============================== prooftrans ============================ Prover9 (64) version 2017-09A, September 2017. Process 5127 was started by veroff on theorem, Sat Jan 4 12:55:08 2020 The command was "prover9 -f Ka_to_aK1.in". ============================== end of head =========================== ============================== end of input ========================== ============================== PROOF ================================= % -------- Comments from original proof -------- % Proof 1 at 114.85 (+ 3.29) seconds: "aK1". % Length of proof is 2167. % Level of proof is 183. % Maximum clause weight is 107.000. % Given clauses 2171 (11.863 givens/level). 1 x * y = z & x * u = z -> y = u # label(non_clause). [assumption]. 2 x * y = z & u * y = z -> x = u # label(non_clause). [assumption]. 3 x * y = x * z -> y = z # label(non_clause). [assumption]. 4 x * y = z * y -> x = 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(K(x,y),z,u) = 1 # label("aK1") # 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 K(a(x,y,z),u) = 1 # label("Ka"). [assumption]. 46 a(K(c1,c2),c3,c4) != 1 # label("aK1") # answer("aK1"). [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 1 * x != y | x = y. [para(11(a,1),19(a,2))]. 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) \ ((x * 1) * y) = a(x,1,y). [para(11(a,1),22(a,2,1,2)),flip(a)]. 72 (x * (y * z)) * a(x,y,z) = (x * y) * z. [para(22(a,2),14(a,1,2))]. 73 (x * y) \ ((x * (y / z)) * z) = a(x,y / z,z). [para(16(a,1),22(a,2,1,2)),flip(a)]. 74 (x * y) * K(y,x) = y * x. [para(24(a,2),14(a,1,2))]. 75 x \ ((y \ x) * y) = K(y \ x,y). [para(14(a,1),24(a,2,1)),flip(a)]. 76 ((x \ y) * x) \ y = K(x,x \ y). [para(14(a,1),24(a,2,2)),flip(a)]. 77 x \ (y * (x / y)) = K(y,x / y). [para(16(a,1),24(a,2,1)),flip(a)]. 78 (x * (y / x)) \ y = K(y / x,x). [para(16(a,1),24(a,2,2)),flip(a)]. 79 (x * y) * L(z,y,x) = x * (y * z). [para(26(a,2),14(a,1,2))]. 80 x \ (y * ((y \ x) * z)) = L(z,y \ x,y). [para(14(a,1),26(a,2,1)),flip(a)]. 81 L(x \ y,x,z) = (z * x) \ (z * y). [para(14(a,1),26(a,2,2,2))]. 82 x \ ((x / y) * (y * z)) = L(z,y,x / y). [para(16(a,1),26(a,2,1)),flip(a)]. 83 (x * y) / (y * 1) = R(x,y,1). [para(12(a,1),28(a,2,1)),flip(a)]. 84 R(x,x \ y,z) = (y * z) / ((x \ y) * z). [para(14(a,1),28(a,2,1,1))]. 85 R(x,y,z) * (y * z) = (x * y) * z. [para(28(a,2),16(a,1,1))]. 86 R(x / y,y,z) = (x * z) / (y * z). [para(16(a,1),28(a,2,1,1))]. 87 ((x * (y / z)) * z) / y = R(x,y / z,z). [para(16(a,1),28(a,2,2)),flip(a)]. 88 T(1,x) = x \ x. [para(11(a,1),30(a,2,2))]. 90 x * T(y,x) = y * x. [para(30(a,2),14(a,1,2))]. 91 T(x,x \ y) = (x \ y) \ y. [para(14(a,1),30(a,2,2))]. 92 T(x / y,y) = y \ x. [para(16(a,1),30(a,2,2))]. 93 T(a(x,y,z),u) = a(x,y,z). [hyper(35,a,45,a)]. 94 1 \ (x * 1) = x. [hyper(18,a,12,a,b,47,a(flip)),flip(a)]. 95 (x * (x \ 1)) \ y = y. [para(14(a,2),47(a,1,1))]. 96 ((1 / x) * x) \ y = y. [para(16(a,2),47(a,1,1))]. 98 x / (y * (y \ 1)) = x. [para(14(a,2),55(a,1,2))]. 99 x / ((1 / y) * y) = x. [para(16(a,2),55(a,1,2))]. 100 (x * (y * z)) / L(z,y,x) = x * y. [para(26(a,2),57(a,1,2))]. 101 (x * y) / T(x,y) = y. [para(30(a,2),57(a,1,2))]. 102 R(x,y,z) \ ((x * y) * z) = y * z. [para(28(a,2),59(a,1,1))]. 103 T(1,x) = 1. [para(88(a,2),48(a,1))]. 107 (x * (x \ 1)) * y != z | y = z. [para(14(a,2),63(a,1,1))]. 108 R(x,x \ 1,y) = y / ((x \ 1) * y). [para(49(a,1),28(a,2,1))]. 109 x \ ((x * y) * (y \ 1)) = a(x,y,y \ 1). [para(51(a,1),22(a,2,1)),flip(a)]. 110 L(x \ 1,x,y) = (y * x) \ y. [para(51(a,1),26(a,2,2))]. 111 R(1 / x,x,y) = y / (x * y). [para(58(a,1),28(a,2,1))]. 112 T((x * y) / x,x) = y. [hyper(17,a,16,a(flip),b,90,a)]. 113 (x * T(y,x)) / x = y. [hyper(18,a,16,a,b,90,a(flip)),flip(a)]. 114 x \ (y * T(x,y)) = y. [hyper(17,a,14,a,b,90,a(flip)),flip(a)]. 115 (x \ y) * T(x,x \ y) = y. [para(90(a,2),14(a,1))]. 116 x * (y * (y \ T(z,x))) = z * x. [para(14(a,2),90(a,1,2))]. 117 x * y != z * x | T(z,x) = y. [para(90(a,1),19(a,1)),flip(a)]. 118 x * T(y,x) != z * x | z = y. [para(90(a,2),20(a,2)),flip(a)]. 119 (x * (y * T(z,x * y))) \ (z * (x * y)) = a(x,y,T(z,x * y)). [para(90(a,1),22(a,2,2)),flip(a)]. 120 (x * y) \ (x * (z * y)) = L(T(z,y),y,x). [para(90(a,1),26(a,2,2,2)),flip(a)]. 121 ((x * y) * z) / (T(x,y) * z) = R(y,T(x,y),z). [para(90(a,1),28(a,2,1,1)),flip(a)]. 122 x * T(T(y,x),z) = T(y,z) * x. [para(36(a,1),90(a,1,2))]. 123 x * L(T(y,x),z,u) = L(y,z,u) * x. [para(38(a,2),90(a,1,2))]. 124 x * R(T(y,x),z,u) = R(y,z,u) * x. [para(40(a,2),90(a,1,2))]. 125 T(T(x / y,z),y) = T(y \ x,z). [para(92(a,1),36(a,1,1)),flip(a)]. 126 K(x \ 1,x) = (x \ 1) * x. [para(95(a,1),24(a,2))]. 127 x * ((x \ 1) * y) = L(y,x \ 1,x). [para(95(a,1),26(a,2)),flip(a)]. 128 K(x,1 / x) = x * (1 / x). [para(96(a,1),24(a,2))]. 129 (1 / x) * (x * y) = L(y,x,1 / x). [para(96(a,1),26(a,2)),flip(a)]. 130 (x * y) * (y \ 1) = R(x,y,y \ 1). [para(98(a,1),28(a,2)),flip(a)]. 131 (x * (1 / y)) * y = R(x,1 / y,y). [para(99(a,1),28(a,2)),flip(a)]. 132 x / T(y,y \ x) = y \ x. [para(14(a,1),101(a,1,1))]. 133 T(T((x * y) / x,z),x) = T(y,z). [para(112(a,1),36(a,1,1)),flip(a)]. 134 x \ (y * (y \ x)) = 1. [para(12(a,1),52(a,1,2,2,2))]. 135 x \ ((x * y) * L(z,y,x)) = y * z. [para(26(a,2),52(a,1,2,2))]. 136 x * (x \ y) = y * 1. [para(134(a,1),14(a,1,2)),flip(a)]. 138 x * (y * (y \ z)) = x * z. [para(13(a,1),53(a,1,2,2,2))]. 139 L(x \ (y \ z),x,y) = (y * x) \ z. [para(53(a,1),26(a,2,2))]. 140 x * (x \ (y * z)) = y * (u * (u \ z)). [para(52(a,1),53(a,1,2,2,2)),flip(a)]. 141 ((x * (x \ y)) / z) \ y = z. [hyper(66,a,60,a)]. 142 (x / y) * y = 1 * x. [para(50(a,1),60(a,1,1,1))]. 144 ((x / y) * y) / z = x / z. [para(16(a,1),61(a,1,1,1,1))]. 145 R((x / y) / z,z,y) = x / (z * y). [para(62(a,1),28(a,2,1))]. 146 ((x * y) / z) * z = ((x / u) * u) * y. [para(61(a,1),62(a,1,1,1,1)),flip(a)]. 147 ((x \ y) * x) * K(x,x \ y) = y. [para(74(a,2),14(a,1))]. 148 x * K(y \ x,y) = (y \ x) * y. [para(14(a,1),74(a,1,1))]. 149 (x * y) * z != y * x | K(y,x) = z. [para(74(a,1),19(a,1)),flip(a)]. 150 (x * y) / (x * K(x,y)) = R(y,x,K(x,y)). [para(74(a,1),28(a,2,1)),flip(a)]. 151 (x * y) * K(T(x,y),y) = T(x,y) * y. [para(90(a,1),74(a,1,1))]. 152 T(T(x,y),x \ z) = T((x \ z) \ z,y). [para(91(a,1),36(a,1,1)),flip(a)]. 153 T(x,a(y,z,u)) = x. [hyper(33,a,93,a)]. 154 a(x,y,z) * u = u * a(x,y,z). [para(93(a,1),90(a,1,2)),flip(a)]. 155 (x * a(y,z,u)) / x = a(y,z,u). [para(93(a,1),113(a,1,1,2))]. 156 K(x,a(y,z,u)) = 1. [hyper(34,a,153,a)]. 157 (x \ y) * z != y | T(x,x \ y) = z. [para(115(a,1),19(a,1)),flip(a)]. 158 L(T(x,x \ y),x \ y,z) = (z * (x \ y)) \ (z * y). [para(115(a,1),26(a,2,2,2))]. 159 K(x \ 1,x) / x = x \ 1. [hyper(70,a,126,a(flip))]. 160 (x \ 1) \ K(x \ 1,x) = x. [hyper(66,a,126,a(flip))]. 161 (x * K(y \ 1,y)) \ ((x * (y \ 1)) * y) = a(x,y \ 1,y). [para(126(a,2),22(a,2,1,2)),flip(a)]. 162 (x * (y \ 1)) \ (x * K(y \ 1,y)) = L(y,y \ 1,x). [para(126(a,2),26(a,2,2,2)),flip(a)]. 163 x \ K(x \ 1,x) = T(x \ 1,x). [para(126(a,2),30(a,2,2)),flip(a)]. 164 K(x,1 / x) / (1 / x) = x. [hyper(70,a,128,a(flip))]. 165 (x / (y * (y \ z))) * z = x. [para(138(a,1),16(a,1))]. 166 x / (y \ ((x / z) * z)) = y. [para(144(a,1),57(a,1))]. 167 R(x,y,y \ z) * z = (x * y) * (y \ z). [para(28(a,2),165(a,1,1))]. 168 x / L(y,z,x / (z * y)) = (x / (z * y)) * z. [para(26(a,2),166(a,1,2))]. 169 x * y != x * z | z = y. [para(12(a,1),64(a,1))]. 170 (x * y) / y = R(x,y,1). [para(12(a,1),83(a,1,2))]. 171 R(x,y,1) = x. [para(170(a,1),15(a,1))]. 172 L(x \ 1,x,y / x) = y \ (y / x). [para(16(a,1),110(a,2,1))]. 173 R((x * y) \ x,z,u) = L(R(y \ 1,z,u),y,x). [para(110(a,1),42(a,1,1))]. 174 L(L(x \ 1,y,z),x,u) = L((u * x) \ u,y,z). [para(110(a,1),43(a,1,1)),flip(a)]. 175 x / L(y \ 1,y,x) = x * y. [para(110(a,2),57(a,1,2))]. 176 L(x,1 / x,y) = (y * (1 / x)) \ y. [para(59(a,1),110(a,1,1))]. 177 R(1 / x,x,x \ y) = (x \ y) / y. [para(14(a,1),111(a,2,2))]. 178 T(x / (y * x),z) = R(T(1 / y,z),y,x). [para(111(a,1),40(a,2,1)),flip(a)]. 179 R(R(1 / x,y,z),x,u) = R(u / (x * u),y,z). [para(111(a,1),44(a,1,1)),flip(a)]. 180 R(1 / x,x,y) \ y = x * y. [para(111(a,2),59(a,1,1))]. 181 x * T(T(y,x),z) != u * x | T(y,z) = u. [para(36(a,1),118(a,1,2)),flip(b)]. 182 x / L(y,1 / y,x) = x * (1 / y). [para(59(a,1),175(a,1,2,1))]. 183 R(x,x \ 1,y) \ y = (x \ 1) * y. [para(57(a,1),180(a,1,1,1))]. 184 K(x,1 / x) \ 1 = K(1 / x,x). [para(128(a,2),78(a,1,1))]. 185 L(x \ T(y,z),x,z) = (z * x) \ (y * z). [para(116(a,1),26(a,2,2))]. 186 x * T(x \ (y * x),z) = T(y,z) * x. [para(30(a,1),122(a,1,2,1))]. 187 T(x / y,z) * y = y * T(y \ x,z). [para(92(a,1),122(a,1,2,1)),flip(a)]. 188 T((x * y) / x,z) * x = x * T(y,z). [para(112(a,1),122(a,1,2,1)),flip(a)]. 189 (x \ y) * T((x \ y) \ y,z) = T(x,z) * (x \ y). [para(91(a,1),122(a,1,2,1))]. 190 T(x,T(x,y) \ z) * y = y * ((T(x,y) \ z) \ z). [para(91(a,1),122(a,1,2)),flip(a)]. 191 (x * T(x \ y,z)) / x = T(y / x,z). [para(125(a,1),113(a,1,1,2))]. 193 (x * T(y,z)) / x = T((x * y) / x,z). [para(133(a,1),113(a,1,1,2))]. 194 T((((x * y) / x) \ z) \ z,x) = T(y,((x * y) / x) \ z). [para(91(a,1),133(a,1,1))]. 196 K(x \ 1,x) * K(x,x \ 1) = 1. [para(126(a,2),147(a,1,1))]. 197 K(K(x,1 / x) \ 1,K(x,1 / x)) = K(1 / x,x) * K(x,1 / x). [para(184(a,1),126(a,2,1))]. 198 K(x \ 1,x) * y != 1 | K(x,x \ 1) = y. [para(196(a,1),19(a,1)),flip(a)]. 199 (x * y) \ (x * y) = a(x,1,y). [para(12(a,1),71(a,1,2,1))]. 200 a(x,1,y) = 1. [para(199(a,1),48(a,1))]. 201 L(x,1,y) = x. [hyper(31,a,200,a)]. 204 x * L(y,z \ x,z) = z * ((z \ x) * y). [para(14(a,1),79(a,1,1))]. 205 x * L(y,z,x / z) = (x / z) * (z * y). [para(16(a,1),79(a,1,1))]. 206 (x * y) * z != x * (y * u) | L(u,y,x) = z. [para(79(a,1),19(a,1)),flip(a)]. 207 (x * (y * z)) \ ((x * y) * (L(z,y,x) * u)) = L(u,L(z,y,x),x * y). [para(79(a,1),26(a,2,1)),flip(a)]. 208 (x * (y * z)) \ (x * (y * (z * u))) = L(L(u,z,y),y * z,x). [para(79(a,1),26(a,2,2,2)),flip(a)]. 209 ((x * (y * z)) * u) / (L(z,y,x) * u) = R(x * y,L(z,y,x),u). [para(79(a,1),28(a,2,1,1)),flip(a)]. 210 (x * y) * T(L(z,y,x),u) = x * (y * T(z,u)). [para(38(a,1),79(a,1,2))]. 211 (x * y) * L(L(z,y,x),u,w) = x * (y * L(z,u,w)). [para(43(a,1),79(a,1,2))]. 212 (x * y) * L(z,T(x,y),y) = y * (T(x,y) * z). [para(90(a,1),79(a,1,1))]. 213 K(x \ 1,x) * L(y,x,x \ 1) = (x \ 1) * (x * y). [para(126(a,2),79(a,1,1))]. 214 L((x \ y) \ z,x \ y,x) = y \ (x * z). [para(14(a,1),81(a,2,1))]. 215 L(x \ y,x,z / x) = z \ ((z / x) * y). [para(16(a,1),81(a,2,1))]. 216 T((x * y) \ (x * z),u) = L(T(y \ z,u),y,x). [para(81(a,1),38(a,2,1)),flip(a)]. 217 R((x * y) \ (x * z),u,w) = L(R(y \ z,u,w),y,x). [para(81(a,1),42(a,1,1))]. 218 L(L(x \ y,z,u),x,w) = L((w * x) \ (w * y),z,u). [para(81(a,1),43(a,1,1)),flip(a)]. 219 L(T(x,y) \ z,T(x,y),y) = (x * y) \ (y * z). [para(90(a,1),81(a,2,1))]. 220 L((x \ 1) \ y,x \ 1,x) = x * y. [para(81(a,2),95(a,1))]. 221 L(x \ y,x,1 / x) = (1 / x) * y. [para(81(a,2),96(a,1))]. 222 L(x \ y,x,y \ 1) = ((y \ 1) * x) \ K(y \ 1,y). [para(126(a,2),81(a,2,2))]. 223 x / L(y \ z,y,x / z) = (x / z) * y. [para(81(a,2),166(a,1,2))]. 224 L(x \ ((y * x) / y),x,y) = K(y,(y * x) / y). [para(81(a,2),77(a,1))]. 225 R(x,y / z,z) * y = (x * (y / z)) * z. [para(16(a,1),85(a,1,2))]. 226 (x * y) * z != u * (y * z) | R(x,y,z) = u. [para(85(a,1),20(a,1))]. 227 (R(x,y,z) * ((y * z) * u)) \ (((x * y) * z) * u) = a(R(x,y,z),y * z,u). [para(85(a,1),22(a,2,2,1)),flip(a)]. 228 (((x * y) * z) * u) / ((y * z) * u) = R(R(x,y,z),y * z,u). [para(85(a,1),28(a,2,1,1)),flip(a)]. 229 ((x * R(y,z,u)) * (z * u)) / ((y * z) * u) = R(x,R(y,z,u),z * u). [para(85(a,1),28(a,2,2)),flip(a)]. 230 L(R(x,y,z),u,w) * (y * z) = (L(x,u,w) * y) * z. [para(42(a,1),85(a,1,1))]. 231 R(R(x,y,z),u,w) * (y * z) = (R(x,u,w) * y) * z. [para(44(a,1),85(a,1,1))]. 232 R(x,y,T(z,y)) * (z * y) = (x * y) * T(z,y). [para(90(a,1),85(a,1,2))]. 233 R(x,y \ 1,y) * K(y \ 1,y) = (x * (y \ 1)) * y. [para(126(a,2),85(a,1,2))]. 234 R(x,y,1 / y) * K(y,1 / y) = (x * y) * (1 / y). [para(128(a,2),85(a,1,2))]. 235 R(x,R(y,z,u),z * u) * ((y * z) * u) = (x * R(y,z,u)) * (z * u). [para(85(a,1),85(a,1,2))]. 236 R(x / y,y,x \ z) = z / (y * (x \ z)). [para(14(a,1),86(a,2,1))]. 237 R(x / y,y,y \ z) = (x * (y \ z)) / z. [para(14(a,1),86(a,2,2))]. 238 R(x / (y / z),y / z,z) = (x * z) / y. [para(16(a,1),86(a,2,2))]. 239 T((x * y) / (z * y),u) = R(T(x / z,u),z,y). [para(86(a,1),40(a,2,1)),flip(a)]. 240 R(x / y,y,T(z,y)) = (x * T(z,y)) / (z * y). [para(90(a,1),86(a,2,2))]. 241 R(x / y,y,y \ 1) = x * (y \ 1). [para(86(a,2),98(a,1))]. 242 R(x / (1 / y),1 / y,y) = x * y. [para(86(a,2),99(a,1))]. 243 R((x * y) / z,z,K(y,x)) = (y * x) / (z * K(y,x)). [para(74(a,1),86(a,2,1))]. 244 R((x \ 1) / y,y,x) = K(x \ 1,x) / (y * x). [para(126(a,2),86(a,2,1))]. 245 (x * (1 / y)) / K(y,1 / y) = R(x / y,y,1 / y). [para(128(a,2),86(a,2,2)),flip(a)]. 246 (x * y) / L(z,y / z,x) = x * (y / z). [para(16(a,1),100(a,1,1,2))]. 247 (x * y) / L(T(z,z \ y),z \ y,x) = x * (z \ y). [para(115(a,1),100(a,1,1,2))]. 248 (x * ((y \ z) * y)) / L(K(y \ z,y),z,x) = x * z. [para(148(a,1),100(a,1,1,2))]. 249 R(x,x \ y,z) \ (y * z) = (x \ y) * z. [para(14(a,1),102(a,1,2,1))]. 250 R(x,T(y,x),z) \ ((y * x) * z) = T(y,x) * z. [para(90(a,1),102(a,1,2,1))]. 251 R(x * y,K(y,x),z) \ ((y * x) * z) = K(y,x) * z. [para(74(a,1),102(a,1,2,1))]. 252 R(x,y,K(y,x)) \ (y * x) = y * K(y,x). [para(74(a,1),102(a,1,2))]. 253 R(x * y,L(z,y,x),u) \ ((x * (y * z)) * u) = L(z,y,x) * u. [para(79(a,1),102(a,1,2,1))]. 254 R(x,x \ 1,(x \ 1) \ y) = ((x \ 1) \ y) / y. [para(14(a,1),108(a,2,2))]. 255 R(x \ 1,(x \ 1) \ 1,y) = y / (T(x,x \ 1) * y). [para(91(a,2),108(a,2,2,1))]. 256 x / K(x \ 1,x) = R(x,x \ 1,x). [para(126(a,2),108(a,2,2)),flip(a)]. 257 L(x,y \ 1,y) / ((y \ 1) * x) = y. [hyper(70,a,127,a)]. 258 x \ L(y,x \ 1,x) = (x \ 1) * y. [hyper(66,a,127,a)]. 259 x * K(x \ 1,x) = L(x,x \ 1,x). [para(126(a,2),127(a,1,2))]. 260 L(x,y,1 / y) / (y * x) = 1 / y. [hyper(70,a,129,a)]. 261 (1 / x) \ L(y,x,1 / x) = x * y. [hyper(66,a,129,a)]. 262 L(T(x,y),y,1 / y) = (1 / y) * (x * y). [para(90(a,1),129(a,1,2)),flip(a)]. 263 R(x,y,y \ 1) / (y \ 1) = x * y. [hyper(70,a,130,a)]. 264 (x \ 1) \ R(y,x,x \ 1) = T(y * x,x \ 1). [para(130(a,1),30(a,2,2)),flip(a)]. 265 K(x \ 1,x) * (x \ 1) = R(x \ 1,x,x \ 1). [para(126(a,2),130(a,1,1))]. 266 R(x,1 / y,y) / y = x * (1 / y). [hyper(70,a,131,a)]. 267 K(x,1 / x) * x = R(x,1 / x,x). [para(128(a,2),131(a,1,1))]. 268 L(T(x \ (y \ z),u),x,y) = T((y * x) \ z,u). [para(139(a,1),38(a,2,1))]. 269 L(R(x \ (y \ z),u,w),x,y) = R((y * x) \ z,u,w). [para(139(a,1),42(a,1,1)),flip(a)]. 270 T(x \ (x / y),z) = L(T(y \ 1,z),y,x / y). [para(172(a,1),38(a,2,1)),flip(a)]. 271 L(x \ 1,x,y / x) * y = (y / x) * K(y \ (y / x),y). [para(172(a,2),148(a,2,1)),flip(a)]. 272 K(x,1 / x) \ x = L(x,1 / x,x). [para(128(a,2),176(a,2,1)),flip(a)]. 273 L(T(x \ y,z),x,1 / x) = T((1 / x) * y,z). [para(221(a,1),38(a,2,1))]. 274 L(R(x \ y,z,u),x,1 / x) = R((1 / x) * y,z,u). [para(221(a,1),42(a,1,1)),flip(a)]. 275 L(L(x \ y,z,u),x,1 / x) = L((1 / x) * y,z,u). [para(221(a,1),43(a,1,1)),flip(a)]. 276 L(K(x \ 1,x) \ y,K(x \ 1,x),x) = L(x,x \ 1,x) \ (x * y). [para(259(a,1),81(a,2,1))]. 277 L(R(x,1 / y,y),z,u) / y = L(x,z,u) * (1 / y). [para(42(a,1),266(a,1,1))]. 278 L(x / y,z,u) * y = y * L(y \ x,z,u). [para(92(a,1),123(a,1,2,1)),flip(a)]. 279 L(a(x,y,z),u,w) * v5 = v5 * L(a(x,y,z),u,w). [para(93(a,1),123(a,1,2,1)),flip(a)]. 280 x * (y * T(z,x * y)) = L(z,y,x) * (x * y). [para(123(a,1),79(a,1)),flip(a)]. 281 x \ (L(y,z,x) * (x * z)) = z * T(y,x * z). [para(123(a,1),135(a,1,2))]. 283 R(x / y,z,u) * y = y * R(y \ x,z,u). [para(92(a,1),124(a,1,2,1)),flip(a)]. 284 R((x * y) / x,z,u) * x = x * R(y,z,u). [para(112(a,1),124(a,1,2,1)),flip(a)]. 285 x \ L(R(T(y,x \ 1),z,u),x \ 1,x) = R(y,z,u) * (x \ 1). [para(124(a,1),258(a,2))]. 286 x * (y * (y \ z)) != u * w | u \ (x * z) = w. [para(140(a,1),19(a,1))]. 287 ((x / y) * y) * z != u * w | (x * z) / w = u. [para(146(a,1),20(a,1))]. 288 R(x,y,K(T(x,y),y)) \ (T(x,y) * y) = y * K(T(x,y),y). [para(151(a,1),102(a,1,2))]. 289 T(T(x,((x \ y) \ y) \ z),x \ y) = (((x \ y) \ y) \ z) \ z. [para(152(a,2),91(a,1))]. 290 T(T(x \ y,z),(x \ y) \ y) = T(T(x,x \ y) \ y,z). [para(91(a,2),152(a,2,1,1))]. 291 T((x * (y / z)) / x,z) = (x * (z \ y)) / x. [para(92(a,1),193(a,1,1,2)),flip(a)]. 292 ((x * y) * z) / ((y * z) * a(x,y,z)) = R(x,y * z,a(x,y,z)). [para(72(a,1),28(a,2,1)),flip(a)]. 293 x * a(x,y,y \ 1) = (x * y) * (y \ 1). [para(51(a,1),72(a,1,1))]. 294 a(x,y,z) * (x * (y * z)) = (x * y) * z. [para(72(a,1),154(a,2))]. 295 a(x,y,z) = ((x * y) * z) / (x * (y * z)). [para(72(a,1),155(a,1,1)),flip(a)]. 296 L(T(x,y \ z),y \ z,y) = z \ (y * (x * (y \ z))). [para(90(a,1),80(a,1,2,2)),flip(a)]. 297 x \ (y * K(y \ x,1 / (y \ x))) = L(1 / (y \ x),y \ x,y). [para(128(a,2),80(a,1,2,2))]. 298 T((x * y) / x,x * y) = L(y,x,(x * y) / x). [para(82(a,1),30(a,2))]. 299 L(T(x,y),y,z / y) = z \ ((z / y) * (x * y)). [para(90(a,1),82(a,1,2,2)),flip(a)]. 300 x \ ((x / (y * z)) * R(y,z,z \ 1)) = L(z \ 1,y * z,x / (y * z)). [para(130(a,1),82(a,1,2,2))]. 301 (K((x / y) \ 1,x / y) * y) / x = R((x / y) \ 1,x / y,y). [para(126(a,2),87(a,1,1,1))]. 302 a(x / y,y,y \ 1) = (x / y) \ (x * (y \ 1)). [para(16(a,1),109(a,1,2,1)),flip(a)]. 303 a(1 / x,x,x \ 1) = (1 / x) \ (x \ 1). [para(58(a,1),109(a,1,2)),flip(a)]. 304 x \ R(x,y,y \ 1) = a(x,y,y \ 1). [para(130(a,1),109(a,1,2))]. 305 L(T(x,y),y,x) = T(x,x * y). [para(120(a,1),30(a,2)),flip(a)]. 306 T(L(x,y,x),y) = T(x,x * y). [para(305(a,1),38(a,1)),flip(a)]. 307 L(T(T(x,y),z),y,x) = T(T(x,x * y),z). [para(305(a,1),38(a,2,1))]. 308 L(R(T(x,y),z,u),y,x) = R(T(x,x * y),z,u). [para(305(a,1),42(a,1,1)),flip(a)]. 309 x * T(y,y * x) = L(y,x,y) * x. [para(305(a,1),123(a,1,2))]. 310 T((x * y) / x,y * x) = L(y,x,y). [hyper(18,a,188,a,b,309,a(flip)),flip(a)]. 311 T(x / y,(y \ x) * y) = L(y \ x,y,y \ x). [hyper(18,a,187,a,b,309,a(flip)),flip(a)]. 312 L(R(x,y,y \ z),u,w) * z = (L(x,u,w) * y) * (y \ z). [para(42(a,1),167(a,1,1))]. 313 R(R(x,y,y \ z),u,w) * z = (R(x,u,w) * y) * (y \ z). [para(44(a,1),167(a,1,1))]. 314 T(x / (y * x),y) = R(y \ 1,y,x). [para(92(a,1),178(a,2,1))]. 315 T((x \ y) / (x * (x \ y)),z) * y = (T(1 / x,z) * x) * (x \ y). [para(178(a,2),167(a,1,1))]. 316 (x / (y * x)) * y = y * R(y \ 1,y,x). [para(314(a,1),90(a,1,2)),flip(a)]. 317 R(x \ 1,x,x \ 1) = T(x \ 1,x). [para(98(a,1),314(a,1,1)),flip(a)]. 318 K(x,y) = L(x \ T(x,y),x,y). [para(185(a,2),24(a,2))]. 320 x * ((x \ y) * T(z,y)) = L(z,x \ y,x) * y. [para(204(a,1),123(a,1))]. 321 x * R(L(y,z,x / z),u,w) = (x / z) * (z * R(y,u,w)). [para(42(a,2),205(a,1,2))]. 322 (x / y) * (y * T(z,x)) = L(z,y,x / y) * x. [para(205(a,1),123(a,1))]. 323 L(T((x \ y) \ z,u),x \ y,x) = T(y \ (x * z),u). [para(214(a,1),38(a,2,1))]. 324 L(R((x \ y) \ z,u,w),x \ y,x) = R(y \ (x * z),u,w). [para(214(a,1),42(a,1,1)),flip(a)]. 325 L(L((x \ y) \ z,u,w),x \ y,x) = L(y \ (x * z),u,w). [para(214(a,1),43(a,1,1)),flip(a)]. 327 R(T(x / (y / z),u),y / z,z) = T((x * z) / y,u). [para(238(a,1),40(a,2,1))]. 328 R(R(x / (y / z),u,w),y / z,z) = R((x * z) / y,u,w). [para(238(a,1),44(a,1,1)),flip(a)]. 329 (x * y) / L(z * y,y / (z * y),x) = x * R(1 / z,z,y). [para(111(a,2),246(a,2,2))]. 330 R(x,x \ (y / z),z) \ y = (x \ (y / z)) * z. [para(16(a,1),249(a,1,2))]. 331 R(x \ y,(x \ y) \ y,z) \ (y * z) = T(x,x \ y) * z. [para(91(a,2),249(a,2,1))]. 332 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),252(a,1,1))]. 333 a(x,y \ 1,y) * (x * K(y \ 1,y)) = (x * (y \ 1)) * y. [para(126(a,2),294(a,1,2,2))]. 334 (((x / (y * z)) * y) * z) / x = a(x / (y * z),y,z). [para(16(a,1),295(a,2,2)),flip(a)]. 335 (x * y) * T(T(x,x * y),z) = x * (y * T(T(x,y),z)). [para(307(a,1),79(a,1,2))]. 336 (x * L(x \ y,z,u)) / x = L(y / x,z,u). [hyper(70,a,278,a)]. 337 (x * R(x \ y,z,u)) \ (x * R(y / x,z,u)) = K(x,R(y / x,z,u)). [para(283(a,1),24(a,2,1)),flip(a)]. 338 (x * R(x \ y,z,u)) \ R(y / x,z,u) = L(x \ 1,x,R(y / x,z,u)). [para(283(a,1),110(a,2,1)),flip(a)]. 339 ((x * y) / (z * y)) * z = z * R(z \ x,z,y). [para(86(a,1),283(a,1,1))]. 340 (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(150(a,1),283(a,1,1,1)),flip(a)]. 341 R((x * y) / x,z,u) = (x * R(y,z,u)) / x. [hyper(70,a,284,a),flip(a)]. 342 ((x * (y / z)) / x) * z = z * ((x * (z \ y)) / x). [para(291(a,1),90(a,1,2)),flip(a)]. 343 L((x * y) / x,z,u) = (x * L(y,z,u)) / x. [para(13(a,1),336(a,1,1,2,1)),flip(a)]. 344 (x * ((y * x) \ y)) / x = L(1 / x,x,y). [para(110(a,1),336(a,1,1,2))]. 345 ((x \ y) * (y \ x)) / (x \ y) = L(1 / (x \ y),x \ y,x). [para(14(a,1),344(a,1,1,2,1))]. 346 R((x * (1 / y)) / x,y,z) = (x * (z / (y * z))) / x. [para(111(a,1),341(a,2,1,2))]. 347 R((x * ((y / z) / u)) / x,u,z) = (x * (y / (u * z))) / x. [para(145(a,1),341(a,2,1,2))]. 348 L((x * (y \ z)) / x,y,u) = (x * ((u * y) \ (u * z))) / x. [para(81(a,1),343(a,2,1,2))]. 349 L((x * ((y \ z) \ u)) / x,y \ z,y) = (x * (z \ (y * u))) / x. [para(214(a,1),343(a,2,1,2))]. 350 x \ ((x * (1 / y)) * y) = a(x,1 / y,y). [para(12(a,1),73(a,1,1))]. 351 x \ R(x,1 / y,y) = a(x,1 / y,y). [para(131(a,1),350(a,1,2))]. 352 L(L(x \ 1,y * x,z),x,y) = (z * (y * x)) \ (z * y). [para(174(a,2),81(a,1))]. 353 L(L(x \ 1,y * x,z / (y * x)),x,y) = z \ ((z / (y * x)) * y). [para(174(a,2),215(a,1))]. 354 R(x / (y * x),y,y \ 1) = R(1 * (y \ 1),y,x). [para(241(a,1),179(a,1,1)),flip(a)]. 355 (x * y) * T((x * y) \ x,z) = x * (y * T(y \ 1,z)). [para(110(a,1),210(a,1,2,1))]. 356 (x * y) * T((x * y) \ (x * z),u) = x * (y * T(y \ z,u)). [para(81(a,1),210(a,1,2,1))]. 357 (x * y) * T((x * y) \ z,u) = x * (y * T(y \ (x \ z),u)). [para(139(a,1),210(a,1,2,1))]. 358 (x * y) * R((y * T(x,y)) \ y,z,u) = y * (T(x,y) * R(T(x,y) \ 1,z,u)). [para(173(a,2),212(a,1,2))]. 359 R(T(x,x * y),y,T(x,y)) = T(x,y). [hyper(17,a,124,a,b,232,a(flip)),flip(a)]. 360 R(T(x / y,y * z),y,z) = (y * z) \ (x * z). [para(239(a,1),92(a,1))]. 361 T((x * y) / (z * y),z) = R(z \ x,z,y). [para(92(a,1),239(a,2,1))]. 362 R(x,y,z) = T(((y * x) * z) / (y * z),y). [para(112(a,1),239(a,2,1)),flip(a)]. 363 R(T(x / y,z),y,u) * (y * u) = (y * u) * T((y * u) \ (x * u),z). [para(239(a,1),187(a,1,1))]. 364 T((x * (y \ z)) / z,y) = R(y \ x,y,y \ z). [para(14(a,1),361(a,1,1,2))]. 365 R((x / y) \ z,x / y,y) = T((z * y) / x,x / y). [para(16(a,1),361(a,1,1,2)),flip(a)]. 366 T(R(x \ y,x,z),x * z) = T((x * z) \ (y * z),x). [para(361(a,1),125(a,1,1))]. 367 T(((1 / x) * y) * x,1 / x) = R(y,1 / x,x). [para(99(a,1),362(a,2,1)),flip(a)]. 368 T(R(x / y,y,T(z,y)),z * y) = (z * y) \ (x * T(z,y)). [para(240(a,2),92(a,1,1))]. 369 K(x \ 1,x) / L(x,y,K(x \ 1,x) / (y * x)) = R((x \ 1) / y,y,x) * y. [para(244(a,2),168(a,2,1))]. 370 R(x,T(y,x),T(z,y * x)) \ (z * (y * x)) = T(y,x) * T(z,y * x). [para(90(a,1),250(a,1,2))]. 371 R(x,x \ 1,T(x,x \ 1)) = ((x \ 1) \ 1) / 1. [para(91(a,2),254(a,1,3))]. 373 (1 / x) \ T(((1 / x) * x) \ y,z) = x * T(x \ ((1 / x) \ y),z). [para(268(a,1),261(a,1,2))]. 