)]. 471 x * (L(x,y,z) \ 1) = L(x,y,z) \ x. [para(470(a,1),327(a,1,2))]. 472 R(x / (x * y),z,u) * (x * y) = (x * y) * R(L(y \ 1,y,x),z,u). [para(142(a,2),224(a,2,2,1))]. 473 R((x * y) / (x * z),u,w) * (x * z) = (x * z) * R(L(z \ y,z,x),u,w). [para(76(a,2),224(a,2,2,1))]. 475 T(x,R(x \ 1,y,z)) = x. [hyper(23,a,82,a,b,227,a),flip(a)]. 476 T(x \ 1,R(x,y,z)) = x \ 1. [para(156(a,1),475(a,1,2,1))]. 477 R(x,y,z) * (x \ 1) = x \ R(x,y,z). [para(476(a,1),327(a,1,2))]. 478 R(x,y,z) / x = x \ R(x,y,z). [para(477(a,1),390(a,1)),flip(a)]. 480 (x \ R(x,y,z)) \ R(x,y,z) = x. [para(478(a,1),66(a,1,1))]. 481 (x / y) \ R(x / y,y,y \ 1) = (x * (y \ 1)) / (x / y). [para(434(a,1),478(a,1,1)),flip(a)]. 482 (x \ ((y * x) / y)) \ 1 = (y / (y * x)) * x. [para(262(a,2),358(a,1))]. 483 R(x,L(x,y,z),u) = x. [para(310(a,2),303(a,1))]. 484 (x * L(x,y,z)) * u = x * (L(x,y,z) * u). [para(483(a,1),79(a,1,1)),flip(a)]. 485 T(x \ 1,x \ y) = T(x \ 1,x * y). [para(330(a,1),337(a,1,2)),flip(a)]. 486 (x \ T(y,x)) / (x \ 1) = T(y,x * x). [para(148(a,1),402(a,1,1))]. 487 (((x \ y) * x) \ 1) * y = K(x,x * y). [para(244(a,1),408(a,1,1))]. 488 ((x \ y) * x) \ y = K(x,x * y). [para(487(a,1),318(a,1)),flip(a)]. 489 K(x,x \ y) = K(x,x * y). [para(488(a,1),71(a,1)),flip(a)]. 490 K(x,x * (x * y)) = K(x,y). [para(19(a,1),489(a,1,2)),flip(a)]. 491 K(x,x * (y * x)) = K(x,T(y,x)). [para(36(a,2),489(a,1,2)),flip(a)]. 492 K(x,(x * x) / y) = K(x,y \ 1). [para(263(a,1),490(a,1,2))]. 493 K(x \ (x \ y),x) = (x * y) \ (y * x). [para(82(a,1),456(a,1,2)),flip(a)]. 494 K(x \ (x \ y),x) = K(y,x). [para(493(a,2),30(a,2)),flip(a)]. 495 K(x \ y,x) = K(x * y,x). [para(19(a,1),494(a,1,1,2))]. 496 (R(x,y,z) \ x) * R(x,y,z) = x. [hyper(23,a,223,a,b,458,a)]. 498 x / R(x,y,z) = R(x,y,z) \ x. [hyper(24,a,22,a,b,496,a),flip(a)]. 499 T(R(x,y,z) \ 1,x) = x \ (x / R(x,y,z)). [para(498(a,2),325(a,2,2))]. 500 (x * y) / (z \ ((z * x) * y)) = R(z,x,y) \ z. [para(101(a,1),461(a,1,1))]. 501 x * ((x \ R(x,y,z)) * u) = R(x,y,z) * u. [para(464(a,1),458(a,1,2)),flip(a)]. 502 (x \ ((y * x) / y)) \ 1 = x * (y / (y * x)). [para(482(a,2),362(a,1))]. 503 L(x,L(y,z,u),y) = x. [hyper(23,a,74,a,b,484,a),flip(a)]. 504 x * ((x \ L(x,y,z)) * u) = L(x,y,z) * u. [hyper(23,a,89,a,b,484,a(flip)),flip(a)]. 505 L(x,(y * z) \ y,z \ 1) = x. [para(142(a,1),503(a,1,2))]. 506 (x \ L(x,y,z)) \ 1 = L(x,y,z) \ x. [para(503(a,1),259(a,1)),flip(a)]. 507 (x \ L(x,y,z)) \ u = L(x,y,z) \ (x * u). [para(503(a,1),267(a,1)),flip(a)]. 509 L(x,y,L(y,z,u)) = x. [para(303(a,1),503(a,1,2))]. 510 T(x,x * L(x,y,z)) = x. [para(503(a,1),220(a,2))]. 511 (L(x,y,z) \ x) \ 1 = x \ L(x,y,z). [para(509(a,1),259(a,1)),flip(a)]. 513 (L(x,y,z) \ u) / (x \ u) = L(x,y,z) \ x. [para(509(a,1),272(a,1,2))]. 514 (x \ L(x,y,z)) * x = L(x,y,z). [para(510(a,1),250(a,1,2))]. 515 L(x,y,z) / x = x \ L(x,y,z). [para(510(a,1),252(a,1,2))]. 516 (x \ L(x,y,z)) \ 1 = x / L(x,y,z). [para(510(a,1),346(a,1,1)),flip(a)]. 517 (x \ L(x,y,z)) \ u = (L(x,y,z) \ x) * u. [para(506(a,1),318(a,1,1)),flip(a)]. 519 x / L(x,y,z) = L(x,y,z) \ x. [para(516(a,1),506(a,1))]. 520 (L(x,y,z) \ x) * L(x,y,z) = x. [para(519(a,1),22(a,1,1))]. 521 (L(x \ 1,x,x / y) \ (x \ 1)) * (y \ (y / x)) = x \ 1. [para(445(a,1),520(a,1,2))]. 523 (x * R(x,y,z)) * u = x * (R(x,y,z) * u). [para(501(a,1),89(a,1,2)),flip(a)]. 524 L(x,y,z) \ (x * u) = (L(x,y,z) \ x) * u. [para(517(a,1),507(a,1)),flip(a)]. 525 R(x,R(x,y,z),u) = x. [hyper(24,a,79,a,b,523,a(flip)),flip(a)]. 526 R(x,y,z) * (x * u) = x * (R(x,y,z) * u). [para(523(a,1),459(a,1)),flip(a)]. 527 R(T(x,y),R(x,z,u),w) = T(x,y). [para(525(a,1),46(a,2,1))]. 528 (x \ R(x,y,z)) * (x * u) = R(x,y,z) * u. [hyper(23,a,501,a,b,526,a(flip)),flip(a)]. 529 x * (R(x,y,z) * (x \ u)) = R(x,y,z) * u. [para(20(a,1),526(a,1,2)),flip(a)]. 530 x * (R(x,y,z) * T(u,x)) = R(x,y,z) * (u * x). [para(82(a,1),526(a,1,2)),flip(a)]. 531 (R(x,y,z) * u) / (x * u) = x \ R(x,y,z). [hyper(24,a,22,a,b,528,a),flip(a)]. 532 (x \ R(x,y,z)) * u = R(x,y,z) * (x \ u). [para(20(a,1),528(a,1,2))]. 533 R(x \ R(x,y,z),x * u,w) = ((R(x,y,z) * u) * w) / ((x * u) * w). [para(528(a,1),34(a,2,1,1))]. 534 x \ (R(x,y,z) * u) = R(x,y,z) * (x \ u). [hyper(23,a,20,a,b,529,a),flip(a)]. 535 x / (y * (R(y,z,u) \ x)) = y \ R(y,z,u). [para(20(a,1),531(a,1,1))]. 536 (R(x,y,z) * (x \ u)) / u = x \ R(x,y,z). [para(20(a,1),531(a,1,2))]. 537 ((x * y) * z) / (x * (y * z)) = x \ R(x,y,z). [para(79(a,1),531(a,1,1))]. 538 (R(R(x,y,z),u,w) * (y * z)) / ((x * y) * z) = R(x,y,z) \ R(R(x,y,z),u,w). [para(79(a,1),531(a,1,2))]. 539 x \ (R(y,z,u) * (y \ x)) = T(y \ R(y,z,u),x). [para(532(a,1),36(a,2,2)),flip(a)]. 540 (R(x,y,z) \ x) \ u = R(x,y,z) * (x \ u). [para(532(a,1),463(a,2))]. 541 (x \ R(x,y,z)) \ u = x * (R(x,y,z) \ u). [para(535(a,1),66(a,1,1))]. 542 x / (R(y,z,u) * (y \ x)) = R(y,z,u) \ y. [para(540(a,1),65(a,1,2))]. 543 x * (R(x,y,z) \ 1) = R(x,y,z) \ x. [para(541(a,1),462(a,1))]. 544 (R(x,y,z) \ x) * u = x * (R(x,y,z) \ u). [para(541(a,1),465(a,1)),flip(a)]. 545 T(R(x,y,z) \ 1,x) = R(x,y,z) \ 1. [hyper(23,a,327,a,b,543,a),flip(a)]. 546 T(x,R(x,y,z) \ 1) = x. [hyper(39,a,545,a)]. 547 x \ (x / R(x,y,z)) = R(x,y,z) \ 1. [para(545(a,1),499(a,1)),flip(a)]. 548 T(x,y) * (R(x,z,u) \ 1) = R(x,z,u) \ T(x,y). [para(546(a,1),329(a,1,2,1)),flip(a)]. 549 (x * y) \ ((z * x) * y) = R(T(z,x * y),x,y). [para(111(a,2),46(a,2)),flip(a)]. 550 (x * (x * (y * z))) / (y * z) = R(x * x,y,z). [para(51(a,1),134(a,1,1))]. 551 x \ ((x * y) * (1 / y)) = a(x,y,1 / y). [para(18(a,1),164(a,1,1))]. 552 x \ ((x * y) * (y \ 1)) = a(x,y,1 / y). [para(155(a,1),551(a,1,2,2))]. 553 x \ ((x * y) * (y \ 1)) = a(x,y,y \ 1). [para(155(a,1),552(a,2,3))]. 554 a(x / y,y,y \ 1) = (x / y) \ (x * (y \ 1)). [para(22(a,1),553(a,1,2,1)),flip(a)]. 555 T((x * y) / (z * y),z) = R(z \ x,z,y). [para(84(a,1),194(a,2,1))]. 556 T(T((x * y) / (z * y),u),z) = T(R(z \ x,z,y),u). [para(555(a,1),42(a,1,1)),flip(a)]. 557 T(x,x * ((y * x) / y)) = x. [para(204(a,2),237(a,1))]. 558 ((x * y) / x) / y = y \ ((x * y) / x). [para(557(a,1),252(a,1,2))]. 559 L(x,x * y,x) * (x \ y) = (x \ y) * T(x,y). [para(312(a,1),221(a,1,1))]. 560 (x \ y) * L(z,y,x \ 1) = x \ (y * z). [para(331(a,2),318(a,1))]. 561 (T(x,y) * (x \ 1)) * z = T(x,y) * (x \ z). [para(374(a,1),332(a,1,1)),flip(a)]. 562 (x \ T(x,y)) * z = T(x,y) * (x \ z). [para(377(a,1),561(a,1,1))]. 563 (T(x,y) * (x \ z)) / z = x \ T(x,y). [hyper(24,a,22,a,b,562,a),flip(a)]. 564 x * (T(x,y) * (x \ x)) = T(x * T(x,y),x). [para(562(a,1),138(a,1,2))]. 565 (T(x,y) * z) / (x * z) = x \ T(x,y). [para(19(a,1),563(a,1,1,2))]. 566 (x \ T(x,y)) \ (T(x,y) * z) = x * z. [para(565(a,1),66(a,1,1))]. 567 (x \ T(x,y)) \ z = x * (T(x,y) \ z). [para(20(a,1),566(a,1,2))]. 568 T(x * T(x,y),x) = x * (T(x,y) * 1). [para(60(a,1),564(a,1,2,2)),flip(a)]. 569 T(x * T(x,y),x) = x * T(x,y). [para(18(a,1),568(a,2,2))]. 571 T(x,x * T(x,y)) = x. [hyper(39,a,569,a)]. 572 T(x,y) / x = x \ T(x,y). [para(571(a,1),252(a,1,2))]. 573 (x \ T(x,y)) \ z = (x / T(x,y)) * z. [para(572(a,1),358(a,1,1))]. 574 (x \ T(x,y)) \ z = (T(x,y) \ x) * z. [para(299(a,1),573(a,2,1))]. 575 (T(x,y) \ x) * (T(x,y) * z) = x * z. [para(574(a,1),566(a,1))]. 576 (T(x,y) \ x) * z = x * (T(x,y) \ z). [para(574(a,1),567(a,1))]. 577 (x * y) / (T(x,z) * y) = T(x,z) \ x. [hyper(24,a,22,a,b,575,a),flip(a)]. 578 x * (T(x,y) \ 1) = T(x,y) \ x. [hyper(24,a,18,a,b,576,a),flip(a)]. 579 K(x,T(x,y) \ 1) = 1. [hyper(23,a,328,a,b,576,a),flip(a)]. 580 T(x,T(x,y) \ 1) = x. [hyper(41,a,579,a)]. 581 T(x,y) * (T(x,z) \ 1) = T(x,z) \ T(x,y). [para(580(a,1),329(a,1,2,1)),flip(a)]. 582 x \ (T(x,y) \ x) = T(x,y) \ 1. [hyper(23,a,20,a,b,578,a),flip(a)]. 583 ((T(x,y) \ x) * z) / (T(x,y) \ z) = R(x,T(x,y) \ 1,z). [para(578(a,1),324(a,1,1,1))]. 584 R(x \ 1,x * y,z) = R(x,y,z) \ 1. [para(348(a,2),344(a,1))]. 585 R(x,x \ y,z) \ 1 = R(x \ 1,y,z). [para(20(a,1),584(a,1,2)),flip(a)]. 586 (x * y) / (z * ((z \ x) * y)) = R(z,x,y) \ z. [para(213(a,1),500(a,1,2))]. 587 T(x \ R(x,y,z),x * (y * z)) = (x * (y * z)) \ ((x * y) * z). [para(537(a,1),84(a,1,1))]. 588 R(x * x,y,z) = x * x. [para(550(a,1),132(a,1))]. 589 R(T(x * x,y),z,u) = T(x * x,y). [para(588(a,1),46(a,2,1))]. 591 T(x * x,y) \ (z * u) = (T(x * x,y) \ z) * u. [para(589(a,1),197(a,1,1))]. 592 a(x / y,y,y \ 1) = (y / x) * (x * (y \ 1)). [para(554(a,2),358(a,1))]. 593 (x * y) / (z * ((z \ y) * T(x,y))) = R(z,y,T(x,y)) \ z. [para(82(a,1),586(a,1,1))]. 594 a(x,y,z) = (x \ (y * z)) \ ((x \ y) * z). [para(284(a,2),28(a,2))]. 596 (x \ (y * (x \ 1))) * x = T(y,x) * (x \ 1). [para(378(a,1),329(a,1))]. 597 (T(x,y) * (y \ 1)) / y = y \ (x * (y \ 1)). [hyper(24,a,22,a,b,596,a),flip(a)]. 598 x \ (y * (x \ 1)) = T(y,x) / (x * x). [para(597(a,1),401(a,1))]. 599 x \ ((x * (x * y)) * (x \ 1)) = (x * (y * x)) / (x * x). [para(103(a,1),598(a,2,1))]. 600 T(x,y) / (y * y) = T(x / (y * y),y). [para(598(a,1),403(a,2)),flip(a)]. 601 x * ((y \ (y \ 1)) * z) = (x / (y * y)) * z. [para(416(a,1),428(a,1,1)),flip(a)]. 602 (x / (y * y)) * z = x * (y \ (y \ z)). [para(291(a,1),601(a,1,2)),flip(a)]. 603 L(x,y / (y * z),z) = x. [hyper(23,a,74,a,b,451,a),flip(a)]. 604 (x * (y / (y * x))) \ z = (y / (y * x)) \ (x \ z). [para(603(a,1),177(a,1)),flip(a)]. 605 T(x,x * (y / (y * x))) = x. [para(603(a,1),364(a,2))]. 606 (x * (y / (y * x))) \ z = ((y * x) / y) * (x \ z). [para(604(a,2),358(a,1))]. 607 x * (x * ((y * z) / ((x * y) * z))) = R(x,x * y,z). [para(95(a,1),211(a,1)),flip(a)]. 608 L(R(x,x,y),z,u) * (x * y) = (x * L(x,z,u)) * y. [para(214(a,1),184(a,2,1))]. 609 L(K(x,y),y * x,x * y) = K(y,x) \ 1. [para(30(a,2),260(a,2,1))]. 610 (x \ (y * z)) \ ((x \ y) * z) = a(x \ 1,y,z). [para(318(a,1),323(a,1,2,1))]. 611 a(x \ 1,y,z) = a(x,y,z). [para(610(a,1),594(a,2)),flip(a)]. 612 a(x / y,z,u) = a(y / x,z,u). [para(343(a,1),611(a,1,1))]. 613 L(x \ 1,y,x \ 1) * y = y * T(x \ 1,x * y). [para(485(a,1),336(a,2,2))]. 614 T(T((x * y) / (z * y),u),z) = R(T(z \ x,u),z,y). [para(556(a,2),46(a,2)),flip(a)]. 615 x * (x * (R(x,y,z) \ 1)) = R(x,x * y,z). [para(344(a,1),607(a,1,2,2))]. 616 (x * x) / R(x,y,z) = R(x,x * y,z). [para(615(a,1),263(a,1)),flip(a)]. 617 x * (R(x,y,z) \ x) = R(x,x * y,z). [para(543(a,1),615(a,1,2))]. 618 x \ R(x,x * y,z) = R(x,y,z) \ x. [hyper(23,a,20,a,b,617,a),flip(a)]. 619 x * (R(x,x * y,z) \ x) = R(x,(x * x) * y,z). [para(131(a,2),617(a,2,2))]. 620 x / R(x,x * y,z) = x \ R(x,y,z). [para(617(a,1),535(a,1,2))]. 621 (R(x,y,z) \ x) * x = R(x,x * y,z). [para(617(a,1),544(a,2))]. 622 R(x,x * y,z) \ x = x \ R(x,y,z). [para(620(a,1),498(a,1)),flip(a)]. 623 R(x,x * y,z) \ 1 = x \ (x \ R(x,y,z)). [para(620(a,1),547(a,1,2)),flip(a)]. 624 x \ R(x,x \ y,z) = R(x,y,z) \ x. [para(20(a,1),622(a,1,1,2)),flip(a)]. 625 x * (R(x,x * y,z) \ u) = (x \ R(x,y,z)) * u. [para(622(a,1),544(a,1,1)),flip(a)]. 626 R(x,(x * x) * y,z) = x * (x \ R(x,y,z)). [para(622(a,1),619(a,1,2)),flip(a)]. 627 R(x,(x * x) * y,z) = R(x,y,z). [para(626(a,2),20(a,1))]. 628 R(x,x * (x * y),z) = R(x,y,z). [para(131(a,1),627(a,1,2))]. 629 R(x,x \ y,z) = R(x,x * y,z). [para(20(a,1),628(a,1,2,2)),flip(a)]. 630 R(x,x * y,z) \ (y * z) = (x \ y) * z. [para(629(a,1),197(a,1,1))]. 632 R(x,x * y,z) \ 1 = R(x \ 1,y,z). [para(629(a,1),585(a,1,1))]. 633 R(x,x * y,z) = R(x \ 1,y,z) \ 1. [para(632(a,1),156(a,1,1)),flip(a)]. 634 x \ (x \ R(x,y,z)) = R(x \ 1,y,z). [para(632(a,1),623(a,1)),flip(a)]. 635 x * R(x \ 1,y,z) = x \ R(x,y,z). [para(634(a,1),20(a,1,2))]. 636 x * (R(x \ 1,y,z) * u) = x \ (R(x,y,z) * u). [para(634(a,1),265(a,1,2,1))]. 637 x * (R(x,x * y,z) \ u) = R(x,y,z) * (x \ u). [para(625(a,2),532(a,1))]. 638 x * (R(x \ 1,y,z) * u) = R(x,y,z) * (x \ u). [para(636(a,2),534(a,1))]. 639 x * (y * R(y \ (x \ y),z,u)) = R(x,z,u) * (x \ y). [para(366(a,2),638(a,1,2))]. 640 (x * L(x,y,z)) * u = L(x,y,z) * (x * u). [para(182(a,1),608(a,1,1,1)),flip(a)]. 641 L(x,y,z) \ ((x * L(x,y,z)) * u) = x * u. [hyper(23,a,20,a,b,640,a(flip)),flip(a)]. 642 L(x,y,z) * (x * u) = x * (L(x,y,z) * u). [para(640(a,1),484(a,1))]. 643 L(x,y,z) \ (x * (L(x,y,z) * u)) = x * u. [para(484(a,1),641(a,1,2))]. 644 x * (L(x,y,z) * (x \ u)) = L(x,y,z) * u. [para(20(a,1),642(a,1,2)),flip(a)]. 645 L(x,y,z) * (x * (L(x,y,z) \ u)) = x * u. [para(20(a,1),642(a,2,2))]. 646 (L(x,y,z) \ x) * (L(x,y,z) * u) = x * u. [para(643(a,1),524(a,1)),flip(a)]. 647 (x \ L(x,y,z)) * u = L(x,y,z) * (x \ u). [hyper(23,a,504,a,b,644,a),flip(a)]. 648 (x * y) / (x * (L(x,z,u) \ y)) = L(x,z,u). [hyper(24,a,22,a,b,645,a),flip(a)]. 649 (x * y) / (L(x,z,u) * y) = L(x,z,u) \ x. [hyper(24,a,22,a,b,646,a),flip(a)]. 650 (L(x,y,z) \ x) * u = x * (L(x,y,z) \ u). [para(20(a,1),646(a,1,2))]. 652 T(x,L(x,y,z) \ x) = x. [hyper(23,a,82,a,b,650,a),flip(a)]. 653 K(x,L(x,y,z) \ x) = 1. [hyper(40,a,652,a)]. 654 T(x \ 1,x * (y * y)) = T(x,y * y) \ 1. [para(202(a,1),380(a,2,1))]. 655 T(x,y * y) \ 1 = T(x \ 1,y * y). [para(654(a,1),431(a,1))]. 656 L(x,y,R(T(y,z),u,w)) = x. [hyper(23,a,74,a,b,436,a),flip(a)]. 657 L(x,y,R((y \ z) \ z,u,w)) = x. [para(83(a,1),656(a,1,3,1))]. 658 x \ ((y \ (y \ z)) * (y * (y * x))) = T(z,y * (y * x)). [para(285(a,1),444(a,1,2))]. 659 x \ (x * (x * (y * (x \ 1)))) = (x * (y * x)) / (x * x). [para(51(a,1),599(a,1,2))]. 660 x \ (T(y,z * z) * x) = T(y,z * (z * x)). [para(420(a,1),658(a,1,2))]. 661 T(T(x,y * y),z) = T(x,y * (y * z)). [para(660(a,1),36(a,2))]. 662 T(T(x,y),z * z) = T(x,z * (z * y)). [para(661(a,1),42(a,1)),flip(a)]. 663 x \ (x * T(y,x \ 1)) = (x * (y * x)) / (x * x). [para(347(a,1),659(a,1,2,2))]. 664 (x * (y * x)) / (x * x) = T(y,x \ 1). [para(663(a,1),19(a,1))]. 665 T(x * y,x) / (x * x) = T(x \ y,x \ 1). [para(138(a,1),664(a,1,1))]. 666 T((x * y) / (x * x),x) = T(x \ y,x \ 1). [para(665(a,1),600(a,1)),flip(a)]. 667 (x * (x * ((y * z) * u))) / (z * u) = R(x * (x * y),z,u). [para(51(a,1),94(a,1,1))]. 668 (x * (y \ 1)) / (x / y) = (x / y) \ (x * (y \ 1)). [para(434(a,1),481(a,1,2)),flip(a)]. 669 (x * (y \ 1)) / (x / y) = (y / x) * (x * (y \ 1)). [para(668(a,2),358(a,1))]. 670 (x * (T(x,y) \ z)) / (T(x,y) \ z) = R(x,T(x,y) \ 1,z). [para(576(a,1),583(a,1,1))]. 671 (x * y) / (L(x,z * y,z) * y) = R(z,y,T(x,y)) \ z. [para(455(a,1),593(a,1,2))]. 672 R(x,y,T(z,y)) \ x = L(z,x * y,x) \ z. [para(671(a,1),649(a,1))]. 673 (R(x,y,T(z,y)) \ x) \ 1 = z \ L(z,x * y,x). [para(672(a,2),511(a,1,1))]. 674 L(x,y * (y * z),y) \ x = y \ R(y,z,T(x,y * z)). [para(672(a,1),622(a,1))]. 676 x \ R(x,y,T(z,y)) = z \ L(z,x * y,x). [para(673(a,1),460(a,1)),flip(a)]. 677 R(x,y,T(z,y)) = x * (z \ L(z,x * y,x)). [para(676(a,1),20(a,1,2)),flip(a)]. 678 R(x,x * y,T(z,x * y)) = x * (z \ L(z,y,x)). [para(313(a,1),677(a,2,2,2))]. 679 R(x,y,T(z,x * y)) \ x = z \ L(z,y,x). [hyper(23,a,617,a,b,678,a(flip)),flip(a)]. 680 (x \ L(x,y,z)) * R(z,y,T(x,z * y)) = z. [para(679(a,1),496(a,1,1))]. 681 L(x,y,z) \ x = z \ R(z,y,T(x,z * y)). [para(313(a,1),674(a,1,1))]. 682 L(x,y,z) * (z \ R(z,y,T(x,z * y))) = x. [para(681(a,1),20(a,1,2))]. 683 R(x,y,T(z,x * y)) = x * (L(z,y,x) \ z). [para(681(a,2),20(a,1,2)),flip(a)]. 684 (x \ R(x,y,T(z,x * y))) * L(z,y,x) = z. [para(681(a,1),520(a,1,1))]. 685 L(x,R(y,z,u),T(y,w)) * (T(y,w) \ T(y,w)) = x. [para(527(a,1),682(a,1,2,2))]. 686 R(x,y,T(z,x * y)) * (x \ L(z,y,x)) = z. [para(684(a,1),532(a,1)),flip(a)]. 687 L(x,R(y,z,u),T(y,w)) * 1 = x. [para(60(a,1),685(a,1,2))]. 688 L(x,R(y,z,u),T(y,w)) = x. [hyper(24,a,18,a,b,687,a)]. 690 L(x,R(y / z,u,w),z \ y) = x. [para(84(a,1),688(a,1,3))]. 691 T(R(x,y,z),T(x,u)) / T(x,u) = T(x,u) \ R(x,y,z). [para(688(a,1),441(a,1,2))]. 692 R(T(x,T(x,y)),z,u) / T(x,y) = T(x,y) \ R(x,z,u). [para(46(a,2),691(a,1,1))]. 693 R(x,y,z) / T(x,u) = T(x,u) \ R(x,y,z). [para(115(a,1),692(a,1,1,1))]. 694 x * (x * (((y * z) * u) / (z * u))) = R(x * (x * y),z,u). [para(667(a,1),211(a,1)),flip(a)]. 695 R(x,T(x,y) \ 1,z) = x. [para(670(a,1),21(a,1))]. 696 R(x * (x * y),z,u) = x * (x * R(y,z,u)). [para(34(a,2),694(a,1,2,2)),flip(a)]. 697 x * (x * R(T(y,x),z,u)) = R(x * (y * x),z,u). [para(82(a,1),696(a,1,1,2)),flip(a)]. 698 R(x * (x * T(y,x * x)),z,u) = R(y,z,u) * (x * x). [para(696(a,2),226(a,1))]. 699 R(x * (y * x),z,u) = x * (R(y,z,u) * x). [para(110(a,1),697(a,1,2)),flip(a)]. 700 x \ R(x * (y * x),z,u) = R(y,z,u) * x. [hyper(23,a,20,a,b,699,a(flip)),flip(a)]. 701 (x * (y * x)) \ R(x * (z * x),u,w) = T(y,x) \ (x \ (R(z,u,w) * x)). [para(699(a,2),287(a,1,2))]. 702 x \ R(x * y,z,u) = R(y / x,z,u) * x. [para(22(a,1),700(a,1,2,1,2))]. 703 x \ R(x * y,z,u) = x * R(x \ y,z,u). [para(702(a,2),224(a,1))]. 704 L(x \ (y * R(y \ z,u,w)),x,y) = (y * x) \ R(y * z,u,w). [para(703(a,1),177(a,1,1,2))]. 705 R(x * (y * y),z,u) = R(x,z,u) * (y * y). [para(136(a,1),698(a,1,1))]. 706 (x \ 1) \ T(x \ 1,x * y) = ((x * y) \ y) * x. [para(156(a,1),385(a,2,2))]. 707 (x \ 1) \ T(x \ 1,x * y) = x * ((x * y) \ y). [para(706(a,2),381(a,1))]. 708 (x * y) * T(L(y \ 1,y,x),z) = (x * y) * T((x * y) \ x,z). [para(231(a,1),139(a,1))]. 709 R((x / y) * (z * z),z \ (z \ 1),y) = x / (z \ (z \ y)). [para(415(a,1),293(a,1,1))]. 710 x / (y \ (y \ z)) = (x / z) * (y * y). [para(709(a,1),426(a,1))]. 711 (x / (y * z)) * (y * y) = x / (y \ z). [para(19(a,1),710(a,1,2,2)),flip(a)]. 712 (x * y) / (z \ y) = R(x / z,z,y) * (z * z). [para(80(a,2),711(a,1,1)),flip(a)]. 713 R((x / y) * (y * y),y,z) = (x * z) / (y \ z). [para(712(a,2),705(a,2))]. 714 R(x / (y \ 1),y,z) = (x * z) / (y \ z). [para(397(a,1),713(a,1,1))]. 715 R(x,y,z) = ((x * (y \ 1)) * z) / (y \ z). [para(21(a,1),714(a,1,1))]. 716 R(L(x,y,z) \ x,x,u) = ((L(x,y,z) \ 1) * u) / (x \ u). [para(513(a,1),714(a,1,1))]. 717 R(x,y \ 1,z) = R(x,y,z). [para(715(a,2),324(a,1)),flip(a)]. 718 R(x,y,y) / y = x * (y \ 1). [para(717(a,1),207(a,1,1))]. 719 (x * (y \ 1)) \ R(x,y,y) = y. [para(717(a,1),209(a,1,2))]. 720 R(x / (y \ 1),y,y) = x * y. [para(717(a,1),210(a,1))]. 721 R(x,T(x,y),z) = x. [para(717(a,1),695(a,1))]. 722 (x * T(x,y)) * z = x * (T(x,y) * z). [para(721(a,1),79(a,1,1)),flip(a)]. 723 R(T(x / (y \ 1),z),y,y) / y = (y \ 1) * T((y \ 1) \ x,z). [para(718(a,2),139(a,1))]. 725 (T(x,y) * (R(x,z,u) \ 1)) \ T(x,y) = R(x,z,u). [para(527(a,1),719(a,1,2))]. 726 R(T(x / (y \ 1),z),y,y) = T(x * y,z). [para(720(a,1),46(a,2,1))]. 727 L(x,T(y,z),y) = x. [hyper(23,a,74,a,b,722,a),flip(a)]. 728 T(x,y) * (x * z) = x * (T(x,y) * z). [para(722(a,1),235(a,1)),flip(a)]. 729 x * (T(x,y) * (x \ z)) = T(x,y) * z. [para(722(a,1),281(a,1))]. 730 L(x,y,(z * y) / z) = x. [para(104(a,1),727(a,1,2))]. 731 L(x,(y \ z) \ z,y) = x. [para(83(a,1),727(a,1,2))]. 732 x \ (T(x,y) * z) = T(x,y) * (x \ z). [hyper(23,a,20,a,b,729,a),flip(a)]. 733 x \ (T(x,y) * z) = (x \ T(x,y)) * z. [para(732(a,2),562(a,2)),flip(a)]. 734 (R(x,y,z) \ T(x,u)) \ T(x,u) = R(x,y,z). [para(548(a,1),725(a,1,1))]. 735 R(L(x,y,z) \ x,x,u) = (L(x,y,z) \ u) / (x \ u). [para(318(a,1),716(a,2,1))]. 736 R(L(x,y,z) \ x,x,u) = L(x,y,z) \ x. [para(735(a,2),513(a,1))]. 738 L(x,y,y * x) \ z = ((y * x) \ y) * z. [para(19(a,1),396(a,1,1,2)),flip(a)]. 739 a(x,y,z) = T(x \ R(x,y,z),x * (y * z)). [para(587(a,2),28(a,2))]. 740 T(T(x \ R(x,y,z),u),x * (y * z)) = T(a(x,y,z),u). [para(739(a,2),42(a,1,1)),flip(a)]. 741 a(x,y,z) = T(T(R(x,y,z) / x,x * (y * z)),x). [para(739(a,2),112(a,2)),flip(a)]. 742 T((x * (y \ R(y,z,u))) / x,y * (z * u)) = (x * a(y,z,u)) / x. [para(739(a,2),233(a,1,1,2)),flip(a)]. 743 T(R(x,y,z) \ R(R(x,y,z),u,x),x * (R(x,y,z) * T(u,x))) = a(R(x,y,z),u,x). [para(530(a,2),739(a,2,2)),flip(a)]. 744 T(T((R(x,y,z) * u) / (x * u),x * (y * z)),x) = R(a(x,y,z),x,u). [para(739(a,2),614(a,2,1))]. 745 a(x,y,z) = T(T(x \ R(x,y,z),x * (y * z)),x). [para(478(a,1),741(a,2,1,1))]. 746 T(a(x,y,z),x) = a(x,y,z). [para(739(a,2),745(a,2,1)),flip(a)]. 747 a(x,y,z) * x = x * a(x,y,z). [para(746(a,1),82(a,1,2)),flip(a)]. 748 (x * a(x,y,z)) / x = a(x,y,z). [para(746(a,1),105(a,1,1,2))]. 749 ((x * (x * y)) * a(x * (x * y),z,u)) / y = a(x * (x * y),z,u) * (x * x). [para(747(a,1),418(a,1,1))]. 750 (x \ y) \ R(x \ z,u,w) = (x * y) \ R(x * z,u,w). [para(704(a,1),267(a,1)),flip(a)]. 751 (x * y) * T((x * y) \ x,z) = (x * y) * L(T(y \ 1,z),y,x). [para(44(a,2),708(a,1,2)),flip(a)]. 752 (x \ 1) * T((x \ 1) \ y,z) = T(y * x,z) / x. [para(726(a,1),723(a,1,1)),flip(a)]. 753 (x \ 1) * T(x * y,z) = T(y * x,z) / x. [para(330(a,1),752(a,1,2,1))]. 754 T(x * y,z) / y = y \ T(y * x,z). [para(753(a,1),318(a,1))]. 755 x \ T(x * (y / x),z) = T(y,z) / x. [para(22(a,1),754(a,1,1,1)),flip(a)]. 756 T(x * y,y) / y = (y \ x) * y. [para(754(a,2),146(a,1))]. 757 ((x \ y) * x) * x = T(y * x,x). [para(756(a,1),22(a,1,1))]. 758 T((x * y) * x,x) = (y * x) * x. [para(19(a,1),757(a,1,1,1)),flip(a)]. 759 (x * T(y * x,x)) / (x * x) = T((x \ y) * x,x \ 1). [para(757(a,1),664(a,1,1,2))]. 760 T((x \ y) * x,x \ 1) = ((y * x) * x) / (x * x). [para(82(a,1),759(a,1,1)),flip(a)]. 761 T((x \ y) * x,x \ 1) = R(y,x,x). [para(760(a,2),34(a,2)),flip(a)]. 762 (x * y) * T((x * y) \ x,z) = x * (y * T(y \ 1,z)). [para(751(a,2),74(a,1))]. 763 (x * (x * (y * z))) \ (x * (x * (y * (z * u)))) = L(u,z,x * (x * y)). [para(51(a,1),92(a,1,2))]. 764 (x * y) * T(L(y \ z,y,x),u) = (x * y) * T((x * y) \ (x * z),u). [para(232(a,1),139(a,1))]. 765 (x * y) * R(L(y \ 1,y,x),z,u) = (x * y) * R((x * y) \ x,z,u). [para(472(a,1),224(a,1))]. 767 T(T(x \ R(x,y,z),x * (y * z)),x) = R(a(x,y,z),x,u). [para(531(a,1),744(a,1,1,1))]. 769 R(a(x,y,z),x,u) = a(x,y,z). [para(767(a,1),745(a,2)),flip(a)]. 770 (a(x,y,z) * x) * u = a(x,y,z) * (x * u). [para(769(a,1),79(a,1,1)),flip(a)]. 771 L(x,y,a(y,z,u)) = x. [hyper(23,a,74,a,b,770,a),flip(a)]. 772 (x * a(x,y,z)) * u = a(x,y,z) * (x * u). [para(747(a,1),770(a,1,1))]. 773 L(x,y,z * (z * u)) = (u * y) \ (u * (y * x)). [para(763(a,1),212(a,1))]. 774 L(x,y,z * (z * u)) = L(x,y,u). [para(773(a,2),32(a,2)),flip(a)]. 776 L(x,y,z \ u) = L(x,y,z * u). [para(20(a,1),774(a,1,3,2)),flip(a)]. 777 L(x,y,(z / u) * z) = L(x,y,u). [para(22(a,1),774(a,1,3,2))]. 778 L(x,y,z * (u * z)) = L(x,y,T(u,z)). [para(82(a,1),774(a,1,3,2))]. 779 L(x,y,(z * u) * (u * z)) = L(x,y,K(u,z)). [para(69(a,1),774(a,1,3,2))]. 780 L(x,y,z * ((z \ u) * w)) = L(x,y,z * ((z * u) * w)). [para(89(a,1),774(a,1,3,2)),flip(a)]. 781 L(x,y,(z \ u) * w) = L(x,y,(z * u) * w). [para(89(a,1),774(a,1,3)),flip(a)]. 782 L(x,y,(z \ (z \ u)) * (z \ u)) = L(x,y,T(z,u)). [para(254(a,1),774(a,1,3,2))]. 783 L(x,y,(z * z) / u) = L(x,y,u \ 1). [para(263(a,1),774(a,1,3))]. 784 L(x,y,z / u) = L(x,y,u / z). [para(360(a,1),774(a,1,3))]. 785 L(x,y,z * L(z,u * z,u)) = L(x,y,a(u,z,z)). [para(453(a,2),774(a,1,3,2))]. 786 L(x,y,R(z * (z * u),w,v5)) = L(x,y,R(u,w,v5)). [para(696(a,2),774(a,1,3))]. 787 L(x,y,z \ 1) = L(x,y,z). [para(18(a,1),776(a,2,3))]. 788 L(x,y / z,z * y) = x. [para(776(a,1),236(a,1))]. 789 L(x,y,T(z / u,z)) = L(x,y,((u / z) * u) * u). [para(370(a,2),776(a,1,3))]. 790 L(x,y,y \ (z * z)) = x. [para(776(a,2),429(a,1))]. 792 L(x \ (x / y),y,x * (x / y)) = ((x \ (x / y)) \ y) \ y. [para(776(a,1),442(a,1))]. 793 L(x,R(y / z,u,w),z * y) = x. [para(776(a,1),690(a,1))]. 794 L(x \ L(y \ z,y,u),x,u * y) = ((u \ y) * x) \ (u \ z). [para(776(a,1),275(a,1))]. 795 T(x * x,y) \ (y \ (x * x)) = y \ 1. [para(790(a,1),395(a,1)),flip(a)]. 796 L(x,L(y \ 1,z,u),y) = x. [para(787(a,1),503(a,1))]. 797 L(x,(y * z) \ y,z) = x. [para(787(a,1),505(a,1))]. 798 (x \ y) * L(z,y,x) = x \ (y * z). [para(787(a,1),560(a,1,2))]. 799 x * T(y \ 1,y * x) = L(y \ 1,x,y) * x. [para(787(a,1),613(a,1,1)),flip(a)]. 800 L(x,y \ z,z \ y) = x. [para(20(a,1),797(a,1,2,1))]. 801 L(x,y \ z,z * y) = x. [para(800(a,1),776(a,1)),flip(a)]. 802 L(x,y,z * (z / y)) = x. [para(66(a,1),801(a,1,2))]. 803 (x * L(x \ 1,y,z)) \ u = L(x \ 1,y,z) \ (x \ u). [para(796(a,1),177(a,1)),flip(a)]. 804 L(x,y,(z * (z * u)) * (z * w)) = L(x,y,u \ (z \ w)). [para(282(a,1),777(a,1,3,1))]. 805 L(x,y,(z * (z * u)) * z) = L(x,y,u \ (z \ 1)). [para(289(a,1),777(a,1,3,1))]. 806 L(L(x,y,y / z),z,z / y) = x. [para(784(a,1),304(a,1,1))]. 807 L(x,x,x / y) = y \ (y / (x \ 1)). [para(784(a,1),432(a,1))]. 808 L(x,y,z / (z * y)) = x. [para(784(a,1),730(a,1))]. 809 ((x / (x * y)) * y) \ (x / (x * y)) = y \ 1. [para(808(a,1),142(a,1)),flip(a)]. 810 ((x / (x * y)) * y) * z = (x / (x * y)) * (y * z). [para(808(a,1),74(a,1,2))]. 811 ((x / (x * y)) * y) \ z = y \ ((x / (x * y)) \ z). [para(808(a,1),177(a,1)),flip(a)]. 812 L(x,y / (z * (u * y)),z * (u \ 1)) = x. [para(350(a,1),793(a,1,2))]. 813 (x * (y \ z)) \ (x * (y \ (z * u))) = L(L(u,z,y),y \ z,x). [para(798(a,1),32(a,2,2,2)),flip(a)]. 814 (x \ y) * L(L(z,y,x),u,w) = x \ (y * L(z,u,w)). [para(49(a,1),798(a,1,2))]. 815 T(x,y) \ (x * z) = (T(x,y) \ x) * z. [para(234(a,1),798(a,1,2)),flip(a)]. 816 x \ (((y * x) / y) * z) = (x \ ((y * x) / y)) * z. [para(237(a,1),798(a,1,2)),flip(a)]. 817 (x \ y) * T((x \ y) \ 1,z) = x \ (y * T(y \ x,z)). [para(261(a,1),798(a,1,2))]. 818 L(x,y,T(z \ u,z)) = L(x,y,T(z * u,z)). [para(138(a,1),778(a,1,3)),flip(a)]. 819 L(x,y,T((z \ u) * z,z)) = L(x,y,z * T(u * z,z)). [para(757(a,1),778(a,1,3,2)),flip(a)]. 820 L(x,y,(z * z) / u) = L(x,y,u). [para(783(a,2),787(a,1))]. 821 L(x,y,T(z,z * (u * u))) = L(x,y,z \ (u * u)). [para(252(a,1),820(a,1,3)),flip(a)]. 822 L(x,y,z / (u * u)) = L(x,y,z). [para(820(a,1),784(a,1)),flip(a)]. 823 L(x,y,z * (u * u)) = L(x,y,z). [para(21(a,1),822(a,1,3)),flip(a)]. 824 L(x,y,(z * u) * u) = L(x,y,R(z,u,u)). [para(34(a,2),822(a,1,3)),flip(a)]. 825 (x * (y * (y * z))) \ ((x * (y * y)) * (z * u)) = L(u,z,x). [para(823(a,1),419(a,2))]. 826 (T(x,y) \ x) * y = T(y,T(x,y)). [para(815(a,1),107(a,1))]. 827 T(x,y) \ (x * z) = x * (T(x,y) \ z). [para(815(a,2),576(a,1))]. 828 x * (T(x,y) \ y) = T(y,T(x,y)). [para(826(a,1),576(a,1)),flip(a)]. 829 T(x,T(y,x)) / (T(y,x) \ x) = y. [hyper(24,a,22,a,b,828,a),flip(a)]. 830 x \ T(y,T(x,y)) = T(x,y) \ y. [hyper(23,a,20,a,b,828,a),flip(a)]. 831 (x * y) / (x * (T(x,z) \ y)) = T(x,z). [para(827(a,1),65(a,1,2))]. 832 (((x * y) * (y * x)) * z) \ (((x * y) * (y * x)) * (z * u)) = L(u,z,K(y,x)). [para(779(a,1),32(a,1)),flip(a)]. 833 (x * (y / (y * x))) \ (y / (y * x)) = x \ 1. [para(362(a,1),809(a,1,1))]. 834 T(x \ 1,x * (y / (y * x))) = x \ 1. [para(833(a,1),349(a,2))]. 835 L(x \ 1,y,x) * y = y * ((x * y) \ y). [para(349(a,1),799(a,1,2)),flip(a)]. 836 L(x,y,(z * (z \ u)) * (z \ u)) = L(x,y,T(z,u)). [para(782(a,1),781(a,1)),flip(a)]. 837 L(x,y,z * ((z \ u) * u)) = L(x,y,a(z,u,u)). [para(435(a,1),785(a,1,3))]. 838 L(x,y,R(z \ u,w,v5)) = L(x,y,R(z * u,w,v5)). [para(20(a,1),786(a,1,3,1,2)),flip(a)]. 839 L(x,y,T(z / u,z)) = L(x,y,R(u / z,u,u)). [para(789(a,2),824(a,1))]. 840 L(x,y,z * (z * (u * z))) = L(x,y,u \ (z \ 1)). [para(51(a,1),805(a,1,3))]. 841 (x * (y / (y * x))) * z = (y / (y * x)) * (x * z). [para(362(a,1),810(a,1,1))]. 842 (x * (y / (y * x))) \ z = x \ ((y / (y * x)) \ z). [para(362(a,1),811(a,1,1))]. 843 L(x,y,T(z,z * (u * u))) = L(x,y,z * (u * u)). [para(821(a,2),776(a,1))]. 844 L(x,y,z * (u \ z)) = L(x,y,T(u,z)). [para(20(a,1),836(a,1,3,1))]. 845 L(x,y,T(z / u,z)) = L(x,y,z * u). [para(66(a,1),844(a,1,3,2)),flip(a)]. 846 L(x,y,R(z / u,z,z)) = L(x,y,u * z). [para(845(a,1),839(a,1)),flip(a)]. 847 L(x,y,R((y \ z) * z,u,w)) = x. [para(838(a,1),657(a,1))]. 848 L(x,y,z \ (u \ 1)) = L(x,y,z * u). [para(840(a,1),774(a,1))]. 850 L(x,y,z * (u \ 1)) = L(x,y,z * u). [para(848(a,1),776(a,1)),flip(a)]. 851 L(x,y / (z * (u * y)),z * u) = x. [para(850(a,1),812(a,1))]. 852 L(x,(y * z) * (u / (y * (z * u))),y * z) = x. [para(851(a,1),303(a,1,1))]. 853 ((x * y) * z) / (x * (y * z)) = (x * y) * (z / (x * (y * z))). [para(851(a,1),196(a,1,2))]. 854 x \ ((y / (y * x)) \ z) = ((y * x) / y) * (x \ z). [para(842(a,1),606(a,1))]. 855 L(x,y,T(z,z * (u * u))) = L(x,y,z). [para(843(a,2),823(a,1))]. 856 L(x,y,T(z,u * u)) = L(x,y,z). [para(423(a,1),855(a,1,3))]. 858 L(x,y,R(T(z,u * u),w,v5)) = L(x,y,R(z,w,v5)). [para(46(a,2),856(a,1,3))]. 859 x \ (((y * x) / y) * z) = ((y * x) / y) * (x \ z). [para(358(a,1),854(a,1,2))]. 860 (x \ ((y * x) / y)) * z = ((y * x) / y) * (x \ z). [para(859(a,1),816(a,1)),flip(a)]. 861 L(x,y,z * ((z * u) * u)) = L(x,y,a(z,u,u)). [para(780(a,1),837(a,1))]. 862 L(x,y,z * (z * (u * (z * w)))) = L(x,y,u \ (z \ w)). [para(51(a,1),804(a,1,3))]. 863 L(x,y,T((z \ u) * z,z)) = L(x,y,(u * z) * z). [para(82(a,1),819(a,2,3))]. 864 L(x,y,T((z \ u) * z,z)) = L(x,y,R(u,z,z)). [para(863(a,2),824(a,1))]. 865 L(x,y,z \ (u \ w)) = L(x,y,z * (u * w)). [para(862(a,1),774(a,1))]. 867 L(x,y,z * (u \ w)) = L(x,y,z * (u * w)). [para(865(a,1),776(a,1)),flip(a)]. 868 L(x,y,z * (u * (u * w))) = L(x,y,z * w). [para(19(a,1),867(a,1,3,2)),flip(a)]. 869 L(x,y,(z \ u) * (u \ z)) = L(x,y,(u \ z) * (z * u)). [para(384(a,1),867(a,1,3))]. 871 ((x \ (x / y)) \ y) \ y = x \ (x / y). [para(792(a,1),802(a,1))]. 872 x / (y \ (y / x)) = (y \ (y / x)) \ x. [para(871(a,1),65(a,1,2))]. 873 (x * (y * (y * z))) \ (x * (y * (y * (z * u)))) = L(u,z,x). [para(411(a,1),825(a,1,2))]. 875 L(x,y * (y * z),u) = L(x,z,u). [para(873(a,1),93(a,1)),flip(a)]. 876 L(x,y \ z,u) = L(x,y * z,u). [para(20(a,1),875(a,1,2,2)),flip(a)]. 877 L(x,(y / z) * y,u) = L(x,z,u). [para(22(a,1),875(a,1,2,2))]. 878 L(x,y * (z * y),u) = L(x,T(z,y),u). [para(82(a,1),875(a,1,2,2))]. 879 L(x,(y * z) * (z * y),u) = L(x,K(z,y),u). [para(69(a,1),875(a,1,2,2))]. 880 L(x,(y \ z) * u,w) = L(x,(y * z) * u,w). [para(89(a,1),875(a,1,2)),flip(a)]. 881 L(x,T(y,y * z),u) = L(x,(y \ z) * z,u). [para(250(a,1),875(a,1,2,2)),flip(a)]. 882 L(x,(y * y) / z,u) = L(x,z \ 1,u). [para(263(a,1),875(a,1,2))]. 883 L(x,T(y \ 1,z),u) = L(x,z * (y \ z),u). [para(327(a,1),875(a,1,2,2)),flip(a)]. 884 L(x,y / z,u) = L(x,z / y,u). [para(360(a,1),875(a,1,2))]. 887 L(x,y \ 1,z) = L(x,y,z). [para(18(a,1),876(a,2,2))]. 888 (x * (y \ z)) * L(u,y * z,x) = x * ((y \ z) * u). [para(876(a,1),74(a,1,2))]. 889 L(x,(y \ z) * z,y) = x. [para(876(a,1),731(a,1))]. 890 L(x,y * z,z * y) = x. [para(876(a,1),801(a,1))]. 892 L(x,y * z,z / y) = x. [para(66(a,1),889(a,1,2,1))]. 893 (x * ((x \ y) * y)) \ z = ((x \ y) * y) \ (x \ z). [para(889(a,1),177(a,1)),flip(a)]. 894 ((x * y) * (y * x)) * z = (x * y) * ((y * x) * z). [para(890(a,1),74(a,1,2))]. 895 T(x * y,(x * y) * (y * x)) = T(x * y,y * x). [para(890(a,1),203(a,1)),flip(a)]. 896 L(x,K(y,z),z * y) = x. [para(890(a,1),315(a,1,1))]. 897 K(x,y) \ 1 = K(y,x). [para(890(a,1),609(a,1)),flip(a)]. 898 K(x,y) * K(y,x) = 1. [para(897(a,1),20(a,1,2))]. 899 1 / K(x,y) = K(y,x). [para(897(a,1),65(a,1,2))]. 900 K(x,y) \ z = K(y,x) * z. [para(897(a,1),318(a,1,1)),flip(a)]. 901 K(x,y) * (K(y,x) * z) = z. [para(897(a,1),321(a,1,2,1))]. 902 x / (K(y,z) * x) = K(z,y). [para(897(a,1),340(a,2))]. 903 T(x * y,K(y,x)) / (y * x) = K(x,y). [para(897(a,1),345(a,2))]. 904 R(K(x,y),K(y,x) * z,u) = R(K(y,x),z,u) \ 1. [para(897(a,1),584(a,1,1))]. 905 a(K(x,y),z,u) = a(K(y,x),z,u). [para(897(a,1),611(a,1,1))]. 906 R(K(x,y),K(x,y) * z,u) = R(K(y,x),z,u) \ 1. [para(897(a,1),633(a,2,1,1))]. 907 K(x,y) * (K(y,x) / (x * y)) = K(x,y) \ ((y * x) \ 1). [para(897(a,1),379(a,1,2,1))]. 908 R(x,K(y,z),u) = R(x,K(z,y),u). [para(897(a,1),717(a,1,2))]. 909 L(x,y,K(z,u)) = L(x,y,K(u,z)). [para(897(a,1),787(a,1,3))]. 910 L(K(x,y),z,K(y,x)) * z = z * ((K(y,x) * z) \ z). [para(897(a,1),835(a,1,1,1))]. 911 (x * y) * (K(y,x) * z) = (y * x) * z. [para(896(a,1),176(a,1,2)),flip(a)]. 912 K(x,y) \ ((y * x) \ z) = (x * y) \ z. [para(896(a,1),199(a,1))]. 914 L(x,x,y) = (y * (x \ 1)) \ y. [para(887(a,1),161(a,1))]. 915 x / L(y,y,x) = x * (y \ 1). [para(887(a,1),162(a,1,2))]. 916 L(L(x,y * (z \ 1),y),z,y) = x. [para(887(a,1),308(a,1))]. 917 L(x * y,x,y) = (y \ (x \ 1)) \ 1. [para(887(a,1),351(a,1))]. 918 L(x,y,L(y \ 1,z,u)) = x. [para(887(a,1),509(a,1))]. 919 (x * (y \ z)) / L(z,y,x) = x * (y \ 1). [para(887(a,1),333(a,1,2))]. 920 L(x * (y * z),x,y) = (y \ (x \ 1)) \ z. [para(887(a,1),352(a,1))]. 921 L(x,K(y,z),u) = L(x,K(z,y),u). [para(897(a,1),887(a,1,2))]. 922 T(x * y,K(y,x)) = K(x,y) * (y * x). [para(900(a,1),122(a,1)),flip(a)]. 923 R(K(x,y),K(y,x) * z,u) \ K(x,y) = K(x,y) \ R(K(x,y),z,u). [para(901(a,1),618(a,1,2,2)),flip(a)]. 924 (L(x \ 1,y,z) * x) \ u = x \ (L(x \ 1,y,z) \ u). [para(918(a,1),177(a,1)),flip(a)]. 925 L(x / y,x / y,z) = (z * (y / x)) \ z. [para(343(a,1),914(a,2,1,2))]. 926 L(K(x,y),K(x,y),z) = (z * K(y,x)) \ z. [para(897(a,1),914(a,2,1,2))]. 927 (x * y) * ((y / x) \ 1) = (x * y) / (y / x). [para(788(a,1),915(a,1,2)),flip(a)]. 928 L(x,(y * (y * z)) * (y * u),w) = L(x,z \ (y \ u),w). [para(282(a,1),877(a,1,2,1))]. 929 L(x,(y * (y * z)) * y,u) = L(x,z \ (y \ 1),u). [para(289(a,1),877(a,1,2,1))]. 930 K(x,y) / L(z,z,K(y,x)) = K(x,y) * (z \ 1). [para(909(a,1),915(a,1,2))]. 931 L(x,y * (z \ 1),y) = L(x,y * z,y). [para(916(a,1),303(a,1,1)),flip(a)]. 932 L(x,K(y,z),y * z) = x. [para(921(a,1),896(a,1))]. 933 ((x * y) \ K(x,y)) \ z = K(x,y) \ ((x * y) * z). [para(932(a,1),267(a,1)),flip(a)]. 934 L(x * y,x,y) * z = (y \ (x \ 1)) \ z. [para(917(a,2),318(a,1,1))]. 935 L(x,(y * y) / z,u) = L(x,z,u). [para(882(a,2),887(a,1))]. 936 L(x,y / (z * z),u) = L(x,y,u). [para(935(a,1),884(a,1)),flip(a)]. 937 L(x,y * (z * z),u) = L(x,y,u). [para(21(a,1),936(a,1,2)),flip(a)]. 938 L(x,(y * z) * z,u) = L(x,R(y,z,z),u). [para(34(a,2),936(a,1,2)),flip(a)]. 939 ((x * y) * z) / (K(x,y) * z) = y * x. [hyper(24,a,22,a,b,911,a),flip(a)]. 940 (x * y) \ ((y * x) * z) = K(y,x) * z. [hyper(23,a,20,a,b,911,a),flip(a)]. 941 K(x,y) * ((x * y) \ z) = (y * x) \ z. [para(912(a,1),20(a,1,2))]. 942 x * (y \ ((y * (x \ 1)) * z)) = L(z,y * x,y). [para(931(a,1),446(a,2))]. 943 L(x,K(y,z) * (y * z),u) = L(x,z * y,u). [para(939(a,1),935(a,1,2)),flip(a)]. 944 (x * y) \ (y * (x * z)) = K(y,x) * L(z,x,y). [para(74(a,1),940(a,1,2))]. 945 (x * (y \ 1)) * L(z,y,x) = x * (y \ z). [para(919(a,1),22(a,1,1))]. 946 (a(x,y,z) \ (x \ 1)) \ u = x * (a(x,y,z) * u). [para(920(a,1),771(a,1))]. 947 L(K(x,y),K(x,y),z) / z = (z * K(y,x)) \ 1. [para(926(a,2),320(a,1,1))]. 948 (a(x,y,z) \ (x \ 1)) \ u = (x * a(x,y,z)) * u. [para(771(a,1),934(a,1,1)),flip(a)]. 951 L(x,T(y,y * z),u) = L(x,(y * z) * z,u). [para(881(a,2),880(a,1))]. 952 (x * y) / (y / x) = (x * y) * (x / y). [para(343(a,1),927(a,1,2)),flip(a)]. 953 L(x,(y * (y \ z)) * (y \ z),u) = L(x,T(y,z),u). [para(20(a,1),951(a,1,2,2)),flip(a)]. 954 x * (y * ((y \ (x \ 1)) * z)) = L(z,y * x,y). [para(213(a,1),942(a,1,2))]. 955 K(x,y) * L(x,y,x) = T(x,y * x). [para(944(a,1),36(a,2)),flip(a)]. 956 x * ((x \ (y \ 1)) * y) = a(x,y,y). [hyper(23,a,453,a(flip),b,954,a)]. 957 x * (y * (R(y,y * (x \ 1),z) \ ((x \ 1) * z))) = L(z,y * x,y). [para(630(a,2),954(a,1,2,2))]. 958 x * R(x \ 1,y \ 1,y) = a(x,y,y). [para(335(a,2),956(a,1,2))]. 959 x \ R(x,y \ 1,y) = a(x,y,y). [para(958(a,1),635(a,1)),flip(a)]. 960 x * R(x \ 1,y,y) = a(x,y,y). [para(717(a,1),958(a,1,2))]. 961 R(x,y \ 1,y) \ a(x,y,y) = T(x \ 1,R(x,y \ 1,y)). [para(959(a,1),325(a,2,2)),flip(a)]. 962 x \ R(x,y,y) = a(x,y,y). [para(717(a,1),959(a,1,2))]. 963 x * a(x,y,y) = R(x,y,y). [para(962(a,1),20(a,1,2))]. 964 a(x,y,y) \ R(x,y,y) = x. [para(962(a,1),480(a,1,1))]. 965 (R(x,y,y) \ x) * z = a(x,y,y) \ z. [para(962(a,1),465(a,1,1)),flip(a)]. 966 x * (a(x,y,y) * z) = R(x,y,y) * z. [para(962(a,1),501(a,1,2,1))]. 967 R(x \ 1,y,y) = x \ a(x,y,y). [para(962(a,1),634(a,1,2)),flip(a)]. 968 R(x,x * y,y) = a(x,y,y) \ x. [para(965(a,1),621(a,1)),flip(a)]. 969 T(x * y,K(y,x)) = T(x * y,y * x). [para(895(a,1),248(a,1)),flip(a)]. 970 T(x * y,K(y,x)) = (x \ 1) \ y. [para(969(a,2),439(a,1))]. 971 K(x,y) / T(y * x,K(x,y)) = (y * x) \ K(x,y). [para(969(a,2),257(a,1,2))]. 972 T(x * y,K(y,x)) = x * y. [para(970(a,2),330(a,1))]. 973 K(x,y) = (x * y) / (y * x). [para(972(a,1),903(a,1,1)),flip(a)]. 974 K(x,y) * (y * x) = x * y. [para(972(a,1),922(a,1)),flip(a)]. 975 (x * y) / (T(x,y) * y) = K(y,T(x,y)). [para(82(a,1),973(a,2,1)),flip(a)]. 976 (T(x,y) * y) / (x * y) = K(T(x,y),y). [para(82(a,1),973(a,2,2)),flip(a)]. 977 ((x * y) * z) / ((y * x) * z) = R(K(x,y),y * x,z). [para(973(a,2),80(a,1,1)),flip(a)]. 978 (x \ y) / (y * (x \ 1)) = K(x \ 1,y). [para(318(a,1),973(a,2,1)),flip(a)]. 979 ((K(x,y) * z) * K(y,x)) / z = K(K(x,y) * z,K(y,x)). [para(901(a,1),973(a,2,2)),flip(a)]. 980 K(x \ y,x) * y = (x \ y) * x. [para(20(a,1),974(a,1,2))]. 981 K(x * y,x) * y = (x \ y) * x. [para(495(a,1),980(a,1,1))]. 982 ((x \ y) * x) / y = K(x * y,x). [hyper(24,a,22,a,b,981,a),flip(a)]. 983 K(x,T(y,x)) = T(y,x) \ y. [para(975(a,1),577(a,1))]. 984 T(x,y) * K(y,T(x,y)) = x. [para(983(a,2),20(a,1,2))]. 985 K(x,T(y,x)) * T(y,x) = y. [para(983(a,2),298(a,1,1))]. 987 T(x,y) \ (x * z) = K(y,T(x,y)) * z. [para(983(a,2),815(a,2,1))]. 988 L(x,K(y,T(z,y)),u) = L(x,T(z,y) * z,u). [para(983(a,2),876(a,1,2))]. 989 (x \ y) * K(x,T(y / x,x)) = y / x. [para(84(a,1),984(a,1,1))]. 990 K(T(x,y),y) * x = T(x,y). [hyper(23,a,901,a,b,985,a),flip(a)]. 991 K(x,x \ y) * T(y / x,x) = y / x. [para(84(a,1),985(a,1,1,2))]. 992 K(T(x,y),y) = x \ T(x,y). [para(976(a,1),565(a,1))]. 993 x * K(T(x,y),y) = T(x,y). [para(992(a,2),20(a,1,2))]. 994 (x / y) \ T(x / y,y) = K(y \ x,y). [para(84(a,1),992(a,1,1)),flip(a)]. 995 K(T(x \ 1,y),y) = x * T(x \ 1,y). [para(992(a,2),330(a,1))]. 997 (x / y) * K(T(x / y,y),y) = y \ x. [para(993(a,2),84(a,1))]. 998 T(x,y) * (K(y,T(x,y)) * z) = x * z. [para(987(a,1),20(a,1,2))]. 999 K(x,T(y,x)) * (y \ z) = T(y,x) \ z. [para(20(a,1),987(a,1,2)),flip(a)]. 1000 (x \ y) * K(x,x \ y) = y / x. [para(84(a,1),989(a,1,2,2))]. 1001 (x \ y) * K(x,x * y) = y / x. [para(489(a,1),1000(a,1,2))]. 1002 (x \ y) \ (y / x) = K(x,x * y). [hyper(23,a,20,a,b,1001,a),flip(a)]. 1003 K(x,x * (x * y)) = y \ ((x * y) / x). [para(19(a,1),1002(a,1,1)),flip(a)]. 1004 K(x,x * y) * T(y / x,x) = y / x. [para(489(a,1),991(a,1,1))]. 1005 (x / y) \ T(x / y,y) = K(y * x,y). [para(994(a,2),495(a,1))]. 1006 (x / y) * K(y \ x,y) = y \ x. [para(84(a,1),997(a,1,2,1))]. 1007 (x / y) * K(y * x,y) = y \ x. [para(495(a,1),1006(a,1,2))]. 1008 (x / y) * (x \ y) = K(x * y,x). [hyper(23,a,359,a,b,1007,a),flip(a)]. 1010 (x \ y) * (x / y) = K(x * y,x). [para(1008(a,1),368(a,1)),flip(a)]. 1012 L(x,y,(z \ u) * K(z * u,z)) = L(x,y,z / u). [para(1010(a,1),774(a,1,3,2))]. 1013 K(x,y) = y \ ((x * y) / x). [para(1003(a,1),490(a,1)),flip(a)]. 1014 (x * y) / x = y * K(x,y). [para(1013(a,2),20(a,1,2)),flip(a)]. 1015 x * (y / (y * x)) = K(y,x) \ 1. [para(1013(a,2),502(a,1,1)),flip(a)]. 1016 K(x,y) = ((x * y) / x) / y. [para(1013(a,2),558(a,2)),flip(a)]. 1017 ((x * y) / x) * (y \ z) = K(x,y) * z. [para(1013(a,2),860(a,1,1)),flip(a)]. 1018 (x * K(y,x)) * y = y * x. [para(1014(a,1),22(a,1,1))]. 1019 x / (x / y) = y * K(x / y,y). [para(22(a,1),1014(a,1,1))]. 1020 T(x * K(y,x),y) = x. [para(1014(a,1),104(a,1,1))]. 1021 L(x,y * K(z,y),y) = x. [para(1014(a,1),237(a,1,2))]. 1022 a(x / (x * y),z,u) = a(y * K(x,y),z,u). [para(1014(a,1),612(a,1,1)),flip(a)]. 1023 T(T(x * K(y,x),z),y) = T(x,z). [para(1020(a,1),42(a,1,1)),flip(a)]. 1024 T(x * K(y,x),z) * y = y * T(x,z). [para(1020(a,1),108(a,1,2,1)),flip(a)]. 1025 x / L(y,x * K(y,x),y) = y \ (x * K(y,x)). [para(1020(a,1),441(a,1,1))]. 1026 L(x,K(y,z),z) = x. [para(1021(a,1),303(a,1))]. 1027 (x * K(y,x)) \ z = K(y,x) \ (x \ z). [para(1021(a,1),270(a,1))]. 1028 (x * K(y,x)) * z = x * (K(y,x) * z). [para(1026(a,1),74(a,1,2))]. 1029 L(x,K(y,z),y) = x. [para(1026(a,1),921(a,1)),flip(a)]. 1030 (x * K(x,y)) * z = x * (K(x,y) * z). [para(1029(a,1),74(a,1,2))]. 1031 x \ (K(x,y) * z) = (x \ K(x,y)) * z. [para(1029(a,1),798(a,1,2)),flip(a)]. 1032 (x * K(y,x)) \ 1 = K(x,y) / x. [para(1029(a,1),947(a,1,1)),flip(a)]. 1033 (x * y) / x = K(x,y) * y. [para(1016(a,2),22(a,1,1)),flip(a)]. 1035 (x * K(y,x)) / x = K(y,x). [para(1014(a,1),1016(a,2,1)),flip(a)]. 1036 K(x,y) * y = y * K(x,y). [para(1033(a,1),1014(a,1))]. 1037 T(K(x,y),y) = K(x,y). [para(1035(a,1),104(a,1,1))]. 1038 T(x,K(y,x)) = x. [hyper(39,a,1037,a)]. 1040 T(x,y) * K(z,x) = K(z,x) * T(x,y). [para(1038(a,1),108(a,1,2,1)),flip(a)]. 1041 K(x,y) = x * (y / (y * x)). [para(1015(a,2),897(a,1)),flip(a)]. 1042 x \ K(x,y) = y / (y * x). [hyper(23,a,20,a,b,1041,a(flip)),flip(a)]. 1043 K(x,y) = (y / (y * x)) * x. [para(1041(a,2),362(a,2)),flip(a)]. 1044 K(x,y) / x = y / (y * x). [para(1041(a,2),363(a,1,1))]. 1045 x * ((y / (y * x)) * z) = K(x,y) * z. [para(1041(a,2),451(a,1,1)),flip(a)]. 1046 T(x,K(x,y)) = x. [para(1041(a,2),605(a,1,2))]. 1047 ((x * y) / x) * (y \ z) = K(y,x) \ z. [para(1041(a,2),606(a,1,1)),flip(a)]. 1048 T(x \ 1,K(x,y)) = x \ 1. [para(1041(a,2),834(a,1,2))]. 1049 (x / (x * y)) * (y * z) = K(y,x) * z. [para(1041(a,2),841(a,1,1)),flip(a)]. 1050 K(x,y) * x = x * K(x,y). [para(1046(a,1),82(a,1,2))]. 1051 T(x,T(y,x) \ y) = x. [para(983(a,1),1046(a,1,2))]. 1052 (T(x,y) \ x) * y = y * (T(x,y) \ x). [para(1051(a,1),82(a,1,2))]. 1053 K(x,y) = ((y * x) / y) \ x. [para(1043(a,2),358(a,2)),flip(a)]. 1054 K(x,y) / x = x \ K(x,y). [para(1044(a,2),1042(a,2)),flip(a)]. 1055 K(x,y) * (x \ 1) = x \ K(x,y). [para(1048(a,1),327(a,1,2))]. 1056 (x * K(y,x)) \ 1 = x \ K(x,y). [para(1032(a,2),1054(a,1))]. 1057 (x \ 1) / (x \ K(x,y)) = K(y,x). [para(1055(a,1),902(a,1,2))]. 1058 (x * K(y,x)) \ z = (x \ K(x,y)) * z. [para(1056(a,1),318(a,1,1)),flip(a)]. 1059 K(x,y) * (y * z) = ((x * y) / x) * z. [para(19(a,1),1017(a,1,2)),flip(a)]. 1060 T(x,y) * K(z,T(x,y)) = T(x * K(z,x),y). [hyper(24,a,1018,a,b,1024,a),flip(a)]. 1061 T(x * K(x \ y,x),y) = L(x,x \ y,x). [hyper(24,a,221,a,b,1024,a)]. 1062 T(x * K(y,x),x * y) = L(x,y,x). [hyper(24,a,217,a(flip),b,1024,a)]. 1063 (x * K(y,x)) \ z = K(x,y) * (x \ z). [para(1027(a,2),900(a,1))]. 1064 ((x * y) / x) * z = y * (K(x,y) * z). [para(1014(a,2),1028(a,1,1))]. 1065 x \ (K(x,y) * z) = (y / (y * x)) * z. [para(1042(a,1),1031(a,2,1))]. 1066 K(x,y) \ (x * z) = ((y * x) / y) * z. [para(19(a,1),1047(a,1,2)),flip(a)]. 1067 K(x,y) * (x \ z) = (y / (y * x)) * z. [para(20(a,1),1049(a,1,2)),flip(a)]. 1068 K(x,y) * (x * z) = x * (K(x,y) * z). [para(1049(a,1),1045(a,1,2)),flip(a)]. 1069 x * (T(y,x) \ y) = T(x,T(y,x)). [para(1052(a,1),826(a,1))]. 1070 x * K(x,T(y,x)) = T(x,T(y,x)). [para(983(a,2),1069(a,1,2))]. 1071 x / (K(y,z) * (y \ x)) = y * K(z,y). [para(1063(a,1),65(a,1,2))]. 1072 (x \ K(x,y)) * z = K(x,y) * (x \ z). [para(1063(a,1),1058(a,1)),flip(a)]. 1073 K(x,y) * (y * z) = y * (K(x,y) * z). [para(1064(a,1),1059(a,2))]. 1074 K(x,y) \ (x * z) = (K(y,x) * x) * z. [para(1033(a,1),1066(a,2,1))]. 1075 K(x,y) * (x \ (y * x)) = y. [para(1067(a,2),22(a,1))]. 1076 x \ (K(x,y) * z) = K(x,y) * (x \ z). [para(1067(a,2),1065(a,2))]. 1077 K(x,y) * T(y,x) = y. [para(36(a,2),1075(a,1,2))]. 1078 K(x,y / x) = K(x,x * y). [hyper(24,a,1004,a,b,1077,a)]. 1079 K(x,T(y,x)) = K(x,y). [hyper(24,a,985,a,b,1077,a),flip(a)]. 1080 K(x,y) = T(y,x) \ y. [hyper(24,a,298,a,b,1077,a)]. 1081 T(x,y) = K(x,y) * x. [hyper(23,a,901,a,b,1077,a)]. 1082 K(x,T(y,z)) * T(T(y,x),z) = T(y,z). [para(42(a,1),1077(a,1,2))]. 1083 K(x,R(y,z,u)) * R(T(y,x),z,u) = R(y,z,u). [para(46(a,2),1077(a,1,2))]. 1084 L(x \ y,x,K(z,y)) = (K(z,y) \ x) \ T(y,z). [para(1077(a,1),267(a,1,1,2))]. 1085 L(x,y,K(z,u) * u) = L(x,y,T(u,z)). [para(1077(a,1),774(a,1,3,2))]. 1086 K(x,y) = T(x,y) / x. [para(1077(a,1),902(a,1,2)),flip(a)]. 1087 (x * y) * T(y,x) = (y * x) * y. [para(1077(a,1),911(a,1,2)),flip(a)]. 1088 T(x,y) * T(x,y) = x * T(T(x,y),y). [para(1077(a,1),998(a,1,2))]. 1089 T(x,y) * K(y,x) = x. [para(1077(a,1),1040(a,2))]. 1090 (x / (x * y)) * T(x,y) = y \ x. [para(1077(a,1),1065(a,1,2)),flip(a)]. 1091 K(x,T(T(y,x),z)) = K(x,T(y,z)). [para(42(a,1),1079(a,1,2))]. 1092 K(x,x * (y * x)) = K(x,y). [para(1079(a,1),491(a,2))]. 1093 T(x,y) \ (x * z) = K(y,x) * z. [para(1079(a,1),987(a,2,1))]. 1094 T(x,y) * (K(y,x) * z) = x * z. [para(1079(a,1),998(a,1,2,1))]. 1095 K(x,y) * (y \ z) = T(y,x) \ z. [para(1079(a,1),999(a,1,1))]. 1096 T(x,T(y,x)) = x * K(x,y). [para(1079(a,1),1070(a,1,2)),flip(a)]. 1097 T(T(x,y),z) \ T(x,z) = K(y,T(x,z)). [para(42(a,1),1080(a,2,1)),flip(a)]. 1098 K(x,y) * (T(y,x) * z) = y * z. [para(1080(a,2),575(a,1,1))]. 1099 x * (T(x,y) \ z) = K(y,x) * z. [para(1080(a,2),576(a,1,1)),flip(a)]. 1100 K(x,y) = y * (T(y,x) \ 1). [para(1080(a,2),578(a,2)),flip(a)]. 1101 T(x,y) \ 1 = x \ K(y,x). [para(1080(a,2),582(a,1,2)),flip(a)]. 1102 (x * y) / (T(x,z) * y) = K(z,x). [para(1080(a,2),577(a,2))]. 1103 ((x * y) * y) \ ((y * x) * y) = K(y,(y * x) * y). [para(758(a,1),1080(a,2,1)),flip(a)]. 1104 T(x,y) = (x * x) / (x * K(y,x)). [para(1080(a,2),831(a,1,2,2)),flip(a)]. 1105 K(T(x,y),y) = K(x,y). [hyper(24,a,990,a,b,1081,a(flip)),flip(a)]. 1106 (x * T(y,z)) / L(y,K(y,z),x) = x * K(y,z). [para(1081(a,2),99(a,1,1,2))]. 1107 T(x,y) = x * K(x,y). [para(1081(a,2),1050(a,1))]. 1108 K(x,y) = x \ T(x,y). [para(1086(a,2),572(a,1))]. 1109 R(T(x,y),z,u) * K(y,R(x,z,u)) = R(x,z,u). [para(46(a,2),1089(a,1,1))]. 1110 K(R(T(x,y),z,u),y) = K(R(x,z,u),y). [para(46(a,2),1105(a,1,1))]. 1111 x * T(x \ 1,y) = K(x \ 1,y). [para(1105(a,1),995(a,1)),flip(a)]. 1112 T(x * K(y,x),T(y,x)) = x. [para(1105(a,1),1020(a,1,1,2))]. 1113 K(x,y) * T(x,y) = T(T(x,y),y). [para(1105(a,1),1081(a,2,1)),flip(a)]. 1114 K(x,y) * T(K(y,x),z) = K(K(y,x),z). [hyper(23,a,901,a,b,1107,a(flip)),flip(a)]. 1115 (x * y) \ (x * T(y,z)) = L(K(y,z),y,x). [para(1107(a,2),32(a,2,2,2)),flip(a)]. 1116 x * (y * K(y,x)) = y * x. [para(1107(a,1),82(a,1,2))]. 1117 (x * y) * L(K(y,z),y,x) = x * T(y,z). [para(1107(a,2),74(a,2,2))]. 1118 (x \ y) * K(x * y,x) = T(x \ y,x). [para(495(a,1),1107(a,2,2)),flip(a)]. 1119 L(x,y,z * T(z,u)) = L(x,y,K(z,u)). [para(1107(a,2),774(a,1,3,2))]. 1120 x * (K(x,y) * z) = T(x,y) * z. [para(1107(a,2),1030(a,1,1)),flip(a)]. 1121 T(x,y) * K(x,y) = T(T(x,y),y). [para(1105(a,1),1107(a,2,2)),flip(a)]. 1122 T(x,y) \ T(T(x,z),y) = K(T(x,y),z). [para(42(a,1),1108(a,2,2)),flip(a)]. 1123 L(x,y,z) \ L(T(x,u),y,z) = K(L(x,y,z),u). [para(44(a,2),1108(a,2,2)),flip(a)]. 1124 x \ ((x \ y) \ y) = K(x,x * y). [para(249(a,1),1108(a,2,2)),flip(a)]. 1125 T(x,y) * (x \ z) = K(x,y) * z. [para(1108(a,2),562(a,1,1)),flip(a)]. 1126 K(x \ 1,x * y) = x * ((x * y) \ y). [para(1108(a,2),707(a,1))]. 1127 x \ (T(x,y) * z) = K(x,y) * z. [para(1108(a,2),733(a,2,1))]. 1128 K(x / y,y) = K(y * x,y). [para(1108(a,2),1005(a,1))]. 1130 K(x,(y * (x \ 1)) / x) = K(x,T(y,x \ 1)). [para(347(a,1),1078(a,2,2))]. 1131 T(x,T(y,x)) = T(x,y). [para(1096(a,2),1107(a,2)),flip(a)]. 1132 T(T(x,y),T(z,x)) = T(T(x,z),y). [para(1131(a,1),42(a,1,1)),flip(a)]. 1133 T(x,y / x) = T(x,x \ y). [para(84(a,1),1131(a,1,2)),flip(a)]. 1134 (x * y) / T(y,x) = T(x,y). [para(1131(a,1),117(a,1,2))]. 1135 L(T(x,y),T(y,x),x) = T(x,x * T(y,x)). [para(1131(a,1),203(a,1,1))]. 1136 T(x,x * (y * x)) = T(x,y). [para(1131(a,1),247(a,2))]. 1137 T(x,y) / (T(y,x) \ x) = y. [para(1131(a,1),829(a,1,1))]. 1138 T(x,y) \ y = x \ T(y,x). [para(1131(a,1),830(a,1,2)),flip(a)]. 1139 T(x,y * K(x,y)) = T(x,y). [para(1020(a,1),1131(a,1,2)),flip(a)]. 1140 K(x,y) * K(z,K(y,x)) = T(K(y,x),z) \ 1. [hyper(23,a,901,a,b,1100,a(flip)),flip(a)]. 1141 L(T(x,y),y * K(x,y),T(x,y)) = (T(x,y) \ (y * K(x,y))) \ y. [para(1112(a,1),440(a,1,2)),flip(a)]. 1143 K((x * (y \ 1)) / y,y) = K(T(x,y \ 1),y). [para(347(a,1),1128(a,2,1))]. 1144 x / (x / y) = y * K(y * x,y). [para(1128(a,1),1019(a,2,2))]. 1145 T(x,y / x) = T(x,x * y). [para(1133(a,2),246(a,1))]. 1146 T(x,y) * T(y,x) = x * y. [para(1134(a,1),22(a,1,1))]. 1147 x / (y \ T(x,y)) = T(y,x). [para(1138(a,1),65(a,1,2))]. 1148 (T(x,y) \ y) * K(x,x * T(y,x)) = T(y,x) / x. [para(1138(a,2),1001(a,1,1))]. 1149 T(x,(y * (x \ 1)) / x) = T(x,T(y,x \ 1)). [para(347(a,1),1145(a,2,2))]. 1150 (T(x,y) * (T(y,x) * z)) \ ((x * y) * z) = a(T(x,y),T(y,x),z). [para(1146(a,1),28(a,2,2,1)),flip(a)]. 1151 (x * y) \ (T(x,y) * (T(y,x) * z)) = L(z,T(y,x),T(x,y)). [para(1146(a,1),32(a,2,1)),flip(a)]. 1152 T(T(x,y),x \ T(y,x)) = (x \ T(y,x)) \ y. [para(1147(a,1),84(a,1,1))]. 1153 R(x,y,x) * (y * x) = (y * x) * T(x,y). [para(1087(a,2),79(a,2))]. 1154 T(x,y) * ((y * x) / ((x * y) * x)) = K(T(x,y),y * x). [para(1087(a,1),1041(a,2,2,2)),flip(a)]. 1155 K(x,T(y,K(z,T(y,x)))) = K(x,T(y,x)). [para(1038(a,1),1091(a,1,2)),flip(a)]. 1156 L(x,y * K(z,y),u) = L(x,T(y,z),u). [para(1094(a,1),937(a,1,2))]. 1157 T(x,y) * (y * x) = x * (x * y). [para(974(a,1),1094(a,1,2))]. 1158 K(x,y) * (T(x,y) \ z) = x \ z. [hyper(23,a,901,a,b,1095,a),flip(a)]. 1159 K(x,y) * (y \ x) = y \ T(x,y). [para(1095(a,2),1138(a,1))]. 1160 K(x,y) * (x * z) = T(x,y) * z. [hyper(23,a,901,a,b,1098,a),flip(a)]. 1162 R(K(x,y),T(y,x) * z,u) \ 1 = ((T(y,x) * z) * u) / ((y * z) * u). [para(1098(a,1),344(a,1,2,1)),flip(a)]. 1163 x \ (K(y,x) * z) = T(x,y) \ z. [hyper(23,a,20,a,b,1099,a),flip(a)]. 1164 (x * y) * T((x * y) \ x,z) = x * K(y \ 1,z). [para(1111(a,1),762(a,2,2))]. 1165 x \ (y * T(y \ x,z)) = K((x \ y) \ 1,z). [para(1111(a,1),817(a,1)),flip(a)]. 1166 (x * ((K(x,y) * z) * u)) \ ((T(x,y) * z) * u) = a(x,K(x,y) * z,u). [para(1120(a,1),28(a,2,2,1)),flip(a)]. 1168 T(x,y) * (T(y,x) * z) = x * (y * z). [para(1098(a,1),1120(a,1,2)),flip(a)]. 1169 L(x,y,z * ((z \ u) * u)) = L(x,y,K(z,z * u)). [para(1124(a,1),865(a,1,3)),flip(a)]. 1170 T(x,y) \ ((x \ T(y,x)) \ y) = K(T(x,y),T(x,y) * y). [para(1138(a,1),1124(a,1,2,1))]. 1171 T(x,y) \ (K(x,y) * z) = x \ z. [hyper(23,a,20,a,b,1125,a),flip(a)]. 1172 K(x,y) * (z * x) = T(x,y) * T(z,x). [para(36(a,2),1125(a,1,2)),flip(a)]. 1173 T(x / y,z) * y = K(x / y,z) * x. [para(66(a,1),1125(a,1,2))]. 1174 T(x,y) * (z / (z * x)) = K(x,y) * K(x,z). [para(1042(a,1),1125(a,1,2))]. 1175 T(x,y) * (T(x,z) \ 1) = K(x,y) * K(z,x). [para(1101(a,2),1125(a,1,2))]. 1176 x \ T(T(x,y),y) = K(x,y) * K(x,y). [para(1121(a,1),1127(a,1,2))]. 1177 T(T(x,x * y),T(z,x)) = T(T(x,z),x \ y). [para(246(a,1),1132(a,1,1))]. 1178 (x / (x / y)) * z = y * (K(y * x,y) * z). [para(1144(a,2),1028(a,1,1))]. 1179 ((x * y) * T(y,x)) \ (y * (y * x)) = K(T(y,x),x * y). [para(1157(a,1),30(a,2,2)),flip(a)]. 1180 (x * (x * y)) \ (T(x,y) * ((y * x) * z)) = L(z,y * x,T(x,y)). [para(1157(a,1),32(a,2,1)),flip(a)]. 1181 K(x,y) * (T(x,y) \ T(x,z)) = K(x,z). [para(1158(a,2),1108(a,2)),flip(a)]. 1182 K(T(x,y \ 1),y) * (x * (y \ 1)) = y \ T(T(x,y \ 1),y). [para(326(a,1),1159(a,1,2))]. 1183 ((T(x,y) * z) * u) / ((x * z) * u) = R(K(x,y),x * z,u). [para(1160(a,1),34(a,2,1,1)),flip(a)]. 1184 (x * y) \ (T(x,z) * y) = T(K(x,z),x * y). [para(1160(a,1),36(a,2,2)),flip(a)]. 1185 L(x,T(y,z) * z,u) = L(x,z * y,u). [para(1160(a,1),943(a,1,2))]. 1186 T(x,y) \ (T(y,x) \ z) = x \ (y \ z). [para(1158(a,1),1163(a,1,2)),flip(a)]. 1187 T(x,y) \ (y * K(x,y)) = x \ y. [para(1036(a,1),1171(a,1,2))]. 1188 x \ (y * K(x,y)) = K(x,y) * (x \ y). [para(1187(a,1),1158(a,1,2)),flip(a)]. 1189 (K(x,y) * (x \ z)) \ ((x \ K(x,y)) * (z * u)) = L(u,z,x \ K(x,y)). [para(1072(a,1),32(a,2,1)),flip(a)]. 1190 (K(x,y) * z) \ (y * (K(x,y) * z)) = L(T(y,z),z,K(x,y)). [para(1073(a,1),106(a,1,2))]. 1191 K(x,y) \ (x * z) = (K(x,y) \ x) * z. [para(900(a,2),1074(a,2,1))]. 1192 L(x,y,(z * u) / z) = L(x,y,T(u,z)). [para(1033(a,2),1085(a,1,3))]. 1193 T(x,y) * K(y,T(x,z)) = K(z,T(x,y)) * T(x,z). [para(1097(a,1),1099(a,1,2))]. 1194 L(x,y,(z / (u * u)) * (u \ (z * (u \ 1)))) = L(x,y,K(z / (u * u),u)). [para(403(a,1),1119(a,1,3,2))]. 1195 (x * T(y,x)) \ (T(y,z) * x) = L(K(T(y,x),z),T(y,x),x). [para(1122(a,1),180(a,1,1)),flip(a)]. 1196 K(x,T(y,K(z,T(y,x)))) = K(x,y). [para(1155(a,2),1079(a,1))]. 1197 K(x,y) * T(T(y,x),K(z,T(y,x))) = T(y,K(z,T(y,x))). [para(1196(a,1),1082(a,1,1))]. 1198 (x * (y * z)) / (T(y,x) * z) = T(x,y). [hyper(24,a,22,a,b,1168,a),flip(a)]. 1199 (x \ y) * (T(x,y / x) * z) = (y / x) * (x * z). [para(84(a,1),1168(a,1,1))]. 1200 (T(x / y,z) * y) / x = K(x / y,z). [hyper(24,a,22,a,b,1173,a(flip)),flip(a)]. 1201 K(x / y,z) * x = y * T(y \ x,z). [para(1173(a,1),139(a,1))]. 1202 (R(x,y,z) * (K(x,u) * K(x,u))) / T(T(x,u),u) = x \ R(x,y,z). [para(1176(a,1),536(a,1,1,2))]. 1203 L(x,y,K(y,z)) = x. [hyper(23,a,798,a,b,1191,a(flip)),flip(a)]. 1204 L(x,y,T(z,y) \ z) = x. [para(983(a,1),1203(a,1,3))]. 1205 L(x,y,T(z,y) * z) = x. [para(1204(a,1),776(a,1)),flip(a)]. 1206 L(x,y,z * T(z,y)) = x. [para(116(a,1),1205(a,1,3))]. 1207 ((x * T(x,y)) * y) \ ((x * T(x,y)) * (y * z)) = z. [para(1206(a,1),32(a,1)),flip(a)]. 1208 L(x,y,T(z * u,z) / z) = L(x,y,T((z \ u) * z,z)). [para(138(a,1),1192(a,1,3,1))]. 1209 (x * (R(y,z,u) * w)) / (R(T(y,x),z,u) * w) = T(x,R(y,z,u)). [para(46(a,2),1198(a,1,2,1))]. 1210 (x * (y * (a(T(y,x),z,z) * u))) / (R(T(y,x),z,z) * u) = T(x,y). [para(966(a,1),1198(a,1,2))]. 1211 (x * T(x \ y,z)) / y = K(y / x,z). [para(139(a,1),1200(a,1,1))]. 1212 K((x * y) / x,z) * (x * y) = x * T(y,z). [para(19(a,1),1201(a,2,2,1))]. 1213 x \ (y * T(y \ x,z)) = T(K(x / y,z),x). [para(1201(a,1),36(a,2,2)),flip(a)]. 1214 ((x * y) * T((x * y) \ ((z * x) * y),u)) / ((z * x) * y) = K(R(z,x,y),u). [para(34(a,2),1211(a,2,1))]. 1215 T(x * K(x * y,x),y) = L(x,x \ y,x). [para(495(a,1),1061(a,1,1,2))]. 1216 L(T(x,y),T(y,x),x) = T(x,y * x). [para(82(a,1),1135(a,2,2))]. 1217 (x * y) * T(y,y * (x * y)) = R(y,x,y) * (x * y). [para(1136(a,2),1153(a,2,2)),flip(a)]. 1218 T(x * K(x * y,x),y) = L(x,x * y,x). [para(1215(a,2),312(a,1))]. 1219 T(x / (x / y),x) = L(y,y * x,y). [para(1144(a,2),1218(a,1,1))]. 1220 K(x,T(y,x \ 1)) = K(x,y / (x * x)). [para(401(a,1),1130(a,1,2)),flip(a)]. 1221 K(T(x,y \ 1),y) = K(x / (y * y),y). [para(401(a,1),1143(a,1,1)),flip(a)]. 1222 T(x,T(y,x \ 1)) = T(x,y / (x * x)). [para(401(a,1),1149(a,1,2)),flip(a)]. 1223 K(((x * y) \ x) \ 1,z) = (x * y) \ (x * T(y,z)). [para(19(a,1),1165(a,1,2,2,1)),flip(a)]. 1224 T(x,y) \ T(x,z) = K(x,z) * K(y,x). [para(1175(a,1),581(a,1)),flip(a)]. 1225 K(x,y) * (K(x,z) * K(y,x)) = K(x,z). [para(1224(a,1),1181(a,1,2))]. 1226 K(x,y) * K(z,x) = K(z,x) * K(x,y). [hyper(23,a,901,a,b,1225,a)]. 1229 T(T(x,y),x \ z) = T(T(x,y),x * z). [para(1177(a,1),1132(a,1))]. 1230 T(T(x,y),x * T(y,x)) = (x \ T(y,x)) \ y. [para(1229(a,1),1152(a,1))]. 1231 (x / (x / y)) * x = y * ((y \ x) * y). [para(981(a,1),1178(a,2,2))]. 1232 T(x * y,x) = (y / (y / x)) * y. [para(1231(a,2),138(a,1)),flip(a)]. 1233 T(x * y,x) / y = y / (y / x). [hyper(24,a,22,a,b,1232,a(flip)),flip(a)]. 1234 ((x / y) / x) * T(y * x,y) = x. [hyper(23,a,359,a,b,1232,a(flip)),flip(a)]. 1235 L(x,T(y * z,y),u) = L(x,z / y,u). [para(1232(a,2),877(a,1,2))]. 1236 x \ T(x * y,y) = x / (x / y). [para(1233(a,1),754(a,1)),flip(a)]. 1237 x / T(y * x,y) = (x / y) / x. [hyper(24,a,22,a,b,1234,a),flip(a)]. 1238 T(x * y,y) = x * (x / (x / y)). [para(1236(a,1),20(a,1,2)),flip(a)]. 1239 T(x * (y \ x),y \ x) = x * (x / y). [para(65(a,1),1238(a,2,2,2))]. 1240 T(K(x / y,z),x) = K((x \ y) \ 1,z). [para(1213(a,1),1165(a,1))]. 1241 K((x \ (y \ x)) \ 1,z) = T(K(y,z),x). [para(65(a,1),1240(a,1,1,1)),flip(a)]. 1242 K((T(x,y) \ (T(y,x) \ x)) \ 1,z) = T(K(y,z),T(x,y)). [para(1137(a,1),1240(a,1,1,1)),flip(a)]. 1243 K(T(x \ 1,y) \ 1,z) = T(K(x,z),y). [para(325(a,2),1241(a,1,1,1))]. 1244 K(T((x \ 1) \ 1,y * y),z) = T(K(x,z),y * y). [para(655(a,1),1243(a,1,1))]. 1245 (x \ T(y,x)) \ y = T(T(x,y),y * x). [para(82(a,1),1230(a,1,2)),flip(a)]. 1246 x / L(y,T(x,y),y) = y \ (x * K(y,x)). [para(1156(a,1),1025(a,1,2))]. 1247 x / L(y,T(x,y),y) = K(y,x) * (y \ x). [para(1246(a,2),1188(a,1))]. 1248 L(x \ y,x,K(z,y)) = (K(y,z) * x) \ T(y,z). [para(900(a,1),1084(a,2,1))]. 1249 R(K(x,y),T(x,y) * z,u) \ 1 = R(K(y,x),x * z,u). [para(1098(a,1),906(a,1,2)),flip(a)]. 1250 L(x,y * (y * (z * y)),u) = L(x,z \ (y \ 1),u). [para(51(a,1),929(a,1,2))]. 1251 ((x * y) \ K(x,y)) \ z = K(y,x) * ((x * y) * z). [para(933(a,2),900(a,1))]. 1252 (x * a(x,y,z)) * u = x * (a(x,y,z) * u). [para(948(a,1),946(a,1))]. 1253 a(x,y,z) * (x * u) = x * (a(x,y,z) * u). [para(1252(a,1),772(a,1)),flip(a)]. 1254 x * (a(x,y,z) * (x \ u)) = a(x,y,z) * u. [para(20(a,1),1253(a,1,2)),flip(a)]. 1255 L(x,y * (z \ y),u) = L(x,T(z,y),u). [para(20(a,1),953(a,1,2,1))]. 1256 L(x,T(y \ 1,z),u) = L(x,T(y,z),u). [para(1255(a,1),883(a,2))]. 1257 K(x,y) / (y * x) = (y * x) \ K(x,y). [para(972(a,1),971(a,1,2))]. 1258 L(x,y,T(z \ u,z)) = L(x,y,z / u). [para(1118(a,1),1012(a,1,3))]. 1259 L(x,y,T(z * u,z)) = L(x,y,z / u). [para(1258(a,1),818(a,1)),flip(a)]. 1260 (T(x,y) \ y) * K(x,y * x) = T(y,x) / x. [para(82(a,1),1148(a,1,2,2))]. 1261 L(x,y,K(z,z * u)) = L(x,y,a(z,u,u)). [para(1169(a,1),837(a,1))]. 1262 L(x,y,K(z * u,z)) = L(x,y,a(z,u,u)). [para(1261(a,1),909(a,1)),flip(a)]. 1263 L(x,y,a(z,u * z,u * z)) = L(x,y,K(z,u)). [para(1092(a,1),1261(a,1,3)),flip(a)]. 1264 K(x,T(y,z)) * T(T(y,x),K(x,T(y,z))) = K(z,T(y,x)) * T(y,z). [para(1193(a,1),82(a,2))]. 1265 (x \ y) * (T(x,x * y) * z) = (y / x) * (x * z). [para(1145(a,1),1199(a,1,2,1))]. 1266 (x * (T(x,y) * y)) \ ((x * T(x,y)) * (y * z)) = z. [para(722(a,1),1207(a,1,1))]. 1267 L(K(x,y),x,z) = K(((z * x) \ z) \ 1,y). [para(1223(a,2),1115(a,1)),flip(a)]. 1268 K(L(x \ 1,x,y) \ 1,z) = L(K(x,z),x,y). [para(142(a,2),1267(a,2,1,1)),flip(a)]. 1269 K(T(x,y * y),z) = T(K(x,z),y * y). [para(156(a,1),1244(a,1,1,1))]. 1270 K(T(x,y * y),z) \ 1 = T(K(x,z) \ 1,y * y). [para(1269(a,2),655(a,1,1))]. 1271 L(x,y \ (z \ 1),u) = L(x,y * z,u). [para(1250(a,1),875(a,1))]. 1273 L(x,y * (z \ 1),u) = L(x,y * z,u). [para(1271(a,1),876(a,1)),flip(a)]. 1274 (x \ y) * ((y / x) * (x * z)) = ((x \ y) * y) * z. [para(1265(a,1),253(a,1,2))]. 1275 (x * (T(x,y) * y)) \ (x * (T(x,y) * (y * z))) = z. [para(722(a,1),1266(a,1,2))]. 1276 T(K(x,y) \ 1,z * z) = K(y,T(x,z * z)). [para(1270(a,1),897(a,1))]. 1277 K(x,T(y,z * z)) = T(K(x,y),z * z). [para(897(a,1),1276(a,1,1)),flip(a)]. 1278 K(T(x,y * y),z) = K(x,T(z,y * y)). [para(1277(a,2),1269(a,2))]. 1279 L(L(x,y,T(z,y)),T(z,y) * y,z) = x. [para(1275(a,1),174(a,1)),flip(a)]. 1280 L(L(x,y,T(z,y)),y * z,z) = x. [para(1279(a,1),1185(a,1)),flip(a)]. 1281 L(L(x,y,T(y \ z,y)),z,y \ z) = x. [para(20(a,1),1280(a,1,2))]. 1282 L(x,y * (z * y),y) = L(x,z,T(y,z)). [para(1280(a,1),303(a,1,1))]. 1283 L(x,T(y,z) * z,T(y,z)) = L(x,z * y,y). [para(308(a,1),1280(a,1,1)),flip(a)]. 1284 L(x,T(y,z),z) = L(x,y,T(z,y)). [para(1280(a,1),314(a,1,1))]. 1285 L(x,T(y,y * z),y * z) = L(x,y,y / z). [para(1284(a,2),1259(a,1))]. 1286 L(L(x,y,y / z),z,y \ z) = x. [para(1258(a,1),1281(a,1,1))]. 1287 L(L(x,y,y / z),z,y * z) = x. [para(1286(a,1),776(a,1)),flip(a)]. 1288 L(x,y,z / y) = L(x,y,z * y). [para(304(a,1),1287(a,1,1)),flip(a)]. 1289 L(x \ (x / y),x,y * x) = y \ 1. [para(445(a,1),1287(a,1,1))]. 1290 L(x,y,y / z) = L(x,y,z * y). [para(806(a,1),1287(a,1,1)),flip(a)]. 1291 L(x,y,(z * y) * y) = L(x,y,z). [para(21(a,1),1288(a,1,3)),flip(a)]. 1292 L(x \ 1,x,y * x) = y \ (y / x). [para(1288(a,1),144(a,1))]. 1293 L(x,x,y * x) = y \ (y / (x \ 1)). [para(1288(a,1),432(a,1))]. 1294 x * L(y,z,x * z) = (x / z) * (z * y). [para(1288(a,1),173(a,1,2))]. 1295 (x \ 1) \ L(T(y \ (y / x),z),y,x * y) = K(L(y \ (y / x),y,x * y),z). [para(1289(a,1),1123(a,1,1))]. 1296 ((x * y) * y) \ (x * y) = x \ (x / y). [para(1292(a,1),142(a,1)),flip(a)]. 1297 L(x,y \ 1,T(y * z,y \ 1)) = L(x,(y * z) * z,y * z). [para(322(a,1),1282(a,1,2,2)),flip(a)]. 1298 x * K(L(y \ 1,y,x * y) \ 1,z) = (x / y) * (y * K(y,z)). [para(1268(a,2),1294(a,1,2))]. 1299 x \ L(x,x * y,y) = a(T(y,x),x,x). [para(1283(a,1),452(a,1,2))]. 1300 L(x,y * z,T(z,y)) = L(x,y * z,z). [para(1283(a,1),1185(a,1)),flip(a)]. 1301 T(L(K(x,y),z,K(y,x)),z) = (K(y,x) * z) \ z. [hyper(23,a,82,a,b,910,a(flip)),flip(a)]. 1302 L(x,y * x,x) = R(x,y,x). [hyper(24,a,217,a(flip),b,1217,a(flip)),flip(a)]. 1303 R(x,y / x,x) = L(x,y,x). [para(22(a,1),1302(a,1,2)),flip(a)]. 1304 L(T(x,y),z * x,x) = T(R(x,z,x),y). [para(1302(a,1),44(a,2,1))]. 1305 L(x,y,x) * ((y / x) * x) = (x * (y / x)) * x. [para(1303(a,1),79(a,1,1))]. 1306 L(T(x,y),z * x,x) = R(T(x,y),z,x). [para(1304(a,2),46(a,2)),flip(a)]. 1307 L(x,y,x) * y = (x * (y / x)) * x. [para(22(a,1),1305(a,1,2))]. 1308 T(L(x,y,x) * y,x) = ((y / x) * x) * x. [para(1307(a,2),758(a,1,1))]. 1309 T(L(x,y,x) * y,x) = y * x. [para(22(a,1),1308(a,2,1))]. 1310 (L(x,y,x) * y) * x = x * (y * x). [para(1309(a,1),82(a,1,2)),flip(a)]. 1311 L(R(x,y,x),y,x) = x. [hyper(24,a,184,a,b,1310,a(flip)),flip(a)]. 1312 R(L(x,y,x),y,x) = x. [hyper(24,a,79,a,b,1310,a(flip)),flip(a)]. 1313 R(x,x \ y,x) = L(x,y,x). [para(1311(a,1),302(a,1,1)),flip(a)]. 1314 L(x,x * y,x) = R(x,y,x). [para(1311(a,1),303(a,1,1))]. 1315 R(x,x * y,x) = L(x,y,x). [para(1311(a,1),308(a,1,1)),flip(a)]. 1316 x \ T(y * x,y) = R(y,x,y). [para(1314(a,1),316(a,1)),flip(a)]. 1317 R(x,y,x) * (x \ y) = (x \ y) * T(x,y). [para(1314(a,1),559(a,1,1))]. 1318 T(x * K(x * y,x),y) = R(x,y,x). [para(1314(a,1),1218(a,2))]. 1319 T(x / (x / y),x) = R(y,x,y). [para(1314(a,1),1219(a,2))]. 1320 L(x,y,x) \ x = x \ R(x,y,x). [para(1315(a,1),622(a,1,1))]. 1321 x * R(y,x,y) = T(y * x,y). [para(1316(a,1),20(a,1,2))]. 1322 T(x,R(y,x,y)) = T(x,x / (x / y)). [para(1319(a,1),1131(a,1,2))]. 1323 (x / T(y * x,y)) * T(x,R(y,x,y)) = R(y,x,y) \ x. [para(1321(a,1),1090(a,1,1,2))]. 1324 T(x,y) * K(x * y,T(x,y)) = R(x,y,x). [para(1318(a,1),1060(a,2))]. 1325 T(x,y) * K(y * T(x,y),T(x,y)) = R(x,y,x). [para(82(a,2),1324(a,1,2,1))]. 1326 K(x,y) * (K(y,x) / (x * y)) = (x * y) \ 1. [para(907(a,2),912(a,1))]. 1327 K(x,y) * ((x * y) \ K(y,x)) = (x * y) \ 1. [para(1257(a,1),1326(a,1,2))]. 1328 (x * y) \ K(x,y) = (y * x) \ 1. [para(1327(a,1),941(a,1)),flip(a)]. 1329 K(x,y) * ((y * x) * z) = ((x * y) \ 1) \ z. [para(1328(a,1),1251(a,1,1)),flip(a)]. 1330 K(x,y) * ((y * x) * z) = (x * y) * z. [para(1329(a,2),330(a,1))]. 1331 ((x * y) * z) / ((y * x) * z) = K(x,y). [hyper(24,a,22,a,b,1330,a),flip(a)]. 1332 R(K(x,y),y * x,z) = K(x,y). [para(1331(a,1),977(a,1)),flip(a)]. 1333 R(K(x,T(y,x)),T(y,x) * x,z) = K(x,y). [para(1332(a,2),1079(a,1))]. 1335 R(K(x,y),T(y,x) * x,z) = K(x,y). [para(1079(a,1),1333(a,1,1))]. 1336 ((T(x,y) * y) * z) / ((K(y,x) * (T(x,y) * y)) * z) = K(y,x) \ 1. [para(1335(a,1),344(a,2,1))]. 1337 (x * L(x \ 1,y,z)) \ u = x \ (L(x \ 1,y,z) \ u). [para(216(a,1),924(a,1,1))]. 1338 L(x,y * (y * (z * (y * u))),w) = L(x,z \ (y \ u),w). [para(51(a,1),928(a,1,2))]. 1339 T(x,y) * (R(x,y,x) \ 1) = K(T(x,y),y * x). [para(344(a,1),1154(a,1,2))]. 1340 R(x,y,x) \ T(x,y) = K(T(x,y),y * x). [para(1339(a,1),548(a,1)),flip(a)]. 1341 T(x,y) \ T(T(x,y),y * x) = K(T(x,y),T(x,y) * y). [para(1245(a,1),1170(a,1,2))]. 1342 (((x * y) * T(y,x)) \ (y * y)) * x = K(T(y,x),x * y). [para(1179(a,1),391(a,1)),flip(a)]. 1343 T(x,K(y,T(x,z))) = K(z,x) * T(x,z). [para(1038(a,1),1197(a,1,2)),flip(a)]. 1345 T(x,K(y,T(x,z))) = x. [para(1343(a,2),1077(a,1))]. 1346 T(T(x,y),K(z,T(x,u))) = T(x,y). [para(1345(a,1),42(a,1,1)),flip(a)]. 1350 L(x,y,T(z * u,z) / z) = L(x,y,R(u,z,z)). [para(1208(a,2),864(a,1))]. 1351 T(K(x,y),T(z,x)) = K((z \ (x \ z)) \ 1,y). [para(1186(a,1),1242(a,1,1,1)),flip(a)]. 1352 T(K(x,y),T(z,x)) = T(K(x,y),z). [para(1351(a,2),1241(a,1))]. 1353 T(x,y) * T(K(y,z),x) = K(y,z) * T(x,y). [para(1352(a,1),82(a,1,2))]. 1354 K(x,y) * (K(y,z) * x) = K(y,z) * T(x,y). [para(1353(a,1),1172(a,2))]. 1355 (K(x,y) * T(z,x)) / L(z,K(x,y),K(z,x)) = K(z,x) * K(x,y). [para(1354(a,1),99(a,1,1))]. 1356 ((x / y) / x) * T(x,R(y,x,y)) = R(y,x,y) \ x. [para(1237(a,1),1323(a,1,1))]. 1357 L(x \ 1,y,z) \ (x \ u) = x \ (L(x \ 1,y,z) \ u). [para(1337(a,1),803(a,1)),flip(a)]. 1358 L(x,y \ (z \ u),w) = L(x,y * (z * u),w). [para(1338(a,1),875(a,1))]. 1360 L(x,y * (z \ u),w) = L(x,y * (z * u),w). [para(1358(a,1),876(a,1)),flip(a)]. 1361 L(x,y * (z * (z * u)),w) = L(x,y * u,w). [para(19(a,1),1360(a,1,2,2)),flip(a)]. 1362 L(x,(y \ z) * (z \ y),u) = L(x,(z \ y) * (y * z),u). [para(384(a,1),1360(a,1,2))]. 1363 L(x,y * R(z,z * u,w),v5) = L(x,y * (R(z,u,w) \ 1),v5). [para(615(a,1),1361(a,1,2,2))]. 1364 K(T(x,y),T(x,y) * y) = K(T(x,y),y * x). [para(1341(a,1),1108(a,2)),flip(a)]. 1365 (((x * y) * x) \ (x * x)) * y = K(T(x,y),y * x). [para(1087(a,1),1342(a,1,1,1))]. 1366 K(T(x,y),y * x) = K(x,x * y). [para(1365(a,1),408(a,1))]. 1367 R(x,y,x) \ T(x,y) = K(x,x * y). [para(1366(a,1),1340(a,2))]. 1368 K(x,x * y) \ T(x,y) = R(x,y,x). [para(1367(a,1),734(a,1,1))]. 1369 K(x * y,x) * T(x,y) = R(x,y,x). [para(1368(a,1),900(a,1)),flip(a)]. 1370 R(x,y,x) / T(x,y) = K(x * y,x). [hyper(24,a,22,a,b,1369,a),flip(a)]. 1371 (x \ (L(x \ 1,x,x / y) \ 1)) * (y \ (y / x)) = x \ 1. [para(1357(a,1),521(a,1,1))]. 1372 R(x,y \ 1,y) \ a(x,y,y) = x \ 1. [para(961(a,2),476(a,1))]. 1374 R(x,y,y) \ a(x,y,y) = x \ 1. [para(717(a,1),1372(a,1,1))]. 1375 (x * y) \ (x * (y * z)) = L(z,T(y,x),T(x,y)). [para(1168(a,1),1151(a,1,2))]. 1376 L(x,T(y,z),T(z,y)) = L(x,y,z). [para(1375(a,1),32(a,2)),flip(a)]. 1377 L(T(x,y),y,K(z,x)) = T(x,K(z,x) * y). [para(1190(a,1),36(a,2)),flip(a)]. 1378 (x \ (L(x \ 1,x,y * x) \ 1)) * (y \ (y / x)) = x \ 1. [para(1290(a,1),1371(a,1,1,2,1))]. 1379 ((x \ y) * z) \ (x \ u) = ((x * y) * z) \ (x * u). [para(794(a,1),201(a,1))]. 1380 (x * ((x \ y) * y)) \ z = ((x * y) * y) \ (x * z). [para(1379(a,1),893(a,2))]. 1381 (x * ((x \ y) * y)) \ y = x \ (x / y). [para(1380(a,2),1296(a,1))]. 1382 x / (y \ (y / x)) = y * ((y \ x) * x). [para(1381(a,1),65(a,1,2))]. 1383 (x \ (x / y)) \ y = x * ((x \ y) * y). [para(1382(a,1),872(a,1)),flip(a)]. 1384 x * L(x,y * x,y) = (y \ (y / x)) \ x. [para(1383(a,2),435(a,2))]. 1385 (x * L(x,y * x,y)) / x = (y \ (y / x)) \ 1. [para(1384(a,2),320(a,1,1))]. 1386 L(x,y * x,y) = (y \ (y / x)) \ 1. [para(1385(a,1),218(a,1)),flip(a)]. 1387 x \ ((y \ (y / x)) \ 1) = a(y,x,x). [para(1386(a,1),452(a,1,2))]. 1388 (x \ (x / y)) \ 1 = y * a(x,y,y). [para(1386(a,1),453(a,1))]. 1389 (x \ 1) \ (L(x,x,y * x) \ 1) = a(y,x \ 1,x \ 1). [para(1293(a,2),1387(a,1,2,1))]. 1390 (x \ (x / y)) \ z = (y * a(x,y,y)) * z. [para(1388(a,1),318(a,1,1)),flip(a)]. 1391 K(x,(x * x) / (y \ (y / z))) = K(x,z * a(y,z,z)). [para(1388(a,1),492(a,2,2))]. 1392 L(x \ 1,x,y * x) \ 1 = x * a(y,x,x). [para(1292(a,2),1388(a,1,1))]. 1393 (x \ (x * a(y,x,x))) * (y \ (y / x)) = x \ 1. [para(1392(a,1),1378(a,1,1,2))]. 1394 a(x,y,y) * (x \ (x / y)) = y \ 1. [para(19(a,1),1393(a,1,1))]. 1396 a(K(x,y),z,z) * (K(y,x) \ (K(y,x) / z)) = z \ 1. [para(905(a,1),1394(a,1,1))]. 1397 a(x,y,y) * (x / y) = x * (y \ 1). [para(1394(a,1),1254(a,1,2)),flip(a)]. 1398 (x * (y \ 1)) / (x / y) = a(x,y,y). [hyper(24,a,22,a,b,1397,a),flip(a)]. 1399 (x / y) * (y * (x \ 1)) = a(y,x,x). [para(1398(a,1),669(a,1)),flip(a)]. 1400 a(x / y,y,y \ 1) = a(x,y,y). [para(1399(a,1),592(a,2))]. 1401 a(x * (y * y),y \ 1,(y \ 1) \ 1) = a(x * y,y \ 1,y \ 1). [para(400(a,1),1400(a,1,1))]. 1402 K(x,(y \ (y / z)) \ 1) = K(x,z * a(y,z,z)). [para(1391(a,1),492(a,1)),flip(a)]. 1403 a(K(x,y),z,z) * (K(x,y) * (K(y,x) / z)) = z \ 1. [para(900(a,1),1396(a,1,2))]. 1404 K(x,y) * (a(K(x,y),z,z) * (K(y,x) / z)) = z \ 1. [para(1403(a,1),1253(a,1)),flip(a)]. 1405 R(K(x,y),z,z) * (K(y,x) / z) = z \ 1. [para(1404(a,1),966(a,1)),flip(a)]. 1406 x * (L(x,x,y * x) \ 1) = a(y,x \ 1,x \ 1). [para(1389(a,1),330(a,1)),flip(a)]. 1407 a(x,y \ 1,y \ 1) = L(y,y,x * y) \ y. [para(1406(a,1),471(a,1))]. 1408 a(x * y,y \ 1,y \ 1) = L(y,y,x) \ y. [para(1291(a,1),1407(a,2,1))]. 1409 (x * (y \ z)) \ (x * (y \ (z * u))) = L(L(u,z,y),y * z,x). [para(813(a,2),876(a,1))]. 1410 (x * y) * (z / (x * (y * z))) = x \ R(x,y,z). [para(853(a,1),537(a,1))]. 1411 L(x,y \ R(y,z,u),y * z) = x. [para(1410(a,1),852(a,1,2))]. 1412 L(x,y * R(y,z,u),y * z) = x. [para(1411(a,1),876(a,1)),flip(a)]. 1413 L(x,y * R(y,y * z,u),z) = x. [para(1412(a,1),774(a,1)),flip(a)]. 1414 K(T(x,y \ 1),y) * (x * (y \ 1)) = T(x,y) * (y \ 1). [para(1182(a,2),329(a,1))]. 1415 K(T(x,y \ 1),y) = K(x,y). [hyper(24,a,1160,a,b,1414,a)]. 1416 (x * (y \ 1)) / (T(x,y) * (y \ 1)) = K(y,T(x,y \ 1)). [para(1414(a,1),902(a,1,2))]. 1418 K(x / (y * y),y) = K(x,y). [para(1415(a,1),1221(a,1)),flip(a)]. 1419 K(x,T(y,x \ 1)) = K(x,y). [para(1416(a,1),1102(a,1))]. 1420 K(x \ 1,T(y,x)) = K(x \ 1,y). [para(156(a,1),1419(a,1,2,2))]. 1421 T(x,T(y,x \ 1)) = x * K(x,y). [para(1419(a,1),1107(a,2,2))]. 1423 K(x,y / (x * x)) = K(x,y). [para(1419(a,1),1220(a,1)),flip(a)]. 1424 K(x,R(y / x,x,x)) = K(x,y * x). [para(80(a,2),1423(a,1,2))]. 1425 ((x \ 1) * T(y,x)) / (x \ 1) = T(y,x) * K(x \ 1,y). [para(1420(a,1),1014(a,2,2))]. 1426 T(x,T(y,x \ 1)) = T(x,y). [para(1421(a,2),1107(a,2)),flip(a)]. 1427 T(x \ 1,T(y,x)) = T(x \ 1,y). [para(156(a,1),1426(a,1,2,2))]. 1428 T(x,y / (x * x)) = T(x,y). [para(1426(a,1),1222(a,1)),flip(a)]. 1429 L(x,T(y,z),T(T(z,y \ 1),y)) = L(x,y,T(z,y \ 1)). [para(1426(a,1),1376(a,1,2))]. 1430 T(x,(y * x) * x) = T(x,R(y,x,x)). [para(34(a,2),1428(a,1,2)),flip(a)]. 1431 L(x,T(y \ 1,z),T(T(z,y),y \ 1)) = L(x,y \ 1,T(z,y)). [para(1427(a,1),1376(a,1,2))]. 1432 (x \ T(y,x)) / (x \ 1) = T(y,x) * K(x \ 1,y). [para(318(a,1),1425(a,1,1))]. 1433 T(x,y) * K(y \ 1,x) = T(x,y * y). [para(1432(a,1),486(a,1))]. 1434 L(x,T(y,z),T(T(z,y),y \ 1)) = L(x,y,T(z,y \ 1)). [para(42(a,1),1429(a,1,3))]. 1435 L(x,R(y,z,z),y * z) = L(x,y \ 1,T(y * z,y \ 1)). [para(1297(a,2),938(a,1)),flip(a)]. 1436 L(x,R(y,z,z),y * z) = L(x,y,T(y * z,y \ 1)). [para(1435(a,2),887(a,1))]. 1437 L(x,y * R(z,z * u,w),v5) = L(x,y * R(z,u,w),v5). [para(1363(a,2),1273(a,1))]. 1438 L(x,y * R(y,z,u),z) = x. [para(1437(a,1),1413(a,1))]. 1439 L(x,y * (z * R(z,y,u)),y) = x. [para(1438(a,1),303(a,1,1))]. 1440 L(x,y \ R(y \ 1,z,u),z) = x. [para(318(a,1),1438(a,1,2))]. 1441 (x * (y \ R(y,x,z))) * u = x * ((y \ R(y,x,z)) * u). [para(1438(a,1),888(a,1,2))]. 1442 a(x,x * (y * R(y,x,z)),u) = 1. [hyper(38,a,1439,a)]. 1443 L(x,y * R(y \ 1,z,u),z) = x. [para(1440(a,1),876(a,1)),flip(a)]. 1444 L(x,a(y,z,z),z) = x. [para(960(a,1),1443(a,1,2))]. 1445 x / (a(y,x,x) \ 1) = x * a(y,x,x). [para(1444(a,1),145(a,1,2))]. 1446 (x * a(y,x,x)) * z = x * (a(y,x,x) * z). [para(1444(a,1),74(a,1,2))]. 1447 K(x,(y \ (y / z)) \ 1) = K(x,z / (a(y,z,z) \ 1)). [para(1445(a,2),1402(a,2,2))]. 1448 (x \ (x / y)) \ z = y * (a(x,y,y) * z). [para(1446(a,1),1390(a,2))]. 1449 L(x * (a(y,x,x) * z),y * (y / x),y) = (y / x) \ (y * z). [para(1448(a,1),311(a,1,1))]. 1450 (x * (y \ R(y,x,z))) * u = x * (R(y,x,z) * (y \ u)). [para(532(a,1),1441(a,2,2))]. 1451 L(x,T(y,z),T(T(z,y),y \ 1)) = L(x,y \ 1,T(z,y)). [para(1431(a,1),1256(a,1)),flip(a)]. 1452 L(x,y \ 1,T(z,y)) = L(x,y,T(z,y \ 1)). [para(1451(a,1),1434(a,1))]. 1453 L(x,y,T(z,y \ 1)) = L(x,y,T(z,y)). [para(1452(a,1),887(a,1))]. 1454 L(x,R(y,z,z),y * z) = L(x,y,T(y * z,y)). [para(1453(a,1),1436(a,2))]. 1455 L(x,R(y,z,z),y * z) = L(x,y,y / z). [para(1454(a,2),1259(a,1))]. 1456 L(x,R(y,z,z),y * z) = L(x,y,z * y). [para(1455(a,2),1290(a,1))]. 1457 L(T(x,y),y * K(x,y),T(x,y)) = (x \ y) \ y. [para(1187(a,1),1141(a,2,1))]. 1458 (x * (y * z)) \ ((x * y) * z) = a(T(x,y),T(y,x),z). [para(1168(a,1),1150(a,1,1))]. 1459 a(T(x,y),T(y,x),z) = a(x,y,z). [para(1458(a,1),28(a,2)),flip(a)]. 1460 a(T(x,y),T(T(y,x),x),z) = a(x,T(y,x),z). [para(1131(a,1),1459(a,1,1))]. 1461 x \ (y \ (y \ (T(y,x) * ((x * y) * z)))) = L(z,x * y,T(y,x)). [para(1180(a,1),443(a,1)),flip(a)]. 1462 x * K(y * a(x,y,y),z) = (x / y) * (y * K(y,z)). [para(1392(a,1),1298(a,1,2,1))]. 1463 x * K(y * a(x,y,y),z) = (x / y) * T(y,z). [para(1107(a,2),1462(a,2,2))]. 1464 x \ (y \ (K(y,x) * ((x * y) * z))) = L(z,x * y,T(y,x)). [para(1127(a,1),1461(a,1,2,2))]. 1465 x \ (y \ ((y * x) * z)) = L(z,x * y,T(y,x)). [para(1330(a,1),1464(a,1,2,2))]. 1466 L(x,y * z,T(z,y)) = L(x,z * y,z). [para(1465(a,1),309(a,1))]. 1467 L(x,y * z,z) = L(x,z * y,z). [para(1466(a,1),1300(a,1)),flip(a)]. 1468 L(L(x,y,z),y * z,z) = x. [para(1467(a,2),303(a,1))]. 1469 L(L(x,y * z,z),y,z) = x. [para(1467(a,2),308(a,1,1))]. 1470 x \ L(x,x * y,y) = a(y,x,x). [para(1467(a,2),452(a,1,2))]. 1471 L(x,y * (y / z),y) = L(x,z,y). [para(1467(a,1),877(a,1))]. 1472 L(x,(y * z) * z,y * z) = L(x,T(y,z),y * z). [para(1467(a,1),878(a,1))]. 1473 L(x,T(y,z),z) = L(x,y,z). [para(1468(a,1),314(a,1,1))]. 1474 L(L(x,y,z * y),z,z * y) = x. [para(875(a,1),1469(a,1,1))]. 1475 L(T(x,y),y,x) = T(x,y * x). [para(1473(a,1),1216(a,1))]. 1476 K(x,y) * (x \ y) = y / L(x,y,x). [para(1473(a,1),1247(a,1,2)),flip(a)]. 1477 L(x,y,y / z) = L(x,y,y * z). [para(1473(a,1),1285(a,1)),flip(a)]. 1478 (x * T(y,x)) \ (T(y,z) * x) = L(K(T(y,x),z),y,x). [para(1473(a,1),1195(a,2))]. 1479 T(x,y * x) = T(x,x * y). [para(1475(a,1),203(a,1))]. 1480 K(x,y) * L(x,y,x) = T(x,x * y). [para(1479(a,1),955(a,2))]. 1481 T(x,x * y) * K(y * x,x) = x. [para(1479(a,1),1089(a,1,1))]. 1482 T(x,x * (y * x)) = T(x,R(y,x,x)). [para(1479(a,1),1430(a,1))]. 1483 x \ L(x,y,x * y) = a(x * y,x,x). [para(875(a,1),1470(a,1,2))]. 1484 x \ L(x,T(y,x),y * x) = a(y * x,x,x). [para(878(a,1),1470(a,1,2))]. 1485 a(T(x,y),y,y) = a(x,y,y). [para(1470(a,1),1299(a,1)),flip(a)]. 1486 L(x * (a(y,x,x) * z),x,y) = (y / x) \ (y * z). [para(1471(a,1),1449(a,1))]. 1487 L(x,y,y * x) = x * a(y * x,x,x). [para(454(a,1),1474(a,1,1))]. 1488 L(x,x,x * y) = y \ (y / (x \ 1)). [para(1477(a,1),807(a,1))]. 1489 K(x * y,y) = K(y * x,y). [hyper(23,a,1089,a,b,1481,a)]. 1490 T(x * K(x * y,x),y * x) = x. [para(1489(a,1),1020(a,1,1,2))]. 1491 x / (x / y) = y * K(x * y,y). [para(1489(a,2),1144(a,2,2))]. 1492 R(x,y,x) / T(x,y) = K(y * x,x). [para(1489(a,2),1370(a,2))]. 1493 T(x / (x / y),x * y) = y. [para(1144(a,2),1490(a,1,1))]. 1494 T(x * y,x / (x / y)) = T(x * y,y). [para(1493(a,1),1131(a,1,2)),flip(a)]. 1495 (x / (x / y)) \ T(x * y,x / (x / y)) = y \ (x * y). [para(1493(a,1),1138(a,1,1)),flip(a)]. 1496 R(x,y,x) = y / (y / T(x,y)). [para(1491(a,2),1325(a,1)),flip(a)]. 1497 R(x,y,x) \ y = y / T(x,y). [para(1496(a,2),66(a,1,1))]. 1498 (T(x,y) \ y) * K(T(x,y),T(x,y) * y) = R(x,y,x) \ y. [para(1497(a,2),1001(a,2))]. 1499 ((x / y) / x) * T(x,R(y,x,y)) = x / T(y,x). [para(1497(a,1),1356(a,2))]. 1500 K(x,y) = (y \ x) / (x / L(y,x,y)). [para(1476(a,1),902(a,1,2)),flip(a)]. 1501 (x * y) / (K(x,y) * L(x,y,x)) = R(x,x * y,x) \ (x * y). [para(1480(a,2),1497(a,2,2)),flip(a)]. 1502 T(x,R(y,x,x)) = T(x,y). [para(1482(a,1),1136(a,1))]. 1503 K(x,R(y,x,x)) = x \ T(x,y). [para(1502(a,1),1108(a,2,2))]. 1504 K(x,R(y,x,x)) = K(x,y). [para(1503(a,2),1108(a,2)),flip(a)]. 1505 K(x,y / x) = K(x,y * x). [para(1504(a,1),1424(a,1))]. 1506 K(x,y * x) = K(x,x * y). [para(1505(a,1),1078(a,1))]. 1507 ((x * y) * y) \ ((y * x) * y) = K(y,y * (y * x)). [para(1506(a,1),1103(a,2))]. 1508 (T(x,y) \ y) * K(x,x * y) = T(y,x) / x. [para(1506(a,1),1260(a,1,2))]. 1509 K(T(x,y),y * T(x,y)) = K(T(x,y),y * x). [para(1506(a,2),1364(a,1))]. 1510 T(x,y) \ R(x,y,x) = K(y * x,x). [para(1492(a,1),693(a,1)),flip(a)]. 1511 K(x,y) * (y \ R(y,x,y)) = K(x * y,y). [para(1510(a,1),1095(a,2))]. 1512 K(T(x,y),y * x) = K(T(x,y),x * y). [para(82(a,1),1509(a,1,2)),flip(a)]. 1513 K(T(x,y),x * y) = K(x,x * y). [para(1512(a,1),1366(a,1))]. 1514 L(x,R(y,z,z),y * z) = L(x,T(y,z),y * z). [para(1472(a,1),938(a,1)),flip(a)]. 1515 L(x,T(y,z),y * z) = L(x,y,z * y). [para(1514(a,1),1456(a,1))]. 1516 x \ L(x,y,x * y) = a(y * x,x,x). [para(1515(a,1),1484(a,1,2))]. 1517 a(x * y,y,y) = a(y * x,y,y). [para(1516(a,1),1483(a,1))]. 1518 L(x * (a(y,x,x) * z),x,y) = (x / y) * (y * z). [para(1486(a,2),358(a,1))]. 1519 K(x,y) = ((y * x) * x) \ ((x * y) * x). [para(1507(a,2),490(a,1)),flip(a)]. 1520 (x * (y * x)) \ ((x * y) * x) = K(y * x,x) * K(x,y). [para(1519(a,2),941(a,1,2)),flip(a)]. 1521 (x * y) \ (T(x,z) * y) = L(K(T(x,y),z),x,y). [para(82(a,1),1478(a,1,1))]. 1522 L(K(T(x,y),z),x,y) = T(K(x,z),x * y). [para(1521(a,1),1184(a,1))]. 1523 (x / (x / y)) \ T(x * y,x / (x / y)) = T(x,y). [para(1495(a,2),36(a,2)),flip(a)]. 1524 (x / (x / y)) \ T(x * y,y) = T(x,y). [para(1494(a,1),1523(a,1,2))]. 1525 ((x / y) / x) * T(x * y,y) = T(x,y). [para(1524(a,1),358(a,1)),flip(a)]. 1526 (x / y) * T(y * (x \ y),x \ y) = T(y,x \ y). [para(65(a,1),1525(a,1,1,1))]. 1527 L(x,y,z * (((u / w) / u) * T(u,w))) = L(x,y,z * T(u * w,w)). [para(1525(a,1),868(a,1,3,2,2))]. 1528 (x / y) * (y * (y / x)) = T(y,x \ y). [para(1239(a,1),1526(a,1,2))]. 1529 T(x,x / y) = T(x,y \ x). [para(1528(a,1),369(a,1)),flip(a)]. 1530 T(x,R(y,x,y)) = T(x,(x / y) \ x). [para(1529(a,1),1322(a,2))]. 1531 T(x,R(y,x,y)) = T(x,y). [para(66(a,1),1530(a,2,2))]. 1532 ((x / y) / x) * T(x,y) = x / T(y,x). [para(1531(a,1),1499(a,1,2))]. 1533 K(x * y,y) * K(y,x) = a(y,x,y). [para(1520(a,1),28(a,2)),flip(a)]. 1534 K(x,y) * K(y * x,x) = a(x,y,x). [para(1533(a,1),1226(a,2))]. 1535 K(x * y,x) * K(x,y) = a(x,y,x). [para(1489(a,1),1533(a,1,1))]. 1536 K(x,y) * a(y,x,y) = K(x * y,y). [hyper(23,a,901,a,b,1534,a),flip(a)]. 1537 K(x,y) * K(x * y,x) = a(x,y,x). [para(1489(a,1),1534(a,1,2))]. 1538 (((x \ y) * x) / y) * K(x,y) = a(x,y,x). [para(982(a,2),1535(a,1,1))]. 1539 x \ R(x,y,x) = a(x,y,x). [hyper(23,a,1511,a,b,1536,a),flip(a)]. 1541 L(x,y,x) \ x = a(x,y,x). [para(1539(a,1),1320(a,2))]. 1542 a(x,y,x) * L(x,y,x) = x. [para(1541(a,1),520(a,1,1))]. 1543 (x * y) / L(L(y,z,y),a(y,z,y),x) = x * a(y,z,y). [para(1542(a,1),99(a,1,1,2))]. 1544 (T(x,y) \ y) * K(T(x,y),y * T(x,y)) = R(x,y,x) \ y. [para(1506(a,2),1498(a,1,2))]. 1545 (T(x,y) \ y) * K(T(x,y),x * y) = R(x,y,x) \ y. [para(82(a,1),1544(a,1,2,2))]. 1546 (T(x,y) \ y) * K(x,x * y) = R(x,y,x) \ y. [para(1513(a,1),1545(a,1,2))]. 1547 R(x,y,x) \ y = T(y,x) / x. [para(1546(a,1),1508(a,1))]. 1548 T(x,y) / y = x / T(y,x). [para(1547(a,1),1497(a,1))]. 1549 (x / T(y,x)) * y = T(x,y). [para(1548(a,1),22(a,1,1))]. 1550 (x / y) * (y * K(x,y)) = T(x,y * K(x,y)). [para(1020(a,1),1549(a,1,1,2))]. 1551 T(x,y) = (x / y) * (y * K(x,y)). [para(1550(a,2),1139(a,1)),flip(a)]. 1552 (x / y) * T(y,x) = x * K(y,x). [hyper(23,a,359,a,b,1551,a(flip)),flip(a)]. 1553 (x * (y \ 1)) * T(L(y,y,x),x) = x * K(L(y,y,x),x). [para(915(a,1),1552(a,1,1))]. 1554 (x * (y \ 1)) * L(T(y,x),y,x) = x * K(L(y,y,x),x). [para(44(a,2),1553(a,1,2))]. 1555 x * K(L(y,y,x),x) = x * (y \ T(y,x)). [para(1554(a,1),945(a,1))]. 1556 x * K(L(y,y,x),x) = x * K(y,x). [para(1108(a,2),1555(a,2,2))]. 1557 T(x * K(y,x),L(y,y,x)) = x. [para(1556(a,1),1020(a,1,1))]. 1558 T(x,L(y,y,x)) = T(x,y). [para(1557(a,1),1023(a,1,1)),flip(a)]. 1559 (x * y) / (K(x,y) * L(x,y,x)) = L(x,y,x) \ (x * y). [para(1315(a,1),1501(a,2,1))]. 1560 (x * y) / (K(x,y) * L(x,y,x)) = (L(x,y,x) \ x) * y. [para(1559(a,2),524(a,1))]. 1561 (x * y) / T(x,x * y) = (L(x,y,x) \ x) * y. [para(1480(a,1),1560(a,1,2))]. 1562 (L(x,y,x) \ x) * y = T(x * y,x) / x. [para(1561(a,1),1548(a,2)),flip(a)]. 1563 T(x * y,x) / x = a(x,y,x) * y. [para(1541(a,1),1562(a,1,1)),flip(a)]. 1564 R(K(x,y),K(y,x) * z,u) \ K(x,y) = K(y,x) * R(K(x,y),z,u). [para(923(a,2),900(a,1))]. 1565 x * (y * (R(y,y * (x \ 1),z) \ (x \ z))) = L(z,y * x,y). [para(318(a,1),957(a,1,2,2,2))]. 1566 x * (R(y,x \ 1,z) * (y \ (x \ z))) = L(z,y * x,y). [para(637(a,1),1565(a,1,2))]. 1567 x * (R(y,x,z) * (y \ (x \ z))) = L(z,y * x,y). [para(717(a,1),1566(a,1,2,1))]. 1568 R(x * (K(x,y) * K(x,y)),z,u) / T(T(x,y),y) = x \ R(x,z,u). [para(705(a,2),1202(a,1,1))]. 1569 K(x,T(y,z)) * T(y,x) = K(z,T(y,x)) * T(y,z). [para(1346(a,1),1264(a,1,2))]. 1570 (K(x,T(y,z)) * T(y,x)) / L(y,K(y,z),K(z,T(y,x))) = K(z,T(y,x)) * K(y,z). [para(1569(a,1),1106(a,1,1))]. 1572 ((T(x,y) * y) * z) / ((x * y) * z) = K(y,x) \ 1. [para(1098(a,1),1336(a,1,2,1))]. 1574 a(x * (y * y),y \ 1,y) = a(x * y,y \ 1,y \ 1). [para(156(a,1),1401(a,1,3))]. 1575 L(x,y,z * T(u * w,w)) = L(x,y,z * (u / T(w,u))). [para(1532(a,1),1527(a,1,3,2)),flip(a)]. 1576 L(x,y,z * (T(u,w) / w)) = L(x,y,z * T(u * w,w)). [para(1548(a,2),1575(a,2,3,2)),flip(a)]. 1577 (R(K(x,y),z,u) \ 1) \ K(y,x) = K(x,y) * R(K(y,x),z,u). [para(904(a,1),1564(a,1,1))]. 1578 R(K(x,y),z,u) * K(y,x) = K(x,y) * R(K(y,x),z,u). [para(1577(a,1),330(a,1)),flip(a)]. 1579 K(x,y) * R(K(y,x),T(x,y) * z,u) = R(K(y,x),x * z,u) \ K(y,x). [para(1249(a,1),1577(a,1,1)),flip(a)]. 1580 R(T(x,y) * K(x,y),z,u) / T(T(x,y),y) = x \ R(x,z,u). [para(1120(a,1),1568(a,1,1,1))]. 1581 R(T(T(x,y),y),z,u) / T(T(x,y),y) = x \ R(x,z,u). [para(1121(a,1),1580(a,1,1,1))]. 1582 T(T(x,y),y) \ R(T(T(x,y),y),z,u) = x \ R(x,z,u). [para(1581(a,1),478(a,1)),flip(a)]. 1583 (x * y) * T((x * y) \ (x * z),u) = (x * y) * L(T(y \ z,u),y,x). [para(44(a,2),764(a,1,2)),flip(a)]. 1584 (x * y) * R((x * y) \ x,z,u) = (x * y) * L(R(y \ 1,z,u),y,x). [para(48(a,1),765(a,1,2)),flip(a)]. 1589 (K(x,y) * (x \ z)) \ (K(x,y) * (x \ (z * u))) = L(u,z,x \ K(x,y)). [para(1072(a,1),1189(a,1,2))]. 1590 (x * y) * T((x * y) \ (x * z),u) = x * (y * T(y \ z,u)). [para(1583(a,2),74(a,1))]. 1591 (x * y) * R((x * y) \ x,z,u) = x * (y * R(y \ 1,z,u)). [para(1584(a,2),74(a,1))]. 1592 (x * y) * R((x * y) \ x,z,u) = x * (y \ R(y,z,u)). [para(635(a,1),1591(a,2,2))]. 1593 (x / y) * (y * R(((y \ x) * x) \ (y \ x),z,u)) = x \ R(x,z,u). [hyper(23,a,1274,a,b,1592,a(flip)),flip(a)]. 1594 (x / y) * (y * R(((y * x) * x) \ (y * x),z,u)) = x \ R(x,z,u). [para(1379(a,1),1593(a,1,2,2,1))]. 1595 (x / y) * (y * R(y \ (y / x),z,u)) = x \ R(x,z,u). [para(1296(a,1),1594(a,1,2,2,1))]. 1596 ((x \ y) / y) * (y * R(y \ x,z,u)) = (x \ y) \ R(x \ y,z,u). [para(65(a,1),1595(a,1,2,2,1,2))]. 1597 (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). [para(99(a,1),1595(a,1,2,2,1,2))]. 1598 (x \ 1) * (y * R(y \ x,z,u)) = (x \ y) \ R(x \ y,z,u). [para(320(a,1),1596(a,1,1))]. 1599 (x \ y) \ R(x \ y,z,u) = x \ (y * R(y \ x,z,u)). [para(1598(a,1),318(a,1))]. 1601 (x * y) \ R(x * y,z,u) = x \ (y * R(y \ x,z,u)). [para(1599(a,1),750(a,1)),flip(a)]. 1602 L(L(x,y,z),z * y,K(z,u)) = L(x,y,z \ K(z,u)). [para(1589(a,1),1409(a,1)),flip(a)]. 1603 L(L(x,y,z),z * y,K(z,u)) = L(x,y,z * K(z,u)). [para(1602(a,2),776(a,1))]. 1604 L(L(x,y,z),z * y,K(z,u)) = L(x,y,T(z,u)). [para(1107(a,2),1603(a,2,3))]. 1605 L(L(x,y,z),z * y,T(z,u)) = L(x,z * (z * y),K(z,u)). [para(303(a,1),1604(a,1,1)),flip(a)]. 1606 L(L(x,y,z),z * y,T(z,u)) = L(x,y,K(z,u)). [para(1605(a,2),875(a,1))]. 1608 (x * (y * x)) \ R(x * (z * x),u,w) = T(y,x) \ T(R(z,u,w),x). [para(36(a,2),701(a,2,2))]. 1609 (x * (y * x)) \ R(x * (z * x),u,w) = T(y,x) \ R(T(z,x),u,w). [para(46(a,2),1608(a,2,2))]. 1610 x \ ((y * x) * R((y * x) \ x,z,u)) = T(y,x) \ R(T(y,x),z,u). [para(1609(a,1),1601(a,1)),flip(a)]. 1611 L(x,y,z * (u \ (u \ (u \ (z * (u \ 1)))))) = L(x,y,K(z / (u * u),u)). [para(602(a,1),1194(a,1,3))]. 1612 L(x,y,z * (u \ ((u \ (u \ z)) * (u \ 1)))) = L(x,y,K(z / (u * u),u)). [para(285(a,1),1611(a,1,3,2,2))]. 1613 L(x,y,z * (u * ((u \ (u \ z)) * (u \ 1)))) = L(x,y,K(z / (u * u),u)). [para(1612(a,1),867(a,1)),flip(a)]. 1614 L(x,y,K(z / (u * u),u)) = L(x,y,z * (u \ (z * (u \ 1)))). [para(265(a,1),1613(a,1,3,2)),flip(a)]. 1615 L(x,y,K(z / (u * u),u)) = L(x,y,z * (u * (z * (u \ 1)))). [para(1614(a,2),867(a,1))]. 1616 L(x,y,K(z / (u * u),u)) = L(x,y,z * T(z,u \ 1)). [para(347(a,1),1615(a,2,3,2))]. 1617 L(x,y,K(z / (u * u),u)) = L(x,y,K(z,u \ 1)). [para(1616(a,2),1119(a,1))]. 1618 L(x,y,K(z,u \ 1)) = L(x,y,K(z,u)). [para(1418(a,1),1617(a,1,3)),flip(a)]. 1619 L(x,y,K(z,u \ 1)) = L(x,y,K(u,z)). [para(1618(a,2),909(a,1))]. 1620 (x * (x * (y * (z * u)))) \ ((x * (x * (y * z))) * u) = a(x * (x * y),z,u). [para(51(a,1),91(a,1,2,1))]. 1621 (x * y) * R(L(y \ z,y,x),u,w) = (x * y) * R((x * y) \ (x * z),u,w). [para(473(a,1),224(a,1))]. 1624 ((x * y) * ((y * x) * z)) \ (((x * y) * (y * x)) * (z * u)) = L(u,z,K(y,x)). [para(894(a,1),832(a,1,1))]. 1625 ((x * y) * T(R(T(z,x * y),x,y),u)) / ((z * x) * y) = K(R(z,x,y),u). [para(549(a,1),1214(a,1,1,2,1))]. 1626 ((x * y) * R(T(T(z,x * y),u),x,y)) / ((z * x) * y) = K(R(z,x,y),u). [para(46(a,2),1625(a,1,1,2))]. 1627 (R(T(x,y),z,u) * (z * u)) / ((x * z) * u) = K(R(x,z,u),y). [para(222(a,1),1626(a,1,1))]. 1628 ((T(x,y) * z) * u) / ((x * z) * u) = K(R(x,z,u),y). [para(79(a,1),1627(a,1,1))]. 1629 R(K(x,y),x * z,u) = K(R(x,z,u),y). [para(1628(a,1),1183(a,1)),flip(a)]. 1630 K(R(x,y,z),y) = K(y,x) \ 1. [para(1628(a,1),1572(a,1))]. 1631 R(K(x,y),T(y,x) * z,u) \ 1 = K(R(y,z,u),x). [para(1628(a,1),1162(a,2))]. 1632 K(R(x,y,z),y) = K(x,y). [para(1630(a,2),897(a,1))]. 1633 T(x,R(y,x,z)) = (x * x) / (x * K(y,x)). [para(1632(a,1),1104(a,2,2,2))]. 1634 K(R(x,x \ y,z),u) = R(K(x,u),y,z). [para(20(a,1),1629(a,1,2)),flip(a)]. 1635 R(K(x,y),x * (z / (z * x)),u) = K(x,y). [para(450(a,1),1629(a,2,1))]. 1636 R(K(x,y),T(x,y) * z,u) = K(R(T(x,y),z,u),y). [para(1105(a,1),1629(a,1,1))]. 1637 K(R(x,x * y,z),u) = R(K(x,u),y,z). [para(629(a,1),1634(a,1,1))]. 1638 R(K(x,y),z,x) = K(L(x,z,x),y). [para(1313(a,1),1634(a,1,1)),flip(a)]. 1639 K(x,R(y,y * z,u)) = R(K(y,x),z,u) \ 1. [para(1637(a,1),897(a,1,1)),flip(a)]. 1640 R(K(x,y),K(x,z) * u,w) = K(R(x,T(x,z) * u,w),y). [para(1120(a,1),1637(a,1,1,2)),flip(a)]. 1641 K(R(x,T(x,y) * z,u),y) = R(K(T(x,y),y),z,u). [para(1637(a,1),1110(a,1)),flip(a)]. 1642 T(x,R(y,x,z)) = T(x,y). [para(1633(a,2),1104(a,2)),flip(a)]. 1643 R(x,y,z) * T(y,x) = y * R(x,y,z). [para(1642(a,1),82(a,1,2))]. 1647 T(x,y) \ (x * R(y,x,z)) = T(R(y,x,z),T(x,y)). [para(1643(a,1),36(a,2,2)),flip(a)]. 1648 R(K(x,y),K(x,z),u) = K(x,y). [para(1041(a,2),1635(a,1,2))]. 1649 R(K(x,y),K(z,x),u) = K(x,y). [para(1648(a,1),908(a,1)),flip(a)]. 1650 (K(x,y) * K(z,x)) * u = K(x,y) * (K(z,x) * u). [para(1649(a,1),79(a,1,1)),flip(a)]. 1651 R(K(x,y),T(y,x) * z,u) = K(R(y,z,u),x) \ 1. [para(1631(a,1),156(a,1,1)),flip(a)]. 1652 R(K(x,y),T(x,y) * z,u) = K(R(x,z,u),y). [para(1636(a,2),1110(a,1))]. 1653 R(K(x,y),y * z,u) = K(R(y,z,u),x) \ 1. [para(1652(a,1),1249(a,1,1)),flip(a)]. 1654 R(K(x,y),y * z,u) = K(x,R(y,z,u)). [para(1653(a,2),897(a,1))]. 1656 R(K(x,y),x * z,u) * K(y,x) = K(x,y) * K(y,R(x,z,u)). [para(1654(a,1),1578(a,2,2))]. 1657 K(R(x,T(x,y) * z,u),y) = R(K(x,y),z,u). [para(1105(a,1),1641(a,2,1))]. 1658 T(R(x,y,z),T(y,x)) = K(x,y) * R(x,y,z). [para(1647(a,1),1093(a,1))]. 1659 R(T(x,T(y,x)),y,z) = K(x,y) * R(x,y,z). [para(1658(a,1),46(a,2))]. 1660 K(x,y) * R(x,y,z) = R(T(x,y),y,z). [para(1131(a,1),1659(a,1,1)),flip(a)]. 1661 T(x,y) \ R(T(x,y),y,z) = x \ R(x,y,z). [para(1660(a,1),1171(a,1,2))]. 1662 (x \ y) \ R(T(y / x,x),x,z) = (y / x) \ R(y / x,x,z). [para(84(a,1),1661(a,1,1))]. 1663 L(x,K(y,z),K(z,u)) = x. [hyper(23,a,74,a,b,1650,a),flip(a)]. 1664 L(x,K(y,z),K(u,z)) = x. [para(1663(a,1),909(a,1)),flip(a)]. 1665 L(x,K(y,z),K(u,y)) = x. [para(1664(a,1),921(a,1)),flip(a)]. 1666 (K(x,y) * T(z,x)) / z = K(z,x) * K(x,y). [para(1665(a,1),1355(a,1,2))]. 1667 R(K(x,y),T(y,x) * z,u) = K(x,R(y,z,u)). [para(1651(a,2),897(a,1))]. 1668 R(K(x,y),y * z,u) \ K(x,y) = K(y,x) * K(x,R(y,z,u)). [para(1667(a,1),1579(a,1,2)),flip(a)]. 1669 R(K(x,y),K(x,y) * z,u) = R(K(x,y),z,u). [para(1640(a,2),1657(a,1))]. 1670 R(K(x,y),z,u) \ 1 = R(K(y,x),z,u). [para(1669(a,1),906(a,1)),flip(a)]. 1671 R(K(x,y),z,u) \ K(x,y) = K(x,y) * R(K(y,x),z,u). [para(1670(a,1),543(a,1,2)),flip(a)]. 1672 K(x,R(y,y * z,u)) = R(K(x,y),z,u). [para(1670(a,1),1639(a,2))]. 1673 K(R(x,y,z),u) * K(u,x) = K(x,u) * K(u,R(x,y,z)). [para(1629(a,1),1656(a,1,1))]. 1674 K(x,y) * K(R(y,z,u),x) = K(y,x) * K(x,R(y,z,u)). [para(1673(a,1),1226(a,2))]. 1675 (x / y) \ R(x / y,y,z) = (y \ x) \ R(y \ x,y,z). [para(84(a,1),1662(a,1,2,1)),flip(a)]. 1676 (x \ y) \ R(x \ y,x,z) = (x / y) * R(y / x,x,z). [para(1675(a,1),358(a,1))]. 1677 x \ (y * R(y \ x,x,z)) = (x / y) * R(y / x,x,z). [para(1676(a,1),1599(a,1)),flip(a)]. 1678 x \ ((y \ x) * R((y \ x) \ x,x,z)) = y * R((y \ x) / x,x,z). [para(65(a,1),1677(a,2,1))]. 1679 x \ (R(y,x,z) * (y \ x)) = y * R((y \ x) / x,x,z). [para(225(a,1),1678(a,1,2))]. 1680 x * R((x \ y) / y,y,z) = T(x \ R(x,y,z),y). [para(1679(a,1),539(a,1))]. 1681 T(x \ R(x,y,z),y) = x * R(x \ 1,y,z). [para(320(a,1),1680(a,1,2,1)),flip(a)]. 1683 T(x \ R(x,y,z),y) = x \ R(x,y,z). [para(1681(a,2),635(a,1))]. 1684 (x * (y \ R(y,x,z))) / x = y \ R(y,x,z). [para(1683(a,1),105(a,1,1,2))]. 1685 T(x \ R(x,y,z),x * (y * z)) = T(a(x,y,z),y). [para(1683(a,1),740(a,1,1))]. 1686 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). [para(1684(a,1),1518(a,2,1))]. 1687 T(a(x,y,z),y) = a(x,y,z). [para(1685(a,1),739(a,2)),flip(a)]. 1688 a(x,y,z) * y = y * a(x,y,z). [para(1687(a,1),82(a,1,2)),flip(a)]. 1689 a(x,y \ 1,z) * (y \ 1) = y \ a(x,y \ 1,z). [para(1687(a,1),326(a,1,2)),flip(a)]. 1690 T(x * y,x) / x = y * a(x,y,x). [para(1688(a,1),1563(a,2))]. 1691 L(x,y,z * (T(u * z,u) / u)) = L(x,y,a(u,z,u)). [para(1690(a,2),774(a,1,3,2))]. 1692 L(x,y,z * a(u,z,u)) = L(x,y,R(z,u,u)). [para(1690(a,1),1350(a,1,3))]. 1693 L(x,y,z * T((u * z) * u,u)) = L(x,y,a(u,z,u)). [para(1691(a,1),1576(a,1)),flip(a)]. 1694 L(x,y,z * ((z * u) * u)) = L(x,y,a(u,z,u)). [para(758(a,1),1693(a,1,3,2))]. 1695 L(x,y,a(z,u,u)) = L(x,y,a(u,z,u)). [para(1694(a,1),861(a,1)),flip(a)]. 1696 (x * (x * (y * (z * u)))) \ (x * (x * ((y * z) * u))) = a(x * (x * y),z,u). [para(51(a,1),1620(a,1,2))]. 1697 (x * y) * R((x * y) \ (x * z),u,w) = (x * y) * L(R(y \ z,u,w),y,x). [para(48(a,1),1621(a,1,2)),flip(a)]. 1698 ((x * y) * ((y * x) * z)) \ ((x * y) * ((y * x) * (z * u))) = L(u,z,K(y,x)). [para(894(a,1),1624(a,1,2))]. 1699 a(x * (x * y),z,u) = (y * (z * u)) \ ((y * z) * u). [para(1696(a,1),212(a,1))]. 1700 a(x * (x * y),z,u) = a(y,z,u). [para(1699(a,2),28(a,2)),flip(a)]. 1702 a(x \ y,z,u) = a(x * y,z,u). [para(20(a,1),1700(a,1,1,2)),flip(a)]. 1703 a((x / y) * x,z,u) = a(y,z,u). [para(22(a,1),1700(a,1,1,2))]. 1704 a(x * (y * x),z,u) = a(T(y,x),z,u). [para(82(a,1),1700(a,1,1,2))]. 1706 a(x * ((x \ y) * z),u,w) = a(x * ((x * y) * z),u,w). [para(89(a,1),1700(a,1,1,2)),flip(a)]. 1707 a((x \ y) * z,u,w) = a((x * y) * z,u,w). [para(89(a,1),1700(a,1,1)),flip(a)]. 1708 a((x * x) / y,z,u) = a(y \ 1,z,u). [para(263(a,1),1700(a,1,1))]. 1709 a(x * L(x,y * x,y),z,u) = a(a(y,x,x),z,u). [para(453(a,2),1700(a,1,1,2))]. 1710 a(R(x \ 1,y,y),z,u) = a(x * a(x,y,y),z,u). [para(960(a,1),1700(a,1,1,2)),flip(a)]. 1711 a(K(x,y) * y,z,u) = a(T(y,x),z,u). [para(1077(a,1),1700(a,1,1,2))]. 1712 a(x * T(x,y),z,u) = a(K(x,y),z,u). [para(1107(a,2),1700(a,1,1,2))]. 1713 ((x \ y) * (T(x,x * y) * z)) \ (y * z) = a(x * y,T(x,x * y),z). [para(1702(a,1),255(a,2))]. 1714 a(K(x \ 1,x * y),z,u) = a(x \ ((x * y) \ y),z,u). [para(1126(a,2),1702(a,2,1)),flip(a)]. 1715 a((x * (x * y)) * (x * z),u,w) = a(y \ (x \ z),u,w). [para(282(a,1),1703(a,1,1,1))]. 1716 a((x * x) / y,z,u) = a(y,z,u). [para(1708(a,2),611(a,1))]. 1717 a(x / (y * y),z,u) = a(x,z,u). [para(1716(a,1),612(a,1)),flip(a)]. 1718 a(R(x,x * y,z),u,w) = a(R(x,y,z),u,w). [para(616(a,1),1716(a,1,1))]. 1719 a(x * K(y,x),z,u) = a(T(x,y),z,u). [para(1104(a,2),1716(a,1,1)),flip(a)]. 1720 a(x * (y * y),z,u) = a(x,z,u). [para(21(a,1),1717(a,1,1)),flip(a)]. 1721 a((x * y) * y,z,u) = a(R(x,y,y),z,u). [para(34(a,2),1717(a,1,1)),flip(a)]. 1722 a(x / (y \ 1),z,u) = a(x / y,z,u). [para(398(a,1),1717(a,1,1)),flip(a)]. 1723 ((x * (y * y)) * (z * u)) \ (((x * (y * y)) * z) * u) = a(x,z,u). [para(1720(a,1),28(a,1)),flip(a)]. 1724 a(T(T(x,y),y),z,u) = a(x,z,u). [para(985(a,1),1711(a,1,1)),flip(a)]. 1725 a((x / (y * y)) * (y \ (x * (y \ 1))),z,u) = a(K(x / (y * y),y),z,u). [para(403(a,1),1712(a,1,1,2))]. 1726 a(x / (x * y),z,u) = a(T(y,x),z,u). [para(1719(a,1),1022(a,2))]. 1727 a((x \ 1) / y,z,u) = a(y / x,z,u). [para(1722(a,1),612(a,1)),flip(a)]. 1728 a(x / T(y * x,y),z,u) = a(T(R(y,x,y),x),z,u). [para(1321(a,1),1726(a,1,1,2))]. 1729 a(x * (y * x),x,x) = a(R(y,x,x),x,x). [para(1721(a,1),1517(a,1)),flip(a)]. 1730 a(R(x,y,y),y,y) = a(T(x,y),y,y). [para(1729(a,1),1704(a,1))]. 1731 a(R(x,y,y),y,y) = a(x,y,y). [para(1730(a,2),1485(a,1))]. 1732 R(R(x,y,y) \ 1,y,y) = R(x,y,y) \ a(x,y,y). [para(1731(a,1),967(a,2,2))]. 1733 R(R(x,y,y),R(x,y,y) * y,y) = a(x,y,y) \ R(x,y,y). [para(1731(a,1),968(a,2,1))]. 1734 a(x * ((x \ y) * y),z,u) = a(a(x,y,y),z,u). [para(435(a,1),1709(a,1,1))]. 1735 a(R(x \ 1,y,y),z,u) = a(R(x,y,y),z,u). [para(963(a,1),1710(a,2,1))]. 1736 R(R(x,y,y) \ 1,y,y) = x \ 1. [para(1732(a,2),1374(a,1))]. 1737 R((x * y) \ 1,y,y) = (x / (y \ 1)) \ 1. [para(720(a,1),1736(a,1,1,1))]. 1739 R((x * y) \ 1,y,y) = (y \ 1) / x. [para(1737(a,2),343(a,1))]. 1740 (x \ 1) / (y / x) = R(y \ 1,x,x). [para(22(a,1),1739(a,1,1,1)),flip(a)]. 1741 (((x * y) \ 1) * y) * y = ((y \ 1) / x) * (y * y). [para(1739(a,1),79(a,1,1)),flip(a)]. 1742 R(x \ 1,y,y) \ 1 = (x / y) / (y \ 1). [para(1740(a,1),343(a,1,1))]. 1743 a((x \ 1) / ((y / x) \ 1),z,u) = a(R(y \ 1,x,x),z,u). [para(1740(a,1),1722(a,2,1))]. 1744 R(x,x * y,y) = (x / y) / (y \ 1). [para(1742(a,1),633(a,2))]. 1745 K(R(x,x * y,y),z) * (x / y) = (y \ 1) * T((y \ 1) \ (x / y),z). [para(1744(a,2),1201(a,1,1,1))]. 1746 (((x * y) \ 1) * y) * y = T(y / x,y * y). [para(1741(a,2),294(a,1))]. 1747 T(x / y,x * x) = ((y * x) \ x) * x. [para(318(a,1),1746(a,1,1)),flip(a)]. 1748 L(x,y * z,R(T(z / y,z * z),u,w)) = x. [para(1747(a,2),847(a,1,3,1))]. 1749 L(x,y * z,R(z / y,u,w)) = x. [para(1748(a,1),858(a,1)),flip(a)]. 1750 L(x,y * (z \ 1),u / (y * (z * u))) = x. [para(350(a,1),1749(a,1,3))]. 1752 L(x,y * z,u / (y * (z * u))) = x. [para(1750(a,1),1273(a,1)),flip(a)]. 1753 x / ((y * z) \ (y * (z * x))) = (x / (y * (z * x))) * (y * z). [para(1752(a,1),205(a,1,2))]. 1754 a(T(R(x,y,x),y),z,u) = a((y / x) / y,z,u). [para(1237(a,1),1728(a,1,1)),flip(a)]. 1755 a(x * ((x * y) * y),z,u) = a(a(x,y,y),z,u). [para(1706(a,1),1734(a,1))]. 1756 a(x * (x * (y * (x * z))),u,w) = a(y \ (x \ z),u,w). [para(51(a,1),1715(a,1,1))]. 1757 a(x \ (y \ z),u,w) = a(x * (y * z),u,w). [para(1756(a,1),1700(a,1))]. 1759 a(x * (y \ z),u,w) = a(x * (y * z),u,w). [para(1757(a,1),1702(a,1)),flip(a)]. 1760 a(K(x \ 1,x * y),z,u) = a(x * ((x * y) * y),z,u). [para(1757(a,1),1714(a,2))]. 1761 R(R(x,y,y),R(x,y,y) * y,y) = x. [para(1733(a,2),964(a,1))]. 1762 R(K(R(x,y,y),z),y,y) = K(x,z). [para(1761(a,1),1637(a,1,1)),flip(a)]. 1763 K(R(x,y,y),z) * (y \ 1) = K(x,z) / y. [para(1762(a,1),718(a,1,1)),flip(a)]. 1764 K(x,R(y,z,z)) * (K(y,x) / z) = z \ 1. [hyper(23,a,901,a,b,1763,a),flip(a)]. 1765 R(K(x,y),z,z) = K(x,R(y,z,z)). [hyper(24,a,1405,a,b,1764,a),flip(a)]. 1766 K(R(x,y,y),z) \ 1 = R(K(z,x),y,y). [para(1765(a,2),897(a,2))]. 1767 K(x,R(y,z,z)) * 1 = R(K(x,y),z,z). [para(1766(a,1),900(a,1)),flip(a)]. 1768 a((x \ 1) / (x / y),z,u) = a(R(y \ 1,x,x),z,u). [para(343(a,1),1743(a,1,1,2))]. 1769 a(R(x \ 1,y,y),z,u) = a((y / x) / y,z,u). [para(1768(a,1),1727(a,1))]. 1770 a((x / y) / x,z,u) = a(R(y,x,x),z,u). [para(1769(a,1),1735(a,1))]. 1771 a(T(R(x,y,x),y),z,u) = a(R(x,y,y),z,u). [para(1770(a,1),1754(a,2))]. 1772 a(R(T(x,y),y,x),z,u) = a(R(x,y,y),z,u). [para(46(a,2),1771(a,1,1))]. 1773 (x / (y * (z * x))) * (y * z) = x / L(x,z,y). [para(32(a,2),1753(a,1,2)),flip(a)]. 1774 (x / (y * (z * x))) * (y * z) = L(x,z,y) \ x. [para(1773(a,2),519(a,1))]. 1775 (L(x * y,z / (x * (y * z)),x * y) * (z / (x * (y * z)))) * (x * y) = (x * y) * (L(z,y,x) \ z). [para(1774(a,1),1310(a,2,2))]. 1776 (x * (y * (y * (z * u)))) \ (((x * (y * y)) * z) * u) = a(x,z,u). [para(411(a,1),1723(a,1,1))]. 1777 (x * (y * (y * (z * u)))) \ ((x * (y * (y * z))) * u) = a(x,z,u). [para(411(a,1),1776(a,1,2,1))]. 1778 a(x,y * (y * z),u) = a(x,z,u). [para(1777(a,1),90(a,1)),flip(a)]. 1779 a(x,y \ z,u) = a(x,y * z,u). [para(20(a,1),1778(a,1,2,2)),flip(a)]. 1780 a(x,(y / z) * y,u) = a(x,z,u). [para(22(a,1),1778(a,1,2,2))]. 1781 a(x,(y \ z) * u,w) = a(x,(y * z) * u,w). [para(89(a,1),1778(a,1,2)),flip(a)]. 1782 a(x,T(y,y * z),u) = a(x,(y \ z) * z,u). [para(250(a,1),1778(a,1,2,2)),flip(a)]. 1783 a(x,K(y,z) * T(y,z),u) = a(x,y,u). [para(1081(a,2),1778(a,1,2,2))]. 1785 a(x * (y * y),y * 1,y) = a(x * y,y \ 1,y \ 1). [para(1779(a,1),1574(a,1))]. 1786 a(x,y \ 1,z) * (y \ 1) = y \ a(x,y * 1,z). [para(1779(a,1),1689(a,2,2))]. 1787 a(x,(y * (y * z)) * (y * u),w) = a(x,z \ (y \ u),w). [para(282(a,1),1780(a,1,2,1))]. 1788 a(x,T(y * z,y),u) = a(x,z / y,u). [para(1232(a,2),1780(a,1,2))]. 1789 a(x,T(T(y,z),z),u) = a(x,y,u). [para(1113(a,1),1783(a,1,2))]. 1790 a(T(x,y),y,z) = a(x,T(y,x),z). [para(1789(a,1),1460(a,1))]. 1792 a(x,T(y,y * z),u) = a(x,(y * z) * z,u). [para(1782(a,2),1781(a,1))]. 1793 a(x,y \ 1,z) * (y \ 1) = y \ a(x,y,z). [para(18(a,1),1786(a,2,2,2))]. 1794 a(x,y * 1,z) * (y \ 1) = y \ a(x,y,z). [para(1779(a,1),1793(a,1,1))]. 1795 a(x,y,z) * (y \ 1) = y \ a(x,y,z). [para(18(a,1),1794(a,1,1,2))]. 1796 a(x * (y * y),y,y) = a(x * y,y \ 1,y \ 1). [para(18(a,1),1785(a,1,2))]. 1797 a(x * y,y \ 1,y \ 1) = a(x,y,y). [para(1796(a,1),1720(a,1))]. 1798 L(x,x,y) \ x = a(y,x,x). [para(1797(a,1),1408(a,1)),flip(a)]. 1800 a(x,y,y) * L(y,y,x) = y. [para(1798(a,1),520(a,1,1))]. 1801 R(x,y,y) * L(y,y,x) = x * y. [para(1800(a,1),966(a,1,2)),flip(a)]. 1802 T(R(x,y,y),L(y,y,x)) = L(y,y,x) \ (x * y). [para(1801(a,1),36(a,2,2))]. 1803 R(T(x,L(y,y,x)),y,y) = L(y,y,x) \ (x * y). [para(1802(a,1),46(a,2))]. 1804 L(x,x,y) \ (y * x) = R(T(y,x),x,x). [para(1558(a,1),1803(a,1,1)),flip(a)]. 1805 a(x,y * (y * (z * (y * u))),w) = a(x,z \ (y \ u),w). [para(51(a,1),1787(a,1,2))]. 1806 a(x,y \ (z \ u),w) = a(x,y * (z * u),w). [para(1805(a,1),1778(a,1))]. 1808 a(x,y * (z \ u),w) = a(x,y * (z * u),w). [para(1806(a,1),1779(a,1)),flip(a)]. 1809 a(x * y,T(x,x * y),z) = ((y / x) * (x * z)) \ (y * z). [para(1265(a,1),1713(a,1,1)),flip(a)]. 1810 a(x * y,T(x,x * y),z) = a(y / x,x,z). [para(1809(a,2),68(a,1))]. 1811 R(K(x,y),z,z) * (x / z) = (z \ 1) * T((z \ 1) \ (x / z),y). [para(1637(a,1),1745(a,1,1))]. 1812 K(x,R(y,z,z)) * (x / z) = (z \ 1) * T((z \ 1) \ (x / z),y). [para(1765(a,1),1811(a,1,1))]. 1813 K(x,R(y,z,z)) * (x / z) = (z \ 1) * T(z * (x / z),y). [para(330(a,1),1812(a,2,2,1))]. 1814 K(x,R(y,z,z)) * (x / z) = z \ T(z * (x / z),y). [para(1813(a,2),318(a,1))]. 1815 K(x,R(y,z,z)) * (x / z) = T(x,y) / z. [para(1814(a,2),755(a,1))]. 1816 a(x * (y \ (y \ (y \ (x * (y \ 1))))),z,u) = a(K(x / (y * y),y),z,u). [para(602(a,1),1725(a,1,1))]. 1817 a(x * (y \ ((y \ (y \ x)) * (y \ 1))),z,u) = a(K(x / (y * y),y),z,u). [para(285(a,1),1816(a,1,1,2,2))]. 1818 a(x * (y * ((y \ (y \ x)) * (y \ 1))),z,u) = a(K(x / (y * y),y),z,u). [para(1817(a,1),1759(a,1)),flip(a)]. 1819 a(K(x / (y * y),y),z,u) = a(x * (y \ (x * (y \ 1))),z,u). [para(265(a,1),1818(a,1,1,2)),flip(a)]. 1820 a(K(x / (y * y),y),z,u) = a(x * (y * (x * (y \ 1))),z,u). [para(1819(a,2),1759(a,1))]. 1821 a(K(x / (y * y),y),z,u) = a(x * T(x,y \ 1),z,u). [para(347(a,1),1820(a,2,1,2))]. 1822 a(K(x / (y * y),y),z,u) = a(K(x,y \ 1),z,u). [para(1821(a,2),1712(a,1))]. 1823 a(K(x,y \ 1),z,u) = a(K(x,y),z,u). [para(1418(a,1),1822(a,1,1)),flip(a)]. 1824 a(K(x \ 1,y),z,u) = a(K(y,x),z,u). [para(1823(a,1),905(a,1)),flip(a)]. 1825 a(x * ((x * y) * y),z,u) = a(K(x * y,x),z,u). [para(1824(a,1),1760(a,1)),flip(a)]. 1826 a(K(x * y,x),z,u) = a(a(x,y,y),z,u). [para(1825(a,1),1755(a,1))]. 1827 (x * y) * R((x * y) \ (x * z),u,w) = x * (y * R(y \ z,u,w)). [para(1697(a,2),74(a,1))]. 1828 (x * y) * R((x * y) \ z,u,w) = x * (y * R(y \ (x \ z),u,w)). [para(20(a,1),1827(a,1,2,1,2))]. 1829 (x * y) * R((x * y) \ y,z,u) = R(x,z,u) * (x \ y). [para(1828(a,2),639(a,1))]. 1830 T(x,y) \ R(T(x,y),z,u) = y \ (R(x,z,u) * (x \ y)). [para(1829(a,1),1610(a,1,2)),flip(a)]. 1831 T(x,y) \ R(T(x,y),z,u) = T(x \ R(x,z,u),y). [para(1830(a,2),539(a,1))]. 1832 (R(T(x,y),z,u) \ T(x,y)) * w = T(x \ R(x,z,u),y) \ w. [para(1831(a,1),465(a,1,1)),flip(a)]. 1833 T(x \ R(x,y,y),z) = a(T(x,z),y,y). [para(1831(a,1),962(a,1))]. 1834 K(x,y) * R(T(y,x),z,u) = y * T(y \ R(y,z,u),x). [para(1831(a,1),1099(a,1,2)),flip(a)]. 1835 T(T(x,y) \ R(T(x,y),z,u),y) = x \ R(x,z,u). [para(1831(a,1),1582(a,1))]. 1836 a(T(x,y),z,z) = T(a(x,z,z),y). [para(962(a,1),1833(a,1,1)),flip(a)]. 1837 T(T(x \ R(x,y,z),u),u) = x \ R(x,y,z). [para(1831(a,1),1835(a,1,1))]. 1838 (x * (y \ R(y,z,u))) / x = T(y \ R(y,z,u),x). [para(1837(a,1),105(a,1,1,2))]. 1839 T(a(x,y,z),x * (y * z)) = x \ R(x,y,z). [para(739(a,2),1837(a,1,1))]. 1840 a(x,y,z) * K(a(x,y,z),x * (y * z)) = x \ R(x,y,z). [para(1839(a,1),1107(a,1)),flip(a)]. 1841 T(T(x \ R(x,y,z),u),x * (y * z)) = (u * a(x,y,z)) / u. [para(1838(a,1),742(a,1,1))]. 1842 (x * (y \ R(y,z,u))) / x = (y \ R(y,z,u)) * K(y \ R(y,z,u),x). [para(1838(a,2),1107(a,1))]. 1843 (x * a(y,z,u)) / x = T(a(y,z,u),x). [para(1841(a,1),740(a,1))]. 1844 T(a(x,y,z),u) * (u / (u * a(x,y,z))) = 1. [para(1843(a,1),354(a,1,1))]. 1845 L(x,x,x * ((x \ 1) * a(y,z,u))) = ((x \ 1) * a(y,z,u)) \ T(a(y,z,u),x \ 1). [para(1843(a,1),1488(a,2,2))]. 1846 K(a(x,y,z),u) * K(a(x,y,z),u) = 1. [para(1844(a,1),1174(a,1)),flip(a)]. 1847 K(a(x,y,z),u) = K(u,a(x,y,z)). [hyper(24,a,898,a,b,1846,a)]. 1848 a(x,y,z) * K(x * (y * z),a(x,y,z)) = x \ R(x,y,z). [para(1847(a,1),1840(a,1,2))]. 1849 K(x \ R(x,y,z),u) = K(u,x \ R(x,y,z)). [hyper(23,a,1014,a(flip),b,1842,a(flip))]. 1850 L(L(x,y,z * u),(z * u) * y,u * z) = L(x,y,K(z,u)). [para(1698(a,1),174(a,1)),flip(a)]. 1851 ((x * (x * y)) * a(y,z,u)) / y = a(x * (x * y),z,u) * (x * x). [para(1700(a,1),749(a,1,1,2))]. 1852 (x * (x * (y * a(y,z,u)))) / y = a(x * (x * y),z,u) * (x * x). [para(51(a,1),1851(a,1,1))]. 1854 a(x * (x * y),z,u) * (x * x) = x * (x * ((y * a(y,z,u)) / y)). [para(1852(a,1),211(a,1))]. 1855 a(x * (x * y),z,u) * (x * x) = x * (x * a(y,z,u)). [para(748(a,1),1854(a,2,2,2))]. 1856 a(x,y,z) * (u * u) = u * (u * a(x,y,z)). [para(1700(a,1),1855(a,1,1))]. 1857 T((a(x,y,z) * (u * u)) / (u * u),u) = T(u \ (u * a(x,y,z)),u \ 1). [para(1856(a,2),666(a,1,1,1))]. 1859 T(x \ (x * a(y,z,u)),x \ 1) = T(a(y,z,u),x). [para(21(a,1),1857(a,1,1)),flip(a)]. 1860 T(a(x,y,z),u \ 1) = T(a(x,y,z),u). [para(19(a,1),1859(a,1,1))]. 1863 x * L(T(y \ (y / x),z),y,x * y) = K(L(y \ (y / x),y,x * y),z). [para(1295(a,1),330(a,1)),flip(a)]. 1864 (x / y) * (y * T(y \ (y / x),z)) = K(L(y \ (y / x),y,x * y),z). [para(1863(a,1),1294(a,1)),flip(a)]. 1865 (x / y) * (y * T(y \ (y / x),z)) = K(x \ 1,z). [para(1289(a,1),1864(a,2,1))]. 1866 (L(x,y,z) / (z * (y * x))) * ((z * (y * x)) * T((z * (y * x)) \ (z * y),u)) = K(L(x,y,z) \ 1,u). [para(99(a,1),1865(a,1,2,2,1,2))]. 1868 T(x * x,y * z) \ ((((y * z) \ (x * x)) * y) * z) = a((y * z) * (x * x),y,z). [para(394(a,2),1702(a,1))]. 1869 ((R(x,y,z) * u) * w) / ((x * u) * w) = R(x,u,w) \ R(R(x,u,w),y,z). [para(185(a,1),538(a,1,1))]. 1870 R(x \ R(x,y,z),x * u,w) = R(x,u,w) \ R(R(x,u,w),y,z). [para(1869(a,1),533(a,2))]. 1871 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). [para(584(a,1),1870(a,2,1))]. 1872 (K(x,T(y,z)) * T(y,x)) / y = K(z,T(y,x)) * K(y,z). [para(1663(a,1),1570(a,1,2))]. 1873 K(x,T(y,z)) * K(y,x) = K(y,z) * K(z,T(y,x)). [para(1872(a,1),1666(a,1))]. 1874 T(x * x,y * z) \ ((((y * z) \ (x * x)) * y) * z) = a(y * z,y,z). [para(1868(a,2),1720(a,1))]. 1875 (T(x * x,y * z) \ (((y * z) \ (x * x)) * y)) * z = a(y * z,y,z). [para(1874(a,1),591(a,1)),flip(a)]. 1877 ((T(x * x,y * z) \ ((y * z) \ (x * x))) * y) * z = a(y * z,y,z). [para(591(a,1),1875(a,1,1))]. 1878 (((x * y) \ 1) * x) * y = a(x * y,x,y). [para(795(a,1),1877(a,1,1,1))]. 1879 ((x * y) \ x) * y = a(x * y,x,y). [para(318(a,1),1878(a,1,1))]. 1880 x * ((y * x) \ y) = a(y * x,y,x). [para(1879(a,1),388(a,1)),flip(a)]. 1881 a(x * (x \ y),x,x \ y) = (x \ y) * (y \ x). [para(20(a,1),1880(a,1,2,1)),flip(a)]. 1882 (x \ y) * (y \ x) = a(y,x,x \ y). [para(20(a,1),1881(a,1,1)),flip(a)]. 1883 L(x,y,(z \ u) * (u * z)) = L(x,y,a(z,u,u \ z)). [para(1882(a,1),869(a,1,3)),flip(a)]. 1884 L(x,(y \ z) * (z * y),u) = L(x,a(y,z,z \ y),u). [para(1882(a,1),1362(a,1,2)),flip(a)]. 1885 L(x,y,(z * u) * (u * z)) = L(x,y,a(z,u,u \ z)). [para(1883(a,1),781(a,1)),flip(a)]. 1886 L(x,(y * z) * (z * y),u) = L(x,a(y,z,z \ y),u). [para(1884(a,1),880(a,1)),flip(a)]. 1887 L(x,y,a(z,u,u \ z)) = L(x,y,K(u,z)). [para(1885(a,1),779(a,1))]. 1888 L(x,a(y,z,z \ y),u) = L(x,K(z,y),u). [para(1886(a,1),879(a,1))]. 1889 ((x \ 1) * a(y,z,u)) \ T(a(y,z,u),x \ 1) = L(x,x,a(y,z,u)). [para(321(a,1),1845(a,1,3)),flip(a)]. 1890 (x \ a(y,z,u)) \ T(a(y,z,u),x \ 1) = L(x,x,a(y,z,u)). [para(318(a,1),1889(a,1,1))]. 