id stringlengths 9 9 | index int64 1 200 | difficulty stringclasses 1
value | eq1_id int64 54 4.65k | eq2_id int64 221 4.58k | equation1 stringlengths 19 27 | equation2 stringlengths 19 27 | answer bool 2
classes |
|---|---|---|---|---|---|---|---|
hard_0001 | 1 | hard | 706 | 4,204 | x = y * (y * ((x * y) * x)) | x * y = ((z * x) * w) * y | false |
hard_0002 | 2 | hard | 4,555 | 4,437 | x * (y * z) = (z * w) * w | x * (y * x) = (x * y) * z | false |
hard_0003 | 3 | hard | 286 | 1,238 | x = ((y * y) * z) * x | x = x * (((y * x) * x) * x) | true |
hard_0004 | 4 | hard | 4,634 | 4,340 | (x * y) * x = (x * z) * w | x * (y * y) = x * (z * y) | false |
hard_0005 | 5 | hard | 2,805 | 3,891 | x = ((y * z) * (z * x)) * y | x * x = (y * (y * y)) * y | false |
hard_0006 | 6 | hard | 363 | 373 | x * x = (x * y) * z | x * x = (y * z) * w | false |
hard_0007 | 7 | hard | 2,343 | 3,446 | x = (y * (y * (y * z))) * x | x * y = z * (w * (w * y)) | true |
hard_0008 | 8 | hard | 646 | 1,020 | x = x * (y * ((y * z) * y)) | x = x * ((x * (x * x)) * x) | false |
hard_0009 | 9 | hard | 2,656 | 2,863 | x = ((x * x) * (y * z)) * y | x = ((x * (y * x)) * x) * y | false |
hard_0010 | 10 | hard | 4,609 | 4,341 | (x * x) * y = (y * y) * z | x * (y * y) = x * (z * z) | false |
hard_0011 | 11 | hard | 1,880 | 2,031 | x = (x * (y * z)) * (w * y) | x = (y * (z * w)) * (u * z) | false |
hard_0012 | 12 | hard | 4,653 | 4,270 | (x * y) * x = (z * w) * u | x * (x * x) = x * (y * y) | false |
hard_0013 | 13 | hard | 4,208 | 3,356 | x * y = ((z * y) * x) * x | x * y = y * (y * (y * y)) | true |
hard_0014 | 14 | hard | 1,480 | 572 | x = (y * x) * (x * (x * z)) | x = y * (z * (z * (x * y))) | false |
hard_0015 | 15 | hard | 3,265 | 4,269 | x * x = x * (y * (z * y)) | x * (x * x) = x * (y * x) | false |
hard_0016 | 16 | hard | 1,446 | 1,448 | x = (x * y) * (x * (y * z)) | x = (x * y) * (x * (z * y)) | false |
hard_0017 | 17 | hard | 1,286 | 2,891 | x = y * (((x * y) * x) * y) | x = ((x * (y * z)) * z) * y | false |
hard_0018 | 18 | hard | 2,105 | 1,229 | x = ((y * x) * y) * (z * z) | x = x * (((x * y) * x) * y) | true |
hard_0019 | 19 | hard | 3,926 | 3,920 | x * y = (x * (y * x)) * z | x * y = (x * (x * z)) * x | false |
hard_0020 | 20 | hard | 4,508 | 4,527 | x * (y * z) = (x * x) * z | x * (y * z) = (y * y) * x | false |
hard_0021 | 21 | hard | 907 | 221 | x = y * ((y * x) * (x * y)) | x = (y * (x * y)) * x | false |
hard_0022 | 22 | hard | 3,961 | 3,722 | x * y = (y * (y * x)) * x | x * y = (x * y) * (x * y) | false |
hard_0023 | 23 | hard | 164 | 3,470 | x = (x * y) * (z * z) | x * x = x * ((y * z) * w) | true |