374 (x / y) * (y * T(y \ 1,z)) = x * T(x \ (x / y),z). [para(270(a,2),205(a,1,2)),flip(a)]. 375 (1 / x) * ((x \ y) * x) = T((1 / x) * y,x). [para(273(a,1),262(a,1)),flip(a)]. 376 (1 / x) * ((x \ 1) * x) = T(1 / x,x). [para(12(a,1),375(a,2,1))]. 377 T((1 / x) * y,x) != (1 / x) * z | (x \ y) * x = z. [para(375(a,1),19(a,1))]. 378 (1 / x) * ((x \ 1) * x) = x \ 1. [para(376(a,2),92(a,1))]. 379 (1 / (1 / x)) * (x * (1 / x)) = (1 / x) \ 1. [para(59(a,1),378(a,1,2,1))]. 380 (1 / x) * K(x \ 1,x) = x \ 1. [para(126(a,2),378(a,1,2))]. 381 (1 / x) \ (x \ 1) = K(x \ 1,x). [hyper(66,a,380,a)]. 382 R(x / (1 / y),1 / y,K(y \ 1,y)) = (x * K(y \ 1,y)) / (y \ 1). [para(380(a,1),86(a,2,2))]. 383 K((x \ 1) \ 1,x \ 1) = x \ ((x \ 1) \ 1). [para(57(a,1),381(a,1,1)),flip(a)]. 384 a(1 / x,x,x \ 1) = K(x \ 1,x). [para(381(a,1),303(a,2))]. 385 T(x,K(y \ 1,y)) = x. [para(384(a,1),153(a,1,2))]. 386 K(x,K(y \ 1,y)) = 1. [para(384(a,1),156(a,1,2))]. 387 T(K(x \ 1,x),y) = K(x \ 1,x). [hyper(33,a,385,a)]. 388 K(x \ 1,x) \ (y * K(x \ 1,x)) = y. [para(385(a,1),30(a,1)),flip(a)]. 389 T(x,K(y,1 / y)) = x. [para(59(a,1),385(a,1,2,1))]. 390 K(x \ 1,x) * y = y * K(x \ 1,x). [para(385(a,1),90(a,1,2))]. 391 x / K(y \ 1,y) = K(y \ 1,y) \ x. [para(385(a,1),92(a,1))]. 392 (x * K(y \ 1,y)) / x = K(y \ 1,y). [para(385(a,1),101(a,1,2))]. 393 T(x,(y \ 1) * y) = x. [para(126(a,1),385(a,1,2))]. 394 K(x,K(y,1 / y)) = 1. [para(59(a,1),386(a,1,2,1))]. 395 K(x,1 / x) * y = y * K(x,1 / x). [para(389(a,1),90(a,1,2))]. 396 x / K(y,1 / y) = K(y,1 / y) \ x. [para(389(a,1),92(a,1))]. 397 T(x,y * (1 / y)) = x. [para(128(a,1),389(a,1,2))]. 398 (K(x \ 1,x) \ y) \ y = K(x \ 1,x). [para(387(a,1),91(a,1)),flip(a)]. 399 L(K(x \ 1,x),y,z) * u = u * L(K(x \ 1,x),y,z). [para(387(a,1),123(a,1,2,1)),flip(a)]. 400 K(x \ 1,x) \ (x \ 1) = 1 / x. [para(380(a,1),388(a,1,2))]. 401 R(1 / x,x,K(y \ 1,y)) = K(y \ 1,y) / (K(y \ 1,y) * x). [para(390(a,2),111(a,2,2))]. 402 K(x,x \ 1) * K(x \ 1,x) = 1. [para(390(a,1),196(a,1))]. 403 L(x \ y,x,K(z \ 1,z)) = (x * K(z \ 1,z)) \ (K(z \ 1,z) * y). [para(390(a,1),81(a,2,1))]. 404 R(x / y,y,K(z \ 1,z)) = (x * K(z \ 1,z)) / (K(z \ 1,z) * y). [para(390(a,2),86(a,2,2))]. 405 (x \ 1) * K(x \ 1,x) = R(x \ 1,x,x \ 1). [para(390(a,1),265(a,1))]. 406 K(x,x \ 1) \ 1 = K(x \ 1,x). [hyper(66,a,402,a)]. 407 K(x \ 1,x) \ x = R(x,x \ 1,x). [para(391(a,1),256(a,1))]. 408 L(x,x \ 1,x) / x = K(x \ 1,x). [para(259(a,1),392(a,1,1))]. 409 x * K(x,1 / x) = R(x,1 / x,x). [para(395(a,1),267(a,1))]. 410 (1 / (1 / x)) * (x * (1 / x)) = x. [para(379(a,2),59(a,1))]. 411 (1 / (1 / x)) * K(x,1 / x) = x. [para(128(a,2),410(a,1,2))]. 412 K(x,1 / x) * (1 / (1 / x)) = x. [para(411(a,1),395(a,2))]. 413 x / (1 / (1 / x)) = K(x,1 / x). [hyper(70,a,412,a)]. 414 K(x,1 / x) \ x = 1 / (1 / x). [hyper(66,a,412,a)]. 415 L(x,1 / x,x) = 1 / (1 / x). [para(414(a,1),272(a,1)),flip(a)]. 416 L(K(x \ 1,x),y,z) * (z * y) = z * (y * K(x \ 1,x)). [para(387(a,1),280(a,1,2,2)),flip(a)]. 417 T(L(x,y,(y * x) / y),y) = T(y \ (y * x),y * x). [para(298(a,1),125(a,1,1))]. 418 T(((x * y) * z) / (x * z),x * y) = R(L(y,x,(x * y) / x),x,z). [para(298(a,1),239(a,2,1))]. 419 T(((x / y) * y) \ ((x / y) * z),y) = x \ ((x / y) * ((y \ z) * y)). [para(299(a,1),216(a,2))]. 420 x \ ((x / y) * ((y \ 1) * y)) = T(x \ (x / y),y). [para(299(a,1),270(a,2)),flip(a)]. 421 T(x,(y / z) \ (y * (z \ 1))) = x. [para(302(a,1),153(a,1,2))]. 422 L(((x / y) \ (x * (y \ 1))) \ z,a(x / y,y,y \ 1),x / y) = (x * (y \ 1)) \ ((x / y) * z). [para(302(a,2),214(a,1,2))]. 423 ((x / y) \ (x * (y \ 1))) * (x / y) = x * (y \ 1). [para(421(a,1),115(a,1,2))]. 424 (x * y) * R(T(x,x * y),z,u) = x * (y * R(T(x,y),z,u)). [para(308(a,1),79(a,1,2))]. 425 L(x \ 1,x,x \ 1) = 1 / x. [para(311(a,1),393(a,1))]. 426 x \ (L(y,x \ z,x) * z) = (x \ z) * T(y,z). [hyper(66,a,320,a)]. 427 (x / y) \ (L(z,y,x / y) * x) = y * T(z,x). [hyper(66,a,322,a)]. 428 L(x,y,z / y) * z != (z / y) * u | y * T(x,z) = u. [para(322(a,1),19(a,1))]. 429 T((x * (y \ z)) / z,y) * z = ((y \ x) * y) * (y \ z). [para(364(a,2),167(a,1,1))]. 430 R(x,1 / x,x) = T(x,1 / x). [para(58(a,1),367(a,1,1)),flip(a)]. 431 x * K(x,1 / x) = T(x,1 / x). [para(430(a,1),409(a,2))]. 432 R(x,x \ 1,T(x,x \ 1)) = (x \ 1) \ 1. [para(371(a,2),55(a,1))]. 433 (x \ 1) * K(x \ 1,x) = T(x \ 1,x). [para(405(a,2),317(a,1))]. 434 (x \ y) * T((x \ y) \ z,y) = x \ ((y \ (x * z)) * y). [para(214(a,1),426(a,1,2,1)),flip(a)]. 435 T(x,L(a(y,z,u),w,v5)) = x. [hyper(118,a,279,a)]. 436 T(x,L(K(y \ 1,y),z,u)) = x. [para(384(a,1),435(a,1,2,1))]. 437 T(x,L(y \ ((y \ 1) \ 1),z,u)) = x. [para(383(a,1),436(a,1,2,1))]. 438 T(x,L(y \ T(y,y \ 1),z,u)) = x. [para(91(a,2),437(a,1,2,1,2))]. 439 T(x,K(y,y \ 1)) = x. [para(318(a,2),438(a,1,2))]. 440 T(K(x,x \ 1),y) = K(x,x \ 1). [hyper(33,a,439,a)]. 441 (K(x,x \ 1) \ y) * K(x,x \ 1) = y. [hyper(17,a,375,a,b,439,a(flip)),flip(a)]. 442 K(x,x \ 1) * y = y * K(x,x \ 1). [para(439(a,1),90(a,1,2))]. 443 x \ (K(y,y \ 1) * x) = K(y,y \ 1). [para(439(a,1),114(a,1,2,2))]. 444 K(x,x \ 1) * y != z * K(x,x \ 1) | z = y. [para(439(a,1),118(a,1,2))]. 445 L(K(x,x \ 1),y,z) * (z * y) = z * (y * K(x,x \ 1)). [para(440(a,1),280(a,1,2,2)),flip(a)]. 446 (x * K(y,y \ 1)) \ (K(y,y \ 1) * (x * z)) = L(z,x,K(y,y \ 1)). [para(442(a,1),26(a,2,1)),flip(a)]. 447 (x * (K(y,y \ 1) * z)) * a(x,z,K(y,y \ 1)) = (x * z) * K(y,y \ 1). [para(442(a,2),72(a,1,1,2))]. 448 R(x,x \ y,K(z,z \ 1)) \ (K(z,z \ 1) * y) = (x \ y) * K(z,z \ 1). [para(442(a,2),249(a,1,2))]. 449 (x * y) * K(z,z \ 1) != u * (K(z,z \ 1) * y) | R(x,y,K(z,z \ 1)) = u. [para(442(a,2),226(a,2,2))]. 450 (x \ y) * ((z * ((x \ y) \ y)) / z) = ((z * x) / z) * (x \ y). [para(57(a,1),342(a,1,1,1,2)),flip(a)]. 451 R(x / (y * x),y,y \ 1) = R(y \ 1,y,x). [para(11(a,1),354(a,2,1))]. 452 R(x / y,y / x,(y / x) \ 1) = R((y / x) \ 1,y / x,x). [para(16(a,1),451(a,1,1,2))]. 453 x \ ((x / y) * K(y \ 1,y)) = T(x \ (x / y),y). [para(126(a,2),420(a,1,2,2))]. 454 (x * (y \ 1)) \ (((x / y) \ (x * (y \ 1))) * (z * (x / y))) = L(T(z,x / y),x / y,(x / y) \ (x * (y \ 1))). [para(423(a,1),120(a,1,1))]. 455 (x * (y \ 1)) \ (K(y \ 1,y) * x) = L(y,y \ 1,x). [para(390(a,2),162(a,1,2))]. 456 (x * y) * L((x * y) \ z,u,w) = x * (y * L(y \ (x \ z),u,w)). [para(139(a,1),211(a,1,2,1))]. 457 (x * y) * L(T(x,x * y),z,u) = x * (y * L(T(x,y),z,u)). [para(305(a,1),211(a,1,2,1))]. 459 K(x \ 1,x) * T(((x \ 1) * x) \ y,z) = (x \ 1) * (x * T(x \ ((x \ 1) \ y),z)). [para(268(a,1),213(a,1,2))]. 460 (x * y) * L((y * T(x,y)) \ (y * z),u,w) = y * (T(x,y) * L(T(x,y) \ z,u,w)). [para(218(a,1),212(a,1,2))]. 461 L((x * y) / (z * y),u,w) * (z * y) = (L(x / z,u,w) * z) * y. [para(86(a,1),230(a,1,1,1))]. 462 (L(x / (y / z),u,w) * (y / z)) * z = L((x * z) / y,u,w) * ((y / z) * z). [para(238(a,1),230(a,1,1,1)),flip(a)]. 463 x \ ((L(y,z,x) * x) * z) = z * T(R(y,x,z),x * z). [para(230(a,1),281(a,1,2))]. 464 R(R(x,y \ 1,y),z,u) * K(y \ 1,y) = (R(x,z,u) * (y \ 1)) * y. [para(126(a,2),231(a,1,2))]. 465 R((x * y) / (z * y),u,w) * (z * y) = (R(x / z,u,w) * z) * y. [para(86(a,1),231(a,1,1,1))]. 466 (R(x,y,y \ (z * u)) * z) * u = (R(x,z,u) * y) * (y \ (z * u)). [para(231(a,1),167(a,1))]. 467 (R(x,(y * z) / u,u) * y) * z = (R(x,y,z) * ((y * z) / u)) * u. [para(231(a,1),225(a,1))]. 468 (R(x,y,T(z,y)) * z) * y = (R(x,z,y) * y) * T(z,y). [para(231(a,1),232(a,1))]. 469 K(x \ 1,x) \ ((y * (x \ 1)) * x) = R(y,x \ 1,x). [para(233(a,1),388(a,1,2))]. 470 K(x \ 1,x) * R(y,x \ 1,x) = (y * (x \ 1)) * x. [para(233(a,1),390(a,2))]. 471 K(x,1 / x) \ (y * (1 / x)) = R(y / x,x,1 / x). [para(245(a,1),396(a,1)),flip(a)]. 472 (x * y) / L(T(z \ y,(z \ y) \ y),(z \ y) \ y,x) = x * T(z,z \ y). [para(91(a,2),247(a,2,2))]. 473 ((x * (y \ z)) * y) / L(K(y \ z,y),z,R(x,y \ z,y)) = R(x,y \ z,y) * z. [para(85(a,1),248(a,1,1))]. 474 (x * y) * R((x * y) \ z,u,w) = x * (y * R(y \ (x \ z),u,w)). [para(269(a,1),79(a,1,2))]. 475 (1 / x) * (x * R(x \ y,z,u)) = R((1 / x) * y,z,u). [para(274(a,1),129(a,2))]. 476 (1 / x) \ L((1 / x) * y,z,u) = x * L(x \ y,z,u). [para(275(a,1),261(a,1,2))]. 477 L((1 / x) * T(x,y),x,y) = L(K(x,y),x,1 / x). [para(318(a,2),275(a,1,1)),flip(a)]. 478 L(R(x / (1 / y),1 / y,y),z,u) / y = (1 / y) * L((1 / y) \ x,z,u). [para(277(a,2),278(a,1))]. 479 L(R(T(x,y \ z),u,w),y \ z,y) = R(z \ (y * (x * (y \ z))),u,w). [para(296(a,1),42(a,1,1)),flip(a)]. 480 (x \ y) * (y \ (x * (z * (x \ y)))) = L(z,x \ y,x) * (x \ y). [para(296(a,1),123(a,1,2))]. 481 (x \ 1) * T((x \ 1) \ y,z) = x \ T(1 \ (x * y),z). [para(323(a,1),258(a,1,2)),flip(a)]. 482 x * ((x \ y) * T((x \ y) \ z,u)) = y * T(y \ (x * z),u). [para(323(a,1),204(a,1,2)),flip(a)]. 483 (T(x / (y / z),u) * (y / z)) * z = T((x * z) / y,u) * y. [para(327(a,1),225(a,1,1)),flip(a)]. 484 ((R(1 / x,x,x \ (y * z)) * y) * z) / (x \ (y * z)) = a((x \ (y * z)) / (y * z),y,z). [para(177(a,2),334(a,1,1,1,1))]. 485 ((x * (y / (z * y))) / x) * (z * y) = (((x * (1 / z)) / x) * z) * y. [para(346(a,1),85(a,1,1))]. 486 ((x * (y / ((1 / y) * y))) / x) / y = ((x * (1 / (1 / y))) / x) * (1 / y). [para(346(a,1),266(a,1,1))]. 487 ((x * ((y \ z) / (y * (y \ z)))) / x) * z = (((x * (1 / y)) / x) * y) * (y \ z). [para(346(a,1),167(a,1,1))]. 488 R(T(x \ y,x * z),x,z) = T((x * z) \ (y * z),x). [para(366(a,1),40(a,2))]. 489 L(T(x,y),y,(y * x) / y) = T(y \ (y * x),y * x). [para(417(a,1),38(a,2))]. 490 K(x \ 1,x) * y != (z * (x \ 1)) * x | R(z,x \ 1,x) = y. [para(470(a,1),19(a,1)),flip(a)]. 491 K(x \ 1,x) * R(R(y,x \ 1,x),z,u) = (R(y,z,u) * (x \ 1)) * x. [para(44(a,1),470(a,1,2))]. 492 T((x * y) \ ((x * z) * y),x) = R(T(z,x * y),x,y). [para(13(a,1),488(a,1,1,1)),flip(a)]. 493 L(T(x,y),y,(y * x) / y) = T(x,y * x). [para(13(a,1),489(a,2,1))]. 494 R(T(x,y * x),y,x) = T(x,y). [para(13(a,1),492(a,1,1)),flip(a)]. 495 R(T(x,y),y / x,x) = T(x,y / x). [para(16(a,1),494(a,1,1,2))]. 496 x * R(T(y,x * y),x,y) = y * x. [para(494(a,2),90(a,1,2))]. 497 R(x,x \ 1,x) = T(x,x \ 1). [para(393(a,1),494(a,1,1))]. 498 R(1 / x,x,1 / x) = T(1 / x,x). [para(397(a,1),494(a,1,1))]. 499 R(x,x \ 1,x) = (x \ 1) \ 1. [para(497(a,2),91(a,1))]. 500 K(x \ 1,x) \ x = T(x,x \ 1). [para(497(a,1),407(a,2))]. 501 x / K(x \ 1,x) = (x \ 1) \ 1. [para(499(a,1),256(a,2))]. 502 K(x \ 1,x) * T(x,x \ 1) = x. [para(500(a,1),14(a,1,2))]. 503 ((x \ 1) \ 1) \ x = K(x \ 1,x). [para(501(a,1),59(a,1,1))]. 504 R(((x / y) \ 1) \ 1,K((x / y) \ 1,x / y),y) = x / (K((x / y) \ 1,x / y) * y). [para(501(a,1),145(a,1,1))]. 505 K(x \ 1,x) * ((x \ 1) \ 1) = x. [para(91(a,1),502(a,1,2))]. 506 R(1 / x,x,1 / x) = x \ 1. [para(498(a,2),92(a,1))]. 507 (x \ 1) \ (1 / x) = x * (1 / x). [para(506(a,1),180(a,1,1))]. 508 (R(1 / x,y,z) * x) * (1 / x) = R(x \ 1,y,z) * (x * (1 / x)). [para(506(a,1),231(a,1,1,1)),flip(a)]. 509 (x \ 1) \ (1 / x) = K(x,1 / x). [para(507(a,2),128(a,2)),flip(a)]. 510 (x \ 1) * K(x,1 / x) = 1 / x. [para(509(a,1),14(a,1,2))]. 511 K(x,1 / x) * (x \ 1) = 1 / x. [para(510(a,1),395(a,2))]. 512 x * (y * T(T(x,y),z)) = T(x,z) * (x * y). [para(335(a,1),122(a,1))]. 513 T(x,y) * (x * z) = x * (T(x,y) * z). [para(122(a,1),512(a,1,2)),flip(a)]. 514 x \ (T(x,y) * z) = T(x,y) * (x \ z). [hyper(286,a,513,a)]. 515 T(x,y) \ (x * (T(x,y) * z)) = x * z. [hyper(66,a,513,a)]. 516 x * (T(x,y) * (x \ z)) = T(x,y) * z. [para(14(a,1),513(a,1,2)),flip(a)]. 517 (x / y) * (T(x / y,z) * y) = T(x / y,z) * x. [para(16(a,1),513(a,1,2)),flip(a)]. 518 x * (T(x,y) * T(z,x)) = T(x,y) * (z * x). [para(90(a,1),513(a,1,2)),flip(a)]. 519 (x / y) * (T(x / y,y) * z) = (y \ x) * ((x / y) * z). [para(92(a,1),513(a,1,1)),flip(a)]. 520 T(x,y) * (x \ 1) = x \ T(x,y). [para(12(a,1),514(a,1,2)),flip(a)]. 521 x \ (T(x,y) * (x / z)) = T(x,y) * L(z \ 1,z,x / z). [para(172(a,2),514(a,2,2))]. 522 T(x,y) \ (x \ T(x,y)) = x \ 1. [hyper(66,a,520,a)]. 523 (x \ T(x,y)) \ (T(x,y) * ((x \ 1) * z)) = L(z,x \ 1,T(x,y)). [para(520(a,1),26(a,2,1)),flip(a)]. 524 (x \ 1) * T((x \ 1) \ 1,y) = x \ T(x,y). [para(520(a,1),189(a,2))]. 525 x * (T(x,y) \ 1) = T(x,y) \ x. [para(51(a,1),515(a,1,2)),flip(a)]. 526 x \ (T(x,y) \ x) = T(x,y) \ 1. [hyper(66,a,525,a)]. 527 T((T(x,y) \ x) / x,x) = T(x,y) \ 1. [para(525(a,1),112(a,1,1,1))]. 528 T((1 / x) * (T(x,y) \ x),x) = (1 / x) * ((T(x,y) \ 1) * x). [para(526(a,1),375(a,1,2,1)),flip(a)]. 529 T(x,y) * (x \ L(z,x \ T(x,y),x)) = (x \ T(x,y)) * z. [hyper(17,a,204,a(flip),b,516,a)]. 531 (x / y) * (y * T(y \ x,z)) = T(x / y,z) * x. [para(187(a,1),517(a,1,2))]. 532 (1 / x) \ T(1 / x,y) = x * T(x \ 1,y). [hyper(17,a,136,a,b,531,a),flip(a)]. 533 (x * y) * T((y * T(x,y)) \ y,z) = y * (T(x,y) * T(T(x,y) \ 1,z)). [para(90(a,1),355(a,1,1))]. 534 (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(79(a,1),355(a,1,1))]. 535 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(164(a,1),374(a,1,1)),flip(a)]. 536 ((x \ y) * x) * (x \ z) = z * T(z \ (y * (x \ z)),x). [para(429(a,1),187(a,1))]. 537 (x \ y) * T((x \ y) \ 1,y) = x \ ((y \ x) * y). [para(12(a,1),434(a,2,2,1,2))]. 538 x \ ((L(y,z,x) * x) * z) = z * R(T(y,x * z),x,z). [para(40(a,2),463(a,2,2))]. 539 (1 / x) * (x * R(x \ 1,y,z)) = R(1 / x,y,z). [para(12(a,1),475(a,2,1))]. 540 (1 / x) * (((y * z) / (x * z)) * x) = R((1 / x) * y,x,z). [para(339(a,2),475(a,1,2))]. 541 (1 / x) \ R(1 / x,y,z) = x * R(x \ 1,y,z). [hyper(66,a,539,a)]. 542 (1 / x) * ((y / (x * y)) * x) = R(1 / x,x,y). [para(316(a,2),539(a,1,2))]. 544 x * R(x \ 1,y,y \ 1) = a(1 / x,y,y \ 1). [para(541(a,1),304(a,1))]. 545 (1 / x) \ L((1 / x) * K(x \ 1,x),y,z) = x * L(T(x \ 1,x),y,z). [para(163(a,1),476(a,2,2,1))]. 546 (x \ 1) * T((x \ 1) \ y,z) = x \ T(x * y,z). [para(47(a,1),481(a,2,2,1))]. 547 (x / y) * ((y \ x) * z) = (y \ x) * ((x / y) * z). [para(92(a,1),519(a,1,2,1))]. 548 (x \ (x * y)) * (((x * y) / x) * z) = ((x * y) / x) * (y * z). [para(112(a,1),519(a,1,2,1)),flip(a)]. 549 (x \ y) \ ((y / x) * z) = (y / x) * ((x \ y) \ z). [hyper(286,a,547,a)]. 550 (x \ y) * ((y / x) * ((x \ y) \ z)) = (y / x) * z. [para(14(a,1),547(a,1,2)),flip(a)]. 551 (x / y) * ((y \ x) \ 1) = (y \ x) \ (x / y). [para(12(a,1),549(a,1,2)),flip(a)]. 552 (x / y) * ((y \ x) \ ((x / y) \ z)) = (y \ x) \ z. [para(14(a,1),549(a,1,2)),flip(a)]. 553 (x / (x / y)) * (((x / y) \ x) \ z) = y \ ((x / (x / y)) * z). [para(59(a,1),549(a,1,1)),flip(a)]. 554 (1 / x) * T(x,x \ 1) = (x \ 1) \ (1 / x). [para(91(a,2),551(a,1,2))]. 555 (x / y) \ ((y \ x) \ z) = (y \ x) \ ((x / y) \ z). [hyper(66,a,552,a)]. 556 (x \ (x * y)) \ (((x * y) / x) \ z) = ((x * y) / x) \ (y \ z). [para(13(a,1),555(a,1,2,1)),flip(a)]. 557 ((x \ 1) * x) * (x \ y) = y * T(y \ (x \ y),x). [para(11(a,1),536(a,2,2,1,2))]. 558 x * T(x \ (K(y \ 1,y) * ((y \ 1) \ x)),y \ 1) = (y * (y \ 1)) * ((y \ 1) \ x). [para(160(a,1),536(a,1,1,1)),flip(a)]. 559 K(x \ 1,x) * (x \ y) = y * T(y \ (x \ y),x). [para(126(a,2),557(a,1,1))]. 560 x \ (y \ ((L(z,x,y) * y) * x)) = R(T(z,y * x),y,x). [hyper(66,a,538,a(flip))]. 561 K(x \ (x / y),x) = y * T(y \ 1,x). [hyper(428,a,271,a),flip(a)]. 562 x \ K(y \ (y / x),y) = T(x \ 1,y). [hyper(66,a,561,a(flip))]. 563 T(x,y) * ((T(x,y) \ 1) * x) = x * K(x \ (x / T(x,y)),x). [para(561(a,2),518(a,1,2)),flip(a)]. 564 K(x \ (x / (y \ 1)),x) = y \ T(y,x). [para(561(a,2),524(a,1))]. 565 L(x \ 1,x,y) \ K(y \ (y * x),y) = T(L(x \ 1,x,y) \ 1,y). [para(175(a,1),562(a,1,2,1,2))]. 566 K(x \ (x / ((y / x) \ 1)),x) = (y / x) \ (x \ y). [para(92(a,1),564(a,2,2))]. 567 L((x * (y \ z)) / z,u,w) * z = (L(x / y,u,w) * y) * (y \ z). [para(237(a,1),312(a,1,1,1))]. 568 (x / y) * (y * R(y \ 1,z,u)) = x * R(x \ (x / y),z,u). [para(172(a,1),321(a,1,2,1)),flip(a)]. 569 (x \ 1) * R((x \ 1) \ y,z,u) = x \ R(1 \ (x * y),z,u). [para(324(a,1),258(a,1,2)),flip(a)]. 570 (x \ 1) * L((x \ 1) \ y,z,u) = x \ L(1 \ (x * y),z,u). [para(325(a,1),258(a,1,2)),flip(a)]. 571 R(x / (1 / y),z,u) * (1 / y) = R((x * y) / 1,z,u) / y. [para(328(a,1),266(a,1,1)),flip(a)]. 572 T(x,x \ y) * z = ((x \ y) \ y) * z. [para(331(a,1),249(a,1))]. 573 ((x \ y) \ y) * T(z,T(x,x \ y)) = z * T(x,x \ y). [para(572(a,1),90(a,1))]. 574 (((x * ((y / z) / u)) / x) * u) * z = ((x * (y / (u * z))) / x) * (u * z). [para(347(a,1),85(a,1,1)),flip(a)]. 575 (x * y) * ((z * ((x * y) \ (x * u))) / z) = x * (y * ((z * (y \ u)) / z)). [para(348(a,1),79(a,1,2))]. 576 R(T(x / y,z * y),y,T(z,y)) = (z * y) \ (x * T(z,y)). [para(368(a,1),40(a,2))]. 577 L(K(x \ 1,x),y,z) * (z * y) = z * (K(x \ 1,x) * y). [para(390(a,2),416(a,2,2))]. 578 (1 / x) * ((y * (x \ 1)) * x) = R((1 / x) * y,x,x \ 1). [para(98(a,1),540(a,1,2,1))]. 579 T(T(x,x \ y) \ y,(((x \ y) \ y) \ y) \ z) = ((((x \ y) \ y) \ y) \ z) \ z. [para(289(a,1),290(a,1)),flip(a)]. 580 x * R(1 / y,y,z) = x * (z / (y * z)). [para(329(a,1),246(a,1))]. 581 (x * (y / (z * y))) / R(1 / z,z,y) = x. [hyper(70,a,580,a)]. 582 K((x / (y * x)) \ 1,x / (y * x)) = ((x / (y * x)) \ 1) * R(1 / y,y,x). [para(580(a,2),126(a,2))]. 583 K(x / (y * x),(x / (y * x)) \ z) = (((x / (y * x)) \ z) * R(1 / y,y,x)) \ z. [para(580(a,2),76(a,1,1)),flip(a)]. 584 x * (y * R(T(x,y),z,u)) = R(x,z,u) * (x * y). [para(424(a,1),124(a,1))]. 585 R(x,y,z) * (x * u) = x * (R(x,y,z) * u). [para(124(a,1),584(a,1,2)),flip(a)]. 586 x \ (R(x,y,z) * u) = R(x,y,z) * (x \ u). [hyper(286,a,585,a)]. 587 (R(x,y,z) * u) \ (x * (R(x,y,z) * u)) = L(T(x,u),u,R(x,y,z)). [para(585(a,1),120(a,1,2))]. 588 R(x,y,z) * (x \ 1) = x \ R(x,y,z). [para(12(a,1),586(a,1,2)),flip(a)]. 589 R(x / y,y / x,(y / x) \ 1) = T((1 * x) / y,y / x). [para(452(a,2),365(a,1))]. 590 R(x / y,y / x,(y / x) \ 1) = T(x / y,y / x). [para(11(a,1),589(a,2,1,1))]. 591 x * (y * L(T(x,y),z,u)) = L(x,z,u) * (x * y). [para(457(a,1),123(a,1))]. 592 L(x,y,z) * (x * u) = x * (L(x,y,z) * u). [para(123(a,1),591(a,1,2)),flip(a)]. 593 L(x,y,z) \ (x * (L(x,y,z) * u)) = x * u. [hyper(66,a,592,a)]. 594 L(x,y,z) \ (x * u) = x * (L(x,y,z) \ u). [hyper(17,a,140,a,b,592,a),flip(a)]. 595 x * (L(x,y,z) \ 1) = L(x,y,z) \ x. [para(51(a,1),593(a,1,2)),flip(a)]. 596 x \ (L(x,y,z) \ x) = L(x,y,z) \ 1. [hyper(66,a,595,a)]. 597 (x \ (y \ z)) \ (((y * x) \ z) \ (x \ (y \ z))) = L(x \ (y \ z),x,y) \ 1. [para(139(a,1),596(a,1,2,1))]. 598 x * (L(x,1 / x,x) \ y) = (1 / (1 / x)) \ (x * y). [para(415(a,1),594(a,1,1)),flip(a)]. 599 (1 / (1 / x)) \ (x * y) = x * ((1 / (1 / x)) \ y). [para(415(a,1),598(a,1,2,1)),flip(a)]. 600 x * ((x \ y) * T((x \ y) \ 1,z)) = y * T(y \ x,z). [para(12(a,1),482(a,2,2,1,2))]. 601 x * T(x \ y,z) = y * K(z \ (z / (y \ x)),z). [para(561(a,2),600(a,1,2)),flip(a)]. 602 x \ (y * K(z \ (z / (y \ x)),z)) = T(x \ y,z). [hyper(66,a,601,a)]. 603 (x / y) * T(y,z) = x * K(z \ (z / (x \ (x / y))),z). [para(59(a,1),601(a,1,2,1))]. 604 x \ (y * K((y \ x) \ 1,y \ x)) = T(x \ y,y \ x). [para(54(a,1),602(a,1,2,2,1,2))]. 605 K(x \ (x / (y \ (y / z))),x) = y \ ((y / z) * T(z,x)). [hyper(66,a,603,a(flip)),flip(a)]. 606 x \ (K((y \ x) \ 1,y \ x) * y) = T(x \ y,y \ x). [para(390(a,2),604(a,1,2))]. 607 K((x \ y) \ 1,x \ y) * x = y * T(y \ x,x \ y). [para(606(a,1),14(a,1,2)),flip(a)]. 609 K(((x * y) \ x) \ 1,L(y \ 1,y,x)) * (x * y) = x * T(x \ (x * y),(x * y) \ x). [para(110(a,2),607(a,1,1,2))]. 610 ((x / y) * T((x / y) \ z,u)) * y = T((z * y) / x,u) * x. [para(187(a,1),483(a,1,1))]. 611 ((x * y) / x) * (y * z) = y * (((x * y) / x) * z). [para(13(a,1),548(a,1,1)),flip(a)]. 612 x * (((y * x) / y) * (x \ z)) = ((y * x) / y) * z. [para(14(a,1),611(a,1,2)),flip(a)]. 613 ((x * y) / x) * (y \ 1) = y \ ((x * y) / x). [hyper(17,a,136,a,b,612,a)]. 614 ((x * y) / x) \ (y \ ((x * y) / x)) = y \ 1. [hyper(66,a,613,a)]. 615 (x / (x / y)) \ (y \ (((x / y) * y) / (x / y))) = y \ 1. [para(16(a,1),614(a,1,1,1))]. 616 (x / (x / y)) \ (y \ (x / (x / y))) = y \ 1. [para(16(a,1),615(a,1,2,2,1))]. 618 x \ ((y / (y / x)) * z) = (y / (y / x)) * (x \ z). [para(59(a,1),553(a,1,2,1)),flip(a)]. 619 ((x * y) / x) \ (y \ z) = y \ (((x * y) / x) \ z). [para(13(a,1),556(a,1,1)),flip(a)]. 620 ((x * y) / x) \ (y \ ((x * y) / x)) = (x \ (x * y)) \ 1. [para(48(a,1),556(a,1,2)),flip(a)]. 621 x \ (((y * x) / y) \ x) = ((y * x) / y) \ 1. [para(48(a,1),619(a,1,2)),flip(a)]. 622 ((x * y) / x) \ (y \ (x * y)) = y \ x. [para(59(a,1),619(a,2,2))]. 623 ((x * y) / x) \ T(x,y) = y \ x. [para(30(a,2),622(a,1,2))]. 624 T(x,y) / (y \ x) = (x * y) / x. [para(623(a,1),57(a,1,2))]. 625 ((x * y) * x) / (x * y) = T(x * y,x) / y. [para(13(a,1),624(a,1,2)),flip(a)]. 626 x * (((y * x) / y) \ 1) = ((y * x) / y) \ x. [para(621(a,1),14(a,1,2))]. 627 (((x * y) / x) \ 1) * T(y,((x * y) / x) \ 1) = ((x * y) / x) \ y. [para(626(a,1),90(a,2))]. 628 L(x,T(x,y) \ 1,T(x,y)) = x * K(x \ (x / T(x,y)),x). [para(563(a,1),127(a,1)),flip(a)]. 629 K(x \ 1,x) * R(K(x \ 1,x) \ (K(x \ 1,x) / x),y,z) = (x \ 1) * (x * R(x \ 1,y,z)). [para(159(a,1),568(a,1,1)),flip(a)]. 630 (x \ 1) * R((x \ 1) \ y,z,u) = x \ R(x * y,z,u). [para(47(a,1),569(a,2,2,1))]. 631 (x \ 1) * R((x \ 1) \ 1,y,z) = x \ R(x,y,z). [para(94(a,1),569(a,2,2,1))]. 632 (x \ 1) * L((x \ 1) \ y,z,u) = x \ L(x * y,z,u). [para(47(a,1),570(a,2,2,1))]. 633 R(x / (1 / y),z,u) * (1 / y) = R(x * y,z,u) / y. [para(55(a,1),571(a,2,1,1))]. 634 (1 / x) * R((1 / x) \ y,z,u) = R(y * x,z,u) / x. [para(633(a,1),283(a,1)),flip(a)]. 635 (1 / x) * R((1 / x) \ 1,y,z) = R(x,y,z) / x. [para(11(a,1),634(a,2,1,1))]. 636 (1 / x) * R(x,y,z) = R(x,y,z) / x. [para(59(a,1),635(a,1,2,1))]. 637 (R(x,y,z) / x) / R(x,y,z) = 1 / x. [hyper(70,a,636,a)]. 638 R(x \ 1,y,z) / (x \ 1) = x * R(x \ 1,y,z). [para(57(a,1),636(a,1,1)),flip(a)]. 639 ((x / y) * T((x / y) \ z,u)) * y = x * T(x \ (z * y),u). [para(610(a,2),187(a,1))]. 640 ((x / y) * T((x / y) \ x,z)) * y = x * T(y,z). [para(610(a,2),188(a,1))]. 641 (1 / x) * T((1 / x) \ 1,y) = T(x,y) / x. [hyper(18,a,142,a,b,640,a)]. 642 ((x / y) * T(y,z)) * y = x * T(y,z). [para(59(a,1),640(a,1,1,2,1))]. 643 (x * T(y,z)) / y = (x / y) * T(y,z). [hyper(70,a,642,a)]. 644 (1 / x) * T(x,y) = T(x,y) / x. [hyper(18,a,142,a,b,642,a)]. 645 (x * T(y,z)) * y = (x * y) * T(y,z). [para(15(a,1),642(a,1,1,1))]. 646 T((x / y) * T(y,z),y) = y \ (x * T(y,z)). [para(642(a,1),30(a,2,2))]. 647 (T(x,y) / x) / T(x,y) = 1 / x. [hyper(70,a,644,a)]. 648 T(x,y) \ (T(x,y) / x) = T(1 / x,T(x,y)). [para(644(a,1),30(a,2,2)),flip(a)]. 649 T(x \ 1,y) / (x \ 1) = x * T(x \ 1,y). [para(57(a,1),644(a,1,1)),flip(a)]. 650 L(T(x,y) \ z,T(x,y),1 / x) = (T(x,y) / x) \ ((1 / x) * z). [para(644(a,1),81(a,2,1))]. 651 (1 / x) * a(1 / x,T(x,y),T(x,y) \ 1) = (T(x,y) / x) * (T(x,y) \ 1). [para(644(a,1),293(a,2,1))]. 652 L(K(x,y),x,1 / x) = L(T(x,y) / x,x,y). [para(644(a,1),477(a,1,1)),flip(a)]. 653 (x \ 1) \ (1 / x) = T(x,x \ 1) / x. [para(644(a,1),554(a,1)),flip(a)]. 654 (x / y) * T(y,x) = (y * x) / y. [para(90(a,1),643(a,1,1)),flip(a)]. 655 (x / (y / z)) * T(y / z,z) = (x * (z \ y)) / (y / z). [para(92(a,1),643(a,1,1,2)),flip(a)]. 656 (L(x \ 1,x,y) * y) / L(x \ 1,x,y) = (y * x) * T(L(x \ 1,x,y),y). [para(175(a,1),654(a,1,1)),flip(a)]. 657 (L(x,1 / x,y) * y) / L(x,1 / x,y) = (y * (1 / x)) * T(L(x,1 / x,y),y). [para(182(a,1),654(a,1,1)),flip(a)]. 