mirror of
https://github.com/AdaCore/why3.git
synced 2026-02-12 12:34:55 -08:00
277 lines
19 KiB
XML
277 lines
19 KiB
XML
<?xml version="1.0" encoding="UTF-8"?>
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<!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
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"https://www.why3.org/why3session.dtd">
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<why3session shape_version="6">
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<prover id="1" name="Alt-Ergo" version="2.6.0" timelimit="5" steplimit="0" memlimit="1000"/>
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<prover id="2" name="Z3" version="4.12.2" timelimit="5" steplimit="0" memlimit="1000"/>
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<prover id="3" name="Coq" version="8.19.2" timelimit="0" steplimit="0" memlimit="0"/>
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<prover id="8" name="CVC3" version="2.4.1" timelimit="5" steplimit="0" memlimit="1000"/>
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<file format="whyml" proved="true">
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<path name=".."/><path name="queens.mlw"/>
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<theory name="NQueensSetsTermination" proved="true">
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<goal name="t'vc" expl="VC for t" proved="true">
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<transf name="split_goal_right" proved="true" >
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<goal name="t'vc.0" expl="loop invariant init" proved="true">
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<proof prover="1"><result status="valid" time="0.010000" steps="14"/></proof>
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</goal>
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<goal name="t'vc.1" expl="precondition" proved="true">
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<proof prover="1"><result status="valid" time="0.000000" steps="0"/></proof>
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</goal>
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<goal name="t'vc.2" expl="variant decrease" proved="true">
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<proof prover="1"><result status="valid" time="0.100000" steps="482"/></proof>
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</goal>
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<goal name="t'vc.3" expl="loop variant decrease" proved="true">
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<proof prover="1"><result status="valid" time="0.020000" steps="119"/></proof>
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</goal>
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<goal name="t'vc.4" expl="loop invariant preservation" proved="true">
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<proof prover="1"><result status="valid" time="0.020000" steps="69"/></proof>
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</goal>
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</transf>
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</goal>
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</theory>
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<theory name="Solution" proved="true">
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<goal name="partial_solution_eq_prefix" proved="true">
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<proof prover="1"><result status="valid" time="0.010000" steps="69"/></proof>
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</goal>
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<goal name="no_duplicate" proved="true">
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<proof prover="2"><result status="valid" time="0.020000" steps="11143"/></proof>
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<proof prover="8"><result status="valid" time="0.010000"/></proof>
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</goal>
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</theory>
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<theory name="NQueensSets" proved="true">
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<goal name="t3'vc" expl="VC for t3" proved="true">
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<transf name="split_vc" proved="true" >
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<goal name="t3'vc.0" expl="assertion" proved="true">
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<proof prover="1"><result status="valid" time="0.270099" steps="1988"/></proof>
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</goal>
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<goal name="t3'vc.1" expl="loop invariant init" proved="true">
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<proof prover="1"><result status="valid" time="0.020000" steps="145"/></proof>
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</goal>
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<goal name="t3'vc.2" expl="loop invariant init" proved="true">
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<proof prover="1"><result status="valid" time="0.010000" steps="22"/></proof>
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</goal>
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<goal name="t3'vc.3" expl="loop invariant init" proved="true">
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<proof prover="1"><result status="valid" time="0.010000" steps="26"/></proof>
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</goal>
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<goal name="t3'vc.4" expl="loop invariant init" proved="true">
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<proof prover="1"><result status="valid" time="0.010000" steps="23"/></proof>
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</goal>
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<goal name="t3'vc.5" expl="loop invariant init" proved="true">
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<proof prover="1"><result status="valid" time="0.010000" steps="24"/></proof>
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</goal>
