TSTP Solution File: NUM513+3 by nanoCoP---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : nanoCoP---2.0
% Problem : NUM513+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : nanocop.sh %s %d
% Computer : n008.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 203.83s 197.90s
% Output : Proof 203.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM513+3 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.12 % Command : nanocop.sh %s %d
% 0.12/0.33 % Computer : n008.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 17:22:24 EDT 2023
% 0.12/0.33 % CPUTime :
% 203.83/197.90
% 203.83/197.90 /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 203.83/197.90 Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 203.83/197.90 %-----------------------------------------------------
% 203.83/197.90 ncf(matrix, plain, [(1067 ^ _201938) ^ [] : [-(xk = sdtasdt0(xr, sdtsldt0(xk, xr)))], (1069 ^ _201938) ^ [] : [-(aNaturalNumber0(sdtsldt0(xn, xr)))], (1071 ^ _201938) ^ [] : [-(xn = sdtasdt0(xr, sdtsldt0(xn, xr)))], (1073 ^ _201938) ^ [] : [sdtasdt0(xp, sdtsldt0(xk, xr)) = sdtasdt0(sdtsldt0(xn, xr), xm)], (1065 ^ _201938) ^ [] : [-(aNaturalNumber0(sdtsldt0(xk, xr)))], !, (930 ^ _169303) ^ [] : [-(sdtpldt0(xn, 926 ^ []) = xp)], (714 ^ _169303) ^ [_190950, _190952] : [aNaturalNumber0(_190952), aNaturalNumber0(_190950), -(_190952 = sz00), doDivides0(_190952, _190950), 729 ^ _169303 : [(730 ^ _169303) ^ [_191360] : [aNaturalNumber0(_191360), -(sdtasdt0(_191360, sdtsldt0(_190950, _190952)) = sdtsldt0(sdtasdt0(_191360, _190950), _190952))]]], (266 ^ _169303) ^ [_177849] : [aNaturalNumber0(_177849), -(_177849 = sz00), 273 ^ _169303 : [(274 ^ _169303) ^ [_178111, _178113] : [aNaturalNumber0(_178113), aNaturalNumber0(_178111), 283 ^ _169303 : [(286 ^ _169303) ^ [] : [sdtasdt0(_178113, _177849) = sdtasdt0(_178111, _177849)], (284 ^ _169303) ^ [] : [sdtasdt0(_177849, _178113) = sdtasdt0(_177849, _178111)]], -(_178113 = _178111)]]], (1049 ^ _169303) ^ [] : [-(sdtpldt0(sdtsldt0(xn, xr), 1045 ^ []) = xn)], (148 ^ _169303) ^ [_174111, _174113] : [-(aNaturalNumber0(sdtasdt0(_174113, _174111))), aNaturalNumber0(_174113), aNaturalNumber0(_174111)], (72 ^ _169303) ^ [_171658, _171660] : [-(aNaturalNumber0(_171658)), _171660 = _171658, aNaturalNumber0(_171660)], (949 ^ _169303) ^ [] : [xk = sz00], (519 ^ _169303) ^ [_185448, _185450] : [aNaturalNumber0(_185450), aNaturalNumber0(_185448), -(_185450 = sz00), -(sdtlseqdt0(_185448, sdtasdt0(_185448, _185450)))], (122 ^ _169303) ^ [_173383] : [aNaturalNumber0(_173383), true___, -(true___)], (960 ^ _169303) ^ [] : [-(aNaturalNumber0(958 ^ []))], (551 ^ _169303) ^ [_186303, _186305] : [aNaturalNumber0(_186305), aNaturalNumber0(_186303), -(iLess0(_186305, _186303)), -(_186305 = _186303), sdtlseqdt0(_186305, _186303)], (290 ^ _169303) ^ [_178622, _178624] : [aNaturalNumber0(_178624), aNaturalNumber0(_178622), sdtpldt0(_178624, _178622) = sz00, 301 ^ _169303 : [(304 ^ _169303) ^ [] : [-(_178622 = sz00)], (302 ^ _169303) ^ [] : [-(_178624 = sz00)]]], (998 ^ _169303) ^ [] : [-(aNaturalNumber0(996 ^ []))], (1013 ^ _169303) ^ [] : [1015 ^ _169303 : [(1020 ^ _169303) ^ [] : [-(doDivides0(xr, xn))], (1018 ^ _169303) ^ [] : [-(xn = sdtasdt0(xr, 1014 ^ []))], (1016 ^ _169303) ^ [] : [-(aNaturalNumber0(1014 ^ []))]], 1022 ^ _169303 : [(1027 ^ _169303) ^ [] : [-(doDivides0(xr, xm))], (1025 ^ _169303) ^ [] : [-(xm = sdtasdt0(xr, 1021 ^ []))], (1023 ^ _169303) ^ [] : [-(aNaturalNumber0(1021 ^ []))]]], (1040 ^ _169303) ^ [] : [sdtsldt0(xn, xr) = xn], (917 ^ _169303) ^ [_197331] : [aNaturalNumber0(_197331), sdtpldt0(xp, _197331) = xm], (802 ^ _169303) ^ [] : [-(aNaturalNumber0(xn))], (736 ^ _169303) ^ [_191601] : [aNaturalNumber0(_191601), 739 ^ _169303 : [(740 ^ _169303) ^ [] : [isPrime0(_191601), 743 ^ _169303 : [(748 ^ _169303) ^ [_191993] : [aNaturalNumber0(_191993), doDivides0(_191993, _191601), -(_191993 = sz10), -(_191993 = _191601)], (746 ^ _169303) ^ [] : [_191601 = sz10], (744 ^ _169303) ^ [] : [_191601 = sz00]]], (762 ^ _169303) ^ [] : [-(isPrime0(_191601)), -(_191601 = sz00), -(_191601 = sz10), 772 ^ _169303 : [(779 ^ _169303) ^ [] : [771 ^ [_191601] = _191601], (773 ^ _169303) ^ [] : [-(aNaturalNumber0(771 ^ [_191601]))], (777 ^ _169303) ^ [] : [771 ^ [_191601] = sz10], (775 ^ _169303) ^ [] : [-(doDivides0(771 ^ [_191601], _191601))]]]]], (943 ^ _169303) ^ [] : [-(aNaturalNumber0(xk))], (1032 ^ _169303) ^ [] : [-(xn = sdtasdt0(xr, 1028 ^ []))], (569 ^ _169303) ^ [_186781, _186783] : [aNaturalNumber0(_186783), aNaturalNumber0(_186781), 576 ^ _169303 : [(586 ^ _169303) ^ [] : [-(doDivides0(_186783, _186781)), 587 ^ _169303 : [(588 ^ _169303) ^ [_187341] : [aNaturalNumber0(_187341), _186781 = sdtasdt0(_186783, _187341)]]], (577 ^ _169303) ^ [] : [doDivides0(_186783, _186781), 581 ^ _169303 : [(584 ^ _169303) ^ [] : [-(_186781 = sdtasdt0(_186783, 580 ^ [_186781, _186783]))], (582 ^ _169303) ^ [] : [-(aNaturalNumber0(580 ^ [_186781, _186783]))]]]]], (136 ^ _169303) ^ [] : [sz10 = sz00], (1034 ^ _169303) ^ [] : [-(doDivides0(xr, xn))], (405 ^ _169303) ^ [_182033, _182035, _182037] : [aNaturalNumber0(_182037), aNaturalNumber0(_182035), aNaturalNumber0(_182033), -(sdtlseqdt0(_182037, _182033)), sdtlseqdt0(_182037, _182035), sdtlseqdt0(_182035, _182033)], (4 ^ _169303) ^ [_169534, _169536] : [_169536 = _169534, -(_169534 = _169536)], (966 ^ _169303) ^ [] : [xr = sz00], (1000 ^ _169303) ^ [] : [-(sdtasdt0(xn, xm) = sdtasdt0(xr, 996 ^ []))], (928 ^ _169303) ^ [] : [-(aNaturalNumber0(926 ^ []))], (1036 ^ _169303) ^ [] : [-(aNaturalNumber0(sdtsldt0(xn, xr)))], (246 ^ _169303) ^ [_177272, _177274, _177276] : [259 ^ _169303 : [(262 ^ _169303) ^ [] : [sdtpldt0(_177274, _177276) = sdtpldt0(_177272, _177276)], (260 ^ _169303) ^ [] : [sdtpldt0(_177276, _177274) = sdtpldt0(_177276, _177272)]], -(_177274 = _177272), aNaturalNumber0(_177276), aNaturalNumber0(_177274), aNaturalNumber0(_177272)], (214 ^ _169303) ^ [_176151] : [aNaturalNumber0(_176151), 217 ^ _169303 : [(220 ^ _169303) ^ [] : [-(_176151 = sdtasdt0(sz10, _176151))], (218 ^ _169303) ^ [] : [-(sdtasdt0(_176151, sz10) = _176151)]]], (903 ^ _169303) ^ [] : [-(aNaturalNumber0(901 ^ []))], (900 ^ _169303) ^ [] : [-(isPrime0(xp))], (878 ^ _169303) ^ [] : [xp = sz10], (1038 ^ _169303) ^ [] : [-(xn = sdtasdt0(xr, sdtsldt0(xn, xr)))], (158 ^ _169303) ^ [_174410, _174412] : [-(sdtpldt0(_174412, _174410) = sdtpldt0(_174410, _174412)), aNaturalNumber0(_174412), aNaturalNumber0(_174410)], (168 ^ _169303) ^ [_174731, _174733, _174735] : [-(sdtpldt0(sdtpldt0(_174735, _174733), _174731) = sdtpldt0(_174735, sdtpldt0(_174733, _174731))), aNaturalNumber0(_174735), aNaturalNumber0(_174733), aNaturalNumber0(_174731)], (44 ^ _169303) ^ [_170818, _170820, _170822, _170824] : [-(doDivides0(_170822, _170818)), doDivides0(_170824, _170820), _170824 = _170822, _170820 = _170818], (880 ^ _169303) ^ [_196223] : [-(_196223 = sz10), -(_196223 = xp), aNaturalNumber0(_196223), 885 ^ _169303 : [(886 ^ _169303) ^ [_196426] : [aNaturalNumber0(_196426), xp = sdtasdt0(_196223, _196426)], (892 ^ _169303) ^ [] : [doDivides0(_196223, xp)]]], (925 ^ _169303) ^ [] : [xn = xp], (804 ^ _169303) ^ [] : [-(aNaturalNumber0(xm))], (58 ^ _169303) ^ [_171262, _171264, _171266, _171268] : [-(sdtlseqdt0(_171266, _171262)), sdtlseqdt0(_171268, _171264), _171268 = _171266, _171264 = _171262], (324 ^ _169303) ^ [_179571, _179573] : [aNaturalNumber0(_179573), aNaturalNumber0(_179571), 331 ^ _169303 : [(341 ^ _169303) ^ [] : [-(sdtlseqdt0(_179573, _179571)), 342 ^ _169303 : [(343 ^ _169303) ^ [_180131] : [aNaturalNumber0(_180131), sdtpldt0(_179573, _180131) = _179571]]], (332 ^ _169303) ^ [] : [sdtlseqdt0(_179573, _179571), 336 ^ _169303 : [(339 ^ _169303) ^ [] : [-(sdtpldt0(_179573, 335 ^ [_179571, _179573]) = _179571)], (337 ^ _169303) ^ [] : [-(aNaturalNumber0(335 ^ [_179571, _179573]))]]]]], (10 ^ _169303) ^ [_169738, _169740, _169742] : [-(_169742 = _169738), _169742 = _169740, _169740 = _169738], (82 ^ _169303) ^ [_171995, _171997, _171999, _172001] : [-(sdtmndt0(_172001, _171997) = sdtmndt0(_171999, _171995)), _172001 = _171999, _171997 = _171995], (1047 ^ _169303) ^ [] : [-(aNaturalNumber0(1045 ^ []))], (1063 ^ _169303) ^ [] : [-(sdtasdt0(xn, xm) = sdtasdt0(sdtsldt0(sdtasdt0(xp, xk), xr), xr))], (955 ^ _169303) ^ [] : [xk = sz10], (951 ^ _169303) ^ [] : [xk = sz10], (1057 ^ _169303) ^ [] : [-(sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr) = sdtasdt0(xn, xm))], (995 ^ _169303) ^ [] : [-(sdtpldt0(xr, 991 ^ []) = xk)], (915 ^ _169303) ^ [] : [sdtlseqdt0(xp, xn)], (1044 ^ _169303) ^ [] : [-(xn = sdtasdt0(xr, sdtsldt0(xn, xr)))], (990 ^ _169303) ^ [] : [-(isPrime0(xr))], (230 ^ _169303) ^ [_176725, _176727, _176729] : [241 ^ _169303 : [(244 ^ _169303) ^ [] : [-(sdtasdt0(sdtpldt0(_176727, _176725), _176729) = sdtpldt0(sdtasdt0(_176727, _176729), sdtasdt0(_176725, _176729)))], (242 ^ _169303) ^ [] : [-(sdtasdt0(_176729, sdtpldt0(_176727, _176725)) = sdtpldt0(sdtasdt0(_176729, _176727), sdtasdt0(_176729, _176725)))]], aNaturalNumber0(_176729), aNaturalNumber0(_176727), aNaturalNumber0(_176725)], (182 ^ _169303) ^ [_175137] : [aNaturalNumber0(_175137), 185 ^ _169303 : [(188 ^ _169303) ^ [] : [-(_175137 = sdtpldt0(sz00, _175137))], (186 ^ _169303) ^ [] : [-(sdtpldt0(_175137, sz00) = _175137)]]], (1007 ^ _169303) ^ [] : [-(aNaturalNumber0(1005 ^ []))], (1042 ^ _169303) ^ [] : [-(aNaturalNumber0(sdtsldt0(xn, xr)))], (134 ^ _169303) ^ [] : [-(aNaturalNumber0(sz10))], (962 ^ _169303) ^ [] : [-(xk = sdtasdt0(xr, 958 ^ []))], (652 ^ _169303) ^ [_189274, _189276, _189278] : [aNaturalNumber0(_189278), aNaturalNumber0(_189276), aNaturalNumber0(_189274), -(doDivides0(_189278, sdtpldt0(_189276, _189274))), doDivides0(_189278, _189276), doDivides0(_189278, _189274)], (200 ^ _169303) ^ [_175745, _175747, _175749] : [-(sdtasdt0(sdtasdt0(_175749, _175747), _175745) = sdtasdt0(_175749, sdtasdt0(_175747, _175745))), aNaturalNumber0(_175749), aNaturalNumber0(_175747), aNaturalNumber0(_175745)], (674 ^ _169303) ^ [_189880, _189882, _189884] : [aNaturalNumber0(_189884), aNaturalNumber0(_189882), aNaturalNumber0(_189880), -(doDivides0(_189884, _189880)), doDivides0(_189884, _189882), doDivides0(_189884, sdtpldt0(_189882, _189880))], (222 ^ _169303) ^ [_176424] : [aNaturalNumber0(_176424), 225 ^ _169303 : [(228 ^ _169303) ^ [] : [-(sz00 = sdtasdt0(sz00, _176424))], (226 ^ _169303) ^ [] : [-(sdtasdt0(_176424, sz00) = sz00)]]], (1055 ^ _169303) ^ [] : [-(xn = sdtasdt0(xr, sdtsldt0(xn, xr)))], (381 ^ _169303) ^ [_181342] : [aNaturalNumber0(_181342), -(sdtlseqdt0(_181342, _181342))], (533 ^ _169303) ^ [_185843, _185845] : [aNaturalNumber0(_185845), aNaturalNumber0(_185843), iLess0(_185845, _185843), true___, -(true___)], (1059 ^ _169303) ^ [] : [-(aNaturalNumber0(sdtsldt0(sdtasdt0(xp, xk), xr)))], (923 ^ _169303) ^ [] : [sdtlseqdt0(xp, xm)], (306 ^ _169303) ^ [_179089, _179091] : [aNaturalNumber0(_179091), aNaturalNumber0(_179089), sdtasdt0(_179091, _179089) = sz00, -(_179091 = sz00), -(_179089 = sz00)], (443 ^ _169303) ^ [_183082, _183084] : [aNaturalNumber0(_183084), aNaturalNumber0(_183082), -(_183084 = _183082), sdtlseqdt0(_183084, _183082), 458 ^ _169303 : [(459 ^ _169303) ^ [_183526] : [aNaturalNumber0(_183526), 462 ^ _169303 : [(469 ^ _169303) ^ [] : [-(sdtlseqdt0(sdtpldt0(_183084, _183526), sdtpldt0(_183082, _183526)))], (463 ^ _169303) ^ [] : [sdtpldt0(_183526, _183084) = sdtpldt0(_183526, _183082)], (467 ^ _169303) ^ [] : [sdtpldt0(_183084, _183526) = sdtpldt0(_183082, _183526)], (465 ^ _169303) ^ [] : [-(sdtlseqdt0(sdtpldt0(_183526, _183084), sdtpldt0(_183526, _183082)))]]]]], (1051 ^ _169303) ^ [] : [-(sdtlseqdt0(sdtsldt0(xn, xr), xn))], (1002 ^ _169303) ^ [] : [-(doDivides0(xr, sdtasdt0(xn, xm)))], (905 ^ _169303) ^ [] : [-(sdtasdt0(xn, xm) = sdtasdt0(xp, 901 ^ []))], (947 ^ _169303) ^ [] : [-(xk = sdtsldt0(sdtasdt0(xn, xm), xp))], (808 ^ _169303) ^ [_193712, _193714, _193716] : [aNaturalNumber0(_193716), aNaturalNumber0(_193714), aNaturalNumber0(_193712), iLess0(sdtpldt0(sdtpldt0(_193716, _193714), _193712), sdtpldt0(sdtpldt0(xn, xm), xp)), 862 ^ _169303 : [(867 ^ _169303) ^ [] : [-(doDivides0(_193712, _193716))], (865 ^ _169303) ^ [] : [-(_193716 = sdtasdt0(_193712, 861 ^ [_193712, _193714, _193716]))], (863 ^ _169303) ^ [] : [-(aNaturalNumber0(861 ^ [_193712, _193714, _193716]))]], 869 ^ _169303 : [(874 ^ _169303) ^ [] : [-(doDivides0(_193712, _193714))], (872 ^ _169303) ^ [] : [-(_193714 = sdtasdt0(_193712, 868 ^ [_193712, _193714, _193716]))], (870 ^ _169303) ^ [] : [-(aNaturalNumber0(868 ^ [_193712, _193714, _193716]))]], 847 ^ _169303 : [(848 ^ _169303) ^ [_195133] : [aNaturalNumber0(_195133), sdtasdt0(_193716, _193714) = sdtasdt0(_193712, _195133)], (854 ^ _169303) ^ [] : [doDivides0(_193712, sdtasdt0(_193716, _193714))]], 823 ^ _169303 : [(824 ^ _169303) ^ [] : [-(_193712 = sz00), -(_193712 = sz10), 832 ^ _169303 : [(842 ^ _169303) ^ [] : [831 ^ [_193712, _193714, _193716] = sz10], (840 ^ _169303) ^ [] : [-(doDivides0(831 ^ [_193712, _193714, _193716], _193712))], (844 ^ _169303) ^ [] : [831 ^ [_193712, _193714, _193716] = _193712], (833 ^ _169303) ^ [] : [-(aNaturalNumber0(831 ^ [_193712, _193714, _193716]))], (836 ^ _169303) ^ [] : [-(aNaturalNumber0(834 ^ [_193712, _193714, _193716]))], (838 ^ _169303) ^ [] : [-(_193712 = sdtasdt0(831 ^ [_193712, _193714, _193716], 834 ^ [_193712, _193714, _193716]))]]], (846 ^ _169303) ^ [] : [isPrime0(_193712)]]], (1053 ^ _169303) ^ [] : [-(aNaturalNumber0(sdtsldt0(xn, xr)))], (968 ^ _169303) ^ [] : [xr = sz10], (2 ^ _169303) ^ [_169427] : [-(_169427 = _169427)], (957 ^ _169303) ^ [] : [-(aNaturalNumber0(xr))], (471 ^ _169303) ^ [_184050, _184052, _184054] : [aNaturalNumber0(_184054), aNaturalNumber0(_184052), aNaturalNumber0(_184050), 494 ^ _169303 : [(501 ^ _169303) ^ [] : [-(sdtlseqdt0(sdtasdt0(_184052, _184054), sdtasdt0(_184050, _184054)))], (495 ^ _169303) ^ [] : [sdtasdt0(_184054, _184052) = sdtasdt0(_184054, _184050)], (499 ^ _169303) ^ [] : [sdtasdt0(_184052, _184054) = sdtasdt0(_184050, _184054)], (497 ^ _169303) ^ [] : [-(sdtlseqdt0(sdtasdt0(_184054, _184052), sdtasdt0(_184054, _184050)))]], -(_184054 = sz00), -(_184052 = _184050), sdtlseqdt0(_184052, _184050)], (34 ^ _169303) ^ [_170495, _170497] : [-(isPrime0(_170495)), _170497 = _170495, isPrime0(_170497)], (92 ^ _169303) ^ [_172354, _172356, _172358, _172360] : [-(sdtpldt0(_172360, _172356) = sdtpldt0(_172358, _172354)), _172360 = _172358, _172356 = _172354], (351 ^ _169303) ^ [_180414, _180416] : [aNaturalNumber0(_180416), aNaturalNumber0(_180414), sdtlseqdt0(_180416, _180414), 362 ^ _169303 : [(371 ^ _169303) ^ [_181020] : [-(_181020 = sdtmndt0(_180414, _180416)), aNaturalNumber0(_181020), sdtpldt0(_180416, _181020) = _180414], (363 ^ _169303) ^ [_180761] : [_180761 = sdtmndt0(_180414, _180416), 366 ^ _169303 : [(369 ^ _169303) ^ [] : [-(sdtpldt0(_180416, _180761) = _180414)], (367 ^ _169303) ^ [] : [-(aNaturalNumber0(_180761))]]]]], (1030 ^ _169303) ^ [] : [-(aNaturalNumber0(1028 ^ []))], (937 ^ _169303) ^ [] : [-(aNaturalNumber0(935 ^ []))], (102 ^ _169303) ^ [_172713, _172715, _172717, _172719] : [-(sdtasdt0(_172719, _172715) = sdtasdt0(_172717, _172713)), _172719 = _172717, _172715 = _172713], (964 ^ _169303) ^ [] : [-(doDivides0(xr, xk))], (1004 ^ _169303) ^ [] : [xk = xp], (907 ^ _169303) ^ [] : [-(doDivides0(xp, sdtasdt0(xn, xm)))], (696 ^ _169303) ^ [_190472, _190474] : [aNaturalNumber0(_190474), aNaturalNumber0(_190472), -(sdtlseqdt0(_190474, _190472)), doDivides0(_190474, _190472), -(_190472 = sz00)], (132 ^ _169303) ^ [] : [-(aNaturalNumber0(sz00))], (387 ^ _169303) ^ [_181544, _181546] : [aNaturalNumber0(_181546), aNaturalNumber0(_181544), -(_181546 = _181544), sdtlseqdt0(_181546, _181544), sdtlseqdt0(_181544, _181546)], (953 ^ _169303) ^ [] : [xk = sz00], (909 ^ _169303) ^ [_197084] : [aNaturalNumber0(_197084), sdtpldt0(xp, _197084) = xn], (20 ^ _169303) ^ [_170079, _170081, _170083, _170085] : [-(iLess0(_170083, _170079)), iLess0(_170085, _170081), _170085 = _170083, _170081 = _170079], (945 ^ _169303) ^ [] : [-(sdtasdt0(xn, xm) = sdtasdt0(xp, xk))], (876 ^ _169303) ^ [] : [xp = sz00], (1011 ^ _169303) ^ [] : [-(sdtlseqdt0(xk, xp))], (503 ^ _169303) ^ [_185000] : [aNaturalNumber0(_185000), -(_185000 = sz00), -(_185000 = sz10), 514 ^ _169303 : [(517 ^ _169303) ^ [] : [-(sdtlseqdt0(sz10, _185000))], (515 ^ _169303) ^ [] : [sz10 = _185000]]], (630 ^ _169303) ^ [_188674, _188676, _188678] : [aNaturalNumber0(_188678), aNaturalNumber0(_188676), aNaturalNumber0(_188674), -(doDivides0(_188678, _188674)), doDivides0(_188678, _188676), doDivides0(_188676, _188674)], (783 ^ _169303) ^ [_192945] : [795 ^ _169303 : [(800 ^ _169303) ^ [] : [-(isPrime0(794 ^ [_192945]))], (798 ^ _169303) ^ [] : [-(doDivides0(794 ^ [_192945], _192945))], (796 ^ _169303) ^ [] : [-(aNaturalNumber0(794 ^ [_192945]))]], aNaturalNumber0(_192945), -(_192945 = sz00), -(_192945 = sz10)], (1061 ^ _169303) ^ [] : [-(sdtasdt0(xp, xk) = sdtasdt0(xr, sdtsldt0(sdtasdt0(xp, xk), xr)))], (112 ^ _169303) ^ [_173052, _173054, _173056, _173058] : [-(sdtsldt0(_173058, _173054) = sdtsldt0(_173056, _173052)), _173058 = _173056, _173054 = _173052], (993 ^ _169303) ^ [] : [-(aNaturalNumber0(991 ^ []))], (427 ^ _169303) ^ [_182619, _182621] : [aNaturalNumber0(_182621), aNaturalNumber0(_182619), -(sdtlseqdt0(_182621, _182619)), 438 ^ _169303 : [(441 ^ _169303) ^ [] : [-(sdtlseqdt0(_182619, _182621))], (439 ^ _169303) ^ [] : [_182619 = _182621]]], (138 ^ _169303) ^ [_173812, _173814] : [-(aNaturalNumber0(sdtpldt0(_173814, _173812))), aNaturalNumber0(_173814), aNaturalNumber0(_173812)], (970 ^ _169303) ^ [_198846] : [-(_198846 = sz10), -(_198846 = xr), aNaturalNumber0(_198846), 975 ^ _169303 : [(976 ^ _169303) ^ [_199049] : [aNaturalNumber0(_199049), xr = sdtasdt0(_198846, _199049)], (982 ^ _169303) ^ [] : [doDivides0(_198846, xr)]]], (806 ^ _169303) ^ [] : [-(aNaturalNumber0(xp))], (1009 ^ _169303) ^ [] : [-(sdtpldt0(xk, 1005 ^ []) = xp)], (932 ^ _169303) ^ [] : [-(sdtlseqdt0(xn, xp))], (934 ^ _169303) ^ [] : [xm = xp], (941 ^ _169303) ^ [] : [-(sdtlseqdt0(xm, xp))], (939 ^ _169303) ^ [] : [-(sdtpldt0(xm, 935 ^ []) = xp)], (190 ^ _169303) ^ [_175424, _175426] : [-(sdtasdt0(_175426, _175424) = sdtasdt0(_175424, _175426)), aNaturalNumber0(_175426), aNaturalNumber0(_175424)], (596 ^ _169303) ^ [_187624, _187626] : [aNaturalNumber0(_187626), aNaturalNumber0(_187624), -(_187626 = sz00), doDivides0(_187626, _187624), 611 ^ _169303 : [(620 ^ _169303) ^ [_188322] : [-(_188322 = sdtsldt0(_187624, _187626)), aNaturalNumber0(_188322), _187624 = sdtasdt0(_187626, _188322)], (612 ^ _169303) ^ [_188063] : [_188063 = sdtsldt0(_187624, _187626), 615 ^ _169303 : [(618 ^ _169303) ^ [] : [-(_187624 = sdtasdt0(_187626, _188063))], (616 ^ _169303) ^ [] : [-(aNaturalNumber0(_188063))]]]]]], input).
% 203.83/197.90 ncf('1',plain,[-(xk = sdtasdt0(xr, sdtsldt0(xk, xr)))],start(1067 ^ 0)).
% 203.83/197.90 ncf('1.1',plain,[xk = sdtasdt0(xr, sdtsldt0(xk, xr)), -(sdtpldt0(xk, sdtsldt0(sdtasdt0(xp, xk), xr)) = sdtpldt0(sdtasdt0(xr, sdtsldt0(xk, xr)), sdtasdt0(sdtsldt0(xn, xr), xm))), sdtsldt0(sdtasdt0(xp, xk), xr) = sdtasdt0(sdtsldt0(xn, xr), xm)],extension(92 ^ 1,bind([[_172354, _172356, _172358, _172360], [sdtasdt0(sdtsldt0(xn, xr), xm), sdtsldt0(sdtasdt0(xp, xk), xr), sdtasdt0(xr, sdtsldt0(xk, xr)), xk]]))).
% 203.83/197.90 ncf('1.1.1',plain,[sdtpldt0(xk, sdtsldt0(sdtasdt0(xp, xk), xr)) = sdtpldt0(sdtasdt0(xr, sdtsldt0(xk, xr)), sdtasdt0(sdtsldt0(xn, xr), xm)), -(sdtpldt0(sdtasdt0(xr, sdtsldt0(xk, xr)), sdtasdt0(xp, sdtsldt0(xk, xr))) = sdtpldt0(sdtasdt0(xr, sdtsldt0(xk, xr)), sdtasdt0(sdtsldt0(xn, xr), xm))), sdtpldt0(sdtasdt0(xr, sdtsldt0(xk, xr)), sdtasdt0(xp, sdtsldt0(xk, xr))) = sdtpldt0(xk, sdtsldt0(sdtasdt0(xp, xk), xr))],extension(10 ^ 2,bind([[_169738, _169740, _169742], [sdtpldt0(sdtasdt0(xr, sdtsldt0(xk, xr)), sdtasdt0(sdtsldt0(xn, xr), xm)), sdtpldt0(xk, sdtsldt0(sdtasdt0(xp, xk), xr)), sdtpldt0(sdtasdt0(xr, sdtsldt0(xk, xr)), sdtasdt0(xp, sdtsldt0(xk, xr)))]]))).
% 203.83/197.90 ncf('1.1.1.1',plain,[sdtpldt0(sdtasdt0(xr, sdtsldt0(xk, xr)), sdtasdt0(xp, sdtsldt0(xk, xr))) = sdtpldt0(sdtasdt0(xr, sdtsldt0(xk, xr)), sdtasdt0(sdtsldt0(xn, xr), xm)), -(sdtasdt0(xp, sdtsldt0(xk, xr)) = sdtasdt0(sdtsldt0(xn, xr), xm)), aNaturalNumber0(sdtasdt0(xr, sdtsldt0(xk, xr))), aNaturalNumber0(sdtasdt0(xp, sdtsldt0(xk, xr))), aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm))],extension(246 ^ 3,bind([[_177272, _177274, _177276], [sdtasdt0(sdtsldt0(xn, xr), xm), sdtasdt0(xp, sdtsldt0(xk, xr)), sdtasdt0(xr, sdtsldt0(xk, xr))]]))).
% 203.83/197.90 ncf('1.1.1.1.1',plain,[sdtasdt0(xp, sdtsldt0(xk, xr)) = sdtasdt0(sdtsldt0(xn, xr), xm)],extension(1073 ^ 4)).
