<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
"http://why3.lri.fr/why3session.dtd">
<why3session shape_version="6">
<prover id="0" name="Z3" version="4.7.1" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="2" name="Alt-Ergo" version="2.3.0" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="4" name="CVC4" version="1.6" timelimit="5" steplimit="0" memlimit="1000"/>
<file format="whyml" proved="true">
<path name=".."/><path name="three_idem_ring.mlw"/>
<theory name="Top" proved="true">
 <goal name="mul&#39;vc" expl="VC for mul" proved="true">
 <proof prover="4"><result status="valid" time="0.01" steps="899"/></proof>
 </goal>
 <goal name="Exponentiation.Assoc" proved="true">
 <proof prover="4"><result status="valid" time="0.01" steps="869"/></proof>
 </goal>
 <goal name="Exponentiation.Unit_def_l" proved="true">
 <proof prover="4"><result status="valid" time="0.00" steps="916"/></proof>
 </goal>
 <goal name="Exponentiation.Unit_def_r" proved="true">
 <proof prover="4"><result status="valid" time="0.01" steps="960"/></proof>
 </goal>
 <goal name="Exponentiation.Power_0" proved="true">
 <proof prover="4"><result status="valid" time="0.01" steps="1240"/></proof>
 </goal>
 <goal name="Exponentiation.Power_s" proved="true">
 <proof prover="4"><result status="valid" time="0.01" steps="1581"/></proof>
 </goal>
 <goal name="simpl_left" proved="true">
 <proof prover="2"><result status="valid" time="0.08" steps="22"/></proof>
 </goal>
 <goal name="simpl_right" proved="true">
 <proof prover="4"><result status="valid" time="0.01" steps="2313"/></proof>
 </goal>
 <goal name="zero_star_l" proved="true">
 <proof prover="2"><result status="valid" time="0.03" steps="36"/></proof>
 </goal>
 <goal name="zero_star_r" proved="true">
 <proof prover="2"><result status="valid" time="0.05" steps="42"/></proof>
 </goal>
 <goal name="neg_star_r" proved="true">
 <proof prover="2"><result status="valid" time="4.80" steps="152"/></proof>
 </goal>
 <goal name="neg_star_l" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="neg_star_l.0" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="2629"/></proof>
  </goal>
  <goal name="neg_star_l.1" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="2184"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="neg_neg" proved="true">
 <proof prover="4"><result status="valid" time="0.01" steps="2528"/></proof>
 </goal>
 <goal name="null_add" proved="true">
 <proof prover="4"><result status="valid" time="0.01" steps="2926"/></proof>
 </goal>
 <goal name="mul_star_l&#39;vc" expl="VC for mul_star_l" proved="true">
 <proof prover="4"><result status="valid" time="0.01" steps="3460"/></proof>
 </goal>
 <goal name="mul_star_r&#39;vc" expl="VC for mul_star_r" proved="true">
 <proof prover="4"><result status="valid" time="0.02" steps="3590"/></proof>
 </goal>
 <goal name="null_star_l" proved="true">
 <proof prover="4"><result status="valid" time="0.01" steps="3118"/></proof>
 </goal>
 <goal name="null_star_r" proved="true">
 <proof prover="4"><result status="valid" time="0.01" steps="3244"/></proof>
 </goal>
 <goal name="null_mul_congr" proved="true">
 <proof prover="2"><result status="valid" time="0.03" steps="18"/></proof>
 </goal>
 <goal name="all_null6" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="all_null6.0" proved="true">
  <proof prover="0"><result status="valid" time="0.08" steps="118499"/></proof>
  </goal>
  <goal name="all_null6.1" proved="true">
  <proof prover="4"><result status="valid" time="0.03" steps="3167"/></proof>
  </goal>
  <goal name="all_null6.2" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="4447"/></proof>
  </goal>
  <goal name="all_null6.3" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="3250"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="all_split" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="all_split.0" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="6366"/></proof>
  </goal>
  <goal name="all_split.1" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="3586"/></proof>
  </goal>
  <goal name="all_split.2" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="3628"/></proof>
  </goal>
  <goal name="all_split.3" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="3583"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="free_split" proved="true">
 <proof prover="4"><result status="valid" time="0.01" steps="3783"/></proof>
 </goal>
 <goal name="null_2_idem" proved="true">
 <proof prover="4"><result status="valid" time="0.20" steps="62507"/></proof>
 </goal>
 <goal name="null2_comm" proved="true">
 <proof prover="4"><result status="valid" time="0.19" steps="63670"/></proof>
 </goal>
 <goal name="swap_equality" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="swap_equality.0" proved="true">
  <proof prover="0"><result status="valid" time="2.39" steps="1101324"/></proof>
  </goal>
  <goal name="swap_equality.1" proved="true">
  <proof prover="4"><result status="valid" time="0.10" steps="31320"/></proof>
  </goal>
  <goal name="swap_equality.2" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="4173"/></proof>
  </goal>
  <goal name="swap_equality.3" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="4180"/></proof>
  </goal>
  <goal name="swap_equality.4" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="4304"/></proof>
  </goal>
  <goal name="swap_equality.5" proved="true">
  <proof prover="4"><result status="valid" time="3.58" steps="85072"/></proof>
  </goal>
  <goal name="swap_equality.6" proved="true">
  <proof prover="0"><result status="valid" time="0.54" steps="221774"/></proof>
  </goal>
  <goal name="swap_equality.7" proved="true">
  <proof prover="4"><result status="valid" time="0.09" steps="30624"/></proof>
  </goal>
  <goal name="swap_equality.8" proved="true">
  <proof prover="4"><result status="valid" time="0.03" steps="10621"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="null3_comm" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="null3_comm.0" proved="true">
  <proof prover="4"><result status="valid" time="0.04" steps="12326"/></proof>
  </goal>
  <goal name="null3_comm.1" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="4446"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="commutative" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="commutative.0" proved="true">
  <proof prover="2"><result status="valid" time="0.35" steps="88"/></proof>
  </goal>
  <goal name="commutative.1" proved="true">
  <proof prover="4"><result status="valid" time="0.09" steps="30460"/></proof>
  </goal>
  <goal name="commutative.2" proved="true">
  <proof prover="4"><result status="valid" time="0.09" steps="30454"/></proof>
  </goal>
  <goal name="commutative.3" proved="true">
  <proof prover="4"><result status="valid" time="0.08" steps="30639"/></proof>
  </goal>
  <goal name="commutative.4" proved="true">
  <proof prover="4"><result status="valid" time="0.09" steps="30626"/></proof>
  </goal>
  <goal name="commutative.5" proved="true">
  <proof prover="4"><result status="valid" time="0.06" steps="19525"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
</file>
</why3session>
