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<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
"http://why3.lri.fr/why3session.dtd">
<why3session shape_version="4">
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<prover id="1" name="Alt-Ergo" version="1.01" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="2" name="CVC4" version="1.4" timelimit="2" steplimit="0" memlimit="0"/>
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<file name="../avl.mlw">
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<theory name="SelectionTypes">
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 <goal name="rebuild_aternative_def" expl="">
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 <proof prover="1" timelimit="2" memlimit="0"><result status="valid" time="0.07" steps="88"/></proof>
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 </goal>
</theory>
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<theory name="AVL">
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 <goal name="M.M.assoc" expl="">
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 <proof prover="1"><result status="valid" time="0.00" steps="1"/></proof>
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 </goal>
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 <goal name="M.M.neutral" expl="">
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 <proof prover="1"><result status="valid" time="0.01" steps="3"/></proof>
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 </goal>
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 <goal name="WP_parameter real_height_nonnegative" expl="VC for real_height_nonnegative">
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 <proof prover="1" timelimit="2" memlimit="0"><result status="valid" time="0.02" steps="28"/></proof>
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 </goal>
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 <goal name="rotation_preserve_model" expl="">
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 <proof prover="1" timelimit="2" memlimit="0"><result status="valid" time="0.02" steps="6"/></proof>
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 </goal>
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 <goal name="WP_parameter height" expl="VC for height">
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 <proof prover="1" timelimit="2" memlimit="0"><result status="valid" time="0.02" steps="22"/></proof>
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 </goal>
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 <goal name="WP_parameter total" expl="VC for total">
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 <proof prover="1" timelimit="2" memlimit="0"><result status="valid" time="0.02" steps="27"/></proof>
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 </goal>
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 <goal name="WP_parameter empty" expl="VC for empty">
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 <proof prover="1" timelimit="2" memlimit="0"><result status="valid" time="0.02" steps="8"/></proof>
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 </goal>
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 <goal name="WP_parameter node" expl="VC for node">
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 <proof prover="1" timelimit="2" memlimit="0"><result status="valid" time="0.03" steps="98"/></proof>
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 </goal>
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 <goal name="WP_parameter singleton" expl="VC for singleton">
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 <proof prover="1" timelimit="2" memlimit="0"><result status="valid" time="0.04" steps="63"/></proof>
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 </goal>
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 <goal name="WP_parameter is_empty" expl="VC for is_empty">
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 <proof prover="1" timelimit="2" memlimit="0"><result status="valid" time="0.02" steps="68"/></proof>
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 </goal>
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 <goal name="WP_parameter view" expl="VC for view">
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 <proof prover="1" timelimit="2" memlimit="0"><result status="valid" time="0.07" steps="257"/></proof>
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 </goal>
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 <goal name="WP_parameter balance" expl="VC for balance">
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 <transf name="split_goal_wp">
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  <goal name="WP_parameter balance.1" expl="precondition">
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  <proof prover="1"><result status="valid" time="0.01" steps="5"/></proof>
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  </goal>
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  <goal name="WP_parameter balance.2" expl="precondition">
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  <proof prover="1"><result status="valid" time="0.01" steps="5"/></proof>
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  </goal>
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  <goal name="WP_parameter balance.3" expl="precondition">
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  <proof prover="1"><result status="valid" time="0.01" steps="6"/></proof>
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  </goal>
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  <goal name="WP_parameter balance.4" expl="unreachable point">
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  <proof prover="1"><result status="valid" time="0.02" steps="33"/></proof>
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  </goal>
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  <goal name="WP_parameter balance.5" expl="precondition">
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  <proof prover="1"><result status="valid" time="0.02" steps="35"/></proof>
