TSTP Solution File: NUM505+1 by nanoCoP---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : NUM505+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n017.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 11:44:48 EDT 2023

% Result   : Theorem 0.45s 1.37s
% Output   : Proof 0.45s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : NUM505+1 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n017.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 16:10:30 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.45/1.37  
% 0.45/1.37  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 0.45/1.37  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.45/1.37  %-----------------------------------------------------
% 0.45/1.37  ncf(matrix, plain, [(874 ^ _114542) ^ [] : [sdtlseqdt0(xp, xk)], (876 ^ _114542) ^ [] : [-(xk = xp), sdtlseqdt0(xk, xp)], (82 ^ _114542) ^ [_117254, _117256, _117258, _117260] : [-(sdtmndt0(_117260, _117256) = sdtmndt0(_117258, _117254)), _117260 = _117258, _117256 = _117254], (92 ^ _114542) ^ [_117613, _117615, _117617, _117619] : [-(sdtpldt0(_117619, _117615) = sdtpldt0(_117617, _117613)), _117619 = _117617, _117615 = _117613], (102 ^ _114542) ^ [_117972, _117974, _117976, _117978] : [-(sdtsldt0(_117978, _117974) = sdtsldt0(_117976, _117972)), _117978 = _117976, _117974 = _117972], (112 ^ _114542) ^ [_118311, _118313, _118315, _118317] : [-(sdtasdt0(_118317, _118313) = sdtasdt0(_118315, _118311)), _118317 = _118315, _118313 = _118311], (2 ^ _114542) ^ [_114686] : [-(_114686 = _114686)], (4 ^ _114542) ^ [_114793, _114795] : [_114795 = _114793, -(_114793 = _114795)], (10 ^ _114542) ^ [_114997, _114999, _115001] : [-(_115001 = _114997), _115001 = _114999, _114999 = _114997], (20 ^ _114542) ^ [_115338, _115340, _115342, _115344] : [-(iLess0(_115342, _115338)), iLess0(_115344, _115340), _115344 = _115342, _115340 = _115338], (34 ^ _114542) ^ [_115754, _115756] : [-(aNaturalNumber0(_115754)), _115756 = _115754, aNaturalNumber0(_115756)], (44 ^ _114542) ^ [_116049, _116051] : [-(isPrime0(_116049)), _116051 = _116049, isPrime0(_116051)], (54 ^ _114542) ^ [_116372, _116374, _116376, _116378] : [-(doDivides0(_116376, _116372)), doDivides0(_116378, _116374), _116378 = _116376, _116374 = _116372], (68 ^ _114542) ^ [_116796, _116798, _116800, _116802] : [-(sdtlseqdt0(_116800, _116796)), sdtlseqdt0(_116802, _116798), _116802 = _116800, _116798 = _116796], (122 ^ _114542) ^ [_118642] : [aNaturalNumber0(_118642), true___, -(true___)], (132 ^ _114542) ^ [] : [-(aNaturalNumber0(sz00))], (134 ^ _114542) ^ [] : [-(aNaturalNumber0(sz10))], (136 ^ _114542) ^ [] : [sz10 = sz00], (138 ^ _114542) ^ [_119071, _119073] : [-(aNaturalNumber0(sdtpldt0(_119073, _119071))), aNaturalNumber0(_119073), aNaturalNumber0(_119071)], (148 ^ _114542) ^ [_119370, _119372] : [-(aNaturalNumber0(sdtasdt0(_119372, _119370))), aNaturalNumber0(_119372), aNaturalNumber0(_119370)], (158 ^ _114542) ^ [_119669, _119671] : [-(sdtpldt0(_119671, _119669) = sdtpldt0(_119669, _119671)), aNaturalNumber0(_119671), aNaturalNumber0(_119669)], (168 ^ _114542) ^ [_119990, _119992, _119994] : [-(sdtpldt0(sdtpldt0(_119994, _119992), _119990) = sdtpldt0(_119994, sdtpldt0(_119992, _119990))), aNaturalNumber0(_119994), aNaturalNumber0(_119992), aNaturalNumber0(_119990)], (182 ^ _114542) ^ [_120396] : [aNaturalNumber0(_120396), 185 ^ _114542 : [(186 ^ _114542) ^ [] : [-(sdtpldt0(_120396, sz00) = _120396)], (188 ^ _114542) ^ [] : [-(_120396 = sdtpldt0(sz00, _120396))]]], (190 ^ _114542) ^ [_120683, _120685] : [-(sdtasdt0(_120685, _120683) = sdtasdt0(_120683, _120685)), aNaturalNumber0(_120685), aNaturalNumber0(_120683)], (200 ^ _114542) ^ [_121004, _121006, _121008] : [-(sdtasdt0(sdtasdt0(_121008, _121006), _121004) = sdtasdt0(_121008, sdtasdt0(_121006, _121004))), aNaturalNumber0(_121008), aNaturalNumber0(_121006), aNaturalNumber0(_121004)], (214 ^ _114542) ^ [_121410] : [aNaturalNumber0(_121410), 217 ^ _114542 : [(218 ^ _114542) ^ [] : [-(sdtasdt0(_121410, sz10) = _121410)], (220 ^ _114542) ^ [] : [-(_121410 = sdtasdt0(sz10, _121410))]]], (222 ^ _114542) ^ [_121683] : [aNaturalNumber0(_121683), 225 ^ _114542 : [(226 ^ _114542) ^ [] : [-(sdtasdt0(_121683, sz00) = sz00)], (228 ^ _114542) ^ [] : [-(sz00 = sdtasdt0(sz00, _121683))]]], (230 ^ _114542) ^ [_121984, _121986, _121988] : [241 ^ _114542 : [(242 ^ _114542) ^ [] : [-(sdtasdt0(_121988, sdtpldt0(_121986, _121984)) = sdtpldt0(sdtasdt0(_121988, _121986), sdtasdt0(_121988, _121984)))], (244 ^ _114542) ^ [] : [-(sdtasdt0(sdtpldt0(_121986, _121984), _121988) = sdtpldt0(sdtasdt0(_121986, _121988), sdtasdt0(_121984, _121988)))]], aNaturalNumber0(_121988), aNaturalNumber0(_121986), aNaturalNumber0(_121984)], (246 ^ _114542) ^ [_122531, _122533, _122535] : [259 ^ _114542 : [(260 ^ _114542) ^ [] : [sdtpldt0(_122535, _122533) = sdtpldt0(_122535, _122531)], (262 ^ _114542) ^ [] : [sdtpldt0(_122533, _122535) = sdtpldt0(_122531, _122535)]], -(_122533 = _122531), aNaturalNumber0(_122535), aNaturalNumber0(_122533), aNaturalNumber0(_122531)], (266 ^ _114542) ^ [_123108] : [aNaturalNumber0(_123108), -(_123108 = sz00), 273 ^ _114542 : [(274 ^ _114542) ^ [_123370, _123372] : [aNaturalNumber0(_123372), aNaturalNumber0(_123370), 283 ^ _114542 : [(284 ^ _114542) ^ [] : [sdtasdt0(_123108, _123372) = sdtasdt0(_123108, _123370)], (286 ^ _114542) ^ [] : [sdtasdt0(_123372, _123108) = sdtasdt0(_123370, _123108)]], -(_123372 = _123370)]]], (290 ^ _114542) ^ [_123881, _123883] : [aNaturalNumber0(_123883), aNaturalNumber0(_123881), sdtpldt0(_123883, _123881) = sz00, 301 ^ _114542 : [(302 ^ _114542) ^ [] : [-(_123883 = sz00)], (304 ^ _114542) ^ [] : [-(_123881 = sz00)]]], (306 ^ _114542) ^ [_124348, _124350] : [aNaturalNumber0(_124350), aNaturalNumber0(_124348), sdtasdt0(_124350, _124348) = sz00, -(_124350 = sz00), -(_124348 = sz00)], (324 ^ _114542) ^ [_124830, _124832] : [aNaturalNumber0(_124832), aNaturalNumber0(_124830), 331 ^ _114542 : [(332 ^ _114542) ^ [] : [sdtlseqdt0(_124832, _124830), 336 ^ _114542 : [(337 ^ _114542) ^ [] : [-(aNaturalNumber0(335 ^ [_124830, _124832]))], (339 ^ _114542) ^ [] : [-(sdtpldt0(_124832, 335 ^ [_124830, _124832]) = _124830)]]], (341 ^ _114542) ^ [] : [-(sdtlseqdt0(_124832, _124830)), 342 ^ _114542 : [(343 ^ _114542) ^ [_125390] : [aNaturalNumber0(_125390), sdtpldt0(_124832, _125390) = _124830]]]]], (351 ^ _114542) ^ [_125673, _125675] : [aNaturalNumber0(_125675), aNaturalNumber0(_125673), sdtlseqdt0(_125675, _125673), 362 ^ _114542 : [(363 ^ _114542) ^ [_126020] : [_126020 = sdtmndt0(_125673, _125675), 366 ^ _114542 : [(367 ^ _114542) ^ [] : [-(aNaturalNumber0(_126020))], (369 ^ _114542) ^ [] : [-(sdtpldt0(_125675, _126020) = _125673)]]], (371 ^ _114542) ^ [_126279] : [-(_126279 = sdtmndt0(_125673, _125675)), aNaturalNumber0(_126279), sdtpldt0(_125675, _126279) = _125673]]], (381 ^ _114542) ^ [_126601] : [aNaturalNumber0(_126601), -(sdtlseqdt0(_126601, _126601))], (387 ^ _114542) ^ [_126803, _126805] : [aNaturalNumber0(_126805), aNaturalNumber0(_126803), -(_126805 = _126803), sdtlseqdt0(_126805, _126803), sdtlseqdt0(_126803, _126805)], (405 ^ _114542) ^ [_127292, _127294, _127296] : [aNaturalNumber0(_127296), aNaturalNumber0(_127294), aNaturalNumber0(_127292), -(sdtlseqdt0(_127296, _127292)), sdtlseqdt0(_127296, _127294), sdtlseqdt0(_127294, _127292)], (427 ^ _114542) ^ [_127878, _127880] : [aNaturalNumber0(_127880), aNaturalNumber0(_127878), -(sdtlseqdt0(_127880, _127878)), 438 ^ _114542 : [(439 ^ _114542) ^ [] : [_127878 = _127880], (441 ^ _114542) ^ [] : [-(sdtlseqdt0(_127878, _127880))]]], (443 ^ _114542) ^ [_128341, _128343] : [aNaturalNumber0(_128343), aNaturalNumber0(_128341), -(_128343 = _128341), sdtlseqdt0(_128343, _128341), 458 ^ _114542 : [(459 ^ _114542) ^ [_128785] : [aNaturalNumber0(_128785), 462 ^ _114542 : [(463 ^ _114542) ^ [] : [sdtpldt0(_128785, _128343) = sdtpldt0(_128785, _128341)], (465 ^ _114542) ^ [] : [-(sdtlseqdt0(sdtpldt0(_128785, _128343), sdtpldt0(_128785, _128341)))], (467 ^ _114542) ^ [] : [sdtpldt0(_128343, _128785) = sdtpldt0(_128341, _128785)], (469 ^ _114542) ^ [] : [-(sdtlseqdt0(sdtpldt0(_128343, _128785), sdtpldt0(_128341, _128785)))]]]]], (471 ^ _114542) ^ [_129309, _129311, _129313] : [aNaturalNumber0(_129313), aNaturalNumber0(_129311), aNaturalNumber0(_129309), 494 ^ _114542 : [(495 ^ _114542) ^ [] : [sdtasdt0(_129313, _129311) = sdtasdt0(_129313, _129309)], (497 ^ _114542) ^ [] : [-(sdtlseqdt0(sdtasdt0(_129313, _129311), sdtasdt0(_129313, _129309)))], (499 ^ _114542) ^ [] : [sdtasdt0(_129311, _129313) = sdtasdt0(_129309, _129313)], (501 ^ _114542) ^ [] : [-(sdtlseqdt0(sdtasdt0(_129311, _129313), sdtasdt0(_129309, _129313)))]], -(_129313 = sz00), -(_129311 = _129309), sdtlseqdt0(_129311, _129309)], (503 ^ _114542) ^ [_130259] : [aNaturalNumber0(_130259), -(_130259 = sz00), -(_130259 = sz10), 514 ^ _114542 : [(515 ^ _114542) ^ [] : [sz10 = _130259], (517 ^ _114542) ^ [] : [-(sdtlseqdt0(sz10, _130259))]]], (519 ^ _114542) ^ [_130707, _130709] : [aNaturalNumber0(_130709), aNaturalNumber0(_130707), -(_130709 = sz00), -(sdtlseqdt0(_130707, sdtasdt0(_130707, _130709)))], (533 ^ _114542) ^ [_131102, _131104] : [aNaturalNumber0(_131104), aNaturalNumber0(_131102), iLess0(_131104, _131102), true___, -(true___)], (551 ^ _114542) ^ [_131562, _131564] : [aNaturalNumber0(_131564), aNaturalNumber0(_131562), -(iLess0(_131564, _131562)), -(_131564 = _131562), sdtlseqdt0(_131564, _131562)], (569 ^ _114542) ^ [_132040, _132042] : [aNaturalNumber0(_132042), aNaturalNumber0(_132040), 576 ^ _114542 : [(577 ^ _114542) ^ [] : [doDivides0(_132042, _132040), 581 ^ _114542 : [(582 ^ _114542) ^ [] : [-(aNaturalNumber0(580 ^ [_132040, _132042]))], (584 ^ _114542) ^ [] : [-(_132040 = sdtasdt0(_132042, 580 ^ [_132040, _132042]))]]], (586 ^ _114542) ^ [] : [-(doDivides0(_132042, _132040)), 587 ^ _114542 : [(588 ^ _114542) ^ [_132600] : [aNaturalNumber0(_132600), _132040 = sdtasdt0(_132042, _132600)]]]]], (596 ^ _114542) ^ [_132883, _132885] : [aNaturalNumber0(_132885), aNaturalNumber0(_132883), -(_132885 = sz00), doDivides0(_132885, _132883), 611 ^ _114542 : [(612 ^ _114542) ^ [_133322] : [_133322 = sdtsldt0(_132883, _132885), 615 ^ _114542 : [(616 ^ _114542) ^ [] : [-(aNaturalNumber0(_133322))], (618 ^ _114542) ^ [] : [-(_132883 = sdtasdt0(_132885, _133322))]]], (620 ^ _114542) ^ [_133581] : [-(_133581 = sdtsldt0(_132883, _132885)), aNaturalNumber0(_133581), _132883 = sdtasdt0(_132885, _133581)]]], (630 ^ _114542) ^ [_133933, _133935, _133937] : [aNaturalNumber0(_133937), aNaturalNumber0(_133935), aNaturalNumber0(_133933), -(doDivides0(_133937, _133933)), doDivides0(_133937, _133935), doDivides0(_133935, _133933)], (652 ^ _114542) ^ [_134533, _134535, _134537] : [aNaturalNumber0(_134537), aNaturalNumber0(_134535), aNaturalNumber0(_134533), -(doDivides0(_134537, sdtpldt0(_134535, _134533))), doDivides0(_134537, _134535), doDivides0(_134537, _134533)], (674 ^ _114542) ^ [_135139, _135141, _135143] : [aNaturalNumber0(_135143), aNaturalNumber0(_135141), aNaturalNumber0(_135139), -(doDivides0(_135143, _135139)), doDivides0(_135143, _135141), doDivides0(_135143, sdtpldt0(_135141, _135139))], (696 ^ _114542) ^ [_135731, _135733] : [aNaturalNumber0(_135733), aNaturalNumber0(_135731), -(sdtlseqdt0(_135733, _135731)), doDivides0(_135733, _135731), -(_135731 = sz00)], (714 ^ _114542) ^ [_136209, _136211] : [aNaturalNumber0(_136211), aNaturalNumber0(_136209), -(_136211 = sz00), doDivides0(_136211, _136209), 729 ^ _114542 : [(730 ^ _114542) ^ [_136619] : [aNaturalNumber0(_136619), -(sdtasdt0(_136619, sdtsldt0(_136209, _136211)) = sdtsldt0(sdtasdt0(_136619, _136209), _136211))]]], (736 ^ _114542) ^ [_136860] : [aNaturalNumber0(_136860), 739 ^ _114542 : [(762 ^ _114542) ^ [] : [-(isPrime0(_136860)), -(_136860 = sz00), -(_136860 = sz10), 772 ^ _114542 : [(773 ^ _114542) ^ [] : [-(aNaturalNumber0(771 ^ [_136860]))], (775 ^ _114542) ^ [] : [-(doDivides0(771 ^ [_136860], _136860))], (777 ^ _114542) ^ [] : [771 ^ [_136860] = sz10], (779 ^ _114542) ^ [] : [771 ^ [_136860] = _136860]]], (740 ^ _114542) ^ [] : [isPrime0(_136860), 743 ^ _114542 : [(744 ^ _114542) ^ [] : [_136860 = sz00], (746 ^ _114542) ^ [] : [_136860 = sz10], (748 ^ _114542) ^ [_137252] : [aNaturalNumber0(_137252), doDivides0(_137252, _136860), -(_137252 = sz10), -(_137252 = _136860)]]]]], (783 ^ _114542) ^ [_138204] : [795 ^ _114542 : [(796 ^ _114542) ^ [] : [-(aNaturalNumber0(794 ^ [_138204]))], (798 ^ _114542) ^ [] : [-(doDivides0(794 ^ [_138204], _138204))], (800 ^ _114542) ^ [] : [-(isPrime0(794 ^ [_138204]))]], aNaturalNumber0(_138204), -(_138204 = sz00), -(_138204 = sz10)], (802 ^ _114542) ^ [] : [-(aNaturalNumber0(xn))], (804 ^ _114542) ^ [] : [-(aNaturalNumber0(xm))], (806 ^ _114542) ^ [] : [-(aNaturalNumber0(xp))], (838 ^ _114542) ^ [] : [-(isPrime0(xp))], (840 ^ _114542) ^ [] : [-(doDivides0(xp, sdtasdt0(xn, xm)))], (842 ^ _114542) ^ [] : [sdtlseqdt0(xp, xn)], (844 ^ _114542) ^ [] : [sdtlseqdt0(xp, xm)], (846 ^ _114542) ^ [] : [xn = xp], (848 ^ _114542) ^ [] : [-(sdtlseqdt0(xn, xp))], (850 ^ _114542) ^ [] : [xm = xp], (852 ^ _114542) ^ [] : [-(sdtlseqdt0(xm, xp))], (854 ^ _114542) ^ [] : [-(xk = sdtsldt0(sdtasdt0(xn, xm), xp))], (856 ^ _114542) ^ [] : [xk = sz00], (858 ^ _114542) ^ [] : [xk = sz10], (860 ^ _114542) ^ [] : [xk = sz00], (862 ^ _114542) ^ [] : [xk = sz10], (864 ^ _114542) ^ [] : [-(aNaturalNumber0(xr))], (866 ^ _114542) ^ [] : [-(doDivides0(xr, xk))], (868 ^ _114542) ^ [] : [-(isPrime0(xr))], (870 ^ _114542) ^ [] : [-(sdtlseqdt0(xr, xk))], (872 ^ _114542) ^ [] : [-(doDivides0(xr, sdtasdt0(xn, xm)))], (808 ^ _114542) ^ [_138971, _138973, _138975] : [aNaturalNumber0(_138975), aNaturalNumber0(_138973), aNaturalNumber0(_138971), isPrime0(_138971), doDivides0(_138971, sdtasdt0(_138975, _138973)), iLess0(sdtpldt0(sdtpldt0(_138975, _138973), _138971), sdtpldt0(sdtpldt0(xn, xm), xp)), -(doDivides0(_138971, _138975)), -(doDivides0(_138971, _138973))]], input).
