[
  {
    "id": "true_2739_2736",
    "eq1_id": 2739,
    "eq2_id": 2736,
    "equation1": "x = ((y ◇ y) ◇ (x ◇ z)) ◇ x",
    "equation2": "x = ((y ◇ y) ◇ (x ◇ y)) ◇ x",
    "answer": true
  },
  {
    "id": "true_3268_3253",
    "eq1_id": 3268,
    "eq2_id": 3253,
    "equation1": "x ◇ x = y ◇ (x ◇ (x ◇ x))",
    "equation2": "x ◇ x = x ◇ (x ◇ (x ◇ x))",
    "answer": true
  },
  {
    "id": "false_1876_1895",
    "eq1_id": 1876,
    "eq2_id": 1895,
    "equation1": "x = (x ◇ (y ◇ z)) ◇ (z ◇ y)",
    "equation2": "x = (y ◇ (x ◇ y)) ◇ (x ◇ y)",
    "answer": false
  },
  {
    "id": "false_4084_3555",
    "eq1_id": 4084,
    "eq2_id": 3555,
    "equation1": "x ◇ x = ((y ◇ x) ◇ y) ◇ y",
    "equation2": "x ◇ y = y ◇ ((y ◇ x) ◇ x)",
    "answer": false
  },
  {
    "id": "false_2699_3474",
    "eq1_id": 2699,
    "eq2_id": 3474,
    "equation1": "x = ((y ◇ x) ◇ (x ◇ y)) ◇ x",
    "equation2": "x ◇ x = y ◇ ((x ◇ y) ◇ x)",
    "answer": false
  },
  {
    "id": "false_430_2263",
    "eq1_id": 430,
    "eq2_id": 2263,
    "equation1": "x = x ◇ (y ◇ (x ◇ (y ◇ y)))",
    "equation2": "x = (x ◇ (y ◇ (y ◇ x))) ◇ x",
    "answer": false
  },
  {
    "id": "false_2327_4629",
    "eq1_id": 2327,
    "eq2_id": 4629,
    "equation1": "x = (y ◇ (y ◇ (x ◇ x))) ◇ x",
    "equation2": "(x ◇ y) ◇ x = (x ◇ y) ◇ y",
    "answer": false
  },
  {
    "id": "false_3068_4074",
    "eq1_id": 3068,
    "eq2_id": 4074,
    "equation1": "x = (((x ◇ y) ◇ x) ◇ y) ◇ x",
    "equation2": "x ◇ x = ((x ◇ y) ◇ y) ◇ y",
    "answer": false
  },
  {
    "id": "false_3917_4118",
    "eq1_id": 3917,
    "eq2_id": 4118,
    "equation1": "x ◇ y = (x ◇ (x ◇ y)) ◇ x",
    "equation2": "x ◇ y = ((x ◇ x) ◇ x) ◇ y",
    "answer": false
  },
  {
    "id": "false_2917_28",
    "eq1_id": 2917,
    "eq2_id": 28,
    "equation1": "x = ((y ◇ (x ◇ y)) ◇ z) ◇ z",
    "equation2": "x = (y ◇ x) ◇ x",
    "answer": false
  },
  {
    "id": "true_2942_5",
    "eq1_id": 2942,
    "eq2_id": 5,
    "equation1": "x = ((y ◇ (y ◇ x)) ◇ z) ◇ x",
    "equation2": "x = y ◇ x",
    "answer": true
  },
  {
    "id": "true_3108_4642",
    "eq1_id": 3108,
    "eq2_id": 4642,
    "equation1": "x = (((y ◇ x) ◇ x) ◇ z) ◇ x",
    "equation2": "(x ◇ y) ◇ x = (z ◇ x) ◇ x",
    "answer": true
  },
  {
    "id": "true_193_191",
    "eq1_id": 193,
    "eq2_id": 191,
    "equation1": "x = (y ◇ z) ◇ (y ◇ w)",
    "equation2": "x = (y ◇ z) ◇ (y ◇ y)",
    "answer": true
  },
  {
    "id": "true_4238_4230",
    "eq1_id": 4238,
    "eq2_id": 4230,
    "equation1": "x ◇ y = ((z ◇ z) ◇ w) ◇ y",
    "equation2": "x ◇ y = ((z ◇ z) ◇ y) ◇ y",
    "answer": true
  },
  {
    "id": "false_1865_1454",
    "eq1_id": 1865,
    "eq2_id": 1454,
    "equation1": "x = (x ◇ (y ◇ y)) ◇ (z ◇ z)",
    "equation2": "x = (x ◇ y) ◇ (y ◇ (y ◇ x))",
    "answer": false
  },
  {
    "id": "false_203_2673",
    "eq1_id": 203,
    "eq2_id": 2673,
    "equation1": "x = (x ◇ (x ◇ x)) ◇ x",
    "equation2": "x = ((x ◇ y) ◇ (y ◇ y)) ◇ y",
    "answer": false
  },
  {
    "id": "true_1167_2000",
    "eq1_id": 1167,
    "eq2_id": 2000,
    "equation1": "x = y ◇ ((z ◇ (y ◇ y)) ◇ x)",
    "equation2": "x = (y ◇ (z ◇ z)) ◇ (z ◇ x)",
    "answer": true
  },
  {
    "id": "false_619_1322",
    "eq1_id": 619,
    "eq2_id": 1322,
    "equation1": "x = x ◇ (x ◇ ((y ◇ x) ◇ x))",
    "equation2": "x = y ◇ (((y ◇ y) ◇ x) ◇ x)",
    "answer": false
  },
  {
    "id": "false_825_167",
    "eq1_id": 825,
    "eq2_id": 167,
    "equation1": "x = x ◇ ((x ◇ y) ◇ (y ◇ x))",
    "equation2": "x = (y ◇ x) ◇ (x ◇ y)",
    "answer": false
  },
  {
    "id": "false_1922_125",
    "eq1_id": 1922,
    "eq2_id": 125,
    "equation1": "x = (y ◇ (y ◇ x)) ◇ (x ◇ y)",
    "equation2": "x = y ◇ ((y ◇ x) ◇ y)",
    "answer": false
  },
  {
    "id": "false_4157_39",
    "eq1_id": 4157,
    "eq2_id": 39,
    "equation1": "x ◇ y = ((y ◇ x) ◇ y) ◇ x",
    "equation2": "x ◇ x = y ◇ x",
    "answer": false
  },
  {
    "id": "true_3291_3304",
    "eq1_id": 3291,
    "eq2_id": 3304,
    "equation1": "x ◇ x = y ◇ (z ◇ (x ◇ w))",
    "equation2": "x ◇ x = y ◇ (z ◇ (w ◇ u))",
    "answer": true
  },
  {
    "id": "true_1698_555",
    "eq1_id": 1698,
    "eq2_id": 555,
    "equation1": "x = (y ◇ x) ◇ ((y ◇ z) ◇ y)",
    "equation2": "x = y ◇ (z ◇ (y ◇ (x ◇ y)))",
    "answer": true
  },
  {
    "id": "false_731_2663",
    "eq1_id": 731,
    "eq2_id": 2663,
    "equation1": "x = y ◇ (y ◇ ((z ◇ z) ◇ x))",
    "equation2": "x = ((x ◇ y) ◇ (x ◇ y)) ◇ y",
    "answer": false
  },
  {
    "id": "false_1232_73",
    "eq1_id": 1232,
    "eq2_id": 73,
    "equation1": "x = x ◇ (((x ◇ y) ◇ y) ◇ y)",
    "equation2": "x = y ◇ (y ◇ (x ◇ y))",
    "answer": false
  },
  {
    "id": "false_1045_910",
    "eq1_id": 1045,
