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="CVC4" version="1.8" timelimit="5" steplimit="0" memlimit="1000"/>
6 <prover id="1" name="Alt-Ergo" version="2.4.2" timelimit="5" steplimit="0" memlimit="1000"/>
7 <prover id="2" name="Z3" version="4.12.2" timelimit="5" steplimit="0" memlimit="1000"/>
8 <prover id="3" name="CVC4" version="1.5" timelimit="5" steplimit="0" memlimit="1000"/>
9 <prover id="4" name="CVC4" version="1.7" timelimit="1" steplimit="0" memlimit="1000"/>
10 <prover id="5" name="Alt-Ergo" version="2.3.0" timelimit="1" steplimit="0" memlimit="1000"/>
11 <prover id="6" name="CVC5" version="1.0.5" timelimit="1" steplimit="0" memlimit="1000"/>
12 <prover id="7" name="Alt-Ergo" version="2.3.3" timelimit="5" steplimit="0" memlimit="1000"/>
13 <file format="whyml" proved="true">
14 <path name=".."/><path name="skew_heaps.mlw"/>
15 <theory name="Heap" proved="true">
16 <goal name="empty'vc" expl="VC for empty" proved="true">
17 <proof prover="5"><result status="valid" time="0.000000" steps="0"/></proof>
20 <theory name="SkewHeaps" proved="true">
21 <goal name="root_is_min'vc" expl="VC for root_is_min" proved="true">
22 <proof prover="1"><result status="valid" time="8.661145" steps="52934"/></proof>
24 <goal name="empty'vc" expl="VC for empty" proved="true">
25 <proof prover="1"><result status="valid" time="0.000000" steps="21"/></proof>
27 <goal name="get_min'vc" expl="VC for get_min" proved="true">
28 <proof prover="7"><result status="valid" time="0.000000" steps="35"/></proof>
30 <goal name="merge'vc" expl="VC for merge" proved="true">
31 <transf name="split_vc" proved="true" >
32 <goal name="merge'vc.0" expl="variant decrease" proved="true">
33 <proof prover="4"><result status="valid" time="0.060000" steps="5121"/></proof>
35 <goal name="merge'vc.1" expl="precondition" proved="true">
36 <proof prover="4"><result status="valid" time="0.040000" steps="3516"/></proof>
38 <goal name="merge'vc.2" expl="variant decrease" proved="true">
39 <proof prover="4"><result status="valid" time="0.070000" steps="5176"/></proof>
41 <goal name="merge'vc.3" expl="precondition" proved="true">
42 <proof prover="4"><result status="valid" time="0.040000" steps="3520"/></proof>
44 <goal name="merge'vc.4" expl="postcondition" proved="true">
45 <transf name="split_vc" proved="true" >
46 <goal name="merge'vc.4.0" expl="postcondition" proved="true">
47 <proof prover="4"><result status="valid" time="0.030000" steps="3401"/></proof>
49 <goal name="merge'vc.4.1" expl="postcondition" proved="true">
50 <proof prover="4"><result status="valid" time="0.040000" steps="3713"/></proof>
52 <goal name="merge'vc.4.2" expl="postcondition" proved="true">
53 <proof prover="4"><result status="valid" time="0.040000" steps="3713"/></proof>
55 <goal name="merge'vc.4.3" expl="postcondition" proved="true">
56 <proof prover="6"><result status="valid" time="1.010611" steps="86343"/></proof>
60 <goal name="merge'vc.5" expl="postcondition" proved="true">
61 <transf name="split_vc" proved="true" >
62 <goal name="merge'vc.5.0" expl="postcondition" proved="true">
63 <proof prover="4"><result status="valid" time="0.050000" steps="3626"/></proof>
65 <goal name="merge'vc.5.1" expl="postcondition" proved="true">
66 <proof prover="4"><result status="valid" time="0.030000" steps="3924"/></proof>
68 <goal name="merge'vc.5.2" expl="postcondition" proved="true">
69 <proof prover="4"><result status="valid" time="0.040000" steps="3924"/></proof>
71 <goal name="merge'vc.5.3" expl="postcondition" proved="true">
72 <proof prover="6"><result status="valid" time="0.040000" steps="9774"/></proof>
76 <goal name="merge'vc.6" expl="postcondition" proved="true">
77 <transf name="split_vc" proved="true" >
78 <goal name="merge'vc.6.0" expl="postcondition" proved="true">
79 <proof prover="4"><result status="valid" time="0.040000" steps="3637"/></proof>
81 <goal name="merge'vc.6.1" expl="postcondition" proved="true">
82 <proof prover="4"><result status="valid" time="0.030000" steps="3921"/></proof>
84 <goal name="merge'vc.6.2" expl="postcondition" proved="true">
85 <proof prover="4"><result status="valid" time="0.040000" steps="3921"/></proof>
87 <goal name="merge'vc.6.3" expl="postcondition" proved="true">
