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<interps>

<source>ring19.out</source>

<heading><![CDATA[
Mace4 (32) version 2009-02A, February 2009.
Process 11177 was started by mccune on cleo,
Wed Feb 25 09:31:59 2009
The command was "/home/mccune/bin/mace4 -f ring19.in".
]]></heading>

<input><![CDATA[
formulas(assumptions).
g(x) = M * x.
f(x,y) = (H * x) + (K * y).
f(f(a,b),c) != f(a,f(b,c)).
end_of_list.

formulas(assumptions).
g(f(g(f(y,f(x,z))),f(y,f(f(x,x),g(x))))) = z.
end_of_list.
]]></input>

  <interp size="19" number="1" seconds="5">

    <op0 type="function">
      <sym><![CDATA[H]]></sym>
      <v>17</v>
    </op0>

    <op0 type="function">
      <sym><![CDATA[K]]></sym>
      <v>14</v>
    </op0>

    <op0 type="function">
      <sym><![CDATA[M]]></sym>
      <v>7</v>
    </op0>

    <op0 type="function">
      <sym><![CDATA[a]]></sym>
      <v>0</v>
    </op0>

    <op0 type="function">
      <sym><![CDATA[b]]></sym>
      <v>0</v>
    </op0>

    <op0 type="function">
      <sym><![CDATA[c]]></sym>
      <v>1</v>
    </op0>

    <op1 type="function">
        <sym><![CDATA[g]]></sym>
        <head><i>0</i><i>1</i><i>2</i><i>3</i><i>4</i><i>5</i><i>6</i><i>7</i><i>8</i><i>9</i><i>10</i><i>11</i><i>12</i><i>13</i><i>14</i><i>15</i><i>16</i><i>17</i><i>18</i></head>
        <row> <v>0</v><v>7</v><v>14</v><v>2</v><v>9</v><v>16</v><v>4</v><v>11</v><v>18</v><v>6</v><v>13</v><v>1</v><v>8</v><v>15</v><v>3</v><v>10</v><v>17</v><v>5</v><v>12</v></row>
    </op1>

