<?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="698"/></proof>
 </goal>
 <goal name="Exponentiation.Assoc" proved="true">
 <proof prover="4"><result status="valid" time="0.01" steps="668"/></proof>
 </goal>
 <goal name="Exponentiation.Unit_def_l" proved="true">
 <proof prover="4"><result status="valid" time="0.00" steps="715"/></proof>
 </goal>
 <goal name="Exponentiation.Unit_def_r" proved="true">
 <proof prover="4"><result status="valid" time="0.01" steps="759"/></proof>
 </goal>
 <goal name="Exponentiation.Power_0" proved="true">
 <proof prover="4"><result status="valid" time="0.01" steps="872"/></proof>
 </goal>
 <goal name="Exponentiation.Power_s" proved="true">
 <proof prover="4"><result status="valid" time="0.01" steps="1176"/></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="2311"/></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="2627"/></proof>
  </goal>
  <goal name="neg_star_l.1" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="2182"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="neg_neg" proved="true">
 <proof prover="4"><result status="valid" time="0.01" steps="2526"/></proof>
 </goal>
 <goal name="null_add" proved="true">
 <proof prover="4"><result status="valid" time="0.01" steps="2924"/></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="3458"/></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="3588"/></proof>
 </goal>
 <goal name="null_star_l" proved="true">
 <proof prover="4"><result status="valid" time="0.01" steps="3116"/></proof>
 </goal>
 <goal name="null_star_r" proved="true">
 <proof prover="4"><result status="valid" time="0.01" steps="3242"/></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="118504"/></proof>
  </goal>
  <goal name="all_null6.1" proved="true">
  <proof prover="4"><result status="valid" time="0.03" steps="3165"/></proof>
  </goal>
  <goal name="all_null6.2" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="4445"/></proof>
  </goal>
  <goal name="all_null6.3" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="3248"/></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="6364"/></proof>
  </goal>
  <goal name="all_split.1" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="3584"/></proof>
  </goal>
  <goal name="all_split.2" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="3626"/></proof>
  </goal>
  <goal name="all_split.3" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="3581"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="free_split" proved="true">
 <proof prover="4"><result status="valid" time="0.01" steps="3781"/></proof>
 </goal>
 <goal name="null_2_idem" proved="true">
 <proof prover="4"><result status="valid" time="0.20" steps="62505"/></proof>
 </goal>
 <goal name="null2_comm" proved="true">
 <proof prover="4"><result status="valid" time="0.25" steps="63668"/></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="31318"/></proof>
  </goal>
  <goal name="swap_equality.2" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="4171"/></proof>
  </goal>
  <goal name="swap_equality.3" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="4178"/></proof>
  </goal>
  <goal name="swap_equality.4" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="4302"/></proof>
  </goal>
  <goal name="swap_equality.5" proved="true">
  <proof prover="4"><result status="valid" time="3.59" steps="85070"/></proof>
  </goal>
  <goal name="swap_equality.6" proved="true">
  <proof prover="0"><result status="valid" time="0.54" steps="221825"/></proof>
  </goal>
  <goal name="swap_equality.7" proved="true">
  <proof prover="4"><result status="valid" time="0.09" steps="30622"/></proof>
  </goal>
  <goal name="swap_equality.8" proved="true">
  <proof prover="4"><result status="valid" time="0.15" steps="10619"/></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="12324"/></proof>
  </goal>
  <goal name="null3_comm.1" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="4444"/></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="30458"/></proof>
  </goal>
  <goal name="commutative.2" proved="true">
  <proof prover="4"><result status="valid" time="0.09" steps="30452"/></proof>
  </goal>
  <goal name="commutative.3" proved="true">
  <proof prover="4"><result status="valid" time="0.08" steps="30637"/></proof>
  </goal>
  <goal name="commutative.4" proved="true">
  <proof prover="4"><result status="valid" time="0.09" steps="30624"/></proof>
  </goal>
  <goal name="commutative.5" proved="true">
  <proof prover="4"><result status="valid" time="0.06" steps="19523"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
</file>
</why3session>
