============================== Prover9 =============================== Prover9 (64) version 2017-09A, September 2017. Process 5364 was started by veroff on theorem, Sat Jan 4 12:57:07 2020 The command was "prover9 -f aK1_to_aK2.in". ============================== end of head =========================== ============================== INPUT ================================= % Reading from file aK1_to_aK2.in assign(order,kbo). set(lex_order_vars). set(para_from_small). clear(back_demod). set(restrict_denials). 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) # label("associator"). (x * y) \ (y * x) = K(y,x) # label("commutator"). (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(assumptions). a(K(x,y),z,u) = 1 # label("aK1"). end_of_list. formulas(goals). a(x,K(y,z),u) = 1 # label("aK2"). end_of_list. formulas(hints). a(x,K(y,z),u) = K(y,z) * K(z,y). a(x,K(y,z),u) = K(y,z) * K(z,(x / y) \ x). K(x,y) * K(y,(z / x) \ z) = a(z,K(x,y),u). K(x,((y * (z \ u)) / u) \ w) = K(x,(y / z) \ w). K(x,R(y,z,u) \ w) = K(x,y \ w). K(x,R(y,z,u) \ w) = K(x,T(y \ 1,y) * w). K(x,R(y,z,u) \ w) = K(x,T(((y \ 1) \ 1) \ 1,y) * w). K(x,R(T(((y \ 1) \ 1) \ 1,y) \ 1,z,u) \ w) = K(x,R(y,z,u) \ w). K(x,R(T(((y \ 1) \ 1) \ 1,y) \ 1,z,u) \ w) = K(x,R((y \ 1) \ 1,z,u) \ w). K(x,R(T(((y \ 1) \ 1) \ 1,y) \ 1,z,u) \ w) = K(x,((R((y \ 1) \ 1,z,u) \ 1) \ 1) \ w). K(x,(T(R((y \ 1) \ 1,z,u) \ 1,y) \ 1) \ w) = K(x,((R((y \ 1) \ 1,z,u) \ 1) \ 1) \ w). ((x \ 1) * (R((x \ 1) \ 1,y,z) \ 1)) / (1 / x) = T(R((x \ 1) \ 1,y,z) \ 1,x). K(x,y) * (R(x \ 1,z,u) \ 1) = T(R(x \ 1,z,u) \ 1,y). T(R(x \ 1,y,z) \ 1,u) = K(x,u) * (R(x \ 1,y,z) \ 1). T(R(x \ 1,y,z) \ 1,T(u,1)) = K(x,u) * (R(x \ 1,y,z) \ 1). K(x,y) * (R(x \ 1,z,u) \ 1) = T(R(x \ 1,z,u) \ 1,T(y,1)). K(x,y) * T(R(x \ 1,z,u) \ 1,x) = T(R(x \ 1,z,u) \ 1,T(y,1)). K((1 / x) \ 1,y) * T(R(x \ 1,z,u) \ 1,x) = T(R(x \ 1,z,u) \ 1,T(y,1)). K(x,R(y \ 1,z,u) \ w) = K(x,y * w). K(x,T(y * z,z)) = K(x,R(z \ 1,u,w) \ y). K(x,R(y \ 1,z,u) \ w) = K(x,T(w * y,y)). K(x,T(y / (z \ 1),z)) = K(x,R(z \ 1,u,w) \ y). K(x,((R(y \ 1,z,u) / w) * y) \ 1) = K(x,T(w,y)). K(x,T(y,z)) = K(x,((R(z \ 1,u,w) / y) * z) \ 1). K(x,1 / ((R(y \ 1,z,u) / w) * y)) = K(x,T(w,y)). K(x,1 / ((R(y \ 1,z,u) / w) * ((1 / y) \ 1))) = K(x,T(w,y)). K(x,T(y,z)) = K(x,1 / ((R(z \ 1,u,w) / y) * ((1 / z) \ 1))). K(x,1 / ((R(y \ 1,z,u) / w) * (1 / (1 / y)))) = K(x,T(w,y)). K(x,T(y,z)) = K(x,1 / ((R(z \ 1,u,w) / y) * (1 / (1 / z)))). K(x,(1 / (1 / (1 / y))) / (R(y \ 1,z,u) / w)) = K(x,T(w,y)). K(x,T(y,z)) = K(x,(1 / (1 / (1 / z))) / (R(z \ 1,u,w) / y)). K(x,R(1 / (1 / (1 / y)),z,u) / (R(y \ 1,z,u) / w)) = K(x,T(w,y)). K(x,R(1 / (1 / (1 / y)),z,u) / (R(y \ 1,z,u) / w)) = K(T(x,y \ 1),w). K(T(x,y \ 1),z) = K(x,R(1 / (1 / (1 / y)),u,w) / (R(y \ 1,u,w) / z)). R(T(x \ 1,y) \ 1,z,u) = T(R(x,z,u) \ 1,y) \ 1. R(((x \ 1) \ 1) * K(y,x \ 1),z,u) = T(R(x,z,u) \ 1,y) \ 1. R((x \ 1) \ 1,y,z) * K(u,x \ 1) = T(R(x,y,z) \ 1,u) \ 1. K(x,(R(1 / (1 / (1 / y)),z,u) * w) / R(y \ 1,z,u)) = K(T(x,y \ 1),w). R(1 / (1 / x),y,z) = 1 / (1 / R(x,y,z)). 1 / (1 / R(x,y,z)) = R(1 / (1 / x),y,z). K(R(1 / x,y,z) \ 1,u) * T(R(x \ 1,y,z) \ 1,x) = T(R(x \ 1,y,z) \ 1,T(u,1)). R(1 / (1 / x),y,z) \ 1 = 1 / R(x,y,z). 1 / R(x,y,z) = R(1 / (1 / x),y,z) \ 1. 1 / R(x \ 1,y,z) = R(1 / x,y,z) \ 1. R((x \ 1) \ 1,y,z) * K(u,R(x,y,z) \ 1) = T(R(x,y,z) \ 1,u) \ 1. 1 / R((x \ 1) \ 1,y,z) = R(x,y,z) \ 1. R((x \ 1) \ 1,y,z) = (R(x,y,z) \ 1) \ 1. (R(x,y,z) \ 1) \ 1 = R((x \ 1) \ 1,y,z). 1 / (R((x \ 1) \ 1,y,z) \ 1) = (R(x,y,z) \ 1) \ 1. K(x,R((y \ 1) \ 1,z,u) \ w) = K(x,R(y,z,u) \ w). (R(x,y,z) \ u) * K(x \ 1,x) = R((x \ 1) \ 1,y,z) \ u. R((x \ 1) \ 1,y,z) \ u = (R(x,y,z) \ u) * K(x \ 1,x). K(x \ 1,x) * (R(x,y,z) \ u) = R((x \ 1) \ 1,y,z) \ u. (K(x \ 1,x) * (R(x,y,z) \ u)) * 1 = R((x \ 1) \ 1,y,z) \ u. (K(x \ 1,x) * (R(x,y,z) \ u)) * a(R((x \ 1) \ 1,y,z),K(x \ 1,x),(R((x \ 1) \ 1,y,z) * K(x \ 1,x)) \ u) = R((x \ 1) \ 1,y,z) \ u. (K(x \ 1,x) * ((R((x \ 1) \ 1,y,z) * K(x \ 1,x)) \ u)) * a(R((x \ 1) \ 1,y,z),K(x \ 1,x),(R((x \ 1) \ 1,y,z) * K(x \ 1,x)) \ u) = R((x \ 1) \ 1,y,z) \ u. (K(x \ 1,x) * ((R((x \ 1) \ 1,y,z) * K(x \ 1,x)) \ u)) * a(R((x \ 1) \ 1,y,z),K(x \ 1,x),(R((x \ 1) \ 1,y,z) * K(x \ 1,x)) \ u) = R(R((x \ 1) \ 1,y,z),K(x \ 1,x) * (R(x,y,z) \ u),1) \ u. R(R((x \ 1) \ 1,y,z),K(x \ 1,x) * (R(x,y,z) \ u),1) \ u = (K(x \ 1,x) * ((R((x \ 1) \ 1,y,z) * K(x \ 1,x)) \ u)) * a(R((x \ 1) \ 1,y,z),K(x \ 1,x),(R((x \ 1) \ 1,y,z) * K(x \ 1,x)) \ u). K(x,((R(y \ 1,z,u) / (w / (y \ 1))) * y) \ 1) = K(x,R(y \ 1,z,u) \ w). K(x,((R(y \ 1,z,u) / (w / (y \ 1))) * y) \ 1) = K(x,T(w / R(y \ 1,z,u),y)). K(x,((R(y \ 1,z,u) / (w / (y \ 1))) * y) \ 1) = K(T(x,y \ 1),w / R(y \ 1,z,u)). K(x,((R(y \ 1,z,u) / (w / (y \ 1))) * y) \ 1) = K(T(x,y \ 1),w / R(1 / y,z,u)). K(x,((R(y \ 1,z,u) / (w / (y \ 1))) * y) \ 1) = K(T(x,y \ 1),w * (R(1 / y,z,u) \ 1)). K(x,((R(y \ 1,z,u) / (w / (y \ 1))) * y) \ 1) = K(x,((1 / y) * (w * (R(1 / y,z,u) \ 1))) * y). K(x,((1 / y) * (z * (R(1 / y,u,w) \ 1))) / (y \ 1)) = K(x,((R(y \ 1,u,w) / (z / (y \ 1))) * y) \ 1). K(x,(R(1 / y,z,u) * (w * (R(1 / y,z,u) \ 1))) / R(y \ 1,z,u)) = K(x,((R(y \ 1,z,u) / (w / (y \ 1))) * y) \ 1). K(x,(R(1 / y,z,u) * (w * (R(1 / y,z,u) \ 1))) / R(y \ 1,z,u)) = K(x,(y \ 1) / (R(y \ 1,z,u) / (w / (y \ 1)))). K(x,(R(1 / y,z,u) * (w * (R(1 / y,z,u) \ 1))) / R(y \ 1,z,u)) = K(x,((y \ 1) * (w / (y \ 1))) / R(y \ 1,z,u)). K(x,(R(1 / y,z,u) * (w * (R(1 / y,z,u) \ 1))) / R(y \ 1,z,u)) = K(x,((y \ 1) * (w / (y \ 1))) / R(1 / y,z,u)). K(x,(R(1 / y,z,u) * (w * (R(1 / y,z,u) \ 1))) / R(y \ 1,z,u)) = K(x,((y \ 1) * (w / (y \ 1))) * (R(1 / y,z,u) \ 1)). K(x,(R(1 / y,z,u) * (w * (R(1 / y,z,u) \ 1))) / R(y \ 1,z,u)) = K(x,((1 / y) * (w / (1 / y))) * (R(1 / y,z,u) \ 1)). K(x,(R(1 / y,z,u) * (w * (R(1 / y,z,u) \ 1))) / R(y \ 1,z,u)) = K(x,(R(1 / y,z,u) * (w / R(1 / y,z,u))) * (R(1 / y,z,u) \ 1)). K(x,(R(1 / y,z,u) * (w / R(1 / y,z,u))) * (R(1 / y,z,u) \ 1)) = K(x,(R(1 / y,z,u) * (w * (R(1 / y,z,u) \ 1))) / R(y \ 1,z,u)). K(x,y / R(1 / z,u,w)) = K(x,y / R(z \ 1,u,w)). K(T(x,y \ 1),R(y \ 1,z,u) \ w) = K(x,w / R(1 / y,z,u)). K(x,R(y / R(1 / z,u,w),z \ 1,z)) = K(T(x,z \ 1),R(z \ 1,u,w) \ y). ((x \ 1) * (R(x \ 1,y,z) \ u)) * x = R(u / R(1 / x,y,z),x \ 1,x). (x / y) * (R(x / y,z,u) \ w) = (y \ x) * (R(y \ x,z,u) \ w). (x \ y) * (R(x \ y,z,u) \ w) = (y / x) * (R(y / x,z,u) \ w). K(x,x \ y) * (R(y / x,z,u) \ w) = R(x \ y,z,u) \ w. (K(x,x \ y) * (R(y / x,z,u) \ w)) * 1 = R(x \ y,z,u) \ w. (K(x,x \ y) * (R(y / x,z,u) \ w)) * a(R(x \ y,z,u),K(x,x \ y),(R(x \ y,z,u) * K(x,x \ y)) \ w) = R(x \ y,z,u) \ w. (K(x,y) * (R(y * K(x,y),z,u) \ w)) * a(R(y,z,u),K(x,y),(R(y,z,u) * K(x,y)) \ w) = R(y,z,u) \ w. (K(x,y) * ((R(y,z,u) * K(x,y)) \ w)) * a(R(y,z,u),K(x,y),(R(y,z,u) * K(x,y)) \ w) = R(y,z,u) \ w. R(x,y,z) * (u / R(x,y,z)) = x * (u / x). R(x,y,z) * (u / R(x,y,z)) = u * K(x,x \ u). K(x,R(x,y,z) \ u) = K(x,x \ u). K(x,R(x,y,z) \ u) = K(x,u / x). K(x,y / x) = K(x,R(x,z,u) \ y). K(x,x * (R(x,y,z) \ u)) = K(x,u). T(x,x * (R(x,y,z) \ u)) = x * K(x,u). T(x,x * (R(x,y,z) \ u)) = T(x,u). T(x,y) = T(x,x * (R(x,z,u) \ y)). T(x,R(x,y,z) * u) = T(x,x * u). T(x,x * y) = T(x,R(x,z,u) * y). T(x,R(x,y,z) * u) = (K(x * u,x) / x) \ 1. K(R(x,y,z) * u,x) = K(x * u,x). K(x * y,x) = K(R(x,z,u) * y,x). K(R(x,y,z) * u,T(x,u)) = K(x * u,x). K(R(x,y,z) * u,T(x,u)) = K(x * u,R(x,y,z)). K(R(x,y,z) * u,T(x,u)) = K(u * T(x,u),R(x,y,z)). K(x * T(y,x),R(y,z,u)) = K(R(y,z,u) * x,T(y,x)). (x * (R(T(x,y),z,u) * y)) \ ((x * y) * R(T(x,y),z,u)) = K(y * T(x,y),R(x,z,u)). ((T(x,x * y) * y) * R(T(x,y),z,u)) \ ((x * y) * R(T(x,y),z,u)) = K(y * T(x,y),R(x,z,u)). (R(T(x,y),z,u) * w) * T(x,w) = (T(x,y) * w) * R(T(x,w),z,u). (T(x,y) * z) * R(T(x,z),u,w) = (R(T(x,y),u,w) * z) * T(x,z). (T(x,y) * z) * R(T(x,K(x,y) * z),u,w) = (R(T(x,y),u,w) * z) * T(x,z). (T(x,y) * z) * R(T(x,K(R(x,u,w),y) * z),u,w) = (R(T(x,y),u,w) * z) * T(x,z). (x * (K(x,y) * z)) * R(T(x,K(R(x,u,w),y) * z),u,w) = (R(T(x,y),u,w) * z) * T(x,z). (x * (K(R(x,y,z),u) * w)) * R(T(x,K(R(x,y,z),u) * w),y,z) = (R(T(x,u),y,z) * w) * T(x,w). (x * (K(R(x,y,z),u) * w)) * R(T(x,K(R(x,y,z),u) * w),y,z) = (R(T(x,u),y,z) * w) * T(x,K(x,u) * w). (x * (K(R(x,y,z),u) * w)) * R(T(x,K(R(x,y,z),u) * w),y,z) = (R(T(x,u),y,z) * w) * T(x,K(R(x,y,z),u) * w). K(x,y) * K(y,((z * (x \ u)) / u) \ z) = a(z,K(x,y),u). K(x,y) * T(K(y,z / ((z * (x \ u)) / u)),z) = a(z,K(x,y),u). K(x,y) * T((z * u) / (z * (K(x,y) * u)),z) = a(z,K(x,y),u). (x * y) / (x * (T(K(z,u),w) * y)) = T((x * y) / (x * (K(z,u) * y)),w). (x * y) / (x * (K(T(z \ 1,u) \ 1,w) * y)) = T((x * y) / (x * (K(z,w) * y)),u). (x * y) / (x * (K(T(z \ 1,u) \ 1,w) * y)) = T((x * (K(w,z) * y)) / (x * y),u). (x * y) / (x * (K(z,u) * y)) = K(u,x / ((x * (z \ y)) / y)). L(K(x,T(T(y,z),u * z)),z,u) = (u * z) / (u * (K(y,x) * z)). (x * y) / (x * (K(T(z \ 1,u) \ 1,w) * y)) = (x * (T(K(w,z),u) * y)) / (x * y). (x * (T(K(y,z),u) * w)) / (x * w) = (x * w) / (x * (K(T(z \ 1,u) \ 1,y) * w)). (x * (K(y,z) * u)) / (x * u) = (x * u) / (x * (K(z,y) * u)). (x * (y * T(K(z,u),y))) / (x * y) = (x * y) / (x * (K(u,z) * y)). (x * y) / (x * (K(z,u) * y)) = (x * (y * T(K(u,z),y))) / (x * y). R((x * y) / (x * (K(z,u) * y)),w,v5) = (x * y) / (x * (K(z,u) * y)). R((x * y) / (x * (K(z,u) * y)),w,v5) = ((x * (K(z,u) * y)) * L(T(K(u,z),y),y,x)) / (x * (K(z,u) * y)). ((x * (K(y,z) * u)) * L(T(K(z,y),u),u,x)) / (x * (K(y,z) * u)) = R((x * u) / (x * (K(y,z) * u)),w,v5). ((x * (K(y,z) * u)) * L(R(T(K(z,y),u),w,v5),u,x)) / (x * (K(y,z) * u)) = R((x * u) / (x * (K(y,z) * u)),w,v5). K(x,((1 / (1 / R(1 / y,z,u))) * w) / R(y \ 1,z,u)) = K(T(x,y \ 1),w). K(x,x * (R(x,y,z) \ (u / x))) = K(x,R(x,y,z) \ u). K(x,R(x,y,z) \ u) = K(x,x * (R(x,y,z) \ (u / x))). K(x,((1 / (1 / R(1 / y,z,u))) * w) / R(y \ 1,z,u)) = K(x,((1 / y) * w) * y). K(x,((y \ 1) * z) * y) = K(T(x,y \ 1),z). K(x,y / (z \ 1)) = K(x,y * z). K(x,y * z) = K(x,y / (z \ 1)). K(x,R(y,z,u) / w) = K(x,y / w). K(x,T(y \ 1,y) * z) = K(x,y \ z). K(x,(y \ 1) * z) = K(x,y \ z). K(x,R(x,y,z) \ (u * x)) = K(x,x * (R(x,y,z) \ u)). K(x,x * (R(x,y,z) \ u)) = K(x,R(x,y,z) \ (u * x)). K(x,T(y * z,z)) = K(x,z * y). K(x,(y \ 1) \ z) = K(x,y * z). K(x,y * z) = K(x,(y \ 1) \ z). K(x,T(y * z,y)) = K(x,z * y). K(x,y \ R(y * z,u,w)) = K(x,z). K(x,y * R(z,u,w)) = K(x,y * z). K(x,y * R(y \ z,u,w)) = K(x,z). K(x,T(y * R(y \ z,u,w),z)) = K(x,z). ((x * R(x \ y,z,u)) * ((y * w) / y)) \ ((x * R(x \ y,z,u)) * w) = K(w,T(x * R(x \ y,z,u),y)). K(x,((1 / (1 / R(y / z,u,w))) * v5) / R(z \ y,u,w)) = K(x,((y / z) * v5) / (z \ y)). (R(x / y,z,u) * w) / R(y \ x,z,u) = ((x / y) * w) / (y \ x). (K(x,x \ y) * z) * K(x \ y,z) = ((y / x) * z) / (x \ y). (K(x,x \ y) * z) * K(T(x \ y,z),z) = ((y / x) * z) / (x \ y). (K(x,x \ y) * z) * K(T(x \ y,z),K(x,x \ y) * z) = ((y / x) * z) / (x \ y). (K(x,x \ y) * z) * K(z \ ((x \ y) * z),K(x,x \ y) * z) = ((y / x) * z) / (x \ y). ((x * R(x \ y,z,u)) * ((y * w) / y)) \ (w * (x * R(x \ T(y,w),z,u))) = K(w,T(x * R(x \ y,z,u),y)). K(x,y) * (z * R(z \ x,u,w)) = z * R(z \ T(x,y),u,w). K(x,y) * (z * R(z \ x,u,w)) = z * R(z \ (x * K(x,y)),u,w). (x * R(x \ y,z,u)) * K(w,v5) = x * R(x \ (y * K(w,v5)),z,u). (x * R(K(y,z) * (K(z,y) * (x \ u)),w,v5)) * K(z,y) = x * R(x \ (u * K(z,y)),w,v5). (x * (K(y,z) * R(K(z,y) * (x \ u),w,v5))) * K(z,y) = x * R(x \ (u * K(z,y)),w,v5). (x * (K(y,z) * R(K(z,y) * (x \ u),w,v5))) * K(z,y) = x * R(x \ (u * ((x * K(y,z)) \ x)),w,v5). (x * (K(y,z) * R(K(y,z) \ (x \ u),w,v5))) * K(z,y) = x * R(x \ (u * ((x * K(y,z)) \ x)),w,v5). L(K(x,T(T(y,z),u * z)),z,u) = K(x,u / ((u * (y \ z)) / z)). L(T(K(x,T(y,z)),u * z),z,u) = K(x,u / ((u * (y \ z)) / z)). T(L(K(x,T(y,z)),z,u),u * z) = K(x,u / ((u * (y \ z)) / z)). T(K(x,L(T(y,z),y \ z,u)),u * z) = K(x,u / ((u * (y \ z)) / z)). T(K(x,L(T(y,z),y \ z,u)),u * z) = K(x,(u * z) / (u * (y \ z))). K(x,T((y * (z \ u)) \ (y * u),y * (z \ u))) = T(K(x,L(T(z,u),z \ u,y)),y * u). T(K(x,(y * (z \ u)) \ (y * u)),y * (z \ u)) = T(K(x,L(T(z,u),z \ u,y)),y * u). T(K(x,L(T(y,z),y \ z,u)),u * z) = T(K(x,(u * (y \ z)) \ (u * z)),u * (y \ z)). T(K(x,L(T(y,y \ z),y \ z,u)),u * z) = T(K(x,(u * (y \ z)) \ (u * z)),u * (y \ z)). T(K(x,(y * (z \ u)) \ (y * u)),y * (z \ u)) = T(K(x,L(T(z,z \ u),z \ u,y)),y * u). K(x,L(T(y,z),y \ z,u)) = L(K(x,T(y,z)),z,u). K(x,L(T(y,z),y \ z,u)) = L(T(K(x,y),z),z,u). L(T(K(x,y),z),z,u) = K(x,L(T(y,z),y \ z,u)). K(x,T(L(T(T(y,z),u * z),y \ z,u),u * z)) = L(T(K(x,y),z),z,u). T(K(x,L(T(T(y,z),u * z),y \ z,u)),u * z) = L(T(K(x,y),z),z,u). T(K(x,L(T(T(y,y \ z),u * z),y \ z,u)),u * z) = L(T(K(x,y),z),z,u). T(K(x,T(L(T(y,y \ z),y \ z,u),u * z)),u * z) = L(T(K(x,y),z),z,u). T(K(T(x,y * z),L(T(u,u \ z),u \ z,y)),y * z) = L(T(K(x,u),z),z,y). T(K(T(x,y * z),L(T(u,u \ z),u \ z,y)),y * z) = K(x,((y * z) \ (y * (u \ z))) \ 1). K(x,((y * z) \ (y * (u \ z))) \ 1) = T(K(T(x,y * z),L(T(u,u \ z),u \ z,y)),y * z). K(x,(y \ (y / z)) \ 1) = T(K(T(x,y),z),y). T(K(T(x,y),z),y) = K(x,(y \ (y / z)) \ 1). K(x,T(y,z \ 1) / (y / z)) = T(K(T(x,y),z),y). T(K(T(x,y),z),y) = K(x,T(y,z \ 1) / (y / z)). K(x,(T(y,z \ 1) * z) / y) = T(K(T(x,y),z),y). x * (K(y,x \ 1) * K(y,x)) = (T(y,x \ 1) * x) / y. x * (K(y,(y * x) \ y) * K(y,x)) = (T(y,x \ 1) * x) / y. x * (K(y,(y * x) \ (1 * y)) * K(y,x)) = (T(y,x \ 1) * x) / y. x * (K(y,((y * x) / y) \ 1) * K(y,x)) = (T(y,x \ 1) * x) / y. x * (K(y,((y * x) / y) \ 1) * K(y,x)) = K(y,x \ 1) * ((y * x) / y). K(x,y \ 1) * ((x * y) / x) = y * (K(x,((x * y) / x) \ 1) * K(x,y)). K(x,(x * y) \ x) * ((x * y) / x) = y * (K(x,((x * y) / x) \ 1) * K(x,y)). K(x,(x * y) \ (1 * x)) * ((x * y) / x) = y * (K(x,((x * y) / x) \ 1) * K(x,y)). K(x,(y \ 1) / z) = K(x,(z * y) \ 1). K(x,(y * z) \ K(z \ 1,z)) = K(x,(z \ 1) / y). K(x,R((y \ 1) / z,z,y)) = K(x,(z * y) \ K(y \ 1,y)). K(x,y * (K(z,y \ 1) * K(z,y))) = T(K(T(x,z),y),z). T(K(T(x,y),z),y) = K(x,z * (K(y,z \ 1) * K(y,z))). T(K(x,(y * z) / y),y) = K(x,z * (K(y,z \ 1) * K(y,z))). K(x,y * (K(z,y \ 1) * K(z,y))) = T(K(x,(z * y) / z),z). K(x,y * (K(z,(z * y) \ z) * K(z,y))) = T(K(x,(z * y) / z),z). K(x,y * (K(z,(z * y) \ (1 * z)) * K(z,y))) = T(K(x,(z * y) / z),z). K(x,y / (z * (1 / u))) = K(x,y / (z * (u \ 1))). K(x,(y / (z \ 1)) / u) = K(x,y / (u * (1 / z))). K(x,y / (z * (1 / u))) = K(x,(y / (u \ 1)) / z). K(x,(y / (z \ 1)) * (u \ 1)) = K(x,y / (u * (1 / z))). K(x,(y / (z \ 1)) * (u \ 1)) = K(x,(y / (1 / z)) / u). K(x,(y / (1 / z)) * u) = K(x,(y / (z \ 1)) * u). K(x,(((y / (z \ 1)) \ 1) \ 1) * u) = K(x,(y / (1 / z)) * u). K(T(x,y \ 1),z) = K(x,T(z,y)). K(x,T(y * z,z)) = K(x,T(y * z,y)). K(x,T(y * z,y)) = K(x,T(y * z,z)). K(x,T(y / R(z \ 1,u,w),z)) = K(x,R(z \ 1,u,w) \ y). K(x,R(y \ 1,z,u) \ w) = K(x,T(w / R(y \ 1,z,u),y)). K(x,T(y,z \ 1)) = K(x,T(y,z)). K(x,y) * K(x,K(z,y)) = K(x,T(y,z \ 1)). K(x,K(y \ 1,z)) = K(x,K(y,z)). K(x,K(y \ 1,z)) = K(y,K(x,z)). K(x,K(y,z)) = K(y,K(x \ 1,z)). K(x,K(y,z \ 1)) = K(z,K(x,y)). K(x,K(y,z \ 1)) = K(x,K(y,z)). K(x,K(y,z \ y)) = K(x,K(y,z)). K(x,y / z) * K(z \ y,x) = K(x,K(y,z \ y)). K(x,y / z) * K((y \ z) \ 1,x) = K(x,K(y,z \ y)). K(x,(y / z) \ 1) * K((z \ y) \ 1,x) = K(x,K(z,y \ z)). K(x,(y / z) \ 1) * K((z \ y) \ 1,x) = K(z,K(x,y \ z)). K(x,y * (K(z,((z * y) / z) \ 1) * K(z,y))) = T(K(x,(z * y) / z),z). K(x,((x * y) / x) \ 1) * ((x * y) / x) = y * (K(x,((x * y) / x) \ 1) * K(x,y)). ((x * y) / x) * K(x,z) = y * (K(x,z) * K(x,y)). ((x * y) / x) * K(x,z) = (y * K(x,z)) * K(x,y). (x * K(y,z)) * K(y,u) = (x * K(y,u)) * K(y,z). T(K(x,y) * (z * K(x,u)),K(x,y)) = (z * K(x,y)) * K(x,u). T((K(x,y) * z) * K(x,u),K(x,y)) = (z * K(x,y)) * K(x,u). T(x * K(y,z),K(y,u)) = T(x,K(y,u)) * K(y,z). K(x,y) * T(T(z,K(x,y)),K(x,u)) = T(z * K(x,y),K(x,u)). T(x * K(y,z),K(y,u)) = K(y,z) * T(T(x,K(y,z)),K(y,u)). T(K(x,y) * z,K(x,u)) = K(x,y) * T(z,K(x,u)). K(x,y) * T(z,K(x,u)) = T(K(x,y) * z,K(x,u)). K(x,(y / z) \ 1) * K((z \ y) \ 1,x) = K(z,K(x,(z \ y) \ 1)). K(x,y \ K(y,z)) * K(y \ 1,x) = K(z,K(x,y \ 1)). K(x,y \ K(y,z)) \ K(z,K(x,y \ 1)) = K(y \ 1,x). L(K(x,T(T(y,z),u * z)),z,u) = (u * (K(x,y) * z)) / (u * z). (x * (K(y,z) * u)) / (x * u) = L(K(y,T(T(z,u),x * u)),u,x). K(x,((1 / y) * z) * y) = K(T(x,y \ 1),z). R(x * K(y,z),u,w) = R(x,u,w) * K(y,z). K(x,K(y,K(x,z) * u)) * (K(x,w) * u) = K(x,w) * T(u,K(x,y)). R(K(x,y) * T(z,K(y,x)),u,w) = R(z,u,w) * K(x,y). (x * y) * K(z,x) = x * (y * K(z,x)). x * (y * K(z,x)) = (x * y) * K(z,x). K(x,y / z) * K(z \ y,x) = K(x,K(y,z)). K(x,y / z) * K(z \ y,x) = K(x,K(z,y)). K(x,K(y,z \ 1)) = K(x,K(y,z \ y)). K(x,K(y,z \ y)) = K(x,K(y,z \ 1)). K(x,K(y,y \ z)) = K(x,K(y,z)). K(x,K(y,z)) = K(x,K(y,y \ z)). K(x,K(y,y * z)) = K(x,K(y,z)). K(x,K(y,y * z)) = K(y,K(x,z)). K(x,K(y,z)) = K(y,K(x,x * z)). K(x,K(y,x * z)) = K(x,K(y,z)). K(x,K(y,z)) = K(x,K(y,x * z)). K(x,K(y,x \ z)) = K(x,K(y,z)). K(x,K(y,z)) = K(x,K(y,x \ z)). x * y != z * T(z \ x,K(u,w)) | y = K(u,K(w,z \ x)). T(x * (K(y,x) * z),K(x,y)) = x * (z * K(y,x)). x * T(x \ y,K(x,z)) = y * K(x,K(z,y)). x * K(y,K(z,x)) = y * T(y \ x,K(y,z)). T(x * y,K(x,z)) = x * T(y,K(x,z)). x * T(y,K(x,z)) = T(x * y,K(x,z)). x * T(x \ y,K(x,z)) = T(y,K(x,z)). x * T(x \ y,K(x,z)) = T(y,K(z,x)). x * T(x \ y,K(z,x)) = T(y,K(z,x)). T(x,K(y,z)) = z * T(z \ x,K(y,z)). T(x * y,K(z,x)) = x * T(y,K(z,x)). x * T(y,K(z,x)) = T(x * y,K(z,x)). K(x,y / z) * K(z \ y,x) = K(x,K(z,z \ y)). K(x,T(R((y \ 1) / z,z,y),K(y,y \ 1))) = K(x,(z * y) \ K(y \ 1,y)). x * (K(y,x) * (z * K(x,y))) = T(x * z,K(y,x)). T(x * y,K(z,x)) = x * (K(z,x) * (y * K(x,z))). K(x \ y,z) * K(z,y / x) = K(z,K(x,x \ y)). K(x,y \ K(y,z)) \ K(z,K(x,y \ 1)) = K(y \ K(y,z),T(x,z)). K(1 / R(x \ 1,y,z),u) * T(R(x \ 1,y,z) \ 1,x) = T(R(x \ 1,y,z) \ 1,T(u,1)). K(x \ K(x,y),T(z,y)) = K(x \ 1,z). K(x,K(y \ K(y,x),z)) = K(x,K(z,y \ 1)). K(x \ K(x,y),z) = K(x \ 1,T(z,y)). K(x,K(y,z)) * (K(y,u) * x) = K(y,u) * T(x,K(y,z)). K(x,T(y,z)) * (z * x) = z * T(x,y). K(T(x,y),z) * (y * x) = y * T(x,z). T(x * (K(y,x) * z),K(x,y)) = (x * z) * K(y,x). K(x,T(K(y,z) / u,K(z,y))) = K(x,u \ K(y,z)). K(x,y) * R(T(z,K(y,x)),u,w) = R(z,u,w) * K(x,y). K(x,y) * (y * (z * K(y,x))) = T(y * z,K(x,y)). T(x,K(y,z)) = T(x,K(z,y)). K(x,y) * T(z,K(y,x)) = z * K(x,y). T(K(x,y) * z,K(y,x)) = z * K(x,y). x * K(y,z) = T(K(y,z) * x,K(z,y)). K(x,y) * (z * K(y,x)) = T(z,K(x,y)). T(x,K(y,z)) = K(y,z) * (x * K(z,y)). (K(x,y) * z) * K(y,x) = T(z,K(x,y)). T(x,K(y,z)) = (K(y,z) * x) * K(z,y). (K(x,y) * z) / K(x,y) = T(z,K(x,y)). K(x,K(y,K(x,z) * u)) = K(u,K(x,y)). K(x,y) * K(x,K(z,y)) = K(x,T(y,z)). K(x,T(y,z)) = K(x,y) * K(x,K(z,y)). K(x \ y,z) * K(z,y / x) = K(x,K(z,x \ y)). (x * ((y * z) / y)) \ (z * (K(y,z) * x)) = K(z,T(x,y)). K(x / y,z) * (y \ x) = T(y \ x,T(z,x)). T(x \ y,T(z,y)) = K(y / x,z) * (x \ y). K(((x * y) / x) \ 1,z) = K(y \ 1,T(z,x)). K(x \ 1,T(y,z)) = K(((z * x) / z) \ 1,y). (x * (y * K(z,u))) / (x * y) = L(K(z,T(u,x * y)),y,x). L(K(x,T(y,z * u)),u,z) = (z * (u * K(x,y))) / (z * u). K(T(x,y),z) * (y * x) = (y * x) * K(x,z). K(x,T(y \ z,y)) = K(x,z / y). K(x,T(L(T(y,z),u,w),z)) = K(x,L(y,u,w)). K(T(x,y),K(z,x) * u) = K(T(x,y),u). K(T(x,y),R(y,z,u) \ w) = K(x,w / R(y,z,u)). K(T(x,y \ 1),R(z,y \ 1,y)) = K(x,((1 / y) * z) * y). K(x,(y * z) / y) = K(T(x,y),z). K(T(x,y),z) = K(x,(y * z) / y). K((x * y) / x,z) = K(y,T(z,x)). K(x,T(y,z)) = K((z * x) / z,y). K(x,T(T(y,z),z)) = K(x,y). K(x \ y,T(z,y)) = K(y / x,z). K(x / y,z) = K(y \ x,T(z,x)). K(T(x,y),T(z,y)) = K(x,z). (x * K(y,z)) / x = K(y,T(z,x)). T(K(x,T(y,z)),z) = K(x,y). T(K(x,y),z) * z = z * K(x,y). T(T(K(x,y),z),z) = K(x,y). K(x,y) \ K(z,K(y,x)) = K(y,T(x,z)). K(K(x,y) * z,K(x,u)) = K(z,K(x,u)). K(x,y) * K(x,K(z,y)) = T(K(x,y),z). K(x,K(y,T(z,x))) = K(x,K(z,y)). K(x,y) * K(z,K(x,y)) = T(K(x,y),z). T(K(x,y),z) = K(x,y) * K(z,K(x,y)). K(x,y) * K(y,T(x,z)) = K(z,K(y,x)). K(K(x,y),z) = K(z,K(x,y)). K(x,K(y,z)) = K(x,K(z,y)). K(x,K(y,T(z,x))) = K(z,K(x,y)). x * T(x \ y,K(z,u)) = y * K(z,K(u,x \ y)). x * K(y,K(z,x)) = T(x,K(y,z)). T(x,K(y,z)) = x * K(y,K(z,x)). K(x,K(y,z)) * z = T(z,K(x,y)). T(x,K(y,z)) = K(y,K(z,x)) * x. K(x,K(y,z)) = K(z,K(x,y)). K(x,K(y,z)) = K(y,K(x,z)). K(K(x,y) * z,K(x,u)) = K(K(z,x),u). K(K(x,y),z) = K(K(y,u) * x,K(y,z)). K(x,K(y,z)) * K(K(x,z),y) = 1. K(x,y) * K(x,K(y,z)) = T(K(x,y),z). T(K(x,y),z) = K(x,y) * K(x,K(y,z)). (K(x,y) * z) / K(x,y) = z * K(x,K(y,z)). K(K(x,y),z) = K(x,K(y,z)). K(x,K(y,z)) = K(z,K(y,x)). K(x * y,K(y,z)) = K(x,K(y,z)). K(x * y,K(y,z)) = K(y * x,K(y,z)). K(K(x,y),y * z) = K(z * y,K(y,x)). T(K(x,y),z * y) * K(y,x) = K(K(x,y),y * z). T(K(x,y),z * y) = T(K(x,y),y * z). K(x,y * K(y * z,y \ 1)) = T(K(x,y),z * y). K(x,((((y \ 1) * (R((y \ 1) \ 1,z,u) \ 1)) / (1 / y)) \ 1) \ w) = K(x,((R((y \ 1) \ 1,z,u) \ 1) \ 1) \ w). K(x,T(y \ 1,z * y) \ 1) = K(x,y * K(y * z,y \ 1)). K(x,(y \ 1) \ K(z,u)) = K(x,y * K(z,u)). K(x,y * K(z,u)) = K(x,(y \ 1) \ K(z,u)). K(x,T(y * z,y)) = K(x,(z \ 1) \ y). K(x,T(y / (z \ 1),u)) = K(x,T(y * z,u)). K(x,T(y * z,u)) = K(x,T(y / (z \ 1),u)). K(x,T(y * (1 / z),u)) = K(x,T(y / z,u)). K(x,T(y / z,u)) = K(x,T(y * (1 / z),u)). K(x,(((y / (1 / z)) \ 1) \ 1) * u) = K(x,(((y / (z \ 1)) \ 1) \ 1) * u). K(x,((y / (1 / z)) \ 1) \ u) = K(x,((y / (z \ 1)) \ 1) \ u). K(x,((y / (z \ 1)) \ 1) \ u) = K(x,((y / (1 / z)) \ 1) \ u). (x \ 1) \ K(x * y,x \ 1) = T(x \ 1,y * x) \ 1. T(x \ 1,y * x) \ 1 = (x \ 1) \ K(x * y,x \ 1). x \ K(x \ 1,x * y) = T(x \ 1,y * x). x * T(x \ 1,y * x) = K(x \ 1,x * y). K(x \ 1,x * y) = x * T(x \ 1,y * x). K(x,T(y / (1 / (1 / z)),u)) = K(x,T(y / z,u)). K(x,T(y / z,u)) = K(x,T(y / (1 / (1 / z)),u)). K(x \ 1,(x \ 1) \ y) = K(x \ 1,x * y). K(x \ 1,x * y) = K(x \ 1,(x \ 1) \ y). K(x,T((y \ 1) \ 1,z) * u) = K(x,T(y,z) * u). K(x,T(y \ 1,y) * z) = K(x,(y \ 1) * z). K(x,(y \ K(z \ 1,z)) * u) = K(x,(y \ 1) * u). K(x,((y \ 1) \ 1) \ z) = K(x,y \ z). K(x,T(y * K(z \ 1,z),u)) = K(x,T(y,u)). K(x,y \ K(z \ 1,z)) = K(x,y \ 1). K(x,((1 / (1 / y)) * z) / u) = K(x,(y * z) / u). K(x,(y \ K(z \ 1,z)) \ u) = K(x,(y \ 1) \ u). K(x,((y \ 1) \ 1) * z) = K(x,y * z). K(x,K(y \ 1,y) * z) = K(x,z). K(x,y) = K(x,K(z \ 1,z) * y). K(x,y * K(z \ 1,z)) = K(x,y). K(x,y * K(z,z \ 1)) = K(x,y). (x \ (K(y \ 1,y) * z)) / (((u * x) / u) \ (K(y \ 1,y) * z)) = K(u,x * K(y,y \ 1)). K(x,(x \ 1) \ (R(x,y,z) \ u)) = K(x,R(x,y,z) \ (u * x)). K(x,R(x,y,z) \ (u * x)) = K(x,(x \ 1) \ (R(x,y,z) \ u)). K(R(x,y,z),(x \ 1) \ (R(x,y,z) \ u)) = K(x,R(x,y,z) \ (u * x)). K(R(x,y,z),(x \ 1) \ (R(x,y,z) \ u)) = K(x,(x \ R(x,y,z)) \ u). (x \ (K(y \ 1,y) * z)) / ((K(y,y \ 1) * ((u * x) / u)) \ z) = K(u,x * K(y,y \ 1)). (x * (y * K(z,z \ 1))) / u = K(z,z \ 1) * ((x * y) / u). K(x,x \ 1) * ((y * z) / u) = (y * (z * K(x,x \ 1))) / u. R((x * y) / (x * (K(z,u) * y)),x * (K(z,u) * y),L(T(K(u,z),y),y,x)) = (x * (y * T(K(u,z),y))) / (x * y). ((x * (K(y,z) * u)) * R(L(T(K(z,y),u),u,x),w,v5)) / (x * (K(y,z) * u)) = R((x * u) / (x * (K(y,z) * u)),w,v5). R((x * y) / (x * (K(z,u) * y)),w,v5) = ((x * (K(z,u) * y)) * R(L(T(K(u,z),y),y,x),w,v5)) / (x * (K(z,u) * y)). (x * (K(y,z) * u)) * L(T(K(z,y),u),u,x) = x * u. x / L(T(K(y,z),u),w,v5) = x * L(T(K(z,y),u),w,v5). x * L(T(K(y,z),u),w,v5) = x / L(T(K(z,y),u),w,v5). K(x,(x \ 1) * y) = K(x,x \ y). K(T(x \ y,x),x) \ 1 = K(x,(x \ 1) * y). K(T((x \ 1) * y,x),x) = K(T(x \ y,x),x). K(T(x \ y,x),x) = K(T((x \ 1) * y,x),x). K(T((1 / x) * y,x),x) = K(T(x \ y,x),x). K((1 / x) * (y * x),x) = K(T(y,x),x). K((1 / x) * y,x) = K(x \ y,x). K((x \ 1) * y,x) = K(x \ y,x). K(x \ y,x) = K((x \ 1) * y,x). K(x \ ((x \ 1) \ y),x) = K(y,x). K(x \ ((x \ 1) \ y),x) = K(y,(x \ 1) \ 1). K(x \ ((x \ 1) \ y),x) = K(y,((x \ 1) \ y) / y). K(x,((y \ 1) \ x) / x) = K(y \ ((y \ 1) \ x),y). K(x,T(y,z \ 1) / (y / z)) = K(x,(y \ (y / z)) \ 1). K(x,(y \ (y / z)) \ 1) = K(x,T(y,z \ 1) / (y / z)). ((1 / x) \ y) \ ((1 / x) \ T(y,x)) = K(x \ ((x \ 1) \ y),x). K(x,L(x \ 1,y,z)) * ((z * y) / u) = (z * (y * K(x,x \ 1))) / u. (x * (y * K(z,z \ 1))) / u = K(z,L(z \ 1,y,x)) * ((x * y) / u). K(x,L(x \ 1,y,z)) * (z * y) = z * (y * K(x,x \ 1)). K(x,L(x \ 1,y,z)) = K(x,L(x,y,z) \ 1). K(x,L(x,y,z) \ 1) = K(x,L(x \ 1,y,z)). K((1 / x) \ 1,L(x,y,z) \ 1) = K(x,L(x \ 1,y,z)). K(x,L(x \ 1,y,z)) = K((1 / x) \ 1,L(x,y,z) \ 1). K(L(1 / x,y,z) \ 1,x \ 1) = K(x,L(x \ 1,y,z)). L(K(x \ 1,x),y,z) \ 1 = K(x,L(x \ 1,y,z)). K(R(x,y,z) * u,T(x,u)) = K(R(x,y,z) * u,x). K(x * y,K(x,y) * z) = K(x * y,z). K(x,K(y,y \ x) * z) = K(x,z). K(x,y) = K(x,K(z,z \ x) * y). K(x,K(y \ x,y) * z) = K(x,z). K(x,y) = K(x,K(z \ x,z) * y). K(x,x \ (x * y)) = K(x,K(z \ x,z) * y). K(x,(y * (y \ x)) \ (x * z)) = K(x,K(y \ x,y) * z). K(x,K(y \ x,y) * z) = K(x,(y * (y \ x)) \ (x * z)). K(x,(x \ y) \ z) = K(x,y \ (z * x)). (R(x / y,z,u) * w) / R(y \ x,z,u) = (K(y,y \ x) * w) * K(y \ x,w). K(x,(y / x) \ z) = K(x,(x \ y) \ z). K(x,K(y,x) * z) = K(x,z). K(x,y * K(z,x)) = K(x,y). K(x,y) = K(x,y * K(z,x)). K(x,y * K(x,z)) = K(x,y). K(x \ ((1 / x) \ y),x) = K(x \ ((x \ 1) \ y),x). K(K(x,y) * z,x) = K(z,x). K(x,y * K(x,z)) = u / (K(y,x) * u). x / (K(y,z) * x) = K(z,y * K(z,u)). K(x * K(y,z),y) = K(x,y). K((x / y) * T(y,z),y) = K(x,y). K(x,y) = K((x / y) * T(y,z),y). K(x \ (y * T(x,z)),x) = K(y,x). K(x,y) = K(y \ (x * T(y,z)),y). K(x / T(y,z),y) = K(y \ x,y). K(((x \ y) \ y) \ z,x) = K(x \ z,x). K(T(x,y) \ z,x) = K(x \ z,x). K(T(x,y) \ z,x) = z \ ((x \ z) * x). x \ ((y \ x) * y) = K(T(y,z) \ x,y). K(x * y,K(y,z)) = K(z,K(y,x)). (x * y) \ T(x * y,K(y,z)) = K(z,K(y,x)). (x * y) \ (y * T(x,T(y,z))) = K(z,K(y,x)). K(x,(y / x) \ z) = K(x,y \ (z * x)). K(x,y \ (z * x)) = K(x,(y / x) \ z). K(x,T(y / (z / x),y)) = K(x,z \ (y * x)). K(x,y \ (z * x)) = K(x,T(z / (y / x),z)). T(K(x,y),z) * K(y,x) = K(z,K(y,x)). K(x,K(y,z)) * K(x,K(z,y)) = 1. (x * y) \ (y * (x * T(K(x,y),z))) = K(z,K(y,x)). K(K(x,y),z) = K(z,K(y,x)). K(x,K(y,z)) = K(K(z,y),x). T(K(x,L(T(y,y \ z),y \ z,u)),u * (y \ z)) = T(K(x,L(T(y,y \ z),y \ z,u)),u * z). K(x,(y * z) \ y) = K(x,z \ 1). K(x,y \ 1) = K(x,(z * y) \ z). T(K(x,y),z / y) = T(K(x,y),z). T(K(x,y),z) = T(K(x,y),z / y). K(x,T((y * x) / z,y)) = K(x,z \ (y * x)). K(x / T(y,z),y) = K(T(y,z) \ x,y). K(x,(y \ z) \ 1) = K(x,z \ y). K(x,y \ z) = K(x,(z \ y) \ 1). T(K(x,y),z * y) = T(K(x,y),z). T(K(x,y),z * x) = K(x,T(y,z)). K(T(x,y),K(y,z)) = K(x,K(y,z)). K(x / y,T(z,y)) = K(y \ x,z). K(x \ y,z) = K(y / x,T(z,x)). K(x,y) * T(K(y,x),z) = K(z,K(x,y)). K(T(x,y),z) = K(x,T(z,y)). x * T(K(x,y),z) = T(x,T(y,z)). T(x,T(y,z)) = x * T(K(x,y),z). T(K(x,y / z),y) = K(x,z \ y). T(K(x,y),z * y) = K(x,T(y,z)). K(x,y) * K(z,x) = K(z,x) * K(x,y). K(x,T(y,z)) = T(K(x,y),z). T(K(x,y),z) = K(x,T(y,z)). x * K(y,T(z,x)) = K(y,z) * x. K(x,y) * z = z * K(x,T(y,z)). (x * y) / T(T(x,y),z) = K(z,x) * y. T(x,K(x,y) * z) = T(x,z). T(x,y) = T(x,K(x,z) * y). T(T(x,y),K(z,x) * u) = T(T(x,u),y). T(T(x,y),z) = T(T(x,z),K(u,x) * y). T(x,K(y,x) * z) = T(x,z). T(x,y * K(z,x)) = T(x,y). T(x,y) = T(x,y * K(z,x)). T(x,y * K(x,z)) = T(x,y). T(x,y) = T(x,y * K(x,z)). K(R(x,y,z),(x \ 1) \ (R(x,y,z) \ u)) = K(R(x,y,z),(x \ R(x,y,z)) \ u). K(R(x,y,z),(x \ R(x,y,z)) \ u) = K(R(x,y,z),(x \ 1) \ (R(x,y,z) \ u)). K(x,(y * (x / y)) \ (x * z)) = K(x,K(y \ x,y) * z). K(x,(x * y) \ z) = K(x,y \ (x \ z)). K(x,L(y,z,x)) = K(x,y). L(K(x,y),z * y,u) = K(x,L(y,z,u)). K(x,L(y,z,u)) = L(K(x,y),z * y,u). x * L(K(T(y \ 1,z) \ 1,u),w,v5) = x / L(T(K(u,y),z),w,v5). x / L(T(K(y,z),u),w,v5) = x * L(K(T(z \ 1,u) \ 1,y),w,v5). K(x,L(y,z / y,u)) = L(K(x,y),z,u). L(K(x,y),z,u) = K(x,L(y,z / y,u)). x * y != x / L(K(z,u),w,v5) | y = K(u,L(z,w / z,v5)). x / L(K(y,z),u,w) = x * L(K(z,y),u,w). (x * L(K(y,z),u,w)) \ x = L(K(z,y),u,w). x \ (y * (x * K(y,z))) != K(y,z) * u | T(y,x) = u. x \ (y * (x * K(y,z))) != K(y,z) * u | u = T(y,x). x * (K(y,z) * T(y,x)) = y * (x * K(y,z)). (x * y) * K(x,z) = x * (y * K(x,z)). x * K(y,L(z,u / z,w)) = x / L(K(z,y),u,w). x / L(K(y,z),u,w) = x * K(z,L(y,u / y,w)). L(K(x,y),z,x) = K(x,y). K(L(x,y / x,z),u) = L(K(x,u),y,z). K((x * (y / z)) \ (x * y),u) = L(K(z,u),y,x). L(K(x,y),z,u) = K((u * (z / x)) \ (u * z),y). L(K(x \ y,z),y,u) = K((u * x) \ (u * y),z). K((x * y) \ (x * z),u) = L(K(y \ z,u),z,x). K(x * y,K(x,z)) = K(y,K(x,z)). K(x,y / ((y / z) * K(z \ 1,y))) = K(x,(y \ (y / z)) \ 1). T(x * y,K(y,z)) = y * T(x,T(y,z)). K(x,y) * K(y,T(x,z)) = K(x * z,K(x,y)). K(T(x \ 1,y) \ 1,z) = T(K(x,z),y). (x * ((y * z) / y)) \ (x * z) = K(z,y). K(x,y) * K(y,T(x,z)) = K(z,K(x,y)). K(x,K(y,z)) = K(y,z) * K(z,T(y,x)). T(K(x,y),z) \ 1 = K(y,T(x,z)). T(K(x,y),K(x,z)) = K(x,y). K(x,y) = T(K(x,y),K(x,z)). K(T(x,y),z) = T(K(x,z),y). T(K(x,y),z) = K(T(x,z),y). T(K(x,y),z * x) = K(T(x,z),y). K(T(x,y),z) = T(K(x,z),y * x). T(K(x / y,z),x) = K(y \ x,z). K(x \ y,z) = T(K(y / x,z),y). K(T(x,y) \ 1,z) = T(K(x \ 1,z),y). (x \ (x / y)) * x = (x / y) * K(y \ 1,x). (x / y) * K(y \ 1,x) = (x \ (x / y)) * x. K((x \ y) \ y,z) = T(K(x,z),y). K(L(x \ y,z,u) \ 1,w) = L(K(y \ x,w),z,u). L(K(x \ y,z),u,w) = K(L(y \ x,u,w) \ 1,z). K(L(x \ y,x,z) \ 1,u) = K((z * y) \ (z * x),u). K(x \ (x / y),z) = K(y \ 1,z). K(x \ 1,y) = K(z \ (z / x),y). K((x \ y) \ 1,z) = K(y \ x,z). x \ (K(y,z) * ((T(y,z) \ x) * y)) = K(T(y,z) \ x,y). ((1 / x) \ y) \ ((1 / x) \ T(y,z)) = K(x \ ((1 / x) \ y),z). x \ (y * (x * K(y,z))) = K(y,z) * T(y,x * K(y,z)). L(x,K(x,y),z) = x. x = L(x,K(x,y),z). K(x,y * K(z,y \ 1)) = T(K(x,y),z). (x * ((y * z) / y)) * K(z,y) = x * z. (x * K(L(y \ 1,z,u) \ 1,w)) \ x = L(K(w,y),z,u). ((x * K(y,z)) * R((x * K(y,z)) \ u,w,v5)) * K(z,y) = x * R(x \ (u * ((x * K(y,z)) \ x)),w,v5). x / K(y,z) = x * K(z,y). (x * K(y,z)) * K(z,y) = x. x * (K(y,z) * T(y,x)) = (y * x) * K(y,z). (x * y) * K(x,z) = y * (K(x,z) * T(x,y)). (x * K(y,z)) \ x = K(z,y). (x * K(y,z)) \ (x * T(y,z)) = y. K(x,y) * (z * T(y,x)) = T(z * y,K(y,x)). (x / y) * T(y,z) = x * K(y,z). x * K(y,z) = (x / y) * T(y,z). x * T(x \ y,z) = y * K(x \ y,z). x * K(y \ x,z) = y * T(y \ x,z). x \ (y * T(y \ x,z)) = K(y \ x,z). (x * y) * K(y,z) = x * T(y,z). (x * y) \ (x * T(y,z)) = K(y,z). L(K(x,y),x,z) = K(x,y). L(K(x,y),x,z) = K(y,x) \ 1. K(x,y) \ 1 = L(K(y,x),y,z). K((x \ 1) \ 1,L(x \ 1,y,z)) = L(K(x \ 1,x),y,z) \ 1. L(K(x \ 1,x),y,z) \ 1 = K((x \ 1) \ 1,L(x \ 1,y,z)). L(K(x,y),z,u) \ 1 = L(K(y,x),z,u). K(L(x \ 1,y,z) \ 1,u) = L(K(u,x),y,z) \ 1. L(K(x,y),z,u) \ 1 = K(L(y \ 1,z,u) \ 1,x). K(L(1 / x,y,z) \ 1,u) = L(K(u,x),y,z) \ 1. L(K(x,y),z,u) \ 1 = K(L(1 / y,z,u) \ 1,x). K(x,L(x,y,z) \ 1) * (z * y) = z * (y * K(x,x \ 1)). K(x,L(y \ 1,z,u) \ 1) = L(K(x,y),z,u). L(K(x,y),z,u) = K(x,L(y \ 1,z,u) \ 1). K(x,L(1 / y,z,u) \ 1) = L(K(x,y),z,u). L(K(x,y),z,u) = K(x,L(1 / y,z,u) \ 1). L(K(x,y \ 1),z,u) = K(x,L(y,z,u) \ 1). K(L(x,y,z) \ 1,u \ 1) = K(x \ 1,L(u,y,z) \ 1). (x * y) * K(z,L(u,y,x) \ 1) = x * (y * K(z,u \ 1)). (x * y) * K(z,L(u,y,x) \ 1) = x * (K(z,y / (y * u)) * y). x * (K(y,z / (z * u)) * z) = (x * z) * K(y,L(u,z,x) \ 1). x * (K(y,z / (x \ (x * (z * u)))) * z) = (x * z) * K(y,L(u,z,x) \ 1). K(x,(y * z) / u) * (y * z) = y * (K(x,z / (y \ u)) * z). x * (K(y,z / (x \ u)) * z) = K(y,(x * z) / u) * (x * z). x * (y * R(K(z,(y \ (x \ u)) \ 1),w,v5)) = K(z,(x * y) / u) * (x * y). x * (y * R(y \ ((x \ z) * ((u * ((x \ z) \ y)) / u)),w,v5)) = K(u,(x * y) / z) * (x * y). x * (y * R(y \ (x \ (z * ((u * (z \ (x * y))) / u))),w,v5)) = K(u,(x * y) / z) * (x * y). (K(x,x \ y) * z) * K(z \ (K(x \ y,x) * ((y / x) * z)),K(x,x \ y) * z) = ((y / x) * z) / (x \ y). K(x,((y * z) \ (y * (u \ z))) \ 1) = L(T(K(x,u),z),z,y). K(x,((y * z) \ (y * (u \ z))) \ 1) = (y * z) \ (y * (K(x,u) * z)). (x * y) \ (x * (K(z,u) * y)) = K(z,((x * y) \ (x * (u \ y))) \ 1). (x * y) \ (x * (((z * u) / z) * (u \ y))) = K(z,((x * y) \ (x * (u \ y))) \ 1). (x * y) \ (x * ((z \ y) * T((u * z) / u,z \ y))) = K(u,((x * y) \ (x * (z \ y))) \ 1). (x * y) \ ((x * (z \ y)) * L(T((u * z) / u,z \ y),z \ y,x)) = K(u,((x * y) \ (x * (z \ y))) \ 1). (R(x / y,z,u) * w) / R(y \ x,z,u) = (K(y,y \ x) * w) * K(y \ x,K(y,y \ x) * w). ((R(T(x,x * y),z,u) * y) * T(x,y)) \ ((x * y) * R(T(x,y),z,u)) = K(y * T(x,y),R(x,z,u)). ((T(R(x,y,z),x * u) * u) * T(x,u)) \ ((x * u) * R(T(x,u),y,z)) = K(u * T(x,u),R(x,y,z)). (x * y) \ ((x * (z \ y)) * L((u * T(z,z \ y)) / u,z \ y,x)) = K(u,((x * y) \ (x * (z \ y))) \ 1). K(x,y) * ((z * u) / (z * (T(K(x,y),z) * u))) = a(z,K(x,y),u). K(x,y) * ((z * u) / (z * (T(K(x,y),z) * u))) = a(z,T(K(x,y),z),u). K(x,y) * ((z * u) / (z * (T(K(x,y),z) * u))) = a(z,K((z \ (x \ z)) \ 1,y),u). a(x,K((x \ (y \ x)) \ 1,z),u) = K(y,z) * ((x * u) / (x * (T(K(y,z),x) * u))). (K(x,y) * (z * u)) / (z * (T(K(x,y),z) * u)) = a(z,K((z \ (x \ z)) \ 1,y),u). (K(x,y) * (z * u)) / (z * (K((z \ (x \ z)) \ 1,y) * u)) = a(z,K((z \ (x \ z)) \ 1,y),u). T(x * R(x \ y,z,u),y) = x * R(x \ y,z,u). K(x,y) * (z * R(z \ x,u,w)) = (z * R(z \ x,u,w)) * K(x,y). T(x * R(x \ y,z,u),w) = x * R(x \ T(y,w),z,u). x * (y * R(y \ T(z,x),u,w)) = (y * R(y \ z,u,w)) * x. x * (y * R(y \ (x \ (z * x)),u,w)) = (y * R(y \ z,u,w)) * x. ((x \ y) \ y) * (z * R(z \ (T(x,x \ y) \ u),w,v5)) = z * (x * R(x \ (z \ u),w,v5)). T(x,y) * (z * R(z \ (T(x,y) \ u),w,v5)) = z * (x * R(x \ (z \ u),w,v5)). K(T((1 / x) * y,x),x) = K(T((x \ 1) * y,x),x). K(T(K(x,x \ 1) * y,x),x) = K(T(y,x),x). K((1 / x) * y,x) = K((x \ 1) * y,x). K(K(x,x \ 1) * y,x) = K(y,x). K(K(x,x \ 1) * y,x) = K(y,(x \ 1) \ 1). K(x,(y \ 1) \ 1) = K(K(y,y \ 1) * x,y). K(K(x \ 1,x) * y,(x \ 1) \ 1) = K(y,x). K(x,y) = K(K(y \ 1,y) * x,(y \ 1) \ 1). K(K(x \ 1,x) * y,(x \ 1) \ 1) = (x * y) \ (y * x). (x * y) \ (y * x) = K(K(x \ 1,x) * y,(x \ 1) \ 1). K(x,y \ 1) * y = y * K(x,y \ 1). K(x,(y * z) / (y * (z * u))) * (y * z) = (y * z) * K(x,L(u,z,y) \ 1). (x * y) * K(z,L(u,y,x) \ 1) = K(z,(x * y) / (x * (y * u))) * (x * y). K(x,y / (y * z)) * y = y * K(x,z \ 1). x * K(y,z \ 1) = K(y,x / (x * z)) * x. T(K(x,y / z),y) = K(x,(y \ z) \ 1). x * K(y,(x \ z) \ 1) = K(y,x / z) * x. x * R(K(y,(x \ z) \ 1),u,w) = K(y,x / z) * x. x * R(K(y,(x \ z) \ 1),u,w) = R(K(y,x / z),u,w) * x. R(K(x,y / z),u,w) * y = y * R(K(x,(y \ z) \ 1),u,w). a(x,T(y,x),z) = a(x,y,z). a(x,K(y,x) * z,u) = a(x,z,u). a(x,y,z) = a(x,K(u,x) * y,z). a(x,K(y,x) * z,u) = (x * (z * u)) \ ((x * z) * u). (x * (y * z)) \ ((x * y) * z) = a(x,K(u,x) * y,z). (x * (y * z)) \ (K(x,u) * (K(u,x) * ((x * y) * z))) = a(x,K(u,x) * y,z). a(x,K(y,x) * z,u) = (x * (z * u)) \ (K(x,y) * (K(y,x) * ((x * z) * u))). K(x,((y \ 1) \ x) / x) = ((1 / y) \ x) \ ((1 / y) \ T(x,y)). ((1 / x) \ y) \ ((1 / x) \ T(y,x)) = K(y,((x \ 1) \ y) / y). x * R(1 / (1 / y),y \ 1,(1 / y) \ x) = (1 / y) \ T(x,y). ((x \ 1) * (R((x \ 1) \ 1,y,z) \ 1)) / (1 / x) = K(x \ 1,x) * (R((x \ 1) \ 1,y,z) \ 1). K(x \ 1,x) * (R((x \ 1) \ 1,y,z) \ 1) = ((x \ 1) * (R((x \ 1) \ 1,y,z) \ 1)) / (1 / x). (x * (R(x \ 1,y,z) \ 1)) / x = R(x \ 1,y,z) \ 1. T(R(x \ 1,y,z) \ 1,x) = R(x \ 1,y,z) \ 1. R(x \ 1,y,z) \ 1 = T(R(x \ 1,y,z) \ 1,x). T(R(x,y,z) \ 1,x \ 1) = R(x,y,z) \ 1. T(x,R(y,z,u) \ 1) = T(x,y \ 1). T(x,R(y,z,u) \ 1) = T(x,z / (y * z)). x * R(1 / (1 / y),1 / y,(1 / y) \ x) = (1 / y) \ T(x,y). K(x,T(y * z,y \ 1)) = K(x,T(y * z,z)). x * R(1 / y,y,y \ x) = y \ T(x,y \ 1). x \ T(y,x \ 1) = y * R(1 / x,x,x \ y). K(x,T(y,z \ 1)) = K(x,T(y,z \ y)). T(x,x \ (y \ x)) = T(x,y \ 1). T(x,y \ 1) = T(x,x \ (y \ x)). x \ T(y,x \ 1) = y * ((x \ y) / y). T(x,(y * z) / ((u * y) * z)) = T(x,R(u,y,z) \ 1). T(x,(y \ z) / z) = T(x,y \ 1). T(x,y / (z * y)) = T(x,z \ 1). K(x,R(y,z,u) \ 1) = K(x,y \ 1). K(x,R(y,z,u) \ 1) = K(x,z / (y * z)). K(x,y / K(y \ 1,z)) = T(K(x,y),z). K((x / (y * x)) \ 1,z / (u * z)) * (y * x) = T(y,u \ 1) * x. (x * ((y * (x \ z)) / y)) / z = K(y,z / x). K(x,T(1 / y,z) \ 1) = K(x,y / K(y \ 1,z)). K(x,(y \ z) / z) = K(x,y \ 1). K(x,y \ 1) = K(x,(y \ z) / z). K(x,(y * z) / ((u * y) * z)) = K(x,R(u,y,z) \ 1). K(x,R(y,z,u) \ 1) = K(x,(z * u) / ((y * z) * u)). K(x,y / (z * y)) = K(x,z \ 1). K(x,y \ 1) = K(x,z / (y * z)). K(x,(y / z) \ 1) = K(x,z / y). R(K(x,y / z),y / z,z) = K(x,(z / y) \ 1). R(K(x,y / z),y / z,z) = K(x,T((z / y) \ 1,y \ z)). R(K(x,y / z),y / z,z) = K(x,T(z / y,y / z) \ 1). K(x,T(y / z,z / y) \ 1) = R(K(x,z / y),z / y,y). T(K(x,(y / z) \ 1),z / y) = R(K(x,z / y),z / y,y). (R(x / y,z,u) * w) / R(y \ x,z,u) = (K(y,y \ x) * w) * K(R(y \ x,z,u),K(y,y \ x) * w). R(x \ y,z,u) * (K(x,x \ y) * w) = R(y / x,z,u) * w. T((x * ((y * (x \ z)) / y)) / z,z / x) = R(K(y,z / x),z / x,x). K(x,(y * (x / z)) \ u) = K(x,(y * (z \ x)) \ u). (T(x,x * y) * y) * R(T(x,y),z,u) = x * (R(T(x,y),z,u) * y). (x * (y \ ((z \ (y * (x \ u))) * z))) \ u = K(z,(x * (z / y)) \ u). (T(x,x * y) * y) * R(T(x,y),z,u) = T(x,y) * (R(x,z,u) * y). L(K(x \ y,x) * z,K(x,x \ y),y) = (x * (y / x)) \ (y * z). (x * (y / x)) \ (y * z) = L(K(x \ y,x) * z,K(x,x \ y),y). (x \ K(x \ 1,y)) \ 1 = (x \ 1) \ K(y,x \ 1). (x \ 1) \ K(y,x \ 1) = (x \ K(x \ 1,y)) \ 1. (x \ 1) \ (K(x \ 1,y) \ z) = (x \ K(x \ 1,y)) \ z. (x \ K(x \ 1,y)) \ z = (x \ 1) \ (K(x \ 1,y) \ z). (x * K(x,y)) \ z = x \ (K(x,y) \ z). x \ (K(x,y) \ z) = (x * K(x,y)) \ z. x * ((x * K(x,y)) \ z) = K(x,y) \ z. K(x,y) \ z = x * ((x * K(x,y)) \ z). (x * y) \ (y * (x * T(K(x,y),z))) = K(y,x) * T(K(x,y),z). R(T(x,y),z,u) * (x * w) = T(x,y) * (R(x,z,u) * w). T(x,y) * (R(x,z,u) * w) = R(T(x,y),z,u) * (x * w). T(x,y) * (R(x,z,u) * (x \ w)) = R(T(x,y),z,u) * w. (x * y) * z != x * (y * K(u \ 1,w)) | K(L(u,y,x) \ 1,w) = z. x * (y * K(z \ 1,u)) != (x * y) * w | K(L(z,y,x) \ 1,u) = w. (x * (R(T(x,y),z,u) * y)) \ ((x * y) * R(T(x,y),z,u)) = K(R(x,z,u) * y,T(x,y)). T(x,y) * (R(x,z,u) * w) = x * (R(T(x,y),z,u) * w). x * (R(T(x,y),z,u) * w) = T(x,y) * (R(x,z,u) * w). K(x,y) * (R(x,z,u) * w) = R(T(x,y),z,u) * w. ((x \ y) \ y) * (z * R(z \ (T(x,x \ y) \ (u * z)),w,v5)) = (x * R(x \ u,w,v5)) * z. T(x,y) * (z * R(z \ (T(x,y) \ u),w,v5)) = z * (T(x,z) * R(T(x,z) \ (z \ u),w,v5)). x * (T(y,x) * R(T(y,x) \ (x \ z),u,w)) = T(y,v5) * (x * R(x \ (T(y,v5) \ z),u,w)). (x * (((y \ ((x \ z) * u)) * y) / u)) \ z = K(y,(x * (y / u)) \ z). (x * (y \ ((z \ (y * (x \ u))) * z))) \ u = K(z,(x * (y \ z)) \ u). ((x * y) / x) * T(x,z) = y * (K(x,z) * T(x,y)). x * (K(y,z) * T(y,x)) = ((y * x) / y) * T(y,z). ((T(R(x,y,z),u * T(x,u)) * u) * T(x,u)) \ ((x * u) * R(T(x,u),y,z)) = K(u * T(x,u),R(x,y,z)). K(R(x,y,z) \ 1,u) = K(x \ 1,u). K(R(x,y,z) \ 1,u) = K(y / (x * y),u). K((x / (y * x)) \ 1,z) * (y * x) != u * x | T(y,z) = u. (x * K(y \ 1,z)) / x = K(((x * y) / x) \ 1,z). ((K(x,y) * z) * u) / (z * (K((z \ (x \ z)) \ 1,y) * u)) = a(z,K((z \ (x \ z)) \ 1,y),u). a(x,K((x \ (y \ x)) \ 1,z),u) = ((K(y,z) * x) * u) / (x * (K((x \ (y \ x)) \ 1,z) * u)). K((x \ (y \ x)) \ 1,z) = T(K(y,z),x). T(K(x,y),z) = K((z \ (x \ z)) \ 1,y). x * K((x \ (y \ x)) \ 1,z) = K(y,z) * x. ((x / (y \ 1)) \ 1) \ K(y \ 1,y) = ((x / (1 / y)) \ 1) \ 1. ((x / (1 / y)) \ 1) \ 1 = ((x / (y \ 1)) \ 1) \ K(y \ 1,y). (x * (K(y,x) * (z * u))) \ (K(y,x) * ((x * z) * u)) = a(x,K(y,x) * z,u). K((x \ y) \ y,z) = K(T(x,y),z). K(T(x,y),z) = K((x \ y) \ y,z). L((x \ y) \ y,y / x,(x \ z) \ z) = T(x,y). K(x,L(T(T(y,y \ z),u),w,v5)) = K(x,L(T(T(y,z),u),w,v5)). L(T(x,x \ y),y / x,(x \ z) \ z) = T(x,y). L(T(x,x \ y),y / x,x) = T(x,y). R(T(T(x,y),z),x \ y,x) = T(T(x,x \ y),z). L(T(x,y / x),y / x,x) = T(x,y). R(T(x,y),x \ y,x) = T(x,x \ y). T(x,x * (y / x)) = T(x,y). T(x,y) = T(x,x * (y / x)). T(x,(x \ y) * x) = T(x,y). T(x,y * x) = T(x,x * y). T(x,x * y) = T(x,y * x). T(x,(y \ 1) \ x) = T(x,x * y). ((1 / x) * (R(1 / x,y,z) \ u)) * x = R(u / R(1 / x,y,z),x \ 1,x). T(x,x * T(y,y \ 1)) = T(x,(y \ 1) \ x). (x / R(y,z,u)) * y = y * (R(y,z,u) \ x). x * (R(x,y,z) \ u) = (u / R(x,y,z)) * x. T(x,y * T(z,z \ 1)) = T(x,y / (z \ 1)). R(x,y,z) * (u / R(x,y,z)) = u * K(x,R(x,y,z) \ u). x * K(y,R(y,z,u) \ x) = R(y,z,u) * (x / R(y,z,u)). K(R(x,y,z),u) * x = T(x,u). T(x,y) = K(R(x,z,u),y) * x. K((x * y) / (z * y),u) = K(x / z,u). K(R(x,y,z),u) = K(x,u). T(x,R(y,z,u)) \ x = K(y,x). K(x,y) = T(y,R(x,z,u)) \ y. T(x,y * (z \ 1)) = T(x,y / z). T(x,(y * z) / (u * z)) = T(x,y / u). x * R(y,x,y) = T(y * x,y). (T(x,x * y) * y) * R(T(x,y),z,u) = R(T(x,y),z,u) * (x * y). R(T(x,y),z,u) * (x * y) = (T(x,x * y) * y) * R(T(x,y),z,u). T(x,R(y,z,u)) = T(x,y). T(x,y) = T(x,R(y,z,u)). T(x / R(y,z,u),y) = R(y,z,u) \ x. R(x,y,z) * T(u,x) = u * R(x,y,z). K(x,T(y \ 1,z) \ 1) = T(K(x,y),z). K(x,T(1 / y,z) \ 1) = T(K(x,y),z). K(x,T(y,z) \ 1) = T(K(x,y \ 1),z). T(K(x,y \ 1),z) = K(x,T(y,z) \ 1). x * (y * R(y \ (x \ (z * ((u * (z \ (x * y))) / u))),w,v5)) = (x * y) * R(K(u,((x * y) \ z) \ 1),w,v5). (x * y) * R(K(z,((x * y) \ u) \ 1),w,v5) = x * (y * R(y \ (x \ (u * ((z * (u \ (x * y))) / z))),w,v5)). (x * y) \ ((x * (z \ y)) * ((u * L(T(z,z \ y),z \ y,x)) / u)) = K(u,((x * y) \ (x * (z \ y))) \ 1). R((x * ((y * (x \ z)) / y)) / z,u,w) * z = z * R(K(y,(z \ x) \ 1),u,w). T(x,y) * R(T(y,x),z,u) = x * R(y,z,u). x * R(y,z,u) = T(x,y) * R(T(y,x),z,u). T(x,y) * R(T(x,y) \ z,u,w) = x * R(x \ z,u,w). x * R(x \ y,z,u) = T(x,w) * R(T(x,w) \ y,z,u). K(L(x,y,z) \ 1,x) = K(x \ 1,L(x,y,z)). K(L(x \ 1,y,z) \ 1,u) = L(K(x,u),y,z). L(K(x,y),z,u) = K(L(x \ 1,z,u) \ 1,y). (x * y) * K(L(z,y,x) \ 1,u) = x * (y * K(z \ 1,u)). L(K(x \ 1,y),z,u) = K(L(x,z,u) \ 1,y). (K(x \ 1,x) * y) * ((x \ 1) \ 1) = y * x. (x * (y * T(y \ (x \ z),u))) \ z = K(u,(x * y) \ z). (x * T(x \ y,z)) \ y = K(z,x \ y). ((x / y) * T(y,z)) \ x = K(z,y). K(x,y) = ((z / y) * T(y,x)) \ z. x * y != (z / u) * u | y = x \ z. (x * y) / T(T(x,y),z) = y * K(z,T(x,y)). x * K(y,T(z,x)) = (z * x) / T(T(z,x),y). (x * K(y \ z,y)) * ((y \ z) \ z) = x * y. (x * T(y,z)) * K(z,y) = x * y. x * T(y,z) != (u * T(y,z)) * y | x = u * y. (x / y) * K(z,y) = x / T(y,z). x / T(y,z) = (x / y) * K(z,y). (x * K(y,z)) * T(z,y) = x * z. (x * K(y,z)) \ (x * z) = T(z,y). (K(x,x \ y) * z) * K((K(x,x \ y) * z) \ ((y / x) * z),K(x,x \ y) * z) = ((y / x) * z) / (x \ y). ((x / y) * z) / (y \ x) = (K(y,y \ x) * z) * K((K(y,y \ x) * z) \ ((x / y) * z),K(y,y \ x) * z). K((x * y) / ((z * x) * y),u) = K(R(z,x,y) \ 1,u). K(R(x,y,z) \ 1,u) = K((y * z) / ((x * y) * z),u). K(x / (y * x),z) = K(y \ 1,z). K(x \ 1,y) = K(z / (x * z),y). K((x / (y * x)) \ 1,z) * (y * x) = T(y,z) * x. K((x / y) \ 1,z) = K(y / x,z). x * y != z * T(z \ y,u) | x = K(y / z,u). x * (T(y,z) * (y \ T(y,x))) = ((y * x) / y) * T(y,z). ((x / y) * z) / (K(y,y \ x) * z) = y \ x. (x * K((x \ y) \ 1,z)) / x = K((y / x) \ 1,z). K((x / y) \ 1,z) * y = x * T(x \ y,z). T(x,y) * (x \ z) = z * K((z \ (x \ z)) \ 1,y). x * K((x \ (y \ x)) \ 1,z) = T(y,z) * (y \ x). x * T(x \ y,z) != y * u | K((y \ x) \ 1,z) = u. L(K(x,y),y,z) = K(x,y). K(x \ 1,(x \ 1) \ y) = x * T(x \ 1,y * x). (x * (K(y,x) * z)) \ u = (x * z) \ (K(x,y) * u). K(x \ y,x) * ((x \ y) \ z) = (y / x) \ z. (x / y) \ z = K(y \ x,y) * ((y \ x) \ z). (x \ (K(y \ 1,y) * z)) / (((u * (x * K(y,y \ 1))) / u) \ z) = K(u,x * K(y,y \ 1)). (x * y) * K(z,y) = x * (y * K(z,y)). K(L(x,y,x),z) = K(x,z). (x * (y / x)) \ (y * (K(x,x \ y) * z)) = L(z,K(x,x \ y),y). L(x,K(y,y \ z),z) = (y * (z / y)) \ (z * (K(y,y \ z) * x)). (x \ y) \ K(x \ y,x) = (y / x) \ 1. (x / y) \ 1 = (y \ x) \ K(y \ x,y). (x / (y \ 1)) \ K(y,y \ 1) = (x / (1 / y)) \ 1. (x / (1 / y)) \ 1 = (x / (y \ 1)) \ K(y,y \ 1). K(x \ y,x) * ((y / x) * z) = (x \ y) * z. (x \ y) * z = K(x \ y,x) * ((y / x) * z). K(x,x * (y \ 1)) = K(x,y \ x). x \ T(x,y * (x \ 1)) = K(x,x \ y). x * K(y,y \ x) = y * (x / y). ((T(x,y * z) * y) * z) \ ((x * y) * z) = K(y * z,x). K(x,x / y) = K(x,y \ x). K(x,y / x) = K(x,x \ y). K(x,x \ y) = K(x,y / x). K(x,T(y,x)) = K(x,y). K(x,y) = K(x,T(y,x)). x / (x / y) = y * K(y \ x,y). K(T(x,y),y) \ 1 = K(y,x). K(x \ (y * T(x,z)),x) = K((y / x) * T(x,z),x). K(x / y,y) = K(y \ x,y). K(x \ y,x) = K(y / x,x). K(T(x,y),y) = K(x,y). K(x,y) = K(T(x,y),y). ((x * y) / x) \ 1 = y \ K(y,x). x \ K(x,y) = ((y * x) / y) \ 1. K(T(x,y),y) = x \ T(x,y). K(x,y) = ((y * x) / y) \ x. ((x * y) / x) \ y = K(y,x). K(L(x,y,x),z) = u / (K(z,x) * u). x / (K(y,z) * x) = K(L(z,u,z),y). T(K(x,y),z) * K(y,x) = K(K(x,y),z). K(K(x,y),z) = T(K(x,y),z) * K(y,x). (x * K(y,x)) \ x = K(x,y). (x * y) \ ((y * x) * T(K(x,y),z)) = K(y,x) * T(K(x,y),z). (K(x,y) * z) \ 1 = z \ K(y,x). x * K(y,z) != 1 | K(z,y) = x. x * K(y,z) != 1 | x = K(z,y). (K(x,y) * z) \ u = z \ (K(y,x) * u). x \ (K(y,z) * u) = (K(z,y) * x) \ u. K(x,y) * T(K(y,x),z) = K(K(y,x),z). x * y != T(x,z) | y = K(x,z). K(x \ y,x) * (y / x) = x \ y. K(x,x \ y) * z != y / x | z = x \ y. ((x * y) / x) \ z = K(y,x) * (y \ z). K(x,y) * (x \ z) = ((y * x) / y) \ z. K(x,y) * z != y \ u | z = ((x * y) / x) \ u. K(x,y) * K(y,x) = 1. 1 = K(x,y) * K(y,x). K(x,y) \ z = K(y,x) * z. x / (K(y,z) * x) = K(z,y). K(x,y) \ 1 = K(y,x). K(x,y) = K(y,x) \ 1. K(x,y) * (z * K(y,x)) = T(z,K(y,x)). T(x,K(y,z)) = K(z,y) * (x * K(y,z)). K(x,y) * ((K(y,x) * z) * u) = z * u. x * y = K(z,u) * ((K(u,z) * x) * y). (x * y) \ ((K(x \ z,x) * y) * ((x \ z) \ z)) = K(K(x \ z,x) * y,(x \ z) \ z). (x * y) / T(T(x,z),K(z,x) * y) = K(z,x) * y. K(x,y) * (K(y,x) * z) = z. T(x,y) * z != x * (K(x,y) * u) | z = u. (x * (K(y,x) * z)) * u = K(y,x) * ((x * z) * u). T(x,y) * (K(y,x) * z) = x * z. x * y = T(x,z) * (K(z,x) * y). K(x,y) * z != y * u | z = T(y,x) * u. (x \ y) / (((z * x) / z) \ y) = K(z,x). (x * (y * K(z,y))) / K(z,y) = x * y. (K(x,y) * ((R(y,z,u) * K(x,y)) \ w)) * a(R(y,z,u),K(x,y),(R(y,z,u) * K(x,y)) \ w) = R(R(y,z,u),K(x,y) * ((R(y,z,u) * K(x,y)) \ w),1) \ w. R(R(x,y,z),K(u,x) * ((R(x,y,z) * K(u,x)) \ w),1) \ w = (K(u,x) * ((R(x,y,z) * K(u,x)) \ w)) * a(R(x,y,z),K(u,x),(R(x,y,z) * K(u,x)) \ w). a(R(x,y,z),K(u,x),w) = 1. a(x,K(y,x),z) = 1. K(x,y) * (y * z) = y * (K(x,y) * z). x * (K(y,x) * z) = K(y,x) * (x * z). L(x,K(y,z),z) = x. K(x,y) * (((x * y) / x) \ z) = y \ z. x \ y = K(z,x) * (((z * x) / z) \ y). (x * ((y * z) / y)) / K(y,z) = x * z. x * y = (x * ((z * y) / z)) / K(z,y). K(x,y) * (z * T(y,x)) = y * T(z,T(y,x)). T(x,(y \ 1) \ x) = T(x,y * x). T(x,y) = (K(y,x) / x) \ 1. (K(x,y) / y) \ 1 = T(y,x). T(x,x / y) = T(x,y \ x). T(x,y) * R(T(y,x),z,u) = R(y,z,u) * T(x,y). T(x,y / x) = T(x,x \ y). T(x,x \ y) = T(x,y / x). T(x,T(y,x)) = T(x,y). T(x,y) = T(x,T(y,x)). T(x,y) = (x \ (y * x)) \ (y * x). (x \ (y * x)) \ (y * x) = T(x,y). K(x,y / (z * K(u,y))) = K(x,T(y,u) / z). (x \ 1) * K(y,x) = T(x,y) \ 1. K(x,y) / y = 1 / T(y,x). K(x,y) = y * (T(y,x) \ 1). x * (T(x,y) \ 1) = K(y,x). T(x,y) * K(y,x) = x. K(x,y) * (T(y,x) * z) = y * z. x * y = K(z,x) * (T(x,z) * y). L(T(x,y),K(y,x),z) = (z * K(y,x)) \ (z * x). K(x,y) = T(y,x) \ y. T(x,y) \ x = K(y,x). K(x,y) * T(y,x) = y. x = K(y,x) * T(x,y). x * y != T(x,z) * u | y = K(x,z) * u. T(x,y) \ (x * y) = T(y,x). T(x,y) * T(y,x) = x * y. x * (T(y,x) * (y \ z)) = ((y * x) / y) * z. ((x * y) / x) * z = y * (T(x,y) * (x \ z)). (x * K(y,x)) * z = x * (K(y,x) * z). R(x \ y,z,u) * (K(x,R(x \ y,z,u)) * w) = R(y / x,z,u) * w. R(x / y,z,u) * w = R(y \ x,z,u) * (K(y,R(y \ x,z,u)) * w). (x * ((y * z) / y)) \ (z * (K(y,z) * x)) = K((y * z) / y,x). K((x * y) / x,z) = (z * ((x * y) / x)) \ (y * (K(x,y) * z)). (x \ y) * (K(x,x \ y) * z) = (y / x) * z. (x / y) * z = (y \ x) * (K(y,y \ x) * z). x \ (((y * x) / y) * z) = K(y,x) * z. (x / ((y * z) / y)) * z = x / K(y,z). x / K(y,z) = (x / ((y * z) / y)) * z. T(x * ((y * (x \ 1)) / y),z) = K(y,T(x,z) \ 1). K(x,T(y,z) \ 1) = T(y * ((x * (y \ 1)) / x),z). (x * ((y * (x \ z)) / y)) / z = K(y,(x / z) \ 1). K(x,(y / z) \ 1) = (y * ((x * (y \ z)) / x)) / z. x \ (y * ((z * (y \ x)) / z)) = K(z,(x \ y) \ 1). K(x,(y \ z) \ 1) = y \ (z * ((x * (z \ y)) / x)). K(x,y) * ((T(x,y) \ z) * u) = (x \ z) * u. (x \ y) * z = K(x,u) * ((T(x,u) \ y) * z). (x * (K(R(x,y,z),u) * w)) * R(T(x,K(R(x,y,z),u) * w),y,z) = (T(R(x,y,z),u) * w) * T(x,K(R(x,y,z),u) * w). (T(R(x,y,z),u) * w) * T(x,K(R(x,y,z),u) * w) = (x * (K(R(x,y,z),u) * w)) * R(T(x,K(R(x,y,z),u) * w),y,z). x * R(K(x,y) * z,u,w) = T(x,y) * R(z,u,w). K(x / y,z) * x = y * T(y \ x,z). (x / y) * z != T(x / y,u) * x | z = y * T(y \ x,u). L(x * T(x \ 1,y),z,u) = K(L(x,z,u) \ 1,y). K(L(x,y,z) \ 1,u) = L(x * T(x \ 1,u),y,z). K(x \ (x / T(y,z)),x) = T(K(y \ 1,x),z). T(K(x \ 1,y),z) = K(y \ (y / T(x,z)),y). (x * T(x \ y,z)) / y = K((x / y) \ 1,z). K((x / y) \ 1,z) = (x * T(x \ y,z)) / y. x * T(x \ y,z) = y * K((y \ x) \ 1,z). x * K((x \ y) \ 1,z) = y * T(y \ x,z). K(x \ 1,y) / x = T(1 / x,y). K(x,y) * (T(x,y) \ z) = x \ z. x * (K(x,y) * z) = T(x,y) * z. T(x,y) * (R(x,z,u) * (x \ w)) = K(x,y) * (R(x,z,u) * w). K(x,y) * (R(x,z,u) * w) = T(x,y) * (R(x,z,u) * (x \ w)). K(x,y) * ((x * z) / u) = (T(x,y) * z) / u. (T(x,y) * z) / u = K(x,y) * ((x * z) / u). K(x,y) * (z * x) = T(x,y) * T(z,x). K(R(x,y,z),u) * (R(x,y,z) * w) = R(T(x,u),y,z) * w. T(x,T(y / z,y)) = T(x,z \ y). T(x,L(y,z,y)) = T(x,y). T(x,y) = T(x,L(y,z,y)). R(K(x,y),x,(x * K(x,y)) \ z) \ z = x * ((x * K(x,y)) \ z). T(x,L(y,z,y)) = x * K(x,y). T(x,y) != x * z | K(x,y) = z. (x * K(x,y)) / x = K(x,y). T(K(x,y),x) = K(x,y). x * T(x \ 1,y) = K(x \ 1,y). K(x \ 1,y) = x * T(x \ 1,y). T(x,K(x,y)) = x. x \ T(x,y * (z \ 1)) = K(x,y / z). K(x,y) = T(x,y) * (x \ 1). T(x,y) * (x \ 1) = K(x,y). (x * y) * T(K(y,x),z) = x * (y * T(K(y,x),z)). x * (y * T(K(y,x),z)) = (x * y) * T(K(y,x),z). (x * y) \ (x * T(y,z)) = L(K(y,z),y,x). L(K(x,y),x,z) = (z * x) \ (z * T(x,y)). T(x,y) = x * K(x,y). x * K(x,y) = T(x,y). T(x,y) * (x \ z) = K(x,y) * z. K(x,y) * (x * z) = T(x,y) * z. T(x,y) * z = K(x,y) * (x * z). (x * K(y,z)) \ (x * T(y,z)) = L(y,K(y,z),x). L(x,K(x,y),z) = (z * K(x,y)) \ (z * T(x,y)). K(x,y) = x \ T(x,y). x \ T(x,y) = K(x,y). T(x,y) = K(x,y) * x. ((x * y) / x) * z = y * (K(x,y) * z). x * (K(y,x) * z) = ((y * x) / y) * z. L(x \ y,x,x \ y) = T(y / x,y). L(x,y,(z \ u) \ u) = L(x,y,z). L(x,y,T(z,u)) = L(x,y,z). L(x,y,z) = L(x,y,T(z,u)). L(x,y,z / u) = L(x,y,u \ z). K(x,y) * (y * x) = x * y. x * y = K(x,y) * (y * x). (x * y) / ((z * y) / z) = x / K(z,y). T(x * K(y,x),y) = x. x / (x / y) = y * K(x / y,y). (x * K(y,x)) * y = y * x. (x \ y) * K(x,x \ y) = y / x. x / y = (y \ x) * K(y,y \ x). x * ((y * (x \ 1)) / y) = K(y,x \ 1). K(x,y \ 1) = y * ((x * (y \ 1)) / x). T((((x * (y / z)) / x) * z) / y,y / z) = R(K(x,y / z),y / z,z). R(K(x,y / z),y / z,z) = T((((x * (y / z)) / x) * z) / y,y / z). (x * y) / x = y * K(x,y). L(x,y,(z * u) / z) = L(x,y,u). ((x * y) / x) * (y \ z) = K(x,y) * z. K(x,x \ y) * (x \ y) = y / x. x / y = K(y,y \ x) * (y \ x). K(x,y) = y \ ((x * y) / x). x \ ((y * x) / y) = K(y,x). (x * y) / x = K(x,y) * y. K(x,y) * y = (x * y) / x. (x * y) \ ((y * x) * x) = K(y,x) * x. R(x,K(y,z),z) = x. R(x,y * T(y \ 1,z),z) = x. (x * ((y \ 1) \ (z * T(z \ 1,y)))) / ((y \ 1) \ (z * T(z \ 1,y))) = R(x,z * T(z \ 1,y),y). (x * (y * T(y \ 1,z))) * ((z \ 1) \ 1) = x * ((z \ 1) \ (y * T(y \ 1,z))). (x * (y * T(y \ 1,z))) * ((z \ 1) \ 1) = x * (y * ((z \ (y \ ((z \ 1) \ 1))) * z)). L(T(x,y),K(z,x),u) = T(x,y). L(x,K(y,x),z) = x. (x * (y * K(z,y))) \ ((x * (y * K(z,y))) * y) = L(y,K(z,y),x). (x * y) / (y * K(z,y)) = x / K(z,y). (x * K(y,z)) * z = x * (z * K(y,z)). x * (y * K(z,y)) = (x * K(z,y)) * y. x * (y * K(y \ (y * z),y)) = (x * K(z,y)) * y. (x * K(y,z)) * z = x * (z * K(z \ (z * y),z)). (x * K(y \ z,y)) * y = x * (y * K(y \ z,y)). x * (y * K(y \ z,y)) = (x * K(y \ z,y)) * y. x * ((y \ z) * ((z \ T(y,y \ z)) * z)) = (x * K(z \ y,z)) * z. (x * K(y \ z,y)) * y = x * ((z \ y) * ((y \ T(z,z \ y)) * y)). ((x \ (y * z)) * x) / z = z \ ((x \ (z * y)) * x). x \ ((y \ (x * z)) * y) = ((y \ (z * x)) * y) / x. (x \ 1) * ((y \ ((x \ 1) \ z)) * y) = x \ ((y \ (x * z)) * y). (x \ 1) * ((y \ ((x \ 1) \ z)) * y) = x \ ((y \ (1 \ (x * z))) * y). x \ ((y \ (1 \ (x * z))) * y) = (x \ 1) * ((y \ ((x \ 1) \ z)) * y). (x * y) * L((z \ (y \ ((z \ 1) \ 1))) * z,y,x) = (x * (y * T(y \ 1,z))) * ((z \ 1) \ 1). (x * (y \ z)) * L((z \ T(y,y \ z)) * z,y \ z,x) = (x * K(z \ y,z)) * z. L((x \ ((y \ z) \ u)) * x,y \ z,y) = (x \ (z \ (y * u))) * x. L((x \ y) * x,z,u) = (x \ L(y,z,u)) * x. (x \ L(y,z,u)) * x = L((x \ y) * x,z,u). (x \ L(x * y,z,u)) * x = L(y * x,z,u). L(x * y,z,u) / y = y \ L(y * x,z,u). (x \ 1) * L((x \ 1) \ y,z,u) = L(y * x,z,u) / x. (x \ 1) * L(T(1 / x,1 / (1 / x)) \ y,z,u) = L(y * x,z,u) / x. (x \ 1) * L(T((1 / (1 / x)) \ 1,1 / (1 / x)) \ y,z,u) = L(y * x,z,u) / x. T(1 / x,1 / (1 / x)) * L(T((1 / (1 / x)) \ 1,1 / (1 / x)) \ y,z,u) = L(y * x,z,u) / x. T((1 / (1 / x)) \ 1,1 / (1 / x)) * L(T((1 / (1 / x)) \ 1,1 / (1 / x)) \ y,z,u) = L(y * x,z,u) / x. T((1 / x) \ 1,1 / x) * L(T((1 / x) \ 1,1 / x) \ y,z,u) = x * L(x \ y,z,u). T(x \ 1,x) * L(T(x \ 1,x) \ y,z,u) = x \ L(x * y,z,u). x \ L(x * y,z,u) = T(x \ 1,x) * L(T(x \ 1,x) \ y,z,u). T(x \ L(x * ((x * y) / x),z,u),x) = x \ L(x * y,z,u). x \ L(x * y,z,u) = T(x \ L(x * ((x * y) / x),z,u),x). T(x \ L(x * ((x * y) / x),z,u),(x \ 1) \ 1) = x \ L(x * y,z,u). T(x \ L(x * ((((x \ 1) \ 1) * y) / ((x \ 1) \ 1)),z,u),(x \ 1) \ 1) = x \ L(x * y,z,u). T(x \ L(x * ((((x \ 1) \ 1) * y) / ((x \ 1) \ 1)),z,u),(x \ 1) \ 1) = (x \ 1) * L((x \ 1) \ y,z,u). T(x \ L(x * ((((x \ 1) \ 1) * y) / ((x \ 1) \ 1)),z,u),(x \ 1) \ 1) = (x \ 1) * L((((x \ 1) \ 1) \ K(x,x \ 1)) \ y,z,u). ((1 / x) \ y) \ (y * R(1 / (1 / x),x \ 1,(1 / x) \ y)) = K(y,((x \ 1) \ y) / y). (x \ 1) * ((y \ ((x \ 1) \ z)) * y) = ((y \ (z * x)) * y) / x. ((x \ (y * z)) * x) / z = (z \ 1) * ((x \ ((z \ 1) \ y)) * x). ((x \ (y / (z \ 1))) * x) * (z \ 1) = ((x \ (y * z)) * x) / z. (x * y) \ ((y * x) * x) = (y * x) / y. (x * y) / x = (y * x) \ ((x * y) * y). L(x \ T(x * y,y),x,y) = (x * y) / x. ((x \ (y / z)) * x) * z = z * ((x \ (z \ y)) * x). x * ((y \ (x \ z)) * y) = ((y \ (z / x)) * y) * x. x * (y \ T(y * (x \ z),x)) = ((x \ (z * y)) * x) / y. R((x * y) / x,x,T(y,x)) = x \ T(x * y,y). T((x \ (y / z)) * x,z) = (x \ (z \ y)) * x. T(x * y,z) / y = y \ T(y * x,z). T((x \ y) * x,z) = (x \ T(y,z)) * x. (x \ T(y,z)) * x = T((x \ y) * x,z). (x \ T(x * y,z)) * x = T(y * x,z). (x \ T(x * (y / x),z)) * x = T(y,z). T(x,y) = (z \ T(z * (x / z),y)) * z. K(x \ 1,x) * T(K(x,x \ 1) * y,z) = T(y,z). T(x,y) = K(z \ 1,z) * T(K(z,z \ 1) * x,y). T(K(x \ 1,x) * y,z) = K(x \ 1,x) * T(y,z). K(x \ 1,x) * T(y,z) = T(K(x \ 1,x) * y,z). T(K(x \ 1,x) * y,z) = T(y,z) * K(x \ 1,x). T(x * K(y \ 1,y),z) = T(x,z) * K(y \ 1,y). T(x,y) * K(z \ 1,z) = T(x * K(z \ 1,z),y). T(x,y) * K(z \ 1,R(z,u,w)) = T(x * K(z \ 1,z),y). T(x,y) * T(K(z \ 1,R(z,u,w)),x * y) = T(x * K(z \ 1,z),y). T(x * K(y \ 1,y),z) = T(x,z) * T(K(y \ 1,R(y,u,w)),x * z). T(x \ L(x * ((((x \ 1) \ 1) * y) / ((x \ 1) \ 1)),z,u),(x \ 1) \ 1) = (x \ 1) * L(K(x \ 1,x) * ((((x \ 1) \ 1) \ 1) \ y),z,u). L(K(x \ 1,x) * y,z,u) = K(x \ 1,x) * L(y,z,u). K(x \ 1,x) * L(y,z,u) = L(K(x \ 1,x) * y,z,u). L(K(x \ 1,x) * y,z,u) = L(y,z,u) * K(x \ 1,x). L(x,y,z) * K(u \ 1,u) = L(K(u \ 1,u) * x,y,z). (x * y) \ (x * (K(z \ 1,z) * (y * u))) = L(u,y,x) * K(z \ 1,z). ((1 / x) \ y) \ (y * R(1 / (1 / x),x \ 1,(1 / x) \ y)) = K(y,((1 / x) \ y) / y). K(x \ 1,x) * ((y \ 1) \ z) = (y \ K(x,x \ 1)) \ z. (x \ K(y,y \ 1)) \ z = K(y \ 1,y) * ((x \ 1) \ z). (x \ K(y,y \ 1)) \ 1 = (x \ 1) \ K(y \ 1,y). (x \ 1) \ K(y \ 1,y) = (x \ K(y,y \ 1)) \ 1. ((x \ 1) \ y) * K(z,z \ 1) = (x \ K(z \ 1,z)) \ y. (x \ 1) \ (K(y \ 1,y) * z) = (x \ K(y,y \ 1)) \ z. (x \ K(y,y \ 1)) \ z = (x \ 1) \ (K(y \ 1,y) * z). (x \ 1) \ T(x \ 1,y * ((z \ 1) \ 1)) = x * T(x \ 1,y * z). R(1 / (1 / x),x \ 1,(1 / x) \ y) = ((1 / x) \ y) / y. T(x,y) * T(K(z \ 1,R(z,u,w)),x * y) = y \ ((x * K(z \ 1,z)) * y). x \ ((y * K(z \ 1,z)) * x) = T(y,x) * T(K(z \ 1,R(z,u,w)),y * x). ((x * (y * T(y \ 1,z))) * ((z \ 1) \ 1)) / ((z \ 1) \ (y * T(y \ 1,z))) = R(x,y * T(y \ 1,z),z). T(x,y * ((z \ 1) \ 1)) = T(x,y * z). T(x,y * T(z,z \ 1)) = T(x,y * z). R(x,1 / y,z) = R(x,y \ 1,z). R(x,K(y \ 1,y),z) = x. R(x,y,K(z \ 1,R(z,u,w))) = x. (x * y) \ ((x * (y * z)) * K(u \ 1,u)) = L(z,y,x) * K(u \ 1,u). R(x,y,(z \ 1) \ 1) = R(x,y,z). R(x,y,z) = R(x,y,(z \ 1) \ 1). x \ (K(y,y \ 1) * z) = (x \ z) * K(y,y \ 1). T(x,y * K(z,z \ 1)) = T(x,y). R(x,y,K(z \ 1,z)) = x. (x \ 1) * K(y,y \ 1) = x \ K(y,y \ 1). x \ K(y,y \ 1) = (x \ 1) * K(y,y \ 1). R(x,y,K(z,z \ 1)) = x. (x * y) * K(z,z \ 1) = x * (K(z,z \ 1) * y). K(x,L(x \ 1,y,z)) = K(x,x \ 1). (x * y) * K(z,L(z \ 1,u,w)) = x * (K(z,z \ 1) * y). (x * y) * K(z,L(z \ 1,u,w)) = x * (K(z,1 / z) * y). (x * y) * K(z,L(z \ 1,u,w)) = x * (K((1 / z) \ 1,1 / z) * y). (x * y) * K(z,L(1 / z,u,w)) = x * (K((1 / z) \ 1,1 / z) * y). (x * y) * K(z \ 1,L(z,u,w)) = x * (K(z \ 1,z) * y). (x * y) * K(z \ 1,z) = x * (K(z \ 1,z) * y). x * (K(y \ 1,y) * z) = (x * z) * K(y \ 1,y). (x * y) \ (x * (K(z \ 1,z) * (y * u))) = L(K(z \ 1,z) * u,y,x). L(K(x \ 1,x) * y,z,u) = (u * z) \ (u * (K(x \ 1,x) * (z * y))). x \ (K(y \ 1,y) * z) = K(y \ 1,y) * (x \ z). (x \ 1) \ (K(y,y \ 1) * z) = (x \ K(y \ 1,y)) \ z. (x \ K(y \ 1,y)) \ z = (x \ 1) \ (K(y,y \ 1) * z). K(x \ 1,x) * ((y \ 1) * z) = (y \ K(x \ 1,x)) * z. (x \ K(y \ 1,y)) * z = K(y \ 1,y) * ((x \ 1) * z). K(x \ 1,x) * (y * z) = y * (K(x \ 1,x) * z). (x \ 1) * K(y \ 1,y) = x \ K(y \ 1,y). x \ K(y \ 1,y) = (x \ 1) * K(y \ 1,y). L(K(x \ 1,x),y,z) = K(x \ 1,x). L(K(x \ 1,x),y,z) = K(x \ 1,L(x,y,z)). K(x \ 1,L(x,y,z)) = L(K(x \ 1,x),y,z). K(L(x,y,z) \ 1,L(x,y,z)) = K(x \ 1,L(x,y,z)). L(T(x,x \ 1),y,z) \ L(x,y,z) = K(L(x,y,z) \ 1,L(x,y,z)). L(T(x,x \ 1),y,z) = (L(x,y,z) \ 1) \ 1. L(T(x,(y * x) \ y),y,z) = (L(x,y,z) \ 1) \ 1. T(L(x,y,z),(y * x) \ y) = (L(x,y,z) \ 1) \ 1. T(L(x,y,z),(y * x) \ y) = (((z * y) \ (z * (y * x))) \ 1) \ 1. T(L(x,y,z),(y * x) \ (z \ (z * y))) = (((z * y) \ (z * (y * x))) \ 1) \ 1. T(x \ (y * z),z \ (y \ x)) = ((x \ (y * z)) \ 1) \ 1. x \ ((y * z) * K(x \ (y * z),(y * z) \ x)) = T(x \ (y * z),z \ (y \ x)). K(((x * y) \ z) \ 1,y \ (x \ z)) = K(z \ (x * y),(x * y) \ z). K(((x * y) \ z) \ 1,(x * y) \ z) = K(((x * y) \ z) \ 1,y \ (x \ z)). K(((x * y) \ z) \ 1,y \ (x \ z)) = K(((x * y) \ z) \ 1,(x * y) \ z). (1 / ((x * y) \ z)) \ (((x * y) \ z) \ 1) = K(((x * y) \ z) \ 1,y \ (x \ z)). ((((x * y) \ z) \ (y \ (x \ z))) / (y \ (x \ z))) \ (((x * y) \ z) \ 1) = K(((x * y) \ z) \ 1,y \ (x \ z)). ((((x * y) \ z) \ (y \ (x \ z))) / (y \ (x \ z))) \ (((x * y) \ z) \ 1) = K((y \ (x \ z)) \ (((x * y) \ z) \ (y \ (x \ z))),y \ (x \ z)). ((((x * y) \ z) \ (y \ (x \ z))) / (y \ (x \ z))) \ (((x * y) \ z) \ 1) = K((y \ (x \ z)) \ ((y \ (x \ z)) / ((x * y) \ z)),y \ (x \ z)). K((x \ (y \ z)) \ ((x \ (y \ z)) / ((y * x) \ z)),x \ (y \ z)) = ((((y * x) \ z) \ (x \ (y \ z))) / (x \ (y \ z))) \ (((y * x) \ z) \ 1). K((x \ (y \ z)) \ ((x \ (y \ z)) / ((1 / ((y * x) \ z)) \ 1)),x \ (y \ z)) = ((((y * x) \ z) \ (x \ (y \ z))) / (x \ (y \ z))) \ (((y * x) \ z) \ 1). R(R(x,1 / y,z),K(y \ 1,y),(1 / y) * z) = R(x,y \ 1,z). R(R(x,1 / y,z),K(y \ 1,(y \ 1) \ 1),(1 / y) * z) = R(x,y \ 1,z). R(R(x,1 / y,z),K(y \ 1,(y \ 1) \ 1),(1 / y) * z) = R(x,K(y \ 1,y) / y,z). R(R(x,1 / y,z),K(y \ 1,(y \ 1) \ 1),(1 / y) * z) = R(x,K(y \ 1,(y \ 1) \ 1) / y,z). R(x,K(y \ 1,(y \ 1) \ 1) / y,z) = R(R(x,1 / y,z),K(y \ 1,(y \ 1) \ 1),(1 / y) * z). R(R(x,1 / y,K(z \ 1,z)),K(z \ 1,(z \ 1) \ 1) / y,u) = R(R(x,1 / y,u),K(z \ 1,(z \ 1) \ 1),(1 / y) * u). R(R(x,1 / y,K(z,z \ 1)),K(z,z \ 1) / y,u) = R(R(x,1 / y,u),K(z,z \ 1),(1 / y) * u). R(R(x,y,K(z,z \ 1)),y * K(z,z \ 1),u) = R(R(x,y,u),K(z,z \ 1),y * u). R(R(x,y,z),K(u,u \ 1),y * z) = R(R(x,y,K(u,u \ 1)),y * K(u,u \ 1),z). K(x,x \ 1) * ((y * z) / (K(x,x \ 1) * z)) = R(y,K(x,x \ 1),z). R(x,K(y,y \ 1),z) = K(y,y \ 1) * ((x * z) / (K(y,y \ 1) * z)). R(x,(y * K(z \ 1,z)) \ y,u) = K(z,z \ 1) * ((x * u) / (K(z,z \ 1) * u)). R(x,(y * ((1 / (1 / z)) * (z \ 1))) \ y,u) = K(z,z \ 1) * ((x * u) / (K(z,z \ 1) * u)). R(x,(y * ((1 / (1 / z)) * (z \ 1))) \ y,u) = (K(z,z \ 1) * (x * u)) / (K(z,z \ 1) * u). R(x,(y * ((1 / (1 / z)) * (z \ 1))) \ y,u) = (K(z,z \ 1) * (x * u)) / (L(K(z,z \ 1),K(z \ 1,z),y) * u). R(x,(y * ((1 / (1 / z)) * (z \ 1))) \ y,u) = (K(z,z \ 1) * (x * u)) / (L(K(z,z \ 1),(1 / (1 / z)) * (z \ 1),y) * u). R(x,(y * ((1 / (1 / z)) * (z \ 1))) \ y,u) = (K(z,z \ 1) * (x * u)) / (L(L(K(z,z \ 1),z \ 1,1 / (1 / z)),(1 / (1 / z)) * (z \ 1),y) * u). R(x,(y * ((1 / (1 / z)) * (z \ 1))) \ y,u) = ((x * K(z,z \ 1)) * u) / (L(L(K(z,z \ 1),z \ 1,1 / (1 / z)),(1 / (1 / z)) * (z \ 1),y) * u). ((x * K(y,y \ 1)) * z) / (L(L(K(y,y \ 1),y \ 1,1 / (1 / y)),(1 / (1 / y)) * (y \ 1),u) * z) = R(x,(u * ((1 / (1 / y)) * (y \ 1))) \ u,z). ((x * ((y * K(z \ 1,z)) \ y)) * u) / (L(L(K(z,z \ 1),z \ 1,1 / (1 / z)),(1 / (1 / z)) * (z \ 1),y) * u) = R(x,(y * ((1 / (1 / z)) * (z \ 1))) \ y,u). K(x \ 1,L(x,y,z)) = K(x \ 1,x). K(x \ 1,x) = K(x \ 1,L(x,y,z)). R(K(x \ 1,L(x,y,z)),z,y) = K(x \ 1,x). T(K(x \ 1,L(x,y,z)),u) = K(x \ 1,L(x,y,z)). T(x,K(y \ 1,L(y,z,u))) = x. T(x,K(1 / y,L(y,z,u))) = x. T(x,K(y,L(y \ 1,z,u))) = x. x \ T(x,L(x \ 1,y,z)) = K(x,L(x \ 1,y,z)). K(x,L(x \ 1,y,z)) = x \ T(x,L(x \ 1,y,z)). K(L(x \ 1,y,z) \ (L(x \ 1,y,z) * x),L(x \ 1,y,z)) = x \ T(x,L(x \ 1,y,z)). K(L(x \ 1,y,z) \ ((1 / x) \ L(x \ 1,y,z)),L(x \ 1,y,z)) = x \ T(x,L(x \ 1,y,z)). (x * y) * ((z \ L(y \ ((z \ 1) \ 1),y,x)) * z) = (x * (y * T(y \ 1,z))) * ((z \ 1) \ 1). (x * K(y,x)) \ x = K(y,x) \ 1. T(L(x \ 1,x,y) \ 1,y) \ (L(x \ 1,x,y) \ 1) = (y * K(x,y)) \ y. (x * K(y,x)) \ x = T(L(y \ 1,y,x) \ 1,x) \ (L(y \ 1,y,x) \ 1). (x * (y \ T(y,x))) \ x = T(y,x) \ y. ((L(x,x \ 1,y) * y) / L(x,x \ 1,y)) \ y = T(x,y) \ x. ((L(x,x \ 1,y) * y) / L(x,x \ 1,y)) \ y = (x \ T(x,y)) \ 1. ((L(x,x \ 1,y) * y) / L(x,x \ 1,y)) \ y = (y \ (y * (x \ T(x,y)))) \ 1. (x \ (x * (y \ T(y,x)))) \ 1 = ((L(y,y \ 1,x) * x) / L(y,y \ 1,x)) \ x. (x \ ((y * x) / y)) \ 1 = ((y * x) / y) \ x. (x \ ((y * x) / y)) * (((y * x) / y) \ x) = 1. (x \ ((y * x) / y)) * ((((y * x) / y) \ 1) * ((x \ 1) \ 1)) = 1. (x \ ((y * x) / y)) * ((((y * x) / y) \ 1) * (((y \ (y * x)) \ 1) \ 1)) = 1. (x \ ((y * x) / y)) * ((((y * x) / y) \ 1) * T((((y * x) / y) \ 1) \ 1,y)) = 1. x \ ((y * z) * K(((y * z) \ x) \ 1,z \ (y \ x))) = T(x \ (y * z),z \ (y \ x)). x \ (y * K(x \ y,y \ x)) = ((x \ y) \ 1) \ 1. x \ (y * K(x \ y,y \ x)) = T(x \ y,y \ x). K((x \ y) \ 1,x \ y) = K(y \ x,x \ y). K(x \ y,y \ x) = K((y \ x) \ 1,y \ x). T(1 / x,y / (y / x)) = x \ 1. ((x \ y) * (y \ x)) \ ((y \ x) * (x \ y)) = K((x \ y) \ 1,x \ y). (1 / (1 / (x \ y))) * (y \ x) = (y \ x) * (x \ y). ((x \ y) * (y \ x)) / (x \ y) = 1 / (1 / (y \ x)). L(1 / (x \ y),x \ y,x) = 1 / (1 / (y \ x)). (x / (x / y)) \ (y \ (x / (x / y))) = T(1 / y,x / (x / y)). T(1 / x,y / (y / x)) = (y / (y / x)) \ (x \ (y / (y / x))). (1 / x) * (y / (y / x)) = x \ (y / (y / x)). x \ (y / (y / x)) = (1 / x) * (y / (y / x)). ((x / y) \ x) \ (x / (x / y)) = (1 / y) * (x / (x / y)). (1 / x) * (y / (y / x)) = ((y / x) \ y) \ (y / (y / x)). (1 / (x \ y)) * (y / x) = (x \ y) \ (y / x). ((x \ y) \ (y / x)) / (y / x) = 1 / (x \ y). K(x / y,(x / y) \ 1) = (y \ x) * (1 / (y \ x)). x \ (K(x / y,y / x) * y) = L(1 / (y \ x),y \ x,y). (x \ y) * (1 / (x \ y)) = K(y / x,x / y). K(x / y,y / x) = (y \ x) * (1 / (y \ x)). K(x \ y,(x \ y) \ 1) = K(y / x,x / y). K(x / y,y / x) = K(y \ x,(y \ x) \ 1). x * y != (x \ 1) \ 1 | y = K(x,x \ 1). (x \ y) * K(y / x,x / y) = ((x \ y) \ 1) \ 1. ((x \ y) \ 1) \ 1 = (x \ y) * K(y / x,x / y). (R((x \ y) \ 1,z,u) / ((x \ y) * R((x \ y) \ 1,z,u))) \ 1 = (x \ y) * K(y / x,x / y). (R((x \ y) \ 1,z,u) / ((x \ y) * R((x \ y) \ 1,z,u))) \ 1 = K(y / x,x / y) * (x \ y). R(R(x,y,z),y * z,K(z,z \ 1)) = R(x,y,(z \ 1) \ 1). R(x,y,(z \ 1) \ 1) = R(R(x,y,z),y * z,K(z,z \ 1)). R(R(x,y,z),y * z,K(z,z \ 1)) = ((x * y) * ((z \ 1) \ 1)) / (y * ((z \ 1) \ 1)). ((x * y) * ((z \ 1) \ 1)) / (y * ((z \ 1) \ 1)) = R(R(x,y,z),y * z,K(z,z \ 1)). R(T(K(x \ 1,L(x,y,z)),z * y),z,y) = K(x \ 1,x). R(T(K(x \ 1,L(x,y,z)),z * y),z,y) = y \ (y * K(x \ 1,x)). R(T(K(x \ 1,L(x,y,z)),z * y),z,y) = y \ (z \ (z * (y * K(x \ 1,x)))). x \ (y \ (y * (x * K(z \ 1,z)))) = R(T(K(z \ 1,L(z,x,y)),y * x),y,x). x \ (y \ (L(K(z \ 1,z),x,y) * (y * x))) = R(T(K(z \ 1,L(z,x,y)),y * x),y,x). (L(x,x \ 1,y) * y) / L(x,x \ 1,y) = y * (x \ T(x,y)). (L(x,x \ 1,y) * y) / L(x,1 / x,y) = y * (x \ T(x,y)). L(x,1 / x,y) = L(x,x \ 1,y). L(L(x,y * (1 / x),K(x \ 1,x)),1 / x,y) = L(x,x \ 1,y). (((x \ 1) \ 1) * y) / ((x \ 1) \ 1) = (x * y) / x. (((x \ 1) \ 1) * y) / ((x \ 1) \ 1) = (y / x) * T(x,y). (x / y) * T(y,x) = (((y \ 1) \ 1) * x) / ((y \ 1) \ 1). (x / ((y \ 1) \ 1)) * T((y \ 1) \ 1,z) = (x / y) * T(y,z). (x / ((y \ 1) \ 1)) * T((y \ 1) \ 1,z) = x * (x \ ((x / y) * T(y,z))). K((x \ 1) \ 1,y) = K(x,y). K(x,y) = K((x \ 1) \ 1,y). K(1 / x,y) = K(x \ 1,y). K(x \ 1,y) = K(1 / x,y). (x * (y \ 1)) \ ((y \ 1) * x) = K(1 / y,x). K(1 / x,y) = (y * (x \ 1)) \ ((x \ 1) * y). (x * (1 / y)) \ ((1 / y) * z) = (x * (y \ 1)) \ ((y \ 1) * z). T(L(x \ 1,x,y) \ 1,y) \ (L(x \ 1,x,y) \ 1) = K(x,y) \ 1. K(x,y) \ 1 = T(L(x \ 1,x,y) \ 1,y) \ (L(x \ 1,x,y) \ 1). (x \ T(x,y)) \ 1 = T(x,y) \ x. (x \ T(x,y)) * (T(x,y) \ x) = 1. (x \ T(x,y)) * (T(x,y) \ x) = T(1,y). (x \ T(x,y)) * (T(x,y) \ x) = T(x * (x \ 1),y). T(x * (x \ 1),y) = (x \ T(x,y)) * (T(x,y) \ x). T(x * L(x \ 1,x,x \ T(x,y)),y) = (x \ T(x,y)) * (T(x,y) \ x). L(T(x,y \ 1) \ z,T(x,y \ 1),y \ 1) = (x * (1 / y)) \ ((1 / y) * z). L(T(x,x \ 1),y,z) \ L(x,y,z) = K(x \ 1,L(x,y,z)). L(T(x,x \ 1),y,z) \ L(x,y,z) = x * T(x \ 1,L(x,y,z)). L(T(x,x \ 1),y,z) \ L(x,y,z) = T(1 / x,L(x,y,z)) * x. x \ (y \ ((L(K(z \ 1,z),x,y) * y) * x)) = R(T(K(z \ 1,L(z,x,y)),y * x),y,x). L(K(x \ 1,L(x,y,z)),y,z) = L(K(x \ 1,x),y,z). L(K(x \ 1,L(x,y,z)),y,z) = K(L(x,y,z) \ 1,L(x,y,z)). x * T(x \ 1,L(x,y,z)) = K(x \ 1,L(x,y,z)). K(x \ 1,L(x,y,z)) = x * T(x \ 1,L(x,y,z)). (x \ 1) * y != T(x \ 1,z) | y = x * T(x \ 1,z). (x \ 1) * K(x \ 1,L(x,y,z)) = T(x \ 1,L(x,y,z)). T(x \ 1,L(x,y,z)) = (x \ 1) * K(x \ 1,L(x,y,z)). (T(x,((y * x) / y) \ 1) \ ((((y * x) / y) \ 1) \ 1)) * ((((y * x) / y) \ 1) * T((((y * x) / y) \ 1) \ 1,y)) = 1. (T(x \ 1,y) \ (x \ 1)) * (x * T(x \ 1,y)) = 1. (T(x,y) \ x) * (x \ T(x,y)) = 1. T((T(x,y) \ x) * (x \ T(x,y)),z) = (T(x,y) \ x) * (x \ T(x,y)). (x \ 1) * (T(x,y) \ x) = T(x,y) \ 1. (x \ 1) * (T(x,y) \ x) = T(1 / T(x,y),x). T(1 / T(x,y),x) = (x \ 1) * (T(x,y) \ x). (1 / x) * (T(x,y) \ x) = 1 / T(x,y). 1 / T(x,y) = (1 / x) * (T(x,y) \ x). L(T(x,y) \ 1,x,x \ 1) = 1 / T(x,y). L(1 / T((x \ 1) \ 1,y),x,x \ 1) = 1 / T(x,y). K(x \ (x / T(y \ (y / z),z)),x) = y \ ((y / z) * T(z,x)). x * (T((x \ y) * z,x) / z) = ((x \ (y * z)) * x) / z. ((x \ (y * z)) * x) / z = x * (T((x \ y) * z,x) / z). T(x / y,y / x) \ 1 = T((x / y) \ 1,y \ x). T((1 * x) / y,y / x) \ 1 = T((x / y) \ 1,y \ x). T(x * L(x \ 1,x,x \ T(x,y)),y) = (x \ T(x,y)) * (x * (T(x,y) \ 1)). (x \ T(x,y)) * (x * (T(x,y) \ 1)) = T(x * L(x \ 1,x,x \ T(x,y)),y). L(1 / T((x \ 1) \ 1,y),x,x \ 1) = T(1 / (1 / x),y) \ 1. K(x,x \ 1) * (T(x,y) \ z) = T(1 / (1 / x),y) \ z. R((x / y) \ 1,x / y,y) \ 1 = T((y / x) \ 1,x \ y). K(x,T((y / z) \ 1,z \ y)) = K(x,(y / z) \ 1). L(T(x,x \ 1),y,z) \ L(x,y,z) = (L(x,y,z) \ (L(x,y,z) / x)) * x. R(x,T(1 / x,y),x) = T(x,x \ 1). T(x,T(1 / x,y)) = T(x,x \ 1). T(x,T(1 / x,y)) = T(x,1 / x). T(x,1 / x) = T(x,T(1 / x,y)). T((x / y) \ 1,x / y) = T((x / y) \ 1,y \ x). T((x / y) \ 1,y \ x) = T((x / y) \ 1,x / y). T((1 / x) \ 1,1 / x) = T(x,T(1 / x,y)). T(x,T(1 / x,y)) = T((1 / x) \ 1,1 / x). T(x \ 1,T(x,y)) = T(x \ 1,x). T(x \ 1,x) = T(x \ 1,T(x,y)). T(1 / x,T(x,y)) = x \ 1. K(x,y) = (L(x \ 1,x,y) \ 1) \ T(L(x \ 1,x,y) \ 1,y). (x \ 1) * (x * T(x \ 1,y)) = T(x \ 1,y). L(x,y,z) \ ((x \ 1) * L(x,y,z)) = (x \ 1) * K(x \ 1,L(x,y,z)). (x \ 1) * K(x \ 1,y) = x \ K(x \ 1,y). x \ K(x \ 1,y) = (x \ 1) * K(x \ 1,y). R(x,x \ 1,K(x \ 1,y)) = x. R(x,x \ 1,K(x \ 1,y)) = 1 / (x \ 1). (L(x,1 / x,y) * y) / L(x,1 / x,y) = y * (x \ T(x,y)). K(x,y) / (x * K(x,y)) = 1 / x. L(K(x,y),x,1 / x) = K(x,y). T(K(x \ (x / (y \ (y / z))),x),z) = y \ ((y / z) * T(z,x)). T(x,y) * L(z,x,x \ T(x,y)) = (x \ T(x,y)) * (x * z). T(x,y) != z * x | x \ T(x,y) = z. T(x,x \ T(x,y)) = x. T((T(x,y) \ x) * (x \ T(x,y)),z) = (T(x,y) \ x) * (T(x,y) / x). T(x \ T(x,L(x \ 1,y,z)),L(x \ 1,y,z) * x) = K(L(x \ 1,y,z) \ ((1 / x) \ L(x \ 1,y,z)),L(x \ 1,y,z)). L(x \ 1,x,x \ T(x,y)) = T(1 / x,T(x,y)). (x \ 1) \ T(x \ 1,y) = x * T(x \ 1,y). (1 / x) * T(x,y) = x \ T(x,y). K(x,y) = L(T(x,y) / x,x,y). (x \ T(x,y)) * x = T(x,y). T(x,y) / x = x \ T(x,y). x \ T(x,y) = T(x,y) / x. K(x,x \ 1) * T(1 / (1 / x),y) = T(x,y). K(x,x \ 1) * (T(x,y) \ z) = (1 / (1 / T(x,y))) \ z. K(T(x,y),T(x,y) \ 1) = K(x,x \ 1). K(T(x,y),T(x,y) \ 1) = x / (1 / (1 / x)). x / (1 / (1 / x)) = K(T(x,y),T(x,y) \ 1). x / (((1 / (1 / x)) * y) / y) = K(T(x,y),T(x,y) \ 1). ((x \ (y / (1 / z))) * x) * (1 / z) = ((x \ (y * z)) * x) / z. ((x \ (y * z)) * x) / z = ((x \ (y / (1 / z))) * x) * (1 / z). x / ((y * (1 / (1 / T(x,y)))) / y) = K(T(x,y),T(x,y) \ 1). ((x * y) / z) / ((x * (1 / (1 / y))) / z) = K(y,y \ 1). L(L(x,y * (1 / x),K(x \ 1,x)),1 / x,y) = (y * (x \ 1)) \ (K(x \ 1,x) * y). R(x / y,y,1 / y) = x * (y \ 1). x * (y \ 1) = R(x / y,y,1 / y). (x * y) * (y \ 1) = R(x,y,1 / y). R(x,y,1 / y) = (x * y) * (y \ 1). R((x \ (y / (1 / z))) * x,z \ 1,z) = (x \ (y * z)) * x. R(x,y \ 1,y) / y = x * (1 / y). R(x / (1 / y),y \ 1,y) = x * y. (x * (1 / y)) * y = R(x,y \ 1,y). R(x,1 / y,y) = R(x,y \ 1,y). (x / ((y \ 1) \ 1)) * T((y \ 1) \ 1,z) = x * K(z \ (z / T(x \ (x / y),y)),z). x \ (x / T(y,y \ 1)) = T(x \ (x / y),y). (x / y) * K(y \ 1,y) = x / T(y,y \ 1). ((x * y) * ((z \ 1) \ 1)) / ((y * z) * K(z,z \ 1)) = R(R(x,y,z),y * z,K(z,z \ 1)). R(x,y,K(y,y \ 1)) = x. (x * y) * K(y,y \ 1) = x * ((y \ 1) \ 1). (((x \ 1) \ 1) \ y) * T(x,x \ 1) = (x \ y) * x. (x \ y) * x = (((x \ 1) \ 1) \ y) * T(x,x \ 1). (x * y) * K(y,y \ 1) = x * T(y,y \ 1). x * T(y,y \ 1) = (x * y) * K(y,y \ 1). K(x \ 1,x) * (y * T(x,x \ 1)) = y * x. (x / (1 / y)) \ K(y \ 1,y) = (x / (y \ 1)) \ 1. (x * y) * ((((z \ 1) \ 1) \ L(y \ ((z \ 1) \ 1),y,x)) * T(z,z \ 1)) = (x * (y * T(y \ 1,z))) * ((z \ 1) \ 1). K(x,x \ 1) * (y * x) = y * T(x,x \ 1). (x / (y \ 1)) * K(y \ 1,y) = x / (1 / y). x / (1 / y) = (x / (y \ 1)) * K(y \ 1,y). (1 / x) * (y / (1 / x)) = (x \ 1) * (y / (x \ 1)). ((x \ 1) \ 1) * T(y,x) = y * T(x,x \ 1). T(x,x \ 1) * T(y,x) = y * T(x,x \ 1). T(x,T(y,y \ 1)) = T(x,y). (x \ 1) * T(y * x,x \ 1) = R(y,x,1 / x). L(T(x,y \ 1) \ z,T(x,1 / y),y \ 1) = (x * (1 / y)) \ ((1 / y) * z). T(((1 / x) * y) * x,x \ 1) = R(y,1 / x,x). T(x,(y \ 1) \ 1) = T(x,y). T(x,y) = T(x,(y \ 1) \ 1). T(x,1 / y) = T(x,y \ 1). T(x,1 / (1 / y)) = T(x,y). T(x,y) = T(x,1 / (1 / y)). K(x \ 1,x) * (y / (x \ 1)) = y / (1 / x). x / (1 / y) = K(y \ 1,y) * (x / (y \ 1)). R(x,1 / y,K(y \ 1,y)) = x. R(x,y,K(y \ 1,y)) = x. (1 / (1 / x)) * T(y,x) = y * (1 / (1 / x)). x * (1 / (1 / y)) = (1 / (1 / y)) * T(x,y). K(x \ 1,x) * ((y * x) / z) = (y * (1 / (1 / x))) / z. (x * (1 / (1 / y))) / z = K(y \ 1,y) * ((x * y) / z). (x / (1 / (1 / y))) * K(y \ 1,y) = x / y. x / y = (x / (1 / (1 / y))) * K(y \ 1,y). (x / y) * (1 / (1 / y)) = x * K(y \ 1,y). K(x \ 1,x) * (y * x) = y * (1 / (1 / x)). x * (1 / (1 / y)) = K(y \ 1,y) * (x * y). (x * (1 / (1 / y))) / y = x * K(y \ 1,y). x * y != K(z \ 1,z) * (u * y) | x = u * K(z \ 1,z). (x / y) * (1 / (1 / y)) = K(y \ 1,y) * x. K(x \ 1,x) * y = (y / x) * (1 / (1 / x)). K((x / y) / x,x / (x / y)) = K(y \ 1,y). T((x / y) / x,x / (x / y)) = K(y \ 1,y) * ((x / y) / x). K(x \ 1,x) * ((y / x) / y) = T((y / x) / y,y / (y / x)). K(x \ 1,(y / x) \ y) * ((y / x) / y) = T((y / x) / y,y / (y / x)). (R((x \ y) \ 1,z,u) / ((x \ y) * R((x \ y) \ 1,z,u))) \ 1 = K(x / y,y / x) \ (x \ y). K((x \ y) \ 1,x \ y) * (x / y) = T(x / y,y / x). K((x \ y) \ 1,x \ y) = K(x / y,y / x). K(x / y,y / x) = K((x \ y) \ 1,x \ y). x * y != z * T(z \ y,y \ z) | x = K((y \ z) \ 1,y \ z). K(x / y,y / x) * x = y * T(y \ x,x \ y). T(x \ y,y \ x) = ((x \ y) \ 1) \ 1. T(x,(y * x) \ y) = (x \ 1) \ 1. x * y != x * T(z,z \ u) | y = (z \ u) \ u. T(x,(y * x) \ y) = T(x,x \ 1). T(x,x \ 1) = T(x,(y * x) \ y). x * T(y,(x * y) \ x) = x * T(y,y \ 1). x * T(x \ (x * y),(x * y) \ x) = x * T(y,y \ 1). x * T(x \ (x * y),(x * y) \ x) = x * (y * K(y,y \ 1)). L(K(x,x \ 1),x,y) * (y * x) = y * T(y \ (y * x),(y * x) \ y). K(((x * y) \ x) \ 1,L(y \ 1,y,x)) = L(K(y,y \ 1),y,x). K(((x * y) \ x) \ 1,L(y \ 1,y,x)) = L(K((y \ 1) \ 1,y \ 1),y,x). K(L(x,y,z) \ 1,L(x,y,z)) = L(K(x \ 1,x),y,z). x * (L(y,z,u) \ y) != (L(y,z,u) \ 1) * y | x = L(K(y \ 1,y),z,u). K(L(x,y,z) \ 1,L(x,y,z)) * (L(x,y,z) \ x) = (L(x,y,z) \ 1) * x. (L(x,y,z) \ 1) * x = K(L(x,y,z) \ 1,L(x,y,z)) * (L(x,y,z) \ x). (1 / L(x,y,z)) \ ((L(x,y,z) \ 1) * (L(x,y,z) \ x)) = (L(x,y,z) \ 1) * x. (((x * y) \ z) \ (y \ (x \ z))) / (y \ (x \ z)) = 1 / ((x * y) \ z). x \ ((y * z) * K((z \ (y \ x)) \ (((y * z) \ x) \ (z \ (y \ x))),z \ (y \ x))) = T(x \ (y * z),z \ (y \ x)). (x \ (y \ z)) / ((y * x) \ z) = ((y * x) \ z) \ (x \ (y \ z)). ((x * y) \ z) \ (y \ (x \ z)) = (y \ (x \ z)) / ((x * y) \ z). (1 / L(x,y,z)) \ ((L(x,y,z) \ 1) * (x * (L(x,y,z) \ 1))) = (L(x,y,z) \ 1) * x. (((x * y) \ z) \ (y \ (x \ z))) / (y \ (x \ z)) = 1 / L(y \ (x \ z),y,x). (L(x,y,z) \ x) / x = 1 / L(x,y,z). L(x \ (y \ z),x,y) \ (x \ (y \ z)) = (x \ (y \ z)) / ((y * x) \ z). (x \ (y \ z)) / ((y * x) \ z) = L(x \ (y \ z),x,y) \ (x \ (y \ z)). x / L(x,y,z) = L(x,y,z) \ x. L(x,y,z) * T(L(x,y,z) \ x,u) = x. L(x,y,z) * T(((L(x,y,z) * (z * y)) / (z * y)) \ x,u) = x. ((L(x,y,z) * (z * y)) / (z * y)) * T(((L(x,y,z) * (z * y)) / (z * y)) \ x,u) = x. ((L(x,y,z) * (z * y)) / (z * y)) * T(((L(x,y,z) * (z * y)) / (z * y)) \ x,u) = (x * (z * y)) / (z * y). (x \ 1) * T(y * x,1 / x) = R(y,x,1 / x). (x \ 1) \ R(y,x,1 / x) = T(y * x,1 / x). L(T(x * y,1 / y),1 / y,K(y \ 1,y)) = (y \ 1) \ R(x,y,1 / y). L(T(x * y,1 / y),1 / y,(1 / y) \ (y \ 1)) = (y \ 1) \ R(x,y,1 / y). L(T(x * y,1 / y),1 / y,(1 / y) \ (1 * (y \ 1))) = (y \ 1) \ R(x,y,1 / y). (x \ 1) \ R(y,x,1 / x) = L(T(y * x,1 / x),1 / x,(1 / x) \ (1 * (x \ 1))). (x \ 1) \ (K(x \ 1,x) * (R(y,x,1 / x) * K(x,x \ 1))) = L(T(y * x,1 / x),1 / x,(1 / x) \ (1 * (x \ 1))). (x \ 1) \ (((1 / x) \ (x \ 1)) * (R(y,x,1 / x) * K(x,x \ 1))) = L(T(y * x,1 / x),1 / x,(1 / x) \ (1 * (x \ 1))). (x \ 1) \ (((1 / x) \ (1 * (x \ 1))) * (R(y,x,1 / x) * K(x,x \ 1))) = L(T(y * x,1 / x),1 / x,(1 / x) \ (1 * (x \ 1))). R(x,T(y,x),K(z \ 1,R(z,u,w))) \ ((y * K(z \ 1,z)) * x) = T(y,x) * T(K(z \ 1,R(z,u,w)),y * x). (R(x \ 1,y,z) / (x * R(x \ 1,y,z))) \ 1 = K(x \ 1,x) \ x. (R(x \ 1,y,z) / (x * R(x \ 1,y,z))) \ 1 = ((x \ 1) * x) \ x. ((x \ 1) * x) \ x = (R(x \ 1,y,z) / (x * R(x \ 1,y,z))) \ 1. ((x / (y * x)) * y) \ y = (x / (y * x)) \ 1. ((x / (y * x)) * y) * ((x / (y * x)) \ 1) = y. ((x / (y * x)) * ((y * x) / x)) * ((x / (y * x)) \ 1) = y. ((x / y) * (y / x)) * ((x / y) \ 1) = y / x. ((x / y) * (y / x)) * ((x / y) \ 1) = T(y / x,(x / y) * (y / x)). L(T(x / y,y / x),y / x,((y / x) * (x / y)) / (y / x)) = ((y / x) * (x / y)) * ((y / x) \ 1). (1 * (x \ 1)) \ (((1 / x) \ (1 * (x \ 1))) * (R(y,x,1 / x) * K(x,x \ 1))) = L(T(y * x,1 / x),1 / x,(1 / x) \ (1 * (x \ 1))). K(x,x \ 1) * ((R(y,z,u) * (z * u)) / (K(x,x \ 1) * (z * u))) = R(R(y,z,K(x,x \ 1)),z * K(x,x \ 1),u). K(x,x \ 1) * (((y * z) * u) / (K(x,x \ 1) * (z * u))) = R(R(y,z,K(x,x \ 1)),z * K(x,x \ 1),u). R(R(x,y,K(z,z \ 1)),y * K(z,z \ 1),u) = K(z,z \ 1) * (((x * y) * u) / (K(z,z \ 1) * (y * u))). (K(x,x \ 1) * ((y * z) * u)) / (K(x,x \ 1) * (z * u)) = R(R(y,z,K(x,x \ 1)),z * K(x,x \ 1),u). R(R(x,1 / y,K(y \ 1,y)),y \ 1,K((y \ 1) \ 1,y \ 1)) = x. R(R(x,1 / y,K(y \ 1,y)),y \ 1,K(y,y \ 1)) = x. R(R(x,y,K(z \ 1,z)),y * K(z \ 1,z),K(z,z \ 1)) = x. R(R(x,y,K(z \ 1,z)),y * K(z \ 1,z),K(z,z \ 1)) = (x * y) / y. L(L(x,y * (1 / x),K(x \ 1,x)),1 / x,y) = R(y / x,x,1 / x) \ (K(x \ 1,x) * y). a(R((x \ 1) \ 1,y,z),K(x \ 1,x),u) = 1. a(R(x \ 1,y,z),K(x,x \ 1),u) = 1. a(R(x \ 1,y,z),K(x,x \ 1),u) = (R(1 / x,y,z) * u) \ (R(1 / x,y,z) * u). (R(1 / x,y,z) * u) \ (R(1 / x,y,z) * u) = a(R(x \ 1,y,z),K(x,x \ 1),u). T(((1 / x) * y) * x,x \ 1) = R(y,x \ 1,x). R(x,y \ 1,y) = T(((1 / y) * x) * y,y \ 1). (x \ 1) \ R((1 / x) * y,x,x \ 1) = R(y,x \ 1,x). (1 * (x \ 1)) \ R((1 / x) * y,x,x \ 1) = R(y,x \ 1,x). L(R(x,y \ 1,y),K(y \ 1,y),1 / y) = (1 * (y \ 1)) \ R((1 / y) * x,y,y \ 1). (R(x,y,K(y \ 1,y)) / y) * (1 / (1 / y)) != z * K(y \ 1,y) | z = x. x * K(y \ 1,y) != (R(z,y,K(y \ 1,y)) / y) * (1 / (1 / y)) | x = z. (R(x,y,K(y \ 1,y)) / y) * (1 / (1 / y)) = x * K(y \ 1,y). (R(x,y,K(y \ 1,y)) / y) * (1 / (1 / y)) = x * (L(y,y \ 1,y) / y). (R(x,y,K(y \ 1,y)) / y) * L(y,y \ 1,y) = x * (L(y,y \ 1,y) / y). R(x,K(y \ 1,y),z) = R(x,z,K(y \ 1,y)). R(K(x \ 1,x) * (K(x,x \ 1) * y),K(x \ 1,x),z) = R(y,z,K(x \ 1,x)). K(x \ 1,x) * R(K(x,x \ 1) * y,K(x \ 1,x),z) = R(y,z,K(x \ 1,x)). K(x \ 1,x) * R(y / K(x \ 1,x),K(x \ 1,x),z) = R(y,z,K(x \ 1,x)). R(x,y,K(z \ 1,z)) = K(z \ 1,z) * R(x / K(z \ 1,z),K(z \ 1,z),y). T((T(x,y) \ x) * (T(x,y) / x),z) = (T(x,y) \ x) * (T(x,y) / x). x * ((y \ (x \ ((y \ 1) \ 1))) * y) = (y \ 1) \ (x * T(x \ 1,y)). (x \ 1) \ (y * T(y \ 1,x)) = y * ((x \ (y \ ((x \ 1) \ 1))) * x). ((x * (y * T(y \ 1,z))) * ((z \ 1) \ 1)) / ((z \ 1) \ (y * T(y \ 1,z))) = R(x,y * T(y \ 1,z),(z \ 1) \ 1). R(x,y * T(y \ 1,z),(z \ 1) \ 1) = ((x * (y * T(y \ 1,z))) * ((z \ 1) \ 1)) / ((z \ 1) \ (y * T(y \ 1,z))). (x * T(x \ 1,y)) * ((y \ 1) \ 1) = (y \ 1) \ (x * T(x \ 1,y)). (x \ 1) \ (y * T(y \ 1,x)) = (y * T(y \ 1,x)) * ((x \ 1) \ 1). T(x,x \ 1) * (y * T(y \ 1,x)) = (x \ 1) \ (y * T(y \ 1,x)). K(x / y,(x / y) \ 1) != (y \ x) * z | ((y \ x) \ (x / y)) / (x / y) = z. (x \ y) * (((x \ y) \ (y / x)) / (y / x)) = K(y / x,(y / x) \ 1). (x \ y) * (((x \ y) \ (y / x)) / (y / x)) = x \ (K(y / x,(y / x) \ 1) * x). R(x \ 1,y,z) * (K(x,x \ 1) * u) = R(1 / x,y,z) * u. R(x \ 1,y,z) * (K(x \ 1,x) \ u) = R(1 / x,y,z) * u. T(x,((y * x) / y) \ 1) \ ((((z * x) / z) \ 1) \ 1) = x \ ((z * x) / z). ((x \ 1) \ 1) \ ((((y * x) / y) \ 1) \ 1) = x \ ((y * x) / y). x \ ((y * x) / y) = ((x \ 1) \ 1) \ ((((y * x) / y) \ 1) \ 1). K(x \ 1,x) * ((((y * x) / y) \ 1) \ 1) = (y * x) / y. L(1 / T((x \ 1) \ 1,y),x,x \ 1) = K(x,x \ 1) * (T(x,y) \ 1). R((x * y) / y,y,K(z \ 1,z)) = K(z \ 1,z) * R(x / K(z \ 1,z),K(z \ 1,z),y). L(x,K(y \ 1,y),1 / y) = x. L(x,K(y \ 1,y),z / (y * z)) = x. L(x,K(y,y \ 1),y) = x. L(x,K(y,y \ 1),y) = L(x,y,K(y,y \ 1)). L(x,y,K(y,y \ 1)) = L(x,K(y,y \ 1),y). ((x \ 1) \ 1) \ (x * (K(x,x \ 1) * y)) = L(y,x,K(x,x \ 1)). ((x \ 1) \ 1) \ (K(x,x \ 1) * (x * y)) = L(y,x,K(x,x \ 1)). R(x / y,y,K(z \ 1,z)) = K(z \ 1,z) * (x / (K(z \ 1,z) * y)). K(x,((1 / y) \ z) / z) = K(x,((y \ 1) \ z) / z). K(x,((y \ 1) \ z) / z) = K(x,((1 / y) \ z) / z). ((((1 / x) \ y) / y) \ 1) \ 1 = ((x \ 1) \ y) / y. 1 / (((x \ 1) \ y) / y) = (((1 / x) \ y) / y) \ 1. (((1 / x) \ y) / y) \ 1 = 1 / (((x \ 1) \ y) / y). (((1 / (1 / x)) \ y) / y) \ 1 = 1 / ((x \ y) / y). ((1 / (1 / x)) \ y) / y = 1 / (1 / ((x \ y) / y)). (1 / (1 / ((x \ y) / y))) * y = (1 / (1 / x)) \ y. K(x,x \ 1) * (x \ y) = (1 / (1 / ((x \ y) / y))) * y. K(x / (y \ x),(y \ x) / x) = K(y,y \ 1). K(x / (y * x),(x / (y * x)) \ 1) = K(y \ 1,y). K(x / y,y / x) \ z = K(y / x,x / y) * z. K(x / y,y / x) * z = K(y / x,x / y) \ z. K(x / (y \ x),(y \ x) / x) = K(y,(x / (y \ x)) \ 1). K(x,(y / (x \ y)) \ 1) = K(y / (x \ y),(x \ y) / y). K(x / (y * x),(x / (y * x)) \ 1) = K(y,y \ 1) \ 1. K(x / y,(x / y) \ 1) = K(x / y,y / x). K(x / y,y / x) = K(x / y,(x / y) \ 1). K(x,y / (x * y)) = K(x,x \ 1). K((x * y) / y,y / (x * y)) = K(x,x \ 1). x * (y * z) != T(y,y \ 1) * z | x = K(y,y \ 1). K((x * y) / y,y / (x * y)) * (x * y) = T(x,x \ 1) * y. T(x \ T(x,L(x \ 1,y,z)),u) = x \ T(x,L(x \ 1,y,z)). T(x,y \ T(y,L(y \ 1,z,u))) = x. R(R((x \ 1) \ 1,y,z),K(x \ 1,x) * (R(x,y,z) \ u),a(R((x \ 1) \ 1,y,z),K(x \ 1,x),(R((x \ 1) \ 1,y,z) * K(x \ 1,x)) \ u)) \ u = (K(x \ 1,x) * ((R((x \ 1) \ 1,y,z) * K(x \ 1,x)) \ u)) * a(R((x \ 1) \ 1,y,z),K(x \ 1,x),(R((x \ 1) \ 1,y,z) * K(x \ 1,x)) \ u). R((x \ 1) \ 1,y,z) * K(x \ 1,x) = R(x,y,z). R(T(x,x \ 1),y,z) * K(x \ 1,x) = R(x,y,z). (x \ y) * (((x \ y) \ (y / x)) / (y / x)) = x \ (y * L(y \ x,y / x,x / y)). x \ (y * L(y \ x,y / x,x / y)) = (x \ y) * (((x \ y) \ (y / x)) / (y / x)). ((x / y) * (x \ y)) / (x / y) = L(x \ y,x / y,y / x). L(x \ y,x / y,y / x) = ((x / y) * (x \ y)) / (x / y). R((x / y) * K(y \ 1,y),y,K(y,y \ 1)) = x / T(y,y \ 1). L(T(x / y,y),y / x,x / y) = ((y / x) * (y \ x)) / (y / x). R((K(x \ 1,x) * y) / x,x,K(x,x \ 1)) = y / T(x,x \ 1). x / T(y,y \ 1) = R((K(y \ 1,y) * x) / y,y,K(y,y \ 1)). (R(1 / x,y,z) * K(x \ 1,x)) * (K(x \ 1,x) \ u) = R(1 / x,y,z) * u. R(1 / x,y,z) * u = (R(1 / x,y,z) * K(x \ 1,x)) * (K(x \ 1,x) \ u). R(1 / x,K(x \ 1,x),y) = 1 / x. R(1 / x,K(1 / x,x),y) = 1 / x. R(x,K(x,x \ 1),y) = x. x \ (K(y \ x,(y \ x) \ 1) * y) = L(1 / (y \ x),y \ x,y). K(x \ 1,x) * ((((y * x) / y) \ 1) \ 1) = (1 / x) \ (((y * x) / y) * (x \ 1)). (1 / x) \ (((y * x) / y) * (x \ 1)) = K(x \ 1,x) * ((((y * x) / y) \ 1) \ 1). K(x / y,y / x) * x = y * (((y \ x) \ 1) \ 1). T(x \ y,x / y) = ((x \ y) \ 1) \ 1. T(((x / y) \ 1) \ 1,y) = T(y \ x,y / x). T(x / y,y / x) = ((x / y) \ 1) \ 1. R((x / y) \ 1,x / y,y) \ 1 = T((y / x) \ 1,y / x). T((x / y) \ 1,x / y) = R((y / x) \ 1,y / x,x) \ 1. T((1 * x) / y,y / x) = ((x / y) \ 1) \ 1. ((x / y) \ 1) \ 1 = T((1 * x) / y,y / x). R((x / y) \ 1,x / y,y) = ((y / x) \ 1) \ 1. R(x \ 1,x,y) = ((y / (x * y)) \ 1) \ 1. ((x / (y * x)) \ 1) \ 1 = R(y \ 1,y,x). T(x / (y * x),T(y,y \ 1)) = ((x / (y * x)) \ 1) \ 1. K((x / (y * x)) \ 1,x / (y * x)) * (y * x) = T(y,y \ 1) * x. T(x,y / (x * y)) = T(x,x \ 1). T(x,x \ 1) = T(x,y / (x * y)). T(T(1 / (1 / x),y),x \ 1) = T(x,y). T(x,y) = T(T(1 / (1 / x),y),x \ 1). T(1 / (1 / x),x \ 1) = x. T(1 / (1 / x),y / (x * y)) = x. L(x,y / (x * y),x) = 1 / (1 / x). (x \ 1) * ((((y * x) / y) \ 1) \ 1) = ((y * x) / y) * (x \ 1). (x * ((y \ 1) \ 1)) / x = (((x * y) / x) \ 1) \ 1. R(x,T(y,x),T(K(z \ 1,R(z,u,w)),y * x)) \ ((y * K(z \ 1,z)) * x) = T(y,x) * T(K(z \ 1,R(z,u,w)),y * x). L(K(x \ 1,x),y,z) * (z * y) = z * (K(x \ 1,x) * y). ((x / (y * x)) * y) / R(1 / y,y,x) = L(y,x / (y * x),y). T(L(x / y,y / x,x / y),y) = ((y / x) * (y \ x)) / (y / x). K(((x * y) \ x) \ 1,L(y \ 1,y,x)) * (x * y) = x * T(x \ (x * y),(x * y) \ x). T((1 / x) * (T(x,y) \ x),x) = (x \ 1) * (T(x,y) \ x). K((x \ y) \ 1,x \ y) * x = y * T(y \ x,x \ y). x * T(x \ y,y \ x) = K((y \ x) \ 1,y \ x) * y. L(L((1 / x) \ 1,y * (1 / x),K(x \ 1,x)),1 / x,y) = R(y / x,x,1 / x) \ (K(x \ 1,x) * y). K(x \ 1,x) * (y * (1 / x)) = R(y / x,x,1 / x). R(x / y,y,1 / y) = K(y \ 1,y) * (x * (1 / y)). L(R(x,y \ 1,y),a(1 / y,y,y \ 1),1 / y) = (1 * (y \ 1)) \ R((1 / y) * x,y,y \ 1). L(K(x,x \ 1),y,1 / (1 / x)) = K(x,x \ 1). K(x,x \ 1) \ (y * (1 / x)) = R(y / x,x,1 / x). K(x \ 1,x) \ ((y * (x \ 1)) * x) = R(y,x \ 1,x). R(T(x,y * K(z,z \ 1)),y,K(z,z \ 1)) = T(x,y). T(x,y) = R(T(x,y * K(z,z \ 1)),y,K(z,z \ 1)). K((x / y) / x,x / (x / y)) * x = (x / y) * (1 / (1 / y)). x \ (K(x / y,y / x) * y) = 1 / (1 / (x \ y)). (x * K(y,y \ 1)) \ ((x * z) * K(y,y \ 1)) = z. (((x * y) / x) \ 1) * ((y \ 1) \ 1) = ((x * y) / x) \ y. T((x * y) / x,((z * y) / z) \ 1) = (x * ((y \ 1) \ 1)) / x. (x * ((y \ 1) \ 1)) / x = T((x * y) / x,((z * y) / z) \ 1). T(x,((y * x) / y) \ 1) = (x \ 1) \ 1. K(x / y,y / x) * y = x * (1 / (1 / (x \ y))). (x * K(y \ 1,y)) \ K(y \ 1,y) = x \ 1. (x * K(y,y \ 1)) * z = (x * z) * K(y,y \ 1). (K(x,x \ 1) * ((y * z) * u)) / ((z * K(x,x \ 1)) * u) = R(R(y,z,K(x,x \ 1)),z * K(x,x \ 1),u). (R(x \ 1,y,z) * (K(x,x \ 1) * u)) \ (R(1 / x,y,z) * u) = a(R(x \ 1,y,z),K(x,x \ 1),u). a(R(x \ 1,y,z),K(x,x \ 1),u) = (R(x \ 1,y,z) * (K(x,x \ 1) * u)) \ (R(1 / x,y,z) * u). ((x * y) / z) * K(x \ 1,x) = ((1 / (1 / x)) * y) / z. ((1 / (1 / x)) * y) / z = ((x * y) / z) * K(x \ 1,x). R(x / (1 / y),1 / y,K(y \ 1,y)) = K(y \ 1,y) * (x / (y \ 1)). K(x \ 1,R(x,y,z)) * (u * w) = (u * K(x \ 1,x)) * w. (x * K(y \ 1,y)) * z = K(y \ 1,R(y,u,w)) * (x * z). (1 / x) * ((T(x,y) \ 1) * x) = (x \ 1) * (T(x,y) \ x). (x * (y \ 1)) \ (((x / y) \ (x * (y \ 1))) * (z * (x / y))) = L(T(z,x / y),x / y,(x / y) \ (x * (y \ 1))). R(x,L(x \ 1,y,z),T(x,L(x \ 1,y,z))) = T(x,L(x \ 1,y,z)). T(x,x * L(x \ 1,y,z)) = x. 1 / ((R(x,y,z) \ 1) * K(x \ 1,x)) = (R(x,y,z) \ 1) \ 1. 