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Commit dcb6c555 authored by Andrei Paskevich's avatar Andrei Paskevich
Browse files

update prover identifiers in Coq proofs

parent 0cb3c6a5
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Showing with 94 additions and 94 deletions
examples/check-builtin/real/why3session.xml
View file @ dcb6c555
<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE why3session SYSTEM "/home/marche/why3/share/why3session.dtd">
<!DOCTYPE why3session SYSTEM "/home/andrei/prj/why-git/share/why3session.dtd">
<why3session
name="check-builtin/real/why3session.xml" shape_version="2">
name="examples/check-builtin/real/why3session.xml" shape_version="2">
<prover
id="0"
name="Alt-Ergo"
......@@ -40,13 +40,13 @@
expanded="true">
<theory
name="Test"
locfile="check-builtin/real/../real.why"
locfile="examples/check-builtin/real/../real.why"
loclnum="1" loccnumb="7" loccnume="11"
verified="true"
expanded="false">
<goal
name="G1"
locfile="check-builtin/real/../real.why"
locfile="examples/check-builtin/real/../real.why"
loclnum="3" loccnumb="7" loccnume="9"
sum="9d01d2b58c8039b40fe8082e9bb9cedc"
proved="true"
......@@ -111,7 +111,7 @@
</goal>
<goal
name="G2"
locfile="check-builtin/real/../real.why"
locfile="examples/check-builtin/real/../real.why"
loclnum="4" loccnumb="7" loccnume="9"
sum="e9f427dfcc75690a3a5f9b4d2b7d3327"
proved="true"
......@@ -168,7 +168,7 @@
</goal>
<goal
name="G3"
locfile="check-builtin/real/../real.why"
locfile="examples/check-builtin/real/../real.why"
loclnum="5" loccnumb="7" loccnume="9"
sum="fb068fd1bb87e531b24e317c5436367f"
proved="true"
......@@ -218,13 +218,13 @@
</theory>
<theory
name="TestInfix"
locfile="check-builtin/real/../real.why"
locfile="examples/check-builtin/real/../real.why"
loclnum="8" loccnumb="7" loccnume="16"
verified="true"
expanded="false">
<goal
name="Add"
locfile="check-builtin/real/../real.why"
locfile="examples/check-builtin/real/../real.why"
loclnum="10" loccnumb="7" loccnume="10"
sum="f0a10a146dafb71211cd816e932b7e5b"
proved="true"
......@@ -281,7 +281,7 @@
</goal>
<goal
name="Sub"
locfile="check-builtin/real/../real.why"
locfile="examples/check-builtin/real/../real.why"
loclnum="11" loccnumb="7" loccnume="10"
sum="5ae49ab292dd37e18dde314db68ac554"
proved="true"
......@@ -338,7 +338,7 @@
</goal>
<goal
name="Neg"
locfile="check-builtin/real/../real.why"
locfile="examples/check-builtin/real/../real.why"
loclnum="12" loccnumb="7" loccnume="10"
sum="5f2b467053fb1d185282edf5e642bf79"
proved="true"
......@@ -395,7 +395,7 @@
</goal>
<goal
name="Mul"
locfile="check-builtin/real/../real.why"
locfile="examples/check-builtin/real/../real.why"
loclnum="13" loccnumb="7" loccnume="10"
sum="f1b9dbdabb722a965ee8acf67e6b37ab"
proved="true"
......@@ -452,7 +452,7 @@
</goal>
<goal
name="Div"
locfile="check-builtin/real/../real.why"
locfile="examples/check-builtin/real/../real.why"
loclnum="14" loccnumb="7" loccnume="10"
sum="fc6768829934bc33395105daf89e64b9"
proved="true"
......@@ -509,7 +509,7 @@
</goal>
<goal
name="Inv"
locfile="check-builtin/real/../real.why"
locfile="examples/check-builtin/real/../real.why"
loclnum="15" loccnumb="7" loccnume="10"
sum="0e7c6d415b84eecf6be7dc96c2d3e515"
proved="true"
......@@ -559,13 +559,13 @@
</theory>
<theory
name="SquareTest"
locfile="check-builtin/real/../real.why"
locfile="examples/check-builtin/real/../real.why"