658 K(x \ (x / (x \ (x / y))),x) = x \ ((y * x) / y). [para(654(a,1),605(a,2,2))]. 659 (x * y) / T(y,z) = (x / T(y,z)) * y. [hyper(287,a,645,a)]. 660 (x * y) * T(y,x) = (y * x) * y. [para(90(a,1),645(a,1,1)),flip(a)]. 661 R((x * y) / x,x,T(y,x)) = ((y * x) * y) / (y * x). [para(660(a,1),240(a,2,1))]. 662 R(T((x * y) / x,y * x),x,T(y,x)) = (y * x) \ ((y * x) * y). [para(660(a,1),576(a,2,2))]. 663 T(x,x \ 1) / x = K(x,1 / x). [para(653(a,1),509(a,1))]. 664 K(x,1 / x) * x = T(x,x \ 1). [para(663(a,1),16(a,1,1))]. 665 x * K(x,1 / x) = T(x,x \ 1). [para(664(a,1),395(a,1)),flip(a)]. 666 T(x,1 / x) = T(x,x \ 1). [para(665(a,1),431(a,1)),flip(a)]. 667 T(x,1 / x) = (x \ 1) \ 1. [para(666(a,2),91(a,1))]. 668 T(x \ 1,x) = ((x \ 1) \ 1) \ 1. [para(57(a,1),667(a,1,2))]. 669 1 / T(x \ 1,x) = (x \ 1) \ 1. [para(668(a,2),57(a,1,2))]. 670 T(x,x \ 1) \ 1 = T(x \ 1,x). [para(91(a,2),668(a,2,1)),flip(a)]. 671 1 / ((x \ 1) * K(x \ 1,x)) = (x \ 1) \ 1. [para(433(a,2),669(a,1,2))]. 672 (1 / T(x,y)) * x = x / T(x,y). [para(11(a,1),659(a,1,1)),flip(a)]. 673 (x * y) / T(y,z) != u * y | x / T(y,z) = u. [para(659(a,2),20(a,1))]. 674 (x * y) / T(y,y \ z) = (x / ((y \ z) \ z)) * y. [para(91(a,1),659(a,2,1,2))]. 675 (x / T(x,y)) / x = 1 / T(x,y). [hyper(70,a,672,a)]. 676 K(x \ (x / (1 / y)),x) = T(y,x) / y. [para(641(a,1),561(a,2))]. 677 K(x \ (x / (1 / (y / (x * y)))),x) = R(x \ 1,x,y) / (y / (x * y)). [para(314(a,1),676(a,2,1))]. 678 T(x * K(y \ (y / (x \ (x / z))),y),z) = z \ (x * T(z,y)). [para(603(a,1),646(a,1,1))]. 679 L(x \ 1,x,T(x,y) / x) = T(1 / x,T(x,y)). [para(648(a,1),172(a,2))]. 680 x / T(y,y \ z) = x / ((y \ z) \ z). [hyper(673,a,674,a)]. 681 (x / ((y \ z) \ z)) * T((y \ z) \ z,u) = x * K(u \ (u / (x \ (x / T(y,y \ z)))),u). [para(680(a,2),603(a,2,2,1,2,2,2))]. 682 R((x * y) / x,x,T(y,x)) = T(y * x,y) / x. [para(661(a,2),625(a,1))]. 683 (x * (y \ z)) / (z / y) = (x / (z / y)) * (y \ z). [para(92(a,1),655(a,1,2)),flip(a)]. 684 (1 / (x / y)) * (y \ x) = (y \ x) / (x / y). [para(11(a,1),683(a,1,1)),flip(a)]. 685 (x / ((y * z) / y)) * (y \ (y * z)) = (x * z) / ((y * z) / y). [para(13(a,1),683(a,1,1,2)),flip(a)]. 686 (x \ (x * y)) / ((x * y) / x) = (1 / ((x * y) / x)) * y. [para(13(a,1),684(a,1,2)),flip(a)]. 687 (1 / ((x * y) / x)) * y = y / ((x * y) / x). [para(13(a,1),686(a,1,1)),flip(a)]. 688 (x / ((y * x) / y)) / x = 1 / ((y * x) / y). [hyper(70,a,687,a)]. 689 (x * T(x \ (y * z),u)) / z = (x / z) * T((x / z) \ y,u). [hyper(70,a,639,a)]. 690 (((x / y) \ z) * (x / y)) * y = x * T(x \ (z * y),x / y). [para(90(a,1),639(a,1,1))]. 691 (x * y) / ((z * y) / z) = (x / ((z * y) / z)) * y. [para(13(a,1),685(a,1,2)),flip(a)]. 692 (x / y) * T((x / y) \ 1,z) = (x * T(x \ y,z)) / y. [para(11(a,1),689(a,1,1,2,1,2)),flip(a)]. 693 K(x \ (x / (y / z)),x) = (y * T(y \ z,x)) / z. [para(692(a,1),561(a,2))]. 694 K(x \ (x / ((y * z) / y)),x) = (y * (z * T(z \ 1,x))) / y. [para(355(a,1),693(a,2,1))]. 695 K((x / y) \ 1,x / y) * y = x * T(x \ (1 * y),x / y). [para(126(a,2),690(a,1,1))]. 696 K(x \ (x / ((y * x) / y)),x) = (y * ((x \ 1) * x)) / y. [para(90(a,1),694(a,2,1,2))]. 697 K(x \ (x / ((y * x) / y)),x) = (y * K(x \ 1,x)) / y. [para(126(a,2),696(a,2,1,2))]. 698 K(x \ (x / ((y * x) / y)),x) = K(x \ 1,x). [para(697(a,2),392(a,1))]. 700 ((x * y) / x) \ K(y \ 1,y) = T(((x * y) / x) \ 1,y). [para(698(a,1),562(a,1,2))]. 701 K((x / y) \ 1,x / y) * y = x * T(x \ y,x / y). [para(11(a,1),695(a,2,2,1,2))]. 702 K((x / (y * x)) \ 1,x / (y * x)) * (y * x) = T(y,x / (y * x)) * x. [para(701(a,2),186(a,1))]. 703 (K((x / y) \ 1,x / y) * y) / x = T(y / x,x / y). [para(701(a,2),191(a,1,1))]. 704 (L(x,y,z) * (z * y)) \ (x * (z * y)) = a(z,y,T(x,z * y)). [para(280(a,1),119(a,1,1))]. 705 (L(x,y,z) * (z * y)) * a(z,y,T(x,z * y)) = x * (z * y). [para(704(a,1),14(a,1,2))]. 706 ((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(704(a,1),689(a,1,1,2,1)),flip(a)]. 707 R(x,y * ((x * y) \ z),a(x,y,(x * y) \ z)) \ z = (y * ((x * y) \ z)) * a(x,y,(x * y) \ z). [para(292(a,1),141(a,1,1))]. 708 x \ (K(y \ x,1 / (y \ x)) * y) = L(1 / (y \ x),y \ x,y). [para(395(a,2),297(a,1,2))]. 709 R((x / (y * x)) \ 1,R(1 / y,y,x),y * x) = (K((x / (y * x)) \ 1,x / (y * x)) * (y * x)) / x. [para(111(a,2),301(a,2,2)),flip(a)]. 710 x * ((x \ y) * ((z * ((x \ y) \ u)) / z)) = y * ((z * (y \ (x * u))) / z). [para(349(a,1),204(a,1,2)),flip(a)]. 711 R(1 / x,x,K(y \ 1,y)) * (K(y \ 1,y) * x) = K(y \ 1,y). [para(401(a,2),16(a,1,1))]. 712 (x \ 1) * (x * (y * (x \ 1))) = L(y,x \ 1,x) * (x \ 1). [para(47(a,1),480(a,1,2))]. 713 L(x,T(x,y) \ 1,T(x,y)) * (T(x,y) \ 1) = (T(x,y) \ 1) * (T(x,y) * (T(x,y) \ x)). [para(525(a,1),712(a,1,2,2)),flip(a)]. 714 L((x * y) / x,y \ 1,y) * (y \ 1) = (y \ 1) * (((x * y) / x) * 1). [para(612(a,1),712(a,1,2)),flip(a)]. 715 R(L(x,y,x),y,T(x,y)) = (x * y) \ ((x * y) * x). [para(310(a,1),662(a,1,1))]. 716 L(R(x,y,T(x,y)),y,x) = (x * y) \ ((x * y) * x). [para(715(a,1),42(a,1)),flip(a)]. 717 L(R(x,y,T(x,y)),y,x) = x. [para(716(a,2),13(a,1))]. 718 L((x * R(y,z,T(y,z))) / x,z,y) = (x * y) / x. [para(717(a,1),343(a,2,1,2))]. 719 L(R((x * y) / x,z,T(y,z)),z,y) = (x * y) / x. [para(341(a,2),718(a,1,1))]. 720 x * (K(y \ 1,y) * z) != K(y \ 1,y) | R(1 / z,z,K(y \ 1,y)) = x. [para(711(a,1),20(a,1)),flip(a)]. 721 K(1 / x,x) * K(x,1 / x) = 1. [para(197(a,1),394(a,1))]. 723 L(K(x \ 1,x) \ y,K(x \ 1,x),x) = x * (L(x,x \ 1,x) \ y). [para(276(a,2),594(a,1))]. 724 T((x \ y) / y,z) * y = (T(1 / x,z) * x) * (x \ y). [para(14(a,1),315(a,1,1,1,2))]. 725 (T(1 / x,y) * x) * (x \ z) = z * T(z \ (x \ z),y). [para(724(a,1),187(a,1))]. 726 (x * T(x \ 1,y)) * (x \ z) = z * T(z \ (x \ z),y). [para(187(a,1),725(a,1,1))]. 727 (x * T(x \ (y \ x),z)) / (y \ x) = y * T(y \ 1,z). [hyper(70,a,726,a)]. 728 (x \ (y \ x)) * x = (y * T(y \ 1,x)) * (y \ x). [para(726(a,2),90(a,1)),flip(a)]. 729 (x \ T(x,y)) * ((x \ 1) \ z) = z * T(z \ ((x \ 1) \ z),y). [para(524(a,1),726(a,1,1))]. 730 (T(x,y) * T(T(x,y) \ 1,x \ T(x,y))) * (T(x,y) \ (x \ T(x,y))) = ((x \ T(x,y)) \ (x \ 1)) * (x \ T(x,y)). [para(522(a,1),728(a,1,1,2)),flip(a)]. 731 (T(x,y) * T(T(x,y) \ 1,x)) * (T(x,y) \ x) = (T(x,y) \ 1) * x. [para(526(a,1),728(a,1,1)),flip(a)]. 732 (L(x,y,z) * T(L(x,y,z) \ 1,x)) * (L(x,y,z) \ x) = (L(x,y,z) \ 1) * x. [para(596(a,1),728(a,1,1)),flip(a)]. 733 (((x * y) * z) * T(((x * y) * z) \ (y * z),u)) / (R(x,y,z) \ ((x * y) * z)) = R(x,y,z) * T(R(x,y,z) \ 1,u). [para(102(a,1),727(a,1,1,2,1,2))]. 734 x * T(x \ ((1 / x) \ y),z) = (1 / x) \ T(y,z). [para(96(a,1),373(a,1,2,1)),flip(a)]. 735 T(((x * y) * z) / (x * z),x * y) = L(R(y,x,z),x,(x * y) / x). [para(418(a,2),42(a,1))]. 736 x \ ((x / y) * ((y \ z) * y)) = T(x \ ((x / y) * z),y). [para(16(a,1),419(a,1,1,1)),flip(a)]. 737 T(K(x \ (x / (y \ (y / z))),x),z) = y \ ((y / z) * ((z \ T(z,x)) * z)). [para(605(a,2),736(a,2,1)),flip(a)]. 738 (x * y) * L((x * y) \ (z * y),u,w) = (L(z / x,u,w) * x) * y. [para(461(a,1),278(a,1)),flip(a)]. 739 (x * y) * R((x * y) \ (z * y),u,w) = (R(z / x,u,w) * x) * y. [para(465(a,1),283(a,1)),flip(a)]. 740 (x * y) * ((z * ((x * y) \ y)) / z) = (((z * (1 / x)) / z) * x) * y. [para(485(a,1),342(a,1)),flip(a)]. 741 (R(1 / x,y,z) * x) * (1 / x) = R(x \ 1,y,z) * K(x,1 / x). [para(128(a,2),508(a,2,2))]. 742 T(L(x \ 1,x,y) \ 1,y) = L(x \ 1,x,y) \ K(x,y). [para(13(a,1),565(a,1,2,1)),flip(a)]. 743 K(x,y) = L(x \ 1,x,y) * T(L(x \ 1,x,y) \ 1,y). [para(742(a,2),14(a,1,2)),flip(a)]. 744 (L(x / y,z,u) * y) * (y \ w) = w * L(w \ (x * (y \ w)),z,u). [para(567(a,1),278(a,1))]. 745 L(T(x,y),y,R(x,z,u)) = T(x,R(x,z,u) * y). [para(587(a,1),30(a,2)),flip(a)]. 746 R(x,y,z) \ (T(x,R(x,y,z) * (R(x,y,z) \ u)) * u) = (R(x,y,z) \ u) * T(T(x,R(x,y,z) \ u),u). [para(745(a,1),426(a,1,2,1))]. 747 L(R(x,y,y \ 1),y,(y * x) / y) = T((y * x) * (y \ 1),y * x). [para(98(a,1),735(a,1,1)),flip(a)]. 748 L(R(x,y,x),y,(y * x) / y) = x. [para(735(a,1),112(a,1))]. 749 ((x * y) / x) \ (y * (x * y)) = x * T(R(y,x,y),x * y). [para(748(a,1),427(a,1,2,1))]. 750 ((x * y) / x) \ (y * (x * y)) = x * R(T(y,x * y),x,y). [para(40(a,2),749(a,2,2))]. 751 ((x * y) / x) \ (y * (x * y)) = y * x. [para(750(a,2),496(a,1))]. 752 ((L(x,y,z) \ x) / x) \ ((L(x,y,z) \ 1) * (x * (L(x,y,z) \ 1))) = (L(x,y,z) \ 1) * x. [para(595(a,1),751(a,1,1,1))]. 753 x * (y * L(y \ (x \ (z * y)),u,w)) = (L(z / x,u,w) * x) * y. [para(738(a,1),456(a,1)),flip(a)]. 754 (x * y) * R((x * y) \ (z * y),u,w) = (x * R(x \ z,u,w)) * y. [para(283(a,1),739(a,2,1))]. 755 (x * y) * R((x * y) \ ((x * z) * y),u,w) = (x * R(z,u,w)) * y. [para(284(a,1),739(a,2,1))]. 756 (x * y) * ((z * ((x * y) \ y)) / z) = (x * ((z * (x \ 1)) / z)) * y. [para(342(a,1),740(a,2,1))]. 757 (x * R(x \ 1,y,z)) * (1 / x) = R(x \ 1,y,z) * K(x,1 / x). [para(283(a,1),741(a,1,1))]. 758 (x * L(x \ y,z,u)) * (x \ w) = w * L(w \ (y * (x \ w)),z,u). [para(278(a,1),744(a,1,1))]. 759 x * (y * L(y \ (x \ (z * y)),u,w)) = (x * L(x \ z,u,w)) * y. [para(278(a,1),753(a,2,1))]. 760 (x * y) * R((x * y) \ y,z,u) = (x * R(x \ 1,z,u)) * y. [para(11(a,1),754(a,1,2,1,2))]. 761 x * (y * R(y \ (x \ (z * y)),u,w)) = (x * R(x \ z,u,w)) * y. [para(754(a,1),474(a,1)),flip(a)]. 762 x * (y * R(y \ (x \ y),z,u)) = (x * R(x \ 1,z,u)) * y. [para(760(a,1),474(a,1)),flip(a)]. 763 (x \ T(x,y)) \ ((T(x,y) * R(T(x,y) \ 1,z,u)) * (x \ 1)) = L(R((x \ 1) \ (T(x,y) \ (x \ 1)),z,u),x \ 1,T(x,y)). [para(762(a,1),523(a,1,2))]. 764 (x * R(y,z,u)) * y = (x * y) * R(y,z,u). [para(13(a,1),755(a,1,2,1)),flip(a)]. 765 (x * R(x \ y,z,u)) * (x \ y) = y * R(x \ y,z,u). [para(14(a,1),764(a,2,1))]. 766 x * L(x \ (1 * (y \ x)),y,y \ 1) = (y * (1 / y)) * (y \ x). [para(425(a,1),758(a,1,1,2)),flip(a)]. 767 x * L(x \ (1 * (y \ x)),y,y \ 1) = K(y,1 / y) * (y \ x). [para(128(a,2),766(a,2,1))]. 768 x * L(x \ (y \ x),y,y \ 1) = K(y,1 / y) * (y \ x). [para(11(a,1),767(a,1,2,1,2))]. 769 x * L(x \ (x \ (y * x)),z,u) = T(x * L(x \ y,z,u),x). [hyper(117,a,759,a),flip(a)]. 770 x * (y * L(y \ (x \ y),z,u)) = (x * L(x \ 1,z,u)) * y. [para(11(a,1),759(a,1,2,2,1,2,2))]. 771 (x * L(x \ (y / z),u,w)) * z = x * (z * L(z \ (x \ y),u,w)). [para(16(a,1),759(a,1,2,2,1,2,2)),flip(a)]. 772 T(x * L(x \ y,z,u),x) = x * L(x \ T(y,x),z,u). [para(30(a,2),769(a,1,2,1,2)),flip(a)]. 773 T(x * L(x \ 1,y,z),x) = x * L(x \ 1,y,z). [para(103(a,1),772(a,2,2,1,2))]. 774 T(x * L(x \ y,x,1 / x),x) = x * ((1 / x) * T(y,x)). [para(221(a,1),772(a,2,2))]. 775 T(x,x * L(x \ 1,y,z)) = x. [hyper(33,a,773,a)]. 776 R(x,L(x \ 1,y,z),T(x,L(x \ 1,y,z))) = T(x,L(x \ 1,y,z)). [para(775(a,1),359(a,1,1))]. 777 T(x * ((1 / x) * y),x) = x * ((1 / x) * T(y,x)). [para(221(a,1),774(a,1,1,2))]. 778 T(x * ((1 / x) * ((1 / x) \ ((1 / (1 / x)) \ y))),x) = x * ((1 / (1 / x)) \ T(y,x)). [para(734(a,1),777(a,2,2))]. 779 x * (y * L(y \ (x \ y),x,x \ 1)) = (x * (1 / x)) * y. [para(425(a,1),770(a,2,1,2))]. 780 x * (K(x,1 / x) * (x \ y)) = (x * (1 / x)) * y. [para(768(a,1),779(a,1,2))]. 781 x * (K(x,1 / x) * (x \ y)) = K(x,1 / x) * y. [para(128(a,2),780(a,2,1))]. 782 x \ (y * (x * L(x \ (y \ z),u,w))) = T(y * L(y \ (z / x),u,w),x). [para(771(a,1),30(a,2,2)),flip(a)]. 783 ((x * R(y,y \ z,u)) * ((y \ z) * u)) / (z * u) = R(x,R(y,y \ z,u),(y \ z) * u). [para(14(a,1),229(a,1,2,1))]. 784 R(x,R(y,y \ 1,z),(y \ 1) * z) * z = (x * R(y,y \ 1,z)) * ((y \ 1) * z). [para(49(a,1),235(a,1,2))]. 785 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(314(a,2),235(a,1,1))]. 786 (x * R(x \ 1,x,y)) \ (x * R(1 / x,x,y)) = K(x,y / (x * y)). [para(111(a,1),337(a,2,2))]. 787 (x * y) * T((x * y) \ (z * y),u) = (T(z / x,u) * x) * y. [para(363(a,1),85(a,1))]. 788 (x * y) * T((x * y) \ (z * y),u) = (x * T(x \ z,u)) * y. [para(187(a,1),787(a,2,1))]. 789 x * (y * T(y \ (x \ (z * y)),u)) = (x * T(x \ z,u)) * y. [para(788(a,1),357(a,1)),flip(a)]. 790 x * (y * T(y \ (x \ y),z)) = (x * T(x \ 1,z)) * y. [para(11(a,1),789(a,1,2,2,1,2,2))]. 791 (x * T(x \ (y / z),u)) * z = x * (z * T(z \ (x \ y),u)). [para(16(a,1),789(a,1,2,2,1,2,2)),flip(a)]. 792 x * ((y \ (x \ (z * y))) * y) = (x * T(x \ z,y)) * y. [para(90(a,1),789(a,1,2))]. 793 ((x * y) * T((x * y) \ x,z)) * u = (x * y) * (u * T(u \ L(y \ u,y,x),z)). [para(81(a,2),789(a,1,2,2,1,2)),flip(a)]. 794 (x * T(x \ 1,y)) * x = x * (x * T(x \ 1,y)). [para(48(a,1),790(a,1,2,2,1,2)),flip(a)]. 795 (x * T(x \ 1,y)) * y = x * ((y \ (x \ y)) * y). [para(90(a,1),790(a,1,2)),flip(a)]. 796 x * (y \ T(y * (x \ (y \ 1)),z)) = (x * T(x \ 1,z)) * (y \ 1). [para(546(a,1),790(a,1,2))]. 797 x * (K(x \ 1,x) * (x \ y)) = (x * T(x \ 1,x)) * y. [para(559(a,2),790(a,1,2))]. 798 (x \ 1) * ((x \ T(x,y)) * ((x \ 1) \ z)) = ((x \ 1) * T((x \ 1) \ 1,y)) * z. [para(729(a,2),790(a,1,2))]. 799 T(x,x * T(x \ 1,y)) = x. [hyper(117,a,794,a)]. 800 R(x,(x * T(x \ 1,y)) / x,x) = T(x,(x * T(x \ 1,y)) / x). [para(799(a,1),495(a,1,1))]. 801 T(x \ 1,x \ T(x,y)) = x \ 1. [para(524(a,1),799(a,1,2))]. 802 (x \ T(x,y)) * (x \ 1) = (x \ 1) * (x \ T(x,y)). [para(801(a,1),90(a,1,2))]. 803 (x \ y) * ((y \ T(x,x \ y)) * y) = ((x \ y) * T((x \ y) \ 1,y)) * y. [para(91(a,2),795(a,2,2,1,2)),flip(a)]. 804 ((x * (y \ z)) * T((x * (y \ z)) \ x,z)) * z = (x * (y \ z)) * ((z \ L(T(y,y \ z),y \ z,x)) * z). [para(158(a,2),792(a,1,2,1,2)),flip(a)]. 805 x * (K(x \ 1,x) * (x \ y)) = ((x \ 1) * x) * y. [para(90(a,1),797(a,2,1))]. 806 x * (K(x \ 1,x) * (x \ y)) = K(x \ 1,x) * y. [para(126(a,2),805(a,2,1))]. 807 x \ (K(x \ 1,x) * y) = K(x \ 1,x) * (x \ y). [hyper(66,a,806,a)]. 808 K(x \ 1,x) * (x * y) = x * (K(x \ 1,x) * y). [para(13(a,1),806(a,1,2,2)),flip(a)]. 809 (x \ 1) * (y * T(y \ ((x \ 1) \ z),u)) = (x \ T(x * (z / y),u)) * y. [para(546(a,1),791(a,1,1)),flip(a)]. 810 T(x,(x * T(x \ 1,y)) / x) = R(x,T(1 / x,y),x). [para(191(a,1),800(a,1,2)),flip(a)]. 811 R(x,T(1 / x,y),x) = T(x,T(1 / x,y)). [para(191(a,1),810(a,1,2)),flip(a)]. 812 L((1 / x) \ y,1 / x,K(x \ 1,x)) = (x \ 1) \ (K(x \ 1,x) * y). [para(380(a,1),403(a,2,1))]. 813 R(T(x,x \ 1),y,z) * K(x \ 1,x) = (R(x,y,z) * (x \ 1)) * x. [para(497(a,1),464(a,1,1,1))]. 814 R(T(x,x \ 1),y,z) * K(x \ 1,x) = (x \ R(x,y,z)) * x. [para(588(a,1),813(a,2,1))]. 815 x \ R(1 \ (x * (y * (x \ 1))),z,u) = R(y,z,u) * (x \ 1). [para(479(a,1),285(a,1,2))]. 816 x \ R(x * (y * (x \ 1)),z,u) = R(y,z,u) * (x \ 1). [para(47(a,1),815(a,1,2,1))]. 817 K(x \ 1,x) * R(R(x,x \ 1,x),y,z) = (x \ R(x,y,z)) * x. [para(588(a,1),491(a,2,1))]. 818 K(x \ 1,x) * R(K(x \ 1,x) \ x,y,z) = (x \ R(x,y,z)) * x. [para(407(a,2),817(a,1,2,1))]. 819 L((x * y) / x,y \ 1,y) * (y \ 1) = (y \ 1) * ((x * y) / x). [para(12(a,1),714(a,2,2))]. 821 (x * R(x \ 1,x,x \ y)) \ R(1 / x,x,x \ y) = L(x \ 1,x,(x \ y) / y). [para(177(a,1),338(a,2,3))]. 822 ((x * (1 / (1 / y))) / x) * (1 / y) = ((x * y) / x) / y. [para(99(a,1),486(a,1,1,1,2)),flip(a)]. 823 (1 / x) * ((y * ((1 / x) \ 1)) / y) = ((y * x) / y) / x. [para(822(a,1),342(a,1)),flip(a)]. 824 (1 / x) * ((y * x) / y) = ((y * x) / y) / x. [para(59(a,1),823(a,1,2,1,2))]. 825 x * (T(y,x) * T(T(y,x) \ 1,z)) = (y * x) * T((y * x) \ x,z). [para(90(a,1),533(a,1,2,1,1)),flip(a)]. 826 x * (T(y,x) * T(T(y,x) \ 1,z)) = y * (x * T(x \ (y \ x),z)). [para(825(a,2),357(a,1))]. 827 x * K(y \ (y / T(z,x)),y) = z * (x * T(x \ (z \ x),y)). [para(561(a,2),826(a,1,2))]. 828 (x * T(x \ 1,y)) * z = z * K(y \ (y / T(x,z)),y). [para(827(a,2),790(a,1)),flip(a)]. 829 T(x * T(x \ 1,y),z) = K(y \ (y / T(x,z)),y). [hyper(117,a,828,a(flip))]. 830 T(x * T(x \ 1,y),x \ y) = K(y \ (x \ y),y). [para(132(a,1),829(a,2,1,2))]. 831 T(x,y) * T(T(x,y) \ 1,z) = T(x * T(x \ 1,z),y). [para(829(a,2),561(a,1)),flip(a)]. 832 K(x \ (x / T(y,z)),x) = T(K(x \ (x / y),x),z). [para(561(a,2),829(a,1,1)),flip(a)]. 833 K(x \ (x / T(x,y)),x) = T(K(x \ 1,x),y). [para(54(a,1),832(a,2,1,1,2))]. 834 K(x \ (x / T(x,y)),x) = K(x \ 1,x). [para(833(a,2),387(a,1))]. 836 T(x * T(x \ 1,x),y) * (T(x,y) \ x) = (T(x,y) \ 1) * x. [para(831(a,1),731(a,1,1))]. 837 T((x \ 1) * x,y) * (T(x,y) \ x) = (T(x,y) \ 1) * x. [para(90(a,1),836(a,1,1,1))]. 838 T(K(x \ 1,x),y) * (T(x,y) \ x) = (T(x,y) \ 1) * x. [para(126(a,2),837(a,1,1,1))]. 839 K(x \ 1,x) * (T(x,y) \ x) = (T(x,y) \ 1) * x. [para(387(a,1),838(a,1,1))]. 841 (1 / x) \ L(x \ 1,y,z) = x * L(T(x \ 1,x),y,z). [para(380(a,1),545(a,1,2,1))]. 842 (1 / x) \ L(x \ 1,y,z) = L(x \ 1,y,z) * x. [para(841(a,2),123(a,1))]. 843 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(842(a,1),830(a,1,2))]. 844 (((x * ((y / z) / u)) / x) * u) * z = (u * z) * ((x * ((u * z) \ y)) / x). [para(574(a,2),342(a,1))]. 845 (x * y) * ((z * ((x * y) \ u)) / z) = x * (y * ((z * (y \ (x \ u))) / z)). [para(14(a,1),575(a,1,2,1,2,2))]. 846 x \ (y * ((z * (y \ (x * u))) / z)) = (x \ y) * ((z * ((x \ y) \ u)) / z). [hyper(66,a,710,a)]. 847 (x \ y) * ((y \ T(x,x \ y)) * y) = (x \ ((y \ x) * y)) * y. [para(537(a,1),803(a,2,1))]. 848 (x \ y) * ((y \ T(x,x \ y)) * y) = K(y \ x,y) * y. [para(75(a,1),847(a,2,1))]. 849 (x * y) * ((x * ((x * y) \ z)) / x) = (x * ((z / y) / x)) * y. [para(16(a,1),844(a,1,1)),flip(a)]. 850 x * (y * ((z * (y \ (x \ y))) / z)) = (x * ((z * (x \ 1)) / z)) * y. [para(845(a,1),756(a,1))]. 851 x * (y * ((x * (y \ (x \ z))) / x)) = (x * ((z / y) / x)) * y. [para(845(a,1),849(a,1))]. 852 x * (y * ((x * (y \ 1)) / x)) = (x * ((x / y) / x)) * y. [para(48(a,1),851(a,1,2,2,1,2,2))]. 853 (x * (R(y / z,z,y \ u) / x)) * (z * (y \ u)) = x * ((z * (y \ u)) * ((x * ((z * (y \ u)) \ (x \ u))) / x)). [para(236(a,2),851(a,2,1,2,1)),flip(a)]. 854 (x \ y) * ((z * ((x \ y) \ 1)) / z) = x \ (y * ((z * (y \ x)) / z)). [para(12(a,1),846(a,1,2,2,1,2,2)),flip(a)]. 855 x \ ((y * x) * ((z * ((y * x) \ x)) / z)) = T(y,x) * ((z * ((x \ (y * x)) \ 1)) / z). [para(30(a,2),854(a,1,1)),flip(a)]. 856 x \ (y * (((y / x) * (y \ x)) / (y / x))) = (x \ y) * (((x \ y) \ (y / x)) / (y / x)). [para(551(a,1),854(a,1,2,1)),flip(a)]. 857 x * T(y,y \ z) = x * ((y \ z) \ z). [para(472(a,1),247(a,1))]. 859 (1 / x) * L((1 / x) \ y,z,u) = L(y * x,z,u) / x. [para(242(a,1),478(a,1,1,1)),flip(a)]. 860 (x \ (y \ z)) \ (((y * x) \ z) \ (x \ (y \ z))) = ((y * x) \ z) \ 1. [para(139(a,1),597(a,2,1))]. 861 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(860(a,1),566(a,2,2))]. 862 (L(x \ 1,x,y) * y) / L(x \ 1,x,y) = y * (x * T(x \ 1,y)). [para(656(a,2),210(a,1))]. 863 (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(862(a,1),620(a,1,1))]. 864 x * (T(y,x) * R(T(y,x) \ 1,z,u)) = (y * x) * R((y * x) \ x,z,u). [para(90(a,1),358(a,1,2,1,1)),flip(a)]. 865 x * (T(y,x) * R(T(y,x) \ 1,z,u)) = (y * R(y \ 1,z,u)) * x. [para(864(a,2),760(a,1))]. 866 T(x,y) * R(T(x,y) \ 1,z,u) = T(x * R(x \ 1,z,u),y). [hyper(117,a,865,a),flip(a)]. 867 (L(x / (y / z),u,w) * (y / z)) * z = L((x * z) / y,u,w) * y. [para(16(a,1),462(a,2,2))]. 868 ((x / y) * L((x / y) \ z,u,w)) * y = L((z * y) / x,u,w) * x. [para(278(a,1),867(a,1,1))]. 869 ((x / y) * L((x / y) \ z,u,w)) * y = x * L(x \ (z * y),u,w). [para(868(a,2),278(a,1))]. 870 ((x / y) * L((x / y) \ x,z,u)) * y = x * L(y,z,u). [para(13(a,1),869(a,2,2,1))]. 871 ((x / y) * L(y,z,u)) * y = x * L(y,z,u). [para(59(a,1),870(a,1,1,2,1))]. 872 (x * L(y,z,u)) / y = (x / y) * L(y,z,u). [hyper(70,a,871,a)]. 873 (1 / x) * L(x,y,z) = L(x,y,z) / x. [hyper(18,a,142,a,b,871,a)]. 874 (R(x,L(y,z,u) / y,y) / y) * L(y,z,u) = x * (L(y,z,u) / y). [hyper(18,a,225,a(flip),b,871,a)]. 875 L(x,y,z) \ (L(x,y,z) / x) = T(1 / x,L(x,y,z)). [para(873(a,1),30(a,2,2)),flip(a)]. 876 ((x / L(y,z,u)) / y) * L(y,z,u) = x / y. [para(16(a,1),872(a,1,1)),flip(a)]. 877 ((x * y) / z) * L(z,y,x) = (x * (y * z)) / z. [para(79(a,1),872(a,1,1)),flip(a)]. 878 (x / L(y,z,u)) / y = (x / y) / L(y,z,u). [hyper(70,a,876,a),flip(a)]. 879 (x / L(x,y,z)) / x = 1 / L(x,y,z). [para(54(a,1),878(a,2,1))]. 880 L(x,y,z) = ((z * y) / x) \ ((z * (y * x)) / x). [hyper(66,a,877,a),flip(a)]. 881 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(875(a,1),330(a,1,1,2))]. 882 (R(x,K(y \ 1,y),y) / y) * L(y,y \ 1,y) = x * (L(y,y \ 1,y) / y). [para(408(a,1),874(a,1,1,1,2))]. 883 ((x * ((y \ z) / z)) / x) * z = (((x * (1 / y)) / x) * y) * (y \ z). [para(14(a,1),487(a,1,1,1,2,2))]. 884 (((x * (1 / y)) / x) * y) * (y \ z) = z * ((x * (z \ (y \ z))) / x). [para(883(a,1),342(a,1))]. 885 x * ((y * (x \ (y \ x))) / y) = (y * (1 / y)) * (y \ x). [para(16(a,1),884(a,1,1)),flip(a)]. 886 (x * ((y * (x \ 1)) / y)) * (x \ z) = z * ((y * (z \ (x \ z))) / y). [para(342(a,1),884(a,1,1))]. 887 (x * ((y * (x \ (z \ x))) / y)) / (z \ x) = z * ((y * (z \ 1)) / y). [hyper(70,a,886,a)]. 888 (x * ((y * (x \ z)) / y)) / ((x / z) \ x) = (x / z) * ((y * ((x / z) \ 1)) / y). [para(59(a,1),887(a,1,1,2,1,2,2))]. 889 (x \ 1) * ((x \ T(x,y)) * ((x \ 1) \ z)) = (x \ T(x,y)) * z. [para(524(a,1),798(a,2,1))]. 890 (x \ T(x,y)) * ((x \ 1) * z) = (x \ 1) * ((x \ T(x,y)) * z). [para(13(a,1),889(a,1,2,2)),flip(a)]. 891 (x \ T(x,y)) \ R((x \ 1) * ((x \ T(x,y)) * ((x \ T(x,y)) \ 1)),z,u) = R(x \ 1,z,u) * ((x \ T(x,y)) \ 1). [para(890(a,1),816(a,1,2,1))]. 892 (x / y) * ((z * ((x / y) \ 1)) / z) = (x * ((z * (x \ y)) / z)) / y. [para(59(a,1),888(a,1,2)),flip(a)]. 893 (((x \ 1) * (x \ T(x,y))) * x) / L(K(x \ 1,x),1,R(x \ T(x,y),x \ 1,x)) = R(x \ T(x,y),x \ 1,x) * 1. [para(802(a,1),473(a,1,1,1))]. 894 (L(x,1 / x,y) * y) / L(x,1 / x,y) = y * ((1 / x) * T(x,y)). [para(657(a,2),210(a,1))]. 895 (x * y) * (z * T(z \ L(y \ z,y,x),u)) = (x * (y * T(y \ 1,u))) * z. [para(355(a,1),793(a,1,1)),flip(a)]. 896 K(x \ 1,x) * T(K(x \ 1,x) \ y,z) = (x \ 1) * (x * T(x \ ((x \ 1) \ y),z)). [para(126(a,2),459(a,1,2,1,1))]. 897 (x * y) * L((x * y) \ (y * z),u,w) = y * (T(x,y) * L(T(x,y) \ z,u,w)). [para(90(a,1),460(a,1,2,1,1))]. 898 x * (T(y,x) * L(T(y,x) \ z,u,w)) = y * (x * L(x \ (y \ (x * z)),u,w)). [para(897(a,1),456(a,1))]. 899 x \ (y * (x * L(x \ (y \ (x * z)),u,w))) = T(y,x) * L(T(y,x) \ z,u,w). [hyper(66,a,898,a)]. 900 x * (T(y,x) * L(T(y,x) \ 1,z,u)) = y * (x * L(x \ (y \ x),z,u)). [para(12(a,1),898(a,2,2,2,1,2,2))]. 901 x * (T(y,x) * L(T(y,x) \ 1,z,u)) = (y * L(y \ 1,z,u)) * x. [para(900(a,2),770(a,1))]. 902 T(x,y) * L(T(x,y) \ 1,z,u) = T(x * L(x \ 1,z,u),y). [hyper(117,a,901,a),flip(a)]. 903 T(x * L(x \ 1,y,z),u) / T(x,u) = L(1 / T(x,u),y,z). [para(902(a,1),336(a,1,1))]. 904 T(x * L(x \ 1,T(x,y),x / T(x,y)),y) = x \ (T(x,y) * (x / T(x,y))). [para(902(a,1),521(a,2)),flip(a)]. 905 T((x / T(x,y)) * (T(x,y) * (x \ 1)),y) = x \ (T(x,y) * (x / T(x,y))). [para(205(a,1),904(a,1,1))]. 906 T((x / T(x,y)) * (x \ T(x,y)),y) = x \ (T(x,y) * (x / T(x,y))). [para(520(a,1),905(a,1,1,2))]. 907 T((x / T(x,y)) * (x \ T(x,y)),y) = K(T(x,y),x / T(x,y)). [para(906(a,2),77(a,1))]. 908 T(x * L(x \ ((y * z) / y),u,w),y) = T(x,y) * L(T(x,y) \ z,u,w). [para(899(a,1),782(a,1)),flip(a)]. 909 T(x \ L(x * ((y * z) / y),u,w),y) = T(x \ 1,y) * L(T(x \ 1,y) \ z,u,w). [para(632(a,1),908(a,1,1))]. 910 x * T(x \ (K(y \ 1,y) * ((y \ 1) \ x)),y \ 1) = (y \ 1) \ x. [hyper(107,a,558,a(flip)),flip(a)]. 