%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : RNG112+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n015.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 11:49:52 EDT 2023

% Result   : Theorem 44.03s 42.90s
% Output   : Proof 44.03s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem  : RNG112+1 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.13  % Command  : nanocop.sh %s %d
% 0.13/0.34  % Computer : n015.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Thu May 18 20:38:07 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 44.03/42.90  
% 44.03/42.90  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 44.03/42.90  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 44.03/42.90  %-----------------------------------------------------
% 44.03/42.90  ncf(matrix, plain, [(972 ^ _167456) ^ [_167501] : [aElementOf0(_167501, xI), -(_167501 = sz00), 980 ^ _167456 : [(985 ^ _167456) ^ [] : [-(iLess0(sbrdtbr0(979 ^ [_167501]), sbrdtbr0(_167501)))], (983 ^ _167456) ^ [] : [979 ^ [_167501] = sz00], (981 ^ _167456) ^ [] : [-(aElementOf0(979 ^ [_167501], xI))]]], !, (224 ^ _134977) ^ [_142463] : [aElement0(_142463), true___, -(true___)], (920 ^ _134977) ^ [] : [-(aElement0(xa))], (719 ^ _134977) ^ [_158860, _158862] : [732 ^ _134977 : [(735 ^ _134977) ^ [] : [-(aElement0(731 ^ [_158860, _158862]))], (737 ^ _134977) ^ [] : [-(_158862 = sdtpldt0(sdtasdt0(730 ^ [_158860, _158862], _158860), 731 ^ [_158860, _158862]))], (739 ^ _134977) ^ [] : [-(731 ^ [_158860, _158862] = sz00), -(iLess0(sbrdtbr0(731 ^ [_158860, _158862]), sbrdtbr0(_158860)))], (733 ^ _134977) ^ [] : [-(aElement0(730 ^ [_158860, _158862]))]], aElement0(_158862), aElement0(_158860), -(_158860 = sz00)], (254 ^ _134977) ^ [_143327, _143329] : [-(aElement0(sdtasdt0(_143329, _143327))), aElement0(_143329), aElement0(_143327)], (859 ^ _134977) ^ [_163413] : [aElement0(_163413), 862 ^ _134977 : [(863 ^ _134977) ^ [_163604] : [_163604 = slsdtgt0(_163413), 866 ^ _134977 : [(878 ^ _134977) ^ [_164192] : [-(aElementOf0(_164192, _163604)), 879 ^ _134977 : [(880 ^ _134977) ^ [_164292] : [aElement0(_164292), sdtasdt0(_163413, _164292) = _164192]]], (869 ^ _134977) ^ [_163859] : [aElementOf0(_163859, _163604), 873 ^ _134977 : [(876 ^ _134977) ^ [] : [-(sdtasdt0(_163413, 872 ^ [_163413, _163604, _163859]) = _163859)], (874 ^ _134977) ^ [] : [-(aElement0(872 ^ [_163413, _163604, _163859]))]]], (867 ^ _134977) ^ [] : [-(aSet0(_163604))]]], (888 ^ _134977) ^ [_164537] : [-(_164537 = slsdtgt0(_163413)), aSet0(_164537), 905 ^ _134977 : [(910 ^ _134977) ^ [] : [aElementOf0(893 ^ [_163413, _164537], _164537)], (908 ^ _134977) ^ [] : [-(sdtasdt0(_163413, 904 ^ [_163413, _164537]) = 893 ^ [_163413, _164537])], (906 ^ _134977) ^ [] : [-(aElement0(904 ^ [_163413, _164537]))]], 896 ^ _134977 : [(899 ^ _134977) ^ [_164909] : [aElement0(_164909), sdtasdt0(_163413, _164909) = 893 ^ [_163413, _164537]], (897 ^ _134977) ^ [] : [-(aElementOf0(893 ^ [_163413, _164537], _164537))]]]]], (2 ^ _134977) ^ [_135101] : [-(_135101 = _135101)], (48 ^ _134977) ^ [_136657, _136659, _136661, _136663] : [-(aDivisorOf0(_136661, _136657)), aDivisorOf0(_136663, _136659), _136663 = _136661, _136659 = _136657], (681 ^ _134977) ^ [_157853] : [aNaturalNumber0(_157853), true___, -(true___)], (238 ^ _134977) ^ [_142824] : [aElement0(_142824), -(aElement0(smndt0(_142824)))], (62 ^ _134977) ^ [_137101, _137103, _137105, _137107] : [-(doDivides0(_137105, _137101)), doDivides0(_137107, _137103), _137107 = _137105, _137103 = _137101], (236 ^ _134977) ^ [] : [-(aElement0(sz10))], (10 ^ _134977) ^ [_135412, _135414, _135416] : [-(_135416 = _135412), _135416 = _135414, _135414 = _135412], (360 ^ _134977) ^ [_146749] : [aElement0(_146749), 363 ^ _134977 : [(366 ^ _134977) ^ [] : [-(sz00 = sdtasdt0(sz00, _146749))], (364 ^ _134977) ^ [] : [-(sdtasdt0(_146749, sz00) = sz00)]]], (505 ^ _134977) ^ [_151901, _151903] : [aSet0(_151903), aSet0(_151901), 512 ^ _134977 : [(513 ^ _134977) ^ [_152177] : [_152177 = sdtasasdt0(_151903, _151901), 516 ^ _134977 : [(527 ^ _134977) ^ [_152694] : [-(aElementOf0(_152694, _152177)), aElementOf0(_152694, _151903), aElementOf0(_152694, _151901)], (519 ^ _134977) ^ [_152435] : [aElementOf0(_152435, _152177), 522 ^ _134977 : [(525 ^ _134977) ^ [] : [-(aElementOf0(_152435, _151901))], (523 ^ _134977) ^ [] : [-(aElementOf0(_152435, _151903))]]], (517 ^ _134977) ^ [] : [-(aSet0(_152177))]]], (537 ^ _134977) ^ [_152980] : [-(_152980 = sdtasasdt0(_151903, _151901)), aSet0(_152980), 553 ^ _134977 : [(558 ^ _134977) ^ [] : [aElementOf0(542 ^ [_151901, _151903, _152980], _152980)], (556 ^ _134977) ^ [] : [-(aElementOf0(542 ^ [_151901, _151903, _152980], _151901))], (554 ^ _134977) ^ [] : [-(aElementOf0(542 ^ [_151901, _151903, _152980], _151903))]], 545 ^ _134977 : [(548 ^ _134977) ^ [] : [aElementOf0(542 ^ [_151901, _151903, _152980], _151903), aElementOf0(542 ^ [_151901, _151903, _152980], _151901)], (546 ^ _134977) ^ [] : [-(aElementOf0(542 ^ [_151901, _151903, _152980], _152980))]]]]], (607 ^ _134977) ^ [_155485, _155487] : [-(aIdeal0(sdtpldt1(_155487, _155485))), aIdeal0(_155487), aIdeal0(_155485)], (368 ^ _134977) ^ [_147036, _147038] : [aElement0(_147038), aElement0(_147036), sdtasdt0(_147038, _147036) = sz00, -(_147038 = sz00), -(_147036 = sz00)], (212 ^ _134977) ^ [_142003, _142005] : [_142005 = _142003, -(slsdtgt0(_142005) = slsdtgt0(_142003))], (38 ^ _134977) ^ [_136334, _136336] : [-(aNaturalNumber0(_136334)), _136336 = _136334, aNaturalNumber0(_136336)], (947 ^ _134977) ^ [] : [943 ^ [] = sz00], (304 ^ _134977) ^ [_144921, _144923] : [-(sdtasdt0(_144923, _144921) = sdtasdt0(_144921, _144923)), aElement0(_144923), aElement0(_144921)], (90 ^ _134977) ^ [_137961, _137963] : [-(aSet0(_137961)), _137963 = _137961, aSet0(_137963)], (651 ^ _134977) ^ [_156775, _156777] : [aIdeal0(_156777), aIdeal0(_156775), 661 ^ _134977 : [(664 ^ _134977) ^ [] : [aElementOf0(660 ^ [_156775, _156777], sdtpldt1(_156777, _156775))], (662 ^ _134977) ^ [] : [-(aElement0(660 ^ [_156775, _156777]))]], 665 ^ _134977 : [(666 ^ _134977) ^ [_157273, _157275] : [674 ^ _134977 : [(679 ^ _134977) ^ [] : [-(sdteqdtlpzmzozddtrp0(673 ^ [_156775, _156777, _157273, _157275], _157273, _156775))], (677 ^ _134977) ^ [] : [-(sdteqdtlpzmzozddtrp0(673 ^ [_156775, _156777, _157273, _157275], _157275, _156777))], (675 ^ _134977) ^ [] : [-(aElement0(673 ^ [_156775, _156777, _157273, _157275]))]], aElement0(_157275), aElement0(_157273)]]], (794 ^ _134977) ^ [_161344, _161346] : [aElement0(_161346), aElement0(_161344), 801 ^ _134977 : [(820 ^ _134977) ^ [_162212] : [-(aGcdOfAnd0(_162212, _161346, _161344)), aDivisorOf0(_162212, _161346), aDivisorOf0(_162212, _161344), 830 ^ _134977 : [(835 ^ _134977) ^ [] : [doDivides0(829 ^ [_161344, _161346, _162212], _162212)], (833 ^ _134977) ^ [] : [-(aDivisorOf0(829 ^ [_161344, _161346, _162212], _161344))], (831 ^ _134977) ^ [] : [-(aDivisorOf0(829 ^ [_161344, _161346, _162212], _161346))]]], (802 ^ _134977) ^ [_161625] : [aGcdOfAnd0(_161625, _161346, _161344), 805 ^ _134977 : [(810 ^ _134977) ^ [_161926] : [-(doDivides0(_161926, _161625)), aDivisorOf0(_161926, _161346), aDivisorOf0(_161926, _161344)], (808 ^ _134977) ^ [] : [-(aDivisorOf0(_161625, _161344))], (806 ^ _134977) ^ [] : [-(aDivisorOf0(_161625, _161346))]]]]], (398 ^ _134977) ^ [_147811] : [aSet0(_147811), 401 ^ _134977 : [(402 ^ _134977) ^ [_147941] : [aElementOf0(_147941, _147811), -(aElement0(_147941))]]], (274 ^ _134977) ^ [_143947, _143949, _143951] : [-(sdtpldt0(sdtpldt0(_143951, _143949), _143947) = sdtpldt0(_143951, sdtpldt0(_143949, _143947))), aElement0(_143951), aElement0(_143949), aElement0(_143947)], (945 ^ _134977) ^ [] : [-(aElementOf0(943 ^ [], sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))))], (182 ^ _134977) ^ [_140954, _140956, _140958, _140960] : [-(sdtpldt0(_140960, _140956) = sdtpldt0(_140958, _140954)), _140960 = _140958, _140956 = _140954], (76 ^ _134977) ^ [_137545, _137547, _137549, _137551] : [-(misRelativelyPrime0(_137549, _137545)), misRelativelyPrime0(_137551, _137547), _137551 = _137549, _137547 = _137545], (839 ^ _134977) ^ [_162877, _162879] : [aElement0(_162879), aElement0(_162877), 846 ^ _134977 : [(853 ^ _134977) ^ [] : [aGcdOfAnd0(sz10, _162879, _162877), -(misRelativelyPrime0(_162879, _162877))], (847 ^ _134977) ^ [] : [misRelativelyPrime0(_162879, _162877), -(aGcdOfAnd0(sz10, _162879, _162877))]]], (234 ^ _134977) ^ [] : [-(aElement0(sz00))], (940 ^ _134977) ^ [] : [-(aElementOf0(sz00, slsdtgt0(xb)))], (176 ^ _134977) ^ [_140708, _140710] : [_140710 = _140708, -(smndt0(_140710) = smndt0(_140708))], (924 ^ _134977) ^ [] : [xa = sz00, xb = sz00], (4 ^ _134977) ^ [_135208, _135210] : [_135210 = _135208, -(_135208 = _135210)], (930 ^ _134977) ^ [] : [-(aGcdOfAnd0(xc, xa, xb))], (914 ^ _134977) ^ [_165476] : [aElement0(_165476), -(aIdeal0(slsdtgt0(_165476)))], (288 ^ _134977) ^ [_144353] : [aElement0(_144353), 291 ^ _134977 : [(294 ^ _134977) ^ [] : [-(_144353 = sdtpldt0(sz00, _144353))], (292 ^ _134977) ^ [] : [-(sdtpldt0(_144353, sz00) = _144353)]]], (152 ^ _134977) ^ [_139907, _139909, _139911, _139913] : [-(iLess0(_139911, _139907)), iLess0(_139913, _139909), _139913 = _139911, _139909 = _139907], (922 ^ _134977) ^ [] : [-(aElement0(xb))], (701 ^ _134977) ^ [_158400, _158402] : [aNaturalNumber0(_158402), aNaturalNumber0(_158400), iLess0(_158402, _158400), true___, -(true___)], (938 ^ _134977) ^ [] : [-(aElementOf0(xa, slsdtgt0(xa)))], (166 ^ _134977) ^ [_140377, _140379, _140381, _140383] : [-(sdtasasdt0(_140383, _140379) = sdtasasdt0(_140381, _140377)), _140383 = _140381, _140379 = _140377], (352 ^ _134977) ^ [_146468] : [aElement0(_146468), 355 ^ _134977 : [(358 ^ _134977) ^ [] : [-(smndt0(_146468) = sdtasdt0(_146468, smndt0(sz10)))], (356 ^ _134977) ^ [] : [-(sdtasdt0(smndt0(sz10), _146468) = smndt0(_146468))]]], (128 ^ _134977) ^ [_139160, _139162] : [-(aIdeal0(_139160)), _139162 = _139160, aIdeal0(_139162)], (386 ^ _134977) ^ [] : [sz10 = sz00], (328 ^ _134977) ^ [_145648] : [aElement0(_145648), 331 ^ _134977 : [(334 ^ _134977) ^ [] : [-(_145648 = sdtasdt0(sz10, _145648))], (332 ^ _134977) ^ [] : [-(sdtasdt0(_145648, sz10) = _145648)]]], (110 ^ _134977) ^ [_138607, _138609, _138611, _138613, _138615, _138617] : [-(aGcdOfAnd0(_138615, _138611, _138607)), aGcdOfAnd0(_138617, _138613, _138609), _138617 = _138615, _138613 = _138611, _138609 = _138607], (627 ^ _134977) ^ [_156097, _156099, _156101] : [aElement0(_156101), aElement0(_156099), aIdeal0(_156097), 638 ^ _134977 : [(645 ^ _134977) ^ [] : [aElementOf0(sdtpldt0(_156101, smndt0(_156099)), _156097), -(sdteqdtlpzmzozddtrp0(_156101, _156099, _156097))], (639 ^ _134977) ^ [] : [sdteqdtlpzmzozddtrp0(_156101, _156099, _156097), -(aElementOf0(sdtpldt0(_156101, smndt0(_156099)), _156097))]]], (934 ^ _134977) ^ [] : [-(xI = sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))], (202 ^ _134977) ^ [_141672, _141674, _141676, _141678] : [-(sdtpldt1(_141678, _141674) = sdtpldt1(_141676, _141672)), _141678 = _141676, _141674 = _141672], (432 ^ _134977) ^ [_148921, _148923] : [aSet0(_148923), aSet0(_148921), 439 ^ _134977 : [(440 ^ _134977) ^ [_149216] : [_149216 = sdtpldt1(_148923, _148921), 443 ^ _134977 : [(458 ^ _134977) ^ [_150053] : [-(aElementOf0(_150053, _149216)), 459 ^ _134977 : [(460 ^ _134977) ^ [_150183, _150185] : [aElementOf0(_150185, _148923), aElementOf0(_150183, _148921), sdtpldt0(_150185, _150183) = _150053]]], (446 ^ _134977) ^ [_149493] : [aElementOf0(_149493, _149216), 451 ^ _134977 : [(456 ^ _134977) ^ [] : [-(sdtpldt0(449 ^ [_148921, _148923, _149216, _149493], 450 ^ [_148921, _148923, _149216, _149493]) = _149493)], (454 ^ _134977) ^ [] : [-(aElementOf0(450 ^ [_148921, _148923, _149216, _149493], _148921))], (452 ^ _134977) ^ [] : [-(aElementOf0(449 ^ [_148921, _148923, _149216, _149493], _148923))]]], (444 ^ _134977) ^ [] : [-(aSet0(_149216))]]], (472 ^ _134977) ^ [_150551] : [-(_150551 = sdtpldt1(_148923, _148921)), aSet0(_150551), 494 ^ _134977 : [(497 ^ _134977) ^ [] : [-(aElementOf0(493 ^ [_148921, _148923, _150551], _148921))], (499 ^ _134977) ^ [] : [-(sdtpldt0(492 ^ [_148921, _148923, _150551], 493 ^ [_148921, _148923, _150551]) = 477 ^ [_148921, _148923, _150551])], (501 ^ _134977) ^ [] : [aElementOf0(477 ^ [_148921, _148923, _150551], _150551)], (495 ^ _134977) ^ [] : [-(aElementOf0(492 ^ [_148921, _148923, _150551], _148923))]], 480 ^ _134977 : [(483 ^ _134977) ^ [_150980, _150982] : [aElementOf0(_150982, _148923), aElementOf0(_150980, _148921), sdtpldt0(_150982, _150980) = 477 ^ [_148921, _148923, _150551]], (481 ^ _134977) ^ [] : [-(aElementOf0(477 ^ [_148921, _148923, _150551], _150551))]]]]], (336 ^ _134977) ^ [_145949, _145951, _145953] : [347 ^ _134977 : [(350 ^ _134977) ^ [] : [-(sdtasdt0(sdtpldt0(_145951, _145949), _145953) = sdtpldt0(sdtasdt0(_145951, _145953), sdtasdt0(_145949, _145953)))], (348 ^ _134977) ^ [] : [-(sdtasdt0(_145953, sdtpldt0(_145951, _145949)) = sdtpldt0(sdtasdt0(_145953, _145951), sdtasdt0(_145953, _145949)))]], aElement0(_145953), aElement0(_145951), aElement0(_145949)], (264 ^ _134977) ^ [_143626, _143628] : [-(sdtpldt0(_143628, _143626) = sdtpldt0(_143626, _143628)), aElement0(_143628), aElement0(_143626)], (244 ^ _134977) ^ [_143028, _143030] : [-(aElement0(sdtpldt0(_143030, _143028))), aElement0(_143030), aElement0(_143028)], (562 ^ _134977) ^ [_153850] : [aIdeal0(_153850), 565 ^ _134977 : [(568 ^ _134977) ^ [_154082] : [aElementOf0(_154082, _153850), 571 ^ _134977 : [(578 ^ _134977) ^ [_154455] : [aElement0(_154455), -(aElementOf0(sdtasdt0(_154455, _154082), _153850))], (572 ^ _134977) ^ [_154263] : [aElementOf0(_154263, _153850), -(aElementOf0(sdtpldt0(_154082, _154263), _153850))]]], (566 ^ _134977) ^ [] : [-(aSet0(_153850))]]], (745 ^ _134977) ^ [_159807, _159809] : [aElement0(_159809), aElement0(_159807), 752 ^ _134977 : [(762 ^ _134977) ^ [] : [-(doDivides0(_159809, _159807)), 763 ^ _134977 : [(764 ^ _134977) ^ [_160367] : [aElement0(_160367), sdtasdt0(_159809, _160367) = _159807]]], (753 ^ _134977) ^ [] : [doDivides0(_159809, _159807), 757 ^ _134977 : [(760 ^ _134977) ^ [] : [-(sdtasdt0(_159809, 756 ^ [_159807, _159809]) = _159807)], (758 ^ _134977) ^ [] : [-(aElement0(756 ^ [_159807, _159809]))]]]]], (192 ^ _134977) ^ [_141313, _141315, _141317, _141319] : [-(sdtasdt0(_141319, _141315) = sdtasdt0(_141317, _141313)), _141319 = _141317, _141315 = _141313], (942 ^ _134977) ^ [] : [-(aElementOf0(xb, slsdtgt0(xb)))], (691 ^ _134977) ^ [_158108] : [-(aNaturalNumber0(sbrdtbr0(_158108))), aElement0(_158108), -(_158108 = sz00)], (314 ^ _134977) ^ [_145242, _145244, _145246] : [-(sdtasdt0(sdtasdt0(_145246, _145244), _145242) = sdtasdt0(_145246, sdtasdt0(_145244, _145242))), aElement0(_145246), aElement0(_145244), aElement0(_145242)], (584 ^ _134977) ^ [_154645] : [-(aIdeal0(_154645)), aSet0(_154645), 590 ^ _134977 : [(593 ^ _134977) ^ [] : [595 ^ _134977 : [(598 ^ _134977) ^ [] : [aElementOf0(sdtpldt0(589 ^ [_154645], 594 ^ [_154645]), _154645)], (596 ^ _134977) ^ [] : [-(aElementOf0(594 ^ [_154645], _154645))]], 600 ^ _134977 : [(603 ^ _134977) ^ [] : [aElementOf0(sdtasdt0(599 ^ [_154645], 589 ^ [_154645]), _154645)], (601 ^ _134977) ^ [] : [-(aElement0(599 ^ [_154645]))]]], (591 ^ _134977) ^ [] : [-(aElementOf0(589 ^ [_154645], _154645))]]], (20 ^ _134977) ^ [_135781, _135783, _135785, _135787, _135789, _135791] : [-(sdteqdtlpzmzozddtrp0(_135789, _135785, _135781)), sdteqdtlpzmzozddtrp0(_135791, _135787, _135783), _135791 = _135789, _135787 = _135785, _135783 = _135781], (772 ^ _134977) ^ [_160636] : [aElement0(_160636), 775 ^ _134977 : [(784 ^ _134977) ^ [_161038] : [-(aDivisorOf0(_161038, _160636)), aElement0(_161038), doDivides0(_161038, _160636)], (776 ^ _134977) ^ [_160801] : [aDivisorOf0(_160801, _160636), 779 ^ _134977 : [(782 ^ _134977) ^ [] : [-(doDivides0(_160801, _160636))], (780 ^ _134977) ^ [] : [-(aElement0(_160801))]]]]], (949 ^ _134977) ^ [_166403] : [aElementOf0(_166403, xI), -(_166403 = sz00), 957 ^ _134977 : [(962 ^ _134977) ^ [_166874] : [iLess0(sbrdtbr0(_166874), sbrdtbr0(956 ^ [_166403])), aElementOf0(_166874, xI), -(_166874 = sz00)], (960 ^ _134977) ^ [] : [956 ^ [_166403] = sz00], (958 ^ _134977) ^ [] : [-(aElementOf0(956 ^ [_166403], xI))]]], (388 ^ _134977) ^ [_147556] : [aSet0(_147556), true___, -(true___)], (100 ^ _134977) ^ [_138256, _138258] : [-(aElement0(_138256)), _138258 = _138256, aElement0(_138258)], (296 ^ _134977) ^ [_144626] : [aElement0(_144626), 299 ^ _134977 : [(302 ^ _134977) ^ [] : [-(sz00 = sdtpldt0(smndt0(_144626), _144626))], (300 ^ _134977) ^ [] : [-(sdtpldt0(_144626, smndt0(_144626)) = sz00)]]], (936 ^ _134977) ^ [] : [-(aElementOf0(sz00, slsdtgt0(xa)))], (932 ^ _134977) ^ [] : [-(aIdeal0(xI))], (408 ^ _134977) ^ [_148156, _148158] : [aSet0(_148158), aSet0(_148156), -(_148158 = _148156), 420 ^ _134977 : [(423 ^ _134977) ^ [] : [aElementOf0(419 ^ [_148156, _148158], _148156)], (421 ^ _134977) ^ [] : [-(aElementOf0(419 ^ [_148156, _148158], _148158))]], 425 ^ _134977 : [(428 ^ _134977) ^ [] : [aElementOf0(424 ^ [_148156, _148158], _148158)], (426 ^ _134977) ^ [] : [-(aElementOf0(424 ^ [_148156, _148158], _148156))]]], (218 ^ _134977) ^ [_142201, _142203] : [_142203 = _142201, -(sbrdtbr0(_142203) = sbrdtbr0(_142201))], (138 ^ _134977) ^ [_139483, _139485, _139487, _139489] : [-(aElementOf0(_139487, _139483)), aElementOf0(_139489, _139485), _139489 = _139487, _139485 = _139483], (617 ^ _134977) ^ [_155784, _155786] : [-(aIdeal0(sdtasasdt0(_155786, _155784))), aIdeal0(_155786), aIdeal0(_155784)]], input).
% 44.03/42.90  ncf('1',plain,[aElementOf0(979 ^ [943 ^ []], xI), -(979 ^ [943 ^ []] = sz00), 983 : 979 ^ [979 ^ [943 ^ []]] = sz00],start(972 ^ 0,bind([[_167501], [979 ^ [943 ^ []]]]))).
% 44.03/42.90  ncf('1.1',plain,[-(aElementOf0(979 ^ [943 ^ []], xI)), aElementOf0(943 ^ [], xI), -(943 ^ [] = sz00)],extension(972 ^ 1,bind([[_167501], [943 ^ []]]))).