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<goal name="t3'vc.6" expl="precondition" proved="true">
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<proof prover="1"><result status="valid" time="0.010000" steps="32"/></proof>
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</goal>
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<goal name="t3'vc.7" expl="variant decrease" proved="true">
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<proof prover="1"><result status="valid" time="0.100000" steps="601"/></proof>
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</goal>
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<goal name="t3'vc.8" expl="precondition" proved="true">
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<transf name="split_vc" proved="true" >
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<goal name="t3'vc.8.0" expl="precondition" proved="true">
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<proof prover="1"><result status="valid" time="0.010000" steps="42"/></proof>
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</goal>
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<goal name="t3'vc.8.1" expl="precondition" proved="true">
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<proof prover="1"><result status="valid" time="0.100000" steps="581"/></proof>
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</goal>
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<goal name="t3'vc.8.2" expl="precondition" proved="true">
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<proof prover="1"><result status="valid" time="0.010000" steps="42"/></proof>
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</goal>
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<goal name="t3'vc.8.3" expl="precondition" proved="true">
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<proof prover="1"><result status="valid" time="0.040000" steps="235"/></proof>
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</goal>
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<goal name="t3'vc.8.4" expl="precondition" proved="true">
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<proof prover="1"><result status="valid" time="0.040000" steps="235"/></proof>
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</goal>
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<goal name="t3'vc.8.5" expl="precondition" proved="true">
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<proof prover="1"><result status="valid" time="0.296394" steps="2636"/></proof>
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</goal>
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<goal name="t3'vc.8.6" expl="precondition" proved="true">
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<proof prover="1"><result status="valid" time="0.675719" steps="7060"/></proof>
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<transf name="remove" proved="true" arg1="zero,one,(-),(>),(<=),(>=),get,set,(!),(==),subset,is_empty,singleton,disjoint,eq_sol,partial_solution,solution,lt_sol,sorted,d,Assoc1,Unit_def_l,Unit_def_r,Inv_def_l,Inv_def_r,Comm1,Assoc,Mul_distr_l,Mul_distr_r,Comm,Unitary,NonTrivialRing,Refl,Trans,Antisymm,Total,ZeroLessOne,CompatOrderAdd,CompatOrderMult,extensionality,subset_refl,subset_trans,is_empty_empty,empty_is_empty,add_def,mem_singleton,add_remove,remove_add,subset_remove,union_def,subset_union_1,subset_union_2,inter_def,subset_inter_1,subset_inter_2,diff_def,subset_diff,pick_def,disjoint_inter_empty,disjoint_diff_eq,disjoint_diff_s2,filter_def,subset_filter,map_def,mem_map,cardinal_nonneg,cardinal_empty,cardinal_add,cardinal_remove,cardinal_subset,subset_eq,cardinal1,cardinal_union,cardinal_inter_disjoint,cardinal_diff,cardinal_filter,cardinal_map,min_elt_def,max_elt_def,interval_def,cardinal_interval,mk'spec,choose'spec,partial_solution_eq_prefix,no_duplicate,H17,H16,H14,H13,H12,H11,Ensures11,Ensures10,Assert,H10,H9,H7,H6,H5,H4,LoopInvariant3,LoopInvariant2,LoopInvariant,H3,Ensures7,Ensures6,Ensures5,Ensures4,Ensures3,Ensures2,Ensures">
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<goal name="t3'vc.8.6.0" expl="precondition" proved="true">
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<proof prover="1"><result status="valid" time="0.000000" steps="55"/></proof>
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</goal>
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</transf>
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</goal>
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<goal name="t3'vc.8.7" expl="precondition" proved="true">
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<proof prover="1"><result status="valid" time="0.295901" steps="3902"/></proof>
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</goal>
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<goal name="t3'vc.8.8" expl="precondition" proved="true">
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<proof prover="1"><result status="valid" time="1.995672" steps="15037"/></proof>
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<transf name="remove" proved="true" arg1="zero,one,(-),(>),(<=),(>=),get,set,(!),(==),subset,is_empty,singleton,disjoint,eq_sol,partial_solution,solution,lt_sol,sorted,d,Assoc1,Unit_def_l,Unit_def_r,Inv_def_l,Inv_def_r,Comm1,Assoc,Mul_distr_l,Mul_distr_r,Comm,Unitary,NonTrivialRing,Refl,Trans,Antisymm,Total,ZeroLessOne,CompatOrderAdd,CompatOrderMult,extensionality,subset_refl,subset_trans,is_empty_empty,empty_is_empty,mem_singleton,remove_def,add_remove,remove_add,subset_remove,union_def,subset_union_1,subset_union_2,inter_def,subset_inter_1,subset_inter_2,diff_def,subset_diff,pick_def,disjoint_inter_empty,disjoint_diff_eq,disjoint_diff_s2,filter_def,subset_filter,map_def,mem_map,cardinal_nonneg,cardinal_empty,cardinal_add,cardinal_remove,cardinal_subset,subset_eq,cardinal1,cardinal_union,cardinal_inter_disjoint,cardinal_diff,cardinal_filter,cardinal_map,min_elt_def,max_elt_def,interval_def,cardinal_interval,mk'spec,choose'spec,partial_solution_eq_prefix,no_duplicate,H16,H15,H14,H12,H11,H10,Ensures11,Ensures10,Assert,H9,H8,H6,H5,H4,H3,LoopInvariant3,LoopInvariant2,LoopInvariant,H2,Ensures7,Ensures6,Ensures5,Ensures3,Ensures1,Ensures,H1">
