playing with bitvectors

tests/bitvector.why

+
+theory BitVector
+
+  use export bool.Bool
+  use import int.Int
+
+  function size : int
+
+  type bv
+
+  function nth bv int: bool
+
+  function bvzero : bv
+  axiom Nth_zero:
+    forall n:int. 0 <= n < size -> nth bvzero n = False
+
+  function bvone : bv
+  axiom Nth_one:
+    forall n:int. 0 <= n < size -> nth bvone n = True
+
+  predicate eq (v1 v2 : bv) =
+    forall n:int. 0 <= n < size -> nth v1 n = nth v2 n
+
+  axiom extensionality:
+    forall v1 v2 : bv. eq v1 v2 -> v1 = v2
+
+  function bw_and (v1 v2 : bv) : bv
+  axiom Nth_bw_and:
+    forall v1 v2:bv, n:int. 0 <= n < size ->
+      nth (bw_and v1 v2) n = andb (nth v1 n) (nth v2 n)
+
+  function bw_or (v1 v2 : bv) : bv
+  axiom Nth_bw_or:
+    forall v1 v2:bv, n:int. 0 <= n < size ->
+      nth (bw_or v1 v2) n = orb (nth v1 n) (nth v2 n)
+
+  function bw_xor (v1 v2 : bv) : bv
+  axiom Nth_bw_xor:
+    forall v1 v2:bv, n:int. 0 <= n < size ->
+      nth (bw_xor v1 v2) n = xorb (nth v1 n) (nth v2 n)
+
+  function bw_not (v : bv) : bv
+  axiom Nth_bw_not:
+    forall v:bv, n:int. 0 <= n < size ->
+      nth (bw_not v) n = notb (nth v n)
+
+  (* logical shift right *)
+  function lsr bv int : bv
+
+  axiom lsr_nth_low:
+    forall b:bv, n s:int.
+      0 <= n < size -> 0 <= s ->
+        n+s < size -> nth (lsr b s) n = nth b (n+s)
+
+  axiom lsr_nth_high:
+    forall b:bv, n s:int.
+      0 <= n < size -> 0 <= s ->
+        n+s >= size -> nth (lsr b s) n = False
+
+  (* arithmetic shift right *)
+  function asr bv int : bv
+
+  axiom asr_nth_low:
+    forall b:bv, n s:int.
+      0 <= n < size -> 0 <= s ->
+        n+s < size -> nth (asr b s) n = nth b (n+s)
+
+  axiom asr_nth_high:
+    forall b:bv, n s:int.
+      0 <= n < size -> 0 <= s ->
+        n+s >= size -> nth (asr b s) n = nth b (size-1)
+
+  (* logical shift left *)
+  function lsl bv int : bv
+
+  axiom lsl_nth_high:
+    forall b:bv, n s:int.
+      0 <= n < size -> 0 <= s ->
+        0 <= n-s -> nth (lsl b s) n = nth b (n-s)
+
+  axiom lsl_nth_low:
+    forall b:bv, n s:int.
+      0 <= n < size -> 0 <= s ->
+        0 > n-s -> nth (lsl b s) n = False
+
+  (* conversion to/from integers *)
+
+  function to_nat_aux bv int : int
+    (* (to_nat_aux b i) returns the non-negative integer whose
+       binary repr is b[size-1..i] *)
+
+  axiom to_nat_aux_zero :
+    forall b:bv, i:int.
+      0 <= i < size ->
+        nth b i = False ->
+          to_nat_aux b i = 2 * to_nat_aux b (i+1)
+
+  axiom to_nat_aux_one :
+    forall b:bv, i:int.
+      0 <= i < size ->
+        nth b i = True ->
+          to_nat_aux b i = 1 + 2 * to_nat_aux b (i+1)
+
+  axiom to_nat_aux_high :
+    forall b:bv, i:int.
+      i >= size ->
+        to_nat_aux b i = 0
+
+  function to_nat (b:bv) : int = to_nat_aux b 0
+
+
+  function to_int_aux bv int : int
+    (* (to_int_aux b i) returns the integer whose
+       2-complement binary repr is b[size-1..i] *)
+
+  axiom to_int_aux_zero :
+    forall b:bv, i:int.
+      0 <= i < size-1 ->
+        nth b i = False ->
+          to_int_aux b i = 2 * to_int_aux b (i+1)
+
+  axiom to_int_aux_one :
+    forall b:bv, i:int.
