<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
"http://why3.lri.fr/why3session.dtd">
<why3session shape_version="6">
<prover id="0" name="Alt-Ergo" version="2.0.0" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="1" name="Z3" version="3.2" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="2" name="Z3" version="4.7.1" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="3" name="Vampire" version="4.2.2" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="4" name="Eprover" version="2.0" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="5" name="CVC4" version="1.7" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="6" name="Alt-Ergo" version="2.4.1" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="7" name="Alt-Ergo" version="2.4.2" timelimit="5" steplimit="0" memlimit="2000"/>
<prover id="8" name="CVC3" version="2.4.1" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="9" name="Alt-Ergo" version="2.3.3" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="10" name="CVC4" version="1.8" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="11" name="Z3" version="4.8.10" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="12" name="CVC5" version="1.0.5" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="13" name="Alt-Ergo" version="2.4.3" timelimit="5" steplimit="0" memlimit="1000"/>
<file format="whyml" proved="true">
<path name=".."/><path name="euler_sieve.mlw"/>
<theory name="ArithmeticResults" proved="true">
 <goal name="mult_croissance_locale&#39;vc" expl="VC for mult_croissance_locale" proved="true">
 <proof prover="9"><result status="valid" time="0.000000" steps="10"/></proof>
 </goal>
 <goal name="mult_croissance&#39;vc" expl="VC for mult_croissance" proved="true">
 <proof prover="9"><result status="valid" time="0.010000" steps="16"/></proof>
 </goal>
 <goal name="comp_mult_2&#39;vc" expl="VC for comp_mult_2" proved="true">
 <proof prover="9"><result status="valid" time="0.010000" steps="12"/></proof>
 </goal>
 <goal name="div_croissance_locale1&#39;vc" expl="VC for div_croissance_locale1" proved="true">
 <proof prover="10"><result status="valid" time="0.270000" steps="35858"/></proof>
 </goal>
 <goal name="div_croissance1&#39;vc" expl="VC for div_croissance1" proved="true">
 <proof prover="9"><result status="valid" time="0.020000" steps="37"/></proof>
 </goal>
 <goal name="div_croissance_locale2&#39;vc" expl="VC for div_croissance_locale2" proved="true">
 <proof prover="10"><result status="valid" time="0.240000" steps="45824"/></proof>
 </goal>
 <goal name="div_croissance2&#39;vc" expl="VC for div_croissance2" proved="true">
 <proof prover="9"><result status="valid" time="0.020000" steps="43"/></proof>
 </goal>
 <goal name="div_mult_1&#39;vc" expl="VC for div_mult_1" proved="true">
 <proof prover="10"><result status="valid" time="0.280000" steps="48521"/></proof>
 </goal>
 <goal name="mult_borne_sous_exp&#39;vc" expl="VC for mult_borne_sous_exp" proved="true">
 <proof prover="9"><result status="valid" time="0.300000" steps="387"/></proof>
 </goal>
 <goal name="sq_ineq&#39;vc" expl="VC for sq_ineq" proved="true">
 <proof prover="10"><result status="valid" time="0.180000" steps="37965"/></proof>
 </goal>
</theory>
<theory name="DivisibilityResults" proved="true">
 <goal name="divides_div&#39;vc" expl="VC for divides_div" proved="true">
 <proof prover="9"><result status="valid" time="0.050000" steps="77"/></proof>
 </goal>
 <goal name="divides_inf&#39;vc" expl="VC for divides_inf" proved="true">
 <proof prover="9"><result status="valid" time="0.040000" steps="68"/></proof>
 </goal>
 <goal name="not_prime_divider_limits&#39;vc" expl="VC for not_prime_divider_limits" proved="true">
 <proof prover="9"><result status="valid" time="0.010000" steps="46"/></proof>
 </goal>
 <goal name="no_prod_impl_no_divider&#39;vc" expl="VC for no_prod_impl_no_divider" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="no_prod_impl_no_divider&#39;vc.0" expl="postcondition" proved="true">
  <transf name="case" proved="true" arg1="(exists k:int. (2 &lt;= k /\ k &lt; n) /\ not k = i /\ divides k i)">
   <goal name="no_prod_impl_no_divider&#39;vc.0.0" expl="true case (postcondition)" proved="true">
   <transf name="destruct" proved="true" arg1="H">
    <goal name="no_prod_impl_no_divider&#39;vc.0.0.0" expl="true case (postcondition)" proved="true">
    <transf name="destruct" proved="true" arg1="H">
     <goal name="no_prod_impl_no_divider&#39;vc.0.0.0.0" expl="destruct premise" proved="true">
     <transf name="introduce_exists" proved="true" >
      <goal name="no_prod_impl_no_divider&#39;vc.0.0.0.0.0" expl="destruct premise" proved="true">
      <transf name="assert" proved="true" arg1="(exists l:int. l * k = i)">
       <goal name="no_prod_impl_no_divider&#39;vc.0.0.0.0.0.0" expl="asserted formula" proved="true">
       <proof prover="9"><result status="valid" time="0.020000" steps="53"/></proof>
       </goal>
       <goal name="no_prod_impl_no_divider&#39;vc.0.0.0.0.0.1" expl="destruct premise" proved="true">
       <transf name="introduce_exists" proved="true" >
        <goal name="no_prod_impl_no_divider&#39;vc.0.0.0.0.0.1.0" expl="destruct premise" proved="true">
        <transf name="exists" proved="true" arg1="k">
         <goal name="no_prod_impl_no_divider&#39;vc.0.0.0.0.0.1.0.0" proved="true">
         <transf name="exists" proved="true" arg1="l">
          <goal name="no_prod_impl_no_divider&#39;vc.0.0.0.0.0.1.0.0.0" proved="true">
          <transf name="case" proved="true" arg1="(l = i)">
           <goal name="no_prod_impl_no_divider&#39;vc.0.0.0.0.0.1.0.0.0.0" expl="true case" proved="true">
           <transf name="assert" proved="true" arg1="(k = 1)">
            <goal name="no_prod_impl_no_divider&#39;vc.0.0.0.0.0.1.0.0.0.0.0" expl="asserted formula" proved="true">
            <proof prover="3"><result status="valid" time="0.080000"/></proof>
            </goal>
            <goal name="no_prod_impl_no_divider&#39;vc.0.0.0.0.0.1.0.0.0.0.1" expl="true case" proved="true">
            <proof prover="9"><result status="valid" time="0.010000" steps="24"/></proof>
            </goal>
           </transf>
           </goal>
           <goal name="no_prod_impl_no_divider&#39;vc.0.0.0.0.0.1.0.0.0.1" expl="false case" proved="true">
           <proof prover="9"><result status="valid" time="2.920000" steps="443"/></proof>
           </goal>
          </transf>
          </goal>
         </transf>
         </goal>
        </transf>
        </goal>
       </transf>
       </goal>
      </transf>
      </goal>
     </transf>
     </goal>
     <goal name="no_prod_impl_no_divider&#39;vc.0.0.0.1" expl="true case (postcondition)" proved="true">
     <proof prover="9"><result status="valid" time="0.010000" steps="12"/></proof>
     </goal>
    </transf>
    </goal>
   </transf>
   </goal>
   <goal name="no_prod_impl_no_divider&#39;vc.0.1" expl="false case (postcondition)" proved="true">
   <proof prover="9"><result status="valid" time="0.010000" steps="22"/></proof>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
 <goal name="not_prime_impl_divisor_under_sqrt&#39;vc" expl="VC for not_prime_impl_divisor_under_sqrt" proved="true">
 <proof prover="9"><result status="valid" time="0.030000" steps="162"/></proof>
 </goal>
</theory>
<theory name="EulerSieveSpec" proved="true">
 <goal name="conservation_all_eliminated_marked_on_marked_change&#39;vc" expl="VC for conservation_all_eliminated_marked_on_marked_change" proved="true">
 <proof prover="9"><result status="valid" time="0.060000" steps="177"/></proof>
 </goal>
 <goal name="conservation_all_eliminated_marked_on_nexts_change&#39;vc" expl="VC for conservation_all_eliminated_marked_on_nexts_change" proved="true">
 <transf name="inline_goal" proved="true" >
  <goal name="conservation_all_eliminated_marked_on_nexts_change&#39;vc.0" expl="VC for conservation_all_eliminated_marked_on_nexts_change" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="conservation_all_eliminated_marked_on_nexts_change&#39;vc.0.0" expl="postcondition" proved="true">
   <transf name="split_vc" proved="true" >
    <goal name="conservation_all_eliminated_marked_on_nexts_change&#39;vc.0.0.0" expl="postcondition" proved="true">
    <proof prover="9"><result status="valid" time="0.020000" steps="51"/></proof>
    </goal>
    <goal name="conservation_all_eliminated_marked_on_nexts_change&#39;vc.0.0.1" expl="postcondition" proved="true">
    <proof prover="9"><result status="valid" time="0.552011" steps="1741"/></proof>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
</theory>
<theory name="EulerSieve" proved="true">
 <goal name="multiples_of_marked_are_marked&#39;vc" expl="VC for multiples_of_marked_are_marked" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="multiples_of_marked_are_marked&#39;vc.0" expl="postcondition" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="multiples_of_marked_are_marked&#39;vc.0.0" expl="postcondition" proved="true">
   <proof prover="9"><result status="valid" time="0.020000" steps="28"/></proof>
   </goal>
   <goal name="multiples_of_marked_are_marked&#39;vc.0.1" expl="postcondition" proved="true">
   <proof prover="9"><result status="valid" time="0.010000" steps="28"/></proof>
   </goal>
   <goal name="multiples_of_marked_are_marked&#39;vc.0.2" expl="postcondition" proved="true">
   <proof prover="9"><result status="valid" time="0.010000" steps="28"/></proof>
   </goal>
   <goal name="multiples_of_marked_are_marked&#39;vc.0.3" expl="postcondition" proved="true">
   <proof prover="9"><result status="valid" time="0.010000" steps="28"/></proof>
   </goal>
   <goal name="multiples_of_marked_are_marked&#39;vc.0.4" expl="VC for multiples_of_marked_are_marked" proved="true">
   <transf name="inline_all" proved="true" >
    <goal name="multiples_of_marked_are_marked&#39;vc.0.4.0" expl="VC for multiples_of_marked_are_marked" proved="true">
    <proof prover="8"><result status="valid" time="0.040000"/></proof>
    <transf name="remove" proved="true" arg1="Assoc1,Unit_def_l,Unit_def_r,Inv_def_l,Inv_def_r,Comm1,Assoc,Mul_distr_l,Mul_distr_r,Comm,Unitary,NonTrivialRing,Refl,ZeroLessOne,CompatOrderAdd,CompatOrderMult,Abs_le,Abs_pos,Mod_bound,Div_unique,Div_bound,Mod_1,Div_1,Div_inf,Div_inf_neg,Mod_0,Div_1_left,Div_minus1_left,Mod_minus1_left,Div_mult,Mod_mult,Div_mod1,Div_bound1,Mod_bound1,Div_sign_pos,Div_sign_neg,Mod_sign_pos,Mod_sign_neg,Rounds_toward_zero,Div_11,Mod_11,Div_inf1,Mod_inf,Div_mult1,Mod_mult1,even_or_odd,even_not_odd,even_odd,odd_even,even_even,odd_odd,even_2k,odd_2k1,even_mod2,divides&#39;spec,divides_refl,divides_1_n,divides_0,divides_left,divides_right,divides_oppr,divides_oppl,divides_oppr_rev,divides_oppl_rev,divides_plusr,divides_minusr,divides_multl,divides_multr,divides_factorl,divides_factorr,divides_n_1,divides_antisym,divides_trans,divides_bounds,mod_divides_euclidean,mod_divides_computer,divides_mod_computer,odd_divides,prime_2,prime_3,prime_divisors,small_divisors,even_prime,odd_prime,mult_croissance_locale,mult_croissance,comp_mult_2,div_croissance_locale1,div_croissance1,div_croissance_locale2,div_croissance2,div_mult_1,sq_ineq,divides_div,divides_inf,not_prime_divider_limits,no_prod_impl_no_divider,not_prime_impl_divisor_under_sqrt,length_nonnegative,(==)&#39;spec,create&#39;spec,empty&#39;def,set&#39;spec,set&#39;def,([&lt;-])&#39;def,singleton&#39;spec,cons&#39;spec,snoc&#39;spec,([..])&#39;spec,([..])&#39;def,([_..])&#39;def,([.._])&#39;def,(++)&#39;spec,conservation_all_eliminated_marked_on_marked_change,conservation_all_eliminated_marked_on_nexts_change,H13,H12,Requires,H11,H10,H9,H8,H7,H6,H5,H4,H3,H">
     <goal name="multiples_of_marked_are_marked&#39;vc.0.4.0.0" expl="VC for multiples_of_marked_are_marked" proved="true">
     <proof prover="8"><result status="valid" time="0.010000"/></proof>
     <proof prover="10"><result status="valid" time="0.030000" steps="6438"/></proof>
     <proof prover="11"><result status="valid" time="0.010000" steps="20965"/></proof>
     </goal>
    </transf>
    </goal>
   </transf>
   </goal>
   <goal name="multiples_of_marked_are_marked&#39;vc.0.5" expl="VC for multiples_of_marked_are_marked" proved="true">
   <transf name="assert" proved="true" arg1="(k * (i * j) = i*j + (k-1)*(i*j))">
    <goal name="multiples_of_marked_are_marked&#39;vc.0.5.0" expl="asserted formula" proved="true">
    <proof prover="9"><result status="valid" time="0.020000" steps="29"/></proof>
    </goal>
    <goal name="multiples_of_marked_are_marked&#39;vc.0.5.1" expl="VC for multiples_of_marked_are_marked" proved="true">
    <transf name="assert" proved="true" arg1="((k-1)*(i*j) &gt;= 0)">
     <goal name="multiples_of_marked_are_marked&#39;vc.0.5.1.0" expl="asserted formula" proved="true">
     <proof prover="9"><result status="valid" time="0.020000" steps="32"/></proof>
     </goal>
     <goal name="multiples_of_marked_are_marked&#39;vc.0.5.1.1" expl="VC for multiples_of_marked_are_marked" proved="true">
     <proof prover="9"><result status="valid" time="0.020000" steps="32"/></proof>
     </goal>
    </transf>
    </goal>
   </transf>
   </goal>
   <goal name="multiples_of_marked_are_marked&#39;vc.0.6" expl="VC for multiples_of_marked_are_marked" proved="true">
   <transf name="unfold" proved="true" arg1="previously_marked_multiples" arg2="in" arg3="Requires">
    <goal name="multiples_of_marked_are_marked&#39;vc.0.6.0" expl="VC for multiples_of_marked_are_marked" proved="true">
    <transf name="unfold" proved="true" arg1="all_multiples_marked" arg2="in" arg3="Requires">
     <goal name="multiples_of_marked_are_marked&#39;vc.0.6.0.0" expl="VC for multiples_of_marked_are_marked" proved="true">
     <proof prover="1"><result status="valid" time="0.040000"/></proof>
     <transf name="remove" proved="true" arg1="zero,one,(-),even,([]),inv_nexts,all_eliminated_marked,all_eliminated_marked_partial,is_copy,not_marked_impl_next_not_marked_partial,all_primes,all_multiples_marked,previously_marked_multiples,only_multiples_marked,prime_multiples_marked,inv_remove_products,Assoc1,Unit_def_r,Mul_distr_l,Refl,Trans,Div_unique,Div_bound,Div_minus1_left,Div_sign_pos,even_not_odd,odd_not_even,even_odd,odd_2k1,divides_left,divides_oppr_rev,divides_multl,divides_multr,divides_mod_euclidean,mod_divides_computer,prime_divisors,odd_prime,mult_croissance_locale,comp_mult_2,sq_ineq,divides_div,no_prod_impl_no_divider,create&#39;spec,empty&#39;def,set&#39;spec,set&#39;def,singleton&#39;spec,cons&#39;spec,snoc&#39;spec,([..])&#39;spec,([..])&#39;def,(++)&#39;spec,conservation_all_eliminated_marked_on_marked_change,conservation_all_eliminated_marked_on_nexts_change">
      <goal name="multiples_of_marked_are_marked&#39;vc.0.6.0.0.0" expl="VC for multiples_of_marked_are_marked" proved="true">
      <proof prover="1"><result status="valid" time="0.030000"/></proof>
      <proof prover="3"><result status="valid" time="0.110000"/></proof>
      </goal>
     </transf>
     </goal>
    </transf>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
 <goal name="prev_and_new_impl_all_multiples_marked&#39;vc" expl="VC for prev_and_new_impl_all_multiples_marked" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="prev_and_new_impl_all_multiples_marked&#39;vc.0" expl="assertion" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="prev_and_new_impl_all_multiples_marked&#39;vc.0.0" expl="assertion" proved="true">
   <transf name="unfold" proved="true" arg1="previously_marked_multiples" arg2="in" arg3="Requires2">
    <goal name="prev_and_new_impl_all_multiples_marked&#39;vc.0.0.0" expl="assertion" proved="true">
    <transf name="unfold" proved="true" arg1="all_multiples_marked" arg2="in" arg3="Requires2">
     <goal name="prev_and_new_impl_all_multiples_marked&#39;vc.0.0.0.0" expl="assertion" proved="true">
     <proof prover="9"><result status="valid" time="0.030000" steps="77"/></proof>
     </goal>
    </transf>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="prev_and_new_impl_all_multiples_marked&#39;vc.1" expl="assertion" proved="true">
  <proof prover="9"><result status="valid" time="0.090000" steps="151"/></proof>
  </goal>
  <goal name="prev_and_new_impl_all_multiples_marked&#39;vc.2" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.010000" steps="26"/></proof>
  </goal>
  <goal name="prev_and_new_impl_all_multiples_marked&#39;vc.3" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.010000" steps="27"/></proof>
  </goal>
  <goal name="prev_and_new_impl_all_multiples_marked&#39;vc.4" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.010000" steps="26"/></proof>
  </goal>
  <goal name="prev_and_new_impl_all_multiples_marked&#39;vc.5" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="27"/></proof>
  </goal>
  <goal name="prev_and_new_impl_all_multiples_marked&#39;vc.6" expl="assertion" proved="true">
  <proof prover="9"><result status="valid" time="0.010000" steps="26"/></proof>
  </goal>
  <goal name="prev_and_new_impl_all_multiples_marked&#39;vc.7" expl="assertion" proved="true">
  <proof prover="9"><result status="valid" time="0.250000" steps="256"/></proof>
  </goal>
  <goal name="prev_and_new_impl_all_multiples_marked&#39;vc.8" expl="assertion" proved="true">
  <proof prover="9"><result status="valid" time="0.010000" steps="26"/></proof>
  </goal>
  <goal name="prev_and_new_impl_all_multiples_marked&#39;vc.9" expl="assertion" proved="true">
  <proof prover="9"><result status="valid" time="0.030000" steps="82"/></proof>
  </goal>
  <goal name="prev_and_new_impl_all_multiples_marked&#39;vc.10" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.050000" steps="120"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="conservation_only_multiples_marked&#39;vc" expl="VC for conservation_only_multiples_marked" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="conservation_only_multiples_marked&#39;vc.0" expl="assertion" proved="true">
  <proof prover="9"><result status="valid" time="0.120000" steps="234"/></proof>
  </goal>
  <goal name="conservation_only_multiples_marked&#39;vc.1" expl="assertion" proved="true">
  <proof prover="9"><result status="valid" time="0.100000" steps="137"/></proof>
  </goal>
  <goal name="conservation_only_multiples_marked&#39;vc.2" expl="assertion" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="20"/></proof>
  </goal>
  <goal name="conservation_only_multiples_marked&#39;vc.3" expl="postcondition" proved="true">
  <transf name="inline_goal" proved="true" >
   <goal name="conservation_only_multiples_marked&#39;vc.3.0" expl="postcondition" proved="true">
   <transf name="split_vc" proved="true" >
    <goal name="conservation_only_multiples_marked&#39;vc.3.0.0" expl="postcondition" proved="true">
    <transf name="case" proved="true" arg1="(k = i * j)">
     <goal name="conservation_only_multiples_marked&#39;vc.3.0.0.0" expl="true case (postcondition)" proved="true">
     <proof prover="9"><result status="valid" time="0.030000" steps="61"/></proof>
     </goal>
     <goal name="conservation_only_multiples_marked&#39;vc.3.0.0.1" expl="false case (postcondition)" proved="true">
     <proof prover="9"><result status="valid" time="0.100000" steps="172"/></proof>
     </goal>
    </transf>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
 <goal name="conservation_previously_marked_multiples&#39;vc" expl="VC for conservation_previously_marked_multiples" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="conservation_previously_marked_multiples&#39;vc.0" expl="assertion" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="67"/></proof>
  </goal>
  <goal name="conservation_previously_marked_multiples&#39;vc.1" expl="assertion" proved="true">
  <proof prover="9"><result status="valid" time="0.030000" steps="92"/></proof>
  </goal>
  <goal name="conservation_previously_marked_multiples&#39;vc.2" expl="assertion" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="conservation_previously_marked_multiples&#39;vc.2.0" expl="assertion" proved="true">
   <proof prover="9"><result status="valid" time="0.020000" steps="32"/></proof>
   </goal>
   <goal name="conservation_previously_marked_multiples&#39;vc.2.1" expl="VC for conservation_previously_marked_multiples" proved="true">
   <proof prover="9"><result status="valid" time="0.080000" steps="234"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="conservation_previously_marked_multiples&#39;vc.3" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="26"/></proof>
  </goal>
  <goal name="conservation_previously_marked_multiples&#39;vc.4" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="28"/></proof>
  </goal>
  <goal name="conservation_previously_marked_multiples&#39;vc.5" expl="assertion" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="conservation_previously_marked_multiples&#39;vc.5.0" expl="assertion" proved="true">
   <proof prover="3"><result status="valid" time="0.593397"/></proof>
   </goal>
   <goal name="conservation_previously_marked_multiples&#39;vc.5.1" expl="VC for conservation_previously_marked_multiples" proved="true">
   <proof prover="9"><result status="valid" time="0.040000" steps="109"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="conservation_previously_marked_multiples&#39;vc.6" expl="assertion" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="conservation_previously_marked_multiples&#39;vc.6.0" expl="assertion" proved="true">
   <transf name="inline_goal" proved="true" >
    <goal name="conservation_previously_marked_multiples&#39;vc.6.0.0" expl="assertion" proved="true">
    <transf name="split_vc" proved="true" >
     <goal name="conservation_previously_marked_multiples&#39;vc.6.0.0.0" expl="assertion" proved="true">
     <proof prover="9"><result status="valid" time="0.020000" steps="30"/></proof>
     </goal>
     <goal name="conservation_previously_marked_multiples&#39;vc.6.0.0.1" expl="assertion" proved="true">
     <proof prover="9"><result status="valid" time="0.020000" steps="30"/></proof>
     </goal>
     <goal name="conservation_previously_marked_multiples&#39;vc.6.0.0.2" expl="assertion" proved="true">
     <proof prover="9"><result status="valid" time="0.020000" steps="38"/></proof>
     </goal>
    </transf>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="conservation_previously_marked_multiples&#39;vc.7" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="73"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="conservation_previously_marked_multiples_on_marked_change" proved="true">
 <transf name="inline_goal" proved="true" >
  <goal name="conservation_previously_marked_multiples_on_marked_change.0" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="conservation_previously_marked_multiples_on_marked_change.0.0" proved="true">
   <transf name="inline_goal" proved="true" >
    <goal name="conservation_previously_marked_multiples_on_marked_change.0.0.0" proved="true">
    <transf name="split_vc" proved="true" >
     <goal name="conservation_previously_marked_multiples_on_marked_change.0.0.0.0" proved="true">
     <proof prover="9"><result status="valid" time="0.010000" steps="12"/></proof>
     </goal>
     <goal name="conservation_previously_marked_multiples_on_marked_change.0.0.0.1" proved="true">
     <proof prover="4"><result status="valid" time="0.130000"/></proof>
     <transf name="remove" proved="true" arg1="zero,one,(-),(&gt;),(&lt;=),(&gt;=),abs,even,odd,divides,prime,([]),singleton,cons,snoc,(++),inv_nexts,all_eliminated_marked,all_eliminated_marked_partial,not_marked_impl_next_not_marked,is_copy,not_marked_impl_next_not_marked_partial,all_primes,previously_marked_multiples,only_multiples_marked,prime_multiples_marked,inv_remove_products,ordered,all_inf_or_eq,Assoc1,Unit_def_l,Unit_def_r,Inv_def_l,Inv_def_r,Comm1,Assoc,Mul_distr_l,Mul_distr_r,Unitary,NonTrivialRing,ZeroLessOne,CompatOrderAdd,CompatOrderMult,Abs_le,Abs_pos,Div_mod,Mod_bound,Div_unique,Div_bound,Mod_1,Div_inf,Mod_0,Div_1_left,Div_minus1_left,Mod_1_left,Mod_minus1_left,Div_mult,Mod_mult,Div_mod1,Div_bound1,Mod_bound1,Div_sign_pos,Div_sign_neg,Mod_sign_pos,Mod_sign_neg,Rounds_toward_zero,Div_11,Mod_11,Div_inf1,Mod_inf,Div_mult1,Mod_mult1,even_or_odd,even_not_odd,odd_not_even,even_odd,odd_even,even_even,odd_odd,even_2k,odd_2k1,even_mod2,divides&#39;spec,divides_1_n,divides_0,divides_left,divides_right,divides_oppr,divides_oppl,divides_plusr,divides_minusr,divides_multl,divides_multr,divides_factorl,divides_factorr,divides_trans,divides_bounds,mod_divides_euclidean,divides_mod_euclidean,mod_divides_computer,divides_mod_computer,even_divides,odd_divides,not_prime_1,prime_2,prime_3,prime_divisors,small_divisors,even_prime,odd_prime,mult_croissance_locale,mult_croissance,comp_mult_2,div_croissance_locale1,div_croissance1,div_croissance_locale2,div_croissance2,div_mult_1,mult_borne_sous_exp,sq_ineq,divides_div,divides_inf,not_prime_divider_limits,no_prod_impl_no_divider,not_prime_impl_divisor_under_sqrt,(==)&#39;spec,create&#39;spec,empty&#39;def,set&#39;def,cons&#39;spec,snoc&#39;spec,([..])&#39;spec,([..])&#39;def,([_..])&#39;def,([.._])&#39;def,(++)&#39;spec,conservation_all_eliminated_marked_on_marked_change,conservation_all_eliminated_marked_on_nexts_change,multiples_of_marked_are_marked,prev_and_new_impl_all_multiples_marked,conservation_only_multiples_marked,conservation_previously_marked_multiples">
      <goal name="conservation_previously_marked_multiples_on_marked_change.0.0.0.1.0" proved="true">
      <proof prover="3"><result status="valid" time="0.040000"/></proof>
      <proof prover="4" timelimit="1"><result status="valid" time="0.185042"/></proof>
      <proof prover="9"><result status="valid" time="0.100000" steps="543"/></proof>
      </goal>
     </transf>
     </goal>
     <goal name="conservation_previously_marked_multiples_on_marked_change.0.0.0.2" proved="true">
     <transf name="inline_all" proved="true" >
      <goal name="conservation_previously_marked_multiples_on_marked_change.0.0.0.2.0" proved="true">
      <proof prover="11"><result status="valid" time="0.164235" steps="595736"/></proof>
      </goal>
     </transf>
     </goal>
    </transf>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
 <goal name="conservation_not_marked_impl_next_not_marked&#39;vc" expl="VC for conservation_not_marked_impl_next_not_marked" proved="true">
 <proof prover="9"><result status="valid" time="0.330000" steps="430"/></proof>
 </goal>
 <goal name="unchanged_other_elements&#39;vc" expl="VC for unchanged_other_elements" proved="true">
 <proof prover="9"><result status="valid" time="0.030000" steps="67"/></proof>
 </goal>
 <goal name="t&#39;vc" expl="VC for t" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="t&#39;vc.0" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.010000" steps="10"/></proof>
  </goal>
  <goal name="t&#39;vc.1" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.010000" steps="12"/></proof>
  </goal>
  <goal name="t&#39;vc.2" expl="type invariant" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="14"/></proof>
  </goal>
  <goal name="t&#39;vc.3" expl="type invariant" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="47"/></proof>
  </goal>
  <goal name="t&#39;vc.4" expl="type invariant" proved="true">
  <proof prover="9"><result status="valid" time="0.030000" steps="161"/></proof>
  </goal>
  <goal name="t&#39;vc.5" expl="type invariant" proved="true">
  <proof prover="9"><result status="valid" time="0.040000" steps="222"/></proof>
  </goal>
  <goal name="t&#39;vc.6" expl="type invariant" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="28"/></proof>
  </goal>
  <goal name="t&#39;vc.7" expl="type invariant" proved="true">
  <proof prover="9"><result status="valid" time="0.010000" steps="26"/></proof>
  </goal>
  <goal name="t&#39;vc.8" expl="type invariant" proved="true">
  <proof prover="9"><result status="valid" time="0.030000" steps="267"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="remove_products&#39;vc" expl="VC for remove_products" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="remove_products&#39;vc.0" expl="division by zero" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="25"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.1" expl="integer overflow" proved="true">
  <proof prover="9"><result status="valid" time="0.040000" steps="130"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.2" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="61"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.3" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="63"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.4" expl="assertion" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="remove_products&#39;vc.4.0" expl="assertion" proved="true">
   <proof prover="9"><result status="valid" time="0.030000" steps="74"/></proof>
   </goal>
   <goal name="remove_products&#39;vc.4.1" expl="VC for remove_products" proved="true">
   <proof prover="9"><result status="valid" time="0.080000" steps="78"/></proof>
   </goal>
   <goal name="remove_products&#39;vc.4.2" expl="VC for remove_products" proved="true">
   <proof prover="9"><result status="valid" time="0.310000" steps="452"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="remove_products&#39;vc.5" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.080000" steps="206"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.6" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.030000" steps="83"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.7" expl="integer overflow" proved="true">
  <proof prover="9"><result status="valid" time="0.080000" steps="82"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.8" expl="precondition" proved="true">
  <proof prover="5"><result status="valid" time="0.210000" steps="46096"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.9" expl="precondition" proved="true">
  <transf name="assert" proved="true" arg1="(mod (int63&#39;int n) 2 = 1)">
   <goal name="remove_products&#39;vc.9.0" expl="asserted formula" proved="true">
   <proof prover="9"><result status="valid" time="0.340913" steps="342"/></proof>
   </goal>
   <goal name="remove_products&#39;vc.9.1" expl="precondition" proved="true">
   <proof prover="9"><result status="valid" time="0.040000" steps="86"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="remove_products&#39;vc.10" expl="precondition" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="remove_products&#39;vc.10.0" expl="precondition" proved="true">
   <proof prover="9"><result status="valid" time="0.030000" steps="86"/></proof>
   </goal>
   <goal name="remove_products&#39;vc.10.1" expl="precondition" proved="true">
   <proof prover="9"><result status="valid" time="0.110000" steps="90"/></proof>
   </goal>
   <goal name="remove_products&#39;vc.10.2" expl="precondition" proved="true">
   <proof prover="9"><result status="valid" time="0.110000" steps="90"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="remove_products&#39;vc.11" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.030000" steps="91"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.12" expl="assertion" proved="true">
  <transf name="inline_goal" proved="true" >
   <goal name="remove_products&#39;vc.12.0" expl="assertion" proved="true">
   <transf name="split_vc" proved="true" >
    <goal name="remove_products&#39;vc.12.0.0" expl="assertion" proved="true">
    <proof prover="9"><result status="valid" time="0.030000" steps="86"/></proof>
    </goal>
    <goal name="remove_products&#39;vc.12.0.1" expl="assertion" proved="true">
    <proof prover="9"><result status="valid" time="0.030000" steps="86"/></proof>
    </goal>
    <goal name="remove_products&#39;vc.12.0.2" expl="assertion" proved="true">
    <proof prover="9"><result status="valid" time="0.120000" steps="92"/></proof>
    </goal>
    <goal name="remove_products&#39;vc.12.0.3" expl="assertion" proved="true">
    <proof prover="9"><result status="valid" time="0.030000" steps="86"/></proof>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="remove_products&#39;vc.13" expl="assertion" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="remove_products&#39;vc.13.0" expl="assertion" proved="true">
   <proof prover="9"><result status="valid" time="0.030000" steps="91"/></proof>
   </goal>
   <goal name="remove_products&#39;vc.13.1" expl="assertion" proved="true">
   <proof prover="9"><result status="valid" time="0.130000" steps="95"/></proof>
   </goal>
   <goal name="remove_products&#39;vc.13.2" expl="VC for remove_products" proved="true">
   <proof prover="9"><result status="valid" time="0.240000" steps="403"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="remove_products&#39;vc.14" expl="assertion" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="remove_products&#39;vc.14.0" expl="assertion" proved="true">
   <proof prover="9"><result status="valid" time="0.030000" steps="93"/></proof>
   </goal>
   <goal name="remove_products&#39;vc.14.1" expl="assertion" proved="true">
   <proof prover="9"><result status="valid" time="0.030000" steps="93"/></proof>
   </goal>
   <goal name="remove_products&#39;vc.14.2" expl="assertion" proved="true">
   <proof prover="9"><result status="valid" time="0.140000" steps="97"/></proof>
   </goal>
   <goal name="remove_products&#39;vc.14.3" expl="VC for remove_products" proved="true">
   <proof prover="9"><result status="valid" time="1.547595" steps="437"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="remove_products&#39;vc.15" expl="assertion" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="remove_products&#39;vc.15.0" expl="assertion" proved="true">
   <transf name="inline_goal" proved="true" >
    <goal name="remove_products&#39;vc.15.0.0" expl="assertion" proved="true">
    <transf name="split_vc" proved="true" >
     <goal name="remove_products&#39;vc.15.0.0.0" expl="assertion" proved="true">
     <proof prover="9"><result status="valid" time="0.120000" steps="99"/></proof>
     </goal>
     <goal name="remove_products&#39;vc.15.0.0.1" expl="assertion" proved="true">
     <proof prover="9"><result status="valid" time="0.030000" steps="95"/></proof>
     </goal>
     <goal name="remove_products&#39;vc.15.0.0.2" expl="assertion" proved="true">
     <proof prover="9"><result status="valid" time="0.130000" steps="99"/></proof>
     </goal>
     <goal name="remove_products&#39;vc.15.0.0.3" expl="assertion" proved="true">
     <proof prover="9"><result status="valid" time="0.857071" steps="444"/></proof>
     </goal>
    </transf>
    </goal>
   </transf>
   </goal>
   <goal name="remove_products&#39;vc.15.1" expl="VC for remove_products" proved="true">
   <proof prover="0"><result status="valid" time="1.360000" steps="762"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="remove_products&#39;vc.16" expl="assertion" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="remove_products&#39;vc.16.0" expl="assertion" proved="true">
   <proof prover="10" timelimit="10"><result status="valid" time="9.500217" steps="604618"/></proof>
   </goal>
   <goal name="remove_products&#39;vc.16.1" expl="VC for remove_products" proved="true">
   <proof prover="9"><result status="valid" time="0.640000" steps="437"/></proof>
   <proof prover="10"><result status="valid" time="0.340000" steps="75215"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="remove_products&#39;vc.17" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.030000" steps="97"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.18" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.040000" steps="98"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.19" expl="assertion" proved="true">
  <proof prover="9"><result status="valid" time="0.120000" steps="103"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.20" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.030000" steps="101"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.21" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.040000" steps="102"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.22" expl="precondition" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="remove_products&#39;vc.22.0" expl="precondition" proved="true">
   <proof prover="9"><result status="valid" time="0.040000" steps="107"/></proof>
   </goal>
   <goal name="remove_products&#39;vc.22.1" expl="precondition" proved="true">
   <proof prover="10" timelimit="1"><result status="valid" time="0.180000" steps="41411"/></proof>
   </goal>
   <goal name="remove_products&#39;vc.22.2" expl="precondition" proved="true">
   <proof prover="10" timelimit="1"><result status="valid" time="0.450000" steps="75069"/></proof>
   </goal>
   <goal name="remove_products&#39;vc.22.3" expl="precondition" proved="true">
   <proof prover="9"><result status="valid" time="0.040000" steps="107"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="remove_products&#39;vc.23" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.040000" steps="111"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.24" expl="precondition" proved="true">
  <proof prover="8"><result status="valid" time="1.012360"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.25" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.040000" steps="111"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.26" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.040000" steps="111"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.27" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.170000" steps="301"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.28" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.040000" steps="118"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.29" expl="assertion" proved="true">
  <transf name="inline_goal" proved="true" >
   <goal name="remove_products&#39;vc.29.0" expl="assertion" proved="true">
   <transf name="split_vc" proved="true" >
    <goal name="remove_products&#39;vc.29.0.0" expl="assertion" proved="true">
    <proof prover="9"><result status="valid" time="0.040000" steps="113"/></proof>
    </goal>
    <goal name="remove_products&#39;vc.29.0.1" expl="assertion" proved="true">
    <proof prover="9"><result status="valid" time="0.040000" steps="113"/></proof>
    </goal>
    <goal name="remove_products&#39;vc.29.0.2" expl="assertion" proved="true">
    <proof prover="9"><result status="valid" time="0.704228" steps="627"/></proof>
    </goal>
    <goal name="remove_products&#39;vc.29.0.3" expl="VC for remove_products" proved="true">
