1 <?xml version="1.0" encoding="UTF-8"?>
2 <!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
3 "https://www.why3.org/why3session.dtd">
4 <why3session shape_version="6">
5 <prover id="1" name="CVC5" version="1.0.5" timelimit="1" steplimit="0" memlimit="1000"/>
6 <prover id="2" name="Z3" version="4.8.10" timelimit="1" steplimit="0" memlimit="1000"/>
7 <file format="whyml" proved="true">
8 <path name=".."/><path name="bubble_sort.mlw"/>
9 <theory name="BubbleSort" proved="true">
10 <goal name="bubble_sort'vc" expl="VC for bubble_sort" proved="true">
11 <transf name="split_goal_right" proved="true" >
12 <goal name="bubble_sort'vc.0" expl="loop invariant init" proved="true">
13 <proof prover="2"><result status="valid" time="0.074041" steps="37444"/></proof>
15 <goal name="bubble_sort'vc.1" expl="loop invariant init" proved="true">
16 <proof prover="2"><result status="valid" time="0.057119" steps="45392"/></proof>
18 <goal name="bubble_sort'vc.2" expl="loop invariant init" proved="true">
19 <proof prover="2"><result status="valid" time="0.046590" steps="40572"/></proof>
21 <goal name="bubble_sort'vc.3" expl="loop invariant init" proved="true">
22 <proof prover="2"><result status="valid" time="0.038935" steps="18109"/></proof>
24 <goal name="bubble_sort'vc.4" expl="loop invariant init" proved="true">
25 <proof prover="2"><result status="valid" time="0.044603" steps="18137"/></proof>
27 <goal name="bubble_sort'vc.5" expl="loop invariant init" proved="true">
28 <proof prover="2"><result status="valid" time="0.052953" steps="42326"/></proof>
30 <goal name="bubble_sort'vc.6" expl="loop invariant init" proved="true">
31 <proof prover="2"><result status="valid" time="0.048709" steps="42373"/></proof>
33 <goal name="bubble_sort'vc.7" expl="index in array bounds" proved="true">
34 <proof prover="2"><result status="valid" time="0.045909" steps="44348"/></proof>
36 <goal name="bubble_sort'vc.8" expl="index in array bounds" proved="true">
37 <proof prover="2"><result status="valid" time="0.047368" steps="43996"/></proof>
39 <goal name="bubble_sort'vc.9" expl="precondition" proved="true">
40 <proof prover="2"><result status="valid" time="0.052246" steps="47991"/></proof>
42 <goal name="bubble_sort'vc.10" expl="loop invariant preservation" proved="true">
43 <proof prover="1"><result status="valid" time="0.170284" steps="10453"/></proof>
45 <goal name="bubble_sort'vc.11" expl="loop invariant preservation" proved="true">
46 <proof prover="1"><result status="valid" time="0.362711" steps="26859"/></proof>
48 <goal name="bubble_sort'vc.12" expl="loop invariant preservation" proved="true">
49 <proof prover="2"><result status="valid" time="0.248655" steps="460615"/></proof>
51 <goal name="bubble_sort'vc.13" expl="loop invariant preservation" proved="true">
52 <proof prover="1"><result status="valid" time="0.281755" steps="18928"/></proof>
54 <goal name="bubble_sort'vc.14" expl="loop invariant preservation" proved="true">
55 <proof prover="2"><result status="valid" time="0.038080" steps="19805"/></proof>
57 <goal name="bubble_sort'vc.15" expl="loop invariant preservation" proved="true">
58 <proof prover="2"><result status="valid" time="0.039327" steps="19837"/></proof>
60 <goal name="bubble_sort'vc.16" expl="loop invariant preservation" proved="true">
61 <proof prover="2"><result status="valid" time="0.061210" steps="45904"/></proof>
63 <goal name="bubble_sort'vc.17" expl="loop invariant preservation" proved="true">
64 <proof prover="2"><result status="valid" time="0.058018" steps="53395"/></proof>
66 <goal name="bubble_sort'vc.18" expl="loop invariant preservation" proved="true">
