id string | input string | target string | answer string | metadata dict |
|---|---|---|---|---|
hard2_0171 | Equation 1: x = y * ((x * (x * y)) * y)
Equation 2: x * y = (x * (z * z)) * w
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | False | True | {
"equation1": "x = y * ((x * (x * y)) * y)",
"equation2": "x * y = (x * (z * z)) * w",
"difficulty": "hard",
"index": 171
} |
hard2_0172 | Equation 1: x = y * ((x * (x * y)) * y)
Equation 2: x = ((y * y) * z) * (z * x)
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | False | True | {
"equation1": "x = y * ((x * (x * y)) * y)",
"equation2": "x = ((y * y) * z) * (z * x)",
"difficulty": "hard",
"index": 172
} |
hard2_0175 | Equation 1: x = ((y * z) * (z * x)) * y
Equation 2: x = ((x * (x * y)) * x) * y
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | False | True | {
"equation1": "x = ((y * z) * (z * x)) * y",
"equation2": "x = ((x * (x * y)) * x) * y",
"difficulty": "hard",
"index": 175
} |
hard2_0176 | Equation 1: x = ((x * (y * y)) * z) * x
Equation 2: x = ((x * (y * z)) * w) * x
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | False | True | {
"equation1": "x = ((x * (y * y)) * z) * x",
"equation2": "x = ((x * (y * z)) * w) * x",
"difficulty": "hard",
"index": 176
} |
hard2_0177 | Equation 1: x = (y * ((y * x) * x)) * y
Equation 2: x = (y * (x * (z * y))) * x
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | False | True | {
"equation1": "x = (y * ((y * x) * x)) * y",
"equation2": "x = (y * (x * (z * y))) * x",
"difficulty": "hard",
"index": 177
} |
hard2_0179 | Equation 1: x = (y * x) * (x * (z * y))
Equation 2: (x * y) * x = (y * x) * x
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | False | True | {
"equation1": "x = (y * x) * (x * (z * y))",
"equation2": "(x * y) * x = (y * x) * x",
"difficulty": "hard",
"index": 179
} |
hard2_0180 | Equation 1: x * x = (y * (z * w)) * u
Equation 2: x * (y * z) = (z * x) * y
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | False | True | {
"equation1": "x * x = (y * (z * w)) * u",
"equation2": "x * (y * z) = (z * x) * y",
"difficulty": "hard",
"index": 180
} |
hard2_0181 | Equation 1: x = x * (y * ((y * z) * y))
Equation 2: x = ((x * (x * y)) * z) * x
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | False | True | {
"equation1": "x = x * (y * ((y * z) * y))",
"equation2": "x = ((x * (x * y)) * z) * x",
"difficulty": "hard",
"index": 181
} |
hard2_0182 | Equation 1: x = y * ((x * (x * y)) * y)
Equation 2: x * y = z * (y * (z * w))
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | False | True | {
"equation1": "x = y * ((x * (x * y)) * y)",
"equation2": "x * y = z * (y * (z * w))",
"difficulty": "hard",
"index": 182
} |
hard2_0186 | Equation 1: x = y * (x * ((x * x) * z))
Equation 2: x = y * (y * (x * (x * z)))
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | True | False | {
"equation1": "x = y * (x * ((x * x) * z))",
"equation2": "x = y * (y * (x * (x * z)))",
"difficulty": "hard",
"index": 186
} |
hard2_0187 | Equation 1: x = (y * z) * (z * x)
Equation 2: x = y * ((y * (z * y)) * x)
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | False | True | {
"equation1": "x = (y * z) * (z * x)",
"equation2": "x = y * ((y * (z * y)) * x)",
"difficulty": "hard",
"index": 187
} |
hard2_0188 | Equation 1: (x * y) * z = (z * w) * x
Equation 2: (x * x) * y = (z * w) * y
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | False | True | {
"equation1": "(x * y) * z = (z * w) * x",
"equation2": "(x * x) * y = (z * w) * y",
"difficulty": "hard",
"index": 188
} |
hard2_0194 | Equation 1: x = (y * ((y * x) * x)) * y