% 203.83/197.90 ncf('1.1.1.1.2',plain,[-(aNaturalNumber0(sdtasdt0(xr, sdtsldt0(xk, xr)))), aNaturalNumber0(xr), aNaturalNumber0(sdtsldt0(xk, xr))],extension(148 ^ 4,bind([[_174111, _174113], [sdtsldt0(xk, xr), xr]]))).
% 203.83/197.90 ncf('1.1.1.1.2.1',plain,[-(aNaturalNumber0(xr))],extension(957 ^ 5)).
% 203.83/197.90 ncf('1.1.1.1.2.2',plain,[-(aNaturalNumber0(sdtsldt0(xk, xr)))],extension(1065 ^ 5)).
% 203.83/197.90 ncf('1.1.1.1.3',plain,[-(aNaturalNumber0(sdtasdt0(xp, sdtsldt0(xk, xr)))), aNaturalNumber0(xp), aNaturalNumber0(sdtsldt0(xk, xr))],extension(148 ^ 4,bind([[_174111, _174113], [sdtsldt0(xk, xr), xp]]))).
% 203.83/197.90 ncf('1.1.1.1.3.1',plain,[-(aNaturalNumber0(xp))],extension(806 ^ 5)).
% 203.83/197.90 ncf('1.1.1.1.3.2',plain,[-(aNaturalNumber0(sdtsldt0(xk, xr)))],extension(1065 ^ 5)).
% 203.83/197.90 ncf('1.1.1.1.4',plain,[-(aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm))), aNaturalNumber0(sdtsldt0(xn, xr)), aNaturalNumber0(xm)],extension(148 ^ 4,bind([[_174111, _174113], [xm, sdtsldt0(xn, xr)]]))).
% 203.83/197.90 ncf('1.1.1.1.4.1',plain,[-(aNaturalNumber0(sdtsldt0(xn, xr)))],extension(1069 ^ 5)).
% 203.83/197.90 ncf('1.1.1.1.4.2',plain,[-(aNaturalNumber0(xm))],extension(804 ^ 5)).
% 203.83/197.90 ncf('1.1.1.2',plain,[-(sdtpldt0(sdtasdt0(xr, sdtsldt0(xk, xr)), sdtasdt0(xp, sdtsldt0(xk, xr))) = sdtpldt0(xk, sdtsldt0(sdtasdt0(xp, xk), xr))), sdtasdt0(xr, sdtsldt0(xk, xr)) = xk, sdtasdt0(xp, sdtsldt0(xk, xr)) = sdtsldt0(sdtasdt0(xp, xk), xr)],extension(92 ^ 3,bind([[_172354, _172356, _172358, _172360], [sdtsldt0(sdtasdt0(xp, xk), xr), sdtasdt0(xp, sdtsldt0(xk, xr)), xk, sdtasdt0(xr, sdtsldt0(xk, xr))]]))).
% 203.83/197.90 ncf('1.1.1.2.1',plain,[-(sdtasdt0(xr, sdtsldt0(xk, xr)) = xk), xk = sdtasdt0(xr, sdtsldt0(xk, xr))],extension(4 ^ 4,bind([[_169534, _169536], [sdtasdt0(xr, sdtsldt0(xk, xr)), xk]]))).
% 203.83/197.90 ncf('1.1.1.2.1.1',plain,[-(xk = sdtasdt0(xr, sdtsldt0(xk, xr)))],reduction('1')).
% 203.83/197.90 ncf('1.1.1.2.2',plain,[-(sdtasdt0(xp, sdtsldt0(xk, xr)) = sdtsldt0(sdtasdt0(xp, xk), xr)), 730 : aNaturalNumber0(xp), 730 : aNaturalNumber0(xr), 730 : aNaturalNumber0(xk), 730 : -(xr = sz00), 730 : doDivides0(xr, xk)],extension(714 ^ 4,bind([[_190950, _190952, _191360], [xk, xr, xp]]))).
% 203.83/197.90 ncf('1.1.1.2.2.1',plain,[-(aNaturalNumber0(xp))],extension(806 ^ 7)).
% 203.83/197.90 ncf('1.1.1.2.2.2',plain,[-(aNaturalNumber0(xr))],extension(957 ^ 5)).
% 203.83/197.90 ncf('1.1.1.2.2.3',plain,[-(aNaturalNumber0(xk))],extension(943 ^ 5)).
% 203.83/197.90 ncf('1.1.1.2.2.4',plain,[xr = sz00],extension(966 ^ 5)).
% 203.83/197.90 ncf('1.1.1.2.2.5',plain,[-(doDivides0(xr, xk))],extension(964 ^ 5)).
% 203.83/197.90 ncf('1.1.2',plain,[-(sdtsldt0(sdtasdt0(xp, xk), xr) = sdtasdt0(sdtsldt0(xn, xr), xm)), 274 : aNaturalNumber0(sdtsldt0(sdtasdt0(xp, xk), xr)), 274 : aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm)), 286 : sdtasdt0(sdtsldt0(sdtasdt0(xp, xk), xr), xr) = sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr), 274 : aNaturalNumber0(xr), 274 : -(xr = sz00)],extension(266 ^ 2,bind([[_177849, _178111, _178113], [xr, sdtasdt0(sdtsldt0(xn, xr), xm), sdtsldt0(sdtasdt0(xp, xk), xr)]]))).