1 / ((x \ 1) * K(x \ 1,x)) = (x \ 1) \ 1. (x \ 1) * K(x \ 1,x) = T(x \ 1,x). a(x,y,z) = ((x * y) * z) / (x * (y * z)). ((x * y) * z) / (x * (y * z)) = a(x,y,z). ((L(x,y,z) * (z * y)) / (z * y)) * T(((L(x,y,z) * (z * y)) / (z * y)) \ x,u) = ((L(x,y,z) * (z * y)) * a(z,y,T(x,z * y))) / (z * y). (x * a(y,z,u)) / x = a(y,z,u). T(a(x,y,z),u) = a(x,y,z). T(x,a(y,z,u)) = x. K(x,a(y,z,u)) = 1. K(x,a(y / (z * u),z,u)) = 1. K(x,a(R(y,z,u),z,u)) = 1. K(x,x \ 1) * y != z | K(x \ 1,x) * z = y. T(x,((y * x) / y) \ 1) = ((y \ (y * x)) \ 1) \ 1. ((x \ (x * y)) \ 1) \ 1 = T(y,((x * y) / x) \ 1). (1 / (1 / (x / y))) * y = y * (1 / (1 / (y \ x))). x * (1 / (1 / (x \ y))) = (1 / (1 / (y / x))) * x. T(((x / y) \ 1) \ 1,y) = ((y \ x) \ 1) \ 1. ((x \ y) \ 1) \ 1 = T(((y / x) \ 1) \ 1,x). K(x,y) / T((z \ 1) \ 1,u) = K(x,y) * (T(z,u) \ 1). K(x,y) * (T(z,u) \ 1) = K(x,y) / T((z \ 1) \ 1,u). (T(x,y) \ 1) \ 1 = T((x \ 1) \ 1,y). 1 / T((x \ 1) \ 1,y) = T(x,y) \ 1. 1 / T(x \ 1,y) = T(1 / x,y) \ 1. T(1 / x,y) \ 1 = 1 / T(x \ 1,y). K(T(x,y),T(x,y) \ 1) * T(1 / (1 / x),y) = T(x,y). x * (1 / (1 / T(y,x))) = (1 / (1 / y)) * x. T(1 / (1 / x),y) \ 1 = 1 / T(x,y). 1 / (1 / T(x,y)) = T(1 / (1 / x),y). T(1 / (1 / x),y) = 1 / (1 / T(x,y)). L(x,T(x,y) \ 1,T(x,y)) = 1 / (1 / x). L(T(K(x,x \ 1),y),y,1 / (1 / x)) = K(x,x \ 1). ((1 / x) \ (y * T(y \ 1,x))) * K(x,x \ 1) = T(x,x \ 1) * (y * T(y \ 1,x)). T((T(x,y) \ x) * (T(x,y) / x),z) = (T(x,y) \ x) * (T(x,y) / ((T(x,y) \ x) * T(x,y))). (x * y) \ ((1 / (1 / x)) * y) = K(x \ 1,x). L(K(x,x \ 1),K(x \ 1,x),y) = K(x,x \ 1). R(R(x,y,K(z \ 1,z)),y * K(z \ 1,z),K(z,z \ 1)) = (x * y) / ((y * K(z \ 1,z)) * K(z,z \ 1)). (x * y) / ((y * K(z \ 1,z)) * K(z,z \ 1)) = R(R(x,y,K(z \ 1,z)),y * K(z \ 1,z),K(z,z \ 1)). (x * K(y,y \ 1)) \ z = x \ (K(y \ 1,y) * z). x \ (K(y \ 1,y) * z) = (x * K(y,y \ 1)) \ z. (K(x \ 1,x) * y) * K(x,x \ 1) = y. x = (K(y \ 1,y) * x) * K(y,y \ 1). (K(x,x \ 1) * y) \ y = K(x \ 1,x). (x * K(y \ 1,y)) \ x = K(y,y \ 1). (x * K(y \ 1,y)) * K(y,y \ 1) = x. x = (x * K(y \ 1,y)) * K(y,y \ 1). (x * K(y \ 1,y)) \ z = x \ (K(y,y \ 1) * z). x \ (K(y,y \ 1) * z) = (x * K(y \ 1,y)) \ z. x * K(x \ (x / T(x,y)),x) = 1 / (1 / x). ((1 / (1 / x)) * y) \ (x * y) = K(x,x \ 1). (x * y) * K(x,x \ 1) = ((x \ 1) \ 1) * y. (x * y) * K(x,x \ 1) = T(x,x \ 1) * y. ((1 / x) \ y) * K(x,x \ 1) = (x \ 1) \ y. K(x \ 1,x) * (y * K(x,x \ 1)) = y. (x * y) * K(z,z \ 1) != u * (K(z,z \ 1) * y) | R(x,y,K(z,z \ 1)) = u. R(x,x \ y,K(z,z \ 1)) \ (K(z,z \ 1) * y) = (x \ y) * K(z,z \ 1). (x * K(y,y \ 1)) * z = K(y,y \ 1) * (x * z). (1 / x) * K(y,y \ 1) = K(y,y \ 1) / x. (x * K(y,y \ 1)) \ (K(y,y \ 1) * (x * z)) = L(z,x,K(y,y \ 1)). L(x,y,K(z,z \ 1)) = (y * K(z,z \ 1)) \ (K(z,z \ 1) * (y * x)). R(x \ 1,y,z) * K(x,x \ 1) = R(1 / x,y,z). R(1 / x,y,z) = R(x \ 1,y,z) * K(x,x \ 1). K(x,x \ 1) * y != R(1 / x,z,u) * w | y = R(x \ 1,z,u) * w. K(x,1 / x) \ (y * (1 / x)) = R(y / x,x,1 / x). 1 / T(x \ 1,x) = (x \ 1) \ 1. T(x \ 1,x) = ((x \ 1) \ 1) \ 1. T(x,1 / x) = (x \ 1) \ 1. T(x,1 / x) = T(x,x \ 1). x * K(x,1 / x) = T(x,1 / x). (x * y) * K(y,y \ 1) != z * ((y \ 1) \ 1) | R(x,y,K(y,y \ 1)) = z. ((x \ 1) \ 1) \ (x * (K(x,x \ 1) * y)) = L(y,K(x,x \ 1),x). L(x,K(y,y \ 1),y) = ((y \ 1) \ 1) \ (y * (K(y,y \ 1) * x)). (x * K(y,y \ 1)) / T(y,y \ 1) = R(x / y,y,K(y,y \ 1)). R(x / y,y,K(y,y \ 1)) = (x * K(y,y \ 1)) / T(y,y \ 1). x * K(x,x \ 1) = (x \ 1) \ 1. (T(x,x \ 1) * y) / (K(x,x \ 1) * y) = R(x,K(x,x \ 1),y). R(x,K(x,x \ 1),y) = (T(x,x \ 1) * y) / (K(x,x \ 1) * y). x * K(x,x \ 1) = T(x,x \ 1). x * K(x,1 / x) = T(x,x \ 1). x \ (K(y \ x,1 / (y \ x)) * y) = L(1 / (y \ x),y \ x,y). x * K(x,1 / x) = R(x,1 / x,x). (R(x,K(y \ 1,y),y) / y) * L(y,y \ 1,y) = x * (L(y,y \ 1,y) / y). L(x,x \ 1,x) / x = K(x \ 1,x). x / K(y \ 1,y) = K(y,y \ 1) * x. x \ (K((y \ x) \ 1,y \ x) * y) = T(x \ y,y \ x). R(1 / x,y,z) * K(x \ 1,x) = R(x \ 1,y,z). K(x \ 1,x) * R(y,x \ 1,x) = (y * (x \ 1)) * x. (x * (y \ 1)) \ (K(y \ 1,y) * x) = L(y,y \ 1,x). (x \ 1) * K(x \ 1,x) = R(x \ 1,x,x \ 1). (K(x \ 1,x) * y) / z = (y / z) * K(x \ 1,x). (x * K(y \ 1,y)) / z = K(y \ 1,y) * (x / z). (x * K(y \ 1,y)) * z = K(y \ 1,y) * (x * z). R(x / y,y,K(z \ 1,z)) = (x * K(z \ 1,z)) / (K(z \ 1,z) * y). K(x,x \ 1) * (y * K(x \ 1,x)) = y. K(x,a(R(y,z,u),z,u)) = K(x,y \ R(y,z,u)). K(x,y \ R(y,z,u)) = K(x,a(R(y,z,u),z,u)). K(x,L(1 / y,z,u)) = K(x,L(y \ 1,z,u)). K(x,L(y \ 1,z,u)) = K(x,L(1 / y,z,u)). R(1 / x,x,1 / x) = x \ 1. ((x \ 1) \ 1) \ x = K(x \ 1,x). T(x / (y * x),T(y,y \ 1)) = R(y \ 1,y,x). L(1 / T((x \ 1) \ 1,y),x,x \ 1) = K(x,x \ 1) / T((x \ 1) \ 1,y). K(x,x \ 1) / T((x \ 1) \ 1,y) = L(1 / T((x \ 1) \ 1,y),x,x \ 1). L(K(x,x \ 1),y,z) * (z * y) = z * (y * K(x,x \ 1)). x * (y * K(z,z \ 1)) = L(K(z,z \ 1),y,x) * (x * y). K(x \ 1,x) * (T(x,y) \ x) = (T(x,y) \ 1) * x. K(x \ (x / T(x,y)),x) = K(x \ 1,x). L(K(x \ 1,x),y,z) * (z * y) = z * (y * K(x \ 1,x)). x * (y * K(z \ 1,z)) = L(K(z \ 1,z),y,x) * (x * y). ((x / y) \ (x * (y \ 1))) * (x / y) = x * (y \ 1). x / K(x \ 1,x) = (x \ 1) \ 1. T(K(x \ 1,R(x,y,z)),u) = K(x \ 1,R(x,y,z)). T(1 / x,T(x,x \ 1)) = x \ 1. R(T(x,x \ 1),y,z) * K(x \ 1,x) = (R(x,y,z) * (x \ 1)) * x. R(x,x \ 1,x) = (x \ 1) \ 1. L(x,y / (x * y),x) * (y / (x * y)) = (y / (x * y)) * x. (x / (y * x)) * y = L(y,x / (y * x),y) * (x / (y * x)). T(L(x,y / (x * y),x),y / (x * y)) = x. T(x * (y / (x * y)),z) = x * (y / (x * y)). K(x / y,y / x) * z = z * K(x / y,y / x). L(R(x / y,y / x,(y / x) \ 1),y / x,((y / x) * (x / y)) / (y / x)) = ((y / x) * (x / y)) * ((y / x) \ 1). ((x / y) * (y / x)) / (x / y) = L(y / x,x / y,y / x). T(x,y * (z / (y * z))) = x. K(x,x \ 1) * y != z * K(x,x \ 1) | z = y. x \ (K(y,y \ 1) * x) = K(y,y \ 1). K(x,x \ 1) * y = y * K(x,x \ 1). T(K(x,x \ 1),y) = K(x,x \ 1). x / K(y,1 / y) = K(y,1 / y) \ x. K(x,1 / x) * y = y * K(x,1 / x). T(x,K(y \ 1,R(y,z,u))) = x. T(x,K(y / z,z / y)) = x. (x * K(y \ 1,y)) / x = K(y \ 1,y). x / K(y \ 1,y) = K(y \ 1,y) \ x. K(x \ 1,x) * y = y * K(x \ 1,x). T(K(x \ 1,x),y) = K(x \ 1,x). T(x,K(y,y \ 1)) = x. R(1 / x,x,1 / x) = T(1 / x,x). T(x,K(y,1 / y)) = x. T(x * L(x \ 1,y,z),x) = x * L(x \ 1,y,z). T(1,x) = 1. T(x,1) = x. R(x,x \ 1,x) = T(x,x \ 1). T(x,K(y \ 1,y)) = x. T(x,y * (1 / y)) = x. T(x,(y \ 1) * y) = x. T(x,(y / z) * (z / y)) = x. T(x,(y / z) \ (y * (z \ 1))) = x. T(x \ R(x,y,z),u) = x \ R(x,y,z). K(x,y \ R(y,z,u)) = 1. T(x,y \ R(y,z,u)) = x. T(x,(y / (z * y)) * z) = x. T(x,y * R(y \ 1,z,u)) = x. T(x * R(x \ 1,y,z),u) = x * R(x \ 1,y,z). x * R(x \ 1,y,z) = T(x * R(x \ 1,y,z),u). T((x \ (K(y,x) * (x * y))) * R((x \ (K(y,x) * (x * y))) \ 1,z,u),w) = y * R(y \ 1,z,u). T((x \ (K(y,x) * (x * y))) * R(T(K(K(y,x),x * y) * y,x) \ 1,z,u),w) = y * R(y \ 1,z,u). T((x \ (K(y,x) * (x * y))) * R(T(K(K(y,x),x * y) * y,x) \ 1,z,u),w) = y * R((x \ (x * y)) \ 1,z,u). T((x \ (K(y,x) * (x * y))) * R(T(K(K(y,x),x * y) * y,x) \ 1,z,u),w) = (x \ (x * y)) * R((x \ (x * y)) \ 1,z,u). T((x \ (K(y,x) * (x * y))) * R(T(K(K(y,x),x * y) * y,x) \ 1,z,u),w) = T(((x * y) / x) * R(((x * y) / x) \ 1,z,u),x). T((x \ (K(y,x) * (x * y))) * R(T(K(K(y,x),x * y) * y,x) \ 1,z,u),w) = T(T(((x * y) / x) * R(((x * y) / x) \ 1,z,u),w),x). T(T(((x * y) / x) * R(((x * y) / x) \ 1,z,u),w),x) = T((x \ (K(y,x) * (x * y))) * R(T(K(K(y,x),x * y) * y,x) \ 1,z,u),w). T(T(x * R(x \ 1,y,z),u),w) = T(x * R(x \ 1,y,z),w). T((x \ (K(y,x) * (x * y))) * R((x \ (K(y,x) * (x * y))) \ 1,z,u),w) = T(y * R(y \ 1,z,u),w). T(T(K(K(x,y),y * x) * x,y) * R((y \ (K(x,y) * (y * x))) \ 1,z,u),w) = T(x * R(x \ 1,z,u),w). T(T(K(K(x,y),y * x) * x,y) * R((y \ (K(x,y) * (y * x))) \ 1,z,u),w) = T(x * R((y \ (y * x)) \ 1,z,u),w). T(T(K(K(x,y),y * x) * x,y) * R((y \ (K(x,y) * (y * x))) \ 1,z,u),w) = T((y \ (y * x)) * R((y \ (y * x)) \ 1,z,u),w). T(T(K(K(x,y),y * x) * x,y) * R((y \ (K(x,y) * (y * x))) \ 1,z,u),w) = T(T(((y * x) / y) * R(((y * x) / y) \ 1,z,u),w),y). T(T(((x * y) / x) * R(((x * y) / x) \ 1,z,u),w),x) = T(T(K(K(y,x),x * y) * y,x) * R((x \ (K(y,x) * (x * y))) \ 1,z,u),w). T(T((K(x,y) * ((y * x) / y)) * R((K(x,y) * ((y * x) / y)) \ 1,z,u),w),y) = T((y \ (K(x,y) * (y * x))) * R(T(K(K(x,y),y * x) * x,y) \ 1,z,u),w). T(T((K(x,y) * ((y * x) / y)) * R((K(x,y) * ((y * x) / y)) \ 1,z,u),w),y) = T(T(K(K(x,y),y * x) * x,y) * R((y \ (K(x,y) * (y * x))) \ 1,z,u),w). T(T((K(x,y) * ((y * x) / y)) * R(((K(x,y) * (y * x)) / y) \ 1,z,u),w),y) = T((y \ (K(x,y) * (y * x))) * R(T(K(K(x,y),y * x) * x,y) \ 1,z,u),w). T(T((K(x,y) * ((y * x) / y)) * R(((K(x,y) * (y * x)) / y) \ 1,z,u),w),y) = T(T(K(K(x,y),y * x) * x,y) * R((y \ (K(x,y) * (y * x))) \ 1,z,u),w). T(x \ L(x * ((((x \ 1) \ 1) * y) / ((x \ 1) \ 1)),z,u),(x \ 1) \ 1) = (x \ 1) * (K(x \ 1,x) * L((((x \ 1) \ 1) \ 1) \ y,z,u)). T(x \ L(x * ((((x \ 1) \ 1) * y) / ((x \ 1) \ 1)),z,u),(x \ 1) \ 1) = (x \ 1) * (K(x \ 1,x) * L(T(x \ 1,(x \ 1) \ 1) \ y,z,u)). (x \ 1) * (K(x \ 1,x) * L(T(x \ 1,(x \ 1) \ 1) \ y,z,u)) = T(x \ L(x * ((((x \ 1) \ 1) * y) / ((x \ 1) \ 1)),z,u),(x \ 1) \ 1). (x \ (K(y,x) * (x * y))) * R((x \ (K(y,x) * (x * y))) \ 1,z,u) = T(y * R(y \ 1,z,u),x). T(x * R(x \ 1,y,z),u) = (u \ (K(x,u) * (u * x))) * R((u \ (K(x,u) * (u * x))) \ 1,y,z). T((K(K(x,y),y * x) * x) * R((K(K(x,y),y * x) * x) \ 1,z,u),y) = (y \ (K(x,y) * (y * x))) * R((y \ (K(x,y) * (y * x))) \ 1,z,u). T(T(x,L(x \ 1,y,z)) / x,L(x \ 1,y,z) * x) = K(L(x \ 1,y,z) \ ((1 / x) \ L(x \ 1,y,z)),L(x \ 1,y,z)). T(x,x \ y) * (z * T(z \ 1,x)) = (z * T(z \ 1,x)) * ((x \ y) \ y). (x * T(x \ 1,y)) * ((y \ z) \ z) = T(y,y \ z) * (x * T(x \ 1,y)). (1 / x) \ (y * T(y \ 1,x)) = x * (y * T(y \ 1,x)). (1 / x) \ (x \ (x * (y * T(y \ 1,x)))) = x * (y * T(y \ 1,x)). ((x * ((y * ((1 / (1 / z)) * (z \ 1))) \ y)) * u) / (L(L(K(z,z \ 1),z \ 1,1 / (1 / z)),(1 / (1 / z)) * (z \ 1),y) * u) = R(x,(y * ((1 / (1 / z)) * (z \ 1))) \ y,u). T((T(x,y) \ x) * (x \ T(x,y)),y) = 1. T((T(x,y) \ x) * (x \ T(x,y)),y) = K(T(x,y),T(x,y) \ x). (x * T(x \ 1,y)) * z != y * (x * T(x \ 1,y)) | z = y. (1 / x) \ (x \ ((L(y \ 1,y,x) * x) / L(y \ 1,y,x))) = x * (y * T(y \ 1,x)). (1 / x) \ (((y * x) / y) * (x \ 1)) = (y * x) / y. (x \ 1) \ ((y * (x \ 1)) / y) = x * ((y * (x \ 1)) / y). x * ((y * (x \ 1)) / y) = (x \ 1) \ ((y * (x \ 1)) / y). (1 / x) \ (x \ ((y * x) / y)) = (y * x) / y. (1 / x) * ((y * x) / y) = x \ ((y * x) / y). (x * y) / x != z * y | y \ ((x * y) / x) = z. T(1 / T(x,y),x) = T(x,y) \ 1. L(K(x,x \ 1),x \ 1,y / (1 / x)) = ((y / (1 / x)) * (x \ 1)) \ y. T((T(x,y) \ x) * (x \ T(x,y)),y) = K(T(x,y),x / T(x,y)). (T(x,y) \ x) / x = 1 / T(x,y). x * T(y,z) != y | T(y,z) \ y = x. x != y * T(x,z) | T(x,z) \ x = y. x / T(x,y) = T(x,y) \ x. (T(x,y) \ x) * T(x,y) = x. K(T(x,y),T(x,y) \ x) = 1. (x \ 1) \ (1 / x) = K(x,x \ 1). ((x * y) / x) / y = y \ ((x * y) / x). (x \ ((y * x) / y)) * x = (y * x) / y. T(T(x,y),T(x,y) \ x) = T(x,y). (x * T(x \ 1,y)) * ((T(y,x * T(x \ 1,y)) \ z) \ z) = T(y,y \ z) * (x * T(x \ 1,y)). T(x,x \ y) * (z * T(z \ 1,x)) = (z * T(z \ 1,x)) * ((T(x,z * T(z \ 1,x)) \ y) \ y). (x * T(x \ 1,y)) * y = y * (x * T(x \ 1,y)). T(x,x \ ((y * x) / y)) = x. T(x,y * T(y \ 1,x)) = x. T(x,y) * K(z,x) = K(z,x) * T(x,y). K(x,y) * T(y,z) = T(y,z) * K(x,y). ((x * K(y,z)) * z) \ ((x * (z * K(y,z))) * z) = L(z,K(y,z),x). L(x,K(y,x),z) = ((z * K(y,x)) * x) \ ((z * (x * K(y,x))) * x). (x \ y) * ((y \ T(x,x \ y)) * y) = y * K(y \ x,y). (x \ 1) * K(x,x \ 1) = 1 / x. (x * K(y,x)) * z = K(y,x) * (x * z). T(x,K(y,x)) = x. K(x,y) * y = y * K(x,y). T(L(x,T(x,y) \ 1,T(x,y)),y) = 1 / (1 / T(x,y)). 1 / (1 / T(x,y)) = T(L(x,T(x,y) \ 1,T(x,y)),y). L(x,x \ 1,x) = 1 / (1 / x). 1 / (1 / x) = L(x,x \ 1,x). R(K(x,y),z,u) = (y * K(x,y)) * (y \ 1). x * K(x \ 1,x) = 1 / (1 / x). x * (y \ 1) != K(y \ 1,y) | x = 1 / (1 / y). (x * K(y,x)) * (x \ 1) = K(y,x). (x * K(y,x)) \ K(y,x) = x \ 1. (x * K(y,x)) \ (L(y \ 1,y,x) * T(L(y \ 1,y,x) \ 1,x)) = x \ 1. (x * (y * T(y \ 1,x))) \ (y * T(y \ 1,x)) = x \ 1. x \ 1 = (x * (y * T(y \ 1,x))) \ (y * T(y \ 1,x)). (L(x \ 1,x,y) \ (L(x \ 1,x,y) * y)) \ 1 = (y * (x * T(x \ 1,y))) \ (x * T(x \ 1,y)). (x * (y * T(y \ 1,x))) \ (y * T(y \ 1,x)) = (L(y \ 1,y,x) \ (L(y \ 1,y,x) * x)) \ 1. (x * (y * T(y \ 1,x))) \ (x \ (x * (y * T(y \ 1,x)))) = (L(y \ 1,y,x) \ (L(y \ 1,y,x) * x)) \ 1. (K(x,y) * z) * R((K(x,y) * z) \ u,w,v5) = z * R(z \ u,w,v5). (K(x,y) * z) * R((K(x,y) * z) \ u,w,v5) = z * R((K(x,y) * z) \ (K(x,y) * u),w,v5). x * R((K(y,z) * x) \ (K(y,z) * u),w,v5) = (K(y,z) * x) * R((K(y,z) * x) \ u,w,v5). x * R(T(K(y,z) * (u / (K(y,z) * x)),K(y,z) * x),w,v5) = (K(y,z) * x) * R((K(y,z) * x) \ u,w,v5). K(R(x,y,z) \ 1,R(x,y,z)) = K(x \ 1,x). x * (y * z) != (K(u,w) * y) * z | x = K(u,w). K(R(x,y,z) \ 1,R(x,y,z)) * (y * z) = (K(x \ 1,x) * y) * z. K(R(x,y,z) \ 1,R(x,y,z)) * (y * z) = ((x * T(x \ 1,R(x,y,z))) * y) * z. K(R(x,y,z) \ 1,R(x,y,z)) * (y * z) = (x * (y * T(y \ (x \ y),R(x,y,z)))) * z. K(R(x,y,z) \ 1,R(x,y,z)) * (y * z) = ((x * y) * T((x * y) \ y,R(x,y,z))) * z. ((x * y) * z) * T(((x * y) * z) \ (y * z),R(x,y,z)) = K(R(x,y,z) \ 1,R(x,y,z)) * (y * z). ((x * y) * z) * T(((x * y) * z) \ (y * z),R(x,y,z)) = ((R(x,y,z) \ 1) * R(x,y,z)) * (y * z). ((R(x,y,z) \ 1) * R(x,y,z)) * (y * z) = ((x * y) * z) * T(((x * y) * z) \ (y * z),R(x,y,z)). T((x * y) / ((z * x) * y),R(z,x,y)) * ((z * x) * y) = ((R(z,x,y) \ 1) * R(z,x,y)) * (x * y). x * (T(T(y,x),z) * R(T(T(y,x),z) \ (x \ u),w,v5)) = T(y,z) * (x * R(x \ (T(y,z) \ u),w,v5)). x * (T(T(y,x),z) * R(T(T(y,x),z) \ (x \ u),w,v5)) = (T(y,z) * x) * R((T(y,z) * x) \ u,w,v5). x * T(R(K(y,z) * (u / (K(y,z) * x)),w,v5),K(y,z) * x) = (K(y,z) * x) * R((K(y,z) * x) \ u,w,v5). (x * (y \ z)) * ((z \ L(T(y,y \ z),y \ z,x)) * z) = (x * K(z \ y,z)) * z. (x * (y \ z)) * ((z \ L(T(y,y \ z),y \ z,x)) * z) = (x * (y \ ((z \ y) * z))) * z. (x * (y \ z)) * ((z \ L(T(y,y \ z),y \ z,x)) * z) = (x * ((y \ z) * T((y \ z) \ 1,z))) * z. (x * ((y \ z) * T((y \ z) \ 1,z))) * z = (x * (y \ z)) * ((z \ L(T(y,y \ z),y \ z,x)) * z). L(K(x \ 1,x),y,z) * (L(x,y,z) \ x) = (L(x,y,z) \ 1) * x. L((x \ 1) * x,y,z) * (L(x,y,z) \ x) = (L(x,y,z) \ 1) * x. L(x * T(x \ 1,L(x,y,z)),y,z) = K(L(x,y,z) \ 1,L(x,y,z)). K(L(x,y,z) \ 1,L(x,y,z)) = L(x * T(x \ 1,L(x,y,z)),y,z). L(x * T(x \ 1,x),y,z) * (L(x,y,z) \ x) = (L(x,y,z) \ 1) * x. L(x * T(x \ 1,L(x,y,z)),y,z) = (L(x,y,z) \ 1) * L(x,y,z). L(x,y,z) * T(L(x,y,z) \ 1,u) = L(x * T(x \ 1,u),y,z). L(x * T(x \ 1,y),z,u) = L(x,z,u) * T(L(x,z,u) \ 1,y). (x * y) * (L(z,y,x) * T(L(z,y,x) \ 1,u)) = x * (y * (z * T(z \ 1,u))). (x * y) * (L(z,y,x) * T(L(z,y,x) \ 1,u)) = x * ((y * z) * T((y * z) \ y,u)). (x * (y * z)) * T((x * (y * z)) \ (x * y),u) = (x * y) * (L(z,y,x) * T(L(z,y,x) \ 1,u)). T(x / (y * x),T(y,x / (y * x))) = ((x / (y * x)) \ 1) \ 1. R((x / (y * x)) \ 1,R(1 / y,y,x),y * x) = T(y,x / (y * x)). R((x / (y * x)) \ 1,R(1 / y,y,x),y * x) = T((y * x) / x,x / (y * x)). x \ (K(x,x \ 1) * T(1 / (1 / x),y)) = T(x,y) / x. K(x,x \ 1) * T(1 / (1 / x),y) = x * (T(x,y) / x). K(x,1 / x) * T(1 / (1 / x),y) = x * (T(x,y) / x). K(x,1 / x) * T(K(x,1 / x) \ (K(x,1 / x) / (1 / x)),y) = x * (T(x,y) / x). T(K(x,x \ 1),y) / T((x \ 1) \ 1,y) = L(1 / T((x \ 1) \ 1,y),x,x \ 1). T(K((x \ 1) \ 1,x \ 1),y) / T((x \ 1) \ 1,y) = L(1 / T((x \ 1) \ 1,y),x,x \ 1). T(((x \ 1) \ 1) * (x \ 1),y) / T((x \ 1) \ 1,y) = L(1 / T((x \ 1) \ 1,y),x,x \ 1). L(K(x \ 1,x) \ ((y * (x \ 1)) * x),a(1 / x,x,x \ 1),1 / x) = (1 * (x \ 1)) \ R((1 / x) * y,x,x \ 1). L(K(x \ 1,x) \ y,a(1 / x,x,x \ 1),1 / x) = (1 * (x \ 1)) \ ((1 / x) * y). L(((1 / x) \ (x \ 1)) \ y,a(1 / x,x,x \ 1),1 / x) = (1 * (x \ 1)) \ ((1 / x) * y). K(x,T(y \ R(y,z,u),(R(y,z,u) * z) * u)) = K(x,a(R(y,z,u),z,u)). K(x,T(R(y,z,u) / y,(R(y,z,u) * z) * u)) = K(x,a(R(y,z,u),z,u)). K(x,a(R(y,z,u),z,u)) = K(x,T(R(y,z,u) / y,(R(y,z,u) * z) * u)). (x * T(x \ 1,y)) * ((y \ 1) \ 1) = x * ((y \ (x \ ((y \ 1) \ 1))) * y). x * ((y \ (x \ ((y \ 1) \ 1))) * y) = (x * T(x \ 1,y)) * ((y \ 1) \ 1). (x \ 1) \ T((x \ 1) * y,x) = (x \ y) * x. (x \ y) * x = (x \ 1) \ T((x \ 1) * y,x). (x \ ((x \ 1) \ y)) * x = (x \ 1) \ T(y,x). T((1 / x) * ((x \ 1) \ y),x) = (1 / x) * ((x \ 1) \ T(y,x)). (1 / x) * ((x \ 1) \ T(y,x)) = T((1 / x) * ((x \ 1) \ y),x). T((1 / x) * ((x \ 1) \ y),x) = K(x,x \ 1) * T(y,x). T(K(x,x \ 1) * y,x) = K(x,x \ 1) * T(y,x). T(x * ((1 / (1 / x)) \ y),x) = K(x,x \ 1) * T(y,x). x * L(x \ y,x / y,y / x) = K(x / y,(x / y) \ 1) * y. T(((x \ 1) \ 1) * ((x \ 1) * 1),y) / T((x \ 1) \ 1,y) = L(1 / T((x \ 1) \ 1,y),x,x \ 1). L(((x \ 1) \ 1) \ y,x,x \ 1) = (x \ 1) * y. L(x,(y \ 1) \ 1,y \ 1) = L(x,y,y \ 1). L(x,y,y \ 1) = L(x,(y \ 1) \ 1,y \ 1). L(x,1 / y,y) = L(x,y \ 1,y). K(x,x \ 1) * L(y,x \ 1,x) = x * ((1 / x) * y). K(x / y,y / x) * y = (1 / (1 / (y / x))) * x. (x \ 1) * (K(x \ 1,(x \ 1) \ 1) * L(T(x \ 1,(x \ 1) \ 1) \ y,z,u)) = T(x \ L(x * ((((x \ 1) \ 1) * y) / ((x \ 1) \ 1)),z,u),(x \ 1) \ 1). T(x \ L(x * ((((x \ 1) \ 1) * y) / ((x \ 1) \ 1)),z,u),(x \ 1) \ 1) = (x \ 1) * (K(x \ 1,(x \ 1) \ 1) * L(T(x \ 1,(x \ 1) \ 1) \ y,z,u)). T(x,x \ 1) * ((x \ 1) * y) = x * ((1 / x) * y). x * ((1 / x) * y) = T(x,x \ 1) * ((x \ 1) * y). (T(x,x \ 1) * y) / (K(x,x \ 1) * y) = x. L(T(K(x,x \ 1),y),y,1 / (1 / x)) = ((1 / (1 / x)) * y) \ (x * y). ((1 / (1 / x)) * y) \ (x * y) = L(T(K(x,x \ 1),y),y,1 / (1 / x)). x * (K(x,x \ 1) * y) = T(x,x \ 1) * y. (1 / (1 / x)) * (K(x,x \ 1) * y) = x * y. x * y = (1 / (1 / x)) * (K(x,x \ 1) * y). K(x,x \ 1) * y != x * z | y = (1 / (1 / x)) * z. K(x,x \ 1) * (x * y) = x * (K(x,x \ 1) * y). x * (K(x,x \ 1) * y) = K(x,x \ 1) * (x * y). K(x,x \ 1) * (x \ y) = (1 / (1 / x)) \ y. x * y != K(x,x \ 1) * z | y = (1 / (1 / x)) \ z. K(x,T((R(y,z,u) * z) / (y * z),(R(y,z,u) * z) * u)) = K(x,a(R(y,z,u),z,u)). x * (K(x,x \ 1) * (x \ y)) = K(x,x \ 1) * y. K(x,T(y / z,y * u)) = K(x,(z * u) \ (y * u)). K(x,T(y / (1 / z),u)) = K(x,T(y * z,u)). K(x,T(y * z,u)) = K(x,T(y / (1 / z),u)). K(x \ 1,x) * (y * x) = (1 / (1 / x)) * T(y,x). K((x / y) \ 1,x / y) * x = (1 / (1 / (x / y))) * y. (1 / (1 / x)) * (x \ 1) = K(x \ 1,x). K(x \ 1,x) = (1 / (1 / x)) * (x \ 1). K(x,x \ 1) * L(y,x \ 1,x) = T(x,x \ 1) * ((x \ 1) * y). K(x,x \ 1) * (x * y) = ((x \ 1) \ 1) * y. K(x,x \ 1) * (y * x) = T(x,x \ 1) * T(y,x). T(x * ((1 / x) * ((1 / x) \ ((1 / (1 / x)) \ y))),x) = K(x,x \ 1) * T(y,x). K(x \ 1,x) * (x * y) = (1 / (1 / x)) * y. K(x,L(y,z,y)) = K(x,y). K(x,y) = K(x,L(y,z,y)). K(x,L(T(y,y \ z),u,w)) = K(x,L(T(y,z),u,w)). K(x,x \ 1) * (x * y) = T(x,x \ 1) * y. T(x,x \ 1) * y = K(x,x \ 1) * (x * y). K(x,x \ 1) * x = T(x,x \ 1). K(x,1 / x) * x = T(x,x \ 1). x * ((1 / (1 / x)) \ y) = K(x,x \ 1) * y. K(x,x \ 1) * ((1 / (1 / x)) * y) = x * y. x * y = K(x,x \ 1) * ((1 / (1 / x)) * y). K(x,T(y / z,y)) = K(x,z \ y). K(x,y \ z) = K(x,T(z / y,z)). K(x,1 / x) \ T(x,x \ 1) = x. x / (1 / (1 / x)) = K(x,x \ 1). K(x,x \ 1) * (1 / (1 / x)) = x. K(x,(y \ z) \ z) = K(x,T(y,z)). x * L(x \ (1 * y),x / y,y / x) = K(x / y,(x / y) \ 1) * y. K(x,x \ 1) * y != x * ((1 / x) * z) | L(z,1 / x,x) = y. R(x,y,1 / y) * K(y,y \ 1) = (x * y) * (1 / y). x * (K(x,x \ 1) * (x \ y)) = K(x,1 / x) * y. K(x,1 / x) \ ((x \ 1) \ 1) = x. K(x,x \ 1) \ x = 1 / (1 / x). K(x,x \ 1) = x * (1 / x). K(x,(y \ 1) \ 1) = K(x,y). K(x,y) = K(x,(y \ 1) \ 1). K(x,1 / y) = K(x,y \ 1). K(x,y \ 1) = K(x,1 / y). ((T(x,y * z) * y) * z) \ ((x * y) * z) = K(y * z,T(x,y * z)). K(x,T(y,z * y)) = K(x,T(y,z)). K(x,T(y,z)) = K(x,T(y,z * y)). K(x,T((y * z) / u,w)) = K(x,T(y / (u / z),w)). K(x,T(y,y \ z)) = K(x,T(y,z)). K(x,T((y * z) / (u * z),w)) = K(x,T(y / u,w)). K(x,T(y,y * z)) = K(x,T(y,z)). K(x,T(y,z)) = K(x,T(y,y * z)). K(x,(y * z) / u) = K(x,y / (u / z)). K(x,T(y \ 1,y)) = K(x,y \ 1). K(x,y * (z \ 1)) = K(x,y / z). K(x,(y / z) / u) = K(x,y / (u * z)). K(x,y / (z * u)) = K(x,(y / u) / z). K(x,(y * z) / (u * z)) = K(x,y / u). K(x,L(R(y,z,u),w,v5)) = K(x,L(y,w,v5)). K(x,R(y,z,u)) = K(x,y). (R(x,y,z) * u) * K(u,x) = u * R(x,y,z). x * R(y,z,u) = (R(y,z,u) * x) * K(x,y). x * R(K(x,y) * (K(x,y) \ y),z,u) = (R(y,z,u) * x) * K(x,y). x * (K(x,y) * R(K(x,y) \ y,z,u)) = (R(y,z,u) * x) * K(x,y). (R(x,y,z) * u) * K(u,x) = u * (K(u,x) * R(K(u,x) \ x,y,z)). (x * K(x,y)) * R((x * K(x,y)) \ (x * y),z,u) = (R(y,z,u) * x) * K(x,y). L(R(x,T(1 / x,L(x,y,z)),x),y,z) \ L(x,y,z) = (L(x,y,z) \ (L(x,y,z) / x)) * x. ((T(x,y * z) * y) * z) \ ((x * y) * z) = K(y * z,R(T(x,y * z),y,z)). ((T(x,y * z) * y) * z) \ ((x * y) * z) = K(y * z,(y * z) \ ((x * y) * z)). K(x / (y * x),(x / (y * x)) \ 1) = K(y,x / (y * x)) \ 1. ((x / (y * x)) \ 1) * R(1 / y,y,x) = K(y,x / (y * x)). K(x,y / (x * y)) = ((y / (x * y)) \ 1) * R(1 / x,x,y). T((1 / x) * T((1 / x) \ 1,L(x \ 1,y,z)),L(x \ 1,y,z) * x) = K(L(x \ 1,y,z) \ ((1 / x) \ L(x \ 1,y,z)),L(x \ 1,y,z)). (1 / x) \ L(x \ 1,y,z) = L(x \ 1,y,z) * x. x * T(x \ 1,R(x,y,z)) = K(x \ 1,x). T(x / y,y / x) != z * (x / y) | K(x / y,y / x) = z. K((x * y) / y,y / (x * y)) = ((y / (x * y)) \ 1) * R(1 / x,x,y). K(x / y,y / x) * (x / y) = T(x / y,y / x). K(x / y,y / x) * x = y * T(y \ x,y / x). K(x / y,(x / y) \ 1) * z = K(y / x,x / y) \ z. K(x / y,y / x) \ z = K(y / x,(y / x) \ 1) * z. K((x \ 1) \ 1,x \ 1) = K(x,x \ 1). K(x,x \ 1) = K((x \ 1) \ 1,x \ 1). K((x / y) \ 1,x / y) = K(y / x,x / y). K(x / y,y / x) = K((y / x) \ 1,y / x). K(1 / x,x) = K(x \ 1,x). K(x / (y * x),y) = K(y \ 1,y). K(x \ 1,x) = K(y / (x * y),x). (1 / x) \ L(x \ 1,y,z) = x * L(T(x \ 1,x),y,z). R(x / (1 / y),1 / y,K(y \ 1,y)) = (x * K(y \ 1,y)) / (y \ 1). x * T(x \ 1,R((1 / x) \ 1,y,z)) = K(x \ 1,x). (1 / x) * K(x \ 1,x) = x \ 1. (1 / x) \ (x \ 1) = K(x \ 1,x). K(x \ 1,x) = (1 / x) \ (x \ 1). a(x / (y * x),y,y \ 1) = K(y \ 1,y). a(1 / x,x,x \ 1) = K(x \ 1,x). a(R(1 / x,y,z),x,x \ 1) = K(x \ 1,x). a(R(1 / x,y,z),x,x \ 1) = R(x \ 1,y,z) / R(1 / x,y,z). R(x \ 1,y,z) / R(1 / x,y,z) = a(R(1 / x,y,z),x,x \ 1). a(x / (y * x),y,y \ 1) = K(x / (y * x),y). K(x / (y * x),y) = a(x / (y * x),y,y \ 1). K(x \ (x * (y / (x * y))),x) = a(y / (x * y),x,x \ 1). K(x \ (x / (1 / (y / (x * y)))),x) = a(y / (x * y),x,x \ 1). x / (1 / (y / (x * y))) = x * (y / (x * y)). x * L(x \ (1 * y),x / y,y / x) = ((x / y) * (1 / (x / y))) * y. ((x / y) * (1 / (x / y))) * y = x * L(x \ (1 * y),x / y,y / x). L((x / (y * x)) \ 1,x / (y * x),y) = 1 / (x / (y * x)). L((x / y) \ 1,x / y,y / x) = 1 / (x / y). L(x \ 1,x,(x \ y) / y) = 1 / x. 1 / x = L(x \ 1,x,(x \ y) / y). (x * R(x \ 1,y,z)) \ R(1 / x,y,z) = 1 / x. ((x / (y * x)) * y) / R(1 / y,y,x) = 1 / (1 / y). x * T(x \ 1,R((1 / x) \ 1,y,z)) = (1 / x) \ (x \ 1). (1 / x) \ (x \ 1) = x * T(x \ 1,R((1 / x) \ 1,y,z)). T(1 / x,R((1 / x) \ 1,y,z)) = x \ 1. T(x,R(x \ 1,y,z)) = (x \ 1) \ 1. T(1 / x,R(x,y,z)) = x \ 1. R(x,y,z) * (x \ 1) = (1 / x) * R(x,y,z). R(x \ 1,x,y) / (y / (x * y)) = a(y / (x * y),x,x \ 1). R((x \ 1) / (x * (x \ 1)),y,z) / R(1 / x,y,z) = a(R(1 / x,y,z),x,x \ 1). R(1 / x,x,y) / (1 / x) = (y / (x * y)) * x. (1 / x) * y != R(1 / x,x,z) | y = (z / (x * z)) * x. (1 / x) * R(x,y,z) = x \ R(x,y,z). R(x,y,y \ 1) / x = a(x,y,y \ 1). (x * R(x \ 1,y,z)) * (1 / x) = R(1 / x,y,z). x * (R(x,y,z) / x) = R(x,y,z). R(x,y,z) / x = x \ R(x,y,z). (x \ R(x,y,z)) * x = R(x,y,z). (R(x,y,z) * (x \ 1)) * x = R(x,y,z). R(x,y,z) = (R(x,y,z) * (x \ 1)) * x. R(K(x \ 1,x) * (K(x,x \ 1) * x),y,z) = (R(x,y,z) * (x \ 1)) * x. K(x \ 1,x) * R(K(x,x \ 1) * x,y,z) = (R(x,y,z) * (x \ 1)) * x. L(T(x,1 / y) \ z,T(x,1 / y),y \ 1) = (x * (1 / y)) \ ((1 / y) * z). L(x,y,1 / z) = L(x,y,z \ 1). L(x,y,K(z,u) * w) = L(x,y,w). L(x,L(y,z,K(u,w)),K(u,w) * z) = L(x,y,z). L(L(x,y,z),z * y,K(u,w)) = L(x,L(y,z,K(u,w)),K(u,w) * z). L(x,L(y,z,K(u,w)),K(u,w) * z) = L(L(x,y,z),z * y,K(u,w)). K(x \ 1,x) * R(K(x,x \ 1) * x,y,z) = ((x \ 1) * R((x \ 1) \ 1,y,z)) * x. K(x \ 1,x) * T(K(x,x \ 1) * y,z) = (x \ T(x * (y / x),z)) * x. K(x \ 1,x) * T(K(x \ 1,x) \ y,z) = (x \ T(x * (y / x),z)) * x. T(T(((K(x,y) * (y * x)) / y) * R(((K(x,y) * (y * x)) / y) \ 1,z,u),w),y) = T((y \ (K(x,y) * (y * x))) * R(T(K(K(x,y),y * x) * x,y) \ 1,z,u),w). T(T(((K(x,y) * (y * x)) / y) * R(((K(x,y) * (y * x)) / y) \ 1,z,u),w),y) = T(T(K(K(x,y),y * x) * x,y) * R((y \ (K(x,y) * (y * x))) \ 1,z,u),w). T((K(K(x,y),y * x) * x) * R((K(K(x,y),y * x) * x) \ 1,z,u),y) = (y \ (K(x,y) * (y * x))) * R(T(K(K(x,y),y * x) * x,y) \ 1,z,u). (x \ (K(y,x) * (x * y))) * R(T(K(K(y,x),x * y) * y,x) \ 1,z,u) = T((K(K(y,x),x * y) * y) * R((K(K(y,x),x * y) * y) \ 1,z,u),x). T(K(K(x,y),y * x) * x,y) = y \ (K(x,y) * (y * x)). x \ (K(y,x) * (x * y)) = T(K(K(y,x),x * y) * y,x). K(K(x,y),y * x) * (x * y) = K(x,y) * (y * x). K(K(x,y),y * x) * (x * y) = K(x,y) * ((y * x) / 1). K(x,y) * ((y * x) / 1) = K(K(x,y),y * x) * (x * y). T(x,y) * ((z * (T(x,y) \ 1)) / z) = T(x * ((z * (x \ 1)) / z),y). T(x * ((y * (x \ 1)) / y),z) = T(x,z) * ((y * (T(x,z) \ 1)) / y). x \ ((y * ((z * (y \ 1)) / z)) * x) = T(y,x) * ((z * (T(y,x) \ 1)) / z). x \ ((y * x) * ((z * ((y * x) \ x)) / z)) = T(y,x) * ((z * (T(y,x) \ 1)) / z). (K(x,y) * (z * u)) \ (K(x,y) * (z * (u * w))) = L(w,L(u,z,K(x,y)),K(x,y) * z). K(x \ 1,x) * R(K(x \ 1,x) \ x,y,z) = ((x \ 1) * R((x \ 1) \ 1,y,z)) * x. T(x \ L(x * ((y * z) / y),u,w),y) = T(x \ 1,y) * L(T(x \ 1,y) \ z,u,w). T(x * L(x \ ((y * z) / y),u,w),y) = T(x,y) * L(T(x,y) \ z,u,w). T(x,y) * L(T(x,y) \ z,u,w) = T(x * L(x \ ((y * z) / y),u,w),y). T((x / T(x,y)) * (x \ T(x,y)),y) = K(T(x,y),x / T(x,y)). T((x / T(x,y)) * (x \ T(x,y)),y) = x \ (T(x,y) * (x / T(x,y))). T((x / T(x,y)) * (T(x,y) * (x \ 1)),y) = x \ (T(x,y) * (x / T(x,y))). T(x * L(x \ 1,T(x,y),x / T(x,y)),y) = x \ (T(x,y) * (x / T(x,y))). x \ (T(x,y) * (x / T(x,y))) = T(x * L(x \ 1,T(x,y),x / T(x,y)),y). T(x * L(x \ 1,y,z),u) / T(x,u) = L(1 / T(x,u),y,z). T(x,y) * L(T(x,y) \ 1,z,u) = T(x * L(x \ 1,z,u),y). T(x * L(x \ 1,y,z),u) = T(x,u) * L(T(x,u) \ 1,y,z). x * (T(y,x) * L(T(y,x) \ 1,z,u)) = (y * L(y \ 1,z,u)) * x. x * (T(y,x) * L(T(y,x) \ 1,z,u)) = y * (x * L(x \ (y \ x),z,u)). x \ (y * (x * L(x \ (y \ (x * z)),u,w))) = T(y,x) * L(T(y,x) \ z,u,w). x * (T(y,x) * L(T(y,x) \ z,u,w)) = y * (x * L(x \ (y \ (x * z)),u,w)). (x * y) * L((x * y) \ (y * z),u,w) = y * (T(x,y) * L(T(x,y) \ z,u,w)). K(x \ 1,x) * T(K(x \ 1,x) \ y,z) = (x \ 1) * (x * T(x \ ((x \ 1) \ y),z)). K(x,y) * ((y * x) / K(x * y,K(K(x,y),y * x))) = K(K(x,y),y * x) * (x * y). K(K(x,y),y * x) * (x * y) = K(x,y) * ((y * x) / K(x * y,K(K(x,y),y * x))). (x * y) * (z * T(z \ L(y \ z,y,x),u)) = (x * (y * T(y \ 1,u))) * z. (x * (y * T(y \ 1,z))) * u = (x * y) * (u * T(u \ L(y \ u,y,x),z)). (L(x,1 / x,y) * y) / L(x,1 / x,y) = y * ((1 / x) * T(x,y)). T(T((x / y) * R((x / y) \ 1,z,u),w),y) = T((y \ x) * R((y \ x) \ 1,z,u),w). T((x \ y) * R((x \ y) \ 1,z,u),w) = T(T((y / x) * R((y / x) \ 1,z,u),w),x). T((x / y) * R((x / y) \ 1,z,u),y) = (y \ x) * R((y \ x) \ 1,z,u). (x / y) * ((z * ((x / y) \ 1)) / z) = (x * ((z * (x \ y)) / z)) / y. (x * ((y * (x \ z)) / y)) / z = (x / z) * ((y * ((x / z) \ 1)) / y). T((x / y) * R((x / y) \ 1,z,u),y) = (y \ x) * R(T(x / y,y) \ 1,z,u). (x \ y) * R(T(y / x,x) \ 1,z,u) = T((y / x) * R((y / x) \ 1,z,u),x). T(x,y) * R(T(x,y) \ 1,z,u) = T(x * R(x \ 1,z,u),y). T(x * R(x \ 1,y,z),u) = T(x,u) * R(T(x,u) \ 1,y,z). x * (T(y,x) * R(T(y,x) \ 1,z,u)) = (y * R(y \ 1,z,u)) * x. x * (T(y,x) * R(T(y,x) \ 1,z,u)) = (y * x) * R((y * x) \ x,z,u). (x * y) * R((x * y) \ y,z,u) = y * (T(x,y) * R(T(x,y) \ 1,z,u)). (x * ((y * (x \ z)) / y)) / ((x / z) \ x) = (x / z) * ((y * ((x / z) \ 1)) / y). (x * ((y * (x \ (z \ x))) / y)) / (z \ x) = z * ((y * (z \ 1)) / y). (x * ((y * (x \ 1)) / y)) * (x \ z) = z * ((y * (z \ (x \ z))) / y). (((x * (1 / y)) / x) * y) * (y \ z) = z * ((x * (z \ (y \ z))) / x). ((x * ((y \ z) / z)) / x) * z = (((x * (1 / y)) / x) * y) * (y \ z). R(L(x,y,z),T(1 / x,L(x,y,z)),x) \ L(x,y,z) = (L(x,y,z) \ (L(x,y,z) / x)) * x. L(x,y,z) = ((z * y) * x) \ ((z * (y * x)) * x). ((x * y) * z) \ ((x * (y * z)) * z) = L(z,y,x). (x / L(x,y,z)) / x = 1 / L(x,y,z). ((x / L(y,z,u)) * y) \ (x * y) = L(y,z,u). (x / L(y,z,u)) / y = (x / y) / L(y,z,u). (x / y) / L(y,z,u) = (x / L(y,z,u)) / y. ((x / L(y,z,u)) * y) * L(y,z,u) = x * y. x * y = ((x / L(y,z,u)) * y) * L(y,z,u). ((x / L(y,z,u)) / y) * L(y,z,u) = x / y. x / y = ((x / L(y,z,u)) / y) * L(y,z,u). L(x,y,z) \ (L(x,y,z) / x) = T(1 / x,L(x,y,z)). T(1 / x,L(x,y,z)) = L(x,y,z) \ (L(x,y,z) / x). (x * L(y,z,u)) * y = (x * y) * L(y,z,u). (R(x,L(y,z,u) / y,y) / y) * L(y,z,u) = x * (L(y,z,u) / y). x * y != R(z,u / y,y) * u | x = z * (u / y). (1 / x) * L(x,y,z) = L(x,y,z) / x. (x * L(y,z,u)) / y = (x / y) * L(y,z,u). ((x / y) * L(y,z,u)) * y = x * L(y,z,u). ((x / y) * L((x / y) \ x,z,u)) * y = x * L(y,z,u). ((x / y) * L((x / y) \ z,u,w)) * y = x * L(x \ (z * y),u,w). ((x / y) * L((x / y) \ z,u,w)) * y = L((z * y) / x,u,w) * x. (L(x / (y / z),u,w) * (y / z)) * z = L((x * z) / y,u,w) * y. (x * (y * T(y \ 1,x))) \ (x \ ((L(y \ 1,y,x) * x) / L(y \ 1,y,x))) = (L(y \ 1,y,x) \ (L(y \ 1,y,x) * x)) \ 1. (L(x \ 1,x,y) * y) / L(x \ 1,x,y) = y * (x * T(x \ 1,y)). K((x \ (y \ z)) \ ((x \ (y \ z)) / (((((y * x) \ z) \ (x \ (y \ z))) / (x \ (y \ z))) \ 1)),x \ (y \ z)) = ((((y * x) \ z) \ (x \ (y \ z))) / (x \ (y \ z))) \ (((y * x) \ z) \ 1). (x \ (y \ z)) \ (((y * x) \ z) \ (x \ (y \ z))) = ((y * x) \ z) \ 1. (1 / x) * L((1 / x) \ y,z,u) = L(y * x,z,u) / x. L(x * y,z,u) / y = (1 / y) * L((1 / y) \ x,z,u). x * T(y,y \ z) = x * ((y \ z) \ z). x \ (y * (((y / x) * (y \ x)) / (y / x))) = (x \ y) * (((x \ y) \ (y / x)) / (y / x)). (x \ y) * (((x \ y) \ (y / x)) / (y / x)) = x \ (y * (((y / x) * (y \ x)) / (y / x))). x \ ((y * x) * ((z * ((y * x) \ x)) / z)) = T(y,x) * ((z * ((x \ (y * x)) \ 1)) / z). T(x,y) * ((z * ((y \ (x * y)) \ 1)) / z) = y \ ((x * y) * ((z * ((x * y) \ y)) / z)). (x \ y) * ((z * ((x \ y) \ 1)) / z) = x \ (y * ((z * (y \ x)) / z)). x \ (y * ((z * (y \ x)) / z)) = (x \ y) * ((z * ((x \ y) \ 1)) / z). R((x \ y) * x,z,u) = (x \ R(y,z,u)) * x. (x \ R(y,z,u)) * x = R((x \ y) * x,z,u). x \ R(x * (y / x),z,u) = R(y,z,u) / x. R(x,y,z) / u = u \ R(u * (x / u),y,z). (x \ R(x * y,z,u)) * x = R(y * x,z,u). R(x * y,z,u) / y = y \ R(y * x,z,u). (x \ 1) * R((x \ 1) \ y,z,u) = R(y * x,z,u) / x. ((x \ (y / (1 / z))) * x) * (1 / z) = x * (T((x \ y) * z,x) / z). x * (T((x \ y) * z,x) / z) = ((x \ (y / (1 / z))) * x) * (1 / z). (1 / x) * T((1 / x) \ y,z) = T(y * x,z) / x. (1 / x) * T((1 / x) \ (y / x),z) = T(y,z) / x. T(x,y) / z = (1 / z) * T((1 / z) \ (x / z),y). (x \ y) * ((y \ T(x,x \ y)) * y) = K(y \ x,y) * y. (x \ y) * ((y \ T(x,x \ y)) * y) = (x \ ((y \ x) * y)) * y. (T(x,y) * (R(x,z,u) * y)) \ ((x * y) * R(T(x,y),z,u)) = K(R(x,z,u) * y,T(x,y)). K(R(x,y,z) * u,T(x,u)) = (T(x,u) * (R(x,y,z) * u)) \ ((x * u) * R(T(x,u),y,z)). (R(x,y,z) * u) * T(x,u) = (x * u) * R(T(x,u),y,z). (x * y) * R(T(x,y),z,u) = (R(x,z,u) * y) * T(x,y). (x * y) * R(y \ (x * y),z,u) = (R(x,z,u) * y) * T(x,y). (R(x,y,z) * u) * T(x,u) = (x * u) * R(u \ (x * u),y,z). (R(x,y,z) * u) * (u \ (x * u)) = (x * u) * R(u \ (x * u),y,z). x \ (y * ((z * (y \ (x * u))) / z)) = (x \ y) * ((z * ((x \ y) \ u)) / z). (x \ 1) * R(K(x,x \ 1) * ((1 / x) \ y),z,u) = R(y * x,z,u) / x. (x * y) \ ((y * x) * T(K(x,y),z)) = K(y,x) * T(K(y,x) \ 1,z). (x * y) * (K(y,x) * T(K(y,x) \ 1,z)) = (y * x) * T(K(x,y),z). (x * y) * K(z \ (z / K(y,x)),z) = (y * x) * T(K(x,y),z). (x * y) * T(K(y,x),z) = (y * x) * K(z \ (z / K(x,y)),z). T(K(x \ 1,x),y) * (T(x,y) \ x) = (T(x,y) \ 1) * x. T((x \ 1) * x,y) * (T(x,y) \ x) = (T(x,y) \ 1) * x. T(x * T(x \ 1,x),y) * (T(x,y) \ x) = (T(x,y) \ 1) * x. K(x \ (x / T(x,y)),x) = T(K(x \ 1,x),y). K(x \ (x / T(y,z)),x) = T(K(x \ (x / y),x),z). T(K(x \ (x / y),x),z) = K(x \ (x / T(y,z)),x). T(x,y) * T(T(x,y) \ 1,z) = T(x * T(x \ 1,z),y). T(x * T(x \ 1,y),z) = T(x,z) * T(T(x,z) \ 1,y). T(x * T(x \ 1,y),x \ y) = K(y \ (x \ y),y). T(x * T(x \ 1,y),z) = K(y \ (y / T(x,z)),y). (x * T(x \ 1,y)) * z = z * K(y \ (y / T(x,z)),y). x * K(y \ (y / T(z,x)),y) = (z * T(z \ 1,y)) * x. x * K(y \ (y / T(z,x)),y) = z * (x * T(x \ (z \ x),y)). x * (T(y,x) * T(T(y,x) \ 1,z)) = y * (x * T(x \ (y \ x),z)). x * (T(y,x) * T(T(y,x) \ 1,z)) = (y * x) * T((y * x) \ x,z). (x * y) * T((x * y) \ y,z) = y * (T(x,y) * T(T(x,y) \ 1,z)). (1 / x) * ((y * x) / y) = ((y * x) / y) / x. (1 / x) * ((y * ((1 / x) \ 1)) / y) = ((y * x) / y) / x. ((x * y) / x) / y = (1 / y) * ((x * ((1 / y) \ 1)) / x). ((x * (1 / (1 / y))) / x) * (1 / y) = ((x * y) / x) / y. ((x * y) / x) / y = ((x * (1 / (1 / y))) / x) * (1 / y). (x * R(x \ 1,x,x \ y)) \ R(1 / x,x,x \ y) = L(x \ 1,x,(x \ y) / y). R(x,T(1 / x,y),x) = T(x,T(1 / x,y)). T(x,T(1 / x,y)) = R(x,T(1 / x,y),x). T(x,(x * T(x \ 1,y)) / x) = R(x,T(1 / x,y),x). R(x,T(1 / x,y),x) = T(x,(x * T(x \ 1,y)) / x). ((1 / x) * ((1 / x) \ T(y,z))) / x = (1 / x) * T((1 / x) \ (y / x),z). ((x \ (y / (z \ 1))) * x) * (z \ 1) = x * (z \ T(z * (x \ y),x)). x * (y \ T(y * (x \ z),x)) = ((x \ (z / (y \ 1))) * x) * (y \ 1). (x \ 1) * (y * T(y \ ((x \ 1) \ z),u)) = (x \ T(x * (z / y),u)) * y. (x \ T(x * (y / z),u)) * z = (x \ 1) * (z * T(z \ ((x \ 1) \ y),u)). x * (y * T(y \ (x \ z),x)) = ((x \ (z / y)) * x) * y. ((x \ (y / z)) * x) * z = x * (z * T(z \ (x \ y),x)). (x * (y * T(y \ (x \ z),u))) / y = x * T(x \ (z / y),u). K(x \ 1,x) * y != (((x \ 1) \ 1) \ z) * u | (x \ z) * u = y. K(x \ 1,x) * (x \ y) = ((x \ 1) \ 1) \ y. x \ (K(x \ 1,x) * y) = K(x \ 1,x) * (x \ y). x * (K(x \ 1,x) * (x \ y)) = K(x \ 1,x) * y. x * (K(x \ 1,x) * (x \ y)) = ((x \ 1) * x) * y. ((x * (y \ z)) * T((x * (y \ z)) \ x,z)) * z = (x * (y \ z)) * ((z \ L(T(y,y \ z),y \ z,x)) * z). (x * (y \ z)) * ((z \ L(T(y,y \ z),y \ z,x)) * z) = ((x * (y \ z)) * T((x * (y \ z)) \ x,z)) * z. (x \ y) * ((y \ T(x,x \ y)) * y) = ((x \ y) * T((x \ y) \ 1,y)) * y. ((x \ y) * T((x \ y) \ 1,y)) * y = (x \ y) * ((y \ T(x,x \ y)) * y). R(x,(x * T(x \ 1,y)) / x,x) = T(x,(x * T(x \ 1,y)) / x). T(x,x * T(x \ 1,y)) = x. x * (K(x \ 1,x) * (x \ y)) = (x * T(x \ 1,x)) * y. x * (y \ T(y * (x \ (y \ 1)),z)) = (x * T(x \ 1,z)) * (y \ 1). (x * T(x \ 1,y)) * y = x * ((y \ (x \ y)) * y). x * ((y \ (x \ y)) * y) = (x * T(x \ 1,y)) * y. (x * T(x \ 1,y)) * x = x * (x * T(x \ 1,y)). x * (x * T(x \ 1,y)) = (x * T(x \ 1,y)) * x. ((x * y) * T((x * y) \ x,z)) * u = (x * y) * (u * T(u \ L(y \ u,y,x),z)). (x * y) * (z * T(z \ L(y \ z,y,x),u)) = ((x * y) * T((x * y) \ x,u)) * z. x * ((y \ (x \ (z * y))) * y) = (x * T(x \ z,y)) * y. (x * T(x \ (y / z),u)) * z = x * (z * T(z \ (x \ y),u)). x * (y * T(y \ (x \ z),u)) = (x * T(x \ (z / y),u)) * y. x * (y * T(y \ (x \ y),z)) = (x * T(x \ 1,z)) * y. x * (y * T(y \ (x \ (z * y)),u)) = (x * T(x \ z,u)) * y. (x * T(x \ y,z)) * u = x * (u * T(u \ (x \ (y * u)),z)). (x * y) * T((x * y) \ (z * y),u) = (x * T(x \ z,u)) * y. (x * y) * T((x * y) \ (z * y),u) = (T(z / x,u) * x) * y. (x * (T(y,z) * u)) / (x * u) = T((x * (y * u)) / (x * u),z). (x * (y * T(T(z,y),u))) / (x * y) = T((x * (z * y)) / (x * y),u). (x * (y * T(z,u))) / (x * y) = T((x * (y * z)) / (x * y),u). T((x * y) / (R(z,x,y) * (x * y)),R(z,x,y)) * ((z * x) * y) = ((R(z,x,y) \ 1) * R(z,x,y)) * (x * y). (K(x,y) * (z * u)) \ ((K(x,y) * z) * (u * w)) = L(w,L(u,z,K(x,y)),K(x,y) * z). x \ (y * (x * L(x \ (y \ z),u,w))) = T(y * L(y \ (z / x),u,w),x). T(x * L(x \ (y / z),u,w),z) = z \ (x * (z * L(z \ (x \ y),u,w))). ((x \ y) \ y) * (z * R(z \ (T(x,x \ y) \ (u * z)),w,v5)) = (T(x,x \ y) * R(T(x,x \ y) \ u,w,v5)) * z. (T(x,x \ y) * R(T(x,x \ y) \ z,u,w)) * v5 = ((x \ y) \ y) * (v5 * R(v5 \ (T(x,x \ y) \ (z * v5)),u,w)). x * (K(x,1 / x) * (x \ y)) = K(x,1 / x) * y. x * (K(x,1 / x) * (x \ y)) = (x * (1 / x)) * y. x * (y * L(y \ (x \ y),x,x \ 1)) = (x * (1 / x)) * y. T(x * ((1 / x) * ((1 / x) \ ((1 / (1 / x)) \ y))),x) = x * ((1 / (1 / x)) \ T(y,x)). T(x * ((1 / x) * y),x) = x * ((1 / x) * T(y,x)). T(x * L(x \ y,x,1 / x),x) = x * ((1 / x) * T(y,x)). T(x * L(x \ y,z,u),x) = x * L(x \ T(y,x),z,u). x * L(x \ T(y,x),z,u) = T(x * L(x \ y,z,u),x). (x * L(x \ (y / z),u,w)) * z = x * (z * L(z \ (x \ y),u,w)). x * (y * L(y \ (x \ z),u,w)) = (x * L(x \ (z / y),u,w)) * y. x * (y * L(y \ (x \ y),z,u)) = (x * L(x \ 1,z,u)) * y. x * L(x \ (x \ (y * x)),z,u) = T(x * L(x \ y,z,u),x). T(x * L(x \ y,z,u),x) = x * L(x \ (x \ (y * x)),z,u). x * L(x \ (y \ x),y,y \ 1) = K(y,1 / y) * (y \ x). x * L(x \ (1 * (y \ x)),y,y \ 1) = K(y,1 / y) * (y \ x). x * L(x \ (1 * (y \ x)),y,y \ 1) = (y * (1 / y)) * (y \ x). (x * (1 / x)) * (x \ y) = y * L(y \ (1 * (x \ y)),x,x \ 1). (x * R(T(y,x),z,u)) * (x \ (y * x)) = (y * x) * R(x \ (y * x),z,u). (x * R(x \ y,z,u)) * (x \ y) = y * R(x \ y,z,u). (x * R(y,z,u)) * y = (x * y) * R(y,z,u). (x * y) * R(y,z,u) = (x * R(y,z,u)) * y. x * (y * R(y \ (x \ (z * y)),u,w)) = (x * R(x \ z,u,w)) * y. (x * R(x \ y,z,u)) * w = x * (w * R(w \ (x \ (y * w)),z,u)). x * (y * L(y \ (x \ (z * y)),u,w)) = (x * L(x \ z,u,w)) * y. (x * R(x \ y,z,u)) * (x \ w) = w * R(w \ (y * (x \ w)),z,u). (x * L(x \ y,z,u)) * (x \ w) = w * L(w \ (y * (x \ w)),z,u). (x * y) * ((z * ((x * y) \ y)) / z) = (x * ((z * (x \ 1)) / z)) * y. K(x \ 1,x) * R(((x \ 1) * x) \ x,y,z) = ((x \ 1) * R((x \ 1) \ 1,y,z)) * x. (x * y) * R((x * y) \ y,z,u) = (x * R(x \ 1,z,u)) * y. (x * y) * R((x * y) \ ((x * z) * y),u,w) = (x * R(z,u,w)) * y. (x * y) * R((x * y) \ (z * y),u,w) = (x * R(x \ z,u,w)) * y. (x * y) * R((x * y) \ y,z,u) = (R(1 / x,z,u) * x) * y. x * (y * L(y \ (x \ (z * y)),u,w)) = (L(z / x,u,w) * x) * y. (L(x / y,z,u) * y) * w = y * (w * L(w \ (y \ (x * w)),z,u)). x * (T(T(y,x),z) * R(T(T(y,x),z) \ (x \ u),w,v5)) = (T(y,z) * x) * R((x * T(T(y,x),z)) \ u,w,v5). (T(x,y) * z) * R((z * T(T(x,z),y)) \ u,w,v5) = z * (T(T(x,z),y) * R(T(T(x,z),y) \ (z \ u),w,v5)). ((L(x,y,z) \ x) / x) \ ((L(x,y,z) \ 1) * (x * (L(x,y,z) \ 1))) = (L(x,y,z) \ 1) * x. ((x * y) / x) \ (y * (x * y)) = y * x. ((x * y) / x) \ (y * (x * y)) = x * R(T(y,x * y),x,y). ((x * y) / x) \ (y * (x * y)) = x * T(R(y,x,y),x * y). L(R(x,y,x),y,(y * x) / y) = x. L(R(x,y,y \ 1),y,(y * x) / y) = T((y * x) * (y \ 1),y * x). T((x * y) * (x \ 1),x * y) = L(R(y,x,x \ 1),x,(x * y) / x). R(x \ 1,y,z) / (x * R(x \ 1,y,z)) = x \ 1. (x \ 1) * (x * R(x \ 1,y,z)) = R(x \ 1,y,z). (R(x / y,z,u) * y) * (y \ w) = w * R(w \ (x * (y \ w)),z,u). (L(x / y,z,u) * y) * (y \ w) = w * L(w \ (x * (y \ w)),z,u). K(x,y) = L(x \ 1,x,y) * T(L(x \ 1,x,y) \ 1,y). L(x \ 1,x,y) * T(L(x \ 1,x,y) \ 1,y) = K(x,y). T(L(x \ 1,x,y) \ 1,y) = L(x \ 1,x,y) \ K(x,y). L(x \ 1,x,y) \ K(x,y) = T(L(x \ 1,x,y) \ 1,y). (x * y) * ((z * ((x * y) \ y)) / z) = (((z * (1 / x)) / z) * x) * y. (((x * (1 / y)) / x) * y) * z = (y * z) * ((x * ((y * z) \ z)) / x). (x * y) * R((x * y) \ (z * y),u,w) = (R(z / x,u,w) * x) * y. (R(x / y,z,u) * y) * w = (y * w) * R((y * w) \ (x * w),z,u). (x * y) * L((x * y) \ (z * y),u,w) = (L(z / x,u,w) * x) * y. (L(x / y,z,u) * y) * w = (y * w) * L((y * w) \ (x * w),z,u). (x * y) * R((y * T(x,y)) \ y,z,u) = y * (T(x,y) * R(T(x,y) \ 1,z,u)). (x * y) * R((x * y) \ z,u,w) = x * (y * R(y \ (x \ z),u,w)). (x * y) * R((x * y) \ x,z,u) = x * (y * R(y \ 1,z,u)). T(((x * y) * z) / (x * z),x * y) = L(R(y,x,z),x,(x * y) / x). T(K(x \ (x / (y \ (y / z))),x),z) = y \ ((y / z) * ((z \ T(z,x)) * z)). x \ ((x / y) * ((y \ T(y,z)) * y)) = T(K(z \ (z / (x \ (x / y))),z),y). x \ ((x / y) * ((y \ z) * y)) = T(x \ ((x / y) * z),y). T(x \ ((x / y) * z),y) = x \ ((x / y) * ((y \ z) * y)). x * T(x \ ((1 / x) \ y),z) = (1 / x) \ T(y,z). (1 / x) \ T(y,z) = x * T(x \ ((1 / x) \ y),z). (T(x,y) * T(T(x,y) \ 1,x)) * (T(x,y) \ x) = (T(x,y) \ 1) * x. (T(x,y) \ 1) * x = (T(x,y) * T(T(x,y) \ 1,x)) * (T(x,y) \ x). (L(x,y,z) * T(L(x,y,z) \ 1,x)) * (L(x,y,z) \ x) = (L(x,y,z) \ 1) * x. (L(x,y,z) \ 1) * x = (L(x,y,z) * T(L(x,y,z) \ 1,x)) * (L(x,y,z) \ x). (x \ (y \ x)) * x = (y * T(y \ 1,x)) * (y \ x). (x * T(x \ 1,y)) * (x \ y) = (y \ (x \ y)) * y. (x * T(x \ 1,y)) * (x \ z) = z * T(z \ (x \ z),y). (T(1 / x,y) * x) * (x \ z) = z * T(z \ (x \ z),y). T((x \ y) / y,z) * y = (T(1 / x,z) * x) * (x \ y). L(R((x * y) / x,z,T(y,z)),z,y) = (x * y) / x. L((x * R(y,z,T(y,z))) / x,z,y) = (x * y) / x. L(R(x,y,T(x,y)),y,x) = x. L(R(x,y,T(x,y)),y,x) = (x * y) \ ((x * y) * x). (x * y) \ ((x * y) * x) = L(R(x,y,T(x,y)),y,x). R(L(x,y,x),y,T(x,y)) = (x * y) \ ((x * y) * x). T(x,x / (y \ 1)) = T(x,y * x). x \ ((y * (x * y)) / y) = T(y,y / (x \ 1)). x \ ((y * (1 \ (x * y))) / y) = T(y,y / (x \ 1)). x * T(K(y,z) * R(u / (K(y,z) * x),w,v5),K(y,z) * x) = (K(y,z) * x) * R((K(y,z) * x) \ u,w,v5). x * T(K(y,z) * u,K(y,z) * x) = u * (K(y,z) * x). x * ((x \ y) * ((z * ((x \ y) \ u)) / z)) = y * ((z * (y \ (x * u))) / z). x * ((y * (x \ (z * u))) / y) = z * ((z \ x) * ((y * ((z \ x) \ u)) / y)). R((x / (y * x)) \ 1,R(1 / y,y,x),y * x) = (K((x / (y * x)) \ 1,x / (y * x)) * (y * x)) / x. (K((x / (y * x)) \ 1,x / (y * x)) * (y * x)) / x = R((x / (y * x)) \ 1,R(1 / y,y,x),y * x). R(x,y * ((x * y) \ z),a(x,y,(x * y) \ z)) \ z = (y * ((x * y) \ z)) * a(x,y,(x * y) \ z). ((L(x,y,z) * (z * y)) / (z * y)) * T(((L(x,y,z) * (z * y)) / (z * y)) \ x,u) = ((L(x,y,z) * (z * y)) * T(a(z,y,T(x,z * y)),u)) / (z * y). ((L(x,y,z) * (z * y)) * T(a(z,y,T(x,z * y)),u)) / (z * y) = ((L(x,y,z) * (z * y)) / (z * y)) * T(((L(x,y,z) * (z * y)) / (z * y)) \ x,u). (L(x,y,z) * (z * y)) * a(z,y,T(x,z * y)) = x * (z * y). (L(x,y,z) * (z * y)) \ (x * (z * y)) = a(z,y,T(x,z * y)). K((x / y) \ 1,x / y) * (y / x) = T(y / x,x / y). T(x / y,y / x) = K((y / x) \ 1,y / x) * (x / y). (K((x / y) \ 1,x / y) * y) / x = T(y / x,x / y). K((x / (y * x)) \ 1,x / (y * x)) * (y * x) = T(y,x / (y * x)) * x. K((x / y) \ 1,x / y) * y = x * T(x \ y,x / y). K((x / y) \ 1,x / y) * y = x * T(x \ (1 * y),x / y). (x / y) * T((x / y) \ z,x) = ((x \ (z * y)) * x) / y. ((x \ (y * z)) * x) / z = (x / z) * T((x / z) \ y,x). (x / y) * T((x / y) \ 1,z) = (x * T(x \ y,z)) / y. (x * T(x \ y,z)) / y = (x / y) * T((x / y) \ 1,z). (x * y) / ((z * y) / z) = (x / ((z * y) / z)) * y. (x / ((y * z) / y)) * z = (x * z) / ((y * z) / y). (((x / y) \ z) * (x / y)) * y = x * T(x \ (z * y),x / y). (x * T(x \ (y * z),u)) / z = (x / z) * T((x / z) \ y,u). (x / ((y * z) / y)) * (y \ (y * z)) = (x * z) / ((y * z) / y). (x * y) / ((z * y) / z) = (x / ((z * y) / z)) * (z \ (z * y)). (x * (y \ z)) / (z / y) = (x / (z / y)) * (y \ z). (x / (y / z)) * (z \ y) = (x * (z \ y)) / (y / z). R((x * y) / x,x,T(y,x)) = T(y * x,y) / x. (x / ((y \ z) \ z)) * T((y \ z) \ z,u) = x * K(u \ (u / (x \ (x / T(y,y \ z)))),u). x / T(y,y \ z) = x / ((y \ z) \ z). L(x \ 1,x,T(x,y) / x) = T(1 / x,T(x,y)). K(x \ (x / (1 / (y / (x * y)))),x) = R(x \ 1,x,y) / (y / (x * y)). K(x \ (x / (1 / y)),x) = T(y,x) / y. (x / T(x,y)) / x = 1 / T(x,y). (x * y) / T(y,y \ z) = (x / ((y \ z) \ z)) * y. (x * y) / T(y,z) != u * y | x / T(y,z) = u. (x / T(y,z)) / y = (x / y) / T(y,z). (x / y) / T(y,z) = (x / T(y,z)) / y. R(T((x * y) / x,y * x),x,T(y,x)) = (y * x) \ ((y * x) * y). R((x * y) / x,x,T(y,x)) = ((y * x) * y) / (y * x). (x * y) * T(y,x) = (y * x) * y. (x * y) * x = (y * x) * T(x,y). (x * y) / T(y,z) = (x / T(y,z)) * y. x \ ((y * (x * y)) / y) = T(y,x * y). T(x,y * x) = y \ ((x * (y * x)) / x). K(x \ (x / (x \ (x / y))),x) = x \ ((y * x) / y). (L(x,1 / x,y) * y) / L(x,1 / x,y) = (y * (1 / x)) * T(L(x,1 / x,y),y). (x * (1 / y)) * T(L(y,1 / y,x),x) = (L(y,1 / y,x) * x) / L(y,1 / y,x). (L(x \ 1,x,y) * y) / L(x \ 1,x,y) = (y * x) * T(L(x \ 1,x,y),y). (x * y) * T(L(y \ 1,y,x),x) = (L(y \ 1,y,x) * x) / L(y \ 1,y,x). T(x,y) = (y / x) \ ((x * y) / x). (x / y) \ ((y * x) / y) = T(y,x). (x / (y / z)) * T(y / z,z) = (x * (z \ y)) / (y / z). (x * (y \ z)) / (z / y) = (x / (z / y)) * T(z / y,y). (x / y) * T(y,x) = (y * x) / y. (x * y) / x = (y / x) * T(x,y). ((x / T(y,z)) / y) * T(y,z) = x / y. x / y = ((x / T(y,z)) / y) * T(y,z). L(K(x,y),x,1 / x) = L(T(x,y) / x,x,y). L(T(x,y) / x,x,y) = L(K(x,y),x,1 / x). T(x \ 1,y) / (x \ 1) = x * T(x \ 1,y). x * T(x \ 1,y) = T(x \ 1,y) / (x \ 1). T(x,y) \ (T(x,y) / x) = T(1 / x,T(x,y)). T(1 / x,T(x,y)) = T(x,y) \ (T(x,y) / x). T((x / y) * T(y,z),y) = y \ (x * T(y,z)). (x * T(y,z)) * y = (x * y) * T(y,z). (1 / x) * T(x,y) = T(x,y) / x. ((x / y) * T(y,z)) \ (x * T(y,z)) = y. (x * T(y,z)) / y = (x / y) * T(y,z). ((x / y) * T(y,z)) * y = x * T(y,z). (1 / x) * T((1 / x) \ 1,y) = T(x,y) / x. x * y != 1 * z | x = z / y. ((x / y) * T((x / y) \ x,z)) * y = x * T(y,z). ((x / y) * T((x / y) \ z,u)) * y = x * T(x \ (z * y),u). x \ T(y,y / (x * y)) = y * ((x \ y) / y). (((x * y) / x) \ 1) * T(y,((x * y) / x) \ 1) = ((x * y) / x) \ y. x * (((y * x) / y) \ 1) = ((y * x) / y) \ x. (x * y) * L((x \ y) / y,y,x) = T(y,y / (x * y)). x \ L((y * ((x \ 1) \ y)) / y,x \ 1,x) = T(y,y / (x \ 1)). x * ((y * (x \ y)) / y) = T(y,y / x). T(x,x / y) = y * ((x * (y \ x)) / x). ((x * y) * x) / (x * y) = T(x * y,x) / y. T(x * y,x) / y = ((x * y) * x) / (x * y). ((x * (x / y)) / x) * y = T(x,x / y). T(x,x / y) = ((x * (x / y)) / x) * y. T(x,y) / (y \ x) = (x * y) / x. T(x,y) = ((x * y) / x) * (y \ x). ((x * y) / x) * (y \ x) = T(x,y). ((x * y) / x) \ T(x,y) = y \ x. ((x * y) / x) \ (y \ (x * y)) = y \ x. x \ (((y * x) / y) \ x) = ((y * x) / y) \ 1. ((x * y) / x) \ 1 = y \ (((x * y) / x) \ y). ((x * y) / x) \ (y \ ((x * y) / x)) = (x \ (x * y)) \ 1. (x \ (x * y)) \ 1 = ((x * y) / x) \ (y \ ((x * y) / x)). ((x * y) / x) \ (y \ z) = y \ (((x * y) / x) \ z). x \ (((y * x) / y) \ z) = ((y * x) / y) \ (x \ z). (x / (x / y)) \ (y \ (x / (x / y))) = y \ 1. (x / (x / y)) \ (y \ (((x / y) * y) / (x / y))) = y \ 1. ((x * y) / x) \ (y \ ((x * y) / x)) = y \ 1. ((x * y) / x) * (y \ 1) = y \ ((x * y) / x). x \ ((y * x) / y) = ((y * x) / y) * (x \ 1). x * (((y * x) / y) * (x \ z)) = ((y * x) / y) * z. ((x * y) / x) * z = y * (((x * y) / x) * (y \ z)). ((x * y) / x) * (y * z) = y * (((x * y) / x) * z). x * (((y * x) / y) * z) = ((y * x) / y) * (x * z). L(x,T(x,y) \ 1,T(x,y)) = x * K(x \ (x / T(x,y)),x). x * K(x \ (x / T(x,y)),x) = L(x,T(x,y) \ 1,T(x,y)). (R(x,y,z) / x) / R(x,y,z) = 1 / x. (1 / x) * R(x,y,z) = R(x,y,z) / x. (x \ 1) * (K(x,x \ 1) * R((1 / x) \ y,z,u)) = R(y * x,z,u) / x. (1 / x) * R((1 / x) \ 1,y,z) = R(x,y,z) / x. (1 / x) * R((1 / x) \ y,z,u) = R(y * x,z,u) / x. R(x * y,z,u) / y = (1 / y) * R((1 / y) \ x,z,u). R(x / (1 / y),z,u) * (1 / y) = R(x * y,z,u) / y. (x \ 1) * L((x \ 1) \ y,z,u) = x \ L(x * y,z,u). (x \ 1) * R((x \ 1) \ y,z,u) = x \ R(x * y,z,u). ((x / y) * T((x / y) \ z,u)) * y = T((z * y) / x,u) * x. K(x \ (x / (y \ (y / z))),x) = y \ ((y / z) * T(z,x)). x \ ((x / y) * T(y,z)) = K(z \ (z / (x \ (x / y))),z). K(x * y,K(K(x,y),y * x)) = 1. K(x * K(y,z),K(K(y,z),x)) = 1. T(x * K(y,z),K(K(y,z),x)) = x * K(y,z). x * K(y,z) = T(x * K(y,z),K(K(y,z),x)). K(K(x,y),z) \ (K(x,y) * z) = z * K(x,y). (x \ (x * y)) \ (((x * y) / x) \ z) = ((x * y) / x) \ (y \ z). ((x * y) / x) \ (y \ z) = (x \ (x * y)) \ (((x * y) / x) \ z). L(T(x,y) \ 1,x,x \ 1) = (1 / x) * (T(x,y) \ x). (1 / x) * (T(x,y) \ x) = L(T(x,y) \ 1,x,x \ 1). L(x \ 1,x,x \ 1) = 1 / x. 1 / x = L(x \ 1,x,x \ 1). (1 / x) * (x * y) = L(y,x,x \ 1). K(x \ 1,x) * R(1 / x,y,z) = (x \ 1) * (x * R(x \ 1,y,z)). (x \ 1) * (x * R(x \ 1,y,z)) = K(x \ 1,x) * R(1 / x,y,z). (1 / x) \ L(y,x,x \ 1) = x * y. (x \ 1) * y != K(x \ 1,x) * L(z,x,x \ 1) | y = x * z. (x \ 1) * ((1 / x) \ y) = K(x \ 1,x) * y. (x \ 1) \ (K(x \ 1,x) * y) = (1 / x) \ y. (1 / x) \ y = (x \ 1) \ (K(x \ 1,x) * y). (1 / x) * ((x \ 1) \ (K(x \ 1,x) * y)) = y. x = (1 / y) * ((y \ 1) \ (K(y \ 1,y) * x)). (x \ y) * z != (y / x) * u | z = (y / x) * ((x \ y) \ u). ((x \ 1) \ 1) \ ((x \ 1) \ y) = x \ ((1 / x) \ y). x \ ((1 / x) \ y) = ((x \ 1) \ 1) \ ((x \ 1) \ y). ((x \ 1) \ 1) \ K(x,x \ 1) = x \ 1. x \ 1 = ((x \ 1) \ 1) \ K(x,x \ 1). (1 / x) * (K(x \ 1,x) * y) = (x \ 1) * y. K(x,x \ 1) \ ((x \ 1) \ 1) = x. x \ (K(x \ 1,x) * y) = ((x \ 1) \ 1) \ y. K(x \ 1,x) * ((x \ 1) \ 1) = x. (1 / x) \ ((x \ 1) * y) = K(x \ 1,x) * y. K(x \ 1,x) * y = (1 / x) \ ((x \ 1) * y). K(x \ 1,x) * ((x \ 1) \ y) = (1 / x) \ y. K(x,x \ 1) * ((1 / x) \ y) = (x \ 1) \ y. (x \ 1) \ y = K(x,x \ 1) * ((1 / x) \ y). (x / y) \ ((y \ x) \ z) = (y \ x) \ ((x / y) \ z). (x \ 1) * (K(x,x \ 1) * y) = (1 / x) * y. (x / y) * ((y \ x) \ ((x / y) \ z)) = (y \ x) \ z. (x \ y) \ z = (y / x) * ((x \ y) \ ((y / x) \ z)). (x / y) * ((y \ x) \ 1) = (y \ x) \ (x / y). (x \ y) \ (y / x) = (y / x) * ((x \ y) \ 1). (x \ y) * ((y / x) * ((x \ y) \ z)) = (y / x) * z. (x / y) * z = (y \ x) * ((x / y) * ((y \ x) \ z)). (x \ y) \ ((y / x) * z) = (y / x) * ((x \ y) \ z). (x \ (x * y)) * (((x * y) / x) * z) = ((x * y) / x) * (y * z). ((x * y) / x) * (y * z) = (x \ (x * y)) * (((x * y) / x) * z). (x / y) * ((y \ x) * z) = (y \ x) * ((x / y) * z). x \ (y * K((y \ x) \ 1,y \ x)) = T(x \ y,y \ x). (x / y) * T(y,z) = x * K(z \ (z / (x \ (x / y))),z). (x * y) * T((x * y) \ (y * x),z) = (y * x) * K(z \ (z / K(x,y)),z). x \ (y * K(z \ (z / (y \ x)),z)) = T(x \ y,z). x * T(x \ y,z) = y * K(z \ (z / (y \ x)),z). x * K(y \ (y / (x \ z)),y) = z * T(z \ x,y). (1 / x) \ T(1 / x,y) = x * T(x \ 1,y). T(x,y) * (x \ T(x,z)) = T(x,z) * (x \ T(x,y)). (x / y) * (y * T(y \ x,z)) = T(x / y,z) * x. K(K(x,y),K(x,y) * z) \ (K(x,y) * z) = z * K(x,y). K(K(x,y),z) \ z = T(z,K(x,y)). T(x,K(y,z)) = K(K(y,z),x) \ x. 1 / (x \ K(K(y,z),x)) = T(x,K(y,z)). T(x,K(y,z)) * (x \ K(K(y,z),x)) = 1. T(x,y) * ((T(x,y) \ 1) * x) = x * K(x \ (x / T(x,y)),x). x * K(x \ (x / T(x,y)),x) = T(x,y) * ((T(x,y) \ 1) * x). T((1 / x) * (T(x,y) \ x),x) = (1 / x) * ((T(x,y) \ 1) * x). (1 / x) * ((T(x,y) \ 1) * x) = T((1 / x) * (T(x,y) \ x),x). T((T(x,y) \ x) / x,x) = T(x,y) \ 1. x \ (T(x,y) \ x) = T(x,y) \ 1. x * (T(x,y) \ 1) = T(x,y) \ x. T(x,y) \ x = x * (T(x,y) \ 1). (x / y) * (T(x / y,y) * z) = (y \ x) * ((x / y) * z). (x \ y) * ((y / x) * z) = (y / x) * (T(y / x,x) * z). T(x,y) \ (x * z) = x * (T(x,y) \ z). x * (T(x,y) \ z) = T(x,y) \ (x * z). T(x,K(y,z)) * (x \ K(K(y,z),x)) = x \ x. x \ x = T(x,K(y,z)) * (x \ K(K(y,z),x)). x \ (T(x,y) * T(x,z)) = T(x,z) * (x \ T(x,y)). x \ (T(x,y) * (x / z)) = T(x,y) * L(z \ 1,z,x / z). T(x,y) * (x \ (T(x,y) \ z)) = x \ z. x \ y = T(x,z) * (x \ (T(x,z) \ y)). (x / y) * (T(x / y,z) * y) = T(x / y,z) * x. x * (T(x,y) * T(z,x)) = T(x,y) * (z * 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) = T(x,y) * (x \ z). x * (T(x,y) * (x \ z)) = T(x,y) * z. x * T(x \ (y * x),z) = y * (T(y,z) * (y \ x)). x * (T(x,y) * (x \ z)) = z * T(z \ (x * z),y). x * ((x \ y) * T((x \ y) \ 1,z)) = y * T(y \ x,z). (x \ (y \ z)) \ (((y * x) \ z) \ (x \ (y \ z))) = L(x \ (y \ z),x,y) \ 1. x \ (L(x,y,z) \ x) = L(x,y,z) \ 1. x * (L(x,y,z) \ 1) = L(x,y,z) \ x. L(x,y,z) \ x = x * (L(x,y,z) \ 1). L(x,y,z) \ (x * u) = x * (L(x,y,z) \ u). x * (L(x,y,z) \ u) = L(x,y,z) \ (x * u). x * y != z * (u * (u \ w)) | y = x \ (z * w). L(x,y,z) * (x * u) = x * (L(x,y,z) * u). x * (L(x,y,z) * u) = L(x,y,z) * (x * u). x * (y * L(T(x,y),z,u)) = L(x,z,u) * (x * y). R(x / y,y / x,(y / x) \ 1) = T(x / y,y / x). R(x / y,y / x,(y / x) \ 1) = T((1 * x) / y,y / x). R(x,y,x) * T(y,x) = T(x * y,x). R(x,y,x) * (x \ (y * x)) = T(x * y,x). T(x * y,x) = R(x,y,x) * (x \ (y * x)). (x \ 1) * R((x \ 1) \ 1,y,z) = x \ R(x,y,z). R(x,y,z) * (x \ (y * z)) = x \ ((x * y) * z). x \ ((x * y) * z) = R(x,y,z) * (x \ (y * z)). R(x,y,z) * (x \ 1) = x \ R(x,y,z). x \ R(x,y,z) = R(x,y,z) * (x \ 1). 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) * u) = R(x,y,z) * (x \ u). 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(T(x,y),z,u)) = R(x,z,u) * (x * y). ((x * ((y * z) \ y)) * u) / (L(z \ 1,z,y) * u) = R(x,(y * z) \ y,u). R(x,(y * z) \ y,u) = ((x * ((y * z) \ y)) * u) / (L(z \ 1,z,y) * u). L(x \ 1,x,y) * z = ((y * x) \ y) * z. K(x / (y * x),(x / (y * x)) \ z) = (((x / (y * x)) \ z) * R(1 / y,y,x)) \ z. (((x / (y * x)) \ z) * R(1 / y,y,x)) \ z = K(x / (y * x),(x / (y * x)) \ z). K((x / (y * x)) \ 1,x / (y * x)) = ((x / (y * x)) \ 1) * R(1 / y,y,x). (x * (y / (z * y))) / R(1 / z,z,y) = x. x * R(1 / y,y,z) = x * (z / (y * z)). T(x,K(y,z)) * K(K(y,z),x) = x. T(x,K(y,z)) \ x = K(K(y,z),x). K(K(x,y),z) = T(z,K(x,y)) \ z. K(K(x,y),K(x,y) \ z) = K(K(x,y),z). K(K(x,y),z) = K(K(x,y),K(x,y) \ z). K(K(x,y),K(x,y) * z) = K(K(x,y),z). K(K(x,y),z) = K(K(x,y),K(x,y) * z). (x * K(y,z)) \ (K(y,z) * x) = K(K(y,z),K(y,z) * x). K(K(x,y),K(x,y) * z) = (z * K(x,y)) \ (K(x,y) * z). R(x \ 1,y,z) / R(1 / x,y,z) = K(x \ 1,x). K(x \ 1,x) * R(1 / x,y,z) = R(x \ 1,y,z). K(x,x \ 1) * (R(x \ 1,y,z) * u) = R(1 / x,y,z) * u. R(1 / x,y,z) * u = K(x,x \ 1) * (R(x \ 1,y,z) * u). K(x,x \ 1) * R(x \ 1,y,z) = R(1 / x,y,z). R(1 / x,y,z) = K(x,x \ 1) * R(x \ 1,y,z). R(K(x,y) * z,u,w) = K(x,y) * R(z,u,w). x / (K(y \ 1,y) * x) = K(y,y \ 1). K(x \ 1,x) * y != z | K(x,x \ 1) * z = y. x != K(y \ 1,y) * z | K(y,y \ 1) * x = z. K(x,x \ 1) \ y = K(x \ 1,x) * y. K(x \ 1,x) * y = K(x,x \ 1) \ y. (1 / x) * ((x \ 1) \ y) = K(x,x \ 1) * y. K(x,x \ 1) * ((x \ 1) * y) = (1 / x) * y. (1 / x) * y = K(x,x \ 1) * ((x \ 1) * y). K(x,x \ 1) \ 1 = K(x \ 1,x). K(x,x \ 1) * (x \ 1) = 1 / x. K(x,x \ 1) * K(x \ 1,x) = 1. K(x \ 1,x) * (K(x,x \ 1) * y) = y. K(x \ 1,x) \ y = K(x,x \ 1) * y. (1 / x) * ((y * (x \ 1)) * x) = R((1 / x) * y,x,x \ 1). R(T(x / y,z * y),y,T(z,y)) = (z * y) \ (x * T(z,y)). (x * (y * (x \ 1))) / x = (x * (y / x)) * (x \ 1). ((x \ y) \ y) * T(z,T(x,x \ y)) = z * T(x,x \ y). (T(x,x \ y) * z) \ (z * ((x \ y) \ y)) = K(z,(x \ y) \ y). K(x,(y \ z) \ z) = (T(y,y \ z) * x) \ (x * ((y \ z) \ z)). T(x,x \ y) * z = ((x \ y) \ y) * z. R(x / (1 / y),z,u) * (1 / y) = R((x * y) / 1,z,u) / y. R((x * y) / 1,z,u) / y = R(x / (1 / y),z,u) * (1 / y). (x \ 1) * L((x \ 1) \ y,z,u) = x \ L(1 \ (x * y),z,u). x \ L(1 \ (x * y),z,u) = (x \ 1) * L((x \ 1) \ y,z,u). (x \ 1) * R((x \ 1) \ y,z,u) = x \ R(1 \ (x * y),z,u). x \ R(1 \ (x * y),z,u) = (x \ 1) * R((x \ 1) \ y,z,u). R((x * (y \ z)) / z,u,w) * z = (R(x / y,u,w) * y) * (y \ z). L((x * (y \ z)) / z,u,w) * z = (L(x / y,u,w) * y) * (y \ z). (K(x,y) * ((z * u) * w)) / (u * w) = R(K(x,y) * z,u,w). K(x \ (x / ((y / x) \ 1)),x) = (y / x) \ (x \ y). L(x,y,z \ T(z,u)) = x. L(x \ 1,x,y) \ K(y \ (y * x),y) = T(L(x \ 1,x,y) \ 1,y). K(x \ (x / (y \ 1)),x) = y \ T(y,x). x \ K(y \ (y / x),y) = T(x \ 1,y). K(x \ (x / y),x) = y * T(y \ 1,x). x * T(x \ 1,y) = K(y \ (y / x),y). R(K(x \ 1,x),K(x,x \ 1),y) \ y = K(x,x \ 1) * y. x \ (y \ ((L(z,x,y) * y) * x)) = R(T(z,y * x),y,x). K(x \ 1,x) * (x \ y) = y * T(y \ (x \ y),x). ((x \ 1) * x) * (x \ y) = y * T(y \ (x \ y),x). T(x,y) * (x \ 1) = x \ T(x,y). x \ T(x,y) = T(x,y) * (x \ 1). (x \ 1) * T((x \ 1) \ 1,y) = x \ T(x,y). (x \ 1) * T((x \ 1) \ y,z) = x \ T(x * y,z). (1 / x) \ L((1 / x) * K(x \ 1,x),y,z) = x * L(T(x \ 1,x),y,z). (1 / x) * ((y / (x * y)) * x) = R(1 / x,x,y). (1 / x) \ R(1 / x,y,z) = x * R(x \ 1,y,z). (1 / x) * (((y * z) / (x * z)) * x) = R((1 / x) * y,x,z). (1 / x) * (x * R(x \ 1,y,z)) = R(1 / x,y,z). x \ ((L(y,z,x) * x) * z) = z * R(T(y,x * z),x,z). (x \ y) * T((x \ y) \ 1,y) = x \ ((y \ x) * y). ((x \ y) * x) * (x \ z) = z * T(z \ (y * (x \ z)),x). R(K(x,y),z,u) \ (w * (K(x,y) * v5)) = v5 * T(w,K(x,y) * v5). K(x,1 / x) * T(K(x,1 / x) \ (K(x,1 / x) / (1 / x)),y) = x * ((1 / x) * T((1 / x) \ 1,y)). x * ((1 / x) * T((1 / x) \ 1,y)) = K(x,1 / x) * T(K(x,1 / x) \ (K(x,1 / x) / (1 / x)),y). (x * (y * z)) * T(((x * y) * L(z,y,x)) \ (x * y),u) = (x * y) * (L(z,y,x) * T(L(z,y,x) \ 1,u)). (x * y) * T((y * T(x,y)) \ y,z) = y * (T(x,y) * T(T(x,y) \ 1,z)). x * R(T(y,x * y),x,y) = y * x. R(T(x,y),y / x,x) = T(x,y / x). R(T(x,y * x),y,x) = T(x,y). T(x,y) = R(T(x,y * x),y,x). L(T(x,y),y,(y * x) / y) = T(x,y * x). T((x * y) \ ((x * z) * y),x) = R(T(z,x * y),x,y). R(T(x,y * z),y,z) = T((y * z) \ ((y * x) * z),y). L(T(x,y),y,(y * x) / y) = T(y \ (y * x),y * x). R(T(x \ y,x * z),x,z) = T((x * z) \ (y * z),x). ((x * ((y \ z) / (y * (y \ z)))) / x) * z = (((x * (1 / y)) / x) * y) * (y \ z). ((x * (y / ((1 / y) * y))) / x) / y = ((x * (1 / (1 / y))) / x) * (1 / y). ((x * (y / (z * y))) / x) * (z * y) = (((x * (1 / z)) / x) * z) * y. (T(x / (y / z),u) * (y / z)) * z = T((x * z) / y,u) * y. T((x * y) / z,u) * z = (T(x / (z / y),u) * (z / y)) * y. x * ((x \ y) * T((x \ y) \ z,u)) = y * T(y \ (x * z),u). x * T(x \ (y * z),u) = y * ((y \ x) * T((y \ x) \ z,u)). (x \ 1) * T((x \ 1) \ y,z) = x \ T(1 \ (x * y),z). x \ T(1 \ (x * y),z) = (x \ 1) * T((x \ 1) \ y,z). L(R(x / (1 / y),1 / y,y),z,u) / y = (1 / y) * L((1 / y) \ x,z,u). L((1 / x) * T(x,y),x,y) = L(K(x,y),x,1 / x). L(K(x,y),x,1 / x) = L((1 / x) * T(x,y),x,y). (1 / x) \ L((1 / x) * y,z,u) = x * L(x \ y,z,u). (1 / x) * (x * R(x \ y,z,u)) = R((1 / x) * y,z,u). (x * y) / L(T(z \ y,(z \ y) \ y),(z \ y) \ y,x) = x * T(z,z \ y). R((x * y) / (z * y),u,w) * (z * y) = (R(x / z,u,w) * z) * y. R(R(x,y \ 1,y),z,u) * K(y \ 1,y) = (R(x,z,u) * (y \ 1)) * y. x \ ((L(y,z,x) * x) * z) = z * T(R(y,x,z),x * z). (L(x / (y / z),u,w) * (y / z)) * z = L((x * z) / y,u,w) * ((y / z) * z). L((x * y) / z,u,w) * ((z / y) * y) = (L(x / (z / y),u,w) * (z / y)) * y. (L(K(x,y),z,u) * w) * v5 = L(K(x,y),z,u) * (w * v5). L(K(x,y),z,u) * (w * v5) = (L(K(x,y),z,u) * w) * v5. L((x * y) / (z * y),u,w) * (z * y) = (L(x / z,u,w) * z) * y. (x * y) * L((y * T(x,y)) \ (y * z),u,w) = y * (T(x,y) * L(T(x,y) \ z,u,w)). (x * y) * R((x * y) \ (x * z),u,w) = x * (y * R(y \ z,u,w)). K(x \ 1,x) * T(((x \ 1) * x) \ y,z) = (x \ 1) * (x * T(x \ ((x \ 1) \ y),z)). (x * y) * L(T(x,x * y),z,u) = x * (y * L(T(x,y),z,u)). (x * y) * L((x * y) \ z,u,w) = x * (y * L(y \ (x \ z),u,w)). x \ ((x / y) * K(y \ 1,y)) = T(x \ (x / y),y). T(T(x,x * y) * y,T(x,y)) = x * y. R(x / y,y / x,(y / x) \ 1) = R((y / x) \ 1,y / x,x). R(x / (y * x),y,y \ 1) = R(y \ 1,y,x). (x \ y) * ((z * ((x \ y) \ y)) / z) = ((z * x) / z) * (x \ y). ((x * y) / x) * (y \ z) = (y \ z) * ((x * ((y \ z) \ z)) / x). (K(x,y) * (y * x)) / K(x * y,K(K(x,y),y * x)) = K(K(x,y),y * x) * (x * y). (R(T(x,y * z),y,z) * (y * z)) \ ((x * y) * z) = K(y * z,(y * z) \ ((x * y) * z)). (x \ y) * T((x \ y) \ z,y) = x \ ((y \ (x * z)) * y). x \ ((y \ (x * z)) * y) = (x \ y) * T((x \ y) \ z,y). R(x,1 / x,x) = T(x,1 / x). T(x,1 / x) = R(x,1 / x,x). T((x * (y \ z)) / z,y) * z = ((y \ x) * y) * (y \ z). (x * y) \ ((z * x) * y) = R(T(z,x * y),x,y). R(T(x,y * z),y,z) = (y * z) \ ((x * y) * z). L(x,y,z / y) * z != (z / y) * u | y * T(x,z) = u. (x / y) \ (L(z,y,x / y) * x) = y * T(z,x). T(((x * y) * z) / (x * z),x * y) = R(L(y,x,(x * y) / x),x,z). T(L(x,y,(y * x) / y),y) = T(y \ (y * x),y * x). x \ (L(y,x \ z,x) * z) = (x \ z) * T(y,z). (x * y) * R(T(x,x * y),z,u) = x * (y * R(T(x,y),z,u)). x \ ((x / y) * ((y \ 1) * y)) = T(x \ (x / y),y). T(x \ (x / y),y) = x \ ((x / y) * ((y \ 1) * y)). T(((x / y) * y) \ ((x / y) * z),y) = x \ ((x / y) * ((y \ z) * y)). L(((x / y) \ (x * (y \ 1))) \ z,a(x / y,y,y \ 1),x / y) = (x * (y \ 1)) \ ((x / y) * z). K(x,y) \ (z * (K(x,y) * u)) = u * T(z,K(x,y) * u). T((1 / x) * y,x) != (1 / x) * z | (x \ y) * x = z. (1 / x) * ((x \ y) * x) = T((1 / x) * y,x). T((1 / x) * y,x) = (1 / x) * ((x \ y) * x). (x / y) * (y * T(y \ 1,z)) = x * T(x \ (x / y),z). x * T(x \ (x / y),z) = (x / y) * (y * T(y \ 1,z)). (1 / x) \ T(((1 / x) * x) \ y,z) = x * T(x \ ((1 / x) \ y),z). R(x,T(y,x),T(z,y * x)) \ (z * (y * x)) = T(y,x) * T(z,y * x). T(R(x / y,y,T(z,y)),z * y) = (z * y) \ (x * T(z,y)). T(((1 / x) * y) * x,1 / x) = R(y,1 / x,x). R(x,1 / y,y) = T(((1 / y) * x) * y,1 / y). T(R(x \ y,x,z),x * z) = T((x * z) \ (y * z),x). R((x / y) \ z,x / y,y) = T((z * y) / x,x / y). T((x * y) / z,z / y) = R((z / y) \ x,z / y,y). T((x * (y \ z)) / z,y) = R(y \ x,y,y \ z). R(T(x / y,z),y,u) * (y * u) = (y * u) * T((y * u) \ (x * u),z). R(x,y,z) = T(((y * x) * z) / (y * z),y). T(((x * y) * z) / (x * z),x) = R(y,x,z). T((x * y) / (z * y),z) = R(z \ x,z,y). R(T(x / y,y * z),y,z) = (y * z) \ (x * z). (T(x,x * y) * y) * T(x,y) = T(x,y) * (x * y). T(x,y) * (x * y) = (T(x,x * y) * y) * T(x,y). R(T(x,y),x \ y,T(x,x \ y)) = T(x,x \ y). R(T(x,x * y),y,T(x,y)) = T(x,y). T(x,y) = R(T(x,x * y),y,T(x,y)). x * y != R(z,u,w) * x | y = R(T(z,x),u,w). x * (y * T(y \ T(y,x),z)) = (x * y) * T(K(y,x),z). (x * y) * T(K(y,x),z) = x * (y * T(y \ T(y,x),z)). (x * y) * T((x * y) \ z,u) = x * (y * T(y \ (x \ z),u)). (x * y) * T((x * y) \ (x * z),u) = x * (y * T(y \ z,u)). (x * y) * T((x * y) \ x,z) = x * (y * T(y \ 1,z)). R(x / (y * x),y,y \ 1) = R(1 * (y \ 1),y,x). R(1 * (x \ 1),x,y) = R(y / (x * y),x,x \ 1). L(L(x \ 1,y * x,z),x,y) = (z * (y * x)) \ (z * y). L((x * ((y \ z) \ u)) / x,y \ z,y) = (x * (z \ (y * u))) / x. L(((x * y) * z) / (x * y),y,x) = (x * (y * z)) / (x * y). R((x * (y / z)) / x,z,z \ 1) = (x * (y * (z \ 1))) / x. R((x * (1 / y)) / x,y,z) = (x * (z / (y * z))) / x. ((x \ y) * (y \ x)) / (x \ y) = L(1 / (x \ y),x \ y,x). L((x \ y) / z,z,x) = (z * ((x * z) \ y)) / z. (x * ((y * x) \ z)) / x = L((y \ z) / x,x,y). (x * ((y * x) \ y)) / x = L(1 / x,x,y). L((x * y) / x,z,u) = (x * L(y,z,u)) / x. (x * L(y,z,u)) / x = L((x * y) / x,z,u). ((x * (y / z)) / x) * z = z * ((x * (z \ y)) / x). x * ((y * (x \ z)) / y) = ((y * (z / x)) / y) * x. R((x * y) / x,z,u) = (x * R(y,z,u)) / x. (x * R(y,z,u)) / x = R((x * y) / x,z,u). (x * K(x,y)) * R((x * K(x,y)) \ (x * y),z,u) = R(R(y,x,K(x,y)),z,u) * (x * K(x,y)). R(R(x,y,K(y,x)),z,u) * (y * K(y,x)) = (y * K(y,x)) * R((y * K(y,x)) \ (y * x),z,u). ((x * y) / (z * y)) * z = z * R(z \ x,z,y). (x * R(x \ y,z,u)) \ R(y / x,z,u) = L(x \ 1,x,R(y / x,z,u)). L(x \ 1,x,R(y / x,z,u)) = (x * R(x \ y,z,u)) \ R(y / x,z,u). (x * R(x \ y,z,u)) / x = R(y / x,z,u). (x * L(x \ y,z,u)) / x = L(y / x,z,u). L(R(x,y,K(y,L(x,z,u))),z,u) \ (y * L(x,z,u)) = y * K(y,L(x,z,u)). R(x * y,(x * y) \ x,z) \ (x * z) = L(y \ 1,y,x) * z. R(x \ y,(x \ y) \ y,z) \ (y * z) = T(x,x \ y) * z. R(x,x \ (y / z),z) \ y = (x \ (y / z)) * z. (x * y) / L(z * y,y / (z * y),x) = x * R(1 / z,z,y). R(R(x / (y / z),u,w),y / z,z) = R((x * z) / y,u,w). R((x * y) / z,u,w) = R(R(x / (z / y),u,w),z / y,y). R(T(x / (y / z),u),y / z,z) = T((x * z) / y,u). K(x,y) = L(x \ T(x,y),x,y). L(x \ y,x,y / x) = T(y / x,y). T(x / y,x) = L(y \ x,y,x / y). L(L((x \ y) \ z,u,w),x \ y,x) = L(y \ (x * z),u,w). L(x \ (y * z),u,w) = L(L((y \ x) \ z,u,w),y \ x,y). L(R((x \ y) \ z,u,w),x \ y,x) = R(y \ (x * z),u,w). R(x \ (y * z),u,w) = L(R((y \ x) \ z,u,w),y \ x,y). L(T((x \ y) \ z,u),x \ y,x) = T(y \ (x * z),u). (x / y) * (y * T(z,x)) = L(z,y,x / y) * x. T((x * y) / x,x * y) = L(y,x,(x * y) / x). x * ((x \ y) * T(z,y)) = L(z,x \ y,x) * y. R(x \ 1,x,x \ 1) = T(x \ 1,x). T(x \ 1,x) = R(x \ 1,x,x \ 1). (x / (y * x)) * y = y * R(y \ 1,y,x). x * R(x \ 1,x,y) = (y / (x * y)) * x. T((x \ y) / (x * (x \ y)),z) * y = (T(1 / x,z) * x) * (x \ y). T(x / (y * x),y) = R(y \ 1,y,x). R(R(x,y,y \ z),u,w) * z = (R(x,u,w) * y) * (y \ z). L(R(x,y,y \ z),u,w) * z = (L(x,u,w) * y) * (y \ z). T((x * y) / x,y * x) = L(y,x,y). L(x,y,x) = T((y * x) / y,x * y). x * y != y * T(z,u) | x = T((y * z) / y,u). x * T(y,y * x) = L(y,x,y) * x. L(R(T(x,y),z,u),y,x) = R(T(x,x * y),z,u). R(T(x,x * y),z,u) = L(R(T(x,y),z,u),y,x). T(L(x,y,x),y) = T(x,x * y). T(x,x * y) = T(L(x,y,x),y). L(T(x,y),y,x) = T(x,x * y). T(x,x * y) = L(T(x,y),y,x). L(T(x,y),y,z / y) = z \ ((z / y) * (x * y)). x \ ((x / y) * (z * y)) = L(T(z,y),y,x / y). x \ R(x,y,y \ 1) = a(x,y,y \ 1). a(1 / x,x,x \ 1) = (1 / x) \ (x \ 1). (1 / x) \ (x \ 1) = a(1 / x,x,x \ 1). a(x / y,y,y \ 1) = (x / y) \ (x * (y \ 1)). (x / y) \ (x * (y \ 1)) = a(x / y,y,y \ 1). (K((x / y) \ 1,x / y) * y) / x = R((x / y) \ 1,x / y,y). x \ (y * K(y \ x,1 / (y \ x))) = L(1 / (y \ x),y \ x,y). R(x,y * z,a(x,y,z)) \ ((x * y) * z) = (y * z) * a(x,y,z). K(K(x,y),K(x,y) \ z) = T(z,K(x,y)) \ z. T(x,K(y,z)) \ x = K(K(y,z),K(y,z) \ x). T(K(x,y) * (z / u),u) = u \ (K(x,y) * z). (K(x,y) \ z) * K(x,y) = T(z,K(x,y)). T(x,K(y,z)) = (K(y,z) \ x) * K(y,z). (K(x,y) * ((z * u) * w)) / (u * w) = K(x,y) * R(z,u,w). (K(x,y) * z) / u = K(x,y) * (z / u). R(T(K(x,y),z),u,w) = T(K(x,y),z). x \ (K(y,z) * (u * x)) = T(K(y,z) * u,x). T(K(x,y) * z,u) = u \ (K(x,y) * (z * u)). ((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)) \ (u * (K(x,y) * z)) = K(u,K(x,y) * z). K(x,K(y,z) * u) = (K(y,z) * (u * x)) \ (x * (K(y,z) * u)). (x * (K(y,z) * (u * w))) \ ((x * (K(y,z) * u)) * w) = a(x,K(y,z) * u,w). a(x,K(y,z) * u,w) = (x * (K(y,z) * (u * w))) \ ((x * (K(y,z) * u)) * w). K(x,y) * z != (K(x,y) * u) * w | u * w = z. (K(x,y) * z) * u != K(x,y) * w | z * u = w. (K(x,y) * z) * (z \ u) = K(x,y) * u. R(K(x,y),z,u) = K(x,y). K(x,y) = R(K(x,y),z,u). x * (y * z) != (u * y) * z | x = R(u,y,z). T(K(x,y) * z,K(x,y)) = z * K(x,y). T((x * (y / z)) / x,z) = (x * (z \ y)) / x. (x * (y \ z)) / x = T((x * (z / y)) / x,y). ((x * y) * T(L(z,y,x),u)) / (x * y) = T((x * (y * z)) / (x * y),u). ((x / y) * y) * z != u * w | (x * z) / w = u. x * (y * (y \ z)) != u * w | u \ (x * z) = w. (x \ y) * R((x \ y) \ y,z,u) = R(x,z,u) * (x \ y). R((x * y) / x,z,u) * x = x * R(y,z,u). x * R(y,z,u) = R((x * y) / x,z,u) * x. R(x / y,z,u) * y = y * R(y \ x,z,u). x * R(x \ y,z,u) = R(y / x,z,u) * x. x \ (L(y,z,x) * (x * z)) = z * T(y,x * z). x * (y * T(z,x * y)) = L(z,y,x) * (x * y). L(x,y,z) * (z * y) = z * (y * T(x,z * y)). L(x / y,z,u) * y = y * L(y \ x,z,u). x * L(x \ y,z,u) = L(y / x,z,u) * x. L(R(x,1 / y,y),z,u) / y = L(x,z,u) * (1 / y). R(x / y,y,x \ z) \ z = y * (x \ z). L(L(x \ y,z,u),x,1 / x) = L((1 / x) * y,z,u). L((1 / x) * y,z,u) = L(L(x \ y,z,u),x,1 / x). L(R(x \ y,z,u),x,1 / x) = R((1 / x) * y,z,u). R((1 / x) * y,z,u) = L(R(x \ y,z,u),x,1 / x). L(T(x \ y,z),x,1 / x) = T((1 / x) * y,z). x * K(x \ 1,x) = L(x,x \ 1,x). L((x \ 1) \ y,x \ 1,x) = x * y. x * y = L((x \ 1) \ y,x \ 1,x). L(x \ 1,x,y / x) * y = (y / x) * K(y \ (y / x),y). (x / y) * K(x \ (x / y),x) = L(y \ 1,y,x / y) * x. T(x \ (x / y),z) = L(T(y \ 1,z),y,x / y). L(T(x \ 1,y),x,z / x) = T(z \ (z / x),y). (K(x,y) * z) \ u = z \ (K(x,y) \ u). L(T(x \ (y \ z),u),x,y) = T((y * x) \ z,u). x \ L(y,x \ 1,x) = (x \ 1) * y. K(x,1 / x) * x = R(x,1 / x,x). R(x,1 / y,y) / y = x * (1 / y). K(x \ 1,x) * (x \ 1) = R(x \ 1,x,x \ 1). (x \ 1) \ R(y,x,x \ 1) = T(y * x,x \ 1). T(x * y,y \ 1) = (y \ 1) \ R(x,y,y \ 1). R(x,y,y \ 1) != z * (y \ 1) | x * y = z. R(x,y,y \ 1) / (y \ 1) = x * y. L(T(x,y),y,1 / y) = (1 / y) * (x * y). (1 / x) * (y * x) = L(T(y,x),x,1 / x). (1 / x) \ L(y,x,1 / x) = x * y. L(x,y,1 / y) / (y * x) = 1 / y. x / K(x \ 1,x) = R(x,x \ 1,x). R(x,x \ 1,x) = x / K(x \ 1,x). R(x * y,L(z,y,x),u) \ ((x * (y * z)) * u) = L(z,y,x) * u. R(x,y,K(y,x)) \ (y * x) = y * K(y,x). R(x * y,K(y,x),z) \ ((y * x) * z) = K(y,x) * z. R(x,T(y,x),z) \ ((y * x) * z) = T(y,x) * z. R(x,x \ y,z) \ (y * z) = (x \ y) * z. (x * y) / L(T(z,z \ y),z \ y,x) = x * (z \ y). (x * (y * z)) / L(T(y,z),z,x) = x * z. (K(x,y) * (z * u)) / u = K(x,y) * z. (x * y) / L(z,y / z,x) = x * (y / z). R((x * y) / z,z,L(u,y,x)) = (x * (y * u)) / (z * L(u,y,x)). R((x \ 1) / y,y,x) = K(x \ 1,x) / (y * x). (x * (1 / y)) / K(y,1 / y) = R(x / y,y,1 / y). R(x / y,y,1 / y) = (x * (1 / y)) / K(y,1 / y). R(x / (1 / y),1 / y,y) = x * y. R(x / y,y,y \ 1) = x * (y \ 1). R(x / y,y,T(z,y)) = (x * T(z,y)) / (z * y). R(x / y,y,z) \ (x * z) = y * z. T((x * y) / (z * y),u) = R(T(x / z,u),z,y). R(T(x / y,z),y,u) = T((x * u) / (y * u),z). R(x / (y / z),y / z,z) = (x * z) / y. R(x / y,y,y \ z) = (x * (y \ z)) / z. R(x,R(y,z,u),z * u) * ((y * z) * u) = (x * R(y,z,u)) * (z * u). R(x,y \ 1,y) * K(y \ 1,y) = (x * (y \ 1)) * y. R(x,y,T(z,y)) * (z * y) = (x * y) * T(z,y). R(R(x,y,z),u,w) * (y * z) = (R(x,u,w) * y) * z. L(R(x,y,z),u,w) * (y * z) = (L(x,u,w) * y) * z. (((x * y) * z) * u) / ((y * z) * u) = R(R(x,y,z),y * z,u). R(R(x,y,z),y * z,u) = (((x * y) * z) * u) / ((y * z) * u). ((x * y) * z) \ ((R(x,y,z) * y) * z) = a(R(x,y,z),y,z). a(R(x,y,z),y,z) = ((x * y) * z) \ ((R(x,y,z) * y) * z). (x * y) * z != u * (y * z) | R(x,y,z) = u. R(x,y / z,z) * y = (x * (y / z)) * z. L(x \ y,x,1 / x) = (1 / x) * y. L(x \ T(y,z),x,z) = (z * x) \ (y * z). L(T(x,y) \ z,T(x,y),y) = (x * y) \ (y * z). (K(x,y) * z) \ (K(x,y) * u) = z \ u. L(L(x \ y,z,u),x,w) = L((w * x) \ (w * y),z,u). L((x * y) \ (x * z),u,w) = L(L(y \ z,u,w),y,x). R((x * y) \ (x * z),u,w) = L(R(y \ z,u,w),y,x). T((x * y) \ (x * z),u) = L(T(y \ z,u),y,x). L(T(x \ y,z),x,u) = T((u * x) \ (u * y),z). L(x \ y,x,z / y) = ((z / y) * x) \ z. L(x \ y,x,z / x) = z \ ((z / x) * y). L((x \ y) \ z,x \ y,x) = y \ (x * z). K(x \ 1,x) * L(y,x,x \ 1) = (x \ 1) * (x * y). (x * y) * L(z,T(x,y),y) = y * (T(x,y) * z). (K(x,y) * z) * u = K(x,y) * (z * u). (x * y) * L(L(z,y,x),u,w) = x * (y * L(z,u,w)). (x * y) * T(L(z,y,x),u) = x * (y * T(z,u)). (x * (y * z)) \ (x * (y * (z * u))) = L(L(u,z,y),y * z,x). L(L(x,y,z),z * y,u) = (u * (z * y)) \ (u * (z * (y * x))). (x * (y * z)) \ ((x * y) * (L(z,y,x) * u)) = L(u,L(z,y,x),x * y). L(x,L(y,z,u),u * z) = (u * (z * y)) \ ((u * z) * (L(y,z,u) * x)). (x * y) * z != x * (y * u) | L(u,y,x) = z. x * (y * z) != (x * y) * u | L(z,y,x) = u. x * L(y,z,x / z) = (x / z) * (z * y). x * L(y,z \ x,z) = z * ((z \ x) * y). x * ((x \ 1) * y) = L(y,x \ 1,x). L(x,y \ 1,y) = y * ((y \ 1) * x). K(x \ 1,x) \ (x \ 1) = 1 / x. K(x,1 / x) \ x = 1 / (1 / x). 1 / (x \ K(y,z)) = K(y,z) \ x. K(x,y) \ z = 1 / (z \ K(x,y)). K(x,y) \ (K(x,y) / z) = 1 / z. L(K(x,x \ 1),K(x \ 1,x),y) = (y * K(x \ 1,x)) \ y. K(x \ 1,x) * K(x,x \ 1) = 1. K(x,y) * (1 / z) = K(x,y) / z. K(x,y) / z = K(x,y) * (1 / z). R((x \ 1) * x,K(x,x \ 1),y) \ y = K(x,x \ 1) * y. T((((x * y) / x) \ z) \ z,x) = T(y,((x * y) / x) \ z). (x * T(y,z)) / x = T((x * y) / x,z). x * T(x \ y,z) != u * x | T(y / x,z) = u. x * T(x \ y,z) != u * x | u = T(y / x,z). (x * T(x \ y,z)) / x = T(y / x,z). T(x,T(x,y) \ z) * y = y * ((T(x,y) \ z) \ z). x * ((T(y,x) \ z) \ z) = T(y,T(y,x) \ z) * x. (x \ y) * T((x \ y) \ y,z) = T(x,z) * (x \ y). T((x * y) / x,z) * x = x * T(y,z). x * T(y,z) = T((x * y) / x,z) * x. T(x,y) * T(x,z) = T(x,z) * T(x,y). T(x / y,z) * y = y * T(y \ x,z). x * T(x \ y,z) = T(y / x,z) * x. x * T(x \ (y * x),z) = T(y,z) * x. K(x \ 1,x) \ 1 = K(x,x \ 1). R(x,x \ 1,y) \ y = (x \ 1) * y. K(x,y) / (z \ 1) = K(x,y) * z. x / L(y,1 / y,x) = x * (1 / y). x * T(T(y,x),z) != u * x | T(y,z) = u. x * T(T(y,x),z) != u * x | u = T(y,z). R(1 / x,x,y) \ y = x * y. R(R(1 / x,y,z),x,u) = R(u / (x * u),y,z). R(x / (y * x),z,u) = R(R(1 / y,z,u),y,x). T(x / (y * x),z) = R(T(1 / y,z),y,x). R(T(1 / x,y),x,z) = T(z / (x * z),y). R(1 / x,x,x \ y) = (x \ y) / y. x / L(y \ 1,y,x) = x * y. L(L(x \ 1,y,z),x,u) = L((u * x) \ u,y,z). L((x * y) \ x,z,u) = L(L(y \ 1,z,u),y,x). L(x \ 1,x,y / x) = y \ (y / x). R(x,y,1) = x. (x * y) / y = R(x,y,1). x * 1 != y * z | y \ x = z. x * 1 != y * z | z = y \ x. x * y != x * z | z = y. R(x,y,y \ z) * z = (x * y) * (y \ z). x \ K(x \ 1,x) = T(x \ 1,x). T(x \ 1,x) = x \ K(x \ 1,x). (x * (y \ 1)) \ (x * K(y \ 1,y)) = L(y,y \ 1,x). L(x,x \ 1,y) = (y * (x \ 1)) \ (y * K(x \ 1,x)). K(x \ 1,x) / x = x \ 1. x / (y \ ((x / z) * z)) = y. (x / (y * (y \ z))) * z = x. (x / y) * y = z * (z \ x). K(x,1 / x) / (1 / x) = x. L(T(x,x \ y),x \ y,z) = (z * (x \ y)) \ (z * y). (x \ y) * z != y | T(x,x \ y) = z. x != (y \ x) * z | T(y,y \ x) = z. x / K(y,y \ x) = (y \ x) * y. (x * y) * K(K(x,y),y * x) = K(x,y) * (y * x). K(x,y) \ (x * y) = T(y * x,K(x,y)). T(x * y,K(y,x)) = K(y,x) \ (y * x). (x * y) / (x * K(x,y)) = R(y,x,K(x,y)). R(x,y,K(y,x)) = (y * x) / (y * K(y,x)). (x * y) * z != y * x | K(y,x) = z. x * y != (y * x) * z | K(x,y) = z. x * K(y,x / y) = y * (x / y). x * K(y \ x,y) = (y \ x) * y. K(x \ 1,x) = (x \ 1) * x. ((x * y) / z) * z = ((x / u) * u) * y. ((x / y) * y) * z = ((x * z) / u) * u. R((x / y) / z,z,y) = x / (z * y). ((x / y) * y) / z = x / z. (x / y) * y = 1 * x. x * (x \ (y * z)) = y * (u * (u \ z)). x * (y * (y \ z)) = u * (u \ (x * z)). L(x \ (y \ z),x,y) = (y * x) \ z. x * (y * (y \ z)) = x * z. x \ ((x * y) * L(z,y,x)) = y * z. (x / y) \ (z * (z \ x)) = y. T(T((x * y) / x,z),x) = T(y,z). T(x,y) = T(T((z * x) / z,y),z). x / T(y,y \ x) = y \ x. T(x,T(x,y)) = x. (x * (1 / y)) * y = R(x,1 / y,y). R(x,1 / y,y) = (x * (1 / y)) * y. (x * y) * (y \ 1) = R(x,y,y \ 1). R(x,y,y \ 1) = (x * y) * (y \ 1). (1 / x) * (x * y) = L(y,x,1 / x). L(x,y,1 / y) = (1 / y) * (y * x). K(x,1 / x) = x * (1 / x). T(T(x / y,z),y) = T(y \ x,z). T(x \ y,z) = T(T(y / x,z),x). x * R(T(y,x),z,u) = R(y,z,u) * x. x * L(T(y,x),z,u) = L(y,z,u) * x. x * T(T(y,x),z) = T(y,z) * x. T(x,y) \ (x * y) = T(y,T(x,y)). T(x,T(y,x)) = T(y,x) \ (y * x). (x * y) \ (x * (z * y)) = L(T(z,y),y,x). L(T(x,y),y,z) = (z * y) \ (z * (x * y)). (x * (y * T(z,x * y))) \ (z * (x * y)) = a(x,y,T(z,x * y)). a(x,y,T(z,x * y)) = (x * (y * T(z,x * y))) \ (z * (x * y)). x * T(y,x) != z * x | z = y. x * y != y * T(z,y) | x = z. x * y != z * x | T(z,x) = y. x * y != y * z | T(x,y) = z. (x \ y) * T(x,x \ y) = y. x \ (y * T(x,y)) = y. x = y \ (x * T(y,x)). x * y != z | y = x \ z. (x * T(y,x)) / x = y. x = (y * T(x,y)) / y. x * y != z | x = z / y. T((x * y) / x,x) = y. x * y != ((x * z) / u) * u | y = z. R(1 / x,x,y) = y / (x * y). L(x \ 1,x,y) = (y * x) \ y. x \ ((x * y) * (y \ 1)) = a(x,y,y \ 1). a(x,y,y \ 1) = x \ ((x * y) * (y \ 1)). R(x,x \ 1,y) = y / ((x \ 1) * y). (x * (x \ 1)) * y != z | y = z. x * (y * (y \ 1)) != z | x = z. ((x / (y / z)) \ x) \ y = z. R(x,y,z) \ ((x * y) * z) = y * z. (x * y) / T(x,y) = y. (x * (y * z)) / L(z,y,x) = x * y. (x * y) / K(x,y) = y * x. T(T(x,y),x) = T(x,y). T(x,y) = T(T(x,y),x). x / ((1 / y) * y) = x. x / (y * (y \ 1)) = x. ((1 / x) * x) \ y = y. L(x,y,K(z,u)) = x. T(x / y,y) = y \ x. T(x,x \ y) = (x \ y) \ y. x * T(y,x) = y * x. T(x,x) = x. ((x * (y / z)) * z) / y = R(x,y / z,z). R(x,y / z,z) = ((x * (y / z)) * z) / y. R(x / y,y,z) = (x * z) / (y * z). R(x,y,z) * (y * z) = (x * y) * z. (x * y) / (y * 1) = R(x,y,1). R(x,y,1) = (x * y) / (y * 1). L(x,y / x,z) = (z * (y / x)) \ (z * y). L(x \ y,x,z) = (z * x) \ (z * y). x \ (y * ((y \ x) * z)) = L(z,y \ x,y). L(x,y \ z,y) = z \ (y * ((y \ z) * x)). (x * y) * L(z,y,x) = x * (y * z). x \ (y * (x / y)) = K(y,x / y). K(x,y / x) = y \ (x * (y / x)). ((x \ y) * x) \ y = K(x,x \ y). K(x,x \ y) = ((x \ y) * x) \ y. x \ ((y \ x) * y) = K(y \ x,y). K(x \ y,x) = y \ ((x \ y) * x). (x * y) * K(y,x) = y * x. (x * (y * z)) * a(x,y,z) = (x * y) * z. x * y != z | z / y = x. x != y * z | x / z = y. x * (y \ z) != z | x = y. x * 1 != y | x = y. x * y != z | x \ z = y. x != y * z | y \ x = z. x \ (x * (y * z)) != y * u | u = z. x * y != z \ (z * (x * u)) | y = u. (x * y) * 1 != x * z | z = y. x * y != (x * z) * 1 | y = z. x * y != x | 1 = y. x != x * y | 1 = y. (((x / y) / z) * z) * y = x. (((x * y) / z) * z) / y = x. ((x * (x \ y)) / z) * z = y. (x / y) \ x = y. ((1 / x) * x) * y = y. x / (y \ x) = y. x * (((x \ y) * z) / z) = y. x / 1 = x. x / x = 1. x * (y * (y \ (x \ z))) = z. x \ (y * (y \ (x * z))) = z. x * (y * (y \ 1)) = x. x * (x \ (1 * y)) = y. (x * (x \ 1)) * y = y. x \ x = 1. 1 \ x = x. a(c1,K(c2,c3),c4) != 1. a(K(x,y),z,u) = 1. R(R(x,y,z),u,w) = R(R(x,u,w),y,z). L(L(x,y,z),u,w) = L(L(x,u,w),y,z). R(L(x,y,z),u,w) = L(R(x,u,w),y,z). L(R(x,y,z),u,w) = R(L(x,u,w),y,z). R(T(x,y),z,u) = T(R(x,z,u),y). T(R(x,y,z),u) = R(T(x,u),y,z). L(T(x,y),z,u) = T(L(x,z,u),y). T(L(x,y,z),u) = L(T(x,u),y,z). T(T(x,y),z) = T(T(x,z),y). K(x,y) != 1 | T(x,y) = x. T(x,y) != x | K(x,y) = 1. T(x,y) != x | T(y,x) = y. L(x,y,z) != x | a(z,y,x) = 1. a(x,y,z) != 1 | L(z,y,x) = z. T(x,y) = y \ (x * y). x \ (y * x) = T(y,x). R(x,y,z) = ((x * y) * z) / (y * z). ((x * y) * z) / (y * z) = R(x,y,z). L(x,y,z) = (z * y) \ (z * (y * x)). (x * y) \ (x * (y * z)) = L(z,y,x). K(x,y) = (y * x) \ (x * y). (x * y) \ (y * x) = K(y,x). a(x,y,z) = (x * (y * z)) \ ((x * y) * z). (x * (y * z)) \ ((x * y) * z) = a(x,y,z). x * y != z * y | x = z. x * y != x * z | y = z. x * y != z | u * y != z | u = x. x * y != z | x * u != z | u = y. (x / y) * y = x. (x * y) / y = x. x * (x \ y) = y. x \ (x * y) = y. x * 1 = x. 1 * x = x. a(x,K(y,z),u) = 1. 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(x,K(y,z),u) = 1 # label("aK2") # 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) # label("associator"). [assumption]. (x * y) \ (y * x) = K(y,x) # label("commutator"). [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]. a(K(x,y),z,u) = 1 # label("aK1"). [assumption]. a(c1,K(c2,c3),c4) != 1 # label("aK2"). [deny(10)]. end_of_list. formulas(demodulators). end_of_list. % 3211 hints input. ============================== PREDICATE ELIMINATION ================= No predicates eliminated. ============================== end predicate elimination ============= Auto_denials: % copying label "aK2" to answer in negative clause Term ordering decisions: Function symbol KB weights: 1=1. c1=1. c2=1. c3=1. c4=1. *=1. T=1. \=1. K=1. /=1. L=1. R=1. a=1. Predicate symbol precedence: predicate_order([ = ]). Function symbol precedence: function_order([ 1, c1, c2, c3, c4, *, 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) % assign(para_lit_limit, 3). % (nonunit Horn with equality) Auto_process settings: (no changes). kept: 11 1 * x = x. [assumption]. kept: 12 x * 1 = x. [assumption]. kept: 13 x \ (x * y) = y. [assumption]. kept: 14 x * (x \ y) = y. [assumption]. kept: 15 (x * y) / y = x. [assumption]. kept: 16 (x / y) * y = x. [assumption]. kept: 17 x * y != z | x * u != z | u = y. [clausify(1)]. kept: 18 x * y != z | u * y != z | u = x. [clausify(2)]. kept: 19 x * y != x * z | y = z. [clausify(3)]. kept: 20 x * y != z * y | x = z. [clausify(4)]. 