    <proof prover="9"><result status="valid" time="0.150000" steps="119"/></proof>
    </goal>
    <goal name="remove_products&#39;vc.29.0.4" expl="VC for remove_products" proved="true">
    <transf name="case" proved="true" arg1="(j &lt; x)">
     <goal name="remove_products&#39;vc.29.0.4.0" expl="true case" proved="true">
     <proof prover="9"><result status="valid" time="0.040000" steps="122"/></proof>
     </goal>
     <goal name="remove_products&#39;vc.29.0.4.1" expl="false case" proved="true">
     <transf name="unfold" proved="true" arg1="all_eliminated_marked_partial" arg2="in" arg3="Requires4">
      <goal name="remove_products&#39;vc.29.0.4.1.0" expl="false case" proved="true">
      <proof prover="10" timelimit="10"><result status="valid" time="8.078439" steps="575085"/></proof>
      </goal>
     </transf>
     </goal>
    </transf>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="remove_products&#39;vc.30" expl="variant decrease" proved="true">
  <proof prover="10"><result status="valid" time="0.460000" steps="81687"/></proof>
  <proof prover="11"><result status="valid" time="0.110000" steps="373940"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.31" expl="precondition" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="remove_products&#39;vc.31.0" expl="precondition" proved="true">
   <proof prover="9"><result status="valid" time="0.040000" steps="115"/></proof>
   </goal>
   <goal name="remove_products&#39;vc.31.1" expl="precondition" proved="true">
   <proof prover="9"><result status="valid" time="0.040000" steps="115"/></proof>
   </goal>
   <goal name="remove_products&#39;vc.31.2" expl="precondition" proved="true">
   <proof prover="9"><result status="valid" time="0.040000" steps="115"/></proof>
   </goal>
   <goal name="remove_products&#39;vc.31.3" expl="precondition" proved="true">
   <proof prover="9"><result status="valid" time="0.040000" steps="115"/></proof>
   </goal>
   <goal name="remove_products&#39;vc.31.4" expl="precondition" proved="true">
   <proof prover="9"><result status="valid" time="0.040000" steps="115"/></proof>
   </goal>
   <goal name="remove_products&#39;vc.31.5" expl="precondition" proved="true">
   <proof prover="9"><result status="valid" time="0.040000" steps="115"/></proof>
   </goal>
   <goal name="remove_products&#39;vc.31.6" expl="precondition" proved="true">
   <proof prover="10"><result status="valid" time="0.527248" steps="82794"/></proof>
   <proof prover="11"><result status="valid" time="0.120000" steps="373778"/></proof>
   </goal>
   <goal name="remove_products&#39;vc.31.7" expl="precondition" proved="true">
   <proof prover="10"><result status="valid" time="0.280000" steps="60804"/></proof>
   <proof prover="11"><result status="valid" time="0.120000" steps="414140"/></proof>
   </goal>
   <goal name="remove_products&#39;vc.31.8" expl="precondition" proved="true">
   <proof prover="10" timelimit="1"><result status="valid" time="0.270000" steps="60411"/></proof>
   <proof prover="12"><result status="valid" time="0.551355" steps="50746"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="remove_products&#39;vc.32" expl="precondition" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="remove_products&#39;vc.32.0" expl="precondition" proved="true">
   <transf name="inline_goal" proved="true" >
    <goal name="remove_products&#39;vc.32.0.0" expl="precondition" proved="true">
    <transf name="split_all_full" proved="true" >
     <goal name="remove_products&#39;vc.32.0.0.0" expl="VC for remove_products" proved="true">
     <proof prover="9"><result status="valid" time="0.160000" steps="125"/></proof>
     </goal>
     <goal name="remove_products&#39;vc.32.0.0.1" expl="VC for remove_products" proved="true">
     <proof prover="9"><result status="valid" time="0.420000" steps="599"/></proof>
     </goal>
     <goal name="remove_products&#39;vc.32.0.0.2" expl="VC for remove_products" proved="true">
     <transf name="unfold" proved="true" arg1="inv_remove_products" arg2="in" arg3="Requires8">
      <goal name="remove_products&#39;vc.32.0.0.2.0" expl="VC for remove_products" proved="true">
      <transf name="split_premise_right" proved="true" >
       <goal name="remove_products&#39;vc.32.0.0.2.0.0" expl="VC for remove_products" proved="true">
       <transf name="inline_goal" proved="true" >
        <goal name="remove_products&#39;vc.32.0.0.2.0.0.0" expl="VC for remove_products" proved="true">
        <transf name="unfold" proved="true" arg1="all_primes" arg2="in" arg3="Requires11">
         <goal name="remove_products&#39;vc.32.0.0.2.0.0.0.0" expl="VC for remove_products" proved="true">
         <transf name="split_vc" proved="true" >
          <goal name="remove_products&#39;vc.32.0.0.2.0.0.0.0.0" expl="VC for remove_products" proved="true">
          <transf name="instantiate" proved="true" arg1="Requires11" arg2="i">
           <goal name="remove_products&#39;vc.32.0.0.2.0.0.0.0.0.0" expl="VC for remove_products" proved="true">
           <proof prover="9"><result status="valid" time="0.560000" steps="643"/></proof>
           </goal>
          </transf>
          </goal>
          <goal name="remove_products&#39;vc.32.0.0.2.0.0.0.0.1" expl="VC for remove_products" proved="true">
          <transf name="instantiate" proved="true" arg1="Requires11" arg2="i">
           <goal name="remove_products&#39;vc.32.0.0.2.0.0.0.0.1.0" expl="VC for remove_products" proved="true">
           <proof prover="9"><result status="valid" time="0.560000" steps="660"/></proof>
           </goal>
          </transf>
          </goal>
         </transf>
         </goal>
        </transf>
        </goal>
       </transf>
       </goal>
      </transf>
      </goal>
     </transf>
     </goal>
     <goal name="remove_products&#39;vc.32.0.0.3" expl="VC for remove_products" proved="true">
     <proof prover="9"><result status="valid" time="0.160000" steps="125"/></proof>
     </goal>
     <goal name="remove_products&#39;vc.32.0.0.4" expl="VC for remove_products" proved="true">
     <proof prover="9"><result status="valid" time="0.400000" steps="611"/></proof>
     </goal>
     <goal name="remove_products&#39;vc.32.0.0.5" expl="VC for remove_products" proved="true">
     <proof prover="9"><result status="valid" time="0.160000" steps="125"/></proof>
     </goal>
    </transf>
    </goal>
   </transf>
   </goal>
   <goal name="remove_products&#39;vc.32.1" expl="precondition" proved="true">
   <proof prover="5"><result status="valid" time="0.100000" steps="33851"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="remove_products&#39;vc.33" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.920000" steps="505"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.34" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.050000" steps="126"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.35" expl="precondition" proved="true">
  <proof prover="10"><result status="valid" time="0.290000" steps="61872"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.36" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.050000" steps="129"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.37" expl="precondition" proved="true">
  <transf name="inline_goal" proved="true" >
   <goal name="remove_products&#39;vc.37.0" expl="precondition" proved="true">
   <transf name="split_vc" proved="true" >
    <goal name="remove_products&#39;vc.37.0.0" expl="precondition" proved="true">
    <proof prover="9"><result status="valid" time="0.160000" steps="133"/></proof>
    </goal>
    <goal name="remove_products&#39;vc.37.0.1" expl="precondition" proved="true">
    <proof prover="9"><result status="valid" time="0.160000" steps="133"/></proof>
    </goal>
    <goal name="remove_products&#39;vc.37.0.2" expl="precondition" proved="true">
    <proof prover="9"><result status="valid" time="0.040000" steps="129"/></proof>
    </goal>
    <goal name="remove_products&#39;vc.37.0.3" expl="precondition" proved="true">
    <transf name="case" proved="true" arg1="(i = p)">
     <goal name="remove_products&#39;vc.37.0.3.0" expl="true case (precondition)" proved="true">
     <transf name="remove" proved="true" arg1="H24,H23,H22">
      <goal name="remove_products&#39;vc.37.0.3.0.0" expl="true case (precondition)" proved="true">
      <proof prover="9"><result status="valid" time="2.714563" steps="703"/></proof>
      </goal>
     </transf>
     </goal>
     <goal name="remove_products&#39;vc.37.0.3.1" expl="false case (precondition)" proved="true">
     <transf name="assert" proved="true" arg1="(forall i. 0 &lt;= i &lt; div (length marked_old - 1) n -&gt; i &lt;&gt; p -&gt; (nexts t)[i] = (nexts t1)[i])">
      <goal name="remove_products&#39;vc.37.0.3.1.0" expl="asserted formula" proved="true">
      <proof prover="9"><result status="valid" time="0.200000" steps="149"/></proof>
      </goal>
      <goal name="remove_products&#39;vc.37.0.3.1.1" expl="false case (precondition)" proved="true">
      <transf name="inline_all" proved="true" >
       <goal name="remove_products&#39;vc.37.0.3.1.1.0" expl="false case (precondition)" proved="true">
       <proof prover="2"><result status="valid" time="0.112585" steps="348188"/></proof>
       </goal>
      </transf>
      </goal>
     </transf>
     </goal>
    </transf>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="remove_products&#39;vc.38" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.390000" steps="639"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.39" expl="precondition" proved="true">
  <transf name="inline_goal" proved="true" >
   <goal name="remove_products&#39;vc.39.0" expl="precondition" proved="true">
   <transf name="split_vc" proved="true" >
    <goal name="remove_products&#39;vc.39.0.0" expl="precondition" proved="true">
    <proof prover="9"><result status="valid" time="0.160000" steps="137"/></proof>
    </goal>
    <goal name="remove_products&#39;vc.39.0.1" expl="precondition" proved="true">
    <proof prover="9"><result status="valid" time="0.170000" steps="137"/></proof>
    </goal>
    <goal name="remove_products&#39;vc.39.0.2" expl="precondition" proved="true">
    <proof prover="9"><result status="valid" time="0.040000" steps="133"/></proof>
    </goal>
    <goal name="remove_products&#39;vc.39.0.3" expl="precondition" proved="true">
    <proof prover="9"><result status="valid" time="0.190000" steps="137"/></proof>
    </goal>
    <goal name="remove_products&#39;vc.39.0.4" expl="precondition" proved="true">
    <transf name="unfold" proved="true" arg1="not_marked_impl_next_not_marked_partial" arg2="in" arg3="Requires8">
     <goal name="remove_products&#39;vc.39.0.4.0" expl="precondition" proved="true">
     <transf name="split_premise_right" proved="true" >
      <goal name="remove_products&#39;vc.39.0.4.0.0" expl="precondition" proved="true">
      <transf name="instantiate" proved="true" arg1="Requires8" arg2="i">
       <goal name="remove_products&#39;vc.39.0.4.0.0.0" expl="precondition" proved="true">
       <proof prover="10"><result status="valid" time="0.640000" steps="98438"/></proof>
       </goal>
      </transf>
      </goal>
     </transf>
     </goal>
    </transf>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="remove_products&#39;vc.40" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.050000" steps="135"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.41" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.040000" steps="129"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.42" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.040000" steps="129"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.43" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.040000" steps="129"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.44" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.040000" steps="129"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.45" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.040000" steps="129"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.46" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.040000" steps="129"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.47" expl="assertion" proved="true">
  <proof prover="10"><result status="valid" time="0.860000" steps="112597"/></proof>
  <proof prover="11"><result status="valid" time="0.090000" steps="291869"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.48" expl="variant decrease" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="remove_products&#39;vc.48.0" expl="variant decrease" proved="true">
   <proof prover="9"><result status="valid" time="0.030000" steps="99"/></proof>
   </goal>
   <goal name="remove_products&#39;vc.48.1" expl="variant decrease" proved="true">
   <proof prover="10"><result status="valid" time="0.427149" steps="73933"/></proof>
   <proof prover="11"><result status="valid" time="0.100000" steps="291163"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="remove_products&#39;vc.49" expl="precondition" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="remove_products&#39;vc.49.0" expl="precondition" proved="true">
   <proof prover="9"><result status="valid" time="0.030000" steps="99"/></proof>
   </goal>
   <goal name="remove_products&#39;vc.49.1" expl="precondition" proved="true">
   <proof prover="9"><result status="valid" time="0.030000" steps="99"/></proof>
   </goal>
   <goal name="remove_products&#39;vc.49.2" expl="precondition" proved="true">
   <proof prover="9"><result status="valid" time="0.040000" steps="99"/></proof>
   </goal>
   <goal name="remove_products&#39;vc.49.3" expl="precondition" proved="true">
   <proof prover="9"><result status="valid" time="0.040000" steps="99"/></proof>
   </goal>
   <goal name="remove_products&#39;vc.49.4" expl="precondition" proved="true">
   <proof prover="9"><result status="valid" time="0.030000" steps="99"/></proof>
   </goal>
   <goal name="remove_products&#39;vc.49.5" expl="precondition" proved="true">
   <proof prover="9"><result status="valid" time="0.030000" steps="99"/></proof>
   </goal>
   <goal name="remove_products&#39;vc.49.6" expl="precondition" proved="true">
   <proof prover="10"><result status="valid" time="0.407911" steps="73923"/></proof>
   <proof prover="11"><result status="valid" time="0.080000" steps="247473"/></proof>
   </goal>
   <goal name="remove_products&#39;vc.49.7" expl="precondition" proved="true">
   <proof prover="9"><result status="valid" time="0.030000" steps="99"/></proof>
   </goal>
   <goal name="remove_products&#39;vc.49.8" expl="precondition" proved="true">
   <proof prover="10"><result status="valid" time="0.377999" steps="55746"/></proof>
   <proof prover="12"><result status="valid" time="0.459106" steps="47037"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="remove_products&#39;vc.50" expl="precondition" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="remove_products&#39;vc.50.0" expl="precondition" proved="true">
   <transf name="inline_goal" proved="true" >
    <goal name="remove_products&#39;vc.50.0.0" expl="precondition" proved="true">
    <transf name="split_all_full" proved="true" >
     <goal name="remove_products&#39;vc.50.0.0.0" expl="VC for remove_products" proved="true">
     <proof prover="9"><result status="valid" time="0.130000" steps="110"/></proof>
     </goal>
     <goal name="remove_products&#39;vc.50.0.0.1" expl="VC for remove_products" proved="true">
     <proof prover="9"><result status="valid" time="0.290000" steps="432"/></proof>
     </goal>
     <goal name="remove_products&#39;vc.50.0.0.2" expl="VC for remove_products" proved="true">
     <transf name="unfold" proved="true" arg1="inv_remove_products" arg2="in" arg3="Requires8">
      <goal name="remove_products&#39;vc.50.0.0.2.0" expl="VC for remove_products" proved="true">
      <transf name="split_premise_right" proved="true" >
       <goal name="remove_products&#39;vc.50.0.0.2.0.0" expl="VC for remove_products" proved="true">
       <transf name="inline_goal" proved="true" >
        <goal name="remove_products&#39;vc.50.0.0.2.0.0.0" expl="VC for remove_products" proved="true">
        <transf name="unfold" proved="true" arg1="all_primes" arg2="in" arg3="Requires11">
         <goal name="remove_products&#39;vc.50.0.0.2.0.0.0.0" expl="VC for remove_products" proved="true">
         <transf name="split_vc" proved="true" >
          <goal name="remove_products&#39;vc.50.0.0.2.0.0.0.0.0" expl="VC for remove_products" proved="true">
          <transf name="instantiate" proved="true" arg1="Requires11" arg2="i">
           <goal name="remove_products&#39;vc.50.0.0.2.0.0.0.0.0.0" expl="VC for remove_products" proved="true">
           <proof prover="9"><result status="valid" time="0.360000" steps="470"/></proof>
           </goal>
          </transf>
          </goal>
          <goal name="remove_products&#39;vc.50.0.0.2.0.0.0.0.1" expl="VC for remove_products" proved="true">
          <transf name="instantiate" proved="true" arg1="Requires11" arg2="i">
           <goal name="remove_products&#39;vc.50.0.0.2.0.0.0.0.1.0" expl="VC for remove_products" proved="true">
           <proof prover="9"><result status="valid" time="0.340000" steps="464"/></proof>
           </goal>
          </transf>
          </goal>
         </transf>
         </goal>
        </transf>
        </goal>
       </transf>
       </goal>
      </transf>
      </goal>
     </transf>
     </goal>
     <goal name="remove_products&#39;vc.50.0.0.3" expl="VC for remove_products" proved="true">
     <proof prover="9"><result status="valid" time="0.140000" steps="110"/></proof>
     </goal>
     <goal name="remove_products&#39;vc.50.0.0.4" expl="VC for remove_products" proved="true">
     <proof prover="9"><result status="valid" time="0.270000" steps="421"/></proof>
     </goal>
     <goal name="remove_products&#39;vc.50.0.0.5" expl="VC for remove_products" proved="true">
     <proof prover="9"><result status="valid" time="0.130000" steps="110"/></proof>
     </goal>
    </transf>
    </goal>
   </transf>
   </goal>
   <goal name="remove_products&#39;vc.50.1" expl="precondition" proved="true">
   <proof prover="5"><result status="valid" time="0.080000" steps="32075"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="remove_products&#39;vc.51" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.640000" steps="457"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.52" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.040000" steps="113"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.53" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.775794" steps="467"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.54" expl="precondition" proved="true">
  <proof prover="11"><result status="valid" time="0.100000" steps="325529"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.55" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.040000" steps="117"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.56" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.040000" steps="118"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.57" expl="precondition" proved="true">
  <transf name="inline_goal" proved="true" >
   <goal name="remove_products&#39;vc.57.0" expl="precondition" proved="true">
   <transf name="split_vc" proved="true" >
    <goal name="remove_products&#39;vc.57.0.0" expl="precondition" proved="true">
    <proof prover="9"><result status="valid" time="0.140000" steps="120"/></proof>
    </goal>
    <goal name="remove_products&#39;vc.57.0.1" expl="precondition" proved="true">
    <proof prover="9"><result status="valid" time="0.140000" steps="120"/></proof>
    </goal>
    <goal name="remove_products&#39;vc.57.0.2" expl="precondition" proved="true">
    <proof prover="9"><result status="valid" time="0.040000" steps="118"/></proof>
    </goal>
    <goal name="remove_products&#39;vc.57.0.3" expl="precondition" proved="true">
    <proof prover="9"><result status="valid" time="0.170000" steps="120"/></proof>
    </goal>
    <goal name="remove_products&#39;vc.57.0.4" expl="precondition" proved="true">
    <transf name="unfold" proved="true" arg1="not_marked_impl_next_not_marked_partial" arg2="in" arg3="Requires8">
     <goal name="remove_products&#39;vc.57.0.4.0" expl="precondition" proved="true">
     <transf name="split_premise_right" proved="true" >
      <goal name="remove_products&#39;vc.57.0.4.0.0" expl="precondition" proved="true">
      <transf name="instantiate" proved="true" arg1="Requires8" arg2="i">
       <goal name="remove_products&#39;vc.57.0.4.0.0.0" expl="precondition" proved="true">
       <proof prover="10"><result status="valid" time="0.520000" steps="88088"/></proof>
       </goal>
      </transf>
      </goal>
     </transf>
     </goal>
    </transf>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="remove_products&#39;vc.58" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.040000" steps="120"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.59" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.040000" steps="113"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.60" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.040000" steps="113"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.61" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.030000" steps="113"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.62" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.040000" steps="113"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.63" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.030000" steps="113"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.64" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.030000" steps="113"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.65" expl="assertion" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="remove_products&#39;vc.65.0" expl="assertion" proved="true">
   <proof prover="9"><result status="valid" time="0.030000" steps="74"/></proof>
   </goal>
   <goal name="remove_products&#39;vc.65.1" expl="VC for remove_products" proved="true">
   <proof prover="11"><result status="valid" time="0.080000" steps="212456"/></proof>
   </goal>
   <goal name="remove_products&#39;vc.65.2" expl="VC for remove_products" proved="true">
   <proof prover="9"><result status="valid" time="0.612364" steps="538"/></proof>
   </goal>
   <goal name="remove_products&#39;vc.65.3" expl="VC for remove_products" proved="true">
   <proof prover="9"><result status="valid" time="0.120000" steps="291"/></proof>
   </goal>
   <goal name="remove_products&#39;vc.65.4" expl="VC for remove_products" proved="true">
   <proof prover="9"><result status="valid" time="0.100000" steps="84"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="remove_products&#39;vc.66" expl="precondition" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="remove_products&#39;vc.66.0" expl="precondition" proved="true">
   <proof prover="10"><result status="valid" time="0.240000" steps="59682"/></proof>
   <proof prover="12"><result status="valid" time="0.618215" steps="49746"/></proof>
   </goal>
   <goal name="remove_products&#39;vc.66.1" expl="precondition" proved="true">
   <proof prover="9"><result status="valid" time="0.030000" steps="80"/></proof>
   </goal>
   <goal name="remove_products&#39;vc.66.2" expl="VC for remove_products" proved="true">
   <transf name="split_vc" proved="true" >
    <goal name="remove_products&#39;vc.66.2.0" expl="VC for remove_products" proved="true">
    <transf name="split_vc" proved="true" >
     <goal name="remove_products&#39;vc.66.2.0.0" expl="VC for remove_products" proved="true">
     <proof prover="7"><result status="valid" time="0.513681" steps="5233"/></proof>
     </goal>
    </transf>
    </goal>
    <goal name="remove_products&#39;vc.66.2.1" expl="VC for remove_products" proved="true">
    <proof prover="10" timelimit="1"><result status="valid" time="0.150000" steps="37064"/></proof>
    </goal>
   </transf>
   </goal>
   <goal name="remove_products&#39;vc.66.3" expl="VC for remove_products" proved="true">
   <proof prover="10"><result status="valid" time="0.307326" steps="61707"/></proof>
   <proof prover="11"><result status="valid" time="0.070000" steps="224418"/></proof>
   </goal>
   <goal name="remove_products&#39;vc.66.4" expl="VC for remove_products" proved="true">
   <proof prover="9"><result status="valid" time="0.030000" steps="76"/></proof>
   </goal>
   <goal name="remove_products&#39;vc.66.5" expl="VC for remove_products" proved="true">
   <proof prover="11"><result status="valid" time="0.090000" steps="266243"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="remove_products&#39;vc.67" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.030000" steps="78"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.68" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="78"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.69" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.030000" steps="78"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.70" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="78"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.71" expl="postcondition" proved="true">
  <transf name="inline_goal" proved="true" >
   <goal name="remove_products&#39;vc.71.0" expl="postcondition" proved="true">
   <transf name="split_vc" proved="true" >
    <goal name="remove_products&#39;vc.71.0.0" expl="postcondition" proved="true">
    <proof prover="9"><result status="valid" time="0.060000" steps="82"/></proof>
    </goal>
    <goal name="remove_products&#39;vc.71.0.1" expl="postcondition" proved="true">
    <proof prover="9"><result status="valid" time="0.070000" steps="82"/></proof>
    </goal>
    <goal name="remove_products&#39;vc.71.0.2" expl="postcondition" proved="true">
    <proof prover="9"><result status="valid" time="0.030000" steps="78"/></proof>
    </goal>
    <goal name="remove_products&#39;vc.71.0.3" expl="postcondition" proved="true">
    <transf name="unfold" proved="true" arg1="prime_multiples_marked" arg2="in" arg3="Requires2">
     <goal name="remove_products&#39;vc.71.0.3.0" expl="postcondition" proved="true">
     <transf name="split_all_right" proved="true" >
      <goal name="remove_products&#39;vc.71.0.3.0.0" expl="postcondition" proved="true">
      <transf name="case" proved="true" arg1="(i &lt; (nexts t)[x])">
       <goal name="remove_products&#39;vc.71.0.3.0.0.0" expl="true case (postcondition)" proved="true">
       <proof prover="9"><result status="valid" time="0.080000" steps="96"/></proof>
       </goal>
       <goal name="remove_products&#39;vc.71.0.3.0.0.1" expl="false case (postcondition)" proved="true">
       <proof prover="9"><result status="valid" time="0.160000" steps="321"/></proof>
       </goal>
      </transf>
      </goal>
     </transf>
     </goal>
    </transf>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="remove_products&#39;vc.72" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.030000" steps="80"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.73" expl="precondition" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="remove_products&#39;vc.73.0" expl="precondition" proved="true">
   <proof prover="10"><result status="valid" time="0.406438" steps="58372"/></proof>
   <proof prover="12"><result status="valid" time="0.522483" steps="51373"/></proof>
   </goal>
   <goal name="remove_products&#39;vc.73.1" expl="precondition" proved="true">
   <proof prover="9"><result status="valid" time="0.030000" steps="78"/></proof>
   </goal>
   <goal name="remove_products&#39;vc.73.2" expl="VC for remove_products" proved="true">
   <proof prover="6"><result status="valid" time="2.000000" steps="23393"/></proof>
   </goal>
   <goal name="remove_products&#39;vc.73.3" expl="VC for remove_products" proved="true">
   <proof prover="10"><result status="valid" time="0.430812" steps="60739"/></proof>
   <proof prover="11"><result status="valid" time="0.080000" steps="220233"/></proof>
   </goal>
   <goal name="remove_products&#39;vc.73.4" expl="VC for remove_products" proved="true">
   <proof prover="9"><result status="valid" time="0.020000" steps="74"/></proof>
   </goal>
   <goal name="remove_products&#39;vc.73.5" expl="VC for remove_products" proved="true">
   <proof prover="11"><result status="valid" time="0.090000" steps="257420"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="remove_products&#39;vc.74" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="76"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.75" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="76"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.76" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.030000" steps="76"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.77" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.030000" steps="76"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.78" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.060000" steps="79"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.79" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.030000" steps="78"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.80" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.030000" steps="86"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.81" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.040000" steps="79"/></proof>
  <transf name="remove" proved="true" arg1="zero1,one1,(-),(&gt;),(&lt;=),(&gt;=),abs,int63&#39;maxInt,int63&#39;minInt,min_int63,max_int63,to_int,in_bounds,zero,one,even,odd,divides,prime,([]),singleton,cons,snoc,(++),inv_nexts,all_eliminated_marked,all_eliminated_marked_partial,not_marked_impl_next_not_marked,is_copy,not_marked_impl_next_not_marked_partial,all_primes,all_multiples_marked,previously_marked_multiples,prime_multiples_marked,inv_remove_products,ordered,all_inf_or_eq,max,marked_old,Assoc1,Unit_def_l,Unit_def_r,Inv_def_l,Inv_def_r,Comm1,Assoc,Mul_distr_l,Mul_distr_r,Comm,Unitary,NonTrivialRing,Refl,Trans,Antisymm,Total,ZeroLessOne,CompatOrderAdd,CompatOrderMult,Abs_le,Abs_pos,Div_mod,Mod_bound,Div_unique,Div_bound,Mod_1,Div_1,Div_inf,Div_inf_neg,Mod_0,Div_1_left,Div_minus1_left,Mod_1_left,Mod_minus1_left,Div_mult,Mod_mult,Div_mod1,Div_bound1,Mod_bound1,Div_sign_pos,Div_sign_neg,Mod_sign_pos,Mod_sign_neg,Rounds_toward_zero,Div_11,Mod_11,Div_inf1,Mod_inf,Div_mult1,Mod_mult1,to_int_in_bounds,extensionality,max_int&#39;def,min_int&#39;def,even_or_odd,even_not_odd,odd_not_even,even_odd,odd_even,even_even,odd_odd,even_2k,odd_2k1,even_mod2,divides&#39;spec,divides_refl,divides_1_n,divides_0,divides_left,divides_right,divides_oppr,divides_oppl,divides_oppr_rev,divides_oppl_rev,divides_plusr,divides_minusr,divides_multl,divides_multr,divides_factorl,divides_factorr,divides_n_1,divides_antisym,divides_trans,divides_bounds,mod_divides_euclidean,divides_mod_euclidean,mod_divides_computer,divides_mod_computer,even_divides,odd_divides,not_prime_1,prime_2,prime_3,prime_divisors,small_divisors,even_prime,odd_prime,mult_croissance_locale,mult_croissance,comp_mult_2,div_croissance_locale1,div_croissance1,div_croissance_locale2,div_croissance2,div_mult_1,mult_borne_sous_exp,sq_ineq,divides_div,divides_inf,not_prime_divider_limits,no_prod_impl_no_divider,not_prime_impl_divisor_under_sqrt,length_nonnegative,(==)&#39;spec,create&#39;spec,empty&#39;def,set&#39;spec,set&#39;def,([&lt;-])&#39;def,singleton&#39;spec,cons&#39;spec,snoc&#39;spec,([..])&#39;spec,([..])&#39;def,([_..])&#39;def,([.._])&#39;def,(++)&#39;spec,conservation_all_eliminated_marked_on_marked_change,conservation_all_eliminated_marked_on_nexts_change,multiples_of_marked_are_marked,prev_and_new_impl_all_multiples_marked,conservation_only_multiples_marked,conservation_previously_marked_multiples,conservation_previously_marked_multiples_on_marked_change,conservation_not_marked_impl_next_not_marked,unchanged_other_elements,t&#39;invariant,H2,H1,H,Requires4,Requires3,Requires1,Ensures1,Ensures,Requires">
   <goal name="remove_products&#39;vc.81.0" expl="precondition" proved="true">
   <proof prover="0"><result status="valid" time="0.000000" steps="16"/></proof>
   <proof prover="9"><result status="valid" time="0.000000" steps="32"/></proof>
   <proof prover="11"><result status="valid" time="0.020000" steps="35647"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="remove_products&#39;vc.82" expl="integer overflow" proved="true">
  <proof prover="9"><result status="valid" time="0.030000" steps="31"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.83" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="31"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.84" expl="precondition" proved="true">
  <transf name="assert" proved="true" arg1="(mod (int63&#39;int n) 2 = 1)">
   <goal name="remove_products&#39;vc.84.0" expl="asserted formula" proved="true">
   <proof prover="10"><result status="valid" time="0.170000" steps="37352"/></proof>
   <proof prover="11"><result status="valid" time="0.060000" steps="124438"/></proof>
   </goal>
   <goal name="remove_products&#39;vc.84.1" expl="precondition" proved="true">
   <proof prover="9"><result status="valid" time="0.080000" steps="37"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="remove_products&#39;vc.85" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.040000" steps="109"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.86" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="42"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.87" expl="assertion" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="remove_products&#39;vc.87.0" expl="assertion" proved="true">
   <proof prover="9"><result status="valid" time="0.060000" steps="179"/></proof>
   </goal>
   <goal name="remove_products&#39;vc.87.1" expl="assertion" proved="true">
   <proof prover="10"><result status="valid" time="0.370352" steps="53612"/></proof>
   </goal>
   <goal name="remove_products&#39;vc.87.2" expl="VC for remove_products" proved="true">
   <proof prover="10"><result status="valid" time="0.170000" steps="43249"/></proof>
   <proof prover="11"><result status="valid" time="0.070000" steps="177327"/></proof>
   </goal>
   <goal name="remove_products&#39;vc.87.3" expl="VC for remove_products" proved="true">
   <proof prover="9"><result status="valid" time="0.040000" steps="49"/></proof>
   </goal>
   <goal name="remove_products&#39;vc.87.4" expl="VC for remove_products" proved="true">
   <proof prover="9"><result status="valid" time="0.040000" steps="43"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="remove_products&#39;vc.88" expl="precondition" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="remove_products&#39;vc.88.0" expl="precondition" proved="true">
   <proof prover="9"><result status="valid" time="0.020000" steps="37"/></proof>
   </goal>
   <goal name="remove_products&#39;vc.88.1" expl="precondition" proved="true">
   <proof prover="9"><result status="valid" time="0.020000" steps="37"/></proof>
   </goal>
   <goal name="remove_products&#39;vc.88.2" expl="precondition" proved="true">
   <proof prover="9"><result status="valid" time="0.020000" steps="37"/></proof>
   </goal>
   <goal name="remove_products&#39;vc.88.3" expl="precondition" proved="true">
   <proof prover="9"><result status="valid" time="0.020000" steps="37"/></proof>
   </goal>
   <goal name="remove_products&#39;vc.88.4" expl="precondition" proved="true">
   <proof prover="10"><result status="valid" time="0.200000" steps="47209"/></proof>
   <proof prover="11"><result status="valid" time="0.060000" steps="170463"/></proof>
   </goal>
   <goal name="remove_products&#39;vc.88.5" expl="precondition" proved="true">
   <proof prover="9"><result status="valid" time="0.020000" steps="37"/></proof>
   </goal>
   <goal name="remove_products&#39;vc.88.6" expl="precondition" proved="true">
   <proof prover="10"><result status="valid" time="0.240000" steps="53111"/></proof>
   <proof prover="11"><result status="valid" time="0.070000" steps="187279"/></proof>
   </goal>
   <goal name="remove_products&#39;vc.88.7" expl="precondition" proved="true">
   <proof prover="9"><result status="valid" time="0.020000" steps="37"/></proof>
   </goal>
   <goal name="remove_products&#39;vc.88.8" expl="precondition" proved="true">
   <proof prover="11"><result status="valid" time="0.080000" steps="171201"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="remove_products&#39;vc.89" expl="precondition" proved="true">
  <transf name="inline_goal" proved="true" >
   <goal name="remove_products&#39;vc.89.0" expl="precondition" proved="true">
   <transf name="split_vc" proved="true" >
    <goal name="remove_products&#39;vc.89.0.0" expl="precondition" proved="true">
    <proof prover="10"><result status="valid" time="0.180000" steps="44962"/></proof>
    <proof prover="11"><result status="valid" time="0.070000" steps="190360"/></proof>
    </goal>
    <goal name="remove_products&#39;vc.89.0.1" expl="precondition" proved="true">
    <proof prover="11"><result status="valid" time="0.060000" steps="172689"/></proof>
    </goal>
    <goal name="remove_products&#39;vc.89.0.2" expl="precondition" proved="true">
    <transf name="assert" proved="true" arg1="(n * n &gt; n)">
     <goal name="remove_products&#39;vc.89.0.2.0" expl="asserted formula" proved="true">
     <proof prover="11"><result status="valid" time="0.070000" steps="165841"/></proof>
     </goal>
     <goal name="remove_products&#39;vc.89.0.2.1" expl="precondition" proved="true">
     <proof prover="10"><result status="valid" time="0.349603" steps="55658"/></proof>
     </goal>
    </transf>
    </goal>
    <goal name="remove_products&#39;vc.89.0.3" expl="precondition" proved="true">
    <proof prover="10"><result status="valid" time="0.150000" steps="39445"/></proof>
    <proof prover="11"><result status="valid" time="0.060000" steps="165038"/></proof>
    </goal>
    <goal name="remove_products&#39;vc.89.0.4" expl="precondition" proved="true">
    <proof prover="11"><result status="valid" time="0.070000" steps="175279"/></proof>
    </goal>
    <goal name="remove_products&#39;vc.89.0.5" expl="precondition" proved="true">
    <proof prover="10"><result status="valid" time="0.160000" steps="41115"/></proof>
    <proof prover="11"><result status="valid" time="0.060000" steps="174476"/></proof>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="remove_products&#39;vc.90" expl="precondition" proved="true">
