Skip to content

GitLab

Commit 579f0073 authored by Mário Pereira's avatar Mário Pereira
Browse files
Options

updated proof sessions

parent 3766147e
Expand all Hide whitespace changes
Inline Side-by-side
Showing with 1717 additions and 2265 deletions
examples/TODO
View file @ 579f0073
add_list.mlw
arm.mlw
bag.mlw
bellman_ford.mlw
......@@ -16,12 +15,9 @@ division.mlw
dyck.mlw
edit_distance.mlw
esterel.mlw
euler001.mlw
euler002.mlw
ewd673.mlw
fibonacci.mlw
find.mlw
finger_trees.mlw
finite_tarski.mlw
flag2.mlw
foveoos11_challenge1.mlw
......@@ -39,7 +35,6 @@ lcp.mlw
linear_probing.mlw
linked_list_rev.mlw
maximum_subarray.mlw
mergesort_list.mlw
my_cosine.mlw
optimal_replay.mlw
patience.mlw
......@@ -55,7 +50,6 @@ schorr_waite_via_recursion.mlw
sieve.mlw
skew_heaps.mlw
snapshotable_trees.mlw
sorted_list.mlw
sudoku.mlw
sum_of_digits.mlw
there_and_back_again.mlw
......
examples/add_list/why3session.xml
View file @ 579f0073
......@@ -2,31 +2,25 @@
<!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
"http://why3.lri.fr/why3session.dtd">
<why3session shape_version="4">
<prover id="0" name="CVC3" version="2.4.1" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="2" name="Z3" version="3.2" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="3" name="Alt-Ergo" version="0.99.1" timelimit="5" steplimit="0" memlimit="1000"/>
<file name="../add_list.mlw" expanded="true">
<prover id="1" name="Alt-Ergo" version="1.30" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="4" name="Z3" version="4.4.1" timelimit="1" steplimit="0" memlimit="1000"/>
<file name="../add_list.mlw">
<theory name="SumList" sum="d41d8cd98f00b204e9800998ecf8427e">
</theory>
<theory name="AddListRec" sum="f062b1e05a91602624b37c4b34762555" expanded="true">
<goal name="WP_parameter sum" expl="VC for sum" expanded="true">
<proof prover="0"><result status="valid" time="0.01"/></proof>
<proof prover="2"><result status="valid" time="0.02"/></proof>
<proof prover="3"><result status="valid" time="0.02" steps="49"/></proof>
<theory name="AddListRec" sum="b22282c439ddd5fa9976e2048ec06a22">
<goal name="VC sum" expl="VC for sum">
<proof prover="1"><result status="valid" time="0.02" steps="200"/></proof>
</goal>
<goal name="WP_parameter main" expl="VC for main" expanded="true">
<proof prover="0"><result status="valid" time="0.02"/></proof>
<proof prover="2"><result status="valid" time="0.02"/></proof>
<goal name="VC main" expl="VC for main">
<proof prover="4"><result status="valid" time="0.02"/></proof>
</goal>
</theory>
<theory name="AddListImp" sum="7ac8c0163d88693d0911255c23bfb93d" expanded="true">
<goal name="WP_parameter sum" expl="VC for sum" expanded="true">
<proof prover="0"><result status="valid" time="0.02"/></proof>
<proof prover="2"><result status="valid" time="0.02"/></proof>
<theory name="AddListImp" sum="f7b23f93ac300ff2dca6f1bdf5f7fec6">
<goal name="VC sum" expl="VC for sum">
<proof prover="4"><result status="valid" time="0.02"/></proof>
</goal>
<goal name="WP_parameter main" expl="VC for main" expanded="true">
<proof prover="0"><result status="valid" time="0.02"/></proof>
<proof prover="2"><result status="valid" time="0.02"/></proof>
<goal name="VC main" expl="VC for main">
<proof prover="4"><result status="valid" time="0.01"/></proof>
</goal>
</theory>
</file>
......