Equation 2: x = (y * (x * (y * x))) * y
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | False | True | {
"equation1": "x = (y * ((y * x) * x)) * y",
"equation2": "x = (y * (x * (y * x))) * y",
"difficulty": "hard",
"index": 194
} |
hard2_0195 | Equation 1: x * (x * y) = (z * y) * w
Equation 2: x * (y * x) = (z * z) * x
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | False | True | {
"equation1": "x * (x * y) = (z * y) * w",
"equation2": "x * (y * x) = (z * z) * x",
"difficulty": "hard",
"index": 195
} |
hard2_0196 | Equation 1: x = (y * ((y * x) * x)) * y
Equation 2: x = x * ((y * y) * (z * y))
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | False | True | {
"equation1": "x = (y * ((y * x) * x)) * y",
"equation2": "x = x * ((y * y) * (z * y))",
"difficulty": "hard",
"index": 196
} |
hard2_0197 | Equation 1: x * x = y * (z * (y * w))
Equation 2: x * x = y * (z * (x * z))
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | False | True | {
"equation1": "x * x = y * (z * (y * w))",
"equation2": "x * x = y * (z * (x * z))",
"difficulty": "hard",
"index": 197
} |
hard2_0199 | Equation 1: x = ((x * y) * (x * z)) * w
Equation 2: x = ((x * (x * x)) * x) * y
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | True | False | {
"equation1": "x = ((x * y) * (x * z)) * w",
"equation2": "x = ((x * (x * x)) * x) * y",
"difficulty": "hard",
"index": 199
} |
normal_0029 | Equation 1: x = x * (x * ((y * z) * z))
Equation 2: x = (x * x) * (y * (z * y))
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | False | True | {
"equation1": "x = x * (x * ((y * z) * z))",
"equation2": "x = (x * x) * (y * (z * y))",
"difficulty": "normal",
"index": 29
} |
normal_0050 | Equation 1: x = (y * x) * (y * (z * y))
Equation 2: x = ((y * z) * w) * (y * w)
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | True | False | {
"equation1": "x = (y * x) * (y * (z * y))",
"equation2": "x = ((y * z) * w) * (y * w)",
"difficulty": "normal",
"index": 50
} |
normal_0053 | Equation 1: x = (y * x) * (x * (z * x))
Equation 2: x = (((y * z) * w) * w) * x
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | False | True | {
"equation1": "x = (y * x) * (x * (z * x))",
"equation2": "x = (((y * z) * w) * w) * x",
"difficulty": "normal",
"index": 53
} |
normal_0062 | Equation 1: x = ((y * x) * (y * z)) * y
Equation 2: x = ((y * z) * (y * w)) * u
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | True | False | {
"equation1": "x = ((y * x) * (y * z)) * y",
"equation2": "x = ((y * z) * (y * w)) * u",
"difficulty": "normal",
"index": 62
} |
normal_0094 | Equation 1: x * (x * y) = z * (x * z)
Equation 2: x * y = (z * w) * w
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | False | True | {
"equation1": "x * (x * y) = z * (x * z)",
"equation2": "x * y = (z * w) * w",
"difficulty": "normal",
"index": 94
} |
normal_0161 | Equation 1: x = y * (y * ((x * z) * z))
Equation 2: x * y = y * ((z * x) * z)
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | True | False | {
"equation1": "x = y * (y * ((x * z) * z))",
"equation2": "x * y = y * ((z * x) * z)",
"difficulty": "normal",
"index": 161
} |
normal_0176 | Equation 1: x = ((y * x) * x) * (y * y)
Equation 2: (x * y) * x = (z * x) * y
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | False | True | {
"equation1": "x = ((y * x) * x) * (y * y)",
"equation2": "(x * y) * x = (z * x) * y",
"difficulty": "normal",
"index": 176
} |
normal_0183 | Equation 1: x = ((y * (z * w)) * y) * x
Equation 2: x * y = ((y * x) * x) * z
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | False | True | {