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<goal name="t3'vc.8.8.0" expl="precondition" proved="true">
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<proof prover="1"><result status="valid" time="0.000000" steps="56"/></proof>
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</goal>
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</transf>
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</goal>
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<goal name="t3'vc.8.9" expl="precondition" proved="true">
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<proof prover="1"><result status="valid" time="0.435262" steps="3375"/></proof>
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</goal>
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<goal name="t3'vc.8.10" expl="precondition" proved="true">
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<proof prover="1"><result status="valid" time="1.955307" steps="15008"/></proof>
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<transf name="remove" proved="true" arg1="zero,one,(-),(>),(<=),(>=),get,set,(!),(==),subset,is_empty,singleton,disjoint,eq_sol,partial_solution,solution,lt_sol,sorted,d,Assoc1,Unit_def_l,Unit_def_r,Inv_def_l,Inv_def_r,Comm1,Assoc,Mul_distr_l,Mul_distr_r,Comm,Unitary,NonTrivialRing,Refl,Trans,Antisymm,Total,ZeroLessOne,CompatOrderAdd,CompatOrderMult,extensionality,subset_refl,subset_trans,is_empty_empty,empty_is_empty,mem_singleton,remove_def,add_remove,remove_add,subset_remove,union_def,subset_union_1,subset_union_2,inter_def,subset_inter_1,subset_inter_2,diff_def,subset_diff,pick_def,disjoint_inter_empty,disjoint_diff_eq,disjoint_diff_s2,filter_def,subset_filter,map_def,mem_map,cardinal_nonneg,cardinal_empty,cardinal_add,cardinal_remove,cardinal_subset,subset_eq,cardinal1,cardinal_union,cardinal_inter_disjoint,cardinal_diff,cardinal_filter,cardinal_map,min_elt_def,max_elt_def,interval_def,cardinal_interval,mk'spec,choose'spec,partial_solution_eq_prefix,no_duplicate,H16,H15,H14,H13,H11,H10,Ensures11,Ensures10,Assert,H9,H8,H6,H5,H4,H3,LoopInvariant3,LoopInvariant2,LoopInvariant,H2,Ensures6,Ensures4,Ensures3,Ensures2,Ensures1,Ensures,H1">
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<goal name="t3'vc.8.10.0" expl="precondition" proved="true">
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<proof prover="1"><result status="valid" time="0.000000" steps="54"/></proof>
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</goal>
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</transf>
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</goal>
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<goal name="t3'vc.8.11" expl="precondition" proved="true">
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<transf name="inline_goal" proved="true" >
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<goal name="t3'vc.8.11.0" expl="precondition" proved="true">
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<transf name="split_vc" proved="true" >
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<goal name="t3'vc.8.11.0.0" expl="precondition" proved="true">
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<proof prover="1"><result status="valid" time="0.240000" steps="1368"/></proof>
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</goal>
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<goal name="t3'vc.8.11.0.1" expl="precondition" proved="true">
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<proof prover="1"><result status="valid" time="0.210000" steps="1110"/></proof>
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</goal>
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<goal name="t3'vc.8.11.0.2" expl="precondition" proved="true">
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<proof prover="1"><result status="valid" time="0.292926" steps="3243"/></proof>
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</goal>
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<goal name="t3'vc.8.11.0.3" expl="precondition" proved="true">
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<proof prover="1"><result status="valid" time="0.312696" steps="3245"/></proof>
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</goal>
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<goal name="t3'vc.8.11.0.4" expl="precondition" proved="true">
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<proof prover="1"><result status="valid" time="0.306536" steps="3240"/></proof>
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</goal>
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</transf>
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</goal>
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</transf>
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</goal>
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</transf>
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</goal>
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<goal name="t3'vc.9" expl="loop variant decrease" proved="true">
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<proof prover="1"><result status="valid" time="0.030000" steps="101"/></proof>
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</goal>
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<goal name="t3'vc.10" expl="loop invariant preservation" proved="true">
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<transf name="split_vc" proved="true" >
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<goal name="t3'vc.10.0" expl="loop invariant preservation" proved="true">
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<proof prover="1"><result status="valid" time="0.020000" steps="58"/></proof>
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</goal>
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<goal name="t3'vc.10.1" expl="loop invariant preservation" proved="true">
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<proof prover="1"><result status="valid" time="0.020000" steps="58"/></proof>
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</goal>