    "eq2_id": 910,
    "equation1": "x = x ◇ ((y ◇ (y ◇ x)) ◇ x)",
    "equation2": "x = y ◇ ((y ◇ x) ◇ (y ◇ y))",
    "answer": false
  },
  {
    "id": "true_1617_1615",
    "eq1_id": 1617,
    "eq2_id": 1615,
    "equation1": "x = (y ◇ z) ◇ (w ◇ (z ◇ u))",
    "equation2": "x = (y ◇ z) ◇ (w ◇ (z ◇ z))",
    "answer": true
  },
  {
    "id": "true_1604_1822",
    "eq1_id": 1604,
    "eq2_id": 1822,
    "equation1": "x = (y ◇ z) ◇ (w ◇ (x ◇ y))",
    "equation2": "x = (y ◇ z) ◇ ((w ◇ w) ◇ y)",
    "answer": true
  },
  {
    "id": "false_4608_3050",
    "eq1_id": 4608,
    "eq2_id": 3050,
    "equation1": "(x ◇ x) ◇ y = (y ◇ y) ◇ x",
    "equation2": "x = (((x ◇ x) ◇ x) ◇ x) ◇ x",
    "answer": false
  },
  {
    "id": "true_1202_1055",
    "eq1_id": 1202,
    "eq2_id": 1055,
    "equation1": "x = y ◇ ((z ◇ (w ◇ y)) ◇ x)",
    "equation2": "x = x ◇ ((y ◇ (z ◇ x)) ◇ x)",
    "answer": true
  },
  {
    "id": "true_2111_1755",
    "eq1_id": 2111,
    "eq2_id": 1755,
    "equation1": "x = ((y ◇ x) ◇ z) ◇ (y ◇ x)",
    "equation2": "x = (y ◇ z) ◇ ((x ◇ x) ◇ x)",
    "answer": true
  },
  {
    "id": "false_825_2663",
    "eq1_id": 825,
    "eq2_id": 2663,
    "equation1": "x = x ◇ ((x ◇ y) ◇ (y ◇ x))",
    "equation2": "x = ((x ◇ y) ◇ (x ◇ y)) ◇ y",
    "answer": false
  },
  {
    "id": "true_282_2133",
    "eq1_id": 282,
    "eq2_id": 2133,
    "equation1": "x = ((y ◇ y) ◇ x) ◇ z",
    "equation2": "x = ((y ◇ y) ◇ x) ◇ (z ◇ w)",
    "answer": true
  },
  {
    "id": "false_3749_4320",
    "eq1_id": 3749,
    "eq2_id": 4320,
    "equation1": "x ◇ y = (y ◇ x) ◇ (x ◇ y)",
    "equation2": "x ◇ (y ◇ x) = y ◇ (x ◇ x)",
    "answer": false
  },
  {
    "id": "true_1120_714",
    "eq1_id": 1120,
    "eq2_id": 714,
    "equation1": "x = y ◇ ((y ◇ (y ◇ x)) ◇ y)",
    "equation2": "x = y ◇ (y ◇ ((y ◇ x) ◇ y))",
    "answer": true
  },
  {
    "id": "false_4458_3867",
    "eq1_id": 4458,
    "eq2_id": 3867,
    "equation1": "x ◇ (y ◇ x) = (z ◇ y) ◇ z",
    "equation2": "x ◇ x = (x ◇ (y ◇ x)) ◇ x",
    "answer": false
  },
  {
    "id": "true_3568_3565",
    "eq1_id": 3568,
    "eq2_id": 3565,
    "equation1": "x ◇ y = y ◇ ((z ◇ x) ◇ w)",
    "equation2": "x ◇ y = y ◇ ((z ◇ x) ◇ x)",
    "answer": true
  },
  {
    "id": "true_4150_4134",
    "eq1_id": 4150,
    "eq2_id": 4134,
    "equation1": "x ◇ y = ((x ◇ z) ◇ w) ◇ y",
    "equation2": "x ◇ y = ((x ◇ y) ◇ z) ◇ y",
    "answer": true
  },
  {
    "id": "false_4364_3474",
    "eq1_id": 4364,
    "eq2_id": 3474,
    "equation1": "x ◇ (y ◇ z) = y ◇ (z ◇ x)",
    "equation2": "x ◇ x = y ◇ ((x ◇ y) ◇ x)",
    "answer": false
  },
  {
    "id": "true_2497_2441",
    "eq1_id": 2497,
    "eq2_id": 2441,
    "equation1": "x = (y ◇ ((x ◇ x) ◇ y)) ◇ y",
    "equation2": "x = (x ◇ ((x ◇ x) ◇ x)) ◇ x",
    "answer": true
  },
  {
    "id": "true_143_1425",
    "eq1_id": 143,
    "eq2_id": 1425,
    "equation1": "x = y ◇ ((z ◇ z) ◇ y)",
    "equation2": "x = y ◇ (((z ◇ w) ◇ u) ◇ v)",
    "answer": true
  },
  {
    "id": "true_4520_4476",
    "eq1_id": 4520,
    "eq2_id": 4476,
    "equation1": "x ◇ (y ◇ z) = (x ◇ w) ◇ z",
    "equation2": "x ◇ (y ◇ y) = (x ◇ z) ◇ y",
    "answer": true
  },
  {
    "id": "false_3665_640",
    "eq1_id": 3665,
    "eq2_id": 640,
    "equation1": "x ◇ x = (x ◇ y) ◇ (x ◇ y)",
    "equation2": "x = x ◇ (y ◇ ((y ◇ x) ◇ y))",
    "answer": false
  },
  {
    "id": "true_305_295",
    "eq1_id": 305,
    "eq2_id": 295,
    "equation1": "x = ((y ◇ z) ◇ w) ◇ w",
    "equation2": "x = ((y ◇ z) ◇ y) ◇ y",
    "answer": true
  },
  {
    "id": "false_1202_2541",
    "eq1_id": 1202,
    "eq2_id": 2541,
    "equation1": "x = y ◇ ((z ◇ (w ◇ y)) ◇ x)",
    "equation2": "x = (y ◇ ((y ◇ y) ◇ x)) ◇ y",
    "answer": false
  },
  {
    "id": "false_28_4081",
    "eq1_id": 28,
    "eq2_id": 4081,
    "equation1": "x = (y ◇ x) ◇ x",
    "equation2": "x ◇ x = ((y ◇ x) ◇ x) ◇ y",
    "answer": false
  },
  {
    "id": "true_1595_1593",
    "eq1_id": 1595,
    "eq2_id": 1593,
    "equation1": "x = (y ◇ z) ◇ (z ◇ (z ◇ y))",
    "equation2": "x = (y ◇ z) ◇ (z ◇ (y ◇ w))",
    "answer": true
  },
  {
    "id": "true_3083_3094",
    "eq1_id": 3083,
    "eq2_id": 3094,
    "equation1": "x = (((x ◇ y) ◇ y) ◇ z) ◇ z",
    "equation2": "x = (((x ◇ y) ◇ z) ◇ z) ◇ y",
    "answer": true
  },
  {
    "id": "false_833_3546",
    "eq1_id": 833,
    "eq2_id": 3546,
    "equation1": "x = x ◇ ((y ◇ x) ◇ (x ◇ y))",
    "equation2": "x ◇ y = y ◇ ((x ◇ x) ◇ y)",
    "answer": false
  },
  {
    "id": "false_452_255",
    "eq1_id": 452,
    "eq2_id": 255,
    "equation1": "x = x ◇ (y ◇ (z ◇ (y ◇ z)))",
    "equation2": "x = ((x ◇ x) ◇ x) ◇ x",
    "answer": false
  },
  {
    "id": "true_2230_2205",
    "eq1_id": 2230,