hard_0024 | 24 | hard | 706 | 860 | x = y * (y * ((x * y) * x)) | x = x * ((y * z) * (z * x)) | false |
hard_0025 | 25 | hard | 3,008 | 1,131 | x = ((y * (z * z)) * x) * y | x = y * ((y * (z * x)) * z) | false |
hard_0026 | 26 | hard | 2,890 | 3,261 | x = ((x * (y * z)) * z) * x | x * x = x * (y * (y * x)) | false |
hard_0027 | 27 | hard | 54 | 2,695 | x = x * (y * (x * z)) | x = ((x * y) * (z * w)) * u | true |
hard_0028 | 28 | hard | 3,583 | 4,406 | x * y = z * ((x * x) * y) | x * (x * y) = (y * x) * y | false |
hard_0029 | 29 | hard | 1,738 | 3,972 | x = (y * y) * ((z * x) * x) | x * y = (y * (z * x)) * y | false |
hard_0030 | 30 | hard | 2,301 | 4,303 | x = (y * (x * (y * x))) * y | x * (x * y) = z * (y * x) | false |
hard_0031 | 31 | hard | 2,089 | 900 | x = ((y * x) * x) * (x * z) | x = y * ((x * z) * (z * w)) | false |
hard_0032 | 32 | hard | 2,089 | 404 | x = ((y * x) * x) * (x * z) | x * y = (z * z) * z | false |
hard_0033 | 33 | hard | 2,994 | 2,623 | x = ((y * (z * y)) * y) * x | x = (y * ((z * w) * y)) * x | false |
hard_0034 | 34 | hard | 386 | 3,639 | x * y = (y * x) * z | x * y = z * ((w * y) * y) | true |
hard_0035 | 35 | hard | 868 | 2,243 | x = x * ((y * z) * (w * u)) | x = (x * (x * (y * x))) * x | true |
hard_0036 | 36 | hard | 3,290 | 3,264 | x * x = y * (z * (x * z)) | x * x = x * (y * (z * x)) | false |
hard_0037 | 37 | hard | 1,336 | 419 | x = y * (((y * z) * y) * x) | x = x * (x * (y * (y * x))) | false |
hard_0038 | 38 | hard | 3,919 | 3,330 | x * y = (x * (x * y)) * z | x * y = x * (z * (y * y)) | false |
hard_0039 | 39 | hard | 830 | 1,229 | x = x * ((x * y) * (z * z)) | x = x * (((x * y) * x) * y) | false |
hard_0040 | 40 | hard | 1,070 | 3,950 | x = x * ((y * (z * w)) * w) | x * y = (x * (z * w)) * u | true |
hard_0041 | 41 | hard | 3,118 | 3,441 | x = (((y * x) * y) * z) * x | x * y = z * (w * (z * y)) | true |
hard_0042 | 42 | hard | 168 | 431 | x = (y * x) * (x * z) | x = x * (y * (x * (y * z))) | false |
hard_0043 | 43 | hard | 3,277 | 3,473 | x * x = y * (x * (z * w)) | x * x = y * ((x * x) * z) | false |
hard_0044 | 44 | hard | 234 | 3,065 | x = (y * (y * z)) * x | x = (((x * y) * x) * x) * x | true |
hard_0045 | 45 | hard | 1,480 | 1,882 | x = (y * x) * (x * (x * z)) | x = (x * (y * z)) * (w * w) | false |
hard_0046 | 46 | hard | 3,550 | 3,282 | x * y = y * ((x * y) * z) | x * x = y * (y * (y * y)) | true |
hard_0047 | 47 | hard | 1,486 | 913 | x = (y * x) * (x * (z * z)) | x = y * ((y * x) * (z * y)) | false |
hard_0048 | 48 | hard | 242 | 3,197 | x = (y * (z * y)) * x | x = (((y * z) * y) * y) * x | false |
hard_0049 | 49 | hard | 4,541 | 4,578 | x * (y * z) = (z * x) * y | x * (y * z) = (w * u) * y | false |