  <proof prover="11"><result status="valid" time="0.080000" steps="172897"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.91" expl="precondition" proved="true">
  <proof prover="10"><result status="valid" time="0.140000" steps="39551"/></proof>
  <proof prover="11"><result status="valid" time="0.070000" steps="173407"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.92" expl="precondition" proved="true">
  <proof prover="10"><result status="valid" time="0.220000" steps="48613"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.93" expl="precondition" proved="true">
  <proof prover="8"><result status="valid" time="1.407268"/></proof>
  <transf name="remove" proved="true" arg1="zero1,one1,(-),(&gt;),(&lt;=),(&gt;=),abs,int63&#39;maxInt,int63&#39;minInt,min_int63,max_int63,to_int,in_bounds,zero,one,even,odd,divides,prime,([]),singleton,cons,snoc,(++),inv_nexts,not_marked_impl_next_not_marked,is_copy,not_marked_impl_next_not_marked_partial,all_primes,all_multiples_marked,previously_marked_multiples,only_multiples_marked,prime_multiples_marked,inv_remove_products,ordered,all_inf_or_eq,max,marked_copy,Assoc1,Unit_def_l,Unit_def_r,Inv_def_l,Inv_def_r,Comm1,Assoc,Mul_distr_l,Mul_distr_r,Comm,Unitary,NonTrivialRing,Refl,Trans,Antisymm,Total,ZeroLessOne,CompatOrderAdd,CompatOrderMult,Abs_le,Abs_pos,Div_mod,Mod_bound,Div_unique,Div_bound,Mod_1,Div_1,Div_inf,Div_inf_neg,Mod_0,Div_1_left,Div_minus1_left,Mod_1_left,Mod_minus1_left,Div_mult,Mod_mult,Div_mod1,Div_bound1,Mod_bound1,Div_sign_pos,Div_sign_neg,Mod_sign_pos,Mod_sign_neg,Rounds_toward_zero,Div_11,Mod_11,Div_inf1,Mod_inf,Div_mult1,Mod_mult1,to_int_in_bounds,extensionality,max_int&#39;def,min_int&#39;def,even_or_odd,even_not_odd,odd_not_even,even_odd,odd_even,even_even,odd_odd,even_2k,odd_2k1,even_mod2,divides&#39;spec,divides_refl,divides_1_n,divides_0,divides_left,divides_right,divides_oppr,divides_oppl,divides_oppr_rev,divides_oppl_rev,divides_plusr,divides_minusr,divides_multl,divides_multr,divides_factorl,divides_factorr,divides_n_1,divides_antisym,divides_trans,divides_bounds,mod_divides_euclidean,divides_mod_euclidean,mod_divides_computer,divides_mod_computer,even_divides,odd_divides,not_prime_1,prime_2,prime_3,prime_divisors,small_divisors,even_prime,odd_prime,mult_croissance_locale,mult_croissance,comp_mult_2,div_croissance_locale1,div_croissance1,div_croissance_locale2,div_croissance2,div_mult_1,mult_borne_sous_exp,sq_ineq,divides_div,divides_inf,not_prime_divider_limits,no_prod_impl_no_divider,not_prime_impl_divisor_under_sqrt,length_nonnegative,(==)&#39;spec,create&#39;spec,empty&#39;def,set&#39;spec,set&#39;def,([&lt;-])&#39;def,singleton&#39;spec,cons&#39;spec,snoc&#39;spec,([..])&#39;spec,([..])&#39;def,([_..])&#39;def,([.._])&#39;def,(++)&#39;spec,conservation_all_eliminated_marked_on_marked_change,conservation_all_eliminated_marked_on_nexts_change,multiples_of_marked_are_marked,prev_and_new_impl_all_multiples_marked,conservation_only_multiples_marked,conservation_previously_marked_multiples,conservation_previously_marked_multiples_on_marked_change,conservation_not_marked_impl_next_not_marked,unchanged_other_elements,H4,H3,H2,Requires8,Requires7,Requires6,Requires5,Ensures5,Ensures4,Ensures3,Ensures2,H,Ensures1,Ensures,Assert,Requires3,Requires2,Requires1,Requires">
   <goal name="remove_products&#39;vc.93.0" expl="precondition" proved="true">
   <proof prover="8" timelimit="1"><result status="valid" time="0.020000"/></proof>
   <proof prover="9"><result status="valid" time="0.100000" steps="174"/></proof>
   <proof prover="10"><result status="valid" time="0.060000" steps="9957"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="remove_products&#39;vc.94" expl="precondition" proved="true">
  <transf name="inline_goal" proved="true" >
   <goal name="remove_products&#39;vc.94.0" expl="precondition" proved="true">
   <transf name="split_vc" proved="true" >
    <goal name="remove_products&#39;vc.94.0.0" expl="precondition" proved="true">
    <proof prover="10"><result status="valid" time="0.150000" steps="41569"/></proof>
    <proof prover="11"><result status="valid" time="0.060000" steps="179695"/></proof>
    </goal>
    <goal name="remove_products&#39;vc.94.0.1" expl="precondition" proved="true">
    <proof prover="10"><result status="valid" time="0.180000" steps="44007"/></proof>
    <proof prover="11"><result status="valid" time="0.060000" steps="168899"/></proof>
    </goal>
    <goal name="remove_products&#39;vc.94.0.2" expl="precondition" proved="true">
    <proof prover="9"><result status="valid" time="0.020000" steps="54"/></proof>
    <proof prover="10"><result status="valid" time="0.150000" steps="39545"/></proof>
    </goal>
    <goal name="remove_products&#39;vc.94.0.3" expl="precondition" proved="true">
    <proof prover="11"><result status="valid" time="0.070000" steps="189844"/></proof>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="remove_products&#39;vc.95" expl="precondition" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="remove_products&#39;vc.95.0" expl="precondition" proved="true">
   <transf name="inline_goal" proved="true" >
    <goal name="remove_products&#39;vc.95.0.0" expl="precondition" proved="true">
    <transf name="split_all_full" proved="true" >
     <goal name="remove_products&#39;vc.95.0.0.0" expl="VC for remove_products" proved="true">
     <proof prover="10"><result status="valid" time="0.200000" steps="47981"/></proof>
     <proof prover="11"><result status="valid" time="0.080000" steps="199540"/></proof>
     </goal>
     <goal name="remove_products&#39;vc.95.0.0.1" expl="VC for remove_products" proved="true">
     <proof prover="9"><result status="valid" time="0.020000" steps="55"/></proof>
     <proof prover="10"><result status="valid" time="0.110000" steps="41337"/></proof>
     </goal>
     <goal name="remove_products&#39;vc.95.0.0.2" expl="VC for remove_products" proved="true">
     <proof prover="10"><result status="valid" time="0.280000" steps="61361"/></proof>
     <proof prover="11"><result status="valid" time="0.080000" steps="215212"/></proof>
     </goal>
     <goal name="remove_products&#39;vc.95.0.0.3" expl="VC for remove_products" proved="true">
     <proof prover="10"><result status="valid" time="0.260000" steps="55321"/></proof>
     </goal>
    </transf>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="remove_products&#39;vc.96" expl="precondition" proved="true">
  <transf name="inline_goal" proved="true" >
   <goal name="remove_products&#39;vc.96.0" expl="precondition" proved="true">
   <transf name="split_vc" proved="true" >
    <goal name="remove_products&#39;vc.96.0.0" expl="precondition" proved="true">
    <proof prover="10"><result status="valid" time="0.150000" steps="41584"/></proof>
    <proof prover="11"><result status="valid" time="0.080000" steps="194821"/></proof>
    </goal>
    <goal name="remove_products&#39;vc.96.0.1" expl="precondition" proved="true">
    <proof prover="10"><result status="valid" time="0.180000" steps="44268"/></proof>
    <proof prover="11"><result status="valid" time="0.060000" steps="171733"/></proof>
    </goal>
    <goal name="remove_products&#39;vc.96.0.2" expl="precondition" proved="true">
    <proof prover="9"><result status="valid" time="0.020000" steps="57"/></proof>
    <proof prover="10"><result status="valid" time="0.150000" steps="39578"/></proof>
    <proof prover="11"><result status="valid" time="0.060000" steps="156850"/></proof>
    </goal>
    <goal name="remove_products&#39;vc.96.0.3" expl="precondition" proved="true">
    <proof prover="11"><result status="valid" time="0.060000" steps="196553"/></proof>
    </goal>
    <goal name="remove_products&#39;vc.96.0.4" expl="precondition" proved="true">
    <transf name="inline_all" proved="true" >
     <goal name="remove_products&#39;vc.96.0.4.0" expl="precondition" proved="true">
     <proof prover="11"><result status="valid" time="0.613671" steps="808135"/></proof>
     </goal>
    </transf>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="remove_products&#39;vc.97" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="59"/></proof>
  <proof prover="10"><result status="valid" time="0.150000" steps="40210"/></proof>
  <proof prover="11"><result status="valid" time="0.070000" steps="172717"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.98" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.050000" steps="54"/></proof>
  <proof prover="10"><result status="valid" time="0.180000" steps="44479"/></proof>
  <proof prover="11"><result status="valid" time="0.060000" steps="167844"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.99" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="58"/></proof>
  <proof prover="10"><result status="valid" time="0.110000" steps="37338"/></proof>
  <proof prover="11"><result status="valid" time="0.020000" steps="11658"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.100" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="58"/></proof>
  <proof prover="10"><result status="valid" time="0.110000" steps="37341"/></proof>
  <proof prover="11"><result status="valid" time="0.020000" steps="11663"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.101" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="58"/></proof>
  <proof prover="10"><result status="valid" time="0.110000" steps="37344"/></proof>
  <proof prover="11"><result status="valid" time="0.020000" steps="11668"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.102" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="58"/></proof>
  <proof prover="10"><result status="valid" time="0.100000" steps="37347"/></proof>
  <proof prover="11"><result status="valid" time="0.020000" steps="11673"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.103" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="58"/></proof>
  <proof prover="10"><result status="valid" time="0.120000" steps="37350"/></proof>
  <proof prover="11"><result status="valid" time="0.020000" steps="11678"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.104" expl="precondition" proved="true">
  <proof prover="10"><result status="valid" time="0.280000" steps="61017"/></proof>
  <proof prover="11"><result status="valid" time="0.070000" steps="191636"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.105" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="60"/></proof>
  <proof prover="10"><result status="valid" time="0.120000" steps="38971"/></proof>
  <proof prover="11"><result status="valid" time="0.020000" steps="12368"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.106" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="60"/></proof>
  <proof prover="10"><result status="valid" time="0.120000" steps="38977"/></proof>
  <proof prover="11"><result status="valid" time="0.020000" steps="12373"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.107" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.050000" steps="62"/></proof>
  <proof prover="10"><result status="valid" time="0.200000" steps="46260"/></proof>
  <proof prover="11"><result status="valid" time="0.070000" steps="177326"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.108" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="62"/></proof>
  <proof prover="10"><result status="valid" time="0.120000" steps="38988"/></proof>
  <proof prover="11"><result status="valid" time="0.020000" steps="12383"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.109" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="62"/></proof>
  <proof prover="10"><result status="valid" time="0.110000" steps="38991"/></proof>
  <proof prover="11"><result status="valid" time="0.020000" steps="12388"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.110" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="55"/></proof>
  <proof prover="10"><result status="valid" time="0.120000" steps="37258"/></proof>
  <proof prover="11"><result status="valid" time="0.010000" steps="11621"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.111" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="55"/></proof>
  <proof prover="10"><result status="valid" time="0.110000" steps="37261"/></proof>
  <proof prover="11"><result status="valid" time="0.020000" steps="11626"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.112" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="55"/></proof>
  <proof prover="10"><result status="valid" time="0.110000" steps="37264"/></proof>
  <proof prover="11"><result status="valid" time="0.020000" steps="11631"/></proof>
  </goal>
  <goal name="remove_products&#39;vc.113" expl="postcondition" proved="true">
  <transf name="inline_goal" proved="true" >
   <goal name="remove_products&#39;vc.113.0" expl="postcondition" proved="true">
   <transf name="split_vc" proved="true" >
    <goal name="remove_products&#39;vc.113.0.0" expl="postcondition" proved="true">
    <transf name="unfold" proved="true" arg1="only_multiples_marked" arg2="in" arg3="Ensures5">
     <goal name="remove_products&#39;vc.113.0.0.0" expl="postcondition" proved="true">
     <transf name="instantiate" proved="true" arg1="Ensures5" arg2="k">
      <goal name="remove_products&#39;vc.113.0.0.0.0" expl="postcondition" proved="true">
      <proof prover="0"><result status="valid" time="0.817033" steps="295"/></proof>
      <transf name="remove" proved="true" arg1="zero1,one1,(-),(&gt;),(&lt;=),(&gt;=),abs,int63&#39;maxInt,int63&#39;minInt,min_int63,max_int63,to_int,in_bounds,zero,one,even,odd,divides,prime,([]),singleton,cons,snoc,(++),all_eliminated_marked,all_eliminated_marked_partial,not_marked_impl_next_not_marked,is_copy,not_marked_impl_next_not_marked_partial,all_primes,all_multiples_marked,previously_marked_multiples,only_multiples_marked,prime_multiples_marked,inv_remove_products,ordered,all_inf_or_eq,max,marked_old,marked_copy,Assoc1,Unit_def_l,Unit_def_r,Inv_def_l,Inv_def_r,Comm1,Assoc,Mul_distr_l,Mul_distr_r,Comm,Unitary,NonTrivialRing,Refl,Trans,Antisymm,Total,ZeroLessOne,CompatOrderAdd,CompatOrderMult,Abs_le,Abs_pos,Div_mod,Mod_bound,Div_unique,Div_bound,Mod_1,Div_1,Div_inf,Div_inf_neg,Mod_0,Div_1_left,Div_minus1_left,Mod_1_left,Mod_minus1_left,Div_mult,Mod_mult,Div_mod1,Div_bound1,Mod_bound1,Div_sign_pos,Div_sign_neg,Mod_sign_pos,Mod_sign_neg,Rounds_toward_zero,Div_11,Mod_11,Div_inf1,Mod_inf,Div_mult1,Mod_mult1,to_int_in_bounds,extensionality,max_int&#39;def,min_int&#39;def,even_or_odd,even_not_odd,odd_not_even,even_odd,odd_even,even_even,odd_odd,even_2k,odd_2k1,even_mod2,divides&#39;spec,divides_refl,divides_1_n,divides_0,divides_left,divides_right,divides_oppr,divides_oppl,divides_oppr_rev,divides_oppl_rev,divides_plusr,divides_minusr,divides_multl,divides_multr,divides_factorl,divides_factorr,divides_n_1,divides_antisym,divides_trans,divides_bounds,mod_divides_euclidean,divides_mod_euclidean,mod_divides_computer,divides_mod_computer,even_divides,odd_divides,not_prime_1,prime_2,prime_3,prime_divisors,small_divisors,even_prime,odd_prime,mult_croissance_locale,mult_croissance,comp_mult_2,div_croissance_locale1,div_croissance1,div_croissance_locale2,div_croissance2,div_mult_1,mult_borne_sous_exp,sq_ineq,divides_div,divides_inf,not_prime_divider_limits,no_prod_impl_no_divider,not_prime_impl_divisor_under_sqrt,length_nonnegative,(==)&#39;spec,create&#39;spec,empty&#39;def,set&#39;spec,set&#39;def,([&lt;-])&#39;def,singleton&#39;spec,cons&#39;spec,snoc&#39;spec,([..])&#39;spec,([..])&#39;def,([_..])&#39;def,([.._])&#39;def,(++)&#39;spec,conservation_all_eliminated_marked_on_marked_change,conservation_all_eliminated_marked_on_nexts_change,multiples_of_marked_are_marked,prev_and_new_impl_all_multiples_marked,conservation_only_multiples_marked,conservation_previously_marked_multiples,conservation_previously_marked_multiples_on_marked_change,conservation_not_marked_impl_next_not_marked,unchanged_other_elements,H8,H6,Requires3,Requires2,Requires1,Requires,Ensures16,Ensures15,Ensures14,Ensures13,H5,Ensures12,Ensures11,Assert,Ensures10,Ensures9,Ensures8,Ensures7,Ensures6,Ensures5,Ensures4,Ensures3,Ensures2,Ensures1,Ensures">
       <goal name="remove_products&#39;vc.113.0.0.0.0.0" expl="postcondition" proved="true">
       <proof prover="0"><result status="valid" time="0.060000" steps="61"/></proof>
       <proof prover="9"><result status="valid" time="0.050000" steps="91"/></proof>
       <proof prover="11"><result status="valid" time="0.020000" steps="49116"/></proof>
       </goal>
      </transf>
      </goal>
     </transf>
     </goal>
    </transf>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
 <goal name="previously_marked_multiples_impl_prime&#39;vc" expl="VC for previously_marked_multiples_impl_prime" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="previously_marked_multiples_impl_prime&#39;vc.0" expl="assertion" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="previously_marked_multiples_impl_prime&#39;vc.0.0" expl="assertion" proved="true">
   <transf name="inline_all" proved="true" >
    <goal name="previously_marked_multiples_impl_prime&#39;vc.0.0.0" expl="assertion" proved="true">
    <proof prover="11"><result status="valid" time="0.100000" steps="226158"/></proof>
    </goal>
   </transf>
   </goal>
   <goal name="previously_marked_multiples_impl_prime&#39;vc.0.1" expl="VC for previously_marked_multiples_impl_prime" proved="true">
   <proof prover="9"><result status="valid" time="0.447313" steps="631"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="previously_marked_multiples_impl_prime&#39;vc.1" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.030000" steps="80"/></proof>
  <proof prover="10"><result status="valid" time="0.160000" steps="39404"/></proof>
  <proof prover="11"><result status="valid" time="0.060000" steps="131850"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="only_multiples_marked_impl_not_marked&#39;vc" expl="VC for only_multiples_marked_impl_not_marked" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="only_multiples_marked_impl_not_marked&#39;vc.0" expl="assertion" proved="true">
  <proof prover="9"><result status="valid" time="0.030000" steps="73"/></proof>
  </goal>
  <goal name="only_multiples_marked_impl_not_marked&#39;vc.1" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.527998" steps="402"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
<theory name="EulerSieveImpl" proved="true">
 <goal name="conservation_inv_arr_on_mark&#39;vc" expl="VC for conservation_inv_arr_on_mark" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="conservation_inv_arr_on_mark&#39;vc.0" expl="assertion" proved="true">
  <proof prover="9"><result status="valid" time="0.322715" steps="144"/></proof>
  <proof prover="10"><result status="valid" time="0.150000" steps="35640"/></proof>
  </goal>
  <goal name="conservation_inv_arr_on_mark&#39;vc.1" expl="assertion" proved="true">
  <proof prover="9"><result status="valid" time="0.340126" steps="179"/></proof>
  <proof prover="10"><result status="valid" time="0.150000" steps="34408"/></proof>
  <proof prover="11"><result status="valid" time="0.060000" steps="137932"/></proof>
  </goal>
  <goal name="conservation_inv_arr_on_mark&#39;vc.2" expl="postcondition" proved="true">
  <transf name="assert" proved="true" arg1="(abs arr[i] = abs arr[i &lt;- - arr[i]][i])">
   <goal name="conservation_inv_arr_on_mark&#39;vc.2.0" expl="asserted formula" proved="true">
   <proof prover="9"><result status="valid" time="0.160000" steps="141"/></proof>
   <proof prover="10"><result status="valid" time="0.160000" steps="34897"/></proof>
   <proof prover="11"><result status="valid" time="0.050000" steps="140977"/></proof>
   </goal>
   <goal name="conservation_inv_arr_on_mark&#39;vc.2.1" expl="postcondition" proved="true">
   <transf name="case" proved="true" arg1="(j = i)">
    <goal name="conservation_inv_arr_on_mark&#39;vc.2.1.0" expl="true case (postcondition)" proved="true">
    <proof prover="9"><result status="valid" time="0.246506" steps="181"/></proof>
    <proof prover="10"><result status="valid" time="0.160000" steps="35012"/></proof>
    </goal>
    <goal name="conservation_inv_arr_on_mark&#39;vc.2.1.1" expl="false case (postcondition)" proved="true">
    <proof prover="9"><result status="valid" time="1.959155" steps="722"/></proof>
    <proof prover="10"><result status="valid" time="0.190000" steps="40300"/></proof>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
 <goal name="conservation_inv_arr_on_jump&#39;vc" expl="VC for conservation_inv_arr_on_jump" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="conservation_inv_arr_on_jump&#39;vc.0" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="22"/></proof>
  <proof prover="10"><result status="valid" time="0.100000" steps="30435"/></proof>
  <proof prover="11"><result status="valid" time="0.020000" steps="9318"/></proof>
  </goal>
  <goal name="conservation_inv_arr_on_jump&#39;vc.1" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="22"/></proof>
  <proof prover="10"><result status="valid" time="0.130000" steps="32221"/></proof>
  <proof prover="11"><result status="valid" time="0.060000" steps="119271"/></proof>
  </goal>
  <goal name="conservation_inv_arr_on_jump&#39;vc.2" expl="assertion" proved="true">
  <proof prover="9"><result status="valid" time="2.289727" steps="347"/></proof>
  <proof prover="10"><result status="valid" time="0.150000" steps="36012"/></proof>
  </goal>
  <goal name="conservation_inv_arr_on_jump&#39;vc.3" expl="assertion" proved="true">
  <proof prover="9"><result status="valid" time="3.429227" steps="335"/></proof>
  <proof prover="10"><result status="valid" time="0.160000" steps="36294"/></proof>
  </goal>
  <goal name="conservation_inv_arr_on_jump&#39;vc.4" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="5.774406" steps="2893"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="t&#39;vc" expl="VC for t" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="t&#39;vc.0" expl="array creation size" proved="true">
  <proof prover="9"><result status="valid" time="0.010000" steps="10"/></proof>
  <proof prover="10"><result status="valid" time="0.090000" steps="26190"/></proof>
  <proof prover="11"><result status="valid" time="0.020000" steps="7444"/></proof>
  </goal>
  <goal name="t&#39;vc.1" expl="index in array bounds" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="12"/></proof>
  <proof prover="10"><result status="valid" time="0.110000" steps="31228"/></proof>
  <proof prover="11"><result status="valid" time="0.010000" steps="15773"/></proof>
  </goal>
  <goal name="t&#39;vc.2" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.010000" steps="16"/></proof>
  <proof prover="10"><result status="valid" time="0.100000" steps="31114"/></proof>
  <proof prover="11"><result status="valid" time="0.020000" steps="9507"/></proof>
  </goal>
  <goal name="t&#39;vc.3" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="18"/></proof>
  <proof prover="10"><result status="valid" time="0.120000" steps="36403"/></proof>
  <proof prover="11"><result status="valid" time="0.020000" steps="11789"/></proof>
  </goal>
  <goal name="t&#39;vc.4" expl="type invariant" proved="true">
  <proof prover="9"><result status="valid" time="0.010000" steps="20"/></proof>
  <proof prover="10"><result status="valid" time="0.120000" steps="36730"/></proof>
  <proof prover="11"><result status="valid" time="0.020000" steps="19406"/></proof>
  </goal>
  <goal name="t&#39;vc.5" expl="type invariant" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="62"/></proof>
  <proof prover="10"><result status="valid" time="0.240000" steps="41025"/></proof>
  </goal>
  <goal name="t&#39;vc.6" expl="type invariant" proved="true">
  <proof prover="9"><result status="valid" time="0.000000" steps="26"/></proof>
  <proof prover="10"><result status="valid" time="0.120000" steps="36940"/></proof>
  <proof prover="11"><result status="valid" time="0.020000" steps="12063"/></proof>
  </goal>
  <goal name="t&#39;vc.7" expl="type invariant" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="27"/></proof>
  <proof prover="10"><result status="valid" time="0.110000" steps="37008"/></proof>
  <proof prover="11"><result status="valid" time="0.020000" steps="19650"/></proof>
  </goal>
  <goal name="t&#39;vc.8" expl="type invariant" proved="true">
  <proof prover="9"><result status="valid" time="0.040000" steps="190"/></proof>
  <proof prover="10"><result status="valid" time="0.190000" steps="44049"/></proof>
  </goal>
  <goal name="t&#39;vc.9" expl="type invariant" proved="true">
  <proof prover="9"><result status="valid" time="0.171635" steps="255"/></proof>
  <proof prover="10"><result status="valid" time="0.185629" steps="44740"/></proof>
  </goal>
  <goal name="t&#39;vc.10" expl="type invariant" proved="true">
  <proof prover="9"><result status="valid" time="0.010000" steps="36"/></proof>
  <proof prover="10"><result status="valid" time="0.150000" steps="39653"/></proof>
  <proof prover="11"><result status="valid" time="0.030000" steps="183951"/></proof>
  </goal>
  <goal name="t&#39;vc.11" expl="type invariant" proved="true">
  <proof prover="9"><result status="valid" time="0.040000" steps="34"/></proof>
  <proof prover="10"><result status="valid" time="0.200000" steps="39859"/></proof>
  </goal>
  <goal name="t&#39;vc.12" expl="type invariant" proved="true">
  <proof prover="9"><result status="valid" time="0.251208" steps="343"/></proof>
  <proof prover="10"><result status="valid" time="0.140000" steps="43842"/></proof>
  </goal>
  <goal name="t&#39;vc.13" expl="type invariant" proved="true">
  <proof prover="10"><result status="valid" time="0.210000" steps="46702"/></proof>
  </goal>
  <goal name="t&#39;vc.14" expl="type invariant" proved="true">
  <proof prover="9"><result status="valid" time="2.683099" steps="998"/></proof>
  <proof prover="10"><result status="valid" time="0.250000" steps="47265"/></proof>
  </goal>
  <goal name="t&#39;vc.15" expl="type invariant" proved="true">
  <proof prover="9"><result status="valid" time="0.459628" steps="340"/></proof>
  <proof prover="10"><result status="valid" time="0.210000" steps="44991"/></proof>
  <proof prover="11"><result status="valid" time="0.100000" steps="199182"/></proof>
  </goal>
  <goal name="t&#39;vc.16" expl="type invariant" proved="true">
  <proof prover="9"><result status="valid" time="4.162421" steps="884"/></proof>
  <proof prover="10"><result status="valid" time="0.210000" steps="49223"/></proof>
  <proof prover="11"><result status="valid" time="0.330000" steps="736277"/></proof>
  </goal>
  <goal name="t&#39;vc.17" expl="type invariant" proved="true">
  <proof prover="10"><result status="valid" time="0.210000" steps="50108"/></proof>
  </goal>
  <goal name="t&#39;vc.18" expl="type invariant" proved="true">
  <proof prover="9"><result status="valid" time="4.649233" steps="1533"/></proof>
  <proof prover="10"><result status="valid" time="0.240000" steps="51308"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="create&#39;vc" expl="VC for create" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="create&#39;vc.0" expl="integer overflow" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="16"/></proof>
  <proof prover="10"><result status="valid" time="0.140000" steps="31856"/></proof>
  <proof prover="11"><result status="valid" time="0.050000" steps="108131"/></proof>
  </goal>
  <goal name="create&#39;vc.1" expl="division by zero" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="16"/></proof>
  <proof prover="10"><result status="valid" time="0.100000" steps="28751"/></proof>
  <proof prover="11"><result status="valid" time="0.020000" steps="8522"/></proof>
  </goal>
  <goal name="create&#39;vc.2" expl="integer overflow" proved="true">
  <proof prover="9"><result status="valid" time="0.040000" steps="70"/></proof>
  <proof prover="10"><result status="valid" time="0.140000" steps="32174"/></proof>
  <proof prover="11"><result status="valid" time="0.060000" steps="110349"/></proof>
  </goal>
  <goal name="create&#39;vc.3" expl="integer overflow" proved="true">
  <proof prover="9"><result status="valid" time="0.040000" steps="81"/></proof>
  <proof prover="10"><result status="valid" time="0.140000" steps="32284"/></proof>
  <proof prover="11"><result status="valid" time="0.050000" steps="111235"/></proof>
  </goal>
  <goal name="create&#39;vc.4" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="20"/></proof>
  <proof prover="10"><result status="valid" time="0.120000" steps="30562"/></proof>
  <proof prover="11"><result status="valid" time="0.050000" steps="107443"/></proof>
  </goal>
  <goal name="create&#39;vc.5" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="30"/></proof>
  <proof prover="10"><result status="valid" time="0.110000" steps="34368"/></proof>
  <proof prover="11"><result status="valid" time="0.020000" steps="10777"/></proof>
  </goal>
  <goal name="create&#39;vc.6" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="24"/></proof>
  <proof prover="10"><result status="valid" time="0.150000" steps="36165"/></proof>
  <proof prover="11"><result status="valid" time="0.060000" steps="152241"/></proof>
  </goal>
  <goal name="create&#39;vc.7" expl="array creation size" proved="true">
  <proof prover="9"><result status="valid" time="0.030000" steps="30"/></proof>
  <proof prover="10"><result status="valid" time="0.200000" steps="44829"/></proof>
  <proof prover="11"><result status="valid" time="0.080000" steps="193000"/></proof>
  </goal>
  <goal name="create&#39;vc.8" expl="integer overflow" proved="true">
  <proof prover="9"><result status="valid" time="0.030000" steps="32"/></proof>
  <proof prover="10"><result status="valid" time="0.170000" steps="42338"/></proof>
  <proof prover="11"><result status="valid" time="0.080000" steps="194111"/></proof>
  </goal>
  <goal name="create&#39;vc.9" expl="loop invariant init" proved="true">
  <proof prover="9"><result status="valid" time="0.050000" steps="141"/></proof>
  <proof prover="10"><result status="valid" time="0.200000" steps="48553"/></proof>
  </goal>
  <goal name="create&#39;vc.10" expl="integer overflow" proved="true">
  <proof prover="9"><result status="valid" time="0.040000" steps="42"/></proof>
  <proof prover="10"><result status="valid" time="0.180000" steps="42565"/></proof>
  <proof prover="11"><result status="valid" time="0.070000" steps="200379"/></proof>
  </goal>
  <goal name="create&#39;vc.11" expl="integer overflow" proved="true">
  <proof prover="9"><result status="valid" time="0.040000" steps="44"/></proof>
  <proof prover="10"><result status="valid" time="0.200000" steps="45539"/></proof>
  <proof prover="11"><result status="valid" time="0.080000" steps="200262"/></proof>
  </goal>
  <goal name="create&#39;vc.12" expl="integer overflow" proved="true">
  <proof prover="9"><result status="valid" time="0.040000" steps="48"/></proof>
  <proof prover="10"><result status="valid" time="0.190000" steps="47244"/></proof>
  <proof prover="11"><result status="valid" time="0.080000" steps="212936"/></proof>
  </goal>
  <goal name="create&#39;vc.13" expl="integer overflow" proved="true">
  <proof prover="9"><result status="valid" time="0.040000" steps="50"/></proof>
  <proof prover="10"><result status="valid" time="0.190000" steps="47365"/></proof>
  <proof prover="11"><result status="valid" time="0.080000" steps="216617"/></proof>
  </goal>
  <goal name="create&#39;vc.14" expl="index in array bounds" proved="true">
  <proof prover="9"><result status="valid" time="0.030000" steps="46"/></proof>
  <proof prover="10"><result status="valid" time="0.170000" steps="45930"/></proof>
  <proof prover="11"><result status="valid" time="0.080000" steps="203856"/></proof>
  </goal>
  <goal name="create&#39;vc.15" expl="loop invariant preservation" proved="true">
  <proof prover="9"><result status="valid" time="2.834821" steps="2876"/></proof>
  <proof prover="10"><result status="valid" time="0.220000" steps="49454"/></proof>
  </goal>
  <goal name="create&#39;vc.16" expl="integer overflow" proved="true">
  <proof prover="9"><result status="valid" time="0.030000" steps="38"/></proof>
  <proof prover="10"><result status="valid" time="0.200000" steps="45535"/></proof>
  <proof prover="11"><result status="valid" time="0.070000" steps="198086"/></proof>
  </goal>
  <goal name="create&#39;vc.17" expl="division by zero" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="38"/></proof>
  <proof prover="10"><result status="valid" time="0.120000" steps="40302"/></proof>
  <proof prover="11"><result status="valid" time="0.020000" steps="13264"/></proof>
  </goal>
  <goal name="create&#39;vc.18" expl="integer overflow" proved="true">
  <proof prover="9"><result status="valid" time="0.040000" steps="41"/></proof>
  <proof prover="10"><result status="valid" time="0.200000" steps="45764"/></proof>
  <proof prover="11"><result status="valid" time="0.080000" steps="200479"/></proof>
  </goal>
  <goal name="create&#39;vc.19" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="40"/></proof>
  <proof prover="10"><result status="valid" time="0.120000" steps="40333"/></proof>
  <proof prover="11"><result status="valid" time="0.020000" steps="22227"/></proof>
  </goal>
  <goal name="create&#39;vc.20" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="40"/></proof>
  <proof prover="10"><result status="valid" time="0.150000" steps="42436"/></proof>
  <proof prover="11"><result status="valid" time="0.070000" steps="202361"/></proof>
  </goal>
  <goal name="create&#39;vc.21" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.050000" steps="43"/></proof>
  <proof prover="10"><result status="valid" time="0.220000" steps="49752"/></proof>
  </goal>
  <goal name="create&#39;vc.22" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.060000" steps="45"/></proof>
  <proof prover="10"><result status="valid" time="0.200000" steps="48253"/></proof>
  <proof prover="11"><result status="valid" time="0.080000" steps="218049"/></proof>
  </goal>
  <goal name="create&#39;vc.23" expl="precondition" proved="true">
  <proof prover="10"><result status="valid" time="0.220000" steps="51471"/></proof>
  </goal>
  <goal name="create&#39;vc.24" expl="precondition" proved="true">
  <proof prover="10"><result status="valid" time="0.506278" steps="58209"/></proof>
  </goal>
  <goal name="create&#39;vc.25" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.060000" steps="57"/></proof>
  <proof prover="10"><result status="valid" time="0.210000" steps="49175"/></proof>
  <proof prover="11"><result status="valid" time="0.080000" steps="219255"/></proof>
  </goal>
  <goal name="create&#39;vc.26" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.110000" steps="227"/></proof>
  <proof prover="10"><result status="valid" time="0.220000" steps="50259"/></proof>
  </goal>
  <goal name="create&#39;vc.27" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.712571" steps="497"/></proof>
  <proof prover="10"><result status="valid" time="0.260000" steps="51775"/></proof>
  </goal>
  <goal name="create&#39;vc.28" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="1.306523" steps="1424"/></proof>
  <proof prover="10"><result status="valid" time="0.250000" steps="53539"/></proof>
  </goal>
  <goal name="create&#39;vc.29" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.650000" steps="846"/></proof>
  <proof prover="10"><result status="valid" time="0.240000" steps="52891"/></proof>
  </goal>
  <goal name="create&#39;vc.30" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="1.103240" steps="1144"/></proof>
  <proof prover="10"><result status="valid" time="0.397299" steps="54160"/></proof>
  </goal>
  <goal name="create&#39;vc.31" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="1.070000" steps="1208"/></proof>
  <proof prover="10"><result status="valid" time="0.260000" steps="53434"/></proof>
  </goal>
  <goal name="create&#39;vc.32" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="3.643352" steps="2307"/></proof>
  <proof prover="10"><result status="valid" time="0.250000" steps="52667"/></proof>
  </goal>
  <goal name="create&#39;vc.33" expl="precondition" proved="true">
  <proof prover="10"><result status="valid" time="0.260000" steps="55354"/></proof>
  </goal>
  <goal name="create&#39;vc.34" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="58"/></proof>
  <proof prover="10"><result status="valid" time="0.130000" steps="40485"/></proof>
  <proof prover="11"><result status="valid" time="0.020000" steps="13354"/></proof>
  </goal>
  <goal name="create&#39;vc.35" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.300000" steps="432"/></proof>
  <proof prover="10"><result status="valid" time="0.230000" steps="52711"/></proof>
  </goal>
  <goal name="create&#39;vc.36" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.492365" steps="264"/></proof>
  <proof prover="10"><result status="valid" time="0.240000" steps="53377"/></proof>
  </goal>
  <goal name="create&#39;vc.37" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.070000" steps="72"/></proof>
  <proof prover="10"><result status="valid" time="0.250000" steps="54056"/></proof>
  <proof prover="11"><result status="valid" time="0.080000" steps="228162"/></proof>
  </goal>
  <goal name="create&#39;vc.38" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="1.153152" steps="676"/></proof>
  <proof prover="10"><result status="valid" time="0.260000" steps="52024"/></proof>
  <proof prover="11"><result status="valid" time="0.090000" steps="252367"/></proof>
  </goal>
  <goal name="create&#39;vc.39" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="1.212821" steps="787"/></proof>
  <proof prover="10"><result status="valid" time="0.260000" steps="54948"/></proof>
  <proof prover="11"><result status="valid" time="0.090000" steps="251685"/></proof>
  </goal>
  <goal name="create&#39;vc.40" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.510616" steps="558"/></proof>
  <proof prover="10"><result status="valid" time="0.250000" steps="53815"/></proof>
  <proof prover="11"><result status="valid" time="0.090000" steps="226392"/></proof>
  </goal>
  <goal name="create&#39;vc.41" expl="out of loop bounds" proved="true">
  <proof prover="9"><result status="valid" time="0.050000" steps="35"/></proof>
  <proof prover="10"><result status="valid" time="0.210000" steps="51783"/></proof>
