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="0" name="Z3" version="4.11.2" timelimit="1" steplimit="0" memlimit="1000"/>
6 <prover id="1" name="Alt-Ergo" version="2.0.0" timelimit="5" steplimit="0" memlimit="1000"/>
7 <prover id="3" name="Alt-Ergo" version="2.3.0" timelimit="1" steplimit="0" memlimit="1000"/>
8 <file format="whyml" proved="true">
9 <path name=".."/><path name="counting_sort.mlw"/>
10 <theory name="Spec" proved="true">
11 <goal name="k'vc" expl="VC for k" proved="true">
12 <proof prover="3"><result status="valid" time="0.000000" steps="0"/></proof>
14 <goal name="eqlt'vc" expl="VC for eqlt" proved="true">
15 <proof prover="1"><result status="valid" time="0.760000" steps="777"/></proof>
18 <theory name="CountingSort" proved="true">
19 <goal name="counting_sort'vc" expl="VC for counting_sort" proved="true">
20 <transf name="split_goal_right" proved="true" >
21 <goal name="counting_sort'vc.0" expl="array creation size" proved="true">
22 <proof prover="1"><result status="valid" time="0.000000" steps="4"/></proof>
24 <goal name="counting_sort'vc.1" expl="loop invariant init" proved="true">
25 <proof prover="1"><result status="valid" time="0.000000" steps="16"/></proof>
27 <goal name="counting_sort'vc.2" expl="index in array bounds" proved="true">
28 <proof prover="1"><result status="valid" time="0.000000" steps="9"/></proof>
30 <goal name="counting_sort'vc.3" expl="index in array bounds" proved="true">
31 <proof prover="1"><result status="valid" time="0.000000" steps="12"/></proof>
33 <goal name="counting_sort'vc.4" expl="index in array bounds" proved="true">
34 <proof prover="1"><result status="valid" time="0.000000" steps="12"/></proof>
36 <goal name="counting_sort'vc.5" expl="loop invariant preservation" proved="true">
37 <proof prover="1"><result status="valid" time="0.060000" steps="88"/></proof>
39 <goal name="counting_sort'vc.6" expl="loop invariant init" proved="true">
40 <proof prover="1"><result status="valid" time="0.110000" steps="175"/></proof>
42 <goal name="counting_sort'vc.7" expl="loop invariant init" proved="true">
43 <proof prover="1"><result status="valid" time="0.000000" steps="11"/></proof>
45 <goal name="counting_sort'vc.8" expl="loop invariant init" proved="true">
46 <proof prover="1"><result status="valid" time="0.000000" steps="10"/></proof>
48 <goal name="counting_sort'vc.9" expl="loop invariant init" proved="true">
49 <proof prover="1"><result status="valid" time="0.000000" steps="10"/></proof>
51 <goal name="counting_sort'vc.10" expl="index in array bounds" proved="true">
52 <proof prover="1"><result status="valid" time="0.000000" steps="13"/></proof>
54 <goal name="counting_sort'vc.11" expl="loop invariant init" proved="true">
55 <proof prover="1"><result status="valid" time="0.000000" steps="14"/></proof>
57 <goal name="counting_sort'vc.12" expl="loop invariant init" proved="true">
58 <proof prover="1"><result status="valid" time="0.000000" steps="15"/></proof>
60 <goal name="counting_sort'vc.13" expl="loop invariant init" proved="true">
61 <proof prover="1"><result status="valid" time="0.000000" steps="22"/></proof>
63 <goal name="counting_sort'vc.14" expl="loop invariant init" proved="true">
64 <proof prover="1"><result status="valid" time="0.000000" steps="22"/></proof>
66 <goal name="counting_sort'vc.15" expl="loop invariant init" proved="true">
67 <proof prover="1"><result status="valid" time="0.060000" steps="154"/></proof>
69 <goal name="counting_sort'vc.16" expl="index in array bounds" proved="true">
70 <proof prover="1"><result status="valid" time="0.080000" steps="166"/></proof>
72 <goal name="counting_sort'vc.17" expl="loop invariant preservation" proved="true">
73 <proof prover="1"><result status="valid" time="0.010000" steps="24"/></proof>
75 <goal name="counting_sort'vc.18" expl="loop invariant preservation" proved="true">
76 <proof prover="1"><result status="valid" time="0.040000" steps="69"/></proof>
78 <goal name="counting_sort'vc.19" expl="loop invariant preservation" proved="true">
79 <proof prover="1"><result status="valid" time="0.040000" steps="79"/></proof>
81 <goal name="counting_sort'vc.20" expl="loop invariant preservation" proved="true">
82 <proof prover="0"><result status="valid" time="0.590000" steps="1313254"/></proof>
84 <goal name="counting_sort'vc.21" expl="loop invariant preservation" proved="true">