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  </goal>
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  <goal name="WP_parameter balance.6" expl="precondition">
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  <proof prover="1"><result status="valid" time="0.02" steps="39"/></proof>
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  </goal>
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  <goal name="WP_parameter balance.7" expl="precondition">
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  <proof prover="1"><result status="valid" time="0.04" steps="83"/></proof>
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  </goal>
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  <goal name="WP_parameter balance.8" expl="precondition">
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  <proof prover="1"><result status="valid" time="0.06" steps="125"/></proof>
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  </goal>
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  <goal name="WP_parameter balance.9" expl="postcondition">
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  <proof prover="1"><result status="valid" time="0.02" steps="63"/></proof>
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  </goal>
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  <goal name="WP_parameter balance.10" expl="postcondition">
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  <proof prover="1"><result status="valid" time="0.14" steps="209"/></proof>
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  </goal>
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  <goal name="WP_parameter balance.11" expl="precondition">
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  <proof prover="1"><result status="valid" time="0.02" steps="10"/></proof>
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  </goal>
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  <goal name="WP_parameter balance.12" expl="unreachable point">
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  <proof prover="1"><result status="valid" time="0.03" steps="83"/></proof>
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  </goal>
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  <goal name="WP_parameter balance.13" expl="precondition">
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  <proof prover="1"><result status="valid" time="0.16" steps="341"/></proof>
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  </goal>
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  <goal name="WP_parameter balance.14" expl="precondition">
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  <proof prover="1"><result status="valid" time="0.33" steps="504"/></proof>
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  </goal>
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  <goal name="WP_parameter balance.15" expl="precondition">
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  <proof prover="1"><result status="valid" time="0.54" steps="883"/></proof>
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  </goal>
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  <goal name="WP_parameter balance.16" expl="postcondition">
  <proof prover="1"><result status="valid" time="0.18" steps="313"/></proof>
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  </goal>
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  <goal name="WP_parameter balance.17" expl="postcondition">
  <proof prover="1"><result status="valid" time="0.86" steps="986"/></proof>
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  </goal>
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  <goal name="WP_parameter balance.18" expl="precondition">
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  <proof prover="1"><result status="valid" time="0.02" steps="7"/></proof>
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  </goal>
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  <goal name="WP_parameter balance.19" expl="unreachable point">
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  <proof prover="1"><result status="valid" time="0.03" steps="34"/></proof>
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  </goal>
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  <goal name="WP_parameter balance.20" expl="precondition">
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  <proof prover="1"><result status="valid" time="0.04" steps="36"/></proof>
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  </goal>
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  <goal name="WP_parameter balance.21" expl="precondition">
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  <proof prover="1"><result status="valid" time="0.03" steps="40"/></proof>
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  </goal>
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  <goal name="WP_parameter balance.22" expl="precondition">
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  <proof prover="1"><result status="valid" time="0.05" steps="84"/></proof>
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  </goal>
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  <goal name="WP_parameter balance.23" expl="precondition">
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  <proof prover="1"><result status="valid" time="0.08" steps="128"/></proof>
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  </goal>
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  <goal name="WP_parameter balance.24" expl="postcondition">
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  <proof prover="1"><result status="valid" time="0.02" steps="68"/></proof>
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  </goal>
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  <goal name="WP_parameter balance.25" expl="postcondition">
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  <proof prover="1"><result status="valid" time="0.14" steps="195"/></proof>
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  </goal>
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  <goal name="WP_parameter balance.26" expl="precondition">