    "eq2_id": 2205,
    "equation1": "x = ((y ◇ z) ◇ w) ◇ (w ◇ w)",
    "equation2": "x = ((y ◇ z) ◇ z) ◇ (z ◇ z)",
    "answer": true
  },
  {
    "id": "false_919_872",
    "eq1_id": 919,
    "eq2_id": 872,
    "equation1": "x = y ◇ ((y ◇ y) ◇ (y ◇ x))",
    "equation2": "x = y ◇ ((x ◇ x) ◇ (y ◇ x))",
    "answer": false
  },
  {
    "id": "true_4616_4623",
    "eq1_id": 4616,
    "eq2_id": 4623,
    "equation1": "(x ◇ x) ◇ y = (z ◇ x) ◇ z",
    "equation2": "(x ◇ x) ◇ y = (z ◇ z) ◇ w",
    "answer": true
  },
  {
    "id": "false_1491_2866",
    "eq1_id": 1491,
    "eq2_id": 2866,
    "equation1": "x = (y ◇ x) ◇ (y ◇ (y ◇ x))",
    "equation2": "x = ((x ◇ (y ◇ x)) ◇ y) ◇ y",
    "answer": false
  },
  {
    "id": "false_376_4635",
    "eq1_id": 376,
    "eq2_id": 4635,
    "equation1": "x ◇ y = (x ◇ x) ◇ z",
    "equation2": "(x ◇ y) ◇ x = (y ◇ x) ◇ x",
    "answer": false
  },
  {
    "id": "false_437_3722",
    "eq1_id": 437,
    "eq2_id": 3722,
    "equation1": "x = x ◇ (y ◇ (y ◇ (x ◇ y)))",
    "equation2": "x ◇ y = (x ◇ y) ◇ (x ◇ y)",
    "answer": false
  },
  {
    "id": "true_4530_4576",
    "eq1_id": 4530,
    "eq2_id": 4576,
    "equation1": "x ◇ (y ◇ z) = (y ◇ y) ◇ w",
    "equation2": "x ◇ (y ◇ z) = (w ◇ w) ◇ u",
    "answer": true
  },
  {
    "id": "false_1673_1731",
    "eq1_id": 1673,
    "eq2_id": 1731,
    "equation1": "x = (x ◇ y) ◇ ((z ◇ z) ◇ y)",
    "equation2": "x = (y ◇ y) ◇ ((y ◇ y) ◇ x)",
    "answer": false
  },
  {
    "id": "false_3758_1861",
    "eq1_id": 3758,
    "eq2_id": 1861,
    "equation1": "x ◇ y = (y ◇ y) ◇ (x ◇ x)",
    "equation2": "x = (x ◇ (y ◇ y)) ◇ (y ◇ y)",
    "answer": false
  },
  {
    "id": "false_504_670",
    "eq1_id": 504,
    "eq2_id": 670,
    "equation1": "x = y ◇ (y ◇ (x ◇ (y ◇ y)))",
    "equation2": "x = y ◇ (x ◇ ((x ◇ y) ◇ y))",
    "answer": false
  },
  {
    "id": "true_4098_4090",
    "eq1_id": 4098,
    "eq2_id": 4090,
    "equation1": "x ◇ x = ((y ◇ y) ◇ z) ◇ z",
    "equation2": "x ◇ x = ((y ◇ y) ◇ x) ◇ x",
    "answer": true
  },
  {
    "id": "true_2599_2594",
    "eq1_id": 2599,
    "eq2_id": 2594,
    "equation1": "x = (y ◇ ((z ◇ y) ◇ w)) ◇ w",
    "equation2": "x = (y ◇ ((z ◇ y) ◇ z)) ◇ z",
    "answer": true
  },
  {
    "id": "true_1022_99",
    "eq1_id": 1022,
    "eq2_id": 99,
    "equation1": "x = x ◇ ((x ◇ (x ◇ y)) ◇ x)",
    "equation2": "x = x ◇ ((x ◇ x) ◇ x)",
    "answer": true
  },
  {
    "id": "true_425_1630",
    "eq1_id": 425,
    "eq2_id": 1630,
    "equation1": "x = x ◇ (x ◇ (y ◇ (z ◇ w)))",
    "equation2": "x = (x ◇ x) ◇ ((x ◇ x) ◇ y)",
    "answer": true
  },
  {
    "id": "false_4072_1120",
    "eq1_id": 4072,
    "eq2_id": 1120,
    "equation1": "x ◇ x = ((x ◇ y) ◇ x) ◇ z",
    "equation2": "x = y ◇ ((y ◇ (y ◇ x)) ◇ y)",
    "answer": false
  },
  {
    "id": "true_608_593",
    "eq1_id": 608,
    "eq2_id": 593,
    "equation1": "x = y ◇ (z ◇ (w ◇ (u ◇ x)))",
    "equation2": "x = y ◇ (z ◇ (w ◇ (y ◇ x)))",
    "answer": true
  },
  {
    "id": "true_2930_2914",
    "eq1_id": 2930,
    "eq2_id": 2914,
    "equation1": "x = ((y ◇ (x ◇ z)) ◇ z) ◇ w",
    "equation2": "x = ((y ◇ (x ◇ y)) ◇ y) ◇ z",
    "answer": true
  },
  {
    "id": "false_5_2866",
    "eq1_id": 5,
    "eq2_id": 2866,
    "equation1": "x = y ◇ x",
    "equation2": "x = ((x ◇ (y ◇ x)) ◇ y) ◇ y",
    "answer": false
  },
  {
    "id": "false_413_642",
    "eq1_id": 413,
    "eq2_id": 642,
    "equation1": "x = x ◇ (x ◇ (x ◇ (y ◇ x)))",
    "equation2": "x = x ◇ (y ◇ ((y ◇ y) ◇ x))",
    "answer": false
  },
  {
    "id": "true_3541_3537",
    "eq1_id": 3541,
    "eq2_id": 3537,
    "equation1": "x ◇ y = x ◇ ((z ◇ w) ◇ y)",
    "equation2": "x ◇ y = x ◇ ((z ◇ z) ◇ y)",
    "answer": true
  },
  {
    "id": "false_1721_2291",
    "eq1_id": 1721,
    "eq2_id": 2291,
    "equation1": "x = (y ◇ y) ◇ ((x ◇ y) ◇ x)",
    "equation2": "x = (y ◇ (x ◇ (x ◇ x))) ◇ y",
    "answer": false
  },
  {
    "id": "true_2430_2318",
    "eq1_id": 2430,
    "eq2_id": 2318,
    "equation1": "x = (y ◇ (z ◇ (w ◇ w))) ◇ x",
    "equation2": "x = (y ◇ (x ◇ (z ◇ z))) ◇ x",
    "answer": true
  },
  {
    "id": "false_1983_1021",
    "eq1_id": 1983,
    "eq2_id": 1021,
    "equation1": "x = (y ◇ (z ◇ y)) ◇ (z ◇ x)",
    "equation2": "x = x ◇ ((x ◇ (x ◇ x)) ◇ y)",
    "answer": false
  },
  {
    "id": "false_3533_3871",
    "eq1_id": 3533,
    "eq2_id": 3871,
    "equation1": "x ◇ y = x ◇ ((z ◇ y) ◇ y)",
    "equation2": "x ◇ x = (x ◇ (y ◇ y)) ◇ y",
    "answer": false
  },
  {
    "id": "true_2860_3458",
    "eq1_id": 2860,
    "eq2_id": 3458,
    "equation1": "x = ((x ◇ (x ◇ y)) ◇ z) ◇ z",
    "equation2": "x ◇ x = x ◇ ((x ◇ y) ◇ x)",
    "answer": true
  },
  {
    "id": "false_2098_221",
    "eq1_id": 2098,