67 <proof prover="2"><result status="valid" time="0.042461" steps="19329"/></proof>
69 <goal name="bubble_sort'vc.19" expl="loop invariant preservation" proved="true">
70 <proof prover="1"><result status="valid" time="0.219863" steps="11499"/></proof>
72 <goal name="bubble_sort'vc.20" expl="loop invariant preservation" proved="true">
73 <proof prover="2"><result status="valid" time="0.060108" steps="48572"/></proof>
75 <goal name="bubble_sort'vc.21" expl="out of loop bounds" proved="true">
76 <proof prover="2"><result status="valid" time="0.057150" steps="42368"/></proof>
78 <goal name="bubble_sort'vc.22" expl="postcondition" proved="true">
79 <proof prover="2"><result status="valid" time="0.036539" steps="17777"/></proof>
81 <goal name="bubble_sort'vc.23" expl="postcondition" proved="true">
82 <proof prover="2"><result status="valid" time="0.057784" steps="41477"/></proof>
84 <goal name="bubble_sort'vc.24" expl="out of loop bounds" proved="true">
85 <proof prover="2"><result status="valid" time="0.058298" steps="40156"/></proof>
89 <goal name="test1'vc" expl="VC for test1" proved="true">
90 <proof prover="2"><result status="valid" time="0.071961" steps="53318"/></proof>
92 <goal name="test2'vc" expl="VC for test2" proved="true">
93 <proof prover="2"><result status="valid" time="0.053707" steps="68050"/></proof>
95 <goal name="bench'vc" expl="VC for bench" proved="true">
96 <proof prover="2"><result status="valid" time="0.042430" steps="39375"/></proof>
99 <theory name="TAOCP" proved="true">
100 <goal name="bubble_sort'vc" expl="VC for bubble_sort" proved="true">
101 <transf name="split_vc" proved="true" >
102 <goal name="bubble_sort'vc.0" expl="loop invariant init" proved="true">
103 <proof prover="2"><result status="valid" time="0.028105" steps="2791"/></proof>
105 <goal name="bubble_sort'vc.1" expl="loop invariant init" proved="true">
106 <proof prover="2"><result status="valid" time="0.058850" steps="37268"/></proof>
108 <goal name="bubble_sort'vc.2" expl="loop invariant init" proved="true">
109 <proof prover="2"><result status="valid" time="0.028942" steps="2903"/></proof>
111 <goal name="bubble_sort'vc.3" expl="loop invariant init" proved="true">
112 <proof prover="2"><result status="valid" time="0.045459" steps="40458"/></proof>
114 <goal name="bubble_sort'vc.4" expl="loop invariant init" proved="true">
115 <proof prover="2"><result status="valid" time="0.060056" steps="3080"/></proof>
117 <goal name="bubble_sort'vc.5" expl="loop invariant init" proved="true">
118 <proof prover="2"><result status="valid" time="0.037537" steps="3085"/></proof>
120 <goal name="bubble_sort'vc.6" expl="loop invariant init" proved="true">
121 <proof prover="2"><result status="valid" time="0.041097" steps="42003"/></proof>
123 <goal name="bubble_sort'vc.7" expl="loop invariant init" proved="true">
124 <proof prover="2"><result status="valid" time="0.058038" steps="41685"/></proof>
126 <goal name="bubble_sort'vc.8" expl="loop invariant init" proved="true">
127 <proof prover="2"><result status="valid" time="0.058054" steps="47567"/></proof>
129 <goal name="bubble_sort'vc.9" expl="loop invariant init" proved="true">
130 <proof prover="2"><result status="valid" time="0.034576" steps="3201"/></proof>
132 <goal name="bubble_sort'vc.10" expl="index in array bounds" proved="true">
133 <proof prover="2"><result status="valid" time="0.056669" steps="43528"/></proof>
135 <goal name="bubble_sort'vc.11" expl="index in array bounds" proved="true">
136 <proof prover="2"><result status="valid" time="0.046853" steps="43131"/></proof>
