TSTP Solution File: NUM507+3 by nanoCoP---2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : nanoCoP---2.0
% Problem : NUM507+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : nanocop.sh %s %d
% Computer : n025.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 11:44:49 EDT 2023
% Result : Theorem 240.11s 232.31s
% Output : Proof 240.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : NUM507+3 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.12 % Command : nanocop.sh %s %d
% 0.12/0.33 % Computer : n025.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 17:29:48 EDT 2023
% 0.12/0.33 % CPUTime :
% 240.11/232.31
% 240.11/232.31 /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 240.11/232.31 Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 240.11/232.31 %-----------------------------------------------------
% 240.11/232.31 ncf(matrix, plain, [(1013 ^ _197354) ^ [] : [-(sdtpldt0(sdtpldt0(xn, xm), xr) = sdtpldt0(sdtpldt0(xn, xm), xp)), 1016 ^ _197354 : [(1023 ^ _197354) ^ [] : [sdtlseqdt0(sdtpldt0(sdtpldt0(xn, xm), xr), sdtpldt0(sdtpldt0(xn, xm), xp))], (1017 ^ _197354) ^ [_197496] : [aNaturalNumber0(_197496), sdtpldt0(sdtpldt0(sdtpldt0(xn, xm), xr), _197496) = sdtpldt0(sdtpldt0(xn, xm), xp)]]], !, (943 ^ _166284) ^ [] : [-(aNaturalNumber0(xk))], (951 ^ _166284) ^ [] : [xk = sz10], (551 ^ _166284) ^ [_183284, _183286] : [aNaturalNumber0(_183286), aNaturalNumber0(_183284), -(iLess0(_183286, _183284)), -(_183286 = _183284), sdtlseqdt0(_183286, _183284)], (1007 ^ _166284) ^ [] : [-(aNaturalNumber0(1005 ^ []))], (696 ^ _166284) ^ [_187453, _187455] : [aNaturalNumber0(_187455), aNaturalNumber0(_187453), -(sdtlseqdt0(_187455, _187453)), doDivides0(_187455, _187453), -(_187453 = sz00)], (405 ^ _166284) ^ [_179014, _179016, _179018] : [aNaturalNumber0(_179018), aNaturalNumber0(_179016), aNaturalNumber0(_179014), -(sdtlseqdt0(_179018, _179014)), sdtlseqdt0(_179018, _179016), sdtlseqdt0(_179016, _179014)], (1009 ^ _166284) ^ [] : [-(sdtpldt0(xk, 1005 ^ []) = xp)], (427 ^ _166284) ^ [_179600, _179602] : [aNaturalNumber0(_179602), aNaturalNumber0(_179600), -(sdtlseqdt0(_179602, _179600)), 438 ^ _166284 : [(439 ^ _166284) ^ [] : [_179600 = _179602], (441 ^ _166284) ^ [] : [-(sdtlseqdt0(_179600, _179602))]]], (947 ^ _166284) ^ [] : [-(xk = sdtsldt0(sdtasdt0(xn, xm), xp))], (1000 ^ _166284) ^ [] : [-(sdtasdt0(xn, xm) = sdtasdt0(xr, 996 ^ []))], (230 ^ _166284) ^ [_173706, _173708, _173710] : [241 ^ _166284 : [(242 ^ _166284) ^ [] : [-(sdtasdt0(_173710, sdtpldt0(_173708, _173706)) = sdtpldt0(sdtasdt0(_173710, _173708), sdtasdt0(_173710, _173706)))], (244 ^ _166284) ^ [] : [-(sdtasdt0(sdtpldt0(_173708, _173706), _173710) = sdtpldt0(sdtasdt0(_173708, _173710), sdtasdt0(_173706, _173710)))]], aNaturalNumber0(_173710), aNaturalNumber0(_173708), aNaturalNumber0(_173706)], (966 ^ _166284) ^ [] : [xr = sz00], (246 ^ _166284) ^ [_174253, _174255, _174257] : [259 ^ _166284 : [(260 ^ _166284) ^ [] : [sdtpldt0(_174257, _174255) = sdtpldt0(_174257, _174253)], (262 ^ _166284) ^ [] : [sdtpldt0(_174255, _174257) = sdtpldt0(_174253, _174257)]], -(_174255 = _174253), aNaturalNumber0(_174257), aNaturalNumber0(_174255), aNaturalNumber0(_174253)], (934 ^ _166284) ^ [] : [xm = xp], (351 ^ _166284) ^ [_177395, _177397] : [aNaturalNumber0(_177397), aNaturalNumber0(_177395), sdtlseqdt0(_177397, _177395), 362 ^ _166284 : [(363 ^ _166284) ^ [_177742] : [_177742 = sdtmndt0(_177395, _177397), 366 ^ _166284 : [(367 ^ _166284) ^ [] : [-(aNaturalNumber0(_177742))], (369 ^ _166284) ^ [] : [-(sdtpldt0(_177397, _177742) = _177395)]]], (371 ^ _166284) ^ [_178001] : [-(_178001 = sdtmndt0(_177395, _177397)), aNaturalNumber0(_178001), sdtpldt0(_177397, _178001) = _177395]]], (503 ^ _166284) ^ [_181981] : [aNaturalNumber0(_181981), -(_181981 = sz00), -(_181981 = sz10), 514 ^ _166284 : [(515 ^ _166284) ^ [] : [sz10 = _181981], (517 ^ _166284) ^ [] : [-(sdtlseqdt0(sz10, _181981))]]], (802 ^ _166284) ^ [] : [-(aNaturalNumber0(xn))], (112 ^ _166284) ^ [_170033, _170035, _170037, _170039] : [-(sdtpldt0(_170039, _170035) = sdtpldt0(_170037, _170033)), _170039 = _170037, _170035 = _170033], (266 ^ _166284) ^ [_174830] : [aNaturalNumber0(_174830), -(_174830 = sz00), 273 ^ _166284 : [(274 ^ _166284) ^ [_175092, _175094] : [aNaturalNumber0(_175094), aNaturalNumber0(_175092), 283 ^ _166284 : [(284 ^ _166284) ^ [] : [sdtasdt0(_174830, _175094) = sdtasdt0(_174830, _175092)], (286 ^ _166284) ^ [] : [sdtasdt0(_175094, _174830) = sdtasdt0(_175092, _174830)]], -(_175094 = _175092)]]], (808 ^ _166284) ^ [_190693, _190695, _190697] : [aNaturalNumber0(_190697), aNaturalNumber0(_190695), aNaturalNumber0(_190693), iLess0(sdtpldt0(sdtpldt0(_190697, _190695), _190693), sdtpldt0(sdtpldt0(xn, xm), xp)), 862 ^ _166284 : [(863 ^ _166284) ^ [] : [-(aNaturalNumber0(861 ^ [_190693, _190695, _190697]))], (867 ^ _166284) ^ [] : [-(doDivides0(_190693, _190697))], (865 ^ _166284) ^ [] : [-(_190697 = sdtasdt0(_190693, 861 ^ [_190693, _190695, _190697]))]], 869 ^ _166284 : [(870 ^ _166284) ^ [] : [-(aNaturalNumber0(868 ^ [_190693, _190695, _190697]))], (874 ^ _166284) ^ [] : [-(doDivides0(_190693, _190695))], (872 ^ _166284) ^ [] : [-(_190695 = sdtasdt0(_190693, 868 ^ [_190693, _190695, _190697]))]], 847 ^ _166284 : [(854 ^ _166284) ^ [] : [doDivides0(_190693, sdtasdt0(_190697, _190695))], (848 ^ _166284) ^ [_192114] : [aNaturalNumber0(_192114), sdtasdt0(_190697, _190695) = sdtasdt0(_190693, _192114)]], 823 ^ _166284 : [(846 ^ _166284) ^ [] : [isPrime0(_190693)], (824 ^ _166284) ^ [] : [-(_190693 = sz00), -(_190693 = sz10), 832 ^ _166284 : [(838 ^ _166284) ^ [] : [-(_190693 = sdtasdt0(831 ^ [_190693, _190695, _190697], 834 ^ [_190693, _190695, _190697]))], (836 ^ _166284) ^ [] : [-(aNaturalNumber0(834 ^ [_190693, _190695, _190697]))], (842 ^ _166284) ^ [] : [831 ^ [_190693, _190695, _190697] = sz10], (844 ^ _166284) ^ [] : [831 ^ [_190693, _190695, _190697] = _190693], (833 ^ _166284) ^ [] : [-(aNaturalNumber0(831 ^ [_190693, _190695, _190697]))], (840 ^ _166284) ^ [] : [-(doDivides0(831 ^ [_190693, _190695, _190697], _190693))]]]]], (915 ^ _166284) ^ [] : [sdtlseqdt0(xp, xn)], (443 ^ _166284) ^ [_180063, _180065] : [aNaturalNumber0(_180065), aNaturalNumber0(_180063), -(_180065 = _180063), sdtlseqdt0(_180065, _180063), 458 ^ _166284 : [(459 ^ _166284) ^ [_180507] : [aNaturalNumber0(_180507), 462 ^ _166284 : [(467 ^ _166284) ^ [] : [sdtpldt0(_180065, _180507) = sdtpldt0(_180063, _180507)], (463 ^ _166284) ^ [] : [sdtpldt0(_180507, _180065) = sdtpldt0(_180507, _180063)], (465 ^ _166284) ^ [] : [-(sdtlseqdt0(sdtpldt0(_180507, _180065), sdtpldt0(_180507, _180063)))], (469 ^ _166284) ^ [] : [-(sdtlseqdt0(sdtpldt0(_180065, _180507), sdtpldt0(_180063, _180507)))]]]]], (907 ^ _166284) ^ [] : [-(doDivides0(xp, sdtasdt0(xn, xm)))], (1002 ^ _166284) ^ [] : [-(doDivides0(xr, sdtasdt0(xn, xm)))], (804 ^ _166284) ^ [] : [-(aNaturalNumber0(xm))], (903 ^ _166284) ^ [] : [-(aNaturalNumber0(901 ^ []))], (937 ^ _166284) ^ [] : [-(aNaturalNumber0(935 ^ []))], (925 ^ _166284) ^ [] : [xn = xp], (917 ^ _166284) ^ [_194312] : [aNaturalNumber0(_194312), sdtpldt0(xp, _194312) = xm], (569 ^ _166284) ^ [_183762, _183764] : [aNaturalNumber0(_183764), aNaturalNumber0(_183762), 576 ^ _166284 : [(577 ^ _166284) ^ [] : [doDivides0(_183764, _183762), 581 ^ _166284 : [(582 ^ _166284) ^ [] : [-(aNaturalNumber0(580 ^ [_183762, _183764]))], (584 ^ _166284) ^ [] : [-(_183762 = sdtasdt0(_183764, 580 ^ [_183762, _183764]))]]], (586 ^ _166284) ^ [] : [-(doDivides0(_183764, _183762)), 587 ^ _166284 : [(588 ^ _166284) ^ [_184322] : [aNaturalNumber0(_184322), _183762 = sdtasdt0(_183764, _184322)]]]]], (136 ^ _166284) ^ [] : [sz10 = sz00], (993 ^ _166284) ^ [] : [-(aNaturalNumber0(991 ^ []))], (960 ^ _166284) ^ [] : [-(aNaturalNumber0(958 ^ []))], (92 ^ _166284) ^ [_169335, _169337, _169339, _169341] : [-(sdtsldt0(_169341, _169337) = sdtsldt0(_169339, _169335)), _169341 = _169339, _169337 = _169335], (880 ^ _166284) ^ [_193204] : [-(_193204 = sz10), -(_193204 = xp), aNaturalNumber0(_193204), 885 ^ _166284 : [(892 ^ _166284) ^ [] : [doDivides0(_193204, xp)], (886 ^ _166284) ^ [_193407] : [aNaturalNumber0(_193407), xp = sdtasdt0(_193204, _193407)]]], (82 ^ _166284) ^ [_168976, _168978, _168980, _168982] : [-(sdtmndt0(_168982, _168978) = sdtmndt0(_168980, _168976)), _168982 = _168980, _168978 = _168976], (158 ^ _166284) ^ [_171391, _171393] : [-(sdtpldt0(_171393, _171391) = sdtpldt0(_171391, _171393)), aNaturalNumber0(_171393), aNaturalNumber0(_171391)], (596 ^ _166284) ^ [_184605, _184607] : [aNaturalNumber0(_184607), aNaturalNumber0(_184605), -(_184607 = sz00), doDivides0(_184607, _184605), 611 ^ _166284 : [(612 ^ _166284) ^ [_185044] : [_185044 = sdtsldt0(_184605, _184607), 615 ^ _166284 : [(616 ^ _166284) ^ [] : [-(aNaturalNumber0(_185044))], (618 ^ _166284) ^ [] : [-(_184605 = sdtasdt0(_184607, _185044))]]], (620 ^ _166284) ^ [_185303] : [-(_185303 = sdtsldt0(_184605, _184607)), aNaturalNumber0(_185303), _184605 = sdtasdt0(_184607, _185303)]]], (122 ^ _166284) ^ [_170364] : [aNaturalNumber0(_170364), true___, -(true___)], (905 ^ _166284) ^ [] : [-(sdtasdt0(xn, xm) = sdtasdt0(xp, 901 ^ []))], (182 ^ _166284) ^ [_172118] : [aNaturalNumber0(_172118), 185 ^ _166284 : [(186 ^ _166284) ^ [] : [-(sdtpldt0(_172118, sz00) = _172118)], (188 ^ _166284) ^ [] : [-(_172118 = sdtpldt0(sz00, _172118))]]], (995 ^ _166284) ^ [] : [-(sdtpldt0(xr, 991 ^ []) = xk)], (68 ^ _166284) ^ [_168518, _168520, _168522, _168524] : [-(sdtlseqdt0(_168522, _168518)), sdtlseqdt0(_168524, _168520), _168524 = _168522, _168520 = _168518], (4 ^ _166284) ^ [_166515, _166517] : [_166517 = _166515, -(_166515 = _166517)], (736 ^ _166284) ^ [_188582] : [aNaturalNumber0(_188582), 739 ^ _166284 : [(762 ^ _166284) ^ [] : [-(isPrime0(_188582)), -(_188582 = sz00), -(_188582 = sz10), 772 ^ _166284 : [(777 ^ _166284) ^ [] : [771 ^ [_188582] = sz10], (773 ^ _166284) ^ [] : [-(aNaturalNumber0(771 ^ [_188582]))], (775 ^ _166284) ^ [] : [-(doDivides0(771 ^ [_188582], _188582))], (779 ^ _166284) ^ [] : [771 ^ [_188582] = _188582]]], (740 ^ _166284) ^ [] : [isPrime0(_188582), 743 ^ _166284 : [(744 ^ _166284) ^ [] : [_188582 = sz00], (748 ^ _166284) ^ [_188974] : [aNaturalNumber0(_188974), doDivides0(_188974, _188582), -(_188974 = sz10), -(_188974 = _188582)], (746 ^ _166284) ^ [] : [_188582 = sz10]]]]], (387 ^ _166284) ^ [_178525, _178527] : [aNaturalNumber0(_178527), aNaturalNumber0(_178525), -(_178527 = _178525), sdtlseqdt0(_178527, _178525), sdtlseqdt0(_178525, _178527)], (970 ^ _166284) ^ [_195827] : [-(_195827 = sz10), -(_195827 = xr), aNaturalNumber0(_195827), 975 ^ _166284 : [(982 ^ _166284) ^ [] : [doDivides0(_195827, xr)], (976 ^ _166284) ^ [_196030] : [aNaturalNumber0(_196030), xr = sdtasdt0(_195827, _196030)]]], (290 ^ _166284) ^ [_175603, _175605] : [aNaturalNumber0(_175605), aNaturalNumber0(_175603), sdtpldt0(_175605, _175603) = sz00, 301 ^ _166284 : [(302 ^ _166284) ^ [] : [-(_175605 = sz00)], (304 ^ _166284) ^ [] : [-(_175603 = sz00)]]], (783 ^ _166284) ^ [_189926] : [795 ^ _166284 : [(796 ^ _166284) ^ [] : [-(aNaturalNumber0(794 ^ [_189926]))], (800 ^ _166284) ^ [] : [-(isPrime0(794 ^ [_189926]))], (798 ^ _166284) ^ [] : [-(doDivides0(794 ^ [_189926], _189926))]], aNaturalNumber0(_189926), -(_189926 = sz00), -(_189926 = sz10)], (878 ^ _166284) ^ [] : [xp = sz10], (900 ^ _166284) ^ [] : [-(isPrime0(xp))], (533 ^ _166284) ^ [_182824, _182826] : [aNaturalNumber0(_182826), aNaturalNumber0(_182824), iLess0(_182826, _182824), true___, -(true___)], (714 ^ _166284) ^ [_187931, _187933] : [aNaturalNumber0(_187933), aNaturalNumber0(_187931), -(_187933 = sz00), doDivides0(_187933, _187931), 729 ^ _166284 : [(730 ^ _166284) ^ [_188341] : [aNaturalNumber0(_188341), -(sdtasdt0(_188341, sdtsldt0(_187931, _187933)) = sdtsldt0(sdtasdt0(_188341, _187931), _187933))]]], (957 ^ _166284) ^ [] : [-(aNaturalNumber0(xr))], (928 ^ _166284) ^ [] : [-(aNaturalNumber0(926 ^ []))], (132 ^ _166284) ^ [] : [-(aNaturalNumber0(sz00))], (909 ^ _166284) ^ [_194065] : [aNaturalNumber0(_194065), sdtpldt0(xp, _194065) = xn], (168 ^ _166284) ^ [_171712, _171714, _171716] : [-(sdtpldt0(sdtpldt0(_171716, _171714), _171712) = sdtpldt0(_171716, sdtpldt0(_171714, _171712))), aNaturalNumber0(_171716), aNaturalNumber0(_171714), aNaturalNumber0(_171712)], (964 ^ _166284) ^ [] : [-(doDivides0(xr, xk))], (953 ^ _166284) ^ [] : [xk = sz00], (214 ^ _166284) ^ [_173132] : [aNaturalNumber0(_173132), 217 ^ _166284 : [(218 ^ _166284) ^ [] : [-(sdtasdt0(_173132, sz10) = _173132)], (220 ^ _166284) ^ [] : [-(_173132 = sdtasdt0(sz10, _173132))]]], (2 ^ _166284) ^ [_166408] : [-(_166408 = _166408)], (324 ^ _166284) ^ [_176552, _176554] : [aNaturalNumber0(_176554), aNaturalNumber0(_176552), 331 ^ _166284 : [(332 ^ _166284) ^ [] : [sdtlseqdt0(_176554, _176552), 336 ^ _166284 : [(337 ^ _166284) ^ [] : [-(aNaturalNumber0(335 ^ [_176552, _176554]))], (339 ^ _166284) ^ [] : [-(sdtpldt0(_176554, 335 ^ [_176552, _176554]) = _176552)]]], (341 ^ _166284) ^ [] : [-(sdtlseqdt0(_176554, _176552)), 342 ^ _166284 : [(343 ^ _166284) ^ [_177112] : [aNaturalNumber0(_177112), sdtpldt0(_176554, _177112) = _176552]]]]], (10 ^ _166284) ^ [_166719, _166721, _166723] : [-(_166723 = _166719), _166723 = _166721, _166721 = _166719], (652 ^ _166284) ^ [_186255, _186257, _186259] : [aNaturalNumber0(_186259), aNaturalNumber0(_186257), aNaturalNumber0(_186255), -(doDivides0(_186259, sdtpldt0(_186257, _186255))), doDivides0(_186259, _186257), doDivides0(_186259, _186255)], (932 ^ _166284) ^ [] : [-(sdtlseqdt0(xn, xp))], (58 ^ _166284) ^ [_168215, _168217] : [-(aNaturalNumber0(_168215)), _168217 = _168215, aNaturalNumber0(_168217)], (1011 ^ _166284) ^ [] : [-(sdtlseqdt0(xk, xp))], (968 ^ _166284) ^ [] : [xr = sz10], (519 ^ _166284) ^ [_182429, _182431] : [aNaturalNumber0(_182431), aNaturalNumber0(_182429), -(_182431 = sz00), -(sdtlseqdt0(_182429, sdtasdt0(_182429, _182431)))], (134 ^ _166284) ^ [] : [-(aNaturalNumber0(sz10))], (945 ^ _166284) ^ [] : [-(sdtasdt0(xn, xm) = sdtasdt0(xp, xk))], (306 ^ _166284) ^ [_176070, _176072] : [aNaturalNumber0(_176072), aNaturalNumber0(_176070), sdtasdt0(_176072, _176070) = sz00, -(_176072 = sz00), -(_176070 = sz00)], (222 ^ _166284) ^ [_173405] : [aNaturalNumber0(_173405), 225 ^ _166284 : [(226 ^ _166284) ^ [] : [-(sdtasdt0(_173405, sz00) = sz00)], (228 ^ _166284) ^ [] : [-(sz00 = sdtasdt0(sz00, _173405))]]], (806 ^ _166284) ^ [] : [-(aNaturalNumber0(xp))], (138 ^ _166284) ^ [_170793, _170795] : [-(aNaturalNumber0(sdtpldt0(_170795, _170793))), aNaturalNumber0(_170795), aNaturalNumber0(_170793)], (148 ^ _166284) ^ [_171092, _171094] : [-(aNaturalNumber0(sdtasdt0(_171094, _171092))), aNaturalNumber0(_171094), aNaturalNumber0(_171092)], (876 ^ _166284) ^ [] : [xp = sz00], (941 ^ _166284) ^ [] : [-(sdtlseqdt0(xm, xp))], (955 ^ _166284) ^ [] : [xk = sz10], (630 ^ _166284) ^ [_185655, _185657, _185659] : [aNaturalNumber0(_185659), aNaturalNumber0(_185657), aNaturalNumber0(_185655), -(doDivides0(_185659, _185655)), doDivides0(_185659, _185657), doDivides0(_185657, _185655)], (1004 ^ _166284) ^ [] : [xk = xp], (34 ^ _166284) ^ [_167476, _167478] : [-(isPrime0(_167476)), _167478 = _167476, isPrime0(_167478)], (381 ^ _166284) ^ [_178323] : [aNaturalNumber0(_178323), -(sdtlseqdt0(_178323, _178323))], (190 ^ _166284) ^ [_172405, _172407] : [-(sdtasdt0(_172407, _172405) = sdtasdt0(_172405, _172407)), aNaturalNumber0(_172407), aNaturalNumber0(_172405)], (998 ^ _166284) ^ [] : [-(aNaturalNumber0(996 ^ []))], (990 ^ _166284) ^ [] : [-(isPrime0(xr))], (939 ^ _166284) ^ [] : [-(sdtpldt0(xm, 935 ^ []) = xp)], (949 ^ _166284) ^ [] : [xk = sz00], (962 ^ _166284) ^ [] : [-(xk = sdtasdt0(xr, 958 ^ []))], (930 ^ _166284) ^ [] : [-(sdtpldt0(xn, 926 ^ []) = xp)], (674 ^ _166284) ^ [_186861, _186863, _186865] : [aNaturalNumber0(_186865), aNaturalNumber0(_186863), aNaturalNumber0(_186861), -(doDivides0(_186865, _186861)), doDivides0(_186865, _186863), doDivides0(_186865, sdtpldt0(_186863, _186861))], (20 ^ _166284) ^ [_167060, _167062, _167064, _167066] : [-(iLess0(_167064, _167060)), iLess0(_167066, _167062), _167066 = _167064, _167062 = _167060], (200 ^ _166284) ^ [_172726, _172728, _172730] : [-(sdtasdt0(sdtasdt0(_172730, _172728), _172726) = sdtasdt0(_172730, sdtasdt0(_172728, _172726))), aNaturalNumber0(_172730), aNaturalNumber0(_172728), aNaturalNumber0(_172726)], (44 ^ _166284) ^ [_167799, _167801, _167803, _167805] : [-(doDivides0(_167803, _167799)), doDivides0(_167805, _167801), _167805 = _167803, _167801 = _167799], (102 ^ _166284) ^ [_169694, _169696, _169698, _169700] : [-(sdtasdt0(_169700, _169696) = sdtasdt0(_169698, _169694)), _169700 = _169698, _169696 = _169694], (471 ^ _166284) ^ [_181031, _181033, _181035] : [aNaturalNumber0(_181035), aNaturalNumber0(_181033), aNaturalNumber0(_181031), 494 ^ _166284 : [(499 ^ _166284) ^ [] : [sdtasdt0(_181033, _181035) = sdtasdt0(_181031, _181035)], (495 ^ _166284) ^ [] : [sdtasdt0(_181035, _181033) = sdtasdt0(_181035, _181031)], (497 ^ _166284) ^ [] : [-(sdtlseqdt0(sdtasdt0(_181035, _181033), sdtasdt0(_181035, _181031)))], (501 ^ _166284) ^ [] : [-(sdtlseqdt0(sdtasdt0(_181033, _181035), sdtasdt0(_181031, _181035)))]], -(_181035 = sz00), -(_181033 = _181031), sdtlseqdt0(_181033, _181031)], (923 ^ _166284) ^ [] : [sdtlseqdt0(xp, xm)]], input).
% 240.11/232.31 ncf('1',plain,[-(sdtpldt0(sdtpldt0(xn, xm), xr) = sdtpldt0(sdtpldt0(xn, xm), xp)), 1023 : sdtlseqdt0(sdtpldt0(sdtpldt0(xn, xm), xr), sdtpldt0(sdtpldt0(xn, xm), xp))],start(1013 ^ 0)).
% 240.11/232.31 ncf('1.1',plain,[sdtpldt0(sdtpldt0(xn, xm), xr) = sdtpldt0(sdtpldt0(xn, xm), xp), -(xr = xp), aNaturalNumber0(sdtpldt0(xn, xm)), aNaturalNumber0(xr), aNaturalNumber0(xp)],extension(246 ^ 1,bind([[_174253, _174255, _174257], [xp, xr, sdtpldt0(xn, xm)]]))).
% 240.11/232.31 ncf('1.1.1',plain,[xr = xp, aNaturalNumber0(xp), aNaturalNumber0(xr), -(sdtlseqdt0(xp, xr))],extension(427 ^ 2,bind([[_179600, _179602], [xr, xp]]))).
% 240.11/232.31 ncf('1.1.1.1',plain,[-(aNaturalNumber0(xp)), xr = xp, aNaturalNumber0(xr)],extension(58 ^ 3,bind([[_168215, _168217], [xp, xr]]))).
% 240.11/232.31 ncf('1.1.1.1.1',plain,[-(xr = xp)],reduction('1.1')).
% 240.11/232.31 ncf('1.1.1.1.2',plain,[-(aNaturalNumber0(xr))],extension(957 ^ 4)).
% 240.11/232.31 ncf('1.1.1.2',plain,[-(aNaturalNumber0(xr))],extension(957 ^ 3)).
% 240.11/232.31 ncf('1.1.1.3',plain,[sdtlseqdt0(xp, xr), aNaturalNumber0(xp), aNaturalNumber0(xr), aNaturalNumber0(xk), -(sdtlseqdt0(xp, xk)), sdtlseqdt0(xr, xk)],extension(405 ^ 3,bind([[_179014, _179016, _179018], [xk, xr, xp]]))).
% 240.11/232.31 ncf('1.1.1.3.1',plain,[-(aNaturalNumber0(xp))],lemmata('[1, 1].x')).
% 240.11/232.31 ncf('1.1.1.3.2',plain,[-(aNaturalNumber0(xr))],lemmata('[1, 1].x')).
% 240.11/232.31 ncf('1.1.1.3.3',plain,[-(aNaturalNumber0(xk))],extension(943 ^ 4)).
% 240.11/232.31 ncf('1.1.1.3.4',plain,[sdtlseqdt0(xp, xk), aNaturalNumber0(xk), aNaturalNumber0(xp), -(xk = xp), sdtlseqdt0(xk, xp)],extension(387 ^ 4,bind([[_178525, _178527], [xp, xk]]))).
% 240.11/232.31 ncf('1.1.1.3.4.1',plain,[-(aNaturalNumber0(xk))],lemmata('[1, 1, 1].x')).
% 240.11/232.31 ncf('1.1.1.3.4.2',plain,[-(aNaturalNumber0(xp))],lemmata('[1, 1, 1].x')).
% 240.11/232.31 ncf('1.1.1.3.4.3',plain,[xk = xp],extension(1004 ^ 5)).
% 240.11/232.31 ncf('1.1.1.3.4.4',plain,[-(sdtlseqdt0(xk, xp))],extension(1011 ^ 5)).
% 240.11/232.31 ncf('1.1.1.3.5',plain,[-(sdtlseqdt0(xr, xk)), aNaturalNumber0(xr), aNaturalNumber0(xk), doDivides0(xr, xk), -(xk = sz00)],extension(696 ^ 4,bind([[_187453, _187455], [xk, xr]]))).
% 240.11/232.31 ncf('1.1.1.3.5.1',plain,[-(aNaturalNumber0(xr))],lemmata('[1, 1, 1].x')).