loclnum="19" loccnumb="7" loccnume="17"
verified="true"
expanded="false">
<goal
name="Sqrt_zero"
locfile="check-builtin/real/../real.why"
locfile="examples/check-builtin/real/../real.why"
loclnum="23" loccnumb="8" loccnume="17"
sum="e1c84be18617065e9d67bb385ddb5f0d"
proved="true"
......@@ -593,7 +593,7 @@
memlimit="0"
obsolete="false"
archived="false">
<result status="valid" time="0.00"/>
<result status="valid" time="0.01"/>
</proof>
<proof
prover="3"
......@@ -617,12 +617,12 @@
memlimit="1000"
obsolete="false"
archived="false">
<result status="valid" time="0.01"/>
<result status="valid" time="0.00"/>
</proof>
</goal>
<goal
name="Sqrt_one"
locfile="check-builtin/real/../real.why"
locfile="examples/check-builtin/real/../real.why"
loclnum="24" loccnumb="8" loccnume="16"
sum="ae5db834377202e2f151940dea8fa810"
proved="true"
......@@ -679,7 +679,7 @@
</goal>
<goal
name="Sqrt_four"
locfile="check-builtin/real/../real.why"
locfile="examples/check-builtin/real/../real.why"
loclnum="25" loccnumb="8" loccnume="17"
sum="41341456f742115dd3f31bf49ff6baad"
proved="true"
......@@ -707,7 +707,7 @@
memlimit="0"
obsolete="false"
archived="false">
<result status="valid" time="0.01"/>
<result status="valid" time="0.00"/>
</proof>
<proof
prover="3"
......@@ -727,23 +727,23 @@
</proof>
<proof
prover="7"
timelimit="65"
timelimit="66"
memlimit="1000"
obsolete="false"
archived="false">
<result status="valid" time="32.58"/>
<result status="valid" time="31.97"/>
</proof>
</goal>
</theory>
<theory
name="ExpLogTest"
locfile="check-builtin/real/../real.why"
locfile="examples/check-builtin/real/../real.why"
loclnum="29" loccnumb="7" loccnume="17"
verified="true"
expanded="false">
<goal
name="Log_e"
locfile="check-builtin/real/../real.why"
locfile="examples/check-builtin/real/../real.why"
loclnum="33" loccnumb="8" loccnume="13"
sum="5d7bdf9229e2fa6545f73bc566dcb09f"
proved="true"
......@@ -755,7 +755,7 @@
memlimit="0"
obsolete="false"
archived="false">
<result status="valid" time="0.01"/>
<result status="valid" time="0.00"/>
</proof>
<proof
prover="2"
......@@ -787,21 +787,21 @@
memlimit="0"
obsolete="false"
archived="false">
<result status="valid" time="0.00"/>
<result status="valid" time="0.01"/>
</proof>
</goal>
</theory>
<theory
name="PowerIntTest"
locfile="check-builtin/real/../real.why"
locfile="examples/check-builtin/real/../real.why"
loclnum="38" loccnumb="7" loccnume="19"
verified="true"
expanded="false">
<goal
name="Pow_2_2"
locfile="check-builtin/real/../real.why"
locfile="examples/check-builtin/real/../real.why"
loclnum="42" loccnumb="8" loccnume="15"
sum="d575c5b256b2d19fc86571c331949c48"
sum="1a1b47860515881ea1a7a3b1cd792a71"
proved="true"
expanded="false"
shape="ainfix =apowerc2.0c2c4.0">
......@@ -835,7 +835,7 @@
memlimit="0"
obsolete="false"
archived="false">
<result status="unknown" time="0.16"/>
<result status="unknown" time="0.15"/>
</proof>
<proof
prover="4"
......@@ -851,7 +851,7 @@
memlimit="0"
obsolete="false"
archived="false">
<result status="timeout" time="3.11"/>
<result status="timeout" time="3.01"/>
</proof>
<proof
prover="1"
......@@ -859,19 +859,19 @@
memlimit="1000"
obsolete="false"
archived="false">
<result status="valid" time="0.01"/>
<result status="valid" time="0.02"/>
</proof>
</goal>
</theory>
<theory
name="PowerRealTest"
locfile="check-builtin/real/../real.why"