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  <proof prover="1"><result status="valid" time="0.01" steps="11"/></proof>
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  </goal>
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  <goal name="WP_parameter balance.27" expl="unreachable point">
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  <proof prover="1"><result status="valid" time="0.03" steps="108"/></proof>
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  </goal>
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  <goal name="WP_parameter balance.28" expl="precondition">
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  <proof prover="1"><result status="valid" time="0.18" steps="342"/></proof>
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  </goal>
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  <goal name="WP_parameter balance.29" expl="precondition">
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  <proof prover="1"><result status="valid" time="0.35" steps="495"/></proof>
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  </goal>
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  <goal name="WP_parameter balance.30" expl="precondition">
  <proof prover="1"><result status="valid" time="0.53" steps="798"/></proof>
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  </goal>
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  <goal name="WP_parameter balance.31" expl="postcondition">
  <proof prover="1"><result status="valid" time="0.16" steps="336"/></proof>
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  </goal>
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  <goal name="WP_parameter balance.32" expl="postcondition">
  <proof prover="1"><result status="valid" time="0.70" steps="979"/></proof>
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  </goal>
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  <goal name="WP_parameter balance.33" expl="precondition">
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  <proof prover="1"><result status="valid" time="0.01" steps="7"/></proof>
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  </goal>
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  <goal name="WP_parameter balance.34" expl="postcondition">
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  <proof prover="1"><result status="valid" time="0.01" steps="11"/></proof>
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  </goal>
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  <goal name="WP_parameter balance.35" expl="postcondition">
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  <proof prover="1"><result status="valid" time="0.02" steps="34"/></proof>
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  </goal>
 </transf>
 </goal>
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 <goal name="WP_parameter decompose_front_node" expl="VC for decompose_front_node">
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 <proof prover="1"><result status="valid" time="0.37" steps="583"/></proof>
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 </goal>
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 <goal name="WP_parameter decompose_front" expl="VC for decompose_front">
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 <proof prover="1" timelimit="2" memlimit="0"><result status="valid" time="0.09" steps="242"/></proof>
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 </goal>
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 <goal name="WP_parameter decompose_back_node" expl="VC for decompose_back_node">
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 <proof prover="1"><result status="valid" time="0.48" steps="726"/></proof>
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 </goal>
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 <goal name="WP_parameter decompose_back" expl="VC for decompose_back">
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 <proof prover="1" timelimit="2" memlimit="0"><result status="valid" time="0.11" steps="302"/></proof>
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 </goal>
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 <goal name="WP_parameter front_node" expl="VC for front_node">
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 <proof prover="1"><result status="valid" time="0.15" steps="309"/></proof>
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 </goal>
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 <goal name="WP_parameter front" expl="VC for front">
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 <proof prover="1"><result status="valid" time="0.08" steps="190"/></proof>
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 </goal>
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 <goal name="WP_parameter back_node" expl="VC for back_node">
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 <proof prover="1" timelimit="2" memlimit="0"><result status="valid" time="0.05" steps="118"/></proof>
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 </goal>
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 <goal name="WP_parameter back" expl="VC for back">
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 <proof prover="1" timelimit="2" memlimit="0"><result status="valid" time="0.03" steps="81"/></proof>
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 </goal>
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 <goal name="WP_parameter fuse" expl="VC for fuse">
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 <proof prover="2"><result status="valid" time="0.24"/></proof>
 </goal>
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 <goal name="WP_parameter cons" expl="VC for cons">
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 <proof prover="1"><result status="valid" time="0.36" steps="562"/></proof>
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 </goal>
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 <goal name="WP_parameter snoc" expl="VC for snoc">
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 <proof prover="1"><result status="valid" time="0.34" steps="563"/></proof>