21 (x * (y * z)) \ ((x * y) * z) = a(x,y,z) # label("associator"). [assumption]. kept: 22 a(x,y,z) = (x * (y * z)) \ ((x * y) * z). [copy(21),flip(a)]. 23 (x * y) \ (y * x) = K(y,x) # label("commutator"). [assumption]. kept: 24 K(x,y) = (y * x) \ (x * y). [copy(23),flip(a)]. 25 (x * y) \ (x * (y * z)) = L(z,y,x). [assumption]. kept: 26 L(x,y,z) = (z * y) \ (z * (y * x)). [copy(25),flip(a)]. 27 ((x * y) * z) / (y * z) = R(x,y,z). [assumption]. kept: 28 R(x,y,z) = ((x * y) * z) / (y * z). [copy(27),flip(a)]. 29 x \ (y * x) = T(y,x). [assumption]. kept: 30 T(x,y) = y \ (x * y). [copy(29),flip(a)]. kept: 31 a(x,y,z) != 1 | L(z,y,x) = z. [clausify(5)]. kept: 32 L(x,y,z) != x | a(z,y,x) = 1. [clausify(6)]. kept: 33 T(x,y) != x | T(y,x) = y. [clausify(7)]. kept: 34 T(x,y) != x | K(x,y) = 1. [clausify(8)]. kept: 35 K(x,y) != 1 | T(x,y) = x. [clausify(9)]. kept: 36 T(T(x,y),z) = T(T(x,z),y). [assumption]. 37 T(L(x,y,z),u) = L(T(x,u),y,z). [assumption]. kept: 38 L(T(x,y),z,u) = T(L(x,z,u),y). [copy(37),flip(a)]. 39 T(R(x,y,z),u) = R(T(x,u),y,z). [assumption]. kept: 40 R(T(x,y),z,u) = T(R(x,z,u),y). [copy(39),flip(a)]. 41 L(R(x,y,z),u,w) = R(L(x,u,w),y,z). [assumption]. kept: 42 R(L(x,y,z),u,w) = L(R(x,u,w),y,z). [copy(41),flip(a)]. kept: 43 L(L(x,y,z),u,w) = L(L(x,u,w),y,z). [assumption]. kept: 44 R(R(x,y,z),u,w) = R(R(x,u,w),y,z). [assumption]. kept: 45 a(K(x,y),z,u) = 1 # label("aK1"). [assumption]. kept: 46 a(c1,K(c2,c3),c4) != 1 # label("aK2") # answer("aK2"). [deny(10)]. ============================== end of process initial clauses ======== ============================== CLAUSES FOR SEARCH ==================== % Clauses after input processing: formulas(usable). 46 a(c1,K(c2,c3),c4) != 1 # label("aK2") # answer("aK2"). [deny(10)]. end_of_list. formulas(sos). 11 1 * x = x. [assumption]. 12 x * 1 = x. [assumption]. 13 x \ (x * y) = y. [assumption]. 14 x * (x \ y) = y. [assumption]. 15 (x * y) / y = x. [assumption]. 16 (x / y) * y = x. [assumption]. 17 x * y != z | x * u != z | u = y. [clausify(1)]. 18 x * y != z | u * y != z | u = x. [clausify(2)]. 19 x * y != x * z | y = z. [clausify(3)]. 20 x * y != z * y | x = z. [clausify(4)]. 22 a(x,y,z) = (x * (y * z)) \ ((x * y) * z). [copy(21),flip(a)]. 24 K(x,y) = (y * x) \ (x * y). [copy(23),flip(a)]. 26 L(x,y,z) = (z * y) \ (z * (y * x)). [copy(25),flip(a)]. 28 R(x,y,z) = ((x * y) * z) / (y * z). [copy(27),flip(a)]. 30 T(x,y) = y \ (x * y). [copy(29),flip(a)]. 31 a(x,y,z) != 1 | L(z,y,x) = z. [clausify(5)]. 32 L(x,y,z) != x | a(z,y,x) = 1. [clausify(6)]. 33 T(x,y) != x | T(y,x) = y. [clausify(7)]. 34 T(x,y) != x | K(x,y) = 1. [clausify(8)]. 35 K(x,y) != 1 | T(x,y) = x. [clausify(9)]. 36 T(T(x,y),z) = T(T(x,z),y). [assumption]. 38 L(T(x,y),z,u) = T(L(x,z,u),y). [copy(37),flip(a)]. 40 R(T(x,y),z,u) = T(R(x,z,u),y). [copy(39),flip(a)]. 42 R(L(x,y,z),u,w) = L(R(x,u,w),y,z). [copy(41),flip(a)]. 43 L(L(x,y,z),u,w) = L(L(x,u,w),y,z). [assumption]. 44 R(R(x,y,z),u,w) = R(R(x,u,w),y,z). [assumption]. 45 a(K(x,y),z,u) = 1 # label("aK1"). [assumption]. end_of_list. formulas(demodulators). end_of_list. % 2458 hints (3211 processed, 753 redundant). ============================== end of clauses for search ============= ============================== SEARCH ================================ % Starting search at 0.16 seconds. given #1 (I,wt=5): 11 1 * x = x. [assumption]. given #2 (I,wt=5): 12 x * 1 = x. [assumption]. given #3 (I,wt=7): 13 x \ (x * y) = y. [assumption]. given #4 (I,wt=7): 14 x * (x \ y) = y. [assumption]. given #5 (I,wt=7): 15 (x * y) / y = x. [assumption]. given #6 (I,wt=7): 16 (x / y) * y = x. [assumption]. given #7 (I,wt=13): 17 x * y != z | x * u != z | u = y. [clausify(1)]. given #8 (I,wt=13): 18 x * y != z | u * y != z | u = x. [clausify(2)]. given #9 (I,wt=10): 19 x * y != x * z | y = z. [clausify(3)]. given #10 (I,wt=10): 20 x * y != z * y | x = z. [clausify(4)]. given #11 (I,wt=16): 22 a(x,y,z) = (x * (y * z)) \ ((x * y) * z). [copy(21),flip(a)]. given #12 (I,wt=11): 24 K(x,y) = (y * x) \ (x * y). [copy(23),flip(a)]. given #13 (I,wt=14): 26 L(x,y,z) = (z * y) \ (z * (y * x)). [copy(25),flip(a)]. given #14 (I,wt=14): 28 R(x,y,z) = ((x * y) * z) / (y * z). [copy(27),flip(a)]. given #15 (I,wt=9): 30 T(x,y) = y \ (x * y). [copy(29),flip(a)]. given #16 (I,wt=12): 31 a(x,y,z) != 1 | L(z,y,x) = z. [clausify(5)]. given #17 (I,wt=12): 32 L(x,y,z) != x | a(z,y,x) = 1. [clausify(6)]. given #18 (I,wt=10): 33 T(x,y) != x | T(y,x) = y. [clausify(7)]. given #19 (I,wt=10): 34 T(x,y) != x | K(x,y) = 1. [clausify(8)]. given #20 (I,wt=10): 35 K(x,y) != 1 | T(x,y) = x. [clausify(9)]. given #21 (I,wt=11): 36 T(T(x,y),z) = T(T(x,z),y). [assumption]. given #22 (I,wt=13): 38 L(T(x,y),z,u) = T(L(x,z,u),y). [copy(37),flip(a)]. given #23 (I,wt=13): 40 R(T(x,y),z,u) = T(R(x,z,u),y). [copy(39),flip(a)]. given #24 (I,wt=15): 42 R(L(x,y,z),u,w) = L(R(x,u,w),y,z). [copy(41),flip(a)]. given #25 (I,wt=15): 43 L(L(x,y,z),u,w) = L(L(x,u,w),y,z). [assumption]. given #26 (I,wt=15): 44 R(R(x,y,z),u,w) = R(R(x,u,w),y,z). [assumption]. given #27 (I,wt=8): 45 a(K(x,y),z,u) = 1 # label("aK1"). [assumption]. given #28 (H,wt=5): 47 1 \ x = x. [para(11(a,1),13(a,1,2))]. given #29 (H,wt=5): 48 x \ x = 1. [para(12(a,1),13(a,1,2))]. given #30 (H,wt=5): 54 x / x = 1. [para(11(a,1),15(a,1,1))]. given #31 (H,wt=5): 55 x / 1 = x. [para(12(a,1),15(a,1,1))]. given #32 (H,wt=5): 84 T(x,x) = x. [para(30(a,2),13(a,1))]. given #33 (H,wt=7): 57 x / (y \ x) = y. [para(14(a,1),15(a,1,1))]. given #34 (H,wt=7): 59 (x / y) \ x = y. [para(16(a,1),13(a,1,2))]. given #35 (H,wt=8): 63 x * y != x | 1 = y. [para(12(a,1),19(a,1)),flip(a)]. given #36 (H,wt=8): 68 x * 1 != y | x = y. [para(12(a,1),20(a,2))]. given #37 (H,wt=8): 88 L(x,y,K(z,u)) = x. [hyper(31,a,45,a)]. given #38 (H,wt=9): 49 (x * (x \ 1)) * y = y. [para(14(a,2),11(a,1,1))]. given #39 (H,wt=9): 50 x * (x \ (1 * y)) = y. [para(14(a,2),11(a,1))]. given #40 (H,wt=9): 51 x * (y * (y \ 1)) = x. [para(14(a,2),12(a,1,2))]. given #41 (H,wt=9): 58 ((1 / x) * x) * y = y. [para(16(a,2),11(a,1,1))]. given #42 (H,wt=9): 85 x * T(y,x) = y * x. [para(30(a,2),14(a,1,2))]. given #43 (H,wt=9): 87 T(x / y,y) = y \ x. [para(16(a,1),30(a,2,2))]. given #44 (H,wt=9): 89 ((1 / x) * x) \ y = y. [para(16(a,2),47(a,1,1))]. given #45 (H,wt=9): 91 x / (y * (y \ 1)) = x. [para(14(a,2),55(a,1,2))]. given #46 (H,wt=9): 92 x / ((1 / y) * y) = x. [para(16(a,2),55(a,1,2))]. given #47 (H,wt=9): 93 T(T(x,y),x) = T(x,y). [para(84(a,1),36(a,1,1)),flip(a)]. given #48 (H,wt=7): 122 T(x,T(x,y)) = x. [hyper(33,a,93,a)]. given #49 (H,wt=9): 96 (x * y) / T(x,y) = y. [para(30(a,2),57(a,1,2))]. given #50 (H,wt=9): 105 T((x * y) / x,x) = y. [hyper(17,a,16,a(flip),b,85,a)]. given #51 (H,wt=9): 106 (x * T(y,x)) / x = y. [hyper(18,a,16,a,b,85,a(flip)),flip(a)]. given #52 (H,wt=9): 107 x \ (y * T(x,y)) = y. [hyper(17,a,14,a,b,85,a(flip)),flip(a)]. given #53 (H,wt=10): 66 x * y != z | x \ z = y. [para(14(a,1),19(a,1)),flip(a)]. given #54 (H,wt=10): 69 x * (y \ z) != z | x = y. [para(14(a,1),20(a,2))]. given #55 (H,wt=10): 70 x * y != z | z / y = x. [para(16(a,1),20(a,1)),flip(a)]. given #56 (H,wt=11): 52 x \ (y * (y \ (x * z))) = z. [para(14(a,2),13(a,1,2))]. given #57 (H,wt=11): 53 x * (y * (y \ (x \ z))) = z. [para(14(a,2),14(a,1,2))]. given #58 (H,wt=11): 56 x * (((x \ y) * z) / z) = y. [para(15(a,2),14(a,1,2))]. given #59 (H,wt=11): 60 ((x * (x \ y)) / z) * z = y. [para(16(a,2),14(a,1))]. given #60 (H,wt=9): 130 (x / y) * y = 1 * x. [para(50(a,1),60(a,1,1,1))]. given #61 (H,wt=11): 61 (((x * y) / z) * z) / y = x. [para(16(a,2),15(a,1,1))]. given #62 (H,wt=11): 62 (((x / y) / z) * z) * y = x. [para(16(a,2),16(a,1,1))]. given #63 (H,wt=11): 72 (x * y) * K(y,x) = y * x. [para(24(a,2),14(a,1,2))]. given #64 (H,wt=11): 86 T(x,x \ y) = (x \ y) \ y. [para(14(a,1),30(a,2,2))]. given #65 (H,wt=11): 94 (x * y) / K(x,y) = y * x. [para(24(a,2),57(a,1,2))]. given #66 (H,wt=11): 98 ((x / (y / z)) \ x) \ y = z. [para(59(a,2),59(a,1,1))]. given #67 (H,wt=11): 108 (x \ y) * T(x,x \ y) = y. [para(85(a,2),14(a,1))]. given #68 (H,wt=11): 118 K(x,1 / x) = x * (1 / x). [para(89(a,1),24(a,2))]. given #69 (H,wt=11): 123 x / T(y,y \ x) = y \ x. [para(14(a,1),96(a,1,1))]. given #70 (H,wt=11): 125 (x / y) \ (z * (z \ x)) = y. [para(16(a,1),52(a,1,2,2,2))]. given #71 (H,wt=11): 127 x * (y * (y \ z)) = x * z. [para(13(a,1),53(a,1,2,2,2))]. given #72 (H,wt=11): 132 ((x / y) * y) / z = x / z. [para(16(a,1),61(a,1,1,1,1))]. given #73 (H,wt=11): 135 K(x \ 1,x) = (x \ 1) * x. [hyper(17,a,49,a,b,72,a)]. given #74 (H,wt=11): 145 K(x,1 / x) / (1 / x) = x. [hyper(70,a,118,a(flip))]. given #75 (H,wt=11): 146 (x / y) * y = z * (z \ x). [para(125(a,1),14(a,1,2))]. given #76 (H,wt=11): 147 (x / (y * (y \ z))) * z = x. [para(127(a,1),16(a,1))]. given #77 (H,wt=11): 148 x / (y \ ((x / z) * z)) = y. [para(132(a,1),57(a,1))]. given #78 (H,wt=11): 149 K(x \ 1,x) / x = x \ 1. [hyper(70,a,135,a(flip))]. given #79 (H,wt=12): 64 (x * y) * 1 != x * z | z = y. [para(12(a,2),19(a,2)),flip(a)]. given #80 (H,wt=10): 154 x * y != x * z | z = y. [para(12(a,1),64(a,1))]. given #81 (H,wt=12): 80 (x * y) / (y * 1) = R(x,y,1). [para(12(a,1),28(a,2,1)),flip(a)]. given #82 (H,wt=10): 156 (x * y) / y = R(x,y,1). [para(12(a,1),80(a,1,2))]. given #83 (H,wt=6): 157 R(x,y,1) = x. [para(156(a,1),15(a,1))]. given #84 (H,wt=12): 99 x * (y * (y \ 1)) != z | x = z. [para(14(a,2),68(a,1,2))]. given #85 (H,wt=12): 100 (x * (x \ 1)) * y != z | y = z. [para(49(a,1),19(a,2))]. given #86 (H,wt=12): 103 L(x \ 1,x,y) = (y * x) \ y. [para(51(a,1),26(a,2,2))]. given #87 (H,wt=12): 104 R(1 / x,x,y) = y / (x * y). [para(58(a,1),28(a,2,1))]. given #88 (H,wt=12): 109 x * y != z * x | T(z,x) = y. [para(85(a,1),19(a,1)),flip(a)]. given #89 (H,wt=12): 110 x * T(y,x) != z * x | z = y. [para(85(a,2),20(a,2)),flip(a)]. given #90 (H,wt=12): 131 1 * x != y * z | x / z = y. [para(130(a,1),20(a,1))]. given #91 (H,wt=12): 155 x * 1 != y * z | y \ x = z. [para(14(a,1),64(a,1,1)),flip(b)]. given #92 (H,wt=12): 160 x / L(y \ 1,y,x) = x * y. [para(103(a,2),57(a,1,2))]. given #93 (H,wt=12): 164 R(1 / x,x,y) \ y = x * y. [para(104(a,2),59(a,1,1))]. given #94 (H,wt=13): 73 x \ ((y \ x) * y) = K(y \ x,y). [para(14(a,1),24(a,2,1)),flip(a)]. given #95 (H,wt=13): 74 ((x \ y) * x) \ y = K(x,x \ y). [para(14(a,1),24(a,2,2)),flip(a)]. given #96 (H,wt=13): 75 x \ (y * (x / y)) = K(y,x / y). [para(16(a,1),24(a,2,1)),flip(a)]. given #97 (H,wt=13): 113 T(x,y) \ (x * y) = T(y,T(x,y)). [para(85(a,1),30(a,2,2)),flip(a)]. given #98 (H,wt=13): 114 x * T(T(y,x),z) = T(y,z) * x. [para(36(a,1),85(a,1,2))]. given #99 (H,wt=13): 117 T(T(x / y,z),y) = T(y \ x,z). [para(87(a,1),36(a,1,1)),flip(a)]. given #100 (H,wt=13): 124 T(T((x * y) / x,z),x) = T(y,z). [para(105(a,1),36(a,1,1)),flip(a)]. given #101 (H,wt=13): 136 x * K(y \ x,y) = (y \ x) * y. [para(14(a,1),72(a,1,1))]. given #102 (H,wt=13): 137 x * K(y,x / y) = y * (x / y). [para(16(a,1),72(a,1,1))]. given #103 (H,wt=13): 142 x / K(y,y \ x) = (y \ x) * y. [para(14(a,1),94(a,1,1))]. given #104 (H,wt=13): 151 x \ K(x \ 1,x) = T(x \ 1,x). [para(135(a,2),30(a,2,2)),flip(a)]. given #105 (H,wt=13): 167 K(x,y) / (z \ 1) = K(x,y) * z. [para(88(a,1),160(a,1,2))]. given #106 (H,wt=13): 169 K(x \ 1,x) \ 1 = K(x,x \ 1). [para(135(a,2),74(a,1,1))]. given #107 (H,wt=13): 182 K(x,y) * (1 / z) = K(x,y) / z. [para(59(a,1),167(a,1,2)),flip(a)]. given #108 (H,wt=13): 183 K(x \ 1,x) * K(x,x \ 1) = 1. [para(169(a,1),14(a,1,2))]. given #109 (H,wt=13): 185 K(x,y) \ (K(x,y) / z) = 1 / z. [hyper(66,a,182,a)]. given #110 (H,wt=13): 186 1 / (x \ K(y,z)) = K(y,z) \ x. [para(57(a,1),185(a,1,2)),flip(a)]. given #111 (H,wt=13): 187 K(x,1 / x) \ x = 1 / (1 / x). [para(145(a,1),185(a,1,2))]. given #112 (H,wt=13): 188 K(x \ 1,x) \ (x \ 1) = 1 / x. [para(149(a,1),185(a,1,2))]. given #113 (H,wt=14): 65 x \ (x * (y * z)) != y * u | u = z. [para(13(a,2),19(a,2)),flip(a)]. given #114 (H,wt=14): 67 ((x * y) / z) * z != x * u | u = y. [para(16(a,2),19(a,2)),flip(a)]. given #115 (H,wt=14): 76 (x * y) * L(z,y,x) = x * (y * z). [para(26(a,2),14(a,1,2))]. given #116 (H,wt=14): 78 L(x \ y,x,z) = (z * x) \ (z * y). [para(14(a,1),26(a,2,2,2))]. given #117 (H,wt=14): 81 R(x,y,z) * (y * z) = (x * y) * z. [para(28(a,2),16(a,1,1))]. given #118 (H,wt=14): 82 R(x / y,y,z) = (x * z) / (y * z). [para(16(a,1),28(a,2,1,1))]. given #119 (H,wt=14): 95 (x * (y * z)) / L(z,y,x) = x * y. [para(26(a,2),57(a,1,2))]. given #120 (H,wt=14): 97 R(x,y,z) \ ((x * y) * z) = y * z. [para(28(a,2),59(a,1,1))]. given #121 (H,wt=14): 101 R(x,x \ 1,y) = y / ((x \ 1) * y). [para(49(a,1),28(a,2,1))]. given #122 (H,wt=14): 119 (1 / x) * (x * y) = L(y,x,1 / x). [para(89(a,1),26(a,2)),flip(a)]. given #123 (H,wt=14): 120 (x * y) * (y \ 1) = R(x,y,y \ 1). [para(91(a,1),28(a,2)),flip(a)]. given #124 (H,wt=14): 121 (x * (1 / y)) * y = R(x,1 / y,y). [para(92(a,1),28(a,2)),flip(a)]. given #125 (H,wt=14): 126 x \ ((x * y) * L(z,y,x)) = y * z. [para(26(a,2),52(a,1,2,2))]. given #126 (H,wt=14): 128 L(x \ (y \ z),x,y) = (y * x) \ z. [para(53(a,1),26(a,2,2))]. given #127 (H,wt=14): 133 R((x / y) / z,z,y) = x / (z * y). [para(62(a,1),28(a,2,1))]. given #128 (H,wt=14): 138 (x * y) * z != y * x | K(y,x) = z. [para(72(a,1),19(a,1)),flip(a)]. given #129 (H,wt=14): 143 (x \ y) * z != y | T(x,x \ y) = z. [para(108(a,1),19(a,1)),flip(a)]. given #130 (H,wt=14): 152 (x / y) * y != z * u | z \ x = u. [para(146(a,2),19(a,1))]. given #131 (H,wt=14): 158 L(x \ 1,x,y / x) = y \ (y / x). [para(16(a,1),103(a,2,1))]. given #132 (H,wt=14): 161 R(1 / x,x,x \ y) = (x \ y) / y. [para(14(a,1),104(a,2,2))]. given #133 (H,wt=14): 166 x / L(y,1 / y,x) = x * (1 / y). [para(59(a,1),160(a,1,2,1))]. given #134 (H,wt=14): 168 R(x,x \ 1,y) \ y = (x \ 1) * y. [para(57(a,1),164(a,1,1,1))]. given #135 (H,wt=14): 189 x * ((x \ 1) * y) = L(y,x \ 1,x). [hyper(100,a,76,a),flip(a)]. given #136 (H,wt=14): 209 L(x \ y,x,1 / x) = (1 / x) * y. [para(78(a,2),89(a,1))]. given #137 (H,wt=14): 222 R(x / y,y,z) \ (x * z) = y * z. [para(82(a,2),59(a,1,1))]. given #138 (H,wt=14): 224 R(x / y,y,y \ 1) = x * (y \ 1). [para(82(a,2),91(a,1))]. given #139 (H,wt=14): 225 R(x / (1 / y),1 / y,y) = x * y. [para(82(a,2),92(a,1))]. given #140 (H,wt=14): 238 x / K(x \ 1,x) = R(x,x \ 1,x). [para(135(a,2),101(a,2,2)),flip(a)]. given #141 (H,wt=14): 239 L(x,y,1 / y) / (y * x) = 1 / y. [hyper(70,a,119,a)]. given #142 (H,wt=14): 240 (1 / x) \ L(y,x,1 / x) = x * y. [hyper(66,a,119,a)]. given #143 (H,wt=14): 242 R(x,y,y \ 1) / (y \ 1) = x * y. [hyper(70,a,120,a)]. given #144 (H,wt=14): 246 R(x,1 / y,y) / y = x * (1 / y). [hyper(70,a,121,a)]. given #145 (H,wt=14): 247 K(x,1 / x) * x = R(x,1 / x,x). [para(118(a,2),121(a,1,1))]. given #146 (H,wt=14): 248 x \ L(y,x \ 1,x) = (x \ 1) * y. [para(49(a,1),126(a,1,2))]. given #147 (H,wt=14): 253 L((x \ 1) \ y,x \ 1,x) = x * y. [para(14(a,1),189(a,1,2)),flip(a)]. given #148 (H,wt=14): 254 x * K(x \ 1,x) = L(x,x \ 1,x). [para(135(a,2),189(a,1,2))]. given #149 (H,wt=15): 115 x * L(T(y,x),z,u) = L(y,z,u) * x. [para(38(a,2),85(a,1,2))]. given #150 (H,wt=15): 116 x * R(T(y,x),z,u) = R(y,z,u) * x. [para(40(a,2),85(a,1,2))]. given #151 (H,wt=15): 129 x * (x \ (y * z)) = y * (u * (u \ z)). [para(52(a,1),53(a,1,2,2,2)),flip(a)]. given #152 (H,wt=15): 134 ((x * y) / z) * z = ((x / u) * u) * y. [para(61(a,1),62(a,1,1,1,1)),flip(a)]. given #153 (H,wt=15): 140 K(x,y) \ (x * y) = T(y * x,K(x,y)). [para(72(a,1),30(a,2,2)),flip(a)]. given #154 (H,wt=15): 170 x * T(x \ (y * x),z) = T(y,z) * x. [para(30(a,1),114(a,1,2,1))]. given #155 (H,wt=15): 171 T(x / y,z) * y = y * T(y \ x,z). [para(87(a,1),114(a,1,2,1)),flip(a)]. given #156 (H,wt=15): 172 T(x,y) * T(x,z) = T(x,z) * T(x,y). [para(122(a,1),114(a,1,2,1))]. given #157 (H,wt=15): 173 T((x * y) / x,z) * x = x * T(y,z). [para(105(a,1),114(a,1,2,1)),flip(a)]. given #158 (H,wt=15): 176 (x * T(x \ y,z)) / x = T(y / x,z). [para(117(a,1),106(a,1,1,2))]. given #159 (H,wt=15): 178 (x * T(y,z)) / x = T((x * y) / x,z). [para(124(a,1),106(a,1,1,2))]. given #160 (H,wt=15): 197 (K(x,y) * z) * u = K(x,y) * (z * u). [para(88(a,1),76(a,1,2))]. given #161 (H,wt=10): 272 R(K(x,y),z,u) = K(x,y). [hyper(18,a,81,a,b,197,a(flip)),flip(a)]. given #162 (H,wt=14): 280 R(T(K(x,y),z),u,w) = T(K(x,y),z). [para(272(a,1),40(a,2,1))]. given #163 (H,wt=15): 206 (K(x,y) * z) \ (K(x,y) * u) = z \ u. [para(78(a,1),88(a,1))]. given #164 (H,wt=15): 230 (K(x,y) * (z * u)) / u = K(x,y) * z. [para(88(a,1),95(a,1,2))]. given #165 (H,wt=15): 250 (K(x,y) * z) \ u = z \ (K(x,y) \ u). [para(128(a,1),88(a,1))]. given #166 (H,wt=15): 271 T(K(x,y) * z,K(x,y)) = z * K(x,y). [hyper(109,a,197,a(flip))]. given #167 (H,wt=15): 273 (K(x,y) * z) * (z \ u) = K(x,y) * u. [para(14(a,1),197(a,2,2))]. given #168 (H,wt=15): 281 (K(x,y) * z) / u = K(x,y) * (z / u). [para(16(a,1),230(a,1,1,2))]. given #169 (H,wt=15): 283 (K(x,y) \ z) * K(x,y) = T(z,K(x,y)). [para(14(a,1),271(a,1,1)),flip(a)]. given #170 (H,wt=16): 71 (x * (y * z)) * a(x,y,z) = (x * y) * z. [para(22(a,2),14(a,1,2))]. given #171 (H,wt=16): 77 x \ (y * ((y \ x) * z)) = L(z,y \ x,y). [para(14(a,1),26(a,2,1)),flip(a)]. given #172 (H,wt=16): 79 L(x,y / x,z) = (z * (y / x)) \ (z * y). [para(16(a,1),26(a,2,2,2))]. given #173 (H,wt=16): 83 ((x * (y / z)) * z) / y = R(x,y / z,z). [para(16(a,1),28(a,2,2)),flip(a)]. given #174 (H,wt=16): 102 x \ ((x * y) * (y \ 1)) = a(x,y,y \ 1). [para(51(a,1),22(a,2,1)),flip(a)]. given #175 (H,wt=15): 291 x \ R(x,y,y \ 1) = a(x,y,y \ 1). [para(120(a,1),102(a,1,2))]. given #176 (H,wt=16): 112 (x * y) \ (x * (z * y)) = L(T(z,y),y,x). [para(85(a,1),26(a,2,2,2)),flip(a)]. given #177 (H,wt=12): 293 L(T(x,y),y,x) = T(x,x * y). [para(112(a,1),30(a,2)),flip(a)]. given #178 (H,wt=12): 294 T(L(x,y,x),y) = T(x,x * y). [para(293(a,1),38(a,1)),flip(a)]. given #179 (H,wt=14): 296 x * T(y,y * x) = L(y,x,y) * x. [para(293(a,1),115(a,1,2))]. given #180 (H,wt=14): 297 T((x * y) / x,y * x) = L(y,x,y). [hyper(18,a,173,a,b,296,a(flip)),flip(a)]. given #181 (H,wt=16): 139 (x * y) / (x * K(x,y)) = R(y,x,K(x,y)). [para(72(a,1),28(a,2,1)),flip(a)]. given #182 (H,wt=16): 153 R(x,y,y \ z) * z = (x * y) * (y \ z). [para(28(a,2),147(a,1,1))]. given #183 (H,wt=16): 162 T(x / (y * x),z) = R(T(1 / y,z),y,x). [para(104(a,1),40(a,2,1)),flip(a)]. given #184 (H,wt=14): 300 T(x / (y * x),y) = R(y \ 1,y,x). [para(87(a,1),162(a,2,1))]. given #185 (H,wt=14): 303 R(x \ 1,x,x \ 1) = T(x \ 1,x). [para(91(a,1),300(a,1,1)),flip(a)]. given #186 (H,wt=16): 165 x * T(T(y,x),z) != u * x | T(y,z) = u. [para(36(a,1),110(a,1,2)),flip(b)]. given #187 (H,wt=16): 190 x * L(y,z \ x,z) = z * ((z \ x) * y). [para(14(a,1),76(a,1,1))]. given #188 (H,wt=16): 191 x * L(y,z,x / z) = (x / z) * (z * y). [para(16(a,1),76(a,1,1))]. given #189 (H,wt=16): 200 L((x \ y) \ z,x \ y,x) = y \ (x * z). [para(14(a,1),78(a,2,1))]. given #190 (H,wt=16): 201 L(x \ y,x,z / x) = z \ ((z / x) * y). [para(16(a,1),78(a,2,1))]. given #191 (H,wt=14): 310 L(x \ y,x,y / x) = T(y / x,y). [para(201(a,2),30(a,2)),flip(a)]. given #192 (H,wt=16): 202 L(x \ y,x,z / y) = ((z / y) * x) \ z. [para(16(a,1),78(a,2,2))]. given #193 (H,wt=16): 208 L(x \ T(y,z),x,z) = (z * x) \ (y * z). [para(85(a,1),78(a,2,2))]. given #194 (H,wt=12): 311 K(x,y) = L(x \ T(x,y),x,y). [para(208(a,2),24(a,2))]. given #195 (H,wt=16): 210 R(x,y / z,z) * y = (x * (y / z)) * z. [para(16(a,1),81(a,1,2))]. given #196 (H,wt=16): 219 R(x / y,y,y \ z) = (x * (y \ z)) / z. [para(14(a,1),82(a,2,2))]. given #197 (H,wt=16): 220 R(x / (y / z),y / z,z) = (x * z) / y. [para(16(a,1),82(a,2,2))]. given #198 (H,wt=16): 229 (x * y) / L(z,y / z,x) = x * (y / z). [para(16(a,1),95(a,1,1,2))]. given #199 (H,wt=16): 231 (x * (y * z)) / L(T(y,z),z,x) = x * z. [para(85(a,1),95(a,1,1,2))]. given #200 (H,wt=16): 233 R(x,x \ y,z) \ (y * z) = (x \ y) * z. [para(14(a,1),97(a,1,2,1))]. given #201 (H,wt=16): 236 R(x,y,K(y,x)) \ (y * x) = y * K(y,x). [para(72(a,1),97(a,1,2))]. given #202 (H,wt=16): 241 L(T(x,y),y,1 / y) = (1 / y) * (x * y). [para(85(a,1),119(a,1,2)),flip(a)]. given #203 (H,wt=16): 258 R(x / y,y,x \ z) \ z = y * (x \ z). [para(14(a,1),222(a,1,2))]. given #204 (H,wt=16): 290 a(1 / x,x,x \ 1) = (1 / x) \ (x \ 1). [para(58(a,1),102(a,1,2)),flip(a)]. given #205 (H,wt=16): 302 (x / (y * x)) * y = y * R(y \ 1,y,x). [para(300(a,1),85(a,1,2)),flip(a)]. given #206 (H,wt=17): 192 (x * y) * z != x * (y * u) | L(u,y,x) = z. [para(76(a,1),19(a,1)),flip(a)]. given #207 (H,wt=17): 211 (x * y) * z != u * (y * z) | R(x,y,z) = u. [para(81(a,1),20(a,1))]. given #208 (H,wt=17): 243 R(x,y,y \ 1) != z * (y \ 1) | x * y = z. [para(120(a,1),20(a,1))]. given #209 (H,wt=17): 260 L(x / y,z,u) * y = y * L(y \ x,z,u). [para(87(a,1),115(a,1,2,1)),flip(a)]. given #210 (H,wt=17): 264 R(x / y,z,u) * y = y * R(y \ x,z,u). [para(87(a,1),116(a,1,2,1)),flip(a)]. given #211 (H,wt=17): 265 R((x * y) / x,z,u) * x = x * R(y,z,u). [para(105(a,1),116(a,1,2,1)),flip(a)]. given #212 (H,wt=17): 270 T((x * (y / z)) / x,z) = (x * (z \ y)) / x. [para(87(a,1),178(a,1,1,2)),flip(a)]. given #213 (H,wt=17): 279 x \ (K(y,z) * (u * x)) = T(K(y,z) * u,x). [para(197(a,1),30(a,2,2)),flip(a)]. given #214 (H,wt=17): 284 T(K(x,y) * (z / u),u) = u \ (K(x,y) * z). [para(281(a,1),87(a,1,1))]. given #215 (H,wt=17): 285 K(K(x,y),K(x,y) \ z) = T(z,K(x,y)) \ z. [para(283(a,1),74(a,1,1)),flip(a)]. given #216 (H,wt=17): 320 (x * L(x \ y,z,u)) / x = L(y / x,z,u). [hyper(70,a,260,a)]. given #217 (H,wt=16): 328 (x * ((y * x) \ y)) / x = L(1 / x,x,y). [para(103(a,1),320(a,1,1,2))]. given #218 (H,wt=17): 321 (x * R(x \ y,z,u)) / x = R(y / x,z,u). [hyper(70,a,264,a)]. given #219 (H,wt=17): 325 R((x * y) / x,z,u) = (x * R(y,z,u)) / x. [hyper(70,a,265,a),flip(a)]. given #220 (H,wt=17): 327 L((x * y) / x,z,u) = (x * L(y,z,u)) / x. [para(13(a,1),320(a,1,1,2,1)),flip(a)]. given #221 (H,wt=18): 159 L(L(x \ 1,y,z),x,u) = L((u * x) \ u,y,z). [para(103(a,1),43(a,1,1)),flip(a)]. given #222 (H,wt=18): 163 R(R(1 / x,y,z),x,u) = R(u / (x * u),y,z). [para(104(a,1),44(a,1,1)),flip(a)]. given #223 (H,wt=18): 177 x * T(x \ y,z) != u * x | T(y / x,z) = u. [para(117(a,1),110(a,1,2)),flip(b)]. given #224 (H,wt=18): 180 x * T(y,z) != u * x | T((x * y) / x,z) = u. [para(124(a,1),110(a,1,2)),flip(b)]. given #225 (H,wt=18): 195 (x * y) * T(L(z,y,x),u) = x * (y * T(z,u)). [para(38(a,1),76(a,1,2))]. given #226 (H,wt=18): 198 (x * y) * L(z,T(x,y),y) = y * (T(x,y) * z). [para(85(a,1),76(a,1,1))]. given #227 (H,wt=18): 203 T((x * y) \ (x * z),u) = L(T(y \ z,u),y,x). [para(78(a,1),38(a,2,1)),flip(a)]. given #228 (H,wt=18): 207 L(T(x,y) \ z,T(x,y),y) = (x * y) \ (y * z). [para(85(a,1),78(a,2,1))]. given #229 (H,wt=18): 216 R(x,y,T(z,y)) * (z * y) = (x * y) * T(z,y). [para(85(a,1),81(a,1,2))]. given #230 (H,wt=14): 341 R(T(x,x * y),y,T(x,y)) = T(x,y). [hyper(17,a,116,a,b,216,a(flip)),flip(a)]. given #231 (H,wt=18): 221 T((x * y) / (z * y),u) = R(T(x / z,u),z,y). [para(82(a,1),40(a,2,1)),flip(a)]. given #232 (H,wt=16): 345 T((x * y) / (z * y),z) = R(z \ x,z,y). [para(87(a,1),221(a,2,1))]. given #233 (H,wt=16): 346 R(x,y,z) = T(((y * x) * z) / (y * z),y). [para(105(a,1),221(a,2,1)),flip(a)]. given #234 (H,wt=18): 223 R(x / y,y,T(z,y)) = (x * T(z,y)) / (z * y). [para(85(a,1),82(a,2,2))]. given #235 (H,wt=18): 227 R((x \ 1) / y,y,x) = K(x \ 1,x) / (y * x). [para(135(a,2),82(a,2,1))]. given #236 (H,wt=18): 234 R(x,T(y,x),z) \ ((y * x) * z) = T(y,x) * z. [para(85(a,1),97(a,1,2,1))]. given #237 (H,wt=18): 244 (x \ 1) \ R(y,x,x \ 1) = T(y * x,x \ 1). [para(120(a,1),30(a,2,2)),flip(a)]. given #238 (H,wt=18): 245 K(x \ 1,x) * (x \ 1) = R(x \ 1,x,x \ 1). [para(135(a,2),120(a,1,1))]. given #239 (H,wt=18): 249 L(T(x \ (y \ z),u),x,y) = T((y * x) \ z,u). [para(128(a,1),38(a,2,1))]. given #240 (H,wt=18): 251 T(x \ (x / y),z) = L(T(y \ 1,z),y,x / y). [para(158(a,1),38(a,2,1)),flip(a)]. given #241 (H,wt=18): 255 L(T(x \ y,z),x,1 / x) = T((1 / x) * y,z). [para(209(a,1),38(a,2,1))]. given #242 (H,wt=17): 356 (1 / x) * ((x \ y) * x) = T((1 / x) * y,x). [para(255(a,1),241(a,1)),flip(a)]. given #243 (H,wt=18): 261 x * (y * T(z,x * y)) = L(z,y,x) * (x * y). [para(115(a,1),76(a,1)),flip(a)]. given #244 (H,wt=18): 262 x \ (L(y,z,x) * (x * z)) = z * T(y,x * z). [para(115(a,1),126(a,1,2))]. given #245 (H,wt=18): 263 R(x,y,z) * u != u * w | R(T(x,u),y,z) = w. [para(116(a,1),19(a,1))]. given #246 (H,wt=18): 267 x * (y * (y \ z)) != u * w | u \ (x * z) = w. [para(129(a,1),19(a,1))]. given #247 (H,wt=18): 268 ((x / y) * y) * z != u * w | (x * z) / w = u. [para(134(a,1),20(a,1))]. given #248 (H,wt=18): 274 K(x,y) * z != (K(x,y) * u) * w | u * w = z. [para(197(a,2),19(a,1)),flip(a)]. given #249 (H,wt=18): 275 (K(x,y) * z) * u != w * (z * u) | K(x,y) = w. [para(197(a,2),20(a,1))]. given #250 (H,wt=18): 289 a(x / y,y,y \ 1) = (x / y) \ (x * (y \ 1)). [para(16(a,1),102(a,1,2,1)),flip(a)]. given #251 (H,wt=18): 292 L(T(x,y),y,z / y) = z \ ((z / y) * (x * y)). [para(16(a,1),112(a,1,1)),flip(a)]. given #252 (H,wt=18): 295 L(R(T(x,y),z,u),y,x) = R(T(x,x * y),z,u). [para(293(a,1),42(a,1,1)),flip(a)]. given #253 (H,wt=18): 304 x * ((x \ y) * T(z,y)) = L(z,x \ y,x) * y. [para(190(a,1),115(a,1))]. given #254 (H,wt=18): 305 T((x * y) / x,x * y) = L(y,x,(x * y) / x). [hyper(109,a,191,a)]. given #255 (H,wt=18): 306 (x / y) * (y * T(z,x)) = L(z,y,x / y) * x. [para(191(a,1),115(a,1))]. given #256 (H,wt=18): 316 R(x,x \ (y / z),z) \ y = (x \ (y / z)) * z. [para(16(a,1),233(a,1,2))]. given #257 (H,wt=18): 323 ((x * y) / (z * y)) * z = z * R(z \ x,z,y). [para(82(a,1),264(a,1,1))]. given #258 (H,wt=18): 329 L((x \ y) / z,z,x) = (z * ((x * z) \ y)) / z. [para(128(a,1),320(a,1,1,2)),flip(a)]. given #259 (H,wt=18): 342 R(T(x,y),x \ y,T(x,x \ y)) = T(x,x \ y). [para(14(a,1),341(a,1,1,2))]. given #260 (H,wt=18): 344 R(T(x / y,y * z),y,z) = (y * z) \ (x * z). [para(221(a,1),87(a,1))]. given #261 (H,wt=18): 348 T((x * (y \ z)) / z,y) = R(y \ x,y,y \ z). [para(14(a,1),345(a,1,1,2))]. given #262 (H,wt=18): 351 T(((1 / x) * y) * x,1 / x) = R(y,1 / x,x). [para(92(a,1),346(a,2,1)),flip(a)]. given #263 (H,wt=12): 370 R(x,1 / x,x) = T(x,1 / x). [para(58(a,1),351(a,1,1)),flip(a)]. given #264 (H,wt=18): 363 x \ (L(y,x \ z,x) * z) = (x \ z) * T(y,z). [hyper(66,a,304,a)]. given #265 (H,wt=18): 366 (x / y) \ (L(z,y,x / y) * x) = y * T(z,x). [hyper(66,a,306,a)]. given #266 (H,wt=18): 368 (x * y) \ ((z * x) * y) = R(T(z,x * y),x,y). [para(15(a,1),344(a,1,1,1)),flip(a)]. given #267 (H,wt=19): 141 (x * y) * K(K(x,y),y * x) = K(x,y) * (y * x). [para(72(a,1),72(a,1,1))]. given #268 (H,wt=19): 174 (x \ y) * T((x \ y) \ y,z) = T(x,z) * (x \ y). [para(86(a,1),114(a,1,2,1))]. given #269 (H,wt=19): 175 T(x,T(x,y) \ z) * y = y * ((T(x,y) \ z) \ z). [para(86(a,1),114(a,1,2)),flip(a)]. given #270 (H,wt=19): 312 R(x,y / z,z) * y != u * z | x * (y / z) = u. [para(210(a,2),20(a,1))]. given #271 (H,wt=19): 326 ((x * (y / z)) / x) * z = z * ((x * (z \ y)) / x). [para(270(a,1),85(a,1,2)),flip(a)]. given #272 (H,wt=19): 336 R(x / (y * x),y,y \ 1) = R(1 * (y \ 1),y,x). [para(224(a,1),163(a,1,1)),flip(a)]. given #273 (H,wt=17): 375 R(x / (y * x),y,y \ 1) = R(y \ 1,y,x). [para(11(a,1),336(a,2,1))]. given #274 (H,wt=19): 343 (T(x,x * y) * y) * T(x,y) = T(x,y) * (x * y). [para(341(a,1),216(a,1,1)),flip(a)]. given #275 (H,wt=15): 377 T(T(x,x * y) * y,T(x,y)) = x * y. [hyper(109,a,343,a(flip))]. given #276 (H,wt=19): 361 x \ ((x / y) * ((y \ 1) * y)) = T(x \ (x / y),y). [para(292(a,1),251(a,2)),flip(a)]. given #277 (H,wt=19): 378 x \ ((x / y) * K(y \ 1,y)) = T(x \ (x / y),y). [para(135(a,2),361(a,1,2,2))]. given #278 (H,wt=20): 144 L(T(x,x \ y),x \ y,z) = (z * (x \ y)) \ (z * y). [para(108(a,1),26(a,2,2,2))]. given #279 (H,wt=20): 150 (x * (y \ 1)) \ (x * K(y \ 1,y)) = L(y,y \ 1,x). [para(135(a,2),26(a,2,2,2)),flip(a)]. given #280 (H,wt=20): 196 (x * y) * L(L(z,y,x),u,w) = x * (y * L(z,u,w)). [para(43(a,1),76(a,1,2))]. given #281 (H,wt=20): 199 K(x \ 1,x) * L(y,x,x \ 1) = (x \ 1) * (x * y). [para(135(a,2),76(a,1,1))]. given #282 (H,wt=20): 204 R((x * y) \ (x * z),u,w) = L(R(y \ z,u,w),y,x). [para(78(a,1),42(a,1,1))]. given #283 (H,wt=20): 205 L(L(x \ y,z,u),x,w) = L((w * x) \ (w * y),z,u). [para(78(a,1),43(a,1,1)),flip(a)]. given #284 (H,wt=20): 214 L(R(x,y,z),u,w) * (y * z) = (L(x,u,w) * y) * z. [para(42(a,1),81(a,1,1))]. given #285 (H,wt=20): 215 R(R(x,y,z),u,w) * (y * z) = (R(x,u,w) * y) * z. [para(44(a,1),81(a,1,1))]. given #286 (H,wt=20): 217 R(x,y \ 1,y) * K(y \ 1,y) = (x * (y \ 1)) * y. [para(135(a,2),81(a,1,2))]. given #287 (H,wt=20): 226 (x * (1 / y)) / K(y,1 / y) = R(x / y,y,1 / y). [para(118(a,2),82(a,2,2)),flip(a)]. given #288 (H,wt=20): 232 (x * y) / L(T(z,z \ y),z \ y,x) = x * (z \ y). [para(108(a,1),95(a,1,1,2))]. given #289 (H,wt=20): 235 R(x * y,K(y,x),z) \ ((y * x) * z) = K(y,x) * z. [para(72(a,1),97(a,1,2,1))]. given #290 (H,wt=20): 256 L(R(x \ y,z,u),x,1 / x) = R((1 / x) * y,z,u). [para(209(a,1),42(a,1,1)),flip(a)]. given #291 (H,wt=20): 257 L(L(x \ y,z,u),x,1 / x) = L((1 / x) * y,z,u). [para(209(a,1),43(a,1,1)),flip(a)]. given #292 (H,wt=19): 394 L((1 / x) * T(x,y),x,y) = L(K(x,y),x,1 / x). [para(311(a,2),257(a,1,1)),flip(a)]. given #293 (H,wt=20): 259 L(R(x,1 / y,y),z,u) / y = L(x,z,u) * (1 / y). [para(42(a,1),246(a,1,1))]. given #294 (H,wt=20): 307 L(T((x \ y) \ z,u),x \ y,x) = T(y \ (x * z),u). [para(200(a,1),38(a,2,1))]. given #295 (H,wt=20): 313 R(T(x / (y / z),u),y / z,z) = T((x * z) / y,u). [para(220(a,1),40(a,2,1))]. given #296 (H,wt=20): 331 R((x * (1 / y)) / x,y,z) = (x * (z / (y * z))) / x. [para(104(a,1),325(a,2,1,2))]. given #297 (H,wt=20): 349 R((x / y) \ z,x / y,y) = T((z * y) / x,x / y). [para(16(a,1),345(a,1,1,2)),flip(a)]. given #298 (H,wt=20): 350 T(R(x \ y,x,z),x * z) = T((x * z) \ (y * z),x). [para(345(a,1),117(a,1,1))]. given #299 (H,wt=20): 357 T((1 / x) * y,x) != (1 / x) * z | (x \ y) * x = z. [para(356(a,1),19(a,1))]. given #300 (H,wt=20): 364 T(L(x,y,(y * x) / y),y) = T(y \ (y * x),y * x). [para(305(a,1),117(a,1,1))]. given #301 (H,wt=20): 402 R(T(x \ y,x * z),x,z) = T((x * z) \ (y * z),x). [para(350(a,1),40(a,2))]. given #302 (H,wt=20): 403 L(T(x,y),y,(y * x) / y) = T(y \ (y * x),y * x). [para(364(a,1),38(a,2))]. given #303 (H,wt=16): 405 L(T(x,y),y,(y * x) / y) = T(x,y * x). [para(13(a,1),403(a,2,1))]. given #304 (H,wt=20): 404 T((x * y) \ ((x * z) * y),x) = R(T(z,x * y),x,y). [para(13(a,1),402(a,1,1,1)),flip(a)]. given #305 (H,wt=12): 406 R(T(x,y * x),y,x) = T(x,y). [para(13(a,1),404(a,1,1)),flip(a)]. given #306 (H,wt=14): 407 R(T(x,y),y / x,x) = T(x,y / x). [para(16(a,1),406(a,1,1,2))]. given #307 (H,wt=14): 408 x * R(T(y,x * y),x,y) = y * x. [para(406(a,2),85(a,1,2))]. given #308 (H,wt=21): 179 T((((x * y) / x) \ z) \ z,x) = T(y,((x * y) / x) \ z). [para(86(a,1),124(a,1,1))]. given #309 (H,wt=21): 266 (x \ y) * R((x \ y) \ y,z,u) = R(x,z,u) * (x \ y). [para(86(a,1),116(a,1,2,1))]. given #310 (H,wt=21): 335 L(L(x \ 1,y * x,z),x,y) = (z * (y * x)) \ (z * y). [para(159(a,2),78(a,1))]. given #311 (H,wt=21): 337 (x * y) * T((x * y) \ x,z) = x * (y * T(y \ 1,z)). [para(103(a,1),195(a,1,2,1))]. given #312 (H,wt=21): 340 x * (y * T(y \ T(y,x),z)) = (x * y) * T(K(y,x),z). [para(311(a,2),195(a,1,2,1)),flip(a)]. given #313 (H,wt=21): 355 (x / y) * (y * T(y \ 1,z)) = x * T(x \ (x / y),z). [para(251(a,2),191(a,1,2)),flip(a)]. given #314 (H,wt=21): 358 K(x,y) \ (z * (K(x,y) * u)) = u * T(z,K(x,y) * u). [para(88(a,1),262(a,1,2,1))]. given #315 (H,wt=21): 367 L(x,y,z / y) * z != (z / y) * u | y * T(x,z) = u. [para(306(a,1),19(a,1))]. given #316 (H,wt=21): 369 T((x * (y \ z)) / z,y) * z = ((y \ x) * y) * (y \ z). [para(348(a,2),153(a,1,1))]. given #317 (H,wt=21): 371 (x \ y) * T((x \ y) \ z,y) = x \ ((y \ (x * z)) * y). [para(200(a,1),363(a,1,2,1)),flip(a)]. given #318 (H,wt=19): 414 (x \ y) * T((x \ y) \ 1,y) = x \ ((y \ x) * y). [para(12(a,1),371(a,2,2,1,2))]. given #319 (H,wt=21): 386 (L(K(x,y),z,u) * w) * v5 = L(K(x,y),z,u) * (w * v5). [para(272(a,1),214(a,1,1,1)),flip(a)]. given #320 (H,wt=21): 388 x \ ((L(y,z,x) * x) * z) = z * T(R(y,x,z),x * z). [para(214(a,1),262(a,1,2))]. given #321 (H,wt=21): 392 (1 / x) * (x * R(x \ y,z,u)) = R((1 / x) * y,z,u). [para(256(a,1),119(a,2))]. given #322 (H,wt=19): 416 (1 / x) * (x * R(x \ 1,y,z)) = R(1 / x,y,z). [para(12(a,1),392(a,2,1))]. given #323 (H,wt=18): 419 (1 / x) * ((y / (x * y)) * x) = R(1 / x,x,y). [para(302(a,2),416(a,1,2))]. given #324 (H,wt=19): 418 (1 / x) \ R(1 / x,y,z) = x * R(x \ 1,y,z). [hyper(66,a,416,a)]. given #325 (H,wt=21): 393 (1 / x) \ L((1 / x) * y,z,u) = x * L(x \ y,z,u). [para(257(a,1),240(a,1,2))]. given #326 (H,wt=21): 396 (x \ 1) * T((x \ 1) \ y,z) = x \ T(1 \ (x * y),z). [para(307(a,1),248(a,1,2)),flip(a)]. given #327 (H,wt=19): 422 (x \ 1) * T((x \ 1) \ y,z) = x \ T(x * y,z). [para(47(a,1),396(a,2,2,1))]. given #328 (H,wt=17): 423 (x \ 1) * T((x \ 1) \ 1,y) = x \ T(x,y). [para(12(a,1),422(a,2,2,1))]. given #329 (H,wt=13): 424 T(x,y) * (x \ 1) = x \ T(x,y). [para(423(a,1),174(a,1)),flip(a)]. given #330 (H,wt=21): 413 ((x \ y) * x) * (x \ z) = z * T(z \ (y * (x \ z)),x). [para(369(a,1),171(a,1))]. given #331 (H,wt=19): 425 ((x \ 1) * x) * (x \ y) = y * T(y \ (x \ y),x). [para(11(a,1),413(a,2,2,1,2))]. given #332 (H,wt=19): 426 K(x \ 1,x) * (x \ y) = y * T(y \ (x \ y),x). [para(135(a,2),425(a,1,1))]. given #333 (H,wt=21): 415 x \ ((L(y,z,x) * x) * z) = z * R(T(y,x * z),x,z). [para(40(a,2),388(a,2,2))]. given #334 (H,wt=21): 420 R(1 / x,x,y) != (1 / x) * z | (y / (x * y)) * x = z. [para(419(a,1),19(a,1))]. given #335 (H,wt=21): 427 x \ (y \ ((L(z,x,y) * y) * x)) = R(T(z,y * x),y,x). [hyper(66,a,415,a(flip))]. given #336 (H,wt=22): 181 R((x \ 1) * x,K(x,x \ 1),y) \ y = K(x,x \ 1) * y. [para(142(a,1),164(a,1,1,1))]. given #337 (H,wt=22): 184 L(K(x,x \ 1),K(x \ 1,x),y) = (y * K(x \ 1,x)) \ y. [para(169(a,1),103(a,1,1))]. given #338 (H,wt=22): 212 ((x * y) * z) \ ((R(x,y,z) * y) * z) = a(R(x,y,z),y,z). [para(81(a,1),22(a,2,1)),flip(a)]. given #339 (H,wt=22): 252 L(x \ 1,x,y / x) * y = (y / x) * K(y \ (y / x),y). [para(158(a,2),136(a,2,1)),flip(a)]. given #340 (H,wt=15): 429 K(x \ (x / y),x) = y * T(y \ 1,x). [hyper(367,a,252,a),flip(a)]. given #341 (H,wt=15): 430 x \ K(y \ (y / x),y) = T(x \ 1,y). [hyper(66,a,429,a(flip))]. given #342 (H,wt=15): 431 K(x \ (x / (y \ 1)),x) = y \ T(y,x). [para(429(a,2),423(a,1))]. given #343 (H,wt=10): 433 L(x,y,z \ T(z,u)) = x. [para(431(a,1),88(a,1,3))]. given #344 (H,wt=19): 434 K(x \ (x / ((y / x) \ 1)),x) = (y / x) \ (x \ y). [para(87(a,1),431(a,2,2))]. given #345 (H,wt=22): 278 ((K(x,y) * (z * u)) * w) / (u * w) = R(K(x,y) * z,u,w). [para(197(a,1),28(a,2,1,1)),flip(a)]. given #346 (H,wt=22): 282 (K(x,y) * ((z * u) * w)) / (u * w) = K(x,y) * R(z,u,w). [para(81(a,1),230(a,1,1,2))]. given #347 (H,wt=22): 298 L(R(x,y,y \ z),u,w) * z = (L(x,u,w) * y) * (y \ z). [para(42(a,1),153(a,1,1))]. given #348 (H,wt=22): 299 R(R(x,y,y \ z),u,w) * z = (R(x,u,w) * y) * (y \ z). [para(44(a,1),153(a,1,1))]. given #349 (H,wt=22): 308 L(R((x \ y) \ z,u,w),x \ y,x) = R(y \ (x * z),u,w). [para(200(a,1),42(a,1,1)),flip(a)]. given #350 (H,wt=22): 309 L(L((x \ y) \ z,u,w),x \ y,x) = L(y \ (x * z),u,w). [para(200(a,1),43(a,1,1)),flip(a)]. given #351 (H,wt=22): 314 R(R(x / (y / z),u,w),y / z,z) = R((x * z) / y,u,w). [para(220(a,1),44(a,1,1)),flip(a)]. given #352 (H,wt=22): 317 R(x \ y,(x \ y) \ y,z) \ (y * z) = T(x,x \ y) * z. [para(86(a,2),233(a,2,1))]. given #353 (H,wt=15): 441 T(x,x \ y) * z = ((x \ y) \ y) * z. [para(317(a,1),233(a,1))]. given #354 (H,wt=21): 443 ((x \ y) \ y) * T(z,T(x,x \ y)) = z * T(x,x \ y). [para(441(a,1),85(a,1))]. given #355 (H,wt=22): 330 ((x \ y) * (y \ x)) / (x \ y) = L(1 / (x \ y),x \ y,x). [para(14(a,1),328(a,1,1,2,1))]. given #356 (H,wt=22): 332 R((x * (y / z)) / x,z,z \ 1) = (x * (y * (z \ 1))) / x. [para(224(a,1),325(a,2,1,2))]. given #357 (H,wt=19): 444 (x * (y * (x \ 1))) / x = (x * (y / x)) * (x \ 1). [para(332(a,1),224(a,1))]. given #358 (H,wt=22): 333 L(((x * y) * z) / (x * y),y,x) = (x * (y * z)) / (x * y). [para(76(a,1),327(a,2,1))]. given #359 (H,wt=22): 352 T(R(x / y,y,T(z,y)),z * y) = (z * y) \ (x * T(z,y)). [para(223(a,2),87(a,1,1))]. given #360 (H,wt=22): 417 (1 / x) * (((y * z) / (x * z)) * x) = R((1 / x) * y,x,z). [para(323(a,2),392(a,1,2))]. given #361 (H,wt=22): 428 R(K(x \ 1,x),K(x,x \ 1),y) \ y = K(x,x \ 1) * y. [para(135(a,2),181(a,1,1,1))]. given #362 (H,wt=15): 447 K(x \ 1,x) \ y = K(x,x \ 1) * y. [para(272(a,1),428(a,1,1))]. => 451 back subsumes hint matchers not on Sos. Reset weight to 518.000. given #363 (H,wt=13): 449 K(x,x \ 1) * K(x \ 1,x) = 1. [para(447(a,1),48(a,1))]. given #364 (H,wt=13): 450 K(x,x \ 1) * (x \ 1) = 1 / x. [para(447(a,1),188(a,1))]. given #365 (H,wt=13): 452 K(x,x \ 1) \ 1 = K(x \ 1,x). [hyper(66,a,449,a)]. given #366 (H,wt=15): 448 K(x \ 1,x) * (K(x,x \ 1) * y) = y. [hyper(65,a,447,a)]. given #367 (H,wt=15): 455 K(x,x \ 1) \ y = K(x \ 1,x) * y. [para(14(a,1),448(a,1,2)),flip(a)]. given #368 (H,wt=15): 457 x / (K(y \ 1,y) * x) = K(y,y \ 1). [para(455(a,1),57(a,1,2))]. given #369 (H,wt=17): 453 K(x,x \ 1) * ((x \ 1) * y) = (1 / x) * y. [para(450(a,1),197(a,1,1)),flip(a)]. given #370 (H,wt=17): 454 (1 / x) * ((x \ 1) \ y) = K(x,x \ 1) * y. [para(450(a,1),273(a,1,1))]. given #371 (H,wt=18): 456 K(x \ 1,x) * y != z | K(x,x \ 1) * z = y. [para(448(a,1),19(a,1)),flip(a)]. given #372 (H,wt=22): 435 (K(x,y) * ((z * u) * w)) / (u * w) = R(K(x,y) * z,u,w). [para(197(a,1),278(a,1,1))]. given #373 (H,wt=17): 458 R(K(x,y) * z,u,w) = K(x,y) * R(z,u,w). [para(435(a,1),282(a,1))]. given #374 (H,wt=19): 459 K(x,x \ 1) * R(x \ 1,y,z) = R(1 / x,y,z). [para(450(a,1),458(a,1,1)),flip(a)]. given #375 (H,wt=19): 462 K(x \ 1,x) * R(1 / x,y,z) = R(x \ 1,y,z). [para(459(a,1),448(a,1,2))]. given #376 (H,wt=19): 463 R(x \ 1,y,z) / R(1 / x,y,z) = K(x \ 1,x). [hyper(70,a,462,a)]. given #377 (H,wt=22): 445 R(T(x / y,z * y),y,T(z,y)) = (z * y) \ (x * T(z,y)). [para(352(a,1),40(a,2))]. given #378 (H,wt=22): 446 (1 / x) * ((y * (x \ 1)) * x) = R((1 / x) * y,x,x \ 1). [para(91(a,1),417(a,1,2,1))]. given #379 (H,wt=23): 194 (x * (y * z)) \ (x * (y * (z * u))) = L(L(u,z,y),y * z,x). [para(76(a,1),26(a,2,2,2)),flip(a)]. given #380 (H,wt=23): 213 (((x * y) * z) * u) / ((y * z) * u) = R(R(x,y,z),y * z,u). [para(81(a,1),28(a,2,1,1)),flip(a)]. given #381 (H,wt=23): 277 (K(x,y) * (z * u)) \ (u * (K(x,y) * z)) = K(u,K(x,y) * z). [para(197(a,1),24(a,2,1)),flip(a)]. given #382 (H,wt=21): 464 (x * K(y,z)) \ (K(y,z) * x) = K(K(y,z),K(y,z) * x). [para(277(a,1),206(a,1)),flip(a)]. given #383 (H,wt=15): 465 K(K(x,y),K(x,y) * z) = K(K(x,y),z). [para(464(a,1),24(a,2)),flip(a)]. given #384 (H,wt=15): 466 K(K(x,y),K(x,y) \ z) = K(K(x,y),z). [para(14(a,1),465(a,1,2)),flip(a)]. given #385 (H,wt=13): 467 T(x,K(y,z)) \ x = K(K(y,z),x). [para(466(a,1),285(a,1)),flip(a)]. given #386 (H,wt=13): 468 T(x,K(y,z)) * K(K(y,z),x) = x. [para(467(a,1),14(a,1,2))]. given #387 (H,wt=23): 315 (x * y) / L(z * y,y / (z * y),x) = x * R(1 / z,z,y). [para(104(a,2),229(a,2,2))]. given #388 (H,wt=16): 469 x * R(1 / y,y,z) = x * (z / (y * z)). [para(315(a,1),229(a,1))]. given #389 (H,wt=16): 470 (x * (y / (z * y))) / R(1 / z,z,y) = x. [hyper(70,a,469,a)]. given #390 (H,wt=23): 318 R(x * y,(x * y) \ x,z) \ (x * z) = L(y \ 1,y,x) * z. [para(103(a,2),233(a,2,1))]. given #391 (H,wt=16): 473 L(x \ 1,x,y) * z = ((y * x) \ y) * z. [para(318(a,1),233(a,1))]. given #392 (H,wt=23): 338 (x * y) * T((x * y) \ (x * z),u) = x * (y * T(y \ z,u)). [para(78(a,1),195(a,1,2,1))]. given #393 (H,wt=23): 339 (x * y) * T((x * y) \ z,u) = x * (y * T(y \ (x \ z),u)). [para(128(a,1),195(a,1,2,1))]. given #394 (H,wt=23): 362 (x * y) * R(T(x,x * y),z,u) = x * (y * R(T(x,y),z,u)). [para(295(a,1),76(a,1,2))]. given #395 (H,wt=19): 475 x * (y * R(T(x,y),z,u)) = R(x,z,u) * (x * y). [para(362(a,1),116(a,1))]. given #396 (H,wt=17): 476 R(x,y,z) * (x * u) = x * (R(x,y,z) * u). [para(116(a,1),475(a,1,2)),flip(a)]. given #397 (H,wt=17): 477 x \ (R(x,y,z) * u) = R(x,y,z) * (x \ u). [hyper(267,a,476,a)]. given #398 (H,wt=15): 479 R(x,y,z) * (x \ 1) = x \ R(x,y,z). [para(12(a,1),477(a,1,2)),flip(a)]. given #399 (H,wt=17): 478 x * (R(x,y,z) * (x \ u)) = R(x,y,z) * u. [para(14(a,1),476(a,1,2)),flip(a)]. given #400 (H,wt=18): 480 R(x,y,z) * (x \ (y * z)) = x \ ((x * y) * z). [para(81(a,1),477(a,1,2)),flip(a)]. given #401 (H,wt=16): 482 R(x,y,x) * (x \ (y * x)) = T(x * y,x). [para(480(a,2),30(a,2)),flip(a)]. given #402 (H,wt=14): 483 R(x,y,x) * T(y,x) = T(x * y,x). [para(30(a,2),482(a,1,2))]. given #403 (H,wt=19): 481 (x \ 1) * R((x \ 1) \ 1,y,z) = x \ R(x,y,z). [para(479(a,1),266(a,2))]. given #404 (H,wt=23): 374 (x \ y) * ((z * ((x \ y) \ y)) / z) = ((z * x) / z) * (x \ y). [para(57(a,1),326(a,1,1,1,2)),flip(a)]. given #405 (H,wt=23): 376 R(x / y,y / x,(y / x) \ 1) = R((y / x) \ 1,y / x,x). [para(16(a,1),375(a,1,1,2))]. given #406 (H,wt=22): 484 R(x / y,y / x,(y / x) \ 1) = T((1 * x) / y,y / x). [para(376(a,2),349(a,1))]. given #407 (H,wt=20): 485 R(x / y,y / x,(y / x) \ 1) = T(x / y,y / x). [para(11(a,1),484(a,2,1,1))]. given #408 (H,wt=23): 380 (x * y) * L(T(x,x * y),z,u) = x * (y * L(T(x,y),z,u)). [para(293(a,1),196(a,1,2,1))]. given #409 (H,wt=19): 486 x * (y * L(T(x,y),z,u)) = L(x,z,u) * (x * y). [para(380(a,1),115(a,1))]. given #410 (H,wt=17): 487 L(x,y,z) * (x * u) = x * (L(x,y,z) * u). [para(115(a,1),486(a,1,2)),flip(a)]. given #411 (H,wt=17): 488 L(x,y,z) \ (x * u) = x * (L(x,y,z) \ u). [hyper(17,a,129,a,b,487,a),flip(a)]. given #412 (H,wt=15): 489 x * (L(x,y,z) \ 1) = L(x,y,z) \ x. [para(12(a,1),488(a,1,2)),flip(a)]. given #413 (H,wt=15): 490 x \ (L(x,y,z) \ x) = L(x,y,z) \ 1. [hyper(66,a,489,a)]. given #414 (H,wt=23): 381 K(x \ 1,x) * L(y,x,x \ 1) != (x \ 1) * z | x * y = z. [para(199(a,2),19(a,1))]. given #415 (H,wt=23): 397 x * ((x \ y) * T((x \ y) \ z,u)) = y * T(y \ (x * z),u). [para(307(a,1),190(a,1,2)),flip(a)]. given #416 (H,wt=19): 493 x * T(x \ (y * x),z) = y * (T(y,z) * (y \ x)). [para(174(a,1),397(a,1,2)),flip(a)]. given #417 (H,wt=15): 494 x * (T(x,y) * (x \ z)) = T(x,y) * z. [para(493(a,1),170(a,1))]. given #418 (H,wt=15): 495 x \ (T(x,y) * z) = T(x,y) * (x \ z). [hyper(66,a,494,a)]. given #419 (H,wt=15): 496 T(x,y) * (x * z) = x * (T(x,y) * z). [para(13(a,1),494(a,1,2,2)),flip(a)]. given #420 (H,wt=15): 499 T(x,y) * (x \ (T(x,y) \ z)) = x \ z. [para(14(a,1),495(a,1,2)),flip(a)]. given #421 (H,wt=15): 503 T(x,y) \ (x * z) = x * (T(x,y) \ z). [hyper(17,a,129,a,b,496,a),flip(a)]. given #422 (H,wt=13): 505 x * (T(x,y) \ 1) = T(x,y) \ x. [para(12(a,1),503(a,1,2)),flip(a)]. given #423 (H,wt=13): 506 x \ (T(x,y) \ x) = T(x,y) \ 1. [hyper(66,a,505,a)]. given #424 (H,wt=15): 507 T((T(x,y) \ x) / x,x) = T(x,y) \ 1. [para(505(a,1),105(a,1,1,1))]. given #425 (H,wt=17): 497 x * (T(x,y) * T(z,x)) = T(x,y) * (z * x). [para(30(a,2),494(a,1,2,2))]. given #426 (H,wt=17): 502 T(x,K(y,z)) * (x \ K(K(y,z),x)) = x \ x. [para(468(a,1),495(a,1,2)),flip(a)]. given #427 (H,wt=15): 510 T(x,K(y,z)) * (x \ K(K(y,z),x)) = 1. [para(502(a,2),48(a,1))]. given #428 (H,wt=15): 511 1 / (x \ K(K(y,z),x)) = T(x,K(y,z)). [hyper(70,a,510,a)]. given #429 (H,wt=13): 513 K(K(x,y),z) \ z = T(z,K(x,y)). [para(511(a,1),186(a,1)),flip(a)]. given #430 (H,wt=19): 498 (x / y) * (T(x / y,z) * y) = T(x / y,z) * x. [para(59(a,1),494(a,1,2,2))]. given #431 (H,wt=19): 501 x \ (T(x,y) * T(x,z)) = T(x,z) * (x \ T(x,y)). [para(172(a,1),495(a,1,2))]. given #432 (H,wt=19): 515 (x / y) * (y * T(y \ x,z)) = T(x / y,z) * x. [para(171(a,1),498(a,1,2))]. given #433 (H,wt=17): 517 (1 / x) \ T(1 / x,y) = x * T(x \ 1,y). [hyper(155,a,515,a(flip))]. given #434 (H,wt=19): 516 T(x,y) * (x \ T(x,z)) = T(x,z) * (x \ T(x,y)). [para(501(a,1),495(a,1))]. given #435 (H,wt=21): 492 x * ((x \ y) * T((x \ y) \ 1,z)) = y * T(y \ x,z). [para(12(a,1),397(a,2,2,1,2))]. given #436 (H,wt=19): 519 x * T(x \ y,z) = y * K(z \ (z / (y \ x)),z). [para(429(a,2),492(a,1,2)),flip(a)]. given #437 (H,wt=19): 520 x \ (y * K(z \ (z / (y \ x)),z)) = T(x \ y,z). [hyper(66,a,519,a)]. given #438 (H,wt=21): 504 (x / y) * (T(x / y,y) * z) = (y \ x) * ((x / y) * z). [para(87(a,1),496(a,1,1)),flip(a)]. given #439 (H,wt=19): 524 (x / y) * ((y \ x) * z) = (y \ x) * ((x / y) * z). [para(87(a,1),504(a,1,2,1))]. given #440 (H,wt=19): 526 (x \ y) \ ((y / x) * z) = (y / x) * ((x \ y) \ z). [hyper(267,a,524,a)]. given #441 (H,wt=17): 528 (x / y) * ((y \ x) \ 1) = (y \ x) \ (x / y). [para(12(a,1),526(a,1,2)),flip(a)]. given #442 (H,wt=19): 527 (x \ y) * ((y / x) * ((x \ y) \ z)) = (y / x) * z. [para(14(a,1),524(a,1,2)),flip(a)]. given #443 (H,wt=17): 531 (x \ 1) * (K(x,x \ 1) * y) = (1 / x) * y. [para(454(a,1),527(a,1,2))]. given #444 (H,wt=19): 529 (x / y) * ((y \ x) \ ((x / y) \ z)) = (y \ x) \ z. [para(14(a,1),526(a,1,2)),flip(a)]. given #445 (H,wt=17): 533 K(x,x \ 1) * ((1 / x) \ y) = (x \ 1) \ y. [para(529(a,1),454(a,1)),flip(a)]. given #446 (H,wt=17): 534 K(x \ 1,x) * ((x \ 1) \ y) = (1 / x) \ y. [para(533(a,1),448(a,1,2))]. given #447 (H,wt=13): 536 K(x \ 1,x) * ((x \ 1) \ 1) = x. [para(534(a,2),59(a,1))]. given #448 (H,wt=13): 538 K(x,x \ 1) \ ((x \ 1) \ 1) = x. [para(536(a,1),455(a,2))]. given #449 (H,wt=17): 535 (1 / x) \ ((x \ 1) * y) = K(x \ 1,x) * y. [para(13(a,1),534(a,1,2)),flip(a)]. given #450 (H,wt=17): 537 x \ (K(x \ 1,x) * y) = ((x \ 1) \ 1) \ y. [para(536(a,1),206(a,1,1))]. given #451 (H,wt=15): 540 ((x \ 1) \ 1) \ K(x,x \ 1) = x \ 1. [para(183(a,1),537(a,1,2)),flip(a)]. given #452 (H,wt=17): 539 (1 / x) * (K(x \ 1,x) * y) = (x \ 1) * y. [para(535(a,1),14(a,1,2))]. given #453 (H,wt=17): 542 (1 / x) * ((x \ 1) \ (K(x \ 1,x) * y)) = y. [hyper(17,a,527,a,b,539,a(flip)),flip(a)]. given #454 (H,wt=17): 543 (x \ 1) \ (K(x \ 1,x) * y) = (1 / x) \ y. [hyper(66,a,542,a),flip(a)]. given #455 (H,wt=17): 544 (x \ 1) * ((1 / x) \ y) = K(x \ 1,x) * y. [para(543(a,1),14(a,1,2))]. given #456 (H,wt=14): 545 (1 / x) \ L(y,x,x \ 1) = x * y. [hyper(17,a,199,a(flip),b,544,a)]. given #457 (H,wt=14): 547 (1 / x) * (x * y) = L(y,x,x \ 1). [para(545(a,1),14(a,1,2))]. given #458 (H,wt=12): 548 L(x \ 1,x,x \ 1) = 1 / x. [hyper(99,a,547,a),flip(a)]. given #459 (H,wt=19): 532 (x / y) \ ((y \ x) \ z) = (y \ x) \ ((x / y) \ z). [hyper(66,a,529,a)]. given #460 (H,wt=19): 541 ((x \ 1) \ 1) \ ((x \ 1) \ y) = x \ ((1 / x) \ y). [para(534(a,1),537(a,1,2)),flip(a)]. given #461 (H,wt=20): 549 L(T(x,y) \ 1,x,x \ 1) = (1 / x) * (T(x,y) \ x). [para(505(a,1),547(a,1,2)),flip(a)]. given #462 (H,wt=21): 514 K(K(x,y),K(x,y) * z) \ (K(x,y) * z) = z * K(x,y). [para(513(a,2),271(a,1))]. given #463 (H,wt=17): 551 K(K(x,y),z) \ (K(x,y) * z) = z * K(x,y). [para(465(a,1),514(a,1,1))]. given #464 (H,wt=17): 552 T(x * K(y,z),K(K(y,z),x)) = x * K(y,z). [para(551(a,1),140(a,1)),flip(a)]. given #465 (H,wt=13): 553 K(x * K(y,z),K(K(y,z),x)) = 1. [hyper(34,a,552,a)]. given #466 (H,wt=13): 554 K(x * y,K(K(x,y),y * x)) = 1. [para(72(a,1),553(a,1,1))]. given #467 (H,wt=21): 522 (x / y) * T(y,z) = x * K(z \ (z / (x \ (x / y))),z). [para(59(a,1),519(a,1,2,1))]. given #468 (H,wt=21): 523 x \ (y * K((y \ x) \ 1,y \ x)) = T(x \ y,y \ x). [para(54(a,1),520(a,1,2,2,1,2))]. given #469 (H,wt=21): 555 K(x \ (x / (y \ (y / z))),x) = y \ ((y / z) * T(z,x)). [hyper(66,a,522,a(flip)),flip(a)]. given #470 (H,wt=22): 500 x \ (T(x,y) * (x / z)) = T(x,y) * L(z \ 1,z,x / z). [para(158(a,2),495(a,2,2))]. given #471 (H,wt=22): 518 T(x / y,z) * x != (x / y) * u | y * T(y \ x,z) = u. [para(515(a,1),19(a,1))]. given #472 (H,wt=22): 530 (x \ y) * z != (y / x) * u | (y / x) * ((x \ y) \ u) = z. [para(527(a,1),19(a,1)),flip(a)]. given #473 (H,wt=23): 398 (T(x / (y / z),u) * (y / z)) * z = T((x * z) / y,u) * y. [para(313(a,1),210(a,1,1)),flip(a)]. given #474 (H,wt=23): 438 (x \ 1) * R((x \ 1) \ y,z,u) = x \ R(1 \ (x * y),z,u). [para(308(a,1),248(a,1,2)),flip(a)]. given #475 (H,wt=21): 557 (x \ 1) * R((x \ 1) \ y,z,u) = x \ R(x * y,z,u). [para(47(a,1),438(a,2,2,1))]. given #476 (H,wt=23): 439 (x \ 1) * L((x \ 1) \ y,z,u) = x \ L(1 \ (x * y),z,u). [para(309(a,1),248(a,1,2)),flip(a)]. given #477 (H,wt=21): 558 (x \ 1) * L((x \ 1) \ y,z,u) = x \ L(x * y,z,u). [para(47(a,1),439(a,2,2,1))]. given #478 (H,wt=23): 440 R(x / (1 / y),z,u) * (1 / y) = R((x * y) / 1,z,u) / y. [para(314(a,1),246(a,1,1)),flip(a)]. given #479 (H,wt=21): 559 R(x / (1 / y),z,u) * (1 / y) = R(x * y,z,u) / y. [para(55(a,1),440(a,2,1,1))]. given #480 (H,wt=21): 560 (1 / x) * R((1 / x) \ y,z,u) = R(y * x,z,u) / x. [para(559(a,1),264(a,1)),flip(a)]. given #481 (H,wt=19): 561 (1 / x) * R((1 / x) \ 1,y,z) = R(x,y,z) / x. [para(11(a,1),560(a,2,1,1))]. given #482 (H,wt=15): 563 (1 / x) * R(x,y,z) = R(x,y,z) / x. [para(59(a,1),561(a,1,2,1))]. given #483 (H,wt=15): 564 (R(x,y,z) / x) / R(x,y,z) = 1 / x. [hyper(70,a,563,a)]. given #484 (H,wt=23): 442 (T(x,x \ y) * z) \ (z * ((x \ y) \ y)) = K(z,(x \ y) \ y). [para(441(a,2),24(a,2,1)),flip(a)]. given #485 (H,wt=23): 460 K(x,x \ 1) * (R(x \ 1,y,z) * u) = R(1 / x,y,z) * u. [para(459(a,1),197(a,1,1)),flip(a)]. given #486 (H,wt=23): 508 T((1 / x) * (T(x,y) \ x),x) = (1 / x) * ((T(x,y) \ 1) * x). [para(506(a,1),356(a,1,2,1)),flip(a)]. given #487 (H,wt=23): 509 T(x,y) * ((T(x,y) \ 1) * x) = x * K(x \ (x / T(x,y)),x). [para(429(a,2),497(a,1,2)),flip(a)]. given #488 (H,wt=22): 565 L(x,T(x,y) \ 1,T(x,y)) = x * K(x \ (x / T(x,y)),x). [para(509(a,1),189(a,1)),flip(a)]. given #489 (H,wt=23): 525 (x \ (x * y)) * (((x * y) / x) * z) = ((x * y) / x) * (y * z). [para(105(a,1),504(a,1,2,1)),flip(a)]. given #490 (H,wt=19): 566 ((x * y) / x) * (y * z) = y * (((x * y) / x) * z). [para(13(a,1),525(a,1,1)),flip(a)]. given #491 (H,wt=19): 567 x * (((y * x) / y) * (x \ z)) = ((y * x) / y) * z. [para(14(a,1),566(a,1,2)),flip(a)]. given #492 (H,wt=17): 568 ((x * y) / x) * (y \ 1) = y \ ((x * y) / x). [hyper(155,a,567,a(flip)),flip(a)]. given #493 (H,wt=17): 569 ((x * y) / x) \ (y \ ((x * y) / x)) = y \ 1. [hyper(66,a,568,a)]. given #494 (H,wt=21): 570 (x / (x / y)) \ (y \ (((x / y) * y) / (x / y))) = y \ 1. [para(16(a,1),569(a,1,1,1))]. given #495 (H,wt=17): 571 (x / (x / y)) \ (y \ (x / (x / y))) = y \ 1. [para(16(a,1),570(a,1,2,2,1))]. => 572 back subsumes hint matchers not on Sos. Reset weight to 521.000. given #496 (H,wt=23): 550 (x \ (x * y)) \ (((x * y) / x) \ z) = ((x * y) / x) \ (y \ z). [para(13(a,1),532(a,1,2,1)),flip(a)]. given #497 (H,wt=19): 573 ((x * y) / x) \ (y \ z) = y \ (((x * y) / x) \ z). [para(13(a,1),550(a,1,1)),flip(a)]. given #498 (H,wt=15): 576 ((x * y) / x) \ (y \ (x * y)) = y \ x. [para(59(a,1),573(a,2,2))]. given #499 (H,wt=13): 577 ((x * y) / x) \ T(x,y) = y \ x. [para(30(a,2),576(a,1,2))]. NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 280 (0.00 of 4.54 sec). given #500 (H,wt=13): 578 T(x,y) = ((x * y) / x) * (y \ x). [para(577(a,1),14(a,1,2)),flip(a)]. given #501 (H,wt=13): 579 T(x,y) / (y \ x) = (x * y) / x. [para(577(a,1),57(a,1,2))]. given #502 (H,wt=15): 580 ((x * (x / y)) / x) * y = T(x,x / y). [para(59(a,1),578(a,2,2)),flip(a)]. given #503 (H,wt=15): 582 x * ((y * (x \ y)) / y) = T(y,y / x). [para(580(a,1),326(a,1)),flip(a)]. given #504 (H,wt=17): 575 x \ (((y * x) / y) \ x) = ((y * x) / y) \ 1. [para(48(a,1),573(a,1,2)),flip(a)]. given #505 (H,wt=17): 581 ((x * y) * x) / (x * y) = T(x * y,x) / y. [para(13(a,1),579(a,1,2)),flip(a)]. given #506 (H,wt=17): 585 x * (((y * x) / y) \ 1) = ((y * x) / y) \ x. [para(575(a,1),14(a,1,2))]. given #507 (H,wt=20): 584 (x * y) * L((x \ y) / y,y,x) = T(y,y / (x * y)). [para(329(a,2),582(a,1,2))]. given #508 (H,wt=17): 587 x \ T(y,y / (x * y)) = y * ((x \ y) / y). [para(584(a,1),126(a,1,2))]. given #509 (H,wt=21): 574 ((x * y) / x) \ (y \ ((x * y) / x)) = (x \ (x * y)) \ 1. [para(48(a,1),550(a,1,2)),flip(a)]. given #510 (H,wt=23): 556 ((x / y) * T((x / y) \ z,u)) * y = T((z * y) / x,u) * x. [para(171(a,1),398(a,1,1))]. given #511 (H,wt=19): 589 ((x / y) * T((x / y) \ x,z)) * y = x * T(y,z). [para(556(a,2),173(a,1))]. given #512 (H,wt=15): 591 ((x / y) * T(y,z)) * y = x * T(y,z). [para(59(a,1),589(a,1,1,2,1))]. given #513 (H,wt=13): 594 (1 / x) * T(x,y) = T(x,y) / x. [hyper(18,a,130,a,b,591,a)]. given #514 (H,wt=15): 592 (x * T(y,z)) / y = (x / y) * T(y,z). [hyper(70,a,591,a)]. given #515 (H,wt=13): 601 (x / y) * T(y,x) = (y * x) / y. [para(85(a,1),592(a,1,1)),flip(a)]. given #516 (H,wt=13): 603 T(x,y) = (y / x) \ ((x * y) / x). [hyper(66,a,601,a),flip(a)]. given #517 (H,wt=15): 593 ((x / y) * T(y,z)) \ (x * T(y,z)) = y. [hyper(66,a,591,a)]. given #518 (H,wt=15): 595 (x * T(y,z)) * y = (x * y) * T(y,z). [para(15(a,1),591(a,1,1,1))]. given #519 (H,wt=13): 610 (x * y) * T(y,x) = (y * x) * y. [para(85(a,1),595(a,1,1)),flip(a)]. given #520 (H,wt=15): 600 ((x / T(y,z)) / y) * T(y,z) = x / y. [para(16(a,1),592(a,1,1)),flip(a)]. given #521 (H,wt=15): 607 x \ ((y * (x * y)) / y) = T(y,x * y). [para(15(a,1),603(a,2,1)),flip(a)]. given #522 (H,wt=15): 608 (x * y) / T(y,z) = (x / T(y,z)) * y. [hyper(268,a,595,a)]. given #523 (H,wt=15): 613 (x / T(y,z)) / y = (x / y) / T(y,z). [hyper(70,a,600,a),flip(a)]. given #524 (H,wt=13): 616 (x / T(x,y)) / x = 1 / T(x,y). [para(54(a,1),613(a,2,1))]. given #525 (H,wt=17): 590 (1 / x) * T((1 / x) \ 1,y) = T(x,y) / x. [hyper(18,a,130,a,b,589,a)]. given #526 (H,wt=15): 617 K(x \ (x / (1 / y)),x) = T(y,x) / y. [para(590(a,1),429(a,2))]. given #527 (H,wt=17): 596 T((x / y) * T(y,z),y) = y \ (x * T(y,z)). [para(591(a,1),30(a,2,2))]. given #528 (H,wt=17): 597 T(x,y) \ (T(x,y) / x) = T(1 / x,T(x,y)). [para(594(a,1),30(a,2,2)),flip(a)]. given #529 (H,wt=17): 598 T(x \ 1,y) / (x \ 1) = x * T(x \ 1,y). [para(57(a,1),594(a,1,1)),flip(a)]. given #530 (H,wt=17): 599 L(K(x,y),x,1 / x) = L(T(x,y) / x,x,y). [para(594(a,1),394(a,1,1)),flip(a)]. given #531 (H,wt=18): 609 (x * T(y,z)) * y != u * T(y,z) | x * y = u. [para(595(a,2),20(a,1))]. given #532 (H,wt=18): 614 (x * y) / T(y,z) != u * y | x / T(y,z) = u. [para(608(a,2),20(a,1))]. given #533 (H,wt=18): 619 L(x \ 1,x,T(x,y) / x) = T(1 / x,T(x,y)). [para(597(a,1),158(a,2))]. given #534 (H,wt=19): 606 K(x \ (x / (x \ (x / y))),x) = x \ ((y * x) / y). [para(601(a,1),555(a,2,2))]. given #535 (H,wt=19): 615 (x * y) / T(y,y \ z) = (x / ((y \ z) \ z)) * y. [para(86(a,1),608(a,2,1,2))]. given #536 (H,wt=15): 620 x / T(y,y \ z) = x / ((y \ z) \ z). [hyper(614,a,615,a)]. given #537 (H,wt=20): 611 R((x * y) / x,x,T(y,x)) = ((y * x) * y) / (y * x). [para(610(a,1),223(a,2,1))]. given #538 (H,wt=18): 622 R((x * y) / x,x,T(y,x)) = T(y * x,y) / x. [para(611(a,2),581(a,1))]. given #539 (H,wt=21): 602 (x / (y / z)) * T(y / z,z) = (x * (z \ y)) / (y / z). [para(87(a,1),592(a,1,1,2)),flip(a)]. given #540 (H,wt=19): 623 (x * (y \ z)) / (z / y) = (x / (z / y)) * (y \ z). [para(87(a,1),602(a,1,2)),flip(a)]. given #541 (H,wt=23): 588 ((x / y) * T((x / y) \ z,u)) * y = x * T(x \ (z * y),u). [para(556(a,2),171(a,1))]. given #542 (H,wt=23): 624 (x / ((y * z) / y)) * (y \ (y * z)) = (x * z) / ((y * z) / y). [para(13(a,1),623(a,1,1,2)),flip(a)]. given #543 (H,wt=19): 627 (x * y) / ((z * y) / z) = (x / ((z * y) / z)) * y. [para(13(a,1),624(a,1,2)),flip(a)]. given #544 (H,wt=23): 625 (x * T(x \ (y * z),u)) / z = (x / z) * T((x / z) \ y,u). [hyper(70,a,588,a)]. given #545 (H,wt=21): 628 (x / y) * T((x / y) \ 1,z) = (x * T(x \ y,z)) / y. [para(11(a,1),625(a,1,1,2,1,2)),flip(a)]. given #546 (H,wt=21): 629 (x / y) * T((x / y) \ z,x) = ((x \ (z * y)) * x) / y. [para(85(a,1),625(a,1,1)),flip(a)]. given #547 (H,wt=23): 626 (((x / y) \ z) * (x / y)) * y = x * T(x \ (z * y),x / y). [para(85(a,1),588(a,1,1))]. given #548 (H,wt=23): 630 K((x / y) \ 1,x / y) * y = x * T(x \ (1 * y),x / y). [para(135(a,2),626(a,1,1))]. given #549 (H,wt=21): 631 K((x / y) \ 1,x / y) * y = x * T(x \ y,x / y). [para(11(a,1),630(a,2,2,1,2))]. given #550 (H,wt=21): 633 (K((x / y) \ 1,x / y) * y) / x = T(y / x,x / y). [para(631(a,2),176(a,1,1))]. given #551 (H,wt=21): 634 K((x / y) \ 1,x / y) * (y / x) = T(y / x,x / y). [para(633(a,1),281(a,1)),flip(a)]. given #552 (H,wt=24): 111 (x * (y * T(z,x * y))) \ (z * (x * y)) = a(x,y,T(z,x * y)). [para(85(a,1),22(a,2,2)),flip(a)]. given #553 (H,wt=23): 635 (L(x,y,z) * (z * y)) \ (x * (z * y)) = a(z,y,T(x,z * y)). [para(261(a,1),111(a,1,1))]. given #554 (H,wt=23): 636 (L(x,y,z) * (z * y)) * a(z,y,T(x,z * y)) = x * (z * y). [para(635(a,1),14(a,1,2))]. given #555 (H,wt=24): 228 R((x * y) / z,z,L(u,y,x)) = (x * (y * u)) / (z * L(u,y,x)). [para(76(a,1),82(a,2,1))]. given #556 (H,wt=24): 237 R(x * y,L(z,y,x),u) \ ((x * (y * z)) * u) = L(z,y,x) * u. [para(76(a,1),97(a,1,2,1))]. given #557 (H,wt=24): 286 R(x,y * z,a(x,y,z)) \ ((x * y) * z) = (y * z) * a(x,y,z). [para(71(a,1),97(a,1,2))]. given #558 (H,wt=24): 287 x \ (y * K(y \ x,1 / (y \ x))) = L(1 / (y \ x),y \ x,y). [para(118(a,2),77(a,1,2,2))]. given #559 (H,wt=24): 288 (K((x / y) \ 1,x / y) * y) / x = R((x / y) \ 1,x / y,y). [para(135(a,2),83(a,1,1,1))]. given #560 (H,wt=24): 334 L((x * ((y \ z) \ u)) / x,y \ z,y) = (x * (z \ (y * u))) / x. [para(200(a,1),327(a,2,1,2))]. given #561 (H,wt=24): 412 R(K(x,y),z,u) \ (w * (K(x,y) * v5)) = v5 * T(w,K(x,y) * v5). [para(272(a,2),358(a,1,1))]. given #562 (H,wt=21): 641 x * T(K(y,z) * u,K(y,z) * x) = u * (K(y,z) * x). [para(412(a,1),97(a,1))]. given #563 (H,wt=24): 583 x \ L((y * ((x \ 1) \ y)) / y,x \ 1,x) = T(y,y / (x \ 1)). [para(582(a,1),248(a,2))]. given #564 (H,wt=19): 643 x \ ((y * (1 \ (x * y))) / y) = T(y,y / (x \ 1)). [para(334(a,1),583(a,1,2))]. given #565 (H,wt=17): 644 x \ ((y * (x * y)) / y) = T(y,y / (x \ 1)). [para(47(a,1),643(a,1,2,1,2))]. given #566 (H,wt=13): 645 T(x,x / (y \ 1)) = T(x,y * x). [para(644(a,1),607(a,1))]. given #567 (H,wt=24): 612 R(T((x * y) / x,y * x),x,T(y,x)) = (y * x) \ ((y * x) * y). [para(610(a,1),445(a,2,2))]. given #568 (H,wt=19): 646 R(L(x,y,x),y,T(x,y)) = (x * y) \ ((x * y) * x). [para(297(a,1),612(a,1,1))]. given #569 (H,wt=19): 647 L(R(x,y,T(x,y)),y,x) = (x * y) \ ((x * y) * x). [para(646(a,1),42(a,1)),flip(a)]. given #570 (H,wt=11): 648 L(R(x,y,T(x,y)),y,x) = x. [para(647(a,2),13(a,1))]. given #571 (H,wt=19): 649 L((x * R(y,z,T(y,z))) / x,z,y) = (x * y) / x. [para(648(a,1),327(a,2,1,2))]. given #572 (H,wt=19): 650 L(R((x * y) / x,z,T(y,z)),z,y) = (x * y) / x. [para(325(a,2),649(a,1,1))]. given #573 (H,wt=25): 301 T((x \ y) / (x * (x \ y)),z) * y = (T(1 / x,z) * x) * (x \ y). [para(162(a,2),153(a,1,1))]. given #574 (H,wt=21): 651 T((x \ y) / y,z) * y = (T(1 / x,z) * x) * (x \ y). [para(14(a,1),301(a,1,1,1,2))]. given #575 (H,wt=21): 652 (T(1 / x,y) * x) * (x \ z) = z * T(z \ (x \ z),y). [para(651(a,1),171(a,1))]. given #576 (H,wt=21): 653 (x * T(x \ 1,y)) * (x \ z) = z * T(z \ (x \ z),y). [para(171(a,1),652(a,1,1))]. given #577 (H,wt=19): 654 (x \ (y \ x)) * x = (y * T(y \ 1,x)) * (y \ x). [para(653(a,2),85(a,1)),flip(a)]. given #578 (H,wt=25): 354 (1 / x) \ T(((1 / x) * x) \ y,z) = x * T(x \ ((1 / x) \ y),z). [para(249(a,1),240(a,1,2))]. given #579 (H,wt=19): 657 x * T(x \ ((1 / x) \ y),z) = (1 / x) \ T(y,z). [para(89(a,1),354(a,1,2,1)),flip(a)]. given #580 (H,wt=25): 360 T(((x / y) * y) \ ((x / y) * z),y) = x \ ((x / y) * ((y \ z) * y)). [para(292(a,1),203(a,2))]. given #581 (H,wt=21): 658 x \ ((x / y) * ((y \ z) * y)) = T(x \ ((x / y) * z),y). [para(16(a,1),360(a,1,1,1)),flip(a)]. given #582 (H,wt=25): 365 T(((x * y) * z) / (x * z),x * y) = R(L(y,x,(x * y) / x),x,z). [para(305(a,1),221(a,2,1))]. given #583 (H,wt=25): 379 (x * y) * L((x * y) \ z,u,w) = x * (y * L(y \ (x \ z),u,w)). [para(128(a,1),196(a,1,2,1))]. given #584 (H,wt=25): 383 (x * y) * R((x * y) \ (x * z),u,w) = x * (y * R(y \ z,u,w)). [para(204(a,2),76(a,1,2))]. given #585 (H,wt=23): 661 (x * y) * R((x * y) \ x,z,u) = x * (y * R(y \ 1,z,u)). [para(12(a,1),383(a,1,2,1,2))]. given #586 (H,wt=25): 385 L((x * y) / (z * y),u,w) * (z * y) = (L(x / z,u,w) * z) * y. [para(82(a,1),214(a,1,1,1))]. given #587 (H,wt=25): 390 R((x * y) / (z * y),u,w) * (z * y) = (R(x / z,u,w) * z) * y. [para(82(a,1),215(a,1,1,1))]. given #588 (H,wt=25): 399 ((x * (y / (z * y))) / x) * (z * y) = (((x * (1 / z)) / x) * z) * y. [para(331(a,1),81(a,1,1))]. given #589 (H,wt=25): 432 L(x \ 1,x,y) \ K(y \ (y * x),y) = T(L(x \ 1,x,y) \ 1,y). [para(160(a,1),430(a,1,2,1,2))]. given #590 (H,wt=21): 667 T(L(x \ 1,x,y) \ 1,y) = L(x \ 1,x,y) \ K(x,y). [para(13(a,1),432(a,1,2,1)),flip(a)]. given #591 (H,wt=21): 668 K(x,y) = L(x \ 1,x,y) * T(L(x \ 1,x,y) \ 1,y). [para(667(a,2),14(a,1,2)),flip(a)]. given #592 (H,wt=25): 436 L((x * (y \ z)) / z,u,w) * z = (L(x / y,u,w) * y) * (y \ z). [para(219(a,1),298(a,1,1,1))]. given #593 (H,wt=25): 437 R((x * (y \ z)) / z,u,w) * z = (R(x / y,u,w) * y) * (y \ z). [para(219(a,1),299(a,1,1,1))]. given #594 (H,wt=25): 546 K(x \ 1,x) * R(1 / x,y,z) = (x \ 1) * (x * R(x \ 1,y,z)). [para(418(a,1),544(a,1,2)),flip(a)]. given #595 (H,wt=19): 671 (x \ 1) * (x * R(x \ 1,y,z)) = R(x \ 1,y,z). [para(546(a,1),462(a,1))]. given #596 (H,wt=19): 672 R(x \ 1,y,z) / (x * R(x \ 1,y,z)) = x \ 1. [hyper(70,a,671,a)]. given #597 (H,wt=25): 586 (((x * y) / x) \ 1) * T(y,((x * y) / x) \ 1) = ((x * y) / x) \ y. [para(585(a,1),85(a,2))]. given #598 (H,wt=25): 656 (T(x,y) * T(T(x,y) \ 1,x)) * (T(x,y) \ x) = (T(x,y) \ 1) * x. [para(506(a,1),654(a,1,1)),flip(a)]. given #599 (H,wt=25): 660 T(((x * y) * z) / (x * z),x * y) = L(R(y,x,z),x,(x * y) / x). [para(365(a,2),42(a,1))]. given #600 (H,wt=13): 674 L(R(x,y,x),y,(y * x) / y) = x. [para(660(a,1),105(a,1))]. given #601 (H,wt=22): 675 ((x * y) / x) \ (y * (x * y)) = x * T(R(y,x,y),x * y). [para(674(a,1),366(a,1,2,1))]. given #602 (H,wt=22): 676 ((x * y) / x) \ (y * (x * y)) = x * R(T(y,x * y),x,y). [para(40(a,2),675(a,2,2))]. given #603 (H,wt=15): 677 ((x * y) / x) \ (y * (x * y)) = y * x. [para(676(a,2),408(a,1))]. given #604 (H,wt=25): 662 (x * y) * R((x * y) \ z,u,w) = x * (y * R(y \ (x \ z),u,w)). [para(14(a,1),383(a,1,2,1,2))]. given #605 (H,wt=25): 664 (x * y) * L((x * y) \ (z * y),u,w) = (L(z / x,u,w) * x) * y. [para(385(a,1),260(a,1)),flip(a)]. given #606 (H,wt=25): 665 (x * y) * R((x * y) \ (z * y),u,w) = (R(z / x,u,w) * x) * y. [para(390(a,1),264(a,1)),flip(a)]. given #607 (H,wt=23): 681 (x * y) * R((x * y) \ y,z,u) = (R(1 / x,z,u) * x) * y. [para(11(a,1),665(a,1,2,1,2))]. given #608 (H,wt=23): 684 (x * y) * R((x * y) \ y,z,u) = (x * R(x \ 1,z,u)) * y. [para(264(a,1),681(a,2,1))]. given #609 (H,wt=25): 666 (x * y) * ((z * ((x * y) \ y)) / z) = (((z * (1 / x)) / z) * x) * y. [para(399(a,1),326(a,1)),flip(a)]. given #610 (H,wt=25): 669 (L(x / y,z,u) * y) * (y \ w) = w * L(w \ (x * (y \ w)),z,u). [para(436(a,1),260(a,1))]. given #611 (H,wt=25): 670 (R(x / y,z,u) * y) * (y \ w) = w * R(w \ (x * (y \ w)),z,u). [para(437(a,1),264(a,1))]. given #612 (H,wt=25): 673 L(R(x,y,y \ 1),y,(y * x) / y) = T((y * x) * (y \ 1),y * x). [para(91(a,1),660(a,1,1)),flip(a)]. given #613 (H,wt=25): 680 x * (y * L(y \ (x \ (z * y)),u,w)) = (L(z / x,u,w) * x) * y. [para(664(a,1),379(a,1)),flip(a)]. given #614 (H,wt=25): 682 (x * y) * R((x * y) \ (z * y),u,w) = (x * R(x \ z,u,w)) * y. [para(264(a,1),665(a,2,1))]. given #615 (H,wt=25): 683 (x * y) * R((x * y) \ ((x * z) * y),u,w) = (x * R(z,u,w)) * y. [para(265(a,1),665(a,2,1))]. given #616 (H,wt=17): 691 (x * R(y,z,u)) * y = (x * y) * R(y,z,u). [para(13(a,1),683(a,1,2,1)),flip(a)]. given #617 (H,wt=21): 692 (x * R(x \ y,z,u)) * (x \ y) = y * R(x \ y,z,u). [para(14(a,1),691(a,2,1))]. given #618 (H,wt=25): 686 (x * y) * ((z * ((x * y) \ y)) / z) = (x * ((z * (x \ 1)) / z)) * y. [para(326(a,1),666(a,2,1))]. given #619 (H,wt=25): 687 (x * L(x \ y,z,u)) * (x \ w) = w * L(w \ (y * (x \ w)),z,u). [para(260(a,1),669(a,1,1))]. given #620 (H,wt=24): 694 x * L(x \ (1 * (y \ x)),y,y \ 1) = (y * (1 / y)) * (y \ x). [para(548(a,1),687(a,1,1,2)),flip(a)]. given #621 (H,wt=24): 695 x * L(x \ (1 * (y \ x)),y,y \ 1) = K(y,1 / y) * (y \ x). [para(118(a,2),694(a,2,1))]. given #622 (H,wt=22): 696 x * L(x \ (y \ x),y,y \ 1) = K(y,1 / y) * (y \ x). [para(11(a,1),695(a,1,2,1,2))]. given #623 (H,wt=25): 688 (x * R(x \ y,z,u)) * (x \ w) = w * R(w \ (y * (x \ w)),z,u). [para(264(a,1),670(a,1,1))]. given #624 (H,wt=25): 689 x * (y * L(y \ (x \ (z * y)),u,w)) = (x * L(x \ z,u,w)) * y. [para(260(a,1),680(a,2,1))]. given #625 (H,wt=23): 697 x * L(x \ (x \ (y * x)),z,u) = T(x * L(x \ y,z,u),x). [hyper(109,a,689,a),flip(a)]. given #626 (H,wt=21): 700 T(x * L(x \ y,z,u),x) = x * L(x \ T(y,x),z,u). [para(30(a,2),697(a,1,2,1,2)),flip(a)]. given #627 (H,wt=22): 701 T(x * L(x \ y,x,1 / x),x) = x * ((1 / x) * T(y,x)). [para(209(a,1),700(a,2,2))]. given #628 (H,wt=19): 702 T(x * ((1 / x) * y),x) = x * ((1 / x) * T(y,x)). [para(209(a,1),701(a,1,1,2))]. given #629 (H,wt=23): 698 x * (y * L(y \ (x \ y),z,u)) = (x * L(x \ 1,z,u)) * y. [para(11(a,1),689(a,1,2,2,1,2,2))]. given #630 (H,wt=22): 704 x * (y * L(y \ (x \ y),x,x \ 1)) = (x * (1 / x)) * y. [para(548(a,1),698(a,2,1,2))]. given #631 (H,wt=19): 705 x * (K(x,1 / x) * (x \ y)) = (x * (1 / x)) * y. [para(696(a,1),704(a,1,2))]. given #632 (H,wt=19): 706 x * (K(x,1 / x) * (x \ y)) = K(x,1 / x) * y. [para(118(a,2),705(a,2,1))]. given #633 (H,wt=25): 690 x * (y * R(y \ (x \ (z * y)),u,w)) = (x * R(x \ z,u,w)) * y. [para(682(a,1),662(a,1)),flip(a)]. given #634 (H,wt=25): 699 (x * L(x \ (y / z),u,w)) * z = x * (z * L(z \ (x \ y),u,w)). [para(16(a,1),689(a,1,2,2,1,2,2)),flip(a)]. given #635 (H,wt=26): 193 (x * (y * z)) \ ((x * y) * (L(z,y,x) * u)) = L(u,L(z,y,x),x * y). [para(76(a,1),26(a,2,1)),flip(a)]. given #636 (H,wt=26): 218 R(x,R(y,z,u),z * u) * ((y * z) * u) = (x * R(y,z,u)) * (z * u). [para(81(a,1),81(a,1,2))]. given #637 (H,wt=26): 269 ((x * y) * T(L(z,y,x),u)) / (x * y) = T((x * (y * z)) / (x * y),u). [para(26(a,2),176(a,1,1,2,1))]. given #638 (H,wt=23): 711 (x * (y * T(z,u))) / (x * y) = T((x * (y * z)) / (x * y),u). [para(195(a,1),269(a,1,1))]. given #639 (H,wt=25): 712 (x * (y * T(T(z,y),u))) / (x * y) = T((x * (z * y)) / (x * y),u). [para(85(a,1),711(a,2,1,1,2))]. given #640 (H,wt=23): 713 (x * (T(y,z) * u)) / (x * u) = T((x * (y * u)) / (x * u),z). [para(114(a,1),712(a,1,1,2))]. given #641 (H,wt=26): 347 R(T(x / y,z),y,u) * (y * u) = (y * u) * T((y * u) \ (x * u),z). [para(221(a,1),171(a,1,1))]. given #642 (H,wt=23): 714 (x * y) * T((x * y) \ (z * y),u) = (T(z / x,u) * x) * y. [para(347(a,1),81(a,1))]. given #643 (H,wt=23): 715 (x * y) * T((x * y) \ (z * y),u) = (x * T(x \ z,u)) * y. [para(171(a,1),714(a,2,1))]. given #644 (H,wt=23): 716 x * (y * T(y \ (x \ (z * y)),u)) = (x * T(x \ z,u)) * y. [para(715(a,1),339(a,1)),flip(a)]. given #645 (H,wt=21): 717 x * (y * T(y \ (x \ y),z)) = (x * T(x \ 1,z)) * y. [para(11(a,1),716(a,1,2,2,1,2,2))]. given #646 (H,wt=19): 721 (x * T(x \ 1,y)) * x = x * (x * T(x \ 1,y)). [para(48(a,1),717(a,1,2,2,1,2)),flip(a)]. given #647 (H,wt=11): 725 T(x,x * T(x \ 1,y)) = x. [hyper(109,a,721,a)]. given #648 (H,wt=19): 722 (x * T(x \ 1,y)) * y = x * ((y \ (x \ y)) * y). [para(85(a,1),717(a,1,2)),flip(a)]. given #649 (H,wt=21): 719 x * ((y \ (x \ (z * y))) * y) = (x * T(x \ z,y)) * y. [para(85(a,1),716(a,1,2))]. given #650 (H,wt=21): 724 x * (K(x \ 1,x) * (x \ y)) = (x * T(x \ 1,x)) * y. [para(426(a,2),717(a,1,2))]. given #651 (H,wt=19): 729 x * (K(x \ 1,x) * (x \ y)) = ((x \ 1) * x) * y. [para(85(a,1),724(a,2,1))]. given #652 (H,wt=19): 730 x * (K(x \ 1,x) * (x \ y)) = K(x \ 1,x) * y. [para(135(a,2),729(a,2,1))]. given #653 (H,wt=19): 731 x \ (K(x \ 1,x) * y) = K(x \ 1,x) * (x \ y). [hyper(66,a,730,a)]. given #654 (H,wt=17): 732 K(x \ 1,x) * (x \ y) = ((x \ 1) \ 1) \ y. [para(731(a,1),537(a,1))]. given #655 (H,wt=23): 718 (x * T(x \ (y / z),u)) * z = x * (z * T(z \ (x \ y),u)). [para(16(a,1),716(a,1,2,2,1,2,2)),flip(a)]. given #656 (H,wt=21): 735 x * (y * T(y \ (x \ z),x)) = ((x \ (z / y)) * x) * y. [para(85(a,1),718(a,1,1)),flip(a)]. given #657 (H,wt=23): 734 (x * (y * T(y \ (x \ z),u))) / y = x * T(x \ (z / y),u). [hyper(70,a,718,a)]. given #658 (H,wt=24): 726 R(x,(x * T(x \ 1,y)) / x,x) = T(x,(x * T(x \ 1,y)) / x). [para(725(a,1),407(a,1,1))]. given #659 (H,wt=20): 739 T(x,(x * T(x \ 1,y)) / x) = R(x,T(1 / x,y),x). [para(176(a,1),726(a,1,2)),flip(a)]. given #660 (H,wt=16): 740 R(x,T(1 / x,y),x) = T(x,T(1 / x,y)). [para(176(a,1),739(a,1,2)),flip(a)]. given #661 (H,wt=24): 733 K(x \ 1,x) * y != (((x \ 1) \ 1) \ z) * u | (x \ z) * u = y. [para(732(a,1),274(a,2,1))]. given #662 (H,wt=25): 723 x * (y \ T(y * (x \ (y \ 1)),z)) = (x * T(x \ 1,z)) * (y \ 1). [para(422(a,1),717(a,1,2))]. given #663 (H,wt=25): 737 ((x \ (y / (z \ 1))) * x) * (z \ 1) = x * (z \ T(z * (x \ y),x)). [para(422(a,1),735(a,1,2)),flip(a)]. given #664 (H,wt=26): 353 R(x,T(y,x),T(z,y * x)) \ (z * (y * x)) = T(y,x) * T(z,y * x). [para(85(a,1),234(a,1,2))]. given #665 (H,wt=26): 389 R(R(x,y \ 1,y),z,u) * K(y \ 1,y) = (R(x,z,u) * (y \ 1)) * y. [para(135(a,2),215(a,1,2))]. given #666 (H,wt=26): 461 R(1 / x,y,z) * u != K(x,x \ 1) * w | R(x \ 1,y,z) * u = w. [para(459(a,1),274(a,2,1)),flip(a)]. given #667 (H,wt=26): 618 K(x \ (x / (1 / (y / (x * y)))),x) = R(x \ 1,x,y) / (y / (x * y)). [para(300(a,1),617(a,2,1))]. given #668 (H,wt=27): 322 (x * R(x \ y,z,u)) \ R(y / x,z,u) = L(x \ 1,x,R(y / x,z,u)). [para(264(a,1),103(a,2,1)),flip(a)]. given #669 (H,wt=27): 400 ((x * (y / ((1 / y) * y))) / x) / y = ((x * (1 / (1 / y))) / x) * (1 / y). [para(331(a,1),246(a,1,1))]. given #670 (H,wt=21): 742 ((x * (1 / (1 / y))) / x) * (1 / y) = ((x * y) / x) / y. [para(92(a,1),400(a,1,1,1,2)),flip(a)]. given #671 (H,wt=21): 743 (1 / x) * ((y * ((1 / x) \ 1)) / y) = ((y * x) / y) / x. [para(742(a,1),326(a,1)),flip(a)]. given #672 (H,wt=17): 744 (1 / x) * ((y * x) / y) = ((y * x) / y) / x. [para(59(a,1),743(a,1,2,1,2))]. given #673 (H,wt=27): 409 (x * y) * T((y * T(x,y)) \ y,z) = y * (T(x,y) * T(T(x,y) \ 1,z)). [para(85(a,1),337(a,1,1))]. given #674 (H,wt=25): 745 x * (T(y,x) * T(T(y,x) \ 1,z)) = (y * x) * T((y * x) \ x,z). [para(85(a,1),409(a,1,2,1,1)),flip(a)]. given #675 (H,wt=25): 746 x * (T(y,x) * T(T(y,x) \ 1,z)) = y * (x * T(x \ (y \ x),z)). [para(745(a,2),339(a,1))]. given #676 (H,wt=23): 747 x * K(y \ (y / T(z,x)),y) = z * (x * T(x \ (z \ x),y)). [para(429(a,2),746(a,1,2))]. given #677 (H,wt=21): 748 (x * T(x \ 1,y)) * z = z * K(y \ (y / T(x,z)),y). [para(747(a,2),717(a,1)),flip(a)]. given #678 (H,wt=19): 749 T(x * T(x \ 1,y),z) = K(y \ (y / T(x,z)),y). [hyper(109,a,748,a(flip))]. given #679 (H,wt=19): 750 T(x * T(x \ 1,y),x \ y) = K(y \ (x \ y),y). [para(123(a,1),749(a,2,1,2))]. given #680 (H,wt=19): 752 K(x \ (x / T(y,z)),x) = T(K(x \ (x / y),x),z). [para(429(a,2),749(a,1,1)),flip(a)]. given #681 (H,wt=17): 753 K(x \ (x / T(x,y)),x) = T(K(x \ 1,x),y). [para(54(a,1),752(a,2,1,1,2))]. given #682 (H,wt=21): 751 T(x,y) * T(T(x,y) \ 1,z) = T(x * T(x \ 1,z),y). [para(749(a,2),429(a,1)),flip(a)]. given #683 (H,wt=23): 754 T(x * T(x \ 1,x),y) * (T(x,y) \ x) = (T(x,y) \ 1) * x. [para(751(a,1),656(a,1,1))]. given #684 (H,wt=21): 755 T((x \ 1) * x,y) * (T(x,y) \ x) = (T(x,y) \ 1) * x. [para(85(a,1),754(a,1,1,1))]. given #685 (H,wt=21): 756 T(K(x \ 1,x),y) * (T(x,y) \ x) = (T(x,y) \ 1) * x. [para(135(a,2),755(a,1,1,1))]. given #686 (H,wt=27): 421 (1 / x) \ L((1 / x) * K(x \ 1,x),y,z) = x * L(T(x \ 1,x),y,z). [para(151(a,1),393(a,2,2,1))]. given #687 (H,wt=27): 474 ((x * ((y * z) \ y)) * u) / (L(z \ 1,z,y) * u) = R(x,(y * z) \ y,u). [para(473(a,2),28(a,2,2)),flip(a)]. given #688 (H,wt=27): 521 (x * y) * T((x * y) \ (y * x),z) = (y * x) * K(z \ (z / K(x,y)),z). [para(24(a,2),519(a,2,2,1,2,2))]. given #689 (H,wt=23): 757 (x * y) * K(z \ (z / K(y,x)),z) = (y * x) * T(K(x,y),z). [para(24(a,2),521(a,1,2,1)),flip(a)]. given #690 (H,wt=25): 758 (x * y) * (K(y,x) * T(K(y,x) \ 1,z)) = (y * x) * T(K(x,y),z). [para(429(a,1),757(a,1,2))]. given #691 (H,wt=25): 759 (x * y) \ ((y * x) * T(K(x,y),z)) = K(y,x) * T(K(y,x) \ 1,z). [hyper(66,a,758,a)]. given #692 (H,wt=27): 562 (x \ 1) * (K(x,x \ 1) * R((1 / x) \ y,z,u)) = R(y * x,z,u) / x. [para(560(a,1),531(a,2))]. given #693 (H,wt=27): 632 K((x / (y * x)) \ 1,x / (y * x)) * (y * x) = T(y,x / (y * x)) * x. [para(631(a,2),170(a,1))]. given #694 (H,wt=27): 640 x * ((x \ y) * ((z * ((x \ y) \ u)) / z)) = y * ((z * (y \ (x * u))) / z). [para(334(a,1),190(a,1,2)),flip(a)]. given #695 (H,wt=27): 659 T(K(x \ (x / (y \ (y / z))),x),z) = y \ ((y / z) * ((z \ T(z,x)) * z)). [para(555(a,2),658(a,2,1)),flip(a)]. given #696 (H,wt=27): 693 (x * R(T(y,x),z,u)) * (x \ (y * x)) = (y * x) * R(x \ (y * x),z,u). [para(30(a,2),692(a,1,1,2,1))]. given #697 (H,wt=25): 762 (R(x,y,z) * u) * (u \ (x * u)) = (x * u) * R(u \ (x * u),y,z). [para(116(a,1),693(a,1,1))]. given #698 (H,wt=23): 763 (x * y) * R(y \ (x * y),z,u) = (R(x,z,u) * y) * T(x,y). [para(30(a,2),762(a,1,2)),flip(a)]. given #699 (H,wt=21): 764 (R(x,y,z) * u) * T(x,u) = (x * u) * R(T(x,u),y,z). [para(30(a,2),763(a,1,2,1)),flip(a)]. given #700 (H,wt=27): 708 x \ (y * (x * L(x \ (y \ z),u,w))) = T(y * L(y \ (z / x),u,w),x). [para(699(a,1),30(a,2,2)),flip(a)]. given #701 (H,wt=27): 727 (x \ y) * ((y \ T(x,x \ y)) * y) = ((x \ y) * T((x \ y) \ 1,y)) * y. [para(86(a,2),722(a,2,2,1,2)),flip(a)]. given #702 (H,wt=23): 766 (x \ y) * ((y \ T(x,x \ y)) * y) = (x \ ((y \ x) * y)) * y. [para(414(a,1),727(a,2,1))]. given #703 (H,wt=21): 767 (x \ y) * ((y \ T(x,x \ y)) * y) = K(y \ x,y) * y. [para(73(a,1),766(a,2,1))]. given #704 (H,wt=27): 736 (x \ 1) * (y * T(y \ ((x \ 1) \ z),u)) = (x \ T(x * (z / y),u)) * y. [para(422(a,1),718(a,1,1)),flip(a)]. given #705 (H,wt=27): 738 ((1 / x) * ((1 / x) \ T(y,z))) / x = (1 / x) * T((1 / x) \ (y / x),z). [para(657(a,1),734(a,1,1,2))]. given #706 (H,wt=19): 768 (1 / x) * T((1 / x) \ (y / x),z) = T(y,z) / x. [para(14(a,1),738(a,1,1)),flip(a)]. given #707 (H,wt=19): 770 (1 / x) * T((1 / x) \ y,z) = T(y * x,z) / x. [para(15(a,1),768(a,1,2,1,2))]. given #708 (H,wt=25): 771 ((x \ (y / (1 / z))) * x) * (1 / z) = x * (T((x \ y) * z,x) / z). [para(770(a,1),735(a,1,2)),flip(a)]. given #709 (H,wt=27): 760 (x \ 1) * R(K(x,x \ 1) * ((1 / x) \ y),z,u) = R(y * x,z,u) / x. [para(458(a,2),562(a,1,2))]. given #710 (H,wt=21): 772 (x \ 1) * R((x \ 1) \ y,z,u) = R(y * x,z,u) / x. [para(533(a,1),760(a,1,2,1))]. given #711 (H,wt=17): 773 R(x * y,z,u) / y = y \ R(y * x,z,u). [para(772(a,1),557(a,1))]. given #712 (H,wt=17): 774 (x \ R(x * y,z,u)) * x = R(y * x,z,u). [para(773(a,1),16(a,1,1))]. given #713 (H,wt=17): 775 x \ R(x * (y / x),z,u) = R(y,z,u) / x. [para(16(a,1),773(a,1,1,1)),flip(a)]. given #714 (H,wt=17): 776 R((x \ y) * x,z,u) = (x \ R(y,z,u)) * x. [para(14(a,1),774(a,1,1,2,1)),flip(a)]. given #715 (H,wt=27): 761 x \ (y * ((z * (y \ (x * u))) / z)) = (x \ y) * ((z * ((x \ y) \ u)) / z). [hyper(66,a,640,a)]. given #716 (H,wt=25): 777 (x \ y) * ((z * ((x \ y) \ 1)) / z) = x \ (y * ((z * (y \ x)) / z)). [para(12(a,1),761(a,1,2,2,1,2,2)),flip(a)]. given #717 (H,wt=28): 276 (x * (K(y,z) * (u * w))) \ ((x * (K(y,z) * u)) * w) = a(x,K(y,z) * u,w). [para(197(a,1),22(a,2,1,2)),flip(a)]. given #718 (H,wt=28): 319 L(R(x,y,K(y,L(x,z,u))),z,u) \ (y * L(x,z,u)) = y * K(y,L(x,z,u)). [para(42(a,1),236(a,1,1))]. given #719 (H,wt=28): 391 (x * y) / L(T(z \ y,(z \ y) \ y),(z \ y) \ y,x) = x * T(z,z \ y). [para(86(a,2),232(a,2,2))]. given #720 (H,wt=15): 780 x * T(y,y \ z) = x * ((y \ z) \ z). [para(391(a,1),232(a,1))]. given #721 (H,wt=18): 781 x * T(y,y \ z) != x * u | (y \ z) \ z = u. [para(780(a,2),19(a,1))]. given #722 (H,wt=28): 395 L(R(x / (1 / y),1 / y,y),z,u) / y = (1 / y) * L((1 / y) \ x,z,u). [para(259(a,2),260(a,1))]. given #723 (H,wt=21): 782 (1 / x) * L((1 / x) \ y,z,u) = L(y * x,z,u) / x. [para(225(a,1),395(a,1,1,1)),flip(a)]. given #724 (H,wt=28): 471 K((x / (y * x)) \ 1,x / (y * x)) = ((x / (y * x)) \ 1) * R(1 / y,y,x). [para(469(a,2),135(a,2))]. given #725 (H,wt=28): 491 (x \ (y \ z)) \ (((y * x) \ z) \ (x \ (y \ z))) = L(x \ (y \ z),x,y) \ 1. [para(128(a,1),490(a,1,2,1))]. given #726 (H,wt=25): 783 (x \ (y \ z)) \ (((y * x) \ z) \ (x \ (y \ z))) = ((y * x) \ z) \ 1. [para(128(a,1),491(a,2,1))]. given #727 (H,wt=28): 604 (L(x \ 1,x,y) * y) / L(x \ 1,x,y) = (y * x) * T(L(x \ 1,x,y),y). [para(160(a,1),601(a,1,1)),flip(a)]. given #728 (H,wt=25): 785 (L(x \ 1,x,y) * y) / L(x \ 1,x,y) = y * (x * T(x \ 1,y)). [para(604(a,2),195(a,1))]. given #729 (H,wt=29): 387 (L(x / (y / z),u,w) * (y / z)) * z = L((x * z) / y,u,w) * ((y / z) * z). [para(220(a,1),214(a,1,1,1)),flip(a)]. given #730 (H,wt=25): 787 (L(x / (y / z),u,w) * (y / z)) * z = L((x * z) / y,u,w) * y. [para(16(a,1),387(a,2,2))]. given #731 (H,wt=25): 788 ((x / y) * L((x / y) \ z,u,w)) * y = L((z * y) / x,u,w) * x. [para(260(a,1),787(a,1,1))]. given #732 (H,wt=25): 789 ((x / y) * L((x / y) \ z,u,w)) * y = x * L(x \ (z * y),u,w). [para(788(a,2),260(a,1))]. given #733 (H,wt=21): 790 ((x / y) * L((x / y) \ x,z,u)) * y = x * L(y,z,u). [para(13(a,1),789(a,2,2,1))]. given #734 (H,wt=17): 791 ((x / y) * L(y,z,u)) * y = x * L(y,z,u). [para(59(a,1),790(a,1,1,2,1))]. given #735 (H,wt=15): 793 (1 / x) * L(x,y,z) = L(x,y,z) / x. [hyper(18,a,130,a,b,791,a)]. given #736 (H,wt=17): 792 (x * L(y,z,u)) / y = (x / y) * L(y,z,u). [hyper(70,a,791,a)]. given #737 (H,wt=17): 795 (x * L(y,z,u)) * y = (x * y) * L(y,z,u). [para(15(a,1),791(a,1,1,1))]. given #738 (H,wt=17): 797 ((x / L(y,z,u)) / y) * L(y,z,u) = x / y. [para(16(a,1),792(a,1,1)),flip(a)]. given #739 (H,wt=17): 798 ((x / L(y,z,u)) * y) * L(y,z,u) = x * y. [para(16(a,1),795(a,1,1)),flip(a)]. given #740 (H,wt=17): 799 (x / L(y,z,u)) / y = (x / y) / L(y,z,u). [hyper(70,a,797,a),flip(a)]. given #741 (H,wt=15): 801 (x / L(x,y,z)) / x = 1 / L(x,y,z). [para(54(a,1),799(a,2,1))]. given #742 (H,wt=17): 800 ((x / L(y,z,u)) * y) \ (x * y) = L(y,z,u). [hyper(66,a,798,a)]. given #743 (H,wt=18): 802 L(x,y,z) = ((z * y) * x) \ ((z * (y * x)) * x). [para(95(a,1),800(a,1,1,1)),flip(a)]. given #744 (H,wt=20): 796 L(x,y,z) \ (L(x,y,z) / x) = T(1 / x,L(x,y,z)). [para(793(a,1),30(a,2,2)),flip(a)]. given #745 (H,wt=25): 794 (R(x,L(y,z,u) / y,y) / y) * L(y,z,u) = x * (L(y,z,u) / y). [hyper(18,a,210,a(flip),b,791,a)]. given #746 (H,wt=29): 401 ((x * ((y \ z) / (y * (y \ z)))) / x) * z = (((x * (1 / y)) / x) * y) * (y \ z). [para(331(a,1),153(a,1,1))]. given #747 (H,wt=25): 804 ((x * ((y \ z) / z)) / x) * z = (((x * (1 / y)) / x) * y) * (y \ z). [para(14(a,1),401(a,1,1,1,2,2))]. given #748 (H,wt=25): 805 (((x * (1 / y)) / x) * y) * (y \ z) = z * ((x * (z \ (y \ z))) / x). [para(804(a,1),326(a,1))]. given #749 (H,wt=25): 806 (x * ((y * (x \ 1)) / y)) * (x \ z) = z * ((y * (z \ (x \ z))) / y). [para(326(a,1),805(a,1,1))]. given #750 (H,wt=25): 807 (x * ((y * (x \ (z \ x))) / y)) / (z \ x) = z * ((y * (z \ 1)) / y). [hyper(70,a,806,a)]. given #751 (H,wt=29): 655 (L(x,y,z) * T(L(x,y,z) \ 1,x)) * (L(x,y,z) \ x) = (L(x,y,z) \ 1) * x. [para(490(a,1),654(a,1,1)),flip(a)]. given #752 (H,wt=29): 663 (x * y) * R((y * T(x,y)) \ y,z,u) = y * (T(x,y) * R(T(x,y) \ 1,z,u)). [para(85(a,1),661(a,1,1))]. given #753 (H,wt=27): 809 x * (T(y,x) * R(T(y,x) \ 1,z,u)) = (y * x) * R((y * x) \ x,z,u). [para(85(a,1),663(a,1,2,1,1)),flip(a)]. given #754 (H,wt=25): 810 x * (T(y,x) * R(T(y,x) \ 1,z,u)) = (y * R(y \ 1,z,u)) * x. [para(809(a,2),684(a,1))]. given #755 (H,wt=23): 811 T(x,y) * R(T(x,y) \ 1,z,u) = T(x * R(x \ 1,z,u),y). [hyper(109,a,810,a),flip(a)]. given #756 (H,wt=29): 808 (x * ((y * (x \ z)) / y)) / ((x / z) \ x) = (x / z) * ((y * ((x / z) \ 1)) / y). [para(59(a,1),807(a,1,1,2,1,2,2))]. given #757 (H,wt=25): 813 (x / y) * ((z * ((x / y) \ 1)) / z) = (x * ((z * (x \ y)) / z)) / y. [para(59(a,1),808(a,1,2)),flip(a)]. given #758 (H,wt=29): 812 T((x / y) * R((x / y) \ 1,z,u),y) = (y \ x) * R(T(x / y,y) \ 1,z,u). [para(87(a,1),811(a,1,1)),flip(a)]. given #759 (H,wt=27): 814 T((x / y) * R((x / y) \ 1,z,u),y) = (y \ x) * R((y \ x) \ 1,z,u). [para(87(a,1),812(a,2,2,1,1))]. given #760 (H,wt=30): 472 K(x / (y * x),(x / (y * x)) \ z) = (((x / (y * x)) \ z) * R(1 / y,y,x)) \ z. [para(469(a,2),74(a,1,1)),flip(a)]. given #761 (H,wt=30): 605 (L(x,1 / x,y) * y) / L(x,1 / x,y) = (y * (1 / x)) * T(L(x,1 / x,y),y). [para(166(a,1),601(a,1,1)),flip(a)]. given #762 (H,wt=25): 816 (L(x,1 / x,y) * y) / L(x,1 / x,y) = y * ((1 / x) * T(x,y)). [para(605(a,2),195(a,1))]. given #763 (H,wt=30): 720 ((x * y) * T((x * y) \ x,z)) * u = (x * y) * (u * T(u \ L(y \ u,y,x),z)). [para(78(a,2),716(a,1,2,2,1,2)),flip(a)]. given #764 (H,wt=28): 817 (x * y) * (z * T(z \ L(y \ z,y,x),u)) = (x * (y * T(y \ 1,u))) * z. [para(337(a,1),720(a,1,1)),flip(a)]. given #765 (H,wt=30): 741 (x * R(x \ 1,x,x \ y)) \ R(1 / x,x,x \ y) = L(x \ 1,x,(x \ y) / y). [para(161(a,1),322(a,2,3))]. given #766 (H,wt=31): 373 (K(x,y) * (y * x)) / K(x * y,K(K(x,y),y * x)) = K(K(x,y),y * x) * (x * y). [para(141(a,1),94(a,1,1))]. given #767 (H,wt=31): 382 K(x \ 1,x) * T(((x \ 1) * x) \ y,z) = (x \ 1) * (x * T(x \ ((x \ 1) \ y),z)). [para(249(a,1),199(a,1,2))]. given #768 (H,wt=31): 384 (x * y) * L((y * T(x,y)) \ (y * z),u,w) = y * (T(x,y) * L(T(x,y) \ z,u,w)). [para(205(a,1),198(a,1,2))]. given #769 (H,wt=29): 820 (x * y) * L((x * y) \ (y * z),u,w) = y * (T(x,y) * L(T(x,y) \ z,u,w)). [para(85(a,1),384(a,1,2,1,1))]. given #770 (H,wt=29): 821 x * (T(y,x) * L(T(y,x) \ z,u,w)) = y * (x * L(x \ (y \ (x * z)),u,w)). [para(820(a,1),379(a,1))]. given #771 (H,wt=27): 823 x * (T(y,x) * L(T(y,x) \ 1,z,u)) = y * (x * L(x \ (y \ x),z,u)). [para(12(a,1),821(a,2,2,2,1,2,2))]. given #772 (H,wt=25): 824 x * (T(y,x) * L(T(y,x) \ 1,z,u)) = (y * L(y \ 1,z,u)) * x. [para(823(a,2),698(a,1))]. given #773 (H,wt=23): 825 T(x,y) * L(T(x,y) \ 1,z,u) = T(x * L(x \ 1,z,u),y). [hyper(109,a,824,a),flip(a)]. given #774 (H,wt=23): 826 T(x * L(x \ 1,y,z),u) / T(x,u) = L(1 / T(x,u),y,z). [para(825(a,1),320(a,1,1))]. given #775 (H,wt=28): 827 T(x * L(x \ 1,T(x,y),x / T(x,y)),y) = x \ (T(x,y) * (x / T(x,y))). [para(825(a,1),500(a,2)),flip(a)]. given #776 (H,wt=27): 828 T((x / T(x,y)) * (T(x,y) * (x \ 1)),y) = x \ (T(x,y) * (x / T(x,y))). [para(191(a,1),827(a,1,1))]. given #777 (H,wt=25): 829 T((x / T(x,y)) * (x \ T(x,y)),y) = x \ (T(x,y) * (x / T(x,y))). [para(424(a,1),828(a,1,1,2))]. given #778 (H,wt=23): 830 T((x / T(x,y)) * (x \ T(x,y)),y) = K(T(x,y),x / T(x,y)). [para(829(a,2),75(a,1))]. given #779 (H,wt=29): 822 x \ (y * (x * L(x \ (y \ (x * z)),u,w))) = T(y,x) * L(T(y,x) \ z,u,w). [hyper(66,a,821,a)]. given #780 (H,wt=27): 831 T(x * L(x \ ((y * z) / y),u,w),y) = T(x,y) * L(T(x,y) \ z,u,w). [para(822(a,1),708(a,1)),flip(a)]. given #781 (H,wt=31): 685 K(x \ 1,x) * R(((x \ 1) * x) \ x,y,z) = ((x \ 1) * R((x \ 1) \ 1,y,z)) * x. [para(135(a,2),684(a,1,1))]. given #782 (H,wt=31): 703 T(x * ((1 / x) * ((1 / x) \ ((1 / (1 / x)) \ y))),x) = x * ((1 / (1 / x)) \ T(y,x)). [para(657(a,1),702(a,2,2))]. given #783 (H,wt=31): 709 (K(x,y) * (z * u)) \ ((K(x,y) * z) * (u * w)) = L(w,L(u,z,K(x,y)),K(x,y) * z). [para(88(a,1),193(a,1,2,2,1))]. given #784 (H,wt=31): 778 x \ ((y * x) * ((z * ((y * x) \ x)) / z)) = T(y,x) * ((z * ((x \ (y * x)) \ 1)) / z). [para(30(a,2),777(a,1,1)),flip(a)]. given #785 (H,wt=29): 835 x \ ((y * x) * ((z * ((y * x) \ x)) / z)) = T(y,x) * ((z * (T(y,x) \ 1)) / z). [para(30(a,2),778(a,2,2,1,2,1))]. given #786 (H,wt=27): 836 x \ ((y * ((z * (y \ 1)) / z)) * x) = T(y,x) * ((z * (T(y,x) \ 1)) / z). [para(686(a,1),835(a,1,2))]. given #787 (H,wt=25): 837 T(x,y) * ((z * (T(x,y) \ 1)) / z) = T(x * ((z * (x \ 1)) / z),y). [para(836(a,1),30(a,2)),flip(a)]. given #788 (H,wt=31): 779 x \ (y * (((y / x) * (y \ x)) / (y / x))) = (x \ y) * (((x \ y) \ (y / x)) / (y / x)). [para(528(a,1),777(a,1,2,1)),flip(a)]. given #789 (H,wt=31): 815 T(T((x / y) * R((x / y) \ 1,z,u),w),y) = T((y \ x) * R((y \ x) \ 1,z,u),w). [para(814(a,1),36(a,1,1)),flip(a)]. given #790 (H,wt=31): 818 K(x,y) * ((y * x) / K(x * y,K(K(x,y),y * x))) = K(K(x,y),y * x) * (x * y). [para(373(a,1),281(a,1)),flip(a)]. given #791 (H,wt=21): 838 K(K(x,y),y * x) * (x * y) = K(x,y) * ((y * x) / 1). [para(554(a,1),818(a,1,2,2)),flip(a)]. given #792 (H,wt=19): 839 K(K(x,y),y * x) * (x * y) = K(x,y) * (y * x). [para(55(a,1),838(a,2,2))]. given #793 (H,wt=21): 841 T(K(K(x,y),y * x) * x,y) = y \ (K(x,y) * (y * x)). [para(839(a,1),279(a,1,2)),flip(a)]. given #794 (H,wt=31): 819 K(x \ 1,x) * T(K(x \ 1,x) \ y,z) = (x \ 1) * (x * T(x \ ((x \ 1) \ y),z)). [para(135(a,2),382(a,1,2,1,1))]. given #795 (H,wt=27): 845 K(x \ 1,x) * T(K(x \ 1,x) \ y,z) = (x \ T(x * (y / x),z)) * x. [para(819(a,2),736(a,1))]. given #796 (H,wt=27): 846 K(x \ 1,x) * T(K(x,x \ 1) * y,z) = (x \ T(x * (y / x),z)) * x. [para(447(a,1),845(a,1,2,1))]. given #797 (H,wt=31): 832 T(x \ L(x * ((y * z) / y),u,w),y) = T(x \ 1,y) * L(T(x \ 1,y) \ z,u,w). [para(558(a,1),831(a,1,1))]. given #798 (H,wt=31): 833 K(x \ 1,x) * R(K(x \ 1,x) \ x,y,z) = ((x \ 1) * R((x \ 1) \ 1,y,z)) * x. [para(135(a,2),685(a,1,2,1,1))]. given #799 (H,wt=31): 834 (K(x,y) * (z * u)) \ (K(x,y) * (z * (u * w))) = L(w,L(u,z,K(x,y)),K(x,y) * z). [para(197(a,1),709(a,1,2))]. given #800 (H,wt=25): 848 L(L(x,y,z),z * y,K(u,w)) = L(x,L(y,z,K(u,w)),K(u,w) * z). [para(834(a,1),194(a,1)),flip(a)]. given #801 (H,wt=18): 849 L(x,L(y,z,K(u,w)),K(u,w) * z) = L(x,y,z). [para(848(a,1),88(a,1))]. given #802 (H,wt=13): 850 L(x,y,K(z,u) * w) = L(x,y,w). [para(88(a,1),849(a,1,2))]. given #803 (H,wt=13): 851 L(x,y,1 / z) = L(x,y,z \ 1). [para(450(a,1),850(a,1,3))]. given #804 (H,wt=28): 852 L(T(x,1 / y) \ z,T(x,1 / y),y \ 1) = (x * (1 / y)) \ ((1 / y) * z). [para(851(a,1),207(a,1))]. given #805 (H,wt=31): 847 K(x \ 1,x) * R(K(x,x \ 1) * x,y,z) = ((x \ 1) * R((x \ 1) \ 1,y,z)) * x. [para(447(a,1),833(a,1,2,1))]. given #806 (H,wt=27): 853 K(x \ 1,x) * R(K(x,x \ 1) * x,y,z) = (R(x,y,z) * (x \ 1)) * x. [para(266(a,1),847(a,2,1))]. given #807 (H,wt=27): 854 R(K(x \ 1,x) * (K(x,x \ 1) * x),y,z) = (R(x,y,z) * (x \ 1)) * x. [para(853(a,1),458(a,2))]. given #808 (H,wt=15): 855 (R(x,y,z) * (x \ 1)) * x = R(x,y,z). [para(448(a,1),854(a,1,1)),flip(a)]. given #809 (H,wt=13): 856 (x \ R(x,y,z)) * x = R(x,y,z). [para(479(a,1),855(a,1,1))]. given #810 (H,wt=13): 857 R(x,y,z) / x = x \ R(x,y,z). [hyper(70,a,856,a)]. given #811 (H,wt=13): 858 x * (R(x,y,z) / x) = R(x,y,z). [para(856(a,1),56(a,1,2,1))]. given #812 (H,wt=15): 860 R(x,y,y \ 1) / x = a(x,y,y \ 1). [para(857(a,2),291(a,1))]. given #813 (H,wt=15): 861 (1 / x) * R(x,y,z) = x \ R(x,y,z). [para(857(a,1),563(a,2))]. given #814 (H,wt=17): 865 R(x,y,z) * (x \ 1) = (1 / x) * R(x,y,z). [para(861(a,2),479(a,2))]. given #815 (H,wt=12): 866 T(1 / x,R(x,y,z)) = x \ 1. [hyper(109,a,865,a)]. given #816 (H,wt=14): 867 T(x,R(x \ 1,y,z)) = (x \ 1) \ 1. [para(57(a,1),866(a,1,1))]. given #817 (H,wt=16): 868 T(1 / x,R((1 / x) \ 1,y,z)) = x \ 1. [para(59(a,1),867(a,2,1))]. given #818 (H,wt=18): 862 R(1 / x,x,y) / (1 / x) = (y / (x * y)) * x. [hyper(17,a,419,a,b,858,a)]. given #819 (H,wt=19): 859 (x * R(x \ 1,y,z)) * (1 / x) = R(1 / x,y,z). [para(418(a,1),856(a,1,1))]. given #820 (H,wt=19): 871 (x * R(x \ 1,y,z)) \ R(1 / x,y,z) = 1 / x. [hyper(66,a,859,a)]. given #821 (H,wt=14): 872 L(x \ 1,x,(x \ y) / y) = 1 / x. [para(871(a,1),741(a,1)),flip(a)]. given #822 (H,wt=18): 873 L((x / y) \ 1,x / y,y / x) = 1 / (x / y). [para(59(a,1),872(a,1,3,1))]. given #823 (H,wt=20): 870 ((x / (y * x)) * y) / R(1 / y,y,x) = 1 / (1 / y). [para(862(a,1),564(a,1,1))]. given #824 (H,wt=22): 869 x * T(x \ 1,R((1 / x) \ 1,y,z)) = (1 / x) \ (x \ 1). [para(868(a,1),517(a,1,2)),flip(a)]. given #825 (H,wt=22): 875 L((x / (y * x)) \ 1,x / (y * x),y) = 1 / (x / (y * x)). [para(15(a,1),873(a,1,3))]. given #826 (H,wt=17): 877 x / (1 / (y / (x * y))) = x * (y / (x * y)). [para(875(a,1),160(a,1,2))]. given #827 (H,wt=23): 864 R(x \ 1,x,y) / (y / (x * y)) = a(y / (x * y),x,x \ 1). [para(375(a,1),860(a,1,1))]. given #828 (H,wt=24): 878 K(x \ (x / (1 / (y / (x * y)))),x) = a(y / (x * y),x,x \ 1). [para(864(a,1),618(a,2))]. given #829 (H,wt=22): 879 K(x \ (x * (y / (x * y))),x) = a(y / (x * y),x,x \ 1). [para(877(a,1),878(a,1,1,2))]. given #830 (H,wt=18): 880 a(x / (y * x),y,y \ 1) = K(x / (y * x),y). [para(13(a,1),879(a,1,1)),flip(a)]. given #831 (H,wt=26): 876 x * L(x \ (1 * y),x / y,y / x) = ((x / y) * (1 / (x / y))) * y. [para(873(a,1),789(a,1,1,2)),flip(a)]. given #832 (H,wt=31): 863 R((x \ 1) / (x * (x \ 1)),y,z) / R(1 / x,y,z) = a(R(1 / x,y,z),x,x \ 1). [para(163(a,1),860(a,1,1))]. given #833 (H,wt=25): 882 a(R(1 / x,y,z),x,x \ 1) = R(x \ 1,y,z) / R(1 / x,y,z). [para(91(a,1),863(a,1,1,1)),flip(a)]. given #834 (H,wt=17): 884 a(R(1 / x,y,z),x,x \ 1) = K(x \ 1,x). [para(882(a,2),463(a,1))]. given #835 (H,wt=14): 885 a(1 / x,x,x \ 1) = K(x \ 1,x). [para(157(a,1),884(a,1,1))]. given #836 (H,wt=13): 888 (1 / x) \ (x \ 1) = K(x \ 1,x). [para(885(a,1),290(a,1)),flip(a)]. given #837 (H,wt=13): 889 (1 / x) * K(x \ 1,x) = x \ 1. [para(888(a,1),14(a,1,2))]. given #838 (H,wt=16): 886 a(x / (y * x),y,y \ 1) = K(y \ 1,y). [para(104(a,1),884(a,1,1))]. given #839 (H,wt=13): 893 K(x / (y * x),y) = K(y \ 1,y). [para(886(a,1),880(a,1)),flip(a)]. given #840 (H,wt=11): 894 K(1 / x,x) = K(x \ 1,x). [para(12(a,1),893(a,1,1,2))]. given #841 (H,wt=15): 897 K((x \ 1) \ 1,x \ 1) = K(x,x \ 1). [para(57(a,1),894(a,1,1)),flip(a)]. given #842 (H,wt=17): 895 K((x / y) \ 1,x / y) = K(y / x,x / y). [para(16(a,1),893(a,1,1,2)),flip(a)]. given #843 (H,wt=19): 899 K(x / y,y / x) * x = y * T(y \ x,y / x). [para(895(a,1),631(a,1,1))]. given #844 (H,wt=19): 900 K(x / y,y / x) * (x / y) = T(x / y,y / x). [para(895(a,1),634(a,1,1))]. given #845 (H,wt=20): 890 x * T(x \ 1,R((1 / x) \ 1,y,z)) = K(x \ 1,x). [para(888(a,1),869(a,2))]. given #846 (H,wt=16): 903 x * T(x \ 1,R(x,y,z)) = K(x \ 1,x). [para(59(a,1),890(a,1,2,2,1))]. given #847 (H,wt=21): 892 (1 / x) \ L(x \ 1,y,z) = x * L(T(x \ 1,x),y,z). [para(889(a,1),421(a,1,2,1))]. given #848 (H,wt=19): 904 (1 / x) \ L(x \ 1,y,z) = L(x \ 1,y,z) * x. [para(892(a,2),115(a,1))]. given #849 (H,wt=21): 898 K(x / y,(x / y) \ 1) * z = K(y / x,x / y) \ z. [para(895(a,1),447(a,1,1)),flip(a)]. given #850 (H,wt=22): 902 T(x / y,y / x) != z * (x / y) | K(x / y,y / x) = z. [para(900(a,1),20(a,1))]. given #851 (H,wt=26): 891 R(x / (1 / y),1 / y,K(y \ 1,y)) = (x * K(y \ 1,y)) / (y \ 1). [para(889(a,1),82(a,2,2))]. given #852 (H,wt=26): 901 K((x * y) / y,y / (x * y)) = ((y / (x * y)) \ 1) * R(1 / x,x,y). [para(895(a,1),471(a,1))]. given #853 (H,wt=22): 906 ((x / (y * x)) \ 1) * R(1 / y,y,x) = K(y,x / (y * x)). [para(15(a,1),901(a,1,1)),flip(a)]. given #854 (H,wt=23): 907 K(x / (y * x),(x / (y * x)) \ 1) = K(y,x / (y * x)) \ 1. [para(906(a,1),472(a,2,1))]. given #855 (H,wt=32): 372 (R(T(x,y * z),y,z) * (y * z)) \ ((x * y) * z) = K(y * z,(y * z) \ ((x * y) * z)). [para(368(a,1),74(a,1,1,1))]. given #856 (H,wt=29): 908 ((T(x,y * z) * y) * z) \ ((x * y) * z) = K(y * z,(y * z) \ ((x * y) * z)). [para(81(a,1),372(a,1,1))]. given #857 (H,wt=28): 909 ((T(x,y * z) * y) * z) \ ((x * y) * z) = K(y * z,R(T(x,y * z),y,z)). [para(368(a,1),908(a,2,2))]. given #858 (H,wt=32): 765 (T(x,y) * (R(x,z,u) * y)) \ ((x * y) * R(T(x,y),z,u)) = K(R(x,z,u) * y,T(x,y)). [para(764(a,1),24(a,2,2)),flip(a)]. given #859 (H,wt=33): 621 (x / ((y \ z) \ z)) * T((y \ z) \ z,u) = x * K(u \ (u / (x \ (x / T(y,y \ z)))),u). [para(620(a,2),522(a,2,2,1,2,2,2))]. given #860 (H,wt=33): 678 ((L(x,y,z) \ x) / x) \ ((L(x,y,z) \ 1) * (x * (L(x,y,z) \ 1))) = (L(x,y,z) \ 1) * x. [para(489(a,1),677(a,1,1,1))]. given #861 (H,wt=33): 803 R(L(x,y,z),T(1 / x,L(x,y,z)),x) \ L(x,y,z) = (L(x,y,z) \ (L(x,y,z) / x)) * x. [para(796(a,1),316(a,1,1,2))]. given #862 (H,wt=33): 910 L(R(x,T(1 / x,L(x,y,z)),x),y,z) \ L(x,y,z) = (L(x,y,z) \ (L(x,y,z) / x)) * x. [para(42(a,1),803(a,1,1))]. given #863 (H,wt=34): 324 (x * K(x,y)) * R((x * K(x,y)) \ (x * y),z,u) = R(R(y,x,K(x,y)),z,u) * (x * K(x,y)). [para(139(a,1),264(a,1,1,1)),flip(a)]. given #864 (H,wt=29): 911 (x * K(x,y)) * R((x * K(x,y)) \ (x * y),z,u) = (R(y,z,u) * x) * K(x,y). [para(324(a,2),215(a,1))]. given #865 (H,wt=25): 912 x * (K(x,y) * R(K(x,y) \ y,z,u)) = (R(y,z,u) * x) * K(x,y). [para(911(a,1),383(a,1)),flip(a)]. given #866 (H,wt=25): 913 x * R(K(x,y) * (K(x,y) \ y),z,u) = (R(y,z,u) * x) * K(x,y). [para(458(a,2),912(a,1,2))]. given #867 (H,wt=17): 914 (R(x,y,z) * u) * K(u,x) = u * R(x,y,z). [para(14(a,1),913(a,1,2,1)),flip(a)]. given #868 (H,wt=10): 915 K(x,R(y,z,u)) = K(x,y). [hyper(138,a,914,a)]. given #869 (H,wt=13): 919 K(x,y * (z \ 1)) = K(x,y / z). [para(224(a,1),915(a,1,2))]. given #870 (H,wt=11): 928 K(x,1 / y) = K(x,y \ 1). [para(11(a,1),919(a,1,2)),flip(a)]. given #871 (H,wt=11): 929 K(x,(y \ 1) \ 1) = K(x,y). [para(57(a,1),928(a,1,2)),flip(a)]. given #872 (H,wt=11): 930 K(x,x \ 1) = x * (1 / x). [para(928(a,1),118(a,1))]. given #873 (H,wt=13): 920 K(x,T(y \ 1,y)) = K(x,y \ 1). [para(303(a,1),915(a,1,2))]. given #874 (H,wt=13): 922 K(x,T(y,y * z)) = K(x,T(y,z)). [para(341(a,1),915(a,1,2)),flip(a)]. given #875 (H,wt=13): 924 K(x,T(y,y \ z)) = K(x,T(y,z)). [para(342(a,1),915(a,1,2))]. given #876 (H,wt=13): 926 K(x,T(y,z * y)) = K(x,T(y,z)). [para(406(a,1),915(a,1,2)),flip(a)]. given #877 (H,wt=13): 931 K(x,x \ 1) \ x = 1 / (1 / x). [para(928(a,1),187(a,1,1))]. given #878 (H,wt=13): 932 K(x,1 / x) \ ((x \ 1) \ 1) = x. [para(928(a,2),538(a,1,1))]. given #879 (H,wt=13): 937 K(x,(y \ z) \ z) = K(x,T(y,z)). [para(86(a,1),924(a,1,2))]. given #880 (H,wt=13): 938 K(x,x \ 1) * (1 / (1 / x)) = x. [para(931(a,1),14(a,1,2))]. given #881 (H,wt=13): 939 x / (1 / (1 / x)) = K(x,x \ 1). [para(931(a,1),57(a,1,2))]. given #882 (H,wt=13): 940 K(x,1 / x) \ T(x,x \ 1) = x. [para(86(a,2),932(a,1,2))]. given #883 (H,wt=13): 941 K(x,T(y / z,y)) = K(x,z \ y). [para(59(a,1),937(a,1,2,1)),flip(a)]. given #884 (H,wt=13): 945 K(x,1 / x) * x = T(x,x \ 1). [para(940(a,1),14(a,1,2))]. given #885 (H,wt=13): 946 K(x,x \ 1) * x = T(x,x \ 1). [para(928(a,1),945(a,1,1))]. given #886 (H,wt=15): 917 K(x,(y * z) / (u * z)) = K(x,y / u). [para(82(a,1),915(a,1,2))]. given #887 (H,wt=15): 918 K(x,(y / z) / u) = K(x,y / (u * z)). [para(133(a,1),915(a,1,2)),flip(a)]. given #888 (H,wt=15): 921 K(x,(y * z) / u) = K(x,y / (u / z)). [para(220(a,1),915(a,1,2))]. given #889 (H,wt=16): 916 K(x,L(R(y,z,u),w,v5)) = K(x,L(y,w,v5)). [para(42(a,1),915(a,1,2))]. given #890 (H,wt=10): 950 K(x,L(y,z,y)) = K(x,y). [para(648(a,1),916(a,1,2)),flip(a)]. given #891 (H,wt=17): 942 K(x,x \ 1) * ((1 / (1 / x)) * y) = x * y. [para(938(a,1),197(a,1,1)),flip(a)]. given #892 (H,wt=17): 943 x * ((1 / (1 / x)) \ y) = K(x,x \ 1) * y. [para(938(a,1),273(a,1,1))]. given #893 (H,wt=17): 947 K(x,x \ 1) * (x * y) = T(x,x \ 1) * y. [para(946(a,1),197(a,1,1)),flip(a)]. given #894 (H,wt=17): 951 K(x \ 1,x) * (x * y) = (1 / (1 / x)) * y. [para(942(a,1),448(a,1,2))]. given #895 (H,wt=15): 957 (1 / (1 / x)) * (x \ 1) = K(x \ 1,x). [hyper(99,a,951,a),flip(a)]. given #896 (H,wt=17): 955 K(x,x \ 1) * (x * y) = ((x \ 1) \ 1) * y. [para(86(a,1),947(a,2,1))]. given #897 (H,wt=18): 960 K(x \ 1,x) != y * (x \ 1) | 1 / (1 / x) = y. [para(957(a,1),20(a,1))]. given #898 (H,wt=19): 923 K(x,T((y * z) / (u * z),w)) = K(x,T(y / u,w)). [para(221(a,2),915(a,1,2))]. given #899 (H,wt=17): 961 K(x,T(y / (1 / z),u)) = K(x,T(y * z,u)). [para(92(a,1),923(a,1,2,1)),flip(a)]. given #900 (H,wt=19): 925 K(x,T((y * z) / u,w)) = K(x,T(y / (u / z),w)). [para(313(a,1),915(a,1,2))]. given #901 (H,wt=19): 933 x * (K(x,x \ 1) * (x \ y)) = K(x,1 / x) * y. [para(928(a,1),706(a,1,2,1))]. given #902 (H,wt=19): 949 K(x,L(T(y,y \ z),u,w)) = K(x,L(T(y,z),u,w)). [para(342(a,1),916(a,1,2,1))]. given #903 (H,wt=19): 954 K(x,x \ 1) * (y * x) = T(x,x \ 1) * T(y,x). [para(85(a,1),947(a,1,2))]. given #904 (H,wt=19): 959 K(x \ 1,x) * (y * x) = (1 / (1 / x)) * T(y,x). [para(85(a,1),951(a,1,2))]. given #905 (H,wt=19): 962 K(x,T(y / z,y * u)) = K(x,(z * u) \ (y * u)). [para(923(a,1),941(a,1))]. given #906 (H,wt=19): 963 x * (K(x,x \ 1) * (x \ y)) = K(x,x \ 1) * y. [para(928(a,1),933(a,2,1))]. given #907 (H,wt=17): 965 K(x,x \ 1) * (x \ y) = (1 / (1 / x)) \ y. [hyper(17,a,943,a,b,963,a)]. given #908 (H,wt=19): 966 K(x,x \ 1) * (x * y) = x * (K(x,x \ 1) * y). [para(13(a,1),963(a,1,2,2)),flip(a)]. given #909 (H,wt=17): 967 (1 / (1 / x)) * (K(x,x \ 1) * y) = x * y. [hyper(17,a,942,a,b,966,a),flip(a)]. given #910 (H,wt=17): 968 x * (K(x,x \ 1) * y) = T(x,x \ 1) * y. [para(966(a,1),947(a,1))]. given #911 (H,wt=17): 970 (T(x,x \ 1) * y) / (K(x,x \ 1) * y) = x. [hyper(70,a,968,a)]. given #912 (H,wt=19): 971 T(x,x \ 1) * ((x \ 1) * y) = x * ((1 / x) * y). [para(453(a,1),968(a,1,2)),flip(a)]. given #913 (H,wt=20): 934 R(x,y,1 / y) * K(y,y \ 1) = (x * y) * (1 / y). [para(930(a,2),81(a,1,2))]. given #914 (H,wt=20): 944 K(x,x \ 1) * y != x * z | (1 / (1 / x)) * z = y. [para(938(a,1),274(a,2,1))]. given #915 (H,wt=20): 948 T(x,x \ 1) * y != z * (x * y) | K(x,x \ 1) = z. [para(946(a,1),275(a,1,1))]. given #916 (H,wt=20): 952 K(x,x \ 1) * y != x * z | (1 / (1 / x)) \ y = z. [para(943(a,1),19(a,1))]. given #917 (H,wt=21): 958 K((x / y) \ 1,x / y) * x = (1 / (1 / (x / y))) * y. [para(16(a,1),951(a,1,2))]. given #918 (H,wt=19): 973 K(x / y,y / x) * y = (1 / (1 / (y / x))) * x. [para(895(a,1),958(a,1,1))]. given #919 (H,wt=23): 935 K(x,x \ 1) * y != x * ((1 / x) * z) | L(z,1 / x,x) = y. [para(930(a,2),192(a,1,1))]. given #920 (H,wt=24): 956 K(x,x \ 1) * L(y,x \ 1,x) = T(x,x \ 1) * ((x \ 1) * y). [para(189(a,1),947(a,1,2))]. given #921 (H,wt=20): 974 K(x,x \ 1) * L(y,x \ 1,x) = x * ((1 / x) * y). [para(956(a,2),971(a,1))]. given #922 (H,wt=13): 975 L(x,1 / y,y) = L(x,y \ 1,y). [hyper(935,a,974,a)]. given #923 (H,wt=17): 976 L(x,(y \ 1) \ 1,y \ 1) = L(x,y,y \ 1). [para(57(a,1),975(a,1,2)),flip(a)]. given #924 (H,wt=18): 977 L(((x \ 1) \ 1) \ y,x,x \ 1) = (x \ 1) * y. [para(976(a,1),253(a,1))]. given #925 (H,wt=25): 927 ((T(x,y * z) * y) * z) \ ((x * y) * z) = K(y * z,T(x,y * z)). [para(915(a,1),909(a,2))]. given #926 (H,wt=26): 936 x * L(x \ (1 * y),x / y,y / x) = K(x / y,(x / y) \ 1) * y. [para(930(a,2),876(a,2,1))]. given #927 (H,wt=24): 980 x * L(x \ y,x / y,y / x) = K(x / y,(x / y) \ 1) * y. [para(11(a,1),936(a,1,2,1,2))]. given #928 (H,wt=26): 969 L(T(K(x,x \ 1),y),y,1 / (1 / x)) = ((1 / (1 / x)) * y) \ (x * y). [para(967(a,1),112(a,1,2)),flip(a)]. given #929 (H,wt=29): 953 T(x * ((1 / x) * ((1 / x) \ ((1 / (1 / x)) \ y))),x) = K(x,x \ 1) * T(y,x). [para(943(a,1),703(a,2))]. given #930 (H,wt=21): 981 T(x * ((1 / (1 / x)) \ y),x) = K(x,x \ 1) * T(y,x). [para(14(a,1),953(a,1,1,2))]. given #931 (H,wt=19): 983 T(K(x,x \ 1) * y,x) = K(x,x \ 1) * T(y,x). [para(943(a,1),981(a,1,1))]. given #932 (H,wt=21): 984 T((1 / x) * ((x \ 1) \ y),x) = K(x,x \ 1) * T(y,x). [para(454(a,2),983(a,1,1))]. given #933 (H,wt=23): 985 T((1 / x) * ((x \ 1) \ y),x) = (1 / x) * ((x \ 1) \ T(y,x)). [para(984(a,2),454(a,2)),flip(a)]. given #934 (H,wt=17): 986 (x \ ((x \ 1) \ y)) * x = (x \ 1) \ T(y,x). [hyper(357,a,985,a)]. given #935 (H,wt=17): 987 (x \ 1) \ T((x \ 1) * y,x) = (x \ y) * x. [para(13(a,1),986(a,1,1,2)),flip(a)]. given #936 (H,wt=27): 988 (x * T(x \ 1,y)) * ((y \ 1) \ 1) = x * ((y \ (x \ ((y \ 1) \ 1))) * y). [para(987(a,1),723(a,1,2)),flip(a)]. given #937 (H,wt=31): 964 K(x,T((R(y,z,u) * z) / (y * z),(R(y,z,u) * z) * u)) = K(x,a(R(y,z,u),z,u)). [para(212(a,1),962(a,2,2))]. given #938 (H,wt=27): 989 K(x,T(R(y,z,u) / y,(R(y,z,u) * z) * u)) = K(x,a(R(y,z,u),z,u)). [para(964(a,1),923(a,1)),flip(a)]. given #939 (H,wt=27): 990 K(x,T(y \ R(y,z,u),(R(y,z,u) * z) * u)) = K(x,a(R(y,z,u),z,u)). [para(857(a,1),989(a,1,2,1))]. given #940 (H,wt=35): 359 L(((x / y) \ (x * (y \ 1))) \ z,a(x / y,y,y \ 1),x / y) = (x * (y \ 1)) \ ((x / y) * z). [para(289(a,2),200(a,1,2))]. given #941 (H,wt=33): 992 L(((1 / x) \ (x \ 1)) \ y,a(1 / x,x,x \ 1),1 / x) = (1 * (x \ 1)) \ ((1 / x) * y). [para(11(a,1),359(a,1,1,1,2))]. given #942 (H,wt=31): 993 L(K(x \ 1,x) \ y,a(1 / x,x,x \ 1),1 / x) = (1 * (x \ 1)) \ ((1 / x) * y). [para(888(a,1),992(a,1,1,1))]. given #943 (H,wt=36): 638 R(x,y * ((x * y) \ z),a(x,y,(x * y) \ z)) \ z = (y * ((x * y) \ z)) * a(x,y,(x * y) \ z). [para(14(a,1),286(a,1,2))]. given #944 (H,wt=36): 978 T(((x \ 1) \ 1) * ((x \ 1) * 1),y) / T((x \ 1) \ 1,y) = L(1 / T((x \ 1) \ 1,y),x,x \ 1). [para(977(a,1),826(a,1,1,1,2))]. given #945 (H,wt=34): 995 T(((x \ 1) \ 1) * (x \ 1),y) / T((x \ 1) \ 1,y) = L(1 / T((x \ 1) \ 1,y),x,x \ 1). [para(12(a,1),978(a,1,1,1,2))]. given #946 (H,wt=34): 996 T(K((x \ 1) \ 1,x \ 1),y) / T((x \ 1) \ 1,y) = L(1 / T((x \ 1) \ 1,y),x,x \ 1). [para(135(a,2),995(a,1,1,1))]. given #947 (H,wt=30): 997 T(K(x,x \ 1),y) / T((x \ 1) \ 1,y) = L(1 / T((x \ 1) \ 1,y),x,x \ 1). [para(897(a,1),996(a,1,1,1))]. given #948 (H,wt=37): 411 K(x,1 / x) * T(K(x,1 / x) \ (K(x,1 / x) / (1 / x)),y) = x * ((1 / x) * T((1 / x) \ 1,y)). [para(145(a,1),355(a,1,1)),flip(a)]. given #949 (H,wt=31): 998 K(x,1 / x) * T(K(x,1 / x) \ (K(x,1 / x) / (1 / x)),y) = x * (T(x,y) / x). [para(590(a,1),411(a,2,2))]. given #950 (H,wt=21): 999 K(x,1 / x) * T(1 / (1 / x),y) = x * (T(x,y) / x). [para(185(a,1),998(a,1,2,1))]. given #951 (H,wt=21): 1001 K(x,x \ 1) * T(1 / (1 / x),y) = x * (T(x,y) / x). [para(928(a,1),999(a,1,1))]. given #952 (H,wt=21): 1002 x \ (K(x,x \ 1) * T(1 / (1 / x),y)) = T(x,y) / x. [hyper(66,a,1001,a(flip))]. given #953 (H,wt=37): 639 R((x / (y * x)) \ 1,R(1 / y,y,x),y * x) = (K((x / (y * x)) \ 1,x / (y * x)) * (y * x)) / x. [para(104(a,2),288(a,2,2)),flip(a)]. given #954 (H,wt=29): 1003 R((x / (y * x)) \ 1,R(1 / y,y,x),y * x) = T((y * x) / x,x / (y * x)). [para(639(a,2),633(a,1))]. given #955 (H,wt=25): 1004 R((x / (y * x)) \ 1,R(1 / y,y,x),y * x) = T(y,x / (y * x)). [para(15(a,1),1003(a,2,1))]. given #956 (H,wt=23): 1005 T(x / (y * x),T(y,x / (y * x))) = ((x / (y * x)) \ 1) \ 1. [para(1004(a,1),867(a,1,2))]. given #957 (H,wt=38): 410 (x * (y * z)) * T(((x * y) * L(z,y,x)) \ (x * y),u) = (x * y) * (L(z,y,x) * T(L(z,y,x) \ 1,u)). [para(76(a,1),337(a,1,1))]. given #958 (H,wt=35): 1006 (x * (y * z)) * T((x * (y * z)) \ (x * y),u) = (x * y) * (L(z,y,x) * T(L(z,y,x) \ 1,u)). [para(76(a,1),410(a,1,2,1,1))]. given #959 (H,wt=31): 1007 (x * y) * (L(z,y,x) * T(L(z,y,x) \ 1,u)) = x * ((y * z) * T((y * z) \ y,u)). [para(1006(a,1),338(a,1))]. given #960 (H,wt=29): 1008 (x * y) * (L(z,y,x) * T(L(z,y,x) \ 1,u)) = x * (y * (z * T(z \ 1,u))). [para(337(a,1),1007(a,2,2))]. given #961 (H,wt=24): 1009 L(x,y,z) * T(L(x,y,z) \ 1,u) = L(x * T(x \ 1,u),y,z). [hyper(192,a,1008,a),flip(a)]. given #962 (H,wt=25): 1010 L(x * T(x \ 1,L(x,y,z)),y,z) = (L(x,y,z) \ 1) * L(x,y,z). [para(1009(a,1),85(a,1))]. given #963 (H,wt=25): 1012 L(x * T(x \ 1,L(x,y,z)),y,z) = K(L(x,y,z) \ 1,L(x,y,z)). [para(1010(a,2),135(a,2)),flip(a)]. given #964 (H,wt=26): 1011 L(x * T(x \ 1,x),y,z) * (L(x,y,z) \ x) = (L(x,y,z) \ 1) * x. [para(1009(a,1),655(a,1,1))]. given #965 (H,wt=24): 1013 L((x \ 1) * x,y,z) * (L(x,y,z) \ x) = (L(x,y,z) \ 1) * x. [para(85(a,1),1011(a,1,1,1))]. given #966 (H,wt=24): 1014 L(K(x \ 1,x),y,z) * (L(x,y,z) \ x) = (L(x,y,z) \ 1) * x. [para(135(a,2),1013(a,1,1,1))]. given #967 (H,wt=27): 1015 (L(x,y,z) \ 1) * x != u * (L(x,y,z) \ x) | L(K(x \ 1,x),y,z) = u. [para(1014(a,1),20(a,1))]. given #968 (H,wt=38): 728 ((x * (y \ z)) * T((x * (y \ z)) \ x,z)) * z = (x * (y \ z)) * ((z \ L(T(y,y \ z),y \ z,x)) * z). [para(144(a,2),719(a,1,2,1,2)),flip(a)]. given #969 (H,wt=36): 1016 (x * (y \ z)) * ((z \ L(T(y,y \ z),y \ z,x)) * z) = (x * ((y \ z) * T((y \ z) \ 1,z))) * z. [para(337(a,1),728(a,1,1)),flip(a)]. given #970 (H,wt=32): 1017 (x * (y \ z)) * ((z \ L(T(y,y \ z),y \ z,x)) * z) = (x * (y \ ((z \ y) * z))) * z. [para(414(a,1),1016(a,2,1,2))]. given #971 (H,wt=30): 1018 (x * (y \ z)) * ((z \ L(T(y,y \ z),y \ z,x)) * z) = (x * K(z \ y,z)) * z. [para(73(a,1),1017(a,2,1,2))]. given #972 (H,wt=39): 642 x * T(K(y,z) * R(u / (K(y,z) * x),w,v5),K(y,z) * x) = (K(y,z) * x) * R((K(y,z) * x) \ u,w,v5). [para(641(a,2),264(a,1))]. given #973 (H,wt=39): 679 x * (T(T(y,x),z) * R(T(T(y,x),z) \ (x \ u),w,v5)) = (T(y,z) * x) * R((x * T(T(y,x),z)) \ u,w,v5). [para(114(a,1),662(a,1,1)),flip(a)]. given #974 (H,wt=37): 1020 x * (T(T(y,x),z) * R(T(T(y,x),z) \ (x \ u),w,v5)) = (T(y,z) * x) * R((T(y,z) * x) \ u,w,v5). [para(114(a,1),679(a,2,2,1,1))]. given #975 (H,wt=37): 1021 x * (T(T(y,x),z) * R(T(T(y,x),z) \ (x \ u),w,v5)) = T(y,z) * (x * R(x \ (T(y,z) \ u),w,v5)). [para(1020(a,2),662(a,1))]. given #976 (H,wt=39): 710 T((x * y) / (R(z,x,y) * (x * y)),R(z,x,y)) * ((z * x) * y) = ((R(z,x,y) \ 1) * R(z,x,y)) * (x * y). [para(300(a,2),218(a,1,1))]. given #977 (H,wt=36): 1022 T((x * y) / ((z * x) * y),R(z,x,y)) * ((z * x) * y) = ((R(z,x,y) \ 1) * R(z,x,y)) * (x * y). [para(81(a,1),710(a,1,1,1,2))]. given #978 (H,wt=36): 1023 ((x * y) * z) * T(((x * y) * z) \ (y * z),R(x,y,z)) = ((R(x,y,z) \ 1) * R(x,y,z)) * (y * z). [para(1022(a,1),171(a,1)),flip(a)]. given #979 (H,wt=36): 1024 ((x * y) * z) * T(((x * y) * z) \ (y * z),R(x,y,z)) = K(R(x,y,z) \ 1,R(x,y,z)) * (y * z). [para(135(a,2),1023(a,2,1))]. given #980 (H,wt=32): 1025 K(R(x,y,z) \ 1,R(x,y,z)) * (y * z) = ((x * y) * T((x * y) \ y,R(x,y,z))) * z. [para(1024(a,1),715(a,1))]. given #981 (H,wt=32): 1026 K(R(x,y,z) \ 1,R(x,y,z)) * (y * z) = (x * (y * T(y \ (x \ y),R(x,y,z)))) * z. [para(339(a,1),1025(a,2,1))]. given #982 (H,wt=30): 1027 K(R(x,y,z) \ 1,R(x,y,z)) * (y * z) = ((x * T(x \ 1,R(x,y,z))) * y) * z. [para(717(a,1),1026(a,2,1))]. given #983 (H,wt=25): 1028 K(R(x,y,z) \ 1,R(x,y,z)) * (y * z) = (K(x \ 1,x) * y) * z. [para(903(a,1),1027(a,2,1,1))]. given #984 (H,wt=17): 1029 K(R(x,y,z) \ 1,R(x,y,z)) = K(x \ 1,x). [hyper(18,a,197,a(flip),b,1028,a)]. given #985 (H,wt=39): 1019 x * T(R(K(y,z) * (u / (K(y,z) * x)),w,v5),K(y,z) * x) = (K(y,z) * x) * R((K(y,z) * x) \ u,w,v5). [para(458(a,2),642(a,1,2,1))]. given #986 (H,wt=39): 1032 x * R(T(K(y,z) * (u / (K(y,z) * x)),K(y,z) * x),w,v5) = (K(y,z) * x) * R((K(y,z) * x) \ u,w,v5). [para(40(a,2),1019(a,1,2))]. given #987 (H,wt=33): 1033 (K(x,y) * z) * R((K(x,y) * z) \ u,w,v5) = z * R((K(x,y) * z) \ (K(x,y) * u),w,v5). [para(284(a,1),1032(a,1,2,1)),flip(a)]. given #988 (H,wt=25): 1034 (K(x,y) * z) * R((K(x,y) * z) \ u,w,v5) = z * R(z \ u,w,v5). [para(206(a,1),1033(a,2,2,1))]. given #989 (H,wt=41): 707 ((x \ y) \ y) * (z * R(z \ (T(x,x \ y) \ (u * z)),w,v5)) = (T(x,x \ y) * R(T(x,x \ y) \ u,w,v5)) * z. [para(690(a,1),441(a,1)),flip(a)]. given #990 (H,wt=42): 994 L(K(x \ 1,x) \ ((y * (x \ 1)) * x),a(1 / x,x,x \ 1),1 / x) = (1 * (x \ 1)) \ R((1 / x) * y,x,x \ 1). [para(446(a,1),993(a,2,2))]. given #991 (H,wt=45): 786 (x * (y * T(y \ 1,x))) \ (x \ ((L(y \ 1,y,x) * x) / L(y \ 1,y,x))) = (L(y \ 1,y,x) \ (L(y \ 1,y,x) * x)) \ 1. [para(785(a,1),574(a,1,1))]. given #992 (H,wt=39): 1036 (x * (y * T(y \ 1,x))) \ (x \ (x * (y * T(y \ 1,x)))) = (L(y \ 1,y,x) \ (L(y \ 1,y,x) * x)) \ 1. [para(785(a,1),786(a,1,2,2))]. given #993 (H,wt=35): 1037 (L(x \ 1,x,y) \ (L(x \ 1,x,y) * y)) \ 1 = (y * (x * T(x \ 1,y))) \ (x * T(x \ 1,y)). [para(13(a,1),1036(a,1,2)),flip(a)]. given #994 (H,wt=21): 1038 (x * (y * T(y \ 1,x))) \ (y * T(y \ 1,x)) = x \ 1. [para(13(a,1),1037(a,1,1)),flip(a)]. given #995 (H,wt=27): 1040 (x * K(y,x)) \ (L(y \ 1,y,x) * T(L(y \ 1,y,x) \ 1,x)) = x \ 1. [para(668(a,2),1038(a,1,1,2))]. given #996 (H,wt=13): 1041 (x * K(y,x)) \ K(y,x) = x \ 1. [para(668(a,2),1040(a,1,2))]. given #997 (H,wt=13): 1042 (x * K(y,x)) * (x \ 1) = K(y,x). [para(1041(a,1),14(a,1,2))]. given #998 (H,wt=13): 1043 x * K(x \ 1,x) = 1 / (1 / x). [hyper(18,a,957,a,b,1042,a)]. given #999 (H,wt=12): 1045 L(x,x \ 1,x) = 1 / (1 / x). [para(1043(a,1),254(a,1)),flip(a)]. given #1000 (H,wt=16): 1044 R(K(x,y),z,u) = (y * K(x,y)) * (y \ 1). [para(1042(a,2),272(a,2))]. given #1001 (H,wt=11): 1047 K(x,y) * y = y * K(x,y). [hyper(243,a,1044,a)]. given #1002 (H,wt=7): 1048 T(x,K(y,x)) = x. [hyper(109,a,1047,a)]. given #1003 (H,wt=11): 1054 T(x,y * T(y \ 1,x)) = x. [para(429(a,1),1048(a,1,2))]. given #1004 (H,wt=11): 1055 T(x,x \ ((y * x) / y)) = x. [para(606(a,1),1048(a,1,2))]. given #1005 (H,wt=13): 1050 (x \ 1) * K(x,x \ 1) = 1 / x. [para(1047(a,1),450(a,1))]. given #1006 (H,wt=13): 1058 T(T(x,y),T(x,y) \ x) = T(x,y). [para(106(a,1),1055(a,1,2,2))]. given #1007 (H,wt=11): 1062 K(T(x,y),T(x,y) \ x) = 1. [hyper(34,a,1058,a)]. given #1008 (H,wt=11): 1063 (T(x,y) \ x) * T(x,y) = x. [para(1058(a,1),108(a,1,2))]. given #1009 (H,wt=11): 1064 x / T(x,y) = T(x,y) \ x. [para(1058(a,1),123(a,1,2))]. given #1010 (H,wt=13): 1061 (x \ 1) \ (1 / x) = K(x,x \ 1). [hyper(66,a,1050,a)]. given #1011 (H,wt=13): 1066 (T(x,y) \ x) / x = 1 / T(x,y). [para(1064(a,1),616(a,1,1))]. given #1012 (H,wt=13): 1069 T(1 / T(x,y),x) = T(x,y) \ 1. [para(1066(a,1),507(a,1,1))]. given #1013 (H,wt=14): 1065 x * T(y,z) != y | T(y,z) \ y = x. [para(1063(a,1),20(a,1)),flip(a)]. given #1014 (H,wt=15): 1049 (x * K(y,x)) * z = K(y,x) * (x * z). [para(1047(a,1),197(a,1,1))]. given #1015 (H,wt=15): 1053 T(x,y) * K(z,x) = K(z,x) * T(x,y). [para(1048(a,1),114(a,1,2,1)),flip(a)]. given #1016 (H,wt=15): 1059 (x \ ((y * x) / y)) * x = (y * x) / y. [para(1055(a,1),108(a,1,2))]. given #1017 (H,wt=15): 1060 ((x * y) / x) / y = y \ ((x * y) / x). [para(1055(a,1),123(a,1,2))]. given #1018 (H,wt=17): 1071 (1 / x) * ((y * x) / y) = x \ ((y * x) / y). [para(1060(a,1),744(a,2))]. given #1019 (H,wt=17): 1072 (1 / x) \ (x \ ((y * x) / y)) = (y * x) / y. [hyper(66,a,1071,a)]. given #1020 (H,wt=18): 1070 (x * y) / x != z * y | y \ ((x * y) / x) = z. [para(1059(a,1),20(a,1))]. given #1021 (H,wt=19): 1056 (x * T(x \ 1,y)) * y = y * (x * T(x \ 1,y)). [para(1054(a,1),85(a,1,2))]. given #1022 (H,wt=19): 1074 (1 / x) \ (((y * x) / y) * (x \ 1)) = (y * x) / y. [para(568(a,2),1072(a,1,2))]. given #1023 (H,wt=20): 1046 T(L(x,T(x,y) \ 1,T(x,y)),y) = 1 / (1 / T(x,y)). [para(1045(a,1),38(a,1)),flip(a)]. given #1024 (H,wt=21): 1051 (x \ y) * ((y \ T(x,x \ y)) * y) = y * K(y \ x,y). [para(1047(a,1),767(a,2))]. given #1025 (H,wt=21): 1073 (x \ 1) \ ((y * (x \ 1)) / y) = x * ((y * (x \ 1)) / y). [para(57(a,1),1071(a,1,1)),flip(a)]. given #1026 (H,wt=22): 1076 (x * T(x \ 1,y)) * z != y * (x * T(x \ 1,y)) | z = y. [para(1056(a,1),19(a,2))]. given #1027 (H,wt=23): 1067 T((T(x,y) \ x) * (x \ T(x,y)),y) = K(T(x,y),x / T(x,y)). [para(1064(a,1),830(a,1,1,1))]. given #1028 (H,wt=23): 1077 T((T(x,y) \ x) * (x \ T(x,y)),y) = K(T(x,y),T(x,y) \ x). [para(1064(a,1),1067(a,2,2))]. given #1029 (H,wt=15): 1078 T((T(x,y) \ x) * (x \ T(x,y)),y) = 1. [para(1077(a,2),1062(a,1))]. given #1030 (H,wt=24): 1052 ((x * K(y,z)) * z) \ ((x * (z * K(y,z))) * z) = L(z,K(y,z),x). [para(1047(a,1),802(a,2,2,1,2)),flip(a)]. given #1031 (H,wt=26): 1068 L(K(x,x \ 1),x \ 1,y / (1 / x)) = ((y / (1 / x)) * (x \ 1)) \ y. [para(1061(a,1),202(a,1,1))]. given #1032 (H,wt=31): 1075 (1 / x) \ (x \ ((L(y \ 1,y,x) * x) / L(y \ 1,y,x))) = x * (y * T(y \ 1,x)). [para(1072(a,2),785(a,1))]. given #1033 (H,wt=25): 1081 (1 / x) \ (x \ (x * (y * T(y \ 1,x)))) = x * (y * T(y \ 1,x)). [para(785(a,1),1075(a,1,2,2))]. given #1034 (H,wt=21): 1082 (1 / x) \ (y * T(y \ 1,x)) = x * (y * T(y \ 1,x)). [para(13(a,1),1081(a,1,2))]. given #1035 (H,wt=35): 1057 (x * T(x \ 1,y)) * ((T(y,x * T(x \ 1,y)) \ z) \ z) = T(y,y \ z) * (x * T(x \ 1,y)). [para(1054(a,1),175(a,1,1,2,1)),flip(a)]. given #1036 (H,wt=27): 1084 T(x,x \ y) * (z * T(z \ 1,x)) = (z * T(z \ 1,x)) * ((x \ y) \ y). [para(1054(a,1),1057(a,1,2,1,1)),flip(a)]. given #1037 (H,wt=50): 905 T((1 / x) * T((1 / x) \ 1,L(x \ 1,y,z)),L(x \ 1,y,z) * x) = K(L(x \ 1,y,z) \ ((1 / x) \ L(x \ 1,y,z)),L(x \ 1,y,z)). [para(904(a,1),750(a,1,2))]. given #1038 (H,wt=44): 1085 T(T(x,L(x \ 1,y,z)) / x,L(x \ 1,y,z) * x) = K(L(x \ 1,y,z) \ ((1 / x) \ L(x \ 1,y,z)),L(x \ 1,y,z)). [para(590(a,1),905(a,1,1))]. given #1039 (H,wt=53): 637 ((L(x,y,z) * (z * y)) / (z * y)) * T(((L(x,y,z) * (z * y)) / (z * y)) \ x,u) = ((L(x,y,z) * (z * y)) * T(a(z,y,T(x,z * y)),u)) / (z * y). [para(635(a,1),625(a,1,1,2,1)),flip(a)]. given #1040 (H,wt=53): 842 T((K(K(x,y),y * x) * x) * R((K(K(x,y),y * x) * x) \ 1,z,u),y) = (y \ (K(x,y) * (y * x))) * R(T(K(K(x,y),y * x) * x,y) \ 1,z,u). [para(841(a,1),811(a,1,1)),flip(a)]. given #1041 (H,wt=51): 1086 T((K(K(x,y),y * x) * x) * R((K(K(x,y),y * x) * x) \ 1,z,u),y) = (y \ (K(x,y) * (y * x))) * R((y \ (K(x,y) * (y * x))) \ 1,z,u). [para(841(a,1),842(a,2,2,1,1))]. given #1042 (H,wt=35): 1087 (x \ (K(y,x) * (x * y))) * R((x \ (K(y,x) * (x * y))) \ 1,z,u) = T(y * R(y \ 1,z,u),x). [para(1034(a,1),1086(a,1,1)),flip(a)]. given #1043 (H,wt=55): 972 (x \ 1) * (K(x \ 1,(x \ 1) \ 1) * L(T(x \ 1,(x \ 1) \ 1) \ y,z,u)) = T(x \ L(x * ((((x \ 1) \ 1) * y) / ((x \ 1) \ 1)),z,u),(x \ 1) \ 1). [para(968(a,2),832(a,2)),flip(a)]. given #1044 (H,wt=51): 1089 T(x \ L(x * ((((x \ 1) \ 1) * y) / ((x \ 1) \ 1)),z,u),(x \ 1) \ 1) = (x \ 1) * (K(x \ 1,x) * L(T(x \ 1,(x \ 1) \ 1) \ y,z,u)). [para(929(a,1),972(a,1,2,1)),flip(a)]. given #1045 (H,wt=49): 1090 T(x \ L(x * ((((x \ 1) \ 1) * y) / ((x \ 1) \ 1)),z,u),(x \ 1) \ 1) = (x \ 1) * (K(x \ 1,x) * L((((x \ 1) \ 1) \ 1) \ y,z,u)). [para(86(a,1),1089(a,2,2,2,1,1))]. given #1046 (H,wt=57): 843 T(T(((K(x,y) * (y * x)) / y) * R(((K(x,y) * (y * x)) / y) \ 1,z,u),w),y) = T(T(K(K(x,y),y * x) * x,y) * R((y \ (K(x,y) * (y * x))) \ 1,z,u),w). [para(841(a,2),815(a,2,1,1))]. given #1047 (H,wt=57): 844 T(T(((K(x,y) * (y * x)) / y) * R(((K(x,y) * (y * x)) / y) \ 1,z,u),w),y) = T((y \ (K(x,y) * (y * x))) * R(T(K(K(x,y),y * x) * x,y) \ 1,z,u),w). [para(841(a,2),815(a,2,1,2,1,1))]. given #1048 (H,wt=57): 1091 T(T((K(x,y) * ((y * x) / y)) * R(((K(x,y) * (y * x)) / y) \ 1,z,u),w),y) = T(T(K(K(x,y),y * x) * x,y) * R((y \ (K(x,y) * (y * x))) \ 1,z,u),w). [para(281(a,1),843(a,1,1,1,1))]. given #1049 (H,wt=57): 1092 T(T((K(x,y) * ((y * x) / y)) * R(((K(x,y) * (y * x)) / y) \ 1,z,u),w),y) = T((y \ (K(x,y) * (y * x))) * R(T(K(K(x,y),y * x) * x,y) \ 1,z,u),w). [para(281(a,1),844(a,1,1,1,1))]. given #1050 (H,wt=57): 1093 T(T((K(x,y) * ((y * x) / y)) * R((K(x,y) * ((y * x) / y)) \ 1,z,u),w),y) = T(T(K(K(x,y),y * x) * x,y) * R((y \ (K(x,y) * (y * x))) \ 1,z,u),w). [para(281(a,1),1091(a,1,1,1,2,1,1))]. given #1051 (H,wt=49): 1095 T(T(K(K(x,y),y * x) * x,y) * R((y \ (K(x,y) * (y * x))) \ 1,z,u),w) = T(T(((y * x) / y) * R(((y * x) / y) \ 1,z,u),w),y). [para(1034(a,1),1093(a,1,1,1)),flip(a)]. given #1052 (H,wt=47): 1096 T(T(K(K(x,y),y * x) * x,y) * R((y \ (K(x,y) * (y * x))) \ 1,z,u),w) = T((y \ (y * x)) * R((y \ (y * x)) \ 1,z,u),w). [para(1095(a,2),815(a,1))]. given #1053 (H,wt=43): 1098 T(T(K(K(x,y),y * x) * x,y) * R((y \ (K(x,y) * (y * x))) \ 1,z,u),w) = T(x * R((y \ (y * x)) \ 1,z,u),w). [para(13(a,1),1096(a,2,1,1))]. given #1054 (H,wt=39): 1099 T(T(K(K(x,y),y * x) * x,y) * R((y \ (K(x,y) * (y * x))) \ 1,z,u),w) = T(x * R(x \ 1,z,u),w). [para(13(a,1),1098(a,2,1,2,1,1))]. given #1055 (H,wt=37): 1100 T((x \ (K(y,x) * (x * y))) * R((x \ (K(y,x) * (x * y))) \ 1,z,u),w) = T(y * R(y \ 1,z,u),w). [para(841(a,1),1099(a,1,1,1))]. given #1056 (H,wt=23): 1101 T(T(x * R(x \ 1,y,z),u),w) = T(x * R(x \ 1,y,z),w). [para(1087(a,1),1100(a,1,1))]. given #1057 (H,wt=57): 1094 T(T((K(x,y) * ((y * x) / y)) * R((K(x,y) * ((y * x) / y)) \ 1,z,u),w),y) = T((y \ (K(x,y) * (y * x))) * R(T(K(K(x,y),y * x) * x,y) \ 1,z,u),w). [para(281(a,1),1092(a,1,1,1,2,1,1))]. given #1058 (H,wt=49): 1102 T((x \ (K(y,x) * (x * y))) * R(T(K(K(y,x),x * y) * y,x) \ 1,z,u),w) = T(T(((x * y) / x) * R(((x * y) / x) \ 1,z,u),w),x). [para(1034(a,1),1094(a,1,1,1)),flip(a)]. given #1059 (H,wt=47): 1104 T((x \ (K(y,x) * (x * y))) * R(T(K(K(y,x),x * y) * y,x) \ 1,z,u),w) = T(((x * y) / x) * R(((x * y) / x) \ 1,z,u),x). [para(1102(a,2),1101(a,1))]. given #1060 (H,wt=45): 1105 T((x \ (K(y,x) * (x * y))) * R(T(K(K(y,x),x * y) * y,x) \ 1,z,u),w) = (x \ (x * y)) * R((x \ (x * y)) \ 1,z,u). [para(1104(a,2),814(a,1))]. given #1061 (H,wt=41): 1107 T((x \ (K(y,x) * (x * y))) * R(T(K(K(y,x),x * y) * y,x) \ 1,z,u),w) = y * R((x \ (x * y)) \ 1,z,u). [para(13(a,1),1105(a,2,1))]. given #1062 (H,wt=37): 1108 T((x \ (K(y,x) * (x * y))) * R(T(K(K(y,x),x * y) * y,x) \ 1,z,u),w) = y * R(y \ 1,z,u). [para(13(a,1),1107(a,2,2,1,1))]. given #1063 (H,wt=35): 1109 T((x \ (K(y,x) * (x * y))) * R((x \ (K(y,x) * (x * y))) \ 1,z,u),w) = y * R(y \ 1,z,u). [para(841(a,1),1108(a,1,1,2,1,1))]. given #1064 (H,wt=19): 1110 T(x * R(x \ 1,y,z),u) = x * R(x \ 1,y,z). [para(1109(a,1),1100(a,1)),flip(a)]. given #1065 (H,wt=12): 1111 T(x,y * R(y \ 1,z,u)) = x. [hyper(33,a,1110,a)]. given #1066 (H,wt=10): 1115 T(x,y \ R(y,z,u)) = x. [para(481(a,1),1111(a,1,2))]. given #1067 (H,wt=10): 1116 K(x,y \ R(y,z,u)) = 1. [hyper(34,a,1115,a)]. given #1068 (H,wt=11): 1114 T(x,(y / (z * y)) * z) = x. [para(302(a,2),1111(a,1,2))]. given #1069 (H,wt=9): 1120 T(x,(y \ 1) * y) = x. [para(91(a,1),1114(a,1,2,1))]. given #1070 (H,wt=5): 1124 T(x,1) = x. [para(1063(a,1),1120(a,1,2))]. given #1071 (H,wt=5): 1126 T(1,x) = 1. [hyper(33,a,1124,a)]. given #1072 (H,wt=9): 1121 T(x,y * (1 / y)) = x. [para(92(a,1),1114(a,1,2,1))]. given #1073 (H,wt=9): 1122 T(x,K(y \ 1,y)) = x. [para(135(a,2),1120(a,1,2))]. given #1074 (H,wt=9): 1129 T(x,K(y,1 / y)) = x. [para(118(a,2),1121(a,1,2))]. given #1075 (H,wt=9): 1131 T(x,K(y,y \ 1)) = x. [para(930(a,2),1121(a,1,2))]. given #1076 (H,wt=11): 1119 T(x,(y / z) * (z / y)) = x. [para(16(a,1),1114(a,1,2,1,2))]. given #1077 (H,wt=11): 1136 T(x,K(y / z,z / y)) = x. [para(895(a,1),1122(a,1,2))]. given #1078 (H,wt=11): 1144 T(x,y * (z / (y * z))) = x. [para(15(a,1),1119(a,1,2,1))]. given #1079 (H,wt=12): 1123 R(x,x \ 1,x) = T(x,x \ 1). [para(1120(a,1),406(a,1,1))]. given #1080 (H,wt=12): 1137 T(x,K(y \ 1,R(y,z,u))) = x. [para(915(a,2),1122(a,1,2))]. given #1081 (H,wt=12): 1151 R(x,x \ 1,x) = (x \ 1) \ 1. [para(1123(a,2),86(a,1))]. given #1082 (H,wt=13): 1118 T(x,(y / z) \ (y * (z \ 1))) = x. [para(224(a,1),1115(a,1,2,2))]. given #1083 (H,wt=13): 1132 T(K(x \ 1,x),y) = K(x \ 1,x). [hyper(33,a,1122,a)]. given #1084 (H,wt=13): 1140 T(K(x,x \ 1),y) = K(x,x \ 1). [hyper(33,a,1131,a)]. given #1085 (H,wt=13): 1153 T(1 / x,T(x,x \ 1)) = x \ 1. [para(1123(a,1),866(a,1,2))]. given #1086 (H,wt=13): 1155 x / K(x \ 1,x) = (x \ 1) \ 1. [para(1151(a,1),238(a,2))]. given #1087 (H,wt=13): 1163 ((x \ 1) \ 1) \ x = K(x \ 1,x). [para(1155(a,1),59(a,1,1))]. given #1088 (H,wt=14): 1130 R(1 / x,x,1 / x) = T(1 / x,x). [para(1121(a,1),406(a,1,1))]. given #1089 (H,wt=12): 1164 R(1 / x,x,1 / x) = x \ 1. [para(1130(a,2),87(a,1))]. given #1090 (H,wt=15): 1117 T(x \ R(x,y,z),u) = x \ R(x,y,z). [hyper(33,a,1115,a)]. given #1091 (H,wt=15): 1133 K(x \ 1,x) * y = y * K(x \ 1,x). [para(1122(a,1),85(a,1,2))]. given #1092 (H,wt=15): 1134 x / K(y \ 1,y) = K(y \ 1,y) \ x. [para(1122(a,1),87(a,1))]. given #1093 (H,wt=15): 1135 (x * K(y \ 1,y)) / x = K(y \ 1,y). [para(1122(a,1),96(a,1,2))]. given #1094 (H,wt=14): 1178 L(x,x \ 1,x) / x = K(x \ 1,x). [para(254(a,1),1135(a,1,1))]. given #1095 (H,wt=15): 1138 K(x,1 / x) * y = y * K(x,1 / x). [para(1129(a,1),85(a,1,2))]. given #1096 (H,wt=13): 1182 x * K(x,1 / x) = T(x,x \ 1). [para(1138(a,1),945(a,1))]. given #1097 (H,wt=13): 1183 x * K(x,x \ 1) = T(x,x \ 1). [para(928(a,1),1182(a,1,2))]. given #1098 (H,wt=13): 1185 x * K(x,x \ 1) = (x \ 1) \ 1. [para(1183(a,2),86(a,1))]. given #1099 (H,wt=14): 1180 x * K(x,1 / x) = R(x,1 / x,x). [para(1138(a,1),247(a,1))]. given #1100 (H,wt=13): 1190 x * K(x,1 / x) = T(x,1 / x). [para(1180(a,2),370(a,1))]. given #1101 (H,wt=11): 1191 T(x,1 / x) = T(x,x \ 1). [para(1190(a,1),1182(a,1))]. given #1102 (H,wt=11): 1192 T(x,1 / x) = (x \ 1) \ 1. [para(1191(a,2),86(a,1))]. given #1103 (H,wt=13): 1193 T(x \ 1,x) = ((x \ 1) \ 1) \ 1. [para(57(a,1),1192(a,1,2))]. given #1104 (H,wt=13): 1194 1 / T(x \ 1,x) = (x \ 1) \ 1. [para(1193(a,2),57(a,1,2))]. given #1105 (H,wt=15): 1139 x / K(y,1 / y) = K(y,1 / y) \ x. [para(1129(a,1),87(a,1))]. given #1106 (H,wt=15): 1141 K(x,x \ 1) * y = y * K(x,x \ 1). [para(1131(a,1),85(a,1,2))]. given #1107 (H,wt=15): 1142 x \ (K(y,y \ 1) * x) = K(y,y \ 1). [para(1131(a,1),107(a,1,2,2))]. given #1108 (H,wt=15): 1158 K(x \ (x / T(x,y)),x) = K(x \ 1,x). [para(1132(a,1),753(a,2))]. given #1109 (H,wt=15): 1167 K(x,x \ 1) * (y * K(x \ 1,x)) = y. [hyper(456,a,1133,a)]. given #1110 (H,wt=15): 1177 x / K(y \ 1,y) = K(y,y \ 1) * x. [para(1134(a,2),447(a,1))]. given #1111 (H,wt=15): 1202 K(x \ 1,x) * (y * K(x,x \ 1)) = y. [para(1141(a,1),448(a,1,2))]. given #1112 (H,wt=15): 1210 (x * K(y \ 1,y)) * K(y,y \ 1) = x. [para(1167(a,1),1141(a,1)),flip(a)]. given #1113 (H,wt=15): 1211 (x * K(y \ 1,y)) \ x = K(y,y \ 1). [para(1167(a,1),1142(a,1,2))]. given #1114 (H,wt=15): 1212 (K(x,x \ 1) * y) \ y = K(x \ 1,x). [para(1177(a,1),59(a,1,1))]. given #1115 (H,wt=15): 1213 (K(x \ 1,x) * y) * K(x,x \ 1) = y. [hyper(154,a,1202,a),flip(a)]. given #1116 (H,wt=16): 1149 T(L(x,y / (x * y),x),y / (x * y)) = x. [para(1144(a,1),294(a,2))]. given #1117 (H,wt=16): 1187 (x \ 1) \ 1 != x * y | K(x,x \ 1) = y. [para(1185(a,1),19(a,1))]. given #1118 (H,wt=17): 1148 T(x * (y / (x * y)),z) = x * (y / (x * y)). [hyper(33,a,1144,a)]. given #1119 (H,wt=17): 1165 K(x,L(1 / y,z,u)) = K(x,L(y \ 1,z,u)). [para(1164(a,1),916(a,1,2,1)),flip(a)]. given #1120 (H,wt=17): 1198 (1 / x) * K(y,y \ 1) = K(y,y \ 1) / x. [para(1141(a,1),182(a,1))]. given #1121 (H,wt=17): 1203 ((1 / x) \ y) * K(x,x \ 1) = (x \ 1) \ y. [para(1141(a,1),533(a,1))]. given #1122 (H,wt=17): 1204 (x * y) * K(x,x \ 1) = T(x,x \ 1) * y. [para(1141(a,1),947(a,1))]. given #1123 (H,wt=17): 1205 (x * y) * K(x,x \ 1) = ((x \ 1) \ 1) * y. [para(1141(a,1),955(a,1))]. given #1124 (H,wt=17): 1206 ((1 / (1 / x)) * y) \ (x * y) = K(x,x \ 1). [para(942(a,1),1142(a,1,2))]. given #1125 (H,wt=17): 1207 x * K(x \ (x / T(x,y)),x) = 1 / (1 / x). [para(1158(a,2),1043(a,1,2))]. given #1126 (H,wt=16): 1221 L(x,T(x,y) \ 1,T(x,y)) = 1 / (1 / x). [para(1207(a,1),565(a,2))]. given #1127 (H,wt=15): 1222 1 / (1 / T(x,y)) = T(1 / (1 / x),y). [para(1221(a,1),1046(a,1,1)),flip(a)]. given #1128 (H,wt=15): 1224 T(1 / (1 / x),y) \ 1 = 1 / T(x,y). [para(1222(a,1),59(a,1,1))]. given #1129 (H,wt=15): 1228 1 / T(x \ 1,y) = T(1 / x,y) \ 1. [para(57(a,1),1224(a,1,1,1,2)),flip(a)]. given #1130 (H,wt=15): 1229 1 / T((x \ 1) \ 1,y) = T(x,y) \ 1. [para(57(a,1),1228(a,2,1,1))]. given #1131 (H,wt=15): 1230 (T(x,y) \ 1) \ 1 = T((x \ 1) \ 1,y). [para(1229(a,1),59(a,1,1))]. given #1132 (H,wt=17): 1217 (x * y) \ ((1 / (1 / x)) * y) = K(x \ 1,x). [para(942(a,1),1212(a,1,1))]. given #1133 (H,wt=17): 1225 x * (1 / (1 / T(y,x))) = (1 / (1 / y)) * x. [para(1222(a,2),85(a,1,2))]. given #1134 (H,wt=17): 1232 T(((x / y) \ 1) \ 1,y) = ((y \ x) \ 1) \ 1. [para(87(a,1),1230(a,1,1,1)),flip(a)]. given #1135 (H,wt=18): 1143 K(x,x \ 1) * y != z * K(x,x \ 1) | z = y. [para(1131(a,1),110(a,1,2))]. given #1136 (H,wt=18): 1162 T(x / (y * x),T(y,y \ 1)) = R(y \ 1,y,x). [para(1153(a,1),162(a,2,1))]. given #1137 (H,wt=18): 1166 K(x,a(R(y,z,u),z,u)) = K(x,y \ R(y,z,u)). [para(1117(a,1),990(a,1,2)),flip(a)]. given #1138 (H,wt=11): 1236 K(x,a(R(y,z,u),z,u)) = 1. [para(1166(a,2),1116(a,1))]. given #1139 (H,wt=12): 1238 K(x,a(y / (z * u),z,u)) = 1. [para(133(a,1),1236(a,1,2,1))]. given #1140 (H,wt=8): 1240 K(x,a(y,z,u)) = 1. [para(15(a,1),1238(a,1,2,1))]. given #1141 (H,wt=8): 1241 T(x,a(y,z,u)) = x. [hyper(35,a,1240,a)]. given #1142 (H,wt=11): 1243 T(a(x,y,z),u) = a(x,y,z). [hyper(33,a,1241,a)]. given #1143 (H,wt=13): 1244 (x * a(y,z,u)) / x = a(y,z,u). [para(1241(a,1),96(a,1,2))]. given #1144 (H,wt=16): 1246 a(x,y,z) = ((x * y) * z) / (x * (y * z)). [para(71(a,1),1244(a,1,1)),flip(a)]. given #1145 (H,wt=18): 1172 (x \ 1) * K(x \ 1,x) = R(x \ 1,x,x \ 1). [para(1133(a,1),245(a,1))]. given #1146 (H,wt=15): 1247 (x \ 1) * K(x \ 1,x) = T(x \ 1,x). [para(1172(a,2),303(a,1))]. given #1147 (H,wt=17): 1248 1 / ((x \ 1) * K(x \ 1,x)) = (x \ 1) \ 1. [para(1247(a,2),1194(a,1,2))]. given #1148 (H,wt=18): 1216 L(K(x,x \ 1),K(x \ 1,x),y) = K(x,x \ 1). [para(1211(a,1),184(a,2))]. given #1149 (H,wt=18): 1235 K(x,x \ 1) * y != z | K(x \ 1,x) * z = y. [para(1213(a,1),1143(a,2))]. given #1150 (H,wt=19): 1128 T(x * L(x \ 1,y,z),x) = x * L(x \ 1,y,z). [para(1126(a,1),700(a,2,2,1,2))]. given #1151 (H,wt=12): 1251 T(x,x * L(x \ 1,y,z)) = x. [hyper(33,a,1128,a)]. given #1152 (H,wt=19): 1147 K(x / y,y / x) * z = z * K(x / y,y / x). [para(1136(a,1),85(a,1,2))]. given #1153 (H,wt=19): 1154 T(K(x \ 1,R(x,y,z)),u) = K(x \ 1,R(x,y,z)). [hyper(33,a,1137,a)]. given #1154 (H,wt=19): 1156 ((x / y) \ (x * (y \ 1))) * (x / y) = x * (y \ 1). [para(1118(a,1),108(a,1,2))]. given #1155 (H,wt=19): 1159 K(x \ 1,x) * (T(x,y) \ x) = (T(x,y) \ 1) * x. [para(1132(a,1),756(a,1,1))]. given #1156 (H,wt=19): 1169 (x * K(y \ 1,y)) * z = K(y \ 1,y) * (x * z). [para(1133(a,1),197(a,1,1))]. given #1157 (H,wt=19): 1170 (x * K(y \ 1,y)) / z = K(y \ 1,y) * (x / z). [para(1133(a,1),281(a,1,1))]. given #1158 (H,wt=19): 1171 (K(x \ 1,x) * y) / z = (y / z) * K(x \ 1,x). [para(1133(a,1),281(a,2))]. given #1159 (H,wt=19): 1175 R(1 / x,y,z) * K(x \ 1,x) = R(x \ 1,y,z). [para(1133(a,1),462(a,1))]. given #1160 (H,wt=19): 1196 R(x \ 1,y,z) * K(x,x \ 1) = R(1 / x,y,z). [hyper(17,a,460,a,b,1141,a),flip(a)]. given #1161 (H,wt=19): 1199 (x * K(y,y \ 1)) * z = K(y,y \ 1) * (x * z). [para(1141(a,1),197(a,1,1))]. given #1162 (H,wt=19): 1209 (x * K(y \ 1,y)) \ z = x \ (K(y,y \ 1) * z). [para(1167(a,1),206(a,1,1)),flip(a)]. given #1163 (H,wt=17): 1263 (x * K(y \ 1,y)) \ K(y \ 1,y) = x \ 1. [para(449(a,1),1209(a,2,2))]. given #1164 (H,wt=19): 1214 (x * K(y,y \ 1)) \ z = x \ (K(y \ 1,y) * z). [para(1202(a,1),206(a,1,1)),flip(a)]. given #1165 (H,wt=19): 1233 (1 / (1 / (x / y))) * y = y * (1 / (1 / (y \ x))). [para(87(a,1),1225(a,1,2,2,2)),flip(a)]. given #1166 (H,wt=19): 1234 T(x,((y * x) / y) \ 1) = ((y \ (y * x)) \ 1) \ 1. [para(1232(a,1),179(a,1)),flip(a)]. given #1167 (H,wt=15): 1265 T(x,((y * x) / y) \ 1) = (x \ 1) \ 1. [para(13(a,1),1234(a,2,1,1))]. given #1168 (H,wt=19): 1262 (x * K(y,y \ 1)) * z = (x * z) * K(y,y \ 1). [para(1199(a,2),1141(a,1))]. given #1169 (H,wt=19): 1264 K(x / y,y / x) * y = x * (1 / (1 / (x \ y))). [para(1233(a,1),973(a,2))]. given #1170 (H,wt=19): 1268 (x * K(y,y \ 1)) \ ((x * z) * K(y,y \ 1)) = z. [hyper(66,a,1262,a)]. given #1171 (H,wt=19): 1269 x \ (K(x / y,y / x) * y) = 1 / (1 / (x \ y)). [hyper(66,a,1264,a(flip))]. given #1172 (H,wt=20): 1173 (x * (y \ 1)) \ (K(y \ 1,y) * x) = L(y,y \ 1,x). [para(1133(a,2),150(a,1,2))]. given #1173 (H,wt=20): 1174 K(x \ 1,x) * R(y,x \ 1,x) = (y * (x \ 1)) * x. [para(1133(a,2),217(a,1))]. given #1174 (H,wt=20): 1195 K(x,1 / x) \ (y * (1 / x)) = R(y / x,x,1 / x). [para(1139(a,1),226(a,1))]. given #1175 (H,wt=20): 1220 L(T(K(x,x \ 1),y),y,1 / (1 / x)) = K(x,x \ 1). [para(1206(a,1),969(a,2))]. given #1176 (H,wt=18): 1274 L(K(x,x \ 1),y,1 / (1 / x)) = K(x,x \ 1). [para(1140(a,1),1220(a,1,1))]. given #1177 (H,wt=20): 1271 R(T(x,y * K(z,z \ 1)),y,K(z,z \ 1)) = T(x,y). [para(1268(a,1),404(a,1,1)),flip(a)]. given #1178 (H,wt=20): 1272 K(x \ 1,x) \ ((y * (x \ 1)) * x) = R(y,x \ 1,x). [hyper(66,a,1174,a)]. given #1179 (H,wt=20): 1273 K(x,x \ 1) \ (y * (1 / x)) = R(y / x,x,1 / x). [para(928(a,1),1195(a,1,1))]. given #1180 (H,wt=20): 1278 K(x \ 1,x) * (y * (1 / x)) = R(y / x,x,1 / x). [para(1273(a,1),455(a,1)),flip(a)]. given #1181 (H,wt=21): 1176 x \ (K((y \ x) \ 1,y \ x) * y) = T(x \ y,y \ x). [para(1133(a,2),523(a,1,2))]. given #1182 (H,wt=21): 1226 K(T(x,y),T(x,y) \ 1) * T(1 / (1 / x),y) = T(x,y). [para(1222(a,1),938(a,1,2))]. given #1183 (H,wt=21): 1231 K(x,y) / T((z \ 1) \ 1,u) = K(x,y) * (T(z,u) \ 1). [para(1229(a,1),182(a,1,2)),flip(a)]. given #1184 (H,wt=21): 1254 (1 / x) * ((T(x,y) \ 1) * x) = (x \ 1) * (T(x,y) \ x). [para(1159(a,1),539(a,1,2))]. given #1185 (H,wt=21): 1259 ((x * y) / z) * K(x \ 1,x) = ((1 / (1 / x)) * y) / z. [para(951(a,1),1171(a,1,1)),flip(a)]. given #1186 (H,wt=21): 1267 (((x * y) / x) \ 1) * ((y \ 1) \ 1) = ((x * y) / x) \ y. [para(1265(a,1),586(a,1,2))]. given #1187 (H,wt=21): 1280 K((x \ y) \ 1,x \ y) * x = y * T(y \ x,x \ y). [para(1176(a,1),14(a,1,2)),flip(a)]. given #1188 (H,wt=21): 1281 T((1 / x) * (T(x,y) \ x),x) = (x \ 1) * (T(x,y) \ x). [para(1254(a,1),508(a,2))]. given #1189 (H,wt=22): 1145 ((x / y) * (y / x)) / (x / y) = L(y / x,x / y,y / x). [para(1119(a,1),297(a,1))]. given #1190 (H,wt=22): 1150 L(x,y / (x * y),x) * (y / (x * y)) = (y / (x * y)) * x. [para(1144(a,1),296(a,1,2)),flip(a)]. given #1191 (H,wt=22): 1157 L(K(x \ 1,x),y,z) * (z * y) = z * (y * K(x \ 1,x)). [para(1132(a,1),261(a,1,2,2)),flip(a)]. given #1192 (H,wt=22): 1160 L(K(x,x \ 1),y,z) * (z * y) = z * (y * K(x,x \ 1)). [para(1140(a,1),261(a,1,2,2)),flip(a)]. given #1193 (H,wt=22): 1256 K(x \ 1,x) * (y * z) != u * z | y * K(x \ 1,x) = u. [para(1169(a,1),20(a,1))]. given #1194 (H,wt=22): 1257 K(x \ 1,R(x,y,z)) * (u * w) = (u * K(x \ 1,x)) * w. [para(915(a,2),1169(a,2,1)),flip(a)]. given #1195 (H,wt=22): 1287 L(K(x \ 1,x),y,z) * (z * y) = z * (K(x \ 1,x) * y). [para(1133(a,2),1157(a,2,2))]. given #1196 (H,wt=23): 1249 1 / ((R(x,y,z) \ 1) * K(x \ 1,x)) = (R(x,y,z) \ 1) \ 1. [para(1029(a,1),1248(a,1,2,2))]. given #1197 (H,wt=23): 1266 T((x * y) / x,((z * y) / z) \ 1) = (x * ((y \ 1) \ 1)) / x. [para(1265(a,1),178(a,1,1,2)),flip(a)]. given #1198 (H,wt=19): 1289 (x * ((y \ 1) \ 1)) / x = (((x * y) / x) \ 1) \ 1. [para(1266(a,1),86(a,1))]. given #1199 (H,wt=23): 1270 K((x / y) / x,x / (x / y)) * x = (x / y) * (1 / (1 / y)). [para(59(a,1),1264(a,2,2,2,2))]. given #1200 (H,wt=23): 1286 ((x / (y * x)) * y) / R(1 / y,y,x) = L(y,x / (y * x),y). [para(1150(a,1),470(a,1,1))]. given #1201 (H,wt=14): 1291 L(x,y / (x * y),x) = 1 / (1 / x). [para(1286(a,1),870(a,1))]. given #1202 (H,wt=13): 1293 T(1 / (1 / x),y / (x * y)) = x. [para(1291(a,1),1149(a,1,1))]. given #1203 (H,wt=11): 1294 T(1 / (1 / x),x \ 1) = x. [para(91(a,1),1293(a,1,2))]. given #1204 (H,wt=15): 1296 T(T(1 / (1 / x),y),x \ 1) = T(x,y). [para(1294(a,1),36(a,1,1)),flip(a)]. given #1205 (H,wt=13): 1297 T(x,y / (x * y)) = T(x,x \ 1). [para(1293(a,1),1296(a,1,1)),flip(a)]. given #1206 (H,wt=21): 1299 T(x / (y * x),T(y,y \ 1)) = ((x / (y * x)) \ 1) \ 1. [para(1297(a,1),1005(a,1,2))]. given #1207 (H,wt=16): 1300 R(x \ 1,x,y) = ((y / (x * y)) \ 1) \ 1. [para(1299(a,1),1162(a,1)),flip(a)]. given #1208 (H,wt=18): 1302 R((x / y) \ 1,x / y,y) = ((y / x) \ 1) \ 1. [para(16(a,1),1300(a,2,1,1,2))]. given #1209 (H,wt=17): 1303 T((1 * x) / y,y / x) = ((x / y) \ 1) \ 1. [para(1302(a,1),349(a,1)),flip(a)]. given #1210 (H,wt=15): 1305 T(x / y,y / x) = ((x / y) \ 1) \ 1. [para(11(a,1),1303(a,1,1,1))]. given #1211 (H,wt=17): 1306 T(((x / y) \ 1) \ 1,y) = T(y \ x,y / x). [para(1305(a,1),117(a,1,1))]. given #1212 (H,wt=15): 1307 T(x \ y,x / y) = ((x \ y) \ 1) \ 1. [para(1306(a,1),1232(a,1))]. given #1213 (H,wt=19): 1308 K(x / y,y / x) * x = y * (((y \ x) \ 1) \ 1). [para(1307(a,1),899(a,2,2))]. given #1214 (H,wt=22): 1304 R((x / y) \ 1,x / y,y) \ 1 = T((y / x) \ 1,y / x). [para(1302(a,2),1193(a,2,1)),flip(a)]. given #1215 (H,wt=23): 1290 (x \ 1) * ((((y * x) / y) \ 1) \ 1) = ((y * x) / y) * (x \ 1). [para(1289(a,1),374(a,1,2))]. given #1216 (H,wt=24): 1181 x \ (K(y \ x,1 / (y \ x)) * y) = L(1 / (y \ x),y \ x,y). [para(1138(a,2),287(a,1,2))]. given #1217 (H,wt=24): 1184 (T(x,x \ 1) * y) / (K(x,x \ 1) * y) = R(x,K(x,x \ 1),y). [para(1183(a,1),28(a,2,1,1)),flip(a)]. given #1218 (H,wt=10): 1311 R(x,K(x,x \ 1),y) = x. [para(1184(a,1),970(a,1))]. given #1219 (H,wt=14): 1312 R(1 / x,K(1 / x,x),y) = 1 / x. [para(59(a,1),1311(a,1,2,2))]. given #1220 (H,wt=14): 1313 R(1 / x,K(x \ 1,x),y) = 1 / x. [para(894(a,1),1312(a,1,2))]. given #1221 (H,wt=24): 1186 (x * K(y,y \ 1)) / T(y,y \ 1) = R(x / y,y,K(y,y \ 1)). [para(1183(a,1),82(a,2,2)),flip(a)]. given #1222 (H,wt=24): 1188 ((x \ 1) \ 1) \ (x * (K(x,x \ 1) * y)) = L(y,K(x,x \ 1),x). [para(1185(a,1),26(a,2,1)),flip(a)]. given #1223 (H,wt=24): 1283 x * T(x \ y,y \ x) != z * y | K((y \ x) \ 1,y \ x) = z. [para(1280(a,1),20(a,1))]. given #1224 (H,wt=24): 1285 T(L(x / y,y / x,x / y),y) = ((y / x) * (y \ x)) / (y / x). [para(1145(a,1),270(a,1,1))]. given #1225 (H,wt=24): 1310 x \ (K(y \ x,(y \ x) \ 1) * y) = L(1 / (y \ x),y \ x,y). [para(928(a,1),1181(a,1,2,1))]. given #1226 (H,wt=24): 1315 R((K(x \ 1,x) * y) / x,x,K(x,x \ 1)) = y / T(x,x \ 1). [para(1213(a,1),1186(a,1,1)),flip(a)]. given #1227 (H,wt=24): 1316 L(T(x / y,y),y / x,x / y) = ((y / x) * (y \ x)) / (y / x). [para(1285(a,1),38(a,2))]. given #1228 (H,wt=22): 1318 ((x / y) * (x \ y)) / (x / y) = L(x \ y,x / y,y / x). [para(87(a,1),1316(a,1,1)),flip(a)]. given #1229 (H,wt=24): 1317 R((x / y) * K(y \ 1,y),y,K(y,y \ 1)) = x / T(y,y \ 1). [para(1171(a,1),1315(a,1,1))]. given #1230 (H,wt=25): 1152 R(T(x,x \ 1),y,z) * K(x \ 1,x) = (R(x,y,z) * (x \ 1)) * x. [para(1123(a,1),389(a,1,1,1))]. given #1231 (H,wt=19): 1320 R(T(x,x \ 1),y,z) * K(x \ 1,x) = R(x,y,z). [para(1152(a,2),855(a,1))]. given #1232 (H,wt=19): 1321 R((x \ 1) \ 1,y,z) * K(x \ 1,x) = R(x,y,z). [para(86(a,1),1320(a,1,1,1))]. given #1233 (H,wt=25): 1252 R(x,L(x \ 1,y,z),T(x,L(x \ 1,y,z))) = T(x,L(x \ 1,y,z)). [para(1251(a,1),341(a,1,1))]. given #1234 (H,wt=14): 1323 T(x,y \ T(y,L(y \ 1,z,u))) = x. [para(1252(a,1),1115(a,1,2,2))]. given #1235 (H,wt=23): 1324 T(x \ T(x,L(x \ 1,y,z)),u) = x \ T(x,L(x \ 1,y,z)). [hyper(33,a,1323,a)]. given #1236 (H,wt=25): 1298 K((x / (y * x)) \ 1,x / (y * x)) * (y * x) = T(y,y \ 1) * x. [para(1297(a,1),632(a,2,1))]. given #1237 (H,wt=23): 1325 K((x * y) / y,y / (x * y)) * (x * y) = T(x,x \ 1) * y. [para(895(a,1),1298(a,1,1))]. given #1238 (H,wt=17): 1327 K((x * y) / y,y / (x * y)) = K(x,x \ 1). [hyper(18,a,947,a,b,1325,a)]. given #1239 (H,wt=13): 1328 K(x,y / (x * y)) = K(x,x \ 1). [para(15(a,1),1327(a,1,1))]. given #1240 (H,wt=17): 1330 K(x / y,(x / y) \ 1) = K(x / y,y / x). [para(16(a,1),1328(a,1,2,2)),flip(a)]. given #1241 (H,wt=19): 1333 K(x / y,y / x) \ z = K(y / x,x / y) * z. [para(1330(a,1),898(a,1,1)),flip(a)]. given #1242 (H,wt=21): 1331 K(x / (y * x),(x / (y * x)) \ 1) = K(y,y \ 1) \ 1. [para(1328(a,1),907(a,2,1))]. given #1243 (H,wt=19): 1334 K(x / (y * x),(x / (y * x)) \ 1) = K(y \ 1,y). [para(1331(a,2),452(a,1))]. given #1244 (H,wt=21): 1332 K(x / (y \ x),(y \ x) / x) = K(y,(x / (y \ x)) \ 1). [para(57(a,1),1330(a,1,1)),flip(a)]. given #1245 (H,wt=17): 1336 K(x / (y \ x),(y \ x) / x) = K(y,y \ 1). [para(57(a,1),1332(a,2,2,1))]. given #1246 (H,wt=21): 1337 K(x,x \ 1) * (x \ y) = (1 / (1 / ((x \ y) / y))) * y. [para(1336(a,1),973(a,1,1))]. given #1247 (H,wt=19): 1338 (1 / (1 / ((x \ y) / y))) * y = (1 / (1 / x)) \ y. [para(1337(a,1),965(a,1))]. given #1248 (H,wt=19): 1339 ((1 / (1 / x)) \ y) / y = 1 / (1 / ((x \ y) / y)). [hyper(70,a,1338,a)]. given #1249 (H,wt=19): 1340 (((1 / (1 / x)) \ y) / y) \ 1 = 1 / ((x \ y) / y). [para(1339(a,2),59(a,1,1))]. given #1250 (H,wt=19): 1341 1 / (((x \ 1) \ y) / y) = (((1 / x) \ y) / y) \ 1. [para(57(a,1),1340(a,1,1,1,1,2)),flip(a)]. given #1251 (H,wt=19): 1342 ((((1 / x) \ y) / y) \ 1) \ 1 = ((x \ 1) \ y) / y. [para(1341(a,1),59(a,1,1))]. given #1252 (H,wt=19): 1343 K(x,((1 / y) \ z) / z) = K(x,((y \ 1) \ z) / z). [para(1342(a,1),929(a,1,2)),flip(a)]. given #1253 (H,wt=26): 1168 R(x / y,y,K(z \ 1,z)) = (x * K(z \ 1,z)) / (K(z \ 1,z) * y). [para(1133(a,2),82(a,2,2))]. given #1254 (H,wt=26): 1197 (x * K(y,y \ 1)) \ (K(y,y \ 1) * (x * z)) = L(z,x,K(y,y \ 1)). [para(1141(a,1),26(a,2,1)),flip(a)]. given #1255 (H,wt=24): 1345 ((x \ 1) \ 1) \ (K(x,x \ 1) * (x * y)) = L(y,x,K(x,x \ 1)). [para(1185(a,1),1197(a,1,1))]. given #1256 (H,wt=24): 1346 ((x \ 1) \ 1) \ (x * (K(x,x \ 1) * y)) = L(y,x,K(x,x \ 1)). [para(966(a,1),1345(a,1,2))]. given #1257 (H,wt=17): 1347 L(x,K(y,y \ 1),y) = L(x,y,K(y,y \ 1)). [para(1346(a,1),1188(a,1)),flip(a)]. given #1258 (H,wt=10): 1348 L(x,K(y,y \ 1),y) = x. [para(1347(a,2),88(a,1))]. given #1259 (H,wt=14): 1349 L(x,K(y \ 1,y),z / (y * z)) = x. [para(1334(a,1),1348(a,1,2))]. given #1260 (H,wt=12): 1350 L(x,K(y \ 1,y),1 / y) = x. [para(12(a,1),1349(a,1,3,2))]. given #1261 (H,wt=26): 1258 R(x / (1 / y),1 / y,K(y \ 1,y)) = K(y \ 1,y) * (x / (y \ 1)). [para(1170(a,1),891(a,2))]. given #1262 (H,wt=26): 1344 R(x / y,y,K(z \ 1,z)) = K(z \ 1,z) * (x / (K(z \ 1,z) * y)). [para(1168(a,2),1170(a,1))]. given #1263 (H,wt=27): 1189 (x * y) * K(y,y \ 1) != z * ((y \ 1) \ 1) | R(x,y,K(y,y \ 1)) = z. [para(1185(a,1),211(a,2,2))]. given #1264 (H,wt=28): 1161 L(1 / T((x \ 1) \ 1,y),x,x \ 1) = K(x,x \ 1) / T((x \ 1) \ 1,y). [para(1140(a,1),997(a,1,1)),flip(a)]. given #1265 (H,wt=26): 1353 L(1 / T((x \ 1) \ 1,y),x,x \ 1) = K(x,x \ 1) * (T(x,y) \ 1). [para(1161(a,2),1231(a,1))]. given #1266 (H,wt=28): 1179 (R(x,K(y \ 1,y),y) / y) * L(y,y \ 1,y) = x * (L(y,y \ 1,y) / y). [para(1178(a,1),794(a,1,1,1,2))]. given #1267 (H,wt=28): 1200 R(x,x \ y,K(z,z \ 1)) \ (K(z,z \ 1) * y) = (x \ y) * K(z,z \ 1). [para(1141(a,2),233(a,1,2))]. given #1268 (H,wt=29): 1201 (x * y) * K(z,z \ 1) != u * (K(z,z \ 1) * y) | R(x,y,K(z,z \ 1)) = u. [para(1141(a,2),211(a,2,2))]. given #1269 (H,wt=29): 1309 K(x \ 1,x) * ((((y * x) / y) \ 1) \ 1) = (1 / x) \ (((y * x) / y) * (x \ 1)). [para(1290(a,1),535(a,1,2)),flip(a)]. given #1270 (H,wt=21): 1354 K(x \ 1,x) * ((((y * x) / y) \ 1) \ 1) = (y * x) / y. [para(1309(a,2),1074(a,1))]. given #1271 (H,wt=23): 1355 ((x \ 1) \ 1) \ ((((y * x) / y) \ 1) \ 1) = x \ ((y * x) / y). [para(1354(a,1),537(a,1,2)),flip(a)]. given #1272 (H,wt=27): 1356 T(x,((y * x) / y) \ 1) \ ((((z * x) / z) \ 1) \ 1) = x \ ((z * x) / z). [para(1265(a,2),1355(a,1,1))]. given #1273 (H,wt=29): 1314 (R(1 / x,y,z) * K(x \ 1,x)) * (K(x \ 1,x) \ u) = R(1 / x,y,z) * u. [para(1313(a,1),299(a,1,1,1)),flip(a)]. given #1274 (H,wt=23): 1357 R(x \ 1,y,z) * (K(x \ 1,x) \ u) = R(1 / x,y,z) * u. [para(1175(a,1),1314(a,1,1))]. given #1275 (H,wt=23): 1358 R(x \ 1,y,z) * (K(x,x \ 1) * u) = R(1 / x,y,z) * u. [para(447(a,1),1357(a,1,2))]. given #1276 (H,wt=30): 1319 (x \ y) * (((x \ y) \ (y / x)) / (y / x)) = x \ (y * L(y \ x,y / x,x / y)). [para(1318(a,1),779(a,1,2,2)),flip(a)]. given #1277 (H,wt=29): 1359 (x \ y) * (((x \ y) \ (y / x)) / (y / x)) = x \ (K(y / x,(y / x) \ 1) * x). [para(980(a,1),1319(a,2,2))]. given #1278 (H,wt=25): 1360 (x \ y) * (((x \ y) \ (y / x)) / (y / x)) = K(y / x,(y / x) \ 1). [para(1359(a,2),1142(a,1))]. given #1279 (H,wt=28): 1361 K(x / y,(x / y) \ 1) != (y \ x) * z | ((y \ x) \ (x / y)) / (x / y) = z. [para(1360(a,1),19(a,1))]. given #1280 (H,wt=31): 1219 ((1 / x) \ (y * T(y \ 1,x))) * K(x,x \ 1) = T(x,x \ 1) * (y * T(y \ 1,x)). [para(1082(a,2),1204(a,1,1))]. given #1281 (H,wt=25): 1363 T(x,x \ 1) * (y * T(y \ 1,x)) = (x \ 1) \ (y * T(y \ 1,x)). [para(1219(a,1),1203(a,1))]. given #1282 (H,wt=25): 1364 (x * T(x \ 1,y)) * ((y \ 1) \ 1) = (y \ 1) \ (x * T(x \ 1,y)). [para(1363(a,1),1084(a,1)),flip(a)]. given #1283 (H,wt=25): 1366 x * ((y \ (x \ ((y \ 1) \ 1))) * y) = (y \ 1) \ (x * T(x \ 1,y)). [para(1364(a,1),988(a,1)),flip(a)]. given #1284 (H,wt=32): 1284 K(((x * y) \ x) \ 1,L(y \ 1,y,x)) * (x * y) = x * T(x \ (x * y),(x * y) \ x). [para(103(a,2),1280(a,1,1,2))]. given #1285 (H,wt=33): 1218 T((T(x,y) \ x) * (T(x,y) / x),z) = (T(x,y) \ x) * (T(x,y) / ((T(x,y) \ x) * T(x,y))). [para(1063(a,1),1148(a,1,1,2,2))]. given #1286 (H,wt=25): 1367 T((T(x,y) \ x) * (T(x,y) / x),z) = (T(x,y) \ x) * (T(x,y) / x). [para(1063(a,1),1218(a,2,2,2))]. given #1287 (H,wt=33): 1351 R((x * y) / y,y,K(z \ 1,z)) = K(z \ 1,z) * R(x / K(z \ 1,z),K(z \ 1,z),y). [para(82(a,2),1344(a,2,2))]. given #1288 (H,wt=29): 1368 K(x \ 1,x) * R(y / K(x \ 1,x),K(x \ 1,x),z) = R(y,z,K(x \ 1,x)). [para(15(a,1),1351(a,1,1)),flip(a)]. given #1289 (H,wt=29): 1369 K(x \ 1,x) * R(K(x,x \ 1) * y,K(x \ 1,x),z) = R(y,z,K(x \ 1,x)). [para(1177(a,1),1368(a,1,2,1))]. given #1290 (H,wt=29): 1370 R(K(x \ 1,x) * (K(x,x \ 1) * y),K(x \ 1,x),z) = R(y,z,K(x \ 1,x)). [para(1369(a,1),458(a,2))]. given #1291 (H,wt=17): 1371 R(x,K(y \ 1,y),z) = R(x,z,K(y \ 1,y)). [para(448(a,1),1370(a,1,1))]. given #1292 (H,wt=28): 1372 (R(x,y,K(y \ 1,y)) / y) * L(y,y \ 1,y) = x * (L(y,y \ 1,y) / y). [para(1371(a,1),1179(a,1,1,1))]. given #1293 (H,wt=27): 1373 (R(x,y,K(y \ 1,y)) / y) * (1 / (1 / y)) = x * (L(y,y \ 1,y) / y). [para(1045(a,1),1372(a,1,2))]. given #1294 (H,wt=24): 1374 (R(x,y,K(y \ 1,y)) / y) * (1 / (1 / y)) = x * K(y \ 1,y). [para(1178(a,1),1373(a,2,2))]. given #1295 (H,wt=27): 1375 (R(x,y,K(y \ 1,y)) / y) * (1 / (1 / y)) != z * K(y \ 1,y) | z = x. [para(1374(a,2),20(a,2)),flip(a)]. given #1296 (H,wt=35): 1277 L(R(x,y \ 1,y),a(1 / y,y,y \ 1),1 / y) = (1 * (y \ 1)) \ R((1 / y) * x,y,y \ 1). [para(1272(a,1),994(a,1,1))]. given #1297 (H,wt=32): 1376 L(R(x,y \ 1,y),K(y \ 1,y),1 / y) = (1 * (y \ 1)) \ R((1 / y) * x,y,y \ 1). [para(885(a,1),1277(a,1,2))]. given #1298 (H,wt=23): 1377 (1 * (x \ 1)) \ R((1 / x) * y,x,x \ 1) = R(y,x \ 1,x). [para(1376(a,1),1350(a,1))]. given #1299 (H,wt=21): 1378 (x \ 1) \ R((1 / x) * y,x,x \ 1) = R(y,x \ 1,x). [para(11(a,1),1377(a,1,1))]. given #1300 (H,wt=18): 1379 T(((1 / x) * y) * x,x \ 1) = R(y,x \ 1,x). [para(1378(a,1),244(a,1)),flip(a)]. given #1301 (H,wt=37): 1260 (R(x \ 1,y,z) * (K(x,x \ 1) * u)) \ (R(1 / x,y,z) * u) = a(R(x \ 1,y,z),K(x,x \ 1),u). [para(1196(a,1),22(a,2,2,1)),flip(a)]. given #1302 (H,wt=31): 1380 a(R(x \ 1,y,z),K(x,x \ 1),u) = (R(1 / x,y,z) * u) \ (R(1 / x,y,z) * u). [para(1358(a,1),1260(a,1,1)),flip(a)]. given #1303 (H,wt=15): 1381 a(R(x \ 1,y,z),K(x,x \ 1),u) = 1. [para(1380(a,2),48(a,1))]. given #1304 (H,wt=17): 1383 a(R((x \ 1) \ 1,y,z),K(x \ 1,x),u) = 1. [para(929(a,1),1381(a,1,2))]. given #1305 (H,wt=38): 1279 L(L((1 / x) \ 1,y * (1 / x),K(x \ 1,x)),1 / x,y) = R(y / x,x,1 / x) \ (K(x \ 1,x) * y). [para(1278(a,1),335(a,2,1))]. given #1306 (H,wt=34): 1384 L(L(x,y * (1 / x),K(x \ 1,x)),1 / x,y) = R(y / x,x,1 / x) \ (K(x \ 1,x) * y). [para(59(a,1),1279(a,1,1,1))]. given #1307 (H,wt=39): 1215 R(R(x,y,K(z \ 1,z)),y * K(z \ 1,z),K(z,z \ 1)) = (x * y) / ((y * K(z \ 1,z)) * K(z,z \ 1)). [para(1210(a,1),213(a,1,1)),flip(a)]. given #1308 (H,wt=27): 1385 R(R(x,y,K(z \ 1,z)),y * K(z \ 1,z),K(z,z \ 1)) = (x * y) / y. [para(1210(a,1),1215(a,2,2))]. given #1309 (H,wt=23): 1386 R(R(x,y,K(z \ 1,z)),y * K(z \ 1,z),K(z,z \ 1)) = x. [para(1385(a,2),15(a,1))]. given #1310 (H,wt=21): 1387 R(R(x,1 / y,K(y \ 1,y)),y \ 1,K(y,y \ 1)) = x. [para(889(a,1),1386(a,1,2))]. given #1311 (H,wt=25): 1388 R(R(x,1 / y,K(y \ 1,y)),y \ 1,K((y \ 1) \ 1,y \ 1)) = x. [para(897(a,2),1387(a,1,3))]. given #1312 (H,wt=39): 1261 (K(x,x \ 1) * ((y * z) * u)) / ((z * K(x,x \ 1)) * u) = R(R(y,z,K(x,x \ 1)),z * K(x,x \ 1),u). [para(1199(a,1),213(a,1,1))]. given #1313 (H,wt=39): 1389 (K(x,x \ 1) * ((y * z) * u)) / (K(x,x \ 1) * (z * u)) = R(R(y,z,K(x,x \ 1)),z * K(x,x \ 1),u). [para(1199(a,1),1261(a,1,2))]. given #1314 (H,wt=39): 1390 K(x,x \ 1) * (((y * z) * u) / (K(x,x \ 1) * (z * u))) = R(R(y,z,K(x,x \ 1)),z * K(x,x \ 1),u). [para(1389(a,1),281(a,1)),flip(a)]. given #1315 (H,wt=40): 1253 (x * (y \ 1)) \ (((x / y) \ (x * (y \ 1))) * (z * (x / y))) = L(T(z,x / y),x / y,(x / y) \ (x * (y \ 1))). [para(1156(a,1),112(a,1,1))]. given #1316 (H,wt=41): 1146 L(R(x / y,y / x,(y / x) \ 1),y / x,((y / x) * (x / y)) / (y / x)) = ((y / x) * (x / y)) * ((y / x) \ 1). [para(1119(a,1),673(a,2))]. given #1317 (H,wt=36): 1393 L(T(x / y,y / x),y / x,((y / x) * (x / y)) / (y / x)) = ((y / x) * (x / y)) * ((y / x) \ 1). [para(485(a,1),1146(a,1,1))]. given #1318 (H,wt=25): 1394 ((x / y) * (y / x)) * ((x / y) \ 1) = T(y / x,(x / y) * (y / x)). [para(1393(a,1),405(a,1))]. given #1319 (H,wt=17): 1395 ((x / y) * (y / x)) * ((x / y) \ 1) = y / x. [para(1394(a,2),1119(a,1))]. given #1320 (H,wt=21): 1396 ((x / (y * x)) * ((y * x) / x)) * ((x / (y * x)) \ 1) = y. [para(1395(a,2),15(a,1))]. given #1321 (H,wt=17): 1397 ((x / (y * x)) * y) * ((x / (y * x)) \ 1) = y. [para(15(a,1),1396(a,1,1,2))]. given #1322 (H,wt=17): 1398 ((x / (y * x)) * y) \ y = (x / (y * x)) \ 1. [hyper(66,a,1397,a)]. given #1323 (H,wt=25): 1399 (R(x \ 1,y,z) / (x * R(x \ 1,y,z))) \ 1 = ((x \ 1) * x) \ x. [para(672(a,1),1398(a,1,1,1)),flip(a)]. given #1324 (H,wt=25): 1400 (R(x \ 1,y,z) / (x * R(x \ 1,y,z))) \ 1 = K(x \ 1,x) \ x. [para(135(a,2),1399(a,2,1))]. given #1325 (H,wt=42): 1365 ((x * (y * T(y \ 1,z))) * ((z \ 1) \ 1)) / ((z \ 1) \ (y * T(y \ 1,z))) = R(x,y * T(y \ 1,z),(z \ 1) \ 1). [para(1364(a,1),28(a,2,2)),flip(a)]. given #1326 (H,wt=42): 1391 K(x,x \ 1) * ((R(y,z,u) * (z * u)) / (K(x,x \ 1) * (z * u))) = R(R(y,z,K(x,x \ 1)),z * K(x,x \ 1),u). [para(81(a,2),1390(a,1,2,1))]. given #1327 (H,wt=44): 1288 R(x,T(y,x),T(K(z \ 1,R(z,u,w)),y * x)) \ ((y * K(z \ 1,z)) * x) = T(y,x) * T(K(z \ 1,R(z,u,w)),y * x). [para(1257(a,1),353(a,1,2))]. given #1328 (H,wt=40): 1401 R(x,T(y,x),K(z \ 1,R(z,u,w))) \ ((y * K(z \ 1,z)) * x) = T(y,x) * T(K(z \ 1,R(z,u,w)),y * x). [para(1154(a,1),1288(a,1,1,3))]. given #1329 (H,wt=49): 1392 (1 * (x \ 1)) \ (((1 / x) \ (1 * (x \ 1))) * (R(y,x,1 / x) * K(x,x \ 1))) = L(T(y * x,1 / x),1 / x,(1 / x) \ (1 * (x \ 1))). [para(934(a,2),1253(a,1,2,2))]. given #1330 (H,wt=47): 1403 (x \ 1) \ (((1 / x) \ (1 * (x \ 1))) * (R(y,x,1 / x) * K(x,x \ 1))) = L(T(y * x,1 / x),1 / x,(1 / x) \ (1 * (x \ 1))). [para(11(a,1),1392(a,1,1))]. given #1331 (H,wt=45): 1404 (x \ 1) \ (((1 / x) \ (x \ 1)) * (R(y,x,1 / x) * K(x,x \ 1))) = L(T(y * x,1 / x),1 / x,(1 / x) \ (1 * (x \ 1))). [para(11(a,1),1403(a,1,2,1,2))]. given #1332 (H,wt=43): 1405 (x \ 1) \ (K(x \ 1,x) * (R(y,x,1 / x) * K(x,x \ 1))) = L(T(y * x,1 / x),1 / x,(1 / x) \ (1 * (x \ 1))). [para(888(a,1),1404(a,1,2,1))]. given #1333 (H,wt=31): 1406 L(T(x * y,1 / y),1 / y,(1 / y) \ (1 * (y \ 1))) = (y \ 1) \ R(x,y,1 / y). [para(1202(a,1),1405(a,1,2)),flip(a)]. given #1334 (H,wt=29): 1407 L(T(x * y,1 / y),1 / y,(1 / y) \ (y \ 1)) = (y \ 1) \ R(x,y,1 / y). [para(11(a,1),1406(a,1,3,2))]. given #1335 (H,wt=27): 1409 L(T(x * y,1 / y),1 / y,K(y \ 1,y)) = (y \ 1) \ R(x,y,1 / y). [para(888(a,1),1407(a,1,3))]. given #1336 (H,wt=18): 1410 (x \ 1) \ R(y,x,1 / x) = T(y * x,1 / x). [para(1409(a,1),88(a,1))]. given #1337 (H,wt=18): 1411 (x \ 1) * T(y * x,1 / x) = R(y,x,1 / x). [para(1410(a,1),14(a,1,2))]. given #1338 (H,wt=51): 1245 ((L(x,y,z) * (z * y)) / (z * y)) * T(((L(x,y,z) * (z * y)) / (z * y)) \ x,u) = ((L(x,y,z) * (z * y)) * a(z,y,T(x,z * y))) / (z * y). [para(1243(a,1),637(a,2,1,2))]. given #1339 (H,wt=39): 1412 ((L(x,y,z) * (z * y)) / (z * y)) * T(((L(x,y,z) * (z * y)) / (z * y)) \ x,u) = (x * (z * y)) / (z * y). [para(636(a,1),1245(a,2,1))]. given #1340 (H,wt=31): 1414 ((L(x,y,z) * (z * y)) / (z * y)) * T(((L(x,y,z) * (z * y)) / (z * y)) \ x,u) = x. [para(1412(a,2),15(a,1))]. given #1341 (H,wt=23): 1415 L(x,y,z) * T(((L(x,y,z) * (z * y)) / (z * y)) \ x,u) = x. [para(15(a,1),1414(a,1,1))]. given #1342 (H,wt=15): 1416 L(x,y,z) * T(L(x,y,z) \ x,u) = x. [para(15(a,1),1415(a,1,2,1,1))]. given #1343 (H,wt=13): 1419 x / L(x,y,z) = L(x,y,z) \ x. [para(1416(a,1),106(a,1,1))]. given #1344 (H,wt=15): 1421 (L(x,y,z) \ x) / x = 1 / L(x,y,z). [para(1419(a,1),801(a,1,1))]. given #1345 (H,wt=26): 1420 L(x \ (y \ z),x,y) \ (x \ (y \ z)) = (x \ (y \ z)) / ((y * x) \ z). [para(128(a,1),1419(a,1,2)),flip(a)]. given #1346 (H,wt=23): 1424 (x \ (y \ z)) / ((y * x) \ z) = ((y * x) \ z) \ (x \ (y \ z)). [para(128(a,1),1420(a,1,1)),flip(a)]. given #1347 (H,wt=28): 1422 (((x * y) \ z) \ (y \ (x \ z))) / (y \ (x \ z)) = 1 / L(y \ (x \ z),y,x). [para(128(a,1),1421(a,1,1,1))]. given #1348 (H,wt=25): 1426 (((x * y) \ z) \ (y \ (x \ z))) / (y \ (x \ z)) = 1 / ((x * y) \ z). [para(128(a,1),1422(a,2,2))]. given #1349 (H,wt=31): 1423 (1 / L(x,y,z)) \ ((L(x,y,z) \ 1) * (x * (L(x,y,z) \ 1))) = (L(x,y,z) \ 1) * x. [para(1421(a,1),678(a,1,1))]. given #1350 (H,wt=29): 1427 (1 / L(x,y,z)) \ ((L(x,y,z) \ 1) * (L(x,y,z) \ x)) = (L(x,y,z) \ 1) * x. [para(489(a,1),1423(a,1,2,2))]. given #1351 (H,wt=27): 1428 K(L(x,y,z) \ 1,L(x,y,z)) * (L(x,y,z) \ x) = (L(x,y,z) \ 1) * x. [para(1427(a,1),535(a,1)),flip(a)]. given #1352 (H,wt=20): 1429 K(L(x,y,z) \ 1,L(x,y,z)) = L(K(x \ 1,x),y,z). [hyper(18,a,1014,a,b,1428,a)]. given #1353 (H,wt=27): 1430 K(((x * y) \ x) \ 1,L(y \ 1,y,x)) = L(K((y \ 1) \ 1,y \ 1),y,x). [para(103(a,1),1429(a,1,1,1))]. given #1354 (H,wt=23): 1431 K(((x * y) \ x) \ 1,L(y \ 1,y,x)) = L(K(y,y \ 1),y,x). [para(897(a,1),1430(a,2,1))]. given #1355 (H,wt=26): 1432 L(K(x,x \ 1),x,y) * (y * x) = y * T(y \ (y * x),(y * x) \ y). [para(1431(a,1),1284(a,1,1))]. given #1356 (H,wt=23): 1433 x * T(x \ (x * y),(x * y) \ x) = x * (y * K(y,y \ 1)). [para(1432(a,1),1160(a,1))]. given #1357 (H,wt=21): 1434 x * T(x \ (x * y),(x * y) \ x) = x * T(y,y \ 1). [para(1183(a,1),1433(a,2,2))]. given #1358 (H,wt=17): 1435 x * T(y,(x * y) \ x) = x * T(y,y \ 1). [para(13(a,1),1434(a,1,2,1))]. given #1359 (H,wt=13): 1436 T(x,(y * x) \ y) = T(x,x \ 1). [hyper(154,a,1435,a),flip(a)]. given #1360 (H,wt=13): 1437 T(x,(y * x) \ y) = (x \ 1) \ 1. [hyper(17,a,780,a(flip),b,1435,a)]. given #1361 (H,wt=15): 1438 T(x \ y,y \ x) = ((x \ y) \ 1) \ 1. [para(14(a,1),1437(a,1,2,1))]. given #1362 (H,wt=19): 1440 K(x / y,y / x) * x = y * T(y \ x,x \ y). [para(1438(a,2),1308(a,2,2))]. given #1363 (H,wt=17): 1441 K((x \ y) \ 1,x \ y) = K(x / y,y / x). [hyper(18,a,1280,a,b,1440,a),flip(a)]. given #1364 (H,wt=21): 1442 K((x \ y) \ 1,x \ y) * (x / y) = T(x / y,y / x). [para(1441(a,2),900(a,1,1))]. given #1365 (H,wt=27): 1444 K(x \ 1,(y / x) \ y) * ((y / x) / y) = T((y / x) / y,y / (y / x)). [para(59(a,1),1442(a,1,1,1,1))]. given #1366 (H,wt=23): 1445 T((x / y) / x,x / (x / y)) = K(y \ 1,y) * ((x / y) / x). [para(59(a,1),1444(a,1,1,2)),flip(a)]. given #1367 (H,wt=17): 1446 K((x / y) / x,x / (x / y)) = K(y \ 1,y). [hyper(902,a,1445,a)]. given #1368 (H,wt=17): 1447 (x / y) * (1 / (1 / y)) = K(y \ 1,y) * x. [para(1446(a,1),1270(a,1,1)),flip(a)]. given #1369 (H,wt=17): 1448 (x * (1 / (1 / y))) / y = x * K(y \ 1,y). [hyper(18,a,1169,a,b,1447,a)]. given #1370 (H,wt=17): 1449 K(x \ 1,x) * (y * x) = y * (1 / (1 / x)). [para(15(a,1),1447(a,1,1)),flip(a)]. given #1371 (H,wt=17): 1450 (x / y) * (1 / (1 / y)) = x * K(y \ 1,y). [para(1447(a,2),1133(a,1))]. given #1372 (H,wt=10): 1455 R(x,y,K(y \ 1,y)) = x. [hyper(1375,a,1450,a)]. given #1373 (H,wt=12): 1456 R(x,1 / y,K(y \ 1,y)) = x. [para(1455(a,1),1388(a,1))]. given #1374 (H,wt=17): 1452 (x / (1 / (1 / y))) * K(y \ 1,y) = x / y. [para(16(a,1),1448(a,1,1)),flip(a)]. given #1375 (H,wt=17): 1454 (1 / (1 / x)) * T(y,x) = y * (1 / (1 / x)). [para(1449(a,1),959(a,1)),flip(a)]. given #1376 (H,wt=11): 1458 T(x,1 / (1 / y)) = T(x,y). [hyper(165,a,1454,a),flip(a)]. given #1377 (H,wt=11): 1459 T(x,1 / y) = T(x,y \ 1). [para(57(a,1),1458(a,1,2,2))]. given #1378 (H,wt=11): 1460 T(x,(y \ 1) \ 1) = T(x,y). [para(57(a,1),1459(a,1,2)),flip(a)]. given #1379 (H,wt=11): 1464 T(x,T(y,y \ 1)) = T(x,y). [para(86(a,2),1460(a,1,2))]. given #1380 (H,wt=17): 1457 K(x \ 1,x) * (y / (x \ 1)) = y / (1 / x). [para(1456(a,1),1258(a,1)),flip(a)]. given #1381 (H,wt=17): 1465 T(x,x \ 1) * T(y,x) = y * T(x,x \ 1). [para(1464(a,1),85(a,1,2))]. given #1382 (H,wt=17): 1467 ((x \ 1) \ 1) * T(y,x) = y * T(x,x \ 1). [para(1464(a,1),443(a,1,2))]. given #1383 (H,wt=17): 1469 (x / (y \ 1)) * K(y \ 1,y) = x / (1 / y). [para(1457(a,1),1133(a,1)),flip(a)]. given #1384 (H,wt=17): 1470 K(x,x \ 1) * (y * x) = y * T(x,x \ 1). [para(1465(a,1),954(a,2))]. given #1385 (H,wt=17): 1473 K(x \ 1,x) * (y * T(x,x \ 1)) = y * x. [hyper(1235,a,1470,a)]. given #1386 (H,wt=17): 1474 (x * y) * K(y,y \ 1) = x * T(y,y \ 1). [para(1470(a,1),1141(a,1)),flip(a)]. given #1387 (H,wt=17): 1476 (x * y) * K(y,y \ 1) = x * ((y \ 1) \ 1). [para(86(a,1),1474(a,2,2))]. given #1388 (H,wt=10): 1477 R(x,y,K(y,y \ 1)) = x. [hyper(1189,a,1476,a)]. given #1389 (H,wt=17): 1479 (x / y) * K(y \ 1,y) = x / T(y,y \ 1). [para(1477(a,1),1317(a,1))]. given #1390 (H,wt=17): 1480 x \ (x / T(y,y \ 1)) = T(x \ (x / y),y). [para(1479(a,1),378(a,1,2))]. given #1391 (H,wt=18): 1461 T(((1 / x) * y) * x,x \ 1) = R(y,1 / x,x). [para(1459(a,1),351(a,1))]. given #1392 (H,wt=13): 1482 R(x,1 / y,y) = R(x,y \ 1,y). [para(1461(a,1),1379(a,1))]. given #1393 (H,wt=14): 1483 (x * (1 / y)) * y = R(x,y \ 1,y). [para(1482(a,1),121(a,2))]. given #1394 (H,wt=14): 1484 R(x / (1 / y),y \ 1,y) = x * y. [para(1482(a,1),225(a,1))]. given #1395 (H,wt=14): 1485 R(x,y \ 1,y) / y = x * (1 / y). [para(1482(a,1),246(a,1,1))]. given #1396 (H,wt=18): 1463 (x \ 1) * T(y * x,x \ 1) = R(y,x,1 / x). [para(1459(a,1),1411(a,1,2))]. given #1397 (H,wt=14): 1487 (x * y) * (y \ 1) = R(x,y,1 / y). [para(1463(a,1),85(a,1)),flip(a)]. given #1398 (H,wt=14): 1488 R(x / y,y,1 / y) = x * (y \ 1). [para(16(a,1),1487(a,1,1)),flip(a)]. given #1399 (H,wt=19): 1468 (1 / x) * (y / (1 / x)) = (x \ 1) * (y / (x \ 1)). [para(1457(a,1),539(a,1,2))]. given #1400 (H,wt=19): 1472 (x / (1 / y)) \ K(y \ 1,y) = (x / (y \ 1)) \ 1. [para(1469(a,1),1263(a,1,1))]. given #1401 (H,wt=19): 1475 (((x \ 1) \ 1) \ y) * T(x,x \ 1) = (x \ y) * x. [hyper(733,a,1473,a),flip(a)]. given #1402 (H,wt=21): 1453 K(x \ 1,x) * ((y * x) / z) = (y * (1 / (1 / x))) / z. [para(1449(a,1),281(a,1,1)),flip(a)]. given #1403 (H,wt=21): 1490 ((x * y) / z) / ((x * (1 / (1 / y))) / z) = K(y,y \ 1). [para(1453(a,1),457(a,1,2))]. given #1404 (H,wt=22): 1486 R((x \ (y / (1 / z))) * x,z \ 1,z) = (x \ (y * z)) * x. [para(1484(a,1),776(a,2,1,2))]. given #1405 (H,wt=23): 1491 x / ((y * (1 / (1 / T(x,y)))) / y) = K(T(x,y),T(x,y) \ 1). [para(106(a,1),1490(a,1,1))]. given #1406 (H,wt=21): 1493 x / (((1 / (1 / x)) * y) / y) = K(T(x,y),T(x,y) \ 1). [para(1225(a,1),1491(a,1,2,1))]. given #1407 (H,wt=17): 1494 K(T(x,y),T(x,y) \ 1) = x / (1 / (1 / x)). [para(15(a,1),1493(a,1,2)),flip(a)]. given #1408 (H,wt=15): 1496 K(T(x,y),T(x,y) \ 1) = K(x,x \ 1). [para(1494(a,2),939(a,1))]. given #1409 (H,wt=17): 1498 K(x,x \ 1) * T(1 / (1 / x),y) = T(x,y). [para(1496(a,1),1226(a,1,1))]. given #1410 (H,wt=11): 1499 T(x,y) / x = x \ T(x,y). [para(1498(a,1),1002(a,1,2)),flip(a)]. given #1411 (H,wt=11): 1501 (x \ T(x,y)) * x = T(x,y). [para(1499(a,1),16(a,1,1))]. given #1412 (H,wt=9): 1508 T(x,x \ T(x,y)) = x. [hyper(143,a,1501,a)]. given #1413 (H,wt=12): 1502 K(x,y) = L(T(x,y) / x,x,y). [para(1499(a,2),311(a,2,1))]. given #1414 (H,wt=12): 1512 L(K(x,y),x,1 / x) = K(x,y). [para(1502(a,2),599(a,2))]. given #1415 (H,wt=13): 1503 (1 / x) * T(x,y) = x \ T(x,y). [para(1499(a,1),594(a,2))]. given #1416 (H,wt=13): 1513 K(x,y) / (x * K(x,y)) = 1 / x. [para(1512(a,1),239(a,1,1))]. given #1417 (H,wt=14): 1509 T(x,y) != z * x | x \ T(x,y) = z. [para(1501(a,1),20(a,1))]. given #1418 (H,wt=16): 1515 R(x,x \ 1,K(x \ 1,y)) = 1 / (x \ 1). [para(1513(a,1),101(a,2))]. given #1419 (H,wt=12): 1516 R(x,x \ 1,K(x \ 1,y)) = x. [para(1515(a,2),57(a,1))]. given #1420 (H,wt=17): 1504 (x \ 1) \ T(x \ 1,y) = x * T(x \ 1,y). [para(1499(a,1),598(a,1))]. given #1421 (H,wt=17): 1517 (x \ 1) * K(x \ 1,y) = x \ K(x \ 1,y). [para(1516(a,1),168(a,1,1)),flip(a)]. given #1422 (H,wt=17): 1519 (x \ 1) * (x * T(x \ 1,y)) = T(x \ 1,y). [para(1504(a,1),14(a,1,2))]. given #1423 (H,wt=18): 1505 L(x \ 1,x,x \ T(x,y)) = T(1 / x,T(x,y)). [para(1499(a,1),619(a,1,3))]. given #1424 (H,wt=11): 1522 T(1 / x,T(x,y)) = x \ 1. [para(1505(a,1),433(a,1))]. given #1425 (H,wt=13): 1523 T(x \ 1,T(x,y)) = T(x \ 1,x). [para(1522(a,1),117(a,1,1)),flip(a)]. given #1426 (H,wt=17): 1525 T((1 / x) \ 1,1 / x) = T(x,T(1 / x,y)). [para(59(a,1),1523(a,1,1)),flip(a)]. given #1427 (H,wt=13): 1527 T(x,T(1 / x,y)) = T(x,1 / x). [para(59(a,1),1525(a,1,1)),flip(a)]. given #1428 (H,wt=13): 1528 T(x,T(1 / x,y)) = T(x,x \ 1). [para(1527(a,2),1191(a,1))]. given #1429 (H,wt=14): 1529 R(x,T(1 / x,y),x) = T(x,x \ 1). [para(1528(a,1),740(a,2))]. given #1430 (H,wt=19): 1526 T((x / y) \ 1,x / y) = T((x / y) \ 1,y \ x). [para(87(a,1),1523(a,1,2)),flip(a)]. given #1431 (H,wt=19): 1532 K(x,T((y / z) \ 1,z \ y)) = K(x,(y / z) \ 1). [para(1526(a,1),920(a,1,2))]. given #1432 (H,wt=20): 1521 T(x \ 1,y) != (x \ 1) * z | x * T(x \ 1,y) = z. [para(1519(a,1),19(a,1))]. given #1433 (H,wt=21): 1497 K(x,x \ 1) * (T(x,y) \ z) = (1 / (1 / T(x,y))) \ z. [para(1496(a,1),965(a,1,1))]. given #1434 (H,wt=21): 1534 K(x,x \ 1) * (T(x,y) \ z) = T(1 / (1 / x),y) \ z. [para(1222(a,1),1497(a,2,1))]. given #1435 (H,wt=22): 1510 T(x,y) * L(z,x,x \ T(x,y)) = (x \ T(x,y)) * (x * z). [para(1501(a,1),76(a,1,1))]. given #1436 (H,wt=22): 1533 R((x / y) \ 1,x / y,y) \ 1 = T((y / x) \ 1,x \ y). [para(1526(a,1),1304(a,2))]. given #1437 (H,wt=21): 1537 T((1 * x) / y,y / x) \ 1 = T((x / y) \ 1,y \ x). [para(349(a,1),1533(a,1,1))]. given #1438 (H,wt=19): 1538 T(x / y,y / x) \ 1 = T((x / y) \ 1,y \ x). [para(11(a,1),1537(a,1,1,1,1))]. given #1439 (H,wt=23): 1492 ((x \ (y / (1 / z))) * x) * (1 / z) = ((x \ (y * z)) * x) / z. [para(1486(a,1),1485(a,1,1)),flip(a)]. given #1440 (H,wt=21): 1539 x * (T((x \ y) * z,x) / z) = ((x \ (y * z)) * x) / z. [para(1492(a,1),771(a,1)),flip(a)]. given #1441 (H,wt=23): 1511 T(K(x \ (x / (y \ (y / z))),x),z) = y \ ((y / z) * T(z,x)). [para(1501(a,1),659(a,2,2,2))]. given #1442 (H,wt=23): 1514 (L(x,1 / x,y) * y) / L(x,1 / x,y) = y * (x \ T(x,y)). [para(1503(a,1),816(a,2,2))]. given #1443 (H,wt=23): 1520 K(x,y) = (L(x \ 1,x,y) \ 1) \ T(L(x \ 1,x,y) \ 1,y). [para(1504(a,2),668(a,2))]. given #1444 (H,wt=23): 1540 K(x \ (x / T(y \ (y / z),z)),x) = y \ ((y / z) * T(z,x)). [para(1511(a,1),752(a,2))]. given #1445 (H,wt=24): 1535 L(1 / T((x \ 1) \ 1,y),x,x \ 1) = T(1 / (1 / x),y) \ 1. [para(1534(a,1),1353(a,2))]. given #1446 (H,wt=20): 1541 L(1 / T((x \ 1) \ 1,y),x,x \ 1) = 1 / T(x,y). [para(1535(a,2),1224(a,1))]. given #1447 (H,wt=16): 1542 L(T(x,y) \ 1,x,x \ 1) = 1 / T(x,y). [para(1229(a,1),1541(a,1,1))]. given #1448 (H,wt=15): 1543 (1 / x) * (T(x,y) \ x) = 1 / T(x,y). [para(1542(a,1),549(a,1)),flip(a)]. given #1449 (H,wt=17): 1544 (x \ 1) * (T(x,y) \ x) = T(1 / T(x,y),x). [para(1543(a,1),1281(a,1,1)),flip(a)]. given #1450 (H,wt=15): 1545 (x \ 1) * (T(x,y) \ x) = T(x,y) \ 1. [para(1544(a,2),1069(a,1))]. given #1451 (H,wt=25): 1507 T((T(x,y) \ x) * (x \ T(x,y)),z) = (T(x,y) \ x) * (T(x,y) / x). [para(1499(a,1),1367(a,1,1,2))]. given #1452 (H,wt=25): 1546 T((T(x,y) \ x) * (x \ T(x,y)),z) = (T(x,y) \ x) * (x \ T(x,y)). [para(1499(a,1),1507(a,2,2))]. given #1453 (H,wt=13): 1547 (T(x,y) \ x) * (x \ T(x,y)) = 1. [para(1546(a,1),1078(a,1))]. given #1454 (H,wt=19): 1549 (T(x \ 1,y) \ (x \ 1)) * (x * T(x \ 1,y)) = 1. [para(1504(a,1),1547(a,1,2))]. given #1455 (H,wt=26): 1518 L(x,y,z) \ ((x \ 1) * L(x,y,z)) = (x \ 1) * K(x \ 1,L(x,y,z)). [para(1516(a,1),319(a,1,1,1))]. given #1456 (H,wt=21): 1551 (x \ 1) * K(x \ 1,L(x,y,z)) = T(x \ 1,L(x,y,z)). [para(1518(a,1),30(a,2)),flip(a)]. given #1457 (H,wt=19): 1552 x * T(x \ 1,L(x,y,z)) = K(x \ 1,L(x,y,z)). [hyper(17,a,1519,a,b,1551,a),flip(a)]. given #1458 (H,wt=23): 1553 L(K(x \ 1,L(x,y,z)),y,z) = K(L(x,y,z) \ 1,L(x,y,z)). [para(1552(a,1),1012(a,1,1))]. given #1459 (H,wt=20): 1554 L(K(x \ 1,L(x,y,z)),y,z) = L(K(x \ 1,x),y,z). [para(1553(a,2),1429(a,1))]. given #1460 (H,wt=27): 1530 L(T(x,x \ 1),y,z) \ L(x,y,z) = (L(x,y,z) \ (L(x,y,z) / x)) * x. [para(1529(a,1),910(a,1,1,1))]. given #1461 (H,wt=24): 1556 L(T(x,x \ 1),y,z) \ L(x,y,z) = T(1 / x,L(x,y,z)) * x. [para(796(a,1),1530(a,2,1))]. given #1462 (H,wt=24): 1558 L(T(x,x \ 1),y,z) \ L(x,y,z) = x * T(x \ 1,L(x,y,z)). [para(1556(a,2),171(a,1))]. given #1463 (H,wt=22): 1559 L(T(x,x \ 1),y,z) \ L(x,y,z) = K(x \ 1,L(x,y,z)). [para(1558(a,2),1552(a,1))]. given #1464 (H,wt=28): 1462 L(T(x,y \ 1) \ z,T(x,1 / y),y \ 1) = (x * (1 / y)) \ ((1 / y) * z). [para(1459(a,1),852(a,1,1,1))]. given #1465 (H,wt=28): 1536 T(x * L(x \ 1,x,x \ T(x,y)),y) = (x \ T(x,y)) * (x * (T(x,y) \ 1)). [para(1510(a,1),825(a,1)),flip(a)]. given #1466 (H,wt=26): 1561 T(x * L(x \ 1,x,x \ T(x,y)),y) = (x \ T(x,y)) * (T(x,y) \ x). [para(505(a,1),1536(a,2,2))]. given #1467 (H,wt=19): 1562 (x \ T(x,y)) * (T(x,y) \ x) = T(x * (x \ 1),y). [para(433(a,1),1561(a,1,1,2)),flip(a)]. given #1468 (H,wt=15): 1563 (x \ T(x,y)) * (T(x,y) \ x) = T(1,y). [para(14(a,1),1562(a,2,1))]. given #1469 (H,wt=13): 1566 (x \ T(x,y)) * (T(x,y) \ x) = 1. [para(1563(a,2),1126(a,1))]. given #1470 (H,wt=13): 1567 (x \ T(x,y)) \ 1 = T(x,y) \ x. [hyper(66,a,1566,a)]. given #1471 (H,wt=25): 