locfile="examples/check-builtin/real/../real.why"
loclnum="47" loccnumb="7" loccnume="20"
verified="true"
expanded="false">
<goal
name="Pow_2_2"
locfile="check-builtin/real/../real.why"
locfile="examples/check-builtin/real/../real.why"
loclnum="51" loccnumb="8" loccnume="15"
sum="ed5264b6afcf21937a5f7b8ee11aa039"
proved="true"
......@@ -891,7 +891,7 @@
memlimit="0"
obsolete="false"
archived="false">
<result status="valid" time="0.00"/>
<result status="valid" time="0.01"/>
</proof>
<proof
prover="7"
......@@ -899,19 +899,19 @@
memlimit="0"
obsolete="false"
archived="false">
<result status="valid" time="0.01"/>
<result status="valid" time="0.00"/>
</proof>
</goal>
</theory>
<theory
name="TrigonometryTest"
locfile="check-builtin/real/../real.why"
locfile="examples/check-builtin/real/../real.why"
loclnum="56" loccnumb="7" loccnume="23"
verified="false"
expanded="true">
<goal
name="Cos_2_pi"
locfile="check-builtin/real/../real.why"
locfile="examples/check-builtin/real/../real.why"
loclnum="62" loccnumb="8" loccnume="16"
sum="b763bfc07b1a5c4fb7524e2b1eb5da99"
proved="true"
......@@ -931,7 +931,7 @@
memlimit="0"
obsolete="false"
archived="false">
<result status="valid" time="0.25"/>
<result status="valid" time="0.24"/>
</proof>
<proof
prover="2"
......@@ -960,7 +960,7 @@
</goal>
<goal
name="Sin_2_pi"
locfile="check-builtin/real/../real.why"
locfile="examples/check-builtin/real/../real.why"
loclnum="63" loccnumb="8" loccnume="16"
sum="72f36a6805c161c41252365985a579a6"
proved="true"
......@@ -972,7 +972,7 @@
memlimit="0"
obsolete="false"
archived="false">
<result status="valid" time="0.15"/>
<result status="valid" time="0.14"/>
</proof>
<proof
prover="0"
......@@ -980,7 +980,7 @@
memlimit="1000"
obsolete="false"
archived="false">
<result status="valid" time="3.93"/>
<result status="valid" time="3.76"/>
</proof>
<proof
prover="2"
......@@ -1004,7 +1004,7 @@
memlimit="0"
obsolete="false"
archived="false">
<result status="valid" time="0.11"/>
<result status="valid" time="0.10"/>
</proof>
<proof
prover="1"
......@@ -1012,12 +1012,12 @@
memlimit="1000"
obsolete="false"
archived="false">
<result status="valid" time="3.32"/>
<result status="valid" time="3.15"/>
</proof>
</goal>
<goal
name="Tan_pi_3"
locfile="check-builtin/real/../real.why"
locfile="examples/check-builtin/real/../real.why"
loclnum="64" loccnumb="8" loccnume="16"
sum="e71f334bf99fde98a5a4921ac5ba65ed"
proved="false"
......@@ -1058,7 +1058,7 @@
</goal>
<goal
name="Atan_1"
locfile="check-builtin/real/../real.why"
locfile="examples/check-builtin/real/../real.why"
loclnum="65" loccnumb="8" loccnume="14"
sum="6e382bffd885c7410f18b54a86f3fe4a"
proved="false"
......
examples/hoare_logic/blocking_semantics/blocking_semantics_WP_wp_conj_1.v
View file @ dcb6c555
......@@ -480,7 +480,7 @@ Unset Implicit Arguments.
Require Why3.
Ltac ae := why3 "alt-ergo" timelimit 2.
Ltac ae10 := why3 "alt-ergo" timelimit 10.
Ltac cvc10 := why3 "cvc3-2.4" timelimit 10.
Ltac cvc10 := why3 "cvc3" timelimit 10.
(* Why3 goal *)
Theorem wp_conj : forall (sigma:(map Z value)) (pi:(list (Z* value)%type))
......
examples/hoare_logic/blocking_semantics/blocking_semantics_WP_wp_reduction_1.v
View file @ dcb6c555
......@@ -561,7 +561,7 @@ Axiom wp_conj : forall (sigma:(map ident value)) (pi:(list (ident*
Require Why3.
Ltac ae := why3 "alt-ergo" timelimit 2.
Ltac ae10 := why3 "alt-ergo" timelimit 10.
