why3session.xml 14.3 KB
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<?xml version="1.0" encoding="UTF-8"?>
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<!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
"http://why3.lri.fr/why3session.dtd">
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<why3session shape_version="4">
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<prover id="0" name="Coq" version="8.4pl4" timelimit="5" memlimit="1000"/>
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<prover id="1" name="Alt-Ergo" version="0.99.1" timelimit="5" memlimit="1000"/>
<prover id="2" name="Alt-Ergo" version="0.95.1" timelimit="5" memlimit="1000"/>
<prover id="3" name="CVC3" version="2.4.1" timelimit="5" memlimit="1000"/>
<prover id="4" name="CVC4" version="1.4" timelimit="5" memlimit="1000"/>
<prover id="5" name="CVC3" version="2.2" timelimit="3" memlimit="1000"/>
<prover id="6" name="Z3" version="4.3.1" timelimit="5" memlimit="1000"/>
<prover id="7" name="Z3" version="3.2" timelimit="3" memlimit="1000"/>
<prover id="8" name="Z3" version="4.3.2" timelimit="5" memlimit="1000"/>
<prover id="9" name="CVC4" version="1.3" timelimit="5" memlimit="1000"/>
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<file name="../triangle_inequality.why" expanded="true">
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<theory name="CauchySchwarzInequality" sum="029d2a2da0bd5b8c118724b66181542e" expanded="true">
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 <goal name="norm2_pos">
 <proof prover="6"><result status="valid" time="0.00"/></proof>
 <proof prover="7"><result status="valid" time="0.01"/></proof>
 <proof prover="8"><result status="valid" time="0.00"/></proof>
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 </goal>
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 <goal name="p_expr">
 <proof prover="5" timelimit="30"><result status="valid" time="0.01"/></proof>
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 <proof prover="6"><result status="valid" time="0.00"/></proof>
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 <proof prover="7"><result status="valid" time="0.00"/></proof>
 <proof prover="8"><result status="valid" time="0.00"/></proof>
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 </goal>
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 <goal name="p_pos">
 <proof prover="1"><result status="valid" time="0.02" steps="3"/></proof>
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 <proof prover="2"><result status="valid" time="0.01"/></proof>
 <proof prover="3"><result status="valid" time="0.01"/></proof>
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 <proof prover="4"><result status="valid" time="0.00"/></proof>
 <proof prover="5"><result status="valid" time="0.01"/></proof>
 <proof prover="9"><result status="valid" time="0.00"/></proof>
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 </goal>
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 <goal name="mul_div_simpl">
 <proof prover="6"><result status="valid" time="0.00"/></proof>
 <proof prover="7"><result status="valid" time="0.02"/></proof>
 <proof prover="8"><result status="valid" time="0.00"/></proof>
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 </goal>
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 <goal name="p_val_part">
 <metas>
  <ls_pos name="one" id="143"
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   ip_theory="Real">
   <ip_library name="real"/>
   <ip_qualid name="one"/>
  </ls_pos>
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  <ls_pos name="infix &lt;" id="144"
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   ip_theory="Real">
   <ip_library name="real"/>
   <ip_qualid name="infix &lt;"/>
  </ls_pos>
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  <ls_pos name="infix &lt;=" id="156"
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   ip_theory="Real">
   <ip_library name="real"/>
   <ip_qualid name="infix &lt;="/>
  </ls_pos>
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  <ls_pos name="infix +" id="1313"
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   ip_theory="Real">
   <ip_library name="real"/>
   <ip_qualid name="infix +"/>
  </ls_pos>
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  <ls_pos name="prefix -" id="1314"
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   ip_theory="Real">
   <ip_library name="real"/>
   <ip_qualid name="prefix -"/>
  </ls_pos>
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  <ls_pos name="infix *" id="1315"
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   ip_theory="Real">
   <ip_library name="real"/>
   <ip_qualid name="infix *"/>
  </ls_pos>
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  <ls_pos name="inv" id="1381"
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   ip_theory="Real">
   <ip_library name="real"/>
   <ip_qualid name="inv"/>
  </ls_pos>
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  <ls_pos name="infix &gt;=" id="1438"
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   ip_theory="Real">
   <ip_library name="real"/>
   <ip_qualid name="infix &gt;="/>
  </ls_pos>
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  <ls_pos name="sqrt" id="2559"
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   ip_theory="Square">
   <ip_library name="real"/>
   <ip_qualid name="sqrt"/>
  </ls_pos>
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  <pr_pos name="Assoc" id="1316"
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   ip_theory="Real">
   <ip_library name="real"/>
   <ip_qualid name="CommutativeGroup"/>
   <ip_qualid name="Assoc"/>
  </pr_pos>
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  <pr_pos name="Unit_def_l" id="1323"
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   ip_theory="Real">