% 0.45/1.37  ncf('1',plain,[sdtlseqdt0(xp, xk)],start(874 ^ 0)).
% 0.45/1.37  ncf('1.1',plain,[-(sdtlseqdt0(xp, xk)), aNaturalNumber0(xp), aNaturalNumber0(xk), 439 : xk = xp],extension(427 ^ 1,bind([[_127878, _127880], [xk, xp]]))).
% 0.45/1.37  ncf('1.1.1',plain,[-(aNaturalNumber0(xp))],extension(806 ^ 2)).
% 0.45/1.37  ncf('1.1.2',plain,[-(aNaturalNumber0(xk)), 612 : xk = sdtsldt0(sdtasdt0(xn, xm), xp), 612 : aNaturalNumber0(xp), 612 : aNaturalNumber0(sdtasdt0(xn, xm)), 612 : -(xp = sz00), 612 : doDivides0(xp, sdtasdt0(xn, xm))],extension(596 ^ 2,bind([[_132883, _132885, _133322], [sdtasdt0(xn, xm), xp, xk]]))).
% 0.45/1.37  ncf('1.1.2.1',plain,[-(xk = sdtsldt0(sdtasdt0(xn, xm), xp))],extension(854 ^ 5)).
% 0.45/1.37  ncf('1.1.2.2',plain,[-(aNaturalNumber0(xp))],lemmata('[1].x')).
% 0.45/1.37  ncf('1.1.2.3',plain,[-(aNaturalNumber0(sdtasdt0(xn, xm))), aNaturalNumber0(xn), aNaturalNumber0(xm)],extension(148 ^ 3,bind([[_119370, _119372], [xm, xn]]))).
% 0.45/1.37  ncf('1.1.2.3.1',plain,[-(aNaturalNumber0(xn))],extension(802 ^ 4)).
% 0.45/1.37  ncf('1.1.2.3.2',plain,[-(aNaturalNumber0(xm))],extension(804 ^ 4)).
% 0.45/1.37  ncf('1.1.2.4',plain,[xp = sz00, 740 : isPrime0(xp), 740 : aNaturalNumber0(xp)],extension(736 ^ 3,bind([[_136860], [xp]]))).
% 0.45/1.37  ncf('1.1.2.4.1',plain,[-(isPrime0(xp))],extension(838 ^ 6)).
% 0.45/1.37  ncf('1.1.2.4.2',plain,[-(aNaturalNumber0(xp))],lemmata('[1, 1].x')).
% 0.45/1.37  ncf('1.1.2.5',plain,[-(doDivides0(xp, sdtasdt0(xn, xm)))],extension(840 ^ 3)).
% 0.45/1.37  ncf('1.1.3',plain,[-(xk = xp), sdtlseqdt0(xk, xp)],extension(876 ^ 4)).
% 0.45/1.37  ncf('1.1.3.1',plain,[-(sdtlseqdt0(xk, xp)), aNaturalNumber0(xk), aNaturalNumber0(xp), 441 : -(sdtlseqdt0(xp, xk))],extension(427 ^ 5,bind([[_127878, _127880], [xp, xk]]))).
% 0.45/1.37  ncf('1.1.3.1.1',plain,[-(aNaturalNumber0(xk))],lemmata('[1].x')).
% 0.45/1.37  ncf('1.1.3.1.2',plain,[-(aNaturalNumber0(xp))],lemmata('[1].x')).
% 0.45/1.37  ncf('1.1.3.1.3',plain,[sdtlseqdt0(xp, xk)],reduction('1')).
% 0.45/1.37  %-----------------------------------------------------
% 0.45/1.37  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------