911 x \ ((y * x) * ((z * ((y * x) \ x)) / z)) = T(y,x) * ((z * (T(y,x) \ 1)) / z). [para(30(a,2),855(a,2,2,1,2,1))]. 912 x \ ((y * ((z * (y \ 1)) / z)) * x) = T(y,x) * ((z * (T(y,x) \ 1)) / z). [para(756(a,1),911(a,1,2))]. 913 T(x,y) * ((z * (T(x,y) \ 1)) / z) = T(x * ((z * (x \ 1)) / z),y). [para(912(a,1),30(a,2)),flip(a)]. 914 K(x \ 1,x) * T(K(x \ 1,x) \ y,z) = (x \ T(x * (y / x),z)) * x. [para(896(a,2),809(a,1))]. 915 L(x,T(x,y) \ 1,T(x,y)) * (T(x,y) \ 1) = (T(x,y) \ 1) * x. [para(14(a,1),713(a,2,2))]. 917 ((R(1 / x,y,z) * x) * (x \ (y * z))) / (x \ (y * z)) = a((x \ (y * z)) / (y * z),y,z). [para(466(a,1),484(a,1,1))]. 918 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),881(a,1,1))]. 919 ((x * R(x \ 1,y,z)) * (x \ (y * z))) / (x \ (y * z)) = a((x \ (y * z)) / (y * z),y,z). [para(283(a,1),917(a,1,1,1))]. 920 a((x \ (y * z)) / (y * z),y,z) = x * R(x \ 1,y,z). [para(919(a,1),15(a,1))]. 921 T(x,y * R(y \ 1,z,u)) = x. [para(920(a,1),153(a,1,2))]. 922 T(x * R(x \ 1,y,z),u) = x * R(x \ 1,y,z). [hyper(33,a,921,a)]. 923 T(x,(y / (z * y)) * z) = x. [para(316(a,2),921(a,1,2))]. 924 T(x,y \ R(y,z,u)) = x. [para(631(a,1),921(a,1,2))]. 925 (x \ R(x,y,z)) * x = R(x,y,z). [para(924(a,1),115(a,1,2))]. 926 R(x,y,z) / x = x \ R(x,y,z). [para(924(a,1),132(a,1,2))]. 927 T(x,y \ T(y,L(y \ 1,z,u))) = x. [para(776(a,1),924(a,1,2,2))]. 928 T(x,((y \ z) / z) * y) = x. [para(14(a,1),923(a,1,2,1,2))]. 929 T(x,(y / z) * (z / y)) = x. [para(16(a,1),923(a,1,2,1,2))]. 930 L((x \ y) / y,x,(x \ y) / y) = (x * ((x \ y) / y)) / x. [para(928(a,1),310(a,1)),flip(a)]. 931 T(x,y * (z / (y * z))) = x. [para(15(a,1),929(a,1,2,1))]. 932 T(x,y * ((y \ z) / z)) = x. [para(57(a,1),929(a,1,2,1))]. 933 ((x / y) * (y / x)) / (x / y) = L(y / x,x / y,y / x). [para(929(a,1),310(a,1))]. 934 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(929(a,1),747(a,2))]. 935 T(x * (y / (x * y)),z) = x * (y / (x * y)). [hyper(33,a,931,a)]. 936 T(L(x,y / (x * y),x),y / (x * y)) = x. [para(931(a,1),306(a,2))]. 937 L(x,y / (x * y),x) * (y / (x * y)) = (y / (x * y)) * x. [para(931(a,1),309(a,1,2)),flip(a)]. 938 (x * (y * ((y \ z) / z))) / x = y * ((y \ z) / z). [para(932(a,1),101(a,1,2))]. 939 (((x \ y) / y) * x) / ((x \ y) / y) = L(x,(x \ y) / y,x). [para(932(a,1),310(a,1))]. 940 x * (R(x,y,z) / x) = R(x,y,z). [para(925(a,1),56(a,1,2,1))]. 941 a(x,y,y \ 1) * x = R(x,y,y \ 1). [para(304(a,1),925(a,1,1))]. 942 (x * R(x \ 1,y,z)) * (1 / x) = R(1 / x,y,z). [para(541(a,1),925(a,1,1))]. 943 R(T(x,x \ 1),y,z) * K(x \ 1,x) = R(x,y,z). [para(925(a,1),814(a,2))]. 944 R(x,y,y \ 1) / x = a(x,y,y \ 1). [para(926(a,2),304(a,1))]. 945 R(x,y,z) * (x \ 1) = R(x,y,z) / x. [para(926(a,2),588(a,2))]. 946 (x \ 1) \ R(x \ 1,y,z) = x * R(x \ 1,y,z). [para(926(a,1),638(a,1))]. 947 R(1 / x,x,y) / (1 / x) = (y / (x * y)) * x. [hyper(17,a,542,a,b,940,a)]. 948 (x \ 1) * (x * R(x \ 1,y,z)) = R(x \ 1,y,z). [para(638(a,1),940(a,1,2))]. 949 T(x \ T(x,L(x \ 1,y,z)),u) = x \ T(x,L(x \ 1,y,z)). [hyper(33,a,927,a)]. 950 a(x \ 1,x,x \ 1) = K(x \ 1,x). [hyper(18,a,265,a,b,941,a)]. 951 R((x \ 1) / (x * (x \ 1)),y,z) / R(1 / x,y,z) = a(R(1 / x,y,z),x,x \ 1). [para(179(a,1),944(a,1,1))]. 952 R(x \ 1,x,y) / (y / (x * y)) = a(y / (x * y),x,x \ 1). [para(451(a,1),944(a,1,1))]. 953 x * R(x \ 1,y,y \ 1) = a(x \ 1,y,y \ 1). [para(944(a,1),638(a,1)),flip(a)]. 954 R(x,y,z) * (x \ 1) = (1 / x) * R(x,y,z). [para(945(a,2),636(a,2)),flip(a)]. 955 T(1 / x,R(x,y,z)) = x \ 1. [hyper(117,a,954,a)]. 956 T(x,R(x \ 1,y,z)) = (x \ 1) \ 1. [para(57(a,1),955(a,1,1))]. 957 T(1 / x,(x \ 1) \ 1) = x \ 1. [para(432(a,1),955(a,1,2))]. 958 T(1 / x,T(x,x \ 1)) = x \ 1. [para(497(a,1),955(a,1,2))]. 959 ((x \ 1) * x) * (x \ y) = y * T(y \ (x \ y),(x \ 1) \ 1). [para(957(a,1),725(a,1,1,1))]. 960 T(x / (y * x),T(y,y \ 1)) = R(y \ 1,y,x). [para(958(a,1),178(a,2,1))]. 961 T(1 / x,R((1 / x) \ 1,y,z)) = x \ 1. [para(59(a,1),956(a,2,1))]. 962 x * T(x \ 1,R((1 / x) \ 1,y,z)) = (1 / x) \ (x \ 1). [para(961(a,1),532(a,1,2)),flip(a)]. 963 ((x / (y * x)) * y) / R(1 / y,y,x) = 1 / (1 / y). [para(947(a,1),637(a,1,1))]. 964 T(x,y) * R(T(x,y) \ 1,z,u) = x * R(x \ 1,z,u). [para(922(a,1),866(a,2))]. 965 ((((x \ y) / y) * x) / ((x \ y) / y)) \ (x * ((x \ y) / y)) = L((x \ y) / y,x,(x \ y) / y). [para(938(a,1),880(a,2,2)),flip(a)]. 966 (x * R(x \ 1,y,z)) \ R(1 / x,y,z) = 1 / x. [hyper(66,a,942,a)]. 967 R((x \ 1) \ 1,y,z) * K(x \ 1,x) = R(x,y,z). [para(91(a,1),943(a,1,1,1))]. 968 R(x \ 1,y,z) / (x * R(x \ 1,y,z)) = x \ 1. [para(946(a,1),57(a,1,2))]. 969 a(1 / x,y,y \ 1) = a(x \ 1,y,y \ 1). [para(953(a,1),544(a,1)),flip(a)]. 970 T(x * R(x \ 1,y,y \ 1),z) = a(T(x,z) \ 1,y,y \ 1). [para(953(a,1),866(a,1)),flip(a)]. 971 (1 / x) * a(x \ 1,T(x,y),T(x,y) \ 1) = (T(x,y) / x) * (T(x,y) \ 1). [para(969(a,1),651(a,1,2))]. 972 L(x \ 1,x,(x \ y) / y) = 1 / x. [para(966(a,1),821(a,1)),flip(a)]. 973 L((x / y) \ 1,x / y,y / x) = 1 / (x / y). [para(59(a,1),972(a,1,3,1))]. 975 L((x / (y * x)) \ 1,x / (y * x),y) = 1 / (x / (y * x)). [para(15(a,1),973(a,1,3))]. 976 x * L(x \ (1 * y),x / y,y / x) = ((x / y) * (1 / (x / y))) * y. [para(973(a,1),869(a,1,1,2)),flip(a)]. 978 T(L(x / y,y / x,x / y),y) = ((y / x) * (y \ x)) / (y / x). [para(933(a,1),291(a,1,1))]. 979 ((x / (y * x)) * y) / R(1 / y,y,x) = L(y,x / (y * x),y). [para(937(a,1),581(a,1,1))]. 980 x * T(x \ 1,R((1 / x) \ 1,y,z)) = K(x \ 1,x). [para(962(a,2),381(a,1))]. 981 x * T(x \ 1,R(x,y,z)) = K(x \ 1,x). [para(59(a,1),980(a,1,2,2,1))]. 982 x / (1 / (y / (x * y))) = x * (y / (x * y)). [para(975(a,1),175(a,1,2))]. 983 K(x \ (x / (1 / (y / (x * y)))),x) = a(y / (x * y),x,x \ 1). [para(952(a,1),677(a,2))]. 984 K(x \ 1,x) * (x \ y) = y * T(y \ (x \ y),(x \ 1) \ 1). [para(126(a,2),959(a,1,1))]. 985 a(T(x,y) \ 1,z,z \ 1) = T(a(x \ 1,z,z \ 1),y). [para(953(a,1),970(a,1,1)),flip(a)]. 986 a(T(x,y) \ 1,z,z \ 1) = a(x \ 1,z,z \ 1). [para(985(a,2),93(a,1))]. 987 a((x / y) \ 1,z,z \ 1) = a((y \ x) \ 1,z,z \ 1). [para(92(a,1),986(a,1,1,1)),flip(a)]. 989 a(x \ 1,T(x,y),T(x,y) \ 1) = K(T(x,y) \ 1,T(x,y)). [para(986(a,1),950(a,1))]. 990 L(x,y / (x * y),x) = 1 / (1 / x). [para(979(a,1),963(a,1))]. 991 L(x,(x \ y) / y,x) = 1 / (1 / x). [para(14(a,1),990(a,1,2,2))]. 992 L(T(x,y),z / (x * z),x) = T(1 / (1 / x),y). [para(990(a,1),38(a,2,1))]. 993 L(x,x \ 1,x) = 1 / (1 / x). [para(98(a,1),990(a,1,2))]. 994 T(1 / (1 / x),y / (x * y)) = x. [para(990(a,1),936(a,1,1))]. 996 T(L(x,T(x,y) \ 1,T(x,y)),y) = 1 / (1 / T(x,y)). [para(993(a,1),38(a,1)),flip(a)]. 997 L(T(x,y),x \ 1,x) = T(1 / (1 / x),y). [para(993(a,1),38(a,2,1))]. 998 x * K(x \ 1,x) = 1 / (1 / x). [para(993(a,1),259(a,2))]. 999 L((x * y) / x,y \ 1,y) = (x * (1 / (1 / y))) / x. [para(993(a,1),343(a,2,1,2))]. 1000 L(K(x \ 1,x) \ y,K(x \ 1,x),x) = x * ((1 / (1 / x)) \ y). [para(993(a,1),723(a,2,2,1))]. 1001 T(1 / (1 / x),x \ 1) = x. [para(98(a,1),994(a,1,2))]. 1003 T(T(1 / (1 / x),y),x \ 1) = T(x,y). [para(1001(a,1),36(a,1,1)),flip(a)]. 1004 (1 / (1 / x)) * y != x * (K(x \ 1,x) * z) | L(z,K(x \ 1,x),x) = y. [para(998(a,1),206(a,1,1))]. 1005 K(x \ 1,x) * x = 1 / (1 / x). [para(998(a,1),390(a,2))]. 1006 x * K(x \ (x / T(x,y)),x) = 1 / (1 / x). [para(834(a,2),998(a,1,2))]. 1008 (1 / (1 / x)) * L(y,x,K(x \ 1,x)) = K(x \ 1,x) * (x * y). [para(1005(a,1),79(a,1,1))]. 1009 K(x \ 1,x) * (x * y) != (1 / (1 / x)) * z | L(y,x,K(x \ 1,x)) = z. [para(1005(a,1),206(a,1,1)),flip(a)]. 1010 (((x \ y) / y) * x) / ((x \ y) / y) = 1 / (1 / x). [para(991(a,1),939(a,2))]. 1011 T(x,y / (x * y)) = T(x,x \ 1). [para(994(a,1),1003(a,1,1)),flip(a)]. 1012 K((x / (y * x)) \ 1,x / (y * x)) * (y * x) = T(y,y \ 1) * x. [para(1011(a,1),702(a,2,1))]. 1013 T(1 / (1 / x),y) / ((x \ 1) * T(x,y)) = x. [para(997(a,1),257(a,1,1))]. 1014 L(x,T(x,y) \ 1,T(x,y)) = 1 / (1 / x). [para(1006(a,1),628(a,2))]. 1015 (1 / (1 / x)) * (T(x,y) \ 1) = (T(x,y) \ 1) * x. [para(1014(a,1),915(a,1,1))]. 1017 L(T(x,y) \ 1,(x \ 1) * T(x,y),T(1 / (1 / x),y) / ((x \ 1) * T(x,y))) = T(1 / (1 / x),y) \ (x * R(x \ 1,T(x,y),T(x,y) \ 1)). [para(1013(a,1),300(a,1,2,1)),flip(a)]. 1019 T(1 / (1 / x),T(x,y) \ 1) = x. [hyper(117,a,1015,a(flip))]. 1021 T(1 / (1 / ((x * y) / x)),y \ 1) = (x * y) / x. [para(112(a,1),1019(a,1,2,1))]. 1022 (1 / (1 / ((x * y) / x))) * (y \ 1) = (y \ 1) * ((x * y) / x). [para(1021(a,1),90(a,1,2)),flip(a)]. 1023 1 / (1 / T(x,y)) = T(1 / (1 / x),y). [para(1014(a,1),996(a,1,1)),flip(a)]. 1024 T(1 / (1 / x),y) \ 1 = 1 / T(x,y). [para(1023(a,1),59(a,1,1))]. 1025 x * (1 / (1 / T(y,x))) = (1 / (1 / y)) * x. [para(1023(a,2),90(a,1,2))]. 1026 T(1 / (1 / (x / y)),y) = 1 / (1 / (y \ x)). [para(92(a,1),1023(a,1,2,2)),flip(a)]. 1028 1 / T(x \ 1,y) = T(1 / x,y) \ 1. [para(57(a,1),1024(a,1,1,1,2)),flip(a)]. 1029 1 / T((x \ 1) \ 1,y) = T(x,y) \ 1. [para(57(a,1),1028(a,2,1,1))]. 1030 (T(x,y) \ 1) \ 1 = T((x \ 1) \ 1,y). [para(1029(a,1),59(a,1,1))]. 1031 T(((x / y) \ 1) \ 1,y) = ((y \ x) \ 1) \ 1. [para(92(a,1),1030(a,1,1,1)),flip(a)]. 1032 (1 / (1 / (x / y))) * y = y * (1 / (1 / (y \ x))). [para(92(a,1),1025(a,1,2,2,2)),flip(a)]. 1034 T(x,((y * x) / y) \ 1) = ((y \ (y * x)) \ 1) \ 1. [para(1031(a,1),194(a,1)),flip(a)]. 1035 T(x,((y * x) / y) \ 1) = (x \ 1) \ 1. [para(13(a,1),1034(a,2,1,1))]. 1036 T((x * y) / x,((z * y) / z) \ 1) = (x * ((y \ 1) \ 1)) / x. [para(1035(a,1),193(a,1,1,2)),flip(a)]. 1037 (((x * y) / x) \ 1) * ((y \ 1) \ 1) = ((x * y) / x) \ y. [para(1035(a,1),627(a,1,2))]. 1038 a(((x * y) / x) \ 1,(y \ 1) \ 1,y \ 1) * ((((x * y) / x) \ 1) * K((y \ 1) \ 1,y \ 1)) = (((x * y) / x) \ y) * (y \ 1). [para(1037(a,1),333(a,2,1))]. 1040 L((x * y) / x,y \ 1,y) = 1 / (1 / ((x * y) / x)). [hyper(18,a,819,a,b,1022,a),flip(a)]. 1041 (x * (1 / (1 / y))) / x = 1 / (1 / ((x * y) / x)). [para(1040(a,1),999(a,1)),flip(a)]. 1042 (x * ((y \ 1) \ 1)) / x = (((x * y) / x) \ 1) \ 1. [para(1036(a,1),91(a,1))]. 1043 (x \ 1) * ((((y * x) / y) \ 1) \ 1) = ((y * x) / y) * (x \ 1). [para(1042(a,1),450(a,1,2))]. 1044 L(T(x / y,y),y / x,x / y) = ((y / x) * (y \ x)) / (y / x). [para(978(a,1),38(a,2))]. 1045 K(x \ (x * (y / (x * y))),x) = a(y / (x * y),x,x \ 1). [para(982(a,1),983(a,1,1,2))]. 1046 a(x / (y * x),y,y \ 1) = K(x / (y * x),y). [para(13(a,1),1045(a,1,1)),flip(a)]. 1048 (1 / (1 / x)) * L(y,x,K(x \ 1,x)) = x * (K(x \ 1,x) * y). [para(1008(a,2),808(a,1))]. 1049 ((x / y) * (x \ y)) / (x / y) = L(x \ y,x / y,y / x). [para(92(a,1),1044(a,1,1)),flip(a)]. 1050 (x \ y) * (((x \ y) \ (y / x)) / (y / x)) = x \ (y * L(y \ x,y / x,x / y)). [para(1049(a,1),856(a,1,2,2)),flip(a)]. 1052 L(x,K(y \ 1,y),y) = L(x,y,K(y \ 1,y)). [hyper(1004,a,1048,a)]. 1053 L(K(x \ 1,x) \ y,x,K(x \ 1,x)) = x * ((1 / (1 / x)) \ y). [para(1052(a,1),1000(a,1))]. 1054 (1 / x) * K(T(x,y) \ 1,T(x,y)) = (T(x,y) / x) * (T(x,y) \ 1). [para(989(a,1),971(a,1,2))]. 1055 a(R(1 / x,y,z),x,x \ 1) = R(x \ 1,y,z) / R(1 / x,y,z). [para(98(a,1),951(a,1,1,1)),flip(a)]. 1057 x * (K(x,y) * R(K(x,y) \ (x \ (x * y)),z,u)) = R(R(y,x,K(x,y)),z,u) * (x * K(x,y)). [para(340(a,1),474(a,1)),flip(a)]. 1058 L((x \ y) / y,x,(x \ y) / y) = (1 / (1 / x)) \ (x * ((x \ y) / y)). [para(1010(a,1),965(a,1,1)),flip(a)]. 1059 L((x \ y) / y,x,(x \ y) / y) = x * ((1 / (1 / x)) \ ((x \ y) / y)). [para(1058(a,2),599(a,1))]. 1061 x * ((1 / (1 / x)) \ ((x \ y) / y)) = (x * ((x \ y) / y)) / x. [para(1059(a,1),930(a,1))]. 1062 R(R(x,y,K(y,x)),z,u) * (y * K(y,x)) = y * (K(y,x) * R(K(y,x) \ x,z,u)). [para(13(a,1),1057(a,1,2,2,1,2)),flip(a)]. 1063 x * (K(x,y) * R(K(x,y) \ y,z,u)) = (R(y,z,u) * x) * K(x,y). [para(1062(a,1),231(a,1))]. 1064 (R(x,y,z) * (x \ 1)) * K(x \ 1,x) = (x \ 1) * ((x \ R(x,y,z)) * x). [para(818(a,1),1063(a,1,2)),flip(a)]. 1065 (R(x,y,z) * (x \ 1)) * K(x \ 1,x) = (x \ 1) * R(x,y,z). [para(925(a,1),1064(a,2,2))]. 1066 K(x \ 1,R(x,y,z)) = K(x \ 1,x). [hyper(149,a,1065,a)]. 1067 T(x,K(y \ 1,R(y,z,u))) = x. [para(1066(a,2),385(a,1,2))]. 1068 K(x \ 1,(x \ 1) \ 1) = K(x \ 1,x). [para(432(a,1),1066(a,1,2))]. 1069 T(K(x \ 1,R(x,y,z)),u) = K(x \ 1,R(x,y,z)). [hyper(33,a,1067,a)]. 1070 L(((1 / x) \ (x \ 1)) \ y,a(1 / x,x,x \ 1),1 / x) = (1 * (x \ 1)) \ ((1 / x) * y). [para(11(a,1),422(a,1,1,1,2))]. 1071 L(K(x \ 1,x) \ y,a(1 / x,x,x \ 1),1 / x) = (1 * (x \ 1)) \ ((1 / x) * y). [para(381(a,1),1070(a,1,1,1))]. 1072 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(578(a,1),1071(a,2,2))]. 1073 K(x \ 1,x) * R(K(x \ 1,x) \ (x \ 1),y,z) = (x \ 1) * (x * R(x \ 1,y,z)). [para(159(a,1),629(a,1,2,1,2))]. 1074 K(x \ 1,x) * R(1 / x,y,z) = (x \ 1) * (x * R(x \ 1,y,z)). [para(400(a,1),1073(a,1,2,1))]. 1075 K(x \ 1,x) * R(1 / x,y,z) = R(x \ 1,y,z). [para(1074(a,2),948(a,1))]. 1076 R(x \ 1,y,z) / R(1 / x,y,z) = K(x \ 1,x). [hyper(70,a,1075,a)]. 1077 K(x \ 1,x) * (y / (x * y)) = R(x \ 1,x,y). [para(111(a,1),1075(a,1,2))]. 1078 R(1 / x,y,z) * K(x \ 1,x) = R(x \ 1,y,z). [para(1075(a,1),390(a,1)),flip(a)]. 1079 (x / (y * x)) * K(y \ 1,y) = R(y \ 1,y,x). [para(1077(a,1),390(a,1)),flip(a)]. 1080 x / L(K(y \ 1,y) \ (y * x),K(y \ 1,y),x / (y * x)) = R(y \ 1,y,x). [para(1079(a,1),223(a,2))]. 1081 a(R(1 / x,y,z),x,x \ 1) = K(x \ 1,x). [para(1076(a,1),1055(a,2))]. 1082 a(x / (y * x),y,y \ 1) = K(y \ 1,y). [para(111(a,1),1081(a,1,1))]. 1084 K(x / (y * x),y) = K(y \ 1,y). [para(1082(a,1),1046(a,1)),flip(a)]. 1085 K(1 / x,x) = K(x \ 1,x). [para(12(a,1),1084(a,1,1,2))]. 1086 K((x \ y) / y,x) = K(x \ 1,x). [para(14(a,1),1084(a,1,1,2))]. 1087 K((x / y) \ 1,x / y) = K(y / x,x / y). [para(16(a,1),1084(a,1,1,2)),flip(a)]. 1089 K((x \ 1) \ 1,x \ 1) = K(x,x \ 1). [para(57(a,1),1085(a,1,1)),flip(a)]. 1090 K(x \ 1,x) * K(x,1 / x) = 1. [para(1085(a,1),721(a,1,1))]. 1091 L((1 / x) \ y,1 / x,K(1 / x,x)) = (x \ 1) \ (K(x \ 1,x) * y). [para(1085(a,2),812(a,1,3))]. 1092 K(x,1 / x) = K(x,x \ 1). [hyper(198,a,1090,a),flip(a)]. 1093 K(x,x \ 1) = x * (1 / x). [para(1092(a,1),128(a,1))]. 1094 K(x,x \ 1) * (1 / (1 / x)) = x. [para(1092(a,1),412(a,1,1))]. 1095 x / (1 / (1 / x)) = K(x,x \ 1). [para(1092(a,1),413(a,2))]. 1096 K(x,x \ 1) \ x = 1 / (1 / x). [para(1092(a,1),414(a,1,1))]. 1097 R(x,y,1 / y) * K(y,y \ 1) = (x * y) * (1 / y). [para(1092(a,1),234(a,1,2))]. 1098 K(x,x \ 1) \ (y * (1 / x)) = R(y / x,x,1 / x). [para(1092(a,1),471(a,1,1))]. 1099 (x \ 1) * K(x,x \ 1) = 1 / x. [para(1092(a,1),510(a,1,2))]. 1100 K(x,x \ 1) * (x \ 1) = 1 / x. [para(1092(a,1),511(a,1,1))]. 1101 K(x,x \ 1) * x = T(x,x \ 1). [para(1092(a,1),664(a,1,1))]. 1102 x * K(x,x \ 1) = T(x,x \ 1). [para(1092(a,1),665(a,1,2))]. 1103 x \ (K(y \ x,(y \ x) \ 1) * y) = L(1 / (y \ x),y \ x,y). [para(1092(a,1),708(a,1,2,1))]. 1104 (x * R(x \ 1,y,z)) * (1 / x) = R(x \ 1,y,z) * K(x,x \ 1). [para(1092(a,1),757(a,2,2))]. 1105 x * (K(x,x \ 1) * (x \ y)) = K(x,1 / x) * y. [para(1092(a,1),781(a,1,2,1))]. 1106 K(x,x \ 1) * y != x * ((1 / x) * z) | L(z,1 / x,x) = y. [para(1093(a,2),206(a,1,1))]. 1107 T((x * y) \ (K(x,x \ 1) * y),x) = R(T(1 / x,x * y),x,y). [para(1093(a,2),492(a,1,1,2,1))]. 1108 x * ((y * (x \ (y \ x))) / y) = K(y,y \ 1) * (y \ x). [para(1093(a,2),885(a,2,1))]. 1109 x * L(x \ (1 * y),x / y,y / x) = K(x / y,(x / y) \ 1) * y. [para(1093(a,2),976(a,2,1))]. 1110 L((1 / (1 / x)) \ y,1 / (1 / x),K(x,x \ 1)) = x \ (K(x,x \ 1) * y). [para(1094(a,1),81(a,2,1))]. 1111 K(T(x,y),T(x,y) \ 1) * T(1 / (1 / x),y) = T(x,y). [para(1023(a,1),1094(a,1,2))]. 1112 ((1 / x) * y) / (K(x,x \ 1) * y) = R(x \ 1,K(x,x \ 1),y). [para(1099(a,1),28(a,2,1,1)),flip(a)]. 1113 (1 / x) / L(y,(x \ 1) / y,K(x,x \ 1)) = K(x,x \ 1) * ((x \ 1) / y). [para(1100(a,1),246(a,1,1))]. 1114 T(x,x \ 1) * y != K(x,x \ 1) * (x * z) | L(z,x,K(x,x \ 1)) = y. [para(1101(a,1),206(a,1,1))]. 1115 (T(x,x \ 1) * y) / (K(x,x \ 1) * y) = R(x,K(x,x \ 1),y). [para(1102(a,1),28(a,2,1,1)),flip(a)]. 1116 x * K(x,x \ 1) = (x \ 1) \ 1. [para(1102(a,2),91(a,1))]. 1117 (x * K(y,y \ 1)) / T(y,y \ 1) = R(x / y,y,K(y,y \ 1)). [para(1102(a,1),86(a,2,2)),flip(a)]. 1119 ((x \ 1) \ 1) \ (x * (K(x,x \ 1) * y)) = L(y,K(x,x \ 1),x). [para(1116(a,1),26(a,2,1)),flip(a)]. 1120 (x * y) * K(y,y \ 1) != z * ((y \ 1) \ 1) | R(x,y,K(y,y \ 1)) = z. [para(1116(a,1),226(a,2,2))]. 1121 ((x \ 1) \ 1) \ (K(x,x \ 1) * (x * y)) = L(y,x,K(x,x \ 1)). [para(1116(a,1),446(a,1,1))]. 1122 ((x \ 1) \ 1) \ K(x,x \ 1) = x \ 1. [para(1089(a,1),160(a,1,2))]. 1123 x * T(x \ (K(y,y \ 1) * (((y \ 1) \ 1) \ x)),(y \ 1) \ 1) = ((y \ 1) \ 1) \ x. [para(1089(a,1),910(a,1,2,1,2,1))]. 1124 T(x,K(y / z,z / y)) = x. [para(1087(a,1),385(a,1,2))]. 1125 K(x / y,y / x) * x = y * T(y \ x,y / x). [para(1087(a,1),701(a,1,1))]. 1126 K((x * y) / y,y / (x * y)) = ((y / (x * y)) \ 1) * R(1 / x,x,y). [para(1087(a,1),582(a,1))]. 1127 K((x * y) / y,y / (x * y)) * (x * y) = T(x,x \ 1) * y. [para(1087(a,1),1012(a,1,1))]. 1128 K(x / y,y / x) * z = z * K(x / y,y / x). [para(1124(a,1),90(a,1,2))]. 1129 x * (K(x,x \ 1) * (x \ y)) = K(x,x \ 1) * y. [para(1092(a,1),1105(a,2,1))]. 1130 x \ (K(x,x \ 1) * y) = K(x,x \ 1) * (x \ y). [hyper(66,a,1129,a)]. 1131 K(x,x \ 1) * (x * y) = x * (K(x,x \ 1) * y). [para(13(a,1),1129(a,1,2,2)),flip(a)]. 1132 (x * y) * K(x,x \ 1) = x * (K(x,x \ 1) * y). [para(1131(a,1),442(a,1)),flip(a)]. 1133 R(x,y,K(x,x \ 1)) = x. [hyper(449,a,1132,a)]. 1134 R(x \ 1,y,K(x \ 1,x)) = x \ 1. [para(1068(a,1),1133(a,1,3))]. 1135 (R(x \ 1,y,z) * ((y * z) / K(x \ 1,x))) * K(x \ 1,x) = ((x \ 1) * y) * z. [para(1134(a,1),467(a,1,1,1)),flip(a)]. 1136 K(x,y / (x * y)) * (x * y) = T(x,x \ 1) * y. [para(15(a,1),1127(a,1,1,1))]. 1138 T((x * y) \ (K(x,x \ 1) * y),x) = (x * y) \ (1 * y). [para(1107(a,2),360(a,1))]. 1139 T((x * y) \ (K(x,x \ 1) * y),x) = (x * y) \ y. [para(11(a,1),1138(a,2,2))]. 1140 ((x \ 1) \ 1) \ (x * (K(x,x \ 1) * y)) = L(y,x,K(x,x \ 1)). [para(1131(a,1),1121(a,1,2))]. 1141 L(x,K(y,y \ 1),y) = L(x,y,K(y,y \ 1)). [para(1140(a,1),1119(a,1)),flip(a)]. 1142 R(x \ 1,y,z) * K(x,x \ 1) = R(1 / x,y,z). [para(1104(a,1),942(a,1))]. 1143 (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(1142(a,1),22(a,2,2,1)),flip(a)]. 1144 K(x,x \ 1) * R(x \ 1,y,z) = R(1 / x,y,z). [para(1142(a,1),442(a,2))]. 1145 (x * R(x \ 1,y,z)) * K(x,x \ 1) = x * R(1 / x,y,z). [para(1144(a,1),1132(a,2,2))]. 1146 (x * R(x \ 1,y,z)) \ (x * R(1 / x,y,z)) = K(x,x \ 1). [hyper(66,a,1145,a)]. 1147 K(x,y / (x * y)) = K(x,x \ 1). [para(1146(a,1),786(a,1)),flip(a)]. 1148 K(x / y,(x / y) \ 1) = K(x / y,y / x). [para(16(a,1),1147(a,1,2,2)),flip(a)]. 1149 K(x,x \ 1) * (x * y) = T(x,x \ 1) * y. [para(1147(a,1),1136(a,1,1))]. 1151 K((x \ y) / y,((x \ y) / y) \ 1) = K((x \ y) / y,x). [para(57(a,1),1148(a,2,2))]. 1152 K((x * y) / y,y / (x * y)) = K(x,x \ 1). [hyper(18,a,1127,a,b,1149,a),flip(a)]. 1153 K(x,x \ 1) * (y * x) = T(x,x \ 1) * T(y,x). [para(90(a,1),1149(a,1,2))]. 1154 K(x,x \ 1) * (x * y) = ((x \ 1) \ 1) * y. [para(91(a,1),1149(a,2,1))]. 1155 K(x,x \ 1) * L(y,x \ 1,x) = T(x,x \ 1) * ((x \ 1) * y). [para(127(a,1),1149(a,1,2))]. 1156 (x * y) * K(x,x \ 1) = T(x,x \ 1) * y. [para(1149(a,1),442(a,1)),flip(a)]. 1157 x * (K(x,x \ 1) * y) = T(x,x \ 1) * y. [para(1149(a,1),1131(a,1)),flip(a)]. 1160 (T(x,x \ 1) * y) / (K(x,x \ 1) * y) = x. [hyper(70,a,1157,a)]. 1161 (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(1157(a,2),909(a,2)),flip(a)]. 1162 K(x,x \ 1) * (T(x,x \ 1) \ y) = x \ y. [para(1160(a,1),141(a,1,1)),flip(a)]. 1163 R(x,K(x,x \ 1),y) = x. [para(1160(a,1),1115(a,1)),flip(a)]. 1164 R(1 / x,K(1 / x,x),y) = 1 / x. [para(59(a,1),1163(a,1,2,2))]. 1165 R(1 / x,K(x \ 1,x),y) = 1 / x. [para(1085(a,1),1164(a,1,2))]. 1166 (R(1 / x,y,z) * K(x \ 1,x)) * (K(x \ 1,x) \ u) = R(1 / x,y,z) * u. [para(1165(a,1),313(a,1,1,1)),flip(a)]. 1167 K(x,x \ 1) * (((x \ 1) \ 1) \ y) = x \ y. [para(91(a,1),1162(a,1,2,1))]. 1168 K((x \ y) / y,((x \ y) / y) \ 1) = K(x \ 1,x). [para(1151(a,2),1086(a,1))]. 1170 K(x \ 1,x) \ ((x \ y) / y) = 1 / (1 / ((x \ y) / y)). [para(1168(a,1),1096(a,1,1))]. 1171 K((x \ y) / y,y / (x \ y)) = K(x \ 1,x). [para(1168(a,1),1148(a,1)),flip(a)]. 1172 x * L(x \ y,x / y,y / x) = K(x / y,(x / y) \ 1) * y. [para(11(a,1),1109(a,1,2,1,2))]. 1173 K(x / (y * x),(x / (y * x)) \ 1) * (y * x) = x * L(x \ (y * x),x / (y * x),y). [para(15(a,1),1172(a,1,2,3)),flip(a)]. 1174 (x \ y) * (((x \ y) \ (y / x)) / (y / x)) = x \ (K(y / x,(y / x) \ 1) * x). [para(1172(a,1),1050(a,2,2))]. 1175 ((x / (y * x)) \ 1) * R(1 / y,y,x) = K(y,x / (y * x)). [para(15(a,1),1126(a,1,1)),flip(a)]. 1176 K(x / (y * x),(x / (y * x)) \ 1) = K(y,x / (y * x)) \ 1. [para(1175(a,1),583(a,2,1))]. 1177 K(x / (y * x),(x / (y * x)) \ 1) = K(y,y \ 1) \ 1. [para(1147(a,1),1176(a,2,1))]. 1178 K(x / (y * x),(x / (y * x)) \ 1) = K(y \ 1,y). [para(1177(a,2),406(a,1))]. 1180 L(x,y,K(y,y \ 1)) = x. [hyper(1114,a,1149,a(flip))]. 1181 L(x,1 / y,K(1 / y,y)) = x. [para(59(a,1),1180(a,1,3,2))]. 1182 L(x,K(y,y \ 1),y) = x. [para(1180(a,1),1141(a,2))]. 1183 L(x,K(y \ 1,y),z / (y * z)) = x. [para(1178(a,1),1182(a,1,2))]. 1184 L(x,1 / y,K(y \ 1,y)) = x. [para(1085(a,1),1181(a,1,3))]. 1185 (x \ 1) \ (K(x \ 1,x) * y) = (1 / x) \ y. [para(1181(a,1),1091(a,1)),flip(a)]. 1186 L(x,1 / (1 / y),K(y,1 / y)) = x. [para(59(a,1),1184(a,1,3,1))]. 1187 L(x,K(y \ 1,y),1 / y) = x. [para(12(a,1),1183(a,1,3,2))]. 1188 L(x,1 / (1 / y),K(y,y \ 1)) = x. [para(1092(a,1),1186(a,1,3))]. 1189 (x \ 1) * ((1 / x) \ y) = K(x \ 1,x) * y. [para(1185(a,1),14(a,1,2))]. 1190 (1 / x) * ((x \ 1) \ (K(x \ 1,x) * y)) = y. [para(1185(a,2),14(a,1,2))]. 1191 (1 / x) \ L(y,x,x \ 1) = x * y. [hyper(17,a,213,a(flip),b,1189,a)]. 1192 (1 / x) * (x * y) = L(y,x,x \ 1). [para(1191(a,1),14(a,1,2))]. 1193 (1 / x) * (K(y \ 1,y) * x) = L(K(y \ 1,y),x,x \ 1). [para(390(a,2),1192(a,1,2))]. 1194 L(T(x,y) \ 1,x,x \ 1) = (1 / x) * (T(x,y) \ x). [para(525(a,1),1192(a,1,2)),flip(a)]. 1195 (1 / x) * (K(x \ 1,x) * y) = (x \ 1) * y. [para(1190(a,1),550(a,1,2)),flip(a)]. 1196 (1 / x) \ ((x \ 1) * y) = K(x \ 1,x) * y. [hyper(66,a,1195,a)]. 1197 (1 / x) * ((T(x,y) \ 1) * x) = (x \ 1) * (T(x,y) \ x). [para(839(a,1),1195(a,1,2))]. 1198 K(x \ 1,x) * ((x \ 1) \ y) = (1 / x) \ y. [para(14(a,1),1196(a,1,2)),flip(a)]. 1199 K(x \ 1,x) * ((((y * x) / y) \ 1) \ 1) = (1 / x) \ (((y * x) / y) * (x \ 1)). [para(1043(a,1),1196(a,1,2)),flip(a)]. 1201 T((1 / x) * (T(x,y) \ x),x) = (x \ 1) * (T(x,y) \ x). [para(1197(a,1),528(a,2))]. 1202 x \ (K(x,x \ 1) * y) = (1 / (1 / x)) \ y. [para(1110(a,1),1188(a,1))]. 1203 x * ((1 / (1 / x)) \ y) = K(x,x \ 1) * y. [para(1202(a,1),14(a,1,2))]. 1204 K(x,x \ 1) * (x \ y) = (1 / (1 / x)) \ y. [para(1202(a,1),1130(a,1)),flip(a)]. 1205 K(x,x \ 1) * ((1 / (1 / x)) * y) = x * y. [para(13(a,1),1203(a,1,2)),flip(a)]. 1206 T(x * ((1 / x) * ((1 / x) \ ((1 / (1 / x)) \ y))),x) = K(x,x \ 1) * T(y,x). [para(1203(a,1),778(a,2))]. 1207 (1 / (1 / x)) \ (((y * x) / y) \ x) = K(x,x \ 1) * (((y * x) / y) \ 1). [para(621(a,1),1204(a,1,2)),flip(a)]. 1208 x * ((y * (x \ (y \ x))) / y) = (1 / (1 / y)) \ x. [para(1204(a,1),1108(a,2))]. 1209 x \ ((1 / (1 / y)) \ x) = (y * (x \ (y \ x))) / y. [hyper(66,a,1208,a)]. 1210 R(x \ 1,y,z) * (K(x \ 1,x) \ u) = R(1 / x,y,z) * u. [para(1078(a,1),1166(a,1,1))]. 