1892 (x \ a(y,z,u)) \ T(a(y,z,u),x) = L(x,x,a(y,z,u)). [para(1860(a,1),1890(a,1,2))]. 1893 L(x,a(y,z,u),x) = L(x,x,a(y,z,u)). [para(1892(a,1),440(a,1)),flip(a)]. 1894 L(x,x,a(y,z,z \ y)) = L(x,K(z,y),x). [para(1893(a,1),1888(a,1))]. 1895 L(x,K(y,z),x) = L(x,x,K(y,z)). [para(1894(a,1),1887(a,1))]. 1896 L(x,K(y,z),x) = L(x,x,K(z,y)). [para(1895(a,2),909(a,1))]. 1897 (x \ K(y,z)) / (K(y,z) / L(x,x,K(z,y))) = K(K(y,z),x). [para(1896(a,1),1500(a,2,2,2)),flip(a)]. 1898 (x \ K(y,z)) / (K(y,z) * (x \ 1)) = K(K(y,z),x). [para(930(a,1),1897(a,1,2))]. 1899 K(x \ 1,K(y,z)) = K(K(y,z),x). [para(1898(a,1),978(a,1)),flip(a)]. 1900 K(K(x,y),z) * (K(x,y) \ u) = T(K(x,y),z \ 1) \ u. [para(1899(a,1),1095(a,1,1))]. 1901 T(K(x,y),z) * K(K(x,y),z) = T(K(x,y),z * z). [para(1899(a,1),1433(a,1,2))]. 1902 T(T(K(x,y),z),z) = T(K(x,y),z * z). [para(1901(a,1),1121(a,1)),flip(a)]. 1903 T(K(x,y),T(z,x) * T(z,x)) = T(T(K(x,y),z),T(z,x)). [para(1352(a,1),1902(a,1,1)),flip(a)]. 1904 x / (T(K(y,z),u \ 1) \ x) = K(y,z) * K(u,K(y,z)). [para(1900(a,1),1071(a,1,2))]. 1905 T(K(x,y),z * T(T(z,x),x)) = T(T(K(x,y),z),T(z,x)). [para(1088(a,1),1903(a,1,2))]. 1906 K(x,y) * K(z,K(x,y)) = T(K(x,y),z \ 1). [para(1904(a,1),65(a,1))]. 1907 T(K(x,y),z \ 1) * z = z * K(x,y). [para(1906(a,1),1018(a,1,1))]. 1908 ((x * y) * (z / (x * (y * z)))) * (x * y) = (x * y) * (L(z,y,x) \ z). [para(851(a,1),1775(a,1,1,1))]. 1910 (x \ R(x,y,z)) * (x * y) = (x * y) * (L(z,y,x) \ z). [para(1410(a,1),1908(a,1,1))]. 1911 (x * y) * (L(z,y,x) \ z) = R(x,y,z) * y. [para(1910(a,1),528(a,1))]. 1912 ((x * y) \ 1) * ((x * (y * z)) * T((x * (y * z)) \ (x * y),u)) = K(L(z,y,x) \ 1,u). [para(342(a,1),1866(a,1,1))]. 1914 ((x * y) \ 1) * (x * ((y * z) * T((y * z) \ y,u))) = K(L(z,y,x) \ 1,u). [para(1590(a,1),1912(a,1,2))]. 1915 ((x * y) \ 1) * (x * (y * K(z \ 1,u))) = K(L(z,y,x) \ 1,u). [para(1164(a,1),1914(a,1,2,2))]. 1916 (x * y) \ (x * (y * K(z \ 1,u))) = K(L(z,y,x) \ 1,u). [para(1915(a,1),318(a,1)),flip(a)]. 1917 L(K(x \ 1,y),z,u) = K(L(x,z,u) \ 1,y). [para(1916(a,1),32(a,2))]. 1918 K(L(x \ 1,y,z) \ 1,u) = L(K(x,u),y,z). [para(156(a,1),1917(a,1,1,1)),flip(a)]. 1920 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). [para(750(a,1),1871(a,1,1))]. 1921 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). [para(18(a,1),1920(a,1,1,1))]. 1922 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). [para(18(a,1),1921(a,1,1,2,1))]. 1923 (R(x,y,z) \ 1) \ R(R(x \ 1,x * y,z),u,w) = R(x \ R(x,u,w),y,z). [para(322(a,1),1922(a,1,2)),flip(a)]. 1924 (R(x,y,z) \ 1) \ R(R(x,y,z) \ 1,u,w) = R(x \ R(x,u,w),y,z). [para(584(a,1),1923(a,1,2,1))]. 1925 (R(x,y,z) * 1) \ R(R(x,y,z) * 1,u,w) = R(x \ R(x,u,w),y,z). [para(1924(a,1),750(a,1)),flip(a)]. 1926 R(x,y,z) \ R(R(x,y,z) * 1,u,w) = R(x \ R(x,u,w),y,z). [para(18(a,1),1925(a,1,1))]. 1927 R(x,y,z) \ R(R(x,y,z),u,w) = R(x \ R(x,u,w),y,z). [para(18(a,1),1926(a,1,2,1))]. 1928 R(x \ R(x,y,y),z,u) = a(R(x,z,u),y,y). [para(1927(a,1),962(a,1))]. 1929 T(R(x \ R(x,y,x),z,u),x * (R(x,z,u) * T(y,x))) = a(R(x,z,u),y,x). [para(1927(a,1),743(a,1,1))]. 1930 a(R(x,y,z),u,u) = R(a(x,u,u),y,z). [para(962(a,1),1928(a,1,1)),flip(a)]. 1931 T(R(a(x,y,x),z,u),x * (R(x,z,u) * T(y,x))) = a(R(x,z,u),y,x). [para(1539(a,1),1929(a,1,1,1))]. 1932 T(R(a(x,y,x),z,u),R(x,z,u) * (y * x)) = a(R(x,z,u),y,x). [para(530(a,1),1931(a,1,2))]. 1933 R(T(a(x,y,x),R(x,z,u) * (y * x)),z,u) = a(R(x,z,u),y,x). [para(1932(a,1),46(a,2))]. 1934 ((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). [para(342(a,1),1597(a,1,1))]. 1936 ((x * y) \ 1) * (x * ((y * z) * R((y * z) \ y,u,w))) = L(z,y,x) \ R(L(z,y,x),u,w). [para(1827(a,1),1934(a,1,2))]. 1937 ((x * y) \ 1) * (x * (y * (z \ R(z,u,w)))) = L(z,y,x) \ R(L(z,y,x),u,w). [para(1592(a,1),1936(a,1,2,2))]. 1938 (x * y) \ (x * (y * (z \ R(z,u,w)))) = L(z,y,x) \ R(L(z,y,x),u,w). [para(1937(a,1),318(a,1)),flip(a)]. 1939 L(x,y,z) \ R(L(x,y,z),u,w) = L(x \ R(x,u,w),y,z). [para(1938(a,1),32(a,2)),flip(a)]. 1940 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). [para(1808(a,1),1686(a,1,1,2,1))]. 1941 L((x * (y \ R(y,x,z))) * (1 * u),x * (y \ R(y,x,z)),x) = (y \ R(y,x,z)) * (x * u). [para(1442(a,1),1940(a,1,1,2,1))]. 1942 L((x * (y \ R(y,x,z))) * u,x * (y \ R(y,x,z)),x) = (y \ R(y,x,z)) * (x * u). [para(17(a,1),1941(a,1,1,2))]. 1944 L(x * (R(y,x,z) * (y \ u)),x * (y \ R(y,x,z)),x) = (y \ R(y,x,z)) * (x * u). [para(1450(a,1),1942(a,1,1))]. 1945 L(x * (R(y,x,z) * (y \ u)),x * (y * R(y,x,z)),x) = (y \ R(y,x,z)) * (x * u). [para(1944(a,1),1360(a,1)),flip(a)]. 1946 (x \ R(x,y,z)) * (y * u) = y * (R(x,y,z) * (x \ u)). [para(1945(a,1),1439(a,1))]. 1947 R(x,y,z) * (x \ (y * u)) = y * (R(x,y,z) * (x \ u)). [para(1946(a,1),532(a,1)),flip(a)]. 1948 R(x,y,z) * (x \ (y * (y \ z))) = L(z,x * y,x). [para(1947(a,2),1567(a,1))]. 1949 R(x,y,z) * (x \ z) = L(z,x * y,x). [para(20(a,1),1948(a,1,2,2))]. 1950 R(x,y,L(z,y,x)) * (x \ L(z,y,x)) = z. [para(1949(a,2),303(a,1))]. 1951 L(x,y * z,y) / x = y \ R(y,z,x). [para(1949(a,1),536(a,1,1))]. 1952 x / L(x,y * z,y) = R(y,z,x) \ y. [para(1949(a,1),542(a,1,2))]. 1953 x \ L(x,y * z,y) = y \ R(y,z,x). [para(1951(a,1),515(a,1)),flip(a)]. 1954 L(x,y * z,y) \ x = R(y,z,x) \ y. [para(1952(a,1),519(a,1)),flip(a)]. 1955 x \ R(x,x \ y,z) = z \ L(z,y,x). [para(20(a,1),1953(a,1,2,2)),flip(a)]. 1956 x \ R(x,x * y,z) = z \ L(z,y,x). [para(313(a,1),1953(a,1,2)),flip(a)]. 1957 K(x,R(y,z,x) \ y) = 1. [para(1954(a,1),653(a,1,2))]. 1958 K(x,y \ R(y,z,x)) = 1. [para(622(a,1),1957(a,1,2))]. 1959 T(x,y \ R(y,z,x)) = x. [hyper(41,a,1958,a)]. 1960 K(x,T(y \ R(y,z,x),u)) = 1. [para(1831(a,1),1958(a,1,2))]. 1961 T(x \ R(x,y,z),z) = x \ R(x,y,z). [hyper(39,a,1959,a)]. 1962 K(x,a(y,z,x)) = 1. [para(739(a,2),1960(a,1,2))]. 1963 T(x,a(y,z,x)) = x. [hyper(41,a,1962,a)]. 1964 a(x,y,z) * z = z * a(x,y,z). [para(1963(a,1),82(a,1,2))]. 1965 R(x,y,z) \ x = z \ L(z,y,x). [para(1955(a,1),624(a,1)),flip(a)]. 1966 L(x,y,z) = x * (R(z,y,x) \ z). [para(1965(a,2),20(a,1,2)),flip(a)]. 1967 R(x,y,z) = x / (z \ L(z,y,x)). [para(1965(a,1),65(a,1,2)),flip(a)]. 1968 (x \ L(x,y,z)) \ 1 = z \ R(z,y,x). [para(1965(a,1),460(a,1,1))]. 1969 (x \ L(x,y,z)) * R(z,y,x) = z. [para(1965(a,1),496(a,1,1))]. 1970 L(x,y,z) = (R(z,y,x) \ z) * x. [para(1965(a,2),514(a,1,1)),flip(a)]. 1971 x * (R(K(y,z),u,x) \ K(y,z)) = L(x,u,K(z,y)). [para(1966(a,1),909(a,1))]. 1972 R(x,y,T(z,x * y)) = R(x,y,z). [hyper(23,a,680,a,b,1969,a),flip(a)]. 1973 L(x,y,z) * R(z,y,x) = x * z. [para(1969(a,1),504(a,1,2)),flip(a)]. 1974 L(x,y,z) * (x \ R(z,y,x)) = z. [para(1969(a,1),647(a,1)),flip(a)]. 1975 R(x,y,z) * L(z,y,x) = x * z. [para(1970(a,2),458(a,1,2))]. 1976 L(x,y,z) = (z \ R(z,y,x)) \ x. [para(1970(a,2),465(a,2)),flip(a)]. 1977 T(x \ R(x,y,z),u) \ z = L(z,y,T(x,u)). [para(1970(a,2),1832(a,1)),flip(a)]. 1978 L(x,y,z) \ x = z \ R(z,y,x). [para(1972(a,1),681(a,2,2))]. 1979 R(x,y,z) = x * (L(z,y,x) \ z). [para(1972(a,1),683(a,1))]. 1980 R(x,y,z) * (x \ L(z,y,x)) = z. [para(1972(a,1),686(a,1,1))]. 1981 (L(x,y,z) * (R(z,y,x) * u)) \ ((x * z) * u) = a(L(x,y,z),R(z,y,x),u). [para(1973(a,1),28(a,2,2,1)),flip(a)]. 1984 (L(x,y,z) \ x) * (z * u) = R(z,y,x) * u. [para(1978(a,2),528(a,1,1))]. 1985 (x \ R(x,y,z)) * u = z * (L(z,y,x) \ u). [para(1978(a,1),650(a,1,1))]. 1986 R(x \ R(x,y,z),z,u) = L(z,y,x) \ z. [para(1978(a,1),736(a,1,1))]. 1987 (x * y) * (x \ R(x,y,z)) = R(x,y,z) * y. [para(1978(a,1),1911(a,1,2))]. 1988 K(x,y) \ R(K(x,y),z,u) = u \ L(u,z,K(x,y)). [para(1669(a,1),1956(a,1,2))]. 1989 x \ R(x,y,z) = (L(z,y,x) \ z) * 1. [para(1968(a,1),517(a,1))]. 1990 R(x,y,L(z,y,x)) = R(x,y,z). [hyper(24,a,1980,a,b,1950,a)]. 1991 (x \ R(x,y,z)) \ z = L(z,y,T(x,z)). [para(1961(a,1),1977(a,1,1))]. 1992 L(x,y,T(z,x)) = L(x,y,z). [para(1991(a,1),1976(a,2)),flip(a)]. 1993 L(L(x,y,z),z * y,T(z,L(x,y,z))) = x. [para(1992(a,2),303(a,1))]. 1994 L(x,y,K(z,L(x,y,z))) = x. [para(1993(a,1),1606(a,1)),flip(a)]. 1995 x * (L(x,y,z) \ (z * u)) = R(z,y,x) * u. [para(1984(a,1),650(a,1)),flip(a)]. 1996 L((x \ R(x,y,z)) \ u,x \ R(x,y,z),x * y) = (R(x,y,z) * y) \ ((x * y) * u). [para(1987(a,1),76(a,2,1))]. 1998 L(x,y,z) * (R(z,y,x) * u) = x * (z * u). [para(1995(a,1),645(a,1,2))]. 1999 x * (L(x,y,z) \ (z * T(y,z))) = y * R(z,y,x). [para(1995(a,2),1643(a,1))]. 2000 x * (L(x,y,z) \ (z * L(x,y,z))) = z * x. [para(1995(a,2),1975(a,1))]. 2001 x * T(y,L(x,z,y)) = y * x. [para(36(a,2),2000(a,1,2))]. 2002 T(x,L(y,z,x)) = x * K(x,y). [hyper(23,a,1116,a,b,2001,a)]. 2005 K(x,L(y,z,x)) = K(x,y). [hyper(23,a,1107,a(flip),b,2002,a(flip)),flip(a)]. 2006 L(x,y,K(z,x)) = x. [para(2005(a,1),1994(a,1,3))]. 2007 L(T(x,y),z,K(u,x)) = T(x,y). [para(2006(a,1),44(a,2,1))]. 2008 L(x,y,K(x,z)) = x. [para(2006(a,1),909(a,1)),flip(a)]. 2009 L(x,y,a(x,z,z)) = x. [para(2006(a,1),1262(a,1)),flip(a)]. 2010 L(K(x,y),z,K(u,x \ 1)) = K((x \ 1) \ 1,y). [para(2006(a,1),1918(a,1,1,1)),flip(a)]. 2011 R(K(x,y),z,y) = K(x,y) / (y \ y). [para(2006(a,1),1967(a,2,2,2))]. 2013 (K(x,y) * z) * x = K(x,y) * (z * x). [para(2008(a,1),74(a,1,2))]. 2014 x * (x \ R(a(x,y,y),z,x)) = a(x,y,y). [para(2009(a,1),1974(a,1,1))]. 2015 T(x,K(y,x) * z) = T(x,z). [para(2007(a,1),1377(a,1)),flip(a)]. 2016 K(K(x,y) * z,y) = T(y,z) \ y. [para(2015(a,1),1080(a,2,1))]. 2017 K(x,K(y,x) * z) = x \ T(x,z). [para(2015(a,1),1108(a,2,2))]. 2018 T(x,T(x,y) * z) = T(x,x * z). [para(1098(a,1),2015(a,1,2)),flip(a)]. 2019 T(x,y * T(z,x)) = T(x,y * z). [para(1212(a,1),2015(a,1,2))]. 2021 K(K(x,y) * z,y) = K(z,y). [para(2016(a,2),1080(a,2)),flip(a)]. 2022 K(K(x,y) * z,x) = K(z,x). [para(901(a,1),2021(a,1,1)),flip(a)]. 2023 K(x * (K(x,y) * z),x) = K(x * z,x). [para(1068(a,1),2022(a,1,1))]. 2024 K(x,K(y,x) * z) = K(x,z). [para(2017(a,2),1108(a,2)),flip(a)]. 2025 K(x,K(x,y) * z) = K(x,z). [para(901(a,1),2024(a,1,2)),flip(a)]. 2026 K(x,y) * K(x * (K(x,z) * y),x) = a(x,K(x,z) * y,x). [para(2025(a,1),1537(a,1,1))]. 2027 R(K(x,y),z,y) = K(x,y) / 1. [para(60(a,1),2011(a,2,2))]. 2029 R(K(x,y),z,y) = K(x,y). [para(2027(a,2),64(a,1))]. 2030 K(x,R(y,z,y)) = K(x,y). [para(2029(a,1),1654(a,1)),flip(a)]. 2031 R(K(x,y),z,x) = K(y,x) \ 1. [para(2029(a,1),1670(a,1,1)),flip(a)]. 2032 K(x,y) * R(T(y,x),z,y) = R(y,z,y). [para(2030(a,1),1083(a,1,1))]. 2033 R(K(x,y),z,x) = K(x,y). [para(2031(a,2),897(a,1))]. 2034 K(L(x,y,x),z) = K(x,z). [para(2033(a,1),1638(a,1)),flip(a)]. 2036 K((x \ y) \ y,z) = K(T(x,y),z). [para(1457(a,1),2034(a,1,1))]. 2038 K(T(x,x \ y),z) = K(T(x,y),z). [para(83(a,2),2036(a,1,1))]. 2039 x \ (K(x,y) * (z * x)) = T(K(x,y) * z,x). [para(2013(a,1),36(a,2,2)),flip(a)]. 2040 x * ((K(x,y) * z) * x) = T(x,y) * (z * x). [para(2013(a,2),1120(a,1,2))]. 2041 T(x,y) \ R(T(x,y),z,x) = x \ R(x,z,x). [para(2032(a,1),1163(a,1,2)),flip(a)]. 2042 x * (x \ a(R(x,y,x),z,z)) = a(x,z,z). [para(1930(a,2),2014(a,1,2,2))]. 2043 x * (x \ a(L(x,y,x),z,z)) = a(x,z,z). [para(1303(a,1),2042(a,1,2,2,1))]. 2044 a(L(x,y,x),z,z) = a(x,z,z). [para(2043(a,1),20(a,1)),flip(a)]. 2045 a(L(T(x,y),y * x,x),z,z) = a(T(x,y),z,z). [para(1283(a,1),2044(a,1,1))]. 2046 K(x,y) * (x \ (z * x)) = T(K(x,y) * z,x). [para(2039(a,1),1076(a,1)),flip(a)]. 2047 (T(x,y) * (z * x)) \ ((T(x,y) * z) * x) = a(x,K(x,y) * z,x). [para(2040(a,1),1166(a,1,1))]. 2048 T(x,y) \ R(T(x,y),z,x) = a(x,z,x). [para(2041(a,2),1539(a,1))]. 2049 T(x \ R(x,y,x),z) = a(x,y,x). [para(2048(a,1),1831(a,1)),flip(a)]. 2050 T(a(x,y,x),z) = a(x,y,x). [para(1539(a,1),2049(a,1,1))]. 2051 a(x,y,x) * z = z * a(x,y,x). [para(2050(a,1),82(a,1,2)),flip(a)]. 2052 a(R(x,y,z),u,x) = R(a(x,u,x),y,z). [para(2050(a,1),1933(a,1,1)),flip(a)]. 2053 (a(x,y,x) * z) * L(u,z,a(x,y,x)) = (z * u) * a(x,y,x). [para(2051(a,1),74(a,2))]. 2054 a(x,y,x) \ a(R(x,z,z),y,x) = a(a(x,y,x),z,z). [para(2052(a,2),962(a,1,2))]. 2056 T(K(x,y) * z,x) = K(x,y) * T(z,x). [para(36(a,2),2046(a,1,2)),flip(a)]. 2057 T(K(x,y) * R(z,u,w),x) = K(x,y) * R(T(z,x),u,w). [para(46(a,2),2056(a,2,2))]. 2058 T(K(x,y) * z,x) / z = K(z,x) * K(x,y). [para(2056(a,2),1666(a,1,1))]. 2059 T(K(x,y) * z,x) / z = K(x,y) * K(z,x). [para(2058(a,2),1226(a,2)),flip(a)]. 2060 L(K(x,y),z,K(u,x \ 1)) = K(x,y). [para(156(a,1),2010(a,2,1))]. 2061 L(K(x,y),z,K(u,x)) = K(x,y). [para(2060(a,1),1618(a,1)),flip(a)]. 2062 L(K(x,y),z,K(x,u)) = K(x,y). [para(2060(a,1),1619(a,1)),flip(a)]. 2063 (K(x,y) * z) \ z = T(K(y,x),z). [para(2061(a,1),1301(a,1,1)),flip(a)]. 2064 T(K(x,y) * z,K(x,y)) = z * K(x,y). [para(2062(a,1),1309(a,1,1,1))]. 2065 x / T(K(y,z),x) = K(z,y) * x. [para(2063(a,1),65(a,1,2))]. 2067 (T(K(x,y),z) / z) * u = (K(y,x) * z) \ u. [para(2065(a,1),358(a,1,1)),flip(a)]. 2068 (K(x,y) * z) * K(y,x) = T(z,K(y,x)). [para(2065(a,1),1549(a,1,1))]. 2069 K(K(x,y) * z,K(y,x)) = T(z,K(y,x)) / z. [para(2068(a,1),979(a,1,1)),flip(a)]. 2070 K(K(x,y) * z,K(y,x)) = K(z,K(y,x)). [para(2069(a,2),1086(a,2)),flip(a)]. 2071 K(K(x,y) * z,K(x,y)) = K(z,K(x,y)). [para(901(a,1),2070(a,1,1)),flip(a)]. 2072 a(a(K(x,y),z,z),u,w) = a(K(z,K(x,y)),u,w). [para(2071(a,1),1826(a,1,1)),flip(a)]. 2073 a(R(T(x,y),y,x),z,z) = a(T(x,y),z,z). [para(1306(a,1),2045(a,1,1))]. 2074 a(R(x,y,y),z,z) = a(T(x,y),z,z). [para(2073(a,1),1772(a,1)),flip(a)]. 2076 x * (K(y,z) * R(K(z,y),u,x)) = L(x,u,K(z,y)). [para(1671(a,1),1971(a,1,2))]. 2077 x * (K(y,z) * K(z,R(y,u,x))) = L(x,y * u,K(y,z)). [para(1668(a,1),1971(a,1,2))]. 2078 x * (L(x,y,z) \ (y * z)) = y * R(z,y,x). [para(82(a,1),1999(a,1,2,2))]. 2079 L(x,y,z) = (x * (y * z)) / (y * R(z,y,x)). [para(2078(a,1),648(a,1,2)),flip(a)]. 2080 T(K(x,y) * R(y,z,u),x) = y * T(y \ R(y,z,u),x). [para(2057(a,2),1834(a,1))]. 2081 T(K(x,y) * R(y,z,u),x) / R(y,z,u) = K(R(y,z,u) / y,x). [para(2080(a,2),1211(a,1,1))]. 2082 a(x,K(x,y) * z,x) = K(x,z) * K(x * z,x). [para(2023(a,1),2026(a,1,2)),flip(a)]. 2083 a(x,K(x,y) * z,x) = a(x,z,x). [para(2082(a,2),1537(a,1))]. 2085 a(x,K(x,y) * z,x) = a(T(x,y),z,x). [para(2047(a,1),28(a,2)),flip(a)]. 2086 a(T(x,y),z,x) = a(x,z,x). [para(2085(a,1),2083(a,1))]. 2087 a((x \ y) \ y,z,x) = a(x,z,x). [para(83(a,1),2086(a,1,1))]. 2089 a((x \ y) * y,z,x) = a(x,z,x). [para(2087(a,1),1702(a,1)),flip(a)]. 2090 a((x * y) * y,z,x) = a(x,z,x). [para(2089(a,1),1707(a,1)),flip(a)]. 2091 a(R(x,y,y),z,x) = a(x,z,x). [para(2090(a,1),1721(a,1)),flip(a)]. 2092 a(a(x,y,x),z,z) = a(x,y,x) \ a(x,y,x). [para(2091(a,1),2054(a,1,2)),flip(a)]. 2093 a(a(x,y,x),z,z) = 1. [para(2092(a,2),60(a,1))]. 2095 L(x,x,a(y,z,y)) = x. [hyper(37,a,2093,a)]. 2097 L(x,x,a(y,z,z)) = x. [para(2095(a,1),1695(a,2))]. 2098 L(x,x,K(y,z)) = x. [para(2097(a,1),1263(a,1)),flip(a)]. 2099 R(T(a(x,y,y),z),z,z) = z \ (a(x,y,y) * z). [para(2097(a,1),1804(a,1,1)),flip(a)]. 2100 a(K(x,y),z,z) = 1. [hyper(38,a,2098,a)]. 2101 K(x,y) * (z \ 1) = K(x,y) / z. [para(2098(a,1),915(a,1,2)),flip(a)]. 2102 (K(x,y) * (z / u)) \ K(x,y) = u / z. [para(2098(a,1),925(a,1)),flip(a)]. 2103 L(x,K(y,z),x) = x. [para(2098(a,1),1895(a,2))]. 2104 R(K(x,y),z,z) = K(x,y) * 1. [para(2100(a,1),963(a,1,2)),flip(a)]. 2105 a(K(x,K(y,z)),u,w) = a(1,u,w). [para(2100(a,1),2072(a,1,1)),flip(a)]. 2106 T(K(x,y),z) / z = z \ K(x,y). [para(2103(a,1),441(a,1,2))]. 2107 K(x,R(y,z,z)) = K(x,y). [hyper(24,a,1767,a,b,2104,a(flip)),flip(a)]. 2108 K(x,y / (z \ 1)) = K(x,y * z). [para(720(a,1),2107(a,1,2)),flip(a)]. 2112 K(x,y) * (x / z) = T(x,y) / z. [para(2107(a,1),1815(a,1,1))]. 2114 K(x,y) / (z \ 1) = K(x,y) * z. [para(156(a,1),2101(a,1,2)),flip(a)]. 2115 a(K(x,K(y,z)),u,w) = 1. [para(2105(a,2),125(a,1))]. 2117 L(x,y,K(z,K(u,w))) = x. [hyper(37,a,2115,a)]. 2119 x * (x \ R(K(y,K(z,u)),w,x)) = K(y,K(z,u)). [para(2117(a,1),1974(a,1,1))]. 2121 (K(x,y) * z) \ u = (z \ K(y,x)) * u. [para(2106(a,1),2067(a,1,1)),flip(a)]. 2122 K(x,R(((y \ 1) * z) \ 1,z,z)) = K(x,(z \ 1) * y). [para(1739(a,2),2108(a,1,2))]. 2123 T(x,y) / (z \ x) = K(x,y) * z. [para(65(a,1),2112(a,1,2)),flip(a)]. 2125 (K(x,y) * z) \ K(x,y) = z \ 1. [para(2114(a,1),66(a,1,1))]. 2126 (K(x,y) * z) \ T(x,y) = z \ x. [para(2123(a,1),66(a,1,1))]. 2127 (K(x,y) \ z) \ 1 = z \ K(x,y). [para(20(a,1),2125(a,1,1)),flip(a)]. 2128 (K(x,y) * z) \ y = z \ T(y,x). [para(901(a,1),2126(a,1,1)),flip(a)]. 2129 L(x \ y,x,K(z,y)) = x \ y. [para(2126(a,1),1248(a,2))]. 2130 a(K(x,y),z,z \ y) = 1. [hyper(38,a,2129,a)]. 2132 a(K(x,y * z),y,z) = 1. [para(19(a,1),2130(a,1,3))]. 2133 (K(x,y) \ z) \ u = (z \ K(x,y)) * u. [para(2127(a,1),318(a,1,1)),flip(a)]. 2136 (x \ K(y,z)) * y = x \ T(y,z). [para(2121(a,1),2128(a,1))]. 2137 ((x / y) \ K(z,u)) * K(u,z) = y / x. [para(2121(a,1),2102(a,1))]. 2139 (x \ T(y,z)) \ ((x \ K(y,z)) * (y * u)) = L(u,y,x \ K(y,z)). [para(2136(a,1),32(a,2,1)),flip(a)]. 2140 x / K(y,z) = x * K(z,y). [para(66(a,1),2137(a,1,1)),flip(a)]. 2141 (x * K(y,z)) \ x = K(z,y). [para(2140(a,1),66(a,1,1))]. 2144 (K(x,y) * z) / K(x,y) = T(z,K(y,x)). [para(2140(a,2),2068(a,1))]. 2145 T(x,K(y,z)) \ x = K(x,K(z,y)). [para(2144(a,1),1053(a,2,1)),flip(a)]. 2146 K(K(x,y),z) = K(z,K(y,x)). [para(2145(a,1),1080(a,2))]. 2147 K(x,K(y,z)) * K(x,K(z,y)) = 1. [para(2146(a,1),898(a,1,1))]. 2148 K(x,y) * K(z,K(y,x)) = T(K(x,y),z). [para(2146(a,1),1107(a,2,2)),flip(a)]. 2149 K(x,y) * T(K(y,x),z) = K(z,K(x,y)). [para(2146(a,1),1114(a,2))]. 2150 T(K(x,y),z) \ 1 = T(K(y,x),z). [para(2148(a,1),1140(a,1)),flip(a)]. 2151 T(K(x,y),z) * T(K(y,x),z) = 1. [para(2150(a,1),20(a,1,2))]. 2152 T(K(x,y),z) * K(y,x) = K(z,K(y,x)). [para(2149(a,1),405(a,2))]. 2153 R(T(a(x,y,y),z),z,z) = T(a(x,y,y),z). [para(2099(a,2),36(a,2)),flip(a)]. 2154 R(T(a(x,y,y),z),z,z) = a(T(x,z),y,y). [para(2153(a,2),1836(a,2)),flip(a)]. 2155 R(a(T(x,y),z,z),y,y) = a(T(x,y),z,z). [para(1836(a,2),2154(a,1,1))]. 2156 a(R(T(x,y),y,y),z,z) = a(T(x,y),z,z). [para(2155(a,1),1930(a,2))]. 2157 a(T(T(x,y),y),z,z) = a(T(x,y),z,z). [para(2156(a,1),2074(a,1)),flip(a)]. 2158 a(T(x,y),z,z) = a(x,z,z). [para(2157(a,1),1724(a,1))]. 2161 (x * (y * (a(y,z,z) * u))) / (R(T(y,x),z,z) * u) = T(x,y). [para(2158(a,1),1210(a,1,1,2,2,1))]. 2165 R(K(x,K(y,z)),u,w) = K(x,K(y,z)). [para(2119(a,1),20(a,1)),flip(a)]. 2166 K(x,R(K(y,z),u,w)) = K(x,K(y,z)). [para(2165(a,1),1654(a,1)),flip(a)]. 2167 K(x,K(y,R(z,u,w))) = K(x,K(y,z)). [para(1654(a,1),2166(a,1,2))]. 2168 K(K(R(x,y,z),u),w) = K(w,K(u,x)). [para(2167(a,1),2146(a,2))]. 2169 K(R(K(x,y),z,u),w) = K(w,K(y,x)). [para(1634(a,1),2168(a,1,1))]. 2170 K(x,R((y \ z) \ 1,z,z)) = K(x,(z \ 1) * y). [para(318(a,1),2122(a,1,2,1,1))]. 2171 K(x,(y \ z) \ 1) = K(x,(z \ 1) * y). [para(2170(a,1),2107(a,1)),flip(a)]. 2172 K(x,(y \ z) \ 1) = K(x,z \ y). [para(318(a,1),2171(a,2,2))]. 2174 K(x,(y / z) \ y) = K(x,z / (a(y,z,z) \ 1)). [para(2172(a,1),1447(a,1))]. 2175 K(x,y / (a(z,y,y) \ 1)) = K(x,y). [para(66(a,1),2174(a,1,2)),flip(a)]. 2176 K(x,y * a(z,y,y)) = K(x,y). [para(1445(a,1),2175(a,1,2))]. 2177 K(x * a(y,x,x),z) = (z \ 1) / (z \ K(z,x)). [para(2176(a,1),1057(a,1,2,2)),flip(a)]. 2178 K(x * a(y,x,x),z) = K(x,z). [para(2177(a,2),1057(a,1))]. 2179 (x / y) * T(y,z) = x * K(y,z). [para(2178(a,1),1463(a,1,2)),flip(a)]. 2180 (x * y) * K(y,z) = x * T(y,z). [para(21(a,1),2179(a,1,1)),flip(a)]. 2183 L(K(x,y),x,z) = K(x,y). [hyper(23,a,1117,a,b,2180,a),flip(a)]. 2184 (x * y) \ (x * T(y,z)) = K(y,z). [hyper(23,a,20,a,b,2180,a),flip(a)]. 2185 (x * (y * z)) \ (x * (y * T(z,u))) = L(K(z,u),y * z,x). [para(2180(a,1),32(a,2,2,2)),flip(a)]. 2186 (x * T(y,z)) \ (x * y) = K(z,y). [para(2180(a,1),2141(a,1,1))]. 2187 L(K(T(x,y),z),x,y) = K(T(x,y),z). [para(2183(a,1),1376(a,1)),flip(a)]. 2189 (x * (y * z)) \ ((x * y) * T(L(z,y,x),u)) = K(L(z,y,x),u). [para(74(a,1),2184(a,1,1))]. 2192 T(K(x,y),x * z) = K(T(x,z),y). [para(2187(a,1),1522(a,1)),flip(a)]. 2193 K(T(x,x \ y),z) = T(K(x,z),y). [para(20(a,1),2192(a,1,2)),flip(a)]. 2194 K(T(x,y),z) = T(K(x,z),y). [para(2193(a,1),2038(a,1)),flip(a)]. 2195 K(x,T(y,z)) * T(K(y,x),z) = 1. [para(2194(a,1),898(a,1,2))]. 2196 K(T(x,y * T(T(y,x),x)),z) = T(T(K(x,z),y),T(y,x)). [para(2194(a,2),1905(a,1))]. 2197 K(x,T(y,z)) = T(K(x,y),z). [hyper(24,a,2151,a,b,2195,a)]. 2199 K(x,y) * K(y,T(x,z)) = K(K(y,x),z). [para(2197(a,2),1114(a,1,2))]. 2200 K(x,T(y,z \ 1)) * z = z * K(x,y). [para(2197(a,2),1907(a,1,1))]. 2202 K(x,y) * K(y,T(x,z)) = K(z,K(x,y)). [para(2197(a,2),2149(a,1,2))]. 2203 K(x,T(y,z)) * K(y,x) = K(z,K(y,x)). [para(2197(a,2),2152(a,1,1))]. 2204 K(T(x,y),z) = K(x,T(z,y)). [para(2197(a,2),2194(a,2))]. 2205 K(x,T(y,z)) * K(y,x) = K(K(x,y),z). [para(2199(a,1),1226(a,2))]. 2206 K(x,T(y,z)) * K(y,x) = K(x,K(y,z)). [para(2202(a,1),1873(a,2))]. 2207 K(x,y) * K(x,K(y,z)) = K(x,T(y,z)). [para(2206(a,1),1225(a,1,2))]. 2208 K(x,K(y,z)) = K(z,K(y,x)). [para(2206(a,1),2203(a,1))]. 2209 K(K(x,y),z) = K(x,K(y,z)). [para(2206(a,1),2205(a,1)),flip(a)]. 2210 1 / K(x,K(y,z)) = K(K(y,x),z). [para(2208(a,1),899(a,1,2))]. 2211 K(K(x,y),z) = K(K(x,z),y). [para(2210(a,1),899(a,1))]. 2212 K(K(x,y),z) = K(y,K(z,x)). [para(2211(a,1),2146(a,1))]. 2213 K(x,K(y,z)) = K(z,K(x,y)). [para(2212(a,1),2209(a,1))]. 2214 T(K(x,y) * K(x,K(y,z)),z) = K(x,y). [para(2213(a,2),1020(a,1,1,2))]. 2215 T(K(x,T(y,z)),z) = K(x,y). [para(2207(a,1),2214(a,1,1))]. 2216 K(x,T(y,z)) * z = z * K(x,y). [para(2215(a,1),82(a,1,2)),flip(a)]. 2217 K(x,T(T(y,z),z)) = K(x,y). [para(2215(a,1),2197(a,2))]. 2219 K(x,T(y,z \ 1)) = K(x,T(y,z)). [hyper(24,a,2200,a,b,2216,a),flip(a)]. 2220 T(K(x,y) * z,K(x,y)) = K(x,T(y,z)) * z. [para(2216(a,2),2064(a,2))]. 2221 K(x,T(y,z \ (z \ (u \ 1)))) = K(x,T(y,u * (z * z))). [para(409(a,1),2219(a,1,2,2))]. 2222 K(T(x,y * T(y,x)),z) = T(T(K(x,z),y),T(y,x)). [para(2019(a,1),2196(a,1,1))]. 2223 T(T(K(x,y),z),T(z,x)) = K(T(x,z * z),y). [para(2019(a,1),2222(a,1,1)),flip(a)]. 2224 T(T(K(x,y),z),T(z,x)) = K(x,T(y,z * z)). [para(2223(a,2),1278(a,1))]. 2225 T(K(x,T(y,z)),T(z,x)) = K(x,T(y,z * z)). [para(2197(a,2),2224(a,1,1))]. 2226 K(T(x,T(y,x)),T(z,y)) = K(x,T(z,y * y)). [para(2225(a,1),2194(a,2))]. 2227 K(T(x,y),T(z,y)) = K(x,T(z,y * y)). [para(1131(a,1),2226(a,1,1))]. 2228 K(x,T(T(y,z),z)) = K(x,T(y,z * z)). [para(2227(a,1),2204(a,1)),flip(a)]. 2229 K(x,T(y,z * z)) = K(x,y). [para(2228(a,1),2217(a,1))]. 2230 K(x,T(y,z * (z * u))) = K(x,T(y,u)). [para(662(a,1),2229(a,1,2))]. 2232 K(x,T(y,z \ u)) = K(x,T(y,z * u)). [para(20(a,1),2230(a,1,2,2,2)),flip(a)]. 2233 K(x,T(y,T(z,z * u))) = K(x,T(y,(z \ u) * u)). [para(250(a,1),2230(a,1,2,2,2)),flip(a)]. 2234 K(x,T(y,(z / u) * (z * z))) = K(x,T(y,u / (z \ 1))). [para(399(a,1),2230(a,1,2,2,2))]. 2235 K(x,T(y,z \ (z \ u))) = K(x,T(y,u)). [para(20(a,1),2232(a,2,2,2))]. 2236 K(x,T(y,z * (u * u))) = K(x,T(y,z \ 1)). [para(2221(a,1),2235(a,1))]. 2237 K(x,T(y,z * (u * u))) = K(x,T(y,z)). [para(2236(a,2),2219(a,1))]. 2239 K(x,T(y,z / (u \ 1))) = K(x,T(y,u / z)). [para(2234(a,1),2237(a,1))]. 2241 (x * (R(y,z,z) * u)) / (R(T(y,x),z,z) * u) = T(x,y). [para(966(a,1),2161(a,1,1,2))]. 2243 T(x,R(y,z,z)) = T(x,y). [para(2241(a,1),1209(a,1)),flip(a)]. 2244 T(x,y / (z \ 1)) = T(x,y * z). [para(720(a,1),2243(a,1,2)),flip(a)]. 2246 K(x,T(y,z / u)) = K(x,T(y,u * z)). [para(2244(a,1),2239(a,1,2)),flip(a)]. 2247 K(x,T(y,(z \ u) * u)) = K(x,T(y,z)). [para(65(a,1),2246(a,1,2,2)),flip(a)]. 2248 K(x,T(y,T(z,z * u))) = K(x,T(y,z)). [para(2247(a,1),2233(a,2))]. 2249 K(x,T(y,T(z,u))) = K(x,T(y,z)). [para(20(a,1),2248(a,1,2,2,2))]. 2251 K(x,K(y,T(z,u))) = K(x,T(y,z)) * K(y,x). [para(2249(a,1),2206(a,1,1)),flip(a)]. 2253 K(x,K(y,T(z,u))) = K(x,K(y,z)). [para(2251(a,2),2206(a,1))]. 2254 K(x,K(y,z \ R(z,u,w))) = K(x,K(y,a(z,u,w))). [para(739(a,2),2253(a,1,2,2)),flip(a)]. 2255 K(x,K(y \ R(y,z,u),w)) = K(x,K(w,a(y,z,u))). [para(1849(a,2),2254(a,1,2))]. 2256 (x * (y * z)) \ ((x * y) * L(T(z,u),y,x)) = K(L(z,y,x),u). [para(44(a,2),2189(a,1,2,2))]. 2257 (x * (y * z)) \ (x * (y * T(z,u))) = K(L(z,y,x),u). [para(74(a,1),2256(a,1,2))]. 2258 L(K(x,y),z * x,u) = K(L(x,z,u),y). [para(2257(a,1),2185(a,1)),flip(a)]. 2259 K(L(x,y / x,z),u) = L(K(x,u),y,z). [para(22(a,1),2258(a,1,2)),flip(a)]. 2260 K(x,y) * K(R(y,z,u),x) = K(R(y,z,u) / y,x). [para(2081(a,1),2059(a,1)),flip(a)]. 2261 K(x,y) * K(R(y,z,u),x) = K(y \ R(y,z,u),x). [para(478(a,1),2260(a,2,1))]. 2262 K(x,y) * K(R(y,z,u),x) = K(x,y \ R(y,z,u)). [para(2261(a,2),1849(a,1))]. 2263 K(x,K(y,z) \ R(K(y,z),u,w)) = K(x,K(y,z)) * K(x,K(z,y)). [para(2169(a,1),2262(a,1,2)),flip(a)]. 2264 (x * T(y,z)) \ ((x * K(y,z)) * (y * u)) = L(u,y,x \ K(y,z)). [para(2139(a,1),284(a,1)),flip(a)]. 2265 K(x,K(y,z) \ R(K(y,z),u,w)) = 1. [para(2263(a,2),2147(a,1))]. 2266 K(x,K(y,z) \ K(R(y,u,w),z)) = 1. [para(1629(a,1),2265(a,1,2,2))]. 2268 K(x,K(y,z) * K(R(z,u,w),y)) = 1. [para(900(a,1),2266(a,1,2))]. 2269 K(x,K(y \ R(y,z,u),w)) = 1. [para(2261(a,1),2268(a,1,2))]. 2270 K(x,K(y,a(z,u,w))) = 1. [para(2269(a,1),2255(a,1)),flip(a)]. 2271 T(x,K(y,a(z,u,w))) = x. [hyper(41,a,2270,a)]. 2273 K(x,T(a(y,z,u),w)) = K(x,a(y,z,u)). [hyper(24,a,2220,a(flip),b,2271,a(flip)),flip(a)]. 2274 K(x,y \ R(y,z,u)) = K(x,a(y,z,u)). [para(1839(a,1),2273(a,1,2))]. 2275 K(x,y \ R(y,z,u)) = K(a(y,z,u),x). [para(2274(a,2),1847(a,2)),flip(a)]. 2276 K(x \ R(x,y,z),u) = K(u,a(x,y,z)). [para(2274(a,1),1849(a,2))]. 2277 K(x,a(y,z,L(u,z,y))) = K(x,y \ R(y,z,u)). [para(1990(a,1),2274(a,1,2,2)),flip(a)]. 2278 K(x,y) * K(R(y,z,u),x) = K(x,a(y,z,u)). [para(2274(a,1),2262(a,2))]. 2279 K(x,a(K(y,z),u,w)) = 1. [para(2274(a,1),2265(a,1))]. 2280 T(x,a(K(y,z),u,w)) = x. [hyper(41,a,2279,a)]. 2281 ((K(x,y) * z) * u) / (K(x,y) * (z * u)) = a(K(x,y),z,u). [para(2280(a,1),300(a,1,2))]. 2282 K(R(x,y,z) \ x,u) = K(u,a(x,x * y,z)). [para(618(a,1),2276(a,1,1))]. 2283 K(x,y) * K(y,R(x,z,u)) = K(y,a(x,z,u)). [para(2278(a,1),1674(a,1)),flip(a)]. 2284 L(x,y * z,K(y,u)) = x * K(u,a(y,z,x)). [para(2283(a,1),2077(a,1,2)),flip(a)]. 2285 K(x,a(y,z,L(u,z,y))) = K(x,a(y,z,u)). [para(2277(a,2),2274(a,1))]. 2286 K(x,y) \ R(K(x,y),z,u) = a(K(x,y),z,u). [para(2281(a,1),537(a,1)),flip(a)]. 2287 x \ L(x,y,K(z,u)) = a(K(z,u),y,x). [para(2286(a,1),1988(a,1)),flip(a)]. 2288 x * a(K(y,z),u,x) = L(x,u,K(y,z)). [para(2287(a,1),20(a,1,2))]. 2289 a(K(x,y),x * z,u) = K(y,a(x,z,u)). [hyper(23,a,2284,a(flip),b,2288,a)]. 2290 x * a(K(y,z),u,x) = L(x,u,K(z,y)). [para(905(a,1),2288(a,1,2))]. 2291 K(x,a(y,y * z,u)) = a(K(y,x),z,u). [para(2289(a,1),1778(a,1))]. 2292 K((x * y) * z,a(x,y,z)) = 1. [para(2289(a,1),2132(a,1))]. 2293 K(x * (y * z),a(x,y,L(z,y,x))) = 1. [para(74(a,1),2292(a,1,1))]. 2294 K(x,a(y,y * z,u)) = a(K(x,y),z,u). [para(2291(a,2),905(a,1))]. 2295 K(x * (y * z),a(x,y,z)) = 1. [para(2293(a,1),2285(a,1)),flip(a)]. 2296 x \ R(x,y,z) = a(x,y,z) * 1. [para(2295(a,1),1848(a,1,2)),flip(a)]. 2297 a(x,y,z) = x \ R(x,y,z). [hyper(24,a,18,a,b,2296,a(flip))]. 2298 a(x,y,z) = L(z,y,x) \ z. [hyper(24,a,1989,a(flip),b,2296,a(flip))]. 2302 R(x,y,z) \ x = a(x,y,z) \ 1. [para(2297(a,2),462(a,1,1)),flip(a)]. 2306 x * (a(x,y,z) * u) = R(x,y,z) * u. [para(2297(a,2),501(a,1,2,1))]. 2308 a(x,y,z) * (x * u) = R(x,y,z) * u. [para(2297(a,2),528(a,1,1))]. 2310 a(x,x * y,z) = R(x,y,z) \ x. [para(2297(a,2),618(a,1))]. 2311 a(x,y,z) = R(x,x * y,z) \ x. [para(2297(a,2),622(a,2)),flip(a)]. 2313 a(x,y,z) = x * R(x \ 1,y,z). [para(2297(a,2),635(a,2)),flip(a)]. 2316 x \ (R(y,z,u) * (y \ x)) = a(T(y,x),z,u). [para(2297(a,2),1830(a,1)),flip(a)]. 2317 T(x \ R(x,y,z),u) = a(T(x,u),y,z). [para(2297(a,2),1831(a,1)),flip(a)]. 2318 R(x \ R(x,y,z),u,w) = a(R(x,u,w),y,z). [para(2297(a,2),1927(a,1)),flip(a)]. 2319 L(x \ R(x,y,z),u,w) = a(L(x,u,w),y,z). [para(2297(a,2),1939(a,1)),flip(a)]. 2320 a(x,y,z) = z \ L(z,x * y,x). [para(2297(a,2),1953(a,2)),flip(a)]. 2322 a(x,x * y,z) = z \ L(z,y,x). [para(2297(a,2),1956(a,1))]. 2323 x * (L(x,y,z) \ u) = a(z,y,x) * u. [para(2297(a,2),1985(a,1,1)),flip(a)]. 2328 a(x,y,z) \ 1 = z \ L(z,y,x). [para(2298(a,2),511(a,1,1))]. 2332 L(x,y,z) \ (x * u) = a(z,y,x) * u. [para(2298(a,2),524(a,2,1))]. 2333 a(x,y,z) * (L(z,y,x) * u) = z * u. [para(2298(a,2),646(a,1,1))]. 2336 a(T(x,y),z,y) = L(y,z,x) \ y. [para(1992(a,1),2298(a,2,1))]. 2340 K(a(x,y,z) \ 1,u) = K(u,a(x,x * y,z)). [para(2302(a,1),2282(a,1,1))]. 2341 a(x,x * y,z) = a(x,y,z) \ 1. [para(2310(a,2),2302(a,1))]. 2343 a(x,x * y,z) \ 1 = a(x,y,z). [para(2311(a,2),2302(a,1)),flip(a)]. 2344 L(x,a(y,z,u),z) = x. [para(2313(a,2),1443(a,1,2))]. 2347 (x * a(y,x,z)) * u = x * (a(y,x,z) * u). [para(2344(a,1),74(a,1,2))]. 2348 (x \ a(y,x,z)) \ 1 = a(y,x,z) \ x. [para(2344(a,1),259(a,1)),flip(a)]. 2349 (x \ a(y,x,z)) \ u = a(y,x,z) \ (x * u). [para(2344(a,1),267(a,1)),flip(a)]. 2350 (x * y) \ (x * L(y,z * u,z)) = L(a(z,u,y),y,x). [para(2320(a,2),76(a,1,1)),flip(a)]. 2356 (x * L(y,z,u)) / L(a(u,u * z,y),y,x) = x * y. [para(2322(a,2),179(a,1,2,1))]. 2357 ((x * y) \ x) * L(L(y,x,x * y),z,u) = a(u,z,L(y,x,x * y)) \ 1. [para(2328(a,2),738(a,1)),flip(a)]. 2358 a(T(x,y),z,y) = a(x,z,y). [para(2336(a,2),2298(a,2)),flip(a)]. 2360 a(x,x * y,z) \ u = a(x,y,z) * u. [para(2341(a,2),330(a,1,1))]. 2366 K(a(x,x * y,z),u) = a(K(u,x),y,z). [para(2294(a,1),1847(a,2))]. 2368 x * (y * a(x,z,y)) = R(x,z,y) * y. [para(1964(a,1),2306(a,1,2))]. 2370 a(T(x,y),z,u) = T(a(x,z,u),y). [para(2297(a,2),2317(a,1,1)),flip(a)]. 2371 a(T(x,y),z,u) \ a(x,z,u) = K(y,a(x,z,u)). [para(2370(a,2),1080(a,2,1)),flip(a)]. 2372 a(T(x,y),y,z) = a(x,y,z). [para(2370(a,2),1687(a,1))]. 2373 a(x,T(y,x),z) = a(x,y,z). [para(2372(a,1),1790(a,1)),flip(a)]. 2374 a(x / y,y,z) = a(y * x,y,z). [para(2373(a,1),1810(a,1)),flip(a)]. 2375 a(x / y,x,z) = a(x * y,x,z). [para(2374(a,1),612(a,1)),flip(a)]. 2376 a(x,y,z) * (u * L(z,y,x)) = z * T(u,L(z,y,x)). [para(36(a,2),2323(a,1,2)),flip(a)]. 2378 a(x,y,z) * (z * u) = z * (a(x,y,z) * u). [para(2332(a,1),2323(a,1,2)),flip(a)]. 2380 a(x,y,z) * (z * x) = z * R(x,y,z). [para(1973(a,1),2333(a,1,2))]. 2386 (x \ a(y,x,z)) \ u = (a(y,x,z) \ x) * u. [para(2348(a,1),318(a,1,1)),flip(a)]. 2388 K(a(x,y,z) \ 1,u) = a(K(u,x),y,z). [para(2341(a,1),2366(a,1,1))]. 2389 (x * y) * L(a(x,z,y),y,x) = R(x,z,y) * y. [para(2368(a,1),74(a,2))]. 2390 x \ ((y \ x) * T(y,x)) = a(T(y,x),x,y). [para(1317(a,1),2316(a,1,2))]. 2391 x \ ((y \ x) * T(y,x)) = a(y,x,y). [para(2390(a,2),2086(a,1))]. 2393 a(R(x,y,z),u,y) = L(y,u,x) \ y. [para(2318(a,1),1986(a,1))]. 2394 a(R(x,y,z),u,w) = R(a(x,u,w),y,z). [para(2297(a,2),2318(a,1,1)),flip(a)]. 2396 a(R(x,y,z),u,y) = a(x,u,y). [para(2393(a,2),2298(a,2)),flip(a)]. 2400 a(L(x,y,x),z,y) = a(x,z,y). [para(1312(a,1),2396(a,1,1)),flip(a)]. 2404 R(a(x,y,z),x * u,w) = a(R(x,u,w),y,z). [para(2394(a,1),1718(a,1))]. 2406 a(L(x,y,z),u,w) = L(a(x,u,w),y,z). [para(2297(a,2),2319(a,1,1)),flip(a)]. 2410 K(x,a(y / z,(y / z) * z,u)) = K(a(z * y,z,u) \ 1,x). [para(2374(a,1),2340(a,1,1,1)),flip(a)]. 2411 (a(x,y,z) * y) * u = y * (a(x,y,z) * u). [para(1688(a,2),2347(a,1,1))]. 2412 a(x,y,z) \ (y * u) = (a(x,y,z) \ y) * u. [para(2386(a,1),2349(a,1)),flip(a)]. 2413 L(x,y,a(z,y,u)) = x. [hyper(23,a,798,a,b,2412,a(flip)),flip(a)]. 2414 (a(x,y,z) * y) * u = a(x,y,z) * (y * u). [para(2413(a,1),74(a,1,2))]. 2415 (a(x,y,z) * (y \ 1)) * u = a(x,y,z) * (y \ u). [para(2413(a,1),945(a,1,2))]. 2417 a(x,y,z) * (y * u) = y * (a(x,y,z) * u). [para(2414(a,1),2411(a,1))]. 2419 (x * y) \ (x * (a(z,x,u) * y)) = T(a(z,x,u),x * y). [para(2417(a,1),36(a,2,2)),flip(a)]. 2421 (x * y) * a(L(x,y,x),z,y) = R(x,z,y) * y. [para(2406(a,2),2389(a,1,2))]. 2422 (x * y) * a(x,z,y) = R(x,z,y) * y. [para(2400(a,1),2421(a,1,2))]. 2423 (x * (R(y,z,u) * u)) / ((y * u) * R(a(y,z,u),y * u,x)) = L(x,y * u,a(y,z,u)). [para(2422(a,1),2079(a,2,1,2)),flip(a)]. 2424 (x \ a(y,x,z)) * u = a(y,x,z) * (x \ u). [para(1795(a,1),2415(a,1,1))]. 2425 (a(x,y,z) * (y \ u)) \ ((y \ a(x,y,z)) * (u * w)) = L(w,u,y \ a(x,y,z)). [para(2424(a,1),32(a,2,1)),flip(a)]. 2426 L(T(a(x,y,z),u),u,y) = T(a(x,y,z),y * u). [para(2419(a,1),106(a,1)),flip(a)]. 2427 L(a(T(x,y),z,u),y,z) = T(a(x,z,u),z * y). [para(2370(a,2),2426(a,1,1))]. 2429 K(a(x * y,x,z) \ 1,u) = K(u,a(y / x,y,z)). [para(22(a,1),2410(a,1,2,2)),flip(a)]. 2430 K(a(x * y,x,z) \ 1,u) = K(u,a(y * x,y,z)). [para(2375(a,1),2429(a,2,2))]. 2431 K(x,a(y * z,y,u)) = a(K(x,z * y),z,u). [para(2430(a,1),2388(a,1))]. 2432 a(L(x,y,z),R(z,y,x),u) = (x * (z * u)) \ ((x * z) * u). [para(1998(a,1),1981(a,1,1)),flip(a)]. 2433 a(L(x,y,z),R(z,y,x),u) = a(x,z,u). [para(2432(a,2),28(a,2)),flip(a)]. 2435 L(a(x,R(y,z,x),u),z,y) = a(x,y,u). [para(2433(a,1),2406(a,1)),flip(a)]. 2436 (a(x,y,z) * (y \ u)) \ (a(x,y,z) * (y \ (u * w))) = L(w,u,y \ a(x,y,z)). [para(2424(a,1),2425(a,1,2))]. 2437 L(L(x,y,z),z * y,a(u,z,w)) = L(x,y,z \ a(u,z,w)). [para(2436(a,1),1409(a,1)),flip(a)]. 2438 L(L(x,y,z),z * y,a(u,z,w)) = L(x,y,z * a(u,z,w)). [para(2437(a,2),776(a,1))]. 2439 (R(x,y,z) * y) \ ((x * y) * u) = (x \ R(x,y,z)) \ u. [para(1996(a,1),1411(a,1))]. 2440 L(x,y,R(z,y,x)) = (z \ R(z,y,x)) \ x. [para(2439(a,1),183(a,1)),flip(a)]. 2441 L(x,y,R(z,y,x)) = L(x,y,z). [para(2440(a,2),1976(a,2)),flip(a)]. 2442 L(x,y * z,R(y,z,x) \ 1) = L(x,y * z,y \ 1). [para(584(a,1),2441(a,1,3))]. 2443 L(x,y * z,R(y,z,x)) = L(x,y * z,y \ 1). [para(2442(a,1),787(a,1)),flip(a)]. 2444 L(x,y * z,R(y,z,x)) = L(x,y * z,y). [para(2443(a,2),787(a,1))]. 2445 R(x,y,z) * (L(z,x * y,x) \ z) = R(R(x,y,z),x * y,z). [para(2444(a,1),1979(a,2,2,1)),flip(a)]. 2446 R(x,y,z) * (R(x,y,z) \ x) = R(R(x,y,z),x * y,z). [para(1954(a,1),2445(a,1,2))]. 2447 R(R(x,y,z),x * y,z) = x. [para(2446(a,1),20(a,1))]. 2448 R(R(x,x * y,z),y,z) = x. [para(2447(a,1),50(a,1)),flip(a)]. 2449 K(x,R(y,y * z,u) \ R(R(y,y * z,u),z,u)) = K(x,R(y,y * z,u)) * K(y,x). [para(2448(a,1),2262(a,1,2,1)),flip(a)]. 2450 K(x,R(y,y * z,u) \ R(R(y,y * z,u),z,u)) = R(K(x,y),z,u) * K(y,x). [para(1672(a,1),2449(a,2,1))]. 2451 K(x,R(y,y * z,u) \ R(R(y,y * z,u),z,u)) = K(y,x) * R(K(x,y),z,u). [para(2450(a,2),406(a,1))]. 2452 K(x,R(y,y * z,u) \ y) = K(y,x) * R(K(x,y),z,u). [para(2448(a,1),2451(a,1,2,2))]. 2453 K(x,y) * R(K(y,x),z,u) = K(y,x \ R(x,z,u)). [para(622(a,1),2452(a,1,2)),flip(a)]. 2454 x * K(y,z \ R(z,u,x)) = L(x,u,K(y,z)). [para(2453(a,1),2076(a,1,2))]. 2455 x * K(a(y,z,x),u) = L(x,z,K(u,y)). [para(2275(a,1),2454(a,1,2))]. 2456 a(K(x,y),z,u) = K(a(x,z,u),y). [hyper(23,a,2290,a,b,2455,a),flip(a)]. 2457 a(K(x,y),z,u) = K(a(y,z,u),x). [hyper(23,a,2288,a,b,2455,a),flip(a)]. 2458 a(K(x,y),z,u) = K(y,a(x,z,u)). [para(2456(a,2),1847(a,1))]. 2459 a(K(x,y),z,u) = K(x,a(y,z,u)). [para(2457(a,2),1847(a,1))]. 2460 x * K(y,a(z,u,x)) = L(x,u,K(z,y)). [para(2458(a,1),2288(a,1,2))]. 2461 K(x * y,a(z,x,u)) = K(z,a(y * x,y,u)). [para(2458(a,1),2431(a,2)),flip(a)]. 2462 K(x,a(y,z,u)) = K(y,a(x,z,u)). [para(2459(a,1),2458(a,1))]. 2463 L(x,y * z,K(y,u)) = L(x,z,K(y,u)). [para(2460(a,1),2284(a,2))]. 2464 (x * (R(y,z,u) * u)) / ((y * u) * a(R(y,u,x),z,u)) = L(x,y * u,a(y,z,u)). [para(2404(a,1),2423(a,1,2,2))]. 2465 (x * (R(y,z,u) * u)) / ((y * u) * a(y,z,u)) = L(x,y * u,a(y,z,u)). [para(2396(a,1),2464(a,1,2,2))]. 2467 (x * (R(y,z,u) * u)) / (R(y,z,u) * u) = L(x,y * u,a(y,z,u)). [para(2422(a,1),2465(a,1,2))]. 2468 L(x,y * z,a(y,u,z)) = x. [para(2467(a,1),21(a,1))]. 2469 L(x,y * z,a(T(z,y),u,y)) = x. [para(2468(a,1),1185(a,1)),flip(a)]. 2470 L(x,y * z,a(z,u,y)) = x. [para(2358(a,1),2469(a,1,3))]. 2471 (a(x,y,z) * (z * x)) \ (a(x,y,z) * (z * (x * u))) = L(u,x,z). [para(2470(a,1),174(a,2))]. 2472 (x * R(y,z,x)) \ (a(y,z,x) * (x * (y * u))) = L(u,y,x). [para(2380(a,1),2471(a,1,1))]. 2473 (x * R(y,z,x)) \ (x * (a(y,z,x) * (y * u))) = L(u,y,x). [para(2378(a,1),2472(a,1,2))]. 2474 (x * R(y,z,x)) \ (x * (R(y,z,x) * u)) = L(u,y,x). [para(2308(a,1),2473(a,1,2,2))]. 2475 L(x,R(y,z,u),u) = L(x,y,u). [para(2474(a,1),32(a,2))]. 2476 a(x,R(y,z,x),u) = L(u,y,x) \ u. [para(2475(a,1),2298(a,2,1))]. 2477 a(x,R(y,z,x),u) = a(x,y,u). [para(2476(a,2),2298(a,2)),flip(a)]. 2478 L(a(x,y,z),u,y) = a(x,y,z). [para(2477(a,1),2435(a,1,1))]. 2480 T(a(x,y,z),y * u) = a(T(x,u),y,z). [para(2478(a,1),2427(a,1)),flip(a)]. 2484 a(T(x,y),z,u) \ a(x,z,u) = K(z * y,a(x,z,u)). [para(2480(a,1),1080(a,2,1)),flip(a)]. 2494 K(x * y,a(z,x,u)) = K(y,a(z,x,u)). [para(2484(a,1),2371(a,1))]. 2495 K(x,a(y * z,y,u)) = K(z,a(x,y,u)). [para(2494(a,1),2462(a,1)),flip(a)]. 2496 K(x,a(y * z,y,u)) = K(y,a(x,z,u)). [para(2494(a,1),2461(a,1)),flip(a)]. 2497 K(x,a(y,z,u)) = K(z,a(y,x,u)). [para(2496(a,1),2495(a,1))]. 2498 x * K(y,a(z,u,x)) = L(x,y,K(z,u)). [para(2497(a,1),2460(a,1,2))]. 2499 L(x,y,K(z,u)) = L(x,u,K(z,y)). [para(2498(a,1),2460(a,1))]. 2501 L(x,y,K(z,z * u)) = L(x,u,K(z,y)). [para(2499(a,1),2463(a,1))]. 2502 L(x,y,a(z,u,u)) = L(x,u,K(z,y)). [para(2501(a,1),1261(a,1)),flip(a)]. 2503 L(x,y,a(z,u,u)) = L(x,y,K(z,u)). [para(2502(a,2),2499(a,1))]. 2504 L(x,y,a(z,u,z)) = L(x,y,K(u,z)). [para(2503(a,1),1695(a,1)),flip(a)]. 2505 L(L(x,y,z),z * y,K(z,u)) = L(x,y,z * a(u,z,u)). [para(2504(a,1),2438(a,1))]. 2506 L(x,y,z * a(u,z,u)) = L(x,y,T(z,u)). [para(2505(a,1),1604(a,1))]. 2507 L(x,y,R(z,u,u)) = L(x,y,T(z,u)). [para(2506(a,1),1692(a,1)),flip(a)]. 2508 L(x,y,T(z / u,z)) = L(x,y,u * z). [para(2507(a,1),846(a,1))]. 2509 L(x,y,z * u) = L(x,y,u * z). [para(2508(a,1),845(a,1))]. 2510 L(L(x,y,z * u),(z * u) * y,u * z) = x. [para(2509(a,1),303(a,1))]. 2515 L(x,y,K(z,u)) = x. [para(2510(a,1),1850(a,1)),flip(a)]. 2516 a(K(x,y),z,u) = 1. [hyper(38,a,2515,a)]. 2518 (K(x,y) * z) * u = K(x,y) * (z * u). [para(2515(a,1),74(a,1,2))]. 2519 (K(x,y) * z) \ (K(x,y) * u) = z \ u. [para(2515(a,1),76(a,1)),flip(a)]. 2520 (K(x,y) \ z) \ u = z \ (K(x,y) * u). [para(2515(a,1),267(a,1)),flip(a)]. 2521 (K(x,y) * z) / u = K(x,y) * (z / u). [para(2515(a,1),196(a,1,2))]. 2526 L(x,y,T(z,u)) = L(x,y,z). [para(2515(a,1),1604(a,1)),flip(a)]. 2534 L(x,y,a(z,u,z)) = x. [para(2515(a,1),2504(a,2))]. 2540 K(a(x,y,z),u) = 1. [para(2516(a,1),2456(a,1)),flip(a)]. 2543 T(a(x,y,z),u) = a(x,y,z). [hyper(41,a,2540,a)]. 2548 (a(x,y,x) * z) * u = (z * u) * a(x,y,x). [para(2534(a,1),2053(a,1,2))]. 2553 L(x,y,z * (u * z)) = L(x,y,u). [para(2526(a,1),778(a,2))]. 2571 x / a(y,z,u) = a(y,z,u) \ x. [para(2543(a,1),252(a,1,2))]. 2578 a(T(x,y),z,u) = a(x,z,u). [para(2543(a,1),2370(a,2))]. 2586 a(x * (y * x),z,u) = a(y,z,u). [para(2578(a,1),1704(a,2))]. 2621 (x * (K(y,z) * (u * w))) \ ((x * (K(y,z) * u)) * w) = a(x,K(y,z) * u,w). [para(2518(a,1),28(a,2,1,2)),flip(a)]. 2622 (K(x,y) * (z * (u * w))) \ (((K(x,y) * z) * u) * w) = a(K(x,y) * z,u,w). [para(2518(a,1),28(a,2,1)),flip(a)]. 2623 (K(x,y) * (z * u)) \ ((K(x,y) * z) * (u * w)) = L(w,u,K(x,y) * z). [para(2518(a,1),32(a,2,1)),flip(a)]. 2624 ((K(x,y) * (z * u)) * w) / (u * w) = R(K(x,y) * z,u,w). [para(2518(a,1),34(a,2,1,1)),flip(a)]. 2632 x \ (K(y,z) * u) = (x \ K(y,z)) * u. [para(2520(a,1),2133(a,1))]. 2646 L(x,K(y,z),u) = x. [hyper(23,a,798,a,b,2632,a(flip)),flip(a)]. 2649 (x * K(y,z)) * u = x * (K(y,z) * u). [para(2646(a,1),74(a,1,2))]. 2650 (x * (K(y,z) * u)) / u = x * K(y,z). [para(2646(a,1),99(a,1,2))]. 2656 L(x,T(y,z) * y,u) = x. [para(2646(a,1),988(a,1)),flip(a)]. 2658 L(x,(y \ z) * (z / y),u) = x. [para(84(a,1),2656(a,1,2,1))]. 2659 L(x,(y * z) * (z / y),u) = x. [para(2658(a,1),880(a,1)),flip(a)]. 2660 L(x,T(L(y / z,z * y,y / z) * (z * y),y / z),u) = x. [para(1309(a,2),2659(a,1,2))]. 2667 (x * T(y,z)) \ (x * (K(y,z) * (y * u))) = L(u,y,x \ K(y,z)). [para(2649(a,1),2264(a,1,2))]. 2670 (x * y) / T(y,z) = x * K(z,y). [para(1077(a,1),2650(a,1,1,2))]. 2671 (x / y) * K(z,y) = x / T(y,z). [para(22(a,1),2670(a,1,1)),flip(a)]. 2672 (x * (y * z)) / T(L(z,y,x),u) = (x * y) * K(u,L(z,y,x)). [para(74(a,1),2670(a,1,1))]. 2673 ((x \ y) * x) / T(y,x) = a(x,y,x). [para(2671(a,1),1538(a,1))]. 2675 a(x,y,x) * T(y,x) = (x \ y) * x. [para(2673(a,1),22(a,1,1))]. 2698 (K(x,y) * ((z * u) * w)) / (u * w) = R(K(x,y) * z,u,w). [para(2518(a,1),2624(a,1,1))]. 2699 K(x,y) * (((z * u) * w) / (u * w)) = R(K(x,y) * z,u,w). [para(2698(a,1),2521(a,1)),flip(a)]. 2700 R(K(x,y) * z,u,w) = K(x,y) * R(z,u,w). [para(34(a,2),2699(a,1,2)),flip(a)]. 2701 R(x * K(y,z),u,w) = R(x,u,w) * K(y,z). [hyper(23,a,699,a(flip),b,2700,a(flip))]. 2704 R(T(x,y),z,u) * K(y,x) = R(x,z,u). [para(1089(a,1),2701(a,1,1)),flip(a)]. 2706 K(x,R(y,z,u)) = K(x,y). [hyper(23,a,1109,a,b,2704,a),flip(a)]. 2708 T(x,R(y,z,u)) = x * K(x,y). [para(2706(a,1),1107(a,2,2))]. 2716 T(x,R(y,z,u)) = T(x,y). [para(2708(a,2),1107(a,2)),flip(a)]. 2731 L(x,T((y / z) * (z * y),y / z),u) = x. [para(892(a,1),2660(a,1,2,1,1))]. 2733 L(x,(y * z) / (z / y),u) = x. [para(2731(a,1),1235(a,1)),flip(a)]. 2734 L(x,(y * z) * (y / z),u) = x. [para(952(a,1),2733(a,1,2))]. 2735 (x * (y * z)) / L(T(z,u),y,x) = (x * y) * K(u,L(z,y,x)). [para(44(a,2),2672(a,1,2))]. 2739 (x * T(y,z)) \ (x * (T(y,z) * u)) = L(u,y,x \ K(y,z)). [para(1160(a,1),2667(a,1,2,2))]. 2740 L(x,y,z \ K(y,u)) = L(x,T(y,u),z). [para(2739(a,1),32(a,2)),flip(a)]. 2741 L(x,y,z * K(y,u)) = L(x,T(y,u),z). [para(2740(a,1),776(a,1)),flip(a)]. 2752 (K(x,y) * (z * u)) \ (K(x,y) * (z * (u * w))) = L(w,u,K(x,y) * z). [para(2518(a,1),2623(a,1,2))]. 2753 L(x,y,K(z,u) * w) = (w * y) \ (w * (y * x)). [para(2752(a,1),2519(a,1))]. 2754 L(x,y,K(z,u) * w) = L(x,y,w). [para(2753(a,2),32(a,2)),flip(a)]. 2755 ((x * K(y,z)) * u) \ ((x * K(y,z)) * (u * w)) = L(w,u,x). [para(2753(a,1),2553(a,1))]. 2760 L(x,y,z * K(u,w)) = L(x,y,z). [para(2200(a,1),2754(a,1,3))]. 2763 L(x,T(y,z),u) = L(x,y,u). [para(2760(a,1),2741(a,1)),flip(a)]. 2765 L(x,(y * z) * z,u) = L(x,y,u). [para(2763(a,1),951(a,1)),flip(a)]. 2766 L(x,y / z,u) = L(x,z * y,u). [para(2763(a,1),1235(a,1)),flip(a)]. 2777 L(x,y / z,u) = L(x,y * z,u). [para(22(a,1),2765(a,1,2,1)),flip(a)]. 2779 (x * y) / L(z,z * y,x) = x * (y / z). [para(2766(a,1),196(a,1,2))]. 2782 L(x,y * z,u) = L(x,z * y,u). [para(2777(a,1),2766(a,1))]. 2787 L(x,(y / z) * (y * z),u) = x. [para(2782(a,1),2734(a,1))]. 2788 L(x,(y \ (y \ z)) * ((y \ z) * T(y,z)),u) = x. [para(256(a,1),2787(a,1,2,1))]. 2793 (x * (y * z)) / L(T(z,u),T(z,u) * (y * z),x) = x * (y * K(u,z)). [para(2670(a,1),2779(a,2,2))]. 2798 L(x,(y * (y \ z)) * ((y \ z) * T(y,z)),u) = x. [para(2788(a,1),880(a,1)),flip(a)]. 2799 L(x,y * ((z \ y) * T(z,y)),u) = x. [para(20(a,1),2798(a,1,2,1))]. 2800 L(x,y \ ((z \ y) * T(z,y)),u) = x. [para(2799(a,1),876(a,2))]. 2801 L(x,a(y,z,y),u) = x. [para(2391(a,1),2800(a,1,2))]. 2802 (x * a(y,z,y)) * u = x * (a(y,z,y) * u). [para(2801(a,1),74(a,1,2))]. 2803 (x * y) / L(y,z,y) = x * a(y,z,y). [para(2801(a,1),1543(a,1,2))]. 2805 (x * (y * (a(z,u,z) * w))) \ (((x * y) * a(z,u,z)) * w) = a(x,y,a(z,u,z) * w). [para(2802(a,2),28(a,2,2)),flip(a)]. 2806 (a(x,y,x) * z) * u = z * (a(x,y,x) * u). [para(2051(a,2),2802(a,1,1))]. 2807 (x * y) * a(z,u,z) = x * (a(z,u,z) * y). [para(2806(a,1),2548(a,1)),flip(a)]. 2810 (x * (K(y,z) * u)) \ ((x * K(y,z)) * (u * w)) = L(w,u,x). [para(2649(a,1),2755(a,1,1))]. 2811 (x * (K(y,z) * u)) \ (x * (K(y,z) * (u * w))) = L(w,u,x). [para(2649(a,1),2810(a,1,2))]. 2812 L(L(x,y,K(z,u)),K(z,u) * y,w) = L(x,y,w). [para(2811(a,1),174(a,1)),flip(a)]. 2813 L(x,K(y,z) * u,w) = L(x,u,w). [para(2515(a,1),2812(a,1,1))]. 2815 L(x,T(y,z) * u,w) = L(x,y * u,w). [para(1098(a,1),2813(a,1,2)),flip(a)]. 2817 L(x,T(y,z) * u,w) = L(x,u * y,w). [para(2815(a,2),2782(a,1))]. 2821 (x * (y * z)) / L(T(z,u),(y * z) * z,x) = x * (y * K(u,z)). [para(2817(a,1),2793(a,1,2))]. 2822 (x * (y * z)) / L(T(z,u),y,x) = x * (y * K(u,z)). [para(2765(a,1),2821(a,1,2))]. 2824 (x * y) * K(z,L(u,y,x)) = x * (y * K(z,u)). [para(2822(a,1),2735(a,1)),flip(a)]. 2831 (K(x,y) * (z * (u * w))) \ ((K(x,y) * (z * u)) * w) = a(K(x,y) * z,u,w). [para(2518(a,1),2622(a,1,2,1))]. 2833 (K(x,y) * (z * (u * w))) \ (K(x,y) * ((z * u) * w)) = a(K(x,y) * z,u,w). [para(2518(a,1),2831(a,1,2))]. 2835 a(K(x,y) * z,u,w) = (z * (u * w)) \ ((z * u) * w). [para(2833(a,1),2519(a,1))]. 2837 ((x * K(y,z)) * (u * w)) \ (((x * K(y,z)) * u) * w) = a(x,u,w). [para(2835(a,1),2586(a,1))]. 2853 (x * (K(y,z) * (u * w))) \ (((x * K(y,z)) * u) * w) = a(x,u,w). [para(2649(a,1),2837(a,1,1))]. 2854 (x * (K(y,z) * (u * w))) \ ((x * (K(y,z) * u)) * w) = a(x,u,w). [para(2649(a,1),2853(a,1,2,1))]. 2855 a(x,K(y,z) * u,w) = a(x,u,w). [para(2854(a,1),2621(a,1)),flip(a)]. 2856 a(x,y * z,u) = a(x,z * y,u). [para(974(a,1),2855(a,1,2))]. 2857 a(x,T(y,z),u) = a(x,y,u). [para(985(a,1),2855(a,1,2)),flip(a)]. 2858 a(x,y * T(z,u),w) = a(x,y * z,w). [para(1212(a,1),2855(a,1,2))]. 2861 a(x,y * K(z,u),w) = a(x,y,w). [para(2200(a,1),2855(a,1,2))]. 2865 a(x,y / z,u) = a(x,z * y,u). [para(2857(a,1),1788(a,1)),flip(a)]. 2866 a(x,(y * z) * z,u) = a(x,y,u). [para(2857(a,1),1792(a,1)),flip(a)]. 2877 a(x,y * (z * K(u,w)),v5) = a(x,y * z,v5). [para(2824(a,1),2861(a,1,2))]. 2878 a(x,L(y,z,y) * (u * y),w) = a(x,u * a(y,z,y),w). [para(2803(a,1),2865(a,1,2)),flip(a)]. 2886 a(x,y * (z * K(u,z)),w) = a(x,y * L(z,u,z),w). [para(1062(a,1),2858(a,1,2,2)),flip(a)]. 2907 a(x,y * L(z,u,z),w) = a(x,y * z,w). [para(2886(a,1),2877(a,1))]. 2908 a(x,L(y,z,y) * u,w) = a(x,u * y,w). [para(2907(a,1),2856(a,1)),flip(a)]. 2910 a(x,y * a(z,u,z),w) = a(x,(y * z) * z,w). [para(2878(a,1),2908(a,1))]. 2911 a(x,y * a(z,u,z),w) = a(x,y,w). [para(2910(a,2),2866(a,1))]. 2913 a(x,a(y,z,y) * u,w) = a(x,u,w). [para(2051(a,2),2911(a,1,2))]. 2915 (x * ((a(y,z,y) * u) * w)) \ ((x * (a(y,z,y) * u)) * w) = a(x,u,w). [para(2913(a,1),28(a,1)),flip(a)]. 2919 (x * (y * (a(z,u,z) * w))) \ ((x * (a(z,u,z) * y)) * w) = a(x,y,w). [para(2806(a,1),2915(a,1,1,2))]. 2986 (x * (y * (a(z,u,z) * w))) \ ((x * (a(z,u,z) * y)) * w) = a(x,y,a(z,u,z) * w). [para(2807(a,1),2805(a,1,2,1))]. 2987 a(x,y,a(z,u,z) * w) = a(x,y,w). [para(2986(a,1),2919(a,1))]. 2988 a(x,y,L(z,u,z)) = a(x,y,z). [para(1542(a,1),2987(a,1,3)),flip(a)]. 2989 a(x,y,(z \ u) * z) = a(x,y,T(u,z)). [para(2675(a,1),2987(a,1,3))]. 2991 a(x,y,(T(z,u) * u) \ (T(z,u) * (z * u))) = a(x,y,T(z,u)). [para(106(a,2),2988(a,1,3))]. 2992 a(x,y,T(z * u,z)) = a(x,y,u * z). [para(19(a,1),2989(a,1,3,1)),flip(a)]. 2993 a(x,y,(T(z,u) * u) \ (z * (T(z,u) * u))) = a(x,y,T(z,u)). [para(728(a,1),2991(a,1,3,2))]. 2994 a(x,y,T(z,T(z,u) * u)) = a(x,y,T(z,u)). [para(36(a,2),2993(a,1,3))]. 2995 a(x,y,T(z,z * u)) = a(x,y,T(z,u)). [para(2018(a,1),2994(a,1,3))]. 2996 a(x,y,T((z \ u) * z,((z \ u) * z) * (z \ 1))) = a(x,y,R(u,z,z)). [para(761(a,1),2995(a,2,3))]. 2998 a(x,y,T((z \ u) * z,R(z \ u,z,z \ 1))) = a(x,y,R(u,z,z)). [para(433(a,1),2996(a,1,3,2))]. 2999 a(x,y,T((z \ u) * z,z \ u)) = a(x,y,R(u,z,z)). [para(2716(a,1),2998(a,1,3))]. 3001 a(x,y,z * (z \ u)) = a(x,y,R(u,z,z)). [para(2999(a,1),2992(a,1)),flip(a)]. 3002 a(x,y,R(z,u,u)) = a(x,y,z). [para(20(a,1),3001(a,1,3)),flip(a)]. 3003 a(x,y,z / (u \ 1)) = a(x,y,z * u). [para(720(a,1),3002(a,1,3)),flip(a)]. 3004 a(x,y,R(((z \ 1) * u) \ 1,u,u)) = a(x,y,(u \ 1) * z). [para(1739(a,2),3003(a,1,3))]. 3005 a(x,y,R((z \ u) \ 1,u,u)) = a(x,y,(u \ 1) * z). [para(318(a,1),3004(a,1,3,1,1))]. 3006 a(x,y,(z \ u) \ 1) = a(x,y,(u \ 1) * z). [para(3005(a,1),3002(a,1)),flip(a)]. 3007 a(x,y,(z \ u) \ 1) = a(x,y,u \ z). [para(318(a,1),3006(a,2,3))]. 3009 a(x,y,(z / u) \ z) = a(x,y,u * a(z,u,u)). [para(1388(a,1),3007(a,1,3)),flip(a)]. 3010 a(x,y,z * a(u,z,z)) = a(x,y,z). [para(66(a,1),3009(a,1,3)),flip(a)]. 3011 a(x,y,L(z,u,u * z)) = a(x,y,z). [para(1487(a,2),3010(a,1,3))]. 3012 ((x * y) \ x) * L(L(y,x,x * y),z,u) = a(u,z,y) \ 1. [para(3011(a,1),2357(a,2,1))]. 3013 (x * y) \ (x * L(y,z,u)) = a(u,z,y) \ 1. [para(3012(a,1),814(a,1)),flip(a)]. 3015 L(a(x,y,z),z,u) = a(x,x * y,z) \ 1. [para(3013(a,1),2350(a,1)),flip(a)]. 3016 L(a(x,y,z),z,u) = a(x,y,z). [para(3015(a,2),2343(a,1))]. 3019 (x * L(y,z,u)) / a(u,u * z,y) = x * y. [para(3016(a,1),2356(a,1,2))]. 3021 a(x,x * y,z) \ (u * L(z,y,x)) = u * z. [para(3019(a,1),2571(a,1)),flip(a)]. 3023 a(x,y,z) * (u * L(z,y,x)) = u * z. [para(3021(a,1),2360(a,1)),flip(a)]. 3026 x * T(y,L(x,z,u)) = y * x. [para(3023(a,1),2376(a,1)),flip(a)]. 3032 K(L(x,y,z),u) = (u * x) \ (x * u). [para(3026(a,1),2186(a,1,1)),flip(a)]. 3034 K(L(x,y,z),u) = K(x,u). [para(3032(a,2),30(a,2)),flip(a)]. 3036 L(K(x,y),z,u) = K(x,y). [para(3034(a,1),2259(a,1)),flip(a)]. 3038 a(x,y,K(z,u)) = 1. [hyper(38,a,3036,a)]. 3039 $F # answer("aK3"). [resolve(3038,a,58,a)]. ============================== end of proof ========================== % Disable descendants (x means already disabled): 58 given #2651 (H,wt=8): 3038 a(x,y,K(z,u)) = 1. [hyper(38,a,3036,a)]. given #2652 (H,wt=15): 3024 a(x,y,z) \ (u * z) = u * L(z,y,x). [hyper(23,a,20,a,b,3023,a),flip(a)]. given #2653 (H,wt=15): 3031 L(x,y,z) * T(u,x) = u * L(x,y,z). [para(303(a,1),3026(a,1,2,2))]. given #2654 (H,wt=15): 3040 (x * y) * K(z,u) = x * (y * K(z,u)). [para(3036(a,1),74(a,1,2))]. given #2655 (H,wt=15): 3041 x \ (y * K(z,u)) = (x \ y) * K(z,u). [para(3036(a,1),560(a,1,2)),flip(a)]. given #2656 (H,wt=15): 3049 (x / y) * L(y,z,u) = a(u,z,y) \ x. [para(22(a,1),3024(a,1,2)),flip(a)]. given #2657 (H,wt=15): 3050 (x * L(y,z,u)) \ (x * y) = a(u,z,y). [para(3024(a,1),2569(a,1,1))]. given #2658 (H,wt=17): 3053 (x \ (y \ z)) * K(y,y * z) = x \ (z / y). [para(1001(a,1),3041(a,1,2)),flip(a)]. given #2659 (H,wt=17): 3054 a(x,y,z * u) \ u = z \ L(z * u,y,x). [para(3049(a,1),353(a,1))]. given #2660 (H,wt=19): 3052 (x * (y * K(z,u))) * w = (x * y) * (K(z,u) * w). [para(3040(a,1),2649(a,1,1))]. given #2661 (H,wt=25): 3055 ((x * y) * L(L(z,y,x),u,w)) \ (x * (y * z)) = a(w,u,L(z,y,x)). [para(74(a,1),3050(a,1,2))]. given #2662 (H,wt=22): 3059 (x * (y * L(z,u,w))) \ (x * (y * z)) = a(w,u,L(z,y,x)). [para(175(a,1),3055(a,1,1))]. given #2663 (H,wt=26): 3058 ((x * y) * (K(z,u) * w)) / ((y * K(z,u)) * w) = R(x,y * K(z,u),w). [para(3052(a,1),34(a,2,1)),flip(a)]. given #2664 (H,wt=26): 3060 ((x * y) * (K(z,u) * w)) / (y * (K(z,u) * w)) = R(x,y * K(z,u),w). [para(2649(a,1),3058(a,1,2))]. given #2665 (H,wt=17): 3061 R(x,y * K(z,u),w) = R(x,y,K(z,u) * w). [para(3060(a,1),34(a,2)),flip(a)]. given #2666 (H,wt=13): 3062 R(x,y,K(z,u) * w) = R(x,y,w). [para(3061(a,1),2892(a,1))]. given #2667 (H,wt=11): 3063 R(x,y,T(z,u)) = R(x,y,z). [para(985(a,1),3062(a,1,3)),flip(a)]. given #2668 (H,wt=13): 3072 R(x,y,T(z,u)) = a(x,y,z) * x. [para(3063(a,2),2303(a,1))]. given #2669 (H,wt=11): 3073 a(x,y,T(z,u)) = a(x,y,z). [hyper(24,a,2303,a(flip),b,3072,a(flip)),flip(a)]. given #2670 (H,wt=13): 3074 a(x,y,z / u) = a(x,y,u \ z). [para(84(a,1),3073(a,1,3)),flip(a)]. given #2671 (H,wt=13): 3075 a(x,y,(z \ u) * z) = a(x,y,u). [para(3073(a,1),2989(a,2))]. given #2672 (H,wt=17): 3077 a(x,y,(z / u) / x) = a(x,y,(x * u) \ z). [para(3074(a,1),2493(a,2))]. given #2673 (H,wt=17): 3078 a(x,y,(z / u) / y) = a(x,y,(y * u) \ z). [para(3074(a,1),2960(a,2))]. given #2674 (H,wt=17): 3079 a(x,y,((z / u) * w) * (u / z)) = a(x,y,w). [para(358(a,1),3075(a,1,3,1))]. given #2675 (H,wt=19): 3080 (x \ y) \ L((x \ y) * x,z,u) = a(u,z,y) \ x. [para(3075(a,1),3054(a,1,1)),flip(a)]. given #2676 (H,wt=15): 3082 L(x,y,z) / (u \ x) = a(z,y,x) \ u. [para(3080(a,1),1588(a,1)),flip(a)]. given #2677 (H,wt=20): 3083 a(x,x * y,L(z,y,x)) \ u = z / (u \ L(z,y,x)). [para(303(a,1),3082(a,1,1)),flip(a)]. given #2678 (H,wt=17): 3084 (a(x,y,z) \ 1) \ u = z / (u \ L(z,y,x)). [para(2365(a,1),3083(a,1,1))]. given #2679 (H,wt=15): 3085 x / (y \ L(x,z,u)) = a(u,z,x) * y. [para(3084(a,1),330(a,1))]. given #2680 (H,wt=17): 3086 x / (y * L(x,z,u)) = a(u,z,x) * (y \ 1). [para(330(a,1),3085(a,1,2))]. given #2681 (H,wt=15): 3088 x / (y * L(x,z,u)) = y \ a(u,z,x). [para(3086(a,2),2572(a,1))]. given #2682 (H,wt=25): 3087 R(x,y,z) / a(L(x,u,w),y,z) = a(w,u,R(x,y,z)) * L(x,u,w). [para(2301(a,1),3085(a,1,2))]. given #2683 (H,wt=25): 3089 a(L(x,y,z),u,w) \ R(x,u,w) = a(z,y,R(x,u,w)) * L(x,y,z). [para(3087(a,1),2571(a,1)),flip(a)]. given #2684 (H,wt=22): 3090 a(x,y,R(z,u,w)) * L(z,y,x) = z * a(x,y,a(z,u,w)). [para(3089(a,1),2973(a,1))]. given #2685 (H,wt=27): 3056 L(a(x,y,z),u * L(z,y,x),w) = (w * (u * L(z,y,x))) \ (w * (u * z)). [para(3050(a,1),76(a,1,1))]. given #2686 (H,wt=20): 3091 L(a(x,y,z),u * L(z,y,x),w) = a(x,y,L(z,u,w)). [para(3056(a,2),3059(a,1))]. given #2687 (H,wt=12): 3093 a(x,y,L(z,u,x)) = a(x,y,z). [para(3091(a,1),2687(a,1))]. given #2688 (H,wt=18): 3094 a(x,y,L(L(z,u,x),w,v5)) = a(x,y,L(z,w,v5)). [para(49(a,1),3093(a,1,3))]. given #2689 (H,wt=20): 3092 a(L(x,y * L(z,u,x),w),u,z) = a(x,u,L(z,y,w)). [para(3091(a,1),2406(a,2))]. given #2690 (H,wt=22): 3099 a(L(x,L(y,z,x) * u,w),z,y) = a(x,z,L(y,T(u,v5),w)). [para(2817(a,1),3092(a,1,1))]. given #2691 (H,wt=27): 3098 a(L(x,y * z,u),w,L(z,x * w,x)) = a(x,w,L(L(z,x * w,x),y,u)). [para(308(a,1),3092(a,1,1,2,2))]. given #2692 (H,wt=28): 3057 (x * (y * (K(z,u) * w))) \ ((x * (y * K(z,u))) * w) = a(x,y,K(z,u) * w). [para(3052(a,2),28(a,2,2)),flip(a)]. given #2693 (H,wt=13): 3100 a(x,y,K(z,u) * w) = a(x,y,w). [para(3057(a,1),2918(a,1))]. given #2694 (H,wt=15): 3102 a(x,y,z * T(u,w)) = a(x,y,z * u). [para(1212(a,1),3100(a,1,3))]. given #2695 (H,wt=15): 3104 a(x,y,T(z,u) / w) = a(x,y,z / w). [para(1815(a,1),3100(a,1,3))]. given #2696 (H,wt=15): 3111 a(x,y,z \ T(u,w)) = a(x,y,u / z). [para(3104(a,1),3074(a,1)),flip(a)]. given #2697 (H,wt=16): 3103 a(x,y,K(z * u,z)) = a(x,y,a(z,u,z)). [para(1537(a,1),3100(a,1,3)),flip(a)]. given #2698 (H,wt=9): 3113 a(x,y,a(z,u,z)) = 1. [para(3103(a,1),3038(a,1))]. given #2699 (H,wt=12): 3114 L(a(x,y,x),z,u) = a(x,y,x). [hyper(37,a,3113,a)]. given #2700 (H,wt=12): 3116 a(L(x,y,z),u,x) = a(x,u,x). [para(3114(a,1),2406(a,2))]. given #2701 (H,wt=14): 3117 L(x * a(x,y,x),y,L(x,z,u)) = x. [para(3116(a,1),2362(a,1,1,2))]. given #2702 (H,wt=12): 3119 L(R(x,y,x),y,L(x,z,u)) = x. [para(1540(a,1),3117(a,1,1))]. given #2703 (H,wt=17): 3101 a(x,y,(z / u) * w) = a(x,y,(u \ z) * w). [para(1161(a,1),3100(a,1,3))]. given #2704 (H,wt=17): 3105 a(x,y,(K(z,u) * w) * v5) = a(x,y,w * v5). [para(2518(a,2),3100(a,1,3))]. given #2705 (H,wt=17): 3106 a(x,y,(z * K(u,w)) * v5) = a(x,y,z * v5). [para(2630(a,1),3100(a,1,3))]. given #2706 (H,wt=17): 3107 a(x,y,(z \ u) \ w) = a(x,y,(z / u) * w). [para(2676(a,1),3100(a,1,3)),flip(a)]. given #2707 (H,wt=17): 3108 a(x,y,(z \ K(u,w)) * v5) = a(x,y,z \ v5). [para(2677(a,1),3100(a,1,3))]. given #2708 (H,wt=17): 3110 a(x,y,z * (u / w)) = a(x,y,z * (w \ u)). [para(84(a,1),3102(a,1,3,2)),flip(a)]. given #2709 (H,wt=17): 3112 a(x,y,(z / u) / w) = a(x,y,w \ (u \ z)). [para(84(a,1),3111(a,1,3,2)),flip(a)]. given #2710 (H,wt=17): 3123 a(x,y,(z \ u) \ w) = a(x,y,(u \ z) * w). [para(3107(a,2),3101(a,1))]. given #2711 (H,wt=17): 3125 a(x,y,((z / u) * w) * (z \ u)) = a(x,y,w). [para(3110(a,1),3079(a,1))]. given #2712 (H,wt=17): 3126 a(x,y,(x * z) \ u) = a(x,y,x \ (z \ u)). [para(3112(a,1),3077(a,1)),flip(a)]. given #2713 (H,wt=17): 3127 a(x,y,(y * z) \ u) = a(x,y,y \ (z \ u)). [para(3112(a,1),3078(a,1)),flip(a)]. given #2714 (H,wt=19): 3124 a(x,y,(T(z,u) * w) \ v5) = a(x,y,(z * w) \ v5). [para(2134(a,1),3108(a,1,3))]. given #2715 (H,wt=20): 3120 L(x,y,z) * (u * R(x,u,x)) = (L(x,y,z) * u) * x. [para(3119(a,1),74(a,1,2)),flip(a)]. given #2716 (H,wt=19): 3132 L(x,y,z) * T(x * u,x) = (L(x,y,z) * u) * x. [para(1321(a,1),3120(a,1,2))]. given #2717 (H,wt=17): 3133 (L(x,y,z) * u) * x = (x * u) * L(x,y,z). [para(3132(a,1),3031(a,1))]. given #2718 (H,wt=17): 3134 (x * (L(x,y,z) \ u)) * L(x,y,z) = u * x. [para(20(a,1),3133(a,1,1)),flip(a)]. given #2719 (H,wt=15): 3135 (x * a(y,z,u)) * L(u,z,y) = x * u. [para(2604(a,1),3134(a,1,1))]. given #2720 (H,wt=15): 3137 (x / a(y,z,u)) * u = x * L(u,z,y). [para(22(a,1),3135(a,1,1)),flip(a)]. given #2721 (H,wt=15): 3138 (a(x,y,z) / u) \ z = u * L(z,y,x). [para(3137(a,1),358(a,2))]. given #2722 (H,wt=15): 3139 x / (y * L(x,z,u)) = a(u,z,x) / y. [para(3138(a,1),65(a,1,2))]. given #2723 (H,wt=13): 3140 a(x,y,z) / u = u \ a(x,y,z). [para(3139(a,1),3088(a,1))]. given #2724 (H,wt=17): 3141 (a(x,y,z) \ u) \ w = (u \ a(x,y,z)) * w. [para(3140(a,1),2605(a,2,1))]. given #2725 (H,wt=21): 3121 a(x,y,((z / u) * w) * v5) = a(x,y,((u \ z) * w) * v5). [para(1161(a,1),3105(a,1,3,1))]. given #2726 (H,wt=17): 3143 a(x,y,((z \ u) * w) * (u \ z)) = a(x,y,w). [para(3121(a,1),3125(a,1))]. given #2727 (H,wt=20): 3145 a(x,y,(z \ (u * w)) * (u \ z)) = a(x,y,L(w,u,z)). [para(798(a,1),3143(a,1,3,1))]. given #2728 (H,wt=21): 3122 a(x,y,((z \ u) \ w) * v5) = a(x,y,((z / u) * w) * v5). [para(2676(a,1),3105(a,1,3,1)),flip(a)]. given #2729 (H,wt=21): 3130 a(x,y,y \ (z \ ((z * y) * u))) = a(x,y,K(z,y) * u). [para(940(a,1),3127(a,1,3)),flip(a)]. given #2730 (H,wt=17): 3147 a(x,y,y \ (z \ ((z * y) * u))) = a(x,y,u). [para(3130(a,2),3100(a,1))]. given #2731 (H,wt=14): 3148 a(x,y,L(z,u * y,u)) = a(x,y,z). [para(309(a,1),3147(a,1,3))]. given #2732 (H,wt=21): 3131 a(x,y,((z / u) * w) \ v5) = a(x,y,((u \ z) * w) \ v5). [para(84(a,1),3124(a,1,3,1,1)),flip(a)]. given #2733 (H,wt=21): 3146 a(x,y,((z \ u) \ w) * v5) = a(x,y,((u \ z) * w) * v5). [para(3122(a,2),3121(a,1))]. given #2734 (H,wt=22): 3129 a(x,x * y,x \ (y \ z)) = (y \ (x \ z)) \ ((x * y) \ z). [para(3126(a,1),2327(a,1))]. given #2735 (H,wt=22): 3144 a(x,y,((z \ u) * w) * ((u * w) \ z)) = a(x,y,a(z,u,w)). [para(595(a,1),3143(a,1,3,1))]. given #2736 (H,wt=22): 3151 a(L(x,y * z,u),w,z) = a(x,w,L(L(z,x * w,x),y,u)). [para(3148(a,1),3098(a,1))]. given #2737 (H,wt=17): 3153 a(L(x,y * z,u),w,z) = a(x,w,L(z,y,u)). [para(3151(a,2),3094(a,1))]. given #2738 (H,wt=17): 3155 a(x,y,L(z,u * z,w)) = a(L(x,u,w),y,z). [para(2765(a,1),3153(a,1,1)),flip(a)]. given #2739 (H,wt=27): 3128 a(x,y,((z \ (u \ w)) * K(u,u * w)) * v5) = a(x,y,((w / u) \ z) \ v5). [para(3053(a,2),3123(a,2,3,1)),flip(a)]. given #2740 (H,wt=27): 3157 a(x,y,((z \ (u \ w)) * K(u,u * w)) * v5) = a(x,y,((u / w) * z) \ v5). [para(358(a,1),3128(a,2,3,1))]. given #2741 (H,wt=21): 3158 a(x,y,((z / u) * w) \ v5) = a(x,y,(w \ (z \ u)) * v5). [para(3157(a,1),3106(a,1))]. given #2742 (H,wt=21): 3160 a(x,y,((z \ u) * w) \ v5) = a(x,y,(w \ (u \ z)) * v5). [para(3158(a,1),3131(a,1)),flip(a)]. given #2743 (H,wt=21): 3161 a(x,y,z / ((u \ w) * v5)) = a(x,y,(v5 \ (w \ u)) * z). [para(3160(a,1),3074(a,2))]. given #2744 (H,wt=30): 3152 a(x,y,(z \ (u \ w)) \ ((u * z) \ w)) = x \ L(x,y,a(u,u * z,u \ (z \ w))). [para(3129(a,1),2970(a,2,3)),flip(a)]. given #2745 (H,wt=28): 3162 a(x,y,(z \ (u \ w)) \ ((u * z) \ w)) = x \ L(x,y,a(u,z,u \ (z \ w))). [para(2361(a,1),3152(a,2,2))]. given #2746 (H,wt=26): 3163 a(x,y,(z \ (u \ w)) \ ((u * z) \ w)) = a(x,y,a(u,z,u \ (z \ w))). [para(3162(a,2),2970(a,1))]. given #2747 (H,wt=32): 2972 (x \ (a(y,z,u) * w)) \ ((a(y,z,u) \ x) \ w) = a(x \ (a(y,z,u) * w),x,a(y,z,u)). [para(267(a,1),2970(a,1,2))]. given #2748 (H,wt=32): 3164 (x \ (a(y,z,u) * w)) \ ((x \ a(y,z,u)) * w) = a(x \ (a(y,z,u) * w),x,a(y,z,u)). [para(3141(a,1),2972(a,1,2))]. given #2749 (H,wt=22): 3165 a(x \ (a(y,z,u) * w),x,a(y,z,u)) = a(x,a(y,z,u),w). [para(3164(a,1),594(a,2)),flip(a)]. given #2750 (H,wt=22): 3166 a(x * (a(y,z,u) * w),x,a(y,z,u)) = a(x,a(y,z,u),w). [para(3165(a,1),1702(a,1)),flip(a)]. given #2751 (H,wt=22): 3167 a(x * (y * a(z,u,w)),y,a(z,u,w)) = a(y,a(z,u,w),x). [para(3165(a,1),2964(a,1)),flip(a)]. given #2752 (H,wt=22): 3168 a(a(x,y,z) * (u * w),u,a(x,y,z)) = a(u,a(x,y,z),w). [para(3166(a,1),2955(a,2))]. given #2753 (H,wt=22): 3169 a((x * a(y,z,u)) / w,x,a(y,z,u)) = a(x,a(y,z,u),w). [para(3167(a,1),2606(a,2))]. given #2754 (H,wt=22): 3171 a(a(x,y,z) / (u / w),u,a(x,y,z)) = a(u,a(x,y,z),w). [para(3169(a,1),2852(a,1)),flip(a)]. given #2755 (H,wt=28): 3170 a(a(x,y,z) * (u * w),u,a(x,y,z)) \ v5 = a(u,u * a(x,y,z),w) * v5. [para(3168(a,2),2359(a,2,1)),flip(a)]. given #2756 (H,wt=24): 3172 a(a(x,y,z) * (u * w),u,a(x,y,z)) = a(u,u * a(x,y,z),w). [hyper(24,a,2696,a(flip),b,3170,a(flip)),flip(a)]. given #2757 (H,wt=17): 3173 a(x,x * a(y,z,u),w) = a(x,a(y,z,u),w). [para(3172(a,1),3168(a,1))]. given #2758 (H,wt=19): 3174 a(x,a(y,z,u),w) \ v5 = a(x,a(y,z,u),w) * v5. [para(3173(a,1),2359(a,1,1)),flip(a)]. given #2759 (H,wt=33): 2809 ((x * a(y,z,u)) * w) \ ((x * w) * a(y,z,u)) = a(x,a(y,z,u),w) \ a(x,w,a(y,z,u)). [para(2598(a,1),2790(a,1,2)),flip(a)]. given #2760 (H,wt=23): 3175 a(x,a(y,z,u),w) \ a(x,w,a(y,z,u)) = a(w,x,a(y,z,u)). [para(2809(a,1),2975(a,1))]. given #2761 (H,wt=23): 3176 a(x,a(y,z,u),w) * a(x,w,a(y,z,u)) = a(w,x,a(y,z,u)). [para(3175(a,1),3174(a,1)),flip(a)]. given #2762 (H,wt=36): 2379 R(T(a(x,y,z),(L(z,y,x) * u) * w),L(z,y,x) * u,w) = ((L(z,y,x) * u) * w) \ ((z * u) * w). [para(2333(a,1),549(a,1,2,1)),flip(a)]. given #2763 (H,wt=29): 3177 R(T(a(x,y,z),(L(z,y,x) * u) * w),L(z,y,x) * u,w) = a(x,y,R(z,u,w)). [para(2379(a,2),2751(a,1))]. given #2764 (H,wt=20): 3178 R(a(x,y,z),L(z,y,x) * u,w) = a(x,y,R(z,u,w)). [para(2543(a,1),3177(a,1,1))]. given #2765 (H,wt=20): 3180 a(L(x,L(y,z,x) * u,w),z,y) = a(x,z,R(y,u,w)). [para(3178(a,1),2933(a,2))]. given #2766 (H,wt=17): 3181 a(x,y,L(z,T(u,w),v5)) = a(x,y,R(z,u,v5)). [para(3180(a,1),3099(a,1)),flip(a)]. given #2767 (H,wt=15): 3182 a(x,y,R(z,u,w)) = a(x,y,L(z,u,w)). [para(81(a,1),3181(a,1,3,2)),flip(a)]. given #2768 (H,wt=22): 3184 a(x,y,L(z,u,w)) * L(z,y,x) = z * a(x,y,a(z,u,w)). [para(3182(a,1),3090(a,1,1))]. given #2769 (H,wt=24): 3183 a(x,y,L(z,u * z,w)) = a(x,y,(u \ w) / ((z \ (u \ 1)) * w)). [para(2916(a,1),3182(a,1,3)),flip(a)]. given #2770 (H,wt=24): 3185 a(x,y,L(z,u * z,w)) = a(x,y,(w \ ((u \ 1) \ z)) * (u \ w)). [para(3183(a,2),3161(a,1))]. given #2771 (H,wt=22): 3186 a(x,y,L(z,u * z,w)) = a(x,y,(w \ (u * z)) * (u \ w)). [para(330(a,1),3185(a,2,3,1,2))]. given #2772 (H,wt=17): 3187 a(x,y,L(z,u * z,w)) = a(x,y,L(z,u,w)). [para(3186(a,2),3145(a,1))]. given #2773 (H,wt=15): 3188 a(L(x,y,z),u,w) = a(x,u,L(w,y,z)). [para(3187(a,1),3155(a,1)),flip(a)]. given #2774 (H,wt=22): 3189 L(x,y,z) * a(z,y,L(x,u,w)) = x * a(w,u,a(z,y,x)). [para(3188(a,1),2693(a,1,2))]. given #2775 (H,wt=22): 3190 a(x,y,L(z,u,w)) * L(z,y,x) = z * a(w,u,a(x,y,z)). [para(3188(a,1),2697(a,1,1))]. given #2776 (H,wt=15): 3192 a(x,y,a(z,u,w)) = a(w,u,a(x,y,z)). [hyper(23,a,3184,a(flip),b,3190,a(flip)),flip(a)]. given #2777 (H,wt=15): 3195 a(x,y,a(z,u,w)) = a(w,y,a(x,u,z)). [para(3192(a,1),3192(a,2)),flip(a)]. given #2778 (H,wt=17): 3196 a(x,y,a(z,u,w)) * a(z,y,a(w,u,x)) = 1. [para(3195(a,1),2695(a,1,1))]. given #2779 (H,wt=17): 3198 a(x,y * z,a(u,w,z)) = a(u,y,a(z,w,x)). [para(3195(a,1),2980(a,1))]. given #2780 (H,wt=19): 3193 a(x,y,a(z / u,w,v5)) = a(v5,w,a(x,y,u * z)). [para(2606(a,2),3192(a,1,3))]. given #2781 (H,wt=19): 3194 a(x * y,z,a(u,w,v5)) = a(u,w,a(v5,z,y * x)). [para(3192(a,2),2618(a,1)),flip(a)]. given #2782 (H,wt=19): 3197 a(x * y,x,a(z,u,w)) = a(z,y,a(w,u,x * y)). [para(3195(a,2),2750(a,1)),flip(a)]. given #2783 (H,wt=19): 3200 a(x,y,a(z,u,w / v5)) = a(x,y,a(z,u,v5 * w)). [para(3193(a,1),3192(a,1)),flip(a)]. given #2784 (H,wt=20): 3199 a(x,y,a(a(x,y,z) / u,w,v5)) = a(v5,w,a(x,y,u)). [para(2950(a,1),3193(a,2,3))]. given #2785 (H,wt=22): 3191 L(x,y,z) * a(z,y,L(x,u,w)) = x * a(z,y,a(w,u,x)). [para(3189(a,1),2643(a,1)),flip(a)]. given #2786 (H,wt=15): 3201 a(x,y,a(z,u,w)) = a(z,u,a(x,y,w)). [hyper(23,a,3189,a(flip),b,3191,a(flip))]. given #2787 (H,wt=15): 3203 a(x,y,a(z,u,w)) = a(w,y,a(z,u,x)). [para(3201(a,1),3192(a,1))]. given #2788 (H,wt=15): 3204 a(x,y,a(z,u,w)) = a(x,y,a(w,u,z)). [para(3201(a,1),3192(a,2))]. given #2789 (H,wt=15): 3205 a(x,y,a(z,u,w)) = a(w,u,a(z,y,x)). [para(3201(a,1),3195(a,1))]. given #2790 (H,wt=17): 3207 a(x,y * z,a(u,w,z)) = a(x,y,a(z,w,u)). [para(3203(a,1),3198(a,2))]. given #2791 (H,wt=19): 3208 a(x,y,a(z / u,w,v5)) = a(x,y,a(v5,w,u / z)). [para(612(a,1),3204(a,1,3))]. given #2792 (H,wt=19): 3209 a(x * y,z,a(u,w,v5)) = a(v5,w,a(u,z,y * x)). [para(3204(a,1),3194(a,1))]. given #2793 (H,wt=19): 3210 a(x / y,z,a(u,w,v5)) = a(v5,w,a(u,z,y / x)). [para(3205(a,1),612(a,1)),flip(a)]. given #2794 (H,wt=22): 3202 a(x,y,a(a(x,y,z) / (u / w),u,z)) = a(u,a(x,y,z),w). [para(3201(a,1),3171(a,1))]. given #2795 (H,wt=17): 3214 a(x,y,a(z,u,y / w)) = a(y,a(z,u,x),w). [para(3202(a,1),3199(a,1)),flip(a)]. given #2796 (H,wt=17): 3215 a(x,y,a(z,u,w * y)) = a(y,a(z,u,x),w). [para(3214(a,1),3200(a,1)),flip(a)]. given #2797 (H,wt=17): 3217 a(x,y,a(z,u,u / w)) = a(u,a(x,y,z),w). [para(3214(a,1),3201(a,1)),flip(a)]. given #2798 (H,wt=17): 3218 a(x * y,x,a(z,u,w)) = a(y,a(w,u,z),x). [para(3215(a,1),3197(a,2))]. given #2799 (H,wt=17): 3219 a(x,y,a(z / u,u,w)) = a(u,a(x,y,w),z). [para(3217(a,1),3208(a,2))]. given #2800 (H,wt=17): 3220 a(x / y,y,a(z,u,w)) = a(y,a(w,u,z),x). [para(3217(a,1),3210(a,2))]. given #2801 (H,wt=17): 3222 a(x,y,a(z,u,w / u)) = a(u,a(x,y,z),w). [para(3219(a,1),3204(a,1)),flip(a)]. given #2802 (H,wt=21): 3221 a(x * (y * z),y,a(u,w,v5)) = a(x * z,a(v5,w,u),y). [para(3218(a,1),2955(a,2))]. given #2803 (H,wt=21): 3223 a(x / (y / z),y,a(u,w,v5)) = a(y,a(v5,w,u),z * x). [para(3220(a,1),2956(a,1)),flip(a)]. given #2804 (H,wt=21): 3224 a(x / (y * z),z,a(u,w,v5)) = a(z,a(v5,w,u),y * x). [para(3223(a,1),2851(a,1)),flip(a)]. given #2805 (H,wt=23): 3206 a(x,a(y,z,u),w) * a(u,w,a(y,z,x)) = a(w,x,a(y,z,u)). [para(3203(a,1),3176(a,1,2))]. given #2806 (H,wt=23): 3211 a(x * (y * z),y,a(x,u,w)) = a(w,u,a(x,z,x * (z * y))). [para(3205(a,1),2985(a,1)),flip(a)]. given #2807 (H,wt=21): 3225 a(x,y,a(z,u,z * (u * w))) = a(z * u,a(x,y,z),w). [para(3211(a,1),3221(a,1))]. given #2808 (H,wt=23): 3213 a(x * (y * z),y,a(u,w,v5)) = a(v5,w,a(u,y,z * (y * x))). [para(3209(a,1),2488(a,1)),flip(a)]. given #2809 (H,wt=23): 3226 a(x / (y * z),z,a(u,w,v5)) = a(v5,w,a(u,z,x * (z * y))). [para(3213(a,1),2846(a,2))]. given #2810 (H,wt=21): 3227 a(x,y,a(z,u,w * (u * v5))) = a(u,a(x,y,z),v5 * w). [para(3226(a,1),3224(a,1))]. given #2811 (H,wt=19): 3228 a(x * y,a(z,u,x),w) = a(y,a(z,u,x),w * x). [para(3227(a,1),3225(a,1)),flip(a)]. given #2812 (H,wt=26): 3212 a(x,y,(z \ (u \ w)) \ ((u * z) \ w)) = a(u \ (z \ w),z,a(u,y,x)). [para(3205(a,1),3163(a,2))]. given #2813 (H,wt=26): 3229 a(x,y,(z \ (u \ w)) \ ((u * z) \ w)) = a(u * (z * w),z,a(u,y,x)). [para(3212(a,2),1757(a,1))]. given #2814 (H,wt=24): 3230 a(x,y,(z \ (u \ w)) \ ((u * z) \ w)) = a(u * w,a(x,y,u),z). [para(3229(a,2),3221(a,1))]. given #2815 (H,wt=24): 3231 a(x,y,(z \ (u \ w)) \ ((u * z) \ w)) = a(w,a(x,y,u),z * u). [para(3230(a,2),3228(a,1))]. given #2816 (H,wt=24): 3232 a(x,y,((z \ u) \ w) * ((z * w) \ u)) = a(u,a(x,y,z),w * z). [para(3231(a,1),3123(a,1)),flip(a)]. given #2817 (H,wt=24): 3233 a(x,y,((z \ u) * w) * ((u * w) \ z)) = a(z,a(x,y,u),w * u). [para(3232(a,1),3146(a,1)),flip(a)]. given #2818 (H,wt=17): 3234 a(x,a(y,z,u),w * u) = a(y,z,a(x,u,w)). [para(3233(a,1),3144(a,1))]. given #2819 (H,wt=17): 3235 a(x,y,a(z,u,w / u)) = a(z,a(x,y,u),w). [para(22(a,1),3234(a,1,3)),flip(a)]. given #2820 (H,wt=15): 3236 a(x,a(y,z,u),w) = a(u,a(y,z,x),w). [para(3235(a,1),3222(a,1))]. given #2821 (H,wt=23): 3237 a(x,a(y,z,u),w) * a(u,w,a(y,z,x)) = a(w,u,a(y,z,x)). [para(3236(a,1),3176(a,1,1))]. given #2822 (H,wt=15): 3238 a(x,y,a(z,u,w)) = a(x,w,a(z,u,y)). [para(3237(a,1),3206(a,1))]. given #2823 (H,wt=17): 3239 a(x,y,a(z,u,w * y)) = a(x,w,a(y,u,z)). [para(3238(a,1),3207(a,1))]. given #2824 (H,wt=15): 3240 a(x,a(y,z,u),w) = a(u,w,a(x,z,y)). [para(3239(a,1),3215(a,1)),flip(a)]. given #2825 (H,wt=23): 3241 a(x,y,a(z,u,w)) * a(z,y,a(w,u,x)) = a(y,z,a(w,u,x)). [para(3240(a,1),3176(a,1,1))]. -------- Proof 5 -------- "aa3". ============================== PROOF ================================= % Proof 5 at 82.23 (+ 1.32) seconds: "aa3". % Length of proof is 2841. % Level of proof is 320. % Maximum clause weight is 50. % Given clauses 2825. 1 x * y = u & x * z = u -> y = z # label(non_clause). [assumption]. 2 y * x = u & z * x = u -> y = z # label(non_clause). [assumption]. 5 a(x,y,z) = 1 -> L(z,y,x) = z # label(non_clause). [assumption]. 6 L(x,y,z) = x -> a(z,y,x) = 1 # label(non_clause). [assumption]. 7 T(x,y) = x -> T(y,x) = y # label(non_clause). [assumption]. 8 T(x,y) = x -> K(x,y) = 1 # label(non_clause). [assumption]. 9 K(x,y) = 1 -> T(x,y) = x # label(non_clause). [assumption]. 12 a(x,y,a(z,u,w)) = 1 # label("aa3") # label(non_clause) # label(goal). [goal]. 17 1 * x = x. [assumption]. 18 x * 1 = x. [assumption]. 19 x \ (x * y) = y. [assumption]. 20 x * (x \ y) = y. [assumption]. 21 (x * y) / y = x. [assumption]. 22 (x / y) * y = x. [assumption]. 23 x * y != z | x * u != z | u = y. [clausify(1)]. 24 x * y != z | u * y != z | u = x. [clausify(2)]. 27 (x * (y * z)) \ ((x * y) * z) = a(x,y,z). [assumption]. 28 a(x,y,z) = (x * (y * z)) \ ((x * y) * z). [copy(27),flip(a)]. 29 (x * y) \ (y * x) = K(y,x). [assumption]. 30 K(x,y) = (y * x) \ (x * y). [copy(29),flip(a)]. 31 (x * y) \ (x * (y * z)) = L(z,y,x). [assumption]. 32 L(x,y,z) = (z * y) \ (z * (y * x)). [copy(31),flip(a)]. 33 ((x * y) * z) / (y * z) = R(x,y,z). [assumption]. 34 R(x,y,z) = ((x * y) * z) / (y * z). [copy(33),flip(a)]. 35 x \ (y * x) = T(y,x). [assumption]. 36 T(x,y) = y \ (x * y). [copy(35),flip(a)]. 37 a(x,y,z) != 1 | L(z,y,x) = z. [clausify(5)]. 38 L(x,y,z) != x | a(z,y,x) = 1. [clausify(6)]. 39 T(x,y) != x | T(y,x) = y. [clausify(7)]. 40 T(x,y) != x | K(x,y) = 1. [clausify(8)]. 41 K(x,y) != 1 | T(x,y) = x. [clausify(9)]. 42 T(T(x,y),z) = T(T(x,z),y). [assumption]. 43 T(L(x,y,z),u) = L(T(x,u),y,z). [assumption]. 44 L(T(x,y),z,u) = T(L(x,z,u),y). [copy(43),flip(a)]. 45 T(R(x,y,z),u) = R(T(x,u),y,z). [assumption]. 46 R(T(x,y),z,u) = T(R(x,z,u),y). [copy(45),flip(a)]. 47 L(R(x,y,z),u,w) = R(L(x,u,w),y,z). [assumption]. 48 R(L(x,y,z),u,w) = L(R(x,u,w),y,z). [copy(47),flip(a)]. 49 L(L(x,y,z),u,w) = L(L(x,u,w),y,z). [assumption]. 50 R(R(x,y,z),u,w) = R(R(x,u,w),y,z). [assumption]. 51 (x * (x * y)) * z = x * (x * (y * z)) # label("LC"). [assumption]. 54 a(c11,c12,a(c13,c14,c15)) != 1 # label("aa3") # answer("aa3"). [deny(12)]. 59 1 \ x = x. [para(17(a,1),19(a,1,2))]. 60 x \ x = 1. [para(18(a,1),19(a,1,2))]. 61 x \ ((x * y) * 1) = y. [para(18(a,2),19(a,1,2))]. 62 x \ (y * (y \ (x * z))) = z. [para(20(a,2),19(a,1,2))]. 64 x / 1 = x. [para(18(a,1),21(a,1,1))]. 65 x / (y \ x) = y. [para(20(a,1),21(a,1,1))]. 66 (x / y) \ x = y. [para(22(a,1),19(a,1,2))]. 67 (x * (y * z)) * a(x,y,z) = (x * y) * z. [para(28(a,2),20(a,1,2))]. 68 ((x / y) * (y * z)) \ (x * z) = a(x / y,y,z). [para(22(a,1),28(a,2,2,1)),flip(a)]. 69 (x * y) * K(y,x) = y * x. [para(30(a,2),20(a,1,2))]. 70 x \ ((y \ x) * y) = K(y \ x,y). [para(20(a,1),30(a,2,1)),flip(a)]. 71 ((x \ y) * x) \ y = K(x,x \ y). [para(20(a,1),30(a,2,2)),flip(a)]. 72 x \ (1 * (x * y)) = L(y,x,1). [para(17(a,1),32(a,2,1)),flip(a)]. 73 (x * 1) \ (x * y) = L(y,1,x). [para(17(a,1),32(a,2,2,2)),flip(a)]. 74 (x * y) * L(z,y,x) = x * (y * z). [para(32(a,2),20(a,1,2))]. 75 x \ (y * ((y \ x) * z)) = L(z,y \ x,y). [para(20(a,1),32(a,2,1)),flip(a)]. 76 L(x \ y,x,z) = (z * x) \ (z * y). [para(20(a,1),32(a,2,2,2))]. 77 x \ ((x / y) * (y * z)) = L(z,y,x / y). [para(22(a,1),32(a,2,1)),flip(a)]. 78 ((x * y) * (y \ z)) / z = R(x,y,y \ z). [para(20(a,1),34(a,2,2)),flip(a)]. 79 R(x,y,z) * (y * z) = (x * y) * z. [para(34(a,2),22(a,1,1))]. 80 R(x / y,y,z) = (x * z) / (y * z). [para(22(a,1),34(a,2,1,1))]. 81 T(x,x) = x. [para(36(a,2),19(a,1))]. 82 x * T(y,x) = y * x. [para(36(a,2),20(a,1,2))]. 83 T(x,x \ y) = (x \ y) \ y. [para(20(a,1),36(a,2,2))]. 84 T(x / y,y) = y \ x. [para(22(a,1),36(a,2,2))]. 85 (x * (x * (y * z))) / z = x * (x * y). [hyper(24,a,22,a,b,51,a),flip(a)]. 86 (x * (x * y)) \ (x * (x * (y * z))) = z. [hyper(23,a,20,a,b,51,a),flip(a)]. 87 x \ ((x * (x * y)) * z) = x * (y * z). [hyper(23,a,20,a,b,51,a(flip)),flip(a)]. 88 (x * (x * 1)) * y = x * (x * y). [para(17(a,1),51(a,2,2,2))]. 89 x * (x * ((x \ y) * z)) = (x * y) * z. [para(20(a,1),51(a,1,1,2)),flip(a)]. 90 (x * (y * (y * (z * u)))) \ ((x * (y * (y * z))) * u) = a(x,y * (y * z),u). [para(51(a,1),28(a,2,1,2)),flip(a)]. 91 (x * (x * (y * (z * u)))) \ (((x * (x * y)) * z) * u) = a(x * (x * y),z,u). [para(51(a,1),28(a,2,1)),flip(a)]. 92 (x * (x * (y * z))) \ ((x * (x * y)) * (z * u)) = L(u,z,x * (x * y)). [para(51(a,1),32(a,2,1)),flip(a)]. 93 (x * (y * (y * z))) \ (x * (y * (y * (z * u)))) = L(u,y * (y * z),x). [para(51(a,1),32(a,2,2,2)),flip(a)]. 94 ((x * (x * (y * z))) * u) / (z * u) = R(x * (x * y),z,u). [para(51(a,1),34(a,2,1,1)),flip(a)]. 95 (x * (x * (y * z))) / ((x * y) * z) = R(x,x * y,z). [para(51(a,1),34(a,2,1)),flip(a)]. 97 ((x * y) / 1) / y = x. [hyper(24,a,22,a,b,64,a(flip)),flip(a)]. 98 T(T(x,y),x) = T(x,y). [para(81(a,1),42(a,1,1)),flip(a)]. 99 (x * (y * z)) / L(z,y,x) = x * y. [para(32(a,2),65(a,1,2))]. 100 (x * y) / T(x,y) = y. [para(36(a,2),65(a,1,2))]. 101 R(x,y,z) \ ((x * y) * z) = y * z. [para(34(a,2),66(a,1,1))]. 102 x \ (y * 1) = x \ y. [para(20(a,1),61(a,1,2,1))]. 103 T(x * (x * y),x) = x * (y * x). [hyper(23,a,51,a(flip),b,82,a)]. 104 T((x * y) / x,x) = y. [hyper(23,a,22,a(flip),b,82,a)]. 105 (x * T(y,x)) / x = y. [hyper(24,a,22,a,b,82,a(flip)),flip(a)]. 106 (x * y) \ (x * (z * y)) = L(T(z,y),y,x). [para(82(a,1),32(a,2,2,2)),flip(a)]. 107 T(x,y) \ (x * y) = T(y,T(x,y)). [para(82(a,1),36(a,2,2)),flip(a)]. 108 x * T(T(y,x),z) = T(y,z) * x. [para(42(a,1),82(a,1,2))]. 109 x * L(T(y,x),z,u) = L(y,z,u) * x. [para(44(a,2),82(a,1,2))]. 110 x * R(T(y,x),z,u) = R(y,z,u) * x. [para(46(a,2),82(a,1,2))]. 111 (x * y) \ ((z * x) * y) = T(R(z,x,y),x * y). [para(34(a,2),84(a,1,1)),flip(a)]. 112 T(T(x / y,z),y) = T(y \ x,z). [para(84(a,1),42(a,1,1)),flip(a)]. 113 ((x * y) / ((1 / z) * z)) / y = x. [para(22(a,2),97(a,1,1,2))]. 114 K(T(x,y),x) = 1. [hyper(40,a,98,a)]. 115 T(x,T(x,y)) = x. [hyper(39,a,98,a)]. 116 T(x,y) * x = x * T(x,y). [para(98(a,1),82(a,1,2)),flip(a)]. 117 (x * y) / T(y,T(x,y)) = T(x,y). [para(82(a,1),100(a,1,1))]. 118 x \ (y * (z * (z \ 1))) = x \ y. [para(20(a,2),102(a,1,2,2))]. 119 K(x,(y * x) / y) = 1. [para(104(a,1),114(a,1,1))]. 120 T(x,(y * x) / y) = x. [hyper(41,a,119,a)]. 121 x * K(y,x / y) = y * (x / y). [para(22(a,1),69(a,1,1))]. 122 K(x,y) \ (x * y) = T(y * x,K(x,y)). [para(69(a,1),36(a,2,2)),flip(a)]. 123 x \ (x * y) = L(y,x,1). [para(17(a,1),72(a,1,2))]. 124 L(x,y,1) = x. [para(123(a,1),19(a,1))]. 125 a(1,x,y) = 1. [hyper(38,a,124,a)]. 126 x \ (x * y) = L(y,1,x). [para(18(a,1),73(a,1,1))]. 127 L(x,1,y) = x. [para(126(a,1),19(a,1))]. 128 K(x \ 1,x) = (x \ 1) * x. [para(70(a,1),59(a,1))]. 129 K(x \ 1,x) / x = x \ 1. [hyper(24,a,22,a,b,128,a(flip)),flip(a)]. 130 (x \ 1) \ K(x \ 1,x) = x. [hyper(23,a,20,a,b,128,a(flip)),flip(a)]. 131 (x * x) * y = x * (x * y). [para(18(a,1),88(a,1,1,2))]. 132 (x * (x * y)) / y = x * x. [hyper(24,a,22,a,b,131,a),flip(a)]. 133 (x * x) \ (x * (x * y)) = y. [hyper(23,a,20,a,b,131,a),flip(a)]. 134 ((x * (x * y)) * z) / (y * z) = R(x * x,y,z). [para(131(a,1),34(a,2,1,1)),flip(a)]. 135 x \ (y * (y * x)) = T(y * y,x). [para(131(a,1),36(a,2,2)),flip(a)]. 136 x * (x * T(y,x * x)) = y * (x * x). [para(131(a,1),82(a,1))]. 137 L(x,y,y) = x. [para(133(a,1),32(a,2))]. 138 x * ((x \ y) * x) = T(x * y,x). [para(20(a,1),103(a,1,1,2)),flip(a)]. 139 T(x / y,z) * y = y * T(y \ x,z). [para(84(a,1),108(a,1,2,1)),flip(a)]. 140 (x * T(x \ y,z)) / x = T(y / x,z). [para(112(a,1),105(a,1,1,2))]. 141 R(x,1 / y,y) / y = x * (1 / y). [para(34(a,2),113(a,1,1))]. 142 L(x \ 1,x,y) = (y * x) \ y. [para(118(a,1),32(a,2))]. 143 L((x \ y) \ 1,x \ y,x) = y \ x. [para(20(a,1),142(a,2,1))]. 144 L(x \ 1,x,y / x) = y \ (y / x). [para(22(a,1),142(a,2,1))]. 145 x / L(y \ 1,y,x) = x * y. [para(142(a,2),65(a,1,2))]. 146 x \ T(x * y,x) = (x \ y) * x. [hyper(23,a,20,a,b,138,a),flip(a)]. 147 x * K(x \ 1,x) = T(x * 1,x). [para(128(a,2),138(a,1,2))]. 148 (x \ (x \ y)) * x = x \ T(y,x). [para(20(a,1),146(a,1,2,1)),flip(a)]. 149 x * K(x \ 1,x) = T(x,x). [para(18(a,1),147(a,2,1))]. 150 x * K(x \ 1,x) = x. [para(149(a,2),81(a,1))]. 151 K(x \ 1,x) = 1. [hyper(23,a,18,a,b,150,a)]. 152 T(x \ 1,x) = x \ 1. [hyper(41,a,151,a)]. 154 (x \ 1) * x = 1. [para(151(a,1),128(a,1)),flip(a)]. 155 1 / x = x \ 1. [para(151(a,1),129(a,1,1))]. 156 (x \ 1) \ 1 = x. [para(151(a,1),130(a,1,2))]. 157 x * (1 / x) = 1. [para(66(a,1),154(a,1,1))]. 160 T(x,x \ 1) = x. [para(156(a,1),83(a,2))]. 161 L(x,x \ 1,y) = (y * (x \ 1)) \ y. [para(156(a,1),142(a,1,1))]. 162 x / L(y,y \ 1,x) = x * (y \ 1). [para(156(a,1),145(a,1,2,1))]. 164 (x * 1) \ ((x * y) * (1 / y)) = a(x,y,1 / y). [para(157(a,1),28(a,2,1,2)),flip(a)]. 165 T(T(x,y),x \ 1) = T(x,y). [para(160(a,1),42(a,1,1)),flip(a)]. 166 K(T(x,y),x \ 1) = 1. [hyper(40,a,165,a)]. 167 K(x \ y,(y / x) \ 1) = 1. [para(84(a,1),166(a,1,1))]. 168 K(x,((y * x) / y) \ 1) = 1. [para(104(a,1),166(a,1,1))]. 169 T(x \ y,(y / x) \ 1) = x \ y. [hyper(41,a,167,a)]. 170 T(x,((y * x) / y) \ 1) = x. [hyper(41,a,168,a)]. 171 (x \ y) \ (x \ T(y,x)) = K(x \ (x \ y),x). [para(148(a,1),70(a,1,2))]. 172 x * L(y,z \ x,z) = z * ((z \ x) * y). [para(20(a,1),74(a,1,1))]. 173 x * L(y,z,x / z) = (x / z) * (z * y). [para(22(a,1),74(a,1,1))]. 174 (x * (y * z)) \ (x * (y * (z * u))) = L(L(u,z,y),y * z,x). [para(74(a,1),32(a,2,2,2)),flip(a)]. 175 (x * y) * L(L(z,y,x),u,w) = x * (y * L(z,u,w)). [para(49(a,1),74(a,1,2))]. 176 (x * y) * L(z,K(x,y),y * x) = (y * x) * (K(x,y) * z). [para(69(a,1),74(a,1,1))]. 177 L(x \ (y \ z),x,y) = (y * x) \ z. [para(20(a,1),76(a,2,2))]. 178 L(x \ (y * x),x,y) = T(y,y * x). [para(76(a,2),36(a,2)),flip(a)]. 179 (x * y) / L(z \ y,z,x) = x * z. [para(76(a,2),65(a,1,2))]. 180 L(x \ T(y,z),x,z) = (z * x) \ (y * z). [para(82(a,1),76(a,2,2))]. 181 L(x \ (y \ ((y * x) * z)),x,y) = z. [para(76(a,2),62(a,1))]. 182 R(x,x,y) = x. [hyper(24,a,131,a(flip),b,79,a)]. 183 (R(x,y,z) * y) \ ((x * y) * z) = L(z,y,R(x,y,z)). [para(79(a,1),32(a,2,2)),flip(a)]. 184 L(R(x,y,z),u,w) * (y * z) = (L(x,u,w) * y) * z. [para(48(a,1),79(a,1,1))]. 185 R(R(x,y,z),u,w) * (y * z) = (R(x,u,w) * y) * z. [para(50(a,1),79(a,1,1))]. 186 R(T(x,y),x,z) = T(x,y). [para(182(a,1),46(a,2,1))]. 187 L(R(x,L(x,y,z),u),y,z) = L(x,y,z). [para(182(a,1),48(a,1)),flip(a)]. 188 R(R(x,y,z),x,u) = R(x,y,z). [para(182(a,1),50(a,1,1)),flip(a)]. 189 R(R(T(x,y),z,u),x,w) = R(T(x,y),z,u). [para(186(a,1),50(a,1,1)),flip(a)]. 190 (T(x,y) * x) * z = T(x,y) * (x * z). [para(186(a,1),79(a,1,1)),flip(a)]. 191 (R(x,y,z) * x) * u = R(x,y,z) * (x * u). [para(188(a,1),79(a,1,1)),flip(a)]. 192 R(1 / x,x,y) = y / (x * y). [para(17(a,1),80(a,2,1))]. 193 R((x / y) / z,z,y) = x / (z * y). [para(22(a,1),80(a,2,1))]. 194 T((x * y) / (z * y),u) = R(T(x / z,u),z,y). [para(80(a,1),46(a,2,1)),flip(a)]. 195 R(x,x \ 1,y) = y / ((x \ 1) * y). [para(65(a,1),192(a,1,1))]. 196 (x * y) / L(z,y / z,x) = x * (y / z). [para(22(a,1),99(a,1,1,2))]. 197 R(x,x \ y,z) \ (y * z) = (x \ y) * z. [para(20(a,1),101(a,1,2,1))]. 198 R(x,y \ 1,y) / y = x * (1 / y). [para(155(a,1),141(a,1,1,2))]. 199 L(K(x,y) \ ((y * x) \ z),K(x,y),y * x) = (x * y) \ z. [para(69(a,1),177(a,2,1))]. 200 (x * x) \ y = x \ (x \ y). [para(177(a,1),137(a,1))]. 201 L(x \ L(y \ z,y,u),x,u * y) = ((u * y) * x) \ (u * z). [para(76(a,2),177(a,1,1,2))]. 202 x \ (x \ (y * (x * x))) = T(y,x * x). [para(200(a,1),36(a,2)),flip(a)]. 203 L(T(x,y),y,x) = T(x,x * y). [para(36(a,2),178(a,1,1))]. 204 T(x,x * ((y * x) / y)) = L(x,(y * x) / y,x). [para(120(a,1),203(a,1,1)),flip(a)]. 205 x / L(y \ z,y,x / z) = (x / z) * y. [para(22(a,1),179(a,1,1))]. 206 R(x,x \ (y / z),z) = y / ((x \ (y / z)) * z). [para(65(a,1),193(a,1,1))]. 207 R(x,y \ 1,y) / y = x * (y \ 1). [para(155(a,1),198(a,2,2))]. 208 (x * (y \ 1)) * y = R(x,y \ 1,y). [para(207(a,1),22(a,1,1))]. 209 (x * (y \ 1)) \ R(x,y \ 1,y) = y. [para(207(a,1),66(a,1,1))]. 210 R(x / (y \ 1),y \ 1,y) = x * y. [para(22(a,1),208(a,1,1)),flip(a)]. 211 (x * (x * y)) / z = x * (x * (y / z)). [para(22(a,1),85(a,1,1,2,2))]. 212 (x * (x * y)) \ (x * (x * z)) = y \ z. [para(20(a,1),86(a,1,2,2,2))]. 213 x \ ((x * y) * z) = x * ((x \ y) * z). [para(20(a,1),87(a,1,2,1,2))]. 214 L(x,y,z) * x = x * L(x,y,z). [para(81(a,1),109(a,1,2,1)),flip(a)]. 215 L(x / y,z,u) * y = y * L(y \ x,z,u). [para(84(a,1),109(a,1,2,1)),flip(a)]. 216 L(x \ 1,y,z) * x = x * L(x \ 1,y,z). [para(152(a,1),109(a,1,2,1)),flip(a)]. 217 x * T(y,y * x) = L(y,x,y) * x. [para(203(a,1),109(a,1,2))]. 218 (x * L(x,y,z)) / x = L(x,y,z). [hyper(24,a,22,a,b,214,a),flip(a)]. 219 T(x,L(x,y,z)) = x. [hyper(23,a,82,a,b,214,a),flip(a)]. 220 T(x,x * L(x,y,z)) = L(x,L(x,y,z),x). [para(219(a,1),203(a,1,1)),flip(a)]. 221 L(x,x \ y,x) * (x \ y) = (x \ y) * T(x,y). [para(20(a,1),217(a,1,2,2)),flip(a)]. 222 x * R(T(T(y,x),z),u,w) = R(T(y,z),u,w) * x. [para(42(a,1),110(a,1,2,1))]. 223 R(x,y,z) * x = x * R(x,y,z). [para(81(a,1),110(a,1,2,1)),flip(a)]. 224 R(x / y,z,u) * y = y * R(y \ x,z,u). [para(84(a,1),110(a,1,2,1)),flip(a)]. 225 (x \ y) * R((x \ y) \ y,z,u) = R(x,z,u) * (x \ y). [para(83(a,1),110(a,1,2,1))]. 226 x * (x * R(T(y,x * x),z,u)) = R(y,z,u) * (x * x). [para(110(a,1),131(a,1)),flip(a)]. 227 R(x \ 1,y,z) * x = x * R(x \ 1,y,z). [para(152(a,1),110(a,1,2,1)),flip(a)]. 228 T(x,R(x,y,z)) = x. [hyper(23,a,82,a,b,223,a),flip(a)]. 229 T(x \ y,R(y / x,z,u)) = T(y / x,x). [para(228(a,1),112(a,1,1)),flip(a)]. 230 x \ (y * (x * x)) = x * T(y,x * x). [hyper(23,a,20,a,b,136,a),flip(a)]. 231 T(x / (x * y),z) * (x * y) = (x * y) * T(L(y \ 1,y,x),z). [para(142(a,2),139(a,2,2,1))]. 232 T((x * y) / (x * z),u) * (x * z) = (x * z) * T(L(z \ y,z,x),u). [para(76(a,2),139(a,2,2,1))]. 233 (x * T(y,z)) / x = T((x * y) / x,z). [para(19(a,1),140(a,1,1,2,1))]. 234 L(x,y,T(y,z)) = x. [hyper(23,a,74,a,b,190,a),flip(a)]. 235 (x * T(x,y)) * z = T(x,y) * (x * z). [para(116(a,1),190(a,1,1))]. 236 L(x,y / z,z \ y) = x. [para(84(a,1),234(a,1,3))]. 237 L(x,(y * z) / y,z) = x. [para(104(a,1),234(a,1,3))]. 238 x * (x * ((x \ y) / z)) = (x * y) / z. [para(20(a,1),211(a,1,1,2)),flip(a)]. 239 (x * (x * y)) \ (x * x) = y \ 1. [para(18(a,1),212(a,1,2,2))]. 240 (x * y) \ (x * (x * z)) = (x \ y) \ z. [para(20(a,1),212(a,1,1,2))]. 241 T(x,x * (x * y)) = y \ (x * y). [para(212(a,1),36(a,2))]. 242 (x * y) \ (x * x) = (x \ y) \ 1. [para(20(a,1),239(a,1,1,2))]. 243 (x * x) / (y \ 1) = x * (x * y). [para(239(a,1),65(a,1,2))]. 244 ((x * y) * z) \ (x * x) = ((x \ y) * z) \ 1. [para(89(a,1),239(a,1,1))]. 245 T(x,x * (x * y)) = T(x,y). [para(241(a,2),36(a,2)),flip(a)]. 246 T(x,x \ y) = T(x,x * y). [para(20(a,1),245(a,1,2,2)),flip(a)]. 247 T(x,x * (y * x)) = T(x,T(y,x)). [para(82(a,1),245(a,1,2,2))]. 248 T(x * y,(x * y) * (y * x)) = T(x * y,K(y,x)). [para(69(a,1),245(a,1,2,2))]. 249 T(x,x * y) = (x \ y) \ y. [para(246(a,1),83(a,1))]. 250 (x \ y) * T(x,x * y) = y. [para(249(a,2),20(a,1,2))]. 251 T(x / y,x) = ((x / y) \ y) \ y. [para(22(a,1),249(a,1,2))]. 252 x / T(y,y * x) = y \ x. [para(249(a,2),65(a,1,2))]. 253 (x \ y) * ((x \ y) * (T(x,x * y) * z)) = ((x \ y) * y) * z. [para(249(a,2),89(a,1,2,2,1))]. 254 (x \ (x \ y)) * T(x,y) = x \ y. [para(20(a,1),250(a,1,2,2))]. 255 ((x \ y) * (T(x,x * y) * z)) \ (y * z) = a(x \ y,T(x,x * y),z). [para(250(a,1),28(a,2,2,1)),flip(a)]. 256 (x \ y) / T(x,y) = x \ (x \ y). [para(20(a,1),252(a,1,2,2))]. 257 K(x,y) / T(y * x,x * y) = (y * x) \ K(x,y). [para(69(a,1),252(a,1,2,2))]. 258 (x \ (x \ y)) \ 1 = y \ (x * x). [para(20(a,1),242(a,1,1)),flip(a)]. 259 L(x \ y,x,y) = (y \ x) \ 1. [para(242(a,1),76(a,2))]. 260 L(K(x,y),y * x,x * y) = ((x * y) \ (y * x)) \ 1. [para(30(a,2),259(a,1,1))]. 261 L(T(x \ y,z),x,y) = T((y \ x) \ 1,z). [para(259(a,1),44(a,2,1))]. 262 (x \ ((y * x) / y)) \ 1 = ((y * x) / y) \ x. [para(259(a,1),237(a,1))]. 263 x * (x * (y \ 1)) = (x * x) / y. [para(156(a,1),243(a,1,2)),flip(a)]. 264 (x \ (y * y)) \ 1 = y \ (y \ x). [para(258(a,1),156(a,1,1))]. 265 x * ((x \ (x \ y)) * z) = x \ (y * z). [para(20(a,1),213(a,1,2,1)),flip(a)]. 266 L(x \ (y * ((y \ x) * z)),x,y) = z. [para(213(a,1),181(a,1,1,2))]. 267 L(x \ (y * z),x,y) = (y \ x) \ z. [para(20(a,1),266(a,1,1,2,2))]. 268 L(x \ y,x,z) = (z \ x) \ (z \ y). [para(20(a,1),267(a,1,1,2))]. 269 L(x \ (y * z),x,z) = (z \ x) \ T(y,z). [para(82(a,1),267(a,1,1,2))]. 270 L((x * y) \ z,x * y,x) = y \ (x \ z). [para(19(a,1),268(a,2,1))]. 271 L(((x * y) * z) \ u,(x * y) * z,x * (y * z)) = a(x,y,z) \ ((x * (y * z)) \ u). [para(28(a,2),268(a,2,1))]. 272 (x \ y) / L(z \ y,z,x) = x \ z. [para(268(a,2),65(a,1,2))]. 273 L(x \ y,x,x / z) = z \ ((x / z) \ y). [para(66(a,1),268(a,2,1))]. 274 (x \ y) \ (x \ z) = (x * y) \ (x * z). [para(268(a,1),76(a,1))]. 275 L(x \ L(y \ z,y,u),x,u \ y) = ((u \ y) * x) \ (u \ z). [para(268(a,2),177(a,1,1,2))]. 276 (x \ 1) / (y \ x) = x \ (x \ y). [para(143(a,1),272(a,1,2))]. 277 x \ (x \ (x / y)) = (x \ 1) / y. [para(66(a,1),276(a,1,2)),flip(a)]. 278 x * ((x \ 1) / y) = x \ (x / y). [para(277(a,1),20(a,1,2))]. 279 ((x \ 1) / y) \ 1 = (x / y) \ (x * x). [para(277(a,1),258(a,1,1))]. 280 T(x * T(x,y),T(x,y)) = x * T(x,y). [hyper(23,a,82,a,b,235,a(flip)),flip(a)]. 281 (x * T(x,y)) * (x \ z) = T(x,y) * z. [para(20(a,1),235(a,2,2))]. 282 (x * y) / (z \ (x \ y)) = x * (x * z). [para(65(a,1),238(a,1,2,2)),flip(a)]. 283 (x \ (x \ y)) \ z = y \ (x * (x * z)). [para(20(a,1),240(a,1,1)),flip(a)]. 284 (x \ y) \ ((x \ z) * u) = (x * y) \ ((x * z) * u). [para(89(a,1),240(a,1,2)),flip(a)]. 285 x \ (x \ (y * z)) = (x \ (x \ y)) * z. [hyper(23,a,20,a,b,265,a),flip(a)]. 286 (x \ (x \ y)) * (x * x) = T(y,x * x). [hyper(23,a,230,a(flip),b,265,a)]. 287 (x * (y * x)) \ (x * z) = T(y,x) \ (x \ z). [para(36(a,2),274(a,1,1)),flip(a)]. 288 T(x * T(x,y),T(x,y)) = T(x,y) * x. [para(280(a,2),116(a,2)),flip(a)]. 289 x / (y \ (x \ 1)) = x * (x * y). [para(18(a,1),282(a,1,1))]. 290 (x \ (x \ y)) \ y = T(x * x,y). [para(283(a,2),135(a,1))]. 291 (x \ (x \ 1)) * y = x \ (x \ y). [para(17(a,1),285(a,1,2,2)),flip(a)]. 292 (x \ (x \ y)) * (y \ z) = x \ (x \ z). [para(20(a,1),285(a,1,2,2)),flip(a)]. 293 R((x / y) / (z \ (z \ 1)),z \ (z \ 1),y) = x / (z \ (z \ y)). [para(291(a,1),193(a,2,2))]. 294 ((x \ 1) / y) * (x * x) = T(x / y,x * x). [para(277(a,1),286(a,1,1))]. 295 T(T(x,y) * x,T(x,y)) = T(x,y) * x. [para(116(a,2),288(a,1,1))]. 296 (x \ (x \ y)) \ (x \ (x \ z)) = y \ z. [hyper(23,a,20,a,b,292,a),flip(a)]. 297 (x \ y) * ((x * y) \ z) = x \ (x \ z). [para(19(a,1),292(a,1,1,2))]. 298 (T(x,y) \ x) * T(x,y) = x. [hyper(23,a,138,a,b,295,a(flip)),flip(a)]. 299 x / T(x,y) = T(x,y) \ x. [hyper(24,a,22,a,b,298,a),flip(a)]. 300 ((x * y) * z) / T(x * (y * z),a(x,y,z)) = a(x,y,z). [para(67(a,1),100(a,1,1))]. 301 L(x,x \ y,x) = y \ T(x * y,x). [para(138(a,1),75(a,1,2)),flip(a)]. 302 L(L(x,y \ z,y),z,y) = x. [para(75(a,1),266(a,1,1))]. 303 L(L(x,y,z),z * y,z) = x. [para(19(a,1),302(a,1,1,2))]. 304 L(L(x,y,z / y),z,z / y) = x. [para(66(a,1),302(a,1,1,2))]. 305 L(x,y \ 1,y) = x. [para(302(a,1),127(a,1)),flip(a)]. 306 L(x,y,y \ 1) = x. [para(156(a,1),305(a,1,2))]. 307 ((x \ 1) * x) \ ((x \ 1) * y) = x \ y. [para(306(a,1),76(a,1)),flip(a)]. 308 L(L(x,y * z,y),z,y) = x. [para(303(a,1),49(a,1)),flip(a)]. 309 x \ (y \ ((y * x) * z)) = L(z,y * x,y). [para(181(a,1),303(a,1,1)),flip(a)]. 310 R(x,L(x,y,z),u) = L(L(x,y,z),z * y,z). [para(187(a,1),303(a,1,1)),flip(a)]. 311 L((x \ y) \ z,x * y,x) = y \ (x * z). [para(267(a,1),303(a,1,1))]. 312 L(x,y \ z,y) = L(x,y * z,y). [para(302(a,1),303(a,1,1)),flip(a)]. 313 L(x,y * (y * z),y) = L(x,z,y). [para(303(a,1),303(a,1,1))]. 314 L(L(x,y * z,z),T(y,z),z) = x. [para(82(a,1),308(a,1,1,2))]. 315 L(L(x,y * z,z * y),K(y,z),z * y) = x. [para(69(a,1),308(a,1,1,2))]. 316 L(x,x * y,x) = y \ T(x * y,x). [para(301(a,1),312(a,1)),flip(a)]. 317 1 \ ((x \ 1) * y) = x \ y. [para(154(a,1),307(a,1,1))]. 318 (x \ 1) * y = x \ y. [para(317(a,1),59(a,1)),flip(a)]. 320 (x \ y) / y = x \ 1. [hyper(24,a,22,a,b,318,a),flip(a)]. 321 x * ((x \ 1) * y) = y. [hyper(23,a,19,a(flip),b,318,a)]. 322 (x \ 1) * (x * y) = y. [para(318(a,2),19(a,1))]. 323 (x \ (y * z)) \ (((x \ 1) * y) * z) = a(x \ 1,y,z). [para(318(a,1),28(a,2,1)),flip(a)]. 324 ((x * (y \ 1)) * z) / (y \ z) = R(x,y \ 1,z). [para(318(a,1),34(a,2,2)),flip(a)]. 325 T(x \ 1,y) = y \ (x \ y). [para(318(a,1),36(a,2,2))]. 326 x \ T(y,x \ 1) = y * (x \ 1). [para(318(a,1),82(a,1))]. 327 x * T(y \ 1,x) = y \ x. [para(318(a,1),82(a,2))]. 328 (x \ y) * K(y,x \ 1) = y * (x \ 1). [para(318(a,1),69(a,1,1))]. 329 x \ T(T(y,x \ 1),z) = T(y,z) * (x \ 1). [para(318(a,1),108(a,1))]. 330 (x \ 1) \ y = x * y. [para(156(a,1),318(a,1,1)),flip(a)]. 331 (x \ y) * L(z,y,x \ 1) = (x \ 1) * (y * z). [para(318(a,1),74(a,1,1))]. 332 R(x,y \ 1,z) * (y \ z) = (x * (y \ 1)) * z. [para(318(a,1),79(a,1,2))]. 333 (x * (y \ z)) / L(z,y \ 1,x) = x * (y \ 1). [para(318(a,1),99(a,1,1,2))]. 334 R(x,x \ 1,y) = y / (x \ y). [para(318(a,1),195(a,2,2))]. 335 R(x \ 1,y \ 1,y) = (x \ (y \ 1)) * y. [para(318(a,1),208(a,1,1)),flip(a)]. 336 L(x \ 1,y,x \ 1) * y = y * T(x \ 1,x \ y). [para(318(a,1),217(a,1,2,2)),flip(a)]. 337 T(x \ 1,(x \ 1) \ y) = T(x \ 1,x \ y). [para(318(a,1),246(a,2,2))]. 338 (x \ (x \ y)) \ z = (y \ (x * x)) * z. [para(258(a,1),318(a,1,1)),flip(a)]. 339 (x \ (y * y)) \ z = (y \ (y \ x)) * z. [para(264(a,1),318(a,1,1)),flip(a)]. 340 x / (y * x) = y \ 1. [para(19(a,1),320(a,1,1))]. 341 K(x,y) / (x * y) = (y * x) \ 1. [para(30(a,2),320(a,1,1))]. 342 L(x,y,z) / (z * (y * x)) = (z * y) \ 1. [para(32(a,2),320(a,1,1))]. 343 (x / y) \ 1 = y / x. [para(66(a,1),320(a,1,1)),flip(a)]. 344 (x * y) / ((z * x) * y) = R(z,x,y) \ 1. [para(101(a,1),320(a,1,1))]. 345 T(x * y,K(y,x)) / (y * x) = K(y,x) \ 1. [para(122(a,1),320(a,1,1))]. 346 T(x,x * y) / y = (x \ y) \ 1. [para(249(a,2),320(a,1,1))]. 347 x * (y * (x \ 1)) = T(y,x \ 1). [para(82(a,1),321(a,1,2))]. 348 R(x \ 1,x * y,z) = (y * z) / ((x * y) * z). [para(322(a,1),34(a,2,1,1))]. 349 T(x \ 1,x * y) = (x * y) \ y. [para(322(a,1),36(a,2,2))]. 350 R((x \ 1) / y,y,x * z) = z / (y * (x * z)). [para(322(a,1),80(a,2,1))]. 351 L(x * y,x \ 1,y) = (y \ (x \ 1)) \ 1. [para(330(a,1),259(a,1,1))]. 352 L(x * (y * z),x \ 1,y) = (y \ (x \ 1)) \ z. [para(330(a,1),267(a,1,1))]. 353 (x / (y * x)) * z = y \ z. [para(340(a,2),318(a,1,1))]. 354 (x / y) * (y / x) = 1. [para(343(a,1),20(a,1,2))]. 355 K(x \ y,x / y) = 1. [para(343(a,1),167(a,1,2))]. 356 T(x,y / (y * x)) = x. [para(343(a,1),170(a,1,2))]. 357 T(x \ y,x / y) = x \ y. [para(343(a,1),169(a,1,2))]. 358 (x / y) \ z = (y / x) * z. [para(343(a,1),318(a,1,1)),flip(a)]. 359 (x / y) * ((y / x) * z) = z. [para(343(a,1),321(a,1,2,1))]. 360 x * ((y / z) * (z / y)) = x. [para(354(a,2),18(a,1,2))]. 361 K((x * y) \ y,x) = 1. [para(21(a,1),355(a,1,2))]. 362 (x / (x * y)) * y = y * (x / (x * y)). [para(356(a,1),82(a,1,2))]. 363 (x * (y / (y * x))) / x = y / (y * x). [para(356(a,1),100(a,1,2))]. 364 T(x,x * (y / (y * x))) = L(x,y / (y * x),x). [para(356(a,1),203(a,1,1)),flip(a)]. 365 T((x * y) \ y,x) = (x * y) \ y. [hyper(41,a,361,a)]. 366 x * R(x \ (y \ x),z,u) = R(y \ 1,z,u) * x. [para(325(a,1),110(a,1,2,1))]. 367 T(x / y,x \ y) = x / y. [hyper(39,a,357,a)]. 368 (x / y) * (x \ y) = (x \ y) * (x / y). [para(357(a,1),82(a,1,2))]. 369 (x / y) * (z * (y / x)) = T(z,y / x). [para(358(a,1),36(a,2)),flip(a)]. 370 T(x / y,x) = ((y / x) * y) \ y. [para(358(a,1),251(a,2,1))]. 371 ((x \ 1) / y) \ 1 = (y / x) * (x * x). [para(358(a,1),279(a,2))]. 372 T(x \ y,y \ x) = T(y / x,x). [para(367(a,1),112(a,1,1)),flip(a)]. 373 R(x,x \ 1,y) = x. [para(334(a,2),65(a,1))]. 374 R(T(x,y),x \ 1,z) = T(x,y). [para(373(a,1),46(a,2,1))]. 375 R(R(x,y,z),x \ 1,u) = R(x,y,z). [para(373(a,1),50(a,1,1)),flip(a)]. 376 R(T(x / y,y),(x / y) \ 1,z) = y \ x. [para(374(a,2),84(a,1))]. 377 T(x,y) * (x \ 1) = x \ T(x,y). [para(165(a,1),326(a,1,2)),flip(a)]. 378 x \ T(T(y,x \ 1),x) = (x \ (y * (x \ 1))) * x. [para(326(a,1),148(a,1,1,2)),flip(a)]. 379 K(x,y) * ((K(x,y) \ 1) / (x * y)) = K(x,y) \ ((y * x) \ 1). [para(341(a,1),278(a,2,2))]. 380 T(x \ 1,x * (y * y)) = (y \ (y \ (x * (y * y)))) \ 1. [para(349(a,2),258(a,2)),flip(a)]. 381 ((x * y) \ y) * x = x * ((x * y) \ y). [para(365(a,1),82(a,1,2)),flip(a)]. 382 T(x \ y,y \ x) = x \ y. [para(372(a,2),84(a,1))]. 383 T(x \ (x * y),(x * y) \ x) = y. [para(372(a,2),104(a,1))]. 384 (x \ y) * (y \ x) = (y \ x) * (x \ y). [para(382(a,1),82(a,1,2))]. 385 (x \ 1) \ T(x \ 1,x * y) = ((x * y) \ y) * ((x \ 1) \ 1). [para(349(a,1),377(a,1,1)),flip(a)]. 386 T(x,(y * x) \ y) = x. [para(19(a,1),383(a,1,1))]. 387 T(x,y \ (y / x)) = x. [para(22(a,1),386(a,1,2,1))]. 388 ((x * y) \ x) * y = y * ((x * y) \ x). [para(386(a,1),82(a,1,2))]. 389 T(K(x,y),(x * y) \ (y * x)) = K(x,y). [para(69(a,1),386(a,1,2,1))]. 390 R(x,y,z) * (x \ 1) = R(x,y,z) / x. [para(375(a,1),207(a,1,1)),flip(a)]. 391 x \ (y * (y * z)) = (x \ (y * y)) * z. [para(338(a,1),283(a,1)),flip(a)]. 392 (x \ (y * y)) * x = T(y * y,x). [para(338(a,1),290(a,1))]. 393 (x \ (y * y)) * (y \ (y \ z)) = x \ z. [para(338(a,1),296(a,1))]. 394 T(x * x,y * z) \ ((((y * z) \ (x * x)) * y) * z) = a((y * z) \ (x * x),y,z). [para(392(a,1),28(a,2,1)),flip(a)]. 395 L(x \ 1,x,x \ (y * y)) = T(y * y,x) \ (x \ (y * y)). [para(392(a,1),142(a,2,1))]. 396 ((x * y) \ ((x * y) \ ((x * y) * x))) * z = L(y,x,x * y) \ z. [para(32(a,2),339(a,1,1)),flip(a)]. 397 (x / y) * (y * y) = x / (y \ 1). [para(371(a,1),343(a,1))]. 398 (x / (y \ 1)) / (y * y) = x / y. [hyper(24,a,22,a,b,397,a),flip(a)]. 399 (x / y) * (y / (x \ 1)) = x * x. [hyper(23,a,359,a,b,397,a),flip(a)]. 400 (x * y) / (y \ 1) = x * (y * y). [para(21(a,1),397(a,1,1)),flip(a)]. 401 (x * (y \ 1)) / y = x / (y * y). [para(21(a,1),398(a,1,1)),flip(a)]. 402 ((x \ (x \ y)) * x) / (x \ 1) = T(y,x * x). [para(400(a,2),286(a,1))]. 403 T(x / (y * y),y) = y \ (x * (y \ 1)). [para(401(a,1),84(a,1,1))]. 404 T(K(x,y),K(y,x)) = K(x,y). [para(30(a,2),389(a,1,2))]. 405 T(K(x,y),z) * K(y,x) = K(y,x) * T(K(x,y),z). [para(404(a,1),108(a,1,2,1)),flip(a)]. 406 R(K(x,y),z,u) * K(y,x) = K(y,x) * R(K(x,y),z,u). [para(404(a,1),110(a,1,2,1)),flip(a)]. 407 x * ((x \ (y * y)) * z) = y * (y * z). [para(391(a,1),20(a,1,2))]. 408 (((x * y) * x) \ (x * x)) * y = K(x,x * y). [para(391(a,1),30(a,2)),flip(a)]. 409 (x * (y * y)) \ z = y \ (y \ (x \ z)). [hyper(23,a,297,a,b,393,a),flip(a)]. 410 x * ((x \ (y * y)) * z) = (y * y) * z. [para(407(a,2),131(a,2)),flip(a)]. 411 (x * (y * y)) * z = x * (y * (y * z)). [para(407(a,1),89(a,1,2)),flip(a)]. 412 x \ (x \ (y \ ((y * x) * x))) = a(y,x,x). [para(409(a,1),28(a,2)),flip(a)]. 413 (x * (y * y)) \ x = y \ (y \ 1). [para(60(a,1),409(a,2,2,2))]. 414 x \ (x / (y * y)) = y \ (y \ 1). [para(22(a,1),413(a,1,1))]. 415 x / (y \ (y \ 1)) = x * (y * y). [para(413(a,1),65(a,1,2))]. 416 x * (y \ (y \ 1)) = x / (y * y). [para(414(a,1),20(a,1,2))]. 417 (x * (y * y)) * z = x * ((y * y) * z). [para(410(a,1),89(a,1,2)),flip(a)]. 418 (x * (y * (y * z))) / z = x * (y * y). [hyper(24,a,22,a,b,411,a),flip(a)]. 419 (x * (y * (y * z))) \ ((x * (y * y)) * (z * u)) = L(u,z,x * (y * y)). [para(411(a,1),32(a,2,1)),flip(a)]. 420 (x \ (x \ y)) * (x * (x * z)) = T(y,x * x) * z. [para(286(a,1),411(a,1,1)),flip(a)]. 421 L(x,y * y,z) = x. [hyper(23,a,74,a,b,417,a),flip(a)]. 422 R(x,y * y,z) = x. [hyper(24,a,79,a,b,417,a(flip)),flip(a)]. 423 T(x,x * (y * y)) = T(x,y * y). [para(421(a,1),203(a,1)),flip(a)]. 424 L(x,y,y / (z * z)) = x. [para(421(a,1),304(a,1,1))]. 425 L(x,y \ (y \ 1),z) = x. [para(318(a,1),421(a,1,2))]. 426 R(x,y \ (y \ 1),z) = x. [para(318(a,1),422(a,1,2))]. 427 L(x,y,y / (z \ (z \ 1))) = x. [para(318(a,1),424(a,1,3,2))]. 428 (x * (y \ (y \ 1))) * z = x * ((y \ (y \ 1)) * z). [para(425(a,1),74(a,1,2))]. 429 L(x,y,y * (z * z)) = x. [para(415(a,1),427(a,1,3))]. 430 T(x,x \ (y * y)) = T(x,y * y). [para(423(a,1),246(a,2))]. 431 T(x \ 1,x * (y * y)) = T(x \ 1,y * y). [para(330(a,1),430(a,1,2))]. 432 L(x,x,y / x) = y \ (y / (x \ 1)). [para(397(a,1),77(a,1,2)),flip(a)]. 433 (x * y) * (y \ 1) = R(x,y,y \ 1). [para(78(a,1),64(a,1)),flip(a)]. 434 R(x / y,y,y \ 1) = x * (y \ 1). [para(22(a,1),433(a,1,1)),flip(a)]. 435 x * L(y,z * x,z) = z * ((z \ x) * y). [para(312(a,1),172(a,1,2))]. 436 (R(T(x,y),z,u) * x) * w = R(T(x,y),z,u) * (x * w). [para(189(a,1),79(a,1,1)),flip(a)]. 437 T(x \ y,R(y / x,z,u)) = x \ y. [para(229(a,2),84(a,1))]. 438 T((x \ 1) \ y,y * x) = (x \ 1) \ y. [para(210(a,1),437(a,1,2))]. 439 T(x * y,y * x) = (x \ 1) \ y. [para(330(a,1),438(a,1,1))]. 440 (x \ y) \ T(y,x) = L(x,y,x). [para(19(a,1),269(a,1,1)),flip(a)]. 441 T(x,y) / L(y,x,y) = y \ x. [para(440(a,1),65(a,1,2))]. 442 L(x \ (x / y),y,x \ (x / y)) = ((x \ (x / y)) \ y) \ y. [para(387(a,1),440(a,1,2)),flip(a)]. 443 (x * (x * y)) \ z = y \ (x \ (x \ z)). [para(270(a,1),177(a,1)),flip(a)]. 444 x \ (y \ (y \ (z * (y * (y * x))))) = T(z,y * (y * x)). [para(443(a,1),36(a,2)),flip(a)]. 445 L(x \ 1,x,x / y) = y \ (y / x). [para(343(a,1),273(a,2,2))]. 446 x * (y \ ((y * (x \ 1)) * z)) = L(z,y * (x \ 1),y). [para(309(a,1),330(a,1)),flip(a)]. 447 R(x \ y,(y / x) \ 1,z) = x \ y. [para(84(a,1),376(a,1,1))]. 448 R(x \ y,x / y,z) = x \ y. [para(343(a,1),447(a,1,2))]. 449 R(x \ (x * y),x / (x * y),z) = y. [para(448(a,2),19(a,1))]. 450 R(x,y / (y * x),z) = x. [para(19(a,1),449(a,1,1))]. 451 (x * (y / (y * x))) * z = x * ((y / (y * x)) * z). [para(450(a,1),79(a,1,1)),flip(a)]. 452 x \ L(x,y * x,y) = a(y,x,x). [para(309(a,1),412(a,1,2))]. 453 L(x,y * x,y) = x * a(y,x,x). [para(452(a,1),20(a,1,2)),flip(a)]. 454 L(x * a(y,x,x),x,y) = x. [para(453(a,1),308(a,1,1))]. 455 x * ((x \ y) * T(z,y)) = L(z,x * y,x) * y. [para(435(a,1),109(a,1))]. 456 (x * y) \ (x * T(y,x)) = K(x \ (x \ y),x). [para(171(a,1),274(a,1)),flip(a)]. 457 L(x,y,R(y,z,u)) = x. [hyper(23,a,74,a,b,191,a),flip(a)]. 458 R(x,y,z) * ((R(x,y,z) \ x) * u) = x * u. [hyper(23,a,89,a,b,191,a(flip)),flip(a)]. 459 (x * R(x,y,z)) * u = R(x,y,z) * (x * u). [para(223(a,1),191(a,1,1))]. 460 (R(x,y,z) \ x) \ 1 = x \ R(x,y,z). [para(457(a,1),259(a,1)),flip(a)]. 461 (R(x,y,z) \ u) / (x \ u) = R(x,y,z) \ x. [para(457(a,1),272(a,1,2))]. 462 (x \ R(x,y,z)) \ 1 = R(x,y,z) \ x. [para(460(a,1),156(a,1,1))]. 463 (R(x,y,z) \ x) \ u = (x \ R(x,y,z)) * u. [para(460(a,1),318(a,1,1)),flip(a)]. 464 (R(x,y,z) \ x) * ((x \ R(x,y,z)) * u) = u. [para(460(a,1),321(a,1,2,1))]. 465 (x \ R(x,y,z)) \ u = (R(x,y,z) \ x) * u. [para(460(a,1),330(a,1,1))]. 466 T(x,L(x \ 1,y,z)) = x. [hyper(23,a,82,a,b,216,a),flip(a)]. 467 K(x,L(x \ 1,y,z)) = 1. [hyper(40,a,466,a)]. 468 K(x \ 1,L(x,y,z)) = 1. [para(156(a,1),467(a,1,2,1))]. 469 K(L(x,y,z) \ 1,x) = 1. [para(303(a,1),468(a,1,2))]. 470 T(L(x,y,z) \ 1,x) = L(x,y,z) \ 1. [hyper(41,a,469,a)]. 471 x * (L(x,y,z) \ 1) = L(x,y,z) \ x. [para(470(a,1),327(a,1,2))]. 472 R(x / (x * y),z,u) * (x * y) = (x * y) * R(L(y \ 1,y,x),z,u). [para(142(a,2),224(a,2,2,1))]. 473 R((x * y) / (x * z),u,w) * (x * z) = (x * z) * R(L(z \ y,z,x),u,w). [para(76(a,2),224(a,2,2,1))]. 474 R(R(x / y,y,z),u,w) * (y * z) = (y * z) * R((y * z) \ (x * z),u,w). [para(80(a,2),224(a,1,1,1))]. 475 T(x,R(x \ 1,y,z)) = x. [hyper(23,a,82,a,b,227,a),flip(a)]. 476 T(x \ 1,R(x,y,z)) = x \ 1. [para(156(a,1),475(a,1,2,1))]. 477 R(x,y,z) * (x \ 1) = x \ R(x,y,z). [para(476(a,1),327(a,1,2))]. 478 R(x,y,z) / x = x \ R(x,y,z). [para(477(a,1),390(a,1)),flip(a)]. 479 (x \ R(x,y,z)) * x = R(x,y,z). [para(478(a,1),22(a,1,1))]. 480 (x \ R(x,y,z)) \ R(x,y,z) = x. [para(478(a,1),66(a,1,1))]. 481 (x / y) \ R(x / y,y,y \ 1) = (x * (y \ 1)) / (x / y). [para(434(a,1),478(a,1,1)),flip(a)]. 482 (x \ ((y * x) / y)) \ 1 = (y / (y * x)) * x. [para(262(a,2),358(a,1))]. 483 R(x,L(x,y,z),u) = x. [para(310(a,2),303(a,1))]. 484 (x * L(x,y,z)) * u = x * (L(x,y,z) * u). [para(483(a,1),79(a,1,1)),flip(a)]. 485 T(x \ 1,x \ y) = T(x \ 1,x * y). [para(330(a,1),337(a,1,2)),flip(a)]. 486 (x \ T(y,x)) / (x \ 1) = T(y,x * x). [para(148(a,1),402(a,1,1))]. 487 (((x \ y) * x) \ 1) * y = K(x,x * y). [para(244(a,1),408(a,1,1))]. 488 ((x \ y) * x) \ y = K(x,x * y). [para(487(a,1),318(a,1)),flip(a)]. 489 K(x,x \ y) = K(x,x * y). [para(488(a,1),71(a,1)),flip(a)]. 490 K(x,x * (x * y)) = K(x,y). [para(19(a,1),489(a,1,2)),flip(a)]. 491 K(x,x * (y * x)) = K(x,T(y,x)). [para(36(a,2),489(a,1,2)),flip(a)]. 492 K(x,(x * x) / y) = K(x,y \ 1). [para(263(a,1),490(a,1,2))]. 493 K(x \ (x \ y),x) = (x * y) \ (y * x). [para(82(a,1),456(a,1,2)),flip(a)]. 494 K(x \ (x \ y),x) = K(y,x). [para(493(a,2),30(a,2)),flip(a)]. 495 K(x \ y,x) = K(x * y,x). [para(19(a,1),494(a,1,1,2))]. 496 (R(x,y,z) \ x) * R(x,y,z) = x. [hyper(23,a,223,a,b,458,a)]. 497 R(x,y,z) \ (x * u) = (R(x,y,z) \ x) * u. [hyper(23,a,20,a,b,458,a),flip(a)]. 498 x / R(x,y,z) = R(x,y,z) \ x. [hyper(24,a,22,a,b,496,a),flip(a)]. 499 T(R(x,y,z) \ 1,x) = x \ (x / R(x,y,z)). [para(498(a,2),325(a,2,2))]. 500 (x * y) / (z \ ((z * x) * y)) = R(z,x,y) \ z. [para(101(a,1),461(a,1,1))]. 501 x * ((x \ R(x,y,z)) * u) = R(x,y,z) * u. [para(464(a,1),458(a,1,2)),flip(a)]. 502 (x \ ((y * x) / y)) \ 1 = x * (y / (y * x)). [para(482(a,2),362(a,1))]. 503 L(x,L(y,z,u),y) = x. [hyper(23,a,74,a,b,484,a),flip(a)]. 504 x * ((x \ L(x,y,z)) * u) = L(x,y,z) * u. [hyper(23,a,89,a,b,484,a(flip)),flip(a)]. 505 L(x,(y * z) \ y,z \ 1) = x. [para(142(a,1),503(a,1,2))]. 506 (x \ L(x,y,z)) \ 1 = L(x,y,z) \ x. [para(503(a,1),259(a,1)),flip(a)]. 507 (x \ L(x,y,z)) \ u = L(x,y,z) \ (x * u). [para(503(a,1),267(a,1)),flip(a)]. 508 L(x,(y \ z) \ u,z \ (y * u)) = x. [para(267(a,1),503(a,1,2))]. 509 L(x,y,L(y,z,u)) = x. [para(303(a,1),503(a,1,2))]. 510 T(x,x * L(x,y,z)) = x. [para(503(a,1),220(a,2))]. 511 (L(x,y,z) \ x) \ 1 = x \ L(x,y,z). [para(509(a,1),259(a,1)),flip(a)]. 512 (L(x,y,z) \ x) \ u = x \ (L(x,y,z) * u). [para(509(a,1),267(a,1)),flip(a)]. 513 (L(x,y,z) \ u) / (x \ u) = L(x,y,z) \ x. [para(509(a,1),272(a,1,2))]. 514 (x \ L(x,y,z)) * x = L(x,y,z). [para(510(a,1),250(a,1,2))]. 515 L(x,y,z) / x = x \ L(x,y,z). [para(510(a,1),252(a,1,2))]. 516 (x \ L(x,y,z)) \ 1 = x / L(x,y,z). [para(510(a,1),346(a,1,1)),flip(a)]. 517 (x \ L(x,y,z)) \ u = (L(x,y,z) \ x) * u. [para(506(a,1),318(a,1,1)),flip(a)]. 518 (L(x,y,z) \ x) \ u = (x \ L(x,y,z)) * u. [para(506(a,1),330(a,1,1))]. 519 x / L(x,y,z) = L(x,y,z) \ x. [para(516(a,1),506(a,1))]. 520 (L(x,y,z) \ x) * L(x,y,z) = x. [para(519(a,1),22(a,1,1))]. 521 (L(x \ 1,x,x / y) \ (x \ 1)) * (y \ (y / x)) = x \ 1. [para(445(a,1),520(a,1,2))]. 522 (x \ R(x,y,z)) \ u = R(x,y,z) \ (x * u). [para(497(a,2),465(a,2))]. 523 (x * R(x,y,z)) * u = x * (R(x,y,z) * u). [para(501(a,1),89(a,1,2)),flip(a)]. 524 L(x,y,z) \ (x * u) = (L(x,y,z) \ x) * u. [para(517(a,1),507(a,1)),flip(a)]. 525 R(x,R(x,y,z),u) = x. [hyper(24,a,79,a,b,523,a(flip)),flip(a)]. 526 R(x,y,z) * (x * u) = x * (R(x,y,z) * u). [para(523(a,1),459(a,1)),flip(a)]. 527 R(T(x,y),R(x,z,u),w) = T(x,y). [para(525(a,1),46(a,2,1))]. 528 (x \ R(x,y,z)) * (x * u) = R(x,y,z) * u. [hyper(23,a,501,a,b,526,a(flip)),flip(a)]. 529 x * (R(x,y,z) * (x \ u)) = R(x,y,z) * u. [para(20(a,1),526(a,1,2)),flip(a)]. 530 x * (R(x,y,z) * T(u,x)) = R(x,y,z) * (u * x). [para(82(a,1),526(a,1,2)),flip(a)]. 531 (R(x,y,z) * u) / (x * u) = x \ R(x,y,z). [hyper(24,a,22,a,b,528,a),flip(a)]. 532 (x \ R(x,y,z)) * u = R(x,y,z) * (x \ u). [para(20(a,1),528(a,1,2))]. 533 R(x \ R(x,y,z),x * u,w) = ((R(x,y,z) * u) * w) / ((x * u) * w). [para(528(a,1),34(a,2,1,1))]. 534 x \ (R(x,y,z) * u) = R(x,y,z) * (x \ u). [hyper(23,a,20,a,b,529,a),flip(a)]. 535 x / (y * (R(y,z,u) \ x)) = y \ R(y,z,u). [para(20(a,1),531(a,1,1))]. 536 (R(x,y,z) * (x \ u)) / u = x \ R(x,y,z). [para(20(a,1),531(a,1,2))]. 537 ((x * y) * z) / (x * (y * z)) = x \ R(x,y,z). [para(79(a,1),531(a,1,1))]. 538 (R(R(x,y,z),u,w) * (y * z)) / ((x * y) * z) = R(x,y,z) \ R(R(x,y,z),u,w). [para(79(a,1),531(a,1,2))]. 539 x \ (R(y,z,u) * (y \ x)) = T(y \ R(y,z,u),x). [para(532(a,1),36(a,2,2)),flip(a)]. 540 (R(x,y,z) \ x) \ u = R(x,y,z) * (x \ u). [para(532(a,1),463(a,2))]. 541 (x \ R(x,y,z)) \ u = x * (R(x,y,z) \ u). [para(535(a,1),66(a,1,1))]. 542 x / (R(y,z,u) * (y \ x)) = R(y,z,u) \ y. [para(540(a,1),65(a,1,2))]. 543 x * (R(x,y,z) \ 1) = R(x,y,z) \ x. [para(541(a,1),462(a,1))]. 