1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
|
<?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="1.0.5" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="1" name="Z3" version="4.12.2" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="2" name="CVC4" version="1.7" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="3" name="Alt-Ergo" version="2.3.0" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="4" name="Alt-Ergo" version="2.4.1" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="5" name="Alt-Ergo" version="2.1.0" timelimit="10" steplimit="0" memlimit="1000"/>
<prover id="7" name="Alt-Ergo" version="2.4.2" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="9" name="Z3" version="4.8.10" timelimit="1" steplimit="0" memlimit="1000"/>
<file format="whyml" proved="true">
<path name=".."/><path name="binary_search.mlw"/>
<theory name="BinarySearch" proved="true">
<goal name="binary_search'vc" expl="VC for binary_search" proved="true">
<proof prover="5"><result status="valid" time="0.050000" steps="319"/></proof>
</goal>
</theory>
<theory name="BinarySearchAnyMidPoint" proved="true">
<goal name="binary_search'vc" expl="VC for binary_search" proved="true">
<proof prover="5"><result status="valid" time="0.010000" steps="66"/></proof>
</goal>
</theory>
<theory name="BinarySearchBranchless" proved="true">
<goal name="binary_search'vc" expl="VC for binary_search" proved="true">
<proof prover="5" timelimit="5"><result status="valid" time="0.310000" steps="629"/></proof>
</goal>
</theory>
<theory name="BinarySearchInt32" proved="true">
<goal name="binary_search'vc" expl="VC for binary_search" proved="true">
<transf name="split_vc" proved="true" >
<goal name="binary_search'vc.0" expl="integer overflow" proved="true">
<proof prover="0"><result status="valid" time="0.030000" steps="1068"/></proof>
</goal>
<goal name="binary_search'vc.1" expl="loop invariant init" proved="true">
<proof prover="0"><result status="valid" time="0.020000" steps="989"/></proof>
</goal>
<goal name="binary_search'vc.2" expl="loop invariant init" proved="true">
<proof prover="0"><result status="valid" time="0.020000" steps="1099"/></proof>
</goal>
<goal name="binary_search'vc.3" expl="integer overflow" proved="true">
<proof prover="0"><result status="valid" time="0.030000" steps="1462"/></proof>
</goal>
<goal name="binary_search'vc.4" expl="division by zero" proved="true">
<proof prover="0"><result status="valid" time="0.030000" steps="1115"/></proof>
</goal>
<goal name="binary_search'vc.5" expl="integer overflow" proved="true">
<proof prover="0"><result status="valid" time="0.040000" steps="3364"/></proof>
</goal>
<goal name="binary_search'vc.6" expl="integer overflow" proved="true">
<proof prover="0"><result status="valid" time="0.030000" steps="3571"/></proof>
</goal>
<goal name="binary_search'vc.7" expl="assertion" proved="true">
<proof prover="0"><result status="valid" time="0.040000" steps="3558"/></proof>
</goal>
<goal name="binary_search'vc.8" expl="index in array bounds" proved="true">
<proof prover="0"><result status="valid" time="0.030000" steps="2629"/></proof>
</goal>
<goal name="binary_search'vc.9" expl="integer overflow" proved="true">
<proof prover="0"><result status="valid" time="0.040000" steps="3967"/></proof>
</goal>
<goal name="binary_search'vc.10" expl="loop variant decrease" proved="true">
<proof prover="0"><result status="valid" time="0.030000" steps="2691"/></proof>
</goal>
<goal name="binary_search'vc.11" expl="loop invariant preservation" proved="true">
<proof prover="0"><result status="valid" time="0.030000" steps="2678"/></proof>
</goal>
<goal name="binary_search'vc.12" expl="loop invariant preservation" proved="true">
<proof prover="0"><result status="valid" time="0.030000" steps="4607"/></proof>
</goal>
<goal name="binary_search'vc.13" expl="index in array bounds" proved="true">
<proof prover="0"><result status="valid" time="0.040000" steps="2661"/></proof>
</goal>
<goal name="binary_search'vc.14" expl="integer overflow" proved="true">
<proof prover="0"><result status="valid" time="0.030000" steps="3969"/></proof>
</goal>
<goal name="binary_search'vc.15" expl="loop variant decrease" proved="true">
<proof prover="0"><result status="valid" time="0.030000" steps="2715"/></proof>
</goal>
<goal name="binary_search'vc.16" expl="loop invariant preservation" proved="true">
<proof prover="0"><result status="valid" time="0.030000" steps="2709"/></proof>
</goal>
<goal name="binary_search'vc.17" expl="loop invariant preservation" proved="true">