1211 (x \ y) * (((x \ y) \ (y / x)) / (y / x)) = K(y / x,(y / x) \ 1). [para(1174(a,2),443(a,1))]. 1212 K(x / y,(x / y) \ 1) != (y \ x) * z | ((y \ x) \ (x / y)) / (x / y) = z. [para(1211(a,1),19(a,1))]. 1214 T(x * ((1 / (1 / x)) \ y),x) = K(x,x \ 1) * T(y,x). [para(14(a,1),1206(a,1,1,2))]. 1216 T(K(x,x \ 1) * y,x) = K(x,x \ 1) * T(y,x). [para(1203(a,1),1214(a,1,1))]. 1217 x * T(x \ (y \ x),(y \ 1) \ 1) = ((y \ 1) \ 1) \ x. [para(1167(a,1),1123(a,1,2,1,2))]. 1218 K(x \ 1,x) * (x \ y) = ((x \ 1) \ 1) \ y. [para(1217(a,1),984(a,2))]. 1219 x \ (K(x \ 1,x) * y) = ((x \ 1) \ 1) \ y. [para(1218(a,1),807(a,2))]. 1220 K(x / (y * x),(x / (y * x)) \ 1) * (y * x) = x * L(T(y,x),x / (y * x),y). [para(30(a,2),1173(a,2,2,1))]. 1221 K(x / (y * x),(x / (y * x)) \ 1) * (y * x) = x * T(1 / (1 / y),x). [para(992(a,1),1220(a,2,2))]. 1222 K(x / (y * x),(x / (y * x)) \ 1) * (y * x) = (1 / (1 / y)) * x. [para(1221(a,2),90(a,1))]. 1224 K(x \ 1,x) * (x * y) = (1 / (1 / x)) * y. [para(1178(a,1),1222(a,1,1))]. 1225 L(x,y,K(y \ 1,y)) = x. [hyper(1009,a,1224,a)]. 1226 K((x / y) \ 1,x / y) * x = (1 / (1 / (x / y))) * y. [para(16(a,1),1224(a,1,2))]. 1227 K(x \ 1,x) * (y * x) = (1 / (1 / x)) * T(y,x). [para(90(a,1),1224(a,1,2))]. 1229 x * ((1 / (1 / x)) \ y) = K(x \ 1,x) \ y. [para(1225(a,1),1053(a,1)),flip(a)]. 1230 K(x \ 1,x) \ ((x \ y) / y) = (x * ((x \ y) / y)) / x. [para(1229(a,1),1061(a,1))]. 1231 K(x \ 1,x) \ y = K(x,x \ 1) * y. [para(1229(a,1),1203(a,1))]. 1232 K(x \ 1,x) * (K(x,x \ 1) * y) = y. [hyper(65,a,1231,a)]. 1233 K(x,x \ 1) * (y * K(x \ 1,x)) = y. [para(1231(a,1),388(a,1))]. 1234 x / K(y \ 1,y) = K(y,y \ 1) * x. [para(1231(a,1),391(a,2))]. 1235 (K(x,x \ 1) * y) \ y = K(x \ 1,x). [para(1231(a,1),398(a,1,1))]. 1236 K(x \ 1,x) * T(K(x,x \ 1) * y,z) = (x \ T(x * (y / x),z)) * x. [para(1231(a,1),914(a,1,2,1))]. 1237 K(x / y,(x / y) \ 1) * z = K(y / x,x / y) \ z. [para(1087(a,1),1231(a,1,1)),flip(a)]. 1238 x / L(K(y,y \ 1) * (y * x),K(y \ 1,y),x / (y * x)) = R(y \ 1,y,x). [para(1231(a,1),1080(a,1,2,1))]. 1239 R(x \ 1,y,z) * (K(x,x \ 1) * u) = R(1 / x,y,z) * u. [para(1231(a,1),1210(a,1,2))]. 1240 K(x,x \ 1) * ((1 / x) \ y) = (x \ 1) \ y. [hyper(17,a,1198,a,b,1232,a)]. 1241 K(x,x \ 1) \ y = K(x \ 1,x) * y. [para(14(a,1),1232(a,1,2)),flip(a)]. 1242 K(x \ 1,x) * (y * K(x,x \ 1)) = y. [para(442(a,1),1232(a,1,2))]. 1243 (1 / x) \ (K(x,x \ 1) * y) = (x \ 1) \ y. [para(1232(a,1),1185(a,1,2)),flip(a)]. 1244 (1 / x) * ((x \ 1) \ y) = K(x,x \ 1) * y. [para(1232(a,1),1190(a,1,2,2))]. 1245 (x \ 1) * (K(x,x \ 1) * y) = (1 / x) * y. [para(1232(a,1),1195(a,1,2)),flip(a)]. 1246 K(x,x \ 1) * y != z | z * K(x \ 1,x) = y. [para(1233(a,1),19(a,1)),flip(a)]. 1247 (x * K(y \ 1,y)) * K(y,y \ 1) = x. [para(1233(a,1),442(a,1)),flip(a)]. 1248 (x * K(y \ 1,y)) \ x = K(y,y \ 1). [para(1233(a,1),443(a,1,2))]. 1249 (R(x \ 1,y,z) * (K(x,x \ 1) * (y * z))) * K(x \ 1,x) = ((x \ 1) * y) * z. [para(1234(a,1),1135(a,1,1,2))]. 1250 x * K(y \ 1,y) != z | K(y,y \ 1) * z = x. [para(1235(a,1),69(a,1,2)),flip(b)]. 1251 (x * y) \ ((1 / (1 / x)) * y) = K(x \ 1,x). [para(1205(a,1),1235(a,1,1))]. 1252 x / (K(y \ 1,y) * x) = K(y,y \ 1). [para(1241(a,1),57(a,1,2))]. 1253 (K(x \ 1,x) * y) * K(x,x \ 1) = y. [para(1241(a,1),441(a,1,1))]. 1254 K(x \ 1,x) * (y * (1 / x)) = R(y / x,x,1 / x). [para(1241(a,1),1098(a,1))]. 1255 ((x * (y \ 1)) * y) * K(y,y \ 1) = R(x,y \ 1,y). [hyper(490,a,1242,a),flip(a)]. 1256 ((1 / x) \ y) * K(x,x \ 1) = (x \ 1) \ y. [hyper(17,a,1198,a,b,1242,a)]. 1257 L((x * K(y,y \ 1)) \ z,x * K(y,y \ 1),K(y \ 1,y)) = x \ (K(y \ 1,y) * z). [para(1242(a,1),81(a,2,1))]. 1258 (1 / x) * ((x \ 1) \ y) = y * K(x,x \ 1). [para(1242(a,1),1190(a,1,2,2))]. 1259 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(1247(a,1),228(a,1,1)),flip(a)]. 1260 (K(x \ 1,x) * y) \ y = K(x,x \ 1). [para(390(a,2),1248(a,1,1))]. 1261 K(x,x \ 1) * y != z | K(x \ 1,x) * z = y. [para(1253(a,1),444(a,2))]. 1262 R((K(x \ 1,x) * y) / x,x,K(x,x \ 1)) = y / T(x,x \ 1). [para(1253(a,1),1117(a,1,1)),flip(a)]. 1263 K(x,x \ 1) * ((x \ 1) * y) = (1 / x) * y. [para(13(a,1),1244(a,1,2)),flip(a)]. 1264 T((1 / x) * ((x \ 1) \ y),x) = K(x,x \ 1) * T(y,x). [para(1244(a,2),1216(a,1,1))]. 1265 ((1 / x) * y) / (K(x,x \ 1) * y) = x \ 1. [hyper(70,a,1245,a)]. 1266 (x \ 1) * (K(x,x \ 1) * R((1 / x) \ y,z,u)) = R(y * x,z,u) / x. [para(1245(a,2),634(a,1))]. 1267 T(x,x \ 1) * ((x \ 1) * y) = x * ((1 / x) * y). [para(1263(a,1),1157(a,1,2)),flip(a)]. 1268 R(x \ 1,K(x,x \ 1),y) = x \ 1. [para(1265(a,1),1112(a,1)),flip(a)]. 1269 R((x \ 1) \ 1,K(x \ 1,x),y) = (x \ 1) \ 1. [para(1068(a,1),1268(a,1,2))]. 1271 x / (K((x / y) \ 1,x / y) * y) = ((x / y) \ 1) \ 1. [para(1269(a,1),504(a,1)),flip(a)]. 1272 K(x,x \ 1) * L(y,x \ 1,x) = x * ((1 / x) * y). [para(1267(a,1),1155(a,2))]. 1273 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(1254(a,1),352(a,2,1))]. 1274 L(x,1 / y,y) = L(x,y \ 1,y). [hyper(1106,a,1272,a)]. 1275 L(x,(y \ 1) \ 1,y \ 1) = L(x,y,y \ 1). [para(57(a,1),1274(a,1,2)),flip(a)]. 1276 L(((x \ 1) \ 1) \ y,x,x \ 1) = (x \ 1) * y. [para(1275(a,1),220(a,1))]. 1277 T(((x \ 1) \ 1) * ((x \ 1) * 1),y) / T((x \ 1) \ 1,y) = L(1 / T((x \ 1) \ 1,y),x,x \ 1). [para(1276(a,1),903(a,1,1,1,2))]. 1278 K(x / y,y / x) * y = (1 / (1 / (y / x))) * x. [para(1087(a,1),1226(a,1,1))]. 1279 K(x / y,y / x) * y = x * (1 / (1 / (x \ y))). [para(1278(a,2),1032(a,1))]. 1280 x \ (K(x / y,y / x) * y) = 1 / (1 / (x \ y)). [hyper(66,a,1279,a(flip))]. 1281 K((x / y) / x,x / (x / y)) * x = (x / y) * (1 / (1 / y)). [para(59(a,1),1279(a,2,2,2,2))]. 1282 (x * y) \ (K(x,x \ 1) * y) = 1 / (1 / ((x * y) \ y)). [para(1152(a,1),1280(a,1,2,1))]. 1283 (x * ((x \ y) / y)) / x = 1 / (1 / ((x \ y) / y)). [para(1230(a,1),1170(a,1))]. 1284 T(1 / (1 / ((x \ y) / y)),y) = (x * (y \ (x \ y))) / x. [para(1283(a,1),291(a,1,1))]. 1285 K(x / y,y / x) \ z = K(y / x,x / y) * z. [para(1148(a,1),1237(a,1,1)),flip(a)]. 1286 T((1 / x) * ((x \ 1) \ y),x) = (1 / x) * ((x \ 1) \ T(y,x)). [para(1264(a,2),1244(a,2)),flip(a)]. 1287 x / (K(y / x,x / y) * y) = ((x / y) \ 1) \ 1. [para(1087(a,1),1271(a,1,2,1))]. 1289 (x * (y \ (x \ y))) / x = 1 / (1 / (y \ (x \ y))). [para(1284(a,1),1026(a,1))]. 1290 1 / (1 / (x \ (y \ x))) = x \ ((1 / (1 / y)) \ x). [para(1289(a,1),1209(a,2)),flip(a)]. 1291 (((x * y) / x) \ y) \ ((1 / (1 / y)) \ (((x * y) / x) \ y)) = 1 / (1 / ((((x * y) / x) \ y) \ (((x * y) / x) \ 1))). [para(621(a,1),1290(a,1,2,2,2)),flip(a)]. 1292 (x \ ((x \ 1) \ y)) * x = (x \ 1) \ T(y,x). [hyper(377,a,1286,a)]. 1293 (x \ 1) \ T((x \ 1) * y,x) = (x \ y) * x. [para(13(a,1),1292(a,1,1,2)),flip(a)]. 1294 (x * T(x \ 1,y)) * ((y \ 1) \ 1) = x * ((y \ (x \ ((y \ 1) \ 1))) * y). [para(1293(a,1),796(a,1,2)),flip(a)]. 1295 x / L(T(y,y \ 1) * x,K(y \ 1,y),x / (y * x)) = R(y \ 1,y,x). [para(1149(a,1),1238(a,1,2,1))]. 1296 x / (T(y,y \ 1) * x) = R(y \ 1,y,x). [para(1183(a,1),1295(a,1,2))]. 1297 R(x \ 1,(x \ 1) \ 1,y) = R(x \ 1,x,y). [para(1296(a,1),255(a,2))]. 1299 (R(1 / x,y,z) * (y * z)) * K(x \ 1,x) = ((x \ 1) * y) * z. [para(1239(a,1),1249(a,1,1))]. 1300 (((1 / x) * y) * z) * K(x \ 1,x) = ((x \ 1) * y) * z. [para(85(a,1),1299(a,1,1))]. 1301 K(x,x \ 1) * (((x \ 1) * y) * z) = ((1 / x) * y) * z. [hyper(1250,a,1300,a)]. 1302 ((1 / x) * ((x \ 1) \ y)) * z = K(x,x \ 1) * (y * z). [para(14(a,1),1301(a,1,2,1)),flip(a)]. 1303 (K(x,x \ 1) * y) * z = K(x,x \ 1) * (y * z). [para(1244(a,1),1302(a,1,1))]. 1304 (x * K(y,y \ 1)) * z = K(y,y \ 1) * (x * z). [para(1258(a,1),1302(a,1,1))]. 1305 L(x,y,K(z,z \ 1)) = x. [hyper(206,a,1303,a)]. 1306 (K(x,x \ 1) * y) \ (K(x,x \ 1) * z) = y \ z. [hyper(17,a,140,a,b,1303,a),flip(a)]. 1307 K(x,x \ 1) * (R(x \ 1,y,z) * u) = R(1 / x,y,z) * u. [para(1144(a,1),1303(a,1,1)),flip(a)]. 1309 K(x,x \ 1) * (1 / y) = K(x,x \ 1) / y. [para(1305(a,1),182(a,1,2)),flip(a)]. 1310 (K(x,x \ 1) * y) / z = K(x,x \ 1) * (y / z). [para(1305(a,1),246(a,1,2))]. 1311 R(K(x,x \ 1) * y,L(z,y,K(x,x \ 1)),u) = ((K(x,x \ 1) * (y * z)) * u) / (z * u). [para(1305(a,1),209(a,1,2,1)),flip(a)]. 1312 (K(x,x \ 1) * (y * z)) \ ((K(x,x \ 1) * y) * (z * u)) = L(u,L(z,y,K(x,x \ 1)),K(x,x \ 1) * y). [para(1305(a,1),207(a,1,2,2,1))]. 1313 L(x,y,K(z \ 1,z)) = x. [para(1068(a,1),1305(a,1,3))]. 1316 K(x,x \ 1) * ((x \ 1) / y) = (1 / x) / y. [para(1305(a,1),1113(a,1,2)),flip(a)]. 1317 (K(x \ 1,x) * y) * z = K(x \ 1,x) * (y * z). [para(1313(a,1),79(a,1,2))]. 1318 (K(x \ 1,x) * y) / z = K(x \ 1,x) * (y / z). [para(1313(a,1),246(a,1,2))]. 1319 R(K(x \ 1,x) * y,L(z,y,K(x \ 1,x)),u) = ((K(x \ 1,x) * (y * z)) * u) / (z * u). [para(1313(a,1),209(a,1,2,1)),flip(a)]. 1322 K(x,x \ 1) / T((y \ 1) \ 1,z) = K(x,x \ 1) * (T(y,z) \ 1). [para(1029(a,1),1309(a,1,2)),flip(a)]. 1323 (1 / x) \ ((1 / x) / y) = (x \ 1) \ ((x \ 1) / y). [para(1316(a,1),1243(a,1,2))]. 1324 (x * y) \ (K(x,x \ 1) * z) = ((1 / (1 / x)) * y) \ z. [para(1205(a,1),1306(a,1,1))]. 1325 (x * K(y \ 1,y)) \ z = x \ (K(y,y \ 1) * z). [para(1233(a,1),1306(a,1,1)),flip(a)]. 1326 R(K(x \ 1,x),y,z) = K(x \ 1,x). [hyper(226,a,1317,a)]. 1328 (x * K(y \ 1,y)) * z = K(y \ 1,y) * (x * z). [para(390(a,1),1317(a,1,1))]. 1329 K(x \ 1,x) * ((x \ y) * z) = (((x \ 1) \ 1) \ y) * z. [para(1218(a,1),1317(a,1,1)),flip(a)]. 1330 (L(K(x \ 1,x),y,z) * u) * w = L(K(x \ 1,x),y,z) * (u * w). [para(1326(a,1),230(a,1,1,1)),flip(a)]. 1331 (K(x \ 1,x) * y) / z = (y / z) * K(x \ 1,x). [para(1318(a,2),390(a,1))]. 1332 (x * K(y \ 1,y)) / z = K(y \ 1,y) * (x / z). [para(390(a,1),1318(a,1,1))]. 1333 K((x / y) \ 1,x / y) * (y / x) = T(y / x,x / y). [para(1318(a,1),703(a,1))]. 1334 (x * K(y \ 1,y)) \ K(y \ 1,y) = x \ 1. [para(402(a,1),1325(a,2,2))]. 1335 (x * K(y \ 1,y)) \ z = x \ (z * K(y,y \ 1)). [para(442(a,1),1325(a,2,2))]. 1336 K(x \ 1,R(x,y,z)) * (u * w) = (u * K(x \ 1,x)) * w. [para(1066(a,2),1328(a,2,1)),flip(a)]. 1337 R((x / y) * K(y \ 1,y),y,K(y,y \ 1)) = x / T(y,y \ 1). [para(1331(a,1),1262(a,1,1))]. 1338 R(x / (1 / y),1 / y,K(y \ 1,y)) = K(y \ 1,y) * (x / (y \ 1)). [para(1332(a,1),382(a,2))]. 1339 R(x / y,y,K(z \ 1,z)) = K(z \ 1,z) * (x / (K(z \ 1,z) * y)). [para(1332(a,1),404(a,2))]. 1340 x \ (((x * (y \ 1)) * y) * K(y,y \ 1)) = a(x,y \ 1,y). [para(1335(a,1),161(a,1))]. 1341 T(((1 / (1 / x)) * y) \ y,x) = (x * y) \ y. [para(1324(a,1),1139(a,1,1))]. 1342 1 / (1 / ((x * y) \ y)) = ((1 / (1 / x)) * y) \ y. [para(1324(a,1),1282(a,1)),flip(a)]. 1343 T(((1 / x) * y) \ y,x \ 1) = ((x \ 1) * y) \ y. [para(57(a,1),1341(a,1,1,1,1,2))]. 1344 T(T(1 / (1 / (((1 / x) * y) \ y)),z / ((((1 / x) * y) \ y) * z)),x \ 1) = ((x \ 1) * y) \ y. [para(994(a,2),1343(a,1,1))]. 1345 K(x \ 1,x) * y != (((x \ 1) \ 1) \ z) * u | (x \ z) * u = y. [para(1329(a,1),19(a,1)),flip(a)]. 1346 K(x / y,y / x) * (x / y) = T(x / y,y / x). [para(1087(a,1),1333(a,1,1))]. 1347 T(x / y,y / x) != z * (x / y) | K(x / y,y / x) = z. [para(1346(a,1),20(a,1))]. 1348 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(1336(a,1),370(a,1,2))]. 1349 x \ R(x,y \ 1,y) = a(x,y \ 1,y). [para(1255(a,1),1340(a,1,2))]. 1350 (x * L(K(y \ 1,y),z,u)) * w = L(K(y \ 1,y),z,u) * (x * w). [para(399(a,1),1330(a,1,1))]. 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(86(a,2),1339(a,2,2))]. 1352 (x * K(y,y \ 1)) \ z = x \ (K(y \ 1,y) * z). [para(1257(a,1),1313(a,1)),flip(a)]. 1353 R(K(x,x \ 1) * y,L(z,y,K(x,x \ 1)),u) = (K(x,x \ 1) * ((y * z) * u)) / (z * u). [para(1303(a,1),1311(a,2,1))]. 1354 R(K(x \ 1,x) * y,L(z,y,K(x \ 1,x)),u) = (K(x \ 1,x) * ((y * z) * u)) / (z * u). [para(1317(a,1),1319(a,2,1))]. 1355 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)]. 1356 K(x \ 1,x) * R(K(x,x \ 1) * y,K(x \ 1,x),z) = R(y,z,K(x \ 1,x)). [para(1234(a,1),1355(a,1,2,1))]. 1357 (K(x,x \ 1) * ((y * z) * u)) / (z * u) = R(K(x,x \ 1) * y,z,u). [para(1305(a,1),1353(a,1,2)),flip(a)]. 1358 K(x,x \ 1) * (((y * z) * u) / (z * u)) = R(K(x,x \ 1) * y,z,u). [para(1357(a,1),1310(a,1)),flip(a)]. 1359 R(K(x,x \ 1) * y,z,u) = K(x,x \ 1) * R(y,z,u). [para(28(a,2),1358(a,1,2)),flip(a)]. 1360 (x \ 1) * R(K(x,x \ 1) * ((1 / x) \ y),z,u) = R(y * x,z,u) / x. [para(1359(a,2),1266(a,1,2))]. 1361 (x \ 1) * R((x \ 1) \ y,z,u) = R(y * x,z,u) / x. [para(1240(a,1),1360(a,1,2,1))]. 1362 R(x * y,z,u) / y = y \ R(y * x,z,u). [para(1361(a,1),630(a,1))]. 1363 x \ R(x * (y / x),z,u) = R(y,z,u) / x. [para(16(a,1),1362(a,1,1,1)),flip(a)]. 1364 R(x * (y / x),z,u) = x * (R(y,z,u) / x). [para(1363(a,1),14(a,1,2)),flip(a)]. 1365 (K(x \ 1,x) * ((y * z) * u)) / (z * u) = R(K(x \ 1,x) * y,z,u). [para(1313(a,1),1354(a,1,2)),flip(a)]. 1366 K(x \ 1,x) * (((y * z) * u) / (z * u)) = R(K(x \ 1,x) * y,z,u). [para(1365(a,1),1318(a,1)),flip(a)]. 1367 R(K(x \ 1,x) * y,z,u) = K(x \ 1,x) * R(y,z,u). [para(28(a,2),1366(a,1,2)),flip(a)]. 1368 R(K(x \ 1,x) * (K(x,x \ 1) * y),K(x \ 1,x),z) = R(y,z,K(x \ 1,x)). [para(1367(a,2),1356(a,1))]. 1369 R(x,K(y \ 1,y),z) = R(x,z,K(y \ 1,y)). [para(1232(a,1),1368(a,1,1))]. 1370 (R(x,y,K(y \ 1,y)) / y) * L(y,y \ 1,y) = x * (L(y,y \ 1,y) / y). [para(1369(a,1),882(a,1,1,1))]. 1371 (R(x,y,K(y \ 1,y)) / y) * (1 / (1 / y)) = x * (L(y,y \ 1,y) / y). [para(993(a,1),1370(a,1,2))]. 1372 (R(x,y,K(y \ 1,y)) / y) * (1 / (1 / y)) = x * K(y \ 1,y). [para(408(a,1),1371(a,2,2))]. 1373 (R(x,y,K(y \ 1,y)) / y) * (1 / (1 / y)) != z * K(y \ 1,y) | z = x. [para(1372(a,2),20(a,2)),flip(a)]. 1374 T(T(((1 / (1 / (1 / x))) * y) \ y,z / ((((1 / x) * y) \ y) * z)),x \ 1) = ((x \ 1) * y) \ y. [para(1342(a,1),1344(a,1,1,1))]. 1375 T(T(((1 / (1 / (1 / x))) * y) \ y,x \ 1),z / ((((1 / x) * y) \ y) * z)) = ((x \ 1) * y) \ y. [para(1374(a,1),36(a,1)),flip(a)]. 1376 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(967(a,1),707(a,1,1,2,2,1))]. 1377 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),1277(a,1,1,1,2))]. 1378 T(K((x \ 1) \ 1,x \ 1),y) / T((x \ 1) \ 1,y) = L(1 / T((x \ 1) \ 1,y),x,x \ 1). [para(126(a,2),1377(a,1,1,1))]. 1379 T(K(x,x \ 1),y) / T((x \ 1) \ 1,y) = L(1 / T((x \ 1) \ 1,y),x,x \ 1). [para(1089(a,1),1378(a,1,1,1))]. 1380 L(1 / T((x \ 1) \ 1,y),x,x \ 1) = K(x,x \ 1) / T((x \ 1) \ 1,y). [para(440(a,1),1379(a,1,1)),flip(a)]. 1382 L(1 / T((x \ 1) \ 1,y),x,x \ 1) = K(x,x \ 1) * (T(x,y) \ 1). [para(1380(a,2),1322(a,1))]. 1383 K(x,1 / x) * T(K(x,1 / x) \ (K(x,1 / x) / (1 / x)),y) = x * (T(x,y) / x). [para(641(a,1),535(a,2,2))]. 1384 K(x,1 / x) * T(K(x,1 / x) \ x,y) = x * (T(x,y) / x). [para(164(a,1),1383(a,1,2,1,2))]. 1385 K(x,1 / x) * T(1 / (1 / x),y) = x * (T(x,y) / x). [para(414(a,1),1384(a,1,2,1))]. 1386 K(x,x \ 1) * T(1 / (1 / x),y) = x * (T(x,y) / x). [para(1092(a,1),1385(a,1,1))]. 1387 x \ (K(x,x \ 1) * T(1 / (1 / x),y)) = T(x,y) / x. [hyper(66,a,1386,a(flip))]. 1388 R((x / (y * x)) \ 1,R(1 / y,y,x),y * x) = T((y * x) / x,x / (y * x)). [para(709(a,2),703(a,1))]. 1389 R((x / (y * x)) \ 1,R(1 / y,y,x),y * x) = T(y,x / (y * x)). [para(15(a,1),1388(a,2,1))]. 1390 T(x / (y * x),T(y,x / (y * x))) = ((x / (y * x)) \ 1) \ 1. [para(1389(a,1),956(a,1,2))]. 1391 T(x / (y * x),T(y,y \ 1)) = ((x / (y * x)) \ 1) \ 1. [para(1011(a,1),1390(a,1,2))]. 1392 R(x \ 1,x,y) = ((y / (x * y)) \ 1) \ 1. [para(1391(a,1),960(a,1)),flip(a)]. 1394 R((x / y) \ 1,x / y,y) = ((y / x) \ 1) \ 1. [para(16(a,1),1392(a,2,1,1,2))]. 1395 T((1 * x) / y,y / x) = ((x / y) \ 1) \ 1. [para(1394(a,1),365(a,1)),flip(a)]. 1396 R((x / y) \ 1,x / y,y) \ 1 = T((y / x) \ 1,y / x). [para(1394(a,2),668(a,2,1)),flip(a)]. 1397 T(x / y,y / x) = ((x / y) \ 1) \ 1. [para(11(a,1),1395(a,1,1,1))]. 1398 T(((x / y) \ 1) \ 1,y) = T(y \ x,y / x). [para(1397(a,1),125(a,1,1))]. 1399 T(x \ y,x / y) = ((x \ y) \ 1) \ 1. [para(1398(a,1),1031(a,1))]. 1400 K(x / y,y / x) * x = y * (((y \ x) \ 1) \ 1). [para(1399(a,1),1125(a,2,2))]. 1401 a(R(x \ 1,y,z),K(x,x \ 1),u) = (R(1 / x,y,z) * u) \ (R(1 / x,y,z) * u). [para(1239(a,1),1143(a,1,1)),flip(a)]. 1402 a(R(x \ 1,y,z),K(x,x \ 1),u) = 1. [para(1401(a,2),48(a,1))]. 1404 a(R((x \ 1) \ 1,y,z),K(x \ 1,x),u) = 1. [para(1068(a,1),1402(a,1,2))]. 1405 (x * (y * z)) * T((x * (y * z)) \ (x * y),u) = (x * y) * (L(z,y,x) * T(L(z,y,x) \ 1,u)). [para(79(a,1),534(a,1,2,1,1))]. 1406 (x * y) * (L(z,y,x) * T(L(z,y,x) \ 1,u)) = x * ((y * z) * T((y * z) \ y,u)). [para(1405(a,1),356(a,1))]. 1407 (x * y) * (L(z,y,x) * T(L(z,y,x) \ 1,u)) = x * (y * (z * T(z \ 1,u))). [para(355(a,1),1406(a,2,2))]. 1408 L(x,y,z) * T(L(x,y,z) \ 1,u) = L(x * T(x \ 1,u),y,z). [hyper(206,a,1407,a),flip(a)]. 1409 L(x * T(x \ 1,L(x,y,z)),y,z) = (L(x,y,z) \ 1) * L(x,y,z). [para(1408(a,1),90(a,1))]. 1410 L(x * T(x \ 1,x),y,z) * (L(x,y,z) \ x) = (L(x,y,z) \ 1) * x. [para(1408(a,1),732(a,1,1))]. 1411 L(x * T(x \ 1,L(x,y,z)),y,z) = K(L(x,y,z) \ 1,L(x,y,z)). [para(1409(a,2),126(a,2)),flip(a)]. 1412 L((x \ 1) * x,y,z) * (L(x,y,z) \ x) = (L(x,y,z) \ 1) * x. [para(90(a,1),1410(a,1,1,1))]. 1413 L(K(x \ 1,x),y,z) * (L(x,y,z) \ x) = (L(x,y,z) \ 1) * x. [para(126(a,2),1412(a,1,1,1))]. 1415 (R(x,y,z) \ u) * T(T(x,R(x,y,z) \ u),u) = R(x,y,z) \ (T(x,u) * u). [para(14(a,1),746(a,1,2,1,2)),flip(a)]. 1416 R(x,y,z) \ (T(x,u) * u) = T(x,u) * (R(x,y,z) \ u). [para(1415(a,1),122(a,1))]. 1417 T(x,y) * (R(x,y,K(T(x,y),y)) \ y) = y * K(T(x,y),y). [para(1416(a,1),288(a,1))]. 1418 (x * (y \ z)) * ((z \ L(T(y,y \ z),y \ z,x)) * z) = (x * ((y \ z) * T((y \ z) \ 1,z))) * z. [para(355(a,1),804(a,1,1)),flip(a)]. 1419 (x * (y \ z)) * ((z \ L(T(y,y \ z),y \ z,x)) * z) = (x * (y \ ((z \ y) * z))) * z. [para(537(a,1),1418(a,2,1,2))]. 1420 (x * (y \ z)) * ((z \ L(T(y,y \ z),y \ z,x)) * z) = (x * K(z \ y,z)) * z. [para(75(a,1),1419(a,2,1,2))]. 1421 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),1273(a,1,1,1))]. 1422 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(85(a,1),785(a,1,1,1,2))]. 1423 ((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(1422(a,1),187(a,1)),flip(a)]. 1424 ((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(126(a,2),1423(a,2,1))]. 1425 K(R(x,y,z) \ 1,R(x,y,z)) * (y * z) = ((x * y) * T((x * y) \ y,R(x,y,z))) * z. [para(1424(a,1),788(a,1))]. 1426 K(R(x,y,z) \ 1,R(x,y,z)) * (y * z) = (x * (y * T(y \ (x \ y),R(x,y,z)))) * z. [para(357(a,1),1425(a,2,1))]. 1427 K(R(x,y,z) \ 1,R(x,y,z)) * (y * z) = ((x * T(x \ 1,R(x,y,z))) * y) * z. [para(790(a,1),1426(a,2,1))]. 1428 K(R(x,y,z) \ 1,R(x,y,z)) * (y * z) = (K(x \ 1,x) * y) * z. [para(981(a,1),1427(a,2,1,1))]. 1429 K(R(x,y,z) \ 1,R(x,y,z)) = K(x \ 1,x). [hyper(18,a,1317,a(flip),b,1428,a)]. 1431 1 / ((R(x,y,z) \ 1) * K(x \ 1,x)) = (R(x,y,z) \ 1) \ 1. [para(1429(a,1),671(a,1,2,2))]. 1432 K(R(x,y,z),R(x,y,z) \ 1) = (K(x \ 1,x) * u) \ u. [para(1429(a,1),1260(a,1,1,1)),flip(a)]. 1434 K(R(x,y,z),R(x,y,z) \ 1) = K(x,x \ 1). [para(1432(a,2),1248(a,1))]. 1435 K(x / (y * z),R((x / z) / y,y,z) \ 1) = K((x / z) / y,((x / z) / y) \ 1). [para(145(a,1),1434(a,1,1))]. 1436 K((x / y) / z,((x / y) / z) \ 1) = K(x / (z * y),(x / (z * y)) \ 1). [para(145(a,1),1435(a,1,2,1)),flip(a)]. 1437 R(R(x,y,K(z \ 1,z)),y * K(z \ 1,z),K(z,z \ 1)) = (x * y) / y. [para(1247(a,1),1259(a,2,2))]. 1438 R(R(x,y,K(z \ 1,z)),y * K(z \ 1,z),K(z,z \ 1)) = x. [para(1437(a,2),15(a,1))]. 1439 R(R(x,1 / y,K(y \ 1,y)),y \ 1,K(y,y \ 1)) = x. [para(380(a,1),1438(a,1,2))]. 1440 R(R(x,1 / y,K(y \ 1,y)),y \ 1,K((y \ 1) \ 1,y \ 1)) = x. [para(1089(a,2),1439(a,1,3))]. 1441 (K(x,x \ 1) * (y * z)) \ (K(x,x \ 1) * (y * (z * u))) = L(u,L(z,y,K(x,x \ 1)),K(x,x \ 1) * y). [para(1303(a,1),1312(a,1,2))]. 1442 L(L(x,y,z),z * y,K(u,u \ 1)) = L(x,L(y,z,K(u,u \ 1)),K(u,u \ 1) * z). [para(1441(a,1),208(a,1)),flip(a)]. 1443 L(x,L(y,z,K(u,u \ 1)),K(u,u \ 1) * z) = L(x,y,z). [para(1442(a,1),1305(a,1))]. 1444 L(x,y,K(z,z \ 1) * u) = L(x,y,u). [para(1305(a,1),1443(a,1,2))]. 1445 L(x,y,1 / z) = L(x,y,z \ 1). [para(1100(a,1),1444(a,1,3))]. 1446 L(x,y,((z \ 1) \ 1) * u) = L(x,y,z * u). [para(1154(a,1),1444(a,1,3))]. 1447 L(T(x,1 / y) \ z,T(x,1 / y),y \ 1) = (x * (1 / y)) \ ((1 / y) * z). [para(1445(a,1),219(a,1))]. 1448 (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(1097(a,2),454(a,1,2,2))]. 1449 (x * (R(y / z,z,y \ u) / x)) * (z * (y \ u)) = x * (z * ((y \ u) * ((x * ((y \ u) \ (z \ (x \ u)))) / x))). [para(845(a,1),853(a,2,2))]. 1450 R(x * ((y / z) / x),z,y \ u) * (z * (y \ u)) = x * (z * ((y \ u) * ((x * ((y \ u) \ (z \ (x \ u)))) / x))). [para(1364(a,2),1449(a,1,1))]. 1451 x * (y * ((z \ u) * ((x * ((z \ u) \ (y \ (x \ u)))) / x))) = ((x * ((z / y) / x)) * y) * (z \ u). [para(1450(a,1),85(a,1))]. 1452 T(x * T(x \ 1,x \ T(x,y)),y) * (T(x,y) \ (x \ T(x,y))) = ((x \ T(x,y)) \ (x \ 1)) * (x \ T(x,y)). [para(831(a,1),730(a,1,1))]. 1453 T(x * (x \ 1),y) * (T(x,y) \ (x \ T(x,y))) = ((x \ T(x,y)) \ (x \ 1)) * (x \ T(x,y)). [para(801(a,1),1452(a,1,1,1,2))]. 1454 T(1,x) * (T(y,x) \ (y \ T(y,x))) = ((y \ T(y,x)) \ (y \ 1)) * (y \ T(y,x)). [para(14(a,1),1453(a,1,1,1))]. 1457 ((x \ T(x,y)) \ (x \ 1)) * (x \ T(x,y)) = 1 * (T(x,y) \ (x \ T(x,y))). [para(103(a,1),1454(a,1,1)),flip(a)]. 1459 ((x \ T(x,y)) \ (x \ 1)) * (x \ T(x,y)) = 1 * (x \ 1). [para(522(a,1),1457(a,2,2))]. 1460 ((x \ T(x,y)) \ (x \ 1)) * (x \ T(x,y)) = x \ 1. [hyper(63,a,1459,a(flip)),flip(a)]. 1462 R(x \ 1,y,z) * ((x \ T(x,u)) \ 1) = (x \ T(x,u)) \ R(x \ 1,y,z). [para(51(a,1),891(a,1,2,1)),flip(a)]. 1464 L(T(x / y,y / x),y / x,((y / x) * (x / y)) / (y / x)) = ((y / x) * (x / y)) * ((y / x) \ 1). [para(590(a,1),934(a,1,1))]. 1465 ((x / y) * (y / x)) * ((x / y) \ 1) = T(y / x,(x / y) * (y / x)). [para(1464(a,1),493(a,1))]. 1466 ((x / y) * (y / x)) * ((x / y) \ 1) = y / x. [para(1465(a,2),929(a,1))]. 1467 ((x / (y * x)) * ((y * x) / x)) * ((x / (y * x)) \ 1) = y. [para(1466(a,2),15(a,1))]. 1468 ((x / (y * x)) * y) * ((x / (y * x)) \ 1) = y. [para(15(a,1),1467(a,1,1,2))]. 1469 ((x / (y * x)) * y) \ y = (x / (y * x)) \ 1. [hyper(66,a,1468,a)]. 1470 (R(x \ 1,y,z) / (x * R(x \ 1,y,z))) \ 1 = ((x \ 1) * x) \ x. [para(968(a,1),1469(a,1,1,1)),flip(a)]. 1471 (R(x \ 1,y,z) / (x * R(x \ 1,y,z))) \ 1 = K(x \ 1,x) \ x. [para(126(a,2),1470(a,2,1))]. 1472 (((x * y) * z) * T(((x * y) * z) \ (y * z),u)) / (y * z) = R(x,y,z) * T(R(x,y,z) \ 1,u). [para(102(a,1),733(a,1,2))]. 1474 (((x * y) * T((x * y) \ y,z)) * u) / (y * u) = R(x,y,u) * T(R(x,y,u) \ 1,z). [para(788(a,1),1472(a,1,1))]. 1475 ((x * (y * T(y \ (x \ y),z))) * u) / (y * u) = R(x,y,u) * T(R(x,y,u) \ 1,z). [para(357(a,1),1474(a,1,1,1))]. 1476 (((x * T(x \ 1,y)) * z) * u) / (z * u) = R(x,z,u) * T(R(x,z,u) \ 1,y). [para(790(a,1),1475(a,1,1,1))]. 1477 R(x,y,z) * T(R(x,y,z) \ 1,u) = R(x * T(x \ 1,u),y,z). [para(1476(a,1),28(a,2)),flip(a)]. 1478 R(x * T(x \ 1,y),z,u) = K(y \ (y / R(x,z,u)),y). [para(1477(a,1),561(a,2)),flip(a)]. 1479 R(T(x,y) / x,z,u) = K(y \ (y / R(1 / x,z,u)),y). [para(641(a,1),1478(a,1,1))]. 1480 (((x \ 1) * (x \ T(x,y))) * x) / K(x \ 1,x) = R(x \ T(x,y),x \ 1,x) * 1. [para(201(a,1),893(a,1,2))]. 1482 K(x,x \ 1) * (((x \ 1) * (x \ T(x,y))) * x) = R(x \ T(x,y),x \ 1,x) * 1. [para(1480(a,1),1234(a,1)),flip(a)]. 1483 R(x \ T(x,y),x \ 1,x) * 1 = ((1 / x) * (x \ T(x,y))) * x. [para(1482(a,1),1301(a,1))]. 