"equation1": "x = ((y * (z * w)) * y) * x",
"equation2": "x * y = ((y * x) * x) * z",
"difficulty": "normal",
"index": 183
} |
normal_0204 | Equation 1: x = (y * (y * (x * y))) * y
Equation 2: x * y = (y * x) * (z * z)
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | False | True | {
"equation1": "x = (y * (y * (x * y))) * y",
"equation2": "x * y = (y * x) * (z * z)",
"difficulty": "normal",
"index": 204
} |
normal_0219 | Equation 1: x = y * (x * (y * (x * z)))
Equation 2: x * x = y * (x * (z * y))
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | True | False | {
"equation1": "x = y * (x * (y * (x * z)))",
"equation2": "x * x = y * (x * (z * y))",
"difficulty": "normal",
"index": 219
} |
normal_0223 | Equation 1: x = ((y * (x * y)) * x) * y
Equation 2: x = ((y * (z * w)) * u) * z
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | False | True | {
"equation1": "x = ((y * (x * y)) * x) * y",
"equation2": "x = ((y * (z * w)) * u) * z",
"difficulty": "normal",
"index": 223
} |
normal_0251 | Equation 1: x = ((y * x) * (x * y)) * y
Equation 2: x * x = x * y
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | False | True | {
"equation1": "x = ((y * x) * (x * y)) * y",
"equation2": "x * x = x * y",
"difficulty": "normal",
"index": 251
} |
normal_0272 | Equation 1: x = (y * ((x * x) * y)) * y
Equation 2: (x * y) * z = (x * z) * w
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | False | True | {
"equation1": "x = (y * ((x * x) * y)) * y",
"equation2": "(x * y) * z = (x * z) * w",
"difficulty": "normal",
"index": 272
} |
normal_0303 | Equation 1: x = (y * (z * x)) * z
Equation 2: x = y * (((z * x) * x) * y)
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | True | False | {
"equation1": "x = (y * (z * x)) * z",
"equation2": "x = y * (((z * x) * x) * y)",
"difficulty": "normal",
"index": 303
} |
normal_0305 | Equation 1: x = (y * y) * ((x * z) * z)
Equation 2: x = x * (y * (z * (y * z)))
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | False | True | {
"equation1": "x = (y * y) * ((x * z) * z)",
"equation2": "x = x * (y * (z * (y * z)))",
"difficulty": "normal",
"index": 305
} |
normal_0307 | Equation 1: x = (y * (x * x)) * (y * y)
Equation 2: (x * y) * y = (z * y) * w
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | False | True | {
"equation1": "x = (y * (x * x)) * (y * y)",
"equation2": "(x * y) * y = (z * y) * w",
"difficulty": "normal",
"index": 307
} |
normal_0324 | Equation 1: x * x = ((y * x) * x) * z
Equation 2: x * x = ((y * z) * z) * x
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | True | False | {
"equation1": "x * x = ((y * x) * x) * z",
"equation2": "x * x = ((y * z) * z) * x",
"difficulty": "normal",
"index": 324
} |
normal_0326 | Equation 1: x = x * (y * ((y * z) * y))
Equation 2: x = ((x * (x * y)) * y) * x
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | False | True | {
"equation1": "x = x * (y * ((y * z) * y))",
"equation2": "x = ((x * (x * y)) * y) * x",
"difficulty": "normal",
"index": 326
} |
normal_0335 | Equation 1: x = y * (x * (x * y))
Equation 2: x = (x * (y * (y * z))) * w
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | False | True | {
"equation1": "x = y * (x * (x * y))",
"equation2": "x = (x * (y * (y * z))) * w",
"difficulty": "normal",
"index": 335
} |
normal_0343 | Equation 1: x = (y * (x * y)) * (x * y)
Equation 2: x = y * (y * (z * (z * z)))
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | False | True | {
"equation1": "x = (y * (x * y)) * (x * y)",
"equation2": "x = y * (y * (z * (z * z)))",
"difficulty": "normal",
"index": 343
} |