   <ip_library name="real"/>
   <ip_qualid name="CommutativeGroup"/>
   <ip_qualid name="Unit_def_l"/>
  </pr_pos>
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  <pr_pos name="Unit_def_r" id="1326"
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   ip_theory="Real">
   <ip_library name="real"/>
   <ip_qualid name="CommutativeGroup"/>
   <ip_qualid name="Unit_def_r"/>
  </pr_pos>
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  <pr_pos name="Inv_def_l" id="1329"
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   ip_theory="Real">
   <ip_library name="real"/>
   <ip_qualid name="CommutativeGroup"/>
   <ip_qualid name="Inv_def_l"/>
  </pr_pos>
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  <pr_pos name="Inv_def_r" id="1332"
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   ip_theory="Real">
   <ip_library name="real"/>
   <ip_qualid name="CommutativeGroup"/>
   <ip_qualid name="Inv_def_r"/>
  </pr_pos>
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  <pr_pos name="Comm" id="1335"
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   ip_theory="Real">
   <ip_library name="real"/>
   <ip_qualid name="CommutativeGroup"/>
   <ip_qualid name="Comm"/>
   <ip_qualid name="Comm"/>
  </pr_pos>
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  <pr_pos name="Assoc" id="1340"
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   ip_theory="Real">
   <ip_library name="real"/>
   <ip_qualid name="Assoc"/>
   <ip_qualid name="Assoc"/>
  </pr_pos>
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  <pr_pos name="Mul_distr_l" id="1347"
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   ip_theory="Real">
   <ip_library name="real"/>
   <ip_qualid name="Mul_distr_l"/>
  </pr_pos>
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  <pr_pos name="Mul_distr_r" id="1354"
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   ip_theory="Real">
   <ip_library name="real"/>
   <ip_qualid name="Mul_distr_r"/>
  </pr_pos>
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  <pr_pos name="Comm" id="1372"
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   ip_theory="Real">
   <ip_library name="real"/>
   <ip_qualid name="Comm"/>
   <ip_qualid name="Comm"/>
  </pr_pos>
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  <pr_pos name="Unitary" id="1377"
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   ip_theory="Real">
   <ip_library name="real"/>
   <ip_qualid name="Unitary"/>
  </pr_pos>
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  <pr_pos name="NonTrivialRing" id="1380"
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   ip_theory="Real">
   <ip_library name="real"/>
   <ip_qualid name="NonTrivialRing"/>
  </pr_pos>
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  <pr_pos name="Inverse" id="1382"
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   ip_theory="Real">
   <ip_library name="real"/>
   <ip_qualid name="Inverse"/>
  </pr_pos>
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  <pr_pos name="add_div" id="1396"
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   ip_theory="Real">
   <ip_library name="real"/>
   <ip_qualid name="add_div"/>
  </pr_pos>
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  <pr_pos name="sub_div" id="1403"
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   ip_theory="Real">
   <ip_library name="real"/>
   <ip_qualid name="sub_div"/>
  </pr_pos>
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  <pr_pos name="neg_div" id="1410"
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   ip_theory="Real">
   <ip_library name="real"/>
   <ip_qualid name="neg_div"/>
  </pr_pos>
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  <pr_pos name="assoc_div_mul" id="1422"
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   ip_theory="Real">
   <ip_library name="real"/>
   <ip_qualid name="assoc_div_mul"/>
  </pr_pos>
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  <pr_pos name="assoc_div_div" id="1429"
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   ip_theory="Real">
   <ip_library name="real"/>
   <ip_qualid name="assoc_div_div"/>
  </pr_pos>
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  <pr_pos name="Refl" id="1447"
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   ip_theory="Real">
   <ip_library name="real"/>
   <ip_qualid name="Refl"/>
  </pr_pos>
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  <pr_pos name="Trans" id="1450"
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   ip_theory="Real">
   <ip_library name="real"/>
   <ip_qualid name="Trans"/>
  </pr_pos>
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  <pr_pos name="Antisymm" id="1457"
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   ip_theory="Real">
   <ip_library name="real"/>
   <ip_qualid name="Antisymm"/>
  </pr_pos>
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  <pr_pos name="Total" id="1462"
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   ip_theory="Real">
   <ip_library name="real"/>
   <ip_qualid name="Total"/>
  </pr_pos>
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  <pr_pos name="ZeroLessOne" id="1467"
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   ip_theory="Real">
   <ip_library name="real"/>
   <ip_qualid name="ZeroLessOne"/>
  </pr_pos>
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  <pr_pos name="CompatOrderAdd" id="1468"
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   ip_theory="Real">
   <ip_library name="real"/>
   <ip_qualid name="CompatOrderAdd"/>
  </pr_pos>
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  <pr_pos name="CompatOrderMult" id="1475"
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   ip_theory="Real">
   <ip_library name="real"/>
   <ip_qualid name="CompatOrderMult"/>
  </pr_pos>
