%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SWV183+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n020.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri May 19 12:20:07 EDT 2023

% Result   : Theorem 0.28s 1.39s
% Output   : Proof 0.28s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SWV183+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.03/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.34  % Computer : n020.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Fri May 19 02:38:02 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.28/1.39  
% 0.28/1.39  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 0.28/1.39  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.28/1.39  %-----------------------------------------------------
% 0.28/1.39  ncf(matrix, plain, [(1188 ^ _212604) ^ [] : [-(leq(n0, 1186 ^ []))], (1190 ^ _212604) ^ [] : [-(leq(1186 ^ [], n4))], (1192 ^ _212604) ^ [] : [a_select2(mu_init, 1186 ^ []) = init], (1055 ^ _212604) ^ [] : [-(gt(loopcounter, n0))], (1057 ^ _212604) ^ [_252973] : [leq(n0, _252973), leq(_252973, n135299), 1064 ^ _212604 : [(1065 ^ _212604) ^ [_253201] : [-(a_select3(q_init, _252973, _253201) = init), leq(n0, _253201), leq(_253201, n4)]]], (1075 ^ _212604) ^ [_253503] : [-(a_select2(rho_init, _253503) = init), leq(n0, _253503), leq(_253503, n4)], (1085 ^ _212604) ^ [_253784] : [-(a_select2(mu_init, _253784) = init), leq(n0, _253784), leq(_253784, n4)], (1095 ^ _212604) ^ [_254065] : [-(a_select2(sigma_init, _254065) = init), leq(n0, _254065), leq(_254065, n4)], (1105 ^ _212604) ^ [_254346] : [-(a_select3(center_init, _254346, n0) = init), leq(n0, _254346), leq(_254346, n4)], (1115 ^ _212604) ^ [] : [gt(loopcounter, n1), 1118 ^ _212604 : [(1119 ^ _212604) ^ [_254691] : [-(a_select2(muold_init, _254691) = init), leq(n0, _254691), leq(_254691, n4)]]], (1129 ^ _212604) ^ [] : [gt(loopcounter, n1), 1132 ^ _212604 : [(1133 ^ _212604) ^ [_255039] : [-(a_select2(rhoold_init, _255039) = init), leq(n0, _255039), leq(_255039, n4)]]], (1143 ^ _212604) ^ [] : [gt(loopcounter, n1), 1146 ^ _212604 : [(1147 ^ _212604) ^ [_255387] : [-(a_select2(sigmaold_init, _255387) = init), leq(n0, _255387), leq(_255387, n4)]]], (1157 ^ _212604) ^ [_255673] : [-(a_select2(muold_init, _255673) = init), leq(n0, _255673), leq(_255673, n4)], (1167 ^ _212604) ^ [_255954] : [-(a_select2(rhoold_init, _255954) = init), leq(n0, _255954), leq(_255954, n4)], (1177 ^ _212604) ^ [_256215] : [-(a_select2(sigmaold_init, _256215) = init), leq(n0, _256215), leq(_256215, n4)], (2 ^ _212604) ^ [_212748] : [-(_212748 = _212748)], (4 ^ _212604) ^ [_212855, _212857] : [_212857 = _212855, -(_212855 = _212857)], (10 ^ _212604) ^ [_213059, _213061, _213063] : [-(_213063 = _213059), _213063 = _213061, _213061 = _213059], (20 ^ _212604) ^ [_213400, _213402, _213404, _213406] : [-(lt(_213404, _213400)), lt(_213406, _213402), _213406 = _213404, _213402 = _213400], (34 ^ _212604) ^ [_213844, _213846, _213848, _213850] : [-(geq(_213848, _213844)), geq(_213850, _213846), _213850 = _213848, _213846 = _213844], (48 ^ _212604) ^ [_214288, _214290, _214292, _214294] : [-(gt(_214292, _214288)), gt(_214294, _214290), _214294 = _214292, _214290 = _214288], (62 ^ _212604) ^ [_214712, _214714, _214716, _214718] : [-(leq(_214716, _214712)), leq(_214718, _214714), _214718 = _214716, _214714 = _214712], (76 ^ _212604) ^ [_215168, _215170, _215172, _215174] : [-(uniform_int_rnd(_215174, _215170) = uniform_int_rnd(_215172, _215168)), _215174 = _215172, _215170 = _215168], (86 ^ _212604) ^ [_215527, _215529, _215531, _215533] : [-(tptp_const_array1(_215533, _215529) = tptp_const_array1(_215531, _215527)), _215533 = _215531, _215529 = _215527], (96 ^ _212604) ^ [_215914, _215916, _215918, _215920, _215922, _215924] : [-(tptp_const_array2(_215924, _215920, _215916) = tptp_const_array2(_215922, _215918, _215914)), _215924 = _215922, _215920 = _215918, _215916 = _215914], (110 ^ _212604) ^ [_216402, _216404, _216406, _216408] : [-(dim(_216408, _216404) = dim(_216406, _216402)), _216408 = _216406, _216404 = _216402], (120 ^ _212604) ^ [_216733, _216735] : [_216735 = _216733, -(inv(_216735) = inv(_216733))], (126 ^ _212604) ^ [_216979, _216981, _216983, _216985] : [-(tptp_msub(_216985, _216981) = tptp_msub(_216983, _216979)), _216985 = _216983, _216981 = _216979], (136 ^ _212604) ^ [_217338, _217340, _217342, _217344] : [-(tptp_madd(_217344, _217340) = tptp_madd(_217342, _217338)), _217344 = _217342, _217340 = _217338], (146 ^ _212604) ^ [_217697, _217699, _217701, _217703] : [-(tptp_mmul(_217703, _217699) = tptp_mmul(_217701, _217697)), _217703 = _217701, _217699 = _217697], (156 ^ _212604) ^ [_218028, _218030] : [_218030 = _218028, -(trans(_218030) = trans(_218028))], (162 ^ _212604) ^ [_218302, _218304, _218306, _218308, _218310, _218312] : [-(sum(_218312, _218308, _218304) = sum(_218310, _218306, _218302)), _218312 = _218310, _218308 = _218306, _218304 = _218302], (176 ^ _212604) ^ [_218790, _218792, _218794, _218796] : [-(plus(_218796, _218792) = plus(_218794, _218790)), _218796 = _218794, _218792 = _218790], (186 ^ _212604) ^ [_219121, _219123] : [_219123 = _219121, -(pred(_219123) = pred(_219121))], (192 ^ _212604) ^ [_219367, _219369, _219371, _219373] : [-(minus(_219373, _219369) = minus(_219371, _219367)), _219373 = _219371, _219369 = _219367], (202 ^ _212604) ^ [_219782, _219784, _219786, _219788, _219790, _219792, _219794, _219796] : [-(tptp_update3(_219796, _219792, _219788, _219784) = tptp_update3(_219794, _219790, _219786, _219782)), _219796 = _219794, _219792 = _219790, _219788 = _219786, _219784 = _219782], (220 ^ _212604) ^ [_220443, _220445, _220447, _220449, _220451, _220453] : [-(tptp_update2(_220453, _220449, _220445) = tptp_update2(_220451, _220447, _220443)), _220453 = _220451, _220449 = _220447, _220445 = _220443], (234 ^ _212604) ^ [_220903, _220905] : [_220905 = _220903, -(succ(_220905) = succ(_220903))], (254 ^ _212604) ^ [_221645, _221647, _221649, _221651] : [-(a_select2(_221651, _221647) = a_select2(_221649, _221645)), _221651 = _221649, _221647 = _221645], (240 ^ _212604) ^ [_221177, _221179, _221181, _221183, _221185, _221187] : [-(a_select3(_221187, _221183, _221179) = a_select3(_221185, _221181, _221177)), _221187 = _221185, _221183 = _221181, _221179 = _221177], (869 ^ _212604) ^ [] : [-(gt(n5, n4))], (871 ^ _212604) ^ [] : [-(gt(n135299, n4))], (873 ^ _212604) ^ [] : [-(gt(n135299, n5))], (875 ^ _212604) ^ [] : [-(gt(n4, tptp_minus_1))], (877 ^ _212604) ^ [] : [-(gt(n5, tptp_minus_1))], (879 ^ _212604) ^ [] : [-(gt(n135299, tptp_minus_1))], (881 ^ _212604) ^ [] : [-(gt(n0, tptp_minus_1))], (883 ^ _212604) ^ [] : [-(gt(n1, tptp_minus_1))], (885 ^ _212604) ^ [] : [-(gt(n2, tptp_minus_1))], (887 ^ _212604) ^ [] : [-(gt(n3, tptp_minus_1))], (889 ^ _212604) ^ [] : [-(gt(n4, n0))], (891 ^ _212604) ^ [] : [-(gt(n5, n0))], (893 ^ _212604) ^ [] : [-(gt(n135299, n0))], (895 ^ _212604) ^ [] : [-(gt(n1, n0))], (897 ^ _212604) ^ [] : [-(gt(n2, n0))], (899 ^ _212604) ^ [] : [-(gt(n3, n0))], (901 ^ _212604) ^ [] : [-(gt(n4, n1))], (903 ^ _212604) ^ [] : [-(gt(n5, n1))], (905 ^ _212604) ^ [] : [-(gt(n135299, n1))], (907 ^ _212604) ^ [] : [-(gt(n2, n1))], (909 ^ _212604) ^ [] : [-(gt(n3, n1))], (911 ^ _212604) ^ [] : [-(gt(n4, n2))], (913 ^ _212604) ^ [] : [-(gt(n5, n2))], (915 ^ _212604) ^ [] : [-(gt(n135299, n2))], (917 ^ _212604) ^ [] : [-(gt(n3, n2))], (919 ^ _212604) ^ [] : [-(gt(n4, n3))], (921 ^ _212604) ^ [] : [-(gt(n5, n3))], (923 ^ _212604) ^ [] : [-(gt(n135299, n3))], (925 ^ _212604) ^ [_249485] : [leq(n0, _249485), leq(_249485, n4), -(_249485 = n0), -(_249485 = n1), -(_249485 = n2), -(_249485 = n3), -(_249485 = n4)], (951 ^ _212604) ^ [_250106] : [leq(n0, _250106), leq(_250106, n5), -(_250106 = n0), -(_250106 = n1), -(_250106 = n2), -(_250106 = n3), -(_250106 = n4), -(_250106 = n5)], (981 ^ _212604) ^ [_250813] : [-(_250813 = n0), leq(n0, _250813), leq(_250813, n0)], (991 ^ _212604) ^ [_251088] : [leq(n0, _251088), leq(_251088, n1), -(_251088 = n0), -(_251088 = n1)], (1005 ^ _212604) ^ [_251451] : [leq(n0, _251451), leq(_251451, n2), -(_251451 = n0), -(_251451 = n1), -(_251451 = n2)], (1045 ^ _212604) ^ [] : [-(succ(succ(succ(succ(n0)))) = n4)], (1047 ^ _212604) ^ [] : [-(succ(succ(succ(succ(succ(n0))))) = n5)], (1049 ^ _212604) ^ [] : [-(succ(n0) = n1)], (1051 ^ _212604) ^ [] : [-(succ(succ(n0)) = n2)], (1053 ^ _212604) ^ [] : [-(succ(succ(succ(n0))) = n3)], (1023 ^ _212604) ^ [_251900] : [leq(n0, _251900), leq(_251900, n3), -(_251900 = n0), -(_251900 = n1), -(_251900 = n2), -(_251900 = n3)], (264 ^ _212604) ^ [_222076, _222078] : [-(gt(_222078, _222076)), -(gt(_222076, _222078)), -(_222078 = _222076)], (274 ^ _212604) ^ [_222391, _222393, _222395] : [-(gt(_222395, _222391)), gt(_222395, _222393), gt(_222393, _222391)], (284 ^ _212604) ^ [_222670] : [gt(_222670, _222670)], (286 ^ _212604) ^ [_222748] : [-(leq(_222748, _222748))], (288 ^ _212604) ^ [_222869, _222871, _222873] : [-(leq(_222873, _222869)), leq(_222873, _222871), leq(_222871, _222869)], (298 ^ _212604) ^ [_223207, _223209] : [lt(_223209, _223207), -(gt(_223207, _223209))], (304 ^ _212604) ^ [_223369, _223371] : [gt(_223369, _223371), -(lt(_223371, _223369))], (310 ^ _212604) ^ [_223610, _223612] : [geq(_223612, _223610), -(leq(_223610, _223612))], (316 ^ _212604) ^ [_223772, _223774] : [leq(_223772, _223774), -(geq(_223774, _223772))], (322 ^ _212604) ^ [_223984, _223986] : [gt(_223984, _223986), -(leq(_223986, _223984))], (328 ^ _212604) ^ [_224194, _224196] : [-(gt(_224194, _224196)), leq(_224196, _224194), -(_224196 = _224194)], (338 ^ _212604) ^ [_224525, _224527] : [leq(_224527, pred(_224525)), -(gt(_224525, _224527))], (344 ^ _212604) ^ [_224691, _224693] : [gt(_224691, _224693), -(leq(_224693, pred(_224691)))], (350 ^ _212604) ^ [_224878] : [-(gt(succ(_224878), _224878))], (352 ^ _212604) ^ [_224987, _224989] : [leq(_224989, _224987), -(leq(_224989, succ(_224987)))], (358 ^ _212604) ^ [_225230, _225232] : [leq(_225232, _225230), -(gt(succ(_225230), _225232))], (364 ^ _212604) ^ [_225396, _225398] : [gt(succ(_225396), _225398), -(leq(_225398, _225396))], (370 ^ _212604) ^ [_225612, _225614] : [leq(n0, _225614), -(leq(uniform_int_rnd(_225612, _225614), _225614))], (376 ^ _212604) ^ [_225828, _225830] : [leq(n0, _225830), -(leq(n0, uniform_int_rnd(_225828, _225830)))], (382 ^ _212604) ^ [_226072, _226074, _226076, _226078] : [-(a_select2(tptp_const_array1(dim(_226076, _226074), _226072), _226078) = _226072), leq(_226076, _226078), leq(_226078, _226074)], (392 ^ _212604) ^ [_226479, _226481, _226483, _226485, _226487, _226489, _226491] : [-(a_select3(tptp_const_array2(dim(_226489, _226487), dim(_226483, _226481), _226479), _226491, _226485) = _226479), leq(_226489, _226491), leq(_226491, _226487), leq(_226483, _226485), leq(_226485, _226481)], (410 ^ _212604) ^ [_227074, _227076] : [413 ^ _212604 : [(414 ^ _212604) ^ [] : [-(leq(n0, 411 ^ [_227074, _227076]))], (416 ^ _212604) ^ [] : [-(leq(411 ^ [_227074, _227076], _227074))], (418 ^ _212604) ^ [] : [-(leq(n0, 412 ^ [_227074, _227076]))], (420 ^ _212604) ^ [] : [-(leq(412 ^ [_227074, _227076], _227074))], (422 ^ _212604) ^ [] : [a_select3(_227076, 411 ^ [_227074, _227076], 412 ^ [_227074, _227076]) = a_select3(_227076, 412 ^ [_227074, _227076], 411 ^ [_227074, _227076])]], 423 ^ _212604 : [(424 ^ _212604) ^ [_227831, _227833] : [-(a_select3(trans(_227076), _227833, _227831) = a_select3(trans(_227076), _227831, _227833)), leq(n0, _227833), leq(_227833, _227074), leq(n0, _227831), leq(_227831, _227074)]]], (442 ^ _212604) ^ [_228378, _228380] : [445 ^ _212604 : [(446 ^ _212604) ^ [] : [-(leq(n0, 