% 203.83/197.90 ncf('1.1.2.1',plain,[-(aNaturalNumber0(sdtsldt0(sdtasdt0(xp, xk), xr))), sdtasdt0(xp, sdtsldt0(xk, xr)) = sdtsldt0(sdtasdt0(xp, xk), xr), aNaturalNumber0(sdtasdt0(xp, sdtsldt0(xk, xr)))],extension(72 ^ 5,bind([[_171658, _171660], [sdtsldt0(sdtasdt0(xp, xk), xr), sdtasdt0(xp, sdtsldt0(xk, xr))]]))).
% 203.83/197.90 ncf('1.1.2.1.1',plain,[-(sdtasdt0(xp, sdtsldt0(xk, xr)) = sdtsldt0(sdtasdt0(xp, xk), xr)), 730 : aNaturalNumber0(xp), 730 : aNaturalNumber0(xr), 730 : aNaturalNumber0(xk), 730 : -(xr = sz00), 730 : doDivides0(xr, xk)],extension(714 ^ 6,bind([[_190950, _190952, _191360], [xk, xr, xp]]))).
% 203.83/197.90 ncf('1.1.2.1.1.1',plain,[-(aNaturalNumber0(xp))],extension(806 ^ 9)).
% 203.83/197.90 ncf('1.1.2.1.1.2',plain,[-(aNaturalNumber0(xr))],extension(957 ^ 7)).
% 203.83/197.90 ncf('1.1.2.1.1.3',plain,[-(aNaturalNumber0(xk))],extension(943 ^ 7)).
% 203.83/197.90 ncf('1.1.2.1.1.4',plain,[xr = sz00],extension(966 ^ 7)).
% 203.83/197.90 ncf('1.1.2.1.1.5',plain,[-(doDivides0(xr, xk))],extension(964 ^ 7)).
% 203.83/197.90 ncf('1.1.2.1.2',plain,[-(aNaturalNumber0(sdtasdt0(xp, sdtsldt0(xk, xr)))), aNaturalNumber0(xp), aNaturalNumber0(sdtsldt0(xk, xr))],extension(148 ^ 6,bind([[_174111, _174113], [sdtsldt0(xk, xr), xp]]))).
% 203.83/197.90 ncf('1.1.2.1.2.1',plain,[-(aNaturalNumber0(xp))],extension(806 ^ 7)).
% 203.83/197.90 ncf('1.1.2.1.2.2',plain,[-(aNaturalNumber0(sdtsldt0(xk, xr)))],extension(1065 ^ 7)).
% 203.83/197.90 ncf('1.1.2.2',plain,[-(aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm))), aNaturalNumber0(sdtsldt0(xn, xr)), aNaturalNumber0(xm)],extension(148 ^ 5,bind([[_174111, _174113], [xm, sdtsldt0(xn, xr)]]))).
% 203.83/197.90 ncf('1.1.2.2.1',plain,[-(aNaturalNumber0(sdtsldt0(xn, xr)))],extension(1069 ^ 6)).
% 203.83/197.90 ncf('1.1.2.2.2',plain,[-(aNaturalNumber0(xm))],extension(804 ^ 6)).
% 203.83/197.90 ncf('1.1.2.3',plain,[-(sdtasdt0(sdtsldt0(sdtasdt0(xp, xk), xr), xr) = sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr)), sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr) = sdtasdt0(sdtsldt0(sdtasdt0(xp, xk), xr), xr)],extension(4 ^ 7,bind([[_169534, _169536], [sdtasdt0(sdtsldt0(sdtasdt0(xp, xk), xr), xr), sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr)]]))).
% 203.83/197.90 ncf('1.1.2.3.1',plain,[-(sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr) = sdtasdt0(sdtsldt0(sdtasdt0(xp, xk), xr), xr)), sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr) = sdtasdt0(xn, xm), sdtasdt0(xn, xm) = sdtasdt0(sdtsldt0(sdtasdt0(xp, xk), xr), xr)],extension(10 ^ 8,bind([[_169738, _169740, _169742], [sdtasdt0(sdtsldt0(sdtasdt0(xp, xk), xr), xr), sdtasdt0(xn, xm), sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr)]]))).
% 203.83/197.90 ncf('1.1.2.3.1.1',plain,[-(sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr) = sdtasdt0(xn, xm))],extension(1057 ^ 9)).
% 203.83/197.90 ncf('1.1.2.3.1.2',plain,[-(sdtasdt0(xn, xm) = sdtasdt0(sdtsldt0(sdtasdt0(xp, xk), xr), xr))],extension(1063 ^ 9)).
% 203.83/197.90 ncf('1.1.2.4',plain,[-(aNaturalNumber0(xr))],extension(957 ^ 3)).
% 203.83/197.90 ncf('1.1.2.5',plain,[xr = sz00, 740 : isPrime0(xr), 740 : aNaturalNumber0(xr)],extension(736 ^ 3,bind([[_191601], [xr]]))).
% 203.83/197.90 ncf('1.1.2.5.1',plain,[-(isPrime0(xr))],extension(990 ^ 6)).
% 203.83/197.90 ncf('1.1.2.5.2',plain,[-(aNaturalNumber0(xr))],lemmata('[1, 1].x')).
% 203.83/197.90 %-----------------------------------------------------
% 203.83/197.90 End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------