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<goal name="t3'vc.10.2" expl="loop invariant preservation" proved="true">
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<proof prover="1"><result status="valid" time="0.010000" steps="58"/></proof>
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</goal>
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<goal name="t3'vc.10.3" expl="loop invariant preservation" proved="true">
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<proof prover="1"><result status="valid" time="0.030000" steps="106"/></proof>
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</goal>
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<goal name="t3'vc.10.4" expl="loop invariant preservation" proved="true">
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<proof prover="1"><result status="valid" time="4.000833" steps="35355"/></proof>
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<transf name="remove" proved="true" arg1="zero,one,(-),(>),(<=),(>=),get,set,(!),(==),subset,is_empty,singleton,disjoint,eq_sol,partial_solution,solution,lt_sol,sorted,d,Assoc1,Unit_def_l,Unit_def_r,Inv_def_l,Inv_def_r,Comm1,Assoc,Mul_distr_l,Mul_distr_r,Comm,Unitary,NonTrivialRing,Refl,Trans,Antisymm,Total,ZeroLessOne,CompatOrderAdd,CompatOrderMult,extensionality,subset_refl,subset_trans,is_empty_empty,empty_is_empty,add_def,mem_singleton,remove_def,add_remove,remove_add,subset_remove,union_def,subset_union_1,subset_union_2,inter_def,subset_inter_1,subset_inter_2,diff_def,subset_diff,pick_def,disjoint_inter_empty,disjoint_diff_eq,disjoint_diff_s2,filter_def,subset_filter,map_def,mem_map,cardinal_nonneg,cardinal_empty,cardinal_add,cardinal_remove,cardinal_subset,subset_eq,cardinal1,cardinal_union,cardinal_inter_disjoint,cardinal_diff,cardinal_filter,cardinal_map,min_elt_def,max_elt_def,interval_def,cardinal_interval,mk'spec,choose'spec,no_duplicate,H21,H20,H19,H17,H15,H14,Ensures15,Ensures14,Assert,H13,H12,H10,H8,H7,LoopInvariant3,LoopInvariant1,LoopInvariant,H6,Ensures11,Ensures8,Ensures7,Ensures6,Ensures5,H,Ensures3">
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<goal name="t3'vc.10.4.0" expl="loop invariant preservation" proved="true">
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<proof prover="1"><result status="valid" time="0.010000" steps="785"/></proof>
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</goal>
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</transf>
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</goal>
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<goal name="t3'vc.10.5" expl="loop invariant preservation" proved="true">
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<transf name="generalize_introduced" proved="true" >
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<goal name="t3'vc.10.5.0" expl="loop invariant preservation" proved="true">
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<proof prover="3"><path name="queens_NQueensSets_VC_t3_2.v"/><result status="valid" time="5.667969"/></proof>
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</goal>
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</transf>
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</goal>
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<goal name="t3'vc.10.6" expl="loop invariant preservation" proved="true">
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<transf name="case" proved="true" arg1="(i = d)">
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<goal name="t3'vc.10.6.0" expl="true case (loop invariant preservation)" proved="true">
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<proof prover="1"><result status="valid" time="0.060000" steps="466"/></proof>
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</goal>
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<goal name="t3'vc.10.6.1" expl="false case (loop invariant preservation)" proved="true">
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<transf name="case" proved="true" arg1="(j = d)">
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<goal name="t3'vc.10.6.1.0" expl="false case (true case. loop invariant preservation)" proved="true">
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<proof prover="1"><result status="valid" time="0.020000" steps="125"/></proof>
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</goal>
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<goal name="t3'vc.10.6.1.1" expl="false case (loop invariant preservation)" proved="true">
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<transf name="apply" proved="true" arg1="H9">
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<goal name="t3'vc.10.6.1.1.0" expl="apply premises" proved="true">
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<proof prover="1"><result status="valid" time="0.060000" steps="388"/></proof>
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</goal>
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<goal name="t3'vc.10.6.1.1.1" expl="apply premises" proved="true">
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<proof prover="1"><result status="valid" time="0.020000" steps="115"/></proof>
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</goal>
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</transf>
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</goal>
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</transf>
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</goal>
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</transf>
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</goal>
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</transf>
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</goal>
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<goal name="t3'vc.11" expl="loop invariant preservation" proved="true">
