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I have a system of equations \begin{align} & (\epsilon_2 = \epsilon_4, \text{ or } \epsilon_1 \epsilon_4 = -1, \text{ or } \epsilon_1 = \epsilon_2), \\ & \text{and } (\epsilon_3 = \epsilon_4, \text{ or } \epsilon_1 \epsilon_4 = -1, \text{ or } \epsilon_1 = \epsilon_3) \\ & \epsilon_1,\epsilon_2,\epsilon_3,\epsilon_4 \in \{1,-1\}. \end{align} The solutions of $\epsilon_1,\ldots, \epsilon_4$ are \begin{align} & 1, 1, 1, 1, \\ & 1, -1, 1, -1, \\ & -1, 1, -1, 1, \\ & -1, -1, -1, -1, \\ & 1, 1, 1, -1, \\ & 1, 1, -1, -1, \\ & 1, -1, -1, -1, \\ & -1, 1, 1, 1, \\ & -1, -1, 1, 1, \\ & -1, -1, -1, 1. \end{align} I obtained this result by writing a small program.

I have other similar system of equations and the number of equations in the system is very large. So I would like to use some software which can solve this kind of system of equations directly. Are there some software which can solve this kind of system of equations? Thank you very much.

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    Have you noted that these $\epsilon$s can be understood as truth values, with $a=b$ if a xor b is false, and $ab=-1$ if a xor b is true? Logic programming is pretty well established... – 2017-01-03

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