A certified basis of 2 identities

This list of identities is a basis, proved in Lean, of 170 semigroups of order six, all of which generate the variety V[2]. Removing the identities that follow from the others leaves 2 identities (Vampire); the variety page shows the shortest known basis.

Identifier sb-6a1c48ba69f61a96 in the data of the bases-min seal.

Certified for

[6, 2] [6, 3] [6, 4] [6, 5] [6, 7] [6, 8] [6, 9] [6, 10] [6, 11] [6, 12] [6, 13] [6, 14] [6, 15] [6, 16] [6, 17] [6, 18] [6, 19] [6, 20] [6, 21] [6, 22] [6, 23] [6, 24] [6, 25] [6, 26] [6, 27] [6, 28] [6, 29] [6, 30] [6, 31] [6, 32] [6, 33] [6, 34] [6, 36] [6, 37] [6, 38] [6, 39] [6, 41] [6, 43] [6, 44] [6, 45] [6, 46] [6, 47] [6, 48] [6, 49] [6, 50] [6, 51] [6, 52] [6, 53] [6, 54] [6, 55] [6, 56] [6, 57] [6, 58] [6, 59] [6, 60] [6, 61] [6, 62] [6, 63] [6, 64] [6, 65] [6, 66] [6, 67] [6, 68] [6, 69] [6, 70] [6, 71] [6, 72] [6, 73] [6, 74] [6, 75] [6, 76] [6, 77] [6, 78] [6, 79] [6, 80] [6, 81] [6, 82] [6, 83] [6, 84] [6, 85] [6, 86] [6, 88] [6, 89] [6, 90] [6, 91] [6, 92] [6, 94] [6, 95] [6, 96] [6, 97] [6, 98] [6, 99] [6, 100] [6, 101] [6, 102] [6, 103] [6, 104] [6, 105] [6, 106] [6, 107] [6, 108] [6, 109] [6, 110] [6, 111] [6, 112] [6, 113] [6, 114] [6, 115] [6, 116] [6, 117] [6, 119] [6, 120] [6, 121] [6, 122] [6, 123] [6, 124] [6, 125] [6, 126] [6, 127] [6, 129] [6, 130] [6, 132] [6, 133] [6, 134] [6, 135] [6, 136] [6, 137] [6, 138] [6, 139] [6, 140] [6, 142] [6, 143] [6, 144] [6, 146] [6, 147] [6, 148] [6, 149] [6, 150] [6, 151] [6, 152] [6, 153] [6, 154] [6, 155] [6, 156] [6, 157] [6, 158] [6, 159] [6, 160] [6, 161] [6, 162] [6, 163] [6, 164] [6, 165] [6, 166] [6, 167] [6, 168] [6, 169] [6, 170] [6, 171] [6, 172] [6, 173] [6, 174] [6, 175] [6, 177] [6, 179] [6, 180] [6, 181] [6, 182] [6, 183] [6, 184]

The identities

x² ≈ y²
x² ≈ xyz