% 44.03/42.90  ncf('1.1.1',plain,[-(aElementOf0(943 ^ [], xI)), aElementOf0(943 ^ [], sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))), 943 ^ [] = 943 ^ [], sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)) = xI],extension(138 ^ 2,bind([[_139483, _139485, _139487, _139489], [xI, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)), 943 ^ [], 943 ^ []]]))).
% 44.03/42.90  ncf('1.1.1.1',plain,[-(aElementOf0(943 ^ [], sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))))],extension(945 ^ 3)).
% 44.03/42.90  ncf('1.1.1.2',plain,[-(943 ^ [] = 943 ^ [])],extension(2 ^ 3,bind([[_135101], [943 ^ []]]))).
% 44.03/42.90  ncf('1.1.1.3',plain,[-(sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)) = xI), xI = sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))],extension(4 ^ 3,bind([[_135208, _135210], [sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)), xI]]))).
% 44.03/42.90  ncf('1.1.1.3.1',plain,[-(xI = sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))],extension(934 ^ 4)).
% 44.03/42.90  ncf('1.1.2',plain,[943 ^ [] = sz00, -(943 ^ [] = 943 ^ []), sz00 = 943 ^ []],extension(10 ^ 2,bind([[_135412, _135414, _135416], [943 ^ [], sz00, 943 ^ []]]))).
% 44.03/42.90  ncf('1.1.2.1',plain,[943 ^ [] = 943 ^ [], -(943 ^ [] = sz00), 943 ^ [] = sz00],extension(10 ^ 3,bind([[_135412, _135414, _135416], [sz00, 943 ^ [], 943 ^ []]]))).
% 44.03/42.90  ncf('1.1.2.1.1',plain,[943 ^ [] = sz00],extension(947 ^ 4)).
% 44.03/42.90  ncf('1.1.2.1.2',plain,[-(943 ^ [] = sz00)],reduction('1.1')).
% 44.03/42.90  ncf('1.1.2.2',plain,[-(sz00 = 943 ^ []), 943 ^ [] = sz00],extension(4 ^ 3,bind([[_135208, _135210], [sz00, 943 ^ []]]))).
% 44.03/42.90  ncf('1.1.2.2.1',plain,[-(943 ^ [] = sz00)],reduction('1.1')).
% 44.03/42.90  ncf('1.2',plain,[979 ^ [943 ^ []] = sz00, aElementOf0(943 ^ [], xI), -(943 ^ [] = sz00)],extension(972 ^ 1,bind([[_167501], [943 ^ []]]))).
% 44.03/42.90  ncf('1.2.1',plain,[-(aElementOf0(943 ^ [], xI)), aElementOf0(943 ^ [], sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))), 943 ^ [] = 943 ^ [], sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)) = xI],extension(138 ^ 2,bind([[_139483, _139485, _139487, _139489], [xI, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)), 943 ^ [], 943 ^ []]]))).
% 44.03/42.90  ncf('1.2.1.1',plain,[-(aElementOf0(943 ^ [], sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))))],extension(945 ^ 3)).
% 44.03/42.90  ncf('1.2.1.2',plain,[-(943 ^ [] = 943 ^ [])],extension(2 ^ 3,bind([[_135101], [943 ^ []]]))).
% 44.03/42.90  ncf('1.2.1.3',plain,[-(sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)) = xI), xI = sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))],extension(4 ^ 3,bind([[_135208, _135210], [sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)), xI]]))).
% 44.03/42.90  ncf('1.2.1.3.1',plain,[-(xI = sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))],extension(934 ^ 4)).
% 44.03/42.90  ncf('1.2.2',plain,[943 ^ [] = sz00, -(943 ^ [] = 943 ^ []), sz00 = 943 ^ []],extension(10 ^ 2,bind([[_135412, _135414, _135416], [943 ^ [], sz00, 943 ^ []]]))).
% 44.03/42.90  ncf('1.2.2.1',plain,[943 ^ [] = 943 ^ [], -(943 ^ [] = sz00), 943 ^ [] = sz00],extension(10 ^ 3,bind([[_135412, _135414, _135416], [sz00, 943 ^ [], 943 ^ []]]))).
% 44.03/42.90  ncf('1.2.2.1.1',plain,[943 ^ [] = sz00],extension(947 ^ 4)).