examples/euler001/why3session.xml
View file @ 579f0073
......@@ -3,134 +3,126 @@
"http://why3.lri.fr/why3session.dtd">
<why3session shape_version="4">
<prover id="0" name="Coq" version="8.6" timelimit="5" steplimit="0" memlimit="0"/>
<prover id="1" name="CVC3" version="2.4.1" timelimit="30" steplimit="0" memlimit="1000"/>
<prover id="2" name="Z3" version="3.2" timelimit="30" steplimit="0" memlimit="1000"/>
<prover id="3" name="Alt-Ergo" version="0.95.2" timelimit="5" steplimit="0" memlimit="1000"/>
<file name="../euler001.mlw" expanded="true">
<theory name="DivModHints" sum="f7fdece9a19249c4382a43566f166530">
<prover id="1" name="CVC3" version="2.4.1" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="4" name="Alt-Ergo" version="1.30" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="5" name="Z3" version="4.4.1" timelimit="30" steplimit="0" memlimit="1000"/>
<file name="../euler001.mlw">
<theory name="DivModHints" sum="effbd5be7df862660bf36edc101d991b">
<goal name="mod_div_unique">
<proof prover="0" edited="euler001_DivModHints_mod_div_unique_1.v"><result status="valid" time="0.34"/></proof>
</goal>
<goal name="mod_succ_1">
<proof prover="0" edited="euler001_DivModHints_mod_succ_1_1.v"><result status="valid" time="0.40"/></proof>
<proof prover="0" edited="euler001_DivModHints_mod_succ_1_1.v"><result status="valid" time="0.62"/></proof>
</goal>
<goal name="mod_succ_2">
<proof prover="0" edited="euler001_DivModHints_mod_succ_2_1.v"><result status="valid" time="0.37"/></proof>
<proof prover="0" edited="euler001_DivModHints_mod_succ_2_1.v"><result status="valid" time="0.61"/></proof>
</goal>
<goal name="div_succ_1">
<proof prover="1"><result status="valid" time="0.04"/></proof>
<proof prover="1" timelimit="30"><result status="valid" time="0.04"/></proof>
</goal>
<goal name="div_succ_2">
<proof prover="1"><result status="valid" time="0.10"/></proof>
<proof prover="2"><result status="valid" time="0.76"/></proof>
<proof prover="3" timelimit="30"><result status="valid" time="1.96" steps="76"/></proof>
<proof prover="1" timelimit="30"><result status="valid" time="0.10"/></proof>
<proof prover="4" timelimit="30"><result status="valid" time="0.17" steps="52"/></proof>
</goal>
<goal name="mod2_mul2">
<proof prover="1" timelimit="5"><result status="valid" time="0.01"/></proof>
<proof prover="2" timelimit="5"><result status="valid" time="0.01"/></proof>
<proof prover="3"><result status="valid" time="0.05" steps="10"/></proof>
<proof prover="1"><result status="valid" time="0.01"/></proof>
<proof prover="4"><result status="valid" time="0.05" steps="10"/></proof>
<proof prover="5" timelimit="5"><result status="valid" time="0.01"/></proof>
</goal>
<goal name="mod2_mul2_aux">
<proof prover="1"><result status="valid" time="0.02"/></proof>
<proof prover="2"><result status="valid" time="0.02"/></proof>
<proof prover="3"><result status="valid" time="0.02" steps="13"/></proof>
<proof prover="1" timelimit="30"><result status="valid" time="0.02"/></proof>
<proof prover="4"><result status="valid" time="0.02" steps="12"/></proof>
<proof prover="5"><result status="valid" time="0.02"/></proof>
</goal>
<goal name="mod2_mul2_aux2">
<proof prover="1" timelimit="35"><result status="valid" time="0.02"/></proof>
<proof prover="2"><result status="valid" time="0.07"/></proof>
<proof prover="3"><result status="valid" time="0.03" steps="19"/></proof>
<proof prover="4"><result status="valid" time="0.03" steps="15"/></proof>
<proof prover="5"><result status="valid" time="0.36"/></proof>
</goal>
<goal name="div2_mul2">
<proof prover="1" timelimit="5"><result status="valid" time="0.06"/></proof>