<proof prover="0"><result status="valid" time="0.040000" steps="4703"/></proof>
</goal>
<goal name="binary_search'vc.18" expl="postcondition" proved="true">
<proof prover="0"><result status="valid" time="0.040000" steps="2818"/></proof>
</goal>
<goal name="binary_search'vc.19" expl="exceptional postcondition" proved="true">
<proof prover="7"><result status="valid" time="0.010000" steps="22"/></proof>
</goal>
</transf>
</goal>
</theory>
<theory name="BinarySearchBoolean" proved="true">
<goal name="binary_search'vc" expl="VC for binary_search" proved="true">
<proof prover="5"><result status="valid" time="0.080000" steps="349"/></proof>
</goal>
</theory>
<theory name="Complexity" proved="true">
<goal name="log2'vc" expl="VC for log2" proved="true">
<proof prover="3"><result status="valid" time="0.020000" steps="4"/></proof>
</goal>
<goal name="log2_monotone'vc" expl="VC for log2_monotone" proved="true">
<proof prover="3"><result status="valid" time="0.060000" steps="104"/></proof>
</goal>
<goal name="upper_bound" proved="true">
<proof prover="1"><result status="valid" time="0.148291" steps="101230"/></proof>
</goal>
<goal name="binary_search'vc" expl="VC for binary_search" proved="true">
<transf name="split_vc" proved="true" >
<goal name="binary_search'vc.0" expl="loop invariant init" proved="true">
<proof prover="3"><result status="valid" time="0.000000" steps="4"/></proof>
</goal>
<goal name="binary_search'vc.1" expl="loop invariant init" proved="true">
<proof prover="3"><result status="valid" time="0.000000" steps="8"/></proof>
</goal>
<goal name="binary_search'vc.2" expl="loop invariant init" proved="true">
<transf name="compute_in_goal" proved="true" >
<goal name="binary_search'vc.2.0" expl="loop invariant init" proved="true">
<proof prover="3"><result status="valid" time="0.000000" steps="10"/></proof>
</goal>
</transf>
</goal>
<goal name="binary_search'vc.3" expl="precondition" proved="true">
<proof prover="3"><result status="valid" time="0.000000" steps="12"/></proof>
</goal>
<goal name="binary_search'vc.4" expl="index in array bounds" proved="true">
<proof prover="3"><result status="valid" time="0.010000" steps="23"/></proof>
</goal>
<goal name="binary_search'vc.5" expl="loop variant decrease" proved="true">
<proof prover="3"><result status="valid" time="0.010000" steps="20"/></proof>
</goal>
<goal name="binary_search'vc.6" expl="loop invariant preservation" proved="true">
<proof prover="3"><result status="valid" time="0.010000" steps="31"/></proof>
</goal>
<goal name="binary_search'vc.7" expl="loop invariant preservation" proved="true">
<proof prover="3"><result status="valid" time="0.010000" steps="64"/></proof>
</goal>
<goal name="binary_search'vc.8" expl="loop invariant preservation" proved="true">
<proof prover="4"><result status="valid" time="0.050000" steps="480"/></proof>
</goal>
<goal name="binary_search'vc.9" expl="index in array bounds" proved="true">
<proof prover="3"><result status="valid" time="0.010000" steps="26"/></proof>
</goal>
<goal name="binary_search'vc.10" expl="loop variant decrease" proved="true">
<proof prover="3"><result status="valid" time="0.010000" steps="22"/></proof>
</goal>
<goal name="binary_search'vc.11" expl="loop invariant preservation" proved="true">
<proof prover="3"><result status="valid" time="0.010000" steps="33"/></proof>
</goal>
<goal name="binary_search'vc.12" expl="loop invariant preservation" proved="true">
<proof prover="2"><result status="valid" time="0.100000" steps="5568"/></proof>
</goal>
<goal name="binary_search'vc.13" expl="loop invariant preservation" proved="true">
<proof prover="3"><result status="valid" time="0.050000" steps="99"/></proof>
</goal>
<goal name="binary_search'vc.14" expl="postcondition" proved="true">
<proof prover="3"><result status="valid" time="0.010000" steps="42"/></proof>
</goal>
<goal name="binary_search'vc.15" expl="postcondition" proved="true">
<proof prover="3"><result status="valid" time="0.010000" steps="59"/></proof>
</goal>
<goal name="binary_search'vc.16" expl="postcondition" proved="true">
<proof prover="3"><result status="valid" time="0.000000" steps="19"/></proof>
</goal>
<goal name="binary_search'vc.17" expl="postcondition" proved="true">
<proof prover="3"><result status="valid" time="0.020000" steps="16"/></proof>
</goal>
</transf>
</goal>
</theory>
<theory name="TwoDimensional" proved="true">
<goal name="search'vc" expl="VC for search" proved="true">
<proof prover="9"><result status="valid" time="0.037675" steps="31396"/></proof>
</goal>
</theory>
</file>
</why3session>
|
