input:
Equation 1: x = y * (y * ((x * y) * x))
Equation 2: x * y = ((z * x) * w) * y

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True

difficulty: hard


input:
Equation 1: x * (y * z) = (z * w) * w
Equation 2: x * (y * x) = (x * y) * z

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x = ((y * z) * (z * x)) * y
Equation 2: x * x = (y * (y * y)) * y

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x = x * (y * ((y * z) * y))
Equation 2: x = x * ((x * (x * x)) * x)

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x = ((x * x) * (y * z)) * y
Equation 2: x = ((x * (y * x)) * x) * y

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x = (y * x) * (x * (x * z))
Equation 2: x = y * (z * (z * (x * y)))

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x * x = x * (y * (z * y))
Equation 2: x * (x * x) = x * (y * x)

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x = (x * y) * (x * (y * z))
Equation 2: x = (x * y) * (x * (z * y))

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x * y = (y * (y * x)) * x
Equation 2: x * y = (x * y) * (x * y)

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x = y * (y * ((x * y) * x))
Equation 2: x = x * ((y * z) * (z * x))

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x = ((y * (z * z)) * x) * y
Equation 2: x = y * ((y * (z * x)) * z)

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x = ((x * (y * z)) * z) * x
Equation 2: x * x = x * (y * (y * x))

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x = x * (y * (x * z))
Equation 2: x = ((x * y) * (z * w)) * u

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: True

answer: False


input:
Equation 1: x * y = z * ((x * x) * y)
Equation 2: x * (x * y) = (y * x) * y

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x = (y * y) * ((z * x) * x)
Equation 2: x * y = (y * (z * x)) * y

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x = (y * (x * (y * x))) * y
Equation 2: x * (x * y) = z * (y * x)

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x = ((y * x) * x) * (x * z)
Equation 2: x = y * ((x * z) * (z * w))

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x = ((y * x) * x) * (x * z)
Equation 2: x * y = (z * z) * z

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x = x * ((y * z) * (w * u))
Equation 2: x = (x * (x * (y * x))) * x

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: True

answer: False


input:
Equation 1: x = y * (((y * z) * y) * x)
Equation 2: x = x * (x * (y * (y * x)))

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: UNPARSEABLE


input:
Equation 1: x * y = (x * (x * y)) * z
Equation 2: x * y = x * (z * (y * y))

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x = (y * x) * (x * z)
Equation 2: x = x * (y * (x * (y * z)))

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x * x = y * (x * (z * w))
Equation 2: x * x = y * ((x * x) * z)

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x = (y * x) * (x * (x * z))
Equation 2: x = (x * (y * z)) * (w * w)

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x = (y * x) * (x * (z * z))
Equation 2: x = y * ((y * x) * (z * y))

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: UNPARSEABLE


input:
Equation 1: x * y = (x * z) * (y * w)
Equation 2: x * y = (x * y) * (z * x)

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x = y * ((z * y) * (y * x))
Equation 2: x = y * (x * ((z * w) * x))

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x * (y * z) = (w * w) * z
Equation 2: x * (y * x) = (x * z) * x

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x = ((y * z) * z) * x
Equation 2: x = x * ((y * (y * x)) * x)

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: True

answer: False


input:
Equation 1: x = x * (y * (z * (x * y)))
Equation 2: x = x * (((y * x) * z) * w)

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: True

answer: False


input:
Equation 1: x = ((y * x) * z) * (z * y)
Equation 2: x = (y * (y * (x * x))) * x

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x = x * ((y * z) * (z * z))
Equation 2: x = (x * ((y * y) * x)) * x

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: True

answer: False


input:
Equation 1: x = x * (y * (z * y))
Equation 2: x = (x * (x * (x * y))) * x

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: True

answer: False


input:
Equation 1: x = ((y * z) * y) * (x * z)
Equation 2: x = (((y * x) * y) * y) * y

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x = (y * (y * x)) * (z * x)
Equation 2: x * y = z * (y * (w * y))

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: True

answer: False


input:
Equation 1: x * x = y * ((x * z) * y)
Equation 2: x * (y * x) = x * (z * x)

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x * (y * z) = (y * w) * w
Equation 2: x * (y * y) = (z * w) * u

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x = y * ((y * (y * x)) * x)
Equation 2: x = (y * (z * y)) * (y * x)

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x * (x * y) = (z * y) * w
Equation 2: x * (x * y) = y * (z * y)

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x = y * ((x * z) * (z * y))
Equation 2: x = ((x * y) * (y * y)) * y

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x = (x * y) * ((x * y) * y)
Equation 2: x = (x * (x * (x * x))) * y