    <op2 type="function">
        <sym><![CDATA[+]]></sym>
        <head>        <i>0</i><i>1</i><i>2</i><i>3</i><i>4</i><i>5</i><i>6</i><i>7</i><i>8</i><i>9</i><i>10</i><i>11</i><i>12</i><i>13</i><i>14</i><i>15</i><i>16</i><i>17</i><i>18</i></head>
        <row><i>0</i> <v>0</v><v>1</v><v>2</v><v>3</v><v>4</v><v>5</v><v>6</v><v>7</v><v>8</v><v>9</v><v>10</v><v>11</v><v>12</v><v>13</v><v>14</v><v>15</v><v>16</v><v>17</v><v>18</v></row>
        <row><i>1</i> <v>1</v><v>2</v><v>3</v><v>4</v><v>5</v><v>6</v><v>7</v><v>8</v><v>9</v><v>10</v><v>11</v><v>12</v><v>13</v><v>14</v><v>15</v><v>16</v><v>17</v><v>18</v><v>0</v></row>
        <row><i>2</i> <v>2</v><v>3</v><v>4</v><v>5</v><v>6</v><v>7</v><v>8</v><v>9</v><v>10</v><v>11</v><v>12</v><v>13</v><v>14</v><v>15</v><v>16</v><v>17</v><v>18</v><v>0</v><v>1</v></row>
        <row><i>3</i> <v>3</v><v>4</v><v>5</v><v>6</v><v>7</v><v>8</v><v>9</v><v>10</v><v>11</v><v>12</v><v>13</v><v>14</v><v>15</v><v>16</v><v>17</v><v>18</v><v>0</v><v>1</v><v>2</v></row>
        <row><i>4</i> <v>4</v><v>5</v><v>6</v><v>7</v><v>8</v><v>9</v><v>10</v><v>11</v><v>12</v><v>13</v><v>14</v><v>15</v><v>16</v><v>17</v><v>18</v><v>0</v><v>1</v><v>2</v><v>3</v></row>
        <row><i>5</i> <v>5</v><v>6</v><v>7</v><v>8</v><v>9</v><v>10</v><v>11</v><v>12</v><v>13</v><v>14</v><v>15</v><v>16</v><v>17</v><v>18</v><v>0</v><v>1</v><v>2</v><v>3</v><v>4</v></row>
        <row><i>6</i> <v>6</v><v>7</v><v>8</v><v>9</v><v>10</v><v>11</v><v>12</v><v>13</v><v>14</v><v>15</v><v>16</v><v>17</v><v>18</v><v>0</v><v>1</v><v>2</v><v>3</v><v>4</v><v>5</v></row>
        <row><i>7</i> <v>7</v><v>8</v><v>9</v><v>10</v><v>11</v><v>12</v><v>13</v><v>14</v><v>15</v><v>16</v><v>17</v><v>18</v><v>0</v><v>1</v><v>2</v><v>3</v><v>4</v><v>5</v><v>6</v></row>
        <row><i>8</i> <v>8</v><v>9</v><v>10</v><v>11</v><v>12</v><v>13</v><v>14</v><v>15</v><v>16</v><v>17</v><v>18</v><v>0</v><v>1</v><v>2</v><v>3</v><v>4</v><v>5</v><v>6</v><v>7</v></row>
        <row><i>9</i> <v>9</v><v>10</v><v>11</v><v>12</v><v>13</v><v>14</v><v>15</v><v>16</v><v>17</v><v>18</v><v>0</v><v>1</v><v>2</v><v>3</v><v>4</v><v>5</v><v>6</v><v>7</v><v>8</v></row>
        <row><i>10</i> <v>10</v><v>11</v><v>12</v><v>13</v><v>14</v><v>15</v><v>16</v><v>17</v><v>18</v><v>0</v><v>1</v><v>2</v><v>3</v><v>4</v><v>5</v><v>6</v><v>7</v><v>8</v><v>9</v></row>
        <row><i>11</i> <v>11</v><v>12</v><v>13</v><v>14</v><v>15</v><v>16</v><v>17</v><v>18</v><v>0</v><v>1</v><v>2</v><v>3</v><v>4</v><v>5</v><v>6</v><v>7</v><v>8</v><v>9</v><v>10</v></row>
        <row><i>12</i> <v>12</v><v>13</v><v>14</v><v>15</v><v>16</v><v>17</v><v>18</v><v>0</v><v>1</v><v>2</v><v>3</v><v>4</v><v>5</v><v>6</v><v>7</v><v>8</v><v>9</v><v>10</v><v>11</v></row>
        <row><i>13</i> <v>13</v><v>14</v><v>15</v><v>16</v><v>17</v><v>18</v><v>0</v><v>1</v><v>2</v><v>3</v><v>4</v><v>5</v><v>6</v><v>7</v><v>8</v><v>9</v><v>10</v><v>11</v><v>12</v></row>
        <row><i>14</i> <v>14</v><v>15</v><v>16</v><v>17</v><v>18</v><v>0</v><v>1</v><v>2</v><v>3</v><v>4</v><v>5</v><v>6</v><v>7</v><v>8</v><v>9</v><v>10</v><v>11</v><v>12</v><v>13</v></row>
        <row><i>15</i> <v>15</v><v>16</v><v>17</v><v>18</v><v>0</v><v>1</v><v>2</v><v>3</v><v>4</v><v>5</v><v>6</v><v>7</v><v>8</v><v>9</v><v>10</v><v>11</v><v>12</v><v>13</v><v>14</v></row>
        <row><i>16</i> <v>16</v><v>17</v><v>18</v><v>0</v><v>1</v><v>2</v><v>3</v><v>4</v><v>5</v><v>6</v><v>7</v><v>8</v><v>9</v><v>10</v><v>11</v><v>12</v><v>13</v><v>14</v><v>15</v></row>
        <row><i>17</i> <v>17</v><v>18</v><v>0</v><v>1</v><v>2</v><v>3</v><v>4</v><v>5</v><v>6</v><v>7</v><v>8</v><v>9</v><v>10</v><v>11</v><v>12</v><v>13</v><v>14</v><v>15</v><v>16</v></row>
        <row><i>18</i> <v>18</v><v>0</v><v>1</v><v>2</v><v>3</v><v>4</v><v>5</v><v>6</v><v>7</v><v>8</v><v>9</v><v>10</v><v>11</v><v>12</v><v>13</v><v>14</v><v>15</v><v>16</v><v>17</v></row>
    </op2>