normal_0356 | Equation 1: x * x = ((y * x) * y) * z
Equation 2: x * y = (y * (z * x)) * z
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | False | True | {
"equation1": "x * x = ((y * x) * y) * z",
"equation2": "x * y = (y * (z * x)) * z",
"difficulty": "normal",
"index": 356
} |
normal_0364 | Equation 1: x = ((y * x) * x) * (x * x)
Equation 2: x = y * (((y * z) * z) * x)
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | False | True | {
"equation1": "x = ((y * x) * x) * (x * x)",
"equation2": "x = y * (((y * z) * z) * x)",
"difficulty": "normal",
"index": 364
} |
normal_0381 | Equation 1: x = (y * ((y * x) * x)) * x
Equation 2: x = (y * ((z * y) * y)) * x
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | False | True | {
"equation1": "x = (y * ((y * x) * x)) * x",
"equation2": "x = (y * ((z * y) * y)) * x",
"difficulty": "normal",
"index": 381
} |
normal_0440 | Equation 1: x * x = y * (z * w)
Equation 2: x * x = (y * (z * y)) * z
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | False | True | {
"equation1": "x * x = y * (z * w)",
"equation2": "x * x = (y * (z * y)) * z",
"difficulty": "normal",
"index": 440
} |
normal_0453 | Equation 1: x = ((y * y) * x) * (x * x)
Equation 2: (x * y) * z = (x * w) * z
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | False | True | {
"equation1": "x = ((y * y) * x) * (x * x)",
"equation2": "(x * y) * z = (x * w) * z",
"difficulty": "normal",
"index": 453
} |
normal_0512 | Equation 1: x * (x * y) = (z * y) * x
Equation 2: (x * y) * x = (z * y) * z
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | False | True | {
"equation1": "x * (x * y) = (z * y) * x",
"equation2": "(x * y) * x = (z * y) * z",
"difficulty": "normal",
"index": 512
} |
normal_0522 | Equation 1: x = (y * y) * (y * (z * x))
Equation 2: x * y = (y * y) * y
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | True | False | {
"equation1": "x = (y * y) * (y * (z * x))",
"equation2": "x * y = (y * y) * y",
"difficulty": "normal",
"index": 522
} |
normal_0543 | Equation 1: x * (y * x) = (z * z) * w
Equation 2: x * y = (y * y) * (z * z)
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | False | True | {
"equation1": "x * (y * x) = (z * z) * w",
"equation2": "x * y = (y * y) * (z * z)",
"difficulty": "normal",
"index": 543
} |
normal_0565 | Equation 1: x = (y * (x * x)) * (y * y)
Equation 2: x = (y * y) * (x * (z * x))
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | False | True | {
"equation1": "x = (y * (x * x)) * (y * y)",
"equation2": "x = (y * y) * (x * (z * x))",
"difficulty": "normal",
"index": 565
} |
normal_0592 | Equation 1: x = (y * y) * ((x * z) * z)
Equation 2: x = (x * y) * (y * (y * y))
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | False | True | {
"equation1": "x = (y * y) * ((x * z) * z)",
"equation2": "x = (x * y) * (y * (y * y))",
"difficulty": "normal",
"index": 592
} |
normal_0619 | Equation 1: x * y = ((z * x) * z) * y
Equation 2: x * (x * x) = x * (y * x)
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | False | True | {
"equation1": "x * y = ((z * x) * z) * y",
"equation2": "x * (x * x) = x * (y * x)",
"difficulty": "normal",
"index": 619
} |
normal_0628 | Equation 1: x = ((y * y) * (x * x)) * y
Equation 2: x = y * (z * ((z * y) * w))
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | False | True | {
"equation1": "x = ((y * y) * (x * x)) * y",
"equation2": "x = y * (z * ((z * y) * w))",
"difficulty": "normal",
"index": 628
} |
normal_0632 | Equation 1: x * y = y * ((z * z) * x)
Equation 2: x * x = (y * (x * x)) * x
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | False | UNPARSEABLE | {
