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<source>noncommutative-ring.out</source>

<heading><![CDATA[
Mace4 (32) version 2009-02A, February 2009.
Process 11175 was started by mccune on cleo,
Wed Feb 25 09:31:58 2009
The command was "/home/mccune/bin/mace4 -f noncommutative-ring.in".
]]></heading>

<input><![CDATA[
formulas(assumptions).
0 + x = x.
x + 0 = x.
-x + x = 0.
x + -x = 0.
(x + y) + z = x + (y + z).
x + y = y + x.
(x * y) * z = x * (y * z).
x * (y + z) = (x * y) + (x * z).
(y + z) * x = (y * x) + (z * x).
--x = x.
-0 = 0.
0 * x = 0.
x * 0 = 0.
1 * x = x.
x * 1 = x.
a * b != b * a.
end_of_list.
]]></input>

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