<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE PROOF SYSTEM "http://a3pat.ensiie.fr/pub/a3pat.dtd">
<PROOF><SIGNATURE><SYMBOLLIST><SYMBOL arity="2" unmarked="="><NAME>Marked_=</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>and</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>or</NAME></SYMBOL><SYMBOL arity="2" unmarked="implies"><NAME>Marked_implies</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>true</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>=</NAME></SYMBOL><SYMBOL arity="1" unmarked="not"><NAME>Marked_not</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>not</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>implies</NAME></SYMBOL><SYMBOL arity="2" unmarked="or"><NAME>Marked_or</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>xor</NAME></SYMBOL></SYMBOLLIST><VARLIST><VAR>z</VAR><VAR>y</VAR><VAR>x</VAR></VARLIST></SIGNATURE><PROPERTY criterion="dp" prop="sntrs"><SYSTEM><REWSYS><RULE><LHS>not(x)</LHS><RHS>xor(x,true)</RHS></RULE><RULE><LHS>implies(x,y)</LHS><RHS>xor(and(x,y),xor(x,true))</RHS></RULE><RULE><LHS>or(x,y)</LHS><RHS>xor(and(x,y),xor(x,y))</RHS></RULE><RULE><LHS>=(x,y)</LHS><RHS>xor(x,xor(y,true))</RHS></RULE></REWSYS></SYSTEM><CRITERION/><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>not(x)</LHS><RHS>xor(x,true)</RHS></RULE><RULE><LHS>implies(x,y)</LHS><RHS>xor(and(x,y),xor(x,true))</RHS></RULE><RULE><LHS>or(x,y)</LHS><RHS>xor(and(x,y),xor(x,y))</RHS></RULE><RULE><LHS>=(x,y)</LHS><RHS>xor(x,xor(y,true))</RHS></RULE></REWSYS><DPLIST/></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST/></DAG></CRITERION></PROPERTY></PROPERTY></PROOF>
