<?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="Alt-Ergo" version="2.3.0" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="1" name="CVC3" version="2.4.1" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="2" name="Z3" version="4.6.0" timelimit="30" steplimit="0" memlimit="1000"/>
<prover id="3" name="Alt-Ergo" version="2.0.0" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="5" name="Coq" version="8.11.2" timelimit="5" steplimit="0" memlimit="0"/>
<file format="whyml" proved="true">
<path name=".."/><path name="euler001.mlw"/>
<theory name="DivModHints" proved="true">
 <goal name="mod_div_unique" proved="true">
 <proof prover="5"><path name="euler001_DivModHints_mod_div_unique_1.v"/><result status="valid" time="0.15"/></proof>
 </goal>
 <goal name="mod_succ_1" proved="true">
 <proof prover="5"><path name="euler001_DivModHints_mod_succ_1_1.v"/><result status="valid" time="0.22"/></proof>
 </goal>
 <goal name="mod_succ_2" proved="true">
 <proof prover="5"><path name="euler001_DivModHints_mod_succ_2_1.v"/><result status="valid" time="0.30"/></proof>
 </goal>
 <goal name="div_succ_1" proved="true">
 <proof prover="1" timelimit="30"><result status="valid" time="0.04"/></proof>
 </goal>
 <goal name="div_succ_2" proved="true">
 <proof prover="1" timelimit="30"><result status="valid" time="0.10"/></proof>
 <proof prover="3" timelimit="30"><result status="valid" time="0.17" steps="41"/></proof>
 </goal>
 <goal name="mod2_mul2" proved="true">
 <proof prover="1"><result status="valid" time="0.01"/></proof>
 <proof prover="2" timelimit="5"><result status="valid" time="0.01" steps="15025"/></proof>
 <proof prover="3"><result status="valid" time="0.05" steps="6"/></proof>
 </goal>
 <goal name="mod2_mul2_aux" proved="true">
 <proof prover="1" timelimit="30"><result status="valid" time="0.02"/></proof>
 <proof prover="2"><result status="valid" time="0.02" steps="8257"/></proof>
 <proof prover="3"><result status="valid" time="0.02" steps="7"/></proof>
 </goal>
 <goal name="mod2_mul2_aux2" proved="true">
 <proof prover="1" timelimit="35"><result status="valid" time="0.02"/></proof>
 <proof prover="2"><result status="valid" time="0.15" steps="253656"/></proof>
 <proof prover="3"><result status="valid" time="0.03" steps="10"/></proof>
 </goal>
 <goal name="div2_mul2" proved="true">
 <proof prover="1"><result status="valid" time="0.06"/></proof>
 <proof prover="2" timelimit="5"><result status="valid" time="0.02" steps="9811"/></proof>
 <proof prover="3"><result status="valid" time="0.01" steps="3"/></proof>
 </goal>
 <goal name="div2_mul2_aux" proved="true">
 <proof prover="1"><result status="valid" time="0.08"/></proof>
 <proof prover="2" timelimit="5"><result status="valid" time="0.01" steps="9006"/></proof>
 <proof prover="3"><result status="valid" time="0.01" steps="5"/></proof>
 </goal>
 <goal name="div2_add" proved="true">
 <proof prover="1"><result status="valid" time="0.04"/></proof>
 <proof prover="2" timelimit="5"><result status="valid" time="0.02" steps="11687"/></proof>
 </goal>
 <goal name="div2_sub" proved="true">
 <proof prover="1"><result status="valid" time="0.04"/></proof>
 <proof prover="2" timelimit="5"><result status="valid" time="0.02" steps="37307"/></proof>
 </goal>
</theory>
<theory name="TriangularNumbers" proved="true">
 <goal name="tr_mod_2" proved="true">
 <proof prover="5" memlimit="1000"><path name="euler001_TriangularNumbers_tr_mod_2_1.v"/><result status="valid" time="0.31"/></proof>
 </goal>
 <goal name="tr_repr" proved="true">
 <proof prover="3"><result status="valid" time="0.01" steps="7"/></proof>
 </goal>
 <goal name="tr_succ" proved="true">
 <proof prover="1"><result status="valid" time="0.02"/></proof>
 <proof prover="3"><result status="valid" time="0.01" steps="5"/></proof>
 </goal>
</theory>
<theory name="SumMultiple" proved="true">
 <goal name="mod_15" proved="true">
 <proof prover="1" timelimit="30"><result status="valid" time="0.13"/></proof>
 <proof prover="3"><result status="valid" time="0.04" steps="28"/></proof>
 </goal>
 <goal name="Closed_formula_0" proved="true">
 <proof prover="1" timelimit="30"><result status="valid" time="0.02"/></proof>
 <proof prover="3"><result status="valid" time="0.06" steps="79"/></proof>
 </goal>
 <goal name="Closed_formula_n" proved="true">
 <proof prover="1" timelimit="10"><result status="valid" time="1.46"/></proof>
 <proof prover="3" timelimit="10"><result status="valid" time="0.06" steps="55"/></proof>
 </goal>
 <goal name="Closed_formula_n_3" proved="true">
 <proof prover="1" timelimit="10"><result status="valid" time="2.35"/></proof>
 </goal>
 <goal name="Closed_formula_n_5" proved="true">
 <proof prover="1"><result status="valid" time="0.35"/></proof>
 </goal>
 <goal name="Closed_formula_n_15" proved="true">
 <proof prover="1"><result status="valid" time="0.28"/></proof>
 </goal>
 <goal name="Closed_formula_ind" proved="true">
 <proof prover="1"><result status="valid" time="0.02"/></proof>
 </goal>
 <goal name="div_15" proved="true">
 <proof prover="1" timelimit="30"><result status="valid" time="0.01"/></proof>
 <proof prover="2"><result status="valid" time="0.02" steps="17086"/></proof>
 <proof prover="3"><result status="valid" time="0.01" steps="9"/></proof>
 </goal>
 <goal name="div_5" proved="true">
 <proof prover="1" timelimit="30"><result status="valid" time="0.01"/></proof>
 <proof prover="2"><result status="valid" time="0.02" steps="17289"/></proof>
 <proof prover="3"><result status="valid" time="0.01" steps="9"/></proof>
 </goal>
 <goal name="div_3" proved="true">
 <proof prover="1" timelimit="30"><result status="valid" time="0.02"/></proof>
 <proof prover="2"><result status="valid" time="0.02" steps="17492"/></proof>
 <proof prover="3"><result status="valid" time="0.01" steps="9"/></proof>
 </goal>
 <goal name="Closed_Formula" proved="true">
 <proof prover="5" timelimit="30" memlimit="1000"><path name="euler001_SumMultiple_Closed_Formula_1.v"/><result status="valid" time="0.40"/></proof>
 </goal>
</theory>
<theory name="Euler001" proved="true">
 <goal name="solve&#39;vc" expl="VC for solve" proved="true">
 <proof prover="3"><result status="valid" time="1.72" steps="349"/></proof>
 </goal>
 <goal name="run&#39;vc" expl="VC for run" proved="true">
 <proof prover="3"><result status="valid" time="0.00" steps="3"/></proof>
 </goal>
 <goal name="bench&#39;vc" expl="VC for bench" proved="true">
 <proof prover="0"><result status="valid" time="0.00" steps="4"/></proof>
 </goal>
</theory>
</file>
</why3session>