<proof prover="2" timelimit="5"><result status="valid" time="0.02"/></proof>
<proof prover="3"><result status="valid" time="0.01" steps="3"/></proof>
<proof prover="1"><result status="valid" time="0.06"/></proof>
<proof prover="4"><result status="valid" time="0.01" steps="3"/></proof>
<proof prover="5" timelimit="5"><result status="valid" time="0.02"/></proof>
</goal>
<goal name="div2_mul2_aux">
<proof prover="1" timelimit="5"><result status="valid" time="0.08"/></proof>
<proof prover="2" timelimit="5"><result status="valid" time="0.01"/></proof>
<proof prover="3"><result status="valid" time="0.01" steps="5"/></proof>
<proof prover="1"><result status="valid" time="0.08"/></proof>
<proof prover="4"><result status="valid" time="0.01" steps="5"/></proof>
<proof prover="5" timelimit="5"><result status="valid" time="0.01"/></proof>
</goal>
<goal name="div2_add">
<proof prover="1" timelimit="5"><result status="valid" time="0.04"/></proof>
<proof prover="2" timelimit="5"><result status="valid" time="0.02"/></proof>
<proof prover="1"><result status="valid" time="0.04"/></proof>
<proof prover="5" timelimit="5"><result status="valid" time="0.02"/></proof>
</goal>
<goal name="div2_sub">
<proof prover="1" timelimit="5"><result status="valid" time="0.04"/></proof>
<proof prover="2" timelimit="5"><result status="valid" time="0.02"/></proof>
<proof prover="1"><result status="valid" time="0.04"/></proof>
<proof prover="5" timelimit="5"><result status="valid" time="0.02"/></proof>
</goal>
</theory>
<theory name="TriangularNumbers" sum="91847fa59365859f1ae00cac3b34c298">
<theory name="TriangularNumbers" sum="ae4c454fb76f596feaa408865bbd5f44">
<goal name="tr_mod_2">
<proof prover="0" memlimit="1000" edited="euler001_TriangularNumbers_tr_mod_2_1.v"><result status="valid" time="0.31"/></proof>
</goal>
<goal name="tr_repr">
<proof prover="2" timelimit="5"><result status="valid" time="0.02"/></proof>
<proof prover="3"><result status="valid" time="0.01" steps="8"/></proof>
<proof prover="4"><result status="valid" time="0.01" steps="7"/></proof>
</goal>
<goal name="tr_succ">
<proof prover="1" timelimit="5"><result status="valid" time="0.02"/></proof>
<proof prover="2" timelimit="5"><result status="valid" time="0.02"/></proof>
<proof prover="3"><result status="valid" time="0.01" steps="5"/></proof>
<proof prover="1"><result status="valid" time="0.02"/></proof>
<proof prover="4"><result status="valid" time="0.01" steps="5"/></proof>
</goal>
</theory>
<theory name="SumMultiple" sum="90bf0acc57cc35c41e0a28734c52e85d">
<theory name="SumMultiple" sum="a61c93a0c45ac61e4e322d6e2ac4865f">
<goal name="mod_15">
<proof prover="1"><result status="valid" time="0.13"/></proof>
<proof prover="3"><result status="valid" time="0.71" steps="86"/></proof>
<proof prover="1" timelimit="30"><result status="valid" time="0.13"/></proof>
<proof prover="4"><result status="valid" time="0.17" steps="76"/></proof>
</goal>
<goal name="Closed_formula_0">
<proof prover="1"><result status="valid" time="0.02"/></proof>
<proof prover="2"><result status="valid" time="0.14"/></proof>
<proof prover="3"><result status="valid" time="0.31" steps="62"/></proof>
<proof prover="1" timelimit="30"><result status="valid" time="0.02"/></proof>
<proof prover="4"><result status="valid" time="0.06" steps="85"/></proof>
</goal>
<goal name="Closed_formula_n">
<proof prover="1" timelimit="10"><result status="valid" time="1.43"/></proof>
<proof prover="3" timelimit="10"><result status="valid" time="4.53" steps="44"/></proof>
<proof prover="1" timelimit="10"><result status="valid" time="2.25"/></proof>