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x = y * ((x * (x * y)) * y)
Equation 2: x = (y * (z * z)) * w

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x = y * (((z * y) * x) * z)
Equation 2: (x * x) * y = (y * z) * z

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x = (y * ((y * x) * x)) * y
Equation 2: x = x * (((x * y) * x) * z)

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x = y * ((x * (x * y)) * y)
Equation 2: (x * y) * z = (z * y) * x

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x = x * (y * ((y * z) * y))
Equation 2: x * y = ((x * y) * x) * x

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x = x * ((x * (y * z)) * z)
Equation 2: x = x * (x * (y * x))

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: True

answer: False


input:
Equation 1: x * (y * z) = z * (w * u)
Equation 2: (x * y) * y = (x * z) * y

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x * y = x * ((z * y) * x)
Equation 2: x * y = x * (x * (y * y))

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x = y * ((z * (y * y)) * x)
Equation 2: x = (y * z) * ((x * z) * x)

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x * y = ((y * y) * x) * x
Equation 2: x * y = (x * (y * y)) * x

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x = y * ((x * (x * y)) * y)
Equation 2: x = ((y * (z * w)) * u) * z

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x * y = (z * (x * w)) * y
Equation 2: x * x = (y * (y * y)) * x

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x * y = (y * (x * z)) * z
Equation 2: x * y = y * ((z * z) * x)

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x = y * ((x * (x * y)) * y)
Equation 2: x = y * (y * (y * (z * w)))

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x = y * ((y * (x * y)) * x)
Equation 2: x = (x * (y * x)) * (x * x)

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x * (y * x) = (z * w) * u
Equation 2: x * (y * z) = (w * x) * w

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x = ((x * (x * y)) * y) * y
Equation 2: x * (y * x) = x * (y * z)

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: (x * y) * z = (w * z) * u
Equation 2: x * (x * x) = y * (z * w)

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x * y = (y * (x * z)) * y
Equation 2: x * x = ((x * x) * y) * x

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x = y * ((x * (x * y)) * y)
Equation 2: x = x * (y * (z * (w * y)))

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x = y * ((y * (y * x)) * x)
Equation 2: x = ((y * z) * z) * (w * x)

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x = x * (y * ((x * z) * y))
Equation 2: x = x * ((y * (z * w)) * w)

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: True

answer: False


input:
Equation 1: x = (y * z) * (z * (x * y))
Equation 2: x = y * (z * (y * (z * x)))

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x = ((y * x) * z) * (z * y)
Equation 2: x = (y * (y * y)) * (x * y)

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x * (x * y) = (z * w) * u
Equation 2: x * (y * z) = y * (x * z)

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x = (y * ((y * x) * x)) * y
Equation 2: x = (((x * y) * x) * x) * x

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x * (y * z) = (z * y) * y
Equation 2: x * (y * z) = (y * z) * w

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x = (x * (x * y)) * y
Equation 2: x * (y * z) = x * (z * y)

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x * y = (y * (x * z)) * y
Equation 2: x * y = ((x * y) * x) * y

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x * (y * z) = (w * u) * u
Equation 2: x * (y * z) = (y * w) * u

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x = (y * y) * (x * (y * x))
Equation 2: x * y = (x * (x * x)) * y

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x = y * ((z * (z * y)) * x)
Equation 2: x * y = (y * (y * x)) * y

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x = y * ((z * y) * (y * x))
Equation 2: x * y = ((z * x) * x) * y

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x = (x * (x * (y * y))) * z
Equation 2: x * x = ((x * y) * z) * w

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: True

answer: False


input:
Equation 1: x = (y * (x * (y * z))) * y
Equation 2: x = y * ((y * (x * x)) * x)

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: True

answer: False


input:
Equation 1: x = (x * ((x * y) * y)) * y
Equation 2: x * y = ((x * y) * y) * x

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x = (y * ((y * x) * x)) * y
Equation 2: x = ((y * (z * x)) * w) * x

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x = y * ((y * (y * x)) * x)
Equation 2: x * (x * y) = y * (x * y)

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x * x = ((y * z) * w) * u
Equation 2: x * (y * z) = (w * u) * z

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x = (y * x) * (x * (y * z))
Equation 2: x * (y * y) = (x * y) * x

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x = y * (((z * x) * x) * x)
Equation 2: x = x * ((x * (x * y)) * x)

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: True

answer: False


input:
Equation 1: x = (((x * y) * y) * x) * y
Equation 2: x * x = x * ((y * z) * x)

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x = (x * ((x * y) * y)) * y
Equation 2: x = (x * y) * (x * (y * z))

