%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SWV173+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n018.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 12:20:06 EDT 2023

% Result   : Theorem 0.36s 1.39s
% Output   : Proof 0.36s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : SWV173+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.12/0.13  % Command  : nanocop.sh %s %d
% 0.13/0.34  % Computer : n018.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Fri May 19 02:43:43 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.36/1.39  
% 0.36/1.39  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 0.36/1.39  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.36/1.39  %-----------------------------------------------------
% 0.36/1.39  ncf(matrix, plain, [(1162 ^ _209766) ^ [] : [-(leq(n0, 1160 ^ []))], (1164 ^ _209766) ^ [] : [-(leq(1160 ^ [], n4))], (1166 ^ _209766) ^ [] : [a_select2(rhoold_init, 1160 ^ []) = init], (1055 ^ _209766) ^ [] : [-(leq(n0, pv10))], (1057 ^ _209766) ^ [] : [-(leq(pv10, n135299))], (1059 ^ _209766) ^ [] : [-(gt(loopcounter, n1))], (1061 ^ _209766) ^ [_250241] : [leq(n0, _250241), leq(_250241, n135299), 1068 ^ _209766 : [(1069 ^ _209766) ^ [_250469] : [-(a_select3(q_init, _250241, _250469) = init), leq(n0, _250469), leq(_250469, n4)]]], (1079 ^ _209766) ^ [_250771] : [-(a_select2(rho_init, _250771) = init), leq(n0, _250771), leq(_250771, n4)], (1089 ^ _209766) ^ [_251052] : [-(a_select2(mu_init, _251052) = init), leq(n0, _251052), leq(_251052, n4)], (1099 ^ _209766) ^ [_251333] : [-(a_select2(sigma_init, _251333) = init), leq(n0, _251333), leq(_251333, n4)], (1109 ^ _209766) ^ [_251614] : [-(a_select3(center_init, _251614, n0) = init), leq(n0, _251614), leq(_251614, n4)], (1119 ^ _209766) ^ [] : [gt(loopcounter, n1), 1122 ^ _209766 : [(1123 ^ _209766) ^ [_251959] : [-(a_select2(muold_init, _251959) = init), leq(n0, _251959), leq(_251959, n4)]]], (1133 ^ _209766) ^ [] : [gt(loopcounter, n1), 1136 ^ _209766 : [(1137 ^ _209766) ^ [_252307] : [-(a_select2(rhoold_init, _252307) = init), leq(n0, _252307), leq(_252307, n4)]]], (1147 ^ _209766) ^ [] : [gt(loopcounter, n1), 1150 ^ _209766 : [(1151 ^ _209766) ^ [_252635] : [-(a_select2(sigmaold_init, _252635) = init), leq(n0, _252635), leq(_252635, n4)]]], (2 ^ _209766) ^ [_209910] : [-(_209910 = _209910)], (4 ^ _209766) ^ [_210017, _210019] : [_210019 = _210017, -(_210017 = _210019)], (10 ^ _209766) ^ [_210221, _210223, _210225] : [-(_210225 = _210221), _210225 = _210223, _210223 = _210221], (20 ^ _209766) ^ [_210562, _210564, _210566, _210568] : [-(lt(_210566, _210562)), lt(_210568, _210564), _210568 = _210566, _210564 = _210562], (34 ^ _209766) ^ [_211006, _211008, _211010, _211012] : [-(geq(_211010, _211006)), geq(_211012, _211008), _211012 = _211010, _211008 = _211006], (48 ^ _209766) ^ [_211450, _211452, _211454, _211456] : [-(gt(_211454, _211450)), gt(_211456, _211452), _211456 = _211454, _211452 = _211450], (62 ^ _209766) ^ [_211874, _211876, _211878, _211880] : [-(leq(_211878, _211874)), leq(_211880, _211876), _211880 = _211878, _211876 = _211874], (76 ^ _209766) ^ [_212330, _212332, _212334, _212336] : [-(uniform_int_rnd(_212336, _212332) = uniform_int_rnd(_212334, _212330)), _212336 = _212334, _212332 = _212330], (86 ^ _209766) ^ [_212689, _212691, _212693, _212695] : [-(tptp_const_array1(_212695, _212691) = tptp_const_array1(_212693, _212689)), _212695 = _212693, _212691 = _212689], (96 ^ _209766) ^ [_213076, _213078, _213080, _213082, _213084, _213086] : [-(tptp_const_array2(_213086, _213082, _213078) = tptp_const_array2(_213084, _213080, _213076)), _213086 = _213084, _213082 = _213080, _213078 = _213076], (110 ^ _209766) ^ [_213564, _213566, _213568, _213570] : [-(dim(_213570, _213566) = dim(_213568, _213564)), _213570 = _213568, _213566 = _213564], (120 ^ _209766) ^ [_213895, _213897] : [_213897 = _213895, -(inv(_213897) = inv(_213895))], (126 ^ _209766) ^ [_214141, _214143, _214145, _214147] : [-(tptp_msub(_214147, _214143) = tptp_msub(_214145, _214141)), _214147 = _214145, _214143 = _214141], (136 ^ _209766) ^ [_214500, _214502, _214504, _214506] : [-(tptp_madd(_214506, _214502) = tptp_madd(_214504, _214500)), _214506 = _214504, _214502 = _214500], (146 ^ _209766) ^ [_214859, _214861, _214863, _214865] : [-(tptp_mmul(_214865, _214861) = tptp_mmul(_214863, _214859)), _214865 = _214863, _214861 = _214859], (156 ^ _209766) ^ [_215190, _215192] : [_215192 = _215190, -(trans(_215192) = trans(_215190))], (162 ^ _209766) ^ [_215464, _215466, _215468, _215470, _215472, _215474] : [-(sum(_215474, _215470, _215466) = sum(_215472, _215468, _215464)), _215474 = _215472, _215470 = _215468, _215466 = _215464], (176 ^ _209766) ^ [_215952, _215954, _215956, _215958] : [-(plus(_215958, _215954) = plus(_215956, _215952)), _215958 = _215956, _215954 = _215952], (186 ^ _209766) ^ [_216283, _216285] : [_216285 = _216283, -(pred(_216285) = pred(_216283))], (192 ^ _209766) ^ [_216529, _216531, _216533, _216535] : [-(minus(_216535, _216531) = minus(_216533, _216529)), _216535 = _216533, _216531 = _216529], (202 ^ _209766) ^ [_216944, _216946, _216948, _216950, _216952, _216954, _216956, _216958] : [-(tptp_update3(_216958, _216954, _216950, _216946) = tptp_update3(_216956, _216952, _216948, _216944)), _216958 = _216956, _216954 = _216952, _216950 = _216948, _216946 = _216944], (220 ^ _209766) ^ [_217605, _217607, _217609, _217611, _217613, _217615] : [-(tptp_update2(_217615, _217611, _217607) = tptp_update2(_217613, _217609, _217605)), _217615 = _217613, _217611 = _217609, _217607 = _217605], (234 ^ _209766) ^ [_218065, _218067] : [_218067 = _218065, -(succ(_218067) = succ(_218065))], (254 ^ _209766) ^ [_218807, _218809, _218811, _218813] : [-(a_select2(_218813, _218809) = a_select2(_218811, _218807)), _218813 = _218811, _218809 = _218807], (240 ^ _209766) ^ [_218339, _218341, _218343, _218345, _218347, _218349] : [-(a_select3(_218349, _218345, _218341) = a_select3(_218347, _218343, _218339)), _218349 = _218347, _218345 = _218343, _218341 = _218339], (869 ^ _209766) ^ [] : [-(gt(n5, n4))], (871 ^ _209766) ^ [] : [-(gt(n135299, n4))], (873 ^ _209766) ^ [] : [-(gt(n135299, n5))], (875 ^ _209766) ^ [] : [-(gt(n4, tptp_minus_1))], (877 ^ _209766) ^ [] : [-(gt(n5, tptp_minus_1))], (879 ^ _209766) ^ [] : [-(gt(n135299, tptp_minus_1))], (881 ^ _209766) ^ [] : [-(gt(n0, tptp_minus_1))], (883 ^ _209766) ^ [] : [-(gt(n1, tptp_minus_1))], (885 ^ _209766) ^ [] : [-(gt(n2, tptp_minus_1))], (887 ^ _209766) ^ [] : [-(gt(n3, tptp_minus_1))], (889 ^ _209766) ^ [] : [-(gt(n4, n0))], (891 ^ _209766) ^ [] : [-(gt(n5, n0))], (893 ^ _209766) ^ [] : [-(gt(n135299, n0))], (895 ^ _209766) ^ [] : [-(gt(n1, n0))], (897 ^ _209766) ^ [] : [-(gt(n2, n0))], (899 ^ _209766) ^ [] : [-(gt(n3, n0))], (901 ^ _209766) ^ [] : [-(gt(n4, n1))], (903 ^ _209766) ^ [] : [-(gt(n5, n1))], (905 ^ _209766) ^ [] : [-(gt(n135299, n1))], (907 ^ _209766) ^ [] : [-(gt(n2, n1))], (909 ^ _209766) ^ [] : [-(gt(n3, n1))], (911 ^ _209766) ^ [] : [-(gt(n4, n2))], (913 ^ _209766) ^ [] : [-(gt(n5, n2))], (915 ^ _209766) ^ [] : [-(gt(n135299, n2))], (917 ^ _209766) ^ [] : [-(gt(n3, n2))], (919 ^ _209766) ^ [] : [-(gt(n4, n3))], (921 ^ _209766) ^ [] : [-(gt(n5, n3))], (923 ^ _209766) ^ [] : [-(gt(n135299, n3))], (925 ^ _209766) ^ [_246647] : [leq(n0, _246647), leq(_246647, n4), -(_246647 = n0), -(_246647 = n1), -(_246647 = n2), -(_246647 = n3), -(_246647 = n4)], (951 ^ _209766) ^ [_247268] : [leq(n0, _247268), leq(_247268, n5), -(_247268 = n0), -(_247268 = n1), -(_247268 = n2), -(_247268 = n3), -(_247268 = n4), -(_247268 = n5)], (981 ^ _209766) ^ [_247975] : [-(_247975 = n0), leq(n0, _247975), leq(_247975, n0)], (991 ^ _209766) ^ [_248250] : [leq(n0, _248250), leq(_248250, n1), -(_248250 = n0), -(_248250 = n1)], (1005 ^ _209766) ^ [_248613] : [leq(n0, _248613), leq(_248613, n2), -(_248613 = n0), -(_248613 = n1), -(_248613 = n2)], (1045 ^ _209766) ^ [] : [-(succ(succ(succ(succ(n0)))) = n4)], (1047 ^ _209766) ^ [] : [-(succ(succ(succ(succ(succ(n0))))) = n5)], (1049 ^ _209766) ^ [] : [-(succ(n0) = n1)], (1051 ^ _209766) ^ [] : [-(succ(succ(n0)) = n2)], (1053 ^ _209766) ^ [] : [-(succ(succ(succ(n0))) = n3)], (1023 ^ _209766) ^ [_249062] : [leq(n0, _249062), leq(_249062, n3), -(_249062 = n0), -(_249062 = n1), -(_249062 = n2), -(_249062 = n3)], (264 ^ _209766) ^ [_219238, _219240] : [-(gt(_219240, _219238)), -(gt(_219238, _219240)), -(_219240 = _219238)], (274 ^ _209766) ^ [_219553, _219555, _219557] : [-(gt(_219557, _219553)), gt(_219557, _219555), gt(_219555, _219553)], (284 ^ _209766) ^ [_219832] : [gt(_219832, _219832)], (286 ^ _209766) ^ [_219910] : [-(leq(_219910, _219910))], (288 ^ _209766) ^ [_220031, _220033, _220035] : [-(leq(_220035, _220031)), leq(_220035, _220033), leq(_220033, _220031)], (298 ^ _209766) ^ [_220369, _220371] : [lt(_220371, _220369), -(gt(_220369, _220371))], (304 ^ _209766) ^ [_220531, _220533] : [gt(_220531, _220533), -(lt(_220533, _220531))], (310 ^ _209766) ^ [_220772, _220774] : [geq(_220774, _220772), -(leq(_220772, _220774))], (316 ^ _209766) ^ [_220934, _220936] : [leq(_220934, _220936), -(geq(_220936, _220934))], (322 ^ _209766) ^ [_221146, _221148] : [gt(_221146, _221148), -(leq(_221148, _221146))], (328 ^ _209766) ^ [_221356, _221358] : [-(gt(_221356, _221358)), leq(_221358, _221356), -(_221358 = _221356)], (338 ^ _209766) ^ [_221687, _221689] : [leq(_221689, pred(_221687)), -(gt(_221687, _221689))], (344 ^ _209766) ^ [_221853, _221855] : [gt(_221853, _221855), -(leq(_221855, pred(_221853)))], (350 ^ _209766) ^ [_222040] : [-(gt(succ(_222040), _222040))], (352 ^ _209766) ^ [_222149, _222151] : [leq(_222151, _222149), -(leq(_222151, succ(_222149)))], (358 ^ _209766) ^ [_222392, _222394] : [leq(_222394, _222392), -(gt(succ(_222392), _222394))], (364 ^ _209766) ^ [_222558, _222560] : [gt(succ(_222558), _222560), -(leq(_222560, _222558))], (370 ^ _209766) ^ [_222774, _222776] : [leq(n0, _222776), -(leq(uniform_int_rnd(_222774, _222776), _222776))], (376 ^ _209766) ^ [_222990, _222992] : [leq(n0, _222992), -(leq(n0, uniform_int_rnd(_222990, _222992)))], (382 ^ _209766) ^ [_223234, _223236, _223238, _223240] : [-(a_select2(tptp_const_array1(dim(_223238, _223236), _223234), _223240) = _223234), leq(_223238, _223240), leq(_223240, _223236)], (392 ^ _209766) ^ [_223641, _223643, _223645, _223647, _223649, _223651, _223653] : [-(a_select3(tptp_const_array2(dim(_223651, _223649), dim(_223645, _223643), _223641), _223653, _223647) = _223641), leq(_223651, _223653), leq(_223653, _223649), leq(_223645, _223647), leq(_223647, _223643)], (410 ^ _209766) ^ [_224236, _224238] : [413 ^ _209766 : [(414 ^ _209766) ^ [] : [-(leq(n0, 411 ^ [_224236, _224238]))], (416 ^ _209766) ^ [] : [-(leq(411 ^ [_224236, _224238], _224236))], (418 ^ _209766) ^ [] : [-(leq(n0, 412 ^ [_224236, _224238]))], (420 ^ _209766) ^ [] : [-(leq(412 ^ [_224236, _224238], _224236))], (422 ^ _209766) ^ [] : [a_select3(_224238, 411 ^ [_224236, _224238], 412 ^ [_224236, _224238]) = a_select3(_224238, 412 ^ [_224236, _224238], 411 ^ [_224236, _224238])]], 423 ^ _209766 : [(424 ^ _209766) ^ [_224993, _224995] : [-(a_select3(trans(_224238), _224995, _224993) = a_select3(trans(_224238), _224993, _224995)), leq(n0, _224995), leq(_224995, _224236), leq(n0, _224993), leq(_224993, _224236)]]], (442 ^ _209766) ^ [_225540, _225542] : [445 ^ _209766 : [(446 ^ _209766) ^ [] : [-(leq(n0, 443 ^ [_225540, _225542]))], (448 ^ _209766) ^ [] : [-(leq(443 ^ [_225540, _225542], _225540))], (450 ^ _209766) ^ [] : [-(leq(n0, 444 ^ [_225540, _225542]))], (452 ^ _209766) ^ [] : [-(leq(444 ^ [_225540, _225542], _225540))], (454 ^ _209766) ^ [] : [a_select3(_225542, 443 ^ [_225540, _225542], 444 ^ [_225540, _225542]) = a_select3(_225542, 444 ^ [_225540, _225542], 443 ^ [_225540, _225542])]], 455 ^ _209766 : [(456 ^ _209766) ^ [_226297, _226299] : [-(a_select3(inv(_225542), _226299, _226297) = a_select3(inv(_225542), _226297, _226299)), leq(n0, _226299), leq(_226299, _225540), leq(n0, _226297), leq(_226297, _225540)]]], (474 ^ _209766) ^ [_226844, _226846] : [477 ^ _209766 : [(478 ^ _209766) ^ [] : [-(leq(n0, 475 ^ [_226844, _226846]))], (480 ^ _209766) ^ [] : [-(leq(475 ^ [_226844, _226846], _226844))], (482 ^ _209766) ^ [] : [-(leq(n0, 476 ^ [_226844, _226846]))], (484 ^ _209766) ^ [] : [-(leq(476 ^ [_226844, _226846], _226844))], (486 ^ _209766) ^ [] : [a_select3(_226846, 475 ^ [_226844, _226846], 476 ^ [_226844, _226846]) = a_select3(_226846, 476 ^ [_226844, _226846], 475 ^ [_226844, _226846])]], 487 ^ _209766 : [(488 ^ _209766) ^ [_227657, _227659, _227661, _227663] : [-(a_select3(tptp_update3(_226846, _227659, _227659, _227657), _227663, _227661) = a_select3(tptp_update3(_226846, _227659, _227659, _227657), _227661, _227663)), leq(n0, _227663), leq(_227663, _226844), leq(n0, _227661), leq(_227661, _226844), leq(n0, _227659), leq(_227659, _226844)]]], (514 ^ _209766) ^ [_228476, _228478, _228480] : [519 ^ _209766 : [(520 ^ _209766) ^ [] : [-(leq(n0, 517 ^ [_228476, _228478, _228480]))], (522 ^ _209766) ^ [] : [-(leq(517 ^ [_228476, _228478, _228480], _228476))], (524 ^ _209766) ^ [] : [-(leq(n0, 518 ^ [_228476, _228478, _228480]))], (526 ^ _209766) ^ [] : [-(leq(518 ^ [_228476, _228478, _228480], _228476))], (528 ^ _209766) ^ [] : [a_select3(_228480, 517 ^ [_228476, _228478, _228480], 518 ^ [_228476, _228478, _228480]) = a_select3(_228480, 518 ^ [_228476, _228478, _228480], 517 ^ [_228476, _228478, _228480])]], 531 ^ _209766 : [(532 ^ _209766) ^ [] : [-(leq(n0, 529 ^ [_228476, _228478, _228480]))], (534 ^ _209766) ^ [] : [-(leq(529 ^ [_228476, _228478, _228480], _228476))], (536 ^ _209766) ^ [] : [-(leq(n0, 530 ^ [_228476, _228478, _228480]))], (538 ^ _209766) ^ [] : [-(leq(530 ^ [_228476, _228478, _228480], _228476))], (540 ^ _209766) ^ [] : [a_select3(_228478, 529 ^ [_228476, _228478, _228480], 530 ^ [_228476, _228478, _228480]) = a_select3(_228478, 530 ^ [_228476, _228478, _228480], 529 ^ [_228476, _228478, _228480])]], 541 ^ _209766 : [(542 ^ _209766) ^ [_229985, _229987] : [-(a_select3(tptp_madd(_228480, _228478), _229987, _229985) = a_select3(tptp_madd(_228480, _228478), _229985, _229987)), leq(n0, _229987), leq(_229987, _228476), leq(n0, _229985), leq(_229985, _228476)]]], (560 ^ _209766) ^ [_230571, _230573, _230575] : [565 ^ _209766 : [(566 ^ _209766) ^ [] : [-(leq(n0, 563 ^ [_230571, _230573, _230575]))], (568 ^ _209766) ^ [] : [-(leq(563 ^ [_230571, _230573, _230575], _230571))], (570 ^ _209766) ^ [] : [-(leq(n0, 564 ^ [_230571, _230573, _230575]))], (572 ^ _209766) ^ [] : [-(leq(564 ^ [_230571, _230573, _230575], _230571))], (574 ^ _209766) ^ [] : [a_select3(_230575, 563 ^ [_230571, _230573, _230575], 564 ^ [_230571, _230573, _230575]) = a_select3(_230575, 564 ^ [_230571, _230573, _230575], 563 ^ [_230571, _230573, _230575])]], 577 ^ _209766 : [(578 ^ _209766) ^ [] : [-(leq(n0, 575 ^ [_230571, _230573, _230575]))], (580 ^ _209766) ^ [] : [-(leq(575 ^ [_230571, _230573, _230575], _230571))], (582 ^ _209766) ^ [] : [-(leq(n0, 576 ^ [_230571, _230573, _230575]))], (584 ^ _209766) ^ [] : [-(leq(576 ^ [_230571, _230573, _230575], _230571))], (586 ^ _209766) ^ [] : [a_select3(_230573, 575 ^ [_230571, _230573, _230575], 576 ^ [_230571, _230573, _230575]) = a_select3(_230573, 576 ^ [_230571, _230573, _230575], 575 ^ [_230571, _230573, _230575])]], 587 ^ _209766 : [(588 ^ _209766) ^ [_232080, _232082] : [-(a_select3(tptp_msub(_230575, _230573), _232082, _232080) = a_select3(tptp_msub(_230575, _230573), _232080, _232082)), leq(n0, _232082), leq(_232082, _230571), leq(n0, _232080), leq(_232080, _230571)]]], (606 ^ _209766) ^ [_232666, _232668, _232670] : [609 ^ _209766 : [(610 ^ _209766) ^ [] : [-(leq(n0, 607 ^ [_232666, _232668, _232670]))], (612 ^ _209766) ^ [] : [-(leq(607 ^ [_232666, _232668, _232670], _232666))], (614 ^ _209766) ^ [] : [-(leq(n0, 608 ^ [_232666, _232668, _232670]))], (616 ^ _209766) ^ [] : [-(leq(608 ^ [_232666, _232668, _232670], _232666))], (618 ^ _209766) ^ [] : [a_select3(_232668, 607 ^ [_232666, _232668, _232670], 608 ^ [_232666, _232668, _232670]) = a_select3(_232668, 608 ^ [_232666, _232668, _232670], 607 ^ [_232666, _232668, _232670])]], 619 ^ _209766 : [(620 ^ _209766) ^ [_233479, _233481] : [-(a_select3(tptp_mmul(_232670, tptp_mmul(_232668, trans(_232670))), _233481, _233479) = a_select3(tptp_mmul(_232670, tptp_mmul(_232668, trans(_232670))), _233479, _233481)), leq(n0, _233481), leq(_233481, _232666), leq(n0, _233479), leq(_233479, _232666)]]], (638 ^ _209766) ^ [_234098, _234100, _234102, _234104] : [641 ^ _209766 : [(642 ^ _209766) ^ [] : [-(leq(n0, 639 ^ [_234098, _234100, _234102, _234104]))], (644 ^ _209766) ^ [] : [-(leq(639 ^ [_234098, _234100, _234102, _234104], _234098))], (646 ^ _209766) ^ [] : [-(leq(n0, 640 ^ [_234098, _234100, _234102, _234104]))], (648 ^ _209766) ^ [] : [-(leq(640 ^ [_234098, _234100, _234102, _234104], _234098))], (650 ^ _209766) ^ [] : [a_select3(_234102, 639 ^ [_234098, _234100, _234102, _234104], 640 ^ [_234098, _234100, _234102, _234104]) = a_select3(_234102, 640 ^ [_234098, _234100, _234102, _234104], 639 ^ [_234098, _234100, _234102, _234104])]], 651 ^ _209766 : [(652 ^ _209766) ^ [_234955, _234957] : [-(a_select3(tptp_mmul(_234104, tptp_mmul(_234102, trans(_234104))), _234957, _234955) = a_select3(tptp_mmul(_234104, tptp_mmul(_234102, trans(_234104))), _234955, _234957)), leq(n0, _234957), leq(_234957, _234100), leq(n0, _234955), leq(_234955, _234100)]]], (670 ^ _209766) ^ [_235650, _235652, _235654, _235656, _235658, _235660, _235662, _235664] : [675 ^ _209766 : [(676 ^ _209766) ^ [] : [-(leq(n0, 673 ^ [_235650, _235652, _235654, _235656, _235658, _235660, _235662, _235664]))], (678 ^ _209766) ^ [] : [-(leq(673 ^ [_235650, _235652, _235654, _235656, _235658, _235660, _235662, _235664], _235650))], (680 ^ _209766) ^ [] : [-(leq(n0, 674 ^ [_235650, _235652, _235654, _235656, _235658, _235660, _235662, _235664]))], (682 ^ _209766) ^ [] : [-(leq(674 ^ [_235650, _235652, _235654, _235656, _235658, _235660, _235662, _235664], _235650))], (684 ^ _209766) ^ [] : [a_select3(_235658, 673 ^ [_235650, _235652, _235654, _235656, _235658, _235660, _235662, _235664], 674 ^ [_235650, _235652, _235654, _235656, _235658, _235660, _235662, _235664]) = a_select3(_235658, 674 ^ [_235650, _235652, _235654, _235656, _235658, _235660, _235662, _235664], 673 ^ [_235650, _235652, _235654, _235656, _235658, _235660, _235662, _235664])]], 689 ^ _209766 : [(690 ^ _209766) ^ [] : [-(leq(n0, 687 ^ [_235650, _235652, _235654, _235656, _235658, _235660, _235662, _235664]))], (692 ^ _209766) ^ [] : [-(leq(687 ^ [_235650, _235652, _235654, _235656, _235658, _235660, _235662, _235664], _235652))], (694 ^ _209766) ^ [] : [-(leq(n0, 688 ^ [_235650, _235652, _235654, _235656, _235658, _235660, _235662, _235664]))], (696 ^ _209766) ^ [] : [-(leq(688 ^ [_235650, _235652, _235654, _235656, _235658, _235660, _235662, _235664], _235652))], (698 ^ _209766) ^ [] : [a_select3(_235664, 687 ^ [_235650, _235652, _235654, _235656, _235658, _235660, _235662, _235664], 688 ^ [_235650, _235652, _235654, _235656, _235658, _235660, _235662, _235664]) = a_select3(_235664, 688 ^ [_235650, _235652, _235654, _235656, _235658, _235660, _235662, _235664], 687 ^ [_235650, _235652, _235654, _235656, _235658, _235660, _235662, _235664])]], 701 ^ _209766 : [(702 ^ _209766) ^ [] : [-(leq(n0, 699 ^ [_235650, _235652, _235654, _235656, _235658, _235660, _235662, _235664]))], (704 ^ _209766) ^ [] : [-(leq(699 ^ [_235650, _235652, _235654, _235656, _235658, _235660, _235662, _235664], _235652))], (706 ^ _209766) ^ [] : [-(leq(n0, 700 ^ [_235650, _235652, _235654, _235656, _235658, _235660, _235662, _235664]))], (708 ^ _209766) ^ [] : [-(leq(700 ^ [_235650, _235652, _235654, _235656, _235658, _235660, _235662, _235664], _235652))], (710 ^ _209766) ^ [] : [a_select3(_235654, 699 ^ [_235650, _235652, _235654, _235656, _235658, _235660, _235662, _235664], 700 ^ [_235650, _235652, _235654, _235656, _235658, _235660, _235662, _235664]) = a_select3(_235654, 700 ^ [_235650, _235652, _235654, _235656, _235658, _235660, _235662, _235664], 699 ^ [_235650, _235652, _235654, _235656, _235658, _235660, _235662, _235664])]], 711 ^ _209766 : [(712 ^ _209766) ^ [_238578, _238580] : [-(a_select3(tptp_madd(_235664, tptp_mmul(_235662, tptp_mmul(tptp_madd(tptp_mmul(_235660, tptp_mmul(_235658, trans(_235660))), tptp_mmul(_235656, tptp_mmul(_235654, trans(_235656)))), trans(_235662)))), _238580, _238578) = a_select3(tptp_madd(_235664, tptp_mmul(_235662, tptp_mmul(tptp_madd(tptp_mmul(_235660, tptp_mmul(_235658, trans(_235660))), tptp_mmul(_235656, tptp_mmul(_235654, trans(_235656)))), trans(_235662)))), _238578, _238580)), leq(n0, _238580), leq(_238580, _235652), leq(n0, _238578), leq(_238578, _235652)]]], (730 ^ _209766) ^ [_239331] : [-(sum(n0, tptp_minus_1, _239331) = n0)], (732 ^ _209766) ^ [_239413] : [-(tptp_float_0_0 = sum(n0, tptp_minus_1, _239413))], (734 ^ _209766) ^ [] : [-(succ(tptp_minus_1) = n0)], (736 ^ _209766) ^ [_239548] : [-(plus(_239548, n1) = succ(_239548))], (738 ^ _209766) ^ [_239631] : [-(plus(n1, _239631) = succ(_239631))], (740 ^ _209766) ^ [_239714] : [-(plus(_239714, n2) = succ(succ(_239714)))], (742 ^ _209766) ^ [_239799] : [-(plus(n2, _239799) = succ(succ(_239799)))], (744 ^ _209766) ^ [_239884] : [-(plus(_239884, n3) = succ(succ(succ(_239884))))], (746 ^ _209766) ^ [_239971] : [-(plus(n3, _239971) = succ(succ(succ(_239971))))], (748 ^ _209766) ^ [_240058] : [-(plus(_240058, n4) = succ(succ(succ(succ(_240058)))))], (750 ^ _209766) ^ [_240147] : [-(plus(n4, _240147) = succ(succ(succ(succ(_240147)))))], (752 ^ _209766) ^ [_240236] : [-(plus(_240236, n5) = succ(succ(succ(succ(succ(_240236))))))], (754 ^ _209766) ^ [_240327] : [-(plus(n5, _240327) = succ(succ(succ(succ(succ(_240327))))))], (756 ^ _209766) ^ [_240418] : [-(minus(_240418, n1) = pred(_240418))], (758 ^ _209766) ^ [_240501] : [-(pred(succ(_240501)) = _240501)], (760 ^ _209766) ^ [_240583] : [-(succ(pred(_240583)) = _240583)], (762 ^ _209766) ^ [_240723, _240725] : [leq(succ(_240725), succ(_240723)), -(leq(_240725, _240723))], (768 ^ _209766) ^ [_240893, _240895] : [leq(_240895, _240893), -(leq(succ(_240895), succ(_240893)))], (774 ^ _209766) ^ [_241113, _241115] : [leq(succ(_241115), _241113), -(gt(_241113, _241115))], (780 ^ _209766) ^ [_241327, _241329] : [leq(minus(_241329, _241327), _241329), -(leq(n0, _241327))], (786 ^ _209766) ^ [_241556, _241558, _241560, _241562] : [-(a_select3(tptp_update3(_241562, _241560, _241558, _241556), _241560, _241558) = _241556)], (788 ^ _209766) ^ [_241748, _241750, _241752, _241754, _241756, _241758, _241760] : [-(a_select3(tptp_update3(_241752, _241760, _241758, _241748), _241756, _241754) = _241750), -(_241760 = _241756), _241758 = _241754, a_select3(_241752, _241756, _241754) = _241750], (802 ^ _209766) ^ [_242291, _242293, _242295, _242297, _242299, _242301] : [-(a_select3(tptp_update3(_242293, _242297, _242295, _242291), _242301, _242299) = _242291), 807 ^ _209766 : [(808 ^ _209766) ^ [] : [-(leq(n0, 805 ^ [_242291, _242293, _242295, _242297, _242299, _242301]))], (810 ^ _209766) ^ [] : [-(leq(n0, 806 ^ [_242291, _242293, _242295, _242297, _242299, _242301]))], (812 ^ _209766) ^ [] : [-(leq(805 ^ [_242291, _242293, _242295, _242297, _242299, _242301], _242297))], (814 ^ _209766) ^ [] : [-(leq(806 ^ [_242291, _242293, _242295, _242297, _242299, _242301], _242295))], (816 ^ _209766) ^ [] : [a_select3(_242293, 805 ^ [_242291, _242293, _242295, _242297, _242299, _242301], 806 ^ [_242291, _242293, _242295, _242297, _242299, _242301]) = _242291]], leq(n0, _242301), leq(_242301, _242297), leq(n0, _242299), leq(_242299, _242295)], (834 ^ _209766) ^ [_243633, _243635, _243637] : [-(a_select2(tptp_update2(_243637, _243635, _243633), _243635) = _243633)], (836 ^ _209766) ^ [_243793, _243795, _243797, _243799, _243801] : [-(a_select2(tptp_update2(_243797, _243801, _243793), _243799) = _243795), -(_243801 = _243799), a_select2(_243797, _243799) = _243795], (865 ^ _209766) ^ [] : [-(true)], (867 ^ _209766) ^ [] : [def = use], (846 ^ _209766) ^ [_244173, _244175, _244177, _244179] : [-(a_select2(tptp_update2(_244175, _244177, _244173), _244179) = _244173), 850 ^ _209766 : [(851 ^ _209766) ^ [] : [-(leq(n0, 849 ^ [_244173, _244175, _244177, _244179]))], (853 ^ _209766) ^ [] : [-(leq(849 ^ [_244173, _244175, _244177, _244179], _244177))], (855 ^ _209766) ^ [] : [a_select2(_244175, 849 ^ [_244173, _244175, _244177, _244179]) = _244173]], leq(n0, _244179), leq(_244179, _244177)]], input).
% 0.36/1.39  ncf('1',plain,[a_select2(rhoold_init, 1160 ^ []) = init],start(1166 ^ 0)).
% 0.36/1.39  ncf('1.1',plain,[-(a_select2(rhoold_init, 1160 ^ []) = init), 1137 : leq(n0, 1160 ^ []), 1137 : leq(1160 ^ [], n4), 1137 : gt(loopcounter, n1)],extension(1133 ^ 1,bind([[_252307], [1160 ^ []]]))).
% 0.36/1.39  ncf('1.1.1',plain,[-(leq(n0, 1160 ^ []))],extension(1162 ^ 4)).
% 0.36/1.39  ncf('1.1.2',plain,[-(leq(1160 ^ [], n4))],extension(1164 ^ 4)).
% 0.36/1.39  ncf('1.1.3',plain,[-(gt(loopcounter, n1))],extension(1059 ^ 2)).
% 0.36/1.39  %-----------------------------------------------------
% 0.36/1.39  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------