544 (R(x,y,z) \ x) * u = x * (R(x,y,z) \ u). [para(541(a,1),465(a,1)),flip(a)]. 545 T(R(x,y,z) \ 1,x) = R(x,y,z) \ 1. [hyper(23,a,327,a,b,543,a),flip(a)]. 546 T(x,R(x,y,z) \ 1) = x. [hyper(39,a,545,a)]. 547 x \ (x / R(x,y,z)) = R(x,y,z) \ 1. [para(545(a,1),499(a,1)),flip(a)]. 548 T(x,y) * (R(x,z,u) \ 1) = R(x,z,u) \ T(x,y). [para(546(a,1),329(a,1,2,1)),flip(a)]. 549 (x * y) \ ((z * x) * y) = R(T(z,x * y),x,y). [para(111(a,2),46(a,2)),flip(a)]. 550 (x * (x * (y * z))) / (y * z) = R(x * x,y,z). [para(51(a,1),134(a,1,1))]. 551 x \ ((x * y) * (1 / y)) = a(x,y,1 / y). [para(18(a,1),164(a,1,1))]. 552 x \ ((x * y) * (y \ 1)) = a(x,y,1 / y). [para(155(a,1),551(a,1,2,2))]. 553 x \ ((x * y) * (y \ 1)) = a(x,y,y \ 1). [para(155(a,1),552(a,2,3))]. 554 a(x / y,y,y \ 1) = (x / y) \ (x * (y \ 1)). [para(22(a,1),553(a,1,2,1)),flip(a)]. 555 T((x * y) / (z * y),z) = R(z \ x,z,y). [para(84(a,1),194(a,2,1))]. 556 T(T((x * y) / (z * y),u),z) = T(R(z \ x,z,y),u). [para(555(a,1),42(a,1,1)),flip(a)]. 557 T(x,x * ((y * x) / y)) = x. [para(204(a,2),237(a,1))]. 558 ((x * y) / x) / y = y \ ((x * y) / x). [para(557(a,1),252(a,1,2))]. 559 L(x,x * y,x) * (x \ y) = (x \ y) * T(x,y). [para(312(a,1),221(a,1,1))]. 560 (x \ y) * L(z,y,x \ 1) = x \ (y * z). [para(331(a,2),318(a,1))]. 561 (T(x,y) * (x \ 1)) * z = T(x,y) * (x \ z). [para(374(a,1),332(a,1,1)),flip(a)]. 562 (x \ T(x,y)) * z = T(x,y) * (x \ z). [para(377(a,1),561(a,1,1))]. 563 (T(x,y) * (x \ z)) / z = x \ T(x,y). [hyper(24,a,22,a,b,562,a),flip(a)]. 564 x * (T(x,y) * (x \ x)) = T(x * T(x,y),x). [para(562(a,1),138(a,1,2))]. 565 (T(x,y) * z) / (x * z) = x \ T(x,y). [para(19(a,1),563(a,1,1,2))]. 566 (x \ T(x,y)) \ (T(x,y) * z) = x * z. [para(565(a,1),66(a,1,1))]. 567 (x \ T(x,y)) \ z = x * (T(x,y) \ z). [para(20(a,1),566(a,1,2))]. 568 T(x * T(x,y),x) = x * (T(x,y) * 1). [para(60(a,1),564(a,1,2,2)),flip(a)]. 569 T(x * T(x,y),x) = x * T(x,y). [para(18(a,1),568(a,2,2))]. 571 T(x,x * T(x,y)) = x. [hyper(39,a,569,a)]. 572 T(x,y) / x = x \ T(x,y). [para(571(a,1),252(a,1,2))]. 573 (x \ T(x,y)) \ z = (x / T(x,y)) * z. [para(572(a,1),358(a,1,1))]. 574 (x \ T(x,y)) \ z = (T(x,y) \ x) * z. [para(299(a,1),573(a,2,1))]. 575 (T(x,y) \ x) * (T(x,y) * z) = x * z. [para(574(a,1),566(a,1))]. 576 (T(x,y) \ x) * z = x * (T(x,y) \ z). [para(574(a,1),567(a,1))]. 577 (x * y) / (T(x,z) * y) = T(x,z) \ x. [hyper(24,a,22,a,b,575,a),flip(a)]. 578 x * (T(x,y) \ 1) = T(x,y) \ x. [hyper(24,a,18,a,b,576,a),flip(a)]. 579 K(x,T(x,y) \ 1) = 1. [hyper(23,a,328,a,b,576,a),flip(a)]. 580 T(x,T(x,y) \ 1) = x. [hyper(41,a,579,a)]. 581 T(x,y) * (T(x,z) \ 1) = T(x,z) \ T(x,y). [para(580(a,1),329(a,1,2,1)),flip(a)]. 582 x \ (T(x,y) \ x) = T(x,y) \ 1. [hyper(23,a,20,a,b,578,a),flip(a)]. 583 ((T(x,y) \ x) * z) / (T(x,y) \ z) = R(x,T(x,y) \ 1,z). [para(578(a,1),324(a,1,1,1))]. 584 R(x \ 1,x * y,z) = R(x,y,z) \ 1. [para(348(a,2),344(a,1))]. 585 R(x,x \ y,z) \ 1 = R(x \ 1,y,z). [para(20(a,1),584(a,1,2)),flip(a)]. 586 (x * y) / (z * ((z \ x) * y)) = R(z,x,y) \ z. [para(213(a,1),500(a,1,2))]. 587 T(x \ R(x,y,z),x * (y * z)) = (x * (y * z)) \ ((x * y) * z). [para(537(a,1),84(a,1,1))]. 588 R(x * x,y,z) = x * x. [para(550(a,1),132(a,1))]. 589 R(T(x * x,y),z,u) = T(x * x,y). [para(588(a,1),46(a,2,1))]. 591 T(x * x,y) \ (z * u) = (T(x * x,y) \ z) * u. [para(589(a,1),197(a,1,1))]. 592 a(x / y,y,y \ 1) = (y / x) * (x * (y \ 1)). [para(554(a,2),358(a,1))]. 593 (x * y) / (z * ((z \ y) * T(x,y))) = R(z,y,T(x,y)) \ z. [para(82(a,1),586(a,1,1))]. 594 a(x,y,z) = (x \ (y * z)) \ ((x \ y) * z). [para(284(a,2),28(a,2))]. 595 (x \ (y * z)) * a(x,y,z) = (x \ y) * z. [para(594(a,2),20(a,1,2))]. 596 (x \ (y * (x \ 1))) * x = T(y,x) * (x \ 1). [para(378(a,1),329(a,1))]. 597 (T(x,y) * (y \ 1)) / y = y \ (x * (y \ 1)). [hyper(24,a,22,a,b,596,a),flip(a)]. 598 x \ (y * (x \ 1)) = T(y,x) / (x * x). [para(597(a,1),401(a,1))]. 599 x \ ((x * (x * y)) * (x \ 1)) = (x * (y * x)) / (x * x). [para(103(a,1),598(a,2,1))]. 600 T(x,y) / (y * y) = T(x / (y * y),y). [para(598(a,1),403(a,2)),flip(a)]. 601 x * ((y \ (y \ 1)) * z) = (x / (y * y)) * z. [para(416(a,1),428(a,1,1)),flip(a)]. 602 (x / (y * y)) * z = x * (y \ (y \ z)). [para(291(a,1),601(a,1,2)),flip(a)]. 603 L(x,y / (y * z),z) = x. [hyper(23,a,74,a,b,451,a),flip(a)]. 604 (x * (y / (y * x))) \ z = (y / (y * x)) \ (x \ z). [para(603(a,1),177(a,1)),flip(a)]. 605 T(x,x * (y / (y * x))) = x. [para(603(a,1),364(a,2))]. 606 (x * (y / (y * x))) \ z = ((y * x) / y) * (x \ z). [para(604(a,2),358(a,1))]. 607 x * (x * ((y * z) / ((x * y) * z))) = R(x,x * y,z). [para(95(a,1),211(a,1)),flip(a)]. 608 L(R(x,x,y),z,u) * (x * y) = (x * L(x,z,u)) * y. [para(214(a,1),184(a,2,1))]. 609 L(K(x,y),y * x,x * y) = K(y,x) \ 1. [para(30(a,2),260(a,2,1))]. 610 (x \ (y * z)) \ ((x \ y) * z) = a(x \ 1,y,z). [para(318(a,1),323(a,1,2,1))]. 611 a(x \ 1,y,z) = a(x,y,z). [para(610(a,1),594(a,2)),flip(a)]. 612 a(x / y,z,u) = a(y / x,z,u). [para(343(a,1),611(a,1,1))]. 613 L(x \ 1,y,x \ 1) * y = y * T(x \ 1,x * y). [para(485(a,1),336(a,2,2))]. 614 T(T((x * y) / (z * y),u),z) = R(T(z \ x,u),z,y). [para(556(a,2),46(a,2)),flip(a)]. 615 x * (x * (R(x,y,z) \ 1)) = R(x,x * y,z). [para(344(a,1),607(a,1,2,2))]. 616 (x * x) / R(x,y,z) = R(x,x * y,z). [para(615(a,1),263(a,1)),flip(a)]. 617 x * (R(x,y,z) \ x) = R(x,x * y,z). [para(543(a,1),615(a,1,2))]. 618 x \ R(x,x * y,z) = R(x,y,z) \ x. [hyper(23,a,20,a,b,617,a),flip(a)]. 619 x * (R(x,x * y,z) \ x) = R(x,(x * x) * y,z). [para(131(a,2),617(a,2,2))]. 620 x / R(x,x * y,z) = x \ R(x,y,z). [para(617(a,1),535(a,1,2))]. 621 (R(x,y,z) \ x) * x = R(x,x * y,z). [para(617(a,1),544(a,2))]. 622 R(x,x * y,z) \ x = x \ R(x,y,z). [para(620(a,1),498(a,1)),flip(a)]. 623 R(x,x * y,z) \ 1 = x \ (x \ R(x,y,z)). [para(620(a,1),547(a,1,2)),flip(a)]. 624 x \ R(x,x \ y,z) = R(x,y,z) \ x. [para(20(a,1),622(a,1,1,2)),flip(a)]. 625 x * (R(x,x * y,z) \ u) = (x \ R(x,y,z)) * u. [para(622(a,1),544(a,1,1)),flip(a)]. 626 R(x,(x * x) * y,z) = x * (x \ R(x,y,z)). [para(622(a,1),619(a,1,2)),flip(a)]. 627 R(x,(x * x) * y,z) = R(x,y,z). [para(626(a,2),20(a,1))]. 628 R(x,x * (x * y),z) = R(x,y,z). [para(131(a,1),627(a,1,2))]. 629 R(x,x \ y,z) = R(x,x * y,z). [para(20(a,1),628(a,1,2,2)),flip(a)]. 630 R(x,x * y,z) \ (y * z) = (x \ y) * z. [para(629(a,1),197(a,1,1))]. 631 R(x,x * (y / z),z) = y / ((x \ (y / z)) * z). [para(629(a,1),206(a,1))]. 632 R(x,x * y,z) \ 1 = R(x \ 1,y,z). [para(629(a,1),585(a,1,1))]. 633 R(x,x * y,z) = R(x \ 1,y,z) \ 1. [para(632(a,1),156(a,1,1)),flip(a)]. 634 x \ (x \ R(x,y,z)) = R(x \ 1,y,z). [para(632(a,1),623(a,1)),flip(a)]. 635 x * R(x \ 1,y,z) = x \ R(x,y,z). [para(634(a,1),20(a,1,2))]. 636 x * (R(x \ 1,y,z) * u) = x \ (R(x,y,z) * u). [para(634(a,1),265(a,1,2,1))]. 637 x * (R(x,x * y,z) \ u) = R(x,y,z) * (x \ u). [para(625(a,2),532(a,1))]. 638 x * (R(x \ 1,y,z) * u) = R(x,y,z) * (x \ u). [para(636(a,2),534(a,1))]. 639 x * (y * R(y \ (x \ y),z,u)) = R(x,z,u) * (x \ y). [para(366(a,2),638(a,1,2))]. 640 (x * L(x,y,z)) * u = L(x,y,z) * (x * u). [para(182(a,1),608(a,1,1,1)),flip(a)]. 641 L(x,y,z) \ ((x * L(x,y,z)) * u) = x * u. [hyper(23,a,20,a,b,640,a(flip)),flip(a)]. 642 L(x,y,z) * (x * u) = x * (L(x,y,z) * u). [para(640(a,1),484(a,1))]. 643 L(x,y,z) \ (x * (L(x,y,z) * u)) = x * u. [para(484(a,1),641(a,1,2))]. 644 x * (L(x,y,z) * (x \ u)) = L(x,y,z) * u. [para(20(a,1),642(a,1,2)),flip(a)]. 645 L(x,y,z) * (x * (L(x,y,z) \ u)) = x * u. [para(20(a,1),642(a,2,2))]. 646 (L(x,y,z) \ x) * (L(x,y,z) * u) = x * u. [para(643(a,1),524(a,1)),flip(a)]. 647 (x \ L(x,y,z)) * u = L(x,y,z) * (x \ u). [hyper(23,a,504,a,b,644,a),flip(a)]. 648 (x * y) / (x * (L(x,z,u) \ y)) = L(x,z,u). [hyper(24,a,22,a,b,645,a),flip(a)]. 649 (x * y) / (L(x,z,u) * y) = L(x,z,u) \ x. [hyper(24,a,22,a,b,646,a),flip(a)]. 650 (L(x,y,z) \ x) * u = x * (L(x,y,z) \ u). [para(20(a,1),646(a,1,2))]. 651 (L(x,y,z) \ x) \ u = L(x,y,z) * (x \ u). [para(647(a,1),518(a,2))]. 652 T(x,L(x,y,z) \ x) = x. [hyper(23,a,82,a,b,650,a),flip(a)]. 653 K(x,L(x,y,z) \ x) = 1. [hyper(40,a,652,a)]. 654 T(x \ 1,x * (y * y)) = T(x,y * y) \ 1. [para(202(a,1),380(a,2,1))]. 655 T(x,y * y) \ 1 = T(x \ 1,y * y). [para(654(a,1),431(a,1))]. 656 L(x,y,R(T(y,z),u,w)) = x. [hyper(23,a,74,a,b,436,a),flip(a)]. 657 L(x,y,R((y \ z) \ z,u,w)) = x. [para(83(a,1),656(a,1,3,1))]. 658 x \ ((y \ (y \ z)) * (y * (y * x))) = T(z,y * (y * x)). [para(285(a,1),444(a,1,2))]. 659 x \ (x * (x * (y * (x \ 1)))) = (x * (y * x)) / (x * x). [para(51(a,1),599(a,1,2))]. 660 x \ (T(y,z * z) * x) = T(y,z * (z * x)). [para(420(a,1),658(a,1,2))]. 661 T(T(x,y * y),z) = T(x,y * (y * z)). [para(660(a,1),36(a,2))]. 662 T(T(x,y),z * z) = T(x,z * (z * y)). [para(661(a,1),42(a,1)),flip(a)]. 663 x \ (x * T(y,x \ 1)) = (x * (y * x)) / (x * x). [para(347(a,1),659(a,1,2,2))]. 664 (x * (y * x)) / (x * x) = T(y,x \ 1). [para(663(a,1),19(a,1))]. 665 T(x * y,x) / (x * x) = T(x \ y,x \ 1). [para(138(a,1),664(a,1,1))]. 666 T((x * y) / (x * x),x) = T(x \ y,x \ 1). [para(665(a,1),600(a,1)),flip(a)]. 667 (x * (x * ((y * z) * u))) / (z * u) = R(x * (x * y),z,u). [para(51(a,1),94(a,1,1))]. 668 (x * (y \ 1)) / (x / y) = (x / y) \ (x * (y \ 1)). [para(434(a,1),481(a,1,2)),flip(a)]. 669 (x * (y \ 1)) / (x / y) = (y / x) * (x * (y \ 1)). [para(668(a,2),358(a,1))]. 670 (x * (T(x,y) \ z)) / (T(x,y) \ z) = R(x,T(x,y) \ 1,z). [para(576(a,1),583(a,1,1))]. 671 (x * y) / (L(x,z * y,z) * y) = R(z,y,T(x,y)) \ z. [para(455(a,1),593(a,1,2))]. 672 R(x,y,T(z,y)) \ x = L(z,x * y,x) \ z. [para(671(a,1),649(a,1))]. 673 (R(x,y,T(z,y)) \ x) \ 1 = z \ L(z,x * y,x). [para(672(a,2),511(a,1,1))]. 674 L(x,y * (y * z),y) \ x = y \ R(y,z,T(x,y * z)). [para(672(a,1),622(a,1))]. 676 x \ R(x,y,T(z,y)) = z \ L(z,x * y,x). [para(673(a,1),460(a,1)),flip(a)]. 677 R(x,y,T(z,y)) = x * (z \ L(z,x * y,x)). [para(676(a,1),20(a,1,2)),flip(a)]. 678 R(x,x * y,T(z,x * y)) = x * (z \ L(z,y,x)). [para(313(a,1),677(a,2,2,2))]. 679 R(x,y,T(z,x * y)) \ x = z \ L(z,y,x). [hyper(23,a,617,a,b,678,a(flip)),flip(a)]. 680 (x \ L(x,y,z)) * R(z,y,T(x,z * y)) = z. [para(679(a,1),496(a,1,1))]. 681 L(x,y,z) \ x = z \ R(z,y,T(x,z * y)). [para(313(a,1),674(a,1,1))]. 682 L(x,y,z) * (z \ R(z,y,T(x,z * y))) = x. [para(681(a,1),20(a,1,2))]. 683 R(x,y,T(z,x * y)) = x * (L(z,y,x) \ z). [para(681(a,2),20(a,1,2)),flip(a)]. 684 (x \ R(x,y,T(z,x * y))) * L(z,y,x) = z. [para(681(a,1),520(a,1,1))]. 685 L(x,R(y,z,u),T(y,w)) * (T(y,w) \ T(y,w)) = x. [para(527(a,1),682(a,1,2,2))]. 686 R(x,y,T(z,x * y)) * (x \ L(z,y,x)) = z. [para(684(a,1),532(a,1)),flip(a)]. 687 L(x,R(y,z,u),T(y,w)) * 1 = x. [para(60(a,1),685(a,1,2))]. 688 L(x,R(y,z,u),T(y,w)) = x. [hyper(24,a,18,a,b,687,a)]. 690 L(x,R(y / z,u,w),z \ y) = x. [para(84(a,1),688(a,1,3))]. 691 T(R(x,y,z),T(x,u)) / T(x,u) = T(x,u) \ R(x,y,z). [para(688(a,1),441(a,1,2))]. 692 R(T(x,T(x,y)),z,u) / T(x,y) = T(x,y) \ R(x,z,u). [para(46(a,2),691(a,1,1))]. 693 R(x,y,z) / T(x,u) = T(x,u) \ R(x,y,z). [para(115(a,1),692(a,1,1,1))]. 694 x * (x * (((y * z) * u) / (z * u))) = R(x * (x * y),z,u). [para(667(a,1),211(a,1)),flip(a)]. 695 R(x,T(x,y) \ 1,z) = x. [para(670(a,1),21(a,1))]. 696 R(x * (x * y),z,u) = x * (x * R(y,z,u)). [para(34(a,2),694(a,1,2,2)),flip(a)]. 697 x * (x * R(T(y,x),z,u)) = R(x * (y * x),z,u). [para(82(a,1),696(a,1,1,2)),flip(a)]. 698 R(x * (x * T(y,x * x)),z,u) = R(y,z,u) * (x * x). [para(696(a,2),226(a,1))]. 699 R(x * (y * x),z,u) = x * (R(y,z,u) * x). [para(110(a,1),697(a,1,2)),flip(a)]. 700 x \ R(x * (y * x),z,u) = R(y,z,u) * x. [hyper(23,a,20,a,b,699,a(flip)),flip(a)]. 701 (x * (y * x)) \ R(x * (z * x),u,w) = T(y,x) \ (x \ (R(z,u,w) * x)). [para(699(a,2),287(a,1,2))]. 702 x \ R(x * y,z,u) = R(y / x,z,u) * x. [para(22(a,1),700(a,1,2,1,2))]. 703 x \ R(x * y,z,u) = x * R(x \ y,z,u). [para(702(a,2),224(a,1))]. 704 L(x \ (y * R(y \ z,u,w)),x,y) = (y * x) \ R(y * z,u,w). [para(703(a,1),177(a,1,1,2))]. 705 R(x * (y * y),z,u) = R(x,z,u) * (y * y). [para(136(a,1),698(a,1,1))]. 706 (x \ 1) \ T(x \ 1,x * y) = ((x * y) \ y) * x. [para(156(a,1),385(a,2,2))]. 707 (x \ 1) \ T(x \ 1,x * y) = x * ((x * y) \ y). [para(706(a,2),381(a,1))]. 708 (x * y) * T(L(y \ 1,y,x),z) = (x * y) * T((x * y) \ x,z). [para(231(a,1),139(a,1))]. 709 R((x / y) * (z * z),z \ (z \ 1),y) = x / (z \ (z \ y)). [para(415(a,1),293(a,1,1))]. 710 x / (y \ (y \ z)) = (x / z) * (y * y). [para(709(a,1),426(a,1))]. 711 (x / (y * z)) * (y * y) = x / (y \ z). [para(19(a,1),710(a,1,2,2)),flip(a)]. 712 (x * y) / (z \ y) = R(x / z,z,y) * (z * z). [para(80(a,2),711(a,1,1)),flip(a)]. 713 R((x / y) * (y * y),y,z) = (x * z) / (y \ z). [para(712(a,2),705(a,2))]. 714 R(x / (y \ 1),y,z) = (x * z) / (y \ z). [para(397(a,1),713(a,1,1))]. 715 R(x,y,z) = ((x * (y \ 1)) * z) / (y \ z). [para(21(a,1),714(a,1,1))]. 716 R(L(x,y,z) \ x,x,u) = ((L(x,y,z) \ 1) * u) / (x \ u). [para(513(a,1),714(a,1,1))]. 717 R(x,y \ 1,z) = R(x,y,z). [para(715(a,2),324(a,1)),flip(a)]. 718 R(x,y,y) / y = x * (y \ 1). [para(717(a,1),207(a,1,1))]. 719 (x * (y \ 1)) \ R(x,y,y) = y. [para(717(a,1),209(a,1,2))]. 720 R(x / (y \ 1),y,y) = x * y. [para(717(a,1),210(a,1))]. 721 R(x,T(x,y),z) = x. [para(717(a,1),695(a,1))]. 722 (x * T(x,y)) * z = x * (T(x,y) * z). [para(721(a,1),79(a,1,1)),flip(a)]. 723 R(T(x / (y \ 1),z),y,y) / y = (y \ 1) * T((y \ 1) \ x,z). [para(718(a,2),139(a,1))]. 724 R(L(x / (y \ 1),z,u),y,y) / y = (y \ 1) * L((y \ 1) \ x,z,u). [para(718(a,2),215(a,1))]. 725 (T(x,y) * (R(x,z,u) \ 1)) \ T(x,y) = R(x,z,u). [para(527(a,1),719(a,1,2))]. 726 R(T(x / (y \ 1),z),y,y) = T(x * y,z). [para(720(a,1),46(a,2,1))]. 727 L(x,T(y,z),y) = x. [hyper(23,a,74,a,b,722,a),flip(a)]. 728 T(x,y) * (x * z) = x * (T(x,y) * z). [para(722(a,1),235(a,1)),flip(a)]. 729 x * (T(x,y) * (x \ z)) = T(x,y) * z. [para(722(a,1),281(a,1))]. 730 L(x,y,(z * y) / z) = x. [para(104(a,1),727(a,1,2))]. 731 L(x,(y \ z) \ z,y) = x. [para(83(a,1),727(a,1,2))]. 732 x \ (T(x,y) * z) = T(x,y) * (x \ z). [hyper(23,a,20,a,b,729,a),flip(a)]. 733 x \ (T(x,y) * z) = (x \ T(x,y)) * z. [para(732(a,2),562(a,2)),flip(a)]. 734 (R(x,y,z) \ T(x,u)) \ T(x,u) = R(x,y,z). [para(548(a,1),725(a,1,1))]. 735 R(L(x,y,z) \ x,x,u) = (L(x,y,z) \ u) / (x \ u). [para(318(a,1),716(a,2,1))]. 736 R(L(x,y,z) \ x,x,u) = L(x,y,z) \ x. [para(735(a,2),513(a,1))]. 738 L(x,y,y * x) \ z = ((y * x) \ y) * z. [para(19(a,1),396(a,1,1,2)),flip(a)]. 739 a(x,y,z) = T(x \ R(x,y,z),x * (y * z)). [para(587(a,2),28(a,2))]. 740 T(T(x \ R(x,y,z),u),x * (y * z)) = T(a(x,y,z),u). [para(739(a,2),42(a,1,1)),flip(a)]. 741 a(x,y,z) = T(T(R(x,y,z) / x,x * (y * z)),x). [para(739(a,2),112(a,2)),flip(a)]. 742 T((x * (y \ R(y,z,u))) / x,y * (z * u)) = (x * a(y,z,u)) / x. [para(739(a,2),233(a,1,1,2)),flip(a)]. 743 T(R(x,y,z) \ R(R(x,y,z),u,x),x * (R(x,y,z) * T(u,x))) = a(R(x,y,z),u,x). [para(530(a,2),739(a,2,2)),flip(a)]. 744 T(T((R(x,y,z) * u) / (x * u),x * (y * z)),x) = R(a(x,y,z),x,u). [para(739(a,2),614(a,2,1))]. 745 a(x,y,z) = T(T(x \ R(x,y,z),x * (y * z)),x). [para(478(a,1),741(a,2,1,1))]. 746 T(a(x,y,z),x) = a(x,y,z). [para(739(a,2),745(a,2,1)),flip(a)]. 747 a(x,y,z) * x = x * a(x,y,z). [para(746(a,1),82(a,1,2)),flip(a)]. 748 (x * a(x,y,z)) / x = a(x,y,z). [para(746(a,1),105(a,1,1,2))]. 749 ((x * (x * y)) * a(x * (x * y),z,u)) / y = a(x * (x * y),z,u) * (x * x). [para(747(a,1),418(a,1,1))]. 750 (x \ y) \ R(x \ z,u,w) = (x * y) \ R(x * z,u,w). [para(704(a,1),267(a,1)),flip(a)]. 751 (x * y) * T((x * y) \ x,z) = (x * y) * L(T(y \ 1,z),y,x). [para(44(a,2),708(a,1,2)),flip(a)]. 752 (x \ 1) * T((x \ 1) \ y,z) = T(y * x,z) / x. [para(726(a,1),723(a,1,1)),flip(a)]. 753 (x \ 1) * T(x * y,z) = T(y * x,z) / x. [para(330(a,1),752(a,1,2,1))]. 754 T(x * y,z) / y = y \ T(y * x,z). [para(753(a,1),318(a,1))]. 755 x \ T(x * (y / x),z) = T(y,z) / x. [para(22(a,1),754(a,1,1,1)),flip(a)]. 756 T(x * y,y) / y = (y \ x) * y. [para(754(a,2),146(a,1))]. 757 ((x \ y) * x) * x = T(y * x,x). [para(756(a,1),22(a,1,1))]. 758 T((x * y) * x,x) = (y * x) * x. [para(19(a,1),757(a,1,1,1)),flip(a)]. 759 (x * T(y * x,x)) / (x * x) = T((x \ y) * x,x \ 1). [para(757(a,1),664(a,1,1,2))]. 760 T((x \ y) * x,x \ 1) = ((y * x) * x) / (x * x). [para(82(a,1),759(a,1,1)),flip(a)]. 761 T((x \ y) * x,x \ 1) = R(y,x,x). [para(760(a,2),34(a,2)),flip(a)]. 762 (x * y) * T((x * y) \ x,z) = x * (y * T(y \ 1,z)). [para(751(a,2),74(a,1))]. 763 (x * (x * (y * z))) \ (x * (x * (y * (z * u)))) = L(u,z,x * (x * y)). [para(51(a,1),92(a,1,2))]. 764 (x * y) * T(L(y \ z,y,x),u) = (x * y) * T((x * y) \ (x * z),u). [para(232(a,1),139(a,1))]. 765 (x * y) * R(L(y \ 1,y,x),z,u) = (x * y) * R((x * y) \ x,z,u). [para(472(a,1),224(a,1))]. 766 L(R(x / (y \ 1),y,y),z,u) / y = (y \ 1) * L((y \ 1) \ x,z,u). [para(48(a,1),724(a,1,1))]. 767 T(T(x \ R(x,y,z),x * (y * z)),x) = R(a(x,y,z),x,u). [para(531(a,1),744(a,1,1,1))]. 769 R(a(x,y,z),x,u) = a(x,y,z). [para(767(a,1),745(a,2)),flip(a)]. 770 (a(x,y,z) * x) * u = a(x,y,z) * (x * u). [para(769(a,1),79(a,1,1)),flip(a)]. 771 L(x,y,a(y,z,u)) = x. [hyper(23,a,74,a,b,770,a),flip(a)]. 772 (x * a(x,y,z)) * u = a(x,y,z) * (x * u). [para(747(a,1),770(a,1,1))]. 773 L(x,y,z * (z * u)) = (u * y) \ (u * (y * x)). [para(763(a,1),212(a,1))]. 774 L(x,y,z * (z * u)) = L(x,y,u). [para(773(a,2),32(a,2)),flip(a)]. 776 L(x,y,z \ u) = L(x,y,z * u). [para(20(a,1),774(a,1,3,2)),flip(a)]. 777 L(x,y,(z / u) * z) = L(x,y,u). [para(22(a,1),774(a,1,3,2))]. 778 L(x,y,z * (u * z)) = L(x,y,T(u,z)). [para(82(a,1),774(a,1,3,2))]. 779 L(x,y,(z * u) * (u * z)) = L(x,y,K(u,z)). [para(69(a,1),774(a,1,3,2))]. 780 L(x,y,z * ((z \ u) * w)) = L(x,y,z * ((z * u) * w)). [para(89(a,1),774(a,1,3,2)),flip(a)]. 781 L(x,y,(z \ u) * w) = L(x,y,(z * u) * w). [para(89(a,1),774(a,1,3)),flip(a)]. 782 L(x,y,(z \ (z \ u)) * (z \ u)) = L(x,y,T(z,u)). [para(254(a,1),774(a,1,3,2))]. 783 L(x,y,(z * z) / u) = L(x,y,u \ 1). [para(263(a,1),774(a,1,3))]. 784 L(x,y,z / u) = L(x,y,u / z). [para(360(a,1),774(a,1,3))]. 785 L(x,y,z * L(z,u * z,u)) = L(x,y,a(u,z,z)). [para(453(a,2),774(a,1,3,2))]. 786 L(x,y,R(z * (z * u),w,v5)) = L(x,y,R(u,w,v5)). [para(696(a,2),774(a,1,3))]. 787 L(x,y,z \ 1) = L(x,y,z). [para(18(a,1),776(a,2,3))]. 788 L(x,y / z,z * y) = x. [para(776(a,1),236(a,1))]. 789 L(x,y,T(z / u,z)) = L(x,y,((u / z) * u) * u). [para(370(a,2),776(a,1,3))]. 790 L(x,y,y \ (z * z)) = x. [para(776(a,2),429(a,1))]. 791 L(x,(y \ z) \ u,z * (y * u)) = x. [para(776(a,1),508(a,1))]. 792 L(x \ (x / y),y,x * (x / y)) = ((x \ (x / y)) \ y) \ y. [para(776(a,1),442(a,1))]. 793 L(x,R(y / z,u,w),z * y) = x. [para(776(a,1),690(a,1))]. 794 L(x \ L(y \ z,y,u),x,u * y) = ((u \ y) * x) \ (u \ z). [para(776(a,1),275(a,1))]. 795 T(x * x,y) \ (y \ (x * x)) = y \ 1. [para(790(a,1),395(a,1)),flip(a)]. 796 L(x,L(y \ 1,z,u),y) = x. [para(787(a,1),503(a,1))]. 797 L(x,(y * z) \ y,z) = x. [para(787(a,1),505(a,1))]. 798 (x \ y) * L(z,y,x) = x \ (y * z). [para(787(a,1),560(a,1,2))]. 799 x * T(y \ 1,y * x) = L(y \ 1,x,y) * x. [para(787(a,1),613(a,1,1)),flip(a)]. 800 L(x,y \ z,z \ y) = x. [para(20(a,1),797(a,1,2,1))]. 801 L(x,y \ z,z * y) = x. [para(800(a,1),776(a,1)),flip(a)]. 802 L(x,y,z * (z / y)) = x. [para(66(a,1),801(a,1,2))]. 803 (x * L(x \ 1,y,z)) \ u = L(x \ 1,y,z) \ (x \ u). [para(796(a,1),177(a,1)),flip(a)]. 804 L(x,y,(z * (z * u)) * (z * w)) = L(x,y,u \ (z \ w)). [para(282(a,1),777(a,1,3,1))]. 805 L(x,y,(z * (z * u)) * z) = L(x,y,u \ (z \ 1)). [para(289(a,1),777(a,1,3,1))]. 806 L(L(x,y,y / z),z,z / y) = x. [para(784(a,1),304(a,1,1))]. 807 L(x,x,x / y) = y \ (y / (x \ 1)). [para(784(a,1),432(a,1))]. 808 L(x,y,z / (z * y)) = x. [para(784(a,1),730(a,1))]. 809 ((x / (x * y)) * y) \ (x / (x * y)) = y \ 1. [para(808(a,1),142(a,1)),flip(a)]. 810 ((x / (x * y)) * y) * z = (x / (x * y)) * (y * z). [para(808(a,1),74(a,1,2))]. 811 ((x / (x * y)) * y) \ z = y \ ((x / (x * y)) \ z). [para(808(a,1),177(a,1)),flip(a)]. 812 L(x,y / (z * (u * y)),z * (u \ 1)) = x. [para(350(a,1),793(a,1,2))]. 813 (x * (y \ z)) \ (x * (y \ (z * u))) = L(L(u,z,y),y \ z,x). [para(798(a,1),32(a,2,2,2)),flip(a)]. 814 (x \ y) * L(L(z,y,x),u,w) = x \ (y * L(z,u,w)). [para(49(a,1),798(a,1,2))]. 815 T(x,y) \ (x * z) = (T(x,y) \ x) * z. [para(234(a,1),798(a,1,2)),flip(a)]. 816 x \ (((y * x) / y) * z) = (x \ ((y * x) / y)) * z. [para(237(a,1),798(a,1,2)),flip(a)]. 817 (x \ y) * T((x \ y) \ 1,z) = x \ (y * T(y \ x,z)). [para(261(a,1),798(a,1,2))]. 818 L(x,y,T(z \ u,z)) = L(x,y,T(z * u,z)). [para(138(a,1),778(a,1,3)),flip(a)]. 819 L(x,y,T((z \ u) * z,z)) = L(x,y,z * T(u * z,z)). [para(757(a,1),778(a,1,3,2)),flip(a)]. 820 L(x,y,(z * z) / u) = L(x,y,u). [para(783(a,2),787(a,1))]. 821 L(x,y,T(z,z * (u * u))) = L(x,y,z \ (u * u)). [para(252(a,1),820(a,1,3)),flip(a)]. 822 L(x,y,z / (u * u)) = L(x,y,z). [para(820(a,1),784(a,1)),flip(a)]. 823 L(x,y,z * (u * u)) = L(x,y,z). [para(21(a,1),822(a,1,3)),flip(a)]. 824 L(x,y,(z * u) * u) = L(x,y,R(z,u,u)). [para(34(a,2),822(a,1,3)),flip(a)]. 825 (x * (y * (y * z))) \ ((x * (y * y)) * (z * u)) = L(u,z,x). [para(823(a,1),419(a,2))]. 826 (T(x,y) \ x) * y = T(y,T(x,y)). [para(815(a,1),107(a,1))]. 827 T(x,y) \ (x * z) = x * (T(x,y) \ z). [para(815(a,2),576(a,1))]. 828 x * (T(x,y) \ y) = T(y,T(x,y)). [para(826(a,1),576(a,1)),flip(a)]. 829 T(x,T(y,x)) / (T(y,x) \ x) = y. [hyper(24,a,22,a,b,828,a),flip(a)]. 830 x \ T(y,T(x,y)) = T(x,y) \ y. [hyper(23,a,20,a,b,828,a),flip(a)]. 831 (x * y) / (x * (T(x,z) \ y)) = T(x,z). [para(827(a,1),65(a,1,2))]. 832 (((x * y) * (y * x)) * z) \ (((x * y) * (y * x)) * (z * u)) = L(u,z,K(y,x)). [para(779(a,1),32(a,1)),flip(a)]. 833 (x * (y / (y * x))) \ (y / (y * x)) = x \ 1. [para(362(a,1),809(a,1,1))]. 834 T(x \ 1,x * (y / (y * x))) = x \ 1. [para(833(a,1),349(a,2))]. 835 L(x \ 1,y,x) * y = y * ((x * y) \ y). [para(349(a,1),799(a,1,2)),flip(a)]. 836 L(x,y,(z * (z \ u)) * (z \ u)) = L(x,y,T(z,u)). [para(782(a,1),781(a,1)),flip(a)]. 837 L(x,y,z * ((z \ u) * u)) = L(x,y,a(z,u,u)). [para(435(a,1),785(a,1,3))]. 838 L(x,y,R(z \ u,w,v5)) = L(x,y,R(z * u,w,v5)). [para(20(a,1),786(a,1,3,1,2)),flip(a)]. 839 L(x,y,T(z / u,z)) = L(x,y,R(u / z,u,u)). [para(789(a,2),824(a,1))]. 840 L(x,y,z * (z * (u * z))) = L(x,y,u \ (z \ 1)). [para(51(a,1),805(a,1,3))]. 841 (x * (y / (y * x))) * z = (y / (y * x)) * (x * z). [para(362(a,1),810(a,1,1))]. 842 (x * (y / (y * x))) \ z = x \ ((y / (y * x)) \ z). [para(362(a,1),811(a,1,1))]. 843 L(x,y,T(z,z * (u * u))) = L(x,y,z * (u * u)). [para(821(a,2),776(a,1))]. 844 L(x,y,z * (u \ z)) = L(x,y,T(u,z)). [para(20(a,1),836(a,1,3,1))]. 845 L(x,y,T(z / u,z)) = L(x,y,z * u). [para(66(a,1),844(a,1,3,2)),flip(a)]. 846 L(x,y,R(z / u,z,z)) = L(x,y,u * z). [para(845(a,1),839(a,1)),flip(a)]. 847 L(x,y,R((y \ z) * z,u,w)) = x. [para(838(a,1),657(a,1))]. 848 L(x,y,z \ (u \ 1)) = L(x,y,z * u). [para(840(a,1),774(a,1))]. 850 L(x,y,z * (u \ 1)) = L(x,y,z * u). [para(848(a,1),776(a,1)),flip(a)]. 851 L(x,y / (z * (u * y)),z * u) = x. [para(850(a,1),812(a,1))]. 852 L(x,(y * z) * (u / (y * (z * u))),y * z) = x. [para(851(a,1),303(a,1,1))]. 853 ((x * y) * z) / (x * (y * z)) = (x * y) * (z / (x * (y * z))). [para(851(a,1),196(a,1,2))]. 854 x \ ((y / (y * x)) \ z) = ((y * x) / y) * (x \ z). [para(842(a,1),606(a,1))]. 855 L(x,y,T(z,z * (u * u))) = L(x,y,z). [para(843(a,2),823(a,1))]. 856 L(x,y,T(z,u * u)) = L(x,y,z). [para(423(a,1),855(a,1,3))]. 858 L(x,y,R(T(z,u * u),w,v5)) = L(x,y,R(z,w,v5)). [para(46(a,2),856(a,1,3))]. 859 x \ (((y * x) / y) * z) = ((y * x) / y) * (x \ z). [para(358(a,1),854(a,1,2))]. 860 (x \ ((y * x) / y)) * z = ((y * x) / y) * (x \ z). [para(859(a,1),816(a,1)),flip(a)]. 861 L(x,y,z * ((z * u) * u)) = L(x,y,a(z,u,u)). [para(780(a,1),837(a,1))]. 862 L(x,y,z * (z * (u * (z * w)))) = L(x,y,u \ (z \ w)). [para(51(a,1),804(a,1,3))]. 863 L(x,y,T((z \ u) * z,z)) = L(x,y,(u * z) * z). [para(82(a,1),819(a,2,3))]. 864 L(x,y,T((z \ u) * z,z)) = L(x,y,R(u,z,z)). [para(863(a,2),824(a,1))]. 865 L(x,y,z \ (u \ w)) = L(x,y,z * (u * w)). [para(862(a,1),774(a,1))]. 867 L(x,y,z * (u \ w)) = L(x,y,z * (u * w)). [para(865(a,1),776(a,1)),flip(a)]. 868 L(x,y,z * (u * (u * w))) = L(x,y,z * w). [para(19(a,1),867(a,1,3,2)),flip(a)]. 869 L(x,y,(z \ u) * (u \ z)) = L(x,y,(u \ z) * (z * u)). [para(384(a,1),867(a,1,3))]. 871 ((x \ (x / y)) \ y) \ y = x \ (x / y). [para(792(a,1),802(a,1))]. 872 x / (y \ (y / x)) = (y \ (y / x)) \ x. [para(871(a,1),65(a,1,2))]. 873 (x * (y * (y * z))) \ (x * (y * (y * (z * u)))) = L(u,z,x). [para(411(a,1),825(a,1,2))]. 875 L(x,y * (y * z),u) = L(x,z,u). [para(873(a,1),93(a,1)),flip(a)]. 876 L(x,y \ z,u) = L(x,y * z,u). [para(20(a,1),875(a,1,2,2)),flip(a)]. 877 L(x,(y / z) * y,u) = L(x,z,u). [para(22(a,1),875(a,1,2,2))]. 878 L(x,y * (z * y),u) = L(x,T(z,y),u). [para(82(a,1),875(a,1,2,2))]. 879 L(x,(y * z) * (z * y),u) = L(x,K(z,y),u). [para(69(a,1),875(a,1,2,2))]. 880 L(x,(y \ z) * u,w) = L(x,(y * z) * u,w). [para(89(a,1),875(a,1,2)),flip(a)]. 881 L(x,T(y,y * z),u) = L(x,(y \ z) * z,u). [para(250(a,1),875(a,1,2,2)),flip(a)]. 882 L(x,(y * y) / z,u) = L(x,z \ 1,u). [para(263(a,1),875(a,1,2))]. 883 L(x,T(y \ 1,z),u) = L(x,z * (y \ z),u). [para(327(a,1),875(a,1,2,2)),flip(a)]. 884 L(x,y / z,u) = L(x,z / y,u). [para(360(a,1),875(a,1,2))]. 887 L(x,y \ 1,z) = L(x,y,z). [para(18(a,1),876(a,2,2))]. 888 (x * (y \ z)) * L(u,y * z,x) = x * ((y \ z) * u). [para(876(a,1),74(a,1,2))]. 889 L(x,(y \ z) * z,y) = x. [para(876(a,1),731(a,1))]. 890 L(x,y * z,z * y) = x. [para(876(a,1),801(a,1))]. 891 L(x,(y \ z) * u,z * (y * u)) = x. [para(876(a,1),791(a,1))]. 892 L(x,y * z,z / y) = x. [para(66(a,1),889(a,1,2,1))]. 893 (x * ((x \ y) * y)) \ z = ((x \ y) * y) \ (x \ z). [para(889(a,1),177(a,1)),flip(a)]. 894 ((x * y) * (y * x)) * z = (x * y) * ((y * x) * z). [para(890(a,1),74(a,1,2))]. 895 T(x * y,(x * y) * (y * x)) = T(x * y,y * x). [para(890(a,1),203(a,1)),flip(a)]. 896 L(x,K(y,z),z * y) = x. [para(890(a,1),315(a,1,1))]. 897 K(x,y) \ 1 = K(y,x). [para(890(a,1),609(a,1)),flip(a)]. 898 K(x,y) * K(y,x) = 1. [para(897(a,1),20(a,1,2))]. 899 1 / K(x,y) = K(y,x). [para(897(a,1),65(a,1,2))]. 900 K(x,y) \ z = K(y,x) * z. [para(897(a,1),318(a,1,1)),flip(a)]. 901 K(x,y) * (K(y,x) * z) = z. [para(897(a,1),321(a,1,2,1))]. 902 x / (K(y,z) * x) = K(z,y). [para(897(a,1),340(a,2))]. 903 T(x * y,K(y,x)) / (y * x) = K(x,y). [para(897(a,1),345(a,2))]. 904 R(K(x,y),K(y,x) * z,u) = R(K(y,x),z,u) \ 1. [para(897(a,1),584(a,1,1))]. 905 a(K(x,y),z,u) = a(K(y,x),z,u). [para(897(a,1),611(a,1,1))]. 906 R(K(x,y),K(x,y) * z,u) = R(K(y,x),z,u) \ 1. [para(897(a,1),633(a,2,1,1))]. 907 K(x,y) * (K(y,x) / (x * y)) = K(x,y) \ ((y * x) \ 1). [para(897(a,1),379(a,1,2,1))]. 908 R(x,K(y,z),u) = R(x,K(z,y),u). [para(897(a,1),717(a,1,2))]. 909 L(x,y,K(z,u)) = L(x,y,K(u,z)). [para(897(a,1),787(a,1,3))]. 910 L(K(x,y),z,K(y,x)) * z = z * ((K(y,x) * z) \ z). [para(897(a,1),835(a,1,1,1))]. 911 (x * y) * (K(y,x) * z) = (y * x) * z. [para(896(a,1),176(a,1,2)),flip(a)]. 912 K(x,y) \ ((y * x) \ z) = (x * y) \ z. [para(896(a,1),199(a,1))]. 914 L(x,x,y) = (y * (x \ 1)) \ y. [para(887(a,1),161(a,1))]. 915 x / L(y,y,x) = x * (y \ 1). [para(887(a,1),162(a,1,2))]. 916 L(L(x,y * (z \ 1),y),z,y) = x. [para(887(a,1),308(a,1))]. 917 L(x * y,x,y) = (y \ (x \ 1)) \ 1. [para(887(a,1),351(a,1))]. 918 L(x,y,L(y \ 1,z,u)) = x. [para(887(a,1),509(a,1))]. 919 (x * (y \ z)) / L(z,y,x) = x * (y \ 1). [para(887(a,1),333(a,1,2))]. 920 L(x * (y * z),x,y) = (y \ (x \ 1)) \ z. [para(887(a,1),352(a,1))]. 921 L(x,K(y,z),u) = L(x,K(z,y),u). [para(897(a,1),887(a,1,2))]. 922 T(x * y,K(y,x)) = K(x,y) * (y * x). [para(900(a,1),122(a,1)),flip(a)]. 923 R(K(x,y),K(y,x) * z,u) \ K(x,y) = K(x,y) \ R(K(x,y),z,u). [para(901(a,1),618(a,1,2,2)),flip(a)]. 924 (L(x \ 1,y,z) * x) \ u = x \ (L(x \ 1,y,z) \ u). [para(918(a,1),177(a,1)),flip(a)]. 925 L(x / y,x / y,z) = (z * (y / x)) \ z. [para(343(a,1),914(a,2,1,2))]. 926 L(K(x,y),K(x,y),z) = (z * K(y,x)) \ z. [para(897(a,1),914(a,2,1,2))]. 927 (x * y) * ((y / x) \ 1) = (x * y) / (y / x). [para(788(a,1),915(a,1,2)),flip(a)]. 928 L(x,(y * (y * z)) * (y * u),w) = L(x,z \ (y \ u),w). [para(282(a,1),877(a,1,2,1))]. 929 L(x,(y * (y * z)) * y,u) = L(x,z \ (y \ 1),u). [para(289(a,1),877(a,1,2,1))]. 930 K(x,y) / L(z,z,K(y,x)) = K(x,y) * (z \ 1). [para(909(a,1),915(a,1,2))]. 931 L(x,y * (z \ 1),y) = L(x,y * z,y). [para(916(a,1),303(a,1,1)),flip(a)]. 932 L(x,K(y,z),y * z) = x. [para(921(a,1),896(a,1))]. 933 ((x * y) \ K(x,y)) \ z = K(x,y) \ ((x * y) * z). [para(932(a,1),267(a,1)),flip(a)]. 934 L(x * y,x,y) * z = (y \ (x \ 1)) \ z. [para(917(a,2),318(a,1,1))]. 935 L(x,(y * y) / z,u) = L(x,z,u). [para(882(a,2),887(a,1))]. 936 L(x,y / (z * z),u) = L(x,y,u). [para(935(a,1),884(a,1)),flip(a)]. 937 L(x,y * (z * z),u) = L(x,y,u). [para(21(a,1),936(a,1,2)),flip(a)]. 938 L(x,(y * z) * z,u) = L(x,R(y,z,z),u). [para(34(a,2),936(a,1,2)),flip(a)]. 939 ((x * y) * z) / (K(x,y) * z) = y * x. [hyper(24,a,22,a,b,911,a),flip(a)]. 940 (x * y) \ ((y * x) * z) = K(y,x) * z. [hyper(23,a,20,a,b,911,a),flip(a)]. 941 K(x,y) * ((x * y) \ z) = (y * x) \ z. [para(912(a,1),20(a,1,2))]. 942 x * (y \ ((y * (x \ 1)) * z)) = L(z,y * x,y). [para(931(a,1),446(a,2))]. 943 L(x,K(y,z) * (y * z),u) = L(x,z * y,u). [para(939(a,1),935(a,1,2)),flip(a)]. 944 (x * y) \ (y * (x * z)) = K(y,x) * L(z,x,y). [para(74(a,1),940(a,1,2))]. 945 (x * (y \ 1)) * L(z,y,x) = x * (y \ z). [para(919(a,1),22(a,1,1))]. 946 (a(x,y,z) \ (x \ 1)) \ u = x * (a(x,y,z) * u). [para(920(a,1),771(a,1))]. 947 L(K(x,y),K(x,y),z) / z = (z * K(y,x)) \ 1. [para(926(a,2),320(a,1,1))]. 948 (a(x,y,z) \ (x \ 1)) \ u = (x * a(x,y,z)) * u. [para(771(a,1),934(a,1,1)),flip(a)]. 949 L(x,(y * z) * u,z * (y * u)) = x. [para(880(a,1),891(a,1))]. 950 L(x,(y * z) * u,T(y,z) * (z * u)) = x. [para(82(a,1),949(a,1,2,1))]. 951 L(x,T(y,y * z),u) = L(x,(y * z) * z,u). [para(881(a,2),880(a,1))]. 952 (x * y) / (y / x) = (x * y) * (x / y). [para(343(a,1),927(a,1,2)),flip(a)]. 953 L(x,(y * (y \ z)) * (y \ z),u) = L(x,T(y,z),u). [para(20(a,1),951(a,1,2,2)),flip(a)]. 954 x * (y * ((y \ (x \ 1)) * z)) = L(z,y * x,y). [para(213(a,1),942(a,1,2))]. 955 K(x,y) * L(x,y,x) = T(x,y * x). [para(944(a,1),36(a,2)),flip(a)]. 956 x * ((x \ (y \ 1)) * y) = a(x,y,y). [hyper(23,a,453,a(flip),b,954,a)]. 957 x * (y * (R(y,y * (x \ 1),z) \ ((x \ 1) * z))) = L(z,y * x,y). [para(630(a,2),954(a,1,2,2))]. 958 x * R(x \ 1,y \ 1,y) = a(x,y,y). [para(335(a,2),956(a,1,2))]. 959 x \ R(x,y \ 1,y) = a(x,y,y). [para(958(a,1),635(a,1)),flip(a)]. 960 x * R(x \ 1,y,y) = a(x,y,y). [para(717(a,1),958(a,1,2))]. 961 R(x,y \ 1,y) \ a(x,y,y) = T(x \ 1,R(x,y \ 1,y)). [para(959(a,1),325(a,2,2)),flip(a)]. 962 x \ R(x,y,y) = a(x,y,y). [para(717(a,1),959(a,1,2))]. 963 x * a(x,y,y) = R(x,y,y). [para(962(a,1),20(a,1,2))]. 964 a(x,y,y) \ R(x,y,y) = x. [para(962(a,1),480(a,1,1))]. 965 (R(x,y,y) \ x) * z = a(x,y,y) \ z. [para(962(a,1),465(a,1,1)),flip(a)]. 966 x * (a(x,y,y) * z) = R(x,y,y) * z. [para(962(a,1),501(a,1,2,1))]. 967 R(x \ 1,y,y) = x \ a(x,y,y). [para(962(a,1),634(a,1,2)),flip(a)]. 968 R(x,x * y,y) = a(x,y,y) \ x. [para(965(a,1),621(a,1)),flip(a)]. 969 T(x * y,K(y,x)) = T(x * y,y * x). [para(895(a,1),248(a,1)),flip(a)]. 970 T(x * y,K(y,x)) = (x \ 1) \ y. [para(969(a,2),439(a,1))]. 971 K(x,y) / T(y * x,K(x,y)) = (y * x) \ K(x,y). [para(969(a,2),257(a,1,2))]. 972 T(x * y,K(y,x)) = x * y. [para(970(a,2),330(a,1))]. 973 K(x,y) = (x * y) / (y * x). [para(972(a,1),903(a,1,1)),flip(a)]. 974 K(x,y) * (y * x) = x * y. [para(972(a,1),922(a,1)),flip(a)]. 975 (x * y) / (T(x,y) * y) = K(y,T(x,y)). [para(82(a,1),973(a,2,1)),flip(a)]. 976 (T(x,y) * y) / (x * y) = K(T(x,y),y). [para(82(a,1),973(a,2,2)),flip(a)]. 977 ((x * y) * z) / ((y * x) * z) = R(K(x,y),y * x,z). [para(973(a,2),80(a,1,1)),flip(a)]. 978 (x \ y) / (y * (x \ 1)) = K(x \ 1,y). [para(318(a,1),973(a,2,1)),flip(a)]. 979 ((K(x,y) * z) * K(y,x)) / z = K(K(x,y) * z,K(y,x)). [para(901(a,1),973(a,2,2)),flip(a)]. 980 K(x \ y,x) * y = (x \ y) * x. [para(20(a,1),974(a,1,2))]. 981 K(x * y,x) * y = (x \ y) * x. [para(495(a,1),980(a,1,1))]. 982 ((x \ y) * x) / y = K(x * y,x). [hyper(24,a,22,a,b,981,a),flip(a)]. 983 K(x,T(y,x)) = T(y,x) \ y. [para(975(a,1),577(a,1))]. 984 T(x,y) * K(y,T(x,y)) = x. [para(983(a,2),20(a,1,2))]. 985 K(x,T(y,x)) * T(y,x) = y. [para(983(a,2),298(a,1,1))]. 987 T(x,y) \ (x * z) = K(y,T(x,y)) * z. [para(983(a,2),815(a,2,1))]. 988 L(x,K(y,T(z,y)),u) = L(x,T(z,y) * z,u). [para(983(a,2),876(a,1,2))]. 989 (x \ y) * K(x,T(y / x,x)) = y / x. [para(84(a,1),984(a,1,1))]. 990 K(T(x,y),y) * x = T(x,y). [hyper(23,a,901,a,b,985,a),flip(a)]. 991 K(x,x \ y) * T(y / x,x) = y / x. [para(84(a,1),985(a,1,1,2))]. 992 K(T(x,y),y) = x \ T(x,y). [para(976(a,1),565(a,1))]. 993 x * K(T(x,y),y) = T(x,y). [para(992(a,2),20(a,1,2))]. 994 (x / y) \ T(x / y,y) = K(y \ x,y). [para(84(a,1),992(a,1,1)),flip(a)]. 995 K(T(x \ 1,y),y) = x * T(x \ 1,y). [para(992(a,2),330(a,1))]. 997 (x / y) * K(T(x / y,y),y) = y \ x. [para(993(a,2),84(a,1))]. 998 T(x,y) * (K(y,T(x,y)) * z) = x * z. [para(987(a,1),20(a,1,2))]. 999 K(x,T(y,x)) * (y \ z) = T(y,x) \ z. [para(20(a,1),987(a,1,2)),flip(a)]. 1000 (x \ y) * K(x,x \ y) = y / x. [para(84(a,1),989(a,1,2,2))]. 1001 (x \ y) * K(x,x * y) = y / x. [para(489(a,1),1000(a,1,2))]. 1002 (x \ y) \ (y / x) = K(x,x * y). [hyper(23,a,20,a,b,1001,a),flip(a)]. 1003 K(x,x * (x * y)) = y \ ((x * y) / x). [para(19(a,1),1002(a,1,1)),flip(a)]. 1004 K(x,x * y) * T(y / x,x) = y / x. [para(489(a,1),991(a,1,1))]. 1005 (x / y) \ T(x / y,y) = K(y * x,y). [para(994(a,2),495(a,1))]. 1006 (x / y) * K(y \ x,y) = y \ x. [para(84(a,1),997(a,1,2,1))]. 1007 (x / y) * K(y * x,y) = y \ x. [para(495(a,1),1006(a,1,2))]. 1008 (x / y) * (x \ y) = K(x * y,x). [hyper(23,a,359,a,b,1007,a),flip(a)]. 1009 K(x * y,x) / (x \ y) = x / y. [hyper(24,a,22,a,b,1008,a),flip(a)]. 1010 (x \ y) * (x / y) = K(x * y,x). [para(1008(a,1),368(a,1)),flip(a)]. 1011 (x \ y) \ K(x * y,x) = x / y. [hyper(23,a,20,a,b,1010,a),flip(a)]. 1012 L(x,y,(z \ u) * K(z * u,z)) = L(x,y,z / u). [para(1010(a,1),774(a,1,3,2))]. 1013 K(x,y) = y \ ((x * y) / x). [para(1003(a,1),490(a,1)),flip(a)]. 1014 (x * y) / x = y * K(x,y). [para(1013(a,2),20(a,1,2)),flip(a)]. 1015 x * (y / (y * x)) = K(y,x) \ 1. [para(1013(a,2),502(a,1,1)),flip(a)]. 1016 K(x,y) = ((x * y) / x) / y. [para(1013(a,2),558(a,2)),flip(a)]. 1017 ((x * y) / x) * (y \ z) = K(x,y) * z. [para(1013(a,2),860(a,1,1)),flip(a)]. 1018 (x * K(y,x)) * y = y * x. [para(1014(a,1),22(a,1,1))]. 1019 x / (x / y) = y * K(x / y,y). [para(22(a,1),1014(a,1,1))]. 1020 T(x * K(y,x),y) = x. [para(1014(a,1),104(a,1,1))]. 1021 L(x,y * K(z,y),y) = x. [para(1014(a,1),237(a,1,2))]. 1022 a(x / (x * y),z,u) = a(y * K(x,y),z,u). [para(1014(a,1),612(a,1,1)),flip(a)]. 1023 T(T(x * K(y,x),z),y) = T(x,z). [para(1020(a,1),42(a,1,1)),flip(a)]. 1024 T(x * K(y,x),z) * y = y * T(x,z). [para(1020(a,1),108(a,1,2,1)),flip(a)]. 1025 x / L(y,x * K(y,x),y) = y \ (x * K(y,x)). [para(1020(a,1),441(a,1,1))]. 1026 L(x,K(y,z),z) = x. [para(1021(a,1),303(a,1))]. 1027 (x * K(y,x)) \ z = K(y,x) \ (x \ z). [para(1021(a,1),270(a,1))]. 1028 (x * K(y,x)) * z = x * (K(y,x) * z). [para(1026(a,1),74(a,1,2))]. 1029 L(x,K(y,z),y) = x. [para(1026(a,1),921(a,1)),flip(a)]. 1030 (x * K(x,y)) * z = x * (K(x,y) * z). [para(1029(a,1),74(a,1,2))]. 1031 x \ (K(x,y) * z) = (x \ K(x,y)) * z. [para(1029(a,1),798(a,1,2)),flip(a)]. 1032 (x * K(y,x)) \ 1 = K(x,y) / x. [para(1029(a,1),947(a,1,1)),flip(a)]. 1033 (x * y) / x = K(x,y) * y. [para(1016(a,2),22(a,1,1)),flip(a)]. 1035 (x * K(y,x)) / x = K(y,x). [para(1014(a,1),1016(a,2,1)),flip(a)]. 1036 K(x,y) * y = y * K(x,y). [para(1033(a,1),1014(a,1))]. 1037 T(K(x,y),y) = K(x,y). [para(1035(a,1),104(a,1,1))]. 1038 T(x,K(y,x)) = x. [hyper(39,a,1037,a)]. 1040 T(x,y) * K(z,x) = K(z,x) * T(x,y). [para(1038(a,1),108(a,1,2,1)),flip(a)]. 1041 K(x,y) = x * (y / (y * x)). [para(1015(a,2),897(a,1)),flip(a)]. 1042 x \ K(x,y) = y / (y * x). [hyper(23,a,20,a,b,1041,a(flip)),flip(a)]. 1043 K(x,y) = (y / (y * x)) * x. [para(1041(a,2),362(a,2)),flip(a)]. 1044 K(x,y) / x = y / (y * x). [para(1041(a,2),363(a,1,1))]. 1045 x * ((y / (y * x)) * z) = K(x,y) * z. [para(1041(a,2),451(a,1,1)),flip(a)]. 1046 T(x,K(x,y)) = x. [para(1041(a,2),605(a,1,2))]. 1047 ((x * y) / x) * (y \ z) = K(y,x) \ z. [para(1041(a,2),606(a,1,1)),flip(a)]. 1048 T(x \ 1,K(x,y)) = x \ 1. [para(1041(a,2),834(a,1,2))]. 1049 (x / (x * y)) * (y * z) = K(y,x) * z. [para(1041(a,2),841(a,1,1)),flip(a)]. 1050 K(x,y) * x = x * K(x,y). [para(1046(a,1),82(a,1,2))]. 1051 T(x,T(y,x) \ y) = x. [para(983(a,1),1046(a,1,2))]. 1052 (T(x,y) \ x) * y = y * (T(x,y) \ x). [para(1051(a,1),82(a,1,2))]. 1053 K(x,y) = ((y * x) / y) \ x. [para(1043(a,2),358(a,2)),flip(a)]. 1054 K(x,y) / x = x \ K(x,y). [para(1044(a,2),1042(a,2)),flip(a)]. 1055 K(x,y) * (x \ 1) = x \ K(x,y). [para(1048(a,1),327(a,1,2))]. 1056 (x * K(y,x)) \ 1 = x \ K(x,y). [para(1032(a,2),1054(a,1))]. 1057 (x \ 1) / (x \ K(x,y)) = K(y,x). [para(1055(a,1),902(a,1,2))]. 1058 (x * K(y,x)) \ z = (x \ K(x,y)) * z. [para(1056(a,1),318(a,1,1)),flip(a)]. 1059 K(x,y) * (y * z) = ((x * y) / x) * z. [para(19(a,1),1017(a,1,2)),flip(a)]. 1060 T(x,y) * K(z,T(x,y)) = T(x * K(z,x),y). [hyper(24,a,1018,a,b,1024,a),flip(a)]. 1061 T(x * K(x \ y,x),y) = L(x,x \ y,x). [hyper(24,a,221,a,b,1024,a)]. 1062 T(x * K(y,x),x * y) = L(x,y,x). [hyper(24,a,217,a(flip),b,1024,a)]. 1063 (x * K(y,x)) \ z = K(x,y) * (x \ z). [para(1027(a,2),900(a,1))]. 1064 ((x * y) / x) * z = y * (K(x,y) * z). [para(1014(a,2),1028(a,1,1))]. 1065 x \ (K(x,y) * z) = (y / (y * x)) * z. [para(1042(a,1),1031(a,2,1))]. 1066 K(x,y) \ (x * z) = ((y * x) / y) * z. [para(19(a,1),1047(a,1,2)),flip(a)]. 1067 K(x,y) * (x \ z) = (y / (y * x)) * z. [para(20(a,1),1049(a,1,2)),flip(a)]. 1068 K(x,y) * (x * z) = x * (K(x,y) * z). [para(1049(a,1),1045(a,1,2)),flip(a)]. 1069 x * (T(y,x) \ y) = T(x,T(y,x)). [para(1052(a,1),826(a,1))]. 1070 x * K(x,T(y,x)) = T(x,T(y,x)). [para(983(a,2),1069(a,1,2))]. 1071 x / (K(y,z) * (y \ x)) = y * K(z,y). [para(1063(a,1),65(a,1,2))]. 1072 (x \ K(x,y)) * z = K(x,y) * (x \ z). [para(1063(a,1),1058(a,1)),flip(a)]. 1073 K(x,y) * (y * z) = y * (K(x,y) * z). [para(1064(a,1),1059(a,2))]. 1074 K(x,y) \ (x * z) = (K(y,x) * x) * z. [para(1033(a,1),1066(a,2,1))]. 1075 K(x,y) * (x \ (y * x)) = y. [para(1067(a,2),22(a,1))]. 1076 x \ (K(x,y) * z) = K(x,y) * (x \ z). [para(1067(a,2),1065(a,2))]. 1077 K(x,y) * T(y,x) = y. [para(36(a,2),1075(a,1,2))]. 1078 K(x,y / x) = K(x,x * y). [hyper(24,a,1004,a,b,1077,a)]. 1079 K(x,T(y,x)) = K(x,y). [hyper(24,a,985,a,b,1077,a),flip(a)]. 1080 K(x,y) = T(y,x) \ y. [hyper(24,a,298,a,b,1077,a)]. 1081 T(x,y) = K(x,y) * x. [hyper(23,a,901,a,b,1077,a)]. 1082 K(x,T(y,z)) * T(T(y,x),z) = T(y,z). [para(42(a,1),1077(a,1,2))]. 1083 K(x,R(y,z,u)) * R(T(y,x),z,u) = R(y,z,u). [para(46(a,2),1077(a,1,2))]. 1084 L(x \ y,x,K(z,y)) = (K(z,y) \ x) \ T(y,z). [para(1077(a,1),267(a,1,1,2))]. 1085 L(x,y,K(z,u) * u) = L(x,y,T(u,z)). [para(1077(a,1),774(a,1,3,2))]. 1086 K(x,y) = T(x,y) / x. [para(1077(a,1),902(a,1,2)),flip(a)]. 1087 (x * y) * T(y,x) = (y * x) * y. [para(1077(a,1),911(a,1,2)),flip(a)]. 1088 T(x,y) * T(x,y) = x * T(T(x,y),y). [para(1077(a,1),998(a,1,2))]. 1089 T(x,y) * K(y,x) = x. [para(1077(a,1),1040(a,2))]. 1090 (x / (x * y)) * T(x,y) = y \ x. [para(1077(a,1),1065(a,1,2)),flip(a)]. 1091 K(x,T(T(y,x),z)) = K(x,T(y,z)). [para(42(a,1),1079(a,1,2))]. 1092 K(x,x * (y * x)) = K(x,y). [para(1079(a,1),491(a,2))]. 1093 T(x,y) \ (x * z) = K(y,x) * z. [para(1079(a,1),987(a,2,1))]. 1094 T(x,y) * (K(y,x) * z) = x * z. [para(1079(a,1),998(a,1,2,1))]. 1095 K(x,y) * (y \ z) = T(y,x) \ z. [para(1079(a,1),999(a,1,1))]. 1096 T(x,T(y,x)) = x * K(x,y). [para(1079(a,1),1070(a,1,2)),flip(a)]. 1097 T(T(x,y),z) \ T(x,z) = K(y,T(x,z)). [para(42(a,1),1080(a,2,1)),flip(a)]. 1098 K(x,y) * (T(y,x) * z) = y * z. [para(1080(a,2),575(a,1,1))]. 1099 x * (T(x,y) \ z) = K(y,x) * z. [para(1080(a,2),576(a,1,1)),flip(a)]. 1100 K(x,y) = y * (T(y,x) \ 1). [para(1080(a,2),578(a,2)),flip(a)]. 1101 T(x,y) \ 1 = x \ K(y,x). [para(1080(a,2),582(a,1,2)),flip(a)]. 1102 (x * y) / (T(x,z) * y) = K(z,x). [para(1080(a,2),577(a,2))]. 1103 ((x * y) * y) \ ((y * x) * y) = K(y,(y * x) * y). [para(758(a,1),1080(a,2,1)),flip(a)]. 1104 T(x,y) = (x * x) / (x * K(y,x)). [para(1080(a,2),831(a,1,2,2)),flip(a)]. 1105 K(T(x,y),y) = K(x,y). [hyper(24,a,990,a,b,1081,a(flip)),flip(a)]. 1106 (x * T(y,z)) / L(y,K(y,z),x) = x * K(y,z). [para(1081(a,2),99(a,1,1,2))]. 1107 T(x,y) = x * K(x,y). [para(1081(a,2),1050(a,1))]. 1108 K(x,y) = x \ T(x,y). [para(1086(a,2),572(a,1))]. 1109 R(T(x,y),z,u) * K(y,R(x,z,u)) = R(x,z,u). [para(46(a,2),1089(a,1,1))]. 1110 K(R(T(x,y),z,u),y) = K(R(x,z,u),y). [para(46(a,2),1105(a,1,1))]. 1111 x * T(x \ 1,y) = K(x \ 1,y). [para(1105(a,1),995(a,1)),flip(a)]. 1112 T(x * K(y,x),T(y,x)) = x. [para(1105(a,1),1020(a,1,1,2))]. 1113 K(x,y) * T(x,y) = T(T(x,y),y). [para(1105(a,1),1081(a,2,1)),flip(a)]. 1114 K(x,y) * T(K(y,x),z) = K(K(y,x),z). [hyper(23,a,901,a,b,1107,a(flip)),flip(a)]. 1115 (x * y) \ (x * T(y,z)) = L(K(y,z),y,x). [para(1107(a,2),32(a,2,2,2)),flip(a)]. 1116 x * (y * K(y,x)) = y * x. [para(1107(a,1),82(a,1,2))]. 1117 (x * y) * L(K(y,z),y,x) = x * T(y,z). [para(1107(a,2),74(a,2,2))]. 1118 (x \ y) * K(x * y,x) = T(x \ y,x). [para(495(a,1),1107(a,2,2)),flip(a)]. 1119 L(x,y,z * T(z,u)) = L(x,y,K(z,u)). [para(1107(a,2),774(a,1,3,2))]. 1120 x * (K(x,y) * z) = T(x,y) * z. [para(1107(a,2),1030(a,1,1)),flip(a)]. 1121 T(x,y) * K(x,y) = T(T(x,y),y). [para(1105(a,1),1107(a,2,2)),flip(a)]. 1122 T(x,y) \ T(T(x,z),y) = K(T(x,y),z). [para(42(a,1),1108(a,2,2)),flip(a)]. 1123 L(x,y,z) \ L(T(x,u),y,z) = K(L(x,y,z),u). [para(44(a,2),1108(a,2,2)),flip(a)]. 1124 x \ ((x \ y) \ y) = K(x,x * y). [para(249(a,1),1108(a,2,2)),flip(a)]. 1125 T(x,y) * (x \ z) = K(x,y) * z. [para(1108(a,2),562(a,1,1)),flip(a)]. 1126 K(x \ 1,x * y) = x * ((x * y) \ y). [para(1108(a,2),707(a,1))]. 1127 x \ (T(x,y) * z) = K(x,y) * z. [para(1108(a,2),733(a,2,1))]. 1128 K(x / y,y) = K(y * x,y). [para(1108(a,2),1005(a,1))]. 1129 x * K(y,y * x) = y * (x / y). [para(1078(a,1),121(a,1,2))]. 1130 K(x,(y * (x \ 1)) / x) = K(x,T(y,x \ 1)). [para(347(a,1),1078(a,2,2))]. 1131 T(x,T(y,x)) = T(x,y). [para(1096(a,2),1107(a,2)),flip(a)]. 1132 T(T(x,y),T(z,x)) = T(T(x,z),y). [para(1131(a,1),42(a,1,1)),flip(a)]. 1133 T(x,y / x) = T(x,x \ y). [para(84(a,1),1131(a,1,2)),flip(a)]. 1134 (x * y) / T(y,x) = T(x,y). [para(1131(a,1),117(a,1,2))]. 1135 L(T(x,y),T(y,x),x) = T(x,x * T(y,x)). [para(1131(a,1),203(a,1,1))]. 1136 T(x,x * (y * x)) = T(x,y). [para(1131(a,1),247(a,2))]. 1137 T(x,y) / (T(y,x) \ x) = y. [para(1131(a,1),829(a,1,1))]. 1138 T(x,y) \ y = x \ T(y,x). [para(1131(a,1),830(a,1,2)),flip(a)]. 1139 T(x,y * K(x,y)) = T(x,y). [para(1020(a,1),1131(a,1,2)),flip(a)]. 1140 K(x,y) * K(z,K(y,x)) = T(K(y,x),z) \ 1. [hyper(23,a,901,a,b,1100,a(flip)),flip(a)]. 1141 L(T(x,y),y * K(x,y),T(x,y)) = (T(x,y) \ (y * K(x,y))) \ y. [para(1112(a,1),440(a,1,2)),flip(a)]. 1143 K((x * (y \ 1)) / y,y) = K(T(x,y \ 1),y). [para(347(a,1),1128(a,2,1))]. 1144 x / (x / y) = y * K(y * x,y). [para(1128(a,1),1019(a,2,2))]. 1145 T(x,y / x) = T(x,x * y). [para(1133(a,2),246(a,1))]. 1146 T(x,y) * T(y,x) = x * y. [para(1134(a,1),22(a,1,1))]. 1147 x / (y \ T(x,y)) = T(y,x). [para(1138(a,1),65(a,1,2))]. 1148 (T(x,y) \ y) * K(x,x * T(y,x)) = T(y,x) / x. [para(1138(a,2),1001(a,1,1))]. 1149 T(x,(y * (x \ 1)) / x) = T(x,T(y,x \ 1)). [para(347(a,1),1145(a,2,2))]. 1150 (T(x,y) * (T(y,x) * z)) \ ((x * y) * z) = a(T(x,y),T(y,x),z). [para(1146(a,1),28(a,2,2,1)),flip(a)]. 1151 (x * y) \ (T(x,y) * (T(y,x) * z)) = L(z,T(y,x),T(x,y)). [para(1146(a,1),32(a,2,1)),flip(a)]. 1152 T(T(x,y),x \ T(y,x)) = (x \ T(y,x)) \ y. [para(1147(a,1),84(a,1,1))]. 1153 R(x,y,x) * (y * x) = (y * x) * T(x,y). [para(1087(a,2),79(a,2))]. 1154 T(x,y) * ((y * x) / ((x * y) * x)) = K(T(x,y),y * x). [para(1087(a,1),1041(a,2,2,2)),flip(a)]. 1155 K(x,T(y,K(z,T(y,x)))) = K(x,T(y,x)). [para(1038(a,1),1091(a,1,2)),flip(a)]. 1156 L(x,y * K(z,y),u) = L(x,T(y,z),u). [para(1094(a,1),937(a,1,2))]. 1157 T(x,y) * (y * x) = x * (x * y). [para(974(a,1),1094(a,1,2))]. 1158 K(x,y) * (T(x,y) \ z) = x \ z. [hyper(23,a,901,a,b,1095,a),flip(a)]. 1159 K(x,y) * (y \ x) = y \ T(x,y). [para(1095(a,2),1138(a,1))]. 1160 K(x,y) * (x * z) = T(x,y) * z. [hyper(23,a,901,a,b,1098,a),flip(a)]. 1161 K(x,y / x) * ((x \ y) * z) = (y / x) * z. [para(84(a,1),1098(a,1,2,1))]. 1162 R(K(x,y),T(y,x) * z,u) \ 1 = ((T(y,x) * z) * u) / ((y * z) * u). [para(1098(a,1),344(a,1,2,1)),flip(a)]. 1163 x \ (K(y,x) * z) = T(x,y) \ z. [hyper(23,a,20,a,b,1099,a),flip(a)]. 1164 (x * y) * T((x * y) \ x,z) = x * K(y \ 1,z). [para(1111(a,1),762(a,2,2))]. 1165 x \ (y * T(y \ x,z)) = K((x \ y) \ 1,z). [para(1111(a,1),817(a,1)),flip(a)]. 1166 (x * ((K(x,y) * z) * u)) \ ((T(x,y) * z) * u) = a(x,K(x,y) * z,u). [para(1120(a,1),28(a,2,2,1)),flip(a)]. 1167 ((T(x,y) * z) * u) / ((K(x,y) * z) * u) = R(x,K(x,y) * z,u). [para(1120(a,1),34(a,2,1,1)),flip(a)]. 1168 T(x,y) * (T(y,x) * z) = x * (y * z). [para(1098(a,1),1120(a,1,2)),flip(a)]. 1169 L(x,y,z * ((z \ u) * u)) = L(x,y,K(z,z * u)). [para(1124(a,1),865(a,1,3)),flip(a)]. 1170 T(x,y) \ ((x \ T(y,x)) \ y) = K(T(x,y),T(x,y) * y). [para(1138(a,1),1124(a,1,2,1))]. 1171 T(x,y) \ (K(x,y) * z) = x \ z. [hyper(23,a,20,a,b,1125,a),flip(a)]. 1172 K(x,y) * (z * x) = T(x,y) * T(z,x). [para(36(a,2),1125(a,1,2)),flip(a)]. 1173 T(x / y,z) * y = K(x / y,z) * x. [para(66(a,1),1125(a,1,2))]. 1174 T(x,y) * (z / (z * x)) = K(x,y) * K(x,z). [para(1042(a,1),1125(a,1,2))]. 1175 T(x,y) * (T(x,z) \ 1) = K(x,y) * K(z,x). [para(1101(a,2),1125(a,1,2))]. 1176 x \ T(T(x,y),y) = K(x,y) * K(x,y). [para(1121(a,1),1127(a,1,2))]. 1177 T(T(x,x * y),T(z,x)) = T(T(x,z),x \ y). [para(246(a,1),1132(a,1,1))]. 1178 (x / (x / y)) * z = y * (K(y * x,y) * z). [para(1144(a,2),1028(a,1,1))]. 1179 ((x * y) * T(y,x)) \ (y * (y * x)) = K(T(y,x),x * y). [para(1157(a,1),30(a,2,2)),flip(a)]. 1180 (x * (x * y)) \ (T(x,y) * ((y * x) * z)) = L(z,y * x,T(x,y)). [para(1157(a,1),32(a,2,1)),flip(a)]. 1181 K(x,y) * (T(x,y) \ T(x,z)) = K(x,z). [para(1158(a,2),1108(a,2)),flip(a)]. 1182 K(T(x,y \ 1),y) * (x * (y \ 1)) = y \ T(T(x,y \ 1),y). [para(326(a,1),1159(a,1,2))]. 1183 ((T(x,y) * z) * u) / ((x * z) * u) = R(K(x,y),x * z,u). [para(1160(a,1),34(a,2,1,1)),flip(a)]. 1184 (x * y) \ (T(x,z) * y) = T(K(x,z),x * y). [para(1160(a,1),36(a,2,2)),flip(a)]. 1185 L(x,T(y,z) * z,u) = L(x,z * y,u). [para(1160(a,1),943(a,1,2))]. 1186 T(x,y) \ (T(y,x) \ z) = x \ (y \ z). [para(1158(a,1),1163(a,1,2)),flip(a)]. 1187 T(x,y) \ (y * K(x,y)) = x \ y. [para(1036(a,1),1171(a,1,2))]. 1188 x \ (y * K(x,y)) = K(x,y) * (x \ y). [para(1187(a,1),1158(a,1,2)),flip(a)]. 1189 (K(x,y) * (x \ z)) \ ((x \ K(x,y)) * (z * u)) = L(u,z,x \ K(x,y)). [para(1072(a,1),32(a,2,1)),flip(a)]. 1190 (K(x,y) * z) \ (y * (K(x,y) * z)) = L(T(y,z),z,K(x,y)). [para(1073(a,1),106(a,1,2))]. 1191 K(x,y) \ (x * z) = (K(x,y) \ x) * z. [para(900(a,2),1074(a,2,1))]. 1192 L(x,y,(z * u) / z) = L(x,y,T(u,z)). [para(1033(a,2),1085(a,1,3))]. 1193 T(x,y) * K(y,T(x,z)) = K(z,T(x,y)) * T(x,z). [para(1097(a,1),1099(a,1,2))]. 1194 L(x,y,(z / (u * u)) * (u \ (z * (u \ 1)))) = L(x,y,K(z / (u * u),u)). [para(403(a,1),1119(a,1,3,2))]. 1195 (x * T(y,x)) \ (T(y,z) * x) = L(K(T(y,x),z),T(y,x),x). [para(1122(a,1),180(a,1,1)),flip(a)]. 1196 K(x,T(y,K(z,T(y,x)))) = K(x,y). [para(1155(a,2),1079(a,1))]. 1197 K(x,y) * T(T(y,x),K(z,T(y,x))) = T(y,K(z,T(y,x))). [para(1196(a,1),1082(a,1,1))]. 1198 (x * (y * z)) / (T(y,x) * z) = T(x,y). [hyper(24,a,22,a,b,1168,a),flip(a)]. 1199 (x \ y) * (T(x,y / x) * z) = (y / x) * (x * z). [para(84(a,1),1168(a,1,1))]. 1200 (T(x / y,z) * y) / x = K(x / y,z). [hyper(24,a,22,a,b,1173,a(flip)),flip(a)]. 1201 K(x / y,z) * x = y * T(y \ x,z). [para(1173(a,1),139(a,1))]. 1202 (R(x,y,z) * (K(x,u) * K(x,u))) / T(T(x,u),u) = x \ R(x,y,z). [para(1176(a,1),536(a,1,1,2))]. 1203 L(x,y,K(y,z)) = x. [hyper(23,a,798,a,b,1191,a(flip)),flip(a)]. 1204 L(x,y,T(z,y) \ z) = x. [para(983(a,1),1203(a,1,3))]. 1205 L(x,y,T(z,y) * z) = x. [para(1204(a,1),776(a,1)),flip(a)]. 1206 L(x,y,z * T(z,y)) = x. [para(116(a,1),1205(a,1,3))]. 1207 ((x * T(x,y)) * y) \ ((x * T(x,y)) * (y * z)) = z. [para(1206(a,1),32(a,1)),flip(a)]. 1208 L(x,y,T(z * u,z) / z) = L(x,y,T((z \ u) * z,z)). [para(138(a,1),1192(a,1,3,1))]. 1209 (x * (R(y,z,u) * w)) / (R(T(y,x),z,u) * w) = T(x,R(y,z,u)). [para(46(a,2),1198(a,1,2,1))]. 1210 (x * (y * (a(T(y,x),z,z) * u))) / (R(T(y,x),z,z) * u) = T(x,y). [para(966(a,1),1198(a,1,2))]. 1211 (x * T(x \ y,z)) / y = K(y / x,z). [para(139(a,1),1200(a,1,1))]. 1212 K((x * y) / x,z) * (x * y) = x * T(y,z). [para(19(a,1),1201(a,2,2,1))]. 1213 x \ (y * T(y \ x,z)) = T(K(x / y,z),x). [para(1201(a,1),36(a,2,2)),flip(a)]. 1214 ((x * y) * T((x * y) \ ((z * x) * y),u)) / ((z * x) * y) = K(R(z,x,y),u). [para(34(a,2),1211(a,2,1))]. 1215 T(x * K(x * y,x),y) = L(x,x \ y,x). [para(495(a,1),1061(a,1,1,2))]. 1216 L(T(x,y),T(y,x),x) = T(x,y * x). [para(82(a,1),1135(a,2,2))]. 1217 (x * y) * T(y,y * (x * y)) = R(y,x,y) * (x * y). [para(1136(a,2),1153(a,2,2)),flip(a)]. 1218 T(x * K(x * y,x),y) = L(x,x * y,x). [para(1215(a,2),312(a,1))]. 1219 T(x / (x / y),x) = L(y,y * x,y). [para(1144(a,2),1218(a,1,1))]. 1220 K(x,T(y,x \ 1)) = K(x,y / (x * x)). [para(401(a,1),1130(a,1,2)),flip(a)]. 1221 K(T(x,y \ 1),y) = K(x / (y * y),y). [para(401(a,1),1143(a,1,1)),flip(a)]. 1222 T(x,T(y,x \ 1)) = T(x,y / (x * x)). [para(401(a,1),1149(a,1,2)),flip(a)]. 1223 K(((x * y) \ x) \ 1,z) = (x * y) \ (x * T(y,z)). [para(19(a,1),1165(a,1,2,2,1)),flip(a)]. 1224 T(x,y) \ T(x,z) = K(x,z) * K(y,x). [para(1175(a,1),581(a,1)),flip(a)]. 1225 K(x,y) * (K(x,z) * K(y,x)) = K(x,z). [para(1224(a,1),1181(a,1,2))]. 1226 K(x,y) * K(z,x) = K(z,x) * K(x,y). [hyper(23,a,901,a,b,1225,a)]. 1229 T(T(x,y),x \ z) = T(T(x,y),x * z). [para(1177(a,1),1132(a,1))]. 1230 T(T(x,y),x * T(y,x)) = (x \ T(y,x)) \ y. [para(1229(a,1),1152(a,1))]. 1231 (x / (x / y)) * x = y * ((y \ x) * y). [para(981(a,1),1178(a,2,2))]. 1232 T(x * y,x) = (y / (y / x)) * y. [para(1231(a,2),138(a,1)),flip(a)]. 1233 T(x * y,x) / y = y / (y / x). [hyper(24,a,22,a,b,1232,a(flip)),flip(a)]. 1234 ((x / y) / x) * T(y * x,y) = x. [hyper(23,a,359,a,b,1232,a(flip)),flip(a)]. 1235 L(x,T(y * z,y),u) = L(x,z / y,u). [para(1232(a,2),877(a,1,2))]. 1236 x \ T(x * y,y) = x / (x / y). [para(1233(a,1),754(a,1)),flip(a)]. 1237 x / T(y * x,y) = (x / y) / x. [hyper(24,a,22,a,b,1234,a),flip(a)]. 1238 T(x * y,y) = x * (x / (x / y)). [para(1236(a,1),20(a,1,2)),flip(a)]. 1239 T(x * (y \ x),y \ x) = x * (x / y). [para(65(a,1),1238(a,2,2,2))]. 1240 T(K(x / y,z),x) = K((x \ y) \ 1,z). [para(1213(a,1),1165(a,1))]. 1241 K((x \ (y \ x)) \ 1,z) = T(K(y,z),x). [para(65(a,1),1240(a,1,1,1)),flip(a)]. 1242 K((T(x,y) \ (T(y,x) \ x)) \ 1,z) = T(K(y,z),T(x,y)). [para(1137(a,1),1240(a,1,1,1)),flip(a)]. 1243 K(T(x \ 1,y) \ 1,z) = T(K(x,z),y). [para(325(a,2),1241(a,1,1,1))]. 1244 K(T((x \ 1) \ 1,y * y),z) = T(K(x,z),y * y). [para(655(a,1),1243(a,1,1))]. 1245 (x \ T(y,x)) \ y = T(T(x,y),y * x). [para(82(a,1),1230(a,1,2)),flip(a)]. 1246 x / L(y,T(x,y),y) = y \ (x * K(y,x)). [para(1156(a,1),1025(a,1,2))]. 1247 x / L(y,T(x,y),y) = K(y,x) * (y \ x). [para(1246(a,2),1188(a,1))]. 1248 L(x \ y,x,K(z,y)) = (K(y,z) * x) \ T(y,z). [para(900(a,1),1084(a,2,1))]. 1249 R(K(x,y),T(x,y) * z,u) \ 1 = R(K(y,x),x * z,u). [para(1098(a,1),906(a,1,2)),flip(a)]. 1250 L(x,y * (y * (z * y)),u) = L(x,z \ (y \ 1),u). [para(51(a,1),929(a,1,2))]. 1251 ((x * y) \ K(x,y)) \ z = K(y,x) * ((x * y) * z). [para(933(a,2),900(a,1))]. 1252 (x * a(x,y,z)) * u = x * (a(x,y,z) * u). [para(948(a,1),946(a,1))]. 1253 a(x,y,z) * (x * u) = x * (a(x,y,z) * u). [para(1252(a,1),772(a,1)),flip(a)]. 1254 x * (a(x,y,z) * (x \ u)) = a(x,y,z) * u. [para(20(a,1),1253(a,1,2)),flip(a)]. 1255 L(x,y * (z \ y),u) = L(x,T(z,y),u). [para(20(a,1),953(a,1,2,1))]. 1256 L(x,T(y \ 1,z),u) = L(x,T(y,z),u). [para(1255(a,1),883(a,2))]. 1257 K(x,y) / (y * x) = (y * x) \ K(x,y). [para(972(a,1),971(a,1,2))]. 1258 L(x,y,T(z \ u,z)) = L(x,y,z / u). [para(1118(a,1),1012(a,1,3))]. 1259 L(x,y,T(z * u,z)) = L(x,y,z / u). [para(1258(a,1),818(a,1)),flip(a)]. 1260 (T(x,y) \ y) * K(x,y * x) = T(y,x) / x. [para(82(a,1),1148(a,1,2,2))]. 1261 L(x,y,K(z,z * u)) = L(x,y,a(z,u,u)). [para(1169(a,1),837(a,1))]. 1262 L(x,y,K(z * u,z)) = L(x,y,a(z,u,u)). [para(1261(a,1),909(a,1)),flip(a)]. 1263 L(x,y,a(z,u * z,u * z)) = L(x,y,K(z,u)). [para(1092(a,1),1261(a,1,3)),flip(a)]. 1264 K(x,T(y,z)) * T(T(y,x),K(x,T(y,z))) = K(z,T(y,x)) * T(y,z). [para(1193(a,1),82(a,2))]. 1265 (x \ y) * (T(x,x * y) * z) = (y / x) * (x * z). [para(1145(a,1),1199(a,1,2,1))]. 1266 (x * (T(x,y) * y)) \ ((x * T(x,y)) * (y * z)) = z. [para(722(a,1),1207(a,1,1))]. 1267 L(K(x,y),x,z) = K(((z * x) \ z) \ 1,y). [para(1223(a,2),1115(a,1)),flip(a)]. 1268 K(L(x \ 1,x,y) \ 1,z) = L(K(x,z),x,y). [para(142(a,2),1267(a,2,1,1)),flip(a)]. 1269 K(T(x,y * y),z) = T(K(x,z),y * y). [para(156(a,1),1244(a,1,1,1))]. 1270 K(T(x,y * y),z) \ 1 = T(K(x,z) \ 1,y * y). [para(1269(a,2),655(a,1,1))]. 1271 L(x,y \ (z \ 1),u) = L(x,y * z,u). [para(1250(a,1),875(a,1))]. 1273 L(x,y * (z \ 1),u) = L(x,y * z,u). [para(1271(a,1),876(a,1)),flip(a)]. 1274 (x \ y) * ((y / x) * (x * z)) = ((x \ y) * y) * z. [para(1265(a,1),253(a,1,2))]. 1275 (x * (T(x,y) * y)) \ (x * (T(x,y) * (y * z))) = z. [para(722(a,1),1266(a,1,2))]. 1276 T(K(x,y) \ 1,z * z) = K(y,T(x,z * z)). [para(1270(a,1),897(a,1))]. 1277 K(x,T(y,z * z)) = T(K(x,y),z * z). [para(897(a,1),1276(a,1,1)),flip(a)]. 1278 K(T(x,y * y),z) = K(x,T(z,y * y)). [para(1277(a,2),1269(a,2))]. 1279 L(L(x,y,T(z,y)),T(z,y) * y,z) = x. [para(1275(a,1),174(a,1)),flip(a)]. 1280 L(L(x,y,T(z,y)),y * z,z) = x. [para(1279(a,1),1185(a,1)),flip(a)]. 1281 L(L(x,y,T(y \ z,y)),z,y \ z) = x. [para(20(a,1),1280(a,1,2))]. 1282 L(x,y * (z * y),y) = L(x,z,T(y,z)). [para(1280(a,1),303(a,1,1))]. 1283 L(x,T(y,z) * z,T(y,z)) = L(x,z * y,y). [para(308(a,1),1280(a,1,1)),flip(a)]. 1284 L(x,T(y,z),z) = L(x,y,T(z,y)). [para(1280(a,1),314(a,1,1))]. 1285 L(x,T(y,y * z),y * z) = L(x,y,y / z). [para(1284(a,2),1259(a,1))]. 1286 L(L(x,y,y / z),z,y \ z) = x. [para(1258(a,1),1281(a,1,1))]. 1287 L(L(x,y,y / z),z,y * z) = x. [para(1286(a,1),776(a,1)),flip(a)]. 1288 L(x,y,z / y) = L(x,y,z * y). [para(304(a,1),1287(a,1,1)),flip(a)]. 1289 L(x \ (x / y),x,y * x) = y \ 1. [para(445(a,1),1287(a,1,1))]. 1290 L(x,y,y / z) = L(x,y,z * y). [para(806(a,1),1287(a,1,1)),flip(a)]. 1291 L(x,y,(z * y) * y) = L(x,y,z). [para(21(a,1),1288(a,1,3)),flip(a)]. 1292 L(x \ 1,x,y * x) = y \ (y / x). [para(1288(a,1),144(a,1))]. 1293 L(x,x,y * x) = y \ (y / (x \ 1)). [para(1288(a,1),432(a,1))]. 1294 x * L(y,z,x * z) = (x / z) * (z * y). [para(1288(a,1),173(a,1,2))]. 1295 (x \ 1) \ L(T(y \ (y / x),z),y,x * y) = K(L(y \ (y / x),y,x * y),z). [para(1289(a,1),1123(a,1,1))]. 1296 ((x * y) * y) \ (x * y) = x \ (x / y). [para(1292(a,1),142(a,1)),flip(a)]. 1297 L(x,y \ 1,T(y * z,y \ 1)) = L(x,(y * z) * z,y * z). [para(322(a,1),1282(a,1,2,2)),flip(a)]. 1298 x * K(L(y \ 1,y,x * y) \ 1,z) = (x / y) * (y * K(y,z)). [para(1268(a,2),1294(a,1,2))]. 1299 x \ L(x,x * y,y) = a(T(y,x),x,x). [para(1283(a,1),452(a,1,2))]. 1300 L(x,y * z,T(z,y)) = L(x,y * z,z). [para(1283(a,1),1185(a,1)),flip(a)]. 1301 T(L(K(x,y),z,K(y,x)),z) = (K(y,x) * z) \ z. [hyper(23,a,82,a,b,910,a(flip)),flip(a)]. 1302 L(x,y * x,x) = R(x,y,x). [hyper(24,a,217,a(flip),b,1217,a(flip)),flip(a)]. 1303 R(x,y / x,x) = L(x,y,x). [para(22(a,1),1302(a,1,2)),flip(a)]. 1304 L(T(x,y),z * x,x) = T(R(x,z,x),y). [para(1302(a,1),44(a,2,1))]. 1305 L(x,y,x) * ((y / x) * x) = (x * (y / x)) * x. [para(1303(a,1),79(a,1,1))]. 1306 L(T(x,y),z * x,x) = R(T(x,y),z,x). [para(1304(a,2),46(a,2)),flip(a)]. 1307 L(x,y,x) * y = (x * (y / x)) * x. [para(22(a,1),1305(a,1,2))]. 1308 T(L(x,y,x) * y,x) = ((y / x) * x) * x. [para(1307(a,2),758(a,1,1))]. 1309 T(L(x,y,x) * y,x) = y * x. [para(22(a,1),1308(a,2,1))]. 1310 (L(x,y,x) * y) * x = x * (y * x). [para(1309(a,1),82(a,1,2)),flip(a)]. 1311 L(R(x,y,x),y,x) = x. [hyper(24,a,184,a,b,1310,a(flip)),flip(a)]. 1312 R(L(x,y,x),y,x) = x. [hyper(24,a,79,a,b,1310,a(flip)),flip(a)]. 1313 R(x,x \ y,x) = L(x,y,x). [para(1311(a,1),302(a,1,1)),flip(a)]. 1314 L(x,x * y,x) = R(x,y,x). [para(1311(a,1),303(a,1,1))]. 1315 R(x,x * y,x) = L(x,y,x). [para(1311(a,1),308(a,1,1)),flip(a)]. 1316 x \ T(y * x,y) = R(y,x,y). [para(1314(a,1),316(a,1)),flip(a)]. 1317 R(x,y,x) * (x \ y) = (x \ y) * T(x,y). [para(1314(a,1),559(a,1,1))]. 1318 T(x * K(x * y,x),y) = R(x,y,x). [para(1314(a,1),1218(a,2))]. 1319 T(x / (x / y),x) = R(y,x,y). [para(1314(a,1),1219(a,2))]. 1320 L(x,y,x) \ x = x \ R(x,y,x). [para(1315(a,1),622(a,1,1))]. 1321 x * R(y,x,y) = T(y * x,y). [para(1316(a,1),20(a,1,2))]. 1322 T(x,R(y,x,y)) = T(x,x / (x / y)). [para(1319(a,1),1131(a,1,2))]. 1323 (x / T(y * x,y)) * T(x,R(y,x,y)) = R(y,x,y) \ x. [para(1321(a,1),1090(a,1,1,2))]. 1324 T(x,y) * K(x * y,T(x,y)) = R(x,y,x). [para(1318(a,1),1060(a,2))]. 1325 T(x,y) * K(y * T(x,y),T(x,y)) = R(x,y,x). [para(82(a,2),1324(a,1,2,1))]. 1326 K(x,y) * (K(y,x) / (x * y)) = (x * y) \ 1. [para(907(a,2),912(a,1))]. 1327 K(x,y) * ((x * y) \ K(y,x)) = (x * y) \ 1. [para(1257(a,1),1326(a,1,2))]. 1328 (x * y) \ K(x,y) = (y * x) \ 1. [para(1327(a,1),941(a,1)),flip(a)]. 1329 K(x,y) * ((y * x) * z) = ((x * y) \ 1) \ z. [para(1328(a,1),1251(a,1,1)),flip(a)]. 1330 K(x,y) * ((y * x) * z) = (x * y) * z. [para(1329(a,2),330(a,1))]. 1331 ((x * y) * z) / ((y * x) * z) = K(x,y). [hyper(24,a,22,a,b,1330,a),flip(a)]. 1332 R(K(x,y),y * x,z) = K(x,y). [para(1331(a,1),977(a,1)),flip(a)]. 1333 R(K(x,T(y,x)),T(y,x) * x,z) = K(x,y). [para(1332(a,2),1079(a,1))]. 1335 R(K(x,y),T(y,x) * x,z) = K(x,y). [para(1079(a,1),1333(a,1,1))]. 1336 ((T(x,y) * y) * z) / ((K(y,x) * (T(x,y) * y)) * z) = K(y,x) \ 1. [para(1335(a,1),344(a,2,1))]. 1337 (x * L(x \ 1,y,z)) \ u = x \ (L(x \ 1,y,z) \ u). [para(216(a,1),924(a,1,1))]. 1338 L(x,y * (y * (z * (y * u))),w) = L(x,z \ (y \ u),w). [para(51(a,1),928(a,1,2))]. 1339 T(x,y) * (R(x,y,x) \ 1) = K(T(x,y),y * x). [para(344(a,1),1154(a,1,2))]. 1340 R(x,y,x) \ T(x,y) = K(T(x,y),y * x). [para(1339(a,1),548(a,1)),flip(a)]. 1341 T(x,y) \ T(T(x,y),y * x) = K(T(x,y),T(x,y) * y). [para(1245(a,1),1170(a,1,2))]. 1342 (((x * y) * T(y,x)) \ (y * y)) * x = K(T(y,x),x * y). [para(1179(a,1),391(a,1)),flip(a)]. 1343 T(x,K(y,T(x,z))) = K(z,x) * T(x,z). [para(1038(a,1),1197(a,1,2)),flip(a)]. 1345 T(x,K(y,T(x,z))) = x. [para(1343(a,2),1077(a,1))]. 1346 T(T(x,y),K(z,T(x,u))) = T(x,y). [para(1345(a,1),42(a,1,1)),flip(a)]. 1350 L(x,y,T(z * u,z) / z) = L(x,y,R(u,z,z)). [para(1208(a,2),864(a,1))]. 1351 T(K(x,y),T(z,x)) = K((z \ (x \ z)) \ 1,y). [para(1186(a,1),1242(a,1,1,1)),flip(a)]. 1352 T(K(x,y),T(z,x)) = T(K(x,y),z). [para(1351(a,2),1241(a,1))]. 1353 T(x,y) * T(K(y,z),x) = K(y,z) * T(x,y). [para(1352(a,1),82(a,1,2))]. 1354 K(x,y) * (K(y,z) * x) = K(y,z) * T(x,y). [para(1353(a,1),1172(a,2))]. 1355 (K(x,y) * T(z,x)) / L(z,K(x,y),K(z,x)) = K(z,x) * K(x,y). [para(1354(a,1),99(a,1,1))]. 1356 ((x / y) / x) * T(x,R(y,x,y)) = R(y,x,y) \ x. [para(1237(a,1),1323(a,1,1))]. 1357 L(x \ 1,y,z) \ (x \ u) = x \ (L(x \ 1,y,z) \ u). [para(1337(a,1),803(a,1)),flip(a)]. 1358 L(x,y \ (z \ u),w) = L(x,y * (z * u),w). [para(1338(a,1),875(a,1))]. 1360 L(x,y * (z \ u),w) = L(x,y * (z * u),w). [para(1358(a,1),876(a,1)),flip(a)]. 1361 L(x,y * (z * (z * u)),w) = L(x,y * u,w). [para(19(a,1),1360(a,1,2,2)),flip(a)]. 1362 L(x,(y \ z) * (z \ y),u) = L(x,(z \ y) * (y * z),u). [para(384(a,1),1360(a,1,2))]. 1363 L(x,y * R(z,z * u,w),v5) = L(x,y * (R(z,u,w) \ 1),v5). [para(615(a,1),1361(a,1,2,2))]. 1364 K(T(x,y),T(x,y) * y) = K(T(x,y),y * x). [para(1341(a,1),1108(a,2)),flip(a)]. 1365 (((x * y) * x) \ (x * x)) * y = K(T(x,y),y * x). [para(1087(a,1),1342(a,1,1,1))]. 1366 K(T(x,y),y * x) = K(x,x * y). [para(1365(a,1),408(a,1))]. 1367 R(x,y,x) \ T(x,y) = K(x,x * y). [para(1366(a,1),1340(a,2))]. 1368 K(x,x * y) \ T(x,y) = R(x,y,x). [para(1367(a,1),734(a,1,1))]. 1369 K(x * y,x) * T(x,y) = R(x,y,x). [para(1368(a,1),900(a,1)),flip(a)]. 1370 R(x,y,x) / T(x,y) = K(x * y,x). [hyper(24,a,22,a,b,1369,a),flip(a)]. 1371 (x \ (L(x \ 1,x,x / y) \ 1)) * (y \ (y / x)) = x \ 1. [para(1357(a,1),521(a,1,1))]. 1372 R(x,y \ 1,y) \ a(x,y,y) = x \ 1. [para(961(a,2),476(a,1))]. 1374 R(x,y,y) \ a(x,y,y) = x \ 1. [para(717(a,1),1372(a,1,1))]. 1375 (x * y) \ (x * (y * z)) = L(z,T(y,x),T(x,y)). [para(1168(a,1),1151(a,1,2))]. 1376 L(x,T(y,z),T(z,y)) = L(x,y,z). [para(1375(a,1),32(a,2)),flip(a)]. 1377 L(T(x,y),y,K(z,x)) = T(x,K(z,x) * y). [para(1190(a,1),36(a,2)),flip(a)]. 1378 (x \ (L(x \ 1,x,y * x) \ 1)) * (y \ (y / x)) = x \ 1. [para(1290(a,1),1371(a,1,1,2,1))]. 1379 ((x \ y) * z) \ (x \ u) = ((x * y) * z) \ (x * u). [para(794(a,1),201(a,1))]. 1380 (x * ((x \ y) * y)) \ z = ((x * y) * y) \ (x * z). [para(1379(a,1),893(a,2))]. 1381 (x * ((x \ y) * y)) \ y = x \ (x / y). [para(1380(a,2),1296(a,1))]. 1382 x / (y \ (y / x)) = y * ((y \ x) * x). [para(1381(a,1),65(a,1,2))]. 1383 (x \ (x / y)) \ y = x * ((x \ y) * y). [para(1382(a,1),872(a,1)),flip(a)]. 1384 x * L(x,y * x,y) = (y \ (y / x)) \ x. [para(1383(a,2),435(a,2))]. 1385 (x * L(x,y * x,y)) / x = (y \ (y / x)) \ 1. [para(1384(a,2),320(a,1,1))]. 1386 L(x,y * x,y) = (y \ (y / x)) \ 1. [para(1385(a,1),218(a,1)),flip(a)]. 1387 x \ ((y \ (y / x)) \ 1) = a(y,x,x). [para(1386(a,1),452(a,1,2))]. 1388 (x \ (x / y)) \ 1 = y * a(x,y,y). [para(1386(a,1),453(a,1))]. 1389 (x \ 1) \ (L(x,x,y * x) \ 1) = a(y,x \ 1,x \ 1). [para(1293(a,2),1387(a,1,2,1))]. 1390 (x \ (x / y)) \ z = (y * a(x,y,y)) * z. [para(1388(a,1),318(a,1,1)),flip(a)]. 1391 K(x,(x * x) / (y \ (y / z))) = K(x,z * a(y,z,z)). [para(1388(a,1),492(a,2,2))]. 1392 L(x \ 1,x,y * x) \ 1 = x * a(y,x,x). [para(1292(a,2),1388(a,1,1))]. 1393 (x \ (x * a(y,x,x))) * (y \ (y / x)) = x \ 1. [para(1392(a,1),1378(a,1,1,2))]. 1394 a(x,y,y) * (x \ (x / y)) = y \ 1. [para(19(a,1),1393(a,1,1))]. 1396 a(K(x,y),z,z) * (K(y,x) \ (K(y,x) / z)) = z \ 1. [para(905(a,1),1394(a,1,1))]. 1397 a(x,y,y) * (x / y) = x * (y \ 1). [para(1394(a,1),1254(a,1,2)),flip(a)]. 1398 (x * (y \ 1)) / (x / y) = a(x,y,y). [hyper(24,a,22,a,b,1397,a),flip(a)]. 1399 (x / y) * (y * (x \ 1)) = a(y,x,x). [para(1398(a,1),669(a,1)),flip(a)]. 1400 a(x / y,y,y \ 1) = a(x,y,y). [para(1399(a,1),592(a,2))]. 1401 a(x * (y * y),y \ 1,(y \ 1) \ 1) = a(x * y,y \ 1,y \ 1). [para(400(a,1),1400(a,1,1))]. 1402 K(x,(y \ (y / z)) \ 1) = K(x,z * a(y,z,z)). [para(1391(a,1),492(a,1)),flip(a)]. 1403 a(K(x,y),z,z) * (K(x,y) * (K(y,x) / z)) = z \ 1. [para(900(a,1),1396(a,1,2))]. 1404 K(x,y) * (a(K(x,y),z,z) * (K(y,x) / z)) = z \ 1. [para(1403(a,1),1253(a,1)),flip(a)]. 1405 R(K(x,y),z,z) * (K(y,x) / z) = z \ 1. [para(1404(a,1),966(a,1)),flip(a)]. 1406 x * (L(x,x,y * x) \ 1) = a(y,x \ 1,x \ 1). [para(1389(a,1),330(a,1)),flip(a)]. 1407 a(x,y \ 1,y \ 1) = L(y,y,x * y) \ y. [para(1406(a,1),471(a,1))]. 1408 a(x * y,y \ 1,y \ 1) = L(y,y,x) \ y. [para(1291(a,1),1407(a,2,1))]. 1409 (x * (y \ z)) \ (x * (y \ (z * u))) = L(L(u,z,y),y * z,x). [para(813(a,2),876(a,1))]. 1410 (x * y) * (z / (x * (y * z))) = x \ R(x,y,z). [para(853(a,1),537(a,1))]. 1411 L(x,y \ R(y,z,u),y * z) = x. [para(1410(a,1),852(a,1,2))]. 1412 L(x,y * R(y,z,u),y * z) = x. [para(1411(a,1),876(a,1)),flip(a)]. 1413 L(x,y * R(y,y * z,u),z) = x. [para(1412(a,1),774(a,1)),flip(a)]. 1414 K(T(x,y \ 1),y) * (x * (y \ 1)) = T(x,y) * (y \ 1). [para(1182(a,2),329(a,1))]. 1415 K(T(x,y \ 1),y) = K(x,y). [hyper(24,a,1160,a,b,1414,a)]. 1416 (x * (y \ 1)) / (T(x,y) * (y \ 1)) = K(y,T(x,y \ 1)). [para(1414(a,1),902(a,1,2))]. 1418 K(x / (y * y),y) = K(x,y). [para(1415(a,1),1221(a,1)),flip(a)]. 1419 K(x,T(y,x \ 1)) = K(x,y). [para(1416(a,1),1102(a,1))]. 1420 K(x \ 1,T(y,x)) = K(x \ 1,y). [para(156(a,1),1419(a,1,2,2))]. 1421 T(x,T(y,x \ 1)) = x * K(x,y). [para(1419(a,1),1107(a,2,2))]. 1423 K(x,y / (x * x)) = K(x,y). [para(1419(a,1),1220(a,1)),flip(a)]. 1424 K(x,R(y / x,x,x)) = K(x,y * x). [para(80(a,2),1423(a,1,2))]. 1425 ((x \ 1) * T(y,x)) / (x \ 1) = T(y,x) * K(x \ 1,y). [para(1420(a,1),1014(a,2,2))]. 1426 T(x,T(y,x \ 1)) = T(x,y). [para(1421(a,2),1107(a,2)),flip(a)]. 1427 T(x \ 1,T(y,x)) = T(x \ 1,y). [para(156(a,1),1426(a,1,2,2))]. 1428 T(x,y / (x * x)) = T(x,y). [para(1426(a,1),1222(a,1)),flip(a)]. 1429 L(x,T(y,z),T(T(z,y \ 1),y)) = L(x,y,T(z,y \ 1)). [para(1426(a,1),1376(a,1,2))]. 1430 T(x,(y * x) * x) = T(x,R(y,x,x)). [para(34(a,2),1428(a,1,2)),flip(a)]. 1431 L(x,T(y \ 1,z),T(T(z,y),y \ 1)) = L(x,y \ 1,T(z,y)). [para(1427(a,1),1376(a,1,2))]. 1432 (x \ T(y,x)) / (x \ 1) = T(y,x) * K(x \ 1,y). [para(318(a,1),1425(a,1,1))]. 1433 T(x,y) * K(y \ 1,x) = T(x,y * y). [para(1432(a,1),486(a,1))]. 1434 L(x,T(y,z),T(T(z,y),y \ 1)) = L(x,y,T(z,y \ 1)). [para(42(a,1),1429(a,1,3))]. 1435 L(x,R(y,z,z),y * z) = L(x,y \ 1,T(y * z,y \ 1)). [para(1297(a,2),938(a,1)),flip(a)]. 1436 L(x,R(y,z,z),y * z) = L(x,y,T(y * z,y \ 1)). [para(1435(a,2),887(a,1))]. 1437 L(x,y * R(z,z * u,w),v5) = L(x,y * R(z,u,w),v5). [para(1363(a,2),1273(a,1))]. 1438 L(x,y * R(y,z,u),z) = x. [para(1437(a,1),1413(a,1))]. 1439 L(x,y * (z * R(z,y,u)),y) = x. [para(1438(a,1),303(a,1,1))]. 1440 L(x,y \ R(y \ 1,z,u),z) = x. [para(318(a,1),1438(a,1,2))]. 1441 (x * (y \ R(y,x,z))) * u = x * ((y \ R(y,x,z)) * u). [para(1438(a,1),888(a,1,2))]. 1442 a(x,x * (y * R(y,x,z)),u) = 1. [hyper(38,a,1439,a)]. 1443 L(x,y * R(y \ 1,z,u),z) = x. [para(1440(a,1),876(a,1)),flip(a)]. 1444 L(x,a(y,z,z),z) = x. [para(960(a,1),1443(a,1,2))]. 1445 x / (a(y,x,x) \ 1) = x * a(y,x,x). [para(1444(a,1),145(a,1,2))]. 1446 (x * a(y,x,x)) * z = x * (a(y,x,x) * z). [para(1444(a,1),74(a,1,2))]. 1447 K(x,(y \ (y / z)) \ 1) = K(x,z / (a(y,z,z) \ 1)). [para(1445(a,2),1402(a,2,2))]. 1448 (x \ (x / y)) \ z = y * (a(x,y,y) * z). [para(1446(a,1),1390(a,2))]. 1449 L(x * (a(y,x,x) * z),y * (y / x),y) = (y / x) \ (y * z). [para(1448(a,1),311(a,1,1))]. 1450 (x * (y \ R(y,x,z))) * u = x * (R(y,x,z) * (y \ u)). [para(532(a,1),1441(a,2,2))]. 1451 L(x,T(y,z),T(T(z,y),y \ 1)) = L(x,y \ 1,T(z,y)). [para(1431(a,1),1256(a,1)),flip(a)]. 1452 L(x,y \ 1,T(z,y)) = L(x,y,T(z,y \ 1)). [para(1451(a,1),1434(a,1))]. 1453 L(x,y,T(z,y \ 1)) = L(x,y,T(z,y)). [para(1452(a,1),887(a,1))]. 1454 L(x,R(y,z,z),y * z) = L(x,y,T(y * z,y)). [para(1453(a,1),1436(a,2))]. 1455 L(x,R(y,z,z),y * z) = L(x,y,y / z). [para(1454(a,2),1259(a,1))]. 1456 L(x,R(y,z,z),y * z) = L(x,y,z * y). [para(1455(a,2),1290(a,1))]. 1457 L(T(x,y),y * K(x,y),T(x,y)) = (x \ y) \ y. [para(1187(a,1),1141(a,2,1))]. 1458 (x * (y * z)) \ ((x * y) * z) = a(T(x,y),T(y,x),z). [para(1168(a,1),1150(a,1,1))]. 1459 a(T(x,y),T(y,x),z) = a(x,y,z). [para(1458(a,1),28(a,2)),flip(a)]. 1460 a(T(x,y),T(T(y,x),x),z) = a(x,T(y,x),z). [para(1131(a,1),1459(a,1,1))]. 1461 x \ (y \ (y \ (T(y,x) * ((x * y) * z)))) = L(z,x * y,T(y,x)). [para(1180(a,1),443(a,1)),flip(a)]. 1462 x * K(y * a(x,y,y),z) = (x / y) * (y * K(y,z)). [para(1392(a,1),1298(a,1,2,1))]. 1463 x * K(y * a(x,y,y),z) = (x / y) * T(y,z). [para(1107(a,2),1462(a,2,2))]. 1464 x \ (y \ (K(y,x) * ((x * y) * z))) = L(z,x * y,T(y,x)). [para(1127(a,1),1461(a,1,2,2))]. 1465 x \ (y \ ((y * x) * z)) = L(z,x * y,T(y,x)). [para(1330(a,1),1464(a,1,2,2))]. 1466 L(x,y * z,T(z,y)) = L(x,z * y,z). [para(1465(a,1),309(a,1))]. 1467 L(x,y * z,z) = L(x,z * y,z). [para(1466(a,1),1300(a,1)),flip(a)]. 1468 L(L(x,y,z),y * z,z) = x. [para(1467(a,2),303(a,1))]. 1469 L(L(x,y * z,z),y,z) = x. [para(1467(a,2),308(a,1,1))]. 1470 x \ L(x,x * y,y) = a(y,x,x). [para(1467(a,2),452(a,1,2))]. 1471 L(x,y * (y / z),y) = L(x,z,y). [para(1467(a,1),877(a,1))]. 1472 L(x,(y * z) * z,y * z) = L(x,T(y,z),y * z). [para(1467(a,1),878(a,1))]. 1473 L(x,T(y,z),z) = L(x,y,z). [para(1468(a,1),314(a,1,1))]. 1474 L(L(x,y,z * y),z,z * y) = x. [para(875(a,1),1469(a,1,1))]. 1475 L(T(x,y),y,x) = T(x,y * x). [para(1473(a,1),1216(a,1))]. 1476 K(x,y) * (x \ y) = y / L(x,y,x). [para(1473(a,1),1247(a,1,2)),flip(a)]. 1477 L(x,y,y / z) = L(x,y,y * z). [para(1473(a,1),1285(a,1)),flip(a)]. 1478 (x * T(y,x)) \ (T(y,z) * x) = L(K(T(y,x),z),y,x). [para(1473(a,1),1195(a,2))]. 1479 T(x,y * x) = T(x,x * y). [para(1475(a,1),203(a,1))]. 1480 K(x,y) * L(x,y,x) = T(x,x * y). [para(1479(a,1),955(a,2))]. 1481 T(x,x * y) * K(y * x,x) = x. [para(1479(a,1),1089(a,1,1))]. 1482 T(x,x * (y * x)) = T(x,R(y,x,x)). [para(1479(a,1),1430(a,1))]. 1483 x \ L(x,y,x * y) = a(x * y,x,x). [para(875(a,1),1470(a,1,2))]. 1484 x \ L(x,T(y,x),y * x) = a(y * x,x,x). [para(878(a,1),1470(a,1,2))]. 1485 a(T(x,y),y,y) = a(x,y,y). [para(1470(a,1),1299(a,1)),flip(a)]. 1486 L(x * (a(y,x,x) * z),x,y) = (y / x) \ (y * z). [para(1471(a,1),1449(a,1))]. 1487 L(x,y,y * x) = x * a(y * x,x,x). [para(454(a,1),1474(a,1,1))]. 1488 L(x,x,x * y) = y \ (y / (x \ 1)). [para(1477(a,1),807(a,1))]. 1489 K(x * y,y) = K(y * x,y). [hyper(23,a,1089,a,b,1481,a)]. 1490 T(x * K(x * y,x),y * x) = x. [para(1489(a,1),1020(a,1,1,2))]. 1491 x / (x / y) = y * K(x * y,y). [para(1489(a,2),1144(a,2,2))]. 1492 R(x,y,x) / T(x,y) = K(y * x,x). [para(1489(a,2),1370(a,2))]. 1493 T(x / (x / y),x * y) = y. [para(1144(a,2),1490(a,1,1))]. 1494 T(x * y,x / (x / y)) = T(x * y,y). [para(1493(a,1),1131(a,1,2)),flip(a)]. 1495 (x / (x / y)) \ T(x * y,x / (x / y)) = y \ (x * y). [para(1493(a,1),1138(a,1,1)),flip(a)]. 1496 R(x,y,x) = y / (y / T(x,y)). [para(1491(a,2),1325(a,1)),flip(a)]. 1497 R(x,y,x) \ y = y / T(x,y). [para(1496(a,2),66(a,1,1))]. 1498 (T(x,y) \ y) * K(T(x,y),T(x,y) * y) = R(x,y,x) \ y. [para(1497(a,2),1001(a,2))]. 1499 ((x / y) / x) * T(x,R(y,x,y)) = x / T(y,x). [para(1497(a,1),1356(a,2))]. 1500 K(x,y) = (y \ x) / (x / L(y,x,y)). [para(1476(a,1),902(a,1,2)),flip(a)]. 1501 (x * y) / (K(x,y) * L(x,y,x)) = R(x,x * y,x) \ (x * y). [para(1480(a,2),1497(a,2,2)),flip(a)]. 1502 T(x,R(y,x,x)) = T(x,y). [para(1482(a,1),1136(a,1))]. 1503 K(x,R(y,x,x)) = x \ T(x,y). [para(1502(a,1),1108(a,2,2))]. 1504 K(x,R(y,x,x)) = K(x,y). [para(1503(a,2),1108(a,2)),flip(a)]. 1505 K(x,y / x) = K(x,y * x). [para(1504(a,1),1424(a,1))]. 1506 K(x,y * x) = K(x,x * y). [para(1505(a,1),1078(a,1))]. 1507 ((x * y) * y) \ ((y * x) * y) = K(y,y * (y * x)). [para(1506(a,1),1103(a,2))]. 1508 (T(x,y) \ y) * K(x,x * y) = T(y,x) / x. [para(1506(a,1),1260(a,1,2))]. 1509 K(T(x,y),y * T(x,y)) = K(T(x,y),y * x). [para(1506(a,2),1364(a,1))]. 1510 T(x,y) \ R(x,y,x) = K(y * x,x). [para(1492(a,1),693(a,1)),flip(a)]. 1511 K(x,y) * (y \ R(y,x,y)) = K(x * y,y). [para(1510(a,1),1095(a,2))]. 1512 K(T(x,y),y * x) = K(T(x,y),x * y). [para(82(a,1),1509(a,1,2)),flip(a)]. 1513 K(T(x,y),x * y) = K(x,x * y). [para(1512(a,1),1366(a,1))]. 1514 L(x,R(y,z,z),y * z) = L(x,T(y,z),y * z). [para(1472(a,1),938(a,1)),flip(a)]. 1515 L(x,T(y,z),y * z) = L(x,y,z * y). [para(1514(a,1),1456(a,1))]. 1516 x \ L(x,y,x * y) = a(y * x,x,x). [para(1515(a,1),1484(a,1,2))]. 1517 a(x * y,y,y) = a(y * x,y,y). [para(1516(a,1),1483(a,1))]. 1518 L(x * (a(y,x,x) * z),x,y) = (x / y) * (y * z). [para(1486(a,2),358(a,1))]. 1519 K(x,y) = ((y * x) * x) \ ((x * y) * x). [para(1507(a,2),490(a,1)),flip(a)]. 1520 (x * (y * x)) \ ((x * y) * x) = K(y * x,x) * K(x,y). [para(1519(a,2),941(a,1,2)),flip(a)]. 1521 (x * y) \ (T(x,z) * y) = L(K(T(x,y),z),x,y). [para(82(a,1),1478(a,1,1))]. 1522 L(K(T(x,y),z),x,y) = T(K(x,z),x * y). [para(1521(a,1),1184(a,1))]. 1523 (x / (x / y)) \ T(x * y,x / (x / y)) = T(x,y). [para(1495(a,2),36(a,2)),flip(a)]. 1524 (x / (x / y)) \ T(x * y,y) = T(x,y). [para(1494(a,1),1523(a,1,2))]. 1525 ((x / y) / x) * T(x * y,y) = T(x,y). [para(1524(a,1),358(a,1)),flip(a)]. 1526 (x / y) * T(y * (x \ y),x \ y) = T(y,x \ y). [para(65(a,1),1525(a,1,1,1))]. 1527 L(x,y,z * (((u / w) / u) * T(u,w))) = L(x,y,z * T(u * w,w)). [para(1525(a,1),868(a,1,3,2,2))]. 1528 (x / y) * (y * (y / x)) = T(y,x \ y). [para(1239(a,1),1526(a,1,2))]. 1529 T(x,x / y) = T(x,y \ x). [para(1528(a,1),369(a,1)),flip(a)]. 1530 T(x,R(y,x,y)) = T(x,(x / y) \ x). [para(1529(a,1),1322(a,2))]. 1531 T(x,R(y,x,y)) = T(x,y). [para(66(a,1),1530(a,2,2))]. 1532 ((x / y) / x) * T(x,y) = x / T(y,x). [para(1531(a,1),1499(a,1,2))]. 1533 K(x * y,y) * K(y,x) = a(y,x,y). [para(1520(a,1),28(a,2)),flip(a)]. 1534 K(x,y) * K(y * x,x) = a(x,y,x). [para(1533(a,1),1226(a,2))]. 1535 K(x * y,x) * K(x,y) = a(x,y,x). [para(1489(a,1),1533(a,1,1))]. 1536 K(x,y) * a(y,x,y) = K(x * y,y). [hyper(23,a,901,a,b,1534,a),flip(a)]. 1537 K(x,y) * K(x * y,x) = a(x,y,x). [para(1489(a,1),1534(a,1,2))]. 1538 (((x \ y) * x) / y) * K(x,y) = a(x,y,x). [para(982(a,2),1535(a,1,1))]. 1539 x \ R(x,y,x) = a(x,y,x). [hyper(23,a,1511,a,b,1536,a),flip(a)]. 1540 x * a(x,y,x) = R(x,y,x). [para(1539(a,1),20(a,1,2))]. 1541 L(x,y,x) \ x = a(x,y,x). [para(1539(a,1),1320(a,2))]. 1542 a(x,y,x) * L(x,y,x) = x. [para(1541(a,1),520(a,1,1))]. 1543 (x * y) / L(L(y,z,y),a(y,z,y),x) = x * a(y,z,y). [para(1542(a,1),99(a,1,1,2))]. 1544 (T(x,y) \ y) * K(T(x,y),y * T(x,y)) = R(x,y,x) \ y. [para(1506(a,2),1498(a,1,2))]. 1545 (T(x,y) \ y) * K(T(x,y),x * y) = R(x,y,x) \ y. [para(82(a,1),1544(a,1,2,2))]. 1546 (T(x,y) \ y) * K(x,x * y) = R(x,y,x) \ y. [para(1513(a,1),1545(a,1,2))]. 1547 R(x,y,x) \ y = T(y,x) / x. [para(1546(a,1),1508(a,1))]. 1548 T(x,y) / y = x / T(y,x). [para(1547(a,1),1497(a,1))]. 1549 (x / T(y,x)) * y = T(x,y). [para(1548(a,1),22(a,1,1))]. 1550 (x / y) * (y * K(x,y)) = T(x,y * K(x,y)). [para(1020(a,1),1549(a,1,1,2))]. 1551 T(x,y) = (x / y) * (y * K(x,y)). [para(1550(a,2),1139(a,1)),flip(a)]. 1552 (x / y) * T(y,x) = x * K(y,x). [hyper(23,a,359,a,b,1551,a(flip)),flip(a)]. 1553 (x * (y \ 1)) * T(L(y,y,x),x) = x * K(L(y,y,x),x). [para(915(a,1),1552(a,1,1))]. 1554 (x * (y \ 1)) * L(T(y,x),y,x) = x * K(L(y,y,x),x). [para(44(a,2),1553(a,1,2))]. 1555 x * K(L(y,y,x),x) = x * (y \ T(y,x)). [para(1554(a,1),945(a,1))]. 1556 x * K(L(y,y,x),x) = x * K(y,x). [para(1108(a,2),1555(a,2,2))]. 1557 T(x * K(y,x),L(y,y,x)) = x. [para(1556(a,1),1020(a,1,1))]. 1558 T(x,L(y,y,x)) = T(x,y). [para(1557(a,1),1023(a,1,1)),flip(a)]. 1559 (x * y) / (K(x,y) * L(x,y,x)) = L(x,y,x) \ (x * y). [para(1315(a,1),1501(a,2,1))]. 1560 (x * y) / (K(x,y) * L(x,y,x)) = (L(x,y,x) \ x) * y. [para(1559(a,2),524(a,1))]. 1561 (x * y) / T(x,x * y) = (L(x,y,x) \ x) * y. [para(1480(a,1),1560(a,1,2))]. 1562 (L(x,y,x) \ x) * y = T(x * y,x) / x. [para(1561(a,1),1548(a,2)),flip(a)]. 1563 T(x * y,x) / x = a(x,y,x) * y. [para(1541(a,1),1562(a,1,1)),flip(a)]. 1564 R(K(x,y),K(y,x) * z,u) \ K(x,y) = K(y,x) * R(K(x,y),z,u). [para(923(a,2),900(a,1))]. 1565 x * (y * (R(y,y * (x \ 1),z) \ (x \ z))) = L(z,y * x,y). [para(318(a,1),957(a,1,2,2,2))]. 1566 x * (R(y,x \ 1,z) * (y \ (x \ z))) = L(z,y * x,y). [para(637(a,1),1565(a,1,2))]. 1567 x * (R(y,x,z) * (y \ (x \ z))) = L(z,y * x,y). [para(717(a,1),1566(a,1,2,1))]. 1568 R(x * (K(x,y) * K(x,y)),z,u) / T(T(x,y),y) = x \ R(x,z,u). [para(705(a,2),1202(a,1,1))]. 1569 K(x,T(y,z)) * T(y,x) = K(z,T(y,x)) * T(y,z). [para(1346(a,1),1264(a,1,2))]. 1570 (K(x,T(y,z)) * T(y,x)) / L(y,K(y,z),K(z,T(y,x))) = K(z,T(y,x)) * K(y,z). [para(1569(a,1),1106(a,1,1))]. 1572 ((T(x,y) * y) * z) / ((x * y) * z) = K(y,x) \ 1. [para(1098(a,1),1336(a,1,2,1))]. 1574 a(x * (y * y),y \ 1,y) = a(x * y,y \ 1,y \ 1). [para(156(a,1),1401(a,1,3))]. 1575 L(x,y,z * T(u * w,w)) = L(x,y,z * (u / T(w,u))). [para(1532(a,1),1527(a,1,3,2)),flip(a)]. 1576 L(x,y,z * (T(u,w) / w)) = L(x,y,z * T(u * w,w)). [para(1548(a,2),1575(a,2,3,2)),flip(a)]. 1577 (R(K(x,y),z,u) \ 1) \ K(y,x) = K(x,y) * R(K(y,x),z,u). [para(904(a,1),1564(a,1,1))]. 1578 R(K(x,y),z,u) * K(y,x) = K(x,y) * R(K(y,x),z,u). [para(1577(a,1),330(a,1)),flip(a)]. 1579 K(x,y) * R(K(y,x),T(x,y) * z,u) = R(K(y,x),x * z,u) \ K(y,x). [para(1249(a,1),1577(a,1,1)),flip(a)]. 1580 R(T(x,y) * K(x,y),z,u) / T(T(x,y),y) = x \ R(x,z,u). [para(1120(a,1),1568(a,1,1,1))]. 1581 R(T(T(x,y),y),z,u) / T(T(x,y),y) = x \ R(x,z,u). [para(1121(a,1),1580(a,1,1,1))]. 1582 T(T(x,y),y) \ R(T(T(x,y),y),z,u) = x \ R(x,z,u). [para(1581(a,1),478(a,1)),flip(a)]. 1583 (x * y) * T((x * y) \ (x * z),u) = (x * y) * L(T(y \ z,u),y,x). [para(44(a,2),764(a,1,2)),flip(a)]. 1584 (x * y) * R((x * y) \ x,z,u) = (x * y) * L(R(y \ 1,z,u),y,x). [para(48(a,1),765(a,1,2)),flip(a)]. 1585 (x \ 1) * L((x \ 1) \ y,z,u) = L(y * x,z,u) / x. [para(720(a,1),766(a,1,1,1)),flip(a)]. 1586 (x \ 1) * L(x * y,z,u) = L(y * x,z,u) / x. [para(330(a,1),1585(a,1,2,1))]. 1587 L(x * y,z,u) / y = y \ L(y * x,z,u). [para(1586(a,1),318(a,1))]. 1588 (x \ y) \ L((x \ y) * x,z,u) = L(y,z,u) / (x \ y). [para(20(a,1),1587(a,1,1,1)),flip(a)]. 1589 (K(x,y) * (x \ z)) \ (K(x,y) * (x \ (z * u))) = L(u,z,x \ K(x,y)). [para(1072(a,1),1189(a,1,2))]. 1590 (x * y) * T((x * y) \ (x * z),u) = x * (y * T(y \ z,u)). [para(1583(a,2),74(a,1))]. 1591 (x * y) * R((x * y) \ x,z,u) = x * (y * R(y \ 1,z,u)). [para(1584(a,2),74(a,1))]. 1592 (x * y) * R((x * y) \ x,z,u) = x * (y \ R(y,z,u)). [para(635(a,1),1591(a,2,2))]. 1593 (x / y) * (y * R(((y \ x) * x) \ (y \ x),z,u)) = x \ R(x,z,u). [hyper(23,a,1274,a,b,1592,a(flip)),flip(a)]. 1594 (x / y) * (y * R(((y * x) * x) \ (y * x),z,u)) = x \ R(x,z,u). [para(1379(a,1),1593(a,1,2,2,1))]. 1595 (x / y) * (y * R(y \ (y / x),z,u)) = x \ R(x,z,u). [para(1296(a,1),1594(a,1,2,2,1))]. 1596 ((x \ y) / y) * (y * R(y \ x,z,u)) = (x \ y) \ R(x \ y,z,u). [para(65(a,1),1595(a,1,2,2,1,2))]. 1597 (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). [para(99(a,1),1595(a,1,2,2,1,2))]. 1598 (x \ 1) * (y * R(y \ x,z,u)) = (x \ y) \ R(x \ y,z,u). [para(320(a,1),1596(a,1,1))]. 1599 (x \ y) \ R(x \ y,z,u) = x \ (y * R(y \ x,z,u)). [para(1598(a,1),318(a,1))]. 1601 (x * y) \ R(x * y,z,u) = x \ (y * R(y \ x,z,u)). [para(1599(a,1),750(a,1)),flip(a)]. 1602 L(L(x,y,z),z * y,K(z,u)) = L(x,y,z \ K(z,u)). [para(1589(a,1),1409(a,1)),flip(a)]. 1603 L(L(x,y,z),z * y,K(z,u)) = L(x,y,z * K(z,u)). [para(1602(a,2),776(a,1))]. 1604 L(L(x,y,z),z * y,K(z,u)) = L(x,y,T(z,u)). [para(1107(a,2),1603(a,2,3))]. 1605 L(L(x,y,z),z * y,T(z,u)) = L(x,z * (z * y),K(z,u)). [para(303(a,1),1604(a,1,1)),flip(a)]. 1606 L(L(x,y,z),z * y,T(z,u)) = L(x,y,K(z,u)). [para(1605(a,2),875(a,1))]. 1608 (x * (y * x)) \ R(x * (z * x),u,w) = T(y,x) \ T(R(z,u,w),x). [para(36(a,2),701(a,2,2))]. 1609 (x * (y * x)) \ R(x * (z * x),u,w) = T(y,x) \ R(T(z,x),u,w). [para(46(a,2),1608(a,2,2))]. 1610 x \ ((y * x) * R((y * x) \ x,z,u)) = T(y,x) \ R(T(y,x),z,u). [para(1609(a,1),1601(a,1)),flip(a)]. 1611 L(x,y,z * (u \ (u \ (u \ (z * (u \ 1)))))) = L(x,y,K(z / (u * u),u)). [para(602(a,1),1194(a,1,3))]. 1612 L(x,y,z * (u \ ((u \ (u \ z)) * (u \ 1)))) = L(x,y,K(z / (u * u),u)). [para(285(a,1),1611(a,1,3,2,2))]. 1613 L(x,y,z * (u * ((u \ (u \ z)) * (u \ 1)))) = L(x,y,K(z / (u * u),u)). [para(1612(a,1),867(a,1)),flip(a)]. 1614 L(x,y,K(z / (u * u),u)) = L(x,y,z * (u \ (z * (u \ 1)))). [para(265(a,1),1613(a,1,3,2)),flip(a)]. 1615 L(x,y,K(z / (u * u),u)) = L(x,y,z * (u * (z * (u \ 1)))). [para(1614(a,2),867(a,1))]. 1616 L(x,y,K(z / (u * u),u)) = L(x,y,z * T(z,u \ 1)). [para(347(a,1),1615(a,2,3,2))]. 1617 L(x,y,K(z / (u * u),u)) = L(x,y,K(z,u \ 1)). [para(1616(a,2),1119(a,1))]. 1618 L(x,y,K(z,u \ 1)) = L(x,y,K(z,u)). [para(1418(a,1),1617(a,1,3)),flip(a)]. 1619 L(x,y,K(z,u \ 1)) = L(x,y,K(u,z)). [para(1618(a,2),909(a,1))]. 1620 (x * (x * (y * (z * u)))) \ ((x * (x * (y * z))) * u) = a(x * (x * y),z,u). [para(51(a,1),91(a,1,2,1))]. 1621 (x * y) * R(L(y \ z,y,x),u,w) = (x * y) * R((x * y) \ (x * z),u,w). [para(473(a,1),224(a,1))]. 1622 (x * y) * R((x * y) \ (z * y),u,w) = (R(z / x,u,w) * x) * y. [para(474(a,1),185(a,1))]. 1623 (x * y) * R((x * y) \ (z * y),u,w) = (x * R(x \ z,u,w)) * y. [para(224(a,1),1622(a,2,1))]. 1624 ((x * y) * ((y * x) * z)) \ (((x * y) * (y * x)) * (z * u)) = L(u,z,K(y,x)). [para(894(a,1),832(a,1,1))]. 1625 ((x * y) * T(R(T(z,x * y),x,y),u)) / ((z * x) * y) = K(R(z,x,y),u). [para(549(a,1),1214(a,1,1,2,1))]. 1626 ((x * y) * R(T(T(z,x * y),u),x,y)) / ((z * x) * y) = K(R(z,x,y),u). [para(46(a,2),1625(a,1,1,2))]. 1627 (R(T(x,y),z,u) * (z * u)) / ((x * z) * u) = K(R(x,z,u),y). [para(222(a,1),1626(a,1,1))]. 1628 ((T(x,y) * z) * u) / ((x * z) * u) = K(R(x,z,u),y). [para(79(a,1),1627(a,1,1))]. 1629 R(K(x,y),x * z,u) = K(R(x,z,u),y). [para(1628(a,1),1183(a,1)),flip(a)]. 1630 K(R(x,y,z),y) = K(y,x) \ 1. [para(1628(a,1),1572(a,1))]. 1631 R(K(x,y),T(y,x) * z,u) \ 1 = K(R(y,z,u),x). [para(1628(a,1),1162(a,2))]. 1632 K(R(x,y,z),y) = K(x,y). [para(1630(a,2),897(a,1))]. 1633 T(x,R(y,x,z)) = (x * x) / (x * K(y,x)). [para(1632(a,1),1104(a,2,2,2))]. 1634 K(R(x,x \ y,z),u) = R(K(x,u),y,z). [para(20(a,1),1629(a,1,2)),flip(a)]. 1635 R(K(x,y),x * (z / (z * x)),u) = K(x,y). [para(450(a,1),1629(a,2,1))]. 1636 R(K(x,y),T(x,y) * z,u) = K(R(T(x,y),z,u),y). [para(1105(a,1),1629(a,1,1))]. 1637 K(R(x,x * y,z),u) = R(K(x,u),y,z). [para(629(a,1),1634(a,1,1))]. 1638 R(K(x,y),z,x) = K(L(x,z,x),y). [para(1313(a,1),1634(a,1,1)),flip(a)]. 1639 K(x,R(y,y * z,u)) = R(K(y,x),z,u) \ 1. [para(1637(a,1),897(a,1,1)),flip(a)]. 1640 R(K(x,y),K(x,z) * u,w) = K(R(x,T(x,z) * u,w),y). [para(1120(a,1),1637(a,1,1,2)),flip(a)]. 1641 K(R(x,T(x,y) * z,u),y) = R(K(T(x,y),y),z,u). [para(1637(a,1),1110(a,1)),flip(a)]. 1642 T(x,R(y,x,z)) = T(x,y). [para(1633(a,2),1104(a,2)),flip(a)]. 1643 R(x,y,z) * T(y,x) = y * R(x,y,z). [para(1642(a,1),82(a,1,2))]. 1647 T(x,y) \ (x * R(y,x,z)) = T(R(y,x,z),T(x,y)). [para(1643(a,1),36(a,2,2)),flip(a)]. 1648 R(K(x,y),K(x,z),u) = K(x,y). [para(1041(a,2),1635(a,1,2))]. 1649 R(K(x,y),K(z,x),u) = K(x,y). [para(1648(a,1),908(a,1)),flip(a)]. 1650 (K(x,y) * K(z,x)) * u = K(x,y) * (K(z,x) * u). [para(1649(a,1),79(a,1,1)),flip(a)]. 1651 R(K(x,y),T(y,x) * z,u) = K(R(y,z,u),x) \ 1. [para(1631(a,1),156(a,1,1)),flip(a)]. 1652 R(K(x,y),T(x,y) * z,u) = K(R(x,z,u),y). [para(1636(a,2),1110(a,1))]. 1653 R(K(x,y),y * z,u) = K(R(y,z,u),x) \ 1. [para(1652(a,1),1249(a,1,1)),flip(a)]. 1654 R(K(x,y),y * z,u) = K(x,R(y,z,u)). [para(1653(a,2),897(a,1))]. 1656 R(K(x,y),x * z,u) * K(y,x) = K(x,y) * K(y,R(x,z,u)). [para(1654(a,1),1578(a,2,2))]. 1657 K(R(x,T(x,y) * z,u),y) = R(K(x,y),z,u). [para(1105(a,1),1641(a,2,1))]. 1658 T(R(x,y,z),T(y,x)) = K(x,y) * R(x,y,z). [para(1647(a,1),1093(a,1))]. 1659 R(T(x,T(y,x)),y,z) = K(x,y) * R(x,y,z). [para(1658(a,1),46(a,2))]. 1660 K(x,y) * R(x,y,z) = R(T(x,y),y,z). [para(1131(a,1),1659(a,1,1)),flip(a)]. 1661 T(x,y) \ R(T(x,y),y,z) = x \ R(x,y,z). [para(1660(a,1),1171(a,1,2))]. 1662 (x \ y) \ R(T(y / x,x),x,z) = (y / x) \ R(y / x,x,z). [para(84(a,1),1661(a,1,1))]. 1663 L(x,K(y,z),K(z,u)) = x. [hyper(23,a,74,a,b,1650,a),flip(a)]. 1664 L(x,K(y,z),K(u,z)) = x. [para(1663(a,1),909(a,1)),flip(a)]. 1665 L(x,K(y,z),K(u,y)) = x. [para(1664(a,1),921(a,1)),flip(a)]. 1666 (K(x,y) * T(z,x)) / z = K(z,x) * K(x,y). [para(1665(a,1),1355(a,1,2))]. 1667 R(K(x,y),T(y,x) * z,u) = K(x,R(y,z,u)). [para(1651(a,2),897(a,1))]. 1668 R(K(x,y),y * z,u) \ K(x,y) = K(y,x) * K(x,R(y,z,u)). [para(1667(a,1),1579(a,1,2)),flip(a)]. 1669 R(K(x,y),K(x,y) * z,u) = R(K(x,y),z,u). [para(1640(a,2),1657(a,1))]. 1670 R(K(x,y),z,u) \ 1 = R(K(y,x),z,u). [para(1669(a,1),906(a,1)),flip(a)]. 1671 R(K(x,y),z,u) \ K(x,y) = K(x,y) * R(K(y,x),z,u). [para(1670(a,1),543(a,1,2)),flip(a)]. 1672 K(x,R(y,y * z,u)) = R(K(x,y),z,u). [para(1670(a,1),1639(a,2))]. 1673 K(R(x,y,z),u) * K(u,x) = K(x,u) * K(u,R(x,y,z)). [para(1629(a,1),1656(a,1,1))]. 1674 K(x,y) * K(R(y,z,u),x) = K(y,x) * K(x,R(y,z,u)). [para(1673(a,1),1226(a,2))]. 1675 (x / y) \ R(x / y,y,z) = (y \ x) \ R(y \ x,y,z). [para(84(a,1),1662(a,1,2,1)),flip(a)]. 1676 (x \ y) \ R(x \ y,x,z) = (x / y) * R(y / x,x,z). [para(1675(a,1),358(a,1))]. 1677 x \ (y * R(y \ x,x,z)) = (x / y) * R(y / x,x,z). [para(1676(a,1),1599(a,1)),flip(a)]. 1678 x \ ((y \ x) * R((y \ x) \ x,x,z)) = y * R((y \ x) / x,x,z). [para(65(a,1),1677(a,2,1))]. 1679 x \ (R(y,x,z) * (y \ x)) = y * R((y \ x) / x,x,z). [para(225(a,1),1678(a,1,2))]. 1680 x * R((x \ y) / y,y,z) = T(x \ R(x,y,z),y). [para(1679(a,1),539(a,1))]. 1681 T(x \ R(x,y,z),y) = x * R(x \ 1,y,z). [para(320(a,1),1680(a,1,2,1)),flip(a)]. 1683 T(x \ R(x,y,z),y) = x \ R(x,y,z). [para(1681(a,2),635(a,1))]. 1684 (x * (y \ R(y,x,z))) / x = y \ R(y,x,z). [para(1683(a,1),105(a,1,1,2))]. 1685 T(x \ R(x,y,z),x * (y * z)) = T(a(x,y,z),y). [para(1683(a,1),740(a,1,1))]. 1686 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). [para(1684(a,1),1518(a,2,1))]. 1687 T(a(x,y,z),y) = a(x,y,z). [para(1685(a,1),739(a,2)),flip(a)]. 1688 a(x,y,z) * y = y * a(x,y,z). [para(1687(a,1),82(a,1,2)),flip(a)]. 1689 a(x,y \ 1,z) * (y \ 1) = y \ a(x,y \ 1,z). [para(1687(a,1),326(a,1,2)),flip(a)]. 1690 T(x * y,x) / x = y * a(x,y,x). [para(1688(a,1),1563(a,2))]. 1691 L(x,y,z * (T(u * z,u) / u)) = L(x,y,a(u,z,u)). [para(1690(a,2),774(a,1,3,2))]. 1692 L(x,y,z * a(u,z,u)) = L(x,y,R(z,u,u)). [para(1690(a,1),1350(a,1,3))]. 1693 L(x,y,z * T((u * z) * u,u)) = L(x,y,a(u,z,u)). [para(1691(a,1),1576(a,1)),flip(a)]. 1694 L(x,y,z * ((z * u) * u)) = L(x,y,a(u,z,u)). [para(758(a,1),1693(a,1,3,2))]. 1695 L(x,y,a(z,u,u)) = L(x,y,a(u,z,u)). [para(1694(a,1),861(a,1)),flip(a)]. 1696 (x * (x * (y * (z * u)))) \ (x * (x * ((y * z) * u))) = a(x * (x * y),z,u). [para(51(a,1),1620(a,1,2))]. 1697 (x * y) * R((x * y) \ (x * z),u,w) = (x * y) * L(R(y \ z,u,w),y,x). [para(48(a,1),1621(a,1,2)),flip(a)]. 1698 ((x * y) * ((y * x) * z)) \ ((x * y) * ((y * x) * (z * u))) = L(u,z,K(y,x)). [para(894(a,1),1624(a,1,2))]. 1699 a(x * (x * y),z,u) = (y * (z * u)) \ ((y * z) * u). [para(1696(a,1),212(a,1))]. 1700 a(x * (x * y),z,u) = a(y,z,u). [para(1699(a,2),28(a,2)),flip(a)]. 1702 a(x \ y,z,u) = a(x * y,z,u). [para(20(a,1),1700(a,1,1,2)),flip(a)]. 1703 a((x / y) * x,z,u) = a(y,z,u). [para(22(a,1),1700(a,1,1,2))]. 1704 a(x * (y * x),z,u) = a(T(y,x),z,u). [para(82(a,1),1700(a,1,1,2))]. 1705 a((x * y) * (x * (y * z)),u,w) = a(L(z,y,x),u,w). [para(74(a,1),1700(a,1,1,2))]. 1706 a(x * ((x \ y) * z),u,w) = a(x * ((x * y) * z),u,w). [para(89(a,1),1700(a,1,1,2)),flip(a)]. 1707 a((x \ y) * z,u,w) = a((x * y) * z,u,w). [para(89(a,1),1700(a,1,1)),flip(a)]. 1708 a((x * x) / y,z,u) = a(y \ 1,z,u). [para(263(a,1),1700(a,1,1))]. 1709 a(x * L(x,y * x,y),z,u) = a(a(y,x,x),z,u). [para(453(a,2),1700(a,1,1,2))]. 1710 a(R(x \ 1,y,y),z,u) = a(x * a(x,y,y),z,u). [para(960(a,1),1700(a,1,1,2)),flip(a)]. 1711 a(K(x,y) * y,z,u) = a(T(y,x),z,u). [para(1077(a,1),1700(a,1,1,2))]. 1712 a(x * T(x,y),z,u) = a(K(x,y),z,u). [para(1107(a,2),1700(a,1,1,2))]. 1713 ((x \ y) * (T(x,x * y) * z)) \ (y * z) = a(x * y,T(x,x * y),z). [para(1702(a,1),255(a,2))]. 1714 a(K(x \ 1,x * y),z,u) = a(x \ ((x * y) \ y),z,u). [para(1126(a,2),1702(a,2,1)),flip(a)]. 1715 a((x * (x * y)) * (x * z),u,w) = a(y \ (x \ z),u,w). [para(282(a,1),1703(a,1,1,1))]. 1716 a((x * x) / y,z,u) = a(y,z,u). [para(1708(a,2),611(a,1))]. 1717 a(x / (y * y),z,u) = a(x,z,u). [para(1716(a,1),612(a,1)),flip(a)]. 1718 a(R(x,x * y,z),u,w) = a(R(x,y,z),u,w). [para(616(a,1),1716(a,1,1))]. 1719 a(x * K(y,x),z,u) = a(T(x,y),z,u). [para(1104(a,2),1716(a,1,1)),flip(a)]. 1720 a(x * (y * y),z,u) = a(x,z,u). [para(21(a,1),1717(a,1,1)),flip(a)]. 1721 a((x * y) * y,z,u) = a(R(x,y,y),z,u). [para(34(a,2),1717(a,1,1)),flip(a)]. 1722 a(x / (y \ 1),z,u) = a(x / y,z,u). [para(398(a,1),1717(a,1,1)),flip(a)]. 1723 ((x * (y * y)) * (z * u)) \ (((x * (y * y)) * z) * u) = a(x,z,u). [para(1720(a,1),28(a,1)),flip(a)]. 1724 a(T(T(x,y),y),z,u) = a(x,z,u). [para(985(a,1),1711(a,1,1)),flip(a)]. 1725 a((x / (y * y)) * (y \ (x * (y \ 1))),z,u) = a(K(x / (y * y),y),z,u). [para(403(a,1),1712(a,1,1,2))]. 1726 a(x / (x * y),z,u) = a(T(y,x),z,u). [para(1719(a,1),1022(a,2))]. 1727 a((x \ 1) / y,z,u) = a(y / x,z,u). [para(1722(a,1),612(a,1)),flip(a)]. 1728 a(x / T(y * x,y),z,u) = a(T(R(y,x,y),x),z,u). [para(1321(a,1),1726(a,1,1,2))]. 1729 a(x * (y * x),x,x) = a(R(y,x,x),x,x). [para(1721(a,1),1517(a,1)),flip(a)]. 1730 a(R(x,y,y),y,y) = a(T(x,y),y,y). [para(1729(a,1),1704(a,1))]. 1731 a(R(x,y,y),y,y) = a(x,y,y). [para(1730(a,2),1485(a,1))]. 1732 R(R(x,y,y) \ 1,y,y) = R(x,y,y) \ a(x,y,y). [para(1731(a,1),967(a,2,2))]. 1733 R(R(x,y,y),R(x,y,y) * y,y) = a(x,y,y) \ R(x,y,y). [para(1731(a,1),968(a,2,1))]. 1734 a(x * ((x \ y) * y),z,u) = a(a(x,y,y),z,u). [para(435(a,1),1709(a,1,1))]. 1735 a(R(x \ 1,y,y),z,u) = a(R(x,y,y),z,u). [para(963(a,1),1710(a,2,1))]. 1736 R(R(x,y,y) \ 1,y,y) = x \ 1. [para(1732(a,2),1374(a,1))]. 1737 R((x * y) \ 1,y,y) = (x / (y \ 1)) \ 1. [para(720(a,1),1736(a,1,1,1))]. 1739 R((x * y) \ 1,y,y) = (y \ 1) / x. [para(1737(a,2),343(a,1))]. 1740 (x \ 1) / (y / x) = R(y \ 1,x,x). [para(22(a,1),1739(a,1,1,1)),flip(a)]. 1741 (((x * y) \ 1) * y) * y = ((y \ 1) / x) * (y * y). [para(1739(a,1),79(a,1,1)),flip(a)]. 1742 R(x \ 1,y,y) \ 1 = (x / y) / (y \ 1). [para(1740(a,1),343(a,1,1))]. 1743 a((x \ 1) / ((y / x) \ 1),z,u) = a(R(y \ 1,x,x),z,u). [para(1740(a,1),1722(a,2,1))]. 1744 R(x,x * y,y) = (x / y) / (y \ 1). [para(1742(a,1),633(a,2))]. 1745 K(R(x,x * y,y),z) * (x / y) = (y \ 1) * T((y \ 1) \ (x / y),z). [para(1744(a,2),1201(a,1,1,1))]. 1746 (((x * y) \ 1) * y) * y = T(y / x,y * y). [para(1741(a,2),294(a,1))]. 1747 T(x / y,x * x) = ((y * x) \ x) * x. [para(318(a,1),1746(a,1,1)),flip(a)]. 1748 L(x,y * z,R(T(z / y,z * z),u,w)) = x. [para(1747(a,2),847(a,1,3,1))]. 1749 L(x,y * z,R(z / y,u,w)) = x. [para(1748(a,1),858(a,1)),flip(a)]. 1750 L(x,y * (z \ 1),u / (y * (z * u))) = x. [para(350(a,1),1749(a,1,3))]. 1752 L(x,y * z,u / (y * (z * u))) = x. [para(1750(a,1),1273(a,1)),flip(a)]. 1753 x / ((y * z) \ (y * (z * x))) = (x / (y * (z * x))) * (y * z). [para(1752(a,1),205(a,1,2))]. 1754 a(T(R(x,y,x),y),z,u) = a((y / x) / y,z,u). [para(1237(a,1),1728(a,1,1)),flip(a)]. 1755 a(x * ((x * y) * y),z,u) = a(a(x,y,y),z,u). [para(1706(a,1),1734(a,1))]. 1756 a(x * (x * (y * (x * z))),u,w) = a(y \ (x \ z),u,w). [para(51(a,1),1715(a,1,1))]. 1757 a(x \ (y \ z),u,w) = a(x * (y * z),u,w). [para(1756(a,1),1700(a,1))]. 1759 a(x * (y \ z),u,w) = a(x * (y * z),u,w). [para(1757(a,1),1702(a,1)),flip(a)]. 1760 a(K(x \ 1,x * y),z,u) = a(x * ((x * y) * y),z,u). [para(1757(a,1),1714(a,2))]. 1761 R(R(x,y,y),R(x,y,y) * y,y) = x. [para(1733(a,2),964(a,1))]. 1762 R(K(R(x,y,y),z),y,y) = K(x,z). [para(1761(a,1),1637(a,1,1)),flip(a)]. 1763 K(R(x,y,y),z) * (y \ 1) = K(x,z) / y. [para(1762(a,1),718(a,1,1)),flip(a)]. 1764 K(x,R(y,z,z)) * (K(y,x) / z) = z \ 1. [hyper(23,a,901,a,b,1763,a),flip(a)]. 1765 R(K(x,y),z,z) = K(x,R(y,z,z)). [hyper(24,a,1405,a,b,1764,a),flip(a)]. 1766 K(R(x,y,y),z) \ 1 = R(K(z,x),y,y). [para(1765(a,2),897(a,2))]. 1767 K(x,R(y,z,z)) * 1 = R(K(x,y),z,z). [para(1766(a,1),900(a,1)),flip(a)]. 1768 a((x \ 1) / (x / y),z,u) = a(R(y \ 1,x,x),z,u). [para(343(a,1),1743(a,1,1,2))]. 1769 a(R(x \ 1,y,y),z,u) = a((y / x) / y,z,u). [para(1768(a,1),1727(a,1))]. 1770 a((x / y) / x,z,u) = a(R(y,x,x),z,u). [para(1769(a,1),1735(a,1))]. 1771 a(T(R(x,y,x),y),z,u) = a(R(x,y,y),z,u). [para(1770(a,1),1754(a,2))]. 1772 a(R(T(x,y),y,x),z,u) = a(R(x,y,y),z,u). [para(46(a,2),1771(a,1,1))]. 1773 (x / (y * (z * x))) * (y * z) = x / L(x,z,y). [para(32(a,2),1753(a,1,2)),flip(a)]. 1774 (x / (y * (z * x))) * (y * z) = L(x,z,y) \ x. [para(1773(a,2),519(a,1))]. 1775 (L(x * y,z / (x * (y * z)),x * y) * (z / (x * (y * z)))) * (x * y) = (x * y) * (L(z,y,x) \ z). [para(1774(a,1),1310(a,2,2))]. 1776 (x * (y * (y * (z * u)))) \ (((x * (y * y)) * z) * u) = a(x,z,u). [para(411(a,1),1723(a,1,1))]. 1777 (x * (y * (y * (z * u)))) \ ((x * (y * (y * z))) * u) = a(x,z,u). [para(411(a,1),1776(a,1,2,1))]. 1778 a(x,y * (y * z),u) = a(x,z,u). [para(1777(a,1),90(a,1)),flip(a)]. 1779 a(x,y \ z,u) = a(x,y * z,u). [para(20(a,1),1778(a,1,2,2)),flip(a)]. 1780 a(x,(y / z) * y,u) = a(x,z,u). [para(22(a,1),1778(a,1,2,2))]. 1781 a(x,(y \ z) * u,w) = a(x,(y * z) * u,w). [para(89(a,1),1778(a,1,2)),flip(a)]. 1782 a(x,T(y,y * z),u) = a(x,(y \ z) * z,u). [para(250(a,1),1778(a,1,2,2)),flip(a)]. 1783 a(x,K(y,z) * T(y,z),u) = a(x,y,u). [para(1081(a,2),1778(a,1,2,2))]. 1785 a(x * (y * y),y * 1,y) = a(x * y,y \ 1,y \ 1). [para(1779(a,1),1574(a,1))]. 1786 a(x,y \ 1,z) * (y \ 1) = y \ a(x,y * 1,z). [para(1779(a,1),1689(a,2,2))]. 1787 a(x,(y * (y * z)) * (y * u),w) = a(x,z \ (y \ u),w). [para(282(a,1),1780(a,1,2,1))]. 1788 a(x,T(y * z,y),u) = a(x,z / y,u). [para(1232(a,2),1780(a,1,2))]. 1789 a(x,T(T(y,z),z),u) = a(x,y,u). [para(1113(a,1),1783(a,1,2))]. 1790 a(T(x,y),y,z) = a(x,T(y,x),z). [para(1789(a,1),1460(a,1))]. 1792 a(x,T(y,y * z),u) = a(x,(y * z) * z,u). [para(1782(a,2),1781(a,1))]. 1793 a(x,y \ 1,z) * (y \ 1) = y \ a(x,y,z). [para(18(a,1),1786(a,2,2,2))]. 1794 a(x,y * 1,z) * (y \ 1) = y \ a(x,y,z). [para(1779(a,1),1793(a,1,1))]. 1795 a(x,y,z) * (y \ 1) = y \ a(x,y,z). [para(18(a,1),1794(a,1,1,2))]. 1796 a(x * (y * y),y,y) = a(x * y,y \ 1,y \ 1). [para(18(a,1),1785(a,1,2))]. 1797 a(x * y,y \ 1,y \ 1) = a(x,y,y). [para(1796(a,1),1720(a,1))]. 1798 L(x,x,y) \ x = a(y,x,x). [para(1797(a,1),1408(a,1)),flip(a)]. 1800 a(x,y,y) * L(y,y,x) = y. [para(1798(a,1),520(a,1,1))]. 1801 R(x,y,y) * L(y,y,x) = x * y. [para(1800(a,1),966(a,1,2)),flip(a)]. 1802 T(R(x,y,y),L(y,y,x)) = L(y,y,x) \ (x * y). [para(1801(a,1),36(a,2,2))]. 1803 R(T(x,L(y,y,x)),y,y) = L(y,y,x) \ (x * y). [para(1802(a,1),46(a,2))]. 1804 L(x,x,y) \ (y * x) = R(T(y,x),x,x). [para(1558(a,1),1803(a,1,1)),flip(a)]. 1805 a(x,y * (y * (z * (y * u))),w) = a(x,z \ (y \ u),w). [para(51(a,1),1787(a,1,2))]. 1806 a(x,y \ (z \ u),w) = a(x,y * (z * u),w). [para(1805(a,1),1778(a,1))]. 1808 a(x,y * (z \ u),w) = a(x,y * (z * u),w). [para(1806(a,1),1779(a,1)),flip(a)]. 1809 a(x * y,T(x,x * y),z) = ((y / x) * (x * z)) \ (y * z). [para(1265(a,1),1713(a,1,1)),flip(a)]. 1810 a(x * y,T(x,x * y),z) = a(y / x,x,z). [para(1809(a,2),68(a,1))]. 1811 R(K(x,y),z,z) * (x / z) = (z \ 1) * T((z \ 1) \ (x / z),y). [para(1637(a,1),1745(a,1,1))]. 1812 K(x,R(y,z,z)) * (x / z) = (z \ 1) * T((z \ 1) \ (x / z),y). [para(1765(a,1),1811(a,1,1))]. 1813 K(x,R(y,z,z)) * (x / z) = (z \ 1) * T(z * (x / z),y). [para(330(a,1),1812(a,2,2,1))]. 1814 K(x,R(y,z,z)) * (x / z) = z \ T(z * (x / z),y). [para(1813(a,2),318(a,1))]. 1815 K(x,R(y,z,z)) * (x / z) = T(x,y) / z. [para(1814(a,2),755(a,1))]. 1816 a(x * (y \ (y \ (y \ (x * (y \ 1))))),z,u) = a(K(x / (y * y),y),z,u). [para(602(a,1),1725(a,1,1))]. 1817 a(x * (y \ ((y \ (y \ x)) * (y \ 1))),z,u) = a(K(x / (y * y),y),z,u). [para(285(a,1),1816(a,1,1,2,2))]. 1818 a(x * (y * ((y \ (y \ x)) * (y \ 1))),z,u) = a(K(x / (y * y),y),z,u). [para(1817(a,1),1759(a,1)),flip(a)]. 1819 a(K(x / (y * y),y),z,u) = a(x * (y \ (x * (y \ 1))),z,u). [para(265(a,1),1818(a,1,1,2)),flip(a)]. 1820 a(K(x / (y * y),y),z,u) = a(x * (y * (x * (y \ 1))),z,u). [para(1819(a,2),1759(a,1))]. 1821 a(K(x / (y * y),y),z,u) = a(x * T(x,y \ 1),z,u). [para(347(a,1),1820(a,2,1,2))]. 1822 a(K(x / (y * y),y),z,u) = a(K(x,y \ 1),z,u). [para(1821(a,2),1712(a,1))]. 1823 a(K(x,y \ 1),z,u) = a(K(x,y),z,u). [para(1418(a,1),1822(a,1,1)),flip(a)]. 1824 a(K(x \ 1,y),z,u) = a(K(y,x),z,u). [para(1823(a,1),905(a,1)),flip(a)]. 1825 a(x * ((x * y) * y),z,u) = a(K(x * y,x),z,u). [para(1824(a,1),1760(a,1)),flip(a)]. 1826 a(K(x * y,x),z,u) = a(a(x,y,y),z,u). [para(1825(a,1),1755(a,1))]. 1827 (x * y) * R((x * y) \ (x * z),u,w) = x * (y * R(y \ z,u,w)). [para(1697(a,2),74(a,1))]. 1828 (x * y) * R((x * y) \ z,u,w) = x * (y * R(y \ (x \ z),u,w)). [para(20(a,1),1827(a,1,2,1,2))]. 1829 (x * y) * R((x * y) \ y,z,u) = R(x,z,u) * (x \ y). [para(1828(a,2),639(a,1))]. 1830 T(x,y) \ R(T(x,y),z,u) = y \ (R(x,z,u) * (x \ y)). [para(1829(a,1),1610(a,1,2)),flip(a)]. 1831 T(x,y) \ R(T(x,y),z,u) = T(x \ R(x,z,u),y). [para(1830(a,2),539(a,1))]. 1832 (R(T(x,y),z,u) \ T(x,y)) * w = T(x \ R(x,z,u),y) \ w. [para(1831(a,1),465(a,1,1)),flip(a)]. 1833 T(x \ R(x,y,y),z) = a(T(x,z),y,y). [para(1831(a,1),962(a,1))]. 1834 K(x,y) * R(T(y,x),z,u) = y * T(y \ R(y,z,u),x). [para(1831(a,1),1099(a,1,2)),flip(a)]. 1835 T(T(x,y) \ R(T(x,y),z,u),y) = x \ R(x,z,u). [para(1831(a,1),1582(a,1))]. 1836 a(T(x,y),z,z) = T(a(x,z,z),y). [para(962(a,1),1833(a,1,1)),flip(a)]. 1837 T(T(x \ R(x,y,z),u),u) = x \ R(x,y,z). [para(1831(a,1),1835(a,1,1))]. 1838 (x * (y \ R(y,z,u))) / x = T(y \ R(y,z,u),x). [para(1837(a,1),105(a,1,1,2))]. 1839 T(a(x,y,z),x * (y * z)) = x \ R(x,y,z). [para(739(a,2),1837(a,1,1))]. 1840 a(x,y,z) * K(a(x,y,z),x * (y * z)) = x \ R(x,y,z). [para(1839(a,1),1107(a,1)),flip(a)]. 1841 T(T(x \ R(x,y,z),u),x * (y * z)) = (u * a(x,y,z)) / u. [para(1838(a,1),742(a,1,1))]. 1842 (x * (y \ R(y,z,u))) / x = (y \ R(y,z,u)) * K(y \ R(y,z,u),x). [para(1838(a,2),1107(a,1))]. 1843 (x * a(y,z,u)) / x = T(a(y,z,u),x). [para(1841(a,1),740(a,1))]. 1844 T(a(x,y,z),u) * (u / (u * a(x,y,z))) = 1. [para(1843(a,1),354(a,1,1))]. 1845 L(x,x,x * ((x \ 1) * a(y,z,u))) = ((x \ 1) * a(y,z,u)) \ T(a(y,z,u),x \ 1). [para(1843(a,1),1488(a,2,2))]. 1846 K(a(x,y,z),u) * K(a(x,y,z),u) = 1. [para(1844(a,1),1174(a,1)),flip(a)]. 1847 K(a(x,y,z),u) = K(u,a(x,y,z)). [hyper(24,a,898,a,b,1846,a)]. 1848 a(x,y,z) * K(x * (y * z),a(x,y,z)) = x \ R(x,y,z). [para(1847(a,1),1840(a,1,2))]. 1849 K(x \ R(x,y,z),u) = K(u,x \ R(x,y,z)). [hyper(23,a,1014,a(flip),b,1842,a(flip))]. 1850 L(L(x,y,z * u),(z * u) * y,u * z) = L(x,y,K(z,u)). [para(1698(a,1),174(a,1)),flip(a)]. 1851 ((x * (x * y)) * a(y,z,u)) / y = a(x * (x * y),z,u) * (x * x). [para(1700(a,1),749(a,1,1,2))]. 1852 (x * (x * (y * a(y,z,u)))) / y = a(x * (x * y),z,u) * (x * x). [para(51(a,1),1851(a,1,1))]. 1854 a(x * (x * y),z,u) * (x * x) = x * (x * ((y * a(y,z,u)) / y)). [para(1852(a,1),211(a,1))]. 1855 a(x * (x * y),z,u) * (x * x) = x * (x * a(y,z,u)). [para(748(a,1),1854(a,2,2,2))]. 1856 a(x,y,z) * (u * u) = u * (u * a(x,y,z)). [para(1700(a,1),1855(a,1,1))]. 1857 T((a(x,y,z) * (u * u)) / (u * u),u) = T(u \ (u * a(x,y,z)),u \ 1). [para(1856(a,2),666(a,1,1,1))]. 1859 T(x \ (x * a(y,z,u)),x \ 1) = T(a(y,z,u),x). [para(21(a,1),1857(a,1,1)),flip(a)]. 1860 T(a(x,y,z),u \ 1) = T(a(x,y,z),u). [para(19(a,1),1859(a,1,1))]. 1863 x * L(T(y \ (y / x),z),y,x * y) = K(L(y \ (y / x),y,x * y),z). [para(1295(a,1),330(a,1)),flip(a)]. 1864 (x / y) * (y * T(y \ (y / x),z)) = K(L(y \ (y / x),y,x * y),z). [para(1863(a,1),1294(a,1)),flip(a)]. 1865 (x / y) * (y * T(y \ (y / x),z)) = K(x \ 1,z). [para(1289(a,1),1864(a,2,1))]. 1866 (L(x,y,z) / (z * (y * x))) * ((z * (y * x)) * T((z * (y * x)) \ (z * y),u)) = K(L(x,y,z) \ 1,u). [para(99(a,1),1865(a,1,2,2,1,2))]. 1868 T(x * x,y * z) \ ((((y * z) \ (x * x)) * y) * z) = a((y * z) * (x * x),y,z). [para(394(a,2),1702(a,1))]. 1869 ((R(x,y,z) * u) * w) / ((x * u) * w) = R(x,u,w) \ R(R(x,u,w),y,z). [para(185(a,1),538(a,1,1))]. 1870 R(x \ R(x,y,z),x * u,w) = R(x,u,w) \ R(R(x,u,w),y,z). [para(1869(a,1),533(a,2))]. 1871 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). [para(584(a,1),1870(a,2,1))]. 1872 (K(x,T(y,z)) * T(y,x)) / y = K(z,T(y,x)) * K(y,z). [para(1663(a,1),1570(a,1,2))]. 1873 K(x,T(y,z)) * K(y,x) = K(y,z) * K(z,T(y,x)). [para(1872(a,1),1666(a,1))]. 1874 T(x * x,y * z) \ ((((y * z) \ (x * x)) * y) * z) = a(y * z,y,z). [para(1868(a,2),1720(a,1))]. 1875 (T(x * x,y * z) \ (((y * z) \ (x * x)) * y)) * z = a(y * z,y,z). [para(1874(a,1),591(a,1)),flip(a)]. 1877 ((T(x * x,y * z) \ ((y * z) \ (x * x))) * y) * z = a(y * z,y,z). [para(591(a,1),1875(a,1,1))]. 1878 (((x * y) \ 1) * x) * y = a(x * y,x,y). [para(795(a,1),1877(a,1,1,1))]. 1879 ((x * y) \ x) * y = a(x * y,x,y). [para(318(a,1),1878(a,1,1))]. 1880 x * ((y * x) \ y) = a(y * x,y,x). [para(1879(a,1),388(a,1)),flip(a)]. 1881 a(x * (x \ y),x,x \ y) = (x \ y) * (y \ x). [para(20(a,1),1880(a,1,2,1)),flip(a)]. 1882 (x \ y) * (y \ x) = a(y,x,x \ y). [para(20(a,1),1881(a,1,1)),flip(a)]. 1883 L(x,y,(z \ u) * (u * z)) = L(x,y,a(z,u,u \ z)). [para(1882(a,1),869(a,1,3)),flip(a)]. 1884 L(x,(y \ z) * (z * y),u) = L(x,a(y,z,z \ y),u). [para(1882(a,1),1362(a,1,2)),flip(a)]. 1885 L(x,y,(z * u) * (u * z)) = L(x,y,a(z,u,u \ z)). [para(1883(a,1),781(a,1)),flip(a)]. 1886 L(x,(y * z) * (z * y),u) = L(x,a(y,z,z \ y),u). [para(1884(a,1),880(a,1)),flip(a)]. 1887 L(x,y,a(z,u,u \ z)) = L(x,y,K(u,z)). [para(1885(a,1),779(a,1))]. 1888 L(x,a(y,z,z \ y),u) = L(x,K(z,y),u). [para(1886(a,1),879(a,1))]. 1889 ((x \ 1) * a(y,z,u)) \ T(a(y,z,u),x \ 1) = L(x,x,a(y,z,u)). [para(321(a,1),1845(a,1,3)),flip(a)]. 1890 (x \ a(y,z,u)) \ T(a(y,z,u),x \ 1) = L(x,x,a(y,z,u)). [para(318(a,1),1889(a,1,1))]. 1892 (x \ a(y,z,u)) \ T(a(y,z,u),x) = L(x,x,a(y,z,u)). [para(1860(a,1),1890(a,1,2))]. 1893 L(x,a(y,z,u),x) = L(x,x,a(y,z,u)). [para(1892(a,1),440(a,1)),flip(a)]. 1894 L(x,x,a(y,z,z \ y)) = L(x,K(z,y),x). [para(1893(a,1),1888(a,1))]. 1895 L(x,K(y,z),x) = L(x,x,K(y,z)). [para(1894(a,1),1887(a,1))]. 1896 L(x,K(y,z),x) = L(x,x,K(z,y)). [para(1895(a,2),909(a,1))]. 1897 (x \ K(y,z)) / (K(y,z) / L(x,x,K(z,y))) = K(K(y,z),x). [para(1896(a,1),1500(a,2,2,2)),flip(a)]. 1898 (x \ K(y,z)) / (K(y,z) * (x \ 1)) = K(K(y,z),x). [para(930(a,1),1897(a,1,2))]. 1899 K(x \ 1,K(y,z)) = K(K(y,z),x). [para(1898(a,1),978(a,1)),flip(a)]. 1900 K(K(x,y),z) * (K(x,y) \ u) = T(K(x,y),z \ 1) \ u. [para(1899(a,1),1095(a,1,1))]. 1901 T(K(x,y),z) * K(K(x,y),z) = T(K(x,y),z * z). [para(1899(a,1),1433(a,1,2))]. 1902 T(T(K(x,y),z),z) = T(K(x,y),z * z). [para(1901(a,1),1121(a,1)),flip(a)]. 1903 T(K(x,y),T(z,x) * T(z,x)) = T(T(K(x,y),z),T(z,x)). [para(1352(a,1),1902(a,1,1)),flip(a)]. 1904 x / (T(K(y,z),u \ 1) \ x) = K(y,z) * K(u,K(y,z)). [para(1900(a,1),1071(a,1,2))]. 1905 T(K(x,y),z * T(T(z,x),x)) = T(T(K(x,y),z),T(z,x)). [para(1088(a,1),1903(a,1,2))]. 1906 K(x,y) * K(z,K(x,y)) = T(K(x,y),z \ 1). [para(1904(a,1),65(a,1))]. 1907 T(K(x,y),z \ 1) * z = z * K(x,y). [para(1906(a,1),1018(a,1,1))]. 1908 ((x * y) * (z / (x * (y * z)))) * (x * y) = (x * y) * (L(z,y,x) \ z). [para(851(a,1),1775(a,1,1,1))]. 1910 (x \ R(x,y,z)) * (x * y) = (x * y) * (L(z,y,x) \ z). [para(1410(a,1),1908(a,1,1))]. 1911 (x * y) * (L(z,y,x) \ z) = R(x,y,z) * y. [para(1910(a,1),528(a,1))]. 1912 ((x * y) \ 1) * ((x * (y * z)) * T((x * (y * z)) \ (x * y),u)) = K(L(z,y,x) \ 1,u). [para(342(a,1),1866(a,1,1))]. 1914 ((x * y) \ 1) * (x * ((y * z) * T((y * z) \ y,u))) = K(L(z,y,x) \ 1,u). [para(1590(a,1),1912(a,1,2))]. 1915 ((x * y) \ 1) * (x * (y * K(z \ 1,u))) = K(L(z,y,x) \ 1,u). [para(1164(a,1),1914(a,1,2,2))]. 1916 (x * y) \ (x * (y * K(z \ 1,u))) = K(L(z,y,x) \ 1,u). [para(1915(a,1),318(a,1)),flip(a)]. 1917 L(K(x \ 1,y),z,u) = K(L(x,z,u) \ 1,y). [para(1916(a,1),32(a,2))]. 1918 K(L(x \ 1,y,z) \ 1,u) = L(K(x,u),y,z). [para(156(a,1),1917(a,1,1,1)),flip(a)]. 1920 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). [para(750(a,1),1871(a,1,1))]. 1921 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). [para(18(a,1),1920(a,1,1,1))]. 1922 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). [para(18(a,1),1921(a,1,1,2,1))]. 1923 (R(x,y,z) \ 1) \ R(R(x \ 1,x * y,z),u,w) = R(x \ R(x,u,w),y,z). [para(322(a,1),1922(a,1,2)),flip(a)]. 1924 (R(x,y,z) \ 1) \ R(R(x,y,z) \ 1,u,w) = R(x \ R(x,u,w),y,z). [para(584(a,1),1923(a,1,2,1))]. 1925 (R(x,y,z) * 1) \ R(R(x,y,z) * 1,u,w) = R(x \ R(x,u,w),y,z). [para(1924(a,1),750(a,1)),flip(a)]. 1926 R(x,y,z) \ R(R(x,y,z) * 1,u,w) = R(x \ R(x,u,w),y,z). [para(18(a,1),1925(a,1,1))]. 1927 R(x,y,z) \ R(R(x,y,z),u,w) = R(x \ R(x,u,w),y,z). [para(18(a,1),1926(a,1,2,1))]. 1928 R(x \ R(x,y,y),z,u) = a(R(x,z,u),y,y). [para(1927(a,1),962(a,1))]. 1929 T(R(x \ R(x,y,x),z,u),x * (R(x,z,u) * T(y,x))) = a(R(x,z,u),y,x). [para(1927(a,1),743(a,1,1))]. 1930 a(R(x,y,z),u,u) = R(a(x,u,u),y,z). [para(962(a,1),1928(a,1,1)),flip(a)]. 