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 </goal>
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 <goal name="WP_parameter join" expl="VC for join">
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 <proof prover="2" timelimit="5" memlimit="1000"><result status="valid" time="0.50"/></proof>
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 </goal>
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 <goal name="WP_parameter concat" expl="VC for concat">
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 <proof prover="2"><result status="valid" time="0.11"/></proof>
 </goal>
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 <goal name="WP_parameter default_split" expl="VC for default_split">
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 <proof prover="1"><result status="valid" time="0.02" steps="1"/></proof>
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 </goal>
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 <goal name="WP_parameter insert" expl="VC for insert">
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 <transf name="split_goal_wp">
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  <goal name="WP_parameter insert.1" expl="precondition">
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  <proof prover="1"><result status="valid" time="0.01" steps="3"/></proof>
  </goal>
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  <goal name="WP_parameter insert.2" expl="postcondition">
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  <proof prover="1"><result status="valid" time="0.02" steps="17"/></proof>
  </goal>
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  <goal name="WP_parameter insert.3" expl="postcondition">
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  <proof prover="1"><result status="valid" time="0.03" steps="78"/></proof>
  </goal>
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  <goal name="WP_parameter insert.4" expl="postcondition">
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  <proof prover="1"><result status="valid" time="0.02" steps="53"/></proof>
  </goal>
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  <goal name="WP_parameter insert.5" expl="precondition">
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  <proof prover="1"><result status="valid" time="0.02" steps="29"/></proof>
  </goal>
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  <goal name="WP_parameter insert.6" expl="precondition">
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  <proof prover="1"><result status="valid" time="0.02" steps="33"/></proof>
  </goal>
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  <goal name="WP_parameter insert.7" expl="precondition">
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  <proof prover="1"><result status="valid" time="0.01" steps="42"/></proof>
  </goal>
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  <goal name="WP_parameter insert.8" expl="precondition">
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  <proof prover="1"><result status="valid" time="0.01" steps="1"/></proof>
  </goal>
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  <goal name="WP_parameter insert.9" expl="variant decrease">
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  <proof prover="1"><result status="valid" time="0.04" steps="113"/></proof>
  </goal>
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  <goal name="WP_parameter insert.10" expl="precondition">
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  <proof prover="1"><result status="valid" time="0.03" steps="53"/></proof>
  </goal>
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  <goal name="WP_parameter insert.11" expl="precondition">
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  <proof prover="1"><result status="valid" time="0.10" steps="123"/></proof>
  </goal>
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  <goal name="WP_parameter insert.12" expl="postcondition">
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  <proof prover="1"><result status="valid" time="0.03" steps="54"/></proof>
  </goal>
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  <goal name="WP_parameter insert.13" expl="postcondition">
  <proof prover="1"><result status="valid" time="2.20" steps="1058"/></proof>
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  </goal>
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  <goal name="WP_parameter insert.14" expl="postcondition">
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  <proof prover="1"><result status="valid" time="0.34" steps="333"/></proof>
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  </goal>
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  <goal name="WP_parameter insert.15" expl="variant decrease">
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  <proof prover="1"><result status="valid" time="0.10" steps="135"/></proof>
  </goal>
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  <goal name="WP_parameter insert.16" expl="precondition">
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  <proof prover="1"><result status="valid" time="0.04" steps="35"/></proof>
  </goal>
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  <goal name="WP_parameter insert.17" expl="precondition">
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  <proof prover="1"><result status="valid" time="0.23" steps="140"/></proof>
  </goal>
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  <goal name="WP_parameter insert.18" expl="postcondition">
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  <proof prover="1"><result status="valid" time="0.03" steps="54"/></proof>
  </goal>
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  <goal name="WP_parameter insert.19" expl="postcondition">
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  <proof prover="1"><result status="valid" time="1.90" steps="983"/></proof>
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  </goal>
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  <goal name="WP_parameter insert.20" expl="postcondition">