Ltac cvc10 := why3 "cvc3-2.4" timelimit 10.
Ltac cvc10 := why3 "cvc3" timelimit 10.
(* Why3 goal *)
Theorem wp_reduction : forall (sigma:(map ident value)) (sigma':(map ident
......
examples/programs/bellman_ford/bellman_ford_Graph_long_path_decomposition_pigeon1_1.v
View file @ dcb6c555
......@@ -256,7 +256,7 @@ Theorem long_path_decomposition_pigeon1 : forall (l:(list vertex))
Require Why3.
Ltac ae := why3 "alt-ergo".
Ltac cvc := why3 "cvc3-2.4".
Ltac cvc := why3 "cvc3".
intros l v H0.
induction H0.
......
examples/programs/bellman_ford/bellman_ford_Graph_long_path_decomposition_pigeon3_1.v
View file @ dcb6c555
......@@ -271,7 +271,7 @@ Theorem long_path_decomposition_pigeon3 : forall (l:(list vertex))
Require Why3.
Ltac ae := why3 "alt-ergo".
Ltac cvc := why3 "cvc3-2.4".
Ltac cvc := why3 "cvc3".
intros l v H1.
destruct H1 as (e & l1 & l2 & l3 & H1).
......
examples/programs/bellman_ford/bf_WP_BellmanFord_WP_parameter_bellman_ford_15.v
View file @ dcb6c555
......@@ -417,7 +417,7 @@ intros (h4, h5).
destruct (get m u) as [] _eqn. 2: intuition.
destruct (get m v) as [] _eqn.
intros hlt. apply key_lemma_1 with v z0.
why3 "z3-3".
why3 "z3".
assert (hu: exists lu: list vertex, path s lu u /\ path_weight lu u = z) by ae.
destruct hu as (lu, (hu1, hu2)).
exists (infix_plpl lu (Cons u Nil)); ae.
......
examples/programs/bellman_ford/bf_WP_BellmanFord_WP_parameter_bellman_ford_17.v
View file @ dcb6c555
......@@ -438,7 +438,7 @@ Axiom key_lemma_2 : forall (m:(map vertex t)), (inv1 m (cardinal vertices)
forall (v:vertex), ~ (negative_cycle v)).
Require Import Why3.
Ltac Z3 := why3 "z3-3".
Ltac Z3 := why3 "z3".
Ltac ae := why3 "alt-ergo".
(* Why3 goal *)
......@@ -498,7 +498,7 @@ destruct (get m1 v) as [] _eqn; auto.
intros l hpath hlength.
destruct (path_right_inversion s v l hpath) as [(h1,h2) | (y, (l', (h1, (h2, h3))))].
(* Nil *)
subst. simpl. why3 "cvc3-2.4".
subst. simpl. why3 "cvc3".
(* Cons *)
rewrite h3; rewrite path_weight_right_extension.
generalize (H6 v H7); clear H6.
......
examples/programs/bellman_ford/bf_WP_BellmanFord_key_lemma_2_1.v
View file @ dcb6c555
......@@ -435,7 +435,7 @@ Definition inv2(m:(map vertex t)) (via:(set1 (vertex* vertex)%type)): Prop :=
Require Import Why3.
Ltac ae := why3 "alt-ergo" timelimit 30.
Ltac Z3 := why3 "z3-3" timelimit 10.
Ltac Z3 := why3 "z3" timelimit 10.
Lemma length_nonneg: forall a, forall l: list a, (length l >= 0)%Z.
induction l; ae.
......
examples/programs/distance/distance_Distance_WP_parameter_distance_1.v
View file @ dcb6c555
......@@ -134,12 +134,12 @@ generalize (h10 k h). intros h10k.
assert (case: (j < get g1 k \/ j = get g1 k \/ j > get g1 k)%Z) by omega.
destruct case.
(* j < g[k] *)
why3 "z3-3" timelimit 5.
why3 "z3" timelimit 5.
destruct H5.
(* j = g[k] *)
ae.
(* j > g[k] *)
why3 "z3-3" timelimit 3.
why3 "z3" timelimit 3.
(* k = 0 *)
ae.
Qed.