% 44.03/42.90  ncf('1.2.2.1.2',plain,[-(943 ^ [] = sz00)],reduction('1.2')).
% 44.03/42.90  ncf('1.2.2.2',plain,[-(sz00 = 943 ^ []), 943 ^ [] = sz00],extension(4 ^ 3,bind([[_135208, _135210], [sz00, 943 ^ []]]))).
% 44.03/42.90  ncf('1.2.2.2.1',plain,[-(943 ^ [] = sz00)],reduction('1.2')).
% 44.03/42.90  ncf('1.3',plain,[-(979 ^ [979 ^ [943 ^ []]] = sz00), aElementOf0(979 ^ [979 ^ [943 ^ []]], xI), 962 : iLess0(sbrdtbr0(979 ^ [956 ^ [979 ^ [979 ^ [943 ^ []]]]]), sbrdtbr0(956 ^ [979 ^ [979 ^ [943 ^ []]]])), 962 : aElementOf0(979 ^ [956 ^ [979 ^ [979 ^ [943 ^ []]]]], xI), 962 : -(979 ^ [956 ^ [979 ^ [979 ^ [943 ^ []]]]] = sz00)],extension(949 ^ 3,bind([[_166403, _166874], [979 ^ [979 ^ [943 ^ []]], 979 ^ [956 ^ [979 ^ [979 ^ [943 ^ []]]]]]]))).
% 44.03/42.90  ncf('1.3.1',plain,[-(aElementOf0(979 ^ [979 ^ [943 ^ []]], xI))],extension(981 ^ 4)).
% 44.03/42.90  ncf('1.3.2',plain,[-(iLess0(sbrdtbr0(979 ^ [956 ^ [979 ^ [979 ^ [943 ^ []]]]]), sbrdtbr0(956 ^ [979 ^ [979 ^ [943 ^ []]]]))), aElementOf0(956 ^ [979 ^ [979 ^ [943 ^ []]]], xI), -(956 ^ [979 ^ [979 ^ [943 ^ []]]] = sz00)],extension(972 ^ 6,bind([[_167501], [956 ^ [979 ^ [979 ^ [943 ^ []]]]]]))).
% 44.03/42.90  ncf('1.3.2.1',plain,[-(aElementOf0(956 ^ [979 ^ [979 ^ [943 ^ []]]], xI))],extension(958 ^ 7)).
% 44.03/42.90  ncf('1.3.2.2',plain,[956 ^ [979 ^ [979 ^ [943 ^ []]]] = sz00],extension(960 ^ 7)).
% 44.03/42.90  ncf('1.3.3',plain,[-(aElementOf0(979 ^ [956 ^ [979 ^ [979 ^ [943 ^ []]]]], xI)), aElementOf0(956 ^ [979 ^ [979 ^ [943 ^ []]]], xI), -(956 ^ [979 ^ [979 ^ [943 ^ []]]] = sz00)],extension(972 ^ 6,bind([[_167501], [956 ^ [979 ^ [979 ^ [943 ^ []]]]]]))).
% 44.03/42.90  ncf('1.3.3.1',plain,[-(aElementOf0(956 ^ [979 ^ [979 ^ [943 ^ []]]], xI))],extension(958 ^ 7)).
% 44.03/42.90  ncf('1.3.3.2',plain,[956 ^ [979 ^ [979 ^ [943 ^ []]]] = sz00],extension(960 ^ 7)).
% 44.03/42.90  ncf('1.3.4',plain,[979 ^ [956 ^ [979 ^ [979 ^ [943 ^ []]]]] = sz00, aElementOf0(956 ^ [979 ^ [979 ^ [943 ^ []]]], xI), -(956 ^ [979 ^ [979 ^ [943 ^ []]]] = sz00)],extension(972 ^ 6,bind([[_167501], [956 ^ [979 ^ [979 ^ [943 ^ []]]]]]))).
% 44.03/42.90  ncf('1.3.4.1',plain,[-(aElementOf0(956 ^ [979 ^ [979 ^ [943 ^ []]]], xI))],extension(958 ^ 7)).
% 44.03/42.90  ncf('1.3.4.2',plain,[956 ^ [979 ^ [979 ^ [943 ^ []]]] = sz00],extension(960 ^ 7)).
% 44.03/42.90  %-----------------------------------------------------
% 44.03/42.90  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------