88 <proof prover="6"><result status="valid" time="0.050000" steps="4974"/></proof>
94 <goal name="add'vc" expl="VC for add" proved="true">
95 <proof prover="7"><result status="valid" time="0.020000" steps="158"/></proof>
97 <goal name="remove_min'vc" expl="VC for remove_min" proved="true">
98 <proof prover="7"><result status="valid" time="0.020000" steps="260"/></proof>
101 <theory name="HeapSort" proved="true">
102 <goal name="heapsort'vc" expl="VC for heapsort" proved="true">
103 <transf name="split_goal_right" proved="true" >
104 <goal name="heapsort'vc.0" expl="loop invariant init" proved="true">
105 <proof prover="7"><result status="valid" time="0.010000" steps="8"/></proof>
107 <goal name="heapsort'vc.1" expl="loop invariant init" proved="true">
108 <proof prover="7"><result status="valid" time="0.020000" steps="34"/></proof>
110 <goal name="heapsort'vc.2" expl="index in array bounds" proved="true">
111 <proof prover="7"><result status="valid" time="0.010000" steps="14"/></proof>
113 <goal name="heapsort'vc.3" expl="precondition" proved="true">
114 <proof prover="7"><result status="valid" time="0.010000" steps="14"/></proof>
116 <goal name="heapsort'vc.4" expl="assertion" proved="true">
117 <proof prover="7"><result status="valid" time="0.020000" steps="36"/></proof>
119 <goal name="heapsort'vc.5" expl="loop invariant preservation" proved="true">
120 <proof prover="7"><result status="valid" time="0.010000" steps="26"/></proof>
122 <goal name="heapsort'vc.6" expl="loop invariant preservation" proved="true">
123 <proof prover="7"><result status="valid" time="0.190000" steps="318"/></proof>
125 <goal name="heapsort'vc.7" expl="loop invariant init" proved="true">
126 <proof prover="7"><result status="valid" time="0.010000" steps="34"/></proof>
128 <goal name="heapsort'vc.8" expl="loop invariant init" proved="true">
129 <proof prover="2"><result status="valid" time="0.020000" steps="58741"/></proof>
130 <proof prover="4"><result status="valid" time="0.070000" steps="15458"/></proof>
131 <proof prover="7"><result status="valid" time="0.010000" steps="14"/></proof>
133 <goal name="heapsort'vc.9" expl="loop invariant init" proved="true">
134 <proof prover="7"><result status="valid" time="0.010000" steps="27"/></proof>
136 <goal name="heapsort'vc.10" expl="loop invariant init" proved="true">
137 <proof prover="7"><result status="valid" time="0.080000" steps="70"/></proof>
139 <goal name="heapsort'vc.11" expl="precondition" proved="true">
140 <proof prover="7"><result status="valid" time="0.010000" steps="30"/></proof>
142 <goal name="heapsort'vc.12" expl="index in array bounds" proved="true">
143 <proof prover="7"><result status="valid" time="0.020000" steps="30"/></proof>
145 <goal name="heapsort'vc.13" expl="precondition" proved="true">
146 <proof prover="7"><result status="valid" time="0.010000" steps="30"/></proof>
148 <goal name="heapsort'vc.14" expl="loop invariant preservation" proved="true">
149 <proof prover="2" timelimit="1"><result status="valid" time="1.242218" steps="1647088"/></proof>
151 <goal name="heapsort'vc.15" expl="loop invariant preservation" proved="true">
152 <proof prover="7"><result status="valid" time="0.020000" steps="50"/></proof>
154 <goal name="heapsort'vc.16" expl="loop invariant preservation" proved="true">
155 <proof prover="3"><result status="valid" time="0.100000" steps="29125"/></proof>
157 <goal name="heapsort'vc.17" expl="loop invariant preservation" proved="true">
158 <proof prover="0"><result status="valid" time="1.257167" steps="134040"/></proof>
160 <goal name="heapsort'vc.18" expl="postcondition" proved="true">
161 <proof prover="7"><result status="valid" time="0.010000" steps="68"/></proof>
163 <goal name="heapsort'vc.19" expl="postcondition" proved="true">
164 <proof prover="7"><result status="valid" time="0.030000" steps="116"/></proof>
166 <goal name="heapsort'vc.20" expl="out of loop bounds" proved="true">
167 <proof prover="7"><result status="valid" time="0.010000" steps="14"/></proof>
169 <goal name="heapsort'vc.21" expl="out of loop bounds" proved="true">
170 <proof prover="7"><result status="valid" time="0.010000" steps="14"/></proof>