    <op2 type="function">
        <sym><![CDATA[*]]></sym>
        <head>        <i>0</i><i>1</i><i>2</i><i>3</i><i>4</i><i>5</i><i>6</i><i>7</i><i>8</i><i>9</i><i>10</i><i>11</i><i>12</i><i>13</i><i>14</i><i>15</i><i>16</i><i>17</i><i>18</i></head>
        <row><i>0</i> <v>0</v><v>0</v><v>0</v><v>0</v><v>0</v><v>0</v><v>0</v><v>0</v><v>0</v><v>0</v><v>0</v><v>0</v><v>0</v><v>0</v><v>0</v><v>0</v><v>0</v><v>0</v><v>0</v></row>
        <row><i>1</i> <v>0</v><v>1</v><v>2</v><v>3</v><v>4</v><v>5</v><v>6</v><v>7</v><v>8</v><v>9</v><v>10</v><v>11</v><v>12</v><v>13</v><v>14</v><v>15</v><v>16</v><v>17</v><v>18</v></row>
        <row><i>2</i> <v>0</v><v>2</v><v>4</v><v>6</v><v>8</v><v>10</v><v>12</v><v>14</v><v>16</v><v>18</v><v>1</v><v>3</v><v>5</v><v>7</v><v>9</v><v>11</v><v>13</v><v>15</v><v>17</v></row>
        <row><i>3</i> <v>0</v><v>3</v><v>6</v><v>9</v><v>12</v><v>15</v><v>18</v><v>2</v><v>5</v><v>8</v><v>11</v><v>14</v><v>17</v><v>1</v><v>4</v><v>7</v><v>10</v><v>13</v><v>16</v></row>
        <row><i>4</i> <v>0</v><v>4</v><v>8</v><v>12</v><v>16</v><v>1</v><v>5</v><v>9</v><v>13</v><v>17</v><v>2</v><v>6</v><v>10</v><v>14</v><v>18</v><v>3</v><v>7</v><v>11</v><v>15</v></row>
        <row><i>5</i> <v>0</v><v>5</v><v>10</v><v>15</v><v>1</v><v>6</v><v>11</v><v>16</v><v>2</v><v>7</v><v>12</v><v>17</v><v>3</v><v>8</v><v>13</v><v>18</v><v>4</v><v>9</v><v>14</v></row>
        <row><i>6</i> <v>0</v><v>6</v><v>12</v><v>18</v><v>5</v><v>11</v><v>17</v><v>4</v><v>10</v><v>16</v><v>3</v><v>9</v><v>15</v><v>2</v><v>8</v><v>14</v><v>1</v><v>7</v><v>13</v></row>
        <row><i>7</i> <v>0</v><v>7</v><v>14</v><v>2</v><v>9</v><v>16</v><v>4</v><v>11</v><v>18</v><v>6</v><v>13</v><v>1</v><v>8</v><v>15</v><v>3</v><v>10</v><v>17</v><v>5</v><v>12</v></row>
        <row><i>8</i> <v>0</v><v>8</v><v>16</v><v>5</v><v>13</v><v>2</v><v>10</v><v>18</v><v>7</v><v>15</v><v>4</v><v>12</v><v>1</v><v>9</v><v>17</v><v>6</v><v>14</v><v>3</v><v>11</v></row>
        <row><i>9</i> <v>0</v><v>9</v><v>18</v><v>8</v><v>17</v><v>7</v><v>16</v><v>6</v><v>15</v><v>5</v><v>14</v><v>4</v><v>13</v><v>3</v><v>12</v><v>2</v><v>11</v><v>1</v><v>10</v></row>
        <row><i>10</i> <v>0</v><v>10</v><v>1</v><v>11</v><v>2</v><v>12</v><v>3</v><v>13</v><v>4</v><v>14</v><v>5</v><v>15</v><v>6</v><v>16</v><v>7</v><v>17</v><v>8</v><v>18</v><v>9</v></row>
        <row><i>11</i> <v>0</v><v>11</v><v>3</v><v>14</v><v>6</v><v>17</v><v>9</v><v>1</v><v>12</v><v>4</v><v>15</v><v>7</v><v>18</v><v>10</v><v>2</v><v>13</v><v>5</v><v>16</v><v>8</v></row>
        <row><i>12</i> <v>0</v><v>12</v><v>5</v><v>17</v><v>10</v><v>3</v><v>15</v><v>8</v><v>1</v><v>13</v><v>6</v><v>18</v><v>11</v><v>4</v><v>16</v><v>9</v><v>2</v><v>14</v><v>7</v></row>
        <row><i>13</i> <v>0</v><v>13</v><v>7</v><v>1</v><v>14</v><v>8</v><v>2</v><v>15</v><v>9</v><v>3</v><v>16</v><v>10</v><v>4</v><v>17</v><v>11</v><v>5</v><v>18</v><v>12</v><v>6</v></row>
        <row><i>14</i> <v>0</v><v>14</v><v>9</v><v>4</v><v>18</v><v>13</v><v>8</v><v>3</v><v>17</v><v>12</v><v>7</v><v>2</v><v>16</v><v>11</v><v>6</v><v>1</v><v>15</v><v>10</v><v>5</v></row>
        <row><i>15</i> <v>0</v><v>15</v><v>11</v><v>7</v><v>3</v><v>18</v><v>14</v><v>10</v><v>6</v><v>2</v><v>17</v><v>13</v><v>9</v><v>5</v><v>1</v><v>16</v><v>12</v><v>8</v><v>4</v></row>
        <row><i>16</i> <v>0</v><v>16</v><v>13</v><v>10</v><v>7</v><v>4</v><v>1</v><v>17</v><v>14</v><v>11</v><v>8</v><v>5</v><v>2</v><v>18</v><v>15</v><v>12</v><v>9</v><v>6</v><v>3</v></row>
        <row><i>17</i> <v>0</v><v>17</v><v>15</v><v>13</v><v>11</v><v>9</v><v>7</v><v>5</v><v>3</v><v>1</v><v>18</v><v>16</v><v>14</v><v>12</v><v>10</v><v>8</v><v>6</v><v>4</v><v>2</v></row>
        <row><i>18</i> <v>0</v><v>18</v><v>17</v><v>16</v><v>15</v><v>14</v><v>13</v><v>12</v><v>11</v><v>10</v><v>9</v><v>8</v><v>7</v><v>6</v><v>5</v><v>4</v><v>3</v><v>2</v><v>1</v></row>
    </op2>