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  <pr_pos name="Sqrt_positive" id="2561"
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   ip_theory="Square">
   <ip_library name="real"/>
   <ip_qualid name="Sqrt_positive"/>
  </pr_pos>
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  <pr_pos name="Sqrt_square" id="2564"
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   ip_theory="Square">
   <ip_library name="real"/>
   <ip_qualid name="Sqrt_square"/>
  </pr_pos>
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  <pr_pos name="Square_sqrt" id="2567"
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   ip_theory="Square">
   <ip_library name="real"/>
   <ip_qualid name="Square_sqrt"/>
  </pr_pos>
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  <pr_pos name="Sqrt_mul" id="2570"
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   ip_theory="Square">
   <ip_library name="real"/>
   <ip_qualid name="Sqrt_mul"/>
  </pr_pos>
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  <pr_pos name="Sqrt_le" id="2575"
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   ip_theory="Square">
   <ip_library name="real"/>
   <ip_qualid name="Sqrt_le"/>
  </pr_pos>
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  <pr_pos name="norm2_pos" id="2836"
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   ip_theory="CauchySchwarzInequality">
   <ip_qualid name="norm2_pos"/>
  </pr_pos>
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  <pr_pos name="p_expr" id="2862"
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   ip_theory="CauchySchwarzInequality">
   <ip_qualid name="p_expr"/>
  </pr_pos>
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  <pr_pos name="p_pos" id="2873"
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   ip_theory="CauchySchwarzInequality">
   <ip_qualid name="p_pos"/>
  </pr_pos>
  <meta name="remove_logic">
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   <meta_arg_ls id="143"/>
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  </meta>
  <meta name="remove_logic">
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   <meta_arg_ls id="144"/>
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  </meta>
  <meta name="remove_logic">
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   <meta_arg_ls id="156"/>
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  </meta>
  <meta name="remove_logic">
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   <meta_arg_ls id="1313"/>
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  </meta>
  <meta name="remove_logic">
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   <meta_arg_ls id="1314"/>
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  </meta>
  <meta name="remove_logic">
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   <meta_arg_ls id="1315"/>
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  </meta>
  <meta name="remove_logic">
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   <meta_arg_ls id="1381"/>
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  </meta>
  <meta name="remove_logic">
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   <meta_arg_ls id="1438"/>
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  </meta>
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  <meta name="remove_logic">
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   <meta_arg_ls id="2559"/>
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  </meta>
  <meta name="remove_prop">
   <meta_arg_pr id="1316"/>
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  </meta>
  <meta name="remove_prop">
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   <meta_arg_pr id="1323"/>
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  </meta>
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   <meta_arg_pr id="1326"/>
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  </meta>
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   <meta_arg_pr id="1329"/>
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  </meta>
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  </meta>
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   <meta_arg_pr id="1335"/>
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  </meta>
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   <meta_arg_pr id="1340"/>
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  </meta>
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   <meta_arg_pr id="1347"/>
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  </meta>
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   <meta_arg_pr id="1354"/>
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  </meta>
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   <meta_arg_pr id="1372"/>
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  </meta>
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   <meta_arg_pr id="1377"/>
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  </meta>
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   <meta_arg_pr id="1380"/>
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  </meta>
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  </meta>
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  </meta>
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  </meta>
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   <meta_arg_pr id="1475"/>
  </meta>
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  </meta>
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  </meta>
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   <meta_arg_pr id="2836"/>
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  </meta>
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   <meta_arg_pr id="2862"/>
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  </meta>
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  <meta name="remove_prop">