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  <proof prover="1"><result status="valid" time="0.40" steps="339"/></proof>
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  </goal>
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  <goal name="WP_parameter insert.21" expl="precondition">
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  <proof prover="1"><result status="valid" time="0.08" steps="85"/></proof>
  </goal>
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  <goal name="WP_parameter insert.22" expl="postcondition">
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  <proof prover="1"><result status="valid" time="0.02" steps="15"/></proof>
  </goal>
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  <goal name="WP_parameter insert.23" expl="postcondition">
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  <proof prover="1"><result status="valid" time="0.08" steps="119"/></proof>
  </goal>
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  <goal name="WP_parameter insert.24" expl="postcondition">
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  <proof prover="1"><result status="valid" time="0.16" steps="154"/></proof>
  </goal>
 </transf>
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 </goal>
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 <goal name="WP_parameter remove" expl="VC for remove">
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 <transf name="split_goal_wp">
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  <goal name="WP_parameter remove.1" expl="precondition">
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  <proof prover="1"><result status="valid" time="0.01" steps="3"/></proof>
  </goal>
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  <goal name="WP_parameter remove.2" expl="postcondition">
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  <proof prover="1"><result status="valid" time="0.02" steps="30"/></proof>
  </goal>
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  <goal name="WP_parameter remove.3" expl="postcondition">
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  <proof prover="1"><result status="valid" time="0.03" steps="62"/></proof>
  </goal>
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  <goal name="WP_parameter remove.4" expl="postcondition">
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  <proof prover="1"><result status="valid" time="0.01" steps="7"/></proof>
  </goal>
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  <goal name="WP_parameter remove.5" expl="precondition">
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  <proof prover="1"><result status="valid" time="0.02" steps="29"/></proof>
  </goal>
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  <goal name="WP_parameter remove.6" expl="precondition">
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  <proof prover="1"><result status="valid" time="0.02" steps="33"/></proof>
  </goal>
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  <goal name="WP_parameter remove.7" expl="precondition">
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  <proof prover="1"><result status="valid" time="0.02" steps="42"/></proof>
  </goal>
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  <goal name="WP_parameter remove.8" expl="precondition">
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  <proof prover="1"><result status="valid" time="0.01" steps="1"/></proof>
  </goal>
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  <goal name="WP_parameter remove.9" expl="variant decrease">
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  <proof prover="1"><result status="valid" time="0.05" steps="113"/></proof>
  </goal>
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  <goal name="WP_parameter remove.10" expl="precondition">
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  <proof prover="1"><result status="valid" time="0.02" steps="53"/></proof>
  </goal>
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  <goal name="WP_parameter remove.11" expl="precondition">
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  <proof prover="1"><result status="valid" time="0.10" steps="123"/></proof>
  </goal>
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  <goal name="WP_parameter remove.12" expl="postcondition">
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  <proof prover="1"><result status="valid" time="0.02" steps="38"/></proof>
  </goal>
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  <goal name="WP_parameter remove.13" expl="postcondition">
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  <proof prover="1"><result status="valid" time="0.69" steps="545"/></proof>
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  </goal>
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  <goal name="WP_parameter remove.14" expl="postcondition">
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  <proof prover="1"><result status="valid" time="0.32" steps="331"/></proof>
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  </goal>
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  <goal name="WP_parameter remove.15" expl="variant decrease">
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  <proof prover="1"><result status="valid" time="0.11" steps="135"/></proof>
  </goal>
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  <goal name="WP_parameter remove.16" expl="precondition">
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  <proof prover="1"><result status="valid" time="0.03" steps="35"/></proof>
  </goal>
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  <goal name="WP_parameter remove.17" expl="precondition">
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  <proof prover="1"><result status="valid" time="0.22" steps="140"/></proof>
  </goal>
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  <goal name="WP_parameter remove.18" expl="postcondition">
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  <proof prover="1"><result status="valid" time="0.04" steps="49"/></proof>
  </goal>