  <proof prover="11"><result status="valid" time="0.080000" steps="220998"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="set_next&#39;vc" expl="VC for set_next" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="set_next&#39;vc.0" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.030000" steps="35"/></proof>
  <proof prover="10"><result status="valid" time="0.200000" steps="43506"/></proof>
  <proof prover="11"><result status="valid" time="0.070000" steps="184500"/></proof>
  </goal>
  <goal name="set_next&#39;vc.1" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.030000" steps="37"/></proof>
  <proof prover="10"><result status="valid" time="0.180000" steps="43559"/></proof>
  <proof prover="11"><result status="valid" time="0.070000" steps="184895"/></proof>
  </goal>
  <goal name="set_next&#39;vc.2" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.040000" steps="39"/></proof>
  <proof prover="10"><result status="valid" time="0.190000" steps="43689"/></proof>
  <proof prover="11"><result status="valid" time="0.070000" steps="185436"/></proof>
  </goal>
  <goal name="set_next&#39;vc.3" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.030000" steps="41"/></proof>
  <proof prover="10"><result status="valid" time="0.200000" steps="43760"/></proof>
  <proof prover="11"><result status="valid" time="0.060000" steps="187498"/></proof>
  </goal>
  <goal name="set_next&#39;vc.4" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.040000" steps="43"/></proof>
  <proof prover="10"><result status="valid" time="0.180000" steps="43800"/></proof>
  <proof prover="11"><result status="valid" time="0.070000" steps="187878"/></proof>
  </goal>
  <goal name="set_next&#39;vc.5" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.040000" steps="49"/></proof>
  <proof prover="10"><result status="valid" time="0.180000" steps="43874"/></proof>
  <proof prover="11"><result status="valid" time="0.070000" steps="188213"/></proof>
  </goal>
  <goal name="set_next&#39;vc.6" expl="division by zero" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="34"/></proof>
  <proof prover="10"><result status="valid" time="0.100000" steps="32922"/></proof>
  <proof prover="11"><result status="valid" time="0.020000" steps="10187"/></proof>
  </goal>
  <goal name="set_next&#39;vc.7" expl="integer overflow" proved="true">
  <proof prover="9"><result status="valid" time="0.090000" steps="188"/></proof>
  <proof prover="10"><result status="valid" time="0.160000" steps="37679"/></proof>
  <proof prover="11"><result status="valid" time="0.060000" steps="149167"/></proof>
  </goal>
  <goal name="set_next&#39;vc.8" expl="index in array bounds" proved="true">
  <proof prover="9"><result status="valid" time="0.050000" steps="98"/></proof>
  <proof prover="10"><result status="valid" time="0.210000" steps="44818"/></proof>
  <proof prover="11"><result status="valid" time="0.070000" steps="187092"/></proof>
  </goal>
  <goal name="set_next&#39;vc.9" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.050000" steps="43"/></proof>
  <proof prover="10"><result status="valid" time="0.190000" steps="42353"/></proof>
  <proof prover="11"><result status="valid" time="0.070000" steps="179838"/></proof>
  </goal>
  <goal name="set_next&#39;vc.10" expl="type invariant" proved="true">
  <proof prover="9"><result status="valid" time="0.050000" steps="46"/></proof>
  <proof prover="10"><result status="valid" time="0.190000" steps="42896"/></proof>
  <proof prover="11"><result status="valid" time="0.080000" steps="184418"/></proof>
  </goal>
  <goal name="set_next&#39;vc.11" expl="type invariant" proved="true">
  <proof prover="9"><result status="valid" time="0.050000" steps="52"/></proof>
  <proof prover="10"><result status="valid" time="0.180000" steps="44822"/></proof>
  <proof prover="11"><result status="valid" time="0.060000" steps="202506"/></proof>
  </goal>
  <goal name="set_next&#39;vc.12" expl="type invariant" proved="true">
  <proof prover="9"><result status="valid" time="0.060000" steps="55"/></proof>
  <proof prover="10"><result status="valid" time="0.190000" steps="45143"/></proof>
  <proof prover="11"><result status="valid" time="0.070000" steps="201869"/></proof>
  </goal>
  <goal name="set_next&#39;vc.13" expl="type invariant" proved="true">
  <proof prover="9"><result status="valid" time="0.060000" steps="57"/></proof>
  <proof prover="10"><result status="valid" time="0.190000" steps="47499"/></proof>
  <proof prover="11"><result status="valid" time="0.080000" steps="211278"/></proof>
  </goal>
  <goal name="set_next&#39;vc.14" expl="type invariant" proved="true">
  <proof prover="10"><result status="valid" time="0.260000" steps="51688"/></proof>
  </goal>
  <goal name="set_next&#39;vc.15" expl="type invariant" proved="true">
  <proof prover="9"><result status="valid" time="0.060000" steps="61"/></proof>
  <proof prover="10"><result status="valid" time="0.200000" steps="45519"/></proof>
  </goal>
  <goal name="set_next&#39;vc.16" expl="type invariant" proved="true">
  <proof prover="9"><result status="valid" time="0.070000" steps="69"/></proof>
  <proof prover="10"><result status="valid" time="0.220000" steps="48777"/></proof>
  <proof prover="11"><result status="valid" time="0.080000" steps="214603"/></proof>
  </goal>
  <goal name="set_next&#39;vc.17" expl="type invariant" proved="true">
  <proof prover="9"><result status="valid" time="1.188384" steps="1205"/></proof>
  <proof prover="10"><result status="valid" time="0.270000" steps="50975"/></proof>
  </goal>
  <goal name="set_next&#39;vc.18" expl="type invariant" proved="true">
  <proof prover="9"><result status="valid" time="0.317731" steps="574"/></proof>
  <proof prover="10"><result status="valid" time="0.230000" steps="48571"/></proof>
  </goal>
  <goal name="set_next&#39;vc.19" expl="type invariant" proved="true">
  <proof prover="10"><result status="valid" time="0.415885" steps="55058"/></proof>
  </goal>
  <goal name="set_next&#39;vc.20" expl="type invariant" proved="true">
  <proof prover="10"><result status="valid" time="0.310000" steps="62018"/></proof>
  </goal>
  <goal name="set_next&#39;vc.21" expl="type invariant" proved="true">
  <proof prover="10"><result status="valid" time="0.509304" steps="63596"/></proof>
  </goal>
  <goal name="set_next&#39;vc.22" expl="type invariant" proved="true">
  <proof prover="10"><result status="valid" time="0.303293" steps="57431"/></proof>
  </goal>
  <goal name="set_next&#39;vc.23" expl="type invariant" proved="true">
  <proof prover="10"><result status="valid" time="0.230000" steps="52027"/></proof>
  </goal>
  <goal name="set_next&#39;vc.24" expl="type invariant" proved="true">
  <proof prover="10"><result status="valid" time="0.300000" steps="60330"/></proof>
  </goal>
  <goal name="set_next&#39;vc.25" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="54"/></proof>
  <proof prover="10"><result status="valid" time="0.120000" steps="37529"/></proof>
  <proof prover="11"><result status="valid" time="0.040000" steps="96242"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="get_next&#39;vc" expl="VC for get_next" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="get_next&#39;vc.0" expl="division by zero" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="26"/></proof>
  <proof prover="10"><result status="valid" time="0.090000" steps="28936"/></proof>
  <proof prover="11"><result status="valid" time="0.020000" steps="8555"/></proof>
  </goal>
  <goal name="get_next&#39;vc.1" expl="integer overflow" proved="true">
  <proof prover="9"><result status="valid" time="0.060000" steps="114"/></proof>
  <proof prover="10"><result status="valid" time="0.140000" steps="33316"/></proof>
  <proof prover="11"><result status="valid" time="0.060000" steps="124345"/></proof>
  </goal>
  <goal name="get_next&#39;vc.2" expl="index in array bounds" proved="true">
  <proof prover="9"><result status="valid" time="0.040000" steps="83"/></proof>
  <proof prover="10"><result status="valid" time="0.170000" steps="40048"/></proof>
  <proof prover="11"><result status="valid" time="0.070000" steps="161755"/></proof>
  </goal>
  <goal name="get_next&#39;vc.3" expl="index in array bounds" proved="true">
  <proof prover="9"><result status="valid" time="0.050000" steps="90"/></proof>
  <proof prover="10"><result status="valid" time="0.180000" steps="41134"/></proof>
  <proof prover="11"><result status="valid" time="0.070000" steps="166826"/></proof>
  </goal>
  <goal name="get_next&#39;vc.4" expl="integer overflow" proved="true">
  <proof prover="9"><result status="valid" time="0.050000" steps="140"/></proof>
  <proof prover="10"><result status="valid" time="0.190000" steps="41962"/></proof>
  </goal>
  <goal name="get_next&#39;vc.5" expl="index in array bounds" proved="true">
  <proof prover="9"><result status="valid" time="0.040000" steps="90"/></proof>
  <proof prover="10"><result status="valid" time="0.180000" steps="41133"/></proof>
  <proof prover="11"><result status="valid" time="0.070000" steps="166704"/></proof>
  </goal>
  <goal name="get_next&#39;vc.6" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.605526" steps="724"/></proof>
  <proof prover="10"><result status="valid" time="0.220000" steps="46001"/></proof>
  </goal>
  <goal name="get_next&#39;vc.7" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.080000" steps="221"/></proof>
  <proof prover="10"><result status="valid" time="0.460000" steps="83949"/></proof>
  </goal>
  <goal name="get_next&#39;vc.8" expl="postcondition" proved="true">
  <transf name="assert" proved="true" arg1="(i &gt;= 3)">
   <goal name="get_next&#39;vc.8.0" expl="asserted formula" proved="true">
   <proof prover="9"><result status="valid" time="0.020000" steps="36"/></proof>
   <proof prover="10"><result status="valid" time="0.100000" steps="32270"/></proof>
   <proof prover="11"><result status="valid" time="0.020000" steps="9902"/></proof>
   </goal>
   <goal name="get_next&#39;vc.8.1" expl="postcondition" proved="true">
   <transf name="case" proved="true" arg1="(i &lt; max t - 1)">
    <goal name="get_next&#39;vc.8.1.0" expl="true case (postcondition)" proved="true">
    <proof prover="9"><result status="valid" time="0.050000" steps="45"/></proof>
    <proof prover="10"><result status="valid" time="0.200000" steps="40592"/></proof>
    <proof prover="11"><result status="valid" time="0.060000" steps="177325"/></proof>
    </goal>
    <goal name="get_next&#39;vc.8.1.1" expl="false case (postcondition)" proved="true">
    <transf name="case" proved="true" arg1="(i = max t)">
     <goal name="get_next&#39;vc.8.1.1.0" expl="false case (true case. postcondition)" proved="true">
     <proof prover="9"><result status="valid" time="0.050000" steps="47"/></proof>
     <proof prover="10"><result status="valid" time="0.140000" steps="37525"/></proof>
     <proof prover="11"><result status="valid" time="0.060000" steps="154282"/></proof>
     </goal>
     <goal name="get_next&#39;vc.8.1.1.1" expl="false case (postcondition)" proved="true">
     <proof prover="9"><result status="valid" time="0.100000" steps="190"/></proof>
     <proof prover="10"><result status="valid" time="0.260000" steps="49795"/></proof>
     </goal>
    </transf>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
 <goal name="set_mark&#39;vc" expl="VC for set_mark" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="set_mark&#39;vc.0" expl="division by zero" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="26"/></proof>
  <proof prover="10"><result status="valid" time="0.100000" steps="28936"/></proof>
  <proof prover="11"><result status="valid" time="0.020000" steps="8555"/></proof>
  </goal>
  <goal name="set_mark&#39;vc.1" expl="integer overflow" proved="true">
  <proof prover="9"><result status="valid" time="0.060000" steps="119"/></proof>
  <proof prover="10"><result status="valid" time="0.160000" steps="33272"/></proof>
  <proof prover="11"><result status="valid" time="0.060000" steps="124231"/></proof>
  </goal>
  <goal name="set_mark&#39;vc.2" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.030000" steps="30"/></proof>
  <proof prover="10"><result status="valid" time="0.190000" steps="42596"/></proof>
  <proof prover="11"><result status="valid" time="0.060000" steps="180402"/></proof>
  </goal>
  <goal name="set_mark&#39;vc.3" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.040000" steps="32"/></proof>
  <proof prover="10"><result status="valid" time="0.190000" steps="42679"/></proof>
  <proof prover="11"><result status="valid" time="0.070000" steps="180695"/></proof>
  </goal>
  <goal name="set_mark&#39;vc.4" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.030000" steps="34"/></proof>
  <proof prover="10"><result status="valid" time="0.180000" steps="42768"/></proof>
  <proof prover="11"><result status="valid" time="0.060000" steps="181108"/></proof>
  </goal>
  <goal name="set_mark&#39;vc.5" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.040000" steps="36"/></proof>
  <proof prover="10"><result status="valid" time="0.180000" steps="42849"/></proof>
  <proof prover="11"><result status="valid" time="0.070000" steps="183391"/></proof>
  </goal>
  <goal name="set_mark&#39;vc.6" expl="index in array bounds" proved="true">
  <proof prover="9"><result status="valid" time="0.040000" steps="87"/></proof>
  <proof prover="10"><result status="valid" time="0.180000" steps="40871"/></proof>
  <proof prover="11"><result status="valid" time="0.060000" steps="166093"/></proof>
  </goal>
  <goal name="set_mark&#39;vc.7" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.070000" steps="44"/></proof>
  <proof prover="10"><result status="valid" time="0.270000" steps="52598"/></proof>
  <proof prover="11"><result status="valid" time="0.080000" steps="182630"/></proof>
  </goal>
  <goal name="set_mark&#39;vc.8" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.140000" steps="197"/></proof>
  <proof prover="10"><result status="valid" time="0.220000" steps="46232"/></proof>
  </goal>
  <goal name="set_mark&#39;vc.9" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.050000" steps="94"/></proof>
  <proof prover="10"><result status="valid" time="0.190000" steps="42693"/></proof>
  <proof prover="11"><result status="valid" time="0.070000" steps="173662"/></proof>
  </goal>
  <goal name="set_mark&#39;vc.10" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.010000" steps="38"/></proof>
  <proof prover="10"><result status="valid" time="0.150000" steps="36547"/></proof>
  <proof prover="11"><result status="valid" time="0.060000" steps="153587"/></proof>
  </goal>
  <goal name="set_mark&#39;vc.11" expl="index in array bounds" proved="true">
  <proof prover="9"><result status="valid" time="0.040000" steps="94"/></proof>
  <proof prover="10"><result status="valid" time="0.190000" steps="42174"/></proof>
  <proof prover="11"><result status="valid" time="0.060000" steps="172042"/></proof>
  </goal>
  <goal name="set_mark&#39;vc.12" expl="integer overflow" proved="true">
  <proof prover="9"><result status="valid" time="0.040000" steps="38"/></proof>
  <proof prover="10"><result status="valid" time="0.170000" steps="39643"/></proof>
  <proof prover="11"><result status="valid" time="0.060000" steps="163216"/></proof>
  </goal>
  <goal name="set_mark&#39;vc.13" expl="index in array bounds" proved="true">
  <proof prover="9"><result status="valid" time="0.050000" steps="105"/></proof>
  <proof prover="10"><result status="valid" time="0.190000" steps="42494"/></proof>
  <proof prover="11"><result status="valid" time="0.070000" steps="177282"/></proof>
  </goal>
  <goal name="set_mark&#39;vc.14" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.050000" steps="44"/></proof>
  <proof prover="10"><result status="valid" time="0.200000" steps="44065"/></proof>
  <proof prover="11"><result status="valid" time="0.070000" steps="193322"/></proof>
  </goal>
  <goal name="set_mark&#39;vc.15" expl="type invariant" proved="true">
  <proof prover="9"><result status="valid" time="0.050000" steps="47"/></proof>
  <proof prover="10"><result status="valid" time="0.200000" steps="44904"/></proof>
  <proof prover="11"><result status="valid" time="0.070000" steps="195712"/></proof>
  </goal>
  <goal name="set_mark&#39;vc.16" expl="type invariant" proved="true">
  <proof prover="9"><result status="valid" time="0.050000" steps="125"/></proof>
  <proof prover="10"><result status="valid" time="0.190000" steps="45429"/></proof>
  <proof prover="11"><result status="valid" time="0.070000" steps="203011"/></proof>
  </goal>
  <goal name="set_mark&#39;vc.17" expl="type invariant" proved="true">
  <proof prover="9"><result status="valid" time="0.060000" steps="56"/></proof>
  <proof prover="10"><result status="valid" time="0.190000" steps="45408"/></proof>
  <proof prover="11"><result status="valid" time="0.080000" steps="204976"/></proof>
  </goal>
  <goal name="set_mark&#39;vc.18" expl="type invariant" proved="true">
  <proof prover="9"><result status="valid" time="0.060000" steps="58"/></proof>
  <proof prover="10"><result status="valid" time="0.210000" steps="48152"/></proof>
  <proof prover="11"><result status="valid" time="0.080000" steps="215902"/></proof>
  </goal>
  <goal name="set_mark&#39;vc.19" expl="type invariant" proved="true">
  <proof prover="9"><result status="valid" time="0.060000" steps="60"/></proof>
  <proof prover="10"><result status="valid" time="0.180000" steps="45427"/></proof>
  <proof prover="11"><result status="valid" time="0.080000" steps="207569"/></proof>
  </goal>
  <goal name="set_mark&#39;vc.20" expl="type invariant" proved="true">
  <proof prover="9"><result status="valid" time="0.060000" steps="62"/></proof>
  <proof prover="10"><result status="valid" time="0.200000" steps="45764"/></proof>
  </goal>
  <goal name="set_mark&#39;vc.21" expl="type invariant" proved="true">
  <proof prover="9"><result status="valid" time="0.429329" steps="260"/></proof>
  <proof prover="10"><result status="valid" time="0.230000" steps="50083"/></proof>
  </goal>
  <goal name="set_mark&#39;vc.22" expl="type invariant" proved="true">
  <proof prover="9"><result status="valid" time="0.080000" steps="72"/></proof>
  <proof prover="10"><result status="valid" time="0.240000" steps="49985"/></proof>
  <proof prover="11"><result status="valid" time="0.080000" steps="230917"/></proof>
  </goal>
  <goal name="set_mark&#39;vc.23" expl="type invariant" proved="true">
  <proof prover="9"><result status="valid" time="0.060000" steps="63"/></proof>
  <proof prover="10"><result status="valid" time="0.200000" steps="47449"/></proof>
  <proof prover="11"><result status="valid" time="0.070000" steps="211228"/></proof>
  </goal>
  <goal name="set_mark&#39;vc.24" expl="type invariant" proved="true">
  <proof prover="10"><result status="valid" time="0.260000" steps="55591"/></proof>
  </goal>
  <goal name="set_mark&#39;vc.25" expl="type invariant" proved="true">
  <proof prover="10"><result status="valid" time="0.428671" steps="58416"/></proof>
  </goal>
  <goal name="set_mark&#39;vc.26" expl="type invariant" proved="true">
  <proof prover="10"><result status="valid" time="0.280000" steps="58052"/></proof>
  </goal>
  <goal name="set_mark&#39;vc.27" expl="type invariant" proved="true">
  <proof prover="10"><result status="valid" time="0.675083" steps="78566"/></proof>
  </goal>
  <goal name="set_mark&#39;vc.28" expl="type invariant" proved="true">
  <proof prover="10"><result status="valid" time="0.220000" steps="51655"/></proof>
  </goal>
  <goal name="set_mark&#39;vc.29" expl="type invariant" proved="true">
  <proof prover="9"><result status="valid" time="0.120000" steps="76"/></proof>
  <proof prover="10"><result status="valid" time="0.370000" steps="66122"/></proof>
  </goal>
  <goal name="set_mark&#39;vc.30" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="56"/></proof>
  <proof prover="10"><result status="valid" time="0.120000" steps="39217"/></proof>
  <proof prover="11"><result status="valid" time="0.040000" steps="102484"/></proof>
  </goal>
  <goal name="set_mark&#39;vc.31" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.040000" steps="36"/></proof>
  <proof prover="10"><result status="valid" time="0.180000" steps="41706"/></proof>
  <proof prover="11"><result status="valid" time="0.070000" steps="177610"/></proof>
  </goal>
  <goal name="set_mark&#39;vc.32" expl="type invariant" proved="true">
  <proof prover="9"><result status="valid" time="0.040000" steps="39"/></proof>
  <proof prover="10"><result status="valid" time="0.180000" steps="42549"/></proof>
  <proof prover="11"><result status="valid" time="0.080000" steps="180228"/></proof>
  </goal>
  <goal name="set_mark&#39;vc.33" expl="type invariant" proved="true">
  <proof prover="9"><result status="valid" time="0.050000" steps="108"/></proof>
  <proof prover="10"><result status="valid" time="0.200000" steps="44780"/></proof>
  <proof prover="11"><result status="valid" time="0.070000" steps="197002"/></proof>
  </goal>
  <goal name="set_mark&#39;vc.34" expl="type invariant" proved="true">
  <proof prover="9"><result status="valid" time="0.050000" steps="48"/></proof>
  <proof prover="10"><result status="valid" time="0.200000" steps="44836"/></proof>
  <proof prover="11"><result status="valid" time="0.080000" steps="198497"/></proof>
  </goal>
  <goal name="set_mark&#39;vc.35" expl="type invariant" proved="true">
  <proof prover="9"><result status="valid" time="0.060000" steps="50"/></proof>
  <proof prover="10"><result status="valid" time="0.190000" steps="44747"/></proof>
  <proof prover="11"><result status="valid" time="0.080000" steps="200579"/></proof>
  </goal>
  <goal name="set_mark&#39;vc.36" expl="type invariant" proved="true">
  <proof prover="9"><result status="valid" time="0.060000" steps="52"/></proof>
  <proof prover="10"><result status="valid" time="0.200000" steps="44864"/></proof>
  <proof prover="11"><result status="valid" time="0.070000" steps="200905"/></proof>
  </goal>
  <goal name="set_mark&#39;vc.37" expl="type invariant" proved="true">
  <proof prover="9"><result status="valid" time="0.060000" steps="54"/></proof>
  <proof prover="10"><result status="valid" time="0.200000" steps="45185"/></proof>
  </goal>
  <goal name="set_mark&#39;vc.38" expl="type invariant" proved="true">
  <proof prover="9"><result status="valid" time="0.419204" steps="223"/></proof>
  <proof prover="10"><result status="valid" time="0.240000" steps="49042"/></proof>
  </goal>
  <goal name="set_mark&#39;vc.39" expl="type invariant" proved="true">
  <proof prover="9"><result status="valid" time="0.070000" steps="64"/></proof>
  <proof prover="10"><result status="valid" time="0.200000" steps="49020"/></proof>
  <proof prover="11"><result status="valid" time="0.080000" steps="221177"/></proof>
  </goal>
  <goal name="set_mark&#39;vc.40" expl="type invariant" proved="true">
  <proof prover="9"><result status="valid" time="0.070000" steps="55"/></proof>
  <proof prover="10"><result status="valid" time="0.210000" steps="46642"/></proof>
  <proof prover="11"><result status="valid" time="0.080000" steps="204551"/></proof>
  </goal>
  <goal name="set_mark&#39;vc.41" expl="type invariant" proved="true">
  <proof prover="9"><result status="valid" time="0.080000" steps="63"/></proof>
  <proof prover="10"><result status="valid" time="0.200000" steps="48637"/></proof>
  </goal>
  <goal name="set_mark&#39;vc.42" expl="type invariant" proved="true">
  <proof prover="9"><result status="valid" time="0.220000" steps="354"/></proof>
  <proof prover="10"><result status="valid" time="0.270000" steps="53987"/></proof>
  </goal>
  <goal name="set_mark&#39;vc.43" expl="type invariant" proved="true">
  <proof prover="9"><result status="valid" time="0.070000" steps="66"/></proof>
  <proof prover="10"><result status="valid" time="0.230000" steps="50055"/></proof>
  <proof prover="11"><result status="valid" time="0.080000" steps="237627"/></proof>
  </goal>
  <goal name="set_mark&#39;vc.44" expl="type invariant" proved="true">
  <proof prover="9"><result status="valid" time="0.080000" steps="66"/></proof>
  <proof prover="10"><result status="valid" time="0.270000" steps="53544"/></proof>
  <proof prover="11"><result status="valid" time="0.090000" steps="235344"/></proof>
  </goal>
  <goal name="set_mark&#39;vc.45" expl="type invariant" proved="true">
  <proof prover="9"><result status="valid" time="0.100000" steps="63"/></proof>
  <proof prover="10"><result status="valid" time="0.230000" steps="50841"/></proof>
  </goal>
  <goal name="set_mark&#39;vc.46" expl="type invariant" proved="true">
  <proof prover="9"><result status="valid" time="0.110000" steps="68"/></proof>
  <proof prover="10"><result status="valid" time="0.319734" steps="62487"/></proof>
  <proof prover="11"><result status="valid" time="0.090000" steps="250494"/></proof>
  </goal>
  <goal name="set_mark&#39;vc.47" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="48"/></proof>
  <proof prover="10"><result status="valid" time="0.120000" steps="37271"/></proof>
  <proof prover="11"><result status="valid" time="0.040000" steps="95571"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="get_mark&#39;vc" expl="VC for get_mark" proved="true">
 <proof prover="9"><result status="valid" time="0.200000" steps="337"/></proof>
 </goal>
 <goal name="get_max&#39;vc" expl="VC for get_max" proved="true">
 <proof prover="9"><result status="valid" time="0.030000" steps="24"/></proof>
 <proof prover="10"><result status="valid" time="0.140000" steps="32819"/></proof>
 <proof prover="11"><result status="valid" time="0.060000" steps="109705"/></proof>
 </goal>
 <goal name="EulerSieve.t&#39;refn&#39;vc" expl="VC for t" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="t&#39;refn&#39;vc.0" expl="VC for t" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="12"/></proof>
  <proof prover="10"><result status="valid" time="0.130000" steps="37420"/></proof>
  <proof prover="11"><result status="valid" time="0.060000" steps="131310"/></proof>
  </goal>
  <goal name="t&#39;refn&#39;vc.1" expl="VC for t" proved="true">
  <proof prover="9"><result status="valid" time="0.030000" steps="12"/></proof>
  <proof prover="10"><result status="valid" time="0.140000" steps="37398"/></proof>
  <proof prover="11"><result status="valid" time="0.050000" steps="131343"/></proof>
  </goal>
  <goal name="t&#39;refn&#39;vc.2" expl="VC for t" proved="true">
  <proof prover="9"><result status="valid" time="0.030000" steps="12"/></proof>
  <proof prover="10"><result status="valid" time="0.170000" steps="47558"/></proof>
  <proof prover="11"><result status="valid" time="0.070000" steps="184189"/></proof>
  </goal>
  <goal name="t&#39;refn&#39;vc.3" expl="VC for t" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="12"/></proof>
  <proof prover="10"><result status="valid" time="0.170000" steps="42407"/></proof>
  <proof prover="11"><result status="valid" time="0.060000" steps="157672"/></proof>
  </goal>
  <goal name="t&#39;refn&#39;vc.4" expl="VC for t" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="12"/></proof>
  <proof prover="10"><result status="valid" time="0.160000" steps="42638"/></proof>
  <proof prover="11"><result status="valid" time="0.060000" steps="157939"/></proof>
  </goal>
  <goal name="t&#39;refn&#39;vc.5" expl="VC for t" proved="true">
  <proof prover="9"><result status="valid" time="0.030000" steps="12"/></proof>
  <proof prover="10"><result status="valid" time="0.140000" steps="37403"/></proof>
  <proof prover="11"><result status="valid" time="0.050000" steps="131529"/></proof>
  </goal>
  <goal name="t&#39;refn&#39;vc.6" expl="VC for t" proved="true">
  <proof prover="9"><result status="valid" time="0.030000" steps="18"/></proof>
  <proof prover="10"><result status="valid" time="0.160000" steps="42945"/></proof>
  <proof prover="11"><result status="valid" time="0.070000" steps="168994"/></proof>
  </goal>
  <goal name="t&#39;refn&#39;vc.7" expl="VC for t" proved="true">
  <proof prover="9"><result status="valid" time="0.040000" steps="20"/></proof>
  <proof prover="10"><result status="valid" time="0.180000" steps="43391"/></proof>
  <proof prover="11"><result status="valid" time="0.060000" steps="170802"/></proof>
  </goal>
  <goal name="t&#39;refn&#39;vc.8" expl="VC for t" proved="true">
  <proof prover="9"><result status="valid" time="0.030000" steps="12"/></proof>
  <proof prover="10"><result status="valid" time="0.160000" steps="41290"/></proof>
  <proof prover="11"><result status="valid" time="0.060000" steps="151400"/></proof>
  </goal>
  <goal name="t&#39;refn&#39;vc.9" expl="VC for t" proved="true">
  <proof prover="9"><result status="valid" time="0.030000" steps="14"/></proof>
  <proof prover="10"><result status="valid" time="0.160000" steps="41641"/></proof>
  <proof prover="11"><result status="valid" time="0.060000" steps="153111"/></proof>
  </goal>
  <goal name="t&#39;refn&#39;vc.10" expl="VC for t" proved="true">
  <proof prover="9"><result status="valid" time="0.030000" steps="14"/></proof>
  <proof prover="10"><result status="valid" time="0.160000" steps="41577"/></proof>
  <proof prover="11"><result status="valid" time="0.060000" steps="153123"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="EulerSieve.create&#39;refn&#39;vc" expl="VC for create&#39;refn" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="create&#39;refn&#39;vc.0" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="14"/></proof>
  <proof prover="10"><result status="valid" time="0.100000" steps="33327"/></proof>
  <proof prover="11"><result status="valid" time="0.020000" steps="17412"/></proof>
  </goal>
  <goal name="create&#39;refn&#39;vc.1" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="32"/></proof>
  <proof prover="10"><result status="valid" time="0.120000" steps="41568"/></proof>
  <proof prover="11"><result status="valid" time="0.020000" steps="13232"/></proof>
  </goal>
  <goal name="create&#39;refn&#39;vc.2" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="32"/></proof>
  <proof prover="10"><result status="valid" time="0.120000" steps="41589"/></proof>
  <proof prover="11"><result status="valid" time="0.020000" steps="22397"/></proof>
  </goal>
  <goal name="create&#39;refn&#39;vc.3" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.040000" steps="38"/></proof>
  <proof prover="10"><result status="valid" time="0.300000" steps="58108"/></proof>
  </goal>
  <goal name="create&#39;refn&#39;vc.4" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.040000" steps="105"/></proof>
  <proof prover="11"><result status="valid" time="0.070000" steps="204379"/></proof>
  </goal>
  <goal name="create&#39;refn&#39;vc.5" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.040000" steps="105"/></proof>
  <proof prover="11"><result status="valid" time="0.070000" steps="205449"/></proof>
  </goal>
  <goal name="create&#39;refn&#39;vc.6" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.030000" steps="42"/></proof>
  <proof prover="10"><result status="valid" time="0.200000" steps="48449"/></proof>
  <proof prover="11"><result status="valid" time="0.080000" steps="202019"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="EulerSieve.set_next&#39;refn&#39;vc" expl="VC for set_next&#39;refn" proved="true">
 <proof prover="9"><result status="valid" time="0.100000" steps="206"/></proof>
 <proof prover="10"><result status="valid" time="0.160000" steps="46677"/></proof>
 </goal>
 <goal name="EulerSieve.get_next&#39;refn&#39;vc" expl="VC for get_next&#39;refn" proved="true">
 <proof prover="9"><result status="valid" time="0.020000" steps="26"/></proof>
 <proof prover="10"><result status="valid" time="0.130000" steps="35583"/></proof>
 <proof prover="11"><result status="valid" time="0.050000" steps="129637"/></proof>
 </goal>
 <goal name="EulerSieve.set_mark&#39;refn&#39;vc" expl="VC for set_mark&#39;refn" proved="true">
 <proof prover="9"><result status="valid" time="0.030000" steps="40"/></proof>
 <proof prover="10"><result status="valid" time="0.180000" steps="41756"/></proof>
 <proof prover="11"><result status="valid" time="0.060000" steps="151801"/></proof>
 </goal>
 <goal name="EulerSieve.get_mark&#39;refn&#39;vc" expl="VC for get_mark&#39;refn" proved="true">
 <proof prover="9"><result status="valid" time="0.020000" steps="26"/></proof>
 <proof prover="10"><result status="valid" time="0.130000" steps="35583"/></proof>
 <proof prover="11"><result status="valid" time="0.050000" steps="129637"/></proof>
 </goal>
 <goal name="EulerSieve.get_max&#39;refn&#39;vc" expl="VC for get_max&#39;refn" proved="true">
 <proof prover="9"><result status="valid" time="0.020000" steps="20"/></proof>
 <proof prover="10"><result status="valid" time="0.100000" steps="33410"/></proof>
 <proof prover="11"><result status="valid" time="0.010000" steps="10062"/></proof>
 </goal>
 <goal name="euler_sieve&#39;vc" expl="VC for euler_sieve" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="euler_sieve&#39;vc.0" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="14"/></proof>
  <proof prover="10"><result status="valid" time="0.100000" steps="33644"/></proof>
  <proof prover="11"><result status="valid" time="0.020000" steps="17698"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.1" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="58"/></proof>
  <proof prover="10"><result status="valid" time="0.180000" steps="45040"/></proof>
  <proof prover="11"><result status="valid" time="0.060000" steps="208582"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.2" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="60"/></proof>
  <proof prover="10"><result status="valid" time="0.130000" steps="42490"/></proof>
  <proof prover="11"><result status="valid" time="0.020000" steps="13656"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.3" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="60"/></proof>
  <proof prover="10"><result status="valid" time="0.140000" steps="42493"/></proof>
  <proof prover="11"><result status="valid" time="0.020000" steps="13661"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.4" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="60"/></proof>
  <proof prover="10"><result status="valid" time="0.120000" steps="42496"/></proof>
  <proof prover="11"><result status="valid" time="0.020000" steps="13666"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.5" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="60"/></proof>
  <proof prover="10"><result status="valid" time="0.130000" steps="42499"/></proof>
  <proof prover="11"><result status="valid" time="0.020000" steps="13671"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.6" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="78"/></proof>
  <proof prover="10"><result status="valid" time="0.180000" steps="45040"/></proof>
  <proof prover="11"><result status="valid" time="0.040000" steps="114375"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.7" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.190000" steps="258"/></proof>
  <proof prover="10"><result status="valid" time="0.270000" steps="56675"/></proof>
  <proof prover="11"><result status="valid" time="0.080000" steps="239819"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.8" expl="division by zero" proved="true">
  <proof prover="9"><result status="valid" time="0.030000" steps="84"/></proof>
  <proof prover="10"><result status="valid" time="0.180000" steps="45288"/></proof>
  <proof prover="11"><result status="valid" time="0.020000" steps="23375"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.9" expl="integer overflow" proved="true">
  <proof prover="9"><result status="valid" time="0.180000" steps="364"/></proof>
  <proof prover="10"><result status="valid" time="0.220000" steps="52360"/></proof>
  <proof prover="11"><result status="valid" time="0.090000" steps="225288"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.10" expl="assertion" proved="true">
  <proof prover="9"><result status="valid" time="0.460000" steps="403"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.11" expl="precondition" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="euler_sieve&#39;vc.11.0" expl="precondition" proved="true">
   <proof prover="9"><result status="valid" time="0.020000" steps="68"/></proof>
   <proof prover="10"><result status="valid" time="0.180000" steps="45155"/></proof>
   <proof prover="11"><result status="valid" time="0.080000" steps="210982"/></proof>
   </goal>
   <goal name="euler_sieve&#39;vc.11.1" expl="precondition" proved="true">
   <proof prover="9"><result status="valid" time="0.060000" steps="72"/></proof>
   <proof prover="10"><result status="valid" time="0.240000" steps="53710"/></proof>
   <proof prover="11"><result status="valid" time="0.080000" steps="260573"/></proof>
   </goal>
   <goal name="euler_sieve&#39;vc.11.2" expl="precondition" proved="true">
   <transf name="unfold" proved="true" arg1="not_marked_impl_next_not_marked" arg2="in" arg3="Ensures5">
    <goal name="euler_sieve&#39;vc.11.2.0" expl="precondition" proved="true">
    <transf name="split_premise_right" proved="true" >
     <goal name="euler_sieve&#39;vc.11.2.0.0" expl="precondition" proved="true">
     <transf name="assert" proved="true" arg1="(int63&#39;int nn &lt;= div (int63&#39;int (max1 t)) (int63&#39;int nn))">
      <goal name="euler_sieve&#39;vc.11.2.0.0.0" expl="asserted formula" proved="true">
      <proof prover="9"><result status="valid" time="0.100000" steps="76"/></proof>
      <proof prover="11"><result status="valid" time="0.100000" steps="282712"/></proof>
      </goal>
      <goal name="euler_sieve&#39;vc.11.2.0.0.1" expl="precondition" proved="true">
      <proof prover="11"><result status="valid" time="0.130000" steps="447953"/></proof>
      </goal>
     </transf>
     </goal>
    </transf>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="euler_sieve&#39;vc.12" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.030000" steps="95"/></proof>
  <proof prover="10"><result status="valid" time="0.190000" steps="47038"/></proof>
  <proof prover="11"><result status="valid" time="0.090000" steps="241168"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.13" expl="assertion" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="euler_sieve&#39;vc.13.0" expl="assertion" proved="true">
   <proof prover="10"><result status="valid" time="0.330000" steps="68319"/></proof>
   <proof prover="11"><result status="valid" time="0.260000" steps="700074"/></proof>