1484 ((1 / x) * (x \ T(x,y))) * x = R(x \ T(x,y),x \ 1,x). [hyper(68,a,1483,a),flip(a)]. 1485 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(469(a,1),1072(a,1,1))]. 1486 L(R(x,y \ 1,y),K(y \ 1,y),1 / y) = (1 * (y \ 1)) \ R((1 / y) * x,y,y \ 1). [para(384(a,1),1485(a,1,2))]. 1487 (1 * (x \ 1)) \ R((1 / x) * y,x,x \ 1) = R(y,x \ 1,x). [para(1486(a,1),1187(a,1))]. 1488 (x \ 1) \ R((1 / x) * y,x,x \ 1) = R(y,x \ 1,x). [para(11(a,1),1487(a,1,1))]. 1489 T(((1 / x) * y) * x,x \ 1) = R(y,x \ 1,x). [para(1488(a,1),264(a,1)),flip(a)]. 1490 L(R((x \ 1) \ (T(x,y) \ (x \ 1)),z,u),x \ 1,T(x,y)) = (x \ T(x,y)) \ ((x * R(x \ 1,z,u)) * (x \ 1)). [para(964(a,1),763(a,1,2,1)),flip(a)]. 1491 L(R((x \ 1) \ (T(x,y) \ (x \ 1)),z,u),x \ 1,T(x,y)) = (x \ T(x,y)) \ (1 * R(x \ 1,z,u)). [para(765(a,1),1490(a,2,2))]. 1493 L(R((x \ 1) \ (T(x,y) \ (x \ 1)),z,u),x \ 1,T(x,y)) = (x \ T(x,y)) \ R(x \ 1,z,u). [para(11(a,1),1491(a,2,2))]. 1494 R((T(x,y) * (x \ 1)) \ (x \ 1),z,u) = (x \ T(x,y)) \ R(x \ 1,z,u). [para(1493(a,1),269(a,1)),flip(a)]. 1495 R((x \ T(x,y)) \ (x \ 1),z,u) = (x \ T(x,y)) \ R(x \ 1,z,u). [para(520(a,1),1494(a,1,1,1))]. 1496 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(1069(a,1),1348(a,1,1,3))]. 1498 (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(862(a,1),863(a,1,2,2))]. 1499 (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),1498(a,1,2)),flip(a)]. 1500 (x * (y * T(y \ 1,x))) \ (y * T(y \ 1,x)) = x \ 1. [para(13(a,1),1499(a,1,1)),flip(a)]. 1502 (x * K(y,x)) \ (L(y \ 1,y,x) * T(L(y \ 1,y,x) \ 1,x)) = x \ 1. [para(743(a,2),1500(a,1,1,2))]. 1503 (x * K(y,x)) \ K(y,x) = x \ 1. [para(743(a,2),1502(a,1,2))]. 1504 (x * K(y,x)) * (x \ 1) = K(y,x). [para(1503(a,1),14(a,1,2))]. 1505 (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),1448(a,1,1))]. 1506 (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),1505(a,1,2,1,2))]. 1507 (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(381(a,1),1506(a,1,2,1))]. 1508 L(T(x * y,1 / y),1 / y,(1 / y) \ (1 * (y \ 1))) = (y \ 1) \ R(x,y,1 / y). [para(1242(a,1),1507(a,1,2)),flip(a)]. 1509 L(T(x * y,1 / y),1 / y,(1 / y) \ (y \ 1)) = (y \ 1) \ R(x,y,1 / y). [para(11(a,1),1508(a,1,3,2))]. 1511 L(T(x * y,1 / y),1 / y,K(y \ 1,y)) = (y \ 1) \ R(x,y,1 / y). [para(381(a,1),1509(a,1,3))]. 1512 (x \ 1) \ R(y,x,1 / x) = T(y * x,1 / x). [para(1511(a,1),1184(a,1))]. 1513 (x \ 1) * T(y * x,1 / x) = R(y,x,1 / x). [para(1512(a,1),14(a,1,2))]. 1514 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(641(a,1),843(a,1,1))]. 1515 L(T(x,y) \ 1,(x \ 1) * T(x,y),T(1 / (1 / x),y) / ((x \ 1) * T(x,y))) = T(1 / (1 / x),y) \ a(x \ 1,T(x,y),T(x,y) \ 1). [para(953(a,1),1017(a,2,2))]. 1516 ((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(93(a,1),706(a,2,1,2))]. 1518 ((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(705(a,1),1516(a,2,1))]. 1519 ((L(x,y,z) * (z * y)) / (z * y)) * T(((L(x,y,z) * (z * y)) / (z * y)) \ x,u) = x. [para(1518(a,2),15(a,1))]. 1520 L(x,y,z) * T(((L(x,y,z) * (z * y)) / (z * y)) \ x,u) = x. [para(15(a,1),1519(a,1,1))]. 1521 L(x,y,z) * T(L(x,y,z) \ x,u) = x. [para(15(a,1),1520(a,1,2,1,1))]. 1524 x / L(x,y,z) = L(x,y,z) \ x. [para(1521(a,1),113(a,1,1))]. 1525 L(x \ (y \ z),x,y) \ (x \ (y \ z)) = (x \ (y \ z)) / ((y * x) \ z). [para(139(a,1),1524(a,1,2)),flip(a)]. 1526 (L(x,y,z) \ x) / x = 1 / L(x,y,z). [para(1524(a,1),879(a,1,1))]. 1527 (((x * y) \ z) \ (y \ (x \ z))) / (y \ (x \ z)) = 1 / L(y \ (x \ z),y,x). [para(139(a,1),1526(a,1,1,1))]. 1528 (1 / L(x,y,z)) \ ((L(x,y,z) \ 1) * (x * (L(x,y,z) \ 1))) = (L(x,y,z) \ 1) * x. [para(1526(a,1),752(a,1,1))]. 1529 (x \ (y \ z)) / ((y * x) \ z) = ((y * x) \ z) \ (x \ (y \ z)). [para(139(a,1),1525(a,1,1)),flip(a)]. 1530 x \ ((y * z) * K((z \ (y \ x)) \ (((y * z) \ x) \ (z \ (y \ x))),z \ (y \ x))) = T(x \ (y * z),z \ (y \ x)). [para(1529(a,1),602(a,1,2,2,1,2))]. 1531 (((x * y) \ z) \ (y \ (x \ z))) / (y \ (x \ z)) = 1 / ((x * y) \ z). [para(139(a,1),1527(a,2,2))]. 1532 (1 / L(x,y,z)) \ ((L(x,y,z) \ 1) * (L(x,y,z) \ x)) = (L(x,y,z) \ 1) * x. [para(595(a,1),1528(a,1,2,2))]. 1533 K(L(x,y,z) \ 1,L(x,y,z)) * (L(x,y,z) \ x) = (L(x,y,z) \ 1) * x. [para(1532(a,1),1196(a,1)),flip(a)]. 1534 K(L(x,y,z) \ 1,L(x,y,z)) = L(K(x \ 1,x),y,z). [hyper(18,a,1413,a,b,1533,a)]. 1535 K(((x * y) \ x) \ 1,L(y \ 1,y,x)) = L(K((y \ 1) \ 1,y \ 1),y,x). [para(110(a,1),1534(a,1,1,1))]. 1536 K(((x * y) \ x) \ 1,L(y \ 1,y,x)) = L(K(y,y \ 1),y,x). [para(1089(a,1),1535(a,2,1))]. 1537 L(K(x,x \ 1),x,y) * (y * x) = y * T(y \ (y * x),(y * x) \ y). [para(1536(a,1),609(a,1,1))]. 1538 x * T(x \ (x * y),(x * y) \ x) = x * (y * K(y,y \ 1)). [para(1537(a,1),445(a,1))]. 1539 x * T(x \ (x * y),(x * y) \ x) = x * T(y,y \ 1). [para(1102(a,1),1538(a,2,2))]. 1540 x * T(y,(x * y) \ x) = x * T(y,y \ 1). [para(13(a,1),1539(a,1,2,1))]. 1541 T(x,(y * x) \ y) = T(x,x \ 1). [hyper(169,a,1540,a),flip(a)]. 1542 T(x,(y * x) \ y) = (x \ 1) \ 1. [hyper(17,a,857,a(flip),b,1540,a)]. 1543 T(x \ y,y \ x) = ((x \ y) \ 1) \ 1. [para(14(a,1),1542(a,1,2,1))]. 1545 T(x \ y,y \ x) \ 1 = T((x \ y) \ 1,x \ y). [para(1543(a,2),668(a,2,1)),flip(a)]. 1546 T(x \ y,x / y) = T(x \ y,y \ x). [para(1543(a,2),1399(a,2))]. 1547 K(x / y,y / x) * x = y * T(y \ x,x \ y). [para(1543(a,2),1400(a,2,2))]. 1548 K((x \ y) \ 1,x \ y) = K(x / y,y / x). [hyper(18,a,607,a,b,1547,a),flip(a)]. 1549 K(((x \ y) \ y) \ 1,(x \ y) \ y) = K(x \ 1,x). [para(1548(a,2),1171(a,1))]. 1550 K((x \ y) \ 1,x \ y) * (x / y) = T(x / y,y / x). [para(1548(a,2),1346(a,1,1))]. 1551 (R((x \ y) \ 1,z,u) / ((x \ y) * R((x \ y) \ 1,z,u))) \ 1 = K(x / y,y / x) \ (x \ y). [para(1548(a,1),1471(a,2,1))]. 1552 K(x \ 1,(y / x) \ y) * ((y / x) / y) = T((y / x) / y,y / (y / x)). [para(59(a,1),1550(a,1,1,1,1))]. 1553 T((x / y) / x,x / (x / y)) = K(y \ 1,y) * ((x / y) / x). [para(59(a,1),1552(a,1,1,2)),flip(a)]. 1554 K((x / y) / x,x / (x / y)) = K(y \ 1,y). [hyper(1347,a,1553,a)]. 1555 (x / y) * (1 / (1 / y)) = K(y \ 1,y) * x. [para(1554(a,1),1281(a,1,1)),flip(a)]. 1556 K(x \ 1,x) * (y * x) = y * (1 / (1 / x)). [para(15(a,1),1555(a,1,1)),flip(a)]. 1557 (x / y) * (1 / (1 / y)) = x * K(y \ 1,y). [para(1555(a,2),390(a,1))]. 1559 (1 / (1 / x)) * T(y,x) = y * (1 / (1 / x)). [para(1556(a,1),1227(a,1)),flip(a)]. 1560 K(x \ 1,x) * ((y * x) / z) = (y * (1 / (1 / x))) / z. [para(1556(a,1),1318(a,1,1)),flip(a)]. 1561 R(x,y,K(y \ 1,y)) = x. [hyper(1373,a,1557,a)]. 1562 R(x,1 / y,K(y \ 1,y)) = x. [para(1561(a,1),1440(a,1))]. 1563 K(x \ 1,x) * (y / (x \ 1)) = y / (1 / x). [para(1562(a,1),1338(a,1)),flip(a)]. 1564 T(x,1 / (1 / y)) = T(x,y). [hyper(181,a,1559,a),flip(a)]. 1565 T((1 / (1 / x)) * K(x \ (x / ((1 / (1 / x)) \ ((1 / (1 / x)) / y))),x),y) = y \ (y * (1 / (1 / x))). [para(1559(a,1),678(a,2,2))]. 1566 T(x,1 / y) = T(x,y \ 1). [para(57(a,1),1564(a,1,2,2))]. 1567 T(x,(y \ 1) \ 1) = T(x,y). [para(57(a,1),1566(a,1,2)),flip(a)]. 1568 T(((1 / x) * y) * x,x \ 1) = R(y,1 / x,x). [para(1566(a,1),367(a,1))]. 1569 T(((1 / (1 / (1 / x))) * y) \ y,x \ 1) = ((1 / x) * y) \ y. [para(1566(a,1),1341(a,1))]. 1570 L(T(x,y \ 1) \ z,T(x,1 / y),y \ 1) = (x * (1 / y)) \ ((1 / y) * z). [para(1566(a,1),1447(a,1,1,1))]. 1571 (x \ 1) * T(y * x,x \ 1) = R(y,x,1 / x). [para(1566(a,1),1513(a,1,2))]. 1573 T(x,T(y,y \ 1)) = T(x,y). [para(91(a,2),1567(a,1,2))]. 1574 T(x,x \ 1) * T(y,x) = y * T(x,x \ 1). [para(1573(a,1),90(a,1,2))]. 1576 ((x \ 1) \ 1) * T(y,x) = y * T(x,x \ 1). [para(1573(a,1),573(a,1,2))]. 1577 R(x,y,y \ 1) / (1 / y) = K(y \ 1,y) * (x * y). [para(263(a,1),1563(a,1,2)),flip(a)]. 1578 K(x,x \ 1) * (y * x) = y * T(x,x \ 1). [para(1574(a,1),1153(a,2))]. 1579 (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(1576(a,1),895(a,1,2))]. 1580 K(x \ 1,x) * (y * T(x,x \ 1)) = y * x. [hyper(1261,a,1578,a)]. 1581 (x * y) * K(y,y \ 1) = x * T(y,y \ 1). [para(1578(a,1),442(a,1)),flip(a)]. 1582 K(x,x \ 1) * (y * x) = y * T(y \ (y * x),(y * x) \ y). [para(1578(a,2),1539(a,2)),flip(a)]. 1583 (((x \ 1) \ 1) \ y) * T(x,x \ 1) = (x \ y) * x. [hyper(1345,a,1580,a),flip(a)]. 1584 (x * y) * K(y,y \ 1) = x * ((y \ 1) \ 1). [para(91(a,1),1581(a,2,2))]. 1585 R(x,y,K(y,y \ 1)) = x. [hyper(1120,a,1584,a)]. 1586 ((x * y) * ((z \ 1) \ 1)) / ((y * z) * K(z,z \ 1)) = R(R(x,y,z),y * z,K(z,z \ 1)). [para(1584(a,1),228(a,1,1))]. 1587 (x / y) * K(y \ 1,y) = x / T(y,y \ 1). [para(1585(a,1),1337(a,1))]. 1588 x \ (x / T(y,y \ 1)) = T(x \ (x / y),y). [para(1587(a,1),453(a,1,2))]. 1589 (x / ((y \ 1) \ 1)) * T((y \ 1) \ 1,z) = x * K(z \ (z / T(x \ (x / y),y)),z). [para(1588(a,1),681(a,2,2,1,2,2))]. 1590 R(x,1 / y,y) = R(x,y \ 1,y). [para(1568(a,1),1489(a,1))]. 1591 R(x,y \ 1,y) / y = x * (1 / y). [para(1590(a,1),266(a,1,1))]. 1592 x \ R(x,y \ 1,y) = a(x,1 / y,y). [para(1590(a,1),351(a,1,2))]. 1593 a(x,1 / y,y) = a(x,y \ 1,y). [para(1592(a,1),1349(a,1))]. 1594 a(x,(y \ 1) \ 1,y \ 1) = a(x,y,y \ 1). [para(57(a,1),1593(a,1,2)),flip(a)]. 1595 a(((x * y) / x) \ 1,y,y \ 1) * ((((x * y) / x) \ 1) * K((y \ 1) \ 1,y \ 1)) = (((x * y) / x) \ y) * (y \ 1). [para(1594(a,1),1038(a,1,1))]. 1596 (x * y) * (y \ 1) = R(x,y,1 / y). [para(1571(a,1),90(a,1)),flip(a)]. 1597 R(x / y,y,1 / y) = x * (y \ 1). [para(16(a,1),1596(a,1,1)),flip(a)]. 1598 L(L(x,y * (1 / x),K(x \ 1,x)),1 / x,y) = (y * (x \ 1)) \ (K(x \ 1,x) * y). [para(1597(a,1),1421(a,2,1))]. 1599 R(x,y,y \ 1) / (1 / y) = x * (1 / (1 / y)). [para(1577(a,2),1556(a,1))]. 1600 K(x \ 1,x) * ((y * x) / y) = 1 / (1 / ((y * x) / y)). [para(1560(a,2),1041(a,1))]. 1601 ((x * y) / z) / ((x * (1 / (1 / y))) / z) = K(y,y \ 1). [para(1560(a,1),1252(a,1,2))]. 1602 K(((x * y) / x) \ 1,(x * y) / x) = K(y \ 1,y). [hyper(18,a,1005,a,b,1600,a),flip(a)]. 1603 K(x \ 1,x) * ((((y * x) / y) \ 1) \ 1) = (y * x) / y. [para(1602(a,1),505(a,1,1))]. 1604 x / ((y * (1 / (1 / T(x,y)))) / y) = K(T(x,y),T(x,y) \ 1). [para(113(a,1),1601(a,1,1))]. 1605 (1 / x) \ (((y * x) / y) * (x \ 1)) = (y * x) / y. [para(1603(a,1),1199(a,1)),flip(a)]. 1606 ((x \ 1) \ 1) \ ((((y * x) / y) \ 1) \ 1) = x \ ((y * x) / y). [para(1603(a,1),1219(a,1,2)),flip(a)]. 1607 (1 / x) \ (x \ ((y * x) / y)) = (y * x) / y. [para(613(a,1),1605(a,1,2))]. 1608 (1 / x) * ((y * x) / y) = x \ ((y * x) / y). [para(1607(a,1),14(a,1,2))]. 1609 (1 / x) \ (x \ ((L(y \ 1,y,x) * x) / L(y \ 1,y,x))) = x * (y * T(y \ 1,x)). [para(1607(a,2),862(a,1))]. 1610 (x \ 1) \ ((y * (x \ 1)) / y) = x * ((y * (x \ 1)) / y). [para(57(a,1),1608(a,1,1)),flip(a)]. 1611 ((x * y) / x) / y = y \ ((x * y) / x). [para(1608(a,1),824(a,1)),flip(a)]. 1612 (x \ ((y * x) / y)) * x = (y * x) / y. [para(1611(a,1),16(a,1,1))]. 1613 T(x,x \ ((y * x) / y)) = x. [hyper(157,a,1612,a)]. 1614 (x * y) / x != z * y | y \ ((x * y) / x) = z. [para(1612(a,1),20(a,1))]. 1615 (x \ ((L(y \ 1,y,x) * x) / L(y \ 1,y,x))) * x = x * (y * T(y \ 1,x)). [para(1612(a,2),862(a,1))]. 1616 T(T(x,y),T(x,y) \ x) = T(x,y). [para(113(a,1),1613(a,1,2,2))]. 1617 K(T(x,y),T(x,y) \ x) = 1. [hyper(34,a,1616,a)]. 1618 (T(x,y) \ x) * T(x,y) = x. [para(1616(a,1),115(a,1,2))]. 1619 x / T(x,y) = T(x,y) \ x. [para(1616(a,1),132(a,1,2))]. 1620 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(1618(a,1),935(a,1,1,2,2))]. 1621 (T(x,y) \ x) / x = 1 / T(x,y). [para(1619(a,1),675(a,1,1))]. 1622 T((T(x,y) \ x) * (x \ T(x,y)),y) = K(T(x,y),x / T(x,y)). [para(1619(a,1),907(a,1,1,1))]. 1623 T(1 / T(x,y),x) = T(x,y) \ 1. [para(1621(a,1),527(a,1,1))]. 1624 T(((1 / x) * y) \ y,z / ((((1 / x) * y) \ y) * z)) = ((x \ 1) * y) \ y. [para(1569(a,1),1375(a,1,1))]. 1626 x / (((1 / (1 / x)) * y) / y) = K(T(x,y),T(x,y) \ 1). [para(1025(a,1),1604(a,1,2,1))]. 1627 K(T(x,y),T(x,y) \ 1) = x / (1 / (1 / x)). [para(15(a,1),1626(a,1,2)),flip(a)]. 1629 K(T(x,y),T(x,y) \ 1) = K(x,x \ 1). [para(1627(a,2),1095(a,1))]. 1630 K(T(x,y) \ 1,T(x,y)) = K(x,x \ 1) \ 1. [para(1629(a,1),406(a,1,1)),flip(a)]. 1631 K(x,x \ 1) * T(1 / (1 / x),y) = T(x,y). [para(1629(a,1),1111(a,1,1))]. 1632 K(x,x \ 1) * R(T(x,y) \ 1,z,u) = R(1 / T(x,y),z,u). [para(1629(a,1),1144(a,1,1))]. 1633 K(x,x \ 1) * (T(x,y) \ z) = (1 / (1 / T(x,y))) \ z. [para(1629(a,1),1204(a,1,1))]. 1634 K(T(x,y) \ 1,T(x,y)) = K(x \ 1,x). [para(1630(a,2),406(a,1))]. 1635 K(x \ 1,x) / T(x,y) = T(x,y) \ 1. [para(1634(a,1),159(a,1,1))]. 1636 a(x \ 1,T(x,y),T(x,y) \ 1) = K(x \ 1,x). [para(1634(a,1),989(a,2))]. 1637 T(x,y) * K(x \ 1,x) = T(1 / (1 / x),y). [hyper(1246,a,1631,a)]. 1638 T(x,y) / x = x \ T(x,y). [para(1631(a,1),1387(a,1,2)),flip(a)]. 1640 (x \ T(x,y)) * x = T(x,y). [para(1638(a,1),16(a,1,1))]. 1641 (x \ T(x,y)) \ T(x,y) = x. [para(1638(a,1),59(a,1,1))]. 1642 K(x,y) = L(T(x,y) / x,x,y). [para(1638(a,2),318(a,2,1))]. 1643 (1 / x) * T(x,y) = x \ T(x,y). [para(1638(a,1),644(a,2))]. 1644 (x \ T(x,y)) / T(x,y) = 1 / x. [para(1638(a,1),647(a,1,1))]. 1645 T(x,y) \ (x \ T(x,y)) = T(1 / x,T(x,y)). [para(1638(a,1),648(a,1,2))]. 1646 (x \ 1) \ T(x \ 1,y) = x * T(x \ 1,y). [para(1638(a,1),649(a,1))]. 1647 L(x \ 1,x,x \ T(x,y)) = T(1 / x,T(x,y)). [para(1638(a,1),679(a,1,3))]. 1648 L(T(x,y) \ z,T(x,y),1 / x) = (x \ T(x,y)) \ ((1 / x) * z). [para(1638(a,1),650(a,2,1))]. 1649 (1 / x) * K(T(x,y) \ 1,T(x,y)) = (x \ T(x,y)) * (T(x,y) \ 1). [para(1638(a,1),1054(a,2,1))]. 1650 R(x \ T(x,y),z,u) = K(y \ (y / R(1 / x,z,u)),y). [para(1638(a,1),1479(a,1,1))]. 1651 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(1638(a,1),1514(a,1,1))]. 1652 T(x,x \ T(x,y)) = x. [hyper(157,a,1640,a)]. 1653 T(x,y) * L(z,x,x \ T(x,y)) = (x \ T(x,y)) * (x * z). [para(1640(a,1),79(a,1,1))]. 1654 T(K(x \ (x / (y \ (y / z))),x),z) = y \ ((y / z) * T(z,x)). [para(1640(a,1),737(a,2,2,2))]. 1655 K(x \ 1,x) / L(x,x \ T(x,y),K(x \ 1,x) / T(x,y)) = R((x \ 1) / (x \ T(x,y)),x \ T(x,y),x) * (x \ T(x,y)). [para(1640(a,1),369(a,1,2,3,2))]. 1656 T((x * y) / x,((x * y) / x) \ y) = (x * y) / x. [para(112(a,1),1652(a,1,2,2))]. 1657 ((T(x,y) \ 1) * (x \ T(x,y))) \ K(T(x,y) \ 1,T(x,y)) = L(x,x \ T(x,y),T(x,y) \ 1). [para(1641(a,1),222(a,1,1)),flip(a)]. 1658 L(K(x,y),x,1 / x) = K(x,y). [para(1642(a,2),652(a,2))]. 1659 K(x,y) / (x * K(x,y)) = 1 / x. [para(1658(a,1),260(a,1,1))]. 1660 (L(x,1 / x,y) * y) / L(x,1 / x,y) = y * (x \ T(x,y)). [para(1643(a,1),894(a,2,2))]. 1661 R(1 / x,x,x \ T(x,y)) = 1 / x. [para(1644(a,1),177(a,2))]. 1662 T(x,y) \ K((x \ T(x,y)) \ (1 / x),x \ T(x,y)) = T(T(x,y) \ 1,x \ T(x,y)). [para(1644(a,1),562(a,1,2,1,2))]. 1663 (x \ T(x,y)) * R((x \ T(x,y)) \ ((x \ T(x,y)) / T(x,y)),z,u) = (1 / x) * (T(x,y) * R(T(x,y) \ 1,z,u)). [para(1644(a,1),568(a,1,1)),flip(a)]. 1664 K((x \ T(x,y)) \ (1 / x),x \ T(x,y)) = T(x * T(x \ 1,x \ T(x,y)),y). [para(1644(a,1),829(a,2,1,2)),flip(a)]. 1665 R(x,x \ 1,K(x \ 1,y)) = 1 / (x \ 1). [para(1659(a,1),108(a,2))]. 1666 (R(1 / x,x \ T(x,y),T(x,x \ T(x,y))) * x) * (x \ T(x,y)) = ((1 / x) * (x \ T(x,y))) * T(x,x \ T(x,y)). [para(1661(a,1),468(a,2,1,1))]. 1667 R(x,x \ 1,K(x \ 1,y)) = x. [para(1665(a,2),57(a,1))]. 1668 L(x,y,z) \ ((x \ 1) * L(x,y,z)) = (x \ 1) * K(x \ 1,L(x,y,z)). [para(1667(a,1),332(a,1,1,1))]. 1669 T(1 / (1 / x),y) \ K(x \ 1,x) = T(x,y) \ 1. [para(1637(a,1),1334(a,1,1))]. 1670 T(1 / x,T(x,y)) = x \ 1. [para(1645(a,1),522(a,1))]. 1672 T(x \ 1,T(x,y)) = T(x \ 1,x). [para(1670(a,1),125(a,1,1)),flip(a)]. 1675 T((1 / x) \ 1,1 / x) = T(x,T(1 / x,y)). [para(59(a,1),1672(a,1,1)),flip(a)]. 1676 T((x / y) \ 1,x / y) = T((x / y) \ 1,y \ x). [para(92(a,1),1672(a,1,2)),flip(a)]. 1677 (x \ 1) * (x * T(x \ 1,y)) = T(x \ 1,y). [para(1646(a,1),14(a,1,2))]. 1678 K(x,y) = (L(x \ 1,x,y) \ 1) \ T(L(x \ 1,x,y) \ 1,y). [para(1646(a,2),743(a,2))]. 1679 T(x,T(1 / x,y)) = T(x,1 / x). [para(59(a,1),1675(a,1,1)),flip(a)]. 1680 T(x,T(1 / x,y)) = T(x,x \ 1). [para(1679(a,2),666(a,1))]. 1681 R(x,T(1 / x,y),x) = T(x,x \ 1). [para(1680(a,1),811(a,2))]. 1682 L(T(x,x \ 1),y,z) \ L(x,y,z) = (L(x,y,z) \ (L(x,y,z) / x)) * x. [para(1681(a,1),918(a,1,1,1))]. 1685 L(T(x,y) \ 1,(x \ 1) * T(x,y),T(1 / (1 / x),y) / ((x \ 1) * T(x,y))) = T(1 / (1 / x),y) \ K(x \ 1,x). [para(1636(a,1),1515(a,2,2))]. 1687 L(x \ 1,x,x \ T(x,y)) = x \ 1. [para(1647(a,2),1670(a,1))]. 1689 x / ((y * x) / y) = ((y * x) / y) \ x. [para(1656(a,1),132(a,1,2))]. 1690 (((x * y) / x) \ y) / y = 1 / ((x * y) / x). [para(1689(a,1),688(a,1,1))]. 1691 R((x / y) \ 1,x / y,y) \ 1 = T((y / x) \ 1,x \ y). [para(1676(a,1),1396(a,2))]. 1692 K(x,x \ 1) * (T(x,y) \ z) = T(1 / (1 / x),y) \ z. [para(1023(a,1),1633(a,2,1))]. 1693 L(1 / T((x \ 1) \ 1,y),x,x \ 1) = T(1 / (1 / x),y) \ 1. [para(1692(a,1),1382(a,2))]. 1694 T(x * L(x \ 1,x,x \ T(x,y)),y) = (x \ T(x,y)) * (x * (T(x,y) \ 1)). [para(1653(a,1),902(a,1)),flip(a)]. 1695 T((1 * x) / y,y / x) \ 1 = T((x / y) \ 1,y \ x). [para(365(a,1),1691(a,1,1))]. 1696 T(x / y,y / x) \ 1 = T((x / y) \ 1,y \ x). [para(11(a,1),1695(a,1,1,1,1))]. 1697 T(x,((y * x) / y) \ 1) \ ((((z * x) / z) \ 1) \ 1) = x \ ((z * x) / z). [para(1035(a,2),1606(a,1,1))]. 1698 T((T(x,y) \ x) * (x \ T(x,y)),y) = K(T(x,y),T(x,y) \ x). [para(1619(a,1),1622(a,2,2))]. 1699 K(x \ (x / T(y \ (y / z),z)),x) = y \ ((y / z) * T(z,x)). [para(1654(a,1),832(a,2))]. 1700 T((T(x,y) \ x) * (x \ T(x,y)),y) = 1. [para(1698(a,2),1617(a,1))]. 1702 L(T(x,y) \ z,T(x,y),x \ 1) = (x \ T(x,y)) \ ((1 / x) * z). [para(1648(a,1),1445(a,1)),flip(a)]. 1703 L(1 / T((x \ 1) \ 1,y),x,x \ 1) = 1 / T(x,y). [para(1693(a,2),1024(a,1))]. 1704 L(T(x,y) \ 1,x,x \ 1) = 1 / T(x,y). [para(1029(a,1),1703(a,1,1))]. 1705 (1 / x) * (T(x,y) \ x) = 1 / T(x,y). [para(1704(a,1),1194(a,1)),flip(a)]. 1706 (x \ 1) * (T(x,y) \ x) = T(1 / T(x,y),x). [para(1705(a,1),1201(a,1,1)),flip(a)]. 1707 (x \ 1) * (T(x,y) \ x) = T(x,y) \ 1. [para(1706(a,2),1623(a,1))]. 1708 (x \ T(x,y)) * (T(x,y) \ 1) = (1 / x) * K(x \ 1,x). [para(1634(a,1),1649(a,1,2)),flip(a)]. 1709 (x \ T(x,y)) * (T(x,y) \ 1) = x \ 1. [para(1708(a,2),380(a,1))]. 1711 (x \ T(x,y)) \ (x \ 1) = T(x,y) \ 1. [hyper(66,a,1709,a)]. 1712 (T(x,y) \ 1) * (x \ T(x,y)) = x \ 1. [para(1711(a,1),1460(a,1,1))]. 1713 (x \ T(x,y)) \ R(x \ 1,z,u) = R(T(x,y) \ 1,z,u). [para(1711(a,1),1495(a,1,1)),flip(a)]. 1714 (x \ 1) / (x \ T(x,y)) = T(x,y) \ 1. [hyper(70,a,1712,a)]. 1715 (x \ T(x,y)) * R(T(x,y) \ 1,z,u) = R(x \ 1,z,u). [para(1713(a,1),14(a,1,2))]. 1716 R(x \ 1,y,z) * ((x \ T(x,u)) \ 1) = R(T(x,u) \ 1,y,z). [para(1713(a,1),1462(a,2))]. 1717 (x \ 1) * K(x \ 1,L(x,y,z)) = T(x \ 1,L(x,y,z)). [para(1668(a,1),30(a,2)),flip(a)]. 1718 x * T(x \ 1,L(x,y,z)) = K(x \ 1,L(x,y,z)). [hyper(17,a,1677,a,b,1717,a),flip(a)]. 1719 L(K(x \ 1,L(x,y,z)),y,z) = K(L(x,y,z) \ 1,L(x,y,z)). [para(1718(a,1),1411(a,1,1))]. 1720 L(K(x \ 1,L(x,y,z)),y,z) = L(K(x \ 1,x),y,z). [para(1719(a,2),1534(a,1))]. 1721 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(1720(a,1),560(a,1,2,2,1,1))]. 1722 (1 / x) \ L(K(y \ 1,y),x,x \ 1) = x * K(y \ 1,L(y,x,x \ 1)). [para(1720(a,1),1191(a,1,2))]. 1723 T(((1 / x) * y) \ y,(((1 / x) * y) \ y) \ 1) = ((x \ 1) * y) \ y. [para(98(a,1),1624(a,1,2))]. 1724 L(T(x,x \ 1),y,z) \ L(x,y,z) = T(1 / x,L(x,y,z)) * x. [para(875(a,1),1682(a,2,1))]. 1726 L(T(x,x \ 1),y,z) \ L(x,y,z) = x * T(x \ 1,L(x,y,z)). [para(1724(a,2),187(a,1))]. 1727 L(T(x,x \ 1),y,z) \ L(x,y,z) = K(x \ 1,L(x,y,z)). [para(1726(a,2),1718(a,1))]. 1728 x * K(y \ 1,L(y,x,x \ 1)) = x * K(y \ 1,y). [para(1722(a,1),1191(a,1))]. 1729 L(T(x,y \ 1) \ z,T(x,y \ 1),y \ 1) = (x * (1 / y)) \ ((1 / y) * z). [para(1566(a,1),1570(a,1,2))]. 1730 T(x * L(x \ 1,x,x \ T(x,y)),y) = (x \ T(x,y)) * (T(x,y) \ x). [para(525(a,1),1694(a,2,2))]. 1731 (x \ T(x,y)) * (T(x,y) \ x) = T(x * (x \ 1),y). [para(1687(a,1),1730(a,1,1,2)),flip(a)]. 1732 (x \ T(x,y)) * (T(x,y) \ x) = T(1,y). [para(14(a,1),1731(a,2,1))]. 1735 (x \ T(x,y)) * (T(x,y) \ x) = 1. [para(1732(a,2),103(a,1))]. 1736 (x \ T(x,y)) \ 1 = T(x,y) \ x. [hyper(66,a,1735,a)]. 1738 T(L(x \ 1,x,y) \ 1,y) \ (L(x \ 1,x,y) \ 1) = K(x,y) \ 1. [para(1678(a,2),1736(a,1,1)),flip(a)]. 1739 R(x \ 1,y,z) * (T(x,u) \ x) = R(T(x,u) \ 1,y,z). [para(1736(a,1),1716(a,1,2))]. 1740 K(x,x \ 1) * (R(x \ 1,y,z) * (T(x,u) \ x)) = R(1 / T(x,u),y,z). [para(1739(a,2),1632(a,1,2))]. 1741 R(1 / x,y,z) * (T(x,u) \ x) = R(1 / T(x,u),y,z). [para(1740(a,1),1307(a,1)),flip(a)]. 1742 (x / (y * x)) * (T(y,z) \ y) = R(1 / T(y,z),y,x). [para(111(a,1),1741(a,1,1))]. 1743 (x * (1 / y)) \ ((1 / y) * z) = (x * (y \ 1)) \ ((y \ 1) * z). [para(1729(a,1),219(a,1))]. 1744 (x * (y \ 1)) \ ((y \ 1) * x) = K(1 / y,x). [para(1743(a,1),24(a,2)),flip(a)]. 1745 K(1 / x,y) = K(x \ 1,y). [para(1744(a,1),24(a,2)),flip(a)]. 1747 (x \ (x * (y * T(y \ 1,x)))) * x = x * (y * T(y \ 1,x)). [para(862(a,1),1615(a,1,1,2))]. 1748 (x * T(x \ 1,y)) * y = y * (x * T(x \ 1,y)). [para(13(a,1),1747(a,1,1))]. 1749 T(x,y * T(y \ 1,x)) = x. [hyper(117,a,1748,a)]. 1751 (x * T(x \ 1,y)) * ((T(y,x * T(x \ 1,y)) \ z) \ z) = T(y,y \ z) * (x * T(x \ 1,y)). [para(1749(a,1),190(a,1,1,2,1)),flip(a)]. 1752 T(x,y \ T(y,x)) = x. [para(524(a,1),1749(a,1,2))]. 1753 T(x,K(y,x)) = x. [para(743(a,2),1749(a,1,2))]. 1754 T(K(x,y),y) = K(x,y). [hyper(33,a,1753,a)]. 1755 K(x,y) * y = y * K(x,y). [para(1753(a,1),90(a,1,2))]. 1756 K(x,y) * (1 / (1 / y)) = (1 / (1 / y)) * K(x,y). [para(1753(a,1),1025(a,1,2,2,2))]. 1757 (x \ T(x,y)) * y = y * (x \ T(x,y)). [para(1752(a,1),90(a,1,2))]. 1758 (x * K(y,x)) * (x \ 1) = R(K(y,x),x,x \ 1). [para(1755(a,1),130(a,1,1))]. 1759 (((x / y) * K(z,x / y)) * y) / x = R(K(z,x / y),x / y,y). [para(1755(a,1),87(a,1,1,1))]. 1760 (x \ y) * ((y \ T(x,x \ y)) * y) = y * K(y \ x,y). [para(1755(a,1),848(a,2))]. 1761 R(x,x \ T(x,y),y) \ (T(x,y) * y) = y * (x \ T(x,y)). [para(1757(a,1),249(a,2))]. 1762 R(K(x,y),y,y \ 1) = K(x,y). [para(1758(a,1),1504(a,1))]. 1763 K(x,y) * (1 / (1 / y)) = K(x,y) / (1 / y). [para(1762(a,1),1599(a,1,1)),flip(a)]. 1764 (1 / (1 / x)) * K(y,x) = K(y,x) / (1 / x). [para(1756(a,1),1763(a,1))]. 1765 T(x,y) * (R(x,x \ T(x,y),y) \ y) = y * (x \ T(x,y)). [para(1761(a,1),1416(a,1)),flip(a)]. 1766 K((x \ T(x,y)) \ (1 / x),x \ T(x,y)) = T(x * (x \ 1),y). [para(801(a,1),1664(a,2,1,2))]. 1767 K((x \ T(x,y)) \ (1 / x),x \ T(x,y)) = T(1,y). [para(14(a,1),1766(a,2,1))]. 1770 K((x \ T(x,y)) \ (1 / x),x \ T(x,y)) = 1. [para(1767(a,2),103(a,1))]. 1772 (x / ((y \ 1) \ 1)) * T((y \ 1) \ 1,z) = x * (x \ ((x / y) * T(y,z))). [para(1699(a,1),1589(a,2,2))]. 1773 (x / ((y \ 1) \ 1)) * T((y \ 1) \ 1,z) = (x / y) * T(y,z). [para(1772(a,2),14(a,1))]. 1774 (((x \ 1) \ 1) * y) / ((x \ 1) \ 1) = (y / x) * T(x,y). [para(1773(a,1),654(a,1)),flip(a)]. 1775 (((x \ 1) \ 1) * y) / ((x \ 1) \ 1) = (x * y) / x. [para(1774(a,2),654(a,1))]. 1776 L(L(x,y * (1 / x),K(x \ 1,x)),1 / x,y) = L(x,x \ 1,y). [para(1598(a,2),455(a,1))]. 1777 L(x,1 / x,y) = L(x,x \ 1,y). [para(1313(a,1),1776(a,1,1))]. 1778 (L(x,x \ 1,y) * y) / L(x,1 / x,y) = y * (x \ T(x,y)). [para(1777(a,1),1660(a,1,1,1))]. 1779 (L(x,x \ 1,y) * y) / L(x,x \ 1,y) = y * (x \ T(x,y)). [para(1777(a,1),1778(a,1,2))]. 1780 ((x * (y \ T(y,x))) \ x) / x = 1 / ((L(y,y \ 1,x) * x) / L(y,y \ 1,x)). [para(1779(a,1),1690(a,1,1,1))]. 