TSTP Solution File: RNG123+4 by nanoCoP---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : RNG123+4 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n006.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri May 19 11:49:54 EDT 2023

% Result   : Theorem 101.59s 98.76s
% Output   : Proof 101.59s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : RNG123+4 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n006.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Thu May 18 20:20:36 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 101.59/98.76  
% 101.59/98.76  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 101.59/98.76  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 101.59/98.76  %-----------------------------------------------------
% 101.59/98.76  ncf(matrix, plain, [(1285 ^ _163496) ^ [] : [aElementOf0(xr, xI)], (1275 ^ _163496) ^ [_206241, _206243] : [aElementOf0(_206243, slsdtgt0(xa)), aElementOf0(_206241, slsdtgt0(xb)), sdtpldt0(_206243, _206241) = xr], (166 ^ _163496) ^ [_168916, _168918, _168920, _168922] : [-(sdtasasdt0(_168922, _168918) = sdtasasdt0(_168920, _168916)), _168922 = _168920, _168918 = _168916], (176 ^ _163496) ^ [_169275, _169277, _169279, _169281] : [-(sdtpldt1(_169281, _169277) = sdtpldt1(_169279, _169275)), _169281 = _169279, _169277 = _169275], (186 ^ _163496) ^ [_169606, _169608] : [_169608 = _169606, -(sbrdtbr0(_169608) = sbrdtbr0(_169606))], (192 ^ _163496) ^ [_169824, _169826] : [_169826 = _169824, -(smndt0(_169826) = smndt0(_169824))], (198 ^ _163496) ^ [_170070, _170072, _170074, _170076] : [-(sdtasdt0(_170076, _170072) = sdtasdt0(_170074, _170070)), _170076 = _170074, _170072 = _170070], (208 ^ _163496) ^ [_170401, _170403] : [_170403 = _170401, -(slsdtgt0(_170403) = slsdtgt0(_170401))], (214 ^ _163496) ^ [_170627, _170629, _170631, _170633] : [-(sdtpldt0(_170633, _170629) = sdtpldt0(_170631, _170627)), _170633 = _170631, _170629 = _170627], (2 ^ _163496) ^ [_163640] : [-(_163640 = _163640)], (4 ^ _163496) ^ [_163747, _163749] : [_163749 = _163747, -(_163747 = _163749)], (10 ^ _163496) ^ [_163951, _163953, _163955] : [-(_163955 = _163951), _163955 = _163953, _163953 = _163951], (20 ^ _163496) ^ [_164320, _164322, _164324, _164326, _164328, _164330] : [-(sdteqdtlpzmzozddtrp0(_164328, _164324, _164320)), sdteqdtlpzmzozddtrp0(_164330, _164326, _164322), _164330 = _164328, _164326 = _164324, _164322 = _164320], (38 ^ _163496) ^ [_164873, _164875] : [-(aNaturalNumber0(_164873)), _164875 = _164873, aNaturalNumber0(_164875)], (48 ^ _163496) ^ [_165196, _165198, _165200, _165202] : [-(misRelativelyPrime0(_165200, _165196)), misRelativelyPrime0(_165202, _165198), _165202 = _165200, _165198 = _165196], (62 ^ _163496) ^ [_165668, _165670, _165672, _165674, _165676, _165678] : [-(aGcdOfAnd0(_165676, _165672, _165668)), aGcdOfAnd0(_165678, _165674, _165670), _165678 = _165676, _165674 = _165672, _165670 = _165668], (80 ^ _163496) ^ [_166221, _166223] : [-(aSet0(_166221)), _166223 = _166221, aSet0(_166223)], (90 ^ _163496) ^ [_166516, _166518] : [-(aIdeal0(_166516)), _166518 = _166516, aIdeal0(_166518)], (100 ^ _163496) ^ [_166839, _166841, _166843, _166845] : [-(aDivisorOf0(_166843, _166839)), aDivisorOf0(_166845, _166841), _166845 = _166843, _166841 = _166839], (114 ^ _163496) ^ [_167283, _167285, _167287, _167289] : [-(doDivides0(_167287, _167283)), doDivides0(_167289, _167285), _167289 = _167287, _167285 = _167283], (128 ^ _163496) ^ [_167699, _167701] : [-(aElement0(_167699)), _167701 = _167699, aElement0(_167701)], (138 ^ _163496) ^ [_168022, _168024, _168026, _168028] : [-(iLess0(_168026, _168022)), iLess0(_168028, _168024), _168028 = _168026, _168024 = _168022], (152 ^ _163496) ^ [_168446, _168448, _168450, _168452] : [-(aElementOf0(_168450, _168446)), aElementOf0(_168452, _168448), _168452 = _168450, _168448 = _168446], (224 ^ _163496) ^ [_171002] : [aElement0(_171002), true___, -(true___)], (234 ^ _163496) ^ [] : [-(aElement0(sz00))], (236 ^ _163496) ^ [] : [-(aElement0(sz10))], (238 ^ _163496) ^ [_171363] : [aElement0(_171363), -(aElement0(smndt0(_171363)))], (244 ^ _163496) ^ [_171567, _171569] : [-(aElement0(sdtpldt0(_171569, _171567))), aElement0(_171569), aElement0(_171567)], (254 ^ _163496) ^ [_171866, _171868] : [-(aElement0(sdtasdt0(_171868, _171866))), aElement0(_171868), aElement0(_171866)], (264 ^ _163496) ^ [_172165, _172167] : [-(sdtpldt0(_172167, _172165) = sdtpldt0(_172165, _172167)), aElement0(_172167), aElement0(_172165)], (274 ^ _163496) ^ [_172486, _172488, _172490] : [-(sdtpldt0(sdtpldt0(_172490, _172488), _172486) = sdtpldt0(_172490, sdtpldt0(_172488, _172486))), aElement0(_172490), aElement0(_172488), aElement0(_172486)], (288 ^ _163496) ^ [_172892] : [aElement0(_172892), 291 ^ _163496 : [(292 ^ _163496) ^ [] : [-(sdtpldt0(_172892, sz00) = _172892)], (294 ^ _163496) ^ [] : [-(_172892 = sdtpldt0(sz00, _172892))]]], (296 ^ _163496) ^ [_173165] : [aElement0(_173165), 299 ^ _163496 : [(300 ^ _163496) ^ [] : [-(sdtpldt0(_173165, smndt0(_173165)) = sz00)], (302 ^ _163496) ^ [] : [-(sz00 = sdtpldt0(smndt0(_173165), _173165))]]], (304 ^ _163496) ^ [_173460, _173462] : [-(sdtasdt0(_173462, _173460) = sdtasdt0(_173460, _173462)), aElement0(_173462), aElement0(_173460)], (314 ^ _163496) ^ [_173781, _173783, _173785] : [-(sdtasdt0(sdtasdt0(_173785, _173783), _173781) = sdtasdt0(_173785, sdtasdt0(_173783, _173781))), aElement0(_173785), aElement0(_173783), aElement0(_173781)], (328 ^ _163496) ^ [_174187] : [aElement0(_174187), 331 ^ _163496 : [(332 ^ _163496) ^ [] : [-(sdtasdt0(_174187, sz10) = _174187)], (334 ^ _163496) ^ [] : [-(_174187 = sdtasdt0(sz10, _174187))]]], (336 ^ _163496) ^ [_174488, _174490, _174492] : [347 ^ _163496 : [(348 ^ _163496) ^ [] : [-(sdtasdt0(_174492, sdtpldt0(_174490, _174488)) = sdtpldt0(sdtasdt0(_174492, _174490), sdtasdt0(_174492, _174488)))], (350 ^ _163496) ^ [] : [-(sdtasdt0(sdtpldt0(_174490, _174488), _174492) = sdtpldt0(sdtasdt0(_174490, _174492), sdtasdt0(_174488, _174492)))]], aElement0(_174492), aElement0(_174490), aElement0(_174488)], (352 ^ _163496) ^ [_175007] : [aElement0(_175007), 355 ^ _163496 : [(356 ^ _163496) ^ [] : [-(sdtasdt0(smndt0(sz10), _175007) = smndt0(_175007))], (358 ^ _163496) ^ [] : [-(smndt0(_175007) = sdtasdt0(_175007, smndt0(sz10)))]]], (360 ^ _163496) ^ [_175288] : [aElement0(_175288), 363 ^ _163496 : [(364 ^ _163496) ^ [] : [-(sdtasdt0(_175288, sz00) = sz00)], (366 ^ _163496) ^ [] : [-(sz00 = sdtasdt0(sz00, _175288))]]], (368 ^ _163496) ^ [_175575, _175577] : [aElement0(_175577), aElement0(_175575), sdtasdt0(_175577, _175575) = sz00, -(_175577 = sz00), -(_175575 = sz00)], (386 ^ _163496) ^ [] : [sz10 = sz00], (388 ^ _163496) ^ [_176095] : [aSet0(_176095), true___, -(true___)], (398 ^ _163496) ^ [_176350] : [aSet0(_176350), 401 ^ _163496 : [(402 ^ _163496) ^ [_176480] : [aElementOf0(_176480, _176350), -(aElement0(_176480))]]], (408 ^ _163496) ^ [_176695, _176697] : [aSet0(_176697), aSet0(_176695), -(_176697 = _176695), 420 ^ _163496 : [(421 ^ _163496) ^ [] : [-(aElementOf0(419 ^ [_176695, _176697], _176697))], (423 ^ _163496) ^ [] : [aElementOf0(419 ^ [_176695, _176697], _176695)]], 425 ^ _163496 : [(426 ^ _163496) ^ [] : [-(aElementOf0(424 ^ [_176695, _176697], _176695))], (428 ^ _163496) ^ [] : [aElementOf0(424 ^ [_176695, _176697], _176697)]]], (432 ^ _163496) ^ [_177460, _177462] : [aSet0(_177462), aSet0(_177460), 439 ^ _163496 : [(472 ^ _163496) ^ [_179090] : [-(_179090 = sdtpldt1(_177462, _177460)), aSet0(_179090), 494 ^ _163496 : [(495 ^ _163496) ^ [] : [-(aElementOf0(492 ^ [_177460, _177462, _179090], _177462))], (497 ^ _163496) ^ [] : [-(aElementOf0(493 ^ [_177460, _177462, _179090], _177460))], (499 ^ _163496) ^ [] : [-(sdtpldt0(492 ^ [_177460, _177462, _179090], 493 ^ [_177460, _177462, _179090]) = 477 ^ [_177460, _177462, _179090])], (501 ^ _163496) ^ [] : [aElementOf0(477 ^ [_177460, _177462, _179090], _179090)]], 480 ^ _163496 : [(481 ^ _163496) ^ [] : [-(aElementOf0(477 ^ [_177460, _177462, _179090], _179090))], (483 ^ _163496) ^ [_179519, _179521] : [aElementOf0(_179521, _177462), aElementOf0(_179519, _177460), sdtpldt0(_179521, _179519) = 477 ^ [_177460, _177462, _179090]]]], (440 ^ _163496) ^ [_177755] : [_177755 = sdtpldt1(_177462, _177460), 443 ^ _163496 : [(444 ^ _163496) ^ [] : [-(aSet0(_177755))], (446 ^ _163496) ^ [_178032] : [aElementOf0(_178032, _177755), 451 ^ _163496 : [(452 ^ _163496) ^ [] : [-(aElementOf0(449 ^ [_177460, _177462, _177755, _178032], _177462))], (454 ^ _163496) ^ [] : [-(aElementOf0(450 ^ [_177460, _177462, _177755, _178032], _177460))], (456 ^ _163496) ^ [] : [-(sdtpldt0(449 ^ [_177460, _177462, _177755, _178032], 450 ^ [_177460, _177462, _177755, _178032]) = _178032)]]], (458 ^ _163496) ^ [_178592] : [-(aElementOf0(_178592, _177755)), 459 ^ _163496 : [(460 ^ _163496) ^ [_178722, _178724] : [aElementOf0(_178724, _177462), aElementOf0(_178722, _177460), sdtpldt0(_178724, _178722) = _178592]]]]]]], (505 ^ _163496) ^ [_180440, _180442] : [aSet0(_180442), aSet0(_180440), 512 ^ _163496 : [(537 ^ _163496) ^ [_181519] : [-(_181519 = sdtasasdt0(_180442, _180440)), aSet0(_181519), 553 ^ _163496 : [(554 ^ _163496) ^ [] : [-(aElementOf0(542 ^ [_180440, _180442, _181519], _180442))], (556 ^ _163496) ^ [] : [-(aElementOf0(542 ^ [_180440, _180442, _181519], _180440))], (558 ^ _163496) ^ [] : [aElementOf0(542 ^ [_180440, _180442, _181519], _181519)]], 545 ^ _163496 : [(546 ^ _163496) ^ [] : [-(aElementOf0(542 ^ [_180440, _180442, _181519], _181519))], (548 ^ _163496) ^ [] : [aElementOf0(542 ^ [_180440, _180442, _181519], _180442), aElementOf0(542 ^ [_180440, _180442, _181519], _180440)]]], (513 ^ _163496) ^ [_180716] : [_180716 = sdtasasdt0(_180442, _180440), 516 ^ _163496 : [(517 ^ _163496) ^ [] : [-(aSet0(_180716))], (519 ^ _163496) ^ [_180974] : [aElementOf0(_180974, _180716), 522 ^ _163496 : [(523 ^ _163496) ^ [] : [-(aElementOf0(_180974, _180442))], (525 ^ _163496) ^ [] : [-(aElementOf0(_180974, _180440))]]], (527 ^ _163496) ^ [_181233] : [-(aElementOf0(_181233, _180716)), aElementOf0(_181233, _180442), aElementOf0(_181233, _180440)]]]]], (584 ^ _163496) ^ [_183184] : [-(aIdeal0(_183184)), aSet0(_183184), 590 ^ _163496 : [(591 ^ _163496) ^ [] : [-(aElementOf0(589 ^ [_183184], _183184))], (593 ^ _163496) ^ [] : [595 ^ _163496 : [(596 ^ _163496) ^ [] : [-(aElementOf0(594 ^ [_183184], _183184))], (598 ^ _163496) ^ [] : [aElementOf0(sdtpldt0(589 ^ [_183184], 594 ^ [_183184]), _183184)]], 600 ^ _163496 : [(601 ^ _163496) ^ [] : [-(aElement0(599 ^ [_183184]))], (603 ^ _163496) ^ [] : [aElementOf0(sdtasdt0(599 ^ [_183184], 589 ^ [_183184]), _183184)]]]]], (562 ^ _163496) ^ [_182389] : [aIdeal0(_182389), 565 ^ _163496 : [(566 ^ _163496) ^ [] : [-(aSet0(_182389))], (568 ^ _163496) ^ [_182621] : [aElementOf0(_182621, _182389), 571 ^ _163496 : [(572 ^ _163496) ^ [_182802] : [aElementOf0(_182802, _182389), -(aElementOf0(sdtpldt0(_182621, _182802), _182389))], (578 ^ _163496) ^ [_182994] : [aElement0(_182994), -(aElementOf0(sdtasdt0(_182994, _182621), _182389))]]]]], (607 ^ _163496) ^ [_184024, _184026] : [-(aIdeal0(sdtpldt1(_184026, _184024))), aIdeal0(_184026), aIdeal0(_184024)], (617 ^ _163496) ^ [_184323, _184325] : [-(aIdeal0(sdtasasdt0(_184325, _184323))), aIdeal0(_184325), aIdeal0(_184323)], (627 ^ _163496) ^ [_184636, _184638, _184640] : [aElement0(_184640), aElement0(_184638), aIdeal0(_184636), 638 ^ _163496 : [(639 ^ _163496) ^ [] : [sdteqdtlpzmzozddtrp0(_184640, _184638, _184636), -(aElementOf0(sdtpldt0(_184640, smndt0(_184638)), _184636))], (645 ^ _163496) ^ [] : [aElementOf0(sdtpldt0(_184640, smndt0(_184638)), _184636), -(sdteqdtlpzmzozddtrp0(_184640, _184638, _184636))]]], (651 ^ _163496) ^ [_185314, _185316] : [aIdeal0(_185316), aIdeal0(_185314), 661 ^ _163496 : [(662 ^ _163496) ^ [] : [-(aElement0(660 ^ [_185314, _185316]))], (664 ^ _163496) ^ [] : [aElementOf0(660 ^ [_185314, _185316], sdtpldt1(_185316, _185314))]], 665 ^ _163496 : [(666 ^ _163496) ^ [_185812, _185814] : [674 ^ _163496 : [(675 ^ _163496) ^ [] : [-(aElement0(673 ^ [_185314, _185316, _185812, _185814]))], (677 ^ _163496) ^ [] : [-(sdteqdtlpzmzozddtrp0(673 ^ [_185314, _185316, _185812, _185814], _185814, _185316))], (679 ^ _163496) ^ [] : [-(sdteqdtlpzmzozddtrp0(673 ^ [_185314, _185316, _185812, _185814], _185812, _185314))]], aElement0(_185814), aElement0(_185812)]]], (681 ^ _163496) ^ [_186392] : [aNaturalNumber0(_186392), true___, -(true___)], (691 ^ _163496) ^ [_186647] : [-(aNaturalNumber0(sbrdtbr0(_186647))), aElement0(_186647), -(_186647 = sz00)], (701 ^ _163496) ^ [_186939, _186941] : [aNaturalNumber0(_186941), aNaturalNumber0(_186939), iLess0(_186941, _186939), true___, -(true___)], (719 ^ _163496) ^ [_187399, _187401] : [732 ^ _163496 : [(733 ^ _163496) ^ [] : [-(aElement0(730 ^ [_187399, _187401]))], (735 ^ _163496) ^ [] : [-(aElement0(731 ^ [_187399, _187401]))], (737 ^ _163496) ^ [] : [-(_187401 = sdtpldt0(sdtasdt0(730 ^ [_187399, _187401], _187399), 731 ^ [_187399, _187401]))], (739 ^ _163496) ^ [] : [-(731 ^ [_187399, _187401] = sz00), -(iLess0(sbrdtbr0(731 ^ [_187399, _187401]), sbrdtbr0(_187399)))]], aElement0(_187401), aElement0(_187399), -(_187399 = sz00)], (745 ^ _163496) ^ [_188346, _188348] : [aElement0(_188348), aElement0(_188346), 752 ^ _163496 : [(753 ^ _163496) ^ [] : [doDivides0(_188348, _188346), 757 ^ _163496 : [(758 ^ _163496) ^ [] : [-(aElement0(756 ^ [_188346, _188348]))], (760 ^ _163496) ^ [] : [-(sdtasdt0(_188348, 756 ^ [_188346, _188348]) = _188346)]]], (762 ^ _163496) ^ [] : [-(doDivides0(_188348, _188346)), 763 ^ _163496 : [(764 ^ _163496) ^ [_188906] : [aElement0(_188906), sdtasdt0(_188348, _188906) = _188346]]]]], (772 ^ _163496) ^ [_189175] : [aElement0(_189175), 775 ^ _163496 : [(776 ^ _163496) ^ [_189340] : [aDivisorOf0(_189340, _189175), 779 ^ _163496 : [(780 ^ _163496) ^ [] : [-(aElement0(_189340))], (782 ^ _163496) ^ [] : [-(doDivides0(_189340, _189175))]]], (784 ^ _163496) ^ [_189577] : [-(aDivisorOf0(_189577, _189175)), aElement0(_189577), doDivides0(_189577, _189175)]]], (794 ^ _163496) ^ [_189883, _189885] : [aElement0(_189885), aElement0(_189883), 801 ^ _163496 : [(802 ^ _163496) ^ [_190164] : [aGcdOfAnd0(_190164, _189885, _189883), 805 ^ _163496 : [(806 ^ _163496) ^ [] : [-(aDivisorOf0(_190164, _189885))], (808 ^ _163496) ^ [] : [-(aDivisorOf0(_190164, _189883))], (810 ^ _163496) ^ [_190465] : [-(doDivides0(_190465, _190164)), aDivisorOf0(_190465, _189885), aDivisorOf0(_190465, _189883)]]], (820 ^ _163496) ^ [_190751] : [-(aGcdOfAnd0(_190751, _189885, _189883)), aDivisorOf0(_190751, _189885), aDivisorOf0(_190751, _189883), 830 ^ _163496 : [(831 ^ _163496) ^ [] : [-(aDivisorOf0(829 ^ [_189883, _189885, _190751], _189885))], (833 ^ _163496) ^ [] : [-(aDivisorOf0(829 ^ [_189883, _189885, _190751], _189883))], (835 ^ _163496) ^ [] : [doDivides0(829 ^ [_189883, _189885, _190751], _190751)]]]]], (839 ^ _163496) ^ [_191416, _191418] : [aElement0(_191418), aElement0(_191416), 846 ^ _163496 : [(847 ^ _163496) ^ [] : [misRelativelyPrime0(_191418, _191416), -(aGcdOfAnd0(sz10, _191418, _191416))], (853 ^ _163496) ^ [] : [aGcdOfAnd0(sz10, _191418, _191416), -(misRelativelyPrime0(_191418, _191416))]]], (859 ^ _163496) ^ [_191952] : [aElement0(_191952), 862 ^ _163496 : [(888 ^ _163496) ^ [_193076] : [-(_193076 = slsdtgt0(_191952)), aSet0(_193076), 905 ^ _163496 : [(906 ^ _163496) ^ [] : [-(aElement0(904 ^ [_191952, _193076]))], (908 ^ _163496) ^ [] : [-(sdtasdt0(_191952, 904 ^ [_191952, _193076]) = 893 ^ [_191952, _193076])], (910 ^ _163496) ^ [] : [aElementOf0(893 ^ [_191952, _193076], _193076)]], 896 ^ _163496 : [(897 ^ _163496) ^ [] : [-(aElementOf0(893 ^ [_191952, _193076], _193076))], (899 ^ _163496) ^ [_193448] : [aElement0(_193448), sdtasdt0(_191952, _193448) = 893 ^ [_191952, _193076]]]], (863 ^ _163496) ^ [_192143] : [_192143 = slsdtgt0(_191952), 866 ^ _163496 : [(867 ^ _163496) ^ [] : [-(aSet0(_192143))], (869 ^ _163496) ^ [_192398] : [aElementOf0(_192398, _192143), 