    "eq2_id": 221,
    "equation1": "x = ((y ◇ x) ◇ y) ◇ (x ◇ y)",
    "equation2": "x = (y ◇ (x ◇ y)) ◇ x",
    "answer": false
  },
  {
    "id": "false_2459_3521",
    "eq1_id": 2459,
    "eq2_id": 3521,
    "equation1": "x = (x ◇ ((y ◇ x) ◇ y)) ◇ x",
    "equation2": "x ◇ y = x ◇ ((y ◇ y) ◇ x)",
    "answer": false
  },
  {
    "id": "true_3829_41",
    "eq1_id": 3829,
    "eq2_id": 41,
    "equation1": "x ◇ y = (z ◇ z) ◇ (z ◇ z)",
    "equation2": "x ◇ x = y ◇ z",
    "answer": true
  },
  {
    "id": "false_4271_4165",
    "eq1_id": 4271,
    "eq2_id": 4165,
    "equation1": "x ◇ (x ◇ x) = x ◇ (y ◇ z)",
    "equation2": "x ◇ y = ((y ◇ y) ◇ x) ◇ y",
    "answer": false
  },
  {
    "id": "true_130_1759",
    "eq1_id": 130,
    "eq2_id": 1759,
    "equation1": "x = y ◇ ((y ◇ z) ◇ x)",
    "equation2": "x = (y ◇ z) ◇ ((x ◇ y) ◇ x)",
    "answer": true
  },
  {
    "id": "true_4466_4458",
    "eq1_id": 4466,
    "eq2_id": 4458,
    "equation1": "x ◇ (y ◇ x) = (z ◇ w) ◇ z",
    "equation2": "x ◇ (y ◇ x) = (z ◇ y) ◇ z",
    "answer": true
  },
  {
    "id": "true_2061_307",
    "eq1_id": 2061,
    "eq2_id": 307,
    "equation1": "x = ((x ◇ y) ◇ y) ◇ (x ◇ y)",
    "equation2": "x ◇ x = x ◇ (x ◇ x)",
    "answer": true
  },
  {
    "id": "true_1738_1258",
    "eq1_id": 1738,
    "eq2_id": 1258,
    "equation1": "x = (y ◇ y) ◇ ((z ◇ x) ◇ x)",
    "equation2": "x = x ◇ (((y ◇ z) ◇ x) ◇ x)",
    "answer": true
  },
  {
    "id": "true_643_614",
    "eq1_id": 643,
    "eq2_id": 614,
    "equation1": "x = x ◇ (y ◇ ((y ◇ y) ◇ y))",
    "equation2": "x = x ◇ (x ◇ ((x ◇ x) ◇ x))",
    "answer": true
  },
  {
    "id": "true_1671_1649",
    "eq1_id": 1671,
    "eq2_id": 1649,
    "equation1": "x = (x ◇ y) ◇ ((z ◇ y) ◇ w)",
    "equation2": "x = (x ◇ y) ◇ ((x ◇ y) ◇ z)",
    "answer": true
  },
  {
    "id": "true_3875_3865",
    "eq1_id": 3875,
    "eq2_id": 3865,
    "equation1": "x ◇ x = (x ◇ (y ◇ z)) ◇ z",
    "equation2": "x ◇ x = (x ◇ (x ◇ y)) ◇ y",
    "answer": true
  },
  {
    "id": "true_2260_2254",
    "eq1_id": 2260,
    "eq2_id": 2254,
    "equation1": "x = (x ◇ (y ◇ (x ◇ z))) ◇ y",
    "equation2": "x = (x ◇ (y ◇ (x ◇ x))) ◇ y",
    "answer": true
  },
  {
    "id": "true_4318_4314",
    "eq1_id": 4318,
    "eq2_id": 4314,
    "equation1": "x ◇ (y ◇ x) = x ◇ (z ◇ z)",
    "equation2": "x ◇ (y ◇ x) = x ◇ (y ◇ y)",
    "answer": true
  },
  {
    "id": "false_3315_2247",
    "eq1_id": 3315,
    "eq2_id": 2247,
    "equation1": "x ◇ y = x ◇ (y ◇ (x ◇ x))",
    "equation2": "x = (x ◇ (x ◇ (y ◇ y))) ◇ y",
    "answer": false
  },
  {
    "id": "true_2425_2351",
    "eq1_id": 2425,
    "eq2_id": 2351,
    "equation1": "x = (y ◇ (z ◇ (w ◇ z))) ◇ x",
    "equation2": "x = (y ◇ (y ◇ (z ◇ y))) ◇ x",
    "answer": true
  },
  {
    "id": "true_1751_1739",
    "eq1_id": 1751,
    "eq2_id": 1739,
    "equation1": "x = (y ◇ y) ◇ ((z ◇ w) ◇ y)",
    "equation2": "x = (y ◇ y) ◇ ((z ◇ x) ◇ y)",
    "answer": true
  },
  {
    "id": "true_2139_2138",
    "eq1_id": 2139,
    "eq2_id": 2138,
    "equation1": "x = ((y ◇ y) ◇ y) ◇ (y ◇ z)",
    "equation2": "x = ((y ◇ y) ◇ y) ◇ (y ◇ y)",
    "answer": true
  },
  {
    "id": "false_2659_3272",
    "eq1_id": 2659,
    "eq2_id": 3272,
    "equation1": "x = ((x ◇ y) ◇ (x ◇ x)) ◇ x",
    "equation2": "x ◇ x = y ◇ (x ◇ (y ◇ y))",
    "answer": false
  },
  {
    "id": "true_2654_2864",
    "eq1_id": 2654,
    "eq2_id": 2864,
    "equation1": "x = ((x ◇ x) ◇ (y ◇ y)) ◇ z",
    "equation2": "x = ((x ◇ (y ◇ x)) ◇ x) ◇ z",
    "answer": true
  },
  {
    "id": "true_2814_2813",
    "eq1_id": 2814,
    "eq2_id": 2813,
    "equation1": "x = ((y ◇ z) ◇ (z ◇ z)) ◇ z",
    "equation2": "x = ((y ◇ z) ◇ (z ◇ z)) ◇ y",
    "answer": true
  },
  {
    "id": "false_872_2444",
    "eq1_id": 872,
    "eq2_id": 2444,
    "equation1": "x = y ◇ ((x ◇ x) ◇ (y ◇ x))",
    "equation2": "x = (x ◇ ((x ◇ x) ◇ y)) ◇ y",
    "answer": false
  },
  {
    "id": "false_3684_1834",
    "eq1_id": 3684,
    "eq2_id": 1834,
    "equation1": "x ◇ x = (y ◇ y) ◇ (x ◇ x)",
    "equation2": "x = (x ◇ (x ◇ x)) ◇ (y ◇ x)",
    "answer": false
  },
  {
    "id": "true_359_4065",
    "eq1_id": 359,
    "eq2_id": 4065,
    "equation1": "x ◇ x = (x ◇ x) ◇ x",
    "equation2": "x ◇ x = ((x ◇ x) ◇ x) ◇ x",
    "answer": true
  },
  {
    "id": "true_2789_898",
    "eq1_id": 2789,
    "eq2_id": 898,
    "equation1": "x = ((y ◇ z) ◇ (y ◇ x)) ◇ z",
    "equation2": "x = y ◇ ((x ◇ z) ◇ (z ◇ y))",
    "answer": true
  },
  {
    "id": "false_1228_1887",
    "eq1_id": 1228,
    "eq2_id": 1887,
    "equation1": "x = x ◇ (((x ◇ y) ◇ x) ◇ x)",
    "equation2": "x = (y ◇ (x ◇ x)) ◇ (y ◇ x)",
    "answer": false
  },
  {
    "id": "true_2935_3138",
    "eq1_id": 2935,
