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<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
"https://www.why3.org/why3session.dtd">
<why3session shape_version="6">
<prover id="0" name="CVC5" version="1.1.2" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="1" name="CVC5" version="1.0.5" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="2" name="Z3" version="4.13.2" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="3" name="CVC4" version="1.8" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="4" name="Alt-Ergo" version="2.6.0" timelimit="5" steplimit="0" memlimit="1000"/>
<file format="whyml" proved="true">
<path name=".."/><path name="vstte12_combinators.mlw"/>
<theory name="Combinators" proved="true">
<goal name="eq'vc" expl="VC for eq" proved="true">
<proof prover="1"><result status="valid" time="0.010000" steps="1036"/></proof>
</goal>
<goal name="subst_c'vc" expl="VC for subst_c" proved="true">
<proof prover="1"><result status="valid" time="0.020000" steps="3322"/></proof>
</goal>
<goal name="subst_c_commute" proved="true">
<transf name="induction_ty_lex" proved="true" >
<goal name="subst_c_commute.0" proved="true">
<proof prover="1"><result status="valid" time="0.020000" steps="4709"/></proof>
</goal>
</transf>
</goal>
<goal name="reduction'vc" expl="VC for reduction" proved="true">
<proof prover="3" timelimit="5"><result status="valid" time="2.874564" steps="1569956"/></proof>
</goal>
<goal name="test_SKK'vc" expl="VC for test_SKK" proved="true">
<proof prover="1"><result status="valid" time="0.010000" steps="2652"/></proof>
</goal>
<goal name="reduce_step'vc" expl="VC for reduce_step" proved="true">
<proof prover="3"><result status="valid" time="0.090000" steps="14990"/></proof>
</goal>
<goal name="value_in_context'vc" expl="VC for value_in_context" proved="true">
<proof prover="1"><result status="valid" time="0.030000" steps="3731"/></proof>
</goal>
<goal name="irreducible_is_value'vc" expl="VC for irreducible_is_value" proved="true">
<proof prover="4"><result status="valid" time="0.070191" steps="677"/></proof>
</goal>
<goal name="reduction2'vc" expl="VC for reduction2" proved="true">
<transf name="split_vc" proved="true" >
<goal name="reduction2'vc.0" expl="variant decrease" proved="true">
<proof prover="3"><result status="valid" time="0.040000" steps="3303"/></proof>
</goal>
<goal name="reduction2'vc.1" expl="precondition" proved="true">
<proof prover="3"><result status="valid" time="0.040000" steps="3655"/></proof>
</goal>
<goal name="reduction2'vc.2" expl="variant decrease" proved="true">
<proof prover="3"><result status="valid" time="0.050000" steps="3389"/></proof>
</goal>
<goal name="reduction2'vc.3" expl="precondition" proved="true">
<proof prover="3"><result status="valid" time="0.040000" steps="4256"/></proof>
</goal>
<goal name="reduction2'vc.4" expl="unreachable point" proved="true">
<proof prover="3"><result status="valid" time="0.080000" steps="15879"/></proof>
</goal>
<goal name="reduction2'vc.5" expl="unreachable point" proved="true">
<proof prover="3"><result status="valid" time="0.050000" steps="4651"/></proof>
</goal>
<goal name="reduction2'vc.6" expl="unreachable point" proved="true">
<proof prover="3"><result status="valid" time="0.040000" steps="3334"/></proof>
</goal>
<goal name="reduction2'vc.7" expl="postcondition" proved="true">
<proof prover="1" timelimit="1"><result status="valid" time="0.050000" steps="10506"/></proof>
</goal>
<goal name="reduction2'vc.8" expl="postcondition" proved="true">
<transf name="split_vc" proved="true" >
<goal name="reduction2'vc.8.0" expl="postcondition" proved="true">
<proof prover="3"><result status="valid" time="0.040000" steps="3203"/></proof>
</goal>
<goal name="reduction2'vc.8.1" expl="postcondition" proved="true">
<proof prover="3"><result status="valid" time="0.504798" steps="186576"/></proof>
</goal>
</transf>
</goal>
</transf>
</goal>
<goal name="ks'vc" expl="VC for ks" proved="true">
<proof prover="1"><result status="valid" time="0.020000" steps="2839"/></proof>
</goal>
<goal name="reduction3'vc" expl="VC for reduction3" proved="true">
<transf name="split_vc" proved="true" >
<goal name="reduction3'vc.0" expl="variant decrease" proved="true">
<proof prover="2"><result status="valid" time="0.004811" steps="2229"/></proof>
</goal>
<goal name="reduction3'vc.1" expl="precondition" proved="true">
<proof prover="3" timelimit="5"><result status="valid" time="0.058131" steps="7557"/></proof>
</goal>
<goal name="reduction3'vc.2" expl="variant decrease" proved="true">
<proof prover="2"><result status="valid" time="0.013261" steps="24909"/></proof>
</goal>
<goal name="reduction3'vc.3" expl="precondition" proved="true">
<proof prover="3" timelimit="5"><result status="valid" time="0.055053" steps="8409"/></proof>
</goal>
<goal name="reduction3'vc.4" expl="unreachable point" proved="true">
<proof prover="4"><result status="valid" time="0.054732" steps="296"/></proof>
</goal>
<goal name="reduction3'vc.5" expl="unreachable point" proved="true">
<proof prover="4"><result status="valid" time="0.036443" steps="111"/></proof>
</goal>
<goal name="reduction3'vc.6" expl="unreachable point" proved="true">
<proof prover="0"><result status="valid" time="0.051503" steps="6173"/></proof>
</goal>
<goal name="reduction3'vc.7" expl="postcondition" proved="true">
<proof prover="3" timelimit="5"><result status="valid" time="0.235672" steps="43742"/></proof>
</goal>
<goal name="reduction3'vc.8" expl="postcondition" proved="true">
<proof prover="0"><result status="valid" time="0.117238" steps="14707"/></proof>
</goal>
<goal name="reduction3'vc.9" expl="postcondition" proved="true">
<proof prover="0"><result status="valid" time="0.075130" steps="9771"/></proof>
</goal>
<goal name="reduction3'vc.10" expl="postcondition" proved="true">
<proof prover="0"><result status="valid" time="0.114376" steps="14804"/></proof>
</goal>
</transf>
</goal>
<goal name="ks_even_odd'vc" expl="VC for ks_even_odd" proved="true">
<proof prover="1"><result status="valid" time="0.030000" steps="6174"/></proof>
</goal>
</theory>
</file>
</why3session>
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