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<transf name="remove" proved="true" arg1="zero,one,(-),(>),(<=),(>=),get,set,(!),(==),subset,is_empty,singleton,disjoint,partial_solution,solution,lt_sol,sorted,d,Assoc1,Unit_def_l,Unit_def_r,Inv_def_l,Inv_def_r,Comm1,Assoc,Mul_distr_l,Mul_distr_r,Comm,Unitary,NonTrivialRing,Refl,Trans,Antisymm,Total,ZeroLessOne,CompatOrderAdd,CompatOrderMult,extensionality,subset_refl,subset_trans,is_empty_empty,empty_is_empty,add_def,mem_singleton,add_remove,remove_add,subset_remove,union_def,subset_union_1,subset_union_2,inter_def,subset_inter_1,subset_inter_2,subset_diff,pick_def,disjoint_inter_empty,disjoint_diff_eq,disjoint_diff_s2,filter_def,subset_filter,map_def,mem_map,cardinal_nonneg,cardinal_empty,cardinal_add,cardinal_remove,cardinal_subset,subset_eq,cardinal1,cardinal_union,cardinal_inter_disjoint,cardinal_diff,cardinal_filter,cardinal_map,min_elt_def,max_elt_def,interval_def,cardinal_interval,mk'spec,choose'spec,partial_solution_eq_prefix,no_duplicate,H22,H20,H19,H18,H17,H16,Ensures15,Ensures14,H15,H14,H13,H12,H11,H10,H9,LoopInvariant3,LoopInvariant1,H8,Ensures11,Ensures10,Ensures9,Ensures8,Ensures7,Ensures6,Ensures5,Ensures4,H7,H5,Ensures3,Ensures">
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<goal name="t3'vc.11.0" expl="loop invariant preservation" proved="true">
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<proof prover="1"><result status="valid" time="3.048996" steps="16201"/></proof>
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</goal>
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</transf>
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</goal>
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<goal name="t3'vc.12" expl="loop invariant preservation" proved="true">
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<transf name="split_vc" proved="true" >
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<goal name="t3'vc.12.0" expl="loop invariant preservation" proved="true">
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<proof prover="1"><result status="valid" time="0.020000" steps="121"/></proof>
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</goal>
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<goal name="t3'vc.12.1" expl="loop invariant preservation" proved="true">
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<proof prover="1"><result status="valid" time="0.030000" steps="122"/></proof>
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</goal>
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<goal name="t3'vc.12.2" expl="loop invariant preservation" proved="true">
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<transf name="instantiate" proved="true" arg1="LoopInvariant3" arg2="t">
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<goal name="t3'vc.12.2.0" expl="loop invariant preservation" proved="true">
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<transf name="instantiate" proved="true" arg1="H14" arg2="t">
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<goal name="t3'vc.12.2.0.0" expl="loop invariant preservation" proved="true">
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<proof prover="1"><result status="valid" time="0.631555" steps="7165"/></proof>
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</goal>
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</transf>
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</goal>
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</transf>
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</goal>
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</transf>
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</goal>
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<goal name="t3'vc.13" expl="loop invariant preservation" proved="true">
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<proof prover="1"><result status="valid" time="0.290000" steps="2867"/></proof>
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</goal>
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<goal name="t3'vc.14" expl="loop invariant preservation" proved="true">
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<proof prover="1"><result status="valid" time="0.170000" steps="2858"/></proof>
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</goal>
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<goal name="t3'vc.15" expl="postcondition" proved="true">
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<transf name="split_vc" proved="true" >
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<goal name="t3'vc.15.0" expl="postcondition" proved="true">
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<proof prover="1"><result status="valid" time="0.000000" steps="32"/></proof>
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</goal>
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<goal name="t3'vc.15.1" expl="postcondition" proved="true">
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<proof prover="1"><result status="valid" time="0.010000" steps="32"/></proof>
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</goal>
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|
<goal name="t3'vc.15.2" expl="postcondition" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.010000" steps="32"/></proof>
|
|
</goal>
|
|
<goal name="t3'vc.15.3" expl="postcondition" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.010000" steps="32"/></proof>
|
|
</goal>
|
|
<goal name="t3'vc.15.4" expl="postcondition" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.604331" steps="6941"/></proof>
|
|
</goal>
|
|
<goal name="t3'vc.15.5" expl="postcondition" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.310000" steps="2296"/></proof>
|
|
</goal>
|
|
<goal name="t3'vc.15.6" expl="postcondition" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.070000" steps="595"/></proof>
|
|
</goal>
|
|
<goal name="t3'vc.15.7" expl="postcondition" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.010000" steps="32"/></proof>
|
|
</goal>
|
|
<goal name="t3'vc.15.8" expl="postcondition" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.010000" steps="32"/></proof>
|
|
</goal>
|
|
</transf>
|
|
</goal>
|
|
<goal name="t3'vc.16" expl="postcondition" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.050000" steps="265"/></proof>
|
|
</goal>
|
|
</transf>
|
|
</goal>
|
|
<goal name="queens3'vc" expl="VC for queens3" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.100000" steps="410"/></proof>
|
|
</goal>
|
|
</theory>
|
|
</file>
|
|
</why3session>
|