    "eq2_id": 3138,
    "equation1": "x = ((y ◇ (x ◇ z)) ◇ w) ◇ u",
    "equation2": "x = (((y ◇ x) ◇ z) ◇ w) ◇ u",
    "answer": true
  },
  {
    "id": "true_1000_894",
    "eq1_id": 1000,
    "eq2_id": 894,
    "equation1": "x = y ◇ ((z ◇ w) ◇ (y ◇ y))",
    "equation2": "x = y ◇ ((x ◇ z) ◇ (y ◇ y))",
    "answer": true
  },
  {
    "id": "false_640_3150",
    "eq1_id": 640,
    "eq2_id": 3150,
    "equation1": "x = x ◇ (y ◇ ((y ◇ x) ◇ y))",
    "equation2": "x = (((y ◇ y) ◇ y) ◇ x) ◇ y",
    "answer": false
  },
  {
    "id": "false_13_4167",
    "eq1_id": 13,
    "eq2_id": 4167,
    "equation1": "x = y ◇ (x ◇ x)",
    "equation2": "x ◇ y = ((y ◇ y) ◇ y) ◇ x",
    "answer": false
  },
  {
    "id": "true_2135_2128",
    "eq1_id": 2135,
    "eq2_id": 2128,
    "equation1": "x = ((y ◇ y) ◇ y) ◇ (x ◇ y)",
    "equation2": "x = ((y ◇ y) ◇ x) ◇ (y ◇ y)",
    "answer": true
  },
  {
    "id": "true_428_3725",
    "eq1_id": 428,
    "eq2_id": 3725,
    "equation1": "x = x ◇ (y ◇ (x ◇ (x ◇ z)))",
    "equation2": "x ◇ y = (x ◇ y) ◇ (y ◇ y)",
    "answer": true
  },
  {
    "id": "false_2709_4291",
    "eq1_id": 2709,
    "eq2_id": 4291,
    "equation1": "x = ((y ◇ x) ◇ (y ◇ y)) ◇ x",
    "equation2": "x ◇ (x ◇ y) = y ◇ (x ◇ y)",
    "answer": false
  },
  {
    "id": "true_4688_4686",
    "eq1_id": 4688,
    "eq2_id": 4686,
    "equation1": "(x ◇ y) ◇ z = (z ◇ w) ◇ u",
    "equation2": "(x ◇ y) ◇ z = (z ◇ w) ◇ x",
    "answer": true
  },
  {
    "id": "true_2623_2517",
    "eq1_id": 2623,
    "eq2_id": 2517,
    "equation1": "x = (y ◇ ((z ◇ w) ◇ y)) ◇ x",
    "equation2": "x = (y ◇ ((x ◇ z) ◇ y)) ◇ x",
    "answer": true
  },
  {
    "id": "false_2243_3660",
    "eq1_id": 2243,
    "eq2_id": 3660,
    "equation1": "x = (x ◇ (x ◇ (y ◇ x))) ◇ x",
    "equation2": "x ◇ x = (x ◇ x) ◇ (x ◇ y)",
    "answer": false
  },
  {
    "id": "false_280_833",
    "eq1_id": 280,
    "eq2_id": 833,
    "equation1": "x = ((y ◇ y) ◇ x) ◇ x",
    "equation2": "x = x ◇ ((y ◇ x) ◇ (x ◇ y))",
    "answer": false
  },
  {
    "id": "true_1874_1871",
    "eq1_id": 1874,
    "eq2_id": 1871,
    "equation1": "x = (x ◇ (y ◇ z)) ◇ (y ◇ w)",
    "equation2": "x = (x ◇ (y ◇ z)) ◇ (y ◇ x)",
    "answer": true
  },
  {
    "id": "true_561_559",
    "eq1_id": 561,
    "eq2_id": 559,
    "equation1": "x = y ◇ (z ◇ (y ◇ (y ◇ w)))",
    "equation2": "x = y ◇ (z ◇ (y ◇ (y ◇ y)))",
    "answer": true
  },
  {
    "id": "false_108_3862",
    "eq1_id": 108,
    "eq2_id": 3862,
    "equation1": "x = x ◇ ((y ◇ y) ◇ y)",
    "equation2": "x ◇ x = (x ◇ (x ◇ x)) ◇ x",
    "answer": false
  },
  {
    "id": "false_2079_24",
    "eq1_id": 2079,
    "eq2_id": 24,
    "equation1": "x = ((x ◇ y) ◇ z) ◇ (z ◇ y)",
    "equation2": "x = (x ◇ x) ◇ y",
    "answer": false
  },
  {
    "id": "true_3286_3278",
    "eq1_id": 3286,
    "eq2_id": 3278,
    "equation1": "x ◇ x = y ◇ (y ◇ (z ◇ z))",
    "equation2": "x ◇ x = y ◇ (y ◇ (x ◇ x))",
    "answer": true
  },
  {
    "id": "true_3504_3496",
    "eq1_id": 3504,
    "eq2_id": 3496,
    "equation1": "x ◇ x = y ◇ ((z ◇ w) ◇ y)",
    "equation2": "x ◇ x = y ◇ ((z ◇ y) ◇ y)",
    "answer": true
  },
  {
    "id": "false_4480_3684",
    "eq1_id": 4480,
    "eq2_id": 3684,
    "equation1": "x ◇ (y ◇ y) = (y ◇ x) ◇ y",
    "equation2": "x ◇ x = (y ◇ y) ◇ (x ◇ x)",
    "answer": false
  },
  {
    "id": "true_1500_498",
    "eq1_id": 1500,
    "eq2_id": 498,
    "equation1": "x = (y ◇ x) ◇ (z ◇ (x ◇ z))",
    "equation2": "x = y ◇ (x ◇ (z ◇ (w ◇ w)))",
    "answer": true
  },
  {
    "id": "false_2925_3674",
    "eq1_id": 2925,
    "eq2_id": 3674,
    "equation1": "x = ((y ◇ (x ◇ z)) ◇ y) ◇ z",
    "equation2": "x ◇ x = (y ◇ x) ◇ (x ◇ x)",
    "answer": false
  },
  {
    "id": "false_4290_3461",
    "eq1_id": 4290,
    "eq2_id": 3461,
    "equation1": "x ◇ (x ◇ y) = y ◇ (x ◇ x)",
    "equation2": "x ◇ x = x ◇ ((y ◇ x) ◇ x)",
    "answer": false
  },
  {
    "id": "false_395_3271",
    "eq1_id": 395,
    "eq2_id": 3271,
    "equation1": "x ◇ y = (z ◇ x) ◇ y",
    "equation2": "x ◇ x = y ◇ (x ◇ (y ◇ x))",
    "answer": false
  },
  {
    "id": "true_2137_1325",
    "eq1_id": 2137,
    "eq2_id": 1325,
    "equation1": "x = ((y ◇ y) ◇ y) ◇ (y ◇ x)",
    "equation2": "x = y ◇ (((y ◇ y) ◇ y) ◇ x)",
    "answer": true
  },
  {
    "id": "true_1788_1700",
    "eq1_id": 1788,
    "eq2_id": 1700,
    "equation1": "x = (y ◇ z) ◇ ((y ◇ w) ◇ u)",
    "equation2": "x = (y ◇ x) ◇ ((y ◇ z) ◇ w)",
    "answer": true
  },
  {
    "id": "true_1253_1251",
    "eq1_id": 1253,
    "eq2_id": 1251,
    "equation1": "x = x ◇ (((y ◇ y) ◇ y) ◇ z)",
    "equation2": "x = x ◇ (((y ◇ y) ◇ y) ◇ x)",
    "answer": true
  },
  {
    "id": "true_691_1976",
    "eq1_id": 691,