   </goal>
   <goal name="euler_sieve&#39;vc.13.1" expl="VC for euler_sieve" proved="true">
   <transf name="unfold" proved="true" arg1="only_multiples_marked" arg2="in" arg3="Ensures4">
    <goal name="euler_sieve&#39;vc.13.1.0" expl="VC for euler_sieve" proved="true">
    <transf name="remove" proved="true" arg1="zero1,one1,(-),abs,int63&#39;maxInt,int63&#39;minInt,min_int63,max_int63,to_int,in_bounds,zero,one,even,odd,divides,prime,singleton,cons,snoc,(++),exchange,all_eliminated_marked_partial,is_copy,not_marked_impl_next_not_marked_partial,all_primes,all_multiples_marked,previously_marked_multiples,only_multiples_marked,prime_multiples_marked,inv_remove_products,ordered,all_inf_or_eq,inv_count,Assoc1,Unit_def_l,Unit_def_r,Inv_def_r,Comm1,Assoc,Mul_distr_l,Mul_distr_r,Comm,Refl,CompatOrderAdd,Abs_le,Abs_pos,Div_mod,Mod_bound,Div_unique,Div_bound,Mod_1,Div_1,Div_inf,Div_inf_neg,Mod_0,Div_1_left,Div_minus1_left,Mod_1_left,Mod_minus1_left,Div_mult,Mod_mult,Div_mod1,Div_bound1,Mod_bound1,Div_sign_pos,Div_sign_neg,Mod_sign_pos,Mod_sign_neg,Rounds_toward_zero,Div_11,Mod_11,Div_inf1,Mod_inf,Div_mult1,Mod_mult1,to_int_in_bounds,extensionality,max_int&#39;def,min_int&#39;def,even_or_odd,even_not_odd,odd_not_even,even_odd,odd_even,even_even,odd_odd,even_2k,odd_2k1,even_mod2,divides&#39;spec,divides_refl,divides_1_n,divides_0,divides_left,divides_right,divides_oppr,divides_oppl,divides_oppr_rev,divides_oppl_rev,divides_plusr,divides_minusr,divides_multl,divides_multr,divides_factorl,divides_factorr,divides_n_1,divides_antisym,divides_trans,divides_bounds,mod_divides_euclidean,divides_mod_euclidean,mod_divides_computer,divides_mod_computer,even_divides,odd_divides,not_prime_1,prime_2,prime_3,prime_divisors,small_divisors,even_prime,odd_prime,mult_croissance_locale,mult_croissance,comp_mult_2,div_croissance_locale1,div_croissance1,div_croissance_locale2,div_croissance2,div_mult_1,mult_borne_sous_exp,sq_ineq,divides_div,divides_inf,not_prime_divider_limits,no_prod_impl_no_divider,not_prime_impl_divisor_under_sqrt,(==)&#39;spec,create&#39;spec,empty&#39;def,set&#39;spec,set&#39;def,([&lt;-])&#39;def,singleton&#39;spec,cons&#39;spec,snoc&#39;spec,([..])&#39;spec,([..])&#39;def,([_..])&#39;def,([.._])&#39;def,(++)&#39;spec,exchange_set,conservation_all_eliminated_marked_on_marked_change,conservation_all_eliminated_marked_on_nexts_change,array63&#39;invariant,conservation_inv_arr_on_mark,conservation_inv_arr_on_jump,multiples_of_marked_are_marked,prev_and_new_impl_all_multiples_marked,conservation_only_multiples_marked,conservation_previously_marked_multiples,conservation_previously_marked_multiples_on_marked_change,conservation_not_marked_impl_next_not_marked,unchanged_other_elements,previously_marked_multiples_impl_prime,only_multiples_marked_impl_not_marked,H18,H17,Ensures13,H16,H15,H14,Ensures12,Ensures11,Ensures10,Ensures9,Ensures8,H13,H10,H9,Requires4,Requires3,Requires2,Requires,H8,Ensures7,Ensures6,Ensures5,H5,Ensures2,Ensures1,H3,Assert,Ensures,H12,H11,H7,H6">
     <goal name="euler_sieve&#39;vc.13.1.0.0" expl="VC for euler_sieve" proved="true">
     <proof prover="9"><result status="valid" time="0.050000" steps="109"/></proof>
     <proof prover="11"><result status="valid" time="0.030000" steps="302904"/></proof>
     </goal>
    </transf>
    </goal>
   </transf>
   </goal>
   <goal name="euler_sieve&#39;vc.13.2" expl="VC for euler_sieve" proved="true">
   <transf name="remove" proved="true" arg1="zero1,one1,(-),(&gt;),(&lt;=),(&gt;=),abs,int63&#39;maxInt,int63&#39;minInt,min_int63,max_int63,to_int,in_bounds,zero,one,even,odd,divides,prime,([]),singleton,cons,snoc,(++),exchange,inv_nexts,all_eliminated_marked,all_eliminated_marked_partial,is_copy,not_marked_impl_next_not_marked_partial,all_multiples_marked,previously_marked_multiples,only_multiples_marked,prime_multiples_marked,inv_remove_products,ordered,all_inf_or_eq,inv_count,Assoc1,Unit_def_l,Unit_def_r,Inv_def_l,Inv_def_r,Comm1,Assoc,Mul_distr_l,Mul_distr_r,Comm,Unitary,NonTrivialRing,Refl,Trans,Antisymm,Total,ZeroLessOne,CompatOrderAdd,CompatOrderMult,Abs_le,Abs_pos,Div_mod,Mod_bound,Div_unique,Div_bound,Mod_1,Div_1,Div_inf,Div_inf_neg,Mod_0,Div_1_left,Div_minus1_left,Mod_1_left,Mod_minus1_left,Div_mult,Mod_mult,Div_mod1,Div_bound1,Mod_bound1,Div_sign_pos,Div_sign_neg,Mod_sign_pos,Mod_sign_neg,Rounds_toward_zero,Div_11,Mod_11,Div_inf1,Mod_inf,Div_mult1,Mod_mult1,to_int_in_bounds,extensionality,max_int&#39;def,min_int&#39;def,even_or_odd,even_not_odd,odd_not_even,even_odd,odd_even,even_even,odd_odd,even_2k,odd_2k1,even_mod2,divides&#39;spec,divides_refl,divides_1_n,divides_0,divides_left,divides_right,divides_oppr,divides_oppl,divides_oppr_rev,divides_oppl_rev,divides_plusr,divides_minusr,divides_multl,divides_multr,divides_factorl,divides_n_1,divides_antisym,divides_trans,divides_bounds,mod_divides_euclidean,divides_mod_euclidean,mod_divides_computer,divides_mod_computer,even_divides,odd_divides,not_prime_1,prime_2,prime_3,small_divisors,even_prime,odd_prime,mult_croissance_locale,mult_croissance,comp_mult_2,div_croissance_locale1,div_croissance1,div_croissance_locale2,div_croissance2,div_mult_1,mult_borne_sous_exp,sq_ineq,divides_div,divides_inf,not_prime_divider_limits,no_prod_impl_no_divider,not_prime_impl_divisor_under_sqrt,length_nonnegative,(==)&#39;spec,(==)&#39;spec&#39;0,create&#39;spec,create&#39;spec&#39;0,empty&#39;def,set&#39;spec,set&#39;spec&#39;0,set&#39;spec&#39;1,set&#39;def,([&lt;-])&#39;def,singleton&#39;spec,singleton&#39;spec&#39;0,cons&#39;spec,cons&#39;spec&#39;0,cons&#39;spec&#39;1,snoc&#39;spec,snoc&#39;spec&#39;0,snoc&#39;spec&#39;1,([..])&#39;spec,([..])&#39;spec&#39;0,([..])&#39;def,([_..])&#39;def,([.._])&#39;def,(++)&#39;spec,(++)&#39;spec&#39;0,(++)&#39;spec&#39;1,exchange_set,conservation_all_eliminated_marked_on_marked_change,conservation_all_eliminated_marked_on_nexts_change,array63&#39;invariant,conservation_inv_arr_on_mark,conservation_inv_arr_on_jump,t&#39;invariant,multiples_of_marked_are_marked,prev_and_new_impl_all_multiples_marked,conservation_only_multiples_marked,conservation_previously_marked_multiples,conservation_previously_marked_multiples_on_marked_change,conservation_not_marked_impl_next_not_marked,unchanged_other_elements,previously_marked_multiples_impl_prime,only_multiples_marked_impl_not_marked,H18,H17,Ensures13,H16,H15,H14,Ensures12,Ensures11,Ensures10,Ensures9,Ensures8,H13,H10,H9,Requires4,Requires3,Requires2,Requires1,Requires,H8,Ensures7,Ensures6,Ensures5,Ensures4,H5,H4,Ensures3,Ensures2,Ensures1,H3,Assert,Ensures,H12,H11,H7,H6">
    <goal name="euler_sieve&#39;vc.13.2.0" expl="VC for euler_sieve" proved="true">
    <proof prover="3"><result status="valid" time="0.424473"/></proof>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="euler_sieve&#39;vc.14" expl="variant decrease" proved="true">
  <proof prover="9"><result status="valid" time="4.845487" steps="749"/></proof>
  <proof prover="10"><result status="valid" time="0.330000" steps="64625"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.15" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="92"/></proof>
  <proof prover="10"><result status="valid" time="0.230000" steps="52576"/></proof>
  <proof prover="11"><result status="valid" time="0.090000" steps="230534"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.16" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.030000" steps="94"/></proof>
  <proof prover="10"><result status="valid" time="0.120000" steps="43041"/></proof>
  <proof prover="11"><result status="valid" time="0.020000" steps="13881"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.17" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.030000" steps="94"/></proof>
  <proof prover="10"><result status="valid" time="0.180000" steps="45564"/></proof>
  <proof prover="11"><result status="valid" time="0.080000" steps="230681"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.18" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.030000" steps="95"/></proof>
  <proof prover="10"><result status="valid" time="0.160000" steps="45576"/></proof>
  <proof prover="11"><result status="valid" time="0.090000" steps="231456"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.19" expl="precondition" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="euler_sieve&#39;vc.19.0" expl="precondition" proved="true">
   <transf name="inline_goal" proved="true" >
    <goal name="euler_sieve&#39;vc.19.0.0" expl="precondition" proved="true">
    <transf name="split_all_full" proved="true" >
     <goal name="euler_sieve&#39;vc.19.0.0.0" expl="VC for euler_sieve" proved="true">
     <proof prover="9"><result status="valid" time="0.070000" steps="78"/></proof>
     <proof prover="10"><result status="valid" time="0.210000" steps="54517"/></proof>
     <proof prover="11"><result status="valid" time="0.100000" steps="276789"/></proof>
     </goal>
     <goal name="euler_sieve&#39;vc.19.0.0.1" expl="VC for euler_sieve" proved="true">
     <proof prover="9"><result status="valid" time="0.070000" steps="78"/></proof>
     <proof prover="10"><result status="valid" time="0.280000" steps="60961"/></proof>
     <proof prover="11"><result status="valid" time="0.100000" steps="263841"/></proof>
     </goal>
     <goal name="euler_sieve&#39;vc.19.0.0.2" expl="VC for euler_sieve" proved="true">
     <proof prover="9"><result status="valid" time="0.030000" steps="74"/></proof>
     <proof prover="10"><result status="valid" time="0.180000" steps="50868"/></proof>
     <proof prover="11"><result status="valid" time="0.080000" steps="232859"/></proof>
     </goal>
     <goal name="euler_sieve&#39;vc.19.0.0.3" expl="VC for euler_sieve" proved="true">
     <proof prover="9"><result status="valid" time="1.500000" steps="337"/></proof>
     <proof prover="11"><result status="valid" time="0.120000" steps="376076"/></proof>
     </goal>
    </transf>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="euler_sieve&#39;vc.20" expl="precondition" proved="true">
  <transf name="inline_goal" proved="true" >
   <goal name="euler_sieve&#39;vc.20.0" expl="precondition" proved="true">
   <transf name="split_vc" proved="true" >
    <goal name="euler_sieve&#39;vc.20.0.0" expl="precondition" proved="true">
    <proof prover="9"><result status="valid" time="0.070000" steps="79"/></proof>
    <proof prover="10"><result status="valid" time="0.180000" steps="48872"/></proof>
    <proof prover="11"><result status="valid" time="0.090000" steps="252706"/></proof>
    </goal>
    <goal name="euler_sieve&#39;vc.20.0.1" expl="precondition" proved="true">
    <proof prover="9"><result status="valid" time="0.070000" steps="79"/></proof>
    <proof prover="10"><result status="valid" time="0.170000" steps="45668"/></proof>
    <proof prover="11"><result status="valid" time="0.090000" steps="230845"/></proof>
    </goal>
    <goal name="euler_sieve&#39;vc.20.0.2" expl="precondition" proved="true">
    <proof prover="10"><result status="valid" time="1.060000" steps="105785"/></proof>
    </goal>
    <goal name="euler_sieve&#39;vc.20.0.3" expl="precondition" proved="true">
    <proof prover="9"><result status="valid" time="0.030000" steps="75"/></proof>
    <proof prover="10"><result status="valid" time="0.140000" steps="42920"/></proof>
    <proof prover="11"><result status="valid" time="0.020000" steps="13821"/></proof>
    </goal>
    <goal name="euler_sieve&#39;vc.20.0.4" expl="precondition" proved="true">
    <transf name="unfold" proved="true" arg1="not_marked_impl_next_not_marked" arg2="in" arg3="Requires">
     <goal name="euler_sieve&#39;vc.20.0.4.0" expl="precondition" proved="true">
     <transf name="split_premise_right" proved="true" >
      <goal name="euler_sieve&#39;vc.20.0.4.0.0" expl="precondition" proved="true">
      <transf name="assert" proved="true" arg1="(int63&#39;int nn &lt;= div (int63&#39;int (max1 t)) (int63&#39;int nn))">
       <goal name="euler_sieve&#39;vc.20.0.4.0.0.0" expl="asserted formula" proved="true">
       <proof prover="9"><result status="valid" time="0.110000" steps="83"/></proof>
       <proof prover="11"><result status="valid" time="0.100000" steps="283737"/></proof>
       </goal>
       <goal name="euler_sieve&#39;vc.20.0.4.0.0.1" expl="precondition" proved="true">
       <proof prover="11"><result status="valid" time="0.140000" steps="432190"/></proof>
       </goal>
      </transf>
      </goal>
     </transf>
     </goal>
    </transf>
    </goal>
    <goal name="euler_sieve&#39;vc.20.0.5" expl="precondition" proved="true">
    <proof prover="9"><result status="valid" time="0.070000" steps="79"/></proof>
    <proof prover="10"><result status="valid" time="0.180000" steps="47285"/></proof>
    <proof prover="11"><result status="valid" time="0.080000" steps="241526"/></proof>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="euler_sieve&#39;vc.21" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.120000" steps="359"/></proof>
  <proof prover="10"><result status="valid" time="0.260000" steps="55852"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.22" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.030000" steps="88"/></proof>
  <proof prover="10"><result status="valid" time="0.170000" steps="45335"/></proof>
  <proof prover="11"><result status="valid" time="0.070000" steps="211266"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.23" expl="assertion" proved="true">
  <transf name="remove" proved="true" arg1="zero1,one1,(-),(&gt;),(&lt;=),(&gt;=),abs,int63&#39;maxInt,int63&#39;minInt,min_int63,max_int63,to_int,in_bounds,zero,one,even,odd,divides,prime,singleton,cons,snoc,(++),exchange,inv_nexts,all_eliminated_marked,all_eliminated_marked_partial,not_marked_impl_next_not_marked,is_copy,not_marked_impl_next_not_marked_partial,only_multiples_marked,prime_multiples_marked,inv_remove_products,ordered,all_inf_or_eq,inv_count,Assoc1,Unit_def_l,Unit_def_r,Inv_def_l,Inv_def_r,Comm1,Assoc,Refl,Trans,CompatOrderAdd,CompatOrderMult,Abs_le,Abs_pos,Div_mod,Mod_bound,Div_unique,Div_bound,Mod_1,Div_1,Div_inf,Div_inf_neg,Mod_0,Div_1_left,Div_minus1_left,Mod_1_left,Mod_minus1_left,Div_mult,Mod_mult,Div_mod1,Div_bound1,Mod_bound1,Div_sign_pos,Div_sign_neg,Mod_sign_pos,Mod_sign_neg,Rounds_toward_zero,Div_11,Mod_11,Div_inf1,Mod_inf,Div_mult1,Mod_mult1,to_int_in_bounds,extensionality,max_int&#39;def,min_int&#39;def,even_or_odd,even_not_odd,odd_not_even,even_odd,odd_even,even_even,even_2k,odd_2k1,even_mod2,divides&#39;spec,divides_refl,divides_1_n,divides_0,divides_left,divides_right,divides_oppr,divides_oppl,divides_oppr_rev,divides_oppl_rev,divides_plusr,divides_minusr,divides_multl,divides_multr,divides_factorl,divides_factorr,divides_n_1,divides_antisym,divides_trans,divides_bounds,mod_divides_euclidean,divides_mod_euclidean,mod_divides_computer,divides_mod_computer,odd_divides,prime_2,prime_3,prime_divisors,small_divisors,even_prime,odd_prime,mult_croissance_locale,mult_croissance,comp_mult_2,div_croissance_locale1,div_croissance1,div_croissance_locale2,div_croissance2,div_mult_1,mult_borne_sous_exp,sq_ineq,divides_div,divides_inf,not_prime_divider_limits,no_prod_impl_no_divider,not_prime_impl_divisor_under_sqrt,(==)&#39;spec,create&#39;spec,empty&#39;def,set&#39;spec,set&#39;def,([&lt;-])&#39;def,singleton&#39;spec,cons&#39;spec,snoc&#39;spec,([..])&#39;spec,([..])&#39;def,([_..])&#39;def,([.._])&#39;def,(++)&#39;spec,exchange_set,conservation_all_eliminated_marked_on_marked_change,conservation_all_eliminated_marked_on_nexts_change,array63&#39;invariant,conservation_inv_arr_on_mark,conservation_inv_arr_on_jump,t&#39;invariant,multiples_of_marked_are_marked,prev_and_new_impl_all_multiples_marked,conservation_only_multiples_marked,conservation_previously_marked_multiples,conservation_previously_marked_multiples_on_marked_change,conservation_not_marked_impl_next_not_marked,unchanged_other_elements,previously_marked_multiples_impl_prime,only_multiples_marked_impl_not_marked,H17,H16,H15,Ensures13,H14,H13,H12,Ensures12,Ensures11,Ensures10,Ensures9,Ensures8,H11,H10,H9,H8,Requires4,Requires3,Requires2,Requires1,Requires,H7,H6,Ensures7,Ensures6,Ensures4,H5,H4,Ensures2,Ensures1,H3,Ensures,H2">
   <goal name="euler_sieve&#39;vc.23.0" expl="assertion" proved="true">
   <proof prover="3" timelimit="1"><result status="valid" time="1.368824"/></proof>
   <proof prover="9"><result status="valid" time="0.030000" steps="258"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="euler_sieve&#39;vc.24" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="88"/></proof>
  <proof prover="10"><result status="valid" time="0.170000" steps="47584"/></proof>
  <proof prover="11"><result status="valid" time="0.080000" steps="223669"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.25" expl="assertion" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="euler_sieve&#39;vc.25.0" expl="assertion" proved="true">
   <proof prover="9"><result status="valid" time="0.070000" steps="69"/></proof>
   </goal>
   <goal name="euler_sieve&#39;vc.25.1" expl="VC for euler_sieve" proved="true">
   <proof prover="11"><result status="valid" time="0.100000" steps="282495"/></proof>
   </goal>
   <goal name="euler_sieve&#39;vc.25.2" expl="VC for euler_sieve" proved="true">
   <proof prover="9"><result status="valid" time="0.933920" steps="408"/></proof>
   <proof prover="11"><result status="valid" time="0.080000" steps="225913"/></proof>
   </goal>
   <goal name="euler_sieve&#39;vc.25.3" expl="VC for euler_sieve" proved="true">
   <proof prover="9"><result status="valid" time="0.100000" steps="71"/></proof>
   </goal>
   <goal name="euler_sieve&#39;vc.25.4" expl="VC for euler_sieve" proved="true">
   <proof prover="9"><result status="valid" time="0.030000" steps="72"/></proof>
   <proof prover="10"><result status="valid" time="0.170000" steps="48576"/></proof>
   <proof prover="11"><result status="valid" time="0.080000" steps="226391"/></proof>
   </goal>
   <goal name="euler_sieve&#39;vc.25.5" expl="VC for euler_sieve" proved="true">
   <proof prover="9"><result status="valid" time="0.070000" steps="71"/></proof>
   <proof prover="10"><result status="valid" time="0.230000" steps="54825"/></proof>
   <proof prover="11"><result status="valid" time="0.090000" steps="270310"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="euler_sieve&#39;vc.26" expl="assertion" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="euler_sieve&#39;vc.26.0" expl="assertion" proved="true">
   <proof prover="9"><result status="valid" time="0.639083" steps="574"/></proof>
   </goal>
   <goal name="euler_sieve&#39;vc.26.1" expl="assertion" proved="true">
   <proof prover="9"><result status="valid" time="0.730000" steps="330"/></proof>
   </goal>
   <goal name="euler_sieve&#39;vc.26.2" expl="VC for euler_sieve" proved="true">
   <proof prover="9"><result status="valid" time="0.705222" steps="332"/></proof>
   </goal>
   <goal name="euler_sieve&#39;vc.26.3" expl="VC for euler_sieve" proved="true">
   <proof prover="9"><result status="valid" time="0.080000" steps="93"/></proof>
   </goal>
   <goal name="euler_sieve&#39;vc.26.4" expl="VC for euler_sieve" proved="true">
   <proof prover="9"><result status="valid" time="0.592435" steps="330"/></proof>
   </goal>
   <goal name="euler_sieve&#39;vc.26.5" expl="VC for euler_sieve" proved="true">
   <proof prover="10"><result status="valid" time="0.297238" steps="64142"/></proof>
   <proof prover="12"><result status="valid" time="0.460741" steps="50955"/></proof>
   <proof prover="13"><result status="valid" time="0.457778" steps="3684"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="euler_sieve&#39;vc.27" expl="postcondition" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="euler_sieve&#39;vc.27.0" expl="postcondition" proved="true">
   <proof prover="9"><result status="valid" time="2.317632" steps="549"/></proof>
   <proof prover="10"><result status="valid" time="0.325109" steps="68391"/></proof>
   <proof prover="11"><result status="valid" time="0.100000" steps="331393"/></proof>
   </goal>
   <goal name="euler_sieve&#39;vc.27.1" expl="postcondition" proved="true">
   <transf name="assert" proved="true" arg1="(forall j k. 2 &lt;= j &lt; (nexts t)[n] -&gt; 2 &lt;= k &lt; length (marked t) -&gt; j * k &lt;&gt; i)">
    <goal name="euler_sieve&#39;vc.27.1.0" expl="asserted formula" proved="true">
    <proof prover="9"><result status="valid" time="0.470000" steps="310"/></proof>
    </goal>
    <goal name="euler_sieve&#39;vc.27.1.1" expl="postcondition" proved="true">
    <proof prover="10"><result status="valid" time="0.290000" steps="60947"/></proof>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="euler_sieve&#39;vc.28" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="34"/></proof>
  <proof prover="10"><result status="valid" time="0.130000" steps="41895"/></proof>
  <proof prover="11"><result status="valid" time="0.020000" steps="13379"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.29" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="35"/></proof>
  <proof prover="10"><result status="valid" time="0.120000" steps="41913"/></proof>
  <proof prover="11"><result status="valid" time="0.010000" steps="13386"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.30" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.150000" steps="169"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.31" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.837346" steps="634"/></proof>
  <transf name="remove" proved="true" arg1="zero1,one1,(-),(&gt;),(&lt;=),(&gt;=),abs,int63&#39;maxInt,int63&#39;minInt,min_int63,max_int63,to_int,in_bounds,zero,one,even,divides,prime,singleton,cons,snoc,(++),exchange,inv_nexts,all_eliminated_marked,all_eliminated_marked_partial,not_marked_impl_next_not_marked,is_copy,not_marked_impl_next_not_marked_partial,all_primes,all_multiples_marked,previously_marked_multiples,prime_multiples_marked,inv_remove_products,ordered,all_inf_or_eq,inv_count,Assoc1,Unit_def_l,Unit_def_r,Inv_def_l,Inv_def_r,Comm1,Assoc,Mul_distr_l,Mul_distr_r,Comm,Unitary,NonTrivialRing,Refl,Trans,Antisymm,Total,ZeroLessOne,CompatOrderAdd,CompatOrderMult,Abs_le,Abs_pos,Div_mod,Mod_bound,Div_unique,Div_bound,Mod_1,Div_1,Div_inf,Div_inf_neg,Mod_0,Div_1_left,Div_minus1_left,Mod_1_left,Mod_minus1_left,Div_mult,Mod_mult,Div_mod1,Div_bound1,Mod_bound1,Div_sign_pos,Div_sign_neg,Mod_sign_pos,Mod_sign_neg,Rounds_toward_zero,Div_11,Mod_11,Div_inf1,Mod_inf,Div_mult1,Mod_mult1,to_int_in_bounds,extensionality,max_int&#39;def,min_int&#39;def,even_or_odd,even_not_odd,odd_not_even,odd_even,even_even,odd_odd,even_2k,odd_2k1,even_mod2,divides&#39;spec,divides_refl,divides_1_n,divides_0,divides_left,divides_right,divides_oppr,divides_oppl,divides_oppr_rev,divides_oppl_rev,divides_plusr,divides_minusr,divides_multl,divides_multr,divides_factorl,divides_factorr,divides_n_1,divides_antisym,divides_trans,divides_bounds,mod_divides_euclidean,divides_mod_euclidean,mod_divides_computer,divides_mod_computer,odd_divides,not_prime_1,prime_2,prime_3,prime_divisors,small_divisors,even_prime,odd_prime,mult_croissance_locale,mult_croissance,comp_mult_2,div_croissance_locale1,div_croissance1,div_croissance_locale2,div_croissance2,div_mult_1,mult_borne_sous_exp,sq_ineq,divides_div,divides_inf,not_prime_divider_limits,no_prod_impl_no_divider,not_prime_impl_divisor_under_sqrt,length_nonnegative,(==)&#39;spec,create&#39;spec,empty&#39;def,set&#39;spec,set&#39;def,([&lt;-])&#39;def,singleton&#39;spec,cons&#39;spec,snoc&#39;spec,([..])&#39;spec,([..])&#39;def,([_..])&#39;def,([.._])&#39;def,(++)&#39;spec,exchange_set,conservation_all_eliminated_marked_on_marked_change,conservation_all_eliminated_marked_on_nexts_change,array63&#39;invariant,conservation_inv_arr_on_mark,conservation_inv_arr_on_jump,multiples_of_marked_are_marked,prev_and_new_impl_all_multiples_marked,conservation_only_multiples_marked,conservation_previously_marked_multiples,conservation_previously_marked_multiples_on_marked_change,conservation_not_marked_impl_next_not_marked,unchanged_other_elements,previously_marked_multiples_impl_prime,only_multiples_marked_impl_not_marked,H6,H5,H4,H3,H2,Ensures4,Ensures3,Ensures2,Ensures1,H,Requires2,Requires1,Requires">
   <goal name="euler_sieve&#39;vc.31.0" expl="precondition" proved="true">
   <proof prover="0"><result status="valid" time="0.030000" steps="67"/></proof>
   <proof prover="9"><result status="valid" time="0.110000" steps="161"/></proof>
   <proof prover="10"><result status="valid" time="0.060000" steps="9519"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="euler_sieve&#39;vc.32" expl="precondition" proved="true">
  <transf name="inline_goal" proved="true" >
   <goal name="euler_sieve&#39;vc.32.0" expl="precondition" proved="true">
   <transf name="split_vc" proved="true" >
    <goal name="euler_sieve&#39;vc.32.0.0" expl="precondition" proved="true">
    <proof prover="9"><result status="valid" time="0.030000" steps="32"/></proof>
    <proof prover="10"><result status="valid" time="0.220000" steps="50838"/></proof>
    <proof prover="11"><result status="valid" time="0.080000" steps="220946"/></proof>
    </goal>
    <goal name="euler_sieve&#39;vc.32.0.1" expl="precondition" proved="true">
    <proof prover="9"><result status="valid" time="0.030000" steps="32"/></proof>
    <proof prover="10"><result status="valid" time="0.200000" steps="49093"/></proof>
    <proof prover="11"><result status="valid" time="0.070000" steps="210294"/></proof>
    </goal>
    <goal name="euler_sieve&#39;vc.32.0.2" expl="precondition" proved="true">
    <proof prover="9"><result status="valid" time="0.020000" steps="30"/></proof>
    <proof prover="10"><result status="valid" time="0.130000" steps="41865"/></proof>
    <proof prover="11"><result status="valid" time="0.020000" steps="13355"/></proof>
    </goal>
    <goal name="euler_sieve&#39;vc.32.0.3" expl="precondition" proved="true">
    <transf name="case" proved="true" arg1="(mod i 2 = 0)">
     <goal name="euler_sieve&#39;vc.32.0.3.0" expl="true case (precondition)" proved="true">
     <transf name="case" proved="true" arg1="(i &lt; max - 1)">
      <goal name="euler_sieve&#39;vc.32.0.3.0.0" expl="true case (precondition)" proved="true">
      <transf name="instantiate" proved="true" arg1="Ensures1" arg2="i">
       <goal name="euler_sieve&#39;vc.32.0.3.0.0.0" expl="true case (precondition)" proved="true">
       <proof prover="10"><result status="valid" time="0.445331" steps="86225"/></proof>
       </goal>
      </transf>
      </goal>
      <goal name="euler_sieve&#39;vc.32.0.3.0.1" expl="false case (true case. precondition)" proved="true">
      <proof prover="9"><result status="valid" time="0.060000" steps="44"/></proof>
      <proof prover="10"><result status="valid" time="0.210000" steps="49694"/></proof>
      <proof prover="11"><result status="valid" time="0.080000" steps="216659"/></proof>
      </goal>
     </transf>
     </goal>
     <goal name="euler_sieve&#39;vc.32.0.3.1" expl="false case (precondition)" proved="true">
     <proof prover="9"><result status="valid" time="0.180000" steps="141"/></proof>
     <proof prover="10"><result status="valid" time="0.300000" steps="62152"/></proof>
     </goal>
    </transf>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="euler_sieve&#39;vc.33" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.754150" steps="943"/></proof>
  <proof prover="10"><result status="valid" time="0.531011" steps="67956"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.34" expl="assertion" proved="true">
  <proof prover="9"><result status="valid" time="0.090000" steps="223"/></proof>
  <proof prover="10"><result status="valid" time="0.240000" steps="53568"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.35" expl="assertion" proved="true">
  <transf name="case" proved="true" arg1="(mod i 2 = 0)">
   <goal name="euler_sieve&#39;vc.35.0" expl="true case (assertion)" proved="true">
   <proof prover="9"><result status="valid" time="0.190000" steps="206"/></proof>
   <proof prover="10"><result status="valid" time="0.240000" steps="54524"/></proof>
   <proof prover="11"><result status="valid" time="0.080000" steps="237023"/></proof>
   </goal>
   <goal name="euler_sieve&#39;vc.35.1" expl="false case (assertion)" proved="true">
   <transf name="split_vc" proved="true" >
    <goal name="euler_sieve&#39;vc.35.1.0" expl="VC for euler_sieve" proved="true">
    <proof prover="9"><result status="valid" time="0.030000" steps="56"/></proof>
    <proof prover="10"><result status="valid" time="0.130000" steps="44086"/></proof>
    <proof prover="11"><result status="valid" time="0.020000" steps="14296"/></proof>
    </goal>
    <goal name="euler_sieve&#39;vc.35.1.1" expl="VC for euler_sieve" proved="true">
    <proof prover="9"><result status="valid" time="0.030000" steps="56"/></proof>
    <proof prover="10"><result status="valid" time="0.140000" steps="44105"/></proof>
    <proof prover="11"><result status="valid" time="0.020000" steps="14307"/></proof>
    </goal>
    <goal name="euler_sieve&#39;vc.35.1.2" expl="VC for euler_sieve" proved="true">
    <proof prover="9"><result status="valid" time="0.842001" steps="907"/></proof>
    <proof prover="10"><result status="valid" time="0.471485" steps="90379"/></proof>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="euler_sieve&#39;vc.36" expl="assertion" proved="true">
  <proof prover="9"><result status="valid" time="3.131419" steps="1437"/></proof>
  <proof prover="10"><result status="valid" time="0.260000" steps="54708"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.37" expl="index in array bounds" proved="true">
  <proof prover="9"><result status="valid" time="0.040000" steps="48"/></proof>
  <proof prover="10"><result status="valid" time="0.210000" steps="52434"/></proof>
  <proof prover="11"><result status="valid" time="0.080000" steps="237142"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.38" expl="loop invariant init" proved="true">
  <proof prover="9"><result status="valid" time="0.040000" steps="52"/></proof>
  <proof prover="10"><result status="valid" time="0.210000" steps="51058"/></proof>
  <proof prover="11"><result status="valid" time="0.080000" steps="229738"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.39" expl="loop invariant init" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="53"/></proof>
  <proof prover="10"><result status="valid" time="0.140000" steps="44201"/></proof>
  <proof prover="11"><result status="valid" time="0.020000" steps="14425"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.40" expl="loop invariant init" proved="true">
  <proof prover="9"><result status="valid" time="0.170000" steps="270"/></proof>
  <proof prover="10"><result status="valid" time="0.250000" steps="54426"/></proof>
  <proof prover="11"><result status="valid" time="0.100000" steps="246906"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.41" expl="loop invariant init" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="55"/></proof>
  <proof prover="10"><result status="valid" time="0.140000" steps="44265"/></proof>
  <proof prover="11"><result status="valid" time="0.020000" steps="14470"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.42" expl="loop invariant init" proved="true">
  <transf name="inline_goal" proved="true" >
   <goal name="euler_sieve&#39;vc.42.0" expl="loop invariant init" proved="true">
   <transf name="split_vc" proved="true" >
    <goal name="euler_sieve&#39;vc.42.0.0" expl="loop invariant init" proved="true">
    <transf name="assert" proved="true" arg1="(forall i. 1 &lt;= i &lt; length (arr t)[0 &lt;- 2] -&gt; (arr t)[i] = (arr t)[0 &lt;- 2][i])">
     <goal name="euler_sieve&#39;vc.42.0.0.0" expl="asserted formula" proved="true">
     <proof prover="9"><result status="valid" time="0.050000" steps="50"/></proof>
     <proof prover="10"><result status="valid" time="0.210000" steps="53153"/></proof>
     <proof prover="11"><result status="valid" time="0.090000" steps="253488"/></proof>
     </goal>
     <goal name="euler_sieve&#39;vc.42.0.0.1" expl="loop invariant init" proved="true">
     <proof prover="9"><result status="valid" time="0.402676" steps="177"/></proof>
     <proof prover="10"><result status="valid" time="0.260000" steps="57099"/></proof>
     <proof prover="11"><result status="valid" time="0.100000" steps="273828"/></proof>
     </goal>
    </transf>
    </goal>
    <goal name="euler_sieve&#39;vc.42.0.1" expl="loop invariant init" proved="true">
    <proof prover="9"><result status="valid" time="0.600000" steps="341"/></proof>
    <proof prover="10"><result status="valid" time="0.260000" steps="56907"/></proof>
    <proof prover="11"><result status="valid" time="0.100000" steps="285952"/></proof>
    </goal>
    <goal name="euler_sieve&#39;vc.42.0.2" expl="loop invariant init" proved="true">
    <proof prover="9"><result status="valid" time="0.355944" steps="275"/></proof>
    <proof prover="10"><result status="valid" time="0.260000" steps="56714"/></proof>
    <proof prover="11"><result status="valid" time="0.100000" steps="273307"/></proof>
    </goal>
    <goal name="euler_sieve&#39;vc.42.0.3" expl="loop invariant init" proved="true">
    <proof prover="9"><result status="valid" time="0.120000" steps="153"/></proof>
    <proof prover="10"><result status="valid" time="0.250000" steps="56711"/></proof>
    <proof prover="11"><result status="valid" time="0.090000" steps="261070"/></proof>
    </goal>
    <goal name="euler_sieve&#39;vc.42.0.4" expl="loop invariant init" proved="true">
    <transf name="assert" proved="true" arg1="(forall i. 1 &lt;= i &lt; length (arr t)[0 &lt;- 2] -&gt; (arr t)[i] = (arr t)[0 &lt;- 2][i])">
     <goal name="euler_sieve&#39;vc.42.0.4.0" expl="asserted formula" proved="true">
     <proof prover="9"><result status="valid" time="0.060000" steps="54"/></proof>
     <proof prover="10"><result status="valid" time="0.223932" steps="53499"/></proof>
     <proof prover="11"><result status="valid" time="0.090000" steps="261907"/></proof>
     </goal>
     <goal name="euler_sieve&#39;vc.42.0.4.1" expl="loop invariant init" proved="true">
     <proof prover="9"><result status="valid" time="0.670522" steps="570"/></proof>
     <proof prover="10"><result status="valid" time="0.456634" steps="62880"/></proof>
     </goal>
    </transf>
    </goal>
    <goal name="euler_sieve&#39;vc.42.0.5" expl="loop invariant init" proved="true">
    <proof prover="9"><result status="valid" time="0.462247" steps="430"/></proof>
    <proof prover="10"><result status="valid" time="0.380000" steps="70737"/></proof>
    <proof prover="11"><result status="valid" time="0.100000" steps="285923"/></proof>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="euler_sieve&#39;vc.43" expl="loop invariant init" proved="true">
  <proof prover="9"><result status="valid" time="0.050000" steps="156"/></proof>
  <proof prover="10"><result status="valid" time="0.331504" steps="52652"/></proof>
  <proof prover="11"><result status="valid" time="0.080000" steps="244837"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.44" expl="loop invariant init" proved="true">
  <proof prover="9"><result status="valid" time="0.325833" steps="373"/></proof>
  <proof prover="10"><result status="valid" time="0.382581" steps="56623"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.45" expl="loop invariant init" proved="true">
  <proof prover="9"><result status="valid" time="0.060000" steps="206"/></proof>
  <proof prover="10"><result status="valid" time="0.270000" steps="58194"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.46" expl="loop invariant init" proved="true">
  <proof prover="9"><result status="valid" time="0.140000" steps="200"/></proof>
  <proof prover="10"><result status="valid" time="0.240000" steps="58207"/></proof>
  <proof prover="11"><result status="valid" time="0.090000" steps="255720"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.47" expl="loop invariant init" proved="true">
  <proof prover="9"><result status="valid" time="0.568899" steps="445"/></proof>
  <proof prover="10"><result status="valid" time="0.404678" steps="59616"/></proof>
  <proof prover="11"><result status="valid" time="0.120000" steps="329849"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.48" expl="integer overflow" proved="true">
  <proof prover="9"><result status="valid" time="0.050000" steps="69"/></proof>
  <proof prover="10"><result status="valid" time="0.220000" steps="54150"/></proof>
  <proof prover="11"><result status="valid" time="0.080000" steps="249420"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.49" expl="integer overflow" proved="true">
  <proof prover="9"><result status="valid" time="0.040000" steps="71"/></proof>
  <proof prover="10"><result status="valid" time="0.230000" steps="54656"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.50" expl="index in array bounds" proved="true">
  <proof prover="9"><result status="valid" time="0.050000" steps="78"/></proof>
  <proof prover="10"><result status="valid" time="0.250000" steps="55793"/></proof>
  <proof prover="11"><result status="valid" time="0.090000" steps="265597"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.51" expl="division by zero" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="74"/></proof>
  <proof prover="10"><result status="valid" time="0.130000" steps="45931"/></proof>
  <proof prover="11"><result status="valid" time="0.020000" steps="15130"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.52" expl="integer overflow" proved="true">
  <proof prover="9"><result status="valid" time="0.110000" steps="293"/></proof>
  <proof prover="10"><result status="valid" time="0.377939" steps="54598"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.53" expl="assertion" proved="true">
  <proof prover="9"><result status="valid" time="0.060000" steps="189"/></proof>
  <proof prover="10"><result status="valid" time="0.358804" steps="54579"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.54" expl="index in array bounds" proved="true">
  <proof prover="9"><result status="valid" time="0.070000" steps="192"/></proof>
  <proof prover="10"><result status="valid" time="0.250000" steps="56371"/></proof>
  <proof prover="11"><result status="valid" time="0.090000" steps="296984"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.55" expl="index in array bounds" proved="true">
  <proof prover="9"><result status="valid" time="0.060000" steps="200"/></proof>