1781 ((x * (y \ T(y,x))) \ x) / x = 1 / (x * (y \ T(y,x))). [para(1779(a,1),1780(a,2,2))]. 1782 (1 / x) \ (x \ (x * (y * T(y \ 1,x)))) = x * (y * T(y \ 1,x)). [para(862(a,1),1609(a,1,2,2))]. 1783 (1 / x) \ (y * T(y \ 1,x)) = x * (y * T(y \ 1,x)). [para(13(a,1),1782(a,1,2))]. 1785 ((1 / x) \ (y * T(y \ 1,x))) * K(x,x \ 1) = T(x,x \ 1) * (y * T(y \ 1,x)). [para(1783(a,2),1156(a,1,1))]. 1786 T(T(x,y) \ 1,x \ T(x,y)) = T(x,y) \ 1. [para(1770(a,1),1662(a,1,2)),flip(a)]. 1787 R(T(x,y) \ 1,z,u) * (x \ T(x,y)) = (x \ T(x,y)) * R(T(x,y) \ 1,z,u). [para(1786(a,1),124(a,1,2,1)),flip(a)]. 1789 R(T(x,y) \ 1,z,u) * (x \ T(x,y)) = R(x \ 1,z,u). [para(1787(a,2),1715(a,1))]. 1791 T(x,x \ 1) * (y * T(y \ 1,x)) = (x \ 1) \ (y * T(y \ 1,x)). [para(1785(a,1),1256(a,1))]. 1792 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(1330(a,1),1721(a,1,2,2))]. 1793 R(T(K(x \ 1,L(x,y,z)),z * y),z,y) = y \ (z \ (z * (y * K(x \ 1,x)))). [para(416(a,1),1792(a,1,2,2)),flip(a)]. 1794 R(T(K(x \ 1,L(x,y,z)),z * y),z,y) = y \ (y * K(x \ 1,x)). [para(13(a,1),1793(a,2,2))]. 1795 R(T(K(x \ 1,L(x,y,z)),z * y),z,y) = K(x \ 1,x). [para(1794(a,2),13(a,1))]. 1797 R(R(x,y,z),y * z,K(z,z \ 1)) = ((x * y) * ((z \ 1) \ 1)) / (y * ((z \ 1) \ 1)). [para(1584(a,1),1586(a,1,2)),flip(a)]. 1798 R(R(x,y,z),y * z,K(z,z \ 1)) = R(x,y,(z \ 1) \ 1). [para(1797(a,2),28(a,2)),flip(a)]. 1799 T((T(x,y) \ x) * (T(x,y) / x),z) = (T(x,y) \ x) * (T(x,y) / x). [para(1618(a,1),1620(a,2,2,2))]. 1800 T((T(x,y) \ x) * (x \ T(x,y)),z) = (T(x,y) \ x) * (T(x,y) / x). [para(1638(a,1),1799(a,1,1,2))]. 1801 T((T(x,y) \ x) * (x \ T(x,y)),z) = (T(x,y) \ x) * (x \ T(x,y)). [para(1638(a,1),1800(a,2,2))]. 1802 (T(x,y) \ x) * (x \ T(x,y)) = 1. [para(1801(a,1),1700(a,1))]. 1804 (T(x \ 1,y) \ (x \ 1)) * (x * T(x \ 1,y)) = 1. [para(1646(a,1),1802(a,1,2))]. 1805 (T(x,((y * x) / y) \ 1) \ ((((y * x) / y) \ 1) \ 1)) * ((((y * x) / y) \ 1) * T((((y * x) / y) \ 1) \ 1,y)) = 1. [para(194(a,1),1804(a,1,1,1))]. 1806 L(x,x \ T(x,y),T(x,y) \ 1) = (x \ 1) \ K(T(x,y) \ 1,T(x,y)). [para(1712(a,1),1657(a,1,1)),flip(a)]. 1807 L(x,x \ T(x,y),T(x,y) \ 1) = (x \ 1) \ K(x \ 1,x). [para(1634(a,1),1806(a,2,2))]. 1809 L(x,x \ T(x,y),T(x,y) \ 1) = x. [para(1807(a,2),160(a,1))]. 1811 (R((x \ y) \ 1,z,u) / ((x \ y) * R((x \ y) \ 1,z,u))) \ 1 = K(y / x,x / y) * (x \ y). [para(1551(a,2),1285(a,1))]. 1812 T(x,x \ y) * (z * T(z \ 1,x)) = (z * T(z \ 1,x)) * ((x \ y) \ y). [para(1749(a,1),1751(a,1,2,1,1)),flip(a)]. 1813 (x * T(x \ 1,y)) * ((y \ 1) \ 1) = (y \ 1) \ (x * T(x \ 1,y)). [para(1812(a,1),1791(a,1))]. 1814 ((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(1813(a,1),28(a,2,2)),flip(a)]. 1815 x * ((y \ (x \ ((y \ 1) \ 1))) * y) = (y \ 1) \ (x * T(x \ 1,y)). [para(1813(a,1),1294(a,1)),flip(a)]. 1816 (R((x \ y) \ 1,z,u) / ((x \ y) * R((x \ y) \ 1,z,u))) \ 1 = (x \ y) * K(y / x,x / y). [para(1811(a,2),1128(a,1))]. 1817 (x \ y) * K(y / x,x / y) = ((x \ y) \ 1) \ 1. [para(968(a,1),1816(a,1,1)),flip(a)]. 1818 K(x \ y,(x \ y) \ 1) = K(y / x,x / y). [hyper(17,a,1116,a,b,1817,a),flip(a)]. 1819 (x \ y) * (1 / (x \ y)) = K(y / x,x / y). [para(1818(a,1),1093(a,1)),flip(a)]. 1820 x \ (K(x / y,y / x) * y) = L(1 / (y \ x),y \ x,y). [para(1818(a,1),1103(a,1,2,1))]. 1821 K(x / y,(x / y) \ 1) = (y \ x) * (1 / (y \ x)). [para(1819(a,2),1148(a,2))]. 1822 ((x \ y) \ (y / x)) / (y / x) = 1 / (x \ y). [hyper(1212,a,1821,a)]. 1823 (1 / (x \ y)) * (y / x) = (x \ y) \ (y / x). [para(1822(a,1),16(a,1,1))]. 1824 ((x / y) \ x) \ (x / (x / y)) = (1 / y) * (x / (x / y)). [para(59(a,1),1823(a,1,1,2)),flip(a)]. 1825 x * (((1 / (x \ y)) * (x \ y)) / (1 / (x \ y))) = (((x \ y) \ (y / x)) / (1 / (x \ y))) * x. [para(1823(a,1),342(a,1,1,1)),flip(a)]. 1826 (1 / x) * (y / (y / x)) = x \ (y / (y / x)). [para(59(a,1),1824(a,1,1)),flip(a)]. 1827 (x / (x / y)) \ (y \ (x / (x / y))) = T(1 / y,x / (x / y)). [para(1826(a,1),30(a,2,2)),flip(a)]. 1828 L(1 / (x \ y),x \ y,x) = 1 / (1 / (y \ x)). [para(1820(a,1),1280(a,1))]. 1829 ((x \ y) * (y \ x)) / (x \ y) = 1 / (1 / (y \ x)). [para(1828(a,1),345(a,2))]. 1830 (1 / (1 / (x \ y))) * (y \ x) = (y \ x) * (x \ y). [para(1829(a,1),16(a,1,1))]. 1831 ((x \ y) * (y \ x)) \ ((y \ x) * (x \ y)) = K((x \ y) \ 1,x \ y). [para(1830(a,1),1251(a,1,2))]. 1832 T(1 / x,y / (y / x)) = x \ 1. [para(1827(a,1),616(a,1))]. 1834 K((x \ y) \ 1,x \ y) = K(y \ x,x \ y). [para(1831(a,1),24(a,2)),flip(a)]. 1835 x \ (y * K(x \ y,y \ x)) = T(x \ y,y \ x). [para(1834(a,1),604(a,1,2,2))]. 1836 K(x \ y,y \ x) * y = x * T(x \ y,y \ x). [para(1834(a,1),607(a,1,1))]. 1837 K(x / y,y / x) = K(y \ x,x \ y). [para(1834(a,1),1548(a,1)),flip(a)]. 1838 K(x \ (y \ x),(y \ x) \ x) = K(y \ 1,y). [para(1834(a,1),1549(a,1))]. 1839 K(x / y,(x / y) \ 1) = K(y \ x,x \ y). [para(1837(a,1),1148(a,2))]. 1840 x / (K(x \ y,y \ x) * y) = ((x / y) \ 1) \ 1. [para(1837(a,1),1287(a,1,2,1))]. 1841 K(x \ y,y \ x) * ((y / x) \ z) = (1 / (1 / (y / x))) \ z. [para(1839(a,1),1204(a,1,1))]. 1842 K((x / y) / z,((x / y) / z) \ 1) = K((z * y) \ x,x \ (z * y)). [para(1839(a,1),1436(a,2))]. 1843 x \ (y * K(x \ y,y \ x)) = ((x \ y) \ 1) \ 1. [para(1835(a,2),1543(a,1))]. 1844 K(x \ (x * y),(x * y) \ x) = K(y,y \ 1). [hyper(18,a,1582,a,b,1836,a)]. 1845 (x * y) / (K((x * y) \ ((z \ x) * y),((z \ x) * y) \ (x * y)) * ((z \ x) * y)) = (R(z,z \ x,y) \ 1) \ 1. [para(84(a,2),1840(a,2,1,1))]. 1846 K(x,x \ 1) * (((y * x) / y) \ z) = (1 / (1 / ((y * x) / y))) \ z. [para(1844(a,1),1841(a,1,1))]. 1847 K((x * y) \ z,z \ (x * y)) = K(x \ (z / y),(z / y) \ x). [para(1842(a,1),1839(a,1))]. 1848 (1 / (1 / x)) \ (((y * x) / y) \ x) = (1 / (1 / ((y * x) / y))) \ 1. [para(1846(a,1),1207(a,2))]. 1849 (1 / (1 / x)) \ (((y * x) / y) \ x) = 1 / ((y * x) / y). [para(1848(a,2),59(a,1))]. 1850 (((x \ y) \ (y / x)) / (1 / (x \ y))) * x = x * (1 / (1 / (x \ y))). [para(16(a,1),1825(a,1,2,1)),flip(a)]. 1851 ((x \ y) \ (y / x)) / (1 / (x \ y)) = 1 / (1 / (y / x)). [hyper(18,a,1032,a,b,1850,a)]. 1853 ((L(x,x \ 1,y) \ (L(x,x \ 1,y) * y)) \ (y * (x \ T(x,y)))) / (1 / (L(x,x \ 1,y) \ (L(x,x \ 1,y) * y))) = 1 / (1 / ((L(x,x \ 1,y) * y) / L(x,x \ 1,y))). [para(1779(a,1),1851(a,1,1,2))]. 1854 T((1 / (1 / x)) * K(x \ (x / (((1 / x) \ 1) \ (((1 / x) \ 1) / y))),x),y) = y \ (y * (1 / (1 / x))). [para(1323(a,1),1565(a,1,1,2,1,2,2))]. 1855 T((1 / (1 / x)) * K(x \ (x / (x \ (((1 / x) \ 1) / y))),x),y) = y \ (y * (1 / (1 / x))). [para(59(a,1),1854(a,1,1,2,1,2,2,1))]. 1856 T((1 / (1 / x)) * K(x \ (x / (x \ (x / y))),x),y) = y \ (y * (1 / (1 / x))). [para(59(a,1),1855(a,1,1,2,1,2,2,2,1))]. 1857 T((1 / (1 / x)) * K(x \ (x / (x \ (x / y))),x),y) = 1 / (1 / x). [para(1856(a,2),13(a,1))]. 1858 T(K(x \ (x / (x \ (x / y))),x) / (1 / x),y) = 1 / (1 / x). [para(1764(a,1),1857(a,1,1))]. 1859 (x * y) / (K(x \ (((z \ x) * y) / y),(((z \ x) * y) / y) \ x) * ((z \ x) * y)) = (R(z,z \ x,y) \ 1) \ 1. [para(1847(a,1),1845(a,1,2,1))]. 1860 (x * y) / (K(x \ (z \ x),(((z \ x) * y) / y) \ x) * ((z \ x) * y)) = (R(z,z \ x,y) \ 1) \ 1. [para(15(a,1),1859(a,1,2,1,1,2))]. 1861 (x * y) / (K(x \ (z \ x),(z \ x) \ x) * ((z \ x) * y)) = (R(z,z \ x,y) \ 1) \ 1. [para(15(a,1),1860(a,1,2,1,2,1))]. 1864 (x * y) / (K(z \ 1,z) * ((z \ x) * y)) = (R(z,z \ x,y) \ 1) \ 1. [para(1838(a,1),1861(a,1,2,1))]. 1865 (R(x,x \ y,z) \ 1) \ 1 = (y * z) / ((((x \ 1) \ 1) \ y) * z). [para(1329(a,1),1864(a,1,2)),flip(a)]. 1867 x \ ((y * z) * K(((y * z) \ x) \ 1,z \ (y \ x))) = T(x \ (y * z),z \ (y \ x)). [para(860(a,1),1530(a,1,2,2,1))]. 1868 (x \ T(x,y)) * R((x \ T(x,y)) \ ((x \ T(x,y)) / T(x,y)),z,u) = (1 / x) * (x * R(x \ 1,z,u)). [para(964(a,1),1663(a,2,2))]. 1869 (x \ T(x,y)) * R((x \ T(x,y)) \ ((x \ T(x,y)) / T(x,y)),z,u) = R(1 / x,z,u). [para(1868(a,2),539(a,1))]. 1871 (x \ T(x,y)) * R((x \ T(x,y)) \ (1 / x),z,u) = R(1 / x,z,u). [para(1644(a,1),1869(a,1,2,1,2))]. 1873 (x \ ((y * x) / y)) * ((((y * x) / y) \ 1) * T((((y * x) / y) \ 1) \ 1,y)) = 1. [para(1697(a,1),1805(a,1,1))]. 1874 (x \ ((y * x) / y)) * ((((y * x) / y) \ 1) * (((y \ (y * x)) \ 1) \ 1)) = 1. [para(1031(a,1),1873(a,1,2,2))]. 1876 (x \ ((y * x) / y)) * ((((y * x) / y) \ 1) * ((x \ 1) \ 1)) = 1. [para(13(a,1),1874(a,1,2,2,1,1))]. 1877 (x \ ((y * x) / y)) * (((y * x) / y) \ x) = 1. [para(1037(a,1),1876(a,1,2))]. 1878 (x \ ((y * x) / y)) \ 1 = ((y * x) / y) \ x. [hyper(66,a,1877,a)]. 1879 ((L(x,x \ 1,y) * y) / L(x,x \ 1,y)) \ y = (y \ (y * (x \ T(x,y)))) \ 1. [para(1779(a,1),1878(a,1,1,2)),flip(a)]. 1880 ((L(x,x \ 1,y) * y) / L(x,x \ 1,y)) \ y = (x \ T(x,y)) \ 1. [para(13(a,1),1879(a,2,1))]. 1882 ((L(x,x \ 1,y) * y) / L(x,x \ 1,y)) \ y = T(x,y) \ x. [para(1880(a,2),1736(a,1))]. 1883 (x * (y \ T(y,x))) \ x = T(y,x) \ y. [para(1779(a,1),1882(a,1,1))]. 1884 T(L(x \ 1,x,y) \ 1,y) \ (L(x \ 1,x,y) \ 1) = (y * K(x,y)) \ y. [para(1678(a,2),1883(a,1,1,2)),flip(a)]. 1885 1 / (x * (y \ T(y,x))) = (T(y,x) \ y) / x. [para(1883(a,1),1781(a,1,1)),flip(a)]. 1886 (x * K(y,x)) \ x = K(y,x) \ 1. [para(1884(a,1),1738(a,1))]. 1887 (x * y) * ((z \ L(y \ ((z \ 1) \ 1),y,x)) * z) = (x * (y * T(y \ 1,z))) * ((z \ 1) \ 1). [para(1583(a,1),1579(a,1,2))]. 1888 a((x \ (x * y)) \ 1,y,y \ 1) * ((((x * y) / x) \ 1) * K((y \ 1) \ 1,y \ 1)) = (((x * y) / x) \ y) * (y \ 1). [para(987(a,1),1595(a,1,1))]. 1889 (R(1 / x,x \ T(x,y),x) * x) * (x \ T(x,y)) = ((1 / x) * (x \ T(x,y))) * T(x,x \ T(x,y)). [para(1652(a,1),1666(a,1,1,1,3))]. 1890 (x * R(x \ 1,x \ T(x,y),x)) * (x \ T(x,y)) = ((1 / x) * (x \ T(x,y))) * T(x,x \ T(x,y)). [para(283(a,1),1889(a,1,1))]. 1892 L(T(x,y) \ 1,(x \ 1) * T(x,y),T(1 / (1 / x),y) / ((x \ 1) * T(x,y))) = T(x,y) \ 1. [para(1685(a,2),1669(a,1))]. 1893 T(1 / (1 / x),y) \ ((T(1 / (1 / x),y) / ((x \ 1) * T(x,y))) * (x \ 1)) = L(T(x,y) \ 1,T(x,y),x \ 1). [para(1892(a,1),353(a,1,1)),flip(a)]. 1894 T(1 / (1 / x),y) \ ((T(1 / (1 / x),y) / ((x \ 1) * T(x,y))) * (x \ 1)) = (x \ T(x,y)) \ ((1 / x) * 1). [para(1893(a,2),1702(a,1))]. 1895 T(1 / (1 / x),y) \ ((T(1 / (1 / x),y) / ((x \ 1) * T(x,y))) * (x \ 1)) = (x \ T(x,y)) \ (1 / x). [para(12(a,1),1894(a,2,2))]. 1896 T(1 / (1 / x),y) \ (x * (x \ 1)) = (x \ T(x,y)) \ (1 / x). [para(1013(a,1),1895(a,1,2,1))]. 1897 T(1 / (1 / x),y) \ 1 = (x \ T(x,y)) \ (1 / x). [para(14(a,1),1896(a,1,2))]. 1899 (x \ T(x,y)) \ (1 / x) = 1 / T(x,y). [para(1897(a,1),1024(a,1))]. 1900 (x \ T(x,y)) * R(1 / T(x,y),z,u) = R(1 / x,z,u). [para(1899(a,1),1871(a,1,2,1))]. 1901 a(x \ 1,x,x \ 1) * ((((y * x) / y) \ 1) * K((x \ 1) \ 1,x \ 1)) = (((y * x) / y) \ x) * (x \ 1). [para(13(a,1),1888(a,1,1,1,1))]. 1902 K(x \ 1,x) * ((((y * x) / y) \ 1) * K((x \ 1) \ 1,x \ 1)) = (((y * x) / y) \ x) * (x \ 1). [para(950(a,1),1901(a,1,1))]. 1903 K(x \ 1,x) * ((((y * x) / y) \ 1) * K(x,x \ 1)) = (((y * x) / y) \ x) * (x \ 1). [para(1089(a,1),1902(a,1,2,2))]. 1904 (((x * y) / x) \ y) * (y \ 1) = ((x * y) / x) \ 1. [para(1903(a,1),1242(a,1))]. 1905 (((x * y) / x) \ y) \ (((x * y) / x) \ 1) = y \ 1. [hyper(66,a,1904,a)]. 1906 (((x * y) / x) \ y) \ ((1 / (1 / y)) \ (((x * y) / x) \ y)) = 1 / (1 / (y \ 1)). [para(1905(a,1),1291(a,2,2,2))]. 1907 (((x * y) / x) \ y) \ ((1 / (1 / y)) \ (((x * y) / x) \ y)) = 1 / y. [para(57(a,1),1906(a,2,2))]. 1909 (((x * y) / x) \ y) \ (1 / ((x * y) / x)) = 1 / y. [para(1849(a,1),1907(a,1,2))]. 1910 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(1651(a,1),949(a,1))]. 1911 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(842(a,1),1910(a,1,1,2))]. 1913 x \ T(x,L(x \ 1,y,z)) = K(x,L(x \ 1,y,z)). [para(13(a,1),1911(a,1,1)),flip(a)]. 1914 T(x,K(y,L(y \ 1,z,u))) = x. [para(1913(a,1),927(a,1,2))]. 1915 T(x,K(1 / y,L(y,z,u))) = x. [para(59(a,1),1914(a,1,2,2,1))]. 1916 T(x,K(y \ 1,L(y,z,u))) = x. [para(1745(a,1),1915(a,1,2))]. 1917 T(K(x \ 1,L(x,y,z)),u) = K(x \ 1,L(x,y,z)). [hyper(33,a,1916,a)]. 1918 R(K(x \ 1,L(x,y,z)),T(u,K(x \ 1,L(x,y,z))),w) = ((u * K(x \ 1,L(x,y,z))) * w) / (u * w). [para(1916(a,1),121(a,1,2,1)),flip(a)]. 1919 R(K(x \ 1,L(x,y,z)),z,y) = K(x \ 1,x). [para(1917(a,1),1795(a,1,1))]. 1921 ((x * K(y \ 1,L(y,z,u))) * w) / (x * w) = R(K(y \ 1,L(y,z,u)),x,w). [para(1916(a,1),1918(a,1,2)),flip(a)]. 1922 R((x \ 1) / (x \ T(x,y)),x \ T(x,y),x) * (x \ T(x,y)) = K(x \ 1,x) / L(x,x \ T(x,y),T(x,y) \ 1). [para(1635(a,1),1655(a,1,2,3)),flip(a)]. 1923 R((x \ 1) / (x \ T(x,y)),x \ T(x,y),x) * (x \ T(x,y)) = K(x \ 1,x) / x. [para(1809(a,1),1922(a,2,2))]. 1924 R((x \ 1) / (x \ T(x,y)),x \ T(x,y),x) * (x \ T(x,y)) = x \ 1. [para(1923(a,2),159(a,1))]. 1925 R(T(x,y) \ 1,x \ T(x,y),x) * (x \ T(x,y)) = x \ 1. [para(1714(a,1),1924(a,1,1,1))]. 1926 R(x \ 1,x \ T(x,y),x) = x \ 1. [para(1925(a,1),1789(a,1)),flip(a)]. 1928 ((1 / x) * (x \ T(x,y))) * T(x,x \ T(x,y)) = (x * (x \ 1)) * (x \ T(x,y)). [para(1926(a,1),1890(a,1,1,2)),flip(a)]. 1929 ((1 / x) * (x \ T(x,y))) * T(x,x \ T(x,y)) = x \ T(x,y). [hyper(107,a,1928,a(flip)),flip(a)]. 1931 ((1 / x) * (x \ T(x,y))) * x = x \ T(x,y). [para(1652(a,1),1929(a,1,2))]. 1932 R(x \ T(x,y),x \ 1,x) = x \ T(x,y). [para(1931(a,1),1484(a,1)),flip(a)]. 1933 R((x * y) \ (x * T(y,z)),y \ 1,y) = L(y \ T(y,z),y,x). [para(1932(a,1),217(a,2,1))]. 1934 R((x * y) \ (y * x),y \ 1,y) = L(y \ T(y,x),y,x). [para(90(a,1),1933(a,1,1,2))]. 1935 R(K(x,y),x \ 1,x) = L(x \ T(x,y),x,y). [para(24(a,2),1934(a,1,1))]. 1936 R(K(x,y),x \ 1,x) = K(x,y). [para(1935(a,2),318(a,2)),flip(a)]. 1937 K(x,y) * (1 / x) = K(x,y) / x. [para(1936(a,1),1591(a,1,1)),flip(a)]. 1938 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(1068(a,1),1161(a,1,2,1)),flip(a)]. 1939 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(91(a,1),1938(a,2,2,2,1,1))]. 1940 (x \ (x * (y \ T(y,x)))) / (1 / (L(y,y \ 1,x) \ (L(y,y \ 1,x) * x))) = 1 / (1 / ((L(y,y \ 1,x) * x) / L(y,y \ 1,x))). [para(13(a,1),1853(a,1,1,1))]. 1941 (x \ T(x,y)) / (1 / (L(x,x \ 1,y) \ (L(x,x \ 1,y) * y))) = 1 / (1 / ((L(x,x \ 1,y) * y) / L(x,x \ 1,y))). [para(13(a,1),1940(a,1,1))]. 1942 1 / (1 / ((L(x,x \ 1,y) * y) / L(x,x \ 1,y))) = (x \ T(x,y)) / (1 / y). [para(13(a,1),1941(a,1,2,2)),flip(a)]. 1944 1 / (1 / (x * (y \ T(y,x)))) = (y \ T(y,x)) / (1 / x). [para(1779(a,1),1942(a,1,2,2))]. 1945 (x \ T(x,y)) / (1 / y) = 1 / ((T(x,y) \ x) / y). [para(1885(a,1),1944(a,1,2)),flip(a)]. 1946 1 / ((T(L(x \ 1,x,y) \ 1,y) \ (L(x \ 1,x,y) \ 1)) / y) = K(x,y) / (1 / y). [para(1678(a,2),1945(a,1,1)),flip(a)]. 1947 1 / ((K(x,y) \ 1) / y) = K(x,y) / (1 / y). [para(1738(a,1),1946(a,1,2,1))]. 1948 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(1531(a,1),861(a,1,1,2,2,1))]. 1949 ((((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),1948(a,1,1,2,2)),flip(a)]. 1951 ((((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(1529(a,1),1949(a,2,1,2))]. 1952 ((((x * y) \ z) \ (y \ (x \ z))) / (y \ (x \ z))) \ (((x * y) \ z) \ 1) = K(((x * y) \ z) \ 1,y \ (x \ z)). [para(860(a,1),1951(a,2,1))]. 1953 (1 / ((x * y) \ z)) \ (((x * y) \ z) \ 1) = K(((x * y) \ z) \ 1,y \ (x \ z)). [para(1531(a,1),1952(a,1,1))]. 1954 K(((x * y) \ z) \ 1,(x * y) \ z) = K(((x * y) \ z) \ 1,y \ (x \ z)). [para(1953(a,1),381(a,1)),flip(a)]. 1955 K(((x * y) \ z) \ 1,y \ (x \ z)) = K(z \ (x * y),(x * y) \ z). [para(1954(a,1),1834(a,1))]. 1956 x \ ((y * z) * K(x \ (y * z),(y * z) \ x)) = T(x \ (y * z),z \ (y \ x)). [para(1955(a,1),1867(a,1,2,2))]. 1957 T(x \ (y * z),z \ (y \ x)) = ((x \ (y * z)) \ 1) \ 1. [para(1956(a,1),1843(a,1))]. 1958 T(L(x,y,z),(y * x) \ (z \ (z * y))) = (((z * y) \ (z * (y * x))) \ 1) \ 1. [para(26(a,2),1957(a,1,1))]. 1959 T(L(x,y,z),(y * x) \ y) = (((z * y) \ (z * (y * x))) \ 1) \ 1. [para(13(a,1),1958(a,1,2,2))]. 1960 T(L(x,y,z),(y * x) \ y) = (L(x,y,z) \ 1) \ 1. [para(26(a,2),1959(a,2,1,1))]. 1961 L(T(x,(y * x) \ y),y,z) = (L(x,y,z) \ 1) \ 1. [para(1960(a,1),38(a,2))]. 1962 L(T(x,x \ 1),y,z) = (L(x,y,z) \ 1) \ 1. [para(1541(a,1),1961(a,1,1))]. 1963 L(T(x,x \ 1),y,z) \ L(x,y,z) = K(L(x,y,z) \ 1,L(x,y,z)). [para(1962(a,2),503(a,1,1))]. 1965 K(L(x,y,z) \ 1,L(x,y,z)) = K(x \ 1,L(x,y,z)). [para(1963(a,1),1727(a,1))]. 1966 L(K(x \ 1,x),y,z) = K(x \ 1,L(x,y,z)). [para(1965(a,1),1534(a,1)),flip(a)]. 1967 (x * K(y \ 1,L(y,z,u))) * w = L(K(y \ 1,y),z,u) * (x * w). [para(1966(a,1),1350(a,1,1,2))]. 1968 x * L(K(y \ 1,y),x,x \ 1) = x * K(y \ 1,y). [para(1966(a,2),1728(a,1,2))]. 1969 L(K(x \ 1,x),y,y \ 1) = K(x \ 1,x). [hyper(169,a,1968,a),flip(a)]. 1970 (1 / x) * (K(y \ 1,y) * x) = K(y \ 1,y). [para(1969(a,1),1193(a,2))]. 1971 R(1 / x,x,K(y \ 1,y)) = 1 / x. [hyper(720,a,1970,a)]. 1973 R(1 / (x \ 1),x \ 1,K(y \ 1,y)) = x. [para(1971(a,2),57(a,1))]. 1975 R(x,x \ 1,K(y \ 1,y)) = x. [para(57(a,1),1973(a,1,1))]. 1976 R(x,x \ 1,K(y,y \ 1)) = x. [para(1089(a,1),1975(a,1,3))]. 1977 (x \ 1) * K(y,y \ 1) = x \ K(y,y \ 1). [para(1976(a,1),183(a,1,1)),flip(a)]. 1978 (x \ 1) \ (K(y \ 1,y) * z) = (x \ K(y,y \ 1)) \ z. [para(1977(a,1),1352(a,1,1)),flip(a)]. 1979 (x * K(y \ 1,L(y,z,u))) * w = K(y \ 1,L(y,z,u)) * (x * w). [para(1966(a,1),1967(a,2,1))]. 1980 (K(x \ 1,L(x,y,z)) * (u * w)) / (u * w) = R(K(x \ 1,L(x,y,z)),u,w). [para(1979(a,1),1921(a,1,1))]. 1981 R(K(x \ 1,L(x,y,z)),u,w) = K(x \ 1,L(x,y,z)). [para(1980(a,1),15(a,1))]. 1982 K(x \ 1,L(x,y,z)) = K(x \ 1,x). [para(1981(a,1),1919(a,1))]. 1985 L(K(x \ 1,x),y,z) = K(x \ 1,x). [para(1982(a,1),1966(a,2))]. 1986 a(x,y,K(z \ 1,z)) = 1. [hyper(32,a,1985,a)]. 1987 K(x \ 1,x) * (y * z) = y * (K(x \ 1,x) * z). [para(1985(a,1),577(a,1,1))]. 1992 a(x,y,K(z,z \ 1)) = 1. [para(1089(a,1),1986(a,1,3))]. 1993 (x * (K(y,y \ 1) * z)) * 1 = (x * z) * K(y,y \ 1). [para(1992(a,1),447(a,1,2))]. 1994 x \ (K(y \ 1,y) * z) = K(y \ 1,y) * (x \ z). [hyper(286,a,1987,a)]. 1996 (x * y) \ (x * (K(z \ 1,z) * (y * u))) = L(K(z \ 1,z) * u,y,x). [para(1987(a,2),26(a,2,2,2)),flip(a)]. 1997 (x * y) * K(z \ 1,z) = x * (K(z \ 1,z) * y). [para(1987(a,1),390(a,1)),flip(a)]. 1999 x \ (K(y \ 1,y) * z) = (x \ z) * K(y \ 1,y). [para(1994(a,2),390(a,1))]. 2000 K(x \ 1,x) * ((y \ 1) \ z) = (y \ K(x,x \ 1)) \ z. [para(1994(a,1),1978(a,1))]. 2001 (x * K(y,y \ 1)) \ z = (x \ z) * K(y \ 1,y). [para(1999(a,1),1352(a,2))]. 2002 (x * y) * K(z,z \ 1) = x * (K(z,z \ 1) * y). [hyper(68,a,1993,a),flip(a)]. 2004 R(x,y,K(z,z \ 1)) = x. [hyper(449,a,2002,a)]. 2007 (x * (K(y,y \ 1) * z)) \ u = ((x * z) \ u) * K(y \ 1,y). [para(2002(a,1),2001(a,1,1))]. 2008 x \ (K(y,y \ 1) * z) = (x \ z) * K(y,y \ 1). [para(2004(a,1),448(a,1,1))]. 2009 R(x,y,K(z \ 1,z)) = x. [para(1068(a,1),2004(a,1,3))]. 2012 R(x,y,(z \ 1) \ 1) = R(x,y,z). [para(2004(a,1),1798(a,1)),flip(a)]. 2014 (x * y) \ ((x * (y * z)) * K(u \ 1,u)) = L(z,y,x) * K(u \ 1,u). [para(2009(a,1),253(a,1,1))]. 2016 R(x,y,K(z \ 1,R(z,u,w))) = x. [para(1066(a,2),2009(a,1,3))]. 2017 R(x,K(y \ 1,y),z) = x. [para(2009(a,1),1369(a,2))]. 2024 R(x,K(y,y \ 1),z) = x. [para(1089(a,1),2017(a,1,2))]. 2026 (x * ((K(y,y \ 1) * z) * u)) \ (((x * K(y,y \ 1)) * z) * u) = a(R(x,K(y,y \ 1),z),K(y,y \ 1) * z,u). [para(2024(a,1),227(a,1,1,1))]. 2028 ((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(2012(a,1),1814(a,2))]. 2029 T(x,y) * T(K(z \ 1,R(z,u,w)),x * y) = y \ ((x * K(z \ 1,z)) * y). [para(2016(a,1),1496(a,1,1)),flip(a)]. 2031 (x * y) \ (x * (K(z \ 1,z) * (y * u))) = L(u,y,x) * K(z \ 1,z). [para(1997(a,1),2014(a,1,2))]. 2032 L(K(x \ 1,x) * y,z,u) = L(y,z,u) * K(x \ 1,x). [para(2031(a,1),1996(a,1)),flip(a)]. 2033 L(K(x \ 1,x) * y,z,u) = K(x \ 1,x) * L(y,z,u). [para(2032(a,2),390(a,2)),flip(a)]. 2034 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(2033(a,2),1939(a,2,2))]. 2035 T(x,y) * T(K(z \ 1,R(z,u,w)),x * y) = T(x * K(z \ 1,z),y). [para(2029(a,2),30(a,2)),flip(a)]. 2036 T(x,y) * K(z \ 1,R(z,u,w)) = T(x * K(z \ 1,z),y). [para(1069(a,1),2035(a,1,2))]. 2037 T(x * K(y \ 1,y),z) = T(x,z) * K(y \ 1,y). [para(171(a,1),2036(a,1,2,2)),flip(a)]. 2039 T(K(x \ 1,x) * y,z) = T(y,z) * K(x \ 1,x). [para(390(a,2),2037(a,1,1))]. 2040 T(K(x \ 1,x) * y,z) = K(x \ 1,x) * T(y,z). [para(2039(a,2),390(a,2)),flip(a)]. 2041 K(x \ 1,x) * T(K(x,x \ 1) * y,z) = T(y,z). [para(1232(a,1),2040(a,1,1)),flip(a)]. 2043 (x \ T(x * (y / x),z)) * x = T(y,z). [para(2041(a,1),1236(a,1)),flip(a)]. 2044 (x \ T(x * y,z)) * x = T(y * x,z). [para(15(a,1),2043(a,1,1,2,1,2))]. 2046 T(x * y,z) / y = y \ T(y * x,z). [hyper(70,a,2044,a)]. 2047 R((x * y) / x,x,T(y,x)) = x \ T(x * y,y). [para(2046(a,1),682(a,2))]. 2048 L(x \ T(x * y,y),x,y) = (x * y) / x. [para(2047(a,1),719(a,1,1))]. 2049 (x * y) \ ((y * x) * x) = (y * x) / y. [para(2048(a,1),185(a,1)),flip(a)]. 2050 (x * (K(y,y \ 1) * (z * u))) \ (((x * K(y,y \ 1)) * z) * u) = a(R(x,K(y,y \ 1),z),K(y,y \ 1) * z,u). [para(1303(a,1),2026(a,1,1,2))]. 2051 (x * (K(y,y \ 1) * (z * u))) \ ((K(y,y \ 1) * (x * z)) * u) = a(R(x,K(y,y \ 1),z),K(y,y \ 1) * z,u). [para(1304(a,1),2050(a,1,2,1))]. 2052 (x * (K(y,y \ 1) * (z * u))) \ (K(y,y \ 1) * ((x * z) * u)) = a(R(x,K(y,y \ 1),z),K(y,y \ 1) * z,u). [para(1303(a,1),2051(a,1,2))]. 2053 ((x * (K(y,y \ 1) * (z * u))) \ ((x * z) * u)) * K(y,y \ 1) = a(R(x,K(y,y \ 1),z),K(y,y \ 1) * z,u). [para(2052(a,1),2008(a,1)),flip(a)]. 2054 (((x * (y * z)) \ ((x * y) * z)) * K(u \ 1,u)) * K(u,u \ 1) = a(R(x,K(u,u \ 1),y),K(u,u \ 1) * y,z). [para(2007(a,1),2053(a,1,1))]. 2055 a(R(x,K(y,y \ 1),z),K(y,y \ 1) * z,u) = (a(x,z,u) * K(y \ 1,y)) * K(y,y \ 1). [para(22(a,2),2054(a,1,1,1)),flip(a)]. 2056 a(R(x,K(y,y \ 1),z),K(y,y \ 1) * z,u) = a(x,z,u). [para(2055(a,2),1247(a,1))]. 2057 a(x,K(y,y \ 1) * z,u) = a(x,z,u). [para(2024(a,1),2056(a,1,1))]. 2059 a(x,R(1 / y,z,u),w) = a(x,R(y \ 1,z,u),w). [para(1144(a,1),2057(a,1,2))]. 2060 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(2000(a,1),2034(a,2,2,1))]. 2061 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(1122(a,1),2060(a,2,2,1,1))]. 2062 T(x \ L(x * ((((x \ 1) \ 1) * y) / ((x \ 1) \ 1)),z,u),(x \ 1) \ 1) = x \ L(x * y,z,u). [para(2061(a,2),632(a,1))]. 2063 T(x \ L(x * ((x * y) / x),z,u),(x \ 1) \ 1) = x \ L(x * y,z,u). [para(1775(a,1),2062(a,1,1,2,1,2))]. 2064 T(x \ L(x * ((x * y) / x),z,u),x) = x \ L(x * y,z,u). [para(2063(a,1),1567(a,1)),flip(a)]. 2065 T(x \ 1,x) * L(T(x \ 1,x) \ y,z,u) = x \ L(x * y,z,u). [para(2064(a,1),909(a,1)),flip(a)]. 2066 T((1 / x) \ 1,1 / x) * L(T((1 / x) \ 1,1 / x) \ y,z,u) = x * L(x \ y,z,u). [para(2065(a,2),476(a,1))]. 2067 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(2066(a,2),859(a,1))]. 2068 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),2067(a,1,1,1))]. 2070 (x \ 1) * L(T((1 / (1 / x)) \ 1,1 / (1 / x)) \ y,z,u) = L(y * x,z,u) / x. [para(1832(a,1),2068(a,1,1))]. 2071 (x \ 1) * L(T(1 / x,1 / (1 / x)) \ y,z,u) = L(y * x,z,u) / x. [para(59(a,1),2070(a,1,2,1,1,1))]. 2074 (x \ 1) * L((x \ 1) \ y,z,u) = L(y * x,z,u) / x. [para(1832(a,1),2071(a,1,2,1,1))]. 2075 L(x * y,z,u) / y = y \ L(y * x,z,u). [para(2074(a,1),632(a,1))]. 2077 (x \ L(x * y,z,u)) * x = L(y * x,z,u). [para(2075(a,1),16(a,1,1))]. 2078 L((x \ y) * x,z,u) = (x \ L(y,z,u)) * x. [para(14(a,1),2077(a,1,1,2,1)),flip(a)]. 2079 (x * (y \ z)) * L((z \ T(y,y \ z)) * z,y \ z,x) = (x * K(z \ y,z)) * z. [para(2078(a,2),1420(a,1,2))]. 