    "eq2_id": 1976,
    "equation1": "x = y ◇ (x ◇ ((z ◇ y) ◇ y))",
    "equation2": "x = (y ◇ (z ◇ y)) ◇ (x ◇ y)",
    "answer": true
  },
  {
    "id": "true_4151_4149",
    "eq1_id": 4151,
    "eq2_id": 4149,
    "equation1": "x ◇ y = ((x ◇ z) ◇ w) ◇ z",
    "equation2": "x ◇ y = ((x ◇ z) ◇ w) ◇ x",
    "answer": true
  },
  {
    "id": "true_2074_2082",
    "eq1_id": 2074,
    "eq2_id": 2082,
    "equation1": "x = ((x ◇ y) ◇ z) ◇ (y ◇ x)",
    "equation2": "x = ((x ◇ y) ◇ z) ◇ (w ◇ x)",
    "answer": true
  },
  {
    "id": "false_1117_4658",
    "eq1_id": 1117,
    "eq2_id": 4658,
    "equation1": "x = y ◇ ((y ◇ (x ◇ z)) ◇ z)",
    "equation2": "(x ◇ y) ◇ y = (y ◇ x) ◇ x",
    "answer": false
  },
  {
    "id": "true_1664_1644",
    "eq1_id": 1664,
    "eq2_id": 1644,
    "equation1": "x = (x ◇ y) ◇ ((z ◇ x) ◇ x)",
    "equation2": "x = (x ◇ y) ◇ ((x ◇ x) ◇ x)",
    "answer": true
  },
  {
    "id": "true_1457_1454",
    "eq1_id": 1457,
    "eq2_id": 1454,
    "equation1": "x = (x ◇ y) ◇ (y ◇ (z ◇ x))",
    "equation2": "x = (x ◇ y) ◇ (y ◇ (y ◇ x))",
    "answer": true
  },
  {
    "id": "true_4082_4109",
    "eq1_id": 4082,
    "eq2_id": 4109,
    "equation1": "x ◇ x = ((y ◇ x) ◇ x) ◇ z",
    "equation2": "x ◇ x = ((y ◇ z) ◇ z) ◇ y",
    "answer": true
  },
  {
    "id": "false_3068_503",
    "eq1_id": 3068,
    "eq2_id": 503,
    "equation1": "x = (((x ◇ y) ◇ x) ◇ y) ◇ x",
    "equation2": "x = y ◇ (y ◇ (x ◇ (y ◇ x)))",
    "answer": false
  },
  {
    "id": "true_2771_2775",
    "eq1_id": 2771,
    "eq2_id": 2775,
    "equation1": "x = ((y ◇ z) ◇ (x ◇ x)) ◇ y",
    "equation2": "x = ((y ◇ z) ◇ (x ◇ y)) ◇ y",
    "answer": true
  },
  {
    "id": "false_1764_616",
    "eq1_id": 1764,
    "eq2_id": 616,
    "equation1": "x = (y ◇ z) ◇ ((x ◇ z) ◇ y)",
    "equation2": "x = x ◇ (x ◇ ((x ◇ y) ◇ x))",
    "answer": false
  },
  {
    "id": "false_907_2534",
    "eq1_id": 907,
    "eq2_id": 2534,
    "equation1": "x = y ◇ ((y ◇ x) ◇ (x ◇ y))",
    "equation2": "x = (y ◇ ((y ◇ x) ◇ y)) ◇ y",
    "answer": false
  },
  {
    "id": "true_4561_4566",
    "eq1_id": 4561,
    "eq2_id": 4566,
    "equation1": "x ◇ (y ◇ z) = (w ◇ x) ◇ u",
    "equation2": "x ◇ (y ◇ z) = (w ◇ y) ◇ u",
    "answer": true
  },
  {
    "id": "false_3529_427",
    "eq1_id": 3529,
    "eq2_id": 427,
    "equation1": "x ◇ y = x ◇ ((z ◇ x) ◇ y)",
    "equation2": "x = x ◇ (y ◇ (x ◇ (x ◇ y)))",
    "answer": false
  },
  {
    "id": "true_1197_1129",
    "eq1_id": 1197,
    "eq2_id": 1129,
    "equation1": "x = y ◇ ((z ◇ (w ◇ x)) ◇ x)",
    "equation2": "x = y ◇ ((y ◇ (z ◇ x)) ◇ x)",
    "answer": true
  },
  {
    "id": "true_2040_2035",
    "eq1_id": 2040,
    "eq2_id": 2035,
    "equation1": "x = ((x ◇ x) ◇ y) ◇ (x ◇ x)",
    "equation2": "x = ((x ◇ x) ◇ x) ◇ (x ◇ x)",
    "answer": true
  },
  {
    "id": "true_773_768",
    "eq1_id": 773,
    "eq2_id": 768,
    "equation1": "x = y ◇ (z ◇ ((y ◇ w) ◇ u))",
    "equation2": "x = y ◇ (z ◇ ((y ◇ z) ◇ w))",
    "answer": true
  },
  {
    "id": "true_3539_3536",
    "eq1_id": 3539,
    "eq2_id": 3536,
    "equation1": "x ◇ y = x ◇ ((z ◇ z) ◇ w)",
    "equation2": "x ◇ y = x ◇ ((z ◇ z) ◇ x)",
    "answer": true
  },
  {
    "id": "false_2584_3078",
    "eq1_id": 2584,
    "eq2_id": 3078,
    "equation1": "x = (y ◇ ((z ◇ y) ◇ x)) ◇ x",
    "equation2": "x = (((x ◇ y) ◇ y) ◇ y) ◇ x",
    "answer": false
  },
  {
    "id": "false_1507_1526",
    "eq1_id": 1507,
    "eq2_id": 1526,
    "equation1": "x = (y ◇ x) ◇ (z ◇ (z ◇ y))",
    "equation2": "x = (y ◇ y) ◇ (y ◇ (x ◇ y))",
    "answer": false
  },
  {
    "id": "false_4507_2507",
    "eq1_id": 4507,
    "eq2_id": 2507,
    "equation1": "x ◇ (y ◇ z) = (x ◇ x) ◇ y",
    "equation2": "x = (y ◇ ((x ◇ y) ◇ y)) ◇ y",
    "answer": false
  },
  {
    "id": "false_4325_1249",
    "eq1_id": 4325,
    "eq2_id": 1249,
    "equation1": "x ◇ (y ◇ x) = y ◇ (z ◇ z)",
    "equation2": "x = x ◇ (((y ◇ y) ◇ x) ◇ y)",
    "answer": false
  },
  {
    "id": "false_4640_1692",
    "eq1_id": 4640,
    "eq2_id": 1692,
    "equation1": "(x ◇ y) ◇ x = (y ◇ z) ◇ z",
    "equation2": "x = (y ◇ x) ◇ ((y ◇ x) ◇ y)",
    "answer": false
  },
  {
    "id": "false_1861_1479",
    "eq1_id": 1861,
    "eq2_id": 1479,
    "equation1": "x = (x ◇ (y ◇ y)) ◇ (y ◇ y)",
    "equation2": "x = (y ◇ x) ◇ (x ◇ (x ◇ y))",
    "answer": false
  },
  {
    "id": "false_1682_411",
    "eq1_id": 1682,
    "eq2_id": 411,
    "equation1": "x = (y ◇ x) ◇ ((x ◇ x) ◇ y)",
    "equation2": "x = x ◇ (x ◇ (x ◇ (x ◇ x)))",
    "answer": false
  },
  {
    "id": "true_2034_2032",
    "eq1_id": 2034,
    "eq2_id": 2032,
    "equation1": "x = (y ◇ (z ◇ w)) ◇ (u ◇ v)",
    "equation2": "x = (y ◇ (z ◇ w)) ◇ (u ◇ w)",
    "answer": true
  },
  {