  <proof prover="10"><result status="valid" time="0.389769" steps="56582"/></proof>
  <proof prover="11"><result status="valid" time="0.100000" steps="305992"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.56" expl="integer overflow" proved="true">
  <proof prover="9"><result status="valid" time="0.274687" steps="339"/></proof>
  <proof prover="10"><result status="valid" time="0.300000" steps="63362"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.57" expl="index in array bounds" proved="true">
  <proof prover="9"><result status="valid" time="0.060000" steps="94"/></proof>
  <proof prover="10"><result status="valid" time="0.376550" steps="56643"/></proof>
  <proof prover="11"><result status="valid" time="0.100000" steps="284766"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.58" expl="index in array bounds" proved="true">
  <proof prover="9"><result status="valid" time="0.070000" steps="218"/></proof>
  <proof prover="10"><result status="valid" time="0.368175" steps="56943"/></proof>
  <proof prover="11"><result status="valid" time="0.120000" steps="324839"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.59" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.070000" steps="224"/></proof>
  <proof prover="10"><result status="valid" time="0.260000" steps="57099"/></proof>
  <proof prover="11"><result status="valid" time="0.100000" steps="311574"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.60" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.720000" steps="1019"/></proof>
  <proof prover="10"><result status="valid" time="0.361929" steps="67727"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.61" expl="assertion" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="euler_sieve&#39;vc.61.0" expl="assertion" proved="true">
   <transf name="unfold" proved="true" arg1="inv_count" arg2="in" arg3="LoopInvariant5">
    <goal name="euler_sieve&#39;vc.61.0.0" expl="assertion" proved="true">
    <transf name="instantiate" proved="true" arg1="LoopInvariant5" arg2="(int63&#39;int p)">
     <goal name="euler_sieve&#39;vc.61.0.0.0" expl="assertion" proved="true">
     <transf name="instantiate" proved="true" arg1="LoopInvariant5" arg2="(int63&#39;int next)">
      <goal name="euler_sieve&#39;vc.61.0.0.0.0" expl="assertion" proved="true">
      <proof prover="10"><result status="valid" time="0.521652" steps="82698"/></proof>
      </goal>
     </transf>
     </goal>
    </transf>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="euler_sieve&#39;vc.62" expl="assertion" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="euler_sieve&#39;vc.62.0" expl="assertion" proved="true">
   <proof prover="9"><result status="valid" time="1.377774" steps="1142"/></proof>
   <proof prover="10"><result status="valid" time="0.434625" steps="64846"/></proof>
   <proof prover="11"><result status="valid" time="0.180000" steps="551615"/></proof>
   </goal>
   <goal name="euler_sieve&#39;vc.62.1" expl="assertion" proved="true">
   <proof prover="9"><result status="valid" time="1.524070" steps="1144"/></proof>
   <proof prover="10"><result status="valid" time="0.370000" steps="77677"/></proof>
   </goal>
   <goal name="euler_sieve&#39;vc.62.2" expl="assertion" proved="true">
   <proof prover="9"><result status="valid" time="0.865925" steps="978"/></proof>
   <proof prover="10"><result status="valid" time="0.316364" steps="65350"/></proof>
   <proof prover="11"><result status="valid" time="0.110000" steps="384457"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="euler_sieve&#39;vc.63" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.030000" steps="104"/></proof>
  <proof prover="10"><result status="valid" time="0.200000" steps="50670"/></proof>
  <proof prover="11"><result status="valid" time="0.080000" steps="254544"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.64" expl="precondition" proved="true">
  <proof prover="11"><result status="valid" time="0.130000" steps="416950"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.65" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="1.410166" steps="525"/></proof>
  <proof prover="10"><result status="valid" time="0.327066" steps="67941"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.66" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.090000" steps="107"/></proof>
  <proof prover="10"><result status="valid" time="0.379425" steps="58779"/></proof>
  <proof prover="11"><result status="valid" time="0.100000" steps="317708"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.67" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.110000" steps="109"/></proof>
  <proof prover="10"><result status="valid" time="0.410000" steps="79556"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.68" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.140000" steps="112"/></proof>
  <proof prover="10"><result status="valid" time="0.495720" steps="86760"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.69" expl="assertion" proved="true">
  <proof prover="9"><result status="valid" time="0.411919" steps="410"/></proof>
  <proof prover="10"><result status="valid" time="0.300000" steps="65682"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.70" expl="assertion" proved="true">
  <transf name="unfold" proved="true" arg1="inv_count" arg2="in" arg3="LoopInvariant5">
   <goal name="euler_sieve&#39;vc.70.0" expl="assertion" proved="true">
   <transf name="split_vc" proved="true" >
    <goal name="euler_sieve&#39;vc.70.0.0" expl="assertion" proved="true">
    <proof prover="9"><result status="valid" time="0.635303" steps="417"/></proof>
    <proof prover="10"><result status="valid" time="2.119470" steps="227651"/></proof>
    </goal>
    <goal name="euler_sieve&#39;vc.70.0.1" expl="assertion" proved="true">
    <proof prover="9"><result status="valid" time="0.655976" steps="402"/></proof>
    <proof prover="11"><result status="valid" time="0.120000" steps="412166"/></proof>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="euler_sieve&#39;vc.71" expl="loop variant decrease" proved="true">
  <proof prover="9"><result status="valid" time="0.080000" steps="111"/></proof>
  <proof prover="10"><result status="valid" time="0.508948" steps="68143"/></proof>
  <proof prover="11"><result status="valid" time="0.120000" steps="414649"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.72" expl="loop invariant preservation" proved="true">
  <proof prover="9"><result status="valid" time="0.030000" steps="108"/></proof>
  <proof prover="10"><result status="valid" time="0.150000" steps="48783"/></proof>
  <proof prover="11"><result status="valid" time="0.020000" steps="27585"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.73" expl="loop invariant preservation" proved="true">
  <proof prover="9"><result status="valid" time="0.030000" steps="108"/></proof>
  <proof prover="10"><result status="valid" time="0.140000" steps="48799"/></proof>
  <proof prover="11"><result status="valid" time="0.020000" steps="27594"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.74" expl="loop invariant preservation" proved="true">
  <proof prover="9"><result status="valid" time="0.030000" steps="110"/></proof>
  <proof prover="10"><result status="valid" time="0.180000" steps="51647"/></proof>
  <proof prover="11"><result status="valid" time="0.090000" steps="259062"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.75" expl="loop invariant preservation" proved="true">
  <proof prover="9"><result status="valid" time="0.030000" steps="111"/></proof>
  <proof prover="10"><result status="valid" time="0.140000" steps="48834"/></proof>
  <proof prover="11"><result status="valid" time="0.020000" steps="16379"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.76" expl="loop invariant preservation" proved="true">
  <transf name="inline_goal" proved="true" >
   <goal name="euler_sieve&#39;vc.76.0" expl="loop invariant preservation" proved="true">
   <transf name="split_vc" proved="true" >
    <goal name="euler_sieve&#39;vc.76.0.0" expl="loop invariant preservation" proved="true">
    <transf name="case" proved="true" arg1="(i &lt;&gt; p)">
     <goal name="euler_sieve&#39;vc.76.0.0.0" expl="true case (loop invariant preservation)" proved="true">
     <proof prover="9"><result status="valid" time="1.137791" steps="415"/></proof>
     <proof prover="10"><result status="valid" time="0.477089" steps="68496"/></proof>
     </goal>
     <goal name="euler_sieve&#39;vc.76.0.0.1" expl="false case (loop invariant preservation)" proved="true">
     <proof prover="9"><result status="valid" time="1.340947" steps="416"/></proof>
     <proof prover="10"><result status="valid" time="0.480702" steps="66891"/></proof>
     </goal>
    </transf>
    </goal>
    <goal name="euler_sieve&#39;vc.76.0.1" expl="loop invariant preservation" proved="true">
    <transf name="case" proved="true" arg1="(i &lt;&gt; p)">
     <goal name="euler_sieve&#39;vc.76.0.1.0" expl="true case (loop invariant preservation)" proved="true">
     <proof prover="9"><result status="valid" time="1.107765" steps="409"/></proof>
     <proof prover="10"><result status="valid" time="0.340551" steps="68520"/></proof>
     <proof prover="11"><result status="valid" time="0.220000" steps="677350"/></proof>
     </goal>
     <goal name="euler_sieve&#39;vc.76.0.1.1" expl="false case (loop invariant preservation)" proved="true">
     <proof prover="9"><result status="valid" time="0.969484" steps="421"/></proof>
     <proof prover="10"><result status="valid" time="0.503139" steps="68298"/></proof>
     <proof prover="11"><result status="valid" time="0.140000" steps="439646"/></proof>
     </goal>
    </transf>
    </goal>
    <goal name="euler_sieve&#39;vc.76.0.2" expl="loop invariant preservation" proved="true">
    <proof prover="9"><result status="valid" time="1.840000" steps="1263"/></proof>
    <proof prover="10"><result status="valid" time="0.330000" steps="67452"/></proof>
    </goal>
    <goal name="euler_sieve&#39;vc.76.0.3" expl="loop invariant preservation" proved="true">
    <proof prover="9"><result status="valid" time="0.507289" steps="390"/></proof>
    <proof prover="10"><result status="valid" time="0.499773" steps="68453"/></proof>
    <proof prover="11"><result status="valid" time="0.130000" steps="421108"/></proof>
    </goal>
    <goal name="euler_sieve&#39;vc.76.0.4" expl="loop invariant preservation" proved="true">
    <proof prover="9"><result status="valid" time="1.036037" steps="416"/></proof>
    </goal>
    <goal name="euler_sieve&#39;vc.76.0.5" expl="loop invariant preservation" proved="true">
    <transf name="case" proved="true" arg1="(i &lt;&gt; p)">
     <goal name="euler_sieve&#39;vc.76.0.5.0" expl="true case (loop invariant preservation)" proved="true">
     <proof prover="8"><result status="valid" time="0.273332"/></proof>
     <transf name="remove" proved="true" arg1="zero1,one1,(-),(&gt;),(&lt;=),(&gt;=),abs,int63&#39;maxInt,int63&#39;minInt,min_int63,max_int63,to_int,in_bounds,zero,one,even,odd,divides,prime,([]),singleton,cons,snoc,(++),inv_nexts,all_eliminated_marked,all_eliminated_marked_partial,not_marked_impl_next_not_marked,is_copy,not_marked_impl_next_not_marked_partial,all_primes,all_multiples_marked,previously_marked_multiples,only_multiples_marked,prime_multiples_marked,inv_remove_products,ordered,all_inf_or_eq,Assoc1,Unit_def_l,Unit_def_r,Inv_def_l,Inv_def_r,Comm1,Assoc,Mul_distr_l,Mul_distr_r,Comm,Unitary,Refl,Antisymm,Total,ZeroLessOne,CompatOrderAdd,CompatOrderMult,Abs_le,Abs_pos,Div_mod,Mod_bound,Div_unique,Div_bound,Mod_1,Div_1,Div_inf,Div_inf_neg,Mod_0,Div_1_left,Div_minus1_left,Mod_1_left,Mod_minus1_left,Div_mult,Mod_mult,Div_mod1,Div_bound1,Mod_bound1,Div_sign_pos,Div_sign_neg,Mod_sign_pos,Mod_sign_neg,Rounds_toward_zero,Div_11,Mod_11,Div_inf1,Mod_inf,Div_mult1,Mod_mult1,to_int_in_bounds,extensionality,max_int&#39;def,min_int&#39;def,even_or_odd,even_not_odd,odd_not_even,even_odd,odd_even,even_even,odd_odd,even_2k,odd_2k1,even_mod2,divides&#39;spec,divides_refl,divides_1_n,divides_0,divides_left,divides_right,divides_oppr,divides_oppl,divides_oppr_rev,divides_oppl_rev,divides_plusr,divides_minusr,divides_multl,divides_multr,divides_factorl,divides_factorr,divides_n_1,divides_antisym,divides_trans,divides_bounds,mod_divides_euclidean,divides_mod_euclidean,mod_divides_computer,divides_mod_computer,even_divides,odd_divides,not_prime_1,prime_2,prime_3,prime_divisors,small_divisors,even_prime,odd_prime,mult_croissance_locale,mult_croissance,comp_mult_2,div_croissance_locale1,div_croissance1,div_croissance_locale2,div_croissance2,div_mult_1,mult_borne_sous_exp,sq_ineq,divides_div,divides_inf,not_prime_divider_limits,no_prod_impl_no_divider,not_prime_impl_divisor_under_sqrt,(==)&#39;spec,create&#39;spec,empty&#39;def,set&#39;spec,set&#39;def,([&lt;-])&#39;def,cons&#39;spec,snoc&#39;spec,([..])&#39;spec,([..])&#39;def,([_..])&#39;def,([.._])&#39;def,(++)&#39;spec,exchange_set,conservation_all_eliminated_marked_on_marked_change,conservation_all_eliminated_marked_on_nexts_change,conservation_inv_arr_on_mark,conservation_inv_arr_on_jump,t&#39;invariant,multiples_of_marked_are_marked,prev_and_new_impl_all_multiples_marked,conservation_only_multiples_marked,conservation_previously_marked_multiples,conservation_previously_marked_multiples_on_marked_change,conservation_not_marked_impl_next_not_marked,unchanged_other_elements,previously_marked_multiples_impl_prime,only_multiples_marked_impl_not_marked,H39,H38,Ensures18,H37,H36,H35,Ensures17,Ensures16,Ensures15,Ensures14,Ensures13,H34,H33,Ensures12,Assert3,Assert2,Assert1,H30,H29,Ensures11,H28,H27,H26,H25,H24,LoopInvariant9,LoopInvariant8,LoopInvariant6,LoopInvariant5,LoopInvariant4,LoopInvariant3,LoopInvariant2,Ensures10,Ensures9,H23,Ensures8,Ensures7,H22,Ensures6,H17,Ensures5,Ensures4,H16,Ensures3,Ensures2,Assert,Ensures,LoopInvariant1,LoopInvariant,H32,H31,H21,H20,H19,H18,H14,H13,H12,H11,H10,H9,H8,H7,H6,H4">
      <goal name="euler_sieve&#39;vc.76.0.5.0.0" expl="true case (loop invariant preservation)" proved="true">
      <proof prover="8"><result status="valid" time="0.020000"/></proof>
      <proof prover="9"><result status="valid" time="0.020000" steps="61"/></proof>
      <proof prover="10"><result status="valid" time="0.040000" steps="6334"/></proof>
      <proof prover="11"><result status="valid" time="0.020000" steps="30624"/></proof>
      </goal>
     </transf>
     </goal>
     <goal name="euler_sieve&#39;vc.76.0.5.1" expl="false case (loop invariant preservation)" proved="true">
     <proof prover="9"><result status="valid" time="1.252738" steps="1177"/></proof>
     <proof prover="10"><result status="valid" time="0.370131" steps="71916"/></proof>
     </goal>
    </transf>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="euler_sieve&#39;vc.77" expl="loop invariant preservation" proved="true">
  <proof prover="10"><result status="valid" time="0.610857" steps="86003"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.78" expl="loop invariant preservation" proved="true">
  <proof prover="10"><result status="valid" time="0.495098" steps="84133"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.79" expl="loop invariant preservation" proved="true">
  <proof prover="9"><result status="valid" time="0.289908" steps="697"/></proof>
  <proof prover="10"><result status="valid" time="0.344818" steps="69867"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.80" expl="loop invariant preservation" proved="true">
  <proof prover="9"><result status="valid" time="1.093897" steps="980"/></proof>
  <proof prover="10"><result status="valid" time="0.310000" steps="69432"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.81" expl="loop invariant preservation" proved="true">
  <transf name="instantiate" proved="true" arg1="LoopInvariant9" arg2="i">
   <goal name="euler_sieve&#39;vc.81.0" expl="loop invariant preservation" proved="true">
   <proof prover="9"><result status="valid" time="1.525473" steps="952"/></proof>
   <proof prover="10"><result status="valid" time="0.518707" steps="71341"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="euler_sieve&#39;vc.82" expl="integer overflow" proved="true">
  <proof prover="9"><result status="valid" time="0.060000" steps="90"/></proof>
  <proof prover="10"><result status="valid" time="0.180000" steps="48941"/></proof>
  <proof prover="11"><result status="valid" time="0.100000" steps="268488"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.83" expl="integer overflow" proved="true">
  <proof prover="9"><result status="valid" time="0.060000" steps="92"/></proof>
  <proof prover="10"><result status="valid" time="0.250000" steps="55195"/></proof>
  <proof prover="11"><result status="valid" time="0.080000" steps="272740"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.84" expl="index in array bounds" proved="true">
  <proof prover="9"><result status="valid" time="0.060000" steps="94"/></proof>
  <proof prover="10"><result status="valid" time="0.375737" steps="56656"/></proof>
  <proof prover="11"><result status="valid" time="0.100000" steps="288033"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.85" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.070000" steps="226"/></proof>
  <proof prover="10"><result status="valid" time="0.376026" steps="56992"/></proof>
  <proof prover="11"><result status="valid" time="0.100000" steps="306629"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.86" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.030000" steps="101"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.87" expl="integer overflow" proved="true">
  <proof prover="9"><result status="valid" time="0.060000" steps="98"/></proof>
  <proof prover="10"><result status="valid" time="0.382974" steps="57193"/></proof>
  <proof prover="11"><result status="valid" time="0.100000" steps="290262"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.88" expl="assertion" proved="true">
  <proof prover="9"><result status="valid" time="0.150000" steps="389"/></proof>
  <proof prover="10"><result status="valid" time="0.393647" steps="58704"/></proof>
  <proof prover="11"><result status="valid" time="0.110000" steps="323877"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.89" expl="loop variant decrease" proved="true">
  <proof prover="10"><result status="valid" time="0.527402" steps="76922"/></proof>
  <proof prover="11"><result status="valid" time="0.110000" steps="336398"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.90" expl="loop invariant preservation" proved="true">
  <proof prover="9"><result status="valid" time="0.486701" steps="380"/></proof>
  <proof prover="10"><result status="valid" time="0.395329" steps="73889"/></proof>
  <proof prover="11"><result status="valid" time="0.110000" steps="326957"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.91" expl="loop invariant preservation" proved="true">
  <proof prover="9"><result status="valid" time="0.384336" steps="395"/></proof>
  <proof prover="10"><result status="valid" time="0.429713" steps="78710"/></proof>
  <proof prover="11"><result status="valid" time="0.110000" steps="330714"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.92" expl="loop invariant preservation" proved="true">
  <proof prover="9"><result status="valid" time="0.100000" steps="348"/></proof>
  <proof prover="10"><result status="valid" time="0.260000" steps="58983"/></proof>
  <proof prover="11"><result status="valid" time="0.100000" steps="314649"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.93" expl="loop invariant preservation" proved="true">
  <proof prover="9"><result status="valid" time="0.080000" steps="112"/></proof>
  <proof prover="10"><result status="valid" time="0.260000" steps="58259"/></proof>
  <proof prover="11"><result status="valid" time="0.100000" steps="317446"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.94" expl="loop invariant preservation" proved="true">
  <transf name="inline_goal" proved="true" >
   <goal name="euler_sieve&#39;vc.94.0" expl="loop invariant preservation" proved="true">
   <transf name="split_vc" proved="true" >
    <goal name="euler_sieve&#39;vc.94.0.0" expl="loop invariant preservation" proved="true">
    <proof prover="9"><result status="valid" time="2.001232" steps="892"/></proof>
    <proof prover="10"><result status="valid" time="0.320000" steps="67648"/></proof>
    <proof prover="11"><result status="valid" time="0.130000" steps="447747"/></proof>
    </goal>
    <goal name="euler_sieve&#39;vc.94.0.1" expl="loop invariant preservation" proved="true">
    <proof prover="10"><result status="valid" time="0.320000" steps="67667"/></proof>
    <proof prover="11"><result status="valid" time="0.130000" steps="443515"/></proof>
    </goal>
    <goal name="euler_sieve&#39;vc.94.0.2" expl="loop invariant preservation" proved="true">
    <proof prover="9"><result status="valid" time="0.529463" steps="761"/></proof>
    <proof prover="10"><result status="valid" time="0.320000" steps="67441"/></proof>
    <proof prover="11"><result status="valid" time="0.110000" steps="365369"/></proof>
    </goal>
    <goal name="euler_sieve&#39;vc.94.0.3" expl="loop invariant preservation" proved="true">
    <proof prover="9"><result status="valid" time="0.399434" steps="492"/></proof>
    <proof prover="10"><result status="valid" time="0.330000" steps="67444"/></proof>
    <proof prover="11"><result status="valid" time="0.120000" steps="363804"/></proof>
    </goal>
    <goal name="euler_sieve&#39;vc.94.0.4" expl="loop invariant preservation" proved="true">
    <transf name="unfold" proved="true" arg1="inv_count" arg2="in" arg3="LoopInvariant7">
     <goal name="euler_sieve&#39;vc.94.0.4.0" expl="loop invariant preservation" proved="true">
     <transf name="split_premise_right" proved="true" >
      <goal name="euler_sieve&#39;vc.94.0.4.0.0" expl="loop invariant preservation" proved="true">
      <transf name="assert" proved="true" arg1="(t_arr[cnt1 &lt;- ((2 * p1) + 1)][i] = t_arr[i])">
       <goal name="euler_sieve&#39;vc.94.0.4.0.0.0" expl="asserted formula" proved="true">
       <proof prover="10"><result status="valid" time="0.410000" steps="79487"/></proof>
       </goal>
       <goal name="euler_sieve&#39;vc.94.0.4.0.0.1" expl="loop invariant preservation" proved="true">
       <transf name="instantiate" proved="true" arg1="LoopInvariant9" arg2="i">
        <goal name="euler_sieve&#39;vc.94.0.4.0.0.1.0" expl="loop invariant preservation" proved="true">
        <transf name="assert" proved="true" arg1="(cnt1 &lt;= i &lt; length t_arr1)">
         <goal name="euler_sieve&#39;vc.94.0.4.0.0.1.0.0" expl="asserted formula" proved="true">
         <proof prover="9"><result status="valid" time="0.120000" steps="101"/></proof>
         <proof prover="10"><result status="valid" time="0.240000" steps="58280"/></proof>
         <proof prover="11"><result status="valid" time="0.120000" steps="369867"/></proof>
         </goal>
         <goal name="euler_sieve&#39;vc.94.0.4.0.0.1.0.1" expl="loop invariant preservation" proved="true">
         <proof prover="8"><result status="valid" time="2.680000"/></proof>
         <transf name="remove" proved="true" arg1="zero1,one1,(-),(&gt;),(&lt;=),(&gt;=),abs,int63&#39;maxInt,int63&#39;minInt,min_int63,max_int63,to_int,in_bounds,zero,one,even,odd,divides,prime,([]),singleton,cons,snoc,(++),exchange,inv_nexts,all_eliminated_marked,all_eliminated_marked_partial,not_marked_impl_next_not_marked,is_copy,not_marked_impl_next_not_marked_partial,all_primes,all_multiples_marked,previously_marked_multiples,only_multiples_marked,prime_multiples_marked,inv_remove_products,ordered,all_inf_or_eq,inv_count,Assoc1,Unit_def_l,Unit_def_r,Inv_def_l,Inv_def_r,Comm1,Assoc,Mul_distr_l,Mul_distr_r,Comm,Unitary,NonTrivialRing,Refl,Trans,Antisymm,Total,ZeroLessOne,CompatOrderAdd,CompatOrderMult,Abs_pos,Div_mod,Div_unique,Mod_1,Div_1,Div_inf,Div_inf_neg,Mod_0,Div_1_left,Div_minus1_left,Mod_1_left,Mod_minus1_left,Div_mult,Mod_mult,Div_mod1,Div_sign_pos,Div_sign_neg,Mod_sign_pos,Mod_sign_neg,Rounds_toward_zero,Div_11,Mod_11,Div_inf1,Mod_inf,Div_mult1,Mod_mult1,to_int_in_bounds,extensionality,max_int&#39;def,min_int&#39;def,even_or_odd,even_not_odd,odd_not_even,even_odd,odd_even,even_even,odd_odd,even_2k,odd_2k1,divides_refl,divides_1_n,divides_0,divides_left,divides_right,divides_oppr,divides_oppl,divides_oppr_rev,divides_oppl_rev,divides_plusr,divides_minusr,divides_multl,divides_multr,divides_factorl,divides_factorr,divides_n_1,divides_antisym,divides_trans,divides_bounds,mod_divides_euclidean,divides_mod_euclidean,mod_divides_computer,divides_mod_computer,not_prime_1,prime_2,prime_3,prime_divisors,small_divisors,even_prime,odd_prime,mult_croissance_locale,mult_croissance,comp_mult_2,div_croissance_locale1,div_croissance1,div_croissance_locale2,div_croissance2,sq_ineq,divides_div,divides_inf,not_prime_divider_limits,no_prod_impl_no_divider,not_prime_impl_divisor_under_sqrt,length_nonnegative,empty&#39;def,set&#39;def,([&lt;-])&#39;def,([..])&#39;def,([_..])&#39;def,([.._])&#39;def,exchange_set,conservation_all_eliminated_marked_on_marked_change,conservation_all_eliminated_marked_on_nexts_change,conservation_inv_arr_on_mark,conservation_inv_arr_on_jump,multiples_of_marked_are_marked,prev_and_new_impl_all_multiples_marked,conservation_only_multiples_marked,conservation_previously_marked_multiples,conservation_previously_marked_multiples_on_marked_change,conservation_not_marked_impl_next_not_marked,unchanged_other_elements,previously_marked_multiples_impl_prime,only_multiples_marked_impl_not_marked,H33,H32,Ensures18,H31,H30,H29,Ensures17,Ensures16,Ensures15,Ensures14,Ensures13,H28,H27,Assert2,Assert1,H24,H23,Ensures10,H22,H21,H20,H19,H18,LoopInvariant15,LoopInvariant14,LoopInvariant7,LoopInvariant6,LoopInvariant3,LoopInvariant2,Ensures9,Ensures8,H17,Ensures7,Ensures6,H16,Ensures5,H11,Ensures4,Ensures3,H10,H9,Ensures2,Ensures1,Ensures,H8,LoopInvariant1,LoopInvariant,H26,H25,H15,H14,H13,H12,H7,H6,H5,H4,H2,(==)&#39;spec3,(==)&#39;spec2,(==)&#39;spec1,(==)&#39;spec,create&#39;spec1,create&#39;spec,set&#39;spec2,set&#39;spec1,set&#39;spec,singleton&#39;spec1,singleton&#39;spec,cons&#39;spec2,cons&#39;spec1,cons&#39;spec,snoc&#39;spec2,snoc&#39;spec1,snoc&#39;spec,([..])&#39;spec1,([..])&#39;spec,(++)&#39;spec2,(++)&#39;spec1,(++)&#39;spec,Abs_le2,Abs_le1,Abs_le,Div_bound3,Div_bound2,Mod_bound3,Mod_bound2,array63&#39;invariant3,array63&#39;invariant2,array63&#39;invariant1,array63&#39;invariant,Mod_bound1,Mod_bound,Div_bound1,Div_bound,divides&#39;spec1,divides&#39;spec,even_mod21,even_mod2,even_divides1,even_divides,odd_divides1,odd_divides,div_mult_11,div_mult_1,mult_borne_sous_exp1,mult_borne_sous_exp,t&#39;invariant22,t&#39;invariant21,t&#39;invariant20,t&#39;invariant19,t&#39;invariant18,t&#39;invariant17,t&#39;invariant16,t&#39;invariant15,t&#39;invariant14,t&#39;invariant13,t&#39;invariant12,t&#39;invariant11,t&#39;invariant10,t&#39;invariant9,t&#39;invariant8,t&#39;invariant7,t&#39;invariant6,t&#39;invariant5,t&#39;invariant4,t&#39;invariant3,t&#39;invariant2,t&#39;invariant1,t&#39;invariant,Ensures12,Ensures11,Assert4,Assert3,LoopInvariant13,LoopInvariant11,LoopInvariant10,LoopInvariant9,LoopInvariant8,LoopInvariant5,LoopInvariant4,h1">
          <goal name="euler_sieve&#39;vc.94.0.4.0.0.1.0.1.0" expl="loop invariant preservation" proved="true">
          <proof prover="8"><result status="valid" time="0.010000"/></proof>
          <proof prover="9"><result status="valid" time="0.020000" steps="30"/></proof>
          <proof prover="10"><result status="valid" time="0.040000" steps="6028"/></proof>
          <proof prover="11"><result status="valid" time="0.020000" steps="25799"/></proof>
          </goal>
         </transf>
         </goal>
        </transf>
        </goal>
       </transf>
       </goal>
      </transf>
      </goal>
     </transf>
     </goal>
    </transf>
    </goal>
    <goal name="euler_sieve&#39;vc.94.0.5" expl="loop invariant preservation" proved="true">
    <proof prover="11"><result status="valid" time="0.180000" steps="531911"/></proof>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="euler_sieve&#39;vc.95" expl="loop invariant preservation" proved="true">
  <transf name="inline_goal" proved="true" >
   <goal name="euler_sieve&#39;vc.95.0" expl="loop invariant preservation" proved="true">
   <transf name="split_vc" proved="true" >
    <goal name="euler_sieve&#39;vc.95.0.0" expl="loop invariant preservation" proved="true">
    <transf name="case" proved="true" arg1="(j = cnt1)">
     <goal name="euler_sieve&#39;vc.95.0.0.0" expl="true case (loop invariant preservation)" proved="true">
     <proof prover="8"><result status="valid" time="3.360574"/></proof>
     <transf name="remove" proved="true" arg1="zero1,one1,(-),(&gt;),(&lt;=),(&gt;=),abs,int63&#39;maxInt,int63&#39;minInt,min_int63,in_bounds,zero,one,even,odd,divides,prime,([]),singleton,cons,snoc,(++),exchange,inv_nexts,all_eliminated_marked,all_eliminated_marked_partial,not_marked_impl_next_not_marked,is_copy,not_marked_impl_next_not_marked_partial,all_primes,all_multiples_marked,previously_marked_multiples,only_multiples_marked,prime_multiples_marked,inv_remove_products,ordered,inv_count,Assoc1,Unit_def_l,Unit_def_r,Inv_def_l,Inv_def_r,Comm1,Assoc,Mul_distr_l,Mul_distr_r,Comm,Unitary,NonTrivialRing,Refl,Trans,Antisymm,Total,ZeroLessOne,CompatOrderAdd,CompatOrderMult,Abs_le,Abs_pos,Div_mod,Mod_bound,Div_unique,Div_bound,Mod_1,Div_1,Div_inf,Div_inf_neg,Mod_0,Div_1_left,Div_minus1_left,Mod_1_left,Mod_minus1_left,Div_mult,Mod_mult,Div_mod1,Div_bound1,Mod_bound1,Div_sign_pos,Div_sign_neg,Mod_sign_pos,Mod_sign_neg,Rounds_toward_zero,Div_11,Mod_11,Div_inf1,Mod_inf,Div_mult1,Mod_mult1,to_int_in_bounds,extensionality,max_int&#39;def,min_int&#39;def,even_or_odd,even_not_odd,odd_not_even,even_odd,odd_even,even_even,odd_odd,even_2k,odd_2k1,even_mod2,divides&#39;spec,divides_refl,divides_1_n,divides_0,divides_left,divides_right,divides_oppr,divides_oppl,divides_oppr_rev,divides_oppl_rev,divides_plusr,divides_minusr,divides_multl,divides_multr,divides_factorl,divides_factorr,divides_n_1,divides_antisym,divides_trans,divides_bounds,mod_divides_euclidean,divides_mod_euclidean,mod_divides_computer,divides_mod_computer,even_divides,odd_divides,not_prime_1,prime_2,prime_3,prime_divisors,small_divisors,even_prime,odd_prime,mult_croissance_locale,mult_croissance,comp_mult_2,div_croissance_locale1,div_croissance1,div_croissance_locale2,div_croissance2,div_mult_1,mult_borne_sous_exp,sq_ineq,divides_div,divides_inf,not_prime_divider_limits,no_prod_impl_no_divider,not_prime_impl_divisor_under_sqrt,length_nonnegative,(==)&#39;spec,create&#39;spec,empty&#39;def,set&#39;def,singleton&#39;spec,cons&#39;spec,snoc&#39;spec,([..])&#39;spec,([..])&#39;def,([_..])&#39;def,([.._])&#39;def,(++)&#39;spec,exchange_set,conservation_all_eliminated_marked_on_marked_change,conservation_all_eliminated_marked_on_nexts_change,conservation_inv_arr_on_mark,conservation_inv_arr_on_jump,multiples_of_marked_are_marked,prev_and_new_impl_all_multiples_marked,conservation_only_multiples_marked,conservation_previously_marked_multiples,conservation_previously_marked_multiples_on_marked_change,conservation_not_marked_impl_next_not_marked,unchanged_other_elements,previously_marked_multiples_impl_prime,only_multiples_marked_impl_not_marked,H32,H31,Ensures17,H30,H29,H28,Ensures16,Ensures15,Ensures14,Ensures13,Ensures12,H27,H26,Ensures11,Assert3,Assert2,Assert1,H23,H22,H20,H19,H18,H17,LoopInvariant10,LoopInvariant9,LoopInvariant8,LoopInvariant7,LoopInvariant5,LoopInvariant4,LoopInvariant3,Ensures9,Ensures8,H16,Ensures7,Ensures6,H15,Ensures5,H10,H9,H8,Ensures1,Ensures,H7,Assert,LoopInvariant2,LoopInvariant1,LoopInvariant,H25,H24,H14,H13,H12,H11,H6,H4">
      <goal name="euler_sieve&#39;vc.95.0.0.0.0" expl="true case (loop invariant preservation)" proved="true">
      <proof prover="8"><result status="valid" time="0.100000"/></proof>
      <proof prover="9"><result status="valid" time="0.080000" steps="158"/></proof>
      <proof prover="11"><result status="valid" time="0.020000" steps="46458"/></proof>
      </goal>
     </transf>
     </goal>
     <goal name="euler_sieve&#39;vc.95.0.0.1" expl="false case (loop invariant preservation)" proved="true">
     <proof prover="9"><result status="valid" time="1.401070" steps="1234"/></proof>
     <proof prover="10"><result status="valid" time="0.512849" steps="70607"/></proof>
     </goal>
    </transf>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="euler_sieve&#39;vc.96" expl="loop invariant preservation" proved="true">
  <transf name="inline_goal" proved="true" >
   <goal name="euler_sieve&#39;vc.96.0" expl="loop invariant preservation" proved="true">
   <transf name="split_vc" proved="true" >
    <goal name="euler_sieve&#39;vc.96.0.0" expl="loop invariant preservation" proved="true">
    <transf name="unfold" proved="true" arg1="all_inf_or_eq" arg2="in" arg3="LoopInvariant7">
     <goal name="euler_sieve&#39;vc.96.0.0.0" expl="loop invariant preservation" proved="true">
     <transf name="instantiate" proved="true" arg1="LoopInvariant7" arg2="i">
      <goal name="euler_sieve&#39;vc.96.0.0.0.0" expl="loop invariant preservation" proved="true">
      <transf name="unfold" proved="true" arg1="inv_count" arg2="in" arg3="LoopInvariant1">
       <goal name="euler_sieve&#39;vc.96.0.0.0.0.0" expl="loop invariant preservation" proved="true">
       <transf name="split_premise_right" proved="true" >
        <goal name="euler_sieve&#39;vc.96.0.0.0.0.0.0" expl="loop invariant preservation" proved="true">
        <transf name="instantiate" proved="true" arg1="LoopInvariant6" arg2="(int63&#39;int p1)">
         <goal name="euler_sieve&#39;vc.96.0.0.0.0.0.0.0" expl="loop invariant preservation" proved="true">
         <proof prover="10"><result status="valid" time="0.620000" steps="103898"/></proof>
         </goal>
        </transf>
        </goal>
       </transf>
       </goal>
      </transf>
      </goal>
     </transf>
     </goal>
    </transf>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="euler_sieve&#39;vc.97" expl="loop invariant preservation" proved="true">
  <proof prover="9"><result status="valid" time="0.280899" steps="764"/></proof>
  <proof prover="10"><result status="valid" time="0.340000" steps="69710"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.98" expl="loop invariant preservation" proved="true">
  <transf name="instantiate" proved="true" arg1="LoopInvariant9" arg2="i">
   <goal name="euler_sieve&#39;vc.98.0" expl="loop invariant preservation" proved="true">
   <proof prover="9"><result status="valid" time="1.630980" steps="1365"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="euler_sieve&#39;vc.99" expl="loop invariant preservation" proved="true">
  <transf name="case" proved="true" arg1="(i &lt; 2 * p1 + 1)">
   <goal name="euler_sieve&#39;vc.99.0" expl="true case (loop invariant preservation)" proved="true">
   <transf name="instantiate" proved="true" arg1="LoopInvariant9" arg2="i">
    <goal name="euler_sieve&#39;vc.99.0.0" expl="true case (loop invariant preservation)" proved="true">
    <proof prover="9"><result status="valid" time="0.767364" steps="841"/></proof>
    <proof prover="10"><result status="valid" time="0.330000" steps="71318"/></proof>
    </goal>
   </transf>
   </goal>
   <goal name="euler_sieve&#39;vc.99.1" expl="false case (loop invariant preservation)" proved="true">
   <transf name="case" proved="true" arg1="(i = 2 * p1 + 1)">
    <goal name="euler_sieve&#39;vc.99.1.0" expl="false case (true case. loop invariant preservation)" proved="true">
    <proof prover="10"><result status="valid" time="0.490000" steps="89421"/></proof>
    <proof prover="11"><result status="valid" time="0.300000" steps="795166"/></proof>
    </goal>
    <goal name="euler_sieve&#39;vc.99.1.1" expl="false case (loop invariant preservation)" proved="true">
    <proof prover="8"><result status="valid" time="2.070000"/></proof>
    <transf name="remove" proved="true" arg1="zero1,one1,(-),(&gt;),(&lt;=),(&gt;=),int63&#39;maxInt,int63&#39;minInt,min_int63,max_int63,in_bounds,zero,one,even,odd,divides,prime,([]),singleton,cons,snoc,(++),exchange,inv_nexts,all_eliminated_marked,all_eliminated_marked_partial,not_marked_impl_next_not_marked,is_copy,not_marked_impl_next_not_marked_partial,all_primes,all_multiples_marked,previously_marked_multiples,only_multiples_marked,prime_multiples_marked,inv_remove_products,ordered,all_inf_or_eq,Assoc1,Unit_def_l,Unit_def_r,Inv_def_l,Inv_def_r,Comm1,Assoc,Mul_distr_l,Mul_distr_r,Comm,Unitary,NonTrivialRing,Refl,Trans,Antisymm,Total,ZeroLessOne,CompatOrderAdd,CompatOrderMult,Abs_le,Abs_pos,Div_mod,Mod_bound,Div_unique,Div_bound,Mod_1,Div_1,Div_inf,Div_inf_neg,Mod_0,Div_1_left,Div_minus1_left,Mod_1_left,Mod_minus1_left,Div_mult,Mod_mult,Div_mod1,Div_bound1,Mod_bound1,Div_sign_pos,Div_sign_neg,Mod_sign_pos,Mod_sign_neg,Rounds_toward_zero,Div_11,Mod_11,Div_inf1,Mod_inf,Div_mult1,Mod_mult1,to_int_in_bounds,extensionality,max_int&#39;def,min_int&#39;def,even_or_odd,even_not_odd,odd_not_even,even_odd,odd_even,even_even,odd_odd,even_2k,odd_2k1,even_mod2,divides&#39;spec,divides_refl,divides_1_n,divides_0,divides_left,divides_right,divides_oppr,divides_oppl,divides_oppr_rev,divides_oppl_rev,divides_plusr,divides_minusr,divides_multl,divides_multr,divides_factorl,divides_factorr,divides_n_1,divides_antisym,divides_trans,divides_bounds,mod_divides_euclidean,divides_mod_euclidean,mod_divides_computer,divides_mod_computer,even_divides,odd_divides,not_prime_1,prime_2,prime_3,prime_divisors,small_divisors,even_prime,odd_prime,mult_croissance_locale,mult_croissance,comp_mult_2,div_croissance_locale1,div_croissance1,div_croissance_locale2,div_croissance2,div_mult_1,mult_borne_sous_exp,sq_ineq,divides_div,divides_inf,not_prime_divider_limits,no_prod_impl_no_divider,not_prime_impl_divisor_under_sqrt,length_nonnegative,(==)&#39;spec,create&#39;spec,empty&#39;def,set&#39;spec,set&#39;def,([&lt;-])&#39;def,singleton&#39;spec,cons&#39;spec,snoc&#39;spec,([..])&#39;spec,([..])&#39;def,([_..])&#39;def,([.._])&#39;def,(++)&#39;spec,exchange_set,conservation_all_eliminated_marked_on_marked_change,conservation_all_eliminated_marked_on_nexts_change,conservation_inv_arr_on_mark,conservation_inv_arr_on_jump,multiples_of_marked_are_marked,prev_and_new_impl_all_multiples_marked,conservation_only_multiples_marked,conservation_previously_marked_multiples,conservation_previously_marked_multiples_on_marked_change,conservation_not_marked_impl_next_not_marked,unchanged_other_elements,previously_marked_multiples_impl_prime,only_multiples_marked_impl_not_marked,H24,H23,H22,Ensures17,H21,H20,H19,Ensures16,Ensures15,Ensures14,Ensures13,Ensures12,H18,H17,H16,Assert4,Assert3,Assert2,H15,Ensures10,H12,H11,H10,LoopInvariant16,LoopInvariant15,LoopInvariant13,LoopInvariant12,LoopInvariant11,LoopInvariant10,LoopInvariant9,Ensures9,Ensures8,H8,Ensures5,H6,Ensures4,Ensures3,H5,H4,Ensures2,Ensures1,Ensures,Assert,LoopInvariant8,LoopInvariant7,LoopInvariant6,LoopInvariant5,LoopInvariant4,LoopInvariant3,LoopInvariant2,LoopInvariant1,LoopInvariant,H2">