1931 T(R(a(x,y,x),z,u),x * (R(x,z,u) * T(y,x))) = a(R(x,z,u),y,x). [para(1539(a,1),1929(a,1,1,1))]. 1932 T(R(a(x,y,x),z,u),R(x,z,u) * (y * x)) = a(R(x,z,u),y,x). [para(530(a,1),1931(a,1,2))]. 1933 R(T(a(x,y,x),R(x,z,u) * (y * x)),z,u) = a(R(x,z,u),y,x). [para(1932(a,1),46(a,2))]. 1934 ((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). [para(342(a,1),1597(a,1,1))]. 1936 ((x * y) \ 1) * (x * ((y * z) * R((y * z) \ y,u,w))) = L(z,y,x) \ R(L(z,y,x),u,w). [para(1827(a,1),1934(a,1,2))]. 1937 ((x * y) \ 1) * (x * (y * (z \ R(z,u,w)))) = L(z,y,x) \ R(L(z,y,x),u,w). [para(1592(a,1),1936(a,1,2,2))]. 1938 (x * y) \ (x * (y * (z \ R(z,u,w)))) = L(z,y,x) \ R(L(z,y,x),u,w). [para(1937(a,1),318(a,1)),flip(a)]. 1939 L(x,y,z) \ R(L(x,y,z),u,w) = L(x \ R(x,u,w),y,z). [para(1938(a,1),32(a,2)),flip(a)]. 1940 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). [para(1808(a,1),1686(a,1,1,2,1))]. 1941 L((x * (y \ R(y,x,z))) * (1 * u),x * (y \ R(y,x,z)),x) = (y \ R(y,x,z)) * (x * u). [para(1442(a,1),1940(a,1,1,2,1))]. 1942 L((x * (y \ R(y,x,z))) * u,x * (y \ R(y,x,z)),x) = (y \ R(y,x,z)) * (x * u). [para(17(a,1),1941(a,1,1,2))]. 1944 L(x * (R(y,x,z) * (y \ u)),x * (y \ R(y,x,z)),x) = (y \ R(y,x,z)) * (x * u). [para(1450(a,1),1942(a,1,1))]. 1945 L(x * (R(y,x,z) * (y \ u)),x * (y * R(y,x,z)),x) = (y \ R(y,x,z)) * (x * u). [para(1944(a,1),1360(a,1)),flip(a)]. 1946 (x \ R(x,y,z)) * (y * u) = y * (R(x,y,z) * (x \ u)). [para(1945(a,1),1439(a,1))]. 1947 R(x,y,z) * (x \ (y * u)) = y * (R(x,y,z) * (x \ u)). [para(1946(a,1),532(a,1)),flip(a)]. 1948 R(x,y,z) * (x \ (y * (y \ z))) = L(z,x * y,x). [para(1947(a,2),1567(a,1))]. 1949 R(x,y,z) * (x \ z) = L(z,x * y,x). [para(20(a,1),1948(a,1,2,2))]. 1950 R(x,y,L(z,y,x)) * (x \ L(z,y,x)) = z. [para(1949(a,2),303(a,1))]. 1951 L(x,y * z,y) / x = y \ R(y,z,x). [para(1949(a,1),536(a,1,1))]. 1952 x / L(x,y * z,y) = R(y,z,x) \ y. [para(1949(a,1),542(a,1,2))]. 1953 x \ L(x,y * z,y) = y \ R(y,z,x). [para(1951(a,1),515(a,1)),flip(a)]. 1954 L(x,y * z,y) \ x = R(y,z,x) \ y. [para(1952(a,1),519(a,1)),flip(a)]. 1955 x \ R(x,x \ y,z) = z \ L(z,y,x). [para(20(a,1),1953(a,1,2,2)),flip(a)]. 1956 x \ R(x,x * y,z) = z \ L(z,y,x). [para(313(a,1),1953(a,1,2)),flip(a)]. 1957 K(x,R(y,z,x) \ y) = 1. [para(1954(a,1),653(a,1,2))]. 1958 K(x,y \ R(y,z,x)) = 1. [para(622(a,1),1957(a,1,2))]. 1959 T(x,y \ R(y,z,x)) = x. [hyper(41,a,1958,a)]. 1960 K(x,T(y \ R(y,z,x),u)) = 1. [para(1831(a,1),1958(a,1,2))]. 1961 T(x \ R(x,y,z),z) = x \ R(x,y,z). [hyper(39,a,1959,a)]. 1962 K(x,a(y,z,x)) = 1. [para(739(a,2),1960(a,1,2))]. 1963 T(x,a(y,z,x)) = x. [hyper(41,a,1962,a)]. 1964 a(x,y,z) * z = z * a(x,y,z). [para(1963(a,1),82(a,1,2))]. 1965 R(x,y,z) \ x = z \ L(z,y,x). [para(1955(a,1),624(a,1)),flip(a)]. 1966 L(x,y,z) = x * (R(z,y,x) \ z). [para(1965(a,2),20(a,1,2)),flip(a)]. 1967 R(x,y,z) = x / (z \ L(z,y,x)). [para(1965(a,1),65(a,1,2)),flip(a)]. 1968 (x \ L(x,y,z)) \ 1 = z \ R(z,y,x). [para(1965(a,1),460(a,1,1))]. 1969 (x \ L(x,y,z)) * R(z,y,x) = z. [para(1965(a,1),496(a,1,1))]. 1970 L(x,y,z) = (R(z,y,x) \ z) * x. [para(1965(a,2),514(a,1,1)),flip(a)]. 1971 x * (R(K(y,z),u,x) \ K(y,z)) = L(x,u,K(z,y)). [para(1966(a,1),909(a,1))]. 1972 R(x,y,T(z,x * y)) = R(x,y,z). [hyper(23,a,680,a,b,1969,a),flip(a)]. 1973 L(x,y,z) * R(z,y,x) = x * z. [para(1969(a,1),504(a,1,2)),flip(a)]. 1974 L(x,y,z) * (x \ R(z,y,x)) = z. [para(1969(a,1),647(a,1)),flip(a)]. 1975 R(x,y,z) * L(z,y,x) = x * z. [para(1970(a,2),458(a,1,2))]. 1976 L(x,y,z) = (z \ R(z,y,x)) \ x. [para(1970(a,2),465(a,2)),flip(a)]. 1977 T(x \ R(x,y,z),u) \ z = L(z,y,T(x,u)). [para(1970(a,2),1832(a,1)),flip(a)]. 1978 L(x,y,z) \ x = z \ R(z,y,x). [para(1972(a,1),681(a,2,2))]. 1979 R(x,y,z) = x * (L(z,y,x) \ z). [para(1972(a,1),683(a,1))]. 1980 R(x,y,z) * (x \ L(z,y,x)) = z. [para(1972(a,1),686(a,1,1))]. 1981 (L(x,y,z) * (R(z,y,x) * u)) \ ((x * z) * u) = a(L(x,y,z),R(z,y,x),u). [para(1973(a,1),28(a,2,2,1)),flip(a)]. 1984 (L(x,y,z) \ x) * (z * u) = R(z,y,x) * u. [para(1978(a,2),528(a,1,1))]. 1985 (x \ R(x,y,z)) * u = z * (L(z,y,x) \ u). [para(1978(a,1),650(a,1,1))]. 1986 R(x \ R(x,y,z),z,u) = L(z,y,x) \ z. [para(1978(a,1),736(a,1,1))]. 1987 (x * y) * (x \ R(x,y,z)) = R(x,y,z) * y. [para(1978(a,1),1911(a,1,2))]. 1988 K(x,y) \ R(K(x,y),z,u) = u \ L(u,z,K(x,y)). [para(1669(a,1),1956(a,1,2))]. 1989 x \ R(x,y,z) = (L(z,y,x) \ z) * 1. [para(1968(a,1),517(a,1))]. 1990 R(x,y,L(z,y,x)) = R(x,y,z). [hyper(24,a,1980,a,b,1950,a)]. 1991 (x \ R(x,y,z)) \ z = L(z,y,T(x,z)). [para(1961(a,1),1977(a,1,1))]. 1992 L(x,y,T(z,x)) = L(x,y,z). [para(1991(a,1),1976(a,2)),flip(a)]. 1993 L(L(x,y,z),z * y,T(z,L(x,y,z))) = x. [para(1992(a,2),303(a,1))]. 1994 L(x,y,K(z,L(x,y,z))) = x. [para(1993(a,1),1606(a,1)),flip(a)]. 1995 x * (L(x,y,z) \ (z * u)) = R(z,y,x) * u. [para(1984(a,1),650(a,1)),flip(a)]. 1996 L((x \ R(x,y,z)) \ u,x \ R(x,y,z),x * y) = (R(x,y,z) * y) \ ((x * y) * u). [para(1987(a,1),76(a,2,1))]. 1998 L(x,y,z) * (R(z,y,x) * u) = x * (z * u). [para(1995(a,1),645(a,1,2))]. 1999 x * (L(x,y,z) \ (z * T(y,z))) = y * R(z,y,x). [para(1995(a,2),1643(a,1))]. 2000 x * (L(x,y,z) \ (z * L(x,y,z))) = z * x. [para(1995(a,2),1975(a,1))]. 2001 x * T(y,L(x,z,y)) = y * x. [para(36(a,2),2000(a,1,2))]. 2002 T(x,L(y,z,x)) = x * K(x,y). [hyper(23,a,1116,a,b,2001,a)]. 2005 K(x,L(y,z,x)) = K(x,y). [hyper(23,a,1107,a(flip),b,2002,a(flip)),flip(a)]. 2006 L(x,y,K(z,x)) = x. [para(2005(a,1),1994(a,1,3))]. 2007 L(T(x,y),z,K(u,x)) = T(x,y). [para(2006(a,1),44(a,2,1))]. 2008 L(x,y,K(x,z)) = x. [para(2006(a,1),909(a,1)),flip(a)]. 2009 L(x,y,a(x,z,z)) = x. [para(2006(a,1),1262(a,1)),flip(a)]. 2010 L(K(x,y),z,K(u,x \ 1)) = K((x \ 1) \ 1,y). [para(2006(a,1),1918(a,1,1,1)),flip(a)]. 2011 R(K(x,y),z,y) = K(x,y) / (y \ y). [para(2006(a,1),1967(a,2,2,2))]. 2013 (K(x,y) * z) * x = K(x,y) * (z * x). [para(2008(a,1),74(a,1,2))]. 2014 x * (x \ R(a(x,y,y),z,x)) = a(x,y,y). [para(2009(a,1),1974(a,1,1))]. 2015 T(x,K(y,x) * z) = T(x,z). [para(2007(a,1),1377(a,1)),flip(a)]. 2016 K(K(x,y) * z,y) = T(y,z) \ y. [para(2015(a,1),1080(a,2,1))]. 2017 K(x,K(y,x) * z) = x \ T(x,z). [para(2015(a,1),1108(a,2,2))]. 2018 T(x,T(x,y) * z) = T(x,x * z). [para(1098(a,1),2015(a,1,2)),flip(a)]. 2019 T(x,y * T(z,x)) = T(x,y * z). [para(1212(a,1),2015(a,1,2))]. 2021 K(K(x,y) * z,y) = K(z,y). [para(2016(a,2),1080(a,2)),flip(a)]. 2022 K(K(x,y) * z,x) = K(z,x). [para(901(a,1),2021(a,1,1)),flip(a)]. 2023 K(x * (K(x,y) * z),x) = K(x * z,x). [para(1068(a,1),2022(a,1,1))]. 2024 K(x,K(y,x) * z) = K(x,z). [para(2017(a,2),1108(a,2)),flip(a)]. 2025 K(x,K(x,y) * z) = K(x,z). [para(901(a,1),2024(a,1,2)),flip(a)]. 2026 K(x,y) * K(x * (K(x,z) * y),x) = a(x,K(x,z) * y,x). [para(2025(a,1),1537(a,1,1))]. 2027 R(K(x,y),z,y) = K(x,y) / 1. [para(60(a,1),2011(a,2,2))]. 2029 R(K(x,y),z,y) = K(x,y). [para(2027(a,2),64(a,1))]. 2030 K(x,R(y,z,y)) = K(x,y). [para(2029(a,1),1654(a,1)),flip(a)]. 2031 R(K(x,y),z,x) = K(y,x) \ 1. [para(2029(a,1),1670(a,1,1)),flip(a)]. 2032 K(x,y) * R(T(y,x),z,y) = R(y,z,y). [para(2030(a,1),1083(a,1,1))]. 2033 R(K(x,y),z,x) = K(x,y). [para(2031(a,2),897(a,1))]. 2034 K(L(x,y,x),z) = K(x,z). [para(2033(a,1),1638(a,1)),flip(a)]. 2036 K((x \ y) \ y,z) = K(T(x,y),z). [para(1457(a,1),2034(a,1,1))]. 2038 K(T(x,x \ y),z) = K(T(x,y),z). [para(83(a,2),2036(a,1,1))]. 2039 x \ (K(x,y) * (z * x)) = T(K(x,y) * z,x). [para(2013(a,1),36(a,2,2)),flip(a)]. 2040 x * ((K(x,y) * z) * x) = T(x,y) * (z * x). [para(2013(a,2),1120(a,1,2))]. 2041 T(x,y) \ R(T(x,y),z,x) = x \ R(x,z,x). [para(2032(a,1),1163(a,1,2)),flip(a)]. 2042 x * (x \ a(R(x,y,x),z,z)) = a(x,z,z). [para(1930(a,2),2014(a,1,2,2))]. 2043 x * (x \ a(L(x,y,x),z,z)) = a(x,z,z). [para(1303(a,1),2042(a,1,2,2,1))]. 2044 a(L(x,y,x),z,z) = a(x,z,z). [para(2043(a,1),20(a,1)),flip(a)]. 2045 a(L(T(x,y),y * x,x),z,z) = a(T(x,y),z,z). [para(1283(a,1),2044(a,1,1))]. 2046 K(x,y) * (x \ (z * x)) = T(K(x,y) * z,x). [para(2039(a,1),1076(a,1)),flip(a)]. 2047 (T(x,y) * (z * x)) \ ((T(x,y) * z) * x) = a(x,K(x,y) * z,x). [para(2040(a,1),1166(a,1,1))]. 2048 T(x,y) \ R(T(x,y),z,x) = a(x,z,x). [para(2041(a,2),1539(a,1))]. 2049 T(x \ R(x,y,x),z) = a(x,y,x). [para(2048(a,1),1831(a,1)),flip(a)]. 2050 T(a(x,y,x),z) = a(x,y,x). [para(1539(a,1),2049(a,1,1))]. 2051 a(x,y,x) * z = z * a(x,y,x). [para(2050(a,1),82(a,1,2)),flip(a)]. 2052 a(R(x,y,z),u,x) = R(a(x,u,x),y,z). [para(2050(a,1),1933(a,1,1)),flip(a)]. 2053 (a(x,y,x) * z) * L(u,z,a(x,y,x)) = (z * u) * a(x,y,x). [para(2051(a,1),74(a,2))]. 2054 a(x,y,x) \ a(R(x,z,z),y,x) = a(a(x,y,x),z,z). [para(2052(a,2),962(a,1,2))]. 2056 T(K(x,y) * z,x) = K(x,y) * T(z,x). [para(36(a,2),2046(a,1,2)),flip(a)]. 2057 T(K(x,y) * R(z,u,w),x) = K(x,y) * R(T(z,x),u,w). [para(46(a,2),2056(a,2,2))]. 2058 T(K(x,y) * z,x) / z = K(z,x) * K(x,y). [para(2056(a,2),1666(a,1,1))]. 2059 T(K(x,y) * z,x) / z = K(x,y) * K(z,x). [para(2058(a,2),1226(a,2)),flip(a)]. 2060 L(K(x,y),z,K(u,x \ 1)) = K(x,y). [para(156(a,1),2010(a,2,1))]. 2061 L(K(x,y),z,K(u,x)) = K(x,y). [para(2060(a,1),1618(a,1)),flip(a)]. 2062 L(K(x,y),z,K(x,u)) = K(x,y). [para(2060(a,1),1619(a,1)),flip(a)]. 2063 (K(x,y) * z) \ z = T(K(y,x),z). [para(2061(a,1),1301(a,1,1)),flip(a)]. 2064 T(K(x,y) * z,K(x,y)) = z * K(x,y). [para(2062(a,1),1309(a,1,1,1))]. 2065 x / T(K(y,z),x) = K(z,y) * x. [para(2063(a,1),65(a,1,2))]. 2067 (T(K(x,y),z) / z) * u = (K(y,x) * z) \ u. [para(2065(a,1),358(a,1,1)),flip(a)]. 2068 (K(x,y) * z) * K(y,x) = T(z,K(y,x)). [para(2065(a,1),1549(a,1,1))]. 2069 K(K(x,y) * z,K(y,x)) = T(z,K(y,x)) / z. [para(2068(a,1),979(a,1,1)),flip(a)]. 2070 K(K(x,y) * z,K(y,x)) = K(z,K(y,x)). [para(2069(a,2),1086(a,2)),flip(a)]. 2071 K(K(x,y) * z,K(x,y)) = K(z,K(x,y)). [para(901(a,1),2070(a,1,1)),flip(a)]. 2072 a(a(K(x,y),z,z),u,w) = a(K(z,K(x,y)),u,w). [para(2071(a,1),1826(a,1,1)),flip(a)]. 2073 a(R(T(x,y),y,x),z,z) = a(T(x,y),z,z). [para(1306(a,1),2045(a,1,1))]. 2074 a(R(x,y,y),z,z) = a(T(x,y),z,z). [para(2073(a,1),1772(a,1)),flip(a)]. 2076 x * (K(y,z) * R(K(z,y),u,x)) = L(x,u,K(z,y)). [para(1671(a,1),1971(a,1,2))]. 2077 x * (K(y,z) * K(z,R(y,u,x))) = L(x,y * u,K(y,z)). [para(1668(a,1),1971(a,1,2))]. 2078 x * (L(x,y,z) \ (y * z)) = y * R(z,y,x). [para(82(a,1),1999(a,1,2,2))]. 2079 L(x,y,z) = (x * (y * z)) / (y * R(z,y,x)). [para(2078(a,1),648(a,1,2)),flip(a)]. 2080 T(K(x,y) * R(y,z,u),x) = y * T(y \ R(y,z,u),x). [para(2057(a,2),1834(a,1))]. 2081 T(K(x,y) * R(y,z,u),x) / R(y,z,u) = K(R(y,z,u) / y,x). [para(2080(a,2),1211(a,1,1))]. 2082 a(x,K(x,y) * z,x) = K(x,z) * K(x * z,x). [para(2023(a,1),2026(a,1,2)),flip(a)]. 2083 a(x,K(x,y) * z,x) = a(x,z,x). [para(2082(a,2),1537(a,1))]. 2085 a(x,K(x,y) * z,x) = a(T(x,y),z,x). [para(2047(a,1),28(a,2)),flip(a)]. 2086 a(T(x,y),z,x) = a(x,z,x). [para(2085(a,1),2083(a,1))]. 2087 a((x \ y) \ y,z,x) = a(x,z,x). [para(83(a,1),2086(a,1,1))]. 2089 a((x \ y) * y,z,x) = a(x,z,x). [para(2087(a,1),1702(a,1)),flip(a)]. 2090 a((x * y) * y,z,x) = a(x,z,x). [para(2089(a,1),1707(a,1)),flip(a)]. 2091 a(R(x,y,y),z,x) = a(x,z,x). [para(2090(a,1),1721(a,1)),flip(a)]. 2092 a(a(x,y,x),z,z) = a(x,y,x) \ a(x,y,x). [para(2091(a,1),2054(a,1,2)),flip(a)]. 2093 a(a(x,y,x),z,z) = 1. [para(2092(a,2),60(a,1))]. 2095 L(x,x,a(y,z,y)) = x. [hyper(37,a,2093,a)]. 2097 L(x,x,a(y,z,z)) = x. [para(2095(a,1),1695(a,2))]. 2098 L(x,x,K(y,z)) = x. [para(2097(a,1),1263(a,1)),flip(a)]. 2099 R(T(a(x,y,y),z),z,z) = z \ (a(x,y,y) * z). [para(2097(a,1),1804(a,1,1)),flip(a)]. 2100 a(K(x,y),z,z) = 1. [hyper(38,a,2098,a)]. 2101 K(x,y) * (z \ 1) = K(x,y) / z. [para(2098(a,1),915(a,1,2)),flip(a)]. 2102 (K(x,y) * (z / u)) \ K(x,y) = u / z. [para(2098(a,1),925(a,1)),flip(a)]. 2103 L(x,K(y,z),x) = x. [para(2098(a,1),1895(a,2))]. 2104 R(K(x,y),z,z) = K(x,y) * 1. [para(2100(a,1),963(a,1,2)),flip(a)]. 2105 a(K(x,K(y,z)),u,w) = a(1,u,w). [para(2100(a,1),2072(a,1,1)),flip(a)]. 2106 T(K(x,y),z) / z = z \ K(x,y). [para(2103(a,1),441(a,1,2))]. 2107 K(x,R(y,z,z)) = K(x,y). [hyper(24,a,1767,a,b,2104,a(flip)),flip(a)]. 2108 K(x,y / (z \ 1)) = K(x,y * z). [para(720(a,1),2107(a,1,2)),flip(a)]. 2112 K(x,y) * (x / z) = T(x,y) / z. [para(2107(a,1),1815(a,1,1))]. 2114 K(x,y) / (z \ 1) = K(x,y) * z. [para(156(a,1),2101(a,1,2)),flip(a)]. 2115 a(K(x,K(y,z)),u,w) = 1. [para(2105(a,2),125(a,1))]. 2117 L(x,y,K(z,K(u,w))) = x. [hyper(37,a,2115,a)]. 2119 x * (x \ R(K(y,K(z,u)),w,x)) = K(y,K(z,u)). [para(2117(a,1),1974(a,1,1))]. 2121 (K(x,y) * z) \ u = (z \ K(y,x)) * u. [para(2106(a,1),2067(a,1,1)),flip(a)]. 2122 K(x,R(((y \ 1) * z) \ 1,z,z)) = K(x,(z \ 1) * y). [para(1739(a,2),2108(a,1,2))]. 2123 T(x,y) / (z \ x) = K(x,y) * z. [para(65(a,1),2112(a,1,2)),flip(a)]. 2125 (K(x,y) * z) \ K(x,y) = z \ 1. [para(2114(a,1),66(a,1,1))]. 2126 (K(x,y) * z) \ T(x,y) = z \ x. [para(2123(a,1),66(a,1,1))]. 2127 (K(x,y) \ z) \ 1 = z \ K(x,y). [para(20(a,1),2125(a,1,1)),flip(a)]. 2128 (K(x,y) * z) \ y = z \ T(y,x). [para(901(a,1),2126(a,1,1)),flip(a)]. 2129 L(x \ y,x,K(z,y)) = x \ y. [para(2126(a,1),1248(a,2))]. 2130 a(K(x,y),z,z \ y) = 1. [hyper(38,a,2129,a)]. 2132 a(K(x,y * z),y,z) = 1. [para(19(a,1),2130(a,1,3))]. 2133 (K(x,y) \ z) \ u = (z \ K(x,y)) * u. [para(2127(a,1),318(a,1,1)),flip(a)]. 2134 ((x * y) \ K(z,x)) * u = (T(x,z) * y) \ u. [para(1160(a,1),2121(a,1,1)),flip(a)]. 2135 (x \ K(y,z)) * K(z,y) = x \ 1. [para(2121(a,1),2125(a,1))]. 2136 (x \ K(y,z)) * y = x \ T(y,z). [para(2121(a,1),2128(a,1))]. 2137 ((x / y) \ K(z,u)) * K(u,z) = y / x. [para(2121(a,1),2102(a,1))]. 2138 (x / y) * K(x,x * y) = (x \ y) \ 1. [para(1011(a,1),2135(a,1,1))]. 2139 (x \ T(y,z)) \ ((x \ K(y,z)) * (y * u)) = L(u,y,x \ K(y,z)). [para(2136(a,1),32(a,2,1)),flip(a)]. 2140 x / K(y,z) = x * K(z,y). [para(66(a,1),2137(a,1,1)),flip(a)]. 2141 (x * K(y,z)) \ x = K(z,y). [para(2140(a,1),66(a,1,1))]. 2143 (x * K(y,z)) \ u = (K(z,y) / x) * u. [para(2140(a,1),358(a,1,1))]. 2144 (K(x,y) * z) / K(x,y) = T(z,K(y,x)). [para(2140(a,2),2068(a,1))]. 2145 T(x,K(y,z)) \ x = K(x,K(z,y)). [para(2144(a,1),1053(a,2,1)),flip(a)]. 2146 K(K(x,y),z) = K(z,K(y,x)). [para(2145(a,1),1080(a,2))]. 2147 K(x,K(y,z)) * K(x,K(z,y)) = 1. [para(2146(a,1),898(a,1,1))]. 2148 K(x,y) * K(z,K(y,x)) = T(K(x,y),z). [para(2146(a,1),1107(a,2,2)),flip(a)]. 2149 K(x,y) * T(K(y,x),z) = K(z,K(x,y)). [para(2146(a,1),1114(a,2))]. 2150 T(K(x,y),z) \ 1 = T(K(y,x),z). [para(2148(a,1),1140(a,1)),flip(a)]. 2151 T(K(x,y),z) * T(K(y,x),z) = 1. [para(2150(a,1),20(a,1,2))]. 2152 T(K(x,y),z) * K(y,x) = K(z,K(y,x)). [para(2149(a,1),405(a,2))]. 2153 R(T(a(x,y,y),z),z,z) = T(a(x,y,y),z). [para(2099(a,2),36(a,2)),flip(a)]. 2154 R(T(a(x,y,y),z),z,z) = a(T(x,z),y,y). [para(2153(a,2),1836(a,2)),flip(a)]. 2155 R(a(T(x,y),z,z),y,y) = a(T(x,y),z,z). [para(1836(a,2),2154(a,1,1))]. 2156 a(R(T(x,y),y,y),z,z) = a(T(x,y),z,z). [para(2155(a,1),1930(a,2))]. 2157 a(T(T(x,y),y),z,z) = a(T(x,y),z,z). [para(2156(a,1),2074(a,1)),flip(a)]. 2158 a(T(x,y),z,z) = a(x,z,z). [para(2157(a,1),1724(a,1))]. 2161 (x * (y * (a(y,z,z) * u))) / (R(T(y,x),z,z) * u) = T(x,y). [para(2158(a,1),1210(a,1,1,2,2,1))]. 2165 R(K(x,K(y,z)),u,w) = K(x,K(y,z)). [para(2119(a,1),20(a,1)),flip(a)]. 2166 K(x,R(K(y,z),u,w)) = K(x,K(y,z)). [para(2165(a,1),1654(a,1)),flip(a)]. 2167 K(x,K(y,R(z,u,w))) = K(x,K(y,z)). [para(1654(a,1),2166(a,1,2))]. 2168 K(K(R(x,y,z),u),w) = K(w,K(u,x)). [para(2167(a,1),2146(a,2))]. 2169 K(R(K(x,y),z,u),w) = K(w,K(y,x)). [para(1634(a,1),2168(a,1,1))]. 2170 K(x,R((y \ z) \ 1,z,z)) = K(x,(z \ 1) * y). [para(318(a,1),2122(a,1,2,1,1))]. 2171 K(x,(y \ z) \ 1) = K(x,(z \ 1) * y). [para(2170(a,1),2107(a,1)),flip(a)]. 2172 K(x,(y \ z) \ 1) = K(x,z \ y). [para(318(a,1),2171(a,2,2))]. 2174 K(x,(y / z) \ y) = K(x,z / (a(y,z,z) \ 1)). [para(2172(a,1),1447(a,1))]. 2175 K(x,y / (a(z,y,y) \ 1)) = K(x,y). [para(66(a,1),2174(a,1,2)),flip(a)]. 2176 K(x,y * a(z,y,y)) = K(x,y). [para(1445(a,1),2175(a,1,2))]. 2177 K(x * a(y,x,x),z) = (z \ 1) / (z \ K(z,x)). [para(2176(a,1),1057(a,1,2,2)),flip(a)]. 2178 K(x * a(y,x,x),z) = K(x,z). [para(2177(a,2),1057(a,1))]. 2179 (x / y) * T(y,z) = x * K(y,z). [para(2178(a,1),1463(a,1,2)),flip(a)]. 2180 (x * y) * K(y,z) = x * T(y,z). [para(21(a,1),2179(a,1,1)),flip(a)]. 2183 L(K(x,y),x,z) = K(x,y). [hyper(23,a,1117,a,b,2180,a),flip(a)]. 2184 (x * y) \ (x * T(y,z)) = K(y,z). [hyper(23,a,20,a,b,2180,a),flip(a)]. 2185 (x * (y * z)) \ (x * (y * T(z,u))) = L(K(z,u),y * z,x). [para(2180(a,1),32(a,2,2,2)),flip(a)]. 2186 (x * T(y,z)) \ (x * y) = K(z,y). [para(2180(a,1),2141(a,1,1))]. 2187 L(K(T(x,y),z),x,y) = K(T(x,y),z). [para(2183(a,1),1376(a,1)),flip(a)]. 2189 (x * (y * z)) \ ((x * y) * T(L(z,y,x),u)) = K(L(z,y,x),u). [para(74(a,1),2184(a,1,1))]. 2192 T(K(x,y),x * z) = K(T(x,z),y). [para(2187(a,1),1522(a,1)),flip(a)]. 2193 K(T(x,x \ y),z) = T(K(x,z),y). [para(20(a,1),2192(a,1,2)),flip(a)]. 2194 K(T(x,y),z) = T(K(x,z),y). [para(2193(a,1),2038(a,1)),flip(a)]. 2195 K(x,T(y,z)) * T(K(y,x),z) = 1. [para(2194(a,1),898(a,1,2))]. 2196 K(T(x,y * T(T(y,x),x)),z) = T(T(K(x,z),y),T(y,x)). [para(2194(a,2),1905(a,1))]. 2197 K(x,T(y,z)) = T(K(x,y),z). [hyper(24,a,2151,a,b,2195,a)]. 2199 K(x,y) * K(y,T(x,z)) = K(K(y,x),z). [para(2197(a,2),1114(a,1,2))]. 2200 K(x,T(y,z \ 1)) * z = z * K(x,y). [para(2197(a,2),1907(a,1,1))]. 2201 K(x,T(y,z)) / z = z \ K(x,y). [para(2197(a,2),2106(a,1,1))]. 2202 K(x,y) * K(y,T(x,z)) = K(z,K(x,y)). [para(2197(a,2),2149(a,1,2))]. 2203 K(x,T(y,z)) * K(y,x) = K(z,K(y,x)). [para(2197(a,2),2152(a,1,1))]. 2204 K(T(x,y),z) = K(x,T(z,y)). [para(2197(a,2),2194(a,2))]. 2205 K(x,T(y,z)) * K(y,x) = K(K(x,y),z). [para(2199(a,1),1226(a,2))]. 2206 K(x,T(y,z)) * K(y,x) = K(x,K(y,z)). [para(2202(a,1),1873(a,2))]. 2207 K(x,y) * K(x,K(y,z)) = K(x,T(y,z)). [para(2206(a,1),1225(a,1,2))]. 2208 K(x,K(y,z)) = K(z,K(y,x)). [para(2206(a,1),2203(a,1))]. 2209 K(K(x,y),z) = K(x,K(y,z)). [para(2206(a,1),2205(a,1)),flip(a)]. 2210 1 / K(x,K(y,z)) = K(K(y,x),z). [para(2208(a,1),899(a,1,2))]. 2211 K(K(x,y),z) = K(K(x,z),y). [para(2210(a,1),899(a,1))]. 2212 K(K(x,y),z) = K(y,K(z,x)). [para(2211(a,1),2146(a,1))]. 2213 K(x,K(y,z)) = K(z,K(x,y)). [para(2212(a,1),2209(a,1))]. 2214 T(K(x,y) * K(x,K(y,z)),z) = K(x,y). [para(2213(a,2),1020(a,1,1,2))]. 2215 T(K(x,T(y,z)),z) = K(x,y). [para(2207(a,1),2214(a,1,1))]. 2216 K(x,T(y,z)) * z = z * K(x,y). [para(2215(a,1),82(a,1,2)),flip(a)]. 2217 K(x,T(T(y,z),z)) = K(x,y). [para(2215(a,1),2197(a,2))]. 2219 K(x,T(y,z \ 1)) = K(x,T(y,z)). [hyper(24,a,2200,a,b,2216,a),flip(a)]. 2220 T(K(x,y) * z,K(x,y)) = K(x,T(y,z)) * z. [para(2216(a,2),2064(a,2))]. 2221 K(x,T(y,z \ (z \ (u \ 1)))) = K(x,T(y,u * (z * z))). [para(409(a,1),2219(a,1,2,2))]. 2222 K(T(x,y * T(y,x)),z) = T(T(K(x,z),y),T(y,x)). [para(2019(a,1),2196(a,1,1))]. 2223 T(T(K(x,y),z),T(z,x)) = K(T(x,z * z),y). [para(2019(a,1),2222(a,1,1)),flip(a)]. 2224 T(T(K(x,y),z),T(z,x)) = K(x,T(y,z * z)). [para(2223(a,2),1278(a,1))]. 2225 T(K(x,T(y,z)),T(z,x)) = K(x,T(y,z * z)). [para(2197(a,2),2224(a,1,1))]. 2226 K(T(x,T(y,x)),T(z,y)) = K(x,T(z,y * y)). [para(2225(a,1),2194(a,2))]. 2227 K(T(x,y),T(z,y)) = K(x,T(z,y * y)). [para(1131(a,1),2226(a,1,1))]. 2228 K(x,T(T(y,z),z)) = K(x,T(y,z * z)). [para(2227(a,1),2204(a,1)),flip(a)]. 2229 K(x,T(y,z * z)) = K(x,y). [para(2228(a,1),2217(a,1))]. 2230 K(x,T(y,z * (z * u))) = K(x,T(y,u)). [para(662(a,1),2229(a,1,2))]. 2232 K(x,T(y,z \ u)) = K(x,T(y,z * u)). [para(20(a,1),2230(a,1,2,2,2)),flip(a)]. 2233 K(x,T(y,T(z,z * u))) = K(x,T(y,(z \ u) * u)). [para(250(a,1),2230(a,1,2,2,2)),flip(a)]. 2234 K(x,T(y,(z / u) * (z * z))) = K(x,T(y,u / (z \ 1))). [para(399(a,1),2230(a,1,2,2,2))]. 2235 K(x,T(y,z \ (z \ u))) = K(x,T(y,u)). [para(20(a,1),2232(a,2,2,2))]. 2236 K(x,T(y,z * (u * u))) = K(x,T(y,z \ 1)). [para(2221(a,1),2235(a,1))]. 2237 K(x,T(y,z * (u * u))) = K(x,T(y,z)). [para(2236(a,2),2219(a,1))]. 2239 K(x,T(y,z / (u \ 1))) = K(x,T(y,u / z)). [para(2234(a,1),2237(a,1))]. 2241 (x * (R(y,z,z) * u)) / (R(T(y,x),z,z) * u) = T(x,y). [para(966(a,1),2161(a,1,1,2))]. 2243 T(x,R(y,z,z)) = T(x,y). [para(2241(a,1),1209(a,1)),flip(a)]. 2244 T(x,y / (z \ 1)) = T(x,y * z). [para(720(a,1),2243(a,1,2)),flip(a)]. 2246 K(x,T(y,z / u)) = K(x,T(y,u * z)). [para(2244(a,1),2239(a,1,2)),flip(a)]. 2247 K(x,T(y,(z \ u) * u)) = K(x,T(y,z)). [para(65(a,1),2246(a,1,2,2)),flip(a)]. 2248 K(x,T(y,T(z,z * u))) = K(x,T(y,z)). [para(2247(a,1),2233(a,2))]. 2249 K(x,T(y,T(z,u))) = K(x,T(y,z)). [para(20(a,1),2248(a,1,2,2,2))]. 2251 K(x,K(y,T(z,u))) = K(x,T(y,z)) * K(y,x). [para(2249(a,1),2206(a,1,1)),flip(a)]. 2253 K(x,K(y,T(z,u))) = K(x,K(y,z)). [para(2251(a,2),2206(a,1))]. 2254 K(x,K(y,z \ R(z,u,w))) = K(x,K(y,a(z,u,w))). [para(739(a,2),2253(a,1,2,2)),flip(a)]. 2255 K(x,K(y \ R(y,z,u),w)) = K(x,K(w,a(y,z,u))). [para(1849(a,2),2254(a,1,2))]. 2256 (x * (y * z)) \ ((x * y) * L(T(z,u),y,x)) = K(L(z,y,x),u). [para(44(a,2),2189(a,1,2,2))]. 2257 (x * (y * z)) \ (x * (y * T(z,u))) = K(L(z,y,x),u). [para(74(a,1),2256(a,1,2))]. 2258 L(K(x,y),z * x,u) = K(L(x,z,u),y). [para(2257(a,1),2185(a,1)),flip(a)]. 2259 K(L(x,y / x,z),u) = L(K(x,u),y,z). [para(22(a,1),2258(a,1,2)),flip(a)]. 2260 K(x,y) * K(R(y,z,u),x) = K(R(y,z,u) / y,x). [para(2081(a,1),2059(a,1)),flip(a)]. 2261 K(x,y) * K(R(y,z,u),x) = K(y \ R(y,z,u),x). [para(478(a,1),2260(a,2,1))]. 2262 K(x,y) * K(R(y,z,u),x) = K(x,y \ R(y,z,u)). [para(2261(a,2),1849(a,1))]. 2263 K(x,K(y,z) \ R(K(y,z),u,w)) = K(x,K(y,z)) * K(x,K(z,y)). [para(2169(a,1),2262(a,1,2)),flip(a)]. 2264 (x * T(y,z)) \ ((x * K(y,z)) * (y * u)) = L(u,y,x \ K(y,z)). [para(2139(a,1),284(a,1)),flip(a)]. 2265 K(x,K(y,z) \ R(K(y,z),u,w)) = 1. [para(2263(a,2),2147(a,1))]. 2266 K(x,K(y,z) \ K(R(y,u,w),z)) = 1. [para(1629(a,1),2265(a,1,2,2))]. 2268 K(x,K(y,z) * K(R(z,u,w),y)) = 1. [para(900(a,1),2266(a,1,2))]. 2269 K(x,K(y \ R(y,z,u),w)) = 1. [para(2261(a,1),2268(a,1,2))]. 2270 K(x,K(y,a(z,u,w))) = 1. [para(2269(a,1),2255(a,1)),flip(a)]. 2271 T(x,K(y,a(z,u,w))) = x. [hyper(41,a,2270,a)]. 2273 K(x,T(a(y,z,u),w)) = K(x,a(y,z,u)). [hyper(24,a,2220,a(flip),b,2271,a(flip)),flip(a)]. 2274 K(x,y \ R(y,z,u)) = K(x,a(y,z,u)). [para(1839(a,1),2273(a,1,2))]. 2275 K(x,y \ R(y,z,u)) = K(a(y,z,u),x). [para(2274(a,2),1847(a,2)),flip(a)]. 2276 K(x \ R(x,y,z),u) = K(u,a(x,y,z)). [para(2274(a,1),1849(a,2))]. 2277 K(x,a(y,z,L(u,z,y))) = K(x,y \ R(y,z,u)). [para(1990(a,1),2274(a,1,2,2)),flip(a)]. 2278 K(x,y) * K(R(y,z,u),x) = K(x,a(y,z,u)). [para(2274(a,1),2262(a,2))]. 2279 K(x,a(K(y,z),u,w)) = 1. [para(2274(a,1),2265(a,1))]. 2280 T(x,a(K(y,z),u,w)) = x. [hyper(41,a,2279,a)]. 2281 ((K(x,y) * z) * u) / (K(x,y) * (z * u)) = a(K(x,y),z,u). [para(2280(a,1),300(a,1,2))]. 2282 K(R(x,y,z) \ x,u) = K(u,a(x,x * y,z)). [para(618(a,1),2276(a,1,1))]. 2283 K(x,y) * K(y,R(x,z,u)) = K(y,a(x,z,u)). [para(2278(a,1),1674(a,1)),flip(a)]. 2284 L(x,y * z,K(y,u)) = x * K(u,a(y,z,x)). [para(2283(a,1),2077(a,1,2)),flip(a)]. 2285 K(x,a(y,z,L(u,z,y))) = K(x,a(y,z,u)). [para(2277(a,2),2274(a,1))]. 2286 K(x,y) \ R(K(x,y),z,u) = a(K(x,y),z,u). [para(2281(a,1),537(a,1)),flip(a)]. 2287 x \ L(x,y,K(z,u)) = a(K(z,u),y,x). [para(2286(a,1),1988(a,1)),flip(a)]. 2288 x * a(K(y,z),u,x) = L(x,u,K(y,z)). [para(2287(a,1),20(a,1,2))]. 2289 a(K(x,y),x * z,u) = K(y,a(x,z,u)). [hyper(23,a,2284,a(flip),b,2288,a)]. 2290 x * a(K(y,z),u,x) = L(x,u,K(z,y)). [para(905(a,1),2288(a,1,2))]. 2291 K(x,a(y,y * z,u)) = a(K(y,x),z,u). [para(2289(a,1),1778(a,1))]. 2292 K((x * y) * z,a(x,y,z)) = 1. [para(2289(a,1),2132(a,1))]. 2293 K(x * (y * z),a(x,y,L(z,y,x))) = 1. [para(74(a,1),2292(a,1,1))]. 2294 K(x,a(y,y * z,u)) = a(K(x,y),z,u). [para(2291(a,2),905(a,1))]. 2295 K(x * (y * z),a(x,y,z)) = 1. [para(2293(a,1),2285(a,1)),flip(a)]. 2296 x \ R(x,y,z) = a(x,y,z) * 1. [para(2295(a,1),1848(a,1,2)),flip(a)]. 2297 a(x,y,z) = x \ R(x,y,z). [hyper(24,a,18,a,b,2296,a(flip))]. 2298 a(x,y,z) = L(z,y,x) \ z. [hyper(24,a,1989,a(flip),b,2296,a(flip))]. 2300 R(x,y,z) = x * a(x,y,z). [para(2297(a,2),20(a,1,2)),flip(a)]. 2301 L(x,y,z) \ L(R(x,u,w),y,z) = a(L(x,y,z),u,w). [para(48(a,1),2297(a,2,2)),flip(a)]. 2302 R(x,y,z) \ x = a(x,y,z) \ 1. [para(2297(a,2),462(a,1,1)),flip(a)]. 2303 R(x,y,z) = a(x,y,z) * x. [para(2297(a,2),479(a,1,1)),flip(a)]. 2306 x * (a(x,y,z) * u) = R(x,y,z) * u. [para(2297(a,2),501(a,1,2,1))]. 2307 R(x,y,z) \ (x * u) = a(x,y,z) \ u. [para(2297(a,2),522(a,1,1)),flip(a)]. 2308 a(x,y,z) * (x * u) = R(x,y,z) * u. [para(2297(a,2),528(a,1,1))]. 2309 R(x,y,z) * (x \ u) = a(x,y,z) * u. [para(2297(a,2),532(a,1,1)),flip(a)]. 2310 a(x,x * y,z) = R(x,y,z) \ x. [para(2297(a,2),618(a,1))]. 2311 a(x,y,z) = R(x,x * y,z) \ x. [para(2297(a,2),622(a,2)),flip(a)]. 2313 a(x,y,z) = x * R(x \ 1,y,z). [para(2297(a,2),635(a,2)),flip(a)]. 2314 L(x,a(y,z,u),y * z) = x. [para(2297(a,2),1411(a,1,2))]. 2315 (x * y) * R((x * y) \ x,z,u) = x * a(y,z,u). [para(2297(a,2),1592(a,2,2))]. 2316 x \ (R(y,z,u) * (y \ x)) = a(T(y,x),z,u). [para(2297(a,2),1830(a,1)),flip(a)]. 2317 T(x \ R(x,y,z),u) = a(T(x,u),y,z). [para(2297(a,2),1831(a,1)),flip(a)]. 2318 R(x \ R(x,y,z),u,w) = a(R(x,u,w),y,z). [para(2297(a,2),1927(a,1)),flip(a)]. 2319 L(x \ R(x,y,z),u,w) = a(L(x,u,w),y,z). [para(2297(a,2),1939(a,1)),flip(a)]. 2320 a(x,y,z) = z \ L(z,x * y,x). [para(2297(a,2),1953(a,2)),flip(a)]. 2321 L(x,y,z) = a(z,y,x) \ x. [para(2297(a,2),1976(a,2,1))]. 2322 a(x,x * y,z) = z \ L(z,y,x). [para(2297(a,2),1956(a,1))]. 2323 x * (L(x,y,z) \ u) = a(z,y,x) * u. [para(2297(a,2),1985(a,1,1)),flip(a)]. 2325 L(L(x,y,z),u,w) \ L(x,u,w) = a(z,y,L(x,u,w)). [para(49(a,1),2298(a,2,1)),flip(a)]. 2326 L(x,y,z) = x / a(z,y,x). [para(2298(a,2),65(a,1,2)),flip(a)]. 2327 a(x,x * y,(x * y) \ z) = (y \ (x \ z)) \ ((x * y) \ z). [para(270(a,1),2298(a,2,1))]. 2328 a(x,y,z) \ 1 = z \ L(z,y,x). [para(2298(a,2),511(a,1,1))]. 2329 a(x,y,z) = z / L(z,y,x). [para(2298(a,2),519(a,2)),flip(a)]. 2331 x \ (L(x,y,z) * u) = a(z,y,x) \ u. [para(2298(a,2),512(a,1,1)),flip(a)]. 2332 L(x,y,z) \ (x * u) = a(z,y,x) * u. [para(2298(a,2),524(a,2,1))]. 2333 a(x,y,z) * (L(z,y,x) * u) = z * u. [para(2298(a,2),646(a,1,1))]. 2334 (x * y) / (L(x,z,u) * y) = a(u,z,x). [para(2298(a,2),649(a,2))]. 2335 L(x,y,z) * (x \ u) = a(z,y,x) \ u. [para(2298(a,2),651(a,1,1)),flip(a)]. 2336 a(T(x,y),z,y) = L(y,z,x) \ y. [para(1992(a,1),2298(a,2,1))]. 2337 R(x,y * (y * z),u) = x * a(x,z,u). [para(1778(a,1),2300(a,2,2))]. 2338 ((x * y) * a(x,y,z)) * u = (x * y) * (a(x,y,z) * u). [para(2314(a,1),74(a,1,2))]. 2340 K(a(x,y,z) \ 1,u) = K(u,a(x,x * y,z)). [para(2302(a,1),2282(a,1,1))]. 2341 a(x,x * y,z) = a(x,y,z) \ 1. [para(2310(a,2),2302(a,1))]. 2342 L(x,y * z,y) = x * a(y,z,x). [para(2311(a,2),1966(a,2,2))]. 2343 a(x,x * y,z) \ 1 = a(x,y,z). [para(2311(a,2),2302(a,1)),flip(a)]. 2344 L(x,a(y,z,u),z) = x. [para(2313(a,2),1443(a,1,2))]. 2347 (x * a(y,x,z)) * u = x * (a(y,x,z) * u). [para(2344(a,1),74(a,1,2))]. 2348 (x \ a(y,x,z)) \ 1 = a(y,x,z) \ x. [para(2344(a,1),259(a,1)),flip(a)]. 2349 (x \ a(y,x,z)) \ u = a(y,x,z) \ (x * u). [para(2344(a,1),267(a,1)),flip(a)]. 2350 (x * y) \ (x * L(y,z * u,z)) = L(a(z,u,y),y,x). [para(2320(a,2),76(a,1,1)),flip(a)]. 2351 a(x,y,L(z,y,x)) = L(z,y,x) \ z. [para(303(a,1),2320(a,2,2))]. 2356 (x * L(y,z,u)) / L(a(u,u * z,y),y,x) = x * y. [para(2322(a,2),179(a,1,2,1))]. 2357 ((x * y) \ x) * L(L(y,x,x * y),z,u) = a(u,z,L(y,x,x * y)) \ 1. [para(2328(a,2),738(a,1)),flip(a)]. 2358 a(T(x,y),z,y) = a(x,z,y). [para(2336(a,2),2298(a,2)),flip(a)]. 2359 a(x,x * y,z) * u = a(x,y,z) \ u. [para(2341(a,2),318(a,1,1))]. 2360 a(x,x * y,z) \ u = a(x,y,z) * u. [para(2341(a,2),330(a,1,1))]. 2361 L(x,y,a(z,z * u,w)) = L(x,y,a(z,u,w)). [para(2341(a,2),787(a,1,3))]. 2362 L(x * a(y,z,x),z,y) = x. [para(2342(a,1),308(a,1,1))]. 2364 a(x,y,L(z,y,x)) = a(x,y,z). [para(2351(a,2),2298(a,2)),flip(a)]. 2365 a(x,x * y,L(z,y,x)) = a(x,y,z) \ 1. [para(2364(a,1),2341(a,2,1))]. 2366 K(a(x,x * y,z),u) = a(K(u,x),y,z). [para(2294(a,1),1847(a,2))]. 2368 x * (y * a(x,z,y)) = R(x,z,y) * y. [para(1964(a,1),2306(a,1,2))]. 2369 R(a(x,y,z),u,w) \ R(x,y,z) = a(a(x,y,z),u,w) \ x. [para(2303(a,2),2307(a,1,2))]. 2370 a(T(x,y),z,u) = T(a(x,z,u),y). [para(2297(a,2),2317(a,1,1)),flip(a)]. 2371 a(T(x,y),z,u) \ a(x,z,u) = K(y,a(x,z,u)). [para(2370(a,2),1080(a,2,1)),flip(a)]. 2372 a(T(x,y),y,z) = a(x,y,z). [para(2370(a,2),1687(a,1))]. 2373 a(x,T(y,x),z) = a(x,y,z). [para(2372(a,1),1790(a,1)),flip(a)]. 2374 a(x / y,y,z) = a(y * x,y,z). [para(2373(a,1),1810(a,1)),flip(a)]. 2375 a(x / y,x,z) = a(x * y,x,z). [para(2374(a,1),612(a,1)),flip(a)]. 2376 a(x,y,z) * (u * L(z,y,x)) = z * T(u,L(z,y,x)). [para(36(a,2),2323(a,1,2)),flip(a)]. 2377 x * (a(y,z,x) \ u) = L(x,z,y) * u. [para(2331(a,1),20(a,1,2))]. 2378 a(x,y,z) * (z * u) = z * (a(x,y,z) * u). [para(2332(a,1),2323(a,1,2)),flip(a)]. 2379 R(T(a(x,y,z),(L(z,y,x) * u) * w),L(z,y,x) * u,w) = ((L(z,y,x) * u) * w) \ ((z * u) * w). [para(2333(a,1),549(a,1,2,1)),flip(a)]. 2380 a(x,y,z) * (z * x) = z * R(x,y,z). [para(1973(a,1),2333(a,1,2))]. 2381 L(a(x,y,z),u,w) * L(z,y,x) = a(w,u,a(x,y,z)) \ z. [para(2321(a,2),2335(a,1,2))]. 2382 R(x,y * (y * z),u) = R(x,z,u). [para(2337(a,2),2300(a,2)),flip(a)]. 2383 R(x,y \ z,u) = R(x,y * z,u). [para(20(a,1),2382(a,1,2,2)),flip(a)]. 2385 R(x,(y \ z) / u,w) = R(x,(y * z) / u,w). [para(238(a,1),2382(a,1,2)),flip(a)]. 2386 (x \ a(y,x,z)) \ u = (a(y,x,z) \ x) * u. [para(2348(a,1),318(a,1,1)),flip(a)]. 2388 K(a(x,y,z) \ 1,u) = a(K(u,x),y,z). [para(2341(a,1),2366(a,1,1))]. 2389 (x * y) * L(a(x,z,y),y,x) = R(x,z,y) * y. [para(2368(a,1),74(a,2))]. 2390 x \ ((y \ x) * T(y,x)) = a(T(y,x),x,y). [para(1317(a,1),2316(a,1,2))]. 2391 x \ ((y \ x) * T(y,x)) = a(y,x,y). [para(2390(a,2),2086(a,1))]. 2393 a(R(x,y,z),u,y) = L(y,u,x) \ y. [para(2318(a,1),1986(a,1))]. 2394 a(R(x,y,z),u,w) = R(a(x,u,w),y,z). [para(2297(a,2),2318(a,1,1)),flip(a)]. 2396 a(R(x,y,z),u,y) = a(x,u,y). [para(2393(a,2),2298(a,2)),flip(a)]. 2400 a(L(x,y,x),z,y) = a(x,z,y). [para(1312(a,1),2396(a,1,1)),flip(a)]. 2404 R(a(x,y,z),x * u,w) = a(R(x,u,w),y,z). [para(2394(a,1),1718(a,1))]. 2406 a(L(x,y,z),u,w) = L(a(x,u,w),y,z). [para(2297(a,2),2319(a,1,1)),flip(a)]. 2407 a(L(x,y,z),u,w) \ a(x,u,w) = a(z,y,a(x,u,w)). [para(2406(a,2),2298(a,2,1)),flip(a)]. 2408 a(x,y,z) \ a(L(x,u * w,u),y,z) = a(u,w,a(x,y,z)). [para(2406(a,2),2320(a,2,2)),flip(a)]. 2409 a(x,y,z) \ a(L(x,u,w),y,z) = a(w,u,a(x,y,z)) \ 1. [para(2406(a,2),2328(a,2,2)),flip(a)]. 2410 K(x,a(y / z,(y / z) * z,u)) = K(a(z * y,z,u) \ 1,x). [para(2374(a,1),2340(a,1,1,1)),flip(a)]. 2411 (a(x,y,z) * y) * u = y * (a(x,y,z) * u). [para(1688(a,2),2347(a,1,1))]. 2412 a(x,y,z) \ (y * u) = (a(x,y,z) \ y) * u. [para(2386(a,1),2349(a,1)),flip(a)]. 2413 L(x,y,a(z,y,u)) = x. [hyper(23,a,798,a,b,2412,a(flip)),flip(a)]. 2414 (a(x,y,z) * y) * u = a(x,y,z) * (y * u). [para(2413(a,1),74(a,1,2))]. 2415 (a(x,y,z) * (y \ 1)) * u = a(x,y,z) * (y \ u). [para(2413(a,1),945(a,1,2))]. 2416 R(a(x,y,z),y,u) = a(x,y,z). [hyper(24,a,79,a,b,2414,a(flip)),flip(a)]. 2417 a(x,y,z) * (y * u) = y * (a(x,y,z) * u). [para(2414(a,1),2411(a,1))]. 2419 (x * y) \ (x * (a(z,x,u) * y)) = T(a(z,x,u),x * y). [para(2417(a,1),36(a,2,2)),flip(a)]. 2420 x * (y * (a(x,y,z) * u)) = R(x,y,z) * (y * u). [para(2417(a,1),2306(a,1,2))]. 2421 (x * y) * a(L(x,y,x),z,y) = R(x,z,y) * y. [para(2406(a,2),2389(a,1,2))]. 2422 (x * y) * a(x,z,y) = R(x,z,y) * y. [para(2400(a,1),2421(a,1,2))]. 2423 (x * (R(y,z,u) * u)) / ((y * u) * R(a(y,z,u),y * u,x)) = L(x,y * u,a(y,z,u)). [para(2422(a,1),2079(a,2,1,2)),flip(a)]. 2424 (x \ a(y,x,z)) * u = a(y,x,z) * (x \ u). [para(1795(a,1),2415(a,1,1))]. 2425 (a(x,y,z) * (y \ u)) \ ((y \ a(x,y,z)) * (u * w)) = L(w,u,y \ a(x,y,z)). [para(2424(a,1),32(a,2,1)),flip(a)]. 2426 L(T(a(x,y,z),u),u,y) = T(a(x,y,z),y * u). [para(2419(a,1),106(a,1)),flip(a)]. 2427 L(a(T(x,y),z,u),y,z) = T(a(x,z,u),z * y). [para(2370(a,2),2426(a,1,1))]. 2428 a(L(x,y,z),u,w) * L(w,u,x) = a(z,y,a(x,u,w)) \ w. [para(2406(a,2),2381(a,1,1))]. 2429 K(a(x * y,x,z) \ 1,u) = K(u,a(y / x,y,z)). [para(22(a,1),2410(a,1,2,2)),flip(a)]. 2430 K(a(x * y,x,z) \ 1,u) = K(u,a(y * x,y,z)). [para(2375(a,1),2429(a,2,2))]. 2431 K(x,a(y * z,y,u)) = a(K(x,z * y),z,u). [para(2430(a,1),2388(a,1))]. 2432 a(L(x,y,z),R(z,y,x),u) = (x * (z * u)) \ ((x * z) * u). [para(1998(a,1),1981(a,1,1)),flip(a)]. 2433 a(L(x,y,z),R(z,y,x),u) = a(x,z,u). [para(2432(a,2),28(a,2)),flip(a)]. 2435 L(a(x,R(y,z,x),u),z,y) = a(x,y,u). [para(2433(a,1),2406(a,1)),flip(a)]. 2436 (a(x,y,z) * (y \ u)) \ (a(x,y,z) * (y \ (u * w))) = L(w,u,y \ a(x,y,z)). [para(2424(a,1),2425(a,1,2))]. 2437 L(L(x,y,z),z * y,a(u,z,w)) = L(x,y,z \ a(u,z,w)). [para(2436(a,1),1409(a,1)),flip(a)]. 2438 L(L(x,y,z),z * y,a(u,z,w)) = L(x,y,z * a(u,z,w)). [para(2437(a,2),776(a,1))]. 2439 (R(x,y,z) * y) \ ((x * y) * u) = (x \ R(x,y,z)) \ u. [para(1996(a,1),1411(a,1))]. 2440 L(x,y,R(z,y,x)) = (z \ R(z,y,x)) \ x. [para(2439(a,1),183(a,1)),flip(a)]. 2441 L(x,y,R(z,y,x)) = L(x,y,z). [para(2440(a,2),1976(a,2)),flip(a)]. 2442 L(x,y * z,R(y,z,x) \ 1) = L(x,y * z,y \ 1). [para(584(a,1),2441(a,1,3))]. 2443 L(x,y * z,R(y,z,x)) = L(x,y * z,y \ 1). [para(2442(a,1),787(a,1)),flip(a)]. 2444 L(x,y * z,R(y,z,x)) = L(x,y * z,y). [para(2443(a,2),787(a,1))]. 2445 R(x,y,z) * (L(z,x * y,x) \ z) = R(R(x,y,z),x * y,z). [para(2444(a,1),1979(a,2,2,1)),flip(a)]. 2446 R(x,y,z) * (R(x,y,z) \ x) = R(R(x,y,z),x * y,z). [para(1954(a,1),2445(a,1,2))]. 2447 R(R(x,y,z),x * y,z) = x. [para(2446(a,1),20(a,1))]. 2448 R(R(x,x * y,z),y,z) = x. [para(2447(a,1),50(a,1)),flip(a)]. 2449 K(x,R(y,y * z,u) \ R(R(y,y * z,u),z,u)) = K(x,R(y,y * z,u)) * K(y,x). [para(2448(a,1),2262(a,1,2,1)),flip(a)]. 2450 K(x,R(y,y * z,u) \ R(R(y,y * z,u),z,u)) = R(K(x,y),z,u) * K(y,x). [para(1672(a,1),2449(a,2,1))]. 2451 K(x,R(y,y * z,u) \ R(R(y,y * z,u),z,u)) = K(y,x) * R(K(x,y),z,u). [para(2450(a,2),406(a,1))]. 2452 K(x,R(y,y * z,u) \ y) = K(y,x) * R(K(x,y),z,u). [para(2448(a,1),2451(a,1,2,2))]. 2453 K(x,y) * R(K(y,x),z,u) = K(y,x \ R(x,z,u)). [para(622(a,1),2452(a,1,2)),flip(a)]. 2454 x * K(y,z \ R(z,u,x)) = L(x,u,K(y,z)). [para(2453(a,1),2076(a,1,2))]. 2455 x * K(a(y,z,x),u) = L(x,z,K(u,y)). [para(2275(a,1),2454(a,1,2))]. 2456 a(K(x,y),z,u) = K(a(x,z,u),y). [hyper(23,a,2290,a,b,2455,a),flip(a)]. 2457 a(K(x,y),z,u) = K(a(y,z,u),x). [hyper(23,a,2288,a,b,2455,a),flip(a)]. 2458 a(K(x,y),z,u) = K(y,a(x,z,u)). [para(2456(a,2),1847(a,1))]. 2459 a(K(x,y),z,u) = K(x,a(y,z,u)). [para(2457(a,2),1847(a,1))]. 2460 x * K(y,a(z,u,x)) = L(x,u,K(z,y)). [para(2458(a,1),2288(a,1,2))]. 2461 K(x * y,a(z,x,u)) = K(z,a(y * x,y,u)). [para(2458(a,1),2431(a,2)),flip(a)]. 2462 K(x,a(y,z,u)) = K(y,a(x,z,u)). [para(2459(a,1),2458(a,1))]. 2463 L(x,y * z,K(y,u)) = L(x,z,K(y,u)). [para(2460(a,1),2284(a,2))]. 2464 (x * (R(y,z,u) * u)) / ((y * u) * a(R(y,u,x),z,u)) = L(x,y * u,a(y,z,u)). [para(2404(a,1),2423(a,1,2,2))]. 2465 (x * (R(y,z,u) * u)) / ((y * u) * a(y,z,u)) = L(x,y * u,a(y,z,u)). [para(2396(a,1),2464(a,1,2,2))]. 2467 (x * (R(y,z,u) * u)) / (R(y,z,u) * u) = L(x,y * u,a(y,z,u)). [para(2422(a,1),2465(a,1,2))]. 2468 L(x,y * z,a(y,u,z)) = x. [para(2467(a,1),21(a,1))]. 2469 L(x,y * z,a(T(z,y),u,y)) = x. [para(2468(a,1),1185(a,1)),flip(a)]. 2470 L(x,y * z,a(z,u,y)) = x. [para(2358(a,1),2469(a,1,3))]. 2471 (a(x,y,z) * (z * x)) \ (a(x,y,z) * (z * (x * u))) = L(u,x,z). [para(2470(a,1),174(a,2))]. 2472 (x * R(y,z,x)) \ (a(y,z,x) * (x * (y * u))) = L(u,y,x). [para(2380(a,1),2471(a,1,1))]. 2473 (x * R(y,z,x)) \ (x * (a(y,z,x) * (y * u))) = L(u,y,x). [para(2378(a,1),2472(a,1,2))]. 2474 (x * R(y,z,x)) \ (x * (R(y,z,x) * u)) = L(u,y,x). [para(2308(a,1),2473(a,1,2,2))]. 2475 L(x,R(y,z,u),u) = L(x,y,u). [para(2474(a,1),32(a,2))]. 2476 a(x,R(y,z,x),u) = L(u,y,x) \ u. [para(2475(a,1),2298(a,2,1))]. 2477 a(x,R(y,z,x),u) = a(x,y,u). [para(2476(a,2),2298(a,2)),flip(a)]. 2478 L(a(x,y,z),u,y) = a(x,y,z). [para(2477(a,1),2435(a,1,1))]. 2479 a(L(x,y,z),z,u) = a(x,z,u). [para(2478(a,1),2406(a,2))]. 2480 T(a(x,y,z),y * u) = a(T(x,u),y,z). [para(2478(a,1),2427(a,1)),flip(a)]. 2482 a((x * y) \ z,x,u) = a(y \ (x \ z),x,u). [para(177(a,1),2479(a,1,1))]. 2483 L(x,y,z) * a(x,z,u) = R(L(x,y,z),z,u). [para(2479(a,1),2300(a,2,2)),flip(a)]. 2484 a(T(x,y),z,u) \ a(x,z,u) = K(z * y,a(x,z,u)). [para(2480(a,1),1080(a,2,1)),flip(a)]. 2486 a(x \ (y \ z),y,u) = a((y * x) * z,y,u). [para(2482(a,1),1702(a,1))]. 2487 L(x,y,z) * a(x,z,u) = L(R(x,z,u),y,z). [para(2483(a,2),48(a,1))]. 2488 a((x * y) * z,x,u) = a(y * (x * z),x,u). [para(2486(a,1),1757(a,1))]. 2489 (x * a(x,y,z)) / L(R(x,y,z),u,y) = a(y,u,x). [para(2487(a,1),2334(a,1,2))]. 2490 a(T(x,y) * (y * z),y,u) = a((x * y) * z,y,u). [para(82(a,1),2488(a,1,1,1)),flip(a)]. 2491 R(x,y,z) / L(R(x,y,z),u,y) = a(y,u,x). [para(2300(a,2),2489(a,1,1))]. 2492 a(x,y,R(z,x,u)) = a(x,y,z). [para(2491(a,1),2329(a,2))]. 2493 a(x,y,(z / u) / x) = a(x,y,z / (x * u)). [para(193(a,1),2492(a,1,3)),flip(a)]. 2494 K(x * y,a(z,x,u)) = K(y,a(z,x,u)). [para(2484(a,1),2371(a,1))]. 2495 K(x,a(y * z,y,u)) = K(z,a(x,y,u)). [para(2494(a,1),2462(a,1)),flip(a)]. 2496 K(x,a(y * z,y,u)) = K(y,a(x,z,u)). [para(2494(a,1),2461(a,1)),flip(a)]. 2497 K(x,a(y,z,u)) = K(z,a(y,x,u)). [para(2496(a,1),2495(a,1))]. 2498 x * K(y,a(z,u,x)) = L(x,y,K(z,u)). [para(2497(a,1),2460(a,1,2))]. 2499 L(x,y,K(z,u)) = L(x,u,K(z,y)). [para(2498(a,1),2460(a,1))]. 2501 L(x,y,K(z,z * u)) = L(x,u,K(z,y)). [para(2499(a,1),2463(a,1))]. 2502 L(x,y,a(z,u,u)) = L(x,u,K(z,y)). [para(2501(a,1),1261(a,1)),flip(a)]. 2503 L(x,y,a(z,u,u)) = L(x,y,K(z,u)). [para(2502(a,2),2499(a,1))]. 2504 L(x,y,a(z,u,z)) = L(x,y,K(u,z)). [para(2503(a,1),1695(a,1)),flip(a)]. 2505 L(L(x,y,z),z * y,K(z,u)) = L(x,y,z * a(u,z,u)). [para(2504(a,1),2438(a,1))]. 2506 L(x,y,z * a(u,z,u)) = L(x,y,T(z,u)). [para(2505(a,1),1604(a,1))]. 2507 L(x,y,R(z,u,u)) = L(x,y,T(z,u)). [para(2506(a,1),1692(a,1)),flip(a)]. 2508 L(x,y,T(z / u,z)) = L(x,y,u * z). [para(2507(a,1),846(a,1))]. 2509 L(x,y,z * u) = L(x,y,u * z). [para(2508(a,1),845(a,1))]. 2510 L(L(x,y,z * u),(z * u) * y,u * z) = x. [para(2509(a,1),303(a,1))]. 2511 L(x,y,z \ u) = L(x,y,u * z). [para(2509(a,1),776(a,2))]. 2513 L(x,y,z * (u * (u * w))) = L(x,y,w * z). [para(2509(a,1),868(a,2))]. 2514 L(x,y,(z * (u * w)) * (z * u)) = L(x,y,L(w,u,z)). [para(32(a,2),2511(a,1,3)),flip(a)]. 2515 L(x,y,K(z,u)) = x. [para(2510(a,1),1850(a,1)),flip(a)]. 2516 a(K(x,y),z,u) = 1. [hyper(38,a,2515,a)]. 2518 (K(x,y) * z) * u = K(x,y) * (z * u). [para(2515(a,1),74(a,1,2))]. 2519 (K(x,y) * z) \ (K(x,y) * u) = z \ u. [para(2515(a,1),76(a,1)),flip(a)]. 2520 (K(x,y) \ z) \ u = z \ (K(x,y) * u). [para(2515(a,1),267(a,1)),flip(a)]. 2521 (K(x,y) * z) / u = K(x,y) * (z / u). [para(2515(a,1),196(a,1,2))]. 2526 L(x,y,T(z,u)) = L(x,y,z). [para(2515(a,1),1604(a,1)),flip(a)]. 2534 L(x,y,a(z,u,z)) = x. [para(2515(a,1),2504(a,2))]. 2539 K(a(x,y,z) \ 1,u) = 1. [para(2516(a,1),2388(a,2))]. 2540 K(a(x,y,z),u) = 1. [para(2516(a,1),2456(a,1)),flip(a)]. 2543 T(a(x,y,z),u) = a(x,y,z). [hyper(41,a,2540,a)]. 2548 (a(x,y,x) * z) * u = (z * u) * a(x,y,x). [para(2534(a,1),2053(a,1,2))]. 2549 T(a(x,y,z) \ 1,u) = a(x,y,z) \ 1. [hyper(41,a,2539,a)]. 2553 L(x,y,z * (u * z)) = L(x,y,u). [para(2526(a,1),778(a,2))]. 2567 a(x,y,z) * u = u * a(x,y,z). [para(2543(a,1),82(a,1,2)),flip(a)]. 2569 (a(x,y,z) \ u) \ u = a(x,y,z). [para(2543(a,1),83(a,1)),flip(a)]. 2570 (a(x,y,z) \ u) * a(x,y,z) = u. [para(2543(a,1),250(a,1,2))]. 2571 x / a(y,z,u) = a(y,z,u) \ x. [para(2543(a,1),252(a,1,2))]. 2572 a(x,y,z) * (u \ 1) = u \ a(x,y,z). [para(2543(a,1),326(a,1,2)),flip(a)]. 2578 a(T(x,y),z,u) = a(x,z,u). [para(2543(a,1),2370(a,2))]. 2584 a(x / y,z,u) = a(y \ x,z,u). [para(84(a,1),2578(a,1,1)),flip(a)]. 2586 a(x * (y * x),z,u) = a(y,z,u). [para(2578(a,1),1704(a,2))]. 2597 a(x,y,z) * (u / a(x,y,z)) = u. [para(2567(a,2),22(a,1))]. 2598 (x * (a(y,z,u) * w)) \ ((x * w) * a(y,z,u)) = a(x,w,a(y,z,u)). [para(2567(a,2),28(a,2,1,2)),flip(a)]. 2601 (x * y) \ ((x * a(z,u,w)) * y) = R(T(a(z,u,w),x * y),x,y). [para(2567(a,1),549(a,1,2,1))]. 2602 x * (y * a(x,z,u)) = R(x,z,u) * y. [para(2567(a,1),2306(a,1,2))]. 2603 (x * y) * a(x,z,u) = R(x,z,u) * y. [para(2567(a,1),2308(a,1))]. 2604 x * (L(x,y,z) \ u) = u * a(z,y,x). [para(2567(a,1),2323(a,2))]. 2605 (a(x,y,z) \ u) \ w = (a(x,y,z) / u) * w. [para(2570(a,1),353(a,1,1,2)),flip(a)]. 2606 a(x / y,z,u) = a(y * x,z,u). [para(2584(a,2),1702(a,1))]. 2609 a(x * a(y,z,x),u,w) = a(L(x,z,y),u,w). [para(2333(a,1),2586(a,1,1))]. 2612 (x * y) / a(z,u,x) = L(x,u,z) * y. [hyper(23,a,2333,a,b,2597,a)]. 2613 a(x / y,z,u) = a(x * y,z,u). [para(2606(a,1),612(a,1)),flip(a)]. 2618 a(x * y,z,u) = a(y * x,z,u). [para(2613(a,1),2606(a,1))]. 2621 (x * (K(y,z) * (u * w))) \ ((x * (K(y,z) * u)) * w) = a(x,K(y,z) * u,w). [para(2518(a,1),28(a,2,1,2)),flip(a)]. 2622 (K(x,y) * (z * (u * w))) \ (((K(x,y) * z) * u) * w) = a(K(x,y) * z,u,w). [para(2518(a,1),28(a,2,1)),flip(a)]. 2623 (K(x,y) * (z * u)) \ ((K(x,y) * z) * (u * w)) = L(w,u,K(x,y) * z). [para(2518(a,1),32(a,2,1)),flip(a)]. 2624 ((K(x,y) * (z * u)) * w) / (u * w) = R(K(x,y) * z,u,w). [para(2518(a,1),34(a,2,1,1)),flip(a)]. 2629 ((T(x,y) * z) * u) / (K(x,y) * (z * u)) = R(x,K(x,y) * z,u). [para(2518(a,1),1167(a,1,2))]. 2630 K(x,T(y,z)) * (z * u) = (z * K(x,y)) * u. [para(2216(a,1),2518(a,1,1)),flip(a)]. 2631 (x \ K(y,z)) * (K(z,y) * u) = x \ u. [para(2519(a,1),2121(a,1)),flip(a)]. 2632 x \ (K(y,z) * u) = (x \ K(y,z)) * u. [para(2520(a,1),2133(a,1))]. 2633 x * (a(y,z,u) \ 1) = a(y,z,u) \ x. [para(2549(a,1),327(a,1,2))]. 2635 (x * y) \ (R(x,z,u) * y) = L(a(x,z,u),y,x). [para(2602(a,1),32(a,2,2)),flip(a)]. 2637 (x * y) \ (R(x,z,u) * y) = a(x,z,u). [hyper(23,a,20,a,b,2603,a),flip(a)]. 2642 (x * y) * (a(x,y,z) * u) = (R(x,y,z) * y) * u. [para(2603(a,1),2338(a,1,1)),flip(a)]. 2643 L(x,y,z) * a(z,y,L(x,u,w)) = L(x,u,w) * a(w,u,L(x,y,z)). [para(2325(a,1),2604(a,1,2))]. 2644 (L(x,y,z) * u) \ (x * u) = a(z,y,x). [para(2612(a,1),66(a,1,1))]. 2645 (x * K(y,z)) \ u = K(z,y) * (x \ u). [hyper(23,a,297,a,b,2631,a),flip(a)]. 2646 L(x,K(y,z),u) = x. [hyper(23,a,798,a,b,2632,a(flip)),flip(a)]. 2649 (x * K(y,z)) * u = x * (K(y,z) * u). [para(2646(a,1),74(a,1,2))]. 2650 (x * (K(y,z) * u)) / u = x * K(y,z). [para(2646(a,1),99(a,1,2))]. 2656 L(x,T(y,z) * y,u) = x. [para(2646(a,1),988(a,1)),flip(a)]. 2658 L(x,(y \ z) * (z / y),u) = x. [para(84(a,1),2656(a,1,2,1))]. 2659 L(x,(y * z) * (z / y),u) = x. [para(2658(a,1),880(a,1)),flip(a)]. 2660 L(x,T(L(y / z,z * y,y / z) * (z * y),y / z),u) = x. [para(1309(a,2),2659(a,1,2))]. 2661 x \ (R(x / y,z,u) * y) = a(x / y,z,u). [para(22(a,1),2637(a,1,1))]. 2662 (L(R(x,y,z),u,w) * (y * z)) \ ((x * y) * z) = a(w,u,R(x,y,z)). [para(79(a,1),2644(a,1,2))]. 2664 K(x * y,x) * (y \ z) = (x * (y / x)) \ z. [para(1129(a,1),2645(a,1,1)),flip(a)]. 2665 (K(x,y) / z) * u = K(x,y) * (z \ u). [para(2645(a,1),2143(a,1)),flip(a)]. 2666 R(x,K(y,z),u) = x. [hyper(24,a,79,a,b,2649,a(flip)),flip(a)]. 2667 (x * T(y,z)) \ (x * (K(y,z) * (y * u))) = L(u,y,x \ K(y,z)). [para(2649(a,1),2264(a,1,2))]. 2668 (x / y) / K(z,u) = x / (K(z,u) * y). [para(2666(a,1),193(a,1))]. 2670 (x * y) / T(y,z) = x * K(z,y). [para(1077(a,1),2650(a,1,1,2))]. 2671 (x / y) * K(z,y) = x / T(y,z). [para(22(a,1),2670(a,1,1)),flip(a)]. 2672 (x * (y * z)) / T(L(z,y,x),u) = (x * y) * K(u,L(z,y,x)). [para(74(a,1),2670(a,1,1))]. 2673 ((x \ y) * x) / T(y,x) = a(x,y,x). [para(2671(a,1),1538(a,1))]. 2675 a(x,y,x) * T(y,x) = (x \ y) * x. [para(2673(a,1),22(a,1,1))]. 2676 K(x * y,x) * ((x \ y) \ z) = (x / y) * z. [para(1009(a,1),2665(a,1,1)),flip(a)]. 2677 K(x,T(y,z)) * (z \ u) = (z \ K(x,y)) * u. [para(2201(a,1),2665(a,1,1)),flip(a)]. 2678 x / (K(y,z) * u) = (x / u) * K(z,y). [para(2668(a,1),2140(a,1))]. 2679 a(L(x,y * z,y),u,w) = a(L(x,z,y),u,w). [para(2342(a,2),2609(a,1,1))]. 2680 K(x,T(y,z)) * (z * u) = z * (K(x,y) * u). [para(2630(a,2),2649(a,1))]. 2681 x \ (y * R(y \ x,z,u)) = a(x / y,z,u). [para(224(a,1),2661(a,1,2))]. 2682 L(x,y,z * (K(u * w,u) * ((u * (w / u)) \ v5))) = L(x,y,(w \ v5) * z). [para(2664(a,1),2513(a,1,3,2,2))]. 2683 a(x,y,z) \ a(L(x,u,w),y,z) = a(w,u,a(x,y,z)). [para(2679(a,1),2408(a,1,2))]. 2685 x \ (y * R(y \ x,z,u)) = a(y * x,z,u). [para(2681(a,2),2606(a,1))]. 2686 (x * (y * z)) \ ((x * y) * R(L(z,y,x),u,w)) = a((x * y) * (x * (y * z)),u,w). [para(32(a,2),2685(a,1,2,2,1))]. 2687 L(a(x,y,z),u,x) = a(x,y,z). [para(2635(a,1),2637(a,1))]. 2692 (x * (y * (a(x,y,z) * u))) \ ((R(x,y,z) * y) * u) = a(x,y,a(x,y,z) * u). [para(2642(a,1),28(a,2,2)),flip(a)]. 2693 L(x,y,z) * a(L(z,u,w),y,x) = x * a(w,u,a(z,y,x)). [para(2683(a,1),2377(a,1,2)),flip(a)]. 2694 a(x,y,a(z,u,w)) \ 1 = a(x,y,a(z,u,w)). [para(2683(a,1),2409(a,1)),flip(a)]. 2695 a(x,y,a(z,u,w)) * a(x,y,a(z,u,w)) = 1. [para(2694(a,1),20(a,1,2))]. 2696 a(x,y,a(z,u,w)) \ v5 = v5 * a(x,y,a(z,u,w)). [para(2694(a,1),2633(a,1,2)),flip(a)]. 2697 a(L(x,y,z),u,w) * L(w,u,x) = w * a(z,y,a(x,u,w)). [para(2696(a,1),2428(a,2))]. 2698 (K(x,y) * ((z * u) * w)) / (u * w) = R(K(x,y) * z,u,w). [para(2518(a,1),2624(a,1,1))]. 2699 K(x,y) * (((z * u) * w) / (u * w)) = R(K(x,y) * z,u,w). [para(2698(a,1),2521(a,1)),flip(a)]. 2700 R(K(x,y) * z,u,w) = K(x,y) * R(z,u,w). [para(34(a,2),2699(a,1,2)),flip(a)]. 2701 R(x * K(y,z),u,w) = R(x,u,w) * K(y,z). [hyper(23,a,699,a(flip),b,2700,a(flip))]. 2704 R(T(x,y),z,u) * K(y,x) = R(x,z,u). [para(1089(a,1),2701(a,1,1)),flip(a)]. 2706 K(x,R(y,z,u)) = K(x,y). [hyper(23,a,1109,a,b,2704,a),flip(a)]. 2708 T(x,R(y,z,u)) = x * K(x,y). [para(2706(a,1),1107(a,2,2))]. 2716 T(x,R(y,z,u)) = T(x,y). [para(2708(a,2),1107(a,2)),flip(a)]. 2717 R(x,y,z) * T(u,x) = u * R(x,y,z). [para(2716(a,1),82(a,1,2))]. 2723 R(x,y,z) * (x \ u) = (u / x) * R(x,y,z). [para(84(a,1),2717(a,1,2))]. 2725 (x / y) * R(y,z,u) = a(y,z,u) * x. [para(2723(a,1),2309(a,1))]. 2726 a(x,y,z) * (u * x) = u * R(x,y,z). [para(21(a,1),2725(a,1,1)),flip(a)]. 2727 L(x,y,z) * R(a(z,y,x),u,w) = a(a(z,y,x),u,w) * x. [para(2326(a,2),2725(a,1,1))]. 2729 (x * y) * a(y,z,u) = x * R(y,z,u). [para(2726(a,1),2567(a,1)),flip(a)]. 2730 (x * (y * z)) \ (x * (y * R(z,u,w))) = L(a(z,u,w),y * z,x). [para(2729(a,1),32(a,2,2,2)),flip(a)]. 2731 L(x,T((y / z) * (z * y),y / z),u) = x. [para(892(a,1),2660(a,1,2,1,1))]. 2733 L(x,(y * z) / (z / y),u) = x. [para(2731(a,1),1235(a,1)),flip(a)]. 2734 L(x,(y * z) * (y / z),u) = x. [para(952(a,1),2733(a,1,2))]. 2735 (x * (y * z)) / L(T(z,u),y,x) = (x * y) * K(u,L(z,y,x)). [para(44(a,2),2672(a,1,2))]. 2736 (x * y) \ ((x * a(z,u,w)) * y) = R(a(z,u,w),x,y). [para(2543(a,1),2601(a,2,1))]. 2738 (((T(x,y) * z) * u) / (z * u)) * K(y,x) = R(x,K(x,y) * z,u). [para(2629(a,1),2678(a,1)),flip(a)]. 2739 (x * T(y,z)) \ (x * (T(y,z) * u)) = L(u,y,x \ K(y,z)). [para(1160(a,1),2667(a,1,2,2))]. 2740 L(x,y,z \ K(y,u)) = L(x,T(y,u),z). [para(2739(a,1),32(a,2)),flip(a)]. 2741 L(x,y,z * K(y,u)) = L(x,T(y,u),z). [para(2740(a,1),776(a,1)),flip(a)]. 2742 R(T(x,y),z,u) * K(y,x) = R(x,K(x,y) * z,u). [para(34(a,2),2738(a,1,1))]. 2743 R(x,K(x,y) * z,u) = R(x,z,u). [para(2742(a,1),2704(a,1))]. 2744 R(x,y * x,z) = R(x,x * y,z). [para(974(a,1),2743(a,1,2)),flip(a)]. 2746 x \ R(x,y * x,z) = R(x,y,z) \ x. [para(2744(a,2),618(a,1,2))]. 2747 a(x,y * x,z) = R(x,y,z) \ x. [para(2746(a,1),2297(a,2))]. 2748 a(x,y * x,z) = a(x,y,z) \ 1. [para(2747(a,2),2302(a,1))]. 2749 a(x * y,y,z) = a(x * y,x,z) \ 1. [para(2748(a,1),1778(a,1)),flip(a)]. 2750 a(x * y,y,a(z,u,w)) = a(x * y,x,a(z,u,w)). [para(2749(a,2),2694(a,1))]. 2751 ((L(x,y,z) * u) * w) \ ((x * u) * w) = a(z,y,R(x,u,w)). [para(184(a,1),2662(a,1,1))]. 2752 (K(x,y) * (z * u)) \ (K(x,y) * (z * (u * w))) = L(w,u,K(x,y) * z). [para(2518(a,1),2623(a,1,2))]. 2753 L(x,y,K(z,u) * w) = (w * y) \ (w * (y * x)). [para(2752(a,1),2519(a,1))]. 2754 L(x,y,K(z,u) * w) = L(x,y,w). [para(2753(a,2),32(a,2)),flip(a)]. 2755 ((x * K(y,z)) * u) \ ((x * K(y,z)) * (u * w)) = L(w,u,x). [para(2753(a,1),2553(a,1))]. 2757 L(x,y,T(z,u) * w) = L(x,y,z * w). [para(1098(a,1),2754(a,1,3)),flip(a)]. 2758 L(x,y,(z / u) * w) = L(x,y,(u \ z) * w). [para(1161(a,1),2754(a,1,3))]. 2759 L(x,y,z * T(u,w)) = L(x,y,z * u). [para(1212(a,1),2754(a,1,3))]. 2760 L(x,y,z * K(u,w)) = L(x,y,z). [para(2200(a,1),2754(a,1,3))]. 2762 L(x,y,z * (K(u,w) * v5)) = L(x,y,z * v5). [para(2680(a,1),2754(a,1,3))]. 2763 L(x,T(y,z),u) = L(x,y,u). [para(2760(a,1),2741(a,1)),flip(a)]. 2765 L(x,(y * z) * z,u) = L(x,y,u). [para(2763(a,1),951(a,1)),flip(a)]. 2766 L(x,y / z,u) = L(x,z * y,u). [para(2763(a,1),1235(a,1)),flip(a)]. 2777 L(x,y / z,u) = L(x,y * z,u). [para(22(a,1),2765(a,1,2,1)),flip(a)]. 2779 (x * y) / L(z,z * y,x) = x * (y / z). [para(2766(a,1),196(a,1,2))]. 2782 L(x,y * z,u) = L(x,z * y,u). [para(2777(a,1),2766(a,1))]. 2787 L(x,(y / z) * (y * z),u) = x. [para(2782(a,1),2734(a,1))]. 2788 L(x,(y \ (y \ z)) * ((y \ z) * T(y,z)),u) = x. [para(256(a,1),2787(a,1,2,1))]. 2789 L(x,(y * z) * u,y * (z * u)) = x. [para(2757(a,1),950(a,1))]. 2790 a(x,y,z) \ ((x * (y * z)) \ u) = ((x * y) * z) \ u. [para(2789(a,1),271(a,1)),flip(a)]. 2792 L(x,y,z * (u / w)) = L(x,y,z * (w \ u)). [para(84(a,1),2759(a,1,3,2)),flip(a)]. 2793 (x * (y * z)) / L(T(z,u),T(z,u) * (y * z),x) = x * (y * K(u,z)). [para(2670(a,1),2779(a,2,2))]. 2794 L(x,y,(z / u) * w) = L(x,y,(u * z) * w). [para(2758(a,2),781(a,1))]. 2795 L(x,y,z * (u * w)) = L(x,y,z * (w * u)). [para(974(a,1),2762(a,1,3,2))]. 2796 L(x,y,z * (u / w)) = L(x,y,z * (w * u)). [para(2792(a,2),867(a,1))]. 2797 L(x,y,z * ((u * w) * u)) = L(x,y,w * z). [para(2795(a,1),2513(a,1))]. 2798 L(x,(y * (y \ z)) * ((y \ z) * T(y,z)),u) = x. [para(2788(a,1),880(a,1)),flip(a)]. 2799 L(x,y * ((z \ y) * T(z,y)),u) = x. [para(20(a,1),2798(a,1,2,1))]. 2800 L(x,y \ ((z \ y) * T(z,y)),u) = x. [para(2799(a,1),876(a,2))]. 2801 L(x,a(y,z,y),u) = x. [para(2391(a,1),2800(a,1,2))]. 2802 (x * a(y,z,y)) * u = x * (a(y,z,y) * u). [para(2801(a,1),74(a,1,2))]. 2803 (x * y) / L(y,z,y) = x * a(y,z,y). [para(2801(a,1),1543(a,1,2))]. 2805 (x * (y * (a(z,u,z) * w))) \ (((x * y) * a(z,u,z)) * w) = a(x,y,a(z,u,z) * w). [para(2802(a,2),28(a,2,2)),flip(a)]. 2806 (a(x,y,x) * z) * u = z * (a(x,y,x) * u). [para(2051(a,2),2802(a,1,1))]. 2807 (x * y) * a(z,u,z) = x * (a(z,u,z) * y). [para(2806(a,1),2548(a,1)),flip(a)]. 2808 ((x * y) * z) \ (x * (y * z)) = a(x,y,z) \ 1. [para(60(a,1),2790(a,1,2)),flip(a)]. 2809 ((x * a(y,z,u)) * w) \ ((x * w) * a(y,z,u)) = a(x,a(y,z,u),w) \ a(x,w,a(y,z,u)). [para(2598(a,1),2790(a,1,2)),flip(a)]. 2810 (x * (K(y,z) * u)) \ ((x * K(y,z)) * (u * w)) = L(w,u,x). [para(2649(a,1),2755(a,1,1))]. 2811 (x * (K(y,z) * u)) \ (x * (K(y,z) * (u * w))) = L(w,u,x). [para(2649(a,1),2810(a,1,2))]. 2812 L(L(x,y,K(z,u)),K(z,u) * y,w) = L(x,y,w). [para(2811(a,1),174(a,1)),flip(a)]. 2813 L(x,K(y,z) * u,w) = L(x,u,w). [para(2515(a,1),2812(a,1,1))]. 2815 L(x,T(y,z) * u,w) = L(x,y * u,w). [para(1098(a,1),2813(a,1,2)),flip(a)]. 2817 L(x,T(y,z) * u,w) = L(x,u * y,w). [para(2815(a,2),2782(a,1))]. 2821 (x * (y * z)) / L(T(z,u),(y * z) * z,x) = x * (y * K(u,z)). [para(2817(a,1),2793(a,1,2))]. 2822 (x * (y * z)) / L(T(z,u),y,x) = x * (y * K(u,z)). [para(2765(a,1),2821(a,1,2))]. 2824 (x * y) * K(z,L(u,y,x)) = x * (y * K(z,u)). [para(2822(a,1),2735(a,1)),flip(a)]. 2826 L(x,y,z * ((u * (w / u)) \ v5)) = L(x,y,(w \ v5) * z). [para(2682(a,1),2762(a,1)),flip(a)]. 2827 L(x,y,z * ((u * (w / u)) * v5)) = L(x,y,(w \ v5) * z). [para(2826(a,1),867(a,1)),flip(a)]. 2829 L(x,y,z * ((u * (w / u)) * v5)) = L(x,y,(w * v5) * z). [para(2827(a,2),781(a,1))]. 2830 L(x,y,(z * u) * ((w * (z / w)) * (u * v5))) = L(x,y,L(v5,u,w * (z / w))). [para(2829(a,1),2514(a,1))]. 2831 (K(x,y) * (z * (u * w))) \ ((K(x,y) * (z * u)) * w) = a(K(x,y) * z,u,w). [para(2518(a,1),2622(a,1,2,1))]. 2832 L(x,y,L(z,u,(u * z) * (w / (u * z)))) = L(x,y,(w / (u * z)) * (w * u)). [para(2830(a,1),2797(a,1))]. 2833 (K(x,y) * (z * (u * w))) \ (K(x,y) * ((z * u) * w)) = a(K(x,y) * z,u,w). [para(2518(a,1),2831(a,1,2))]. 2834 L(x,y,L(z,u,(u * z) * (w / (u * z)))) = L(x,y,((u * z) * w) * (w * u)). [para(2832(a,2),2794(a,1))]. 2835 a(K(x,y) * z,u,w) = (z * (u * w)) \ ((z * u) * w). [para(2833(a,1),2519(a,1))]. 2836 a(K(x,y) * z,u,w) = a(z,u,w). [para(2835(a,2),28(a,2)),flip(a)]. 2837 ((x * K(y,z)) * (u * w)) \ (((x * K(y,z)) * u) * w) = a(x,u,w). [para(2835(a,1),2586(a,1))]. 2839 a(T(x,y) * z,u,w) = a(x * z,u,w). [para(1098(a,1),2836(a,1,1)),flip(a)]. 2840 a((x / y) * z,u,w) = a((y \ x) * z,u,w). [para(1161(a,1),2836(a,1,1))]. 2841 a(x * T(y,z),u,w) = a(x * y,u,w). [para(1212(a,1),2836(a,1,1))]. 2843 a((x * y) * z,y,u) = a(x * (y * z),y,u). [para(2839(a,1),2490(a,1)),flip(a)]. 2844 a((x / y) * z,u,w) = a((y * x) * z,u,w). [para(2840(a,2),1707(a,1))]. 2845 a(x / (y / z),u,w) = a((z \ y) * x,u,w). [para(2840(a,1),2606(a,2))]. 2846 a(x / (y * z),z,u) = a(y * (z * x),z,u). [para(2843(a,1),2606(a,2))]. 2848 a(x / (y * z),u,w) = a((z / y) * x,u,w). [para(2844(a,2),2606(a,2))]. 2849 a(x / (y / z),u,w) = a(x / (z \ y),u,w). [para(2845(a,2),2606(a,2)),flip(a)]. 2850 a((x * y) / z,x,u) = a(y / (z * x),x,u). [para(2846(a,2),2606(a,2))]. 2851 a(x / (y / z),u,w) = a(x / (z * y),u,w). [para(2848(a,2),2606(a,2))]. 2852 a((x * y) / z,x,u) = a(y / (x / z),x,u). [para(2851(a,2),2850(a,2))]. 2853 (x * (K(y,z) * (u * w))) \ (((x * K(y,z)) * u) * w) = a(x,u,w). [para(2649(a,1),2837(a,1,1))]. 2854 (x * (K(y,z) * (u * w))) \ ((x * (K(y,z) * u)) * w) = a(x,u,w). [para(2649(a,1),2853(a,1,2,1))]. 2855 a(x,K(y,z) * u,w) = a(x,u,w). [para(2854(a,1),2621(a,1)),flip(a)]. 2856 a(x,y * z,u) = a(x,z * y,u). [para(974(a,1),2855(a,1,2))]. 2857 a(x,T(y,z),u) = a(x,y,u). [para(985(a,1),2855(a,1,2)),flip(a)]. 2858 a(x,y * T(z,u),w) = a(x,y * z,w). [para(1212(a,1),2855(a,1,2))]. 2861 a(x,y * K(z,u),w) = a(x,y,w). [para(2200(a,1),2855(a,1,2))]. 2862 R(x,K(y,z) * u,w) = a(x,u,w) * x. [para(2855(a,1),2303(a,2,1))]. 2865 a(x,y / z,u) = a(x,z * y,u). [para(2857(a,1),1788(a,1)),flip(a)]. 2866 a(x,(y * z) * z,u) = a(x,y,u). [para(2857(a,1),1792(a,1)),flip(a)]. 2867 R(x,T(y,z),u) = a(x,y,u) * x. [para(2857(a,1),2303(a,2,1))]. 2876 (x * ((y * K(z,u)) * w)) \ ((x * (y * K(z,u))) * w) = a(x,y,w). [para(2861(a,1),28(a,1)),flip(a)]. 2877 a(x,y * (z * K(u,w)),v5) = a(x,y * z,v5). [para(2824(a,1),2861(a,1,2))]. 2878 a(x,L(y,z,y) * (u * y),w) = a(x,u * a(y,z,y),w). [para(2803(a,1),2865(a,1,2)),flip(a)]. 2882 R(x,T(y,z),u) = R(x,y,u). [para(2867(a,2),2303(a,2)),flip(a)]. 2883 R(x,y / z,u) = R(x,z \ y,u). [para(84(a,1),2882(a,1,2)),flip(a)]. 2884 R(x,y / z,u) = R(x,z * y,u). [para(2883(a,2),2383(a,1))]. 2885 R(x,(y * z) / u,w) = R(x,u * (y \ z),w). [para(2884(a,1),2385(a,1)),flip(a)]. 2886 a(x,y * (z * K(u,z)),w) = a(x,y * L(z,u,z),w). [para(1062(a,1),2858(a,1,2,2)),flip(a)]. 2887 a(x,y * T(z,u),w) = a(x,z * y,w). [para(2858(a,2),2856(a,1))]. 2888 R(x,K(y,z) * u,w) = R(x,u,w). [para(2862(a,2),2303(a,2)),flip(a)]. 2892 R(x,y * K(z,u),w) = R(x,y,w). [para(2200(a,1),2888(a,1,2))]. 2894 R(x,y * (z * K(u,w)),v5) = R(x,y * z,v5). [para(2824(a,1),2892(a,1,2))]. 2896 R(x,y * T(z,u),w) = x * a(x,z * y,w). [para(2887(a,1),2300(a,2,2))]. 2897 R(x,y * (z \ u),w) = R(x,y * (z * u),w). [para(2885(a,1),2884(a,1))]. 2898 R(x,y * ((z \ u) \ 1),w) = R(x,y * (z / u),w). [para(2138(a,1),2894(a,1,2,2))]. 2899 R(x,y * T(z,u),w) = R(x,z * y,w). [para(2896(a,2),2300(a,2)),flip(a)]. 2900 R(x,y * ((z \ u) \ u),w) = R(x,z * y,w). [para(83(a,1),2899(a,1,2,2))]. 2901 R(x,y * ((z \ u) * u),w) = R(x,z * y,w). [para(2900(a,1),2897(a,1)),flip(a)]. 2902 R(x,y * ((z \ u) * 1),w) = R(x,y * (z / u),w). [para(2898(a,1),2897(a,1)),flip(a)]. 2903 R(x,y * (z / u),w) = R(x,y * (z \ u),w). [para(18(a,1),2902(a,1,2,2)),flip(a)]. 2904 R(x,y * (z / u),w) = R(x,y * (z * u),w). [para(2903(a,2),2897(a,1))]. 2905 R(x,x * (y * z),z) = y / ((x \ (y / z)) * z). [para(2904(a,1),631(a,1))]. 2906 R(x,x * ((y \ z) * z),z) = (y \ z) / ((x \ (y \ 1)) * z). [para(320(a,1),2905(a,2,2,1,2))]. 2907 a(x,y * L(z,u,z),w) = a(x,y * z,w). [para(2886(a,1),2877(a,1))]. 2908 a(x,L(y,z,y) * u,w) = a(x,u * y,w). [para(2907(a,1),2856(a,1)),flip(a)]. 2910 a(x,y * a(z,u,z),w) = a(x,(y * z) * z,w). [para(2878(a,1),2908(a,1))]. 2911 a(x,y * a(z,u,z),w) = a(x,y,w). [para(2910(a,2),2866(a,1))]. 2913 a(x,a(y,z,y) * u,w) = a(x,u,w). [para(2051(a,2),2911(a,1,2))]. 2915 (x * ((a(y,z,y) * u) * w)) \ ((x * (a(y,z,y) * u)) * w) = a(x,u,w). [para(2913(a,1),28(a,1)),flip(a)]. 2916 R(x,y * x,z) = (y \ z) / ((x \ (y \ 1)) * z). [para(2906(a,1),2901(a,1)),flip(a)]. 2918 (x * (y * (K(z,u) * w))) \ ((x * (y * K(z,u))) * w) = a(x,y,w). [para(2649(a,1),2876(a,1,1,2))]. 2919 (x * (y * (a(z,u,z) * w))) \ ((x * (a(z,u,z) * y)) * w) = a(x,y,w). [para(2806(a,1),2915(a,1,1,2))]. 2920 L(x,y,L(z,u,(u * z) * ((u * z) * w))) = L(x,y,((u * z) * w) * (w * u)). [para(2796(a,1),2834(a,1,3))]. 2921 L(x,y,((z * u) * w) * (w * z)) = L(x,y,L(u,z,w)). [para(774(a,1),2920(a,1,3)),flip(a)]. 2923 L(x,y,((z * u) * w) * (z * w)) = L(x,y,L(u,z,w)). [para(2921(a,1),2795(a,1)),flip(a)]. 2924 a(((x * y) * z) * (x * z),u,w) = L(w,u,L(y,x,z)) \ w. [para(2923(a,1),2298(a,2,1))]. 2925 a(((x * y) * z) * (x * z),u,w) = a(L(y,x,z),u,w). [para(2924(a,2),2298(a,2)),flip(a)]. 2926 (x * y) \ (((x * z) * y) * R(((x * z) * y) \ (x * y),u,w)) = a(L(z,x,y),u,w). [para(2925(a,1),2685(a,2))]. 2927 (R(x,y,z) * (y * u)) \ ((R(x,y,z) * y) * u) = a(x,y,a(x,y,z) * u). [para(2420(a,1),2692(a,1,1))]. 2928 a(x,y,a(x,y,z) * u) = a(R(x,y,z),y,u). [para(2927(a,1),28(a,2)),flip(a)]. 2929 a(x,y,z * a(x,y,u)) = a(R(x,y,u),y,z). [para(2567(a,1),2928(a,1,3))]. 2930 (x * (y * z)) \ ((x * y) * L(R(z,u,w),y,x)) = a((x * y) * (x * (y * z)),u,w). [para(48(a,1),2686(a,1,2,2))]. 2931 (x * y) \ (((x * z) * R((x * z) \ x,u,w)) * y) = a(L(z,x,y),u,w). [para(1623(a,1),2926(a,1,2))]. 2932 (x * y) \ ((x * a(z,u,w)) * y) = a(L(z,x,y),u,w). [para(2315(a,1),2931(a,1,2,1))]. 2933 a(L(x,y,z),u,w) = R(a(x,u,w),y,z). [para(2932(a,1),2736(a,1))]. 2935 a(R(x,y,z),u,w) = a(L(x,y,z),u,w). [para(2933(a,2),2394(a,2))]. 2936 a(L(x,y,z),y,u) = a(x,y,u). [para(2933(a,2),2416(a,1))]. 2937 a(L(x,y,z),u,w) \ R(x,u,w) = a(a(x,u,w),y,z) \ x. [para(2933(a,2),2369(a,1,1))]. 2938 L(x,y,z) * a(L(z,u,w),y,x) = a(a(z,y,x),u,w) * x. [para(2933(a,2),2727(a,1,2))]. 2939 a((x * y) \ z,y,u) = a(y \ (x \ z),y,u). [para(177(a,1),2936(a,1,1))]. 2940 a((x \ y) \ z,y,u) = a(y \ (x * z),y,u). [para(267(a,1),2936(a,1,1))]. 2941 a((x \ y) \ T(z,x),y,u) = a(y \ (z * x),y,u). [para(269(a,1),2936(a,1,1))]. 2942 L(x,y,z) * a(x,y,u) = R(L(x,y,z),y,u). [para(2936(a,1),2300(a,2,2)),flip(a)]. 2946 a(x,y,z * a(x,y,u)) = a(L(x,y,u),y,z). [para(2935(a,1),2929(a,2))]. 2947 a(x \ (y \ z),x,u) = a((y * x) * z,x,u). [para(2939(a,1),1702(a,1))]. 2948 a(x / (y \ z),z,u) = a(z \ (y * x),z,u). [para(2940(a,1),2584(a,2))]. 2949 L(x,y,z) * a(x,y,u) = L(R(x,y,u),y,z). [para(2942(a,2),48(a,1))]. 2950 a(x,y,z * a(x,y,u)) = a(x,y,z). [para(2946(a,2),2936(a,1))]. 2952 a(x \ (y \ z),x,u) = a(y * (x * z),x,u). [para(2947(a,2),2843(a,1))]. 2953 a(x / (y / z),y,u) = a(y \ (z * x),y,u). [para(2948(a,1),2849(a,2))]. 2954 L(R(x,y,z),y,u) \ (x * a(x,y,z)) = a(u,y,x). [para(2949(a,1),2644(a,1,1))]. 2955 a(x * (y * z),y,u) = a(y * (x * z),y,u). [para(2952(a,1),1757(a,1))]. 2956 a((x * y) / z,z,u) = a(y / (z / x),z,u). [para(2953(a,2),2584(a,2))]. 2957 a((x \ y) * T(z,x),y,u) = a(y \ (z * x),y,u). [para(2941(a,1),1702(a,1)),flip(a)]. 2958 L(R(x,y,z),y,u) \ R(x,y,z) = a(u,y,x). [para(2300(a,2),2954(a,1,2))]. 2959 a(x,y,R(z,y,u)) = a(x,y,z). [para(2958(a,1),2298(a,2))]. 2960 a(x,y,(z / u) / y) = a(x,y,z / (y * u)). [para(193(a,1),2959(a,1,3)),flip(a)]. 2961 a(x \ (y * z),x,u) = a((z \ x) * y,x,u). [para(2957(a,1),2841(a,1))]. 2962 a(x \ (y * z),x,u) = a((z * x) * y,x,u). [para(2961(a,2),1707(a,1))]. 2964 a(x \ (y * z),x,u) = a(z * (x * y),x,u). [para(2962(a,2),2843(a,1))]. 2965 a(a(x,y,z),u,w) * z = z * a(w,u,a(x,y,z)). [para(2938(a,1),2693(a,1))]. 2966 a(a(x,y,z),u,w) = a(w,u,a(x,y,z)). [hyper(24,a,2567,a,b,2965,a)]. 2968 a(a(x,y,z),u,w) \ 1 = a(w,u,a(x,y,z)). [para(2966(a,2),2694(a,1,1))]. 2969 a(a(x,y,z),u,w) \ v5 = v5 * a(w,u,a(x,y,z)). [para(2966(a,2),2696(a,1,1))]. 2970 x \ L(x,y,a(z,u,w)) = a(x,y,a(z,u,w)). [para(2968(a,1),2328(a,1)),flip(a)]. 2971 ((a(x,y,z) * u) * w) \ (a(x,y,z) * (u * w)) = a(w,u,a(x,y,z)). [para(2968(a,1),2808(a,2))]. 2972 (x \ (a(y,z,u) * w)) \ ((a(y,z,u) \ x) \ w) = a(x \ (a(y,z,u) * w),x,a(y,z,u)). [para(267(a,1),2970(a,1,2))]. 2973 a(L(x,y,z),u,w) \ R(x,u,w) = x * a(z,y,a(x,u,w)). [para(2969(a,1),2937(a,2))]. 2974 ((a(x,y,z) * u) * w) \ ((u * w) * a(x,y,z)) = a(w,u,a(x,y,z)). [para(2567(a,1),2971(a,1,2))]. 2975 ((x * a(y,z,u)) * w) \ ((x * w) * a(y,z,u)) = a(w,x,a(y,z,u)). [para(2567(a,1),2974(a,1,1,1))]. 2976 (x * (y * z)) \ (x * (y * R(z,u,w))) = a((x * y) * (x * (y * z)),u,w). [para(74(a,1),2930(a,1,2))]. 2977 L(a(x,y,z),u * x,w) = a((w * u) * (w * (u * x)),y,z). [para(2976(a,1),2730(a,1)),flip(a)]. 2978 L(a(x,y,z),u * x,w) = a(L(x,u,w),y,z). [para(2977(a,2),1705(a,1))]. 2979 a(L(x,y,z),u,w) \ a(x,u,w) = a(z,y * x,a(x,u,w)). [para(2978(a,1),2298(a,2,1)),flip(a)]. 2980 a(x,y * z,a(z,u,w)) = a(x,y,a(z,u,w)). [para(2979(a,1),2407(a,1))]. 2981 a(x,y * z,a(y,u,w)) = a(x,z,a(y,u,w)). [para(2980(a,1),2856(a,1)),flip(a)]. 2982 a(x * y,z * u,a(z,w,v5)) = a(y * x,u,a(z,w,v5)). [para(2981(a,1),2618(a,1)),flip(a)]. 2983 a((x * y) * z,y,a(x,u,w)) = a(z * (x * y),z,a(x,u,w)). [para(2982(a,1),2750(a,1))]. 2984 a(x * (y * z),y,a(x,u,w)) = a(z * (x * y),z,a(x,u,w)). [para(2983(a,1),2843(a,1)),flip(a)]. 2985 a(x * (y * z),y,a(x,u,w)) = a(x * (z * y),z,a(x,u,w)). [para(2984(a,2),2955(a,2))]. 2986 (x * (y * (a(z,u,z) * w))) \ ((x * (a(z,u,z) * y)) * w) = a(x,y,a(z,u,z) * w). [para(2807(a,1),2805(a,1,2,1))]. 2987 a(x,y,a(z,u,z) * w) = a(x,y,w). [para(2986(a,1),2919(a,1))]. 2988 a(x,y,L(z,u,z)) = a(x,y,z). [para(1542(a,1),2987(a,1,3)),flip(a)]. 2989 a(x,y,(z \ u) * z) = a(x,y,T(u,z)). [para(2675(a,1),2987(a,1,3))]. 2991 a(x,y,(T(z,u) * u) \ (T(z,u) * (z * u))) = a(x,y,T(z,u)). [para(106(a,2),2988(a,1,3))]. 2992 a(x,y,T(z * u,z)) = a(x,y,u * z). [para(19(a,1),2989(a,1,3,1)),flip(a)]. 2993 a(x,y,(T(z,u) * u) \ (z * (T(z,u) * u))) = a(x,y,T(z,u)). [para(728(a,1),2991(a,1,3,2))]. 2994 a(x,y,T(z,T(z,u) * u)) = a(x,y,T(z,u)). [para(36(a,2),2993(a,1,3))]. 2995 a(x,y,T(z,z * u)) = a(x,y,T(z,u)). [para(2018(a,1),2994(a,1,3))]. 2996 a(x,y,T((z \ u) * z,((z \ u) * z) * (z \ 1))) = a(x,y,R(u,z,z)). [para(761(a,1),2995(a,2,3))]. 2998 a(x,y,T((z \ u) * z,R(z \ u,z,z \ 1))) = a(x,y,R(u,z,z)). [para(433(a,1),2996(a,1,3,2))]. 2999 a(x,y,T((z \ u) * z,z \ u)) = a(x,y,R(u,z,z)). [para(2716(a,1),2998(a,1,3))]. 3001 a(x,y,z * (z \ u)) = a(x,y,R(u,z,z)). [para(2999(a,1),2992(a,1)),flip(a)]. 3002 a(x,y,R(z,u,u)) = a(x,y,z). [para(20(a,1),3001(a,1,3)),flip(a)]. 3003 a(x,y,z / (u \ 1)) = a(x,y,z * u). [para(720(a,1),3002(a,1,3)),flip(a)]. 3004 a(x,y,R(((z \ 1) * u) \ 1,u,u)) = a(x,y,(u \ 1) * z). [para(1739(a,2),3003(a,1,3))]. 3005 a(x,y,R((z \ u) \ 1,u,u)) = a(x,y,(u \ 1) * z). [para(318(a,1),3004(a,1,3,1,1))]. 3006 a(x,y,(z \ u) \ 1) = a(x,y,(u \ 1) * z). [para(3005(a,1),3002(a,1)),flip(a)]. 3007 a(x,y,(z \ u) \ 1) = a(x,y,u \ z). [para(318(a,1),3006(a,2,3))]. 3009 a(x,y,(z / u) \ z) = a(x,y,u * a(z,u,u)). [para(1388(a,1),3007(a,1,3)),flip(a)]. 3010 a(x,y,z * a(u,z,z)) = a(x,y,z). [para(66(a,1),3009(a,1,3)),flip(a)]. 3011 a(x,y,L(z,u,u * z)) = a(x,y,z). [para(1487(a,2),3010(a,1,3))]. 3012 ((x * y) \ x) * L(L(y,x,x * y),z,u) = a(u,z,y) \ 1. [para(3011(a,1),2357(a,2,1))]. 3013 (x * y) \ (x * L(y,z,u)) = a(u,z,y) \ 1. [para(3012(a,1),814(a,1)),flip(a)]. 3015 L(a(x,y,z),z,u) = a(x,x * y,z) \ 1. [para(3013(a,1),2350(a,1)),flip(a)]. 3016 L(a(x,y,z),z,u) = a(x,y,z). [para(3015(a,2),2343(a,1))]. 3019 (x * L(y,z,u)) / a(u,u * z,y) = x * y. [para(3016(a,1),2356(a,1,2))]. 3021 a(x,x * y,z) \ (u * L(z,y,x)) = u * z. [para(3019(a,1),2571(a,1)),flip(a)]. 3023 a(x,y,z) * (u * L(z,y,x)) = u * z. [para(3021(a,1),2360(a,1)),flip(a)]. 3024 a(x,y,z) \ (u * z) = u * L(z,y,x). [hyper(23,a,20,a,b,3023,a),flip(a)]. 3026 x * T(y,L(x,z,u)) = y * x. [para(3023(a,1),2376(a,1)),flip(a)]. 3031 L(x,y,z) * T(u,x) = u * L(x,y,z). [para(303(a,1),3026(a,1,2,2))]. 3032 K(L(x,y,z),u) = (u * x) \ (x * u). [para(3026(a,1),2186(a,1,1)),flip(a)]. 3034 K(L(x,y,z),u) = K(x,u). [para(3032(a,2),30(a,2)),flip(a)]. 3036 L(K(x,y),z,u) = K(x,y). [para(3034(a,1),2259(a,1)),flip(a)]. 3038 a(x,y,K(z,u)) = 1. [hyper(38,a,3036,a)]. 3040 (x * y) * K(z,u) = x * (y * K(z,u)). [para(3036(a,1),74(a,1,2))]. 3041 x \ (y * K(z,u)) = (x \ y) * K(z,u). [para(3036(a,1),560(a,1,2)),flip(a)]. 3049 (x / y) * L(y,z,u) = a(u,z,y) \ x. [para(22(a,1),3024(a,1,2)),flip(a)]. 3050 (x * L(y,z,u)) \ (x * y) = a(u,z,y). [para(3024(a,1),2569(a,1,1))]. 3052 (x * (y * K(z,u))) * w = (x * y) * (K(z,u) * w). [para(3040(a,1),2649(a,1,1))]. 3053 (x \ (y \ z)) * K(y,y * z) = x \ (z / y). [para(1001(a,1),3041(a,1,2)),flip(a)]. 3054 a(x,y,z * u) \ u = z \ L(z * u,y,x). [para(3049(a,1),353(a,1))]. 3055 ((x * y) * L(L(z,y,x),u,w)) \ (x * (y * z)) = a(w,u,L(z,y,x)). [para(74(a,1),3050(a,1,2))]. 3056 L(a(x,y,z),u * L(z,y,x),w) = (w * (u * L(z,y,x))) \ (w * (u * z)). [para(3050(a,1),76(a,1,1))]. 3057 (x * (y * (K(z,u) * w))) \ ((x * (y * K(z,u))) * w) = a(x,y,K(z,u) * w). [para(3052(a,2),28(a,2,2)),flip(a)]. 3058 ((x * y) * (K(z,u) * w)) / ((y * K(z,u)) * w) = R(x,y * K(z,u),w). [para(3052(a,1),34(a,2,1)),flip(a)]. 3059 (x * (y * L(z,u,w))) \ (x * (y * z)) = a(w,u,L(z,y,x)). [para(175(a,1),3055(a,1,1))]. 3060 ((x * y) * (K(z,u) * w)) / (y * (K(z,u) * w)) = R(x,y * K(z,u),w). [para(2649(a,1),3058(a,1,2))]. 3061 R(x,y * K(z,u),w) = R(x,y,K(z,u) * w). [para(3060(a,1),34(a,2)),flip(a)]. 3062 R(x,y,K(z,u) * w) = R(x,y,w). [para(3061(a,1),2892(a,1))]. 3063 R(x,y,T(z,u)) = R(x,y,z). [para(985(a,1),3062(a,1,3)),flip(a)]. 3072 R(x,y,T(z,u)) = a(x,y,z) * x. [para(3063(a,2),2303(a,1))]. 3073 a(x,y,T(z,u)) = a(x,y,z). [hyper(24,a,2303,a(flip),b,3072,a(flip)),flip(a)]. 3074 a(x,y,z / u) = a(x,y,u \ z). [para(84(a,1),3073(a,1,3)),flip(a)]. 3075 a(x,y,(z \ u) * z) = a(x,y,u). [para(3073(a,1),2989(a,2))]. 3077 a(x,y,(z / u) / x) = a(x,y,(x * u) \ z). [para(3074(a,1),2493(a,2))]. 3078 a(x,y,(z / u) / y) = a(x,y,(y * u) \ z). [para(3074(a,1),2960(a,2))]. 3079 a(x,y,((z / u) * w) * (u / z)) = a(x,y,w). [para(358(a,1),3075(a,1,3,1))]. 3080 (x \ y) \ L((x \ y) * x,z,u) = a(u,z,y) \ x. [para(3075(a,1),3054(a,1,1)),flip(a)]. 3082 L(x,y,z) / (u \ x) = a(z,y,x) \ u. [para(3080(a,1),1588(a,1)),flip(a)]. 3083 a(x,x * y,L(z,y,x)) \ u = z / (u \ L(z,y,x)). [para(303(a,1),3082(a,1,1)),flip(a)]. 3084 (a(x,y,z) \ 1) \ u = z / (u \ L(z,y,x)). [para(2365(a,1),3083(a,1,1))]. 3085 x / (y \ L(x,z,u)) = a(u,z,x) * y. [para(3084(a,1),330(a,1))]. 3086 x / (y * L(x,z,u)) = a(u,z,x) * (y \ 1). [para(330(a,1),3085(a,1,2))]. 3087 R(x,y,z) / a(L(x,u,w),y,z) = a(w,u,R(x,y,z)) * L(x,u,w). [para(2301(a,1),3085(a,1,2))]. 3088 x / (y * L(x,z,u)) = y \ a(u,z,x). [para(3086(a,2),2572(a,1))]. 3089 a(L(x,y,z),u,w) \ R(x,u,w) = a(z,y,R(x,u,w)) * L(x,y,z). [para(3087(a,1),2571(a,1)),flip(a)]. 3090 a(x,y,R(z,u,w)) * L(z,y,x) = z * a(x,y,a(z,u,w)). [para(3089(a,1),2973(a,1))]. 3091 L(a(x,y,z),u * L(z,y,x),w) = a(x,y,L(z,u,w)). [para(3056(a,2),3059(a,1))]. 3092 a(L(x,y * L(z,u,x),w),u,z) = a(x,u,L(z,y,w)). [para(3091(a,1),2406(a,2))]. 3093 a(x,y,L(z,u,x)) = a(x,y,z). [para(3091(a,1),2687(a,1))]. 3094 a(x,y,L(L(z,u,x),w,v5)) = a(x,y,L(z,w,v5)). [para(49(a,1),3093(a,1,3))]. 3098 a(L(x,y * z,u),w,L(z,x * w,x)) = a(x,w,L(L(z,x * w,x),y,u)). [para(308(a,1),3092(a,1,1,2,2))]. 3099 a(L(x,L(y,z,x) * u,w),z,y) = a(x,z,L(y,T(u,v5),w)). [para(2817(a,1),3092(a,1,1))]. 3100 a(x,y,K(z,u) * w) = a(x,y,w). [para(3057(a,1),2918(a,1))]. 3101 a(x,y,(z / u) * w) = a(x,y,(u \ z) * w). [para(1161(a,1),3100(a,1,3))]. 3102 a(x,y,z * T(u,w)) = a(x,y,z * u). [para(1212(a,1),3100(a,1,3))]. 3103 a(x,y,K(z * u,z)) = a(x,y,a(z,u,z)). [para(1537(a,1),3100(a,1,3)),flip(a)]. 3104 a(x,y,T(z,u) / w) = a(x,y,z / w). [para(1815(a,1),3100(a,1,3))]. 3105 a(x,y,(K(z,u) * w) * v5) = a(x,y,w * v5). [para(2518(a,2),3100(a,1,3))]. 3106 a(x,y,(z * K(u,w)) * v5) = a(x,y,z * v5). [para(2630(a,1),3100(a,1,3))]. 3107 a(x,y,(z \ u) \ w) = a(x,y,(z / u) * w). [para(2676(a,1),3100(a,1,3)),flip(a)]. 3108 a(x,y,(z \ K(u,w)) * v5) = a(x,y,z \ v5). [para(2677(a,1),3100(a,1,3))]. 3110 a(x,y,z * (u / w)) = a(x,y,z * (w \ u)). [para(84(a,1),3102(a,1,3,2)),flip(a)]. 3111 a(x,y,z \ T(u,w)) = a(x,y,u / z). [para(3104(a,1),3074(a,1)),flip(a)]. 3112 a(x,y,(z / u) / w) = a(x,y,w \ (u \ z)). [para(84(a,1),3111(a,1,3,2)),flip(a)]. 3113 a(x,y,a(z,u,z)) = 1. [para(3103(a,1),3038(a,1))]. 3114 L(a(x,y,x),z,u) = a(x,y,x). [hyper(37,a,3113,a)]. 3116 a(L(x,y,z),u,x) = a(x,u,x). [para(3114(a,1),2406(a,2))]. 3117 L(x * a(x,y,x),y,L(x,z,u)) = x. [para(3116(a,1),2362(a,1,1,2))]. 3119 L(R(x,y,x),y,L(x,z,u)) = x. [para(1540(a,1),3117(a,1,1))]. 3120 L(x,y,z) * (u * R(x,u,x)) = (L(x,y,z) * u) * x. [para(3119(a,1),74(a,1,2)),flip(a)]. 3121 a(x,y,((z / u) * w) * v5) = a(x,y,((u \ z) * w) * v5). [para(1161(a,1),3105(a,1,3,1))]. 3122 a(x,y,((z \ u) \ w) * v5) = a(x,y,((z / u) * w) * v5). [para(2676(a,1),3105(a,1,3,1)),flip(a)]. 3123 a(x,y,(z \ u) \ w) = a(x,y,(u \ z) * w). [para(3107(a,2),3101(a,1))]. 3124 a(x,y,(T(z,u) * w) \ v5) = a(x,y,(z * w) \ v5). [para(2134(a,1),3108(a,1,3))]. 3125 a(x,y,((z / u) * w) * (z \ u)) = a(x,y,w). [para(3110(a,1),3079(a,1))]. 3126 a(x,y,(x * z) \ u) = a(x,y,x \ (z \ u)). [para(3112(a,1),3077(a,1)),flip(a)]. 3127 a(x,y,(y * z) \ u) = a(x,y,y \ (z \ u)). [para(3112(a,1),3078(a,1)),flip(a)]. 3128 a(x,y,((z \ (u \ w)) * K(u,u * w)) * v5) = a(x,y,((w / u) \ z) \ v5). [para(3053(a,2),3123(a,2,3,1)),flip(a)]. 3129 a(x,x * y,x \ (y \ z)) = (y \ (x \ z)) \ ((x * y) \ z). [para(3126(a,1),2327(a,1))]. 3130 a(x,y,y \ (z \ ((z * y) * u))) = a(x,y,K(z,y) * u). [para(940(a,1),3127(a,1,3)),flip(a)]. 3131 a(x,y,((z / u) * w) \ v5) = a(x,y,((u \ z) * w) \ v5). [para(84(a,1),3124(a,1,3,1,1)),flip(a)]. 3132 L(x,y,z) * T(x * u,x) = (L(x,y,z) * u) * x. [para(1321(a,1),3120(a,1,2))]. 3133 (L(x,y,z) * u) * x = (x * u) * L(x,y,z). [para(3132(a,1),3031(a,1))]. 3134 (x * (L(x,y,z) \ u)) * L(x,y,z) = u * x. [para(20(a,1),3133(a,1,1)),flip(a)]. 3135 (x * a(y,z,u)) * L(u,z,y) = x * u. [para(2604(a,1),3134(a,1,1))]. 3137 (x / a(y,z,u)) * u = x * L(u,z,y). [para(22(a,1),3135(a,1,1)),flip(a)]. 3138 (a(x,y,z) / u) \ z = u * L(z,y,x). [para(3137(a,1),358(a,2))]. 3139 x / (y * L(x,z,u)) = a(u,z,x) / y. [para(3138(a,1),65(a,1,2))]. 3140 a(x,y,z) / u = u \ a(x,y,z). [para(3139(a,1),3088(a,1))]. 3141 (a(x,y,z) \ u) \ w = (u \ a(x,y,z)) * w. [para(3140(a,1),2605(a,2,1))]. 3143 a(x,y,((z \ u) * w) * (u \ z)) = a(x,y,w). [para(3121(a,1),3125(a,1))]. 3144 a(x,y,((z \ u) * w) * ((u * w) \ z)) = a(x,y,a(z,u,w)). [para(595(a,1),3143(a,1,3,1))]. 3145 a(x,y,(z \ (u * w)) * (u \ z)) = a(x,y,L(w,u,z)). [para(798(a,1),3143(a,1,3,1))]. 3146 a(x,y,((z \ u) \ w) * v5) = a(x,y,((u \ z) * w) * v5). [para(3122(a,2),3121(a,1))]. 3147 a(x,y,y \ (z \ ((z * y) * u))) = a(x,y,u). [para(3130(a,2),3100(a,1))]. 3148 a(x,y,L(z,u * y,u)) = a(x,y,z). [para(309(a,1),3147(a,1,3))]. 3151 a(L(x,y * z,u),w,z) = a(x,w,L(L(z,x * w,x),y,u)). [para(3148(a,1),3098(a,1))]. 3152 a(x,y,(z \ (u \ w)) \ ((u * z) \ w)) = x \ L(x,y,a(u,u * z,u \ (z \ w))). [para(3129(a,1),2970(a,2,3)),flip(a)]. 3153 a(L(x,y * z,u),w,z) = a(x,w,L(z,y,u)). [para(3151(a,2),3094(a,1))]. 3155 a(x,y,L(z,u * z,w)) = a(L(x,u,w),y,z). [para(2765(a,1),3153(a,1,1)),flip(a)]. 3157 a(x,y,((z \ (u \ w)) * K(u,u * w)) * v5) = a(x,y,((u / w) * z) \ v5). [para(358(a,1),3128(a,2,3,1))]. 3158 a(x,y,((z / u) * w) \ v5) = a(x,y,(w \ (z \ u)) * v5). [para(3157(a,1),3106(a,1))]. 3160 a(x,y,((z \ u) * w) \ v5) = a(x,y,(w \ (u \ z)) * v5). [para(3158(a,1),3131(a,1)),flip(a)]. 3161 a(x,y,z / ((u \ w) * v5)) = a(x,y,(v5 \ (w \ u)) * z). [para(3160(a,1),3074(a,2))]. 3162 a(x,y,(z \ (u \ w)) \ ((u * z) \ w)) = x \ L(x,y,a(u,z,u \ (z \ w))). [para(2361(a,1),3152(a,2,2))]. 3163 a(x,y,(z \ (u \ w)) \ ((u * z) \ w)) = a(x,y,a(u,z,u \ (z \ w))). [para(3162(a,2),2970(a,1))]. 3164 (x \ (a(y,z,u) * w)) \ ((x \ a(y,z,u)) * w) = a(x \ (a(y,z,u) * w),x,a(y,z,u)). [para(3141(a,1),2972(a,1,2))]. 3165 a(x \ (a(y,z,u) * w),x,a(y,z,u)) = a(x,a(y,z,u),w). [para(3164(a,1),594(a,2)),flip(a)]. 3166 a(x * (a(y,z,u) * w),x,a(y,z,u)) = a(x,a(y,z,u),w). [para(3165(a,1),1702(a,1)),flip(a)]. 3167 a(x * (y * a(z,u,w)),y,a(z,u,w)) = a(y,a(z,u,w),x). [para(3165(a,1),2964(a,1)),flip(a)]. 3168 a(a(x,y,z) * (u * w),u,a(x,y,z)) = a(u,a(x,y,z),w). [para(3166(a,1),2955(a,2))]. 3169 a((x * a(y,z,u)) / w,x,a(y,z,u)) = a(x,a(y,z,u),w). [para(3167(a,1),2606(a,2))]. 3170 a(a(x,y,z) * (u * w),u,a(x,y,z)) \ v5 = a(u,u * a(x,y,z),w) * v5. [para(3168(a,2),2359(a,2,1)),flip(a)]. 3171 a(a(x,y,z) / (u / w),u,a(x,y,z)) = a(u,a(x,y,z),w). [para(3169(a,1),2852(a,1)),flip(a)]. 3172 a(a(x,y,z) * (u * w),u,a(x,y,z)) = a(u,u * a(x,y,z),w). [hyper(24,a,2696,a(flip),b,3170,a(flip)),flip(a)]. 3173 a(x,x * a(y,z,u),w) = a(x,a(y,z,u),w). [para(3172(a,1),3168(a,1))]. 3174 a(x,a(y,z,u),w) \ v5 = a(x,a(y,z,u),w) * v5. [para(3173(a,1),2359(a,1,1)),flip(a)]. 3175 a(x,a(y,z,u),w) \ a(x,w,a(y,z,u)) = a(w,x,a(y,z,u)). [para(2809(a,1),2975(a,1))]. 3176 a(x,a(y,z,u),w) * a(x,w,a(y,z,u)) = a(w,x,a(y,z,u)). [para(3175(a,1),3174(a,1)),flip(a)]. 3177 R(T(a(x,y,z),(L(z,y,x) * u) * w),L(z,y,x) * u,w) = a(x,y,R(z,u,w)). [para(2379(a,2),2751(a,1))]. 3178 R(a(x,y,z),L(z,y,x) * u,w) = a(x,y,R(z,u,w)). [para(2543(a,1),3177(a,1,1))]. 3180 a(L(x,L(y,z,x) * u,w),z,y) = a(x,z,R(y,u,w)). [para(3178(a,1),2933(a,2))]. 3181 a(x,y,L(z,T(u,w),v5)) = a(x,y,R(z,u,v5)). [para(3180(a,1),3099(a,1)),flip(a)]. 3182 a(x,y,R(z,u,w)) = a(x,y,L(z,u,w)). [para(81(a,1),3181(a,1,3,2)),flip(a)]. 3183 a(x,y,L(z,u * z,w)) = a(x,y,(u \ w) / ((z \ (u \ 1)) * w)). [para(2916(a,1),3182(a,1,3)),flip(a)]. 3184 a(x,y,L(z,u,w)) * L(z,y,x) = z * a(x,y,a(z,u,w)). [para(3182(a,1),3090(a,1,1))]. 3185 a(x,y,L(z,u * z,w)) = a(x,y,(w \ ((u \ 1) \ z)) * (u \ w)). [para(3183(a,2),3161(a,1))]. 3186 a(x,y,L(z,u * z,w)) = a(x,y,(w \ (u * z)) * (u \ w)). [para(330(a,1),3185(a,2,3,1,2))]. 3187 a(x,y,L(z,u * z,w)) = a(x,y,L(z,u,w)). [para(3186(a,2),3145(a,1))]. 3188 a(L(x,y,z),u,w) = a(x,u,L(w,y,z)). [para(3187(a,1),3155(a,1)),flip(a)]. 3189 L(x,y,z) * a(z,y,L(x,u,w)) = x * a(w,u,a(z,y,x)). [para(3188(a,1),2693(a,1,2))]. 3190 a(x,y,L(z,u,w)) * L(z,y,x) = z * a(w,u,a(x,y,z)). [para(3188(a,1),2697(a,1,1))]. 3191 L(x,y,z) * a(z,y,L(x,u,w)) = x * a(z,y,a(w,u,x)). [para(3189(a,1),2643(a,1)),flip(a)]. 3192 a(x,y,a(z,u,w)) = a(w,u,a(x,y,z)). [hyper(23,a,3184,a(flip),b,3190,a(flip)),flip(a)]. 3193 a(x,y,a(z / u,w,v5)) = a(v5,w,a(x,y,u * z)). [para(2606(a,2),3192(a,1,3))]. 3194 a(x * y,z,a(u,w,v5)) = a(u,w,a(v5,z,y * x)). [para(3192(a,2),2618(a,1)),flip(a)]. 3195 a(x,y,a(z,u,w)) = a(w,y,a(x,u,z)). [para(3192(a,1),3192(a,2)),flip(a)]. 3196 a(x,y,a(z,u,w)) * a(z,y,a(w,u,x)) = 1. [para(3195(a,1),2695(a,1,1))]. 3197 a(x * y,x,a(z,u,w)) = a(z,y,a(w,u,x * y)). [para(3195(a,2),2750(a,1)),flip(a)]. 3198 a(x,y * z,a(u,w,z)) = a(u,y,a(z,w,x)). [para(3195(a,1),2980(a,1))]. 3199 a(x,y,a(a(x,y,z) / u,w,v5)) = a(v5,w,a(x,y,u)). [para(2950(a,1),3193(a,2,3))]. 3200 a(x,y,a(z,u,w / v5)) = a(x,y,a(z,u,v5 * w)). [para(3193(a,1),3192(a,1)),flip(a)]. 3201 a(x,y,a(z,u,w)) = a(z,u,a(x,y,w)). [hyper(23,a,3189,a(flip),b,3191,a(flip))]. 3202 a(x,y,a(a(x,y,z) / (u / w),u,z)) = a(u,a(x,y,z),w). [para(3201(a,1),3171(a,1))]. 3203 a(x,y,a(z,u,w)) = a(w,y,a(z,u,x)). [para(3201(a,1),3192(a,1))]. 3204 a(x,y,a(z,u,w)) = a(x,y,a(w,u,z)). [para(3201(a,1),3192(a,2))]. 3205 a(x,y,a(z,u,w)) = a(w,u,a(z,y,x)). [para(3201(a,1),3195(a,1))]. 3206 a(x,a(y,z,u),w) * a(u,w,a(y,z,x)) = a(w,x,a(y,z,u)). [para(3203(a,1),3176(a,1,2))]. 3207 a(x,y * z,a(u,w,z)) = a(x,y,a(z,w,u)). [para(3203(a,1),3198(a,2))]. 3208 a(x,y,a(z / u,w,v5)) = a(x,y,a(v5,w,u / z)). [para(612(a,1),3204(a,1,3))]. 3209 a(x * y,z,a(u,w,v5)) = a(v5,w,a(u,z,y * x)). [para(3204(a,1),3194(a,1))]. 3210 a(x / y,z,a(u,w,v5)) = a(v5,w,a(u,z,y / x)). [para(3205(a,1),612(a,1)),flip(a)]. 3211 a(x * (y * z),y,a(x,u,w)) = a(w,u,a(x,z,x * (z * y))). [para(3205(a,1),2985(a,1)),flip(a)]. 3212 a(x,y,(z \ (u \ w)) \ ((u * z) \ w)) = a(u \ (z \ w),z,a(u,y,x)). [para(3205(a,1),3163(a,2))]. 3213 a(x * (y * z),y,a(u,w,v5)) = a(v5,w,a(u,y,z * (y * x))). [para(3209(a,1),2488(a,1)),flip(a)]. 3214 a(x,y,a(z,u,y / w)) = a(y,a(z,u,x),w). [para(3202(a,1),3199(a,1)),flip(a)]. 3215 a(x,y,a(z,u,w * y)) = a(y,a(z,u,x),w). [para(3214(a,1),3200(a,1)),flip(a)]. 3217 a(x,y,a(z,u,u / w)) = a(u,a(x,y,z),w). [para(3214(a,1),3201(a,1)),flip(a)]. 3218 a(x * y,x,a(z,u,w)) = a(y,a(w,u,z),x). [para(3215(a,1),3197(a,2))]. 3219 a(x,y,a(z / u,u,w)) = a(u,a(x,y,w),z). [para(3217(a,1),3208(a,2))]. 3220 a(x / y,y,a(z,u,w)) = a(y,a(w,u,z),x). [para(3217(a,1),3210(a,2))]. 3221 a(x * (y * z),y,a(u,w,v5)) = a(x * z,a(v5,w,u),y). [para(3218(a,1),2955(a,2))]. 3222 a(x,y,a(z,u,w / u)) = a(u,a(x,y,z),w). [para(3219(a,1),3204(a,1)),flip(a)]. 3223 a(x / (y / z),y,a(u,w,v5)) = a(y,a(v5,w,u),z * x). [para(3220(a,1),2956(a,1)),flip(a)]. 3224 a(x / (y * z),z,a(u,w,v5)) = a(z,a(v5,w,u),y * x). [para(3223(a,1),2851(a,1)),flip(a)]. 3225 a(x,y,a(z,u,z * (u * w))) = a(z * u,a(x,y,z),w). [para(3211(a,1),3221(a,1))]. 3226 a(x / (y * z),z,a(u,w,v5)) = a(v5,w,a(u,z,x * (z * y))). [para(3213(a,1),2846(a,2))]. 3227 a(x,y,a(z,u,w * (u * v5))) = a(u,a(x,y,z),v5 * w). [para(3226(a,1),3224(a,1))]. 3228 a(x * y,a(z,u,x),w) = a(y,a(z,u,x),w * x). [para(3227(a,1),3225(a,1)),flip(a)]. 3229 a(x,y,(z \ (u \ w)) \ ((u * z) \ w)) = a(u * (z * w),z,a(u,y,x)). [para(3212(a,2),1757(a,1))]. 3230 a(x,y,(z \ (u \ w)) \ ((u * z) \ w)) = a(u * w,a(x,y,u),z). [para(3229(a,2),3221(a,1))]. 3231 a(x,y,(z \ (u \ w)) \ ((u * z) \ w)) = a(w,a(x,y,u),z * u). [para(3230(a,2),3228(a,1))]. 3232 a(x,y,((z \ u) \ w) * ((z * w) \ u)) = a(u,a(x,y,z),w * z). [para(3231(a,1),3123(a,1)),flip(a)]. 3233 a(x,y,((z \ u) * w) * ((u * w) \ z)) = a(z,a(x,y,u),w * u). [para(3232(a,1),3146(a,1)),flip(a)]. 3234 a(x,a(y,z,u),w * u) = a(y,z,a(x,u,w)). [para(3233(a,1),3144(a,1))]. 3235 a(x,y,a(z,u,w / u)) = a(z,a(x,y,u),w). [para(22(a,1),3234(a,1,3)),flip(a)]. 3236 a(x,a(y,z,u),w) = a(u,a(y,z,x),w). [para(3235(a,1),3222(a,1))]. 3237 a(x,a(y,z,u),w) * a(u,w,a(y,z,x)) = a(w,u,a(y,z,x)). [para(3236(a,1),3176(a,1,1))]. 3238 a(x,y,a(z,u,w)) = a(x,w,a(z,u,y)). [para(3237(a,1),3206(a,1))]. 3239 a(x,y,a(z,u,w * y)) = a(x,w,a(y,u,z)). [para(3238(a,1),3207(a,1))]. 3240 a(x,a(y,z,u),w) = a(u,w,a(x,z,y)). [para(3239(a,1),3215(a,1)),flip(a)]. 3241 a(x,y,a(z,u,w)) * a(z,y,a(w,u,x)) = a(y,z,a(w,u,x)). [para(3240(a,1),3176(a,1,1))]. 3242 a(x,y,a(z,u,w)) = 1. [para(3241(a,1),3196(a,1))]. 3243 $F # answer("aa3"). [resolve(3242,a,54,a)]. ============================== end of proof ========================== % Disable descendants (x means already disabled): 54 given #2826 (H,wt=9): 3242 a(x,y,a(z,u,w)) = 1. [para(3241(a,1),3196(a,1))]. -------- Proof 6 -------- "aa1". ============================== PROOF ================================= % Proof 6 at 82.35 (+ 1.32) seconds: "aa1". % Length of proof is 2842. % Level of proof is 321. % Maximum clause weight is 50. % Given clauses 2826. 1 x * y = u & x * z = u -> y = z # label(non_clause). [assumption]. 2 y * x = u & z * x = u -> y = z # label(non_clause). [assumption]. 5 a(x,y,z) = 1 -> L(z,y,x) = z # label(non_clause). [assumption]. 6 L(x,y,z) = x -> a(z,y,x) = 1 # label(non_clause). [assumption]. 7 T(x,y) = x -> T(y,x) = y # label(non_clause). [assumption]. 8 T(x,y) = x -> K(x,y) = 1 # label(non_clause). [assumption]. 9 K(x,y) = 1 -> T(x,y) = x # label(non_clause). [assumption]. 10 a(a(x,y,z),u,w) = 1 # label("aa1") # label(non_clause) # label(goal). [goal]. 17 1 * x = x. [assumption]. 18 x * 1 = x. [assumption]. 19 x \ (x * y) = y. [assumption]. 20 x * (x \ y) = y. [assumption]. 21 (x * y) / y = x. [assumption]. 22 (x / y) * y = x. [assumption]. 23 x * y != z | x * u != z | u = y. [clausify(1)]. 24 x * y != z | u * y != z | u = x. [clausify(2)]. 27 (x * (y * z)) \ ((x * y) * z) = a(x,y,z). [assumption]. 28 a(x,y,z) = (x * (y * z)) \ ((x * y) * z). [copy(27),flip(a)]. 29 (x * y) \ (y * x) = K(y,x). [assumption]. 30 K(x,y) = (y * x) \ (x * y). [copy(29),flip(a)]. 31 (x * y) \ (x * (y * z)) = L(z,y,x). [assumption]. 32 L(x,y,z) = (z * y) \ (z * (y * x)). [copy(31),flip(a)]. 33 ((x * y) * z) / (y * z) = R(x,y,z). [assumption]. 34 R(x,y,z) = ((x * y) * z) / (y * z). [copy(33),flip(a)]. 35 x \ (y * x) = T(y,x). [assumption]. 36 T(x,y) = y \ (x * y). [copy(35),flip(a)]. 37 a(x,y,z) != 1 | L(z,y,x) = z. [clausify(5)]. 38 L(x,y,z) != x | a(z,y,x) = 1. [clausify(6)]. 39 T(x,y) != x | T(y,x) = y. [clausify(7)]. 40 T(x,y) != x | K(x,y) = 1. [clausify(8)]. 41 K(x,y) != 1 | T(x,y) = x. [clausify(9)]. 42 T(T(x,y),z) = T(T(x,z),y). [assumption]. 43 T(L(x,y,z),u) = L(T(x,u),y,z). [assumption]. 44 L(T(x,y),z,u) = T(L(x,z,u),y). [copy(43),flip(a)]. 45 T(R(x,y,z),u) = R(T(x,u),y,z). [assumption]. 46 R(T(x,y),z,u) = T(R(x,z,u),y). [copy(45),flip(a)]. 47 L(R(x,y,z),u,w) = R(L(x,u,w),y,z). [assumption]. 48 R(L(x,y,z),u,w) = L(R(x,u,w),y,z). [copy(47),flip(a)]. 49 L(L(x,y,z),u,w) = L(L(x,u,w),y,z). [assumption]. 50 R(R(x,y,z),u,w) = R(R(x,u,w),y,z). [assumption]. 51 (x * (x * y)) * z = x * (x * (y * z)) # label("LC"). [assumption]. 52 a(a(c1,c2,c3),c4,c5) != 1 # label("aa1") # answer("aa1"). [deny(10)]. 59 1 \ x = x. [para(17(a,1),19(a,1,2))]. 60 x \ x = 1. [para(18(a,1),19(a,1,2))]. 61 x \ ((x * y) * 1) = y. [para(18(a,2),19(a,1,2))]. 62 x \ (y * (y \ (x * z))) = z. [para(20(a,2),19(a,1,2))]. 64 x / 1 = x. [para(18(a,1),21(a,1,1))]. 65 x / (y \ x) = y. [para(20(a,1),21(a,1,1))]. 66 (x / y) \ x = y. [para(22(a,1),19(a,1,2))]. 67 (x * (y * z)) * a(x,y,z) = (x * y) * z. [para(28(a,2),20(a,1,2))]. 68 ((x / y) * (y * z)) \ (x * z) = a(x / y,y,z). [para(22(a,1),28(a,2,2,1)),flip(a)]. 69 (x * y) * K(y,x) = y * x. [para(30(a,2),20(a,1,2))]. 70 x \ ((y \ x) * y) = K(y \ x,y). [para(20(a,1),30(a,2,1)),flip(a)]. 71 ((x \ y) * x) \ y = K(x,x \ y). [para(20(a,1),30(a,2,2)),flip(a)]. 72 x \ (1 * (x * y)) = L(y,x,1). [para(17(a,1),32(a,2,1)),flip(a)]. 73 (x * 1) \ (x * y) = L(y,1,x). [para(17(a,1),32(a,2,2,2)),flip(a)]. 74 (x * y) * L(z,y,x) = x * (y * z). [para(32(a,2),20(a,1,2))]. 75 x \ (y * ((y \ x) * z)) = L(z,y \ x,y). [para(20(a,1),32(a,2,1)),flip(a)]. 76 L(x \ y,x,z) = (z * x) \ (z * y). [para(20(a,1),32(a,2,2,2))]. 77 x \ ((x / y) * (y * z)) = L(z,y,x / y). [para(22(a,1),32(a,2,1)),flip(a)]. 78 ((x * y) * (y \ z)) / z = R(x,y,y \ z). [para(20(a,1),34(a,2,2)),flip(a)]. 79 R(x,y,z) * (y * z) = (x * y) * z. [para(34(a,2),22(a,1,1))]. 80 R(x / y,y,z) = (x * z) / (y * z). [para(22(a,1),34(a,2,1,1))]. 81 T(x,x) = x. [para(36(a,2),19(a,1))]. 82 x * T(y,x) = y * x. [para(36(a,2),20(a,1,2))]. 83 T(x,x \ y) = (x \ y) \ y. [para(20(a,1),36(a,2,2))]. 84 T(x / y,y) = y \ x. [para(22(a,1),36(a,2,2))]. 85 (x * (x * (y * z))) / z = x * (x * y). [hyper(24,a,22,a,b,51,a),flip(a)]. 86 (x * (x * y)) \ (x * (x * (y * z))) = z. [hyper(23,a,20,a,b,51,a),flip(a)]. 87 x \ ((x * (x * y)) * z) = x * (y * z). [hyper(23,a,20,a,b,51,a(flip)),flip(a)]. 88 (x * (x * 1)) * y = x * (x * y). [para(17(a,1),51(a,2,2,2))]. 89 x * (x * ((x \ y) * z)) = (x * y) * z. [para(20(a,1),51(a,1,1,2)),flip(a)]. 90 (x * (y * (y * (z * u)))) \ ((x * (y * (y * z))) * u) = a(x,y * (y * z),u). [para(51(a,1),28(a,2,1,2)),flip(a)]. 91 (x * (x * (y * (z * u)))) \ (((x * (x * y)) * z) * u) = a(x * (x * y),z,u). [para(51(a,1),28(a,2,1)),flip(a)]. 92 (x * (x * (y * z))) \ ((x * (x * y)) * (z * u)) = L(u,z,x * (x * y)). [para(51(a,1),32(a,2,1)),flip(a)]. 93 (x * (y * (y * z))) \ (x * (y * (y * (z * u)))) = L(u,y * (y * z),x). [para(51(a,1),32(a,2,2,2)),flip(a)]. 94 ((x * (x * (y * z))) * u) / (z * u) = R(x * (x * y),z,u). [para(51(a,1),34(a,2,1,1)),flip(a)]. 95 (x * (x * (y * z))) / ((x * y) * z) = R(x,x * y,z). [para(51(a,1),34(a,2,1)),flip(a)]. 97 ((x * y) / 1) / y = x. [hyper(24,a,22,a,b,64,a(flip)),flip(a)]. 98 T(T(x,y),x) = T(x,y). [para(81(a,1),42(a,1,1)),flip(a)]. 99 (x * (y * z)) / L(z,y,x) = x * y. [para(32(a,2),65(a,1,2))]. 100 (x * y) / T(x,y) = y. [para(36(a,2),65(a,1,2))]. 101 R(x,y,z) \ ((x * y) * z) = y * z. [para(34(a,2),66(a,1,1))]. 102 x \ (y * 1) = x \ y. [para(20(a,1),61(a,1,2,1))]. 103 T(x * (x * y),x) = x * (y * x). [hyper(23,a,51,a(flip),b,82,a)]. 104 T((x * y) / x,x) = y. [hyper(23,a,22,a(flip),b,82,a)]. 105 (x * T(y,x)) / x = y. [hyper(24,a,22,a,b,82,a(flip)),flip(a)]. 106 (x * y) \ (x * (z * y)) = L(T(z,y),y,x). [para(82(a,1),32(a,2,2,2)),flip(a)]. 107 T(x,y) \ (x * y) = T(y,T(x,y)). [para(82(a,1),36(a,2,2)),flip(a)]. 108 x * T(T(y,x),z) = T(y,z) * x. [para(42(a,1),82(a,1,2))]. 109 x * L(T(y,x),z,u) = L(y,z,u) * x. [para(44(a,2),82(a,1,2))]. 110 x * R(T(y,x),z,u) = R(y,z,u) * x. [para(46(a,2),82(a,1,2))]. 111 (x * y) \ ((z * x) * y) = T(R(z,x,y),x * y). [para(34(a,2),84(a,1,1)),flip(a)]. 112 T(T(x / y,z),y) = T(y \ x,z). [para(84(a,1),42(a,1,1)),flip(a)]. 113 ((x * y) / ((1 / z) * z)) / y = x. [para(22(a,2),97(a,1,1,2))]. 114 K(T(x,y),x) = 1. [hyper(40,a,98,a)]. 115 T(x,T(x,y)) = x. [hyper(39,a,98,a)]. 116 T(x,y) * x = x * T(x,y). [para(98(a,1),82(a,1,2)),flip(a)]. 117 (x * y) / T(y,T(x,y)) = T(x,y). [para(82(a,1),100(a,1,1))]. 118 x \ (y * (z * (z \ 1))) = x \ y. [para(20(a,2),102(a,1,2,2))]. 119 K(x,(y * x) / y) = 1. [para(104(a,1),114(a,1,1))]. 120 T(x,(y * x) / y) = x. [hyper(41,a,119,a)]. 121 x * K(y,x / y) = y * (x / y). [para(22(a,1),69(a,1,1))]. 122 K(x,y) \ (x * y) = T(y * x,K(x,y)). [para(69(a,1),36(a,2,2)),flip(a)]. 123 x \ (x * y) = L(y,x,1). [para(17(a,1),72(a,1,2))]. 124 L(x,y,1) = x. [para(123(a,1),19(a,1))]. 125 a(1,x,y) = 1. [hyper(38,a,124,a)]. 126 x \ (x * y) = L(y,1,x). [para(18(a,1),73(a,1,1))]. 127 L(x,1,y) = x. [para(126(a,1),19(a,1))]. 128 K(x \ 1,x) = (x \ 1) * x. [para(70(a,1),59(a,1))]. 129 K(x \ 1,x) / x = x \ 1. [hyper(24,a,22,a,b,128,a(flip)),flip(a)]. 130 (x \ 1) \ K(x \ 1,x) = x. [hyper(23,a,20,a,b,128,a(flip)),flip(a)]. 131 (x * x) * y = x * (x * y). [para(18(a,1),88(a,1,1,2))]. 132 (x * (x * y)) / y = x * x. [hyper(24,a,22,a,b,131,a),flip(a)]. 133 (x * x) \ (x * (x * y)) = y. [hyper(23,a,20,a,b,131,a),flip(a)]. 134 ((x * (x * y)) * z) / (y * z) = R(x * x,y,z). [para(131(a,1),34(a,2,1,1)),flip(a)]. 135 x \ (y * (y * x)) = T(y * y,x). [para(131(a,1),36(a,2,2)),flip(a)]. 136 x * (x * T(y,x * x)) = y * (x * x). [para(131(a,1),82(a,1))]. 137 L(x,y,y) = x. [para(133(a,1),32(a,2))]. 138 x * ((x \ y) * x) = T(x * y,x). [para(20(a,1),103(a,1,1,2)),flip(a)]. 139 T(x / y,z) * y = y * T(y \ x,z). [para(84(a,1),108(a,1,2,1)),flip(a)]. 140 (x * T(x \ y,z)) / x = T(y / x,z). [para(112(a,1),105(a,1,1,2))]. 141 R(x,1 / y,y) / y = x * (1 / y). [para(34(a,2),113(a,1,1))]. 142 L(x \ 1,x,y) = (y * x) \ y. [para(118(a,1),32(a,2))]. 143 L((x \ y) \ 1,x \ y,x) = y \ x. [para(20(a,1),142(a,2,1))]. 144 L(x \ 1,x,y / x) = y \ (y / x). [para(22(a,1),142(a,2,1))]. 145 x / L(y \ 1,y,x) = x * y. [para(142(a,2),65(a,1,2))]. 146 x \ T(x * y,x) = (x \ y) * x. [hyper(23,a,20,a,b,138,a),flip(a)]. 147 x * K(x \ 1,x) = T(x * 1,x). [para(128(a,2),138(a,1,2))]. 148 (x \ (x \ y)) * x = x \ T(y,x). [para(20(a,1),146(a,1,2,1)),flip(a)]. 149 x * K(x \ 1,x) = T(x,x). [para(18(a,1),147(a,2,1))]. 150 x * K(x \ 1,x) = x. [para(149(a,2),81(a,1))]. 151 K(x \ 1,x) = 1. [hyper(23,a,18,a,b,150,a)]. 152 T(x \ 1,x) = x \ 1. [hyper(41,a,151,a)]. 154 (x \ 1) * x = 1. [para(151(a,1),128(a,1)),flip(a)]. 155 1 / x = x \ 1. [para(151(a,1),129(a,1,1))]. 156 (x \ 1) \ 1 = x. [para(151(a,1),130(a,1,2))]. 157 x * (1 / x) = 1. [para(66(a,1),154(a,1,1))]. 160 T(x,x \ 1) = x. [para(156(a,1),83(a,2))]. 161 L(x,x \ 1,y) = (y * (x \ 1)) \ y. [para(156(a,1),142(a,1,1))]. 162 x / L(y,y \ 1,x) = x * (y \ 1). [para(156(a,1),145(a,1,2,1))]. 164 (x * 1) \ ((x * y) * (1 / y)) = a(x,y,1 / y). [para(157(a,1),28(a,2,1,2)),flip(a)]. 165 T(T(x,y),x \ 1) = T(x,y). [para(160(a,1),42(a,1,1)),flip(a)]. 166 K(T(x,y),x \ 1) = 1. [hyper(40,a,165,a)]. 167 K(x \ y,(y / x) \ 1) = 1. [para(84(a,1),166(a,1,1))]. 168 K(x,((y * x) / y) \ 1) = 1. [para(104(a,1),166(a,1,1))]. 169 T(x \ y,(y / x) \ 1) = x \ y. [hyper(41,a,167,a)]. 170 T(x,((y * x) / y) \ 1) = x. [hyper(41,a,168,a)]. 171 (x \ y) \ (x \ T(y,x)) = K(x \ (x \ y),x). [para(148(a,1),70(a,1,2))]. 172 x * L(y,z \ x,z) = z * ((z \ x) * y). [para(20(a,1),74(a,1,1))]. 173 x * L(y,z,x / z) = (x / z) * (z * y). [para(22(a,1),74(a,1,1))]. 174 (x * (y * z)) \ (x * (y * (z * u))) = L(L(u,z,y),y * z,x). [para(74(a,1),32(a,2,2,2)),flip(a)]. 175 (x * y) * L(L(z,y,x),u,w) = x * (y * L(z,u,w)). [para(49(a,1),74(a,1,2))]. 176 (x * y) * L(z,K(x,y),y * x) = (y * x) * (K(x,y) * z). [para(69(a,1),74(a,1,1))]. 177 L(x \ (y \ z),x,y) = (y * x) \ z. [para(20(a,1),76(a,2,2))]. 178 L(x \ (y * x),x,y) = T(y,y * x). [para(76(a,2),36(a,2)),flip(a)]. 179 (x * y) / L(z \ y,z,x) = x * z. [para(76(a,2),65(a,1,2))]. 180 L(x \ T(y,z),x,z) = (z * x) \ (y * z). [para(82(a,1),76(a,2,2))]. 181 L(x \ (y \ ((y * x) * z)),x,y) = z. [para(76(a,2),62(a,1))]. 182 R(x,x,y) = x. [hyper(24,a,131,a(flip),b,79,a)]. 183 (R(x,y,z) * y) \ ((x * y) * z) = L(z,y,R(x,y,z)). [para(79(a,1),32(a,2,2)),flip(a)]. 184 L(R(x,y,z),u,w) * (y * z) = (L(x,u,w) * y) * z. [para(48(a,1),79(a,1,1))]. 185 R(R(x,y,z),u,w) * (y * z) = (R(x,u,w) * y) * z. [para(50(a,1),79(a,1,1))]. 186 R(T(x,y),x,z) = T(x,y). [para(182(a,1),46(a,2,1))]. 187 L(R(x,L(x,y,z),u),y,z) = L(x,y,z). [para(182(a,1),48(a,1)),flip(a)]. 188 R(R(x,y,z),x,u) = R(x,y,z). [para(182(a,1),50(a,1,1)),flip(a)]. 189 R(R(T(x,y),z,u),x,w) = R(T(x,y),z,u). [para(186(a,1),50(a,1,1)),flip(a)]. 190 (T(x,y) * x) * z = T(x,y) * (x * z). [para(186(a,1),79(a,1,1)),flip(a)]. 191 (R(x,y,z) * x) * u = R(x,y,z) * (x * u). [para(188(a,1),79(a,1,1)),flip(a)]. 192 R(1 / x,x,y) = y / (x * y). [para(17(a,1),80(a,2,1))]. 193 R((x / y) / z,z,y) = x / (z * y). [para(22(a,1),80(a,2,1))]. 194 T((x * y) / (z * y),u) = R(T(x / z,u),z,y). [para(80(a,1),46(a,2,1)),flip(a)]. 195 R(x,x \ 1,y) = y / ((x \ 1) * y). [para(65(a,1),192(a,1,1))]. 196 (x * y) / L(z,y / z,x) = x * (y / z). [para(22(a,1),99(a,1,1,2))]. 197 R(x,x \ y,z) \ (y * z) = (x \ y) * z. [para(20(a,1),101(a,1,2,1))]. 198 R(x,y \ 1,y) / y = x * (1 / y). [para(155(a,1),141(a,1,1,2))]. 199 L(K(x,y) \ ((y * x) \ z),K(x,y),y * x) = (x * y) \ z. [para(69(a,1),177(a,2,1))]. 200 (x * x) \ y = x \ (x \ y). [para(177(a,1),137(a,1))]. 201 L(x \ L(y \ z,y,u),x,u * y) = ((u * y) * x) \ (u * z). [para(76(a,2),177(a,1,1,2))]. 202 x \ (x \ (y * (x * x))) = T(y,x * x). [para(200(a,1),36(a,2)),flip(a)]. 203 L(T(x,y),y,x) = T(x,x * y). [para(36(a,2),178(a,1,1))]. 204 T(x,x * ((y * x) / y)) = L(x,(y * x) / y,x). [para(120(a,1),203(a,1,1)),flip(a)]. 205 x / L(y \ z,y,x / z) = (x / z) * y. [para(22(a,1),179(a,1,1))]. 206 R(x,x \ (y / z),z) = y / ((x \ (y / z)) * z). [para(65(a,1),193(a,1,1))]. 207 R(x,y \ 1,y) / y = x * (y \ 1). [para(155(a,1),198(a,2,2))]. 208 (x * (y \ 1)) * y = R(x,y \ 1,y). [para(207(a,1),22(a,1,1))]. 209 (x * (y \ 1)) \ R(x,y \ 1,y) = y. [para(207(a,1),66(a,1,1))]. 210 R(x / (y \ 1),y \ 1,y) = x * y. [para(22(a,1),208(a,1,1)),flip(a)]. 211 (x * (x * y)) / z = x * (x * (y / z)). [para(22(a,1),85(a,1,1,2,2))]. 212 (x * (x * y)) \ (x * (x * z)) = y \ z. [para(20(a,1),86(a,1,2,2,2))]. 213 x \ ((x * y) * z) = x * ((x \ y) * z). [para(20(a,1),87(a,1,2,1,2))]. 214 L(x,y,z) * x = x * L(x,y,z). [para(81(a,1),109(a,1,2,1)),flip(a)]. 215 L(x / y,z,u) * y = y * L(y \ x,z,u). [para(84(a,1),109(a,1,2,1)),flip(a)]. 216 L(x \ 1,y,z) * x = x * L(x \ 1,y,z). [para(152(a,1),109(a,1,2,1)),flip(a)]. 217 x * T(y,y * x) = L(y,x,y) * x. [para(203(a,1),109(a,1,2))]. 218 (x * L(x,y,z)) / x = L(x,y,z). [hyper(24,a,22,a,b,214,a),flip(a)]. 219 T(x,L(x,y,z)) = x. [hyper(23,a,82,a,b,214,a),flip(a)]. 220 T(x,x * L(x,y,z)) = L(x,L(x,y,z),x). [para(219(a,1),203(a,1,1)),flip(a)]. 221 L(x,x \ y,x) * (x \ y) = (x \ y) * T(x,y). [para(20(a,1),217(a,1,2,2)),flip(a)]. 222 x * R(T(T(y,x),z),u,w) = R(T(y,z),u,w) * x. [para(42(a,1),110(a,1,2,1))]. 223 R(x,y,z) * x = x * R(x,y,z). [para(81(a,1),110(a,1,2,1)),flip(a)]. 224 R(x / y,z,u) * y = y * R(y \ x,z,u). [para(84(a,1),110(a,1,2,1)),flip(a)]. 225 (x \ y) * R((x \ y) \ y,z,u) = R(x,z,u) * (x \ y). [para(83(a,1),110(a,1,2,1))]. 226 x * (x * R(T(y,x * x),z,u)) = R(y,z,u) * (x * x). [para(110(a,1),131(a,1)),flip(a)]. 227 R(x \ 1,y,z) * x = x * R(x \ 1,y,z). [para(152(a,1),110(a,1,2,1)),flip(a)]. 228 T(x,R(x,y,z)) = x. [hyper(23,a,82,a,b,223,a),flip(a)]. 229 T(x \ y,R(y / x,z,u)) = T(y / x,x). [para(228(a,1),112(a,1,1)),flip(a)]. 230 x \ (y * (x * x)) = x * T(y,x * x). [hyper(23,a,20,a,b,136,a),flip(a)]. 231 T(x / (x * y),z) * (x * y) = (x * y) * T(L(y \ 1,y,x),z). [para(142(a,2),139(a,2,2,1))]. 232 T((x * y) / (x * z),u) * (x * z) = (x * z) * T(L(z \ y,z,x),u). [para(76(a,2),139(a,2,2,1))]. 233 (x * T(y,z)) / x = T((x * y) / x,z). [para(19(a,1),140(a,1,1,2,1))]. 234 L(x,y,T(y,z)) = x. [hyper(23,a,74,a,b,190,a),flip(a)]. 235 (x * T(x,y)) * z = T(x,y) * (x * z). [para(116(a,1),190(a,1,1))]. 236 L(x,y / z,z \ y) = x. [para(84(a,1),234(a,1,3))]. 237 L(x,(y * z) / y,z) = x. [para(104(a,1),234(a,1,3))]. 238 x * (x * ((x \ y) / z)) = (x * y) / z. [para(20(a,1),211(a,1,1,2)),flip(a)]. 239 (x * (x * y)) \ (x * x) = y \ 1. [para(18(a,1),212(a,1,2,2))]. 240 (x * y) \ (x * (x * z)) = (x \ y) \ z. [para(20(a,1),212(a,1,1,2))]. 241 T(x,x * (x * y)) = y \ (x * y). [para(212(a,1),36(a,2))]. 242 (x * y) \ (x * x) = (x \ y) \ 1. [para(20(a,1),239(a,1,1,2))]. 243 (x * x) / (y \ 1) = x * (x * y). [para(239(a,1),65(a,1,2))]. 244 ((x * y) * z) \ (x * x) = ((x \ y) * z) \ 1. [para(89(a,1),239(a,1,1))]. 245 T(x,x * (x * y)) = T(x,y). [para(241(a,2),36(a,2)),flip(a)]. 246 T(x,x \ y) = T(x,x * y). [para(20(a,1),245(a,1,2,2)),flip(a)]. 247 T(x,x * (y * x)) = T(x,T(y,x)). [para(82(a,1),245(a,1,2,2))]. 248 T(x * y,(x * y) * (y * x)) = T(x * y,K(y,x)). [para(69(a,1),245(a,1,2,2))]. 249 T(x,x * y) = (x \ y) \ y. [para(246(a,1),83(a,1))]. 250 (x \ y) * T(x,x * y) = y. [para(249(a,2),20(a,1,2))]. 251 T(x / y,x) = ((x / y) \ y) \ y. [para(22(a,1),249(a,1,2))]. 252 x / T(y,y * x) = y \ x. [para(249(a,2),65(a,1,2))]. 253 (x \ y) * ((x \ y) * (T(x,x * y) * z)) = ((x \ y) * y) * z. [para(249(a,2),89(a,1,2,2,1))]. 254 (x \ (x \ y)) * T(x,y) = x \ y. [para(20(a,1),250(a,1,2,2))]. 255 ((x \ y) * (T(x,x * y) * z)) \ (y * z) = a(x \ y,T(x,x * y),z). [para(250(a,1),28(a,2,2,1)),flip(a)]. 256 (x \ y) / T(x,y) = x \ (x \ y). [para(20(a,1),252(a,1,2,2))]. 257 K(x,y) / T(y * x,x * y) = (y * x) \ K(x,y). [para(69(a,1),252(a,1,2,2))]. 258 (x \ (x \ y)) \ 1 = y \ (x * x). [para(20(a,1),242(a,1,1)),flip(a)]. 259 L(x \ y,x,y) = (y \ x) \ 1. [para(242(a,1),76(a,2))]. 260 L(K(x,y),y * x,x * y) = ((x * y) \ (y * x)) \ 1. [para(30(a,2),259(a,1,1))]. 261 L(T(x \ y,z),x,y) = T((y \ x) \ 1,z). [para(259(a,1),44(a,2,1))]. 262 (x \ ((y * x) / y)) \ 1 = ((y * x) / y) \ x. [para(259(a,1),237(a,1))]. 263 x * (x * (y \ 1)) = (x * x) / y. [para(156(a,1),243(a,1,2)),flip(a)]. 264 (x \ (y * y)) \ 1 = y \ (y \ x). [para(258(a,1),156(a,1,1))]. 265 x * ((x \ (x \ y)) * z) = x \ (y * z). [para(20(a,1),213(a,1,2,1)),flip(a)]. 266 L(x \ (y * ((y \ x) * z)),x,y) = z. [para(213(a,1),181(a,1,1,2))]. 267 L(x \ (y * z),x,y) = (y \ x) \ z. [para(20(a,1),266(a,1,1,2,2))]. 268 L(x \ y,x,z) = (z \ x) \ (z \ y). [para(20(a,1),267(a,1,1,2))]. 269 L(x \ (y * z),x,z) = (z \ x) \ T(y,z). [para(82(a,1),267(a,1,1,2))]. 270 L((x * y) \ z,x * y,x) = y \ (x \ z). [para(19(a,1),268(a,2,1))]. 271 L(((x * y) * z) \ u,(x * y) * z,x * (y * z)) = a(x,y,z) \ ((x * (y * z)) \ u). [para(28(a,2),268(a,2,1))]. 272 (x \ y) / L(z \ y,z,x) = x \ z. [para(268(a,2),65(a,1,2))]. 273 L(x \ y,x,x / z) = z \ ((x / z) \ y). [para(66(a,1),268(a,2,1))]. 274 (x \ y) \ (x \ z) = (x * y) \ (x * z). [para(268(a,1),76(a,1))]. 275 L(x \ L(y \ z,y,u),x,u \ y) = ((u \ y) * x) \ (u \ z). [para(268(a,2),177(a,1,1,2))]. 276 (x \ 1) / (y \ x) = x \ (x \ y). [para(143(a,1),272(a,1,2))]. 277 x \ (x \ (x / y)) = (x \ 1) / y. [para(66(a,1),276(a,1,2)),flip(a)]. 278 x * ((x \ 1) / y) = x \ (x / y). [para(277(a,1),20(a,1,2))]. 279 ((x \ 1) / y) \ 1 = (x / y) \ (x * x). [para(277(a,1),258(a,1,1))]. 280 T(x * T(x,y),T(x,y)) = x * T(x,y). [hyper(23,a,82,a,b,235,a(flip)),flip(a)]. 281 (x * T(x,y)) * (x \ z) = T(x,y) * z. [para(20(a,1),235(a,2,2))]. 282 (x * y) / (z \ (x \ y)) = x * (x * z). [para(65(a,1),238(a,1,2,2)),flip(a)]. 283 (x \ (x \ y)) \ z = y \ (x * (x * z)). [para(20(a,1),240(a,1,1)),flip(a)]. 284 (x \ y) \ ((x \ z) * u) = (x * y) \ ((x * z) * u). [para(89(a,1),240(a,1,2)),flip(a)]. 285 x \ (x \ (y * z)) = (x \ (x \ y)) * z. [hyper(23,a,20,a,b,265,a),flip(a)]. 286 (x \ (x \ y)) * (x * x) = T(y,x * x). [hyper(23,a,230,a(flip),b,265,a)]. 287 (x * (y * x)) \ (x * z) = T(y,x) \ (x \ z). [para(36(a,2),274(a,1,1)),flip(a)]. 288 T(x * T(x,y),T(x,y)) = T(x,y) * x. [para(280(a,2),116(a,2)),flip(a)]. 289 x / (y \ (x \ 1)) = x * (x * y). [para(18(a,1),282(a,1,1))]. 290 (x \ (x \ y)) \ y = T(x * x,y). [para(283(a,2),135(a,1))]. 291 (x \ (x \ 1)) * y = x \ (x \ y). [para(17(a,1),285(a,1,2,2)),flip(a)]. 292 (x \ (x \ y)) * (y \ z) = x \ (x \ z). [para(20(a,1),285(a,1,2,2)),flip(a)]. 293 R((x / y) / (z \ (z \ 1)),z \ (z \ 1),y) = x / (z \ (z \ y)). [para(291(a,1),193(a,2,2))]. 294 ((x \ 1) / y) * (x * x) = T(x / y,x * x). [para(277(a,1),286(a,1,1))]. 295 T(T(x,y) * x,T(x,y)) = T(x,y) * x. [para(116(a,2),288(a,1,1))]. 296 (x \ (x \ y)) \ (x \ (x \ z)) = y \ z. [hyper(23,a,20,a,b,292,a),flip(a)]. 297 (x \ y) * ((x * y) \ z) = x \ (x \ z). [para(19(a,1),292(a,1,1,2))]. 298 (T(x,y) \ x) * T(x,y) = x. [hyper(23,a,138,a,b,295,a(flip)),flip(a)]. 299 x / T(x,y) = T(x,y) \ x. [hyper(24,a,22,a,b,298,a),flip(a)]. 300 ((x * y) * z) / T(x * (y * z),a(x,y,z)) = a(x,y,z). [para(67(a,1),100(a,1,1))]. 301 L(x,x \ y,x) = y \ T(x * y,x). [para(138(a,1),75(a,1,2)),flip(a)]. 302 L(L(x,y \ z,y),z,y) = x. [para(75(a,1),266(a,1,1))]. 303 L(L(x,y,z),z * y,z) = x. [para(19(a,1),302(a,1,1,2))]. 304 L(L(x,y,z / y),z,z / y) = x. [para(66(a,1),302(a,1,1,2))]. 305 L(x,y \ 1,y) = x. [para(302(a,1),127(a,1)),flip(a)]. 306 L(x,y,y \ 1) = x. [para(156(a,1),305(a,1,2))]. 307 ((x \ 1) * x) \ ((x \ 1) * y) = x \ y. [para(306(a,1),76(a,1)),flip(a)]. 308 L(L(x,y * z,y),z,y) = x. [para(303(a,1),49(a,1)),flip(a)]. 309 x \ (y \ ((y * x) * z)) = L(z,y * x,y). [para(181(a,1),303(a,1,1)),flip(a)]. 310 R(x,L(x,y,z),u) = L(L(x,y,z),z * y,z). [para(187(a,1),303(a,1,1)),flip(a)]. 311 L((x \ y) \ z,x * y,x) = y \ (x * z). [para(267(a,1),303(a,1,1))]. 312 L(x,y \ z,y) = L(x,y * z,y). [para(302(a,1),303(a,1,1)),flip(a)]. 313 L(x,y * (y * z),y) = L(x,z,y). [para(303(a,1),303(a,1,1))]. 314 L(L(x,y * z,z),T(y,z),z) = x. [para(82(a,1),308(a,1,1,2))]. 315 L(L(x,y * z,z * y),K(y,z),z * y) = x. [para(69(a,1),308(a,1,1,2))]. 316 L(x,x * y,x) = y \ T(x * y,x). [para(301(a,1),312(a,1)),flip(a)]. 317 1 \ ((x \ 1) * y) = x \ y. [para(154(a,1),307(a,1,1))]. 318 (x \ 1) * y = x \ y. [para(317(a,1),59(a,1)),flip(a)]. 320 (x \ y) / y = x \ 1. [hyper(24,a,22,a,b,318,a),flip(a)]. 321 x * ((x \ 1) * y) = y. [hyper(23,a,19,a(flip),b,318,a)]. 322 (x \ 1) * (x * y) = y. [para(318(a,2),19(a,1))]. 323 (x \ (y * z)) \ (((x \ 1) * y) * z) = a(x \ 1,y,z). [para(318(a,1),28(a,2,1)),flip(a)]. 324 ((x * (y \ 1)) * z) / (y \ z) = R(x,y \ 1,z). [para(318(a,1),34(a,2,2)),flip(a)]. 325 T(x \ 1,y) = y \ (x \ y). [para(318(a,1),36(a,2,2))]. 326 x \ T(y,x \ 1) = y * (x \ 1). [para(318(a,1),82(a,1))]. 327 x * T(y \ 1,x) = y \ x. [para(318(a,1),82(a,2))]. 328 (x \ y) * K(y,x \ 1) = y * (x \ 1). [para(318(a,1),69(a,1,1))]. 329 x \ T(T(y,x \ 1),z) = T(y,z) * (x \ 1). [para(318(a,1),108(a,1))]. 330 (x \ 1) \ y = x * y. [para(156(a,1),318(a,1,1)),flip(a)]. 331 (x \ y) * L(z,y,x \ 1) = (x \ 1) * (y * z). [para(318(a,1),74(a,1,1))]. 332 R(x,y \ 1,z) * (y \ z) = (x * (y \ 1)) * z. [para(318(a,1),79(a,1,2))]. 333 (x * (y \ z)) / L(z,y \ 1,x) = x * (y \ 1). [para(318(a,1),99(a,1,1,2))]. 334 R(x,x \ 1,y) = y / (x \ y). [para(318(a,1),195(a,2,2))]. 335 R(x \ 1,y \ 1,y) = (x \ (y \ 1)) * y. [para(318(a,1),208(a,1,1)),flip(a)]. 336 L(x \ 1,y,x \ 1) * y = y * T(x \ 1,x \ y). [para(318(a,1),217(a,1,2,2)),flip(a)]. 337 T(x \ 1,(x \ 1) \ y) = T(x \ 1,x \ y). [para(318(a,1),246(a,2,2))]. 338 (x \ (x \ y)) \ z = (y \ (x * x)) * z. [para(258(a,1),318(a,1,1)),flip(a)]. 339 (x \ (y * y)) \ z = (y \ (y \ x)) * z. [para(264(a,1),318(a,1,1)),flip(a)]. 340 x / (y * x) = y \ 1. [para(19(a,1),320(a,1,1))]. 341 K(x,y) / (x * y) = (y * x) \ 1. [para(30(a,2),320(a,1,1))]. 342 L(x,y,z) / (z * (y * x)) = (z * y) \ 1. [para(32(a,2),320(a,1,1))]. 343 (x / y) \ 1 = y / x. [para(66(a,1),320(a,1,1)),flip(a)]. 344 (x * y) / ((z * x) * y) = R(z,x,y) \ 1. [para(101(a,1),320(a,1,1))]. 345 T(x * y,K(y,x)) / (y * x) = K(y,x) \ 1. [para(122(a,1),320(a,1,1))]. 346 T(x,x * y) / y = (x \ y) \ 1. [para(249(a,2),320(a,1,1))]. 347 x * (y * (x \ 1)) = T(y,x \ 1). [para(82(a,1),321(a,1,2))]. 348 R(x \ 1,x * y,z) = (y * z) / ((x * y) * z). [para(322(a,1),34(a,2,1,1))]. 349 T(x \ 1,x * y) = (x * y) \ y. [para(322(a,1),36(a,2,2))]. 350 R((x \ 1) / y,y,x * z) = z / (y * (x * z)). [para(322(a,1),80(a,2,1))]. 351 L(x * y,x \ 1,y) = (y \ (x \ 1)) \ 1. [para(330(a,1),259(a,1,1))]. 352 L(x * (y * z),x \ 1,y) = (y \ (x \ 1)) \ z. [para(330(a,1),267(a,1,1))]. 353 (x / (y * x)) * z = y \ z. [para(340(a,2),318(a,1,1))]. 354 (x / y) * (y / x) = 1. [para(343(a,1),20(a,1,2))]. 355 K(x \ y,x / y) = 1. [para(343(a,1),167(a,1,2))]. 356 T(x,y / (y * x)) = x. [para(343(a,1),170(a,1,2))]. 357 T(x \ y,x / y) = x \ y. [para(343(a,1),169(a,1,2))]. 358 (x / y) \ z = (y / x) * z. [para(343(a,1),318(a,1,1)),flip(a)]. 359 (x / y) * ((y / x) * z) = z. [para(343(a,1),321(a,1,2,1))]. 360 x * ((y / z) * (z / y)) = x. [para(354(a,2),18(a,1,2))]. 361 K((x * y) \ y,x) = 1. [para(21(a,1),355(a,1,2))]. 362 (x / (x * y)) * y = y * (x / (x * y)). [para(356(a,1),82(a,1,2))]. 363 (x * (y / (y * x))) / x = y / (y * x). [para(356(a,1),100(a,1,2))]. 364 T(x,x * (y / (y * x))) = L(x,y / (y * x),x). [para(356(a,1),203(a,1,1)),flip(a)]. 365 T((x * y) \ y,x) = (x * y) \ y. [hyper(41,a,361,a)]. 366 x * R(x \ (y \ x),z,u) = R(y \ 1,z,u) * x. [para(325(a,1),110(a,1,2,1))]. 367 T(x / y,x \ y) = x / y. [hyper(39,a,357,a)]. 368 (x / y) * (x \ y) = (x \ y) * (x / y). [para(357(a,1),82(a,1,2))]. 369 (x / y) * (z * (y / x)) = T(z,y / x). [para(358(a,1),36(a,2)),flip(a)]. 370 T(x / y,x) = ((y / x) * y) \ y. [para(358(a,1),251(a,2,1))]. 371 ((x \ 1) / y) \ 1 = (y / x) * (x * x). [para(358(a,1),279(a,2))]. 372 T(x \ y,y \ x) = T(y / x,x). [para(367(a,1),112(a,1,1)),flip(a)]. 373 R(x,x \ 1,y) = x. [para(334(a,2),65(a,1))]. 374 R(T(x,y),x \ 1,z) = T(x,y). [para(373(a,1),46(a,2,1))]. 375 R(R(x,y,z),x \ 1,u) = R(x,y,z). [para(373(a,1),50(a,1,1)),flip(a)]. 376 R(T(x / y,y),(x / y) \ 1,z) = y \ x. [para(374(a,2),84(a,1))]. 377 T(x,y) * (x \ 1) = x \ T(x,y). [para(165(a,1),326(a,1,2)),flip(a)]. 378 x \ T(T(y,x \ 1),x) = (x \ (y * (x \ 1))) * x. [para(326(a,1),148(a,1,1,2)),flip(a)]. 379 K(x,y) * ((K(x,y) \ 1) / (x * y)) = K(x,y) \ ((y * x) \ 1). [para(341(a,1),278(a,2,2))]. 380 T(x \ 1,x * (y * y)) = (y \ (y \ (x * (y * y)))) \ 1. [para(349(a,2),258(a,2)),flip(a)]. 381 ((x * y) \ y) * x = x * ((x * y) \ y). [para(365(a,1),82(a,1,2)),flip(a)]. 382 T(x \ y,y \ x) = x \ y. [para(372(a,2),84(a,1))]. 