    "id": "true_498_488",
    "eq1_id": 498,
    "eq2_id": 488,
    "equation1": "x = y ◇ (x ◇ (z ◇ (w ◇ w)))",
    "equation2": "x = y ◇ (x ◇ (z ◇ (y ◇ y)))",
    "answer": true
  },
  {
    "id": "true_1676_1672",
    "eq1_id": 1676,
    "eq2_id": 1672,
    "equation1": "x = (x ◇ y) ◇ ((z ◇ w) ◇ x)",
    "equation2": "x = (x ◇ y) ◇ ((z ◇ z) ◇ x)",
    "answer": true
  },
  {
    "id": "true_1874_4357",
    "eq1_id": 1874,
    "eq2_id": 4357,
    "equation1": "x = (x ◇ (y ◇ z)) ◇ (y ◇ w)",
    "equation2": "x ◇ (y ◇ z) = x ◇ (y ◇ w)",
    "answer": true
  },
  {
    "id": "false_450_2087",
    "eq1_id": 450,
    "eq2_id": 2087,
    "equation1": "x = x ◇ (y ◇ (z ◇ (y ◇ x)))",
    "equation2": "x = ((y ◇ x) ◇ x) ◇ (x ◇ x)",
    "answer": false
  },
  {
    "id": "true_172_169",
    "eq1_id": 172,
    "eq2_id": 169,
    "equation1": "x = (y ◇ x) ◇ (z ◇ x)",
    "equation2": "x = (y ◇ x) ◇ (y ◇ x)",
    "answer": true
  },
  {
    "id": "false_2474_3951",
    "eq1_id": 2474,
    "eq2_id": 3951,
    "equation1": "x = (x ◇ ((y ◇ y) ◇ z)) ◇ z",
    "equation2": "x ◇ y = (y ◇ (x ◇ x)) ◇ x",
    "answer": false
  },
  {
    "id": "false_2370_1248",
    "eq1_id": 2370,
    "eq2_id": 1248,
    "equation1": "x = (y ◇ (z ◇ (x ◇ y))) ◇ z",
    "equation2": "x = x ◇ (((y ◇ y) ◇ x) ◇ x)",
    "answer": false
  },
  {
    "id": "false_819_212",
    "eq1_id": 819,
    "eq2_id": 212,
    "equation1": "x = x ◇ ((x ◇ x) ◇ (y ◇ x))",
    "equation2": "x = (x ◇ (y ◇ y)) ◇ y",
    "answer": false
  },
  {
    "id": "true_4266_4223",
    "eq1_id": 4266,
    "eq2_id": 4223,
    "equation1": "x ◇ y = ((z ◇ w) ◇ u) ◇ u",
    "equation2": "x ◇ y = ((z ◇ y) ◇ w) ◇ w",
    "answer": true
  },
  {
    "id": "false_4428_3343",
    "eq1_id": 4428,
    "eq2_id": 3343,
    "equation1": "x ◇ (x ◇ y) = (z ◇ w) ◇ y",
    "equation2": "x ◇ y = y ◇ (x ◇ (x ◇ y))",
    "answer": false
  },
  {
    "id": "false_3145_3481",
    "eq1_id": 3145,
    "eq2_id": 3481,
    "equation1": "x = (((y ◇ y) ◇ x) ◇ z) ◇ x",
    "equation2": "x ◇ x = y ◇ ((y ◇ x) ◇ x)",
    "answer": false
  },
  {
    "id": "true_2055_2656",
    "eq1_id": 2055,
    "eq2_id": 2656,
    "equation1": "x = ((x ◇ y) ◇ x) ◇ (y ◇ z)",
    "equation2": "x = ((x ◇ x) ◇ (y ◇ z)) ◇ y",
    "answer": true
  },
  {
    "id": "true_863_862",
    "eq1_id": 863,
    "eq2_id": 862,
    "equation1": "x = x ◇ ((y ◇ z) ◇ (z ◇ w))",
    "equation2": "x = x ◇ ((y ◇ z) ◇ (z ◇ z))",
    "answer": true
  },
  {
    "id": "false_1925_1435",
    "eq1_id": 1925,
    "eq2_id": 1435,
    "equation1": "x = (y ◇ (y ◇ x)) ◇ (y ◇ y)",
    "equation2": "x = (x ◇ x) ◇ (y ◇ (y ◇ y))",
    "answer": false
  },
  {
    "id": "true_689_1350",
    "eq1_id": 689,
    "eq2_id": 1350,
    "equation1": "x = y ◇ (x ◇ ((z ◇ x) ◇ w))",
    "equation2": "x = y ◇ (((z ◇ x) ◇ x) ◇ y)",
    "answer": true
  },
  {
    "id": "false_1117_4688",
    "eq1_id": 1117,
    "eq2_id": 4688,
    "equation1": "x = y ◇ ((y ◇ (x ◇ z)) ◇ z)",
    "equation2": "(x ◇ y) ◇ z = (z ◇ w) ◇ u",
    "answer": false
  },
  {
    "id": "false_1322_2469",
    "eq1_id": 1322,
    "eq2_id": 2469,
    "equation1": "x = y ◇ (((y ◇ y) ◇ x) ◇ x)",
    "equation2": "x = (x ◇ ((y ◇ y) ◇ y)) ◇ x",
    "answer": false
  },
  {
    "id": "false_1790_1722",
    "eq1_id": 1790,
    "eq2_id": 1722,
    "equation1": "x = (y ◇ z) ◇ ((z ◇ x) ◇ y)",
    "equation2": "x = (y ◇ y) ◇ ((x ◇ y) ◇ y)",
    "answer": false
  },
  {
    "id": "true_4199_4157",
    "eq1_id": 4199,
    "eq2_id": 4157,
    "equation1": "x ◇ y = ((z ◇ x) ◇ z) ◇ x",
    "equation2": "x ◇ y = ((y ◇ x) ◇ y) ◇ x",
    "answer": true
  },
  {
    "id": "true_2944_2850",
    "eq1_id": 2944,
    "eq2_id": 2850,
    "equation1": "x = ((y ◇ (y ◇ x)) ◇ z) ◇ z",
    "equation2": "x = ((x ◇ (x ◇ x)) ◇ y) ◇ y",
    "answer": true
  },
  {
    "id": "true_25_23",
    "eq1_id": 25,
    "eq2_id": 23,
    "equation1": "x = (x ◇ y) ◇ x",
    "equation2": "x = (x ◇ x) ◇ x",
    "answer": true
  },
  {
    "id": "true_195_1948",
    "eq1_id": 195,
    "eq2_id": 1948,
    "equation1": "x = (y ◇ z) ◇ (z ◇ y)",
    "equation2": "x = (y ◇ (y ◇ z)) ◇ (y ◇ w)",
    "answer": true
  },
  {
    "id": "false_2070_2699",
    "eq1_id": 2070,
    "eq2_id": 2699,
    "equation1": "x = ((x ◇ y) ◇ z) ◇ (x ◇ x)",
    "equation2": "x = ((y ◇ x) ◇ (x ◇ y)) ◇ x",
    "answer": false
  },
  {
    "id": "true_1785_1783",
    "eq1_id": 1785,
    "eq2_id": 1783,
    "equation1": "x = (y ◇ z) ◇ ((y ◇ w) ◇ y)",
    "equation2": "x = (y ◇ z) ◇ ((y ◇ z) ◇ w)",
    "answer": true
  },
  {
    "id": "true_4461_4433",
    "eq1_id": 4461,
    "eq2_id": 4433,
    "equation1": "x ◇ (y ◇ x) = (z ◇ z) ◇ y",
    "equation2": "x ◇ (y ◇ x) = (x ◇ x) ◇ y",
    "answer": true
  },
  {
