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="Alt-Ergo" version="2.6.0" timelimit="5" steplimit="0" memlimit="1000"/>
6 <prover id="1" name="Z3" version="4.11.2" timelimit="5" steplimit="0" memlimit="1000"/>
7 <prover id="3" name="CVC5" version="1.0.5" timelimit="1" steplimit="0" memlimit="1000"/>
8 <prover id="4" name="CVC4" version="1.6" timelimit="5" steplimit="0" memlimit="1000"/>
9 <file format="whyml" proved="true">
10 <path name=".."/><path name="three_idem_ring.mlw"/>
11 <theory name="Top" proved="true">
12 <goal name="mul'vc" expl="VC for mul" proved="true">
13 <proof prover="4"><result status="valid" time="0.010000" steps="698"/></proof>
15 <goal name="Exponentiation.Assoc" proved="true">
16 <proof prover="4"><result status="valid" time="0.010000" steps="531"/></proof>
18 <goal name="Exponentiation.Unit_def_l" proved="true">
19 <proof prover="4"><result status="valid" time="0.000000" steps="578"/></proof>
21 <goal name="Exponentiation.Unit_def_r" proved="true">
22 <proof prover="4"><result status="valid" time="0.010000" steps="622"/></proof>
24 <goal name="Exponentiation.Power_0" proved="true">
25 <proof prover="4"><result status="valid" time="0.010000" steps="872"/></proof>
27 <goal name="Exponentiation.Power_s" proved="true">
28 <proof prover="4"><result status="valid" time="0.010000" steps="1176"/></proof>
30 <goal name="simpl_left" proved="true">
31 <proof prover="0"><result status="valid" time="0.080000" steps="1420"/></proof>
33 <goal name="simpl_right" proved="true">
34 <proof prover="4"><result status="valid" time="0.010000" steps="1899"/></proof>
36 <goal name="zero_star_l" proved="true">
37 <proof prover="0"><result status="valid" time="0.030000" steps="230"/></proof>
39 <goal name="zero_star_r" proved="true">
40 <proof prover="0"><result status="valid" time="0.050000" steps="342"/></proof>
42 <goal name="neg_star_r" proved="true">
43 <proof prover="0"><result status="valid" time="0.477868" steps="5140"/></proof>
45 <goal name="neg_star_l" proved="true">
46 <transf name="split_vc" proved="true" >
47 <goal name="neg_star_l.0" proved="true">
48 <proof prover="4"><result status="valid" time="0.010000" steps="2211"/></proof>
50 <goal name="neg_star_l.1" proved="true">
51 <proof prover="4"><result status="valid" time="0.010000" steps="1981"/></proof>
55 <goal name="neg_neg" proved="true">
56 <proof prover="4"><result status="valid" time="0.010000" steps="2116"/></proof>
58 <goal name="null_add" proved="true">
59 <proof prover="4"><result status="valid" time="0.010000" steps="2508"/></proof>
61 <goal name="mul_star_l'vc" expl="VC for mul_star_l" proved="true">
62 <proof prover="4"><result status="valid" time="0.010000" steps="3023"/></proof>
64 <goal name="mul_star_r'vc" expl="VC for mul_star_r" proved="true">
65 <proof prover="4"><result status="valid" time="0.020000" steps="3153"/></proof>
67 <goal name="null_star_l" proved="true">
68 <proof prover="4"><result status="valid" time="0.010000" steps="2702"/></proof>
70 <goal name="null_star_r" proved="true">
71 <proof prover="4"><result status="valid" time="0.010000" steps="2828"/></proof>
73 <goal name="null_mul_congr" proved="true">
74 <proof prover="0"><result status="valid" time="0.030000" steps="48"/></proof>
76 <goal name="all_null6" proved="true">
77 <transf name="split_vc" proved="true" >
78 <goal name="all_null6.0" proved="true">
79 <proof prover="1"><result status="valid" time="0.060000" steps="145099"/></proof>
81 <goal name="all_null6.1" proved="true">
82 <proof prover="4"><result status="valid" time="0.030000" steps="2962"/></proof>
84 <goal name="all_null6.2" proved="true">