% 240.11/232.31 ncf('1.1.1.3.5.2',plain,[-(aNaturalNumber0(xk))],lemmata('[1, 1, 1].x')).
% 240.11/232.31 ncf('1.1.1.3.5.3',plain,[-(doDivides0(xr, xk))],extension(964 ^ 5)).
% 240.11/232.31 ncf('1.1.1.3.5.4',plain,[xk = sz00],extension(953 ^ 5)).
% 240.11/232.31 ncf('1.1.2',plain,[-(aNaturalNumber0(sdtpldt0(xn, xm))), sdtpldt0(sdtpldt0(xn, sz00), sdtpldt0(xm, sz00)) = sdtpldt0(xn, xm), aNaturalNumber0(sdtpldt0(sdtpldt0(xn, sz00), sdtpldt0(xm, sz00)))],extension(58 ^ 2,bind([[_168215, _168217], [sdtpldt0(xn, xm), sdtpldt0(sdtpldt0(xn, sz00), sdtpldt0(xm, sz00))]]))).
% 240.11/232.31 ncf('1.1.2.1',plain,[-(sdtpldt0(sdtpldt0(xn, sz00), sdtpldt0(xm, sz00)) = sdtpldt0(xn, xm)), sdtpldt0(xn, sz00) = xn, sdtpldt0(xm, sz00) = xm],extension(112 ^ 3,bind([[_170033, _170035, _170037, _170039], [xm, sdtpldt0(xm, sz00), xn, sdtpldt0(xn, sz00)]]))).
% 240.11/232.31 ncf('1.1.2.1.1',plain,[-(sdtpldt0(xn, sz00) = xn), aNaturalNumber0(xn)],extension(182 ^ 4,bind([[_172118], [xn]]))).
% 240.11/232.31 ncf('1.1.2.1.1.1',plain,[-(aNaturalNumber0(xn))],extension(802 ^ 5)).
% 240.11/232.31 ncf('1.1.2.1.2',plain,[-(sdtpldt0(xm, sz00) = xm), aNaturalNumber0(xm)],extension(182 ^ 4,bind([[_172118], [xm]]))).
% 240.11/232.31 ncf('1.1.2.1.2.1',plain,[-(aNaturalNumber0(xm))],extension(804 ^ 5)).
% 240.11/232.31 ncf('1.1.2.2',plain,[-(aNaturalNumber0(sdtpldt0(sdtpldt0(xn, sz00), sdtpldt0(xm, sz00)))), aNaturalNumber0(sdtpldt0(xn, sz00)), aNaturalNumber0(sdtpldt0(xm, sz00))],extension(138 ^ 3,bind([[_170793, _170795], [sdtpldt0(xm, sz00), sdtpldt0(xn, sz00)]]))).
% 240.11/232.31 ncf('1.1.2.2.1',plain,[-(aNaturalNumber0(sdtpldt0(xn, sz00))), aNaturalNumber0(xn), aNaturalNumber0(sz00)],extension(138 ^ 4,bind([[_170793, _170795], [sz00, xn]]))).
% 240.11/232.31 ncf('1.1.2.2.1.1',plain,[-(aNaturalNumber0(xn))],extension(802 ^ 5)).
% 240.11/232.31 ncf('1.1.2.2.1.2',plain,[-(aNaturalNumber0(sz00))],extension(132 ^ 5)).
% 240.11/232.31 ncf('1.1.2.2.2',plain,[-(aNaturalNumber0(sdtpldt0(xm, sz00))), aNaturalNumber0(xm), aNaturalNumber0(sz00)],extension(138 ^ 4,bind([[_170793, _170795], [sz00, xm]]))).
% 240.11/232.31 ncf('1.1.2.2.2.1',plain,[-(aNaturalNumber0(xm))],extension(804 ^ 5)).
% 240.11/232.31 ncf('1.1.2.2.2.2',plain,[-(aNaturalNumber0(sz00))],extension(132 ^ 5)).
% 240.11/232.31 ncf('1.1.3',plain,[-(aNaturalNumber0(xr))],extension(957 ^ 2)).
% 240.11/232.31 ncf('1.1.4',plain,[-(aNaturalNumber0(xp)), sdtpldt0(xk, 1005 ^ []) = xp, aNaturalNumber0(sdtpldt0(xk, 1005 ^ []))],extension(58 ^ 2,bind([[_168215, _168217], [xp, sdtpldt0(xk, 1005 ^ [])]]))).
% 240.11/232.31 ncf('1.1.4.1',plain,[-(sdtpldt0(xk, 1005 ^ []) = xp)],extension(1009 ^ 3)).
% 240.11/232.31 ncf('1.1.4.2',plain,[-(aNaturalNumber0(sdtpldt0(xk, 1005 ^ []))), sdtpldt0(1005 ^ [], xk) = sdtpldt0(xk, 1005 ^ []), aNaturalNumber0(sdtpldt0(1005 ^ [], xk))],extension(58 ^ 3,bind([[_168215, _168217], [sdtpldt0(xk, 1005 ^ []), sdtpldt0(1005 ^ [], xk)]]))).
% 240.11/232.31 ncf('1.1.4.2.1',plain,[-(sdtpldt0(1005 ^ [], xk) = sdtpldt0(xk, 1005 ^ [])), aNaturalNumber0(1005 ^ []), aNaturalNumber0(xk)],extension(158 ^ 4,bind([[_171391, _171393], [xk, 1005 ^ []]]))).
% 240.11/232.31 ncf('1.1.4.2.1.1',plain,[-(aNaturalNumber0(1005 ^ []))],extension(1007 ^ 5)).
% 240.11/232.31 ncf('1.1.4.2.1.2',plain,[-(aNaturalNumber0(xk))],extension(943 ^ 5)).
% 240.11/232.31 ncf('1.1.4.2.2',plain,[-(aNaturalNumber0(sdtpldt0(1005 ^ [], xk))), aNaturalNumber0(1005 ^ []), aNaturalNumber0(xk)],extension(138 ^ 4,bind([[_170793, _170795], [xk, 1005 ^ []]]))).