<proof prover="4" timelimit="10"><result status="valid" time="0.35" steps="55"/></proof>
</goal>
<goal name="Closed_formula_n_3">
<proof prover="1" timelimit="10"><result status="valid" time="2.40"/></proof>
<proof prover="1" timelimit="10"><result status="valid" time="4.29"/></proof>
</goal>
<goal name="Closed_formula_n_5">
<proof prover="1" timelimit="5"><result status="valid" time="0.31"/></proof>
<proof prover="1"><result status="valid" time="0.58"/></proof>
</goal>
<goal name="Closed_formula_n_15">
<proof prover="1" timelimit="5"><result status="valid" time="0.30"/></proof>
<proof prover="1"><result status="valid" time="0.47"/></proof>
</goal>
<goal name="Closed_formula_ind">
<proof prover="1" timelimit="5"><result status="valid" time="0.02"/></proof>
<proof prover="1"><result status="valid" time="0.02"/></proof>
</goal>
<goal name="div_15">
<proof prover="1"><result status="valid" time="0.01"/></proof>
<proof prover="2"><result status="valid" time="0.02"/></proof>
<proof prover="3"><result status="valid" time="0.01" steps="7"/></proof>
<proof prover="1" timelimit="30"><result status="valid" time="0.01"/></proof>
<proof prover="4"><result status="valid" time="0.01" steps="8"/></proof>
<proof prover="5"><result status="valid" time="0.02"/></proof>
</goal>
<goal name="div_5">
<proof prover="1"><result status="valid" time="0.01"/></proof>
<proof prover="2"><result status="valid" time="0.02"/></proof>
<proof prover="3"><result status="valid" time="0.01" steps="7"/></proof>
<proof prover="1" timelimit="30"><result status="valid" time="0.01"/></proof>
<proof prover="4"><result status="valid" time="0.01" steps="8"/></proof>
<proof prover="5"><result status="valid" time="0.02"/></proof>
</goal>
<goal name="div_3">
<proof prover="1"><result status="valid" time="0.02"/></proof>
<proof prover="2"><result status="valid" time="0.02"/></proof>
<proof prover="3"><result status="valid" time="0.01" steps="7"/></proof>
<proof prover="1" timelimit="30"><result status="valid" time="0.02"/></proof>
<proof prover="4"><result status="valid" time="0.01" steps="8"/></proof>
<proof prover="5"><result status="valid" time="0.02"/></proof>
</goal>
<goal name="Closed_Formula">
<proof prover="0" timelimit="30" memlimit="1000" edited="euler001_SumMultiple_Closed_Formula_1.v"><result status="valid" time="0.36"/></proof>
<proof prover="0" timelimit="30" memlimit="1000" edited="euler001_SumMultiple_Closed_Formula_1.v"><result status="valid" time="0.50"/></proof>
</goal>
</theory>
<theory name="Euler001" sum="dc11d718c4df40f5ebdac9af279bd48f">
<goal name="WP_parameter solve" expl="VC for solve">
<proof prover="1"><result status="valid" time="0.06"/></proof>
<proof prover="2"><result status="valid" time="0.02"/></proof>
</goal>
<goal name="WP_parameter run" expl="VC for run">
<proof prover="3"><result status="valid" time="0.01" steps="2"/></proof>
<theory name="Euler001" sum="28e99cd463469a236e425682a3ae5f63">
<goal name="VC solve" expl="VC for solve">
<proof prover="4"><result status="valid" time="2.18" steps="522"/></proof>
</goal>
<goal name="WP_parameter bench" expl="VC for bench">
<proof prover="3" memlimit="4000"><result status="valid" time="0.01" steps="2"/></proof>
<goal name="VC run" expl="VC for run">
<proof prover="4"><result status="valid" time="0.00" steps="3"/></proof>
</goal>
<goal name="WP_parameter go" expl="VC for go">
<proof prover="3"><result status="valid" time="0.02" steps="52"/></proof>
<goal name="VC bench" expl="VC for bench">
<proof prover="4"><result status="valid" time="0.00" steps="3"/></proof>
</goal>
</theory>
</file>
......