85 <proof prover="0" timelimit="10" memlimit="4000"><result status="valid" time="0.090000" steps="162109"/></proof>
87 <goal name="counting_sort'vc.22" expl="loop invariant preservation" proved="true">
88 <proof prover="1"><result status="valid" time="0.100000" steps="204"/></proof>
90 <goal name="counting_sort'vc.23" expl="loop invariant preservation" proved="true">
91 <proof prover="1"><result status="valid" time="0.000000" steps="19"/></proof>
93 <goal name="counting_sort'vc.24" expl="loop invariant preservation" proved="true">
94 <proof prover="1"><result status="valid" time="0.000000" steps="28"/></proof>
96 <goal name="counting_sort'vc.25" expl="loop invariant preservation" proved="true">
97 <proof prover="1"><result status="valid" time="0.010000" steps="29"/></proof>
99 <goal name="counting_sort'vc.26" expl="out of loop bounds" proved="true">
100 <proof prover="1"><result status="valid" time="0.160000" steps="337"/></proof>
102 <goal name="counting_sort'vc.27" expl="assertion" proved="true">
103 <proof prover="1"><result status="valid" time="0.170000" steps="221"/></proof>
105 <goal name="counting_sort'vc.28" expl="postcondition" proved="true">
106 <proof prover="1"><result status="valid" time="0.000000" steps="28"/></proof>
108 <goal name="counting_sort'vc.29" expl="out of loop bounds" proved="true">
109 <proof prover="1"><result status="valid" time="0.000000" steps="7"/></proof>
111 <goal name="counting_sort'vc.30" expl="out of loop bounds" proved="true">
112 <proof prover="1"><result status="valid" time="0.000000" steps="34"/></proof>
117 <theory name="InPlaceCountingSort" proved="true">
118 <goal name="in_place_counting_sort'vc" expl="VC for in_place_counting_sort" proved="true">
119 <transf name="split_goal_right" proved="true" >
120 <goal name="in_place_counting_sort'vc.0" expl="array creation size" proved="true">
121 <proof prover="1"><result status="valid" time="0.000000" steps="3"/></proof>
123 <goal name="in_place_counting_sort'vc.1" expl="loop invariant init" proved="true">
124 <proof prover="1"><result status="valid" time="0.000000" steps="14"/></proof>
126 <goal name="in_place_counting_sort'vc.2" expl="index in array bounds" proved="true">
127 <proof prover="1"><result status="valid" time="0.000000" steps="8"/></proof>
129 <goal name="in_place_counting_sort'vc.3" expl="index in array bounds" proved="true">
130 <proof prover="1"><result status="valid" time="0.000000" steps="11"/></proof>
132 <goal name="in_place_counting_sort'vc.4" expl="index in array bounds" proved="true">
133 <proof prover="1"><result status="valid" time="0.000000" steps="11"/></proof>
135 <goal name="in_place_counting_sort'vc.5" expl="loop invariant preservation" proved="true">
136 <proof prover="1"><result status="valid" time="0.060000" steps="86"/></proof>
138 <goal name="in_place_counting_sort'vc.6" expl="loop invariant init" proved="true">
139 <proof prover="1"><result status="valid" time="0.110000" steps="171"/></proof>
141 <goal name="in_place_counting_sort'vc.7" expl="loop invariant init" proved="true">
142 <proof prover="1"><result status="valid" time="0.000000" steps="10"/></proof>
144 <goal name="in_place_counting_sort'vc.8" expl="loop invariant init" proved="true">
145 <proof prover="1"><result status="valid" time="0.000000" steps="9"/></proof>
147 <goal name="in_place_counting_sort'vc.9" expl="loop invariant init" proved="true">
148 <proof prover="1"><result status="valid" time="0.010000" steps="9"/></proof>
150 <goal name="in_place_counting_sort'vc.10" expl="index in array bounds" proved="true">
151 <proof prover="1"><result status="valid" time="0.000000" steps="12"/></proof>
153 <goal name="in_place_counting_sort'vc.11" expl="loop invariant init" proved="true">
154 <proof prover="1"><result status="valid" time="0.000000" steps="13"/></proof>
156 <goal name="in_place_counting_sort'vc.12" expl="loop invariant init" proved="true">
157 <proof prover="1"><result status="valid" time="0.000000" steps="14"/></proof>
159 <goal name="in_place_counting_sort'vc.13" expl="loop invariant init" proved="true">
160 <proof prover="1"><result status="valid" time="0.000000" steps="21"/></proof>
162 <goal name="in_place_counting_sort'vc.14" expl="loop invariant init" proved="true">
163 <proof prover="1"><result status="valid" time="0.000000" steps="21"/></proof>