"equation1": "x * y = y * ((z * z) * x)",
"equation2": "x * x = (y * (x * x)) * x",
"difficulty": "normal",
"index": 632
} |
normal_0700 | Equation 1: x = (y * ((x * y) * z)) * z
Equation 2: x * (y * y) = (x * z) * z
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | False | True | {
"equation1": "x = (y * ((x * y) * z)) * z",
"equation2": "x * (y * y) = (x * z) * z",
"difficulty": "normal",
"index": 700
} |
normal_0703 | Equation 1: x * (y * z) = (z * x) * x
Equation 2: x * y = z * ((w * w) * w)
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | False | True | {
"equation1": "x * (y * z) = (z * x) * x",
"equation2": "x * y = z * ((w * w) * w)",
"difficulty": "normal",
"index": 703
} |
normal_0717 | Equation 1: x * x = y * (x * (z * w))
Equation 2: x * y = (y * (z * x)) * z
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | False | True | {
"equation1": "x * x = y * (x * (z * w))",
"equation2": "x * y = (y * (z * x)) * z",
"difficulty": "normal",
"index": 717
} |
normal_0745 | Equation 1: (x * y) * x = (y * z) * w
Equation 2: x * y = x * (x * (x * y))
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | False | True | {
"equation1": "(x * y) * x = (y * z) * w",
"equation2": "x * y = x * (x * (x * y))",
"difficulty": "normal",
"index": 745
} |
normal_0762 | Equation 1: x = y * ((y * x) * (x * z))
Equation 2: x = (y * x) * ((x * z) * y)
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | True | False | {
"equation1": "x = y * ((y * x) * (x * z))",
"equation2": "x = (y * x) * ((x * z) * y)",
"difficulty": "normal",
"index": 762
} |
normal_0802 | Equation 1: x = (((y * y) * z) * w) * x
Equation 2: x = ((y * (x * y)) * x) * x
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | True | False | {
"equation1": "x = (((y * y) * z) * w) * x",
"equation2": "x = ((y * (x * y)) * x) * x",
"difficulty": "normal",
"index": 802
} |
normal_0830 | Equation 1: x = y * (((x * x) * x) * y)
Equation 2: x = (y * x) * ((z * z) * y)
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | False | True | {
"equation1": "x = y * (((x * x) * x) * y)",
"equation2": "x = (y * x) * ((z * z) * y)",
"difficulty": "normal",
"index": 830
} |
normal_0831 | Equation 1: x * (y * z) = (y * y) * x
Equation 2: x * y = (z * x) * (y * x)
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | False | True | {
"equation1": "x * (y * z) = (y * y) * x",
"equation2": "x * y = (z * x) * (y * x)",
"difficulty": "normal",
"index": 831
} |
normal_0832 | Equation 1: x = ((x * x) * y) * (y * z)
Equation 2: x * x = ((x * x) * y) * x
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | False | True | {
"equation1": "x = ((x * x) * y) * (y * z)",
"equation2": "x * x = ((x * x) * y) * x",
"difficulty": "normal",
"index": 832
} |
normal_0837 | Equation 1: x = ((y * (x * x)) * y) * y
Equation 2: x * y = z * ((z * y) * z)
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | False | True | {
"equation1": "x = ((y * (x * x)) * y) * y",
"equation2": "x * y = z * ((z * y) * z)",
"difficulty": "normal",
"index": 837
} |
normal_0846 | Equation 1: x = ((x * (x * y)) * z) * w
Equation 2: x = (y * ((y * x) * z)) * y
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | False | True | {
"equation1": "x = ((x * (x * y)) * z) * w",
"equation2": "x = (y * ((y * x) * z)) * y",
"difficulty": "normal",
"index": 846
} |
normal_0848 | Equation 1: x = (y * x) * (y * (z * y))
Equation 2: x = ((y * z) * w) * (x * x)
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | True | False | {
"equation1": "x = (y * x) * (y * (z * y))",
"equation2": "x = ((y * z) * w) * (x * x)",