    <op2 type="function">
        <sym><![CDATA[f]]></sym>
        <head>        <i>0</i><i>1</i><i>2</i><i>3</i><i>4</i><i>5</i><i>6</i><i>7</i><i>8</i><i>9</i><i>10</i><i>11</i><i>12</i><i>13</i><i>14</i><i>15</i><i>16</i><i>17</i><i>18</i></head>
        <row><i>0</i> <v>0</v><v>14</v><v>9</v><v>4</v><v>18</v><v>13</v><v>8</v><v>3</v><v>17</v><v>12</v><v>7</v><v>2</v><v>16</v><v>11</v><v>6</v><v>1</v><v>15</v><v>10</v><v>5</v></row>
        <row><i>1</i> <v>17</v><v>12</v><v>7</v><v>2</v><v>16</v><v>11</v><v>6</v><v>1</v><v>15</v><v>10</v><v>5</v><v>0</v><v>14</v><v>9</v><v>4</v><v>18</v><v>13</v><v>8</v><v>3</v></row>
        <row><i>2</i> <v>15</v><v>10</v><v>5</v><v>0</v><v>14</v><v>9</v><v>4</v><v>18</v><v>13</v><v>8</v><v>3</v><v>17</v><v>12</v><v>7</v><v>2</v><v>16</v><v>11</v><v>6</v><v>1</v></row>
        <row><i>3</i> <v>13</v><v>8</v><v>3</v><v>17</v><v>12</v><v>7</v><v>2</v><v>16</v><v>11</v><v>6</v><v>1</v><v>15</v><v>10</v><v>5</v><v>0</v><v>14</v><v>9</v><v>4</v><v>18</v></row>
        <row><i>4</i> <v>11</v><v>6</v><v>1</v><v>15</v><v>10</v><v>5</v><v>0</v><v>14</v><v>9</v><v>4</v><v>18</v><v>13</v><v>8</v><v>3</v><v>17</v><v>12</v><v>7</v><v>2</v><v>16</v></row>
        <row><i>5</i> <v>9</v><v>4</v><v>18</v><v>13</v><v>8</v><v>3</v><v>17</v><v>12</v><v>7</v><v>2</v><v>16</v><v>11</v><v>6</v><v>1</v><v>15</v><v>10</v><v>5</v><v>0</v><v>14</v></row>
        <row><i>6</i> <v>7</v><v>2</v><v>16</v><v>11</v><v>6</v><v>1</v><v>15</v><v>10</v><v>5</v><v>0</v><v>14</v><v>9</v><v>4</v><v>18</v><v>13</v><v>8</v><v>3</v><v>17</v><v>12</v></row>
        <row><i>7</i> <v>5</v><v>0</v><v>14</v><v>9</v><v>4</v><v>18</v><v>13</v><v>8</v><v>3</v><v>17</v><v>12</v><v>7</v><v>2</v><v>16</v><v>11</v><v>6</v><v>1</v><v>15</v><v>10</v></row>
        <row><i>8</i> <v>3</v><v>17</v><v>12</v><v>7</v><v>2</v><v>16</v><v>11</v><v>6</v><v>1</v><v>15</v><v>10</v><v>5</v><v>0</v><v>14</v><v>9</v><v>4</v><v>18</v><v>13</v><v>8</v></row>