383 T(x \ (x * y),(x * y) \ x) = y. [para(372(a,2),104(a,1))]. 384 (x \ y) * (y \ x) = (y \ x) * (x \ y). [para(382(a,1),82(a,1,2))]. 385 (x \ 1) \ T(x \ 1,x * y) = ((x * y) \ y) * ((x \ 1) \ 1). [para(349(a,1),377(a,1,1)),flip(a)]. 386 T(x,(y * x) \ y) = x. [para(19(a,1),383(a,1,1))]. 387 T(x,y \ (y / x)) = x. [para(22(a,1),386(a,1,2,1))]. 388 ((x * y) \ x) * y = y * ((x * y) \ x). [para(386(a,1),82(a,1,2))]. 389 T(K(x,y),(x * y) \ (y * x)) = K(x,y). [para(69(a,1),386(a,1,2,1))]. 390 R(x,y,z) * (x \ 1) = R(x,y,z) / x. [para(375(a,1),207(a,1,1)),flip(a)]. 391 x \ (y * (y * z)) = (x \ (y * y)) * z. [para(338(a,1),283(a,1)),flip(a)]. 392 (x \ (y * y)) * x = T(y * y,x). [para(338(a,1),290(a,1))]. 393 (x \ (y * y)) * (y \ (y \ z)) = x \ z. [para(338(a,1),296(a,1))]. 394 T(x * x,y * z) \ ((((y * z) \ (x * x)) * y) * z) = a((y * z) \ (x * x),y,z). [para(392(a,1),28(a,2,1)),flip(a)]. 395 L(x \ 1,x,x \ (y * y)) = T(y * y,x) \ (x \ (y * y)). [para(392(a,1),142(a,2,1))]. 396 ((x * y) \ ((x * y) \ ((x * y) * x))) * z = L(y,x,x * y) \ z. [para(32(a,2),339(a,1,1)),flip(a)]. 397 (x / y) * (y * y) = x / (y \ 1). [para(371(a,1),343(a,1))]. 398 (x / (y \ 1)) / (y * y) = x / y. [hyper(24,a,22,a,b,397,a),flip(a)]. 399 (x / y) * (y / (x \ 1)) = x * x. [hyper(23,a,359,a,b,397,a),flip(a)]. 400 (x * y) / (y \ 1) = x * (y * y). [para(21(a,1),397(a,1,1)),flip(a)]. 401 (x * (y \ 1)) / y = x / (y * y). [para(21(a,1),398(a,1,1)),flip(a)]. 402 ((x \ (x \ y)) * x) / (x \ 1) = T(y,x * x). [para(400(a,2),286(a,1))]. 403 T(x / (y * y),y) = y \ (x * (y \ 1)). [para(401(a,1),84(a,1,1))]. 404 T(K(x,y),K(y,x)) = K(x,y). [para(30(a,2),389(a,1,2))]. 405 T(K(x,y),z) * K(y,x) = K(y,x) * T(K(x,y),z). [para(404(a,1),108(a,1,2,1)),flip(a)]. 406 R(K(x,y),z,u) * K(y,x) = K(y,x) * R(K(x,y),z,u). [para(404(a,1),110(a,1,2,1)),flip(a)]. 407 x * ((x \ (y * y)) * z) = y * (y * z). [para(391(a,1),20(a,1,2))]. 408 (((x * y) * x) \ (x * x)) * y = K(x,x * y). [para(391(a,1),30(a,2)),flip(a)]. 409 (x * (y * y)) \ z = y \ (y \ (x \ z)). [hyper(23,a,297,a,b,393,a),flip(a)]. 410 x * ((x \ (y * y)) * z) = (y * y) * z. [para(407(a,2),131(a,2)),flip(a)]. 411 (x * (y * y)) * z = x * (y * (y * z)). [para(407(a,1),89(a,1,2)),flip(a)]. 412 x \ (x \ (y \ ((y * x) * x))) = a(y,x,x). [para(409(a,1),28(a,2)),flip(a)]. 413 (x * (y * y)) \ x = y \ (y \ 1). [para(60(a,1),409(a,2,2,2))]. 414 x \ (x / (y * y)) = y \ (y \ 1). [para(22(a,1),413(a,1,1))]. 415 x / (y \ (y \ 1)) = x * (y * y). [para(413(a,1),65(a,1,2))]. 416 x * (y \ (y \ 1)) = x / (y * y). [para(414(a,1),20(a,1,2))]. 417 (x * (y * y)) * z = x * ((y * y) * z). [para(410(a,1),89(a,1,2)),flip(a)]. 418 (x * (y * (y * z))) / z = x * (y * y). [hyper(24,a,22,a,b,411,a),flip(a)]. 419 (x * (y * (y * z))) \ ((x * (y * y)) * (z * u)) = L(u,z,x * (y * y)). [para(411(a,1),32(a,2,1)),flip(a)]. 420 (x \ (x \ y)) * (x * (x * z)) = T(y,x * x) * z. [para(286(a,1),411(a,1,1)),flip(a)]. 421 L(x,y * y,z) = x. [hyper(23,a,74,a,b,417,a),flip(a)]. 422 R(x,y * y,z) = x. [hyper(24,a,79,a,b,417,a(flip)),flip(a)]. 423 T(x,x * (y * y)) = T(x,y * y). [para(421(a,1),203(a,1)),flip(a)]. 424 L(x,y,y / (z * z)) = x. [para(421(a,1),304(a,1,1))]. 425 L(x,y \ (y \ 1),z) = x. [para(318(a,1),421(a,1,2))]. 426 R(x,y \ (y \ 1),z) = x. [para(318(a,1),422(a,1,2))]. 427 L(x,y,y / (z \ (z \ 1))) = x. [para(318(a,1),424(a,1,3,2))]. 428 (x * (y \ (y \ 1))) * z = x * ((y \ (y \ 1)) * z). [para(425(a,1),74(a,1,2))]. 429 L(x,y,y * (z * z)) = x. [para(415(a,1),427(a,1,3))]. 430 T(x,x \ (y * y)) = T(x,y * y). [para(423(a,1),246(a,2))]. 431 T(x \ 1,x * (y * y)) = T(x \ 1,y * y). [para(330(a,1),430(a,1,2))]. 432 L(x,x,y / x) = y \ (y / (x \ 1)). [para(397(a,1),77(a,1,2)),flip(a)]. 433 (x * y) * (y \ 1) = R(x,y,y \ 1). [para(78(a,1),64(a,1)),flip(a)]. 434 R(x / y,y,y \ 1) = x * (y \ 1). [para(22(a,1),433(a,1,1)),flip(a)]. 435 x * L(y,z * x,z) = z * ((z \ x) * y). [para(312(a,1),172(a,1,2))]. 436 (R(T(x,y),z,u) * x) * w = R(T(x,y),z,u) * (x * w). [para(189(a,1),79(a,1,1)),flip(a)]. 437 T(x \ y,R(y / x,z,u)) = x \ y. [para(229(a,2),84(a,1))]. 438 T((x \ 1) \ y,y * x) = (x \ 1) \ y. [para(210(a,1),437(a,1,2))]. 439 T(x * y,y * x) = (x \ 1) \ y. [para(330(a,1),438(a,1,1))]. 440 (x \ y) \ T(y,x) = L(x,y,x). [para(19(a,1),269(a,1,1)),flip(a)]. 441 T(x,y) / L(y,x,y) = y \ x. [para(440(a,1),65(a,1,2))]. 442 L(x \ (x / y),y,x \ (x / y)) = ((x \ (x / y)) \ y) \ y. [para(387(a,1),440(a,1,2)),flip(a)]. 443 (x * (x * y)) \ z = y \ (x \ (x \ z)). [para(270(a,1),177(a,1)),flip(a)]. 444 x \ (y \ (y \ (z * (y * (y * x))))) = T(z,y * (y * x)). [para(443(a,1),36(a,2)),flip(a)]. 445 L(x \ 1,x,x / y) = y \ (y / x). [para(343(a,1),273(a,2,2))]. 446 x * (y \ ((y * (x \ 1)) * z)) = L(z,y * (x \ 1),y). [para(309(a,1),330(a,1)),flip(a)]. 447 R(x \ y,(y / x) \ 1,z) = x \ y. [para(84(a,1),376(a,1,1))]. 448 R(x \ y,x / y,z) = x \ y. [para(343(a,1),447(a,1,2))]. 449 R(x \ (x * y),x / (x * y),z) = y. [para(448(a,2),19(a,1))]. 450 R(x,y / (y * x),z) = x. [para(19(a,1),449(a,1,1))]. 451 (x * (y / (y * x))) * z = x * ((y / (y * x)) * z). [para(450(a,1),79(a,1,1)),flip(a)]. 452 x \ L(x,y * x,y) = a(y,x,x). [para(309(a,1),412(a,1,2))]. 453 L(x,y * x,y) = x * a(y,x,x). [para(452(a,1),20(a,1,2)),flip(a)]. 454 L(x * a(y,x,x),x,y) = x. [para(453(a,1),308(a,1,1))]. 455 x * ((x \ y) * T(z,y)) = L(z,x * y,x) * y. [para(435(a,1),109(a,1))]. 456 (x * y) \ (x * T(y,x)) = K(x \ (x \ y),x). [para(171(a,1),274(a,1)),flip(a)]. 457 L(x,y,R(y,z,u)) = x. [hyper(23,a,74,a,b,191,a),flip(a)]. 458 R(x,y,z) * ((R(x,y,z) \ x) * u) = x * u. [hyper(23,a,89,a,b,191,a(flip)),flip(a)]. 459 (x * R(x,y,z)) * u = R(x,y,z) * (x * u). [para(223(a,1),191(a,1,1))]. 460 (R(x,y,z) \ x) \ 1 = x \ R(x,y,z). [para(457(a,1),259(a,1)),flip(a)]. 461 (R(x,y,z) \ u) / (x \ u) = R(x,y,z) \ x. [para(457(a,1),272(a,1,2))]. 462 (x \ R(x,y,z)) \ 1 = R(x,y,z) \ x. [para(460(a,1),156(a,1,1))]. 463 (R(x,y,z) \ x) \ u = (x \ R(x,y,z)) * u. [para(460(a,1),318(a,1,1)),flip(a)]. 464 (R(x,y,z) \ x) * ((x \ R(x,y,z)) * u) = u. [para(460(a,1),321(a,1,2,1))]. 465 (x \ R(x,y,z)) \ u = (R(x,y,z) \ x) * u. [para(460(a,1),330(a,1,1))]. 466 T(x,L(x \ 1,y,z)) = x. [hyper(23,a,82,a,b,216,a),flip(a)]. 467 K(x,L(x \ 1,y,z)) = 1. [hyper(40,a,466,a)]. 468 K(x \ 1,L(x,y,z)) = 1. [para(156(a,1),467(a,1,2,1))]. 469 K(L(x,y,z) \ 1,x) = 1. [para(303(a,1),468(a,1,2))]. 470 T(L(x,y,z) \ 1,x) = L(x,y,z) \ 1. [hyper(41,a,469,a)]. 471 x * (L(x,y,z) \ 1) = L(x,y,z) \ x. [para(470(a,1),327(a,1,2))]. 472 R(x / (x * y),z,u) * (x * y) = (x * y) * R(L(y \ 1,y,x),z,u). [para(142(a,2),224(a,2,2,1))]. 473 R((x * y) / (x * z),u,w) * (x * z) = (x * z) * R(L(z \ y,z,x),u,w). [para(76(a,2),224(a,2,2,1))]. 474 R(R(x / y,y,z),u,w) * (y * z) = (y * z) * R((y * z) \ (x * z),u,w). [para(80(a,2),224(a,1,1,1))]. 475 T(x,R(x \ 1,y,z)) = x. [hyper(23,a,82,a,b,227,a),flip(a)]. 476 T(x \ 1,R(x,y,z)) = x \ 1. [para(156(a,1),475(a,1,2,1))]. 477 R(x,y,z) * (x \ 1) = x \ R(x,y,z). [para(476(a,1),327(a,1,2))]. 478 R(x,y,z) / x = x \ R(x,y,z). [para(477(a,1),390(a,1)),flip(a)]. 479 (x \ R(x,y,z)) * x = R(x,y,z). [para(478(a,1),22(a,1,1))]. 480 (x \ R(x,y,z)) \ R(x,y,z) = x. [para(478(a,1),66(a,1,1))]. 481 (x / y) \ R(x / y,y,y \ 1) = (x * (y \ 1)) / (x / y). [para(434(a,1),478(a,1,1)),flip(a)]. 482 (x \ ((y * x) / y)) \ 1 = (y / (y * x)) * x. [para(262(a,2),358(a,1))]. 483 R(x,L(x,y,z),u) = x. [para(310(a,2),303(a,1))]. 484 (x * L(x,y,z)) * u = x * (L(x,y,z) * u). [para(483(a,1),79(a,1,1)),flip(a)]. 485 T(x \ 1,x \ y) = T(x \ 1,x * y). [para(330(a,1),337(a,1,2)),flip(a)]. 486 (x \ T(y,x)) / (x \ 1) = T(y,x * x). [para(148(a,1),402(a,1,1))]. 487 (((x \ y) * x) \ 1) * y = K(x,x * y). [para(244(a,1),408(a,1,1))]. 488 ((x \ y) * x) \ y = K(x,x * y). [para(487(a,1),318(a,1)),flip(a)]. 489 K(x,x \ y) = K(x,x * y). [para(488(a,1),71(a,1)),flip(a)]. 490 K(x,x * (x * y)) = K(x,y). [para(19(a,1),489(a,1,2)),flip(a)]. 491 K(x,x * (y * x)) = K(x,T(y,x)). [para(36(a,2),489(a,1,2)),flip(a)]. 492 K(x,(x * x) / y) = K(x,y \ 1). [para(263(a,1),490(a,1,2))]. 493 K(x \ (x \ y),x) = (x * y) \ (y * x). [para(82(a,1),456(a,1,2)),flip(a)]. 494 K(x \ (x \ y),x) = K(y,x). [para(493(a,2),30(a,2)),flip(a)]. 495 K(x \ y,x) = K(x * y,x). [para(19(a,1),494(a,1,1,2))]. 496 (R(x,y,z) \ x) * R(x,y,z) = x. [hyper(23,a,223,a,b,458,a)]. 497 R(x,y,z) \ (x * u) = (R(x,y,z) \ x) * u. [hyper(23,a,20,a,b,458,a),flip(a)]. 498 x / R(x,y,z) = R(x,y,z) \ x. [hyper(24,a,22,a,b,496,a),flip(a)]. 499 T(R(x,y,z) \ 1,x) = x \ (x / R(x,y,z)). [para(498(a,2),325(a,2,2))]. 500 (x * y) / (z \ ((z * x) * y)) = R(z,x,y) \ z. [para(101(a,1),461(a,1,1))]. 501 x * ((x \ R(x,y,z)) * u) = R(x,y,z) * u. [para(464(a,1),458(a,1,2)),flip(a)]. 502 (x \ ((y * x) / y)) \ 1 = x * (y / (y * x)). [para(482(a,2),362(a,1))]. 503 L(x,L(y,z,u),y) = x. [hyper(23,a,74,a,b,484,a),flip(a)]. 504 x * ((x \ L(x,y,z)) * u) = L(x,y,z) * u. [hyper(23,a,89,a,b,484,a(flip)),flip(a)]. 505 L(x,(y * z) \ y,z \ 1) = x. [para(142(a,1),503(a,1,2))]. 506 (x \ L(x,y,z)) \ 1 = L(x,y,z) \ x. [para(503(a,1),259(a,1)),flip(a)]. 507 (x \ L(x,y,z)) \ u = L(x,y,z) \ (x * u). [para(503(a,1),267(a,1)),flip(a)]. 508 L(x,(y \ z) \ u,z \ (y * u)) = x. [para(267(a,1),503(a,1,2))]. 509 L(x,y,L(y,z,u)) = x. [para(303(a,1),503(a,1,2))]. 510 T(x,x * L(x,y,z)) = x. [para(503(a,1),220(a,2))]. 511 (L(x,y,z) \ x) \ 1 = x \ L(x,y,z). [para(509(a,1),259(a,1)),flip(a)]. 512 (L(x,y,z) \ x) \ u = x \ (L(x,y,z) * u). [para(509(a,1),267(a,1)),flip(a)]. 513 (L(x,y,z) \ u) / (x \ u) = L(x,y,z) \ x. [para(509(a,1),272(a,1,2))]. 514 (x \ L(x,y,z)) * x = L(x,y,z). [para(510(a,1),250(a,1,2))]. 515 L(x,y,z) / x = x \ L(x,y,z). [para(510(a,1),252(a,1,2))]. 516 (x \ L(x,y,z)) \ 1 = x / L(x,y,z). [para(510(a,1),346(a,1,1)),flip(a)]. 517 (x \ L(x,y,z)) \ u = (L(x,y,z) \ x) * u. [para(506(a,1),318(a,1,1)),flip(a)]. 518 (L(x,y,z) \ x) \ u = (x \ L(x,y,z)) * u. [para(506(a,1),330(a,1,1))]. 519 x / L(x,y,z) = L(x,y,z) \ x. [para(516(a,1),506(a,1))]. 520 (L(x,y,z) \ x) * L(x,y,z) = x. [para(519(a,1),22(a,1,1))]. 521 (L(x \ 1,x,x / y) \ (x \ 1)) * (y \ (y / x)) = x \ 1. [para(445(a,1),520(a,1,2))]. 522 (x \ R(x,y,z)) \ u = R(x,y,z) \ (x * u). [para(497(a,2),465(a,2))]. 523 (x * R(x,y,z)) * u = x * (R(x,y,z) * u). [para(501(a,1),89(a,1,2)),flip(a)]. 524 L(x,y,z) \ (x * u) = (L(x,y,z) \ x) * u. [para(517(a,1),507(a,1)),flip(a)]. 525 R(x,R(x,y,z),u) = x. [hyper(24,a,79,a,b,523,a(flip)),flip(a)]. 526 R(x,y,z) * (x * u) = x * (R(x,y,z) * u). [para(523(a,1),459(a,1)),flip(a)]. 527 R(T(x,y),R(x,z,u),w) = T(x,y). [para(525(a,1),46(a,2,1))]. 528 (x \ R(x,y,z)) * (x * u) = R(x,y,z) * u. [hyper(23,a,501,a,b,526,a(flip)),flip(a)]. 529 x * (R(x,y,z) * (x \ u)) = R(x,y,z) * u. [para(20(a,1),526(a,1,2)),flip(a)]. 530 x * (R(x,y,z) * T(u,x)) = R(x,y,z) * (u * x). [para(82(a,1),526(a,1,2)),flip(a)]. 531 (R(x,y,z) * u) / (x * u) = x \ R(x,y,z). [hyper(24,a,22,a,b,528,a),flip(a)]. 532 (x \ R(x,y,z)) * u = R(x,y,z) * (x \ u). [para(20(a,1),528(a,1,2))]. 533 R(x \ R(x,y,z),x * u,w) = ((R(x,y,z) * u) * w) / ((x * u) * w). [para(528(a,1),34(a,2,1,1))]. 534 x \ (R(x,y,z) * u) = R(x,y,z) * (x \ u). [hyper(23,a,20,a,b,529,a),flip(a)]. 535 x / (y * (R(y,z,u) \ x)) = y \ R(y,z,u). [para(20(a,1),531(a,1,1))]. 536 (R(x,y,z) * (x \ u)) / u = x \ R(x,y,z). [para(20(a,1),531(a,1,2))]. 537 ((x * y) * z) / (x * (y * z)) = x \ R(x,y,z). [para(79(a,1),531(a,1,1))]. 538 (R(R(x,y,z),u,w) * (y * z)) / ((x * y) * z) = R(x,y,z) \ R(R(x,y,z),u,w). [para(79(a,1),531(a,1,2))]. 539 x \ (R(y,z,u) * (y \ x)) = T(y \ R(y,z,u),x). [para(532(a,1),36(a,2,2)),flip(a)]. 540 (R(x,y,z) \ x) \ u = R(x,y,z) * (x \ u). [para(532(a,1),463(a,2))]. 541 (x \ R(x,y,z)) \ u = x * (R(x,y,z) \ u). [para(535(a,1),66(a,1,1))]. 542 x / (R(y,z,u) * (y \ x)) = R(y,z,u) \ y. [para(540(a,1),65(a,1,2))]. 543 x * (R(x,y,z) \ 1) = R(x,y,z) \ x. [para(541(a,1),462(a,1))]. 544 (R(x,y,z) \ x) * u = x * (R(x,y,z) \ u). [para(541(a,1),465(a,1)),flip(a)]. 545 T(R(x,y,z) \ 1,x) = R(x,y,z) \ 1. [hyper(23,a,327,a,b,543,a),flip(a)]. 546 T(x,R(x,y,z) \ 1) = x. [hyper(39,a,545,a)]. 547 x \ (x / R(x,y,z)) = R(x,y,z) \ 1. [para(545(a,1),499(a,1)),flip(a)]. 548 T(x,y) * (R(x,z,u) \ 1) = R(x,z,u) \ T(x,y). [para(546(a,1),329(a,1,2,1)),flip(a)]. 549 (x * y) \ ((z * x) * y) = R(T(z,x * y),x,y). [para(111(a,2),46(a,2)),flip(a)]. 550 (x * (x * (y * z))) / (y * z) = R(x * x,y,z). [para(51(a,1),134(a,1,1))]. 551 x \ ((x * y) * (1 / y)) = a(x,y,1 / y). [para(18(a,1),164(a,1,1))]. 552 x \ ((x * y) * (y \ 1)) = a(x,y,1 / y). [para(155(a,1),551(a,1,2,2))]. 553 x \ ((x * y) * (y \ 1)) = a(x,y,y \ 1). [para(155(a,1),552(a,2,3))]. 554 a(x / y,y,y \ 1) = (x / y) \ (x * (y \ 1)). [para(22(a,1),553(a,1,2,1)),flip(a)]. 555 T((x * y) / (z * y),z) = R(z \ x,z,y). [para(84(a,1),194(a,2,1))]. 556 T(T((x * y) / (z * y),u),z) = T(R(z \ x,z,y),u). [para(555(a,1),42(a,1,1)),flip(a)]. 557 T(x,x * ((y * x) / y)) = x. [para(204(a,2),237(a,1))]. 558 ((x * y) / x) / y = y \ ((x * y) / x). [para(557(a,1),252(a,1,2))]. 559 L(x,x * y,x) * (x \ y) = (x \ y) * T(x,y). [para(312(a,1),221(a,1,1))]. 560 (x \ y) * L(z,y,x \ 1) = x \ (y * z). [para(331(a,2),318(a,1))]. 561 (T(x,y) * (x \ 1)) * z = T(x,y) * (x \ z). [para(374(a,1),332(a,1,1)),flip(a)]. 562 (x \ T(x,y)) * z = T(x,y) * (x \ z). [para(377(a,1),561(a,1,1))]. 563 (T(x,y) * (x \ z)) / z = x \ T(x,y). [hyper(24,a,22,a,b,562,a),flip(a)]. 564 x * (T(x,y) * (x \ x)) = T(x * T(x,y),x). [para(562(a,1),138(a,1,2))]. 565 (T(x,y) * z) / (x * z) = x \ T(x,y). [para(19(a,1),563(a,1,1,2))]. 566 (x \ T(x,y)) \ (T(x,y) * z) = x * z. [para(565(a,1),66(a,1,1))]. 567 (x \ T(x,y)) \ z = x * (T(x,y) \ z). [para(20(a,1),566(a,1,2))]. 568 T(x * T(x,y),x) = x * (T(x,y) * 1). [para(60(a,1),564(a,1,2,2)),flip(a)]. 569 T(x * T(x,y),x) = x * T(x,y). [para(18(a,1),568(a,2,2))]. 571 T(x,x * T(x,y)) = x. [hyper(39,a,569,a)]. 572 T(x,y) / x = x \ T(x,y). [para(571(a,1),252(a,1,2))]. 573 (x \ T(x,y)) \ z = (x / T(x,y)) * z. [para(572(a,1),358(a,1,1))]. 574 (x \ T(x,y)) \ z = (T(x,y) \ x) * z. [para(299(a,1),573(a,2,1))]. 575 (T(x,y) \ x) * (T(x,y) * z) = x * z. [para(574(a,1),566(a,1))]. 576 (T(x,y) \ x) * z = x * (T(x,y) \ z). [para(574(a,1),567(a,1))]. 577 (x * y) / (T(x,z) * y) = T(x,z) \ x. [hyper(24,a,22,a,b,575,a),flip(a)]. 578 x * (T(x,y) \ 1) = T(x,y) \ x. [hyper(24,a,18,a,b,576,a),flip(a)]. 579 K(x,T(x,y) \ 1) = 1. [hyper(23,a,328,a,b,576,a),flip(a)]. 580 T(x,T(x,y) \ 1) = x. [hyper(41,a,579,a)]. 581 T(x,y) * (T(x,z) \ 1) = T(x,z) \ T(x,y). [para(580(a,1),329(a,1,2,1)),flip(a)]. 582 x \ (T(x,y) \ x) = T(x,y) \ 1. [hyper(23,a,20,a,b,578,a),flip(a)]. 583 ((T(x,y) \ x) * z) / (T(x,y) \ z) = R(x,T(x,y) \ 1,z). [para(578(a,1),324(a,1,1,1))]. 584 R(x \ 1,x * y,z) = R(x,y,z) \ 1. [para(348(a,2),344(a,1))]. 585 R(x,x \ y,z) \ 1 = R(x \ 1,y,z). [para(20(a,1),584(a,1,2)),flip(a)]. 586 (x * y) / (z * ((z \ x) * y)) = R(z,x,y) \ z. [para(213(a,1),500(a,1,2))]. 587 T(x \ R(x,y,z),x * (y * z)) = (x * (y * z)) \ ((x * y) * z). [para(537(a,1),84(a,1,1))]. 588 R(x * x,y,z) = x * x. [para(550(a,1),132(a,1))]. 589 R(T(x * x,y),z,u) = T(x * x,y). [para(588(a,1),46(a,2,1))]. 591 T(x * x,y) \ (z * u) = (T(x * x,y) \ z) * u. [para(589(a,1),197(a,1,1))]. 592 a(x / y,y,y \ 1) = (y / x) * (x * (y \ 1)). [para(554(a,2),358(a,1))]. 593 (x * y) / (z * ((z \ y) * T(x,y))) = R(z,y,T(x,y)) \ z. [para(82(a,1),586(a,1,1))]. 594 a(x,y,z) = (x \ (y * z)) \ ((x \ y) * z). [para(284(a,2),28(a,2))]. 595 (x \ (y * z)) * a(x,y,z) = (x \ y) * z. [para(594(a,2),20(a,1,2))]. 596 (x \ (y * (x \ 1))) * x = T(y,x) * (x \ 1). [para(378(a,1),329(a,1))]. 597 (T(x,y) * (y \ 1)) / y = y \ (x * (y \ 1)). [hyper(24,a,22,a,b,596,a),flip(a)]. 598 x \ (y * (x \ 1)) = T(y,x) / (x * x). [para(597(a,1),401(a,1))]. 599 x \ ((x * (x * y)) * (x \ 1)) = (x * (y * x)) / (x * x). [para(103(a,1),598(a,2,1))]. 600 T(x,y) / (y * y) = T(x / (y * y),y). [para(598(a,1),403(a,2)),flip(a)]. 601 x * ((y \ (y \ 1)) * z) = (x / (y * y)) * z. [para(416(a,1),428(a,1,1)),flip(a)]. 602 (x / (y * y)) * z = x * (y \ (y \ z)). [para(291(a,1),601(a,1,2)),flip(a)]. 603 L(x,y / (y * z),z) = x. [hyper(23,a,74,a,b,451,a),flip(a)]. 604 (x * (y / (y * x))) \ z = (y / (y * x)) \ (x \ z). [para(603(a,1),177(a,1)),flip(a)]. 605 T(x,x * (y / (y * x))) = x. [para(603(a,1),364(a,2))]. 606 (x * (y / (y * x))) \ z = ((y * x) / y) * (x \ z). [para(604(a,2),358(a,1))]. 607 x * (x * ((y * z) / ((x * y) * z))) = R(x,x * y,z). [para(95(a,1),211(a,1)),flip(a)]. 608 L(R(x,x,y),z,u) * (x * y) = (x * L(x,z,u)) * y. [para(214(a,1),184(a,2,1))]. 609 L(K(x,y),y * x,x * y) = K(y,x) \ 1. [para(30(a,2),260(a,2,1))]. 610 (x \ (y * z)) \ ((x \ y) * z) = a(x \ 1,y,z). [para(318(a,1),323(a,1,2,1))]. 611 a(x \ 1,y,z) = a(x,y,z). [para(610(a,1),594(a,2)),flip(a)]. 612 a(x / y,z,u) = a(y / x,z,u). [para(343(a,1),611(a,1,1))]. 613 L(x \ 1,y,x \ 1) * y = y * T(x \ 1,x * y). [para(485(a,1),336(a,2,2))]. 614 T(T((x * y) / (z * y),u),z) = R(T(z \ x,u),z,y). [para(556(a,2),46(a,2)),flip(a)]. 615 x * (x * (R(x,y,z) \ 1)) = R(x,x * y,z). [para(344(a,1),607(a,1,2,2))]. 616 (x * x) / R(x,y,z) = R(x,x * y,z). [para(615(a,1),263(a,1)),flip(a)]. 617 x * (R(x,y,z) \ x) = R(x,x * y,z). [para(543(a,1),615(a,1,2))]. 618 x \ R(x,x * y,z) = R(x,y,z) \ x. [hyper(23,a,20,a,b,617,a),flip(a)]. 619 x * (R(x,x * y,z) \ x) = R(x,(x * x) * y,z). [para(131(a,2),617(a,2,2))]. 620 x / R(x,x * y,z) = x \ R(x,y,z). [para(617(a,1),535(a,1,2))]. 621 (R(x,y,z) \ x) * x = R(x,x * y,z). [para(617(a,1),544(a,2))]. 622 R(x,x * y,z) \ x = x \ R(x,y,z). [para(620(a,1),498(a,1)),flip(a)]. 623 R(x,x * y,z) \ 1 = x \ (x \ R(x,y,z)). [para(620(a,1),547(a,1,2)),flip(a)]. 624 x \ R(x,x \ y,z) = R(x,y,z) \ x. [para(20(a,1),622(a,1,1,2)),flip(a)]. 625 x * (R(x,x * y,z) \ u) = (x \ R(x,y,z)) * u. [para(622(a,1),544(a,1,1)),flip(a)]. 626 R(x,(x * x) * y,z) = x * (x \ R(x,y,z)). [para(622(a,1),619(a,1,2)),flip(a)]. 627 R(x,(x * x) * y,z) = R(x,y,z). [para(626(a,2),20(a,1))]. 628 R(x,x * (x * y),z) = R(x,y,z). [para(131(a,1),627(a,1,2))]. 629 R(x,x \ y,z) = R(x,x * y,z). [para(20(a,1),628(a,1,2,2)),flip(a)]. 630 R(x,x * y,z) \ (y * z) = (x \ y) * z. [para(629(a,1),197(a,1,1))]. 631 R(x,x * (y / z),z) = y / ((x \ (y / z)) * z). [para(629(a,1),206(a,1))]. 632 R(x,x * y,z) \ 1 = R(x \ 1,y,z). [para(629(a,1),585(a,1,1))]. 633 R(x,x * y,z) = R(x \ 1,y,z) \ 1. [para(632(a,1),156(a,1,1)),flip(a)]. 634 x \ (x \ R(x,y,z)) = R(x \ 1,y,z). [para(632(a,1),623(a,1)),flip(a)]. 635 x * R(x \ 1,y,z) = x \ R(x,y,z). [para(634(a,1),20(a,1,2))]. 636 x * (R(x \ 1,y,z) * u) = x \ (R(x,y,z) * u). [para(634(a,1),265(a,1,2,1))]. 637 x * (R(x,x * y,z) \ u) = R(x,y,z) * (x \ u). [para(625(a,2),532(a,1))]. 638 x * (R(x \ 1,y,z) * u) = R(x,y,z) * (x \ u). [para(636(a,2),534(a,1))]. 639 x * (y * R(y \ (x \ y),z,u)) = R(x,z,u) * (x \ y). [para(366(a,2),638(a,1,2))]. 640 (x * L(x,y,z)) * u = L(x,y,z) * (x * u). [para(182(a,1),608(a,1,1,1)),flip(a)]. 641 L(x,y,z) \ ((x * L(x,y,z)) * u) = x * u. [hyper(23,a,20,a,b,640,a(flip)),flip(a)]. 642 L(x,y,z) * (x * u) = x * (L(x,y,z) * u). [para(640(a,1),484(a,1))]. 643 L(x,y,z) \ (x * (L(x,y,z) * u)) = x * u. [para(484(a,1),641(a,1,2))]. 644 x * (L(x,y,z) * (x \ u)) = L(x,y,z) * u. [para(20(a,1),642(a,1,2)),flip(a)]. 645 L(x,y,z) * (x * (L(x,y,z) \ u)) = x * u. [para(20(a,1),642(a,2,2))]. 646 (L(x,y,z) \ x) * (L(x,y,z) * u) = x * u. [para(643(a,1),524(a,1)),flip(a)]. 647 (x \ L(x,y,z)) * u = L(x,y,z) * (x \ u). [hyper(23,a,504,a,b,644,a),flip(a)]. 648 (x * y) / (x * (L(x,z,u) \ y)) = L(x,z,u). [hyper(24,a,22,a,b,645,a),flip(a)]. 649 (x * y) / (L(x,z,u) * y) = L(x,z,u) \ x. [hyper(24,a,22,a,b,646,a),flip(a)]. 650 (L(x,y,z) \ x) * u = x * (L(x,y,z) \ u). [para(20(a,1),646(a,1,2))]. 651 (L(x,y,z) \ x) \ u = L(x,y,z) * (x \ u). [para(647(a,1),518(a,2))]. 652 T(x,L(x,y,z) \ x) = x. [hyper(23,a,82,a,b,650,a),flip(a)]. 653 K(x,L(x,y,z) \ x) = 1. [hyper(40,a,652,a)]. 654 T(x \ 1,x * (y * y)) = T(x,y * y) \ 1. [para(202(a,1),380(a,2,1))]. 655 T(x,y * y) \ 1 = T(x \ 1,y * y). [para(654(a,1),431(a,1))]. 656 L(x,y,R(T(y,z),u,w)) = x. [hyper(23,a,74,a,b,436,a),flip(a)]. 657 L(x,y,R((y \ z) \ z,u,w)) = x. [para(83(a,1),656(a,1,3,1))]. 658 x \ ((y \ (y \ z)) * (y * (y * x))) = T(z,y * (y * x)). [para(285(a,1),444(a,1,2))]. 659 x \ (x * (x * (y * (x \ 1)))) = (x * (y * x)) / (x * x). [para(51(a,1),599(a,1,2))]. 660 x \ (T(y,z * z) * x) = T(y,z * (z * x)). [para(420(a,1),658(a,1,2))]. 661 T(T(x,y * y),z) = T(x,y * (y * z)). [para(660(a,1),36(a,2))]. 662 T(T(x,y),z * z) = T(x,z * (z * y)). [para(661(a,1),42(a,1)),flip(a)]. 663 x \ (x * T(y,x \ 1)) = (x * (y * x)) / (x * x). [para(347(a,1),659(a,1,2,2))]. 664 (x * (y * x)) / (x * x) = T(y,x \ 1). [para(663(a,1),19(a,1))]. 665 T(x * y,x) / (x * x) = T(x \ y,x \ 1). [para(138(a,1),664(a,1,1))]. 666 T((x * y) / (x * x),x) = T(x \ y,x \ 1). [para(665(a,1),600(a,1)),flip(a)]. 667 (x * (x * ((y * z) * u))) / (z * u) = R(x * (x * y),z,u). [para(51(a,1),94(a,1,1))]. 668 (x * (y \ 1)) / (x / y) = (x / y) \ (x * (y \ 1)). [para(434(a,1),481(a,1,2)),flip(a)]. 669 (x * (y \ 1)) / (x / y) = (y / x) * (x * (y \ 1)). [para(668(a,2),358(a,1))]. 670 (x * (T(x,y) \ z)) / (T(x,y) \ z) = R(x,T(x,y) \ 1,z). [para(576(a,1),583(a,1,1))]. 671 (x * y) / (L(x,z * y,z) * y) = R(z,y,T(x,y)) \ z. [para(455(a,1),593(a,1,2))]. 672 R(x,y,T(z,y)) \ x = L(z,x * y,x) \ z. [para(671(a,1),649(a,1))]. 673 (R(x,y,T(z,y)) \ x) \ 1 = z \ L(z,x * y,x). [para(672(a,2),511(a,1,1))]. 674 L(x,y * (y * z),y) \ x = y \ R(y,z,T(x,y * z)). [para(672(a,1),622(a,1))]. 676 x \ R(x,y,T(z,y)) = z \ L(z,x * y,x). [para(673(a,1),460(a,1)),flip(a)]. 677 R(x,y,T(z,y)) = x * (z \ L(z,x * y,x)). [para(676(a,1),20(a,1,2)),flip(a)]. 678 R(x,x * y,T(z,x * y)) = x * (z \ L(z,y,x)). [para(313(a,1),677(a,2,2,2))]. 679 R(x,y,T(z,x * y)) \ x = z \ L(z,y,x). [hyper(23,a,617,a,b,678,a(flip)),flip(a)]. 680 (x \ L(x,y,z)) * R(z,y,T(x,z * y)) = z. [para(679(a,1),496(a,1,1))]. 681 L(x,y,z) \ x = z \ R(z,y,T(x,z * y)). [para(313(a,1),674(a,1,1))]. 682 L(x,y,z) * (z \ R(z,y,T(x,z * y))) = x. [para(681(a,1),20(a,1,2))]. 683 R(x,y,T(z,x * y)) = x * (L(z,y,x) \ z). [para(681(a,2),20(a,1,2)),flip(a)]. 684 (x \ R(x,y,T(z,x * y))) * L(z,y,x) = z. [para(681(a,1),520(a,1,1))]. 685 L(x,R(y,z,u),T(y,w)) * (T(y,w) \ T(y,w)) = x. [para(527(a,1),682(a,1,2,2))]. 686 R(x,y,T(z,x * y)) * (x \ L(z,y,x)) = z. [para(684(a,1),532(a,1)),flip(a)]. 687 L(x,R(y,z,u),T(y,w)) * 1 = x. [para(60(a,1),685(a,1,2))]. 688 L(x,R(y,z,u),T(y,w)) = x. [hyper(24,a,18,a,b,687,a)]. 690 L(x,R(y / z,u,w),z \ y) = x. [para(84(a,1),688(a,1,3))]. 691 T(R(x,y,z),T(x,u)) / T(x,u) = T(x,u) \ R(x,y,z). [para(688(a,1),441(a,1,2))]. 692 R(T(x,T(x,y)),z,u) / T(x,y) = T(x,y) \ R(x,z,u). [para(46(a,2),691(a,1,1))]. 693 R(x,y,z) / T(x,u) = T(x,u) \ R(x,y,z). [para(115(a,1),692(a,1,1,1))]. 694 x * (x * (((y * z) * u) / (z * u))) = R(x * (x * y),z,u). [para(667(a,1),211(a,1)),flip(a)]. 695 R(x,T(x,y) \ 1,z) = x. [para(670(a,1),21(a,1))]. 696 R(x * (x * y),z,u) = x * (x * R(y,z,u)). [para(34(a,2),694(a,1,2,2)),flip(a)]. 697 x * (x * R(T(y,x),z,u)) = R(x * (y * x),z,u). [para(82(a,1),696(a,1,1,2)),flip(a)]. 698 R(x * (x * T(y,x * x)),z,u) = R(y,z,u) * (x * x). [para(696(a,2),226(a,1))]. 699 R(x * (y * x),z,u) = x * (R(y,z,u) * x). [para(110(a,1),697(a,1,2)),flip(a)]. 700 x \ R(x * (y * x),z,u) = R(y,z,u) * x. [hyper(23,a,20,a,b,699,a(flip)),flip(a)]. 701 (x * (y * x)) \ R(x * (z * x),u,w) = T(y,x) \ (x \ (R(z,u,w) * x)). [para(699(a,2),287(a,1,2))]. 702 x \ R(x * y,z,u) = R(y / x,z,u) * x. [para(22(a,1),700(a,1,2,1,2))]. 703 x \ R(x * y,z,u) = x * R(x \ y,z,u). [para(702(a,2),224(a,1))]. 704 L(x \ (y * R(y \ z,u,w)),x,y) = (y * x) \ R(y * z,u,w). [para(703(a,1),177(a,1,1,2))]. 705 R(x * (y * y),z,u) = R(x,z,u) * (y * y). [para(136(a,1),698(a,1,1))]. 706 (x \ 1) \ T(x \ 1,x * y) = ((x * y) \ y) * x. [para(156(a,1),385(a,2,2))]. 707 (x \ 1) \ T(x \ 1,x * y) = x * ((x * y) \ y). [para(706(a,2),381(a,1))]. 708 (x * y) * T(L(y \ 1,y,x),z) = (x * y) * T((x * y) \ x,z). [para(231(a,1),139(a,1))]. 709 R((x / y) * (z * z),z \ (z \ 1),y) = x / (z \ (z \ y)). [para(415(a,1),293(a,1,1))]. 710 x / (y \ (y \ z)) = (x / z) * (y * y). [para(709(a,1),426(a,1))]. 711 (x / (y * z)) * (y * y) = x / (y \ z). [para(19(a,1),710(a,1,2,2)),flip(a)]. 712 (x * y) / (z \ y) = R(x / z,z,y) * (z * z). [para(80(a,2),711(a,1,1)),flip(a)]. 713 R((x / y) * (y * y),y,z) = (x * z) / (y \ z). [para(712(a,2),705(a,2))]. 714 R(x / (y \ 1),y,z) = (x * z) / (y \ z). [para(397(a,1),713(a,1,1))]. 715 R(x,y,z) = ((x * (y \ 1)) * z) / (y \ z). [para(21(a,1),714(a,1,1))]. 716 R(L(x,y,z) \ x,x,u) = ((L(x,y,z) \ 1) * u) / (x \ u). [para(513(a,1),714(a,1,1))]. 717 R(x,y \ 1,z) = R(x,y,z). [para(715(a,2),324(a,1)),flip(a)]. 718 R(x,y,y) / y = x * (y \ 1). [para(717(a,1),207(a,1,1))]. 719 (x * (y \ 1)) \ R(x,y,y) = y. [para(717(a,1),209(a,1,2))]. 720 R(x / (y \ 1),y,y) = x * y. [para(717(a,1),210(a,1))]. 721 R(x,T(x,y),z) = x. [para(717(a,1),695(a,1))]. 722 (x * T(x,y)) * z = x * (T(x,y) * z). [para(721(a,1),79(a,1,1)),flip(a)]. 723 R(T(x / (y \ 1),z),y,y) / y = (y \ 1) * T((y \ 1) \ x,z). [para(718(a,2),139(a,1))]. 724 R(L(x / (y \ 1),z,u),y,y) / y = (y \ 1) * L((y \ 1) \ x,z,u). [para(718(a,2),215(a,1))]. 725 (T(x,y) * (R(x,z,u) \ 1)) \ T(x,y) = R(x,z,u). [para(527(a,1),719(a,1,2))]. 726 R(T(x / (y \ 1),z),y,y) = T(x * y,z). [para(720(a,1),46(a,2,1))]. 727 L(x,T(y,z),y) = x. [hyper(23,a,74,a,b,722,a),flip(a)]. 728 T(x,y) * (x * z) = x * (T(x,y) * z). [para(722(a,1),235(a,1)),flip(a)]. 729 x * (T(x,y) * (x \ z)) = T(x,y) * z. [para(722(a,1),281(a,1))]. 730 L(x,y,(z * y) / z) = x. [para(104(a,1),727(a,1,2))]. 731 L(x,(y \ z) \ z,y) = x. [para(83(a,1),727(a,1,2))]. 732 x \ (T(x,y) * z) = T(x,y) * (x \ z). [hyper(23,a,20,a,b,729,a),flip(a)]. 733 x \ (T(x,y) * z) = (x \ T(x,y)) * z. [para(732(a,2),562(a,2)),flip(a)]. 734 (R(x,y,z) \ T(x,u)) \ T(x,u) = R(x,y,z). [para(548(a,1),725(a,1,1))]. 735 R(L(x,y,z) \ x,x,u) = (L(x,y,z) \ u) / (x \ u). [para(318(a,1),716(a,2,1))]. 736 R(L(x,y,z) \ x,x,u) = L(x,y,z) \ x. [para(735(a,2),513(a,1))]. 738 L(x,y,y * x) \ z = ((y * x) \ y) * z. [para(19(a,1),396(a,1,1,2)),flip(a)]. 739 a(x,y,z) = T(x \ R(x,y,z),x * (y * z)). [para(587(a,2),28(a,2))]. 740 T(T(x \ R(x,y,z),u),x * (y * z)) = T(a(x,y,z),u). [para(739(a,2),42(a,1,1)),flip(a)]. 741 a(x,y,z) = T(T(R(x,y,z) / x,x * (y * z)),x). [para(739(a,2),112(a,2)),flip(a)]. 742 T((x * (y \ R(y,z,u))) / x,y * (z * u)) = (x * a(y,z,u)) / x. [para(739(a,2),233(a,1,1,2)),flip(a)]. 743 T(R(x,y,z) \ R(R(x,y,z),u,x),x * (R(x,y,z) * T(u,x))) = a(R(x,y,z),u,x). [para(530(a,2),739(a,2,2)),flip(a)]. 744 T(T((R(x,y,z) * u) / (x * u),x * (y * z)),x) = R(a(x,y,z),x,u). [para(739(a,2),614(a,2,1))]. 745 a(x,y,z) = T(T(x \ R(x,y,z),x * (y * z)),x). [para(478(a,1),741(a,2,1,1))]. 746 T(a(x,y,z),x) = a(x,y,z). [para(739(a,2),745(a,2,1)),flip(a)]. 747 a(x,y,z) * x = x * a(x,y,z). [para(746(a,1),82(a,1,2)),flip(a)]. 748 (x * a(x,y,z)) / x = a(x,y,z). [para(746(a,1),105(a,1,1,2))]. 749 ((x * (x * y)) * a(x * (x * y),z,u)) / y = a(x * (x * y),z,u) * (x * x). [para(747(a,1),418(a,1,1))]. 750 (x \ y) \ R(x \ z,u,w) = (x * y) \ R(x * z,u,w). [para(704(a,1),267(a,1)),flip(a)]. 751 (x * y) * T((x * y) \ x,z) = (x * y) * L(T(y \ 1,z),y,x). [para(44(a,2),708(a,1,2)),flip(a)]. 752 (x \ 1) * T((x \ 1) \ y,z) = T(y * x,z) / x. [para(726(a,1),723(a,1,1)),flip(a)]. 753 (x \ 1) * T(x * y,z) = T(y * x,z) / x. [para(330(a,1),752(a,1,2,1))]. 754 T(x * y,z) / y = y \ T(y * x,z). [para(753(a,1),318(a,1))]. 755 x \ T(x * (y / x),z) = T(y,z) / x. [para(22(a,1),754(a,1,1,1)),flip(a)]. 756 T(x * y,y) / y = (y \ x) * y. [para(754(a,2),146(a,1))]. 757 ((x \ y) * x) * x = T(y * x,x). [para(756(a,1),22(a,1,1))]. 758 T((x * y) * x,x) = (y * x) * x. [para(19(a,1),757(a,1,1,1)),flip(a)]. 759 (x * T(y * x,x)) / (x * x) = T((x \ y) * x,x \ 1). [para(757(a,1),664(a,1,1,2))]. 760 T((x \ y) * x,x \ 1) = ((y * x) * x) / (x * x). [para(82(a,1),759(a,1,1)),flip(a)]. 761 T((x \ y) * x,x \ 1) = R(y,x,x). [para(760(a,2),34(a,2)),flip(a)]. 762 (x * y) * T((x * y) \ x,z) = x * (y * T(y \ 1,z)). [para(751(a,2),74(a,1))]. 763 (x * (x * (y * z))) \ (x * (x * (y * (z * u)))) = L(u,z,x * (x * y)). [para(51(a,1),92(a,1,2))]. 764 (x * y) * T(L(y \ z,y,x),u) = (x * y) * T((x * y) \ (x * z),u). [para(232(a,1),139(a,1))]. 765 (x * y) * R(L(y \ 1,y,x),z,u) = (x * y) * R((x * y) \ x,z,u). [para(472(a,1),224(a,1))]. 766 L(R(x / (y \ 1),y,y),z,u) / y = (y \ 1) * L((y \ 1) \ x,z,u). [para(48(a,1),724(a,1,1))]. 767 T(T(x \ R(x,y,z),x * (y * z)),x) = R(a(x,y,z),x,u). [para(531(a,1),744(a,1,1,1))]. 769 R(a(x,y,z),x,u) = a(x,y,z). [para(767(a,1),745(a,2)),flip(a)]. 770 (a(x,y,z) * x) * u = a(x,y,z) * (x * u). [para(769(a,1),79(a,1,1)),flip(a)]. 771 L(x,y,a(y,z,u)) = x. [hyper(23,a,74,a,b,770,a),flip(a)]. 772 (x * a(x,y,z)) * u = a(x,y,z) * (x * u). [para(747(a,1),770(a,1,1))]. 773 L(x,y,z * (z * u)) = (u * y) \ (u * (y * x)). [para(763(a,1),212(a,1))]. 774 L(x,y,z * (z * u)) = L(x,y,u). [para(773(a,2),32(a,2)),flip(a)]. 776 L(x,y,z \ u) = L(x,y,z * u). [para(20(a,1),774(a,1,3,2)),flip(a)]. 777 L(x,y,(z / u) * z) = L(x,y,u). [para(22(a,1),774(a,1,3,2))]. 778 L(x,y,z * (u * z)) = L(x,y,T(u,z)). [para(82(a,1),774(a,1,3,2))]. 779 L(x,y,(z * u) * (u * z)) = L(x,y,K(u,z)). [para(69(a,1),774(a,1,3,2))]. 780 L(x,y,z * ((z \ u) * w)) = L(x,y,z * ((z * u) * w)). [para(89(a,1),774(a,1,3,2)),flip(a)]. 781 L(x,y,(z \ u) * w) = L(x,y,(z * u) * w). [para(89(a,1),774(a,1,3)),flip(a)]. 782 L(x,y,(z \ (z \ u)) * (z \ u)) = L(x,y,T(z,u)). [para(254(a,1),774(a,1,3,2))]. 783 L(x,y,(z * z) / u) = L(x,y,u \ 1). [para(263(a,1),774(a,1,3))]. 784 L(x,y,z / u) = L(x,y,u / z). [para(360(a,1),774(a,1,3))]. 785 L(x,y,z * L(z,u * z,u)) = L(x,y,a(u,z,z)). [para(453(a,2),774(a,1,3,2))]. 786 L(x,y,R(z * (z * u),w,v5)) = L(x,y,R(u,w,v5)). [para(696(a,2),774(a,1,3))]. 787 L(x,y,z \ 1) = L(x,y,z). [para(18(a,1),776(a,2,3))]. 788 L(x,y / z,z * y) = x. [para(776(a,1),236(a,1))]. 789 L(x,y,T(z / u,z)) = L(x,y,((u / z) * u) * u). [para(370(a,2),776(a,1,3))]. 790 L(x,y,y \ (z * z)) = x. [para(776(a,2),429(a,1))]. 791 L(x,(y \ z) \ u,z * (y * u)) = x. [para(776(a,1),508(a,1))]. 792 L(x \ (x / y),y,x * (x / y)) = ((x \ (x / y)) \ y) \ y. [para(776(a,1),442(a,1))]. 793 L(x,R(y / z,u,w),z * y) = x. [para(776(a,1),690(a,1))]. 794 L(x \ L(y \ z,y,u),x,u * y) = ((u \ y) * x) \ (u \ z). [para(776(a,1),275(a,1))]. 795 T(x * x,y) \ (y \ (x * x)) = y \ 1. [para(790(a,1),395(a,1)),flip(a)]. 796 L(x,L(y \ 1,z,u),y) = x. [para(787(a,1),503(a,1))]. 797 L(x,(y * z) \ y,z) = x. [para(787(a,1),505(a,1))]. 798 (x \ y) * L(z,y,x) = x \ (y * z). [para(787(a,1),560(a,1,2))]. 799 x * T(y \ 1,y * x) = L(y \ 1,x,y) * x. [para(787(a,1),613(a,1,1)),flip(a)]. 800 L(x,y \ z,z \ y) = x. [para(20(a,1),797(a,1,2,1))]. 801 L(x,y \ z,z * y) = x. [para(800(a,1),776(a,1)),flip(a)]. 802 L(x,y,z * (z / y)) = x. [para(66(a,1),801(a,1,2))]. 803 (x * L(x \ 1,y,z)) \ u = L(x \ 1,y,z) \ (x \ u). [para(796(a,1),177(a,1)),flip(a)]. 804 L(x,y,(z * (z * u)) * (z * w)) = L(x,y,u \ (z \ w)). [para(282(a,1),777(a,1,3,1))]. 805 L(x,y,(z * (z * u)) * z) = L(x,y,u \ (z \ 1)). [para(289(a,1),777(a,1,3,1))]. 806 L(L(x,y,y / z),z,z / y) = x. [para(784(a,1),304(a,1,1))]. 807 L(x,x,x / y) = y \ (y / (x \ 1)). [para(784(a,1),432(a,1))]. 808 L(x,y,z / (z * y)) = x. [para(784(a,1),730(a,1))]. 809 ((x / (x * y)) * y) \ (x / (x * y)) = y \ 1. [para(808(a,1),142(a,1)),flip(a)]. 810 ((x / (x * y)) * y) * z = (x / (x * y)) * (y * z). [para(808(a,1),74(a,1,2))]. 811 ((x / (x * y)) * y) \ z = y \ ((x / (x * y)) \ z). [para(808(a,1),177(a,1)),flip(a)]. 812 L(x,y / (z * (u * y)),z * (u \ 1)) = x. [para(350(a,1),793(a,1,2))]. 813 (x * (y \ z)) \ (x * (y \ (z * u))) = L(L(u,z,y),y \ z,x). [para(798(a,1),32(a,2,2,2)),flip(a)]. 814 (x \ y) * L(L(z,y,x),u,w) = x \ (y * L(z,u,w)). [para(49(a,1),798(a,1,2))]. 815 T(x,y) \ (x * z) = (T(x,y) \ x) * z. [para(234(a,1),798(a,1,2)),flip(a)]. 816 x \ (((y * x) / y) * z) = (x \ ((y * x) / y)) * z. [para(237(a,1),798(a,1,2)),flip(a)]. 817 (x \ y) * T((x \ y) \ 1,z) = x \ (y * T(y \ x,z)). [para(261(a,1),798(a,1,2))]. 818 L(x,y,T(z \ u,z)) = L(x,y,T(z * u,z)). [para(138(a,1),778(a,1,3)),flip(a)]. 819 L(x,y,T((z \ u) * z,z)) = L(x,y,z * T(u * z,z)). [para(757(a,1),778(a,1,3,2)),flip(a)]. 820 L(x,y,(z * z) / u) = L(x,y,u). [para(783(a,2),787(a,1))]. 821 L(x,y,T(z,z * (u * u))) = L(x,y,z \ (u * u)). [para(252(a,1),820(a,1,3)),flip(a)]. 822 L(x,y,z / (u * u)) = L(x,y,z). [para(820(a,1),784(a,1)),flip(a)]. 823 L(x,y,z * (u * u)) = L(x,y,z). [para(21(a,1),822(a,1,3)),flip(a)]. 824 L(x,y,(z * u) * u) = L(x,y,R(z,u,u)). [para(34(a,2),822(a,1,3)),flip(a)]. 825 (x * (y * (y * z))) \ ((x * (y * y)) * (z * u)) = L(u,z,x). [para(823(a,1),419(a,2))]. 826 (T(x,y) \ x) * y = T(y,T(x,y)). [para(815(a,1),107(a,1))]. 827 T(x,y) \ (x * z) = x * (T(x,y) \ z). [para(815(a,2),576(a,1))]. 828 x * (T(x,y) \ y) = T(y,T(x,y)). [para(826(a,1),576(a,1)),flip(a)]. 829 T(x,T(y,x)) / (T(y,x) \ x) = y. [hyper(24,a,22,a,b,828,a),flip(a)]. 830 x \ T(y,T(x,y)) = T(x,y) \ y. [hyper(23,a,20,a,b,828,a),flip(a)]. 831 (x * y) / (x * (T(x,z) \ y)) = T(x,z). [para(827(a,1),65(a,1,2))]. 832 (((x * y) * (y * x)) * z) \ (((x * y) * (y * x)) * (z * u)) = L(u,z,K(y,x)). [para(779(a,1),32(a,1)),flip(a)]. 833 (x * (y / (y * x))) \ (y / (y * x)) = x \ 1. [para(362(a,1),809(a,1,1))]. 834 T(x \ 1,x * (y / (y * x))) = x \ 1. [para(833(a,1),349(a,2))]. 835 L(x \ 1,y,x) * y = y * ((x * y) \ y). [para(349(a,1),799(a,1,2)),flip(a)]. 836 L(x,y,(z * (z \ u)) * (z \ u)) = L(x,y,T(z,u)). [para(782(a,1),781(a,1)),flip(a)]. 837 L(x,y,z * ((z \ u) * u)) = L(x,y,a(z,u,u)). [para(435(a,1),785(a,1,3))]. 838 L(x,y,R(z \ u,w,v5)) = L(x,y,R(z * u,w,v5)). [para(20(a,1),786(a,1,3,1,2)),flip(a)]. 839 L(x,y,T(z / u,z)) = L(x,y,R(u / z,u,u)). [para(789(a,2),824(a,1))]. 840 L(x,y,z * (z * (u * z))) = L(x,y,u \ (z \ 1)). [para(51(a,1),805(a,1,3))]. 841 (x * (y / (y * x))) * z = (y / (y * x)) * (x * z). [para(362(a,1),810(a,1,1))]. 842 (x * (y / (y * x))) \ z = x \ ((y / (y * x)) \ z). [para(362(a,1),811(a,1,1))]. 843 L(x,y,T(z,z * (u * u))) = L(x,y,z * (u * u)). [para(821(a,2),776(a,1))]. 844 L(x,y,z * (u \ z)) = L(x,y,T(u,z)). [para(20(a,1),836(a,1,3,1))]. 845 L(x,y,T(z / u,z)) = L(x,y,z * u). [para(66(a,1),844(a,1,3,2)),flip(a)]. 846 L(x,y,R(z / u,z,z)) = L(x,y,u * z). [para(845(a,1),839(a,1)),flip(a)]. 847 L(x,y,R((y \ z) * z,u,w)) = x. [para(838(a,1),657(a,1))]. 848 L(x,y,z \ (u \ 1)) = L(x,y,z * u). [para(840(a,1),774(a,1))]. 850 L(x,y,z * (u \ 1)) = L(x,y,z * u). [para(848(a,1),776(a,1)),flip(a)]. 851 L(x,y / (z * (u * y)),z * u) = x. [para(850(a,1),812(a,1))]. 852 L(x,(y * z) * (u / (y * (z * u))),y * z) = x. [para(851(a,1),303(a,1,1))]. 853 ((x * y) * z) / (x * (y * z)) = (x * y) * (z / (x * (y * z))). [para(851(a,1),196(a,1,2))]. 854 x \ ((y / (y * x)) \ z) = ((y * x) / y) * (x \ z). [para(842(a,1),606(a,1))]. 855 L(x,y,T(z,z * (u * u))) = L(x,y,z). [para(843(a,2),823(a,1))]. 856 L(x,y,T(z,u * u)) = L(x,y,z). [para(423(a,1),855(a,1,3))]. 858 L(x,y,R(T(z,u * u),w,v5)) = L(x,y,R(z,w,v5)). [para(46(a,2),856(a,1,3))]. 859 x \ (((y * x) / y) * z) = ((y * x) / y) * (x \ z). [para(358(a,1),854(a,1,2))]. 860 (x \ ((y * x) / y)) * z = ((y * x) / y) * (x \ z). [para(859(a,1),816(a,1)),flip(a)]. 861 L(x,y,z * ((z * u) * u)) = L(x,y,a(z,u,u)). [para(780(a,1),837(a,1))]. 862 L(x,y,z * (z * (u * (z * w)))) = L(x,y,u \ (z \ w)). [para(51(a,1),804(a,1,3))]. 863 L(x,y,T((z \ u) * z,z)) = L(x,y,(u * z) * z). [para(82(a,1),819(a,2,3))]. 864 L(x,y,T((z \ u) * z,z)) = L(x,y,R(u,z,z)). [para(863(a,2),824(a,1))]. 865 L(x,y,z \ (u \ w)) = L(x,y,z * (u * w)). [para(862(a,1),774(a,1))]. 867 L(x,y,z * (u \ w)) = L(x,y,z * (u * w)). [para(865(a,1),776(a,1)),flip(a)]. 868 L(x,y,z * (u * (u * w))) = L(x,y,z * w). [para(19(a,1),867(a,1,3,2)),flip(a)]. 869 L(x,y,(z \ u) * (u \ z)) = L(x,y,(u \ z) * (z * u)). [para(384(a,1),867(a,1,3))]. 871 ((x \ (x / y)) \ y) \ y = x \ (x / y). [para(792(a,1),802(a,1))]. 872 x / (y \ (y / x)) = (y \ (y / x)) \ x. [para(871(a,1),65(a,1,2))]. 873 (x * (y * (y * z))) \ (x * (y * (y * (z * u)))) = L(u,z,x). [para(411(a,1),825(a,1,2))]. 875 L(x,y * (y * z),u) = L(x,z,u). [para(873(a,1),93(a,1)),flip(a)]. 876 L(x,y \ z,u) = L(x,y * z,u). [para(20(a,1),875(a,1,2,2)),flip(a)]. 877 L(x,(y / z) * y,u) = L(x,z,u). [para(22(a,1),875(a,1,2,2))]. 878 L(x,y * (z * y),u) = L(x,T(z,y),u). [para(82(a,1),875(a,1,2,2))]. 879 L(x,(y * z) * (z * y),u) = L(x,K(z,y),u). [para(69(a,1),875(a,1,2,2))]. 880 L(x,(y \ z) * u,w) = L(x,(y * z) * u,w). [para(89(a,1),875(a,1,2)),flip(a)]. 881 L(x,T(y,y * z),u) = L(x,(y \ z) * z,u). [para(250(a,1),875(a,1,2,2)),flip(a)]. 882 L(x,(y * y) / z,u) = L(x,z \ 1,u). [para(263(a,1),875(a,1,2))]. 883 L(x,T(y \ 1,z),u) = L(x,z * (y \ z),u). [para(327(a,1),875(a,1,2,2)),flip(a)]. 884 L(x,y / z,u) = L(x,z / y,u). [para(360(a,1),875(a,1,2))]. 887 L(x,y \ 1,z) = L(x,y,z). [para(18(a,1),876(a,2,2))]. 888 (x * (y \ z)) * L(u,y * z,x) = x * ((y \ z) * u). [para(876(a,1),74(a,1,2))]. 889 L(x,(y \ z) * z,y) = x. [para(876(a,1),731(a,1))]. 890 L(x,y * z,z * y) = x. [para(876(a,1),801(a,1))]. 891 L(x,(y \ z) * u,z * (y * u)) = x. [para(876(a,1),791(a,1))]. 892 L(x,y * z,z / y) = x. [para(66(a,1),889(a,1,2,1))]. 893 (x * ((x \ y) * y)) \ z = ((x \ y) * y) \ (x \ z). [para(889(a,1),177(a,1)),flip(a)]. 894 ((x * y) * (y * x)) * z = (x * y) * ((y * x) * z). [para(890(a,1),74(a,1,2))]. 895 T(x * y,(x * y) * (y * x)) = T(x * y,y * x). [para(890(a,1),203(a,1)),flip(a)]. 896 L(x,K(y,z),z * y) = x. [para(890(a,1),315(a,1,1))]. 897 K(x,y) \ 1 = K(y,x). [para(890(a,1),609(a,1)),flip(a)]. 898 K(x,y) * K(y,x) = 1. [para(897(a,1),20(a,1,2))]. 899 1 / K(x,y) = K(y,x). [para(897(a,1),65(a,1,2))]. 900 K(x,y) \ z = K(y,x) * z. [para(897(a,1),318(a,1,1)),flip(a)]. 901 K(x,y) * (K(y,x) * z) = z. [para(897(a,1),321(a,1,2,1))]. 902 x / (K(y,z) * x) = K(z,y). [para(897(a,1),340(a,2))]. 903 T(x * y,K(y,x)) / (y * x) = K(x,y). [para(897(a,1),345(a,2))]. 904 R(K(x,y),K(y,x) * z,u) = R(K(y,x),z,u) \ 1. [para(897(a,1),584(a,1,1))]. 905 a(K(x,y),z,u) = a(K(y,x),z,u). [para(897(a,1),611(a,1,1))]. 906 R(K(x,y),K(x,y) * z,u) = R(K(y,x),z,u) \ 1. [para(897(a,1),633(a,2,1,1))]. 907 K(x,y) * (K(y,x) / (x * y)) = K(x,y) \ ((y * x) \ 1). [para(897(a,1),379(a,1,2,1))]. 908 R(x,K(y,z),u) = R(x,K(z,y),u). [para(897(a,1),717(a,1,2))]. 909 L(x,y,K(z,u)) = L(x,y,K(u,z)). [para(897(a,1),787(a,1,3))]. 910 L(K(x,y),z,K(y,x)) * z = z * ((K(y,x) * z) \ z). [para(897(a,1),835(a,1,1,1))]. 911 (x * y) * (K(y,x) * z) = (y * x) * z. [para(896(a,1),176(a,1,2)),flip(a)]. 912 K(x,y) \ ((y * x) \ z) = (x * y) \ z. [para(896(a,1),199(a,1))]. 914 L(x,x,y) = (y * (x \ 1)) \ y. [para(887(a,1),161(a,1))]. 915 x / L(y,y,x) = x * (y \ 1). [para(887(a,1),162(a,1,2))]. 916 L(L(x,y * (z \ 1),y),z,y) = x. [para(887(a,1),308(a,1))]. 917 L(x * y,x,y) = (y \ (x \ 1)) \ 1. [para(887(a,1),351(a,1))]. 918 L(x,y,L(y \ 1,z,u)) = x. [para(887(a,1),509(a,1))]. 919 (x * (y \ z)) / L(z,y,x) = x * (y \ 1). [para(887(a,1),333(a,1,2))]. 920 L(x * (y * z),x,y) = (y \ (x \ 1)) \ z. [para(887(a,1),352(a,1))]. 921 L(x,K(y,z),u) = L(x,K(z,y),u). [para(897(a,1),887(a,1,2))]. 922 T(x * y,K(y,x)) = K(x,y) * (y * x). [para(900(a,1),122(a,1)),flip(a)]. 923 R(K(x,y),K(y,x) * z,u) \ K(x,y) = K(x,y) \ R(K(x,y),z,u). [para(901(a,1),618(a,1,2,2)),flip(a)]. 924 (L(x \ 1,y,z) * x) \ u = x \ (L(x \ 1,y,z) \ u). [para(918(a,1),177(a,1)),flip(a)]. 925 L(x / y,x / y,z) = (z * (y / x)) \ z. [para(343(a,1),914(a,2,1,2))]. 926 L(K(x,y),K(x,y),z) = (z * K(y,x)) \ z. [para(897(a,1),914(a,2,1,2))]. 927 (x * y) * ((y / x) \ 1) = (x * y) / (y / x). [para(788(a,1),915(a,1,2)),flip(a)]. 928 L(x,(y * (y * z)) * (y * u),w) = L(x,z \ (y \ u),w). [para(282(a,1),877(a,1,2,1))]. 929 L(x,(y * (y * z)) * y,u) = L(x,z \ (y \ 1),u). [para(289(a,1),877(a,1,2,1))]. 930 K(x,y) / L(z,z,K(y,x)) = K(x,y) * (z \ 1). [para(909(a,1),915(a,1,2))]. 931 L(x,y * (z \ 1),y) = L(x,y * z,y). [para(916(a,1),303(a,1,1)),flip(a)]. 932 L(x,K(y,z),y * z) = x. [para(921(a,1),896(a,1))]. 933 ((x * y) \ K(x,y)) \ z = K(x,y) \ ((x * y) * z). [para(932(a,1),267(a,1)),flip(a)]. 934 L(x * y,x,y) * z = (y \ (x \ 1)) \ z. [para(917(a,2),318(a,1,1))]. 935 L(x,(y * y) / z,u) = L(x,z,u). [para(882(a,2),887(a,1))]. 936 L(x,y / (z * z),u) = L(x,y,u). [para(935(a,1),884(a,1)),flip(a)]. 937 L(x,y * (z * z),u) = L(x,y,u). [para(21(a,1),936(a,1,2)),flip(a)]. 938 L(x,(y * z) * z,u) = L(x,R(y,z,z),u). [para(34(a,2),936(a,1,2)),flip(a)]. 939 ((x * y) * z) / (K(x,y) * z) = y * x. [hyper(24,a,22,a,b,911,a),flip(a)]. 940 (x * y) \ ((y * x) * z) = K(y,x) * z. [hyper(23,a,20,a,b,911,a),flip(a)]. 941 K(x,y) * ((x * y) \ z) = (y * x) \ z. [para(912(a,1),20(a,1,2))]. 942 x * (y \ ((y * (x \ 1)) * z)) = L(z,y * x,y). [para(931(a,1),446(a,2))]. 943 L(x,K(y,z) * (y * z),u) = L(x,z * y,u). [para(939(a,1),935(a,1,2)),flip(a)]. 944 (x * y) \ (y * (x * z)) = K(y,x) * L(z,x,y). [para(74(a,1),940(a,1,2))]. 945 (x * (y \ 1)) * L(z,y,x) = x * (y \ z). [para(919(a,1),22(a,1,1))]. 946 (a(x,y,z) \ (x \ 1)) \ u = x * (a(x,y,z) * u). [para(920(a,1),771(a,1))]. 947 L(K(x,y),K(x,y),z) / z = (z * K(y,x)) \ 1. [para(926(a,2),320(a,1,1))]. 948 (a(x,y,z) \ (x \ 1)) \ u = (x * a(x,y,z)) * u. [para(771(a,1),934(a,1,1)),flip(a)]. 949 L(x,(y * z) * u,z * (y * u)) = x. [para(880(a,1),891(a,1))]. 950 L(x,(y * z) * u,T(y,z) * (z * u)) = x. [para(82(a,1),949(a,1,2,1))]. 951 L(x,T(y,y * z),u) = L(x,(y * z) * z,u). [para(881(a,2),880(a,1))]. 952 (x * y) / (y / x) = (x * y) * (x / y). [para(343(a,1),927(a,1,2)),flip(a)]. 953 L(x,(y * (y \ z)) * (y \ z),u) = L(x,T(y,z),u). [para(20(a,1),951(a,1,2,2)),flip(a)]. 954 x * (y * ((y \ (x \ 1)) * z)) = L(z,y * x,y). [para(213(a,1),942(a,1,2))]. 955 K(x,y) * L(x,y,x) = T(x,y * x). [para(944(a,1),36(a,2)),flip(a)]. 956 x * ((x \ (y \ 1)) * y) = a(x,y,y). [hyper(23,a,453,a(flip),b,954,a)]. 957 x * (y * (R(y,y * (x \ 1),z) \ ((x \ 1) * z))) = L(z,y * x,y). [para(630(a,2),954(a,1,2,2))]. 958 x * R(x \ 1,y \ 1,y) = a(x,y,y). [para(335(a,2),956(a,1,2))]. 959 x \ R(x,y \ 1,y) = a(x,y,y). [para(958(a,1),635(a,1)),flip(a)]. 960 x * R(x \ 1,y,y) = a(x,y,y). [para(717(a,1),958(a,1,2))]. 961 R(x,y \ 1,y) \ a(x,y,y) = T(x \ 1,R(x,y \ 1,y)). [para(959(a,1),325(a,2,2)),flip(a)]. 962 x \ R(x,y,y) = a(x,y,y). [para(717(a,1),959(a,1,2))]. 963 x * a(x,y,y) = R(x,y,y). [para(962(a,1),20(a,1,2))]. 964 a(x,y,y) \ R(x,y,y) = x. [para(962(a,1),480(a,1,1))]. 965 (R(x,y,y) \ x) * z = a(x,y,y) \ z. [para(962(a,1),465(a,1,1)),flip(a)]. 966 x * (a(x,y,y) * z) = R(x,y,y) * z. [para(962(a,1),501(a,1,2,1))]. 967 R(x \ 1,y,y) = x \ a(x,y,y). [para(962(a,1),634(a,1,2)),flip(a)]. 968 R(x,x * y,y) = a(x,y,y) \ x. [para(965(a,1),621(a,1)),flip(a)]. 969 T(x * y,K(y,x)) = T(x * y,y * x). [para(895(a,1),248(a,1)),flip(a)]. 970 T(x * y,K(y,x)) = (x \ 1) \ y. [para(969(a,2),439(a,1))]. 971 K(x,y) / T(y * x,K(x,y)) = (y * x) \ K(x,y). [para(969(a,2),257(a,1,2))]. 972 T(x * y,K(y,x)) = x * y. [para(970(a,2),330(a,1))]. 973 K(x,y) = (x * y) / (y * x). [para(972(a,1),903(a,1,1)),flip(a)]. 974 K(x,y) * (y * x) = x * y. [para(972(a,1),922(a,1)),flip(a)]. 975 (x * y) / (T(x,y) * y) = K(y,T(x,y)). [para(82(a,1),973(a,2,1)),flip(a)]. 976 (T(x,y) * y) / (x * y) = K(T(x,y),y). [para(82(a,1),973(a,2,2)),flip(a)]. 977 ((x * y) * z) / ((y * x) * z) = R(K(x,y),y * x,z). [para(973(a,2),80(a,1,1)),flip(a)]. 978 (x \ y) / (y * (x \ 1)) = K(x \ 1,y). [para(318(a,1),973(a,2,1)),flip(a)]. 979 ((K(x,y) * z) * K(y,x)) / z = K(K(x,y) * z,K(y,x)). [para(901(a,1),973(a,2,2)),flip(a)]. 980 K(x \ y,x) * y = (x \ y) * x. [para(20(a,1),974(a,1,2))]. 981 K(x * y,x) * y = (x \ y) * x. [para(495(a,1),980(a,1,1))]. 982 ((x \ y) * x) / y = K(x * y,x). [hyper(24,a,22,a,b,981,a),flip(a)]. 983 K(x,T(y,x)) = T(y,x) \ y. [para(975(a,1),577(a,1))]. 984 T(x,y) * K(y,T(x,y)) = x. [para(983(a,2),20(a,1,2))]. 985 K(x,T(y,x)) * T(y,x) = y. [para(983(a,2),298(a,1,1))]. 987 T(x,y) \ (x * z) = K(y,T(x,y)) * z. [para(983(a,2),815(a,2,1))]. 988 L(x,K(y,T(z,y)),u) = L(x,T(z,y) * z,u). [para(983(a,2),876(a,1,2))]. 989 (x \ y) * K(x,T(y / x,x)) = y / x. [para(84(a,1),984(a,1,1))]. 990 K(T(x,y),y) * x = T(x,y). [hyper(23,a,901,a,b,985,a),flip(a)]. 991 K(x,x \ y) * T(y / x,x) = y / x. [para(84(a,1),985(a,1,1,2))]. 992 K(T(x,y),y) = x \ T(x,y). [para(976(a,1),565(a,1))]. 993 x * K(T(x,y),y) = T(x,y). [para(992(a,2),20(a,1,2))]. 994 (x / y) \ T(x / y,y) = K(y \ x,y). [para(84(a,1),992(a,1,1)),flip(a)]. 995 K(T(x \ 1,y),y) = x * T(x \ 1,y). [para(992(a,2),330(a,1))]. 997 (x / y) * K(T(x / y,y),y) = y \ x. [para(993(a,2),84(a,1))]. 998 T(x,y) * (K(y,T(x,y)) * z) = x * z. [para(987(a,1),20(a,1,2))]. 999 K(x,T(y,x)) * (y \ z) = T(y,x) \ z. [para(20(a,1),987(a,1,2)),flip(a)]. 1000 (x \ y) * K(x,x \ y) = y / x. [para(84(a,1),989(a,1,2,2))]. 1001 (x \ y) * K(x,x * y) = y / x. [para(489(a,1),1000(a,1,2))]. 1002 (x \ y) \ (y / x) = K(x,x * y). [hyper(23,a,20,a,b,1001,a),flip(a)]. 1003 K(x,x * (x * y)) = y \ ((x * y) / x). [para(19(a,1),1002(a,1,1)),flip(a)]. 1004 K(x,x * y) * T(y / x,x) = y / x. [para(489(a,1),991(a,1,1))]. 1005 (x / y) \ T(x / y,y) = K(y * x,y). [para(994(a,2),495(a,1))]. 1006 (x / y) * K(y \ x,y) = y \ x. [para(84(a,1),997(a,1,2,1))]. 1007 (x / y) * K(y * x,y) = y \ x. [para(495(a,1),1006(a,1,2))]. 1008 (x / y) * (x \ y) = K(x * y,x). [hyper(23,a,359,a,b,1007,a),flip(a)]. 1009 K(x * y,x) / (x \ y) = x / y. [hyper(24,a,22,a,b,1008,a),flip(a)]. 1010 (x \ y) * (x / y) = K(x * y,x). [para(1008(a,1),368(a,1)),flip(a)]. 1011 (x \ y) \ K(x * y,x) = x / y. [hyper(23,a,20,a,b,1010,a),flip(a)]. 1012 L(x,y,(z \ u) * K(z * u,z)) = L(x,y,z / u). [para(1010(a,1),774(a,1,3,2))]. 1013 K(x,y) = y \ ((x * y) / x). [para(1003(a,1),490(a,1)),flip(a)]. 1014 (x * y) / x = y * K(x,y). [para(1013(a,2),20(a,1,2)),flip(a)]. 1015 x * (y / (y * x)) = K(y,x) \ 1. [para(1013(a,2),502(a,1,1)),flip(a)]. 1016 K(x,y) = ((x * y) / x) / y. [para(1013(a,2),558(a,2)),flip(a)]. 1017 ((x * y) / x) * (y \ z) = K(x,y) * z. [para(1013(a,2),860(a,1,1)),flip(a)]. 1018 (x * K(y,x)) * y = y * x. [para(1014(a,1),22(a,1,1))]. 1019 x / (x / y) = y * K(x / y,y). [para(22(a,1),1014(a,1,1))]. 1020 T(x * K(y,x),y) = x. [para(1014(a,1),104(a,1,1))]. 1021 L(x,y * K(z,y),y) = x. [para(1014(a,1),237(a,1,2))]. 1022 a(x / (x * y),z,u) = a(y * K(x,y),z,u). [para(1014(a,1),612(a,1,1)),flip(a)]. 1023 T(T(x * K(y,x),z),y) = T(x,z). [para(1020(a,1),42(a,1,1)),flip(a)]. 1024 T(x * K(y,x),z) * y = y * T(x,z). [para(1020(a,1),108(a,1,2,1)),flip(a)]. 1025 x / L(y,x * K(y,x),y) = y \ (x * K(y,x)). [para(1020(a,1),441(a,1,1))]. 1026 L(x,K(y,z),z) = x. [para(1021(a,1),303(a,1))]. 1027 (x * K(y,x)) \ z = K(y,x) \ (x \ z). [para(1021(a,1),270(a,1))]. 1028 (x * K(y,x)) * z = x * (K(y,x) * z). [para(1026(a,1),74(a,1,2))]. 1029 L(x,K(y,z),y) = x. [para(1026(a,1),921(a,1)),flip(a)]. 1030 (x * K(x,y)) * z = x * (K(x,y) * z). [para(1029(a,1),74(a,1,2))]. 1031 x \ (K(x,y) * z) = (x \ K(x,y)) * z. [para(1029(a,1),798(a,1,2)),flip(a)]. 1032 (x * K(y,x)) \ 1 = K(x,y) / x. [para(1029(a,1),947(a,1,1)),flip(a)]. 1033 (x * y) / x = K(x,y) * y. [para(1016(a,2),22(a,1,1)),flip(a)]. 1035 (x * K(y,x)) / x = K(y,x). [para(1014(a,1),1016(a,2,1)),flip(a)]. 1036 K(x,y) * y = y * K(x,y). [para(1033(a,1),1014(a,1))]. 1037 T(K(x,y),y) = K(x,y). [para(1035(a,1),104(a,1,1))]. 1038 T(x,K(y,x)) = x. [hyper(39,a,1037,a)]. 1040 T(x,y) * K(z,x) = K(z,x) * T(x,y). [para(1038(a,1),108(a,1,2,1)),flip(a)]. 1041 K(x,y) = x * (y / (y * x)). [para(1015(a,2),897(a,1)),flip(a)]. 1042 x \ K(x,y) = y / (y * x). [hyper(23,a,20,a,b,1041,a(flip)),flip(a)]. 1043 K(x,y) = (y / (y * x)) * x. [para(1041(a,2),362(a,2)),flip(a)]. 1044 K(x,y) / x = y / (y * x). [para(1041(a,2),363(a,1,1))]. 1045 x * ((y / (y * x)) * z) = K(x,y) * z. [para(1041(a,2),451(a,1,1)),flip(a)]. 1046 T(x,K(x,y)) = x. [para(1041(a,2),605(a,1,2))]. 1047 ((x * y) / x) * (y \ z) = K(y,x) \ z. [para(1041(a,2),606(a,1,1)),flip(a)]. 1048 T(x \ 1,K(x,y)) = x \ 1. [para(1041(a,2),834(a,1,2))]. 1049 (x / (x * y)) * (y * z) = K(y,x) * z. [para(1041(a,2),841(a,1,1)),flip(a)]. 1050 K(x,y) * x = x * K(x,y). [para(1046(a,1),82(a,1,2))]. 1051 T(x,T(y,x) \ y) = x. [para(983(a,1),1046(a,1,2))]. 1052 (T(x,y) \ x) * y = y * (T(x,y) \ x). [para(1051(a,1),82(a,1,2))]. 1053 K(x,y) = ((y * x) / y) \ x. [para(1043(a,2),358(a,2)),flip(a)]. 1054 K(x,y) / x = x \ K(x,y). [para(1044(a,2),1042(a,2)),flip(a)]. 1055 K(x,y) * (x \ 1) = x \ K(x,y). [para(1048(a,1),327(a,1,2))]. 1056 (x * K(y,x)) \ 1 = x \ K(x,y). [para(1032(a,2),1054(a,1))]. 1057 (x \ 1) / (x \ K(x,y)) = K(y,x). [para(1055(a,1),902(a,1,2))]. 1058 (x * K(y,x)) \ z = (x \ K(x,y)) * z. [para(1056(a,1),318(a,1,1)),flip(a)]. 1059 K(x,y) * (y * z) = ((x * y) / x) * z. [para(19(a,1),1017(a,1,2)),flip(a)]. 1060 T(x,y) * K(z,T(x,y)) = T(x * K(z,x),y). [hyper(24,a,1018,a,b,1024,a),flip(a)]. 1061 T(x * K(x \ y,x),y) = L(x,x \ y,x). [hyper(24,a,221,a,b,1024,a)]. 1062 T(x * K(y,x),x * y) = L(x,y,x). [hyper(24,a,217,a(flip),b,1024,a)]. 1063 (x * K(y,x)) \ z = K(x,y) * (x \ z). [para(1027(a,2),900(a,1))]. 1064 ((x * y) / x) * z = y * (K(x,y) * z). [para(1014(a,2),1028(a,1,1))]. 1065 x \ (K(x,y) * z) = (y / (y * x)) * z. [para(1042(a,1),1031(a,2,1))]. 1066 K(x,y) \ (x * z) = ((y * x) / y) * z. [para(19(a,1),1047(a,1,2)),flip(a)]. 1067 K(x,y) * (x \ z) = (y / (y * x)) * z. [para(20(a,1),1049(a,1,2)),flip(a)]. 1068 K(x,y) * (x * z) = x * (K(x,y) * z). [para(1049(a,1),1045(a,1,2)),flip(a)]. 1069 x * (T(y,x) \ y) = T(x,T(y,x)). [para(1052(a,1),826(a,1))]. 1070 x * K(x,T(y,x)) = T(x,T(y,x)). [para(983(a,2),1069(a,1,2))]. 1071 x / (K(y,z) * (y \ x)) = y * K(z,y). [para(1063(a,1),65(a,1,2))]. 1072 (x \ K(x,y)) * z = K(x,y) * (x \ z). [para(1063(a,1),1058(a,1)),flip(a)]. 1073 K(x,y) * (y * z) = y * (K(x,y) * z). [para(1064(a,1),1059(a,2))]. 1074 K(x,y) \ (x * z) = (K(y,x) * x) * z. [para(1033(a,1),1066(a,2,1))]. 1075 K(x,y) * (x \ (y * x)) = y. [para(1067(a,2),22(a,1))]. 1076 x \ (K(x,y) * z) = K(x,y) * (x \ z). [para(1067(a,2),1065(a,2))]. 1077 K(x,y) * T(y,x) = y. [para(36(a,2),1075(a,1,2))]. 1078 K(x,y / x) = K(x,x * y). [hyper(24,a,1004,a,b,1077,a)]. 1079 K(x,T(y,x)) = K(x,y). [hyper(24,a,985,a,b,1077,a),flip(a)]. 1080 K(x,y) = T(y,x) \ y. [hyper(24,a,298,a,b,1077,a)]. 1081 T(x,y) = K(x,y) * x. [hyper(23,a,901,a,b,1077,a)]. 1082 K(x,T(y,z)) * T(T(y,x),z) = T(y,z). [para(42(a,1),1077(a,1,2))]. 1083 K(x,R(y,z,u)) * R(T(y,x),z,u) = R(y,z,u). [para(46(a,2),1077(a,1,2))]. 1084 L(x \ y,x,K(z,y)) = (K(z,y) \ x) \ T(y,z). [para(1077(a,1),267(a,1,1,2))]. 1085 L(x,y,K(z,u) * u) = L(x,y,T(u,z)). [para(1077(a,1),774(a,1,3,2))]. 1086 K(x,y) = T(x,y) / x. [para(1077(a,1),902(a,1,2)),flip(a)]. 1087 (x * y) * T(y,x) = (y * x) * y. [para(1077(a,1),911(a,1,2)),flip(a)]. 1088 T(x,y) * T(x,y) = x * T(T(x,y),y). [para(1077(a,1),998(a,1,2))]. 1089 T(x,y) * K(y,x) = x. [para(1077(a,1),1040(a,2))]. 1090 (x / (x * y)) * T(x,y) = y \ x. [para(1077(a,1),1065(a,1,2)),flip(a)]. 1091 K(x,T(T(y,x),z)) = K(x,T(y,z)). [para(42(a,1),1079(a,1,2))]. 1092 K(x,x * (y * x)) = K(x,y). [para(1079(a,1),491(a,2))]. 1093 T(x,y) \ (x * z) = K(y,x) * z. [para(1079(a,1),987(a,2,1))]. 1094 T(x,y) * (K(y,x) * z) = x * z. [para(1079(a,1),998(a,1,2,1))]. 1095 K(x,y) * (y \ z) = T(y,x) \ z. [para(1079(a,1),999(a,1,1))]. 1096 T(x,T(y,x)) = x * K(x,y). [para(1079(a,1),1070(a,1,2)),flip(a)]. 1097 T(T(x,y),z) \ T(x,z) = K(y,T(x,z)). [para(42(a,1),1080(a,2,1)),flip(a)]. 1098 K(x,y) * (T(y,x) * z) = y * z. [para(1080(a,2),575(a,1,1))]. 1099 x * (T(x,y) \ z) = K(y,x) * z. [para(1080(a,2),576(a,1,1)),flip(a)]. 1100 K(x,y) = y * (T(y,x) \ 1). [para(1080(a,2),578(a,2)),flip(a)]. 1101 T(x,y) \ 1 = x \ K(y,x). [para(1080(a,2),582(a,1,2)),flip(a)]. 1102 (x * y) / (T(x,z) * y) = K(z,x). [para(1080(a,2),577(a,2))]. 1103 ((x * y) * y) \ ((y * x) * y) = K(y,(y * x) * y). [para(758(a,1),1080(a,2,1)),flip(a)]. 1104 T(x,y) = (x * x) / (x * K(y,x)). [para(1080(a,2),831(a,1,2,2)),flip(a)]. 1105 K(T(x,y),y) = K(x,y). [hyper(24,a,990,a,b,1081,a(flip)),flip(a)]. 1106 (x * T(y,z)) / L(y,K(y,z),x) = x * K(y,z). [para(1081(a,2),99(a,1,1,2))]. 1107 T(x,y) = x * K(x,y). [para(1081(a,2),1050(a,1))]. 1108 K(x,y) = x \ T(x,y). [para(1086(a,2),572(a,1))]. 1109 R(T(x,y),z,u) * K(y,R(x,z,u)) = R(x,z,u). [para(46(a,2),1089(a,1,1))]. 1110 K(R(T(x,y),z,u),y) = K(R(x,z,u),y). [para(46(a,2),1105(a,1,1))]. 1111 x * T(x \ 1,y) = K(x \ 1,y). [para(1105(a,1),995(a,1)),flip(a)]. 1112 T(x * K(y,x),T(y,x)) = x. [para(1105(a,1),1020(a,1,1,2))]. 1113 K(x,y) * T(x,y) = T(T(x,y),y). [para(1105(a,1),1081(a,2,1)),flip(a)]. 1114 K(x,y) * T(K(y,x),z) = K(K(y,x),z). [hyper(23,a,901,a,b,1107,a(flip)),flip(a)]. 1115 (x * y) \ (x * T(y,z)) = L(K(y,z),y,x). [para(1107(a,2),32(a,2,2,2)),flip(a)]. 1116 x * (y * K(y,x)) = y * x. [para(1107(a,1),82(a,1,2))]. 1117 (x * y) * L(K(y,z),y,x) = x * T(y,z). [para(1107(a,2),74(a,2,2))]. 1118 (x \ y) * K(x * y,x) = T(x \ y,x). [para(495(a,1),1107(a,2,2)),flip(a)]. 1119 L(x,y,z * T(z,u)) = L(x,y,K(z,u)). [para(1107(a,2),774(a,1,3,2))]. 1120 x * (K(x,y) * z) = T(x,y) * z. [para(1107(a,2),1030(a,1,1)),flip(a)]. 1121 T(x,y) * K(x,y) = T(T(x,y),y). [para(1105(a,1),1107(a,2,2)),flip(a)]. 1122 T(x,y) \ T(T(x,z),y) = K(T(x,y),z). [para(42(a,1),1108(a,2,2)),flip(a)]. 1123 L(x,y,z) \ L(T(x,u),y,z) = K(L(x,y,z),u). [para(44(a,2),1108(a,2,2)),flip(a)]. 1124 x \ ((x \ y) \ y) = K(x,x * y). [para(249(a,1),1108(a,2,2)),flip(a)]. 1125 T(x,y) * (x \ z) = K(x,y) * z. [para(1108(a,2),562(a,1,1)),flip(a)]. 1126 K(x \ 1,x * y) = x * ((x * y) \ y). [para(1108(a,2),707(a,1))]. 1127 x \ (T(x,y) * z) = K(x,y) * z. [para(1108(a,2),733(a,2,1))]. 1128 K(x / y,y) = K(y * x,y). [para(1108(a,2),1005(a,1))]. 1129 x * K(y,y * x) = y * (x / y). [para(1078(a,1),121(a,1,2))]. 1130 K(x,(y * (x \ 1)) / x) = K(x,T(y,x \ 1)). [para(347(a,1),1078(a,2,2))]. 1131 T(x,T(y,x)) = T(x,y). [para(1096(a,2),1107(a,2)),flip(a)]. 1132 T(T(x,y),T(z,x)) = T(T(x,z),y). [para(1131(a,1),42(a,1,1)),flip(a)]. 1133 T(x,y / x) = T(x,x \ y). [para(84(a,1),1131(a,1,2)),flip(a)]. 1134 (x * y) / T(y,x) = T(x,y). [para(1131(a,1),117(a,1,2))]. 1135 L(T(x,y),T(y,x),x) = T(x,x * T(y,x)). [para(1131(a,1),203(a,1,1))]. 1136 T(x,x * (y * x)) = T(x,y). [para(1131(a,1),247(a,2))]. 1137 T(x,y) / (T(y,x) \ x) = y. [para(1131(a,1),829(a,1,1))]. 1138 T(x,y) \ y = x \ T(y,x). [para(1131(a,1),830(a,1,2)),flip(a)]. 1139 T(x,y * K(x,y)) = T(x,y). [para(1020(a,1),1131(a,1,2)),flip(a)]. 1140 K(x,y) * K(z,K(y,x)) = T(K(y,x),z) \ 1. [hyper(23,a,901,a,b,1100,a(flip)),flip(a)]. 1141 L(T(x,y),y * K(x,y),T(x,y)) = (T(x,y) \ (y * K(x,y))) \ y. [para(1112(a,1),440(a,1,2)),flip(a)]. 1143 K((x * (y \ 1)) / y,y) = K(T(x,y \ 1),y). [para(347(a,1),1128(a,2,1))]. 1144 x / (x / y) = y * K(y * x,y). [para(1128(a,1),1019(a,2,2))]. 1145 T(x,y / x) = T(x,x * y). [para(1133(a,2),246(a,1))]. 1146 T(x,y) * T(y,x) = x * y. [para(1134(a,1),22(a,1,1))]. 1147 x / (y \ T(x,y)) = T(y,x). [para(1138(a,1),65(a,1,2))]. 1148 (T(x,y) \ y) * K(x,x * T(y,x)) = T(y,x) / x. [para(1138(a,2),1001(a,1,1))]. 1149 T(x,(y * (x \ 1)) / x) = T(x,T(y,x \ 1)). [para(347(a,1),1145(a,2,2))]. 1150 (T(x,y) * (T(y,x) * z)) \ ((x * y) * z) = a(T(x,y),T(y,x),z). [para(1146(a,1),28(a,2,2,1)),flip(a)]. 1151 (x * y) \ (T(x,y) * (T(y,x) * z)) = L(z,T(y,x),T(x,y)). [para(1146(a,1),32(a,2,1)),flip(a)]. 1152 T(T(x,y),x \ T(y,x)) = (x \ T(y,x)) \ y. [para(1147(a,1),84(a,1,1))]. 1153 R(x,y,x) * (y * x) = (y * x) * T(x,y). [para(1087(a,2),79(a,2))]. 1154 T(x,y) * ((y * x) / ((x * y) * x)) = K(T(x,y),y * x). [para(1087(a,1),1041(a,2,2,2)),flip(a)]. 1155 K(x,T(y,K(z,T(y,x)))) = K(x,T(y,x)). [para(1038(a,1),1091(a,1,2)),flip(a)]. 1156 L(x,y * K(z,y),u) = L(x,T(y,z),u). [para(1094(a,1),937(a,1,2))]. 1157 T(x,y) * (y * x) = x * (x * y). [para(974(a,1),1094(a,1,2))]. 1158 K(x,y) * (T(x,y) \ z) = x \ z. [hyper(23,a,901,a,b,1095,a),flip(a)]. 1159 K(x,y) * (y \ x) = y \ T(x,y). [para(1095(a,2),1138(a,1))]. 1160 K(x,y) * (x * z) = T(x,y) * z. [hyper(23,a,901,a,b,1098,a),flip(a)]. 1161 K(x,y / x) * ((x \ y) * z) = (y / x) * z. [para(84(a,1),1098(a,1,2,1))]. 1162 R(K(x,y),T(y,x) * z,u) \ 1 = ((T(y,x) * z) * u) / ((y * z) * u). [para(1098(a,1),344(a,1,2,1)),flip(a)]. 1163 x \ (K(y,x) * z) = T(x,y) \ z. [hyper(23,a,20,a,b,1099,a),flip(a)]. 1164 (x * y) * T((x * y) \ x,z) = x * K(y \ 1,z). [para(1111(a,1),762(a,2,2))]. 1165 x \ (y * T(y \ x,z)) = K((x \ y) \ 1,z). [para(1111(a,1),817(a,1)),flip(a)]. 1166 (x * ((K(x,y) * z) * u)) \ ((T(x,y) * z) * u) = a(x,K(x,y) * z,u). [para(1120(a,1),28(a,2,2,1)),flip(a)]. 1167 ((T(x,y) * z) * u) / ((K(x,y) * z) * u) = R(x,K(x,y) * z,u). [para(1120(a,1),34(a,2,1,1)),flip(a)]. 1168 T(x,y) * (T(y,x) * z) = x * (y * z). [para(1098(a,1),1120(a,1,2)),flip(a)]. 1169 L(x,y,z * ((z \ u) * u)) = L(x,y,K(z,z * u)). [para(1124(a,1),865(a,1,3)),flip(a)]. 1170 T(x,y) \ ((x \ T(y,x)) \ y) = K(T(x,y),T(x,y) * y). [para(1138(a,1),1124(a,1,2,1))]. 1171 T(x,y) \ (K(x,y) * z) = x \ z. [hyper(23,a,20,a,b,1125,a),flip(a)]. 1172 K(x,y) * (z * x) = T(x,y) * T(z,x). [para(36(a,2),1125(a,1,2)),flip(a)]. 1173 T(x / y,z) * y = K(x / y,z) * x. [para(66(a,1),1125(a,1,2))]. 1174 T(x,y) * (z / (z * x)) = K(x,y) * K(x,z). [para(1042(a,1),1125(a,1,2))]. 1175 T(x,y) * (T(x,z) \ 1) = K(x,y) * K(z,x). [para(1101(a,2),1125(a,1,2))]. 1176 x \ T(T(x,y),y) = K(x,y) * K(x,y). [para(1121(a,1),1127(a,1,2))]. 1177 T(T(x,x * y),T(z,x)) = T(T(x,z),x \ y). [para(246(a,1),1132(a,1,1))]. 1178 (x / (x / y)) * z = y * (K(y * x,y) * z). [para(1144(a,2),1028(a,1,1))]. 1179 ((x * y) * T(y,x)) \ (y * (y * x)) = K(T(y,x),x * y). [para(1157(a,1),30(a,2,2)),flip(a)]. 1180 (x * (x * y)) \ (T(x,y) * ((y * x) * z)) = L(z,y * x,T(x,y)). [para(1157(a,1),32(a,2,1)),flip(a)]. 1181 K(x,y) * (T(x,y) \ T(x,z)) = K(x,z). [para(1158(a,2),1108(a,2)),flip(a)]. 1182 K(T(x,y \ 1),y) * (x * (y \ 1)) = y \ T(T(x,y \ 1),y). [para(326(a,1),1159(a,1,2))]. 1183 ((T(x,y) * z) * u) / ((x * z) * u) = R(K(x,y),x * z,u). [para(1160(a,1),34(a,2,1,1)),flip(a)]. 1184 (x * y) \ (T(x,z) * y) = T(K(x,z),x * y). [para(1160(a,1),36(a,2,2)),flip(a)]. 1185 L(x,T(y,z) * z,u) = L(x,z * y,u). [para(1160(a,1),943(a,1,2))]. 1186 T(x,y) \ (T(y,x) \ z) = x \ (y \ z). [para(1158(a,1),1163(a,1,2)),flip(a)]. 1187 T(x,y) \ (y * K(x,y)) = x \ y. [para(1036(a,1),1171(a,1,2))]. 1188 x \ (y * K(x,y)) = K(x,y) * (x \ y). [para(1187(a,1),1158(a,1,2)),flip(a)]. 1189 (K(x,y) * (x \ z)) \ ((x \ K(x,y)) * (z * u)) = L(u,z,x \ K(x,y)). [para(1072(a,1),32(a,2,1)),flip(a)]. 1190 (K(x,y) * z) \ (y * (K(x,y) * z)) = L(T(y,z),z,K(x,y)). [para(1073(a,1),106(a,1,2))]. 1191 K(x,y) \ (x * z) = (K(x,y) \ x) * z. [para(900(a,2),1074(a,2,1))]. 1192 L(x,y,(z * u) / z) = L(x,y,T(u,z)). [para(1033(a,2),1085(a,1,3))]. 1193 T(x,y) * K(y,T(x,z)) = K(z,T(x,y)) * T(x,z). [para(1097(a,1),1099(a,1,2))]. 1194 L(x,y,(z / (u * u)) * (u \ (z * (u \ 1)))) = L(x,y,K(z / (u * u),u)). [para(403(a,1),1119(a,1,3,2))]. 1195 (x * T(y,x)) \ (T(y,z) * x) = L(K(T(y,x),z),T(y,x),x). [para(1122(a,1),180(a,1,1)),flip(a)]. 1196 K(x,T(y,K(z,T(y,x)))) = K(x,y). [para(1155(a,2),1079(a,1))]. 1197 K(x,y) * T(T(y,x),K(z,T(y,x))) = T(y,K(z,T(y,x))). [para(1196(a,1),1082(a,1,1))]. 1198 (x * (y * z)) / (T(y,x) * z) = T(x,y). [hyper(24,a,22,a,b,1168,a),flip(a)]. 1199 (x \ y) * (T(x,y / x) * z) = (y / x) * (x * z). [para(84(a,1),1168(a,1,1))]. 1200 (T(x / y,z) * y) / x = K(x / y,z). [hyper(24,a,22,a,b,1173,a(flip)),flip(a)]. 1201 K(x / y,z) * x = y * T(y \ x,z). [para(1173(a,1),139(a,1))]. 1202 (R(x,y,z) * (K(x,u) * K(x,u))) / T(T(x,u),u) = x \ R(x,y,z). [para(1176(a,1),536(a,1,1,2))]. 1203 L(x,y,K(y,z)) = x. [hyper(23,a,798,a,b,1191,a(flip)),flip(a)]. 1204 L(x,y,T(z,y) \ z) = x. [para(983(a,1),1203(a,1,3))]. 1205 L(x,y,T(z,y) * z) = x. [para(1204(a,1),776(a,1)),flip(a)]. 1206 L(x,y,z * T(z,y)) = x. [para(116(a,1),1205(a,1,3))]. 1207 ((x * T(x,y)) * y) \ ((x * T(x,y)) * (y * z)) = z. [para(1206(a,1),32(a,1)),flip(a)]. 1208 L(x,y,T(z * u,z) / z) = L(x,y,T((z \ u) * z,z)). [para(138(a,1),1192(a,1,3,1))]. 1209 (x * (R(y,z,u) * w)) / (R(T(y,x),z,u) * w) = T(x,R(y,z,u)). [para(46(a,2),1198(a,1,2,1))]. 1210 (x * (y * (a(T(y,x),z,z) * u))) / (R(T(y,x),z,z) * u) = T(x,y). [para(966(a,1),1198(a,1,2))]. 1211 (x * T(x \ y,z)) / y = K(y / x,z). [para(139(a,1),1200(a,1,1))]. 1212 K((x * y) / x,z) * (x * y) = x * T(y,z). [para(19(a,1),1201(a,2,2,1))]. 1213 x \ (y * T(y \ x,z)) = T(K(x / y,z),x). [para(1201(a,1),36(a,2,2)),flip(a)]. 1214 ((x * y) * T((x * y) \ ((z * x) * y),u)) / ((z * x) * y) = K(R(z,x,y),u). [para(34(a,2),1211(a,2,1))]. 1215 T(x * K(x * y,x),y) = L(x,x \ y,x). [para(495(a,1),1061(a,1,1,2))]. 1216 L(T(x,y),T(y,x),x) = T(x,y * x). [para(82(a,1),1135(a,2,2))]. 1217 (x * y) * T(y,y * (x * y)) = R(y,x,y) * (x * y). [para(1136(a,2),1153(a,2,2)),flip(a)]. 1218 T(x * K(x * y,x),y) = L(x,x * y,x). [para(1215(a,2),312(a,1))]. 1219 T(x / (x / y),x) = L(y,y * x,y). [para(1144(a,2),1218(a,1,1))]. 1220 K(x,T(y,x \ 1)) = K(x,y / (x * x)). [para(401(a,1),1130(a,1,2)),flip(a)]. 1221 K(T(x,y \ 1),y) = K(x / (y * y),y). [para(401(a,1),1143(a,1,1)),flip(a)]. 1222 T(x,T(y,x \ 1)) = T(x,y / (x * x)). [para(401(a,1),1149(a,1,2)),flip(a)]. 1223 K(((x * y) \ x) \ 1,z) = (x * y) \ (x * T(y,z)). [para(19(a,1),1165(a,1,2,2,1)),flip(a)]. 1224 T(x,y) \ T(x,z) = K(x,z) * K(y,x). [para(1175(a,1),581(a,1)),flip(a)]. 1225 K(x,y) * (K(x,z) * K(y,x)) = K(x,z). [para(1224(a,1),1181(a,1,2))]. 1226 K(x,y) * K(z,x) = K(z,x) * K(x,y). [hyper(23,a,901,a,b,1225,a)]. 1229 T(T(x,y),x \ z) = T(T(x,y),x * z). [para(1177(a,1),1132(a,1))]. 1230 T(T(x,y),x * T(y,x)) = (x \ T(y,x)) \ y. [para(1229(a,1),1152(a,1))]. 1231 (x / (x / y)) * x = y * ((y \ x) * y). [para(981(a,1),1178(a,2,2))]. 1232 T(x * y,x) = (y / (y / x)) * y. [para(1231(a,2),138(a,1)),flip(a)]. 1233 T(x * y,x) / y = y / (y / x). [hyper(24,a,22,a,b,1232,a(flip)),flip(a)]. 1234 ((x / y) / x) * T(y * x,y) = x. [hyper(23,a,359,a,b,1232,a(flip)),flip(a)]. 1235 L(x,T(y * z,y),u) = L(x,z / y,u). [para(1232(a,2),877(a,1,2))]. 1236 x \ T(x * y,y) = x / (x / y). [para(1233(a,1),754(a,1)),flip(a)]. 1237 x / T(y * x,y) = (x / y) / x. [hyper(24,a,22,a,b,1234,a),flip(a)]. 1238 T(x * y,y) = x * (x / (x / y)). [para(1236(a,1),20(a,1,2)),flip(a)]. 1239 T(x * (y \ x),y \ x) = x * (x / y). [para(65(a,1),1238(a,2,2,2))]. 1240 T(K(x / y,z),x) = K((x \ y) \ 1,z). [para(1213(a,1),1165(a,1))]. 1241 K((x \ (y \ x)) \ 1,z) = T(K(y,z),x). [para(65(a,1),1240(a,1,1,1)),flip(a)]. 1242 K((T(x,y) \ (T(y,x) \ x)) \ 1,z) = T(K(y,z),T(x,y)). [para(1137(a,1),1240(a,1,1,1)),flip(a)]. 1243 K(T(x \ 1,y) \ 1,z) = T(K(x,z),y). [para(325(a,2),1241(a,1,1,1))]. 1244 K(T((x \ 1) \ 1,y * y),z) = T(K(x,z),y * y). [para(655(a,1),1243(a,1,1))]. 1245 (x \ T(y,x)) \ y = T(T(x,y),y * x). [para(82(a,1),1230(a,1,2)),flip(a)]. 1246 x / L(y,T(x,y),y) = y \ (x * K(y,x)). [para(1156(a,1),1025(a,1,2))]. 1247 x / L(y,T(x,y),y) = K(y,x) * (y \ x). [para(1246(a,2),1188(a,1))]. 1248 L(x \ y,x,K(z,y)) = (K(y,z) * x) \ T(y,z). [para(900(a,1),1084(a,2,1))]. 1249 R(K(x,y),T(x,y) * z,u) \ 1 = R(K(y,x),x * z,u). [para(1098(a,1),906(a,1,2)),flip(a)]. 1250 L(x,y * (y * (z * y)),u) = L(x,z \ (y \ 1),u). [para(51(a,1),929(a,1,2))]. 1251 ((x * y) \ K(x,y)) \ z = K(y,x) * ((x * y) * z). [para(933(a,2),900(a,1))]. 1252 (x * a(x,y,z)) * u = x * (a(x,y,z) * u). [para(948(a,1),946(a,1))]. 1253 a(x,y,z) * (x * u) = x * (a(x,y,z) * u). [para(1252(a,1),772(a,1)),flip(a)]. 1254 x * (a(x,y,z) * (x \ u)) = a(x,y,z) * u. [para(20(a,1),1253(a,1,2)),flip(a)]. 1255 L(x,y * (z \ y),u) = L(x,T(z,y),u). [para(20(a,1),953(a,1,2,1))]. 1256 L(x,T(y \ 1,z),u) = L(x,T(y,z),u). [para(1255(a,1),883(a,2))]. 1257 K(x,y) / (y * x) = (y * x) \ K(x,y). [para(972(a,1),971(a,1,2))]. 1258 L(x,y,T(z \ u,z)) = L(x,y,z / u). [para(1118(a,1),1012(a,1,3))]. 1259 L(x,y,T(z * u,z)) = L(x,y,z / u). [para(1258(a,1),818(a,1)),flip(a)]. 1260 (T(x,y) \ y) * K(x,y * x) = T(y,x) / x. [para(82(a,1),1148(a,1,2,2))]. 1261 L(x,y,K(z,z * u)) = L(x,y,a(z,u,u)). [para(1169(a,1),837(a,1))]. 1262 L(x,y,K(z * u,z)) = L(x,y,a(z,u,u)). [para(1261(a,1),909(a,1)),flip(a)]. 1263 L(x,y,a(z,u * z,u * z)) = L(x,y,K(z,u)). [para(1092(a,1),1261(a,1,3)),flip(a)]. 1264 K(x,T(y,z)) * T(T(y,x),K(x,T(y,z))) = K(z,T(y,x)) * T(y,z). [para(1193(a,1),82(a,2))]. 1265 (x \ y) * (T(x,x * y) * z) = (y / x) * (x * z). [para(1145(a,1),1199(a,1,2,1))]. 1266 (x * (T(x,y) * y)) \ ((x * T(x,y)) * (y * z)) = z. [para(722(a,1),1207(a,1,1))]. 1267 L(K(x,y),x,z) = K(((z * x) \ z) \ 1,y). [para(1223(a,2),1115(a,1)),flip(a)]. 1268 K(L(x \ 1,x,y) \ 1,z) = L(K(x,z),x,y). [para(142(a,2),1267(a,2,1,1)),flip(a)]. 1269 K(T(x,y * y),z) = T(K(x,z),y * y). [para(156(a,1),1244(a,1,1,1))]. 1270 K(T(x,y * y),z) \ 1 = T(K(x,z) \ 1,y * y). [para(1269(a,2),655(a,1,1))]. 1271 L(x,y \ (z \ 1),u) = L(x,y * z,u). [para(1250(a,1),875(a,1))]. 1273 L(x,y * (z \ 1),u) = L(x,y * z,u). [para(1271(a,1),876(a,1)),flip(a)]. 1274 (x \ y) * ((y / x) * (x * z)) = ((x \ y) * y) * z. [para(1265(a,1),253(a,1,2))]. 1275 (x * (T(x,y) * y)) \ (x * (T(x,y) * (y * z))) = z. [para(722(a,1),1266(a,1,2))]. 1276 T(K(x,y) \ 1,z * z) = K(y,T(x,z * z)). [para(1270(a,1),897(a,1))]. 1277 K(x,T(y,z * z)) = T(K(x,y),z * z). [para(897(a,1),1276(a,1,1)),flip(a)]. 1278 K(T(x,y * y),z) = K(x,T(z,y * y)). [para(1277(a,2),1269(a,2))]. 1279 L(L(x,y,T(z,y)),T(z,y) * y,z) = x. [para(1275(a,1),174(a,1)),flip(a)]. 1280 L(L(x,y,T(z,y)),y * z,z) = x. [para(1279(a,1),1185(a,1)),flip(a)]. 1281 L(L(x,y,T(y \ z,y)),z,y \ z) = x. [para(20(a,1),1280(a,1,2))]. 1282 L(x,y * (z * y),y) = L(x,z,T(y,z)). [para(1280(a,1),303(a,1,1))]. 1283 L(x,T(y,z) * z,T(y,z)) = L(x,z * y,y). [para(308(a,1),1280(a,1,1)),flip(a)]. 1284 L(x,T(y,z),z) = L(x,y,T(z,y)). [para(1280(a,1),314(a,1,1))]. 1285 L(x,T(y,y * z),y * z) = L(x,y,y / z). [para(1284(a,2),1259(a,1))]. 1286 L(L(x,y,y / z),z,y \ z) = x. [para(1258(a,1),1281(a,1,1))]. 1287 L(L(x,y,y / z),z,y * z) = x. [para(1286(a,1),776(a,1)),flip(a)]. 1288 L(x,y,z / y) = L(x,y,z * y). [para(304(a,1),1287(a,1,1)),flip(a)]. 1289 L(x \ (x / y),x,y * x) = y \ 1. [para(445(a,1),1287(a,1,1))]. 1290 L(x,y,y / z) = L(x,y,z * y). [para(806(a,1),1287(a,1,1)),flip(a)]. 1291 L(x,y,(z * y) * y) = L(x,y,z). [para(21(a,1),1288(a,1,3)),flip(a)]. 1292 L(x \ 1,x,y * x) = y \ (y / x). [para(1288(a,1),144(a,1))]. 1293 L(x,x,y * x) = y \ (y / (x \ 1)). [para(1288(a,1),432(a,1))]. 1294 x * L(y,z,x * z) = (x / z) * (z * y). [para(1288(a,1),173(a,1,2))]. 1295 (x \ 1) \ L(T(y \ (y / x),z),y,x * y) = K(L(y \ (y / x),y,x * y),z). [para(1289(a,1),1123(a,1,1))]. 1296 ((x * y) * y) \ (x * y) = x \ (x / y). [para(1292(a,1),142(a,1)),flip(a)]. 1297 L(x,y \ 1,T(y * z,y \ 1)) = L(x,(y * z) * z,y * z). [para(322(a,1),1282(a,1,2,2)),flip(a)]. 1298 x * K(L(y \ 1,y,x * y) \ 1,z) = (x / y) * (y * K(y,z)). [para(1268(a,2),1294(a,1,2))]. 1299 x \ L(x,x * y,y) = a(T(y,x),x,x). [para(1283(a,1),452(a,1,2))]. 1300 L(x,y * z,T(z,y)) = L(x,y * z,z). [para(1283(a,1),1185(a,1)),flip(a)]. 1301 T(L(K(x,y),z,K(y,x)),z) = (K(y,x) * z) \ z. [hyper(23,a,82,a,b,910,a(flip)),flip(a)]. 1302 L(x,y * x,x) = R(x,y,x). [hyper(24,a,217,a(flip),b,1217,a(flip)),flip(a)]. 1303 R(x,y / x,x) = L(x,y,x). [para(22(a,1),1302(a,1,2)),flip(a)]. 1304 L(T(x,y),z * x,x) = T(R(x,z,x),y). [para(1302(a,1),44(a,2,1))]. 1305 L(x,y,x) * ((y / x) * x) = (x * (y / x)) * x. [para(1303(a,1),79(a,1,1))]. 1306 L(T(x,y),z * x,x) = R(T(x,y),z,x). [para(1304(a,2),46(a,2)),flip(a)]. 1307 L(x,y,x) * y = (x * (y / x)) * x. [para(22(a,1),1305(a,1,2))]. 1308 T(L(x,y,x) * y,x) = ((y / x) * x) * x. [para(1307(a,2),758(a,1,1))]. 1309 T(L(x,y,x) * y,x) = y * x. [para(22(a,1),1308(a,2,1))]. 1310 (L(x,y,x) * y) * x = x * (y * x). [para(1309(a,1),82(a,1,2)),flip(a)]. 1311 L(R(x,y,x),y,x) = x. [hyper(24,a,184,a,b,1310,a(flip)),flip(a)]. 1312 R(L(x,y,x),y,x) = x. [hyper(24,a,79,a,b,1310,a(flip)),flip(a)]. 1313 R(x,x \ y,x) = L(x,y,x). [para(1311(a,1),302(a,1,1)),flip(a)]. 1314 L(x,x * y,x) = R(x,y,x). [para(1311(a,1),303(a,1,1))]. 1315 R(x,x * y,x) = L(x,y,x). [para(1311(a,1),308(a,1,1)),flip(a)]. 1316 x \ T(y * x,y) = R(y,x,y). [para(1314(a,1),316(a,1)),flip(a)]. 1317 R(x,y,x) * (x \ y) = (x \ y) * T(x,y). [para(1314(a,1),559(a,1,1))]. 1318 T(x * K(x * y,x),y) = R(x,y,x). [para(1314(a,1),1218(a,2))]. 1319 T(x / (x / y),x) = R(y,x,y). [para(1314(a,1),1219(a,2))]. 1320 L(x,y,x) \ x = x \ R(x,y,x). [para(1315(a,1),622(a,1,1))]. 1321 x * R(y,x,y) = T(y * x,y). [para(1316(a,1),20(a,1,2))]. 1322 T(x,R(y,x,y)) = T(x,x / (x / y)). [para(1319(a,1),1131(a,1,2))]. 1323 (x / T(y * x,y)) * T(x,R(y,x,y)) = R(y,x,y) \ x. [para(1321(a,1),1090(a,1,1,2))]. 1324 T(x,y) * K(x * y,T(x,y)) = R(x,y,x). [para(1318(a,1),1060(a,2))]. 1325 T(x,y) * K(y * T(x,y),T(x,y)) = R(x,y,x). [para(82(a,2),1324(a,1,2,1))]. 1326 K(x,y) * (K(y,x) / (x * y)) = (x * y) \ 1. [para(907(a,2),912(a,1))]. 1327 K(x,y) * ((x * y) \ K(y,x)) = (x * y) \ 1. [para(1257(a,1),1326(a,1,2))]. 1328 (x * y) \ K(x,y) = (y * x) \ 1. [para(1327(a,1),941(a,1)),flip(a)]. 1329 K(x,y) * ((y * x) * z) = ((x * y) \ 1) \ z. [para(1328(a,1),1251(a,1,1)),flip(a)]. 1330 K(x,y) * ((y * x) * z) = (x * y) * z. [para(1329(a,2),330(a,1))]. 1331 ((x * y) * z) / ((y * x) * z) = K(x,y). [hyper(24,a,22,a,b,1330,a),flip(a)]. 1332 R(K(x,y),y * x,z) = K(x,y). [para(1331(a,1),977(a,1)),flip(a)]. 1333 R(K(x,T(y,x)),T(y,x) * x,z) = K(x,y). [para(1332(a,2),1079(a,1))]. 1335 R(K(x,y),T(y,x) * x,z) = K(x,y). [para(1079(a,1),1333(a,1,1))]. 1336 ((T(x,y) * y) * z) / ((K(y,x) * (T(x,y) * y)) * z) = K(y,x) \ 1. [para(1335(a,1),344(a,2,1))]. 1337 (x * L(x \ 1,y,z)) \ u = x \ (L(x \ 1,y,z) \ u). [para(216(a,1),924(a,1,1))]. 1338 L(x,y * (y * (z * (y * u))),w) = L(x,z \ (y \ u),w). [para(51(a,1),928(a,1,2))]. 1339 T(x,y) * (R(x,y,x) \ 1) = K(T(x,y),y * x). [para(344(a,1),1154(a,1,2))]. 1340 R(x,y,x) \ T(x,y) = K(T(x,y),y * x). [para(1339(a,1),548(a,1)),flip(a)]. 1341 T(x,y) \ T(T(x,y),y * x) = K(T(x,y),T(x,y) * y). [para(1245(a,1),1170(a,1,2))]. 1342 (((x * y) * T(y,x)) \ (y * y)) * x = K(T(y,x),x * y). [para(1179(a,1),391(a,1)),flip(a)]. 1343 T(x,K(y,T(x,z))) = K(z,x) * T(x,z). [para(1038(a,1),1197(a,1,2)),flip(a)]. 1345 T(x,K(y,T(x,z))) = x. [para(1343(a,2),1077(a,1))]. 1346 T(T(x,y),K(z,T(x,u))) = T(x,y). [para(1345(a,1),42(a,1,1)),flip(a)]. 1350 L(x,y,T(z * u,z) / z) = L(x,y,R(u,z,z)). [para(1208(a,2),864(a,1))]. 1351 T(K(x,y),T(z,x)) = K((z \ (x \ z)) \ 1,y). [para(1186(a,1),1242(a,1,1,1)),flip(a)]. 1352 T(K(x,y),T(z,x)) = T(K(x,y),z). [para(1351(a,2),1241(a,1))]. 1353 T(x,y) * T(K(y,z),x) = K(y,z) * T(x,y). [para(1352(a,1),82(a,1,2))]. 1354 K(x,y) * (K(y,z) * x) = K(y,z) * T(x,y). [para(1353(a,1),1172(a,2))]. 1355 (K(x,y) * T(z,x)) / L(z,K(x,y),K(z,x)) = K(z,x) * K(x,y). [para(1354(a,1),99(a,1,1))]. 1356 ((x / y) / x) * T(x,R(y,x,y)) = R(y,x,y) \ x. [para(1237(a,1),1323(a,1,1))]. 1357 L(x \ 1,y,z) \ (x \ u) = x \ (L(x \ 1,y,z) \ u). [para(1337(a,1),803(a,1)),flip(a)]. 1358 L(x,y \ (z \ u),w) = L(x,y * (z * u),w). [para(1338(a,1),875(a,1))]. 1360 L(x,y * (z \ u),w) = L(x,y * (z * u),w). [para(1358(a,1),876(a,1)),flip(a)]. 1361 L(x,y * (z * (z * u)),w) = L(x,y * u,w). [para(19(a,1),1360(a,1,2,2)),flip(a)]. 1362 L(x,(y \ z) * (z \ y),u) = L(x,(z \ y) * (y * z),u). [para(384(a,1),1360(a,1,2))]. 1363 L(x,y * R(z,z * u,w),v5) = L(x,y * (R(z,u,w) \ 1),v5). [para(615(a,1),1361(a,1,2,2))]. 1364 K(T(x,y),T(x,y) * y) = K(T(x,y),y * x). [para(1341(a,1),1108(a,2)),flip(a)]. 1365 (((x * y) * x) \ (x * x)) * y = K(T(x,y),y * x). [para(1087(a,1),1342(a,1,1,1))]. 1366 K(T(x,y),y * x) = K(x,x * y). [para(1365(a,1),408(a,1))]. 1367 R(x,y,x) \ T(x,y) = K(x,x * y). [para(1366(a,1),1340(a,2))]. 1368 K(x,x * y) \ T(x,y) = R(x,y,x). [para(1367(a,1),734(a,1,1))]. 1369 K(x * y,x) * T(x,y) = R(x,y,x). [para(1368(a,1),900(a,1)),flip(a)]. 1370 R(x,y,x) / T(x,y) = K(x * y,x). [hyper(24,a,22,a,b,1369,a),flip(a)]. 1371 (x \ (L(x \ 1,x,x / y) \ 1)) * (y \ (y / x)) = x \ 1. [para(1357(a,1),521(a,1,1))]. 1372 R(x,y \ 1,y) \ a(x,y,y) = x \ 1. [para(961(a,2),476(a,1))]. 1374 R(x,y,y) \ a(x,y,y) = x \ 1. [para(717(a,1),1372(a,1,1))]. 1375 (x * y) \ (x * (y * z)) = L(z,T(y,x),T(x,y)). [para(1168(a,1),1151(a,1,2))]. 1376 L(x,T(y,z),T(z,y)) = L(x,y,z). [para(1375(a,1),32(a,2)),flip(a)]. 1377 L(T(x,y),y,K(z,x)) = T(x,K(z,x) * y). [para(1190(a,1),36(a,2)),flip(a)]. 1378 (x \ (L(x \ 1,x,y * x) \ 1)) * (y \ (y / x)) = x \ 1. [para(1290(a,1),1371(a,1,1,2,1))]. 1379 ((x \ y) * z) \ (x \ u) = ((x * y) * z) \ (x * u). [para(794(a,1),201(a,1))]. 1380 (x * ((x \ y) * y)) \ z = ((x * y) * y) \ (x * z). [para(1379(a,1),893(a,2))]. 1381 (x * ((x \ y) * y)) \ y = x \ (x / y). [para(1380(a,2),1296(a,1))]. 1382 x / (y \ (y / x)) = y * ((y \ x) * x). [para(1381(a,1),65(a,1,2))]. 1383 (x \ (x / y)) \ y = x * ((x \ y) * y). [para(1382(a,1),872(a,1)),flip(a)]. 1384 x * L(x,y * x,y) = (y \ (y / x)) \ x. [para(1383(a,2),435(a,2))]. 1385 (x * L(x,y * x,y)) / x = (y \ (y / x)) \ 1. [para(1384(a,2),320(a,1,1))]. 1386 L(x,y * x,y) = (y \ (y / x)) \ 1. [para(1385(a,1),218(a,1)),flip(a)]. 1387 x \ ((y \ (y / x)) \ 1) = a(y,x,x). [para(1386(a,1),452(a,1,2))]. 1388 (x \ (x / y)) \ 1 = y * a(x,y,y). [para(1386(a,1),453(a,1))]. 1389 (x \ 1) \ (L(x,x,y * x) \ 1) = a(y,x \ 1,x \ 1). [para(1293(a,2),1387(a,1,2,1))]. 1390 (x \ (x / y)) \ z = (y * a(x,y,y)) * z. [para(1388(a,1),318(a,1,1)),flip(a)]. 1391 K(x,(x * x) / (y \ (y / z))) = K(x,z * a(y,z,z)). [para(1388(a,1),492(a,2,2))]. 1392 L(x \ 1,x,y * x) \ 1 = x * a(y,x,x). [para(1292(a,2),1388(a,1,1))]. 1393 (x \ (x * a(y,x,x))) * (y \ (y / x)) = x \ 1. [para(1392(a,1),1378(a,1,1,2))]. 1394 a(x,y,y) * (x \ (x / y)) = y \ 1. [para(19(a,1),1393(a,1,1))]. 1396 a(K(x,y),z,z) * (K(y,x) \ (K(y,x) / z)) = z \ 1. [para(905(a,1),1394(a,1,1))]. 1397 a(x,y,y) * (x / y) = x * (y \ 1). [para(1394(a,1),1254(a,1,2)),flip(a)]. 1398 (x * (y \ 1)) / (x / y) = a(x,y,y). [hyper(24,a,22,a,b,1397,a),flip(a)]. 1399 (x / y) * (y * (x \ 1)) = a(y,x,x). [para(1398(a,1),669(a,1)),flip(a)]. 1400 a(x / y,y,y \ 1) = a(x,y,y). [para(1399(a,1),592(a,2))]. 1401 a(x * (y * y),y \ 1,(y \ 1) \ 1) = a(x * y,y \ 1,y \ 1). [para(400(a,1),1400(a,1,1))]. 1402 K(x,(y \ (y / z)) \ 1) = K(x,z * a(y,z,z)). [para(1391(a,1),492(a,1)),flip(a)]. 1403 a(K(x,y),z,z) * (K(x,y) * (K(y,x) / z)) = z \ 1. [para(900(a,1),1396(a,1,2))]. 1404 K(x,y) * (a(K(x,y),z,z) * (K(y,x) / z)) = z \ 1. [para(1403(a,1),1253(a,1)),flip(a)]. 1405 R(K(x,y),z,z) * (K(y,x) / z) = z \ 1. [para(1404(a,1),966(a,1)),flip(a)]. 1406 x * (L(x,x,y * x) \ 1) = a(y,x \ 1,x \ 1). [para(1389(a,1),330(a,1)),flip(a)]. 1407 a(x,y \ 1,y \ 1) = L(y,y,x * y) \ y. [para(1406(a,1),471(a,1))]. 1408 a(x * y,y \ 1,y \ 1) = L(y,y,x) \ y. [para(1291(a,1),1407(a,2,1))]. 1409 (x * (y \ z)) \ (x * (y \ (z * u))) = L(L(u,z,y),y * z,x). [para(813(a,2),876(a,1))]. 1410 (x * y) * (z / (x * (y * z))) = x \ R(x,y,z). [para(853(a,1),537(a,1))]. 1411 L(x,y \ R(y,z,u),y * z) = x. [para(1410(a,1),852(a,1,2))]. 1412 L(x,y * R(y,z,u),y * z) = x. [para(1411(a,1),876(a,1)),flip(a)]. 1413 L(x,y * R(y,y * z,u),z) = x. [para(1412(a,1),774(a,1)),flip(a)]. 1414 K(T(x,y \ 1),y) * (x * (y \ 1)) = T(x,y) * (y \ 1). [para(1182(a,2),329(a,1))]. 1415 K(T(x,y \ 1),y) = K(x,y). [hyper(24,a,1160,a,b,1414,a)]. 1416 (x * (y \ 1)) / (T(x,y) * (y \ 1)) = K(y,T(x,y \ 1)). [para(1414(a,1),902(a,1,2))]. 1418 K(x / (y * y),y) = K(x,y). [para(1415(a,1),1221(a,1)),flip(a)]. 1419 K(x,T(y,x \ 1)) = K(x,y). [para(1416(a,1),1102(a,1))]. 1420 K(x \ 1,T(y,x)) = K(x \ 1,y). [para(156(a,1),1419(a,1,2,2))]. 1421 T(x,T(y,x \ 1)) = x * K(x,y). [para(1419(a,1),1107(a,2,2))]. 1423 K(x,y / (x * x)) = K(x,y). [para(1419(a,1),1220(a,1)),flip(a)]. 1424 K(x,R(y / x,x,x)) = K(x,y * x). [para(80(a,2),1423(a,1,2))]. 1425 ((x \ 1) * T(y,x)) / (x \ 1) = T(y,x) * K(x \ 1,y). [para(1420(a,1),1014(a,2,2))]. 1426 T(x,T(y,x \ 1)) = T(x,y). [para(1421(a,2),1107(a,2)),flip(a)]. 1427 T(x \ 1,T(y,x)) = T(x \ 1,y). [para(156(a,1),1426(a,1,2,2))]. 1428 T(x,y / (x * x)) = T(x,y). [para(1426(a,1),1222(a,1)),flip(a)]. 1429 L(x,T(y,z),T(T(z,y \ 1),y)) = L(x,y,T(z,y \ 1)). [para(1426(a,1),1376(a,1,2))]. 1430 T(x,(y * x) * x) = T(x,R(y,x,x)). [para(34(a,2),1428(a,1,2)),flip(a)]. 1431 L(x,T(y \ 1,z),T(T(z,y),y \ 1)) = L(x,y \ 1,T(z,y)). [para(1427(a,1),1376(a,1,2))]. 1432 (x \ T(y,x)) / (x \ 1) = T(y,x) * K(x \ 1,y). [para(318(a,1),1425(a,1,1))]. 1433 T(x,y) * K(y \ 1,x) = T(x,y * y). [para(1432(a,1),486(a,1))]. 1434 L(x,T(y,z),T(T(z,y),y \ 1)) = L(x,y,T(z,y \ 1)). [para(42(a,1),1429(a,1,3))]. 1435 L(x,R(y,z,z),y * z) = L(x,y \ 1,T(y * z,y \ 1)). [para(1297(a,2),938(a,1)),flip(a)]. 1436 L(x,R(y,z,z),y * z) = L(x,y,T(y * z,y \ 1)). [para(1435(a,2),887(a,1))]. 1437 L(x,y * R(z,z * u,w),v5) = L(x,y * R(z,u,w),v5). [para(1363(a,2),1273(a,1))]. 1438 L(x,y * R(y,z,u),z) = x. [para(1437(a,1),1413(a,1))]. 1439 L(x,y * (z * R(z,y,u)),y) = x. [para(1438(a,1),303(a,1,1))]. 1440 L(x,y \ R(y \ 1,z,u),z) = x. [para(318(a,1),1438(a,1,2))]. 1441 (x * (y \ R(y,x,z))) * u = x * ((y \ R(y,x,z)) * u). [para(1438(a,1),888(a,1,2))]. 1442 a(x,x * (y * R(y,x,z)),u) = 1. [hyper(38,a,1439,a)]. 1443 L(x,y * R(y \ 1,z,u),z) = x. [para(1440(a,1),876(a,1)),flip(a)]. 1444 L(x,a(y,z,z),z) = x. [para(960(a,1),1443(a,1,2))]. 1445 x / (a(y,x,x) \ 1) = x * a(y,x,x). [para(1444(a,1),145(a,1,2))]. 1446 (x * a(y,x,x)) * z = x * (a(y,x,x) * z). [para(1444(a,1),74(a,1,2))]. 1447 K(x,(y \ (y / z)) \ 1) = K(x,z / (a(y,z,z) \ 1)). [para(1445(a,2),1402(a,2,2))]. 1448 (x \ (x / y)) \ z = y * (a(x,y,y) * z). [para(1446(a,1),1390(a,2))]. 1449 L(x * (a(y,x,x) * z),y * (y / x),y) = (y / x) \ (y * z). [para(1448(a,1),311(a,1,1))]. 1450 (x * (y \ R(y,x,z))) * u = x * (R(y,x,z) * (y \ u)). [para(532(a,1),1441(a,2,2))]. 1451 L(x,T(y,z),T(T(z,y),y \ 1)) = L(x,y \ 1,T(z,y)). [para(1431(a,1),1256(a,1)),flip(a)]. 1452 L(x,y \ 1,T(z,y)) = L(x,y,T(z,y \ 1)). [para(1451(a,1),1434(a,1))]. 1453 L(x,y,T(z,y \ 1)) = L(x,y,T(z,y)). [para(1452(a,1),887(a,1))]. 1454 L(x,R(y,z,z),y * z) = L(x,y,T(y * z,y)). [para(1453(a,1),1436(a,2))]. 1455 L(x,R(y,z,z),y * z) = L(x,y,y / z). [para(1454(a,2),1259(a,1))]. 1456 L(x,R(y,z,z),y * z) = L(x,y,z * y). [para(1455(a,2),1290(a,1))]. 1457 L(T(x,y),y * K(x,y),T(x,y)) = (x \ y) \ y. [para(1187(a,1),1141(a,2,1))]. 1458 (x * (y * z)) \ ((x * y) * z) = a(T(x,y),T(y,x),z). [para(1168(a,1),1150(a,1,1))]. 1459 a(T(x,y),T(y,x),z) = a(x,y,z). [para(1458(a,1),28(a,2)),flip(a)]. 1460 a(T(x,y),T(T(y,x),x),z) = a(x,T(y,x),z). [para(1131(a,1),1459(a,1,1))]. 1461 x \ (y \ (y \ (T(y,x) * ((x * y) * z)))) = L(z,x * y,T(y,x)). [para(1180(a,1),443(a,1)),flip(a)]. 1462 x * K(y * a(x,y,y),z) = (x / y) * (y * K(y,z)). [para(1392(a,1),1298(a,1,2,1))]. 1463 x * K(y * a(x,y,y),z) = (x / y) * T(y,z). [para(1107(a,2),1462(a,2,2))]. 1464 x \ (y \ (K(y,x) * ((x * y) * z))) = L(z,x * y,T(y,x)). [para(1127(a,1),1461(a,1,2,2))]. 1465 x \ (y \ ((y * x) * z)) = L(z,x * y,T(y,x)). [para(1330(a,1),1464(a,1,2,2))]. 1466 L(x,y * z,T(z,y)) = L(x,z * y,z). [para(1465(a,1),309(a,1))]. 1467 L(x,y * z,z) = L(x,z * y,z). [para(1466(a,1),1300(a,1)),flip(a)]. 1468 L(L(x,y,z),y * z,z) = x. [para(1467(a,2),303(a,1))]. 1469 L(L(x,y * z,z),y,z) = x. [para(1467(a,2),308(a,1,1))]. 1470 x \ L(x,x * y,y) = a(y,x,x). [para(1467(a,2),452(a,1,2))]. 1471 L(x,y * (y / z),y) = L(x,z,y). [para(1467(a,1),877(a,1))]. 1472 L(x,(y * z) * z,y * z) = L(x,T(y,z),y * z). [para(1467(a,1),878(a,1))]. 1473 L(x,T(y,z),z) = L(x,y,z). [para(1468(a,1),314(a,1,1))]. 1474 L(L(x,y,z * y),z,z * y) = x. [para(875(a,1),1469(a,1,1))]. 1475 L(T(x,y),y,x) = T(x,y * x). [para(1473(a,1),1216(a,1))]. 1476 K(x,y) * (x \ y) = y / L(x,y,x). [para(1473(a,1),1247(a,1,2)),flip(a)]. 1477 L(x,y,y / z) = L(x,y,y * z). [para(1473(a,1),1285(a,1)),flip(a)]. 1478 (x * T(y,x)) \ (T(y,z) * x) = L(K(T(y,x),z),y,x). [para(1473(a,1),1195(a,2))]. 1479 T(x,y * x) = T(x,x * y). [para(1475(a,1),203(a,1))]. 1480 K(x,y) * L(x,y,x) = T(x,x * y). [para(1479(a,1),955(a,2))]. 1481 T(x,x * y) * K(y * x,x) = x. [para(1479(a,1),1089(a,1,1))]. 1482 T(x,x * (y * x)) = T(x,R(y,x,x)). [para(1479(a,1),1430(a,1))]. 1483 x \ L(x,y,x * y) = a(x * y,x,x). [para(875(a,1),1470(a,1,2))]. 1484 x \ L(x,T(y,x),y * x) = a(y * x,x,x). [para(878(a,1),1470(a,1,2))]. 1485 a(T(x,y),y,y) = a(x,y,y). [para(1470(a,1),1299(a,1)),flip(a)]. 1486 L(x * (a(y,x,x) * z),x,y) = (y / x) \ (y * z). [para(1471(a,1),1449(a,1))]. 1487 L(x,y,y * x) = x * a(y * x,x,x). [para(454(a,1),1474(a,1,1))]. 1488 L(x,x,x * y) = y \ (y / (x \ 1)). [para(1477(a,1),807(a,1))]. 1489 K(x * y,y) = K(y * x,y). [hyper(23,a,1089,a,b,1481,a)]. 1490 T(x * K(x * y,x),y * x) = x. [para(1489(a,1),1020(a,1,1,2))]. 1491 x / (x / y) = y * K(x * y,y). [para(1489(a,2),1144(a,2,2))]. 1492 R(x,y,x) / T(x,y) = K(y * x,x). [para(1489(a,2),1370(a,2))]. 1493 T(x / (x / y),x * y) = y. [para(1144(a,2),1490(a,1,1))]. 1494 T(x * y,x / (x / y)) = T(x * y,y). [para(1493(a,1),1131(a,1,2)),flip(a)]. 1495 (x / (x / y)) \ T(x * y,x / (x / y)) = y \ (x * y). [para(1493(a,1),1138(a,1,1)),flip(a)]. 1496 R(x,y,x) = y / (y / T(x,y)). [para(1491(a,2),1325(a,1)),flip(a)]. 1497 R(x,y,x) \ y = y / T(x,y). [para(1496(a,2),66(a,1,1))]. 1498 (T(x,y) \ y) * K(T(x,y),T(x,y) * y) = R(x,y,x) \ y. [para(1497(a,2),1001(a,2))]. 1499 ((x / y) / x) * T(x,R(y,x,y)) = x / T(y,x). [para(1497(a,1),1356(a,2))]. 1500 K(x,y) = (y \ x) / (x / L(y,x,y)). [para(1476(a,1),902(a,1,2)),flip(a)]. 1501 (x * y) / (K(x,y) * L(x,y,x)) = R(x,x * y,x) \ (x * y). [para(1480(a,2),1497(a,2,2)),flip(a)]. 1502 T(x,R(y,x,x)) = T(x,y). [para(1482(a,1),1136(a,1))]. 1503 K(x,R(y,x,x)) = x \ T(x,y). [para(1502(a,1),1108(a,2,2))]. 1504 K(x,R(y,x,x)) = K(x,y). [para(1503(a,2),1108(a,2)),flip(a)]. 1505 K(x,y / x) = K(x,y * x). [para(1504(a,1),1424(a,1))]. 1506 K(x,y * x) = K(x,x * y). [para(1505(a,1),1078(a,1))]. 1507 ((x * y) * y) \ ((y * x) * y) = K(y,y * (y * x)). [para(1506(a,1),1103(a,2))]. 1508 (T(x,y) \ y) * K(x,x * y) = T(y,x) / x. [para(1506(a,1),1260(a,1,2))]. 1509 K(T(x,y),y * T(x,y)) = K(T(x,y),y * x). [para(1506(a,2),1364(a,1))]. 1510 T(x,y) \ R(x,y,x) = K(y * x,x). [para(1492(a,1),693(a,1)),flip(a)]. 1511 K(x,y) * (y \ R(y,x,y)) = K(x * y,y). [para(1510(a,1),1095(a,2))]. 1512 K(T(x,y),y * x) = K(T(x,y),x * y). [para(82(a,1),1509(a,1,2)),flip(a)]. 1513 K(T(x,y),x * y) = K(x,x * y). [para(1512(a,1),1366(a,1))]. 1514 L(x,R(y,z,z),y * z) = L(x,T(y,z),y * z). [para(1472(a,1),938(a,1)),flip(a)]. 1515 L(x,T(y,z),y * z) = L(x,y,z * y). [para(1514(a,1),1456(a,1))]. 1516 x \ L(x,y,x * y) = a(y * x,x,x). [para(1515(a,1),1484(a,1,2))]. 1517 a(x * y,y,y) = a(y * x,y,y). [para(1516(a,1),1483(a,1))]. 1518 L(x * (a(y,x,x) * z),x,y) = (x / y) * (y * z). [para(1486(a,2),358(a,1))]. 1519 K(x,y) = ((y * x) * x) \ ((x * y) * x). [para(1507(a,2),490(a,1)),flip(a)]. 1520 (x * (y * x)) \ ((x * y) * x) = K(y * x,x) * K(x,y). [para(1519(a,2),941(a,1,2)),flip(a)]. 1521 (x * y) \ (T(x,z) * y) = L(K(T(x,y),z),x,y). [para(82(a,1),1478(a,1,1))]. 1522 L(K(T(x,y),z),x,y) = T(K(x,z),x * y). [para(1521(a,1),1184(a,1))]. 1523 (x / (x / y)) \ T(x * y,x / (x / y)) = T(x,y). [para(1495(a,2),36(a,2)),flip(a)]. 1524 (x / (x / y)) \ T(x * y,y) = T(x,y). [para(1494(a,1),1523(a,1,2))]. 1525 ((x / y) / x) * T(x * y,y) = T(x,y). [para(1524(a,1),358(a,1)),flip(a)]. 1526 (x / y) * T(y * (x \ y),x \ y) = T(y,x \ y). [para(65(a,1),1525(a,1,1,1))]. 1527 L(x,y,z * (((u / w) / u) * T(u,w))) = L(x,y,z * T(u * w,w)). [para(1525(a,1),868(a,1,3,2,2))]. 1528 (x / y) * (y * (y / x)) = T(y,x \ y). [para(1239(a,1),1526(a,1,2))]. 1529 T(x,x / y) = T(x,y \ x). [para(1528(a,1),369(a,1)),flip(a)]. 1530 T(x,R(y,x,y)) = T(x,(x / y) \ x). [para(1529(a,1),1322(a,2))]. 1531 T(x,R(y,x,y)) = T(x,y). [para(66(a,1),1530(a,2,2))]. 1532 ((x / y) / x) * T(x,y) = x / T(y,x). [para(1531(a,1),1499(a,1,2))]. 1533 K(x * y,y) * K(y,x) = a(y,x,y). [para(1520(a,1),28(a,2)),flip(a)]. 1534 K(x,y) * K(y * x,x) = a(x,y,x). [para(1533(a,1),1226(a,2))]. 1535 K(x * y,x) * K(x,y) = a(x,y,x). [para(1489(a,1),1533(a,1,1))]. 1536 K(x,y) * a(y,x,y) = K(x * y,y). [hyper(23,a,901,a,b,1534,a),flip(a)]. 1537 K(x,y) * K(x * y,x) = a(x,y,x). [para(1489(a,1),1534(a,1,2))]. 1538 (((x \ y) * x) / y) * K(x,y) = a(x,y,x). [para(982(a,2),1535(a,1,1))]. 1539 x \ R(x,y,x) = a(x,y,x). [hyper(23,a,1511,a,b,1536,a),flip(a)]. 1540 x * a(x,y,x) = R(x,y,x). [para(1539(a,1),20(a,1,2))]. 1541 L(x,y,x) \ x = a(x,y,x). [para(1539(a,1),1320(a,2))]. 1542 a(x,y,x) * L(x,y,x) = x. [para(1541(a,1),520(a,1,1))]. 1543 (x * y) / L(L(y,z,y),a(y,z,y),x) = x * a(y,z,y). [para(1542(a,1),99(a,1,1,2))]. 1544 (T(x,y) \ y) * K(T(x,y),y * T(x,y)) = R(x,y,x) \ y. [para(1506(a,2),1498(a,1,2))]. 1545 (T(x,y) \ y) * K(T(x,y),x * y) = R(x,y,x) \ y. [para(82(a,1),1544(a,1,2,2))]. 1546 (T(x,y) \ y) * K(x,x * y) = R(x,y,x) \ y. [para(1513(a,1),1545(a,1,2))]. 1547 R(x,y,x) \ y = T(y,x) / x. [para(1546(a,1),1508(a,1))]. 1548 T(x,y) / y = x / T(y,x). [para(1547(a,1),1497(a,1))]. 1549 (x / T(y,x)) * y = T(x,y). [para(1548(a,1),22(a,1,1))]. 1550 (x / y) * (y * K(x,y)) = T(x,y * K(x,y)). [para(1020(a,1),1549(a,1,1,2))]. 1551 T(x,y) = (x / y) * (y * K(x,y)). [para(1550(a,2),1139(a,1)),flip(a)]. 1552 (x / y) * T(y,x) = x * K(y,x). [hyper(23,a,359,a,b,1551,a(flip)),flip(a)]. 1553 (x * (y \ 1)) * T(L(y,y,x),x) = x * K(L(y,y,x),x). [para(915(a,1),1552(a,1,1))]. 1554 (x * (y \ 1)) * L(T(y,x),y,x) = x * K(L(y,y,x),x). [para(44(a,2),1553(a,1,2))]. 1555 x * K(L(y,y,x),x) = x * (y \ T(y,x)). [para(1554(a,1),945(a,1))]. 1556 x * K(L(y,y,x),x) = x * K(y,x). [para(1108(a,2),1555(a,2,2))]. 1557 T(x * K(y,x),L(y,y,x)) = x. [para(1556(a,1),1020(a,1,1))]. 1558 T(x,L(y,y,x)) = T(x,y). [para(1557(a,1),1023(a,1,1)),flip(a)]. 1559 (x * y) / (K(x,y) * L(x,y,x)) = L(x,y,x) \ (x * y). [para(1315(a,1),1501(a,2,1))]. 1560 (x * y) / (K(x,y) * L(x,y,x)) = (L(x,y,x) \ x) * y. [para(1559(a,2),524(a,1))]. 1561 (x * y) / T(x,x * y) = (L(x,y,x) \ x) * y. [para(1480(a,1),1560(a,1,2))]. 1562 (L(x,y,x) \ x) * y = T(x * y,x) / x. [para(1561(a,1),1548(a,2)),flip(a)]. 1563 T(x * y,x) / x = a(x,y,x) * y. [para(1541(a,1),1562(a,1,1)),flip(a)]. 1564 R(K(x,y),K(y,x) * z,u) \ K(x,y) = K(y,x) * R(K(x,y),z,u). [para(923(a,2),900(a,1))]. 1565 x * (y * (R(y,y * (x \ 1),z) \ (x \ z))) = L(z,y * x,y). [para(318(a,1),957(a,1,2,2,2))]. 1566 x * (R(y,x \ 1,z) * (y \ (x \ z))) = L(z,y * x,y). [para(637(a,1),1565(a,1,2))]. 1567 x * (R(y,x,z) * (y \ (x \ z))) = L(z,y * x,y). [para(717(a,1),1566(a,1,2,1))]. 1568 R(x * (K(x,y) * K(x,y)),z,u) / T(T(x,y),y) = x \ R(x,z,u). [para(705(a,2),1202(a,1,1))]. 1569 K(x,T(y,z)) * T(y,x) = K(z,T(y,x)) * T(y,z). [para(1346(a,1),1264(a,1,2))]. 1570 (K(x,T(y,z)) * T(y,x)) / L(y,K(y,z),K(z,T(y,x))) = K(z,T(y,x)) * K(y,z). [para(1569(a,1),1106(a,1,1))]. 1572 ((T(x,y) * y) * z) / ((x * y) * z) = K(y,x) \ 1. [para(1098(a,1),1336(a,1,2,1))]. 1574 a(x * (y * y),y \ 1,y) = a(x * y,y \ 1,y \ 1). [para(156(a,1),1401(a,1,3))]. 1575 L(x,y,z * T(u * w,w)) = L(x,y,z * (u / T(w,u))). [para(1532(a,1),1527(a,1,3,2)),flip(a)]. 1576 L(x,y,z * (T(u,w) / w)) = L(x,y,z * T(u * w,w)). [para(1548(a,2),1575(a,2,3,2)),flip(a)]. 1577 (R(K(x,y),z,u) \ 1) \ K(y,x) = K(x,y) * R(K(y,x),z,u). [para(904(a,1),1564(a,1,1))]. 1578 R(K(x,y),z,u) * K(y,x) = K(x,y) * R(K(y,x),z,u). [para(1577(a,1),330(a,1)),flip(a)]. 1579 K(x,y) * R(K(y,x),T(x,y) * z,u) = R(K(y,x),x * z,u) \ K(y,x). [para(1249(a,1),1577(a,1,1)),flip(a)]. 1580 R(T(x,y) * K(x,y),z,u) / T(T(x,y),y) = x \ R(x,z,u). [para(1120(a,1),1568(a,1,1,1))]. 1581 R(T(T(x,y),y),z,u) / T(T(x,y),y) = x \ R(x,z,u). [para(1121(a,1),1580(a,1,1,1))]. 1582 T(T(x,y),y) \ R(T(T(x,y),y),z,u) = x \ R(x,z,u). [para(1581(a,1),478(a,1)),flip(a)]. 1583 (x * y) * T((x * y) \ (x * z),u) = (x * y) * L(T(y \ z,u),y,x). [para(44(a,2),764(a,1,2)),flip(a)]. 1584 (x * y) * R((x * y) \ x,z,u) = (x * y) * L(R(y \ 1,z,u),y,x). [para(48(a,1),765(a,1,2)),flip(a)]. 1585 (x \ 1) * L((x \ 1) \ y,z,u) = L(y * x,z,u) / x. [para(720(a,1),766(a,1,1,1)),flip(a)]. 1586 (x \ 1) * L(x * y,z,u) = L(y * x,z,u) / x. [para(330(a,1),1585(a,1,2,1))]. 1587 L(x * y,z,u) / y = y \ L(y * x,z,u). [para(1586(a,1),318(a,1))]. 1588 (x \ y) \ L((x \ y) * x,z,u) = L(y,z,u) / (x \ y). [para(20(a,1),1587(a,1,1,1)),flip(a)]. 1589 (K(x,y) * (x \ z)) \ (K(x,y) * (x \ (z * u))) = L(u,z,x \ K(x,y)). [para(1072(a,1),1189(a,1,2))]. 1590 (x * y) * T((x * y) \ (x * z),u) = x * (y * T(y \ z,u)). [para(1583(a,2),74(a,1))]. 1591 (x * y) * R((x * y) \ x,z,u) = x * (y * R(y \ 1,z,u)). [para(1584(a,2),74(a,1))]. 1592 (x * y) * R((x * y) \ x,z,u) = x * (y \ R(y,z,u)). [para(635(a,1),1591(a,2,2))]. 1593 (x / y) * (y * R(((y \ x) * x) \ (y \ x),z,u)) = x \ R(x,z,u). [hyper(23,a,1274,a,b,1592,a(flip)),flip(a)]. 1594 (x / y) * (y * R(((y * x) * x) \ (y * x),z,u)) = x \ R(x,z,u). [para(1379(a,1),1593(a,1,2,2,1))]. 1595 (x / y) * (y * R(y \ (y / x),z,u)) = x \ R(x,z,u). [para(1296(a,1),1594(a,1,2,2,1))]. 1596 ((x \ y) / y) * (y * R(y \ x,z,u)) = (x \ y) \ R(x \ y,z,u). [para(65(a,1),1595(a,1,2,2,1,2))]. 1597 (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). [para(99(a,1),1595(a,1,2,2,1,2))]. 1598 (x \ 1) * (y * R(y \ x,z,u)) = (x \ y) \ R(x \ y,z,u). [para(320(a,1),1596(a,1,1))]. 1599 (x \ y) \ R(x \ y,z,u) = x \ (y * R(y \ x,z,u)). [para(1598(a,1),318(a,1))]. 1601 (x * y) \ R(x * y,z,u) = x \ (y * R(y \ x,z,u)). [para(1599(a,1),750(a,1)),flip(a)]. 1602 L(L(x,y,z),z * y,K(z,u)) = L(x,y,z \ K(z,u)). [para(1589(a,1),1409(a,1)),flip(a)]. 1603 L(L(x,y,z),z * y,K(z,u)) = L(x,y,z * K(z,u)). [para(1602(a,2),776(a,1))]. 1604 L(L(x,y,z),z * y,K(z,u)) = L(x,y,T(z,u)). [para(1107(a,2),1603(a,2,3))]. 1605 L(L(x,y,z),z * y,T(z,u)) = L(x,z * (z * y),K(z,u)). [para(303(a,1),1604(a,1,1)),flip(a)]. 1606 L(L(x,y,z),z * y,T(z,u)) = L(x,y,K(z,u)). [para(1605(a,2),875(a,1))]. 1608 (x * (y * x)) \ R(x * (z * x),u,w) = T(y,x) \ T(R(z,u,w),x). [para(36(a,2),701(a,2,2))]. 1609 (x * (y * x)) \ R(x * (z * x),u,w) = T(y,x) \ R(T(z,x),u,w). [para(46(a,2),1608(a,2,2))]. 1610 x \ ((y * x) * R((y * x) \ x,z,u)) = T(y,x) \ R(T(y,x),z,u). [para(1609(a,1),1601(a,1)),flip(a)]. 1611 L(x,y,z * (u \ (u \ (u \ (z * (u \ 1)))))) = L(x,y,K(z / (u * u),u)). [para(602(a,1),1194(a,1,3))]. 1612 L(x,y,z * (u \ ((u \ (u \ z)) * (u \ 1)))) = L(x,y,K(z / (u * u),u)). [para(285(a,1),1611(a,1,3,2,2))]. 1613 L(x,y,z * (u * ((u \ (u \ z)) * (u \ 1)))) = L(x,y,K(z / (u * u),u)). [para(1612(a,1),867(a,1)),flip(a)]. 1614 L(x,y,K(z / (u * u),u)) = L(x,y,z * (u \ (z * (u \ 1)))). [para(265(a,1),1613(a,1,3,2)),flip(a)]. 1615 L(x,y,K(z / (u * u),u)) = L(x,y,z * (u * (z * (u \ 1)))). [para(1614(a,2),867(a,1))]. 1616 L(x,y,K(z / (u * u),u)) = L(x,y,z * T(z,u \ 1)). [para(347(a,1),1615(a,2,3,2))]. 1617 L(x,y,K(z / (u * u),u)) = L(x,y,K(z,u \ 1)). [para(1616(a,2),1119(a,1))]. 1618 L(x,y,K(z,u \ 1)) = L(x,y,K(z,u)). [para(1418(a,1),1617(a,1,3)),flip(a)]. 1619 L(x,y,K(z,u \ 1)) = L(x,y,K(u,z)). [para(1618(a,2),909(a,1))]. 1620 (x * (x * (y * (z * u)))) \ ((x * (x * (y * z))) * u) = a(x * (x * y),z,u). [para(51(a,1),91(a,1,2,1))]. 1621 (x * y) * R(L(y \ z,y,x),u,w) = (x * y) * R((x * y) \ (x * z),u,w). [para(473(a,1),224(a,1))]. 1622 (x * y) * R((x * y) \ (z * y),u,w) = (R(z / x,u,w) * x) * y. [para(474(a,1),185(a,1))]. 1623 (x * y) * R((x * y) \ (z * y),u,w) = (x * R(x \ z,u,w)) * y. [para(224(a,1),1622(a,2,1))]. 1624 ((x * y) * ((y * x) * z)) \ (((x * y) * (y * x)) * (z * u)) = L(u,z,K(y,x)). [para(894(a,1),832(a,1,1))]. 1625 ((x * y) * T(R(T(z,x * y),x,y),u)) / ((z * x) * y) = K(R(z,x,y),u). [para(549(a,1),1214(a,1,1,2,1))]. 1626 ((x * y) * R(T(T(z,x * y),u),x,y)) / ((z * x) * y) = K(R(z,x,y),u). [para(46(a,2),1625(a,1,1,2))]. 1627 (R(T(x,y),z,u) * (z * u)) / ((x * z) * u) = K(R(x,z,u),y). [para(222(a,1),1626(a,1,1))]. 1628 ((T(x,y) * z) * u) / ((x * z) * u) = K(R(x,z,u),y). [para(79(a,1),1627(a,1,1))]. 1629 R(K(x,y),x * z,u) = K(R(x,z,u),y). [para(1628(a,1),1183(a,1)),flip(a)]. 1630 K(R(x,y,z),y) = K(y,x) \ 1. [para(1628(a,1),1572(a,1))]. 1631 R(K(x,y),T(y,x) * z,u) \ 1 = K(R(y,z,u),x). [para(1628(a,1),1162(a,2))]. 1632 K(R(x,y,z),y) = K(x,y). [para(1630(a,2),897(a,1))]. 1633 T(x,R(y,x,z)) = (x * x) / (x * K(y,x)). [para(1632(a,1),1104(a,2,2,2))]. 1634 K(R(x,x \ y,z),u) = R(K(x,u),y,z). [para(20(a,1),1629(a,1,2)),flip(a)]. 1635 R(K(x,y),x * (z / (z * x)),u) = K(x,y). [para(450(a,1),1629(a,2,1))]. 1636 R(K(x,y),T(x,y) * z,u) = K(R(T(x,y),z,u),y). [para(1105(a,1),1629(a,1,1))]. 1637 K(R(x,x * y,z),u) = R(K(x,u),y,z). [para(629(a,1),1634(a,1,1))]. 1638 R(K(x,y),z,x) = K(L(x,z,x),y). [para(1313(a,1),1634(a,1,1)),flip(a)]. 1639 K(x,R(y,y * z,u)) = R(K(y,x),z,u) \ 1. [para(1637(a,1),897(a,1,1)),flip(a)]. 1640 R(K(x,y),K(x,z) * u,w) = K(R(x,T(x,z) * u,w),y). [para(1120(a,1),1637(a,1,1,2)),flip(a)]. 1641 K(R(x,T(x,y) * z,u),y) = R(K(T(x,y),y),z,u). [para(1637(a,1),1110(a,1)),flip(a)]. 1642 T(x,R(y,x,z)) = T(x,y). [para(1633(a,2),1104(a,2)),flip(a)]. 1643 R(x,y,z) * T(y,x) = y * R(x,y,z). [para(1642(a,1),82(a,1,2))]. 1647 T(x,y) \ (x * R(y,x,z)) = T(R(y,x,z),T(x,y)). [para(1643(a,1),36(a,2,2)),flip(a)]. 1648 R(K(x,y),K(x,z),u) = K(x,y). [para(1041(a,2),1635(a,1,2))]. 1649 R(K(x,y),K(z,x),u) = K(x,y). [para(1648(a,1),908(a,1)),flip(a)]. 1650 (K(x,y) * K(z,x)) * u = K(x,y) * (K(z,x) * u). [para(1649(a,1),79(a,1,1)),flip(a)]. 1651 R(K(x,y),T(y,x) * z,u) = K(R(y,z,u),x) \ 1. [para(1631(a,1),156(a,1,1)),flip(a)]. 1652 R(K(x,y),T(x,y) * z,u) = K(R(x,z,u),y). [para(1636(a,2),1110(a,1))]. 1653 R(K(x,y),y * z,u) = K(R(y,z,u),x) \ 1. [para(1652(a,1),1249(a,1,1)),flip(a)]. 1654 R(K(x,y),y * z,u) = K(x,R(y,z,u)). [para(1653(a,2),897(a,1))]. 1656 R(K(x,y),x * z,u) * K(y,x) = K(x,y) * K(y,R(x,z,u)). [para(1654(a,1),1578(a,2,2))]. 1657 K(R(x,T(x,y) * z,u),y) = R(K(x,y),z,u). [para(1105(a,1),1641(a,2,1))]. 1658 T(R(x,y,z),T(y,x)) = K(x,y) * R(x,y,z). [para(1647(a,1),1093(a,1))]. 1659 R(T(x,T(y,x)),y,z) = K(x,y) * R(x,y,z). [para(1658(a,1),46(a,2))]. 1660 K(x,y) * R(x,y,z) = R(T(x,y),y,z). [para(1131(a,1),1659(a,1,1)),flip(a)]. 1661 T(x,y) \ R(T(x,y),y,z) = x \ R(x,y,z). [para(1660(a,1),1171(a,1,2))]. 1662 (x \ y) \ R(T(y / x,x),x,z) = (y / x) \ R(y / x,x,z). [para(84(a,1),1661(a,1,1))]. 1663 L(x,K(y,z),K(z,u)) = x. [hyper(23,a,74,a,b,1650,a),flip(a)]. 1664 L(x,K(y,z),K(u,z)) = x. [para(1663(a,1),909(a,1)),flip(a)]. 1665 L(x,K(y,z),K(u,y)) = x. [para(1664(a,1),921(a,1)),flip(a)]. 1666 (K(x,y) * T(z,x)) / z = K(z,x) * K(x,y). [para(1665(a,1),1355(a,1,2))]. 1667 R(K(x,y),T(y,x) * z,u) = K(x,R(y,z,u)). [para(1651(a,2),897(a,1))]. 1668 R(K(x,y),y * z,u) \ K(x,y) = K(y,x) * K(x,R(y,z,u)). [para(1667(a,1),1579(a,1,2)),flip(a)]. 1669 R(K(x,y),K(x,y) * z,u) = R(K(x,y),z,u). [para(1640(a,2),1657(a,1))]. 1670 R(K(x,y),z,u) \ 1 = R(K(y,x),z,u). [para(1669(a,1),906(a,1)),flip(a)]. 1671 R(K(x,y),z,u) \ K(x,y) = K(x,y) * R(K(y,x),z,u). [para(1670(a,1),543(a,1,2)),flip(a)]. 1672 K(x,R(y,y * z,u)) = R(K(x,y),z,u). [para(1670(a,1),1639(a,2))]. 1673 K(R(x,y,z),u) * K(u,x) = K(x,u) * K(u,R(x,y,z)). [para(1629(a,1),1656(a,1,1))]. 1674 K(x,y) * K(R(y,z,u),x) = K(y,x) * K(x,R(y,z,u)). [para(1673(a,1),1226(a,2))]. 1675 (x / y) \ R(x / y,y,z) = (y \ x) \ R(y \ x,y,z). [para(84(a,1),1662(a,1,2,1)),flip(a)]. 1676 (x \ y) \ R(x \ y,x,z) = (x / y) * R(y / x,x,z). [para(1675(a,1),358(a,1))]. 1677 x \ (y * R(y \ x,x,z)) = (x / y) * R(y / x,x,z). [para(1676(a,1),1599(a,1)),flip(a)]. 1678 x \ ((y \ x) * R((y \ x) \ x,x,z)) = y * R((y \ x) / x,x,z). [para(65(a,1),1677(a,2,1))]. 1679 x \ (R(y,x,z) * (y \ x)) = y * R((y \ x) / x,x,z). [para(225(a,1),1678(a,1,2))]. 1680 x * R((x \ y) / y,y,z) = T(x \ R(x,y,z),y). [para(1679(a,1),539(a,1))]. 1681 T(x \ R(x,y,z),y) = x * R(x \ 1,y,z). [para(320(a,1),1680(a,1,2,1)),flip(a)]. 1683 T(x \ R(x,y,z),y) = x \ R(x,y,z). [para(1681(a,2),635(a,1))]. 1684 (x * (y \ R(y,x,z))) / x = y \ R(y,x,z). [para(1683(a,1),105(a,1,1,2))]. 1685 T(x \ R(x,y,z),x * (y * z)) = T(a(x,y,z),y). [para(1683(a,1),740(a,1,1))]. 1686 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). [para(1684(a,1),1518(a,2,1))]. 1687 T(a(x,y,z),y) = a(x,y,z). [para(1685(a,1),739(a,2)),flip(a)]. 1688 a(x,y,z) * y = y * a(x,y,z). [para(1687(a,1),82(a,1,2)),flip(a)]. 1689 a(x,y \ 1,z) * (y \ 1) = y \ a(x,y \ 1,z). [para(1687(a,1),326(a,1,2)),flip(a)]. 1690 T(x * y,x) / x = y * a(x,y,x). [para(1688(a,1),1563(a,2))]. 1691 L(x,y,z * (T(u * z,u) / u)) = L(x,y,a(u,z,u)). [para(1690(a,2),774(a,1,3,2))]. 1692 L(x,y,z * a(u,z,u)) = L(x,y,R(z,u,u)). [para(1690(a,1),1350(a,1,3))]. 1693 L(x,y,z * T((u * z) * u,u)) = L(x,y,a(u,z,u)). [para(1691(a,1),1576(a,1)),flip(a)]. 1694 L(x,y,z * ((z * u) * u)) = L(x,y,a(u,z,u)). [para(758(a,1),1693(a,1,3,2))]. 1695 L(x,y,a(z,u,u)) = L(x,y,a(u,z,u)). [para(1694(a,1),861(a,1)),flip(a)]. 1696 (x * (x * (y * (z * u)))) \ (x * (x * ((y * z) * u))) = a(x * (x * y),z,u). [para(51(a,1),1620(a,1,2))]. 1697 (x * y) * R((x * y) \ (x * z),u,w) = (x * y) * L(R(y \ z,u,w),y,x). [para(48(a,1),1621(a,1,2)),flip(a)]. 1698 ((x * y) * ((y * x) * z)) \ ((x * y) * ((y * x) * (z * u))) = L(u,z,K(y,x)). [para(894(a,1),1624(a,1,2))]. 1699 a(x * (x * y),z,u) = (y * (z * u)) \ ((y * z) * u). [para(1696(a,1),212(a,1))]. 1700 a(x * (x * y),z,u) = a(y,z,u). [para(1699(a,2),28(a,2)),flip(a)]. 1702 a(x \ y,z,u) = a(x * y,z,u). [para(20(a,1),1700(a,1,1,2)),flip(a)]. 1703 a((x / y) * x,z,u) = a(y,z,u). [para(22(a,1),1700(a,1,1,2))]. 1704 a(x * (y * x),z,u) = a(T(y,x),z,u). [para(82(a,1),1700(a,1,1,2))]. 1705 a((x * y) * (x * (y * z)),u,w) = a(L(z,y,x),u,w). [para(74(a,1),1700(a,1,1,2))]. 1706 a(x * ((x \ y) * z),u,w) = a(x * ((x * y) * z),u,w). [para(89(a,1),1700(a,1,1,2)),flip(a)]. 1707 a((x \ y) * z,u,w) = a((x * y) * z,u,w). [para(89(a,1),1700(a,1,1)),flip(a)]. 1708 a((x * x) / y,z,u) = a(y \ 1,z,u). [para(263(a,1),1700(a,1,1))]. 1709 a(x * L(x,y * x,y),z,u) = a(a(y,x,x),z,u). [para(453(a,2),1700(a,1,1,2))]. 1710 a(R(x \ 1,y,y),z,u) = a(x * a(x,y,y),z,u). [para(960(a,1),1700(a,1,1,2)),flip(a)]. 1711 a(K(x,y) * y,z,u) = a(T(y,x),z,u). [para(1077(a,1),1700(a,1,1,2))]. 1712 a(x * T(x,y),z,u) = a(K(x,y),z,u). [para(1107(a,2),1700(a,1,1,2))]. 1713 ((x \ y) * (T(x,x * y) * z)) \ (y * z) = a(x * y,T(x,x * y),z). [para(1702(a,1),255(a,2))]. 1714 a(K(x \ 1,x * y),z,u) = a(x \ ((x * y) \ y),z,u). [para(1126(a,2),1702(a,2,1)),flip(a)]. 1715 a((x * (x * y)) * (x * z),u,w) = a(y \ (x \ z),u,w). [para(282(a,1),1703(a,1,1,1))]. 1716 a((x * x) / y,z,u) = a(y,z,u). [para(1708(a,2),611(a,1))]. 1717 a(x / (y * y),z,u) = a(x,z,u). [para(1716(a,1),612(a,1)),flip(a)]. 1718 a(R(x,x * y,z),u,w) = a(R(x,y,z),u,w). [para(616(a,1),1716(a,1,1))]. 1719 a(x * K(y,x),z,u) = a(T(x,y),z,u). [para(1104(a,2),1716(a,1,1)),flip(a)]. 1720 a(x * (y * y),z,u) = a(x,z,u). [para(21(a,1),1717(a,1,1)),flip(a)]. 1721 a((x * y) * y,z,u) = a(R(x,y,y),z,u). [para(34(a,2),1717(a,1,1)),flip(a)]. 1722 a(x / (y \ 1),z,u) = a(x / y,z,u). [para(398(a,1),1717(a,1,1)),flip(a)]. 1723 ((x * (y * y)) * (z * u)) \ (((x * (y * y)) * z) * u) = a(x,z,u). [para(1720(a,1),28(a,1)),flip(a)]. 1724 a(T(T(x,y),y),z,u) = a(x,z,u). [para(985(a,1),1711(a,1,1)),flip(a)]. 1725 a((x / (y * y)) * (y \ (x * (y \ 1))),z,u) = a(K(x / (y * y),y),z,u). [para(403(a,1),1712(a,1,1,2))]. 1726 a(x / (x * y),z,u) = a(T(y,x),z,u). [para(1719(a,1),1022(a,2))]. 1727 a((x \ 1) / y,z,u) = a(y / x,z,u). [para(1722(a,1),612(a,1)),flip(a)]. 1728 a(x / T(y * x,y),z,u) = a(T(R(y,x,y),x),z,u). [para(1321(a,1),1726(a,1,1,2))]. 1729 a(x * (y * x),x,x) = a(R(y,x,x),x,x). [para(1721(a,1),1517(a,1)),flip(a)]. 1730 a(R(x,y,y),y,y) = a(T(x,y),y,y). [para(1729(a,1),1704(a,1))]. 1731 a(R(x,y,y),y,y) = a(x,y,y). [para(1730(a,2),1485(a,1))]. 1732 R(R(x,y,y) \ 1,y,y) = R(x,y,y) \ a(x,y,y). [para(1731(a,1),967(a,2,2))]. 1733 R(R(x,y,y),R(x,y,y) * y,y) = a(x,y,y) \ R(x,y,y). [para(1731(a,1),968(a,2,1))]. 1734 a(x * ((x \ y) * y),z,u) = a(a(x,y,y),z,u). [para(435(a,1),1709(a,1,1))]. 1735 a(R(x \ 1,y,y),z,u) = a(R(x,y,y),z,u). [para(963(a,1),1710(a,2,1))]. 1736 R(R(x,y,y) \ 1,y,y) = x \ 1. [para(1732(a,2),1374(a,1))]. 1737 R((x * y) \ 1,y,y) = (x / (y \ 1)) \ 1. [para(720(a,1),1736(a,1,1,1))]. 1739 R((x * y) \ 1,y,y) = (y \ 1) / x. [para(1737(a,2),343(a,1))]. 1740 (x \ 1) / (y / x) = R(y \ 1,x,x). [para(22(a,1),1739(a,1,1,1)),flip(a)]. 1741 (((x * y) \ 1) * y) * y = ((y \ 1) / x) * (y * y). [para(1739(a,1),79(a,1,1)),flip(a)]. 1742 R(x \ 1,y,y) \ 1 = (x / y) / (y \ 1). [para(1740(a,1),343(a,1,1))]. 1743 a((x \ 1) / ((y / x) \ 1),z,u) = a(R(y \ 1,x,x),z,u). [para(1740(a,1),1722(a,2,1))]. 1744 R(x,x * y,y) = (x / y) / (y \ 1). [para(1742(a,1),633(a,2))]. 1745 K(R(x,x * y,y),z) * (x / y) = (y \ 1) * T((y \ 1) \ (x / y),z). [para(1744(a,2),1201(a,1,1,1))]. 1746 (((x * y) \ 1) * y) * y = T(y / x,y * y). [para(1741(a,2),294(a,1))]. 1747 T(x / y,x * x) = ((y * x) \ x) * x. [para(318(a,1),1746(a,1,1)),flip(a)]. 1748 L(x,y * z,R(T(z / y,z * z),u,w)) = x. [para(1747(a,2),847(a,1,3,1))]. 1749 L(x,y * z,R(z / y,u,w)) = x. [para(1748(a,1),858(a,1)),flip(a)]. 1750 L(x,y * (z \ 1),u / (y * (z * u))) = x. [para(350(a,1),1749(a,1,3))]. 1752 L(x,y * z,u / (y * (z * u))) = x. [para(1750(a,1),1273(a,1)),flip(a)]. 1753 x / ((y * z) \ (y * (z * x))) = (x / (y * (z * x))) * (y * z). [para(1752(a,1),205(a,1,2))]. 1754 a(T(R(x,y,x),y),z,u) = a((y / x) / y,z,u). [para(1237(a,1),1728(a,1,1)),flip(a)]. 1755 a(x * ((x * y) * y),z,u) = a(a(x,y,y),z,u). [para(1706(a,1),1734(a,1))]. 1756 a(x * (x * (y * (x * z))),u,w) = a(y \ (x \ z),u,w). [para(51(a,1),1715(a,1,1))]. 1757 a(x \ (y \ z),u,w) = a(x * (y * z),u,w). [para(1756(a,1),1700(a,1))]. 1759 a(x * (y \ z),u,w) = a(x * (y * z),u,w). [para(1757(a,1),1702(a,1)),flip(a)]. 1760 a(K(x \ 1,x * y),z,u) = a(x * ((x * y) * y),z,u). [para(1757(a,1),1714(a,2))]. 1761 R(R(x,y,y),R(x,y,y) * y,y) = x. [para(1733(a,2),964(a,1))]. 1762 R(K(R(x,y,y),z),y,y) = K(x,z). [para(1761(a,1),1637(a,1,1)),flip(a)]. 1763 K(R(x,y,y),z) * (y \ 1) = K(x,z) / y. [para(1762(a,1),718(a,1,1)),flip(a)]. 1764 K(x,R(y,z,z)) * (K(y,x) / z) = z \ 1. [hyper(23,a,901,a,b,1763,a),flip(a)]. 1765 R(K(x,y),z,z) = K(x,R(y,z,z)). [hyper(24,a,1405,a,b,1764,a),flip(a)]. 1766 K(R(x,y,y),z) \ 1 = R(K(z,x),y,y). [para(1765(a,2),897(a,2))]. 1767 K(x,R(y,z,z)) * 1 = R(K(x,y),z,z). [para(1766(a,1),900(a,1)),flip(a)]. 1768 a((x \ 1) / (x / y),z,u) = a(R(y \ 1,x,x),z,u). [para(343(a,1),1743(a,1,1,2))]. 1769 a(R(x \ 1,y,y),z,u) = a((y / x) / y,z,u). [para(1768(a,1),1727(a,1))]. 1770 a((x / y) / x,z,u) = a(R(y,x,x),z,u). [para(1769(a,1),1735(a,1))]. 1771 a(T(R(x,y,x),y),z,u) = a(R(x,y,y),z,u). [para(1770(a,1),1754(a,2))]. 1772 a(R(T(x,y),y,x),z,u) = a(R(x,y,y),z,u). [para(46(a,2),1771(a,1,1))]. 1773 (x / (y * (z * x))) * (y * z) = x / L(x,z,y). [para(32(a,2),1753(a,1,2)),flip(a)]. 1774 (x / (y * (z * x))) * (y * z) = L(x,z,y) \ x. [para(1773(a,2),519(a,1))]. 1775 (L(x * y,z / (x * (y * z)),x * y) * (z / (x * (y * z)))) * (x * y) = (x * y) * (L(z,y,x) \ z). [para(1774(a,1),1310(a,2,2))]. 1776 (x * (y * (y * (z * u)))) \ (((x * (y * y)) * z) * u) = a(x,z,u). [para(411(a,1),1723(a,1,1))]. 1777 (x * (y * (y * (z * u)))) \ ((x * (y * (y * z))) * u) = a(x,z,u). [para(411(a,1),1776(a,1,2,1))]. 1778 a(x,y * (y * z),u) = a(x,z,u). [para(1777(a,1),90(a,1)),flip(a)]. 