<theory>

<theory_name>theorem_th_prop4_09</theory_name>

<signature>

<type>point</type>
<type>line</type>
<type>circle</type>

<relation_symbol name="eq_point">
<type>point</type>
<type>point</type>
</relation_symbol>


<relation_symbol name="not_eq_point">
<type>point</type>
<type>point</type>
</relation_symbol>


<relation_symbol name="eq_line">
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<type>line</type>
</relation_symbol>


<relation_symbol name="not_eq_line">
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</relation_symbol>


<relation_symbol name="eq_circle">
<type>circle</type>
<type>circle</type>
</relation_symbol>


<relation_symbol name="not_eq_circle">
<type>circle</type>
<type>circle</type>
</relation_symbol>


<relation_symbol name="on">
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<type>line</type>
</relation_symbol>


<relation_symbol name="not_on">
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<relation_symbol name="intersects">
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</relation_symbol>


<relation_symbol name="not_intersects">
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<type>line</type>
</relation_symbol>


<relation_symbol name="onc">
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</relation_symbol>


<relation_symbol name="not_onc">
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<relation_symbol name="inside">
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</relation_symbol>


<relation_symbol name="not_inside">
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<relation_symbol name="center">
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</relation_symbol>


<relation_symbol name="not_center">
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<relation_symbol name="intersectscc">
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<type>circle</type>
</relation_symbol>


<relation_symbol name="not_intersectscc">
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<type>circle</type>
</relation_symbol>


<relation_symbol name="intersectslc">
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<type>line</type>
</relation_symbol>


<relation_symbol name="not_intersectslc">
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<type>line</type>
</relation_symbol>


<relation_symbol name="comp">
<type>point</type>
<type>point</type>
<type>point</type>
<type>point</type>
</relation_symbol>


<relation_symbol name="not_comp">
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<type>point</type>
<type>point</type>
<type>point</type>
</relation_symbol>


<relation_symbol name="bet">
<type>point</type>
<type>point</type>
<type>point</type>
</relation_symbol>


<relation_symbol name="not_bet">
<type>point</type>
<type>point</type>
<type>point</type>
</relation_symbol>


<relation_symbol name="col">
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<type>point</type>
<type>point</type>
</relation_symbol>


<relation_symbol name="not_col">
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<type>point</type>
</relation_symbol>


<relation_symbol name="cong">
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<type>point</type>
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<relation_symbol name="not_cong">
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<type>point</type>
<type>point</type>
<type>point</type>
</relation_symbol>


<relation_symbol name="cong_area">
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<type>point</type>
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<type>point</type>
</relation_symbol>


<relation_symbol name="not_cong_area">
<type>point</type>
<type>point</type>
<type>point</type>
<type>point</type>
<type>point</type>
<type>point</type>
</relation_symbol>


<relation_symbol name="cong_area_leq">
<type>point</type>
<type>point</type>
<type>point</type>
<type>point</type>
<type>point</type>
<type>point</type>
</relation_symbol>


<relation_symbol name="not_cong_area_leq">
<type>point</type>
<type>point</type>
<type>point</type>
<type>point</type>
<type>point</type>
<type>point</type>
</relation_symbol>


<relation_symbol name="cong_area_zero">
<type>point</type>
<type>point</type>
<type>point</type>
</relation_symbol>


<relation_symbol name="not_cong_area_zero">
<type>point</type>
<type>point</type>
<type>point</type>
</relation_symbol>


<relation_symbol name="area_add">
<type>point</type>
<type>point</type>
<type>point</type>
<type>point</type>
<type>point</type>
<type>point</type>
<type>point</type>
<type>point</type>