        <row><i>9</i> <v>1</v><v>15</v><v>10</v><v>5</v><v>0</v><v>14</v><v>9</v><v>4</v><v>18</v><v>13</v><v>8</v><v>3</v><v>17</v><v>12</v><v>7</v><v>2</v><v>16</v><v>11</v><v>6</v></row>
        <row><i>10</i> <v>18</v><v>13</v><v>8</v><v>3</v><v>17</v><v>12</v><v>7</v><v>2</v><v>16</v><v>11</v><v>6</v><v>1</v><v>15</v><v>10</v><v>5</v><v>0</v><v>14</v><v>9</v><v>4</v></row>
        <row><i>11</i> <v>16</v><v>11</v><v>6</v><v>1</v><v>15</v><v>10</v><v>5</v><v>0</v><v>14</v><v>9</v><v>4</v><v>18</v><v>13</v><v>8</v><v>3</v><v>17</v><v>12</v><v>7</v><v>2</v></row>
        <row><i>12</i> <v>14</v><v>9</v><v>4</v><v>18</v><v>13</v><v>8</v><v>3</v><v>17</v><v>12</v><v>7</v><v>2</v><v>16</v><v>11</v><v>6</v><v>1</v><v>15</v><v>10</v><v>5</v><v>0</v></row>
        <row><i>13</i> <v>12</v><v>7</v><v>2</v><v>16</v><v>11</v><v>6</v><v>1</v><v>15</v><v>10</v><v>5</v><v>0</v><v>14</v><v>9</v><v>4</v><v>18</v><v>13</v><v>8</v><v>3</v><v>17</v></row>
        <row><i>14</i> <v>10</v><v>5</v><v>0</v><v>14</v><v>9</v><v>4</v><v>18</v><v>13</v><v>8</v><v>3</v><v>17</v><v>12</v><v>7</v><v>2</v><v>16</v><v>11</v><v>6</v><v>1</v><v>15</v></row>
        <row><i>15</i> <v>8</v><v>3</v><v>17</v><v>12</v><v>7</v><v>2</v><v>16</v><v>11</v><v>6</v><v>1</v><v>15</v><v>10</v><v>5</v><v>0</v><v>14</v><v>9</v><v>4</v><v>18</v><v>13</v></row>
        <row><i>16</i> <v>6</v><v>1</v><v>15</v><v>10</v><v>5</v><v>0</v><v>14</v><v>9</v><v>4</v><v>18</v><v>13</v><v>8</v><v>3</v><v>17</v><v>12</v><v>7</v><v>2</v><v>16</v><v>11</v></row>
        <row><i>17</i> <v>4</v><v>18</v><v>13</v><v>8</v><v>3</v><v>17</v><v>12</v><v>7</v><v>2</v><v>16</v><v>11</v><v>6</v><v>1</v><v>15</v><v>10</v><v>5</v><v>0</v><v>14</v><v>9</v></row>
        <row><i>18</i> <v>2</v><v>16</v><v>11</v><v>6</v><v>1</v><v>15</v><v>10</v><v>5</v><v>0</v><v>14</v><v>9</v><v>4</v><v>18</v><v>13</v><v>8</v><v>3</v><v>17</v><v>12</v><v>7</v></row>
    </op2>
  </interp>

</interps>