    "id": "false_3943_503",
    "eq1_id": 3943,
    "eq2_id": 503,
    "equation1": "x ◇ y = (x ◇ (z ◇ z)) ◇ y",
    "equation2": "x = y ◇ (y ◇ (x ◇ (y ◇ x)))",
    "answer": false
  },
  {
    "id": "false_1243_3481",
    "eq1_id": 1243,
    "eq2_id": 3481,
    "equation1": "x = x ◇ (((y ◇ x) ◇ y) ◇ z)",
    "equation2": "x ◇ x = y ◇ ((y ◇ x) ◇ x)",
    "answer": false
  },
  {
    "id": "false_4508_910",
    "eq1_id": 4508,
    "eq2_id": 910,
    "equation1": "x ◇ (y ◇ z) = (x ◇ x) ◇ z",
    "equation2": "x = y ◇ ((y ◇ x) ◇ (y ◇ y))",
    "answer": false
  },
  {
    "id": "true_616_614",
    "eq1_id": 616,
    "eq2_id": 614,
    "equation1": "x = x ◇ (x ◇ ((x ◇ y) ◇ x))",
    "equation2": "x = x ◇ (x ◇ ((x ◇ x) ◇ x))",
    "answer": true
  },
  {
    "id": "false_3120_4406",
    "eq1_id": 3120,
    "eq2_id": 4406,
    "equation1": "x = (((y ◇ x) ◇ y) ◇ z) ◇ z",
    "equation2": "x ◇ (x ◇ y) = (y ◇ x) ◇ y",
    "answer": false
  },
  {
    "id": "false_3316_1242",
    "eq1_id": 3316,
    "eq2_id": 1242,
    "equation1": "x ◇ y = x ◇ (y ◇ (x ◇ y))",
    "equation2": "x = x ◇ (((y ◇ x) ◇ y) ◇ y)",
    "answer": false
  },
  {
    "id": "false_1039_4291",
    "eq1_id": 1039,
    "eq2_id": 4291,
    "equation1": "x = x ◇ ((y ◇ (x ◇ y)) ◇ y)",
    "equation2": "x ◇ (x ◇ y) = y ◇ (x ◇ y)",
    "answer": false
  },
  {
    "id": "true_404_4236",
    "eq1_id": 404,
    "eq2_id": 4236,
    "equation1": "x ◇ y = (z ◇ z) ◇ z",
    "equation2": "x ◇ y = ((z ◇ z) ◇ z) ◇ w",
    "answer": true
  },
  {
    "id": "false_4120_2504",
    "eq1_id": 4120,
    "eq2_id": 2504,
    "equation1": "x ◇ y = ((x ◇ x) ◇ y) ◇ x",
    "equation2": "x = (y ◇ ((x ◇ y) ◇ x)) ◇ y",
    "answer": false
  },
  {
    "id": "false_2088_1833",
    "eq1_id": 2088,
    "eq2_id": 1833,
    "equation1": "x = ((y ◇ x) ◇ x) ◇ (x ◇ y)",
    "equation2": "x = (x ◇ (x ◇ x)) ◇ (x ◇ y)",
    "answer": false
  },
  {
    "id": "false_4658_2240",
    "eq1_id": 4658,
    "eq2_id": 2240,
    "equation1": "(x ◇ y) ◇ y = (y ◇ x) ◇ x",
    "equation2": "x = (x ◇ (x ◇ (x ◇ y))) ◇ x",
    "answer": false
  },
  {
    "id": "true_3481_3456",
    "eq1_id": 3481,
    "eq2_id": 3456,
    "equation1": "x ◇ x = y ◇ ((y ◇ x) ◇ x)",
    "equation2": "x ◇ x = x ◇ ((x ◇ x) ◇ x)",
    "answer": true
  },
  {
    "id": "true_489_417",
    "eq1_id": 489,
    "eq2_id": 417,
    "equation1": "x = y ◇ (x ◇ (z ◇ (y ◇ z)))",
    "equation2": "x = x ◇ (x ◇ (y ◇ (x ◇ y)))",
    "answer": true
  },
  {
    "id": "false_3556_1454",
    "eq1_id": 3556,
    "eq2_id": 1454,
    "equation1": "x ◇ y = y ◇ ((y ◇ x) ◇ y)",
    "equation2": "x = (x ◇ y) ◇ (y ◇ (y ◇ x))",
    "answer": false
  },
  {
    "id": "false_378_1275",
    "eq1_id": 378,
    "eq2_id": 1275,
    "equation1": "x ◇ y = (x ◇ y) ◇ y",
    "equation2": "x = y ◇ (((x ◇ x) ◇ x) ◇ x)",
    "answer": false
  },
  {
    "id": "true_674_668",
    "eq1_id": 674,
    "eq2_id": 668,
    "equation1": "x = y ◇ (x ◇ ((x ◇ z) ◇ z))",
    "equation2": "x = y ◇ (x ◇ ((x ◇ x) ◇ z))",
    "answer": true
  },
  {
    "id": "false_4436_2100",
    "eq1_id": 4436,
    "eq2_id": 2100,
    "equation1": "x ◇ (y ◇ x) = (x ◇ y) ◇ y",
    "equation2": "x = ((y ◇ x) ◇ y) ◇ (y ◇ x)",
    "answer": false
  },
  {
    "id": "false_4443_2737",
    "eq1_id": 4443,
    "eq2_id": 2737,
    "equation1": "x ◇ (y ◇ x) = (y ◇ x) ◇ y",
    "equation2": "x = ((y ◇ y) ◇ (x ◇ y)) ◇ y",
    "answer": false
  },
  {
    "id": "false_4508_1657",
    "eq1_id": 4508,
    "eq2_id": 1657,
    "equation1": "x ◇ (y ◇ z) = (x ◇ x) ◇ z",
    "equation2": "x = (x ◇ y) ◇ ((y ◇ y) ◇ x)",
    "answer": false
  },
  {
    "id": "false_117_1895",
    "eq1_id": 117,
    "eq2_id": 1895,
    "equation1": "x = y ◇ ((x ◇ y) ◇ x)",
    "equation2": "x = (y ◇ (x ◇ y)) ◇ (x ◇ y)",
    "answer": false
  },
  {
    "id": "true_1636_1839",
    "eq1_id": 1636,
    "eq2_id": 1839,
    "equation1": "x = (x ◇ x) ◇ ((y ◇ x) ◇ z)",
    "equation2": "x = (x ◇ (x ◇ y)) ◇ (x ◇ z)",
    "answer": true
  },
  {
    "id": "false_4271_4598",
    "eq1_id": 4271,
    "eq2_id": 4598,
    "equation1": "x ◇ (x ◇ x) = x ◇ (y ◇ z)",
    "equation2": "(x ◇ x) ◇ y = (x ◇ y) ◇ x",
    "answer": false
  },
  {
    "id": "true_4391_4382",
    "eq1_id": 4391,
    "eq2_id": 4382,
    "equation1": "x ◇ (x ◇ x) = (y ◇ z) ◇ x",
    "equation2": "x ◇ (x ◇ x) = (x ◇ y) ◇ x",
    "answer": true
  },
  {
    "id": "false_58_1860",
    "eq1_id": 58,
    "eq2_id": 1860,
    "equation1": "x = x ◇ (y ◇ (z ◇ x))",
    "equation2": "x = (x ◇ (y ◇ y)) ◇ (y ◇ x)",
    "answer": false
  },
  {
    "id": "false_1634_3867",
    "eq1_id": 1634,
    "eq2_id": 3867,
    "equation1": "x = (x ◇ x) ◇ ((y ◇ x) ◇ x)",
    "equation2": "x ◇ x = (x ◇ (y ◇ x)) ◇ x",
    "answer": false
  }
]