TSTP Solution File: NUM515+3 by nanoCoP---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : nanoCoP---2.0
% Problem : NUM515+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : nanocop.sh %s %d
% Computer : n014.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 11:44:50 EDT 2023
% Result : Theorem 13.54s 13.79s
% Output : Proof 13.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : NUM515+3 : TPTP v8.1.2. Released v4.0.0.
% 0.10/0.12 % Command : nanocop.sh %s %d
% 0.13/0.33 % Computer : n014.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Thu May 18 16:37:57 EDT 2023
% 0.13/0.33 % CPUTime :
% 13.54/13.79
% 13.54/13.79 /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 13.54/13.79 Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.54/13.79 %-----------------------------------------------------
% 13.54/13.79 ncf(matrix, plain, [(1064 ^ _159653) ^ [] : [-(aNaturalNumber0(sdtsldt0(xn, xr)))], (1066 ^ _159653) ^ [] : [-(xn = sdtasdt0(xr, sdtsldt0(xn, xr)))], (1074 ^ _159653) ^ [] : [doDivides0(xp, sdtsldt0(xn, xr))], (1068 ^ _159653) ^ [_192503] : [aNaturalNumber0(_192503), sdtsldt0(xn, xr) = sdtasdt0(xp, _192503)], (1082 ^ _159653) ^ [] : [doDivides0(xp, xm)], (1076 ^ _159653) ^ [_192734] : [aNaturalNumber0(_192734), xm = sdtasdt0(xp, _192734)], (82 ^ _159653) ^ [_162365, _162367, _162369, _162371] : [-(sdtmndt0(_162371, _162367) = sdtmndt0(_162369, _162365)), _162371 = _162369, _162367 = _162365], (92 ^ _159653) ^ [_162724, _162726, _162728, _162730] : [-(sdtpldt0(_162730, _162726) = sdtpldt0(_162728, _162724)), _162730 = _162728, _162726 = _162724], (102 ^ _159653) ^ [_163083, _163085, _163087, _163089] : [-(sdtsldt0(_163089, _163085) = sdtsldt0(_163087, _163083)), _163089 = _163087, _163085 = _163083], (112 ^ _159653) ^ [_163422, _163424, _163426, _163428] : [-(sdtasdt0(_163428, _163424) = sdtasdt0(_163426, _163422)), _163428 = _163426, _163424 = _163422], (2 ^ _159653) ^ [_159797] : [-(_159797 = _159797)], (4 ^ _159653) ^ [_159904, _159906] : [_159906 = _159904, -(_159904 = _159906)], (10 ^ _159653) ^ [_160108, _160110, _160112] : [-(_160112 = _160108), _160112 = _160110, _160110 = _160108], (20 ^ _159653) ^ [_160449, _160451, _160453, _160455] : [-(iLess0(_160453, _160449)), iLess0(_160455, _160451), _160455 = _160453, _160451 = _160449], (34 ^ _159653) ^ [_160865, _160867] : [-(isPrime0(_160865)), _160867 = _160865, isPrime0(_160867)], (44 ^ _159653) ^ [_161188, _161190, _161192, _161194] : [-(sdtlseqdt0(_161192, _161188)), sdtlseqdt0(_161194, _161190), _161194 = _161192, _161190 = _161188], (58 ^ _159653) ^ [_161604, _161606] : [-(aNaturalNumber0(_161604)), _161606 = _161604, aNaturalNumber0(_161606)], (68 ^ _159653) ^ [_161907, _161909, _161911, _161913] : [-(doDivides0(_161911, _161907)), doDivides0(_161913, _161909), _161913 = _161911, _161909 = _161907], (122 ^ _159653) ^ [_163753] : [aNaturalNumber0(_163753), true___, -(true___)], (132 ^ _159653) ^ [] : [-(aNaturalNumber0(sz00))], (134 ^ _159653) ^ [] : [-(aNaturalNumber0(sz10))], (136 ^ _159653) ^ [] : [sz10 = sz00], (138 ^ _159653) ^ [_164182, _164184] : [-(aNaturalNumber0(sdtpldt0(_164184, _164182))), aNaturalNumber0(_164184), aNaturalNumber0(_164182)], (148 ^ _159653) ^ [_164481, _164483] : [-(aNaturalNumber0(sdtasdt0(_164483, _164481))), aNaturalNumber0(_164483), aNaturalNumber0(_164481)], (158 ^ _159653) ^ [_164780, _164782] : [-(sdtpldt0(_164782, _164780) = sdtpldt0(_164780, _164782)), aNaturalNumber0(_164782), aNaturalNumber0(_164780)], (168 ^ _159653) ^ [_165101, _165103, _165105] : [-(sdtpldt0(sdtpldt0(_165105, _165103), _165101) = sdtpldt0(_165105, sdtpldt0(_165103, _165101))), aNaturalNumber0(_165105), aNaturalNumber0(_165103), aNaturalNumber0(_165101)], (182 ^ _159653) ^ [_165507] : [aNaturalNumber0(_165507), 185 ^ _159653 : [(186 ^ _159653) ^ [] : [-(sdtpldt0(_165507, sz00) = _165507)], (188 ^ _159653) ^ [] : [-(_165507 = sdtpldt0(sz00, _165507))]]], (190 ^ _159653) ^ [_165794, _165796] : [-(sdtasdt0(_165796, _165794) = sdtasdt0(_165794, _165796)), aNaturalNumber0(_165796), aNaturalNumber0(_165794)], (200 ^ _159653) ^ [_166115, _166117, _166119] : [-(sdtasdt0(sdtasdt0(_166119, _166117), _166115) = sdtasdt0(_166119, sdtasdt0(_166117, _166115))), aNaturalNumber0(_166119), aNaturalNumber0(_166117), aNaturalNumber0(_166115)], (214 ^ _159653) ^ [_166521] : [aNaturalNumber0(_166521), 217 ^ _159653 : [(218 ^ _159653) ^ [] : [-(sdtasdt0(_166521, sz10) = _166521)], (220 ^ _159653) ^ [] : [-(_166521 = sdtasdt0(sz10, _166521))]]], (222 ^ _159653) ^ [_166794] : [aNaturalNumber0(_166794), 225 ^ _159653 : [(226 ^ _159653) ^ [] : [-(sdtasdt0(_166794, sz00) = sz00)], (228 ^ _159653) ^ [] : [-(sz00 = sdtasdt0(sz00, _166794))]]], (230 ^ _159653) ^ [_167095, _167097, _167099] : [241 ^ _159653 : [(242 ^ _159653) ^ [] : [-(sdtasdt0(_167099, sdtpldt0(_167097, _167095)) = sdtpldt0(sdtasdt0(_167099, _167097), sdtasdt0(_167099, _167095)))], (244 ^ _159653) ^ [] : [-(sdtasdt0(sdtpldt0(_167097, _167095), _167099) = sdtpldt0(sdtasdt0(_167097, _167099), sdtasdt0(_167095, _167099)))]], aNaturalNumber0(_167099), aNaturalNumber0(_167097), aNaturalNumber0(_167095)], (246 ^ _159653) ^ [_167642, _167644, _167646] : [259 ^ _159653 : [(260 ^ _159653) ^ [] : [sdtpldt0(_167646, _167644) = sdtpldt0(_167646, _167642)], (262 ^ _159653) ^ [] : [sdtpldt0(_167644, _167646) = sdtpldt0(_167642, _167646)]], -(_167644 = _167642), aNaturalNumber0(_167646), aNaturalNumber0(_167644), aNaturalNumber0(_167642)], (266 ^ _159653) ^ [_168219] : [aNaturalNumber0(_168219), -(_168219 = sz00), 273 ^ _159653 : [(274 ^ _159653) ^ [_168481, _168483] : [aNaturalNumber0(_168483), aNaturalNumber0(_168481), 283 ^ _159653 : [(284 ^ _159653) ^ [] : [sdtasdt0(_168219, _168483) = sdtasdt0(_168219, _168481)], (286 ^ _159653) ^ [] : [sdtasdt0(_168483, _168219) = sdtasdt0(_168481, _168219)]], -(_168483 = _168481)]]], (290 ^ _159653) ^ [_168992, _168994] : [aNaturalNumber0(_168994), aNaturalNumber0(_168992), sdtpldt0(_168994, _168992) = sz00, 301 ^ _159653 : [(302 ^ _159653) ^ [] : [-(_168994 = sz00)], (304 ^ _159653) ^ [] : [-(_168992 = sz00)]]], (306 ^ _159653) ^ [_169459, _169461] : [aNaturalNumber0(_169461), aNaturalNumber0(_169459), sdtasdt0(_169461, _169459) = sz00, -(_169461 = sz00), -(_169459 = sz00)], (324 ^ _159653) ^ [_169941, _169943] : [aNaturalNumber0(_169943), aNaturalNumber0(_169941), 331 ^ _159653 : [(332 ^ _159653) ^ [] : [sdtlseqdt0(_169943, _169941), 336 ^ _159653 : [(337 ^ _159653) ^ [] : [-(aNaturalNumber0(335 ^ [_169941, _169943]))], (339 ^ _159653) ^ [] : [-(sdtpldt0(_169943, 335 ^ [_169941, _169943]) = _169941)]]], (341 ^ _159653) ^ [] : [-(sdtlseqdt0(_169943, _169941)), 342 ^ _159653 : [(343 ^ _159653) ^ [_170501] : [aNaturalNumber0(_170501), sdtpldt0(_169943, _170501) = _169941]]]]], (351 ^ _159653) ^ [_170784, _170786] : [aNaturalNumber0(_170786), aNaturalNumber0(_170784), sdtlseqdt0(_170786, _170784), 362 ^ _159653 : [(363 ^ _159653) ^ [_171131] : [_171131 = sdtmndt0(_170784, _170786), 366 ^ _159653 : [(367 ^ _159653) ^ [] : [-(aNaturalNumber0(_171131))], (369 ^ _159653) ^ [] : [-(sdtpldt0(_170786, _171131) = _170784)]]], (371 ^ _159653) ^ [_171390] : [-(_171390 = sdtmndt0(_170784, _170786)), aNaturalNumber0(_171390), sdtpldt0(_170786, _171390) = _170784]]], (381 ^ _159653) ^ [_171712] : [aNaturalNumber0(_171712), -(sdtlseqdt0(_171712, _171712))], (387 ^ _159653) ^ [_171914, _171916] : [aNaturalNumber0(_171916), aNaturalNumber0(_171914), -(_171916 = _171914), sdtlseqdt0(_171916, _171914), sdtlseqdt0(_171914, _171916)], (405 ^ _159653) ^ [_172403, _172405, _172407] : [aNaturalNumber0(_172407), aNaturalNumber0(_172405), aNaturalNumber0(_172403), -(sdtlseqdt0(_172407, _172403)), sdtlseqdt0(_172407, _172405), sdtlseqdt0(_172405, _172403)], (427 ^ _159653) ^ [_172989, _172991] : [aNaturalNumber0(_172991), aNaturalNumber0(_172989), -(sdtlseqdt0(_172991, _172989)), 438 ^ _159653 : [(439 ^ _159653) ^ [] : [_172989 = _172991], (441 ^ _159653) ^ [] : [-(sdtlseqdt0(_172989, _172991))]]], (443 ^ _159653) ^ [_173452, _173454] : [aNaturalNumber0(_173454), aNaturalNumber0(_173452), -(_173454 = _173452), sdtlseqdt0(_173454, _173452), 458 ^ _159653 : [(459 ^ _159653) ^ [_173896] : [aNaturalNumber0(_173896), 462 ^ _159653 : [(463 ^ _159653) ^ [] : [sdtpldt0(_173896, _173454) = sdtpldt0(_173896, _173452)], (465 ^ _159653) ^ [] : [-(sdtlseqdt0(sdtpldt0(_173896, _173454), sdtpldt0(_173896, _173452)))], (467 ^ _159653) ^ [] : [sdtpldt0(_173454, _173896) = sdtpldt0(_173452, _173896)], (469 ^ _159653) ^ [] : [-(sdtlseqdt0(sdtpldt0(_173454, _173896), sdtpldt0(_173452, _173896)))]]]]], (471 ^ _159653) ^ [_174420, _174422, _174424] : [aNaturalNumber0(_174424), aNaturalNumber0(_174422), aNaturalNumber0(_174420), 494 ^ _159653 : [(495 ^ _159653) ^ [] : [sdtasdt0(_174424, _174422) = sdtasdt0(_174424, _174420)], (497 ^ _159653) ^ [] : [-(sdtlseqdt0(sdtasdt0(_174424, _174422), sdtasdt0(_174424, _174420)))], (499 ^ _159653) ^ [] : [sdtasdt0(_174422, _174424) = sdtasdt0(_174420, _174424)], (501 ^ _159653) ^ [] : [-(sdtlseqdt0(sdtasdt0(_174422, _174424), sdtasdt0(_174420, _174424)))]], -(_174424 = sz00), -(_174422 = _174420), sdtlseqdt0(_174422, _174420)], (503 ^ _159653) ^ [_175370] : [aNaturalNumber0(_175370), -(_175370 = sz00), -(_175370 = sz10), 514 ^ _159653 : [(515 ^ _159653) ^ [] : [sz10 = _175370], (517 ^ _159653) ^ [] : [-(sdtlseqdt0(sz10, _175370))]]], (519 ^ _159653) ^ [_175818, _175820] : [aNaturalNumber0(_175820), aNaturalNumber0(_175818), -(_175820 = sz00), -(sdtlseqdt0(_175818, sdtasdt0(_175818, _175820)))], (533 ^ _159653) ^ [_176213, _176215] : [aNaturalNumber0(_176215), aNaturalNumber0(_176213), iLess0(_176215, _176213), true___, -(true___)], (551 ^ _159653) ^ [_176673, _176675] : [aNaturalNumber0(_176675), aNaturalNumber0(_176673), -(iLess0(_176675, _176673)), -(_176675 = _176673), sdtlseqdt0(_176675, _176673)], (569 ^ _159653) ^ [_177151, _177153] : [aNaturalNumber0(_177153), aNaturalNumber0(_177151), 576 ^ _159653 : [(577 ^ _159653) ^ [] : [doDivides0(_177153, _177151), 581 ^ _159653 : [(582 ^ _159653) ^ [] : [-(aNaturalNumber0(580 ^ [_177151, _177153]))], (584 ^ _159653) ^ [] : [-(_177151 = sdtasdt0(_177153, 580 ^ [_177151, _177153]))]]], (586 ^ _159653) ^ [] : [-(doDivides0(_177153, _177151)), 587 ^ _159653 : [(588 ^ _159653) ^ [_177711] : [aNaturalNumber0(_177711), _177151 = sdtasdt0(_177153, _177711)]]]]], (596 ^ _159653) ^ [_177994, _177996] : [aNaturalNumber0(_177996), aNaturalNumber0(_177994), -(_177996 = sz00), doDivides0(_177996, _177994), 611 ^ _159653 : [(612 ^ _159653) ^ [_178433] : [_178433 = sdtsldt0(_177994, _177996), 615 ^ _159653 : [(616 ^ _159653) ^ [] : [-(aNaturalNumber0(_178433))], (618 ^ _159653) ^ [] : [-(_177994 = sdtasdt0(_177996, _178433))]]], (620 ^ _159653) ^ [_178692] : [-(_178692 = sdtsldt0(_177994, _177996)), aNaturalNumber0(_178692), _177994 = sdtasdt0(_177996, _178692)]]], (630 ^ _159653) ^ [_179044, _179046, _179048] : [aNaturalNumber0(_179048), aNaturalNumber0(_179046), aNaturalNumber0(_179044), -(doDivides0(_179048, _179044)), doDivides0(_179048, _179046), doDivides0(_179046, _179044)], (652 ^ _159653) ^ [_179644, _179646, _179648] : [aNaturalNumber0(_179648), aNaturalNumber0(_179646), aNaturalNumber0(_179644), -(doDivides0(_179648, sdtpldt0(_179646, _179644))), doDivides0(_179648, _179646), doDivides0(_179648, _179644)], (674 ^ _159653) ^ [_180250, _180252, _180254] : [aNaturalNumber0(_180254), aNaturalNumber0(_180252), aNaturalNumber0(_180250), -(doDivides0(_180254, _180250)), doDivides0(_180254, _180252), doDivides0(_180254, sdtpldt0(_180252, _180250))], (696 ^ _159653) ^ [_180842, _180844] : [aNaturalNumber0(_180844), aNaturalNumber0(_180842), -(sdtlseqdt0(_180844, _180842)), doDivides0(_180844, _180842), -(_180842 = sz00)], (714 ^ _159653) ^ [_181320, _181322] : [aNaturalNumber0(_181322), aNaturalNumber0(_181320), -(_181322 = sz00), doDivides0(_181322, _181320), 729 ^ _159653 : [(730 ^ _159653) ^ [_181730] : [aNaturalNumber0(_181730), -(sdtasdt0(_181730, sdtsldt0(_181320, _181322)) = sdtsldt0(sdtasdt0(_181730, _181320), _181322))]]], (736 ^ _159653) ^ [_181971] : [aNaturalNumber0(_181971), 739 ^ _159653 : [(762 ^ _159653) ^ [] : [-(isPrime0(_181971)), -(_181971 = sz00), -(_181971 = sz10), 772 ^ _159653 : [(773 ^ _159653) ^ [] : [-(aNaturalNumber0(771 ^ [_181971]))], (775 ^ _159653) ^ [] : [-(doDivides0(771 ^ [_181971], _181971))], (777 ^ _159653) ^ [] : [771 ^ [_181971] = sz10], (779 ^ _159653) ^ [] : [771 ^ [_181971] = _181971]]], (740 ^ _159653) ^ [] : [isPrime0(_181971), 743 ^ _159653 : [(744 ^ _159653) ^ [] : [_181971 = sz00], (746 ^ _159653) ^ [] : [_181971 = sz10], (748 ^ _159653) ^ [_182363] : [aNaturalNumber0(_182363), doDivides0(_182363, _181971), -(_182363 = sz10), -(_182363 = _181971)]]]]], (783 ^ _159653) ^ [_183315] : [795 ^ _159653 : [(796 ^ _159653) ^ [] : [-(aNaturalNumber0(794 ^ [_183315]))], (798 ^ _159653) ^ [] : [-(doDivides0(794 ^ [_183315], _183315))], (800 ^ _159653) ^ [] : [-(isPrime0(794 ^ [_183315]))]], aNaturalNumber0(_183315), -(_183315 = sz00), -(_183315 = sz10)], (802 ^ _159653) ^ [] : [-(aNaturalNumber0(xn))], (804 ^ _159653) ^ [] : [-(aNaturalNumber0(xm))], (806 ^ _159653) ^ [] : [-(aNaturalNumber0(xp))], (808 ^ _159653) ^ [_184082, _184084, _184086] : [aNaturalNumber0(_184086), aNaturalNumber0(_184084), aNaturalNumber0(_184082), iLess0(sdtpldt0(sdtpldt0(_184086, _184084), _184082), sdtpldt0(sdtpldt0(xn, xm), xp)), 862 ^ _159653 : [(863 ^ _159653) ^ [] : [-(aNaturalNumber0(861 ^ [_184082, _184084, _184086]))], (865 ^ _159653) ^ [] : [-(_184086 = sdtasdt0(_184082, 861 ^ [_184082, _184084, _184086]))], (867 ^ _159653) ^ [] : [-(doDivides0(_184082, _184086))]], 869 ^ _159653 : [(870 ^ _159653) ^ [] : [-(aNaturalNumber0(868 ^ [_184082, _184084, _184086]))], (872 ^ _159653) ^ [] : [-(_184084 = sdtasdt0(_184082, 868 ^ [_184082, _184084, _184086]))], (874 ^ _159653) ^ [] : [-(doDivides0(_184082, _184084))]], 847 ^ _159653 : [(854 ^ _159653) ^ [] : [doDivides0(_184082, sdtasdt0(_184086, _184084))], (848 ^ _159653) ^ [_185503] : [aNaturalNumber0(_185503), sdtasdt0(_184086, _184084) = sdtasdt0(_184082, _185503)]], 