......
examples/programs/fibonacci/why3session.xml
View file @ dcb6c555
<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE why3session SYSTEM "/home/andrei/prj/why-git/share/why3session.dtd">
<why3session
name="examples/programs/fibonacci/why3session.xml" shape_version="2">
name="programs/fibonacci/why3session.xml" shape_version="2">
<prover
id="0"
name="Alt-Ergo"
......@@ -36,7 +36,7 @@
expanded="true">
<theory
name="Fibonacci"
locfile="examples/programs/fibonacci/../fibonacci.mlw"
locfile="programs/fibonacci/../fibonacci.mlw"
loclnum="2" loccnumb="7" loccnume="16"
verified="true"
expanded="true">
......@@ -45,13 +45,13 @@
</theory>
<theory
name="FibonacciTest"
locfile="examples/programs/fibonacci/../fibonacci.mlw"
locfile="programs/fibonacci/../fibonacci.mlw"
loclnum="14" loccnumb="7" loccnume="20"
verified="true"
expanded="false">
<goal
name="isfib_2_1"
locfile="examples/programs/fibonacci/../fibonacci.mlw"
locfile="programs/fibonacci/../fibonacci.mlw"
loclnum="18" loccnumb="8" loccnume="17"
sum="53cb43c962b6ac473353e3b02dc4b67b"
proved="true"
......@@ -68,7 +68,7 @@
</goal>
<goal
name="isfib_6_8"
locfile="examples/programs/fibonacci/../fibonacci.mlw"
locfile="programs/fibonacci/../fibonacci.mlw"
loclnum="19" loccnumb="8" loccnume="17"
sum="23ec2eb87c0bebe1406c9b91f62e2d92"
proved="true"
......@@ -85,7 +85,7 @@
</goal>
<goal
name="not_isfib_2_2"
locfile="examples/programs/fibonacci/../fibonacci.mlw"
locfile="programs/fibonacci/../fibonacci.mlw"
loclnum="21" loccnumb="8" loccnume="21"
sum="f3cd71efc59ece547b8cfe0932c063ca"
proved="true"
......@@ -135,13 +135,13 @@
</theory>
<theory
name="FibonacciLinear"
locfile="examples/programs/fibonacci/../fibonacci.mlw"
locfile="programs/fibonacci/../fibonacci.mlw"
loclnum="25" loccnumb="7" loccnume="22"
verified="true"
expanded="false">
<goal
name="WP_parameter fib"
locfile="examples/programs/fibonacci/../fibonacci.mlw"
locfile="programs/fibonacci/../fibonacci.mlw"
loclnum="31" loccnumb="6" loccnume="9"
expl="parameter fib"
sum="0524e9e40b90c0c213c0df1110b389f1"
......@@ -162,7 +162,7 @@
</theory>
<theory
name="Mat22"
locfile="examples/programs/fibonacci/../fibonacci.mlw"
locfile="programs/fibonacci/../fibonacci.mlw"
loclnum="46" loccnumb="7" loccnume="12"
verified="true"
expanded="true">
......@@ -171,16 +171,16 @@
</theory>
<theory
name="FibonacciLogarithmic"
locfile="examples/programs/fibonacci/../fibonacci.mlw"
locfile="programs/fibonacci/../fibonacci.mlw"
loclnum="68" loccnumb="7" loccnume="27"
verified="true"
expanded="true">
<goal
name="WP_parameter logfib"
locfile="examples/programs/fibonacci/../fibonacci.mlw"
locfile="programs/fibonacci/../fibonacci.mlw"
loclnum="82" loccnumb="10" loccnume="16"
expl="parameter logfib"
sum="3966dacbc1855018004e996b874f27fa"
sum="49924bf2200f24435af2c0570880fc85"
proved="true"
expanded="true"
