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<!DOCTYPE PROOF SYSTEM "http://a3pat.ensiie.fr/pub/a3pat.dtd">
<PROOF><SIGNATURE><SYMBOLLIST><SYMBOL arity="1" unmarked="not"><NAME>Marked_not</NAME></SYMBOL><SYMBOL arity="2" unmarked="or"><NAME>Marked_or</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>and</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>not</NAME></SYMBOL><SYMBOL arity="2" unmarked="and"><NAME>Marked_and</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>or</NAME></SYMBOL></SYMBOLLIST><VARLIST><VAR>z</VAR><VAR>y</VAR><VAR>x</VAR></VARLIST></SIGNATURE><PROPERTY criterion="dp" prop="sntrs"><SYSTEM><REWSYS><RULE><LHS>or(x,x)</LHS><RHS>x</RHS></RULE><RULE><LHS>and(x,x)</LHS><RHS>x</RHS></RULE><RULE><LHS>not(not(x))</LHS><RHS>x</RHS></RULE><RULE><LHS>not(and(x,y))</LHS><RHS>or(not(x),not(y))</RHS></RULE><RULE><LHS>not(or(x,y))</LHS><RHS>and(not(x),not(y))</RHS></RULE></REWSYS></SYSTEM><CRITERION/><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>or(x,x)</LHS><RHS>x</RHS></RULE><RULE><LHS>and(x,x)</LHS><RHS>x</RHS></RULE><RULE><LHS>not(not(x))</LHS><RHS>x</RHS></RULE><RULE><LHS>not(and(x,y))</LHS><RHS>or(not(x),not(y))</RHS></RULE><RULE><LHS>not(or(x,y))</LHS><RHS>and(not(x),not(y))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_not(and(x,y))</LHS><RHS>Marked_or(not(x),not(y))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_not(and(x,y))</LHS><RHS>Marked_not(x)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_not(and(x,y))</LHS><RHS>Marked_not(y)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_not(or(x,y))</LHS><RHS>Marked_and(not(x),not(y))</RHS></DPRULE><DPRULE num="4"><LHS>Marked_not(or(x,y))</LHS><RHS>Marked_not(x)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_not(or(x,y))</LHS><RHS>Marked_not(y)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><SCC num="0"><NODE ref="1"/><NODE ref="2"/><NODE ref="4"/><NODE ref="5"/></SCC><NONSCC num="1"><NODE ref="3"/></NONSCC><NONSCC num="2"><NODE ref="0"/></NONSCC></CCLIST><EDGE end="2" start="0"/><EDGE end="1" start="0"/></DAG></CRITERION><PROPERTY criterion="sterm" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>or(x,x)</LHS><RHS>x</RHS></RULE><RULE><LHS>and(x,x)</LHS><RHS>x</RHS></RULE><RULE><LHS>not(not(x))</LHS><RHS>x</RHS></RULE><RULE><LHS>not(and(x,y))</LHS><RHS>or(not(x),not(y))</RHS></RULE><RULE><LHS>not(or(x,y))</LHS><RHS>and(not(x),not(y))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_not(and(x,y))</LHS><RHS>Marked_not(x)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_not(and(x,y))</LHS><RHS>Marked_not(y)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_not(or(x,y))</LHS><RHS>Marked_not(x)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_not(or(x,y))</LHS><RHS>Marked_not(y)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_not</NAME></SYMBOL><INT>1</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_not(or(x,y))</LHS><RHS>Marked_not(y)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_not(or(x,y))</LHS><RHS>Marked_not(x)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_not(and(x,y))</LHS><RHS>Marked_not(y)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_not(and(x,y))</LHS><RHS>Marked_not(x)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>or(x,x)</LHS><RHS>x</RHS></RULE><RULE><LHS>and(x,x)</LHS><RHS>x</RHS></RULE><RULE><LHS>not(not(x))</LHS><RHS>x</RHS></RULE><RULE><LHS>not(and(x,y))</LHS><RHS>or(not(x),not(y))</RHS></RULE><RULE><LHS>not(or(x,y))</LHS><RHS>and(not(x),not(y))</RHS></RULE></REWSYS><DPLIST/></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST/></DAG></CRITERION></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROOF>