% 240.11/232.31 ncf('1.1.4.2.2.1',plain,[-(aNaturalNumber0(1005 ^ []))],extension(1007 ^ 5)).
% 240.11/232.31 ncf('1.1.4.2.2.2',plain,[-(aNaturalNumber0(xk))],extension(943 ^ 5)).
% 240.11/232.31 ncf('1.2',plain,[-(sdtlseqdt0(sdtpldt0(sdtpldt0(xn, xm), xr), sdtpldt0(sdtpldt0(xn, xm), xp))), 459 : aNaturalNumber0(sdtpldt0(xn, xm)), 459 : aNaturalNumber0(xr), 459 : aNaturalNumber0(xp), 459 : -(xr = xp), 459 : sdtlseqdt0(xr, xp)],extension(443 ^ 3,bind([[_180063, _180065, _180507], [xp, xr, sdtpldt0(xn, xm)]]))).
% 240.11/232.31 ncf('1.2.1',plain,[-(aNaturalNumber0(sdtpldt0(xn, xm))), sdtpldt0(sdtpldt0(xn, sz00), sdtpldt0(xm, sz00)) = sdtpldt0(xn, xm), aNaturalNumber0(sdtpldt0(sdtpldt0(xn, sz00), sdtpldt0(xm, sz00)))],extension(58 ^ 6,bind([[_168215, _168217], [sdtpldt0(xn, xm), sdtpldt0(sdtpldt0(xn, sz00), sdtpldt0(xm, sz00))]]))).
% 240.11/232.31 ncf('1.2.1.1',plain,[-(sdtpldt0(sdtpldt0(xn, sz00), sdtpldt0(xm, sz00)) = sdtpldt0(xn, xm)), sdtpldt0(xn, sz00) = xn, sdtpldt0(xm, sz00) = xm],extension(112 ^ 7,bind([[_170033, _170035, _170037, _170039], [xm, sdtpldt0(xm, sz00), xn, sdtpldt0(xn, sz00)]]))).
% 240.11/232.31 ncf('1.2.1.1.1',plain,[-(sdtpldt0(xn, sz00) = xn), aNaturalNumber0(xn)],extension(182 ^ 8,bind([[_172118], [xn]]))).
% 240.11/232.31 ncf('1.2.1.1.1.1',plain,[-(aNaturalNumber0(xn))],extension(802 ^ 9)).
% 240.11/232.31 ncf('1.2.1.1.2',plain,[-(sdtpldt0(xm, sz00) = xm), aNaturalNumber0(xm)],extension(182 ^ 8,bind([[_172118], [xm]]))).
% 240.11/232.31 ncf('1.2.1.1.2.1',plain,[-(aNaturalNumber0(xm))],extension(804 ^ 9)).
% 240.11/232.31 ncf('1.2.1.2',plain,[-(aNaturalNumber0(sdtpldt0(sdtpldt0(xn, sz00), sdtpldt0(xm, sz00)))), aNaturalNumber0(sdtpldt0(xn, sz00)), aNaturalNumber0(sdtpldt0(xm, sz00))],extension(138 ^ 7,bind([[_170793, _170795], [sdtpldt0(xm, sz00), sdtpldt0(xn, sz00)]]))).
% 240.11/232.31 ncf('1.2.1.2.1',plain,[-(aNaturalNumber0(sdtpldt0(xn, sz00))), aNaturalNumber0(xn), aNaturalNumber0(sz00)],extension(138 ^ 8,bind([[_170793, _170795], [sz00, xn]]))).
% 240.11/232.31 ncf('1.2.1.2.1.1',plain,[-(aNaturalNumber0(xn))],extension(802 ^ 9)).
% 240.11/232.31 ncf('1.2.1.2.1.2',plain,[-(aNaturalNumber0(sz00))],extension(132 ^ 9)).
% 240.11/232.31 ncf('1.2.1.2.2',plain,[-(aNaturalNumber0(sdtpldt0(xm, sz00))), aNaturalNumber0(xm), aNaturalNumber0(sz00)],extension(138 ^ 8,bind([[_170793, _170795], [sz00, xm]]))).
% 240.11/232.31 ncf('1.2.1.2.2.1',plain,[-(aNaturalNumber0(xm))],extension(804 ^ 9)).
% 240.11/232.31 ncf('1.2.1.2.2.2',plain,[-(aNaturalNumber0(sz00))],extension(132 ^ 9)).
% 240.11/232.31 ncf('1.2.2',plain,[-(aNaturalNumber0(xr))],extension(957 ^ 4)).
% 240.11/232.31 ncf('1.2.3',plain,[-(aNaturalNumber0(xp)), sdtpldt0(xk, 1005 ^ []) = xp, aNaturalNumber0(sdtpldt0(xk, 1005 ^ []))],extension(58 ^ 4,bind([[_168215, _168217], [xp, sdtpldt0(xk, 1005 ^ [])]]))).
% 240.11/232.31 ncf('1.2.3.1',plain,[-(sdtpldt0(xk, 1005 ^ []) = xp)],extension(1009 ^ 5)).
% 240.11/232.31 ncf('1.2.3.2',plain,[-(aNaturalNumber0(sdtpldt0(xk, 1005 ^ []))), sdtpldt0(1005 ^ [], xk) = sdtpldt0(xk, 1005 ^ []), aNaturalNumber0(sdtpldt0(1005 ^ [], xk))],extension(58 ^ 5,bind([[_168215, _168217], [sdtpldt0(xk, 1005 ^ []), sdtpldt0(1005 ^ [], xk)]]))).
% 240.11/232.31 ncf('1.2.3.2.1',plain,[-(sdtpldt0(1005 ^ [], xk) = sdtpldt0(xk, 1005 ^ [])), aNaturalNumber0(1005 ^ []), aNaturalNumber0(xk)],extension(158 ^ 6,bind([[_171391, _171393], [xk, 1005 ^ []]]))).