823 ^ _159653 : [(846 ^ _159653) ^ [] : [isPrime0(_184082)], (824 ^ _159653) ^ [] : [-(_184082 = sz00), -(_184082 = sz10), 832 ^ _159653 : [(833 ^ _159653) ^ [] : [-(aNaturalNumber0(831 ^ [_184082, _184084, _184086]))], (836 ^ _159653) ^ [] : [-(aNaturalNumber0(834 ^ [_184082, _184084, _184086]))], (838 ^ _159653) ^ [] : [-(_184082 = sdtasdt0(831 ^ [_184082, _184084, _184086], 834 ^ [_184082, _184084, _184086]))], (840 ^ _159653) ^ [] : [-(doDivides0(831 ^ [_184082, _184084, _184086], _184082))], (842 ^ _159653) ^ [] : [831 ^ [_184082, _184084, _184086] = sz10], (844 ^ _159653) ^ [] : [831 ^ [_184082, _184084, _184086] = _184082]]]]], (876 ^ _159653) ^ [] : [xp = sz00], (878 ^ _159653) ^ [] : [xp = sz10], (900 ^ _159653) ^ [] : [-(isPrime0(xp))], (903 ^ _159653) ^ [] : [-(aNaturalNumber0(901 ^ []))], (905 ^ _159653) ^ [] : [-(sdtasdt0(xn, xm) = sdtasdt0(xp, 901 ^ []))], (907 ^ _159653) ^ [] : [-(doDivides0(xp, sdtasdt0(xn, xm)))], (880 ^ _159653) ^ [_186593] : [-(_186593 = sz10), -(_186593 = xp), aNaturalNumber0(_186593), 885 ^ _159653 : [(892 ^ _159653) ^ [] : [doDivides0(_186593, xp)], (886 ^ _159653) ^ [_186796] : [aNaturalNumber0(_186796), xp = sdtasdt0(_186593, _186796)]]], (915 ^ _159653) ^ [] : [sdtlseqdt0(xp, xn)], (909 ^ _159653) ^ [_187454] : [aNaturalNumber0(_187454), sdtpldt0(xp, _187454) = xn], (923 ^ _159653) ^ [] : [sdtlseqdt0(xp, xm)], (917 ^ _159653) ^ [_187701] : [aNaturalNumber0(_187701), sdtpldt0(xp, _187701) = xm], (925 ^ _159653) ^ [] : [xn = xp], (928 ^ _159653) ^ [] : [-(aNaturalNumber0(926 ^ []))], (930 ^ _159653) ^ [] : [-(sdtpldt0(xn, 926 ^ []) = xp)], (932 ^ _159653) ^ [] : [-(sdtlseqdt0(xn, xp))], (934 ^ _159653) ^ [] : [xm = xp], (937 ^ _159653) ^ [] : [-(aNaturalNumber0(935 ^ []))], (939 ^ _159653) ^ [] : [-(sdtpldt0(xm, 935 ^ []) = xp)], (941 ^ _159653) ^ [] : [-(sdtlseqdt0(xm, xp))], (943 ^ _159653) ^ [] : [-(aNaturalNumber0(xk))], (945 ^ _159653) ^ [] : [-(sdtasdt0(xn, xm) = sdtasdt0(xp, xk))], (947 ^ _159653) ^ [] : [-(xk = sdtsldt0(sdtasdt0(xn, xm), xp))], (949 ^ _159653) ^ [] : [xk = sz00], (951 ^ _159653) ^ [] : [xk = sz10], (953 ^ _159653) ^ [] : [xk = sz00], (955 ^ _159653) ^ [] : [xk = sz10], (993 ^ _159653) ^ [] : [-(aNaturalNumber0(991 ^ []))], (995 ^ _159653) ^ [] : [-(sdtpldt0(xr, 991 ^ []) = xk)], (998 ^ _159653) ^ [] : [-(aNaturalNumber0(996 ^ []))], (1000 ^ _159653) ^ [] : [-(sdtasdt0(xn, xm) = sdtasdt0(xr, 996 ^ []))], (1002 ^ _159653) ^ [] : [-(doDivides0(xr, sdtasdt0(xn, xm)))], (1004 ^ _159653) ^ [] : [xk = xp], (1007 ^ _159653) ^ [] : [-(aNaturalNumber0(1005 ^ []))], (1009 ^ _159653) ^ [] : [-(sdtpldt0(xk, 1005 ^ []) = xp)], (1011 ^ _159653) ^ [] : [-(sdtlseqdt0(xk, xp))], (1030 ^ _159653) ^ [] : [-(aNaturalNumber0(1028 ^ []))], (1032 ^ _159653) ^ [] : [-(xn = sdtasdt0(xr, 1028 ^ []))], (1034 ^ _159653) ^ [] : [-(doDivides0(xr, xn))], (1036 ^ _159653) ^ [] : [-(aNaturalNumber0(sdtsldt0(xn, xr)))], (1038 ^ _159653) ^ [] : [-(xn = sdtasdt0(xr, sdtsldt0(xn, xr)))], (1040 ^ _159653) ^ [] : [sdtsldt0(xn, xr) = xn], (1042 ^ _159653) ^ [] : [-(aNaturalNumber0(sdtsldt0(xn, xr)))], (1044 ^ _159653) ^ [] : [-(xn = sdtasdt0(xr, sdtsldt0(xn, xr)))], (1047 ^ _159653) ^ [] : [-(aNaturalNumber0(1045 ^ []))], (1049 ^ _159653) ^ [] : [-(sdtpldt0(sdtsldt0(xn, xr), 1045 ^ []) = xn)], (1051 ^ _159653) ^ [] : [-(sdtlseqdt0(sdtsldt0(xn, xr), xn))], (1053 ^ _159653) ^ [] : [-(aNaturalNumber0(sdtsldt0(xn, xr)))], (1055 ^ _159653) ^ [] : [-(xn = sdtasdt0(xr, sdtsldt0(xn, xr)))], (1058 ^ _159653) ^ [] : [-(aNaturalNumber0(1056 ^ []))], (1060 ^ _159653) ^ [] : [-(sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, 1056 ^ []))], (1062 ^ _159653) ^ [] : [-(doDivides0(xp, sdtasdt0(sdtsldt0(xn, xr), xm)))], (1013 ^ _159653) ^ [] : [1015 ^ _159653 : [(1016 ^ _159653) ^ [] : [-(aNaturalNumber0(1014 ^ []))], (1018 ^ _159653) ^ [] : [-(xn = sdtasdt0(xr, 1014 ^ []))], (1020 ^ _159653) ^ [] : [-(doDivides0(xr, xn))]], 1022 ^ _159653 : [(1023 ^ _159653) ^ [] : [-(aNaturalNumber0(1021 ^ []))], (1025 ^ _159653) ^ [] : [-(xm = sdtasdt0(xr, 1021 ^ []))], (1027 ^ _159653) ^ [] : [-(doDivides0(xr, xm))]]], (957 ^ _159653) ^ [] : [-(aNaturalNumber0(xr))], (960 ^ _159653) ^ [] : [-(aNaturalNumber0(958 ^ []))], (962 ^ _159653) ^ [] : [-(xk = sdtasdt0(xr, 958 ^ []))], (964 ^ _159653) ^ [] : [-(doDivides0(xr, xk))], (966 ^ _159653) ^ [] : [xr = sz00], (968 ^ _159653) ^ [] : [xr = sz10], (990 ^ _159653) ^ [] : [-(isPrime0(xr))], (970 ^ _159653) ^ [_189216] : [-(_189216 = sz10), -(_189216 = xr), aNaturalNumber0(_189216), 975 ^ _159653 : [(982 ^ _159653) ^ [] : [doDivides0(_189216, xr)], (976 ^ _159653) ^ [_189419] : [aNaturalNumber0(_189419), xr = sdtasdt0(_189216, _189419)]]]], input).
% 13.54/13.79 ncf('1',plain,[doDivides0(xp, xm)],start(1082 ^ 0)).
% 13.54/13.79 ncf('1.1',plain,[-(doDivides0(xp, xm)), aNaturalNumber0(sdtsldt0(xn, xr)), aNaturalNumber0(xm), aNaturalNumber0(xp), iLess0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp)), 863 : -(aNaturalNumber0(861 ^ [xp, xm, sdtsldt0(xn, xr)])), 854 : doDivides0(xp, sdtasdt0(sdtsldt0(xn, xr), xm)), 846 : isPrime0(xp)],extension(808 ^ 1,bind([[_184082, _184084, _184086], [xp, xm, sdtsldt0(xn, xr)]]))).
% 13.54/13.79 ncf('1.1.1',plain,[-(aNaturalNumber0(sdtsldt0(xn, xr)))],extension(1064 ^ 2)).
% 13.54/13.79 ncf('1.1.2',plain,[-(aNaturalNumber0(xm))],extension(804 ^ 2)).
% 13.54/13.79 ncf('1.1.3',plain,[-(aNaturalNumber0(xp))],extension(806 ^ 2)).
% 13.54/13.79 ncf('1.1.4',plain,[-(iLess0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp))), aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp)), aNaturalNumber0(sdtpldt0(sdtpldt0(xn, xm), xp)), -(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp) = sdtpldt0(sdtpldt0(xn, xm), xp)), sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp))],extension(551 ^ 2,bind([[_176673, _176675], [sdtpldt0(sdtpldt0(xn, xm), xp), sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp)]]))).
% 13.54/13.79 ncf('1.1.4.1',plain,[-(aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp))), aNaturalNumber0(sdtpldt0(sdtsldt0(xn, xr), xm)), aNaturalNumber0(xp)],extension(138 ^ 3,bind([[_164182, _164184], [xp, sdtpldt0(sdtsldt0(xn, xr), xm)]]))).
% 13.54/13.79 ncf('1.1.4.1.1',plain,[-(aNaturalNumber0(sdtpldt0(sdtsldt0(xn, xr), xm))), aNaturalNumber0(sdtsldt0(xn, xr)), aNaturalNumber0(xm)],extension(138 ^ 4,bind([[_164182, _164184], [xm, sdtsldt0(xn, xr)]]))).
% 13.54/13.79 ncf('1.1.4.1.1.1',plain,[-(aNaturalNumber0(sdtsldt0(xn, xr)))],lemmata('[1].x')).
% 13.54/13.79 ncf('1.1.4.1.1.2',plain,[-(aNaturalNumber0(xm))],lemmata('[1].x')).
% 13.54/13.79 ncf('1.1.4.1.2',plain,[-(aNaturalNumber0(xp))],lemmata('[1].x')).
% 13.54/13.79 ncf('1.1.4.2',plain,[-(aNaturalNumber0(sdtpldt0(sdtpldt0(xn, xm), xp))), aNaturalNumber0(sdtpldt0(xn, xm)), aNaturalNumber0(xp)],extension(138 ^ 3,bind([[_164182, _164184], [xp, sdtpldt0(xn, xm)]]))).
% 13.54/13.79 ncf('1.1.4.2.1',plain,[-(aNaturalNumber0(sdtpldt0(xn, xm))), aNaturalNumber0(xn), aNaturalNumber0(xm)],extension(138 ^ 4,bind([[_164182, _164184], [xm, xn]]))).