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x = y * ((y * (y * x)) * x)
Equation 2: x = y * (((z * x) * x) * x)

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x = y * (((z * y) * x) * z)
Equation 2: x * (y * z) = x * (z * y)

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x = ((x * x) * y) * (y * z)
Equation 2: x * x = x * (x * (y * z))

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x = ((x * (y * z)) * z) * x
Equation 2: x = ((x * x) * (y * y)) * x

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x = y * (z * ((z * y) * x))
Equation 2: x = y * (x * ((y * x) * x))

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x = y * ((x * z) * (z * y))
Equation 2: x = y * ((z * x) * (y * z))

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x = (y * (y * x)) * (y * x)
Equation 2: x * y = ((z * y) * w) * y

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x = (x * y) * ((z * w) * x)
Equation 2: x * y = ((x * z) * x) * y

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x * x = y * (z * (w * u))
Equation 2: x * (x * y) = y * (y * x)

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: (x * y) * z = (z * w) * u
Equation 2: x * (y * z) = (y * z) * z

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x = (y * ((y * x) * x)) * y
Equation 2: x * y = z * (w * (x * z))

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x = ((y * (z * y)) * x) * w
Equation 2: x = x * (((y * y) * x) * z)

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: True

answer: False


input:
Equation 1: x = (x * ((x * y) * y)) * y
Equation 2: x * y = ((x * z) * x) * w

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x = (x * (y * z)) * (w * x)
Equation 2: (x * y) * z = (x * w) * z

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x = ((y * x) * z) * (z * y)
Equation 2: x = y * (x * ((z * y) * z))

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
Equation 1: x = (y * (y * (x * y))) * y
Equation 2: x = (x * ((x * x) * x)) * x

Does Equation 1 imply Equation 2 over all magmas?
Answer True or False.

target: False

answer: True


input:
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.

target: False

answer: True


input:
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.

target: False

answer: True


input:
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.

target: False

answer: True


input:
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.

target: False

answer: True


input:
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.

target: False

answer: True


input:
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.

target: False

answer: True


input:
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.

target: False

answer: True


input:
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.

target: False

answer: True


input:
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.

target: False

answer: True


input:
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.

target: True

answer: False


input:
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.

target: False

answer: True


input:
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.

target: False

answer: True


input:
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.

target: False

answer: True


input:
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.

target: False

answer: True


input:
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.

target: False

answer: True


input:
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.

target: False

answer: True


input:
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.

target: True

answer: False


input:
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.

target: False

answer: True

difficulty: normal


input:
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.

target: True

answer: False


input:
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.

target: False

answer: True


input:
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.

target: True

answer: False


input:
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.

target: False

answer: True


input:
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.

target: True

answer: False


input:
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.

target: False

answer: True


input:
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.

target: False

answer: True


input:
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.

target: False

answer: True


input:
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.

target: True

answer: False


input:
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.

target: False

answer: True


input:
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.

target: False

answer: True

equation2: x * x = x * y


input:
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.

target: False

answer: True


input:
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.

target: True

answer: False


input:
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.

target: False

answer: True


input:
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.

target: False

answer: True


input:
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.

target: True

answer: False


input:
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.

target: False

answer: True


input:
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.

target: False

answer: True


input:
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.

target: False

answer: True


input:
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.

target: False

answer: True


input:
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.

target: False

answer: True


input:
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.

target: False

answer: True


input:
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.

target: False

answer: True


input:
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.

target: False

answer: True


input:
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.

target: False

answer: True


input:
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.

target: True

answer: False


input:
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.

target: False

answer: True


input:
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.

target: False

answer: True


input:
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.

target: False

answer: True


input:
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.

target: False

answer: True


input:
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.

target: False

answer: True


input:
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.

target: False

answer: UNPARSEABLE


input:
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.

target: False

answer: True


input:
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.

target: False

answer: True


input:
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.

target: False

answer: True


input:
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.

target: False

answer: True


input:
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.

target: True

answer: False


input:
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.

target: True

answer: False


input:
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.

target: False

answer: True


input:
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.

target: False

answer: True


input:
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.

target: False

answer: True


input:
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.

target: False

answer: True


input:
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.

target: False

answer: True


input:
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.

target: True

answer: False


input:
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.

target: False

answer: True


input:
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.

target: False

answer: True


input:
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.

target: False

answer: True


input:
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.

target: False

answer: True


input:
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.

target: False

answer: True


input:
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.

target: True

answer: False


input:
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.

target: False

answer: True


input:
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.

target: False

answer: True


input:
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.

target: False

answer: True


input:
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.

target: False

answer: True


input:
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.

target: False

answer: True


input:
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.

target: False

answer: True