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   <meta_arg_pr id="2873"/>
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  </meta>
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  <goal name="p_val_part">
  <transf name="eliminate_builtin">
   <goal name="p_val_part.1" expl="1.">
   <proof prover="2" timelimit="45"><result status="valid" time="32.03"/></proof>
   <proof prover="6"><result status="valid" time="0.00"/></proof>
   <proof prover="8"><result status="valid" time="0.00"/></proof>
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   </goal>
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  </transf>
  </goal>
 </metas>
 </goal>
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 <goal name="p_val_part_pos">
 <proof prover="1"><result status="valid" time="0.02" steps="9"/></proof>
 <proof prover="2"><result status="valid" time="0.02"/></proof>
 <proof prover="4"><result status="valid" time="0.00"/></proof>
 <proof prover="9"><result status="valid" time="0.01"/></proof>
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 </goal>
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 <goal name="p_val_part_pos_aux">
 <proof prover="1"><result status="valid" time="0.01" steps="2"/></proof>
 <proof prover="2"><result status="valid" time="0.01"/></proof>
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 </goal>
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 <goal name="CauchySchwarz_aux_non_null">
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 <proof prover="0" edited="triangle_inequality_CauchySchwarzInequality_CauchySchwarz_aux_non_null_1.v"><result status="valid" time="1.24"/></proof>
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 </goal>
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 <goal name="norm_null">
 <proof prover="2"><result status="valid" time="0.06"/></proof>
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 </goal>
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 <goal name="CauchySchwarz_aux_null">
 <proof prover="1"><result status="valid" time="0.06" steps="18"/></proof>
 <proof prover="2"><result status="valid" time="0.06"/></proof>
 <proof prover="3"><result status="valid" time="0.01"/></proof>
 <proof prover="5"><result status="valid" time="0.01"/></proof>
 <proof prover="6"><result status="valid" time="0.00"/></proof>
 <proof prover="7"><result status="valid" time="0.28"/></proof>
 <proof prover="8"><result status="valid" time="0.00"/></proof>
 </goal>
 <goal name="CauchySchwarz_aux">
 <proof prover="1"><result status="valid" time="0.02" steps="8"/></proof>
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 <proof prover="2"><result status="valid" time="0.01"/></proof>
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 <proof prover="3"><result status="valid" time="0.00"/></proof>
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 <proof prover="4"><result status="valid" time="0.01"/></proof>
 <proof prover="5"><result status="valid" time="0.00"/></proof>
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 <proof prover="9"><result status="valid" time="0.01"/></proof>
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 </goal>
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 <goal name="norm_pos">
 <proof prover="1"><result status="valid" time="0.01" steps="4"/></proof>
 <proof prover="2"><result status="valid" time="0.02"/></proof>
 <proof prover="3"><result status="valid" time="0.00"/></proof>
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 <proof prover="4"><result status="valid" time="0.00"/></proof>
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 <proof prover="5"><result status="valid" time="0.01"/></proof>
 <proof prover="6"><result status="valid" time="0.00"/></proof>
 <proof prover="7"><result status="valid" time="0.02"/></proof>
 <proof prover="8"><result status="valid" time="0.01"/></proof>
 <proof prover="9"><result status="valid" time="0.01"/></proof>
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 </goal>
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 <goal name="sqr_le_sqrt">
 <proof prover="1"><result status="valid" time="0.03" steps="18"/></proof>
 <proof prover="2"><result status="valid" time="0.03"/></proof>
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 </goal>
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 <goal name="CauchySchwarz">
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 <proof prover="0" edited="triangle_inequality_CauchySchwarzInequality_CauchySchwarz_1.v"><result status="valid" time="1.47"/></proof>
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 </goal>
</theory>
448
<theory name="TriangleInequality" sum="0e6e449288baab6d459040c11cfc2eb5" expanded="true">
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 <goal name="triangle_aux">
 <proof prover="6"><result status="valid" time="0.00"/></proof>
 <proof prover="8"><result status="valid" time="0.01"/></proof>
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 </goal>
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 <goal name="sqr_sqrt_le">
 <proof prover="1"><result status="valid" time="0.04" steps="17"/></proof>
 <proof prover="2"><result status="valid" time="0.02"/></proof>
 <proof prover="3"><result status="valid" time="0.01"/></proof>
 <proof prover="5"><result status="valid" time="0.01"/></proof>
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 </goal>
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 <goal name="triangle">
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 <proof prover="0" edited="triangle_inequality_TriangleInequality_triangle_1.v"><result status="valid" time="1.27"/></proof>
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 </goal>
</theory>
</file>
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</why3session>