+      0 <= i < size-1 ->
+        nth b i = True ->
+          to_int_aux b i = 1 + 2 * to_int_aux b (i+1)
+
+  axiom to_int_aux_pos :
+    forall b:bv. nth b (size-1) = False ->
+         to_int_aux b (size-1) = 0
+
+  axiom to_int_aux_neg :
+    forall b:bv. nth b (size-1) = True ->
+         to_int_aux b (size-1) = -1
+
+  function to_int (b:bv) : int = to_int_aux b 0
+
+end
+
+
+theory BV32
+
+  function size : int = 32
+
+  clone export BitVector with function size = size
+
+end
+
+
+theory TestBv32
+
+  use import BV32
+  use import int.Int
+
+  goal Test1:
+    let b = bw_and bvzero bvone in nth b 1 = False
+
+  goal Test2:
+    let b = lsr bvone 16 in nth b 15 = True
+
+  goal Test3:
+    let b = lsr bvone 16 in nth b 16 = False
+
+  goal Test4:
+    let b = asr bvone 16 in nth b 15 = True
+
+  goal Test5:
+    let b = asr bvone 16 in nth b 16 = True
+
+  goal Test6:
+    let b = asr (lsr bvone 1) 16 in nth b 16 = False
+
+  goal to_nat_0x00000000:
+    to_nat bvzero = 0
+
+  goal to_nat_0x0000000F:
+    to_nat (lsr bvone 28) = 15
+
+  goal to_nat_0x0000001F:
+    to_nat (lsr bvone 27) = 31
+
+  goal to_nat_0x0000003F:
+    to_nat (lsr bvone 26) = 63
+
+  goal to_nat_0x0000007F:
+    to_nat (lsr bvone 25) = 127
+
+  goal to_nat_0x000000FF:
+    to_nat (lsr bvone 24) = 255
+
+  goal to_nat_0x000001FF:
+    to_nat (lsr bvone 23) = 511
+
+  goal to_nat_0x000003FF:
+    to_nat (lsr bvone 22) = 1023
+
+  goal to_nat_0x000007FF:
+    to_nat (lsr bvone 21) = 2047
+
+  goal to_nat_0x00000FFF:
+    to_nat (lsr bvone 20) = 4095
+
+  goal to_nat_0x00001FFF:
+    to_nat (lsr bvone 19) = 8191
+
+  goal to_nat_0x00003FFF:
+    to_nat (lsr bvone 18) = 16383
+
+  goal to_nat_0x00007FFF:
+    to_nat (lsr bvone 17) = 32767
+
+  goal to_nat_0x0000FFFF:
+    to_nat (lsr bvone 16) = 65535
+
+(*
+  goal to_nat_smoke:
+    to_nat (lsr bvone 16) = 65536
+*)
+
+  goal to_nat_0x0001FFFF:
+    to_nat (lsr bvone 15) = 131071
+
+  goal to_nat_0x0003FFFF:
+    to_nat (lsr bvone 14) = 262143
+
+  goal to_nat_0x0007FFFF:
+    to_nat (lsr bvone 13) = 524287
+
+  goal to_nat_0x000FFFFF:
+    to_nat (lsr bvone 12) = 1048575
+
+  goal to_nat_0x00FFFFFF:
+    to_nat (lsr bvone 8) = 16777215
+
+  goal to_nat_0xFFFFFFFF:
+    to_nat bvone = 4294967295
+
+  goal to_int_0x00000000:
+    to_int bvzero = 0
+
+  goal to_int_0xFFFFFFFF:
+    to_int bvone = -1
+
+  goal to_int_0x7FFFFFFF:
+    to_int (lsr bvone 1) = 2147483647
+
+  goal to_int_0x80000000:
+    to_int (lsl bvone 31) = -2147483648
+
+  goal to_int_0x0000FFFF:
+    to_int (lsr bvone 16) = 65535
+
+  goal to_int_smoke:
+    to_int (lsr bvone 16) = 65536
+
+end
+
+
+(*
+Local Variables:
+compile-command: "why3ide bitvector.why"
+End:
+*)

tests/bitvector/bitvector_TestBv32_to_int_0x80000000_1.v

+(* This file is generated by Why3's Coq driver *)
+(* Beware! Only edit allowed sections below    *)
+Require Import ZArith.
+Require Import Rbase.
+Parameter bv : Type.
+
+Parameter nth: bv -> Z -> bool.