1779 a(x,y \ z,u) = a(x,y * z,u). [para(20(a,1),1778(a,1,2,2)),flip(a)]. 1780 a(x,(y / z) * y,u) = a(x,z,u). [para(22(a,1),1778(a,1,2,2))]. 1781 a(x,(y \ z) * u,w) = a(x,(y * z) * u,w). [para(89(a,1),1778(a,1,2)),flip(a)]. 1782 a(x,T(y,y * z),u) = a(x,(y \ z) * z,u). [para(250(a,1),1778(a,1,2,2)),flip(a)]. 1783 a(x,K(y,z) * T(y,z),u) = a(x,y,u). [para(1081(a,2),1778(a,1,2,2))]. 1785 a(x * (y * y),y * 1,y) = a(x * y,y \ 1,y \ 1). [para(1779(a,1),1574(a,1))]. 1786 a(x,y \ 1,z) * (y \ 1) = y \ a(x,y * 1,z). [para(1779(a,1),1689(a,2,2))]. 1787 a(x,(y * (y * z)) * (y * u),w) = a(x,z \ (y \ u),w). [para(282(a,1),1780(a,1,2,1))]. 1788 a(x,T(y * z,y),u) = a(x,z / y,u). [para(1232(a,2),1780(a,1,2))]. 1789 a(x,T(T(y,z),z),u) = a(x,y,u). [para(1113(a,1),1783(a,1,2))]. 1790 a(T(x,y),y,z) = a(x,T(y,x),z). [para(1789(a,1),1460(a,1))]. 1792 a(x,T(y,y * z),u) = a(x,(y * z) * z,u). [para(1782(a,2),1781(a,1))]. 1793 a(x,y \ 1,z) * (y \ 1) = y \ a(x,y,z). [para(18(a,1),1786(a,2,2,2))]. 1794 a(x,y * 1,z) * (y \ 1) = y \ a(x,y,z). [para(1779(a,1),1793(a,1,1))]. 1795 a(x,y,z) * (y \ 1) = y \ a(x,y,z). [para(18(a,1),1794(a,1,1,2))]. 1796 a(x * (y * y),y,y) = a(x * y,y \ 1,y \ 1). [para(18(a,1),1785(a,1,2))]. 1797 a(x * y,y \ 1,y \ 1) = a(x,y,y). [para(1796(a,1),1720(a,1))]. 1798 L(x,x,y) \ x = a(y,x,x). [para(1797(a,1),1408(a,1)),flip(a)]. 1800 a(x,y,y) * L(y,y,x) = y. [para(1798(a,1),520(a,1,1))]. 1801 R(x,y,y) * L(y,y,x) = x * y. [para(1800(a,1),966(a,1,2)),flip(a)]. 1802 T(R(x,y,y),L(y,y,x)) = L(y,y,x) \ (x * y). [para(1801(a,1),36(a,2,2))]. 1803 R(T(x,L(y,y,x)),y,y) = L(y,y,x) \ (x * y). [para(1802(a,1),46(a,2))]. 1804 L(x,x,y) \ (y * x) = R(T(y,x),x,x). [para(1558(a,1),1803(a,1,1)),flip(a)]. 1805 a(x,y * (y * (z * (y * u))),w) = a(x,z \ (y \ u),w). [para(51(a,1),1787(a,1,2))]. 1806 a(x,y \ (z \ u),w) = a(x,y * (z * u),w). [para(1805(a,1),1778(a,1))]. 1808 a(x,y * (z \ u),w) = a(x,y * (z * u),w). [para(1806(a,1),1779(a,1)),flip(a)]. 1809 a(x * y,T(x,x * y),z) = ((y / x) * (x * z)) \ (y * z). [para(1265(a,1),1713(a,1,1)),flip(a)]. 1810 a(x * y,T(x,x * y),z) = a(y / x,x,z). [para(1809(a,2),68(a,1))]. 1811 R(K(x,y),z,z) * (x / z) = (z \ 1) * T((z \ 1) \ (x / z),y). [para(1637(a,1),1745(a,1,1))]. 1812 K(x,R(y,z,z)) * (x / z) = (z \ 1) * T((z \ 1) \ (x / z),y). [para(1765(a,1),1811(a,1,1))]. 1813 K(x,R(y,z,z)) * (x / z) = (z \ 1) * T(z * (x / z),y). [para(330(a,1),1812(a,2,2,1))]. 1814 K(x,R(y,z,z)) * (x / z) = z \ T(z * (x / z),y). [para(1813(a,2),318(a,1))]. 1815 K(x,R(y,z,z)) * (x / z) = T(x,y) / z. [para(1814(a,2),755(a,1))]. 1816 a(x * (y \ (y \ (y \ (x * (y \ 1))))),z,u) = a(K(x / (y * y),y),z,u). [para(602(a,1),1725(a,1,1))]. 1817 a(x * (y \ ((y \ (y \ x)) * (y \ 1))),z,u) = a(K(x / (y * y),y),z,u). [para(285(a,1),1816(a,1,1,2,2))]. 1818 a(x * (y * ((y \ (y \ x)) * (y \ 1))),z,u) = a(K(x / (y * y),y),z,u). [para(1817(a,1),1759(a,1)),flip(a)]. 1819 a(K(x / (y * y),y),z,u) = a(x * (y \ (x * (y \ 1))),z,u). [para(265(a,1),1818(a,1,1,2)),flip(a)]. 1820 a(K(x / (y * y),y),z,u) = a(x * (y * (x * (y \ 1))),z,u). [para(1819(a,2),1759(a,1))]. 1821 a(K(x / (y * y),y),z,u) = a(x * T(x,y \ 1),z,u). [para(347(a,1),1820(a,2,1,2))]. 1822 a(K(x / (y * y),y),z,u) = a(K(x,y \ 1),z,u). [para(1821(a,2),1712(a,1))]. 1823 a(K(x,y \ 1),z,u) = a(K(x,y),z,u). [para(1418(a,1),1822(a,1,1)),flip(a)]. 1824 a(K(x \ 1,y),z,u) = a(K(y,x),z,u). [para(1823(a,1),905(a,1)),flip(a)]. 1825 a(x * ((x * y) * y),z,u) = a(K(x * y,x),z,u). [para(1824(a,1),1760(a,1)),flip(a)]. 1826 a(K(x * y,x),z,u) = a(a(x,y,y),z,u). [para(1825(a,1),1755(a,1))]. 1827 (x * y) * R((x * y) \ (x * z),u,w) = x * (y * R(y \ z,u,w)). [para(1697(a,2),74(a,1))]. 1828 (x * y) * R((x * y) \ z,u,w) = x * (y * R(y \ (x \ z),u,w)). [para(20(a,1),1827(a,1,2,1,2))]. 1829 (x * y) * R((x * y) \ y,z,u) = R(x,z,u) * (x \ y). [para(1828(a,2),639(a,1))]. 1830 T(x,y) \ R(T(x,y),z,u) = y \ (R(x,z,u) * (x \ y)). [para(1829(a,1),1610(a,1,2)),flip(a)]. 1831 T(x,y) \ R(T(x,y),z,u) = T(x \ R(x,z,u),y). [para(1830(a,2),539(a,1))]. 1832 (R(T(x,y),z,u) \ T(x,y)) * w = T(x \ R(x,z,u),y) \ w. [para(1831(a,1),465(a,1,1)),flip(a)]. 1833 T(x \ R(x,y,y),z) = a(T(x,z),y,y). [para(1831(a,1),962(a,1))]. 1834 K(x,y) * R(T(y,x),z,u) = y * T(y \ R(y,z,u),x). [para(1831(a,1),1099(a,1,2)),flip(a)]. 1835 T(T(x,y) \ R(T(x,y),z,u),y) = x \ R(x,z,u). [para(1831(a,1),1582(a,1))]. 1836 a(T(x,y),z,z) = T(a(x,z,z),y). [para(962(a,1),1833(a,1,1)),flip(a)]. 1837 T(T(x \ R(x,y,z),u),u) = x \ R(x,y,z). [para(1831(a,1),1835(a,1,1))]. 1838 (x * (y \ R(y,z,u))) / x = T(y \ R(y,z,u),x). [para(1837(a,1),105(a,1,1,2))]. 1839 T(a(x,y,z),x * (y * z)) = x \ R(x,y,z). [para(739(a,2),1837(a,1,1))]. 1840 a(x,y,z) * K(a(x,y,z),x * (y * z)) = x \ R(x,y,z). [para(1839(a,1),1107(a,1)),flip(a)]. 1841 T(T(x \ R(x,y,z),u),x * (y * z)) = (u * a(x,y,z)) / u. [para(1838(a,1),742(a,1,1))]. 1842 (x * (y \ R(y,z,u))) / x = (y \ R(y,z,u)) * K(y \ R(y,z,u),x). [para(1838(a,2),1107(a,1))]. 1843 (x * a(y,z,u)) / x = T(a(y,z,u),x). [para(1841(a,1),740(a,1))]. 1844 T(a(x,y,z),u) * (u / (u * a(x,y,z))) = 1. [para(1843(a,1),354(a,1,1))]. 1845 L(x,x,x * ((x \ 1) * a(y,z,u))) = ((x \ 1) * a(y,z,u)) \ T(a(y,z,u),x \ 1). [para(1843(a,1),1488(a,2,2))]. 1846 K(a(x,y,z),u) * K(a(x,y,z),u) = 1. [para(1844(a,1),1174(a,1)),flip(a)]. 1847 K(a(x,y,z),u) = K(u,a(x,y,z)). [hyper(24,a,898,a,b,1846,a)]. 1848 a(x,y,z) * K(x * (y * z),a(x,y,z)) = x \ R(x,y,z). [para(1847(a,1),1840(a,1,2))]. 1849 K(x \ R(x,y,z),u) = K(u,x \ R(x,y,z)). [hyper(23,a,1014,a(flip),b,1842,a(flip))]. 1850 L(L(x,y,z * u),(z * u) * y,u * z) = L(x,y,K(z,u)). [para(1698(a,1),174(a,1)),flip(a)]. 1851 ((x * (x * y)) * a(y,z,u)) / y = a(x * (x * y),z,u) * (x * x). [para(1700(a,1),749(a,1,1,2))]. 1852 (x * (x * (y * a(y,z,u)))) / y = a(x * (x * y),z,u) * (x * x). [para(51(a,1),1851(a,1,1))]. 1854 a(x * (x * y),z,u) * (x * x) = x * (x * ((y * a(y,z,u)) / y)). [para(1852(a,1),211(a,1))]. 1855 a(x * (x * y),z,u) * (x * x) = x * (x * a(y,z,u)). [para(748(a,1),1854(a,2,2,2))]. 1856 a(x,y,z) * (u * u) = u * (u * a(x,y,z)). [para(1700(a,1),1855(a,1,1))]. 1857 T((a(x,y,z) * (u * u)) / (u * u),u) = T(u \ (u * a(x,y,z)),u \ 1). [para(1856(a,2),666(a,1,1,1))]. 1859 T(x \ (x * a(y,z,u)),x \ 1) = T(a(y,z,u),x). [para(21(a,1),1857(a,1,1)),flip(a)]. 1860 T(a(x,y,z),u \ 1) = T(a(x,y,z),u). [para(19(a,1),1859(a,1,1))]. 1863 x * L(T(y \ (y / x),z),y,x * y) = K(L(y \ (y / x),y,x * y),z). [para(1295(a,1),330(a,1)),flip(a)]. 1864 (x / y) * (y * T(y \ (y / x),z)) = K(L(y \ (y / x),y,x * y),z). [para(1863(a,1),1294(a,1)),flip(a)]. 1865 (x / y) * (y * T(y \ (y / x),z)) = K(x \ 1,z). [para(1289(a,1),1864(a,2,1))]. 1866 (L(x,y,z) / (z * (y * x))) * ((z * (y * x)) * T((z * (y * x)) \ (z * y),u)) = K(L(x,y,z) \ 1,u). [para(99(a,1),1865(a,1,2,2,1,2))]. 1868 T(x * x,y * z) \ ((((y * z) \ (x * x)) * y) * z) = a((y * z) * (x * x),y,z). [para(394(a,2),1702(a,1))]. 1869 ((R(x,y,z) * u) * w) / ((x * u) * w) = R(x,u,w) \ R(R(x,u,w),y,z). [para(185(a,1),538(a,1,1))]. 1870 R(x \ R(x,y,z),x * u,w) = R(x,u,w) \ R(R(x,u,w),y,z). [para(1869(a,1),533(a,2))]. 1871 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). [para(584(a,1),1870(a,2,1))]. 1872 (K(x,T(y,z)) * T(y,x)) / y = K(z,T(y,x)) * K(y,z). [para(1663(a,1),1570(a,1,2))]. 1873 K(x,T(y,z)) * K(y,x) = K(y,z) * K(z,T(y,x)). [para(1872(a,1),1666(a,1))]. 1874 T(x * x,y * z) \ ((((y * z) \ (x * x)) * y) * z) = a(y * z,y,z). [para(1868(a,2),1720(a,1))]. 1875 (T(x * x,y * z) \ (((y * z) \ (x * x)) * y)) * z = a(y * z,y,z). [para(1874(a,1),591(a,1)),flip(a)]. 1877 ((T(x * x,y * z) \ ((y * z) \ (x * x))) * y) * z = a(y * z,y,z). [para(591(a,1),1875(a,1,1))]. 1878 (((x * y) \ 1) * x) * y = a(x * y,x,y). [para(795(a,1),1877(a,1,1,1))]. 1879 ((x * y) \ x) * y = a(x * y,x,y). [para(318(a,1),1878(a,1,1))]. 1880 x * ((y * x) \ y) = a(y * x,y,x). [para(1879(a,1),388(a,1)),flip(a)]. 1881 a(x * (x \ y),x,x \ y) = (x \ y) * (y \ x). [para(20(a,1),1880(a,1,2,1)),flip(a)]. 1882 (x \ y) * (y \ x) = a(y,x,x \ y). [para(20(a,1),1881(a,1,1)),flip(a)]. 1883 L(x,y,(z \ u) * (u * z)) = L(x,y,a(z,u,u \ z)). [para(1882(a,1),869(a,1,3)),flip(a)]. 1884 L(x,(y \ z) * (z * y),u) = L(x,a(y,z,z \ y),u). [para(1882(a,1),1362(a,1,2)),flip(a)]. 1885 L(x,y,(z * u) * (u * z)) = L(x,y,a(z,u,u \ z)). [para(1883(a,1),781(a,1)),flip(a)]. 1886 L(x,(y * z) * (z * y),u) = L(x,a(y,z,z \ y),u). [para(1884(a,1),880(a,1)),flip(a)]. 1887 L(x,y,a(z,u,u \ z)) = L(x,y,K(u,z)). [para(1885(a,1),779(a,1))]. 1888 L(x,a(y,z,z \ y),u) = L(x,K(z,y),u). [para(1886(a,1),879(a,1))]. 1889 ((x \ 1) * a(y,z,u)) \ T(a(y,z,u),x \ 1) = L(x,x,a(y,z,u)). [para(321(a,1),1845(a,1,3)),flip(a)]. 1890 (x \ a(y,z,u)) \ T(a(y,z,u),x \ 1) = L(x,x,a(y,z,u)). [para(318(a,1),1889(a,1,1))]. 1892 (x \ a(y,z,u)) \ T(a(y,z,u),x) = L(x,x,a(y,z,u)). [para(1860(a,1),1890(a,1,2))]. 1893 L(x,a(y,z,u),x) = L(x,x,a(y,z,u)). [para(1892(a,1),440(a,1)),flip(a)]. 1894 L(x,x,a(y,z,z \ y)) = L(x,K(z,y),x). [para(1893(a,1),1888(a,1))]. 1895 L(x,K(y,z),x) = L(x,x,K(y,z)). [para(1894(a,1),1887(a,1))]. 1896 L(x,K(y,z),x) = L(x,x,K(z,y)). [para(1895(a,2),909(a,1))]. 1897 (x \ K(y,z)) / (K(y,z) / L(x,x,K(z,y))) = K(K(y,z),x). [para(1896(a,1),1500(a,2,2,2)),flip(a)]. 1898 (x \ K(y,z)) / (K(y,z) * (x \ 1)) = K(K(y,z),x). [para(930(a,1),1897(a,1,2))]. 1899 K(x \ 1,K(y,z)) = K(K(y,z),x). [para(1898(a,1),978(a,1)),flip(a)]. 1900 K(K(x,y),z) * (K(x,y) \ u) = T(K(x,y),z \ 1) \ u. [para(1899(a,1),1095(a,1,1))]. 1901 T(K(x,y),z) * K(K(x,y),z) = T(K(x,y),z * z). [para(1899(a,1),1433(a,1,2))]. 1902 T(T(K(x,y),z),z) = T(K(x,y),z * z). [para(1901(a,1),1121(a,1)),flip(a)]. 1903 T(K(x,y),T(z,x) * T(z,x)) = T(T(K(x,y),z),T(z,x)). [para(1352(a,1),1902(a,1,1)),flip(a)]. 1904 x / (T(K(y,z),u \ 1) \ x) = K(y,z) * K(u,K(y,z)). [para(1900(a,1),1071(a,1,2))]. 1905 T(K(x,y),z * T(T(z,x),x)) = T(T(K(x,y),z),T(z,x)). [para(1088(a,1),1903(a,1,2))]. 1906 K(x,y) * K(z,K(x,y)) = T(K(x,y),z \ 1). [para(1904(a,1),65(a,1))]. 1907 T(K(x,y),z \ 1) * z = z * K(x,y). [para(1906(a,1),1018(a,1,1))]. 1908 ((x * y) * (z / (x * (y * z)))) * (x * y) = (x * y) * (L(z,y,x) \ z). [para(851(a,1),1775(a,1,1,1))]. 1910 (x \ R(x,y,z)) * (x * y) = (x * y) * (L(z,y,x) \ z). [para(1410(a,1),1908(a,1,1))]. 1911 (x * y) * (L(z,y,x) \ z) = R(x,y,z) * y. [para(1910(a,1),528(a,1))]. 1912 ((x * y) \ 1) * ((x * (y * z)) * T((x * (y * z)) \ (x * y),u)) = K(L(z,y,x) \ 1,u). [para(342(a,1),1866(a,1,1))]. 1914 ((x * y) \ 1) * (x * ((y * z) * T((y * z) \ y,u))) = K(L(z,y,x) \ 1,u). [para(1590(a,1),1912(a,1,2))]. 1915 ((x * y) \ 1) * (x * (y * K(z \ 1,u))) = K(L(z,y,x) \ 1,u). [para(1164(a,1),1914(a,1,2,2))]. 1916 (x * y) \ (x * (y * K(z \ 1,u))) = K(L(z,y,x) \ 1,u). [para(1915(a,1),318(a,1)),flip(a)]. 1917 L(K(x \ 1,y),z,u) = K(L(x,z,u) \ 1,y). [para(1916(a,1),32(a,2))]. 1918 K(L(x \ 1,y,z) \ 1,u) = L(K(x,u),y,z). [para(156(a,1),1917(a,1,1,1)),flip(a)]. 1920 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). [para(750(a,1),1871(a,1,1))]. 1921 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). [para(18(a,1),1920(a,1,1,1))]. 1922 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). [para(18(a,1),1921(a,1,1,2,1))]. 1923 (R(x,y,z) \ 1) \ R(R(x \ 1,x * y,z),u,w) = R(x \ R(x,u,w),y,z). [para(322(a,1),1922(a,1,2)),flip(a)]. 1924 (R(x,y,z) \ 1) \ R(R(x,y,z) \ 1,u,w) = R(x \ R(x,u,w),y,z). [para(584(a,1),1923(a,1,2,1))]. 1925 (R(x,y,z) * 1) \ R(R(x,y,z) * 1,u,w) = R(x \ R(x,u,w),y,z). [para(1924(a,1),750(a,1)),flip(a)]. 1926 R(x,y,z) \ R(R(x,y,z) * 1,u,w) = R(x \ R(x,u,w),y,z). [para(18(a,1),1925(a,1,1))]. 1927 R(x,y,z) \ R(R(x,y,z),u,w) = R(x \ R(x,u,w),y,z). [para(18(a,1),1926(a,1,2,1))]. 1928 R(x \ R(x,y,y),z,u) = a(R(x,z,u),y,y). [para(1927(a,1),962(a,1))]. 1929 T(R(x \ R(x,y,x),z,u),x * (R(x,z,u) * T(y,x))) = a(R(x,z,u),y,x). [para(1927(a,1),743(a,1,1))]. 1930 a(R(x,y,z),u,u) = R(a(x,u,u),y,z). [para(962(a,1),1928(a,1,1)),flip(a)]. 1931 T(R(a(x,y,x),z,u),x * (R(x,z,u) * T(y,x))) = a(R(x,z,u),y,x). [para(1539(a,1),1929(a,1,1,1))]. 1932 T(R(a(x,y,x),z,u),R(x,z,u) * (y * x)) = a(R(x,z,u),y,x). [para(530(a,1),1931(a,1,2))]. 1933 R(T(a(x,y,x),R(x,z,u) * (y * x)),z,u) = a(R(x,z,u),y,x). [para(1932(a,1),46(a,2))]. 1934 ((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). [para(342(a,1),1597(a,1,1))]. 1936 ((x * y) \ 1) * (x * ((y * z) * R((y * z) \ y,u,w))) = L(z,y,x) \ R(L(z,y,x),u,w). [para(1827(a,1),1934(a,1,2))]. 1937 ((x * y) \ 1) * (x * (y * (z \ R(z,u,w)))) = L(z,y,x) \ R(L(z,y,x),u,w). [para(1592(a,1),1936(a,1,2,2))]. 1938 (x * y) \ (x * (y * (z \ R(z,u,w)))) = L(z,y,x) \ R(L(z,y,x),u,w). [para(1937(a,1),318(a,1)),flip(a)]. 1939 L(x,y,z) \ R(L(x,y,z),u,w) = L(x \ R(x,u,w),y,z). [para(1938(a,1),32(a,2)),flip(a)]. 1940 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). [para(1808(a,1),1686(a,1,1,2,1))]. 1941 L((x * (y \ R(y,x,z))) * (1 * u),x * (y \ R(y,x,z)),x) = (y \ R(y,x,z)) * (x * u). [para(1442(a,1),1940(a,1,1,2,1))]. 1942 L((x * (y \ R(y,x,z))) * u,x * (y \ R(y,x,z)),x) = (y \ R(y,x,z)) * (x * u). [para(17(a,1),1941(a,1,1,2))]. 1944 L(x * (R(y,x,z) * (y \ u)),x * (y \ R(y,x,z)),x) = (y \ R(y,x,z)) * (x * u). [para(1450(a,1),1942(a,1,1))]. 1945 L(x * (R(y,x,z) * (y \ u)),x * (y * R(y,x,z)),x) = (y \ R(y,x,z)) * (x * u). [para(1944(a,1),1360(a,1)),flip(a)]. 1946 (x \ R(x,y,z)) * (y * u) = y * (R(x,y,z) * (x \ u)). [para(1945(a,1),1439(a,1))]. 1947 R(x,y,z) * (x \ (y * u)) = y * (R(x,y,z) * (x \ u)). [para(1946(a,1),532(a,1)),flip(a)]. 1948 R(x,y,z) * (x \ (y * (y \ z))) = L(z,x * y,x). [para(1947(a,2),1567(a,1))]. 1949 R(x,y,z) * (x \ z) = L(z,x * y,x). [para(20(a,1),1948(a,1,2,2))]. 1950 R(x,y,L(z,y,x)) * (x \ L(z,y,x)) = z. [para(1949(a,2),303(a,1))]. 1951 L(x,y * z,y) / x = y \ R(y,z,x). [para(1949(a,1),536(a,1,1))]. 1952 x / L(x,y * z,y) = R(y,z,x) \ y. [para(1949(a,1),542(a,1,2))]. 1953 x \ L(x,y * z,y) = y \ R(y,z,x). [para(1951(a,1),515(a,1)),flip(a)]. 1954 L(x,y * z,y) \ x = R(y,z,x) \ y. [para(1952(a,1),519(a,1)),flip(a)]. 1955 x \ R(x,x \ y,z) = z \ L(z,y,x). [para(20(a,1),1953(a,1,2,2)),flip(a)]. 1956 x \ R(x,x * y,z) = z \ L(z,y,x). [para(313(a,1),1953(a,1,2)),flip(a)]. 1957 K(x,R(y,z,x) \ y) = 1. [para(1954(a,1),653(a,1,2))]. 1958 K(x,y \ R(y,z,x)) = 1. [para(622(a,1),1957(a,1,2))]. 1959 T(x,y \ R(y,z,x)) = x. [hyper(41,a,1958,a)]. 1960 K(x,T(y \ R(y,z,x),u)) = 1. [para(1831(a,1),1958(a,1,2))]. 1961 T(x \ R(x,y,z),z) = x \ R(x,y,z). [hyper(39,a,1959,a)]. 1962 K(x,a(y,z,x)) = 1. [para(739(a,2),1960(a,1,2))]. 1963 T(x,a(y,z,x)) = x. [hyper(41,a,1962,a)]. 1964 a(x,y,z) * z = z * a(x,y,z). [para(1963(a,1),82(a,1,2))]. 1965 R(x,y,z) \ x = z \ L(z,y,x). [para(1955(a,1),624(a,1)),flip(a)]. 1966 L(x,y,z) = x * (R(z,y,x) \ z). [para(1965(a,2),20(a,1,2)),flip(a)]. 1967 R(x,y,z) = x / (z \ L(z,y,x)). [para(1965(a,1),65(a,1,2)),flip(a)]. 1968 (x \ L(x,y,z)) \ 1 = z \ R(z,y,x). [para(1965(a,1),460(a,1,1))]. 1969 (x \ L(x,y,z)) * R(z,y,x) = z. [para(1965(a,1),496(a,1,1))]. 1970 L(x,y,z) = (R(z,y,x) \ z) * x. [para(1965(a,2),514(a,1,1)),flip(a)]. 1971 x * (R(K(y,z),u,x) \ K(y,z)) = L(x,u,K(z,y)). [para(1966(a,1),909(a,1))]. 1972 R(x,y,T(z,x * y)) = R(x,y,z). [hyper(23,a,680,a,b,1969,a),flip(a)]. 1973 L(x,y,z) * R(z,y,x) = x * z. [para(1969(a,1),504(a,1,2)),flip(a)]. 1974 L(x,y,z) * (x \ R(z,y,x)) = z. [para(1969(a,1),647(a,1)),flip(a)]. 1975 R(x,y,z) * L(z,y,x) = x * z. [para(1970(a,2),458(a,1,2))]. 1976 L(x,y,z) = (z \ R(z,y,x)) \ x. [para(1970(a,2),465(a,2)),flip(a)]. 1977 T(x \ R(x,y,z),u) \ z = L(z,y,T(x,u)). [para(1970(a,2),1832(a,1)),flip(a)]. 1978 L(x,y,z) \ x = z \ R(z,y,x). [para(1972(a,1),681(a,2,2))]. 1979 R(x,y,z) = x * (L(z,y,x) \ z). [para(1972(a,1),683(a,1))]. 1980 R(x,y,z) * (x \ L(z,y,x)) = z. [para(1972(a,1),686(a,1,1))]. 1981 (L(x,y,z) * (R(z,y,x) * u)) \ ((x * z) * u) = a(L(x,y,z),R(z,y,x),u). [para(1973(a,1),28(a,2,2,1)),flip(a)]. 1984 (L(x,y,z) \ x) * (z * u) = R(z,y,x) * u. [para(1978(a,2),528(a,1,1))]. 1985 (x \ R(x,y,z)) * u = z * (L(z,y,x) \ u). [para(1978(a,1),650(a,1,1))]. 1986 R(x \ R(x,y,z),z,u) = L(z,y,x) \ z. [para(1978(a,1),736(a,1,1))]. 1987 (x * y) * (x \ R(x,y,z)) = R(x,y,z) * y. [para(1978(a,1),1911(a,1,2))]. 1988 K(x,y) \ R(K(x,y),z,u) = u \ L(u,z,K(x,y)). [para(1669(a,1),1956(a,1,2))]. 1989 x \ R(x,y,z) = (L(z,y,x) \ z) * 1. [para(1968(a,1),517(a,1))]. 1990 R(x,y,L(z,y,x)) = R(x,y,z). [hyper(24,a,1980,a,b,1950,a)]. 1991 (x \ R(x,y,z)) \ z = L(z,y,T(x,z)). [para(1961(a,1),1977(a,1,1))]. 1992 L(x,y,T(z,x)) = L(x,y,z). [para(1991(a,1),1976(a,2)),flip(a)]. 1993 L(L(x,y,z),z * y,T(z,L(x,y,z))) = x. [para(1992(a,2),303(a,1))]. 1994 L(x,y,K(z,L(x,y,z))) = x. [para(1993(a,1),1606(a,1)),flip(a)]. 1995 x * (L(x,y,z) \ (z * u)) = R(z,y,x) * u. [para(1984(a,1),650(a,1)),flip(a)]. 1996 L((x \ R(x,y,z)) \ u,x \ R(x,y,z),x * y) = (R(x,y,z) * y) \ ((x * y) * u). [para(1987(a,1),76(a,2,1))]. 1998 L(x,y,z) * (R(z,y,x) * u) = x * (z * u). [para(1995(a,1),645(a,1,2))]. 1999 x * (L(x,y,z) \ (z * T(y,z))) = y * R(z,y,x). [para(1995(a,2),1643(a,1))]. 2000 x * (L(x,y,z) \ (z * L(x,y,z))) = z * x. [para(1995(a,2),1975(a,1))]. 2001 x * T(y,L(x,z,y)) = y * x. [para(36(a,2),2000(a,1,2))]. 2002 T(x,L(y,z,x)) = x * K(x,y). [hyper(23,a,1116,a,b,2001,a)]. 2005 K(x,L(y,z,x)) = K(x,y). [hyper(23,a,1107,a(flip),b,2002,a(flip)),flip(a)]. 2006 L(x,y,K(z,x)) = x. [para(2005(a,1),1994(a,1,3))]. 2007 L(T(x,y),z,K(u,x)) = T(x,y). [para(2006(a,1),44(a,2,1))]. 2008 L(x,y,K(x,z)) = x. [para(2006(a,1),909(a,1)),flip(a)]. 2009 L(x,y,a(x,z,z)) = x. [para(2006(a,1),1262(a,1)),flip(a)]. 2010 L(K(x,y),z,K(u,x \ 1)) = K((x \ 1) \ 1,y). [para(2006(a,1),1918(a,1,1,1)),flip(a)]. 2011 R(K(x,y),z,y) = K(x,y) / (y \ y). [para(2006(a,1),1967(a,2,2,2))]. 2013 (K(x,y) * z) * x = K(x,y) * (z * x). [para(2008(a,1),74(a,1,2))]. 2014 x * (x \ R(a(x,y,y),z,x)) = a(x,y,y). [para(2009(a,1),1974(a,1,1))]. 2015 T(x,K(y,x) * z) = T(x,z). [para(2007(a,1),1377(a,1)),flip(a)]. 2016 K(K(x,y) * z,y) = T(y,z) \ y. [para(2015(a,1),1080(a,2,1))]. 2017 K(x,K(y,x) * z) = x \ T(x,z). [para(2015(a,1),1108(a,2,2))]. 2018 T(x,T(x,y) * z) = T(x,x * z). [para(1098(a,1),2015(a,1,2)),flip(a)]. 2019 T(x,y * T(z,x)) = T(x,y * z). [para(1212(a,1),2015(a,1,2))]. 2021 K(K(x,y) * z,y) = K(z,y). [para(2016(a,2),1080(a,2)),flip(a)]. 2022 K(K(x,y) * z,x) = K(z,x). [para(901(a,1),2021(a,1,1)),flip(a)]. 2023 K(x * (K(x,y) * z),x) = K(x * z,x). [para(1068(a,1),2022(a,1,1))]. 2024 K(x,K(y,x) * z) = K(x,z). [para(2017(a,2),1108(a,2)),flip(a)]. 2025 K(x,K(x,y) * z) = K(x,z). [para(901(a,1),2024(a,1,2)),flip(a)]. 2026 K(x,y) * K(x * (K(x,z) * y),x) = a(x,K(x,z) * y,x). [para(2025(a,1),1537(a,1,1))]. 2027 R(K(x,y),z,y) = K(x,y) / 1. [para(60(a,1),2011(a,2,2))]. 2029 R(K(x,y),z,y) = K(x,y). [para(2027(a,2),64(a,1))]. 2030 K(x,R(y,z,y)) = K(x,y). [para(2029(a,1),1654(a,1)),flip(a)]. 2031 R(K(x,y),z,x) = K(y,x) \ 1. [para(2029(a,1),1670(a,1,1)),flip(a)]. 2032 K(x,y) * R(T(y,x),z,y) = R(y,z,y). [para(2030(a,1),1083(a,1,1))]. 2033 R(K(x,y),z,x) = K(x,y). [para(2031(a,2),897(a,1))]. 2034 K(L(x,y,x),z) = K(x,z). [para(2033(a,1),1638(a,1)),flip(a)]. 2036 K((x \ y) \ y,z) = K(T(x,y),z). [para(1457(a,1),2034(a,1,1))]. 2038 K(T(x,x \ y),z) = K(T(x,y),z). [para(83(a,2),2036(a,1,1))]. 2039 x \ (K(x,y) * (z * x)) = T(K(x,y) * z,x). [para(2013(a,1),36(a,2,2)),flip(a)]. 2040 x * ((K(x,y) * z) * x) = T(x,y) * (z * x). [para(2013(a,2),1120(a,1,2))]. 2041 T(x,y) \ R(T(x,y),z,x) = x \ R(x,z,x). [para(2032(a,1),1163(a,1,2)),flip(a)]. 2042 x * (x \ a(R(x,y,x),z,z)) = a(x,z,z). [para(1930(a,2),2014(a,1,2,2))]. 2043 x * (x \ a(L(x,y,x),z,z)) = a(x,z,z). [para(1303(a,1),2042(a,1,2,2,1))]. 2044 a(L(x,y,x),z,z) = a(x,z,z). [para(2043(a,1),20(a,1)),flip(a)]. 2045 a(L(T(x,y),y * x,x),z,z) = a(T(x,y),z,z). [para(1283(a,1),2044(a,1,1))]. 2046 K(x,y) * (x \ (z * x)) = T(K(x,y) * z,x). [para(2039(a,1),1076(a,1)),flip(a)]. 2047 (T(x,y) * (z * x)) \ ((T(x,y) * z) * x) = a(x,K(x,y) * z,x). [para(2040(a,1),1166(a,1,1))]. 2048 T(x,y) \ R(T(x,y),z,x) = a(x,z,x). [para(2041(a,2),1539(a,1))]. 2049 T(x \ R(x,y,x),z) = a(x,y,x). [para(2048(a,1),1831(a,1)),flip(a)]. 2050 T(a(x,y,x),z) = a(x,y,x). [para(1539(a,1),2049(a,1,1))]. 2051 a(x,y,x) * z = z * a(x,y,x). [para(2050(a,1),82(a,1,2)),flip(a)]. 2052 a(R(x,y,z),u,x) = R(a(x,u,x),y,z). [para(2050(a,1),1933(a,1,1)),flip(a)]. 2053 (a(x,y,x) * z) * L(u,z,a(x,y,x)) = (z * u) * a(x,y,x). [para(2051(a,1),74(a,2))]. 2054 a(x,y,x) \ a(R(x,z,z),y,x) = a(a(x,y,x),z,z). [para(2052(a,2),962(a,1,2))]. 2056 T(K(x,y) * z,x) = K(x,y) * T(z,x). [para(36(a,2),2046(a,1,2)),flip(a)]. 2057 T(K(x,y) * R(z,u,w),x) = K(x,y) * R(T(z,x),u,w). [para(46(a,2),2056(a,2,2))]. 2058 T(K(x,y) * z,x) / z = K(z,x) * K(x,y). [para(2056(a,2),1666(a,1,1))]. 2059 T(K(x,y) * z,x) / z = K(x,y) * K(z,x). [para(2058(a,2),1226(a,2)),flip(a)]. 2060 L(K(x,y),z,K(u,x \ 1)) = K(x,y). [para(156(a,1),2010(a,2,1))]. 2061 L(K(x,y),z,K(u,x)) = K(x,y). [para(2060(a,1),1618(a,1)),flip(a)]. 2062 L(K(x,y),z,K(x,u)) = K(x,y). [para(2060(a,1),1619(a,1)),flip(a)]. 2063 (K(x,y) * z) \ z = T(K(y,x),z). [para(2061(a,1),1301(a,1,1)),flip(a)]. 2064 T(K(x,y) * z,K(x,y)) = z * K(x,y). [para(2062(a,1),1309(a,1,1,1))]. 2065 x / T(K(y,z),x) = K(z,y) * x. [para(2063(a,1),65(a,1,2))]. 2067 (T(K(x,y),z) / z) * u = (K(y,x) * z) \ u. [para(2065(a,1),358(a,1,1)),flip(a)]. 2068 (K(x,y) * z) * K(y,x) = T(z,K(y,x)). [para(2065(a,1),1549(a,1,1))]. 2069 K(K(x,y) * z,K(y,x)) = T(z,K(y,x)) / z. [para(2068(a,1),979(a,1,1)),flip(a)]. 2070 K(K(x,y) * z,K(y,x)) = K(z,K(y,x)). [para(2069(a,2),1086(a,2)),flip(a)]. 2071 K(K(x,y) * z,K(x,y)) = K(z,K(x,y)). [para(901(a,1),2070(a,1,1)),flip(a)]. 2072 a(a(K(x,y),z,z),u,w) = a(K(z,K(x,y)),u,w). [para(2071(a,1),1826(a,1,1)),flip(a)]. 2073 a(R(T(x,y),y,x),z,z) = a(T(x,y),z,z). [para(1306(a,1),2045(a,1,1))]. 2074 a(R(x,y,y),z,z) = a(T(x,y),z,z). [para(2073(a,1),1772(a,1)),flip(a)]. 2076 x * (K(y,z) * R(K(z,y),u,x)) = L(x,u,K(z,y)). [para(1671(a,1),1971(a,1,2))]. 2077 x * (K(y,z) * K(z,R(y,u,x))) = L(x,y * u,K(y,z)). [para(1668(a,1),1971(a,1,2))]. 2078 x * (L(x,y,z) \ (y * z)) = y * R(z,y,x). [para(82(a,1),1999(a,1,2,2))]. 2079 L(x,y,z) = (x * (y * z)) / (y * R(z,y,x)). [para(2078(a,1),648(a,1,2)),flip(a)]. 2080 T(K(x,y) * R(y,z,u),x) = y * T(y \ R(y,z,u),x). [para(2057(a,2),1834(a,1))]. 2081 T(K(x,y) * R(y,z,u),x) / R(y,z,u) = K(R(y,z,u) / y,x). [para(2080(a,2),1211(a,1,1))]. 2082 a(x,K(x,y) * z,x) = K(x,z) * K(x * z,x). [para(2023(a,1),2026(a,1,2)),flip(a)]. 2083 a(x,K(x,y) * z,x) = a(x,z,x). [para(2082(a,2),1537(a,1))]. 2085 a(x,K(x,y) * z,x) = a(T(x,y),z,x). [para(2047(a,1),28(a,2)),flip(a)]. 2086 a(T(x,y),z,x) = a(x,z,x). [para(2085(a,1),2083(a,1))]. 2087 a((x \ y) \ y,z,x) = a(x,z,x). [para(83(a,1),2086(a,1,1))]. 2089 a((x \ y) * y,z,x) = a(x,z,x). [para(2087(a,1),1702(a,1)),flip(a)]. 2090 a((x * y) * y,z,x) = a(x,z,x). [para(2089(a,1),1707(a,1)),flip(a)]. 2091 a(R(x,y,y),z,x) = a(x,z,x). [para(2090(a,1),1721(a,1)),flip(a)]. 2092 a(a(x,y,x),z,z) = a(x,y,x) \ a(x,y,x). [para(2091(a,1),2054(a,1,2)),flip(a)]. 2093 a(a(x,y,x),z,z) = 1. [para(2092(a,2),60(a,1))]. 2095 L(x,x,a(y,z,y)) = x. [hyper(37,a,2093,a)]. 2097 L(x,x,a(y,z,z)) = x. [para(2095(a,1),1695(a,2))]. 2098 L(x,x,K(y,z)) = x. [para(2097(a,1),1263(a,1)),flip(a)]. 2099 R(T(a(x,y,y),z),z,z) = z \ (a(x,y,y) * z). [para(2097(a,1),1804(a,1,1)),flip(a)]. 2100 a(K(x,y),z,z) = 1. [hyper(38,a,2098,a)]. 2101 K(x,y) * (z \ 1) = K(x,y) / z. [para(2098(a,1),915(a,1,2)),flip(a)]. 2102 (K(x,y) * (z / u)) \ K(x,y) = u / z. [para(2098(a,1),925(a,1)),flip(a)]. 2103 L(x,K(y,z),x) = x. [para(2098(a,1),1895(a,2))]. 2104 R(K(x,y),z,z) = K(x,y) * 1. [para(2100(a,1),963(a,1,2)),flip(a)]. 2105 a(K(x,K(y,z)),u,w) = a(1,u,w). [para(2100(a,1),2072(a,1,1)),flip(a)]. 2106 T(K(x,y),z) / z = z \ K(x,y). [para(2103(a,1),441(a,1,2))]. 2107 K(x,R(y,z,z)) = K(x,y). [hyper(24,a,1767,a,b,2104,a(flip)),flip(a)]. 2108 K(x,y / (z \ 1)) = K(x,y * z). [para(720(a,1),2107(a,1,2)),flip(a)]. 2112 K(x,y) * (x / z) = T(x,y) / z. [para(2107(a,1),1815(a,1,1))]. 2114 K(x,y) / (z \ 1) = K(x,y) * z. [para(156(a,1),2101(a,1,2)),flip(a)]. 2115 a(K(x,K(y,z)),u,w) = 1. [para(2105(a,2),125(a,1))]. 2117 L(x,y,K(z,K(u,w))) = x. [hyper(37,a,2115,a)]. 2119 x * (x \ R(K(y,K(z,u)),w,x)) = K(y,K(z,u)). [para(2117(a,1),1974(a,1,1))]. 2121 (K(x,y) * z) \ u = (z \ K(y,x)) * u. [para(2106(a,1),2067(a,1,1)),flip(a)]. 2122 K(x,R(((y \ 1) * z) \ 1,z,z)) = K(x,(z \ 1) * y). [para(1739(a,2),2108(a,1,2))]. 2123 T(x,y) / (z \ x) = K(x,y) * z. [para(65(a,1),2112(a,1,2)),flip(a)]. 2125 (K(x,y) * z) \ K(x,y) = z \ 1. [para(2114(a,1),66(a,1,1))]. 2126 (K(x,y) * z) \ T(x,y) = z \ x. [para(2123(a,1),66(a,1,1))]. 2127 (K(x,y) \ z) \ 1 = z \ K(x,y). [para(20(a,1),2125(a,1,1)),flip(a)]. 2128 (K(x,y) * z) \ y = z \ T(y,x). [para(901(a,1),2126(a,1,1)),flip(a)]. 2129 L(x \ y,x,K(z,y)) = x \ y. [para(2126(a,1),1248(a,2))]. 2130 a(K(x,y),z,z \ y) = 1. [hyper(38,a,2129,a)]. 2132 a(K(x,y * z),y,z) = 1. [para(19(a,1),2130(a,1,3))]. 2133 (K(x,y) \ z) \ u = (z \ K(x,y)) * u. [para(2127(a,1),318(a,1,1)),flip(a)]. 2134 ((x * y) \ K(z,x)) * u = (T(x,z) * y) \ u. [para(1160(a,1),2121(a,1,1)),flip(a)]. 2135 (x \ K(y,z)) * K(z,y) = x \ 1. [para(2121(a,1),2125(a,1))]. 2136 (x \ K(y,z)) * y = x \ T(y,z). [para(2121(a,1),2128(a,1))]. 2137 ((x / y) \ K(z,u)) * K(u,z) = y / x. [para(2121(a,1),2102(a,1))]. 2138 (x / y) * K(x,x * y) = (x \ y) \ 1. [para(1011(a,1),2135(a,1,1))]. 2139 (x \ T(y,z)) \ ((x \ K(y,z)) * (y * u)) = L(u,y,x \ K(y,z)). [para(2136(a,1),32(a,2,1)),flip(a)]. 2140 x / K(y,z) = x * K(z,y). [para(66(a,1),2137(a,1,1)),flip(a)]. 2141 (x * K(y,z)) \ x = K(z,y). [para(2140(a,1),66(a,1,1))]. 2143 (x * K(y,z)) \ u = (K(z,y) / x) * u. [para(2140(a,1),358(a,1,1))]. 2144 (K(x,y) * z) / K(x,y) = T(z,K(y,x)). [para(2140(a,2),2068(a,1))]. 2145 T(x,K(y,z)) \ x = K(x,K(z,y)). [para(2144(a,1),1053(a,2,1)),flip(a)]. 2146 K(K(x,y),z) = K(z,K(y,x)). [para(2145(a,1),1080(a,2))]. 2147 K(x,K(y,z)) * K(x,K(z,y)) = 1. [para(2146(a,1),898(a,1,1))]. 2148 K(x,y) * K(z,K(y,x)) = T(K(x,y),z). [para(2146(a,1),1107(a,2,2)),flip(a)]. 2149 K(x,y) * T(K(y,x),z) = K(z,K(x,y)). [para(2146(a,1),1114(a,2))]. 2150 T(K(x,y),z) \ 1 = T(K(y,x),z). [para(2148(a,1),1140(a,1)),flip(a)]. 2151 T(K(x,y),z) * T(K(y,x),z) = 1. [para(2150(a,1),20(a,1,2))]. 2152 T(K(x,y),z) * K(y,x) = K(z,K(y,x)). [para(2149(a,1),405(a,2))]. 2153 R(T(a(x,y,y),z),z,z) = T(a(x,y,y),z). [para(2099(a,2),36(a,2)),flip(a)]. 2154 R(T(a(x,y,y),z),z,z) = a(T(x,z),y,y). [para(2153(a,2),1836(a,2)),flip(a)]. 2155 R(a(T(x,y),z,z),y,y) = a(T(x,y),z,z). [para(1836(a,2),2154(a,1,1))]. 2156 a(R(T(x,y),y,y),z,z) = a(T(x,y),z,z). [para(2155(a,1),1930(a,2))]. 2157 a(T(T(x,y),y),z,z) = a(T(x,y),z,z). [para(2156(a,1),2074(a,1)),flip(a)]. 2158 a(T(x,y),z,z) = a(x,z,z). [para(2157(a,1),1724(a,1))]. 2161 (x * (y * (a(y,z,z) * u))) / (R(T(y,x),z,z) * u) = T(x,y). [para(2158(a,1),1210(a,1,1,2,2,1))]. 2165 R(K(x,K(y,z)),u,w) = K(x,K(y,z)). [para(2119(a,1),20(a,1)),flip(a)]. 2166 K(x,R(K(y,z),u,w)) = K(x,K(y,z)). [para(2165(a,1),1654(a,1)),flip(a)]. 2167 K(x,K(y,R(z,u,w))) = K(x,K(y,z)). [para(1654(a,1),2166(a,1,2))]. 2168 K(K(R(x,y,z),u),w) = K(w,K(u,x)). [para(2167(a,1),2146(a,2))]. 2169 K(R(K(x,y),z,u),w) = K(w,K(y,x)). [para(1634(a,1),2168(a,1,1))]. 2170 K(x,R((y \ z) \ 1,z,z)) = K(x,(z \ 1) * y). [para(318(a,1),2122(a,1,2,1,1))]. 2171 K(x,(y \ z) \ 1) = K(x,(z \ 1) * y). [para(2170(a,1),2107(a,1)),flip(a)]. 2172 K(x,(y \ z) \ 1) = K(x,z \ y). [para(318(a,1),2171(a,2,2))]. 2174 K(x,(y / z) \ y) = K(x,z / (a(y,z,z) \ 1)). [para(2172(a,1),1447(a,1))]. 2175 K(x,y / (a(z,y,y) \ 1)) = K(x,y). [para(66(a,1),2174(a,1,2)),flip(a)]. 2176 K(x,y * a(z,y,y)) = K(x,y). [para(1445(a,1),2175(a,1,2))]. 2177 K(x * a(y,x,x),z) = (z \ 1) / (z \ K(z,x)). [para(2176(a,1),1057(a,1,2,2)),flip(a)]. 2178 K(x * a(y,x,x),z) = K(x,z). [para(2177(a,2),1057(a,1))]. 2179 (x / y) * T(y,z) = x * K(y,z). [para(2178(a,1),1463(a,1,2)),flip(a)]. 2180 (x * y) * K(y,z) = x * T(y,z). [para(21(a,1),2179(a,1,1)),flip(a)]. 2183 L(K(x,y),x,z) = K(x,y). [hyper(23,a,1117,a,b,2180,a),flip(a)]. 2184 (x * y) \ (x * T(y,z)) = K(y,z). [hyper(23,a,20,a,b,2180,a),flip(a)]. 2185 (x * (y * z)) \ (x * (y * T(z,u))) = L(K(z,u),y * z,x). [para(2180(a,1),32(a,2,2,2)),flip(a)]. 2186 (x * T(y,z)) \ (x * y) = K(z,y). [para(2180(a,1),2141(a,1,1))]. 2187 L(K(T(x,y),z),x,y) = K(T(x,y),z). [para(2183(a,1),1376(a,1)),flip(a)]. 2189 (x * (y * z)) \ ((x * y) * T(L(z,y,x),u)) = K(L(z,y,x),u). [para(74(a,1),2184(a,1,1))]. 2192 T(K(x,y),x * z) = K(T(x,z),y). [para(2187(a,1),1522(a,1)),flip(a)]. 2193 K(T(x,x \ y),z) = T(K(x,z),y). [para(20(a,1),2192(a,1,2)),flip(a)]. 2194 K(T(x,y),z) = T(K(x,z),y). [para(2193(a,1),2038(a,1)),flip(a)]. 2195 K(x,T(y,z)) * T(K(y,x),z) = 1. [para(2194(a,1),898(a,1,2))]. 2196 K(T(x,y * T(T(y,x),x)),z) = T(T(K(x,z),y),T(y,x)). [para(2194(a,2),1905(a,1))]. 2197 K(x,T(y,z)) = T(K(x,y),z). [hyper(24,a,2151,a,b,2195,a)]. 2199 K(x,y) * K(y,T(x,z)) = K(K(y,x),z). [para(2197(a,2),1114(a,1,2))]. 2200 K(x,T(y,z \ 1)) * z = z * K(x,y). [para(2197(a,2),1907(a,1,1))]. 2201 K(x,T(y,z)) / z = z \ K(x,y). [para(2197(a,2),2106(a,1,1))]. 2202 K(x,y) * K(y,T(x,z)) = K(z,K(x,y)). [para(2197(a,2),2149(a,1,2))]. 2203 K(x,T(y,z)) * K(y,x) = K(z,K(y,x)). [para(2197(a,2),2152(a,1,1))]. 2204 K(T(x,y),z) = K(x,T(z,y)). [para(2197(a,2),2194(a,2))]. 2205 K(x,T(y,z)) * K(y,x) = K(K(x,y),z). [para(2199(a,1),1226(a,2))]. 2206 K(x,T(y,z)) * K(y,x) = K(x,K(y,z)). [para(2202(a,1),1873(a,2))]. 2207 K(x,y) * K(x,K(y,z)) = K(x,T(y,z)). [para(2206(a,1),1225(a,1,2))]. 2208 K(x,K(y,z)) = K(z,K(y,x)). [para(2206(a,1),2203(a,1))]. 2209 K(K(x,y),z) = K(x,K(y,z)). [para(2206(a,1),2205(a,1)),flip(a)]. 2210 1 / K(x,K(y,z)) = K(K(y,x),z). [para(2208(a,1),899(a,1,2))]. 2211 K(K(x,y),z) = K(K(x,z),y). [para(2210(a,1),899(a,1))]. 2212 K(K(x,y),z) = K(y,K(z,x)). [para(2211(a,1),2146(a,1))]. 2213 K(x,K(y,z)) = K(z,K(x,y)). [para(2212(a,1),2209(a,1))]. 2214 T(K(x,y) * K(x,K(y,z)),z) = K(x,y). [para(2213(a,2),1020(a,1,1,2))]. 2215 T(K(x,T(y,z)),z) = K(x,y). [para(2207(a,1),2214(a,1,1))]. 2216 K(x,T(y,z)) * z = z * K(x,y). [para(2215(a,1),82(a,1,2)),flip(a)]. 2217 K(x,T(T(y,z),z)) = K(x,y). [para(2215(a,1),2197(a,2))]. 2219 K(x,T(y,z \ 1)) = K(x,T(y,z)). [hyper(24,a,2200,a,b,2216,a),flip(a)]. 2220 T(K(x,y) * z,K(x,y)) = K(x,T(y,z)) * z. [para(2216(a,2),2064(a,2))]. 2221 K(x,T(y,z \ (z \ (u \ 1)))) = K(x,T(y,u * (z * z))). [para(409(a,1),2219(a,1,2,2))]. 2222 K(T(x,y * T(y,x)),z) = T(T(K(x,z),y),T(y,x)). [para(2019(a,1),2196(a,1,1))]. 2223 T(T(K(x,y),z),T(z,x)) = K(T(x,z * z),y). [para(2019(a,1),2222(a,1,1)),flip(a)]. 2224 T(T(K(x,y),z),T(z,x)) = K(x,T(y,z * z)). [para(2223(a,2),1278(a,1))]. 2225 T(K(x,T(y,z)),T(z,x)) = K(x,T(y,z * z)). [para(2197(a,2),2224(a,1,1))]. 2226 K(T(x,T(y,x)),T(z,y)) = K(x,T(z,y * y)). [para(2225(a,1),2194(a,2))]. 2227 K(T(x,y),T(z,y)) = K(x,T(z,y * y)). [para(1131(a,1),2226(a,1,1))]. 2228 K(x,T(T(y,z),z)) = K(x,T(y,z * z)). [para(2227(a,1),2204(a,1)),flip(a)]. 2229 K(x,T(y,z * z)) = K(x,y). [para(2228(a,1),2217(a,1))]. 2230 K(x,T(y,z * (z * u))) = K(x,T(y,u)). [para(662(a,1),2229(a,1,2))]. 2232 K(x,T(y,z \ u)) = K(x,T(y,z * u)). [para(20(a,1),2230(a,1,2,2,2)),flip(a)]. 2233 K(x,T(y,T(z,z * u))) = K(x,T(y,(z \ u) * u)). [para(250(a,1),2230(a,1,2,2,2)),flip(a)]. 2234 K(x,T(y,(z / u) * (z * z))) = K(x,T(y,u / (z \ 1))). [para(399(a,1),2230(a,1,2,2,2))]. 2235 K(x,T(y,z \ (z \ u))) = K(x,T(y,u)). [para(20(a,1),2232(a,2,2,2))]. 2236 K(x,T(y,z * (u * u))) = K(x,T(y,z \ 1)). [para(2221(a,1),2235(a,1))]. 2237 K(x,T(y,z * (u * u))) = K(x,T(y,z)). [para(2236(a,2),2219(a,1))]. 2239 K(x,T(y,z / (u \ 1))) = K(x,T(y,u / z)). [para(2234(a,1),2237(a,1))]. 2241 (x * (R(y,z,z) * u)) / (R(T(y,x),z,z) * u) = T(x,y). [para(966(a,1),2161(a,1,1,2))]. 2243 T(x,R(y,z,z)) = T(x,y). [para(2241(a,1),1209(a,1)),flip(a)]. 2244 T(x,y / (z \ 1)) = T(x,y * z). [para(720(a,1),2243(a,1,2)),flip(a)]. 2246 K(x,T(y,z / u)) = K(x,T(y,u * z)). [para(2244(a,1),2239(a,1,2)),flip(a)]. 2247 K(x,T(y,(z \ u) * u)) = K(x,T(y,z)). [para(65(a,1),2246(a,1,2,2)),flip(a)]. 2248 K(x,T(y,T(z,z * u))) = K(x,T(y,z)). [para(2247(a,1),2233(a,2))]. 2249 K(x,T(y,T(z,u))) = K(x,T(y,z)). [para(20(a,1),2248(a,1,2,2,2))]. 2251 K(x,K(y,T(z,u))) = K(x,T(y,z)) * K(y,x). [para(2249(a,1),2206(a,1,1)),flip(a)]. 2253 K(x,K(y,T(z,u))) = K(x,K(y,z)). [para(2251(a,2),2206(a,1))]. 2254 K(x,K(y,z \ R(z,u,w))) = K(x,K(y,a(z,u,w))). [para(739(a,2),2253(a,1,2,2)),flip(a)]. 2255 K(x,K(y \ R(y,z,u),w)) = K(x,K(w,a(y,z,u))). [para(1849(a,2),2254(a,1,2))]. 2256 (x * (y * z)) \ ((x * y) * L(T(z,u),y,x)) = K(L(z,y,x),u). [para(44(a,2),2189(a,1,2,2))]. 2257 (x * (y * z)) \ (x * (y * T(z,u))) = K(L(z,y,x),u). [para(74(a,1),2256(a,1,2))]. 2258 L(K(x,y),z * x,u) = K(L(x,z,u),y). [para(2257(a,1),2185(a,1)),flip(a)]. 2259 K(L(x,y / x,z),u) = L(K(x,u),y,z). [para(22(a,1),2258(a,1,2)),flip(a)]. 2260 K(x,y) * K(R(y,z,u),x) = K(R(y,z,u) / y,x). [para(2081(a,1),2059(a,1)),flip(a)]. 2261 K(x,y) * K(R(y,z,u),x) = K(y \ R(y,z,u),x). [para(478(a,1),2260(a,2,1))]. 2262 K(x,y) * K(R(y,z,u),x) = K(x,y \ R(y,z,u)). [para(2261(a,2),1849(a,1))]. 2263 K(x,K(y,z) \ R(K(y,z),u,w)) = K(x,K(y,z)) * K(x,K(z,y)). [para(2169(a,1),2262(a,1,2)),flip(a)]. 2264 (x * T(y,z)) \ ((x * K(y,z)) * (y * u)) = L(u,y,x \ K(y,z)). [para(2139(a,1),284(a,1)),flip(a)]. 2265 K(x,K(y,z) \ R(K(y,z),u,w)) = 1. [para(2263(a,2),2147(a,1))]. 2266 K(x,K(y,z) \ K(R(y,u,w),z)) = 1. [para(1629(a,1),2265(a,1,2,2))]. 2268 K(x,K(y,z) * K(R(z,u,w),y)) = 1. [para(900(a,1),2266(a,1,2))]. 2269 K(x,K(y \ R(y,z,u),w)) = 1. [para(2261(a,1),2268(a,1,2))]. 2270 K(x,K(y,a(z,u,w))) = 1. [para(2269(a,1),2255(a,1)),flip(a)]. 2271 T(x,K(y,a(z,u,w))) = x. [hyper(41,a,2270,a)]. 2273 K(x,T(a(y,z,u),w)) = K(x,a(y,z,u)). [hyper(24,a,2220,a(flip),b,2271,a(flip)),flip(a)]. 2274 K(x,y \ R(y,z,u)) = K(x,a(y,z,u)). [para(1839(a,1),2273(a,1,2))]. 2275 K(x,y \ R(y,z,u)) = K(a(y,z,u),x). [para(2274(a,2),1847(a,2)),flip(a)]. 2276 K(x \ R(x,y,z),u) = K(u,a(x,y,z)). [para(2274(a,1),1849(a,2))]. 2277 K(x,a(y,z,L(u,z,y))) = K(x,y \ R(y,z,u)). [para(1990(a,1),2274(a,1,2,2)),flip(a)]. 2278 K(x,y) * K(R(y,z,u),x) = K(x,a(y,z,u)). [para(2274(a,1),2262(a,2))]. 2279 K(x,a(K(y,z),u,w)) = 1. [para(2274(a,1),2265(a,1))]. 2280 T(x,a(K(y,z),u,w)) = x. [hyper(41,a,2279,a)]. 2281 ((K(x,y) * z) * u) / (K(x,y) * (z * u)) = a(K(x,y),z,u). [para(2280(a,1),300(a,1,2))]. 2282 K(R(x,y,z) \ x,u) = K(u,a(x,x * y,z)). [para(618(a,1),2276(a,1,1))]. 2283 K(x,y) * K(y,R(x,z,u)) = K(y,a(x,z,u)). [para(2278(a,1),1674(a,1)),flip(a)]. 2284 L(x,y * z,K(y,u)) = x * K(u,a(y,z,x)). [para(2283(a,1),2077(a,1,2)),flip(a)]. 2285 K(x,a(y,z,L(u,z,y))) = K(x,a(y,z,u)). [para(2277(a,2),2274(a,1))]. 2286 K(x,y) \ R(K(x,y),z,u) = a(K(x,y),z,u). [para(2281(a,1),537(a,1)),flip(a)]. 2287 x \ L(x,y,K(z,u)) = a(K(z,u),y,x). [para(2286(a,1),1988(a,1)),flip(a)]. 2288 x * a(K(y,z),u,x) = L(x,u,K(y,z)). [para(2287(a,1),20(a,1,2))]. 2289 a(K(x,y),x * z,u) = K(y,a(x,z,u)). [hyper(23,a,2284,a(flip),b,2288,a)]. 2290 x * a(K(y,z),u,x) = L(x,u,K(z,y)). [para(905(a,1),2288(a,1,2))]. 2291 K(x,a(y,y * z,u)) = a(K(y,x),z,u). [para(2289(a,1),1778(a,1))]. 2292 K((x * y) * z,a(x,y,z)) = 1. [para(2289(a,1),2132(a,1))]. 2293 K(x * (y * z),a(x,y,L(z,y,x))) = 1. [para(74(a,1),2292(a,1,1))]. 2294 K(x,a(y,y * z,u)) = a(K(x,y),z,u). [para(2291(a,2),905(a,1))]. 2295 K(x * (y * z),a(x,y,z)) = 1. [para(2293(a,1),2285(a,1)),flip(a)]. 2296 x \ R(x,y,z) = a(x,y,z) * 1. [para(2295(a,1),1848(a,1,2)),flip(a)]. 2297 a(x,y,z) = x \ R(x,y,z). [hyper(24,a,18,a,b,2296,a(flip))]. 2298 a(x,y,z) = L(z,y,x) \ z. [hyper(24,a,1989,a(flip),b,2296,a(flip))]. 2300 R(x,y,z) = x * a(x,y,z). [para(2297(a,2),20(a,1,2)),flip(a)]. 2301 L(x,y,z) \ L(R(x,u,w),y,z) = a(L(x,y,z),u,w). [para(48(a,1),2297(a,2,2)),flip(a)]. 2302 R(x,y,z) \ x = a(x,y,z) \ 1. [para(2297(a,2),462(a,1,1)),flip(a)]. 2303 R(x,y,z) = a(x,y,z) * x. [para(2297(a,2),479(a,1,1)),flip(a)]. 2306 x * (a(x,y,z) * u) = R(x,y,z) * u. [para(2297(a,2),501(a,1,2,1))]. 2307 R(x,y,z) \ (x * u) = a(x,y,z) \ u. [para(2297(a,2),522(a,1,1)),flip(a)]. 2308 a(x,y,z) * (x * u) = R(x,y,z) * u. [para(2297(a,2),528(a,1,1))]. 2309 R(x,y,z) * (x \ u) = a(x,y,z) * u. [para(2297(a,2),532(a,1,1)),flip(a)]. 2310 a(x,x * y,z) = R(x,y,z) \ x. [para(2297(a,2),618(a,1))]. 2311 a(x,y,z) = R(x,x * y,z) \ x. [para(2297(a,2),622(a,2)),flip(a)]. 2313 a(x,y,z) = x * R(x \ 1,y,z). [para(2297(a,2),635(a,2)),flip(a)]. 2314 L(x,a(y,z,u),y * z) = x. [para(2297(a,2),1411(a,1,2))]. 2315 (x * y) * R((x * y) \ x,z,u) = x * a(y,z,u). [para(2297(a,2),1592(a,2,2))]. 2316 x \ (R(y,z,u) * (y \ x)) = a(T(y,x),z,u). [para(2297(a,2),1830(a,1)),flip(a)]. 2317 T(x \ R(x,y,z),u) = a(T(x,u),y,z). [para(2297(a,2),1831(a,1)),flip(a)]. 2318 R(x \ R(x,y,z),u,w) = a(R(x,u,w),y,z). [para(2297(a,2),1927(a,1)),flip(a)]. 2319 L(x \ R(x,y,z),u,w) = a(L(x,u,w),y,z). [para(2297(a,2),1939(a,1)),flip(a)]. 2320 a(x,y,z) = z \ L(z,x * y,x). [para(2297(a,2),1953(a,2)),flip(a)]. 2321 L(x,y,z) = a(z,y,x) \ x. [para(2297(a,2),1976(a,2,1))]. 2322 a(x,x * y,z) = z \ L(z,y,x). [para(2297(a,2),1956(a,1))]. 2323 x * (L(x,y,z) \ u) = a(z,y,x) * u. [para(2297(a,2),1985(a,1,1)),flip(a)]. 2325 L(L(x,y,z),u,w) \ L(x,u,w) = a(z,y,L(x,u,w)). [para(49(a,1),2298(a,2,1)),flip(a)]. 2326 L(x,y,z) = x / a(z,y,x). [para(2298(a,2),65(a,1,2)),flip(a)]. 2327 a(x,x * y,(x * y) \ z) = (y \ (x \ z)) \ ((x * y) \ z). [para(270(a,1),2298(a,2,1))]. 2328 a(x,y,z) \ 1 = z \ L(z,y,x). [para(2298(a,2),511(a,1,1))]. 2329 a(x,y,z) = z / L(z,y,x). [para(2298(a,2),519(a,2)),flip(a)]. 2331 x \ (L(x,y,z) * u) = a(z,y,x) \ u. [para(2298(a,2),512(a,1,1)),flip(a)]. 2332 L(x,y,z) \ (x * u) = a(z,y,x) * u. [para(2298(a,2),524(a,2,1))]. 2333 a(x,y,z) * (L(z,y,x) * u) = z * u. [para(2298(a,2),646(a,1,1))]. 2334 (x * y) / (L(x,z,u) * y) = a(u,z,x). [para(2298(a,2),649(a,2))]. 2335 L(x,y,z) * (x \ u) = a(z,y,x) \ u. [para(2298(a,2),651(a,1,1)),flip(a)]. 2336 a(T(x,y),z,y) = L(y,z,x) \ y. [para(1992(a,1),2298(a,2,1))]. 2337 R(x,y * (y * z),u) = x * a(x,z,u). [para(1778(a,1),2300(a,2,2))]. 2338 ((x * y) * a(x,y,z)) * u = (x * y) * (a(x,y,z) * u). [para(2314(a,1),74(a,1,2))]. 2340 K(a(x,y,z) \ 1,u) = K(u,a(x,x * y,z)). [para(2302(a,1),2282(a,1,1))]. 2341 a(x,x * y,z) = a(x,y,z) \ 1. [para(2310(a,2),2302(a,1))]. 2342 L(x,y * z,y) = x * a(y,z,x). [para(2311(a,2),1966(a,2,2))]. 2343 a(x,x * y,z) \ 1 = a(x,y,z). [para(2311(a,2),2302(a,1)),flip(a)]. 2344 L(x,a(y,z,u),z) = x. [para(2313(a,2),1443(a,1,2))]. 2347 (x * a(y,x,z)) * u = x * (a(y,x,z) * u). [para(2344(a,1),74(a,1,2))]. 2348 (x \ a(y,x,z)) \ 1 = a(y,x,z) \ x. [para(2344(a,1),259(a,1)),flip(a)]. 2349 (x \ a(y,x,z)) \ u = a(y,x,z) \ (x * u). [para(2344(a,1),267(a,1)),flip(a)]. 2350 (x * y) \ (x * L(y,z * u,z)) = L(a(z,u,y),y,x). [para(2320(a,2),76(a,1,1)),flip(a)]. 2351 a(x,y,L(z,y,x)) = L(z,y,x) \ z. [para(303(a,1),2320(a,2,2))]. 2356 (x * L(y,z,u)) / L(a(u,u * z,y),y,x) = x * y. [para(2322(a,2),179(a,1,2,1))]. 2357 ((x * y) \ x) * L(L(y,x,x * y),z,u) = a(u,z,L(y,x,x * y)) \ 1. [para(2328(a,2),738(a,1)),flip(a)]. 2358 a(T(x,y),z,y) = a(x,z,y). [para(2336(a,2),2298(a,2)),flip(a)]. 2359 a(x,x * y,z) * u = a(x,y,z) \ u. [para(2341(a,2),318(a,1,1))]. 2360 a(x,x * y,z) \ u = a(x,y,z) * u. [para(2341(a,2),330(a,1,1))]. 2361 L(x,y,a(z,z * u,w)) = L(x,y,a(z,u,w)). [para(2341(a,2),787(a,1,3))]. 2362 L(x * a(y,z,x),z,y) = x. [para(2342(a,1),308(a,1,1))]. 2364 a(x,y,L(z,y,x)) = a(x,y,z). [para(2351(a,2),2298(a,2)),flip(a)]. 2365 a(x,x * y,L(z,y,x)) = a(x,y,z) \ 1. [para(2364(a,1),2341(a,2,1))]. 2366 K(a(x,x * y,z),u) = a(K(u,x),y,z). [para(2294(a,1),1847(a,2))]. 2368 x * (y * a(x,z,y)) = R(x,z,y) * y. [para(1964(a,1),2306(a,1,2))]. 2369 R(a(x,y,z),u,w) \ R(x,y,z) = a(a(x,y,z),u,w) \ x. [para(2303(a,2),2307(a,1,2))]. 2370 a(T(x,y),z,u) = T(a(x,z,u),y). [para(2297(a,2),2317(a,1,1)),flip(a)]. 2371 a(T(x,y),z,u) \ a(x,z,u) = K(y,a(x,z,u)). [para(2370(a,2),1080(a,2,1)),flip(a)]. 2372 a(T(x,y),y,z) = a(x,y,z). [para(2370(a,2),1687(a,1))]. 2373 a(x,T(y,x),z) = a(x,y,z). [para(2372(a,1),1790(a,1)),flip(a)]. 2374 a(x / y,y,z) = a(y * x,y,z). [para(2373(a,1),1810(a,1)),flip(a)]. 2375 a(x / y,x,z) = a(x * y,x,z). [para(2374(a,1),612(a,1)),flip(a)]. 2376 a(x,y,z) * (u * L(z,y,x)) = z * T(u,L(z,y,x)). [para(36(a,2),2323(a,1,2)),flip(a)]. 2377 x * (a(y,z,x) \ u) = L(x,z,y) * u. [para(2331(a,1),20(a,1,2))]. 2378 a(x,y,z) * (z * u) = z * (a(x,y,z) * u). [para(2332(a,1),2323(a,1,2)),flip(a)]. 2379 R(T(a(x,y,z),(L(z,y,x) * u) * w),L(z,y,x) * u,w) = ((L(z,y,x) * u) * w) \ ((z * u) * w). [para(2333(a,1),549(a,1,2,1)),flip(a)]. 2380 a(x,y,z) * (z * x) = z * R(x,y,z). [para(1973(a,1),2333(a,1,2))]. 2381 L(a(x,y,z),u,w) * L(z,y,x) = a(w,u,a(x,y,z)) \ z. [para(2321(a,2),2335(a,1,2))]. 2382 R(x,y * (y * z),u) = R(x,z,u). [para(2337(a,2),2300(a,2)),flip(a)]. 2383 R(x,y \ z,u) = R(x,y * z,u). [para(20(a,1),2382(a,1,2,2)),flip(a)]. 2385 R(x,(y \ z) / u,w) = R(x,(y * z) / u,w). [para(238(a,1),2382(a,1,2)),flip(a)]. 2386 (x \ a(y,x,z)) \ u = (a(y,x,z) \ x) * u. [para(2348(a,1),318(a,1,1)),flip(a)]. 2388 K(a(x,y,z) \ 1,u) = a(K(u,x),y,z). [para(2341(a,1),2366(a,1,1))]. 2389 (x * y) * L(a(x,z,y),y,x) = R(x,z,y) * y. [para(2368(a,1),74(a,2))]. 2390 x \ ((y \ x) * T(y,x)) = a(T(y,x),x,y). [para(1317(a,1),2316(a,1,2))]. 2391 x \ ((y \ x) * T(y,x)) = a(y,x,y). [para(2390(a,2),2086(a,1))]. 2393 a(R(x,y,z),u,y) = L(y,u,x) \ y. [para(2318(a,1),1986(a,1))]. 2394 a(R(x,y,z),u,w) = R(a(x,u,w),y,z). [para(2297(a,2),2318(a,1,1)),flip(a)]. 2396 a(R(x,y,z),u,y) = a(x,u,y). [para(2393(a,2),2298(a,2)),flip(a)]. 2400 a(L(x,y,x),z,y) = a(x,z,y). [para(1312(a,1),2396(a,1,1)),flip(a)]. 2404 R(a(x,y,z),x * u,w) = a(R(x,u,w),y,z). [para(2394(a,1),1718(a,1))]. 2406 a(L(x,y,z),u,w) = L(a(x,u,w),y,z). [para(2297(a,2),2319(a,1,1)),flip(a)]. 2407 a(L(x,y,z),u,w) \ a(x,u,w) = a(z,y,a(x,u,w)). [para(2406(a,2),2298(a,2,1)),flip(a)]. 2408 a(x,y,z) \ a(L(x,u * w,u),y,z) = a(u,w,a(x,y,z)). [para(2406(a,2),2320(a,2,2)),flip(a)]. 2409 a(x,y,z) \ a(L(x,u,w),y,z) = a(w,u,a(x,y,z)) \ 1. [para(2406(a,2),2328(a,2,2)),flip(a)]. 2410 K(x,a(y / z,(y / z) * z,u)) = K(a(z * y,z,u) \ 1,x). [para(2374(a,1),2340(a,1,1,1)),flip(a)]. 2411 (a(x,y,z) * y) * u = y * (a(x,y,z) * u). [para(1688(a,2),2347(a,1,1))]. 2412 a(x,y,z) \ (y * u) = (a(x,y,z) \ y) * u. [para(2386(a,1),2349(a,1)),flip(a)]. 2413 L(x,y,a(z,y,u)) = x. [hyper(23,a,798,a,b,2412,a(flip)),flip(a)]. 2414 (a(x,y,z) * y) * u = a(x,y,z) * (y * u). [para(2413(a,1),74(a,1,2))]. 2415 (a(x,y,z) * (y \ 1)) * u = a(x,y,z) * (y \ u). [para(2413(a,1),945(a,1,2))]. 2416 R(a(x,y,z),y,u) = a(x,y,z). [hyper(24,a,79,a,b,2414,a(flip)),flip(a)]. 2417 a(x,y,z) * (y * u) = y * (a(x,y,z) * u). [para(2414(a,1),2411(a,1))]. 2419 (x * y) \ (x * (a(z,x,u) * y)) = T(a(z,x,u),x * y). [para(2417(a,1),36(a,2,2)),flip(a)]. 2420 x * (y * (a(x,y,z) * u)) = R(x,y,z) * (y * u). [para(2417(a,1),2306(a,1,2))]. 2421 (x * y) * a(L(x,y,x),z,y) = R(x,z,y) * y. [para(2406(a,2),2389(a,1,2))]. 2422 (x * y) * a(x,z,y) = R(x,z,y) * y. [para(2400(a,1),2421(a,1,2))]. 2423 (x * (R(y,z,u) * u)) / ((y * u) * R(a(y,z,u),y * u,x)) = L(x,y * u,a(y,z,u)). [para(2422(a,1),2079(a,2,1,2)),flip(a)]. 2424 (x \ a(y,x,z)) * u = a(y,x,z) * (x \ u). [para(1795(a,1),2415(a,1,1))]. 2425 (a(x,y,z) * (y \ u)) \ ((y \ a(x,y,z)) * (u * w)) = L(w,u,y \ a(x,y,z)). [para(2424(a,1),32(a,2,1)),flip(a)]. 2426 L(T(a(x,y,z),u),u,y) = T(a(x,y,z),y * u). [para(2419(a,1),106(a,1)),flip(a)]. 2427 L(a(T(x,y),z,u),y,z) = T(a(x,z,u),z * y). [para(2370(a,2),2426(a,1,1))]. 2428 a(L(x,y,z),u,w) * L(w,u,x) = a(z,y,a(x,u,w)) \ w. [para(2406(a,2),2381(a,1,1))]. 2429 K(a(x * y,x,z) \ 1,u) = K(u,a(y / x,y,z)). [para(22(a,1),2410(a,1,2,2)),flip(a)]. 2430 K(a(x * y,x,z) \ 1,u) = K(u,a(y * x,y,z)). [para(2375(a,1),2429(a,2,2))]. 2431 K(x,a(y * z,y,u)) = a(K(x,z * y),z,u). [para(2430(a,1),2388(a,1))]. 2432 a(L(x,y,z),R(z,y,x),u) = (x * (z * u)) \ ((x * z) * u). [para(1998(a,1),1981(a,1,1)),flip(a)]. 2433 a(L(x,y,z),R(z,y,x),u) = a(x,z,u). [para(2432(a,2),28(a,2)),flip(a)]. 2435 L(a(x,R(y,z,x),u),z,y) = a(x,y,u). [para(2433(a,1),2406(a,1)),flip(a)]. 2436 (a(x,y,z) * (y \ u)) \ (a(x,y,z) * (y \ (u * w))) = L(w,u,y \ a(x,y,z)). [para(2424(a,1),2425(a,1,2))]. 2437 L(L(x,y,z),z * y,a(u,z,w)) = L(x,y,z \ a(u,z,w)). [para(2436(a,1),1409(a,1)),flip(a)]. 2438 L(L(x,y,z),z * y,a(u,z,w)) = L(x,y,z * a(u,z,w)). [para(2437(a,2),776(a,1))]. 2439 (R(x,y,z) * y) \ ((x * y) * u) = (x \ R(x,y,z)) \ u. [para(1996(a,1),1411(a,1))]. 2440 L(x,y,R(z,y,x)) = (z \ R(z,y,x)) \ x. [para(2439(a,1),183(a,1)),flip(a)]. 2441 L(x,y,R(z,y,x)) = L(x,y,z). [para(2440(a,2),1976(a,2)),flip(a)]. 2442 L(x,y * z,R(y,z,x) \ 1) = L(x,y * z,y \ 1). [para(584(a,1),2441(a,1,3))]. 2443 L(x,y * z,R(y,z,x)) = L(x,y * z,y \ 1). [para(2442(a,1),787(a,1)),flip(a)]. 2444 L(x,y * z,R(y,z,x)) = L(x,y * z,y). [para(2443(a,2),787(a,1))]. 2445 R(x,y,z) * (L(z,x * y,x) \ z) = R(R(x,y,z),x * y,z). [para(2444(a,1),1979(a,2,2,1)),flip(a)]. 2446 R(x,y,z) * (R(x,y,z) \ x) = R(R(x,y,z),x * y,z). [para(1954(a,1),2445(a,1,2))]. 2447 R(R(x,y,z),x * y,z) = x. [para(2446(a,1),20(a,1))]. 2448 R(R(x,x * y,z),y,z) = x. [para(2447(a,1),50(a,1)),flip(a)]. 2449 K(x,R(y,y * z,u) \ R(R(y,y * z,u),z,u)) = K(x,R(y,y * z,u)) * K(y,x). [para(2448(a,1),2262(a,1,2,1)),flip(a)]. 2450 K(x,R(y,y * z,u) \ R(R(y,y * z,u),z,u)) = R(K(x,y),z,u) * K(y,x). [para(1672(a,1),2449(a,2,1))]. 2451 K(x,R(y,y * z,u) \ R(R(y,y * z,u),z,u)) = K(y,x) * R(K(x,y),z,u). [para(2450(a,2),406(a,1))]. 2452 K(x,R(y,y * z,u) \ y) = K(y,x) * R(K(x,y),z,u). [para(2448(a,1),2451(a,1,2,2))]. 2453 K(x,y) * R(K(y,x),z,u) = K(y,x \ R(x,z,u)). [para(622(a,1),2452(a,1,2)),flip(a)]. 2454 x * K(y,z \ R(z,u,x)) = L(x,u,K(y,z)). [para(2453(a,1),2076(a,1,2))]. 2455 x * K(a(y,z,x),u) = L(x,z,K(u,y)). [para(2275(a,1),2454(a,1,2))]. 2456 a(K(x,y),z,u) = K(a(x,z,u),y). [hyper(23,a,2290,a,b,2455,a),flip(a)]. 2457 a(K(x,y),z,u) = K(a(y,z,u),x). [hyper(23,a,2288,a,b,2455,a),flip(a)]. 2458 a(K(x,y),z,u) = K(y,a(x,z,u)). [para(2456(a,2),1847(a,1))]. 2459 a(K(x,y),z,u) = K(x,a(y,z,u)). [para(2457(a,2),1847(a,1))]. 2460 x * K(y,a(z,u,x)) = L(x,u,K(z,y)). [para(2458(a,1),2288(a,1,2))]. 2461 K(x * y,a(z,x,u)) = K(z,a(y * x,y,u)). [para(2458(a,1),2431(a,2)),flip(a)]. 2462 K(x,a(y,z,u)) = K(y,a(x,z,u)). [para(2459(a,1),2458(a,1))]. 2463 L(x,y * z,K(y,u)) = L(x,z,K(y,u)). [para(2460(a,1),2284(a,2))]. 2464 (x * (R(y,z,u) * u)) / ((y * u) * a(R(y,u,x),z,u)) = L(x,y * u,a(y,z,u)). [para(2404(a,1),2423(a,1,2,2))]. 2465 (x * (R(y,z,u) * u)) / ((y * u) * a(y,z,u)) = L(x,y * u,a(y,z,u)). [para(2396(a,1),2464(a,1,2,2))]. 2467 (x * (R(y,z,u) * u)) / (R(y,z,u) * u) = L(x,y * u,a(y,z,u)). [para(2422(a,1),2465(a,1,2))]. 2468 L(x,y * z,a(y,u,z)) = x. [para(2467(a,1),21(a,1))]. 2469 L(x,y * z,a(T(z,y),u,y)) = x. [para(2468(a,1),1185(a,1)),flip(a)]. 2470 L(x,y * z,a(z,u,y)) = x. [para(2358(a,1),2469(a,1,3))]. 2471 (a(x,y,z) * (z * x)) \ (a(x,y,z) * (z * (x * u))) = L(u,x,z). [para(2470(a,1),174(a,2))]. 2472 (x * R(y,z,x)) \ (a(y,z,x) * (x * (y * u))) = L(u,y,x). [para(2380(a,1),2471(a,1,1))]. 2473 (x * R(y,z,x)) \ (x * (a(y,z,x) * (y * u))) = L(u,y,x). [para(2378(a,1),2472(a,1,2))]. 2474 (x * R(y,z,x)) \ (x * (R(y,z,x) * u)) = L(u,y,x). [para(2308(a,1),2473(a,1,2,2))]. 2475 L(x,R(y,z,u),u) = L(x,y,u). [para(2474(a,1),32(a,2))]. 2476 a(x,R(y,z,x),u) = L(u,y,x) \ u. [para(2475(a,1),2298(a,2,1))]. 2477 a(x,R(y,z,x),u) = a(x,y,u). [para(2476(a,2),2298(a,2)),flip(a)]. 2478 L(a(x,y,z),u,y) = a(x,y,z). [para(2477(a,1),2435(a,1,1))]. 2479 a(L(x,y,z),z,u) = a(x,z,u). [para(2478(a,1),2406(a,2))]. 2480 T(a(x,y,z),y * u) = a(T(x,u),y,z). [para(2478(a,1),2427(a,1)),flip(a)]. 2482 a((x * y) \ z,x,u) = a(y \ (x \ z),x,u). [para(177(a,1),2479(a,1,1))]. 2483 L(x,y,z) * a(x,z,u) = R(L(x,y,z),z,u). [para(2479(a,1),2300(a,2,2)),flip(a)]. 2484 a(T(x,y),z,u) \ a(x,z,u) = K(z * y,a(x,z,u)). [para(2480(a,1),1080(a,2,1)),flip(a)]. 2486 a(x \ (y \ z),y,u) = a((y * x) * z,y,u). [para(2482(a,1),1702(a,1))]. 2487 L(x,y,z) * a(x,z,u) = L(R(x,z,u),y,z). [para(2483(a,2),48(a,1))]. 2488 a((x * y) * z,x,u) = a(y * (x * z),x,u). [para(2486(a,1),1757(a,1))]. 2489 (x * a(x,y,z)) / L(R(x,y,z),u,y) = a(y,u,x). [para(2487(a,1),2334(a,1,2))]. 2490 a(T(x,y) * (y * z),y,u) = a((x * y) * z,y,u). [para(82(a,1),2488(a,1,1,1)),flip(a)]. 2491 R(x,y,z) / L(R(x,y,z),u,y) = a(y,u,x). [para(2300(a,2),2489(a,1,1))]. 2492 a(x,y,R(z,x,u)) = a(x,y,z). [para(2491(a,1),2329(a,2))]. 2493 a(x,y,(z / u) / x) = a(x,y,z / (x * u)). [para(193(a,1),2492(a,1,3)),flip(a)]. 2494 K(x * y,a(z,x,u)) = K(y,a(z,x,u)). [para(2484(a,1),2371(a,1))]. 2495 K(x,a(y * z,y,u)) = K(z,a(x,y,u)). [para(2494(a,1),2462(a,1)),flip(a)]. 2496 K(x,a(y * z,y,u)) = K(y,a(x,z,u)). [para(2494(a,1),2461(a,1)),flip(a)]. 2497 K(x,a(y,z,u)) = K(z,a(y,x,u)). [para(2496(a,1),2495(a,1))]. 2498 x * K(y,a(z,u,x)) = L(x,y,K(z,u)). [para(2497(a,1),2460(a,1,2))]. 2499 L(x,y,K(z,u)) = L(x,u,K(z,y)). [para(2498(a,1),2460(a,1))]. 2501 L(x,y,K(z,z * u)) = L(x,u,K(z,y)). [para(2499(a,1),2463(a,1))]. 2502 L(x,y,a(z,u,u)) = L(x,u,K(z,y)). [para(2501(a,1),1261(a,1)),flip(a)]. 2503 L(x,y,a(z,u,u)) = L(x,y,K(z,u)). [para(2502(a,2),2499(a,1))]. 2504 L(x,y,a(z,u,z)) = L(x,y,K(u,z)). [para(2503(a,1),1695(a,1)),flip(a)]. 2505 L(L(x,y,z),z * y,K(z,u)) = L(x,y,z * a(u,z,u)). [para(2504(a,1),2438(a,1))]. 2506 L(x,y,z * a(u,z,u)) = L(x,y,T(z,u)). [para(2505(a,1),1604(a,1))]. 2507 L(x,y,R(z,u,u)) = L(x,y,T(z,u)). [para(2506(a,1),1692(a,1)),flip(a)]. 2508 L(x,y,T(z / u,z)) = L(x,y,u * z). [para(2507(a,1),846(a,1))]. 2509 L(x,y,z * u) = L(x,y,u * z). [para(2508(a,1),845(a,1))]. 2510 L(L(x,y,z * u),(z * u) * y,u * z) = x. [para(2509(a,1),303(a,1))]. 2511 L(x,y,z \ u) = L(x,y,u * z). [para(2509(a,1),776(a,2))]. 2513 L(x,y,z * (u * (u * w))) = L(x,y,w * z). [para(2509(a,1),868(a,2))]. 2514 L(x,y,(z * (u * w)) * (z * u)) = L(x,y,L(w,u,z)). [para(32(a,2),2511(a,1,3)),flip(a)]. 2515 L(x,y,K(z,u)) = x. [para(2510(a,1),1850(a,1)),flip(a)]. 2516 a(K(x,y),z,u) = 1. [hyper(38,a,2515,a)]. 2518 (K(x,y) * z) * u = K(x,y) * (z * u). [para(2515(a,1),74(a,1,2))]. 2519 (K(x,y) * z) \ (K(x,y) * u) = z \ u. [para(2515(a,1),76(a,1)),flip(a)]. 2520 (K(x,y) \ z) \ u = z \ (K(x,y) * u). [para(2515(a,1),267(a,1)),flip(a)]. 2521 (K(x,y) * z) / u = K(x,y) * (z / u). [para(2515(a,1),196(a,1,2))]. 2526 L(x,y,T(z,u)) = L(x,y,z). [para(2515(a,1),1604(a,1)),flip(a)]. 2534 L(x,y,a(z,u,z)) = x. [para(2515(a,1),2504(a,2))]. 2539 K(a(x,y,z) \ 1,u) = 1. [para(2516(a,1),2388(a,2))]. 2540 K(a(x,y,z),u) = 1. [para(2516(a,1),2456(a,1)),flip(a)]. 2543 T(a(x,y,z),u) = a(x,y,z). [hyper(41,a,2540,a)]. 2548 (a(x,y,x) * z) * u = (z * u) * a(x,y,x). [para(2534(a,1),2053(a,1,2))]. 2549 T(a(x,y,z) \ 1,u) = a(x,y,z) \ 1. [hyper(41,a,2539,a)]. 2553 L(x,y,z * (u * z)) = L(x,y,u). [para(2526(a,1),778(a,2))]. 2567 a(x,y,z) * u = u * a(x,y,z). [para(2543(a,1),82(a,1,2)),flip(a)]. 2569 (a(x,y,z) \ u) \ u = a(x,y,z). [para(2543(a,1),83(a,1)),flip(a)]. 2570 (a(x,y,z) \ u) * a(x,y,z) = u. [para(2543(a,1),250(a,1,2))]. 2571 x / a(y,z,u) = a(y,z,u) \ x. [para(2543(a,1),252(a,1,2))]. 2572 a(x,y,z) * (u \ 1) = u \ a(x,y,z). [para(2543(a,1),326(a,1,2)),flip(a)]. 2578 a(T(x,y),z,u) = a(x,z,u). [para(2543(a,1),2370(a,2))]. 2584 a(x / y,z,u) = a(y \ x,z,u). [para(84(a,1),2578(a,1,1)),flip(a)]. 2586 a(x * (y * x),z,u) = a(y,z,u). [para(2578(a,1),1704(a,2))]. 2597 a(x,y,z) * (u / a(x,y,z)) = u. [para(2567(a,2),22(a,1))]. 2598 (x * (a(y,z,u) * w)) \ ((x * w) * a(y,z,u)) = a(x,w,a(y,z,u)). [para(2567(a,2),28(a,2,1,2)),flip(a)]. 2601 (x * y) \ ((x * a(z,u,w)) * y) = R(T(a(z,u,w),x * y),x,y). [para(2567(a,1),549(a,1,2,1))]. 2602 x * (y * a(x,z,u)) = R(x,z,u) * y. [para(2567(a,1),2306(a,1,2))]. 2603 (x * y) * a(x,z,u) = R(x,z,u) * y. [para(2567(a,1),2308(a,1))]. 2604 x * (L(x,y,z) \ u) = u * a(z,y,x). [para(2567(a,1),2323(a,2))]. 2605 (a(x,y,z) \ u) \ w = (a(x,y,z) / u) * w. [para(2570(a,1),353(a,1,1,2)),flip(a)]. 2606 a(x / y,z,u) = a(y * x,z,u). [para(2584(a,2),1702(a,1))]. 2609 a(x * a(y,z,x),u,w) = a(L(x,z,y),u,w). [para(2333(a,1),2586(a,1,1))]. 2612 (x * y) / a(z,u,x) = L(x,u,z) * y. [hyper(23,a,2333,a,b,2597,a)]. 2613 a(x / y,z,u) = a(x * y,z,u). [para(2606(a,1),612(a,1)),flip(a)]. 2618 a(x * y,z,u) = a(y * x,z,u). [para(2613(a,1),2606(a,1))]. 2621 (x * (K(y,z) * (u * w))) \ ((x * (K(y,z) * u)) * w) = a(x,K(y,z) * u,w). [para(2518(a,1),28(a,2,1,2)),flip(a)]. 2622 (K(x,y) * (z * (u * w))) \ (((K(x,y) * z) * u) * w) = a(K(x,y) * z,u,w). [para(2518(a,1),28(a,2,1)),flip(a)]. 2623 (K(x,y) * (z * u)) \ ((K(x,y) * z) * (u * w)) = L(w,u,K(x,y) * z). [para(2518(a,1),32(a,2,1)),flip(a)]. 2624 ((K(x,y) * (z * u)) * w) / (u * w) = R(K(x,y) * z,u,w). [para(2518(a,1),34(a,2,1,1)),flip(a)]. 2629 ((T(x,y) * z) * u) / (K(x,y) * (z * u)) = R(x,K(x,y) * z,u). [para(2518(a,1),1167(a,1,2))]. 2630 K(x,T(y,z)) * (z * u) = (z * K(x,y)) * u. [para(2216(a,1),2518(a,1,1)),flip(a)]. 2631 (x \ K(y,z)) * (K(z,y) * u) = x \ u. [para(2519(a,1),2121(a,1)),flip(a)]. 2632 x \ (K(y,z) * u) = (x \ K(y,z)) * u. [para(2520(a,1),2133(a,1))]. 2633 x * (a(y,z,u) \ 1) = a(y,z,u) \ x. [para(2549(a,1),327(a,1,2))]. 2635 (x * y) \ (R(x,z,u) * y) = L(a(x,z,u),y,x). [para(2602(a,1),32(a,2,2)),flip(a)]. 2637 (x * y) \ (R(x,z,u) * y) = a(x,z,u). [hyper(23,a,20,a,b,2603,a),flip(a)]. 2642 (x * y) * (a(x,y,z) * u) = (R(x,y,z) * y) * u. [para(2603(a,1),2338(a,1,1)),flip(a)]. 2643 L(x,y,z) * a(z,y,L(x,u,w)) = L(x,u,w) * a(w,u,L(x,y,z)). [para(2325(a,1),2604(a,1,2))]. 2644 (L(x,y,z) * u) \ (x * u) = a(z,y,x). [para(2612(a,1),66(a,1,1))]. 2645 (x * K(y,z)) \ u = K(z,y) * (x \ u). [hyper(23,a,297,a,b,2631,a),flip(a)]. 2646 L(x,K(y,z),u) = x. [hyper(23,a,798,a,b,2632,a(flip)),flip(a)]. 2649 (x * K(y,z)) * u = x * (K(y,z) * u). [para(2646(a,1),74(a,1,2))]. 2650 (x * (K(y,z) * u)) / u = x * K(y,z). [para(2646(a,1),99(a,1,2))]. 2656 L(x,T(y,z) * y,u) = x. [para(2646(a,1),988(a,1)),flip(a)]. 2658 L(x,(y \ z) * (z / y),u) = x. [para(84(a,1),2656(a,1,2,1))]. 2659 L(x,(y * z) * (z / y),u) = x. [para(2658(a,1),880(a,1)),flip(a)]. 2660 L(x,T(L(y / z,z * y,y / z) * (z * y),y / z),u) = x. [para(1309(a,2),2659(a,1,2))]. 2661 x \ (R(x / y,z,u) * y) = a(x / y,z,u). [para(22(a,1),2637(a,1,1))]. 2662 (L(R(x,y,z),u,w) * (y * z)) \ ((x * y) * z) = a(w,u,R(x,y,z)). [para(79(a,1),2644(a,1,2))]. 2664 K(x * y,x) * (y \ z) = (x * (y / x)) \ z. [para(1129(a,1),2645(a,1,1)),flip(a)]. 2665 (K(x,y) / z) * u = K(x,y) * (z \ u). [para(2645(a,1),2143(a,1)),flip(a)]. 2666 R(x,K(y,z),u) = x. [hyper(24,a,79,a,b,2649,a(flip)),flip(a)]. 2667 (x * T(y,z)) \ (x * (K(y,z) * (y * u))) = L(u,y,x \ K(y,z)). [para(2649(a,1),2264(a,1,2))]. 2668 (x / y) / K(z,u) = x / (K(z,u) * y). [para(2666(a,1),193(a,1))]. 2670 (x * y) / T(y,z) = x * K(z,y). [para(1077(a,1),2650(a,1,1,2))]. 2671 (x / y) * K(z,y) = x / T(y,z). [para(22(a,1),2670(a,1,1)),flip(a)]. 2672 (x * (y * z)) / T(L(z,y,x),u) = (x * y) * K(u,L(z,y,x)). [para(74(a,1),2670(a,1,1))]. 2673 ((x \ y) * x) / T(y,x) = a(x,y,x). [para(2671(a,1),1538(a,1))]. 2675 a(x,y,x) * T(y,x) = (x \ y) * x. [para(2673(a,1),22(a,1,1))]. 2676 K(x * y,x) * ((x \ y) \ z) = (x / y) * z. [para(1009(a,1),2665(a,1,1)),flip(a)]. 2677 K(x,T(y,z)) * (z \ u) = (z \ K(x,y)) * u. [para(2201(a,1),2665(a,1,1)),flip(a)]. 2678 x / (K(y,z) * u) = (x / u) * K(z,y). [para(2668(a,1),2140(a,1))]. 2679 a(L(x,y * z,y),u,w) = a(L(x,z,y),u,w). [para(2342(a,2),2609(a,1,1))]. 2680 K(x,T(y,z)) * (z * u) = z * (K(x,y) * u). [para(2630(a,2),2649(a,1))]. 2681 x \ (y * R(y \ x,z,u)) = a(x / y,z,u). [para(224(a,1),2661(a,1,2))]. 2682 L(x,y,z * (K(u * w,u) * ((u * (w / u)) \ v5))) = L(x,y,(w \ v5) * z). [para(2664(a,1),2513(a,1,3,2,2))]. 2683 a(x,y,z) \ a(L(x,u,w),y,z) = a(w,u,a(x,y,z)). [para(2679(a,1),2408(a,1,2))]. 2685 x \ (y * R(y \ x,z,u)) = a(y * x,z,u). [para(2681(a,2),2606(a,1))]. 2686 (x * (y * z)) \ ((x * y) * R(L(z,y,x),u,w)) = a((x * y) * (x * (y * z)),u,w). [para(32(a,2),2685(a,1,2,2,1))]. 2687 L(a(x,y,z),u,x) = a(x,y,z). [para(2635(a,1),2637(a,1))]. 2692 (x * (y * (a(x,y,z) * u))) \ ((R(x,y,z) * y) * u) = a(x,y,a(x,y,z) * u). [para(2642(a,1),28(a,2,2)),flip(a)]. 2693 L(x,y,z) * a(L(z,u,w),y,x) = x * a(w,u,a(z,y,x)). [para(2683(a,1),2377(a,1,2)),flip(a)]. 2694 a(x,y,a(z,u,w)) \ 1 = a(x,y,a(z,u,w)). [para(2683(a,1),2409(a,1)),flip(a)]. 2695 a(x,y,a(z,u,w)) * a(x,y,a(z,u,w)) = 1. [para(2694(a,1),20(a,1,2))]. 2696 a(x,y,a(z,u,w)) \ v5 = v5 * a(x,y,a(z,u,w)). [para(2694(a,1),2633(a,1,2)),flip(a)]. 2697 a(L(x,y,z),u,w) * L(w,u,x) = w * a(z,y,a(x,u,w)). [para(2696(a,1),2428(a,2))]. 2698 (K(x,y) * ((z * u) * w)) / (u * w) = R(K(x,y) * z,u,w). [para(2518(a,1),2624(a,1,1))]. 2699 K(x,y) * (((z * u) * w) / (u * w)) = R(K(x,y) * z,u,w). [para(2698(a,1),2521(a,1)),flip(a)]. 2700 R(K(x,y) * z,u,w) = K(x,y) * R(z,u,w). [para(34(a,2),2699(a,1,2)),flip(a)]. 2701 R(x * K(y,z),u,w) = R(x,u,w) * K(y,z). [hyper(23,a,699,a(flip),b,2700,a(flip))]. 2704 R(T(x,y),z,u) * K(y,x) = R(x,z,u). [para(1089(a,1),2701(a,1,1)),flip(a)]. 2706 K(x,R(y,z,u)) = K(x,y). [hyper(23,a,1109,a,b,2704,a),flip(a)]. 2708 T(x,R(y,z,u)) = x * K(x,y). [para(2706(a,1),1107(a,2,2))]. 2716 T(x,R(y,z,u)) = T(x,y). [para(2708(a,2),1107(a,2)),flip(a)]. 2717 R(x,y,z) * T(u,x) = u * R(x,y,z). [para(2716(a,1),82(a,1,2))]. 2723 R(x,y,z) * (x \ u) = (u / x) * R(x,y,z). [para(84(a,1),2717(a,1,2))]. 2725 (x / y) * R(y,z,u) = a(y,z,u) * x. [para(2723(a,1),2309(a,1))]. 2726 a(x,y,z) * (u * x) = u * R(x,y,z). [para(21(a,1),2725(a,1,1)),flip(a)]. 2727 L(x,y,z) * R(a(z,y,x),u,w) = a(a(z,y,x),u,w) * x. [para(2326(a,2),2725(a,1,1))]. 2729 (x * y) * a(y,z,u) = x * R(y,z,u). [para(2726(a,1),2567(a,1)),flip(a)]. 2730 (x * (y * z)) \ (x * (y * R(z,u,w))) = L(a(z,u,w),y * z,x). [para(2729(a,1),32(a,2,2,2)),flip(a)]. 2731 L(x,T((y / z) * (z * y),y / z),u) = x. [para(892(a,1),2660(a,1,2,1,1))]. 2733 L(x,(y * z) / (z / y),u) = x. [para(2731(a,1),1235(a,1)),flip(a)]. 2734 L(x,(y * z) * (y / z),u) = x. [para(952(a,1),2733(a,1,2))]. 2735 (x * (y * z)) / L(T(z,u),y,x) = (x * y) * K(u,L(z,y,x)). [para(44(a,2),2672(a,1,2))]. 2736 (x * y) \ ((x * a(z,u,w)) * y) = R(a(z,u,w),x,y). [para(2543(a,1),2601(a,2,1))]. 2738 (((T(x,y) * z) * u) / (z * u)) * K(y,x) = R(x,K(x,y) * z,u). [para(2629(a,1),2678(a,1)),flip(a)]. 2739 (x * T(y,z)) \ (x * (T(y,z) * u)) = L(u,y,x \ K(y,z)). [para(1160(a,1),2667(a,1,2,2))]. 2740 L(x,y,z \ K(y,u)) = L(x,T(y,u),z). [para(2739(a,1),32(a,2)),flip(a)]. 2741 L(x,y,z * K(y,u)) = L(x,T(y,u),z). [para(2740(a,1),776(a,1)),flip(a)]. 2742 R(T(x,y),z,u) * K(y,x) = R(x,K(x,y) * z,u). [para(34(a,2),2738(a,1,1))]. 2743 R(x,K(x,y) * z,u) = R(x,z,u). [para(2742(a,1),2704(a,1))]. 2744 R(x,y * x,z) = R(x,x * y,z). [para(974(a,1),2743(a,1,2)),flip(a)]. 2746 x \ R(x,y * x,z) = R(x,y,z) \ x. [para(2744(a,2),618(a,1,2))]. 2747 a(x,y * x,z) = R(x,y,z) \ x. [para(2746(a,1),2297(a,2))]. 2748 a(x,y * x,z) = a(x,y,z) \ 1. [para(2747(a,2),2302(a,1))]. 2749 a(x * y,y,z) = a(x * y,x,z) \ 1. [para(2748(a,1),1778(a,1)),flip(a)]. 2750 a(x * y,y,a(z,u,w)) = a(x * y,x,a(z,u,w)). [para(2749(a,2),2694(a,1))]. 2751 ((L(x,y,z) * u) * w) \ ((x * u) * w) = a(z,y,R(x,u,w)). [para(184(a,1),2662(a,1,1))]. 2752 (K(x,y) * (z * u)) \ (K(x,y) * (z * (u * w))) = L(w,u,K(x,y) * z). [para(2518(a,1),2623(a,1,2))]. 2753 L(x,y,K(z,u) * w) = (w * y) \ (w * (y * x)). [para(2752(a,1),2519(a,1))]. 2754 L(x,y,K(z,u) * w) = L(x,y,w). [para(2753(a,2),32(a,2)),flip(a)]. 2755 ((x * K(y,z)) * u) \ ((x * K(y,z)) * (u * w)) = L(w,u,x). [para(2753(a,1),2553(a,1))]. 2757 L(x,y,T(z,u) * w) = L(x,y,z * w). [para(1098(a,1),2754(a,1,3)),flip(a)]. 2758 L(x,y,(z / u) * w) = L(x,y,(u \ z) * w). [para(1161(a,1),2754(a,1,3))]. 2759 L(x,y,z * T(u,w)) = L(x,y,z * u). [para(1212(a,1),2754(a,1,3))]. 2760 L(x,y,z * K(u,w)) = L(x,y,z). [para(2200(a,1),2754(a,1,3))]. 2762 L(x,y,z * (K(u,w) * v5)) = L(x,y,z * v5). [para(2680(a,1),2754(a,1,3))]. 2763 L(x,T(y,z),u) = L(x,y,u). [para(2760(a,1),2741(a,1)),flip(a)]. 2765 L(x,(y * z) * z,u) = L(x,y,u). [para(2763(a,1),951(a,1)),flip(a)]. 2766 L(x,y / z,u) = L(x,z * y,u). [para(2763(a,1),1235(a,1)),flip(a)]. 2777 L(x,y / z,u) = L(x,y * z,u). [para(22(a,1),2765(a,1,2,1)),flip(a)]. 2779 (x * y) / L(z,z * y,x) = x * (y / z). [para(2766(a,1),196(a,1,2))]. 2782 L(x,y * z,u) = L(x,z * y,u). [para(2777(a,1),2766(a,1))]. 2787 L(x,(y / z) * (y * z),u) = x. [para(2782(a,1),2734(a,1))]. 2788 L(x,(y \ (y \ z)) * ((y \ z) * T(y,z)),u) = x. [para(256(a,1),2787(a,1,2,1))]. 2789 L(x,(y * z) * u,y * (z * u)) = x. [para(2757(a,1),950(a,1))]. 2790 a(x,y,z) \ ((x * (y * z)) \ u) = ((x * y) * z) \ u. [para(2789(a,1),271(a,1)),flip(a)]. 2792 L(x,y,z * (u / w)) = L(x,y,z * (w \ u)). [para(84(a,1),2759(a,1,3,2)),flip(a)]. 2793 (x * (y * z)) / L(T(z,u),T(z,u) * (y * z),x) = x * (y * K(u,z)). [para(2670(a,1),2779(a,2,2))]. 2794 L(x,y,(z / u) * w) = L(x,y,(u * z) * w). [para(2758(a,2),781(a,1))]. 2795 L(x,y,z * (u * w)) = L(x,y,z * (w * u)). [para(974(a,1),2762(a,1,3,2))]. 2796 L(x,y,z * (u / w)) = L(x,y,z * (w * u)). [para(2792(a,2),867(a,1))]. 2797 L(x,y,z * ((u * w) * u)) = L(x,y,w * z). [para(2795(a,1),2513(a,1))]. 2798 L(x,(y * (y \ z)) * ((y \ z) * T(y,z)),u) = x. [para(2788(a,1),880(a,1)),flip(a)]. 2799 L(x,y * ((z \ y) * T(z,y)),u) = x. [para(20(a,1),2798(a,1,2,1))]. 2800 L(x,y \ ((z \ y) * T(z,y)),u) = x. [para(2799(a,1),876(a,2))]. 2801 L(x,a(y,z,y),u) = x. [para(2391(a,1),2800(a,1,2))]. 2802 (x * a(y,z,y)) * u = x * (a(y,z,y) * u). [para(2801(a,1),74(a,1,2))]. 2803 (x * y) / L(y,z,y) = x * a(y,z,y). [para(2801(a,1),1543(a,1,2))]. 2805 (x * (y * (a(z,u,z) * w))) \ (((x * y) * a(z,u,z)) * w) = a(x,y,a(z,u,z) * w). [para(2802(a,2),28(a,2,2)),flip(a)]. 2806 (a(x,y,x) * z) * u = z * (a(x,y,x) * u). [para(2051(a,2),2802(a,1,1))]. 2807 (x * y) * a(z,u,z) = x * (a(z,u,z) * y). [para(2806(a,1),2548(a,1)),flip(a)]. 2808 ((x * y) * z) \ (x * (y * z)) = a(x,y,z) \ 1. [para(60(a,1),2790(a,1,2)),flip(a)]. 2809 ((x * a(y,z,u)) * w) \ ((x * w) * a(y,z,u)) = a(x,a(y,z,u),w) \ a(x,w,a(y,z,u)). [para(2598(a,1),2790(a,1,2)),flip(a)]. 2810 (x * (K(y,z) * u)) \ ((x * K(y,z)) * (u * w)) = L(w,u,x). [para(2649(a,1),2755(a,1,1))]. 2811 (x * (K(y,z) * u)) \ (x * (K(y,z) * (u * w))) = L(w,u,x). [para(2649(a,1),2810(a,1,2))]. 2812 L(L(x,y,K(z,u)),K(z,u) * y,w) = L(x,y,w). [para(2811(a,1),174(a,1)),flip(a)]. 2813 L(x,K(y,z) * u,w) = L(x,u,w). [para(2515(a,1),2812(a,1,1))]. 2815 L(x,T(y,z) * u,w) = L(x,y * u,w). [para(1098(a,1),2813(a,1,2)),flip(a)]. 2817 L(x,T(y,z) * u,w) = L(x,u * y,w). [para(2815(a,2),2782(a,1))]. 2821 (x * (y * z)) / L(T(z,u),(y * z) * z,x) = x * (y * K(u,z)). [para(2817(a,1),2793(a,1,2))]. 2822 (x * (y * z)) / L(T(z,u),y,x) = x * (y * K(u,z)). [para(2765(a,1),2821(a,1,2))]. 2824 (x * y) * K(z,L(u,y,x)) = x * (y * K(z,u)). [para(2822(a,1),2735(a,1)),flip(a)]. 2826 L(x,y,z * ((u * (w / u)) \ v5)) = L(x,y,(w \ v5) * z). [para(2682(a,1),2762(a,1)),flip(a)]. 2827 L(x,y,z * ((u * (w / u)) * v5)) = L(x,y,(w \ v5) * z). [para(2826(a,1),867(a,1)),flip(a)]. 2829 L(x,y,z * ((u * (w / u)) * v5)) = L(x,y,(w * v5) * z). [para(2827(a,2),781(a,1))]. 2830 L(x,y,(z * u) * ((w * (z / w)) * (u * v5))) = L(x,y,L(v5,u,w * (z / w))). [para(2829(a,1),2514(a,1))]. 2831 (K(x,y) * (z * (u * w))) \ ((K(x,y) * (z * u)) * w) = a(K(x,y) * z,u,w). [para(2518(a,1),2622(a,1,2,1))]. 2832 L(x,y,L(z,u,(u * z) * (w / (u * z)))) = L(x,y,(w / (u * z)) * (w * u)). [para(2830(a,1),2797(a,1))]. 2833 (K(x,y) * (z * (u * w))) \ (K(x,y) * ((z * u) * w)) = a(K(x,y) * z,u,w). [para(2518(a,1),2831(a,1,2))]. 2834 L(x,y,L(z,u,(u * z) * (w / (u * z)))) = L(x,y,((u * z) * w) * (w * u)). [para(2832(a,2),2794(a,1))]. 2835 a(K(x,y) * z,u,w) = (z * (u * w)) \ ((z * u) * w). [para(2833(a,1),2519(a,1))]. 2836 a(K(x,y) * z,u,w) = a(z,u,w). [para(2835(a,2),28(a,2)),flip(a)]. 2837 ((x * K(y,z)) * (u * w)) \ (((x * K(y,z)) * u) * w) = a(x,u,w). [para(2835(a,1),2586(a,1))]. 2839 a(T(x,y) * z,u,w) = a(x * z,u,w). [para(1098(a,1),2836(a,1,1)),flip(a)]. 2840 a((x / y) * z,u,w) = a((y \ x) * z,u,w). [para(1161(a,1),2836(a,1,1))]. 2841 a(x * T(y,z),u,w) = a(x * y,u,w). [para(1212(a,1),2836(a,1,1))]. 2843 a((x * y) * z,y,u) = a(x * (y * z),y,u). [para(2839(a,1),2490(a,1)),flip(a)]. 2844 a((x / y) * z,u,w) = a((y * x) * z,u,w). [para(2840(a,2),1707(a,1))]. 2845 a(x / (y / z),u,w) = a((z \ y) * x,u,w). [para(2840(a,1),2606(a,2))]. 2846 a(x / (y * z),z,u) = a(y * (z * x),z,u). [para(2843(a,1),2606(a,2))]. 2848 a(x / (y * z),u,w) = a((z / y) * x,u,w). [para(2844(a,2),2606(a,2))]. 2849 a(x / (y / z),u,w) = a(x / (z \ y),u,w). [para(2845(a,2),2606(a,2)),flip(a)]. 2850 a((x * y) / z,x,u) = a(y / (z * x),x,u). [para(2846(a,2),2606(a,2))]. 2851 a(x / (y / z),u,w) = a(x / (z * y),u,w). [para(2848(a,2),2606(a,2))]. 2852 a((x * y) / z,x,u) = a(y / (x / z),x,u). [para(2851(a,2),2850(a,2))]. 2853 (x * (K(y,z) * (u * w))) \ (((x * K(y,z)) * u) * w) = a(x,u,w). [para(2649(a,1),2837(a,1,1))]. 2854 (x * (K(y,z) * (u * w))) \ ((x * (K(y,z) * u)) * w) = a(x,u,w). [para(2649(a,1),2853(a,1,2,1))]. 2855 a(x,K(y,z) * u,w) = a(x,u,w). [para(2854(a,1),2621(a,1)),flip(a)]. 2856 a(x,y * z,u) = a(x,z * y,u). [para(974(a,1),2855(a,1,2))]. 2857 a(x,T(y,z),u) = a(x,y,u). [para(985(a,1),2855(a,1,2)),flip(a)]. 2858 a(x,y * T(z,u),w) = a(x,y * z,w). [para(1212(a,1),2855(a,1,2))]. 2861 a(x,y * K(z,u),w) = a(x,y,w). [para(2200(a,1),2855(a,1,2))]. 2862 R(x,K(y,z) * u,w) = a(x,u,w) * x. [para(2855(a,1),2303(a,2,1))]. 2865 a(x,y / z,u) = a(x,z * y,u). [para(2857(a,1),1788(a,1)),flip(a)]. 2866 a(x,(y * z) * z,u) = a(x,y,u). [para(2857(a,1),1792(a,1)),flip(a)]. 2867 R(x,T(y,z),u) = a(x,y,u) * x. [para(2857(a,1),2303(a,2,1))]. 2876 (x * ((y * K(z,u)) * w)) \ ((x * (y * K(z,u))) * w) = a(x,y,w). [para(2861(a,1),28(a,1)),flip(a)]. 2877 a(x,y * (z * K(u,w)),v5) = a(x,y * z,v5). [para(2824(a,1),2861(a,1,2))]. 2878 a(x,L(y,z,y) * (u * y),w) = a(x,u * a(y,z,y),w). [para(2803(a,1),2865(a,1,2)),flip(a)]. 2882 R(x,T(y,z),u) = R(x,y,u). [para(2867(a,2),2303(a,2)),flip(a)]. 2883 R(x,y / z,u) = R(x,z \ y,u). [para(84(a,1),2882(a,1,2)),flip(a)]. 2884 R(x,y / z,u) = R(x,z * y,u). [para(2883(a,2),2383(a,1))]. 2885 R(x,(y * z) / u,w) = R(x,u * (y \ z),w). [para(2884(a,1),2385(a,1)),flip(a)]. 2886 a(x,y * (z * K(u,z)),w) = a(x,y * L(z,u,z),w). [para(1062(a,1),2858(a,1,2,2)),flip(a)]. 2887 a(x,y * T(z,u),w) = a(x,z * y,w). [para(2858(a,2),2856(a,1))]. 2888 R(x,K(y,z) * u,w) = R(x,u,w). [para(2862(a,2),2303(a,2)),flip(a)]. 2892 R(x,y * K(z,u),w) = R(x,y,w). [para(2200(a,1),2888(a,1,2))]. 2894 R(x,y * (z * K(u,w)),v5) = R(x,y * z,v5). [para(2824(a,1),2892(a,1,2))]. 2896 R(x,y * T(z,u),w) = x * a(x,z * y,w). [para(2887(a,1),2300(a,2,2))]. 2897 R(x,y * (z \ u),w) = R(x,y * (z * u),w). [para(2885(a,1),2884(a,1))]. 2898 R(x,y * ((z \ u) \ 1),w) = R(x,y * (z / u),w). [para(2138(a,1),2894(a,1,2,2))]. 2899 R(x,y * T(z,u),w) = R(x,z * y,w). [para(2896(a,2),2300(a,2)),flip(a)]. 2900 R(x,y * ((z \ u) \ u),w) = R(x,z * y,w). [para(83(a,1),2899(a,1,2,2))]. 2901 R(x,y * ((z \ u) * u),w) = R(x,z * y,w). [para(2900(a,1),2897(a,1)),flip(a)]. 2902 R(x,y * ((z \ u) * 1),w) = R(x,y * (z / u),w). [para(2898(a,1),2897(a,1)),flip(a)]. 2903 R(x,y * (z / u),w) = R(x,y * (z \ u),w). [para(18(a,1),2902(a,1,2,2)),flip(a)]. 2904 R(x,y * (z / u),w) = R(x,y * (z * u),w). [para(2903(a,2),2897(a,1))]. 2905 R(x,x * (y * z),z) = y / ((x \ (y / z)) * z). [para(2904(a,1),631(a,1))]. 2906 R(x,x * ((y \ z) * z),z) = (y \ z) / ((x \ (y \ 1)) * z). [para(320(a,1),2905(a,2,2,1,2))]. 2907 a(x,y * L(z,u,z),w) = a(x,y * z,w). [para(2886(a,1),2877(a,1))]. 2908 a(x,L(y,z,y) * u,w) = a(x,u * y,w). [para(2907(a,1),2856(a,1)),flip(a)]. 2910 a(x,y * a(z,u,z),w) = a(x,(y * z) * z,w). [para(2878(a,1),2908(a,1))]. 2911 a(x,y * a(z,u,z),w) = a(x,y,w). [para(2910(a,2),2866(a,1))]. 2913 a(x,a(y,z,y) * u,w) = a(x,u,w). [para(2051(a,2),2911(a,1,2))]. 2915 (x * ((a(y,z,y) * u) * w)) \ ((x * (a(y,z,y) * u)) * w) = a(x,u,w). [para(2913(a,1),28(a,1)),flip(a)]. 2916 R(x,y * x,z) = (y \ z) / ((x \ (y \ 1)) * z). [para(2906(a,1),2901(a,1)),flip(a)]. 2918 (x * (y * (K(z,u) * w))) \ ((x * (y * K(z,u))) * w) = a(x,y,w). [para(2649(a,1),2876(a,1,1,2))]. 2919 (x * (y * (a(z,u,z) * w))) \ ((x * (a(z,u,z) * y)) * w) = a(x,y,w). [para(2806(a,1),2915(a,1,1,2))]. 2920 L(x,y,L(z,u,(u * z) * ((u * z) * w))) = L(x,y,((u * z) * w) * (w * u)). [para(2796(a,1),2834(a,1,3))]. 2921 L(x,y,((z * u) * w) * (w * z)) = L(x,y,L(u,z,w)). [para(774(a,1),2920(a,1,3)),flip(a)]. 2923 L(x,y,((z * u) * w) * (z * w)) = L(x,y,L(u,z,w)). [para(2921(a,1),2795(a,1)),flip(a)]. 2924 a(((x * y) * z) * (x * z),u,w) = L(w,u,L(y,x,z)) \ w. [para(2923(a,1),2298(a,2,1))]. 2925 a(((x * y) * z) * (x * z),u,w) = a(L(y,x,z),u,w). [para(2924(a,2),2298(a,2)),flip(a)]. 2926 (x * y) \ (((x * z) * y) * R(((x * z) * y) \ (x * y),u,w)) = a(L(z,x,y),u,w). [para(2925(a,1),2685(a,2))]. 2927 (R(x,y,z) * (y * u)) \ ((R(x,y,z) * y) * u) = a(x,y,a(x,y,z) * u). [para(2420(a,1),2692(a,1,1))]. 2928 a(x,y,a(x,y,z) * u) = a(R(x,y,z),y,u). [para(2927(a,1),28(a,2)),flip(a)]. 2929 a(x,y,z * a(x,y,u)) = a(R(x,y,u),y,z). [para(2567(a,1),2928(a,1,3))]. 2930 (x * (y * z)) \ ((x * y) * L(R(z,u,w),y,x)) = a((x * y) * (x * (y * z)),u,w). [para(48(a,1),2686(a,1,2,2))]. 2931 (x * y) \ (((x * z) * R((x * z) \ x,u,w)) * y) = a(L(z,x,y),u,w). [para(1623(a,1),2926(a,1,2))]. 2932 (x * y) \ ((x * a(z,u,w)) * y) = a(L(z,x,y),u,w). [para(2315(a,1),2931(a,1,2,1))]. 2933 a(L(x,y,z),u,w) = R(a(x,u,w),y,z). [para(2932(a,1),2736(a,1))]. 2935 a(R(x,y,z),u,w) = a(L(x,y,z),u,w). [para(2933(a,2),2394(a,2))]. 2936 a(L(x,y,z),y,u) = a(x,y,u). [para(2933(a,2),2416(a,1))]. 2937 a(L(x,y,z),u,w) \ R(x,u,w) = a(a(x,u,w),y,z) \ x. [para(2933(a,2),2369(a,1,1))]. 2938 L(x,y,z) * a(L(z,u,w),y,x) = a(a(z,y,x),u,w) * x. [para(2933(a,2),2727(a,1,2))]. 2939 a((x * y) \ z,y,u) = a(y \ (x \ z),y,u). [para(177(a,1),2936(a,1,1))]. 2940 a((x \ y) \ z,y,u) = a(y \ (x * z),y,u). [para(267(a,1),2936(a,1,1))]. 2941 a((x \ y) \ T(z,x),y,u) = a(y \ (z * x),y,u). [para(269(a,1),2936(a,1,1))]. 2942 L(x,y,z) * a(x,y,u) = R(L(x,y,z),y,u). [para(2936(a,1),2300(a,2,2)),flip(a)]. 2946 a(x,y,z * a(x,y,u)) = a(L(x,y,u),y,z). [para(2935(a,1),2929(a,2))]. 2947 a(x \ (y \ z),x,u) = a((y * x) * z,x,u). [para(2939(a,1),1702(a,1))]. 2948 a(x / (y \ z),z,u) = a(z \ (y * x),z,u). [para(2940(a,1),2584(a,2))]. 2949 L(x,y,z) * a(x,y,u) = L(R(x,y,u),y,z). [para(2942(a,2),48(a,1))]. 2950 a(x,y,z * a(x,y,u)) = a(x,y,z). [para(2946(a,2),2936(a,1))]. 2952 a(x \ (y \ z),x,u) = a(y * (x * z),x,u). [para(2947(a,2),2843(a,1))]. 2953 a(x / (y / z),y,u) = a(y \ (z * x),y,u). [para(2948(a,1),2849(a,2))]. 2954 L(R(x,y,z),y,u) \ (x * a(x,y,z)) = a(u,y,x). [para(2949(a,1),2644(a,1,1))]. 2955 a(x * (y * z),y,u) = a(y * (x * z),y,u). [para(2952(a,1),1757(a,1))]. 2956 a((x * y) / z,z,u) = a(y / (z / x),z,u). [para(2953(a,2),2584(a,2))]. 2957 a((x \ y) * T(z,x),y,u) = a(y \ (z * x),y,u). [para(2941(a,1),1702(a,1)),flip(a)]. 2958 L(R(x,y,z),y,u) \ R(x,y,z) = a(u,y,x). [para(2300(a,2),2954(a,1,2))]. 2959 a(x,y,R(z,y,u)) = a(x,y,z). [para(2958(a,1),2298(a,2))]. 2960 a(x,y,(z / u) / y) = a(x,y,z / (y * u)). [para(193(a,1),2959(a,1,3)),flip(a)]. 2961 a(x \ (y * z),x,u) = a((z \ x) * y,x,u). [para(2957(a,1),2841(a,1))]. 2962 a(x \ (y * z),x,u) = a((z * x) * y,x,u). [para(2961(a,2),1707(a,1))]. 2964 a(x \ (y * z),x,u) = a(z * (x * y),x,u). [para(2962(a,2),2843(a,1))]. 2965 a(a(x,y,z),u,w) * z = z * a(w,u,a(x,y,z)). [para(2938(a,1),2693(a,1))]. 2966 a(a(x,y,z),u,w) = a(w,u,a(x,y,z)). [hyper(24,a,2567,a,b,2965,a)]. 2968 a(a(x,y,z),u,w) \ 1 = a(w,u,a(x,y,z)). [para(2966(a,2),2694(a,1,1))]. 2969 a(a(x,y,z),u,w) \ v5 = v5 * a(w,u,a(x,y,z)). [para(2966(a,2),2696(a,1,1))]. 2970 x \ L(x,y,a(z,u,w)) = a(x,y,a(z,u,w)). [para(2968(a,1),2328(a,1)),flip(a)]. 2971 ((a(x,y,z) * u) * w) \ (a(x,y,z) * (u * w)) = a(w,u,a(x,y,z)). [para(2968(a,1),2808(a,2))]. 2972 (x \ (a(y,z,u) * w)) \ ((a(y,z,u) \ x) \ w) = a(x \ (a(y,z,u) * w),x,a(y,z,u)). [para(267(a,1),2970(a,1,2))]. 2973 a(L(x,y,z),u,w) \ R(x,u,w) = x * a(z,y,a(x,u,w)). [para(2969(a,1),2937(a,2))]. 2974 ((a(x,y,z) * u) * w) \ ((u * w) * a(x,y,z)) = a(w,u,a(x,y,z)). [para(2567(a,1),2971(a,1,2))]. 2975 ((x * a(y,z,u)) * w) \ ((x * w) * a(y,z,u)) = a(w,x,a(y,z,u)). [para(2567(a,1),2974(a,1,1,1))]. 2976 (x * (y * z)) \ (x * (y * R(z,u,w))) = a((x * y) * (x * (y * z)),u,w). [para(74(a,1),2930(a,1,2))]. 2977 L(a(x,y,z),u * x,w) = a((w * u) * (w * (u * x)),y,z). [para(2976(a,1),2730(a,1)),flip(a)]. 2978 L(a(x,y,z),u * x,w) = a(L(x,u,w),y,z). [para(2977(a,2),1705(a,1))]. 2979 a(L(x,y,z),u,w) \ a(x,u,w) = a(z,y * x,a(x,u,w)). [para(2978(a,1),2298(a,2,1)),flip(a)]. 2980 a(x,y * z,a(z,u,w)) = a(x,y,a(z,u,w)). [para(2979(a,1),2407(a,1))]. 2981 a(x,y * z,a(y,u,w)) = a(x,z,a(y,u,w)). [para(2980(a,1),2856(a,1)),flip(a)]. 2982 a(x * y,z * u,a(z,w,v5)) = a(y * x,u,a(z,w,v5)). [para(2981(a,1),2618(a,1)),flip(a)]. 2983 a((x * y) * z,y,a(x,u,w)) = a(z * (x * y),z,a(x,u,w)). [para(2982(a,1),2750(a,1))]. 2984 a(x * (y * z),y,a(x,u,w)) = a(z * (x * y),z,a(x,u,w)). [para(2983(a,1),2843(a,1)),flip(a)]. 2985 a(x * (y * z),y,a(x,u,w)) = a(x * (z * y),z,a(x,u,w)). [para(2984(a,2),2955(a,2))]. 2986 (x * (y * (a(z,u,z) * w))) \ ((x * (a(z,u,z) * y)) * w) = a(x,y,a(z,u,z) * w). [para(2807(a,1),2805(a,1,2,1))]. 2987 a(x,y,a(z,u,z) * w) = a(x,y,w). [para(2986(a,1),2919(a,1))]. 2988 a(x,y,L(z,u,z)) = a(x,y,z). [para(1542(a,1),2987(a,1,3)),flip(a)]. 2989 a(x,y,(z \ u) * z) = a(x,y,T(u,z)). [para(2675(a,1),2987(a,1,3))]. 2991 a(x,y,(T(z,u) * u) \ (T(z,u) * (z * u))) = a(x,y,T(z,u)). [para(106(a,2),2988(a,1,3))]. 2992 a(x,y,T(z * u,z)) = a(x,y,u * z). [para(19(a,1),2989(a,1,3,1)),flip(a)]. 2993 a(x,y,(T(z,u) * u) \ (z * (T(z,u) * u))) = a(x,y,T(z,u)). [para(728(a,1),2991(a,1,3,2))]. 2994 a(x,y,T(z,T(z,u) * u)) = a(x,y,T(z,u)). [para(36(a,2),2993(a,1,3))]. 2995 a(x,y,T(z,z * u)) = a(x,y,T(z,u)). [para(2018(a,1),2994(a,1,3))]. 2996 a(x,y,T((z \ u) * z,((z \ u) * z) * (z \ 1))) = a(x,y,R(u,z,z)). [para(761(a,1),2995(a,2,3))]. 2998 a(x,y,T((z \ u) * z,R(z \ u,z,z \ 1))) = a(x,y,R(u,z,z)). [para(433(a,1),2996(a,1,3,2))]. 2999 a(x,y,T((z \ u) * z,z \ u)) = a(x,y,R(u,z,z)). [para(2716(a,1),2998(a,1,3))]. 3001 a(x,y,z * (z \ u)) = a(x,y,R(u,z,z)). [para(2999(a,1),2992(a,1)),flip(a)]. 3002 a(x,y,R(z,u,u)) = a(x,y,z). [para(20(a,1),3001(a,1,3)),flip(a)]. 3003 a(x,y,z / (u \ 1)) = a(x,y,z * u). [para(720(a,1),3002(a,1,3)),flip(a)]. 3004 a(x,y,R(((z \ 1) * u) \ 1,u,u)) = a(x,y,(u \ 1) * z). [para(1739(a,2),3003(a,1,3))]. 3005 a(x,y,R((z \ u) \ 1,u,u)) = a(x,y,(u \ 1) * z). [para(318(a,1),3004(a,1,3,1,1))]. 3006 a(x,y,(z \ u) \ 1) = a(x,y,(u \ 1) * z). [para(3005(a,1),3002(a,1)),flip(a)]. 3007 a(x,y,(z \ u) \ 1) = a(x,y,u \ z). [para(318(a,1),3006(a,2,3))]. 3009 a(x,y,(z / u) \ z) = a(x,y,u * a(z,u,u)). [para(1388(a,1),3007(a,1,3)),flip(a)]. 3010 a(x,y,z * a(u,z,z)) = a(x,y,z). [para(66(a,1),3009(a,1,3)),flip(a)]. 3011 a(x,y,L(z,u,u * z)) = a(x,y,z). [para(1487(a,2),3010(a,1,3))]. 3012 ((x * y) \ x) * L(L(y,x,x * y),z,u) = a(u,z,y) \ 1. [para(3011(a,1),2357(a,2,1))]. 3013 (x * y) \ (x * L(y,z,u)) = a(u,z,y) \ 1. [para(3012(a,1),814(a,1)),flip(a)]. 3015 L(a(x,y,z),z,u) = a(x,x * y,z) \ 1. [para(3013(a,1),2350(a,1)),flip(a)]. 3016 L(a(x,y,z),z,u) = a(x,y,z). [para(3015(a,2),2343(a,1))]. 3019 (x * L(y,z,u)) / a(u,u * z,y) = x * y. [para(3016(a,1),2356(a,1,2))]. 3021 a(x,x * y,z) \ (u * L(z,y,x)) = u * z. [para(3019(a,1),2571(a,1)),flip(a)]. 3023 a(x,y,z) * (u * L(z,y,x)) = u * z. [para(3021(a,1),2360(a,1)),flip(a)]. 3024 a(x,y,z) \ (u * z) = u * L(z,y,x). [hyper(23,a,20,a,b,3023,a),flip(a)]. 3026 x * T(y,L(x,z,u)) = y * x. [para(3023(a,1),2376(a,1)),flip(a)]. 3031 L(x,y,z) * T(u,x) = u * L(x,y,z). [para(303(a,1),3026(a,1,2,2))]. 3032 K(L(x,y,z),u) = (u * x) \ (x * u). [para(3026(a,1),2186(a,1,1)),flip(a)]. 3034 K(L(x,y,z),u) = K(x,u). [para(3032(a,2),30(a,2)),flip(a)]. 3036 L(K(x,y),z,u) = K(x,y). [para(3034(a,1),2259(a,1)),flip(a)]. 3038 a(x,y,K(z,u)) = 1. [hyper(38,a,3036,a)]. 3040 (x * y) * K(z,u) = x * (y * K(z,u)). [para(3036(a,1),74(a,1,2))]. 3041 x \ (y * K(z,u)) = (x \ y) * K(z,u). [para(3036(a,1),560(a,1,2)),flip(a)]. 3049 (x / y) * L(y,z,u) = a(u,z,y) \ x. [para(22(a,1),3024(a,1,2)),flip(a)]. 3050 (x * L(y,z,u)) \ (x * y) = a(u,z,y). [para(3024(a,1),2569(a,1,1))]. 3052 (x * (y * K(z,u))) * w = (x * y) * (K(z,u) * w). [para(3040(a,1),2649(a,1,1))]. 3053 (x \ (y \ z)) * K(y,y * z) = x \ (z / y). [para(1001(a,1),3041(a,1,2)),flip(a)]. 3054 a(x,y,z * u) \ u = z \ L(z * u,y,x). [para(3049(a,1),353(a,1))]. 3055 ((x * y) * L(L(z,y,x),u,w)) \ (x * (y * z)) = a(w,u,L(z,y,x)). [para(74(a,1),3050(a,1,2))]. 3056 L(a(x,y,z),u * L(z,y,x),w) = (w * (u * L(z,y,x))) \ (w * (u * z)). [para(3050(a,1),76(a,1,1))]. 3057 (x * (y * (K(z,u) * w))) \ ((x * (y * K(z,u))) * w) = a(x,y,K(z,u) * w). [para(3052(a,2),28(a,2,2)),flip(a)]. 3058 ((x * y) * (K(z,u) * w)) / ((y * K(z,u)) * w) = R(x,y * K(z,u),w). [para(3052(a,1),34(a,2,1)),flip(a)]. 3059 (x * (y * L(z,u,w))) \ (x * (y * z)) = a(w,u,L(z,y,x)). [para(175(a,1),3055(a,1,1))]. 3060 ((x * y) * (K(z,u) * w)) / (y * (K(z,u) * w)) = R(x,y * K(z,u),w). [para(2649(a,1),3058(a,1,2))]. 3061 R(x,y * K(z,u),w) = R(x,y,K(z,u) * w). [para(3060(a,1),34(a,2)),flip(a)]. 3062 R(x,y,K(z,u) * w) = R(x,y,w). [para(3061(a,1),2892(a,1))]. 3063 R(x,y,T(z,u)) = R(x,y,z). [para(985(a,1),3062(a,1,3)),flip(a)]. 3072 R(x,y,T(z,u)) = a(x,y,z) * x. [para(3063(a,2),2303(a,1))]. 3073 a(x,y,T(z,u)) = a(x,y,z). [hyper(24,a,2303,a(flip),b,3072,a(flip)),flip(a)]. 3074 a(x,y,z / u) = a(x,y,u \ z). [para(84(a,1),3073(a,1,3)),flip(a)]. 3075 a(x,y,(z \ u) * z) = a(x,y,u). [para(3073(a,1),2989(a,2))]. 3077 a(x,y,(z / u) / x) = a(x,y,(x * u) \ z). [para(3074(a,1),2493(a,2))]. 3078 a(x,y,(z / u) / y) = a(x,y,(y * u) \ z). [para(3074(a,1),2960(a,2))]. 3079 a(x,y,((z / u) * w) * (u / z)) = a(x,y,w). [para(358(a,1),3075(a,1,3,1))]. 3080 (x \ y) \ L((x \ y) * x,z,u) = a(u,z,y) \ x. [para(3075(a,1),3054(a,1,1)),flip(a)]. 3082 L(x,y,z) / (u \ x) = a(z,y,x) \ u. [para(3080(a,1),1588(a,1)),flip(a)]. 3083 a(x,x * y,L(z,y,x)) \ u = z / (u \ L(z,y,x)). [para(303(a,1),3082(a,1,1)),flip(a)]. 3084 (a(x,y,z) \ 1) \ u = z / (u \ L(z,y,x)). [para(2365(a,1),3083(a,1,1))]. 3085 x / (y \ L(x,z,u)) = a(u,z,x) * y. [para(3084(a,1),330(a,1))]. 3086 x / (y * L(x,z,u)) = a(u,z,x) * (y \ 1). [para(330(a,1),3085(a,1,2))]. 3087 R(x,y,z) / a(L(x,u,w),y,z) = a(w,u,R(x,y,z)) * L(x,u,w). [para(2301(a,1),3085(a,1,2))]. 3088 x / (y * L(x,z,u)) = y \ a(u,z,x). [para(3086(a,2),2572(a,1))]. 3089 a(L(x,y,z),u,w) \ R(x,u,w) = a(z,y,R(x,u,w)) * L(x,y,z). [para(3087(a,1),2571(a,1)),flip(a)]. 3090 a(x,y,R(z,u,w)) * L(z,y,x) = z * a(x,y,a(z,u,w)). [para(3089(a,1),2973(a,1))]. 3091 L(a(x,y,z),u * L(z,y,x),w) = a(x,y,L(z,u,w)). [para(3056(a,2),3059(a,1))]. 3092 a(L(x,y * L(z,u,x),w),u,z) = a(x,u,L(z,y,w)). [para(3091(a,1),2406(a,2))]. 3093 a(x,y,L(z,u,x)) = a(x,y,z). [para(3091(a,1),2687(a,1))]. 3094 a(x,y,L(L(z,u,x),w,v5)) = a(x,y,L(z,w,v5)). [para(49(a,1),3093(a,1,3))]. 3098 a(L(x,y * z,u),w,L(z,x * w,x)) = a(x,w,L(L(z,x * w,x),y,u)). [para(308(a,1),3092(a,1,1,2,2))]. 3099 a(L(x,L(y,z,x) * u,w),z,y) = a(x,z,L(y,T(u,v5),w)). [para(2817(a,1),3092(a,1,1))]. 3100 a(x,y,K(z,u) * w) = a(x,y,w). [para(3057(a,1),2918(a,1))]. 3101 a(x,y,(z / u) * w) = a(x,y,(u \ z) * w). [para(1161(a,1),3100(a,1,3))]. 3102 a(x,y,z * T(u,w)) = a(x,y,z * u). [para(1212(a,1),3100(a,1,3))]. 3103 a(x,y,K(z * u,z)) = a(x,y,a(z,u,z)). [para(1537(a,1),3100(a,1,3)),flip(a)]. 3104 a(x,y,T(z,u) / w) = a(x,y,z / w). [para(1815(a,1),3100(a,1,3))]. 3105 a(x,y,(K(z,u) * w) * v5) = a(x,y,w * v5). [para(2518(a,2),3100(a,1,3))]. 3106 a(x,y,(z * K(u,w)) * v5) = a(x,y,z * v5). [para(2630(a,1),3100(a,1,3))]. 3107 a(x,y,(z \ u) \ w) = a(x,y,(z / u) * w). [para(2676(a,1),3100(a,1,3)),flip(a)]. 3108 a(x,y,(z \ K(u,w)) * v5) = a(x,y,z \ v5). [para(2677(a,1),3100(a,1,3))]. 3110 a(x,y,z * (u / w)) = a(x,y,z * (w \ u)). [para(84(a,1),3102(a,1,3,2)),flip(a)]. 3111 a(x,y,z \ T(u,w)) = a(x,y,u / z). [para(3104(a,1),3074(a,1)),flip(a)]. 3112 a(x,y,(z / u) / w) = a(x,y,w \ (u \ z)). [para(84(a,1),3111(a,1,3,2)),flip(a)]. 3113 a(x,y,a(z,u,z)) = 1. [para(3103(a,1),3038(a,1))]. 3114 L(a(x,y,x),z,u) = a(x,y,x). [hyper(37,a,3113,a)]. 3116 a(L(x,y,z),u,x) = a(x,u,x). [para(3114(a,1),2406(a,2))]. 3117 L(x * a(x,y,x),y,L(x,z,u)) = x. [para(3116(a,1),2362(a,1,1,2))]. 3119 L(R(x,y,x),y,L(x,z,u)) = x. [para(1540(a,1),3117(a,1,1))]. 3120 L(x,y,z) * (u * R(x,u,x)) = (L(x,y,z) * u) * x. [para(3119(a,1),74(a,1,2)),flip(a)]. 3121 a(x,y,((z / u) * w) * v5) = a(x,y,((u \ z) * w) * v5). [para(1161(a,1),3105(a,1,3,1))]. 3122 a(x,y,((z \ u) \ w) * v5) = a(x,y,((z / u) * w) * v5). [para(2676(a,1),3105(a,1,3,1)),flip(a)]. 3123 a(x,y,(z \ u) \ w) = a(x,y,(u \ z) * w). [para(3107(a,2),3101(a,1))]. 3124 a(x,y,(T(z,u) * w) \ v5) = a(x,y,(z * w) \ v5). [para(2134(a,1),3108(a,1,3))]. 3125 a(x,y,((z / u) * w) * (z \ u)) = a(x,y,w). [para(3110(a,1),3079(a,1))]. 3126 a(x,y,(x * z) \ u) = a(x,y,x \ (z \ u)). [para(3112(a,1),3077(a,1)),flip(a)]. 3127 a(x,y,(y * z) \ u) = a(x,y,y \ (z \ u)). [para(3112(a,1),3078(a,1)),flip(a)]. 3128 a(x,y,((z \ (u \ w)) * K(u,u * w)) * v5) = a(x,y,((w / u) \ z) \ v5). [para(3053(a,2),3123(a,2,3,1)),flip(a)]. 3129 a(x,x * y,x \ (y \ z)) = (y \ (x \ z)) \ ((x * y) \ z). [para(3126(a,1),2327(a,1))]. 3130 a(x,y,y \ (z \ ((z * y) * u))) = a(x,y,K(z,y) * u). [para(940(a,1),3127(a,1,3)),flip(a)]. 3131 a(x,y,((z / u) * w) \ v5) = a(x,y,((u \ z) * w) \ v5). [para(84(a,1),3124(a,1,3,1,1)),flip(a)]. 3132 L(x,y,z) * T(x * u,x) = (L(x,y,z) * u) * x. [para(1321(a,1),3120(a,1,2))]. 3133 (L(x,y,z) * u) * x = (x * u) * L(x,y,z). [para(3132(a,1),3031(a,1))]. 3134 (x * (L(x,y,z) \ u)) * L(x,y,z) = u * x. [para(20(a,1),3133(a,1,1)),flip(a)]. 3135 (x * a(y,z,u)) * L(u,z,y) = x * u. [para(2604(a,1),3134(a,1,1))]. 3137 (x / a(y,z,u)) * u = x * L(u,z,y). [para(22(a,1),3135(a,1,1)),flip(a)]. 3138 (a(x,y,z) / u) \ z = u * L(z,y,x). [para(3137(a,1),358(a,2))]. 3139 x / (y * L(x,z,u)) = a(u,z,x) / y. [para(3138(a,1),65(a,1,2))]. 3140 a(x,y,z) / u = u \ a(x,y,z). [para(3139(a,1),3088(a,1))]. 3141 (a(x,y,z) \ u) \ w = (u \ a(x,y,z)) * w. [para(3140(a,1),2605(a,2,1))]. 3143 a(x,y,((z \ u) * w) * (u \ z)) = a(x,y,w). [para(3121(a,1),3125(a,1))]. 3144 a(x,y,((z \ u) * w) * ((u * w) \ z)) = a(x,y,a(z,u,w)). [para(595(a,1),3143(a,1,3,1))]. 3145 a(x,y,(z \ (u * w)) * (u \ z)) = a(x,y,L(w,u,z)). [para(798(a,1),3143(a,1,3,1))]. 3146 a(x,y,((z \ u) \ w) * v5) = a(x,y,((u \ z) * w) * v5). [para(3122(a,2),3121(a,1))]. 3147 a(x,y,y \ (z \ ((z * y) * u))) = a(x,y,u). [para(3130(a,2),3100(a,1))]. 3148 a(x,y,L(z,u * y,u)) = a(x,y,z). [para(309(a,1),3147(a,1,3))]. 3151 a(L(x,y * z,u),w,z) = a(x,w,L(L(z,x * w,x),y,u)). [para(3148(a,1),3098(a,1))]. 3152 a(x,y,(z \ (u \ w)) \ ((u * z) \ w)) = x \ L(x,y,a(u,u * z,u \ (z \ w))). [para(3129(a,1),2970(a,2,3)),flip(a)]. 3153 a(L(x,y * z,u),w,z) = a(x,w,L(z,y,u)). [para(3151(a,2),3094(a,1))]. 3155 a(x,y,L(z,u * z,w)) = a(L(x,u,w),y,z). [para(2765(a,1),3153(a,1,1)),flip(a)]. 3157 a(x,y,((z \ (u \ w)) * K(u,u * w)) * v5) = a(x,y,((u / w) * z) \ v5). [para(358(a,1),3128(a,2,3,1))]. 3158 a(x,y,((z / u) * w) \ v5) = a(x,y,(w \ (z \ u)) * v5). [para(3157(a,1),3106(a,1))]. 3160 a(x,y,((z \ u) * w) \ v5) = a(x,y,(w \ (u \ z)) * v5). [para(3158(a,1),3131(a,1)),flip(a)]. 3161 a(x,y,z / ((u \ w) * v5)) = a(x,y,(v5 \ (w \ u)) * z). [para(3160(a,1),3074(a,2))]. 3162 a(x,y,(z \ (u \ w)) \ ((u * z) \ w)) = x \ L(x,y,a(u,z,u \ (z \ w))). [para(2361(a,1),3152(a,2,2))]. 3163 a(x,y,(z \ (u \ w)) \ ((u * z) \ w)) = a(x,y,a(u,z,u \ (z \ w))). [para(3162(a,2),2970(a,1))]. 3164 (x \ (a(y,z,u) * w)) \ ((x \ a(y,z,u)) * w) = a(x \ (a(y,z,u) * w),x,a(y,z,u)). [para(3141(a,1),2972(a,1,2))]. 3165 a(x \ (a(y,z,u) * w),x,a(y,z,u)) = a(x,a(y,z,u),w). [para(3164(a,1),594(a,2)),flip(a)]. 3166 a(x * (a(y,z,u) * w),x,a(y,z,u)) = a(x,a(y,z,u),w). [para(3165(a,1),1702(a,1)),flip(a)]. 3167 a(x * (y * a(z,u,w)),y,a(z,u,w)) = a(y,a(z,u,w),x). [para(3165(a,1),2964(a,1)),flip(a)]. 3168 a(a(x,y,z) * (u * w),u,a(x,y,z)) = a(u,a(x,y,z),w). [para(3166(a,1),2955(a,2))]. 3169 a((x * a(y,z,u)) / w,x,a(y,z,u)) = a(x,a(y,z,u),w). [para(3167(a,1),2606(a,2))]. 3170 a(a(x,y,z) * (u * w),u,a(x,y,z)) \ v5 = a(u,u * a(x,y,z),w) * v5. [para(3168(a,2),2359(a,2,1)),flip(a)]. 3171 a(a(x,y,z) / (u / w),u,a(x,y,z)) = a(u,a(x,y,z),w). [para(3169(a,1),2852(a,1)),flip(a)]. 3172 a(a(x,y,z) * (u * w),u,a(x,y,z)) = a(u,u * a(x,y,z),w). [hyper(24,a,2696,a(flip),b,3170,a(flip)),flip(a)]. 3173 a(x,x * a(y,z,u),w) = a(x,a(y,z,u),w). [para(3172(a,1),3168(a,1))]. 3174 a(x,a(y,z,u),w) \ v5 = a(x,a(y,z,u),w) * v5. [para(3173(a,1),2359(a,1,1)),flip(a)]. 3175 a(x,a(y,z,u),w) \ a(x,w,a(y,z,u)) = a(w,x,a(y,z,u)). [para(2809(a,1),2975(a,1))]. 3176 a(x,a(y,z,u),w) * a(x,w,a(y,z,u)) = a(w,x,a(y,z,u)). [para(3175(a,1),3174(a,1)),flip(a)]. 3177 R(T(a(x,y,z),(L(z,y,x) * u) * w),L(z,y,x) * u,w) = a(x,y,R(z,u,w)). [para(2379(a,2),2751(a,1))]. 3178 R(a(x,y,z),L(z,y,x) * u,w) = a(x,y,R(z,u,w)). [para(2543(a,1),3177(a,1,1))]. 3180 a(L(x,L(y,z,x) * u,w),z,y) = a(x,z,R(y,u,w)). [para(3178(a,1),2933(a,2))]. 3181 a(x,y,L(z,T(u,w),v5)) = a(x,y,R(z,u,v5)). [para(3180(a,1),3099(a,1)),flip(a)]. 3182 a(x,y,R(z,u,w)) = a(x,y,L(z,u,w)). [para(81(a,1),3181(a,1,3,2)),flip(a)]. 3183 a(x,y,L(z,u * z,w)) = a(x,y,(u \ w) / ((z \ (u \ 1)) * w)). [para(2916(a,1),3182(a,1,3)),flip(a)]. 3184 a(x,y,L(z,u,w)) * L(z,y,x) = z * a(x,y,a(z,u,w)). [para(3182(a,1),3090(a,1,1))]. 3185 a(x,y,L(z,u * z,w)) = a(x,y,(w \ ((u \ 1) \ z)) * (u \ w)). [para(3183(a,2),3161(a,1))]. 3186 a(x,y,L(z,u * z,w)) = a(x,y,(w \ (u * z)) * (u \ w)). [para(330(a,1),3185(a,2,3,1,2))]. 3187 a(x,y,L(z,u * z,w)) = a(x,y,L(z,u,w)). [para(3186(a,2),3145(a,1))]. 3188 a(L(x,y,z),u,w) = a(x,u,L(w,y,z)). [para(3187(a,1),3155(a,1)),flip(a)]. 3189 L(x,y,z) * a(z,y,L(x,u,w)) = x * a(w,u,a(z,y,x)). [para(3188(a,1),2693(a,1,2))]. 3190 a(x,y,L(z,u,w)) * L(z,y,x) = z * a(w,u,a(x,y,z)). [para(3188(a,1),2697(a,1,1))]. 3191 L(x,y,z) * a(z,y,L(x,u,w)) = x * a(z,y,a(w,u,x)). [para(3189(a,1),2643(a,1)),flip(a)]. 3192 a(x,y,a(z,u,w)) = a(w,u,a(x,y,z)). [hyper(23,a,3184,a(flip),b,3190,a(flip)),flip(a)]. 3193 a(x,y,a(z / u,w,v5)) = a(v5,w,a(x,y,u * z)). [para(2606(a,2),3192(a,1,3))]. 3194 a(x * y,z,a(u,w,v5)) = a(u,w,a(v5,z,y * x)). [para(3192(a,2),2618(a,1)),flip(a)]. 3195 a(x,y,a(z,u,w)) = a(w,y,a(x,u,z)). [para(3192(a,1),3192(a,2)),flip(a)]. 3196 a(x,y,a(z,u,w)) * a(z,y,a(w,u,x)) = 1. [para(3195(a,1),2695(a,1,1))]. 3197 a(x * y,x,a(z,u,w)) = a(z,y,a(w,u,x * y)). [para(3195(a,2),2750(a,1)),flip(a)]. 3198 a(x,y * z,a(u,w,z)) = a(u,y,a(z,w,x)). [para(3195(a,1),2980(a,1))]. 3199 a(x,y,a(a(x,y,z) / u,w,v5)) = a(v5,w,a(x,y,u)). [para(2950(a,1),3193(a,2,3))]. 3200 a(x,y,a(z,u,w / v5)) = a(x,y,a(z,u,v5 * w)). [para(3193(a,1),3192(a,1)),flip(a)]. 3201 a(x,y,a(z,u,w)) = a(z,u,a(x,y,w)). [hyper(23,a,3189,a(flip),b,3191,a(flip))]. 3202 a(x,y,a(a(x,y,z) / (u / w),u,z)) = a(u,a(x,y,z),w). [para(3201(a,1),3171(a,1))]. 3203 a(x,y,a(z,u,w)) = a(w,y,a(z,u,x)). [para(3201(a,1),3192(a,1))]. 3204 a(x,y,a(z,u,w)) = a(x,y,a(w,u,z)). [para(3201(a,1),3192(a,2))]. 3205 a(x,y,a(z,u,w)) = a(w,u,a(z,y,x)). [para(3201(a,1),3195(a,1))]. 3206 a(x,a(y,z,u),w) * a(u,w,a(y,z,x)) = a(w,x,a(y,z,u)). [para(3203(a,1),3176(a,1,2))]. 3207 a(x,y * z,a(u,w,z)) = a(x,y,a(z,w,u)). [para(3203(a,1),3198(a,2))]. 3208 a(x,y,a(z / u,w,v5)) = a(x,y,a(v5,w,u / z)). [para(612(a,1),3204(a,1,3))]. 3209 a(x * y,z,a(u,w,v5)) = a(v5,w,a(u,z,y * x)). [para(3204(a,1),3194(a,1))]. 3210 a(x / y,z,a(u,w,v5)) = a(v5,w,a(u,z,y / x)). [para(3205(a,1),612(a,1)),flip(a)]. 3211 a(x * (y * z),y,a(x,u,w)) = a(w,u,a(x,z,x * (z * y))). [para(3205(a,1),2985(a,1)),flip(a)]. 3212 a(x,y,(z \ (u \ w)) \ ((u * z) \ w)) = a(u \ (z \ w),z,a(u,y,x)). [para(3205(a,1),3163(a,2))]. 3213 a(x * (y * z),y,a(u,w,v5)) = a(v5,w,a(u,y,z * (y * x))). [para(3209(a,1),2488(a,1)),flip(a)]. 3214 a(x,y,a(z,u,y / w)) = a(y,a(z,u,x),w). [para(3202(a,1),3199(a,1)),flip(a)]. 3215 a(x,y,a(z,u,w * y)) = a(y,a(z,u,x),w). [para(3214(a,1),3200(a,1)),flip(a)]. 3217 a(x,y,a(z,u,u / w)) = a(u,a(x,y,z),w). [para(3214(a,1),3201(a,1)),flip(a)]. 3218 a(x * y,x,a(z,u,w)) = a(y,a(w,u,z),x). [para(3215(a,1),3197(a,2))]. 3219 a(x,y,a(z / u,u,w)) = a(u,a(x,y,w),z). [para(3217(a,1),3208(a,2))]. 3220 a(x / y,y,a(z,u,w)) = a(y,a(w,u,z),x). [para(3217(a,1),3210(a,2))]. 3221 a(x * (y * z),y,a(u,w,v5)) = a(x * z,a(v5,w,u),y). [para(3218(a,1),2955(a,2))]. 3222 a(x,y,a(z,u,w / u)) = a(u,a(x,y,z),w). [para(3219(a,1),3204(a,1)),flip(a)]. 3223 a(x / (y / z),y,a(u,w,v5)) = a(y,a(v5,w,u),z * x). [para(3220(a,1),2956(a,1)),flip(a)]. 3224 a(x / (y * z),z,a(u,w,v5)) = a(z,a(v5,w,u),y * x). [para(3223(a,1),2851(a,1)),flip(a)]. 3225 a(x,y,a(z,u,z * (u * w))) = a(z * u,a(x,y,z),w). [para(3211(a,1),3221(a,1))]. 3226 a(x / (y * z),z,a(u,w,v5)) = a(v5,w,a(u,z,x * (z * y))). [para(3213(a,1),2846(a,2))]. 3227 a(x,y,a(z,u,w * (u * v5))) = a(u,a(x,y,z),v5 * w). [para(3226(a,1),3224(a,1))]. 3228 a(x * y,a(z,u,x),w) = a(y,a(z,u,x),w * x). [para(3227(a,1),3225(a,1)),flip(a)]. 3229 a(x,y,(z \ (u \ w)) \ ((u * z) \ w)) = a(u * (z * w),z,a(u,y,x)). [para(3212(a,2),1757(a,1))]. 3230 a(x,y,(z \ (u \ w)) \ ((u * z) \ w)) = a(u * w,a(x,y,u),z). [para(3229(a,2),3221(a,1))]. 3231 a(x,y,(z \ (u \ w)) \ ((u * z) \ w)) = a(w,a(x,y,u),z * u). [para(3230(a,2),3228(a,1))]. 3232 a(x,y,((z \ u) \ w) * ((z * w) \ u)) = a(u,a(x,y,z),w * z). [para(3231(a,1),3123(a,1)),flip(a)]. 3233 a(x,y,((z \ u) * w) * ((u * w) \ z)) = a(z,a(x,y,u),w * u). [para(3232(a,1),3146(a,1)),flip(a)]. 3234 a(x,a(y,z,u),w * u) = a(y,z,a(x,u,w)). [para(3233(a,1),3144(a,1))]. 3235 a(x,y,a(z,u,w / u)) = a(z,a(x,y,u),w). [para(22(a,1),3234(a,1,3)),flip(a)]. 3236 a(x,a(y,z,u),w) = a(u,a(y,z,x),w). [para(3235(a,1),3222(a,1))]. 3237 a(x,a(y,z,u),w) * a(u,w,a(y,z,x)) = a(w,u,a(y,z,x)). [para(3236(a,1),3176(a,1,1))]. 3238 a(x,y,a(z,u,w)) = a(x,w,a(z,u,y)). [para(3237(a,1),3206(a,1))]. 3239 a(x,y,a(z,u,w * y)) = a(x,w,a(y,u,z)). [para(3238(a,1),3207(a,1))]. 3240 a(x,a(y,z,u),w) = a(u,w,a(x,z,y)). [para(3239(a,1),3215(a,1)),flip(a)]. 3241 a(x,y,a(z,u,w)) * a(z,y,a(w,u,x)) = a(y,z,a(w,u,x)). [para(3240(a,1),3176(a,1,1))]. 3242 a(x,y,a(z,u,w)) = 1. [para(3241(a,1),3196(a,1))]. 3245 a(a(x,y,z),u,w) = 1. [para(3242(a,1),2966(a,2))]. 3246 $F # answer("aa1"). [resolve(3245,a,52,a)]. ============================== end of proof ========================== -------- Proof 7 -------- "aa2". ============================== PROOF ================================= % Proof 7 at 82.45 (+ 1.33) seconds: "aa2". % Length of proof is 2842. % Level of proof is 321. % Maximum clause weight is 50. % Given clauses 2826. 1 x * y = u & x * z = u -> y = z # label(non_clause). [assumption]. 2 y * x = u & z * x = u -> y = z # label(non_clause). [assumption]. 5 a(x,y,z) = 1 -> L(z,y,x) = z # label(non_clause). [assumption]. 6 L(x,y,z) = x -> a(z,y,x) = 1 # label(non_clause). [assumption]. 7 T(x,y) = x -> T(y,x) = y # label(non_clause). [assumption]. 8 T(x,y) = x -> K(x,y) = 1 # label(non_clause). [assumption]. 9 K(x,y) = 1 -> T(x,y) = x # label(non_clause). [assumption]. 11 a(x,a(y,z,u),w) = 1 # label("aa2") # label(non_clause) # label(goal). [goal]. 17 1 * x = x. [assumption]. 18 x * 1 = x. [assumption]. 19 x \ (x * y) = y. [assumption]. 20 x * (x \ y) = y. [assumption]. 21 (x * y) / y = x. [assumption]. 22 (x / y) * y = x. [assumption]. 23 x * y != z | x * u != z | u = y. [clausify(1)]. 24 x * y != z | u * y != z | u = x. [clausify(2)]. 27 (x * (y * z)) \ ((x * y) * z) = a(x,y,z). [assumption]. 28 a(x,y,z) = (x * (y * z)) \ ((x * y) * z). [copy(27),flip(a)]. 29 (x * y) \ (y * x) = K(y,x). [assumption]. 30 K(x,y) = (y * x) \ (x * y). [copy(29),flip(a)]. 31 (x * y) \ (x * (y * z)) = L(z,y,x). [assumption]. 32 L(x,y,z) = (z * y) \ (z * (y * x)). [copy(31),flip(a)]. 33 ((x * y) * z) / (y * z) = R(x,y,z). [assumption]. 34 R(x,y,z) = ((x * y) * z) / (y * z). [copy(33),flip(a)]. 35 x \ (y * x) = T(y,x). [assumption]. 36 T(x,y) = y \ (x * y). [copy(35),flip(a)]. 37 a(x,y,z) != 1 | L(z,y,x) = z. [clausify(5)]. 38 L(x,y,z) != x | a(z,y,x) = 1. [clausify(6)]. 39 T(x,y) != x | T(y,x) = y. [clausify(7)]. 40 T(x,y) != x | K(x,y) = 1. [clausify(8)]. 41 K(x,y) != 1 | T(x,y) = x. [clausify(9)]. 42 T(T(x,y),z) = T(T(x,z),y). [assumption]. 43 T(L(x,y,z),u) = L(T(x,u),y,z). [assumption]. 44 L(T(x,y),z,u) = T(L(x,z,u),y). [copy(43),flip(a)]. 45 T(R(x,y,z),u) = R(T(x,u),y,z). [assumption]. 46 R(T(x,y),z,u) = T(R(x,z,u),y). [copy(45),flip(a)]. 47 L(R(x,y,z),u,w) = R(L(x,u,w),y,z). [assumption]. 48 R(L(x,y,z),u,w) = L(R(x,u,w),y,z). [copy(47),flip(a)]. 49 L(L(x,y,z),u,w) = L(L(x,u,w),y,z). [assumption]. 50 R(R(x,y,z),u,w) = R(R(x,u,w),y,z). [assumption]. 51 (x * (x * y)) * z = x * (x * (y * z)) # label("LC"). [assumption]. 53 a(c6,a(c7,c8,c9),c10) != 1 # label("aa2") # answer("aa2"). [deny(11)]. 59 1 \ x = x. [para(17(a,1),19(a,1,2))]. 60 x \ x = 1. [para(18(a,1),19(a,1,2))]. 61 x \ ((x * y) * 1) = y. [para(18(a,2),19(a,1,2))]. 62 x \ (y * (y \ (x * z))) = z. [para(20(a,2),19(a,1,2))]. 64 x / 1 = x. [para(18(a,1),21(a,1,1))]. 65 x / (y \ x) = y. [para(20(a,1),21(a,1,1))]. 66 (x / y) \ x = y. [para(22(a,1),19(a,1,2))]. 67 (x * (y * z)) * a(x,y,z) = (x * y) * z. [para(28(a,2),20(a,1,2))]. 68 ((x / y) * (y * z)) \ (x * z) = a(x / y,y,z). [para(22(a,1),28(a,2,2,1)),flip(a)]. 69 (x * y) * K(y,x) = y * x. [para(30(a,2),20(a,1,2))]. 70 x \ ((y \ x) * y) = K(y \ x,y). [para(20(a,1),30(a,2,1)),flip(a)]. 71 ((x \ y) * x) \ y = K(x,x \ y). [para(20(a,1),30(a,2,2)),flip(a)]. 72 x \ (1 * (x * y)) = L(y,x,1). [para(17(a,1),32(a,2,1)),flip(a)]. 73 (x * 1) \ (x * y) = L(y,1,x). [para(17(a,1),32(a,2,2,2)),flip(a)]. 74 (x * y) * L(z,y,x) = x * (y * z). [para(32(a,2),20(a,1,2))]. 75 x \ (y * ((y \ x) * z)) = L(z,y \ x,y). [para(20(a,1),32(a,2,1)),flip(a)]. 76 L(x \ y,x,z) = (z * x) \ (z * y). [para(20(a,1),32(a,2,2,2))]. 77 x \ ((x / y) * (y * z)) = L(z,y,x / y). [para(22(a,1),32(a,2,1)),flip(a)]. 78 ((x * y) * (y \ z)) / z = R(x,y,y \ z). [para(20(a,1),34(a,2,2)),flip(a)]. 79 R(x,y,z) * (y * z) = (x * y) * z. [para(34(a,2),22(a,1,1))]. 80 R(x / y,y,z) = (x * z) / (y * z). [para(22(a,1),34(a,2,1,1))]. 81 T(x,x) = x. [para(36(a,2),19(a,1))]. 82 x * T(y,x) = y * x. [para(36(a,2),20(a,1,2))]. 83 T(x,x \ y) = (x \ y) \ y. [para(20(a,1),36(a,2,2))]. 84 T(x / y,y) = y \ x. [para(22(a,1),36(a,2,2))]. 85 (x * (x * (y * z))) / z = x * (x * y). [hyper(24,a,22,a,b,51,a),flip(a)]. 86 (x * (x * y)) \ (x * (x * (y * z))) = z. [hyper(23,a,20,a,b,51,a),flip(a)]. 87 x \ ((x * (x * y)) * z) = x * (y * z). [hyper(23,a,20,a,b,51,a(flip)),flip(a)]. 88 (x * (x * 1)) * y = x * (x * y). [para(17(a,1),51(a,2,2,2))]. 89 x * (x * ((x \ y) * z)) = (x * y) * z. [para(20(a,1),51(a,1,1,2)),flip(a)]. 90 (x * (y * (y * (z * u)))) \ ((x * (y * (y * z))) * u) = a(x,y * (y * z),u). [para(51(a,1),28(a,2,1,2)),flip(a)]. 91 (x * (x * (y * (z * u)))) \ (((x * (x * y)) * z) * u) = a(x * (x * y),z,u). [para(51(a,1),28(a,2,1)),flip(a)]. 92 (x * (x * (y * z))) \ ((x * (x * y)) * (z * u)) = L(u,z,x * (x * y)). [para(51(a,1),32(a,2,1)),flip(a)]. 93 (x * (y * (y * z))) \ (x * (y * (y * (z * u)))) = L(u,y * (y * z),x). [para(51(a,1),32(a,2,2,2)),flip(a)]. 94 ((x * (x * (y * z))) * u) / (z * u) = R(x * (x * y),z,u). [para(51(a,1),34(a,2,1,1)),flip(a)]. 95 (x * (x * (y * z))) / ((x * y) * z) = R(x,x * y,z). [para(51(a,1),34(a,2,1)),flip(a)]. 97 ((x * y) / 1) / y = x. [hyper(24,a,22,a,b,64,a(flip)),flip(a)]. 98 T(T(x,y),x) = T(x,y). [para(81(a,1),42(a,1,1)),flip(a)]. 99 (x * (y * z)) / L(z,y,x) = x * y. [para(32(a,2),65(a,1,2))]. 100 (x * y) / T(x,y) = y. [para(36(a,2),65(a,1,2))]. 101 R(x,y,z) \ ((x * y) * z) = y * z. [para(34(a,2),66(a,1,1))]. 102 x \ (y * 1) = x \ y. [para(20(a,1),61(a,1,2,1))]. 103 T(x * (x * y),x) = x * (y * x). [hyper(23,a,51,a(flip),b,82,a)]. 104 T((x * y) / x,x) = y. [hyper(23,a,22,a(flip),b,82,a)]. 105 (x * T(y,x)) / x = y. [hyper(24,a,22,a,b,82,a(flip)),flip(a)]. 106 (x * y) \ (x * (z * y)) = L(T(z,y),y,x). [para(82(a,1),32(a,2,2,2)),flip(a)]. 107 T(x,y) \ (x * y) = T(y,T(x,y)). [para(82(a,1),36(a,2,2)),flip(a)]. 108 x * T(T(y,x),z) = T(y,z) * x. [para(42(a,1),82(a,1,2))]. 109 x * L(T(y,x),z,u) = L(y,z,u) * x. [para(44(a,2),82(a,1,2))]. 110 x * R(T(y,x),z,u) = R(y,z,u) * x. [para(46(a,2),82(a,1,2))]. 111 (x * y) \ ((z * x) * y) = T(R(z,x,y),x * y). [para(34(a,2),84(a,1,1)),flip(a)]. 112 T(T(x / y,z),y) = T(y \ x,z). [para(84(a,1),42(a,1,1)),flip(a)]. 113 ((x * y) / ((1 / z) * z)) / y = x. [para(22(a,2),97(a,1,1,2))]. 114 K(T(x,y),x) = 1. [hyper(40,a,98,a)]. 115 T(x,T(x,y)) = x. [hyper(39,a,98,a)]. 116 T(x,y) * x = x * T(x,y). [para(98(a,1),82(a,1,2)),flip(a)]. 117 (x * y) / T(y,T(x,y)) = T(x,y). [para(82(a,1),100(a,1,1))]. 118 x \ (y * (z * (z \ 1))) = x \ y. [para(20(a,2),102(a,1,2,2))]. 119 K(x,(y * x) / y) = 1. [para(104(a,1),114(a,1,1))]. 120 T(x,(y * x) / y) = x. [hyper(41,a,119,a)]. 121 x * K(y,x / y) = y * (x / y). [para(22(a,1),69(a,1,1))]. 122 K(x,y) \ (x * y) = T(y * x,K(x,y)). [para(69(a,1),36(a,2,2)),flip(a)]. 123 x \ (x * y) = L(y,x,1). [para(17(a,1),72(a,1,2))]. 124 L(x,y,1) = x. [para(123(a,1),19(a,1))]. 125 a(1,x,y) = 1. [hyper(38,a,124,a)]. 126 x \ (x * y) = L(y,1,x). [para(18(a,1),73(a,1,1))]. 127 L(x,1,y) = x. [para(126(a,1),19(a,1))]. 128 K(x \ 1,x) = (x \ 1) * x. [para(70(a,1),59(a,1))]. 129 K(x \ 1,x) / x = x \ 1. [hyper(24,a,22,a,b,128,a(flip)),flip(a)]. 130 (x \ 1) \ K(x \ 1,x) = x. [hyper(23,a,20,a,b,128,a(flip)),flip(a)]. 131 (x * x) * y = x * (x * y). [para(18(a,1),88(a,1,1,2))]. 132 (x * (x * y)) / y = x * x. [hyper(24,a,22,a,b,131,a),flip(a)]. 133 (x * x) \ (x * (x * y)) = y. [hyper(23,a,20,a,b,131,a),flip(a)]. 134 ((x * (x * y)) * z) / (y * z) = R(x * x,y,z). [para(131(a,1),34(a,2,1,1)),flip(a)]. 135 x \ (y * (y * x)) = T(y * y,x). [para(131(a,1),36(a,2,2)),flip(a)]. 136 x * (x * T(y,x * x)) = y * (x * x). [para(131(a,1),82(a,1))]. 137 L(x,y,y) = x. [para(133(a,1),32(a,2))]. 138 x * ((x \ y) * x) = T(x * y,x). [para(20(a,1),103(a,1,1,2)),flip(a)]. 139 T(x / y,z) * y = y * T(y \ x,z). [para(84(a,1),108(a,1,2,1)),flip(a)]. 140 (x * T(x \ y,z)) / x = T(y / x,z). [para(112(a,1),105(a,1,1,2))]. 141 R(x,1 / y,y) / y = x * (1 / y). [para(34(a,2),113(a,1,1))]. 142 L(x \ 1,x,y) = (y * x) \ y. [para(118(a,1),32(a,2))]. 143 L((x \ y) \ 1,x \ y,x) = y \ x. [para(20(a,1),142(a,2,1))]. 144 L(x \ 1,x,y / x) = y \ (y / x). [para(22(a,1),142(a,2,1))]. 145 x / L(y \ 1,y,x) = x * y. [para(142(a,2),65(a,1,2))]. 146 x \ T(x * y,x) = (x \ y) * x. [hyper(23,a,20,a,b,138,a),flip(a)]. 147 x * K(x \ 1,x) = T(x * 1,x). [para(128(a,2),138(a,1,2))]. 148 (x \ (x \ y)) * x = x \ T(y,x). [para(20(a,1),146(a,1,2,1)),flip(a)]. 149 x * K(x \ 1,x) = T(x,x). [para(18(a,1),147(a,2,1))]. 150 x * K(x \ 1,x) = x. [para(149(a,2),81(a,1))]. 151 K(x \ 1,x) = 1. [hyper(23,a,18,a,b,150,a)]. 152 T(x \ 1,x) = x \ 1. [hyper(41,a,151,a)]. 154 (x \ 1) * x = 1. [para(151(a,1),128(a,1)),flip(a)]. 155 1 / x = x \ 1. [para(151(a,1),129(a,1,1))]. 156 (x \ 1) \ 1 = x. [para(151(a,1),130(a,1,2))]. 157 x * (1 / x) = 1. [para(66(a,1),154(a,1,1))]. 160 T(x,x \ 1) = x. [para(156(a,1),83(a,2))]. 161 L(x,x \ 1,y) = (y * (x \ 1)) \ y. [para(156(a,1),142(a,1,1))]. 162 x / L(y,y \ 1,x) = x * (y \ 1). [para(156(a,1),145(a,1,2,1))]. 164 (x * 1) \ ((x * y) * (1 / y)) = a(x,y,1 / y). [para(157(a,1),28(a,2,1,2)),flip(a)]. 165 T(T(x,y),x \ 1) = T(x,y). [para(160(a,1),42(a,1,1)),flip(a)]. 166 K(T(x,y),x \ 1) = 1. [hyper(40,a,165,a)]. 167 K(x \ y,(y / x) \ 1) = 1. [para(84(a,1),166(a,1,1))]. 168 K(x,((y * x) / y) \ 1) = 1. [para(104(a,1),166(a,1,1))]. 169 T(x \ y,(y / x) \ 1) = x \ y. [hyper(41,a,167,a)]. 170 T(x,((y * x) / y) \ 1) = x. [hyper(41,a,168,a)]. 171 (x \ y) \ (x \ T(y,x)) = K(x \ (x \ y),x). [para(148(a,1),70(a,1,2))]. 172 x * L(y,z \ x,z) = z * ((z \ x) * y). [para(20(a,1),74(a,1,1))]. 173 x * L(y,z,x / z) = (x / z) * (z * y). [para(22(a,1),74(a,1,1))]. 174 (x * (y * z)) \ (x * (y * (z * u))) = L(L(u,z,y),y * z,x). [para(74(a,1),32(a,2,2,2)),flip(a)]. 175 (x * y) * L(L(z,y,x),u,w) = x * (y * L(z,u,w)). [para(49(a,1),74(a,1,2))]. 176 (x * y) * L(z,K(x,y),y * x) = (y * x) * (K(x,y) * z). [para(69(a,1),74(a,1,1))]. 177 L(x \ (y \ z),x,y) = (y * x) \ z. [para(20(a,1),76(a,2,2))]. 178 L(x \ (y * x),x,y) = T(y,y * x). [para(76(a,2),36(a,2)),flip(a)]. 179 (x * y) / L(z \ y,z,x) = x * z. [para(76(a,2),65(a,1,2))]. 180 L(x \ T(y,z),x,z) = (z * x) \ (y * z). [para(82(a,1),76(a,2,2))]. 181 L(x \ (y \ ((y * x) * z)),x,y) = z. [para(76(a,2),62(a,1))]. 182 R(x,x,y) = x. [hyper(24,a,131,a(flip),b,79,a)]. 183 (R(x,y,z) * y) \ ((x * y) * z) = L(z,y,R(x,y,z)). [para(79(a,1),32(a,2,2)),flip(a)]. 184 L(R(x,y,z),u,w) * (y * z) = (L(x,u,w) * y) * z. [para(48(a,1),79(a,1,1))]. 185 R(R(x,y,z),u,w) * (y * z) = (R(x,u,w) * y) * z. [para(50(a,1),79(a,1,1))]. 186 R(T(x,y),x,z) = T(x,y). [para(182(a,1),46(a,2,1))]. 187 L(R(x,L(x,y,z),u),y,z) = L(x,y,z). [para(182(a,1),48(a,1)),flip(a)]. 188 R(R(x,y,z),x,u) = R(x,y,z). [para(182(a,1),50(a,1,1)),flip(a)]. 189 R(R(T(x,y),z,u),x,w) = R(T(x,y),z,u). [para(186(a,1),50(a,1,1)),flip(a)]. 190 (T(x,y) * x) * z = T(x,y) * (x * z). [para(186(a,1),79(a,1,1)),flip(a)]. 191 (R(x,y,z) * x) * u = R(x,y,z) * (x * u). [para(188(a,1),79(a,1,1)),flip(a)]. 192 R(1 / x,x,y) = y / (x * y). [para(17(a,1),80(a,2,1))]. 193 R((x / y) / z,z,y) = x / (z * y). [para(22(a,1),80(a,2,1))]. 194 T((x * y) / (z * y),u) = R(T(x / z,u),z,y). [para(80(a,1),46(a,2,1)),flip(a)]. 195 R(x,x \ 1,y) = y / ((x \ 1) * y). [para(65(a,1),192(a,1,1))]. 196 (x * y) / L(z,y / z,x) = x * (y / z). [para(22(a,1),99(a,1,1,2))]. 197 R(x,x \ y,z) \ (y * z) = (x \ y) * z. [para(20(a,1),101(a,1,2,1))]. 198 R(x,y \ 1,y) / y = x * (1 / y). [para(155(a,1),141(a,1,1,2))]. 199 L(K(x,y) \ ((y * x) \ z),K(x,y),y * x) = (x * y) \ z. [para(69(a,1),177(a,2,1))]. 200 (x * x) \ y = x \ (x \ y). [para(177(a,1),137(a,1))]. 201 L(x \ L(y \ z,y,u),x,u * y) = ((u * y) * x) \ (u * z). [para(76(a,2),177(a,1,1,2))]. 202 x \ (x \ (y * (x * x))) = T(y,x * x). [para(200(a,1),36(a,2)),flip(a)]. 203 L(T(x,y),y,x) = T(x,x * y). [para(36(a,2),178(a,1,1))]. 204 T(x,x * ((y * x) / y)) = L(x,(y * x) / y,x). [para(120(a,1),203(a,1,1)),flip(a)]. 205 x / L(y \ z,y,x / z) = (x / z) * y. [para(22(a,1),179(a,1,1))]. 206 R(x,x \ (y / z),z) = y / ((x \ (y / z)) * z). [para(65(a,1),193(a,1,1))]. 207 R(x,y \ 1,y) / y = x * (y \ 1). [para(155(a,1),198(a,2,2))]. 208 (x * (y \ 1)) * y = R(x,y \ 1,y). [para(207(a,1),22(a,1,1))]. 209 (x * (y \ 1)) \ R(x,y \ 1,y) = y. [para(207(a,1),66(a,1,1))]. 210 R(x / (y \ 1),y \ 1,y) = x * y. [para(22(a,1),208(a,1,1)),flip(a)]. 211 (x * (x * y)) / z = x * (x * (y / z)). [para(22(a,1),85(a,1,1,2,2))]. 212 (x * (x * y)) \ (x * (x * z)) = y \ z. [para(20(a,1),86(a,1,2,2,2))]. 213 x \ ((x * y) * z) = x * ((x \ y) * z). [para(20(a,1),87(a,1,2,1,2))]. 214 L(x,y,z) * x = x * L(x,y,z). [para(81(a,1),109(a,1,2,1)),flip(a)]. 215 L(x / y,z,u) * y = y * L(y \ x,z,u). [para(84(a,1),109(a,1,2,1)),flip(a)]. 216 L(x \ 1,y,z) * x = x * L(x \ 1,y,z). [para(152(a,1),109(a,1,2,1)),flip(a)]. 