% 13.54/13.79 ncf('1.1.4.2.1.1',plain,[-(aNaturalNumber0(xn))],extension(802 ^ 5)).
% 13.54/13.79 ncf('1.1.4.2.1.2',plain,[-(aNaturalNumber0(xm))],lemmata('[1].x')).
% 13.54/13.79 ncf('1.1.4.2.2',plain,[-(aNaturalNumber0(xp))],lemmata('[1].x')).
% 13.54/13.79 ncf('1.1.4.3',plain,[sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp) = sdtpldt0(sdtpldt0(xn, xm), xp), -(sdtpldt0(sdtsldt0(xn, xr), xm) = sdtpldt0(xn, xm)), aNaturalNumber0(xp), aNaturalNumber0(sdtpldt0(sdtsldt0(xn, xr), xm)), aNaturalNumber0(sdtpldt0(xn, xm))],extension(246 ^ 3,bind([[_167642, _167644, _167646], [sdtpldt0(xn, xm), sdtpldt0(sdtsldt0(xn, xr), xm), xp]]))).
% 13.54/13.79 ncf('1.1.4.3.1',plain,[sdtpldt0(sdtsldt0(xn, xr), xm) = sdtpldt0(xn, xm), -(sdtsldt0(xn, xr) = xn), aNaturalNumber0(xm), aNaturalNumber0(sdtsldt0(xn, xr)), aNaturalNumber0(xn)],extension(246 ^ 4,bind([[_167642, _167644, _167646], [xn, sdtsldt0(xn, xr), xm]]))).
% 13.54/13.79 ncf('1.1.4.3.1.1',plain,[sdtsldt0(xn, xr) = xn],extension(1040 ^ 5)).
% 13.54/13.79 ncf('1.1.4.3.1.2',plain,[-(aNaturalNumber0(xm))],lemmata('[1].x')).
% 13.54/13.79 ncf('1.1.4.3.1.3',plain,[-(aNaturalNumber0(sdtsldt0(xn, xr)))],lemmata('[1].x')).
% 13.54/13.79 ncf('1.1.4.3.1.4',plain,[-(aNaturalNumber0(xn))],extension(802 ^ 5)).
% 13.54/13.79 ncf('1.1.4.3.2',plain,[-(aNaturalNumber0(xp))],lemmata('[1].x')).
% 13.54/13.79 ncf('1.1.4.3.3',plain,[-(aNaturalNumber0(sdtpldt0(sdtsldt0(xn, xr), xm))), aNaturalNumber0(sdtsldt0(xn, xr)), aNaturalNumber0(xm)],extension(138 ^ 4,bind([[_164182, _164184], [xm, sdtsldt0(xn, xr)]]))).
% 13.54/13.79 ncf('1.1.4.3.3.1',plain,[-(aNaturalNumber0(sdtsldt0(xn, xr)))],lemmata('[1].x')).
% 13.54/13.79 ncf('1.1.4.3.3.2',plain,[-(aNaturalNumber0(xm))],lemmata('[1].x')).
% 13.54/13.79 ncf('1.1.4.3.4',plain,[-(aNaturalNumber0(sdtpldt0(xn, xm))), aNaturalNumber0(xn), aNaturalNumber0(xm)],extension(138 ^ 4,bind([[_164182, _164184], [xm, xn]]))).
% 13.54/13.79 ncf('1.1.4.3.4.1',plain,[-(aNaturalNumber0(xn))],extension(802 ^ 5)).
% 13.54/13.79 ncf('1.1.4.3.4.2',plain,[-(aNaturalNumber0(xm))],lemmata('[1].x')).
% 13.54/13.79 ncf('1.1.4.4',plain,[-(sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp))), 459 : aNaturalNumber0(xp), 459 : aNaturalNumber0(sdtpldt0(sdtsldt0(xn, xr), xm)), 459 : aNaturalNumber0(sdtpldt0(xn, xm)), 459 : -(sdtpldt0(sdtsldt0(xn, xr), xm) = sdtpldt0(xn, xm)), 459 : sdtlseqdt0(sdtpldt0(sdtsldt0(xn, xr), xm), sdtpldt0(xn, xm))],extension(443 ^ 3,bind([[_173452, _173454, _173896], [sdtpldt0(xn, xm), sdtpldt0(sdtsldt0(xn, xr), xm), xp]]))).
% 13.54/13.79 ncf('1.1.4.4.1',plain,[-(aNaturalNumber0(xp))],lemmata('[1].x')).
% 13.54/13.79 ncf('1.1.4.4.2',plain,[-(aNaturalNumber0(sdtpldt0(sdtsldt0(xn, xr), xm))), aNaturalNumber0(sdtsldt0(xn, xr)), aNaturalNumber0(xm)],extension(138 ^ 4,bind([[_164182, _164184], [xm, sdtsldt0(xn, xr)]]))).
% 13.54/13.79 ncf('1.1.4.4.2.1',plain,[-(aNaturalNumber0(sdtsldt0(xn, xr)))],lemmata('[1].x')).
% 13.54/13.79 ncf('1.1.4.4.2.2',plain,[-(aNaturalNumber0(xm))],lemmata('[1].x')).
% 13.54/13.79 ncf('1.1.4.4.3',plain,[-(aNaturalNumber0(sdtpldt0(xn, xm))), aNaturalNumber0(xn), aNaturalNumber0(xm)],extension(138 ^ 4,bind([[_164182, _164184], [xm, xn]]))).