hard_0050 | 50 | hard | 1,274 | 2,647 | x = x * (((y * z) * w) * u) | x = ((x * x) * (x * y)) * y | true |
hard_0051 | 51 | hard | 4,150 | 4,243 | x * y = ((x * z) * w) * y | x * y = ((z * w) * x) * y | false |
hard_0052 | 52 | hard | 169 | 2,056 | x = (y * x) * (y * x) | x = ((x * y) * x) * (z * x) | true |
hard_0053 | 53 | hard | 3,738 | 3,727 | x * y = (x * z) * (y * w) | x * y = (x * y) * (z * x) | false |
hard_0054 | 54 | hard | 4,246 | 4,469 | x * y = ((z * w) * x) * u | x * (y * y) = (x * x) * x | true |
hard_0055 | 55 | hard | 1,400 | 1,364 | x = y * (((z * w) * x) * x) | x = y * (((z * x) * w) * w) | false |
hard_0056 | 56 | hard | 1,953 | 608 | x = (y * (y * z)) * (w * x) | x = y * (z * (w * (u * x))) | true |
hard_0057 | 57 | hard | 964 | 698 | x = y * ((z * y) * (y * x)) | x = y * (x * ((z * w) * x)) | false |
hard_0058 | 58 | hard | 4,574 | 4,438 | x * (y * z) = (w * w) * z | x * (y * x) = (x * z) * x | false |
hard_0059 | 59 | hard | 298 | 1,045 | x = ((y * z) * z) * x | x = x * ((y * (y * x)) * x) | true |
hard_0060 | 60 | hard | 3,184 | 1,288 | x = (((y * z) * x) * z) * x | x = y * (((x * y) * y) * x) | true |
hard_0061 | 61 | hard | 447 | 1,247 | x = x * (y * (z * (x * y))) | x = x * (((y * x) * z) * w) | true |
hard_0062 | 62 | hard | 2,116 | 2,327 | x = ((y * x) * z) * (z * y) | x = (y * (y * (x * x))) * x | false |
hard_0063 | 63 | hard | 302 | 1,217 | x = ((y * z) * w) * x | x = y * ((z * (w * u)) * x) | true |
hard_0064 | 64 | hard | 862 | 2,466 | x = x * ((y * z) * (z * z)) | x = (x * ((y * y) * x)) * x | true |
hard_0065 | 65 | hard | 59 | 2,240 | x = x * (y * (z * y)) | x = (x * (x * (x * y))) * x | true |
hard_0066 | 66 | hard | 2,180 | 3,116 | x = ((y * z) * y) * (x * z) | x = (((y * x) * y) * y) * y | false |
hard_0067 | 67 | hard | 1,927 | 3,409 | x = (y * (y * x)) * (z * x) | x * y = z * (y * (w * y)) | true |
hard_0068 | 68 | hard | 3,478 | 4,316 | x * x = y * ((x * z) * y) | x * (y * x) = x * (z * x) | false |
hard_0069 | 69 | hard | 286 | 532 | x = ((y * y) * z) * x | x = y * (y * (z * (w * x))) | true |
hard_0070 | 70 | hard | 2,105 | 1,229 | x = ((y * x) * y) * (z * z) | x = x * (((x * y) * x) * y) | true |
hard_0071 | 71 | hard | 3,926 | 3,920 | x * y = (x * (y * x)) * z | x * y = (x * (x * z)) * x | false |
hard_0072 | 72 | hard | 4,508 | 4,527 | x * (y * z) = (x * x) * z | x * (y * z) = (y * y) * x | false |
hard_0073 | 73 | hard | 907 | 221 | x = y * ((y * x) * (x * y)) | x = (y * (x * y)) * x | false |
hard_0074 | 74 | hard | 3,961 | 3,722 | x * y = (y * (y * x)) * x | x * y = (x * y) * (x * y) | false |
hard_0075 | 75 | hard | 164 | 3,470 | x = (x * y) * (z * z) | x * x = x * ((y * z) * w) | true |