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  <goal name="WP_parameter remove.19" expl="postcondition">
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  <proof prover="1"><result status="valid" time="1.72" steps="807"/></proof>
  </goal>
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  <goal name="WP_parameter remove.20" expl="postcondition">
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  <proof prover="1"><result status="valid" time="0.37" steps="329"/></proof>
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  </goal>
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  <goal name="WP_parameter remove.21" expl="precondition">
337 338
  <proof prover="1"><result status="valid" time="0.08" steps="85"/></proof>
  </goal>
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339
  <goal name="WP_parameter remove.22" expl="postcondition">
340 341
  <proof prover="1"><result status="valid" time="0.02" steps="15"/></proof>
  </goal>
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342
  <goal name="WP_parameter remove.23" expl="postcondition">
343 344
  <proof prover="1"><result status="valid" time="0.08" steps="107"/></proof>
  </goal>
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345
  <goal name="WP_parameter remove.24" expl="postcondition">
346 347 348
  <proof prover="1"><result status="valid" time="0.10" steps="161"/></proof>
  </goal>
 </transf>
349
 </goal>
350
 <goal name="WP_parameter get" expl="VC for get">
351
 <proof prover="1"><result status="valid" time="0.79" steps="2065"/></proof>
352
 </goal>
353
 <goal name="WP_parameter extract" expl="VC for extract">
354
 <transf name="split_goal_wp">
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355
  <goal name="WP_parameter extract.1" expl="precondition">
356 357
  <proof prover="1"><result status="valid" time="0.01" steps="3"/></proof>
  </goal>
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358
  <goal name="WP_parameter extract.2" expl="postcondition">
359 360
  <proof prover="1"><result status="valid" time="0.02" steps="62"/></proof>
  </goal>
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361
  <goal name="WP_parameter extract.3" expl="postcondition">
362 363
  <proof prover="1"><result status="valid" time="0.02" steps="31"/></proof>
  </goal>
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364
  <goal name="WP_parameter extract.4" expl="precondition">
365 366
  <proof prover="1"><result status="valid" time="0.02" steps="29"/></proof>
  </goal>
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367
  <goal name="WP_parameter extract.5" expl="precondition">
368 369
  <proof prover="1"><result status="valid" time="0.02" steps="33"/></proof>
  </goal>
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370
  <goal name="WP_parameter extract.6" expl="precondition">
371 372
  <proof prover="1"><result status="valid" time="0.01" steps="42"/></proof>
  </goal>
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373
  <goal name="WP_parameter extract.7" expl="precondition">
374 375
  <proof prover="1"><result status="valid" time="0.01" steps="1"/></proof>
  </goal>
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376
  <goal name="WP_parameter extract.8" expl="variant decrease">
377 378
  <proof prover="1"><result status="valid" time="0.05" steps="113"/></proof>
  </goal>
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379
  <goal name="WP_parameter extract.9" expl="precondition">
380 381
  <proof prover="1"><result status="valid" time="0.02" steps="53"/></proof>
  </goal>
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382
  <goal name="WP_parameter extract.10" expl="precondition">
383 384
  <proof prover="1"><result status="valid" time="0.10" steps="137"/></proof>
  </goal>
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385
  <goal name="WP_parameter extract.11" expl="postcondition">
386 387
  <proof prover="1"><result status="valid" time="0.36" steps="439"/></proof>
  </goal>
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388
  <goal name="WP_parameter extract.12" expl="postcondition">
389 390
  <proof prover="1"><result status="valid" time="0.54" steps="446"/></proof>
  </goal>
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391
  <goal name="WP_parameter extract.13" expl="variant decrease">
392 393
  <proof prover="1"><result status="valid" time="0.11" steps="135"/></proof>
  </goal>
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394
  <goal name="WP_parameter extract.14" expl="precondition">
395 396
  <proof prover="1"><result status="valid" time="0.02" steps="35"/></proof>
  </goal>
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397
  <goal name="WP_parameter extract.15" expl="precondition">
398 399
  <proof prover="1"><result status="valid" time="0.19" steps="164"/></proof>
  </goal>
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400
  <goal name="WP_parameter extract.16" expl="postcondition">
401
  <proof prover="1"><result status="valid" time="0.54" steps="714"/></proof>
402
  </goal>
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403
  <goal name="WP_parameter extract.17" expl="postcondition">
404
  <proof prover="1"><result status="valid" time="0.54" steps="525"/></proof>
405
  </goal>
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406
  <goal name="WP_parameter extract.18" expl="precondition">
407 408
  <proof prover="1"><result status="valid" time="0.05" steps="85"/></proof>
  </goal>
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409
  <goal name="WP_parameter extract.19" expl="postcondition">
410 411
  <proof prover="1"><result status="valid" time="0.05" steps="107"/></proof>
  </goal>
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412
  <goal name="WP_parameter extract.20" expl="postcondition">
413 414 415
  <proof prover="1"><result status="valid" time="0.12" steps="163"/></proof>
  </goal>
 </transf>
416
 </goal>
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 <goal name="WP_parameter split" expl="VC for split">
418
 <proof prover="1"><result status="valid" time="1.37" steps="2416"/></proof>
419 420 421 422
 </goal>
</theory>
</file>
</why3session>