% 13.54/13.79 ncf('1.1.4.4.3.1',plain,[-(aNaturalNumber0(xn))],extension(802 ^ 5)).
% 13.54/13.79 ncf('1.1.4.4.3.2',plain,[-(aNaturalNumber0(xm))],lemmata('[1].x')).
% 13.54/13.79 ncf('1.1.4.4.4',plain,[sdtpldt0(sdtsldt0(xn, xr), xm) = sdtpldt0(xn, xm), -(sdtsldt0(xn, xr) = xn), aNaturalNumber0(xm), aNaturalNumber0(sdtsldt0(xn, xr)), aNaturalNumber0(xn)],extension(246 ^ 4,bind([[_167642, _167644, _167646], [xn, sdtsldt0(xn, xr), xm]]))).
% 13.54/13.79 ncf('1.1.4.4.4.1',plain,[sdtsldt0(xn, xr) = xn],extension(1040 ^ 5)).
% 13.54/13.79 ncf('1.1.4.4.4.2',plain,[-(aNaturalNumber0(xm))],lemmata('[1].x')).
% 13.54/13.79 ncf('1.1.4.4.4.3',plain,[-(aNaturalNumber0(sdtsldt0(xn, xr)))],lemmata('[1].x')).
% 13.54/13.79 ncf('1.1.4.4.4.4',plain,[-(aNaturalNumber0(xn))],extension(802 ^ 5)).
% 13.54/13.79 ncf('1.1.4.4.5',plain,[-(sdtlseqdt0(sdtpldt0(sdtsldt0(xn, xr), xm), sdtpldt0(xn, xm))), 459 : aNaturalNumber0(xm), 459 : aNaturalNumber0(sdtsldt0(xn, xr)), 459 : aNaturalNumber0(xn), 459 : -(sdtsldt0(xn, xr) = xn), 459 : sdtlseqdt0(sdtsldt0(xn, xr), xn)],extension(443 ^ 4,bind([[_173452, _173454, _173896], [xn, sdtsldt0(xn, xr), xm]]))).
% 13.54/13.79 ncf('1.1.4.4.5.1',plain,[-(aNaturalNumber0(xm))],lemmata('[1].x')).
% 13.54/13.79 ncf('1.1.4.4.5.2',plain,[-(aNaturalNumber0(sdtsldt0(xn, xr)))],lemmata('[1].x')).
% 13.54/13.79 ncf('1.1.4.4.5.3',plain,[-(aNaturalNumber0(xn))],extension(802 ^ 5)).
% 13.54/13.79 ncf('1.1.4.4.5.4',plain,[sdtsldt0(xn, xr) = xn],extension(1040 ^ 5)).
% 13.54/13.79 ncf('1.1.4.4.5.5',plain,[-(sdtlseqdt0(sdtsldt0(xn, xr), xn))],extension(1051 ^ 5)).
% 13.54/13.79 ncf('1.1.5',plain,[aNaturalNumber0(861 ^ [xp, xm, sdtsldt0(xn, xr)]), sdtsldt0(xn, xr) = sdtasdt0(xp, 861 ^ [xp, xm, sdtsldt0(xn, xr)])],extension(1068 ^ 4,bind([[_192503], [861 ^ [xp, xm, sdtsldt0(xn, xr)]]]))).
% 13.54/13.79 ncf('1.1.5.1',plain,[-(sdtsldt0(xn, xr) = sdtasdt0(xp, 861 ^ [xp, xm, sdtsldt0(xn, xr)]))],extension(865 ^ 5)).
% 13.54/13.79 ncf('1.1.6',plain,[-(doDivides0(xp, sdtasdt0(sdtsldt0(xn, xr), xm)))],extension(1062 ^ 4)).
% 13.54/13.79 ncf('1.1.7',plain,[-(isPrime0(xp)), 762 : -(xp = sz00), 762 : -(xp = sz10), 773 : -(aNaturalNumber0(771 ^ [xp])), 762 : aNaturalNumber0(xp)],extension(736 ^ 4,bind([[_181971], [xp]]))).
% 13.54/13.79 ncf('1.1.7.1',plain,[xp = sz00],extension(876 ^ 7)).
% 13.54/13.79 ncf('1.1.7.2',plain,[xp = sz10],extension(878 ^ 7)).
% 13.54/13.79 ncf('1.1.7.3',plain,[aNaturalNumber0(771 ^ [xp]), -(771 ^ [xp] = sz10), -(771 ^ [xp] = xp), 892 : doDivides0(771 ^ [xp], xp)],extension(880 ^ 9,bind([[_186593], [771 ^ [xp]]]))).
% 13.54/13.79 ncf('1.1.7.3.1',plain,[771 ^ [xp] = sz10],extension(777 ^ 10)).
% 13.54/13.79 ncf('1.1.7.3.2',plain,[771 ^ [xp] = xp],extension(779 ^ 10)).
% 13.54/13.79 ncf('1.1.7.3.3',plain,[-(doDivides0(771 ^ [xp], xp))],extension(775 ^ 12)).
% 13.54/13.79 ncf('1.1.7.4',plain,[-(aNaturalNumber0(xp))],lemmata('[1].x')).
% 13.54/13.79 %-----------------------------------------------------
% 13.54/13.79 End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------