%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SWV185+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n001.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 12:20:08 EDT 2023

% Result   : Theorem 0.35s 1.38s
% Output   : Proof 0.35s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SWV185+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.07/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n001.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 : Fri May 19 03:20:35 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.35/1.38  
% 0.35/1.38  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 0.35/1.38  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.35/1.38  %-----------------------------------------------------
% 0.35/1.38  ncf(matrix, plain, [(1158 ^ _209156) ^ [] : [-(leq(n0, 1156 ^ []))], (1160 ^ _209156) ^ [] : [-(leq(1156 ^ [], n4))], (1162 ^ _209156) ^ [] : [a_select2(rhoold_init, 1156 ^ []) = init], (1055 ^ _209156) ^ [] : [-(gt(loopcounter, n1))], (1057 ^ _209156) ^ [_249525] : [leq(n0, _249525), leq(_249525, n135299), 1064 ^ _209156 : [(1065 ^ _209156) ^ [_249753] : [-(a_select3(q_init, _249525, _249753) = init), leq(n0, _249753), leq(_249753, n4)]]], (1075 ^ _209156) ^ [_250055] : [-(a_select2(rho_init, _250055) = init), leq(n0, _250055), leq(_250055, n4)], (1085 ^ _209156) ^ [_250336] : [-(a_select2(mu_init, _250336) = init), leq(n0, _250336), leq(_250336, n4)], (1095 ^ _209156) ^ [_250617] : [-(a_select2(sigma_init, _250617) = init), leq(n0, _250617), leq(_250617, n4)], (1105 ^ _209156) ^ [_250898] : [-(a_select3(center_init, _250898, n0) = init), leq(n0, _250898), leq(_250898, n4)], (1115 ^ _209156) ^ [] : [gt(loopcounter, n1), 1118 ^ _209156 : [(1119 ^ _209156) ^ [_251243] : [-(a_select2(muold_init, _251243) = init), leq(n0, _251243), leq(_251243, n4)]]], (1129 ^ _209156) ^ [] : [gt(loopcounter, n1), 1132 ^ _209156 : [(1133 ^ _209156) ^ [_251591] : [-(a_select2(rhoold_init, _251591) = init), leq(n0, _251591), leq(_251591, n4)]]], (1143 ^ _209156) ^ [] : [gt(loopcounter, n1), 1146 ^ _209156 : [(1147 ^ _209156) ^ [_251919] : [-(a_select2(sigmaold_init, _251919) = init), leq(n0, _251919), leq(_251919, n4)]]], (2 ^ _209156) ^ [_209300] : [-(_209300 = _209300)], (4 ^ _209156) ^ [_209407, _209409] : [_209409 = _209407, -(_209407 = _209409)], (10 ^ _209156) ^ [_209611, _209613, _209615] : [-(_209615 = _209611), _209615 = _209613, _209613 = _209611], (20 ^ _209156) ^ [_209952, _209954, _209956, _209958] : [-(lt(_209956, _209952)), lt(_209958, _209954), _209958 = _209956, _209954 = _209952], (34 ^ _209156) ^ [_210396, _210398, _210400, _210402] : [-(geq(_210400, _210396)), geq(_210402, _210398), _210402 = _210400, _210398 = _210396], (48 ^ _209156) ^ [_210840, _210842, _210844, _210846] : [-(gt(_210844, _210840)), gt(_210846, _210842), _210846 = _210844, _210842 = _210840], (62 ^ _209156) ^ [_211264, _211266, _211268, _211270] : [-(leq(_211268, _211264)), leq(_211270, _211266), _211270 = _211268, _211266 = _211264], (76 ^ _209156) ^ [_211720, _211722, _211724, _211726] : [-(uniform_int_rnd(_211726, _211722) = uniform_int_rnd(_211724, _211720)), _211726 = _211724, _211722 = _211720], (86 ^ _209156) ^ [_212079, _212081, _212083, _212085] : [-(tptp_const_array1(_212085, _212081) = tptp_const_array1(_212083, _212079)), _212085 = _212083, _212081 = _212079], (96 ^ _209156) ^ [_212466, _212468, _212470, _212472, _212474, _212476] : [-(tptp_const_array2(_212476, _212472, _212468) = tptp_const_array2(_212474, _212470, _212466)), _212476 = _212474, _212472 = _212470, _212468 = _212466], (110 ^ _209156) ^ [_212954, _212956, _212958, _212960] : [-(dim(_212960, _212956) = dim(_212958, _212954)), _212960 = _212958, _212956 = _212954], (120 ^ _209156) ^ [_213285, _213287] : [_213287 = _213285, -(inv(_213287) = inv(_213285))], (126 ^ _209156) ^ [_213531, _213533, _213535, _213537] : [-(tptp_msub(_213537, _213533) = tptp_msub(_213535, _213531)), _213537 = _213535, _213533 = _213531], (136 ^ _209156) ^ [_213890, _213892, _213894, _213896] : [-(tptp_madd(_213896, _213892) = tptp_madd(_213894, _213890)), _213896 = _213894, _213892 = _213890], (146 ^ _209156) ^ [_214249, _214251, _214253, _214255] : [-(tptp_mmul(_214255, _214251) = tptp_mmul(_214253, _214249)), _214255 = _214253, _214251 = _214249], (156 ^ _209156) ^ [_214580, _214582] : [_214582 = _214580, -(trans(_214582) = trans(_214580))], (162 ^ _209156) ^ [_214854, _214856, _214858, _214860, _214862, _214864] : [-(sum(_214864, _214860, _214856) = sum(_214862, _214858, _214854)), _214864 = _214862, _214860 = _214858, _214856 = _214854], (176 ^ _209156) ^ [_215342, _215344, _215346, _215348] : [-(plus(_215348, _215344) = plus(_215346, _215342)), _215348 = _215346, _215344 = _215342], (186 ^ _209156) ^ [_215673, _215675] : [_215675 = _215673, -(pred(_215675) = pred(_215673))], (192 ^ _209156) ^ [_215919, _215921, _215923, _215925] : [-(minus(_215925, _215921) = minus(_215923, _215919)), _215925 = _215923, _215921 = _215919], (202 ^ _209156) ^ [_216334, _216336, _216338, _216340, _216342, _216344, _216346, _216348] : [-(tptp_update3(_216348, _216344, _216340, _216336) = tptp_update3(_216346, _216342, _216338, _216334)), _216348 = _216346, _216344 = _216342, _216340 = _216338, _216336 = _216334], (220 ^ _209156) ^ [_216995, _216997, _216999, _217001, _217003, _217005] : [-(tptp_update2(_217005, _217001, _216997) = tptp_update2(_217003, _216999, _216995)), _217005 = _217003, _217001 = _216999, _216997 = _216995], (234 ^ _209156) ^ [_217455, _217457] : [_217457 = _217455, -(succ(_217457) = succ(_217455))], (254 ^ _209156) ^ [_218197, _218199, _218201, _218203] : [-(a_select2(_218203, _218199) = a_select2(_218201, _218197)), _218203 = _218201, _218199 = _218197], (240 ^ _209156) ^ [_217729, _217731, _217733, _217735, _217737, _217739] : [-(a_select3(_217739, _217735, _217731) = a_select3(_217737, _217733, _217729)), _217739 = _217737, _217735 = _217733, _217731 = _217729], (869 ^ _209156) ^ [] : [-(gt(n5, n4))], (871 ^ _209156) ^ [] : [-(gt(n135299, n4))], (873 ^ _209156) ^ [] : [-(gt(n135299, n5))], (875 ^ _209156) ^ [] : [-(gt(n4, tptp_minus_1))], (877 ^ _209156) ^ [] : [-(gt(n5, tptp_minus_1))], (879 ^ _209156) ^ [] : [-(gt(n135299, tptp_minus_1))], (881 ^ _209156) ^ [] : [-(gt(n0, tptp_minus_1))], (883 ^ _209156) ^ [] : [-(gt(n1, tptp_minus_1))], (885 ^ _209156) ^ [] : [-(gt(n2, tptp_minus_1))], (887 ^ _209156) ^ [] : [-(gt(n3, tptp_minus_1))], (889 ^ _209156) ^ [] : [-(gt(n4, n0))], (891 ^ _209156) ^ [] : [-(gt(n5, n0))], (893 ^ _209156) ^ [] : [-(gt(n135299, n0))], (895 ^ _209156) ^ [] : [-(gt(n1, n0))], (897 ^ _209156) ^ [] : [-(gt(n2, n0))], (899 ^ _209156) ^ [] : [-(gt(n3, n0))], (901 ^ _209156) ^ [] : [-(gt(n4, n1))], (903 ^ _209156) ^ [] : [-(gt(n5, n1))], (905 ^ _209156) ^ [] : [-(gt(n135299, n1))], (907 ^ _209156) ^ [] : [-(gt(n2, n1))], (909 ^ _209156) ^ [] : [-(gt(n3, n1))], (911 ^ _209156) ^ [] : [-(gt(n4, n2))], (913 ^ _209156) ^ [] : [-(gt(n5, n2))], (915 ^ _209156) ^ [] : [-(gt(n135299, n2))], (917 ^ _209156) ^ [] : [-(gt(n3, n2))], (919 ^ _209156) ^ [] : [-(gt(n4, n3))], (921 ^ _209156) ^ [] : [-(gt(n5, n3))], (923 ^ _209156) ^ [] : [-(gt(n135299, n3))], (925 ^ _209156) ^ [_246037] : [leq(n0, _246037), leq(_246037, n4), -(_246037 = n0), -(_246037 = n1), -(_246037 = n2), -(_246037 = n3), -(_246037 = n4)], (951 ^ _209156) ^ [_246658] : [leq(n0, _246658), leq(_246658, n5), -(_246658 = n0), -(_246658 = n1), -(_246658 = n2), -(_246658 = n3), -(_246658 = n4), -(_246658 = n5)], (981 ^ _209156) ^ [_247365] : [-(_247365 = n0), leq(n0, _247365), leq(_247365, n0)], (991 ^ _209156) ^ [_247640] : [leq(n0, _247640), leq(_247640, n1), -(_247640 = n0), -(_247640 = n1)], (1005 ^ _209156) ^ [_248003] : [leq(n0, _248003), leq(_248003, n2), -(_248003 = n0), -(_248003 = n1), -(_248003 = n2)], (1045 ^ _209156) ^ [] : [-(succ(succ(succ(succ(n0)))) = n4)], (1047 ^ _209156) ^ [] : [-(succ(succ(succ(succ(succ(n0))))) = n5)], (1049 ^ _209156) ^ [] : [-(succ(n0) = n1)], (1051 ^ _209156) ^ [] : [-(succ(succ(n0)) = n2)], (1053 ^ _209156) ^ [] : [-(succ(succ(succ(n0))) = n3)], (1023 ^ _209156) ^ [_248452] : [leq(n0, _248452), leq(_248452, n3), -(_248452 = n0), -(_248452 = n1), -(_248452 = n2), -(_248452 = n3)], (264 ^ _209156) ^ [_218628, _218630] : [-(gt(_218630, _218628)), -(gt(_218628, _218630)), -(_218630 = _218628)], (274 ^ _209156) ^ [_218943, _218945, _218947] : [-(gt(_218947, _218943)), gt(_218947, _218945), gt(_218945, _218943)], (284 ^ _209156) ^ [_219222] : [gt(_219222, _219222)], (286 ^ _209156) ^ [_219300] : [-(leq(_219300, _219300))], (288 ^ _209156) ^ [_219421, _219423, _219425] : [-(leq(_219425, _219421)), leq(_219425, _219423), leq(_219423, _219421)], (298 ^ _209156) ^ [_219759, _219761] : [lt(_219761, _219759), -(gt(_219759, _219761))], (304 ^ _209156) ^ [_219921, _219923] : [gt(_219921, _219923), -(lt(_219923, _219921))], (310 ^ _209156) ^ [_220162, _220164] : [geq(_220164, _220162), -(leq(_220162, _220164))], (316 ^ _209156) ^ [_220324, _220326] : [leq(_220324, _220326), -(geq(_220326, _220324))], (322 ^ _209156) ^ [_220536, _220538] : [gt(_220536, _220538), -(leq(_220538, _220536))], (328 ^ _209156) ^ [_220746, _220748] : [-(gt(_220746, _220748)), leq(_220748, _220746), -(_220748 = _220746)], (338 ^ _209156) ^ [_221077, _221079] : [leq(_221079, pred(_221077)), -(gt(_221077, _221079))], (344 ^ _209156) ^ [_221243, _221245] : [gt(_221243, _221245), -(leq(_221245, pred(_221243)))], (350 ^ _209156) ^ [_221430] : [-(gt(succ(_221430), _221430))], (352 ^ _209156) ^ [_221539, _221541] : [leq(_221541, _221539), -(leq(_221541, succ(_221539)))], (358 ^ _209156) ^ [_221782, _221784] : [leq(_221784, _221782), -(gt(succ(_221782), _221784))], (364 ^ _209156) ^ [_221948, _221950] : [gt(succ(_221948), _221950), -(leq(_221950, _221948))], (370 ^ _209156) ^ [_222164, _222166] : [leq(n0, _222166), -(leq(uniform_int_rnd(_222164, _222166), _222166))], (376 ^ _209156) ^ [_222380, _222382] : [leq(n0, _222382), -(leq(n0, uniform_int_rnd(_222380, _222382)))], (382 ^ _209156) ^ [_222624, _222626, _222628, _222630] : [-(a_select2(tptp_const_array1(dim(_222628, _222626), _222624), _222630) = _222624), leq(_222628, _222630), leq(_222630, _222626)], (392 ^ _209156) ^ [_223031, _223033, _223035, _223037, _223039, _223041, _223043] : [-(a_select3(tptp_const_array2(dim(_223041, _223039), dim(_223035, _223033), _223031), _223043, _223037) = _223031), leq(_223041, _223043), leq(_223043, _223039), leq(_223035, _223037), leq(_223037, _223033)], (410 ^ _209156) ^ [_223626, _223628] : [413 ^ _209156 : [(414 ^ _209156) ^ [] : [-(leq(n0, 411 ^ [_223626, _223628]))], (416 ^ _209156) ^ [] : [-(leq(411 ^ [_223626, _223628], _223626))], (418 ^ _209156) ^ [] : [-(leq(n0, 412 ^ [_223626, _223628]))], (420 ^ _209156) ^ [] : [-(leq(412 ^ [_223626, _223628], _223626))], (422 ^ _209156) ^ [] : [a_select3(_223628, 411 ^ [_223626, _223628], 412 ^ [_223626, _223628]) = a_select3(_223628, 412 ^ [_223626, _223628], 411 ^ [_223626, _223628])]], 423 ^ _209156 : [(424 ^ _209156) ^ [_224383, _224385] : [-(a_select3(trans(_223628), _224385, _224383) = a_select3(trans(_223628), _224383, _224385)), leq(n0, _224385), leq(_224385, _223626), leq(n0, _224383), leq(_224383, _223626)]]], (442 ^ _209156) ^ [_224930, _224932] : [445 ^ _209156 : [(446 ^ _209156) ^ [] : [-(leq(n0, 443 ^ [_224930, _224932]))], (448 ^ _209156) ^ [] : [-(leq(443 ^ [_224930, _224932], _224930))], (450 ^ _209156) ^ [] : [-(leq(n0, 444 ^ [_224930, _224932]))], (452 ^ _209156) ^ [] : [-(leq(444 ^ [_224930, _224932], _224930))], (454 ^ _209156) ^ [] : [a_select3(_224932, 443 ^ [_224930, _224932], 444 ^ [_224930, _224932]) = a_select3(_224932, 444 ^ [_224930, _224932], 443 ^ [_224930, _224932])]], 455 ^ _209156 : [(456 ^ _209156) ^ [_225687, _225689] : [-(a_select3(inv(_224932), _225689, _225687) = a_select3(inv(_224932), _225687, _225689)), leq(n0, _225689), leq(_225689, _224930), leq(n0, _225687), leq(_225687, _224930)]]], (474 ^ _209156) ^ [_226234, _226236] : [477 ^ _209156 : [(478 ^ _209156) ^ [] : [-(leq(n0, 475 ^ [_226234, _226236]))], (480 ^ _209156) ^ [] : [-(leq(475 ^ [_226234, _226236], _226234))], (482 ^ _209156) ^ [] : [-(leq(n0, 476 ^ [_226234, _226236]))], (484 ^ _209156) ^ [] : [-(leq(476 ^ [_226234, _226236], _226234))], (486 ^ _209156) ^ [] : [a_select3(_226236, 475 ^ [_226234, _226236], 476 ^ [_226234, _226236]) = a_select3(_226236, 476 ^ [_226234, _226236], 475 ^ [_226234, _226236])]], 487 ^ _209156 : [(488 ^ _209156) ^ [_227047, _227049, _227051, _227053] : [-(a_select3(tptp_update3(_226236, _227049, _227049, _227047), _227053, _227051) = a_select3(tptp_update3(_226236, _227049, _227049, _227047), _227051, _227053)), leq(n0, _227053), leq(_227053, _226234), leq(n0, _227051), leq(_227051, _226234), leq(n0, _227049), leq(_227049, _226234)]]], (514 ^ _209156) ^ [_227866, _227868, _227870] : [519 ^ _209156 : [(520 ^ _209156) ^ [] : [-(leq(n0, 517 ^ [_227866, _227868, _227870]))], (522 ^ _209156) ^ [] : [-(leq(517 ^ [_227866, _227868, _227870], _227866))], (524 ^ _209156) ^ [] : [-(leq(n0, 518 ^ [_227866, _227868, _227870]))], (526 ^ _209156) ^ [] : [-(leq(518 ^ [_227866, _227868, _227870], _227866))], (528 ^ _209156) ^ [] : [a_select3(_227870, 517 ^ [_227866, _227868, _227870], 518 ^ [_227866, _227868, _227870]) = a_select3(_227870, 518 ^ [_227866, _227868, _227870], 517 ^ [_227866, _227868, _227870])]], 531 ^ _209156 : [(532 ^ _209156) ^ [] : [-(leq(n0, 529 ^ [_227866, _227868, _227870]))], (534 ^ _209156) ^ [] : [-(leq(529 ^ [_227866, _227868, _227870], _227866))], (536 ^ _209156) ^ [] : [-(leq(n0, 530 ^ [_227866, _227868, _227870]))], (538 ^ _209156) ^ [] : [-(leq(530 ^ [_227866, _227868, _227870], _227866))], (540 ^ _209156) ^ [] : [a_select3(_227868, 529 ^ [_227866, _227868, _227870], 530 ^ [_227866, _227868, _227870]) = a_select3(_227868, 530 ^ [_227866, _227868, _227870], 529 ^ [_227866, _227868, _227870])]], 541 ^ _209156 : [(542 ^ _209156) ^ [_229375, _229377] : [-(a_select3(tptp_madd(_227870, _227868), _229377, _229375) = a_select3(tptp_madd(_227870, _227868), _229375, _229377)), leq(n0, _229377), leq(_229377, _227866), leq(n0, _229375), leq(_229375, _227866)]]], (560 ^ _209156) ^ [_229961, _229963, _229965] : [565 ^ _209156 : [(566 ^ _209156) ^ [] : [-(leq(n0, 563 ^ [_229961, _229963, _229965]))], (568 ^ _209156) ^ [] : [-(leq(563 ^ [_229961, _229963, _229965], _229961))], (570 ^ _209156) ^ [] : [-(leq(n0, 564 ^ [_229961, _229963, _229965]))], (572 ^ _209156) ^ [] : [-(leq(564 ^ [_229961, _229963, _229965], _229961))], (574 ^ _209156) ^ [] : [a_select3(_229965, 563 ^ [_229961, _229963, _229965], 564 ^ [_229961, _229963, _229965]) = a_select3(_229965, 564 ^ [_229961, _229963, _229965], 563 ^ [_229961, _229963, _229965])]], 577 ^ _209156 : [(578 ^ _209156) ^ [] : [-(leq(n0, 575 ^ [_229961, _229963, _229965]))], (580 ^ _209156) ^ [] : [-(leq(575 ^ [_229961, _229963, _229965], _229961))], (582 ^ _209156) ^ [] : [-(leq(n0, 576 ^ [_229961, _229963, _229965]))], (584 ^ _209156) ^ [] : [-(leq(576 ^ [_229961, _229963, _229965], _229961))], (586 ^ _209156) ^ [] : [a_select3(_229963, 575 ^ [_229961, _229963, _229965], 576 ^ [_229961, _229963, _229965]) = a_select3(_229963, 576 ^ [_229961, _229963, _229965], 575 ^ [_229961, _229963, _229965])]], 587 ^ _209156 : [(588 ^ _209156) ^ [_231470, _231472] : [-(a_select3(tptp_msub(_229965, _229963), _231472, _231470) = a_select3(tptp_msub(_229965, _229963), _231470, _231472)), leq(n0, _231472), leq(_231472, _229961), leq(n0, _231470), leq(_231470, _229961)]]], (606 ^ _209156) ^ [_232056, _232058, _232060] : [609 ^ _209156 : [(610 ^ _209156) ^ [] : [-(leq(n0, 607 ^ [_232056, _232058, _232060]))], (612 ^ _209156) ^ [] : [-(leq(607 ^ [_232056, _232058, _232060], _232056))], (614 ^ _209156) ^ [] : [-(leq(n0, 608 ^ [_232056, _232058, _232060]))], (616 ^ _209156) ^ [] : [-(leq(608 ^ [_232056, _232058, _232060], _232056))], (618 ^ _209156) ^ [] : [a_select3(_232058, 607 ^ [_232056, _232058, _232060], 608 ^ [_232056, _232058, _232060]) = a_select3(_232058, 608 ^ [_232056, _232058, _232060], 607 ^ [_232056, _232058, _232060])]], 619 ^ _209156 : [(620 ^ _209156) ^ [_232869, _232871] : [-(a_select3(tptp_mmul(_232060, tptp_mmul(_232058, trans(_232060))), _232871, _232869) = a_select3(tptp_mmul(_232060, tptp_mmul(_232058, trans(_232060))), _232869, _232871)), leq(n0, _232871), leq(_232871, _232056), leq(n0, _232869), leq(_232869, _232056)]]], (638 ^ _209156) ^ [_233488, _233490, _233492, _233494] : [641 ^ _209156 : [(642 ^ _209156) ^ [] : [-(leq(n0, 639 ^ [_233488, _233490, _233492, _233494]))], (644 ^ _209156) ^ [] : [-(leq(639 ^ [_233488, _233490, _233492, _233494], _233488))], (646 ^ _209156) ^ [] : [-(leq(n0, 640 ^ [_233488, _233490, _233492, _233494]))], (648 ^ _209156) ^ [] : [-(leq(640 ^ [_233488, _233490, _233492, _233494], _233488))], (650 ^ _209156) ^ [] : [a_select3(_233492, 639 ^ [_233488, _233490, _233492, _233494], 640 ^ [_233488, _233490, _233492, _233494]) = a_select3(_233492, 640 ^ [_233488, _233490, _233492, _233494], 639 ^ [_233488, _233490, _233492, _233494])]], 651 ^ _209156 : [(652 ^ _209156) ^ [_234345, _234347] : [-(a_select3(tptp_mmul(_233494, tptp_mmul(_233492, trans(_233494))), _234347, _234345) = a_select3(tptp_mmul(_233494, tptp_mmul(_233492, trans(_233494))), _234345, _234347)), leq(n0, _234347), leq(_234347, _233490), leq(n0, _234345), leq(_234345, _233490)]]], (670 ^ _209156) ^ [_235040, _235042, _235044, _235046, _235048, _235050, _235052, _235054] : [675 ^ _209156 : [(676 ^ _209156) ^ [] : [-(leq(n0, 673 ^ [_235040, _235042, _235044, _235046, _235048, _235050, _235052, _235054]))], (678 ^ _209156) ^ [] : [-(leq(673 ^ [_235040, _235042, _235044, _235046, _235048, _235050, _235052, _235054], _235040))], (680 ^ _209156) ^ [] : [-(leq(n0, 674 ^ [_235040, _235042, _235044, _235046, _235048, _235050, _235052, _235054]))], (682 ^ _209156) ^ [] : [-(leq(674 ^ [_235040, _235042, _235044, _235046, _235048, _235050, _235052, _235054], _235040))], (684 ^ _209156) ^ [] : [a_select3(_235048, 673 ^ [_235040, _235042, _235044, _235046, _235048, _235050, _235052, _235054], 674 ^ [_235040, _235042, _235044, _235046, _235048, _235050, _235052, _235054]) = a_select3(_235048, 674 ^ [_235040, _235042, _235044, _235046, _235048, _235050, _235052, _235054], 673 ^ [_235040, _235042, _235044, _235046, _235048, _235050, _235052, _235054])]], 689 ^ _209156 : [(690 ^ _209156) ^ [] : [-(leq(n0, 687 ^ [_235040, _235042, _235044, _235046, _235048, _235050, _235052, _235054]))], (692 ^ _209156) ^ [] : [-(leq(687 ^ [_235040, _235042, _235044, _235046, _235048, _235050, _235052, _235054], _235042))], (694 ^ _209156) ^ [] : [-(leq(n0, 688 ^ [_235040, _235042, _235044, _235046, _235048, _235050, _235052, _235054]))], (696 ^ _209156) ^ [] : [-(leq(688 ^ [_235040, _235042, _235044, _235046, _235048, _235050, _235052, _235054], _235042))], (698 ^ _209156) ^ [] : [a_select3(_235054, 687 ^ [_235040, _235042, _235044, _235046, _235048, _235050, _235052, _235054], 688 ^ [_235040, _235042, _235044, _235046, _235048, _235050, _235052, _235054]) = a_select3(_235054, 688 ^ [_235040, _235042, _235044, _235046, _235048, _235050, _235052, _235054], 687 ^ [_235040, _235042, _235044, _235046, _235048, _235050, _235052, _235054])]], 701 ^ _209156 : [(702 ^ _209156) ^ [] : [-(leq(n0, 699 ^ [_235040, _235042, _235044, _235046, _235048, _235050, _235052, _235054]))], (704 ^ _209156) ^ [] : [-(leq(699 ^ [_235040, _235042, _235044, _235046, _235048, _235050, _235052, _235054], _235042))], (706 ^ _209156) ^ [] : [-(leq(n0, 700 ^ [_235040, _235042, _235044, _235046, _235048, _235050, _235052, _235054]))], (708 ^ _209156) ^ [] : [-(leq(700 ^ [_235040, _235042, _235044, _235046, _235048, _235050, _235052, _235054], _235042))], (710 ^ _209156) ^ [] : [a_select3(_235044, 699 ^ [_235040, _235042, _235044, _235046, _235048, _235050, _235052, _235054], 700 ^ [_235040, _235042, _235044, _235046, _235048, _235050, _235052, _235054]) = a_select3(_235044, 700 ^ [_235040, _235042, _235044, _235046, _235048, _235050, _235052, _235054], 699 ^ [_235040, _235042, _235044, _235046, _235048, _235050, _235052, _235054])]], 711 ^ _209156 : [(712 ^ _209156) ^ [_237968, _237970] : [-(a_select3(tptp_madd(_235054, tptp_mmul(_235052, tptp_mmul(tptp_madd(tptp_mmul(_235050, tptp_mmul(_235048, trans(_235050))), tptp_mmul(_235046, tptp_mmul(_235044, trans(_235046)))), trans(_235052)))), _237970, _237968) = a_select3(tptp_madd(_235054, tptp_mmul(_235052, tptp_mmul(tptp_madd(tptp_mmul(_235050, tptp_mmul(_235048, trans(_235050))), tptp_mmul(_235046, tptp_mmul(_235044, trans(_235046)))), trans(_235052)))), _237968, _237970)), leq(n0, _237970), leq(_237970, _235042), leq(n0, _237968), leq(_237968, _235042)]]], (730 ^ _209156) ^ [_238721] : [-(sum(n0, tptp_minus_1, _238721) = n0)], (732 ^ _209156) ^ [_238803] : [-(tptp_float_0_0 = sum(n0, tptp_minus_1, _238803))], (734 ^ _209156) ^ [] : [-(succ(tptp_minus_1) = n0)], (736 ^ _209156) ^ [_238938] : [-(plus(_238938, n1) = succ(_238938))], (738 ^ _209156) ^ [_239021] : [-(plus(n1, _239021) = succ(_239021))], (740 ^ _209156) ^ [_239104] : [-(plus(_239104, n2) = succ(succ(_239104)))], (742 ^ _209156) ^ [_239189] : [-(plus(n2, _239189) = succ(succ(_239189)))], (744 ^ _209156) ^ [_239274] : [-(plus(_239274, n3) = succ(succ(succ(_239274))))], (746 ^ _209156) ^ [_239361] : [-(plus(n3, _239361) = succ(succ(succ(_239361))))], (748 ^ _209156) ^ [_239448] : [-(plus(_239448, n4) = succ(succ(succ(succ(_239448)))))], (750 ^ _209156) ^ [_239537] : [-(plus(n4, _239537) = succ(succ(succ(succ(_239537)))))], (752 ^ _209156) ^ [_239626] : [-(plus(_239626, n5) = succ(succ(succ(succ(succ(_239626))))))], (754 ^ _209156) ^ [_239717] : [-(plus(n5, _239717) = succ(succ(succ(succ(succ(_239717))))))], (756 ^ _209156) ^ [_239808] : [-(minus(_239808, n1) = pred(_239808))], (758 ^ _209156) ^ [_239891] : [-(pred(succ(_239891)) = _239891)], (760 ^ _209156) ^ [_239973] : [-(succ(pred(_239973)) = _239973)], (762 ^ _209156) ^ [_240113, _240115] : [leq(succ(_240115), succ(_240113)), -(leq(_240115, _240113))], (768 ^ _209156) ^ [_240283, _240285] : [leq(_240285, _240283), -(leq(succ(_240285), succ(_240283)))], (774 ^ _209156) ^ [_240503, _240505] : [leq(succ(_240505), _240503), -(gt(_240503, _240505))], (780 ^ _209156) ^ [_240717, _240719] : [leq(minus(_240719, _240717), _240719), -(leq(n0, _240717))], (786 ^ _209156) ^ [_240946, _240948, _240950, _240952] : [-(a_select3(tptp_update3(_240952, _240950, _240948, _240946), _240950, _240948) = _240946)], (788 ^ _209156) ^ [_241138, _241140, _241142, _241144, _241146, _241148, _241150] : [-(a_select3(tptp_update3(_241142, _241150, _241148, _241138), _241146, _241144) = _241140), -(_241150 = _241146), _241148 = _241144, a_select3(_241142, _241146, _241144) = _241140], (802 ^ _209156) ^ [_241681, _241683, _241685, _241687, _241689, _241691] : [-(a_select3(tptp_update3(_241683, _241687, _241685, _241681), _241691, _241689) = _241681), 807 ^ _209156 : [(808 ^ _209156) ^ [] : [-(leq(n0, 805 ^ [_241681, _241683, _241685, _241687, _241689, _241691]))], (810 ^ _209156) ^ [] : [-(leq(n0, 806 ^ [_241681, _241683, _241685, _241687, _241689, _241691]))], (812 ^ _209156) ^ [] : [-(leq(805 ^ [_241681, _241683, _241685, _241687, _241689, _241691], _241687))], (814 ^ _209156) ^ [] : [-(leq(806 ^ [_241681, _241683, _241685, _241687, _241689, _241691], _241685))], (816 ^ _209156) ^ [] : [a_select3(_241683, 805 ^ [_241681, _241683, _241685, _241687, _241689, _241691], 806 ^ [_241681, _241683, _241685, _241687, _241689, _241691]) = _241681]], leq(n0, _241691), leq(_241691, _241687), leq(n0, _241689), leq(_241689, _241685)], (834 ^ _209156) ^ [_243023, _243025, _243027] : [-(a_select2(tptp_update2(_243027, _243025, _243023), _243025) = _243023)], (836 ^ _209156) ^ [_243183, _243185, _243187, _243189, _243191] : [-(a_select2(tptp_update2(_243187, _243191, _243183), _243189) = _243185), -(_243191 = _243189), a_select2(_243187, _243189) = _243185], (865 ^ _209156) ^ [] : [-(true)], (867 ^ _209156) ^ [] : [def = use], (846 ^ _209156) ^ [_243563, _243565, _243567, _243569] : [-(a_select2(tptp_update2(_243565, _243567, _243563), _243569) = _243563), 850 ^ _209156 : [(851 ^ _209156) ^ [] : [-(leq(n0, 849 ^ [_243563, _243565, _243567, _243569]))], (853 ^ _209156) ^ [] : [-(leq(849 ^ [_243563, _243565, _243567, _243569], _243567))], (855 ^ _209156) ^ [] : [a_select2(_243565, 849 ^ [_243563, _243565, _243567, _243569]) = _243563]], leq(n0, _243569), leq(_243569, _243567)]], input).
% 0.35/1.38  ncf('1',plain,[a_select2(rhoold_init, 1156 ^ []) = init],start(1162 ^ 0)).
% 0.35/1.38  ncf('1.1',plain,[-(a_select2(rhoold_init, 1156 ^ []) = init), 1133 : leq(n0, 1156 ^ []), 1133 : leq(1156 ^ [], n4), 1133 : gt(loopcounter, n1)],extension(1129 ^ 1,bind([[_251591], [1156 ^ []]]))).
% 0.35/1.38  ncf('1.1.1',plain,[-(leq(n0, 1156 ^ []))],extension(1158 ^ 4)).
% 0.35/1.38  ncf('1.1.2',plain,[-(leq(1156 ^ [], n4))],extension(1160 ^ 4)).
% 0.35/1.38  ncf('1.1.3',plain,[-(gt(loopcounter, n1))],extension(1055 ^ 2)).
% 0.35/1.38  %-----------------------------------------------------
% 0.35/1.38  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------