hard_0076 | 76 | hard | 706 | 860 | x = y * (y * ((x * y) * x)) | x = x * ((y * z) * (z * x)) | false |
hard_0077 | 77 | hard | 3,008 | 1,131 | x = ((y * (z * z)) * x) * y | x = y * ((y * (z * x)) * z) | false |
hard_0078 | 78 | hard | 2,890 | 3,261 | x = ((x * (y * z)) * z) * x | x * x = x * (y * (y * x)) | false |
hard_0079 | 79 | hard | 54 | 2,695 | x = x * (y * (x * z)) | x = ((x * y) * (z * w)) * u | true |
hard_0080 | 80 | hard | 3,583 | 4,406 | x * y = z * ((x * x) * y) | x * (x * y) = (y * x) * y | false |
hard_0081 | 81 | hard | 1,738 | 3,972 | x = (y * y) * ((z * x) * x) | x * y = (y * (z * x)) * y | false |
hard_0082 | 82 | hard | 2,301 | 4,303 | x = (y * (x * (y * x))) * y | x * (x * y) = z * (y * x) | false |
hard_0083 | 83 | hard | 2,089 | 900 | x = ((y * x) * x) * (x * z) | x = y * ((x * z) * (z * w)) | false |
hard_0084 | 84 | hard | 2,089 | 404 | x = ((y * x) * x) * (x * z) | x * y = (z * z) * z | false |
hard_0085 | 85 | hard | 2,994 | 2,623 | x = ((y * (z * y)) * y) * x | x = (y * ((z * w) * y)) * x | false |
hard_0086 | 86 | hard | 386 | 3,639 | x * y = (y * x) * z | x * y = z * ((w * y) * y) | true |
hard_0087 | 87 | hard | 868 | 2,243 | x = x * ((y * z) * (w * u)) | x = (x * (x * (y * x))) * x | true |
hard_0088 | 88 | hard | 3,290 | 3,264 | x * x = y * (z * (x * z)) | x * x = x * (y * (z * x)) | false |
hard_0089 | 89 | hard | 1,336 | 419 | x = y * (((y * z) * y) * x) | x = x * (x * (y * (y * x))) | false |
hard_0090 | 90 | hard | 3,919 | 3,330 | x * y = (x * (x * y)) * z | x * y = x * (z * (y * y)) | false |
hard_0091 | 91 | hard | 830 | 1,229 | x = x * ((x * y) * (z * z)) | x = x * (((x * y) * x) * y) | false |
hard_0092 | 92 | hard | 1,070 | 3,950 | x = x * ((y * (z * w)) * w) | x * y = (x * (z * w)) * u | true |
hard_0093 | 93 | hard | 3,118 | 3,441 | x = (((y * x) * y) * z) * x | x * y = z * (w * (z * y)) | true |
hard_0094 | 94 | hard | 168 | 431 | x = (y * x) * (x * z) | x = x * (y * (x * (y * z))) | false |
hard_0095 | 95 | hard | 3,277 | 3,473 | x * x = y * (x * (z * w)) | x * x = y * ((x * x) * z) | false |
hard_0096 | 96 | hard | 234 | 3,065 | x = (y * (y * z)) * x | x = (((x * y) * x) * x) * x | true |
hard_0097 | 97 | hard | 1,480 | 1,882 | x = (y * x) * (x * (x * z)) | x = (x * (y * z)) * (w * w) | false |
hard_0098 | 98 | hard | 3,550 | 3,282 | x * y = y * ((x * y) * z) | x * x = y * (y * (y * y)) | true |
hard_0099 | 99 | hard | 1,486 | 913 | x = (y * x) * (x * (z * z)) | x = y * ((y * x) * (z * y)) | false |
hard_0100 | 100 | hard | 242 | 3,197 | x = (y * (z * y)) * x | x = (((y * z) * y) * y) * x | false |
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