examples/euler002/why3session.xml
View file @ 579f0073
This diff is collapsed.
examples/fibonacci/why3session.xml
View file @ 579f0073
This diff is collapsed.
examples/finger_trees/why3session.xml
View file @ 579f0073
......@@ -2,420 +2,17 @@
<!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
"http://why3.lri.fr/why3session.dtd">
<why3session shape_version="4">
<prover id="0" name="Alt-Ergo" version="0.99.1" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="1" name="CVC3" version="2.4.1" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="2" name="CVC4" version="1.4" timelimit="5" steplimit="0" memlimit="1000"/>
<file name="../finger_trees.mlw" expanded="true">
<theory name="FingerTrees" sum="ba184d414509c625df9333762a1df473" expanded="true">
<goal name="WP_parameter node_cons_app" expl="VC for node_cons_app">
<transf name="split_goal_wp">
<goal name="WP_parameter node_cons_app.1" expl="1. postcondition">
<proof prover="0"><result status="valid" time="0.04" steps="74"/></proof>
</goal>
<goal name="WP_parameter node_cons_app.2" expl="2. postcondition">
<proof prover="0"><result status="valid" time="0.04" steps="80"/></proof>
</goal>
</transf>
<prover id="3" name="Alt-Ergo" version="1.30" timelimit="5" steplimit="0" memlimit="1000"/>
<file name="../finger_trees.mlw">
<theory name="FingerTrees" sum="bc4cfeb4a57bb9b172602a713c4bf5ce">
<goal name="VC node_cons_app" expl="VC for node_cons_app">
<proof prover="3"><result status="valid" time="0.05" steps="300"/></proof>
</goal>
<goal name="WP_parameter d_cons" expl="VC for d_cons">
<transf name="split_goal_wp">
<goal name="WP_parameter d_cons.1" expl="1. postcondition">
<proof prover="0"><result status="valid" time="0.03" steps="70"/></proof>
</goal>
<goal name="WP_parameter d_cons.2" expl="2. postcondition">
<proof prover="0"><result status="valid" time="0.04" steps="75"/></proof>
</goal>
<goal name="WP_parameter d_cons.3" expl="3. postcondition">
<proof prover="0"><result status="valid" time="0.03" steps="80"/></proof>
</goal>
<goal name="WP_parameter d_cons.4" expl="4. postcondition">
<proof prover="1"><result status="valid" time="0.03"/></proof>
<proof prover="2"><result status="valid" time="0.31"/></proof>
</goal>
</transf>
<goal name="VC d_cons" expl="VC for d_cons">
<proof prover="3"><result status="valid" time="0.32" steps="2032"/></proof>
</goal>
<goal name="WP_parameter cons" expl="VC for cons" expanded="true">
<transf name="split_goal_wp" expanded="true">
<goal name="WP_parameter cons.1" expl="1. postcondition">
<proof prover="0"><result status="valid" time="0.02" steps="29"/></proof>
</goal>
<goal name="WP_parameter cons.2" expl="2. postcondition">
<proof prover="0"><result status="valid" time="0.07" steps="151"/></proof>
</goal>
<goal name="WP_parameter cons.3" expl="3. postcondition">
<proof prover="0"><result status="valid" time="0.18" steps="184"/></proof>
</goal>
<goal name="WP_parameter cons.4" expl="4. assertion">
<proof prover="0"><result status="valid" time="0.11" steps="140"/></proof>