217 x * T(y,y * x) = L(y,x,y) * x. [para(203(a,1),109(a,1,2))]. 218 (x * L(x,y,z)) / x = L(x,y,z). [hyper(24,a,22,a,b,214,a),flip(a)]. 219 T(x,L(x,y,z)) = x. [hyper(23,a,82,a,b,214,a),flip(a)]. 220 T(x,x * L(x,y,z)) = L(x,L(x,y,z),x). [para(219(a,1),203(a,1,1)),flip(a)]. 221 L(x,x \ y,x) * (x \ y) = (x \ y) * T(x,y). [para(20(a,1),217(a,1,2,2)),flip(a)]. 222 x * R(T(T(y,x),z),u,w) = R(T(y,z),u,w) * x. [para(42(a,1),110(a,1,2,1))]. 223 R(x,y,z) * x = x * R(x,y,z). [para(81(a,1),110(a,1,2,1)),flip(a)]. 224 R(x / y,z,u) * y = y * R(y \ x,z,u). [para(84(a,1),110(a,1,2,1)),flip(a)]. 225 (x \ y) * R((x \ y) \ y,z,u) = R(x,z,u) * (x \ y). [para(83(a,1),110(a,1,2,1))]. 226 x * (x * R(T(y,x * x),z,u)) = R(y,z,u) * (x * x). [para(110(a,1),131(a,1)),flip(a)]. 227 R(x \ 1,y,z) * x = x * R(x \ 1,y,z). [para(152(a,1),110(a,1,2,1)),flip(a)]. 228 T(x,R(x,y,z)) = x. [hyper(23,a,82,a,b,223,a),flip(a)]. 229 T(x \ y,R(y / x,z,u)) = T(y / x,x). [para(228(a,1),112(a,1,1)),flip(a)]. 230 x \ (y * (x * x)) = x * T(y,x * x). [hyper(23,a,20,a,b,136,a),flip(a)]. 231 T(x / (x * y),z) * (x * y) = (x * y) * T(L(y \ 1,y,x),z). [para(142(a,2),139(a,2,2,1))]. 232 T((x * y) / (x * z),u) * (x * z) = (x * z) * T(L(z \ y,z,x),u). [para(76(a,2),139(a,2,2,1))]. 233 (x * T(y,z)) / x = T((x * y) / x,z). [para(19(a,1),140(a,1,1,2,1))]. 234 L(x,y,T(y,z)) = x. [hyper(23,a,74,a,b,190,a),flip(a)]. 235 (x * T(x,y)) * z = T(x,y) * (x * z). [para(116(a,1),190(a,1,1))]. 236 L(x,y / z,z \ y) = x. [para(84(a,1),234(a,1,3))]. 237 L(x,(y * z) / y,z) = x. [para(104(a,1),234(a,1,3))]. 238 x * (x * ((x \ y) / z)) = (x * y) / z. [para(20(a,1),211(a,1,1,2)),flip(a)]. 239 (x * (x * y)) \ (x * x) = y \ 1. [para(18(a,1),212(a,1,2,2))]. 240 (x * y) \ (x * (x * z)) = (x \ y) \ z. [para(20(a,1),212(a,1,1,2))]. 241 T(x,x * (x * y)) = y \ (x * y). [para(212(a,1),36(a,2))]. 242 (x * y) \ (x * x) = (x \ y) \ 1. [para(20(a,1),239(a,1,1,2))]. 243 (x * x) / (y \ 1) = x * (x * y). [para(239(a,1),65(a,1,2))]. 244 ((x * y) * z) \ (x * x) = ((x \ y) * z) \ 1. [para(89(a,1),239(a,1,1))]. 245 T(x,x * (x * y)) = T(x,y). [para(241(a,2),36(a,2)),flip(a)]. 246 T(x,x \ y) = T(x,x * y). [para(20(a,1),245(a,1,2,2)),flip(a)]. 247 T(x,x * (y * x)) = T(x,T(y,x)). [para(82(a,1),245(a,1,2,2))]. 248 T(x * y,(x * y) * (y * x)) = T(x * y,K(y,x)). [para(69(a,1),245(a,1,2,2))]. 249 T(x,x * y) = (x \ y) \ y. [para(246(a,1),83(a,1))]. 250 (x \ y) * T(x,x * y) = y. [para(249(a,2),20(a,1,2))]. 251 T(x / y,x) = ((x / y) \ y) \ y. [para(22(a,1),249(a,1,2))]. 252 x / T(y,y * x) = y \ x. [para(249(a,2),65(a,1,2))]. 253 (x \ y) * ((x \ y) * (T(x,x * y) * z)) = ((x \ y) * y) * z. [para(249(a,2),89(a,1,2,2,1))]. 254 (x \ (x \ y)) * T(x,y) = x \ y. [para(20(a,1),250(a,1,2,2))]. 255 ((x \ y) * (T(x,x * y) * z)) \ (y * z) = a(x \ y,T(x,x * y),z). [para(250(a,1),28(a,2,2,1)),flip(a)]. 256 (x \ y) / T(x,y) = x \ (x \ y). [para(20(a,1),252(a,1,2,2))]. 257 K(x,y) / T(y * x,x * y) = (y * x) \ K(x,y). [para(69(a,1),252(a,1,2,2))]. 258 (x \ (x \ y)) \ 1 = y \ (x * x). [para(20(a,1),242(a,1,1)),flip(a)]. 259 L(x \ y,x,y) = (y \ x) \ 1. [para(242(a,1),76(a,2))]. 260 L(K(x,y),y * x,x * y) = ((x * y) \ (y * x)) \ 1. [para(30(a,2),259(a,1,1))]. 261 L(T(x \ y,z),x,y) = T((y \ x) \ 1,z). [para(259(a,1),44(a,2,1))]. 262 (x \ ((y * x) / y)) \ 1 = ((y * x) / y) \ x. [para(259(a,1),237(a,1))]. 263 x * (x * (y \ 1)) = (x * x) / y. [para(156(a,1),243(a,1,2)),flip(a)]. 264 (x \ (y * y)) \ 1 = y \ (y \ x). [para(258(a,1),156(a,1,1))]. 265 x * ((x \ (x \ y)) * z) = x \ (y * z). [para(20(a,1),213(a,1,2,1)),flip(a)]. 266 L(x \ (y * ((y \ x) * z)),x,y) = z. [para(213(a,1),181(a,1,1,2))]. 267 L(x \ (y * z),x,y) = (y \ x) \ z. [para(20(a,1),266(a,1,1,2,2))]. 268 L(x \ y,x,z) = (z \ x) \ (z \ y). [para(20(a,1),267(a,1,1,2))]. 269 L(x \ (y * z),x,z) = (z \ x) \ T(y,z). [para(82(a,1),267(a,1,1,2))]. 270 L((x * y) \ z,x * y,x) = y \ (x \ z). [para(19(a,1),268(a,2,1))]. 271 L(((x * y) * z) \ u,(x * y) * z,x * (y * z)) = a(x,y,z) \ ((x * (y * z)) \ u). [para(28(a,2),268(a,2,1))]. 272 (x \ y) / L(z \ y,z,x) = x \ z. [para(268(a,2),65(a,1,2))]. 273 L(x \ y,x,x / z) = z \ ((x / z) \ y). [para(66(a,1),268(a,2,1))]. 274 (x \ y) \ (x \ z) = (x * y) \ (x * z). [para(268(a,1),76(a,1))]. 275 L(x \ L(y \ z,y,u),x,u \ y) = ((u \ y) * x) \ (u \ z). [para(268(a,2),177(a,1,1,2))]. 276 (x \ 1) / (y \ x) = x \ (x \ y). [para(143(a,1),272(a,1,2))]. 277 x \ (x \ (x / y)) = (x \ 1) / y. [para(66(a,1),276(a,1,2)),flip(a)]. 278 x * ((x \ 1) / y) = x \ (x / y). [para(277(a,1),20(a,1,2))]. 279 ((x \ 1) / y) \ 1 = (x / y) \ (x * x). [para(277(a,1),258(a,1,1))]. 280 T(x * T(x,y),T(x,y)) = x * T(x,y). [hyper(23,a,82,a,b,235,a(flip)),flip(a)]. 281 (x * T(x,y)) * (x \ z) = T(x,y) * z. [para(20(a,1),235(a,2,2))]. 282 (x * y) / (z \ (x \ y)) = x * (x * z). [para(65(a,1),238(a,1,2,2)),flip(a)]. 283 (x \ (x \ y)) \ z = y \ (x * (x * z)). [para(20(a,1),240(a,1,1)),flip(a)]. 284 (x \ y) \ ((x \ z) * u) = (x * y) \ ((x * z) * u). [para(89(a,1),240(a,1,2)),flip(a)]. 285 x \ (x \ (y * z)) = (x \ (x \ y)) * z. [hyper(23,a,20,a,b,265,a),flip(a)]. 286 (x \ (x \ y)) * (x * x) = T(y,x * x). [hyper(23,a,230,a(flip),b,265,a)]. 287 (x * (y * x)) \ (x * z) = T(y,x) \ (x \ z). [para(36(a,2),274(a,1,1)),flip(a)]. 288 T(x * T(x,y),T(x,y)) = T(x,y) * x. [para(280(a,2),116(a,2)),flip(a)]. 289 x / (y \ (x \ 1)) = x * (x * y). [para(18(a,1),282(a,1,1))]. 290 (x \ (x \ y)) \ y = T(x * x,y). [para(283(a,2),135(a,1))]. 291 (x \ (x \ 1)) * y = x \ (x \ y). [para(17(a,1),285(a,1,2,2)),flip(a)]. 292 (x \ (x \ y)) * (y \ z) = x \ (x \ z). [para(20(a,1),285(a,1,2,2)),flip(a)]. 293 R((x / y) / (z \ (z \ 1)),z \ (z \ 1),y) = x / (z \ (z \ y)). [para(291(a,1),193(a,2,2))]. 294 ((x \ 1) / y) * (x * x) = T(x / y,x * x). [para(277(a,1),286(a,1,1))]. 295 T(T(x,y) * x,T(x,y)) = T(x,y) * x. [para(116(a,2),288(a,1,1))]. 296 (x \ (x \ y)) \ (x \ (x \ z)) = y \ z. [hyper(23,a,20,a,b,292,a),flip(a)]. 297 (x \ y) * ((x * y) \ z) = x \ (x \ z). [para(19(a,1),292(a,1,1,2))]. 298 (T(x,y) \ x) * T(x,y) = x. [hyper(23,a,138,a,b,295,a(flip)),flip(a)]. 299 x / T(x,y) = T(x,y) \ x. [hyper(24,a,22,a,b,298,a),flip(a)]. 300 ((x * y) * z) / T(x * (y * z),a(x,y,z)) = a(x,y,z). [para(67(a,1),100(a,1,1))]. 301 L(x,x \ y,x) = y \ T(x * y,x). [para(138(a,1),75(a,1,2)),flip(a)]. 302 L(L(x,y \ z,y),z,y) = x. [para(75(a,1),266(a,1,1))]. 303 L(L(x,y,z),z * y,z) = x. [para(19(a,1),302(a,1,1,2))]. 304 L(L(x,y,z / y),z,z / y) = x. [para(66(a,1),302(a,1,1,2))]. 305 L(x,y \ 1,y) = x. [para(302(a,1),127(a,1)),flip(a)]. 306 L(x,y,y \ 1) = x. [para(156(a,1),305(a,1,2))]. 307 ((x \ 1) * x) \ ((x \ 1) * y) = x \ y. [para(306(a,1),76(a,1)),flip(a)]. 308 L(L(x,y * z,y),z,y) = x. [para(303(a,1),49(a,1)),flip(a)]. 309 x \ (y \ ((y * x) * z)) = L(z,y * x,y). [para(181(a,1),303(a,1,1)),flip(a)]. 310 R(x,L(x,y,z),u) = L(L(x,y,z),z * y,z). [para(187(a,1),303(a,1,1)),flip(a)]. 311 L((x \ y) \ z,x * y,x) = y \ (x * z). [para(267(a,1),303(a,1,1))]. 312 L(x,y \ z,y) = L(x,y * z,y). [para(302(a,1),303(a,1,1)),flip(a)]. 313 L(x,y * (y * z),y) = L(x,z,y). [para(303(a,1),303(a,1,1))]. 314 L(L(x,y * z,z),T(y,z),z) = x. [para(82(a,1),308(a,1,1,2))]. 315 L(L(x,y * z,z * y),K(y,z),z * y) = x. [para(69(a,1),308(a,1,1,2))]. 316 L(x,x * y,x) = y \ T(x * y,x). [para(301(a,1),312(a,1)),flip(a)]. 317 1 \ ((x \ 1) * y) = x \ y. [para(154(a,1),307(a,1,1))]. 318 (x \ 1) * y = x \ y. [para(317(a,1),59(a,1)),flip(a)]. 320 (x \ y) / y = x \ 1. [hyper(24,a,22,a,b,318,a),flip(a)]. 321 x * ((x \ 1) * y) = y. [hyper(23,a,19,a(flip),b,318,a)]. 322 (x \ 1) * (x * y) = y. [para(318(a,2),19(a,1))]. 323 (x \ (y * z)) \ (((x \ 1) * y) * z) = a(x \ 1,y,z). [para(318(a,1),28(a,2,1)),flip(a)]. 324 ((x * (y \ 1)) * z) / (y \ z) = R(x,y \ 1,z). [para(318(a,1),34(a,2,2)),flip(a)]. 325 T(x \ 1,y) = y \ (x \ y). [para(318(a,1),36(a,2,2))]. 326 x \ T(y,x \ 1) = y * (x \ 1). [para(318(a,1),82(a,1))]. 327 x * T(y \ 1,x) = y \ x. [para(318(a,1),82(a,2))]. 328 (x \ y) * K(y,x \ 1) = y * (x \ 1). [para(318(a,1),69(a,1,1))]. 329 x \ T(T(y,x \ 1),z) = T(y,z) * (x \ 1). [para(318(a,1),108(a,1))]. 330 (x \ 1) \ y = x * y. [para(156(a,1),318(a,1,1)),flip(a)]. 331 (x \ y) * L(z,y,x \ 1) = (x \ 1) * (y * z). [para(318(a,1),74(a,1,1))]. 332 R(x,y \ 1,z) * (y \ z) = (x * (y \ 1)) * z. [para(318(a,1),79(a,1,2))]. 333 (x * (y \ z)) / L(z,y \ 1,x) = x * (y \ 1). [para(318(a,1),99(a,1,1,2))]. 334 R(x,x \ 1,y) = y / (x \ y). [para(318(a,1),195(a,2,2))]. 335 R(x \ 1,y \ 1,y) = (x \ (y \ 1)) * y. [para(318(a,1),208(a,1,1)),flip(a)]. 336 L(x \ 1,y,x \ 1) * y = y * T(x \ 1,x \ y). [para(318(a,1),217(a,1,2,2)),flip(a)]. 337 T(x \ 1,(x \ 1) \ y) = T(x \ 1,x \ y). [para(318(a,1),246(a,2,2))]. 338 (x \ (x \ y)) \ z = (y \ (x * x)) * z. [para(258(a,1),318(a,1,1)),flip(a)]. 339 (x \ (y * y)) \ z = (y \ (y \ x)) * z. [para(264(a,1),318(a,1,1)),flip(a)]. 340 x / (y * x) = y \ 1. [para(19(a,1),320(a,1,1))]. 341 K(x,y) / (x * y) = (y * x) \ 1. [para(30(a,2),320(a,1,1))]. 342 L(x,y,z) / (z * (y * x)) = (z * y) \ 1. [para(32(a,2),320(a,1,1))]. 343 (x / y) \ 1 = y / x. [para(66(a,1),320(a,1,1)),flip(a)]. 344 (x * y) / ((z * x) * y) = R(z,x,y) \ 1. [para(101(a,1),320(a,1,1))]. 345 T(x * y,K(y,x)) / (y * x) = K(y,x) \ 1. [para(122(a,1),320(a,1,1))]. 346 T(x,x * y) / y = (x \ y) \ 1. [para(249(a,2),320(a,1,1))]. 347 x * (y * (x \ 1)) = T(y,x \ 1). [para(82(a,1),321(a,1,2))]. 348 R(x \ 1,x * y,z) = (y * z) / ((x * y) * z). [para(322(a,1),34(a,2,1,1))]. 349 T(x \ 1,x * y) = (x * y) \ y. [para(322(a,1),36(a,2,2))]. 350 R((x \ 1) / y,y,x * z) = z / (y * (x * z)). [para(322(a,1),80(a,2,1))]. 351 L(x * y,x \ 1,y) = (y \ (x \ 1)) \ 1. [para(330(a,1),259(a,1,1))]. 352 L(x * (y * z),x \ 1,y) = (y \ (x \ 1)) \ z. [para(330(a,1),267(a,1,1))]. 353 (x / (y * x)) * z = y \ z. [para(340(a,2),318(a,1,1))]. 354 (x / y) * (y / x) = 1. [para(343(a,1),20(a,1,2))]. 355 K(x \ y,x / y) = 1. [para(343(a,1),167(a,1,2))]. 356 T(x,y / (y * x)) = x. [para(343(a,1),170(a,1,2))]. 357 T(x \ y,x / y) = x \ y. [para(343(a,1),169(a,1,2))]. 358 (x / y) \ z = (y / x) * z. [para(343(a,1),318(a,1,1)),flip(a)]. 359 (x / y) * ((y / x) * z) = z. [para(343(a,1),321(a,1,2,1))]. 360 x * ((y / z) * (z / y)) = x. [para(354(a,2),18(a,1,2))]. 361 K((x * y) \ y,x) = 1. [para(21(a,1),355(a,1,2))]. 362 (x / (x * y)) * y = y * (x / (x * y)). [para(356(a,1),82(a,1,2))]. 363 (x * (y / (y * x))) / x = y / (y * x). [para(356(a,1),100(a,1,2))]. 364 T(x,x * (y / (y * x))) = L(x,y / (y * x),x). [para(356(a,1),203(a,1,1)),flip(a)]. 365 T((x * y) \ y,x) = (x * y) \ y. [hyper(41,a,361,a)]. 366 x * R(x \ (y \ x),z,u) = R(y \ 1,z,u) * x. [para(325(a,1),110(a,1,2,1))]. 367 T(x / y,x \ y) = x / y. [hyper(39,a,357,a)]. 368 (x / y) * (x \ y) = (x \ y) * (x / y). [para(357(a,1),82(a,1,2))]. 369 (x / y) * (z * (y / x)) = T(z,y / x). [para(358(a,1),36(a,2)),flip(a)]. 370 T(x / y,x) = ((y / x) * y) \ y. [para(358(a,1),251(a,2,1))]. 371 ((x \ 1) / y) \ 1 = (y / x) * (x * x). [para(358(a,1),279(a,2))]. 372 T(x \ y,y \ x) = T(y / x,x). [para(367(a,1),112(a,1,1)),flip(a)]. 373 R(x,x \ 1,y) = x. [para(334(a,2),65(a,1))]. 374 R(T(x,y),x \ 1,z) = T(x,y). [para(373(a,1),46(a,2,1))]. 375 R(R(x,y,z),x \ 1,u) = R(x,y,z). [para(373(a,1),50(a,1,1)),flip(a)]. 376 R(T(x / y,y),(x / y) \ 1,z) = y \ x. [para(374(a,2),84(a,1))]. 377 T(x,y) * (x \ 1) = x \ T(x,y). [para(165(a,1),326(a,1,2)),flip(a)]. 378 x \ T(T(y,x \ 1),x) = (x \ (y * (x \ 1))) * x. [para(326(a,1),148(a,1,1,2)),flip(a)]. 379 K(x,y) * ((K(x,y) \ 1) / (x * y)) = K(x,y) \ ((y * x) \ 1). [para(341(a,1),278(a,2,2))]. 380 T(x \ 1,x * (y * y)) = (y \ (y \ (x * (y * y)))) \ 1. [para(349(a,2),258(a,2)),flip(a)]. 381 ((x * y) \ y) * x = x * ((x * y) \ y). [para(365(a,1),82(a,1,2)),flip(a)]. 382 T(x \ y,y \ x) = x \ y. [para(372(a,2),84(a,1))]. 383 T(x \ (x * y),(x * y) \ x) = y. [para(372(a,2),104(a,1))]. 384 (x \ y) * (y \ x) = (y \ x) * (x \ y). [para(382(a,1),82(a,1,2))]. 385 (x \ 1) \ T(x \ 1,x * y) = ((x * y) \ y) * ((x \ 1) \ 1). [para(349(a,1),377(a,1,1)),flip(a)]. 386 T(x,(y * x) \ y) = x. [para(19(a,1),383(a,1,1))]. 387 T(x,y \ (y / x)) = x. [para(22(a,1),386(a,1,2,1))]. 388 ((x * y) \ x) * y = y * ((x * y) \ x). [para(386(a,1),82(a,1,2))]. 389 T(K(x,y),(x * y) \ (y * x)) = K(x,y). [para(69(a,1),386(a,1,2,1))]. 390 R(x,y,z) * (x \ 1) = R(x,y,z) / x. [para(375(a,1),207(a,1,1)),flip(a)]. 391 x \ (y * (y * z)) = (x \ (y * y)) * z. [para(338(a,1),283(a,1)),flip(a)]. 392 (x \ (y * y)) * x = T(y * y,x). [para(338(a,1),290(a,1))]. 393 (x \ (y * y)) * (y \ (y \ z)) = x \ z. [para(338(a,1),296(a,1))]. 394 T(x * x,y * z) \ ((((y * z) \ (x * x)) * y) * z) = a((y * z) \ (x * x),y,z). [para(392(a,1),28(a,2,1)),flip(a)]. 395 L(x \ 1,x,x \ (y * y)) = T(y * y,x) \ (x \ (y * y)). [para(392(a,1),142(a,2,1))]. 396 ((x * y) \ ((x * y) \ ((x * y) * x))) * z = L(y,x,x * y) \ z. [para(32(a,2),339(a,1,1)),flip(a)]. 397 (x / y) * (y * y) = x / (y \ 1). [para(371(a,1),343(a,1))]. 398 (x / (y \ 1)) / (y * y) = x / y. [hyper(24,a,22,a,b,397,a),flip(a)]. 399 (x / y) * (y / (x \ 1)) = x * x. [hyper(23,a,359,a,b,397,a),flip(a)]. 400 (x * y) / (y \ 1) = x * (y * y). [para(21(a,1),397(a,1,1)),flip(a)]. 401 (x * (y \ 1)) / y = x / (y * y). [para(21(a,1),398(a,1,1)),flip(a)]. 402 ((x \ (x \ y)) * x) / (x \ 1) = T(y,x * x). [para(400(a,2),286(a,1))]. 403 T(x / (y * y),y) = y \ (x * (y \ 1)). [para(401(a,1),84(a,1,1))]. 404 T(K(x,y),K(y,x)) = K(x,y). [para(30(a,2),389(a,1,2))]. 405 T(K(x,y),z) * K(y,x) = K(y,x) * T(K(x,y),z). [para(404(a,1),108(a,1,2,1)),flip(a)]. 406 R(K(x,y),z,u) * K(y,x) = K(y,x) * R(K(x,y),z,u). [para(404(a,1),110(a,1,2,1)),flip(a)]. 407 x * ((x \ (y * y)) * z) = y * (y * z). [para(391(a,1),20(a,1,2))]. 408 (((x * y) * x) \ (x * x)) * y = K(x,x * y). [para(391(a,1),30(a,2)),flip(a)]. 409 (x * (y * y)) \ z = y \ (y \ (x \ z)). [hyper(23,a,297,a,b,393,a),flip(a)]. 410 x * ((x \ (y * y)) * z) = (y * y) * z. [para(407(a,2),131(a,2)),flip(a)]. 411 (x * (y * y)) * z = x * (y * (y * z)). [para(407(a,1),89(a,1,2)),flip(a)]. 412 x \ (x \ (y \ ((y * x) * x))) = a(y,x,x). [para(409(a,1),28(a,2)),flip(a)]. 413 (x * (y * y)) \ x = y \ (y \ 1). [para(60(a,1),409(a,2,2,2))]. 414 x \ (x / (y * y)) = y \ (y \ 1). [para(22(a,1),413(a,1,1))]. 415 x / (y \ (y \ 1)) = x * (y * y). [para(413(a,1),65(a,1,2))]. 416 x * (y \ (y \ 1)) = x / (y * y). [para(414(a,1),20(a,1,2))]. 417 (x * (y * y)) * z = x * ((y * y) * z). [para(410(a,1),89(a,1,2)),flip(a)]. 418 (x * (y * (y * z))) / z = x * (y * y). [hyper(24,a,22,a,b,411,a),flip(a)]. 419 (x * (y * (y * z))) \ ((x * (y * y)) * (z * u)) = L(u,z,x * (y * y)). [para(411(a,1),32(a,2,1)),flip(a)]. 420 (x \ (x \ y)) * (x * (x * z)) = T(y,x * x) * z. [para(286(a,1),411(a,1,1)),flip(a)]. 421 L(x,y * y,z) = x. [hyper(23,a,74,a,b,417,a),flip(a)]. 422 R(x,y * y,z) = x. [hyper(24,a,79,a,b,417,a(flip)),flip(a)]. 423 T(x,x * (y * y)) = T(x,y * y). [para(421(a,1),203(a,1)),flip(a)]. 424 L(x,y,y / (z * z)) = x. [para(421(a,1),304(a,1,1))]. 425 L(x,y \ (y \ 1),z) = x. [para(318(a,1),421(a,1,2))]. 426 R(x,y \ (y \ 1),z) = x. [para(318(a,1),422(a,1,2))]. 427 L(x,y,y / (z \ (z \ 1))) = x. [para(318(a,1),424(a,1,3,2))]. 428 (x * (y \ (y \ 1))) * z = x * ((y \ (y \ 1)) * z). [para(425(a,1),74(a,1,2))]. 429 L(x,y,y * (z * z)) = x. [para(415(a,1),427(a,1,3))]. 430 T(x,x \ (y * y)) = T(x,y * y). [para(423(a,1),246(a,2))]. 431 T(x \ 1,x * (y * y)) = T(x \ 1,y * y). [para(330(a,1),430(a,1,2))]. 432 L(x,x,y / x) = y \ (y / (x \ 1)). [para(397(a,1),77(a,1,2)),flip(a)]. 433 (x * y) * (y \ 1) = R(x,y,y \ 1). [para(78(a,1),64(a,1)),flip(a)]. 434 R(x / y,y,y \ 1) = x * (y \ 1). [para(22(a,1),433(a,1,1)),flip(a)]. 435 x * L(y,z * x,z) = z * ((z \ x) * y). [para(312(a,1),172(a,1,2))]. 436 (R(T(x,y),z,u) * x) * w = R(T(x,y),z,u) * (x * w). [para(189(a,1),79(a,1,1)),flip(a)]. 437 T(x \ y,R(y / x,z,u)) = x \ y. [para(229(a,2),84(a,1))]. 438 T((x \ 1) \ y,y * x) = (x \ 1) \ y. [para(210(a,1),437(a,1,2))]. 439 T(x * y,y * x) = (x \ 1) \ y. [para(330(a,1),438(a,1,1))]. 440 (x \ y) \ T(y,x) = L(x,y,x). [para(19(a,1),269(a,1,1)),flip(a)]. 441 T(x,y) / L(y,x,y) = y \ x. [para(440(a,1),65(a,1,2))]. 442 L(x \ (x / y),y,x \ (x / y)) = ((x \ (x / y)) \ y) \ y. [para(387(a,1),440(a,1,2)),flip(a)]. 443 (x * (x * y)) \ z = y \ (x \ (x \ z)). [para(270(a,1),177(a,1)),flip(a)]. 444 x \ (y \ (y \ (z * (y * (y * x))))) = T(z,y * (y * x)). [para(443(a,1),36(a,2)),flip(a)]. 445 L(x \ 1,x,x / y) = y \ (y / x). [para(343(a,1),273(a,2,2))]. 446 x * (y \ ((y * (x \ 1)) * z)) = L(z,y * (x \ 1),y). [para(309(a,1),330(a,1)),flip(a)]. 447 R(x \ y,(y / x) \ 1,z) = x \ y. [para(84(a,1),376(a,1,1))]. 448 R(x \ y,x / y,z) = x \ y. [para(343(a,1),447(a,1,2))]. 449 R(x \ (x * y),x / (x * y),z) = y. [para(448(a,2),19(a,1))]. 450 R(x,y / (y * x),z) = x. [para(19(a,1),449(a,1,1))]. 451 (x * (y / (y * x))) * z = x * ((y / (y * x)) * z). [para(450(a,1),79(a,1,1)),flip(a)]. 452 x \ L(x,y * x,y) = a(y,x,x). [para(309(a,1),412(a,1,2))]. 453 L(x,y * x,y) = x * a(y,x,x). [para(452(a,1),20(a,1,2)),flip(a)]. 454 L(x * a(y,x,x),x,y) = x. [para(453(a,1),308(a,1,1))]. 455 x * ((x \ y) * T(z,y)) = L(z,x * y,x) * y. [para(435(a,1),109(a,1))]. 456 (x * y) \ (x * T(y,x)) = K(x \ (x \ y),x). [para(171(a,1),274(a,1)),flip(a)]. 457 L(x,y,R(y,z,u)) = x. [hyper(23,a,74,a,b,191,a),flip(a)]. 458 R(x,y,z) * ((R(x,y,z) \ x) * u) = x * u. [hyper(23,a,89,a,b,191,a(flip)),flip(a)]. 459 (x * R(x,y,z)) * u = R(x,y,z) * (x * u). [para(223(a,1),191(a,1,1))]. 460 (R(x,y,z) \ x) \ 1 = x \ R(x,y,z). [para(457(a,1),259(a,1)),flip(a)]. 461 (R(x,y,z) \ u) / (x \ u) = R(x,y,z) \ x. [para(457(a,1),272(a,1,2))]. 462 (x \ R(x,y,z)) \ 1 = R(x,y,z) \ x. [para(460(a,1),156(a,1,1))]. 463 (R(x,y,z) \ x) \ u = (x \ R(x,y,z)) * u. [para(460(a,1),318(a,1,1)),flip(a)]. 464 (R(x,y,z) \ x) * ((x \ R(x,y,z)) * u) = u. [para(460(a,1),321(a,1,2,1))]. 465 (x \ R(x,y,z)) \ u = (R(x,y,z) \ x) * u. [para(460(a,1),330(a,1,1))]. 466 T(x,L(x \ 1,y,z)) = x. [hyper(23,a,82,a,b,216,a),flip(a)]. 467 K(x,L(x \ 1,y,z)) = 1. [hyper(40,a,466,a)]. 468 K(x \ 1,L(x,y,z)) = 1. [para(156(a,1),467(a,1,2,1))]. 469 K(L(x,y,z) \ 1,x) = 1. [para(303(a,1),468(a,1,2))]. 470 T(L(x,y,z) \ 1,x) = L(x,y,z) \ 1. [hyper(41,a,469,a)]. 471 x * (L(x,y,z) \ 1) = L(x,y,z) \ x. [para(470(a,1),327(a,1,2))]. 472 R(x / (x * y),z,u) * (x * y) = (x * y) * R(L(y \ 1,y,x),z,u). [para(142(a,2),224(a,2,2,1))]. 473 R((x * y) / (x * z),u,w) * (x * z) = (x * z) * R(L(z \ y,z,x),u,w). [para(76(a,2),224(a,2,2,1))]. 474 R(R(x / y,y,z),u,w) * (y * z) = (y * z) * R((y * z) \ (x * z),u,w). [para(80(a,2),224(a,1,1,1))]. 475 T(x,R(x \ 1,y,z)) = x. [hyper(23,a,82,a,b,227,a),flip(a)]. 476 T(x \ 1,R(x,y,z)) = x \ 1. [para(156(a,1),475(a,1,2,1))]. 477 R(x,y,z) * (x \ 1) = x \ R(x,y,z). [para(476(a,1),327(a,1,2))]. 478 R(x,y,z) / x = x \ R(x,y,z). [para(477(a,1),390(a,1)),flip(a)]. 479 (x \ R(x,y,z)) * x = R(x,y,z). [para(478(a,1),22(a,1,1))]. 480 (x \ R(x,y,z)) \ R(x,y,z) = x. [para(478(a,1),66(a,1,1))]. 481 (x / y) \ R(x / y,y,y \ 1) = (x * (y \ 1)) / (x / y). [para(434(a,1),478(a,1,1)),flip(a)]. 482 (x \ ((y * x) / y)) \ 1 = (y / (y * x)) * x. [para(262(a,2),358(a,1))]. 483 R(x,L(x,y,z),u) = x. [para(310(a,2),303(a,1))]. 484 (x * L(x,y,z)) * u = x * (L(x,y,z) * u). [para(483(a,1),79(a,1,1)),flip(a)]. 485 T(x \ 1,x \ y) = T(x \ 1,x * y). [para(330(a,1),337(a,1,2)),flip(a)]. 486 (x \ T(y,x)) / (x \ 1) = T(y,x * x). [para(148(a,1),402(a,1,1))]. 487 (((x \ y) * x) \ 1) * y = K(x,x * y). [para(244(a,1),408(a,1,1))]. 488 ((x \ y) * x) \ y = K(x,x * y). [para(487(a,1),318(a,1)),flip(a)]. 489 K(x,x \ y) = K(x,x * y). [para(488(a,1),71(a,1)),flip(a)]. 490 K(x,x * (x * y)) = K(x,y). [para(19(a,1),489(a,1,2)),flip(a)]. 491 K(x,x * (y * x)) = K(x,T(y,x)). [para(36(a,2),489(a,1,2)),flip(a)]. 492 K(x,(x * x) / y) = K(x,y \ 1). [para(263(a,1),490(a,1,2))]. 493 K(x \ (x \ y),x) = (x * y) \ (y * x). [para(82(a,1),456(a,1,2)),flip(a)]. 494 K(x \ (x \ y),x) = K(y,x). [para(493(a,2),30(a,2)),flip(a)]. 495 K(x \ y,x) = K(x * y,x). [para(19(a,1),494(a,1,1,2))]. 496 (R(x,y,z) \ x) * R(x,y,z) = x. [hyper(23,a,223,a,b,458,a)]. 497 R(x,y,z) \ (x * u) = (R(x,y,z) \ x) * u. [hyper(23,a,20,a,b,458,a),flip(a)]. 498 x / R(x,y,z) = R(x,y,z) \ x. [hyper(24,a,22,a,b,496,a),flip(a)]. 499 T(R(x,y,z) \ 1,x) = x \ (x / R(x,y,z)). [para(498(a,2),325(a,2,2))]. 500 (x * y) / (z \ ((z * x) * y)) = R(z,x,y) \ z. [para(101(a,1),461(a,1,1))]. 501 x * ((x \ R(x,y,z)) * u) = R(x,y,z) * u. [para(464(a,1),458(a,1,2)),flip(a)]. 502 (x \ ((y * x) / y)) \ 1 = x * (y / (y * x)). [para(482(a,2),362(a,1))]. 503 L(x,L(y,z,u),y) = x. [hyper(23,a,74,a,b,484,a),flip(a)]. 504 x * ((x \ L(x,y,z)) * u) = L(x,y,z) * u. [hyper(23,a,89,a,b,484,a(flip)),flip(a)]. 505 L(x,(y * z) \ y,z \ 1) = x. [para(142(a,1),503(a,1,2))]. 506 (x \ L(x,y,z)) \ 1 = L(x,y,z) \ x. [para(503(a,1),259(a,1)),flip(a)]. 507 (x \ L(x,y,z)) \ u = L(x,y,z) \ (x * u). [para(503(a,1),267(a,1)),flip(a)]. 508 L(x,(y \ z) \ u,z \ (y * u)) = x. [para(267(a,1),503(a,1,2))]. 509 L(x,y,L(y,z,u)) = x. [para(303(a,1),503(a,1,2))]. 510 T(x,x * L(x,y,z)) = x. [para(503(a,1),220(a,2))]. 511 (L(x,y,z) \ x) \ 1 = x \ L(x,y,z). [para(509(a,1),259(a,1)),flip(a)]. 512 (L(x,y,z) \ x) \ u = x \ (L(x,y,z) * u). [para(509(a,1),267(a,1)),flip(a)]. 513 (L(x,y,z) \ u) / (x \ u) = L(x,y,z) \ x. [para(509(a,1),272(a,1,2))]. 514 (x \ L(x,y,z)) * x = L(x,y,z). [para(510(a,1),250(a,1,2))]. 515 L(x,y,z) / x = x \ L(x,y,z). [para(510(a,1),252(a,1,2))]. 516 (x \ L(x,y,z)) \ 1 = x / L(x,y,z). [para(510(a,1),346(a,1,1)),flip(a)]. 517 (x \ L(x,y,z)) \ u = (L(x,y,z) \ x) * u. [para(506(a,1),318(a,1,1)),flip(a)]. 518 (L(x,y,z) \ x) \ u = (x \ L(x,y,z)) * u. [para(506(a,1),330(a,1,1))]. 519 x / L(x,y,z) = L(x,y,z) \ x. [para(516(a,1),506(a,1))]. 520 (L(x,y,z) \ x) * L(x,y,z) = x. [para(519(a,1),22(a,1,1))]. 521 (L(x \ 1,x,x / y) \ (x \ 1)) * (y \ (y / x)) = x \ 1. [para(445(a,1),520(a,1,2))]. 522 (x \ R(x,y,z)) \ u = R(x,y,z) \ (x * u). [para(497(a,2),465(a,2))]. 523 (x * R(x,y,z)) * u = x * (R(x,y,z) * u). [para(501(a,1),89(a,1,2)),flip(a)]. 524 L(x,y,z) \ (x * u) = (L(x,y,z) \ x) * u. [para(517(a,1),507(a,1)),flip(a)]. 525 R(x,R(x,y,z),u) = x. [hyper(24,a,79,a,b,523,a(flip)),flip(a)]. 526 R(x,y,z) * (x * u) = x * (R(x,y,z) * u). [para(523(a,1),459(a,1)),flip(a)]. 527 R(T(x,y),R(x,z,u),w) = T(x,y). [para(525(a,1),46(a,2,1))]. 528 (x \ R(x,y,z)) * (x * u) = R(x,y,z) * u. [hyper(23,a,501,a,b,526,a(flip)),flip(a)]. 529 x * (R(x,y,z) * (x \ u)) = R(x,y,z) * u. [para(20(a,1),526(a,1,2)),flip(a)]. 530 x * (R(x,y,z) * T(u,x)) = R(x,y,z) * (u * x). [para(82(a,1),526(a,1,2)),flip(a)]. 531 (R(x,y,z) * u) / (x * u) = x \ R(x,y,z). [hyper(24,a,22,a,b,528,a),flip(a)]. 532 (x \ R(x,y,z)) * u = R(x,y,z) * (x \ u). [para(20(a,1),528(a,1,2))]. 533 R(x \ R(x,y,z),x * u,w) = ((R(x,y,z) * u) * w) / ((x * u) * w). [para(528(a,1),34(a,2,1,1))]. 534 x \ (R(x,y,z) * u) = R(x,y,z) * (x \ u). [hyper(23,a,20,a,b,529,a),flip(a)]. 535 x / (y * (R(y,z,u) \ x)) = y \ R(y,z,u). [para(20(a,1),531(a,1,1))]. 536 (R(x,y,z) * (x \ u)) / u = x \ R(x,y,z). [para(20(a,1),531(a,1,2))]. 537 ((x * y) * z) / (x * (y * z)) = x \ R(x,y,z). [para(79(a,1),531(a,1,1))]. 538 (R(R(x,y,z),u,w) * (y * z)) / ((x * y) * z) = R(x,y,z) \ R(R(x,y,z),u,w). [para(79(a,1),531(a,1,2))]. 539 x \ (R(y,z,u) * (y \ x)) = T(y \ R(y,z,u),x). [para(532(a,1),36(a,2,2)),flip(a)]. 540 (R(x,y,z) \ x) \ u = R(x,y,z) * (x \ u). [para(532(a,1),463(a,2))]. 541 (x \ R(x,y,z)) \ u = x * (R(x,y,z) \ u). [para(535(a,1),66(a,1,1))]. 542 x / (R(y,z,u) * (y \ x)) = R(y,z,u) \ y. [para(540(a,1),65(a,1,2))]. 543 x * (R(x,y,z) \ 1) = R(x,y,z) \ x. [para(541(a,1),462(a,1))]. 544 (R(x,y,z) \ x) * u = x * (R(x,y,z) \ u). [para(541(a,1),465(a,1)),flip(a)]. 545 T(R(x,y,z) \ 1,x) = R(x,y,z) \ 1. [hyper(23,a,327,a,b,543,a),flip(a)]. 546 T(x,R(x,y,z) \ 1) = x. [hyper(39,a,545,a)]. 547 x \ (x / R(x,y,z)) = R(x,y,z) \ 1. [para(545(a,1),499(a,1)),flip(a)]. 548 T(x,y) * (R(x,z,u) \ 1) = R(x,z,u) \ T(x,y). [para(546(a,1),329(a,1,2,1)),flip(a)]. 549 (x * y) \ ((z * x) * y) = R(T(z,x * y),x,y). [para(111(a,2),46(a,2)),flip(a)]. 550 (x * (x * (y * z))) / (y * z) = R(x * x,y,z). [para(51(a,1),134(a,1,1))]. 551 x \ ((x * y) * (1 / y)) = a(x,y,1 / y). [para(18(a,1),164(a,1,1))]. 552 x \ ((x * y) * (y \ 1)) = a(x,y,1 / y). [para(155(a,1),551(a,1,2,2))]. 553 x \ ((x * y) * (y \ 1)) = a(x,y,y \ 1). [para(155(a,1),552(a,2,3))]. 554 a(x / y,y,y \ 1) = (x / y) \ (x * (y \ 1)). [para(22(a,1),553(a,1,2,1)),flip(a)]. 555 T((x * y) / (z * y),z) = R(z \ x,z,y). [para(84(a,1),194(a,2,1))]. 556 T(T((x * y) / (z * y),u),z) = T(R(z \ x,z,y),u). [para(555(a,1),42(a,1,1)),flip(a)]. 557 T(x,x * ((y * x) / y)) = x. [para(204(a,2),237(a,1))]. 558 ((x * y) / x) / y = y \ ((x * y) / x). [para(557(a,1),252(a,1,2))]. 559 L(x,x * y,x) * (x \ y) = (x \ y) * T(x,y). [para(312(a,1),221(a,1,1))]. 560 (x \ y) * L(z,y,x \ 1) = x \ (y * z). [para(331(a,2),318(a,1))]. 561 (T(x,y) * (x \ 1)) * z = T(x,y) * (x \ z). [para(374(a,1),332(a,1,1)),flip(a)]. 562 (x \ T(x,y)) * z = T(x,y) * (x \ z). [para(377(a,1),561(a,1,1))]. 563 (T(x,y) * (x \ z)) / z = x \ T(x,y). [hyper(24,a,22,a,b,562,a),flip(a)]. 564 x * (T(x,y) * (x \ x)) = T(x * T(x,y),x). [para(562(a,1),138(a,1,2))]. 565 (T(x,y) * z) / (x * z) = x \ T(x,y). [para(19(a,1),563(a,1,1,2))]. 566 (x \ T(x,y)) \ (T(x,y) * z) = x * z. [para(565(a,1),66(a,1,1))]. 567 (x \ T(x,y)) \ z = x * (T(x,y) \ z). [para(20(a,1),566(a,1,2))]. 568 T(x * T(x,y),x) = x * (T(x,y) * 1). [para(60(a,1),564(a,1,2,2)),flip(a)]. 569 T(x * T(x,y),x) = x * T(x,y). [para(18(a,1),568(a,2,2))]. 571 T(x,x * T(x,y)) = x. [hyper(39,a,569,a)]. 572 T(x,y) / x = x \ T(x,y). [para(571(a,1),252(a,1,2))]. 573 (x \ T(x,y)) \ z = (x / T(x,y)) * z. [para(572(a,1),358(a,1,1))]. 574 (x \ T(x,y)) \ z = (T(x,y) \ x) * z. [para(299(a,1),573(a,2,1))]. 575 (T(x,y) \ x) * (T(x,y) * z) = x * z. [para(574(a,1),566(a,1))]. 576 (T(x,y) \ x) * z = x * (T(x,y) \ z). [para(574(a,1),567(a,1))]. 577 (x * y) / (T(x,z) * y) = T(x,z) \ x. [hyper(24,a,22,a,b,575,a),flip(a)]. 578 x * (T(x,y) \ 1) = T(x,y) \ x. [hyper(24,a,18,a,b,576,a),flip(a)]. 579 K(x,T(x,y) \ 1) = 1. [hyper(23,a,328,a,b,576,a),flip(a)]. 580 T(x,T(x,y) \ 1) = x. [hyper(41,a,579,a)]. 581 T(x,y) * (T(x,z) \ 1) = T(x,z) \ T(x,y). [para(580(a,1),329(a,1,2,1)),flip(a)]. 582 x \ (T(x,y) \ x) = T(x,y) \ 1. [hyper(23,a,20,a,b,578,a),flip(a)]. 583 ((T(x,y) \ x) * z) / (T(x,y) \ z) = R(x,T(x,y) \ 1,z). [para(578(a,1),324(a,1,1,1))]. 584 R(x \ 1,x * y,z) = R(x,y,z) \ 1. [para(348(a,2),344(a,1))]. 585 R(x,x \ y,z) \ 1 = R(x \ 1,y,z). [para(20(a,1),584(a,1,2)),flip(a)]. 586 (x * y) / (z * ((z \ x) * y)) = R(z,x,y) \ z. [para(213(a,1),500(a,1,2))]. 587 T(x \ R(x,y,z),x * (y * z)) = (x * (y * z)) \ ((x * y) * z). [para(537(a,1),84(a,1,1))]. 588 R(x * x,y,z) = x * x. [para(550(a,1),132(a,1))]. 589 R(T(x * x,y),z,u) = T(x * x,y). [para(588(a,1),46(a,2,1))]. 591 T(x * x,y) \ (z * u) = (T(x * x,y) \ z) * u. [para(589(a,1),197(a,1,1))]. 592 a(x / y,y,y \ 1) = (y / x) * (x * (y \ 1)). [para(554(a,2),358(a,1))]. 593 (x * y) / (z * ((z \ y) * T(x,y))) = R(z,y,T(x,y)) \ z. [para(82(a,1),586(a,1,1))]. 594 a(x,y,z) = (x \ (y * z)) \ ((x \ y) * z). [para(284(a,2),28(a,2))]. 595 (x \ (y * z)) * a(x,y,z) = (x \ y) * z. [para(594(a,2),20(a,1,2))]. 596 (x \ (y * (x \ 1))) * x = T(y,x) * (x \ 1). [para(378(a,1),329(a,1))]. 597 (T(x,y) * (y \ 1)) / y = y \ (x * (y \ 1)). [hyper(24,a,22,a,b,596,a),flip(a)]. 598 x \ (y * (x \ 1)) = T(y,x) / (x * x). [para(597(a,1),401(a,1))]. 599 x \ ((x * (x * y)) * (x \ 1)) = (x * (y * x)) / (x * x). [para(103(a,1),598(a,2,1))]. 600 T(x,y) / (y * y) = T(x / (y * y),y). [para(598(a,1),403(a,2)),flip(a)]. 601 x * ((y \ (y \ 1)) * z) = (x / (y * y)) * z. [para(416(a,1),428(a,1,1)),flip(a)]. 602 (x / (y * y)) * z = x * (y \ (y \ z)). [para(291(a,1),601(a,1,2)),flip(a)]. 603 L(x,y / (y * z),z) = x. [hyper(23,a,74,a,b,451,a),flip(a)]. 604 (x * (y / (y * x))) \ z = (y / (y * x)) \ (x \ z). [para(603(a,1),177(a,1)),flip(a)]. 605 T(x,x * (y / (y * x))) = x. [para(603(a,1),364(a,2))]. 606 (x * (y / (y * x))) \ z = ((y * x) / y) * (x \ z). [para(604(a,2),358(a,1))]. 607 x * (x * ((y * z) / ((x * y) * z))) = R(x,x * y,z). [para(95(a,1),211(a,1)),flip(a)]. 608 L(R(x,x,y),z,u) * (x * y) = (x * L(x,z,u)) * y. [para(214(a,1),184(a,2,1))]. 609 L(K(x,y),y * x,x * y) = K(y,x) \ 1. [para(30(a,2),260(a,2,1))]. 610 (x \ (y * z)) \ ((x \ y) * z) = a(x \ 1,y,z). [para(318(a,1),323(a,1,2,1))]. 611 a(x \ 1,y,z) = a(x,y,z). [para(610(a,1),594(a,2)),flip(a)]. 612 a(x / y,z,u) = a(y / x,z,u). [para(343(a,1),611(a,1,1))]. 613 L(x \ 1,y,x \ 1) * y = y * T(x \ 1,x * y). [para(485(a,1),336(a,2,2))]. 614 T(T((x * y) / (z * y),u),z) = R(T(z \ x,u),z,y). [para(556(a,2),46(a,2)),flip(a)]. 615 x * (x * (R(x,y,z) \ 1)) = R(x,x * y,z). [para(344(a,1),607(a,1,2,2))]. 616 (x * x) / R(x,y,z) = R(x,x * y,z). [para(615(a,1),263(a,1)),flip(a)]. 617 x * (R(x,y,z) \ x) = R(x,x * y,z). [para(543(a,1),615(a,1,2))]. 618 x \ R(x,x * y,z) = R(x,y,z) \ x. [hyper(23,a,20,a,b,617,a),flip(a)]. 619 x * (R(x,x * y,z) \ x) = R(x,(x * x) * y,z). [para(131(a,2),617(a,2,2))]. 620 x / R(x,x * y,z) = x \ R(x,y,z). [para(617(a,1),535(a,1,2))]. 621 (R(x,y,z) \ x) * x = R(x,x * y,z). [para(617(a,1),544(a,2))]. 622 R(x,x * y,z) \ x = x \ R(x,y,z). [para(620(a,1),498(a,1)),flip(a)]. 623 R(x,x * y,z) \ 1 = x \ (x \ R(x,y,z)). [para(620(a,1),547(a,1,2)),flip(a)]. 624 x \ R(x,x \ y,z) = R(x,y,z) \ x. [para(20(a,1),622(a,1,1,2)),flip(a)]. 625 x * (R(x,x * y,z) \ u) = (x \ R(x,y,z)) * u. [para(622(a,1),544(a,1,1)),flip(a)]. 626 R(x,(x * x) * y,z) = x * (x \ R(x,y,z)). [para(622(a,1),619(a,1,2)),flip(a)]. 627 R(x,(x * x) * y,z) = R(x,y,z). [para(626(a,2),20(a,1))]. 628 R(x,x * (x * y),z) = R(x,y,z). [para(131(a,1),627(a,1,2))]. 629 R(x,x \ y,z) = R(x,x * y,z). [para(20(a,1),628(a,1,2,2)),flip(a)]. 630 R(x,x * y,z) \ (y * z) = (x \ y) * z. [para(629(a,1),197(a,1,1))]. 631 R(x,x * (y / z),z) = y / ((x \ (y / z)) * z). [para(629(a,1),206(a,1))]. 632 R(x,x * y,z) \ 1 = R(x \ 1,y,z). [para(629(a,1),585(a,1,1))]. 633 R(x,x * y,z) = R(x \ 1,y,z) \ 1. [para(632(a,1),156(a,1,1)),flip(a)]. 634 x \ (x \ R(x,y,z)) = R(x \ 1,y,z). [para(632(a,1),623(a,1)),flip(a)]. 635 x * R(x \ 1,y,z) = x \ R(x,y,z). [para(634(a,1),20(a,1,2))]. 636 x * (R(x \ 1,y,z) * u) = x \ (R(x,y,z) * u). [para(634(a,1),265(a,1,2,1))]. 637 x * (R(x,x * y,z) \ u) = R(x,y,z) * (x \ u). [para(625(a,2),532(a,1))]. 638 x * (R(x \ 1,y,z) * u) = R(x,y,z) * (x \ u). [para(636(a,2),534(a,1))]. 639 x * (y * R(y \ (x \ y),z,u)) = R(x,z,u) * (x \ y). [para(366(a,2),638(a,1,2))]. 640 (x * L(x,y,z)) * u = L(x,y,z) * (x * u). [para(182(a,1),608(a,1,1,1)),flip(a)]. 641 L(x,y,z) \ ((x * L(x,y,z)) * u) = x * u. [hyper(23,a,20,a,b,640,a(flip)),flip(a)]. 642 L(x,y,z) * (x * u) = x * (L(x,y,z) * u). [para(640(a,1),484(a,1))]. 643 L(x,y,z) \ (x * (L(x,y,z) * u)) = x * u. [para(484(a,1),641(a,1,2))]. 644 x * (L(x,y,z) * (x \ u)) = L(x,y,z) * u. [para(20(a,1),642(a,1,2)),flip(a)]. 645 L(x,y,z) * (x * (L(x,y,z) \ u)) = x * u. [para(20(a,1),642(a,2,2))]. 646 (L(x,y,z) \ x) * (L(x,y,z) * u) = x * u. [para(643(a,1),524(a,1)),flip(a)]. 647 (x \ L(x,y,z)) * u = L(x,y,z) * (x \ u). [hyper(23,a,504,a,b,644,a),flip(a)]. 648 (x * y) / (x * (L(x,z,u) \ y)) = L(x,z,u). [hyper(24,a,22,a,b,645,a),flip(a)]. 649 (x * y) / (L(x,z,u) * y) = L(x,z,u) \ x. [hyper(24,a,22,a,b,646,a),flip(a)]. 650 (L(x,y,z) \ x) * u = x * (L(x,y,z) \ u). [para(20(a,1),646(a,1,2))]. 651 (L(x,y,z) \ x) \ u = L(x,y,z) * (x \ u). [para(647(a,1),518(a,2))]. 652 T(x,L(x,y,z) \ x) = x. [hyper(23,a,82,a,b,650,a),flip(a)]. 653 K(x,L(x,y,z) \ x) = 1. [hyper(40,a,652,a)]. 654 T(x \ 1,x * (y * y)) = T(x,y * y) \ 1. [para(202(a,1),380(a,2,1))]. 655 T(x,y * y) \ 1 = T(x \ 1,y * y). [para(654(a,1),431(a,1))]. 656 L(x,y,R(T(y,z),u,w)) = x. [hyper(23,a,74,a,b,436,a),flip(a)]. 657 L(x,y,R((y \ z) \ z,u,w)) = x. [para(83(a,1),656(a,1,3,1))]. 658 x \ ((y \ (y \ z)) * (y * (y * x))) = T(z,y * (y * x)). [para(285(a,1),444(a,1,2))]. 659 x \ (x * (x * (y * (x \ 1)))) = (x * (y * x)) / (x * x). [para(51(a,1),599(a,1,2))]. 660 x \ (T(y,z * z) * x) = T(y,z * (z * x)). [para(420(a,1),658(a,1,2))]. 661 T(T(x,y * y),z) = T(x,y * (y * z)). [para(660(a,1),36(a,2))]. 662 T(T(x,y),z * z) = T(x,z * (z * y)). [para(661(a,1),42(a,1)),flip(a)]. 663 x \ (x * T(y,x \ 1)) = (x * (y * x)) / (x * x). [para(347(a,1),659(a,1,2,2))]. 664 (x * (y * x)) / (x * x) = T(y,x \ 1). [para(663(a,1),19(a,1))]. 665 T(x * y,x) / (x * x) = T(x \ y,x \ 1). [para(138(a,1),664(a,1,1))]. 666 T((x * y) / (x * x),x) = T(x \ y,x \ 1). [para(665(a,1),600(a,1)),flip(a)]. 667 (x * (x * ((y * z) * u))) / (z * u) = R(x * (x * y),z,u). [para(51(a,1),94(a,1,1))]. 668 (x * (y \ 1)) / (x / y) = (x / y) \ (x * (y \ 1)). [para(434(a,1),481(a,1,2)),flip(a)]. 669 (x * (y \ 1)) / (x / y) = (y / x) * (x * (y \ 1)). [para(668(a,2),358(a,1))]. 670 (x * (T(x,y) \ z)) / (T(x,y) \ z) = R(x,T(x,y) \ 1,z). [para(576(a,1),583(a,1,1))]. 671 (x * y) / (L(x,z * y,z) * y) = R(z,y,T(x,y)) \ z. [para(455(a,1),593(a,1,2))]. 672 R(x,y,T(z,y)) \ x = L(z,x * y,x) \ z. [para(671(a,1),649(a,1))]. 673 (R(x,y,T(z,y)) \ x) \ 1 = z \ L(z,x * y,x). [para(672(a,2),511(a,1,1))]. 674 L(x,y * (y * z),y) \ x = y \ R(y,z,T(x,y * z)). [para(672(a,1),622(a,1))]. 676 x \ R(x,y,T(z,y)) = z \ L(z,x * y,x). [para(673(a,1),460(a,1)),flip(a)]. 677 R(x,y,T(z,y)) = x * (z \ L(z,x * y,x)). [para(676(a,1),20(a,1,2)),flip(a)]. 678 R(x,x * y,T(z,x * y)) = x * (z \ L(z,y,x)). [para(313(a,1),677(a,2,2,2))]. 679 R(x,y,T(z,x * y)) \ x = z \ L(z,y,x). [hyper(23,a,617,a,b,678,a(flip)),flip(a)]. 680 (x \ L(x,y,z)) * R(z,y,T(x,z * y)) = z. [para(679(a,1),496(a,1,1))]. 681 L(x,y,z) \ x = z \ R(z,y,T(x,z * y)). [para(313(a,1),674(a,1,1))]. 682 L(x,y,z) * (z \ R(z,y,T(x,z * y))) = x. [para(681(a,1),20(a,1,2))]. 683 R(x,y,T(z,x * y)) = x * (L(z,y,x) \ z). [para(681(a,2),20(a,1,2)),flip(a)]. 684 (x \ R(x,y,T(z,x * y))) * L(z,y,x) = z. [para(681(a,1),520(a,1,1))]. 685 L(x,R(y,z,u),T(y,w)) * (T(y,w) \ T(y,w)) = x. [para(527(a,1),682(a,1,2,2))]. 686 R(x,y,T(z,x * y)) * (x \ L(z,y,x)) = z. [para(684(a,1),532(a,1)),flip(a)]. 687 L(x,R(y,z,u),T(y,w)) * 1 = x. [para(60(a,1),685(a,1,2))]. 688 L(x,R(y,z,u),T(y,w)) = x. [hyper(24,a,18,a,b,687,a)]. 690 L(x,R(y / z,u,w),z \ y) = x. [para(84(a,1),688(a,1,3))]. 691 T(R(x,y,z),T(x,u)) / T(x,u) = T(x,u) \ R(x,y,z). [para(688(a,1),441(a,1,2))]. 692 R(T(x,T(x,y)),z,u) / T(x,y) = T(x,y) \ R(x,z,u). [para(46(a,2),691(a,1,1))]. 693 R(x,y,z) / T(x,u) = T(x,u) \ R(x,y,z). [para(115(a,1),692(a,1,1,1))]. 694 x * (x * (((y * z) * u) / (z * u))) = R(x * (x * y),z,u). [para(667(a,1),211(a,1)),flip(a)]. 695 R(x,T(x,y) \ 1,z) = x. [para(670(a,1),21(a,1))]. 696 R(x * (x * y),z,u) = x * (x * R(y,z,u)). [para(34(a,2),694(a,1,2,2)),flip(a)]. 697 x * (x * R(T(y,x),z,u)) = R(x * (y * x),z,u). [para(82(a,1),696(a,1,1,2)),flip(a)]. 698 R(x * (x * T(y,x * x)),z,u) = R(y,z,u) * (x * x). [para(696(a,2),226(a,1))]. 699 R(x * (y * x),z,u) = x * (R(y,z,u) * x). [para(110(a,1),697(a,1,2)),flip(a)]. 700 x \ R(x * (y * x),z,u) = R(y,z,u) * x. [hyper(23,a,20,a,b,699,a(flip)),flip(a)]. 701 (x * (y * x)) \ R(x * (z * x),u,w) = T(y,x) \ (x \ (R(z,u,w) * x)). [para(699(a,2),287(a,1,2))]. 702 x \ R(x * y,z,u) = R(y / x,z,u) * x. [para(22(a,1),700(a,1,2,1,2))]. 703 x \ R(x * y,z,u) = x * R(x \ y,z,u). [para(702(a,2),224(a,1))]. 704 L(x \ (y * R(y \ z,u,w)),x,y) = (y * x) \ R(y * z,u,w). [para(703(a,1),177(a,1,1,2))]. 705 R(x * (y * y),z,u) = R(x,z,u) * (y * y). [para(136(a,1),698(a,1,1))]. 706 (x \ 1) \ T(x \ 1,x * y) = ((x * y) \ y) * x. [para(156(a,1),385(a,2,2))]. 707 (x \ 1) \ T(x \ 1,x * y) = x * ((x * y) \ y). [para(706(a,2),381(a,1))]. 708 (x * y) * T(L(y \ 1,y,x),z) = (x * y) * T((x * y) \ x,z). [para(231(a,1),139(a,1))]. 709 R((x / y) * (z * z),z \ (z \ 1),y) = x / (z \ (z \ y)). [para(415(a,1),293(a,1,1))]. 710 x / (y \ (y \ z)) = (x / z) * (y * y). [para(709(a,1),426(a,1))]. 711 (x / (y * z)) * (y * y) = x / (y \ z). [para(19(a,1),710(a,1,2,2)),flip(a)]. 712 (x * y) / (z \ y) = R(x / z,z,y) * (z * z). [para(80(a,2),711(a,1,1)),flip(a)]. 713 R((x / y) * (y * y),y,z) = (x * z) / (y \ z). [para(712(a,2),705(a,2))]. 714 R(x / (y \ 1),y,z) = (x * z) / (y \ z). [para(397(a,1),713(a,1,1))]. 715 R(x,y,z) = ((x * (y \ 1)) * z) / (y \ z). [para(21(a,1),714(a,1,1))]. 716 R(L(x,y,z) \ x,x,u) = ((L(x,y,z) \ 1) * u) / (x \ u). [para(513(a,1),714(a,1,1))]. 717 R(x,y \ 1,z) = R(x,y,z). [para(715(a,2),324(a,1)),flip(a)]. 718 R(x,y,y) / y = x * (y \ 1). [para(717(a,1),207(a,1,1))]. 719 (x * (y \ 1)) \ R(x,y,y) = y. [para(717(a,1),209(a,1,2))]. 720 R(x / (y \ 1),y,y) = x * y. [para(717(a,1),210(a,1))]. 721 R(x,T(x,y),z) = x. [para(717(a,1),695(a,1))]. 722 (x * T(x,y)) * z = x * (T(x,y) * z). [para(721(a,1),79(a,1,1)),flip(a)]. 723 R(T(x / (y \ 1),z),y,y) / y = (y \ 1) * T((y \ 1) \ x,z). [para(718(a,2),139(a,1))]. 724 R(L(x / (y \ 1),z,u),y,y) / y = (y \ 1) * L((y \ 1) \ x,z,u). [para(718(a,2),215(a,1))]. 725 (T(x,y) * (R(x,z,u) \ 1)) \ T(x,y) = R(x,z,u). [para(527(a,1),719(a,1,2))]. 726 R(T(x / (y \ 1),z),y,y) = T(x * y,z). [para(720(a,1),46(a,2,1))]. 727 L(x,T(y,z),y) = x. [hyper(23,a,74,a,b,722,a),flip(a)]. 728 T(x,y) * (x * z) = x * (T(x,y) * z). [para(722(a,1),235(a,1)),flip(a)]. 729 x * (T(x,y) * (x \ z)) = T(x,y) * z. [para(722(a,1),281(a,1))]. 730 L(x,y,(z * y) / z) = x. [para(104(a,1),727(a,1,2))]. 731 L(x,(y \ z) \ z,y) = x. [para(83(a,1),727(a,1,2))]. 732 x \ (T(x,y) * z) = T(x,y) * (x \ z). [hyper(23,a,20,a,b,729,a),flip(a)]. 733 x \ (T(x,y) * z) = (x \ T(x,y)) * z. [para(732(a,2),562(a,2)),flip(a)]. 734 (R(x,y,z) \ T(x,u)) \ T(x,u) = R(x,y,z). [para(548(a,1),725(a,1,1))]. 735 R(L(x,y,z) \ x,x,u) = (L(x,y,z) \ u) / (x \ u). [para(318(a,1),716(a,2,1))]. 736 R(L(x,y,z) \ x,x,u) = L(x,y,z) \ x. [para(735(a,2),513(a,1))]. 738 L(x,y,y * x) \ z = ((y * x) \ y) * z. [para(19(a,1),396(a,1,1,2)),flip(a)]. 739 a(x,y,z) = T(x \ R(x,y,z),x * (y * z)). [para(587(a,2),28(a,2))]. 740 T(T(x \ R(x,y,z),u),x * (y * z)) = T(a(x,y,z),u). [para(739(a,2),42(a,1,1)),flip(a)]. 741 a(x,y,z) = T(T(R(x,y,z) / x,x * (y * z)),x). [para(739(a,2),112(a,2)),flip(a)]. 742 T((x * (y \ R(y,z,u))) / x,y * (z * u)) = (x * a(y,z,u)) / x. [para(739(a,2),233(a,1,1,2)),flip(a)]. 743 T(R(x,y,z) \ R(R(x,y,z),u,x),x * (R(x,y,z) * T(u,x))) = a(R(x,y,z),u,x). [para(530(a,2),739(a,2,2)),flip(a)]. 744 T(T((R(x,y,z) * u) / (x * u),x * (y * z)),x) = R(a(x,y,z),x,u). [para(739(a,2),614(a,2,1))]. 745 a(x,y,z) = T(T(x \ R(x,y,z),x * (y * z)),x). [para(478(a,1),741(a,2,1,1))]. 746 T(a(x,y,z),x) = a(x,y,z). [para(739(a,2),745(a,2,1)),flip(a)]. 747 a(x,y,z) * x = x * a(x,y,z). [para(746(a,1),82(a,1,2)),flip(a)]. 748 (x * a(x,y,z)) / x = a(x,y,z). [para(746(a,1),105(a,1,1,2))]. 749 ((x * (x * y)) * a(x * (x * y),z,u)) / y = a(x * (x * y),z,u) * (x * x). [para(747(a,1),418(a,1,1))]. 750 (x \ y) \ R(x \ z,u,w) = (x * y) \ R(x * z,u,w). [para(704(a,1),267(a,1)),flip(a)]. 751 (x * y) * T((x * y) \ x,z) = (x * y) * L(T(y \ 1,z),y,x). [para(44(a,2),708(a,1,2)),flip(a)]. 752 (x \ 1) * T((x \ 1) \ y,z) = T(y * x,z) / x. [para(726(a,1),723(a,1,1)),flip(a)]. 753 (x \ 1) * T(x * y,z) = T(y * x,z) / x. [para(330(a,1),752(a,1,2,1))]. 754 T(x * y,z) / y = y \ T(y * x,z). [para(753(a,1),318(a,1))]. 755 x \ T(x * (y / x),z) = T(y,z) / x. [para(22(a,1),754(a,1,1,1)),flip(a)]. 756 T(x * y,y) / y = (y \ x) * y. [para(754(a,2),146(a,1))]. 757 ((x \ y) * x) * x = T(y * x,x). [para(756(a,1),22(a,1,1))]. 758 T((x * y) * x,x) = (y * x) * x. [para(19(a,1),757(a,1,1,1)),flip(a)]. 759 (x * T(y * x,x)) / (x * x) = T((x \ y) * x,x \ 1). [para(757(a,1),664(a,1,1,2))]. 760 T((x \ y) * x,x \ 1) = ((y * x) * x) / (x * x). [para(82(a,1),759(a,1,1)),flip(a)]. 761 T((x \ y) * x,x \ 1) = R(y,x,x). [para(760(a,2),34(a,2)),flip(a)]. 762 (x * y) * T((x * y) \ x,z) = x * (y * T(y \ 1,z)). [para(751(a,2),74(a,1))]. 763 (x * (x * (y * z))) \ (x * (x * (y * (z * u)))) = L(u,z,x * (x * y)). [para(51(a,1),92(a,1,2))]. 764 (x * y) * T(L(y \ z,y,x),u) = (x * y) * T((x * y) \ (x * z),u). [para(232(a,1),139(a,1))]. 765 (x * y) * R(L(y \ 1,y,x),z,u) = (x * y) * R((x * y) \ x,z,u). [para(472(a,1),224(a,1))]. 766 L(R(x / (y \ 1),y,y),z,u) / y = (y \ 1) * L((y \ 1) \ x,z,u). [para(48(a,1),724(a,1,1))]. 767 T(T(x \ R(x,y,z),x * (y * z)),x) = R(a(x,y,z),x,u). [para(531(a,1),744(a,1,1,1))]. 769 R(a(x,y,z),x,u) = a(x,y,z). [para(767(a,1),745(a,2)),flip(a)]. 770 (a(x,y,z) * x) * u = a(x,y,z) * (x * u). [para(769(a,1),79(a,1,1)),flip(a)]. 771 L(x,y,a(y,z,u)) = x. [hyper(23,a,74,a,b,770,a),flip(a)]. 772 (x * a(x,y,z)) * u = a(x,y,z) * (x * u). [para(747(a,1),770(a,1,1))]. 773 L(x,y,z * (z * u)) = (u * y) \ (u * (y * x)). [para(763(a,1),212(a,1))]. 774 L(x,y,z * (z * u)) = L(x,y,u). [para(773(a,2),32(a,2)),flip(a)]. 776 L(x,y,z \ u) = L(x,y,z * u). [para(20(a,1),774(a,1,3,2)),flip(a)]. 777 L(x,y,(z / u) * z) = L(x,y,u). [para(22(a,1),774(a,1,3,2))]. 778 L(x,y,z * (u * z)) = L(x,y,T(u,z)). [para(82(a,1),774(a,1,3,2))]. 779 L(x,y,(z * u) * (u * z)) = L(x,y,K(u,z)). [para(69(a,1),774(a,1,3,2))]. 780 L(x,y,z * ((z \ u) * w)) = L(x,y,z * ((z * u) * w)). [para(89(a,1),774(a,1,3,2)),flip(a)]. 781 L(x,y,(z \ u) * w) = L(x,y,(z * u) * w). [para(89(a,1),774(a,1,3)),flip(a)]. 782 L(x,y,(z \ (z \ u)) * (z \ u)) = L(x,y,T(z,u)). [para(254(a,1),774(a,1,3,2))]. 783 L(x,y,(z * z) / u) = L(x,y,u \ 1). [para(263(a,1),774(a,1,3))]. 784 L(x,y,z / u) = L(x,y,u / z). [para(360(a,1),774(a,1,3))]. 785 L(x,y,z * L(z,u * z,u)) = L(x,y,a(u,z,z)). [para(453(a,2),774(a,1,3,2))]. 786 L(x,y,R(z * (z * u),w,v5)) = L(x,y,R(u,w,v5)). [para(696(a,2),774(a,1,3))]. 787 L(x,y,z \ 1) = L(x,y,z). [para(18(a,1),776(a,2,3))]. 788 L(x,y / z,z * y) = x. [para(776(a,1),236(a,1))]. 789 L(x,y,T(z / u,z)) = L(x,y,((u / z) * u) * u). [para(370(a,2),776(a,1,3))]. 790 L(x,y,y \ (z * z)) = x. [para(776(a,2),429(a,1))]. 791 L(x,(y \ z) \ u,z * (y * u)) = x. [para(776(a,1),508(a,1))]. 792 L(x \ (x / y),y,x * (x / y)) = ((x \ (x / y)) \ y) \ y. [para(776(a,1),442(a,1))]. 793 L(x,R(y / z,u,w),z * y) = x. [para(776(a,1),690(a,1))]. 794 L(x \ L(y \ z,y,u),x,u * y) = ((u \ y) * x) \ (u \ z). [para(776(a,1),275(a,1))]. 795 T(x * x,y) \ (y \ (x * x)) = y \ 1. [para(790(a,1),395(a,1)),flip(a)]. 796 L(x,L(y \ 1,z,u),y) = x. [para(787(a,1),503(a,1))]. 797 L(x,(y * z) \ y,z) = x. [para(787(a,1),505(a,1))]. 798 (x \ y) * L(z,y,x) = x \ (y * z). [para(787(a,1),560(a,1,2))]. 799 x * T(y \ 1,y * x) = L(y \ 1,x,y) * x. [para(787(a,1),613(a,1,1)),flip(a)]. 800 L(x,y \ z,z \ y) = x. [para(20(a,1),797(a,1,2,1))]. 801 L(x,y \ z,z * y) = x. [para(800(a,1),776(a,1)),flip(a)]. 802 L(x,y,z * (z / y)) = x. [para(66(a,1),801(a,1,2))]. 803 (x * L(x \ 1,y,z)) \ u = L(x \ 1,y,z) \ (x \ u). [para(796(a,1),177(a,1)),flip(a)]. 804 L(x,y,(z * (z * u)) * (z * w)) = L(x,y,u \ (z \ w)). [para(282(a,1),777(a,1,3,1))]. 805 L(x,y,(z * (z * u)) * z) = L(x,y,u \ (z \ 1)). [para(289(a,1),777(a,1,3,1))]. 806 L(L(x,y,y / z),z,z / y) = x. [para(784(a,1),304(a,1,1))]. 807 L(x,x,x / y) = y \ (y / (x \ 1)). [para(784(a,1),432(a,1))]. 808 L(x,y,z / (z * y)) = x. [para(784(a,1),730(a,1))]. 809 ((x / (x * y)) * y) \ (x / (x * y)) = y \ 1. [para(808(a,1),142(a,1)),flip(a)]. 810 ((x / (x * y)) * y) * z = (x / (x * y)) * (y * z). [para(808(a,1),74(a,1,2))]. 811 ((x / (x * y)) * y) \ z = y \ ((x / (x * y)) \ z). [para(808(a,1),177(a,1)),flip(a)]. 812 L(x,y / (z * (u * y)),z * (u \ 1)) = x. [para(350(a,1),793(a,1,2))]. 813 (x * (y \ z)) \ (x * (y \ (z * u))) = L(L(u,z,y),y \ z,x). [para(798(a,1),32(a,2,2,2)),flip(a)]. 814 (x \ y) * L(L(z,y,x),u,w) = x \ (y * L(z,u,w)). [para(49(a,1),798(a,1,2))]. 815 T(x,y) \ (x * z) = (T(x,y) \ x) * z. [para(234(a,1),798(a,1,2)),flip(a)]. 816 x \ (((y * x) / y) * z) = (x \ ((y * x) / y)) * z. [para(237(a,1),798(a,1,2)),flip(a)]. 817 (x \ y) * T((x \ y) \ 1,z) = x \ (y * T(y \ x,z)). [para(261(a,1),798(a,1,2))]. 818 L(x,y,T(z \ u,z)) = L(x,y,T(z * u,z)). [para(138(a,1),778(a,1,3)),flip(a)]. 819 L(x,y,T((z \ u) * z,z)) = L(x,y,z * T(u * z,z)). [para(757(a,1),778(a,1,3,2)),flip(a)]. 820 L(x,y,(z * z) / u) = L(x,y,u). [para(783(a,2),787(a,1))]. 821 L(x,y,T(z,z * (u * u))) = L(x,y,z \ (u * u)). [para(252(a,1),820(a,1,3)),flip(a)]. 822 L(x,y,z / (u * u)) = L(x,y,z). [para(820(a,1),784(a,1)),flip(a)]. 823 L(x,y,z * (u * u)) = L(x,y,z). [para(21(a,1),822(a,1,3)),flip(a)]. 824 L(x,y,(z * u) * u) = L(x,y,R(z,u,u)). [para(34(a,2),822(a,1,3)),flip(a)]. 825 (x * (y * (y * z))) \ ((x * (y * y)) * (z * u)) = L(u,z,x). [para(823(a,1),419(a,2))]. 826 (T(x,y) \ x) * y = T(y,T(x,y)). [para(815(a,1),107(a,1))]. 827 T(x,y) \ (x * z) = x * (T(x,y) \ z). [para(815(a,2),576(a,1))]. 828 x * (T(x,y) \ y) = T(y,T(x,y)). [para(826(a,1),576(a,1)),flip(a)]. 829 T(x,T(y,x)) / (T(y,x) \ x) = y. [hyper(24,a,22,a,b,828,a),flip(a)]. 830 x \ T(y,T(x,y)) = T(x,y) \ y. [hyper(23,a,20,a,b,828,a),flip(a)]. 831 (x * y) / (x * (T(x,z) \ y)) = T(x,z). [para(827(a,1),65(a,1,2))]. 832 (((x * y) * (y * x)) * z) \ (((x * y) * (y * x)) * (z * u)) = L(u,z,K(y,x)). [para(779(a,1),32(a,1)),flip(a)]. 833 (x * (y / (y * x))) \ (y / (y * x)) = x \ 1. [para(362(a,1),809(a,1,1))]. 834 T(x \ 1,x * (y / (y * x))) = x \ 1. [para(833(a,1),349(a,2))]. 835 L(x \ 1,y,x) * y = y * ((x * y) \ y). [para(349(a,1),799(a,1,2)),flip(a)]. 836 L(x,y,(z * (z \ u)) * (z \ u)) = L(x,y,T(z,u)). [para(782(a,1),781(a,1)),flip(a)]. 837 L(x,y,z * ((z \ u) * u)) = L(x,y,a(z,u,u)). [para(435(a,1),785(a,1,3))]. 838 L(x,y,R(z \ u,w,v5)) = L(x,y,R(z * u,w,v5)). [para(20(a,1),786(a,1,3,1,2)),flip(a)]. 839 L(x,y,T(z / u,z)) = L(x,y,R(u / z,u,u)). [para(789(a,2),824(a,1))]. 840 L(x,y,z * (z * (u * z))) = L(x,y,u \ (z \ 1)). [para(51(a,1),805(a,1,3))]. 841 (x * (y / (y * x))) * z = (y / (y * x)) * (x * z). [para(362(a,1),810(a,1,1))]. 842 (x * (y / (y * x))) \ z = x \ ((y / (y * x)) \ z). [para(362(a,1),811(a,1,1))]. 843 L(x,y,T(z,z * (u * u))) = L(x,y,z * (u * u)). [para(821(a,2),776(a,1))]. 844 L(x,y,z * (u \ z)) = L(x,y,T(u,z)). [para(20(a,1),836(a,1,3,1))]. 845 L(x,y,T(z / u,z)) = L(x,y,z * u). [para(66(a,1),844(a,1,3,2)),flip(a)]. 846 L(x,y,R(z / u,z,z)) = L(x,y,u * z). [para(845(a,1),839(a,1)),flip(a)]. 847 L(x,y,R((y \ z) * z,u,w)) = x. [para(838(a,1),657(a,1))]. 848 L(x,y,z \ (u \ 1)) = L(x,y,z * u). [para(840(a,1),774(a,1))]. 850 L(x,y,z * (u \ 1)) = L(x,y,z * u). [para(848(a,1),776(a,1)),flip(a)]. 851 L(x,y / (z * (u * y)),z * u) = x. [para(850(a,1),812(a,1))]. 852 L(x,(y * z) * (u / (y * (z * u))),y * z) = x. [para(851(a,1),303(a,1,1))]. 853 ((x * y) * z) / (x * (y * z)) = (x * y) * (z / (x * (y * z))). [para(851(a,1),196(a,1,2))]. 854 x \ ((y / (y * x)) \ z) = ((y * x) / y) * (x \ z). [para(842(a,1),606(a,1))]. 855 L(x,y,T(z,z * (u * u))) = L(x,y,z). [para(843(a,2),823(a,1))]. 856 L(x,y,T(z,u * u)) = L(x,y,z). [para(423(a,1),855(a,1,3))]. 858 L(x,y,R(T(z,u * u),w,v5)) = L(x,y,R(z,w,v5)). [para(46(a,2),856(a,1,3))]. 859 x \ (((y * x) / y) * z) = ((y * x) / y) * (x \ z). [para(358(a,1),854(a,1,2))]. 860 (x \ ((y * x) / y)) * z = ((y * x) / y) * (x \ z). [para(859(a,1),816(a,1)),flip(a)]. 861 L(x,y,z * ((z * u) * u)) = L(x,y,a(z,u,u)). [para(780(a,1),837(a,1))]. 862 L(x,y,z * (z * (u * (z * w)))) = L(x,y,u \ (z \ w)). [para(51(a,1),804(a,1,3))]. 863 L(x,y,T((z \ u) * z,z)) = L(x,y,(u * z) * z). [para(82(a,1),819(a,2,3))]. 864 L(x,y,T((z \ u) * z,z)) = L(x,y,R(u,z,z)). [para(863(a,2),824(a,1))]. 865 L(x,y,z \ (u \ w)) = L(x,y,z * (u * w)). [para(862(a,1),774(a,1))]. 867 L(x,y,z * (u \ w)) = L(x,y,z * (u * w)). [para(865(a,1),776(a,1)),flip(a)]. 868 L(x,y,z * (u * (u * w))) = L(x,y,z * w). [para(19(a,1),867(a,1,3,2)),flip(a)]. 869 L(x,y,(z \ u) * (u \ z)) = L(x,y,(u \ z) * (z * u)). [para(384(a,1),867(a,1,3))]. 871 ((x \ (x / y)) \ y) \ y = x \ (x / y). [para(792(a,1),802(a,1))]. 872 x / (y \ (y / x)) = (y \ (y / x)) \ x. [para(871(a,1),65(a,1,2))]. 873 (x * (y * (y * z))) \ (x * (y * (y * (z * u)))) = L(u,z,x). [para(411(a,1),825(a,1,2))]. 875 L(x,y * (y * z),u) = L(x,z,u). [para(873(a,1),93(a,1)),flip(a)]. 876 L(x,y \ z,u) = L(x,y * z,u). [para(20(a,1),875(a,1,2,2)),flip(a)]. 877 L(x,(y / z) * y,u) = L(x,z,u). [para(22(a,1),875(a,1,2,2))]. 878 L(x,y * (z * y),u) = L(x,T(z,y),u). [para(82(a,1),875(a,1,2,2))]. 879 L(x,(y * z) * (z * y),u) = L(x,K(z,y),u). [para(69(a,1),875(a,1,2,2))]. 880 L(x,(y \ z) * u,w) = L(x,(y * z) * u,w). [para(89(a,1),875(a,1,2)),flip(a)]. 881 L(x,T(y,y * z),u) = L(x,(y \ z) * z,u). [para(250(a,1),875(a,1,2,2)),flip(a)]. 882 L(x,(y * y) / z,u) = L(x,z \ 1,u). [para(263(a,1),875(a,1,2))]. 883 L(x,T(y \ 1,z),u) = L(x,z * (y \ z),u). [para(327(a,1),875(a,1,2,2)),flip(a)]. 884 L(x,y / z,u) = L(x,z / y,u). [para(360(a,1),875(a,1,2))]. 887 L(x,y \ 1,z) = L(x,y,z). [para(18(a,1),876(a,2,2))]. 888 (x * (y \ z)) * L(u,y * z,x) = x * ((y \ z) * u). [para(876(a,1),74(a,1,2))]. 889 L(x,(y \ z) * z,y) = x. [para(876(a,1),731(a,1))]. 890 L(x,y * z,z * y) = x. [para(876(a,1),801(a,1))]. 891 L(x,(y \ z) * u,z * (y * u)) = x. [para(876(a,1),791(a,1))]. 892 L(x,y * z,z / y) = x. [para(66(a,1),889(a,1,2,1))]. 893 (x * ((x \ y) * y)) \ z = ((x \ y) * y) \ (x \ z). [para(889(a,1),177(a,1)),flip(a)]. 894 ((x * y) * (y * x)) * z = (x * y) * ((y * x) * z). [para(890(a,1),74(a,1,2))]. 895 T(x * y,(x * y) * (y * x)) = T(x * y,y * x). [para(890(a,1),203(a,1)),flip(a)]. 896 L(x,K(y,z),z * y) = x. [para(890(a,1),315(a,1,1))]. 897 K(x,y) \ 1 = K(y,x). [para(890(a,1),609(a,1)),flip(a)]. 898 K(x,y) * K(y,x) = 1. [para(897(a,1),20(a,1,2))]. 899 1 / K(x,y) = K(y,x). [para(897(a,1),65(a,1,2))]. 900 K(x,y) \ z = K(y,x) * z. [para(897(a,1),318(a,1,1)),flip(a)]. 901 K(x,y) * (K(y,x) * z) = z. [para(897(a,1),321(a,1,2,1))]. 902 x / (K(y,z) * x) = K(z,y). [para(897(a,1),340(a,2))]. 903 T(x * y,K(y,x)) / (y * x) = K(x,y). [para(897(a,1),345(a,2))]. 904 R(K(x,y),K(y,x) * z,u) = R(K(y,x),z,u) \ 1. [para(897(a,1),584(a,1,1))]. 905 a(K(x,y),z,u) = a(K(y,x),z,u). [para(897(a,1),611(a,1,1))]. 906 R(K(x,y),K(x,y) * z,u) = R(K(y,x),z,u) \ 1. [para(897(a,1),633(a,2,1,1))]. 907 K(x,y) * (K(y,x) / (x * y)) = K(x,y) \ ((y * x) \ 1). [para(897(a,1),379(a,1,2,1))]. 908 R(x,K(y,z),u) = R(x,K(z,y),u). [para(897(a,1),717(a,1,2))]. 909 L(x,y,K(z,u)) = L(x,y,K(u,z)). [para(897(a,1),787(a,1,3))]. 910 L(K(x,y),z,K(y,x)) * z = z * ((K(y,x) * z) \ z). [para(897(a,1),835(a,1,1,1))]. 911 (x * y) * (K(y,x) * z) = (y * x) * z. [para(896(a,1),176(a,1,2)),flip(a)]. 912 K(x,y) \ ((y * x) \ z) = (x * y) \ z. [para(896(a,1),199(a,1))]. 914 L(x,x,y) = (y * (x \ 1)) \ y. [para(887(a,1),161(a,1))]. 915 x / L(y,y,x) = x * (y \ 1). [para(887(a,1),162(a,1,2))]. 916 L(L(x,y * (z \ 1),y),z,y) = x. [para(887(a,1),308(a,1))]. 917 L(x * y,x,y) = (y \ (x \ 1)) \ 1. [para(887(a,1),351(a,1))]. 918 L(x,y,L(y \ 1,z,u)) = x. [para(887(a,1),509(a,1))]. 919 (x * (y \ z)) / L(z,y,x) = x * (y \ 1). [para(887(a,1),333(a,1,2))]. 920 L(x * (y * z),x,y) = (y \ (x \ 1)) \ z. [para(887(a,1),352(a,1))]. 921 L(x,K(y,z),u) = L(x,K(z,y),u). [para(897(a,1),887(a,1,2))]. 922 T(x * y,K(y,x)) = K(x,y) * (y * x). [para(900(a,1),122(a,1)),flip(a)]. 923 R(K(x,y),K(y,x) * z,u) \ K(x,y) = K(x,y) \ R(K(x,y),z,u). [para(901(a,1),618(a,1,2,2)),flip(a)]. 924 (L(x \ 1,y,z) * x) \ u = x \ (L(x \ 1,y,z) \ u). [para(918(a,1),177(a,1)),flip(a)]. 925 L(x / y,x / y,z) = (z * (y / x)) \ z. [para(343(a,1),914(a,2,1,2))]. 926 L(K(x,y),K(x,y),z) = (z * K(y,x)) \ z. [para(897(a,1),914(a,2,1,2))]. 927 (x * y) * ((y / x) \ 1) = (x * y) / (y / x). [para(788(a,1),915(a,1,2)),flip(a)]. 928 L(x,(y * (y * z)) * (y * u),w) = L(x,z \ (y \ u),w). [para(282(a,1),877(a,1,2,1))]. 929 L(x,(y * (y * z)) * y,u) = L(x,z \ (y \ 1),u). [para(289(a,1),877(a,1,2,1))]. 930 K(x,y) / L(z,z,K(y,x)) = K(x,y) * (z \ 1). [para(909(a,1),915(a,1,2))]. 931 L(x,y * (z \ 1),y) = L(x,y * z,y). [para(916(a,1),303(a,1,1)),flip(a)]. 932 L(x,K(y,z),y * z) = x. [para(921(a,1),896(a,1))]. 933 ((x * y) \ K(x,y)) \ z = K(x,y) \ ((x * y) * z). [para(932(a,1),267(a,1)),flip(a)]. 934 L(x * y,x,y) * z = (y \ (x \ 1)) \ z. [para(917(a,2),318(a,1,1))]. 935 L(x,(y * y) / z,u) = L(x,z,u). [para(882(a,2),887(a,1))]. 936 L(x,y / (z * z),u) = L(x,y,u). [para(935(a,1),884(a,1)),flip(a)]. 937 L(x,y * (z * z),u) = L(x,y,u). [para(21(a,1),936(a,1,2)),flip(a)]. 938 L(x,(y * z) * z,u) = L(x,R(y,z,z),u). [para(34(a,2),936(a,1,2)),flip(a)]. 939 ((x * y) * z) / (K(x,y) * z) = y * x. [hyper(24,a,22,a,b,911,a),flip(a)]. 940 (x * y) \ ((y * x) * z) = K(y,x) * z. [hyper(23,a,20,a,b,911,a),flip(a)]. 941 K(x,y) * ((x * y) \ z) = (y * x) \ z. [para(912(a,1),20(a,1,2))]. 942 x * (y \ ((y * (x \ 1)) * z)) = L(z,y * x,y). [para(931(a,1),446(a,2))]. 943 L(x,K(y,z) * (y * z),u) = L(x,z * y,u). [para(939(a,1),935(a,1,2)),flip(a)]. 944 (x * y) \ (y * (x * z)) = K(y,x) * L(z,x,y). [para(74(a,1),940(a,1,2))]. 945 (x * (y \ 1)) * L(z,y,x) = x * (y \ z). [para(919(a,1),22(a,1,1))]. 946 (a(x,y,z) \ (x \ 1)) \ u = x * (a(x,y,z) * u). [para(920(a,1),771(a,1))]. 947 L(K(x,y),K(x,y),z) / z = (z * K(y,x)) \ 1. [para(926(a,2),320(a,1,1))]. 948 (a(x,y,z) \ (x \ 1)) \ u = (x * a(x,y,z)) * u. [para(771(a,1),934(a,1,1)),flip(a)]. 949 L(x,(y * z) * u,z * (y * u)) = x. [para(880(a,1),891(a,1))]. 950 L(x,(y * z) * u,T(y,z) * (z * u)) = x. [para(82(a,1),949(a,1,2,1))]. 951 L(x,T(y,y * z),u) = L(x,(y * z) * z,u). [para(881(a,2),880(a,1))]. 952 (x * y) / (y / x) = (x * y) * (x / y). [para(343(a,1),927(a,1,2)),flip(a)]. 953 L(x,(y * (y \ z)) * (y \ z),u) = L(x,T(y,z),u). [para(20(a,1),951(a,1,2,2)),flip(a)]. 954 x * (y * ((y \ (x \ 1)) * z)) = L(z,y * x,y). [para(213(a,1),942(a,1,2))]. 955 K(x,y) * L(x,y,x) = T(x,y * x). [para(944(a,1),36(a,2)),flip(a)]. 956 x * ((x \ (y \ 1)) * y) = a(x,y,y). [hyper(23,a,453,a(flip),b,954,a)]. 957 x * (y * (R(y,y * (x \ 1),z) \ ((x \ 1) * z))) = L(z,y * x,y). [para(630(a,2),954(a,1,2,2))]. 958 x * R(x \ 1,y \ 1,y) = a(x,y,y). [para(335(a,2),956(a,1,2))]. 959 x \ R(x,y \ 1,y) = a(x,y,y). [para(958(a,1),635(a,1)),flip(a)]. 960 x * R(x \ 1,y,y) = a(x,y,y). [para(717(a,1),958(a,1,2))]. 961 R(x,y \ 1,y) \ a(x,y,y) = T(x \ 1,R(x,y \ 1,y)). [para(959(a,1),325(a,2,2)),flip(a)]. 962 x \ R(x,y,y) = a(x,y,y). [para(717(a,1),959(a,1,2))]. 963 x * a(x,y,y) = R(x,y,y). [para(962(a,1),20(a,1,2))]. 964 a(x,y,y) \ R(x,y,y) = x. [para(962(a,1),480(a,1,1))]. 965 (R(x,y,y) \ x) * z = a(x,y,y) \ z. [para(962(a,1),465(a,1,1)),flip(a)]. 966 x * (a(x,y,y) * z) = R(x,y,y) * z. [para(962(a,1),501(a,1,2,1))]. 967 R(x \ 1,y,y) = x \ a(x,y,y). [para(962(a,1),634(a,1,2)),flip(a)]. 968 R(x,x * y,y) = a(x,y,y) \ x. [para(965(a,1),621(a,1)),flip(a)]. 969 T(x * y,K(y,x)) = T(x * y,y * x). [para(895(a,1),248(a,1)),flip(a)]. 970 T(x * y,K(y,x)) = (x \ 1) \ y. [para(969(a,2),439(a,1))]. 971 K(x,y) / T(y * x,K(x,y)) = (y * x) \ K(x,y). [para(969(a,2),257(a,1,2))]. 972 T(x * y,K(y,x)) = x * y. [para(970(a,2),330(a,1))]. 973 K(x,y) = (x * y) / (y * x). [para(972(a,1),903(a,1,1)),flip(a)]. 974 K(x,y) * (y * x) = x * y. [para(972(a,1),922(a,1)),flip(a)]. 975 (x * y) / (T(x,y) * y) = K(y,T(x,y)). [para(82(a,1),973(a,2,1)),flip(a)]. 976 (T(x,y) * y) / (x * y) = K(T(x,y),y). [para(82(a,1),973(a,2,2)),flip(a)]. 977 ((x * y) * z) / ((y * x) * z) = R(K(x,y),y * x,z). [para(973(a,2),80(a,1,1)),flip(a)]. 978 (x \ y) / (y * (x \ 1)) = K(x \ 1,y). [para(318(a,1),973(a,2,1)),flip(a)]. 979 ((K(x,y) * z) * K(y,x)) / z = K(K(x,y) * z,K(y,x)). [para(901(a,1),973(a,2,2)),flip(a)]. 980 K(x \ y,x) * y = (x \ y) * x. [para(20(a,1),974(a,1,2))]. 981 K(x * y,x) * y = (x \ y) * x. [para(495(a,1),980(a,1,1))]. 982 ((x \ y) * x) / y = K(x * y,x). [hyper(24,a,22,a,b,981,a),flip(a)]. 983 K(x,T(y,x)) = T(y,x) \ y. [para(975(a,1),577(a,1))]. 984 T(x,y) * K(y,T(x,y)) = x. [para(983(a,2),20(a,1,2))]. 985 K(x,T(y,x)) * T(y,x) = y. [para(983(a,2),298(a,1,1))]. 987 T(x,y) \ (x * z) = K(y,T(x,y)) * z. [para(983(a,2),815(a,2,1))]. 988 L(x,K(y,T(z,y)),u) = L(x,T(z,y) * z,u). [para(983(a,2),876(a,1,2))]. 989 (x \ y) * K(x,T(y / x,x)) = y / x. [para(84(a,1),984(a,1,1))]. 990 K(T(x,y),y) * x = T(x,y). [hyper(23,a,901,a,b,985,a),flip(a)]. 991 K(x,x \ y) * T(y / x,x) = y / x. [para(84(a,1),985(a,1,1,2))]. 992 K(T(x,y),y) = x \ T(x,y). [para(976(a,1),565(a,1))]. 993 x * K(T(x,y),y) = T(x,y). [para(992(a,2),20(a,1,2))]. 994 (x / y) \ T(x / y,y) = K(y \ x,y). [para(84(a,1),992(a,1,1)),flip(a)]. 995 K(T(x \ 1,y),y) = x * T(x \ 1,y). [para(992(a,2),330(a,1))]. 997 (x / y) * K(T(x / y,y),y) = y \ x. [para(993(a,2),84(a,1))]. 998 T(x,y) * (K(y,T(x,y)) * z) = x * z. [para(987(a,1),20(a,1,2))]. 999 K(x,T(y,x)) * (y \ z) = T(y,x) \ z. [para(20(a,1),987(a,1,2)),flip(a)]. 1000 (x \ y) * K(x,x \ y) = y / x. [para(84(a,1),989(a,1,2,2))]. 1001 (x \ y) * K(x,x * y) = y / x. [para(489(a,1),1000(a,1,2))]. 1002 (x \ y) \ (y / x) = K(x,x * y). [hyper(23,a,20,a,b,1001,a),flip(a)]. 1003 K(x,x * (x * y)) = y \ ((x * y) / x). [para(19(a,1),1002(a,1,1)),flip(a)]. 1004 K(x,x * y) * T(y / x,x) = y / x. [para(489(a,1),991(a,1,1))]. 1005 (x / y) \ T(x / y,y) = K(y * x,y). [para(994(a,2),495(a,1))]. 1006 (x / y) * K(y \ x,y) = y \ x. [para(84(a,1),997(a,1,2,1))]. 1007 (x / y) * K(y * x,y) = y \ x. [para(495(a,1),1006(a,1,2))]. 1008 (x / y) * (x \ y) = K(x * y,x). [hyper(23,a,359,a,b,1007,a),flip(a)]. 1009 K(x * y,x) / (x \ y) = x / y. [hyper(24,a,22,a,b,1008,a),flip(a)]. 1010 (x \ y) * (x / y) = K(x * y,x). [para(1008(a,1),368(a,1)),flip(a)]. 1011 (x \ y) \ K(x * y,x) = x / y. [hyper(23,a,20,a,b,1010,a),flip(a)]. 1012 L(x,y,(z \ u) * K(z * u,z)) = L(x,y,z / u). [para(1010(a,1),774(a,1,3,2))]. 1013 K(x,y) = y \ ((x * y) / x). [para(1003(a,1),490(a,1)),flip(a)]. 1014 (x * y) / x = y * K(x,y). [para(1013(a,2),20(a,1,2)),flip(a)]. 1015 x * (y / (y * x)) = K(y,x) \ 1. [para(1013(a,2),502(a,1,1)),flip(a)]. 1016 K(x,y) = ((x * y) / x) / y. [para(1013(a,2),558(a,2)),flip(a)]. 1017 ((x * y) / x) * (y \ z) = K(x,y) * z. [para(1013(a,2),860(a,1,1)),flip(a)]. 1018 (x * K(y,x)) * y = y * x. [para(1014(a,1),22(a,1,1))]. 1019 x / (x / y) = y * K(x / y,y). [para(22(a,1),1014(a,1,1))]. 1020 T(x * K(y,x),y) = x. [para(1014(a,1),104(a,1,1))]. 1021 L(x,y * K(z,y),y) = x. [para(1014(a,1),237(a,1,2))]. 1022 a(x / (x * y),z,u) = a(y * K(x,y),z,u). [para(1014(a,1),612(a,1,1)),flip(a)]. 1023 T(T(x * K(y,x),z),y) = T(x,z). [para(1020(a,1),42(a,1,1)),flip(a)]. 1024 T(x * K(y,x),z) * y = y * T(x,z). [para(1020(a,1),108(a,1,2,1)),flip(a)]. 1025 x / L(y,x * K(y,x),y) = y \ (x * K(y,x)). [para(1020(a,1),441(a,1,1))]. 1026 L(x,K(y,z),z) = x. [para(1021(a,1),303(a,1))]. 1027 (x * K(y,x)) \ z = K(y,x) \ (x \ z). [para(1021(a,1),270(a,1))]. 1028 (x * K(y,x)) * z = x * (K(y,x) * z). [para(1026(a,1),74(a,1,2))]. 1029 L(x,K(y,z),y) = x. [para(1026(a,1),921(a,1)),flip(a)]. 1030 (x * K(x,y)) * z = x * (K(x,y) * z). [para(1029(a,1),74(a,1,2))]. 1031 x \ (K(x,y) * z) = (x \ K(x,y)) * z. [para(1029(a,1),798(a,1,2)),flip(a)]. 1032 (x * K(y,x)) \ 1 = K(x,y) / x. [para(1029(a,1),947(a,1,1)),flip(a)]. 1033 (x * y) / x = K(x,y) * y. [para(1016(a,2),22(a,1,1)),flip(a)]. 1035 (x * K(y,x)) / x = K(y,x). [para(1014(a,1),1016(a,2,1)),flip(a)]. 1036 K(x,y) * y = y * K(x,y). [para(1033(a,1),1014(a,1))]. 1037 T(K(x,y),y) = K(x,y). [para(1035(a,1),104(a,1,1))]. 1038 T(x,K(y,x)) = x. [hyper(39,a,1037,a)]. 1040 T(x,y) * K(z,x) = K(z,x) * T(x,y). [para(1038(a,1),108(a,1,2,1)),flip(a)]. 1041 K(x,y) = x * (y / (y * x)). [para(1015(a,2),897(a,1)),flip(a)]. 1042 x \ K(x,y) = y / (y * x). [hyper(23,a,20,a,b,1041,a(flip)),flip(a)]. 1043 K(x,y) = (y / (y * x)) * x. [para(1041(a,2),362(a,2)),flip(a)]. 1044 K(x,y) / x = y / (y * x). [para(1041(a,2),363(a,1,1))]. 1045 x * ((y / (y * x)) * z) = K(x,y) * z. [para(1041(a,2),451(a,1,1)),flip(a)]. 1046 T(x,K(x,y)) = x. [para(1041(a,2),605(a,1,2))]. 1047 ((x * y) / x) * (y \ z) = K(y,x) \ z. [para(1041(a,2),606(a,1,1)),flip(a)]. 1048 T(x \ 1,K(x,y)) = x \ 1. [para(1041(a,2),834(a,1,2))]. 1049 (x / (x * y)) * (y * z) = K(y,x) * z. [para(1041(a,2),841(a,1,1)),flip(a)]. 1050 K(x,y) * x = x * K(x,y). [para(1046(a,1),82(a,1,2))]. 1051 T(x,T(y,x) \ y) = x. [para(983(a,1),1046(a,1,2))]. 1052 (T(x,y) \ x) * y = y * (T(x,y) \ x). [para(1051(a,1),82(a,1,2))]. 1053 K(x,y) = ((y * x) / y) \ x. [para(1043(a,2),358(a,2)),flip(a)]. 1054 K(x,y) / x = x \ K(x,y). [para(1044(a,2),1042(a,2)),flip(a)]. 1055 K(x,y) * (x \ 1) = x \ K(x,y). [para(1048(a,1),327(a,1,2))]. 1056 (x * K(y,x)) \ 1 = x \ K(x,y). [para(1032(a,2),1054(a,1))]. 1057 (x \ 1) / (x \ K(x,y)) = K(y,x). [para(1055(a,1),902(a,1,2))]. 1058 (x * K(y,x)) \ z = (x \ K(x,y)) * z. [para(1056(a,1),318(a,1,1)),flip(a)]. 1059 K(x,y) * (y * z) = ((x * y) / x) * z. [para(19(a,1),1017(a,1,2)),flip(a)]. 1060 T(x,y) * K(z,T(x,y)) = T(x * K(z,x),y). [hyper(24,a,1018,a,b,1024,a),flip(a)]. 1061 T(x * K(x \ y,x),y) = L(x,x \ y,x). [hyper(24,a,221,a,b,1024,a)]. 1062 T(x * K(y,x),x * y) = L(x,y,x). [hyper(24,a,217,a(flip),b,1024,a)]. 1063 (x * K(y,x)) \ z = K(x,y) * (x \ z). [para(1027(a,2),900(a,1))]. 1064 ((x * y) / x) * z = y * (K(x,y) * z). [para(1014(a,2),1028(a,1,1))]. 1065 x \ (K(x,y) * z) = (y / (y * x)) * z. [para(1042(a,1),1031(a,2,1))]. 1066 K(x,y) \ (x * z) = ((y * x) / y) * z. [para(19(a,1),1047(a,1,2)),flip(a)]. 1067 K(x,y) * (x \ z) = (y / (y * x)) * z. [para(20(a,1),1049(a,1,2)),flip(a)]. 1068 K(x,y) * (x * z) = x * (K(x,y) * z). [para(1049(a,1),1045(a,1,2)),flip(a)]. 1069 x * (T(y,x) \ y) = T(x,T(y,x)). [para(1052(a,1),826(a,1))]. 1070 x * K(x,T(y,x)) = T(x,T(y,x)). [para(983(a,2),1069(a,1,2))]. 1071 x / (K(y,z) * (y \ x)) = y * K(z,y). [para(1063(a,1),65(a,1,2))]. 1072 (x \ K(x,y)) * z = K(x,y) * (x \ z). [para(1063(a,1),1058(a,1)),flip(a)]. 1073 K(x,y) * (y * z) = y * (K(x,y) * z). [para(1064(a,1),1059(a,2))]. 1074 K(x,y) \ (x * z) = (K(y,x) * x) * z. [para(1033(a,1),1066(a,2,1))]. 1075 K(x,y) * (x \ (y * x)) = y. [para(1067(a,2),22(a,1))]. 1076 x \ (K(x,y) * z) = K(x,y) * (x \ z). [para(1067(a,2),1065(a,2))]. 1077 K(x,y) * T(y,x) = y. [para(36(a,2),1075(a,1,2))]. 1078 K(x,y / x) = K(x,x * y). [hyper(24,a,1004,a,b,1077,a)]. 1079 K(x,T(y,x)) = K(x,y). [hyper(24,a,985,a,b,1077,a),flip(a)]. 1080 K(x,y) = T(y,x) \ y. [hyper(24,a,298,a,b,1077,a)]. 1081 T(x,y) = K(x,y) * x. [hyper(23,a,901,a,b,1077,a)]. 1082 K(x,T(y,z)) * T(T(y,x),z) = T(y,z). [para(42(a,1),1077(a,1,2))]. 1083 K(x,R(y,z,u)) * R(T(y,x),z,u) = R(y,z,u). [para(46(a,2),1077(a,1,2))]. 1084 L(x \ y,x,K(z,y)) = (K(z,y) \ x) \ T(y,z). [para(1077(a,1),267(a,1,1,2))]. 1085 L(x,y,K(z,u) * u) = L(x,y,T(u,z)). [para(1077(a,1),774(a,1,3,2))]. 1086 K(x,y) = T(x,y) / x. [para(1077(a,1),902(a,1,2)),flip(a)]. 1087 (x * y) * T(y,x) = (y * x) * y. [para(1077(a,1),911(a,1,2)),flip(a)]. 1088 T(x,y) * T(x,y) = x * T(T(x,y),y). [para(1077(a,1),998(a,1,2))]. 1089 T(x,y) * K(y,x) = x. [para(1077(a,1),1040(a,2))]. 1090 (x / (x * y)) * T(x,y) = y \ x. [para(1077(a,1),1065(a,1,2)),flip(a)]. 1091 K(x,T(T(y,x),z)) = K(x,T(y,z)). [para(42(a,1),1079(a,1,2))]. 1092 K(x,x * (y * x)) = K(x,y). [para(1079(a,1),491(a,2))]. 1093 T(x,y) \ (x * z) = K(y,x) * z. [para(1079(a,1),987(a,2,1))]. 1094 T(x,y) * (K(y,x) * z) = x * z. [para(1079(a,1),998(a,1,2,1))]. 1095 K(x,y) * (y \ z) = T(y,x) \ z. [para(1079(a,1),999(a,1,1))]. 1096 T(x,T(y,x)) = x * K(x,y). [para(1079(a,1),1070(a,1,2)),flip(a)]. 1097 T(T(x,y),z) \ T(x,z) = K(y,T(x,z)). [para(42(a,1),1080(a,2,1)),flip(a)]. 1098 K(x,y) * (T(y,x) * z) = y * z. [para(1080(a,2),575(a,1,1))]. 1099 x * (T(x,y) \ z) = K(y,x) * z. [para(1080(a,2),576(a,1,1)),flip(a)]. 1100 K(x,y) = y * (T(y,x) \ 1). [para(1080(a,2),578(a,2)),flip(a)]. 1101 T(x,y) \ 1 = x \ K(y,x). [para(1080(a,2),582(a,1,2)),flip(a)]. 1102 (x * y) / (T(x,z) * y) = K(z,x). [para(1080(a,2),577(a,2))]. 1103 ((x * y) * y) \ ((y * x) * y) = K(y,(y * x) * y). [para(758(a,1),1080(a,2,1)),flip(a)]. 1104 T(x,y) = (x * x) / (x * K(y,x)). [para(1080(a,2),831(a,1,2,2)),flip(a)]. 1105 K(T(x,y),y) = K(x,y). [hyper(24,a,990,a,b,1081,a(flip)),flip(a)]. 1106 (x * T(y,z)) / L(y,K(y,z),x) = x * K(y,z). [para(1081(a,2),99(a,1,1,2))]. 1107 T(x,y) = x * K(x,y). [para(1081(a,2),1050(a,1))]. 1108 K(x,y) = x \ T(x,y). [para(1086(a,2),572(a,1))]. 1109 R(T(x,y),z,u) * K(y,R(x,z,u)) = R(x,z,u). [para(46(a,2),1089(a,1,1))]. 1110 K(R(T(x,y),z,u),y) = K(R(x,z,u),y). [para(46(a,2),1105(a,1,1))]. 1111 x * T(x \ 1,y) = K(x \ 1,y). [para(1105(a,1),995(a,1)),flip(a)]. 1112 T(x * K(y,x),T(y,x)) = x. [para(1105(a,1),1020(a,1,1,2))]. 1113 K(x,y) * T(x,y) = T(T(x,y),y). [para(1105(a,1),1081(a,2,1)),flip(a)]. 1114 K(x,y) * T(K(y,x),z) = K(K(y,x),z). [hyper(23,a,901,a,b,1107,a(flip)),flip(a)]. 1115 (x * y) \ (x * T(y,z)) = L(K(y,z),y,x). [para(1107(a,2),32(a,2,2,2)),flip(a)]. 1116 x * (y * K(y,x)) = y * x. [para(1107(a,1),82(a,1,2))]. 1117 (x * y) * L(K(y,z),y,x) = x * T(y,z). [para(1107(a,2),74(a,2,2))]. 1118 (x \ y) * K(x * y,x) = T(x \ y,x). [para(495(a,1),1107(a,2,2)),flip(a)]. 1119 L(x,y,z * T(z,u)) = L(x,y,K(z,u)). [para(1107(a,2),774(a,1,3,2))]. 1120 x * (K(x,y) * z) = T(x,y) * z. [para(1107(a,2),1030(a,1,1)),flip(a)]. 1121 T(x,y) * K(x,y) = T(T(x,y),y). [para(1105(a,1),1107(a,2,2)),flip(a)]. 1122 T(x,y) \ T(T(x,z),y) = K(T(x,y),z). [para(42(a,1),1108(a,2,2)),flip(a)]. 1123 L(x,y,z) \ L(T(x,u),y,z) = K(L(x,y,z),u). [para(44(a,2),1108(a,2,2)),flip(a)]. 1124 x \ ((x \ y) \ y) = K(x,x * y). [para(249(a,1),1108(a,2,2)),flip(a)]. 1125 T(x,y) * (x \ z) = K(x,y) * z. [para(1108(a,2),562(a,1,1)),flip(a)]. 1126 K(x \ 1,x * y) = x * ((x * y) \ y). [para(1108(a,2),707(a,1))]. 1127 x \ (T(x,y) * z) = K(x,y) * z. [para(1108(a,2),733(a,2,1))]. 1128 K(x / y,y) = K(y * x,y). [para(1108(a,2),1005(a,1))]. 1129 x * K(y,y * x) = y * (x / y). [para(1078(a,1),121(a,1,2))]. 1130 K(x,(y * (x \ 1)) / x) = K(x,T(y,x \ 1)). [para(347(a,1),1078(a,2,2))]. 1131 T(x,T(y,x)) = T(x,y). [para(1096(a,2),1107(a,2)),flip(a)]. 1132 T(T(x,y),T(z,x)) = T(T(x,z),y). [para(1131(a,1),42(a,1,1)),flip(a)]. 1133 T(x,y / x) = T(x,x \ y). [para(84(a,1),1131(a,1,2)),flip(a)]. 1134 (x * y) / T(y,x) = T(x,y). [para(1131(a,1),117(a,1,2))]. 1135 L(T(x,y),T(y,x),x) = T(x,x * T(y,x)). [para(1131(a,1),203(a,1,1))]. 1136 T(x,x * (y * x)) = T(x,y). [para(1131(a,1),247(a,2))]. 1137 T(x,y) / (T(y,x) \ x) = y. [para(1131(a,1),829(a,1,1))]. 1138 T(x,y) \ y = x \ T(y,x). [para(1131(a,1),830(a,1,2)),flip(a)]. 1139 T(x,y * K(x,y)) = T(x,y). [para(1020(a,1),1131(a,1,2)),flip(a)]. 1140 K(x,y) * K(z,K(y,x)) = T(K(y,x),z) \ 1. [hyper(23,a,901,a,b,1100,a(flip)),flip(a)]. 1141 L(T(x,y),y * K(x,y),T(x,y)) = (T(x,y) \ (y * K(x,y))) \ y. [para(1112(a,1),440(a,1,2)),flip(a)]. 1143 K((x * (y \ 1)) / y,y) = K(T(x,y \ 1),y). [para(347(a,1),1128(a,2,1))]. 1144 x / (x / y) = y * K(y * x,y). [para(1128(a,1),1019(a,2,2))]. 1145 T(x,y / x) = T(x,x * y). [para(1133(a,2),246(a,1))]. 1146 T(x,y) * T(y,x) = x * y. [para(1134(a,1),22(a,1,1))]. 1147 x / (y \ T(x,y)) = T(y,x). [para(1138(a,1),65(a,1,2))]. 1148 (T(x,y) \ y) * K(x,x * T(y,x)) = T(y,x) / x. [para(1138(a,2),1001(a,1,1))]. 1149 T(x,(y * (x \ 1)) / x) = T(x,T(y,x \ 1)). [para(347(a,1),1145(a,2,2))]. 1150 (T(x,y) * (T(y,x) * z)) \ ((x * y) * z) = a(T(x,y),T(y,x),z). [para(1146(a,1),28(a,2,2,1)),flip(a)]. 1151 (x * y) \ (T(x,y) * (T(y,x) * z)) = L(z,T(y,x),T(x,y)). [para(1146(a,1),32(a,2,1)),flip(a)]. 1152 T(T(x,y),x \ T(y,x)) = (x \ T(y,x)) \ y. [para(1147(a,1),84(a,1,1))]. 1153 R(x,y,x) * (y * x) = (y * x) * T(x,y). [para(1087(a,2),79(a,2))]. 1154 T(x,y) * ((y * x) / ((x * y) * x)) = K(T(x,y),y * x). [para(1087(a,1),1041(a,2,2,2)),flip(a)]. 1155 K(x,T(y,K(z,T(y,x)))) = K(x,T(y,x)). [para(1038(a,1),1091(a,1,2)),flip(a)]. 1156 L(x,y * K(z,y),u) = L(x,T(y,z),u). [para(1094(a,1),937(a,1,2))]. 1157 T(x,y) * (y * x) = x * (x * y). [para(974(a,1),1094(a,1,2))]. 1158 K(x,y) * (T(x,y) \ z) = x \ z. [hyper(23,a,901,a,b,1095,a),flip(a)]. 1159 K(x,y) * (y \ x) = y \ T(x,y). [para(1095(a,2),1138(a,1))]. 1160 K(x,y) * (x * z) = T(x,y) * z. [hyper(23,a,901,a,b,1098,a),flip(a)]. 1161 K(x,y / x) * ((x \ y) * z) = (y / x) * z. [para(84(a,1),1098(a,1,2,1))]. 1162 R(K(x,y),T(y,x) * z,u) \ 1 = ((T(y,x) * z) * u) / ((y * z) * u). [para(1098(a,1),344(a,1,2,1)),flip(a)]. 1163 x \ (K(y,x) * z) = T(x,y) \ z. [hyper(23,a,20,a,b,1099,a),flip(a)]. 1164 (x * y) * T((x * y) \ x,z) = x * K(y \ 1,z). [para(1111(a,1),762(a,2,2))]. 1165 x \ (y * T(y \ x,z)) = K((x \ y) \ 1,z). [para(1111(a,1),817(a,1)),flip(a)]. 1166 (x * ((K(x,y) * z) * u)) \ ((T(x,y) * z) * u) = a(x,K(x,y) * z,u). [para(1120(a,1),28(a,2,2,1)),flip(a)]. 1167 ((T(x,y) * z) * u) / ((K(x,y) * z) * u) = R(x,K(x,y) * z,u). [para(1120(a,1),34(a,2,1,1)),flip(a)]. 1168 T(x,y) * (T(y,x) * z) = x * (y * z). [para(1098(a,1),1120(a,1,2)),flip(a)]. 1169 L(x,y,z * ((z \ u) * u)) = L(x,y,K(z,z * u)). [para(1124(a,1),865(a,1,3)),flip(a)]. 1170 T(x,y) \ ((x \ T(y,x)) \ y) = K(T(x,y),T(x,y) * y). [para(1138(a,1),1124(a,1,2,1))]. 1171 T(x,y) \ (K(x,y) * z) = x \ z. [hyper(23,a,20,a,b,1125,a),flip(a)]. 1172 K(x,y) * (z * x) = T(x,y) * T(z,x). [para(36(a,2),1125(a,1,2)),flip(a)]. 1173 T(x / y,z) * y = K(x / y,z) * x. [para(66(a,1),1125(a,1,2))]. 1174 T(x,y) * (z / (z * x)) = K(x,y) * K(x,z). [para(1042(a,1),1125(a,1,2))]. 1175 T(x,y) * (T(x,z) \ 1) = K(x,y) * K(z,x). [para(1101(a,2),1125(a,1,2))]. 1176 x \ T(T(x,y),y) = K(x,y) * K(x,y). [para(1121(a,1),1127(a,1,2))]. 1177 T(T(x,x * y),T(z,x)) = T(T(x,z),x \ y). [para(246(a,1),1132(a,1,1))]. 1178 (x / (x / y)) * z = y * (K(y * x,y) * z). [para(1144(a,2),1028(a,1,1))]. 1179 ((x * y) * T(y,x)) \ (y * (y * x)) = K(T(y,x),x * y). [para(1157(a,1),30(a,2,2)),flip(a)]. 1180 (x * (x * y)) \ (T(x,y) * ((y * x) * z)) = L(z,y * x,T(x,y)). [para(1157(a,1),32(a,2,1)),flip(a)]. 1181 K(x,y) * (T(x,y) \ T(x,z)) = K(x,z). [para(1158(a,2),1108(a,2)),flip(a)]. 1182 K(T(x,y \ 1),y) * (x * (y \ 1)) = y \ T(T(x,y \ 1),y). [para(326(a,1),1159(a,1,2))]. 1183 ((T(x,y) * z) * u) / ((x * z) * u) = R(K(x,y),x * z,u). [para(1160(a,1),34(a,2,1,1)),flip(a)]. 1184 (x * y) \ (T(x,z) * y) = T(K(x,z),x * y). [para(1160(a,1),36(a,2,2)),flip(a)]. 1185 L(x,T(y,z) * z,u) = L(x,z * y,u). [para(1160(a,1),943(a,1,2))]. 1186 T(x,y) \ (T(y,x) \ z) = x \ (y \ z). [para(1158(a,1),1163(a,1,2)),flip(a)]. 1187 T(x,y) \ (y * K(x,y)) = x \ y. [para(1036(a,1),1171(a,1,2))]. 1188 x \ (y * K(x,y)) = K(x,y) * (x \ y). [para(1187(a,1),1158(a,1,2)),flip(a)]. 1189 (K(x,y) * (x \ z)) \ ((x \ K(x,y)) * (z * u)) = L(u,z,x \ K(x,y)). [para(1072(a,1),32(a,2,1)),flip(a)]. 1190 (K(x,y) * z) \ (y * (K(x,y) * z)) = L(T(y,z),z,K(x,y)). [para(1073(a,1),106(a,1,2))]. 1191 K(x,y) \ (x * z) = (K(x,y) \ x) * z. [para(900(a,2),1074(a,2,1))]. 1192 L(x,y,(z * u) / z) = L(x,y,T(u,z)). [para(1033(a,2),1085(a,1,3))]. 1193 T(x,y) * K(y,T(x,z)) = K(z,T(x,y)) * T(x,z). [para(1097(a,1),1099(a,1,2))]. 1194 L(x,y,(z / (u * u)) * (u \ (z * (u \ 1)))) = L(x,y,K(z / (u * u),u)). [para(403(a,1),1119(a,1,3,2))]. 1195 (x * T(y,x)) \ (T(y,z) * x) = L(K(T(y,x),z),T(y,x),x). [para(1122(a,1),180(a,1,1)),flip(a)]. 1196 K(x,T(y,K(z,T(y,x)))) = K(x,y). [para(1155(a,2),1079(a,1))]. 1197 K(x,y) * T(T(y,x),K(z,T(y,x))) = T(y,K(z,T(y,x))). [para(1196(a,1),1082(a,1,1))]. 1198 (x * (y * z)) / (T(y,x) * z) = T(x,y). [hyper(24,a,22,a,b,1168,a),flip(a)]. 1199 (x \ y) * (T(x,y / x) * z) = (y / x) * (x * z). [para(84(a,1),1168(a,1,1))]. 1200 (T(x / y,z) * y) / x = K(x / y,z). [hyper(24,a,22,a,b,1173,a(flip)),flip(a)]. 1201 K(x / y,z) * x = y * T(y \ x,z). [para(1173(a,1),139(a,1))]. 1202 (R(x,y,z) * (K(x,u) * K(x,u))) / T(T(x,u),u) = x \ R(x,y,z). [para(1176(a,1),536(a,1,1,2))]. 1203 L(x,y,K(y,z)) = x. [hyper(23,a,798,a,b,1191,a(flip)),flip(a)]. 1204 L(x,y,T(z,y) \ z) = x. [para(983(a,1),1203(a,1,3))]. 1205 L(x,y,T(z,y) * z) = x. [para(1204(a,1),776(a,1)),flip(a)]. 1206 L(x,y,z * T(z,y)) = x. [para(116(a,1),1205(a,1,3))]. 1207 ((x * T(x,y)) * y) \ ((x * T(x,y)) * (y * z)) = z. [para(1206(a,1),32(a,1)),flip(a)]. 1208 L(x,y,T(z * u,z) / z) = L(x,y,T((z \ u) * z,z)). [para(138(a,1),1192(a,1,3,1))]. 1209 (x * (R(y,z,u) * w)) / (R(T(y,x),z,u) * w) = T(x,R(y,z,u)). [para(46(a,2),1198(a,1,2,1))]. 1210 (x * (y * (a(T(y,x),z,z) * u))) / (R(T(y,x),z,z) * u) = T(x,y). [para(966(a,1),1198(a,1,2))]. 1211 (x * T(x \ y,z)) / y = K(y / x,z). [para(139(a,1),1200(a,1,1))]. 1212 K((x * y) / x,z) * (x * y) = x * T(y,z). [para(19(a,1),1201(a,2,2,1))]. 1213 x \ (y * T(y \ x,z)) = T(K(x / y,z),x). [para(1201(a,1),36(a,2,2)),flip(a)]. 1214 ((x * y) * T((x * y) \ ((z * x) * y),u)) / ((z * x) * y) = K(R(z,x,y),u). [para(34(a,2),1211(a,2,1))]. 1215 T(x * K(x * y,x),y) = L(x,x \ y,x). [para(495(a,1),1061(a,1,1,2))]. 1216 L(T(x,y),T(y,x),x) = T(x,y * x). [para(82(a,1),1135(a,2,2))]. 1217 (x * y) * T(y,y * (x * y)) = R(y,x,y) * (x * y). [para(1136(a,2),1153(a,2,2)),flip(a)]. 1218 T(x * K(x * y,x),y) = L(x,x * y,x). [para(1215(a,2),312(a,1))]. 1219 T(x / (x / y),x) = L(y,y * x,y). [para(1144(a,2),1218(a,1,1))]. 1220 K(x,T(y,x \ 1)) = K(x,y / (x * x)). [para(401(a,1),1130(a,1,2)),flip(a)]. 1221 K(T(x,y \ 1),y) = K(x / (y * y),y). [para(401(a,1),1143(a,1,1)),flip(a)]. 1222 T(x,T(y,x \ 1)) = T(x,y / (x * x)). [para(401(a,1),1149(a,1,2)),flip(a)]. 1223 K(((x * y) \ x) \ 1,z) = (x * y) \ (x * T(y,z)). [para(19(a,1),1165(a,1,2,2,1)),flip(a)]. 1224 T(x,y) \ T(x,z) = K(x,z) * K(y,x). [para(1175(a,1),581(a,1)),flip(a)]. 1225 K(x,y) * (K(x,z) * K(y,x)) = K(x,z). [para(1224(a,1),1181(a,1,2))]. 1226 K(x,y) * K(z,x) = K(z,x) * K(x,y). [hyper(23,a,901,a,b,1225,a)]. 1229 T(T(x,y),x \ z) = T(T(x,y),x * z). [para(1177(a,1),1132(a,1))]. 1230 T(T(x,y),x * T(y,x)) = (x \ T(y,x)) \ y. [para(1229(a,1),1152(a,1))]. 1231 (x / (x / y)) * x = y * ((y \ x) * y). [para(981(a,1),1178(a,2,2))]. 1232 T(x * y,x) = (y / (y / x)) * y. [para(1231(a,2),138(a,1)),flip(a)]. 1233 T(x * y,x) / y = y / (y / x). [hyper(24,a,22,a,b,1232,a(flip)),flip(a)]. 1234 ((x / y) / x) * T(y * x,y) = x. [hyper(23,a,359,a,b,1232,a(flip)),flip(a)]. 1235 L(x,T(y * z,y),u) = L(x,z / y,u). [para(1232(a,2),877(a,1,2))]. 1236 x \ T(x * y,y) = x / (x / y). [para(1233(a,1),754(a,1)),flip(a)]. 1237 x / T(y * x,y) = (x / y) / x. [hyper(24,a,22,a,b,1234,a),flip(a)]. 1238 T(x * y,y) = x * (x / (x / y)). [para(1236(a,1),20(a,1,2)),flip(a)]. 1239 T(x * (y \ x),y \ x) = x * (x / y). [para(65(a,1),1238(a,2,2,2))]. 1240 T(K(x / y,z),x) = K((x \ y) \ 1,z). [para(1213(a,1),1165(a,1))]. 1241 K((x \ (y \ x)) \ 1,z) = T(K(y,z),x). [para(65(a,1),1240(a,1,1,1)),flip(a)]. 1242 K((T(x,y) \ (T(y,x) \ x)) \ 1,z) = T(K(y,z),T(x,y)). [para(1137(a,1),1240(a,1,1,1)),flip(a)]. 1243 K(T(x \ 1,y) \ 1,z) = T(K(x,z),y). [para(325(a,2),1241(a,1,1,1))]. 1244 K(T((x \ 1) \ 1,y * y),z) = T(K(x,z),y * y). [para(655(a,1),1243(a,1,1))]. 1245 (x \ T(y,x)) \ y = T(T(x,y),y * x). [para(82(a,1),1230(a,1,2)),flip(a)]. 1246 x / L(y,T(x,y),y) = y \ (x * K(y,x)). [para(1156(a,1),1025(a,1,2))]. 1247 x / L(y,T(x,y),y) = K(y,x) * (y \ x). [para(1246(a,2),1188(a,1))]. 1248 L(x \ y,x,K(z,y)) = (K(y,z) * x) \ T(y,z). [para(900(a,1),1084(a,2,1))]. 1249 R(K(x,y),T(x,y) * z,u) \ 1 = R(K(y,x),x * z,u). [para(1098(a,1),906(a,1,2)),flip(a)]. 1250 L(x,y * (y * (z * y)),u) = L(x,z \ (y \ 1),u). [para(51(a,1),929(a,1,2))]. 1251 ((x * y) \ K(x,y)) \ z = K(y,x) * ((x * y) * z). [para(933(a,2),900(a,1))]. 1252 (x * a(x,y,z)) * u = x * (a(x,y,z) * u). [para(948(a,1),946(a,1))]. 1253 a(x,y,z) * (x * u) = x * (a(x,y,z) * u). [para(1252(a,1),772(a,1)),flip(a)]. 1254 x * (a(x,y,z) * (x \ u)) = a(x,y,z) * u. [para(20(a,1),1253(a,1,2)),flip(a)]. 1255 L(x,y * (z \ y),u) = L(x,T(z,y),u). [para(20(a,1),953(a,1,2,1))]. 1256 L(x,T(y \ 1,z),u) = L(x,T(y,z),u). [para(1255(a,1),883(a,2))]. 1257 K(x,y) / (y * x) = (y * x) \ K(x,y). [para(972(a,1),971(a,1,2))]. 1258 L(x,y,T(z \ u,z)) = L(x,y,z / u). [para(1118(a,1),1012(a,1,3))]. 1259 L(x,y,T(z * u,z)) = L(x,y,z / u). [para(1258(a,1),818(a,1)),flip(a)]. 1260 (T(x,y) \ y) * K(x,y * x) = T(y,x) / x. [para(82(a,1),1148(a,1,2,2))]. 1261 L(x,y,K(z,z * u)) = L(x,y,a(z,u,u)). [para(1169(a,1),837(a,1))]. 1262 L(x,y,K(z * u,z)) = L(x,y,a(z,u,u)). [para(1261(a,1),909(a,1)),flip(a)]. 1263 L(x,y,a(z,u * z,u * z)) = L(x,y,K(z,u)). [para(1092(a,1),1261(a,1,3)),flip(a)]. 1264 K(x,T(y,z)) * T(T(y,x),K(x,T(y,z))) = K(z,T(y,x)) * T(y,z). [para(1193(a,1),82(a,2))]. 1265 (x \ y) * (T(x,x * y) * z) = (y / x) * (x * z). [para(1145(a,1),1199(a,1,2,1))]. 1266 (x * (T(x,y) * y)) \ ((x * T(x,y)) * (y * z)) = z. [para(722(a,1),1207(a,1,1))]. 1267 L(K(x,y),x,z) = K(((z * x) \ z) \ 1,y). [para(1223(a,2),1115(a,1)),flip(a)]. 1268 K(L(x \ 1,x,y) \ 1,z) = L(K(x,z),x,y). [para(142(a,2),1267(a,2,1,1)),flip(a)]. 1269 K(T(x,y * y),z) = T(K(x,z),y * y). [para(156(a,1),1244(a,1,1,1))]. 1270 K(T(x,y * y),z) \ 1 = T(K(x,z) \ 1,y * y). [para(1269(a,2),655(a,1,1))]. 1271 L(x,y \ (z \ 1),u) = L(x,y * z,u). [para(1250(a,1),875(a,1))]. 1273 L(x,y * (z \ 1),u) = L(x,y * z,u). [para(1271(a,1),876(a,1)),flip(a)]. 1274 (x \ y) * ((y / x) * (x * z)) = ((x \ y) * y) * z. [para(1265(a,1),253(a,1,2))]. 1275 (x * (T(x,y) * y)) \ (x * (T(x,y) * (y * z))) = z. [para(722(a,1),1266(a,1,2))]. 1276 T(K(x,y) \ 1,z * z) = K(y,T(x,z * z)). [para(1270(a,1),897(a,1))]. 1277 K(x,T(y,z * z)) = T(K(x,y),z * z). [para(897(a,1),1276(a,1,1)),flip(a)]. 1278 K(T(x,y * y),z) = K(x,T(z,y * y)). [para(1277(a,2),1269(a,2))]. 1279 L(L(x,y,T(z,y)),T(z,y) * y,z) = x. [para(1275(a,1),174(a,1)),flip(a)]. 1280 L(L(x,y,T(z,y)),y * z,z) = x. [para(1279(a,1),1185(a,1)),flip(a)]. 1281 L(L(x,y,T(y \ z,y)),z,y \ z) = x. [para(20(a,1),1280(a,1,2))]. 1282 L(x,y * (z * y),y) = L(x,z,T(y,z)). [para(1280(a,1),303(a,1,1))]. 1283 L(x,T(y,z) * z,T(y,z)) = L(x,z * y,y). [para(308(a,1),1280(a,1,1)),flip(a)]. 1284 L(x,T(y,z),z) = L(x,y,T(z,y)). [para(1280(a,1),314(a,1,1))]. 1285 L(x,T(y,y * z),y * z) = L(x,y,y / z). [para(1284(a,2),1259(a,1))]. 1286 L(L(x,y,y / z),z,y \ z) = x. [para(1258(a,1),1281(a,1,1))]. 1287 L(L(x,y,y / z),z,y * z) = x. [para(1286(a,1),776(a,1)),flip(a)]. 1288 L(x,y,z / y) = L(x,y,z * y). [para(304(a,1),1287(a,1,1)),flip(a)]. 1289 L(x \ (x / y),x,y * x) = y \ 1. [para(445(a,1),1287(a,1,1))]. 1290 L(x,y,y / z) = L(x,y,z * y). [para(806(a,1),1287(a,1,1)),flip(a)]. 1291 L(x,y,(z * y) * y) = L(x,y,z). [para(21(a,1),1288(a,1,3)),flip(a)]. 1292 L(x \ 1,x,y * x) = y \ (y / x). [para(1288(a,1),144(a,1))]. 1293 L(x,x,y * x) = y \ (y / (x \ 1)). [para(1288(a,1),432(a,1))]. 1294 x * L(y,z,x * z) = (x / z) * (z * y). [para(1288(a,1),173(a,1,2))]. 1295 (x \ 1) \ L(T(y \ (y / x),z),y,x * y) = K(L(y \ (y / x),y,x * y),z). [para(1289(a,1),1123(a,1,1))]. 1296 ((x * y) * y) \ (x * y) = x \ (x / y). [para(1292(a,1),142(a,1)),flip(a)]. 1297 L(x,y \ 1,T(y * z,y \ 1)) = L(x,(y * z) * z,y * z). [para(322(a,1),1282(a,1,2,2)),flip(a)]. 1298 x * K(L(y \ 1,y,x * y) \ 1,z) = (x / y) * (y * K(y,z)). [para(1268(a,2),1294(a,1,2))]. 1299 x \ L(x,x * y,y) = a(T(y,x),x,x). [para(1283(a,1),452(a,1,2))]. 1300 L(x,y * z,T(z,y)) = L(x,y * z,z). [para(1283(a,1),1185(a,1)),flip(a)]. 1301 T(L(K(x,y),z,K(y,x)),z) = (K(y,x) * z) \ z. [hyper(23,a,82,a,b,910,a(flip)),flip(a)]. 1302 L(x,y * x,x) = R(x,y,x). [hyper(24,a,217,a(flip),b,1217,a(flip)),flip(a)]. 1303 R(x,y / x,x) = L(x,y,x). [para(22(a,1),1302(a,1,2)),flip(a)]. 1304 L(T(x,y),z * x,x) = T(R(x,z,x),y). [para(1302(a,1),44(a,2,1))]. 1305 L(x,y,x) * ((y / x) * x) = (x * (y / x)) * x. [para(1303(a,1),79(a,1,1))]. 1306 L(T(x,y),z * x,x) = R(T(x,y),z,x). [para(1304(a,2),46(a,2)),flip(a)]. 1307 L(x,y,x) * y = (x * (y / x)) * x. [para(22(a,1),1305(a,1,2))]. 1308 T(L(x,y,x) * y,x) = ((y / x) * x) * x. [para(1307(a,2),758(a,1,1))]. 1309 T(L(x,y,x) * y,x) = y * x. [para(22(a,1),1308(a,2,1))]. 1310 (L(x,y,x) * y) * x = x * (y * x). [para(1309(a,1),82(a,1,2)),flip(a)]. 1311 L(R(x,y,x),y,x) = x. [hyper(24,a,184,a,b,1310,a(flip)),flip(a)]. 1312 R(L(x,y,x),y,x) = x. [hyper(24,a,79,a,b,1310,a(flip)),flip(a)]. 1313 R(x,x \ y,x) = L(x,y,x). [para(1311(a,1),302(a,1,1)),flip(a)]. 1314 L(x,x * y,x) = R(x,y,x). [para(1311(a,1),303(a,1,1))]. 1315 R(x,x * y,x) = L(x,y,x). [para(1311(a,1),308(a,1,1)),flip(a)]. 1316 x \ T(y * x,y) = R(y,x,y). [para(1314(a,1),316(a,1)),flip(a)]. 1317 R(x,y,x) * (x \ y) = (x \ y) * T(x,y). [para(1314(a,1),559(a,1,1))]. 1318 T(x * K(x * y,x),y) = R(x,y,x). [para(1314(a,1),1218(a,2))]. 1319 T(x / (x / y),x) = R(y,x,y). [para(1314(a,1),1219(a,2))]. 1320 L(x,y,x) \ x = x \ R(x,y,x). [para(1315(a,1),622(a,1,1))]. 1321 x * R(y,x,y) = T(y * x,y). [para(1316(a,1),20(a,1,2))]. 1322 T(x,R(y,x,y)) = T(x,x / (x / y)). [para(1319(a,1),1131(a,1,2))]. 1323 (x / T(y * x,y)) * T(x,R(y,x,y)) = R(y,x,y) \ x. [para(1321(a,1),1090(a,1,1,2))]. 1324 T(x,y) * K(x * y,T(x,y)) = R(x,y,x). [para(1318(a,1),1060(a,2))]. 1325 T(x,y) * K(y * T(x,y),T(x,y)) = R(x,y,x). [para(82(a,2),1324(a,1,2,1))]. 1326 K(x,y) * (K(y,x) / (x * y)) = (x * y) \ 1. [para(907(a,2),912(a,1))]. 1327 K(x,y) * ((x * y) \ K(y,x)) = (x * y) \ 1. [para(1257(a,1),1326(a,1,2))]. 1328 (x * y) \ K(x,y) = (y * x) \ 1. [para(1327(a,1),941(a,1)),flip(a)]. 1329 K(x,y) * ((y * x) * z) = ((x * y) \ 1) \ z. [para(1328(a,1),1251(a,1,1)),flip(a)]. 1330 K(x,y) * ((y * x) * z) = (x * y) * z. [para(1329(a,2),330(a,1))]. 1331 ((x * y) * z) / ((y * x) * z) = K(x,y). [hyper(24,a,22,a,b,1330,a),flip(a)]. 1332 R(K(x,y),y * x,z) = K(x,y). [para(1331(a,1),977(a,1)),flip(a)]. 1333 R(K(x,T(y,x)),T(y,x) * x,z) = K(x,y). [para(1332(a,2),1079(a,1))]. 1335 R(K(x,y),T(y,x) * x,z) = K(x,y). [para(1079(a,1),1333(a,1,1))]. 1336 ((T(x,y) * y) * z) / ((K(y,x) * (T(x,y) * y)) * z) = K(y,x) \ 1. [para(1335(a,1),344(a,2,1))]. 1337 (x * L(x \ 1,y,z)) \ u = x \ (L(x \ 1,y,z) \ u). [para(216(a,1),924(a,1,1))]. 1338 L(x,y * (y * (z * (y * u))),w) = L(x,z \ (y \ u),w). [para(51(a,1),928(a,1,2))]. 1339 T(x,y) * (R(x,y,x) \ 1) = K(T(x,y),y * x). [para(344(a,1),1154(a,1,2))]. 1340 R(x,y,x) \ T(x,y) = K(T(x,y),y * x). [para(1339(a,1),548(a,1)),flip(a)]. 1341 T(x,y) \ T(T(x,y),y * x) = K(T(x,y),T(x,y) * y). [para(1245(a,1),1170(a,1,2))]. 1342 (((x * y) * T(y,x)) \ (y * y)) * x = K(T(y,x),x * y). [para(1179(a,1),391(a,1)),flip(a)]. 1343 T(x,K(y,T(x,z))) = K(z,x) * T(x,z). [para(1038(a,1),1197(a,1,2)),flip(a)]. 1345 T(x,K(y,T(x,z))) = x. [para(1343(a,2),1077(a,1))]. 1346 T(T(x,y),K(z,T(x,u))) = T(x,y). [para(1345(a,1),42(a,1,1)),flip(a)]. 1350 L(x,y,T(z * u,z) / z) = L(x,y,R(u,z,z)). [para(1208(a,2),864(a,1))]. 1351 T(K(x,y),T(z,x)) = K((z \ (x \ z)) \ 1,y). [para(1186(a,1),1242(a,1,1,1)),flip(a)]. 1352 T(K(x,y),T(z,x)) = T(K(x,y),z). [para(1351(a,2),1241(a,1))]. 1353 T(x,y) * T(K(y,z),x) = K(y,z) * T(x,y). [para(1352(a,1),82(a,1,2))]. 1354 K(x,y) * (K(y,z) * x) = K(y,z) * T(x,y). [para(1353(a,1),1172(a,2))]. 1355 (K(x,y) * T(z,x)) / L(z,K(x,y),K(z,x)) = K(z,x) * K(x,y). [para(1354(a,1),99(a,1,1))]. 1356 ((x / y) / x) * T(x,R(y,x,y)) = R(y,x,y) \ x. [para(1237(a,1),1323(a,1,1))]. 1357 L(x \ 1,y,z) \ (x \ u) = x \ (L(x \ 1,y,z) \ u). [para(1337(a,1),803(a,1)),flip(a)]. 1358 L(x,y \ (z \ u),w) = L(x,y * (z * u),w). [para(1338(a,1),875(a,1))]. 1360 L(x,y * (z \ u),w) = L(x,y * (z * u),w). [para(1358(a,1),876(a,1)),flip(a)]. 1361 L(x,y * (z * (z * u)),w) = L(x,y * u,w). [para(19(a,1),1360(a,1,2,2)),flip(a)]. 1362 L(x,(y \ z) * (z \ y),u) = L(x,(z \ y) * (y * z),u). [para(384(a,1),1360(a,1,2))]. 1363 L(x,y * R(z,z * u,w),v5) = L(x,y * (R(z,u,w) \ 1),v5). [para(615(a,1),1361(a,1,2,2))]. 1364 K(T(x,y),T(x,y) * y) = K(T(x,y),y * x). [para(1341(a,1),1108(a,2)),flip(a)]. 1365 (((x * y) * x) \ (x * x)) * y = K(T(x,y),y * x). [para(1087(a,1),1342(a,1,1,1))]. 1366 K(T(x,y),y * x) = K(x,x * y). [para(1365(a,1),408(a,1))]. 1367 R(x,y,x) \ T(x,y) = K(x,x * y). [para(1366(a,1),1340(a,2))]. 1368 K(x,x * y) \ T(x,y) = R(x,y,x). [para(1367(a,1),734(a,1,1))]. 1369 K(x * y,x) * T(x,y) = R(x,y,x). [para(1368(a,1),900(a,1)),flip(a)]. 1370 R(x,y,x) / T(x,y) = K(x * y,x). [hyper(24,a,22,a,b,1369,a),flip(a)]. 1371 (x \ (L(x \ 1,x,x / y) \ 1)) * (y \ (y / x)) = x \ 1. [para(1357(a,1),521(a,1,1))]. 1372 R(x,y \ 1,y) \ a(x,y,y) = x \ 1. [para(961(a,2),476(a,1))]. 1374 R(x,y,y) \ a(x,y,y) = x \ 1. [para(717(a,1),1372(a,1,1))]. 1375 (x * y) \ (x * (y * z)) = L(z,T(y,x),T(x,y)). [para(1168(a,1),1151(a,1,2))]. 1376 L(x,T(y,z),T(z,y)) = L(x,y,z). [para(1375(a,1),32(a,2)),flip(a)]. 1377 L(T(x,y),y,K(z,x)) = T(x,K(z,x) * y). [para(1190(a,1),36(a,2)),flip(a)]. 1378 (x \ (L(x \ 1,x,y * x) \ 1)) * (y \ (y / x)) = x \ 1. [para(1290(a,1),1371(a,1,1,2,1))]. 1379 ((x \ y) * z) \ (x \ u) = ((x * y) * z) \ (x * u). [para(794(a,1),201(a,1))]. 1380 (x * ((x \ y) * y)) \ z = ((x * y) * y) \ (x * z). [para(1379(a,1),893(a,2))]. 1381 (x * ((x \ y) * y)) \ y = x \ (x / y). [para(1380(a,2),1296(a,1))]. 1382 x / (y \ (y / x)) = y * ((y \ x) * x). [para(1381(a,1),65(a,1,2))]. 1383 (x \ (x / y)) \ y = x * ((x \ y) * y). [para(1382(a,1),872(a,1)),flip(a)]. 1384 x * L(x,y * x,y) = (y \ (y / x)) \ x. [para(1383(a,2),435(a,2))]. 1385 (x * L(x,y * x,y)) / x = (y \ (y / x)) \ 1. [para(1384(a,2),320(a,1,1))]. 1386 L(x,y * x,y) = (y \ (y / x)) \ 1. [para(1385(a,1),218(a,1)),flip(a)]. 1387 x \ ((y \ (y / x)) \ 1) = a(y,x,x). [para(1386(a,1),452(a,1,2))]. 1388 (x \ (x / y)) \ 1 = y * a(x,y,y). [para(1386(a,1),453(a,1))]. 1389 (x \ 1) \ (L(x,x,y * x) \ 1) = a(y,x \ 1,x \ 1). [para(1293(a,2),1387(a,1,2,1))]. 1390 (x \ (x / y)) \ z = (y * a(x,y,y)) * z. [para(1388(a,1),318(a,1,1)),flip(a)]. 1391 K(x,(x * x) / (y \ (y / z))) = K(x,z * a(y,z,z)). [para(1388(a,1),492(a,2,2))]. 1392 L(x \ 1,x,y * x) \ 1 = x * a(y,x,x). [para(1292(a,2),1388(a,1,1))]. 1393 (x \ (x * a(y,x,x))) * (y \ (y / x)) = x \ 1. [para(1392(a,1),1378(a,1,1,2))]. 1394 a(x,y,y) * (x \ (x / y)) = y \ 1. [para(19(a,1),1393(a,1,1))]. 1396 a(K(x,y),z,z) * (K(y,x) \ (K(y,x) / z)) = z \ 1. [para(905(a,1),1394(a,1,1))]. 1397 a(x,y,y) * (x / y) = x * (y \ 1). [para(1394(a,1),1254(a,1,2)),flip(a)]. 1398 (x * (y \ 1)) / (x / y) = a(x,y,y). [hyper(24,a,22,a,b,1397,a),flip(a)]. 1399 (x / y) * (y * (x \ 1)) = a(y,x,x). [para(1398(a,1),669(a,1)),flip(a)]. 1400 a(x / y,y,y \ 1) = a(x,y,y). [para(1399(a,1),592(a,2))]. 1401 a(x * (y * y),y \ 1,(y \ 1) \ 1) = a(x * y,y \ 1,y \ 1). [para(400(a,1),1400(a,1,1))]. 1402 K(x,(y \ (y / z)) \ 1) = K(x,z * a(y,z,z)). [para(1391(a,1),492(a,1)),flip(a)]. 1403 a(K(x,y),z,z) * (K(x,y) * (K(y,x) / z)) = z \ 1. [para(900(a,1),1396(a,1,2))]. 1404 K(x,y) * (a(K(x,y),z,z) * (K(y,x) / z)) = z \ 1. [para(1403(a,1),1253(a,1)),flip(a)]. 1405 R(K(x,y),z,z) * (K(y,x) / z) = z \ 1. [para(1404(a,1),966(a,1)),flip(a)]. 1406 x * (L(x,x,y * x) \ 1) = a(y,x \ 1,x \ 1). [para(1389(a,1),330(a,1)),flip(a)]. 1407 a(x,y \ 1,y \ 1) = L(y,y,x * y) \ y. [para(1406(a,1),471(a,1))]. 1408 a(x * y,y \ 1,y \ 1) = L(y,y,x) \ y. [para(1291(a,1),1407(a,2,1))]. 1409 (x * (y \ z)) \ (x * (y \ (z * u))) = L(L(u,z,y),y * z,x). [para(813(a,2),876(a,1))]. 1410 (x * y) * (z / (x * (y * z))) = x \ R(x,y,z). [para(853(a,1),537(a,1))]. 1411 L(x,y \ R(y,z,u),y * z) = x. [para(1410(a,1),852(a,1,2))]. 1412 L(x,y * R(y,z,u),y * z) = x. [para(1411(a,1),876(a,1)),flip(a)]. 1413 L(x,y * R(y,y * z,u),z) = x. [para(1412(a,1),774(a,1)),flip(a)]. 1414 K(T(x,y \ 1),y) * (x * (y \ 1)) = T(x,y) * (y \ 1). [para(1182(a,2),329(a,1))]. 1415 K(T(x,y \ 1),y) = K(x,y). [hyper(24,a,1160,a,b,1414,a)]. 1416 (x * (y \ 1)) / (T(x,y) * (y \ 1)) = K(y,T(x,y \ 1)). [para(1414(a,1),902(a,1,2))]. 1418 K(x / (y * y),y) = K(x,y). [para(1415(a,1),1221(a,1)),flip(a)]. 1419 K(x,T(y,x \ 1)) = K(x,y). [para(1416(a,1),1102(a,1))]. 1420 K(x \ 1,T(y,x)) = K(x \ 1,y). [para(156(a,1),1419(a,1,2,2))]. 1421 T(x,T(y,x \ 1)) = x * K(x,y). [para(1419(a,1),1107(a,2,2))]. 1423 K(x,y / (x * x)) = K(x,y). [para(1419(a,1),1220(a,1)),flip(a)]. 1424 K(x,R(y / x,x,x)) = K(x,y * x). [para(80(a,2),1423(a,1,2))]. 1425 ((x \ 1) * T(y,x)) / (x \ 1) = T(y,x) * K(x \ 1,y). [para(1420(a,1),1014(a,2,2))]. 1426 T(x,T(y,x \ 1)) = T(x,y). [para(1421(a,2),1107(a,2)),flip(a)]. 1427 T(x \ 1,T(y,x)) = T(x \ 1,y). [para(156(a,1),1426(a,1,2,2))]. 1428 T(x,y / (x * x)) = T(x,y). [para(1426(a,1),1222(a,1)),flip(a)]. 1429 L(x,T(y,z),T(T(z,y \ 1),y)) = L(x,y,T(z,y \ 1)). [para(1426(a,1),1376(a,1,2))]. 1430 T(x,(y * x) * x) = T(x,R(y,x,x)). [para(34(a,2),1428(a,1,2)),flip(a)]. 1431 L(x,T(y \ 1,z),T(T(z,y),y \ 1)) = L(x,y \ 1,T(z,y)). [para(1427(a,1),1376(a,1,2))]. 1432 (x \ T(y,x)) / (x \ 1) = T(y,x) * K(x \ 1,y). [para(318(a,1),1425(a,1,1))]. 1433 T(x,y) * K(y \ 1,x) = T(x,y * y). [para(1432(a,1),486(a,1))]. 1434 L(x,T(y,z),T(T(z,y),y \ 1)) = L(x,y,T(z,y \ 1)). [para(42(a,1),1429(a,1,3))]. 1435 L(x,R(y,z,z),y * z) = L(x,y \ 1,T(y * z,y \ 1)). [para(1297(a,2),938(a,1)),flip(a)]. 1436 L(x,R(y,z,z),y * z) = L(x,y,T(y * z,y \ 1)). [para(1435(a,2),887(a,1))]. 1437 L(x,y * R(z,z * u,w),v5) = L(x,y * R(z,u,w),v5). [para(1363(a,2),1273(a,1))]. 1438 L(x,y * R(y,z,u),z) = x. [para(1437(a,1),1413(a,1))]. 1439 L(x,y * (z * R(z,y,u)),y) = x. [para(1438(a,1),303(a,1,1))]. 1440 L(x,y \ R(y \ 1,z,u),z) = x. [para(318(a,1),1438(a,1,2))]. 1441 (x * (y \ R(y,x,z))) * u = x * ((y \ R(y,x,z)) * u). [para(1438(a,1),888(a,1,2))]. 1442 a(x,x * (y * R(y,x,z)),u) = 1. [hyper(38,a,1439,a)]. 1443 L(x,y * R(y \ 1,z,u),z) = x. [para(1440(a,1),876(a,1)),flip(a)]. 1444 L(x,a(y,z,z),z) = x. [para(960(a,1),1443(a,1,2))]. 1445 x / (a(y,x,x) \ 1) = x * a(y,x,x). [para(1444(a,1),145(a,1,2))]. 1446 (x * a(y,x,x)) * z = x * (a(y,x,x) * z). [para(1444(a,1),74(a,1,2))]. 1447 K(x,(y \ (y / z)) \ 1) = K(x,z / (a(y,z,z) \ 1)). [para(1445(a,2),1402(a,2,2))]. 1448 (x \ (x / y)) \ z = y * (a(x,y,y) * z). [para(1446(a,1),1390(a,2))]. 1449 L(x * (a(y,x,x) * z),y * (y / x),y) = (y / x) \ (y * z). [para(1448(a,1),311(a,1,1))]. 1450 (x * (y \ R(y,x,z))) * u = x * (R(y,x,z) * (y \ u)). [para(532(a,1),1441(a,2,2))]. 1451 L(x,T(y,z),T(T(z,y),y \ 1)) = L(x,y \ 1,T(z,y)). [para(1431(a,1),1256(a,1)),flip(a)]. 1452 L(x,y \ 1,T(z,y)) = L(x,y,T(z,y \ 1)). [para(1451(a,1),1434(a,1))]. 1453 L(x,y,T(z,y \ 1)) = L(x,y,T(z,y)). [para(1452(a,1),887(a,1))]. 1454 L(x,R(y,z,z),y * z) = L(x,y,T(y * z,y)). [para(1453(a,1),1436(a,2))]. 1455 L(x,R(y,z,z),y * z) = L(x,y,y / z). [para(1454(a,2),1259(a,1))]. 1456 L(x,R(y,z,z),y * z) = L(x,y,z * y). [para(1455(a,2),1290(a,1))]. 1457 L(T(x,y),y * K(x,y),T(x,y)) = (x \ y) \ y. [para(1187(a,1),1141(a,2,1))]. 1458 (x * (y * z)) \ ((x * y) * z) = a(T(x,y),T(y,x),z). [para(1168(a,1),1150(a,1,1))]. 1459 a(T(x,y),T(y,x),z) = a(x,y,z). [para(1458(a,1),28(a,2)),flip(a)]. 1460 a(T(x,y),T(T(y,x),x),z) = a(x,T(y,x),z). [para(1131(a,1),1459(a,1,1))]. 1461 x \ (y \ (y \ (T(y,x) * ((x * y) * z)))) = L(z,x * y,T(y,x)). [para(1180(a,1),443(a,1)),flip(a)]. 1462 x * K(y * a(x,y,y),z) = (x / y) * (y * K(y,z)). [para(1392(a,1),1298(a,1,2,1))]. 1463 x * K(y * a(x,y,y),z) = (x / y) * T(y,z). [para(1107(a,2),1462(a,2,2))]. 1464 x \ (y \ (K(y,x) * ((x * y) * z))) = L(z,x * y,T(y,x)). [para(1127(a,1),1461(a,1,2,2))]. 1465 x \ (y \ ((y * x) * z)) = L(z,x * y,T(y,x)). [para(1330(a,1),1464(a,1,2,2))]. 1466 L(x,y * z,T(z,y)) = L(x,z * y,z). [para(1465(a,1),309(a,1))]. 1467 L(x,y * z,z) = L(x,z * y,z). [para(1466(a,1),1300(a,1)),flip(a)]. 1468 L(L(x,y,z),y * z,z) = x. [para(1467(a,2),303(a,1))]. 1469 L(L(x,y * z,z),y,z) = x. [para(1467(a,2),308(a,1,1))]. 1470 x \ L(x,x * y,y) = a(y,x,x). [para(1467(a,2),452(a,1,2))]. 1471 L(x,y * (y / z),y) = L(x,z,y). [para(1467(a,1),877(a,1))]. 1472 L(x,(y * z) * z,y * z) = L(x,T(y,z),y * z). [para(1467(a,1),878(a,1))]. 1473 L(x,T(y,z),z) = L(x,y,z). [para(1468(a,1),314(a,1,1))]. 1474 L(L(x,y,z * y),z,z * y) = x. [para(875(a,1),1469(a,1,1))]. 1475 L(T(x,y),y,x) = T(x,y * x). [para(1473(a,1),1216(a,1))]. 1476 K(x,y) * (x \ y) = y / L(x,y,x). [para(1473(a,1),1247(a,1,2)),flip(a)]. 1477 L(x,y,y / z) = L(x,y,y * z). [para(1473(a,1),1285(a,1)),flip(a)]. 1478 (x * T(y,x)) \ (T(y,z) * x) = L(K(T(y,x),z),y,x). [para(1473(a,1),1195(a,2))]. 1479 T(x,y * x) = T(x,x * y). [para(1475(a,1),203(a,1))]. 1480 K(x,y) * L(x,y,x) = T(x,x * y). [para(1479(a,1),955(a,2))]. 1481 T(x,x * y) * K(y * x,x) = x. [para(1479(a,1),1089(a,1,1))]. 1482 T(x,x * (y * x)) = T(x,R(y,x,x)). [para(1479(a,1),1430(a,1))]. 1483 x \ L(x,y,x * y) = a(x * y,x,x). [para(875(a,1),1470(a,1,2))]. 1484 x \ L(x,T(y,x),y * x) = a(y * x,x,x). [para(878(a,1),1470(a,1,2))]. 1485 a(T(x,y),y,y) = a(x,y,y). [para(1470(a,1),1299(a,1)),flip(a)]. 1486 L(x * (a(y,x,x) * z),x,y) = (y / x) \ (y * z). [para(1471(a,1),1449(a,1))]. 1487 L(x,y,y * x) = x * a(y * x,x,x). [para(454(a,1),1474(a,1,1))]. 1488 L(x,x,x * y) = y \ (y / (x \ 1)). [para(1477(a,1),807(a,1))]. 1489 K(x * y,y) = K(y * x,y). [hyper(23,a,1089,a,b,1481,a)]. 1490 T(x * K(x * y,x),y * x) = x. [para(1489(a,1),1020(a,1,1,2))]. 1491 x / (x / y) = y * K(x * y,y). [para(1489(a,2),1144(a,2,2))]. 1492 R(x,y,x) / T(x,y) = K(y * x,x). [para(1489(a,2),1370(a,2))]. 1493 T(x / (x / y),x * y) = y. [para(1144(a,2),1490(a,1,1))]. 1494 T(x * y,x / (x / y)) = T(x * y,y). [para(1493(a,1),1131(a,1,2)),flip(a)]. 1495 (x / (x / y)) \ T(x * y,x / (x / y)) = y \ (x * y). [para(1493(a,1),1138(a,1,1)),flip(a)]. 1496 R(x,y,x) = y / (y / T(x,y)). [para(1491(a,2),1325(a,1)),flip(a)]. 1497 R(x,y,x) \ y = y / T(x,y). [para(1496(a,2),66(a,1,1))]. 1498 (T(x,y) \ y) * K(T(x,y),T(x,y) * y) = R(x,y,x) \ y. [para(1497(a,2),1001(a,2))]. 1499 ((x / y) / x) * T(x,R(y,x,y)) = x / T(y,x). [para(1497(a,1),1356(a,2))]. 1500 K(x,y) = (y \ x) / (x / L(y,x,y)). [para(1476(a,1),902(a,1,2)),flip(a)]. 1501 (x * y) / (K(x,y) * L(x,y,x)) = R(x,x * y,x) \ (x * y). [para(1480(a,2),1497(a,2,2)),flip(a)]. 1502 T(x,R(y,x,x)) = T(x,y). [para(1482(a,1),1136(a,1))]. 1503 K(x,R(y,x,x)) = x \ T(x,y). [para(1502(a,1),1108(a,2,2))]. 1504 K(x,R(y,x,x)) = K(x,y). [para(1503(a,2),1108(a,2)),flip(a)]. 1505 K(x,y / x) = K(x,y * x). [para(1504(a,1),1424(a,1))]. 1506 K(x,y * x) = K(x,x * y). [para(1505(a,1),1078(a,1))]. 1507 ((x * y) * y) \ ((y * x) * y) = K(y,y * (y * x)). [para(1506(a,1),1103(a,2))]. 1508 (T(x,y) \ y) * K(x,x * y) = T(y,x) / x. [para(1506(a,1),1260(a,1,2))]. 1509 K(T(x,y),y * T(x,y)) = K(T(x,y),y * x). [para(1506(a,2),1364(a,1))]. 1510 T(x,y) \ R(x,y,x) = K(y * x,x). [para(1492(a,1),693(a,1)),flip(a)]. 1511 K(x,y) * (y \ R(y,x,y)) = K(x * y,y). [para(1510(a,1),1095(a,2))]. 1512 K(T(x,y),y * x) = K(T(x,y),x * y). [para(82(a,1),1509(a,1,2)),flip(a)]. 1513 K(T(x,y),x * y) = K(x,x * y). [para(1512(a,1),1366(a,1))]. 1514 L(x,R(y,z,z),y * z) = L(x,T(y,z),y * z). [para(1472(a,1),938(a,1)),flip(a)]. 1515 L(x,T(y,z),y * z) = L(x,y,z * y). [para(1514(a,1),1456(a,1))]. 1516 x \ L(x,y,x * y) = a(y * x,x,x). [para(1515(a,1),1484(a,1,2))]. 1517 a(x * y,y,y) = a(y * x,y,y). [para(1516(a,1),1483(a,1))]. 1518 L(x * (a(y,x,x) * z),x,y) = (x / y) * (y * z). [para(1486(a,2),358(a,1))]. 1519 K(x,y) = ((y * x) * x) \ ((x * y) * x). [para(1507(a,2),490(a,1)),flip(a)]. 1520 (x * (y * x)) \ ((x * y) * x) = K(y * x,x) * K(x,y). [para(1519(a,2),941(a,1,2)),flip(a)]. 1521 (x * y) \ (T(x,z) * y) = L(K(T(x,y),z),x,y). [para(82(a,1),1478(a,1,1))]. 1522 L(K(T(x,y),z),x,y) = T(K(x,z),x * y). [para(1521(a,1),1184(a,1))]. 1523 (x / (x / y)) \ T(x * y,x / (x / y)) = T(x,y). [para(1495(a,2),36(a,2)),flip(a)]. 1524 (x / (x / y)) \ T(x * y,y) = T(x,y). [para(1494(a,1),1523(a,1,2))]. 1525 ((x / y) / x) * T(x * y,y) = T(x,y). [para(1524(a,1),358(a,1)),flip(a)]. 1526 (x / y) * T(y * (x \ y),x \ y) = T(y,x \ y). [para(65(a,1),1525(a,1,1,1))]. 1527 L(x,y,z * (((u / w) / u) * T(u,w))) = L(x,y,z * T(u * w,w)). [para(1525(a,1),868(a,1,3,2,2))]. 1528 (x / y) * (y * (y / x)) = T(y,x \ y). [para(1239(a,1),1526(a,1,2))]. 1529 T(x,x / y) = T(x,y \ x). [para(1528(a,1),369(a,1)),flip(a)]. 1530 T(x,R(y,x,y)) = T(x,(x / y) \ x). [para(1529(a,1),1322(a,2))]. 1531 T(x,R(y,x,y)) = T(x,y). [para(66(a,1),1530(a,2,2))]. 1532 ((x / y) / x) * T(x,y) = x / T(y,x). [para(1531(a,1),1499(a,1,2))]. 1533 K(x * y,y) * K(y,x) = a(y,x,y). [para(1520(a,1),28(a,2)),flip(a)]. 1534 K(x,y) * K(y * x,x) = a(x,y,x). [para(1533(a,1),1226(a,2))]. 1535 K(x * y,x) * K(x,y) = a(x,y,x). [para(1489(a,1),1533(a,1,1))]. 1536 K(x,y) * a(y,x,y) = K(x * y,y). [hyper(23,a,901,a,b,1534,a),flip(a)]. 1537 K(x,y) * K(x * y,x) = a(x,y,x). [para(1489(a,1),1534(a,1,2))]. 1538 (((x \ y) * x) / y) * K(x,y) = a(x,y,x). [para(982(a,2),1535(a,1,1))]. 1539 x \ R(x,y,x) = a(x,y,x). [hyper(23,a,1511,a,b,1536,a),flip(a)]. 1540 x * a(x,y,x) = R(x,y,x). [para(1539(a,1),20(a,1,2))]. 1541 L(x,y,x) \ x = a(x,y,x). [para(1539(a,1),1320(a,2))]. 1542 a(x,y,x) * L(x,y,x) = x. [para(1541(a,1),520(a,1,1))]. 1543 (x * y) / L(L(y,z,y),a(y,z,y),x) = x * a(y,z,y). [para(1542(a,1),99(a,1,1,2))]. 1544 (T(x,y) \ y) * K(T(x,y),y * T(x,y)) = R(x,y,x) \ y. [para(1506(a,2),1498(a,1,2))]. 1545 (T(x,y) \ y) * K(T(x,y),x * y) = R(x,y,x) \ y. [para(82(a,1),1544(a,1,2,2))]. 1546 (T(x,y) \ y) * K(x,x * y) = R(x,y,x) \ y. [para(1513(a,1),1545(a,1,2))]. 1547 R(x,y,x) \ y = T(y,x) / x. [para(1546(a,1),1508(a,1))]. 1548 T(x,y) / y = x / T(y,x). [para(1547(a,1),1497(a,1))]. 1549 (x / T(y,x)) * y = T(x,y). [para(1548(a,1),22(a,1,1))]. 1550 (x / y) * (y * K(x,y)) = T(x,y * K(x,y)). [para(1020(a,1),1549(a,1,1,2))]. 1551 T(x,y) = (x / y) * (y * K(x,y)). [para(1550(a,2),1139(a,1)),flip(a)]. 1552 (x / y) * T(y,x) = x * K(y,x). [hyper(23,a,359,a,b,1551,a(flip)),flip(a)]. 1553 (x * (y \ 1)) * T(L(y,y,x),x) = x * K(L(y,y,x),x). [para(915(a,1),1552(a,1,1))]. 1554 (x * (y \ 1)) * L(T(y,x),y,x) = x * K(L(y,y,x),x). [para(44(a,2),1553(a,1,2))]. 1555 x * K(L(y,y,x),x) = x * (y \ T(y,x)). [para(1554(a,1),945(a,1))]. 1556 x * K(L(y,y,x),x) = x * K(y,x). [para(1108(a,2),1555(a,2,2))]. 1557 T(x * K(y,x),L(y,y,x)) = x. [para(1556(a,1),1020(a,1,1))]. 1558 T(x,L(y,y,x)) = T(x,y). [para(1557(a,1),1023(a,1,1)),flip(a)]. 1559 (x * y) / (K(x,y) * L(x,y,x)) = L(x,y,x) \ (x * y). [para(1315(a,1),1501(a,2,1))]. 1560 (x * y) / (K(x,y) * L(x,y,x)) = (L(x,y,x) \ x) * y. [para(1559(a,2),524(a,1))]. 1561 (x * y) / T(x,x * y) = (L(x,y,x) \ x) * y. [para(1480(a,1),1560(a,1,2))]. 1562 (L(x,y,x) \ x) * y = T(x * y,x) / x. [para(1561(a,1),1548(a,2)),flip(a)]. 1563 T(x * y,x) / x = a(x,y,x) * y. [para(1541(a,1),1562(a,1,1)),flip(a)]. 1564 R(K(x,y),K(y,x) * z,u) \ K(x,y) = K(y,x) * R(K(x,y),z,u). [para(923(a,2),900(a,1))]. 1565 x * (y * (R(y,y * (x \ 1),z) \ (x \ z))) = L(z,y * x,y). [para(318(a,1),957(a,1,2,2,2))]. 1566 x * (R(y,x \ 1,z) * (y \ (x \ z))) = L(z,y * x,y). [para(637(a,1),1565(a,1,2))]. 1567 x * (R(y,x,z) * (y \ (x \ z))) = L(z,y * x,y). [para(717(a,1),1566(a,1,2,1))]. 1568 R(x * (K(x,y) * K(x,y)),z,u) / T(T(x,y),y) = x \ R(x,z,u). [para(705(a,2),1202(a,1,1))]. 1569 K(x,T(y,z)) * T(y,x) = K(z,T(y,x)) * T(y,z). [para(1346(a,1),1264(a,1,2))]. 1570 (K(x,T(y,z)) * T(y,x)) / L(y,K(y,z),K(z,T(y,x))) = K(z,T(y,x)) * K(y,z). [para(1569(a,1),1106(a,1,1))]. 1572 ((T(x,y) * y) * z) / ((x * y) * z) = K(y,x) \ 1. [para(1098(a,1),1336(a,1,2,1))]. 1574 a(x * (y * y),y \ 1,y) = a(x * y,y \ 1,y \ 1). [para(156(a,1),1401(a,1,3))]. 1575 L(x,y,z * T(u * w,w)) = L(x,y,z * (u / T(w,u))). [para(1532(a,1),1527(a,1,3,2)),flip(a)]. 1576 L(x,y,z * (T(u,w) / w)) = L(x,y,z * T(u * w,w)). [para(1548(a,2),1575(a,2,3,2)),flip(a)]. 1577 (R(K(x,y),z,u) \ 1) \ K(y,x) = K(x,y) * R(K(y,x),z,u). [para(904(a,1),1564(a,1,1))]. 1578 R(K(x,y),z,u) * K(y,x) = K(x,y) * R(K(y,x),z,u). [para(1577(a,1),330(a,1)),flip(a)]. 1579 K(x,y) * R(K(y,x),T(x,y) * z,u) = R(K(y,x),x * z,u) \ K(y,x). [para(1249(a,1),1577(a,1,1)),flip(a)]. 1580 R(T(x,y) * K(x,y),z,u) / T(T(x,y),y) = x \ R(x,z,u). [para(1120(a,1),1568(a,1,1,1))]. 1581 R(T(T(x,y),y),z,u) / T(T(x,y),y) = x \ R(x,z,u). [para(1121(a,1),1580(a,1,1,1))]. 1582 T(T(x,y),y) \ R(T(T(x,y),y),z,u) = x \ R(x,z,u). [para(1581(a,1),478(a,1)),flip(a)]. 1583 (x * y) * T((x * y) \ (x * z),u) = (x * y) * L(T(y \ z,u),y,x). [para(44(a,2),764(a,1,2)),flip(a)]. 1584 (x * y) * R((x * y) \ x,z,u) = (x * y) * L(R(y \ 1,z,u),y,x). [para(48(a,1),765(a,1,2)),flip(a)]. 1585 (x \ 1) * L((x \ 1) \ y,z,u) = L(y * x,z,u) / x. [para(720(a,1),766(a,1,1,1)),flip(a)]. 1586 (x \ 1) * L(x * y,z,u) = L(y * x,z,u) / x. [para(330(a,1),1585(a,1,2,1))]. 1587 L(x * y,z,u) / y = y \ L(y * x,z,u). [para(1586(a,1),318(a,1))]. 1588 (x \ y) \ L((x \ y) * x,z,u) = L(y,z,u) / (x \ y). [para(20(a,1),1587(a,1,1,1)),flip(a)]. 1589 (K(x,y) * (x \ z)) \ (K(x,y) * (x \ (z * u))) = L(u,z,x \ K(x,y)). [para(1072(a,1),1189(a,1,2))]. 1590 (x * y) * T((x * y) \ (x * z),u) = x * (y * T(y \ z,u)). [para(1583(a,2),74(a,1))]. 1591 (x * y) * R((x * y) \ x,z,u) = x * (y * R(y \ 1,z,u)). [para(1584(a,2),74(a,1))]. 1592 (x * y) * R((x * y) \ x,z,u) = x * (y \ R(y,z,u)). [para(635(a,1),1591(a,2,2))]. 1593 (x / y) * (y * R(((y \ x) * x) \ (y \ x),z,u)) = x \ R(x,z,u). [hyper(23,a,1274,a,b,1592,a(flip)),flip(a)]. 1594 (x / y) * (y * R(((y * x) * x) \ (y * x),z,u)) = x \ R(x,z,u). [para(1379(a,1),1593(a,1,2,2,1))]. 1595 (x / y) * (y * R(y \ (y / x),z,u)) = x \ R(x,z,u). [para(1296(a,1),1594(a,1,2,2,1))]. 1596 ((x \ y) / y) * (y * R(y \ x,z,u)) = (x \ y) \ R(x \ y,z,u). [para(65(a,1),1595(a,1,2,2,1,2))]. 1597 (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). [para(99(a,1),1595(a,1,2,2,1,2))]. 1598 (x \ 1) * (y * R(y \ x,z,u)) = (x \ y) \ R(x \ y,z,u). [para(320(a,1),1596(a,1,1))]. 1599 (x \ y) \ R(x \ y,z,u) = x \ (y * R(y \ x,z,u)). [para(1598(a,1),318(a,1))]. 1601 (x * y) \ R(x * y,z,u) = x \ (y * R(y \ x,z,u)). [para(1599(a,1),750(a,1)),flip(a)]. 1602 L(L(x,y,z),z * y,K(z,u)) = L(x,y,z \ K(z,u)). [para(1589(a,1),1409(a,1)),flip(a)]. 1603 L(L(x,y,z),z * y,K(z,u)) = L(x,y,z * K(z,u)). [para(1602(a,2),776(a,1))]. 1604 L(L(x,y,z),z * y,K(z,u)) = L(x,y,T(z,u)). [para(1107(a,2),1603(a,2,3))]. 1605 L(L(x,y,z),z * y,T(z,u)) = L(x,z * (z * y),K(z,u)). [para(303(a,1),1604(a,1,1)),flip(a)]. 1606 L(L(x,y,z),z * y,T(z,u)) = L(x,y,K(z,u)). [para(1605(a,2),875(a,1))]. 1608 (x * (y * x)) \ R(x * (z * x),u,w) = T(y,x) \ T(R(z,u,w),x). [para(36(a,2),701(a,2,2))]. 1609 (x * (y * x)) \ R(x * (z * x),u,w) = T(y,x) \ R(T(z,x),u,w). [para(46(a,2),1608(a,2,2))]. 1610 x \ ((y * x) * R((y * x) \ x,z,u)) = T(y,x) \ R(T(y,x),z,u). [para(1609(a,1),1601(a,1)),flip(a)]. 1611 L(x,y,z * (u \ (u \ (u \ (z * (u \ 1)))))) = L(x,y,K(z / (u * u),u)). [para(602(a,1),1194(a,1,3))]. 1612 L(x,y,z * (u \ ((u \ (u \ z)) * (u \ 1)))) = L(x,y,K(z / (u * u),u)). [para(285(a,1),1611(a,1,3,2,2))]. 1613 L(x,y,z * (u * ((u \ (u \ z)) * (u \ 1)))) = L(x,y,K(z / (u * u),u)). [para(1612(a,1),867(a,1)),flip(a)]. 1614 L(x,y,K(z / (u * u),u)) = L(x,y,z * (u \ (z * (u \ 1)))). [para(265(a,1),1613(a,1,3,2)),flip(a)]. 1615 L(x,y,K(z / (u * u),u)) = L(x,y,z * (u * (z * (u \ 1)))). [para(1614(a,2),867(a,1))]. 1616 L(x,y,K(z / (u * u),u)) = L(x,y,z * T(z,u \ 1)). [para(347(a,1),1615(a,2,3,2))]. 1617 L(x,y,K(z / (u * u),u)) = L(x,y,K(z,u \ 1)). [para(1616(a,2),1119(a,1))]. 1618 L(x,y,K(z,u \ 1)) = L(x,y,K(z,u)). [para(1418(a,1),1617(a,1,3)),flip(a)]. 1619 L(x,y,K(z,u \ 1)) = L(x,y,K(u,z)). [para(1618(a,2),909(a,1))]. 1620 (x * (x * (y * (z * u)))) \ ((x * (x * (y * z))) * u) = a(x * (x * y),z,u). [para(51(a,1),91(a,1,2,1))]. 1621 (x * y) * R(L(y \ z,y,x),u,w) = (x * y) * R((x * y) \ (x * z),u,w). [para(473(a,1),224(a,1))]. 1622 (x * y) * R((x * y) \ (z * y),u,w) = (R(z / x,u,w) * x) * y. [para(474(a,1),185(a,1))]. 1623 (x * y) * R((x * y) \ (z * y),u,w) = (x * R(x \ z,u,w)) * y. [para(224(a,1),1622(a,2,1))]. 