%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SWV166+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n022.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 12:20:05 EDT 2023

% Result   : Theorem 0.34s 1.39s
% Output   : Proof 0.34s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SWV166+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.06/0.12  % Command  : nanocop.sh %s %d
% 0.13/0.34  % Computer : n022.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 02:41:31 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.34/1.39  
% 0.34/1.39  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 0.34/1.39  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.34/1.39  %-----------------------------------------------------
% 0.34/1.39  ncf(matrix, plain, [(1164 ^ _210220) ^ [] : [-(leq(n0, 1162 ^ []))], (1166 ^ _210220) ^ [] : [-(leq(1162 ^ [], n4))], (1168 ^ _210220) ^ [] : [a_select2(rhoold_init, 1162 ^ []) = init], (1055 ^ _210220) ^ [] : [n0 = pv90], (1057 ^ _210220) ^ [] : [-(leq(n0, pv40))], (1059 ^ _210220) ^ [] : [-(leq(pv40, n4))], (1061 ^ _210220) ^ [] : [-(gt(loopcounter, n1))], (1063 ^ _210220) ^ [_250747] : [leq(n0, _250747), leq(_250747, n135299), 1070 ^ _210220 : [(1071 ^ _210220) ^ [_250975] : [-(a_select3(q_init, _250747, _250975) = init), leq(n0, _250975), leq(_250975, n4)]]], (1081 ^ _210220) ^ [_251277] : [-(a_select2(rho_init, _251277) = init), leq(n0, _251277), leq(_251277, n4)], (1091 ^ _210220) ^ [_251558] : [-(a_select2(mu_init, _251558) = init), leq(n0, _251558), leq(_251558, pred(pv40))], (1101 ^ _210220) ^ [_251839] : [-(a_select2(sigma_init, _251839) = init), leq(n0, _251839), leq(_251839, pred(pv40))], (1111 ^ _210220) ^ [_252120] : [-(a_select3(center_init, _252120, n0) = init), leq(n0, _252120), leq(_252120, n4)], (1121 ^ _210220) ^ [] : [gt(loopcounter, n1), 1124 ^ _210220 : [(1125 ^ _210220) ^ [_252465] : [-(a_select2(muold_init, _252465) = init), leq(n0, _252465), leq(_252465, n4)]]], (1135 ^ _210220) ^ [] : [gt(loopcounter, n1), 1138 ^ _210220 : [(1139 ^ _210220) ^ [_252813] : [-(a_select2(rhoold_init, _252813) = init), leq(n0, _252813), leq(_252813, n4)]]], (1149 ^ _210220) ^ [] : [gt(loopcounter, n1), 1152 ^ _210220 : [(1153 ^ _210220) ^ [_253141] : [-(a_select2(sigmaold_init, _253141) = init), leq(n0, _253141), leq(_253141, n4)]]], (2 ^ _210220) ^ [_210364] : [-(_210364 = _210364)], (4 ^ _210220) ^ [_210471, _210473] : [_210473 = _210471, -(_210471 = _210473)], (10 ^ _210220) ^ [_210675, _210677, _210679] : [-(_210679 = _210675), _210679 = _210677, _210677 = _210675], (20 ^ _210220) ^ [_211016, _211018, _211020, _211022] : [-(lt(_211020, _211016)), lt(_211022, _211018), _211022 = _211020, _211018 = _211016], (34 ^ _210220) ^ [_211460, _211462, _211464, _211466] : [-(geq(_211464, _211460)), geq(_211466, _211462), _211466 = _211464, _211462 = _211460], (48 ^ _210220) ^ [_211904, _211906, _211908, _211910] : [-(gt(_211908, _211904)), gt(_211910, _211906), _211910 = _211908, _211906 = _211904], (62 ^ _210220) ^ [_212328, _212330, _212332, _212334] : [-(leq(_212332, _212328)), leq(_212334, _212330), _212334 = _212332, _212330 = _212328], (76 ^ _210220) ^ [_212784, _212786, _212788, _212790] : [-(uniform_int_rnd(_212790, _212786) = uniform_int_rnd(_212788, _212784)), _212790 = _212788, _212786 = _212784], (86 ^ _210220) ^ [_213143, _213145, _213147, _213149] : [-(tptp_const_array1(_213149, _213145) = tptp_const_array1(_213147, _213143)), _213149 = _213147, _213145 = _213143], (96 ^ _210220) ^ [_213530, _213532, _213534, _213536, _213538, _213540] : [-(tptp_const_array2(_213540, _213536, _213532) = tptp_const_array2(_213538, _213534, _213530)), _213540 = _213538, _213536 = _213534, _213532 = _213530], (110 ^ _210220) ^ [_214018, _214020, _214022, _214024] : [-(dim(_214024, _214020) = dim(_214022, _214018)), _214024 = _214022, _214020 = _214018], (120 ^ _210220) ^ [_214349, _214351] : [_214351 = _214349, -(inv(_214351) = inv(_214349))], (126 ^ _210220) ^ [_214595, _214597, _214599, _214601] : [-(tptp_msub(_214601, _214597) = tptp_msub(_214599, _214595)), _214601 = _214599, _214597 = _214595], (136 ^ _210220) ^ [_214954, _214956, _214958, _214960] : [-(tptp_madd(_214960, _214956) = tptp_madd(_214958, _214954)), _214960 = _214958, _214956 = _214954], (146 ^ _210220) ^ [_215313, _215315, _215317, _215319] : [-(tptp_mmul(_215319, _215315) = tptp_mmul(_215317, _215313)), _215319 = _215317, _215315 = _215313], (156 ^ _210220) ^ [_215644, _215646] : [_215646 = _215644, -(trans(_215646) = trans(_215644))], (162 ^ _210220) ^ [_215918, _215920, _215922, _215924, _215926, _215928] : [-(sum(_215928, _215924, _215920) = sum(_215926, _215922, _215918)), _215928 = _215926, _215924 = _215922, _215920 = _215918], (176 ^ _210220) ^ [_216406, _216408, _216410, _216412] : [-(plus(_216412, _216408) = plus(_216410, _216406)), _216412 = _216410, _216408 = _216406], (186 ^ _210220) ^ [_216765, _216767, _216769, _216771] : [-(minus(_216771, _216767) = minus(_216769, _216765)), _216771 = _216769, _216767 = _216765], (196 ^ _210220) ^ [_217180, _217182, _217184, _217186, _217188, _217190, _217192, _217194] : [-(tptp_update3(_217194, _217190, _217186, _217182) = tptp_update3(_217192, _217188, _217184, _217180)), _217194 = _217192, _217190 = _217188, _217186 = _217184, _217182 = _217180], (214 ^ _210220) ^ [_217841, _217843, _217845, _217847, _217849, _217851] : [-(tptp_update2(_217851, _217847, _217843) = tptp_update2(_217849, _217845, _217841)), _217851 = _217849, _217847 = _217845, _217843 = _217841], (228 ^ _210220) ^ [_218301, _218303] : [_218303 = _218301, -(succ(_218303) = succ(_218301))], (234 ^ _210220) ^ [_218519, _218521] : [_218521 = _218519, -(pred(_218521) = pred(_218519))], (254 ^ _210220) ^ [_219261, _219263, _219265, _219267] : [-(a_select2(_219267, _219263) = a_select2(_219265, _219261)), _219267 = _219265, _219263 = _219261], (240 ^ _210220) ^ [_218793, _218795, _218797, _218799, _218801, _218803] : [-(a_select3(_218803, _218799, _218795) = a_select3(_218801, _218797, _218793)), _218803 = _218801, _218799 = _218797, _218795 = _218793], (869 ^ _210220) ^ [] : [-(gt(n5, n4))], (871 ^ _210220) ^ [] : [-(gt(n135299, n4))], (873 ^ _210220) ^ [] : [-(gt(n135299, n5))], (875 ^ _210220) ^ [] : [-(gt(n4, tptp_minus_1))], (877 ^ _210220) ^ [] : [-(gt(n5, tptp_minus_1))], (879 ^ _210220) ^ [] : [-(gt(n135299, tptp_minus_1))], (881 ^ _210220) ^ [] : [-(gt(n0, tptp_minus_1))], (883 ^ _210220) ^ [] : [-(gt(n1, tptp_minus_1))], (885 ^ _210220) ^ [] : [-(gt(n2, tptp_minus_1))], (887 ^ _210220) ^ [] : [-(gt(n3, tptp_minus_1))], (889 ^ _210220) ^ [] : [-(gt(n4, n0))], (891 ^ _210220) ^ [] : [-(gt(n5, n0))], (893 ^ _210220) ^ [] : [-(gt(n135299, n0))], (895 ^ _210220) ^ [] : [-(gt(n1, n0))], (897 ^ _210220) ^ [] : [-(gt(n2, n0))], (899 ^ _210220) ^ [] : [-(gt(n3, n0))], (901 ^ _210220) ^ [] : [-(gt(n4, n1))], (903 ^ _210220) ^ [] : [-(gt(n5, n1))], (905 ^ _210220) ^ [] : [-(gt(n135299, n1))], (907 ^ _210220) ^ [] : [-(gt(n2, n1))], (909 ^ _210220) ^ [] : [-(gt(n3, n1))], (911 ^ _210220) ^ [] : [-(gt(n4, n2))], (913 ^ _210220) ^ [] : [-(gt(n5, n2))], (915 ^ _210220) ^ [] : [-(gt(n135299, n2))], (917 ^ _210220) ^ [] : [-(gt(n3, n2))], (919 ^ _210220) ^ [] : [-(gt(n4, n3))], (921 ^ _210220) ^ [] : [-(gt(n5, n3))], (923 ^ _210220) ^ [] : [-(gt(n135299, n3))], (925 ^ _210220) ^ [_247101] : [leq(n0, _247101), leq(_247101, n4), -(_247101 = n0), -(_247101 = n1), -(_247101 = n2), -(_247101 = n3), -(_247101 = n4)], (951 ^ _210220) ^ [_247722] : [leq(n0, _247722), leq(_247722, n5), -(_247722 = n0), -(_247722 = n1), -(_247722 = n2), -(_247722 = n3), -(_247722 = n4), -(_247722 = n5)], (981 ^ _210220) ^ [_248429] : [-(_248429 = n0), leq(n0, _248429), leq(_248429, n0)], (991 ^ _210220) ^ [_248704] : [leq(n0, _248704), leq(_248704, n1), -(_248704 = n0), -(_248704 = n1)], (1005 ^ _210220) ^ [_249067] : [leq(n0, _249067), leq(_249067, n2), -(_249067 = n0), -(_249067 = n1), -(_249067 = n2)], (1045 ^ _210220) ^ [] : [-(succ(succ(succ(succ(n0)))) = n4)], (1047 ^ _210220) ^ [] : [-(succ(succ(succ(succ(succ(n0))))) = n5)], (1049 ^ _210220) ^ [] : [-(succ(n0) = n1)], (1051 ^ _210220) ^ [] : [-(succ(succ(n0)) = n2)], (1053 ^ _210220) ^ [] : [-(succ(succ(succ(n0))) = n3)], (1023 ^ _210220) ^ [_249516] : [leq(n0, _249516), leq(_249516, n3), -(_249516 = n0), -(_249516 = n1), -(_249516 = n2), -(_249516 = n3)], (264 ^ _210220) ^ [_219692, _219694] : [-(gt(_219694, _219692)), -(gt(_219692, _219694)), -(_219694 = _219692)], (274 ^ _210220) ^ [_220007, _220009, _220011] : [-(gt(_220011, _220007)), gt(_220011, _220009), gt(_220009, _220007)], (284 ^ _210220) ^ [_220286] : [gt(_220286, _220286)], (286 ^ _210220) ^ [_220364] : [-(leq(_220364, _220364))], (288 ^ _210220) ^ [_220485, _220487, _220489] : [-(leq(_220489, _220485)), leq(_220489, _220487), leq(_220487, _220485)], (298 ^ _210220) ^ [_220823, _220825] : [lt(_220825, _220823), -(gt(_220823, _220825))], (304 ^ _210220) ^ [_220985, _220987] : [gt(_220985, _220987), -(lt(_220987, _220985))], (310 ^ _210220) ^ [_221226, _221228] : [geq(_221228, _221226), -(leq(_221226, _221228))], (316 ^ _210220) ^ [_221388, _221390] : [leq(_221388, _221390), -(geq(_221390, _221388))], (322 ^ _210220) ^ [_221600, _221602] : [gt(_221600, _221602), -(leq(_221602, _221600))], (328 ^ _210220) ^ [_221810, _221812] : [-(gt(_221810, _221812)), leq(_221812, _221810), -(_221812 = _221810)], (338 ^ _210220) ^ [_222141, _222143] : [leq(_222143, pred(_222141)), -(gt(_222141, _222143))], (344 ^ _210220) ^ [_222307, _222309] : [gt(_222307, _222309), -(leq(_222309, pred(_222307)))], (350 ^ _210220) ^ [_222494] : [-(gt(succ(_222494), _222494))], (352 ^ _210220) ^ [_222603, _222605] : [leq(_222605, _222603), -(leq(_222605, succ(_222603)))], (358 ^ _210220) ^ [_222846, _222848] : [leq(_222848, _222846), -(gt(succ(_222846), _222848))], (364 ^ _210220) ^ [_223012, _223014] : [gt(succ(_223012), _223014), -(leq(_223014, _223012))], (370 ^ _210220) ^ [_223228, _223230] : [leq(n0, _223230), -(leq(uniform_int_rnd(_223228, _223230), _223230))], (376 ^ _210220) ^ [_223444, _223446] : [leq(n0, _223446), -(leq(n0, uniform_int_rnd(_223444, _223446)))], (382 ^ _210220) ^ [_223688, _223690, _223692, _223694] : [-(a_select2(tptp_const_array1(dim(_223692, _223690), _223688), _223694) = _223688), leq(_223692, _223694), leq(_223694, _223690)], (392 ^ _210220) ^ [_224095, _224097, _224099, _224101, _224103, _224105, _224107] : [-(a_select3(tptp_const_array2(dim(_224105, _224103), dim(_224099, _224097), _224095), _224107, _224101) = _224095), leq(_224105, _224107), leq(_224107, _224103), leq(_224099, _224101), leq(_224101, _224097)], (410 ^ _210220) ^ [_224690, _224692] : [413 ^ _210220 : [(414 ^ _210220) ^ [] : [-(leq(n0, 411 ^ [_224690, _224692]))], (416 ^ _210220) ^ [] : [-(leq(411 ^ [_224690, _224692], _224690))], (418 ^ _210220) ^ [] : [-(leq(n0, 412 ^ [_224690, _224692]))], (420 ^ _210220) ^ [] : [-(leq(412 ^ [_224690, _224692], _224690))], (422 ^ _210220) ^ [] : [a_select3(_224692, 411 ^ [_224690, _224692], 412 ^ [_224690, _224692]) = a_select3(_224692, 412 ^ [_224690, _224692], 411 ^ [_224690, _224692])]], 423 ^ _210220 : [(424 ^ _210220) ^ [_225447, _225449] : [-(a_select3(trans(_224692), _225449, _225447) = a_select3(trans(_224692), _225447, _225449)), leq(n0, _225449), leq(_225449, _224690), leq(n0, _225447), leq(_225447, _224690)]]], (442 ^ _210220) ^ [_225994, _225996] : [445 ^ _210220 : [(446 ^ _210220) ^ [] : [-(leq(n0, 443 ^ [_225994, _225996]))], (448 ^ _210220) ^ [] : [-(leq(443 ^ [_225994, _225996], _225994))], (450 ^ _210220) ^ [] : [-(leq(n0, 444 ^ [_225994, _225996]))], (452 ^ _210220) ^ [] : [-(leq(444 ^ [_225994, _225996], _225994))], (454 ^ _210220) ^ [] : [a_select3(_225996, 443 ^ [_225994, _225996], 444 ^ [_225994, _225996]) = a_select3(_225996, 444 ^ [_225994, _225996], 443 ^ [_225994, _225996])]], 455 ^ _210220 : [(456 ^ _210220) ^ [_226751, _226753] : [-(a_select3(inv(_225996), _226753, _226751) = a_select3(inv(_225996), _226751, _226753)), leq(n0, _226753), leq(_226753, _225994), leq(n0, _226751), leq(_226751, _225994)]]], (474 ^ _210220) ^ [_227298, _227300] : [477 ^ _210220 : [(478 ^ _210220) ^ [] : [-(leq(n0, 475 ^ [_227298, _227300]))], (480 ^ _210220) ^ [] : [-(leq(475 ^ [_227298, _227300], _227298))], (482 ^ _210220) ^ [] : [-(leq(n0, 476 ^ [_227298, _227300]))], (484 ^ _210220) ^ [] : [-(leq(476 ^ [_227298, _227300], _227298))], (486 ^ _210220) ^ [] : [a_select3(_227300, 475 ^ [_227298, _227300], 476 ^ [_227298, _227300]) = a_select3(_227300, 476 ^ [_227298, _227300], 475 ^ [_227298, _227300])]], 487 ^ _210220 : [(488 ^ _210220) ^ [_228111, _228113, _228115, _228117] : [-(a_select3(tptp_update3(_227300, _228113, _228113, _228111), _228117, _228115) = a_select3(tptp_update3(_227300, _228113, _228113, _228111), _228115, _228117)), leq(n0, _228117), leq(_228117, _227298), leq(n0, _228115), leq(_228115, _227298), leq(n0, _228113), leq(_228113, _227298)]]], (514 ^ _210220) ^ [_228930, _228932, _228934] : [519 ^ _210220 : [(520 ^ _210220) ^ [] : [-(leq(n0, 517 ^ [_228930, _228932, _228934]))], (522 ^ _210220) ^ [] : [-(leq(517 ^ [_228930, _228932, _228934], _228930))], (524 ^ _210220) ^ [] : [-(leq(n0, 518 ^ [_228930, _228932, _228934]))], (526 ^ _210220) ^ [] : [-(leq(518 ^ [_228930, _228932, _228934], _228930))], (528 ^ _210220) ^ [] : [a_select3(_228934, 517 ^ [_228930, _228932, _228934], 518 ^ [_228930, _228932, _228934]) = a_select3(_228934, 518 ^ [_228930, _228932, _228934], 517 ^ [_228930, _228932, _228934])]], 531 ^ _210220 : [(532 ^ _210220) ^ [] : [-(leq(n0, 529 ^ [_228930, _228932, _228934]))], (534 ^ _210220) ^ [] : [-(leq(529 ^ [_228930, _228932, _228934], _228930))], (536 ^ _210220) ^ [] : [-(leq(n0, 530 ^ [_228930, _228932, _228934]))], (538 ^ _210220) ^ [] : [-(leq(530 ^ [_228930, _228932, _228934], _228930))], (540 ^ _210220) ^ [] : [a_select3(_228932, 529 ^ [_228930, _228932, _228934], 530 ^ [_228930, _228932, _228934]) = a_select3(_228932, 530 ^ [_228930, _228932, _228934], 529 ^ [_228930, _228932, _228934])]], 541 ^ _210220 : [(542 ^ _210220) ^ [_230439, _230441] : [-(a_select3(tptp_madd(_228934, _228932), _230441, _230439) = a_select3(tptp_madd(_228934, _228932), _230439, _230441)), leq(n0, _230441), leq(_230441, _228930), leq(n0, _230439), leq(_230439, _228930)]]], (560 ^ _210220) ^ [_231025, _231027, _231029] : [565 ^ _210220 : [(566 ^ _210220) ^ [] : [-(leq(n0, 563 ^ [_231025, _231027, _231029]))], (568 ^ _210220) ^ [] : [-(leq(563 ^ [_231025, _231027, _231029], _231025))], (570 ^ _210220) ^ [] : [-(leq(n0, 564 ^ [_231025, _231027, _231029]))], (572 ^ _210220) ^ [] : [-(leq(564 ^ [_231025, _231027, _231029], _231025))], (574 ^ _210220) ^ [] : [a_select3(_231029, 563 ^ [_231025, _231027, _231029], 564 ^ [_231025, _231027, _231029]) = a_select3(_231029, 564 ^ [_231025, _231027, _231029], 563 ^ [_231025, _231027, _231029])]], 577 ^ _210220 : [(578 ^ _210220) ^ [] : [-(leq(n0, 575 ^ [_231025, _231027, _231029]))], (580 ^ _210220) ^ [] : [-(leq(575 ^ [_231025, _231027, _231029], _231025))], (582 ^ _210220) ^ [] : [-(leq(n0, 576 ^ [_231025, _231027, _231029]))], (584 ^ _210220) ^ [] : [-(leq(576 ^ [_231025, _231027, _231029], _231025))], (586 ^ _210220) ^ [] : [a_select3(_231027, 575 ^ [_231025, _231027, _231029], 576 ^ [_231025, _231027, _231029]) = a_select3(_231027, 576 ^ [_231025, _231027, _231029], 575 ^ [_231025, _231027, _231029])]], 587 ^ _210220 : [(588 ^ _210220) ^ [_232534, _232536] : [-(a_select3(tptp_msub(_231029, _231027), _232536, _232534) = a_select3(tptp_msub(_231029, _231027), _232534, _232536)), leq(n0, _232536), leq(_232536, _231025), leq(n0, _232534), leq(_232534, _231025)]]], (606 ^ _210220) ^ [_233120, _233122, _233124] : [609 ^ _210220 : [(610 ^ _210220) ^ [] : [-(leq(n0, 607 ^ [_233120, _233122, _233124]))], (612 ^ _210220) ^ [] : [-(leq(607 ^ [_233120, _233122, _233124], _233120))], (614 ^ _210220) ^ [] : [-(leq(n0, 608 ^ [_233120, _233122, _233124]))], (616 ^ _210220) ^ [] : [-(leq(608 ^ [_233120, _233122, _233124], _233120))], (618 ^ _210220) ^ [] : [a_select3(_233122, 607 ^ [_233120, _233122, _233124], 608 ^ [_233120, _233122, _233124]) = a_select3(_233122, 608 ^ [_233120, _233122, _233124], 607 ^ [_233120, _233122, _233124])]], 619 ^ _210220 : [(620 ^ _210220) ^ [_233933, _233935] : [-(a_select3(tptp_mmul(_233124, tptp_mmul(_233122, trans(_233124))), _233935, _233933) = a_select3(tptp_mmul(_233124, tptp_mmul(_233122, trans(_233124))), _233933, _233935)), leq(n0, _233935), leq(_233935, _233120), leq(n0, _233933), leq(_233933, _233120)]]], (638 ^ _210220) ^ [_234552, _234554, _234556, _234558] : [641 ^ _210220 : [(642 ^ _210220) ^ [] : [-(leq(n0, 639 ^ [_234552, _234554, _234556, _234558]))], (644 ^ _210220) ^ [] : [-(leq(639 ^ [_234552, _234554, _234556, _234558], _234552))], (646 ^ _210220) ^ [] : [-(leq(n0, 640 ^ [_234552, _234554, _234556, _234558]))], (648 ^ _210220) ^ [] : [-(leq(640 ^ [_234552, _234554, _234556, _234558], _234552))], (650 ^ _210220) ^ [] : [a_select3(_234556, 639 ^ [_234552, _234554, _234556, _234558], 640 ^ [_234552, _234554, _234556, _234558]) = a_select3(_234556, 640 ^ [_234552, _234554, _234556, _234558], 639 ^ [_234552, _234554, _234556, _234558])]], 651 ^ _210220 : [(652 ^ _210220) ^ [_235409, _235411] : [-(a_select3(tptp_mmul(_234558, tptp_mmul(_234556, trans(_234558))), _235411, _235409) = a_select3(tptp_mmul(_234558, tptp_mmul(_234556, trans(_234558))), _235409, _235411)), leq(n0, _235411), leq(_235411, _234554), leq(n0, _235409), leq(_235409, _234554)]]], (670 ^ _210220) ^ [_236104, _236106, _236108, _236110, _236112, _236114, _236116, _236118] : [675 ^ _210220 : [(676 ^ _210220) ^ [] : [-(leq(n0, 673 ^ [_236104, _236106, _236108, _236110, _236112, _236114, _236116, _236118]))], (678 ^ _210220) ^ [] : [-(leq(673 ^ [_236104, _236106, _236108, _236110, _236112, _236114, _236116, _236118], _236104))], (680 ^ _210220) ^ [] : [-(leq(n0, 674 ^ [_236104, _236106, _236108, _236110, _236112, _236114, _236116, _236118]))], (682 ^ _210220) ^ [] : [-(leq(674 ^ [_236104, _236106, _236108, _236110, _236112, _236114, _236116, _236118], _236104))], (684 ^ _210220) ^ [] : [a_select3(_236112, 673 ^ [_236104, _236106, _236108, _236110, _236112, _236114, _236116, _236118], 674 ^ [_236104, _236106, _236108, _236110, _236112, _236114, _236116, _236118]) = a_select3(_236112, 674 ^ [_236104, _236106, _236108, _236110, _236112, _236114, _236116, _236118], 673 ^ [_236104, _236106, _236108, _236110, _236112, _236114, _236116, _236118])]], 689 ^ _210220 : [(690 ^ _210220) ^ [] : [-(leq(n0, 687 ^ [_236104, _236106, _236108, _236110, _236112, _236114, _236116, _236118]))], (692 ^ _210220) ^ [] : [-(leq(687 ^ [_236104, _236106, _236108, _236110, _236112, _236114, _236116, _236118], _236106))], (694 ^ _210220) ^ [] : [-(leq(n0, 688 ^ [_236104, _236106, _236108, _236110, _236112, _236114, _236116, _236118]))], (696 ^ _210220) ^ [] : [-(leq(688 ^ [_236104, _236106, _236108, _236110, _236112, _236114, _236116, _236118], _236106))], (698 ^ _210220) ^ [] : [a_select3(_236118, 687 ^ [_236104, _236106, _236108, _236110, _236112, _236114, _236116, _236118], 688 ^ [_236104, _236106, _236108, _236110, _236112, _236114, _236116, _236118]) = a_select3(_236118, 688 ^ [_236104, _236106, _236108, _236110, _236112, _236114, _236116, _236118], 687 ^ [_236104, _236106, _236108, _236110, _236112, _236114, _236116, _236118])]], 701 ^ _210220 : [(702 ^ _210220) ^ [] : [-(leq(n0, 699 ^ [_236104, _236106, _236108, _236110, _236112, _236114, _236116, _236118]))], (704 ^ _210220) ^ [] : [-(leq(699 ^ [_236104, _236106, _236108, _236110, _236112, _236114, _236116, _236118], _236106))], (706 ^ _210220) ^ [] : [-(leq(n0, 700 ^ [_236104, _236106, _236108, _236110, _236112, _236114, _236116, _236118]))], (708 ^ _210220) ^ [] : [-(leq(700 ^ [_236104, _236106, _236108, _236110, _236112, _236114, _236116, _236118], _236106))], (710 ^ _210220) ^ [] : [a_select3(_236108, 699 ^ [_236104, _236106, _236108, _236110, _236112, _236114, _236116, _236118], 700 ^ [_236104, _236106, _236108, _236110, _236112, _236114, _236116, _236118]) = a_select3(_236108, 700 ^ [_236104, _236106, _236108, _236110, _236112, _236114, _236116, _236118], 699 ^ [_236104, _236106, _236108, _236110, _236112, _236114, _236116, _236118])]], 711 ^ _210220 : [(712 ^ _210220) ^ [_239032, _239034] : [-(a_select3(tptp_madd(_236118, tptp_mmul(_236116, tptp_mmul(tptp_madd(tptp_mmul(_236114, tptp_mmul(_236112, trans(_236114))), tptp_mmul(_236110, tptp_mmul(_236108, trans(_236110)))), trans(_236116)))), _239034, _239032) = a_select3(tptp_madd(_236118, tptp_mmul(_236116, tptp_mmul(tptp_madd(tptp_mmul(_236114, tptp_mmul(_236112, trans(_236114))), tptp_mmul(_236110, tptp_mmul(_236108, trans(_236110)))), trans(_236116)))), _239032, _239034)), leq(n0, _239034), leq(_239034, _236106), leq(n0, _239032), leq(_239032, _236106)]]], (730 ^ _210220) ^ [_239785] : [-(sum(n0, tptp_minus_1, _239785) = n0)], (732 ^ _210220) ^ [_239867] : [-(tptp_float_0_0 = sum(n0, tptp_minus_1, _239867))], (734 ^ _210220) ^ [] : [-(succ(tptp_minus_1) = n0)], (736 ^ _210220) ^ [_240002] : [-(plus(_240002, n1) = succ(_240002))], (738 ^ _210220) ^ [_240085] : [-(plus(n1, _240085) = succ(_240085))], (740 ^ _210220) ^ [_240168] : [-(plus(_240168, n2) = succ(succ(_240168)))], (742 ^ _210220) ^ [_240253] : [-(plus(n2, _240253) = succ(succ(_240253)))], (744 ^ _210220) ^ [_240338] : [-(plus(_240338, n3) = succ(succ(succ(_240338))))], (746 ^ _210220) ^ [_240425] : [-(plus(n3, _240425) = succ(succ(succ(_240425))))], (748 ^ _210220) ^ [_240512] : [-(plus(_240512, n4) = succ(succ(succ(succ(_240512)))))], (750 ^ _210220) ^ [_240601] : [-(plus(n4, _240601) = succ(succ(succ(succ(_240601)))))], (752 ^ _210220) ^ [_240690] : [-(plus(_240690, n5) = succ(succ(succ(succ(succ(_240690))))))], (754 ^ _210220) ^ [_240781] : [-(plus(n5, _240781) = succ(succ(succ(succ(succ(_240781))))))], (756 ^ _210220) ^ [_240872] : [-(minus(_240872, n1) = pred(_240872))], (758 ^ _210220) ^ [_240955] : [-(pred(succ(_240955)) = _240955)], (760 ^ _210220) ^ [_241037] : [-(succ(pred(_241037)) = _241037)], (762 ^ _210220) ^ [_241177, _241179] : [leq(succ(_241179), succ(_241177)), -(leq(_241179, _241177))], (768 ^ _210220) ^ [_241347, _241349] : [leq(_241349, _241347), -(leq(succ(_241349), succ(_241347)))], (774 ^ _210220) ^ [_241567, _241569] : [leq(succ(_241569), _241567), -(gt(_241567, _241569))], (780 ^ _210220) ^ [_241781, _241783] : [leq(minus(_241783, _241781), _241783), -(leq(n0, _241781))], (786 ^ _210220) ^ [_242010, _242012, _242014, _242016] : [-(a_select3(tptp_update3(_242016, _242014, _242012, _242010), _242014, _242012) = _242010)], (788 ^ _210220) ^ [_242202, _242204, _242206, _242208, _242210, _242212, _242214] : [-(a_select3(tptp_update3(_242206, _242214, _242212, _242202), _242210, _242208) = _242204), -(_242214 = _242210), _242212 = _242208, a_select3(_242206, _242210, _242208) = _242204], (802 ^ _210220) ^ [_242745, _242747, _242749, _242751, _242753, _242755] : [-(a_select3(tptp_update3(_242747, _242751, _242749, _242745), _242755, _242753) = _242745), 807 ^ _210220 : [(808 ^ _210220) ^ [] : [-(leq(n0, 805 ^ [_242745, _242747, _242749, _242751, _242753, _242755]))], (810 ^ _210220) ^ [] : [-(leq(n0, 806 ^ [_242745, _242747, _242749, _242751, _242753, _242755]))], (812 ^ _210220) ^ [] : [-(leq(805 ^ [_242745, _242747, _242749, _242751, _242753, _242755], _242751))], (814 ^ _210220) ^ [] : [-(leq(806 ^ [_242745, _242747, _242749, _242751, _242753, _242755], _242749))], (816 ^ _210220) ^ [] : [a_select3(_242747, 805 ^ [_242745, _242747, _242749, _242751, _242753, _242755], 806 ^ [_242745, _242747, _242749, _242751, _242753, _242755]) = _242745]], leq(n0, _242755), leq(_242755, _242751), leq(n0, _242753), leq(_242753, _242749)], (834 ^ _210220) ^ [_244087, _244089, _244091] : [-(a_select2(tptp_update2(_244091, _244089, _244087), _244089) = _244087)], (836 ^ _210220) ^ [_244247, _244249, _244251, _244253, _244255] : [-(a_select2(tptp_update2(_244251, _244255, _244247), _244253) = _244249), -(_244255 = _244253), a_select2(_244251, _244253) = _244249], (865 ^ _210220) ^ [] : [-(true)], (867 ^ _210220) ^ [] : [def = use], (846 ^ _210220) ^ [_244627, _244629, _244631, _244633] : [-(a_select2(tptp_update2(_244629, _244631, _244627), _244633) = _244627), 850 ^ _210220 : [(851 ^ _210220) ^ [] : [-(leq(n0, 849 ^ [_244627, _244629, _244631, _244633]))], (853 ^ _210220) ^ [] : [-(leq(849 ^ [_244627, _244629, _244631, _244633], _244631))], (855 ^ _210220) ^ [] : [a_select2(_244629, 849 ^ [_244627, _244629, _244631, _244633]) = _244627]], leq(n0, _244633), leq(_244633, _244631)]], input).
% 0.34/1.39  ncf('1',plain,[a_select2(rhoold_init, 1162 ^ []) = init],start(1168 ^ 0)).
% 0.34/1.39  ncf('1.1',plain,[-(a_select2(rhoold_init, 1162 ^ []) = init), 1139 : leq(n0, 1162 ^ []), 1139 : leq(1162 ^ [], n4), 1139 : gt(loopcounter, n1)],extension(1135 ^ 1,bind([[_252813], [1162 ^ []]]))).
% 0.34/1.39  ncf('1.1.1',plain,[-(leq(n0, 1162 ^ []))],extension(1164 ^ 4)).
% 0.34/1.39  ncf('1.1.2',plain,[-(leq(1162 ^ [], n4))],extension(1166 ^ 4)).
% 0.34/1.39  ncf('1.1.3',plain,[-(gt(loopcounter, n1))],extension(1061 ^ 2)).
% 0.34/1.39  %-----------------------------------------------------
% 0.34/1.39  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------