"difficulty": "normal",
"index": 848
} |
normal_0852 | Equation 1: x = y * (y * (x * (y * x)))
Equation 2: x = y * ((z * (x * w)) * x)
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | False | True | {
"equation1": "x = y * (y * (x * (y * x)))",
"equation2": "x = y * ((z * (x * w)) * x)",
"difficulty": "normal",
"index": 852
} |
normal_0882 | Equation 1: x * x = (y * (z * y)) * y
Equation 2: x * x = ((y * x) * y) * z
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | False | True | {
"equation1": "x * x = (y * (z * y)) * y",
"equation2": "x * x = ((y * x) * y) * z",
"difficulty": "normal",
"index": 882
} |
normal_0883 | Equation 1: x = ((y * z) * (w * y)) * x
Equation 2: x * (y * z) = (x * y) * y
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | False | True | {
"equation1": "x = ((y * z) * (w * y)) * x",
"equation2": "x * (y * z) = (x * y) * y",
"difficulty": "normal",
"index": 883
} |
normal_0898 | Equation 1: x = (y * ((y * y) * z)) * x
Equation 2: x = (y * x) * (y * y)
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | False | True | {
"equation1": "x = (y * ((y * y) * z)) * x",
"equation2": "x = (y * x) * (y * y)",
"difficulty": "normal",
"index": 898
} |
normal_0903 | Equation 1: x * y = y * (x * (x * x))
Equation 2: x * y = ((z * y) * z) * x
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | False | True | {
"equation1": "x * y = y * (x * (x * x))",
"equation2": "x * y = ((z * y) * z) * x",
"difficulty": "normal",
"index": 903
} |
normal_0906 | Equation 1: x = ((y * x) * (x * x)) * z
Equation 2: x = y * ((z * x) * (x * y))
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | True | False | {
"equation1": "x = ((y * x) * (x * x)) * z",
"equation2": "x = y * ((z * x) * (x * y))",
"difficulty": "normal",
"index": 906
} |
normal_0907 | Equation 1: x = ((x * (y * x)) * x) * z
Equation 2: x = (x * (y * (z * y))) * w
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | False | True | {
"equation1": "x = ((x * (y * x)) * x) * z",
"equation2": "x = (x * (y * (z * y))) * w",
"difficulty": "normal",
"index": 907
} |
normal_0956 | Equation 1: x = (y * x) * ((x * x) * y)
Equation 2: x = x * ((x * y) * (y * x))
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | False | True | {
"equation1": "x = (y * x) * ((x * x) * y)",
"equation2": "x = x * ((x * y) * (y * x))",
"difficulty": "normal",
"index": 956
} |
normal_0971 | Equation 1: x = (y * (x * z)) * (x * x)
Equation 2: x * y = y * (x * (z * y))
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | False | True | {
"equation1": "x = (y * (x * z)) * (x * x)",
"equation2": "x * y = y * (x * (z * y))",
"difficulty": "normal",
"index": 971
} |
normal_0987 | Equation 1: x * (y * z) = (w * z) * w
Equation 2: x * y = z * ((w * z) * u)
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | False | True | {
"equation1": "x * (y * z) = (w * z) * w",
"equation2": "x * y = z * ((w * z) * u)",
"difficulty": "normal",
"index": 987
} |
normal_0990 | Equation 1: x * (y * y) = (z * x) * x
Equation 2: x * x = ((x * y) * z) * w
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | False | True | {
"equation1": "x * (y * y) = (z * x) * x",
"equation2": "x * x = ((x * y) * z) * w",
"difficulty": "normal",
"index": 990
} |
normal_0997 | Equation 1: x = (y * z) * (x * (z * x))
Equation 2: x * x = (y * (y * y)) * x
Does Equation 1 imply Equation 2 over all magmas?
Answer True or False. | False | True | {
"equation1": "x = (y * z) * (x * (z * x))",
"equation2": "x * x = (y * (y * y)) * x",
"difficulty": "normal",
"index": 997
} |
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