+
+
+Parameter bvzero: bv.
+
+
+Axiom Nth_zero : forall (n:Z), ((0%Z <= n)%Z /\ (n <  32%Z)%Z) ->
+  ((nth bvzero n) = false).
+
+Parameter bvone: bv.
+
+
+Axiom Nth_one : forall (n:Z), ((0%Z <= n)%Z /\ (n <  32%Z)%Z) -> ((nth bvone
+  n) = true).
+
+Definition eq(v1:bv) (v2:bv): Prop := forall (n:Z), ((0%Z <= n)%Z /\
+  (n <  32%Z)%Z) -> ((nth v1 n) = (nth v2 n)).
+
+Axiom extensionality : forall (v1:bv) (v2:bv), (eq v1 v2) -> (v1 = v2).
+
+Parameter bw_and: bv -> bv -> bv.
+
+
+Axiom Nth_bw_and : forall (v1:bv) (v2:bv) (n:Z), ((0%Z <= n)%Z /\
+  (n <  32%Z)%Z) -> ((nth (bw_and v1 v2) n) = (andb (nth v1 n) (nth v2 n))).
+
+Parameter bw_or: bv -> bv -> bv.
+
+
+Axiom Nth_bw_or : forall (v1:bv) (v2:bv) (n:Z), ((0%Z <= n)%Z /\
+  (n <  32%Z)%Z) -> ((nth (bw_or v1 v2) n) = (orb (nth v1 n) (nth v2 n))).
+
+Parameter bw_xor: bv -> bv -> bv.
+
+
+Axiom Nth_bw_xor : forall (v1:bv) (v2:bv) (n:Z), ((0%Z <= n)%Z /\
+  (n <  32%Z)%Z) -> ((nth (bw_xor v1 v2) n) = (xorb (nth v1 n) (nth v2 n))).
+
+Parameter bw_not: bv -> bv.
+
+
+Axiom Nth_bw_not : forall (v:bv) (n:Z), ((0%Z <= n)%Z /\ (n <  32%Z)%Z) ->
+  ((nth (bw_not v) n) = (negb (nth v n))).
+
+Parameter lsr: bv -> Z -> bv.
+
+
+Axiom lsr_nth_low : forall (b:bv) (n:Z) (s:Z), ((0%Z <= n)%Z /\
+  (n <  32%Z)%Z) -> ((0%Z <= s)%Z -> (((n + s)%Z <  32%Z)%Z -> ((nth (lsr b
+  s) n) = (nth b (n + s)%Z)))).
+
+Axiom lsr_nth_high : forall (b:bv) (n:Z) (s:Z), ((0%Z <= n)%Z /\
+  (n <  32%Z)%Z) -> ((0%Z <= s)%Z -> ((32%Z <= (n + s)%Z)%Z -> ((nth (lsr b
+  s) n) = false))).
+
+Parameter asr: bv -> Z -> bv.
+
+
+Axiom asr_nth_low : forall (b:bv) (n:Z) (s:Z), ((0%Z <= n)%Z /\
+  (n <  32%Z)%Z) -> ((0%Z <= s)%Z -> (((n + s)%Z <  32%Z)%Z -> ((nth (asr b
+  s) n) = (nth b (n + s)%Z)))).
+
+Axiom asr_nth_high : forall (b:bv) (n:Z) (s:Z), ((0%Z <= n)%Z /\
+  (n <  32%Z)%Z) -> ((0%Z <= s)%Z -> ((32%Z <= (n + s)%Z)%Z -> ((nth (asr b
+  s) n) = (nth b (32%Z - 1%Z)%Z)))).
+
+Parameter lsl: bv -> Z -> bv.
+
+
+Axiom lsl_nth_high : forall (b:bv) (n:Z) (s:Z), ((0%Z <= n)%Z /\
+  (n <  32%Z)%Z) -> ((0%Z <= s)%Z -> ((0%Z <= (n - s)%Z)%Z -> ((nth (lsl b s)
+  n) = (nth b (n - s)%Z)))).
+
+Axiom lsl_nth_low : forall (b:bv) (n:Z) (s:Z), ((0%Z <= n)%Z /\
+  (n <  32%Z)%Z) -> ((0%Z <= s)%Z -> (((n - s)%Z <  0%Z)%Z -> ((nth (lsl b s)
+  n) = false))).
+
+Parameter to_nat_aux: bv -> Z -> Z.