</goal>
<goal name="WP_parameter cons.5" expl="5. variant decrease">
<proof prover="0"><result status="valid" time="0.02" steps="28"/></proof>
</goal>
<goal name="WP_parameter cons.6" expl="6. postcondition" expanded="true">
<metas
expanded="true">
<ts_pos name="real" arity="0" id="2"
ip_theory="BuiltIn">
<ip_library name="why3"/>
<ip_library name="BuiltIn"/>
<ip_qualid name="real"/>
</ts_pos>
<ts_pos name="bool" arity="0" id="3"
ip_theory="Bool">
<ip_library name="why3"/>
<ip_library name="Bool"/>
<ip_qualid name="bool"/>
</ts_pos>
<ts_pos name="tuple0" arity="0" id="20"
ip_theory="Tuple0">
<ip_library name="why3"/>
<ip_library name="Tuple0"/>
<ip_qualid name="tuple0"/>
</ts_pos>
<ts_pos name="unit" arity="0" id="21"
ip_theory="Unit">
<ip_library name="why3"/>
<ip_library name="Unit"/>
<ip_qualid name="unit"/>
</ts_pos>
<ts_pos name="&apos;mark" arity="0" id="68"
ip_theory="Mark">
<ip_library name="why3"/>
<ip_library name="Mark"/>
<ip_qualid name="&apos;mark"/>
</ts_pos>
<ts_pos name="tuple2" arity="2" id="871"
ip_theory="Tuple2">
<ip_library name="why3"/>
<ip_library name="Tuple2"/>
<ip_qualid name="tuple2"/>
</ts_pos>
<ls_pos name="infix =" id="10"
ip_theory="BuiltIn">
<ip_library name="why3"/>
<ip_library name="BuiltIn"/>
<ip_qualid name="infix ="/>
</ls_pos>
<ls_pos name="zero" id="155"
ip_theory="Int">
<ip_library name="int"/>
<ip_qualid name="zero"/>
</ls_pos>
<ls_pos name="one" id="156"
ip_theory="Int">
<ip_library name="int"/>
<ip_qualid name="one"/>
</ls_pos>
<ls_pos name="infix &lt;" id="157"
ip_theory="Int">
<ip_library name="int"/>
<ip_qualid name="infix &lt;"/>
</ls_pos>
<ls_pos name="infix &gt;" id="160"
ip_theory="Int">
<ip_library name="int"/>
<ip_qualid name="infix &gt;"/>
</ls_pos>
<ls_pos name="infix +" id="1326"
ip_theory="Int">
<ip_library name="int"/>
<ip_qualid name="infix +"/>
</ls_pos>
<ls_pos name="prefix -" id="1327"
ip_theory="Int">
<ip_library name="int"/>
<ip_qualid name="prefix -"/>
</ls_pos>
<ls_pos name="infix *" id="1328"
ip_theory="Int">
<ip_library name="int"/>
<ip_qualid name="infix *"/>
</ls_pos>
<ls_pos name="infix -" id="1376"
ip_theory="Int">
<ip_library name="int"/>
<ip_qualid name="infix -"/>
</ls_pos>
<ls_pos name="infix &gt;=" id="1396"
ip_theory="Int">
<ip_library name="int"/>
<ip_qualid name="infix &gt;="/>
</ls_pos>
<ls_pos name="mem" id="2214"
ip_theory="Mem">
<ip_library name="list"/>
<ip_qualid name="mem"/>
</ls_pos>
<pr_pos name="Assoc" id="1329"
ip_theory="Int">
<ip_library name="int"/>
<ip_qualid name="CommutativeGroup"/>
<ip_qualid name="Assoc"/>
</pr_pos>
<pr_pos name="Unit_def_l" id="1336"
ip_theory="Int">
<ip_library name="int"/>
<ip_qualid name="CommutativeGroup"/>
<ip_qualid name="Unit_def_l"/>
</pr_pos>
<pr_pos name="Unit_def_r" id="1339"
ip_theory="Int">
<ip_library name="int"/>
<ip_qualid name="CommutativeGroup"/>
<ip_qualid name="Unit_def_r"/>
</pr_pos>
<pr_pos name="Inv_def_l" id="1342"
ip_theory="Int">
<ip_library name="int"/>
<ip_qualid name="CommutativeGroup"/>