165 <goal name="in_place_counting_sort'vc.15" expl="loop invariant init" proved="true">
166 <proof prover="1"><result status="valid" time="0.060000" steps="152"/></proof>
168 <goal name="in_place_counting_sort'vc.16" expl="index in array bounds" proved="true">
169 <proof prover="1"><result status="valid" time="0.110000" steps="202"/></proof>
171 <goal name="in_place_counting_sort'vc.17" expl="assertion" proved="true">
172 <proof prover="1"><result status="valid" time="0.060000" steps="85"/></proof>
174 <goal name="in_place_counting_sort'vc.18" expl="loop invariant preservation" proved="true">
175 <proof prover="1"><result status="valid" time="0.000000" steps="23"/></proof>
177 <goal name="in_place_counting_sort'vc.19" expl="loop invariant preservation" proved="true">
178 <proof prover="1"><result status="valid" time="0.040000" steps="69"/></proof>
180 <goal name="in_place_counting_sort'vc.20" expl="loop invariant preservation" proved="true">
181 <proof prover="1"><result status="valid" time="0.050000" steps="84"/></proof>
183 <goal name="in_place_counting_sort'vc.21" expl="loop invariant preservation" proved="true">
184 <proof prover="0"><result status="valid" time="0.190000" steps="394484"/></proof>
186 <goal name="in_place_counting_sort'vc.22" expl="loop invariant preservation" proved="true">
187 <proof prover="0"><result status="valid" time="0.130000" steps="240008"/></proof>
189 <goal name="in_place_counting_sort'vc.23" expl="loop invariant preservation" proved="true">
190 <proof prover="1"><result status="valid" time="0.130000" steps="234"/></proof>
192 <goal name="in_place_counting_sort'vc.24" expl="loop invariant preservation" proved="true">
193 <proof prover="1"><result status="valid" time="0.000000" steps="18"/></proof>
195 <goal name="in_place_counting_sort'vc.25" expl="loop invariant preservation" proved="true">
196 <proof prover="1"><result status="valid" time="0.010000" steps="27"/></proof>
198 <goal name="in_place_counting_sort'vc.26" expl="loop invariant preservation" proved="true">
199 <proof prover="1"><result status="valid" time="0.010000" steps="28"/></proof>
201 <goal name="in_place_counting_sort'vc.27" expl="out of loop bounds" proved="true">
202 <proof prover="1"><result status="valid" time="0.150000" steps="331"/></proof>
204 <goal name="in_place_counting_sort'vc.28" expl="assertion" proved="true">
205 <proof prover="0"><result status="valid" time="0.020000" steps="34333"/></proof>
207 <goal name="in_place_counting_sort'vc.29" expl="postcondition" proved="true">
208 <proof prover="1"><result status="valid" time="0.000000" steps="27"/></proof>
210 <goal name="in_place_counting_sort'vc.30" expl="out of loop bounds" proved="true">
211 <proof prover="1"><result status="valid" time="0.000000" steps="6"/></proof>
213 <goal name="in_place_counting_sort'vc.31" expl="out of loop bounds" proved="true">
214 <proof prover="1"><result status="valid" time="0.000000" steps="25"/></proof>
219 <theory name="Harness" proved="true">
220 <goal name="harness'vc" expl="VC for harness" proved="true">
221 <transf name="split_goal_right" proved="true" >
222 <goal name="harness'vc.0" expl="array creation size" proved="true">
223 <proof prover="1"><result status="valid" time="0.000000" steps="3"/></proof>
225 <goal name="harness'vc.1" expl="index in array bounds" proved="true">
226 <proof prover="1"><result status="valid" time="0.000000" steps="4"/></proof>
228 <goal name="harness'vc.2" expl="precondition" proved="true">
229 <proof prover="1"><result status="valid" time="0.000000" steps="35"/></proof>
231 <goal name="harness'vc.3" expl="assertion" proved="true">
232 <proof prover="0"><result status="valid" time="0.020000" steps="51095"/></proof>
234 <goal name="harness'vc.4" expl="assertion" proved="true">
235 <proof prover="0"><result status="valid" time="0.030000" steps="122236"/></proof>
237 <goal name="harness'vc.5" expl="assertion" proved="true">
238 <proof prover="0"><result status="valid" time="0.040000" steps="177453"/></proof>
240 <goal name="harness'vc.6" expl="assertion" proved="true">
241 <proof prover="0"><result status="valid" time="0.040000" steps="198927"/></proof>
243 <goal name="harness'vc.7" expl="assertion" proved="true">
244 <proof prover="1"><result status="valid" time="0.140000" steps="254"/></proof>