+
+
+Axiom to_nat_aux_zero : forall (b:bv) (i:Z), ((0%Z <= i)%Z /\
+  (i <  32%Z)%Z) -> (((nth b i) = false) -> ((to_nat_aux b
+  i) = (2%Z * (to_nat_aux b (i + 1%Z)%Z))%Z)).
+
+Axiom to_nat_aux_one : forall (b:bv) (i:Z), ((0%Z <= i)%Z /\
+  (i <  32%Z)%Z) -> (((nth b i) = true) -> ((to_nat_aux b
+  i) = (1%Z + (2%Z * (to_nat_aux b (i + 1%Z)%Z))%Z)%Z)).
+
+Axiom to_nat_aux_high : forall (b:bv) (i:Z), (32%Z <= i)%Z -> ((to_nat_aux b
+  i) = 0%Z).
+
+Parameter to_int_aux: bv -> Z -> Z.
+
+
+Axiom to_int_aux_zero : forall (b:bv) (i:Z), ((0%Z <= i)%Z /\
+  (i <  (32%Z - 1%Z)%Z)%Z) -> (((nth b i) = false) -> ((to_int_aux b
+  i) = (2%Z * (to_int_aux b (i + 1%Z)%Z))%Z)).
+
+Axiom to_int_aux_one : forall (b:bv) (i:Z), ((0%Z <= i)%Z /\
+  (i <  (32%Z - 1%Z)%Z)%Z) -> (((nth b i) = true) -> ((to_int_aux b
+  i) = (1%Z + (2%Z * (to_int_aux b (i + 1%Z)%Z))%Z)%Z)).
+
+Axiom to_int_aux_pos : forall (b:bv), ((nth b (32%Z - 1%Z)%Z) = false) ->
+  ((to_int_aux b (32%Z - 1%Z)%Z) = 0%Z).
+
+Axiom to_int_aux_neg : forall (b:bv), ((nth b (32%Z - 1%Z)%Z) = true) ->
+  ((to_int_aux b (32%Z - 1%Z)%Z) = (-1%Z)%Z).
+
+(* YOU MAY EDIT THE CONTEXT BELOW *)
+
+(* DO NOT EDIT BELOW *)
+
+Theorem to_int_0x80000000 : ((to_int_aux (lsl bvone 31%Z)
+  0%Z) = (-2147483648%Z)%Z).
+(* YOU MAY EDIT THE PROOF BELOW *)
+rewrite to_int_aux_zero; auto with zarith.
+2: rewrite lsl_nth_low; auto with zarith.
+rewrite to_int_aux_zero; auto with zarith.
+2: rewrite lsl_nth_low; auto with zarith.
+rewrite to_int_aux_zero; auto with zarith.
+2: rewrite lsl_nth_low; auto with zarith.
+rewrite to_int_aux_zero; auto with zarith.
+2: rewrite lsl_nth_low; auto with zarith.
+rewrite to_int_aux_zero; auto with zarith.
+2: rewrite lsl_nth_low; auto with zarith.
+rewrite to_int_aux_zero; auto with zarith.
+2: rewrite lsl_nth_low; auto with zarith.
+rewrite to_int_aux_zero; auto with zarith.
+2: rewrite lsl_nth_low; auto with zarith.
+rewrite to_int_aux_zero; auto with zarith.
+2: rewrite lsl_nth_low; auto with zarith.
+rewrite to_int_aux_zero; auto with zarith.
+2: rewrite lsl_nth_low; auto with zarith.
+rewrite to_int_aux_zero; auto with zarith.
+2: rewrite lsl_nth_low; auto with zarith.
+rewrite to_int_aux_zero; auto with zarith.
+2: rewrite lsl_nth_low; auto with zarith.
+rewrite to_int_aux_zero; auto with zarith.
+2: rewrite lsl_nth_low; auto with zarith.
+rewrite to_int_aux_zero; auto with zarith.
+2: rewrite lsl_nth_low; auto with zarith.
+rewrite to_int_aux_zero; auto with zarith.
+2: rewrite lsl_nth_low; auto with zarith.
+rewrite to_int_aux_zero; auto with zarith.
+2: rewrite lsl_nth_low; auto with zarith.
+rewrite to_int_aux_zero; auto with zarith.
+2: rewrite lsl_nth_low; auto with zarith.
+rewrite to_int_aux_zero; auto with zarith.
+2: rewrite lsl_nth_low; auto with zarith.
