%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SWV178+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n021.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 12:20:07 EDT 2023

% Result   : Theorem 0.35s 1.40s
% Output   : Proof 0.35s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13  % Problem  : SWV178+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.13/0.14  % Command  : nanocop.sh %s %d
% 0.14/0.36  % Computer : n021.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Fri May 19 02:33:57 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 0.35/1.40  
% 0.35/1.40  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 0.35/1.40  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.35/1.40  %-----------------------------------------------------
% 0.35/1.40  ncf(matrix, plain, [(1162 ^ _209884) ^ [] : [-(leq(n0, 1160 ^ []))], (1164 ^ _209884) ^ [] : [-(leq(1160 ^ [], n4))], (1166 ^ _209884) ^ [] : [a_select2(sigmaold_init, 1160 ^ []) = init], (1055 ^ _209884) ^ [] : [-(leq(n0, pv40))], (1057 ^ _209884) ^ [] : [-(leq(pv40, n4))], (1059 ^ _209884) ^ [] : [-(gt(loopcounter, n1))], (1061 ^ _209884) ^ [_250359] : [leq(n0, _250359), leq(_250359, n135299), 1068 ^ _209884 : [(1069 ^ _209884) ^ [_250587] : [-(a_select3(q_init, _250359, _250587) = init), leq(n0, _250587), leq(_250587, n4)]]], (1079 ^ _209884) ^ [_250889] : [-(a_select2(rho_init, _250889) = init), leq(n0, _250889), leq(_250889, n4)], (1089 ^ _209884) ^ [_251170] : [-(a_select2(mu_init, _251170) = init), leq(n0, _251170), leq(_251170, pred(pv40))], (1099 ^ _209884) ^ [_251451] : [-(a_select2(sigma_init, _251451) = init), leq(n0, _251451), leq(_251451, pred(pv40))], (1109 ^ _209884) ^ [_251732] : [-(a_select3(center_init, _251732, n0) = init), leq(n0, _251732), leq(_251732, n4)], (1119 ^ _209884) ^ [] : [gt(loopcounter, n1), 1122 ^ _209884 : [(1123 ^ _209884) ^ [_252077] : [-(a_select2(muold_init, _252077) = init), leq(n0, _252077), leq(_252077, n4)]]], (1133 ^ _209884) ^ [] : [gt(loopcounter, n1), 1136 ^ _209884 : [(1137 ^ _209884) ^ [_252425] : [-(a_select2(rhoold_init, _252425) = init), leq(n0, _252425), leq(_252425, n4)]]], (1147 ^ _209884) ^ [] : [gt(loopcounter, n1), 1150 ^ _209884 : [(1151 ^ _209884) ^ [_252753] : [-(a_select2(sigmaold_init, _252753) = init), leq(n0, _252753), leq(_252753, n4)]]], (2 ^ _209884) ^ [_210028] : [-(_210028 = _210028)], (4 ^ _209884) ^ [_210135, _210137] : [_210137 = _210135, -(_210135 = _210137)], (10 ^ _209884) ^ [_210339, _210341, _210343] : [-(_210343 = _210339), _210343 = _210341, _210341 = _210339], (20 ^ _209884) ^ [_210680, _210682, _210684, _210686] : [-(lt(_210684, _210680)), lt(_210686, _210682), _210686 = _210684, _210682 = _210680], (34 ^ _209884) ^ [_211124, _211126, _211128, _211130] : [-(geq(_211128, _211124)), geq(_211130, _211126), _211130 = _211128, _211126 = _211124], (48 ^ _209884) ^ [_211568, _211570, _211572, _211574] : [-(gt(_211572, _211568)), gt(_211574, _211570), _211574 = _211572, _211570 = _211568], (62 ^ _209884) ^ [_211992, _211994, _211996, _211998] : [-(leq(_211996, _211992)), leq(_211998, _211994), _211998 = _211996, _211994 = _211992], (76 ^ _209884) ^ [_212448, _212450, _212452, _212454] : [-(uniform_int_rnd(_212454, _212450) = uniform_int_rnd(_212452, _212448)), _212454 = _212452, _212450 = _212448], (86 ^ _209884) ^ [_212807, _212809, _212811, _212813] : [-(tptp_const_array1(_212813, _212809) = tptp_const_array1(_212811, _212807)), _212813 = _212811, _212809 = _212807], (96 ^ _209884) ^ [_213194, _213196, _213198, _213200, _213202, _213204] : [-(tptp_const_array2(_213204, _213200, _213196) = tptp_const_array2(_213202, _213198, _213194)), _213204 = _213202, _213200 = _213198, _213196 = _213194], (110 ^ _209884) ^ [_213682, _213684, _213686, _213688] : [-(dim(_213688, _213684) = dim(_213686, _213682)), _213688 = _213686, _213684 = _213682], (120 ^ _209884) ^ [_214013, _214015] : [_214015 = _214013, -(inv(_214015) = inv(_214013))], (126 ^ _209884) ^ [_214259, _214261, _214263, _214265] : [-(tptp_msub(_214265, _214261) = tptp_msub(_214263, _214259)), _214265 = _214263, _214261 = _214259], (136 ^ _209884) ^ [_214618, _214620, _214622, _214624] : [-(tptp_madd(_214624, _214620) = tptp_madd(_214622, _214618)), _214624 = _214622, _214620 = _214618], (146 ^ _209884) ^ [_214977, _214979, _214981, _214983] : [-(tptp_mmul(_214983, _214979) = tptp_mmul(_214981, _214977)), _214983 = _214981, _214979 = _214977], (156 ^ _209884) ^ [_215308, _215310] : [_215310 = _215308, -(trans(_215310) = trans(_215308))], (162 ^ _209884) ^ [_215582, _215584, _215586, _215588, _215590, _215592] : [-(sum(_215592, _215588, _215584) = sum(_215590, _215586, _215582)), _215592 = _215590, _215588 = _215586, _215584 = _215582], (176 ^ _209884) ^ [_216070, _216072, _216074, _216076] : [-(plus(_216076, _216072) = plus(_216074, _216070)), _216076 = _216074, _216072 = _216070], (186 ^ _209884) ^ [_216429, _216431, _216433, _216435] : [-(minus(_216435, _216431) = minus(_216433, _216429)), _216435 = _216433, _216431 = _216429], (196 ^ _209884) ^ [_216844, _216846, _216848, _216850, _216852, _216854, _216856, _216858] : [-(tptp_update3(_216858, _216854, _216850, _216846) = tptp_update3(_216856, _216852, _216848, _216844)), _216858 = _216856, _216854 = _216852, _216850 = _216848, _216846 = _216844], (214 ^ _209884) ^ [_217505, _217507, _217509, _217511, _217513, _217515] : [-(tptp_update2(_217515, _217511, _217507) = tptp_update2(_217513, _217509, _217505)), _217515 = _217513, _217511 = _217509, _217507 = _217505], (228 ^ _209884) ^ [_217965, _217967] : [_217967 = _217965, -(succ(_217967) = succ(_217965))], (234 ^ _209884) ^ [_218183, _218185] : [_218185 = _218183, -(pred(_218185) = pred(_218183))], (254 ^ _209884) ^ [_218925, _218927, _218929, _218931] : [-(a_select2(_218931, _218927) = a_select2(_218929, _218925)), _218931 = _218929, _218927 = _218925], (240 ^ _209884) ^ [_218457, _218459, _218461, _218463, _218465, _218467] : [-(a_select3(_218467, _218463, _218459) = a_select3(_218465, _218461, _218457)), _218467 = _218465, _218463 = _218461, _218459 = _218457], (869 ^ _209884) ^ [] : [-(gt(n5, n4))], (871 ^ _209884) ^ [] : [-(gt(n135299, n4))], (873 ^ _209884) ^ [] : [-(gt(n135299, n5))], (875 ^ _209884) ^ [] : [-(gt(n4, tptp_minus_1))], (877 ^ _209884) ^ [] : [-(gt(n5, tptp_minus_1))], (879 ^ _209884) ^ [] : [-(gt(n135299, tptp_minus_1))], (881 ^ _209884) ^ [] : [-(gt(n0, tptp_minus_1))], (883 ^ _209884) ^ [] : [-(gt(n1, tptp_minus_1))], (885 ^ _209884) ^ [] : [-(gt(n2, tptp_minus_1))], (887 ^ _209884) ^ [] : [-(gt(n3, tptp_minus_1))], (889 ^ _209884) ^ [] : [-(gt(n4, n0))], (891 ^ _209884) ^ [] : [-(gt(n5, n0))], (893 ^ _209884) ^ [] : [-(gt(n135299, n0))], (895 ^ _209884) ^ [] : [-(gt(n1, n0))], (897 ^ _209884) ^ [] : [-(gt(n2, n0))], (899 ^ _209884) ^ [] : [-(gt(n3, n0))], (901 ^ _209884) ^ [] : [-(gt(n4, n1))], (903 ^ _209884) ^ [] : [-(gt(n5, n1))], (905 ^ _209884) ^ [] : [-(gt(n135299, n1))], (907 ^ _209884) ^ [] : [-(gt(n2, n1))], (909 ^ _209884) ^ [] : [-(gt(n3, n1))], (911 ^ _209884) ^ [] : [-(gt(n4, n2))], (913 ^ _209884) ^ [] : [-(gt(n5, n2))], (915 ^ _209884) ^ [] : [-(gt(n135299, n2))], (917 ^ _209884) ^ [] : [-(gt(n3, n2))], (919 ^ _209884) ^ [] : [-(gt(n4, n3))], (921 ^ _209884) ^ [] : [-(gt(n5, n3))], (923 ^ _209884) ^ [] : [-(gt(n135299, n3))], (925 ^ _209884) ^ [_246765] : [leq(n0, _246765), leq(_246765, n4), -(_246765 = n0), -(_246765 = n1), -(_246765 = n2), -(_246765 = n3), -(_246765 = n4)], (951 ^ _209884) ^ [_247386] : [leq(n0, _247386), leq(_247386, n5), -(_247386 = n0), -(_247386 = n1), -(_247386 = n2), -(_247386 = n3), -(_247386 = n4), -(_247386 = n5)], (981 ^ _209884) ^ [_248093] : [-(_248093 = n0), leq(n0, _248093), leq(_248093, n0)], (991 ^ _209884) ^ [_248368] : [leq(n0, _248368), leq(_248368, n1), -(_248368 = n0), -(_248368 = n1)], (1005 ^ _209884) ^ [_248731] : [leq(n0, _248731), leq(_248731, n2), -(_248731 = n0), -(_248731 = n1), -(_248731 = n2)], (1045 ^ _209884) ^ [] : [-(succ(succ(succ(succ(n0)))) = n4)], (1047 ^ _209884) ^ [] : [-(succ(succ(succ(succ(succ(n0))))) = n5)], (1049 ^ _209884) ^ [] : [-(succ(n0) = n1)], (1051 ^ _209884) ^ [] : [-(succ(succ(n0)) = n2)], (1053 ^ _209884) ^ [] : [-(succ(succ(succ(n0))) = n3)], (1023 ^ _209884) ^ [_249180] : [leq(n0, _249180), leq(_249180, n3), -(_249180 = n0), -(_249180 = n1), -(_249180 = n2), -(_249180 = n3)], (264 ^ _209884) ^ [_219356, _219358] : [-(gt(_219358, _219356)), -(gt(_219356, _219358)), -(_219358 = _219356)], (274 ^ _209884) ^ [_219671, _219673, _219675] : [-(gt(_219675, _219671)), gt(_219675, _219673), gt(_219673, _219671)], (284 ^ _209884) ^ [_219950] : [gt(_219950, _219950)], (286 ^ _209884) ^ [_220028] : [-(leq(_220028, _220028))], (288 ^ _209884) ^ [_220149, _220151, _220153] : [-(leq(_220153, _220149)), leq(_220153, _220151), leq(_220151, _220149)], (298 ^ _209884) ^ [_220487, _220489] : [lt(_220489, _220487), -(gt(_220487, _220489))], (304 ^ _209884) ^ [_220649, _220651] : [gt(_220649, _220651), -(lt(_220651, _220649))], (310 ^ _209884) ^ [_220890, _220892] : [geq(_220892, _220890), -(leq(_220890, _220892))], (316 ^ _209884) ^ [_221052, _221054] : [leq(_221052, _221054), -(geq(_221054, _221052))], (322 ^ _209884) ^ [_221264, _221266] : [gt(_221264, _221266), -(leq(_221266, _221264))], (328 ^ _209884) ^ [_221474, _221476] : [-(gt(_221474, _221476)), leq(_221476, _221474), -(_221476 = _221474)], (338 ^ _209884) ^ [_221805, _221807] : [leq(_221807, pred(_221805)), -(gt(_221805, _221807))], (344 ^ _209884) ^ [_221971, _221973] : [gt(_221971, _221973), -(leq(_221973, pred(_221971)))], (350 ^ _209884) ^ [_222158] : [-(gt(succ(_222158), _222158))], (352 ^ _209884) ^ [_222267, _222269] : [leq(_222269, _222267), -(leq(_222269, succ(_222267)))], (358 ^ _209884) ^ [_222510, _222512] : [leq(_222512, _222510), -(gt(succ(_222510), _222512))], (364 ^ _209884) ^ [_222676, _222678] : [gt(succ(_222676), _222678), -(leq(_222678, _222676))], (370 ^ _209884) ^ [_222892, _222894] : [leq(n0, _222894), -(leq(uniform_int_rnd(_222892, _222894), _222894))], (376 ^ _209884) ^ [_223108, _223110] : [leq(n0, _223110), -(leq(n0, uniform_int_rnd(_223108, _223110)))], (382 ^ _209884) ^ [_223352, _223354, _223356, _223358] : [-(a_select2(tptp_const_array1(dim(_223356, _223354), _223352), _223358) = _223352), leq(_223356, _223358), leq(_223358, _223354)], (392 ^ _209884) ^ [_223759, _223761, _223763, _223765, _223767, _223769, _223771] : [-(a_select3(tptp_const_array2(dim(_223769, _223767), dim(_223763, _223761), _223759), _223771, _223765) = _223759), leq(_223769, _223771), leq(_223771, _223767), leq(_223763, _223765), leq(_223765, _223761)], (410 ^ _209884) ^ [_224354, _224356] : [413 ^ _209884 : [(414 ^ _209884) ^ [] : [-(leq(n0, 411 ^ [_224354, _224356]))], (416 ^ _209884) ^ [] : [-(leq(411 ^ [_224354, _224356], _224354))], (418 ^ _209884) ^ [] : [-(leq(n0, 412 ^ [_224354, _224356]))], (420 ^ _209884) ^ [] : [-(leq(412 ^ [_224354, _224356], _224354))], (422 ^ _209884) ^ [] : [a_select3(_224356, 411 ^ [_224354, _224356], 412 ^ [_224354, _224356]) = a_select3(_224356, 412 ^ [_224354, _224356], 411 ^ [_224354, _224356])]], 423 ^ _209884 : [(424 ^ _209884) ^ [_225111, _225113] : [-(a_select3(trans(_224356), _225113, _225111) = a_select3(trans(_224356), _225111, _225113)), leq(n0, _225113), leq(_225113, _224354), leq(n0, _225111), leq(_225111, _224354)]]], (442 ^ _209884) ^ [_225658, _225660] : [445 ^ _209884 : [(446 ^ _209884) ^ [] : [-(leq(n0, 443 ^ [_225658, _225660]))], (448 ^ _209884) ^ [] : [-(leq(443 ^ [_225658, _225660], _225658))], (450 ^ _209884) ^ [] : [-(leq(n0, 444 ^ [_225658, _225660]))], (452 ^ _209884) ^ [] : [-(leq(444 ^ [_225658, _225660], _225658))], (454 ^ _209884) ^ [] : [a_select3(_225660, 443 ^ [_225658, _225660], 444 ^ [_225658, _225660]) = a_select3(_225660, 444 ^ [_225658, _225660], 443 ^ [_225658, _225660])]], 455 ^ _209884 : [(456 ^ _209884) ^ [_226415, _226417] : [-(a_select3(inv(_225660), _226417, _226415) = a_select3(inv(_225660), _226415, _226417)), leq(n0, _226417), leq(_226417, _225658), leq(n0, _226415), leq(_226415, _225658)]]], (474 ^ _209884) ^ [_226962, _226964] : [477 ^ _209884 : [(478 ^ _209884) ^ [] : [-(leq(n0, 475 ^ [_226962, _226964]))], (480 ^ _209884) ^ [] : [-(leq(475 ^ [_226962, _226964], _226962))], (482 ^ _209884) ^ [] : [-(leq(n0, 476 ^ [_226962, _226964]))], (484 ^ _209884) ^ [] : [-(leq(476 ^ [_226962, _226964], _226962))], (486 ^ _209884) ^ [] : [a_select3(_226964, 475 ^ [_226962, _226964], 476 ^ [_226962, _226964]) = a_select3(_226964, 476 ^ [_226962, _226964], 475 ^ [_226962, _226964])]], 487 ^ _209884 : [(488 ^ _209884) ^ [_227775, _227777, _227779, _227781] : [-(a_select3(tptp_update3(_226964, _227777, _227777, _227775), _227781, _227779) = a_select3(tptp_update3(_226964, _227777, _227777, _227775), _227779, _227781)), leq(n0, _227781), leq(_227781, _226962), leq(n0, _227779), leq(_227779, _226962), leq(n0, _227777), leq(_227777, _226962)]]], (514 ^ _209884) ^ [_228594, _228596, _228598] : [519 ^ _209884 : [(520 ^ _209884) ^ [] : [-(leq(n0, 517 ^ [_228594, _228596, _228598]))], (522 ^ _209884) ^ [] : [-(leq(517 ^ [_228594, _228596, _228598], _228594))], (524 ^ _209884) ^ [] : [-(leq(n0, 518 ^ [_228594, _228596, _228598]))], (526 ^ _209884) ^ [] : [-(leq(518 ^ [_228594, _228596, _228598], _228594))], (528 ^ _209884) ^ [] : [a_select3(_228598, 517 ^ [_228594, _228596, _228598], 518 ^ [_228594, _228596, _228598]) = a_select3(_228598, 518 ^ [_228594, _228596, _228598], 517 ^ [_228594, _228596, _228598])]], 531 ^ _209884 : [(532 ^ _209884) ^ [] : [-(leq(n0, 529 ^ [_228594, _228596, _228598]))], (534 ^ _209884) ^ [] : [-(leq(529 ^ [_228594, _228596, _228598], _228594))], (536 ^ _209884) ^ [] : [-(leq(n0, 530 ^ [_228594, _228596, _228598]))], (538 ^ _209884) ^ [] : [-(leq(530 ^ [_228594, _228596, _228598], _228594))], (540 ^ _209884) ^ [] : [a_select3(_228596, 529 ^ [_228594, _228596, _228598], 530 ^ [_228594, _228596, _228598]) = a_select3(_228596, 530 ^ [_228594, _228596, _228598], 529 ^ [_228594, _228596, _228598])]], 541 ^ _209884 : [(542 ^ _209884) ^ [_230103, _230105] : [-(a_select3(tptp_madd(_228598, _228596), _230105, _230103) = a_select3(tptp_madd(_228598, _228596), _230103, _230105)), leq(n0, _230105), leq(_230105, _228594), leq(n0, _230103), leq(_230103, _228594)]]], (560 ^ _209884) ^ [_230689, _230691, _230693] : [565 ^ _209884 : [(566 ^ _209884) ^ [] : [-(leq(n0, 563 ^ [_230689, _230691, _230693]))], (568 ^ _209884) ^ [] : [-(leq(563 ^ [_230689, _230691, _230693], _230689))], (570 ^ _209884) ^ [] : [-(leq(n0, 564 ^ [_230689, _230691, _230693]))], (572 ^ _209884) ^ [] : [-(leq(564 ^ [_230689, _230691, _230693], _230689))], (574 ^ _209884) ^ [] : [a_select3(_230693, 563 ^ [_230689, _230691, _230693], 564 ^ [_230689, _230691, _230693]) = a_select3(_230693, 564 ^ [_230689, _230691, _230693], 563 ^ [_230689, _230691, _230693])]], 577 ^ _209884 : [(578 ^ _209884) ^ [] : [-(leq(n0, 575 ^ [_230689, _230691, _230693]))], (580 ^ _209884) ^ [] : [-(leq(575 ^ [_230689, _230691, _230693], _230689))], (582 ^ _209884) ^ [] : [-(leq(n0, 576 ^ [_230689, _230691, _230693]))], (584 ^ _209884) ^ [] : [-(leq(576 ^ [_230689, _230691, _230693], _230689))], (586 ^ _209884) ^ [] : [a_select3(_230691, 575 ^ [_230689, _230691, _230693], 576 ^ [_230689, _230691, _230693]) = a_select3(_230691, 576 ^ [_230689, _230691, _230693], 575 ^ [_230689, _230691, _230693])]], 587 ^ _209884 : [(588 ^ _209884) ^ [_232198, _232200] : [-(a_select3(tptp_msub(_230693, _230691), _232200, _232198) = a_select3(tptp_msub(_230693, _230691), _232198, _232200)), leq(n0, _232200), leq(_232200, _230689), leq(n0, _232198), leq(_232198, _230689)]]], (606 ^ _209884) ^ [_232784, _232786, _232788] : [609 ^ _209884 : [(610 ^ _209884) ^ [] : [-(leq(n0, 607 ^ [_232784, _232786, _232788]))], (612 ^ _209884) ^ [] : [-(leq(607 ^ [_232784, _232786, _232788], _232784))], (614 ^ _209884) ^ [] : [-(leq(n0, 608 ^ [_232784, _232786, _232788]))], (616 ^ _209884) ^ [] : [-(leq(608 ^ [_232784, _232786, _232788], _232784))], (618 ^ _209884) ^ [] : [a_select3(_232786, 607 ^ [_232784, _232786, _232788], 608 ^ [_232784, _232786, _232788]) = a_select3(_232786, 608 ^ [_232784, _232786, _232788], 607 ^ [_232784, _232786, _232788])]], 619 ^ _209884 : [(620 ^ _209884) ^ [_233597, _233599] : [-(a_select3(tptp_mmul(_232788, tptp_mmul(_232786, trans(_232788))), _233599, _233597) = a_select3(tptp_mmul(_232788, tptp_mmul(_232786, trans(_232788))), _233597, _233599)), leq(n0, _233599), leq(_233599, _232784), leq(n0, _233597), leq(_233597, _232784)]]], (638 ^ _209884) ^ [_234216, _234218, _234220, _234222] : [641 ^ _209884 : [(642 ^ _209884) ^ [] : [-(leq(n0, 639 ^ [_234216, _234218, _234220, _234222]))], (644 ^ _209884) ^ [] : [-(leq(639 ^ [_234216, _234218, _234220, _234222], _234216))], (646 ^ _209884) ^ [] : [-(leq(n0, 640 ^ [_234216, _234218, _234220, _234222]))], (648 ^ _209884) ^ [] : [-(leq(640 ^ [_234216, _234218, _234220, _234222], _234216))], (650 ^ _209884) ^ [] : [a_select3(_234220, 639 ^ [_234216, _234218, _234220, _234222], 640 ^ [_234216, _234218, _234220, _234222]) = a_select3(_234220, 640 ^ [_234216, _234218, _234220, _234222], 639 ^ [_234216, _234218, _234220, _234222])]], 651 ^ _209884 : [(652 ^ _209884) ^ [_235073, _235075] : [-(a_select3(tptp_mmul(_234222, tptp_mmul(_234220, trans(_234222))), _235075, _235073) = a_select3(tptp_mmul(_234222, tptp_mmul(_234220, trans(_234222))), _235073, _235075)), leq(n0, _235075), leq(_235075, _234218), leq(n0, _235073), leq(_235073, _234218)]]], (670 ^ _209884) ^ [_235768, _235770, _235772, _235774, _235776, _235778, _235780, _235782] : [675 ^ _209884 : [(676 ^ _209884) ^ [] : [-(leq(n0, 673 ^ [_235768, _235770, _235772, _235774, _235776, _235778, _235780, _235782]))], (678 ^ _209884) ^ [] : [-(leq(673 ^ [_235768, _235770, _235772, _235774, _235776, _235778, _235780, _235782], _235768))], (680 ^ _209884) ^ [] : [-(leq(n0, 674 ^ [_235768, _235770, _235772, _235774, _235776, _235778, _235780, _235782]))], (682 ^ _209884) ^ [] : [-(leq(674 ^ [_235768, _235770, _235772, _235774, _235776, _235778, _235780, _235782], _235768))], (684 ^ _209884) ^ [] : [a_select3(_235776, 673 ^ [_235768, _235770, _235772, _235774, _235776, _235778, _235780, _235782], 674 ^ [_235768, _235770, _235772, _235774, _235776, _235778, _235780, _235782]) = a_select3(_235776, 674 ^ [_235768, _235770, _235772, _235774, _235776, _235778, _235780, _235782], 673 ^ [_235768, _235770, _235772, _235774, _235776, _235778, _235780, _235782])]], 689 ^ _209884 : [(690 ^ _209884) ^ [] : [-(leq(n0, 687 ^ [_235768, _235770, _235772, _235774, _235776, _235778, _235780, _235782]))], (692 ^ _209884) ^ [] : [-(leq(687 ^ [_235768, _235770, _235772, _235774, _235776, _235778, _235780, _235782], _235770))], (694 ^ _209884) ^ [] : [-(leq(n0, 688 ^ [_235768, _235770, _235772, _235774, _235776, _235778, _235780, _235782]))], (696 ^ _209884) ^ [] : [-(leq(688 ^ [_235768, _235770, _235772, _235774, _235776, _235778, _235780, _235782], _235770))], (698 ^ _209884) ^ [] : [a_select3(_235782, 687 ^ [_235768, _235770, _235772, _235774, _235776, _235778, _235780, _235782], 688 ^ [_235768, _235770, _235772, _235774, _235776, _235778, _235780, _235782]) = a_select3(_235782, 688 ^ [_235768, _235770, _235772, _235774, _235776, _235778, _235780, _235782], 687 ^ [_235768, _235770, _235772, _235774, _235776, _235778, _235780, _235782])]], 701 ^ _209884 : [(702 ^ _209884) ^ [] : [-(leq(n0, 699 ^ [_235768, _235770, _235772, _235774, _235776, _235778, _235780, _235782]))], (704 ^ _209884) ^ [] : [-(leq(699 ^ [_235768, _235770, _235772, _235774, _235776, _235778, _235780, _235782], _235770))], (706 ^ _209884) ^ [] : [-(leq(n0, 700 ^ [_235768, _235770, _235772, _235774, _235776, _235778, _235780, _235782]))], (708 ^ _209884) ^ [] : [-(leq(700 ^ [_235768, _235770, _235772, _235774, _235776, _235778, _235780, _235782], _235770))], (710 ^ _209884) ^ [] : [a_select3(_235772, 699 ^ [_235768, _235770, _235772, _235774, _235776, _235778, _235780, _235782], 700 ^ [_235768, _235770, _235772, _235774, _235776, _235778, _235780, _235782]) = a_select3(_235772, 700 ^ [_235768, _235770, _235772, _235774, _235776, _235778, _235780, _235782], 699 ^ [_235768, _235770, _235772, _235774, _235776, _235778, _235780, _235782])]], 711 ^ _209884 : [(712 ^ _209884) ^ [_238696, _238698] : [-(a_select3(tptp_madd(_235782, tptp_mmul(_235780, tptp_mmul(tptp_madd(tptp_mmul(_235778, tptp_mmul(_235776, trans(_235778))), tptp_mmul(_235774, tptp_mmul(_235772, trans(_235774)))), trans(_235780)))), _238698, _238696) = a_select3(tptp_madd(_235782, tptp_mmul(_235780, tptp_mmul(tptp_madd(tptp_mmul(_235778, tptp_mmul(_235776, trans(_235778))), tptp_mmul(_235774, tptp_mmul(_235772, trans(_235774)))), trans(_235780)))), _238696, _238698)), leq(n0, _238698), leq(_238698, _235770), leq(n0, _238696), leq(_238696, _235770)]]], (730 ^ _209884) ^ [_239449] : [-(sum(n0, tptp_minus_1, _239449) = n0)], (732 ^ _209884) ^ [_239531] : [-(tptp_float_0_0 = sum(n0, tptp_minus_1, _239531))], (734 ^ _209884) ^ [] : [-(succ(tptp_minus_1) = n0)], (736 ^ _209884) ^ [_239666] : [-(plus(_239666, n1) = succ(_239666))], (738 ^ _209884) ^ [_239749] : [-(plus(n1, _239749) = succ(_239749))], (740 ^ _209884) ^ [_239832] : [-(plus(_239832, n2) = succ(succ(_239832)))], (742 ^ _209884) ^ [_239917] : [-(plus(n2, _239917) = succ(succ(_239917)))], (744 ^ _209884) ^ [_240002] : [-(plus(_240002, n3) = succ(succ(succ(_240002))))], (746 ^ _209884) ^ [_240089] : [-(plus(n3, _240089) = succ(succ(succ(_240089))))], (748 ^ _209884) ^ [_240176] : [-(plus(_240176, n4) = succ(succ(succ(succ(_240176)))))], (750 ^ _209884) ^ [_240265] : [-(plus(n4, _240265) = succ(succ(succ(succ(_240265)))))], (752 ^ _209884) ^ [_240354] : [-(plus(_240354, n5) = succ(succ(succ(succ(succ(_240354))))))], (754 ^ _209884) ^ [_240445] : [-(plus(n5, _240445) = succ(succ(succ(succ(succ(_240445))))))], (756 ^ _209884) ^ [_240536] : [-(minus(_240536, n1) = pred(_240536))], (758 ^ _209884) ^ [_240619] : [-(pred(succ(_240619)) = _240619)], (760 ^ _209884) ^ [_240701] : [-(succ(pred(_240701)) = _240701)], (762 ^ _209884) ^ [_240841, _240843] : [leq(succ(_240843), succ(_240841)), -(leq(_240843, _240841))], (768 ^ _209884) ^ [_241011, _241013] : [leq(_241013, _241011), -(leq(succ(_241013), succ(_241011)))], (774 ^ _209884) ^ [_241231, _241233] : [leq(succ(_241233), _241231), -(gt(_241231, _241233))], (780 ^ _209884) ^ [_241445, _241447] : [leq(minus(_241447, _241445), _241447), -(leq(n0, _241445))], (786 ^ _209884) ^ [_241674, _241676, _241678, _241680] : [-(a_select3(tptp_update3(_241680, _241678, _241676, _241674), _241678, _241676) = _241674)], (788 ^ _209884) ^ [_241866, _241868, _241870, _241872, _241874, _241876, _241878] : [-(a_select3(tptp_update3(_241870, _241878, _241876, _241866), _241874, _241872) = _241868), -(_241878 = _241874), _241876 = _241872, a_select3(_241870, _241874, _241872) = _241868], (802 ^ _209884) ^ [_242409, _242411, _242413, _242415, _242417, _242419] : [-(a_select3(tptp_update3(_242411, _242415, _242413, _242409), _242419, _242417) = _242409), 807 ^ _209884 : [(808 ^ _209884) ^ [] : [-(leq(n0, 805 ^ [_242409, _242411, _242413, _242415, _242417, _242419]))], (810 ^ _209884) ^ [] : [-(leq(n0, 806 ^ [_242409, _242411, _242413, _242415, _242417, _242419]))], (812 ^ _209884) ^ [] : [-(leq(805 ^ [_242409, _242411, _242413, _242415, _242417, _242419], _242415))], (814 ^ _209884) ^ [] : [-(leq(806 ^ [_242409, _242411, _242413, _242415, _242417, _242419], _242413))], (816 ^ _209884) ^ [] : [a_select3(_242411, 805 ^ [_242409, _242411, _242413, _242415, _242417, _242419], 806 ^ [_242409, _242411, _242413, _242415, _242417, _242419]) = _242409]], leq(n0, _242419), leq(_242419, _242415), leq(n0, _242417), leq(_242417, _242413)], (834 ^ _209884) ^ [_243751, _243753, _243755] : [-(a_select2(tptp_update2(_243755, _243753, _243751), _243753) = _243751)], (836 ^ _209884) ^ [_243911, _243913, _243915, _243917, _243919] : [-(a_select2(tptp_update2(_243915, _243919, _243911), _243917) = _243913), -(_243919 = _243917), a_select2(_243915, _243917) = _243913], (865 ^ _209884) ^ [] : [-(true)], (867 ^ _209884) ^ [] : [def = use], (846 ^ _209884) ^ [_244291, _244293, _244295, _244297] : [-(a_select2(tptp_update2(_244293, _244295, _244291), _244297) = _244291), 850 ^ _209884 : [(851 ^ _209884) ^ [] : [-(leq(n0, 849 ^ [_244291, _244293, _244295, _244297]))], (853 ^ _209884) ^ [] : [-(leq(849 ^ [_244291, _244293, _244295, _244297], _244295))], (855 ^ _209884) ^ [] : [a_select2(_244293, 849 ^ [_244291, _244293, _244295, _244297]) = _244291]], leq(n0, _244297), leq(_244297, _244295)]], input).
% 0.35/1.40  ncf('1',plain,[a_select2(sigmaold_init, 1160 ^ []) = init],start(1166 ^ 0)).
% 0.35/1.40  ncf('1.1',plain,[-(a_select2(sigmaold_init, 1160 ^ []) = init), 1151 : leq(n0, 1160 ^ []), 1151 : leq(1160 ^ [], n4), 1151 : gt(loopcounter, n1)],extension(1147 ^ 1,bind([[_252753], [1160 ^ []]]))).
% 0.35/1.40  ncf('1.1.1',plain,[-(leq(n0, 1160 ^ []))],extension(1162 ^ 4)).
% 0.35/1.40  ncf('1.1.2',plain,[-(leq(1160 ^ [], n4))],extension(1164 ^ 4)).
% 0.35/1.40  ncf('1.1.3',plain,[-(gt(loopcounter, n1))],extension(1059 ^ 2)).
% 0.35/1.40  %-----------------------------------------------------
% 0.35/1.40  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------