     <goal name="euler_sieve&#39;vc.99.1.1.0" expl="false case (loop invariant preservation)" proved="true">
     <proof prover="9"><result status="valid" time="0.180000" steps="183"/></proof>
     </goal>
    </transf>
    <transf name="remove" proved="true" arg1="zero1,one1,(-),(&gt;),(&lt;=),(&gt;=),abs,int63&#39;maxInt,int63&#39;minInt,min_int63,in_bounds,zero,one,even,odd,divides,prime,([]),singleton,cons,snoc,(++),exchange,inv_nexts,all_eliminated_marked,all_eliminated_marked_partial,not_marked_impl_next_not_marked,is_copy,not_marked_impl_next_not_marked_partial,all_primes,all_multiples_marked,previously_marked_multiples,only_multiples_marked,prime_multiples_marked,inv_remove_products,ordered,all_inf_or_eq,Assoc1,Unit_def_l,Unit_def_r,Inv_def_l,Inv_def_r,Comm1,Assoc,Mul_distr_l,Mul_distr_r,Comm,Unitary,NonTrivialRing,Refl,Trans,Antisymm,Total,ZeroLessOne,CompatOrderAdd,CompatOrderMult,Abs_pos,Div_mod,Mod_bound,Div_unique,Div_bound,Mod_1,Div_1,Div_inf,Div_inf_neg,Mod_0,Div_1_left,Div_minus1_left,Mod_1_left,Mod_minus1_left,Div_mult,Mod_mult,Div_mod1,Div_bound1,Mod_bound1,Div_sign_pos,Div_sign_neg,Mod_sign_pos,Mod_sign_neg,Div_11,Mod_11,Div_inf1,Mod_inf,Div_mult1,Mod_mult1,to_int_in_bounds,extensionality,max_int&#39;def,min_int&#39;def,even_or_odd,even_not_odd,odd_not_even,even_odd,even_even,odd_odd,even_2k,odd_2k1,even_mod2,divides&#39;spec,divides_refl,divides_1_n,divides_0,divides_left,divides_right,divides_oppr,divides_oppl,divides_oppr_rev,divides_oppl_rev,divides_plusr,divides_minusr,divides_multl,divides_multr,divides_factorl,divides_factorr,divides_n_1,divides_antisym,divides_trans,divides_bounds,mod_divides_euclidean,divides_mod_euclidean,mod_divides_computer,divides_mod_computer,even_divides,odd_divides,not_prime_1,prime_2,prime_3,prime_divisors,small_divisors,mult_croissance_locale,mult_croissance,comp_mult_2,div_croissance_locale1,div_croissance1,div_croissance_locale2,div_croissance2,div_mult_1,mult_borne_sous_exp,sq_ineq,divides_div,divides_inf,not_prime_divider_limits,no_prod_impl_no_divider,not_prime_impl_divisor_under_sqrt,length_nonnegative,(==)&#39;spec,create&#39;spec,empty&#39;def,set&#39;spec,set&#39;def,([&lt;-])&#39;def,singleton&#39;spec,cons&#39;spec,snoc&#39;spec,([..])&#39;spec,([..])&#39;def,([_..])&#39;def,([.._])&#39;def,(++)&#39;spec,exchange_set,conservation_all_eliminated_marked_on_marked_change,conservation_all_eliminated_marked_on_nexts_change,conservation_inv_arr_on_mark,conservation_inv_arr_on_jump,multiples_of_marked_are_marked,prev_and_new_impl_all_multiples_marked,conservation_only_multiples_marked,conservation_previously_marked_multiples,conservation_previously_marked_multiples_on_marked_change,conservation_not_marked_impl_next_not_marked,unchanged_other_elements,previously_marked_multiples_impl_prime,only_multiples_marked_impl_not_marked,H24,H23,H22,Ensures17,H21,H20,H19,Ensures16,Ensures15,Ensures14,Ensures13,Ensures12,H18,H17,H16,Ensures11,Assert4,Assert3,Assert2,H15,Ensures10,H12,H11,H10,LoopInvariant16,LoopInvariant15,LoopInvariant13,LoopInvariant12,LoopInvariant11,LoopInvariant10,LoopInvariant9,Ensures9,Ensures8,H8,Ensures4,Ensures3,H5,H4,Ensures2,Ensures1,Ensures,LoopInvariant8,LoopInvariant6,LoopInvariant5,LoopInvariant4,LoopInvariant3,LoopInvariant2,LoopInvariant,H2">
     <goal name="euler_sieve&#39;vc.99.1.1.0" expl="false case (loop invariant preservation)" proved="true">
     <proof prover="8" timelimit="1"><result status="valid" time="0.050000"/></proof>
     </goal>
    </transf>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="euler_sieve&#39;vc.100" expl="integer overflow" proved="true">
  <proof prover="9"><result status="valid" time="0.060000" steps="84"/></proof>
  <proof prover="10"><result status="valid" time="0.190000" steps="48858"/></proof>
  <proof prover="11"><result status="valid" time="0.080000" steps="255189"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.101" expl="integer overflow" proved="true">
  <proof prover="9"><result status="valid" time="0.060000" steps="86"/></proof>
  <proof prover="10"><result status="valid" time="0.240000" steps="55016"/></proof>
  <proof prover="11"><result status="valid" time="0.090000" steps="258865"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.102" expl="index in array bounds" proved="true">
  <proof prover="9"><result status="valid" time="0.070000" steps="88"/></proof>
  <proof prover="10"><result status="valid" time="0.260000" steps="56451"/></proof>
  <proof prover="11"><result status="valid" time="0.090000" steps="288777"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.103" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.070000" steps="215"/></proof>
  <proof prover="10"><result status="valid" time="0.250000" steps="56818"/></proof>
  <proof prover="11"><result status="valid" time="0.100000" steps="297667"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.104" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.030000" steps="91"/></proof>
  <proof prover="10"><result status="valid" time="0.310000" steps="63790"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.105" expl="integer overflow" proved="true">
  <proof prover="9"><result status="valid" time="0.060000" steps="92"/></proof>
  <proof prover="10"><result status="valid" time="0.240000" steps="56929"/></proof>
  <proof prover="11"><result status="valid" time="0.090000" steps="275179"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.106" expl="integer overflow" proved="true">
  <proof prover="9"><result status="valid" time="0.070000" steps="94"/></proof>
  <proof prover="10"><result status="valid" time="0.375391" steps="56962"/></proof>
  <proof prover="11"><result status="valid" time="0.100000" steps="286632"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.107" expl="assertion" proved="true">
  <proof prover="9"><result status="valid" time="0.140000" steps="374"/></proof>
  <proof prover="10"><result status="valid" time="0.388926" steps="57961"/></proof>
  <proof prover="11"><result status="valid" time="0.100000" steps="308961"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.108" expl="loop variant decrease" proved="true">
  <proof prover="9"><result status="valid" time="0.070000" steps="97"/></proof>
  <proof prover="10"><result status="valid" time="0.280000" steps="60437"/></proof>
  <proof prover="11"><result status="valid" time="0.100000" steps="300526"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.109" expl="loop invariant preservation" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="90"/></proof>
  <proof prover="10"><result status="valid" time="0.180000" steps="50497"/></proof>
  <proof prover="11"><result status="valid" time="0.080000" steps="246738"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.110" expl="loop invariant preservation" proved="true">
  <proof prover="9"><result status="valid" time="0.060000" steps="98"/></proof>
  <proof prover="10"><result status="valid" time="0.270000" steps="57215"/></proof>
  <proof prover="11"><result status="valid" time="0.100000" steps="301789"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.111" expl="loop invariant preservation" proved="true">
  <proof prover="9"><result status="valid" time="0.080000" steps="103"/></proof>
  <proof prover="10"><result status="valid" time="0.260000" steps="57437"/></proof>
  <proof prover="11"><result status="valid" time="0.080000" steps="310327"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.112" expl="loop invariant preservation" proved="true">
  <proof prover="9"><result status="valid" time="0.080000" steps="105"/></proof>
  <proof prover="10"><result status="valid" time="0.260000" steps="57783"/></proof>
  <proof prover="11"><result status="valid" time="0.100000" steps="315478"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.113" expl="loop invariant preservation" proved="true">
  <transf name="inline_goal" proved="true" >
   <goal name="euler_sieve&#39;vc.113.0" expl="loop invariant preservation" proved="true">
   <transf name="split_vc" proved="true" >
    <goal name="euler_sieve&#39;vc.113.0.0" expl="loop invariant preservation" proved="true">
    <proof prover="9"><result status="valid" time="2.737395" steps="1381"/></proof>
    <proof prover="10"><result status="valid" time="0.456634" steps="69124"/></proof>
    <proof prover="11"><result status="valid" time="0.120000" steps="434018"/></proof>
    </goal>
    <goal name="euler_sieve&#39;vc.113.0.1" expl="loop invariant preservation" proved="true">
    <proof prover="10"><result status="valid" time="0.310000" steps="68232"/></proof>
    <proof prover="11"><result status="valid" time="0.130000" steps="429185"/></proof>
    </goal>
    <goal name="euler_sieve&#39;vc.113.0.2" expl="loop invariant preservation" proved="true">
    <proof prover="9"><result status="valid" time="0.729504" steps="1013"/></proof>
    <proof prover="10"><result status="valid" time="0.431171" steps="68966"/></proof>
    <proof prover="11"><result status="valid" time="0.120000" steps="358712"/></proof>
    </goal>
    <goal name="euler_sieve&#39;vc.113.0.3" expl="loop invariant preservation" proved="true">
    <proof prover="9"><result status="valid" time="0.350000" steps="375"/></proof>
    <proof prover="10"><result status="valid" time="0.483077" steps="68203"/></proof>
    <proof prover="11"><result status="valid" time="0.110000" steps="357200"/></proof>
    </goal>
    <goal name="euler_sieve&#39;vc.113.0.4" expl="loop invariant preservation" proved="true">
    <transf name="unfold" proved="true" arg1="inv_count" arg2="in" arg3="LoopInvariant7">
     <goal name="euler_sieve&#39;vc.113.0.4.0" expl="loop invariant preservation" proved="true">
     <transf name="split_premise_right" proved="true" >
      <goal name="euler_sieve&#39;vc.113.0.4.0.0" expl="loop invariant preservation" proved="true">
      <transf name="assert" proved="true" arg1="(t_arr[cnt1 &lt;- ((2 * p1) + 1)][i] = t_arr[i])">
       <goal name="euler_sieve&#39;vc.113.0.4.0.0.0" expl="asserted formula" proved="true">
       <proof prover="10"><result status="valid" time="0.420000" steps="79620"/></proof>
       </goal>
       <goal name="euler_sieve&#39;vc.113.0.4.0.0.1" expl="loop invariant preservation" proved="true">
       <transf name="instantiate" proved="true" arg1="LoopInvariant9" arg2="i">
        <goal name="euler_sieve&#39;vc.113.0.4.0.0.1.0" expl="loop invariant preservation" proved="true">
        <transf name="assert" proved="true" arg1="(cnt1 &lt;= i &lt; length t_arr1)">
         <goal name="euler_sieve&#39;vc.113.0.4.0.0.1.0.0" expl="asserted formula" proved="true">
         <proof prover="9"><result status="valid" time="0.120000" steps="94"/></proof>
         <proof prover="10"><result status="valid" time="0.230000" steps="58202"/></proof>
         <proof prover="11"><result status="valid" time="0.130000" steps="361875"/></proof>
         </goal>
         <goal name="euler_sieve&#39;vc.113.0.4.0.0.1.0.1" expl="loop invariant preservation" proved="true">
         <proof prover="8"><result status="valid" time="1.380000"/></proof>
         <transf name="remove" proved="true" arg1="zero1,one1,(-),(&gt;),(&lt;=),(&gt;=),abs,int63&#39;maxInt,int63&#39;minInt,min_int63,max_int63,to_int,in_bounds,zero,one,even,odd,divides,prime,([]),singleton,cons,snoc,(++),exchange,inv_nexts,all_eliminated_marked,all_eliminated_marked_partial,not_marked_impl_next_not_marked,is_copy,not_marked_impl_next_not_marked_partial,all_primes,all_multiples_marked,previously_marked_multiples,only_multiples_marked,prime_multiples_marked,inv_remove_products,ordered,all_inf_or_eq,inv_count,Assoc1,Unit_def_l,Unit_def_r,Inv_def_l,Inv_def_r,Comm1,Assoc,Mul_distr_l,Mul_distr_r,Comm,Unitary,NonTrivialRing,Refl,Trans,Antisymm,Total,ZeroLessOne,CompatOrderAdd,CompatOrderMult,Abs_pos,Div_mod,Div_unique,Mod_1,Div_1,Div_inf,Div_inf_neg,Mod_0,Div_1_left,Div_minus1_left,Mod_1_left,Mod_minus1_left,Div_mult,Mod_mult,Div_mod1,Div_sign_pos,Div_sign_neg,Mod_sign_pos,Mod_sign_neg,Rounds_toward_zero,Div_11,Mod_11,Div_inf1,Mod_inf,Div_mult1,Mod_mult1,to_int_in_bounds,extensionality,max_int&#39;def,min_int&#39;def,even_or_odd,even_not_odd,odd_not_even,even_odd,odd_even,even_even,odd_odd,even_2k,odd_2k1,divides_refl,divides_1_n,divides_0,divides_left,divides_right,divides_oppr,divides_oppl,divides_oppr_rev,divides_oppl_rev,divides_plusr,divides_minusr,divides_multl,divides_multr,divides_factorl,divides_factorr,divides_n_1,divides_antisym,divides_trans,divides_bounds,mod_divides_euclidean,divides_mod_euclidean,mod_divides_computer,divides_mod_computer,not_prime_1,prime_2,prime_3,prime_divisors,small_divisors,even_prime,odd_prime,mult_croissance_locale,mult_croissance,comp_mult_2,div_croissance_locale1,div_croissance1,div_croissance_locale2,div_croissance2,sq_ineq,divides_div,divides_inf,not_prime_divider_limits,no_prod_impl_no_divider,not_prime_impl_divisor_under_sqrt,length_nonnegative,empty&#39;def,set&#39;def,([&lt;-])&#39;def,([..])&#39;def,([_..])&#39;def,([.._])&#39;def,exchange_set,conservation_all_eliminated_marked_on_marked_change,conservation_all_eliminated_marked_on_nexts_change,conservation_inv_arr_on_mark,conservation_inv_arr_on_jump,multiples_of_marked_are_marked,prev_and_new_impl_all_multiples_marked,conservation_only_multiples_marked,conservation_previously_marked_multiples,conservation_previously_marked_multiples_on_marked_change,conservation_not_marked_impl_next_not_marked,unchanged_other_elements,previously_marked_multiples_impl_prime,only_multiples_marked_impl_not_marked,H27,H26,Ensures18,H25,H24,H23,Ensures17,Ensures16,Ensures15,Ensures14,Ensures13,H22,H21,Assert2,Assert1,H18,H17,Ensures10,H16,H15,H14,H13,H12,LoopInvariant15,LoopInvariant14,LoopInvariant7,LoopInvariant6,LoopInvariant3,LoopInvariant2,Ensures9,Ensures8,H11,Ensures7,Ensures6,H10,Ensures5,Ensures4,H9,H8,Ensures3,Ensures2,Ensures1,Ensures,LoopInvariant1,LoopInvariant,H20,H19,H7,H6,H5,H4,H2,(==)&#39;spec3,(==)&#39;spec2,(==)&#39;spec1,(==)&#39;spec,create&#39;spec1,create&#39;spec,set&#39;spec2,set&#39;spec1,set&#39;spec,singleton&#39;spec1,singleton&#39;spec,cons&#39;spec2,cons&#39;spec1,cons&#39;spec,snoc&#39;spec2,snoc&#39;spec1,snoc&#39;spec,([..])&#39;spec1,([..])&#39;spec,(++)&#39;spec2,(++)&#39;spec1,(++)&#39;spec,Abs_le2,Abs_le1,Abs_le,Div_bound3,Div_bound2,Mod_bound3,Mod_bound2,array63&#39;invariant3,array63&#39;invariant2,array63&#39;invariant1,array63&#39;invariant,Mod_bound1,Mod_bound,Div_bound1,Div_bound,divides&#39;spec1,divides&#39;spec,even_mod21,even_mod2,even_divides1,even_divides,odd_divides1,odd_divides,div_mult_11,div_mult_1,mult_borne_sous_exp1,mult_borne_sous_exp,t&#39;invariant22,t&#39;invariant21,t&#39;invariant20,t&#39;invariant19,t&#39;invariant18,t&#39;invariant17,t&#39;invariant16,t&#39;invariant15,t&#39;invariant14,t&#39;invariant13,t&#39;invariant12,t&#39;invariant11,t&#39;invariant10,t&#39;invariant9,t&#39;invariant8,t&#39;invariant7,t&#39;invariant6,t&#39;invariant5,t&#39;invariant4,t&#39;invariant3,t&#39;invariant2,t&#39;invariant1,t&#39;invariant,Ensures12,Ensures11,Assert4,Assert3,LoopInvariant13,LoopInvariant11,LoopInvariant10,LoopInvariant9,LoopInvariant8,LoopInvariant5,LoopInvariant4,h1">
          <goal name="euler_sieve&#39;vc.113.0.4.0.0.1.0.1.0" expl="loop invariant preservation" proved="true">
          <proof prover="8"><result status="valid" time="0.010000"/></proof>
          <proof prover="9"><result status="valid" time="0.020000" steps="30"/></proof>
          <proof prover="10"><result status="valid" time="0.040000" steps="6027"/></proof>
          <proof prover="11"><result status="valid" time="0.020000" steps="25799"/></proof>
          </goal>
         </transf>
         </goal>
        </transf>
        </goal>
       </transf>
       </goal>
      </transf>
      </goal>
     </transf>
     </goal>
    </transf>
    </goal>
    <goal name="euler_sieve&#39;vc.113.0.5" expl="loop invariant preservation" proved="true">
    <proof prover="11"><result status="valid" time="0.140000" steps="493575"/></proof>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="euler_sieve&#39;vc.114" expl="loop invariant preservation" proved="true">
  <transf name="inline_goal" proved="true" >
   <goal name="euler_sieve&#39;vc.114.0" expl="loop invariant preservation" proved="true">
   <transf name="split_vc" proved="true" >
    <goal name="euler_sieve&#39;vc.114.0.0" expl="loop invariant preservation" proved="true">
    <transf name="unfold" proved="true" arg1="ordered" arg2="in" arg3="LoopInvariant7">
     <goal name="euler_sieve&#39;vc.114.0.0.0" expl="loop invariant preservation" proved="true">
     <transf name="instantiate" proved="true" arg1="LoopInvariant7" arg2="i">
      <goal name="euler_sieve&#39;vc.114.0.0.0.0" expl="loop invariant preservation" proved="true">
      <transf name="instantiate" proved="true" arg1="Hinst" arg2="j">
       <goal name="euler_sieve&#39;vc.114.0.0.0.0.0" expl="loop invariant preservation" proved="true">
       <transf name="case" proved="true" arg1="(j = cnt1)">
        <goal name="euler_sieve&#39;vc.114.0.0.0.0.0.0" expl="true case (loop invariant preservation)" proved="true">
        <proof prover="9"><result status="valid" time="1.199016" steps="1368"/></proof>
        <proof prover="10"><result status="valid" time="0.471110" steps="69248"/></proof>
        </goal>
        <goal name="euler_sieve&#39;vc.114.0.0.0.0.0.1" expl="false case (loop invariant preservation)" proved="true">
        <proof prover="9"><result status="valid" time="0.290000" steps="592"/></proof>
        <proof prover="10"><result status="valid" time="0.408165" steps="60412"/></proof>
        </goal>
       </transf>
       </goal>
      </transf>
      </goal>
     </transf>
     </goal>
    </transf>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="euler_sieve&#39;vc.115" expl="loop invariant preservation" proved="true">
  <transf name="inline_goal" proved="true" >
   <goal name="euler_sieve&#39;vc.115.0" expl="loop invariant preservation" proved="true">
   <transf name="split_vc" proved="true" >
    <goal name="euler_sieve&#39;vc.115.0.0" expl="loop invariant preservation" proved="true">
    <transf name="unfold" proved="true" arg1="all_inf_or_eq" arg2="in" arg3="LoopInvariant7">
     <goal name="euler_sieve&#39;vc.115.0.0.0" expl="loop invariant preservation" proved="true">
     <transf name="instantiate" proved="true" arg1="LoopInvariant7" arg2="i">
      <goal name="euler_sieve&#39;vc.115.0.0.0.0" expl="loop invariant preservation" proved="true">
      <transf name="case" proved="true" arg1="(i &lt; cnt1)">
       <goal name="euler_sieve&#39;vc.115.0.0.0.0.0" expl="true case (loop invariant preservation)" proved="true">
       <proof prover="9"><result status="valid" time="0.170000" steps="374"/></proof>
       <proof prover="10"><result status="valid" time="0.270000" steps="59472"/></proof>
       <proof prover="11"><result status="valid" time="0.160000" steps="492848"/></proof>
       </goal>
       <goal name="euler_sieve&#39;vc.115.0.0.0.0.1" expl="false case (loop invariant preservation)" proved="true">
       <proof prover="9"><result status="valid" time="1.348692" steps="1203"/></proof>
       <proof prover="10"><result status="valid" time="0.485629" steps="70679"/></proof>
       </goal>
      </transf>
      </goal>
     </transf>
     </goal>
    </transf>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="euler_sieve&#39;vc.116" expl="loop invariant preservation" proved="true">
  <proof prover="9"><result status="valid" time="0.220000" steps="535"/></proof>
  <proof prover="10"><result status="valid" time="0.335805" steps="70550"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.117" expl="loop invariant preservation" proved="true">
  <transf name="case" proved="true" arg1="(i &lt; cnt1)">
   <goal name="euler_sieve&#39;vc.117.0" expl="true case (loop invariant preservation)" proved="true">
   <proof prover="9"><result status="valid" time="0.796739" steps="1076"/></proof>
   <proof prover="10"><result status="valid" time="0.496857" steps="70448"/></proof>
   </goal>
   <goal name="euler_sieve&#39;vc.117.1" expl="false case (loop invariant preservation)" proved="true">
   <proof prover="9"><result status="valid" time="1.137262" steps="1282"/></proof>
   <proof prover="10"><result status="valid" time="0.410785" steps="76383"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="euler_sieve&#39;vc.118" expl="loop invariant preservation" proved="true">
  <transf name="case" proved="true" arg1="(i &lt; 2 * p1 + 1)">
   <goal name="euler_sieve&#39;vc.118.0" expl="true case (loop invariant preservation)" proved="true">
   <transf name="instantiate" proved="true" arg1="LoopInvariant9" arg2="i">
    <goal name="euler_sieve&#39;vc.118.0.0" expl="true case (loop invariant preservation)" proved="true">
    <proof prover="9"><result status="valid" time="0.634054" steps="838"/></proof>
    <proof prover="10"><result status="valid" time="0.341353" steps="72488"/></proof>
    </goal>
   </transf>
   </goal>
   <goal name="euler_sieve&#39;vc.118.1" expl="false case (loop invariant preservation)" proved="true">
   <transf name="case" proved="true" arg1="(i = 2 * p1 + 1)">
    <goal name="euler_sieve&#39;vc.118.1.0" expl="false case (true case. loop invariant preservation)" proved="true">
    <proof prover="10"><result status="valid" time="0.700000" steps="97768"/></proof>
    <proof prover="11"><result status="valid" time="0.300000" steps="726462"/></proof>
    </goal>
    <goal name="euler_sieve&#39;vc.118.1.1" expl="false case (loop invariant preservation)" proved="true">
    <proof prover="9"><result status="valid" time="5.381771" steps="1445"/></proof>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="euler_sieve&#39;vc.119" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.050000" steps="75"/></proof>
  <proof prover="10"><result status="valid" time="0.250000" steps="55955"/></proof>
  <proof prover="11"><result status="valid" time="0.090000" steps="258144"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.120" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.332142" steps="282"/></proof>
  <proof prover="10"><result status="valid" time="1.020000" steps="126275"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.121" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="1.221513" steps="824"/></proof>
  <proof prover="10"><result status="valid" time="1.410000" steps="142186"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.122" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.243386" steps="310"/></proof>
  <proof prover="10"><result status="valid" time="0.290000" steps="66680"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.123" expl="postcondition" proved="true">
  <proof prover="10"><result status="valid" time="0.440781" steps="84220"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.124" expl="assertion" proved="true">
  <proof prover="9"><result status="valid" time="0.140000" steps="221"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.125" expl="assertion" proved="true">
  <proof prover="9"><result status="valid" time="0.180000" steps="258"/></proof>
  <proof prover="10"><result status="valid" time="2.143452" steps="319022"/></proof>
  <proof prover="11"><result status="valid" time="0.298313" steps="551331"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.126" expl="assertion" proved="true">
  <proof prover="9"><result status="valid" time="0.717347" steps="297"/></proof>
  <proof prover="10"><result status="valid" time="0.230000" steps="50619"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.127" expl="index in array bounds" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="36"/></proof>
  <proof prover="10"><result status="valid" time="0.210000" steps="49413"/></proof>
  <proof prover="11"><result status="valid" time="0.080000" steps="214746"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.128" expl="loop invariant init" proved="true">
  <proof prover="9"><result status="valid" time="0.030000" steps="40"/></proof>
  <proof prover="10"><result status="valid" time="0.200000" steps="48015"/></proof>
  <proof prover="11"><result status="valid" time="0.080000" steps="214687"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.129" expl="loop invariant init" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="41"/></proof>
  <proof prover="10"><result status="valid" time="0.130000" steps="42445"/></proof>
  <proof prover="11"><result status="valid" time="0.020000" steps="13669"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.130" expl="loop invariant init" proved="true">
  <proof prover="9"><result status="valid" time="0.100000" steps="186"/></proof>
  <proof prover="10"><result status="valid" time="0.230000" steps="50627"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.131" expl="loop invariant init" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="43"/></proof>
  <proof prover="10"><result status="valid" time="0.140000" steps="42509"/></proof>
  <proof prover="11"><result status="valid" time="0.020000" steps="13714"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.132" expl="loop invariant init" proved="true">
  <transf name="inline_goal" proved="true" >
   <goal name="euler_sieve&#39;vc.132.0" expl="loop invariant init" proved="true">
   <transf name="split_vc" proved="true" >
    <goal name="euler_sieve&#39;vc.132.0.0" expl="loop invariant init" proved="true">
    <transf name="assert" proved="true" arg1="(forall i. 1 &lt;= i &lt; length (arr t)[0 &lt;- 2] -&gt; (arr t)[i] = (arr t)[0 &lt;- 2][i])">
     <goal name="euler_sieve&#39;vc.132.0.0.0" expl="asserted formula" proved="true">
     <proof prover="9"><result status="valid" time="0.040000" steps="44"/></proof>
     <proof prover="10"><result status="valid" time="0.210000" steps="50206"/></proof>
     <proof prover="11"><result status="valid" time="0.080000" steps="238330"/></proof>
     </goal>
     <goal name="euler_sieve&#39;vc.132.0.0.1" expl="loop invariant init" proved="true">
     <proof prover="9"><result status="valid" time="0.330000" steps="143"/></proof>
     <proof prover="10"><result status="valid" time="0.240000" steps="53300"/></proof>
     <proof prover="11"><result status="valid" time="0.080000" steps="245532"/></proof>
     </goal>
    </transf>
    </goal>
    <goal name="euler_sieve&#39;vc.132.0.1" expl="loop invariant init" proved="true">
    <proof prover="9"><result status="valid" time="0.368625" steps="263"/></proof>
    <proof prover="10"><result status="valid" time="0.240000" steps="53172"/></proof>
    <proof prover="11"><result status="valid" time="0.090000" steps="250927"/></proof>
    </goal>
    <goal name="euler_sieve&#39;vc.132.0.2" expl="loop invariant init" proved="true">
    <proof prover="9"><result status="valid" time="0.130000" steps="199"/></proof>
    <proof prover="10"><result status="valid" time="0.240000" steps="52966"/></proof>
    <proof prover="11"><result status="valid" time="0.090000" steps="239387"/></proof>
    </goal>
    <goal name="euler_sieve&#39;vc.132.0.3" expl="loop invariant init" proved="true">
    <proof prover="9"><result status="valid" time="0.080000" steps="121"/></proof>
    <proof prover="10"><result status="valid" time="0.250000" steps="52963"/></proof>
    <proof prover="11"><result status="valid" time="0.090000" steps="238436"/></proof>
    </goal>
    <goal name="euler_sieve&#39;vc.132.0.4" expl="loop invariant init" proved="true">
    <transf name="assert" proved="true" arg1="(forall i. 1 &lt;= i &lt; length (arr t)[0 &lt;- 2] -&gt; (arr t)[i] = (arr t)[0 &lt;- 2][i])">
     <goal name="euler_sieve&#39;vc.132.0.4.0" expl="asserted formula" proved="true">
     <proof prover="9"><result status="valid" time="0.060000" steps="48"/></proof>
     <proof prover="10"><result status="valid" time="0.220000" steps="50552"/></proof>
     <proof prover="11"><result status="valid" time="0.090000" steps="246142"/></proof>
     </goal>
     <goal name="euler_sieve&#39;vc.132.0.4.1" expl="loop invariant init" proved="true">
     <proof prover="9"><result status="valid" time="0.844351" steps="830"/></proof>
     <proof prover="10"><result status="valid" time="0.300000" steps="59014"/></proof>
     <proof prover="11"><result status="valid" time="0.120000" steps="324288"/></proof>
     </goal>
    </transf>
    </goal>
    <goal name="euler_sieve&#39;vc.132.0.5" expl="loop invariant init" proved="true">
    <proof prover="9"><result status="valid" time="0.170000" steps="254"/></proof>
    <proof prover="10"><result status="valid" time="0.301162" steps="65509"/></proof>
    <proof prover="11"><result status="valid" time="0.090000" steps="256507"/></proof>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="euler_sieve&#39;vc.133" expl="loop invariant init" proved="true">
  <proof prover="9"><result status="valid" time="0.040000" steps="116"/></proof>
  <proof prover="10"><result status="valid" time="0.200000" steps="49571"/></proof>
  <proof prover="11"><result status="valid" time="0.080000" steps="229720"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.134" expl="loop invariant init" proved="true">
  <proof prover="9"><result status="valid" time="0.110000" steps="305"/></proof>
  <proof prover="10"><result status="valid" time="0.240000" steps="52824"/></proof>
  <proof prover="11"><result status="valid" time="0.080000" steps="234909"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.135" expl="loop invariant init" proved="true">
  <proof prover="9"><result status="valid" time="0.040000" steps="164"/></proof>
  <proof prover="10"><result status="valid" time="0.260000" steps="54089"/></proof>
  <proof prover="11"><result status="valid" time="0.090000" steps="247853"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.136" expl="loop invariant init" proved="true">
  <proof prover="9"><result status="valid" time="0.110000" steps="297"/></proof>
  <proof prover="10"><result status="valid" time="0.240000" steps="54095"/></proof>
  <proof prover="11"><result status="valid" time="0.080000" steps="237384"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.137" expl="loop invariant init" proved="true">
  <proof prover="9"><result status="valid" time="0.370000" steps="577"/></proof>
  <proof prover="10"><result status="valid" time="0.260000" steps="55367"/></proof>
  <proof prover="11"><result status="valid" time="0.120000" steps="294310"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.138" expl="integer overflow" proved="true">
  <proof prover="9"><result status="valid" time="0.040000" steps="57"/></proof>
  <proof prover="10"><result status="valid" time="0.190000" steps="51031"/></proof>
  <proof prover="11"><result status="valid" time="0.080000" steps="234432"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.139" expl="integer overflow" proved="true">
  <proof prover="9"><result status="valid" time="0.040000" steps="59"/></proof>
  <proof prover="10"><result status="valid" time="0.200000" steps="51129"/></proof>
  <proof prover="11"><result status="valid" time="0.080000" steps="234842"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.140" expl="index in array bounds" proved="true">
  <proof prover="9"><result status="valid" time="0.050000" steps="66"/></proof>
  <proof prover="10"><result status="valid" time="0.220000" steps="52679"/></proof>
  <proof prover="11"><result status="valid" time="0.080000" steps="250517"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.141" expl="division by zero" proved="true">
  <proof prover="9"><result status="valid" time="0.030000" steps="62"/></proof>
  <proof prover="10"><result status="valid" time="0.120000" steps="44175"/></proof>
  <proof prover="11"><result status="valid" time="0.020000" steps="14374"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.142" expl="integer overflow" proved="true">
  <proof prover="9"><result status="valid" time="0.080000" steps="240"/></proof>
  <proof prover="10"><result status="valid" time="0.210000" steps="51457"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.143" expl="assertion" proved="true">
  <proof prover="9"><result status="valid" time="0.060000" steps="162"/></proof>
  <proof prover="10"><result status="valid" time="0.220000" steps="51468"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.144" expl="index in array bounds" proved="true">
  <proof prover="9"><result status="valid" time="0.050000" steps="165"/></proof>
  <proof prover="10"><result status="valid" time="0.240000" steps="53225"/></proof>
  <proof prover="11"><result status="valid" time="0.090000" steps="279258"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.145" expl="index in array bounds" proved="true">
  <proof prover="9"><result status="valid" time="0.050000" steps="173"/></proof>
  <proof prover="10"><result status="valid" time="0.250000" steps="53436"/></proof>
  <proof prover="11"><result status="valid" time="0.100000" steps="287984"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.146" expl="integer overflow" proved="true">
  <proof prover="9"><result status="valid" time="0.396657" steps="277"/></proof>
  <proof prover="10"><result status="valid" time="0.280000" steps="58742"/></proof>
  <proof prover="11"><result status="valid" time="0.100000" steps="308133"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.147" expl="index in array bounds" proved="true">
  <proof prover="9"><result status="valid" time="0.060000" steps="82"/></proof>
  <proof prover="10"><result status="valid" time="0.240000" steps="53506"/></proof>
  <proof prover="11"><result status="valid" time="0.090000" steps="273791"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.148" expl="index in array bounds" proved="true">
  <proof prover="9"><result status="valid" time="0.070000" steps="191"/></proof>
  <proof prover="10"><result status="valid" time="0.240000" steps="53797"/></proof>
  <proof prover="11"><result status="valid" time="0.100000" steps="305661"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.149" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.060000" steps="197"/></proof>
  <proof prover="10"><result status="valid" time="0.240000" steps="53948"/></proof>
  <proof prover="11"><result status="valid" time="0.100000" steps="298034"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.150" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.643201" steps="995"/></proof>
  <proof prover="10"><result status="valid" time="0.320000" steps="62894"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.151" expl="assertion" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="euler_sieve&#39;vc.151.0" expl="assertion" proved="true">
   <transf name="unfold" proved="true" arg1="inv_count" arg2="in" arg3="LoopInvariant5">
    <goal name="euler_sieve&#39;vc.151.0.0" expl="assertion" proved="true">
    <transf name="instantiate" proved="true" arg1="LoopInvariant5" arg2="(int63&#39;int p)">
     <goal name="euler_sieve&#39;vc.151.0.0.0" expl="assertion" proved="true">
     <transf name="instantiate" proved="true" arg1="LoopInvariant5" arg2="(int63&#39;int next)">
      <goal name="euler_sieve&#39;vc.151.0.0.0.0" expl="assertion" proved="true">
      <proof prover="10"><result status="valid" time="0.330000" steps="75450"/></proof>
      </goal>
     </transf>
     </goal>
    </transf>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="euler_sieve&#39;vc.152" expl="assertion" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="euler_sieve&#39;vc.152.0" expl="assertion" proved="true">
   <proof prover="9"><result status="valid" time="0.652696" steps="838"/></proof>
   <proof prover="10"><result status="valid" time="0.415887" steps="60432"/></proof>
   <proof prover="11"><result status="valid" time="0.180000" steps="542272"/></proof>
   </goal>
   <goal name="euler_sieve&#39;vc.152.1" expl="assertion" proved="true">
   <proof prover="9"><result status="valid" time="1.093455" steps="1148"/></proof>
   <proof prover="10"><result status="valid" time="0.517058" steps="72248"/></proof>
   </goal>
   <goal name="euler_sieve&#39;vc.152.2" expl="assertion" proved="true">
   <proof prover="9"><result status="valid" time="0.299424" steps="321"/></proof>
   <proof prover="10"><result status="valid" time="0.280000" steps="59699"/></proof>
   <proof prover="11"><result status="valid" time="0.120000" steps="361540"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="euler_sieve&#39;vc.153" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.030000" steps="92"/></proof>
  <proof prover="10"><result status="valid" time="0.190000" steps="48861"/></proof>
  <proof prover="11"><result status="valid" time="0.080000" steps="243014"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.154" expl="precondition" proved="true">
  <proof prover="10"><result status="valid" time="3.307129" steps="326347"/></proof>
  <proof prover="11"><result status="valid" time="0.140000" steps="407016"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.155" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="1.055861" steps="422"/></proof>
  <proof prover="10"><result status="valid" time="0.418946" steps="74685"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.156" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.080000" steps="95"/></proof>
  <proof prover="10"><result status="valid" time="0.250000" steps="55636"/></proof>
  <proof prover="11"><result status="valid" time="0.100000" steps="307729"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.157" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.100000" steps="97"/></proof>
  <proof prover="10"><result status="valid" time="0.550238" steps="73403"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.158" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.130000" steps="100"/></proof>