1624 ((x * y) * ((y * x) * z)) \ (((x * y) * (y * x)) * (z * u)) = L(u,z,K(y,x)). [para(894(a,1),832(a,1,1))]. 1625 ((x * y) * T(R(T(z,x * y),x,y),u)) / ((z * x) * y) = K(R(z,x,y),u). [para(549(a,1),1214(a,1,1,2,1))]. 1626 ((x * y) * R(T(T(z,x * y),u),x,y)) / ((z * x) * y) = K(R(z,x,y),u). [para(46(a,2),1625(a,1,1,2))]. 1627 (R(T(x,y),z,u) * (z * u)) / ((x * z) * u) = K(R(x,z,u),y). [para(222(a,1),1626(a,1,1))]. 1628 ((T(x,y) * z) * u) / ((x * z) * u) = K(R(x,z,u),y). [para(79(a,1),1627(a,1,1))]. 1629 R(K(x,y),x * z,u) = K(R(x,z,u),y). [para(1628(a,1),1183(a,1)),flip(a)]. 1630 K(R(x,y,z),y) = K(y,x) \ 1. [para(1628(a,1),1572(a,1))]. 1631 R(K(x,y),T(y,x) * z,u) \ 1 = K(R(y,z,u),x). [para(1628(a,1),1162(a,2))]. 1632 K(R(x,y,z),y) = K(x,y). [para(1630(a,2),897(a,1))]. 1633 T(x,R(y,x,z)) = (x * x) / (x * K(y,x)). [para(1632(a,1),1104(a,2,2,2))]. 1634 K(R(x,x \ y,z),u) = R(K(x,u),y,z). [para(20(a,1),1629(a,1,2)),flip(a)]. 1635 R(K(x,y),x * (z / (z * x)),u) = K(x,y). [para(450(a,1),1629(a,2,1))]. 1636 R(K(x,y),T(x,y) * z,u) = K(R(T(x,y),z,u),y). [para(1105(a,1),1629(a,1,1))]. 1637 K(R(x,x * y,z),u) = R(K(x,u),y,z). [para(629(a,1),1634(a,1,1))]. 1638 R(K(x,y),z,x) = K(L(x,z,x),y). [para(1313(a,1),1634(a,1,1)),flip(a)]. 1639 K(x,R(y,y * z,u)) = R(K(y,x),z,u) \ 1. [para(1637(a,1),897(a,1,1)),flip(a)]. 1640 R(K(x,y),K(x,z) * u,w) = K(R(x,T(x,z) * u,w),y). [para(1120(a,1),1637(a,1,1,2)),flip(a)]. 1641 K(R(x,T(x,y) * z,u),y) = R(K(T(x,y),y),z,u). [para(1637(a,1),1110(a,1)),flip(a)]. 1642 T(x,R(y,x,z)) = T(x,y). [para(1633(a,2),1104(a,2)),flip(a)]. 1643 R(x,y,z) * T(y,x) = y * R(x,y,z). [para(1642(a,1),82(a,1,2))]. 1647 T(x,y) \ (x * R(y,x,z)) = T(R(y,x,z),T(x,y)). [para(1643(a,1),36(a,2,2)),flip(a)]. 1648 R(K(x,y),K(x,z),u) = K(x,y). [para(1041(a,2),1635(a,1,2))]. 1649 R(K(x,y),K(z,x),u) = K(x,y). [para(1648(a,1),908(a,1)),flip(a)]. 1650 (K(x,y) * K(z,x)) * u = K(x,y) * (K(z,x) * u). [para(1649(a,1),79(a,1,1)),flip(a)]. 1651 R(K(x,y),T(y,x) * z,u) = K(R(y,z,u),x) \ 1. [para(1631(a,1),156(a,1,1)),flip(a)]. 1652 R(K(x,y),T(x,y) * z,u) = K(R(x,z,u),y). [para(1636(a,2),1110(a,1))]. 1653 R(K(x,y),y * z,u) = K(R(y,z,u),x) \ 1. [para(1652(a,1),1249(a,1,1)),flip(a)]. 1654 R(K(x,y),y * z,u) = K(x,R(y,z,u)). [para(1653(a,2),897(a,1))]. 1656 R(K(x,y),x * z,u) * K(y,x) = K(x,y) * K(y,R(x,z,u)). [para(1654(a,1),1578(a,2,2))]. 1657 K(R(x,T(x,y) * z,u),y) = R(K(x,y),z,u). [para(1105(a,1),1641(a,2,1))]. 1658 T(R(x,y,z),T(y,x)) = K(x,y) * R(x,y,z). [para(1647(a,1),1093(a,1))]. 1659 R(T(x,T(y,x)),y,z) = K(x,y) * R(x,y,z). [para(1658(a,1),46(a,2))]. 1660 K(x,y) * R(x,y,z) = R(T(x,y),y,z). [para(1131(a,1),1659(a,1,1)),flip(a)]. 1661 T(x,y) \ R(T(x,y),y,z) = x \ R(x,y,z). [para(1660(a,1),1171(a,1,2))]. 1662 (x \ y) \ R(T(y / x,x),x,z) = (y / x) \ R(y / x,x,z). [para(84(a,1),1661(a,1,1))]. 1663 L(x,K(y,z),K(z,u)) = x. [hyper(23,a,74,a,b,1650,a),flip(a)]. 1664 L(x,K(y,z),K(u,z)) = x. [para(1663(a,1),909(a,1)),flip(a)]. 1665 L(x,K(y,z),K(u,y)) = x. [para(1664(a,1),921(a,1)),flip(a)]. 1666 (K(x,y) * T(z,x)) / z = K(z,x) * K(x,y). [para(1665(a,1),1355(a,1,2))]. 1667 R(K(x,y),T(y,x) * z,u) = K(x,R(y,z,u)). [para(1651(a,2),897(a,1))]. 1668 R(K(x,y),y * z,u) \ K(x,y) = K(y,x) * K(x,R(y,z,u)). [para(1667(a,1),1579(a,1,2)),flip(a)]. 1669 R(K(x,y),K(x,y) * z,u) = R(K(x,y),z,u). [para(1640(a,2),1657(a,1))]. 1670 R(K(x,y),z,u) \ 1 = R(K(y,x),z,u). [para(1669(a,1),906(a,1)),flip(a)]. 1671 R(K(x,y),z,u) \ K(x,y) = K(x,y) * R(K(y,x),z,u). [para(1670(a,1),543(a,1,2)),flip(a)]. 1672 K(x,R(y,y * z,u)) = R(K(x,y),z,u). [para(1670(a,1),1639(a,2))]. 1673 K(R(x,y,z),u) * K(u,x) = K(x,u) * K(u,R(x,y,z)). [para(1629(a,1),1656(a,1,1))]. 1674 K(x,y) * K(R(y,z,u),x) = K(y,x) * K(x,R(y,z,u)). [para(1673(a,1),1226(a,2))]. 1675 (x / y) \ R(x / y,y,z) = (y \ x) \ R(y \ x,y,z). [para(84(a,1),1662(a,1,2,1)),flip(a)]. 1676 (x \ y) \ R(x \ y,x,z) = (x / y) * R(y / x,x,z). [para(1675(a,1),358(a,1))]. 1677 x \ (y * R(y \ x,x,z)) = (x / y) * R(y / x,x,z). [para(1676(a,1),1599(a,1)),flip(a)]. 1678 x \ ((y \ x) * R((y \ x) \ x,x,z)) = y * R((y \ x) / x,x,z). [para(65(a,1),1677(a,2,1))]. 1679 x \ (R(y,x,z) * (y \ x)) = y * R((y \ x) / x,x,z). [para(225(a,1),1678(a,1,2))]. 1680 x * R((x \ y) / y,y,z) = T(x \ R(x,y,z),y). [para(1679(a,1),539(a,1))]. 1681 T(x \ R(x,y,z),y) = x * R(x \ 1,y,z). [para(320(a,1),1680(a,1,2,1)),flip(a)]. 1683 T(x \ R(x,y,z),y) = x \ R(x,y,z). [para(1681(a,2),635(a,1))]. 1684 (x * (y \ R(y,x,z))) / x = y \ R(y,x,z). [para(1683(a,1),105(a,1,1,2))]. 1685 T(x \ R(x,y,z),x * (y * z)) = T(a(x,y,z),y). [para(1683(a,1),740(a,1,1))]. 1686 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). [para(1684(a,1),1518(a,2,1))]. 1687 T(a(x,y,z),y) = a(x,y,z). [para(1685(a,1),739(a,2)),flip(a)]. 1688 a(x,y,z) * y = y * a(x,y,z). [para(1687(a,1),82(a,1,2)),flip(a)]. 1689 a(x,y \ 1,z) * (y \ 1) = y \ a(x,y \ 1,z). [para(1687(a,1),326(a,1,2)),flip(a)]. 1690 T(x * y,x) / x = y * a(x,y,x). [para(1688(a,1),1563(a,2))]. 1691 L(x,y,z * (T(u * z,u) / u)) = L(x,y,a(u,z,u)). [para(1690(a,2),774(a,1,3,2))]. 1692 L(x,y,z * a(u,z,u)) = L(x,y,R(z,u,u)). [para(1690(a,1),1350(a,1,3))]. 1693 L(x,y,z * T((u * z) * u,u)) = L(x,y,a(u,z,u)). [para(1691(a,1),1576(a,1)),flip(a)]. 1694 L(x,y,z * ((z * u) * u)) = L(x,y,a(u,z,u)). [para(758(a,1),1693(a,1,3,2))]. 1695 L(x,y,a(z,u,u)) = L(x,y,a(u,z,u)). [para(1694(a,1),861(a,1)),flip(a)]. 1696 (x * (x * (y * (z * u)))) \ (x * (x * ((y * z) * u))) = a(x * (x * y),z,u). [para(51(a,1),1620(a,1,2))]. 1697 (x * y) * R((x * y) \ (x * z),u,w) = (x * y) * L(R(y \ z,u,w),y,x). [para(48(a,1),1621(a,1,2)),flip(a)]. 1698 ((x * y) * ((y * x) * z)) \ ((x * y) * ((y * x) * (z * u))) = L(u,z,K(y,x)). [para(894(a,1),1624(a,1,2))]. 1699 a(x * (x * y),z,u) = (y * (z * u)) \ ((y * z) * u). [para(1696(a,1),212(a,1))]. 1700 a(x * (x * y),z,u) = a(y,z,u). [para(1699(a,2),28(a,2)),flip(a)]. 1702 a(x \ y,z,u) = a(x * y,z,u). [para(20(a,1),1700(a,1,1,2)),flip(a)]. 1703 a((x / y) * x,z,u) = a(y,z,u). [para(22(a,1),1700(a,1,1,2))]. 1704 a(x * (y * x),z,u) = a(T(y,x),z,u). [para(82(a,1),1700(a,1,1,2))]. 1705 a((x * y) * (x * (y * z)),u,w) = a(L(z,y,x),u,w). [para(74(a,1),1700(a,1,1,2))]. 1706 a(x * ((x \ y) * z),u,w) = a(x * ((x * y) * z),u,w). [para(89(a,1),1700(a,1,1,2)),flip(a)]. 1707 a((x \ y) * z,u,w) = a((x * y) * z,u,w). [para(89(a,1),1700(a,1,1)),flip(a)]. 1708 a((x * x) / y,z,u) = a(y \ 1,z,u). [para(263(a,1),1700(a,1,1))]. 1709 a(x * L(x,y * x,y),z,u) = a(a(y,x,x),z,u). [para(453(a,2),1700(a,1,1,2))]. 1710 a(R(x \ 1,y,y),z,u) = a(x * a(x,y,y),z,u). [para(960(a,1),1700(a,1,1,2)),flip(a)]. 1711 a(K(x,y) * y,z,u) = a(T(y,x),z,u). [para(1077(a,1),1700(a,1,1,2))]. 1712 a(x * T(x,y),z,u) = a(K(x,y),z,u). [para(1107(a,2),1700(a,1,1,2))]. 1713 ((x \ y) * (T(x,x * y) * z)) \ (y * z) = a(x * y,T(x,x * y),z). [para(1702(a,1),255(a,2))]. 1714 a(K(x \ 1,x * y),z,u) = a(x \ ((x * y) \ y),z,u). [para(1126(a,2),1702(a,2,1)),flip(a)]. 1715 a((x * (x * y)) * (x * z),u,w) = a(y \ (x \ z),u,w). [para(282(a,1),1703(a,1,1,1))]. 1716 a((x * x) / y,z,u) = a(y,z,u). [para(1708(a,2),611(a,1))]. 1717 a(x / (y * y),z,u) = a(x,z,u). [para(1716(a,1),612(a,1)),flip(a)]. 1718 a(R(x,x * y,z),u,w) = a(R(x,y,z),u,w). [para(616(a,1),1716(a,1,1))]. 1719 a(x * K(y,x),z,u) = a(T(x,y),z,u). [para(1104(a,2),1716(a,1,1)),flip(a)]. 1720 a(x * (y * y),z,u) = a(x,z,u). [para(21(a,1),1717(a,1,1)),flip(a)]. 1721 a((x * y) * y,z,u) = a(R(x,y,y),z,u). [para(34(a,2),1717(a,1,1)),flip(a)]. 1722 a(x / (y \ 1),z,u) = a(x / y,z,u). [para(398(a,1),1717(a,1,1)),flip(a)]. 1723 ((x * (y * y)) * (z * u)) \ (((x * (y * y)) * z) * u) = a(x,z,u). [para(1720(a,1),28(a,1)),flip(a)]. 1724 a(T(T(x,y),y),z,u) = a(x,z,u). [para(985(a,1),1711(a,1,1)),flip(a)]. 1725 a((x / (y * y)) * (y \ (x * (y \ 1))),z,u) = a(K(x / (y * y),y),z,u). [para(403(a,1),1712(a,1,1,2))]. 1726 a(x / (x * y),z,u) = a(T(y,x),z,u). [para(1719(a,1),1022(a,2))]. 1727 a((x \ 1) / y,z,u) = a(y / x,z,u). [para(1722(a,1),612(a,1)),flip(a)]. 1728 a(x / T(y * x,y),z,u) = a(T(R(y,x,y),x),z,u). [para(1321(a,1),1726(a,1,1,2))]. 1729 a(x * (y * x),x,x) = a(R(y,x,x),x,x). [para(1721(a,1),1517(a,1)),flip(a)]. 1730 a(R(x,y,y),y,y) = a(T(x,y),y,y). [para(1729(a,1),1704(a,1))]. 1731 a(R(x,y,y),y,y) = a(x,y,y). [para(1730(a,2),1485(a,1))]. 1732 R(R(x,y,y) \ 1,y,y) = R(x,y,y) \ a(x,y,y). [para(1731(a,1),967(a,2,2))]. 1733 R(R(x,y,y),R(x,y,y) * y,y) = a(x,y,y) \ R(x,y,y). [para(1731(a,1),968(a,2,1))]. 1734 a(x * ((x \ y) * y),z,u) = a(a(x,y,y),z,u). [para(435(a,1),1709(a,1,1))]. 1735 a(R(x \ 1,y,y),z,u) = a(R(x,y,y),z,u). [para(963(a,1),1710(a,2,1))]. 1736 R(R(x,y,y) \ 1,y,y) = x \ 1. [para(1732(a,2),1374(a,1))]. 1737 R((x * y) \ 1,y,y) = (x / (y \ 1)) \ 1. [para(720(a,1),1736(a,1,1,1))]. 1739 R((x * y) \ 1,y,y) = (y \ 1) / x. [para(1737(a,2),343(a,1))]. 1740 (x \ 1) / (y / x) = R(y \ 1,x,x). [para(22(a,1),1739(a,1,1,1)),flip(a)]. 1741 (((x * y) \ 1) * y) * y = ((y \ 1) / x) * (y * y). [para(1739(a,1),79(a,1,1)),flip(a)]. 1742 R(x \ 1,y,y) \ 1 = (x / y) / (y \ 1). [para(1740(a,1),343(a,1,1))]. 1743 a((x \ 1) / ((y / x) \ 1),z,u) = a(R(y \ 1,x,x),z,u). [para(1740(a,1),1722(a,2,1))]. 1744 R(x,x * y,y) = (x / y) / (y \ 1). [para(1742(a,1),633(a,2))]. 1745 K(R(x,x * y,y),z) * (x / y) = (y \ 1) * T((y \ 1) \ (x / y),z). [para(1744(a,2),1201(a,1,1,1))]. 1746 (((x * y) \ 1) * y) * y = T(y / x,y * y). [para(1741(a,2),294(a,1))]. 1747 T(x / y,x * x) = ((y * x) \ x) * x. [para(318(a,1),1746(a,1,1)),flip(a)]. 1748 L(x,y * z,R(T(z / y,z * z),u,w)) = x. [para(1747(a,2),847(a,1,3,1))]. 1749 L(x,y * z,R(z / y,u,w)) = x. [para(1748(a,1),858(a,1)),flip(a)]. 1750 L(x,y * (z \ 1),u / (y * (z * u))) = x. [para(350(a,1),1749(a,1,3))]. 1752 L(x,y * z,u / (y * (z * u))) = x. [para(1750(a,1),1273(a,1)),flip(a)]. 1753 x / ((y * z) \ (y * (z * x))) = (x / (y * (z * x))) * (y * z). [para(1752(a,1),205(a,1,2))]. 1754 a(T(R(x,y,x),y),z,u) = a((y / x) / y,z,u). [para(1237(a,1),1728(a,1,1)),flip(a)]. 1755 a(x * ((x * y) * y),z,u) = a(a(x,y,y),z,u). [para(1706(a,1),1734(a,1))]. 1756 a(x * (x * (y * (x * z))),u,w) = a(y \ (x \ z),u,w). [para(51(a,1),1715(a,1,1))]. 1757 a(x \ (y \ z),u,w) = a(x * (y * z),u,w). [para(1756(a,1),1700(a,1))]. 1759 a(x * (y \ z),u,w) = a(x * (y * z),u,w). [para(1757(a,1),1702(a,1)),flip(a)]. 1760 a(K(x \ 1,x * y),z,u) = a(x * ((x * y) * y),z,u). [para(1757(a,1),1714(a,2))]. 1761 R(R(x,y,y),R(x,y,y) * y,y) = x. [para(1733(a,2),964(a,1))]. 1762 R(K(R(x,y,y),z),y,y) = K(x,z). [para(1761(a,1),1637(a,1,1)),flip(a)]. 1763 K(R(x,y,y),z) * (y \ 1) = K(x,z) / y. [para(1762(a,1),718(a,1,1)),flip(a)]. 1764 K(x,R(y,z,z)) * (K(y,x) / z) = z \ 1. [hyper(23,a,901,a,b,1763,a),flip(a)]. 1765 R(K(x,y),z,z) = K(x,R(y,z,z)). [hyper(24,a,1405,a,b,1764,a),flip(a)]. 1766 K(R(x,y,y),z) \ 1 = R(K(z,x),y,y). [para(1765(a,2),897(a,2))]. 1767 K(x,R(y,z,z)) * 1 = R(K(x,y),z,z). [para(1766(a,1),900(a,1)),flip(a)]. 1768 a((x \ 1) / (x / y),z,u) = a(R(y \ 1,x,x),z,u). [para(343(a,1),1743(a,1,1,2))]. 1769 a(R(x \ 1,y,y),z,u) = a((y / x) / y,z,u). [para(1768(a,1),1727(a,1))]. 1770 a((x / y) / x,z,u) = a(R(y,x,x),z,u). [para(1769(a,1),1735(a,1))]. 1771 a(T(R(x,y,x),y),z,u) = a(R(x,y,y),z,u). [para(1770(a,1),1754(a,2))]. 1772 a(R(T(x,y),y,x),z,u) = a(R(x,y,y),z,u). [para(46(a,2),1771(a,1,1))]. 1773 (x / (y * (z * x))) * (y * z) = x / L(x,z,y). [para(32(a,2),1753(a,1,2)),flip(a)]. 1774 (x / (y * (z * x))) * (y * z) = L(x,z,y) \ x. [para(1773(a,2),519(a,1))]. 1775 (L(x * y,z / (x * (y * z)),x * y) * (z / (x * (y * z)))) * (x * y) = (x * y) * (L(z,y,x) \ z). [para(1774(a,1),1310(a,2,2))]. 1776 (x * (y * (y * (z * u)))) \ (((x * (y * y)) * z) * u) = a(x,z,u). [para(411(a,1),1723(a,1,1))]. 1777 (x * (y * (y * (z * u)))) \ ((x * (y * (y * z))) * u) = a(x,z,u). [para(411(a,1),1776(a,1,2,1))]. 1778 a(x,y * (y * z),u) = a(x,z,u). [para(1777(a,1),90(a,1)),flip(a)]. 1779 a(x,y \ z,u) = a(x,y * z,u). [para(20(a,1),1778(a,1,2,2)),flip(a)]. 1780 a(x,(y / z) * y,u) = a(x,z,u). [para(22(a,1),1778(a,1,2,2))]. 1781 a(x,(y \ z) * u,w) = a(x,(y * z) * u,w). [para(89(a,1),1778(a,1,2)),flip(a)]. 1782 a(x,T(y,y * z),u) = a(x,(y \ z) * z,u). [para(250(a,1),1778(a,1,2,2)),flip(a)]. 1783 a(x,K(y,z) * T(y,z),u) = a(x,y,u). [para(1081(a,2),1778(a,1,2,2))]. 1785 a(x * (y * y),y * 1,y) = a(x * y,y \ 1,y \ 1). [para(1779(a,1),1574(a,1))]. 1786 a(x,y \ 1,z) * (y \ 1) = y \ a(x,y * 1,z). [para(1779(a,1),1689(a,2,2))]. 1787 a(x,(y * (y * z)) * (y * u),w) = a(x,z \ (y \ u),w). [para(282(a,1),1780(a,1,2,1))]. 1788 a(x,T(y * z,y),u) = a(x,z / y,u). [para(1232(a,2),1780(a,1,2))]. 1789 a(x,T(T(y,z),z),u) = a(x,y,u). [para(1113(a,1),1783(a,1,2))]. 1790 a(T(x,y),y,z) = a(x,T(y,x),z). [para(1789(a,1),1460(a,1))]. 1792 a(x,T(y,y * z),u) = a(x,(y * z) * z,u). [para(1782(a,2),1781(a,1))]. 1793 a(x,y \ 1,z) * (y \ 1) = y \ a(x,y,z). [para(18(a,1),1786(a,2,2,2))]. 1794 a(x,y * 1,z) * (y \ 1) = y \ a(x,y,z). [para(1779(a,1),1793(a,1,1))]. 1795 a(x,y,z) * (y \ 1) = y \ a(x,y,z). [para(18(a,1),1794(a,1,1,2))]. 1796 a(x * (y * y),y,y) = a(x * y,y \ 1,y \ 1). [para(18(a,1),1785(a,1,2))]. 1797 a(x * y,y \ 1,y \ 1) = a(x,y,y). [para(1796(a,1),1720(a,1))]. 1798 L(x,x,y) \ x = a(y,x,x). [para(1797(a,1),1408(a,1)),flip(a)]. 1800 a(x,y,y) * L(y,y,x) = y. [para(1798(a,1),520(a,1,1))]. 1801 R(x,y,y) * L(y,y,x) = x * y. [para(1800(a,1),966(a,1,2)),flip(a)]. 1802 T(R(x,y,y),L(y,y,x)) = L(y,y,x) \ (x * y). [para(1801(a,1),36(a,2,2))]. 1803 R(T(x,L(y,y,x)),y,y) = L(y,y,x) \ (x * y). [para(1802(a,1),46(a,2))]. 1804 L(x,x,y) \ (y * x) = R(T(y,x),x,x). [para(1558(a,1),1803(a,1,1)),flip(a)]. 1805 a(x,y * (y * (z * (y * u))),w) = a(x,z \ (y \ u),w). [para(51(a,1),1787(a,1,2))]. 1806 a(x,y \ (z \ u),w) = a(x,y * (z * u),w). [para(1805(a,1),1778(a,1))]. 1808 a(x,y * (z \ u),w) = a(x,y * (z * u),w). [para(1806(a,1),1779(a,1)),flip(a)]. 1809 a(x * y,T(x,x * y),z) = ((y / x) * (x * z)) \ (y * z). [para(1265(a,1),1713(a,1,1)),flip(a)]. 1810 a(x * y,T(x,x * y),z) = a(y / x,x,z). [para(1809(a,2),68(a,1))]. 1811 R(K(x,y),z,z) * (x / z) = (z \ 1) * T((z \ 1) \ (x / z),y). [para(1637(a,1),1745(a,1,1))]. 1812 K(x,R(y,z,z)) * (x / z) = (z \ 1) * T((z \ 1) \ (x / z),y). [para(1765(a,1),1811(a,1,1))]. 1813 K(x,R(y,z,z)) * (x / z) = (z \ 1) * T(z * (x / z),y). [para(330(a,1),1812(a,2,2,1))]. 1814 K(x,R(y,z,z)) * (x / z) = z \ T(z * (x / z),y). [para(1813(a,2),318(a,1))]. 1815 K(x,R(y,z,z)) * (x / z) = T(x,y) / z. [para(1814(a,2),755(a,1))]. 1816 a(x * (y \ (y \ (y \ (x * (y \ 1))))),z,u) = a(K(x / (y * y),y),z,u). [para(602(a,1),1725(a,1,1))]. 1817 a(x * (y \ ((y \ (y \ x)) * (y \ 1))),z,u) = a(K(x / (y * y),y),z,u). [para(285(a,1),1816(a,1,1,2,2))]. 1818 a(x * (y * ((y \ (y \ x)) * (y \ 1))),z,u) = a(K(x / (y * y),y),z,u). [para(1817(a,1),1759(a,1)),flip(a)]. 1819 a(K(x / (y * y),y),z,u) = a(x * (y \ (x * (y \ 1))),z,u). [para(265(a,1),1818(a,1,1,2)),flip(a)]. 1820 a(K(x / (y * y),y),z,u) = a(x * (y * (x * (y \ 1))),z,u). [para(1819(a,2),1759(a,1))]. 1821 a(K(x / (y * y),y),z,u) = a(x * T(x,y \ 1),z,u). [para(347(a,1),1820(a,2,1,2))]. 1822 a(K(x / (y * y),y),z,u) = a(K(x,y \ 1),z,u). [para(1821(a,2),1712(a,1))]. 1823 a(K(x,y \ 1),z,u) = a(K(x,y),z,u). [para(1418(a,1),1822(a,1,1)),flip(a)]. 1824 a(K(x \ 1,y),z,u) = a(K(y,x),z,u). [para(1823(a,1),905(a,1)),flip(a)]. 1825 a(x * ((x * y) * y),z,u) = a(K(x * y,x),z,u). [para(1824(a,1),1760(a,1)),flip(a)]. 1826 a(K(x * y,x),z,u) = a(a(x,y,y),z,u). [para(1825(a,1),1755(a,1))]. 1827 (x * y) * R((x * y) \ (x * z),u,w) = x * (y * R(y \ z,u,w)). [para(1697(a,2),74(a,1))]. 1828 (x * y) * R((x * y) \ z,u,w) = x * (y * R(y \ (x \ z),u,w)). [para(20(a,1),1827(a,1,2,1,2))]. 1829 (x * y) * R((x * y) \ y,z,u) = R(x,z,u) * (x \ y). [para(1828(a,2),639(a,1))]. 1830 T(x,y) \ R(T(x,y),z,u) = y \ (R(x,z,u) * (x \ y)). [para(1829(a,1),1610(a,1,2)),flip(a)]. 1831 T(x,y) \ R(T(x,y),z,u) = T(x \ R(x,z,u),y). [para(1830(a,2),539(a,1))]. 1832 (R(T(x,y),z,u) \ T(x,y)) * w = T(x \ R(x,z,u),y) \ w. [para(1831(a,1),465(a,1,1)),flip(a)]. 1833 T(x \ R(x,y,y),z) = a(T(x,z),y,y). [para(1831(a,1),962(a,1))]. 1834 K(x,y) * R(T(y,x),z,u) = y * T(y \ R(y,z,u),x). [para(1831(a,1),1099(a,1,2)),flip(a)]. 1835 T(T(x,y) \ R(T(x,y),z,u),y) = x \ R(x,z,u). [para(1831(a,1),1582(a,1))]. 1836 a(T(x,y),z,z) = T(a(x,z,z),y). [para(962(a,1),1833(a,1,1)),flip(a)]. 1837 T(T(x \ R(x,y,z),u),u) = x \ R(x,y,z). [para(1831(a,1),1835(a,1,1))]. 1838 (x * (y \ R(y,z,u))) / x = T(y \ R(y,z,u),x). [para(1837(a,1),105(a,1,1,2))]. 1839 T(a(x,y,z),x * (y * z)) = x \ R(x,y,z). [para(739(a,2),1837(a,1,1))]. 1840 a(x,y,z) * K(a(x,y,z),x * (y * z)) = x \ R(x,y,z). [para(1839(a,1),1107(a,1)),flip(a)]. 1841 T(T(x \ R(x,y,z),u),x * (y * z)) = (u * a(x,y,z)) / u. [para(1838(a,1),742(a,1,1))]. 1842 (x * (y \ R(y,z,u))) / x = (y \ R(y,z,u)) * K(y \ R(y,z,u),x). [para(1838(a,2),1107(a,1))]. 1843 (x * a(y,z,u)) / x = T(a(y,z,u),x). [para(1841(a,1),740(a,1))]. 1844 T(a(x,y,z),u) * (u / (u * a(x,y,z))) = 1. [para(1843(a,1),354(a,1,1))]. 1845 L(x,x,x * ((x \ 1) * a(y,z,u))) = ((x \ 1) * a(y,z,u)) \ T(a(y,z,u),x \ 1). [para(1843(a,1),1488(a,2,2))]. 1846 K(a(x,y,z),u) * K(a(x,y,z),u) = 1. [para(1844(a,1),1174(a,1)),flip(a)]. 1847 K(a(x,y,z),u) = K(u,a(x,y,z)). [hyper(24,a,898,a,b,1846,a)]. 1848 a(x,y,z) * K(x * (y * z),a(x,y,z)) = x \ R(x,y,z). [para(1847(a,1),1840(a,1,2))]. 1849 K(x \ R(x,y,z),u) = K(u,x \ R(x,y,z)). [hyper(23,a,1014,a(flip),b,1842,a(flip))]. 1850 L(L(x,y,z * u),(z * u) * y,u * z) = L(x,y,K(z,u)). [para(1698(a,1),174(a,1)),flip(a)]. 1851 ((x * (x * y)) * a(y,z,u)) / y = a(x * (x * y),z,u) * (x * x). [para(1700(a,1),749(a,1,1,2))]. 1852 (x * (x * (y * a(y,z,u)))) / y = a(x * (x * y),z,u) * (x * x). [para(51(a,1),1851(a,1,1))]. 1854 a(x * (x * y),z,u) * (x * x) = x * (x * ((y * a(y,z,u)) / y)). [para(1852(a,1),211(a,1))]. 1855 a(x * (x * y),z,u) * (x * x) = x * (x * a(y,z,u)). [para(748(a,1),1854(a,2,2,2))]. 1856 a(x,y,z) * (u * u) = u * (u * a(x,y,z)). [para(1700(a,1),1855(a,1,1))]. 1857 T((a(x,y,z) * (u * u)) / (u * u),u) = T(u \ (u * a(x,y,z)),u \ 1). [para(1856(a,2),666(a,1,1,1))]. 1859 T(x \ (x * a(y,z,u)),x \ 1) = T(a(y,z,u),x). [para(21(a,1),1857(a,1,1)),flip(a)]. 1860 T(a(x,y,z),u \ 1) = T(a(x,y,z),u). [para(19(a,1),1859(a,1,1))]. 1863 x * L(T(y \ (y / x),z),y,x * y) = K(L(y \ (y / x),y,x * y),z). [para(1295(a,1),330(a,1)),flip(a)]. 1864 (x / y) * (y * T(y \ (y / x),z)) = K(L(y \ (y / x),y,x * y),z). [para(1863(a,1),1294(a,1)),flip(a)]. 1865 (x / y) * (y * T(y \ (y / x),z)) = K(x \ 1,z). [para(1289(a,1),1864(a,2,1))]. 1866 (L(x,y,z) / (z * (y * x))) * ((z * (y * x)) * T((z * (y * x)) \ (z * y),u)) = K(L(x,y,z) \ 1,u). [para(99(a,1),1865(a,1,2,2,1,2))]. 1868 T(x * x,y * z) \ ((((y * z) \ (x * x)) * y) * z) = a((y * z) * (x * x),y,z). [para(394(a,2),1702(a,1))]. 1869 ((R(x,y,z) * u) * w) / ((x * u) * w) = R(x,u,w) \ R(R(x,u,w),y,z). [para(185(a,1),538(a,1,1))]. 1870 R(x \ R(x,y,z),x * u,w) = R(x,u,w) \ R(R(x,u,w),y,z). [para(1869(a,1),533(a,2))]. 1871 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). [para(584(a,1),1870(a,2,1))]. 1872 (K(x,T(y,z)) * T(y,x)) / y = K(z,T(y,x)) * K(y,z). [para(1663(a,1),1570(a,1,2))]. 1873 K(x,T(y,z)) * K(y,x) = K(y,z) * K(z,T(y,x)). [para(1872(a,1),1666(a,1))]. 1874 T(x * x,y * z) \ ((((y * z) \ (x * x)) * y) * z) = a(y * z,y,z). [para(1868(a,2),1720(a,1))]. 1875 (T(x * x,y * z) \ (((y * z) \ (x * x)) * y)) * z = a(y * z,y,z). [para(1874(a,1),591(a,1)),flip(a)]. 1877 ((T(x * x,y * z) \ ((y * z) \ (x * x))) * y) * z = a(y * z,y,z). [para(591(a,1),1875(a,1,1))]. 1878 (((x * y) \ 1) * x) * y = a(x * y,x,y). [para(795(a,1),1877(a,1,1,1))]. 1879 ((x * y) \ x) * y = a(x * y,x,y). [para(318(a,1),1878(a,1,1))]. 1880 x * ((y * x) \ y) = a(y * x,y,x). [para(1879(a,1),388(a,1)),flip(a)]. 1881 a(x * (x \ y),x,x \ y) = (x \ y) * (y \ x). [para(20(a,1),1880(a,1,2,1)),flip(a)]. 1882 (x \ y) * (y \ x) = a(y,x,x \ y). [para(20(a,1),1881(a,1,1)),flip(a)]. 1883 L(x,y,(z \ u) * (u * z)) = L(x,y,a(z,u,u \ z)). [para(1882(a,1),869(a,1,3)),flip(a)]. 1884 L(x,(y \ z) * (z * y),u) = L(x,a(y,z,z \ y),u). [para(1882(a,1),1362(a,1,2)),flip(a)]. 1885 L(x,y,(z * u) * (u * z)) = L(x,y,a(z,u,u \ z)). [para(1883(a,1),781(a,1)),flip(a)]. 1886 L(x,(y * z) * (z * y),u) = L(x,a(y,z,z \ y),u). [para(1884(a,1),880(a,1)),flip(a)]. 1887 L(x,y,a(z,u,u \ z)) = L(x,y,K(u,z)). [para(1885(a,1),779(a,1))]. 1888 L(x,a(y,z,z \ y),u) = L(x,K(z,y),u). [para(1886(a,1),879(a,1))]. 1889 ((x \ 1) * a(y,z,u)) \ T(a(y,z,u),x \ 1) = L(x,x,a(y,z,u)). [para(321(a,1),1845(a,1,3)),flip(a)]. 1890 (x \ a(y,z,u)) \ T(a(y,z,u),x \ 1) = L(x,x,a(y,z,u)). [para(318(a,1),1889(a,1,1))]. 1892 (x \ a(y,z,u)) \ T(a(y,z,u),x) = L(x,x,a(y,z,u)). [para(1860(a,1),1890(a,1,2))]. 1893 L(x,a(y,z,u),x) = L(x,x,a(y,z,u)). [para(1892(a,1),440(a,1)),flip(a)]. 1894 L(x,x,a(y,z,z \ y)) = L(x,K(z,y),x). [para(1893(a,1),1888(a,1))]. 1895 L(x,K(y,z),x) = L(x,x,K(y,z)). [para(1894(a,1),1887(a,1))]. 1896 L(x,K(y,z),x) = L(x,x,K(z,y)). [para(1895(a,2),909(a,1))]. 1897 (x \ K(y,z)) / (K(y,z) / L(x,x,K(z,y))) = K(K(y,z),x). [para(1896(a,1),1500(a,2,2,2)),flip(a)]. 1898 (x \ K(y,z)) / (K(y,z) * (x \ 1)) = K(K(y,z),x). [para(930(a,1),1897(a,1,2))]. 1899 K(x \ 1,K(y,z)) = K(K(y,z),x). [para(1898(a,1),978(a,1)),flip(a)]. 1900 K(K(x,y),z) * (K(x,y) \ u) = T(K(x,y),z \ 1) \ u. [para(1899(a,1),1095(a,1,1))]. 1901 T(K(x,y),z) * K(K(x,y),z) = T(K(x,y),z * z). [para(1899(a,1),1433(a,1,2))]. 1902 T(T(K(x,y),z),z) = T(K(x,y),z * z). [para(1901(a,1),1121(a,1)),flip(a)]. 1903 T(K(x,y),T(z,x) * T(z,x)) = T(T(K(x,y),z),T(z,x)). [para(1352(a,1),1902(a,1,1)),flip(a)]. 1904 x / (T(K(y,z),u \ 1) \ x) = K(y,z) * K(u,K(y,z)). [para(1900(a,1),1071(a,1,2))]. 1905 T(K(x,y),z * T(T(z,x),x)) = T(T(K(x,y),z),T(z,x)). [para(1088(a,1),1903(a,1,2))]. 1906 K(x,y) * K(z,K(x,y)) = T(K(x,y),z \ 1). [para(1904(a,1),65(a,1))]. 1907 T(K(x,y),z \ 1) * z = z * K(x,y). [para(1906(a,1),1018(a,1,1))]. 1908 ((x * y) * (z / (x * (y * z)))) * (x * y) = (x * y) * (L(z,y,x) \ z). [para(851(a,1),1775(a,1,1,1))]. 1910 (x \ R(x,y,z)) * (x * y) = (x * y) * (L(z,y,x) \ z). [para(1410(a,1),1908(a,1,1))]. 1911 (x * y) * (L(z,y,x) \ z) = R(x,y,z) * y. [para(1910(a,1),528(a,1))]. 1912 ((x * y) \ 1) * ((x * (y * z)) * T((x * (y * z)) \ (x * y),u)) = K(L(z,y,x) \ 1,u). [para(342(a,1),1866(a,1,1))]. 1914 ((x * y) \ 1) * (x * ((y * z) * T((y * z) \ y,u))) = K(L(z,y,x) \ 1,u). [para(1590(a,1),1912(a,1,2))]. 1915 ((x * y) \ 1) * (x * (y * K(z \ 1,u))) = K(L(z,y,x) \ 1,u). [para(1164(a,1),1914(a,1,2,2))]. 1916 (x * y) \ (x * (y * K(z \ 1,u))) = K(L(z,y,x) \ 1,u). [para(1915(a,1),318(a,1)),flip(a)]. 1917 L(K(x \ 1,y),z,u) = K(L(x,z,u) \ 1,y). [para(1916(a,1),32(a,2))]. 1918 K(L(x \ 1,y,z) \ 1,u) = L(K(x,u),y,z). [para(156(a,1),1917(a,1,1,1)),flip(a)]. 1920 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). [para(750(a,1),1871(a,1,1))]. 1921 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). [para(18(a,1),1920(a,1,1,1))]. 1922 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). [para(18(a,1),1921(a,1,1,2,1))]. 1923 (R(x,y,z) \ 1) \ R(R(x \ 1,x * y,z),u,w) = R(x \ R(x,u,w),y,z). [para(322(a,1),1922(a,1,2)),flip(a)]. 1924 (R(x,y,z) \ 1) \ R(R(x,y,z) \ 1,u,w) = R(x \ R(x,u,w),y,z). [para(584(a,1),1923(a,1,2,1))]. 1925 (R(x,y,z) * 1) \ R(R(x,y,z) * 1,u,w) = R(x \ R(x,u,w),y,z). [para(1924(a,1),750(a,1)),flip(a)]. 1926 R(x,y,z) \ R(R(x,y,z) * 1,u,w) = R(x \ R(x,u,w),y,z). [para(18(a,1),1925(a,1,1))]. 1927 R(x,y,z) \ R(R(x,y,z),u,w) = R(x \ R(x,u,w),y,z). [para(18(a,1),1926(a,1,2,1))]. 1928 R(x \ R(x,y,y),z,u) = a(R(x,z,u),y,y). [para(1927(a,1),962(a,1))]. 1929 T(R(x \ R(x,y,x),z,u),x * (R(x,z,u) * T(y,x))) = a(R(x,z,u),y,x). [para(1927(a,1),743(a,1,1))]. 1930 a(R(x,y,z),u,u) = R(a(x,u,u),y,z). [para(962(a,1),1928(a,1,1)),flip(a)]. 1931 T(R(a(x,y,x),z,u),x * (R(x,z,u) * T(y,x))) = a(R(x,z,u),y,x). [para(1539(a,1),1929(a,1,1,1))]. 1932 T(R(a(x,y,x),z,u),R(x,z,u) * (y * x)) = a(R(x,z,u),y,x). [para(530(a,1),1931(a,1,2))]. 1933 R(T(a(x,y,x),R(x,z,u) * (y * x)),z,u) = a(R(x,z,u),y,x). [para(1932(a,1),46(a,2))]. 1934 ((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). [para(342(a,1),1597(a,1,1))]. 1936 ((x * y) \ 1) * (x * ((y * z) * R((y * z) \ y,u,w))) = L(z,y,x) \ R(L(z,y,x),u,w). [para(1827(a,1),1934(a,1,2))]. 1937 ((x * y) \ 1) * (x * (y * (z \ R(z,u,w)))) = L(z,y,x) \ R(L(z,y,x),u,w). [para(1592(a,1),1936(a,1,2,2))]. 1938 (x * y) \ (x * (y * (z \ R(z,u,w)))) = L(z,y,x) \ R(L(z,y,x),u,w). [para(1937(a,1),318(a,1)),flip(a)]. 1939 L(x,y,z) \ R(L(x,y,z),u,w) = L(x \ R(x,u,w),y,z). [para(1938(a,1),32(a,2)),flip(a)]. 1940 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). [para(1808(a,1),1686(a,1,1,2,1))]. 1941 L((x * (y \ R(y,x,z))) * (1 * u),x * (y \ R(y,x,z)),x) = (y \ R(y,x,z)) * (x * u). [para(1442(a,1),1940(a,1,1,2,1))]. 1942 L((x * (y \ R(y,x,z))) * u,x * (y \ R(y,x,z)),x) = (y \ R(y,x,z)) * (x * u). [para(17(a,1),1941(a,1,1,2))]. 1944 L(x * (R(y,x,z) * (y \ u)),x * (y \ R(y,x,z)),x) = (y \ R(y,x,z)) * (x * u). [para(1450(a,1),1942(a,1,1))]. 1945 L(x * (R(y,x,z) * (y \ u)),x * (y * R(y,x,z)),x) = (y \ R(y,x,z)) * (x * u). [para(1944(a,1),1360(a,1)),flip(a)]. 1946 (x \ R(x,y,z)) * (y * u) = y * (R(x,y,z) * (x \ u)). [para(1945(a,1),1439(a,1))]. 1947 R(x,y,z) * (x \ (y * u)) = y * (R(x,y,z) * (x \ u)). [para(1946(a,1),532(a,1)),flip(a)]. 1948 R(x,y,z) * (x \ (y * (y \ z))) = L(z,x * y,x). [para(1947(a,2),1567(a,1))]. 1949 R(x,y,z) * (x \ z) = L(z,x * y,x). [para(20(a,1),1948(a,1,2,2))]. 1950 R(x,y,L(z,y,x)) * (x \ L(z,y,x)) = z. [para(1949(a,2),303(a,1))]. 1951 L(x,y * z,y) / x = y \ R(y,z,x). [para(1949(a,1),536(a,1,1))]. 1952 x / L(x,y * z,y) = R(y,z,x) \ y. [para(1949(a,1),542(a,1,2))]. 1953 x \ L(x,y * z,y) = y \ R(y,z,x). [para(1951(a,1),515(a,1)),flip(a)]. 1954 L(x,y * z,y) \ x = R(y,z,x) \ y. [para(1952(a,1),519(a,1)),flip(a)]. 1955 x \ R(x,x \ y,z) = z \ L(z,y,x). [para(20(a,1),1953(a,1,2,2)),flip(a)]. 1956 x \ R(x,x * y,z) = z \ L(z,y,x). [para(313(a,1),1953(a,1,2)),flip(a)]. 1957 K(x,R(y,z,x) \ y) = 1. [para(1954(a,1),653(a,1,2))]. 1958 K(x,y \ R(y,z,x)) = 1. [para(622(a,1),1957(a,1,2))]. 1959 T(x,y \ R(y,z,x)) = x. [hyper(41,a,1958,a)]. 1960 K(x,T(y \ R(y,z,x),u)) = 1. [para(1831(a,1),1958(a,1,2))]. 1961 T(x \ R(x,y,z),z) = x \ R(x,y,z). [hyper(39,a,1959,a)]. 1962 K(x,a(y,z,x)) = 1. [para(739(a,2),1960(a,1,2))]. 1963 T(x,a(y,z,x)) = x. [hyper(41,a,1962,a)]. 1964 a(x,y,z) * z = z * a(x,y,z). [para(1963(a,1),82(a,1,2))]. 1965 R(x,y,z) \ x = z \ L(z,y,x). [para(1955(a,1),624(a,1)),flip(a)]. 1966 L(x,y,z) = x * (R(z,y,x) \ z). [para(1965(a,2),20(a,1,2)),flip(a)]. 1967 R(x,y,z) = x / (z \ L(z,y,x)). [para(1965(a,1),65(a,1,2)),flip(a)]. 1968 (x \ L(x,y,z)) \ 1 = z \ R(z,y,x). [para(1965(a,1),460(a,1,1))]. 1969 (x \ L(x,y,z)) * R(z,y,x) = z. [para(1965(a,1),496(a,1,1))]. 1970 L(x,y,z) = (R(z,y,x) \ z) * x. [para(1965(a,2),514(a,1,1)),flip(a)]. 1971 x * (R(K(y,z),u,x) \ K(y,z)) = L(x,u,K(z,y)). [para(1966(a,1),909(a,1))]. 1972 R(x,y,T(z,x * y)) = R(x,y,z). [hyper(23,a,680,a,b,1969,a),flip(a)]. 1973 L(x,y,z) * R(z,y,x) = x * z. [para(1969(a,1),504(a,1,2)),flip(a)]. 1974 L(x,y,z) * (x \ R(z,y,x)) = z. [para(1969(a,1),647(a,1)),flip(a)]. 1975 R(x,y,z) * L(z,y,x) = x * z. [para(1970(a,2),458(a,1,2))]. 1976 L(x,y,z) = (z \ R(z,y,x)) \ x. [para(1970(a,2),465(a,2)),flip(a)]. 1977 T(x \ R(x,y,z),u) \ z = L(z,y,T(x,u)). [para(1970(a,2),1832(a,1)),flip(a)]. 1978 L(x,y,z) \ x = z \ R(z,y,x). [para(1972(a,1),681(a,2,2))]. 1979 R(x,y,z) = x * (L(z,y,x) \ z). [para(1972(a,1),683(a,1))]. 1980 R(x,y,z) * (x \ L(z,y,x)) = z. [para(1972(a,1),686(a,1,1))]. 1981 (L(x,y,z) * (R(z,y,x) * u)) \ ((x * z) * u) = a(L(x,y,z),R(z,y,x),u). [para(1973(a,1),28(a,2,2,1)),flip(a)]. 1984 (L(x,y,z) \ x) * (z * u) = R(z,y,x) * u. [para(1978(a,2),528(a,1,1))]. 1985 (x \ R(x,y,z)) * u = z * (L(z,y,x) \ u). [para(1978(a,1),650(a,1,1))]. 1986 R(x \ R(x,y,z),z,u) = L(z,y,x) \ z. [para(1978(a,1),736(a,1,1))]. 1987 (x * y) * (x \ R(x,y,z)) = R(x,y,z) * y. [para(1978(a,1),1911(a,1,2))]. 1988 K(x,y) \ R(K(x,y),z,u) = u \ L(u,z,K(x,y)). [para(1669(a,1),1956(a,1,2))]. 1989 x \ R(x,y,z) = (L(z,y,x) \ z) * 1. [para(1968(a,1),517(a,1))]. 1990 R(x,y,L(z,y,x)) = R(x,y,z). [hyper(24,a,1980,a,b,1950,a)]. 1991 (x \ R(x,y,z)) \ z = L(z,y,T(x,z)). [para(1961(a,1),1977(a,1,1))]. 1992 L(x,y,T(z,x)) = L(x,y,z). [para(1991(a,1),1976(a,2)),flip(a)]. 1993 L(L(x,y,z),z * y,T(z,L(x,y,z))) = x. [para(1992(a,2),303(a,1))]. 1994 L(x,y,K(z,L(x,y,z))) = x. [para(1993(a,1),1606(a,1)),flip(a)]. 1995 x * (L(x,y,z) \ (z * u)) = R(z,y,x) * u. [para(1984(a,1),650(a,1)),flip(a)]. 1996 L((x \ R(x,y,z)) \ u,x \ R(x,y,z),x * y) = (R(x,y,z) * y) \ ((x * y) * u). [para(1987(a,1),76(a,2,1))]. 1998 L(x,y,z) * (R(z,y,x) * u) = x * (z * u). [para(1995(a,1),645(a,1,2))]. 1999 x * (L(x,y,z) \ (z * T(y,z))) = y * R(z,y,x). [para(1995(a,2),1643(a,1))]. 2000 x * (L(x,y,z) \ (z * L(x,y,z))) = z * x. [para(1995(a,2),1975(a,1))]. 2001 x * T(y,L(x,z,y)) = y * x. [para(36(a,2),2000(a,1,2))]. 2002 T(x,L(y,z,x)) = x * K(x,y). [hyper(23,a,1116,a,b,2001,a)]. 2005 K(x,L(y,z,x)) = K(x,y). [hyper(23,a,1107,a(flip),b,2002,a(flip)),flip(a)]. 2006 L(x,y,K(z,x)) = x. [para(2005(a,1),1994(a,1,3))]. 2007 L(T(x,y),z,K(u,x)) = T(x,y). [para(2006(a,1),44(a,2,1))]. 2008 L(x,y,K(x,z)) = x. [para(2006(a,1),909(a,1)),flip(a)]. 2009 L(x,y,a(x,z,z)) = x. [para(2006(a,1),1262(a,1)),flip(a)]. 2010 L(K(x,y),z,K(u,x \ 1)) = K((x \ 1) \ 1,y). [para(2006(a,1),1918(a,1,1,1)),flip(a)]. 2011 R(K(x,y),z,y) = K(x,y) / (y \ y). [para(2006(a,1),1967(a,2,2,2))]. 2013 (K(x,y) * z) * x = K(x,y) * (z * x). [para(2008(a,1),74(a,1,2))]. 2014 x * (x \ R(a(x,y,y),z,x)) = a(x,y,y). [para(2009(a,1),1974(a,1,1))]. 2015 T(x,K(y,x) * z) = T(x,z). [para(2007(a,1),1377(a,1)),flip(a)]. 2016 K(K(x,y) * z,y) = T(y,z) \ y. [para(2015(a,1),1080(a,2,1))]. 2017 K(x,K(y,x) * z) = x \ T(x,z). [para(2015(a,1),1108(a,2,2))]. 2018 T(x,T(x,y) * z) = T(x,x * z). [para(1098(a,1),2015(a,1,2)),flip(a)]. 2019 T(x,y * T(z,x)) = T(x,y * z). [para(1212(a,1),2015(a,1,2))]. 2021 K(K(x,y) * z,y) = K(z,y). [para(2016(a,2),1080(a,2)),flip(a)]. 2022 K(K(x,y) * z,x) = K(z,x). [para(901(a,1),2021(a,1,1)),flip(a)]. 2023 K(x * (K(x,y) * z),x) = K(x * z,x). [para(1068(a,1),2022(a,1,1))]. 2024 K(x,K(y,x) * z) = K(x,z). [para(2017(a,2),1108(a,2)),flip(a)]. 2025 K(x,K(x,y) * z) = K(x,z). [para(901(a,1),2024(a,1,2)),flip(a)]. 2026 K(x,y) * K(x * (K(x,z) * y),x) = a(x,K(x,z) * y,x). [para(2025(a,1),1537(a,1,1))]. 2027 R(K(x,y),z,y) = K(x,y) / 1. [para(60(a,1),2011(a,2,2))]. 2029 R(K(x,y),z,y) = K(x,y). [para(2027(a,2),64(a,1))]. 2030 K(x,R(y,z,y)) = K(x,y). [para(2029(a,1),1654(a,1)),flip(a)]. 2031 R(K(x,y),z,x) = K(y,x) \ 1. [para(2029(a,1),1670(a,1,1)),flip(a)]. 2032 K(x,y) * R(T(y,x),z,y) = R(y,z,y). [para(2030(a,1),1083(a,1,1))]. 2033 R(K(x,y),z,x) = K(x,y). [para(2031(a,2),897(a,1))]. 2034 K(L(x,y,x),z) = K(x,z). [para(2033(a,1),1638(a,1)),flip(a)]. 2036 K((x \ y) \ y,z) = K(T(x,y),z). [para(1457(a,1),2034(a,1,1))]. 2038 K(T(x,x \ y),z) = K(T(x,y),z). [para(83(a,2),2036(a,1,1))]. 2039 x \ (K(x,y) * (z * x)) = T(K(x,y) * z,x). [para(2013(a,1),36(a,2,2)),flip(a)]. 2040 x * ((K(x,y) * z) * x) = T(x,y) * (z * x). [para(2013(a,2),1120(a,1,2))]. 2041 T(x,y) \ R(T(x,y),z,x) = x \ R(x,z,x). [para(2032(a,1),1163(a,1,2)),flip(a)]. 2042 x * (x \ a(R(x,y,x),z,z)) = a(x,z,z). [para(1930(a,2),2014(a,1,2,2))]. 2043 x * (x \ a(L(x,y,x),z,z)) = a(x,z,z). [para(1303(a,1),2042(a,1,2,2,1))]. 2044 a(L(x,y,x),z,z) = a(x,z,z). [para(2043(a,1),20(a,1)),flip(a)]. 2045 a(L(T(x,y),y * x,x),z,z) = a(T(x,y),z,z). [para(1283(a,1),2044(a,1,1))]. 2046 K(x,y) * (x \ (z * x)) = T(K(x,y) * z,x). [para(2039(a,1),1076(a,1)),flip(a)]. 2047 (T(x,y) * (z * x)) \ ((T(x,y) * z) * x) = a(x,K(x,y) * z,x). [para(2040(a,1),1166(a,1,1))]. 2048 T(x,y) \ R(T(x,y),z,x) = a(x,z,x). [para(2041(a,2),1539(a,1))]. 2049 T(x \ R(x,y,x),z) = a(x,y,x). [para(2048(a,1),1831(a,1)),flip(a)]. 2050 T(a(x,y,x),z) = a(x,y,x). [para(1539(a,1),2049(a,1,1))]. 2051 a(x,y,x) * z = z * a(x,y,x). [para(2050(a,1),82(a,1,2)),flip(a)]. 2052 a(R(x,y,z),u,x) = R(a(x,u,x),y,z). [para(2050(a,1),1933(a,1,1)),flip(a)]. 2053 (a(x,y,x) * z) * L(u,z,a(x,y,x)) = (z * u) * a(x,y,x). [para(2051(a,1),74(a,2))]. 2054 a(x,y,x) \ a(R(x,z,z),y,x) = a(a(x,y,x),z,z). [para(2052(a,2),962(a,1,2))]. 2056 T(K(x,y) * z,x) = K(x,y) * T(z,x). [para(36(a,2),2046(a,1,2)),flip(a)]. 2057 T(K(x,y) * R(z,u,w),x) = K(x,y) * R(T(z,x),u,w). [para(46(a,2),2056(a,2,2))]. 2058 T(K(x,y) * z,x) / z = K(z,x) * K(x,y). [para(2056(a,2),1666(a,1,1))]. 2059 T(K(x,y) * z,x) / z = K(x,y) * K(z,x). [para(2058(a,2),1226(a,2)),flip(a)]. 2060 L(K(x,y),z,K(u,x \ 1)) = K(x,y). [para(156(a,1),2010(a,2,1))]. 2061 L(K(x,y),z,K(u,x)) = K(x,y). [para(2060(a,1),1618(a,1)),flip(a)]. 2062 L(K(x,y),z,K(x,u)) = K(x,y). [para(2060(a,1),1619(a,1)),flip(a)]. 2063 (K(x,y) * z) \ z = T(K(y,x),z). [para(2061(a,1),1301(a,1,1)),flip(a)]. 2064 T(K(x,y) * z,K(x,y)) = z * K(x,y). [para(2062(a,1),1309(a,1,1,1))]. 2065 x / T(K(y,z),x) = K(z,y) * x. [para(2063(a,1),65(a,1,2))]. 2067 (T(K(x,y),z) / z) * u = (K(y,x) * z) \ u. [para(2065(a,1),358(a,1,1)),flip(a)]. 2068 (K(x,y) * z) * K(y,x) = T(z,K(y,x)). [para(2065(a,1),1549(a,1,1))]. 2069 K(K(x,y) * z,K(y,x)) = T(z,K(y,x)) / z. [para(2068(a,1),979(a,1,1)),flip(a)]. 2070 K(K(x,y) * z,K(y,x)) = K(z,K(y,x)). [para(2069(a,2),1086(a,2)),flip(a)]. 2071 K(K(x,y) * z,K(x,y)) = K(z,K(x,y)). [para(901(a,1),2070(a,1,1)),flip(a)]. 2072 a(a(K(x,y),z,z),u,w) = a(K(z,K(x,y)),u,w). [para(2071(a,1),1826(a,1,1)),flip(a)]. 2073 a(R(T(x,y),y,x),z,z) = a(T(x,y),z,z). [para(1306(a,1),2045(a,1,1))]. 2074 a(R(x,y,y),z,z) = a(T(x,y),z,z). [para(2073(a,1),1772(a,1)),flip(a)]. 2076 x * (K(y,z) * R(K(z,y),u,x)) = L(x,u,K(z,y)). [para(1671(a,1),1971(a,1,2))]. 2077 x * (K(y,z) * K(z,R(y,u,x))) = L(x,y * u,K(y,z)). [para(1668(a,1),1971(a,1,2))]. 2078 x * (L(x,y,z) \ (y * z)) = y * R(z,y,x). [para(82(a,1),1999(a,1,2,2))]. 2079 L(x,y,z) = (x * (y * z)) / (y * R(z,y,x)). [para(2078(a,1),648(a,1,2)),flip(a)]. 2080 T(K(x,y) * R(y,z,u),x) = y * T(y \ R(y,z,u),x). [para(2057(a,2),1834(a,1))]. 2081 T(K(x,y) * R(y,z,u),x) / R(y,z,u) = K(R(y,z,u) / y,x). [para(2080(a,2),1211(a,1,1))]. 2082 a(x,K(x,y) * z,x) = K(x,z) * K(x * z,x). [para(2023(a,1),2026(a,1,2)),flip(a)]. 2083 a(x,K(x,y) * z,x) = a(x,z,x). [para(2082(a,2),1537(a,1))]. 2085 a(x,K(x,y) * z,x) = a(T(x,y),z,x). [para(2047(a,1),28(a,2)),flip(a)]. 2086 a(T(x,y),z,x) = a(x,z,x). [para(2085(a,1),2083(a,1))]. 2087 a((x \ y) \ y,z,x) = a(x,z,x). [para(83(a,1),2086(a,1,1))]. 2089 a((x \ y) * y,z,x) = a(x,z,x). [para(2087(a,1),1702(a,1)),flip(a)]. 2090 a((x * y) * y,z,x) = a(x,z,x). [para(2089(a,1),1707(a,1)),flip(a)]. 2091 a(R(x,y,y),z,x) = a(x,z,x). [para(2090(a,1),1721(a,1)),flip(a)]. 2092 a(a(x,y,x),z,z) = a(x,y,x) \ a(x,y,x). [para(2091(a,1),2054(a,1,2)),flip(a)]. 2093 a(a(x,y,x),z,z) = 1. [para(2092(a,2),60(a,1))]. 2095 L(x,x,a(y,z,y)) = x. [hyper(37,a,2093,a)]. 2097 L(x,x,a(y,z,z)) = x. [para(2095(a,1),1695(a,2))]. 2098 L(x,x,K(y,z)) = x. [para(2097(a,1),1263(a,1)),flip(a)]. 2099 R(T(a(x,y,y),z),z,z) = z \ (a(x,y,y) * z). [para(2097(a,1),1804(a,1,1)),flip(a)]. 2100 a(K(x,y),z,z) = 1. [hyper(38,a,2098,a)]. 2101 K(x,y) * (z \ 1) = K(x,y) / z. [para(2098(a,1),915(a,1,2)),flip(a)]. 2102 (K(x,y) * (z / u)) \ K(x,y) = u / z. [para(2098(a,1),925(a,1)),flip(a)]. 2103 L(x,K(y,z),x) = x. [para(2098(a,1),1895(a,2))]. 2104 R(K(x,y),z,z) = K(x,y) * 1. [para(2100(a,1),963(a,1,2)),flip(a)]. 2105 a(K(x,K(y,z)),u,w) = a(1,u,w). [para(2100(a,1),2072(a,1,1)),flip(a)]. 2106 T(K(x,y),z) / z = z \ K(x,y). [para(2103(a,1),441(a,1,2))]. 2107 K(x,R(y,z,z)) = K(x,y). [hyper(24,a,1767,a,b,2104,a(flip)),flip(a)]. 2108 K(x,y / (z \ 1)) = K(x,y * z). [para(720(a,1),2107(a,1,2)),flip(a)]. 2112 K(x,y) * (x / z) = T(x,y) / z. [para(2107(a,1),1815(a,1,1))]. 2114 K(x,y) / (z \ 1) = K(x,y) * z. [para(156(a,1),2101(a,1,2)),flip(a)]. 2115 a(K(x,K(y,z)),u,w) = 1. [para(2105(a,2),125(a,1))]. 2117 L(x,y,K(z,K(u,w))) = x. [hyper(37,a,2115,a)]. 2119 x * (x \ R(K(y,K(z,u)),w,x)) = K(y,K(z,u)). [para(2117(a,1),1974(a,1,1))]. 2121 (K(x,y) * z) \ u = (z \ K(y,x)) * u. [para(2106(a,1),2067(a,1,1)),flip(a)]. 2122 K(x,R(((y \ 1) * z) \ 1,z,z)) = K(x,(z \ 1) * y). [para(1739(a,2),2108(a,1,2))]. 2123 T(x,y) / (z \ x) = K(x,y) * z. [para(65(a,1),2112(a,1,2)),flip(a)]. 2125 (K(x,y) * z) \ K(x,y) = z \ 1. [para(2114(a,1),66(a,1,1))]. 2126 (K(x,y) * z) \ T(x,y) = z \ x. [para(2123(a,1),66(a,1,1))]. 2127 (K(x,y) \ z) \ 1 = z \ K(x,y). [para(20(a,1),2125(a,1,1)),flip(a)]. 2128 (K(x,y) * z) \ y = z \ T(y,x). [para(901(a,1),2126(a,1,1)),flip(a)]. 2129 L(x \ y,x,K(z,y)) = x \ y. [para(2126(a,1),1248(a,2))]. 2130 a(K(x,y),z,z \ y) = 1. [hyper(38,a,2129,a)]. 2132 a(K(x,y * z),y,z) = 1. [para(19(a,1),2130(a,1,3))]. 2133 (K(x,y) \ z) \ u = (z \ K(x,y)) * u. [para(2127(a,1),318(a,1,1)),flip(a)]. 2134 ((x * y) \ K(z,x)) * u = (T(x,z) * y) \ u. [para(1160(a,1),2121(a,1,1)),flip(a)]. 2135 (x \ K(y,z)) * K(z,y) = x \ 1. [para(2121(a,1),2125(a,1))]. 2136 (x \ K(y,z)) * y = x \ T(y,z). [para(2121(a,1),2128(a,1))]. 2137 ((x / y) \ K(z,u)) * K(u,z) = y / x. [para(2121(a,1),2102(a,1))]. 2138 (x / y) * K(x,x * y) = (x \ y) \ 1. [para(1011(a,1),2135(a,1,1))]. 2139 (x \ T(y,z)) \ ((x \ K(y,z)) * (y * u)) = L(u,y,x \ K(y,z)). [para(2136(a,1),32(a,2,1)),flip(a)]. 2140 x / K(y,z) = x * K(z,y). [para(66(a,1),2137(a,1,1)),flip(a)]. 2141 (x * K(y,z)) \ x = K(z,y). [para(2140(a,1),66(a,1,1))]. 2143 (x * K(y,z)) \ u = (K(z,y) / x) * u. [para(2140(a,1),358(a,1,1))]. 2144 (K(x,y) * z) / K(x,y) = T(z,K(y,x)). [para(2140(a,2),2068(a,1))]. 2145 T(x,K(y,z)) \ x = K(x,K(z,y)). [para(2144(a,1),1053(a,2,1)),flip(a)]. 2146 K(K(x,y),z) = K(z,K(y,x)). [para(2145(a,1),1080(a,2))]. 2147 K(x,K(y,z)) * K(x,K(z,y)) = 1. [para(2146(a,1),898(a,1,1))]. 2148 K(x,y) * K(z,K(y,x)) = T(K(x,y),z). [para(2146(a,1),1107(a,2,2)),flip(a)]. 2149 K(x,y) * T(K(y,x),z) = K(z,K(x,y)). [para(2146(a,1),1114(a,2))]. 2150 T(K(x,y),z) \ 1 = T(K(y,x),z). [para(2148(a,1),1140(a,1)),flip(a)]. 2151 T(K(x,y),z) * T(K(y,x),z) = 1. [para(2150(a,1),20(a,1,2))]. 2152 T(K(x,y),z) * K(y,x) = K(z,K(y,x)). [para(2149(a,1),405(a,2))]. 2153 R(T(a(x,y,y),z),z,z) = T(a(x,y,y),z). [para(2099(a,2),36(a,2)),flip(a)]. 2154 R(T(a(x,y,y),z),z,z) = a(T(x,z),y,y). [para(2153(a,2),1836(a,2)),flip(a)]. 2155 R(a(T(x,y),z,z),y,y) = a(T(x,y),z,z). [para(1836(a,2),2154(a,1,1))]. 2156 a(R(T(x,y),y,y),z,z) = a(T(x,y),z,z). [para(2155(a,1),1930(a,2))]. 2157 a(T(T(x,y),y),z,z) = a(T(x,y),z,z). [para(2156(a,1),2074(a,1)),flip(a)]. 2158 a(T(x,y),z,z) = a(x,z,z). [para(2157(a,1),1724(a,1))]. 2161 (x * (y * (a(y,z,z) * u))) / (R(T(y,x),z,z) * u) = T(x,y). [para(2158(a,1),1210(a,1,1,2,2,1))]. 2165 R(K(x,K(y,z)),u,w) = K(x,K(y,z)). [para(2119(a,1),20(a,1)),flip(a)]. 2166 K(x,R(K(y,z),u,w)) = K(x,K(y,z)). [para(2165(a,1),1654(a,1)),flip(a)]. 2167 K(x,K(y,R(z,u,w))) = K(x,K(y,z)). [para(1654(a,1),2166(a,1,2))]. 2168 K(K(R(x,y,z),u),w) = K(w,K(u,x)). [para(2167(a,1),2146(a,2))]. 2169 K(R(K(x,y),z,u),w) = K(w,K(y,x)). [para(1634(a,1),2168(a,1,1))]. 2170 K(x,R((y \ z) \ 1,z,z)) = K(x,(z \ 1) * y). [para(318(a,1),2122(a,1,2,1,1))]. 2171 K(x,(y \ z) \ 1) = K(x,(z \ 1) * y). [para(2170(a,1),2107(a,1)),flip(a)]. 2172 K(x,(y \ z) \ 1) = K(x,z \ y). [para(318(a,1),2171(a,2,2))]. 2174 K(x,(y / z) \ y) = K(x,z / (a(y,z,z) \ 1)). [para(2172(a,1),1447(a,1))]. 2175 K(x,y / (a(z,y,y) \ 1)) = K(x,y). [para(66(a,1),2174(a,1,2)),flip(a)]. 2176 K(x,y * a(z,y,y)) = K(x,y). [para(1445(a,1),2175(a,1,2))]. 2177 K(x * a(y,x,x),z) = (z \ 1) / (z \ K(z,x)). [para(2176(a,1),1057(a,1,2,2)),flip(a)]. 2178 K(x * a(y,x,x),z) = K(x,z). [para(2177(a,2),1057(a,1))]. 2179 (x / y) * T(y,z) = x * K(y,z). [para(2178(a,1),1463(a,1,2)),flip(a)]. 2180 (x * y) * K(y,z) = x * T(y,z). [para(21(a,1),2179(a,1,1)),flip(a)]. 2183 L(K(x,y),x,z) = K(x,y). [hyper(23,a,1117,a,b,2180,a),flip(a)]. 2184 (x * y) \ (x * T(y,z)) = K(y,z). [hyper(23,a,20,a,b,2180,a),flip(a)]. 2185 (x * (y * z)) \ (x * (y * T(z,u))) = L(K(z,u),y * z,x). [para(2180(a,1),32(a,2,2,2)),flip(a)]. 2186 (x * T(y,z)) \ (x * y) = K(z,y). [para(2180(a,1),2141(a,1,1))]. 2187 L(K(T(x,y),z),x,y) = K(T(x,y),z). [para(2183(a,1),1376(a,1)),flip(a)]. 2189 (x * (y * z)) \ ((x * y) * T(L(z,y,x),u)) = K(L(z,y,x),u). [para(74(a,1),2184(a,1,1))]. 2192 T(K(x,y),x * z) = K(T(x,z),y). [para(2187(a,1),1522(a,1)),flip(a)]. 2193 K(T(x,x \ y),z) = T(K(x,z),y). [para(20(a,1),2192(a,1,2)),flip(a)]. 2194 K(T(x,y),z) = T(K(x,z),y). [para(2193(a,1),2038(a,1)),flip(a)]. 2195 K(x,T(y,z)) * T(K(y,x),z) = 1. [para(2194(a,1),898(a,1,2))]. 2196 K(T(x,y * T(T(y,x),x)),z) = T(T(K(x,z),y),T(y,x)). [para(2194(a,2),1905(a,1))]. 2197 K(x,T(y,z)) = T(K(x,y),z). [hyper(24,a,2151,a,b,2195,a)]. 2199 K(x,y) * K(y,T(x,z)) = K(K(y,x),z). [para(2197(a,2),1114(a,1,2))]. 2200 K(x,T(y,z \ 1)) * z = z * K(x,y). [para(2197(a,2),1907(a,1,1))]. 2201 K(x,T(y,z)) / z = z \ K(x,y). [para(2197(a,2),2106(a,1,1))]. 2202 K(x,y) * K(y,T(x,z)) = K(z,K(x,y)). [para(2197(a,2),2149(a,1,2))]. 2203 K(x,T(y,z)) * K(y,x) = K(z,K(y,x)). [para(2197(a,2),2152(a,1,1))]. 2204 K(T(x,y),z) = K(x,T(z,y)). [para(2197(a,2),2194(a,2))]. 2205 K(x,T(y,z)) * K(y,x) = K(K(x,y),z). [para(2199(a,1),1226(a,2))]. 2206 K(x,T(y,z)) * K(y,x) = K(x,K(y,z)). [para(2202(a,1),1873(a,2))]. 2207 K(x,y) * K(x,K(y,z)) = K(x,T(y,z)). [para(2206(a,1),1225(a,1,2))]. 2208 K(x,K(y,z)) = K(z,K(y,x)). [para(2206(a,1),2203(a,1))]. 2209 K(K(x,y),z) = K(x,K(y,z)). [para(2206(a,1),2205(a,1)),flip(a)]. 2210 1 / K(x,K(y,z)) = K(K(y,x),z). [para(2208(a,1),899(a,1,2))]. 2211 K(K(x,y),z) = K(K(x,z),y). [para(2210(a,1),899(a,1))]. 2212 K(K(x,y),z) = K(y,K(z,x)). [para(2211(a,1),2146(a,1))]. 2213 K(x,K(y,z)) = K(z,K(x,y)). [para(2212(a,1),2209(a,1))]. 2214 T(K(x,y) * K(x,K(y,z)),z) = K(x,y). [para(2213(a,2),1020(a,1,1,2))]. 2215 T(K(x,T(y,z)),z) = K(x,y). [para(2207(a,1),2214(a,1,1))]. 2216 K(x,T(y,z)) * z = z * K(x,y). [para(2215(a,1),82(a,1,2)),flip(a)]. 2217 K(x,T(T(y,z),z)) = K(x,y). [para(2215(a,1),2197(a,2))]. 2219 K(x,T(y,z \ 1)) = K(x,T(y,z)). [hyper(24,a,2200,a,b,2216,a),flip(a)]. 2220 T(K(x,y) * z,K(x,y)) = K(x,T(y,z)) * z. [para(2216(a,2),2064(a,2))]. 2221 K(x,T(y,z \ (z \ (u \ 1)))) = K(x,T(y,u * (z * z))). [para(409(a,1),2219(a,1,2,2))]. 2222 K(T(x,y * T(y,x)),z) = T(T(K(x,z),y),T(y,x)). [para(2019(a,1),2196(a,1,1))]. 2223 T(T(K(x,y),z),T(z,x)) = K(T(x,z * z),y). [para(2019(a,1),2222(a,1,1)),flip(a)]. 2224 T(T(K(x,y),z),T(z,x)) = K(x,T(y,z * z)). [para(2223(a,2),1278(a,1))]. 2225 T(K(x,T(y,z)),T(z,x)) = K(x,T(y,z * z)). [para(2197(a,2),2224(a,1,1))]. 2226 K(T(x,T(y,x)),T(z,y)) = K(x,T(z,y * y)). [para(2225(a,1),2194(a,2))]. 2227 K(T(x,y),T(z,y)) = K(x,T(z,y * y)). [para(1131(a,1),2226(a,1,1))]. 2228 K(x,T(T(y,z),z)) = K(x,T(y,z * z)). [para(2227(a,1),2204(a,1)),flip(a)]. 2229 K(x,T(y,z * z)) = K(x,y). [para(2228(a,1),2217(a,1))]. 2230 K(x,T(y,z * (z * u))) = K(x,T(y,u)). [para(662(a,1),2229(a,1,2))]. 2232 K(x,T(y,z \ u)) = K(x,T(y,z * u)). [para(20(a,1),2230(a,1,2,2,2)),flip(a)]. 2233 K(x,T(y,T(z,z * u))) = K(x,T(y,(z \ u) * u)). [para(250(a,1),2230(a,1,2,2,2)),flip(a)]. 2234 K(x,T(y,(z / u) * (z * z))) = K(x,T(y,u / (z \ 1))). [para(399(a,1),2230(a,1,2,2,2))]. 2235 K(x,T(y,z \ (z \ u))) = K(x,T(y,u)). [para(20(a,1),2232(a,2,2,2))]. 2236 K(x,T(y,z * (u * u))) = K(x,T(y,z \ 1)). [para(2221(a,1),2235(a,1))]. 2237 K(x,T(y,z * (u * u))) = K(x,T(y,z)). [para(2236(a,2),2219(a,1))]. 2239 K(x,T(y,z / (u \ 1))) = K(x,T(y,u / z)). [para(2234(a,1),2237(a,1))]. 2241 (x * (R(y,z,z) * u)) / (R(T(y,x),z,z) * u) = T(x,y). [para(966(a,1),2161(a,1,1,2))]. 2243 T(x,R(y,z,z)) = T(x,y). [para(2241(a,1),1209(a,1)),flip(a)]. 2244 T(x,y / (z \ 1)) = T(x,y * z). [para(720(a,1),2243(a,1,2)),flip(a)]. 2246 K(x,T(y,z / u)) = K(x,T(y,u * z)). [para(2244(a,1),2239(a,1,2)),flip(a)]. 2247 K(x,T(y,(z \ u) * u)) = K(x,T(y,z)). [para(65(a,1),2246(a,1,2,2)),flip(a)]. 2248 K(x,T(y,T(z,z * u))) = K(x,T(y,z)). [para(2247(a,1),2233(a,2))]. 2249 K(x,T(y,T(z,u))) = K(x,T(y,z)). [para(20(a,1),2248(a,1,2,2,2))]. 2251 K(x,K(y,T(z,u))) = K(x,T(y,z)) * K(y,x). [para(2249(a,1),2206(a,1,1)),flip(a)]. 2253 K(x,K(y,T(z,u))) = K(x,K(y,z)). [para(2251(a,2),2206(a,1))]. 2254 K(x,K(y,z \ R(z,u,w))) = K(x,K(y,a(z,u,w))). [para(739(a,2),2253(a,1,2,2)),flip(a)]. 2255 K(x,K(y \ R(y,z,u),w)) = K(x,K(w,a(y,z,u))). [para(1849(a,2),2254(a,1,2))]. 2256 (x * (y * z)) \ ((x * y) * L(T(z,u),y,x)) = K(L(z,y,x),u). [para(44(a,2),2189(a,1,2,2))]. 2257 (x * (y * z)) \ (x * (y * T(z,u))) = K(L(z,y,x),u). [para(74(a,1),2256(a,1,2))]. 2258 L(K(x,y),z * x,u) = K(L(x,z,u),y). [para(2257(a,1),2185(a,1)),flip(a)]. 2259 K(L(x,y / x,z),u) = L(K(x,u),y,z). [para(22(a,1),2258(a,1,2)),flip(a)]. 2260 K(x,y) * K(R(y,z,u),x) = K(R(y,z,u) / y,x). [para(2081(a,1),2059(a,1)),flip(a)]. 2261 K(x,y) * K(R(y,z,u),x) = K(y \ R(y,z,u),x). [para(478(a,1),2260(a,2,1))]. 2262 K(x,y) * K(R(y,z,u),x) = K(x,y \ R(y,z,u)). [para(2261(a,2),1849(a,1))]. 2263 K(x,K(y,z) \ R(K(y,z),u,w)) = K(x,K(y,z)) * K(x,K(z,y)). [para(2169(a,1),2262(a,1,2)),flip(a)]. 2264 (x * T(y,z)) \ ((x * K(y,z)) * (y * u)) = L(u,y,x \ K(y,z)). [para(2139(a,1),284(a,1)),flip(a)]. 2265 K(x,K(y,z) \ R(K(y,z),u,w)) = 1. [para(2263(a,2),2147(a,1))]. 2266 K(x,K(y,z) \ K(R(y,u,w),z)) = 1. [para(1629(a,1),2265(a,1,2,2))]. 2268 K(x,K(y,z) * K(R(z,u,w),y)) = 1. [para(900(a,1),2266(a,1,2))]. 2269 K(x,K(y \ R(y,z,u),w)) = 1. [para(2261(a,1),2268(a,1,2))]. 2270 K(x,K(y,a(z,u,w))) = 1. [para(2269(a,1),2255(a,1)),flip(a)]. 2271 T(x,K(y,a(z,u,w))) = x. [hyper(41,a,2270,a)]. 2273 K(x,T(a(y,z,u),w)) = K(x,a(y,z,u)). [hyper(24,a,2220,a(flip),b,2271,a(flip)),flip(a)]. 2274 K(x,y \ R(y,z,u)) = K(x,a(y,z,u)). [para(1839(a,1),2273(a,1,2))]. 2275 K(x,y \ R(y,z,u)) = K(a(y,z,u),x). [para(2274(a,2),1847(a,2)),flip(a)]. 2276 K(x \ R(x,y,z),u) = K(u,a(x,y,z)). [para(2274(a,1),1849(a,2))]. 2277 K(x,a(y,z,L(u,z,y))) = K(x,y \ R(y,z,u)). [para(1990(a,1),2274(a,1,2,2)),flip(a)]. 2278 K(x,y) * K(R(y,z,u),x) = K(x,a(y,z,u)). [para(2274(a,1),2262(a,2))]. 2279 K(x,a(K(y,z),u,w)) = 1. [para(2274(a,1),2265(a,1))]. 2280 T(x,a(K(y,z),u,w)) = x. [hyper(41,a,2279,a)]. 2281 ((K(x,y) * z) * u) / (K(x,y) * (z * u)) = a(K(x,y),z,u). [para(2280(a,1),300(a,1,2))]. 2282 K(R(x,y,z) \ x,u) = K(u,a(x,x * y,z)). [para(618(a,1),2276(a,1,1))]. 2283 K(x,y) * K(y,R(x,z,u)) = K(y,a(x,z,u)). [para(2278(a,1),1674(a,1)),flip(a)]. 2284 L(x,y * z,K(y,u)) = x * K(u,a(y,z,x)). [para(2283(a,1),2077(a,1,2)),flip(a)]. 2285 K(x,a(y,z,L(u,z,y))) = K(x,a(y,z,u)). [para(2277(a,2),2274(a,1))]. 2286 K(x,y) \ R(K(x,y),z,u) = a(K(x,y),z,u). [para(2281(a,1),537(a,1)),flip(a)]. 2287 x \ L(x,y,K(z,u)) = a(K(z,u),y,x). [para(2286(a,1),1988(a,1)),flip(a)]. 2288 x * a(K(y,z),u,x) = L(x,u,K(y,z)). [para(2287(a,1),20(a,1,2))]. 2289 a(K(x,y),x * z,u) = K(y,a(x,z,u)). [hyper(23,a,2284,a(flip),b,2288,a)]. 2290 x * a(K(y,z),u,x) = L(x,u,K(z,y)). [para(905(a,1),2288(a,1,2))]. 2291 K(x,a(y,y * z,u)) = a(K(y,x),z,u). [para(2289(a,1),1778(a,1))]. 2292 K((x * y) * z,a(x,y,z)) = 1. [para(2289(a,1),2132(a,1))]. 2293 K(x * (y * z),a(x,y,L(z,y,x))) = 1. [para(74(a,1),2292(a,1,1))]. 2294 K(x,a(y,y * z,u)) = a(K(x,y),z,u). [para(2291(a,2),905(a,1))]. 2295 K(x * (y * z),a(x,y,z)) = 1. [para(2293(a,1),2285(a,1)),flip(a)]. 2296 x \ R(x,y,z) = a(x,y,z) * 1. [para(2295(a,1),1848(a,1,2)),flip(a)]. 2297 a(x,y,z) = x \ R(x,y,z). [hyper(24,a,18,a,b,2296,a(flip))]. 2298 a(x,y,z) = L(z,y,x) \ z. [hyper(24,a,1989,a(flip),b,2296,a(flip))]. 2300 R(x,y,z) = x * a(x,y,z). [para(2297(a,2),20(a,1,2)),flip(a)]. 2301 L(x,y,z) \ L(R(x,u,w),y,z) = a(L(x,y,z),u,w). [para(48(a,1),2297(a,2,2)),flip(a)]. 2302 R(x,y,z) \ x = a(x,y,z) \ 1. [para(2297(a,2),462(a,1,1)),flip(a)]. 2303 R(x,y,z) = a(x,y,z) * x. [para(2297(a,2),479(a,1,1)),flip(a)]. 2306 x * (a(x,y,z) * u) = R(x,y,z) * u. [para(2297(a,2),501(a,1,2,1))]. 2307 R(x,y,z) \ (x * u) = a(x,y,z) \ u. [para(2297(a,2),522(a,1,1)),flip(a)]. 2308 a(x,y,z) * (x * u) = R(x,y,z) * u. [para(2297(a,2),528(a,1,1))]. 2309 R(x,y,z) * (x \ u) = a(x,y,z) * u. [para(2297(a,2),532(a,1,1)),flip(a)]. 2310 a(x,x * y,z) = R(x,y,z) \ x. [para(2297(a,2),618(a,1))]. 2311 a(x,y,z) = R(x,x * y,z) \ x. [para(2297(a,2),622(a,2)),flip(a)]. 2313 a(x,y,z) = x * R(x \ 1,y,z). [para(2297(a,2),635(a,2)),flip(a)]. 2314 L(x,a(y,z,u),y * z) = x. [para(2297(a,2),1411(a,1,2))]. 2315 (x * y) * R((x * y) \ x,z,u) = x * a(y,z,u). [para(2297(a,2),1592(a,2,2))]. 2316 x \ (R(y,z,u) * (y \ x)) = a(T(y,x),z,u). [para(2297(a,2),1830(a,1)),flip(a)]. 2317 T(x \ R(x,y,z),u) = a(T(x,u),y,z). [para(2297(a,2),1831(a,1)),flip(a)]. 2318 R(x \ R(x,y,z),u,w) = a(R(x,u,w),y,z). [para(2297(a,2),1927(a,1)),flip(a)]. 2319 L(x \ R(x,y,z),u,w) = a(L(x,u,w),y,z). [para(2297(a,2),1939(a,1)),flip(a)]. 2320 a(x,y,z) = z \ L(z,x * y,x). [para(2297(a,2),1953(a,2)),flip(a)]. 2321 L(x,y,z) = a(z,y,x) \ x. [para(2297(a,2),1976(a,2,1))]. 2322 a(x,x * y,z) = z \ L(z,y,x). [para(2297(a,2),1956(a,1))]. 2323 x * (L(x,y,z) \ u) = a(z,y,x) * u. [para(2297(a,2),1985(a,1,1)),flip(a)]. 2325 L(L(x,y,z),u,w) \ L(x,u,w) = a(z,y,L(x,u,w)). [para(49(a,1),2298(a,2,1)),flip(a)]. 2326 L(x,y,z) = x / a(z,y,x). [para(2298(a,2),65(a,1,2)),flip(a)]. 2327 a(x,x * y,(x * y) \ z) = (y \ (x \ z)) \ ((x * y) \ z). [para(270(a,1),2298(a,2,1))]. 2328 a(x,y,z) \ 1 = z \ L(z,y,x). [para(2298(a,2),511(a,1,1))]. 2329 a(x,y,z) = z / L(z,y,x). [para(2298(a,2),519(a,2)),flip(a)]. 2331 x \ (L(x,y,z) * u) = a(z,y,x) \ u. [para(2298(a,2),512(a,1,1)),flip(a)]. 2332 L(x,y,z) \ (x * u) = a(z,y,x) * u. [para(2298(a,2),524(a,2,1))]. 2333 a(x,y,z) * (L(z,y,x) * u) = z * u. [para(2298(a,2),646(a,1,1))]. 2334 (x * y) / (L(x,z,u) * y) = a(u,z,x). [para(2298(a,2),649(a,2))]. 2335 L(x,y,z) * (x \ u) = a(z,y,x) \ u. [para(2298(a,2),651(a,1,1)),flip(a)]. 2336 a(T(x,y),z,y) = L(y,z,x) \ y. [para(1992(a,1),2298(a,2,1))]. 2337 R(x,y * (y * z),u) = x * a(x,z,u). [para(1778(a,1),2300(a,2,2))]. 2338 ((x * y) * a(x,y,z)) * u = (x * y) * (a(x,y,z) * u). [para(2314(a,1),74(a,1,2))]. 2340 K(a(x,y,z) \ 1,u) = K(u,a(x,x * y,z)). [para(2302(a,1),2282(a,1,1))]. 2341 a(x,x * y,z) = a(x,y,z) \ 1. [para(2310(a,2),2302(a,1))]. 2342 L(x,y * z,y) = x * a(y,z,x). [para(2311(a,2),1966(a,2,2))]. 2343 a(x,x * y,z) \ 1 = a(x,y,z). [para(2311(a,2),2302(a,1)),flip(a)]. 2344 L(x,a(y,z,u),z) = x. [para(2313(a,2),1443(a,1,2))]. 2347 (x * a(y,x,z)) * u = x * (a(y,x,z) * u). [para(2344(a,1),74(a,1,2))]. 2348 (x \ a(y,x,z)) \ 1 = a(y,x,z) \ x. [para(2344(a,1),259(a,1)),flip(a)]. 2349 (x \ a(y,x,z)) \ u = a(y,x,z) \ (x * u). [para(2344(a,1),267(a,1)),flip(a)]. 2350 (x * y) \ (x * L(y,z * u,z)) = L(a(z,u,y),y,x). [para(2320(a,2),76(a,1,1)),flip(a)]. 2351 a(x,y,L(z,y,x)) = L(z,y,x) \ z. [para(303(a,1),2320(a,2,2))]. 2356 (x * L(y,z,u)) / L(a(u,u * z,y),y,x) = x * y. [para(2322(a,2),179(a,1,2,1))]. 2357 ((x * y) \ x) * L(L(y,x,x * y),z,u) = a(u,z,L(y,x,x * y)) \ 1. [para(2328(a,2),738(a,1)),flip(a)]. 2358 a(T(x,y),z,y) = a(x,z,y). [para(2336(a,2),2298(a,2)),flip(a)]. 2359 a(x,x * y,z) * u = a(x,y,z) \ u. [para(2341(a,2),318(a,1,1))]. 2360 a(x,x * y,z) \ u = a(x,y,z) * u. [para(2341(a,2),330(a,1,1))]. 2361 L(x,y,a(z,z * u,w)) = L(x,y,a(z,u,w)). [para(2341(a,2),787(a,1,3))]. 2362 L(x * a(y,z,x),z,y) = x. [para(2342(a,1),308(a,1,1))]. 2364 a(x,y,L(z,y,x)) = a(x,y,z). [para(2351(a,2),2298(a,2)),flip(a)]. 2365 a(x,x * y,L(z,y,x)) = a(x,y,z) \ 1. [para(2364(a,1),2341(a,2,1))]. 2366 K(a(x,x * y,z),u) = a(K(u,x),y,z). [para(2294(a,1),1847(a,2))]. 2368 x * (y * a(x,z,y)) = R(x,z,y) * y. [para(1964(a,1),2306(a,1,2))]. 2369 R(a(x,y,z),u,w) \ R(x,y,z) = a(a(x,y,z),u,w) \ x. [para(2303(a,2),2307(a,1,2))]. 2370 a(T(x,y),z,u) = T(a(x,z,u),y). [para(2297(a,2),2317(a,1,1)),flip(a)]. 2371 a(T(x,y),z,u) \ a(x,z,u) = K(y,a(x,z,u)). [para(2370(a,2),1080(a,2,1)),flip(a)]. 2372 a(T(x,y),y,z) = a(x,y,z). [para(2370(a,2),1687(a,1))]. 2373 a(x,T(y,x),z) = a(x,y,z). [para(2372(a,1),1790(a,1)),flip(a)]. 2374 a(x / y,y,z) = a(y * x,y,z). [para(2373(a,1),1810(a,1)),flip(a)]. 2375 a(x / y,x,z) = a(x * y,x,z). [para(2374(a,1),612(a,1)),flip(a)]. 2376 a(x,y,z) * (u * L(z,y,x)) = z * T(u,L(z,y,x)). [para(36(a,2),2323(a,1,2)),flip(a)]. 2377 x * (a(y,z,x) \ u) = L(x,z,y) * u. [para(2331(a,1),20(a,1,2))]. 2378 a(x,y,z) * (z * u) = z * (a(x,y,z) * u). [para(2332(a,1),2323(a,1,2)),flip(a)]. 2379 R(T(a(x,y,z),(L(z,y,x) * u) * w),L(z,y,x) * u,w) = ((L(z,y,x) * u) * w) \ ((z * u) * w). [para(2333(a,1),549(a,1,2,1)),flip(a)]. 2380 a(x,y,z) * (z * x) = z * R(x,y,z). [para(1973(a,1),2333(a,1,2))]. 2381 L(a(x,y,z),u,w) * L(z,y,x) = a(w,u,a(x,y,z)) \ z. [para(2321(a,2),2335(a,1,2))]. 2382 R(x,y * (y * z),u) = R(x,z,u). [para(2337(a,2),2300(a,2)),flip(a)]. 2383 R(x,y \ z,u) = R(x,y * z,u). [para(20(a,1),2382(a,1,2,2)),flip(a)]. 2385 R(x,(y \ z) / u,w) = R(x,(y * z) / u,w). [para(238(a,1),2382(a,1,2)),flip(a)]. 2386 (x \ a(y,x,z)) \ u = (a(y,x,z) \ x) * u. [para(2348(a,1),318(a,1,1)),flip(a)]. 2388 K(a(x,y,z) \ 1,u) = a(K(u,x),y,z). [para(2341(a,1),2366(a,1,1))]. 2389 (x * y) * L(a(x,z,y),y,x) = R(x,z,y) * y. [para(2368(a,1),74(a,2))]. 2390 x \ ((y \ x) * T(y,x)) = a(T(y,x),x,y). [para(1317(a,1),2316(a,1,2))]. 2391 x \ ((y \ x) * T(y,x)) = a(y,x,y). [para(2390(a,2),2086(a,1))]. 2393 a(R(x,y,z),u,y) = L(y,u,x) \ y. [para(2318(a,1),1986(a,1))]. 2394 a(R(x,y,z),u,w) = R(a(x,u,w),y,z). [para(2297(a,2),2318(a,1,1)),flip(a)]. 2396 a(R(x,y,z),u,y) = a(x,u,y). [para(2393(a,2),2298(a,2)),flip(a)]. 2400 a(L(x,y,x),z,y) = a(x,z,y). [para(1312(a,1),2396(a,1,1)),flip(a)]. 2404 R(a(x,y,z),x * u,w) = a(R(x,u,w),y,z). [para(2394(a,1),1718(a,1))]. 2406 a(L(x,y,z),u,w) = L(a(x,u,w),y,z). [para(2297(a,2),2319(a,1,1)),flip(a)]. 2407 a(L(x,y,z),u,w) \ a(x,u,w) = a(z,y,a(x,u,w)). [para(2406(a,2),2298(a,2,1)),flip(a)]. 2408 a(x,y,z) \ a(L(x,u * w,u),y,z) = a(u,w,a(x,y,z)). [para(2406(a,2),2320(a,2,2)),flip(a)]. 2409 a(x,y,z) \ a(L(x,u,w),y,z) = a(w,u,a(x,y,z)) \ 1. [para(2406(a,2),2328(a,2,2)),flip(a)]. 2410 K(x,a(y / z,(y / z) * z,u)) = K(a(z * y,z,u) \ 1,x). [para(2374(a,1),2340(a,1,1,1)),flip(a)]. 2411 (a(x,y,z) * y) * u = y * (a(x,y,z) * u). [para(1688(a,2),2347(a,1,1))]. 2412 a(x,y,z) \ (y * u) = (a(x,y,z) \ y) * u. [para(2386(a,1),2349(a,1)),flip(a)]. 2413 L(x,y,a(z,y,u)) = x. [hyper(23,a,798,a,b,2412,a(flip)),flip(a)]. 2414 (a(x,y,z) * y) * u = a(x,y,z) * (y * u). [para(2413(a,1),74(a,1,2))]. 2415 (a(x,y,z) * (y \ 1)) * u = a(x,y,z) * (y \ u). [para(2413(a,1),945(a,1,2))]. 2416 R(a(x,y,z),y,u) = a(x,y,z). [hyper(24,a,79,a,b,2414,a(flip)),flip(a)]. 2417 a(x,y,z) * (y * u) = y * (a(x,y,z) * u). [para(2414(a,1),2411(a,1))]. 2419 (x * y) \ (x * (a(z,x,u) * y)) = T(a(z,x,u),x * y). [para(2417(a,1),36(a,2,2)),flip(a)]. 2420 x * (y * (a(x,y,z) * u)) = R(x,y,z) * (y * u). [para(2417(a,1),2306(a,1,2))]. 2421 (x * y) * a(L(x,y,x),z,y) = R(x,z,y) * y. [para(2406(a,2),2389(a,1,2))]. 2422 (x * y) * a(x,z,y) = R(x,z,y) * y. [para(2400(a,1),2421(a,1,2))]. 2423 (x * (R(y,z,u) * u)) / ((y * u) * R(a(y,z,u),y * u,x)) = L(x,y * u,a(y,z,u)). [para(2422(a,1),2079(a,2,1,2)),flip(a)]. 2424 (x \ a(y,x,z)) * u = a(y,x,z) * (x \ u). [para(1795(a,1),2415(a,1,1))]. 2425 (a(x,y,z) * (y \ u)) \ ((y \ a(x,y,z)) * (u * w)) = L(w,u,y \ a(x,y,z)). [para(2424(a,1),32(a,2,1)),flip(a)]. 2426 L(T(a(x,y,z),u),u,y) = T(a(x,y,z),y * u). [para(2419(a,1),106(a,1)),flip(a)]. 2427 L(a(T(x,y),z,u),y,z) = T(a(x,z,u),z * y). [para(2370(a,2),2426(a,1,1))]. 2428 a(L(x,y,z),u,w) * L(w,u,x) = a(z,y,a(x,u,w)) \ w. [para(2406(a,2),2381(a,1,1))]. 2429 K(a(x * y,x,z) \ 1,u) = K(u,a(y / x,y,z)). [para(22(a,1),2410(a,1,2,2)),flip(a)]. 2430 K(a(x * y,x,z) \ 1,u) = K(u,a(y * x,y,z)). [para(2375(a,1),2429(a,2,2))]. 2431 K(x,a(y * z,y,u)) = a(K(x,z * y),z,u). [para(2430(a,1),2388(a,1))]. 2432 a(L(x,y,z),R(z,y,x),u) = (x * (z * u)) \ ((x * z) * u). [para(1998(a,1),1981(a,1,1)),flip(a)]. 2433 a(L(x,y,z),R(z,y,x),u) = a(x,z,u). [para(2432(a,2),28(a,2)),flip(a)]. 2435 L(a(x,R(y,z,x),u),z,y) = a(x,y,u). [para(2433(a,1),2406(a,1)),flip(a)]. 2436 (a(x,y,z) * (y \ u)) \ (a(x,y,z) * (y \ (u * w))) = L(w,u,y \ a(x,y,z)). [para(2424(a,1),2425(a,1,2))]. 2437 L(L(x,y,z),z * y,a(u,z,w)) = L(x,y,z \ a(u,z,w)). [para(2436(a,1),1409(a,1)),flip(a)]. 2438 L(L(x,y,z),z * y,a(u,z,w)) = L(x,y,z * a(u,z,w)). [para(2437(a,2),776(a,1))]. 2439 (R(x,y,z) * y) \ ((x * y) * u) = (x \ R(x,y,z)) \ u. [para(1996(a,1),1411(a,1))]. 2440 L(x,y,R(z,y,x)) = (z \ R(z,y,x)) \ x. [para(2439(a,1),183(a,1)),flip(a)]. 2441 L(x,y,R(z,y,x)) = L(x,y,z). [para(2440(a,2),1976(a,2)),flip(a)]. 2442 L(x,y * z,R(y,z,x) \ 1) = L(x,y * z,y \ 1). [para(584(a,1),2441(a,1,3))]. 2443 L(x,y * z,R(y,z,x)) = L(x,y * z,y \ 1). [para(2442(a,1),787(a,1)),flip(a)]. 2444 L(x,y * z,R(y,z,x)) = L(x,y * z,y). [para(2443(a,2),787(a,1))]. 2445 R(x,y,z) * (L(z,x * y,x) \ z) = R(R(x,y,z),x * y,z). [para(2444(a,1),1979(a,2,2,1)),flip(a)]. 2446 R(x,y,z) * (R(x,y,z) \ x) = R(R(x,y,z),x * y,z). [para(1954(a,1),2445(a,1,2))]. 2447 R(R(x,y,z),x * y,z) = x. [para(2446(a,1),20(a,1))]. 2448 R(R(x,x * y,z),y,z) = x. [para(2447(a,1),50(a,1)),flip(a)]. 2449 K(x,R(y,y * z,u) \ R(R(y,y * z,u),z,u)) = K(x,R(y,y * z,u)) * K(y,x). [para(2448(a,1),2262(a,1,2,1)),flip(a)]. 2450 K(x,R(y,y * z,u) \ R(R(y,y * z,u),z,u)) = R(K(x,y),z,u) * K(y,x). [para(1672(a,1),2449(a,2,1))]. 2451 K(x,R(y,y * z,u) \ R(R(y,y * z,u),z,u)) = K(y,x) * R(K(x,y),z,u). [para(2450(a,2),406(a,1))]. 2452 K(x,R(y,y * z,u) \ y) = K(y,x) * R(K(x,y),z,u). [para(2448(a,1),2451(a,1,2,2))]. 2453 K(x,y) * R(K(y,x),z,u) = K(y,x \ R(x,z,u)). [para(622(a,1),2452(a,1,2)),flip(a)]. 2454 x * K(y,z \ R(z,u,x)) = L(x,u,K(y,z)). [para(2453(a,1),2076(a,1,2))]. 2455 x * K(a(y,z,x),u) = L(x,z,K(u,y)). [para(2275(a,1),2454(a,1,2))]. 2456 a(K(x,y),z,u) = K(a(x,z,u),y). [hyper(23,a,2290,a,b,2455,a),flip(a)]. 2457 a(K(x,y),z,u) = K(a(y,z,u),x). [hyper(23,a,2288,a,b,2455,a),flip(a)]. 2458 a(K(x,y),z,u) = K(y,a(x,z,u)). [para(2456(a,2),1847(a,1))]. 2459 a(K(x,y),z,u) = K(x,a(y,z,u)). [para(2457(a,2),1847(a,1))]. 2460 x * K(y,a(z,u,x)) = L(x,u,K(z,y)). [para(2458(a,1),2288(a,1,2))]. 2461 K(x * y,a(z,x,u)) = K(z,a(y * x,y,u)). [para(2458(a,1),2431(a,2)),flip(a)]. 2462 K(x,a(y,z,u)) = K(y,a(x,z,u)). [para(2459(a,1),2458(a,1))]. 2463 L(x,y * z,K(y,u)) = L(x,z,K(y,u)). [para(2460(a,1),2284(a,2))]. 2464 (x * (R(y,z,u) * u)) / ((y * u) * a(R(y,u,x),z,u)) = L(x,y * u,a(y,z,u)). [para(2404(a,1),2423(a,1,2,2))]. 2465 (x * (R(y,z,u) * u)) / ((y * u) * a(y,z,u)) = L(x,y * u,a(y,z,u)). [para(2396(a,1),2464(a,1,2,2))]. 2467 (x * (R(y,z,u) * u)) / (R(y,z,u) * u) = L(x,y * u,a(y,z,u)). [para(2422(a,1),2465(a,1,2))]. 2468 L(x,y * z,a(y,u,z)) = x. [para(2467(a,1),21(a,1))]. 2469 L(x,y * z,a(T(z,y),u,y)) = x. [para(2468(a,1),1185(a,1)),flip(a)]. 2470 L(x,y * z,a(z,u,y)) = x. [para(2358(a,1),2469(a,1,3))]. 2471 (a(x,y,z) * (z * x)) \ (a(x,y,z) * (z * (x * u))) = L(u,x,z). [para(2470(a,1),174(a,2))]. 2472 (x * R(y,z,x)) \ (a(y,z,x) * (x * (y * u))) = L(u,y,x). [para(2380(a,1),2471(a,1,1))]. 2473 (x * R(y,z,x)) \ (x * (a(y,z,x) * (y * u))) = L(u,y,x). [para(2378(a,1),2472(a,1,2))]. 2474 (x * R(y,z,x)) \ (x * (R(y,z,x) * u)) = L(u,y,x). [para(2308(a,1),2473(a,1,2,2))]. 2475 L(x,R(y,z,u),u) = L(x,y,u). [para(2474(a,1),32(a,2))]. 2476 a(x,R(y,z,x),u) = L(u,y,x) \ u. [para(2475(a,1),2298(a,2,1))]. 2477 a(x,R(y,z,x),u) = a(x,y,u). [para(2476(a,2),2298(a,2)),flip(a)]. 2478 L(a(x,y,z),u,y) = a(x,y,z). [para(2477(a,1),2435(a,1,1))]. 2479 a(L(x,y,z),z,u) = a(x,z,u). [para(2478(a,1),2406(a,2))]. 2480 T(a(x,y,z),y * u) = a(T(x,u),y,z). [para(2478(a,1),2427(a,1)),flip(a)]. 2482 a((x * y) \ z,x,u) = a(y \ (x \ z),x,u). [para(177(a,1),2479(a,1,1))]. 2483 L(x,y,z) * a(x,z,u) = R(L(x,y,z),z,u). [para(2479(a,1),2300(a,2,2)),flip(a)]. 2484 a(T(x,y),z,u) \ a(x,z,u) = K(z * y,a(x,z,u)). [para(2480(a,1),1080(a,2,1)),flip(a)]. 2486 a(x \ (y \ z),y,u) = a((y * x) * z,y,u). [para(2482(a,1),1702(a,1))]. 2487 L(x,y,z) * a(x,z,u) = L(R(x,z,u),y,z). [para(2483(a,2),48(a,1))]. 2488 a((x * y) * z,x,u) = a(y * (x * z),x,u). [para(2486(a,1),1757(a,1))]. 2489 (x * a(x,y,z)) / L(R(x,y,z),u,y) = a(y,u,x). [para(2487(a,1),2334(a,1,2))]. 2490 a(T(x,y) * (y * z),y,u) = a((x * y) * z,y,u). [para(82(a,1),2488(a,1,1,1)),flip(a)]. 2491 R(x,y,z) / L(R(x,y,z),u,y) = a(y,u,x). [para(2300(a,2),2489(a,1,1))]. 2492 a(x,y,R(z,x,u)) = a(x,y,z). [para(2491(a,1),2329(a,2))]. 2493 a(x,y,(z / u) / x) = a(x,y,z / (x * u)). [para(193(a,1),2492(a,1,3)),flip(a)]. 2494 K(x * y,a(z,x,u)) = K(y,a(z,x,u)). [para(2484(a,1),2371(a,1))]. 2495 K(x,a(y * z,y,u)) = K(z,a(x,y,u)). [para(2494(a,1),2462(a,1)),flip(a)]. 2496 K(x,a(y * z,y,u)) = K(y,a(x,z,u)). [para(2494(a,1),2461(a,1)),flip(a)]. 2497 K(x,a(y,z,u)) = K(z,a(y,x,u)). [para(2496(a,1),2495(a,1))]. 2498 x * K(y,a(z,u,x)) = L(x,y,K(z,u)). [para(2497(a,1),2460(a,1,2))]. 2499 L(x,y,K(z,u)) = L(x,u,K(z,y)). [para(2498(a,1),2460(a,1))]. 2501 L(x,y,K(z,z * u)) = L(x,u,K(z,y)). [para(2499(a,1),2463(a,1))]. 2502 L(x,y,a(z,u,u)) = L(x,u,K(z,y)). [para(2501(a,1),1261(a,1)),flip(a)]. 2503 L(x,y,a(z,u,u)) = L(x,y,K(z,u)). [para(2502(a,2),2499(a,1))]. 2504 L(x,y,a(z,u,z)) = L(x,y,K(u,z)). [para(2503(a,1),1695(a,1)),flip(a)]. 2505 L(L(x,y,z),z * y,K(z,u)) = L(x,y,z * a(u,z,u)). [para(2504(a,1),2438(a,1))]. 2506 L(x,y,z * a(u,z,u)) = L(x,y,T(z,u)). [para(2505(a,1),1604(a,1))]. 2507 L(x,y,R(z,u,u)) = L(x,y,T(z,u)). [para(2506(a,1),1692(a,1)),flip(a)]. 2508 L(x,y,T(z / u,z)) = L(x,y,u * z). [para(2507(a,1),846(a,1))]. 2509 L(x,y,z * u) = L(x,y,u * z). [para(2508(a,1),845(a,1))]. 2510 L(L(x,y,z * u),(z * u) * y,u * z) = x. [para(2509(a,1),303(a,1))]. 2511 L(x,y,z \ u) = L(x,y,u * z). [para(2509(a,1),776(a,2))]. 2513 L(x,y,z * (u * (u * w))) = L(x,y,w * z). [para(2509(a,1),868(a,2))]. 2514 L(x,y,(z * (u * w)) * (z * u)) = L(x,y,L(w,u,z)). [para(32(a,2),2511(a,1,3)),flip(a)]. 2515 L(x,y,K(z,u)) = x. [para(2510(a,1),1850(a,1)),flip(a)]. 2516 a(K(x,y),z,u) = 1. [hyper(38,a,2515,a)]. 2518 (K(x,y) * z) * u = K(x,y) * (z * u). [para(2515(a,1),74(a,1,2))]. 2519 (K(x,y) * z) \ (K(x,y) * u) = z \ u. [para(2515(a,1),76(a,1)),flip(a)]. 2520 (K(x,y) \ z) \ u = z \ (K(x,y) * u). [para(2515(a,1),267(a,1)),flip(a)]. 2521 (K(x,y) * z) / u = K(x,y) * (z / u). [para(2515(a,1),196(a,1,2))]. 2526 L(x,y,T(z,u)) = L(x,y,z). [para(2515(a,1),1604(a,1)),flip(a)]. 2534 L(x,y,a(z,u,z)) = x. [para(2515(a,1),2504(a,2))]. 2539 K(a(x,y,z) \ 1,u) = 1. [para(2516(a,1),2388(a,2))]. 2540 K(a(x,y,z),u) = 1. [para(2516(a,1),2456(a,1)),flip(a)]. 2543 T(a(x,y,z),u) = a(x,y,z). [hyper(41,a,2540,a)]. 2548 (a(x,y,x) * z) * u = (z * u) * a(x,y,x). [para(2534(a,1),2053(a,1,2))]. 2549 T(a(x,y,z) \ 1,u) = a(x,y,z) \ 1. [hyper(41,a,2539,a)]. 2553 L(x,y,z * (u * z)) = L(x,y,u). [para(2526(a,1),778(a,2))]. 2567 a(x,y,z) * u = u * a(x,y,z). [para(2543(a,1),82(a,1,2)),flip(a)]. 2569 (a(x,y,z) \ u) \ u = a(x,y,z). [para(2543(a,1),83(a,1)),flip(a)]. 2570 (a(x,y,z) \ u) * a(x,y,z) = u. [para(2543(a,1),250(a,1,2))]. 2571 x / a(y,z,u) = a(y,z,u) \ x. [para(2543(a,1),252(a,1,2))]. 2572 a(x,y,z) * (u \ 1) = u \ a(x,y,z). [para(2543(a,1),326(a,1,2)),flip(a)]. 2578 a(T(x,y),z,u) = a(x,z,u). [para(2543(a,1),2370(a,2))]. 2584 a(x / y,z,u) = a(y \ x,z,u). [para(84(a,1),2578(a,1,1)),flip(a)]. 2586 a(x * (y * x),z,u) = a(y,z,u). [para(2578(a,1),1704(a,2))]. 2597 a(x,y,z) * (u / a(x,y,z)) = u. [para(2567(a,2),22(a,1))]. 2598 (x * (a(y,z,u) * w)) \ ((x * w) * a(y,z,u)) = a(x,w,a(y,z,u)). [para(2567(a,2),28(a,2,1,2)),flip(a)]. 2601 (x * y) \ ((x * a(z,u,w)) * y) = R(T(a(z,u,w),x * y),x,y). [para(2567(a,1),549(a,1,2,1))]. 2602 x * (y * a(x,z,u)) = R(x,z,u) * y. [para(2567(a,1),2306(a,1,2))]. 2603 (x * y) * a(x,z,u) = R(x,z,u) * y. [para(2567(a,1),2308(a,1))]. 2604 x * (L(x,y,z) \ u) = u * a(z,y,x). [para(2567(a,1),2323(a,2))]. 2605 (a(x,y,z) \ u) \ w = (a(x,y,z) / u) * w. [para(2570(a,1),353(a,1,1,2)),flip(a)]. 2606 a(x / y,z,u) = a(y * x,z,u). [para(2584(a,2),1702(a,1))]. 2609 a(x * a(y,z,x),u,w) = a(L(x,z,y),u,w). [para(2333(a,1),2586(a,1,1))]. 2612 (x * y) / a(z,u,x) = L(x,u,z) * y. [hyper(23,a,2333,a,b,2597,a)]. 2613 a(x / y,z,u) = a(x * y,z,u). [para(2606(a,1),612(a,1)),flip(a)]. 2618 a(x * y,z,u) = a(y * x,z,u). [para(2613(a,1),2606(a,1))]. 2621 (x * (K(y,z) * (u * w))) \ ((x * (K(y,z) * u)) * w) = a(x,K(y,z) * u,w). [para(2518(a,1),28(a,2,1,2)),flip(a)]. 2622 (K(x,y) * (z * (u * w))) \ (((K(x,y) * z) * u) * w) = a(K(x,y) * z,u,w). [para(2518(a,1),28(a,2,1)),flip(a)]. 2623 (K(x,y) * (z * u)) \ ((K(x,y) * z) * (u * w)) = L(w,u,K(x,y) * z). [para(2518(a,1),32(a,2,1)),flip(a)]. 2624 ((K(x,y) * (z * u)) * w) / (u * w) = R(K(x,y) * z,u,w). [para(2518(a,1),34(a,2,1,1)),flip(a)]. 2629 ((T(x,y) * z) * u) / (K(x,y) * (z * u)) = R(x,K(x,y) * z,u). [para(2518(a,1),1167(a,1,2))]. 2630 K(x,T(y,z)) * (z * u) = (z * K(x,y)) * u. [para(2216(a,1),2518(a,1,1)),flip(a)]. 2631 (x \ K(y,z)) * (K(z,y) * u) = x \ u. [para(2519(a,1),2121(a,1)),flip(a)]. 2632 x \ (K(y,z) * u) = (x \ K(y,z)) * u. [para(2520(a,1),2133(a,1))]. 2633 x * (a(y,z,u) \ 1) = a(y,z,u) \ x. [para(2549(a,1),327(a,1,2))]. 2635 (x * y) \ (R(x,z,u) * y) = L(a(x,z,u),y,x). [para(2602(a,1),32(a,2,2)),flip(a)]. 2637 (x * y) \ (R(x,z,u) * y) = a(x,z,u). [hyper(23,a,20,a,b,2603,a),flip(a)]. 2642 (x * y) * (a(x,y,z) * u) = (R(x,y,z) * y) * u. [para(2603(a,1),2338(a,1,1)),flip(a)]. 2643 L(x,y,z) * a(z,y,L(x,u,w)) = L(x,u,w) * a(w,u,L(x,y,z)). [para(2325(a,1),2604(a,1,2))]. 2644 (L(x,y,z) * u) \ (x * u) = a(z,y,x). [para(2612(a,1),66(a,1,1))]. 2645 (x * K(y,z)) \ u = K(z,y) * (x \ u). [hyper(23,a,297,a,b,2631,a),flip(a)]. 2646 L(x,K(y,z),u) = x. [hyper(23,a,798,a,b,2632,a(flip)),flip(a)]. 2649 (x * K(y,z)) * u = x * (K(y,z) * u). [para(2646(a,1),74(a,1,2))]. 2650 (x * (K(y,z) * u)) / u = x * K(y,z). [para(2646(a,1),99(a,1,2))]. 2656 L(x,T(y,z) * y,u) = x. [para(2646(a,1),988(a,1)),flip(a)]. 2658 L(x,(y \ z) * (z / y),u) = x. [para(84(a,1),2656(a,1,2,1))]. 2659 L(x,(y * z) * (z / y),u) = x. [para(2658(a,1),880(a,1)),flip(a)]. 2660 L(x,T(L(y / z,z * y,y / z) * (z * y),y / z),u) = x. [para(1309(a,2),2659(a,1,2))]. 2661 x \ (R(x / y,z,u) * y) = a(x / y,z,u). [para(22(a,1),2637(a,1,1))]. 2662 (L(R(x,y,z),u,w) * (y * z)) \ ((x * y) * z) = a(w,u,R(x,y,z)). [para(79(a,1),2644(a,1,2))]. 2664 K(x * y,x) * (y \ z) = (x * (y / x)) \ z. [para(1129(a,1),2645(a,1,1)),flip(a)]. 2665 (K(x,y) / z) * u = K(x,y) * (z \ u). [para(2645(a,1),2143(a,1)),flip(a)]. 2666 R(x,K(y,z),u) = x. [hyper(24,a,79,a,b,2649,a(flip)),flip(a)]. 2667 (x * T(y,z)) \ (x * (K(y,z) * (y * u))) = L(u,y,x \ K(y,z)). [para(2649(a,1),2264(a,1,2))]. 2668 (x / y) / K(z,u) = x / (K(z,u) * y). [para(2666(a,1),193(a,1))]. 2670 (x * y) / T(y,z) = x * K(z,y). [para(1077(a,1),2650(a,1,1,2))]. 2671 (x / y) * K(z,y) = x / T(y,z). [para(22(a,1),2670(a,1,1)),flip(a)]. 2672 (x * (y * z)) / T(L(z,y,x),u) = (x * y) * K(u,L(z,y,x)). [para(74(a,1),2670(a,1,1))]. 2673 ((x \ y) * x) / T(y,x) = a(x,y,x). [para(2671(a,1),1538(a,1))]. 2675 a(x,y,x) * T(y,x) = (x \ y) * x. [para(2673(a,1),22(a,1,1))]. 2676 K(x * y,x) * ((x \ y) \ z) = (x / y) * z. [para(1009(a,1),2665(a,1,1)),flip(a)]. 2677 K(x,T(y,z)) * (z \ u) = (z \ K(x,y)) * u. [para(2201(a,1),2665(a,1,1)),flip(a)]. 2678 x / (K(y,z) * u) = (x / u) * K(z,y). [para(2668(a,1),2140(a,1))]. 2679 a(L(x,y * z,y),u,w) = a(L(x,z,y),u,w). [para(2342(a,2),2609(a,1,1))]. 2680 K(x,T(y,z)) * (z * u) = z * (K(x,y) * u). [para(2630(a,2),2649(a,1))]. 2681 x \ (y * R(y \ x,z,u)) = a(x / y,z,u). [para(224(a,1),2661(a,1,2))]. 2682 L(x,y,z * (K(u * w,u) * ((u * (w / u)) \ v5))) = L(x,y,(w \ v5) * z). [para(2664(a,1),2513(a,1,3,2,2))]. 2683 a(x,y,z) \ a(L(x,u,w),y,z) = a(w,u,a(x,y,z)). [para(2679(a,1),2408(a,1,2))]. 2685 x \ (y * R(y \ x,z,u)) = a(y * x,z,u). [para(2681(a,2),2606(a,1))]. 2686 (x * (y * z)) \ ((x * y) * R(L(z,y,x),u,w)) = a((x * y) * (x * (y * z)),u,w). [para(32(a,2),2685(a,1,2,2,1))]. 2687 L(a(x,y,z),u,x) = a(x,y,z). [para(2635(a,1),2637(a,1))]. 2692 (x * (y * (a(x,y,z) * u))) \ ((R(x,y,z) * y) * u) = a(x,y,a(x,y,z) * u). [para(2642(a,1),28(a,2,2)),flip(a)]. 2693 L(x,y,z) * a(L(z,u,w),y,x) = x * a(w,u,a(z,y,x)). [para(2683(a,1),2377(a,1,2)),flip(a)]. 2694 a(x,y,a(z,u,w)) \ 1 = a(x,y,a(z,u,w)). [para(2683(a,1),2409(a,1)),flip(a)]. 2695 a(x,y,a(z,u,w)) * a(x,y,a(z,u,w)) = 1. [para(2694(a,1),20(a,1,2))]. 2696 a(x,y,a(z,u,w)) \ v5 = v5 * a(x,y,a(z,u,w)). [para(2694(a,1),2633(a,1,2)),flip(a)]. 2697 a(L(x,y,z),u,w) * L(w,u,x) = w * a(z,y,a(x,u,w)). [para(2696(a,1),2428(a,2))]. 2698 (K(x,y) * ((z * u) * w)) / (u * w) = R(K(x,y) * z,u,w). [para(2518(a,1),2624(a,1,1))]. 2699 K(x,y) * (((z * u) * w) / (u * w)) = R(K(x,y) * z,u,w). [para(2698(a,1),2521(a,1)),flip(a)]. 2700 R(K(x,y) * z,u,w) = K(x,y) * R(z,u,w). [para(34(a,2),2699(a,1,2)),flip(a)]. 2701 R(x * K(y,z),u,w) = R(x,u,w) * K(y,z). [hyper(23,a,699,a(flip),b,2700,a(flip))]. 2704 R(T(x,y),z,u) * K(y,x) = R(x,z,u). [para(1089(a,1),2701(a,1,1)),flip(a)]. 2706 K(x,R(y,z,u)) = K(x,y). [hyper(23,a,1109,a,b,2704,a),flip(a)]. 2708 T(x,R(y,z,u)) = x * K(x,y). [para(2706(a,1),1107(a,2,2))]. 2716 T(x,R(y,z,u)) = T(x,y). [para(2708(a,2),1107(a,2)),flip(a)]. 2717 R(x,y,z) * T(u,x) = u * R(x,y,z). [para(2716(a,1),82(a,1,2))]. 2723 R(x,y,z) * (x \ u) = (u / x) * R(x,y,z). [para(84(a,1),2717(a,1,2))]. 2725 (x / y) * R(y,z,u) = a(y,z,u) * x. [para(2723(a,1),2309(a,1))]. 2726 a(x,y,z) * (u * x) = u * R(x,y,z). [para(21(a,1),2725(a,1,1)),flip(a)]. 2727 L(x,y,z) * R(a(z,y,x),u,w) = a(a(z,y,x),u,w) * x. [para(2326(a,2),2725(a,1,1))]. 2729 (x * y) * a(y,z,u) = x * R(y,z,u). [para(2726(a,1),2567(a,1)),flip(a)]. 2730 (x * (y * z)) \ (x * (y * R(z,u,w))) = L(a(z,u,w),y * z,x). [para(2729(a,1),32(a,2,2,2)),flip(a)]. 2731 L(x,T((y / z) * (z * y),y / z),u) = x. [para(892(a,1),2660(a,1,2,1,1))]. 2733 L(x,(y * z) / (z / y),u) = x. [para(2731(a,1),1235(a,1)),flip(a)]. 2734 L(x,(y * z) * (y / z),u) = x. [para(952(a,1),2733(a,1,2))]. 2735 (x * (y * z)) / L(T(z,u),y,x) = (x * y) * K(u,L(z,y,x)). [para(44(a,2),2672(a,1,2))]. 2736 (x * y) \ ((x * a(z,u,w)) * y) = R(a(z,u,w),x,y). [para(2543(a,1),2601(a,2,1))]. 2738 (((T(x,y) * z) * u) / (z * u)) * K(y,x) = R(x,K(x,y) * z,u). [para(2629(a,1),2678(a,1)),flip(a)]. 2739 (x * T(y,z)) \ (x * (T(y,z) * u)) = L(u,y,x \ K(y,z)). [para(1160(a,1),2667(a,1,2,2))]. 2740 L(x,y,z \ K(y,u)) = L(x,T(y,u),z). [para(2739(a,1),32(a,2)),flip(a)]. 2741 L(x,y,z * K(y,u)) = L(x,T(y,u),z). [para(2740(a,1),776(a,1)),flip(a)]. 2742 R(T(x,y),z,u) * K(y,x) = R(x,K(x,y) * z,u). [para(34(a,2),2738(a,1,1))]. 2743 R(x,K(x,y) * z,u) = R(x,z,u). [para(2742(a,1),2704(a,1))]. 2744 R(x,y * x,z) = R(x,x * y,z). [para(974(a,1),2743(a,1,2)),flip(a)]. 2746 x \ R(x,y * x,z) = R(x,y,z) \ x. [para(2744(a,2),618(a,1,2))]. 2747 a(x,y * x,z) = R(x,y,z) \ x. [para(2746(a,1),2297(a,2))]. 2748 a(x,y * x,z) = a(x,y,z) \ 1. [para(2747(a,2),2302(a,1))]. 2749 a(x * y,y,z) = a(x * y,x,z) \ 1. [para(2748(a,1),1778(a,1)),flip(a)]. 2750 a(x * y,y,a(z,u,w)) = a(x * y,x,a(z,u,w)). [para(2749(a,2),2694(a,1))]. 2751 ((L(x,y,z) * u) * w) \ ((x * u) * w) = a(z,y,R(x,u,w)). [para(184(a,1),2662(a,1,1))]. 2752 (K(x,y) * (z * u)) \ (K(x,y) * (z * (u * w))) = L(w,u,K(x,y) * z). [para(2518(a,1),2623(a,1,2))]. 2753 L(x,y,K(z,u) * w) = (w * y) \ (w * (y * x)). [para(2752(a,1),2519(a,1))]. 2754 L(x,y,K(z,u) * w) = L(x,y,w). [para(2753(a,2),32(a,2)),flip(a)]. 2755 ((x * K(y,z)) * u) \ ((x * K(y,z)) * (u * w)) = L(w,u,x). [para(2753(a,1),2553(a,1))]. 2757 L(x,y,T(z,u) * w) = L(x,y,z * w). [para(1098(a,1),2754(a,1,3)),flip(a)]. 2758 L(x,y,(z / u) * w) = L(x,y,(u \ z) * w). [para(1161(a,1),2754(a,1,3))]. 2759 L(x,y,z * T(u,w)) = L(x,y,z * u). [para(1212(a,1),2754(a,1,3))]. 2760 L(x,y,z * K(u,w)) = L(x,y,z). [para(2200(a,1),2754(a,1,3))]. 2762 L(x,y,z * (K(u,w) * v5)) = L(x,y,z * v5). [para(2680(a,1),2754(a,1,3))]. 2763 L(x,T(y,z),u) = L(x,y,u). [para(2760(a,1),2741(a,1)),flip(a)]. 2765 L(x,(y * z) * z,u) = L(x,y,u). [para(2763(a,1),951(a,1)),flip(a)]. 2766 L(x,y / z,u) = L(x,z * y,u). [para(2763(a,1),1235(a,1)),flip(a)]. 2777 L(x,y / z,u) = L(x,y * z,u). [para(22(a,1),2765(a,1,2,1)),flip(a)]. 2779 (x * y) / L(z,z * y,x) = x * (y / z). [para(2766(a,1),196(a,1,2))]. 2782 L(x,y * z,u) = L(x,z * y,u). [para(2777(a,1),2766(a,1))]. 2787 L(x,(y / z) * (y * z),u) = x. [para(2782(a,1),2734(a,1))]. 2788 L(x,(y \ (y \ z)) * ((y \ z) * T(y,z)),u) = x. [para(256(a,1),2787(a,1,2,1))]. 2789 L(x,(y * z) * u,y * (z * u)) = x. [para(2757(a,1),950(a,1))]. 2790 a(x,y,z) \ ((x * (y * z)) \ u) = ((x * y) * z) \ u. [para(2789(a,1),271(a,1)),flip(a)]. 2792 L(x,y,z * (u / w)) = L(x,y,z * (w \ u)). [para(84(a,1),2759(a,1,3,2)),flip(a)]. 2793 (x * (y * z)) / L(T(z,u),T(z,u) * (y * z),x) = x * (y * K(u,z)). [para(2670(a,1),2779(a,2,2))]. 2794 L(x,y,(z / u) * w) = L(x,y,(u * z) * w). [para(2758(a,2),781(a,1))]. 2795 L(x,y,z * (u * w)) = L(x,y,z * (w * u)). [para(974(a,1),2762(a,1,3,2))]. 2796 L(x,y,z * (u / w)) = L(x,y,z * (w * u)). [para(2792(a,2),867(a,1))]. 2797 L(x,y,z * ((u * w) * u)) = L(x,y,w * z). [para(2795(a,1),2513(a,1))]. 2798 L(x,(y * (y \ z)) * ((y \ z) * T(y,z)),u) = x. [para(2788(a,1),880(a,1)),flip(a)]. 2799 L(x,y * ((z \ y) * T(z,y)),u) = x. [para(20(a,1),2798(a,1,2,1))]. 2800 L(x,y \ ((z \ y) * T(z,y)),u) = x. [para(2799(a,1),876(a,2))]. 2801 L(x,a(y,z,y),u) = x. [para(2391(a,1),2800(a,1,2))]. 2802 (x * a(y,z,y)) * u = x * (a(y,z,y) * u). [para(2801(a,1),74(a,1,2))]. 2803 (x * y) / L(y,z,y) = x * a(y,z,y). [para(2801(a,1),1543(a,1,2))]. 2805 (x * (y * (a(z,u,z) * w))) \ (((x * y) * a(z,u,z)) * w) = a(x,y,a(z,u,z) * w). [para(2802(a,2),28(a,2,2)),flip(a)]. 2806 (a(x,y,x) * z) * u = z * (a(x,y,x) * u). [para(2051(a,2),2802(a,1,1))]. 2807 (x * y) * a(z,u,z) = x * (a(z,u,z) * y). [para(2806(a,1),2548(a,1)),flip(a)]. 2808 ((x * y) * z) \ (x * (y * z)) = a(x,y,z) \ 1. [para(60(a,1),2790(a,1,2)),flip(a)]. 2809 ((x * a(y,z,u)) * w) \ ((x * w) * a(y,z,u)) = a(x,a(y,z,u),w) \ a(x,w,a(y,z,u)). [para(2598(a,1),2790(a,1,2)),flip(a)]. 2810 (x * (K(y,z) * u)) \ ((x * K(y,z)) * (u * w)) = L(w,u,x). [para(2649(a,1),2755(a,1,1))]. 2811 (x * (K(y,z) * u)) \ (x * (K(y,z) * (u * w))) = L(w,u,x). [para(2649(a,1),2810(a,1,2))]. 2812 L(L(x,y,K(z,u)),K(z,u) * y,w) = L(x,y,w). [para(2811(a,1),174(a,1)),flip(a)]. 2813 L(x,K(y,z) * u,w) = L(x,u,w). [para(2515(a,1),2812(a,1,1))]. 2815 L(x,T(y,z) * u,w) = L(x,y * u,w). [para(1098(a,1),2813(a,1,2)),flip(a)]. 2817 L(x,T(y,z) * u,w) = L(x,u * y,w). [para(2815(a,2),2782(a,1))]. 2821 (x * (y * z)) / L(T(z,u),(y * z) * z,x) = x * (y * K(u,z)). [para(2817(a,1),2793(a,1,2))]. 2822 (x * (y * z)) / L(T(z,u),y,x) = x * (y * K(u,z)). [para(2765(a,1),2821(a,1,2))]. 2824 (x * y) * K(z,L(u,y,x)) = x * (y * K(z,u)). [para(2822(a,1),2735(a,1)),flip(a)]. 2826 L(x,y,z * ((u * (w / u)) \ v5)) = L(x,y,(w \ v5) * z). [para(2682(a,1),2762(a,1)),flip(a)]. 2827 L(x,y,z * ((u * (w / u)) * v5)) = L(x,y,(w \ v5) * z). [para(2826(a,1),867(a,1)),flip(a)]. 2829 L(x,y,z * ((u * (w / u)) * v5)) = L(x,y,(w * v5) * z). [para(2827(a,2),781(a,1))]. 2830 L(x,y,(z * u) * ((w * (z / w)) * (u * v5))) = L(x,y,L(v5,u,w * (z / w))). [para(2829(a,1),2514(a,1))]. 2831 (K(x,y) * (z * (u * w))) \ ((K(x,y) * (z * u)) * w) = a(K(x,y) * z,u,w). [para(2518(a,1),2622(a,1,2,1))]. 2832 L(x,y,L(z,u,(u * z) * (w / (u * z)))) = L(x,y,(w / (u * z)) * (w * u)). [para(2830(a,1),2797(a,1))]. 2833 (K(x,y) * (z * (u * w))) \ (K(x,y) * ((z * u) * w)) = a(K(x,y) * z,u,w). [para(2518(a,1),2831(a,1,2))]. 2834 L(x,y,L(z,u,(u * z) * (w / (u * z)))) = L(x,y,((u * z) * w) * (w * u)). [para(2832(a,2),2794(a,1))]. 2835 a(K(x,y) * z,u,w) = (z * (u * w)) \ ((z * u) * w). [para(2833(a,1),2519(a,1))]. 2836 a(K(x,y) * z,u,w) = a(z,u,w). [para(2835(a,2),28(a,2)),flip(a)]. 2837 ((x * K(y,z)) * (u * w)) \ (((x * K(y,z)) * u) * w) = a(x,u,w). [para(2835(a,1),2586(a,1))]. 2839 a(T(x,y) * z,u,w) = a(x * z,u,w). [para(1098(a,1),2836(a,1,1)),flip(a)]. 2840 a((x / y) * z,u,w) = a((y \ x) * z,u,w). [para(1161(a,1),2836(a,1,1))]. 2841 a(x * T(y,z),u,w) = a(x * y,u,w). [para(1212(a,1),2836(a,1,1))]. 2843 a((x * y) * z,y,u) = a(x * (y * z),y,u). [para(2839(a,1),2490(a,1)),flip(a)]. 2844 a((x / y) * z,u,w) = a((y * x) * z,u,w). [para(2840(a,2),1707(a,1))]. 2845 a(x / (y / z),u,w) = a((z \ y) * x,u,w). [para(2840(a,1),2606(a,2))]. 2846 a(x / (y * z),z,u) = a(y * (z * x),z,u). [para(2843(a,1),2606(a,2))]. 2848 a(x / (y * z),u,w) = a((z / y) * x,u,w). [para(2844(a,2),2606(a,2))]. 2849 a(x / (y / z),u,w) = a(x / (z \ y),u,w). [para(2845(a,2),2606(a,2)),flip(a)]. 2850 a((x * y) / z,x,u) = a(y / (z * x),x,u). [para(2846(a,2),2606(a,2))]. 2851 a(x / (y / z),u,w) = a(x / (z * y),u,w). [para(2848(a,2),2606(a,2))]. 2852 a((x * y) / z,x,u) = a(y / (x / z),x,u). [para(2851(a,2),2850(a,2))]. 2853 (x * (K(y,z) * (u * w))) \ (((x * K(y,z)) * u) * w) = a(x,u,w). [para(2649(a,1),2837(a,1,1))]. 2854 (x * (K(y,z) * (u * w))) \ ((x * (K(y,z) * u)) * w) = a(x,u,w). [para(2649(a,1),2853(a,1,2,1))]. 2855 a(x,K(y,z) * u,w) = a(x,u,w). [para(2854(a,1),2621(a,1)),flip(a)]. 2856 a(x,y * z,u) = a(x,z * y,u). [para(974(a,1),2855(a,1,2))]. 2857 a(x,T(y,z),u) = a(x,y,u). [para(985(a,1),2855(a,1,2)),flip(a)]. 2858 a(x,y * T(z,u),w) = a(x,y * z,w). [para(1212(a,1),2855(a,1,2))]. 2861 a(x,y * K(z,u),w) = a(x,y,w). [para(2200(a,1),2855(a,1,2))]. 2862 R(x,K(y,z) * u,w) = a(x,u,w) * x. [para(2855(a,1),2303(a,2,1))]. 2865 a(x,y / z,u) = a(x,z * y,u). [para(2857(a,1),1788(a,1)),flip(a)]. 2866 a(x,(y * z) * z,u) = a(x,y,u). [para(2857(a,1),1792(a,1)),flip(a)]. 2867 R(x,T(y,z),u) = a(x,y,u) * x. [para(2857(a,1),2303(a,2,1))]. 2876 (x * ((y * K(z,u)) * w)) \ ((x * (y * K(z,u))) * w) = a(x,y,w). [para(2861(a,1),28(a,1)),flip(a)]. 2877 a(x,y * (z * K(u,w)),v5) = a(x,y * z,v5). [para(2824(a,1),2861(a,1,2))]. 2878 a(x,L(y,z,y) * (u * y),w) = a(x,u * a(y,z,y),w). [para(2803(a,1),2865(a,1,2)),flip(a)]. 2882 R(x,T(y,z),u) = R(x,y,u). [para(2867(a,2),2303(a,2)),flip(a)]. 2883 R(x,y / z,u) = R(x,z \ y,u). [para(84(a,1),2882(a,1,2)),flip(a)]. 2884 R(x,y / z,u) = R(x,z * y,u). [para(2883(a,2),2383(a,1))]. 2885 R(x,(y * z) / u,w) = R(x,u * (y \ z),w). [para(2884(a,1),2385(a,1)),flip(a)]. 2886 a(x,y * (z * K(u,z)),w) = a(x,y * L(z,u,z),w). [para(1062(a,1),2858(a,1,2,2)),flip(a)]. 2887 a(x,y * T(z,u),w) = a(x,z * y,w). [para(2858(a,2),2856(a,1))]. 2888 R(x,K(y,z) * u,w) = R(x,u,w). [para(2862(a,2),2303(a,2)),flip(a)]. 2892 R(x,y * K(z,u),w) = R(x,y,w). [para(2200(a,1),2888(a,1,2))]. 2894 R(x,y * (z * K(u,w)),v5) = R(x,y * z,v5). [para(2824(a,1),2892(a,1,2))]. 2896 R(x,y * T(z,u),w) = x * a(x,z * y,w). [para(2887(a,1),2300(a,2,2))]. 2897 R(x,y * (z \ u),w) = R(x,y * (z * u),w). [para(2885(a,1),2884(a,1))]. 2898 R(x,y * ((z \ u) \ 1),w) = R(x,y * (z / u),w). [para(2138(a,1),2894(a,1,2,2))]. 2899 R(x,y * T(z,u),w) = R(x,z * y,w). [para(2896(a,2),2300(a,2)),flip(a)]. 2900 R(x,y * ((z \ u) \ u),w) = R(x,z * y,w). [para(83(a,1),2899(a,1,2,2))]. 2901 R(x,y * ((z \ u) * u),w) = R(x,z * y,w). [para(2900(a,1),2897(a,1)),flip(a)]. 2902 R(x,y * ((z \ u) * 1),w) = R(x,y * (z / u),w). [para(2898(a,1),2897(a,1)),flip(a)]. 2903 R(x,y * (z / u),w) = R(x,y * (z \ u),w). [para(18(a,1),2902(a,1,2,2)),flip(a)]. 2904 R(x,y * (z / u),w) = R(x,y * (z * u),w). [para(2903(a,2),2897(a,1))]. 2905 R(x,x * (y * z),z) = y / ((x \ (y / z)) * z). [para(2904(a,1),631(a,1))]. 2906 R(x,x * ((y \ z) * z),z) = (y \ z) / ((x \ (y \ 1)) * z). [para(320(a,1),2905(a,2,2,1,2))]. 2907 a(x,y * L(z,u,z),w) = a(x,y * z,w). [para(2886(a,1),2877(a,1))]. 2908 a(x,L(y,z,y) * u,w) = a(x,u * y,w). [para(2907(a,1),2856(a,1)),flip(a)]. 2910 a(x,y * a(z,u,z),w) = a(x,(y * z) * z,w). [para(2878(a,1),2908(a,1))]. 2911 a(x,y * a(z,u,z),w) = a(x,y,w). [para(2910(a,2),2866(a,1))]. 2913 a(x,a(y,z,y) * u,w) = a(x,u,w). [para(2051(a,2),2911(a,1,2))]. 2915 (x * ((a(y,z,y) * u) * w)) \ ((x * (a(y,z,y) * u)) * w) = a(x,u,w). [para(2913(a,1),28(a,1)),flip(a)]. 2916 R(x,y * x,z) = (y \ z) / ((x \ (y \ 1)) * z). [para(2906(a,1),2901(a,1)),flip(a)]. 2918 (x * (y * (K(z,u) * w))) \ ((x * (y * K(z,u))) * w) = a(x,y,w). [para(2649(a,1),2876(a,1,1,2))]. 2919 (x * (y * (a(z,u,z) * w))) \ ((x * (a(z,u,z) * y)) * w) = a(x,y,w). [para(2806(a,1),2915(a,1,1,2))]. 2920 L(x,y,L(z,u,(u * z) * ((u * z) * w))) = L(x,y,((u * z) * w) * (w * u)). [para(2796(a,1),2834(a,1,3))]. 2921 L(x,y,((z * u) * w) * (w * z)) = L(x,y,L(u,z,w)). [para(774(a,1),2920(a,1,3)),flip(a)]. 2923 L(x,y,((z * u) * w) * (z * w)) = L(x,y,L(u,z,w)). [para(2921(a,1),2795(a,1)),flip(a)]. 2924 a(((x * y) * z) * (x * z),u,w) = L(w,u,L(y,x,z)) \ w. [para(2923(a,1),2298(a,2,1))]. 2925 a(((x * y) * z) * (x * z),u,w) = a(L(y,x,z),u,w). [para(2924(a,2),2298(a,2)),flip(a)]. 2926 (x * y) \ (((x * z) * y) * R(((x * z) * y) \ (x * y),u,w)) = a(L(z,x,y),u,w). [para(2925(a,1),2685(a,2))]. 2927 (R(x,y,z) * (y * u)) \ ((R(x,y,z) * y) * u) = a(x,y,a(x,y,z) * u). [para(2420(a,1),2692(a,1,1))]. 2928 a(x,y,a(x,y,z) * u) = a(R(x,y,z),y,u). [para(2927(a,1),28(a,2)),flip(a)]. 2929 a(x,y,z * a(x,y,u)) = a(R(x,y,u),y,z). [para(2567(a,1),2928(a,1,3))]. 2930 (x * (y * z)) \ ((x * y) * L(R(z,u,w),y,x)) = a((x * y) * (x * (y * z)),u,w). [para(48(a,1),2686(a,1,2,2))]. 2931 (x * y) \ (((x * z) * R((x * z) \ x,u,w)) * y) = a(L(z,x,y),u,w). [para(1623(a,1),2926(a,1,2))]. 2932 (x * y) \ ((x * a(z,u,w)) * y) = a(L(z,x,y),u,w). [para(2315(a,1),2931(a,1,2,1))]. 2933 a(L(x,y,z),u,w) = R(a(x,u,w),y,z). [para(2932(a,1),2736(a,1))]. 2935 a(R(x,y,z),u,w) = a(L(x,y,z),u,w). [para(2933(a,2),2394(a,2))]. 2936 a(L(x,y,z),y,u) = a(x,y,u). [para(2933(a,2),2416(a,1))]. 2937 a(L(x,y,z),u,w) \ R(x,u,w) = a(a(x,u,w),y,z) \ x. [para(2933(a,2),2369(a,1,1))]. 2938 L(x,y,z) * a(L(z,u,w),y,x) = a(a(z,y,x),u,w) * x. [para(2933(a,2),2727(a,1,2))]. 2939 a((x * y) \ z,y,u) = a(y \ (x \ z),y,u). [para(177(a,1),2936(a,1,1))]. 2940 a((x \ y) \ z,y,u) = a(y \ (x * z),y,u). [para(267(a,1),2936(a,1,1))]. 2941 a((x \ y) \ T(z,x),y,u) = a(y \ (z * x),y,u). [para(269(a,1),2936(a,1,1))]. 2942 L(x,y,z) * a(x,y,u) = R(L(x,y,z),y,u). [para(2936(a,1),2300(a,2,2)),flip(a)]. 2946 a(x,y,z * a(x,y,u)) = a(L(x,y,u),y,z). [para(2935(a,1),2929(a,2))]. 2947 a(x \ (y \ z),x,u) = a((y * x) * z,x,u). [para(2939(a,1),1702(a,1))]. 2948 a(x / (y \ z),z,u) = a(z \ (y * x),z,u). [para(2940(a,1),2584(a,2))]. 2949 L(x,y,z) * a(x,y,u) = L(R(x,y,u),y,z). [para(2942(a,2),48(a,1))]. 2950 a(x,y,z * a(x,y,u)) = a(x,y,z). [para(2946(a,2),2936(a,1))]. 2952 a(x \ (y \ z),x,u) = a(y * (x * z),x,u). [para(2947(a,2),2843(a,1))]. 2953 a(x / (y / z),y,u) = a(y \ (z * x),y,u). [para(2948(a,1),2849(a,2))]. 2954 L(R(x,y,z),y,u) \ (x * a(x,y,z)) = a(u,y,x). [para(2949(a,1),2644(a,1,1))]. 2955 a(x * (y * z),y,u) = a(y * (x * z),y,u). [para(2952(a,1),1757(a,1))]. 2956 a((x * y) / z,z,u) = a(y / (z / x),z,u). [para(2953(a,2),2584(a,2))]. 2957 a((x \ y) * T(z,x),y,u) = a(y \ (z * x),y,u). [para(2941(a,1),1702(a,1)),flip(a)]. 2958 L(R(x,y,z),y,u) \ R(x,y,z) = a(u,y,x). [para(2300(a,2),2954(a,1,2))]. 2959 a(x,y,R(z,y,u)) = a(x,y,z). [para(2958(a,1),2298(a,2))]. 2960 a(x,y,(z / u) / y) = a(x,y,z / (y * u)). [para(193(a,1),2959(a,1,3)),flip(a)]. 2961 a(x \ (y * z),x,u) = a((z \ x) * y,x,u). [para(2957(a,1),2841(a,1))]. 2962 a(x \ (y * z),x,u) = a((z * x) * y,x,u). [para(2961(a,2),1707(a,1))]. 2964 a(x \ (y * z),x,u) = a(z * (x * y),x,u). [para(2962(a,2),2843(a,1))]. 2965 a(a(x,y,z),u,w) * z = z * a(w,u,a(x,y,z)). [para(2938(a,1),2693(a,1))]. 2966 a(a(x,y,z),u,w) = a(w,u,a(x,y,z)). [hyper(24,a,2567,a,b,2965,a)]. 2968 a(a(x,y,z),u,w) \ 1 = a(w,u,a(x,y,z)). [para(2966(a,2),2694(a,1,1))]. 2969 a(a(x,y,z),u,w) \ v5 = v5 * a(w,u,a(x,y,z)). [para(2966(a,2),2696(a,1,1))]. 2970 x \ L(x,y,a(z,u,w)) = a(x,y,a(z,u,w)). [para(2968(a,1),2328(a,1)),flip(a)]. 2971 ((a(x,y,z) * u) * w) \ (a(x,y,z) * (u * w)) = a(w,u,a(x,y,z)). [para(2968(a,1),2808(a,2))]. 2972 (x \ (a(y,z,u) * w)) \ ((a(y,z,u) \ x) \ w) = a(x \ (a(y,z,u) * w),x,a(y,z,u)). [para(267(a,1),2970(a,1,2))]. 2973 a(L(x,y,z),u,w) \ R(x,u,w) = x * a(z,y,a(x,u,w)). [para(2969(a,1),2937(a,2))]. 2974 ((a(x,y,z) * u) * w) \ ((u * w) * a(x,y,z)) = a(w,u,a(x,y,z)). [para(2567(a,1),2971(a,1,2))]. 2975 ((x * a(y,z,u)) * w) \ ((x * w) * a(y,z,u)) = a(w,x,a(y,z,u)). [para(2567(a,1),2974(a,1,1,1))]. 2976 (x * (y * z)) \ (x * (y * R(z,u,w))) = a((x * y) * (x * (y * z)),u,w). [para(74(a,1),2930(a,1,2))]. 2977 L(a(x,y,z),u * x,w) = a((w * u) * (w * (u * x)),y,z). [para(2976(a,1),2730(a,1)),flip(a)]. 2978 L(a(x,y,z),u * x,w) = a(L(x,u,w),y,z). [para(2977(a,2),1705(a,1))]. 2979 a(L(x,y,z),u,w) \ a(x,u,w) = a(z,y * x,a(x,u,w)). [para(2978(a,1),2298(a,2,1)),flip(a)]. 2980 a(x,y * z,a(z,u,w)) = a(x,y,a(z,u,w)). [para(2979(a,1),2407(a,1))]. 2981 a(x,y * z,a(y,u,w)) = a(x,z,a(y,u,w)). [para(2980(a,1),2856(a,1)),flip(a)]. 2982 a(x * y,z * u,a(z,w,v5)) = a(y * x,u,a(z,w,v5)). [para(2981(a,1),2618(a,1)),flip(a)]. 2983 a((x * y) * z,y,a(x,u,w)) = a(z * (x * y),z,a(x,u,w)). [para(2982(a,1),2750(a,1))]. 2984 a(x * (y * z),y,a(x,u,w)) = a(z * (x * y),z,a(x,u,w)). [para(2983(a,1),2843(a,1)),flip(a)]. 2985 a(x * (y * z),y,a(x,u,w)) = a(x * (z * y),z,a(x,u,w)). [para(2984(a,2),2955(a,2))]. 2986 (x * (y * (a(z,u,z) * w))) \ ((x * (a(z,u,z) * y)) * w) = a(x,y,a(z,u,z) * w). [para(2807(a,1),2805(a,1,2,1))]. 2987 a(x,y,a(z,u,z) * w) = a(x,y,w). [para(2986(a,1),2919(a,1))]. 2988 a(x,y,L(z,u,z)) = a(x,y,z). [para(1542(a,1),2987(a,1,3)),flip(a)]. 2989 a(x,y,(z \ u) * z) = a(x,y,T(u,z)). [para(2675(a,1),2987(a,1,3))]. 2991 a(x,y,(T(z,u) * u) \ (T(z,u) * (z * u))) = a(x,y,T(z,u)). [para(106(a,2),2988(a,1,3))]. 2992 a(x,y,T(z * u,z)) = a(x,y,u * z). [para(19(a,1),2989(a,1,3,1)),flip(a)]. 2993 a(x,y,(T(z,u) * u) \ (z * (T(z,u) * u))) = a(x,y,T(z,u)). [para(728(a,1),2991(a,1,3,2))]. 2994 a(x,y,T(z,T(z,u) * u)) = a(x,y,T(z,u)). [para(36(a,2),2993(a,1,3))]. 2995 a(x,y,T(z,z * u)) = a(x,y,T(z,u)). [para(2018(a,1),2994(a,1,3))]. 2996 a(x,y,T((z \ u) * z,((z \ u) * z) * (z \ 1))) = a(x,y,R(u,z,z)). [para(761(a,1),2995(a,2,3))]. 2998 a(x,y,T((z \ u) * z,R(z \ u,z,z \ 1))) = a(x,y,R(u,z,z)). [para(433(a,1),2996(a,1,3,2))]. 2999 a(x,y,T((z \ u) * z,z \ u)) = a(x,y,R(u,z,z)). [para(2716(a,1),2998(a,1,3))]. 3001 a(x,y,z * (z \ u)) = a(x,y,R(u,z,z)). [para(2999(a,1),2992(a,1)),flip(a)]. 3002 a(x,y,R(z,u,u)) = a(x,y,z). [para(20(a,1),3001(a,1,3)),flip(a)]. 3003 a(x,y,z / (u \ 1)) = a(x,y,z * u). [para(720(a,1),3002(a,1,3)),flip(a)]. 3004 a(x,y,R(((z \ 1) * u) \ 1,u,u)) = a(x,y,(u \ 1) * z). [para(1739(a,2),3003(a,1,3))]. 3005 a(x,y,R((z \ u) \ 1,u,u)) = a(x,y,(u \ 1) * z). [para(318(a,1),3004(a,1,3,1,1))]. 3006 a(x,y,(z \ u) \ 1) = a(x,y,(u \ 1) * z). [para(3005(a,1),3002(a,1)),flip(a)]. 3007 a(x,y,(z \ u) \ 1) = a(x,y,u \ z). [para(318(a,1),3006(a,2,3))]. 3009 a(x,y,(z / u) \ z) = a(x,y,u * a(z,u,u)). [para(1388(a,1),3007(a,1,3)),flip(a)]. 3010 a(x,y,z * a(u,z,z)) = a(x,y,z). [para(66(a,1),3009(a,1,3)),flip(a)]. 3011 a(x,y,L(z,u,u * z)) = a(x,y,z). [para(1487(a,2),3010(a,1,3))]. 3012 ((x * y) \ x) * L(L(y,x,x * y),z,u) = a(u,z,y) \ 1. [para(3011(a,1),2357(a,2,1))]. 3013 (x * y) \ (x * L(y,z,u)) = a(u,z,y) \ 1. [para(3012(a,1),814(a,1)),flip(a)]. 3015 L(a(x,y,z),z,u) = a(x,x * y,z) \ 1. [para(3013(a,1),2350(a,1)),flip(a)]. 3016 L(a(x,y,z),z,u) = a(x,y,z). [para(3015(a,2),2343(a,1))]. 3019 (x * L(y,z,u)) / a(u,u * z,y) = x * y. [para(3016(a,1),2356(a,1,2))]. 3021 a(x,x * y,z) \ (u * L(z,y,x)) = u * z. [para(3019(a,1),2571(a,1)),flip(a)]. 3023 a(x,y,z) * (u * L(z,y,x)) = u * z. [para(3021(a,1),2360(a,1)),flip(a)]. 3024 a(x,y,z) \ (u * z) = u * L(z,y,x). [hyper(23,a,20,a,b,3023,a),flip(a)]. 3026 x * T(y,L(x,z,u)) = y * x. [para(3023(a,1),2376(a,1)),flip(a)]. 3031 L(x,y,z) * T(u,x) = u * L(x,y,z). [para(303(a,1),3026(a,1,2,2))]. 3032 K(L(x,y,z),u) = (u * x) \ (x * u). [para(3026(a,1),2186(a,1,1)),flip(a)]. 3034 K(L(x,y,z),u) = K(x,u). [para(3032(a,2),30(a,2)),flip(a)]. 3036 L(K(x,y),z,u) = K(x,y). [para(3034(a,1),2259(a,1)),flip(a)]. 3038 a(x,y,K(z,u)) = 1. [hyper(38,a,3036,a)]. 3040 (x * y) * K(z,u) = x * (y * K(z,u)). [para(3036(a,1),74(a,1,2))]. 3041 x \ (y * K(z,u)) = (x \ y) * K(z,u). [para(3036(a,1),560(a,1,2)),flip(a)]. 3049 (x / y) * L(y,z,u) = a(u,z,y) \ x. [para(22(a,1),3024(a,1,2)),flip(a)]. 3050 (x * L(y,z,u)) \ (x * y) = a(u,z,y). [para(3024(a,1),2569(a,1,1))]. 3052 (x * (y * K(z,u))) * w = (x * y) * (K(z,u) * w). [para(3040(a,1),2649(a,1,1))]. 3053 (x \ (y \ z)) * K(y,y * z) = x \ (z / y). [para(1001(a,1),3041(a,1,2)),flip(a)]. 3054 a(x,y,z * u) \ u = z \ L(z * u,y,x). [para(3049(a,1),353(a,1))]. 3055 ((x * y) * L(L(z,y,x),u,w)) \ (x * (y * z)) = a(w,u,L(z,y,x)). [para(74(a,1),3050(a,1,2))]. 3056 L(a(x,y,z),u * L(z,y,x),w) = (w * (u * L(z,y,x))) \ (w * (u * z)). [para(3050(a,1),76(a,1,1))]. 3057 (x * (y * (K(z,u) * w))) \ ((x * (y * K(z,u))) * w) = a(x,y,K(z,u) * w). [para(3052(a,2),28(a,2,2)),flip(a)]. 3058 ((x * y) * (K(z,u) * w)) / ((y * K(z,u)) * w) = R(x,y * K(z,u),w). [para(3052(a,1),34(a,2,1)),flip(a)]. 3059 (x * (y * L(z,u,w))) \ (x * (y * z)) = a(w,u,L(z,y,x)). [para(175(a,1),3055(a,1,1))]. 3060 ((x * y) * (K(z,u) * w)) / (y * (K(z,u) * w)) = R(x,y * K(z,u),w). [para(2649(a,1),3058(a,1,2))]. 3061 R(x,y * K(z,u),w) = R(x,y,K(z,u) * w). [para(3060(a,1),34(a,2)),flip(a)]. 3062 R(x,y,K(z,u) * w) = R(x,y,w). [para(3061(a,1),2892(a,1))]. 3063 R(x,y,T(z,u)) = R(x,y,z). [para(985(a,1),3062(a,1,3)),flip(a)]. 3072 R(x,y,T(z,u)) = a(x,y,z) * x. [para(3063(a,2),2303(a,1))]. 3073 a(x,y,T(z,u)) = a(x,y,z). [hyper(24,a,2303,a(flip),b,3072,a(flip)),flip(a)]. 3074 a(x,y,z / u) = a(x,y,u \ z). [para(84(a,1),3073(a,1,3)),flip(a)]. 3075 a(x,y,(z \ u) * z) = a(x,y,u). [para(3073(a,1),2989(a,2))]. 3077 a(x,y,(z / u) / x) = a(x,y,(x * u) \ z). [para(3074(a,1),2493(a,2))]. 3078 a(x,y,(z / u) / y) = a(x,y,(y * u) \ z). [para(3074(a,1),2960(a,2))]. 3079 a(x,y,((z / u) * w) * (u / z)) = a(x,y,w). [para(358(a,1),3075(a,1,3,1))]. 3080 (x \ y) \ L((x \ y) * x,z,u) = a(u,z,y) \ x. [para(3075(a,1),3054(a,1,1)),flip(a)]. 3082 L(x,y,z) / (u \ x) = a(z,y,x) \ u. [para(3080(a,1),1588(a,1)),flip(a)]. 3083 a(x,x * y,L(z,y,x)) \ u = z / (u \ L(z,y,x)). [para(303(a,1),3082(a,1,1)),flip(a)]. 3084 (a(x,y,z) \ 1) \ u = z / (u \ L(z,y,x)). [para(2365(a,1),3083(a,1,1))]. 3085 x / (y \ L(x,z,u)) = a(u,z,x) * y. [para(3084(a,1),330(a,1))]. 3086 x / (y * L(x,z,u)) = a(u,z,x) * (y \ 1). [para(330(a,1),3085(a,1,2))]. 3087 R(x,y,z) / a(L(x,u,w),y,z) = a(w,u,R(x,y,z)) * L(x,u,w). [para(2301(a,1),3085(a,1,2))]. 3088 x / (y * L(x,z,u)) = y \ a(u,z,x). [para(3086(a,2),2572(a,1))]. 3089 a(L(x,y,z),u,w) \ R(x,u,w) = a(z,y,R(x,u,w)) * L(x,y,z). [para(3087(a,1),2571(a,1)),flip(a)]. 3090 a(x,y,R(z,u,w)) * L(z,y,x) = z * a(x,y,a(z,u,w)). [para(3089(a,1),2973(a,1))]. 3091 L(a(x,y,z),u * L(z,y,x),w) = a(x,y,L(z,u,w)). [para(3056(a,2),3059(a,1))]. 3092 a(L(x,y * L(z,u,x),w),u,z) = a(x,u,L(z,y,w)). [para(3091(a,1),2406(a,2))]. 3093 a(x,y,L(z,u,x)) = a(x,y,z). [para(3091(a,1),2687(a,1))]. 3094 a(x,y,L(L(z,u,x),w,v5)) = a(x,y,L(z,w,v5)). [para(49(a,1),3093(a,1,3))]. 3098 a(L(x,y * z,u),w,L(z,x * w,x)) = a(x,w,L(L(z,x * w,x),y,u)). [para(308(a,1),3092(a,1,1,2,2))]. 3099 a(L(x,L(y,z,x) * u,w),z,y) = a(x,z,L(y,T(u,v5),w)). [para(2817(a,1),3092(a,1,1))]. 3100 a(x,y,K(z,u) * w) = a(x,y,w). [para(3057(a,1),2918(a,1))]. 3101 a(x,y,(z / u) * w) = a(x,y,(u \ z) * w). [para(1161(a,1),3100(a,1,3))]. 3102 a(x,y,z * T(u,w)) = a(x,y,z * u). [para(1212(a,1),3100(a,1,3))]. 3103 a(x,y,K(z * u,z)) = a(x,y,a(z,u,z)). [para(1537(a,1),3100(a,1,3)),flip(a)]. 3104 a(x,y,T(z,u) / w) = a(x,y,z / w). [para(1815(a,1),3100(a,1,3))]. 3105 a(x,y,(K(z,u) * w) * v5) = a(x,y,w * v5). [para(2518(a,2),3100(a,1,3))]. 3106 a(x,y,(z * K(u,w)) * v5) = a(x,y,z * v5). [para(2630(a,1),3100(a,1,3))]. 3107 a(x,y,(z \ u) \ w) = a(x,y,(z / u) * w). [para(2676(a,1),3100(a,1,3)),flip(a)]. 3108 a(x,y,(z \ K(u,w)) * v5) = a(x,y,z \ v5). [para(2677(a,1),3100(a,1,3))]. 3110 a(x,y,z * (u / w)) = a(x,y,z * (w \ u)). [para(84(a,1),3102(a,1,3,2)),flip(a)]. 3111 a(x,y,z \ T(u,w)) = a(x,y,u / z). [para(3104(a,1),3074(a,1)),flip(a)]. 3112 a(x,y,(z / u) / w) = a(x,y,w \ (u \ z)). [para(84(a,1),3111(a,1,3,2)),flip(a)]. 3113 a(x,y,a(z,u,z)) = 1. [para(3103(a,1),3038(a,1))]. 3114 L(a(x,y,x),z,u) = a(x,y,x). [hyper(37,a,3113,a)]. 3116 a(L(x,y,z),u,x) = a(x,u,x). [para(3114(a,1),2406(a,2))]. 3117 L(x * a(x,y,x),y,L(x,z,u)) = x. [para(3116(a,1),2362(a,1,1,2))]. 3119 L(R(x,y,x),y,L(x,z,u)) = x. [para(1540(a,1),3117(a,1,1))]. 3120 L(x,y,z) * (u * R(x,u,x)) = (L(x,y,z) * u) * x. [para(3119(a,1),74(a,1,2)),flip(a)]. 3121 a(x,y,((z / u) * w) * v5) = a(x,y,((u \ z) * w) * v5). [para(1161(a,1),3105(a,1,3,1))]. 3122 a(x,y,((z \ u) \ w) * v5) = a(x,y,((z / u) * w) * v5). [para(2676(a,1),3105(a,1,3,1)),flip(a)]. 3123 a(x,y,(z \ u) \ w) = a(x,y,(u \ z) * w). [para(3107(a,2),3101(a,1))]. 3124 a(x,y,(T(z,u) * w) \ v5) = a(x,y,(z * w) \ v5). [para(2134(a,1),3108(a,1,3))]. 3125 a(x,y,((z / u) * w) * (z \ u)) = a(x,y,w). [para(3110(a,1),3079(a,1))]. 3126 a(x,y,(x * z) \ u) = a(x,y,x \ (z \ u)). [para(3112(a,1),3077(a,1)),flip(a)]. 3127 a(x,y,(y * z) \ u) = a(x,y,y \ (z \ u)). [para(3112(a,1),3078(a,1)),flip(a)]. 3128 a(x,y,((z \ (u \ w)) * K(u,u * w)) * v5) = a(x,y,((w / u) \ z) \ v5). [para(3053(a,2),3123(a,2,3,1)),flip(a)]. 3129 a(x,x * y,x \ (y \ z)) = (y \ (x \ z)) \ ((x * y) \ z). [para(3126(a,1),2327(a,1))]. 3130 a(x,y,y \ (z \ ((z * y) * u))) = a(x,y,K(z,y) * u). [para(940(a,1),3127(a,1,3)),flip(a)]. 3131 a(x,y,((z / u) * w) \ v5) = a(x,y,((u \ z) * w) \ v5). [para(84(a,1),3124(a,1,3,1,1)),flip(a)]. 3132 L(x,y,z) * T(x * u,x) = (L(x,y,z) * u) * x. [para(1321(a,1),3120(a,1,2))]. 3133 (L(x,y,z) * u) * x = (x * u) * L(x,y,z). [para(3132(a,1),3031(a,1))]. 3134 (x * (L(x,y,z) \ u)) * L(x,y,z) = u * x. [para(20(a,1),3133(a,1,1)),flip(a)]. 3135 (x * a(y,z,u)) * L(u,z,y) = x * u. [para(2604(a,1),3134(a,1,1))]. 3137 (x / a(y,z,u)) * u = x * L(u,z,y). [para(22(a,1),3135(a,1,1)),flip(a)]. 3138 (a(x,y,z) / u) \ z = u * L(z,y,x). [para(3137(a,1),358(a,2))]. 3139 x / (y * L(x,z,u)) = a(u,z,x) / y. [para(3138(a,1),65(a,1,2))]. 3140 a(x,y,z) / u = u \ a(x,y,z). [para(3139(a,1),3088(a,1))]. 3141 (a(x,y,z) \ u) \ w = (u \ a(x,y,z)) * w. [para(3140(a,1),2605(a,2,1))]. 3143 a(x,y,((z \ u) * w) * (u \ z)) = a(x,y,w). [para(3121(a,1),3125(a,1))]. 3144 a(x,y,((z \ u) * w) * ((u * w) \ z)) = a(x,y,a(z,u,w)). [para(595(a,1),3143(a,1,3,1))]. 3145 a(x,y,(z \ (u * w)) * (u \ z)) = a(x,y,L(w,u,z)). [para(798(a,1),3143(a,1,3,1))]. 3146 a(x,y,((z \ u) \ w) * v5) = a(x,y,((u \ z) * w) * v5). [para(3122(a,2),3121(a,1))]. 3147 a(x,y,y \ (z \ ((z * y) * u))) = a(x,y,u). [para(3130(a,2),3100(a,1))]. 3148 a(x,y,L(z,u * y,u)) = a(x,y,z). [para(309(a,1),3147(a,1,3))]. 3151 a(L(x,y * z,u),w,z) = a(x,w,L(L(z,x * w,x),y,u)). [para(3148(a,1),3098(a,1))]. 3152 a(x,y,(z \ (u \ w)) \ ((u * z) \ w)) = x \ L(x,y,a(u,u * z,u \ (z \ w))). [para(3129(a,1),2970(a,2,3)),flip(a)]. 3153 a(L(x,y * z,u),w,z) = a(x,w,L(z,y,u)). [para(3151(a,2),3094(a,1))]. 3155 a(x,y,L(z,u * z,w)) = a(L(x,u,w),y,z). [para(2765(a,1),3153(a,1,1)),flip(a)]. 3157 a(x,y,((z \ (u \ w)) * K(u,u * w)) * v5) = a(x,y,((u / w) * z) \ v5). [para(358(a,1),3128(a,2,3,1))]. 3158 a(x,y,((z / u) * w) \ v5) = a(x,y,(w \ (z \ u)) * v5). [para(3157(a,1),3106(a,1))]. 3160 a(x,y,((z \ u) * w) \ v5) = a(x,y,(w \ (u \ z)) * v5). [para(3158(a,1),3131(a,1)),flip(a)]. 3161 a(x,y,z / ((u \ w) * v5)) = a(x,y,(v5 \ (w \ u)) * z). [para(3160(a,1),3074(a,2))]. 3162 a(x,y,(z \ (u \ w)) \ ((u * z) \ w)) = x \ L(x,y,a(u,z,u \ (z \ w))). [para(2361(a,1),3152(a,2,2))]. 3163 a(x,y,(z \ (u \ w)) \ ((u * z) \ w)) = a(x,y,a(u,z,u \ (z \ w))). [para(3162(a,2),2970(a,1))]. 3164 (x \ (a(y,z,u) * w)) \ ((x \ a(y,z,u)) * w) = a(x \ (a(y,z,u) * w),x,a(y,z,u)). [para(3141(a,1),2972(a,1,2))]. 3165 a(x \ (a(y,z,u) * w),x,a(y,z,u)) = a(x,a(y,z,u),w). [para(3164(a,1),594(a,2)),flip(a)]. 3166 a(x * (a(y,z,u) * w),x,a(y,z,u)) = a(x,a(y,z,u),w). [para(3165(a,1),1702(a,1)),flip(a)]. 3167 a(x * (y * a(z,u,w)),y,a(z,u,w)) = a(y,a(z,u,w),x). [para(3165(a,1),2964(a,1)),flip(a)]. 3168 a(a(x,y,z) * (u * w),u,a(x,y,z)) = a(u,a(x,y,z),w). [para(3166(a,1),2955(a,2))]. 3169 a((x * a(y,z,u)) / w,x,a(y,z,u)) = a(x,a(y,z,u),w). [para(3167(a,1),2606(a,2))]. 3170 a(a(x,y,z) * (u * w),u,a(x,y,z)) \ v5 = a(u,u * a(x,y,z),w) * v5. [para(3168(a,2),2359(a,2,1)),flip(a)]. 3171 a(a(x,y,z) / (u / w),u,a(x,y,z)) = a(u,a(x,y,z),w). [para(3169(a,1),2852(a,1)),flip(a)]. 3172 a(a(x,y,z) * (u * w),u,a(x,y,z)) = a(u,u * a(x,y,z),w). [hyper(24,a,2696,a(flip),b,3170,a(flip)),flip(a)]. 3173 a(x,x * a(y,z,u),w) = a(x,a(y,z,u),w). [para(3172(a,1),3168(a,1))]. 3174 a(x,a(y,z,u),w) \ v5 = a(x,a(y,z,u),w) * v5. [para(3173(a,1),2359(a,1,1)),flip(a)]. 3175 a(x,a(y,z,u),w) \ a(x,w,a(y,z,u)) = a(w,x,a(y,z,u)). [para(2809(a,1),2975(a,1))]. 3176 a(x,a(y,z,u),w) * a(x,w,a(y,z,u)) = a(w,x,a(y,z,u)). [para(3175(a,1),3174(a,1)),flip(a)]. 3177 R(T(a(x,y,z),(L(z,y,x) * u) * w),L(z,y,x) * u,w) = a(x,y,R(z,u,w)). [para(2379(a,2),2751(a,1))]. 3178 R(a(x,y,z),L(z,y,x) * u,w) = a(x,y,R(z,u,w)). [para(2543(a,1),3177(a,1,1))]. 3180 a(L(x,L(y,z,x) * u,w),z,y) = a(x,z,R(y,u,w)). [para(3178(a,1),2933(a,2))]. 3181 a(x,y,L(z,T(u,w),v5)) = a(x,y,R(z,u,v5)). [para(3180(a,1),3099(a,1)),flip(a)]. 3182 a(x,y,R(z,u,w)) = a(x,y,L(z,u,w)). [para(81(a,1),3181(a,1,3,2)),flip(a)]. 3183 a(x,y,L(z,u * z,w)) = a(x,y,(u \ w) / ((z \ (u \ 1)) * w)). [para(2916(a,1),3182(a,1,3)),flip(a)]. 3184 a(x,y,L(z,u,w)) * L(z,y,x) = z * a(x,y,a(z,u,w)). [para(3182(a,1),3090(a,1,1))]. 3185 a(x,y,L(z,u * z,w)) = a(x,y,(w \ ((u \ 1) \ z)) * (u \ w)). [para(3183(a,2),3161(a,1))]. 3186 a(x,y,L(z,u * z,w)) = a(x,y,(w \ (u * z)) * (u \ w)). [para(330(a,1),3185(a,2,3,1,2))]. 3187 a(x,y,L(z,u * z,w)) = a(x,y,L(z,u,w)). [para(3186(a,2),3145(a,1))]. 3188 a(L(x,y,z),u,w) = a(x,u,L(w,y,z)). [para(3187(a,1),3155(a,1)),flip(a)]. 3189 L(x,y,z) * a(z,y,L(x,u,w)) = x * a(w,u,a(z,y,x)). [para(3188(a,1),2693(a,1,2))]. 3190 a(x,y,L(z,u,w)) * L(z,y,x) = z * a(w,u,a(x,y,z)). [para(3188(a,1),2697(a,1,1))]. 3191 L(x,y,z) * a(z,y,L(x,u,w)) = x * a(z,y,a(w,u,x)). [para(3189(a,1),2643(a,1)),flip(a)]. 3192 a(x,y,a(z,u,w)) = a(w,u,a(x,y,z)). [hyper(23,a,3184,a(flip),b,3190,a(flip)),flip(a)]. 3193 a(x,y,a(z / u,w,v5)) = a(v5,w,a(x,y,u * z)). [para(2606(a,2),3192(a,1,3))]. 3194 a(x * y,z,a(u,w,v5)) = a(u,w,a(v5,z,y * x)). [para(3192(a,2),2618(a,1)),flip(a)]. 3195 a(x,y,a(z,u,w)) = a(w,y,a(x,u,z)). [para(3192(a,1),3192(a,2)),flip(a)]. 3196 a(x,y,a(z,u,w)) * a(z,y,a(w,u,x)) = 1. [para(3195(a,1),2695(a,1,1))]. 3197 a(x * y,x,a(z,u,w)) = a(z,y,a(w,u,x * y)). [para(3195(a,2),2750(a,1)),flip(a)]. 3198 a(x,y * z,a(u,w,z)) = a(u,y,a(z,w,x)). [para(3195(a,1),2980(a,1))]. 3199 a(x,y,a(a(x,y,z) / u,w,v5)) = a(v5,w,a(x,y,u)). [para(2950(a,1),3193(a,2,3))]. 3200 a(x,y,a(z,u,w / v5)) = a(x,y,a(z,u,v5 * w)). [para(3193(a,1),3192(a,1)),flip(a)]. 3201 a(x,y,a(z,u,w)) = a(z,u,a(x,y,w)). [hyper(23,a,3189,a(flip),b,3191,a(flip))]. 3202 a(x,y,a(a(x,y,z) / (u / w),u,z)) = a(u,a(x,y,z),w). [para(3201(a,1),3171(a,1))]. 3203 a(x,y,a(z,u,w)) = a(w,y,a(z,u,x)). [para(3201(a,1),3192(a,1))]. 3204 a(x,y,a(z,u,w)) = a(x,y,a(w,u,z)). [para(3201(a,1),3192(a,2))]. 3205 a(x,y,a(z,u,w)) = a(w,u,a(z,y,x)). [para(3201(a,1),3195(a,1))]. 3206 a(x,a(y,z,u),w) * a(u,w,a(y,z,x)) = a(w,x,a(y,z,u)). [para(3203(a,1),3176(a,1,2))]. 3207 a(x,y * z,a(u,w,z)) = a(x,y,a(z,w,u)). [para(3203(a,1),3198(a,2))]. 3208 a(x,y,a(z / u,w,v5)) = a(x,y,a(v5,w,u / z)). [para(612(a,1),3204(a,1,3))]. 3209 a(x * y,z,a(u,w,v5)) = a(v5,w,a(u,z,y * x)). [para(3204(a,1),3194(a,1))]. 3210 a(x / y,z,a(u,w,v5)) = a(v5,w,a(u,z,y / x)). [para(3205(a,1),612(a,1)),flip(a)]. 3211 a(x * (y * z),y,a(x,u,w)) = a(w,u,a(x,z,x * (z * y))). [para(3205(a,1),2985(a,1)),flip(a)]. 3212 a(x,y,(z \ (u \ w)) \ ((u * z) \ w)) = a(u \ (z \ w),z,a(u,y,x)). [para(3205(a,1),3163(a,2))]. 3213 a(x * (y * z),y,a(u,w,v5)) = a(v5,w,a(u,y,z * (y * x))). [para(3209(a,1),2488(a,1)),flip(a)]. 3214 a(x,y,a(z,u,y / w)) = a(y,a(z,u,x),w). [para(3202(a,1),3199(a,1)),flip(a)]. 3215 a(x,y,a(z,u,w * y)) = a(y,a(z,u,x),w). [para(3214(a,1),3200(a,1)),flip(a)]. 3217 a(x,y,a(z,u,u / w)) = a(u,a(x,y,z),w). [para(3214(a,1),3201(a,1)),flip(a)]. 3218 a(x * y,x,a(z,u,w)) = a(y,a(w,u,z),x). [para(3215(a,1),3197(a,2))]. 3219 a(x,y,a(z / u,u,w)) = a(u,a(x,y,w),z). [para(3217(a,1),3208(a,2))]. 3220 a(x / y,y,a(z,u,w)) = a(y,a(w,u,z),x). [para(3217(a,1),3210(a,2))]. 3221 a(x * (y * z),y,a(u,w,v5)) = a(x * z,a(v5,w,u),y). [para(3218(a,1),2955(a,2))]. 3222 a(x,y,a(z,u,w / u)) = a(u,a(x,y,z),w). [para(3219(a,1),3204(a,1)),flip(a)]. 3223 a(x / (y / z),y,a(u,w,v5)) = a(y,a(v5,w,u),z * x). [para(3220(a,1),2956(a,1)),flip(a)]. 3224 a(x / (y * z),z,a(u,w,v5)) = a(z,a(v5,w,u),y * x). [para(3223(a,1),2851(a,1)),flip(a)]. 3225 a(x,y,a(z,u,z * (u * w))) = a(z * u,a(x,y,z),w). [para(3211(a,1),3221(a,1))]. 3226 a(x / (y * z),z,a(u,w,v5)) = a(v5,w,a(u,z,x * (z * y))). [para(3213(a,1),2846(a,2))]. 3227 a(x,y,a(z,u,w * (u * v5))) = a(u,a(x,y,z),v5 * w). [para(3226(a,1),3224(a,1))]. 3228 a(x * y,a(z,u,x),w) = a(y,a(z,u,x),w * x). [para(3227(a,1),3225(a,1)),flip(a)]. 3229 a(x,y,(z \ (u \ w)) \ ((u * z) \ w)) = a(u * (z * w),z,a(u,y,x)). [para(3212(a,2),1757(a,1))]. 3230 a(x,y,(z \ (u \ w)) \ ((u * z) \ w)) = a(u * w,a(x,y,u),z). [para(3229(a,2),3221(a,1))]. 3231 a(x,y,(z \ (u \ w)) \ ((u * z) \ w)) = a(w,a(x,y,u),z * u). [para(3230(a,2),3228(a,1))]. 3232 a(x,y,((z \ u) \ w) * ((z * w) \ u)) = a(u,a(x,y,z),w * z). [para(3231(a,1),3123(a,1)),flip(a)]. 3233 a(x,y,((z \ u) * w) * ((u * w) \ z)) = a(z,a(x,y,u),w * u). [para(3232(a,1),3146(a,1)),flip(a)]. 3234 a(x,a(y,z,u),w * u) = a(y,z,a(x,u,w)). [para(3233(a,1),3144(a,1))]. 3235 a(x,y,a(z,u,w / u)) = a(z,a(x,y,u),w). [para(22(a,1),3234(a,1,3)),flip(a)]. 3236 a(x,a(y,z,u),w) = a(u,a(y,z,x),w). [para(3235(a,1),3222(a,1))]. 3237 a(x,a(y,z,u),w) * a(u,w,a(y,z,x)) = a(w,u,a(y,z,x)). [para(3236(a,1),3176(a,1,1))]. 3238 a(x,y,a(z,u,w)) = a(x,w,a(z,u,y)). [para(3237(a,1),3206(a,1))]. 3239 a(x,y,a(z,u,w * y)) = a(x,w,a(y,u,z)). [para(3238(a,1),3207(a,1))]. 3240 a(x,a(y,z,u),w) = a(u,w,a(x,z,y)). [para(3239(a,1),3215(a,1)),flip(a)]. 3241 a(x,y,a(z,u,w)) * a(z,y,a(w,u,x)) = a(y,z,a(w,u,x)). [para(3240(a,1),3176(a,1,1))]. 3242 a(x,y,a(z,u,w)) = 1. [para(3241(a,1),3196(a,1))]. 3248 a(x,a(y,z,u),w) = 1. [para(3242(a,1),3165(a,1)),flip(a)]. 3249 $F # answer("aa2"). [resolve(3248,a,53,a)]. ============================== end of proof ========================== ============================== STATISTICS ============================ Given=2826. Generated=10478970. Kept=3218. proofs=7. Usable=2823. Sos=381. Demods=0. Limbo=3, Disabled=44. Hints=3753. Kept_by_rule=0, Deleted_by_rule=10432637. Forward_subsumed=43115. Back_subsumed=5. Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0. Demod_attempts=0. Demod_rewrites=0. Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. Nonunit_fsub_feature_tests=2. Nonunit_bsub_feature_tests=21. Megabytes=11.05. User_CPU=82.50, System_CPU=1.33, Wall_clock=84. ============================== end of statistics ===================== ============================== end of search ========================= THEOREM PROVED THEOREM PROVED Exiting with 7 proofs. ------ process 3835 exit (max_proofs) ------  Process 3835 exit (max_proofs) Mon Feb 20 13:27:39 2012