<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE proofdatabase
SYSTEM "http://www.logic.at/ceres/xml/4.0/proofdatabase.dtd">
<proofdatabase>
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 </definitionlist>
 <axiomset/>
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            </conjunctiveformula>
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          </formulalist>
         </sequent>
         <rule symbol="⋁:l" type="orl">
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           <formulalist>
            <conjunctiveformula type="or">
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              <constantatomformula symbol="P">
               <variable symbol="m"/>
               <variable symbol="k"/>
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              <variable symbol="m"/>
              <variable symbol="k"/>
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            </conjunctiveformula>
           </formulalist>
           <formulalist>
            <conjunctiveformula type="impl">
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              <constantatomformula symbol="Q">
               <variable symbol="m"/>
               <variable symbol="k"/>
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             <conjunctiveformula type="neg">
              <constantatomformula symbol="P">
               <variable symbol="m"/>
               <variable symbol="k"/>
              </constantatomformula>
             </conjunctiveformula>
            </conjunctiveformula>
            <conjunctiveformula type="impl">
             <conjunctiveformula type="neg">
              <constantatomformula symbol="Q">
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               <variable symbol="k"/>
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          </sequent>
          <rule symbol="¬:l" type="negl">
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            <formulalist>
             <conjunctiveformula type="neg">
              <constantatomformula symbol="P">
               <variable symbol="m"/>
               <variable symbol="k"/>
              </constantatomformula>
             </conjunctiveformula>
            </formulalist>
            <formulalist>
             <conjunctiveformula type="impl">
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               <constantatomformula symbol="Q">
                <variable symbol="m"/>
                <variable symbol="k"/>
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                <variable symbol="m"/>
                <variable symbol="k"/>
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              </conjunctiveformula>
             </conjunctiveformula>
            </formulalist>
           </sequent>
           <rule symbol="π:r" type="permr" param="(1 2)">
            <sequent>
             <formulalist/>
             <formulalist>
              <conjunctiveformula type="impl">
               <conjunctiveformula type="neg">
                <constantatomformula symbol="Q">
                 <variable symbol="m"/>
                 <variable symbol="k"/>
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                <constantatomformula symbol="P">
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              <constantatomformula symbol="P">
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               <variable symbol="k"/>
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            <rule symbol="⊃:r" type="implr">
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              <formulalist/>
              <formulalist>
               <constantatomformula symbol="P">
                <variable symbol="m"/>
                <variable symbol="k"/>
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               <conjunctiveformula type="impl">
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                  <variable symbol="m"/>
                  <variable symbol="k"/>
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             <rule symbol="¬:l" type="negl">
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               <formulalist>
                <conjunctiveformula type="neg">
                 <constantatomformula symbol="Q">
                  <variable symbol="m"/>
                  <variable symbol="k"/>
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                </conjunctiveformula>
               </formulalist>
               <formulalist>
                <constantatomformula symbol="P">
                 <variable symbol="m"/>
                 <variable symbol="k"/>
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                <conjunctiveformula type="neg">
                 <constantatomformula symbol="P">
                  <variable symbol="m"/>
                  <variable symbol="k"/>
                 </constantatomformula>
                </conjunctiveformula>
               </formulalist>
              </sequent>
              <rule symbol="w:r" type="weakr">
               <sequent>
                <formulalist/>
                <formulalist>
                 <constantatomformula symbol="P">
                  <variable symbol="m"/>
                  <variable symbol="k"/>
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                 <constantatomformula symbol="Q">
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                  <variable symbol="k"/>
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               </sequent>
               <rule symbol="¬:r" type="negr">
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                 <formulalist/>
                 <formulalist>
                  <constantatomformula symbol="P">
                   <variable symbol="m"/>
                   <variable symbol="k"/>
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                    <variable symbol="m"/>
                    <variable symbol="k"/>
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                <rule type="axiom">
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                  <formulalist>
                   <constantatomformula symbol="P">
                    <variable symbol="m"/>
                    <variable symbol="k"/>
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                  <formulalist>
                   <constantatomformula symbol="P">
                    <variable symbol="m"/>
                    <variable symbol="k"/>
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                 </sequent>
                </rule>
               </rule>
              </rule>
             </rule>
            </rule>
           </rule>
          </rule>
          <rule symbol="⊃:r" type="implr">
           <sequent>
            <formulalist>
             <constantatomformula symbol="Q">
              <variable symbol="m"/>
              <variable symbol="k"/>
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            </formulalist>
            <formulalist>
             <conjunctiveformula type="impl">
              <conjunctiveformula type="neg">
               <constantatomformula symbol="Q">
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                <variable symbol="k"/>
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               <constantatomformula symbol="P">
                <variable symbol="m"/>
                <variable symbol="k"/>
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              </conjunctiveformula>
             </conjunctiveformula>
            </formulalist>
           </sequent>
           <rule symbol="w:r" type="weakr">
            <sequent>
             <formulalist>
              <conjunctiveformula type="neg">
               <constantatomformula symbol="Q">
                <variable symbol="m"/>
                <variable symbol="k"/>
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              <constantatomformula symbol="Q">
               <variable symbol="m"/>
               <variable symbol="k"/>
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             </formulalist>
             <formulalist>
              <conjunctiveformula type="neg">
               <constantatomformula symbol="P">
                <variable symbol="m"/>
                <variable symbol="k"/>
               </constantatomformula>
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             </formulalist>
            </sequent>
            <rule symbol="¬:l" type="negl">
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              <formulalist>
               <conjunctiveformula type="neg">
                <constantatomformula symbol="Q">
                 <variable symbol="m"/>
                 <variable symbol="k"/>
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               </conjunctiveformula>
               <constantatomformula symbol="Q">
                <variable symbol="m"/>
                <variable symbol="k"/>
               </constantatomformula>
              </formulalist>
              <formulalist/>
             </sequent>
             <rule type="axiom">
              <sequent>
               <formulalist>
                <constantatomformula symbol="Q">
                 <variable symbol="m"/>
                 <variable symbol="k"/>
                </constantatomformula>
               </formulalist>
               <formulalist>
                <constantatomformula symbol="Q">
                 <variable symbol="m"/>
                 <variable symbol="k"/>
                </constantatomformula>
               </formulalist>
              </sequent>
             </rule>
            </rule>
           </rule>
          </rule>
         </rule>
        </rule>
       </rule>
      </rule>
     </rule>
    </rule>
   </rule>
  </rule>
 </proof>
 <variabledefinitions/>
</proofdatabase>