1569 T(L(x \ 1,x,y) \ 1,y) \ (L(x \ 1,x,y) \ 1) = K(x,y) \ 1. [para(1520(a,2),1567(a,1,1)),flip(a)]. given #1472 (H,wt=28): 1560 L(T(x,y \ 1) \ z,T(x,y \ 1),y \ 1) = (x * (1 / y)) \ ((1 / y) * z). [para(1459(a,1),1462(a,1,2))]. given #1473 (H,wt=23): 1570 (x * (1 / y)) \ ((1 / y) * z) = (x * (y \ 1)) \ ((y \ 1) * z). [para(1560(a,1),207(a,1))]. given #1474 (H,wt=17): 1571 (x * (y \ 1)) \ ((y \ 1) * x) = K(1 / y,x). [para(1570(a,1),24(a,2)),flip(a)]. given #1475 (H,wt=11): 1572 K(1 / x,y) = K(x \ 1,y). [para(1571(a,1),24(a,2)),flip(a)]. given #1476 (H,wt=11): 1573 K((x \ 1) \ 1,y) = K(x,y). [para(57(a,1),1572(a,1,1)),flip(a)]. given #1477 (H,wt=31): 1481 (x / ((y \ 1) \ 1)) * T((y \ 1) \ 1,z) = x * K(z \ (z / T(x \ (x / y),y)),z). [para(1480(a,1),621(a,2,2,1,2,2))]. given #1478 (H,wt=27): 1574 (x / ((y \ 1) \ 1)) * T((y \ 1) \ 1,z) = x * (x \ ((x / y) * T(y,z))). [para(1540(a,1),1481(a,2,2))]. given #1479 (H,wt=23): 1575 (x / ((y \ 1) \ 1)) * T((y \ 1) \ 1,z) = (x / y) * T(y,z). [para(1574(a,2),14(a,1))]. given #1480 (H,wt=21): 1576 (((x \ 1) \ 1) * y) / ((x \ 1) \ 1) = (y / x) * T(x,y). [para(1575(a,1),601(a,1)),flip(a)]. given #1481 (H,wt=19): 1577 (((x \ 1) \ 1) * y) / ((x \ 1) \ 1) = (x * y) / x. [para(1576(a,2),601(a,1))]. given #1482 (H,wt=31): 1489 L(L(x,y * (1 / x),K(x \ 1,x)),1 / x,y) = (y * (x \ 1)) \ (K(x \ 1,x) * y). [para(1488(a,1),1384(a,2,1))]. given #1483 (H,wt=24): 1578 L(L(x,y * (1 / x),K(x \ 1,x)),1 / x,y) = L(x,x \ 1,y). [para(1489(a,2),1173(a,1))]. given #1484 (H,wt=13): 1579 L(x,1 / x,y) = L(x,x \ 1,y). [para(88(a,1),1578(a,1,1))]. given #1485 (H,wt=23): 1580 (L(x,x \ 1,y) * y) / L(x,1 / x,y) = y * (x \ T(x,y)). [para(1579(a,1),1514(a,1,1,1))]. given #1486 (H,wt=23): 1581 (L(x,x \ 1,y) * y) / L(x,x \ 1,y) = y * (x \ T(x,y)). [para(1579(a,1),1580(a,1,2))]. given #1487 (H,wt=32): 1555 x \ (y \ ((L(K(z \ 1,z),x,y) * y) * x)) = R(T(K(z \ 1,L(z,x,y)),y * x),y,x). [para(1554(a,1),427(a,1,2,2,1,1))]. given #1488 (H,wt=32): 1582 x \ (y \ (L(K(z \ 1,z),x,y) * (y * x))) = R(T(K(z \ 1,L(z,x,y)),y * x),y,x). [para(386(a,1),1555(a,1,2,2))]. given #1489 (H,wt=29): 1583 R(T(K(x \ 1,L(x,y,z)),z * y),z,y) = y \ (z \ (z * (y * K(x \ 1,x)))). [para(1157(a,1),1582(a,1,2,2)),flip(a)]. given #1490 (H,wt=25): 1584 R(T(K(x \ 1,L(x,y,z)),z * y),z,y) = y \ (y * K(x \ 1,x)). [para(13(a,1),1583(a,2,2))]. given #1491 (H,wt=21): 1585 R(T(K(x \ 1,L(x,y,z)),z * y),z,y) = K(x \ 1,x). [para(1584(a,2),13(a,1))]. given #1492 (H,wt=33): 1478 ((x * y) * ((z \ 1) \ 1)) / ((y * z) * K(z,z \ 1)) = R(R(x,y,z),y * z,K(z,z \ 1)). [para(1476(a,1),213(a,1,1))]. given #1493 (H,wt=31): 1587 R(R(x,y,z),y * z,K(z,z \ 1)) = ((x * y) * ((z \ 1) \ 1)) / (y * ((z \ 1) \ 1)). [para(1476(a,1),1478(a,1,2)),flip(a)]. given #1494 (H,wt=22): 1588 R(R(x,y,z),y * z,K(z,z \ 1)) = R(x,y,(z \ 1) \ 1). [para(1587(a,2),28(a,2)),flip(a)]. given #1495 (H,wt=35): 1443 (R((x \ y) \ 1,z,u) / ((x \ y) * R((x \ y) \ 1,z,u))) \ 1 = K(x / y,y / x) \ (x \ y). [para(1441(a,1),1400(a,2,1))]. given #1496 (H,wt=35): 1589 (R((x \ y) \ 1,z,u) / ((x \ y) * R((x \ y) \ 1,z,u))) \ 1 = K(y / x,x / y) * (x \ y). [para(1443(a,2),1333(a,1))]. given #1497 (H,wt=35): 1590 (R((x \ y) \ 1,z,u) / ((x \ y) * R((x \ y) \ 1,z,u))) \ 1 = (x \ y) * K(y / x,x / y). [para(1589(a,2),1147(a,1))]. given #1498 (H,wt=19): 1591 (x \ y) * K(y / x,x / y) = ((x \ y) \ 1) \ 1. [para(672(a,1),1590(a,1,1)),flip(a)]. given #1499 (H,wt=17): 1592 K(x \ y,(x \ y) \ 1) = K(y / x,x / y). [hyper(17,a,1185,a,b,1591,a),flip(a)]. given #1500 (H,wt=17): 1593 (x \ y) * (1 / (x \ y)) = K(y / x,x / y). [para(1592(a,1),930(a,1)),flip(a)]. given #1501 (H,wt=19): 1595 K(x / y,(x / y) \ 1) = (y \ x) * (1 / (y \ x)). [para(1593(a,2),1330(a,2))]. given #1502 (H,wt=17): 1596 ((x \ y) \ (y / x)) / (y / x) = 1 / (x \ y). [hyper(1361,a,1595,a)]. given #1503 (H,wt=17): 1597 (1 / (x \ y)) * (y / x) = (x \ y) \ (y / x). [para(1596(a,1),16(a,1,1))]. given #1504 (H,wt=21): 1598 ((x / y) \ x) \ (x / (x / y)) = (1 / y) * (x / (x / y)). [para(59(a,1),1597(a,1,1,2)),flip(a)]. given #1505 (H,wt=17): 1599 (1 / x) * (y / (y / x)) = x \ (y / (y / x)). [para(59(a,1),1598(a,1,1)),flip(a)]. given #1506 (H,wt=22): 1594 x \ (K(x / y,y / x) * y) = L(1 / (y \ x),y \ x,y). [para(1592(a,1),1310(a,1,2,1))]. given #1507 (H,wt=18): 1601 L(1 / (x \ y),x \ y,x) = 1 / (1 / (y \ x)). [para(1594(a,1),1269(a,1))]. given #1508 (H,wt=19): 1602 ((x \ y) * (y \ x)) / (x \ y) = 1 / (1 / (y \ x)). [para(1601(a,1),330(a,2))]. given #1509 (H,wt=19): 1603 (1 / (1 / (x \ y))) * (y \ x) = (y \ x) * (x \ y). [para(1602(a,1),16(a,1,1))]. given #1510 (H,wt=23): 1600 (x / (x / y)) \ (y \ (x / (x / y))) = T(1 / y,x / (x / y)). [para(1599(a,1),30(a,2,2)),flip(a)]. given #1511 (H,wt=13): 1605 T(1 / x,y / (y / x)) = x \ 1. [para(1600(a,1),571(a,1))]. given #1512 (H,wt=25): 1604 ((x \ y) * (y \ x)) \ ((y \ x) * (x \ y)) = K((x \ y) \ 1,x \ y). [para(1603(a,1),1217(a,1,2))]. given #1513 (H,wt=17): 1607 K((x \ y) \ 1,x \ y) = K(y \ x,x \ y). [para(1604(a,1),24(a,2)),flip(a)]. given #1514 (H,wt=19): 1608 x \ (y * K(x \ y,y \ x)) = T(x \ y,y \ x). [para(1607(a,1),523(a,1,2,2))]. given #1515 (H,wt=19): 1609 x \ (y * K(x \ y,y \ x)) = ((x \ y) \ 1) \ 1. [para(1608(a,2),1438(a,1))]. given #1516 (H,wt=41): 1425 x \ ((y * z) * K((z \ (y \ x)) \ (((y * z) \ x) \ (z \ (y \ x))),z \ (y \ x))) = T(x \ (y * z),z \ (y \ x)). [para(1424(a,1),520(a,1,2,2,1,2))]. given #1517 (H,wt=31): 1610 x \ ((y * z) * K(((y * z) \ x) \ 1,z \ (y \ x))) = T(x \ (y * z),z \ (y \ x)). [para(783(a,1),1425(a,1,2,2,1))]. given #1518 (H,wt=41): 1550 (T(x,((y * x) / y) \ 1) \ ((((y * x) / y) \ 1) \ 1)) * ((((y * x) / y) \ 1) * T((((y * x) / y) \ 1) \ 1,y)) = 1. [para(179(a,1),1549(a,1,1,1))]. given #1519 (H,wt=29): 1611 (x \ ((y * x) / y)) * ((((y * x) / y) \ 1) * T((((y * x) / y) \ 1) \ 1,y)) = 1. [para(1356(a,1),1550(a,1,1))]. given #1520 (H,wt=27): 1612 (x \ ((y * x) / y)) * ((((y * x) / y) \ 1) * (((y \ (y * x)) \ 1) \ 1)) = 1. [para(1232(a,1),1611(a,1,2,2))]. given #1521 (H,wt=23): 1614 (x \ ((y * x) / y)) * ((((y * x) / y) \ 1) * ((x \ 1) \ 1)) = 1. [para(13(a,1),1612(a,1,2,2,1,1))]. given #1522 (H,wt=17): 1615 (x \ ((y * x) / y)) * (((y * x) / y) \ x) = 1. [para(1267(a,1),1614(a,1,2))]. given #1523 (H,wt=17): 1616 (x \ ((y * x) / y)) \ 1 = ((y * x) / y) \ x. [hyper(66,a,1615,a)]. given #1524 (H,wt=29): 1617 ((L(x,x \ 1,y) * y) / L(x,x \ 1,y)) \ y = (y \ (y * (x \ T(x,y)))) \ 1. [para(1581(a,1),1616(a,1,1,2)),flip(a)]. given #1525 (H,wt=25): 1618 ((L(x,x \ 1,y) * y) / L(x,x \ 1,y)) \ y = (x \ T(x,y)) \ 1. [para(13(a,1),1617(a,2,1))]. given #1526 (H,wt=23): 1620 ((L(x,x \ 1,y) * y) / L(x,x \ 1,y)) \ y = T(x,y) \ x. [para(1618(a,2),1567(a,1))]. given #1527 (H,wt=15): 1621 (x * (y \ T(y,x))) \ x = T(y,x) \ y. [para(1581(a,1),1620(a,1,1))]. given #1528 (H,wt=27): 1622 T(L(x \ 1,x,y) \ 1,y) \ (L(x \ 1,x,y) \ 1) = (y * K(x,y)) \ y. [para(1520(a,2),1621(a,1,1,2)),flip(a)]. given #1529 (H,wt=13): 1623 (x * K(y,x)) \ x = K(y,x) \ 1. [para(1622(a,1),1569(a,1))]. given #1530 (H,wt=42): 1471 (x * y) * ((((z \ 1) \ 1) \ L(y \ ((z \ 1) \ 1),y,x)) * T(z,z \ 1)) = (x * (y * T(y \ 1,z))) * ((z \ 1) \ 1). [para(1467(a,1),817(a,1,2))]. given #1531 (H,wt=34): 1624 (x * y) * ((z \ L(y \ ((z \ 1) \ 1),y,x)) * z) = (x * (y * T(y \ 1,z))) * ((z \ 1) \ 1). [para(1475(a,1),1471(a,1,2))]. given #1532 (H,wt=44): 1506 T(x \ T(x,L(x \ 1,y,z)),L(x \ 1,y,z) * x) = K(L(x \ 1,y,z) \ ((1 / x) \ L(x \ 1,y,z)),L(x \ 1,y,z)). [para(1499(a,1),1085(a,1,1))]. given #1533 (H,wt=35): 1625 K(L(x \ 1,y,z) \ ((1 / x) \ L(x \ 1,y,z)),L(x \ 1,y,z)) = x \ T(x,L(x \ 1,y,z)). [para(1506(a,1),1324(a,1))]. given #1534 (H,wt=33): 1626 K(L(x \ 1,y,z) \ (L(x \ 1,y,z) * x),L(x \ 1,y,z)) = x \ T(x,L(x \ 1,y,z)). [para(904(a,1),1625(a,1,1,2))]. given #1535 (H,wt=19): 1628 x \ T(x,L(x \ 1,y,z)) = K(x,L(x \ 1,y,z)). [para(13(a,1),1626(a,1,1)),flip(a)]. given #1536 (H,wt=12): 1629 T(x,K(y,L(y \ 1,z,u))) = x. [para(1628(a,1),1323(a,1,2))]. given #1537 (H,wt=12): 1630 T(x,K(1 / y,L(y,z,u))) = x. [para(59(a,1),1629(a,1,2,2,1))]. given #1538 (H,wt=12): 1631 T(x,K(y \ 1,L(y,z,u))) = x. [para(1572(a,1),1630(a,1,2))]. given #1539 (H,wt=19): 1632 T(K(x \ 1,L(x,y,z)),u) = K(x \ 1,L(x,y,z)). [hyper(33,a,1631,a)]. given #1540 (H,wt=17): 1633 R(K(x \ 1,L(x,y,z)),z,y) = K(x \ 1,x). [para(1632(a,1),1585(a,1,1))]. given #1541 (H,wt=14): 1634 K(x \ 1,L(x,y,z)) = K(x \ 1,x). [para(1633(a,1),272(a,1)),flip(a)]. given #1542 (H,wt=62): 1080 ((x * ((y * ((1 / (1 / z)) * (z \ 1))) \ y)) * u) / (L(L(K(z,z \ 1),z \ 1,1 / (1 / z)),(1 / (1 / z)) * (z \ 1),y) * u) = R(x,(y * ((1 / (1 / z)) * (z \ 1))) \ y,u). [para(1068(a,2),474(a,1,2,1,1))]. given #1543 (H,wt=58): 1638 ((x * ((y * K(z \ 1,z)) \ y)) * u) / (L(L(K(z,z \ 1),z \ 1,1 / (1 / z)),(1 / (1 / z)) * (z \ 1),y) * u) = R(x,(y * ((1 / (1 / z)) * (z \ 1))) \ y,u). [para(957(a,1),1080(a,1,1,1,2,1,2))]. given #1544 (H,wt=54): 1639 R(x,(y * ((1 / (1 / z)) * (z \ 1))) \ y,u) = ((x * K(z,z \ 1)) * u) / (L(L(K(z,z \ 1),z \ 1,1 / (1 / z)),(1 / (1 / z)) * (z \ 1),y) * u). [para(1211(a,1),1638(a,1,1,1,2)),flip(a)]. given #1545 (H,wt=54): 1641 R(x,(y * ((1 / (1 / z)) * (z \ 1))) \ y,u) = (K(z,z \ 1) * (x * u)) / (L(L(K(z,z \ 1),z \ 1,1 / (1 / z)),(1 / (1 / z)) * (z \ 1),y) * u). [para(1199(a,1),1639(a,2,1))]. given #1546 (H,wt=45): 1642 R(x,(y * ((1 / (1 / z)) * (z \ 1))) \ y,u) = (K(z,z \ 1) * (x * u)) / (L(K(z,z \ 1),(1 / (1 / z)) * (z \ 1),y) * u). [para(1274(a,1),1641(a,2,2,1,1))]. given #1547 (H,wt=41): 1643 R(x,(y * ((1 / (1 / z)) * (z \ 1))) \ y,u) = (K(z,z \ 1) * (x * u)) / (L(K(z,z \ 1),K(z \ 1,z),y) * u). [para(957(a,1),1642(a,2,2,1,2))]. given #1548 (H,wt=34): 1645 R(x,(y * ((1 / (1 / z)) * (z \ 1))) \ y,u) = (K(z,z \ 1) * (x * u)) / (K(z,z \ 1) * u). [para(1216(a,1),1643(a,2,2,1))]. given #1549 (H,wt=34): 1646 R(x,(y * ((1 / (1 / z)) * (z \ 1))) \ y,u) = K(z,z \ 1) * ((x * u) / (K(z,z \ 1) * u)). [para(1645(a,2),281(a,1))]. given #1550 (H,wt=30): 1648 R(x,(y * K(z \ 1,z)) \ y,u) = K(z,z \ 1) * ((x * u) / (K(z,z \ 1) * u)). [para(957(a,1),1646(a,1,2,1,2))]. given #1551 (H,wt=26): 1649 K(x,x \ 1) * ((y * z) / (K(x,x \ 1) * z)) = R(y,K(x,x \ 1),z). [para(1211(a,1),1648(a,1,2)),flip(a)]. given #1552 (H,wt=31): 1650 R(R(x,y,K(z,z \ 1)),y * K(z,z \ 1),u) = R(R(x,y,u),K(z,z \ 1),y * u). [para(1649(a,1),1391(a,1)),flip(a)]. given #1553 (H,wt=37): 1651 R(R(x,1 / y,K(z,z \ 1)),K(z,z \ 1) / y,u) = R(R(x,1 / y,u),K(z,z \ 1),(1 / y) * u). [para(1198(a,1),1650(a,1,2))]. given #1554 (H,wt=45): 1652 R(R(x,1 / y,K(z \ 1,z)),K(z \ 1,(z \ 1) \ 1) / y,u) = R(R(x,1 / y,u),K(z \ 1,(z \ 1) \ 1),(1 / y) * u). [para(929(a,1),1651(a,1,1,3))]. given #1555 (H,wt=36): 1653 R(R(x,1 / y,z),K(y \ 1,(y \ 1) \ 1),(1 / y) * z) = R(x,K(y \ 1,(y \ 1) \ 1) / y,z). [para(1456(a,1),1652(a,1,1)),flip(a)]. given #1556 (H,wt=32): 1654 R(R(x,1 / y,z),K(y \ 1,(y \ 1) \ 1),(1 / y) * z) = R(x,K(y \ 1,y) / y,z). [para(929(a,1),1653(a,2,2,1))]. given #1557 (H,wt=28): 1655 R(R(x,1 / y,z),K(y \ 1,(y \ 1) \ 1),(1 / y) * z) = R(x,y \ 1,z). [para(149(a,1),1654(a,2,2))]. given #1558 (H,wt=24): 1656 R(R(x,1 / y,z),K(y \ 1,y),(1 / y) * z) = R(x,y \ 1,z). [para(929(a,1),1655(a,1,2))]. given #1559 (H,wt=63): 784 K((x \ (y \ z)) \ ((x \ (y \ z)) / (((((y * x) \ z) \ (x \ (y \ z))) / (x \ (y \ z))) \ 1)),x \ (y \ z)) = ((((y * x) \ z) \ (x \ (y \ z))) / (x \ (y \ z))) \ (((y * x) \ z) \ 1). [para(783(a,1),434(a,2,2))]. given #1560 (H,wt=53): 1657 K((x \ (y \ z)) \ ((x \ (y \ z)) / ((1 / ((y * x) \ z)) \ 1)),x \ (y \ z)) = ((((y * x) \ z) \ (x \ (y \ z))) / (x \ (y \ z))) \ (((y * x) \ z) \ 1). [para(1426(a,1),784(a,1,1,2,2,1))]. given #1561 (H,wt=49): 1658 ((((x * y) \ z) \ (y \ (x \ z))) / (y \ (x \ z))) \ (((x * y) \ z) \ 1) = K((y \ (x \ z)) \ ((y \ (x \ z)) / ((x * y) \ z)),y \ (x \ z)). [para(59(a,1),1657(a,1,1,2,2)),flip(a)]. given #1562 (H,wt=49): 1660 ((((x * y) \ z) \ (y \ (x \ z))) / (y \ (x \ z))) \ (((x * y) \ z) \ 1) = K((y \ (x \ z)) \ (((x * y) \ z) \ (y \ (x \ z))),y \ (x \ z)). [para(1424(a,1),1658(a,2,1,2))]. given #1563 (H,wt=39): 1661 ((((x * y) \ z) \ (y \ (x \ z))) / (y \ (x \ z))) \ (((x * y) \ z) \ 1) = K(((x * y) \ z) \ 1,y \ (x \ z)). [para(783(a,1),1660(a,2,1))]. given #1564 (H,wt=29): 1662 (1 / ((x * y) \ z)) \ (((x * y) \ z) \ 1) = K(((x * y) \ z) \ 1,y \ (x \ z)). [para(1426(a,1),1661(a,1,1))]. given #1565 (H,wt=27): 1663 K(((x * y) \ z) \ 1,(x * y) \ z) = K(((x * y) \ z) \ 1,y \ (x \ z)). [para(1662(a,1),888(a,1)),flip(a)]. given #1566 (H,wt=25): 1664 K(((x * y) \ z) \ 1,y \ (x \ z)) = K(z \ (x * y),(x * y) \ z). [para(1663(a,1),1607(a,1))]. given #1567 (H,wt=29): 1665 x \ ((y * z) * K(x \ (y * z),(y * z) \ x)) = T(x \ (y * z),z \ (y \ x)). [para(1664(a,1),1610(a,1,2,2))]. given #1568 (H,wt=21): 1666 T(x \ (y * z),z \ (y \ x)) = ((x \ (y * z)) \ 1) \ 1. [para(1665(a,1),1609(a,1))]. given #1569 (H,wt=28): 1667 T(L(x,y,z),(y * x) \ (z \ (z * y))) = (((z * y) \ (z * (y * x))) \ 1) \ 1. [para(26(a,2),1666(a,1,1))]. given #1570 (H,wt=24): 1668 T(L(x,y,z),(y * x) \ y) = (((z * y) \ (z * (y * x))) \ 1) \ 1. [para(13(a,1),1667(a,1,2,2))]. given #1571 (H,wt=19): 1669 T(L(x,y,z),(y * x) \ y) = (L(x,y,z) \ 1) \ 1. [para(26(a,2),1668(a,2,1,1))]. given #1572 (H,wt=19): 1670 L(T(x,(y * x) \ y),y,z) = (L(x,y,z) \ 1) \ 1. [para(1669(a,1),38(a,2))]. given #1573 (H,wt=17): 1671 L(T(x,x \ 1),y,z) = (L(x,y,z) \ 1) \ 1. [para(1436(a,1),1670(a,1,1))]. given #1574 (H,wt=25): 1672 L(T(x,x \ 1),y,z) \ L(x,y,z) = K(L(x,y,z) \ 1,L(x,y,z)). [para(1671(a,2),1163(a,1,1))]. given #1575 (H,wt=20): 1674 K(L(x,y,z) \ 1,L(x,y,z)) = K(x \ 1,L(x,y,z)). [para(1672(a,1),1559(a,1))]. given #1576 (H,wt=17): 1675 L(K(x \ 1,x),y,z) = K(x \ 1,L(x,y,z)). [para(1674(a,1),1429(a,1)),flip(a)]. given #1577 (H,wt=14): 1676 L(K(x \ 1,x),y,z) = K(x \ 1,x). [para(1675(a,2),1634(a,1))]. given #1578 (H,wt=17): 1677 (x \ 1) * K(y \ 1,y) = x \ K(y \ 1,y). [para(1676(a,1),248(a,1,2)),flip(a)]. given #1579 (H,wt=19): 1678 K(x \ 1,x) * (y * z) = y * (K(x \ 1,x) * z). [para(1676(a,1),1287(a,1,1))]. given #1580 (H,wt=19): 1683 x \ (K(y \ 1,y) * z) = K(y \ 1,y) * (x \ z). [hyper(267,a,1678,a)]. given #1581 (H,wt=19): 1686 (x * y) * K(z \ 1,z) = x * (K(z \ 1,z) * y). [para(1678(a,1),1133(a,1)),flip(a)]. given #1582 (H,wt=21): 1681 K(x \ 1,x) * ((y \ 1) * z) = (y \ K(x \ 1,x)) * z. [para(1677(a,1),1169(a,1,1)),flip(a)]. given #1583 (H,wt=21): 1682 (x \ 1) \ (K(y,y \ 1) * z) = (x \ K(y \ 1,y)) \ z. [para(1677(a,1),1209(a,1,1)),flip(a)]. given #1584 (H,wt=22): 1688 (x * y) * K(z \ 1,L(z,u,w)) = x * (K(z \ 1,z) * y). [para(1634(a,2),1686(a,1,2))]. given #1585 (H,wt=26): 1685 (x * y) \ (x * (K(z \ 1,z) * (y * u))) = L(K(z \ 1,z) * u,y,x). [para(1678(a,2),26(a,2,2,2)),flip(a)]. given #1586 (H,wt=26): 1689 (x * y) * K(z,L(1 / z,u,w)) = x * (K((1 / z) \ 1,1 / z) * y). [para(59(a,1),1688(a,1,2,1))]. given #1587 (H,wt=26): 1690 (x * y) * K(z,L(z \ 1,u,w)) = x * (K((1 / z) \ 1,1 / z) * y). [para(1165(a,1),1689(a,1,2))]. given #1588 (H,wt=22): 1691 (x * y) * K(z,L(z \ 1,u,w)) = x * (K(z,1 / z) * y). [para(59(a,1),1690(a,2,2,1,1))]. given #1589 (H,wt=22): 1692 (x * y) * K(z,L(z \ 1,u,w)) = x * (K(z,z \ 1) * y). [para(928(a,1),1691(a,2,2,1))]. given #1590 (H,wt=14): 1693 K(x,L(x \ 1,y,z)) = K(x,x \ 1). [hyper(1076,a,1692,a)]. given #1591 (H,wt=19): 1694 (x * y) * K(z,z \ 1) = x * (K(z,z \ 1) * y). [para(88(a,1),1692(a,1,2,2))]. given #1592 (H,wt=10): 1695 R(x,y,K(z,z \ 1)) = x. [hyper(1201,a,1694,a)]. given #1593 (H,wt=10): 1698 R(x,y,K(z \ 1,z)) = x. [para(929(a,1),1695(a,1,3))]. given #1594 (H,wt=10): 1707 R(x,K(y \ 1,y),z) = x. [para(1698(a,1),1371(a,2))]. given #1595 (H,wt=13): 1699 T(x,y * K(z,z \ 1)) = T(x,y). [para(1695(a,1),1271(a,1))]. given #1596 (H,wt=13): 1703 R(x,y,(z \ 1) \ 1) = R(x,y,z). [para(1695(a,1),1588(a,1)),flip(a)]. given #1597 (H,wt=13): 1706 R(x,y,K(z \ 1,R(z,u,w))) = x. [para(915(a,2),1698(a,1,3))]. given #1598 (H,wt=13): 1714 R(x,1 / y,z) = R(x,y \ 1,z). [para(1707(a,1),1656(a,1))]. given #1599 (H,wt=15): 1715 T(x,y * T(z,z \ 1)) = T(x,y * z). [para(1474(a,1),1699(a,1,2))]. given #1600 (H,wt=15): 1716 T(x,y * ((z \ 1) \ 1)) = T(x,y * z). [para(1476(a,1),1699(a,1,2))]. given #1601 (H,wt=17): 1697 (x \ 1) * K(y,y \ 1) = x \ K(y,y \ 1). [para(1695(a,1),168(a,1,1)),flip(a)]. given #1602 (H,wt=19): 1700 x \ (K(y,y \ 1) * z) = (x \ z) * K(y,y \ 1). [para(1695(a,1),1200(a,1,1))]. given #1603 (H,wt=21): 1721 (x \ 1) \ (K(y \ 1,y) * z) = (x \ K(y,y \ 1)) \ z. [para(1697(a,1),1214(a,1,1)),flip(a)]. given #1604 (H,wt=19): 1723 (x \ K(y,y \ 1)) \ 1 = (x \ 1) \ K(y \ 1,y). [para(12(a,1),1721(a,1,2)),flip(a)]. given #1605 (H,wt=21): 1722 ((x \ 1) \ y) * K(z,z \ 1) = (x \ K(z \ 1,z)) \ y. [para(1700(a,1),1682(a,1))]. given #1606 (H,wt=21): 1724 K(x \ 1,x) * ((y \ 1) \ z) = (y \ K(x,x \ 1)) \ z. [para(1721(a,1),1683(a,1)),flip(a)]. given #1607 (H,wt=22): 1719 R(1 / (1 / x),x \ 1,(1 / x) \ y) = ((1 / x) \ y) / y. [para(1714(a,1),161(a,1))]. given #1608 (H,wt=25): 1720 (x \ 1) \ T(x \ 1,y * ((z \ 1) \ 1)) = x * T(x \ 1,y * z). [para(1716(a,1),1504(a,2,2))]. given #1609 (H,wt=26): 1705 (x * y) \ ((x * (y * z)) * K(u \ 1,u)) = L(z,y,x) * K(u \ 1,u). [para(1698(a,1),237(a,1,1))]. given #1610 (H,wt=26): 1726 (x * y) \ (x * (K(z \ 1,z) * (y * u))) = L(u,y,x) * K(z \ 1,z). [para(1686(a,1),1705(a,1,2))]. given #1611 (H,wt=21): 1727 L(K(x \ 1,x) * y,z,u) = L(y,z,u) * K(x \ 1,x). [para(1726(a,1),1685(a,1)),flip(a)]. given #1612 (H,wt=21): 1728 L(K(x \ 1,x) * y,z,u) = K(x \ 1,x) * L(y,z,u). [para(1727(a,2),1133(a,2)),flip(a)]. given #1613 (H,wt=28): 1718 T(x,y) * T(K(z \ 1,R(z,u,w)),x * y) = y \ ((x * K(z \ 1,z)) * y). [para(1706(a,1),1401(a,1,1)),flip(a)]. given #1614 (H,wt=26): 1730 T(x,y) * T(K(z \ 1,R(z,u,w)),x * y) = T(x * K(z \ 1,z),y). [para(1718(a,2),30(a,2)),flip(a)]. given #1615 (H,wt=22): 1731 T(x,y) * K(z \ 1,R(z,u,w)) = T(x * K(z \ 1,z),y). [para(1154(a,1),1730(a,1,2))]. given #1616 (H,wt=19): 1732 T(x * K(y \ 1,y),z) = T(x,z) * K(y \ 1,y). [para(157(a,1),1731(a,1,2,2)),flip(a)]. given #1617 (H,wt=19): 1734 T(K(x \ 1,x) * y,z) = T(y,z) * K(x \ 1,x). [para(1133(a,2),1732(a,1,1))]. given #1618 (H,wt=19): 1735 T(K(x \ 1,x) * y,z) = K(x \ 1,x) * T(y,z). [para(1734(a,2),1133(a,2)),flip(a)]. given #1619 (H,wt=19): 1736 K(x \ 1,x) * T(K(x,x \ 1) * y,z) = T(y,z). [para(448(a,1),1735(a,1,1)),flip(a)]. given #1620 (H,wt=15): 1738 (x \ T(x * (y / x),z)) * x = T(y,z). [para(1736(a,1),846(a,1)),flip(a)]. given #1621 (H,wt=15): 1739 (x \ T(x * y,z)) * x = T(y * x,z). [para(15(a,1),1738(a,1,1,2,1,2))]. given #1622 (H,wt=15): 1740 T((x \ y) * x,z) = (x \ T(y,z)) * x. [para(56(a,1),1738(a,1,1,2,1)),flip(a)]. given #1623 (H,wt=15): 1742 T(x * y,z) / y = y \ T(y * x,z). [hyper(70,a,1739,a)]. given #1624 (H,wt=17): 1743 T((x \ (y / z)) * x,z) = (x \ (z \ y)) * x. [para(87(a,1),1740(a,2,1,2))]. given #1625 (H,wt=18): 1744 R((x * y) / x,x,T(y,x)) = x \ T(x * y,y). [para(1742(a,1),622(a,2))]. given #1626 (H,wt=16): 1747 L(x \ T(x * y,y),x,y) = (x * y) / x. [para(1744(a,1),650(a,1,1))]. given #1627 (H,wt=15): 1748 (x * y) \ ((y * x) * x) = (y * x) / y. [para(1747(a,1),208(a,1)),flip(a)]. given #1628 (H,wt=19): 1746 ((x \ (y / z)) * x) * z = z * ((x \ (z \ y)) * x). [para(1743(a,1),85(a,1,2)),flip(a)]. given #1629 (H,wt=21): 1745 x * (y \ T(y * (x \ z),x)) = ((x \ (z * y)) * x) / y. [para(1742(a,1),1539(a,1,2))]. given #1630 (H,wt=23): 1749 ((x \ (y / (z \ 1))) * x) * (z \ 1) = ((x \ (y * z)) * x) / z. [para(1745(a,1),737(a,2))]. given #1631 (H,wt=23): 1750 (x \ 1) * ((y \ ((x \ 1) \ z)) * y) = ((y \ (z * x)) * y) / x. [para(1749(a,1),1746(a,1)),flip(a)]. given #1632 (H,wt=32): 1725 ((1 / x) \ y) \ (y * R(1 / (1 / x),x \ 1,(1 / x) \ y)) = K(y,((1 / x) \ y) / y). [para(1719(a,2),75(a,1,2,2))]. given #1633 (H,wt=32): 1751 ((1 / x) \ y) \ (y * R(1 / (1 / x),x \ 1,(1 / x) \ y)) = K(y,((x \ 1) \ y) / y). [para(1725(a,2),1343(a,1))]. given #1634 (H,wt=38): 1717 ((x * (y * T(y \ 1,z))) * ((z \ 1) \ 1)) / ((z \ 1) \ (y * T(y \ 1,z))) = R(x,y * T(y \ 1,z),z). [para(1703(a,1),1365(a,2))]. given #1635 (H,wt=49): 1729 T(x \ L(x * ((((x \ 1) \ 1) * y) / ((x \ 1) \ 1)),z,u),(x \ 1) \ 1) = (x \ 1) * L(K(x \ 1,x) * ((((x \ 1) \ 1) \ 1) \ y),z,u). [para(1728(a,2),1090(a,2,2))]. given #1636 (H,wt=47): 1752 T(x \ L(x * ((((x \ 1) \ 1) * y) / ((x \ 1) \ 1)),z,u),(x \ 1) \ 1) = (x \ 1) * L((((x \ 1) \ 1) \ K(x,x \ 1)) \ y,z,u). [para(1724(a,1),1729(a,2,2,1))]. given #1637 (H,wt=39): 1753 T(x \ L(x * ((((x \ 1) \ 1) * y) / ((x \ 1) \ 1)),z,u),(x \ 1) \ 1) = (x \ 1) * L((x \ 1) \ y,z,u). [para(540(a,1),1752(a,2,2,1,1))]. given #1638 (H,wt=35): 1754 T(x \ L(x * ((((x \ 1) \ 1) * y) / ((x \ 1) \ 1)),z,u),(x \ 1) \ 1) = x \ L(x * y,z,u). [para(1753(a,2),558(a,1))]. given #1639 (H,wt=27): 1755 T(x \ L(x * ((x * y) / x),z,u),(x \ 1) \ 1) = x \ L(x * y,z,u). [para(1577(a,1),1754(a,1,1,2,1,2))]. given #1640 (H,wt=23): 1756 T(x \ L(x * ((x * y) / x),z,u),x) = x \ L(x * y,z,u). [para(1755(a,1),1460(a,1)),flip(a)]. given #1641 (H,wt=25): 1757 T(x \ 1,x) * L(T(x \ 1,x) \ y,z,u) = x \ L(x * y,z,u). [para(1756(a,1),832(a,1)),flip(a)]. given #1642 (H,wt=33): 1758 T((1 / x) \ 1,1 / x) * L(T((1 / x) \ 1,1 / x) \ y,z,u) = x * L(x \ y,z,u). [para(1757(a,2),393(a,1))]. given #1643 (H,wt=41): 1759 T((1 / (1 / x)) \ 1,1 / (1 / x)) * L(T((1 / (1 / x)) \ 1,1 / (1 / x)) \ y,z,u) = L(y * x,z,u) / x. [para(1758(a,2),782(a,1))]. given #1644 (H,wt=37): 1760 T(1 / x,1 / (1 / x)) * L(T((1 / (1 / x)) \ 1,1 / (1 / x)) \ y,z,u) = L(y * x,z,u) / x. [para(59(a,1),1759(a,1,1,1))]. given #1645 (H,wt=31): 1762 (x \ 1) * L(T((1 / (1 / x)) \ 1,1 / (1 / x)) \ y,z,u) = L(y * x,z,u) / x. [para(1605(a,1),1760(a,1,1))]. given #1646 (H,wt=27): 1763 (x \ 1) * L(T(1 / x,1 / (1 / x)) \ y,z,u) = L(y * x,z,u) / x. [para(59(a,1),1762(a,1,2,1,1,1))]. given #1647 (H,wt=21): 1766 (x \ 1) * L((x \ 1) \ y,z,u) = L(y * x,z,u) / x. [para(1605(a,1),1763(a,1,2,1,1))]. given #1648 (H,wt=17): 1767 L(x * y,z,u) / y = y \ L(y * x,z,u). [para(1766(a,1),558(a,1))]. given #1649 (H,wt=17): 1769 (x \ L(x * y,z,u)) * x = L(y * x,z,u). [para(1767(a,1),16(a,1,1))]. given #1650 (H,wt=17): 1770 L((x \ y) * x,z,u) = (x \ L(y,z,u)) * x. [para(14(a,1),1769(a,1,1,2,1)),flip(a)]. given #1651 (H,wt=24): 1771 L((x \ ((y \ z) \ u)) * x,y \ z,y) = (x \ (z \ (y * u))) * x. [para(200(a,1),1770(a,2,1,2))]. given #1652 (H,wt=25): 1774 (x \ 1) * ((y \ ((x \ 1) \ z)) * y) = x \ ((y \ (1 \ (x * z))) * y). [para(1771(a,1),248(a,1,2)),flip(a)]. given #1653 (H,wt=23): 1775 (x \ 1) * ((y \ ((x \ 1) \ z)) * y) = x \ ((y \ (x * z)) * y). [para(47(a,1),1774(a,2,2,1,2))]. given #1654 (H,wt=19): 1776 ((x \ (y * z)) * x) / z = z \ ((x \ (z * y)) * x). [para(1775(a,1),1750(a,1)),flip(a)]. given #1655 (H,wt=30): 1772 (x * (y \ z)) * L((z \ T(y,y \ z)) * z,y \ z,x) = (x * K(z \ y,z)) * z. [para(1770(a,2),1018(a,1,2))]. given #1656 (H,wt=25): 1777 x * ((y \ z) * ((z \ T(y,y \ z)) * z)) = (x * K(z \ y,z)) * z. [para(1772(a,1),76(a,1)),flip(a)]. given #1657 (H,wt=19): 1778 (x * K(y \ z,y)) * y = x * (y * K(y \ z,y)). [para(1051(a,1),1777(a,1,2)),flip(a)]. given #1658 (H,wt=19): 1779 x * (y * K(y \ (y * z),y)) = (x * K(z,y)) * y. [para(13(a,1),1778(a,1,1,2,1)),flip(a)]. given #1659 (H,wt=15): 1780 (x * K(y,z)) * z = x * (z * K(y,z)). [para(13(a,1),1779(a,1,2,2,1)),flip(a)]. given #1660 (H,wt=15): 1781 (x * y) / (y * K(z,y)) = x / K(z,y). [hyper(268,a,1780,a)]. given #1661 (H,wt=24): 1782 (x * (y * K(z,y))) \ ((x * (y * K(z,y))) * y) = L(y,K(z,y),x). [para(1780(a,1),1052(a,1,1))]. given #1662 (H,wt=8): 1783 L(x,K(y,x),z) = x. [para(1782(a,1),13(a,1))]. given #1663 (H,wt=12): 1784 L(T(x,y),K(z,x),u) = T(x,y). [para(1783(a,1),38(a,2,1))]. given #1664 (H,wt=34): 1773 (x * y) * L((z \ (y \ ((z \ 1) \ 1))) * z,y,x) = (x * (y * T(y \ 1,z))) * ((z \ 1) \ 1). [para(1770(a,2),1624(a,1,2))]. given #1665 (H,wt=31): 1785 (x * (y * T(y \ 1,z))) * ((z \ 1) \ 1) = x * (y * ((z \ (y \ ((z \ 1) \ 1))) * z)). [para(1773(a,1),76(a,1))]. given #1666 (H,wt=29): 1786 (x * (y * T(y \ 1,z))) * ((z \ 1) \ 1) = x * ((z \ 1) \ (y * T(y \ 1,z))). [para(1366(a,1),1785(a,2,2))]. given #1667 (H,wt=36): 1787 (x * ((y \ 1) \ (z * T(z \ 1,y)))) / ((y \ 1) \ (z * T(z \ 1,y))) = R(x,z * T(z \ 1,y),y). [para(1786(a,1),1717(a,1,1))]. given #1668 (H,wt=12): 1788 R(x,y * T(y \ 1,z),z) = x. [para(1787(a,1),15(a,1))]. given #1669 (H,wt=8): 1789 R(x,K(y,z),z) = x. [para(668(a,2),1788(a,1,2))]. given #1670 (H,wt=15): 1790 (x * y) \ ((y * x) * x) = K(y,x) * x. [para(1789(a,1),235(a,1,1))]. given #1671 (H,wt=11): 1791 (x * y) / x = K(x,y) * y. [para(1790(a,1),1748(a,1)),flip(a)]. given #1672 (H,wt=11): 1792 K(x,y) = y \ ((x * y) / x). [hyper(1070,a,1791,a),flip(a)]. given #1673 (H,wt=11): 1796 (x * y) / x = y * K(x,y). [para(1791(a,2),1047(a,1))]. given #1674 (H,wt=9): 1803 T(x * K(y,x),y) = x. [para(1796(a,1),105(a,1,1))]. given #1675 (H,wt=11): 1801 (x * K(y,x)) * y = y * x. [para(1796(a,1),16(a,1,1))]. given #1676 (H,wt=11): 1805 K(x,y) * (y * x) = x * y. [para(1801(a,1),1049(a,1)),flip(a)]. given #1677 (H,wt=13): 1793 K(x,x \ y) * (x \ y) = y / x. [para(14(a,1),1791(a,1,1)),flip(a)]. given #1678 (H,wt=13): 1795 L(x,y,(z * u) / z) = L(x,y,u). [para(1791(a,2),850(a,1,3))]. given #1679 (H,wt=11): 1812 L(x,y,T(z,u)) = L(x,y,z). [para(106(a,1),1795(a,1,3)),flip(a)]. given #1680 (H,wt=13): 1800 (x \ y) * K(x,x \ y) = y / x. [para(14(a,1),1796(a,1,1)),flip(a)]. given #1681 (H,wt=13): 1802 x / (x / y) = y * K(x / y,y). [para(16(a,1),1796(a,1,1))]. given #1682 (H,wt=13): 1811 L(x,y,z / u) = L(x,y,u \ z). [para(1793(a,1),850(a,1,3))]. given #1683 (H,wt=13): 1813 L(x,y,(z \ u) \ u) = L(x,y,z). [para(86(a,1),1812(a,1,3))]. given #1684 (H,wt=14): 1814 L(x \ y,x,x \ y) = T(y / x,y). [para(1811(a,1),310(a,1))]. given #1685 (H,wt=15): 1794 ((x * y) / x) * (y \ z) = K(x,y) * z. [para(1791(a,2),273(a,1,1))]. given #1686 (H,wt=9): 1817 T(x,y) = K(x,y) * x. [para(1794(a,1),578(a,2))]. given #1687 (H,wt=9): 1818 K(x,y) = x \ T(x,y). [hyper(1509,a,1817,a),flip(a)]. given #1688 (H,wt=7): 1830 T(x,K(x,y)) = x. [para(1818(a,2),1508(a,1,2))]. given #1689 (H,wt=9): 1825 T(x,y) = x * K(x,y). [para(1818(a,2),14(a,1,2)),flip(a)]. given #1690 (H,wt=9): 1832 T(K(x,y),x) = K(x,y). [hyper(33,a,1830,a)]. given #1691 (H,wt=11): 1828 K(x,y) = T(x,y) * (x \ 1). [para(1818(a,2),424(a,2)),flip(a)]. given #1692 (H,wt=11): 1833 (x * K(x,y)) / x = K(x,y). [para(1830(a,1),96(a,1,2))]. given #1693 (H,wt=12): 1834 T(x,y) != x * z | K(x,y) = z. [para(1825(a,2),19(a,1))]. given #1694 (H,wt=12): 1840 T(x,L(y,z,y)) = x * K(x,y). [para(950(a,1),1825(a,2,2))]. given #1695 (H,wt=10): 1845 T(x,L(y,z,y)) = T(x,y). [para(1840(a,2),1825(a,2)),flip(a)]. given #1696 (H,wt=13): 1821 K(x,y) * (x * z) = T(x,y) * z. [para(1817(a,2),197(a,1,1)),flip(a)]. given #1697 (H,wt=13): 1822 T(x,y) * (x \ z) = K(x,y) * z. [para(1817(a,2),273(a,1,1))]. given #1698 (H,wt=13): 1831 x * T(x \ 1,y) = K(x \ 1,y). [para(1818(a,2),1504(a,1)),flip(a)]. given #1699 (H,wt=13): 1846 T(x,T(y / z,y)) = T(x,z \ y). [para(1814(a,1),1845(a,1,2))]. given #1700 (H,wt=13): 1853 x * (K(x,y) * z) = T(x,y) * z. [para(1822(a,1),494(a,1,2))]. given #1701 (H,wt=13): 1854 K(x,y) * (T(x,y) \ z) = x \ z. [para(1822(a,1),499(a,1))]. given #1702 (H,wt=13): 1855 K(x \ 1,y) / x = T(1 / x,y). [para(1831(a,1),176(a,1,1))]. given #1703 (H,wt=15): 1799 x * ((y * (x \ 1)) / y) = K(y,x \ 1). [para(1792(a,2),1073(a,1)),flip(a)]. given #1704 (H,wt=15): 1804 (x * y) / ((z * y) / z) = x / K(z,y). [para(1796(a,2),1781(a,1,2))]. given #1705 (H,wt=15): 1816 ((x * y) / x) * z = y * (K(x,y) * z). [para(1794(a,1),567(a,1,2)),flip(a)]. given #1706 (H,wt=15): 1829 x \ T(x,y * (z \ 1)) = K(x,y / z). [para(1818(a,1),919(a,1))]. given #1707 (H,wt=15): 1848 K(x,y) * (z * x) = T(x,y) * T(z,x). [para(85(a,1),1821(a,1,2))]. given #1708 (H,wt=11): 1885 T(x,y) * T(y,x) = x * y. [para(1848(a,1),1805(a,1))]. given #1709 (H,wt=9): 1887 K(x,y) * T(y,x) = y. [hyper(17,a,1853,a,b,1885,a(flip)),flip(a)]. given #1710 (H,wt=9): 1888 K(x,y) = T(y,x) \ y. [hyper(1065,a,1887,a),flip(a)]. given #1711 (H,wt=9): 1894 T(x,y) * K(y,x) = x. [para(1887(a,1),1053(a,2))]. given #1712 (H,wt=11): 1886 T(x,y) \ (x * y) = T(y,x). [hyper(66,a,1885,a)]. given #1713 (H,wt=9): 1903 T(x,T(y,x)) = T(x,y). [para(1886(a,1),113(a,1)),flip(a)]. given #1714 (H,wt=11): 1898 K(x,y) = y * (T(y,x) \ 1). [para(1888(a,2),505(a,2)),flip(a)]. given #1715 (H,wt=11): 1899 K(x,y) / y = 1 / T(y,x). [para(1888(a,2),1066(a,1,1))]. given #1716 (H,wt=11): 1904 T(x,y / x) = T(x,x \ y). [para(87(a,1),1903(a,1,2)),flip(a)]. given #1717 (H,wt=11): 1906 T(x,x / y) = T(x,y \ x). [para(1903(a,1),1846(a,1))]. given #1718 (H,wt=11): 1907 T(x,y) = (K(y,x) / x) \ 1. [para(1899(a,2),59(a,1,1)),flip(a)]. given #1719 (H,wt=13): 1891 K(x,y) * (T(y,x) * z) = y * z. [para(1887(a,1),197(a,1,1)),flip(a)]. given #1720 (H,wt=13): 1900 (x \ 1) * K(y,x) = T(x,y) \ 1. [para(1888(a,2),1545(a,1,2))]. given #1721 (H,wt=13): 1902 T(x,y) = (x \ (y * x)) \ (y * x). [para(30(a,1),1886(a,1,1)),flip(a)]. given #1722 (H,wt=13): 1911 T(x,(y \ 1) \ x) = T(x,y * x). [para(1906(a,1),645(a,1))]. given #1723 (H,wt=15): 1865 K(x / y,z) * x = y * T(y \ x,z). [hyper(17,a,515,a,b,1853,a)]. given #1724 (H,wt=15): 1877 (x / ((y * z) / y)) * z = x / K(y,z). [para(1804(a,1),627(a,1)),flip(a)]. given #1725 (H,wt=15): 1878 x \ (((y * x) / y) * z) = K(y,x) * z. [hyper(66,a,1816,a(flip))]. given #1726 (H,wt=15): 1882 (x * K(y,x)) * z = x * (K(y,x) * z). [para(1796(a,1),1816(a,1,1))]. given #1727 (H,wt=8): 1917 L(x,K(y,z),z) = x. [hyper(192,a,1882,a)]. given #1728 (H,wt=8): 1919 a(x,K(y,x),z) = 1. [hyper(32,a,1917,a)]. given #1729 (H,wt=11): 1920 a(R(x,y,z),K(u,x),w) = 1. [para(915(a,1),1919(a,1,2))]. given #1730 (H,wt=15): 1914 (x * ((y * z) / y)) / K(y,z) = x * z. [para(15(a,1),1877(a,1,1)),flip(a)]. given #1731 (H,wt=15): 1915 K(x,y) * (((x * y) / x) \ z) = y \ z. [para(14(a,1),1878(a,1,2)),flip(a)]. given #1732 (H,wt=15): 1918 K(x,y) * (y * z) = y * (K(x,y) * z). [para(1882(a,1),1049(a,1)),flip(a)]. given #1733 (H,wt=13): 1928 T(x,y) * (K(y,x) * z) = x * z. [hyper(17,a,1891,a,b,1918,a),flip(a)]. given #1734 (H,wt=11): 1930 K(x,y) * (K(y,x) * z) = z. [hyper(17,a,1853,a(flip),b,1928,a)]. given #1735 (H,wt=9): 1935 K(x,y) \ 1 = K(y,x). [hyper(99,a,1930,a),flip(a)]. given #1736 (H,wt=9): 1938 K(x,y) * K(y,x) = 1. [hyper(63,a,1930,a),flip(a)]. given #1737 (H,wt=11): 1936 x / (K(y,z) * x) = K(z,y). [hyper(70,a,1930,a)]. given #1738 (H,wt=11): 1937 K(x,y) \ z = K(y,x) * z. [hyper(66,a,1930,a)]. given #1739 (H,wt=11): 1948 (x * K(y,x)) \ x = K(x,y). [para(1935(a,1),1623(a,2))]. given #1740 (H,wt=11): 1954 K(x,y) = ((y * x) / y) \ x. [para(1796(a,2),1948(a,1,1)),flip(a)]. given #1741 (H,wt=11): 1956 K(T(x,y),y) = x \ T(x,y). [para(106(a,1),1954(a,2,1))]. given #1742 (H,wt=9): 1958 K(T(x,y),y) = K(x,y). [para(1956(a,2),1818(a,2)),flip(a)]. given #1743 (H,wt=11): 1959 K(x / y,y) = K(y \ x,y). [para(87(a,1),1958(a,1,1)),flip(a)]. given #1744 (H,wt=11): 1962 K(T(x,y),y) \ 1 = K(y,x). [para(1958(a,2),1935(a,1,1))]. given #1745 (H,wt=9): 1964 K(x,T(y,x)) = K(x,y). [para(1962(a,1),1935(a,1)),flip(a)]. given #1746 (H,wt=11): 1965 K(x,y / x) = K(x,x \ y). [para(87(a,1),1964(a,1,2)),flip(a)]. given #1747 (H,wt=11): 1966 K(x,x / y) = K(x,y \ x). [para(1964(a,1),941(a,1))]. given #1748 (H,wt=12): 1944 x * K(y,z) != 1 | K(z,y) = x. [para(1935(a,1),69(a,1,2)),flip(b)]. given #1749 (H,wt=13): 1940 K(x \ y,x) * (y / x) = x \ y. [hyper(17,a,1793,a,b,1930,a)]. given #1750 (H,wt=13): 1946 (K(x,y) * z) \ 1 = z \ K(y,x). [para(1935(a,1),250(a,2,2))]. given #1751 (H,wt=13): 1957 ((x * y) / x) \ 1 = y \ K(y,x). [para(1954(a,2),575(a,1,2)),flip(a)]. given #1752 (H,wt=13): 1963 x / (x / y) = y * K(y \ x,y). [para(1959(a,1),1802(a,2,2))]. given #1753 (H,wt=13): 1968 x * K(y,y \ x) = y * (x / y). [para(1965(a,1),137(a,1,2))]. given #1754 (H,wt=13): 1970 K(x,x * (y \ 1)) = K(x,y \ x). [para(1966(a,1),919(a,2))]. given #1755 (H,wt=14): 1951 K(L(x,y,x),z) = u / (K(z,x) * u). [para(950(a,1),1936(a,1,2,1)),flip(a)]. given #1756 (H,wt=10): 1981 K(L(x,y,x),z) = K(x,z). [para(1951(a,2),1936(a,1))]. given #1757 (H,wt=15): 1924 (x * (y * K(z,y))) / K(z,y) = x * y. [para(1796(a,1),1914(a,1,1,2))]. given #1758 (H,wt=15): 1925 (x \ y) / (((z * x) / z) \ y) = K(z,x). [hyper(70,a,1915,a)]. given #1759 (H,wt=15): 1933 K(x,y) * ((K(y,x) * z) * u) = z * u. [hyper(274,a,1930,a),flip(a)]. given #1760 (H,wt=15): 1934 K(x,y) * (z * K(y,x)) = T(z,K(y,x)). [hyper(109,a,1930,a),flip(a)]. given #1761 (H,wt=15): 1939 ((x * y) / x) \ z = K(y,x) * (y \ z). [hyper(17,a,1915,a,b,1930,a),flip(a)]. given #1762 (H,wt=15): 1941 K(x,y) * T(K(y,x),z) = K(K(y,x),z). [hyper(17,a,1825,a(flip),b,1930,a)]. given #1763 (H,wt=15): 1943 (K(x,y) * z) \ u = z \ (K(y,x) * u). [para(1930(a,1),206(a,1,1)),flip(a)]. given #1764 (H,wt=15): 1949 T(K(x,y),z) * K(y,x) = K(K(x,y),z). [para(1935(a,1),1828(a,2,2)),flip(a)]. given #1765 (H,wt=15): 1969 x \ T(x,y * (x \ 1)) = K(x,x \ y). [para(1965(a,1),1829(a,2))]. given #1766 (H,wt=15): 1976 (x \ y) \ K(x \ y,x) = (y / x) \ 1. [para(1793(a,1),1946(a,1,1)),flip(a)]. given #1767 (H,wt=15): 1982 (x * y) * K(z,y) = x * (y * K(z,y)). [para(1924(a,1),16(a,1,1))]. given #1768 (H,wt=10): 1988 L(K(x,y),y,z) = K(x,y). [hyper(192,a,1982,a)]. given #1769 (H,wt=16): 1807 K(x,x \ y) * z != y / x | x \ y = z. [para(1793(a,1),19(a,1)),flip(a)]. given #1770 (H,wt=16): 1826 (x * y) \ (x * T(y,z)) = L(K(y,z),y,x). [para(1818(a,2),78(a,1,1)),flip(a)]. given #1771 (H,wt=16): 1866 T(x,y) * z != x * u | K(x,y) * z = u. [para(1853(a,1),19(a,1))]. given #1772 (H,wt=16): 1867 T(x,y) * z != x * (K(x,y) * u) | z = u. [para(1853(a,2),19(a,2))]. given #1773 (H,wt=16): 1892 K(x,y) * z != y * u | T(y,x) * u = z. [para(1887(a,1),274(a,2,1))]. given #1774 (H,wt=17): 1851 K(x,y) * ((x * z) / u) = (T(x,y) * z) / u. [para(1821(a,1),281(a,1,1)),flip(a)]. given #1775 (H,wt=17): 1856 x * T(x \ y,z) = y * K((y \ x) \ 1,z). [para(1831(a,1),492(a,1,2)),flip(a)]. given #1776 (H,wt=17): 1858 (x * T(x \ y,z)) / y = K((x / y) \ 1,z). [para(1831(a,1),628(a,1)),flip(a)]. given #1777 (H,wt=17): 1860 K(x \ (x / T(y,z)),x) = T(K(y \ 1,x),z). [para(1831(a,1),749(a,1,1)),flip(a)]. given #1778 (H,wt=17): 1873 K(x,y) * ((T(x,y) \ z) * u) = (x \ z) * u. [para(1854(a,1),197(a,1,1)),flip(a)]. given #1779 (H,wt=17): 1879 (x \ y) * (K(x,x \ y) * z) = (y / x) * z. [para(14(a,1),1816(a,1,1,1)),flip(a)]. given #1780 (H,wt=17): 1884 x * (T(y,x) * (y \ z)) = ((y * x) / y) * z. [para(1822(a,2),1816(a,2,2)),flip(a)]. given #1781 (H,wt=17): 1901 K(x,y / (z * K(u,y))) = K(x,T(y,u) / z). [para(1894(a,1),917(a,1,2,1))]. given #1782 (H,wt=17): 1912 K(x,y) * (z * T(y,x)) = y * T(z,T(y,x)). [para(85(a,1),1891(a,1,2))]. given #1783 (H,wt=17): 1971 K(x \ y,x) * ((y / x) * z) = (x \ y) * z. [para(1940(a,1),197(a,1,1)),flip(a)]. given #1784 (H,wt=17): 1984 K(x \ y,x) * ((x \ y) \ z) = (y / x) \ z. [para(14(a,1),1939(a,1,1,1)),flip(a)]. given #1785 (H,wt=17): 1993 K((x / y) \ 1,z) * y = x * T(x \ y,z). [para(1858(a,1),16(a,1,1))]. given #1786 (H,wt=13): 2001 K((x / y) \ 1,z) = K(y / x,z). [hyper(18,a,1865,a,b,1993,a)]. given #1787 (H,wt=13): 2005 K(x / (y * x),z) = K(y \ 1,z). [para(15(a,1),2001(a,1,1,1)),flip(a)]. given #1788 (H,wt=17): 1995 ((x / y) * z) / (K(y,y \ x) * z) = y \ x. [hyper(70,a,1879,a)]. given #1789 (H,wt=18): 1820 (x * K(y,z)) \ (x * T(y,z)) = L(y,K(y,z),x). [para(1817(a,2),26(a,2,2,2)),flip(a)]. given #1790 (H,wt=18): 1889 L(T(x,y),K(y,x),z) = (z * K(y,x)) \ (z * x). [para(1887(a,1),26(a,2,2,2))]. given #1791 (H,wt=13): 2010 (x * K(y,z)) \ (x * z) = T(z,y). [para(1889(a,1),1784(a,1))]. given #1792 (H,wt=13): 2011 (x * K(y,z)) * T(z,y) = x * z. [para(2010(a,1),14(a,1,2))]. given #1793 (H,wt=13): 2012 (x / y) * K(z,y) = x / T(y,z). [para(2010(a,1),148(a,1,2)),flip(a)]. given #1794 (H,wt=13): 2014 (x * T(y,z)) * K(z,y) = x * y. [hyper(18,a,595,a(flip),b,2011,a)]. given #1795 (H,wt=13): 2019 ((x / y) * T(y,z)) \ x = K(z,y). [hyper(17,a,146,a(flip),b,2014,a),flip(a)]. given #1796 (H,wt=15): 2020 (x * T(x \ y,z)) \ y = K(z,x \ y). [para(57(a,1),2019(a,1,1,1))]. given #1797 (H,wt=17): 2015 (x * K(y \ z,y)) * ((y \ z) \ z) = x * y. [para(86(a,1),2011(a,1,2))]. given #1798 (H,wt=17): 2016 (x * y) / T(T(x,y),z) = y * K(z,T(x,y)). [para(96(a,1),2012(a,1,1)),flip(a)]. given #1799 (H,wt=17): 2022 (K(x \ 1,x) * y) * ((x \ 1) \ 1) = y * x. [para(1133(a,2),2015(a,1,1))]. given #1800 (H,wt=18): 1913 x * T(x \ y,z) != u * y | K(y / x,z) = u. [para(1865(a,1),20(a,1))]. given #1801 (H,wt=18): 1927 x \ y != K(z,x) * u | ((z * x) / z) \ y = u. [para(1915(a,1),19(a,1))]. given #1802 (H,wt=19): 1827 (x * y) * T(K(y,x),z) = x * (y * T(K(y,x),z)). [para(1818(a,2),340(a,1,2,2,1)),flip(a)]. given #1803 (H,wt=19): 1862 L(x * T(x \ 1,y),z,u) = K(L(x,z,u) \ 1,y). [para(1831(a,1),1009(a,1)),flip(a)]. given #1804 (H,wt=17): 2024 L(K(x \ 1,y),z,u) = K(L(x,z,u) \ 1,y). [para(1831(a,1),1862(a,1,1))]. given #1805 (H,wt=17): 2026 K(L(x \ 1,y,z) \ 1,u) = L(K(x,u),y,z). [para(1573(a,1),2024(a,1,1)),flip(a)]. given #1806 (H,wt=17): 2028 K(L(x,y,z) \ 1,x) = K(x \ 1,L(x,y,z)). [para(2024(a,1),1675(a,1))]. given #1807 (H,wt=19): 1868 x * R(K(x,y) * z,u,w) = T(x,y) * R(z,u,w). [para(458(a,2),1853(a,1,2))]. given #1808 (H,wt=17): 2030 T(x,y) * R(T(y,x),z,u) = x * R(y,z,u). [para(1887(a,1),1868(a,1,2,1)),flip(a)]. given #1809 (H,wt=19): 1874 x \ (y * ((z * (y \ x)) / z)) = K(z,(x \ y) \ 1). [para(1799(a,1),777(a,1)),flip(a)]. given #1810 (H,wt=19): 1875 (x * ((y * (x \ z)) / y)) / z = K(y,(x / z) \ 1). [para(1799(a,1),813(a,1)),flip(a)]. given #1811 (H,wt=19): 1876 T(x * ((y * (x \ 1)) / y),z) = K(y,T(x,z) \ 1). [para(1799(a,1),837(a,1)),flip(a)]. given #1812 (H,wt=15): 2034 K(x,T(y,z) \ 1) = T(K(x,y \ 1),z). [para(1799(a,1),1876(a,1,1)),flip(a)]. given #1813 (H,wt=15): 2035 K(x,T(1 / y,z) \ 1) = T(K(x,y),z). [para(59(a,1),2034(a,2,1,2))]. given #1814 (H,wt=15): 2036 K(x,T(y \ 1,z) \ 1) = T(K(x,y),z). [para(929(a,1),2034(a,2,1))]. given #1815 (H,wt=19): 1905 T(x,y) * R(T(y,x),z,u) = R(y,z,u) * T(x,y). [para(1903(a,1),116(a,1,2,1))]. given #1816 (H,wt=15): 2037 R(x,y,z) * T(u,x) = u * R(x,y,z). [para(1905(a,1),2030(a,1))]. given #1817 (H,wt=10): 2039 T(x,R(y,z,u)) = T(x,y). [hyper(165,a,2037,a),flip(a)]. given #1818 (H,wt=12): 2042 x * R(y,x,y) = T(y * x,y). [para(2037(a,1),483(a,1))]. given #1819 (H,wt=12): 2047 T(x,R(y,z,u)) \ x = K(y,x). [para(2039(a,2),1888(a,2,1)),flip(a)]. given #1820 (H,wt=10): 2048 K(R(x,y,z),u) = K(x,u). [para(2047(a,1),1888(a,2))]. given #1821 (H,wt=12): 2050 K(R(x,y,z),u) * x = T(x,u). [para(2048(a,2),1817(a,2,1)),flip(a)]. given #1822 (H,wt=13): 2046 T(x,y * (z \ 1)) = T(x,y / z). [para(224(a,1),2039(a,1,2))]. given #1823 (H,wt=15): 2038 T(x / R(y,z,u),y) = R(y,z,u) \ x. [hyper(177,a,2037,a)]. given #1824 (H,wt=15): 2045 T(x,(y * z) / (u * z)) = T(x,y / u). [para(82(a,1),2039(a,1,2))]. given #1825 (H,wt=15): 2049 K((x * y) / (z * y),u) = K(x / z,u). [para(82(a,1),2048(a,1,1))]. given #1826 (H,wt=17): 2052 T(x,y * T(z,z \ 1)) = T(x,y / (z \ 1)). [para(86(a,2),2046(a,1,2,2))]. given #1827 (H,wt=17): 2053 (x / R(y,z,u)) * y = y * (R(y,z,u) \ x). [para(2038(a,1),85(a,1,2)),flip(a)]. given #1828 (H,wt=17): 2054 T(x,x * T(y,y \ 1)) = T(x,(y \ 1) \ x). [para(2052(a,2),1906(a,1))]. given #1829 (H,wt=13): 2056 T(x,(y \ 1) \ x) = T(x,x * y). [para(2054(a,1),1715(a,1))]. given #1830 (H,wt=11): 2057 T(x,y * x) = T(x,x * y). [para(2056(a,1),1911(a,1)),flip(a)]. given #1831 (H,wt=11): 2058 T(x,(x \ y) * x) = T(x,y). [para(14(a,1),2057(a,2,2))]. given #1832 (H,wt=11): 2059 T(x,x * (y / x)) = T(x,y). [para(16(a,1),2057(a,1,2)),flip(a)]. given #1833 (H,wt=14): 2060 R(T(x,y),x \ y,x) = T(x,x \ y). [para(2058(a,1),406(a,1,1))]. given #1834 (H,wt=14): 2061 L(T(x,y / x),y / x,x) = T(x,y). [para(2059(a,1),293(a,2))]. given #1835 (H,wt=14): 2063 L(T(x,x \ y),y / x,x) = T(x,y). [para(1904(a,1),2061(a,1,1))]. given #1836 (H,wt=18): 2062 R(T(T(x,y),z),x \ y,x) = T(T(x,x \ y),z). [para(2060(a,1),40(a,2,1))]. given #1837 (H,wt=18): 2064 L(T(x,x \ y),y / x,(x \ z) \ z) = T(x,y). [para(2063(a,1),1813(a,2))]. given #1838 (H,wt=18): 2066 L((x \ y) \ y,y / x,(x \ z) \ z) = T(x,y). [para(86(a,1),2064(a,1,1))]. given #1839 (H,wt=13): 2067 K((x \ y) \ y,z) = K(T(x,y),z). [para(2066(a,1),1981(a,1,1)),flip(a)]. given #1840 (H,wt=19): 1929 (x * (K(y,x) * z)) * u = K(y,x) * ((x * z) * u). [para(1918(a,1),197(a,1,1))]. given #1841 (H,wt=19): 1931 (x * y) / T(T(x,z),K(z,x) * y) = K(z,x) * y. [para(1928(a,1),96(a,1,1))]. given #1842 (H,wt=19): 1961 K(x \ (y * T(x,z)),x) = K((y / x) * T(x,z),x). [para(596(a,1),1958(a,1,1))]. given #1843 (H,wt=19): 1975 (x / (y \ 1)) \ K(y,y \ 1) = (x / (1 / y)) \ 1. [para(1457(a,1),1946(a,1,1)),flip(a)]. given #1844 (H,wt=19): 1985 (x * (K(y,x) * z)) \ u = (x * z) \ (K(x,y) * u). [para(1918(a,1),1943(a,1,1))]. given #1845 (H,wt=19): 1986 K(x \ 1,(x \ 1) \ y) = x * T(x \ 1,y * x). [para(1969(a,1),1720(a,1))]. given #1846 (H,wt=19): 1992 T(x,y) * (x \ z) = z * K((z \ (x \ z)) \ 1,y). [para(1856(a,1),174(a,1)),flip(a)]. given #1847 (H,wt=17): 2070 x * K((x \ (y \ x)) \ 1,z) = K(y,z) * x. [para(1992(a,1),1822(a,1))]. given #1848 (H,wt=15): 2071 K((x \ (y \ x)) \ 1,z) = T(K(y,z),x). [hyper(109,a,2070,a),flip(a)]. given #1849 (H,wt=19): 1994 (x * K((x \ y) \ 1,z)) / x = K((y / x) \ 1,z). [para(1856(a,1),1858(a,1,1))]. given #1850 (H,wt=19): 2003 K((x / (y * x)) \ 1,z) * (y * x) = T(y,z) * x. [para(1993(a,2),170(a,1))]. given #1851 (H,wt=19): 2073 (x * K(y \ 1,z)) / x = K(((x * y) / x) \ 1,z). [para(13(a,1),1994(a,1,1,2,1,1))]. given #1852 (H,wt=20): 1991 x * T(x \ y,z) != y * u | K((y \ x) \ 1,z) = u. [para(1856(a,2),19(a,1))]. given #1853 (H,wt=20): 2006 K((x * y) / ((z * x) * y),u) = K(R(z,x,y) \ 1,u). [para(28(a,2),2001(a,1,1,1)),flip(a)]. given #1854 (H,wt=16): 2076 K(R(x,y,z) \ 1,u) = K(y / (x * y),u). [para(2006(a,1),2049(a,1))]. given #1855 (H,wt=14): 2077 K(R(x,y,z) \ 1,u) = K(x \ 1,u). [para(2076(a,2),2005(a,1))]. given #1856 (H,wt=21): 1967 ((T(x,y * z) * y) * z) \ ((x * y) * z) = K(y * z,x). [para(1964(a,1),927(a,2))]. given #1857 (H,wt=21): 1997 x * (T(y,z) * (y \ T(y,x))) = ((y * x) / y) * T(y,z). [para(516(a,1),1884(a,1,2))]. given #1858 (H,wt=19): 2082 ((x * y) / x) * T(x,z) = y * (K(x,z) * T(x,y)). [para(1822(a,1),1997(a,1,2)),flip(a)]. given #1859 (H,wt=21): 2021 (x * (y * T(y \ (x \ z),u))) \ z = K(u,(x * y) \ z). [para(339(a,1),2020(a,1,1))]. given #1860 (H,wt=21): 2029 T(x,y) * R(T(x,y) \ z,u,w) = x * R(x \ z,u,w). [para(1854(a,1),1868(a,1,2,1)),flip(a)]. given #1861 (H,wt=22): 1847 K(R(x,y,z),u) * (R(x,y,z) * w) = R(T(x,u),y,z) * w. [para(40(a,2),1821(a,2,1))]. given #1862 (H,wt=19): 2088 K(x,y) * (R(x,z,u) * w) = R(T(x,y),z,u) * w. [para(2048(a,1),1847(a,1,1))]. given #1863 (H,wt=21): 2089 T(x,y) * (R(x,z,u) * w) = x * (R(T(x,y),z,u) * w). [para(2088(a,1),1853(a,1,2)),flip(a)]. given #1864 (H,wt=22): 2025 (x * y) * K(L(z,y,x) \ 1,u) = x * (y * K(z \ 1,u)). [para(2024(a,1),76(a,1,2))]. given #1865 (H,wt=22): 2051 R(x,y,z) * (u / R(x,y,z)) = u * K(x,R(x,y,z) \ u). [para(2048(a,1),1968(a,1,2)),flip(a)]. given #1866 (H,wt=22): 2074 K((x / (y * x)) \ 1,z) * (y * x) != u * x | T(y,z) = u. [para(2003(a,2),20(a,1))]. given #1867 (H,wt=23): 1852 T(x,y) * (R(x,z,u) * (x \ w)) = K(x,y) * (R(x,z,u) * w). [para(478(a,1),1821(a,1,2)),flip(a)]. given #1868 (H,wt=21): 2093 T(x,y) * (R(x,z,u) * (x \ w)) = R(T(x,y),z,u) * w. [para(1852(a,2),2088(a,1))]. given #1869 (H,wt=21): 2094 R(T(x,y),z,u) * (x * w) = T(x,y) * (R(x,z,u) * w). [para(13(a,1),2093(a,1,2,2)),flip(a)]. given #1870 (H,wt=23): 1880 (x * ((y * z) / y)) \ (z * (K(y,z) * x)) = K((y * z) / y,x). [para(1816(a,1),24(a,2,2)),flip(a)]. given #1871 (H,wt=23): 1947 (x * y) \ ((y * x) * T(K(x,y),z)) = K(y,x) * T(K(x,y),z). [para(1935(a,1),759(a,2,2,1))]. given #1872 (H,wt=23): 2065 K(x,L(T(T(y,y \ z),u),w,v5)) = K(x,L(T(T(y,z),u),w,v5)). [para(2062(a,1),916(a,1,2,1))]. given #1873 (H,wt=23): 2069 ((x / (y \ 1)) \ 1) \ K(y \ 1,y) = ((x / (1 / y)) \ 1) \ 1. [para(1975(a,1),1723(a,1,1)),flip(a)]. given #1874 (H,wt=23): 2095 (x * y) \ (y * (x * T(K(x,y),z))) = K(y,x) * T(K(x,y),z). [para(1827(a,1),1947(a,1,2))]. given #1875 (H,wt=24): 1842 R(K(x,y),x,(x * K(x,y)) \ z) \ z = x * ((x * K(x,y)) \ z). [para(1833(a,1),258(a,1,1,1))]. given #1876 (H,wt=15): 2096 x * ((x * K(x,y)) \ z) = K(x,y) \ z. [para(272(a,1),1842(a,1,1)),flip(a)]. given #1877 (H,wt=15): 2097 (x * K(x,y)) \ z = x \ (K(x,y) \ z). [hyper(66,a,2096,a),flip(a)]. given #1878 (H,wt=21): 2099 (x \ 1) \ (K(x \ 1,y) \ z) = (x \ K(x \ 1,y)) \ z. [para(1517(a,1),2097(a,1,1)),flip(a)]. given #1879 (H,wt=19): 2100 (x \ K(x \ 1,y)) \ 1 = (x \ 1) \ K(y,x \ 1). [para(1935(a,1),2099(a,1,2)),flip(a)]. given #1880 (H,wt=24): 1980 (x * (y / x)) \ (y * (K(x,x \ y) * z)) = L(z,K(x,x \ y),y). [para(1968(a,1),26(a,2,1)),flip(a)]. given #1881 (H,wt=24): 2101 L(K(x \ y,x) * z,K(x,x \ y),y) = (x * (y / x)) \ (y * z). [para(1930(a,1),1980(a,1,2,2)),flip(a)]. given #1882 (H,wt=25): 2041 (T(x,x * y) * y) * R(T(x,y),z,u) = R(T(x,y),z,u) * (x * y). [para(377(a,1),2037(a,1,2)),flip(a)]. given #1883 (H,wt=25): 2083 (x * (y \ ((z \ (y * (x \ u))) * z))) \ u = K(z,(x * (y \ z)) \ u). [para(371(a,1),2021(a,1,1,2))]. given #1884 (H,wt=25): 2084 (x * (((y \ ((x \ z) * u)) * y) / u)) \ z = K(y,(x * (y / u)) \ z). [para(629(a,1),2021(a,1,1,2))]. given #1885 (H,wt=25): 2092 (x * y) * z != x * (y * K(u \ 1,w)) | K(L(u,y,x) \ 1,w) = z. [para(2025(a,1),19(a,1)),flip(a)]. given #1886 (H,wt=25): 2102 (T(x,x * y) * y) * R(T(x,y),z,u) = T(x,y) * (R(x,z,u) * y). [para(2041(a,2),2094(a,1))]. given #1887 (H,wt=25): 2103 (x * (y \ ((z \ (y * (x \ u))) * z))) \ u = K(z,(x * (z / y)) \ u). [para(1776(a,1),2084(a,1,1,2))]. given #1888 (H,wt=19): 2105 K(x,(y * (x / z)) \ u) = K(x,(y * (z \ x)) \ u). [para(2103(a,1),2083(a,1))]. given #1889 (H,wt=25): 2104 (T(x,x * y) * y) * R(T(x,y),z,u) = x * (R(T(x,y),z,u) * y). [para(2102(a,2),2089(a,1))]. given #1890 (H,wt=26): 1798 T((((x * (y / z)) / x) * z) / y,y / z) = R(K(x,y / z),y / z,z). [para(1792(a,2),349(a,1,1)),flip(a)]. given #1891 (H,wt=26): 1881 R(x \ y,z,u) * (K(x,R(x \ y,z,u)) * w) = R(y / x,z,u) * w. [para(321(a,1),1816(a,1,1)),flip(a)]. given #1892 (H,wt=23): 2107 R(x \ y,z,u) * (K(x,x \ y) * w) = R(y / x,z,u) * w. [para(915(a,1),1881(a,1,2,1))]. given #1893 (H,wt=26): 2106 T((x * ((y * (x \ z)) / y)) / z,z / x) = R(K(y,z / x),z / x,x). [para(326(a,1),1798(a,1,1,1))]. given #1894 (H,wt=22): 2112 T(K(x,(y / z) \ 1),z / y) = R(K(x,z / y),z / y,y). [para(1875(a,1),2106(a,1,1))]. given #1895 (H,wt=22): 2113 R(K(x,y / z),y / z,z) = K(x,T(z / y,y / z) \ 1). [para(2112(a,1),2034(a,2)),flip(a)]. given #1896 (H,wt=22): 2114 R(K(x,y / z),y / z,z) = K(x,T((z / y) \ 1,y \ z)). [para(1538(a,1),2113(a,2,2))]. given #1897 (H,wt=18): 2115 R(K(x,y / z),y / z,z) = K(x,(z / y) \ 1). [para(2114(a,2),1532(a,1))]. given #1898 (H,wt=13): 2116 K(x,(y / z) \ 1) = K(x,z / y). [para(2115(a,1),272(a,1))]. given #1899 (H,wt=13): 2117 K(x,y / (z * y)) = K(x,z \ 1). [para(15(a,1),2116(a,1,2,1)),flip(a)]. given #1900 (H,wt=13): 2119 K(x,(y \ z) / z) = K(x,y \ 1). [para(57(a,1),2116(a,1,2,1)),flip(a)]. given #1901 (H,wt=17): 2122 (x * ((y * (x \ z)) / y)) / z = K(y,z / x). [para(2116(a,1),1875(a,2))]. given #1902 (H,wt=19): 2121 K(x,T(1 / y,z) \ 1) = K(x,y / K(y \ 1,z)). [para(1855(a,1),2116(a,1,2,1))]. given #1903 (H,wt=15): 2124 K(x,y / K(y \ 1,z)) = T(K(x,y),z). [para(2121(a,1),2035(a,1))]. given #1904 (H,wt=20): 2118 K(x,(y * z) / ((u * y) * z)) = K(x,R(u,y,z) \ 1). [para(28(a,2),2116(a,1,2,1)),flip(a)]. given #1905 (H,wt=16): 2125 K(x,R(y,z,u) \ 1) = K(x,z / (y * z)). [para(2118(a,1),917(a,1))]. given #1906 (H,wt=14): 2127 K(x,R(y,z,u) \ 1) = K(x,y \ 1). [para(2125(a,2),2117(a,1))]. given #1907 (H,wt=25): 2123 K((x / (y * x)) \ 1,z / (u * z)) * (y * x) = T(y,u \ 1) * x. [para(2117(a,2),2003(a,1,1))]. given #1908 (H,wt=13): 2129 T(x,y / (z * y)) = T(x,z \ 1). [hyper(2074,a,2123,a)]. given #1909 (H,wt=13): 2132 T(x,(y \ z) / z) = T(x,y \ 1). [para(14(a,1),2129(a,1,2,2))]. given #1910 (H,wt=13): 2136 T(x,x \ (y \ x)) = T(x,y \ 1). [para(2132(a,1),1904(a,1)),flip(a)]. given #1911 (H,wt=15): 2134 x \ T(y,x \ 1) = y * ((x \ y) / y). [para(2129(a,1),587(a,1,2))]. given #1912 (H,wt=15): 2137 K(x,T(y,z \ 1)) = K(x,T(y,z \ y)). [para(2136(a,1),924(a,1,2))]. given #1913 (H,wt=17): 2140 K(x,T(y * z,y \ 1)) = K(x,T(y * z,z)). [para(13(a,1),2137(a,2,2,2))]. given #1914 (H,wt=18): 2138 x * R(1 / y,y,y \ x) = y \ T(x,y \ 1). [para(161(a,2),2134(a,2,2)),flip(a)]. given #1915 (H,wt=20): 2133 T(x,(y * z) / ((u * y) * z)) = T(x,R(u,y,z) \ 1). [para(81(a,1),2129(a,1,2,2))]. given #1916 (H,wt=16): 2142 T(x,R(y,z,u) \ 1) = T(x,z / (y * z)). [para(2133(a,1),2045(a,1))]. given #1917 (H,wt=14): 2144 T(x,R(y,z,u) \ 1) = T(x,y \ 1). [para(2142(a,2),2129(a,1))]. given #1918 (H,wt=17): 2145 T(R(x,y,z) \ 1,x \ 1) = R(x,y,z) \ 1. [para(2144(a,1),84(a,1))]. given #1919 (H,wt=19): 2147 T(R(x \ 1,y,z) \ 1,x) = R(x \ 1,y,z) \ 1. [para(2145(a,1),1460(a,1)),flip(a)]. given #1920 (H,wt=21): 2148 (x * (R(x \ 1,y,z) \ 1)) / x = R(x \ 1,y,z) \ 1. [para(2147(a,1),106(a,1,1,2))]. given #1921 (H,wt=24): 2141 x * R(1 / (1 / y),1 / y,(1 / y) \ x) = (1 / y) \ T(x,y). [para(59(a,1),2138(a,2,2,2))]. given #1922 (H,wt=24): 2150 x * R(1 / (1 / y),y \ 1,(1 / y) \ x) = (1 / y) \ T(x,y). [para(1714(a,1),2141(a,1,2))]. given #1923 (H,wt=23): 2151 K(x,((y \ 1) \ x) / x) = ((1 / y) \ x) \ ((1 / y) \ T(x,y)). [para(2150(a,1),1751(a,1,2)),flip(a)]. given #1924 (H,wt=28): 2055 ((1 / x) * (R(1 / x,y,z) \ u)) * x = R(u / R(1 / x,y,z),x \ 1,x). [para(2053(a,1),1483(a,1,1))]. given #1925 (H,wt=28): 2068 (x * (K(y,x) * (z * u))) \ (K(y,x) * ((x * z) * u)) = a(x,K(y,x) * z,u). [para(1929(a,1),276(a,1,2))]. given #1926 (H,wt=28): 2152 (x * (y * z)) \ (K(x,u) * (K(u,x) * ((x * y) * z))) = a(x,K(u,x) * y,z). [para(2068(a,1),1985(a,1)),flip(a)]. given #1927 (H,wt=20): 2153 a(x,K(y,x) * z,u) = (x * (z * u)) \ ((x * z) * u). [para(1930(a,1),2152(a,1,2)),flip(a)]. given #1928 (H,wt=13): 2154 a(x,K(y,x) * z,u) = a(x,z,u). [para(2153(a,2),22(a,2)),flip(a)]. given #1929 (H,wt=11): 2156 a(x,T(y,x),z) = a(x,y,z). [para(1817(a,2),2154(a,1,2))]. given #1930 (H,wt=29): 2031 R((x * ((y * (x \ z)) / y)) / z,u,w) * z = z * R(K(y,(z \ x) \ 1),u,w). [para(1874(a,1),264(a,2,2,1))]. given #1931 (H,wt=23): 2157 x * R(K(y,(x \ z) \ 1),u,w) = R(K(y,x / z),u,w) * x. [para(2122(a,1),2031(a,1,1,1)),flip(a)]. given #1932 (H,wt=20): 2158 x * R(K(y,(x \ z) \ 1),u,w) = K(y,x / z) * x. [para(272(a,1),2157(a,2,1))]. given #1933 (H,wt=17): 2159 x * K(y,(x \ z) \ 1) = K(y,x / z) * x. [para(157(a,1),2158(a,1,2))]. given #1934 (H,wt=15): 2161 T(K(x,y / z),y) = K(x,(y \ z) \ 1). [hyper(109,a,2159,a)]. given #1935 (H,wt=17): 2162 K(x,y / (y * z)) * y = y * K(x,z \ 1). [para(13(a,1),2159(a,1,2,2,1)),flip(a)]. given #1936 (H,wt=15): 2164 K(x,y \ 1) * y = y * K(x,y \ 1). [para(2117(a,1),2162(a,1,1))]. given #1937 (H,wt=28): 2163 K(x,(y * z) / (y * (z * u))) * (y * z) = (y * z) * K(x,L(u,z,y) \ 1). [para(26(a,2),2159(a,1,2,2,1)),flip(a)]. given #1938 (H,wt=31): 1932 (x * y) \ ((K(x \ z,x) * y) * ((x \ z) \ z)) = K(K(x \ z,x) * y,(x \ z) \ z). [para(1928(a,1),442(a,1,1))]. given #1939 (H,wt=21): 2165 K(K(x \ 1,x) * y,(x \ 1) \ 1) = (x * y) \ (y * x). [para(2022(a,1),1932(a,1,2)),flip(a)]. given #1940 (H,wt=17): 2166 K(K(x \ 1,x) * y,(x \ 1) \ 1) = K(y,x). [para(2165(a,2),24(a,2)),flip(a)]. given #1941 (H,wt=17): 2167 K(K(x,x \ 1) * y,x) = K(y,(x \ 1) \ 1). [para(448(a,1),2166(a,1,1)),flip(a)]. given #1942 (H,wt=13): 2168 K(K(x,x \ 1) * y,x) = K(y,x). [para(2167(a,2),929(a,1))]. given #1943 (H,wt=15): 2169 K((1 / x) * y,x) = K((x \ 1) * y,x). [para(453(a,1),2168(a,1,1))]. given #1944 (H,wt=17): 2170 K(T(K(x,x \ 1) * y,x),x) = K(T(y,x),x). [para(983(a,2),2168(a,1,1))]. given #1945 (H,wt=19): 2171 K(T((1 / x) * y,x),x) = K(T((x \ 1) * y,x),x). [para(453(a,1),2170(a,1,1,1))]. given #1946 (H,wt=32): 2091 (x * (R(T(x,y),z,u) * y)) \ ((x * y) * R(T(x,y),z,u)) = K(R(x,z,u) * y,T(x,y)). [para(2089(a,1),765(a,1,1))]. given #1947 (H,wt=33): 1983 (x \ (K(y \ 1,y) * z)) / (((u * (x * K(y,y \ 1))) / u) \ z) = K(u,x * K(y,y \ 1)). [para(1214(a,1),1925(a,1,1))]. given #1948 (H,wt=33): 2085 T(x,y) * (z * R(z \ (T(x,y) \ u),w,v5)) = z * (T(x,z) * R(T(x,z) \ (z \ u),w,v5)). [para(2029(a,1),1021(a,1,2)),flip(a)]. given #1949 (H,wt=29): 2172 T(x,y) * (z * R(z \ (T(x,y) \ u),w,v5)) = z * (x * R(x \ (z \ u),w,v5)). [para(2029(a,1),2085(a,2,2))]. given #1950 (H,wt=33): 2086 ((x \ y) \ y) * (z * R(z \ (T(x,x \ y) \ (u * z)),w,v5)) = (x * R(x \ u,w,v5)) * z. [para(2029(a,1),707(a,2,1))]. given #1951 (H,wt=33): 2174 ((x \ y) \ y) * (z * R(z \ (T(x,x \ y) \ u),w,v5)) = z * (x * R(x \ (z \ u),w,v5)). [para(86(a,1),2172(a,1,1))]. given #1952 (H,wt=25): 2177 x * (y * R(y \ (x \ (z * x)),u,w)) = (y * R(y \ z,u,w)) * x. [para(2174(a,1),2086(a,1))]. given #1953 (H,wt=23): 2178 x * (y * R(y \ T(z,x),u,w)) = (y * R(y \ z,u,w)) * x. [para(30(a,2),2177(a,1,2,2,1,2))]. given #1954 (H,wt=21): 2179 T(x * R(x \ y,z,u),w) = x * R(x \ T(y,w),z,u). [hyper(109,a,2178,a)]. given #1955 (H,wt=19): 2181 T(x * R(x \ y,z,u),y) = x * R(x \ y,z,u). [para(84(a,1),2179(a,2,2,1,2))]. given #1956 (H,wt=25): 2180 K(x,y) * (z * R(z \ x,u,w)) = (z * R(z \ x,u,w)) * K(x,y). [para(1830(a,1),2178(a,1,2,2,1,2))]. given #1957 (H,wt=34): 2072 ((K(x,y) * z) * u) / (z * (K((z \ (x \ z)) \ 1,y) * u)) = a(z,K((z \ (x \ z)) \ 1,y),u). [para(2070(a,1),1246(a,2,1,1)),flip(a)]. given #1958 (H,wt=34): 2182 (K(x,y) * (z * u)) / (z * (K((z \ (x \ z)) \ 1,y) * u)) = a(z,K((z \ (x \ z)) \ 1,y),u). [para(197(a,1),2072(a,1,1))]. given #1959 (H,wt=30): 2183 (K(x,y) * (z * u)) / (z * (T(K(x,y),z) * u)) = a(z,K((z \ (x \ z)) \ 1,y),u). [para(2071(a,1),2182(a,1,2,2,1))]. given #1960 (H,wt=30): 2184 K(x,y) * ((z * u) / (z * (T(K(x,y),z) * u))) = a(z,K((z \ (x \ z)) \ 1,y),u). [para(2183(a,1),281(a,1)),flip(a)]. given #1961 (H,wt=26): 2185 K(x,y) * ((z * u) / (z * (T(K(x,y),z) * u))) = a(z,T(K(x,y),z),u). [para(2071(a,1),2184(a,2,2))]. given #1962 (H,wt=24): 2186 K(x,y) * ((z * u) / (z * (T(K(x,y),z) * u))) = a(z,K(x,y),u). [para(2185(a,2),2156(a,1))]. given #1963 (H,wt=35): 2149 ((x \ 1) * (R((x \ 1) \ 1,y,z) \ 1)) / (1 / x) = K(x \ 1,x) * (R((x \ 1) \ 1,y,z) \ 1). [para(2148(a,1),1457(a,1,2)),flip(a)]. given #1964 (H,wt=38): 2032 (x * y) \ ((x * (z \ y)) * ((u * L(T(z,z \ y),z \ y,x)) / u)) = K(u,((x * y) \ (x * (z \ y))) \ 1). [para(144(a,2),1874(a,1,2,2,1,2))]. given #1965 (H,wt=38): 2081 ((T(R(x,y,z),u * T(x,u)) * u) * T(x,u)) \ ((x * u) * R(T(x,u),y,z)) = K(u * T(x,u),R(x,y,z)). [para(764(a,1),1967(a,1,2))]. given #1966 (H,wt=36): 2188 ((T(R(x,y,z),x * u) * u) * T(x,u)) \ ((x * u) * R(T(x,u),y,z)) = K(u * T(x,u),R(x,y,z)). [para(85(a,1),2081(a,1,1,1,1,2))]. given #1967 (H,wt=36): 2189 ((R(T(x,x * y),z,u) * y) * T(x,y)) \ ((x * y) * R(T(x,y),z,u)) = K(y * T(x,y),R(x,z,u)). [para(40(a,2),2188(a,1,1,1,1))]. given #1968 (H,wt=38): 2110 (R(x / y,z,u) * w) / R(y \ x,z,u) = (K(y,y \ x) * w) * K(R(y \ x,z,u),K(y,y \ x) * w). [para(2107(a,1),1796(a,1,1))]. given #1969 (H,wt=35): 2190 (R(x / y,z,u) * w) / R(y \ x,z,u) = (K(y,y \ x) * w) * K(y \ x,K(y,y \ x) * w). [para(2048(a,1),2110(a,2,2))]. given #1970 (H,wt=38): 2187 (x * y) \ ((x * (z \ y)) * L((u * T(z,z \ y)) / u,z \ y,x)) = K(u,((x * y) \ (x * (z \ y))) \ 1). [para(327(a,2),2032(a,1,2,2))]. given #1971 (H,wt=38): 2192 (x * y) \ ((x * (z \ y)) * L(T((u * z) / u,z \ y),z \ y,x)) = K(u,((x * y) \ (x * (z \ y))) \ 1). [para(178(a,1),2187(a,1,2,2,1))]. given #1972 (H,wt=33): 2193 (x * y) \ (x * ((z \ y) * T((u * z) / u,z \ y))) = K(u,((x * y) \ (x * (z \ y))) \ 1). [para(76(a,1),2192(a,1,2))]. given #1973 (H,wt=29): 2194 (x * y) \ (x * (((z * u) / z) * (u \ y))) = K(z,((x * y) \ (x * (u \ y))) \ 1). [para(85(a,1),2193(a,1,2,2))]. given #1974 (H,wt=25): 2195 K(x,((y * z) \ (y * (u \ z))) \ 1) = (y * z) \ (y * (K(x,u) * z)). [para(1794(a,1),2194(a,1,2,2)),flip(a)]. given #1975 (H,wt=22): 2196 K(x,((y * z) \ (y * (u \ z))) \ 1) = L(T(K(x,u),z),z,y). [para(2195(a,2),112(a,1))]. given #1976 (H,wt=39): 2009 (K(x,x \ y) * z) * K((K(x,x \ y) * z) \ ((y / x) * z),K(x,x \ y) * z) = ((y / x) * z) / (x \ y). [para(1995(a,1),1963(a,1,2)),flip(a)]. given #1977 (H,wt=39): 2033 x * (y * R(y \ (x \ (z * ((u * (z \ (x * y))) / u))),w,v5)) = (x * y) * R(K(u,((x * y) \ z) \ 1),w,v5). [para(1874(a,1),662(a,1,2,1)),flip(a)]. given #1978 (H,wt=34): 2198 x * (y * R(y \ (x \ (z * ((u * (z \ (x * y))) / u))),w,v5)) = K(u,(x * y) / z) * (x * y). [para(2033(a,2),2158(a,1))]. given #1979 (H,wt=34): 2199 x * (y * R(y \ ((x \ z) * ((u * ((x \ z) \ y)) / u)),w,v5)) = K(u,(x * y) / z) * (x * y). [para(761(a,1),2198(a,1,2,2,1,2))]. given #1980 (H,wt=28): 2201 x * (y * R(K(z,(y \ (x \ u)) \ 1),w,v5)) = K(z,(x * y) / u) * (x * y). [para(1874(a,1),2199(a,1,2,2,1))]. given #1981 (H,wt=23): 2202 K(x,(y * z) / u) * (y * z) = y * (K(x,z / (y \ u)) * z). [para(2158(a,1),2201(a,1,2)),flip(a)]. given #1982 (H,wt=28): 2203 x * (K(y,z / (x \ (x * (z * u)))) * z) = (x * z) * K(y,L(u,z,x) \ 1). [para(2202(a,1),2163(a,1))]. given #1983 (H,wt=24): 2204 (x * y) * K(z,L(u,y,x) \ 1) = x * (K(z,y / (y * u)) * y). [para(13(a,1),2203(a,1,2,1,2,2)),flip(a)]. given #1984 (H,wt=22): 2206 (x * y) * K(z,L(u,y,x) \ 1) = x * (y * K(z,u \ 1)). [para(2162(a,1),2204(a,2,2))]. given #1985 (H,wt=17): 2208 L(K(x,y \ 1),z,u) = K(x,L(y,z,u) \ 1). [hyper(192,a,2206,a)]. given #1986 (H,wt=17): 2209 K(x,L(1 / y,z,u) \ 1) = L(K(x,y),z,u). [para(59(a,1),2208(a,1,1,2)),flip(a)]. given #1987 (H,wt=17): 2210 K(x,L(y \ 1,z,u) \ 1) = L(K(x,y),z,u). [para(929(a,1),2208(a,1,1)),flip(a)]. given #1988 (H,wt=19): 2213 K(L(1 / x,y,z) \ 1,u) = L(K(u,x),y,z) \ 1. [para(2209(a,1),1935(a,1,1)),flip(a)]. given #1989 (H,wt=19): 2214 K(L(x \ 1,y,z) \ 1,u) = L(K(u,x),y,z) \ 1. [para(2210(a,1),1935(a,1,1)),flip(a)]. given #1990 (H,wt=15): 2215 L(K(x,y),z,u) \ 1 = L(K(y,x),z,u). [para(2214(a,1),2026(a,1))]. given #1991 (H,wt=12): 2217 L(K(x,y),x,z) = K(y,x) \ 1. [para(1988(a,1),2215(a,1,1)),flip(a)]. given #1992 (H,wt=10): 2218 L(K(x,y),x,z) = K(x,y). [para(2217(a,2),1935(a,1))]. given #1993 (H,wt=13): 2221 (x * y) \ (x * T(y,z)) = K(y,z). [para(2218(a,1),1826(a,2))]. given #1994 (H,wt=13): 2222 (x * y) * K(y,z) = x * T(y,z). [para(2221(a,1),14(a,1,2))]. given #1995 (H,wt=13): 2227 (x / y) * T(y,z) = x * K(y,z). [para(16(a,1),2222(a,1,1)),flip(a)]. given #1996 (H,wt=11): 2231 (x * K(y,z)) \ x = K(z,y). [para(2227(a,1),2019(a,1,1))]. given #1997 (H,wt=11): 2233 (x * K(y,z)) * K(z,y) = x. [para(2231(a,1),14(a,1,2))]. given #1998 (H,wt=11): 2234 x / K(y,z) = x * K(z,y). [para(2231(a,1),57(a,1,2))]. given #1999 (H,wt=13): 2230 (x * K(y,z)) \ (x * T(y,z)) = y. [para(2227(a,1),593(a,1,1))]. given #2000 (H,wt=8): 2241 L(x,K(x,y),z) = x. [para(2230(a,1),1820(a,1)),flip(a)]. given #2001 (H,wt=15): 2223 x \ (y * T(y \ x,z)) = K(y \ x,z). [para(14(a,1),2221(a,1,1))]. given #2002 (H,wt=15): 2226 x * T(x \ y,z) = y * K(x \ y,z). [para(14(a,1),2222(a,1,1)),flip(a)]. given #2003 (H,wt=13): 2246 K((x \ y) \ 1,z) = K(y \ x,z). [hyper(1991,a,2226,a)]. given #2004 (H,wt=13): 2249 K(x \ (x / y),z) = K(y \ 1,z). [para(59(a,1),2246(a,1,1,1)),flip(a)]. given #2005 (H,wt=13): 2252 K((x \ y) \ y,z) = T(K(x,z),y). [para(2246(a,1),2071(a,1))]. given #2006 (H,wt=11): 2261 K(T(x,y),z) = T(K(x,z),y). [para(2252(a,1),2067(a,1)),flip(a)]. given #2007 (H,wt=11): 2262 T(K(x,y),K(x,z)) = K(x,y). [para(1830(a,1),2261(a,1,1)),flip(a)]. given #2008 (H,wt=13): 2258 T(K(x / y,z),x) = K(y \ x,z). [para(59(a,1),2252(a,1,1,1)),flip(a)]. given #2009 (H,wt=13): 2260 T(K(x,y),z * x) = K(T(x,z),y). [para(1902(a,2),2252(a,1,1)),flip(a)]. given #2010 (H,wt=13): 2263 T(K(x,y),z) \ 1 = K(y,T(x,z)). [para(2261(a,1),1935(a,1,1))]. given #2011 (H,wt=15): 2239 (x * ((y * z) / y)) * K(z,y) = x * z. [para(2234(a,1),1914(a,1))]. given #2012 (H,wt=15): 2240 K(x,y * K(z,y \ 1)) = T(K(x,y),z). [para(2234(a,1),2124(a,1,2))]. given #2013 (H,wt=15): 2256 K(T(x,y) \ 1,z) = T(K(x \ 1,z),y). [para(2249(a,1),1860(a,1))]. given #2014 (H,wt=15): 2264 K(x,y) * K(y,T(x,z)) = K(z,K(x,y)). [para(2263(a,1),1898(a,2,2)),flip(a)]. given #2015 (H,wt=15): 2265 (x * ((y * z) / y)) \ (x * z) = K(z,y). [hyper(66,a,2239,a)]. given #2016 (H,wt=15): 2266 K(T(x \ 1,y) \ 1,z) = T(K(x,z),y). [para(1573(a,1),2256(a,2,1))]. given #2017 (H,wt=17): 2229 K(x,y) * (z * T(y,x)) = T(z * y,K(y,x)). [para(2222(a,1),1934(a,1,2))]. given #2018 (H,wt=15): 2269 T(x * y,K(y,z)) = y * T(x,T(y,z)). [para(2229(a,1),1912(a,1))]. given #2019 (H,wt=17): 2232 x * (K(y,z) * T(y,x)) = (y * x) * K(y,z). [para(2227(a,1),2082(a,1)),flip(a)]. given #2020 (H,wt=17): 2253 (x \ (x / y)) * x = (x / y) * K(y \ 1,x). [para(2249(a,1),136(a,1,2)),flip(a)]. given #2021 (H,wt=17): 2268 K(x,y) * K(y,T(x,z)) = K(x * z,K(x,y)). [para(922(a,1),2264(a,1,2))]. given #2022 (H,wt=13): 2271 K(x * y,K(x,z)) = K(y,K(x,z)). [para(2268(a,1),2264(a,1))]. given #2023 (H,wt=19): 2251 K(L(x \ y,z,u) \ 1,w) = L(K(y \ x,w),z,u). [para(2246(a,1),2024(a,1,1)),flip(a)]. given #2024 (H,wt=20): 2250 K(L(x \ y,x,z) \ 1,u) = K((z * y) \ (z * x),u). [para(78(a,2),2246(a,1,1,1))]. given #2025 (H,wt=18): 2272 L(K(x \ y,z),y,u) = K((u * x) \ (u * y),z). [para(2250(a,1),2251(a,1)),flip(a)]. given #2026 (H,wt=18): 2273 K((x * (y / z)) \ (x * y),u) = L(K(z,u),y,x). [para(59(a,1),2272(a,1,1,1)),flip(a)]. given #2027 (H,wt=15): 2274 K(L(x,y / x,z),u) = L(K(x,u),y,z). [para(79(a,2),2273(a,1,1))]. given #2028 (H,wt=10): 2275 L(K(x,y),z,x) = K(x,y). [para(2274(a,1),1981(a,1))]. given #2029 (H,wt=15): 2277 (x * y) * K(x,z) = x * (y * K(x,z)). [para(2275(a,1),76(a,1,2))]. given #2030 (H,wt=17): 2278 x * (K(y,z) * T(y,x)) = y * (x * K(y,z)). [para(2277(a,1),2232(a,2))]. given #2031 (H,wt=19): 2276 x * K(y,L(z,u / z,w)) = x / L(K(z,y),u,w). [para(2274(a,1),2234(a,1,2)),flip(a)]. given #2032 (H,wt=20): 2279 x \ (y * (x * K(y,z))) != K(y,z) * u | T(y,x) = u. [para(2278(a,1),65(a,1,2)),flip(b)]. given #2033 (H,wt=21): 2207 K(L(x,y,z) \ 1,u \ 1) = K(x \ 1,L(u,y,z) \ 1). [hyper(2092,a,2206,a)]. given #2034 (H,wt=21): 2237 (x * K(L(y \ 1,z,u) \ 1,w)) \ x = L(K(w,y),z,u). [para(2231(a,2),2210(a,1))]. given #2035 (H,wt=17): 2281 (x * L(K(y,z),u,w)) \ x = L(K(z,y),u,w). [para(2026(a,1),2237(a,1,1,2))]. given #2036 (H,wt=17): 2282 x / L(K(y,z),u,w) = x * L(K(z,y),u,w). [para(2281(a,1),57(a,1,2))]. given #2037 (H,wt=15): 2284 K(x,L(y,z / y,u)) = L(K(x,y),z,u). [hyper(17,a,2276,a,b,2282,a(flip)),flip(a)]. given #2038 (H,wt=15): 2286 L(K(x,y),z * y,u) = K(x,L(y,z,u)). [para(15(a,1),2284(a,1,2,2)),flip(a)]. given #2039 (H,wt=10): 2288 K(x,L(y,z,x)) = K(x,y). [para(2286(a,1),2275(a,1))]. given #2040 (H,wt=15): 2289 K(x,(x * y) \ z) = K(x,y \ (x \ z)). [para(128(a,1),2288(a,1,2))]. given #2041 (H,wt=21): 2242 x \ (y * (x * K(y,z))) = K(y,z) * T(y,x * K(y,z)). [para(2241(a,1),262(a,1,2,1))]. given #2042 (H,wt=11): 2292 T(x,y * K(x,z)) = T(x,y). [hyper(2279,a,2242,a),flip(a)]. given #2043 (H,wt=11): 2293 T(x,y * K(z,x)) = T(x,y). [para(2233(a,1),2292(a,1,2)),flip(a)]. given #2044 (H,wt=11): 2294 T(x,K(y,x) * z) = T(x,z). [para(2070(a,1),2293(a,1,2))]. given #2045 (H,wt=11): 2296 T(x,K(x,y) * z) = T(x,z). [para(1930(a,1),2294(a,1,2)),flip(a)]. given #2046 (H,wt=15): 2295 T(T(x,y),K(z,x) * u) = T(T(x,u),y). [para(2294(a,1),36(a,1,1)),flip(a)]. given #2047 (H,wt=15): 2297 (x * y) / T(T(x,y),z) = K(z,x) * y. [para(2295(a,1),1931(a,1,2))]. given #2048 (H,wt=13): 2298 x * K(y,T(z,x)) = K(y,z) * x. [para(2297(a,1),2016(a,1)),flip(a)]. given #2049 (H,wt=11): 2300 K(x,T(y,z)) = T(K(x,y),z). [hyper(109,a,2298,a),flip(a)]. given #2050 (H,wt=11): 2305 K(T(x,y),z) = K(x,T(z,y)). [para(2300(a,2),2261(a,2))]. given #2051 (H,wt=13): 2302 T(K(x,y),z * y) = K(x,T(y,z)). [para(2300(a,1),926(a,1))]. given #2052 (H,wt=13): 2303 T(K(x,y / z),y) = K(x,z \ y). [para(2300(a,1),941(a,1))]. given #2053 (H,wt=13): 2304 x * T(K(x,y),z) = T(x,T(y,z)). [para(2300(a,1),1825(a,2,2)),flip(a)]. given #2054 (H,wt=13): 2307 K(x / y,T(z,y)) = K(y \ x,z). [para(87(a,1),2305(a,1,1)),flip(a)]. given #2055 (H,wt=13): 2308 K(T(x,y),K(y,z)) = K(x,K(y,z)). [para(1832(a,1),2305(a,2,2))]. given #2056 (H,wt=13): 2309 T(K(x,y),z * x) = K(x,T(y,z)). [para(2305(a,1),2260(a,2))]. given #2057 (H,wt=13): 2310 T(K(x,y),z * y) = T(K(x,y),z). [para(2302(a,2),2300(a,1))]. given #2058 (H,wt=13): 2311 K(x,(y \ z) \ 1) = K(x,z \ y). [para(2303(a,1),2161(a,1)),flip(a)]. given #2059 (H,wt=13): 2314 T(K(x,y),z / y) = T(K(x,y),z). [para(16(a,1),2310(a,1,2)),flip(a)]. given #2060 (H,wt=13): 2315 K(x,(y * z) \ y) = K(x,z \ 1). [para(13(a,1),2311(a,1,2,1)),flip(a)]. given #2061 (H,wt=15): 2301 K(x,y) * K(z,x) = K(z,x) * K(x,y). [para(1830(a,1),2298(a,1,2,2))]. given #2062 (H,wt=15): 2306 K(x,y) * T(K(y,x),z) = K(z,K(x,y)). [para(2300(a,1),2264(a,1,2))]. given #2063 (H,wt=11): 2317 K(K(x,y),z) = K(z,K(y,x)). [para(2306(a,1),1941(a,1)),flip(a)]. given #2064 (H,wt=13): 2319 K(x,K(y,z)) * K(x,K(z,y)) = 1. [para(2317(a,1),1938(a,1,1))]. given #2065 (H,wt=15): 2312 K(x / T(y,z),y) = K(T(y,z) \ x,y). [para(122(a,1),2307(a,1,2))]. given #2066 (H,wt=15): 2320 T(K(x,y),z) * K(y,x) = K(z,K(y,x)). [para(2317(a,1),1949(a,2))]. given #2067 (H,wt=17): 2313 K(x,T((y * x) / z,y)) = K(x,z \ (y * x)). [para(2309(a,1),2303(a,1))]. given #2068 (H,wt=17): 2321 K(x,T(y / (z / x),y)) = K(x,z \ (y * x)). [para(2313(a,1),925(a,1)),flip(a)]. given #2069 (H,wt=15): 2322 K(x,(y / x) \ z) = K(x,y \ (z * x)). [para(2321(a,1),941(a,1)),flip(a)]. given #2070 (H,wt=19): 2318 (x * y) \ (y * (x * T(K(x,y),z))) = K(z,K(y,x)). [para(2306(a,1),2095(a,2))]. given #2071 (H,wt=17): 2323 (x * y) \ (y * T(x,T(y,z))) = K(z,K(y,x)). [para(2304(a,1),2318(a,1,2,2))]. given #2072 (H,wt=17): 2324 (x * y) \ T(x * y,K(y,z)) = K(z,K(y,x)). [para(2269(a,2),2323(a,1,2))]. given #2073 (H,wt=13): 2325 K(x * y,K(y,z)) = K(z,K(y,x)). [para(2324(a,1),1818(a,2))]. given #2074 (H,wt=21): 2245 x \ (K(y,z) * ((T(y,z) \ x) * y)) = K(T(y,z) \ x,y). [para(1848(a,2),2223(a,1,2))]. given #2075 (H,wt=15): 2326 K(T(x,y) \ z,x) = z \ ((x \ z) * x). [para(1873(a,1),2245(a,1,2)),flip(a)]. given #2076 (H,wt=13): 2327 K(T(x,y) \ z,x) = K(x \ z,x). [para(2326(a,2),73(a,1))]. given #2077 (H,wt=13): 2331 K(x / T(y,z),y) = K(y \ x,y). [para(2327(a,1),2312(a,2))]. given #2078 (H,wt=13): 2332 K(x \ (y * T(x,z)),x) = K(y,x). [para(15(a,1),2331(a,1,1)),flip(a)]. given #2079 (H,wt=13): 2334 K((x / y) * T(y,z),y) = K(x,y). [para(2332(a,1),1961(a,1)),flip(a)]. given #2080 (H,wt=11): 2335 K(x * K(y,z),y) = K(x,y). [para(2227(a,1),2334(a,1,1))]. given #2081 (H,wt=11): 2338 K(K(x,y) * z,x) = K(z,x). [para(2298(a,1),2335(a,1,1))]. given #2082 (H,wt=15): 2329 K(((x \ y) \ y) \ z,x) = K(x \ z,x). [para(86(a,1),2327(a,1,1,1))]. given #2083 (H,wt=15): 2337 K(x,y * K(x,z)) = u / (K(y,x) * u). [para(2335(a,1),1936(a,1,2,1)),flip(a)]. given #2084 (H,wt=11): 2341 K(x,y * K(x,z)) = K(x,y). [para(2337(a,2),1936(a,1))]. given #2085 (H,wt=11): 2342 K(x,y * K(z,x)) = K(x,y). [para(2233(a,1),2341(a,1,2)),flip(a)]. given #2086 (H,wt=11): 2343 K(x,K(y,x) * z) = K(x,z). [para(2070(a,1),2342(a,1,2))]. given #2087 (H,wt=15): 2344 K(x,(y / x) \ z) = K(x,(x \ y) \ z). [para(1984(a,1),2343(a,1,2))]. given #2088 (H,wt=15): 2346 K(x,(x \ y) \ z) = K(x,y \ (z * x)). [para(2344(a,1),2322(a,1))]. given #2089 (H,wt=19): 2340 K(x \ ((1 / x) \ y),x) = K(x \ ((x \ 1) \ y),x). [para(541(a,1),2329(a,1,1))]. given #2090 (H,wt=21): 2290 K(x,(y * (x / y)) \ (x * z)) = K(x,K(y \ x,y) * z). [para(2101(a,1),2288(a,1,2))]. given #2091 (H,wt=21): 2347 K(x,(y * (y \ x)) \ (x * z)) = K(x,K(y \ x,y) * z). [para(2290(a,1),2105(a,1)),flip(a)]. given #2092 (H,wt=17): 2348 K(x,x \ (x * y)) = K(x,K(z \ x,z) * y). [para(14(a,1),2347(a,1,2,1))]. given #2093 (H,wt=13): 2349 K(x,K(y \ x,y) * z) = K(x,z). [para(13(a,1),2348(a,1,2)),flip(a)]. given #2094 (H,wt=13): 2350 K(x,K(y,y \ x) * z) = K(x,z). [para(1930(a,1),2349(a,1,2)),flip(a)]. given #2095 (H,wt=15): 2351 K(x * y,K(x,y) * z) = K(x * y,z). [para(13(a,1),2350(a,1,2,1,2))]. given #2096 (H,wt=19): 2352 K(R(x,y,z) * u,T(x,u)) = K(R(x,y,z) * u,x). [para(2050(a,1),2351(a,1,2))]. given #2097 (H,wt=22): 2211 K(x,L(x,y,z) \ 1) * (z * y) = z * (y * K(x,x \ 1)). [para(2208(a,1),1160(a,1,1))]. given #2098 (H,wt=22): 2280 x / L(K(y,z),u,w) != x * v5 | K(z,L(y,u / y,w)) = v5. [para(2276(a,1),19(a,1))]. given #2099 (H,wt=23): 2216 K((x \ 1) \ 1,L(x \ 1,y,z)) = L(K(x \ 1,x),y,z) \ 1. [para(2214(a,1),2028(a,1)),flip(a)]. given #2100 (H,wt=19): 2353 L(K(x \ 1,x),y,z) \ 1 = K(x,L(x \ 1,y,z)). [para(2216(a,1),1573(a,1))]. given #2101 (H,wt=21): 2354 K(L(1 / x,y,z) \ 1,x \ 1) = K(x,L(x \ 1,y,z)). [para(2353(a,1),2213(a,2))]. given #2102 (H,wt=21): 2355 K((1 / x) \ 1,L(x,y,z) \ 1) = K(x,L(x \ 1,y,z)). [para(2354(a,1),2207(a,1)),flip(a)]. given #2103 (H,wt=17): 2356 K(x,L(x \ 1,y,z)) = K(x,L(x,y,z) \ 1). [para(59(a,1),2355(a,1,1)),flip(a)]. given #2104 (H,wt=22): 2357 K(x,L(x \ 1,y,z)) * (z * y) = z * (y * K(x,x \ 1)). [para(2356(a,2),2211(a,1,1))]. given #2105 (H,wt=23): 2244 ((1 / x) \ y) \ ((1 / x) \ T(y,z)) = K(x \ ((1 / x) \ y),z). [para(657(a,1),2223(a,1,2))]. given #2106 (H,wt=23): 2270 K(x,y / ((y / z) * K(z \ 1,y))) = K(x,(y \ (y / z)) \ 1). [para(2253(a,1),2117(a,1,2,2))]. given #2107 (H,wt=21): 2360 K(x,T(y,z \ 1) / (y / z)) = K(x,(y \ (y / z)) \ 1). [para(2270(a,1),1901(a,1)),flip(a)]. given #2108 (H,wt=23): 2359 ((1 / x) \ y) \ ((1 / x) \ T(y,x)) = K(x \ ((x \ 1) \ y),x). [para(2244(a,2),2340(a,1))]. given #2109 (H,wt=19): 2361 K(x \ ((x \ 1) \ y),x) = K(y,((x \ 1) \ y) / y). [para(2359(a,1),2151(a,2)),flip(a)]. given #2110 (H,wt=17): 2362 K(x \ ((x \ 1) \ y),x) = K(y,(x \ 1) \ 1). [para(2361(a,2),2119(a,1))]. given #2111 (H,wt=13): 2363 K(x \ ((x \ 1) \ y),x) = K(y,x). [para(2362(a,2),929(a,1))]. given #2112 (H,wt=13): 2365 K((x \ 1) * y,x) = K(x \ y,x). [para(13(a,1),2363(a,1,1,2)),flip(a)]. given #2113 (H,wt=13): 2366 K((1 / x) * y,x) = K(x \ y,x). [para(2365(a,1),2169(a,2))]. given #2114 (H,wt=15): 2367 K((1 / x) * (y * x),x) = K(T(y,x),x). [para(30(a,2),2366(a,2,1))]. given #2115 (H,wt=17): 2368 K(T((1 / x) * y,x),x) = K(T(x \ y,x),x). [para(356(a,1),2367(a,1,1))]. given #2116 (H,wt=17): 2369 K(T((x \ 1) * y,x),x) = K(T(x \ y,x),x). [para(2368(a,1),2171(a,1)),flip(a)]. given #2117 (H,wt=17): 2370 K(T(x \ y,x),x) \ 1 = K(x,(x \ 1) * y). [para(2369(a,1),1962(a,1,1))]. given #2118 (H,wt=13): 2371 K(x,(x \ 1) * y) = K(x,x \ y). [para(2370(a,1),1962(a,1))]. given #2119 (H,wt=25): 2285 x * L(K(T(y \ 1,z) \ 1,u),w,v5) = x / L(T(K(u,y),z),w,v5). [para(2036(a,1),2282(a,1,2,1)),flip(a)]. given #2120 (H,wt=21): 2372 x / L(T(K(y,z),u),w,v5) = x * L(T(K(z,y),u),w,v5). [para(2266(a,1),2285(a,1,2,1)),flip(a)]. given #2121 (H,wt=20): 2373 (x * (K(y,z) * u)) * L(T(K(z,y),u),u,x) = x * u. [para(2372(a,1),231(a,1))]. given #2122 (H,wt=26): 2358 K(x,L(x \ 1,y,z)) * ((z * y) / u) = (z * (y * K(x,x \ 1))) / u. [para(2357(a,1),281(a,1,1)),flip(a)]. given #2123 (H,wt=23): 2376 (x * (y * K(z,z \ 1))) / u = K(z,z \ 1) * ((x * y) / u). [para(1693(a,1),2358(a,1,1)),flip(a)]. given #2124 (H,wt=29): 2291 K(R(x,y,z),(x \ 1) \ (R(x,y,z) \ u)) = K(R(x,y,z),(x \ R(x,y,z)) \ u). [para(479(a,1),2289(a,1,2,1)),flip(a)]. given #2125 (H,wt=26): 2379 K(R(x,y,z),(x \ 1) \ (R(x,y,z) \ u)) = K(x,(x \ R(x,y,z)) \ u). [para(2291(a,2),2048(a,1))]. given #2126 (H,wt=26): 2381 K(R(x,y,z),(x \ 1) \ (R(x,y,z) \ u)) = K(x,R(x,y,z) \ (u * x)). [para(2379(a,2),2346(a,1))]. given #2127 (H,wt=23): 2382 K(x,(x \ 1) \ (R(x,y,z) \ u)) = K(x,R(x,y,z) \ (u * x)). [para(2381(a,1),2048(a,1)),flip(a)]. given #2128 (H,wt=29): 2345 (R(x / y,z,u) * w) / R(y \ x,z,u) = (K(y,y \ x) * w) * K(y \ x,w). [para(2343(a,1),2190(a,2,2))]. given #2129 (H,wt=33): 2378 (x \ (K(y \ 1,y) * z)) / ((K(y,y \ 1) * ((u * x) / u)) \ z) = K(u,x * K(y,y \ 1)). [para(2376(a,1),1983(a,1,2,1))]. given #2130 (H,wt=33): 2385 (x \ (K(y \ 1,y) * z)) / (((u * x) / u) \ (K(y \ 1,y) * z)) = K(u,x * K(y,y \ 1)). [para(1943(a,1),2378(a,1,2))]. given #2131 (H,wt=13): 2386 K(x,y * K(z,z \ 1)) = K(x,y). [para(2385(a,1),1925(a,1))]. given #2132 (H,wt=13): 2387 K(x,y * K(z \ 1,z)) = K(x,y). [para(929(a,1),2386(a,1,2,2))]. given #2133 (H,wt=13): 2388 K(x,K(y \ 1,y) * z) = K(x,z). [para(1213(a,1),2386(a,1,2)),flip(a)]. given #2134 (H,wt=15): 2389 K(x,((y \ 1) \ 1) * z) = K(x,y * z). [para(1205(a,1),2386(a,1,2))]. given #2135 (H,wt=15): 2393 K(x,y \ K(z \ 1,z)) = K(x,y \ 1). [para(1677(a,1),2387(a,1,2))]. given #2136 (H,wt=15): 2395 K(x,((y \ 1) \ 1) \ z) = K(x,y \ z). [para(732(a,1),2388(a,1,2))]. given #2137 (H,wt=17): 2394 K(x,T(y * K(z \ 1,z),u)) = K(x,T(y,u)). [para(1732(a,2),2387(a,1,2))]. given #2138 (H,wt=17): 2397 K(x,T(y \ 1,y) * z) = K(x,(y \ 1) * z). [para(1821(a,1),2388(a,1,2))]. given #2139 (H,wt=17): 2399 K(x \ 1,(x \ 1) \ y) = K(x \ 1,x * y). [para(2389(a,1),2371(a,1)),flip(a)]. given #2140 (H,wt=17): 2401 x * T(x \ 1,y * x) = K(x \ 1,x * y). [para(2399(a,1),1986(a,1)),flip(a)]. given #2141 (H,wt=17): 2402 x \ K(x \ 1,x * y) = T(x \ 1,y * x). [hyper(66,a,2401,a)]. given #2142 (H,wt=19): 2390 K(x,(y \ K(z \ 1,z)) \ u) = K(x,(y \ 1) \ u). [para(1722(a,1),2386(a,1,2))]. given #2143 (H,wt=19): 2392 K(x,((1 / (1 / y)) * z) / u) = K(x,(y * z) / u). [para(1259(a,1),2387(a,1,2))]. given #2144 (H,wt=19): 2396 K(x,(y \ K(z \ 1,z)) * u) = K(x,(y \ 1) * u). [para(1681(a,1),2388(a,1,2))]. given #2145 (H,wt=19): 2398 K(x,T((y \ 1) \ 1,z) * u) = K(x,T(y,z) * u). [para(1230(a,1),2389(a,1,2,1))]. given #2146 (H,wt=19): 2400 K(x,T(y / (1 / (1 / z)),u)) = K(x,T(y / z,u)). [para(1452(a,1),2394(a,1,2,1)),flip(a)]. given #2147 (H,wt=17): 2406 K(x,T(y * (1 / z),u)) = K(x,T(y / z,u)). [para(2400(a,1),961(a,1)),flip(a)]. given #2148 (H,wt=17): 2407 K(x,T(y / (z \ 1),u)) = K(x,T(y * z,u)). [para(57(a,1),2406(a,1,2,1,2)),flip(a)]. given #2149 (H,wt=15): 2408 K(x,T(y * z,y)) = K(x,(z \ 1) \ y). [para(2407(a,1),941(a,1))]. given #2150 (H,wt=17): 2409 K(x,(y \ 1) \ K(z,u)) = K(x,y * K(z,u)). [para(271(a,1),2408(a,1,2)),flip(a)]. given #2151 (H,wt=21): 2403 (x \ 1) \ K(x * y,x \ 1) = T(x \ 1,y * x) \ 1. [para(2402(a,1),2100(a,1,1)),flip(a)]. given #2152 (H,wt=23): 2404 K(x,((y / (1 / z)) \ 1) \ u) = K(x,((y / (z \ 1)) \ 1) \ u). [para(1472(a,1),2390(a,1,2,1)),flip(a)]. given #2153 (H,wt=23): 2410 K(x,T(y \ 1,z * y) \ 1) = K(x,y * K(y * z,y \ 1)). [para(2403(a,1),2409(a,1,2))]. given #2154 (H,wt=19): 2412 K(x,y * K(y * z,y \ 1)) = T(K(x,y),z * y). [para(2410(a,1),2036(a,1))]. given #2155 (H,wt=15): 2413 T(K(x,y),z * y) = T(K(x,y),y * z). [para(2412(a,1),2240(a,1))]. given #2156 (H,wt=19): 2414 T(K(x,y),z * y) * K(y,x) = K(K(x,y),y * z). [para(2413(a,2),1949(a,1,1))]. given #2157 (H,wt=15): 2415 K(K(x,y),y * z) = K(z * y,K(y,x)). [para(2414(a,1),2320(a,1))]. given #2158 (H,wt=15): 2416 K(x * y,K(y,z)) = K(y * x,K(y,z)). [para(2415(a,1),2317(a,1))]. given #2159 (H,wt=13): 2417 K(x * y,K(y,z)) = K(x,K(y,z)). [para(2416(a,2),2271(a,1))]. given #2160 (H,wt=11): 2418 K(x,K(y,z)) = K(z,K(y,x)). [para(2417(a,1),2325(a,1))]. given #2161 (H,wt=11): 2419 K(K(x,y),z) = K(x,K(y,z)). [para(2418(a,1),2317(a,2))]. given #2162 (H,wt=13): 2422 K(x,K(y,z)) * K(K(x,z),y) = 1. [para(2419(a,2),2319(a,1,2))]. given #2163 (H,wt=11): 2424 K(x,K(y,z)) = K(y,K(x,z)). [hyper(1944,a,2422,a)]. given #2164 (H,wt=11): 2425 K(x,K(y,z)) = K(z,K(x,y)). [para(2424(a,1),2418(a,1))]. given #2165 (H,wt=11): 2430 K(x,K(y,z)) = K(x,K(z,y)). [para(2425(a,1),2418(a,1))]. given #2166 (H,wt=11): 2431 K(K(x,y),z) = K(z,K(x,y)). [para(2425(a,1),2419(a,2))]. given #2167 (H,wt=13): 2426 K(x,K(y,z)) * z = T(z,K(x,y)). [para(2425(a,2),1817(a,2,1)),flip(a)]. given #2168 (H,wt=13): 2427 x * K(y,K(z,x)) = T(x,K(y,z)). [para(2425(a,2),1825(a,2,2)),flip(a)]. given #2169 (H,wt=13): 2429 K(x,K(y,T(z,x))) = K(z,K(x,y)). [para(2425(a,2),2308(a,1))]. given #2170 (H,wt=13): 2434 K(x,K(y,T(z,x))) = K(x,K(z,y)). [para(2429(a,2),2424(a,1))]. given #2171 (H,wt=15): 2421 K(x,y) * K(x,K(y,z)) = T(K(x,y),z). [para(2419(a,1),1825(a,2,2)),flip(a)]. given #2172 (H,wt=15): 2423 K(K(x,y) * z,K(x,u)) = K(K(z,x),u). [para(2338(a,1),2419(a,1,1)),flip(a)]. given #2173 (H,wt=15): 2432 K(x,y) * K(y,T(x,z)) = K(z,K(y,x)). [para(2430(a,1),2264(a,2))]. given #2174 (H,wt=15): 2433 K(x,y) * K(z,K(x,y)) = T(K(x,y),z). [para(2431(a,1),1825(a,2,2)),flip(a)]. given #2175 (H,wt=11): 2438 T(T(K(x,y),z),z) = K(x,y). [para(2433(a,1),1803(a,1,1))]. given #2176 (H,wt=11): 2440 T(K(x,T(y,z)),z) = K(x,y). [para(2300(a,2),2438(a,1,1))]. given #2177 (H,wt=11): 2442 K(T(x,y),T(z,y)) = K(x,z). [para(2440(a,1),2261(a,2))]. given #2178 (H,wt=11): 2444 K(x,T(T(y,z),z)) = K(x,y). [para(2440(a,1),2300(a,2))]. given #2179 (H,wt=13): 2439 T(K(x,y),z) * z = z * K(x,y). [para(2433(a,1),1801(a,1,1))]. given #2180 (H,wt=13): 2441 (x * K(y,z)) / x = K(y,T(z,x)). [para(2440(a,1),106(a,1,1,2))]. given #2181 (H,wt=13): 2443 K(x \ y,T(z,y)) = K(y / x,z). [para(2440(a,1),2258(a,1)),flip(a)]. given #2182 (H,wt=13): 2445 K((x * y) / x,z) = K(y,T(z,x)). [para(105(a,1),2442(a,1,1)),flip(a)]. given #2183 (H,wt=13): 2446 K(x,(y * z) / y) = K(T(x,y),z). [para(105(a,1),2442(a,1,2)),flip(a)]. given #2184 (H,wt=13): 2451 K(x,T(y \ z,y)) = K(x,z / y). [para(87(a,1),2444(a,1,2,1))]. given #2185 (H,wt=15): 2435 K(x,y) * K(x,K(z,y)) = T(K(x,y),z). [para(2430(a,1),2421(a,1,2))]. given #2186 (H,wt=15): 2436 K(K(x,y) * z,K(x,u)) = K(z,K(x,u)). [para(2423(a,2),2419(a,1))]. given #2187 (H,wt=15): 2437 K(x,y) \ K(z,K(y,x)) = K(y,T(x,z)). [hyper(66,a,2432,a)]. given #2188 (H,wt=15): 2449 K(T(x,y),K(z,x) * u) = K(T(x,y),u). [para(2442(a,1),2343(a,1,2,1))]. given #2189 (H,wt=15): 2458 K(x,y) * K(x,K(z,y)) = K(x,T(y,z)). [para(2435(a,2),2300(a,2)),flip(a)]. given #2190 (H,wt=15): 2459 K(x,K(y,K(x,z) * u)) = K(u,K(x,y)). [para(2436(a,1),2425(a,2))]. given #2191 (H,wt=17): 2420 (K(x,y) * z) / K(x,y) = z * K(x,K(y,z)). [para(2419(a,1),1796(a,2,2))]. given #2192 (H,wt=15): 2460 (K(x,y) * z) / K(x,y) = T(z,K(x,y)). [para(2420(a,2),2427(a,1))]. given #2193 (H,wt=15): 2461 (K(x,y) * z) * K(y,x) = T(z,K(x,y)). [para(2460(a,1),2234(a,1)),flip(a)]. given #2194 (H,wt=15): 2462 K(x,y) * (z * K(y,x)) = T(z,K(x,y)). [para(2461(a,1),197(a,1)),flip(a)]. given #2195 (H,wt=11): 2465 T(x,K(y,z)) = T(x,K(z,y)). [para(2462(a,1),1934(a,1))]. given #2196 (H,wt=15): 2463 T(K(x,y) * z,K(y,x)) = z * K(x,y). [para(1930(a,1),2461(a,1,1)),flip(a)]. given #2197 (H,wt=15): 2464 K(x,y) * T(z,K(y,x)) = z * K(x,y). [para(2461(a,1),1933(a,1,2))]. given #2198 (H,wt=17): 2450 K(x,T(L(T(y,z),u,w),z)) = K(x,L(y,u,w)). [para(38(a,2),2444(a,1,2,1))]. given #2199 (H,wt=17): 2452 K(T(x,y),z) * (y * x) = (y * x) * K(x,z). [para(2260(a,1),2439(a,1,1))]. given #2200 (H,wt=15): 2470 K(T(x,y),z) * (y * x) = y * T(x,z). [para(2452(a,2),2222(a,1))]. given #2201 (H,wt=15): 2471 K(x,T(y,z)) * (z * x) = z * T(x,y). [para(2305(a,1),2470(a,1,1))]. given #2202 (H,wt=17): 2454 K(((x * y) / x) \ 1,z) = K(y \ 1,T(z,x)). [para(2441(a,1),2073(a,1)),flip(a)]. given #2203 (H,wt=15): 2473 K(x \ K(x,y),z) = K(x \ 1,T(z,y)). [para(1957(a,1),2454(a,1,1))]. given #2204 (H,wt=15): 2475 K(x \ K(x,y),T(z,y)) = K(x \ 1,z). [para(2473(a,2),2444(a,1))]. given #2205 (H,wt=17): 2455 K(x / y,z) * (y \ x) = T(y \ x,T(z,x)). [para(2443(a,1),1817(a,2,1)),flip(a)]. given #2206 (H,wt=17): 2474 K(x,K(y \ K(y,x),z)) = K(x,K(z,y \ 1)). [para(2473(a,2),2434(a,1,2))]. given #2207 (H,wt=19): 2428 x * T(x \ y,K(z,u)) = y * K(z,K(u,x \ y)). [para(2425(a,2),2226(a,2,2))]. given #2208 (H,wt=19): 2448 K(T(x,y),R(y,z,u) \ w) = K(x,w / R(y,z,u)). [para(2038(a,1),2442(a,1,2))]. given #2209 (H,wt=19): 2457 K(x \ y,z) * K(z,y / x) = K(x,K(z,x \ y)). [para(2451(a,1),2432(a,1,2))]. given #2210 (H,wt=19): 2466 K(x,y) * (y * (z * K(y,x))) = T(y * z,K(x,y)). [para(2277(a,1),2462(a,1,2))]. given #2211 (H,wt=19): 2468 K(x,T(K(y,z) / u,K(z,y))) = K(x,u \ K(y,z)). [para(2465(a,1),941(a,1,2))]. given #2212 (H,wt=19): 2469 T(x * (K(y,x) * z),K(x,y)) = (x * z) * K(y,x). [para(1918(a,1),2463(a,1,1))]. given #2213 (H,wt=19): 2479 