138 <goal name="bubble_sort'vc.12" expl="precondition" proved="true">
139 <proof prover="2"><result status="valid" time="0.055598" steps="47568"/></proof>
141 <goal name="bubble_sort'vc.13" expl="loop invariant preservation" proved="true">
142 <proof prover="2"><result status="valid" time="0.027964" steps="48109"/></proof>
144 <goal name="bubble_sort'vc.14" expl="loop invariant preservation" proved="true">
145 <proof prover="1"><result status="valid" time="0.144297" steps="9153"/></proof>
147 <goal name="bubble_sort'vc.15" expl="loop invariant preservation" proved="true">
148 <proof prover="2"><result status="valid" time="0.203598" steps="388080"/></proof>
150 <goal name="bubble_sort'vc.16" expl="loop invariant preservation" proved="true">
151 <proof prover="1"><result status="valid" time="0.165283" steps="14207"/></proof>
153 <goal name="bubble_sort'vc.17" expl="loop invariant preservation" proved="true">
154 <proof prover="1"><result status="valid" time="0.144219" steps="12280"/></proof>
156 <goal name="bubble_sort'vc.18" expl="loop invariant preservation" proved="true">
157 <proof prover="2"><result status="valid" time="0.080244" steps="255289"/></proof>
159 <goal name="bubble_sort'vc.19" expl="loop invariant preservation" proved="true">
160 <proof prover="2"><result status="valid" time="0.046612" steps="43168"/></proof>
162 <goal name="bubble_sort'vc.20" expl="loop invariant preservation" proved="true">
163 <proof prover="2"><result status="valid" time="0.026049" steps="3272"/></proof>
165 <goal name="bubble_sort'vc.21" expl="loop invariant preservation" proved="true">
166 <proof prover="2"><result status="valid" time="0.040069" steps="45194"/></proof>
168 <goal name="bubble_sort'vc.22" expl="loop invariant preservation" proved="true">
169 <transf name="split_vc" proved="true" >
170 <goal name="bubble_sort'vc.22.0" expl="loop invariant preservation" proved="true">
171 <proof prover="2"><result status="valid" time="0.034692" steps="44844"/></proof>
175 <goal name="bubble_sort'vc.23" expl="loop invariant preservation" proved="true">
176 <proof prover="1"><result status="valid" time="0.206065" steps="22027"/></proof>
178 <goal name="bubble_sort'vc.24" expl="loop invariant preservation" proved="true">
179 <proof prover="2"><result status="valid" time="0.026466" steps="3388"/></proof>
181 <goal name="bubble_sort'vc.25" expl="loop variant decrease" proved="true">
182 <proof prover="2"><result status="valid" time="0.051195" steps="47768"/></proof>
184 <goal name="bubble_sort'vc.26" expl="loop invariant preservation" proved="true">
185 <proof prover="2"><result status="valid" time="0.044204" steps="47395"/></proof>
187 <goal name="bubble_sort'vc.27" expl="loop invariant preservation" proved="true">
188 <proof prover="2"><result status="valid" time="0.024583" steps="3236"/></proof>
190 <goal name="bubble_sort'vc.28" expl="loop invariant preservation" proved="true">
191 <proof prover="2"><result status="valid" time="0.038398" steps="53587"/></proof>
193 <goal name="bubble_sort'vc.29" expl="loop invariant preservation" proved="true">
194 <proof prover="2"><result status="valid" time="0.044270" steps="68021"/></proof>
196 <goal name="bubble_sort'vc.30" expl="out of loop bounds" proved="true">
197 <proof prover="2"><result status="valid" time="0.051902" steps="45758"/></proof>
199 <goal name="bubble_sort'vc.31" expl="postcondition" proved="true">
200 <proof prover="2"><result status="valid" time="0.031893" steps="3063"/></proof>
202 <goal name="bubble_sort'vc.32" expl="postcondition" proved="true">
203 <proof prover="2"><result status="valid" time="0.160555" steps="1594806"/></proof>