873 ^ _163496 : [(874 ^ _163496) ^ [] : [-(aElement0(872 ^ [_191952, _192143, _192398]))], (876 ^ _163496) ^ [] : [-(sdtasdt0(_191952, 872 ^ [_191952, _192143, _192398]) = _192398)]]], (878 ^ _163496) ^ [_192731] : [-(aElementOf0(_192731, _192143)), 879 ^ _163496 : [(880 ^ _163496) ^ [_192831] : [aElement0(_192831), sdtasdt0(_191952, _192831) = _192731]]]]]]], (914 ^ _163496) ^ [_194015] : [aElement0(_194015), -(aIdeal0(slsdtgt0(_194015)))], (920 ^ _163496) ^ [] : [-(aElement0(xa))], (922 ^ _163496) ^ [] : [-(aElement0(xb))], (924 ^ _163496) ^ [] : [xa = sz00, xb = sz00], (930 ^ _163496) ^ [] : [-(aElement0(xc))], (933 ^ _163496) ^ [] : [-(aElement0(931 ^ []))], (935 ^ _163496) ^ [] : [-(sdtasdt0(xc, 931 ^ []) = xa)], (937 ^ _163496) ^ [] : [-(doDivides0(xc, xa))], (939 ^ _163496) ^ [] : [-(aDivisorOf0(xc, xa))], (941 ^ _163496) ^ [] : [-(aElement0(xc))], (944 ^ _163496) ^ [] : [-(aElement0(942 ^ []))], (946 ^ _163496) ^ [] : [-(sdtasdt0(xc, 942 ^ []) = xb)], (948 ^ _163496) ^ [] : [-(doDivides0(xc, xb))], (950 ^ _163496) ^ [] : [-(aDivisorOf0(xc, xb))], (987 ^ _163496) ^ [] : [-(aGcdOfAnd0(xc, xa, xb))], (952 ^ _163496) ^ [_195075] : [980 ^ _163496 : [(981 ^ _163496) ^ [] : [-(aElement0(979 ^ [_195075]))], (983 ^ _163496) ^ [] : [-(sdtasdt0(_195075, 979 ^ [_195075]) = xc)], (985 ^ _163496) ^ [] : [-(doDivides0(_195075, xc))]], 969 ^ _163496 : [(976 ^ _163496) ^ [] : [doDivides0(_195075, xb)], (978 ^ _163496) ^ [] : [aDivisorOf0(_195075, xb)], (970 ^ _163496) ^ [_195676] : [aElement0(_195676), sdtasdt0(_195075, _195676) = xb]], 955 ^ _163496 : [(968 ^ _163496) ^ [] : [aDivisorOf0(_195075, xa)], (956 ^ _163496) ^ [] : [aElement0(_195075), 959 ^ _163496 : [(966 ^ _163496) ^ [] : [doDivides0(_195075, xa)], (960 ^ _163496) ^ [_195380] : [aElement0(_195380), sdtasdt0(_195075, _195380) = xa]]]]], (989 ^ _163496) ^ [] : [-(aSet0(xI))], (991 ^ _163496) ^ [_196367] : [aElementOf0(_196367, xI), 994 ^ _163496 : [(995 ^ _163496) ^ [_196542] : [aElementOf0(_196542, xI), -(aElementOf0(sdtpldt0(_196367, _196542), xI))], (1001 ^ _163496) ^ [_196726] : [aElement0(_196726), -(aElementOf0(sdtasdt0(_196726, _196367), xI))]]], (1007 ^ _163496) ^ [] : [-(aIdeal0(xI))], (1009 ^ _163496) ^ [_197017] : [aElementOf0(_197017, slsdtgt0(xa)), 1013 ^ _163496 : [(1014 ^ _163496) ^ [] : [-(aElement0(1012 ^ [_197017]))], (1016 ^ _163496) ^ [] : [-(sdtasdt0(xa, 1012 ^ [_197017]) = _197017)]]], (1018 ^ _163496) ^ [_197314] : [-(aElementOf0(_197314, slsdtgt0(xa))), 1019 ^ _163496 : [(1020 ^ _163496) ^ [_197406] : [aElement0(_197406), sdtasdt0(xa, _197406) = _197314]]], (1028 ^ _163496) ^ [_197687] : [aElementOf0(_197687, slsdtgt0(xb)), 1032 ^ _163496 : [(1033 ^ _163496) ^ [] : [-(aElement0(1031 ^ [_197687]))], (1035 ^ _163496) ^ [] : [-(sdtasdt0(xb, 1031 ^ [_197687]) = _197687)]]], (1037 ^ _163496) ^ [_197984] : [-(aElementOf0(_197984, slsdtgt0(xb))), 1038 ^ _163496 : [(1039 ^ _163496) ^ [_198076] : [aElement0(_198076), sdtasdt0(xb, _198076) = _197984]]], (1073 ^ _163496) ^ [] : [-(xI = sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))], (1047 ^ _163496) ^ [_198357] : [aElementOf0(_198357, xI), 1052 ^ _163496 : [(1053 ^ _163496) ^ [] : [-(aElementOf0(1050 ^ [_198357], slsdtgt0(xa)))], (1055 ^ _163496) ^ [] : [-(aElementOf0(1051 ^ [_198357], slsdtgt0(xb)))], (1057 ^ _163496) ^ [] : [-(sdtpldt0(1050 ^ [_198357], 1051 ^ [_198357]) = _198357)]]], (1059 ^ _163496) ^ [_198821] : [-(aElementOf0(_198821, xI)), 1060 ^ _163496 : [(1061 ^ _163496) ^ [_198939, _198941] : [aElementOf0(_198941, slsdtgt0(xa)), aElementOf0(_198939, slsdtgt0(xb)), sdtpldt0(_198941, _198939) = _198821]]], (1076 ^ _163496) ^ [] : [-(aElement0(1074 ^ []))], (1078 ^ _163496) ^ [] : [-(sdtasdt0(xa, 1074 ^ []) = sz00)], (1080 ^ _163496) ^ [] : [-(aElementOf0(sz00, slsdtgt0(xa)))], (1083 ^ _163496) ^ [] : [-(aElement0(1081 ^ []))], (1085 ^ _163496) ^ [] : [-(sdtasdt0(xa, 1081 ^ []) = xa)], (1087 ^ _163496) ^ [] : [-(aElementOf0(xa, slsdtgt0(xa)))], (1090 ^ _163496) ^ [] : [-(aElement0(1088 ^ []))], (1092 ^ _163496) ^ [] : [-(sdtasdt0(xb, 1088 ^ []) = sz00)], (1094 ^ _163496) ^ [] : [-(aElementOf0(sz00, slsdtgt0(xb)))], (1097 ^ _163496) ^ [] : [-(aElement0(1095 ^ []))], (1099 ^ _163496) ^ [] : [-(sdtasdt0(xb, 1095 ^ []) = xb)], (1101 ^ _163496) ^ [] : [-(aElementOf0(xb, slsdtgt0(xb)))], (1104 ^ _163496) ^ [_200372] : [aElementOf0(_200372, slsdtgt0(xa)), 1108 ^ _163496 : [(1109 ^ _163496) ^ [] : [-(aElement0(1107 ^ [_200372]))], (1111 ^ _163496) ^ [] : [-(sdtasdt0(xa, 1107 ^ [_200372]) = _200372)]]], (1113 ^ _163496) ^ [_200669] : [-(aElementOf0(_200669, slsdtgt0(xa))), 1114 ^ _163496 : [(1115 ^ _163496) ^ [_200761] : [aElement0(_200761), sdtasdt0(xa, _200761) = _200669]]], (1144 ^ _163496) ^ [] : [-(aElementOf0(1141 ^ [], slsdtgt0(xa)))], (1146 ^ _163496) ^ [] : [-(aElementOf0(1142 ^ [], slsdtgt0(xb)))], (1148 ^ _163496) ^ [] : [-(sdtpldt0(1141 ^ [], 1142 ^ []) = 1102 ^ [])], (1150 ^ _163496) ^ [] : [-(aElementOf0(1102 ^ [], sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))))], (1152 ^ _163496) ^ [] : [1102 ^ [] = sz00], (1123 ^ _163496) ^ [_201042] : [aElementOf0(_201042, slsdtgt0(xb)), 1127 ^ _163496 : [(1128 ^ _163496) ^ [] : [-(aElement0(1126 ^ [_201042]))], (1130 ^ _163496) ^ [] : [-(sdtasdt0(xb, 1126 ^ [_201042]) = _201042)]]], (1132 ^ _163496) ^ [_201339] : [-(aElementOf0(_201339, slsdtgt0(xb))), 1133 ^ _163496 : [(1134 ^ _163496) ^ [_201431] : [aElement0(_201431), sdtasdt0(xb, _201431) = _201339]]], (1156 ^ _163496) ^ [] : [-(aElementOf0(1153 ^ [], slsdtgt0(xa)))], (1158 ^ _163496) ^ [] : [-(aElementOf0(1154 ^ [], slsdtgt0(xb)))], (1160 ^ _163496) ^ [] : [-(sdtpldt0(1153 ^ [], 1154 ^ []) = xu)], (1162 ^ _163496) ^ [] : [-(aElementOf0(xu, xI))], (1164 ^ _163496) ^ [] : [xu = sz00], (1166 ^ _163496) ^ [_202433] : [iLess0(sbrdtbr0(_202433), sbrdtbr0(xu)), -(_202433 = sz00), 1169 ^ _163496 : [(1180 ^ _163496) ^ [] : [aElementOf0(_202433, xI)], (1170 ^ _163496) ^ [_202621, _202623] : [aElementOf0(_202623, slsdtgt0(xa)), aElementOf0(_202621, slsdtgt0(xb)), sdtpldt0(_202623, _202621) = _202433]]], (1186 ^ _163496) ^ [] : [1187 ^ _163496 : [(1194 ^ _163496) ^ [] : [doDivides0(xu, xa)], (1196 ^ _163496) ^ [] : [aDivisorOf0(xu, xa)], (1188 ^ _163496) ^ [_203126] : [aElement0(_203126), sdtasdt0(xu, _203126) = xa]], 1197 ^ _163496 : [(1204 ^ _163496) ^ [] : [doDivides0(xu, xb)], (1206 ^ _163496) ^ [] : [aDivisorOf0(xu, xb)], (1198 ^ _163496) ^ [_203409] : [aElement0(_203409), sdtasdt0(xu, _203409) = xb]]], (1210 ^ _163496) ^ [] : [-(aElement0(1207 ^ []))], (1212 ^ _163496) ^ [] : [-(aElement0(1208 ^ []))], (1214 ^ _163496) ^ [] : [-(xu = sdtpldt0(sdtasdt0(xa, 1207 ^ []), sdtasdt0(xb, 1208 ^ [])))], (1217 ^ _163496) ^ [] : [-(aElement0(1215 ^ []))], (1219 ^ _163496) ^ [] : [-(sdtasdt0(xu, 1215 ^ []) = xa)], (1221 ^ _163496) ^ [] : [-(doDivides0(xu, xa))], (1229 ^ _163496) ^ [] : [doDivides0(xu, xb)], (1223 ^ _163496) ^ [_204203] : [aElement0(_204203), sdtasdt0(xu, _204203) = xb], (1243 ^ _163496) ^ [] : [xr = sz00], (1247 ^ _163496) ^ [] : [-(aElementOf0(1244 ^ [], slsdtgt0(xa)))], (1249 ^ _163496) ^ [] : [-(aElementOf0(1245 ^ [], slsdtgt0(xb)))], (1251 ^ _163496) ^ [] : [-(sdtpldt0(1244 ^ [], 1245 ^ []) = smndt0(sdtasdt0(xq, xu)))], (1253 ^ _163496) ^ [] : [-(aElementOf0(smndt0(sdtasdt0(xq, xu)), xI))], (1257 ^ _163496) ^ [] : [-(aElementOf0(1254 ^ [], slsdtgt0(xa)))], (1259 ^ _163496) ^ [] : [-(aElementOf0(1255 ^ [], slsdtgt0(xb)))], (1261 ^ _163496) ^ [] : [-(sdtpldt0(1254 ^ [], 1255 ^ []) = xb)], (1265 ^ _163496) ^ [] : [-(aElementOf0(1262 ^ [], slsdtgt0(xa)))], (1267 ^ _163496) ^ [] : [-(aElementOf0(1263 ^ [], slsdtgt0(xb)))], (1269 ^ _163496) ^ [] : [-(sdtpldt0(1262 ^ [], 1263 ^ []) = xb)], (1271 ^ _163496) ^ [] : [-(aElementOf0(xb, xI))], (1273 ^ _163496) ^ [] : [-(xr = sdtpldt0(smndt0(sdtasdt0(xq, xu)), xb))], (1231 ^ _163496) ^ [] : [-(aElement0(xq))], (1233 ^ _163496) ^ [] : [-(aElement0(xr))], (1235 ^ _163496) ^ [] : [-(xb = sdtpldt0(sdtasdt0(xq, xu), xr))], (1237 ^ _163496) ^ [] : [-(xr = sz00), -(iLess0(sbrdtbr0(xr), sbrdtbr0(xu)))]], input).
% 101.59/98.76  ncf('1',plain,[aElementOf0(xr, xI)],start(1285 ^ 0)).
% 101.59/98.76  ncf('1.1',plain,[-(aElementOf0(xr, xI)), aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq, xu)), xb), xI), sdtpldt0(smndt0(sdtasdt0(xq, xu)), xb) = xr, xI = xI],extension(152 ^ 1,bind([[_168446, _168448, _168450, _168452], [xI, xI, xr, sdtpldt0(smndt0(sdtasdt0(xq, xu)), xb)]]))).
% 101.59/98.76  ncf('1.1.1',plain,[-(aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq, xu)), xb), xI)), 572 : aElementOf0(xb, xI), 572 : aElementOf0(smndt0(sdtasdt0(xq, xu)), xI), 568 : aIdeal0(xI)],extension(562 ^ 2,bind([[_182389, _182621, _182802], [xI, smndt0(sdtasdt0(xq, xu)), xb]]))).
% 101.59/98.76  ncf('1.1.1.1',plain,[-(aElementOf0(xb, xI))],extension(1271 ^ 7)).
% 101.59/98.76  ncf('1.1.1.2',plain,[-(aElementOf0(smndt0(sdtasdt0(xq, xu)), xI))],extension(1253 ^ 5)).
% 101.59/98.76  ncf('1.1.1.3',plain,[-(aIdeal0(xI))],extension(1007 ^ 3)).
% 101.59/98.76  ncf('1.1.2',plain,[-(sdtpldt0(smndt0(sdtasdt0(xq, xu)), xb) = xr), xr = sdtpldt0(smndt0(sdtasdt0(xq, xu)), xb)],extension(4 ^ 2,bind([[_163747, _163749], [sdtpldt0(smndt0(sdtasdt0(xq, xu)), xb), xr]]))).
% 101.59/98.76  ncf('1.1.2.1',plain,[-(xr = sdtpldt0(smndt0(sdtasdt0(xq, xu)), xb))],extension(1273 ^ 3)).
% 101.59/98.76  ncf('1.1.3',plain,[-(xI = xI)],extension(2 ^ 2,bind([[_163640], [xI]]))).
% 101.59/98.76  %-----------------------------------------------------
% 101.59/98.76  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------