K(x \ y,z) * K(z,y / x) = K(z,K(x,x \ y)). [para(2457(a,2),2424(a,1))]. given #2214 (H,wt=19): 2480 x * (K(y,x) * (z * K(x,y))) = T(x * z,K(y,x)). [para(2466(a,1),1918(a,1)),flip(a)]. given #2215 (H,wt=15): 2483 T(x * y,K(z,x)) = x * T(y,K(z,x)). [para(2462(a,1),2480(a,1,2)),flip(a)]. given #2216 (H,wt=15): 2484 x * T(x \ y,K(z,x)) = T(y,K(z,x)). [para(14(a,1),2483(a,1,1)),flip(a)]. given #2217 (H,wt=15): 2486 x * T(x \ y,K(x,z)) = T(y,K(z,x)). [para(2465(a,1),2484(a,1,2))]. given #2218 (H,wt=15): 2487 x * T(x \ y,K(x,z)) = T(y,K(x,z)). [para(2486(a,2),2465(a,1))]. given #2219 (H,wt=15): 2488 T(x * y,K(x,z)) = x * T(y,K(x,z)). [para(13(a,1),2487(a,1,2,1)),flip(a)]. given #2220 (H,wt=17): 2489 x * T(x \ y,K(x,z)) = y * K(x,K(z,y)). [para(2487(a,2),2427(a,2)),flip(a)]. given #2221 (H,wt=13): 2491 K(x,K(y,x \ z)) = K(x,K(y,z)). [hyper(17,a,2428,a(flip),b,2489,a(flip)),flip(a)]. given #2222 (H,wt=13): 2492 K(x,K(y,x * z)) = K(x,K(y,z)). [para(13(a,1),2491(a,1,2,2)),flip(a)]. given #2223 (H,wt=13): 2493 K(x,K(y,y * z)) = K(y,K(x,z)). [para(2492(a,1),2424(a,1)),flip(a)]. given #2224 (H,wt=13): 2494 K(x,K(y,y * z)) = K(x,K(y,z)). [para(2493(a,2),2424(a,1))]. given #2225 (H,wt=13): 2495 K(x,K(y,y \ z)) = K(x,K(y,z)). [para(14(a,1),2494(a,1,2,2)),flip(a)]. given #2226 (H,wt=15): 2496 K(x,K(y,z \ 1)) = K(x,K(y,z \ y)). [para(1970(a,1),2494(a,1,2)),flip(a)]. given #2227 (H,wt=19): 2482 K(x,y / z) * K(z \ y,x) = K(x,K(z,z \ y)). [para(2479(a,1),2301(a,2))]. given #2228 (H,wt=17): 2497 K(x,y / z) * K(z \ y,x) = K(x,K(z,y)). [para(2482(a,2),2495(a,1))]. given #2229 (H,wt=17): 2498 K(x,y / z) * K(z \ y,x) = K(x,K(y,z)). [para(2497(a,2),2430(a,1))]. given #2230 (H,wt=19): 2490 T(x * (K(y,x) * z),K(x,y)) = x * (z * K(y,x)). [para(2463(a,1),2488(a,2,2))]. given #2231 (H,wt=15): 2499 (x * y) * K(z,x) = x * (y * K(z,x)). [para(2490(a,1),2469(a,1)),flip(a)]. given #2232 (H,wt=21): 2456 (x * ((y * z) / y)) \ (z * (K(y,z) * x)) = K(z,T(x,y)). [para(2445(a,1),1880(a,2))]. given #2233 (H,wt=21): 2467 K(x,y) * R(T(z,K(y,x)),u,w) = R(z,u,w) * K(x,y). [para(2465(a,1),116(a,1,2,1))]. given #2234 (H,wt=21): 2472 K(x,K(y,z)) * (K(y,u) * x) = K(y,u) * T(x,K(y,z)). [para(2262(a,1),2471(a,1,1,2))]. given #2235 (H,wt=21): 2500 R(K(x,y) * T(z,K(y,x)),u,w) = R(z,u,w) * K(x,y). [para(2467(a,1),458(a,2))]. given #2236 (H,wt=17): 2502 R(x * K(y,z),u,w) = R(x,u,w) * K(y,z). [para(2464(a,1),2500(a,1,1))]. given #2237 (H,wt=22): 2447 K(T(x,y \ 1),R(z,y \ 1,y)) = K(x,((1 / y) * z) * y). [para(1379(a,1),2442(a,1,2))]. given #2238 (H,wt=17): 2504 K(x,((1 / y) * z) * y) = K(T(x,y \ 1),z). [para(2447(a,1),915(a,1))]. given #2239 (H,wt=22): 2453 (x * (y * K(z,u))) / (x * y) = L(K(z,T(u,x * y)),y,x). [para(2441(a,1),333(a,1,1)),flip(a)]. given #2240 (H,wt=22): 2478 x * T(x \ y,K(z,u)) != y * w | K(z,K(u,x \ y)) = w. [para(2428(a,2),19(a,1))]. given #2241 (H,wt=24): 2506 L(K(x,T(T(y,z),u * z)),z,u) = (u * (K(x,y) * z)) / (u * z). [para(2298(a,1),2453(a,1,1,2)),flip(a)]. given #2242 (H,wt=25): 2477 K(x,y \ K(y,z)) \ K(z,K(x,y \ 1)) = K(y \ K(y,z),T(x,z)). [para(2474(a,1),2437(a,1,2))]. given #2243 (H,wt=21): 2507 K(x,y \ K(y,z)) \ K(z,K(x,y \ 1)) = K(y \ 1,x). [para(2477(a,2),2475(a,1))]. given #2244 (H,wt=21): 2508 K(x,y \ K(y,z)) * K(y \ 1,x) = K(z,K(x,y \ 1)). [para(2507(a,1),14(a,1,2))]. given #2245 (H,wt=25): 2501 K(x,K(y,K(x,z) * u)) * (K(x,w) * u) = K(x,w) * T(u,K(x,y)). [para(2459(a,2),2472(a,1,1))]. given #2246 (H,wt=19): 2511 T(K(x,y) * z,K(x,u)) = K(x,y) * T(z,K(x,u)). [para(2501(a,1),2426(a,1)),flip(a)]. given #2247 (H,wt=23): 2512 K(x,y) * T(T(z,K(x,y)),K(x,u)) = T(z * K(x,y),K(x,u)). [para(85(a,1),2511(a,1,1)),flip(a)]. given #2248 (H,wt=19): 2513 T(x * K(y,z),K(y,u)) = T(x,K(y,u)) * K(y,z). [para(2512(a,1),114(a,1))]. given #2249 (H,wt=23): 2514 T((K(x,y) * z) * K(x,u),K(x,y)) = (z * K(x,y)) * K(x,u). [para(271(a,1),2513(a,2,1))]. given #2250 (H,wt=23): 2515 T(K(x,y) * (z * K(x,u)),K(x,y)) = (z * K(x,y)) * K(x,u). [para(197(a,1),2514(a,1,1))]. given #2251 (H,wt=19): 2516 (x * K(y,z)) * K(y,u) = (x * K(y,u)) * K(y,z). [para(2515(a,1),271(a,1))]. given #2252 (H,wt=19): 2517 ((x * y) / x) * K(x,z) = (y * K(x,z)) * K(x,y). [para(1796(a,2),2516(a,1,1))]. given #2253 (H,wt=19): 2518 ((x * y) / x) * K(x,z) = y * (K(x,z) * K(x,y)). [para(2517(a,2),2499(a,1))]. given #2254 (H,wt=25): 2510 K(x,(y / z) \ 1) * K((z \ y) \ 1,x) = K(z,K(x,(z \ y) \ 1)). [para(1976(a,1),2508(a,1,1,2))]. given #2255 (H,wt=23): 2521 K(x,(y / z) \ 1) * K((z \ y) \ 1,x) = K(z,K(x,y \ z)). [para(2311(a,1),2510(a,2,2))]. given #2256 (H,wt=23): 2522 K(x,(y / z) \ 1) * K((z \ y) \ 1,x) = K(x,K(z,y \ z)). [para(2521(a,2),2424(a,1))]. given #2257 (H,wt=21): 2523 K(x,y / z) * K((y \ z) \ 1,x) = K(x,K(y,z \ y)). [para(2116(a,1),2522(a,1,1))]. given #2258 (H,wt=19): 2524 K(x,y / z) * K(z \ y,x) = K(x,K(y,z \ y)). [para(2246(a,1),2523(a,1,2))]. given #2259 (H,wt=13): 2525 K(x,K(y,z \ y)) = K(x,K(y,z)). [para(2524(a,1),2498(a,1))]. given #2260 (H,wt=13): 2526 K(x,K(y,z \ 1)) = K(x,K(y,z)). [para(2525(a,1),2496(a,2))]. given #2261 (H,wt=13): 2527 K(x,K(y,z \ 1)) = K(z,K(x,y)). [para(2526(a,2),2425(a,1))]. given #2262 (H,wt=13): 2528 K(x,K(y \ 1,z)) = K(y,K(x,z)). [para(2527(a,1),2430(a,1)),flip(a)]. given #2263 (H,wt=13): 2529 K(x,K(y \ 1,z)) = K(x,K(y,z)). [para(2528(a,2),2424(a,1))]. given #2264 (H,wt=17): 2530 K(x,y) * K(x,K(z,y)) = K(x,T(y,z \ 1)). [para(2529(a,1),2458(a,1,2))]. given #2265 (H,wt=13): 2531 K(x,T(y,z \ 1)) = K(x,T(y,z)). [para(2530(a,1),2458(a,1))]. given #2266 (H,wt=13): 2534 K(T(x,y \ 1),z) = K(x,T(z,y)). [para(2531(a,1),2305(a,2))]. given #2267 (H,wt=15): 2533 K(x,T(y * z,z)) = K(x,T(y * z,y)). [para(2531(a,1),2140(a,1)),flip(a)]. given #2268 (H,wt=23): 2532 K(x,T(y / R(z \ 1,u,w),z)) = K(x,R(z \ 1,u,w) \ y). [para(2038(a,1),2531(a,1,2)),flip(a)]. given #2269 (H,wt=27): 2405 K(x,(((y / (1 / z)) \ 1) \ 1) * u) = K(x,(((y / (z \ 1)) \ 1) \ 1) * u). [para(2069(a,1),2396(a,1,2,1))]. given #2270 (H,wt=23): 2535 K(x,(((y / (z \ 1)) \ 1) \ 1) * u) = K(x,(y / (1 / z)) * u). [para(2405(a,1),2389(a,1))]. given #2271 (H,wt=19): 2536 K(x,(y / (1 / z)) * u) = K(x,(y / (z \ 1)) * u). [para(2535(a,1),2389(a,1))]. given #2272 (H,wt=21): 2537 K(x,(y / (z \ 1)) * (u \ 1)) = K(x,(y / (1 / z)) / u). [para(2536(a,1),919(a,1))]. given #2273 (H,wt=21): 2538 K(x,(y / (z \ 1)) * (u \ 1)) = K(x,y / (u * (1 / z))). [para(2537(a,2),918(a,1))]. given #2274 (H,wt=19): 2539 K(x,(y / (z \ 1)) / u) = K(x,y / (u * (1 / z))). [para(2538(a,1),919(a,1)),flip(a)]. given #2275 (H,wt=19): 2540 K(x,y / (z * (1 / u))) = K(x,y / (z * (u \ 1))). [para(2539(a,1),918(a,1))]. given #2276 (H,wt=27): 2520 K(x,y * (K(z,((z * y) / z) \ 1) * K(z,y))) = T(K(x,(z * y) / z),z). [para(2518(a,1),2240(a,1,2))]. given #2277 (H,wt=27): 2541 K(x,y * (K(z,(z * y) \ (1 * z)) * K(z,y))) = T(K(x,(z * y) / z),z). [para(2322(a,1),2520(a,1,2,2,1))]. given #2278 (H,wt=25): 2542 K(x,y * (K(z,(z * y) \ z) * K(z,y))) = T(K(x,(z * y) / z),z). [para(11(a,1),2541(a,1,2,2,1,2,2))]. given #2279 (H,wt=23): 2543 T(K(x,(y * z) / y),y) = K(x,z * (K(y,z \ 1) * K(y,z))). [para(2315(a,1),2542(a,1,2,2,1)),flip(a)]. given #2280 (H,wt=21): 2545 K(x,y * (K(z,y \ 1) * K(z,y))) = T(K(T(x,z),y),z). [para(2446(a,1),2543(a,1,1)),flip(a)]. given #2281 (H,wt=28): 2481 K(x,T(R((y \ 1) / z,z,y),K(y,y \ 1))) = K(x,(z * y) \ K(y \ 1,y)). [para(227(a,2),2468(a,1,2,1))]. given #2282 (H,wt=22): 2546 K(x,R((y \ 1) / z,z,y)) = K(x,(z * y) \ K(y \ 1,y)). [para(1131(a,1),2481(a,1,2))]. given #2283 (H,wt=19): 2547 K(x,(y * z) \ K(z \ 1,z)) = K(x,(z \ 1) / y). [para(2546(a,1),915(a,1))]. given #2284 (H,wt=15): 2550 K(x,(y \ 1) / z) = K(x,(z * y) \ 1). [para(2547(a,1),2393(a,1))]. given #2285 (H,wt=31): 2519 K(x,((x * y) / x) \ 1) * ((x * y) / x) = y * (K(x,((x * y) / x) \ 1) * K(x,y)). [para(2518(a,1),2164(a,2))]. given #2286 (H,wt=31): 2552 K(x,(x * y) \ (1 * x)) * ((x * y) / x) = y * (K(x,((x * y) / x) \ 1) * K(x,y)). [para(2322(a,1),2519(a,1,1))]. given #2287 (H,wt=29): 2553 K(x,(x * y) \ x) * ((x * y) / x) = y * (K(x,((x * y) / x) \ 1) * K(x,y)). [para(11(a,1),2552(a,1,1,2,2))]. given #2288 (H,wt=27): 2554 x * (K(y,((y * x) / y) \ 1) * K(y,x)) = K(y,x \ 1) * ((y * x) / y). [para(2315(a,1),2553(a,1,1)),flip(a)]. given #2289 (H,wt=25): 2555 x * (K(y,((y * x) / y) \ 1) * K(y,x)) = (T(y,x \ 1) * x) / y. [para(2554(a,2),1851(a,1))]. given #2290 (H,wt=25): 2557 x * (K(y,(y * x) \ (1 * y)) * K(y,x)) = (T(y,x \ 1) * x) / y. [para(2322(a,1),2555(a,1,2,1))]. given #2291 (H,wt=23): 2558 x * (K(y,(y * x) \ y) * K(y,x)) = (T(y,x \ 1) * x) / y. [para(11(a,1),2557(a,1,2,1,2,2))]. given #2292 (H,wt=21): 2559 x * (K(y,x \ 1) * K(y,x)) = (T(y,x \ 1) * x) / y. [para(2315(a,1),2558(a,1,2,1))]. given #2293 (H,wt=19): 2561 K(x,(T(y,z \ 1) * z) / y) = T(K(T(x,y),z),y). [para(2559(a,1),2545(a,1,2))]. given #2294 (H,wt=19): 2562 K(x,T(y,z \ 1) / (y / z)) = T(K(T(x,y),z),y). [para(2561(a,1),921(a,1)),flip(a)]. given #2295 (H,wt=17): 2563 K(x,(y \ (y / z)) \ 1) = T(K(T(x,y),z),y). [para(2562(a,1),2360(a,1)),flip(a)]. given #2296 (H,wt=34): 2476 K(1 / R(x \ 1,y,z),u) * T(R(x \ 1,y,z) \ 1,x) = T(R(x \ 1,y,z) \ 1,T(u,1)). [para(2147(a,2),2455(a,1,2))]. given #2297 (H,wt=34): 2564 T(K(T(x,y * z),L(T(u,u \ z),u \ z,y)),y * z) = K(x,((y * z) \ (y * (u \ z))) \ 1). [para(232(a,1),2563(a,1,2,1,2)),flip(a)]. given #2298 (H,wt=29): 2565 T(K(T(x,y * z),L(T(u,u \ z),u \ z,y)),y * z) = L(T(K(x,u),z),z,y). [para(2564(a,2),2196(a,1))]. given #2299 (H,wt=29): 2566 T(K(x,T(L(T(y,y \ z),y \ z,u),u * z)),u * z) = L(T(K(x,y),z),z,u). [para(2305(a,1),2565(a,1,1))]. given #2300 (H,wt=29): 2567 T(K(x,L(T(T(y,y \ z),u * z),y \ z,u)),u * z) = L(T(K(x,y),z),z,u). [para(38(a,2),2566(a,1,1,2))]. given #2301 (H,wt=27): 2568 T(K(x,L(T(T(y,z),u * z),y \ z,u)),u * z) = L(T(K(x,y),z),z,u). [para(2065(a,1),2567(a,1,1))]. given #2302 (H,wt=27): 2569 K(x,T(L(T(T(y,z),u * z),y \ z,u),u * z)) = L(T(K(x,y),z),z,u). [para(2568(a,1),2300(a,2))]. given #2303 (H,wt=19): 2570 K(x,L(T(y,z),y \ z,u)) = L(T(K(x,y),z),z,u). [para(2569(a,1),2450(a,1)),flip(a)]. given #2304 (H,wt=19): 2571 K(x,L(T(y,z),y \ z,u)) = L(K(x,T(y,z)),z,u). [para(2300(a,2),2570(a,2,1))]. given #2305 (H,wt=35): 2316 T(K(x,L(T(y,y \ z),y \ z,u)),u * (y \ z)) = T(K(x,L(T(y,y \ z),y \ z,u)),u * z). [para(232(a,1),2314(a,1,2))]. given #2306 (H,wt=34): 2573 T(K(x,L(T(y,y \ z),y \ z,u)),u * z) = T(K(x,(u * (y \ z)) \ (u * z)),u * (y \ z)). [para(144(a,1),2316(a,1,1,2)),flip(a)]. given #2307 (H,wt=32): 2574 T(K(x,(y * (z \ u)) \ (y * u)),y * (z \ u)) = T(K(x,L(T(z,u),z \ u,y)),y * u). [para(949(a,1),2573(a,1,1)),flip(a)]. given #2308 (H,wt=32): 2575 K(x,T((y * (z \ u)) \ (y * u),y * (z \ u))) = T(K(x,L(T(z,u),z \ u,y)),y * u). [para(2574(a,1),2300(a,2))]. given #2309 (H,wt=26): 2576 T(K(x,L(T(y,z),y \ z,u)),u * z) = K(x,(u * z) / (u * (y \ z))). [para(2575(a,1),2451(a,1))]. given #2310 (H,wt=26): 2577 T(K(x,L(T(y,z),y \ z,u)),u * z) = K(x,u / ((u * (y \ z)) / z)). [para(2576(a,2),921(a,1))]. given #2311 (H,wt=24): 2578 T(L(K(x,T(y,z)),z,u),u * z) = K(x,u / ((u * (y \ z)) / z)). [para(2571(a,1),2577(a,1,1))]. given #2312 (H,wt=24): 2579 L(T(K(x,T(y,z)),u * z),z,u) = K(x,u / ((u * (y \ z)) / z)). [para(2578(a,1),38(a,2))]. given #2313 (H,wt=24): 2580 L(K(x,T(T(y,z),u * z)),z,u) = K(x,u / ((u * (y \ z)) / z)). [para(2300(a,2),2579(a,1,1))]. given #2314 (H,wt=37): 2235 ((x * K(y,z)) * R((x * K(y,z)) \ u,w,v5)) * K(z,y) = x * R(x \ (u * ((x * K(y,z)) \ x)),w,v5). [para(2231(a,1),688(a,1,2))]. given #2315 (H,wt=37): 2581 (x * (K(y,z) * R(K(y,z) \ (x \ u),w,v5))) * K(z,y) = x * R(x \ (u * ((x * K(y,z)) \ x)),w,v5). [para(662(a,1),2235(a,1,1))]. given #2316 (H,wt=37): 2582 (x * (K(y,z) * R(K(z,y) * (x \ u),w,v5))) * K(z,y) = x * R(x \ (u * ((x * K(y,z)) \ x)),w,v5). [para(1937(a,1),2581(a,1,1,2,2,1))]. given #2317 (H,wt=33): 2583 (x * (K(y,z) * R(K(z,y) * (x \ u),w,v5))) * K(z,y) = x * R(x \ (u * K(z,y)),w,v5). [para(2231(a,1),2582(a,2,2,1,2,2))]. given #2318 (H,wt=33): 2584 (x * R(K(y,z) * (K(z,y) * (x \ u)),w,v5)) * K(z,y) = x * R(x \ (u * K(z,y)),w,v5). [para(458(a,2),2583(a,1,1,2))]. given #2319 (H,wt=25): 2586 (x * R(x \ y,z,u)) * K(w,v5) = x * R(x \ (y * K(w,v5)),z,u). [para(1930(a,1),2584(a,1,1,2,1))]. given #2320 (H,wt=25): 2588 K(x,y) * (z * R(z \ x,u,w)) = z * R(z \ (x * K(x,y)),u,w). [para(2586(a,1),2180(a,2))]. given #2321 (H,wt=23): 2589 K(x,y) * (z * R(z \ x,u,w)) = z * R(z \ T(x,y),u,w). [para(1825(a,2),2588(a,2,2,1,2))]. given #2322 (H,wt=39): 2197 (K(x,x \ y) * z) * K(z \ (K(x \ y,x) * ((y / x) * z)),K(x,x \ y) * z) = ((y / x) * z) / (x \ y). [para(1943(a,1),2009(a,1,2,1))]. given #2323 (H,wt=33): 2591 (K(x,x \ y) * z) * K(z \ ((x \ y) * z),K(x,x \ y) * z) = ((y / x) * z) / (x \ y). [para(1971(a,1),2197(a,1,2,1,2))]. given #2324 (H,wt=31): 2592 (K(x,x \ y) * z) * K(T(x \ y,z),K(x,x \ y) * z) = ((y / x) * z) / (x \ y). [para(30(a,2),2591(a,1,2,1))]. given #2325 (H,wt=25): 2593 (K(x,x \ y) * z) * K(T(x \ y,z),z) = ((y / x) * z) / (x \ y). [para(2449(a,1),2592(a,1,2))]. given #2326 (H,wt=23): 2594 (K(x,x \ y) * z) * K(x \ y,z) = ((y / x) * z) / (x \ y). [para(1958(a,1),2593(a,1,2))]. given #2327 (H,wt=25): 2596 (R(x / y,z,u) * w) / R(y \ x,z,u) = ((x / y) * w) / (y \ x). [para(2594(a,1),2345(a,2))]. given #2328 (H,wt=33): 2597 K(x,((1 / (1 / R(y / z,u,w))) * v5) / R(z \ y,u,w)) = K(x,((y / z) * v5) / (z \ y)). [para(2596(a,1),2392(a,2,2))]. given #2329 (H,wt=40): 2590 ((x * R(x \ y,z,u)) * ((y * w) / y)) \ (w * (x * R(x \ T(y,w),z,u))) = K(w,T(x * R(x \ y,z,u),y)). [para(2589(a,1),2456(a,1,2,2))]. given #2330 (H,wt=38): 2598 ((x * R(x \ y,z,u)) * ((y * w) / y)) \ ((x * R(x \ y,z,u)) * w) = K(w,T(x * R(x \ y,z,u),y)). [para(2178(a,1),2590(a,1,2))]. given #2331 (H,wt=16): 2599 K(x,T(y * R(y \ z,u,w),z)) = K(x,z). [para(2598(a,1),2265(a,1))]. given #2332 (H,wt=14): 2600 K(x,y * R(y \ z,u,w)) = K(x,z). [para(2181(a,1),2599(a,1,2))]. given #2333 (H,wt=14): 2602 K(x,y * R(z,u,w)) = K(x,y * z). [para(13(a,1),2600(a,1,2,2,1))]. given #2334 (H,wt=13): 2604 K(x,T(y * z,y)) = K(x,z * y). [para(2042(a,1),2602(a,1,2))]. given #2335 (H,wt=13): 2605 K(x,(y \ 1) \ z) = K(x,y * z). [para(2604(a,1),2408(a,1)),flip(a)]. given #2336 (H,wt=13): 2606 K(x,T(y * z,z)) = K(x,z * y). [para(2604(a,1),2533(a,2))]. given #2337 (H,wt=13): 2608 K(x,(y \ 1) * z) = K(x,y \ z). [para(2605(a,1),2395(a,1))]. given #2338 (H,wt=14): 2603 K(x,y \ R(y * z,u,w)) = K(x,z). [para(557(a,1),2600(a,1,2))]. given #2339 (H,wt=14): 2611 K(x,R(y,z,u) / w) = K(x,y / w). [para(775(a,1),2603(a,1,2))]. given #2340 (H,wt=13): 2612 K(x,y / (z \ 1)) = K(x,y * z). [para(242(a,1),2611(a,1,2)),flip(a)]. given #2341 (H,wt=15): 2610 K(x,T(y \ 1,y) * z) = K(x,y \ z). [para(2608(a,1),2397(a,2))]. given #2342 (H,wt=17): 2613 K(x,((y \ 1) * z) * y) = K(T(x,y \ 1),z). [para(2612(a,1),2446(a,1))]. given #2343 (H,wt=21): 2607 K(x,R(x,y,z) \ (u * x)) = K(x,x * (R(x,y,z) \ u)). [para(2605(a,1),2382(a,1)),flip(a)]. given #2344 (H,wt=21): 2615 K(x,x * (R(x,y,z) \ (u / x))) = K(x,R(x,y,z) \ u). [para(16(a,1),2607(a,1,2,2)),flip(a)]. given #2345 (H,wt=31): 2614 K(x,((1 / (1 / R(1 / y,z,u))) * w) / R(y \ 1,z,u)) = K(x,((1 / y) * w) * y). [para(2612(a,1),2597(a,2))]. given #2346 (H,wt=29): 2616 K(x,((1 / (1 / R(1 / y,z,u))) * w) / R(y \ 1,z,u)) = K(T(x,y \ 1),w). [para(2614(a,2),2504(a,1))]. given #2347 (H,wt=41): 2375 R((x * y) / (x * (K(z,u) * y)),x * (K(z,u) * y),L(T(K(u,z),y),y,x)) = (x * (y * T(K(u,z),y))) / (x * y). [para(2373(a,1),228(a,2,2))]. given #2348 (H,wt=41): 2411 K(x,((((y \ 1) * (R((y \ 1) \ 1,z,u) \ 1)) / (1 / y)) \ 1) \ w) = K(x,((R((y \ 1) \ 1,z,u) \ 1) \ 1) \ w). [para(2148(a,1),2404(a,2,2,1,1))]. given #2349 (H,wt=42): 2374 ((x * (K(y,z) * u)) * R(L(T(K(z,y),u),u,x),w,v5)) / (x * (K(y,z) * u)) = R((x * u) / (x * (K(y,z) * u)),w,v5). [para(2373(a,1),325(a,1,1,1)),flip(a)]. given #2350 (H,wt=42): 2617 ((x * (K(y,z) * u)) * L(R(T(K(z,y),u),w,v5),u,x)) / (x * (K(y,z) * u)) = R((x * u) / (x * (K(y,z) * u)),w,v5). [para(42(a,1),2374(a,1,1,2))]. given #2351 (H,wt=39): 2618 R((x * y) / (x * (K(z,u) * y)),w,v5) = ((x * (K(z,u) * y)) * L(T(K(u,z),y),y,x)) / (x * (K(z,u) * y)). [para(280(a,1),2617(a,1,1,2,1)),flip(a)]. given #2352 (H,wt=26): 2620 R((x * y) / (x * (K(z,u) * y)),w,v5) = (x * y) / (x * (K(z,u) * y)). [para(2373(a,1),2618(a,2,1))]. given #2353 (H,wt=25): 2622 (x * (y * T(K(z,u),y))) / (x * y) = (x * y) / (x * (K(u,z) * y)). [para(2620(a,1),2375(a,1)),flip(a)]. given #2354 (H,wt=23): 2623 (x * (K(y,z) * u)) / (x * u) = (x * u) / (x * (K(z,y) * u)). [para(85(a,1),2622(a,1,1,2))]. given #2355 (H,wt=24): 2626 L(K(x,T(T(y,z),u * z)),z,u) = (u * z) / (u * (K(y,x) * z)). [para(2623(a,1),2506(a,2))]. given #2356 (H,wt=23): 2627 (x * y) / (x * (K(z,u) * y)) = K(u,x / ((x * (z \ y)) / y)). [para(2626(a,1),2580(a,1))]. given #2357 (H,wt=31): 2625 (x * y) / (x * (K(T(z \ 1,u) \ 1,w) * y)) = (x * (T(K(w,z),u) * y)) / (x * y). [para(2036(a,1),2623(a,1,1,2,1)),flip(a)]. given #2358 (H,wt=31): 2628 (x * y) / (x * (K(T(z \ 1,u) \ 1,w) * y)) = T((x * (K(w,z) * y)) / (x * y),u). [para(2625(a,2),713(a,1))]. given #2359 (H,wt=31): 2629 (x * y) / (x * (K(T(z \ 1,u) \ 1,w) * y)) = T((x * y) / (x * (K(z,w) * y)),u). [para(2623(a,1),2628(a,2,1))]. given #2360 (H,wt=27): 2630 (x * y) / (x * (T(K(z,u),w) * y)) = T((x * y) / (x * (K(z,u) * y)),w). [para(2266(a,1),2629(a,1,2,2,1))]. given #2361 (H,wt=24): 2631 K(x,y) * T((z * u) / (z * (K(x,y) * u)),z) = a(z,K(x,y),u). [para(2630(a,1),2186(a,1,2))]. given #2362 (H,wt=24): 2632 K(x,y) * T(K(y,z / ((z * (x \ u)) / u)),z) = a(z,K(x,y),u). [para(2627(a,1),2631(a,1,2,1))]. given #2363 (H,wt=22): 2633 K(x,y) * K(y,((z * (x \ u)) / u) \ z) = a(z,K(x,y),u). [para(2303(a,1),2632(a,1,2))]. given #2364 (H,wt=44): 1869 (x * (K(R(x,y,z),u) * w)) * R(T(x,K(R(x,y,z),u) * w),y,z) = (T(R(x,y,z),u) * w) * T(x,K(R(x,y,z),u) * w). [para(1853(a,1),764(a,1,1)),flip(a)]. given #2365 (H,wt=44): 2634 (x * (K(R(x,y,z),u) * w)) * R(T(x,K(R(x,y,z),u) * w),y,z) = (R(T(x,u),y,z) * w) * T(x,K(R(x,y,z),u) * w). [para(40(a,2),1869(a,2,1,1))]. given #2366 (H,wt=41): 2635 (x * (K(R(x,y,z),u) * w)) * R(T(x,K(R(x,y,z),u) * w),y,z) = (R(T(x,u),y,z) * w) * T(x,K(x,u) * w). [para(2048(a,1),2634(a,2,2,2,1))]. given #2367 (H,wt=37): 2637 (x * (K(R(x,y,z),u) * w)) * R(T(x,K(R(x,y,z),u) * w),y,z) = (R(T(x,u),y,z) * w) * T(x,w). [para(2296(a,1),2635(a,2,2))]. given #2368 (H,wt=34): 2638 (x * (K(x,y) * z)) * R(T(x,K(R(x,u,w),y) * z),u,w) = (R(T(x,y),u,w) * z) * T(x,z). [para(2048(a,1),2637(a,1,1,2,1))]. given #2369 (H,wt=32): 2640 (T(x,y) * z) * R(T(x,K(R(x,u,w),y) * z),u,w) = (R(T(x,y),u,w) * z) * T(x,z). [para(1853(a,1),2638(a,1,1))]. given #2370 (H,wt=29): 2642 (T(x,y) * z) * R(T(x,K(x,y) * z),u,w) = (R(T(x,y),u,w) * z) * T(x,z). [para(2048(a,1),2640(a,1,2,1,2,1))]. given #2371 (H,wt=25): 2644 (R(T(x,y),z,u) * w) * T(x,w) = (T(x,y) * w) * R(T(x,w),z,u). [para(2296(a,1),2642(a,1,2,1)),flip(a)]. given #2372 (H,wt=36): 2645 ((T(x,x * y) * y) * R(T(x,y),z,u)) \ ((x * y) * R(T(x,y),z,u)) = K(y * T(x,y),R(x,z,u)). [para(2644(a,1),2189(a,1,1))]. given #2373 (H,wt=32): 2647 (x * (R(T(x,y),z,u) * y)) \ ((x * y) * R(T(x,y),z,u)) = K(y * T(x,y),R(x,z,u)). [para(2104(a,1),2645(a,1,1))]. given #2374 (H,wt=21): 2648 K(R(x,y,z) * u,T(x,u)) = K(u * T(x,u),R(x,y,z)). [para(2647(a,1),2091(a,1)),flip(a)]. given #2375 (H,wt=19): 2649 K(R(x,y,z) * u,T(x,u)) = K(x * u,R(x,y,z)). [para(85(a,1),2648(a,2,1))]. given #2376 (H,wt=16): 2650 K(R(x,y,z) * u,T(x,u)) = K(x * u,x). [para(2649(a,2),915(a,1))]. given #2377 (H,wt=14): 2652 K(R(x,y,z) * u,x) = K(x * u,x). [para(2650(a,1),2352(a,1)),flip(a)]. given #2378 (H,wt=18): 2653 T(x,R(x,y,z) * u) = (K(x * u,x) / x) \ 1. [para(2652(a,1),1907(a,2,1,1))]. given #2379 (H,wt=14): 2655 T(x,R(x,y,z) * u) = T(x,x * u). [para(2653(a,2),1907(a,2)),flip(a)]. given #2380 (H,wt=14): 2656 T(x,x * (R(x,y,z) \ u)) = T(x,u). [para(14(a,1),2655(a,1,2)),flip(a)]. given #2381 (H,wt=16): 2657 T(x,x * (R(x,y,z) \ u)) = x * K(x,u). [para(2656(a,2),1825(a,1))]. given #2382 (H,wt=14): 2658 K(x,x * (R(x,y,z) \ u)) = K(x,u). [hyper(1834,a,2657,a)]. given #2383 (H,wt=14): 2659 K(x,R(x,y,z) \ u) = K(x,u / x). [para(2658(a,1),2615(a,1)),flip(a)]. given #2384 (H,wt=14): 2660 K(x,R(x,y,z) \ u) = K(x,x \ u). [para(2659(a,2),1965(a,1))]. given #2385 (H,wt=19): 2662 R(x,y,z) * (u / R(x,y,z)) = u * K(x,x \ u). [para(2660(a,1),2051(a,2,2))]. given #2386 (H,wt=17): 2663 R(x,y,z) * (u / R(x,y,z)) = x * (u / x). [para(2662(a,2),1968(a,1))]. given #2387 (H,wt=56): 1923 (K(x,y) * ((R(y,z,u) * K(x,y)) \ w)) * a(R(y,z,u),K(x,y),(R(y,z,u) * K(x,y)) \ w) = R(R(y,z,u),K(x,y) * ((R(y,z,u) * K(x,y)) \ w),1) \ w. [para(1920(a,1),638(a,1,1,3)),flip(a)]. given #2388 (H,wt=40): 2665 (K(x,y) * ((R(y,z,u) * K(x,y)) \ w)) * a(R(y,z,u),K(x,y),(R(y,z,u) * K(x,y)) \ w) = R(y,z,u) \ w. [para(157(a,1),1923(a,2,1))]. given #2389 (H,wt=40): 2667 (K(x,y) * (R(y * K(x,y),z,u) \ w)) * a(R(y,z,u),K(x,y),(R(y,z,u) * K(x,y)) \ w) = R(y,z,u) \ w. [para(2502(a,2),2665(a,1,1,2,1))]. given #2390 (H,wt=50): 2668 (K(x,x \ y) * (R(y / x,z,u) \ w)) * a(R(x \ y,z,u),K(x,x \ y),(R(x \ y,z,u) * K(x,x \ y)) \ w) = R(x \ y,z,u) \ w. [para(1800(a,1),2667(a,1,1,2,1,1))]. given #2391 (H,wt=25): 2669 (K(x,x \ y) * (R(y / x,z,u) \ w)) * 1 = R(x \ y,z,u) \ w. [para(1920(a,1),2668(a,1,2))]. given #2392 (H,wt=23): 2670 K(x,x \ y) * (R(y / x,z,u) \ w) = R(x \ y,z,u) \ w. [hyper(68,a,2669,a)]. given #2393 (H,wt=25): 2672 (x / y) * (R(x / y,z,u) \ w) = (y \ x) * (R(y \ x,z,u) \ w). [para(2670(a,1),1879(a,1,2)),flip(a)]. given #2394 (H,wt=28): 2673 ((x \ 1) * (R(x \ 1,y,z) \ u)) * x = R(u / R(1 / x,y,z),x \ 1,x). [para(2672(a,1),2055(a,1,1))]. given #2395 (H,wt=30): 2674 K(x,R(y / R(1 / z,u,w),z \ 1,z)) = K(T(x,z \ 1),R(z \ 1,u,w) \ y). [para(2673(a,1),2613(a,1,2))]. given #2396 (H,wt=25): 2675 K(T(x,y \ 1),R(y \ 1,z,u) \ w) = K(x,w / R(1 / y,z,u)). [para(2674(a,1),915(a,1))]. given #2397 (H,wt=21): 2677 K(x,y / R(1 / z,u,w)) = K(x,y / R(z \ 1,u,w)). [para(2675(a,1),2448(a,1))]. given #2398 (H,wt=53): 2678 K(x,(R(1 / y,z,u) * (w * (R(1 / y,z,u) \ 1))) / R(y \ 1,z,u)) = K(x,(R(1 / y,z,u) * (w / R(1 / y,z,u))) * (R(1 / y,z,u) \ 1)). [para(444(a,1),2677(a,1,2)),flip(a)]. given #2399 (H,wt=47): 2679 K(x,(R(1 / y,z,u) * (w * (R(1 / y,z,u) \ 1))) / R(y \ 1,z,u)) = K(x,((1 / y) * (w / (1 / y))) * (R(1 / y,z,u) \ 1)). [para(2663(a,1),2678(a,2,2,1))]. given #2400 (H,wt=47): 2680 K(x,(R(1 / y,z,u) * (w * (R(1 / y,z,u) \ 1))) / R(y \ 1,z,u)) = K(x,((y \ 1) * (w / (y \ 1))) * (R(1 / y,z,u) \ 1)). [para(1468(a,1),2679(a,2,2,1))]. given #2401 (H,wt=45): 2682 K(x,(R(1 / y,z,u) * (w * (R(1 / y,z,u) \ 1))) / R(y \ 1,z,u)) = K(x,((y \ 1) * (w / (y \ 1))) / R(1 / y,z,u)). [para(2680(a,2),919(a,1))]. given #2402 (H,wt=45): 2683 K(x,(R(1 / y,z,u) * (w * (R(1 / y,z,u) \ 1))) / R(y \ 1,z,u)) = K(x,((y \ 1) * (w / (y \ 1))) / R(y \ 1,z,u)). [para(2682(a,2),2677(a,1))]. given #2403 (H,wt=45): 2684 K(x,(R(1 / y,z,u) * (w * (R(1 / y,z,u) \ 1))) / R(y \ 1,z,u)) = K(x,(y \ 1) / (R(y \ 1,z,u) / (w / (y \ 1)))). [para(2683(a,2),921(a,1))]. given #2404 (H,wt=45): 2685 K(x,(R(1 / y,z,u) * (w * (R(1 / y,z,u) \ 1))) / R(y \ 1,z,u)) = K(x,((R(y \ 1,z,u) / (w / (y \ 1))) * y) \ 1). [para(2684(a,2),2550(a,1))]. given #2405 (H,wt=39): 2686 K(x,((1 / y) * (z * (R(1 / y,u,w) \ 1))) / (y \ 1)) = K(x,((R(y \ 1,u,w) / (z / (y \ 1))) * y) \ 1). [para(2596(a,1),2685(a,1,2))]. given #2406 (H,wt=37): 2688 K(x,((R(y \ 1,z,u) / (w / (y \ 1))) * y) \ 1) = K(x,((1 / y) * (w * (R(1 / y,z,u) \ 1))) * y). [para(2686(a,1),2612(a,1))]. given #2407 (H,wt=35): 2689 K(x,((R(y \ 1,z,u) / (w / (y \ 1))) * y) \ 1) = K(T(x,y \ 1),w * (R(1 / y,z,u) \ 1)). [para(2688(a,2),2504(a,1))]. given #2408 (H,wt=33): 2690 K(x,((R(y \ 1,z,u) / (w / (y \ 1))) * y) \ 1) = K(T(x,y \ 1),w / R(1 / y,z,u)). [para(2689(a,2),919(a,1))]. given #2409 (H,wt=33): 2691 K(x,((R(y \ 1,z,u) / (w / (y \ 1))) * y) \ 1) = K(T(x,y \ 1),w / R(y \ 1,z,u)). [para(2690(a,2),2677(a,1))]. given #2410 (H,wt=31): 2692 K(x,((R(y \ 1,z,u) / (w / (y \ 1))) * y) \ 1) = K(x,T(w / R(y \ 1,z,u),y)). [para(2691(a,2),2534(a,1))]. given #2411 (H,wt=29): 2693 K(x,((R(y \ 1,z,u) / (w / (y \ 1))) * y) \ 1) = K(x,R(y \ 1,z,u) \ w). [para(2692(a,2),2532(a,1))]. given #2412 (H,wt=107): 1322 R(R((x \ 1) \ 1,y,z),K(x \ 1,x) * (R(x,y,z) \ u),a(R((x \ 1) \ 1,y,z),K(x \ 1,x),(R((x \ 1) \ 1,y,z) * K(x \ 1,x)) \ u)) \ u = (K(x \ 1,x) * ((R((x \ 1) \ 1,y,z) * K(x \ 1,x)) \ u)) * a(R((x \ 1) \ 1,y,z),K(x \ 1,x),(R((x \ 1) \ 1,y,z) * K(x \ 1,x)) \ u). [para(1321(a,1),638(a,1,1,2,2,1))]. given #2413 (H,wt=78): 2694 (K(x \ 1,x) * ((R((x \ 1) \ 1,y,z) * K(x \ 1,x)) \ u)) * a(R((x \ 1) \ 1,y,z),K(x \ 1,x),(R((x \ 1) \ 1,y,z) * K(x \ 1,x)) \ u) = R(R((x \ 1) \ 1,y,z),K(x \ 1,x) * (R(x,y,z) \ u),1) \ u. [para(1383(a,1),1322(a,1,1,3)),flip(a)]. given #2414 (H,wt=64): 2695 (K(x \ 1,x) * ((R((x \ 1) \ 1,y,z) * K(x \ 1,x)) \ u)) * a(R((x \ 1) \ 1,y,z),K(x \ 1,x),(R((x \ 1) \ 1,y,z) * K(x \ 1,x)) \ u) = R((x \ 1) \ 1,y,z) \ u. [para(157(a,1),2694(a,2,1))]. given #2415 (H,wt=54): 2698 (K(x \ 1,x) * (R(x,y,z) \ u)) * a(R((x \ 1) \ 1,y,z),K(x \ 1,x),(R((x \ 1) \ 1,y,z) * K(x \ 1,x)) \ u) = R((x \ 1) \ 1,y,z) \ u. [para(1321(a,1),2695(a,1,1,2,1))]. given #2416 (H,wt=25): 2699 (K(x \ 1,x) * (R(x,y,z) \ u)) * 1 = R((x \ 1) \ 1,y,z) \ u. [para(1383(a,1),2698(a,1,2))]. given #2417 (H,wt=23): 2700 K(x \ 1,x) * (R(x,y,z) \ u) = R((x \ 1) \ 1,y,z) \ u. [hyper(68,a,2699,a)]. given #2418 (H,wt=21): 2703 K(x,R((y \ 1) \ 1,z,u) \ w) = K(x,R(y,z,u) \ w). [para(2700(a,1),2388(a,1,2))]. given #2419 (H,wt=23): 2702 (R(x,y,z) \ u) * K(x \ 1,x) = R((x \ 1) \ 1,y,z) \ u. [para(2700(a,1),1133(a,1)),flip(a)]. given #2420 (H,wt=21): 2704 1 / (R((x \ 1) \ 1,y,z) \ 1) = (R(x,y,z) \ 1) \ 1. [para(2702(a,1),1249(a,1,2))]. given #2421 (H,wt=17): 2705 R((x \ 1) \ 1,y,z) = (R(x,y,z) \ 1) \ 1. [para(2704(a,1),57(a,1)),flip(a)]. given #2422 (H,wt=17): 2706 1 / R((x \ 1) \ 1,y,z) = R(x,y,z) \ 1. [para(2705(a,2),57(a,1,2))]. given #2423 (H,wt=17): 2708 1 / R(x \ 1,y,z) = R(1 / x,y,z) \ 1. [para(59(a,1),2706(a,1,2,1,1))]. given #2424 (H,wt=17): 2709 R(1 / (1 / x),y,z) \ 1 = 1 / R(x,y,z). [para(98(a,1),2706(a,1,2,1)),flip(a)]. given #2425 (H,wt=17): 2711 R(1 / (1 / x),y,z) = 1 / (1 / R(x,y,z)). [para(2709(a,1),57(a,1,2)),flip(a)]. given #2426 (H,wt=28): 2707 R((x \ 1) \ 1,y,z) * K(u,R(x,y,z) \ 1) = T(R(x,y,z) \ 1,u) \ 1. [para(2705(a,2),1900(a,1,1))]. given #2427 (H,wt=25): 2713 R((x \ 1) \ 1,y,z) * K(u,x \ 1) = T(R(x,y,z) \ 1,u) \ 1. [para(2127(a,1),2707(a,1,2))]. given #2428 (H,wt=25): 2715 R(((x \ 1) \ 1) * K(y,x \ 1),z,u) = T(R(x,z,u) \ 1,y) \ 1. [para(2713(a,1),2502(a,2))]. given #2429 (H,wt=21): 2716 R(T(x \ 1,y) \ 1,z,u) = T(R(x,z,u) \ 1,y) \ 1. [para(1900(a,1),2715(a,1,1))]. given #2430 (H,wt=29): 2712 K(x,(R(1 / (1 / (1 / y)),z,u) * w) / R(y \ 1,z,u)) = K(T(x,y \ 1),w). [para(2711(a,2),2616(a,1,2,1,1))]. given #2431 (H,wt=29): 2717 K(x,R(1 / (1 / (1 / y)),z,u) / (R(y \ 1,z,u) / w)) = K(T(x,y \ 1),w). [para(2712(a,1),921(a,1)),flip(a)]. given #2432 (H,wt=27): 2718 K(x,R(1 / (1 / (1 / y)),z,u) / (R(y \ 1,z,u) / w)) = K(x,T(w,y)). [para(2717(a,2),2534(a,1))]. given #2433 (H,wt=24): 2719 K(x,(1 / (1 / (1 / y))) / (R(y \ 1,z,u) / w)) = K(x,T(w,y)). [para(2718(a,1),2611(a,1)),flip(a)]. given #2434 (H,wt=24): 2720 K(x,1 / ((R(y \ 1,z,u) / w) * (1 / (1 / y)))) = K(x,T(w,y)). [para(2719(a,1),918(a,1)),flip(a)]. given #2435 (H,wt=24): 2722 K(x,1 / ((R(y \ 1,z,u) / w) * ((1 / y) \ 1))) = K(x,T(w,y)). [para(2720(a,1),2540(a,1)),flip(a)]. given #2436 (H,wt=20): 2723 K(x,1 / ((R(y \ 1,z,u) / w) * y)) = K(x,T(w,y)). [para(59(a,1),2722(a,1,2,2,2))]. given #2437 (H,wt=20): 2724 K(x,((R(y \ 1,z,u) / w) * y) \ 1) = K(x,T(w,y)). [para(2723(a,1),928(a,1)),flip(a)]. given #2438 (H,wt=20): 2725 K(x,T(y / (z \ 1),z)) = K(x,R(z \ 1,u,w) \ y). [para(2724(a,1),2693(a,1))]. given #2439 (H,wt=18): 2726 K(x,T(y * z,z)) = K(x,R(z \ 1,u,w) \ y). [para(2725(a,1),2407(a,1)),flip(a)]. given #2440 (H,wt=16): 2728 K(x,R(y \ 1,z,u) \ w) = K(x,y * w). [para(2726(a,1),2606(a,1))]. given #2441 (H,wt=34): 2710 K(R(1 / x,y,z) \ 1,u) * T(R(x \ 1,y,z) \ 1,x) = T(R(x \ 1,y,z) \ 1,T(u,1)). [para(2708(a,1),2476(a,1,1,1))]. given #2442 (H,wt=31): 2729 K((1 / x) \ 1,y) * T(R(x \ 1,z,u) \ 1,x) = T(R(x \ 1,z,u) \ 1,T(y,1)). [para(2077(a,1),2710(a,1,1))]. given #2443 (H,wt=27): 2730 K(x,y) * T(R(x \ 1,z,u) \ 1,x) = T(R(x \ 1,z,u) \ 1,T(y,1)). [para(59(a,1),2729(a,1,1,1))]. given #2444 (H,wt=25): 2732 T(R(x \ 1,y,z) \ 1,T(u,1)) = K(x,u) * (R(x \ 1,y,z) \ 1). [para(2147(a,1),2730(a,1,2)),flip(a)]. given #2445 (H,wt=23): 2733 K(x,y) * (R(x \ 1,z,u) \ 1) = T(R(x \ 1,z,u) \ 1,y). [para(1124(a,1),2732(a,1,2)),flip(a)]. given #2446 (H,wt=31): 2734 ((x \ 1) * (R((x \ 1) \ 1,y,z) \ 1)) / (1 / x) = T(R((x \ 1) \ 1,y,z) \ 1,x). [para(2733(a,1),2149(a,2))]. given #2447 (H,wt=35): 2735 K(x,(T(R((y \ 1) \ 1,z,u) \ 1,y) \ 1) \ w) = K(x,((R((y \ 1) \ 1,z,u) \ 1) \ 1) \ w). [para(2734(a,1),2411(a,1,2,1,1))]. given #2448 (H,wt=35): 2736 K(x,R(T(((y \ 1) \ 1) \ 1,y) \ 1,z,u) \ w) = K(x,((R((y \ 1) \ 1,z,u) \ 1) \ 1) \ w). [para(2716(a,2),2735(a,1,2,1))]. given #2449 (H,wt=31): 2737 K(x,R(T(((y \ 1) \ 1) \ 1,y) \ 1,z,u) \ w) = K(x,R((y \ 1) \ 1,z,u) \ w). [para(2736(a,2),2395(a,1))]. given #2450 (H,wt=27): 2738 K(x,R(T(((y \ 1) \ 1) \ 1,y) \ 1,z,u) \ w) = K(x,R(y,z,u) \ w). [para(2737(a,2),2703(a,1))]. given #2451 (H,wt=22): 2739 K(x,R(y,z,u) \ w) = K(x,T(((y \ 1) \ 1) \ 1,y) * w). [para(2738(a,1),2728(a,1))]. given #2452 (H,wt=18): 2740 K(x,R(y,z,u) \ w) = K(x,T(y \ 1,y) * w). [para(2739(a,2),2398(a,1))]. given #2453 (H,wt=14): 2742 K(x,R(y,z,u) \ w) = K(x,y \ w). [para(2740(a,2),2610(a,1))]. given #2454 (H,wt=19): 2743 K(x,((y * (z \ u)) / u) \ w) = K(x,(y / z) \ w). [para(219(a,1),2742(a,1,2,1))]. given #2455 (H,wt=18): 2744 a(x,K(y,z),u) = K(y,z) * K(z,(x / y) \ x). [para(2743(a,1),2633(a,1,2)),flip(a)]. given #2456 (H,wt=14): 2745 a(x,K(y,z),u) = K(y,z) * K(z,y). [para(59(a,1),2744(a,2,2,2))]. -------- Proof 1 -------- "aK2". ============================== PROOF ================================= % Proof 1 at 135.64 (+ 4.07) seconds: "aK2". % Length of proof is 2446. % Level of proof is 239. % Maximum clause weight is 107.000. % Given clauses 2456 (10.276 givens/level). 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(x,K(y,z),u) = 1 # label("aK2") # label(non_clause) # label(goal). [goal]. 11 1 * x = x. [assumption]. 12 x * 1 = x. [assumption]. 13 x \ (x * y) = y. [assumption]. 14 x * (x \ y) = y. [assumption]. 15 (x * y) / y = x. [assumption]. 16 (x / y) * y = x. [assumption]. 17 x * y != z | x * u != z | u = y. [clausify(1)]. 18 x * y != z | u * y != z | u = x. [clausify(2)]. 19 x * y != x * z | y = z. [clausify(3)]. 20 x * y != z * y | x = z. [clausify(4)]. 21 (x * (y * z)) \ ((x * y) * z) = a(x,y,z) # label("associator"). [assumption]. 22 a(x,y,z) = (x * (y * z)) \ ((x * y) * z). [copy(21),flip(a)]. 23 (x * y) \ (y * x) = K(y,x) # label("commutator"). [assumption]. 24 K(x,y) = (y * x) \ (x * y). [copy(23),flip(a)]. 25 (x * y) \ (x * (y * z)) = L(z,y,x). [assumption]. 26 L(x,y,z) = (z * y) \ (z * (y * x)). [copy(25),flip(a)]. 27 ((x * y) * z) / (y * z) = R(x,y,z). [assumption]. 28 R(x,y,z) = ((x * y) * z) / (y * z). [copy(27),flip(a)]. 29 x \ (y * x) = T(y,x). [assumption]. 30 T(x,y) = y \ (x * y). [copy(29),flip(a)]. 31 a(x,y,z) != 1 | L(z,y,x) = z. [clausify(5)]. 32 L(x,y,z) != x | a(z,y,x) = 1. [clausify(6)]. 33 T(x,y) != x | T(y,x) = y. [clausify(7)]. 34 T(x,y) != x | K(x,y) = 1. [clausify(8)]. 35 K(x,y) != 1 | T(x,y) = x. [clausify(9)]. 36 T(T(x,y),z) = T(T(x,z),y). [assumption]. 37 T(L(x,y,z),u) = L(T(x,u),y,z). [assumption]. 38 L(T(x,y),z,u) = T(L(x,z,u),y). [copy(37),flip(a)]. 39 T(R(x,y,z),u) = R(T(x,u),y,z). [assumption]. 40 R(T(x,y),z,u) = T(R(x,z,u),y). [copy(39),flip(a)]. 41 L(R(x,y,z),u,w) = R(L(x,u,w),y,z). [assumption]. 42 R(L(x,y,z),u,w) = L(R(x,u,w),y,z). [copy(41),flip(a)]. 43 L(L(x,y,z),u,w) = L(L(x,u,w),y,z). [assumption]. 44 R(R(x,y,z),u,w) = R(R(x,u,w),y,z). [assumption]. 45 a(K(x,y),z,u) = 1 # label("aK1"). [assumption]. 46 a(c1,K(c2,c3),c4) != 1 # label("aK2") # answer("aK2"). [deny(10)]. 47 1 \ x = x. [para(11(a,1),13(a,1,2))]. 48 x \ x = 1. [para(12(a,1),13(a,1,2))]. 49 (x * (x \ 1)) * y = y. [para(14(a,2),11(a,1,1))]. 50 x * (x \ (1 * y)) = y. [para(14(a,2),11(a,1))]. 51 x * (y * (y \ 1)) = x. [para(14(a,2),12(a,1,2))]. 52 x \ (y * (y \ (x * z))) = z. [para(14(a,2),13(a,1,2))]. 53 x * (y * (y \ (x \ z))) = z. [para(14(a,2),14(a,1,2))]. 54 x / x = 1. [para(11(a,1),15(a,1,1))]. 55 x / 1 = x. [para(12(a,1),15(a,1,1))]. 56 x * (((x \ y) * z) / z) = y. [para(15(a,2),14(a,1,2))]. 57 x / (y \ x) = y. [para(14(a,1),15(a,1,1))]. 58 ((1 / x) * x) * y = y. [para(16(a,2),11(a,1,1))]. 59 (x / y) \ x = y. [para(16(a,1),13(a,1,2))]. 60 ((x * (x \ y)) / z) * z = y. [para(16(a,2),14(a,1))]. 61 (((x * y) / z) * z) / y = x. [para(16(a,2),15(a,1,1))]. 62 (((x / y) / z) * z) * y = x. [para(16(a,2),16(a,1,1))]. 63 x * y != x | 1 = y. [para(12(a,1),19(a,1)),flip(a)]. 64 (x * y) * 1 != x * z | z = y. [para(12(a,2),19(a,2)),flip(a)]. 65 x \ (x * (y * z)) != y * u | u = z. [para(13(a,2),19(a,2)),flip(a)]. 66 x * y != z | x \ z = y. [para(14(a,1),19(a,1)),flip(a)]. 68 x * 1 != y | x = y. [para(12(a,1),20(a,2))]. 69 x * (y \ z) != z | x = y. [para(14(a,1),20(a,2))]. 70 x * y != z | z / y = x. [para(16(a,1),20(a,1)),flip(a)]. 71 (x * (y * z)) * a(x,y,z) = (x * y) * z. [para(22(a,2),14(a,1,2))]. 72 (x * y) * K(y,x) = y * x. [para(24(a,2),14(a,1,2))]. 73 x \ ((y \ x) * y) = K(y \ x,y). [para(14(a,1),24(a,2,1)),flip(a)]. 74 ((x \ y) * x) \ y = K(x,x \ y). [para(14(a,1),24(a,2,2)),flip(a)]. 75 x \ (y * (x / y)) = K(y,x / y). [para(16(a,1),24(a,2,1)),flip(a)]. 76 (x * y) * L(z,y,x) = x * (y * z). [para(26(a,2),14(a,1,2))]. 77 x \ (y * ((y \ x) * z)) = L(z,y \ x,y). [para(14(a,1),26(a,2,1)),flip(a)]. 78 L(x \ y,x,z) = (z * x) \ (z * y). [para(14(a,1),26(a,2,2,2))]. 79 L(x,y / x,z) = (z * (y / x)) \ (z * y). [para(16(a,1),26(a,2,2,2))]. 80 (x * y) / (y * 1) = R(x,y,1). [para(12(a,1),28(a,2,1)),flip(a)]. 81 R(x,y,z) * (y * z) = (x * y) * z. [para(28(a,2),16(a,1,1))]. 82 R(x / y,y,z) = (x * z) / (y * z). [para(16(a,1),28(a,2,1,1))]. 83 ((x * (y / z)) * z) / y = R(x,y / z,z). [para(16(a,1),28(a,2,2)),flip(a)]. 84 T(x,x) = x. [para(30(a,2),13(a,1))]. 85 x * T(y,x) = y * x. [para(30(a,2),14(a,1,2))]. 86 T(x,x \ y) = (x \ y) \ y. [para(14(a,1),30(a,2,2))]. 87 T(x / y,y) = y \ x. [para(16(a,1),30(a,2,2))]. 88 L(x,y,K(z,u)) = x. [hyper(31,a,45,a)]. 89 ((1 / x) * x) \ y = y. [para(16(a,2),47(a,1,1))]. 91 x / (y * (y \ 1)) = x. [para(14(a,2),55(a,1,2))]. 92 x / ((1 / y) * y) = x. [para(16(a,2),55(a,1,2))]. 93 T(T(x,y),x) = T(x,y). [para(84(a,1),36(a,1,1)),flip(a)]. 94 (x * y) / K(x,y) = y * x. [para(24(a,2),57(a,1,2))]. 95 (x * (y * z)) / L(z,y,x) = x * y. [para(26(a,2),57(a,1,2))]. 96 (x * y) / T(x,y) = y. [para(30(a,2),57(a,1,2))]. 97 R(x,y,z) \ ((x * y) * z) = y * z. [para(28(a,2),59(a,1,1))]. 98 ((x / (y / z)) \ x) \ y = z. [para(59(a,2),59(a,1,1))]. 99 x * (y * (y \ 1)) != z | x = z. [para(14(a,2),68(a,1,2))]. 100 (x * (x \ 1)) * y != z | y = z. [para(49(a,1),19(a,2))]. 101 R(x,x \ 1,y) = y / ((x \ 1) * y). [para(49(a,1),28(a,2,1))]. 102 x \ ((x * y) * (y \ 1)) = a(x,y,y \ 1). [para(51(a,1),22(a,2,1)),flip(a)]. 103 L(x \ 1,x,y) = (y * x) \ y. [para(51(a,1),26(a,2,2))]. 104 R(1 / x,x,y) = y / (x * y). [para(58(a,1),28(a,2,1))]. 105 T((x * y) / x,x) = y. [hyper(17,a,16,a(flip),b,85,a)]. 106 (x * T(y,x)) / x = y. [hyper(18,a,16,a,b,85,a(flip)),flip(a)]. 107 x \ (y * T(x,y)) = y. [hyper(17,a,14,a,b,85,a(flip)),flip(a)]. 108 (x \ y) * T(x,x \ y) = y. [para(85(a,2),14(a,1))]. 109 x * y != z * x | T(z,x) = y. [para(85(a,1),19(a,1)),flip(a)]. 110 x * T(y,x) != z * x | z = y. [para(85(a,2),20(a,2)),flip(a)]. 111 (x * (y * T(z,x * y))) \ (z * (x * y)) = a(x,y,T(z,x * y)). [para(85(a,1),22(a,2,2)),flip(a)]. 112 (x * y) \ (x * (z * y)) = L(T(z,y),y,x). [para(85(a,1),26(a,2,2,2)),flip(a)]. 113 T(x,y) \ (x * y) = T(y,T(x,y)). [para(85(a,1),30(a,2,2)),flip(a)]. 114 x * T(T(y,x),z) = T(y,z) * x. [para(36(a,1),85(a,1,2))]. 115 x * L(T(y,x),z,u) = L(y,z,u) * x. [para(38(a,2),85(a,1,2))]. 116 x * R(T(y,x),z,u) = R(y,z,u) * x. [para(40(a,2),85(a,1,2))]. 117 T(T(x / y,z),y) = T(y \ x,z). [para(87(a,1),36(a,1,1)),flip(a)]. 118 K(x,1 / x) = x * (1 / x). [para(89(a,1),24(a,2))]. 119 (1 / x) * (x * y) = L(y,x,1 / x). [para(89(a,1),26(a,2)),flip(a)]. 120 (x * y) * (y \ 1) = R(x,y,y \ 1). [para(91(a,1),28(a,2)),flip(a)]. 121 (x * (1 / y)) * y = R(x,1 / y,y). [para(92(a,1),28(a,2)),flip(a)]. 122 T(x,T(x,y)) = x. [hyper(33,a,93,a)]. 123 x / T(y,y \ x) = y \ x. [para(14(a,1),96(a,1,1))]. 124 T(T((x * y) / x,z),x) = T(y,z). [para(105(a,1),36(a,1,1)),flip(a)]. 125 (x / y) \ (z * (z \ x)) = y. [para(16(a,1),52(a,1,2,2,2))]. 126 x \ ((x * y) * L(z,y,x)) = y * z. [para(26(a,2),52(a,1,2,2))]. 127 x * (y * (y \ z)) = x * z. [para(13(a,1),53(a,1,2,2,2))]. 128 L(x \ (y \ z),x,y) = (y * x) \ z. [para(53(a,1),26(a,2,2))]. 129 x * (x \ (y * z)) = y * (u * (u \ z)). [para(52(a,1),53(a,1,2,2,2)),flip(a)]. 130 (x / y) * y = 1 * x. [para(50(a,1),60(a,1,1,1))]. 132 ((x / y) * y) / z = x / z. [para(16(a,1),61(a,1,1,1,1))]. 133 R((x / y) / z,z,y) = x / (z * y). [para(62(a,1),28(a,2,1))]. 134 ((x * y) / z) * z = ((x / u) * u) * y. [para(61(a,1),62(a,1,1,1,1)),flip(a)]. 135 K(x \ 1,x) = (x \ 1) * x. [hyper(17,a,49,a,b,72,a)]. 136 x * K(y \ x,y) = (y \ x) * y. [para(14(a,1),72(a,1,1))]. 137 x * K(y,x / y) = y * (x / y). [para(16(a,1),72(a,1,1))]. 138 (x * y) * z != y * x | K(y,x) = z. [para(72(a,1),19(a,1)),flip(a)]. 139 (x * y) / (x * K(x,y)) = R(y,x,K(x,y)). [para(72(a,1),28(a,2,1)),flip(a)]. 140 K(x,y) \ (x * y) = T(y * x,K(x,y)). [para(72(a,1),30(a,2,2)),flip(a)]. 141 (x * y) * K(K(x,y),y * x) = K(x,y) * (y * x). [para(72(a,1),72(a,1,1))]. 142 x / K(y,y \ x) = (y \ x) * y. [para(14(a,1),94(a,1,1))]. 143 (x \ y) * z != y | T(x,x \ y) = z. [para(108(a,1),19(a,1)),flip(a)]. 144 L(T(x,x \ y),x \ y,z) = (z * (x \ y)) \ (z * y). [para(108(a,1),26(a,2,2,2))]. 145 K(x,1 / x) / (1 / x) = x. [hyper(70,a,118,a(flip))]. 146 (x / y) * y = z * (z \ x). [para(125(a,1),14(a,1,2))]. 147 (x / (y * (y \ z))) * z = x. [para(127(a,1),16(a,1))]. 148 x / (y \ ((x / z) * z)) = y. [para(132(a,1),57(a,1))]. 149 K(x \ 1,x) / x = x \ 1. [hyper(70,a,135,a(flip))]. 150 (x * (y \ 1)) \ (x * K(y \ 1,y)) = L(y,y \ 1,x). [para(135(a,2),26(a,2,2,2)),flip(a)]. 151 x \ K(x \ 1,x) = T(x \ 1,x). [para(135(a,2),30(a,2,2)),flip(a)]. 153 R(x,y,y \ z) * z = (x * y) * (y \ z). [para(28(a,2),147(a,1,1))]. 154 x * y != x * z | z = y. [para(12(a,1),64(a,1))]. 155 x * 1 != y * z | y \ x = z. [para(14(a,1),64(a,1,1)),flip(b)]. 156 (x * y) / y = R(x,y,1). [para(12(a,1),80(a,1,2))]. 157 R(x,y,1) = x. [para(156(a,1),15(a,1))]. 158 L(x \ 1,x,y / x) = y \ (y / x). [para(16(a,1),103(a,2,1))]. 159 L(L(x \ 1,y,z),x,u) = L((u * x) \ u,y,z). [para(103(a,1),43(a,1,1)),flip(a)]. 160 x / L(y \ 1,y,x) = x * y. [para(103(a,2),57(a,1,2))]. 161 R(1 / x,x,x \ y) = (x \ y) / y. [para(14(a,1),104(a,2,2))]. 162 T(x / (y * x),z) = R(T(1 / y,z),y,x). [para(104(a,1),40(a,2,1)),flip(a)]. 163 R(R(1 / x,y,z),x,u) = R(u / (x * u),y,z). [para(104(a,1),44(a,1,1)),flip(a)]. 164 R(1 / x,x,y) \ y = x * y. [para(104(a,2),59(a,1,1))]. 165 x * T(T(y,x),z) != u * x | T(y,z) = u. [para(36(a,1),110(a,1,2)),flip(b)]. 166 x / L(y,1 / y,x) = x * (1 / y). [para(59(a,1),160(a,1,2,1))]. 167 K(x,y) / (z \ 1) = K(x,y) * z. [para(88(a,1),160(a,1,2))]. 168 R(x,x \ 1,y) \ y = (x \ 1) * y. [para(57(a,1),164(a,1,1,1))]. 169 K(x \ 1,x) \ 1 = K(x,x \ 1). [para(135(a,2),74(a,1,1))]. 170 x * T(x \ (y * x),z) = T(y,z) * x. [para(30(a,1),114(a,1,2,1))]. 171 T(x / y,z) * y = y * T(y \ x,z). [para(87(a,1),114(a,1,2,1)),flip(a)]. 172 T(x,y) * T(x,z) = T(x,z) * T(x,y). [para(122(a,1),114(a,1,2,1))]. 173 T((x * y) / x,z) * x = x * T(y,z). [para(105(a,1),114(a,1,2,1)),flip(a)]. 174 (x \ y) * T((x \ y) \ y,z) = T(x,z) * (x \ y). [para(86(a,1),114(a,1,2,1))]. 175 T(x,T(x,y) \ z) * y = y * ((T(x,y) \ z) \ z). [para(86(a,1),114(a,1,2)),flip(a)]. 176 (x * T(x \ y,z)) / x = T(y / x,z). [para(117(a,1),106(a,1,1,2))]. 177 x * T(x \ y,z) != u * x | T(y / x,z) = u. [para(117(a,1),110(a,1,2)),flip(b)]. 178 (x * T(y,z)) / x = T((x * y) / x,z). [para(124(a,1),106(a,1,1,2))]. 179 T((((x * y) / x) \ z) \ z,x) = T(y,((x * y) / x) \ z). [para(86(a,1),124(a,1,1))]. 181 R((x \ 1) * x,K(x,x \ 1),y) \ y = K(x,x \ 1) * y. [para(142(a,1),164(a,1,1,1))]. 182 K(x,y) * (1 / z) = K(x,y) / z. [para(59(a,1),167(a,1,2)),flip(a)]. 183 K(x \ 1,x) * K(x,x \ 1) = 1. [para(169(a,1),14(a,1,2))]. 184 L(K(x,x \ 1),K(x \ 1,x),y) = (y * K(x \ 1,x)) \ y. [para(169(a,1),103(a,1,1))]. 185 K(x,y) \ (K(x,y) / z) = 1 / z. [hyper(66,a,182,a)]. 186 1 / (x \ K(y,z)) = K(y,z) \ x. [para(57(a,1),185(a,1,2)),flip(a)]. 187 K(x,1 / x) \ x = 1 / (1 / x). [para(145(a,1),185(a,1,2))]. 188 K(x \ 1,x) \ (x \ 1) = 1 / x. [para(149(a,1),185(a,1,2))]. 189 x * ((x \ 1) * y) = L(y,x \ 1,x). [hyper(100,a,76,a),flip(a)]. 190 x * L(y,z \ x,z) = z * ((z \ x) * y). [para(14(a,1),76(a,1,1))]. 191 x * L(y,z,x / z) = (x / z) * (z * y). [para(16(a,1),76(a,1,1))]. 192 (x * y) * z != x * (y * u) | L(u,y,x) = z. [para(76(a,1),19(a,1)),flip(a)]. 193 (x * (y * z)) \ ((x * y) * (L(z,y,x) * u)) = L(u,L(z,y,x),x * y). [para(76(a,1),26(a,2,1)),flip(a)]. 194 (x * (y * z)) \ (x * (y * (z * u))) = L(L(u,z,y),y * z,x). [para(76(a,1),26(a,2,2,2)),flip(a)]. 195 (x * y) * T(L(z,y,x),u) = x * (y * T(z,u)). [para(38(a,1),76(a,1,2))]. 196 (x * y) * L(L(z,y,x),u,w) = x * (y * L(z,u,w)). [para(43(a,1),76(a,1,2))]. 197 (K(x,y) * z) * u = K(x,y) * (z * u). [para(88(a,1),76(a,1,2))]. 198 (x * y) * L(z,T(x,y),y) = y * (T(x,y) * z). [para(85(a,1),76(a,1,1))]. 199 K(x \ 1,x) * L(y,x,x \ 1) = (x \ 1) * (x * y). [para(135(a,2),76(a,1,1))]. 200 L((x \ y) \ z,x \ y,x) = y \ (x * z). [para(14(a,1),78(a,2,1))]. 201 L(x \ y,x,z / x) = z \ ((z / x) * y). [para(16(a,1),78(a,2,1))]. 202 L(x \ y,x,z / y) = ((z / y) * x) \ z. [para(16(a,1),78(a,2,2))]. 203 T((x * y) \ (x * z),u) = L(T(y \ z,u),y,x). [para(78(a,1),38(a,2,1)),flip(a)]. 204 R((x * y) \ (x * z),u,w) = L(R(y \ z,u,w),y,x). [para(78(a,1),42(a,1,1))]. 205 L(L(x \ y,z,u),x,w) = L((w * x) \ (w * y),z,u). [para(78(a,1),43(a,1,1)),flip(a)]. 206 (K(x,y) * z) \ (K(x,y) * u) = z \ u. [para(78(a,1),88(a,1))]. 207 L(T(x,y) \ z,T(x,y),y) = (x * y) \ (y * z). [para(85(a,1),78(a,2,1))]. 208 L(x \ T(y,z),x,z) = (z * x) \ (y * z). [para(85(a,1),78(a,2,2))]. 209 L(x \ y,x,1 / x) = (1 / x) * y. [para(78(a,2),89(a,1))]. 210 R(x,y / z,z) * y = (x * (y / z)) * z. [para(16(a,1),81(a,1,2))]. 211 (x * y) * z != u * (y * z) | R(x,y,z) = u. [para(81(a,1),20(a,1))]. 212 ((x * y) * z) \ ((R(x,y,z) * y) * z) = a(R(x,y,z),y,z). [para(81(a,1),22(a,2,1)),flip(a)]. 213 (((x * y) * z) * u) / ((y * z) * u) = R(R(x,y,z),y * z,u). [para(81(a,1),28(a,2,1,1)),flip(a)]. 214 L(R(x,y,z),u,w) * (y * z) = (L(x,u,w) * y) * z. [para(42(a,1),81(a,1,1))]. 215 R(R(x,y,z),u,w) * (y * z) = (R(x,u,w) * y) * z. [para(44(a,1),81(a,1,1))]. 216 R(x,y,T(z,y)) * (z * y) = (x * y) * T(z,y). [para(85(a,1),81(a,1,2))]. 217 R(x,y \ 1,y) * K(y \ 1,y) = (x * (y \ 1)) * y. [para(135(a,2),81(a,1,2))]. 218 R(x,R(y,z,u),z * u) * ((y * z) * u) = (x * R(y,z,u)) * (z * u). [para(81(a,1),81(a,1,2))]. 219 R(x / y,y,y \ z) = (x * (y \ z)) / z. [para(14(a,1),82(a,2,2))]. 220 R(x / (y / z),y / z,z) = (x * z) / y. [para(16(a,1),82(a,2,2))]. 221 T((x * y) / (z * y),u) = R(T(x / z,u),z,y). [para(82(a,1),40(a,2,1)),flip(a)]. 222 R(x / y,y,z) \ (x * z) = y * z. [para(82(a,2),59(a,1,1))]. 223 R(x / y,y,T(z,y)) = (x * T(z,y)) / (z * y). [para(85(a,1),82(a,2,2))]. 224 R(x / y,y,y \ 1) = x * (y \ 1). [para(82(a,2),91(a,1))]. 225 R(x / (1 / y),1 / y,y) = x * y. [para(82(a,2),92(a,1))]. 226 (x * (1 / y)) / K(y,1 / y) = R(x / y,y,1 / y). [para(118(a,2),82(a,2,2)),flip(a)]. 227 R((x \ 1) / y,y,x) = K(x \ 1,x) / (y * x). [para(135(a,2),82(a,2,1))]. 228 R((x * y) / z,z,L(u,y,x)) = (x * (y * u)) / (z * L(u,y,x)). [para(76(a,1),82(a,2,1))]. 229 (x * y) / L(z,y / z,x) = x * (y / z). [para(16(a,1),95(a,1,1,2))]. 230 (K(x,y) * (z * u)) / u = K(x,y) * z. [para(88(a,1),95(a,1,2))]. 231 (x * (y * z)) / L(T(y,z),z,x) = x * z. [para(85(a,1),95(a,1,1,2))]. 232 (x * y) / L(T(z,z \ y),z \ y,x) = x * (z \ y). [para(108(a,1),95(a,1,1,2))]. 233 R(x,x \ y,z) \ (y * z) = (x \ y) * z. [para(14(a,1),97(a,1,2,1))]. 234 R(x,T(y,x),z) \ ((y * x) * z) = T(y,x) * z. [para(85(a,1),97(a,1,2,1))]. 235 R(x * y,K(y,x),z) \ ((y * x) * z) = K(y,x) * z. [para(72(a,1),97(a,1,2,1))]. 236 R(x,y,K(y,x)) \ (y * x) = y * K(y,x). [para(72(a,1),97(a,1,2))]. 237 R(x * y,L(z,y,x),u) \ ((x * (y * z)) * u) = L(z,y,x) * u. [para(76(a,1),97(a,1,2,1))]. 238 x / K(x \ 1,x) = R(x,x \ 1,x). [para(135(a,2),101(a,2,2)),flip(a)]. 239 L(x,y,1 / y) / (y * x) = 1 / y. [hyper(70,a,119,a)]. 240 (1 / x) \ L(y,x,1 / x) = x * y. [hyper(66,a,119,a)]. 241 L(T(x,y),y,1 / y) = (1 / y) * (x * y). [para(85(a,1),119(a,1,2)),flip(a)]. 242 R(x,y,y \ 1) / (y \ 1) = x * y. [hyper(70,a,120,a)]. 243 R(x,y,y \ 1) != z * (y \ 1) | x * y = z. [para(120(a,1),20(a,1))]. 244 (x \ 1) \ R(y,x,x \ 1) = T(y * x,x \ 1). [para(120(a,1),30(a,2,2)),flip(a)]. 245 K(x \ 1,x) * (x \ 1) = R(x \ 1,x,x \ 1). [para(135(a,2),120(a,1,1))]. 246 R(x,1 / y,y) / y = x * (1 / y). [hyper(70,a,121,a)]. 247 K(x,1 / x) * x = R(x,1 / x,x). [para(118(a,2),121(a,1,1))]. 248 x \ L(y,x \ 1,x) = (x \ 1) * y. [para(49(a,1),126(a,1,2))]. 249 L(T(x \ (y \ z),u),x,y) = T((y * x) \ z,u). [para(128(a,1),38(a,2,1))]. 250 (K(x,y) * z) \ u = z \ (K(x,y) \ u). [para(128(a,1),88(a,1))]. 251 T(x \ (x / y),z) = L(T(y \ 1,z),y,x / y). [para(158(a,1),38(a,2,1)),flip(a)]. 252 L(x \ 1,x,y / x) * y = (y / x) * K(y \ (y / x),y). [para(158(a,2),136(a,2,1)),flip(a)]. 253 L((x \ 1) \ y,x \ 1,x) = x * y. [para(14(a,1),189(a,1,2)),flip(a)]. 254 x * K(x \ 1,x) = L(x,x \ 1,x). [para(135(a,2),189(a,1,2))]. 255 L(T(x \ y,z),x,1 / x) = T((1 / x) * y,z). [para(209(a,1),38(a,2,1))]. 256 L(R(x \ y,z,u),x,1 / x) = R((1 / x) * y,z,u). [para(209(a,1),42(a,1,1)),flip(a)]. 257 L(L(x \ y,z,u),x,1 / x) = L((1 / x) * y,z,u). [para(209(a,1),43(a,1,1)),flip(a)]. 258 R(x / y,y,x \ z) \ z = y * (x \ z). [para(14(a,1),222(a,1,2))]. 259 L(R(x,1 / y,y),z,u) / y = L(x,z,u) * (1 / y). [para(42(a,1),246(a,1,1))]. 260 L(x / y,z,u) * y = y * L(y \ x,z,u). [para(87(a,1),115(a,1,2,1)),flip(a)]. 261 x * (y * T(z,x * y)) = L(z,y,x) * (x * y). [para(115(a,1),76(a,1)),flip(a)]. 262 x \ (L(y,z,x) * (x * z)) = z * T(y,x * z). [para(115(a,1),126(a,1,2))]. 264 R(x / y,z,u) * y = y * R(y \ x,z,u). [para(87(a,1),116(a,1,2,1)),flip(a)]. 265 R((x * y) / x,z,u) * x = x * R(y,z,u). [para(105(a,1),116(a,1,2,1)),flip(a)]. 266 (x \ y) * R((x \ y) \ y,z,u) = R(x,z,u) * (x \ y). [para(86(a,1),116(a,1,2,1))]. 267 x * (y * (y \ z)) != u * w | u \ (x * z) = w. [para(129(a,1),19(a,1))]. 268 ((x / y) * y) * z != u * w | (x * z) / w = u. [para(134(a,1),20(a,1))]. 269 ((x * y) * T(L(z,y,x),u)) / (x * y) = T((x * (y * z)) / (x * y),u). [para(26(a,2),176(a,1,1,2,1))]. 270 T((x * (y / z)) / x,z) = (x * (z \ y)) / x. [para(87(a,1),178(a,1,1,2)),flip(a)]. 271 T(K(x,y) * z,K(x,y)) = z * K(x,y). [hyper(109,a,197,a(flip))]. 272 R(K(x,y),z,u) = K(x,y). [hyper(18,a,81,a,b,197,a(flip)),flip(a)]. 273 (K(x,y) * z) * (z \ u) = K(x,y) * u. [para(14(a,1),197(a,2,2))]. 274 K(x,y) * z != (K(x,y) * u) * w | u * w = z. [para(197(a,2),19(a,1)),flip(a)]. 276 (x * (K(y,z) * (u * w))) \ ((x * (K(y,z) * u)) * w) = a(x,K(y,z) * u,w). [para(197(a,1),22(a,2,1,2)),flip(a)]. 277 (K(x,y) * (z * u)) \ (u * (K(x,y) * z)) = K(u,K(x,y) * z). [para(197(a,1),24(a,2,1)),flip(a)]. 278 ((K(x,y) * (z * u)) * w) / (u * w) = R(K(x,y) * z,u,w). [para(197(a,1),28(a,2,1,1)),flip(a)]. 279 x \ (K(y,z) * (u * x)) = T(K(y,z) * u,x). [para(197(a,1),30(a,2,2)),flip(a)]. 280 R(T(K(x,y),z),u,w) = T(K(x,y),z). [para(272(a,1),40(a,2,1))]. 281 (K(x,y) * z) / u = K(x,y) * (z / u). [para(16(a,1),230(a,1,1,2))]. 282 (K(x,y) * ((z * u) * w)) / (u * w) = K(x,y) * R(z,u,w). [para(81(a,1),230(a,1,1,2))]. 283 (K(x,y) \ z) * K(x,y) = T(z,K(x,y)). [para(14(a,1),271(a,1,1)),flip(a)]. 284 T(K(x,y) * (z / u),u) = u \ (K(x,y) * z). [para(281(a,1),87(a,1,1))]. 285 K(K(x,y),K(x,y) \ z) = T(z,K(x,y)) \ z. [para(283(a,1),74(a,1,1)),flip(a)]. 286 R(x,y * z,a(x,y,z)) \ ((x * y) * z) = (y * z) * a(x,y,z). [para(71(a,1),97(a,1,2))]. 287 x \ (y * K(y \ x,1 / (y \ x))) = L(1 / (y \ x),y \ x,y). [para(118(a,2),77(a,1,2,2))]. 288 (K((x / y) \ 1,x / y) * y) / x = R((x / y) \ 1,x / y,y). [para(135(a,2),83(a,1,1,1))]. 289 a(x / y,y,y \ 1) = (x / y) \ (x * (y \ 1)). [para(16(a,1),102(a,1,2,1)),flip(a)]. 290 a(1 / x,x,x \ 1) = (1 / x) \ (x \ 1). [para(58(a,1),102(a,1,2)),flip(a)]. 291 x \ R(x,y,y \ 1) = a(x,y,y \ 1). [para(120(a,1),102(a,1,2))]. 292 L(T(x,y),y,z / y) = z \ ((z / y) * (x * y)). [para(16(a,1),112(a,1,1)),flip(a)]. 293 L(T(x,y),y,x) = T(x,x * y). [para(112(a,1),30(a,2)),flip(a)]. 294 T(L(x,y,x),y) = T(x,x * y). [para(293(a,1),38(a,1)),flip(a)]. 295 L(R(T(x,y),z,u),y,x) = R(T(x,x * y),z,u). [para(293(a,1),42(a,1,1)),flip(a)]. 296 x * T(y,y * x) = L(y,x,y) * x. [para(293(a,1),115(a,1,2))]. 297 T((x * y) / x,y * x) = L(y,x,y). [hyper(18,a,173,a,b,296,a(flip)),flip(a)]. 298 L(R(x,y,y \ z),u,w) * z = (L(x,u,w) * y) * (y \ z). [para(42(a,1),153(a,1,1))]. 299 R(R(x,y,y \ z),u,w) * z = (R(x,u,w) * y) * (y \ z). [para(44(a,1),153(a,1,1))]. 300 T(x / (y * x),y) = R(y \ 1,y,x). [para(87(a,1),162(a,2,1))]. 301 T((x \ y) / (x * (x \ y)),z) * y = (T(1 / x,z) * x) * (x \ y). [para(162(a,2),153(a,1,1))]. 302 (x / (y * x)) * y = y * R(y \ 1,y,x). [para(300(a,1),85(a,1,2)),flip(a)]. 303 R(x \ 1,x,x \ 1) = T(x \ 1,x). [para(91(a,1),300(a,1,1)),flip(a)]. 304 x * ((x \ y) * T(z,y)) = L(z,x \ y,x) * y. [para(190(a,1),115(a,1))]. 305 T((x * y) / x,x * y) = L(y,x,(x * y) / x). [hyper(109,a,191,a)]. 306 (x / y) * (y * T(z,x)) = L(z,y,x / y) * x. [para(191(a,1),115(a,1))]. 307 L(T((x \ y) \ z,u),x \ y,x) = T(y \ (x * z),u). [para(200(a,1),38(a,2,1))]. 308 L(R((x \ y) \ z,u,w),x \ y,x) = R(y \ (x * z),u,w). [para(200(a,1),42(a,1,1)),flip(a)]. 309 L(L((x \ y) \ z,u,w),x \ y,x) = L(y \ (x * z),u,w). [para(200(a,1),43(a,1,1)),flip(a)]. 310 L(x \ y,x,y / x) = T(y / x,y). [para(201(a,2),30(a,2)),flip(a)]. 311 K(x,y) = L(x \ T(x,y),x,y). [para(208(a,2),24(a,2))]. 313 R(T(x / (y / z),u),y / z,z) = T((x * z) / y,u). [para(220(a,1),40(a,2,1))]. 314 R(R(x / (y / z),u,w),y / z,z) = R((x * z) / y,u,w). [para(220(a,1),44(a,1,1)),flip(a)]. 315 (x * y) / L(z * y,y / (z * y),x) = x * R(1 / z,z,y). [para(104(a,2),229(a,2,2))]. 316 R(x,x \ (y / z),z) \ y = (x \ (y / z)) * z. [para(16(a,1),233(a,1,2))]. 317 R(x \ y,(x \ y) \ y,z) \ (y * z) = T(x,x \ y) * z. [para(86(a,2),233(a,2,1))]. 318 R(x * y,(x * y) \ x,z) \ (x * z) = L(y \ 1,y,x) * z. [para(103(a,2),233(a,2,1))]. 319 L(R(x,y,K(y,L(x,z,u))),z,u) \ (y * L(x,z,u)) = y * K(y,L(x,z,u)). [para(42(a,1),236(a,1,1))]. 320 (x * L(x \ y,z,u)) / x = L(y / x,z,u). [hyper(70,a,260,a)]. 321 (x * R(x \ y,z,u)) / x = R(y / x,z,u). [hyper(70,a,264,a)]. 322 (x * R(x \ y,z,u)) \ R(y / x,z,u) = L(x \ 1,x,R(y / x,z,u)). [para(264(a,1),103(a,2,1)),flip(a)]. 323 ((x * y) / (z * y)) * z = z * R(z \ x,z,y). [para(82(a,1),264(a,1,1))]. 324 (x * K(x,y)) * R((x * K(x,y)) \ (x * y),z,u) = R(R(y,x,K(x,y)),z,u) * (x * K(x,y)). [para(139(a,1),264(a,1,1,1)),flip(a)]. 325 R((x * y) / x,z,u) = (x * R(y,z,u)) / x. [hyper(70,a,265,a),flip(a)]. 326 ((x * (y / z)) / x) * z = z * ((x * (z \ y)) / x). [para(270(a,1),85(a,1,2)),flip(a)]. 327 L((x * y) / x,z,u) = (x * L(y,z,u)) / x. [para(13(a,1),320(a,1,1,2,1)),flip(a)]. 328 (x * ((y * x) \ y)) / x = L(1 / x,x,y). [para(103(a,1),320(a,1,1,2))]. 329 L((x \ y) / z,z,x) = (z * ((x * z) \ y)) / z. [para(128(a,1),320(a,1,1,2)),flip(a)]. 330 ((x \ y) * (y \ x)) / (x \ y) = L(1 / (x \ y),x \ y,x). [para(14(a,1),328(a,1,1,2,1))]. 331 R((x * (1 / y)) / x,y,z) = (x * (z / (y * z))) / x. [para(104(a,1),325(a,2,1,2))]. 332 R((x * (y / z)) / x,z,z \ 1) = (x * (y * (z \ 1))) / x. [para(224(a,1),325(a,2,1,2))]. 333 L(((x * y) * z) / (x * y),y,x) = (x * (y * z)) / (x * y). [para(76(a,1),327(a,2,1))]. 334 L((x * ((y \ z) \ u)) / x,y \ z,y) = (x * (z \ (y * u))) / x. [para(200(a,1),327(a,2,1,2))]. 335 L(L(x \ 1,y * x,z),x,y) = (z * (y * x)) \ (z * y). [para(159(a,2),78(a,1))]. 336 R(x / (y * x),y,y \ 1) = R(1 * (y \ 1),y,x). [para(224(a,1),163(a,1,1)),flip(a)]. 337 (x * y) * T((x * y) \ x,z) = x * (y * T(y \ 1,z)). [para(103(a,1),195(a,1,2,1))]. 338 (x * y) * T((x * y) \ (x * z),u) = x * (y * T(y \ z,u)). [para(78(a,1),195(a,1,2,1))]. 339 (x * y) * T((x * y) \ z,u) = x * (y * T(y \ (x \ z),u)). [para(128(a,1),195(a,1,2,1))]. 340 x * (y * T(y \ T(y,x),z)) = (x * y) * T(K(y,x),z). [para(311(a,2),195(a,1,2,1)),flip(a)]. 341 R(T(x,x * y),y,T(x,y)) = T(x,y). [hyper(17,a,116,a,b,216,a(flip)),flip(a)]. 342 R(T(x,y),x \ y,T(x,x \ y)) = T(x,x \ y). [para(14(a,1),341(a,1,1,2))]. 343 (T(x,x * y) * y) * T(x,y) = T(x,y) * (x * y). [para(341(a,1),216(a,1,1)),flip(a)]. 344 R(T(x / y,y * z),y,z) = (y * z) \ (x * z). [para(221(a,1),87(a,1))]. 345 T((x * y) / (z * y),z) = R(z \ x,z,y). [para(87(a,1),221(a,2,1))]. 346 R(x,y,z) = T(((y * x) * z) / (y * z),y). [para(105(a,1),221(a,2,1)),flip(a)]. 347 R(T(x / y,z),y,u) * (y * u) = (y * u) * T((y * u) \ (x * u),z). [para(221(a,1),171(a,1,1))]. 348 T((x * (y \ z)) / z,y) = R(y \ x,y,y \ z). [para(14(a,1),345(a,1,1,2))]. 349 R((x / y) \ z,x / y,y) = T((z * y) / x,x / y). [para(16(a,1),345(a,1,1,2)),flip(a)]. 350 T(R(x \ y,x,z),x * z) = T((x * z) \ (y * z),x). [para(345(a,1),117(a,1,1))]. 351 T(((1 / x) * y) * x,1 / x) = R(y,1 / x,x). [para(92(a,1),346(a,2,1)),flip(a)]. 352 T(R(x / y,y,T(z,y)),z * y) = (z * y) \ (x * T(z,y)). [para(223(a,2),87(a,1,1))]. 353 R(x,T(y,x),T(z,y * x)) \ (z * (y * x)) = T(y,x) * T(z,y * x). [para(85(a,1),234(a,1,2))]. 354 (1 / x) \ T(((1 / x) * x) \ y,z) = x * T(x \ ((1 / x) \ y),z). [para(249(a,1),240(a,1,2))]. 355 (x / y) * (y * T(y \ 1,z)) = x * T(x \ (x / y),z). [para(251(a,2),191(a,1,2)),flip(a)]. 356 (1 / x) * ((x \ y) * x) = T((1 / x) * y,x). [para(255(a,1),241(a,1)),flip(a)]. 357 T((1 / x) * y,x) != (1 / x) * z | (x \ y) * x = z. [para(356(a,1),19(a,1))]. 358 K(x,y) \ (z * (K(x,y) * u)) = u * T(z,K(x,y) * u). [para(88(a,1),262(a,1,2,1))]. 359 L(((x / y) \ (x * (y \ 1))) \ z,a(x / y,y,y \ 1),x / y) = (x * (y \ 1)) \ ((x / y) * z). [para(289(a,2),200(a,1,2))]. 360 T(((x / y) * y) \ ((x / y) * z),y) = x \ ((x / y) * ((y \ z) * y)). [para(292(a,1),203(a,2))]. 361 x \ ((x / y) * ((y \ 1) * y)) = T(x \ (x / y),y). [para(292(a,1),251(a,2)),flip(a)]. 362 (x * y) * R(T(x,x * y),z,u) = x * (y * R(T(x,y),z,u)). [para(295(a,1),76(a,1,2))]. 363 x \ (L(y,x \ z,x) * z) = (x \ z) * T(y,z). [hyper(66,a,304,a)]. 364 T(L(x,y,(y * x) / y),y) = T(y \ (y * x),y * x). [para(305(a,1),117(a,1,1))]. 365 T(((x * y) * z) / (x * z),x * y) = R(L(y,x,(x * y) / x),x,z). [para(305(a,1),221(a,2,1))]. 366 (x / y) \ (L(z,y,x / y) * x) = y * T(z,x). [hyper(66,a,306,a)]. 367 L(x,y,z / y) * z != (z / y) * u | y * T(x,z) = u. [para(306(a,1),19(a,1))]. 368 (x * y) \ ((z * x) * y) = R(T(z,x * y),x,y). [para(15(a,1),344(a,1,1,1)),flip(a)]. 369 T((x * (y \ z)) / z,y) * z = ((y \ x) * y) * (y \ z). [para(348(a,2),153(a,1,1))]. 370 R(x,1 / x,x) = T(x,1 / x). [para(58(a,1),351(a,1,1)),flip(a)]. 371 (x \ y) * T((x \ y) \ z,y) = x \ ((y \ (x * z)) * y). [para(200(a,1),363(a,1,2,1)),flip(a)]. 372 (R(T(x,y * z),y,z) * (y * z)) \ ((x * y) * z) = K(y * z,(y * z) \ ((x * y) * z)). [para(368(a,1),74(a,1,1,1))]. 373 (K(x,y) * (y * x)) / K(x * y,K(K(x,y),y * x)) = K(K(x,y),y * x) * (x * y). [para(141(a,1),94(a,1,1))]. 374 (x \ y) * ((z * ((x \ y) \ y)) / z) = ((z * x) / z) * (x \ y). [para(57(a,1),326(a,1,1,1,2)),flip(a)]. 375 R(x / (y * x),y,y \ 1) = R(y \ 1,y,x). [para(11(a,1),336(a,2,1))]. 376 R(x / y,y / x,(y / x) \ 1) = R((y / x) \ 1,y / x,x). [para(16(a,1),375(a,1,1,2))]. 377 T(T(x,x * y) * y,T(x,y)) = x * y. [hyper(109,a,343,a(flip))]. 378 x \ ((x / y) * K(y \ 1,y)) = T(x \ (x / y),y). [para(135(a,2),361(a,1,2,2))]. 379 (x * y) * L((x * y) \ z,u,w) = x * (y * L(y \ (x \ z),u,w)). [para(128(a,1),196(a,1,2,1))]. 380 (x * y) * L(T(x,x * y),z,u) = x * (y * L(T(x,y),z,u)). [para(293(a,1),196(a,1,2,1))]. 382 K(x \ 1,x) * T(((x \ 1) * x) \ y,z) = (x \ 1) * (x * T(x \ ((x \ 1) \ y),z)). [para(249(a,1),199(a,1,2))]. 383 (x * y) * R((x * y) \ (x * z),u,w) = x * (y * R(y \ z,u,w)). [para(204(a,2),76(a,1,2))]. 384 (x * y) * L((y * T(x,y)) \ (y * z),u,w) = y * (T(x,y) * L(T(x,y) \ z,u,w)). [para(205(a,1),198(a,1,2))]. 385 L((x * y) / (z * y),u,w) * (z * y) = (L(x / z,u,w) * z) * y. [para(82(a,1),214(a,1,1,1))]. 386 (L(K(x,y),z,u) * w) * v5 = L(K(x,y),z,u) * (w * v5). [para(272(a,1),214(a,1,1,1)),flip(a)]. 387 (L(x / (y / z),u,w) * (y / z)) * z = L((x * z) / y,u,w) * ((y / z) * z). [para(220(a,1),214(a,1,1,1)),flip(a)]. 388 x \ ((L(y,z,x) * x) * z) = z * T(R(y,x,z),x * z). [para(214(a,1),262(a,1,2))]. 389 R(R(x,y \ 1,y),z,u) * K(y \ 1,y) = (R(x,z,u) * (y \ 1)) * y. [para(135(a,2),215(a,1,2))]. 390 R((x * y) / (z * y),u,w) * (z * y) = (R(x / z,u,w) * z) * y. [para(82(a,1),215(a,1,1,1))]. 391 (x * y) / L(T(z \ y,(z \ y) \ y),(z \ y) \ y,x) = x * T(z,z \ y). [para(86(a,2),232(a,2,2))]. 392 (1 / x) * (x * R(x \ y,z,u)) = R((1 / x) * y,z,u). [para(256(a,1),119(a,2))]. 393 (1 / x) \ L((1 / x) * y,z,u) = x * L(x \ y,z,u). [para(257(a,1),240(a,1,2))]. 394 L((1 / x) * T(x,y),x,y) = L(K(x,y),x,1 / x). [para(311(a,2),257(a,1,1)),flip(a)]. 395 L(R(x / (1 / y),1 / y,y),z,u) / y = (1 / y) * L((1 / y) \ x,z,u). [para(259(a,2),260(a,1))]. 396 (x \ 1) * T((x \ 1) \ y,z) = x \ T(1 \ (x * y),z). [para(307(a,1),248(a,1,2)),flip(a)]. 397 x * ((x \ y) * T((x \ y) \ z,u)) = y * T(y \ (x * z),u). [para(307(a,1),190(a,1,2)),flip(a)]. 398 (T(x / (y / z),u) * (y / z)) * z = T((x * z) / y,u) * y. [para(313(a,1),210(a,1,1)),flip(a)]. 399 ((x * (y / (z * y))) / x) * (z * y) = (((x * (1 / z)) / x) * z) * y. [para(331(a,1),81(a,1,1))]. 400 ((x * (y / ((1 / y) * y))) / x) / y = ((x * (1 / (1 / y))) / x) * (1 / y). [para(331(a,1),246(a,1,1))]. 401 ((x * ((y \ z) / (y * (y \ z)))) / x) * z = (((x * (1 / y)) / x) * y) * (y \ z). [para(331(a,1),153(a,1,1))]. 402 R(T(x \ y,x * z),x,z) = T((x * z) \ (y * z),x). [para(350(a,1),40(a,2))]. 403 L(T(x,y),y,(y * x) / y) = T(y \ (y * x),y * x). [para(364(a,1),38(a,2))]. 404 T((x * y) \ ((x * z) * y),x) = R(T(z,x * y),x,y). [para(13(a,1),402(a,1,1,1)),flip(a)]. 405 L(T(x,y),y,(y * x) / y) = T(x,y * x). [para(13(a,1),403(a,2,1))]. 406 R(T(x,y * x),y,x) = T(x,y). [para(13(a,1),404(a,1,1)),flip(a)]. 407 R(T(x,y),y / x,x) = T(x,y / x). [para(16(a,1),406(a,1,1,2))]. 408 x * R(T(y,x * y),x,y) = y * x. [para(406(a,2),85(a,1,2))]. 409 (x * y) * T((y * T(x,y)) \ y,z) = y * (T(x,y) * T(T(x,y) \ 1,z)). [para(85(a,1),337(a,1,1))]. 410 (x * (y * z)) * T(((x * y) * L(z,y,x)) \ (x * y),u) = (x * y) * (L(z,y,x) * T(L(z,y,x) \ 1,u)). [para(76(a,1),337(a,1,1))]. 411 K(x,1 / x) * T(K(x,1 / x) \ (K(x,1 / x) / (1 / x)),y) = x * ((1 / x) * T((1 / x) \ 1,y)). [para(145(a,1),355(a,1,1)),flip(a)]. 412 R(K(x,y),z,u) \ (w * (K(x,y) * v5)) = v5 * T(w,K(x,y) * v5). [para(272(a,2),358(a,1,1))]. 413 ((x \ y) * x) * (x \ z) = z * T(z \ (y * (x \ z)),x). [para(369(a,1),171(a,1))]. 414 (x \ y) * T((x \ y) \ 1,y) = x \ ((y \ x) * y). [para(12(a,1),371(a,2,2,1,2))]. 415 x \ ((L(y,z,x) * x) * z) = z * R(T(y,x * z),x,z). [para(40(a,2),388(a,2,2))]. 416 (1 / x) * (x * R(x \ 1,y,z)) = R(1 / x,y,z). [para(12(a,1),392(a,2,1))]. 417 (1 / x) * (((y * z) / (x * z)) * x) = R((1 / x) * y,x,z). [para(323(a,2),392(a,1,2))]. 418 (1 / x) \ R(1 / x,y,z) = x * R(x \ 1,y,z). [hyper(66,a,416,a)]. 419 (1 / x) * ((y / (x * y)) * x) = R(1 / x,x,y). [para(302(a,2),416(a,1,2))]. 421 (1 / x) \ L((1 / x) * K(x \ 1,x),y,z) = x * L(T(x \ 1,x),y,z). [para(151(a,1),393(a,2,2,1))]. 422 (x \ 1) * T((x \ 1) \ y,z) = x \ T(x * y,z). [para(47(a,1),396(a,2,2,1))]. 423 (x \ 1) * T((x \ 1) \ 1,y) = x \ T(x,y). [para(12(a,1),422(a,2,2,1))]. 424 T(x,y) * (x \ 1) = x \ T(x,y). [para(423(a,1),174(a,1)),flip(a)]. 425 ((x \ 1) * x) * (x \ y) = y * T(y \ (x \ y),x). [para(11(a,1),413(a,2,2,1,2))]. 426 K(x \ 1,x) * (x \ y) = y * T(y \ (x \ y),x). [para(135(a,2),425(a,1,1))]. 427 x \ (y \ ((L(z,x,y) * y) * x)) = R(T(z,y * x),y,x). [hyper(66,a,415,a(flip))]. 428 R(K(x \ 1,x),K(x,x \ 1),y) \ y = K(x,x \ 1) * y. [para(135(a,2),181(a,1,1,1))]. 429 K(x \ (x / y),x) = y * T(y \ 1,x). [hyper(367,a,252,a),flip(a)]. 430 x \ K(y \ (y / x),y) = T(x \ 1,y). [hyper(66,a,429,a(flip))]. 431 K(x \ (x / (y \ 1)),x) = y \ T(y,x). [para(429(a,2),423(a,1))]. 432 L(x \ 1,x,y) \ K(y \ (y * x),y) = T(L(x \ 1,x,y) \ 1,y). [para(160(a,1),430(a,1,2,1,2))]. 433 L(x,y,z \ T(z,u)) = x. [para(431(a,1),88(a,1,3))]. 434 K(x \ (x / ((y / x) \ 1)),x) = (y / x) \ (x \ y). [para(87(a,1),431(a,2,2))]. 435 (K(x,y) * ((z * u) * w)) / (u * w) = R(K(x,y) * z,u,w). [para(197(a,1),278(a,1,1))]. 436 L((x * (y \ z)) / z,u,w) * z = (L(x / y,u,w) * y) * (y \ z). [para(219(a,1),298(a,1,1,1))]. 437 R((x * (y \ z)) / z,u,w) * z = (R(x / y,u,w) * y) * (y \ z). [para(219(a,1),299(a,1,1,1))]. 438 (x \ 1) * R((x \ 1) \ y,z,u) = x \ R(1 \ (x * y),z,u). [para(308(a,1),248(a,1,2)),flip(a)]. 439 (x \ 1) * L((x \ 1) \ y,z,u) = x \ L(1 \ (x * y),z,u). [para(309(a,1),248(a,1,2)),flip(a)]. 440 R(x / (1 / y),z,u) * (1 / y) = R((x * y) / 1,z,u) / y. [para(314(a,1),246(a,1,1)),flip(a)]. 441 T(x,x \ y) * z = ((x \ y) \ y) * z. [para(317(a,1),233(a,1))]. 442 (T(x,x \ y) * z) \ (z * ((x \ y) \ y)) = K(z,(x \ y) \ y). [para(441(a,2),24(a,2,1)),flip(a)]. 443 ((x \ y) \ y) * T(z,T(x,x \ y)) = z * T(x,x \ y). [para(441(a,1),85(a,1))]. 444 (x * (y * (x \ 1))) / x = (x * (y / x)) * (x \ 1). [para(332(a,1),224(a,1))]. 445 R(T(x / y,z * y),y,T(z,y)) = (z * y) \ (x * T(z,y)). [para(352(a,1),40(a,2))]. 446 (1 / x) * ((y * (x \ 1)) * x) = R((1 / x) * y,x,x \ 1). [para(91(a,1),417(a,1,2,1))]. 447 K(x \ 1,x) \ y = K(x,x \ 1) * y. [para(272(a,1),428(a,1,1))]. 448 K(x \ 1,x) * (K(x,x \ 1) * y) = y. [hyper(65,a,447,a)]. 449 K(x,x \ 1) * K(x \ 1,x) = 1. [para(447(a,1),48(a,1))]. 450 K(x,x \ 1) * (x \ 1) = 1 / x. [para(447(a,1),188(a,1))]. 452 K(x,x \ 1) \ 1 = K(x \ 1,x). [hyper(66,a,449,a)]. 453 K(x,x \ 1) * ((x \ 1) * y) = (1 / x) * y. [para(450(a,1),197(a,1,1)),flip(a)]. 454 (1 / x) * ((x \ 1) \ y) = K(x,x \ 1) * y. [para(450(a,1),273(a,1,1))]. 455 K(x,x \ 1) \ y = K(x \ 1,x) * y. [para(14(a,1),448(a,1,2)),flip(a)]. 456 K(x \ 1,x) * y != z | K(x,x \ 1) * z = y. [para(448(a,1),19(a,1)),flip(a)]. 457 x / (K(y \ 1,y) * x) = K(y,y \ 1). [para(455(a,1),57(a,1,2))]. 458 R(K(x,y) * z,u,w) = K(x,y) * R(z,u,w). [para(435(a,1),282(a,1))]. 459 K(x,x \ 1) * R(x \ 1,y,z) = R(1 / x,y,z). [para(450(a,1),458(a,1,1)),flip(a)]. 460 K(x,x \ 1) * (R(x \ 1,y,z) * u) = R(1 / x,y,z) * u. [para(459(a,1),197(a,1,1)),flip(a)]. 462 K(x \ 1,x) * R(1 / x,y,z) = R(x \ 1,y,z). [para(459(a,1),448(a,1,2))]. 463 R(x \ 1,y,z) / R(1 / x,y,z) = K(x \ 1,x). [hyper(70,a,462,a)]. 464 (x * K(y,z)) \ (K(y,z) * x) = K(K(y,z),K(y,z) * x). [para(277(a,1),206(a,1)),flip(a)]. 465 K(K(x,y),K(x,y) * z) = K(K(x,y),z). [para(464(a,1),24(a,2)),flip(a)]. 466 K(K(x,y),K(x,y) \ z) = K(K(x,y),z). [para(14(a,1),465(a,1,2)),flip(a)]. 467 T(x,K(y,z)) \ x = K(K(y,z),x). [para(466(a,1),285(a,1)),flip(a)]. 468 T(x,K(y,z)) * K(K(y,z),x) = x. [para(467(a,1),14(a,1,2))]. 469 x * R(1 / y,y,z) = x * (z / (y * z)). [para(315(a,1),229(a,1))]. 470 (x * (y / (z * y))) / R(1 / z,z,y) = x. [hyper(70,a,469,a)]. 471 K((x / (y * x)) \ 1,x / (y * x)) = ((x / (y * x)) \ 1) * R(1 / y,y,x). [para(469(a,2),135(a,2))]. 472 K(x / (y * x),(x / (y * x)) \ z) = (((x / (y * x)) \ z) * R(1 / y,y,x)) \ z. [para(469(a,2),74(a,1,1)),flip(a)]. 473 L(x \ 1,x,y) * z = ((y * x) \ y) * z. [para(318(a,1),233(a,1))]. 474 ((x * ((y * z) \ y)) * u) / (L(z \ 1,z,y) * u) = R(x,(y * z) \ y,u). [para(473(a,2),28(a,2,2)),flip(a)]. 475 x * (y * R(T(x,y),z,u)) = R(x,z,u) * (x * y). [para(362(a,1),116(a,1))]. 476 R(x,y,z) * (x * u) = x * (R(x,y,z) * u). [para(116(a,1),475(a,1,2)),flip(a)]. 477 x \ (R(x,y,z) * u) = R(x,y,z) * (x \ u). [hyper(267,a,476,a)]. 478 x * (R(x,y,z) * (x \ u)) = R(x,y,z) * u. [para(14(a,1),476(a,1,2)),flip(a)]. 479 R(x,y,z) * (x \ 1) = x \ R(x,y,z). [para(12(a,1),477(a,1,2)),flip(a)]. 480 R(x,y,z) * (x \ (y * z)) = x \ ((x * y) * z). [para(81(a,1),477(a,1,2)),flip(a)]. 481 (x \ 1) * R((x \ 1) \ 1,y,z) = x \ R(x,y,z). [para(479(a,1),266(a,2))]. 482 R(x,y,x) * (x \ (y * x)) = T(x * y,x). [para(480(a,2),30(a,2)),flip(a)]. 483 R(x,y,x) * T(y,x) = T(x * y,x). [para(30(a,2),482(a,1,2))]. 484 R(x / y,y / x,(y / x) \ 1) = T((1 * x) / y,y / x). [para(376(a,2),349(a,1))]. 485 R(x / y,y / x,(y / x) \ 1) = T(x / y,y / x). [para(11(a,1),484(a,2,1,1))]. 486 x * (y * L(T(x,y),z,u)) = L(x,z,u) * (x * y). [para(380(a,1),115(a,1))]. 487 L(x,y,z) * (x * u) = x * (L(x,y,z) * u). [para(115(a,1),486(a,1,2)),flip(a)]. 488 L(x,y,z) \ (x * u) = x * (L(x,y,z) \ u). [hyper(17,a,129,a,b,487,a),flip(a)]. 489 x * (L(x,y,z) \ 1) = L(x,y,z) \ x. [para(12(a,1),488(a,1,2)),flip(a)]. 490 x \ (L(x,y,z) \ x) = L(x,y,z) \ 1. [hyper(66,a,489,a)]. 491 (x \ (y \ z)) \ (((y * x) \ z) \ (x \ (y \ z))) = L(x \ (y \ z),x,y) \ 1. [para(128(a,1),490(a,1,2,1))]. 492 x * ((x \ y) * T((x \ y) \ 1,z)) = y * T(y \ x,z). [para(12(a,1),397(a,2,2,1,2))]. 493 x * T(x \ (y * x),z) = y * (T(y,z) * (y \ x)). [para(174(a,1),397(a,1,2)),flip(a)]. 494 x * (T(x,y) * (x \ z)) = T(x,y) * z. [para(493(a,1),170(a,1))]. 495 x \ (T(x,y) * z) = T(x,y) * (x \ z). [hyper(66,a,494,a)]. 496 T(x,y) * (x * z) = x * (T(x,y) * z). [para(13(a,1),494(a,1,2,2)),flip(a)]. 497 x * (T(x,y) * T(z,x)) = T(x,y) * (z * x). [para(30(a,2),494(a,1,2,2))]. 498 (x / y) * (T(x / y,z) * y) = T(x / y,z) * x. [para(59(a,1),494(a,1,2,2))]. 499 T(x,y) * (x \ (T(x,y) \ z)) = x \ z. [para(14(a,1),495(a,1,2)),flip(a)]. 500 x \ (T(x,y) * (x / z)) = T(x,y) * L(z \ 1,z,x / z). [para(158(a,2),495(a,2,2))]. 501 x \ (T(x,y) * T(x,z)) = T(x,z) * (x \ T(x,y)). [para(172(a,1),495(a,1,2))]. 502 T(x,K(y,z)) * (x \ K(K(y,z),x)) = x \ x. [para(468(a,1),495(a,1,2)),flip(a)]. 503 T(x,y) \ (x * z) = x * (T(x,y) \ z). [hyper(17,a,129,a,b,496,a),flip(a)]. 504 (x / y) * (T(x / y,y) * z) = (y \ x) * ((x / y) * z). [para(87(a,1),496(a,1,1)),flip(a)]. 505 x * (T(x,y) \ 1) = T(x,y) \ x. [para(12(a,1),503(a,1,2)),flip(a)]. 506 x \ (T(x,y) \ x) = T(x,y) \ 1. [hyper(66,a,505,a)]. 507 T((T(x,y) \ x) / x,x) = T(x,y) \ 1. [para(505(a,1),105(a,1,1,1))]. 508 T((1 / x) * (T(x,y) \ x),x) = (1 / x) * ((T(x,y) \ 1) * x). [para(506(a,1),356(a,1,2,1)),flip(a)]. 509 T(x,y) * ((T(x,y) \ 1) * x) = x * K(x \ (x / T(x,y)),x). [para(429(a,2),497(a,1,2)),flip(a)]. 510 T(x,K(y,z)) * (x \ K(K(y,z),x)) = 1. [para(502(a,2),48(a,1))]. 511 1 / (x \ K(K(y,z),x)) = T(x,K(y,z)). [hyper(70,a,510,a)]. 513 K(K(x,y),z) \ z = T(z,K(x,y)). [para(511(a,1),186(a,1)),flip(a)]. 514 K(K(x,y),K(x,y) * z) \ (K(x,y) * z) = z * K(x,y). [para(513(a,2),271(a,1))]. 515 (x / y) * (y * T(y \ x,z)) = T(x / y,z) * x. [para(171(a,1),498(a,1,2))]. 516 T(x,y) * (x \ T(x,z)) = T(x,z) * (x \ T(x,y)). [para(501(a,1),495(a,1))]. 517 (1 / x) \ T(1 / x,y) = x * T(x \ 1,y). [hyper(155,a,515,a(flip))]. 519 x * T(x \ y,z) = y * K(z \ (z / (y \ x)),z). [para(429(a,2),492(a,1,2)),flip(a)]. 520 x \ (y * K(z \ (z / (y \ x)),z)) = T(x \ y,z). [hyper(66,a,519,a)]. 521 (x * y) * T((x * y) \ (y * x),z) = (y * x) * K(z \ (z / K(x,y)),z). [para(24(a,2),519(a,2,2,1,2,2))]. 522 (x / y) * T(y,z) = x * K(z \ (z / (x \ (x / y))),z). [para(59(a,1),519(a,1,2,1))]. 523 x \ (y * K((y \ x) \ 1,y \ x)) = T(x \ y,y \ x). [para(54(a,1),520(a,1,2,2,1,2))]. 524 (x / y) * ((y \ x) * z) = (y \ x) * ((x / y) * z). [para(87(a,1),504(a,1,2,1))]. 525 (x \ (x * y)) * (((x * y) / x) * z) = ((x * y) / x) * (y * z). [para(105(a,1),504(a,1,2,1)),flip(a)]. 526 (x \ y) \ ((y / x) * z) = (y / x) * ((x \ y) \ z). [hyper(267,a,524,a)]. 527 (x \ y) * ((y / x) * ((x \ y) \ z)) = (y / x) * z. [para(14(a,1),524(a,1,2)),flip(a)]. 528 (x / y) * ((y \ x) \ 1) = (y \ x) \ (x / y). [para(12(a,1),526(a,1,2)),flip(a)]. 529 (x / y) * ((y \ x) \ ((x / y) \ z)) = (y \ x) \ z. [para(14(a,1),526(a,1,2)),flip(a)]. 531 (x \ 1) * (K(x,x \ 1) * y) = (1 / x) * y. [para(454(a,1),527(a,1,2))]. 532 (x / y) \ ((y \ x) \ z) = (y \ x) \ ((x / y) \ z). [hyper(66,a,529,a)]. 533 K(x,x \ 1) * ((1 / x) \ y) = (x \ 1) \ y. [para(529(a,1),454(a,1)),flip(a)]. 534 K(x \ 1,x) * ((x \ 1) \ y) = (1 / x) \ y. [para(533(a,1),448(a,1,2))]. 535 (1 / x) \ ((x \ 1) * y) = K(x \ 1,x) * y. [para(13(a,1),534(a,1,2)),flip(a)]. 536 K(x \ 1,x) * ((x \ 1) \ 1) = x. [para(534(a,2),59(a,1))]. 537 x \ (K(x \ 1,x) * y) = ((x \ 1) \ 1) \ y. [para(536(a,1),206(a,1,1))]. 538 K(x,x \ 1) \ ((x \ 1) \ 1) = x. [para(536(a,1),455(a,2))]. 539 (1 / x) * (K(x \ 1,x) * y) = (x \ 1) * y. [para(535(a,1),14(a,1,2))]. 540 ((x \ 1) \ 1) \ K(x,x \ 1) = x \ 1. [para(183(a,1),537(a,1,2)),flip(a)]. 541 ((x \ 1) \ 1) \ ((x \ 1) \ y) = x \ ((1 / x) \ y). [para(534(a,1),537(a,1,2)),flip(a)]. 542 (1 / x) * ((x \ 1) \ (K(x \ 1,x) * y)) = y. [hyper(17,a,527,a,b,539,a(flip)),flip(a)]. 543 (x \ 1) \ (K(x \ 1,x) * y) = (1 / x) \ y. [hyper(66,a,542,a),flip(a)]. 544 (x \ 1) * ((1 / x) \ y) = K(x \ 1,x) * y. [para(543(a,1),14(a,1,2))]. 545 (1 / x) \ L(y,x,x \ 1) = x * y. [hyper(17,a,199,a(flip),b,544,a)]. 546 K(x \ 1,x) * R(1 / x,y,z) = (x \ 1) * (x * R(x \ 1,y,z)). [para(418(a,1),544(a,1,2)),flip(a)]. 547 (1 / x) * (x * y) = L(y,x,x \ 1). [para(545(a,1),14(a,1,2))]. 548 L(x \ 1,x,x \ 1) = 1 / x. [hyper(99,a,547,a),flip(a)]. 549 L(T(x,y) \ 1,x,x \ 1) = (1 / x) * (T(x,y) \ x). [para(505(a,1),547(a,1,2)),flip(a)]. 550 (x \ (x * y)) \ (((x * y) / x) \ z) = ((x * y) / x) \ (y \ z). [para(13(a,1),532(a,1,2,1)),flip(a)]. 551 K(K(x,y),z) \ (K(x,y) * z) = z * K(x,y). [para(465(a,1),514(a,1,1))]. 552 T(x * K(y,z),K(K(y,z),x)) = x * K(y,z). [para(551(a,1),140(a,1)),flip(a)]. 553 K(x * K(y,z),K(K(y,z),x)) = 1. [hyper(34,a,552,a)]. 554 K(x * y,K(K(x,y),y * x)) = 1. [para(72(a,1),553(a,1,1))]. 555 K(x \ (x / (y \ (y / z))),x) = y \ ((y / z) * T(z,x)). [hyper(66,a,522,a(flip)),flip(a)]. 556 ((x / y) * T((x / y) \ z,u)) * y = T((z * y) / x,u) * x. [para(171(a,1),398(a,1,1))]. 557 (x \ 1) * R((x \ 1) \ y,z,u) = x \ R(x * y,z,u). [para(47(a,1),438(a,2,2,1))]. 558 (x \ 1) * L((x \ 1) \ y,z,u) = x \ L(x * y,z,u). [para(47(a,1),439(a,2,2,1))]. 559 R(x / (1 / y),z,u) * (1 / y) = R(x * y,z,u) / y. [para(55(a,1),440(a,2,1,1))]. 560 (1 / x) * R((1 / x) \ y,z,u) = R(y * x,z,u) / x. [para(559(a,1),264(a,1)),flip(a)]. 561 (1 / x) * R((1 / x) \ 1,y,z) = R(x,y,z) / x. [para(11(a,1),560(a,2,1,1))]. 562 (x \ 1) * (K(x,x \ 1) * R((1 / x) \ y,z,u)) = R(y * x,z,u) / x. [para(560(a,1),531(a,2))]. 563 (1 / x) * R(x,y,z) = R(x,y,z) / x. [para(59(a,1),561(a,1,2,1))]. 564 (R(x,y,z) / x) / R(x,y,z) = 1 / x. [hyper(70,a,563,a)]. 565 L(x,T(x,y) \ 1,T(x,y)) = x * K(x \ (x / T(x,y)),x). [para(509(a,1),189(a,1)),flip(a)]. 566 ((x * y) / x) * (y * z) = y * (((x * y) / x) * z). [para(13(a,1),525(a,1,1)),flip(a)]. 567 x * (((y * x) / y) * (x \ z)) = ((y * x) / y) * z. [para(14(a,1),566(a,1,2)),flip(a)]. 568 ((x * y) / x) * (y \ 1) = y \ ((x * y) / x). [hyper(155,a,567,a(flip)),flip(a)]. 569 ((x * y) / x) \ (y \ ((x * y) / x)) = y \ 1. [hyper(66,a,568,a)]. 570 (x / (x / y)) \ (y \ (((x / y) * y) / (x / y))) = y \ 1. [para(16(a,1),569(a,1,1,1))]. 571 (x / (x / y)) \ (y \ (x / (x / y))) = y \ 1. [para(16(a,1),570(a,1,2,2,1))]. 573 ((x * y) / x) \ (y \ z) = y \ (((x * y) / x) \ z). [para(13(a,1),550(a,1,1)),flip(a)]. 574 ((x * y) / x) \ (y \ ((x * y) / x)) = (x \ (x * y)) \ 1. [para(48(a,1),550(a,1,2)),flip(a)]. 575 x \ (((y * x) / y) \ x) = ((y * x) / y) \ 1. [para(48(a,1),573(a,1,2)),flip(a)]. 576 ((x * y) / x) \ (y \ (x * y)) = y \ x. [para(59(a,1),573(a,2,2))]. 577 ((x * y) / x) \ T(x,y) = y \ x. [para(30(a,2),576(a,1,2))]. 578 T(x,y) = ((x * y) / x) * (y \ x). [para(577(a,1),14(a,1,2)),flip(a)]. 579 T(x,y) / (y \ x) = (x * y) / x. [para(577(a,1),57(a,1,2))]. 580 ((x * (x / y)) / x) * y = T(x,x / y). [para(59(a,1),578(a,2,2)),flip(a)]. 581 ((x * y) * x) / (x * y) = T(x * y,x) / y. [para(13(a,1),579(a,1,2)),flip(a)]. 582 x * ((y * (x \ y)) / y) = T(y,y / x). [para(580(a,1),326(a,1)),flip(a)]. 583 x \ L((y * ((x \ 1) \ y)) / y,x \ 1,x) = T(y,y / (x \ 1)). [para(582(a,1),248(a,2))]. 584 (x * y) * L((x \ y) / y,y,x) = T(y,y / (x * y)). [para(329(a,2),582(a,1,2))]. 585 x * (((y * x) / y) \ 1) = ((y * x) / y) \ x. [para(575(a,1),14(a,1,2))]. 586 (((x * y) / x) \ 1) * T(y,((x * y) / x) \ 1) = ((x * y) / x) \ y. [para(585(a,1),85(a,2))]. 587 x \ T(y,y / (x * y)) = y * ((x \ y) / y). [para(584(a,1),126(a,1,2))]. 588 ((x / y) * T((x / y) \ z,u)) * y = x * T(x \ (z * y),u). [para(556(a,2),171(a,1))]. 589 ((x / y) * T((x / y) \ x,z)) * y = x * T(y,z). [para(556(a,2),173(a,1))]. 590 (1 / x) * T((1 / x) \ 1,y) = T(x,y) / x. [hyper(18,a,130,a,b,589,a)]. 591 ((x / y) * T(y,z)) * y = x * T(y,z). [para(59(a,1),589(a,1,1,2,1))]. 592 (x * T(y,z)) / y = (x / y) * T(y,z). [hyper(70,a,591,a)]. 593 ((x / y) * T(y,z)) \ (x * T(y,z)) = y. [hyper(66,a,591,a)]. 594 (1 / x) * T(x,y) = T(x,y) / x. [hyper(18,a,130,a,b,591,a)]. 595 (x * T(y,z)) * y = (x * y) * T(y,z). [para(15(a,1),591(a,1,1,1))]. 596 T((x / y) * T(y,z),y) = y \ (x * T(y,z)). [para(591(a,1),30(a,2,2))]. 597 T(x,y) \ (T(x,y) / x) = T(1 / x,T(x,y)). [para(594(a,1),30(a,2,2)),flip(a)]. 598 T(x \ 1,y) / (x \ 1) = x * T(x \ 1,y). [para(57(a,1),594(a,1,1)),flip(a)]. 599 L(K(x,y),x,1 / x) = L(T(x,y) / x,x,y). [para(594(a,1),394(a,1,1)),flip(a)]. 600 ((x / T(y,z)) / y) * T(y,z) = x / y. [para(16(a,1),592(a,1,1)),flip(a)]. 601 (x / y) * T(y,x) = (y * x) / y. [para(85(a,1),592(a,1,1)),flip(a)]. 602 (x / (y / z)) * T(y / z,z) = (x * (z \ y)) / (y / z). [para(87(a,1),592(a,1,1,2)),flip(a)]. 603 T(x,y) = (y / x) \ ((x * y) / x). [hyper(66,a,601,a),flip(a)]. 604 (L(x \ 1,x,y) * y) / L(x \ 1,x,y) = (y * x) * T(L(x \ 1,x,y),y). [para(160(a,1),601(a,1,1)),flip(a)]. 605 (L(x,1 / x,y) * y) / L(x,1 / x,y) = (y * (1 / x)) * T(L(x,1 / x,y),y). [para(166(a,1),601(a,1,1)),flip(a)]. 606 K(x \ (x / (x \ (x / y))),x) = x \ ((y * x) / y). [para(601(a,1),555(a,2,2))]. 607 x \ ((y * (x * y)) / y) = T(y,x * y). [para(15(a,1),603(a,2,1)),flip(a)]. 608 (x * y) / T(y,z) = (x / T(y,z)) * y. [hyper(268,a,595,a)]. 610 (x * y) * T(y,x) = (y * x) * y. [para(85(a,1),595(a,1,1)),flip(a)]. 611 R((x * y) / x,x,T(y,x)) = ((y * x) * y) / (y * x). [para(610(a,1),223(a,2,1))]. 612 R(T((x * y) / x,y * x),x,T(y,x)) = (y * x) \ ((y * x) * y). [para(610(a,1),445(a,2,2))]. 613 (x / T(y,z)) / y = (x / y) / T(y,z). [hyper(70,a,600,a),flip(a)]. 614 (x * y) / T(y,z) != u * y | x / T(y,z) = u. [para(608(a,2),20(a,1))]. 615 (x * y) / T(y,y \ z) = (x / ((y \ z) \ z)) * y. [para(86(a,1),608(a,2,1,2))]. 616 (x / T(x,y)) / x = 1 / T(x,y). [para(54(a,1),613(a,2,1))]. 617 K(x \ (x / (1 / y)),x) = T(y,x) / y. [para(590(a,1),429(a,2))]. 618 K(x \ (x / (1 / (y / (x * y)))),x) = R(x \ 1,x,y) / (y / (x * y)). [para(300(a,1),617(a,2,1))]. 619 L(x \ 1,x,T(x,y) / x) = T(1 / x,T(x,y)). [para(597(a,1),158(a,2))]. 620 x / T(y,y \ z) = x / ((y \ z) \ z). [hyper(614,a,615,a)]. 621 (x / ((y \ z) \ z)) * T((y \ z) \ z,u) = x * K(u \ (u / (x \ (x / T(y,y \ z)))),u). [para(620(a,2),522(a,2,2,1,2,2,2))]. 622 R((x * y) / x,x,T(y,x)) = T(y * x,y) / x. [para(611(a,2),581(a,1))]. 623 (x * (y \ z)) / (z / y) = (x / (z / y)) * (y \ z). [para(87(a,1),602(a,1,2)),flip(a)]. 624 (x / ((y * z) / y)) * (y \ (y * z)) = (x * z) / ((y * z) / y). [para(13(a,1),623(a,1,1,2)),flip(a)]. 625 (x * T(x \ (y * z),u)) / z = (x / z) * T((x / z) \ y,u). [hyper(70,a,588,a)]. 626 (((x / y) \ z) * (x / y)) * y = x * T(x \ (z * y),x / y). [para(85(a,1),588(a,1,1))]. 627 (x * y) / ((z * y) / z) = (x / ((z * y) / z)) * y. [para(13(a,1),624(a,1,2)),flip(a)]. 628 (x / y) * T((x / y) \ 1,z) = (x * T(x \ y,z)) / y. [para(11(a,1),625(a,1,1,2,1,2)),flip(a)]. 629 (x / y) * T((x / y) \ z,x) = ((x \ (z * y)) * x) / y. [para(85(a,1),625(a,1,1)),flip(a)]. 630 K((x / y) \ 1,x / y) * y = x * T(x \ (1 * y),x / y). [para(135(a,2),626(a,1,1))]. 631 K((x / y) \ 1,x / y) * y = x * T(x \ y,x / y). [para(11(a,1),630(a,2,2,1,2))]. 632 K((x / (y * x)) \ 1,x / (y * x)) * (y * x) = T(y,x / (y * x)) * x. [para(631(a,2),170(a,1))]. 633 (K((x / y) \ 1,x / y) * y) / x = T(y / x,x / y). [para(631(a,2),176(a,1,1))]. 634 K((x / y) \ 1,x / y) * (y / x) = T(y / x,x / y). [para(633(a,1),281(a,1)),flip(a)]. 635 (L(x,y,z) * (z * y)) \ (x * (z * y)) = a(z,y,T(x,z * y)). [para(261(a,1),111(a,1,1))]. 636 (L(x,y,z) * (z * y)) * a(z,y,T(x,z * y)) = x * (z * y). [para(635(a,1),14(a,1,2))]. 637 ((L(x,y,z) * (z * y)) / (z * y)) * T(((L(x,y,z) * (z * y)) / (z * y)) \ x,u) = ((L(x,y,z) * (z * y)) * T(a(z,y,T(x,z * y)),u)) / (z * y). [para(635(a,1),625(a,1,1,2,1)),flip(a)]. 638 R(x,y * ((x * y) \ z),a(x,y,(x * y) \ z)) \ z = (y * ((x * y) \ z)) * a(x,y,(x * y) \ z). [para(14(a,1),286(a,1,2))]. 639 R((x / (y * x)) \ 1,R(1 / y,y,x),y * x) = (K((x / (y * x)) \ 1,x / (y * x)) * (y * x)) / x. [para(104(a,2),288(a,2,2)),flip(a)]. 640 x * ((x \ y) * ((z * ((x \ y) \ u)) / z)) = y * ((z * (y \ (x * u))) / z). [para(334(a,1),190(a,1,2)),flip(a)]. 641 x * T(K(y,z) * u,K(y,z) * x) = u * (K(y,z) * x). [para(412(a,1),97(a,1))]. 642 x * T(K(y,z) * R(u / (K(y,z) * x),w,v5),K(y,z) * x) = (K(y,z) * x) * R((K(y,z) * x) \ u,w,v5). [para(641(a,2),264(a,1))]. 643 x \ ((y * (1 \ (x * y))) / y) = T(y,y / (x \ 1)). [para(334(a,1),583(a,1,2))]. 644 x \ ((y * (x * y)) / y) = T(y,y / (x \ 1)). [para(47(a,1),643(a,1,2,1,2))]. 645 T(x,x / (y \ 1)) = T(x,y * x). [para(644(a,1),607(a,1))]. 646 R(L(x,y,x),y,T(x,y)) = (x * y) \ ((x * y) * x). [para(297(a,1),612(a,1,1))]. 647 L(R(x,y,T(x,y)),y,x) = (x * y) \ ((x * y) * x). [para(646(a,1),42(a,1)),flip(a)]. 648 L(R(x,y,T(x,y)),y,x) = x. [para(647(a,2),13(a,1))]. 649 L((x * R(y,z,T(y,z))) / x,z,y) = (x * y) / x. [para(648(a,1),327(a,2,1,2))]. 650 L(R((x * y) / x,z,T(y,z)),z,y) = (x * y) / x. [para(325(a,2),649(a,1,1))]. 651 T((x \ y) / y,z) * y = (T(1 / x,z) * x) * (x \ y). [para(14(a,1),301(a,1,1,1,2))]. 652 (T(1 / x,y) * x) * (x \ z) = z * T(z \ (x \ z),y). [para(651(a,1),171(a,1))]. 653 (x * T(x \ 1,y)) * (x \ z) = z * T(z \ (x \ z),y). [para(171(a,1),652(a,1,1))]. 654 (x \ (y \ x)) * x = (y * T(y \ 1,x)) * (y \ x). [para(653(a,2),85(a,1)),flip(a)]. 655 (L(x,y,z) * T(L(x,y,z) \ 1,x)) * (L(x,y,z) \ x) = (L(x,y,z) \ 1) * x. [para(490(a,1),654(a,1,1)),flip(a)]. 656 (T(x,y) * T(T(x,y) \ 1,x)) * (T(x,y) \ x) = (T(x,y) \ 1) * x. [para(506(a,1),654(a,1,1)),flip(a)]. 657 x * T(x \ ((1 / x) \ y),z) = (1 / x) \ T(y,z). [para(89(a,1),354(a,1,2,1)),flip(a)]. 658 x \ ((x / y) * ((y \ z) * y)) = T(x \ ((x / y) * z),y). [para(16(a,1),360(a,1,1,1)),flip(a)]. 659 T(K(x \ (x / (y \ (y / z))),x),z) = y \ ((y / z) * ((z \ T(z,x)) * z)). [para(555(a,2),658(a,2,1)),flip(a)]. 660 T(((x * y) * z) / (x * z),x * y) = L(R(y,x,z),x,(x * y) / x). [para(365(a,2),42(a,1))]. 661 (x * y) * R((x * y) \ x,z,u) = x * (y * R(y \ 1,z,u)). [para(12(a,1),383(a,1,2,1,2))]. 662 (x * y) * R((x * y) \ z,u,w) = x * (y * R(y \ (x \ z),u,w)). [para(14(a,1),383(a,1,2,1,2))]. 663 (x * y) * R((y * T(x,y)) \ y,z,u) = y * (T(x,y) * R(T(x,y) \ 1,z,u)). [para(85(a,1),661(a,1,1))]. 664 (x * y) * L((x * y) \ (z * y),u,w) = (L(z / x,u,w) * x) * y. [para(385(a,1),260(a,1)),flip(a)]. 665 (x * y) * R((x * y) \ (z * y),u,w) = (R(z / x,u,w) * x) * y. [para(390(a,1),264(a,1)),flip(a)]. 666 (x * y) * ((z * ((x * y) \ y)) / z) = (((z * (1 / x)) / z) * x) * y. [para(399(a,1),326(a,1)),flip(a)]. 667 T(L(x \ 1,x,y) \ 1,y) = L(x \ 1,x,y) \ K(x,y). [para(13(a,1),432(a,1,2,1)),flip(a)]. 668 K(x,y) = L(x \ 1,x,y) * T(L(x \ 1,x,y) \ 1,y). [para(667(a,2),14(a,1,2)),flip(a)]. 669 (L(x / y,z,u) * y) * (y \ w) = w * L(w \ (x * (y \ w)),z,u). [para(436(a,1),260(a,1))]. 670 (R(x / y,z,u) * y) * (y \ w) = w * R(w \ (x * (y \ w)),z,u). [para(437(a,1),264(a,1))]. 671 (x \ 1) * (x * R(x \ 1,y,z)) = R(x \ 1,y,z). [para(546(a,1),462(a,1))]. 672 R(x \ 1,y,z) / (x * R(x \ 1,y,z)) = x \ 1. [hyper(70,a,671,a)]. 