+rewrite to_int_aux_zero; auto with zarith.
+2: rewrite lsl_nth_low; auto with zarith.
+rewrite to_int_aux_zero; auto with zarith.
+2: rewrite lsl_nth_low; auto with zarith.
+rewrite to_int_aux_zero; auto with zarith.
+2: rewrite lsl_nth_low; auto with zarith.
+rewrite to_int_aux_zero; auto with zarith.
+2: rewrite lsl_nth_low; auto with zarith.
+rewrite to_int_aux_zero; auto with zarith.
+2: rewrite lsl_nth_low; auto with zarith.
+rewrite to_int_aux_zero; auto with zarith.
+2: rewrite lsl_nth_low; auto with zarith.
+rewrite to_int_aux_zero; auto with zarith.
+2: rewrite lsl_nth_low; auto with zarith.
+rewrite to_int_aux_zero; auto with zarith.
+2: rewrite lsl_nth_low; auto with zarith.
+rewrite to_int_aux_zero; auto with zarith.
+2: rewrite lsl_nth_low; auto with zarith.
+rewrite to_int_aux_zero; auto with zarith.
+2: rewrite lsl_nth_low; auto with zarith.
+rewrite to_int_aux_zero; auto with zarith.
+2: rewrite lsl_nth_low; auto with zarith.
+rewrite to_int_aux_zero; auto with zarith.
+2: rewrite lsl_nth_low; auto with zarith.
+rewrite to_int_aux_zero; auto with zarith.
+2: rewrite lsl_nth_low; auto with zarith.
+rewrite to_int_aux_zero; auto with zarith.
+2: rewrite lsl_nth_low; auto with zarith.
+rewrite to_int_aux_neg; auto with zarith.
+rewrite lsl_nth_high; auto with zarith.
+rewrite Nth_one; auto with zarith.
+Qed.
+(* DO NOT EDIT BELOW *)
+
+

tests/bitvector/why3session.xml

+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE why3session SYSTEM "why3session.dtd">
+<why3session
+ name="bitvector/why3session.xml">
+ <prover
+  id="alt-ergo"
+  name="Alt-Ergo"
+  version="0.93"/>
+ <prover
+  id="coq"
+  name="Coq"
+  version="8.2pl1"/>
+ <prover
+  id="cvc3"
+  name="CVC3"
+  version="2.2"/>
+ <prover
+  id="eprover"
+  name="Eprover"
+  version="1.4 Namring"/>
+ <prover
+  id="gappa"
+  name="Gappa"
+  version="0.15.1"/>
+ <prover
+  id="simplify"
+  name="Simplify"
+  version="1.5.4"/>
+ <prover
+  id="spass"
+  name="Spass"
+  version="3.7"/>
+ <prover
+  id="vampire"
+  name="Vampire"
+  version="0.6"/>
+ <prover
+  id="verit"
+  name="veriT"
+  version="dev"/>
+ <prover
+  id="yices"
+  name="Yices"
+  version="1.0.25"/>
+ <prover
+  id="z3"
+  name="Z3"
+  version="2.19"/>
+ <file
+  name="../bitvector.why"
+  verified="false"
+  expanded="true">
+  <theory
+   name="BitVector"
+   verified="true"
+   expanded="true">
+  </theory>
+  <theory
+   name="BV32"
+   verified="true"
+   expanded="true">
+  </theory>
+  <theory
+   name="TestBv32"
+   verified="false"
+   expanded="true">
+   <goal
+    name="Test1"
+    sum="081a5423810d47ab1fe2b0a82b35eb24"
+    proved="true"
+    expanded="true"
+    shape="Labw_andabvzeroabvoneainfix =anthV0c1aFalse">
+    <proof
+     prover="z3"
+     timelimit="10"
+     edited=""
+     obsolete="false">
+     <result status="valid" time="0.02"/>
+    </proof>
+   </goal>
+   <goal
+    name="Test2"
+    sum="0dfd1f488bc3a073e572644d428b8479"
+    proved="true"
+    expanded="true"
+    shape="Lalsrabvonec16ainfix =anthV0c15aTrue">
+    <proof
+     prover="z3"
+     timelimit="10"
+     edited=""
+     obsolete="false">
+     <result status="valid" time="0.02"/>
+    </proof>
+   </goal>
+   <goal
+    name="Test3"
+    sum="3d3025e93d04d19b4a65c7e91de25997"
+    proved="true"
+    expanded="true"
+    shape="Lalsrabvonec16ainfix =anthV0c16aFalse">
+    <proof
+     prover="z3"
+     timelimit="10"