<ip_qualid name="Inv_def_l"/>
</pr_pos>
<pr_pos name="Inv_def_r" id="1345"
ip_theory="Int">
<ip_library name="int"/>
<ip_qualid name="CommutativeGroup"/>
<ip_qualid name="Inv_def_r"/>
</pr_pos>
<pr_pos name="Comm" id="1348"
ip_theory="Int">
<ip_library name="int"/>
<ip_qualid name="CommutativeGroup"/>
<ip_qualid name="Comm"/>
<ip_qualid name="Comm"/>
</pr_pos>
<pr_pos name="Assoc" id="1353"
ip_theory="Int">
<ip_library name="int"/>
<ip_qualid name="Assoc"/>
<ip_qualid name="Assoc"/>
</pr_pos>
<pr_pos name="Mul_distr_l" id="1360"
ip_theory="Int">
<ip_library name="int"/>
<ip_qualid name="Mul_distr_l"/>
</pr_pos>
<pr_pos name="Mul_distr_r" id="1367"
ip_theory="Int">
<ip_library name="int"/>
<ip_qualid name="Mul_distr_r"/>
</pr_pos>
<pr_pos name="Comm" id="1385"
ip_theory="Int">
<ip_library name="int"/>
<ip_qualid name="Comm"/>
<ip_qualid name="Comm"/>
</pr_pos>
<pr_pos name="Unitary" id="1390"
ip_theory="Int">
<ip_library name="int"/>
<ip_qualid name="Unitary"/>
</pr_pos>
<pr_pos name="NonTrivialRing" id="1393"
ip_theory="Int">
<ip_library name="int"/>
<ip_qualid name="NonTrivialRing"/>
</pr_pos>
<pr_pos name="Refl" id="1405"
ip_theory="Int">
<ip_library name="int"/>
<ip_qualid name="Refl"/>
</pr_pos>
<pr_pos name="Trans" id="1408"
ip_theory="Int">
<ip_library name="int"/>
<ip_qualid name="Trans"/>
</pr_pos>
<pr_pos name="Antisymm" id="1415"
ip_theory="Int">
<ip_library name="int"/>
<ip_qualid name="Antisymm"/>
</pr_pos>
<pr_pos name="Total" id="1420"
ip_theory="Int">
<ip_library name="int"/>
<ip_qualid name="Total"/>
</pr_pos>
<pr_pos name="ZeroLessOne" id="1425"
ip_theory="Int">
<ip_library name="int"/>
<ip_qualid name="ZeroLessOne"/>
</pr_pos>
<pr_pos name="CompatOrderAdd" id="1426"
ip_theory="Int">
<ip_library name="int"/>
<ip_qualid name="CompatOrderAdd"/>
</pr_pos>
<pr_pos name="CompatOrderMult" id="1433"
ip_theory="Int">
<ip_library name="int"/>
<ip_qualid name="CompatOrderMult"/>
</pr_pos>
<pr_pos name="Length_nonnegative" id="2207"
ip_theory="Length">
<ip_library name="list"/>
<ip_qualid name="Length_nonnegative"/>
</pr_pos>
<pr_pos name="Length_nil" id="2210"
ip_theory="Length">
<ip_library name="list"/>
<ip_qualid name="Length_nil"/>
</pr_pos>
<pr_pos name="Append_l_nil" id="3612"
ip_theory="Append">
<ip_library name="list"/>
<ip_qualid name="Append_l_nil"/>
</pr_pos>
<pr_pos name="Append_length" id="3615"
ip_theory="Append">
<ip_library name="list"/>
<ip_qualid name="Append_length"/>
</pr_pos>
<pr_pos name="mem_append" id="3620"
ip_theory="Append">
<ip_library name="list"/>
<ip_qualid name="mem_append"/>
</pr_pos>
<pr_pos name="mem_decomp" id="3627"
ip_theory="Append">
<ip_library name="list"/>
<ip_qualid name="mem_decomp"/>
</pr_pos>
<meta name="remove_logic">
<meta_arg_ls id="10"/>
</meta>
<meta name="remove_logic">
<meta_arg_ls id="155"/>
</meta>
<meta name="remove_logic">
<meta_arg_ls id="156"/>
</meta>
<meta name="remove_logic">
<meta_arg_ls id="157"/>
</meta>
<meta name="remove_logic">
<meta_arg_ls id="160"/>
</meta>