673 L(R(x,y,y \ 1),y,(y * x) / y) = T((y * x) * (y \ 1),y * x). [para(91(a,1),660(a,1,1)),flip(a)]. 674 L(R(x,y,x),y,(y * x) / y) = x. [para(660(a,1),105(a,1))]. 675 ((x * y) / x) \ (y * (x * y)) = x * T(R(y,x,y),x * y). [para(674(a,1),366(a,1,2,1))]. 676 ((x * y) / x) \ (y * (x * y)) = x * R(T(y,x * y),x,y). [para(40(a,2),675(a,2,2))]. 677 ((x * y) / x) \ (y * (x * y)) = y * x. [para(676(a,2),408(a,1))]. 678 ((L(x,y,z) \ x) / x) \ ((L(x,y,z) \ 1) * (x * (L(x,y,z) \ 1))) = (L(x,y,z) \ 1) * x. [para(489(a,1),677(a,1,1,1))]. 679 x * (T(T(y,x),z) * R(T(T(y,x),z) \ (x \ u),w,v5)) = (T(y,z) * x) * R((x * T(T(y,x),z)) \ u,w,v5). [para(114(a,1),662(a,1,1)),flip(a)]. 680 x * (y * L(y \ (x \ (z * y)),u,w)) = (L(z / x,u,w) * x) * y. [para(664(a,1),379(a,1)),flip(a)]. 681 (x * y) * R((x * y) \ y,z,u) = (R(1 / x,z,u) * x) * y. [para(11(a,1),665(a,1,2,1,2))]. 682 (x * y) * R((x * y) \ (z * y),u,w) = (x * R(x \ z,u,w)) * y. [para(264(a,1),665(a,2,1))]. 683 (x * y) * R((x * y) \ ((x * z) * y),u,w) = (x * R(z,u,w)) * y. [para(265(a,1),665(a,2,1))]. 684 (x * y) * R((x * y) \ y,z,u) = (x * R(x \ 1,z,u)) * y. [para(264(a,1),681(a,2,1))]. 685 K(x \ 1,x) * R(((x \ 1) * x) \ x,y,z) = ((x \ 1) * R((x \ 1) \ 1,y,z)) * x. [para(135(a,2),684(a,1,1))]. 686 (x * y) * ((z * ((x * y) \ y)) / z) = (x * ((z * (x \ 1)) / z)) * y. [para(326(a,1),666(a,2,1))]. 687 (x * L(x \ y,z,u)) * (x \ w) = w * L(w \ (y * (x \ w)),z,u). [para(260(a,1),669(a,1,1))]. 688 (x * R(x \ y,z,u)) * (x \ w) = w * R(w \ (y * (x \ w)),z,u). [para(264(a,1),670(a,1,1))]. 689 x * (y * L(y \ (x \ (z * y)),u,w)) = (x * L(x \ z,u,w)) * y. [para(260(a,1),680(a,2,1))]. 690 x * (y * R(y \ (x \ (z * y)),u,w)) = (x * R(x \ z,u,w)) * y. [para(682(a,1),662(a,1)),flip(a)]. 691 (x * R(y,z,u)) * y = (x * y) * R(y,z,u). [para(13(a,1),683(a,1,2,1)),flip(a)]. 692 (x * R(x \ y,z,u)) * (x \ y) = y * R(x \ y,z,u). [para(14(a,1),691(a,2,1))]. 693 (x * R(T(y,x),z,u)) * (x \ (y * x)) = (y * x) * R(x \ (y * x),z,u). [para(30(a,2),692(a,1,1,2,1))]. 694 x * L(x \ (1 * (y \ x)),y,y \ 1) = (y * (1 / y)) * (y \ x). [para(548(a,1),687(a,1,1,2)),flip(a)]. 695 x * L(x \ (1 * (y \ x)),y,y \ 1) = K(y,1 / y) * (y \ x). [para(118(a,2),694(a,2,1))]. 696 x * L(x \ (y \ x),y,y \ 1) = K(y,1 / y) * (y \ x). [para(11(a,1),695(a,1,2,1,2))]. 697 x * L(x \ (x \ (y * x)),z,u) = T(x * L(x \ y,z,u),x). [hyper(109,a,689,a),flip(a)]. 698 x * (y * L(y \ (x \ y),z,u)) = (x * L(x \ 1,z,u)) * y. [para(11(a,1),689(a,1,2,2,1,2,2))]. 699 (x * L(x \ (y / z),u,w)) * z = x * (z * L(z \ (x \ y),u,w)). [para(16(a,1),689(a,1,2,2,1,2,2)),flip(a)]. 700 T(x * L(x \ y,z,u),x) = x * L(x \ T(y,x),z,u). [para(30(a,2),697(a,1,2,1,2)),flip(a)]. 701 T(x * L(x \ y,x,1 / x),x) = x * ((1 / x) * T(y,x)). [para(209(a,1),700(a,2,2))]. 702 T(x * ((1 / x) * y),x) = x * ((1 / x) * T(y,x)). [para(209(a,1),701(a,1,1,2))]. 703 T(x * ((1 / x) * ((1 / x) \ ((1 / (1 / x)) \ y))),x) = x * ((1 / (1 / x)) \ T(y,x)). [para(657(a,1),702(a,2,2))]. 704 x * (y * L(y \ (x \ y),x,x \ 1)) = (x * (1 / x)) * y. [para(548(a,1),698(a,2,1,2))]. 705 x * (K(x,1 / x) * (x \ y)) = (x * (1 / x)) * y. [para(696(a,1),704(a,1,2))]. 706 x * (K(x,1 / x) * (x \ y)) = K(x,1 / x) * y. [para(118(a,2),705(a,2,1))]. 707 ((x \ y) \ y) * (z * R(z \ (T(x,x \ y) \ (u * z)),w,v5)) = (T(x,x \ y) * R(T(x,x \ y) \ u,w,v5)) * z. [para(690(a,1),441(a,1)),flip(a)]. 708 x \ (y * (x * L(x \ (y \ z),u,w))) = T(y * L(y \ (z / x),u,w),x). [para(699(a,1),30(a,2,2)),flip(a)]. 709 (K(x,y) * (z * u)) \ ((K(x,y) * z) * (u * w)) = L(w,L(u,z,K(x,y)),K(x,y) * z). [para(88(a,1),193(a,1,2,2,1))]. 710 T((x * y) / (R(z,x,y) * (x * y)),R(z,x,y)) * ((z * x) * y) = ((R(z,x,y) \ 1) * R(z,x,y)) * (x * y). [para(300(a,2),218(a,1,1))]. 711 (x * (y * T(z,u))) / (x * y) = T((x * (y * z)) / (x * y),u). [para(195(a,1),269(a,1,1))]. 712 (x * (y * T(T(z,y),u))) / (x * y) = T((x * (z * y)) / (x * y),u). [para(85(a,1),711(a,2,1,1,2))]. 713 (x * (T(y,z) * u)) / (x * u) = T((x * (y * u)) / (x * u),z). [para(114(a,1),712(a,1,1,2))]. 714 (x * y) * T((x * y) \ (z * y),u) = (T(z / x,u) * x) * y. [para(347(a,1),81(a,1))]. 715 (x * y) * T((x * y) \ (z * y),u) = (x * T(x \ z,u)) * y. [para(171(a,1),714(a,2,1))]. 716 x * (y * T(y \ (x \ (z * y)),u)) = (x * T(x \ z,u)) * y. [para(715(a,1),339(a,1)),flip(a)]. 717 x * (y * T(y \ (x \ y),z)) = (x * T(x \ 1,z)) * y. [para(11(a,1),716(a,1,2,2,1,2,2))]. 718 (x * T(x \ (y / z),u)) * z = x * (z * T(z \ (x \ y),u)). [para(16(a,1),716(a,1,2,2,1,2,2)),flip(a)]. 719 x * ((y \ (x \ (z * y))) * y) = (x * T(x \ z,y)) * y. [para(85(a,1),716(a,1,2))]. 720 ((x * y) * T((x * y) \ x,z)) * u = (x * y) * (u * T(u \ L(y \ u,y,x),z)). [para(78(a,2),716(a,1,2,2,1,2)),flip(a)]. 721 (x * T(x \ 1,y)) * x = x * (x * T(x \ 1,y)). [para(48(a,1),717(a,1,2,2,1,2)),flip(a)]. 722 (x * T(x \ 1,y)) * y = x * ((y \ (x \ y)) * y). [para(85(a,1),717(a,1,2)),flip(a)]. 723 x * (y \ T(y * (x \ (y \ 1)),z)) = (x * T(x \ 1,z)) * (y \ 1). [para(422(a,1),717(a,1,2))]. 724 x * (K(x \ 1,x) * (x \ y)) = (x * T(x \ 1,x)) * y. [para(426(a,2),717(a,1,2))]. 725 T(x,x * T(x \ 1,y)) = x. [hyper(109,a,721,a)]. 726 R(x,(x * T(x \ 1,y)) / x,x) = T(x,(x * T(x \ 1,y)) / x). [para(725(a,1),407(a,1,1))]. 727 (x \ y) * ((y \ T(x,x \ y)) * y) = ((x \ y) * T((x \ y) \ 1,y)) * y. [para(86(a,2),722(a,2,2,1,2)),flip(a)]. 728 ((x * (y \ z)) * T((x * (y \ z)) \ x,z)) * z = (x * (y \ z)) * ((z \ L(T(y,y \ z),y \ z,x)) * z). [para(144(a,2),719(a,1,2,1,2)),flip(a)]. 729 x * (K(x \ 1,x) * (x \ y)) = ((x \ 1) * x) * y. [para(85(a,1),724(a,2,1))]. 730 x * (K(x \ 1,x) * (x \ y)) = K(x \ 1,x) * y. [para(135(a,2),729(a,2,1))]. 731 x \ (K(x \ 1,x) * y) = K(x \ 1,x) * (x \ y). [hyper(66,a,730,a)]. 732 K(x \ 1,x) * (x \ y) = ((x \ 1) \ 1) \ y. [para(731(a,1),537(a,1))]. 733 K(x \ 1,x) * y != (((x \ 1) \ 1) \ z) * u | (x \ z) * u = y. [para(732(a,1),274(a,2,1))]. 734 (x * (y * T(y \ (x \ z),u))) / y = x * T(x \ (z / y),u). [hyper(70,a,718,a)]. 735 x * (y * T(y \ (x \ z),x)) = ((x \ (z / y)) * x) * y. [para(85(a,1),718(a,1,1)),flip(a)]. 736 (x \ 1) * (y * T(y \ ((x \ 1) \ z),u)) = (x \ T(x * (z / y),u)) * y. [para(422(a,1),718(a,1,1)),flip(a)]. 737 ((x \ (y / (z \ 1))) * x) * (z \ 1) = x * (z \ T(z * (x \ y),x)). [para(422(a,1),735(a,1,2)),flip(a)]. 738 ((1 / x) * ((1 / x) \ T(y,z))) / x = (1 / x) * T((1 / x) \ (y / x),z). [para(657(a,1),734(a,1,1,2))]. 739 T(x,(x * T(x \ 1,y)) / x) = R(x,T(1 / x,y),x). [para(176(a,1),726(a,1,2)),flip(a)]. 740 R(x,T(1 / x,y),x) = T(x,T(1 / x,y)). [para(176(a,1),739(a,1,2)),flip(a)]. 741 (x * R(x \ 1,x,x \ y)) \ R(1 / x,x,x \ y) = L(x \ 1,x,(x \ y) / y). [para(161(a,1),322(a,2,3))]. 742 ((x * (1 / (1 / y))) / x) * (1 / y) = ((x * y) / x) / y. [para(92(a,1),400(a,1,1,1,2)),flip(a)]. 743 (1 / x) * ((y * ((1 / x) \ 1)) / y) = ((y * x) / y) / x. [para(742(a,1),326(a,1)),flip(a)]. 744 (1 / x) * ((y * x) / y) = ((y * x) / y) / x. [para(59(a,1),743(a,1,2,1,2))]. 745 x * (T(y,x) * T(T(y,x) \ 1,z)) = (y * x) * T((y * x) \ x,z). [para(85(a,1),409(a,1,2,1,1)),flip(a)]. 746 x * (T(y,x) * T(T(y,x) \ 1,z)) = y * (x * T(x \ (y \ x),z)). [para(745(a,2),339(a,1))]. 747 x * K(y \ (y / T(z,x)),y) = z * (x * T(x \ (z \ x),y)). [para(429(a,2),746(a,1,2))]. 748 (x * T(x \ 1,y)) * z = z * K(y \ (y / T(x,z)),y). [para(747(a,2),717(a,1)),flip(a)]. 749 T(x * T(x \ 1,y),z) = K(y \ (y / T(x,z)),y). [hyper(109,a,748,a(flip))]. 750 T(x * T(x \ 1,y),x \ y) = K(y \ (x \ y),y). [para(123(a,1),749(a,2,1,2))]. 751 T(x,y) * T(T(x,y) \ 1,z) = T(x * T(x \ 1,z),y). [para(749(a,2),429(a,1)),flip(a)]. 752 K(x \ (x / T(y,z)),x) = T(K(x \ (x / y),x),z). [para(429(a,2),749(a,1,1)),flip(a)]. 753 K(x \ (x / T(x,y)),x) = T(K(x \ 1,x),y). [para(54(a,1),752(a,2,1,1,2))]. 754 T(x * T(x \ 1,x),y) * (T(x,y) \ x) = (T(x,y) \ 1) * x. [para(751(a,1),656(a,1,1))]. 755 T((x \ 1) * x,y) * (T(x,y) \ x) = (T(x,y) \ 1) * x. [para(85(a,1),754(a,1,1,1))]. 756 T(K(x \ 1,x),y) * (T(x,y) \ x) = (T(x,y) \ 1) * x. [para(135(a,2),755(a,1,1,1))]. 757 (x * y) * K(z \ (z / K(y,x)),z) = (y * x) * T(K(x,y),z). [para(24(a,2),521(a,1,2,1)),flip(a)]. 758 (x * y) * (K(y,x) * T(K(y,x) \ 1,z)) = (y * x) * T(K(x,y),z). [para(429(a,1),757(a,1,2))]. 759 (x * y) \ ((y * x) * T(K(x,y),z)) = K(y,x) * T(K(y,x) \ 1,z). [hyper(66,a,758,a)]. 760 (x \ 1) * R(K(x,x \ 1) * ((1 / x) \ y),z,u) = R(y * x,z,u) / x. [para(458(a,2),562(a,1,2))]. 761 x \ (y * ((z * (y \ (x * u))) / z)) = (x \ y) * ((z * ((x \ y) \ u)) / z). [hyper(66,a,640,a)]. 762 (R(x,y,z) * u) * (u \ (x * u)) = (x * u) * R(u \ (x * u),y,z). [para(116(a,1),693(a,1,1))]. 763 (x * y) * R(y \ (x * y),z,u) = (R(x,z,u) * y) * T(x,y). [para(30(a,2),762(a,1,2)),flip(a)]. 764 (R(x,y,z) * u) * T(x,u) = (x * u) * R(T(x,u),y,z). [para(30(a,2),763(a,1,2,1)),flip(a)]. 765 (T(x,y) * (R(x,z,u) * y)) \ ((x * y) * R(T(x,y),z,u)) = K(R(x,z,u) * y,T(x,y)). [para(764(a,1),24(a,2,2)),flip(a)]. 766 (x \ y) * ((y \ T(x,x \ y)) * y) = (x \ ((y \ x) * y)) * y. [para(414(a,1),727(a,2,1))]. 767 (x \ y) * ((y \ T(x,x \ y)) * y) = K(y \ x,y) * y. [para(73(a,1),766(a,2,1))]. 768 (1 / x) * T((1 / x) \ (y / x),z) = T(y,z) / x. [para(14(a,1),738(a,1,1)),flip(a)]. 770 (1 / x) * T((1 / x) \ y,z) = T(y * x,z) / x. [para(15(a,1),768(a,1,2,1,2))]. 771 ((x \ (y / (1 / z))) * x) * (1 / z) = x * (T((x \ y) * z,x) / z). [para(770(a,1),735(a,1,2)),flip(a)]. 772 (x \ 1) * R((x \ 1) \ y,z,u) = R(y * x,z,u) / x. [para(533(a,1),760(a,1,2,1))]. 773 R(x * y,z,u) / y = y \ R(y * x,z,u). [para(772(a,1),557(a,1))]. 774 (x \ R(x * y,z,u)) * x = R(y * x,z,u). [para(773(a,1),16(a,1,1))]. 775 x \ R(x * (y / x),z,u) = R(y,z,u) / x. [para(16(a,1),773(a,1,1,1)),flip(a)]. 776 R((x \ y) * x,z,u) = (x \ R(y,z,u)) * x. [para(14(a,1),774(a,1,1,2,1)),flip(a)]. 777 (x \ y) * ((z * ((x \ y) \ 1)) / z) = x \ (y * ((z * (y \ x)) / z)). [para(12(a,1),761(a,1,2,2,1,2,2)),flip(a)]. 778 x \ ((y * x) * ((z * ((y * x) \ x)) / z)) = T(y,x) * ((z * ((x \ (y * x)) \ 1)) / z). [para(30(a,2),777(a,1,1)),flip(a)]. 779 x \ (y * (((y / x) * (y \ x)) / (y / x))) = (x \ y) * (((x \ y) \ (y / x)) / (y / x)). [para(528(a,1),777(a,1,2,1)),flip(a)]. 780 x * T(y,y \ z) = x * ((y \ z) \ z). [para(391(a,1),232(a,1))]. 782 (1 / x) * L((1 / x) \ y,z,u) = L(y * x,z,u) / x. [para(225(a,1),395(a,1,1,1)),flip(a)]. 783 (x \ (y \ z)) \ (((y * x) \ z) \ (x \ (y \ z))) = ((y * x) \ z) \ 1. [para(128(a,1),491(a,2,1))]. 784 K((x \ (y \ z)) \ ((x \ (y \ z)) / (((((y * x) \ z) \ (x \ (y \ z))) / (x \ (y \ z))) \ 1)),x \ (y \ z)) = ((((y * x) \ z) \ (x \ (y \ z))) / (x \ (y \ z))) \ (((y * x) \ z) \ 1). [para(783(a,1),434(a,2,2))]. 785 (L(x \ 1,x,y) * y) / L(x \ 1,x,y) = y * (x * T(x \ 1,y)). [para(604(a,2),195(a,1))]. 786 (x * (y * T(y \ 1,x))) \ (x \ ((L(y \ 1,y,x) * x) / L(y \ 1,y,x))) = (L(y \ 1,y,x) \ (L(y \ 1,y,x) * x)) \ 1. [para(785(a,1),574(a,1,1))]. 787 (L(x / (y / z),u,w) * (y / z)) * z = L((x * z) / y,u,w) * y. [para(16(a,1),387(a,2,2))]. 788 ((x / y) * L((x / y) \ z,u,w)) * y = L((z * y) / x,u,w) * x. [para(260(a,1),787(a,1,1))]. 789 ((x / y) * L((x / y) \ z,u,w)) * y = x * L(x \ (z * y),u,w). [para(788(a,2),260(a,1))]. 790 ((x / y) * L((x / y) \ x,z,u)) * y = x * L(y,z,u). [para(13(a,1),789(a,2,2,1))]. 791 ((x / y) * L(y,z,u)) * y = x * L(y,z,u). [para(59(a,1),790(a,1,1,2,1))]. 792 (x * L(y,z,u)) / y = (x / y) * L(y,z,u). [hyper(70,a,791,a)]. 793 (1 / x) * L(x,y,z) = L(x,y,z) / x. [hyper(18,a,130,a,b,791,a)]. 794 (R(x,L(y,z,u) / y,y) / y) * L(y,z,u) = x * (L(y,z,u) / y). [hyper(18,a,210,a(flip),b,791,a)]. 795 (x * L(y,z,u)) * y = (x * y) * L(y,z,u). [para(15(a,1),791(a,1,1,1))]. 796 L(x,y,z) \ (L(x,y,z) / x) = T(1 / x,L(x,y,z)). [para(793(a,1),30(a,2,2)),flip(a)]. 797 ((x / L(y,z,u)) / y) * L(y,z,u) = x / y. [para(16(a,1),792(a,1,1)),flip(a)]. 798 ((x / L(y,z,u)) * y) * L(y,z,u) = x * y. [para(16(a,1),795(a,1,1)),flip(a)]. 799 (x / L(y,z,u)) / y = (x / y) / L(y,z,u). [hyper(70,a,797,a),flip(a)]. 800 ((x / L(y,z,u)) * y) \ (x * y) = L(y,z,u). [hyper(66,a,798,a)]. 801 (x / L(x,y,z)) / x = 1 / L(x,y,z). [para(54(a,1),799(a,2,1))]. 802 L(x,y,z) = ((z * y) * x) \ ((z * (y * x)) * x). [para(95(a,1),800(a,1,1,1)),flip(a)]. 803 R(L(x,y,z),T(1 / x,L(x,y,z)),x) \ L(x,y,z) = (L(x,y,z) \ (L(x,y,z) / x)) * x. [para(796(a,1),316(a,1,1,2))]. 804 ((x * ((y \ z) / z)) / x) * z = (((x * (1 / y)) / x) * y) * (y \ z). [para(14(a,1),401(a,1,1,1,2,2))]. 805 (((x * (1 / y)) / x) * y) * (y \ z) = z * ((x * (z \ (y \ z))) / x). [para(804(a,1),326(a,1))]. 806 (x * ((y * (x \ 1)) / y)) * (x \ z) = z * ((y * (z \ (x \ z))) / y). [para(326(a,1),805(a,1,1))]. 807 (x * ((y * (x \ (z \ x))) / y)) / (z \ x) = z * ((y * (z \ 1)) / y). [hyper(70,a,806,a)]. 808 (x * ((y * (x \ z)) / y)) / ((x / z) \ x) = (x / z) * ((y * ((x / z) \ 1)) / y). [para(59(a,1),807(a,1,1,2,1,2,2))]. 809 x * (T(y,x) * R(T(y,x) \ 1,z,u)) = (y * x) * R((y * x) \ x,z,u). [para(85(a,1),663(a,1,2,1,1)),flip(a)]. 810 x * (T(y,x) * R(T(y,x) \ 1,z,u)) = (y * R(y \ 1,z,u)) * x. [para(809(a,2),684(a,1))]. 811 T(x,y) * R(T(x,y) \ 1,z,u) = T(x * R(x \ 1,z,u),y). [hyper(109,a,810,a),flip(a)]. 812 T((x / y) * R((x / y) \ 1,z,u),y) = (y \ x) * R(T(x / y,y) \ 1,z,u). [para(87(a,1),811(a,1,1)),flip(a)]. 813 (x / y) * ((z * ((x / y) \ 1)) / z) = (x * ((z * (x \ y)) / z)) / y. [para(59(a,1),808(a,1,2)),flip(a)]. 814 T((x / y) * R((x / y) \ 1,z,u),y) = (y \ x) * R((y \ x) \ 1,z,u). [para(87(a,1),812(a,2,2,1,1))]. 815 T(T((x / y) * R((x / y) \ 1,z,u),w),y) = T((y \ x) * R((y \ x) \ 1,z,u),w). [para(814(a,1),36(a,1,1)),flip(a)]. 816 (L(x,1 / x,y) * y) / L(x,1 / x,y) = y * ((1 / x) * T(x,y)). [para(605(a,2),195(a,1))]. 817 (x * y) * (z * T(z \ L(y \ z,y,x),u)) = (x * (y * T(y \ 1,u))) * z. [para(337(a,1),720(a,1,1)),flip(a)]. 818 K(x,y) * ((y * x) / K(x * y,K(K(x,y),y * x))) = K(K(x,y),y * x) * (x * y). [para(373(a,1),281(a,1)),flip(a)]. 819 K(x \ 1,x) * T(K(x \ 1,x) \ y,z) = (x \ 1) * (x * T(x \ ((x \ 1) \ y),z)). [para(135(a,2),382(a,1,2,1,1))]. 820 (x * y) * L((x * y) \ (y * z),u,w) = y * (T(x,y) * L(T(x,y) \ z,u,w)). [para(85(a,1),384(a,1,2,1,1))]. 821 x * (T(y,x) * L(T(y,x) \ z,u,w)) = y * (x * L(x \ (y \ (x * z)),u,w)). [para(820(a,1),379(a,1))]. 822 x \ (y * (x * L(x \ (y \ (x * z)),u,w))) = T(y,x) * L(T(y,x) \ z,u,w). [hyper(66,a,821,a)]. 823 x * (T(y,x) * L(T(y,x) \ 1,z,u)) = y * (x * L(x \ (y \ x),z,u)). [para(12(a,1),821(a,2,2,2,1,2,2))]. 824 x * (T(y,x) * L(T(y,x) \ 1,z,u)) = (y * L(y \ 1,z,u)) * x. [para(823(a,2),698(a,1))]. 825 T(x,y) * L(T(x,y) \ 1,z,u) = T(x * L(x \ 1,z,u),y). [hyper(109,a,824,a),flip(a)]. 826 T(x * L(x \ 1,y,z),u) / T(x,u) = L(1 / T(x,u),y,z). [para(825(a,1),320(a,1,1))]. 827 T(x * L(x \ 1,T(x,y),x / T(x,y)),y) = x \ (T(x,y) * (x / T(x,y))). [para(825(a,1),500(a,2)),flip(a)]. 828 T((x / T(x,y)) * (T(x,y) * (x \ 1)),y) = x \ (T(x,y) * (x / T(x,y))). [para(191(a,1),827(a,1,1))]. 829 T((x / T(x,y)) * (x \ T(x,y)),y) = x \ (T(x,y) * (x / T(x,y))). [para(424(a,1),828(a,1,1,2))]. 830 T((x / T(x,y)) * (x \ T(x,y)),y) = K(T(x,y),x / T(x,y)). [para(829(a,2),75(a,1))]. 831 T(x * L(x \ ((y * z) / y),u,w),y) = T(x,y) * L(T(x,y) \ z,u,w). [para(822(a,1),708(a,1)),flip(a)]. 832 T(x \ L(x * ((y * z) / y),u,w),y) = T(x \ 1,y) * L(T(x \ 1,y) \ z,u,w). [para(558(a,1),831(a,1,1))]. 833 K(x \ 1,x) * R(K(x \ 1,x) \ x,y,z) = ((x \ 1) * R((x \ 1) \ 1,y,z)) * x. [para(135(a,2),685(a,1,2,1,1))]. 834 (K(x,y) * (z * u)) \ (K(x,y) * (z * (u * w))) = L(w,L(u,z,K(x,y)),K(x,y) * z). [para(197(a,1),709(a,1,2))]. 835 x \ ((y * x) * ((z * ((y * x) \ x)) / z)) = T(y,x) * ((z * (T(y,x) \ 1)) / z). [para(30(a,2),778(a,2,2,1,2,1))]. 836 x \ ((y * ((z * (y \ 1)) / z)) * x) = T(y,x) * ((z * (T(y,x) \ 1)) / z). [para(686(a,1),835(a,1,2))]. 837 T(x,y) * ((z * (T(x,y) \ 1)) / z) = T(x * ((z * (x \ 1)) / z),y). [para(836(a,1),30(a,2)),flip(a)]. 838 K(K(x,y),y * x) * (x * y) = K(x,y) * ((y * x) / 1). [para(554(a,1),818(a,1,2,2)),flip(a)]. 839 K(K(x,y),y * x) * (x * y) = K(x,y) * (y * x). [para(55(a,1),838(a,2,2))]. 841 T(K(K(x,y),y * x) * x,y) = y \ (K(x,y) * (y * x)). [para(839(a,1),279(a,1,2)),flip(a)]. 842 T((K(K(x,y),y * x) * x) * R((K(K(x,y),y * x) * x) \ 1,z,u),y) = (y \ (K(x,y) * (y * x))) * R(T(K(K(x,y),y * x) * x,y) \ 1,z,u). [para(841(a,1),811(a,1,1)),flip(a)]. 843 T(T(((K(x,y) * (y * x)) / y) * R(((K(x,y) * (y * x)) / y) \ 1,z,u),w),y) = T(T(K(K(x,y),y * x) * x,y) * R((y \ (K(x,y) * (y * x))) \ 1,z,u),w). [para(841(a,2),815(a,2,1,1))]. 844 T(T(((K(x,y) * (y * x)) / y) * R(((K(x,y) * (y * x)) / y) \ 1,z,u),w),y) = T((y \ (K(x,y) * (y * x))) * R(T(K(K(x,y),y * x) * x,y) \ 1,z,u),w). [para(841(a,2),815(a,2,1,2,1,1))]. 845 K(x \ 1,x) * T(K(x \ 1,x) \ y,z) = (x \ T(x * (y / x),z)) * x. [para(819(a,2),736(a,1))]. 846 K(x \ 1,x) * T(K(x,x \ 1) * y,z) = (x \ T(x * (y / x),z)) * x. [para(447(a,1),845(a,1,2,1))]. 847 K(x \ 1,x) * R(K(x,x \ 1) * x,y,z) = ((x \ 1) * R((x \ 1) \ 1,y,z)) * x. [para(447(a,1),833(a,1,2,1))]. 848 L(L(x,y,z),z * y,K(u,w)) = L(x,L(y,z,K(u,w)),K(u,w) * z). [para(834(a,1),194(a,1)),flip(a)]. 849 L(x,L(y,z,K(u,w)),K(u,w) * z) = L(x,y,z). [para(848(a,1),88(a,1))]. 850 L(x,y,K(z,u) * w) = L(x,y,w). [para(88(a,1),849(a,1,2))]. 851 L(x,y,1 / z) = L(x,y,z \ 1). [para(450(a,1),850(a,1,3))]. 852 L(T(x,1 / y) \ z,T(x,1 / y),y \ 1) = (x * (1 / y)) \ ((1 / y) * z). [para(851(a,1),207(a,1))]. 853 K(x \ 1,x) * R(K(x,x \ 1) * x,y,z) = (R(x,y,z) * (x \ 1)) * x. [para(266(a,1),847(a,2,1))]. 854 R(K(x \ 1,x) * (K(x,x \ 1) * x),y,z) = (R(x,y,z) * (x \ 1)) * x. [para(853(a,1),458(a,2))]. 855 (R(x,y,z) * (x \ 1)) * x = R(x,y,z). [para(448(a,1),854(a,1,1)),flip(a)]. 856 (x \ R(x,y,z)) * x = R(x,y,z). [para(479(a,1),855(a,1,1))]. 857 R(x,y,z) / x = x \ R(x,y,z). [hyper(70,a,856,a)]. 858 x * (R(x,y,z) / x) = R(x,y,z). [para(856(a,1),56(a,1,2,1))]. 859 (x * R(x \ 1,y,z)) * (1 / x) = R(1 / x,y,z). [para(418(a,1),856(a,1,1))]. 860 R(x,y,y \ 1) / x = a(x,y,y \ 1). [para(857(a,2),291(a,1))]. 861 (1 / x) * R(x,y,z) = x \ R(x,y,z). [para(857(a,1),563(a,2))]. 862 R(1 / x,x,y) / (1 / x) = (y / (x * y)) * x. [hyper(17,a,419,a,b,858,a)]. 863 R((x \ 1) / (x * (x \ 1)),y,z) / R(1 / x,y,z) = a(R(1 / x,y,z),x,x \ 1). [para(163(a,1),860(a,1,1))]. 864 R(x \ 1,x,y) / (y / (x * y)) = a(y / (x * y),x,x \ 1). [para(375(a,1),860(a,1,1))]. 865 R(x,y,z) * (x \ 1) = (1 / x) * R(x,y,z). [para(861(a,2),479(a,2))]. 866 T(1 / x,R(x,y,z)) = x \ 1. [hyper(109,a,865,a)]. 867 T(x,R(x \ 1,y,z)) = (x \ 1) \ 1. [para(57(a,1),866(a,1,1))]. 868 T(1 / x,R((1 / x) \ 1,y,z)) = x \ 1. [para(59(a,1),867(a,2,1))]. 869 x * T(x \ 1,R((1 / x) \ 1,y,z)) = (1 / x) \ (x \ 1). [para(868(a,1),517(a,1,2)),flip(a)]. 870 ((x / (y * x)) * y) / R(1 / y,y,x) = 1 / (1 / y). [para(862(a,1),564(a,1,1))]. 871 (x * R(x \ 1,y,z)) \ R(1 / x,y,z) = 1 / x. [hyper(66,a,859,a)]. 872 L(x \ 1,x,(x \ y) / y) = 1 / x. [para(871(a,1),741(a,1)),flip(a)]. 873 L((x / y) \ 1,x / y,y / x) = 1 / (x / y). [para(59(a,1),872(a,1,3,1))]. 875 L((x / (y * x)) \ 1,x / (y * x),y) = 1 / (x / (y * x)). [para(15(a,1),873(a,1,3))]. 876 x * L(x \ (1 * y),x / y,y / x) = ((x / y) * (1 / (x / y))) * y. [para(873(a,1),789(a,1,1,2)),flip(a)]. 877 x / (1 / (y / (x * y))) = x * (y / (x * y)). [para(875(a,1),160(a,1,2))]. 878 K(x \ (x / (1 / (y / (x * y)))),x) = a(y / (x * y),x,x \ 1). [para(864(a,1),618(a,2))]. 879 K(x \ (x * (y / (x * y))),x) = a(y / (x * y),x,x \ 1). [para(877(a,1),878(a,1,1,2))]. 880 a(x / (y * x),y,y \ 1) = K(x / (y * x),y). [para(13(a,1),879(a,1,1)),flip(a)]. 882 a(R(1 / x,y,z),x,x \ 1) = R(x \ 1,y,z) / R(1 / x,y,z). [para(91(a,1),863(a,1,1,1)),flip(a)]. 884 a(R(1 / x,y,z),x,x \ 1) = K(x \ 1,x). [para(882(a,2),463(a,1))]. 885 a(1 / x,x,x \ 1) = K(x \ 1,x). [para(157(a,1),884(a,1,1))]. 886 a(x / (y * x),y,y \ 1) = K(y \ 1,y). [para(104(a,1),884(a,1,1))]. 888 (1 / x) \ (x \ 1) = K(x \ 1,x). [para(885(a,1),290(a,1)),flip(a)]. 889 (1 / x) * K(x \ 1,x) = x \ 1. [para(888(a,1),14(a,1,2))]. 890 x * T(x \ 1,R((1 / x) \ 1,y,z)) = K(x \ 1,x). [para(888(a,1),869(a,2))]. 891 R(x / (1 / y),1 / y,K(y \ 1,y)) = (x * K(y \ 1,y)) / (y \ 1). [para(889(a,1),82(a,2,2))]. 892 (1 / x) \ L(x \ 1,y,z) = x * L(T(x \ 1,x),y,z). [para(889(a,1),421(a,1,2,1))]. 893 K(x / (y * x),y) = K(y \ 1,y). [para(886(a,1),880(a,1)),flip(a)]. 894 K(1 / x,x) = K(x \ 1,x). [para(12(a,1),893(a,1,1,2))]. 895 K((x / y) \ 1,x / y) = K(y / x,x / y). [para(16(a,1),893(a,1,1,2)),flip(a)]. 897 K((x \ 1) \ 1,x \ 1) = K(x,x \ 1). [para(57(a,1),894(a,1,1)),flip(a)]. 898 K(x / y,(x / y) \ 1) * z = K(y / x,x / y) \ z. [para(895(a,1),447(a,1,1)),flip(a)]. 899 K(x / y,y / x) * x = y * T(y \ x,y / x). [para(895(a,1),631(a,1,1))]. 900 K(x / y,y / x) * (x / y) = T(x / y,y / x). [para(895(a,1),634(a,1,1))]. 901 K((x * y) / y,y / (x * y)) = ((y / (x * y)) \ 1) * R(1 / x,x,y). [para(895(a,1),471(a,1))]. 902 T(x / y,y / x) != z * (x / y) | K(x / y,y / x) = z. [para(900(a,1),20(a,1))]. 903 x * T(x \ 1,R(x,y,z)) = K(x \ 1,x). [para(59(a,1),890(a,1,2,2,1))]. 904 (1 / x) \ L(x \ 1,y,z) = L(x \ 1,y,z) * x. [para(892(a,2),115(a,1))]. 905 T((1 / x) * T((1 / x) \ 1,L(x \ 1,y,z)),L(x \ 1,y,z) * x) = K(L(x \ 1,y,z) \ ((1 / x) \ L(x \ 1,y,z)),L(x \ 1,y,z)). [para(904(a,1),750(a,1,2))]. 906 ((x / (y * x)) \ 1) * R(1 / y,y,x) = K(y,x / (y * x)). [para(15(a,1),901(a,1,1)),flip(a)]. 907 K(x / (y * x),(x / (y * x)) \ 1) = K(y,x / (y * x)) \ 1. [para(906(a,1),472(a,2,1))]. 908 ((T(x,y * z) * y) * z) \ ((x * y) * z) = K(y * z,(y * z) \ ((x * y) * z)). [para(81(a,1),372(a,1,1))]. 909 ((T(x,y * z) * y) * z) \ ((x * y) * z) = K(y * z,R(T(x,y * z),y,z)). [para(368(a,1),908(a,2,2))]. 910 L(R(x,T(1 / x,L(x,y,z)),x),y,z) \ L(x,y,z) = (L(x,y,z) \ (L(x,y,z) / x)) * x. [para(42(a,1),803(a,1,1))]. 911 (x * K(x,y)) * R((x * K(x,y)) \ (x * y),z,u) = (R(y,z,u) * x) * K(x,y). [para(324(a,2),215(a,1))]. 912 x * (K(x,y) * R(K(x,y) \ y,z,u)) = (R(y,z,u) * x) * K(x,y). [para(911(a,1),383(a,1)),flip(a)]. 913 x * R(K(x,y) * (K(x,y) \ y),z,u) = (R(y,z,u) * x) * K(x,y). [para(458(a,2),912(a,1,2))]. 914 (R(x,y,z) * u) * K(u,x) = u * R(x,y,z). [para(14(a,1),913(a,1,2,1)),flip(a)]. 915 K(x,R(y,z,u)) = K(x,y). [hyper(138,a,914,a)]. 916 K(x,L(R(y,z,u),w,v5)) = K(x,L(y,w,v5)). [para(42(a,1),915(a,1,2))]. 917 K(x,(y * z) / (u * z)) = K(x,y / u). [para(82(a,1),915(a,1,2))]. 918 K(x,(y / z) / u) = K(x,y / (u * z)). [para(133(a,1),915(a,1,2)),flip(a)]. 919 K(x,y * (z \ 1)) = K(x,y / z). [para(224(a,1),915(a,1,2))]. 920 K(x,T(y \ 1,y)) = K(x,y \ 1). [para(303(a,1),915(a,1,2))]. 921 K(x,(y * z) / u) = K(x,y / (u / z)). [para(220(a,1),915(a,1,2))]. 922 K(x,T(y,y * z)) = K(x,T(y,z)). [para(341(a,1),915(a,1,2)),flip(a)]. 923 K(x,T((y * z) / (u * z),w)) = K(x,T(y / u,w)). [para(221(a,2),915(a,1,2))]. 924 K(x,T(y,y \ z)) = K(x,T(y,z)). [para(342(a,1),915(a,1,2))]. 925 K(x,T((y * z) / u,w)) = K(x,T(y / (u / z),w)). [para(313(a,1),915(a,1,2))]. 926 K(x,T(y,z * y)) = K(x,T(y,z)). [para(406(a,1),915(a,1,2)),flip(a)]. 927 ((T(x,y * z) * y) * z) \ ((x * y) * z) = K(y * z,T(x,y * z)). [para(915(a,1),909(a,2))]. 928 K(x,1 / y) = K(x,y \ 1). [para(11(a,1),919(a,1,2)),flip(a)]. 929 K(x,(y \ 1) \ 1) = K(x,y). [para(57(a,1),928(a,1,2)),flip(a)]. 930 K(x,x \ 1) = x * (1 / x). [para(928(a,1),118(a,1))]. 931 K(x,x \ 1) \ x = 1 / (1 / x). [para(928(a,1),187(a,1,1))]. 932 K(x,1 / x) \ ((x \ 1) \ 1) = x. [para(928(a,2),538(a,1,1))]. 933 x * (K(x,x \ 1) * (x \ y)) = K(x,1 / x) * y. [para(928(a,1),706(a,1,2,1))]. 934 R(x,y,1 / y) * K(y,y \ 1) = (x * y) * (1 / y). [para(930(a,2),81(a,1,2))]. 935 K(x,x \ 1) * y != x * ((1 / x) * z) | L(z,1 / x,x) = y. [para(930(a,2),192(a,1,1))]. 936 x * L(x \ (1 * y),x / y,y / x) = K(x / y,(x / y) \ 1) * y. [para(930(a,2),876(a,2,1))]. 937 K(x,(y \ z) \ z) = K(x,T(y,z)). [para(86(a,1),924(a,1,2))]. 938 K(x,x \ 1) * (1 / (1 / x)) = x. [para(931(a,1),14(a,1,2))]. 939 x / (1 / (1 / x)) = K(x,x \ 1). [para(931(a,1),57(a,1,2))]. 940 K(x,1 / x) \ T(x,x \ 1) = x. [para(86(a,2),932(a,1,2))]. 941 K(x,T(y / z,y)) = K(x,z \ y). [para(59(a,1),937(a,1,2,1)),flip(a)]. 942 K(x,x \ 1) * ((1 / (1 / x)) * y) = x * y. [para(938(a,1),197(a,1,1)),flip(a)]. 943 x * ((1 / (1 / x)) \ y) = K(x,x \ 1) * y. [para(938(a,1),273(a,1,1))]. 945 K(x,1 / x) * x = T(x,x \ 1). [para(940(a,1),14(a,1,2))]. 946 K(x,x \ 1) * x = T(x,x \ 1). [para(928(a,1),945(a,1,1))]. 947 K(x,x \ 1) * (x * y) = T(x,x \ 1) * y. [para(946(a,1),197(a,1,1)),flip(a)]. 949 K(x,L(T(y,y \ z),u,w)) = K(x,L(T(y,z),u,w)). [para(342(a,1),916(a,1,2,1))]. 950 K(x,L(y,z,y)) = K(x,y). [para(648(a,1),916(a,1,2)),flip(a)]. 951 K(x \ 1,x) * (x * y) = (1 / (1 / x)) * y. [para(942(a,1),448(a,1,2))]. 953 T(x * ((1 / x) * ((1 / x) \ ((1 / (1 / x)) \ y))),x) = K(x,x \ 1) * T(y,x). [para(943(a,1),703(a,2))]. 954 K(x,x \ 1) * (y * x) = T(x,x \ 1) * T(y,x). [para(85(a,1),947(a,1,2))]. 955 K(x,x \ 1) * (x * y) = ((x \ 1) \ 1) * y. [para(86(a,1),947(a,2,1))]. 956 K(x,x \ 1) * L(y,x \ 1,x) = T(x,x \ 1) * ((x \ 1) * y). [para(189(a,1),947(a,1,2))]. 957 (1 / (1 / x)) * (x \ 1) = K(x \ 1,x). [hyper(99,a,951,a),flip(a)]. 958 K((x / y) \ 1,x / y) * x = (1 / (1 / (x / y))) * y. [para(16(a,1),951(a,1,2))]. 959 K(x \ 1,x) * (y * x) = (1 / (1 / x)) * T(y,x). [para(85(a,1),951(a,1,2))]. 961 K(x,T(y / (1 / z),u)) = K(x,T(y * z,u)). [para(92(a,1),923(a,1,2,1)),flip(a)]. 962 K(x,T(y / z,y * u)) = K(x,(z * u) \ (y * u)). [para(923(a,1),941(a,1))]. 963 x * (K(x,x \ 1) * (x \ y)) = K(x,x \ 1) * y. [para(928(a,1),933(a,2,1))]. 964 K(x,T((R(y,z,u) * z) / (y * z),(R(y,z,u) * z) * u)) = K(x,a(R(y,z,u),z,u)). [para(212(a,1),962(a,2,2))]. 965 K(x,x \ 1) * (x \ y) = (1 / (1 / x)) \ y. [hyper(17,a,943,a,b,963,a)]. 966 K(x,x \ 1) * (x * y) = x * (K(x,x \ 1) * y). [para(13(a,1),963(a,1,2,2)),flip(a)]. 967 (1 / (1 / x)) * (K(x,x \ 1) * y) = x * y. [hyper(17,a,942,a,b,966,a),flip(a)]. 968 x * (K(x,x \ 1) * y) = T(x,x \ 1) * y. [para(966(a,1),947(a,1))]. 969 L(T(K(x,x \ 1),y),y,1 / (1 / x)) = ((1 / (1 / x)) * y) \ (x * y). [para(967(a,1),112(a,1,2)),flip(a)]. 970 (T(x,x \ 1) * y) / (K(x,x \ 1) * y) = x. [hyper(70,a,968,a)]. 971 T(x,x \ 1) * ((x \ 1) * y) = x * ((1 / x) * y). [para(453(a,1),968(a,1,2)),flip(a)]. 972 (x \ 1) * (K(x \ 1,(x \ 1) \ 1) * L(T(x \ 1,(x \ 1) \ 1) \ y,z,u)) = T(x \ L(x * ((((x \ 1) \ 1) * y) / ((x \ 1) \ 1)),z,u),(x \ 1) \ 1). [para(968(a,2),832(a,2)),flip(a)]. 973 K(x / y,y / x) * y = (1 / (1 / (y / x))) * x. [para(895(a,1),958(a,1,1))]. 974 K(x,x \ 1) * L(y,x \ 1,x) = x * ((1 / x) * y). [para(956(a,2),971(a,1))]. 975 L(x,1 / y,y) = L(x,y \ 1,y). [hyper(935,a,974,a)]. 976 L(x,(y \ 1) \ 1,y \ 1) = L(x,y,y \ 1). [para(57(a,1),975(a,1,2)),flip(a)]. 977 L(((x \ 1) \ 1) \ y,x,x \ 1) = (x \ 1) * y. [para(976(a,1),253(a,1))]. 978 T(((x \ 1) \ 1) * ((x \ 1) * 1),y) / T((x \ 1) \ 1,y) = L(1 / T((x \ 1) \ 1,y),x,x \ 1). [para(977(a,1),826(a,1,1,1,2))]. 980 x * L(x \ y,x / y,y / x) = K(x / y,(x / y) \ 1) * y. [para(11(a,1),936(a,1,2,1,2))]. 981 T(x * ((1 / (1 / x)) \ y),x) = K(x,x \ 1) * T(y,x). [para(14(a,1),953(a,1,1,2))]. 983 T(K(x,x \ 1) * y,x) = K(x,x \ 1) * T(y,x). [para(943(a,1),981(a,1,1))]. 984 T((1 / x) * ((x \ 1) \ y),x) = K(x,x \ 1) * T(y,x). [para(454(a,2),983(a,1,1))]. 985 T((1 / x) * ((x \ 1) \ y),x) = (1 / x) * ((x \ 1) \ T(y,x)). [para(984(a,2),454(a,2)),flip(a)]. 986 (x \ ((x \ 1) \ y)) * x = (x \ 1) \ T(y,x). [hyper(357,a,985,a)]. 987 (x \ 1) \ T((x \ 1) * y,x) = (x \ y) * x. [para(13(a,1),986(a,1,1,2)),flip(a)]. 988 (x * T(x \ 1,y)) * ((y \ 1) \ 1) = x * ((y \ (x \ ((y \ 1) \ 1))) * y). [para(987(a,1),723(a,1,2)),flip(a)]. 989 K(x,T(R(y,z,u) / y,(R(y,z,u) * z) * u)) = K(x,a(R(y,z,u),z,u)). [para(964(a,1),923(a,1)),flip(a)]. 990 K(x,T(y \ R(y,z,u),(R(y,z,u) * z) * u)) = K(x,a(R(y,z,u),z,u)). [para(857(a,1),989(a,1,2,1))]. 992 L(((1 / x) \ (x \ 1)) \ y,a(1 / x,x,x \ 1),1 / x) = (1 * (x \ 1)) \ ((1 / x) * y). [para(11(a,1),359(a,1,1,1,2))]. 993 L(K(x \ 1,x) \ y,a(1 / x,x,x \ 1),1 / x) = (1 * (x \ 1)) \ ((1 / x) * y). [para(888(a,1),992(a,1,1,1))]. 994 L(K(x \ 1,x) \ ((y * (x \ 1)) * x),a(1 / x,x,x \ 1),1 / x) = (1 * (x \ 1)) \ R((1 / x) * y,x,x \ 1). [para(446(a,1),993(a,2,2))]. 995 T(((x \ 1) \ 1) * (x \ 1),y) / T((x \ 1) \ 1,y) = L(1 / T((x \ 1) \ 1,y),x,x \ 1). [para(12(a,1),978(a,1,1,1,2))]. 996 T(K((x \ 1) \ 1,x \ 1),y) / T((x \ 1) \ 1,y) = L(1 / T((x \ 1) \ 1,y),x,x \ 1). [para(135(a,2),995(a,1,1,1))]. 997 T(K(x,x \ 1),y) / T((x \ 1) \ 1,y) = L(1 / T((x \ 1) \ 1,y),x,x \ 1). [para(897(a,1),996(a,1,1,1))]. 998 K(x,1 / x) * T(K(x,1 / x) \ (K(x,1 / x) / (1 / x)),y) = x * (T(x,y) / x). [para(590(a,1),411(a,2,2))]. 999 K(x,1 / x) * T(1 / (1 / x),y) = x * (T(x,y) / x). [para(185(a,1),998(a,1,2,1))]. 1001 K(x,x \ 1) * T(1 / (1 / x),y) = x * (T(x,y) / x). [para(928(a,1),999(a,1,1))]. 1002 x \ (K(x,x \ 1) * T(1 / (1 / x),y)) = T(x,y) / x. [hyper(66,a,1001,a(flip))]. 1003 R((x / (y * x)) \ 1,R(1 / y,y,x),y * x) = T((y * x) / x,x / (y * x)). [para(639(a,2),633(a,1))]. 1004 R((x / (y * x)) \ 1,R(1 / y,y,x),y * x) = T(y,x / (y * x)). [para(15(a,1),1003(a,2,1))]. 1005 T(x / (y * x),T(y,x / (y * x))) = ((x / (y * x)) \ 1) \ 1. [para(1004(a,1),867(a,1,2))]. 1006 (x * (y * z)) * T((x * (y * z)) \ (x * y),u) = (x * y) * (L(z,y,x) * T(L(z,y,x) \ 1,u)). [para(76(a,1),410(a,1,2,1,1))]. 1007 (x * y) * (L(z,y,x) * T(L(z,y,x) \ 1,u)) = x * ((y * z) * T((y * z) \ y,u)). [para(1006(a,1),338(a,1))]. 1008 (x * y) * (L(z,y,x) * T(L(z,y,x) \ 1,u)) = x * (y * (z * T(z \ 1,u))). [para(337(a,1),1007(a,2,2))]. 1009 L(x,y,z) * T(L(x,y,z) \ 1,u) = L(x * T(x \ 1,u),y,z). [hyper(192,a,1008,a),flip(a)]. 1010 L(x * T(x \ 1,L(x,y,z)),y,z) = (L(x,y,z) \ 1) * L(x,y,z). [para(1009(a,1),85(a,1))]. 1011 L(x * T(x \ 1,x),y,z) * (L(x,y,z) \ x) = (L(x,y,z) \ 1) * x. [para(1009(a,1),655(a,1,1))]. 1012 L(x * T(x \ 1,L(x,y,z)),y,z) = K(L(x,y,z) \ 1,L(x,y,z)). [para(1010(a,2),135(a,2)),flip(a)]. 1013 L((x \ 1) * x,y,z) * (L(x,y,z) \ x) = (L(x,y,z) \ 1) * x. [para(85(a,1),1011(a,1,1,1))]. 1014 L(K(x \ 1,x),y,z) * (L(x,y,z) \ x) = (L(x,y,z) \ 1) * x. [para(135(a,2),1013(a,1,1,1))]. 1016 (x * (y \ z)) * ((z \ L(T(y,y \ z),y \ z,x)) * z) = (x * ((y \ z) * T((y \ z) \ 1,z))) * z. [para(337(a,1),728(a,1,1)),flip(a)]. 1017 (x * (y \ z)) * ((z \ L(T(y,y \ z),y \ z,x)) * z) = (x * (y \ ((z \ y) * z))) * z. [para(414(a,1),1016(a,2,1,2))]. 1018 (x * (y \ z)) * ((z \ L(T(y,y \ z),y \ z,x)) * z) = (x * K(z \ y,z)) * z. [para(73(a,1),1017(a,2,1,2))]. 1019 x * T(R(K(y,z) * (u / (K(y,z) * x)),w,v5),K(y,z) * x) = (K(y,z) * x) * R((K(y,z) * x) \ u,w,v5). [para(458(a,2),642(a,1,2,1))]. 1020 x * (T(T(y,x),z) * R(T(T(y,x),z) \ (x \ u),w,v5)) = (T(y,z) * x) * R((T(y,z) * x) \ u,w,v5). [para(114(a,1),679(a,2,2,1,1))]. 1021 x * (T(T(y,x),z) * R(T(T(y,x),z) \ (x \ u),w,v5)) = T(y,z) * (x * R(x \ (T(y,z) \ u),w,v5)). [para(1020(a,2),662(a,1))]. 1022 T((x * y) / ((z * x) * y),R(z,x,y)) * ((z * x) * y) = ((R(z,x,y) \ 1) * R(z,x,y)) * (x * y). [para(81(a,1),710(a,1,1,1,2))]. 1023 ((x * y) * z) * T(((x * y) * z) \ (y * z),R(x,y,z)) = ((R(x,y,z) \ 1) * R(x,y,z)) * (y * z). [para(1022(a,1),171(a,1)),flip(a)]. 1024 ((x * y) * z) * T(((x * y) * z) \ (y * z),R(x,y,z)) = K(R(x,y,z) \ 1,R(x,y,z)) * (y * z). [para(135(a,2),1023(a,2,1))]. 1025 K(R(x,y,z) \ 1,R(x,y,z)) * (y * z) = ((x * y) * T((x * y) \ y,R(x,y,z))) * z. [para(1024(a,1),715(a,1))]. 1026 K(R(x,y,z) \ 1,R(x,y,z)) * (y * z) = (x * (y * T(y \ (x \ y),R(x,y,z)))) * z. [para(339(a,1),1025(a,2,1))]. 1027 K(R(x,y,z) \ 1,R(x,y,z)) * (y * z) = ((x * T(x \ 1,R(x,y,z))) * y) * z. [para(717(a,1),1026(a,2,1))]. 1028 K(R(x,y,z) \ 1,R(x,y,z)) * (y * z) = (K(x \ 1,x) * y) * z. [para(903(a,1),1027(a,2,1,1))]. 1029 K(R(x,y,z) \ 1,R(x,y,z)) = K(x \ 1,x). [hyper(18,a,197,a(flip),b,1028,a)]. 1032 x * R(T(K(y,z) * (u / (K(y,z) * x)),K(y,z) * x),w,v5) = (K(y,z) * x) * R((K(y,z) * x) \ u,w,v5). [para(40(a,2),1019(a,1,2))]. 1033 (K(x,y) * z) * R((K(x,y) * z) \ u,w,v5) = z * R((K(x,y) * z) \ (K(x,y) * u),w,v5). [para(284(a,1),1032(a,1,2,1)),flip(a)]. 1034 (K(x,y) * z) * R((K(x,y) * z) \ u,w,v5) = z * R(z \ u,w,v5). [para(206(a,1),1033(a,2,2,1))]. 1036 (x * (y * T(y \ 1,x))) \ (x \ (x * (y * T(y \ 1,x)))) = (L(y \ 1,y,x) \ (L(y \ 1,y,x) * x)) \ 1. [para(785(a,1),786(a,1,2,2))]. 1037 (L(x \ 1,x,y) \ (L(x \ 1,x,y) * y)) \ 1 = (y * (x * T(x \ 1,y))) \ (x * T(x \ 1,y)). [para(13(a,1),1036(a,1,2)),flip(a)]. 1038 (x * (y * T(y \ 1,x))) \ (y * T(y \ 1,x)) = x \ 1. [para(13(a,1),1037(a,1,1)),flip(a)]. 1040 (x * K(y,x)) \ (L(y \ 1,y,x) * T(L(y \ 1,y,x) \ 1,x)) = x \ 1. [para(668(a,2),1038(a,1,1,2))]. 1041 (x * K(y,x)) \ K(y,x) = x \ 1. [para(668(a,2),1040(a,1,2))]. 1042 (x * K(y,x)) * (x \ 1) = K(y,x). [para(1041(a,1),14(a,1,2))]. 1043 x * K(x \ 1,x) = 1 / (1 / x). [hyper(18,a,957,a,b,1042,a)]. 1044 R(K(x,y),z,u) = (y * K(x,y)) * (y \ 1). [para(1042(a,2),272(a,2))]. 1045 L(x,x \ 1,x) = 1 / (1 / x). [para(1043(a,1),254(a,1)),flip(a)]. 1046 T(L(x,T(x,y) \ 1,T(x,y)),y) = 1 / (1 / T(x,y)). [para(1045(a,1),38(a,1)),flip(a)]. 1047 K(x,y) * y = y * K(x,y). [hyper(243,a,1044,a)]. 1048 T(x,K(y,x)) = x. [hyper(109,a,1047,a)]. 1049 (x * K(y,x)) * z = K(y,x) * (x * z). [para(1047(a,1),197(a,1,1))]. 1050 (x \ 1) * K(x,x \ 1) = 1 / x. [para(1047(a,1),450(a,1))]. 1051 (x \ y) * ((y \ T(x,x \ y)) * y) = y * K(y \ x,y). [para(1047(a,1),767(a,2))]. 1052 ((x * K(y,z)) * z) \ ((x * (z * K(y,z))) * z) = L(z,K(y,z),x). [para(1047(a,1),802(a,2,2,1,2)),flip(a)]. 1053 T(x,y) * K(z,x) = K(z,x) * T(x,y). [para(1048(a,1),114(a,1,2,1)),flip(a)]. 1054 T(x,y * T(y \ 1,x)) = x. [para(429(a,1),1048(a,1,2))]. 1055 T(x,x \ ((y * x) / y)) = x. [para(606(a,1),1048(a,1,2))]. 1056 (x * T(x \ 1,y)) * y = y * (x * T(x \ 1,y)). [para(1054(a,1),85(a,1,2))]. 1057 (x * T(x \ 1,y)) * ((T(y,x * T(x \ 1,y)) \ z) \ z) = T(y,y \ z) * (x * T(x \ 1,y)). [para(1054(a,1),175(a,1,1,2,1)),flip(a)]. 1058 T(T(x,y),T(x,y) \ x) = T(x,y). [para(106(a,1),1055(a,1,2,2))]. 1059 (x \ ((y * x) / y)) * x = (y * x) / y. [para(1055(a,1),108(a,1,2))]. 1060 ((x * y) / x) / y = y \ ((x * y) / x). [para(1055(a,1),123(a,1,2))]. 1061 (x \ 1) \ (1 / x) = K(x,x \ 1). [hyper(66,a,1050,a)]. 1062 K(T(x,y),T(x,y) \ x) = 1. [hyper(34,a,1058,a)]. 1063 (T(x,y) \ x) * T(x,y) = x. [para(1058(a,1),108(a,1,2))]. 1064 x / T(x,y) = T(x,y) \ x. [para(1058(a,1),123(a,1,2))]. 1065 x * T(y,z) != y | T(y,z) \ y = x. [para(1063(a,1),20(a,1)),flip(a)]. 1066 (T(x,y) \ x) / x = 1 / T(x,y). [para(1064(a,1),616(a,1,1))]. 1067 T((T(x,y) \ x) * (x \ T(x,y)),y) = K(T(x,y),x / T(x,y)). [para(1064(a,1),830(a,1,1,1))]. 1068 L(K(x,x \ 1),x \ 1,y / (1 / x)) = ((y / (1 / x)) * (x \ 1)) \ y. [para(1061(a,1),202(a,1,1))]. 1069 T(1 / T(x,y),x) = T(x,y) \ 1. [para(1066(a,1),507(a,1,1))]. 1070 (x * y) / x != z * y | y \ ((x * y) / x) = z. [para(1059(a,1),20(a,1))]. 1071 (1 / x) * ((y * x) / y) = x \ ((y * x) / y). [para(1060(a,1),744(a,2))]. 1072 (1 / x) \ (x \ ((y * x) / y)) = (y * x) / y. [hyper(66,a,1071,a)]. 1073 (x \ 1) \ ((y * (x \ 1)) / y) = x * ((y * (x \ 1)) / y). [para(57(a,1),1071(a,1,1)),flip(a)]. 1074 (1 / x) \ (((y * x) / y) * (x \ 1)) = (y * x) / y. [para(568(a,2),1072(a,1,2))]. 1075 (1 / x) \ (x \ ((L(y \ 1,y,x) * x) / L(y \ 1,y,x))) = x * (y * T(y \ 1,x)). [para(1072(a,2),785(a,1))]. 1076 (x * T(x \ 1,y)) * z != y * (x * T(x \ 1,y)) | z = y. [para(1056(a,1),19(a,2))]. 1077 T((T(x,y) \ x) * (x \ T(x,y)),y) = K(T(x,y),T(x,y) \ x). [para(1064(a,1),1067(a,2,2))]. 1078 T((T(x,y) \ x) * (x \ T(x,y)),y) = 1. [para(1077(a,2),1062(a,1))]. 1080 ((x * ((y * ((1 / (1 / z)) * (z \ 1))) \ y)) * u) / (L(L(K(z,z \ 1),z \ 1,1 / (1 / z)),(1 / (1 / z)) * (z \ 1),y) * u) = R(x,(y * ((1 / (1 / z)) * (z \ 1))) \ y,u). [para(1068(a,2),474(a,1,2,1,1))]. 1081 (1 / x) \ (x \ (x * (y * T(y \ 1,x)))) = x * (y * T(y \ 1,x)). [para(785(a,1),1075(a,1,2,2))]. 1082 (1 / x) \ (y * T(y \ 1,x)) = x * (y * T(y \ 1,x)). [para(13(a,1),1081(a,1,2))]. 1084 T(x,x \ y) * (z * T(z \ 1,x)) = (z * T(z \ 1,x)) * ((x \ y) \ y). [para(1054(a,1),1057(a,1,2,1,1)),flip(a)]. 1085 T(T(x,L(x \ 1,y,z)) / x,L(x \ 1,y,z) * x) = K(L(x \ 1,y,z) \ ((1 / x) \ L(x \ 1,y,z)),L(x \ 1,y,z)). [para(590(a,1),905(a,1,1))]. 1086 T((K(K(x,y),y * x) * x) * R((K(K(x,y),y * x) * x) \ 1,z,u),y) = (y \ (K(x,y) * (y * x))) * R((y \ (K(x,y) * (y * x))) \ 1,z,u). [para(841(a,1),842(a,2,2,1,1))]. 1087 (x \ (K(y,x) * (x * y))) * R((x \ (K(y,x) * (x * y))) \ 1,z,u) = T(y * R(y \ 1,z,u),x). [para(1034(a,1),1086(a,1,1)),flip(a)]. 1089 T(x \ L(x * ((((x \ 1) \ 1) * y) / ((x \ 1) \ 1)),z,u),(x \ 1) \ 1) = (x \ 1) * (K(x \ 1,x) * L(T(x \ 1,(x \ 1) \ 1) \ y,z,u)). [para(929(a,1),972(a,1,2,1)),flip(a)]. 1090 T(x \ L(x * ((((x \ 1) \ 1) * y) / ((x \ 1) \ 1)),z,u),(x \ 1) \ 1) = (x \ 1) * (K(x \ 1,x) * L((((x \ 1) \ 1) \ 1) \ y,z,u)). [para(86(a,1),1089(a,2,2,2,1,1))]. 1091 T(T((K(x,y) * ((y * x) / y)) * R(((K(x,y) * (y * x)) / y) \ 1,z,u),w),y) = T(T(K(K(x,y),y * x) * x,y) * R((y \ (K(x,y) * (y * x))) \ 1,z,u),w). [para(281(a,1),843(a,1,1,1,1))]. 1092 T(T((K(x,y) * ((y * x) / y)) * R(((K(x,y) * (y * x)) / y) \ 1,z,u),w),y) = T((y \ (K(x,y) * (y * x))) * R(T(K(K(x,y),y * x) * x,y) \ 1,z,u),w). [para(281(a,1),844(a,1,1,1,1))]. 1093 T(T((K(x,y) * ((y * x) / y)) * R((K(x,y) * ((y * x) / y)) \ 1,z,u),w),y) = T(T(K(K(x,y),y * x) * x,y) * R((y \ (K(x,y) * (y * x))) \ 1,z,u),w). [para(281(a,1),1091(a,1,1,1,2,1,1))]. 1094 T(T((K(x,y) * ((y * x) / y)) * R((K(x,y) * ((y * x) / y)) \ 1,z,u),w),y) = T((y \ (K(x,y) * (y * x))) * R(T(K(K(x,y),y * x) * x,y) \ 1,z,u),w). [para(281(a,1),1092(a,1,1,1,2,1,1))]. 1095 T(T(K(K(x,y),y * x) * x,y) * R((y \ (K(x,y) * (y * x))) \ 1,z,u),w) = T(T(((y * x) / y) * R(((y * x) / y) \ 1,z,u),w),y). [para(1034(a,1),1093(a,1,1,1)),flip(a)]. 1096 T(T(K(K(x,y),y * x) * x,y) * R((y \ (K(x,y) * (y * x))) \ 1,z,u),w) = T((y \ (y * x)) * R((y \ (y * x)) \ 1,z,u),w). [para(1095(a,2),815(a,1))]. 1098 T(T(K(K(x,y),y * x) * x,y) * R((y \ (K(x,y) * (y * x))) \ 1,z,u),w) = T(x * R((y \ (y * x)) \ 1,z,u),w). [para(13(a,1),1096(a,2,1,1))]. 1099 T(T(K(K(x,y),y * x) * x,y) * R((y \ (K(x,y) * (y * x))) \ 1,z,u),w) = T(x * R(x \ 1,z,u),w). [para(13(a,1),1098(a,2,1,2,1,1))]. 1100 T((x \ (K(y,x) * (x * y))) * R((x \ (K(y,x) * (x * y))) \ 1,z,u),w) = T(y * R(y \ 1,z,u),w). [para(841(a,1),1099(a,1,1,1))]. 1101 T(T(x * R(x \ 1,y,z),u),w) = T(x * R(x \ 1,y,z),w). [para(1087(a,1),1100(a,1,1))]. 1102 T((x \ (K(y,x) * (x * y))) * R(T(K(K(y,x),x * y) * y,x) \ 1,z,u),w) = T(T(((x * y) / x) * R(((x * y) / x) \ 1,z,u),w),x). [para(1034(a,1),1094(a,1,1,1)),flip(a)]. 1104 T((x \ (K(y,x) * (x * y))) * R(T(K(K(y,x),x * y) * y,x) \ 1,z,u),w) = T(((x * y) / x) * R(((x * y) / x) \ 1,z,u),x). [para(1102(a,2),1101(a,1))]. 1105 T((x \ (K(y,x) * (x * y))) * R(T(K(K(y,x),x * y) * y,x) \ 1,z,u),w) = (x \ (x * y)) * R((x \ (x * y)) \ 1,z,u). [para(1104(a,2),814(a,1))]. 1107 T((x \ (K(y,x) * (x * y))) * R(T(K(K(y,x),x * y) * y,x) \ 1,z,u),w) = y * R((x \ (x * y)) \ 1,z,u). [para(13(a,1),1105(a,2,1))]. 1108 T((x \ (K(y,x) * (x * y))) * R(T(K(K(y,x),x * y) * y,x) \ 1,z,u),w) = y * R(y \ 1,z,u). [para(13(a,1),1107(a,2,2,1,1))]. 1109 T((x \ (K(y,x) * (x * y))) * R((x \ (K(y,x) * (x * y))) \ 1,z,u),w) = y * R(y \ 1,z,u). [para(841(a,1),1108(a,1,1,2,1,1))]. 1110 T(x * R(x \ 1,y,z),u) = x * R(x \ 1,y,z). [para(1109(a,1),1100(a,1)),flip(a)]. 1111 T(x,y * R(y \ 1,z,u)) = x. [hyper(33,a,1110,a)]. 1114 T(x,(y / (z * y)) * z) = x. [para(302(a,2),1111(a,1,2))]. 1115 T(x,y \ R(y,z,u)) = x. [para(481(a,1),1111(a,1,2))]. 1116 K(x,y \ R(y,z,u)) = 1. [hyper(34,a,1115,a)]. 1117 T(x \ R(x,y,z),u) = x \ R(x,y,z). [hyper(33,a,1115,a)]. 1118 T(x,(y / z) \ (y * (z \ 1))) = x. [para(224(a,1),1115(a,1,2,2))]. 1119 T(x,(y / z) * (z / y)) = x. [para(16(a,1),1114(a,1,2,1,2))]. 1120 T(x,(y \ 1) * y) = x. [para(91(a,1),1114(a,1,2,1))]. 1121 T(x,y * (1 / y)) = x. [para(92(a,1),1114(a,1,2,1))]. 1122 T(x,K(y \ 1,y)) = x. [para(135(a,2),1120(a,1,2))]. 1123 R(x,x \ 1,x) = T(x,x \ 1). [para(1120(a,1),406(a,1,1))]. 1124 T(x,1) = x. [para(1063(a,1),1120(a,1,2))]. 1126 T(1,x) = 1. [hyper(33,a,1124,a)]. 1128 T(x * L(x \ 1,y,z),x) = x * L(x \ 1,y,z). [para(1126(a,1),700(a,2,2,1,2))]. 1129 T(x,K(y,1 / y)) = x. [para(118(a,2),1121(a,1,2))]. 1130 R(1 / x,x,1 / x) = T(1 / x,x). [para(1121(a,1),406(a,1,1))]. 1131 T(x,K(y,y \ 1)) = x. [para(930(a,2),1121(a,1,2))]. 1132 T(K(x \ 1,x),y) = K(x \ 1,x). [hyper(33,a,1122,a)]. 1133 K(x \ 1,x) * y = y * K(x \ 1,x). [para(1122(a,1),85(a,1,2))]. 1134 x / K(y \ 1,y) = K(y \ 1,y) \ x. [para(1122(a,1),87(a,1))]. 1135 (x * K(y \ 1,y)) / x = K(y \ 1,y). [para(1122(a,1),96(a,1,2))]. 1136 T(x,K(y / z,z / y)) = x. [para(895(a,1),1122(a,1,2))]. 1137 T(x,K(y \ 1,R(y,z,u))) = x. [para(915(a,2),1122(a,1,2))]. 1138 K(x,1 / x) * y = y * K(x,1 / x). [para(1129(a,1),85(a,1,2))]. 1139 x / K(y,1 / y) = K(y,1 / y) \ x. [para(1129(a,1),87(a,1))]. 1140 T(K(x,x \ 1),y) = K(x,x \ 1). [hyper(33,a,1131,a)]. 1141 K(x,x \ 1) * y = y * K(x,x \ 1). [para(1131(a,1),85(a,1,2))]. 1142 x \ (K(y,y \ 1) * x) = K(y,y \ 1). [para(1131(a,1),107(a,1,2,2))]. 1143 K(x,x \ 1) * y != z * K(x,x \ 1) | z = y. [para(1131(a,1),110(a,1,2))]. 1144 T(x,y * (z / (y * z))) = x. [para(15(a,1),1119(a,1,2,1))]. 1145 ((x / y) * (y / x)) / (x / y) = L(y / x,x / y,y / x). [para(1119(a,1),297(a,1))]. 1146 L(R(x / y,y / x,(y / x) \ 1),y / x,((y / x) * (x / y)) / (y / x)) = ((y / x) * (x / y)) * ((y / x) \ 1). [para(1119(a,1),673(a,2))]. 1147 K(x / y,y / x) * z = z * K(x / y,y / x). [para(1136(a,1),85(a,1,2))]. 1148 T(x * (y / (x * y)),z) = x * (y / (x * y)). [hyper(33,a,1144,a)]. 1149 T(L(x,y / (x * y),x),y / (x * y)) = x. [para(1144(a,1),294(a,2))]. 1150 L(x,y / (x * y),x) * (y / (x * y)) = (y / (x * y)) * x. [para(1144(a,1),296(a,1,2)),flip(a)]. 1151 R(x,x \ 1,x) = (x \ 1) \ 1. [para(1123(a,2),86(a,1))]. 1152 R(T(x,x \ 1),y,z) * K(x \ 1,x) = (R(x,y,z) * (x \ 1)) * x. [para(1123(a,1),389(a,1,1,1))]. 1153 T(1 / x,T(x,x \ 1)) = x \ 1. [para(1123(a,1),866(a,1,2))]. 1154 T(K(x \ 1,R(x,y,z)),u) = K(x \ 1,R(x,y,z)). [hyper(33,a,1137,a)]. 1155 x / K(x \ 1,x) = (x \ 1) \ 1. [para(1151(a,1),238(a,2))]. 1156 ((x / y) \ (x * (y \ 1))) * (x / y) = x * (y \ 1). [para(1118(a,1),108(a,1,2))]. 1157 L(K(x \ 1,x),y,z) * (z * y) = z * (y * K(x \ 1,x)). [para(1132(a,1),261(a,1,2,2)),flip(a)]. 1158 K(x \ (x / T(x,y)),x) = K(x \ 1,x). [para(1132(a,1),753(a,2))]. 1159 K(x \ 1,x) * (T(x,y) \ x) = (T(x,y) \ 1) * x. [para(1132(a,1),756(a,1,1))]. 1160 L(K(x,x \ 1),y,z) * (z * y) = z * (y * K(x,x \ 1)). [para(1140(a,1),261(a,1,2,2)),flip(a)]. 1161 L(1 / T((x \ 1) \ 1,y),x,x \ 1) = K(x,x \ 1) / T((x \ 1) \ 1,y). [para(1140(a,1),997(a,1,1)),flip(a)]. 1162 T(x / (y * x),T(y,y \ 1)) = R(y \ 1,y,x). [para(1153(a,1),162(a,2,1))]. 1163 ((x \ 1) \ 1) \ x = K(x \ 1,x). [para(1155(a,1),59(a,1,1))]. 1164 R(1 / x,x,1 / x) = x \ 1. [para(1130(a,2),87(a,1))]. 1165 K(x,L(1 / y,z,u)) = K(x,L(y \ 1,z,u)). [para(1164(a,1),916(a,1,2,1)),flip(a)]. 1166 K(x,a(R(y,z,u),z,u)) = K(x,y \ R(y,z,u)). [para(1117(a,1),990(a,1,2)),flip(a)]. 1167 K(x,x \ 1) * (y * K(x \ 1,x)) = y. [hyper(456,a,1133,a)]. 1168 R(x / y,y,K(z \ 1,z)) = (x * K(z \ 1,z)) / (K(z \ 1,z) * y). [para(1133(a,2),82(a,2,2))]. 1169 (x * K(y \ 1,y)) * z = K(y \ 1,y) * (x * z). [para(1133(a,1),197(a,1,1))]. 1170 (x * K(y \ 1,y)) / z = K(y \ 1,y) * (x / z). [para(1133(a,1),281(a,1,1))]. 1171 (K(x \ 1,x) * y) / z = (y / z) * K(x \ 1,x). [para(1133(a,1),281(a,2))]. 1172 (x \ 1) * K(x \ 1,x) = R(x \ 1,x,x \ 1). [para(1133(a,1),245(a,1))]. 1173 (x * (y \ 1)) \ (K(y \ 1,y) * x) = L(y,y \ 1,x). [para(1133(a,2),150(a,1,2))]. 1174 K(x \ 1,x) * R(y,x \ 1,x) = (y * (x \ 1)) * x. [para(1133(a,2),217(a,1))]. 1175 R(1 / x,y,z) * K(x \ 1,x) = R(x \ 1,y,z). [para(1133(a,1),462(a,1))]. 1176 x \ (K((y \ x) \ 1,y \ x) * y) = T(x \ y,y \ x). [para(1133(a,2),523(a,1,2))]. 1177 x / K(y \ 1,y) = K(y,y \ 1) * x. [para(1134(a,2),447(a,1))]. 1178 L(x,x \ 1,x) / x = K(x \ 1,x). [para(254(a,1),1135(a,1,1))]. 1179 (R(x,K(y \ 1,y),y) / y) * L(y,y \ 1,y) = x * (L(y,y \ 1,y) / y). [para(1178(a,1),794(a,1,1,1,2))]. 1180 x * K(x,1 / x) = R(x,1 / x,x). [para(1138(a,1),247(a,1))]. 1181 x \ (K(y \ x,1 / (y \ x)) * y) = L(1 / (y \ x),y \ x,y). [para(1138(a,2),287(a,1,2))]. 1182 x * K(x,1 / x) = T(x,x \ 1). [para(1138(a,1),945(a,1))]. 1183 x * K(x,x \ 1) = T(x,x \ 1). [para(928(a,1),1182(a,1,2))]. 1184 (T(x,x \ 1) * y) / (K(x,x \ 1) * y) = R(x,K(x,x \ 1),y). [para(1183(a,1),28(a,2,1,1)),flip(a)]. 1185 x * K(x,x \ 1) = (x \ 1) \ 1. [para(1183(a,2),86(a,1))]. 1186 (x * K(y,y \ 1)) / T(y,y \ 1) = R(x / y,y,K(y,y \ 1)). [para(1183(a,1),82(a,2,2)),flip(a)]. 1188 ((x \ 1) \ 1) \ (x * (K(x,x \ 1) * y)) = L(y,K(x,x \ 1),x). [para(1185(a,1),26(a,2,1)),flip(a)]. 1189 (x * y) * K(y,y \ 1) != z * ((y \ 1) \ 1) | R(x,y,K(y,y \ 1)) = z. [para(1185(a,1),211(a,2,2))]. 1190 x * K(x,1 / x) = T(x,1 / x). [para(1180(a,2),370(a,1))]. 1191 T(x,1 / x) = T(x,x \ 1). [para(1190(a,1),1182(a,1))]. 1192 T(x,1 / x) = (x \ 1) \ 1. [para(1191(a,2),86(a,1))]. 1193 T(x \ 1,x) = ((x \ 1) \ 1) \ 1. [para(57(a,1),1192(a,1,2))]. 1194 1 / T(x \ 1,x) = (x \ 1) \ 1. [para(1193(a,2),57(a,1,2))]. 1195 K(x,1 / x) \ (y * (1 / x)) = R(y / x,x,1 / x). [para(1139(a,1),226(a,1))]. 1196 R(x \ 1,y,z) * K(x,x \ 1) = R(1 / x,y,z). [hyper(17,a,460,a,b,1141,a),flip(a)]. 1197 (x * K(y,y \ 1)) \ (K(y,y \ 1) * (x * z)) = L(z,x,K(y,y \ 1)). [para(1141(a,1),26(a,2,1)),flip(a)]. 1198 (1 / x) * K(y,y \ 1) = K(y,y \ 1) / x. [para(1141(a,1),182(a,1))]. 1199 (x * K(y,y \ 1)) * z = K(y,y \ 1) * (x * z). [para(1141(a,1),197(a,1,1))]. 1200 R(x,x \ y,K(z,z \ 1)) \ (K(z,z \ 1) * y) = (x \ y) * K(z,z \ 1). [para(1141(a,2),233(a,1,2))]. 1201 (x * y) * K(z,z \ 1) != u * (K(z,z \ 1) * y) | R(x,y,K(z,z \ 1)) = u. [para(1141(a,2),211(a,2,2))]. 1202 K(x \ 1,x) * (y * K(x,x \ 1)) = y. [para(1141(a,1),448(a,1,2))]. 1203 ((1 / x) \ y) * K(x,x \ 1) = (x \ 1) \ y. [para(1141(a,1),533(a,1))]. 1204 (x * y) * K(x,x \ 1) = T(x,x \ 1) * y. [para(1141(a,1),947(a,1))]. 1205 (x * y) * K(x,x \ 1) = ((x \ 1) \ 1) * y. [para(1141(a,1),955(a,1))]. 1206 ((1 / (1 / x)) * y) \ (x * y) = K(x,x \ 1). [para(942(a,1),1142(a,1,2))]. 1207 x * K(x \ (x / T(x,y)),x) = 1 / (1 / x). [para(1158(a,2),1043(a,1,2))]. 1209 (x * K(y \ 1,y)) \ z = x \ (K(y,y \ 1) * z). [para(1167(a,1),206(a,1,1)),flip(a)]. 1210 (x * K(y \ 1,y)) * K(y,y \ 1) = x. [para(1167(a,1),1141(a,1)),flip(a)]. 1211 (x * K(y \ 1,y)) \ x = K(y,y \ 1). [para(1167(a,1),1142(a,1,2))]. 1212 (K(x,x \ 1) * y) \ y = K(x \ 1,x). [para(1177(a,1),59(a,1,1))]. 1213 (K(x \ 1,x) * y) * K(x,x \ 1) = y. [hyper(154,a,1202,a),flip(a)]. 1214 (x * K(y,y \ 1)) \ z = x \ (K(y \ 1,y) * z). [para(1202(a,1),206(a,1,1)),flip(a)]. 1215 R(R(x,y,K(z \ 1,z)),y * K(z \ 1,z),K(z,z \ 1)) = (x * y) / ((y * K(z \ 1,z)) * K(z,z \ 1)). [para(1210(a,1),213(a,1,1)),flip(a)]. 1216 L(K(x,x \ 1),K(x \ 1,x),y) = K(x,x \ 1). [para(1211(a,1),184(a,2))]. 1217 (x * y) \ ((1 / (1 / x)) * y) = K(x \ 1,x). [para(942(a,1),1212(a,1,1))]. 1218 T((T(x,y) \ x) * (T(x,y) / x),z) = (T(x,y) \ x) * (T(x,y) / ((T(x,y) \ x) * T(x,y))). [para(1063(a,1),1148(a,1,1,2,2))]. 1219 ((1 / x) \ (y * T(y \ 1,x))) * K(x,x \ 1) = T(x,x \ 1) * (y * T(y \ 1,x)). [para(1082(a,2),1204(a,1,1))]. 1220 L(T(K(x,x \ 1),y),y,1 / (1 / x)) = K(x,x \ 1). [para(1206(a,1),969(a,2))]. 1221 L(x,T(x,y) \ 1,T(x,y)) = 1 / (1 / x). [para(1207(a,1),565(a,2))]. 1222 1 / (1 / T(x,y)) = T(1 / (1 / x),y). [para(1221(a,1),1046(a,1,1)),flip(a)]. 1224 T(1 / (1 / x),y) \ 1 = 1 / T(x,y). [para(1222(a,1),59(a,1,1))]. 1225 x * (1 / (1 / T(y,x))) = (1 / (1 / y)) * x. [para(1222(a,2),85(a,1,2))]. 1226 K(T(x,y),T(x,y) \ 1) * T(1 / (1 / x),y) = T(x,y). [para(1222(a,1),938(a,1,2))]. 1228 1 / T(x \ 1,y) = T(1 / x,y) \ 1. [para(57(a,1),1224(a,1,1,1,2)),flip(a)]. 1229 1 / T((x \ 1) \ 1,y) = T(x,y) \ 1. [para(57(a,1),1228(a,2,1,1))]. 1230 (T(x,y) \ 1) \ 1 = T((x \ 1) \ 1,y). [para(1229(a,1),59(a,1,1))]. 1231 K(x,y) / T((z \ 1) \ 1,u) = K(x,y) * (T(z,u) \ 1). [para(1229(a,1),182(a,1,2)),flip(a)]. 1232 T(((x / y) \ 1) \ 1,y) = ((y \ x) \ 1) \ 1. [para(87(a,1),1230(a,1,1,1)),flip(a)]. 1233 (1 / (1 / (x / y))) * y = y * (1 / (1 / (y \ x))). [para(87(a,1),1225(a,1,2,2,2)),flip(a)]. 1234 T(x,((y * x) / y) \ 1) = ((y \ (y * x)) \ 1) \ 1. [para(1232(a,1),179(a,1)),flip(a)]. 1235 K(x,x \ 1) * y != z | K(x \ 1,x) * z = y. [para(1213(a,1),1143(a,2))]. 1236 K(x,a(R(y,z,u),z,u)) = 1. [para(1166(a,2),1116(a,1))]. 1238 K(x,a(y / (z * u),z,u)) = 1. [para(133(a,1),1236(a,1,2,1))]. 1240 K(x,a(y,z,u)) = 1. [para(15(a,1),1238(a,1,2,1))]. 1241 T(x,a(y,z,u)) = x. [hyper(35,a,1240,a)]. 1243 T(a(x,y,z),u) = a(x,y,z). [hyper(33,a,1241,a)]. 1244 (x * a(y,z,u)) / x = a(y,z,u). [para(1241(a,1),96(a,1,2))]. 1245 ((L(x,y,z) * (z * y)) / (z * y)) * T(((L(x,y,z) * (z * y)) / (z * y)) \ x,u) = ((L(x,y,z) * (z * y)) * a(z,y,T(x,z * y))) / (z * y). [para(1243(a,1),637(a,2,1,2))]. 1246 a(x,y,z) = ((x * y) * z) / (x * (y * z)). [para(71(a,1),1244(a,1,1)),flip(a)]. 1247 (x \ 1) * K(x \ 1,x) = T(x \ 1,x). [para(1172(a,2),303(a,1))]. 1248 1 / ((x \ 1) * K(x \ 1,x)) = (x \ 1) \ 1. [para(1247(a,2),1194(a,1,2))]. 1249 1 / ((R(x,y,z) \ 1) * K(x \ 1,x)) = (R(x,y,z) \ 1) \ 1. [para(1029(a,1),1248(a,1,2,2))]. 1251 T(x,x * L(x \ 1,y,z)) = x. [hyper(33,a,1128,a)]. 1252 R(x,L(x \ 1,y,z),T(x,L(x \ 1,y,z))) = T(x,L(x \ 1,y,z)). [para(1251(a,1),341(a,1,1))]. 1253 (x * (y \ 1)) \ (((x / y) \ (x * (y \ 1))) * (z * (x / y))) = L(T(z,x / y),x / y,(x / y) \ (x * (y \ 1))). [para(1156(a,1),112(a,1,1))]. 1254 (1 / x) * ((T(x,y) \ 1) * x) = (x \ 1) * (T(x,y) \ x). [para(1159(a,1),539(a,1,2))]. 1257 K(x \ 1,R(x,y,z)) * (u * w) = (u * K(x \ 1,x)) * w. [para(915(a,2),1169(a,2,1)),flip(a)]. 1258 R(x / (1 / y),1 / y,K(y \ 1,y)) = K(y \ 1,y) * (x / (y \ 1)). [para(1170(a,1),891(a,2))]. 1259 ((x * y) / z) * K(x \ 1,x) = ((1 / (1 / x)) * y) / z. [para(951(a,1),1171(a,1,1)),flip(a)]. 1260 (R(x \ 1,y,z) * (K(x,x \ 1) * u)) \ (R(1 / x,y,z) * u) = a(R(x \ 1,y,z),K(x,x \ 1),u). [para(1196(a,1),22(a,2,2,1)),flip(a)]. 1261 (K(x,x \ 1) * ((y * z) * u)) / ((z * K(x,x \ 1)) * u) = R(R(y,z,K(x,x \ 1)),z * K(x,x \ 1),u). [para(1199(a,1),213(a,1,1))]. 1262 (x * K(y,y \ 1)) * z = (x * z) * K(y,y \ 1). [para(1199(a,2),1141(a,1))]. 1263 (x * K(y \ 1,y)) \ K(y \ 1,y) = x \ 1. [para(449(a,1),1209(a,2,2))]. 1264 K(x / y,y / x) * y = x * (1 / (1 / (x \ y))). [para(1233(a,1),973(a,2))]. 1265 T(x,((y * x) / y) \ 1) = (x \ 1) \ 1. [para(13(a,1),1234(a,2,1,1))]. 1266 T((x * y) / x,((z * y) / z) \ 1) = (x * ((y \ 1) \ 1)) / x. [para(1265(a,1),178(a,1,1,2)),flip(a)]. 1267 (((x * y) / x) \ 1) * ((y \ 1) \ 1) = ((x * y) / x) \ y. [para(1265(a,1),586(a,1,2))]. 1268 (x * K(y,y \ 1)) \ ((x * z) * K(y,y \ 1)) = z. [hyper(66,a,1262,a)]. 1269 x \ (K(x / y,y / x) * y) = 1 / (1 / (x \ y)). [hyper(66,a,1264,a(flip))]. 1270 K((x / y) / x,x / (x / y)) * x = (x / y) * (1 / (1 / y)). [para(59(a,1),1264(a,2,2,2,2))]. 1271 R(T(x,y * K(z,z \ 1)),y,K(z,z \ 1)) = T(x,y). [para(1268(a,1),404(a,1,1)),flip(a)]. 1272 K(x \ 1,x) \ ((y * (x \ 1)) * x) = R(y,x \ 1,x). [hyper(66,a,1174,a)]. 1273 K(x,x \ 1) \ (y * (1 / x)) = R(y / x,x,1 / x). [para(928(a,1),1195(a,1,1))]. 1274 L(K(x,x \ 1),y,1 / (1 / x)) = K(x,x \ 1). [para(1140(a,1),1220(a,1,1))]. 1277 L(R(x,y \ 1,y),a(1 / y,y,y \ 1),1 / y) = (1 * (y \ 1)) \ R((1 / y) * x,y,y \ 1). [para(1272(a,1),994(a,1,1))]. 1278 K(x \ 1,x) * (y * (1 / x)) = R(y / x,x,1 / x). [para(1273(a,1),455(a,1)),flip(a)]. 1279 L(L((1 / x) \ 1,y * (1 / x),K(x \ 1,x)),1 / x,y) = R(y / x,x,1 / x) \ (K(x \ 1,x) * y). [para(1278(a,1),335(a,2,1))]. 1280 K((x \ y) \ 1,x \ y) * x = y * T(y \ x,x \ y). [para(1176(a,1),14(a,1,2)),flip(a)]. 1281 T((1 / x) * (T(x,y) \ x),x) = (x \ 1) * (T(x,y) \ x). [para(1254(a,1),508(a,2))]. 1284 K(((x * y) \ x) \ 1,L(y \ 1,y,x)) * (x * y) = x * T(x \ (x * y),(x * y) \ x). [para(103(a,2),1280(a,1,1,2))]. 1285 T(L(x / y,y / x,x / y),y) = ((y / x) * (y \ x)) / (y / x). [para(1145(a,1),270(a,1,1))]. 1286 ((x / (y * x)) * y) / R(1 / y,y,x) = L(y,x / (y * x),y). [para(1150(a,1),470(a,1,1))]. 1287 L(K(x \ 1,x),y,z) * (z * y) = z * (K(x \ 1,x) * y). [para(1133(a,2),1157(a,2,2))]. 1288 R(x,T(y,x),T(K(z \ 1,R(z,u,w)),y * x)) \ ((y * K(z \ 1,z)) * x) = T(y,x) * T(K(z \ 1,R(z,u,w)),y * x). [para(1257(a,1),353(a,1,2))]. 1289 (x * ((y \ 1) \ 1)) / x = (((x * y) / x) \ 1) \ 1. [para(1266(a,1),86(a,1))]. 1290 (x \ 1) * ((((y * x) / y) \ 1) \ 1) = ((y * x) / y) * (x \ 1). [para(1289(a,1),374(a,1,2))]. 1291 L(x,y / (x * y),x) = 1 / (1 / x). [para(1286(a,1),870(a,1))]. 1293 T(1 / (1 / x),y / (x * y)) = x. [para(1291(a,1),1149(a,1,1))]. 1294 T(1 / (1 / x),x \ 1) = x. [para(91(a,1),1293(a,1,2))]. 1296 T(T(1 / (1 / x),y),x \ 1) = T(x,y). [para(1294(a,1),36(a,1,1)),flip(a)]. 1297 T(x,y / (x * y)) = T(x,x \ 1). [para(1293(a,1),1296(a,1,1)),flip(a)]. 1298 K((x / (y * x)) \ 1,x / (y * x)) * (y * x) = T(y,y \ 1) * x. [para(1297(a,1),632(a,2,1))]. 1299 T(x / (y * x),T(y,y \ 1)) = ((x / (y * x)) \ 1) \ 1. [para(1297(a,1),1005(a,1,2))]. 1300 R(x \ 1,x,y) = ((y / (x * y)) \ 1) \ 1. [para(1299(a,1),1162(a,1)),flip(a)]. 1302 R((x / y) \ 1,x / y,y) = ((y / x) \ 1) \ 1. [para(16(a,1),1300(a,2,1,1,2))]. 1303 T((1 * x) / y,y / x) = ((x / y) \ 1) \ 1. [para(1302(a,1),349(a,1)),flip(a)]. 1304 R((x / y) \ 1,x / y,y) \ 1 = T((y / x) \ 1,y / x). [para(1302(a,2),1193(a,2,1)),flip(a)]. 1305 T(x / y,y / x) = ((x / y) \ 1) \ 1. [para(11(a,1),1303(a,1,1,1))]. 1306 T(((x / y) \ 1) \ 1,y) = T(y \ x,y / x). [para(1305(a,1),117(a,1,1))]. 1307 T(x \ y,x / y) = ((x \ y) \ 1) \ 1. [para(1306(a,1),1232(a,1))]. 1308 K(x / y,y / x) * x = y * (((y \ x) \ 1) \ 1). [para(1307(a,1),899(a,2,2))]. 1309 K(x \ 1,x) * ((((y * x) / y) \ 1) \ 1) = (1 / x) \ (((y * x) / y) * (x \ 1)). [para(1290(a,1),535(a,1,2)),flip(a)]. 1310 x \ (K(y \ x,(y \ x) \ 1) * y) = L(1 / (y \ x),y \ x,y). [para(928(a,1),1181(a,1,2,1))]. 1311 R(x,K(x,x \ 1),y) = x. [para(1184(a,1),970(a,1))]. 1312 R(1 / x,K(1 / x,x),y) = 1 / x. [para(59(a,1),1311(a,1,2,2))]. 1313 R(1 / x,K(x \ 1,x),y) = 1 / x. [para(894(a,1),1312(a,1,2))]. 1314 (R(1 / x,y,z) * K(x \ 1,x)) * (K(x \ 1,x) \ u) = R(1 / x,y,z) * u. [para(1313(a,1),299(a,1,1,1)),flip(a)]. 1315 R((K(x \ 1,x) * y) / x,x,K(x,x \ 1)) = y / T(x,x \ 1). [para(1213(a,1),1186(a,1,1)),flip(a)]. 1316 L(T(x / y,y),y / x,x / y) = ((y / x) * (y \ x)) / (y / x). [para(1285(a,1),38(a,2))]. 1317 R((x / y) * K(y \ 1,y),y,K(y,y \ 1)) = x / T(y,y \ 1). [para(1171(a,1),1315(a,1,1))]. 1318 ((x / y) * (x \ y)) / (x / y) = L(x \ y,x / y,y / x). [para(87(a,1),1316(a,1,1)),flip(a)]. 1319 (x \ y) * (((x \ y) \ (y / x)) / (y / x)) = x \ (y * L(y \ x,y / x,x / y)). [para(1318(a,1),779(a,1,2,2)),flip(a)]. 1320 R(T(x,x \ 1),y,z) * K(x \ 1,x) = R(x,y,z). [para(1152(a,2),855(a,1))]. 1321 R((x \ 1) \ 1,y,z) * K(x \ 1,x) = R(x,y,z). [para(86(a,1),1320(a,1,1,1))]. 1322 R(R((x \ 1) \ 1,y,z),K(x \ 1,x) * (R(x,y,z) \ u),a(R((x \ 1) \ 1,y,z),K(x \ 1,x),(R((x \ 1) \ 1,y,z) * K(x \ 1,x)) \ u)) \ u = (K(x \ 1,x) * ((R((x \ 1) \ 1,y,z) * K(x \ 1,x)) \ u)) * a(R((x \ 1) \ 1,y,z),K(x \ 1,x),(R((x \ 1) \ 1,y,z) * K(x \ 1,x)) \ u). [para(1321(a,1),638(a,1,1,2,2,1))]. 1323 T(x,y \ T(y,L(y \ 1,z,u))) = x. [para(1252(a,1),1115(a,1,2,2))]. 1324 T(x \ T(x,L(x \ 1,y,z)),u) = x \ T(x,L(x \ 1,y,z)). [hyper(33,a,1323,a)]. 1325 K((x * y) / y,y / (x * y)) * (x * y) = T(x,x \ 1) * y. [para(895(a,1),1298(a,1,1))]. 1327 K((x * y) / y,y / (x * y)) = K(x,x \ 1). [hyper(18,a,947,a,b,1325,a)]. 1328 K(x,y / (x * y)) = K(x,x \ 1). [para(15(a,1),1327(a,1,1))]. 1330 K(x / y,(x / y) \ 1) = K(x / y,y / x). [para(16(a,1),1328(a,1,2,2)),flip(a)]. 1331 K(x / (y * x),(x / (y * x)) \ 1) = K(y,y \ 1) \ 1. [para(1328(a,1),907(a,2,1))]. 1332 K(x / (y \ x),(y \ x) / x) = K(y,(x / (y \ x)) \ 1). [para(57(a,1),1330(a,1,1)),flip(a)]. 1333 K(x / y,y / x) \ z = K(y / x,x / y) * z. [para(1330(a,1),898(a,1,1)),flip(a)]. 1334 K(x / (y * x),(x / (y * x)) \ 1) = K(y \ 1,y). [para(1331(a,2),452(a,1))]. 1336 K(x / (y \ x),(y \ x) / x) = K(y,y \ 1). [para(57(a,1),1332(a,2,2,1))]. 1337 K(x,x \ 1) * (x \ y) = (1 / (1 / ((x \ y) / y))) * y. [para(1336(a,1),973(a,1,1))]. 1338 (1 / (1 / ((x \ y) / y))) * y = (1 / (1 / x)) \ y. [para(1337(a,1),965(a,1))]. 1339 ((1 / (1 / x)) \ y) / y = 1 / (1 / ((x \ y) / y)). [hyper(70,a,1338,a)]. 1340 (((1 / (1 / x)) \ y) / y) \ 1 = 1 / ((x \ y) / y). [para(1339(a,2),59(a,1,1))]. 1341 1 / (((x \ 1) \ y) / y) = (((1 / x) \ y) / y) \ 1. [para(57(a,1),1340(a,1,1,1,1,2)),flip(a)]. 1342 ((((1 / x) \ y) / y) \ 1) \ 1 = ((x \ 1) \ y) / y. [para(1341(a,1),59(a,1,1))]. 1343 K(x,((1 / y) \ z) / z) = K(x,((y \ 1) \ z) / z). [para(1342(a,1),929(a,1,2)),flip(a)]. 1344 R(x / y,y,K(z \ 1,z)) = K(z \ 1,z) * (x / (K(z \ 1,z) * y)). [para(1168(a,2),1170(a,1))]. 1345 ((x \ 1) \ 1) \ (K(x,x \ 1) * (x * y)) = L(y,x,K(x,x \ 1)). [para(1185(a,1),1197(a,1,1))]. 1346 ((x \ 1) \ 1) \ (x * (K(x,x \ 1) * y)) = L(y,x,K(x,x \ 1)). [para(966(a,1),1345(a,1,2))]. 1347 L(x,K(y,y \ 1),y) = L(x,y,K(y,y \ 1)). [para(1346(a,1),1188(a,1)),flip(a)]. 1348 L(x,K(y,y \ 1),y) = x. [para(1347(a,2),88(a,1))]. 1349 L(x,K(y \ 1,y),z / (y * z)) = x. [para(1334(a,1),1348(a,1,2))]. 1350 L(x,K(y \ 1,y),1 / y) = x. [para(12(a,1),1349(a,1,3,2))]. 1351 R((x * y) / y,y,K(z \ 1,z)) = K(z \ 1,z) * R(x / K(z \ 1,z),K(z \ 1,z),y). [para(82(a,2),1344(a,2,2))]. 1353 L(1 / T((x \ 1) \ 1,y),x,x \ 1) = K(x,x \ 1) * (T(x,y) \ 1). [para(1161(a,2),1231(a,1))]. 1354 K(x \ 1,x) * ((((y * x) / y) \ 1) \ 1) = (y * x) / y. [para(1309(a,2),1074(a,1))]. 1355 ((x \ 1) \ 1) \ ((((y * x) / y) \ 1) \ 1) = x \ ((y * x) / y). [para(1354(a,1),537(a,1,2)),flip(a)]. 1356 T(x,((y * x) / y) \ 1) \ ((((z * x) / z) \ 1) \ 1) = x \ ((z * x) / z). [para(1265(a,2),1355(a,1,1))]. 1357 R(x \ 1,y,z) * (K(x \ 1,x) \ u) = R(1 / x,y,z) * u. [para(1175(a,1),1314(a,1,1))]. 1358 R(x \ 1,y,z) * (K(x,x \ 1) * u) = R(1 / x,y,z) * u. [para(447(a,1),1357(a,1,2))]. 1359 (x \ y) * (((x \ y) \ (y / x)) / (y / x)) = x \ (K(y / x,(y / x) \ 1) * x). [para(980(a,1),1319(a,2,2))]. 1360 (x \ y) * (((x \ y) \ (y / x)) / (y / x)) = K(y / x,(y / x) \ 1). [para(1359(a,2),1142(a,1))]. 1361 K(x / y,(x / y) \ 1) != (y \ x) * z | ((y \ x) \ (x / y)) / (x / y) = z. [para(1360(a,1),19(a,1))]. 1363 T(x,x \ 1) * (y * T(y \ 1,x)) = (x \ 1) \ (y * T(y \ 1,x)). [para(1219(a,1),1203(a,1))]. 1364 (x * T(x \ 1,y)) * ((y \ 1) \ 1) = (y \ 1) \ (x * T(x \ 1,y)). [para(1363(a,1),1084(a,1)),flip(a)]. 1365 ((x * (y * T(y \ 1,z))) * ((z \ 1) \ 1)) / ((z \ 1) \ (y * T(y \ 1,z))) = R(x,y * T(y \ 1,z),(z \ 1) \ 1). [para(1364(a,1),28(a,2,2)),flip(a)]. 1366 x * ((y \ (x \ ((y \ 1) \ 1))) * y) = (y \ 1) \ (x * T(x \ 1,y)). [para(1364(a,1),988(a,1)),flip(a)]. 1367 T((T(x,y) \ x) * (T(x,y) / x),z) = (T(x,y) \ x) * (T(x,y) / x). [para(1063(a,1),1218(a,2,2,2))]. 1368 K(x \ 1,x) * R(y / K(x \ 1,x),K(x \ 1,x),z) = R(y,z,K(x \ 1,x)). [para(15(a,1),1351(a,1,1)),flip(a)]. 1369 K(x \ 1,x) * R(K(x,x \ 1) * y,K(x \ 1,x),z) = R(y,z,K(x \ 1,x)). [para(1177(a,1),1368(a,1,2,1))]. 1370 R(K(x \ 1,x) * (K(x,x \ 1) * y),K(x \ 1,x),z) = R(y,z,K(x \ 1,x)). [para(1369(a,1),458(a,2))]. 1371 R(x,K(y \ 1,y),z) = R(x,z,K(y \ 1,y)). [para(448(a,1),1370(a,1,1))]. 1372 (R(x,y,K(y \ 1,y)) / y) * L(y,y \ 1,y) = x * (L(y,y \ 1,y) / y). [para(1371(a,1),1179(a,1,1,1))]. 1373 (R(x,y,K(y \ 1,y)) / y) * (1 / (1 / y)) = x * (L(y,y \ 1,y) / y). [para(1045(a,1),1372(a,1,2))]. 1374 (R(x,y,K(y \ 1,y)) / y) * (1 / (1 / y)) = x * K(y \ 1,y). [para(1178(a,1),1373(a,2,2))]. 1375 (R(x,y,K(y \ 1,y)) / y) * (1 / (1 / y)) != z * K(y \ 1,y) | z = x. [para(1374(a,2),20(a,2)),flip(a)]. 1376 L(R(x,y \ 1,y),K(y \ 1,y),1 / y) = (1 * (y \ 1)) \ R((1 / y) * x,y,y \ 1). [para(885(a,1),1277(a,1,2))]. 1377 (1 * (x \ 1)) \ R((1 / x) * y,x,x \ 1) = R(y,x \ 1,x). [para(1376(a,1),1350(a,1))]. 1378 (x \ 1) \ R((1 / x) * y,x,x \ 1) = R(y,x \ 1,x). [para(11(a,1),1377(a,1,1))]. 1379 T(((1 / x) * y) * x,x \ 1) = R(y,x \ 1,x). [para(1378(a,1),244(a,1)),flip(a)]. 1380 a(R(x \ 1,y,z),K(x,x \ 1),u) = (R(1 / x,y,z) * u) \ (R(1 / x,y,z) * u). [para(1358(a,1),1260(a,1,1)),flip(a)]. 1381 a(R(x \ 1,y,z),K(x,x \ 1),u) = 1. [para(1380(a,2),48(a,1))]. 1383 a(R((x \ 1) \ 1,y,z),K(x \ 1,x),u) = 1. [para(929(a,1),1381(a,1,2))]. 1384 L(L(x,y * (1 / x),K(x \ 1,x)),1 / x,y) = R(y / x,x,1 / x) \ (K(x \ 1,x) * y). [para(59(a,1),1279(a,1,1,1))]. 1385 R(R(x,y,K(z \ 1,z)),y * K(z \ 1,z),K(z,z \ 1)) = (x * y) / y. [para(1210(a,1),1215(a,2,2))]. 1386 R(R(x,y,K(z \ 1,z)),y * K(z \ 1,z),K(z,z \ 1)) = x. [para(1385(a,2),15(a,1))]. 1387 R(R(x,1 / y,K(y \ 1,y)),y \ 1,K(y,y \ 1)) = x. [para(889(a,1),1386(a,1,2))]. 1388 R(R(x,1 / y,K(y \ 1,y)),y \ 1,K((y \ 1) \ 1,y \ 1)) = x. [para(897(a,2),1387(a,1,3))]. 1389 (K(x,x \ 1) * ((y * z) * u)) / (K(x,x \ 1) * (z * u)) = R(R(y,z,K(x,x \ 1)),z * K(x,x \ 1),u). [para(1199(a,1),1261(a,1,2))]. 1390 K(x,x \ 1) * (((y * z) * u) / (K(x,x \ 1) * (z * u))) = R(R(y,z,K(x,x \ 1)),z * K(x,x \ 1),u). [para(1389(a,1),281(a,1)),flip(a)]. 1391 K(x,x \ 1) * ((R(y,z,u) * (z * u)) / (K(x,x \ 1) * (z * u))) = R(R(y,z,K(x,x \ 1)),z * K(x,x \ 1),u). [para(81(a,2),1390(a,1,2,1))]. 1392 (1 * (x \ 1)) \ (((1 / x) \ (1 * (x \ 1))) * (R(y,x,1 / x) * K(x,x \ 1))) = L(T(y * x,1 / x),1 / x,(1 / x) \ (1 * (x \ 1))). [para(934(a,2),1253(a,1,2,2))]. 1393 L(T(x / y,y / x),y / x,((y / x) * (x / y)) / (y / x)) = ((y / x) * (x / y)) * ((y / x) \ 1). [para(485(a,1),1146(a,1,1))]. 1394 ((x / y) * (y / x)) * ((x / y) \ 1) = T(y / x,(x / y) * (y / x)). [para(1393(a,1),405(a,1))]. 1395 ((x / y) * (y / x)) * ((x / y) \ 1) = y / x. [para(1394(a,2),1119(a,1))]. 1396 ((x / (y * x)) * ((y * x) / x)) * ((x / (y * x)) \ 1) = y. [para(1395(a,2),15(a,1))]. 1397 ((x / (y * x)) * y) * ((x / (y * x)) \ 1) = y. [para(15(a,1),1396(a,1,1,2))]. 1398 ((x / (y * x)) * y) \ y = (x / (y * x)) \ 1. [hyper(66,a,1397,a)]. 1399 (R(x \ 1,y,z) / (x * R(x \ 1,y,z))) \ 1 = ((x \ 1) * x) \ x. [para(672(a,1),1398(a,1,1,1)),flip(a)]. 1400 (R(x \ 1,y,z) / (x * R(x \ 1,y,z))) \ 1 = K(x \ 1,x) \ x. [para(135(a,2),1399(a,2,1))]. 1401 R(x,T(y,x),K(z \ 1,R(z,u,w))) \ ((y * K(z \ 1,z)) * x) = T(y,x) * T(K(z \ 1,R(z,u,w)),y * x). [para(1154(a,1),1288(a,1,1,3))]. 1403 (x \ 1) \ (((1 / x) \ (1 * (x \ 1))) * (R(y,x,1 / x) * K(x,x \ 1))) = L(T(y * x,1 / x),1 / x,(1 / x) \ (1 * (x \ 1))). [para(11(a,1),1392(a,1,1))]. 1404 (x \ 1) \ (((1 / x) \ (x \ 1)) * (R(y,x,1 / x) * K(x,x \ 1))) = L(T(y * x,1 / x),1 / x,(1 / x) \ (1 * (x \ 1))). [para(11(a,1),1403(a,1,2,1,2))]. 1405 (x \ 1) \ (K(x \ 1,x) * (R(y,x,1 / x) * K(x,x \ 1))) = L(T(y * x,1 / x),1 / x,(1 / x) \ (1 * (x \ 1))). [para(888(a,1),1404(a,1,2,1))]. 1406 L(T(x * y,1 / y),1 / y,(1 / y) \ (1 * (y \ 1))) = (y \ 1) \ R(x,y,1 / y). [para(1202(a,1),1405(a,1,2)),flip(a)]. 1407 L(T(x * y,1 / y),1 / y,(1 / y) \ (y \ 1)) = (y \ 1) \ R(x,y,1 / y). [para(11(a,1),1406(a,1,3,2))]. 1409 L(T(x * y,1 / y),1 / y,K(y \ 1,y)) = (y \ 1) \ R(x,y,1 / y). [para(888(a,1),1407(a,1,3))]. 1410 (x \ 1) \ R(y,x,1 / x) = T(y * x,1 / x). [para(1409(a,1),88(a,1))]. 1411 (x \ 1) * T(y * x,1 / x) = R(y,x,1 / x). [para(1410(a,1),14(a,1,2))]. 1412 ((L(x,y,z) * (z * y)) / (z * y)) * T(((L(x,y,z) * (z * y)) / (z * y)) \ x,u) = (x * (z * y)) / (z * y). [para(636(a,1),1245(a,2,1))]. 1414 ((L(x,y,z) * (z * y)) / (z * y)) * T(((L(x,y,z) * (z * y)) / (z * y)) \ x,u) = x. [para(1412(a,2),15(a,1))]. 1415 L(x,y,z) * T(((L(x,y,z) * (z * y)) / (z * y)) \ x,u) = x. [para(15(a,1),1414(a,1,1))]. 1416 L(x,y,z) * T(L(x,y,z) \ x,u) = x. [para(15(a,1),1415(a,1,2,1,1))]. 1419 x / L(x,y,z) = L(x,y,z) \ x. [para(1416(a,1),106(a,1,1))]. 1420 L(x \ (y \ z),x,y) \ (x \ (y \ z)) = (x \ (y \ z)) / ((y * x) \ z). [para(128(a,1),1419(a,1,2)),flip(a)]. 1421 (L(x,y,z) \ x) / x = 1 / L(x,y,z). [para(1419(a,1),801(a,1,1))]. 1422 (((x * y) \ z) \ (y \ (x \ z))) / (y \ (x \ z)) = 1 / L(y \ (x \ z),y,x). [para(128(a,1),1421(a,1,1,1))]. 1423 (1 / L(x,y,z)) \ ((L(x,y,z) \ 1) * (x * (L(x,y,z) \ 1))) = (L(x,y,z) \ 1) * x. [para(1421(a,1),678(a,1,1))]. 1424 (x \ (y \ z)) / ((y * x) \ z) = ((y * x) \ z) \ (x \ (y \ z)). [para(128(a,1),1420(a,1,1)),flip(a)]. 1425 x \ ((y * z) * K((z \ (y \ x)) \ (((y * z) \ x) \ (z \ (y \ x))),z \ (y \ x))) = T(x \ (y * z),z \ (y \ x)). [para(1424(a,1),520(a,1,2,2,1,2))]. 1426 (((x * y) \ z) \ (y \ (x \ z))) / (y \ (x \ z)) = 1 / ((x * y) \ z). [para(128(a,1),1422(a,2,2))]. 1427 (1 / L(x,y,z)) \ ((L(x,y,z) \ 1) * (L(x,y,z) \ x)) = (L(x,y,z) \ 1) * x. [para(489(a,1),1423(a,1,2,2))]. 1428 K(L(x,y,z) \ 1,L(x,y,z)) * (L(x,y,z) \ x) = (L(x,y,z) \ 1) * x. [para(1427(a,1),535(a,1)),flip(a)]. 1429 K(L(x,y,z) \ 1,L(x,y,z)) = L(K(x \ 1,x),y,z). [hyper(18,a,1014,a,b,1428,a)]. 1430 K(((x * y) \ x) \ 1,L(y \ 1,y,x)) = L(K((y \ 1) \ 1,y \ 1),y,x). [para(103(a,1),1429(a,1,1,1))]. 1431 K(((x * y) \ x) \ 1,L(y \ 1,y,x)) = L(K(y,y \ 1),y,x). [para(897(a,1),1430(a,2,1))]. 1432 L(K(x,x \ 1),x,y) * (y * x) = y * T(y \ (y * x),(y * x) \ y). [para(1431(a,1),1284(a,1,1))]. 1433 x * T(x \ (x * y),(x * y) \ x) = x * (y * K(y,y \ 1)). [para(1432(a,1),1160(a,1))]. 1434 x * T(x \ (x * y),(x * y) \ x) = x * T(y,y \ 1). [para(1183(a,1),1433(a,2,2))]. 1435 x * T(y,(x * y) \ x) = x * T(y,y \ 1). [para(13(a,1),1434(a,1,2,1))]. 1436 T(x,(y * x) \ y) = T(x,x \ 1). [hyper(154,a,1435,a),flip(a)]. 1437 T(x,(y * x) \ y) = (x \ 1) \ 1. [hyper(17,a,780,a(flip),b,1435,a)]. 1438 T(x \ y,y \ x) = ((x \ y) \ 1) \ 1. [para(14(a,1),1437(a,1,2,1))]. 1440 K(x / y,y / x) * x = y * T(y \ x,x \ y). [para(1438(a,2),1308(a,2,2))]. 1441 K((x \ y) \ 1,x \ y) = K(x / y,y / x). [hyper(18,a,1280,a,b,1440,a),flip(a)]. 1442 K((x \ y) \ 1,x \ y) * (x / y) = T(x / y,y / x). [para(1441(a,2),900(a,1,1))]. 1443 (R((x \ y) \ 1,z,u) / ((x \ y) * R((x \ y) \ 1,z,u))) \ 1 = K(x / y,y / x) \ (x \ y). [para(1441(a,1),1400(a,2,1))]. 1444 K(x \ 1,(y / x) \ y) * ((y / x) / y) = T((y / x) / y,y / (y / x)). [para(59(a,1),1442(a,1,1,1,1))]. 1445 T((x / y) / x,x / (x / y)) = K(y \ 1,y) * ((x / y) / x). [para(59(a,1),1444(a,1,1,2)),flip(a)]. 1446 K((x / y) / x,x / (x / y)) = K(y \ 1,y). [hyper(902,a,1445,a)]. 1447 (x / y) * (1 / (1 / y)) = K(y \ 1,y) * x. [para(1446(a,1),1270(a,1,1)),flip(a)]. 1448 (x * (1 / (1 / y))) / y = x * K(y \ 1,y). [hyper(18,a,1169,a,b,1447,a)]. 1449 K(x \ 1,x) * (y * x) = y * (1 / (1 / x)). [para(15(a,1),1447(a,1,1)),flip(a)]. 1450 (x / y) * (1 / (1 / y)) = x * K(y \ 1,y). [para(1447(a,2),1133(a,1))]. 1452 (x / (1 / (1 / y))) * K(y \ 1,y) = x / y. [para(16(a,1),1448(a,1,1)),flip(a)]. 1453 K(x \ 1,x) * ((y * x) / z) = (y * (1 / (1 / x))) / z. [para(1449(a,1),281(a,1,1)),flip(a)]. 1454 (1 / (1 / x)) * T(y,x) = y * (1 / (1 / x)). [para(1449(a,1),959(a,1)),flip(a)]. 1455 R(x,y,K(y \ 1,y)) = x. [hyper(1375,a,1450,a)]. 1456 R(x,1 / y,K(y \ 1,y)) = x. [para(1455(a,1),1388(a,1))]. 1457 K(x \ 1,x) * (y / (x \ 1)) = y / (1 / x). [para(1456(a,1),1258(a,1)),flip(a)]. 1458 T(x,1 / (1 / y)) = T(x,y). [hyper(165,a,1454,a),flip(a)]. 1459 T(x,1 / y) = T(x,y \ 1). [para(57(a,1),1458(a,1,2,2))]. 1460 T(x,(y \ 1) \ 1) = T(x,y). [para(57(a,1),1459(a,1,2)),flip(a)]. 1461 T(((1 / x) * y) * x,x \ 1) = R(y,1 / x,x). [para(1459(a,1),351(a,1))]. 1462 L(T(x,y \ 1) \ z,T(x,1 / y),y \ 1) = (x * (1 / y)) \ ((1 / y) * z). [para(1459(a,1),852(a,1,1,1))]. 1463 (x \ 1) * T(y * x,x \ 1) = R(y,x,1 / x). [para(1459(a,1),1411(a,1,2))]. 1464 T(x,T(y,y \ 1)) = T(x,y). [para(86(a,2),1460(a,1,2))]. 1465 T(x,x \ 1) * T(y,x) = y * T(x,x \ 1). [para(1464(a,1),85(a,1,2))]. 1467 ((x \ 1) \ 1) * T(y,x) = y * T(x,x \ 1). [para(1464(a,1),443(a,1,2))]. 1468 (1 / x) * (y / (1 / x)) = (x \ 1) * (y / (x \ 1)). [para(1457(a,1),539(a,1,2))]. 1469 (x / (y \ 1)) * K(y \ 1,y) = x / (1 / y). [para(1457(a,1),1133(a,1)),flip(a)]. 1470 K(x,x \ 1) * (y * x) = y * T(x,x \ 1). [para(1465(a,1),954(a,2))]. 1471 (x * y) * ((((z \ 1) \ 1) \ L(y \ ((z \ 1) \ 1),y,x)) * T(z,z \ 1)) = (x * (y * T(y \ 1,z))) * ((z \ 1) \ 1). [para(1467(a,1),817(a,1,2))]. 1472 (x / (1 / y)) \ K(y \ 1,y) = (x / (y \ 1)) \ 1. [para(1469(a,1),1263(a,1,1))]. 1473 K(x \ 1,x) * (y * T(x,x \ 1)) = y * x. [hyper(1235,a,1470,a)]. 1474 (x * y) * K(y,y \ 1) = x * T(y,y \ 1). [para(1470(a,1),1141(a,1)),flip(a)]. 1475 (((x \ 1) \ 1) \ y) * T(x,x \ 1) = (x \ y) * x. [hyper(733,a,1473,a),flip(a)]. 1476 (x * y) * K(y,y \ 1) = x * ((y \ 1) \ 1). [para(86(a,1),1474(a,2,2))]. 1477 R(x,y,K(y,y \ 1)) = x. [hyper(1189,a,1476,a)]. 1478 ((x * y) * ((z \ 1) \ 1)) / ((y * z) * K(z,z \ 1)) = R(R(x,y,z),y * z,K(z,z \ 1)). [para(1476(a,1),213(a,1,1))]. 1479 (x / y) * K(y \ 1,y) = x / T(y,y \ 1). [para(1477(a,1),1317(a,1))]. 1480 x \ (x / T(y,y \ 1)) = T(x \ (x / y),y). [para(1479(a,1),378(a,1,2))]. 1481 (x / ((y \ 1) \ 1)) * T((y \ 1) \ 1,z) = x * K(z \ (z / T(x \ (x / y),y)),z). [para(1480(a,1),621(a,2,2,1,2,2))]. 1482 R(x,1 / y,y) = R(x,y \ 1,y). [para(1461(a,1),1379(a,1))]. 1483 (x * (1 / y)) * y = R(x,y \ 1,y). [para(1482(a,1),121(a,2))]. 1484 R(x / (1 / y),y \ 1,y) = x * y. [para(1482(a,1),225(a,1))]. 1485 R(x,y \ 1,y) / y = x * (1 / y). [para(1482(a,1),246(a,1,1))]. 1486 R((x \ (y / (1 / z))) * x,z \ 1,z) = (x \ (y * z)) * x. [para(1484(a,1),776(a,2,1,2))]. 1487 (x * y) * (y \ 1) = R(x,y,1 / y). [para(1463(a,1),85(a,1)),flip(a)]. 1488 R(x / y,y,1 / y) = x * (y \ 1). [para(16(a,1),1487(a,1,1)),flip(a)]. 1489 L(L(x,y * (1 / x),K(x \ 1,x)),1 / x,y) = (y * (x \ 1)) \ (K(x \ 1,x) * y). [para(1488(a,1),1384(a,2,1))]. 1490 ((x * y) / z) / ((x * (1 / (1 / y))) / z) = K(y,y \ 1). [para(1453(a,1),457(a,1,2))]. 1491 x / ((y * (1 / (1 / T(x,y)))) / y) = K(T(x,y),T(x,y) \ 1). [para(106(a,1),1490(a,1,1))]. 1492 ((x \ (y / (1 / z))) * x) * (1 / z) = ((x \ (y * z)) * x) / z. [para(1486(a,1),1485(a,1,1)),flip(a)]. 1493 x / (((1 / (1 / x)) * y) / y) = K(T(x,y),T(x,y) \ 1). [para(1225(a,1),1491(a,1,2,1))]. 1494 K(T(x,y),T(x,y) \ 1) = x / (1 / (1 / x)). [para(15(a,1),1493(a,1,2)),flip(a)]. 1496 K(T(x,y),T(x,y) \ 1) = K(x,x \ 1). [para(1494(a,2),939(a,1))]. 1497 K(x,x \ 1) * (T(x,y) \ z) = (1 / (1 / T(x,y))) \ z. [para(1496(a,1),965(a,1,1))]. 1498 K(x,x \ 1) * T(1 / (1 / x),y) = T(x,y). [para(1496(a,1),1226(a,1,1))]. 1499 T(x,y) / x = x \ T(x,y). [para(1498(a,1),1002(a,1,2)),flip(a)]. 1501 (x \ T(x,y)) * x = T(x,y). [para(1499(a,1),16(a,1,1))]. 1502 K(x,y) = L(T(x,y) / x,x,y). [para(1499(a,2),311(a,2,1))]. 1503 (1 / x) * T(x,y) = x \ T(x,y). [para(1499(a,1),594(a,2))]. 1504 (x \ 1) \ T(x \ 1,y) = x * T(x \ 1,y). [para(1499(a,1),598(a,1))]. 1505 L(x \ 1,x,x \ T(x,y)) = T(1 / x,T(x,y)). [para(1499(a,1),619(a,1,3))]. 1506 T(x \ T(x,L(x \ 1,y,z)),L(x \ 1,y,z) * x) = K(L(x \ 1,y,z) \ ((1 / x) \ L(x \ 1,y,z)),L(x \ 1,y,z)). [para(1499(a,1),1085(a,1,1))]. 1507 T((T(x,y) \ x) * (x \ T(x,y)),z) = (T(x,y) \ x) * (T(x,y) / x). [para(1499(a,1),1367(a,1,1,2))]. 1508 T(x,x \ T(x,y)) = x. [hyper(143,a,1501,a)]. 1509 T(x,y) != z * x | x \ T(x,y) = z. [para(1501(a,1),20(a,1))]. 1510 T(x,y) * L(z,x,x \ T(x,y)) = (x \ T(x,y)) * (x * z). [para(1501(a,1),76(a,1,1))]. 1511 T(K(x \ (x / (y \ (y / z))),x),z) = y \ ((y / z) * T(z,x)). [para(1501(a,1),659(a,2,2,2))]. 1512 L(K(x,y),x,1 / x) = K(x,y). [para(1502(a,2),599(a,2))]. 1513 K(x,y) / (x * K(x,y)) = 1 / x. [para(1512(a,1),239(a,1,1))]. 1514 (L(x,1 / x,y) * y) / L(x,1 / x,y) = y * (x \ T(x,y)). [para(1503(a,1),816(a,2,2))]. 1515 R(x,x \ 1,K(x \ 1,y)) = 1 / (x \ 1). [para(1513(a,1),101(a,2))]. 1516 R(x,x \ 1,K(x \ 1,y)) = x. [para(1515(a,2),57(a,1))]. 1517 (x \ 1) * K(x \ 1,y) = x \ K(x \ 1,y). [para(1516(a,1),168(a,1,1)),flip(a)]. 1518 L(x,y,z) \ ((x \ 1) * L(x,y,z)) = (x \ 1) * K(x \ 1,L(x,y,z)). [para(1516(a,1),319(a,1,1,1))]. 1519 (x \ 1) * (x * T(x \ 1,y)) = T(x \ 1,y). [para(1504(a,1),14(a,1,2))]. 1520 K(x,y) = (L(x \ 1,x,y) \ 1) \ T(L(x \ 1,x,y) \ 1,y). [para(1504(a,2),668(a,2))]. 1522 T(1 / x,T(x,y)) = x \ 1. [para(1505(a,1),433(a,1))]. 1523 T(x \ 1,T(x,y)) = T(x \ 1,x). [para(1522(a,1),117(a,1,1)),flip(a)]. 1525 T((1 / x) \ 1,1 / x) = T(x,T(1 / x,y)). [para(59(a,1),1523(a,1,1)),flip(a)]. 1526 T((x / y) \ 1,x / y) = T((x / y) \ 1,y \ x). [para(87(a,1),1523(a,1,2)),flip(a)]. 1527 T(x,T(1 / x,y)) = T(x,1 / x). [para(59(a,1),1525(a,1,1)),flip(a)]. 1528 T(x,T(1 / x,y)) = T(x,x \ 1). [para(1527(a,2),1191(a,1))]. 1529 R(x,T(1 / x,y),x) = T(x,x \ 1). [para(1528(a,1),740(a,2))]. 1530 L(T(x,x \ 1),y,z) \ L(x,y,z) = (L(x,y,z) \ (L(x,y,z) / x)) * x. [para(1529(a,1),910(a,1,1,1))]. 1532 K(x,T((y / z) \ 1,z \ y)) = K(x,(y / z) \ 1). [para(1526(a,1),920(a,1,2))]. 1533 R((x / y) \ 1,x / y,y) \ 1 = T((y / x) \ 1,x \ y). [para(1526(a,1),1304(a,2))]. 1534 K(x,x \ 1) * (T(x,y) \ z) = T(1 / (1 / x),y) \ z. [para(1222(a,1),1497(a,2,1))]. 1535 L(1 / T((x \ 1) \ 1,y),x,x \ 1) = T(1 / (1 / x),y) \ 1. [para(1534(a,1),1353(a,2))]. 1536 T(x * L(x \ 1,x,x \ T(x,y)),y) = (x \ T(x,y)) * (x * (T(x,y) \ 1)). [para(1510(a,1),825(a,1)),flip(a)]. 1537 T((1 * x) / y,y / x) \ 1 = T((x / y) \ 1,y \ x). [para(349(a,1),1533(a,1,1))]. 1538 T(x / y,y / x) \ 1 = T((x / y) \ 1,y \ x). [para(11(a,1),1537(a,1,1,1,1))]. 1539 x * (T((x \ y) * z,x) / z) = ((x \ (y * z)) * x) / z. [para(1492(a,1),771(a,1)),flip(a)]. 1540 K(x \ (x / T(y \ (y / z),z)),x) = y \ ((y / z) * T(z,x)). [para(1511(a,1),752(a,2))]. 1541 L(1 / T((x \ 1) \ 1,y),x,x \ 1) = 1 / T(x,y). [para(1535(a,2),1224(a,1))]. 1542 L(T(x,y) \ 1,x,x \ 1) = 1 / T(x,y). [para(1229(a,1),1541(a,1,1))]. 1543 (1 / x) * (T(x,y) \ x) = 1 / T(x,y). [para(1542(a,1),549(a,1)),flip(a)]. 1544 (x \ 1) * (T(x,y) \ x) = T(1 / T(x,y),x). [para(1543(a,1),1281(a,1,1)),flip(a)]. 1545 (x \ 1) * (T(x,y) \ x) = T(x,y) \ 1. [para(1544(a,2),1069(a,1))]. 1546 T((T(x,y) \ x) * (x \ T(x,y)),z) = (T(x,y) \ x) * (x \ T(x,y)). [para(1499(a,1),1507(a,2,2))]. 1547 (T(x,y) \ x) * (x \ T(x,y)) = 1. [para(1546(a,1),1078(a,1))]. 1549 (T(x \ 1,y) \ (x \ 1)) * (x * T(x \ 1,y)) = 1. [para(1504(a,1),1547(a,1,2))]. 1550 (T(x,((y * x) / y) \ 1) \ ((((y * x) / y) \ 1) \ 1)) * ((((y * x) / y) \ 1) * T((((y * x) / y) \ 1) \ 1,y)) = 1. [para(179(a,1),1549(a,1,1,1))]. 1551 (x \ 1) * K(x \ 1,L(x,y,z)) = T(x \ 1,L(x,y,z)). [para(1518(a,1),30(a,2)),flip(a)]. 1552 x * T(x \ 1,L(x,y,z)) = K(x \ 1,L(x,y,z)). [hyper(17,a,1519,a,b,1551,a),flip(a)]. 1553 L(K(x \ 1,L(x,y,z)),y,z) = K(L(x,y,z) \ 1,L(x,y,z)). [para(1552(a,1),1012(a,1,1))]. 1554 L(K(x \ 1,L(x,y,z)),y,z) = L(K(x \ 1,x),y,z). [para(1553(a,2),1429(a,1))]. 1555 x \ (y \ ((L(K(z \ 1,z),x,y) * y) * x)) = R(T(K(z \ 1,L(z,x,y)),y * x),y,x). [para(1554(a,1),427(a,1,2,2,1,1))]. 1556 L(T(x,x \ 1),y,z) \ L(x,y,z) = T(1 / x,L(x,y,z)) * x. [para(796(a,1),1530(a,2,1))]. 1558 L(T(x,x \ 1),y,z) \ L(x,y,z) = x * T(x \ 1,L(x,y,z)). [para(1556(a,2),171(a,1))]. 1559 L(T(x,x \ 1),y,z) \ L(x,y,z) = K(x \ 1,L(x,y,z)). [para(1558(a,2),1552(a,1))]. 1560 L(T(x,y \ 1) \ z,T(x,y \ 1),y \ 1) = (x * (1 / y)) \ ((1 / y) * z). [para(1459(a,1),1462(a,1,2))]. 1561 T(x * L(x \ 1,x,x \ T(x,y)),y) = (x \ T(x,y)) * (T(x,y) \ x). [para(505(a,1),1536(a,2,2))]. 1562 (x \ T(x,y)) * (T(x,y) \ x) = T(x * (x \ 1),y). [para(433(a,1),1561(a,1,1,2)),flip(a)]. 1563 (x \ T(x,y)) * (T(x,y) \ x) = T(1,y). [para(14(a,1),1562(a,2,1))]. 1566 (x \ T(x,y)) * (T(x,y) \ x) = 1. [para(1563(a,2),1126(a,1))]. 1567 (x \ T(x,y)) \ 1 = T(x,y) \ x. [hyper(66,a,1566,a)]. 1569 T(L(x \ 1,x,y) \ 1,y) \ (L(x \ 1,x,y) \ 1) = K(x,y) \ 1. [para(1520(a,2),1567(a,1,1)),flip(a)]. 1570 (x * (1 / y)) \ ((1 / y) * z) = (x * (y \ 1)) \ ((y \ 1) * z). [para(1560(a,1),207(a,1))]. 1571 (x * (y \ 1)) \ ((y \ 1) * x) = K(1 / y,x). [para(1570(a,1),24(a,2)),flip(a)]. 1572 K(1 / x,y) = K(x \ 1,y). [para(1571(a,1),24(a,2)),flip(a)]. 1573 K((x \ 1) \ 1,y) = K(x,y). [para(57(a,1),1572(a,1,1)),flip(a)]. 1574 (x / ((y \ 1) \ 1)) * T((y \ 1) \ 1,z) = x * (x \ ((x / y) * T(y,z))). [para(1540(a,1),1481(a,2,2))]. 1575 (x / ((y \ 1) \ 1)) * T((y \ 1) \ 1,z) = (x / y) * T(y,z). [para(1574(a,2),14(a,1))]. 1576 (((x \ 1) \ 1) * y) / ((x \ 1) \ 1) = (y / x) * T(x,y). [para(1575(a,1),601(a,1)),flip(a)]. 1577 (((x \ 1) \ 1) * y) / ((x \ 1) \ 1) = (x * y) / x. [para(1576(a,2),601(a,1))]. 1578 L(L(x,y * (1 / x),K(x \ 1,x)),1 / x,y) = L(x,x \ 1,y). [para(1489(a,2),1173(a,1))]. 1579 L(x,1 / x,y) = L(x,x \ 1,y). [para(88(a,1),1578(a,1,1))]. 1580 (L(x,x \ 1,y) * y) / L(x,1 / x,y) = y * (x \ T(x,y)). [para(1579(a,1),1514(a,1,1,1))]. 1581 (L(x,x \ 1,y) * y) / L(x,x \ 1,y) = y * (x \ T(x,y)). [para(1579(a,1),1580(a,1,2))]. 1582 x \ (y \ (L(K(z \ 1,z),x,y) * (y * x))) = R(T(K(z \ 1,L(z,x,y)),y * x),y,x). [para(386(a,1),1555(a,1,2,2))]. 1583 R(T(K(x \ 1,L(x,y,z)),z * y),z,y) = y \ (z \ (z * (y * K(x \ 1,x)))). [para(1157(a,1),1582(a,1,2,2)),flip(a)]. 1584 R(T(K(x \ 1,L(x,y,z)),z * y),z,y) = y \ (y * K(x \ 1,x)). [para(13(a,1),1583(a,2,2))]. 1585 R(T(K(x \ 1,L(x,y,z)),z * y),z,y) = K(x \ 1,x). [para(1584(a,2),13(a,1))]. 1587 R(R(x,y,z),y * z,K(z,z \ 1)) = ((x * y) * ((z \ 1) \ 1)) / (y * ((z \ 1) \ 1)). [para(1476(a,1),1478(a,1,2)),flip(a)]. 1588 R(R(x,y,z),y * z,K(z,z \ 1)) = R(x,y,(z \ 1) \ 1). [para(1587(a,2),28(a,2)),flip(a)]. 1589 (R((x \ y) \ 1,z,u) / ((x \ y) * R((x \ y) \ 1,z,u))) \ 1 = K(y / x,x / y) * (x \ y). [para(1443(a,2),1333(a,1))]. 1590 (R((x \ y) \ 1,z,u) / ((x \ y) * R((x \ y) \ 1,z,u))) \ 1 = (x \ y) * K(y / x,x / y). [para(1589(a,2),1147(a,1))]. 1591 (x \ y) * K(y / x,x / y) = ((x \ y) \ 1) \ 1. [para(672(a,1),1590(a,1,1)),flip(a)]. 1592 K(x \ y,(x \ y) \ 1) = K(y / x,x / y). [hyper(17,a,1185,a,b,1591,a),flip(a)]. 1593 (x \ y) * (1 / (x \ y)) = K(y / x,x / y). [para(1592(a,1),930(a,1)),flip(a)]. 1594 x \ (K(x / y,y / x) * y) = L(1 / (y \ x),y \ x,y). [para(1592(a,1),1310(a,1,2,1))]. 1595 K(x / y,(x / y) \ 1) = (y \ x) * (1 / (y \ x)). [para(1593(a,2),1330(a,2))]. 1596 ((x \ y) \ (y / x)) / (y / x) = 1 / (x \ y). [hyper(1361,a,1595,a)]. 1597 (1 / (x \ y)) * (y / x) = (x \ y) \ (y / x). [para(1596(a,1),16(a,1,1))]. 1598 ((x / y) \ x) \ (x / (x / y)) = (1 / y) * (x / (x / y)). [para(59(a,1),1597(a,1,1,2)),flip(a)]. 1599 (1 / x) * (y / (y / x)) = x \ (y / (y / x)). [para(59(a,1),1598(a,1,1)),flip(a)]. 1600 (x / (x / y)) \ (y \ (x / (x / y))) = T(1 / y,x / (x / y)). [para(1599(a,1),30(a,2,2)),flip(a)]. 1601 L(1 / (x \ y),x \ y,x) = 1 / (1 / (y \ x)). [para(1594(a,1),1269(a,1))]. 1602 ((x \ y) * (y \ x)) / (x \ y) = 1 / (1 / (y \ x)). [para(1601(a,1),330(a,2))]. 1603 (1 / (1 / (x \ y))) * (y \ x) = (y \ x) * (x \ y). [para(1602(a,1),16(a,1,1))]. 1604 ((x \ y) * (y \ x)) \ ((y \ x) * (x \ y)) = K((x \ y) \ 1,x \ y). [para(1603(a,1),1217(a,1,2))]. 1605 T(1 / x,y / (y / x)) = x \ 1. [para(1600(a,1),571(a,1))]. 1607 K((x \ y) \ 1,x \ y) = K(y \ x,x \ y). [para(1604(a,1),24(a,2)),flip(a)]. 1608 x \ (y * K(x \ y,y \ x)) = T(x \ y,y \ x). [para(1607(a,1),523(a,1,2,2))]. 1609 x \ (y * K(x \ y,y \ x)) = ((x \ y) \ 1) \ 1. [para(1608(a,2),1438(a,1))]. 1610 x \ ((y * z) * K(((y * z) \ x) \ 1,z \ (y \ x))) = T(x \ (y * z),z \ (y \ x)). [para(783(a,1),1425(a,1,2,2,1))]. 1611 (x \ ((y * x) / y)) * ((((y * x) / y) \ 1) * T((((y * x) / y) \ 1) \ 1,y)) = 1. [para(1356(a,1),1550(a,1,1))]. 1612 (x \ ((y * x) / y)) * ((((y * x) / y) \ 1) * (((y \ (y * x)) \ 1) \ 1)) = 1. [para(1232(a,1),1611(a,1,2,2))]. 1614 (x \ ((y * x) / y)) * ((((y * x) / y) \ 1) * ((x \ 1) \ 1)) = 1. [para(13(a,1),1612(a,1,2,2,1,1))]. 1615 (x \ ((y * x) / y)) * (((y * x) / y) \ x) = 1. [para(1267(a,1),1614(a,1,2))]. 1616 (x \ ((y * x) / y)) \ 1 = ((y * x) / y) \ x. [hyper(66,a,1615,a)]. 1617 ((L(x,x \ 1,y) * y) / L(x,x \ 1,y)) \ y = (y \ (y * (x \ T(x,y)))) \ 1. [para(1581(a,1),1616(a,1,1,2)),flip(a)]. 1618 ((L(x,x \ 1,y) * y) / L(x,x \ 1,y)) \ y = (x \ T(x,y)) \ 1. [para(13(a,1),1617(a,2,1))]. 1620 ((L(x,x \ 1,y) * y) / L(x,x \ 1,y)) \ y = T(x,y) \ x. [para(1618(a,2),1567(a,1))]. 1621 (x * (y \ T(y,x))) \ x = T(y,x) \ y. [para(1581(a,1),1620(a,1,1))]. 1622 T(L(x \ 1,x,y) \ 1,y) \ (L(x \ 1,x,y) \ 1) = (y * K(x,y)) \ y. [para(1520(a,2),1621(a,1,1,2)),flip(a)]. 1623 (x * K(y,x)) \ x = K(y,x) \ 1. [para(1622(a,1),1569(a,1))]. 1624 (x * y) * ((z \ L(y \ ((z \ 1) \ 1),y,x)) * z) = (x * (y * T(y \ 1,z))) * ((z \ 1) \ 1). [para(1475(a,1),1471(a,1,2))]. 1625 K(L(x \ 1,y,z) \ ((1 / x) \ L(x \ 1,y,z)),L(x \ 1,y,z)) = x \ T(x,L(x \ 1,y,z)). [para(1506(a,1),1324(a,1))]. 1626 K(L(x \ 1,y,z) \ (L(x \ 1,y,z) * x),L(x \ 1,y,z)) = x \ T(x,L(x \ 1,y,z)). [para(904(a,1),1625(a,1,1,2))]. 1628 x \ T(x,L(x \ 1,y,z)) = K(x,L(x \ 1,y,z)). [para(13(a,1),1626(a,1,1)),flip(a)]. 1629 T(x,K(y,L(y \ 1,z,u))) = x. [para(1628(a,1),1323(a,1,2))]. 1630 T(x,K(1 / y,L(y,z,u))) = x. [para(59(a,1),1629(a,1,2,2,1))]. 1631 T(x,K(y \ 1,L(y,z,u))) = x. [para(1572(a,1),1630(a,1,2))]. 1632 T(K(x \ 1,L(x,y,z)),u) = K(x \ 1,L(x,y,z)). [hyper(33,a,1631,a)]. 1633 R(K(x \ 1,L(x,y,z)),z,y) = K(x \ 1,x). [para(1632(a,1),1585(a,1,1))]. 1634 K(x \ 1,L(x,y,z)) = K(x \ 1,x). [para(1633(a,1),272(a,1)),flip(a)]. 