85 <proof prover="4"><result status="valid" time="0.010000" steps="4070"/></proof>
87 <goal name="all_null6.3" proved="true">
88 <proof prover="4"><result status="valid" time="0.010000" steps="3043"/></proof>
92 <goal name="all_split" proved="true">
93 <transf name="split_vc" proved="true" >
94 <goal name="all_split.0" proved="true">
95 <proof prover="4"><result status="valid" time="0.020000" steps="5918"/></proof>
97 <goal name="all_split.1" proved="true">
98 <proof prover="4"><result status="valid" time="0.010000" steps="3183"/></proof>
100 <goal name="all_split.2" proved="true">
101 <proof prover="4"><result status="valid" time="0.010000" steps="3225"/></proof>
103 <goal name="all_split.3" proved="true">
104 <proof prover="4"><result status="valid" time="0.020000" steps="3380"/></proof>
108 <goal name="free_split" proved="true">
109 <proof prover="4"><result status="valid" time="0.010000" steps="3366"/></proof>
111 <goal name="null_2_idem" proved="true">
112 <proof prover="3"><result status="valid" time="0.309560" steps="58886"/></proof>
114 <goal name="null2_comm" proved="true">
115 <proof prover="4"><result status="valid" time="0.250000" steps="63003"/></proof>
117 <goal name="swap_equality" proved="true">
118 <transf name="split_vc" proved="true" >
119 <goal name="swap_equality.0" proved="true">
120 <proof prover="1"><result status="valid" time="3.660000" steps="1622691"/></proof>
122 <goal name="swap_equality.1" proved="true">
123 <proof prover="4"><result status="valid" time="0.100000" steps="30866"/></proof>
125 <goal name="swap_equality.2" proved="true">
126 <proof prover="4"><result status="valid" time="0.010000" steps="3970"/></proof>
128 <goal name="swap_equality.3" proved="true">
129 <proof prover="4"><result status="valid" time="0.020000" steps="3977"/></proof>
131 <goal name="swap_equality.4" proved="true">
132 <proof prover="4"><result status="valid" time="0.010000" steps="4101"/></proof>
134 <goal name="swap_equality.5" proved="true">
135 <proof prover="4"><result status="valid" time="3.590000" steps="85959"/></proof>
137 <goal name="swap_equality.6" proved="true">
138 <proof prover="1"><result status="valid" time="1.140000" steps="378990"/></proof>
140 <goal name="swap_equality.7" proved="true">
141 <proof prover="4"><result status="valid" time="0.090000" steps="30149"/></proof>
143 <goal name="swap_equality.8" proved="true">
144 <proof prover="4"><result status="valid" time="0.150000" steps="10164"/></proof>
148 <goal name="null3_comm" proved="true">
149 <transf name="split_vc" proved="true" >
150 <goal name="null3_comm.0" proved="true">
151 <proof prover="4"><result status="valid" time="0.040000" steps="11878"/></proof>
153 <goal name="null3_comm.1" proved="true">
154 <proof prover="4"><result status="valid" time="0.020000" steps="4241"/></proof>
158 <goal name="commutative" proved="true">
159 <transf name="split_vc" proved="true" >
160 <goal name="commutative.0" proved="true">
161 <proof prover="0"><result status="valid" time="0.024062" steps="482"/></proof>
163 <goal name="commutative.1" proved="true">
164 <proof prover="4"><result status="valid" time="0.090000" steps="30018"/></proof>
166 <goal name="commutative.2" proved="true">
167 <proof prover="4"><result status="valid" time="0.090000" steps="30008"/></proof>
169 <goal name="commutative.3" proved="true">
170 <proof prover="4"><result status="valid" time="0.080000" steps="30187"/></proof>
172 <goal name="commutative.4" proved="true">
173 <proof prover="4"><result status="valid" time="0.090000" steps="30174"/></proof>
175 <goal name="commutative.5" proved="true">
176 <proof prover="4"><result status="valid" time="0.060000" steps="19077"/></proof>