% 240.11/232.31 ncf('1.2.3.2.1.1',plain,[-(aNaturalNumber0(1005 ^ []))],extension(1007 ^ 7)).
% 240.11/232.31 ncf('1.2.3.2.1.2',plain,[-(aNaturalNumber0(xk))],extension(943 ^ 7)).
% 240.11/232.31 ncf('1.2.3.2.2',plain,[-(aNaturalNumber0(sdtpldt0(1005 ^ [], xk))), aNaturalNumber0(1005 ^ []), aNaturalNumber0(xk)],extension(138 ^ 6,bind([[_170793, _170795], [xk, 1005 ^ []]]))).
% 240.11/232.31 ncf('1.2.3.2.2.1',plain,[-(aNaturalNumber0(1005 ^ []))],extension(1007 ^ 7)).
% 240.11/232.31 ncf('1.2.3.2.2.2',plain,[-(aNaturalNumber0(xk))],extension(943 ^ 7)).
% 240.11/232.31 ncf('1.2.4',plain,[xr = xp, aNaturalNumber0(xp), aNaturalNumber0(xr), -(sdtlseqdt0(xp, xr))],extension(427 ^ 4,bind([[_179600, _179602], [xr, xp]]))).
% 240.11/232.31 ncf('1.2.4.1',plain,[-(aNaturalNumber0(xp))],lemmata('[1].x')).
% 240.11/232.31 ncf('1.2.4.2',plain,[-(aNaturalNumber0(xr))],lemmata('[1].x')).
% 240.11/232.31 ncf('1.2.4.3',plain,[sdtlseqdt0(xp, xr), aNaturalNumber0(xp), aNaturalNumber0(xr), aNaturalNumber0(xk), -(sdtlseqdt0(xp, xk)), sdtlseqdt0(xr, xk)],extension(405 ^ 5,bind([[_179014, _179016, _179018], [xk, xr, xp]]))).
% 240.11/232.31 ncf('1.2.4.3.1',plain,[-(aNaturalNumber0(xp))],lemmata('[2, 1].x')).
% 240.11/232.31 ncf('1.2.4.3.2',plain,[-(aNaturalNumber0(xr))],lemmata('[2, 1].x')).
% 240.11/232.31 ncf('1.2.4.3.3',plain,[-(aNaturalNumber0(xk))],extension(943 ^ 6)).
% 240.11/232.31 ncf('1.2.4.3.4',plain,[sdtlseqdt0(xp, xk), aNaturalNumber0(xk), aNaturalNumber0(xp), -(xk = xp), sdtlseqdt0(xk, xp)],extension(387 ^ 6,bind([[_178525, _178527], [xp, xk]]))).
% 240.11/232.31 ncf('1.2.4.3.4.1',plain,[-(aNaturalNumber0(xk))],lemmata('[4, 2, 1].x')).
% 240.11/232.31 ncf('1.2.4.3.4.2',plain,[-(aNaturalNumber0(xp))],lemmata('[4, 2, 1].x')).
% 240.11/232.31 ncf('1.2.4.3.4.3',plain,[xk = xp],extension(1004 ^ 7)).
% 240.11/232.31 ncf('1.2.4.3.4.4',plain,[-(sdtlseqdt0(xk, xp))],extension(1011 ^ 7)).
% 240.11/232.31 ncf('1.2.4.3.5',plain,[-(sdtlseqdt0(xr, xk)), aNaturalNumber0(xr), aNaturalNumber0(xk), doDivides0(xr, xk), -(xk = sz00)],extension(696 ^ 6,bind([[_187453, _187455], [xk, xr]]))).
% 240.11/232.31 ncf('1.2.4.3.5.1',plain,[-(aNaturalNumber0(xr))],lemmata('[4, 2, 1].x')).
% 240.11/232.31 ncf('1.2.4.3.5.2',plain,[-(aNaturalNumber0(xk))],lemmata('[4, 2, 1].x')).
% 240.11/232.31 ncf('1.2.4.3.5.3',plain,[-(doDivides0(xr, xk))],extension(964 ^ 7)).
% 240.11/232.31 ncf('1.2.4.3.5.4',plain,[xk = sz00],extension(953 ^ 7)).
% 240.11/232.31 ncf('1.2.5',plain,[-(sdtlseqdt0(xr, xp)), aNaturalNumber0(xr), aNaturalNumber0(xk), aNaturalNumber0(xp), sdtlseqdt0(xr, xk), sdtlseqdt0(xk, xp)],extension(405 ^ 4,bind([[_179014, _179016, _179018], [xp, xk, xr]]))).
% 240.11/232.31 ncf('1.2.5.1',plain,[-(aNaturalNumber0(xr))],lemmata('[1].x')).
% 240.11/232.31 ncf('1.2.5.2',plain,[-(aNaturalNumber0(xk))],extension(943 ^ 5)).
% 240.11/232.31 ncf('1.2.5.3',plain,[-(aNaturalNumber0(xp))],lemmata('[1].x')).
% 240.11/232.31 ncf('1.2.5.4',plain,[-(sdtlseqdt0(xr, xk)), aNaturalNumber0(xr), aNaturalNumber0(xk), doDivides0(xr, xk), -(xk = sz00)],extension(696 ^ 5,bind([[_187453, _187455], [xk, xr]]))).
% 240.11/232.31 ncf('1.2.5.4.1',plain,[-(aNaturalNumber0(xr))],lemmata('[2, 1].x')).
% 240.11/232.31 ncf('1.2.5.4.2',plain,[-(aNaturalNumber0(xk))],lemmata('[2, 1].x')).
% 240.11/232.31 ncf('1.2.5.4.3',plain,[-(doDivides0(xr, xk))],extension(964 ^ 6)).
% 240.11/232.31 ncf('1.2.5.4.4',plain,[xk = sz00],extension(953 ^ 6)).
% 240.11/232.31 ncf('1.2.5.5',plain,[-(sdtlseqdt0(xk, xp))],extension(1011 ^ 5)).
% 240.11/232.31 %-----------------------------------------------------
% 240.11/232.31 End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------