+     edited=""
+     obsolete="false">
+     <result status="valid" time="0.03"/>
+    </proof>
+   </goal>
+   <goal
+    name="Test4"
+    sum="8f1766048b98478855859610a82ced71"
+    proved="true"
+    expanded="true"
+    shape="Laasrabvonec16ainfix =anthV0c15aTrue">
+    <proof
+     prover="z3"
+     timelimit="10"
+     edited=""
+     obsolete="false">
+     <result status="valid" time="0.03"/>
+    </proof>
+   </goal>
+   <goal
+    name="Test5"
+    sum="7f73dfdaefe18506af991f371f3f457b"
+    proved="true"
+    expanded="true"
+    shape="Laasrabvonec16ainfix =anthV0c16aTrue">
+    <proof
+     prover="z3"
+     timelimit="10"
+     edited=""
+     obsolete="false">
+     <result status="valid" time="0.04"/>
+    </proof>
+   </goal>
+   <goal
+    name="Test6"
+    sum="b191056321013bfe380ec980009cccc9"
+    proved="true"
+    expanded="true"
+    shape="Laasralsrabvonec1c16ainfix =anthV0c16aFalse">
+    <proof
+     prover="z3"
+     timelimit="10"
+     edited=""
+     obsolete="false">
+     <result status="valid" time="0.03"/>
+    </proof>
+   </goal>
+   <goal
+    name="to_nat_0x00000000"
+    sum="3ee0fe188bb040f08b4279f413f39835"
+    proved="true"
+    expanded="true"
+    shape="ainfix =ato_natabvzeroc0">
+    <proof
+     prover="z3"
+     timelimit="10"
+     edited=""
+     obsolete="false">
+     <result status="valid" time="0.39"/>
+    </proof>
+   </goal>
+   <goal
+    name="to_nat_0x0000000F"
+    sum="fb89baa5a9ff9705440a2ec8e5599398"
+    proved="false"
+    expanded="true"
+    shape="ainfix =ato_natalsrabvonec28c15">
+    <proof
+     prover="z3"
+     timelimit="10"
+     edited=""
+     obsolete="false">
+     <result status="timeout" time="60.15"/>
+    </proof>
+   </goal>
+   <goal
+    name="to_nat_0x0000001F"
+    sum="6e0fb9b6b86dd2e94af40ec0a80b4a58"
+    proved="false"
+    expanded="true"
+    shape="ainfix =ato_natalsrabvonec27c31">
+    <proof
+     prover="z3"
+     timelimit="60"
+     edited=""
+     obsolete="false">
+     <result status="timeout" time="60.15"/>
+    </proof>
+   </goal>
+   <goal
+    name="to_nat_0x0000003F"
+    sum="122cf1440c33fffe9ddb16ae7e8819c9"
+    proved="false"
+    expanded="true"
+    shape="ainfix =ato_natalsrabvonec26c63">
+    <proof
+     prover="z3"
+     timelimit="60"
+     edited=""
+     obsolete="false">
+     <result status="timeout" time="60.05"/>
+    </proof>
+   </goal>
+   <goal
+    name="to_nat_0x0000007F"
+    sum="b509cc35c184038ba6cff7c07f17834d"
+    proved="false"
+    expanded="true"
+    shape="ainfix =ato_natalsrabvonec25c127">
+    <proof
+     prover="z3"
+     timelimit="60"
+     edited=""
+     obsolete="false">
+     <result status="timeout" time="60.09"/>
+    </proof>
+   </goal>
+   <goal
+    name="to_nat_0x000000FF"
+    sum="807b63c6feb2d47472dc142d58ab099d"
+    proved="false"
+    expanded="true"
+    shape="ainfix =ato_natalsrabvonec24c255">
+    <proof
+     prover="z3"
+     timelimit="10"
+     edited=""
+     obsolete="false">
+     <result status="timeout" time="60.09"/>
+    </proof>
+   </goal>
+   <goal
+    name="to_nat_0x000001FF"
+    sum="786fa4285e60143b7c2e29b9abb612a7"
+    proved="false"
+    expanded="true"
+    shape="ainfix =ato_natalsrabvonec23c511">
+    <proof
+     prover="z3"
+     timelimit="60"
+     edited=""
+     obsolete="false">
+     <result status="timeout" time="60.09"/>
+    </proof>
+   </goal>
+   <goal