1638 ((x * ((y * K(z \ 1,z)) \ y)) * u) / (L(L(K(z,z \ 1),z \ 1,1 / (1 / z)),(1 / (1 / z)) * (z \ 1),y) * u) = R(x,(y * ((1 / (1 / z)) * (z \ 1))) \ y,u). [para(957(a,1),1080(a,1,1,1,2,1,2))]. 1639 R(x,(y * ((1 / (1 / z)) * (z \ 1))) \ y,u) = ((x * K(z,z \ 1)) * u) / (L(L(K(z,z \ 1),z \ 1,1 / (1 / z)),(1 / (1 / z)) * (z \ 1),y) * u). [para(1211(a,1),1638(a,1,1,1,2)),flip(a)]. 1641 R(x,(y * ((1 / (1 / z)) * (z \ 1))) \ y,u) = (K(z,z \ 1) * (x * u)) / (L(L(K(z,z \ 1),z \ 1,1 / (1 / z)),(1 / (1 / z)) * (z \ 1),y) * u). [para(1199(a,1),1639(a,2,1))]. 1642 R(x,(y * ((1 / (1 / z)) * (z \ 1))) \ y,u) = (K(z,z \ 1) * (x * u)) / (L(K(z,z \ 1),(1 / (1 / z)) * (z \ 1),y) * u). [para(1274(a,1),1641(a,2,2,1,1))]. 1643 R(x,(y * ((1 / (1 / z)) * (z \ 1))) \ y,u) = (K(z,z \ 1) * (x * u)) / (L(K(z,z \ 1),K(z \ 1,z),y) * u). [para(957(a,1),1642(a,2,2,1,2))]. 1645 R(x,(y * ((1 / (1 / z)) * (z \ 1))) \ y,u) = (K(z,z \ 1) * (x * u)) / (K(z,z \ 1) * u). [para(1216(a,1),1643(a,2,2,1))]. 1646 R(x,(y * ((1 / (1 / z)) * (z \ 1))) \ y,u) = K(z,z \ 1) * ((x * u) / (K(z,z \ 1) * u)). [para(1645(a,2),281(a,1))]. 1648 R(x,(y * K(z \ 1,z)) \ y,u) = K(z,z \ 1) * ((x * u) / (K(z,z \ 1) * u)). [para(957(a,1),1646(a,1,2,1,2))]. 1649 K(x,x \ 1) * ((y * z) / (K(x,x \ 1) * z)) = R(y,K(x,x \ 1),z). [para(1211(a,1),1648(a,1,2)),flip(a)]. 1650 R(R(x,y,K(z,z \ 1)),y * K(z,z \ 1),u) = R(R(x,y,u),K(z,z \ 1),y * u). [para(1649(a,1),1391(a,1)),flip(a)]. 1651 R(R(x,1 / y,K(z,z \ 1)),K(z,z \ 1) / y,u) = R(R(x,1 / y,u),K(z,z \ 1),(1 / y) * u). [para(1198(a,1),1650(a,1,2))]. 1652 R(R(x,1 / y,K(z \ 1,z)),K(z \ 1,(z \ 1) \ 1) / y,u) = R(R(x,1 / y,u),K(z \ 1,(z \ 1) \ 1),(1 / y) * u). [para(929(a,1),1651(a,1,1,3))]. 1653 R(R(x,1 / y,z),K(y \ 1,(y \ 1) \ 1),(1 / y) * z) = R(x,K(y \ 1,(y \ 1) \ 1) / y,z). [para(1456(a,1),1652(a,1,1)),flip(a)]. 1654 R(R(x,1 / y,z),K(y \ 1,(y \ 1) \ 1),(1 / y) * z) = R(x,K(y \ 1,y) / y,z). [para(929(a,1),1653(a,2,2,1))]. 1655 R(R(x,1 / y,z),K(y \ 1,(y \ 1) \ 1),(1 / y) * z) = R(x,y \ 1,z). [para(149(a,1),1654(a,2,2))]. 1656 R(R(x,1 / y,z),K(y \ 1,y),(1 / y) * z) = R(x,y \ 1,z). [para(929(a,1),1655(a,1,2))]. 1657 K((x \ (y \ z)) \ ((x \ (y \ z)) / ((1 / ((y * x) \ z)) \ 1)),x \ (y \ z)) = ((((y * x) \ z) \ (x \ (y \ z))) / (x \ (y \ z))) \ (((y * x) \ z) \ 1). [para(1426(a,1),784(a,1,1,2,2,1))]. 1658 ((((x * y) \ z) \ (y \ (x \ z))) / (y \ (x \ z))) \ (((x * y) \ z) \ 1) = K((y \ (x \ z)) \ ((y \ (x \ z)) / ((x * y) \ z)),y \ (x \ z)). [para(59(a,1),1657(a,1,1,2,2)),flip(a)]. 1660 ((((x * y) \ z) \ (y \ (x \ z))) / (y \ (x \ z))) \ (((x * y) \ z) \ 1) = K((y \ (x \ z)) \ (((x * y) \ z) \ (y \ (x \ z))),y \ (x \ z)). [para(1424(a,1),1658(a,2,1,2))]. 1661 ((((x * y) \ z) \ (y \ (x \ z))) / (y \ (x \ z))) \ (((x * y) \ z) \ 1) = K(((x * y) \ z) \ 1,y \ (x \ z)). [para(783(a,1),1660(a,2,1))]. 1662 (1 / ((x * y) \ z)) \ (((x * y) \ z) \ 1) = K(((x * y) \ z) \ 1,y \ (x \ z)). [para(1426(a,1),1661(a,1,1))]. 1663 K(((x * y) \ z) \ 1,(x * y) \ z) = K(((x * y) \ z) \ 1,y \ (x \ z)). [para(1662(a,1),888(a,1)),flip(a)]. 1664 K(((x * y) \ z) \ 1,y \ (x \ z)) = K(z \ (x * y),(x * y) \ z). [para(1663(a,1),1607(a,1))]. 1665 x \ ((y * z) * K(x \ (y * z),(y * z) \ x)) = T(x \ (y * z),z \ (y \ x)). [para(1664(a,1),1610(a,1,2,2))]. 1666 T(x \ (y * z),z \ (y \ x)) = ((x \ (y * z)) \ 1) \ 1. [para(1665(a,1),1609(a,1))]. 1667 T(L(x,y,z),(y * x) \ (z \ (z * y))) = (((z * y) \ (z * (y * x))) \ 1) \ 1. [para(26(a,2),1666(a,1,1))]. 1668 T(L(x,y,z),(y * x) \ y) = (((z * y) \ (z * (y * x))) \ 1) \ 1. [para(13(a,1),1667(a,1,2,2))]. 1669 T(L(x,y,z),(y * x) \ y) = (L(x,y,z) \ 1) \ 1. [para(26(a,2),1668(a,2,1,1))]. 1670 L(T(x,(y * x) \ y),y,z) = (L(x,y,z) \ 1) \ 1. [para(1669(a,1),38(a,2))]. 1671 L(T(x,x \ 1),y,z) = (L(x,y,z) \ 1) \ 1. [para(1436(a,1),1670(a,1,1))]. 1672 L(T(x,x \ 1),y,z) \ L(x,y,z) = K(L(x,y,z) \ 1,L(x,y,z)). [para(1671(a,2),1163(a,1,1))]. 1674 K(L(x,y,z) \ 1,L(x,y,z)) = K(x \ 1,L(x,y,z)). [para(1672(a,1),1559(a,1))]. 1675 L(K(x \ 1,x),y,z) = K(x \ 1,L(x,y,z)). [para(1674(a,1),1429(a,1)),flip(a)]. 1676 L(K(x \ 1,x),y,z) = K(x \ 1,x). [para(1675(a,2),1634(a,1))]. 1677 (x \ 1) * K(y \ 1,y) = x \ K(y \ 1,y). [para(1676(a,1),248(a,1,2)),flip(a)]. 1678 K(x \ 1,x) * (y * z) = y * (K(x \ 1,x) * z). [para(1676(a,1),1287(a,1,1))]. 1681 K(x \ 1,x) * ((y \ 1) * z) = (y \ K(x \ 1,x)) * z. [para(1677(a,1),1169(a,1,1)),flip(a)]. 1682 (x \ 1) \ (K(y,y \ 1) * z) = (x \ K(y \ 1,y)) \ z. [para(1677(a,1),1209(a,1,1)),flip(a)]. 1683 x \ (K(y \ 1,y) * z) = K(y \ 1,y) * (x \ z). [hyper(267,a,1678,a)]. 1685 (x * y) \ (x * (K(z \ 1,z) * (y * u))) = L(K(z \ 1,z) * u,y,x). [para(1678(a,2),26(a,2,2,2)),flip(a)]. 1686 (x * y) * K(z \ 1,z) = x * (K(z \ 1,z) * y). [para(1678(a,1),1133(a,1)),flip(a)]. 1688 (x * y) * K(z \ 1,L(z,u,w)) = x * (K(z \ 1,z) * y). [para(1634(a,2),1686(a,1,2))]. 1689 (x * y) * K(z,L(1 / z,u,w)) = x * (K((1 / z) \ 1,1 / z) * y). [para(59(a,1),1688(a,1,2,1))]. 1690 (x * y) * K(z,L(z \ 1,u,w)) = x * (K((1 / z) \ 1,1 / z) * y). [para(1165(a,1),1689(a,1,2))]. 1691 (x * y) * K(z,L(z \ 1,u,w)) = x * (K(z,1 / z) * y). [para(59(a,1),1690(a,2,2,1,1))]. 1692 (x * y) * K(z,L(z \ 1,u,w)) = x * (K(z,z \ 1) * y). [para(928(a,1),1691(a,2,2,1))]. 1693 K(x,L(x \ 1,y,z)) = K(x,x \ 1). [hyper(1076,a,1692,a)]. 1694 (x * y) * K(z,z \ 1) = x * (K(z,z \ 1) * y). [para(88(a,1),1692(a,1,2,2))]. 1695 R(x,y,K(z,z \ 1)) = x. [hyper(1201,a,1694,a)]. 1697 (x \ 1) * K(y,y \ 1) = x \ K(y,y \ 1). [para(1695(a,1),168(a,1,1)),flip(a)]. 1698 R(x,y,K(z \ 1,z)) = x. [para(929(a,1),1695(a,1,3))]. 1699 T(x,y * K(z,z \ 1)) = T(x,y). [para(1695(a,1),1271(a,1))]. 1700 x \ (K(y,y \ 1) * z) = (x \ z) * K(y,y \ 1). [para(1695(a,1),1200(a,1,1))]. 1703 R(x,y,(z \ 1) \ 1) = R(x,y,z). [para(1695(a,1),1588(a,1)),flip(a)]. 1705 (x * y) \ ((x * (y * z)) * K(u \ 1,u)) = L(z,y,x) * K(u \ 1,u). [para(1698(a,1),237(a,1,1))]. 1706 R(x,y,K(z \ 1,R(z,u,w))) = x. [para(915(a,2),1698(a,1,3))]. 1707 R(x,K(y \ 1,y),z) = x. [para(1698(a,1),1371(a,2))]. 1714 R(x,1 / y,z) = R(x,y \ 1,z). [para(1707(a,1),1656(a,1))]. 1715 T(x,y * T(z,z \ 1)) = T(x,y * z). [para(1474(a,1),1699(a,1,2))]. 1716 T(x,y * ((z \ 1) \ 1)) = T(x,y * z). [para(1476(a,1),1699(a,1,2))]. 1717 ((x * (y * T(y \ 1,z))) * ((z \ 1) \ 1)) / ((z \ 1) \ (y * T(y \ 1,z))) = R(x,y * T(y \ 1,z),z). [para(1703(a,1),1365(a,2))]. 1718 T(x,y) * T(K(z \ 1,R(z,u,w)),x * y) = y \ ((x * K(z \ 1,z)) * y). [para(1706(a,1),1401(a,1,1)),flip(a)]. 1719 R(1 / (1 / x),x \ 1,(1 / x) \ y) = ((1 / x) \ y) / y. [para(1714(a,1),161(a,1))]. 1720 (x \ 1) \ T(x \ 1,y * ((z \ 1) \ 1)) = x * T(x \ 1,y * z). [para(1716(a,1),1504(a,2,2))]. 1721 (x \ 1) \ (K(y \ 1,y) * z) = (x \ K(y,y \ 1)) \ z. [para(1697(a,1),1214(a,1,1)),flip(a)]. 1722 ((x \ 1) \ y) * K(z,z \ 1) = (x \ K(z \ 1,z)) \ y. [para(1700(a,1),1682(a,1))]. 1723 (x \ K(y,y \ 1)) \ 1 = (x \ 1) \ K(y \ 1,y). [para(12(a,1),1721(a,1,2)),flip(a)]. 1724 K(x \ 1,x) * ((y \ 1) \ z) = (y \ K(x,x \ 1)) \ z. [para(1721(a,1),1683(a,1)),flip(a)]. 1725 ((1 / x) \ y) \ (y * R(1 / (1 / x),x \ 1,(1 / x) \ y)) = K(y,((1 / x) \ y) / y). [para(1719(a,2),75(a,1,2,2))]. 1726 (x * y) \ (x * (K(z \ 1,z) * (y * u))) = L(u,y,x) * K(z \ 1,z). [para(1686(a,1),1705(a,1,2))]. 1727 L(K(x \ 1,x) * y,z,u) = L(y,z,u) * K(x \ 1,x). [para(1726(a,1),1685(a,1)),flip(a)]. 1728 L(K(x \ 1,x) * y,z,u) = K(x \ 1,x) * L(y,z,u). [para(1727(a,2),1133(a,2)),flip(a)]. 1729 T(x \ L(x * ((((x \ 1) \ 1) * y) / ((x \ 1) \ 1)),z,u),(x \ 1) \ 1) = (x \ 1) * L(K(x \ 1,x) * ((((x \ 1) \ 1) \ 1) \ y),z,u). [para(1728(a,2),1090(a,2,2))]. 1730 T(x,y) * T(K(z \ 1,R(z,u,w)),x * y) = T(x * K(z \ 1,z),y). [para(1718(a,2),30(a,2)),flip(a)]. 1731 T(x,y) * K(z \ 1,R(z,u,w)) = T(x * K(z \ 1,z),y). [para(1154(a,1),1730(a,1,2))]. 1732 T(x * K(y \ 1,y),z) = T(x,z) * K(y \ 1,y). [para(157(a,1),1731(a,1,2,2)),flip(a)]. 1734 T(K(x \ 1,x) * y,z) = T(y,z) * K(x \ 1,x). [para(1133(a,2),1732(a,1,1))]. 1735 T(K(x \ 1,x) * y,z) = K(x \ 1,x) * T(y,z). [para(1734(a,2),1133(a,2)),flip(a)]. 1736 K(x \ 1,x) * T(K(x,x \ 1) * y,z) = T(y,z). [para(448(a,1),1735(a,1,1)),flip(a)]. 1738 (x \ T(x * (y / x),z)) * x = T(y,z). [para(1736(a,1),846(a,1)),flip(a)]. 1739 (x \ T(x * y,z)) * x = T(y * x,z). [para(15(a,1),1738(a,1,1,2,1,2))]. 1740 T((x \ y) * x,z) = (x \ T(y,z)) * x. [para(56(a,1),1738(a,1,1,2,1)),flip(a)]. 1742 T(x * y,z) / y = y \ T(y * x,z). [hyper(70,a,1739,a)]. 1743 T((x \ (y / z)) * x,z) = (x \ (z \ y)) * x. [para(87(a,1),1740(a,2,1,2))]. 1744 R((x * y) / x,x,T(y,x)) = x \ T(x * y,y). [para(1742(a,1),622(a,2))]. 1745 x * (y \ T(y * (x \ z),x)) = ((x \ (z * y)) * x) / y. [para(1742(a,1),1539(a,1,2))]. 1746 ((x \ (y / z)) * x) * z = z * ((x \ (z \ y)) * x). [para(1743(a,1),85(a,1,2)),flip(a)]. 1747 L(x \ T(x * y,y),x,y) = (x * y) / x. [para(1744(a,1),650(a,1,1))]. 1748 (x * y) \ ((y * x) * x) = (y * x) / y. [para(1747(a,1),208(a,1)),flip(a)]. 1749 ((x \ (y / (z \ 1))) * x) * (z \ 1) = ((x \ (y * z)) * x) / z. [para(1745(a,1),737(a,2))]. 1750 (x \ 1) * ((y \ ((x \ 1) \ z)) * y) = ((y \ (z * x)) * y) / x. [para(1749(a,1),1746(a,1)),flip(a)]. 1751 ((1 / x) \ y) \ (y * R(1 / (1 / x),x \ 1,(1 / x) \ y)) = K(y,((x \ 1) \ y) / y). [para(1725(a,2),1343(a,1))]. 1752 T(x \ L(x * ((((x \ 1) \ 1) * y) / ((x \ 1) \ 1)),z,u),(x \ 1) \ 1) = (x \ 1) * L((((x \ 1) \ 1) \ K(x,x \ 1)) \ y,z,u). [para(1724(a,1),1729(a,2,2,1))]. 1753 T(x \ L(x * ((((x \ 1) \ 1) * y) / ((x \ 1) \ 1)),z,u),(x \ 1) \ 1) = (x \ 1) * L((x \ 1) \ y,z,u). [para(540(a,1),1752(a,2,2,1,1))]. 1754 T(x \ L(x * ((((x \ 1) \ 1) * y) / ((x \ 1) \ 1)),z,u),(x \ 1) \ 1) = x \ L(x * y,z,u). [para(1753(a,2),558(a,1))]. 1755 T(x \ L(x * ((x * y) / x),z,u),(x \ 1) \ 1) = x \ L(x * y,z,u). [para(1577(a,1),1754(a,1,1,2,1,2))]. 1756 T(x \ L(x * ((x * y) / x),z,u),x) = x \ L(x * y,z,u). [para(1755(a,1),1460(a,1)),flip(a)]. 1757 T(x \ 1,x) * L(T(x \ 1,x) \ y,z,u) = x \ L(x * y,z,u). [para(1756(a,1),832(a,1)),flip(a)]. 1758 T((1 / x) \ 1,1 / x) * L(T((1 / x) \ 1,1 / x) \ y,z,u) = x * L(x \ y,z,u). [para(1757(a,2),393(a,1))]. 1759 T((1 / (1 / x)) \ 1,1 / (1 / x)) * L(T((1 / (1 / x)) \ 1,1 / (1 / x)) \ y,z,u) = L(y * x,z,u) / x. [para(1758(a,2),782(a,1))]. 1760 T(1 / x,1 / (1 / x)) * L(T((1 / (1 / x)) \ 1,1 / (1 / x)) \ y,z,u) = L(y * x,z,u) / x. [para(59(a,1),1759(a,1,1,1))]. 1762 (x \ 1) * L(T((1 / (1 / x)) \ 1,1 / (1 / x)) \ y,z,u) = L(y * x,z,u) / x. [para(1605(a,1),1760(a,1,1))]. 1763 (x \ 1) * L(T(1 / x,1 / (1 / x)) \ y,z,u) = L(y * x,z,u) / x. [para(59(a,1),1762(a,1,2,1,1,1))]. 1766 (x \ 1) * L((x \ 1) \ y,z,u) = L(y * x,z,u) / x. [para(1605(a,1),1763(a,1,2,1,1))]. 1767 L(x * y,z,u) / y = y \ L(y * x,z,u). [para(1766(a,1),558(a,1))]. 1769 (x \ L(x * y,z,u)) * x = L(y * x,z,u). [para(1767(a,1),16(a,1,1))]. 1770 L((x \ y) * x,z,u) = (x \ L(y,z,u)) * x. [para(14(a,1),1769(a,1,1,2,1)),flip(a)]. 1771 L((x \ ((y \ z) \ u)) * x,y \ z,y) = (x \ (z \ (y * u))) * x. [para(200(a,1),1770(a,2,1,2))]. 1772 (x * (y \ z)) * L((z \ T(y,y \ z)) * z,y \ z,x) = (x * K(z \ y,z)) * z. [para(1770(a,2),1018(a,1,2))]. 1773 (x * y) * L((z \ (y \ ((z \ 1) \ 1))) * z,y,x) = (x * (y * T(y \ 1,z))) * ((z \ 1) \ 1). [para(1770(a,2),1624(a,1,2))]. 1774 (x \ 1) * ((y \ ((x \ 1) \ z)) * y) = x \ ((y \ (1 \ (x * z))) * y). [para(1771(a,1),248(a,1,2)),flip(a)]. 1775 (x \ 1) * ((y \ ((x \ 1) \ z)) * y) = x \ ((y \ (x * z)) * y). [para(47(a,1),1774(a,2,2,1,2))]. 1776 ((x \ (y * z)) * x) / z = z \ ((x \ (z * y)) * x). [para(1775(a,1),1750(a,1)),flip(a)]. 1777 x * ((y \ z) * ((z \ T(y,y \ z)) * z)) = (x * K(z \ y,z)) * z. [para(1772(a,1),76(a,1)),flip(a)]. 1778 (x * K(y \ z,y)) * y = x * (y * K(y \ z,y)). [para(1051(a,1),1777(a,1,2)),flip(a)]. 1779 x * (y * K(y \ (y * z),y)) = (x * K(z,y)) * y. [para(13(a,1),1778(a,1,1,2,1)),flip(a)]. 1780 (x * K(y,z)) * z = x * (z * K(y,z)). [para(13(a,1),1779(a,1,2,2,1)),flip(a)]. 1781 (x * y) / (y * K(z,y)) = x / K(z,y). [hyper(268,a,1780,a)]. 1782 (x * (y * K(z,y))) \ ((x * (y * K(z,y))) * y) = L(y,K(z,y),x). [para(1780(a,1),1052(a,1,1))]. 1783 L(x,K(y,x),z) = x. [para(1782(a,1),13(a,1))]. 1784 L(T(x,y),K(z,x),u) = T(x,y). [para(1783(a,1),38(a,2,1))]. 1785 (x * (y * T(y \ 1,z))) * ((z \ 1) \ 1) = x * (y * ((z \ (y \ ((z \ 1) \ 1))) * z)). [para(1773(a,1),76(a,1))]. 1786 (x * (y * T(y \ 1,z))) * ((z \ 1) \ 1) = x * ((z \ 1) \ (y * T(y \ 1,z))). [para(1366(a,1),1785(a,2,2))]. 1787 (x * ((y \ 1) \ (z * T(z \ 1,y)))) / ((y \ 1) \ (z * T(z \ 1,y))) = R(x,z * T(z \ 1,y),y). [para(1786(a,1),1717(a,1,1))]. 1788 R(x,y * T(y \ 1,z),z) = x. [para(1787(a,1),15(a,1))]. 1789 R(x,K(y,z),z) = x. [para(668(a,2),1788(a,1,2))]. 1790 (x * y) \ ((y * x) * x) = K(y,x) * x. [para(1789(a,1),235(a,1,1))]. 1791 (x * y) / x = K(x,y) * y. [para(1790(a,1),1748(a,1)),flip(a)]. 1792 K(x,y) = y \ ((x * y) / x). [hyper(1070,a,1791,a),flip(a)]. 1793 K(x,x \ y) * (x \ y) = y / x. [para(14(a,1),1791(a,1,1)),flip(a)]. 1794 ((x * y) / x) * (y \ z) = K(x,y) * z. [para(1791(a,2),273(a,1,1))]. 1795 L(x,y,(z * u) / z) = L(x,y,u). [para(1791(a,2),850(a,1,3))]. 1796 (x * y) / x = y * K(x,y). [para(1791(a,2),1047(a,1))]. 1798 T((((x * (y / z)) / x) * z) / y,y / z) = R(K(x,y / z),y / z,z). [para(1792(a,2),349(a,1,1)),flip(a)]. 1799 x * ((y * (x \ 1)) / y) = K(y,x \ 1). [para(1792(a,2),1073(a,1)),flip(a)]. 1800 (x \ y) * K(x,x \ y) = y / x. [para(14(a,1),1796(a,1,1)),flip(a)]. 1801 (x * K(y,x)) * y = y * x. [para(1796(a,1),16(a,1,1))]. 1802 x / (x / y) = y * K(x / y,y). [para(16(a,1),1796(a,1,1))]. 1803 T(x * K(y,x),y) = x. [para(1796(a,1),105(a,1,1))]. 1804 (x * y) / ((z * y) / z) = x / K(z,y). [para(1796(a,2),1781(a,1,2))]. 1805 K(x,y) * (y * x) = x * y. [para(1801(a,1),1049(a,1)),flip(a)]. 1811 L(x,y,z / u) = L(x,y,u \ z). [para(1793(a,1),850(a,1,3))]. 1812 L(x,y,T(z,u)) = L(x,y,z). [para(106(a,1),1795(a,1,3)),flip(a)]. 1813 L(x,y,(z \ u) \ u) = L(x,y,z). [para(86(a,1),1812(a,1,3))]. 1814 L(x \ y,x,x \ y) = T(y / x,y). [para(1811(a,1),310(a,1))]. 1816 ((x * y) / x) * z = y * (K(x,y) * z). [para(1794(a,1),567(a,1,2)),flip(a)]. 1817 T(x,y) = K(x,y) * x. [para(1794(a,1),578(a,2))]. 1818 K(x,y) = x \ T(x,y). [hyper(1509,a,1817,a),flip(a)]. 1820 (x * K(y,z)) \ (x * T(y,z)) = L(y,K(y,z),x). [para(1817(a,2),26(a,2,2,2)),flip(a)]. 1821 K(x,y) * (x * z) = T(x,y) * z. [para(1817(a,2),197(a,1,1)),flip(a)]. 1822 T(x,y) * (x \ z) = K(x,y) * z. [para(1817(a,2),273(a,1,1))]. 1825 T(x,y) = x * K(x,y). [para(1818(a,2),14(a,1,2)),flip(a)]. 1826 (x * y) \ (x * T(y,z)) = L(K(y,z),y,x). [para(1818(a,2),78(a,1,1)),flip(a)]. 1827 (x * y) * T(K(y,x),z) = x * (y * T(K(y,x),z)). [para(1818(a,2),340(a,1,2,2,1)),flip(a)]. 1828 K(x,y) = T(x,y) * (x \ 1). [para(1818(a,2),424(a,2)),flip(a)]. 1829 x \ T(x,y * (z \ 1)) = K(x,y / z). [para(1818(a,1),919(a,1))]. 1830 T(x,K(x,y)) = x. [para(1818(a,2),1508(a,1,2))]. 1831 x * T(x \ 1,y) = K(x \ 1,y). [para(1818(a,2),1504(a,1)),flip(a)]. 1832 T(K(x,y),x) = K(x,y). [hyper(33,a,1830,a)]. 1833 (x * K(x,y)) / x = K(x,y). [para(1830(a,1),96(a,1,2))]. 1834 T(x,y) != x * z | K(x,y) = z. [para(1825(a,2),19(a,1))]. 1840 T(x,L(y,z,y)) = x * K(x,y). [para(950(a,1),1825(a,2,2))]. 1842 R(K(x,y),x,(x * K(x,y)) \ z) \ z = x * ((x * K(x,y)) \ z). [para(1833(a,1),258(a,1,1,1))]. 1845 T(x,L(y,z,y)) = T(x,y). [para(1840(a,2),1825(a,2)),flip(a)]. 1846 T(x,T(y / z,y)) = T(x,z \ y). [para(1814(a,1),1845(a,1,2))]. 1847 K(R(x,y,z),u) * (R(x,y,z) * w) = R(T(x,u),y,z) * w. [para(40(a,2),1821(a,2,1))]. 1848 K(x,y) * (z * x) = T(x,y) * T(z,x). [para(85(a,1),1821(a,1,2))]. 1851 K(x,y) * ((x * z) / u) = (T(x,y) * z) / u. [para(1821(a,1),281(a,1,1)),flip(a)]. 1852 T(x,y) * (R(x,z,u) * (x \ w)) = K(x,y) * (R(x,z,u) * w). [para(478(a,1),1821(a,1,2)),flip(a)]. 1853 x * (K(x,y) * z) = T(x,y) * z. [para(1822(a,1),494(a,1,2))]. 1854 K(x,y) * (T(x,y) \ z) = x \ z. [para(1822(a,1),499(a,1))]. 1855 K(x \ 1,y) / x = T(1 / x,y). [para(1831(a,1),176(a,1,1))]. 1856 x * T(x \ y,z) = y * K((y \ x) \ 1,z). [para(1831(a,1),492(a,1,2)),flip(a)]. 1858 (x * T(x \ y,z)) / y = K((x / y) \ 1,z). [para(1831(a,1),628(a,1)),flip(a)]. 1860 K(x \ (x / T(y,z)),x) = T(K(y \ 1,x),z). [para(1831(a,1),749(a,1,1)),flip(a)]. 1862 L(x * T(x \ 1,y),z,u) = K(L(x,z,u) \ 1,y). [para(1831(a,1),1009(a,1)),flip(a)]. 1865 K(x / y,z) * x = y * T(y \ x,z). [hyper(17,a,515,a,b,1853,a)]. 1868 x * R(K(x,y) * z,u,w) = T(x,y) * R(z,u,w). [para(458(a,2),1853(a,1,2))]. 1869 (x * (K(R(x,y,z),u) * w)) * R(T(x,K(R(x,y,z),u) * w),y,z) = (T(R(x,y,z),u) * w) * T(x,K(R(x,y,z),u) * w). [para(1853(a,1),764(a,1,1)),flip(a)]. 1873 K(x,y) * ((T(x,y) \ z) * u) = (x \ z) * u. [para(1854(a,1),197(a,1,1)),flip(a)]. 1874 x \ (y * ((z * (y \ x)) / z)) = K(z,(x \ y) \ 1). [para(1799(a,1),777(a,1)),flip(a)]. 1875 (x * ((y * (x \ z)) / y)) / z = K(y,(x / z) \ 1). [para(1799(a,1),813(a,1)),flip(a)]. 1876 T(x * ((y * (x \ 1)) / y),z) = K(y,T(x,z) \ 1). [para(1799(a,1),837(a,1)),flip(a)]. 1877 (x / ((y * z) / y)) * z = x / K(y,z). [para(1804(a,1),627(a,1)),flip(a)]. 1878 x \ (((y * x) / y) * z) = K(y,x) * z. [hyper(66,a,1816,a(flip))]. 1879 (x \ y) * (K(x,x \ y) * z) = (y / x) * z. [para(14(a,1),1816(a,1,1,1)),flip(a)]. 1880 (x * ((y * z) / y)) \ (z * (K(y,z) * x)) = K((y * z) / y,x). [para(1816(a,1),24(a,2,2)),flip(a)]. 1881 R(x \ y,z,u) * (K(x,R(x \ y,z,u)) * w) = R(y / x,z,u) * w. [para(321(a,1),1816(a,1,1)),flip(a)]. 1882 (x * K(y,x)) * z = x * (K(y,x) * z). [para(1796(a,1),1816(a,1,1))]. 1884 x * (T(y,x) * (y \ z)) = ((y * x) / y) * z. [para(1822(a,2),1816(a,2,2)),flip(a)]. 1885 T(x,y) * T(y,x) = x * y. [para(1848(a,1),1805(a,1))]. 1886 T(x,y) \ (x * y) = T(y,x). [hyper(66,a,1885,a)]. 1887 K(x,y) * T(y,x) = y. [hyper(17,a,1853,a,b,1885,a(flip)),flip(a)]. 1888 K(x,y) = T(y,x) \ y. [hyper(1065,a,1887,a),flip(a)]. 1889 L(T(x,y),K(y,x),z) = (z * K(y,x)) \ (z * x). [para(1887(a,1),26(a,2,2,2))]. 1891 K(x,y) * (T(y,x) * z) = y * z. [para(1887(a,1),197(a,1,1)),flip(a)]. 1894 T(x,y) * K(y,x) = x. [para(1887(a,1),1053(a,2))]. 1898 K(x,y) = y * (T(y,x) \ 1). [para(1888(a,2),505(a,2)),flip(a)]. 1899 K(x,y) / y = 1 / T(y,x). [para(1888(a,2),1066(a,1,1))]. 1900 (x \ 1) * K(y,x) = T(x,y) \ 1. [para(1888(a,2),1545(a,1,2))]. 1901 K(x,y / (z * K(u,y))) = K(x,T(y,u) / z). [para(1894(a,1),917(a,1,2,1))]. 1902 T(x,y) = (x \ (y * x)) \ (y * x). [para(30(a,1),1886(a,1,1)),flip(a)]. 1903 T(x,T(y,x)) = T(x,y). [para(1886(a,1),113(a,1)),flip(a)]. 1904 T(x,y / x) = T(x,x \ y). [para(87(a,1),1903(a,1,2)),flip(a)]. 1905 T(x,y) * R(T(y,x),z,u) = R(y,z,u) * T(x,y). [para(1903(a,1),116(a,1,2,1))]. 1906 T(x,x / y) = T(x,y \ x). [para(1903(a,1),1846(a,1))]. 1907 T(x,y) = (K(y,x) / x) \ 1. [para(1899(a,2),59(a,1,1)),flip(a)]. 1911 T(x,(y \ 1) \ x) = T(x,y * x). [para(1906(a,1),645(a,1))]. 1912 K(x,y) * (z * T(y,x)) = y * T(z,T(y,x)). [para(85(a,1),1891(a,1,2))]. 1914 (x * ((y * z) / y)) / K(y,z) = x * z. [para(15(a,1),1877(a,1,1)),flip(a)]. 1915 K(x,y) * (((x * y) / x) \ z) = y \ z. [para(14(a,1),1878(a,1,2)),flip(a)]. 1917 L(x,K(y,z),z) = x. [hyper(192,a,1882,a)]. 1918 K(x,y) * (y * z) = y * (K(x,y) * z). [para(1882(a,1),1049(a,1)),flip(a)]. 1919 a(x,K(y,x),z) = 1. [hyper(32,a,1917,a)]. 1920 a(R(x,y,z),K(u,x),w) = 1. [para(915(a,1),1919(a,1,2))]. 1923 (K(x,y) * ((R(y,z,u) * K(x,y)) \ w)) * a(R(y,z,u),K(x,y),(R(y,z,u) * K(x,y)) \ w) = R(R(y,z,u),K(x,y) * ((R(y,z,u) * K(x,y)) \ w),1) \ w. [para(1920(a,1),638(a,1,1,3)),flip(a)]. 1924 (x * (y * K(z,y))) / K(z,y) = x * y. [para(1796(a,1),1914(a,1,1,2))]. 1925 (x \ y) / (((z * x) / z) \ y) = K(z,x). [hyper(70,a,1915,a)]. 1928 T(x,y) * (K(y,x) * z) = x * z. [hyper(17,a,1891,a,b,1918,a),flip(a)]. 1929 (x * (K(y,x) * z)) * u = K(y,x) * ((x * z) * u). [para(1918(a,1),197(a,1,1))]. 1930 K(x,y) * (K(y,x) * z) = z. [hyper(17,a,1853,a(flip),b,1928,a)]. 1931 (x * y) / T(T(x,z),K(z,x) * y) = K(z,x) * y. [para(1928(a,1),96(a,1,1))]. 1932 (x * y) \ ((K(x \ z,x) * y) * ((x \ z) \ z)) = K(K(x \ z,x) * y,(x \ z) \ z). [para(1928(a,1),442(a,1,1))]. 1933 K(x,y) * ((K(y,x) * z) * u) = z * u. [hyper(274,a,1930,a),flip(a)]. 1934 K(x,y) * (z * K(y,x)) = T(z,K(y,x)). [hyper(109,a,1930,a),flip(a)]. 1935 K(x,y) \ 1 = K(y,x). [hyper(99,a,1930,a),flip(a)]. 1936 x / (K(y,z) * x) = K(z,y). [hyper(70,a,1930,a)]. 1937 K(x,y) \ z = K(y,x) * z. [hyper(66,a,1930,a)]. 1938 K(x,y) * K(y,x) = 1. [hyper(63,a,1930,a),flip(a)]. 1939 ((x * y) / x) \ z = K(y,x) * (y \ z). [hyper(17,a,1915,a,b,1930,a),flip(a)]. 1940 K(x \ y,x) * (y / x) = x \ y. [hyper(17,a,1793,a,b,1930,a)]. 1941 K(x,y) * T(K(y,x),z) = K(K(y,x),z). [hyper(17,a,1825,a(flip),b,1930,a)]. 1943 (K(x,y) * z) \ u = z \ (K(y,x) * u). [para(1930(a,1),206(a,1,1)),flip(a)]. 1944 x * K(y,z) != 1 | K(z,y) = x. [para(1935(a,1),69(a,1,2)),flip(b)]. 1946 (K(x,y) * z) \ 1 = z \ K(y,x). [para(1935(a,1),250(a,2,2))]. 1947 (x * y) \ ((y * x) * T(K(x,y),z)) = K(y,x) * T(K(x,y),z). [para(1935(a,1),759(a,2,2,1))]. 1948 (x * K(y,x)) \ x = K(x,y). [para(1935(a,1),1623(a,2))]. 1949 T(K(x,y),z) * K(y,x) = K(K(x,y),z). [para(1935(a,1),1828(a,2,2)),flip(a)]. 1951 K(L(x,y,x),z) = u / (K(z,x) * u). [para(950(a,1),1936(a,1,2,1)),flip(a)]. 1954 K(x,y) = ((y * x) / y) \ x. [para(1796(a,2),1948(a,1,1)),flip(a)]. 1956 K(T(x,y),y) = x \ T(x,y). [para(106(a,1),1954(a,2,1))]. 1957 ((x * y) / x) \ 1 = y \ K(y,x). [para(1954(a,2),575(a,1,2)),flip(a)]. 1958 K(T(x,y),y) = K(x,y). [para(1956(a,2),1818(a,2)),flip(a)]. 1959 K(x / y,y) = K(y \ x,y). [para(87(a,1),1958(a,1,1)),flip(a)]. 1961 K(x \ (y * T(x,z)),x) = K((y / x) * T(x,z),x). [para(596(a,1),1958(a,1,1))]. 1962 K(T(x,y),y) \ 1 = K(y,x). [para(1958(a,2),1935(a,1,1))]. 1963 x / (x / y) = y * K(y \ x,y). [para(1959(a,1),1802(a,2,2))]. 1964 K(x,T(y,x)) = K(x,y). [para(1962(a,1),1935(a,1)),flip(a)]. 1965 K(x,y / x) = K(x,x \ y). [para(87(a,1),1964(a,1,2)),flip(a)]. 1966 K(x,x / y) = K(x,y \ x). [para(1964(a,1),941(a,1))]. 1967 ((T(x,y * z) * y) * z) \ ((x * y) * z) = K(y * z,x). [para(1964(a,1),927(a,2))]. 1968 x * K(y,y \ x) = y * (x / y). [para(1965(a,1),137(a,1,2))]. 1969 x \ T(x,y * (x \ 1)) = K(x,x \ y). [para(1965(a,1),1829(a,2))]. 1970 K(x,x * (y \ 1)) = K(x,y \ x). [para(1966(a,1),919(a,2))]. 1971 K(x \ y,x) * ((y / x) * z) = (x \ y) * z. [para(1940(a,1),197(a,1,1)),flip(a)]. 1975 (x / (y \ 1)) \ K(y,y \ 1) = (x / (1 / y)) \ 1. [para(1457(a,1),1946(a,1,1)),flip(a)]. 1976 (x \ y) \ K(x \ y,x) = (y / x) \ 1. [para(1793(a,1),1946(a,1,1)),flip(a)]. 1980 (x * (y / x)) \ (y * (K(x,x \ y) * z)) = L(z,K(x,x \ y),y). [para(1968(a,1),26(a,2,1)),flip(a)]. 1981 K(L(x,y,x),z) = K(x,z). [para(1951(a,2),1936(a,1))]. 1982 (x * y) * K(z,y) = x * (y * K(z,y)). [para(1924(a,1),16(a,1,1))]. 1983 (x \ (K(y \ 1,y) * z)) / (((u * (x * K(y,y \ 1))) / u) \ z) = K(u,x * K(y,y \ 1)). [para(1214(a,1),1925(a,1,1))]. 1984 K(x \ y,x) * ((x \ y) \ z) = (y / x) \ z. [para(14(a,1),1939(a,1,1,1)),flip(a)]. 1985 (x * (K(y,x) * z)) \ u = (x * z) \ (K(x,y) * u). [para(1918(a,1),1943(a,1,1))]. 1986 K(x \ 1,(x \ 1) \ y) = x * T(x \ 1,y * x). [para(1969(a,1),1720(a,1))]. 1988 L(K(x,y),y,z) = K(x,y). [hyper(192,a,1982,a)]. 1991 x * T(x \ y,z) != y * u | K((y \ x) \ 1,z) = u. [para(1856(a,2),19(a,1))]. 1992 T(x,y) * (x \ z) = z * K((z \ (x \ z)) \ 1,y). [para(1856(a,1),174(a,1)),flip(a)]. 1993 K((x / y) \ 1,z) * y = x * T(x \ y,z). [para(1858(a,1),16(a,1,1))]. 1994 (x * K((x \ y) \ 1,z)) / x = K((y / x) \ 1,z). [para(1856(a,1),1858(a,1,1))]. 1995 ((x / y) * z) / (K(y,y \ x) * z) = y \ x. [hyper(70,a,1879,a)]. 1997 x * (T(y,z) * (y \ T(y,x))) = ((y * x) / y) * T(y,z). [para(516(a,1),1884(a,1,2))]. 2001 K((x / y) \ 1,z) = K(y / x,z). [hyper(18,a,1865,a,b,1993,a)]. 2003 K((x / (y * x)) \ 1,z) * (y * x) = T(y,z) * x. [para(1993(a,2),170(a,1))]. 2005 K(x / (y * x),z) = K(y \ 1,z). [para(15(a,1),2001(a,1,1,1)),flip(a)]. 2006 K((x * y) / ((z * x) * y),u) = K(R(z,x,y) \ 1,u). [para(28(a,2),2001(a,1,1,1)),flip(a)]. 2009 (K(x,x \ y) * z) * K((K(x,x \ y) * z) \ ((y / x) * z),K(x,x \ y) * z) = ((y / x) * z) / (x \ y). [para(1995(a,1),1963(a,1,2)),flip(a)]. 2010 (x * K(y,z)) \ (x * z) = T(z,y). [para(1889(a,1),1784(a,1))]. 2011 (x * K(y,z)) * T(z,y) = x * z. [para(2010(a,1),14(a,1,2))]. 2012 (x / y) * K(z,y) = x / T(y,z). [para(2010(a,1),148(a,1,2)),flip(a)]. 2014 (x * T(y,z)) * K(z,y) = x * y. [hyper(18,a,595,a(flip),b,2011,a)]. 2015 (x * K(y \ z,y)) * ((y \ z) \ z) = x * y. [para(86(a,1),2011(a,1,2))]. 2016 (x * y) / T(T(x,y),z) = y * K(z,T(x,y)). [para(96(a,1),2012(a,1,1)),flip(a)]. 2019 ((x / y) * T(y,z)) \ x = K(z,y). [hyper(17,a,146,a(flip),b,2014,a),flip(a)]. 2020 (x * T(x \ y,z)) \ y = K(z,x \ y). [para(57(a,1),2019(a,1,1,1))]. 2021 (x * (y * T(y \ (x \ z),u))) \ z = K(u,(x * y) \ z). [para(339(a,1),2020(a,1,1))]. 2022 (K(x \ 1,x) * y) * ((x \ 1) \ 1) = y * x. [para(1133(a,2),2015(a,1,1))]. 2024 L(K(x \ 1,y),z,u) = K(L(x,z,u) \ 1,y). [para(1831(a,1),1862(a,1,1))]. 2025 (x * y) * K(L(z,y,x) \ 1,u) = x * (y * K(z \ 1,u)). [para(2024(a,1),76(a,1,2))]. 2026 K(L(x \ 1,y,z) \ 1,u) = L(K(x,u),y,z). [para(1573(a,1),2024(a,1,1)),flip(a)]. 2028 K(L(x,y,z) \ 1,x) = K(x \ 1,L(x,y,z)). [para(2024(a,1),1675(a,1))]. 2029 T(x,y) * R(T(x,y) \ z,u,w) = x * R(x \ z,u,w). [para(1854(a,1),1868(a,1,2,1)),flip(a)]. 2030 T(x,y) * R(T(y,x),z,u) = x * R(y,z,u). [para(1887(a,1),1868(a,1,2,1)),flip(a)]. 2031 R((x * ((y * (x \ z)) / y)) / z,u,w) * z = z * R(K(y,(z \ x) \ 1),u,w). [para(1874(a,1),264(a,2,2,1))]. 2032 (x * y) \ ((x * (z \ y)) * ((u * L(T(z,z \ y),z \ y,x)) / u)) = K(u,((x * y) \ (x * (z \ y))) \ 1). [para(144(a,2),1874(a,1,2,2,1,2))]. 2033 x * (y * R(y \ (x \ (z * ((u * (z \ (x * y))) / u))),w,v5)) = (x * y) * R(K(u,((x * y) \ z) \ 1),w,v5). [para(1874(a,1),662(a,1,2,1)),flip(a)]. 2034 K(x,T(y,z) \ 1) = T(K(x,y \ 1),z). [para(1799(a,1),1876(a,1,1)),flip(a)]. 2035 K(x,T(1 / y,z) \ 1) = T(K(x,y),z). [para(59(a,1),2034(a,2,1,2))]. 2036 K(x,T(y \ 1,z) \ 1) = T(K(x,y),z). [para(929(a,1),2034(a,2,1))]. 2037 R(x,y,z) * T(u,x) = u * R(x,y,z). [para(1905(a,1),2030(a,1))]. 2038 T(x / R(y,z,u),y) = R(y,z,u) \ x. [hyper(177,a,2037,a)]. 2039 T(x,R(y,z,u)) = T(x,y). [hyper(165,a,2037,a),flip(a)]. 2041 (T(x,x * y) * y) * R(T(x,y),z,u) = R(T(x,y),z,u) * (x * y). [para(377(a,1),2037(a,1,2)),flip(a)]. 2042 x * R(y,x,y) = T(y * x,y). [para(2037(a,1),483(a,1))]. 2045 T(x,(y * z) / (u * z)) = T(x,y / u). [para(82(a,1),2039(a,1,2))]. 2046 T(x,y * (z \ 1)) = T(x,y / z). [para(224(a,1),2039(a,1,2))]. 2047 T(x,R(y,z,u)) \ x = K(y,x). [para(2039(a,2),1888(a,2,1)),flip(a)]. 2048 K(R(x,y,z),u) = K(x,u). [para(2047(a,1),1888(a,2))]. 2049 K((x * y) / (z * y),u) = K(x / z,u). [para(82(a,1),2048(a,1,1))]. 2050 K(R(x,y,z),u) * x = T(x,u). [para(2048(a,2),1817(a,2,1)),flip(a)]. 2051 R(x,y,z) * (u / R(x,y,z)) = u * K(x,R(x,y,z) \ u). [para(2048(a,1),1968(a,1,2)),flip(a)]. 2052 T(x,y * T(z,z \ 1)) = T(x,y / (z \ 1)). [para(86(a,2),2046(a,1,2,2))]. 2053 (x / R(y,z,u)) * y = y * (R(y,z,u) \ x). [para(2038(a,1),85(a,1,2)),flip(a)]. 2054 T(x,x * T(y,y \ 1)) = T(x,(y \ 1) \ x). [para(2052(a,2),1906(a,1))]. 2055 ((1 / x) * (R(1 / x,y,z) \ u)) * x = R(u / R(1 / x,y,z),x \ 1,x). [para(2053(a,1),1483(a,1,1))]. 2056 T(x,(y \ 1) \ x) = T(x,x * y). [para(2054(a,1),1715(a,1))]. 2057 T(x,y * x) = T(x,x * y). [para(2056(a,1),1911(a,1)),flip(a)]. 2058 T(x,(x \ y) * x) = T(x,y). [para(14(a,1),2057(a,2,2))]. 2059 T(x,x * (y / x)) = T(x,y). [para(16(a,1),2057(a,1,2)),flip(a)]. 2060 R(T(x,y),x \ y,x) = T(x,x \ y). [para(2058(a,1),406(a,1,1))]. 2061 L(T(x,y / x),y / x,x) = T(x,y). [para(2059(a,1),293(a,2))]. 2062 R(T(T(x,y),z),x \ y,x) = T(T(x,x \ y),z). [para(2060(a,1),40(a,2,1))]. 2063 L(T(x,x \ y),y / x,x) = T(x,y). [para(1904(a,1),2061(a,1,1))]. 2064 L(T(x,x \ y),y / x,(x \ z) \ z) = T(x,y). [para(2063(a,1),1813(a,2))]. 2065 K(x,L(T(T(y,y \ z),u),w,v5)) = K(x,L(T(T(y,z),u),w,v5)). [para(2062(a,1),916(a,1,2,1))]. 2066 L((x \ y) \ y,y / x,(x \ z) \ z) = T(x,y). [para(86(a,1),2064(a,1,1))]. 2067 K((x \ y) \ y,z) = K(T(x,y),z). [para(2066(a,1),1981(a,1,1)),flip(a)]. 2068 (x * (K(y,x) * (z * u))) \ (K(y,x) * ((x * z) * u)) = a(x,K(y,x) * z,u). [para(1929(a,1),276(a,1,2))]. 2069 ((x / (y \ 1)) \ 1) \ K(y \ 1,y) = ((x / (1 / y)) \ 1) \ 1. [para(1975(a,1),1723(a,1,1)),flip(a)]. 2070 x * K((x \ (y \ x)) \ 1,z) = K(y,z) * x. [para(1992(a,1),1822(a,1))]. 2071 K((x \ (y \ x)) \ 1,z) = T(K(y,z),x). [hyper(109,a,2070,a),flip(a)]. 2072 ((K(x,y) * z) * u) / (z * (K((z \ (x \ z)) \ 1,y) * u)) = a(z,K((z \ (x \ z)) \ 1,y),u). [para(2070(a,1),1246(a,2,1,1)),flip(a)]. 2073 (x * K(y \ 1,z)) / x = K(((x * y) / x) \ 1,z). [para(13(a,1),1994(a,1,1,2,1,1))]. 2074 K((x / (y * x)) \ 1,z) * (y * x) != u * x | T(y,z) = u. [para(2003(a,2),20(a,1))]. 2076 K(R(x,y,z) \ 1,u) = K(y / (x * y),u). [para(2006(a,1),2049(a,1))]. 2077 K(R(x,y,z) \ 1,u) = K(x \ 1,u). [para(2076(a,2),2005(a,1))]. 2081 ((T(R(x,y,z),u * T(x,u)) * u) * T(x,u)) \ ((x * u) * R(T(x,u),y,z)) = K(u * T(x,u),R(x,y,z)). [para(764(a,1),1967(a,1,2))]. 2082 ((x * y) / x) * T(x,z) = y * (K(x,z) * T(x,y)). [para(1822(a,1),1997(a,1,2)),flip(a)]. 2083 (x * (y \ ((z \ (y * (x \ u))) * z))) \ u = K(z,(x * (y \ z)) \ u). [para(371(a,1),2021(a,1,1,2))]. 2084 (x * (((y \ ((x \ z) * u)) * y) / u)) \ z = K(y,(x * (y / u)) \ z). [para(629(a,1),2021(a,1,1,2))]. 2085 T(x,y) * (z * R(z \ (T(x,y) \ u),w,v5)) = z * (T(x,z) * R(T(x,z) \ (z \ u),w,v5)). [para(2029(a,1),1021(a,1,2)),flip(a)]. 2086 ((x \ y) \ y) * (z * R(z \ (T(x,x \ y) \ (u * z)),w,v5)) = (x * R(x \ u,w,v5)) * z. [para(2029(a,1),707(a,2,1))]. 2088 K(x,y) * (R(x,z,u) * w) = R(T(x,y),z,u) * w. [para(2048(a,1),1847(a,1,1))]. 2089 T(x,y) * (R(x,z,u) * w) = x * (R(T(x,y),z,u) * w). [para(2088(a,1),1853(a,1,2)),flip(a)]. 2091 (x * (R(T(x,y),z,u) * y)) \ ((x * y) * R(T(x,y),z,u)) = K(R(x,z,u) * y,T(x,y)). [para(2089(a,1),765(a,1,1))]. 2092 (x * y) * z != x * (y * K(u \ 1,w)) | K(L(u,y,x) \ 1,w) = z. [para(2025(a,1),19(a,1)),flip(a)]. 2093 T(x,y) * (R(x,z,u) * (x \ w)) = R(T(x,y),z,u) * w. [para(1852(a,2),2088(a,1))]. 2094 R(T(x,y),z,u) * (x * w) = T(x,y) * (R(x,z,u) * w). [para(13(a,1),2093(a,1,2,2)),flip(a)]. 2095 (x * y) \ (y * (x * T(K(x,y),z))) = K(y,x) * T(K(x,y),z). [para(1827(a,1),1947(a,1,2))]. 2096 x * ((x * K(x,y)) \ z) = K(x,y) \ z. [para(272(a,1),1842(a,1,1)),flip(a)]. 2097 (x * K(x,y)) \ z = x \ (K(x,y) \ z). [hyper(66,a,2096,a),flip(a)]. 2099 (x \ 1) \ (K(x \ 1,y) \ z) = (x \ K(x \ 1,y)) \ z. [para(1517(a,1),2097(a,1,1)),flip(a)]. 2100 (x \ K(x \ 1,y)) \ 1 = (x \ 1) \ K(y,x \ 1). [para(1935(a,1),2099(a,1,2)),flip(a)]. 2101 L(K(x \ y,x) * z,K(x,x \ y),y) = (x * (y / x)) \ (y * z). [para(1930(a,1),1980(a,1,2,2)),flip(a)]. 2102 (T(x,x * y) * y) * R(T(x,y),z,u) = T(x,y) * (R(x,z,u) * y). [para(2041(a,2),2094(a,1))]. 2103 (x * (y \ ((z \ (y * (x \ u))) * z))) \ u = K(z,(x * (z / y)) \ u). [para(1776(a,1),2084(a,1,1,2))]. 2104 (T(x,x * y) * y) * R(T(x,y),z,u) = x * (R(T(x,y),z,u) * y). [para(2102(a,2),2089(a,1))]. 2105 K(x,(y * (x / z)) \ u) = K(x,(y * (z \ x)) \ u). [para(2103(a,1),2083(a,1))]. 2106 T((x * ((y * (x \ z)) / y)) / z,z / x) = R(K(y,z / x),z / x,x). [para(326(a,1),1798(a,1,1,1))]. 2107 R(x \ y,z,u) * (K(x,x \ y) * w) = R(y / x,z,u) * w. [para(915(a,1),1881(a,1,2,1))]. 2110 (R(x / y,z,u) * w) / R(y \ x,z,u) = (K(y,y \ x) * w) * K(R(y \ x,z,u),K(y,y \ x) * w). [para(2107(a,1),1796(a,1,1))]. 2112 T(K(x,(y / z) \ 1),z / y) = R(K(x,z / y),z / y,y). [para(1875(a,1),2106(a,1,1))]. 2113 R(K(x,y / z),y / z,z) = K(x,T(z / y,y / z) \ 1). [para(2112(a,1),2034(a,2)),flip(a)]. 2114 R(K(x,y / z),y / z,z) = K(x,T((z / y) \ 1,y \ z)). [para(1538(a,1),2113(a,2,2))]. 2115 R(K(x,y / z),y / z,z) = K(x,(z / y) \ 1). [para(2114(a,2),1532(a,1))]. 2116 K(x,(y / z) \ 1) = K(x,z / y). [para(2115(a,1),272(a,1))]. 2117 K(x,y / (z * y)) = K(x,z \ 1). [para(15(a,1),2116(a,1,2,1)),flip(a)]. 2118 K(x,(y * z) / ((u * y) * z)) = K(x,R(u,y,z) \ 1). [para(28(a,2),2116(a,1,2,1)),flip(a)]. 2119 K(x,(y \ z) / z) = K(x,y \ 1). [para(57(a,1),2116(a,1,2,1)),flip(a)]. 2121 K(x,T(1 / y,z) \ 1) = K(x,y / K(y \ 1,z)). [para(1855(a,1),2116(a,1,2,1))]. 2122 (x * ((y * (x \ z)) / y)) / z = K(y,z / x). [para(2116(a,1),1875(a,2))]. 2123 K((x / (y * x)) \ 1,z / (u * z)) * (y * x) = T(y,u \ 1) * x. [para(2117(a,2),2003(a,1,1))]. 2124 K(x,y / K(y \ 1,z)) = T(K(x,y),z). [para(2121(a,1),2035(a,1))]. 2125 K(x,R(y,z,u) \ 1) = K(x,z / (y * z)). [para(2118(a,1),917(a,1))]. 2127 K(x,R(y,z,u) \ 1) = K(x,y \ 1). [para(2125(a,2),2117(a,1))]. 2129 T(x,y / (z * y)) = T(x,z \ 1). [hyper(2074,a,2123,a)]. 2132 T(x,(y \ z) / z) = T(x,y \ 1). [para(14(a,1),2129(a,1,2,2))]. 2133 T(x,(y * z) / ((u * y) * z)) = T(x,R(u,y,z) \ 1). [para(81(a,1),2129(a,1,2,2))]. 2134 x \ T(y,x \ 1) = y * ((x \ y) / y). [para(2129(a,1),587(a,1,2))]. 2136 T(x,x \ (y \ x)) = T(x,y \ 1). [para(2132(a,1),1904(a,1)),flip(a)]. 2137 K(x,T(y,z \ 1)) = K(x,T(y,z \ y)). [para(2136(a,1),924(a,1,2))]. 2138 x * R(1 / y,y,y \ x) = y \ T(x,y \ 1). [para(161(a,2),2134(a,2,2)),flip(a)]. 2140 K(x,T(y * z,y \ 1)) = K(x,T(y * z,z)). [para(13(a,1),2137(a,2,2,2))]. 2141 x * R(1 / (1 / y),1 / y,(1 / y) \ x) = (1 / y) \ T(x,y). [para(59(a,1),2138(a,2,2,2))]. 2142 T(x,R(y,z,u) \ 1) = T(x,z / (y * z)). [para(2133(a,1),2045(a,1))]. 2144 T(x,R(y,z,u) \ 1) = T(x,y \ 1). [para(2142(a,2),2129(a,1))]. 2145 T(R(x,y,z) \ 1,x \ 1) = R(x,y,z) \ 1. [para(2144(a,1),84(a,1))]. 2147 T(R(x \ 1,y,z) \ 1,x) = R(x \ 1,y,z) \ 1. [para(2145(a,1),1460(a,1)),flip(a)]. 2148 (x * (R(x \ 1,y,z) \ 1)) / x = R(x \ 1,y,z) \ 1. [para(2147(a,1),106(a,1,1,2))]. 2149 ((x \ 1) * (R((x \ 1) \ 1,y,z) \ 1)) / (1 / x) = K(x \ 1,x) * (R((x \ 1) \ 1,y,z) \ 1). [para(2148(a,1),1457(a,1,2)),flip(a)]. 2150 x * R(1 / (1 / y),y \ 1,(1 / y) \ x) = (1 / y) \ T(x,y). [para(1714(a,1),2141(a,1,2))]. 2151 K(x,((y \ 1) \ x) / x) = ((1 / y) \ x) \ ((1 / y) \ T(x,y)). [para(2150(a,1),1751(a,1,2)),flip(a)]. 2152 (x * (y * z)) \ (K(x,u) * (K(u,x) * ((x * y) * z))) = a(x,K(u,x) * y,z). [para(2068(a,1),1985(a,1)),flip(a)]. 2153 a(x,K(y,x) * z,u) = (x * (z * u)) \ ((x * z) * u). [para(1930(a,1),2152(a,1,2)),flip(a)]. 2154 a(x,K(y,x) * z,u) = a(x,z,u). [para(2153(a,2),22(a,2)),flip(a)]. 2156 a(x,T(y,x),z) = a(x,y,z). [para(1817(a,2),2154(a,1,2))]. 2157 x * R(K(y,(x \ z) \ 1),u,w) = R(K(y,x / z),u,w) * x. [para(2122(a,1),2031(a,1,1,1)),flip(a)]. 2158 x * R(K(y,(x \ z) \ 1),u,w) = K(y,x / z) * x. [para(272(a,1),2157(a,2,1))]. 2159 x * K(y,(x \ z) \ 1) = K(y,x / z) * x. [para(157(a,1),2158(a,1,2))]. 2161 T(K(x,y / z),y) = K(x,(y \ z) \ 1). [hyper(109,a,2159,a)]. 2162 K(x,y / (y * z)) * y = y * K(x,z \ 1). [para(13(a,1),2159(a,1,2,2,1)),flip(a)]. 2163 K(x,(y * z) / (y * (z * u))) * (y * z) = (y * z) * K(x,L(u,z,y) \ 1). [para(26(a,2),2159(a,1,2,2,1)),flip(a)]. 2164 K(x,y \ 1) * y = y * K(x,y \ 1). [para(2117(a,1),2162(a,1,1))]. 2165 K(K(x \ 1,x) * y,(x \ 1) \ 1) = (x * y) \ (y * x). [para(2022(a,1),1932(a,1,2)),flip(a)]. 2166 K(K(x \ 1,x) * y,(x \ 1) \ 1) = K(y,x). [para(2165(a,2),24(a,2)),flip(a)]. 2167 K(K(x,x \ 1) * y,x) = K(y,(x \ 1) \ 1). [para(448(a,1),2166(a,1,1)),flip(a)]. 2168 K(K(x,x \ 1) * y,x) = K(y,x). [para(2167(a,2),929(a,1))]. 2169 K((1 / x) * y,x) = K((x \ 1) * y,x). [para(453(a,1),2168(a,1,1))]. 2170 K(T(K(x,x \ 1) * y,x),x) = K(T(y,x),x). [para(983(a,2),2168(a,1,1))]. 2171 K(T((1 / x) * y,x),x) = K(T((x \ 1) * y,x),x). [para(453(a,1),2170(a,1,1,1))]. 2172 T(x,y) * (z * R(z \ (T(x,y) \ u),w,v5)) = z * (x * R(x \ (z \ u),w,v5)). [para(2029(a,1),2085(a,2,2))]. 2174 ((x \ y) \ y) * (z * R(z \ (T(x,x \ y) \ u),w,v5)) = z * (x * R(x \ (z \ u),w,v5)). [para(86(a,1),2172(a,1,1))]. 2177 x * (y * R(y \ (x \ (z * x)),u,w)) = (y * R(y \ z,u,w)) * x. [para(2174(a,1),2086(a,1))]. 2178 x * (y * R(y \ T(z,x),u,w)) = (y * R(y \ z,u,w)) * x. [para(30(a,2),2177(a,1,2,2,1,2))]. 2179 T(x * R(x \ y,z,u),w) = x * R(x \ T(y,w),z,u). [hyper(109,a,2178,a)]. 2180 K(x,y) * (z * R(z \ x,u,w)) = (z * R(z \ x,u,w)) * K(x,y). [para(1830(a,1),2178(a,1,2,2,1,2))]. 2181 T(x * R(x \ y,z,u),y) = x * R(x \ y,z,u). [para(84(a,1),2179(a,2,2,1,2))]. 2182 (K(x,y) * (z * u)) / (z * (K((z \ (x \ z)) \ 1,y) * u)) = a(z,K((z \ (x \ z)) \ 1,y),u). [para(197(a,1),2072(a,1,1))]. 2183 (K(x,y) * (z * u)) / (z * (T(K(x,y),z) * u)) = a(z,K((z \ (x \ z)) \ 1,y),u). [para(2071(a,1),2182(a,1,2,2,1))]. 2184 K(x,y) * ((z * u) / (z * (T(K(x,y),z) * u))) = a(z,K((z \ (x \ z)) \ 1,y),u). [para(2183(a,1),281(a,1)),flip(a)]. 2185 K(x,y) * ((z * u) / (z * (T(K(x,y),z) * u))) = a(z,T(K(x,y),z),u). [para(2071(a,1),2184(a,2,2))]. 2186 K(x,y) * ((z * u) / (z * (T(K(x,y),z) * u))) = a(z,K(x,y),u). [para(2185(a,2),2156(a,1))]. 2187 (x * y) \ ((x * (z \ y)) * L((u * T(z,z \ y)) / u,z \ y,x)) = K(u,((x * y) \ (x * (z \ y))) \ 1). [para(327(a,2),2032(a,1,2,2))]. 2188 ((T(R(x,y,z),x * u) * u) * T(x,u)) \ ((x * u) * R(T(x,u),y,z)) = K(u * T(x,u),R(x,y,z)). [para(85(a,1),2081(a,1,1,1,1,2))]. 2189 ((R(T(x,x * y),z,u) * y) * T(x,y)) \ ((x * y) * R(T(x,y),z,u)) = K(y * T(x,y),R(x,z,u)). [para(40(a,2),2188(a,1,1,1,1))]. 2190 (R(x / y,z,u) * w) / R(y \ x,z,u) = (K(y,y \ x) * w) * K(y \ x,K(y,y \ x) * w). [para(2048(a,1),2110(a,2,2))]. 2192 (x * y) \ ((x * (z \ y)) * L(T((u * z) / u,z \ y),z \ y,x)) = K(u,((x * y) \ (x * (z \ y))) \ 1). [para(178(a,1),2187(a,1,2,2,1))]. 2193 (x * y) \ (x * ((z \ y) * T((u * z) / u,z \ y))) = K(u,((x * y) \ (x * (z \ y))) \ 1). [para(76(a,1),2192(a,1,2))]. 2194 (x * y) \ (x * (((z * u) / z) * (u \ y))) = K(z,((x * y) \ (x * (u \ y))) \ 1). [para(85(a,1),2193(a,1,2,2))]. 2195 K(x,((y * z) \ (y * (u \ z))) \ 1) = (y * z) \ (y * (K(x,u) * z)). [para(1794(a,1),2194(a,1,2,2)),flip(a)]. 2196 K(x,((y * z) \ (y * (u \ z))) \ 1) = L(T(K(x,u),z),z,y). [para(2195(a,2),112(a,1))]. 2197 (K(x,x \ y) * z) * K(z \ (K(x \ y,x) * ((y / x) * z)),K(x,x \ y) * z) = ((y / x) * z) / (x \ y). [para(1943(a,1),2009(a,1,2,1))]. 2198 x * (y * R(y \ (x \ (z * ((u * (z \ (x * y))) / u))),w,v5)) = K(u,(x * y) / z) * (x * y). [para(2033(a,2),2158(a,1))]. 2199 x * (y * R(y \ ((x \ z) * ((u * ((x \ z) \ y)) / u)),w,v5)) = K(u,(x * y) / z) * (x * y). [para(761(a,1),2198(a,1,2,2,1,2))]. 2201 x * (y * R(K(z,(y \ (x \ u)) \ 1),w,v5)) = K(z,(x * y) / u) * (x * y). [para(1874(a,1),2199(a,1,2,2,1))]. 2202 K(x,(y * z) / u) * (y * z) = y * (K(x,z / (y \ u)) * z). [para(2158(a,1),2201(a,1,2)),flip(a)]. 2203 x * (K(y,z / (x \ (x * (z * u)))) * z) = (x * z) * K(y,L(u,z,x) \ 1). [para(2202(a,1),2163(a,1))]. 2204 (x * y) * K(z,L(u,y,x) \ 1) = x * (K(z,y / (y * u)) * y). [para(13(a,1),2203(a,1,2,1,2,2)),flip(a)]. 2206 (x * y) * K(z,L(u,y,x) \ 1) = x * (y * K(z,u \ 1)). [para(2162(a,1),2204(a,2,2))]. 2207 K(L(x,y,z) \ 1,u \ 1) = K(x \ 1,L(u,y,z) \ 1). [hyper(2092,a,2206,a)]. 2208 L(K(x,y \ 1),z,u) = K(x,L(y,z,u) \ 1). [hyper(192,a,2206,a)]. 2209 K(x,L(1 / y,z,u) \ 1) = L(K(x,y),z,u). [para(59(a,1),2208(a,1,1,2)),flip(a)]. 2210 K(x,L(y \ 1,z,u) \ 1) = L(K(x,y),z,u). [para(929(a,1),2208(a,1,1)),flip(a)]. 2211 K(x,L(x,y,z) \ 1) * (z * y) = z * (y * K(x,x \ 1)). [para(2208(a,1),1160(a,1,1))]. 2213 K(L(1 / x,y,z) \ 1,u) = L(K(u,x),y,z) \ 1. [para(2209(a,1),1935(a,1,1)),flip(a)]. 2214 K(L(x \ 1,y,z) \ 1,u) = L(K(u,x),y,z) \ 1. [para(2210(a,1),1935(a,1,1)),flip(a)]. 2215 L(K(x,y),z,u) \ 1 = L(K(y,x),z,u). [para(2214(a,1),2026(a,1))]. 2216 K((x \ 1) \ 1,L(x \ 1,y,z)) = L(K(x \ 1,x),y,z) \ 1. [para(2214(a,1),2028(a,1)),flip(a)]. 2217 L(K(x,y),x,z) = K(y,x) \ 1. [para(1988(a,1),2215(a,1,1)),flip(a)]. 2218 L(K(x,y),x,z) = K(x,y). [para(2217(a,2),1935(a,1))]. 2221 (x * y) \ (x * T(y,z)) = K(y,z). [para(2218(a,1),1826(a,2))]. 2222 (x * y) * K(y,z) = x * T(y,z). [para(2221(a,1),14(a,1,2))]. 2223 x \ (y * T(y \ x,z)) = K(y \ x,z). [para(14(a,1),2221(a,1,1))]. 2226 x * T(x \ y,z) = y * K(x \ y,z). [para(14(a,1),2222(a,1,1)),flip(a)]. 2227 (x / y) * T(y,z) = x * K(y,z). [para(16(a,1),2222(a,1,1)),flip(a)]. 2229 K(x,y) * (z * T(y,x)) = T(z * y,K(y,x)). [para(2222(a,1),1934(a,1,2))]. 2230 (x * K(y,z)) \ (x * T(y,z)) = y. [para(2227(a,1),593(a,1,1))]. 2231 (x * K(y,z)) \ x = K(z,y). [para(2227(a,1),2019(a,1,1))]. 2232 x * (K(y,z) * T(y,x)) = (y * x) * K(y,z). [para(2227(a,1),2082(a,1)),flip(a)]. 2233 (x * K(y,z)) * K(z,y) = x. [para(2231(a,1),14(a,1,2))]. 2234 x / K(y,z) = x * K(z,y). [para(2231(a,1),57(a,1,2))]. 2235 ((x * K(y,z)) * R((x * K(y,z)) \ u,w,v5)) * K(z,y) = x * R(x \ (u * ((x * K(y,z)) \ x)),w,v5). [para(2231(a,1),688(a,1,2))]. 2237 (x * K(L(y \ 1,z,u) \ 1,w)) \ x = L(K(w,y),z,u). [para(2231(a,2),2210(a,1))]. 2239 (x * ((y * z) / y)) * K(z,y) = x * z. [para(2234(a,1),1914(a,1))]. 2240 K(x,y * K(z,y \ 1)) = T(K(x,y),z). [para(2234(a,1),2124(a,1,2))]. 2241 L(x,K(x,y),z) = x. [para(2230(a,1),1820(a,1)),flip(a)]. 2242 x \ (y * (x * K(y,z))) = K(y,z) * T(y,x * K(y,z)). [para(2241(a,1),262(a,1,2,1))]. 2244 ((1 / x) \ y) \ ((1 / x) \ T(y,z)) = K(x \ ((1 / x) \ y),z). [para(657(a,1),2223(a,1,2))]. 2245 x \ (K(y,z) * ((T(y,z) \ x) * y)) = K(T(y,z) \ x,y). [para(1848(a,2),2223(a,1,2))]. 2246 K((x \ y) \ 1,z) = K(y \ x,z). [hyper(1991,a,2226,a)]. 2249 K(x \ (x / y),z) = K(y \ 1,z). [para(59(a,1),2246(a,1,1,1)),flip(a)]. 2250 K(L(x \ y,x,z) \ 1,u) = K((z * y) \ (z * x),u). [para(78(a,2),2246(a,1,1,1))]. 2251 K(L(x \ y,z,u) \ 1,w) = L(K(y \ x,w),z,u). [para(2246(a,1),2024(a,1,1)),flip(a)]. 2252 K((x \ y) \ y,z) = T(K(x,z),y). [para(2246(a,1),2071(a,1))]. 2253 (x \ (x / y)) * x = (x / y) * K(y \ 1,x). [para(2249(a,1),136(a,1,2)),flip(a)]. 2256 K(T(x,y) \ 1,z) = T(K(x \ 1,z),y). [para(2249(a,1),1860(a,1))]. 2258 T(K(x / y,z),x) = K(y \ x,z). [para(59(a,1),2252(a,1,1,1)),flip(a)]. 2260 T(K(x,y),z * x) = K(T(x,z),y). [para(1902(a,2),2252(a,1,1)),flip(a)]. 2261 K(T(x,y),z) = T(K(x,z),y). [para(2252(a,1),2067(a,1)),flip(a)]. 2262 T(K(x,y),K(x,z)) = K(x,y). [para(1830(a,1),2261(a,1,1)),flip(a)]. 2263 T(K(x,y),z) \ 1 = K(y,T(x,z)). [para(2261(a,1),1935(a,1,1))]. 2264 K(x,y) * K(y,T(x,z)) = K(z,K(x,y)). [para(2263(a,1),1898(a,2,2)),flip(a)]. 2265 (x * ((y * z) / y)) \ (x * z) = K(z,y). [hyper(66,a,2239,a)]. 2266 K(T(x \ 1,y) \ 1,z) = T(K(x,z),y). [para(1573(a,1),2256(a,2,1))]. 2268 K(x,y) * K(y,T(x,z)) = K(x * z,K(x,y)). [para(922(a,1),2264(a,1,2))]. 2269 T(x * y,K(y,z)) = y * T(x,T(y,z)). [para(2229(a,1),1912(a,1))]. 2270 K(x,y / ((y / z) * K(z \ 1,y))) = K(x,(y \ (y / z)) \ 1). [para(2253(a,1),2117(a,1,2,2))]. 2271 K(x * y,K(x,z)) = K(y,K(x,z)). [para(2268(a,1),2264(a,1))]. 2272 L(K(x \ y,z),y,u) = K((u * x) \ (u * y),z). [para(2250(a,1),2251(a,1)),flip(a)]. 2273 K((x * (y / z)) \ (x * y),u) = L(K(z,u),y,x). [para(59(a,1),2272(a,1,1,1)),flip(a)]. 2274 K(L(x,y / x,z),u) = L(K(x,u),y,z). [para(79(a,2),2273(a,1,1))]. 2275 L(K(x,y),z,x) = K(x,y). [para(2274(a,1),1981(a,1))]. 2276 x * K(y,L(z,u / z,w)) = x / L(K(z,y),u,w). [para(2274(a,1),2234(a,1,2)),flip(a)]. 2277 (x * y) * K(x,z) = x * (y * K(x,z)). [para(2275(a,1),76(a,1,2))]. 2278 x * (K(y,z) * T(y,x)) = y * (x * K(y,z)). [para(2277(a,1),2232(a,2))]. 2279 x \ (y * (x * K(y,z))) != K(y,z) * u | T(y,x) = u. [para(2278(a,1),65(a,1,2)),flip(b)]. 2281 (x * L(K(y,z),u,w)) \ x = L(K(z,y),u,w). [para(2026(a,1),2237(a,1,1,2))]. 2282 x / L(K(y,z),u,w) = x * L(K(z,y),u,w). [para(2281(a,1),57(a,1,2))]. 2284 K(x,L(y,z / y,u)) = L(K(x,y),z,u). [hyper(17,a,2276,a,b,2282,a(flip)),flip(a)]. 2285 x * L(K(T(y \ 1,z) \ 1,u),w,v5) = x / L(T(K(u,y),z),w,v5). [para(2036(a,1),2282(a,1,2,1)),flip(a)]. 2286 L(K(x,y),z * y,u) = K(x,L(y,z,u)). [para(15(a,1),2284(a,1,2,2)),flip(a)]. 2288 K(x,L(y,z,x)) = K(x,y). [para(2286(a,1),2275(a,1))]. 2289 K(x,(x * y) \ z) = K(x,y \ (x \ z)). [para(128(a,1),2288(a,1,2))]. 2290 K(x,(y * (x / y)) \ (x * z)) = K(x,K(y \ x,y) * z). [para(2101(a,1),2288(a,1,2))]. 2291 K(R(x,y,z),(x \ 1) \ (R(x,y,z) \ u)) = K(R(x,y,z),(x \ R(x,y,z)) \ u). [para(479(a,1),2289(a,1,2,1)),flip(a)]. 2292 T(x,y * K(x,z)) = T(x,y). [hyper(2279,a,2242,a),flip(a)]. 2293 T(x,y * K(z,x)) = T(x,y). [para(2233(a,1),2292(a,1,2)),flip(a)]. 2294 T(x,K(y,x) * z) = T(x,z). [para(2070(a,1),2293(a,1,2))]. 2295 T(T(x,y),K(z,x) * u) = T(T(x,u),y). [para(2294(a,1),36(a,1,1)),flip(a)]. 2296 T(x,K(x,y) * z) = T(x,z). [para(1930(a,1),2294(a,1,2)),flip(a)]. 2297 (x * y) / T(T(x,y),z) = K(z,x) * y. [para(2295(a,1),1931(a,1,2))]. 2298 x * K(y,T(z,x)) = K(y,z) * x. [para(2297(a,1),2016(a,1)),flip(a)]. 2300 K(x,T(y,z)) = T(K(x,y),z). [hyper(109,a,2298,a),flip(a)]. 2301 K(x,y) * K(z,x) = K(z,x) * K(x,y). [para(1830(a,1),2298(a,1,2,2))]. 2302 T(K(x,y),z * y) = K(x,T(y,z)). [para(2300(a,1),926(a,1))]. 2303 T(K(x,y / z),y) = K(x,z \ y). [para(2300(a,1),941(a,1))]. 2304 x * T(K(x,y),z) = T(x,T(y,z)). [para(2300(a,1),1825(a,2,2)),flip(a)]. 2305 K(T(x,y),z) = K(x,T(z,y)). [para(2300(a,2),2261(a,2))]. 2306 K(x,y) * T(K(y,x),z) = K(z,K(x,y)). [para(2300(a,1),2264(a,1,2))]. 2307 K(x / y,T(z,y)) = K(y \ x,z). [para(87(a,1),2305(a,1,1)),flip(a)]. 2308 K(T(x,y),K(y,z)) = K(x,K(y,z)). [para(1832(a,1),2305(a,2,2))]. 2309 T(K(x,y),z * x) = K(x,T(y,z)). [para(2305(a,1),2260(a,2))]. 2310 T(K(x,y),z * y) = T(K(x,y),z). [para(2302(a,2),2300(a,1))]. 2311 K(x,(y \ z) \ 1) = K(x,z \ y). [para(2303(a,1),2161(a,1)),flip(a)]. 2312 K(x / T(y,z),y) = K(T(y,z) \ x,y). [para(122(a,1),2307(a,1,2))]. 2313 K(x,T((y * x) / z,y)) = K(x,z \ (y * x)). [para(2309(a,1),2303(a,1))]. 2314 T(K(x,y),z / y) = T(K(x,y),z). [para(16(a,1),2310(a,1,2)),flip(a)]. 2315 K(x,(y * z) \ y) = K(x,z \ 1). [para(13(a,1),2311(a,1,2,1)),flip(a)]. 2316 T(K(x,L(T(y,y \ z),y \ z,u)),u * (y \ z)) = T(K(x,L(T(y,y \ z),y \ z,u)),u * z). [para(232(a,1),2314(a,1,2))]. 2317 K(K(x,y),z) = K(z,K(y,x)). [para(2306(a,1),1941(a,1)),flip(a)]. 2318 (x * y) \ (y * (x * T(K(x,y),z))) = K(z,K(y,x)). [para(2306(a,1),2095(a,2))]. 2319 K(x,K(y,z)) * K(x,K(z,y)) = 1. [para(2317(a,1),1938(a,1,1))]. 2320 T(K(x,y),z) * K(y,x) = K(z,K(y,x)). [para(2317(a,1),1949(a,2))]. 2321 K(x,T(y / (z / x),y)) = K(x,z \ (y * x)). [para(2313(a,1),925(a,1)),flip(a)]. 2322 K(x,(y / x) \ z) = K(x,y \ (z * x)). [para(2321(a,1),941(a,1)),flip(a)]. 2323 (x * y) \ (y * T(x,T(y,z))) = K(z,K(y,x)). [para(2304(a,1),2318(a,1,2,2))]. 2324 (x * y) \ T(x * y,K(y,z)) = K(z,K(y,x)). [para(2269(a,2),2323(a,1,2))]. 2325 K(x * y,K(y,z)) = K(z,K(y,x)). [para(2324(a,1),1818(a,2))]. 2326 K(T(x,y) \ z,x) = z \ ((x \ z) * x). [para(1873(a,1),2245(a,1,2)),flip(a)]. 2327 K(T(x,y) \ z,x) = K(x \ z,x). [para(2326(a,2),73(a,1))]. 2329 K(((x \ y) \ y) \ z,x) = K(x \ z,x). [para(86(a,1),2327(a,1,1,1))]. 2331 K(x / T(y,z),y) = K(y \ x,y). [para(2327(a,1),2312(a,2))]. 2332 K(x \ (y * T(x,z)),x) = K(y,x). [para(15(a,1),2331(a,1,1)),flip(a)]. 2334 K((x / y) * T(y,z),y) = K(x,y). [para(2332(a,1),1961(a,1)),flip(a)]. 2335 K(x * K(y,z),y) = K(x,y). [para(2227(a,1),2334(a,1,1))]. 2337 K(x,y * K(x,z)) = u / (K(y,x) * u). [para(2335(a,1),1936(a,1,2,1)),flip(a)]. 2338 K(K(x,y) * z,x) = K(z,x). [para(2298(a,1),2335(a,1,1))]. 2340 K(x \ ((1 / x) \ y),x) = K(x \ ((x \ 1) \ y),x). [para(541(a,1),2329(a,1,1))]. 2341 K(x,y * K(x,z)) = K(x,y). [para(2337(a,2),1936(a,1))]. 2342 K(x,y * K(z,x)) = K(x,y). [para(2233(a,1),2341(a,1,2)),flip(a)]. 2343 K(x,K(y,x) * z) = K(x,z). [para(2070(a,1),2342(a,1,2))]. 2344 K(x,(y / x) \ z) = K(x,(x \ y) \ z). [para(1984(a,1),2343(a,1,2))]. 2345 (R(x / y,z,u) * w) / R(y \ x,z,u) = (K(y,y \ x) * w) * K(y \ x,w). [para(2343(a,1),2190(a,2,2))]. 2346 K(x,(x \ y) \ z) = K(x,y \ (z * x)). [para(2344(a,1),2322(a,1))]. 2347 K(x,(y * (y \ x)) \ (x * z)) = K(x,K(y \ x,y) * z). [para(2290(a,1),2105(a,1)),flip(a)]. 2348 K(x,x \ (x * y)) = K(x,K(z \ x,z) * y). [para(14(a,1),2347(a,1,2,1))]. 2349 K(x,K(y \ x,y) * z) = K(x,z). [para(13(a,1),2348(a,1,2)),flip(a)]. 2350 K(x,K(y,y \ x) * z) = K(x,z). [para(1930(a,1),2349(a,1,2)),flip(a)]. 2351 K(x * y,K(x,y) * z) = K(x * y,z). [para(13(a,1),2350(a,1,2,1,2))]. 2352 K(R(x,y,z) * u,T(x,u)) = K(R(x,y,z) * u,x). [para(2050(a,1),2351(a,1,2))]. 2353 L(K(x \ 1,x),y,z) \ 1 = K(x,L(x \ 1,y,z)). [para(2216(a,1),1573(a,1))]. 2354 K(L(1 / x,y,z) \ 1,x \ 1) = K(x,L(x \ 1,y,z)). [para(2353(a,1),2213(a,2))]. 2355 K((1 / x) \ 1,L(x,y,z) \ 1) = K(x,L(x \ 1,y,z)). [para(2354(a,1),2207(a,1)),flip(a)]. 2356 K(x,L(x \ 1,y,z)) = K(x,L(x,y,z) \ 1). [para(59(a,1),2355(a,1,1)),flip(a)]. 2357 K(x,L(x \ 1,y,z)) * (z * y) = z * (y * K(x,x \ 1)). [para(2356(a,2),2211(a,1,1))]. 2358 K(x,L(x \ 1,y,z)) * ((z * y) / u) = (z * (y * K(x,x \ 1))) / u. [para(2357(a,1),281(a,1,1)),flip(a)]. 2359 ((1 / x) \ y) \ ((1 / x) \ T(y,x)) = K(x \ ((x \ 1) \ y),x). [para(2244(a,2),2340(a,1))]. 2360 K(x,T(y,z \ 1) / (y / z)) = K(x,(y \ (y / z)) \ 1). [para(2270(a,1),1901(a,1)),flip(a)]. 2361 K(x \ ((x \ 1) \ y),x) = K(y,((x \ 1) \ y) / y). [para(2359(a,1),2151(a,2)),flip(a)]. 2362 K(x \ ((x \ 1) \ y),x) = K(y,(x \ 1) \ 1). [para(2361(a,2),2119(a,1))]. 2363 K(x \ ((x \ 1) \ y),x) = K(y,x). [para(2362(a,2),929(a,1))]. 2365 K((x \ 1) * y,x) = K(x \ y,x). [para(13(a,1),2363(a,1,1,2)),flip(a)]. 2366 K((1 / x) * y,x) = K(x \ y,x). [para(2365(a,1),2169(a,2))]. 2367 K((1 / x) * (y * x),x) = K(T(y,x),x). [para(30(a,2),2366(a,2,1))]. 2368 K(T((1 / x) * y,x),x) = K(T(x \ y,x),x). [para(356(a,1),2367(a,1,1))]. 2369 K(T((x \ 1) * y,x),x) = K(T(x \ y,x),x). [para(2368(a,1),2171(a,1)),flip(a)]. 2370 K(T(x \ y,x),x) \ 1 = K(x,(x \ 1) * y). [para(2369(a,1),1962(a,1,1))]. 2371 K(x,(x \ 1) * y) = K(x,x \ y). [para(2370(a,1),1962(a,1))]. 2372 x / L(T(K(y,z),u),w,v5) = x * L(T(K(z,y),u),w,v5). [para(2266(a,1),2285(a,1,2,1)),flip(a)]. 2373 (x * (K(y,z) * u)) * L(T(K(z,y),u),u,x) = x * u. [para(2372(a,1),231(a,1))]. 2374 ((x * (K(y,z) * u)) * R(L(T(K(z,y),u),u,x),w,v5)) / (x * (K(y,z) * u)) = R((x * u) / (x * (K(y,z) * u)),w,v5). [para(2373(a,1),325(a,1,1,1)),flip(a)]. 2375 R((x * y) / (x * (K(z,u) * y)),x * (K(z,u) * y),L(T(K(u,z),y),y,x)) = (x * (y * T(K(u,z),y))) / (x * y). [para(2373(a,1),228(a,2,2))]. 2376 (x * (y * K(z,z \ 1))) / u = K(z,z \ 1) * ((x * y) / u). [para(1693(a,1),2358(a,1,1)),flip(a)]. 2378 (x \ (K(y \ 1,y) * z)) / ((K(y,y \ 1) * ((u * x) / u)) \ z) = K(u,x * K(y,y \ 1)). [para(2376(a,1),1983(a,1,2,1))]. 2379 K(R(x,y,z),(x \ 1) \ (R(x,y,z) \ u)) = K(x,(x \ R(x,y,z)) \ u). [para(2291(a,2),2048(a,1))]. 2381 K(R(x,y,z),(x \ 1) \ (R(x,y,z) \ u)) = K(x,R(x,y,z) \ (u * x)). [para(2379(a,2),2346(a,1))]. 2382 K(x,(x \ 1) \ (R(x,y,z) \ u)) = K(x,R(x,y,z) \ (u * x)). [para(2381(a,1),2048(a,1)),flip(a)]. 2385 (x \ (K(y \ 1,y) * z)) / (((u * x) / u) \ (K(y \ 1,y) * z)) = K(u,x * K(y,y \ 1)). [para(1943(a,1),2378(a,1,2))]. 2386 K(x,y * K(z,z \ 1)) = K(x,y). [para(2385(a,1),1925(a,1))]. 2387 K(x,y * K(z \ 1,z)) = K(x,y). [para(929(a,1),2386(a,1,2,2))]. 2388 K(x,K(y \ 1,y) * z) = K(x,z). [para(1213(a,1),2386(a,1,2)),flip(a)]. 2389 K(x,((y \ 1) \ 1) * z) = K(x,y * z). [para(1205(a,1),2386(a,1,2))]. 2390 K(x,(y \ K(z \ 1,z)) \ u) = K(x,(y \ 1) \ u). [para(1722(a,1),2386(a,1,2))]. 2392 K(x,((1 / (1 / y)) * z) / u) = K(x,(y * z) / u). [para(1259(a,1),2387(a,1,2))]. 2393 K(x,y \ K(z \ 1,z)) = K(x,y \ 1). [para(1677(a,1),2387(a,1,2))]. 2394 K(x,T(y * K(z \ 1,z),u)) = K(x,T(y,u)). [para(1732(a,2),2387(a,1,2))]. 2395 K(x,((y \ 1) \ 1) \ z) = K(x,y \ z). [para(732(a,1),2388(a,1,2))]. 2396 K(x,(y \ K(z \ 1,z)) * u) = K(x,(y \ 1) * u). [para(1681(a,1),2388(a,1,2))]. 2397 K(x,T(y \ 1,y) * z) = K(x,(y \ 1) * z). [para(1821(a,1),2388(a,1,2))]. 2398 K(x,T((y \ 1) \ 1,z) * u) = K(x,T(y,z) * u). [para(1230(a,1),2389(a,1,2,1))]. 2399 K(x \ 1,(x \ 1) \ y) = K(x \ 1,x * y). [para(2389(a,1),2371(a,1)),flip(a)]. 2400 K(x,T(y / (1 / (1 / z)),u)) = K(x,T(y / z,u)). [para(1452(a,1),2394(a,1,2,1)),flip(a)]. 2401 x * T(x \ 1,y * x) = K(x \ 1,x * y). [para(2399(a,1),1986(a,1)),flip(a)]. 2402 x \ K(x \ 1,x * y) = T(x \ 1,y * x). [hyper(66,a,2401,a)]. 2403 (x \ 1) \ K(x * y,x \ 1) = T(x \ 1,y * x) \ 1. [para(2402(a,1),2100(a,1,1)),flip(a)]. 2404 K(x,((y / (1 / z)) \ 1) \ u) = K(x,((y / (z \ 1)) \ 1) \ u). [para(1472(a,1),2390(a,1,2,1)),flip(a)]. 2405 K(x,(((y / (1 / z)) \ 1) \ 1) * u) = K(x,(((y / (z \ 1)) \ 1) \ 1) * u). [para(2069(a,1),2396(a,1,2,1))]. 2406 K(x,T(y * (1 / z),u)) = K(x,T(y / z,u)). [para(2400(a,1),961(a,1)),flip(a)]. 2407 K(x,T(y / (z \ 1),u)) = K(x,T(y * z,u)). [para(57(a,1),2406(a,1,2,1,2)),flip(a)]. 2408 K(x,T(y * z,y)) = K(x,(z \ 1) \ y). [para(2407(a,1),941(a,1))]. 2409 K(x,(y \ 1) \ K(z,u)) = K(x,y * K(z,u)). [para(271(a,1),2408(a,1,2)),flip(a)]. 2410 K(x,T(y \ 1,z * y) \ 1) = K(x,y * K(y * z,y \ 1)). [para(2403(a,1),2409(a,1,2))]. 2411 K(x,((((y \ 1) * (R((y \ 1) \ 1,z,u) \ 1)) / (1 / y)) \ 1) \ w) = K(x,((R((y \ 1) \ 1,z,u) \ 1) \ 1) \ w). [para(2148(a,1),2404(a,2,2,1,1))]. 2412 K(x,y * K(y * z,y \ 1)) = T(K(x,y),z * y). [para(2410(a,1),2036(a,1))]. 2413 T(K(x,y),z * y) = T(K(x,y),y * z). [para(2412(a,1),2240(a,1))]. 2414 T(K(x,y),z * y) * K(y,x) = K(K(x,y),y * z). [para(2413(a,2),1949(a,1,1))]. 2415 K(K(x,y),y * z) = K(z * y,K(y,x)). [para(2414(a,1),2320(a,1))]. 2416 K(x * y,K(y,z)) = K(y * x,K(y,z)). [para(2415(a,1),2317(a,1))]. 2417 K(x * y,K(y,z)) = K(x,K(y,z)). [para(2416(a,2),2271(a,1))]. 2418 K(x,K(y,z)) = K(z,K(y,x)). [para(2417(a,1),2325(a,1))]. 2419 K(K(x,y),z) = K(x,K(y,z)). [para(2418(a,1),2317(a,2))]. 2420 (K(x,y) * z) / K(x,y) = z * K(x,K(y,z)). [para(2419(a,1),1796(a,2,2))]. 2421 K(x,y) * K(x,K(y,z)) = T(K(x,y),z). [para(2419(a,1),1825(a,2,2)),flip(a)]. 2422 K(x,K(y,z)) * K(K(x,z),y) = 1. [para(2419(a,2),2319(a,1,2))]. 2423 K(K(x,y) * z,K(x,u)) = K(K(z,x),u). [para(2338(a,1),2419(a,1,1)),flip(a)]. 2424 K(x,K(y,z)) = K(y,K(x,z)). [hyper(1944,a,2422,a)]. 2425 K(x,K(y,z)) = K(z,K(x,y)). [para(2424(a,1),2418(a,1))]. 2426 K(x,K(y,z)) * z = T(z,K(x,y)). [para(2425(a,2),1817(a,2,1)),flip(a)]. 2427 x * K(y,K(z,x)) = T(x,K(y,z)). [para(2425(a,2),1825(a,2,2)),flip(a)]. 2428 x * T(x \ y,K(z,u)) = y * K(z,K(u,x \ y)). [para(2425(a,2),2226(a,2,2))]. 2429 K(x,K(y,T(z,x))) = K(z,K(x,y)). [para(2425(a,2),2308(a,1))]. 2430 K(x,K(y,z)) = K(x,K(z,y)). [para(2425(a,1),2418(a,1))]. 2431 K(K(x,y),z) = K(z,K(x,y)). [para(2425(a,1),2419(a,2))]. 2432 K(x,y) * K(y,T(x,z)) = K(z,K(y,x)). [para(2430(a,1),2264(a,2))]. 2433 K(x,y) * K(z,K(x,y)) = T(K(x,y),z). [para(2431(a,1),1825(a,2,2)),flip(a)]. 2434 K(x,K(y,T(z,x))) = K(x,K(z,y)). [para(2429(a,2),2424(a,1))]. 2435 K(x,y) * K(x,K(z,y)) = T(K(x,y),z). [para(2430(a,1),2421(a,1,2))]. 2436 K(K(x,y) * z,K(x,u)) = K(z,K(x,u)). [para(2423(a,2),2419(a,1))]. 2437 K(x,y) \ K(z,K(y,x)) = K(y,T(x,z)). [hyper(66,a,2432,a)]. 2438 T(T(K(x,y),z),z) = K(x,y). [para(2433(a,1),1803(a,1,1))]. 2439 T(K(x,y),z) * z = z * K(x,y). [para(2433(a,1),1801(a,1,1))]. 2440 T(K(x,T(y,z)),z) = K(x,y). [para(2300(a,2),2438(a,1,1))]. 2441 (x * K(y,z)) / x = K(y,T(z,x)). [para(2440(a,1),106(a,1,1,2))]. 2442 K(T(x,y),T(z,y)) = K(x,z). [para(2440(a,1),2261(a,2))]. 2443 K(x \ y,T(z,y)) = K(y / x,z). [para(2440(a,1),2258(a,1)),flip(a)]. 2444 K(x,T(T(y,z),z)) = K(x,y). [para(2440(a,1),2300(a,2))]. 2445 K((x * y) / x,z) = K(y,T(z,x)). [para(105(a,1),2442(a,1,1)),flip(a)]. 2446 K(x,(y * z) / y) = K(T(x,y),z). [para(105(a,1),2442(a,1,2)),flip(a)]. 2447 K(T(x,y \ 1),R(z,y \ 1,y)) = K(x,((1 / y) * z) * y). [para(1379(a,1),2442(a,1,2))]. 2448 K(T(x,y),R(y,z,u) \ w) = K(x,w / R(y,z,u)). [para(2038(a,1),2442(a,1,2))]. 2449 K(T(x,y),K(z,x) * u) = K(T(x,y),u). [para(2442(a,1),2343(a,1,2,1))]. 2450 K(x,T(L(T(y,z),u,w),z)) = K(x,L(y,u,w)). [para(38(a,2),2444(a,1,2,1))]. 2451 K(x,T(y \ z,y)) = K(x,z / y). [para(87(a,1),2444(a,1,2,1))]. 2452 K(T(x,y),z) * (y * x) = (y * x) * K(x,z). [para(2260(a,1),2439(a,1,1))]. 2453 (x * (y * K(z,u))) / (x * y) = L(K(z,T(u,x * y)),y,x). [para(2441(a,1),333(a,1,1)),flip(a)]. 2454 K(((x * y) / x) \ 1,z) = K(y \ 1,T(z,x)). [para(2441(a,1),2073(a,1)),flip(a)]. 2455 K(x / y,z) * (y \ x) = T(y \ x,T(z,x)). [para(2443(a,1),1817(a,2,1)),flip(a)]. 2456 (x * ((y * z) / y)) \ (z * (K(y,z) * x)) = K(z,T(x,y)). [para(2445(a,1),1880(a,2))]. 2457 K(x \ y,z) * K(z,y / x) = K(x,K(z,x \ y)). [para(2451(a,1),2432(a,1,2))]. 2458 K(x,y) * K(x,K(z,y)) = K(x,T(y,z)). [para(2435(a,2),2300(a,2)),flip(a)]. 2459 K(x,K(y,K(x,z) * u)) = K(u,K(x,y)). [para(2436(a,1),2425(a,2))]. 2460 (K(x,y) * z) / K(x,y) = T(z,K(x,y)). [para(2420(a,2),2427(a,1))]. 2461 (K(x,y) * z) * K(y,x) = T(z,K(x,y)). [para(2460(a,1),2234(a,1)),flip(a)]. 2462 K(x,y) * (z * K(y,x)) = T(z,K(x,y)). [para(2461(a,1),197(a,1)),flip(a)]. 2463 T(K(x,y) * z,K(y,x)) = z * K(x,y). [para(1930(a,1),2461(a,1,1)),flip(a)]. 2464 K(x,y) * T(z,K(y,x)) = z * K(x,y). [para(2461(a,1),1933(a,1,2))]. 2465 T(x,K(y,z)) = T(x,K(z,y)). [para(2462(a,1),1934(a,1))]. 2466 K(x,y) * (y * (z * K(y,x))) = T(y * z,K(x,y)). [para(2277(a,1),2462(a,1,2))]. 2467 K(x,y) * R(T(z,K(y,x)),u,w) = R(z,u,w) * K(x,y). [para(2465(a,1),116(a,1,2,1))]. 2468 K(x,T(K(y,z) / u,K(z,y))) = K(x,u \ K(y,z)). [para(2465(a,1),941(a,1,2))]. 2469 T(x * (K(y,x) * z),K(x,y)) = (x * z) * K(y,x). [para(1918(a,1),2463(a,1,1))]. 2470 K(T(x,y),z) * (y * x) = y * T(x,z). [para(2452(a,2),2222(a,1))]. 2471 K(x,T(y,z)) * (z * x) = z * T(x,y). [para(2305(a,1),2470(a,1,1))]. 2472 K(x,K(y,z)) * (K(y,u) * x) = K(y,u) * T(x,K(y,z)). [para(2262(a,1),2471(a,1,1,2))]. 2473 K(x \ K(x,y),z) = K(x \ 1,T(z,y)). [para(1957(a,1),2454(a,1,1))]. 2474 K(x,K(y \ K(y,x),z)) = K(x,K(z,y \ 1)). [para(2473(a,2),2434(a,1,2))]. 2475 K(x \ K(x,y),T(z,y)) = K(x \ 1,z). [para(2473(a,2),2444(a,1))]. 2476 K(1 / R(x \ 1,y,z),u) * T(R(x \ 1,y,z) \ 1,x) = T(R(x \ 1,y,z) \ 1,T(u,1)). [para(2147(a,2),2455(a,1,2))]. 2477 K(x,y \ K(y,z)) \ K(z,K(x,y \ 1)) = K(y \ K(y,z),T(x,z)). [para(2474(a,1),2437(a,1,2))]. 2479 K(x \ y,z) * K(z,y / x) = K(z,K(x,x \ y)). [para(2457(a,2),2424(a,1))]. 2480 x * (K(y,x) * (z * K(x,y))) = T(x * z,K(y,x)). [para(2466(a,1),1918(a,1)),flip(a)]. 2481 K(x,T(R((y \ 1) / z,z,y),K(y,y \ 1))) = K(x,(z * y) \ K(y \ 1,y)). [para(227(a,2),2468(a,1,2,1))]. 2482 K(x,y / z) * K(z \ y,x) = K(x,K(z,z \ y)). [para(2479(a,1),2301(a,2))]. 2483 T(x * y,K(z,x)) = x * T(y,K(z,x)). [para(2462(a,1),2480(a,1,2)),flip(a)]. 2484 x * T(x \ y,K(z,x)) = T(y,K(z,x)). [para(14(a,1),2483(a,1,1)),flip(a)]. 2486 x * T(x \ y,K(x,z)) = T(y,K(z,x)). [para(2465(a,1),2484(a,1,2))]. 2487 x * T(x \ y,K(x,z)) = T(y,K(x,z)). [para(2486(a,2),2465(a,1))]. 2488 T(x * y,K(x,z)) = x * T(y,K(x,z)). [para(13(a,1),2487(a,1,2,1)),flip(a)]. 2489 x * T(x \ y,K(x,z)) = y * K(x,K(z,y)). [para(2487(a,2),2427(a,2)),flip(a)]. 2490 T(x * (K(y,x) * z),K(x,y)) = x * (z * K(y,x)). [para(2463(a,1),2488(a,2,2))]. 2491 K(x,K(y,x \ z)) = K(x,K(y,z)). [hyper(17,a,2428,a(flip),b,2489,a(flip)),flip(a)]. 2492 K(x,K(y,x * z)) = K(x,K(y,z)). [para(13(a,1),2491(a,1,2,2)),flip(a)]. 2493 K(x,K(y,y * z)) = K(y,K(x,z)). [para(2492(a,1),2424(a,1)),flip(a)]. 2494 K(x,K(y,y * z)) = K(x,K(y,z)). [para(2493(a,2),2424(a,1))]. 2495 K(x,K(y,y \ z)) = K(x,K(y,z)). [para(14(a,1),2494(a,1,2,2)),flip(a)]. 2496 K(x,K(y,z \ 1)) = K(x,K(y,z \ y)). [para(1970(a,1),2494(a,1,2)),flip(a)]. 2497 K(x,y / z) * K(z \ y,x) = K(x,K(z,y)). [para(2482(a,2),2495(a,1))]. 2498 K(x,y / z) * K(z \ y,x) = K(x,K(y,z)). [para(2497(a,2),2430(a,1))]. 2499 (x * y) * K(z,x) = x * (y * K(z,x)). [para(2490(a,1),2469(a,1)),flip(a)]. 2500 R(K(x,y) * T(z,K(y,x)),u,w) = R(z,u,w) * K(x,y). [para(2467(a,1),458(a,2))]. 2501 K(x,K(y,K(x,z) * u)) * (K(x,w) * u) = K(x,w) * T(u,K(x,y)). [para(2459(a,2),2472(a,1,1))]. 2502 R(x * K(y,z),u,w) = R(x,u,w) * K(y,z). [para(2464(a,1),2500(a,1,1))]. 2504 K(x,((1 / y) * z) * y) = K(T(x,y \ 1),z). [para(2447(a,1),915(a,1))]. 2506 L(K(x,T(T(y,z),u * z)),z,u) = (u * (K(x,y) * z)) / (u * z). [para(2298(a,1),2453(a,1,1,2)),flip(a)]. 2507 K(x,y \ K(y,z)) \ K(z,K(x,y \ 1)) = K(y \ 1,x). [para(2477(a,2),2475(a,1))]. 2508 K(x,y \ K(y,z)) * K(y \ 1,x) = K(z,K(x,y \ 1)). [para(2507(a,1),14(a,1,2))]. 2510 K(x,(y / z) \ 1) * K((z \ y) \ 1,x) = K(z,K(x,(z \ y) \ 1)). [para(1976(a,1),2508(a,1,1,2))]. 2511 T(K(x,y) * z,K(x,u)) = K(x,y) * T(z,K(x,u)). [para(2501(a,1),2426(a,1)),flip(a)]. 2512 K(x,y) * T(T(z,K(x,y)),K(x,u)) = T(z * K(x,y),K(x,u)). [para(85(a,1),2511(a,1,1)),flip(a)]. 2513 T(x * K(y,z),K(y,u)) = T(x,K(y,u)) * K(y,z). [para(2512(a,1),114(a,1))]. 2514 T((K(x,y) * z) * K(x,u),K(x,y)) = (z * K(x,y)) * K(x,u). [para(271(a,1),2513(a,2,1))]. 2515 T(K(x,y) * (z * K(x,u)),K(x,y)) = (z * K(x,y)) * K(x,u). [para(197(a,1),2514(a,1,1))]. 2516 (x * K(y,z)) * K(y,u) = (x * K(y,u)) * K(y,z). [para(2515(a,1),271(a,1))]. 2517 ((x * y) / x) * K(x,z) = (y * K(x,z)) * K(x,y). [para(1796(a,2),2516(a,1,1))]. 2518 ((x * y) / x) * K(x,z) = y * (K(x,z) * K(x,y)). [para(2517(a,2),2499(a,1))]. 2519 K(x,((x * y) / x) \ 1) * ((x * y) / x) = y * (K(x,((x * y) / x) \ 1) * K(x,y)). [para(2518(a,1),2164(a,2))]. 2520 K(x,y * (K(z,((z * y) / z) \ 1) * K(z,y))) = T(K(x,(z * y) / z),z). [para(2518(a,1),2240(a,1,2))]. 2521 K(x,(y / z) \ 1) * K((z \ y) \ 1,x) = K(z,K(x,y \ z)). [para(2311(a,1),2510(a,2,2))]. 2522 K(x,(y / z) \ 1) * K((z \ y) \ 1,x) = K(x,K(z,y \ z)). [para(2521(a,2),2424(a,1))]. 2523 K(x,y / z) * K((y \ z) \ 1,x) = K(x,K(y,z \ y)). [para(2116(a,1),2522(a,1,1))]. 2524 K(x,y / z) * K(z \ y,x) = K(x,K(y,z \ y)). [para(2246(a,1),2523(a,1,2))]. 2525 K(x,K(y,z \ y)) = K(x,K(y,z)). [para(2524(a,1),2498(a,1))]. 2526 K(x,K(y,z \ 1)) = K(x,K(y,z)). [para(2525(a,1),2496(a,2))]. 2527 K(x,K(y,z \ 1)) = K(z,K(x,y)). [para(2526(a,2),2425(a,1))]. 2528 K(x,K(y \ 1,z)) = K(y,K(x,z)). [para(2527(a,1),2430(a,1)),flip(a)]. 2529 K(x,K(y \ 1,z)) = K(x,K(y,z)). [para(2528(a,2),2424(a,1))]. 2530 K(x,y) * K(x,K(z,y)) = K(x,T(y,z \ 1)). [para(2529(a,1),2458(a,1,2))]. 2531 K(x,T(y,z \ 1)) = K(x,T(y,z)). [para(2530(a,1),2458(a,1))]. 2532 K(x,T(y / R(z \ 1,u,w),z)) = K(x,R(z \ 1,u,w) \ y). [para(2038(a,1),2531(a,1,2)),flip(a)]. 2533 K(x,T(y * z,z)) = K(x,T(y * z,y)). [para(2531(a,1),2140(a,1)),flip(a)]. 2534 K(T(x,y \ 1),z) = K(x,T(z,y)). [para(2531(a,1),2305(a,2))]. 2535 K(x,(((y / (z \ 1)) \ 1) \ 1) * u) = K(x,(y / (1 / z)) * u). [para(2405(a,1),2389(a,1))]. 2536 K(x,(y / (1 / z)) * u) = K(x,(y / (z \ 1)) * u). [para(2535(a,1),2389(a,1))]. 2537 K(x,(y / (z \ 1)) * (u \ 1)) = K(x,(y / (1 / z)) / u). [para(2536(a,1),919(a,1))]. 2538 K(x,(y / (z \ 1)) * (u \ 1)) = K(x,y / (u * (1 / z))). [para(2537(a,2),918(a,1))]. 2539 K(x,(y / (z \ 1)) / u) = K(x,y / (u * (1 / z))). [para(2538(a,1),919(a,1)),flip(a)]. 2540 K(x,y / (z * (1 / u))) = K(x,y / (z * (u \ 1))). [para(2539(a,1),918(a,1))]. 2541 K(x,y * (K(z,(z * y) \ (1 * z)) * K(z,y))) = T(K(x,(z * y) / z),z). [para(2322(a,1),2520(a,1,2,2,1))]. 2542 K(x,y * (K(z,(z * y) \ z) * K(z,y))) = T(K(x,(z * y) / z),z). [para(11(a,1),2541(a,1,2,2,1,2,2))]. 2543 T(K(x,(y * z) / y),y) = K(x,z * (K(y,z \ 1) * K(y,z))). [para(2315(a,1),2542(a,1,2,2,1)),flip(a)]. 2545 K(x,y * (K(z,y \ 1) * K(z,y))) = T(K(T(x,z),y),z). [para(2446(a,1),2543(a,1,1)),flip(a)]. 2546 K(x,R((y \ 1) / z,z,y)) = K(x,(z * y) \ K(y \ 1,y)). [para(1131(a,1),2481(a,1,2))]. 2547 K(x,(y * z) \ K(z \ 1,z)) = K(x,(z \ 1) / y). [para(2546(a,1),915(a,1))]. 2550 K(x,(y \ 1) / z) = K(x,(z * y) \ 1). [para(2547(a,1),2393(a,1))]. 2552 K(x,(x * y) \ (1 * x)) * ((x * y) / x) = y * (K(x,((x * y) / x) \ 1) * K(x,y)). [para(2322(a,1),2519(a,1,1))]. 2553 K(x,(x * y) \ x) * ((x * y) / x) = y * (K(x,((x * y) / x) \ 1) * K(x,y)). [para(11(a,1),2552(a,1,1,2,2))]. 2554 x * (K(y,((y * x) / y) \ 1) * K(y,x)) = K(y,x \ 1) * ((y * x) / y). [para(2315(a,1),2553(a,1,1)),flip(a)]. 2555 x * (K(y,((y * x) / y) \ 1) * K(y,x)) = (T(y,x \ 1) * x) / y. [para(2554(a,2),1851(a,1))]. 2557 x * (K(y,(y * x) \ (1 * y)) * K(y,x)) = (T(y,x \ 1) * x) / y. [para(2322(a,1),2555(a,1,2,1))]. 2558 x * (K(y,(y * x) \ y) * K(y,x)) = (T(y,x \ 1) * x) / y. [para(11(a,1),2557(a,1,2,1,2,2))]. 2559 x * (K(y,x \ 1) * K(y,x)) = (T(y,x \ 1) * x) / y. [para(2315(a,1),2558(a,1,2,1))]. 2561 K(x,(T(y,z \ 1) * z) / y) = T(K(T(x,y),z),y). [para(2559(a,1),2545(a,1,2))]. 2562 K(x,T(y,z \ 1) / (y / z)) = T(K(T(x,y),z),y). [para(2561(a,1),921(a,1)),flip(a)]. 2563 K(x,(y \ (y / z)) \ 1) = T(K(T(x,y),z),y). [para(2562(a,1),2360(a,1)),flip(a)]. 2564 T(K(T(x,y * z),L(T(u,u \ z),u \ z,y)),y * z) = K(x,((y * z) \ (y * (u \ z))) \ 1). [para(232(a,1),2563(a,1,2,1,2)),flip(a)]. 2565 T(K(T(x,y * z),L(T(u,u \ z),u \ z,y)),y * z) = L(T(K(x,u),z),z,y). [para(2564(a,2),2196(a,1))]. 2566 T(K(x,T(L(T(y,y \ z),y \ z,u),u * z)),u * z) = L(T(K(x,y),z),z,u). [para(2305(a,1),2565(a,1,1))]. 2567 T(K(x,L(T(T(y,y \ z),u * z),y \ z,u)),u * z) = L(T(K(x,y),z),z,u). [para(38(a,2),2566(a,1,1,2))]. 2568 T(K(x,L(T(T(y,z),u * z),y \ z,u)),u * z) = L(T(K(x,y),z),z,u). [para(2065(a,1),2567(a,1,1))]. 2569 K(x,T(L(T(T(y,z),u * z),y \ z,u),u * z)) = L(T(K(x,y),z),z,u). [para(2568(a,1),2300(a,2))]. 2570 K(x,L(T(y,z),y \ z,u)) = L(T(K(x,y),z),z,u). [para(2569(a,1),2450(a,1)),flip(a)]. 2571 K(x,L(T(y,z),y \ z,u)) = L(K(x,T(y,z)),z,u). [para(2300(a,2),2570(a,2,1))]. 2573 T(K(x,L(T(y,y \ z),y \ z,u)),u * z) = T(K(x,(u * (y \ z)) \ (u * z)),u * (y \ z)). [para(144(a,1),2316(a,1,1,2)),flip(a)]. 2574 T(K(x,(y * (z \ u)) \ (y * u)),y * (z \ u)) = T(K(x,L(T(z,u),z \ u,y)),y * u). [para(949(a,1),2573(a,1,1)),flip(a)]. 2575 K(x,T((y * (z \ u)) \ (y * u),y * (z \ u))) = T(K(x,L(T(z,u),z \ u,y)),y * u). [para(2574(a,1),2300(a,2))]. 2576 T(K(x,L(T(y,z),y \ z,u)),u * z) = K(x,(u * z) / (u * (y \ z))). [para(2575(a,1),2451(a,1))]. 2577 T(K(x,L(T(y,z),y \ z,u)),u * z) = K(x,u / ((u * (y \ z)) / z)). [para(2576(a,2),921(a,1))]. 2578 T(L(K(x,T(y,z)),z,u),u * z) = K(x,u / ((u * (y \ z)) / z)). [para(2571(a,1),2577(a,1,1))]. 2579 L(T(K(x,T(y,z)),u * z),z,u) = K(x,u / ((u * (y \ z)) / z)). [para(2578(a,1),38(a,2))]. 2580 L(K(x,T(T(y,z),u * z)),z,u) = K(x,u / ((u * (y \ z)) / z)). [para(2300(a,2),2579(a,1,1))]. 2581 (x * (K(y,z) * R(K(y,z) \ (x \ u),w,v5))) * K(z,y) = x * R(x \ (u * ((x * K(y,z)) \ x)),w,v5). [para(662(a,1),2235(a,1,1))]. 2582 (x * (K(y,z) * R(K(z,y) * (x \ u),w,v5))) * K(z,y) = x * R(x \ (u * ((x * K(y,z)) \ x)),w,v5). [para(1937(a,1),2581(a,1,1,2,2,1))]. 2583 (x * (K(y,z) * R(K(z,y) * (x \ u),w,v5))) * K(z,y) = x * R(x \ (u * K(z,y)),w,v5). [para(2231(a,1),2582(a,2,2,1,2,2))]. 2584 (x * R(K(y,z) * (K(z,y) * (x \ u)),w,v5)) * K(z,y) = x * R(x \ (u * K(z,y)),w,v5). [para(458(a,2),2583(a,1,1,2))]. 2586 (x * R(x \ y,z,u)) * K(w,v5) = x * R(x \ (y * K(w,v5)),z,u). [para(1930(a,1),2584(a,1,1,2,1))]. 2588 K(x,y) * (z * R(z \ x,u,w)) = z * R(z \ (x * K(x,y)),u,w). [para(2586(a,1),2180(a,2))]. 2589 K(x,y) * (z * R(z \ x,u,w)) = z * R(z \ T(x,y),u,w). [para(1825(a,2),2588(a,2,2,1,2))]. 2590 ((x * R(x \ y,z,u)) * ((y * w) / y)) \ (w * (x * R(x \ T(y,w),z,u))) = K(w,T(x * R(x \ y,z,u),y)). [para(2589(a,1),2456(a,1,2,2))]. 2591 (K(x,x \ y) * z) * K(z \ ((x \ y) * z),K(x,x \ y) * z) = ((y / x) * z) / (x \ y). [para(1971(a,1),2197(a,1,2,1,2))]. 2592 (K(x,x \ y) * z) * K(T(x \ y,z),K(x,x \ y) * z) = ((y / x) * z) / (x \ y). [para(30(a,2),2591(a,1,2,1))]. 2593 (K(x,x \ y) * z) * K(T(x \ y,z),z) = ((y / x) * z) / (x \ y). [para(2449(a,1),2592(a,1,2))]. 2594 (K(x,x \ y) * z) * K(x \ y,z) = ((y / x) * z) / (x \ y). [para(1958(a,1),2593(a,1,2))]. 2596 (R(x / y,z,u) * w) / R(y \ x,z,u) = ((x / y) * w) / (y \ x). [para(2594(a,1),2345(a,2))]. 2597 K(x,((1 / (1 / R(y / z,u,w))) * v5) / R(z \ y,u,w)) = K(x,((y / z) * v5) / (z \ y)). [para(2596(a,1),2392(a,2,2))]. 2598 ((x * R(x \ y,z,u)) * ((y * w) / y)) \ ((x * R(x \ y,z,u)) * w) = K(w,T(x * R(x \ y,z,u),y)). [para(2178(a,1),2590(a,1,2))]. 2599 K(x,T(y * R(y \ z,u,w),z)) = K(x,z). [para(2598(a,1),2265(a,1))]. 2600 K(x,y * R(y \ z,u,w)) = K(x,z). [para(2181(a,1),2599(a,1,2))]. 2602 K(x,y * R(z,u,w)) = K(x,y * z). [para(13(a,1),2600(a,1,2,2,1))]. 2603 K(x,y \ R(y * z,u,w)) = K(x,z). [para(557(a,1),2600(a,1,2))]. 2604 K(x,T(y * z,y)) = K(x,z * y). [para(2042(a,1),2602(a,1,2))]. 2605 K(x,(y \ 1) \ z) = K(x,y * z). [para(2604(a,1),2408(a,1)),flip(a)]. 2606 K(x,T(y * z,z)) = K(x,z * y). [para(2604(a,1),2533(a,2))]. 2607 K(x,R(x,y,z) \ (u * x)) = K(x,x * (R(x,y,z) \ u)). [para(2605(a,1),2382(a,1)),flip(a)]. 2608 K(x,(y \ 1) * z) = K(x,y \ z). [para(2605(a,1),2395(a,1))]. 2610 K(x,T(y \ 1,y) * z) = K(x,y \ z). [para(2608(a,1),2397(a,2))]. 2611 K(x,R(y,z,u) / w) = K(x,y / w). [para(775(a,1),2603(a,1,2))]. 2612 K(x,y / (z \ 1)) = K(x,y * z). [para(242(a,1),2611(a,1,2)),flip(a)]. 2613 K(x,((y \ 1) * z) * y) = K(T(x,y \ 1),z). [para(2612(a,1),2446(a,1))]. 2614 K(x,((1 / (1 / R(1 / y,z,u))) * w) / R(y \ 1,z,u)) = K(x,((1 / y) * w) * y). [para(2612(a,1),2597(a,2))]. 2615 K(x,x * (R(x,y,z) \ (u / x))) = K(x,R(x,y,z) \ u). [para(16(a,1),2607(a,1,2,2)),flip(a)]. 2616 K(x,((1 / (1 / R(1 / y,z,u))) * w) / R(y \ 1,z,u)) = K(T(x,y \ 1),w). [para(2614(a,2),2504(a,1))]. 2617 ((x * (K(y,z) * u)) * L(R(T(K(z,y),u),w,v5),u,x)) / (x * (K(y,z) * u)) = R((x * u) / (x * (K(y,z) * u)),w,v5). [para(42(a,1),2374(a,1,1,2))]. 2618 R((x * y) / (x * (K(z,u) * y)),w,v5) = ((x * (K(z,u) * y)) * L(T(K(u,z),y),y,x)) / (x * (K(z,u) * y)). [para(280(a,1),2617(a,1,1,2,1)),flip(a)]. 2620 R((x * y) / (x * (K(z,u) * y)),w,v5) = (x * y) / (x * (K(z,u) * y)). [para(2373(a,1),2618(a,2,1))]. 2622 (x * (y * T(K(z,u),y))) / (x * y) = (x * y) / (x * (K(u,z) * y)). [para(2620(a,1),2375(a,1)),flip(a)]. 2623 (x * (K(y,z) * u)) / (x * u) = (x * u) / (x * (K(z,y) * u)). [para(85(a,1),2622(a,1,1,2))]. 2625 (x * y) / (x * (K(T(z \ 1,u) \ 1,w) * y)) = (x * (T(K(w,z),u) * y)) / (x * y). [para(2036(a,1),2623(a,1,1,2,1)),flip(a)]. 2626 L(K(x,T(T(y,z),u * z)),z,u) = (u * z) / (u * (K(y,x) * z)). [para(2623(a,1),2506(a,2))]. 2627 (x * y) / (x * (K(z,u) * y)) = K(u,x / ((x * (z \ y)) / y)). [para(2626(a,1),2580(a,1))]. 2628 (x * y) / (x * (K(T(z \ 1,u) \ 1,w) * y)) = T((x * (K(w,z) * y)) / (x * y),u). [para(2625(a,2),713(a,1))]. 2629 (x * y) / (x * (K(T(z \ 1,u) \ 1,w) * y)) = T((x * y) / (x * (K(z,w) * y)),u). [para(2623(a,1),2628(a,2,1))]. 2630 (x * y) / (x * (T(K(z,u),w) * y)) = T((x * y) / (x * (K(z,u) * y)),w). [para(2266(a,1),2629(a,1,2,2,1))]. 2631 K(x,y) * T((z * u) / (z * (K(x,y) * u)),z) = a(z,K(x,y),u). [para(2630(a,1),2186(a,1,2))]. 2632 K(x,y) * T(K(y,z / ((z * (x \ u)) / u)),z) = a(z,K(x,y),u). [para(2627(a,1),2631(a,1,2,1))]. 2633 K(x,y) * K(y,((z * (x \ u)) / u) \ z) = a(z,K(x,y),u). [para(2303(a,1),2632(a,1,2))]. 2634 (x * (K(R(x,y,z),u) * w)) * R(T(x,K(R(x,y,z),u) * w),y,z) = (R(T(x,u),y,z) * w) * T(x,K(R(x,y,z),u) * w). [para(40(a,2),1869(a,2,1,1))]. 2635 (x * (K(R(x,y,z),u) * w)) * R(T(x,K(R(x,y,z),u) * w),y,z) = (R(T(x,u),y,z) * w) * T(x,K(x,u) * w). [para(2048(a,1),2634(a,2,2,2,1))]. 2637 (x * (K(R(x,y,z),u) * w)) * R(T(x,K(R(x,y,z),u) * w),y,z) = (R(T(x,u),y,z) * w) * T(x,w). [para(2296(a,1),2635(a,2,2))]. 2638 (x * (K(x,y) * z)) * R(T(x,K(R(x,u,w),y) * z),u,w) = (R(T(x,y),u,w) * z) * T(x,z). [para(2048(a,1),2637(a,1,1,2,1))]. 2640 (T(x,y) * z) * R(T(x,K(R(x,u,w),y) * z),u,w) = (R(T(x,y),u,w) * z) * T(x,z). [para(1853(a,1),2638(a,1,1))]. 2642 (T(x,y) * z) * R(T(x,K(x,y) * z),u,w) = (R(T(x,y),u,w) * z) * T(x,z). [para(2048(a,1),2640(a,1,2,1,2,1))]. 2644 (R(T(x,y),z,u) * w) * T(x,w) = (T(x,y) * w) * R(T(x,w),z,u). [para(2296(a,1),2642(a,1,2,1)),flip(a)]. 2645 ((T(x,x * y) * y) * R(T(x,y),z,u)) \ ((x * y) * R(T(x,y),z,u)) = K(y * T(x,y),R(x,z,u)). [para(2644(a,1),2189(a,1,1))]. 2647 (x * (R(T(x,y),z,u) * y)) \ ((x * y) * R(T(x,y),z,u)) = K(y * T(x,y),R(x,z,u)). [para(2104(a,1),2645(a,1,1))]. 2648 K(R(x,y,z) * u,T(x,u)) = K(u * T(x,u),R(x,y,z)). [para(2647(a,1),2091(a,1)),flip(a)]. 2649 K(R(x,y,z) * u,T(x,u)) = K(x * u,R(x,y,z)). [para(85(a,1),2648(a,2,1))]. 2650 K(R(x,y,z) * u,T(x,u)) = K(x * u,x). [para(2649(a,2),915(a,1))]. 2652 K(R(x,y,z) * u,x) = K(x * u,x). [para(2650(a,1),2352(a,1)),flip(a)]. 2653 T(x,R(x,y,z) * u) = (K(x * u,x) / x) \ 1. [para(2652(a,1),1907(a,2,1,1))]. 2655 T(x,R(x,y,z) * u) = T(x,x * u). [para(2653(a,2),1907(a,2)),flip(a)]. 2656 T(x,x * (R(x,y,z) \ u)) = T(x,u). [para(14(a,1),2655(a,1,2)),flip(a)]. 2657 T(x,x * (R(x,y,z) \ u)) = x * K(x,u). [para(2656(a,2),1825(a,1))]. 2658 K(x,x * (R(x,y,z) \ u)) = K(x,u). [hyper(1834,a,2657,a)]. 2659 K(x,R(x,y,z) \ u) = K(x,u / x). [para(2658(a,1),2615(a,1)),flip(a)]. 2660 K(x,R(x,y,z) \ u) = K(x,x \ u). [para(2659(a,2),1965(a,1))]. 2662 R(x,y,z) * (u / R(x,y,z)) = u * K(x,x \ u). [para(2660(a,1),2051(a,2,2))]. 2663 R(x,y,z) * (u / R(x,y,z)) = x * (u / x). [para(2662(a,2),1968(a,1))]. 2665 (K(x,y) * ((R(y,z,u) * K(x,y)) \ w)) * a(R(y,z,u),K(x,y),(R(y,z,u) * K(x,y)) \ w) = R(y,z,u) \ w. [para(157(a,1),1923(a,2,1))]. 2667 (K(x,y) * (R(y * K(x,y),z,u) \ w)) * a(R(y,z,u),K(x,y),(R(y,z,u) * K(x,y)) \ w) = R(y,z,u) \ w. [para(2502(a,2),2665(a,1,1,2,1))]. 2668 (K(x,x \ y) * (R(y / x,z,u) \ w)) * a(R(x \ y,z,u),K(x,x \ y),(R(x \ y,z,u) * K(x,x \ y)) \ w) = R(x \ y,z,u) \ w. [para(1800(a,1),2667(a,1,1,2,1,1))]. 2669 (K(x,x \ y) * (R(y / x,z,u) \ w)) * 1 = R(x \ y,z,u) \ w. [para(1920(a,1),2668(a,1,2))]. 2670 K(x,x \ y) * (R(y / x,z,u) \ w) = R(x \ y,z,u) \ w. [hyper(68,a,2669,a)]. 2672 (x / y) * (R(x / y,z,u) \ w) = (y \ x) * (R(y \ x,z,u) \ w). [para(2670(a,1),1879(a,1,2)),flip(a)]. 2673 ((x \ 1) * (R(x \ 1,y,z) \ u)) * x = R(u / R(1 / x,y,z),x \ 1,x). [para(2672(a,1),2055(a,1,1))]. 2674 K(x,R(y / R(1 / z,u,w),z \ 1,z)) = K(T(x,z \ 1),R(z \ 1,u,w) \ y). [para(2673(a,1),2613(a,1,2))]. 2675 K(T(x,y \ 1),R(y \ 1,z,u) \ w) = K(x,w / R(1 / y,z,u)). [para(2674(a,1),915(a,1))]. 2677 K(x,y / R(1 / z,u,w)) = K(x,y / R(z \ 1,u,w)). [para(2675(a,1),2448(a,1))]. 2678 K(x,(R(1 / y,z,u) * (w * (R(1 / y,z,u) \ 1))) / R(y \ 1,z,u)) = K(x,(R(1 / y,z,u) * (w / R(1 / y,z,u))) * (R(1 / y,z,u) \ 1)). [para(444(a,1),2677(a,1,2)),flip(a)]. 2679 K(x,(R(1 / y,z,u) * (w * (R(1 / y,z,u) \ 1))) / R(y \ 1,z,u)) = K(x,((1 / y) * (w / (1 / y))) * (R(1 / y,z,u) \ 1)). [para(2663(a,1),2678(a,2,2,1))]. 2680 K(x,(R(1 / y,z,u) * (w * (R(1 / y,z,u) \ 1))) / R(y \ 1,z,u)) = K(x,((y \ 1) * (w / (y \ 1))) * (R(1 / y,z,u) \ 1)). [para(1468(a,1),2679(a,2,2,1))]. 2682 K(x,(R(1 / y,z,u) * (w * (R(1 / y,z,u) \ 1))) / R(y \ 1,z,u)) = K(x,((y \ 1) * (w / (y \ 1))) / R(1 / y,z,u)). [para(2680(a,2),919(a,1))]. 2683 K(x,(R(1 / y,z,u) * (w * (R(1 / y,z,u) \ 1))) / R(y \ 1,z,u)) = K(x,((y \ 1) * (w / (y \ 1))) / R(y \ 1,z,u)). [para(2682(a,2),2677(a,1))]. 2684 K(x,(R(1 / y,z,u) * (w * (R(1 / y,z,u) \ 1))) / R(y \ 1,z,u)) = K(x,(y \ 1) / (R(y \ 1,z,u) / (w / (y \ 1)))). [para(2683(a,2),921(a,1))]. 2685 K(x,(R(1 / y,z,u) * (w * (R(1 / y,z,u) \ 1))) / R(y \ 1,z,u)) = K(x,((R(y \ 1,z,u) / (w / (y \ 1))) * y) \ 1). [para(2684(a,2),2550(a,1))]. 2686 K(x,((1 / y) * (z * (R(1 / y,u,w) \ 1))) / (y \ 1)) = K(x,((R(y \ 1,u,w) / (z / (y \ 1))) * y) \ 1). [para(2596(a,1),2685(a,1,2))]. 2688 K(x,((R(y \ 1,z,u) / (w / (y \ 1))) * y) \ 1) = K(x,((1 / y) * (w * (R(1 / y,z,u) \ 1))) * y). [para(2686(a,1),2612(a,1))]. 2689 K(x,((R(y \ 1,z,u) / (w / (y \ 1))) * y) \ 1) = K(T(x,y \ 1),w * (R(1 / y,z,u) \ 1)). [para(2688(a,2),2504(a,1))]. 2690 K(x,((R(y \ 1,z,u) / (w / (y \ 1))) * y) \ 1) = K(T(x,y \ 1),w / R(1 / y,z,u)). [para(2689(a,2),919(a,1))]. 2691 K(x,((R(y \ 1,z,u) / (w / (y \ 1))) * y) \ 1) = K(T(x,y \ 1),w / R(y \ 1,z,u)). [para(2690(a,2),2677(a,1))]. 2692 K(x,((R(y \ 1,z,u) / (w / (y \ 1))) * y) \ 1) = K(x,T(w / R(y \ 1,z,u),y)). [para(2691(a,2),2534(a,1))]. 2693 K(x,((R(y \ 1,z,u) / (w / (y \ 1))) * y) \ 1) = K(x,R(y \ 1,z,u) \ w). [para(2692(a,2),2532(a,1))]. 2694 (K(x \ 1,x) * ((R((x \ 1) \ 1,y,z) * K(x \ 1,x)) \ u)) * a(R((x \ 1) \ 1,y,z),K(x \ 1,x),(R((x \ 1) \ 1,y,z) * K(x \ 1,x)) \ u) = R(R((x \ 1) \ 1,y,z),K(x \ 1,x) * (R(x,y,z) \ u),1) \ u. [para(1383(a,1),1322(a,1,1,3)),flip(a)]. 2695 (K(x \ 1,x) * ((R((x \ 1) \ 1,y,z) * K(x \ 1,x)) \ u)) * a(R((x \ 1) \ 1,y,z),K(x \ 1,x),(R((x \ 1) \ 1,y,z) * K(x \ 1,x)) \ u) = R((x \ 1) \ 1,y,z) \ u. [para(157(a,1),2694(a,2,1))]. 2698 (K(x \ 1,x) * (R(x,y,z) \ u)) * a(R((x \ 1) \ 1,y,z),K(x \ 1,x),(R((x \ 1) \ 1,y,z) * K(x \ 1,x)) \ u) = R((x \ 1) \ 1,y,z) \ u. [para(1321(a,1),2695(a,1,1,2,1))]. 2699 (K(x \ 1,x) * (R(x,y,z) \ u)) * 1 = R((x \ 1) \ 1,y,z) \ u. [para(1383(a,1),2698(a,1,2))]. 2700 K(x \ 1,x) * (R(x,y,z) \ u) = R((x \ 1) \ 1,y,z) \ u. [hyper(68,a,2699,a)]. 2702 (R(x,y,z) \ u) * K(x \ 1,x) = R((x \ 1) \ 1,y,z) \ u. [para(2700(a,1),1133(a,1)),flip(a)]. 2703 K(x,R((y \ 1) \ 1,z,u) \ w) = K(x,R(y,z,u) \ w). [para(2700(a,1),2388(a,1,2))]. 2704 1 / (R((x \ 1) \ 1,y,z) \ 1) = (R(x,y,z) \ 1) \ 1. [para(2702(a,1),1249(a,1,2))]. 2705 R((x \ 1) \ 1,y,z) = (R(x,y,z) \ 1) \ 1. [para(2704(a,1),57(a,1)),flip(a)]. 2706 1 / R((x \ 1) \ 1,y,z) = R(x,y,z) \ 1. [para(2705(a,2),57(a,1,2))]. 2707 R((x \ 1) \ 1,y,z) * K(u,R(x,y,z) \ 1) = T(R(x,y,z) \ 1,u) \ 1. [para(2705(a,2),1900(a,1,1))]. 2708 1 / R(x \ 1,y,z) = R(1 / x,y,z) \ 1. [para(59(a,1),2706(a,1,2,1,1))]. 2709 R(1 / (1 / x),y,z) \ 1 = 1 / R(x,y,z). [para(98(a,1),2706(a,1,2,1)),flip(a)]. 2710 K(R(1 / x,y,z) \ 1,u) * T(R(x \ 1,y,z) \ 1,x) = T(R(x \ 1,y,z) \ 1,T(u,1)). [para(2708(a,1),2476(a,1,1,1))]. 2711 R(1 / (1 / x),y,z) = 1 / (1 / R(x,y,z)). [para(2709(a,1),57(a,1,2)),flip(a)]. 2712 K(x,(R(1 / (1 / (1 / y)),z,u) * w) / R(y \ 1,z,u)) = K(T(x,y \ 1),w). [para(2711(a,2),2616(a,1,2,1,1))]. 2713 R((x \ 1) \ 1,y,z) * K(u,x \ 1) = T(R(x,y,z) \ 1,u) \ 1. [para(2127(a,1),2707(a,1,2))]. 2715 R(((x \ 1) \ 1) * K(y,x \ 1),z,u) = T(R(x,z,u) \ 1,y) \ 1. [para(2713(a,1),2502(a,2))]. 2716 R(T(x \ 1,y) \ 1,z,u) = T(R(x,z,u) \ 1,y) \ 1. [para(1900(a,1),2715(a,1,1))]. 2717 K(x,R(1 / (1 / (1 / y)),z,u) / (R(y \ 1,z,u) / w)) = K(T(x,y \ 1),w). [para(2712(a,1),921(a,1)),flip(a)]. 2718 K(x,R(1 / (1 / (1 / y)),z,u) / (R(y \ 1,z,u) / w)) = K(x,T(w,y)). [para(2717(a,2),2534(a,1))]. 2719 K(x,(1 / (1 / (1 / y))) / (R(y \ 1,z,u) / w)) = K(x,T(w,y)). [para(2718(a,1),2611(a,1)),flip(a)]. 2720 K(x,1 / ((R(y \ 1,z,u) / w) * (1 / (1 / y)))) = K(x,T(w,y)). [para(2719(a,1),918(a,1)),flip(a)]. 2722 K(x,1 / ((R(y \ 1,z,u) / w) * ((1 / y) \ 1))) = K(x,T(w,y)). [para(2720(a,1),2540(a,1)),flip(a)]. 2723 K(x,1 / ((R(y \ 1,z,u) / w) * y)) = K(x,T(w,y)). [para(59(a,1),2722(a,1,2,2,2))]. 2724 K(x,((R(y \ 1,z,u) / w) * y) \ 1) = K(x,T(w,y)). [para(2723(a,1),928(a,1)),flip(a)]. 2725 K(x,T(y / (z \ 1),z)) = K(x,R(z \ 1,u,w) \ y). [para(2724(a,1),2693(a,1))]. 2726 K(x,T(y * z,z)) = K(x,R(z \ 1,u,w) \ y). [para(2725(a,1),2407(a,1)),flip(a)]. 2728 K(x,R(y \ 1,z,u) \ w) = K(x,y * w). [para(2726(a,1),2606(a,1))]. 2729 K((1 / x) \ 1,y) * T(R(x \ 1,z,u) \ 1,x) = T(R(x \ 1,z,u) \ 1,T(y,1)). [para(2077(a,1),2710(a,1,1))]. 2730 K(x,y) * T(R(x \ 1,z,u) \ 1,x) = T(R(x \ 1,z,u) \ 1,T(y,1)). [para(59(a,1),2729(a,1,1,1))]. 2732 T(R(x \ 1,y,z) \ 1,T(u,1)) = K(x,u) * (R(x \ 1,y,z) \ 1). [para(2147(a,1),2730(a,1,2)),flip(a)]. 2733 K(x,y) * (R(x \ 1,z,u) \ 1) = T(R(x \ 1,z,u) \ 1,y). [para(1124(a,1),2732(a,1,2)),flip(a)]. 2734 ((x \ 1) * (R((x \ 1) \ 1,y,z) \ 1)) / (1 / x) = T(R((x \ 1) \ 1,y,z) \ 1,x). [para(2733(a,1),2149(a,2))]. 2735 K(x,(T(R((y \ 1) \ 1,z,u) \ 1,y) \ 1) \ w) = K(x,((R((y \ 1) \ 1,z,u) \ 1) \ 1) \ w). [para(2734(a,1),2411(a,1,2,1,1))]. 2736 K(x,R(T(((y \ 1) \ 1) \ 1,y) \ 1,z,u) \ w) = K(x,((R((y \ 1) \ 1,z,u) \ 1) \ 1) \ w). [para(2716(a,2),2735(a,1,2,1))]. 2737 K(x,R(T(((y \ 1) \ 1) \ 1,y) \ 1,z,u) \ w) = K(x,R((y \ 1) \ 1,z,u) \ w). [para(2736(a,2),2395(a,1))]. 2738 K(x,R(T(((y \ 1) \ 1) \ 1,y) \ 1,z,u) \ w) = K(x,R(y,z,u) \ w). [para(2737(a,2),2703(a,1))]. 2739 K(x,R(y,z,u) \ w) = K(x,T(((y \ 1) \ 1) \ 1,y) * w). [para(2738(a,1),2728(a,1))]. 2740 K(x,R(y,z,u) \ w) = K(x,T(y \ 1,y) * w). [para(2739(a,2),2398(a,1))]. 2742 K(x,R(y,z,u) \ w) = K(x,y \ w). [para(2740(a,2),2610(a,1))]. 2743 K(x,((y * (z \ u)) / u) \ w) = K(x,(y / z) \ w). [para(219(a,1),2742(a,1,2,1))]. 2744 a(x,K(y,z),u) = K(y,z) * K(z,(x / y) \ x). [para(2743(a,1),2633(a,1,2)),flip(a)]. 2745 a(x,K(y,z),u) = K(y,z) * K(z,y). [para(59(a,1),2744(a,2,2,2))]. 2749 a(x,K(y,z),u) = 1. [para(2745(a,2),1938(a,1))]. 2750 $F # answer("aK2"). [resolve(2749,a,46,a)]. ============================== end of proof ========================== ============================== STATISTICS ============================ Given=2456. Generated=9633316. Kept=2731. proofs=1. Usable=2455. Sos=271. Demods=0. Limbo=2, Disabled=30. Hints=3211. Kept_by_rule=0, Deleted_by_rule=9605389. Forward_subsumed=25196. Back_subsumed=2. 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=1377. Nonunit_bsub_feature_tests=75. Megabytes=12.21. User_CPU=135.70, System_CPU=4.08, Wall_clock=140. ============================== end of statistics ===================== ============================== end of search ========================= THEOREM PROVED THEOREM PROVED Exiting with 1 proof. ------ process 5364 exit (max_proofs) ------  Process 5364 exit (max_proofs) Sat Jan 4 12:59:27 2020