%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SWV186+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n005.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 1.41s
% Output   : Proof 0.35s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : SWV186+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.03/0.14  % Command  : nanocop.sh %s %d
% 0.14/0.35  % Computer : n005.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Fri May 19 02:10:23 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 0.35/1.41  
% 0.35/1.41  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 0.35/1.41  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.35/1.41  %-----------------------------------------------------
% 0.35/1.41  ncf(matrix, plain, [(1146 ^ _208128) ^ [] : [-(leq(n0, 1144 ^ []))], (1148 ^ _208128) ^ [] : [-(leq(1144 ^ [], n4))], (1150 ^ _208128) ^ [] : [a_select2(muold_init, 1144 ^ []) = init], (1055 ^ _208128) ^ [] : [-(gt(loopcounter, n1))], (1057 ^ _208128) ^ [_248497] : [leq(n0, _248497), leq(_248497, n135299), 1064 ^ _208128 : [(1065 ^ _208128) ^ [_248725] : [-(a_select3(q_init, _248497, _248725) = init), leq(n0, _248725), leq(_248725, n4)]]], (1075 ^ _208128) ^ [_249027] : [-(a_select3(center_init, _249027, n0) = init), leq(n0, _249027), leq(_249027, n4)], (1085 ^ _208128) ^ [_249310] : [-(a_select2(muold_init, _249310) = init), leq(n0, _249310), leq(_249310, n4)], (1095 ^ _208128) ^ [_249591] : [-(a_select2(rhoold_init, _249591) = init), leq(n0, _249591), leq(_249591, n4)], (1105 ^ _208128) ^ [_249872] : [-(a_select2(sigmaold_init, _249872) = init), leq(n0, _249872), leq(_249872, n4)], (1115 ^ _208128) ^ [_250153] : [-(a_select2(mu_init, _250153) = init), leq(n0, _250153), leq(_250153, n4)], (1125 ^ _208128) ^ [_250434] : [-(a_select2(rho_init, _250434) = init), leq(n0, _250434), leq(_250434, n4)], (1135 ^ _208128) ^ [_250695] : [-(a_select2(sigma_init, _250695) = init), leq(n0, _250695), leq(_250695, n4)], (2 ^ _208128) ^ [_208272] : [-(_208272 = _208272)], (4 ^ _208128) ^ [_208379, _208381] : [_208381 = _208379, -(_208379 = _208381)], (10 ^ _208128) ^ [_208583, _208585, _208587] : [-(_208587 = _208583), _208587 = _208585, _208585 = _208583], (20 ^ _208128) ^ [_208924, _208926, _208928, _208930] : [-(lt(_208928, _208924)), lt(_208930, _208926), _208930 = _208928, _208926 = _208924], (34 ^ _208128) ^ [_209368, _209370, _209372, _209374] : [-(geq(_209372, _209368)), geq(_209374, _209370), _209374 = _209372, _209370 = _209368], (48 ^ _208128) ^ [_209812, _209814, _209816, _209818] : [-(gt(_209816, _209812)), gt(_209818, _209814), _209818 = _209816, _209814 = _209812], (62 ^ _208128) ^ [_210236, _210238, _210240, _210242] : [-(leq(_210240, _210236)), leq(_210242, _210238), _210242 = _210240, _210238 = _210236], (76 ^ _208128) ^ [_210692, _210694, _210696, _210698] : [-(uniform_int_rnd(_210698, _210694) = uniform_int_rnd(_210696, _210692)), _210698 = _210696, _210694 = _210692], (86 ^ _208128) ^ [_211051, _211053, _211055, _211057] : [-(tptp_const_array1(_211057, _211053) = tptp_const_array1(_211055, _211051)), _211057 = _211055, _211053 = _211051], (96 ^ _208128) ^ [_211438, _211440, _211442, _211444, _211446, _211448] : [-(tptp_const_array2(_211448, _211444, _211440) = tptp_const_array2(_211446, _211442, _211438)), _211448 = _211446, _211444 = _211442, _211440 = _211438], (110 ^ _208128) ^ [_211926, _211928, _211930, _211932] : [-(dim(_211932, _211928) = dim(_211930, _211926)), _211932 = _211930, _211928 = _211926], (120 ^ _208128) ^ [_212257, _212259] : [_212259 = _212257, -(inv(_212259) = inv(_212257))], (126 ^ _208128) ^ [_212503, _212505, _212507, _212509] : [-(tptp_msub(_212509, _212505) = tptp_msub(_212507, _212503)), _212509 = _212507, _212505 = _212503], (136 ^ _208128) ^ [_212862, _212864, _212866, _212868] : [-(tptp_madd(_212868, _212864) = tptp_madd(_212866, _212862)), _212868 = _212866, _212864 = _212862], (146 ^ _208128) ^ [_213221, _213223, _213225, _213227] : [-(tptp_mmul(_213227, _213223) = tptp_mmul(_213225, _213221)), _213227 = _213225, _213223 = _213221], (156 ^ _208128) ^ [_213552, _213554] : [_213554 = _213552, -(trans(_213554) = trans(_213552))], (162 ^ _208128) ^ [_213826, _213828, _213830, _213832, _213834, _213836] : [-(sum(_213836, _213832, _213828) = sum(_213834, _213830, _213826)), _213836 = _213834, _213832 = _213830, _213828 = _213826], (176 ^ _208128) ^ [_214314, _214316, _214318, _214320] : [-(plus(_214320, _214316) = plus(_214318, _214314)), _214320 = _214318, _214316 = _214314], (186 ^ _208128) ^ [_214645, _214647] : [_214647 = _214645, -(pred(_214647) = pred(_214645))], (192 ^ _208128) ^ [_214891, _214893, _214895, _214897] : [-(minus(_214897, _214893) = minus(_214895, _214891)), _214897 = _214895, _214893 = _214891], (202 ^ _208128) ^ [_215306, _215308, _215310, _215312, _215314, _215316, _215318, _215320] : [-(tptp_update3(_215320, _215316, _215312, _215308) = tptp_update3(_215318, _215314, _215310, _215306)), _215320 = _215318, _215316 = _215314, _215312 = _215310, _215308 = _215306], (220 ^ _208128) ^ [_215967, _215969, _215971, _215973, _215975, _215977] : [-(tptp_update2(_215977, _215973, _215969) = tptp_update2(_215975, _215971, _215967)), _215977 = _215975, _215973 = _215971, _215969 = _215967], (234 ^ _208128) ^ [_216427, _216429] : [_216429 = _216427, -(succ(_216429) = succ(_216427))], (254 ^ _208128) ^ [_217169, _217171, _217173, _217175] : [-(a_select2(_217175, _217171) = a_select2(_217173, _217169)), _217175 = _217173, _217171 = _217169], (240 ^ _208128) ^ [_216701, _216703, _216705, _216707, _216709, _216711] : [-(a_select3(_216711, _216707, _216703) = a_select3(_216709, _216705, _216701)), _216711 = _216709, _216707 = _216705, _216703 = _216701], (869 ^ _208128) ^ [] : [-(gt(n5, n4))], (871 ^ _208128) ^ [] : [-(gt(n135299, n4))], (873 ^ _208128) ^ [] : [-(gt(n135299, n5))], (875 ^ _208128) ^ [] : [-(gt(n4, tptp_minus_1))], (877 ^ _208128) ^ [] : [-(gt(n5, tptp_minus_1))], (879 ^ _208128) ^ [] : [-(gt(n135299, tptp_minus_1))], (881 ^ _208128) ^ [] : [-(gt(n0, tptp_minus_1))], (883 ^ _208128) ^ [] : [-(gt(n1, tptp_minus_1))], (885 ^ _208128) ^ [] : [-(gt(n2, tptp_minus_1))], (887 ^ _208128) ^ [] : [-(gt(n3, tptp_minus_1))], (889 ^ _208128) ^ [] : [-(gt(n4, n0))], (891 ^ _208128) ^ [] : [-(gt(n5, n0))], (893 ^ _208128) ^ [] : [-(gt(n135299, n0))], (895 ^ _208128) ^ [] : [-(gt(n1, n0))], (897 ^ _208128) ^ [] : [-(gt(n2, n0))], (899 ^ _208128) ^ [] : [-(gt(n3, n0))], (901 ^ _208128) ^ [] : [-(gt(n4, n1))], (903 ^ _208128) ^ [] : [-(gt(n5, n1))], (905 ^ _208128) ^ [] : [-(gt(n135299, n1))], (907 ^ _208128) ^ [] : [-(gt(n2, n1))], (909 ^ _208128) ^ [] : [-(gt(n3, n1))], (911 ^ _208128) ^ [] : [-(gt(n4, n2))], (913 ^ _208128) ^ [] : [-(gt(n5, n2))], (915 ^ _208128) ^ [] : [-(gt(n135299, n2))], (917 ^ _208128) ^ [] : [-(gt(n3, n2))], (919 ^ _208128) ^ [] : [-(gt(n4, n3))], (921 ^ _208128) ^ [] : [-(gt(n5, n3))], (923 ^ _208128) ^ [] : [-(gt(n135299, n3))], (925 ^ _208128) ^ [_245009] : [leq(n0, _245009), leq(_245009, n4), -(_245009 = n0), -(_245009 = n1), -(_245009 = n2), -(_245009 = n3), -(_245009 = n4)], (951 ^ _208128) ^ [_245630] : [leq(n0, _245630), leq(_245630, n5), -(_245630 = n0), -(_245630 = n1), -(_245630 = n2), -(_245630 = n3), -(_245630 = n4), -(_245630 = n5)], (981 ^ _208128) ^ [_246337] : [-(_246337 = n0), leq(n0, _246337), leq(_246337, n0)], (991 ^ _208128) ^ [_246612] : [leq(n0, _246612), leq(_246612, n1), -(_246612 = n0), -(_246612 = n1)], (1005 ^ _208128) ^ [_246975] : [leq(n0, _246975), leq(_246975, n2), -(_246975 = n0), -(_246975 = n1), -(_246975 = n2)], (1045 ^ _208128) ^ [] : [-(succ(succ(succ(succ(n0)))) = n4)], (1047 ^ _208128) ^ [] : [-(succ(succ(succ(succ(succ(n0))))) = n5)], (1049 ^ _208128) ^ [] : [-(succ(n0) = n1)], (1051 ^ _208128) ^ [] : [-(succ(succ(n0)) = n2)], (1053 ^ _208128) ^ [] : [-(succ(succ(succ(n0))) = n3)], (1023 ^ _208128) ^ [_247424] : [leq(n0, _247424), leq(_247424, n3), -(_247424 = n0), -(_247424 = n1), -(_247424 = n2), -(_247424 = n3)], (264 ^ _208128) ^ [_217600, _217602] : [-(gt(_217602, _217600)), -(gt(_217600, _217602)), -(_217602 = _217600)], (274 ^ _208128) ^ [_217915, _217917, _217919] : [-(gt(_217919, _217915)), gt(_217919, _217917), gt(_217917, _217915)], (284 ^ _208128) ^ [_218194] : [gt(_218194, _218194)], (286 ^ _208128) ^ [_218272] : [-(leq(_218272, _218272))], (288 ^ _208128) ^ [_218393, _218395, _218397] : [-(leq(_218397, _218393)), leq(_218397, _218395), leq(_218395, _218393)], (298 ^ _208128) ^ [_218731, _218733] : [lt(_218733, _218731), -(gt(_218731, _218733))], (304 ^ _208128) ^ [_218893, _218895] : [gt(_218893, _218895), -(lt(_218895, _218893))], (310 ^ _208128) ^ [_219134, _219136] : [geq(_219136, _219134), -(leq(_219134, _219136))], (316 ^ _208128) ^ [_219296, _219298] : [leq(_219296, _219298), -(geq(_219298, _219296))], (322 ^ _208128) ^ [_219508, _219510] : [gt(_219508, _219510), -(leq(_219510, _219508))], (328 ^ _208128) ^ [_219718, _219720] : [-(gt(_219718, _219720)), leq(_219720, _219718), -(_219720 = _219718)], (338 ^ _208128) ^ [_220049, _220051] : [leq(_220051, pred(_220049)), -(gt(_220049, _220051))], (344 ^ _208128) ^ [_220215, _220217] : [gt(_220215, _220217), -(leq(_220217, pred(_220215)))], (350 ^ _208128) ^ [_220402] : [-(gt(succ(_220402), _220402))], (352 ^ _208128) ^ [_220511, _220513] : [leq(_220513, _220511), -(leq(_220513, succ(_220511)))], (358 ^ _208128) ^ [_220754, _220756] : [leq(_220756, _220754), -(gt(succ(_220754), _220756))], (364 ^ _208128) ^ [_220920, _220922] : [gt(succ(_220920), _220922), -(leq(_220922, _220920))], (370 ^ _208128) ^ [_221136, _221138] : [leq(n0, _221138), -(leq(uniform_int_rnd(_221136, _221138), _221138))], (376 ^ _208128) ^ [_221352, _221354] : [leq(n0, _221354), -(leq(n0, uniform_int_rnd(_221352, _221354)))], (382 ^ _208128) ^ [_221596, _221598, _221600, _221602] : [-(a_select2(tptp_const_array1(dim(_221600, _221598), _221596), _221602) = _221596), leq(_221600, _221602), leq(_221602, _221598)], (392 ^ _208128) ^ [_222003, _222005, _222007, _222009, _222011, _222013, _222015] : [-(a_select3(tptp_const_array2(dim(_222013, _222011), dim(_222007, _222005), _222003), _222015, _222009) = _222003), leq(_222013, _222015), leq(_222015, _222011), leq(_222007, _222009), leq(_222009, _222005)], (410 ^ _208128) ^ [_222598, _222600] : [413 ^ _208128 : [(414 ^ _208128) ^ [] : [-(leq(n0, 411 ^ [_222598, _222600]))], (416 ^ _208128) ^ [] : [-(leq(411 ^ [_222598, _222600], _222598))], (418 ^ _208128) ^ [] : [-(leq(n0, 412 ^ [_222598, _222600]))], (420 ^ _208128) ^ [] : [-(leq(412 ^ [_222598, _222600], _222598))], (422 ^ _208128) ^ [] : [a_select3(_222600, 411 ^ [_222598, _222600], 412 ^ [_222598, _222600]) = a_select3(_222600, 412 ^ [_222598, _222600], 411 ^ [_222598, _222600])]], 423 ^ _208128 : [(424 ^ _208128) ^ [_223355, _223357] : [-(a_select3(trans(_222600), _223357, _223355) = a_select3(trans(_222600), _223355, _223357)), leq(n0, _223357), leq(_223357, _222598), leq(n0, _223355), leq(_223355, _222598)]]], (442 ^ _208128) ^ [_223902, _223904] : [445 ^ _208128 : [(446 ^ _208128) ^ [] : [-(leq(n0, 443 ^ [_223902, _223904]))], (448 ^ _208128) ^ [] : [-(leq(443 ^ [_223902, _223904], _223902))], (450 ^ _208128) ^ [] : [-(leq(n0, 444 ^ [_223902, _223904]))], (452 ^ _208128) ^ [] : [-(leq(444 ^ [_223902, _223904], _223902))], (454 ^ _208128) ^ [] : [a_select3(_223904, 443 ^ [_223902, _223904], 444 ^ [_223902, _223904]) = a_select3(_223904, 444 ^ [_223902, _223904], 443 ^ [_223902, _223904])]], 455 ^ _208128 : [(456 ^ _208128) ^ [_224659, _224661] : [-(a_select3(inv(_223904), _224661, _224659) = a_select3(inv(_223904), _224659, _224661)), leq(n0, _224661), leq(_224661, _223902), leq(n0, _224659), leq(_224659, _223902)]]], (474 ^ _208128) ^ [_225206, _225208] : [477 ^ _208128 : [(478 ^ _208128) ^ [] : [-(leq(n0, 475 ^ [_225206, _225208]))], (480 ^ _208128) ^ [] : [-(leq(475 ^ [_225206, _225208], _225206))], (482 ^ _208128) ^ [] : [-(leq(n0, 476 ^ [_225206, _225208]))], (484 ^ _208128) ^ [] : [-(leq(476 ^ [_225206, _225208], _225206))], (486 ^ _208128) ^ [] : [a_select3(_225208, 475 ^ [_225206, _225208], 476 ^ [_225206, _225208]) = a_select3(_225208, 476 ^ [_225206, _225208], 475 ^ [_225206, _225208])]], 487 ^ _208128 : [(488 ^ _208128) ^ [_226019, _226021, _226023, _226025] : [-(a_select3(tptp_update3(_225208, _226021, _226021, _226019), _226025, _226023) = a_select3(tptp_update3(_225208, _226021, _226021, _226019), _226023, _226025)), leq(n0, _226025), leq(_226025, _225206), leq(n0, _226023), leq(_226023, _225206), leq(n0, _226021), leq(_226021, _225206)]]], (514 ^ _208128) ^ [_226838, _226840, _226842] : [519 ^ _208128 : [(520 ^ _208128) ^ [] : [-(leq(n0, 517 ^ [_226838, _226840, _226842]))], (522 ^ _208128) ^ [] : [-(leq(517 ^ [_226838, _226840, _226842], _226838))], (524 ^ _208128) ^ [] : [-(leq(n0, 518 ^ [_226838, _226840, _226842]))], (526 ^ _208128) ^ [] : [-(leq(518 ^ [_226838, _226840, _226842], _226838))], (528 ^ _208128) ^ [] : [a_select3(_226842, 517 ^ [_226838, _226840, _226842], 518 ^ [_226838, _226840, _226842]) = a_select3(_226842, 518 ^ [_226838, _226840, _226842], 517 ^ [_226838, _226840, _226842])]], 531 ^ _208128 : [(532 ^ _208128) ^ [] : [-(leq(n0, 529 ^ [_226838, _226840, _226842]))], (534 ^ _208128) ^ [] : [-(leq(529 ^ [_226838, _226840, _226842], _226838))], (536 ^ _208128) ^ [] : [-(leq(n0, 530 ^ [_226838, _226840, _226842]))], (538 ^ _208128) ^ [] : [-(leq(530 ^ [_226838, _226840, _226842], _226838))], (540 ^ _208128) ^ [] : [a_select3(_226840, 529 ^ [_226838, _226840, _226842], 530 ^ [_226838, _226840, _226842]) = a_select3(_226840, 530 ^ [_226838, _226840, _226842], 529 ^ [_226838, _226840, _226842])]], 541 ^ _208128 : [(542 ^ _208128) ^ [_228347, _228349] : [-(a_select3(tptp_madd(_226842, _226840), _228349, _228347) = a_select3(tptp_madd(_226842, _226840), _228347, _228349)), leq(n0, _228349), leq(_228349, _226838), leq(n0, _228347), leq(_228347, _226838)]]], (560 ^ _208128) ^ [_228933, _228935, _228937] : [565 ^ _208128 : [(566 ^ _208128) ^ [] : [-(leq(n0, 563 ^ [_228933, _228935, _228937]))], (568 ^ _208128) ^ [] : [-(leq(563 ^ [_228933, _228935, _228937], _228933))], (570 ^ _208128) ^ [] : [-(leq(n0, 564 ^ [_228933, _228935, _228937]))], (572 ^ _208128) ^ [] : [-(leq(564 ^ [_228933, _228935, _228937], _228933))], (574 ^ _208128) ^ [] : [a_select3(_228937, 563 ^ [_228933, _228935, _228937], 564 ^ [_228933, _228935, _228937]) = a_select3(_228937, 564 ^ [_228933, _228935, _228937], 563 ^ [_228933, _228935, _228937])]], 577 ^ _208128 : [(578 ^ _208128) ^ [] : [-(leq(n0, 575 ^ [_228933, _228935, _228937]))], (580 ^ _208128) ^ [] : [-(leq(575 ^ [_228933, _228935, _228937], _228933))], (582 ^ _208128) ^ [] : [-(leq(n0, 576 ^ [_228933, _228935, _228937]))], (584 ^ _208128) ^ [] : [-(leq(576 ^ [_228933, _228935, _228937], _228933))], (586 ^ _208128) ^ [] : [a_select3(_228935, 575 ^ [_228933, _228935, _228937], 576 ^ [_228933, _228935, _228937]) = a_select3(_228935, 576 ^ [_228933, _228935, _228937], 575 ^ [_228933, _228935, _228937])]], 587 ^ _208128 : [(588 ^ _208128) ^ [_230442, _230444] : [-(a_select3(tptp_msub(_228937, _228935), _230444, _230442) = a_select3(tptp_msub(_228937, _228935), _230442, _230444)), leq(n0, _230444), leq(_230444, _228933), leq(n0, _230442), leq(_230442, _228933)]]], (606 ^ _208128) ^ [_231028, _231030, _231032] : [609 ^ _208128 : [(610 ^ _208128) ^ [] : [-(leq(n0, 607 ^ [_231028, _231030, _231032]))], (612 ^ _208128) ^ [] : [-(leq(607 ^ [_231028, _231030, _231032], _231028))], (614 ^ _208128) ^ [] : [-(leq(n0, 608 ^ [_231028, _231030, _231032]))], (616 ^ _208128) ^ [] : [-(leq(608 ^ [_231028, _231030, _231032], _231028))], (618 ^ _208128) ^ [] : [a_select3(_231030, 607 ^ [_231028, _231030, _231032], 608 ^ [_231028, _231030, _231032]) = a_select3(_231030, 608 ^ [_231028, _231030, _231032], 607 ^ [_231028, _231030, _231032])]], 619 ^ _208128 : [(620 ^ _208128) ^ [_231841, _231843] : [-(a_select3(tptp_mmul(_231032, tptp_mmul(_231030, trans(_231032))), _231843, _231841) = a_select3(tptp_mmul(_231032, tptp_mmul(_231030, trans(_231032))), _231841, _231843)), leq(n0, _231843), leq(_231843, _231028), leq(n0, _231841), leq(_231841, _231028)]]], (638 ^ _208128) ^ [_232460, _232462, _232464, _232466] : [641 ^ _208128 : [(642 ^ _208128) ^ [] : [-(leq(n0, 639 ^ [_232460, _232462, _232464, _232466]))], (644 ^ _208128) ^ [] : [-(leq(639 ^ [_232460, _232462, _232464, _232466], _232460))], (646 ^ _208128) ^ [] : [-(leq(n0, 640 ^ [_232460, _232462, _232464, _232466]))], (648 ^ _208128) ^ [] : [-(leq(640 ^ [_232460, _232462, _232464, _232466], _232460))], (650 ^ _208128) ^ [] : [a_select3(_232464, 639 ^ [_232460, _232462, _232464, _232466], 640 ^ [_232460, _232462, _232464, _232466]) = a_select3(_232464, 640 ^ [_232460, _232462, _232464, _232466], 639 ^ [_232460, _232462, _232464, _232466])]], 651 ^ _208128 : [(652 ^ _208128) ^ [_233317, _233319] : [-(a_select3(tptp_mmul(_232466, tptp_mmul(_232464, trans(_232466))), _233319, _233317) = a_select3(tptp_mmul(_232466, tptp_mmul(_232464, trans(_232466))), _233317, _233319)), leq(n0, _233319), leq(_233319, _232462), leq(n0, _233317), leq(_233317, _232462)]]], (670 ^ _208128) ^ [_234012, _234014, _234016, _234018, _234020, _234022, _234024, _234026] : [675 ^ _208128 : [(676 ^ _208128) ^ [] : [-(leq(n0, 673 ^ [_234012, _234014, _234016, _234018, _234020, _234022, _234024, _234026]))], (678 ^ _208128) ^ [] : [-(leq(673 ^ [_234012, _234014, _234016, _234018, _234020, _234022, _234024, _234026], _234012))], (680 ^ _208128) ^ [] : [-(leq(n0, 674 ^ [_234012, _234014, _234016, _234018, _234020, _234022, _234024, _234026]))], (682 ^ _208128) ^ [] : [-(leq(674 ^ [_234012, _234014, _234016, _234018, _234020, _234022, _234024, _234026], _234012))], (684 ^ _208128) ^ [] : [a_select3(_234020, 673 ^ [_234012, _234014, _234016, _234018, _234020, _234022, _234024, _234026], 674 ^ [_234012, _234014, _234016, _234018, _234020, _234022, _234024, _234026]) = a_select3(_234020, 674 ^ [_234012, _234014, _234016, _234018, _234020, _234022, _234024, _234026], 673 ^ [_234012, _234014, _234016, _234018, _234020, _234022, _234024, _234026])]], 689 ^ _208128 : [(690 ^ _208128) ^ [] : [-(leq(n0, 687 ^ [_234012, _234014, _234016, _234018, _234020, _234022, _234024, _234026]))], (692 ^ _208128) ^ [] : [-(leq(687 ^ [_234012, _234014, _234016, _234018, _234020, _234022, _234024, _234026], _234014))], (694 ^ _208128) ^ [] : [-(leq(n0, 688 ^ [_234012, _234014, _234016, _234018, _234020, _234022, _234024, _234026]))], (696 ^ _208128) ^ [] : [-(leq(688 ^ [_234012, _234014, _234016, _234018, _234020, _234022, _234024, _234026], _234014))], (698 ^ _208128) ^ [] : [a_select3(_234026, 687 ^ [_234012, _234014, _234016, _234018, _234020, _234022, _234024, _234026], 688 ^ [_234012, _234014, _234016, _234018, _234020, _234022, _234024, _234026]) = a_select3(_234026, 688 ^ [_234012, _234014, _234016, _234018, _234020, _234022, _234024, _234026], 687 ^ [_234012, _234014, _234016, _234018, _234020, _234022, _234024, _234026])]], 701 ^ _208128 : [(702 ^ _208128) ^ [] : [-(leq(n0, 699 ^ [_234012, _234014, _234016, _234018, _234020, _234022, _234024, _234026]))], (704 ^ _208128) ^ [] : [-(leq(699 ^ [_234012, _234014, _234016, _234018, _234020, _234022, _234024, _234026], _234014))], (706 ^ _208128) ^ [] : [-(leq(n0, 700 ^ [_234012, _234014, _234016, _234018, _234020, _234022, _234024, _234026]))], (708 ^ _208128) ^ [] : [-(leq(700 ^ [_234012, _234014, _234016, _234018, _234020, _234022, _234024, _234026], _234014))], (710 ^ _208128) ^ [] : [a_select3(_234016, 699 ^ [_234012, _234014, _234016, _234018, _234020, _234022, _234024, _234026], 700 ^ [_234012, _234014, _234016, _234018, _234020, _234022, _234024, _234026]) = a_select3(_234016, 700 ^ [_234012, _234014, _234016, _234018, _234020, _234022, _234024, _234026], 699 ^ [_234012, _234014, _234016, _234018, _234020, _234022, _234024, _234026])]], 711 ^ _208128 : [(712 ^ _208128) ^ [_236940, _236942] : [-(a_select3(tptp_madd(_234026, tptp_mmul(_234024, tptp_mmul(tptp_madd(tptp_mmul(_234022, tptp_mmul(_234020, trans(_234022))), tptp_mmul(_234018, tptp_mmul(_234016, trans(_234018)))), trans(_234024)))), _236942, _236940) = a_select3(tptp_madd(_234026, tptp_mmul(_234024, tptp_mmul(tptp_madd(tptp_mmul(_234022, tptp_mmul(_234020, trans(_234022))), tptp_mmul(_234018, tptp_mmul(_234016, trans(_234018)))), trans(_234024)))), _236940, _236942)), leq(n0, _236942), leq(_236942, _234014), leq(n0, _236940), leq(_236940, _234014)]]], (730 ^ _208128) ^ [_237693] : [-(sum(n0, tptp_minus_1, _237693) = n0)], (732 ^ _208128) ^ [_237775] : [-(tptp_float_0_0 = sum(n0, tptp_minus_1, _237775))], (734 ^ _208128) ^ [] : [-(succ(tptp_minus_1) = n0)], (736 ^ _208128) ^ [_237910] : [-(plus(_237910, n1) = succ(_237910))], (738 ^ _208128) ^ [_237993] : [-(plus(n1, _237993) = succ(_237993))], (740 ^ _208128) ^ [_238076] : [-(plus(_238076, n2) = succ(succ(_238076)))], (742 ^ _208128) ^ [_238161] : [-(plus(n2, _238161) = succ(succ(_238161)))], (744 ^ _208128) ^ [_238246] : [-(plus(_238246, n3) = succ(succ(succ(_238246))))], (746 ^ _208128) ^ [_238333] : [-(plus(n3, _238333) = succ(succ(succ(_238333))))], (748 ^ _208128) ^ [_238420] : [-(plus(_238420, n4) = succ(succ(succ(succ(_238420)))))], (750 ^ _208128) ^ [_238509] : [-(plus(n4, _238509) = succ(succ(succ(succ(_238509)))))], (752 ^ _208128) ^ [_238598] : [-(plus(_238598, n5) = succ(succ(succ(succ(succ(_238598))))))], (754 ^ _208128) ^ [_238689] : [-(plus(n5, _238689) = succ(succ(succ(succ(succ(_238689))))))], (756 ^ _208128) ^ [_238780] : [-(minus(_238780, n1) = pred(_238780))], (758 ^ _208128) ^ [_238863] : [-(pred(succ(_238863)) = _238863)], (760 ^ _208128) ^ [_238945] : [-(succ(pred(_238945)) = _238945)], (762 ^ _208128) ^ [_239085, _239087] : [leq(succ(_239087), succ(_239085)), -(leq(_239087, _239085))], (768 ^ _208128) ^ [_239255, _239257] : [leq(_239257, _239255), -(leq(succ(_239257), succ(_239255)))], (774 ^ _208128) ^ [_239475, _239477] : [leq(succ(_239477), _239475), -(gt(_239475, _239477))], (780 ^ _208128) ^ [_239689, _239691] : [leq(minus(_239691, _239689), _239691), -(leq(n0, _239689))], (786 ^ _208128) ^ [_239918, _239920, _239922, _239924] : [-(a_select3(tptp_update3(_239924, _239922, _239920, _239918), _239922, _239920) = _239918)], (788 ^ _208128) ^ [_240110, _240112, _240114, _240116, _240118, _240120, _240122] : [-(a_select3(tptp_update3(_240114, _240122, _240120, _240110), _240118, _240116) = _240112), -(_240122 = _240118), _240120 = _240116, a_select3(_240114, _240118, _240116) = _240112], (802 ^ _208128) ^ [_240653, _240655, _240657, _240659, _240661, _240663] : [-(a_select3(tptp_update3(_240655, _240659, _240657, _240653), _240663, _240661) = _240653), 807 ^ _208128 : [(808 ^ _208128) ^ [] : [-(leq(n0, 805 ^ [_240653, _240655, _240657, _240659, _240661, _240663]))], (810 ^ _208128) ^ [] : [-(leq(n0, 806 ^ [_240653, _240655, _240657, _240659, _240661, _240663]))], (812 ^ _208128) ^ [] : [-(leq(805 ^ [_240653, _240655, _240657, _240659, _240661, _240663], _240659))], (814 ^ _208128) ^ [] : [-(leq(806 ^ [_240653, _240655, _240657, _240659, _240661, _240663], _240657))], (816 ^ _208128) ^ [] : [a_select3(_240655, 805 ^ [_240653, _240655, _240657, _240659, _240661, _240663], 806 ^ [_240653, _240655, _240657, _240659, _240661, _240663]) = _240653]], leq(n0, _240663), leq(_240663, _240659), leq(n0, _240661), leq(_240661, _240657)], (834 ^ _208128) ^ [_241995, _241997, _241999] : [-(a_select2(tptp_update2(_241999, _241997, _241995), _241997) = _241995)], (836 ^ _208128) ^ [_242155, _242157, _242159, _242161, _242163] : [-(a_select2(tptp_update2(_242159, _242163, _242155), _242161) = _242157), -(_242163 = _242161), a_select2(_242159, _242161) = _242157], (865 ^ _208128) ^ [] : [-(true)], (867 ^ _208128) ^ [] : [def = use], (846 ^ _208128) ^ [_242535, _242537, _242539, _242541] : [-(a_select2(tptp_update2(_242537, _242539, _242535), _242541) = _242535), 850 ^ _208128 : [(851 ^ _208128) ^ [] : [-(leq(n0, 849 ^ [_242535, _242537, _242539, _242541]))], (853 ^ _208128) ^ [] : [-(leq(849 ^ [_242535, _242537, _242539, _242541], _242539))], (855 ^ _208128) ^ [] : [a_select2(_242537, 849 ^ [_242535, _242537, _242539, _242541]) = _242535]], leq(n0, _242541), leq(_242541, _242539)]], input).
% 0.35/1.41  ncf('1',plain,[a_select2(muold_init, 1144 ^ []) = init],start(1150 ^ 0)).
% 0.35/1.41  ncf('1.1',plain,[-(a_select2(muold_init, 1144 ^ []) = init), leq(n0, 1144 ^ []), leq(1144 ^ [], n4)],extension(1085 ^ 1,bind([[_249310], [1144 ^ []]]))).
% 0.35/1.41  ncf('1.1.1',plain,[-(leq(n0, 1144 ^ []))],extension(1146 ^ 2)).
% 0.35/1.41  ncf('1.1.2',plain,[-(leq(1144 ^ [], n4))],extension(1148 ^ 2)).
% 0.35/1.41  %-----------------------------------------------------
% 0.35/1.41  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------