+    name="to_nat_0x000003FF"
+    sum="18f97e041d6198984ab8fb7066f768c5"
+    proved="true"
+    expanded="true"
+    shape="ainfix =ato_natalsrabvonec22c1023">
+    <proof
+     prover="z3"
+     timelimit="10"
+     edited=""
+     obsolete="false">
+     <result status="valid" time="7.05"/>
+    </proof>
+   </goal>
+   <goal
+    name="to_nat_0x000007FF"
+    sum="72aca8f2d706a6e73f0d8c2cced5e2ef"
+    proved="false"
+    expanded="true"
+    shape="ainfix =ato_natalsrabvonec21c2047">
+    <proof
+     prover="z3"
+     timelimit="60"
+     edited=""
+     obsolete="false">
+     <result status="timeout" time="60.13"/>
+    </proof>
+   </goal>
+   <goal
+    name="to_nat_0x00000FFF"
+    sum="b4ea4d76ba6dc41af9643cb2f42ab39e"
+    proved="true"
+    expanded="true"
+    shape="ainfix =ato_natalsrabvonec20c4095">
+    <proof
+     prover="z3"
+     timelimit="10"
+     edited=""
+     obsolete="false">
+     <result status="valid" time="4.88"/>
+    </proof>
+   </goal>
+   <goal
+    name="to_nat_0x00001FFF"
+    sum="067985c11f18ce7ab4bcc254515b87ae"
+    proved="true"
+    expanded="true"
+    shape="ainfix =ato_natalsrabvonec19c8191">
+    <proof
+     prover="z3"
+     timelimit="10"
+     edited=""
+     obsolete="false">
+     <result status="valid" time="1.48"/>
+    </proof>
+   </goal>
+   <goal
+    name="to_nat_0x00003FFF"
+    sum="105f55630dc561de4d3a055aab69dc72"
+    proved="true"
+    expanded="true"
+    shape="ainfix =ato_natalsrabvonec18c16383">
+    <proof
+     prover="z3"
+     timelimit="10"
+     edited=""
+     obsolete="false">
+     <result status="valid" time="2.05"/>
+    </proof>
+   </goal>
+   <goal
+    name="to_nat_0x00007FFF"
+    sum="4a874d91c8315f4d53804f68617e471f"
+    proved="true"
+    expanded="true"
+    shape="ainfix =ato_natalsrabvonec17c32767">
+    <proof
+     prover="z3"
+     timelimit="60"
+     edited=""
+     obsolete="false">
+     <result status="valid" time="2.38"/>
+    </proof>
+   </goal>
+   <goal
+    name="to_nat_0x0000FFFF"
+    sum="e46d6ab315bd19684656be9b766d2458"
+    proved="true"
+    expanded="true"
+    shape="ainfix =ato_natalsrabvonec16c65535">
+    <proof
+     prover="z3"
+     timelimit="10"
+     edited=""
+     obsolete="false">
+     <result status="valid" time="2.18"/>
+    </proof>
+   </goal>
+   <goal
+    name="to_nat_0x0001FFFF"
+    sum="eeb0c825010f74e0c8d8d239cdda9b51"
+    proved="true"
+    expanded="true"
+    shape="ainfix =ato_natalsrabvonec15c131071">
+    <proof
+     prover="z3"
+     timelimit="10"
+     edited=""
+     obsolete="false">
+     <result status="valid" time="8.78"/>
+    </proof>
+   </goal>
+   <goal
+    name="to_nat_0x0003FFFF"
+    sum="824f93245a9d850c4ca4b985258b4efd"
+    proved="false"
+    expanded="true"
+    shape="ainfix =ato_natalsrabvonec14c262143">
+    <proof
+     prover="z3"
+     timelimit="10"
+     edited=""
+     obsolete="false">
+     <result status="timeout" time="60.03"/>
+    </proof>
+   </goal>
+   <goal
+    name="to_nat_0x000FFFFF"
+    sum="d04683dfab1c0c421bcf4fb8f45dce6a"
+    proved="false"
+    expanded="true"
+    shape="ainfix =ato_natalsrabvonec12c1048575">
+    <proof
+     prover="z3"
+     timelimit="10"
+     edited=""
+     obsolete="false">
+     <result status="timeout" time="60.13"/>
+    </proof>
+   </goal>
+   <goal
+    name="to_nat_0x00FFFFFF"
+    sum="902cfbbedcb85d73bd0b09d2b7a6f5ff"