shape="iainfix =V0c0ainfix =apoweramk tc1c1c1c0V0amk tainfix +c1c0c0c0c1iainfix =amodV0c2c0ainfix =apoweramk tc1c1c1c0V0amk tainfix +V3V4V4V4V3Lainfix *V2ainfix +V1ainfix +V1V2Lainfix +ainfix *V1V1ainfix *V2V2ainfix =apoweramk tc1c1c1c0V0amk tainfix +V5V6V6V6V5Lainfix +ainfix *ainfix +V1V2ainfix +V1V2ainfix *V2V2Lainfix *V2ainfix +V1ainfix +V1V2Iainfix =apoweramk tc1c1c1c0adivV0c2amk tainfix +V1V2V2V2V1FAainfix &gt;=adivV0c2c0Aainfix &lt;adivV0c2V0Aainfix &lt;=c0V0Iainfix &gt;=V0c0F">
......@@ -192,10 +192,10 @@
expanded="true">
<goal
name="WP_parameter logfib.1"
locfile="examples/programs/fibonacci/../fibonacci.mlw"
locfile="programs/fibonacci/../fibonacci.mlw"
loclnum="82" loccnumb="10" loccnume="16"
expl="normal postcondition"
sum="adf3fda094b1f16d576b23cf13147c8d"
sum="00aa5f8fcdddef70d5665548b1986d96"
proved="true"
expanded="true"
shape="ainfix =apoweramk tc1c1c1c0V0amk tainfix +c1c0c0c0c1Iainfix =V0c0Iainfix &gt;=V0c0F">
......@@ -236,10 +236,10 @@
</goal>
<goal
name="WP_parameter logfib.2"
locfile="examples/programs/fibonacci/../fibonacci.mlw"
locfile="programs/fibonacci/../fibonacci.mlw"
loclnum="82" loccnumb="10" loccnume="16"
expl="variant decreases"
sum="4464035e38e634573f8cf479606f0013"
sum="01a989f467c67e8551c8707a051cf515"
proved="true"
expanded="true"
shape="ainfix &lt;adivV0c2V0Aainfix &lt;=c0V0Iainfix =V0c0NIainfix &gt;=V0c0F">
......@@ -251,15 +251,15 @@
memlimit="1000"
obsolete="false"
archived="false">
<result status="valid" time="0.00"/>
<result status="valid" time="0.01"/>
</proof>
</goal>
<goal
name="WP_parameter logfib.3"
locfile="examples/programs/fibonacci/../fibonacci.mlw"
locfile="programs/fibonacci/../fibonacci.mlw"
loclnum="82" loccnumb="10" loccnume="16"
expl="precondition"
sum="914eb29f581e4f81f1dc88e3cd6a2125"
sum="ec53c68db6b793ce5dd13c260a850beb"
proved="true"
expanded="true"
shape="ainfix &gt;=adivV0c2c0Iainfix =V0c0NIainfix &gt;=V0c0F">
......@@ -284,10 +284,10 @@
</goal>
<goal
name="WP_parameter logfib.4"
locfile="examples/programs/fibonacci/../fibonacci.mlw"
locfile="programs/fibonacci/../fibonacci.mlw"
loclnum="82" loccnumb="10" loccnume="16"
expl="normal postcondition"
sum="c8a4a4717b459e34b8d3a05ff9c7fb31"
sum="8054b2592b4645e2207abf30a53e8434"
proved="true"
expanded="false"
shape="iainfix =amodV0c2c0ainfix =apoweramk tc1c1c1c0V0amk tainfix +V3V4V4V4V3Lainfix *V2ainfix +V1ainfix +V1V2Lainfix +ainfix *V1V1ainfix *V2V2ainfix =apoweramk tc1c1c1c0V0amk tainfix +V5V6V6V6V5Lainfix +ainfix *ainfix +V1V2ainfix +V1V2ainfix *V2V2Lainfix *V2ainfix +V1ainfix +V1V2Iainfix =apoweramk tc1c1c1c0adivV0c2amk tainfix +V1V2V2V2V1FIainfix &gt;=adivV0c2c0Aainfix &lt;adivV0c2V0Aainfix &lt;=c0V0Iainfix =V0c0NIainfix &gt;=V0c0F">
......@@ -300,16 +300,16 @@
edited="fibonacci_WP_FibonacciLogarithmic_WP_parameter_logfib_1.v"
obsolete="false"
archived="false">
<result status="valid" time="0.62"/>
<result status="valid" time="0.63"/>
</proof>
</goal>
</transf>
</goal>
<goal
name="fib_m"
locfile="examples/programs/fibonacci/../fibonacci.mlw"
locfile="programs/fibonacci/../fibonacci.mlw"
loclnum="105" loccnumb="8" loccnume="13"
sum="e8605b6494a93cb6a637cf1c1f211395"
sum="3b9e61634104ae731da8aac4b1e65d66"
proved="true"