  <proof prover="10"><result status="valid" time="0.632346" steps="79844"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.159" expl="assertion" proved="true">
  <proof prover="9"><result status="valid" time="0.473164" steps="357"/></proof>
  <proof prover="10"><result status="valid" time="0.290000" steps="60995"/></proof>
  <proof prover="11"><result status="valid" time="0.190000" steps="553528"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.160" expl="assertion" proved="true">
  <proof prover="9"><result status="valid" time="0.601224" steps="745"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.161" expl="loop variant decrease" proved="true">
  <proof prover="9"><result status="valid" time="0.080000" steps="99"/></proof>
  <proof prover="10"><result status="valid" time="0.449943" steps="64653"/></proof>
  <proof prover="11"><result status="valid" time="0.130000" steps="378508"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.162" expl="loop invariant preservation" proved="true">
  <proof prover="9"><result status="valid" time="0.040000" steps="96"/></proof>
  <proof prover="10"><result status="valid" time="0.130000" steps="47027"/></proof>
  <proof prover="11"><result status="valid" time="0.030000" steps="26473"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.163" expl="loop invariant preservation" proved="true">
  <proof prover="9"><result status="valid" time="0.040000" steps="96"/></proof>
  <proof prover="10"><result status="valid" time="0.140000" steps="47043"/></proof>
  <proof prover="11"><result status="valid" time="0.020000" steps="26482"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.164" expl="loop invariant preservation" proved="true">
  <proof prover="9"><result status="valid" time="0.040000" steps="98"/></proof>
  <proof prover="10"><result status="valid" time="0.190000" steps="49823"/></proof>
  <proof prover="11"><result status="valid" time="0.090000" steps="247507"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.165" expl="loop invariant preservation" proved="true">
  <proof prover="9"><result status="valid" time="0.040000" steps="99"/></proof>
  <proof prover="10"><result status="valid" time="0.140000" steps="47078"/></proof>
  <proof prover="11"><result status="valid" time="0.020000" steps="15623"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.166" expl="loop invariant preservation" proved="true">
  <transf name="inline_goal" proved="true" >
   <goal name="euler_sieve&#39;vc.166.0" expl="loop invariant preservation" proved="true">
   <transf name="split_vc" proved="true" >
    <goal name="euler_sieve&#39;vc.166.0.0" expl="loop invariant preservation" proved="true">
    <transf name="case" proved="true" arg1="(i &lt;&gt; p)">
     <goal name="euler_sieve&#39;vc.166.0.0.0" expl="true case (loop invariant preservation)" proved="true">
     <proof prover="9"><result status="valid" time="0.921377" steps="369"/></proof>
     <proof prover="10"><result status="valid" time="0.460317" steps="63622"/></proof>
     </goal>
     <goal name="euler_sieve&#39;vc.166.0.0.1" expl="false case (loop invariant preservation)" proved="true">
     <proof prover="9"><result status="valid" time="1.311597" steps="368"/></proof>
     <proof prover="10"><result status="valid" time="0.445461" steps="62914"/></proof>
     <proof prover="11"><result status="valid" time="0.510000" steps="1131265"/></proof>
     </goal>
    </transf>
    </goal>
    <goal name="euler_sieve&#39;vc.166.0.1" expl="loop invariant preservation" proved="true">
    <transf name="case" proved="true" arg1="(i &lt;&gt; p)">
     <goal name="euler_sieve&#39;vc.166.0.1.0" expl="true case (loop invariant preservation)" proved="true">
     <proof prover="9"><result status="valid" time="0.678794" steps="364"/></proof>
     <proof prover="10"><result status="valid" time="0.457942" steps="63637"/></proof>
     <proof prover="11"><result status="valid" time="0.200000" steps="579379"/></proof>
     </goal>
     <goal name="euler_sieve&#39;vc.166.0.1.1" expl="false case (loop invariant preservation)" proved="true">
     <proof prover="9"><result status="valid" time="0.698761" steps="375"/></proof>
     <proof prover="10"><result status="valid" time="0.448279" steps="63069"/></proof>
     <proof prover="11"><result status="valid" time="0.120000" steps="381564"/></proof>
     </goal>
    </transf>
    </goal>
    <goal name="euler_sieve&#39;vc.166.0.2" expl="loop invariant preservation" proved="true">
    <proof prover="9"><result status="valid" time="1.215433" steps="1154"/></proof>
    <proof prover="10"><result status="valid" time="0.452560" steps="63919"/></proof>
    </goal>
    <goal name="euler_sieve&#39;vc.166.0.3" expl="loop invariant preservation" proved="true">
    <proof prover="9"><result status="valid" time="0.542627" steps="341"/></proof>
    <proof prover="10"><result status="valid" time="0.300000" steps="64168"/></proof>
    <proof prover="11"><result status="valid" time="0.120000" steps="373158"/></proof>
    </goal>
    <goal name="euler_sieve&#39;vc.166.0.4" expl="loop invariant preservation" proved="true">
    <proof prover="9"><result status="valid" time="0.916003" steps="369"/></proof>
    <proof prover="10"><result status="valid" time="0.386830" steps="69185"/></proof>
    </goal>
    <goal name="euler_sieve&#39;vc.166.0.5" expl="loop invariant preservation" proved="true">
    <transf name="case" proved="true" arg1="(i &lt;&gt; p)">
     <goal name="euler_sieve&#39;vc.166.0.5.0" expl="true case (loop invariant preservation)" proved="true">
     <proof prover="9" timelimit="20"><result status="valid" time="7.925868" steps="4955"/></proof>
     </goal>
     <goal name="euler_sieve&#39;vc.166.0.5.1" expl="false case (loop invariant preservation)" proved="true">
     <proof prover="9"><result status="valid" time="1.338191" steps="1288"/></proof>
     <proof prover="10"><result status="valid" time="0.336726" steps="65307"/></proof>
     </goal>
    </transf>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="euler_sieve&#39;vc.167" expl="loop invariant preservation" proved="true">
  <proof prover="10"><result status="valid" time="0.512805" steps="68118"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.168" expl="loop invariant preservation" proved="true">
  <proof prover="9"><result status="valid" time="1.814574" steps="2022"/></proof>
  <proof prover="10"><result status="valid" time="0.439557" steps="77222"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.169" expl="loop invariant preservation" proved="true">
  <proof prover="9"><result status="valid" time="0.240000" steps="578"/></proof>
  <proof prover="10"><result status="valid" time="0.325253" steps="65429"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.170" expl="loop invariant preservation" proved="true">
  <proof prover="9"><result status="valid" time="1.050000" steps="830"/></proof>
  <proof prover="10"><result status="valid" time="0.300000" steps="65325"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.171" expl="loop invariant preservation" proved="true">
  <proof prover="10"><result status="valid" time="0.975435" steps="147592"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.172" expl="integer overflow" proved="true">
  <proof prover="9"><result status="valid" time="0.050000" steps="78"/></proof>
  <proof prover="10"><result status="valid" time="0.180000" steps="47117"/></proof>
  <proof prover="11"><result status="valid" time="0.090000" steps="257619"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.173" expl="integer overflow" proved="true">
  <proof prover="9"><result status="valid" time="0.050000" steps="80"/></proof>
  <proof prover="10"><result status="valid" time="0.240000" steps="52117"/></proof>
  <proof prover="11"><result status="valid" time="0.080000" steps="261983"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.174" expl="index in array bounds" proved="true">
  <proof prover="9"><result status="valid" time="0.060000" steps="82"/></proof>
  <proof prover="10"><result status="valid" time="0.250000" steps="53519"/></proof>
  <proof prover="11"><result status="valid" time="0.090000" steps="277049"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.175" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.070000" steps="199"/></proof>
  <proof prover="10"><result status="valid" time="0.240000" steps="53846"/></proof>
  <proof prover="11"><result status="valid" time="0.100000" steps="292589"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.176" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.040000" steps="89"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.177" expl="integer overflow" proved="true">
  <proof prover="9"><result status="valid" time="0.060000" steps="86"/></proof>
  <proof prover="10"><result status="valid" time="0.230000" steps="54047"/></proof>
  <proof prover="11"><result status="valid" time="0.080000" steps="279675"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.178" expl="assertion" proved="true">
  <proof prover="9"><result status="valid" time="0.240000" steps="372"/></proof>
  <proof prover="10"><result status="valid" time="0.240000" steps="54452"/></proof>
  <proof prover="11"><result status="valid" time="0.110000" steps="311169"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.179" expl="loop variant decrease" proved="true">
  <proof prover="9"><result status="valid" time="0.413237" steps="723"/></proof>
  <proof prover="10"><result status="valid" time="0.340000" steps="69262"/></proof>
  <proof prover="11"><result status="valid" time="0.100000" steps="315277"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.180" expl="loop invariant preservation" proved="true">
  <proof prover="9"><result status="valid" time="0.336930" steps="318"/></proof>
  <proof prover="10"><result status="valid" time="0.320000" steps="68062"/></proof>
  <proof prover="11"><result status="valid" time="0.100000" steps="307290"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.181" expl="loop invariant preservation" proved="true">
  <proof prover="9"><result status="valid" time="0.270142" steps="318"/></proof>
  <proof prover="10"><result status="valid" time="0.510338" steps="71449"/></proof>
  <proof prover="11"><result status="valid" time="0.110000" steps="316692"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.182" expl="loop invariant preservation" proved="true">
  <proof prover="9"><result status="valid" time="0.090000" steps="308"/></proof>
  <proof prover="10"><result status="valid" time="0.230000" steps="54634"/></proof>
  <proof prover="11"><result status="valid" time="0.100000" steps="301103"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.183" expl="loop invariant preservation" proved="true">
  <proof prover="9"><result status="valid" time="0.070000" steps="100"/></proof>
  <proof prover="10"><result status="valid" time="0.250000" steps="55062"/></proof>
  <proof prover="11"><result status="valid" time="0.100000" steps="303766"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.184" expl="loop invariant preservation" proved="true">
  <transf name="inline_goal" proved="true" >
   <goal name="euler_sieve&#39;vc.184.0" expl="loop invariant preservation" proved="true">
   <transf name="split_vc" proved="true" >
    <goal name="euler_sieve&#39;vc.184.0.0" expl="loop invariant preservation" proved="true">
    <proof prover="9"><result status="valid" time="2.263203" steps="1047"/></proof>
    <proof prover="10"><result status="valid" time="0.300000" steps="64130"/></proof>
    <proof prover="11"><result status="valid" time="0.140000" steps="386614"/></proof>
    </goal>
    <goal name="euler_sieve&#39;vc.184.0.1" expl="loop invariant preservation" proved="true">
    <proof prover="9"><result status="valid" time="3.528033" steps="1880"/></proof>
    <proof prover="10"><result status="valid" time="0.290000" steps="63310"/></proof>
    <proof prover="11"><result status="valid" time="0.120000" steps="384002"/></proof>
    </goal>
    <goal name="euler_sieve&#39;vc.184.0.2" expl="loop invariant preservation" proved="true">
    <proof prover="9"><result status="valid" time="0.476651" steps="664"/></proof>
    <proof prover="10"><result status="valid" time="0.451190" steps="64017"/></proof>
    <proof prover="11"><result status="valid" time="0.110000" steps="326811"/></proof>
    </goal>
    <goal name="euler_sieve&#39;vc.184.0.3" expl="loop invariant preservation" proved="true">
    <proof prover="9"><result status="valid" time="0.378894" steps="435"/></proof>
    <proof prover="10"><result status="valid" time="0.438509" steps="63054"/></proof>
    <proof prover="11"><result status="valid" time="0.120000" steps="325527"/></proof>
    </goal>
    <goal name="euler_sieve&#39;vc.184.0.4" expl="loop invariant preservation" proved="true">
    <transf name="unfold" proved="true" arg1="inv_count" arg2="in" arg3="LoopInvariant7">
     <goal name="euler_sieve&#39;vc.184.0.4.0" expl="loop invariant preservation" proved="true">
     <transf name="split_premise_right" proved="true" >
      <goal name="euler_sieve&#39;vc.184.0.4.0.0" expl="loop invariant preservation" proved="true">
      <transf name="assert" proved="true" arg1="(t_arr[cnt1 &lt;- ((2 * p1) + 1)][i] = t_arr[i])">
       <goal name="euler_sieve&#39;vc.184.0.4.0.0.0" expl="asserted formula" proved="true">
       <proof prover="10"><result status="valid" time="0.360000" steps="73988"/></proof>
       </goal>
       <goal name="euler_sieve&#39;vc.184.0.4.0.0.1" expl="loop invariant preservation" proved="true">
       <transf name="instantiate" proved="true" arg1="LoopInvariant9" arg2="i">
        <goal name="euler_sieve&#39;vc.184.0.4.0.0.1.0" expl="loop invariant preservation" proved="true">
        <transf name="assert" proved="true" arg1="(cnt1 &lt;= i &lt; length t_arr1)">
         <goal name="euler_sieve&#39;vc.184.0.4.0.0.1.0.0" expl="asserted formula" proved="true">
         <proof prover="9"><result status="valid" time="0.110000" steps="95"/></proof>
         <proof prover="10"><result status="valid" time="0.230000" steps="56374"/></proof>
         <proof prover="11"><result status="valid" time="0.120000" steps="354560"/></proof>
         </goal>
         <goal name="euler_sieve&#39;vc.184.0.4.0.0.1.0.1" expl="loop invariant preservation" proved="true">
         <proof prover="9"><result status="valid" time="5.128159" steps="3181"/></proof>
         </goal>
        </transf>
        </goal>
       </transf>
       </goal>
      </transf>
      </goal>
     </transf>
     </goal>
    </transf>
    </goal>
    <goal name="euler_sieve&#39;vc.184.0.5" expl="loop invariant preservation" proved="true">
    <proof prover="11"><result status="valid" time="0.160000" steps="466587"/></proof>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="euler_sieve&#39;vc.185" expl="loop invariant preservation" proved="true">
  <transf name="inline_goal" proved="true" >
   <goal name="euler_sieve&#39;vc.185.0" expl="loop invariant preservation" proved="true">
   <transf name="introduce_premises" proved="true" >
    <goal name="euler_sieve&#39;vc.185.0.0" expl="loop invariant preservation" proved="true">
    <transf name="split_all_full" proved="true" >
     <goal name="euler_sieve&#39;vc.185.0.0.0" expl="loop invariant preservation" proved="true">
     <transf name="case" proved="true" arg1="(j = cnt1)">
      <goal name="euler_sieve&#39;vc.185.0.0.0.0" expl="true case (loop invariant preservation)" proved="true">
      <proof prover="10"><result status="valid" time="0.399472" steps="71326"/></proof>
      </goal>
      <goal name="euler_sieve&#39;vc.185.0.0.0.1" expl="false case (loop invariant preservation)" proved="true">
      <proof prover="9"><result status="valid" time="0.346138" steps="473"/></proof>
      <proof prover="10"><result status="valid" time="0.410000" steps="73073"/></proof>
      </goal>
     </transf>
     </goal>
    </transf>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="euler_sieve&#39;vc.186" expl="loop invariant preservation" proved="true">
  <transf name="inline_goal" proved="true" >
   <goal name="euler_sieve&#39;vc.186.0" expl="loop invariant preservation" proved="true">
   <transf name="split_vc" proved="true" >
    <goal name="euler_sieve&#39;vc.186.0.0" expl="loop invariant preservation" proved="true">
    <transf name="unfold" proved="true" arg1="all_inf_or_eq" arg2="in" arg3="LoopInvariant7">
     <goal name="euler_sieve&#39;vc.186.0.0.0" expl="loop invariant preservation" proved="true">
     <transf name="instantiate" proved="true" arg1="LoopInvariant7" arg2="i">
      <goal name="euler_sieve&#39;vc.186.0.0.0.0" expl="loop invariant preservation" proved="true">
      <transf name="unfold" proved="true" arg1="inv_count" arg2="in" arg3="LoopInvariant1">
       <goal name="euler_sieve&#39;vc.186.0.0.0.0.0" expl="loop invariant preservation" proved="true">
       <transf name="split_premise_right" proved="true" >
        <goal name="euler_sieve&#39;vc.186.0.0.0.0.0.0" expl="loop invariant preservation" proved="true">
        <transf name="instantiate" proved="true" arg1="LoopInvariant6" arg2="(int63&#39;int p1)">
         <goal name="euler_sieve&#39;vc.186.0.0.0.0.0.0.0" expl="loop invariant preservation" proved="true">
         <proof prover="10"><result status="valid" time="0.660000" steps="95683"/></proof>
         </goal>
        </transf>
        </goal>
       </transf>
       </goal>
      </transf>
      </goal>
     </transf>
     </goal>
    </transf>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="euler_sieve&#39;vc.187" expl="loop invariant preservation" proved="true">
  <proof prover="9"><result status="valid" time="0.200000" steps="663"/></proof>
  <proof prover="10"><result status="valid" time="0.458143" steps="65076"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.188" expl="loop invariant preservation" proved="true">
  <transf name="instantiate" proved="true" arg1="LoopInvariant9" arg2="i">
   <goal name="euler_sieve&#39;vc.188.0" expl="loop invariant preservation" proved="true">
   <proof prover="9"><result status="valid" time="1.687141" steps="1727"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="euler_sieve&#39;vc.189" expl="loop invariant preservation" proved="true">
  <transf name="case" proved="true" arg1="(i &lt; 2 * p1 + 1)">
   <goal name="euler_sieve&#39;vc.189.0" expl="true case (loop invariant preservation)" proved="true">
   <transf name="instantiate" proved="true" arg1="LoopInvariant9" arg2="i">
    <goal name="euler_sieve&#39;vc.189.0.0" expl="true case (loop invariant preservation)" proved="true">
    <proof prover="9"><result status="valid" time="0.548755" steps="752"/></proof>
    <proof prover="10"><result status="valid" time="0.300000" steps="65598"/></proof>
    </goal>
   </transf>
   </goal>
   <goal name="euler_sieve&#39;vc.189.1" expl="false case (loop invariant preservation)" proved="true">
   <transf name="case" proved="true" arg1="(i = 2 * p1 + 1)">
    <goal name="euler_sieve&#39;vc.189.1.0" expl="false case (true case. loop invariant preservation)" proved="true">
    <proof prover="10"><result status="valid" time="0.330000" steps="66677"/></proof>
    <proof prover="11"><result status="valid" time="0.290000" steps="742002"/></proof>
    </goal>
    <goal name="euler_sieve&#39;vc.189.1.1" expl="false case (loop invariant preservation)" proved="true">
    <proof prover="9"><result status="valid" time="2.026177" steps="1184"/></proof>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="euler_sieve&#39;vc.190" expl="integer overflow" proved="true">
  <proof prover="9"><result status="valid" time="0.040000" steps="72"/></proof>
  <proof prover="10"><result status="valid" time="0.190000" steps="47034"/></proof>
  <proof prover="11"><result status="valid" time="0.090000" steps="244059"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.191" expl="integer overflow" proved="true">
  <proof prover="9"><result status="valid" time="0.050000" steps="74"/></proof>
  <proof prover="10"><result status="valid" time="0.240000" steps="51946"/></proof>
  <proof prover="11"><result status="valid" time="0.090000" steps="248044"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.192" expl="index in array bounds" proved="true">
  <proof prover="9"><result status="valid" time="0.060000" steps="76"/></proof>
  <proof prover="10"><result status="valid" time="0.240000" steps="53322"/></proof>
  <proof prover="11"><result status="valid" time="0.090000" steps="276132"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.193" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.060000" steps="188"/></proof>
  <proof prover="10"><result status="valid" time="0.240000" steps="53672"/></proof>
  <proof prover="11"><result status="valid" time="0.080000" steps="284599"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.194" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.030000" steps="79"/></proof>
  <proof prover="10"><result status="valid" time="0.280000" steps="59940"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.195" expl="integer overflow" proved="true">
  <proof prover="9"><result status="valid" time="0.050000" steps="80"/></proof>
  <proof prover="10"><result status="valid" time="0.260000" steps="53785"/></proof>
  <proof prover="11"><result status="valid" time="0.090000" steps="264515"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.196" expl="integer overflow" proved="true">
  <proof prover="9"><result status="valid" time="0.060000" steps="82"/></proof>
  <proof prover="10"><result status="valid" time="0.240000" steps="53822"/></proof>
  <proof prover="11"><result status="valid" time="0.090000" steps="266125"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.197" expl="assertion" proved="true">
  <proof prover="9"><result status="valid" time="0.160000" steps="331"/></proof>
  <proof prover="10"><result status="valid" time="0.240000" steps="54203"/></proof>
  <proof prover="11"><result status="valid" time="0.100000" steps="300000"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.198" expl="loop variant decrease" proved="true">
  <proof prover="9"><result status="valid" time="0.060000" steps="85"/></proof>
  <proof prover="10"><result status="valid" time="0.260000" steps="57148"/></proof>
  <proof prover="11"><result status="valid" time="0.100000" steps="287251"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.199" expl="loop invariant preservation" proved="true">
  <proof prover="9"><result status="valid" time="0.030000" steps="78"/></proof>
  <proof prover="10"><result status="valid" time="0.180000" steps="48673"/></proof>
  <proof prover="11"><result status="valid" time="0.080000" steps="235573"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.200" expl="loop invariant preservation" proved="true">
  <proof prover="9"><result status="valid" time="0.060000" steps="86"/></proof>
  <proof prover="10"><result status="valid" time="0.240000" steps="54073"/></proof>
  <proof prover="11"><result status="valid" time="0.100000" steps="288861"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.201" expl="loop invariant preservation" proved="true">
  <proof prover="9"><result status="valid" time="0.070000" steps="91"/></proof>
  <proof prover="10"><result status="valid" time="0.250000" steps="54303"/></proof>
  <proof prover="11"><result status="valid" time="0.100000" steps="287017"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.202" expl="loop invariant preservation" proved="true">
  <proof prover="9"><result status="valid" time="0.060000" steps="93"/></proof>
  <proof prover="10"><result status="valid" time="0.250000" steps="54588"/></proof>
  <proof prover="11"><result status="valid" time="0.100000" steps="290874"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.203" expl="loop invariant preservation" proved="true">
  <transf name="inline_goal" proved="true" >
   <goal name="euler_sieve&#39;vc.203.0" expl="loop invariant preservation" proved="true">
   <transf name="split_vc" proved="true" >
    <goal name="euler_sieve&#39;vc.203.0.0" expl="loop invariant preservation" proved="true">
    <proof prover="10"><result status="valid" time="0.467122" steps="65073"/></proof>
    <proof prover="11"><result status="valid" time="0.120000" steps="364757"/></proof>
    </goal>
    <goal name="euler_sieve&#39;vc.203.0.1" expl="loop invariant preservation" proved="true">
    <proof prover="9"><result status="valid" time="1.321906" steps="986"/></proof>
    <proof prover="10"><result status="valid" time="0.320000" steps="64168"/></proof>
    <proof prover="11"><result status="valid" time="0.120000" steps="361912"/></proof>
    </goal>
    <goal name="euler_sieve&#39;vc.203.0.2" expl="loop invariant preservation" proved="true">
    <proof prover="9"><result status="valid" time="0.532859" steps="897"/></proof>
    <proof prover="10"><result status="valid" time="0.458024" steps="64966"/></proof>
    <proof prover="11"><result status="valid" time="0.100000" steps="315117"/></proof>
    </goal>
    <goal name="euler_sieve&#39;vc.203.0.3" expl="loop invariant preservation" proved="true">
    <proof prover="9"><result status="valid" time="0.276386" steps="330"/></proof>
    <proof prover="10"><result status="valid" time="0.300000" steps="64122"/></proof>
    <proof prover="11"><result status="valid" time="0.110000" steps="313899"/></proof>
    </goal>
    <goal name="euler_sieve&#39;vc.203.0.4" expl="loop invariant preservation" proved="true">
    <transf name="unfold" proved="true" arg1="inv_count" arg2="in" arg3="LoopInvariant7">
     <goal name="euler_sieve&#39;vc.203.0.4.0" expl="loop invariant preservation" proved="true">
     <transf name="split_premise_right" proved="true" >
      <goal name="euler_sieve&#39;vc.203.0.4.0.0" expl="loop invariant preservation" proved="true">
      <transf name="assert" proved="true" arg1="(t_arr[cnt1 &lt;- ((2 * p1) + 1)][i] = t_arr[i])">
       <goal name="euler_sieve&#39;vc.203.0.4.0.0.0" expl="asserted formula" proved="true">
       <proof prover="10"><result status="valid" time="0.370000" steps="74257"/></proof>
       </goal>
       <goal name="euler_sieve&#39;vc.203.0.4.0.0.1" expl="loop invariant preservation" proved="true">
       <transf name="instantiate" proved="true" arg1="LoopInvariant9" arg2="i">
        <goal name="euler_sieve&#39;vc.203.0.4.0.0.1.0" expl="loop invariant preservation" proved="true">
        <transf name="assert" proved="true" arg1="(cnt1 &lt;= i &lt; length t_arr1)">
         <goal name="euler_sieve&#39;vc.203.0.4.0.0.1.0.0" expl="asserted formula" proved="true">
         <proof prover="9"><result status="valid" time="0.100000" steps="88"/></proof>
         <proof prover="10"><result status="valid" time="0.230000" steps="56296"/></proof>
         <proof prover="11"><result status="valid" time="0.120000" steps="346758"/></proof>
         </goal>
         <goal name="euler_sieve&#39;vc.203.0.4.0.0.1.0.1" expl="loop invariant preservation" proved="true">
         <proof prover="8"><result status="valid" time="1.900000"/></proof>
         <transf name="remove" proved="true" arg1="zero1,one1,(-),(&gt;),(&lt;=),(&gt;=),abs,int63&#39;maxInt,int63&#39;minInt,min_int63,max_int63,to_int,in_bounds,zero,one,even,odd,divides,prime,([]),singleton,cons,snoc,(++),exchange,inv_nexts,all_eliminated_marked,all_eliminated_marked_partial,not_marked_impl_next_not_marked,is_copy,not_marked_impl_next_not_marked_partial,all_primes,all_multiples_marked,previously_marked_multiples,only_multiples_marked,prime_multiples_marked,inv_remove_products,ordered,all_inf_or_eq,inv_count,Assoc1,Unit_def_l,Unit_def_r,Inv_def_l,Inv_def_r,Comm1,Assoc,Mul_distr_l,Mul_distr_r,Comm,Unitary,NonTrivialRing,Refl,Trans,Antisymm,Total,ZeroLessOne,CompatOrderAdd,CompatOrderMult,Abs_pos,Div_mod,Div_unique,Mod_1,Div_1,Div_inf,Div_inf_neg,Mod_0,Div_1_left,Div_minus1_left,Mod_1_left,Mod_minus1_left,Div_mult,Mod_mult,Div_mod1,Div_sign_pos,Div_sign_neg,Mod_sign_pos,Mod_sign_neg,Rounds_toward_zero,Div_11,Mod_11,Div_inf1,Mod_inf,Div_mult1,Mod_mult1,to_int_in_bounds,extensionality,max_int&#39;def,min_int&#39;def,even_or_odd,even_not_odd,odd_not_even,even_odd,odd_even,even_even,odd_odd,even_2k,odd_2k1,divides_refl,divides_1_n,divides_0,divides_left,divides_right,divides_oppr,divides_oppl,divides_oppr_rev,divides_oppl_rev,divides_plusr,divides_minusr,divides_multl,divides_multr,divides_factorl,divides_factorr,divides_n_1,divides_antisym,divides_trans,divides_bounds,mod_divides_euclidean,divides_mod_euclidean,mod_divides_computer,divides_mod_computer,not_prime_1,prime_2,prime_3,prime_divisors,small_divisors,even_prime,odd_prime,mult_croissance_locale,mult_croissance,comp_mult_2,div_croissance_locale1,div_croissance1,div_croissance_locale2,div_croissance2,sq_ineq,divides_div,divides_inf,not_prime_divider_limits,no_prod_impl_no_divider,not_prime_impl_divisor_under_sqrt,length_nonnegative,empty&#39;def,set&#39;def,([&lt;-])&#39;def,([..])&#39;def,([_..])&#39;def,([.._])&#39;def,exchange_set,conservation_all_eliminated_marked_on_marked_change,conservation_all_eliminated_marked_on_nexts_change,conservation_inv_arr_on_mark,conservation_inv_arr_on_jump,multiples_of_marked_are_marked,prev_and_new_impl_all_multiples_marked,conservation_only_multiples_marked,conservation_previously_marked_multiples,conservation_previously_marked_multiples_on_marked_change,conservation_not_marked_impl_next_not_marked,unchanged_other_elements,previously_marked_multiples_impl_prime,only_multiples_marked_impl_not_marked,H24,H23,Ensures16,Ensures15,Ensures14,Ensures13,H22,H21,Assert2,Assert1,H18,H17,Ensures10,H16,H15,H14,H13,H12,LoopInvariant15,LoopInvariant14,LoopInvariant7,LoopInvariant6,LoopInvariant3,LoopInvariant2,Ensures9,Ensures8,H11,Ensures7,Ensures6,H10,Ensures5,Ensures4,H9,H8,Ensures3,Ensures2,Ensures1,Ensures,LoopInvariant1,LoopInvariant,H20,H19,H7,H6,H5,H4,H2,(==)&#39;spec3,(==)&#39;spec2,(==)&#39;spec1,(==)&#39;spec,create&#39;spec1,create&#39;spec,set&#39;spec2,set&#39;spec1,set&#39;spec,singleton&#39;spec1,singleton&#39;spec,cons&#39;spec2,cons&#39;spec1,cons&#39;spec,snoc&#39;spec2,snoc&#39;spec1,snoc&#39;spec,([..])&#39;spec1,([..])&#39;spec,(++)&#39;spec2,(++)&#39;spec1,(++)&#39;spec,Abs_le2,Abs_le1,Abs_le,Div_bound3,Div_bound2,Mod_bound3,Mod_bound2,array63&#39;invariant3,array63&#39;invariant2,array63&#39;invariant1,array63&#39;invariant,Mod_bound1,Mod_bound,Div_bound1,Div_bound,divides&#39;spec1,divides&#39;spec,even_mod21,even_mod2,even_divides1,even_divides,odd_divides1,odd_divides,div_mult_11,div_mult_1,mult_borne_sous_exp1,mult_borne_sous_exp,t&#39;invariant22,t&#39;invariant21,t&#39;invariant20,t&#39;invariant19,t&#39;invariant18,t&#39;invariant17,t&#39;invariant16,t&#39;invariant15,t&#39;invariant14,t&#39;invariant13,t&#39;invariant12,t&#39;invariant11,t&#39;invariant10,t&#39;invariant9,t&#39;invariant8,t&#39;invariant7,t&#39;invariant6,t&#39;invariant5,t&#39;invariant4,t&#39;invariant3,t&#39;invariant2,t&#39;invariant1,t&#39;invariant,Ensures12,Ensures11,Assert4,Assert3,LoopInvariant13,LoopInvariant11,LoopInvariant10,LoopInvariant9,LoopInvariant8,LoopInvariant5,LoopInvariant4,h1">
          <goal name="euler_sieve&#39;vc.203.0.4.0.0.1.0.1.0" expl="loop invariant preservation" proved="true">
          <proof prover="8"><result status="valid" time="0.010000"/></proof>
          <proof prover="9"><result status="valid" time="0.020000" steps="30"/></proof>
          <proof prover="10"><result status="valid" time="0.030000" steps="6014"/></proof>
          <proof prover="11"><result status="valid" time="0.020000" steps="25726"/></proof>
          </goal>
         </transf>
         </goal>
        </transf>
        </goal>
       </transf>
       </goal>
      </transf>
      </goal>
     </transf>
     </goal>
    </transf>
    </goal>
    <goal name="euler_sieve&#39;vc.203.0.5" expl="loop invariant preservation" proved="true">
    <proof prover="11"><result status="valid" time="0.140000" steps="416815"/></proof>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="euler_sieve&#39;vc.204" expl="loop invariant preservation" proved="true">
  <transf name="inline_goal" proved="true" >
   <goal name="euler_sieve&#39;vc.204.0" expl="loop invariant preservation" proved="true">
   <transf name="split_vc" proved="true" >
    <goal name="euler_sieve&#39;vc.204.0.0" expl="loop invariant preservation" proved="true">
    <transf name="unfold" proved="true" arg1="ordered" arg2="in" arg3="LoopInvariant7">
     <goal name="euler_sieve&#39;vc.204.0.0.0" expl="loop invariant preservation" proved="true">
     <transf name="instantiate" proved="true" arg1="LoopInvariant7" arg2="i">
      <goal name="euler_sieve&#39;vc.204.0.0.0.0" expl="loop invariant preservation" proved="true">
      <transf name="instantiate" proved="true" arg1="Hinst" arg2="j">
       <goal name="euler_sieve&#39;vc.204.0.0.0.0.0" expl="loop invariant preservation" proved="true">
       <transf name="case" proved="true" arg1="(j = cnt1)">
        <goal name="euler_sieve&#39;vc.204.0.0.0.0.0.0" expl="true case (loop invariant preservation)" proved="true">
        <proof prover="9"><result status="valid" time="1.793397" steps="1983"/></proof>
        <proof prover="10"><result status="valid" time="0.312530" steps="65045"/></proof>
        </goal>
        <goal name="euler_sieve&#39;vc.204.0.0.0.0.0.1" expl="false case (loop invariant preservation)" proved="true">
        <proof prover="9"><result status="valid" time="0.140000" steps="349"/></proof>
        <proof prover="10"><result status="valid" time="0.260000" steps="56829"/></proof>
        </goal>
       </transf>
       </goal>
      </transf>
      </goal>
     </transf>
     </goal>
    </transf>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="euler_sieve&#39;vc.205" expl="loop invariant preservation" proved="true">
  <transf name="inline_goal" proved="true" >
   <goal name="euler_sieve&#39;vc.205.0" expl="loop invariant preservation" proved="true">
   <transf name="split_vc" proved="true" >
    <goal name="euler_sieve&#39;vc.205.0.0" expl="loop invariant preservation" proved="true">
    <transf name="unfold" proved="true" arg1="all_inf_or_eq" arg2="in" arg3="LoopInvariant7">
     <goal name="euler_sieve&#39;vc.205.0.0.0" expl="loop invariant preservation" proved="true">
     <transf name="instantiate" proved="true" arg1="LoopInvariant7" arg2="i">
      <goal name="euler_sieve&#39;vc.205.0.0.0.0" expl="loop invariant preservation" proved="true">
      <transf name="case" proved="true" arg1="(i &lt; cnt1)">
       <goal name="euler_sieve&#39;vc.205.0.0.0.0.0" expl="true case (loop invariant preservation)" proved="true">
       <proof prover="9"><result status="valid" time="0.130000" steps="414"/></proof>
       <proof prover="10"><result status="valid" time="0.260000" steps="56199"/></proof>
       <proof prover="11"><result status="valid" time="0.140000" steps="420154"/></proof>
       </goal>
       <goal name="euler_sieve&#39;vc.205.0.0.0.0.1" expl="false case (loop invariant preservation)" proved="true">
       <proof prover="9"><result status="valid" time="0.710000" steps="1036"/></proof>
       <proof prover="10"><result status="valid" time="0.466218" steps="65329"/></proof>
       </goal>
      </transf>
      </goal>
     </transf>
     </goal>
    </transf>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="euler_sieve&#39;vc.206" expl="loop invariant preservation" proved="true">
  <proof prover="9"><result status="valid" time="0.180000" steps="461"/></proof>
  <proof prover="10"><result status="valid" time="0.320000" steps="65884"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.207" expl="loop invariant preservation" proved="true">
  <proof prover="9"><result status="valid" time="2.836681" steps="2302"/></proof>
  <proof prover="10"><result status="valid" time="0.723325" steps="98172"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.208" expl="loop invariant preservation" proved="true">
  <transf name="case" proved="true" arg1="(i &lt; 2 * p1 + 1)">
   <goal name="euler_sieve&#39;vc.208.0" expl="true case (loop invariant preservation)" proved="true">
   <transf name="instantiate" proved="true" arg1="LoopInvariant9" arg2="i">
    <goal name="euler_sieve&#39;vc.208.0.0" expl="true case (loop invariant preservation)" proved="true">
    <proof prover="9"><result status="valid" time="0.811888" steps="1239"/></proof>
    <proof prover="10"><result status="valid" time="0.320333" steps="67755"/></proof>
    </goal>
   </transf>
   </goal>
   <goal name="euler_sieve&#39;vc.208.1" expl="false case (loop invariant preservation)" proved="true">
   <transf name="case" proved="true" arg1="(i = 2 * p1 + 1)">
    <goal name="euler_sieve&#39;vc.208.1.0" expl="false case (true case. loop invariant preservation)" proved="true">
    <proof prover="10"><result status="valid" time="0.610000" steps="90293"/></proof>
    <proof prover="11"><result status="valid" time="0.270000" steps="677299"/></proof>
    </goal>
    <goal name="euler_sieve&#39;vc.208.1.1" expl="false case (loop invariant preservation)" proved="true">
    <proof prover="9"><result status="valid" time="2.860000" steps="1395"/></proof>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="euler_sieve&#39;vc.209" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.040000" steps="63"/></proof>
  <proof prover="10"><result status="valid" time="0.210000" steps="52830"/></proof>
  <proof prover="11"><result status="valid" time="0.080000" steps="245343"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.210" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.210000" steps="401"/></proof>
  <proof prover="10"><result status="valid" time="0.850000" steps="115171"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.211" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="1.222760" steps="1346"/></proof>
  <proof prover="10"><result status="valid" time="1.090000" steps="124124"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.212" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.220000" steps="261"/></proof>
  <proof prover="10"><result status="valid" time="0.280000" steps="62353"/></proof>
  </goal>
  <goal name="euler_sieve&#39;vc.213" expl="postcondition" proved="true">
  <proof prover="10"><result status="valid" time="0.910000" steps="123614"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
</file>
</why3session>