+    proved="false"
+    expanded="true"
+    shape="ainfix =ato_natalsrabvonec8c16777215">
+    <proof
+     prover="z3"
+     timelimit="10"
+     edited=""
+     obsolete="false">
+     <result status="timeout" time="60.04"/>
+    </proof>
+   </goal>
+   <goal
+    name="to_nat_0xFFFFFFFF"
+    sum="c70042c7154928630e1b273268a7183e"
+    proved="false"
+    expanded="true"
+    shape="ainfix =ato_natabvonec4294967295">
+    <proof
+     prover="cvc3"
+     timelimit="10"
+     edited=""
+     obsolete="false">
+     <result status="timeout" time="10.07"/>
+    </proof>
+    <proof
+     prover="z3"
+     timelimit="10"
+     edited=""
+     obsolete="false">
+     <result status="timeout" time="60.14"/>
+    </proof>
+   </goal>
+   <goal
+    name="to_int_0x00000000"
+    sum="4c23b9ed9193d3c37ef9e733540a327c"
+    proved="true"
+    expanded="true"
+    shape="ainfix =ato_intabvzeroc0">
+    <proof
+     prover="z3"
+     timelimit="10"
+     edited=""
+     obsolete="false">
+     <result status="valid" time="0.66"/>
+    </proof>
+   </goal>
+   <goal
+    name="to_int_0xFFFFFFFF"
+    sum="b67e811fa21693b3e83d2f78ad81e595"
+    proved="false"
+    expanded="true"
+    shape="ainfix =ato_intabvoneaprefix -c1">
+    <proof
+     prover="cvc3"
+     timelimit="10"
+     edited=""
+     obsolete="false">
+     <result status="timeout" time="10.12"/>
+    </proof>
+    <proof
+     prover="z3"
+     timelimit="10"
+     edited=""
+     obsolete="false">
+     <result status="timeout" time="60.24"/>
+    </proof>
+   </goal>
+   <goal
+    name="to_int_0x7FFFFFFF"
+    sum="b43f3227975796a99b4c5d89bb68e71d"
+    proved="false"
+    expanded="true"
+    shape="ainfix =ato_intalsrabvonec1c2147483647">
+    <proof
+     prover="cvc3"
+     timelimit="10"
+     edited=""
+     obsolete="false">
+     <result status="timeout" time="10.01"/>
+    </proof>
+    <proof
+     prover="z3"
+     timelimit="10"
+     edited=""
+     obsolete="false">
+     <result status="timeout" time="60.07"/>
+    </proof>
+   </goal>
+   <goal
+    name="to_int_0x80000000"
+    sum="90671c46d5853282c420d64d5e4b54ea"
+    proved="true"
+    expanded="true"
+    shape="ainfix =ato_intalslabvonec31aprefix -c2147483648">
+    <proof
+     prover="coq"
+     timelimit="60"
+     edited="bitvector_TestBv32_to_int_0x80000000_1.v"
+     obsolete="false">
+     <result status="valid" time="2.14"/>
+    </proof>
+   </goal>
+   <goal
+    name="to_int_0x0000FFFF"
+    sum="a192b2b655efc71ff855dbb9ca06c3e8"
+    proved="true"
+    expanded="true"
+    shape="ainfix =ato_intalsrabvonec16c65535">
+    <proof
+     prover="cvc3"
+     timelimit="10"
+     edited=""
+     obsolete="false">
+     <result status="timeout" time="10.07"/>
+    </proof>
+    <proof
+     prover="z3"
+     timelimit="10"
+     edited=""
+     obsolete="false">
+     <result status="valid" time="2.52"/>
+    </proof>
+   </goal>
+   <goal
+    name="to_int_smoke"
+    sum="10a66934825245363a2f0b4459f03657"
+    proved="false"
+    expanded="true"
+    shape="ainfix =ato_intalsrabvonec16c65536">
+    <proof
+     prover="cvc3"
+     timelimit="10"
+     edited=""
+     obsolete="false">
+     <result status="timeout" time="10.07"/>
+    </proof>
+    <proof
+     prover="z3"
+     timelimit="10"
+     edited=""
+     obsolete="false"><undone/>
+     
+    </proof>
+   </goal>
+  </theory>
+ </file>
+</why3session>