2080 (x * y) * L((z \ (y \ ((z \ 1) \ 1))) * z,y,x) = (x * (y * T(y \ 1,z))) * ((z \ 1) \ 1). [para(2078(a,2),1887(a,1,2))]. 2081 x * ((y \ z) * ((z \ T(y,y \ z)) * z)) = (x * K(z \ y,z)) * z. [para(2079(a,1),79(a,1)),flip(a)]. 2082 (x * K(y \ z,y)) * y = x * (y * K(y \ z,y)). [para(1760(a,1),2081(a,1,2)),flip(a)]. 2083 x * (y * K(y \ (y * z),y)) = (x * K(z,y)) * y. [para(13(a,1),2082(a,1,1,2,1)),flip(a)]. 2084 (x * K(y,z)) * z = x * (z * K(y,z)). [para(13(a,1),2083(a,1,2,2,1)),flip(a)]. 2085 (x * y) / (y * K(z,y)) = x / K(z,y). [hyper(287,a,2084,a)]. 2086 (x * (y * T(y \ 1,z))) * ((z \ 1) \ 1) = x * (y * ((z \ (y \ ((z \ 1) \ 1))) * z)). [para(2080(a,1),79(a,1))]. 2087 (x * (y * T(y \ 1,z))) * ((z \ 1) \ 1) = x * ((z \ 1) \ (y * T(y \ 1,z))). [para(1815(a,1),2086(a,2,2))]. 2088 (x * ((y \ 1) \ (z * T(z \ 1,y)))) / ((y \ 1) \ (z * T(z \ 1,y))) = R(x,z * T(z \ 1,y),y). [para(2087(a,1),2028(a,1,1))]. 2089 R(x,y * T(y \ 1,z),z) = x. [para(2088(a,1),15(a,1))]. 2090 R(x,y \ T(y,z),z) = x. [para(524(a,1),2089(a,1,2))]. 2091 R(x,K(y,z),z) = x. [para(743(a,2),2089(a,1,2))]. 2092 (x * y) \ ((y * x) * x) = K(y,x) * x. [para(2091(a,1),251(a,1,1))]. 2093 T(x,y) * (x \ y) = y * (x \ T(x,y)). [para(2090(a,1),1765(a,1,2,1))]. 2094 (x * y) / x = K(x,y) * y. [para(2092(a,1),2049(a,1)),flip(a)]. 2095 K(x,y) = y \ ((x * y) / x). [hyper(1614,a,2094,a),flip(a)]. 2097 (x * y) / x = y * K(x,y). [para(2094(a,2),1755(a,1))]. 2098 L(K(x,y \ z),y \ z,y) = z \ (y * ((x * (y \ z)) / x)). [para(2095(a,2),214(a,1,1))]. 2099 T((((x * (y / z)) / x) * z) / y,y / z) = R(K(x,y / z),y / z,z). [para(2095(a,2),365(a,1,1)),flip(a)]. 2100 K(x \ (x / (x \ (x / y))),x) = K(y,x). [para(2095(a,2),658(a,2))]. 2101 x * T(x \ (((y * (x / z)) / y) * z),x / z) = (K(y,x / z) * (x / z)) * z. [para(2095(a,2),690(a,1,1,1)),flip(a)]. 2102 x * ((y * (x \ 1)) / y) = K(y,x \ 1). [para(2095(a,2),1610(a,1)),flip(a)]. 2104 (x * K(y,x)) * y = y * x. [para(2097(a,1),16(a,1,1))]. 2105 T(x * K(y,x),y) = x. [para(2097(a,1),112(a,1,1))]. 2106 L(x \ ((y * x) / y),x,y) = K(y,x * K(y,x)). [para(2097(a,1),224(a,2,2))]. 2107 R(x * K(y,x),y,K(x,y)) = (x * y) / (y * K(x,y)). [para(2097(a,1),243(a,1,1))]. 2108 (x \ y) * (((x \ y) \ y) * K(z,(x \ y) \ y)) = ((z * x) / z) * (x \ y). [para(2097(a,1),450(a,1,2))]. 2109 (x * y) / ((z * y) / z) = x / K(z,y). [para(2097(a,2),2085(a,1,2))]. 2110 ((x * K(y,x)) \ x) * R(T(x * K(y,x),y) \ 1,z,u) = R((x * K(y,x)) \ 1,z,u). [para(2105(a,1),1715(a,1,1,2))]. 2111 ((x * K(y,x)) \ x) * R(1 / T(x * K(y,x),y),z,u) = R(1 / (x * K(y,x)),z,u). [para(2105(a,1),1900(a,1,1,2))]. 2112 x \ ((x * y) / (y * K(x,y))) = K(y * K(x,y),x). [para(2104(a,1),2095(a,2,2,1)),flip(a)]. 2114 T(K(x,y) / (1 / y),x) = 1 / (1 / y). [para(2100(a,1),1858(a,1,1,1))]. 2115 (x * ((x / y) / x)) * y = x * K(x,y \ 1). [para(2102(a,1),852(a,1,2)),flip(a)]. 2116 x * (y * ((z * (y \ (x \ y))) / z)) = K(z,x \ 1) * y. [para(2102(a,1),850(a,2,1))]. 2117 x \ (y * ((z * (y \ x)) / z)) = K(z,(x \ y) \ 1). [para(2102(a,1),854(a,1)),flip(a)]. 2119 (x * ((y * (x \ z)) / y)) / z = K(y,(x / z) \ 1). [para(2102(a,1),892(a,1)),flip(a)]. 2120 T(x * ((y * (x \ 1)) / y),z) = K(y,T(x,z) \ 1). [para(2102(a,1),913(a,1)),flip(a)]. 2121 ((x * y) / ((x * y) / x)) * (x \ z) = x \ ((x / K(x,y)) * z). [para(2109(a,1),618(a,1,2,1)),flip(a)]. 2122 (x / ((y * z) / y)) * z = x / K(y,z). [para(2109(a,1),691(a,1)),flip(a)]. 2123 (x * ((y * z) / y)) / K(y,z) = x * z. [para(15(a,1),2122(a,1,1)),flip(a)]. 2124 (x * (y * K(z,y))) / K(z,y) = x * y. [para(2097(a,1),2123(a,1,1,2))]. 2125 (x * y) * K(z,y) = x * (y * K(z,y)). [para(2124(a,1),16(a,1,1))]. 2126 R(x,y,K(z,y)) = x. [hyper(226,a,2125,a)]. 2127 L(K(x,y),y,z) = K(x,y). [hyper(206,a,2125,a)]. 2128 x * ((x \ y) * K(z,x \ y)) = y * K(z,x \ y). [para(14(a,1),2125(a,1,1)),flip(a)]. 2129 T(x,y) * (x \ y) = y * K(T(x,y),y). [para(2126(a,1),1417(a,1,2,1))]. 2132 K(T(x,y),y) = x \ T(x,y). [hyper(17,a,2093,a(flip),b,2129,a(flip))]. 2133 K(x,y * K(x,y)) = L(K(x,y),y,x). [para(2095(a,2),2106(a,1,1)),flip(a)]. 2134 K(x,y * K(x,y)) = K(x,y). [para(2133(a,2),2127(a,1))]. 2136 K(x * K(y,x),y) = y \ (y / K(y,x)). [para(2085(a,1),2112(a,1,2)),flip(a)]. 2137 K(x,T(y,z) \ 1) = T(K(x,y \ 1),z). [para(2102(a,1),2120(a,1,1)),flip(a)]. 2138 R(x * K(y,x),y,K(x,y)) = x / K(x,y). [para(2107(a,2),2085(a,1))]. 2139 x / K(x,y) = x * K(y,x). [para(2138(a,1),2126(a,1))]. 2140 (x * K(y,x)) \ x = K(x,y). [para(2139(a,1),59(a,1,1))]. 2141 K(x * K(y,x),y) = y \ (y * K(x,y)). [para(2139(a,1),2136(a,2,2))]. 2142 L(K(x,y) \ z,(x * K(y,x)) \ x,x * K(y,x)) = x \ ((x * K(y,x)) * z). [para(2140(a,1),214(a,1,1,1))]. 2143 K(x,y) \ 1 = K(y,x). [para(2140(a,1),1886(a,1)),flip(a)]. 2144 K(x,y) = ((y * x) / y) \ x. [para(2097(a,2),2140(a,1,1)),flip(a)]. 2145 K(x,y) * K(y,x) = 1. [para(2143(a,1),14(a,1,2))]. 2146 1 / K(x,y) = K(y,x). [para(2143(a,1),57(a,1,2))]. 2147 K(K(x,y) \ 1,K(x,y)) = K(y,x) * K(x,y). [para(2143(a,1),126(a,2,1))]. 2148 a((K(x,y) \ (z * u)) / (z * u),z,u) = K(x,y) * R(K(y,x),z,u). [para(2143(a,1),920(a,2,2,1))]. 2149 K(x,y) / (1 / y) = 1 / (K(y,x) / y). [para(2143(a,1),1947(a,1,2,1)),flip(a)]. 2150 (K(x,y) \ 1) \ 1 = K(x,y). [para(2143(a,2),2143(a,1,1))]. 2155 ((x * y) / x) \ 1 = y \ K(y,x). [para(2144(a,2),621(a,1,2)),flip(a)]. 2156 K(x,y) / x = 1 / ((y * x) / y). [para(2144(a,2),1690(a,1,1))]. 2157 K(x,y) \ (1 / ((y * x) / y)) = 1 / x. [para(2144(a,2),1909(a,1,1))]. 2158 R(x \ T(x,y),z,u) = (K(y \ (y / R(1 / x,z,u)),y) \ 1) \ 1. [para(2150(a,2),1650(a,2))]. 2159 (x * K(y,x)) \ 1 = x \ K(x,y). [para(2097(a,1),2155(a,1,1))]. 2160 L(x \ y,x,K(x,z) / x) = K(x,z) \ ((1 / ((z * x) / z)) * y). [para(2156(a,1),215(a,2,2,1))]. 2161 1 / (x * K(y,x)) = K(x,y) / x. [para(2097(a,1),2156(a,2,2)),flip(a)]. 2162 (K(x,y) / x) \ 1 = x * K(y,x). [para(2161(a,1),59(a,1,1))]. 2163 K(x * K(y,x),y) = K(x,y). [para(2141(a,2),13(a,1))]. 2164 K((x * y) / x,x) = K(y,x). [para(2097(a,2),2163(a,1,1))]. 2166 K(T(x,y),y) = K(x,y). [para(113(a,1),2164(a,1,1)),flip(a)]. 2168 K(x,y) = x \ T(x,y). [para(2166(a,1),2132(a,1))]. 2169 T(x,y) = x * K(x,y). [para(2168(a,2),14(a,1,2)),flip(a)]. 2170 K(x,y) = T(x,y) * (x \ 1). [para(2168(a,2),520(a,2)),flip(a)]. 2171 T(x,y) * (x \ L(z,K(x,y),x)) = (x \ T(x,y)) * z. [para(2168(a,2),529(a,1,2,2,2))]. 2172 T(x \ 1,K(x,y)) = x \ 1. [para(2168(a,2),801(a,1,2))]. 2173 T(x,y) = K(x,y) * x. [para(2168(a,2),1640(a,1,1)),flip(a)]. 2174 x * T(x \ 1,y) = K(x \ 1,y). [para(2168(a,2),1646(a,1)),flip(a)]. 2183 K(x,y) * (x \ 1) = (x \ 1) * K(x,y). [para(2172(a,1),90(a,1,2))]. 2185 x * T(x \ y,z) = y * K((y \ x) \ 1,z). [para(2174(a,1),600(a,1,2)),flip(a)]. 2187 (x * T(x \ y,z)) / y = K((x / y) \ 1,z). [para(2174(a,1),692(a,1)),flip(a)]. 2190 T(x,K(x \ 1,y)) = x. [para(2174(a,1),799(a,1,2))]. 2194 T(1 / x,K(x,y)) = 1 / x. [para(59(a,1),2190(a,1,2,1))]. 2195 K(x,y) * (1 / x) = (1 / x) * K(x,y). [para(2194(a,1),90(a,1,2))]. 2196 T(1 / (K(x,y) / x),y) = 1 / (1 / x). [para(2149(a,1),2114(a,1,1))]. 2197 (1 / x) * K(x,y) = K(x,y) / x. [para(2195(a,1),1937(a,1))]. 2198 ((1 / x) * K(x,y)) \ K(x,y) = x. [para(2197(a,2),59(a,1,1))]. 2199 L(x,y,(((1 / z) \ 1) \ 1) * K(z,u)) = L(x,y,K(z,u) / z). [para(2197(a,1),1446(a,2,3))]. 2200 K(K(x,y) \ 1,K(x,y)) = 1. [para(2147(a,2),2145(a,1))]. 2204 T(x,y) * (x \ z) = z * K((z \ (x \ z)) \ 1,y). [para(2185(a,1),189(a,1)),flip(a)]. 2206 (x * K((x \ y) \ 1,z)) / x = K((y / x) \ 1,z). [para(2185(a,1),2187(a,1,1))]. 2207 T(x,y) * (x \ L(z,K(x,y),x)) = K(x,y) * z. [para(2168(a,2),2171(a,2,1))]. 2208 T(x,y) * (x \ L(z,K(x,y),x)) != K(x,y) * u | u = z. [para(2207(a,2),19(a,2)),flip(a)]. 2209 ((x * ((x / y) / x)) * y) * (x \ z) = x * (K(x,y \ 1) * (x \ z)). [para(2116(a,1),1451(a,1,2)),flip(a)]. 2210 L(K(x,y \ z),y \ z,y) = K(x,(z \ y) \ 1). [para(2098(a,2),2117(a,1))]. 2211 K(x,(y \ z) \ 1) = K(x,z \ y). [para(2210(a,1),2127(a,1))]. 2212 K(x,(y \ 1) \ 1) = K(x,y). [para(47(a,1),2211(a,2,2))]. 2213 K(x,T(((1 / y) * z) \ z,y \ 1)) = K(x,(z \ ((y \ 1) * z)) \ 1). [para(1343(a,2),2211(a,2,2)),flip(a)]. 2215 K(x,T(y \ z,u) \ 1) = T(K(x,z \ y),u). [para(2211(a,1),2137(a,2,1))]. 2216 K((x \ y) \ 1,z) = K(z,y \ x) \ 1. [para(2211(a,1),2143(a,1,1)),flip(a)]. 2217 K(x,1 / y) = K(x,y \ 1). [para(59(a,1),2212(a,1,2,1)),flip(a)]. 2218 K(x,T(y,y \ 1)) = K(x,y). [para(91(a,2),2212(a,1,2))]. 2219 K(x,T(y \ 1,y)) = K(x,y \ 1). [para(668(a,2),2212(a,1,2))]. 2220 K(x,R(y,y \ z,u)) = K(x,(z * u) / ((((y \ 1) \ 1) \ z) * u)). [para(1865(a,1),2212(a,1,2)),flip(a)]. 2221 K(x,T(y \ 1,z) \ 1) = T(K(x,y),z). [para(2212(a,1),2137(a,2,1))]. 2222 K(x,((1 / y) * z) \ z) = K(x,((y \ 1) * z) \ z). [para(1723(a,1),2218(a,1,2)),flip(a)]. 2223 K(x,T((y / z) \ 1,z \ y)) = K(x,(y / z) \ 1). [para(1676(a,1),2219(a,1,2))]. 2224 K((x \ y) \ 1,z) = K(y \ x,z). [para(2216(a,2),2143(a,1))]. 2226 T(x,y) * (x \ z) = z * K((x \ z) \ z,y). [para(2224(a,1),2204(a,2,2))]. 2227 (x * K(y \ x,z)) / x = K((y / x) \ 1,z). [para(2224(a,1),2206(a,1,1,2))]. 2228 K(x,T(T(y \ z,u),w) \ 1) = T(T(K(x,z \ y),u),w). [para(2215(a,1),2137(a,2,1))]. 2229 ((T(x,y) * (x \ z)) / z) \ K(K((x \ z) \ z,y) \ 1,K((x \ z) \ z,y)) = T(((z * K((x \ z) \ z,y)) / z) \ 1,K((x \ z) \ z,y)). [para(2226(a,2),700(a,1,1,1))]. 2230 x \ ((x / K(x,y)) * z) = (x / K(x,y)) * (x \ z). [para(2109(a,1),2121(a,1,1)),flip(a)]. 2231 x \ ((x * K(y,x)) * z) = (x / K(x,y)) * (x \ z). [para(2139(a,1),2230(a,1,2,1))]. 2232 x \ ((x * K(y,x)) * z) = (x * K(y,x)) * (x \ z). [para(2139(a,1),2231(a,2,1))]. 2233 L(x,y,(z \ 1) * K(z,u)) = L(x,y,K(z,u) / z). [para(59(a,1),2199(a,1,3,1,1))]. 2234 K(x,(1 * y) / (T(T(z,z \ 1) \ 1,(((z \ 1) \ 1) \ 1) \ 1) * y)) = K(x,R((z \ 1) \ 1,((z \ 1) \ 1) \ 1,y)). [para(579(a,2),2220(a,2,2,2,1)),flip(a)]. 2235 (R(T(x,y) / x,z,u) \ 1) \ 1 = R(x \ T(x,y),z,u). [para(1479(a,2),2158(a,2,1,1)),flip(a)]. 2236 R(x \ T(x,y),x,z) = (((T(x,y) * z) / (x * z)) \ 1) \ 1. [para(86(a,1),2235(a,1,1,1)),flip(a)]. 2237 R(T(x,y) / x,x,z) = (((T(x,y) * z) / (x * z)) \ 1) \ 1. [para(1638(a,2),2236(a,1,1))]. 2238 (((T(x,y) * z) / (x * z)) \ 1) \ 1 = (T(x,y) * z) / (x * z). [para(2237(a,1),86(a,1))]. 2239 (((T(x,y) * (x \ z)) / z) \ 1) \ 1 = (T(x,y) * (x \ z)) / (x * (x \ z)). [para(14(a,1),2238(a,1,1,1,2))]. 2240 ((x * ((x / (y \ 1)) / x)) * (y \ 1)) * (x \ z) = x * (K(x,y) * (x \ z)). [para(2212(a,1),2209(a,2,2,1))]. 2241 K(x,T(((1 / y) * z) \ z,y \ 1)) = K(x,T(y \ 1,z) \ 1). [para(30(a,2),2213(a,2,2,1))]. 2242 K(x,T(((1 / y) * z) \ z,y \ 1)) = T(K(x,y),z). [para(2241(a,2),2221(a,1))]. 2243 K(x,((y \ 1) * z) \ z) = T(K(x,y),z). [para(1343(a,1),2242(a,1,2))]. 2244 K(x,((1 / y) * z) \ z) = T(K(x,y),z). [para(2243(a,1),2222(a,2))]. 2245 T(K(x,y),K(y,z)) = K(x,y). [para(2198(a,1),2244(a,1,2)),flip(a)]. 2246 T(K(x,y),K(z,x)) = K(x,y). [hyper(33,a,2245,a)]. 2247 T((x * ((y * (x \ z)) / y)) / z,z / x) = R(K(y,z / x),z / x,x). [para(342(a,1),2099(a,1,1,1))]. 2248 T(K(x,(y / z) \ 1),z / y) = R(K(x,z / y),z / y,y). [para(2119(a,1),2247(a,1,1))]. 2249 R(K(x,y / z),y / z,z) = K(x,T(z / y,y / z) \ 1). [para(2248(a,1),2137(a,2)),flip(a)]. 2250 R(K(x,y / z),y / z,z) = K(x,T((z / y) \ 1,y \ z)). [para(1696(a,1),2249(a,2,2))]. 2251 R(K(x,y / z),y / z,z) = K(x,(z / y) \ 1). [para(2250(a,2),2223(a,1))]. 2252 ((x * y) / x) * (y \ z) = z * K(x,(y \ z) \ z). [para(2108(a,1),2128(a,1))]. 2253 (x * K(y,x)) * (x \ z) = z * K(y,(x \ z) \ z). [para(2097(a,1),2252(a,1,1))]. 2254 (((T(x,y) * (x \ z)) / z) \ 1) \ 1 = (T(x,y) * (x \ z)) / z. [para(14(a,1),2239(a,2,2))]. 2255 1 / ((T(x,y) * (x \ z)) / z) = ((T(x,y) * (x \ z)) / z) \ 1. [para(2254(a,1),57(a,1,2))]. 2256 (x * K(x,(y \ 1) \ 1)) * (x \ z) = x * (K(x,y) * (x \ z)). [para(2115(a,1),2240(a,1,1))]. 2257 (x * K(x,y)) * (x \ z) = x * (K(x,y) * (x \ z)). [para(2212(a,1),2256(a,1,1,2))]. 2258 x * (K(x,y) * (x \ z)) = T(x,y) * (x \ z). [para(2169(a,2),2257(a,1,1)),flip(a)]. 2259 T(x,y) * (x \ (x * z)) = x * (K(x,y) * z). [para(13(a,1),2258(a,1,2,2)),flip(a)]. 2260 x * (K(x,y) * z) = T(x,y) * z. [para(13(a,1),2259(a,1,2)),flip(a)]. 2262 x \ (T(x,y) * z) = K(x,y) * z. [hyper(66,a,2260,a)]. 2265 T(x,y) * (x \ z) = K(x,y) * z. [hyper(17,a,516,a,b,2260,a),flip(a)]. 2270 K(x,y) * (x \ 1) = x \ K(x,y). [para(2170(a,2),2262(a,1,2)),flip(a)]. 2271 L(x,K(y,z),y) = x. [hyper(2208,a,2265,a)]. 2277 L(x,K(y,z),y * K(z,y)) = x. [para(2163(a,1),2271(a,1,2))]. 2278 (x \ 1) * K(x,y) = x \ K(x,y). [para(2270(a,1),2183(a,1)),flip(a)]. 2279 L(x,y,K(z,u) / z) = L(x,y,z \ K(z,u)). [para(2278(a,1),2233(a,1,3)),flip(a)]. 2280 L(x \ y,x,x \ K(x,z)) = K(x,z) \ ((K(x,z) / x) * y). [para(2279(a,1),215(a,1))]. 2281 L(x \ y,x,x \ K(x,z)) = K(x,z) \ ((1 / ((z * x) / z)) * y). [para(2279(a,1),2160(a,1))]. 2282 K(x,y) * (z * R(z \ L(x \ z,x,x \ K(x,y)),u,w)) = (K(x,y) * R(K(x,y) \ (1 / ((y * x) / y)),u,w)) * z. [para(2281(a,2),761(a,1,2,2,1,2))]. 2283 L(K(x,y) \ z,K(x,y),x * K(y,x)) = x \ ((x * K(y,x)) * z). [para(2140(a,1),2142(a,1,2))]. 2284 L(K(x,y) \ z,K(x,y),x * K(y,x)) = (x * K(y,x)) * (x \ z). [para(2283(a,2),2232(a,1))]. 2285 (x * K(y,x)) * (x \ z) = K(x,y) \ z. [para(2284(a,1),2277(a,1))]. 2286 x * K(y,(z \ x) \ x) = K(z,y) \ x. [para(2285(a,1),2253(a,1)),flip(a)]. 2287 x * T(x \ (((y * (x / z)) / y) * z),x / z) = ((x / z) * K(y,x / z)) * z. [para(1755(a,1),2101(a,2,1))]. 2288 x * T(x \ (y * ((z * (y \ x)) / z)),x / y) = ((x / y) * K(z,x / y)) * y. [para(342(a,1),2287(a,1,2,1,2))]. 2289 ((x / y) * K(z,x / y)) * y = x * T(K(z,(x \ y) \ 1),x / y). [para(2117(a,1),2288(a,1,2,1)),flip(a)]. 2290 ((x / y) * K(z,x / y)) * y = x * K(z,T(x \ y,x / y) \ 1). [para(2137(a,2),2289(a,2,2))]. 2291 ((x / y) * K(z,x / y)) * y = x * K(z,T(x \ y,y \ x) \ 1). [para(1546(a,1),2290(a,2,2,2,1))]. 2292 ((x / y) * K(z,x / y)) * y = x * K(z,T((x \ y) \ 1,x \ y)). [para(1545(a,1),2291(a,2,2,2))]. 2293 ((x / y) * K(z,x / y)) * y = x * K(z,(x \ y) \ 1). [para(2219(a,1),2292(a,2,2))]. 2294 R(K(x,y / z),y / z,z) = (y * K(x,(y \ z) \ 1)) / y. [para(2293(a,1),1759(a,1,1)),flip(a)]. 2295 (x * K(y,(x \ z) \ 1)) / x = K(y,(z / x) \ 1). [para(2294(a,1),2251(a,1))]. 2296 (x * K(y,z \ x)) / x = K(y,(z / x) \ 1). [para(2211(a,1),2295(a,1,1,2))]. 2297 K(x,((y \ z) / z) \ 1) = (K(y,x) \ z) / z. [para(2286(a,1),2296(a,1,1)),flip(a)]. 2298 K(x,y) * R(T(x * K(y,x),y) \ 1,z,u) = R((x * K(y,x)) \ 1,z,u). [para(2140(a,1),2110(a,1,1))]. 2299 R((x * K(y,x)) \ 1,z,u) = K(x,y) * R(x \ 1,z,u). [para(2105(a,1),2298(a,1,2,1,1)),flip(a)]. 2300 K(x,y) * R(x \ 1,z,u) = R(x \ K(x,y),z,u). [para(2159(a,1),2299(a,1,1)),flip(a)]. 2301 (R(x \ K(x,y),z,u) * w) / (R(x \ 1,z,u) * w) = R(K(x,y),R(x \ 1,z,u),w). [para(2300(a,1),28(a,2,1,1)),flip(a)]. 2302 (R(x \ K(x,y),z,u) * w) / ((R(x \ 1,z,u) * w) * a(K(x,y),R(x \ 1,z,u),w)) = R(K(x,y),R(x \ 1,z,u) * w,a(K(x,y),R(x \ 1,z,u),w)). [para(2300(a,1),292(a,1,1,1))]. 2303 (R(x \ K(x,y),(x \ 1) \ z,u) * (((x \ 1) \ z) * u)) / (z * u) = R(K(x,y),R(x \ 1,(x \ 1) \ z,u),((x \ 1) \ z) * u). [para(2300(a,1),783(a,1,1,1))]. 2304 K(x,y) * R(1 / T(x * K(y,x),y),z,u) = R(1 / (x * K(y,x)),z,u). [para(2140(a,1),2111(a,1,1))]. 2305 R(1 / (x * K(y,x)),z,u) = K(x,y) * R(1 / x,z,u). [para(2105(a,1),2304(a,1,2,1,2)),flip(a)]. 2306 K(x,y) * R(1 / x,z,u) = R(K(x,y) / x,z,u). [para(2161(a,1),2305(a,1,1)),flip(a)]. 2307 (R(K(x,y) / x,z,u) * w) / (K(x,y) * (R(1 / x,z,u) * w)) = a(K(x,y),R(1 / x,z,u),w). [para(2306(a,1),295(a,2,1,1)),flip(a)]. 2308 (R(K(x,y) / x,z,u) * w) / (K(x,y) * (R(1 / x,z,u) * w)) = a(K(x,y),R(x \ 1,z,u),w). [para(2307(a,2),2059(a,1))]. 2309 K(x,(1 * y) / (T(T(z \ 1,z),(((z \ 1) \ 1) \ 1) \ 1) * y)) = K(x,R((z \ 1) \ 1,((z \ 1) \ 1) \ 1,y)). [para(670(a,1),2234(a,1,2,2,1,1))]. 2310 K(x,(1 * y) / (T(T(z \ 1,z),(((z \ 1) \ 1) \ 1) \ 1) * y)) = K(x,R((z \ 1) \ 1,z \ 1,y)). [para(1297(a,1),2309(a,2,2))]. 2311 K(x,y) * (z * R(z \ L(x \ z,x,x \ K(x,y)),u,w)) = (K(x,y) * R(1 / x,u,w)) * z. [para(2157(a,1),2282(a,2,1,2,1))]. 2313 K(x,y) * (z * R(z \ L(x \ z,x,x \ K(x,y)),u,w)) = R(K(x,y) / x,u,w) * z. [para(2306(a,1),2311(a,2,1))]. 2314 R(K(x,y),R(x \ 1,(x \ 1) \ z,u),((x \ 1) \ z) * u) = (((x \ K(x,y)) * ((x \ 1) \ z)) * u) / (z * u). [para(85(a,1),2303(a,1,1)),flip(a)]. 2315 T(((x * K((y \ x) \ x,z)) / x) \ 1,K((y \ x) \ x,z)) = ((T(y,z) * (y \ x)) / x) \ 1. [para(2200(a,1),2229(a,1,2)),flip(a)]. 2317 T(K(((x \ y) / y) \ 1,z) \ 1,K((x \ y) \ y,z)) = ((T(x,z) * (x \ y)) / y) \ 1. [para(2227(a,1),2315(a,1,1,1))]. 2318 T(K(x,((y \ z) / z) \ 1),K((y \ z) \ z,x)) = ((T(y,x) * (y \ z)) / z) \ 1. [para(2143(a,1),2317(a,1,1))]. 2319 ((T(x,y) * (x \ z)) / z) \ 1 = K(y,((x \ z) / z) \ 1). [para(2318(a,1),2246(a,1))]. 2321 1 / ((T(x,y) * (x \ z)) / z) = K(y,((x \ z) / z) \ 1). [para(2319(a,1),2255(a,2))]. 2322 1 / ((K(x,y) * z) / z) = K(y,((x \ z) / z) \ 1). [para(2265(a,1),2321(a,1,2,1))]. 2323 K(x,((y \ z) / z) \ 1) = 1 / K(y,x). [para(15(a,1),2322(a,1,2)),flip(a)]. 2325 K(x,((y \ z) / z) \ 1) = K(x,y). [para(2323(a,2),2146(a,1))]. 2326 K(x,(y / z) \ 1) = K(x,z / y). [para(59(a,1),2325(a,1,2,1,1))]. 2328 (K(x,y) \ z) / z = K(y,x). [para(2325(a,1),2297(a,1)),flip(a)]. 2329 x / (K(y,z) * x) = K(z,y). [para(13(a,1),2328(a,1,1))]. 2330 K(x,y) \ z = K(y,x) * z. [para(2328(a,1),16(a,1,1)),flip(a)]. 2331 K(x,y) * R(K(y,x),z,u) = a(K(y,x),z,u). [para(2328(a,1),2148(a,1,1)),flip(a)]. 2334 K(x,y) = y / T(y,x). [para(2173(a,2),2329(a,1,2)),flip(a)]. 2336 K(x,y) = (1 / T(y,x)) * y. [para(2334(a,2),672(a,2)),flip(a)]. 2337 K(x,y) = T(y,x) \ y. [para(2334(a,2),1619(a,1))]. 2341 (x \ 1) * K(y,x) = T(x,y) \ 1. [para(2337(a,2),1707(a,1,2))]. 2342 (x / (y * x)) * K(z,y) = R(1 / T(y,z),y,x). [para(2337(a,2),1742(a,1,2))]. 2343 L(x \ y,x,x \ K(x,z)) = K(z,x) * ((K(x,z) / x) * y). [para(2330(a,1),2280(a,2))]. 2344 K(x,y / (z * y)) = K(x,z \ 1). [para(15(a,1),2326(a,1,2,1)),flip(a)]. 2347 ((((x \ 1) * y) / (R(x,x \ 1,y) * ((x \ 1) * y))) * K(z,R(x,x \ 1,y))) * y = ((1 / T(R(x,x \ 1,y),z)) * R(x,x \ 1,y)) * ((x \ 1) * y). [para(2342(a,2),784(a,1,1))]. 2348 ((((x \ 1) * y) / ((x * (x \ 1)) * y)) * K(z,R(x,x \ 1,y))) * y = ((1 / T(R(x,x \ 1,y),z)) * R(x,x \ 1,y)) * ((x \ 1) * y). [para(85(a,1),2347(a,1,1,1,2))]. 2349 ((((x \ 1) * y) / y) * K(z,R(x,x \ 1,y))) * y = ((1 / T(R(x,x \ 1,y),z)) * R(x,x \ 1,y)) * ((x \ 1) * y). [para(49(a,1),2348(a,1,1,1,2))]. 2350 ((1 / T(R(x,x \ 1,y),z)) * R(x,x \ 1,y)) * ((x \ 1) * y) = ((x \ 1) * K(z,R(x,x \ 1,y))) * y. [para(15(a,1),2349(a,1,1,1)),flip(a)]. 2352 ((x \ 1) * K(y,R(x,x \ 1,z))) * z = K(y,R(x,x \ 1,z)) * ((x \ 1) * z). [para(2336(a,2),2350(a,1,1)),flip(a)]. 2353 (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(1404(a,1),1376(a,1,1,3)),flip(a)]. 2354 (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(171(a,1),2353(a,2,1))]. 2357 (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(967(a,1),2354(a,1,1,2,1))]. 2358 (K(x \ 1,x) * (R(x,y,z) \ u)) * 1 = R((x \ 1) \ 1,y,z) \ u. [para(1404(a,1),2357(a,1,2))]. 2359 K(x \ 1,x) * (R(x,y,z) \ u) = R((x \ 1) \ 1,y,z) \ u. [hyper(68,a,2358,a)]. 2361 (R(x,y,z) \ u) * K(x \ 1,x) = R((x \ 1) \ 1,y,z) \ u. [para(2359(a,1),390(a,1)),flip(a)]. 2362 1 / (R((x \ 1) \ 1,y,z) \ 1) = (R(x,y,z) \ 1) \ 1. [para(2361(a,1),1431(a,1,2))]. 2363 R((x \ 1) \ 1,y,z) = (R(x,y,z) \ 1) \ 1. [para(2362(a,1),57(a,1)),flip(a)]. 2364 K(x,R((y \ 1) \ 1,z,u)) = K(x,R(y,z,u)). [para(2363(a,2),2212(a,1,2))]. 2365 K(x,(1 * y) / (T(T(z \ 1,z),(((z \ 1) \ 1) \ 1) \ 1) * y)) = K(x,R(z,z \ 1,y)). [para(2364(a,1),2310(a,2))]. 2366 K(x,y / (T(T(z \ 1,z),(((z \ 1) \ 1) \ 1) \ 1) * y)) = K(x,R(z,z \ 1,y)). [para(11(a,1),2365(a,1,2,1))]. 2367 K(x,y / (T(T(z \ 1,z),(z \ 1) \ 1) * y)) = K(x,R(z,z \ 1,y)). [para(1567(a,1),2366(a,1,2,2,1))]. 2368 K(x,y / (T(T(z \ 1,z),z) * y)) = K(x,R(z,z \ 1,y)). [para(1567(a,1),2367(a,1,2,2,1))]. 2369 K(x,R(y,y \ 1,z)) = K(x,T(T(y \ 1,y),y) \ 1). [para(2368(a,1),2344(a,1))]. 2370 T(T(K(x,1 \ y),y),y) = K(x,R(y,y \ 1,z)). [para(2369(a,2),2228(a,1)),flip(a)]. 2372 T(T(K(x,y),y),y) = K(x,R(y,y \ 1,z)). [para(47(a,1),2370(a,1,1,1,2))]. 2373 K(x,R(y,y \ 1,z)) = T(K(x,y),y). [para(1754(a,1),2372(a,1,1)),flip(a)]. 2374 K(x,R(y,y \ 1,z)) = K(x,y). [para(2373(a,2),1754(a,1))]. 2375 K(x,R(y,y \ 1,z)) * ((y \ 1) * z) = ((y \ 1) * K(x,y)) * z. [para(2374(a,1),2352(a,1,1,2)),flip(a)]. 2376 K(x,R(y,y \ 1,z)) * ((y \ 1) * z) = (T(y,x) \ 1) * z. [para(2341(a,1),2375(a,2,1))]. 2378 K(x,y) * ((y \ 1) * z) = (T(y,x) \ 1) * z. [para(2374(a,1),2376(a,1,1))]. 2379 K(x,1 / (K(y,x) / y)) * (((1 / (K(y,x) / y)) \ 1) * z) = ((1 / (1 / y)) \ 1) * z. [para(2196(a,1),2378(a,2,1,1))]. 2381 K(x,(K(y,x) / y) \ 1) * (((1 / (K(y,x) / y)) \ 1) * z) = ((1 / (1 / y)) \ 1) * z. [para(2217(a,1),2379(a,1,1))]. 2382 K(x,y * K(x,y)) * (((1 / (K(y,x) / y)) \ 1) * z) = ((1 / (1 / y)) \ 1) * z. [para(2162(a,1),2381(a,1,1,2))]. 2383 K(x,y) * (((1 / (K(y,x) / y)) \ 1) * z) = ((1 / (1 / y)) \ 1) * z. [para(2134(a,1),2382(a,1,1))]. 2384 K(x,y) * ((K(y,x) / y) * z) = ((1 / (1 / y)) \ 1) * z. [para(59(a,1),2383(a,1,2,1))]. 2385 K(x,y) * ((K(y,x) / y) * z) = (1 / y) * z. [para(59(a,1),2384(a,2,1))]. 2388 L(x \ y,x,x \ K(x,z)) = (1 / x) * y. [para(2385(a,1),2343(a,2))]. 2389 K(x,y) * (z * R(z \ ((1 / x) * z),u,w)) = R(K(x,y) / x,u,w) * z. [para(2388(a,1),2313(a,1,2,2,1,2))]. 2391 K(x,y) * (z * R(T(1 / x,z),u,w)) = R(K(x,y) / x,u,w) * z. [para(30(a,2),2389(a,1,2,2,1))]. 2393 K(x,y) * (R(1 / x,z,u) * w) = R(K(x,y) / x,z,u) * w. [para(124(a,1),2391(a,1,2))]. 2394 (R(K(x,y) / x,z,u) * w) / (R(K(x,y) / x,z,u) * w) = a(K(x,y),R(x \ 1,z,u),w). [para(2393(a,1),2308(a,1,2))]. 2395 a(K(x,y),R(x \ 1,z,u),w) = 1. [para(2394(a,1),54(a,1))]. 2397 R(K(x,y),R(x \ 1,z,u) * w,a(K(x,y),R(x \ 1,z,u),w)) = (R(x \ K(x,y),z,u) * w) / ((R(x \ 1,z,u) * w) * 1). [para(2395(a,1),2302(a,1,2,2)),flip(a)]. 2398 R(K(x,y),R(x \ 1,z,u) * w,a(K(x,y),R(x \ 1,z,u),w)) = (R(x \ K(x,y),z,u) * w) / (R(x \ 1,z,u) * w). [para(12(a,1),2397(a,2,2))]. 2400 R(K(x,y),R(x \ 1,z,u) * w,a(K(x,y),R(x \ 1,z,u),w)) = R(K(x,y),R(x \ 1,z,u),w). [para(2398(a,2),2301(a,1))]. 2401 R(K(x,y),R(x \ 1,z,u) * w,1) = R(K(x,y),R(x \ 1,z,u),w). [para(2395(a,1),2400(a,1,3))]. 2402 R(K(x,y),R(x \ 1,z,u),w) = K(x,y). [para(2401(a,1),171(a,1))]. 2404 R(K(x,y),x \ 1,z) = K(x,y). [para(171(a,1),2402(a,1,2))]. 2405 (((x \ K(x,y)) * ((x \ 1) \ z)) * u) / (z * u) = K(x,y). [para(2402(a,1),2314(a,1)),flip(a)]. 2406 (K(x,y) * (x \ 1)) * ((x \ 1) \ z) = K(x,y) * z. [para(2404(a,1),167(a,1,1)),flip(a)]. 2408 (x \ K(x,y)) * ((x \ 1) \ z) = K(x,y) * z. [para(2270(a,1),2406(a,1,1))]. 2409 K(x,y) * ((((y \ K(y,x)) * ((y \ 1) \ z)) * u) / (z * u)) = 1. [para(2405(a,2),2145(a,1,2))]. 2411 K(x,y) * (((K(y,x) * z) * u) / (z * u)) = 1. [para(2408(a,1),2409(a,1,2,1,1))]. 2412 K(x,y) * R(K(y,x),z,u) = 1. [para(28(a,2),2411(a,1,2))]. 2416 a(K(x,y),z,u) = 1. [para(2412(a,1),2331(a,1)),flip(a)]. 2417 $F # answer("aK1"). [resolve(2416,a,46,a)]. ============================== end of proof ==========================