443 ^ [_228378, _228380]))], (448 ^ _212604) ^ [] : [-(leq(443 ^ [_228378, _228380], _228378))], (450 ^ _212604) ^ [] : [-(leq(n0, 444 ^ [_228378, _228380]))], (452 ^ _212604) ^ [] : [-(leq(444 ^ [_228378, _228380], _228378))], (454 ^ _212604) ^ [] : [a_select3(_228380, 443 ^ [_228378, _228380], 444 ^ [_228378, _228380]) = a_select3(_228380, 444 ^ [_228378, _228380], 443 ^ [_228378, _228380])]], 455 ^ _212604 : [(456 ^ _212604) ^ [_229135, _229137] : [-(a_select3(inv(_228380), _229137, _229135) = a_select3(inv(_228380), _229135, _229137)), leq(n0, _229137), leq(_229137, _228378), leq(n0, _229135), leq(_229135, _228378)]]], (474 ^ _212604) ^ [_229682, _229684] : [477 ^ _212604 : [(478 ^ _212604) ^ [] : [-(leq(n0, 475 ^ [_229682, _229684]))], (480 ^ _212604) ^ [] : [-(leq(475 ^ [_229682, _229684], _229682))], (482 ^ _212604) ^ [] : [-(leq(n0, 476 ^ [_229682, _229684]))], (484 ^ _212604) ^ [] : [-(leq(476 ^ [_229682, _229684], _229682))], (486 ^ _212604) ^ [] : [a_select3(_229684, 475 ^ [_229682, _229684], 476 ^ [_229682, _229684]) = a_select3(_229684, 476 ^ [_229682, _229684], 475 ^ [_229682, _229684])]], 487 ^ _212604 : [(488 ^ _212604) ^ [_230495, _230497, _230499, _230501] : [-(a_select3(tptp_update3(_229684, _230497, _230497, _230495), _230501, _230499) = a_select3(tptp_update3(_229684, _230497, _230497, _230495), _230499, _230501)), leq(n0, _230501), leq(_230501, _229682), leq(n0, _230499), leq(_230499, _229682), leq(n0, _230497), leq(_230497, _229682)]]], (514 ^ _212604) ^ [_231314, _231316, _231318] : [519 ^ _212604 : [(520 ^ _212604) ^ [] : [-(leq(n0, 517 ^ [_231314, _231316, _231318]))], (522 ^ _212604) ^ [] : [-(leq(517 ^ [_231314, _231316, _231318], _231314))], (524 ^ _212604) ^ [] : [-(leq(n0, 518 ^ [_231314, _231316, _231318]))], (526 ^ _212604) ^ [] : [-(leq(518 ^ [_231314, _231316, _231318], _231314))], (528 ^ _212604) ^ [] : [a_select3(_231318, 517 ^ [_231314, _231316, _231318], 518 ^ [_231314, _231316, _231318]) = a_select3(_231318, 518 ^ [_231314, _231316, _231318], 517 ^ [_231314, _231316, _231318])]], 531 ^ _212604 : [(532 ^ _212604) ^ [] : [-(leq(n0, 529 ^ [_231314, _231316, _231318]))], (534 ^ _212604) ^ [] : [-(leq(529 ^ [_231314, _231316, _231318], _231314))], (536 ^ _212604) ^ [] : [-(leq(n0, 530 ^ [_231314, _231316, _231318]))], (538 ^ _212604) ^ [] : [-(leq(530 ^ [_231314, _231316, _231318], _231314))], (540 ^ _212604) ^ [] : [a_select3(_231316, 529 ^ [_231314, _231316, _231318], 530 ^ [_231314, _231316, _231318]) = a_select3(_231316, 530 ^ [_231314, _231316, _231318], 529 ^ [_231314, _231316, _231318])]], 541 ^ _212604 : [(542 ^ _212604) ^ [_232823, _232825] : [-(a_select3(tptp_madd(_231318, _231316), _232825, _232823) = a_select3(tptp_madd(_231318, _231316), _232823, _232825)), leq(n0, _232825), leq(_232825, _231314), leq(n0, _232823), leq(_232823, _231314)]]], (560 ^ _212604) ^ [_233409, _233411, _233413] : [565 ^ _212604 : [(566 ^ _212604) ^ [] : [-(leq(n0, 563 ^ [_233409, _233411, _233413]))], (568 ^ _212604) ^ [] : [-(leq(563 ^ [_233409, _233411, _233413], _233409))], (570 ^ _212604) ^ [] : [-(leq(n0, 564 ^ [_233409, _233411, _233413]))], (572 ^ _212604) ^ [] : [-(leq(564 ^ [_233409, _233411, _233413], _233409))], (574 ^ _212604) ^ [] : [a_select3(_233413, 563 ^ [_233409, _233411, _233413], 564 ^ [_233409, _233411, _233413]) = a_select3(_233413, 564 ^ [_233409, _233411, _233413], 563 ^ [_233409, _233411, _233413])]], 577 ^ _212604 : [(578 ^ _212604) ^ [] : [-(leq(n0, 575 ^ [_233409, _233411, _233413]))], (580 ^ _212604) ^ [] : [-(leq(575 ^ [_233409, _233411, _233413], _233409))], (582 ^ _212604) ^ [] : [-(leq(n0, 576 ^ [_233409, _233411, _233413]))], (584 ^ _212604) ^ [] : [-(leq(576 ^ [_233409, _233411, _233413], _233409))], (586 ^ _212604) ^ [] : [a_select3(_233411, 575 ^ [_233409, _233411, _233413], 576 ^ [_233409, _233411, _233413]) = a_select3(_233411, 576 ^ [_233409, _233411, _233413], 575 ^ [_233409, _233411, _233413])]], 587 ^ _212604 : [(588 ^ _212604) ^ [_234918, _234920] : [-(a_select3(tptp_msub(_233413, _233411), _234920, _234918) = a_select3(tptp_msub(_233413, _233411), _234918, _234920)), leq(n0, _234920), leq(_234920, _233409), leq(n0, _234918), leq(_234918, _233409)]]], (606 ^ _212604) ^ [_235504, _235506, _235508] : [609 ^ _212604 : [(610 ^ _212604) ^ [] : [-(leq(n0, 607 ^ [_235504, _235506, _235508]))], (612 ^ _212604) ^ [] : [-(leq(607 ^ [_235504, _235506, _235508], _235504))], (614 ^ _212604) ^ [] : [-(leq(n0, 608 ^ [_235504, _235506, _235508]))], (616 ^ _212604) ^ [] : [-(leq(608 ^ [_235504, _235506, _235508], _235504))], (618 ^ _212604) ^ [] : [a_select3(_235506, 607 ^ [_235504, _235506, _235508], 608 ^ [_235504, _235506, _235508]) = a_select3(_235506, 608 ^ [_235504, _235506, _235508], 607 ^ [_235504, _235506, _235508])]], 619 ^ _212604 : [(620 ^ _212604) ^ [_236317, _236319] : [-(a_select3(tptp_mmul(_235508, tptp_mmul(_235506, trans(_235508))), _236319, _236317) = a_select3(tptp_mmul(_235508, tptp_mmul(_235506, trans(_235508))), _236317, _236319)), leq(n0, _236319), leq(_236319, _235504), leq(n0, _236317), leq(_236317, _235504)]]], (638 ^ _212604) ^ [_236936, _236938, _236940, _236942] : [641 ^ _212604 : [(642 ^ _212604) ^ [] : [-(leq(n0, 639 ^ [_236936, _236938, _236940, _236942]))], (644 ^ _212604) ^ [] : [-(leq(639 ^ [_236936, _236938, _236940, _236942], _236936))], (646 ^ _212604) ^ [] : [-(leq(n0, 640 ^ [_236936, _236938, _236940, _236942]))], (648 ^ _212604) ^ [] : [-(leq(640 ^ [_236936, _236938, _236940, _236942], _236936))], (650 ^ _212604) ^ [] : [a_select3(_236940, 639 ^ [_236936, _236938, _236940, _236942], 640 ^ [_236936, _236938, _236940, _236942]) = a_select3(_236940, 640 ^ [_236936, _236938, _236940, _236942], 639 ^ [_236936, _236938, _236940, _236942])]], 651 ^ _212604 : [(652 ^ _212604) ^ [_237793, _237795] : [-(a_select3(tptp_mmul(_236942, tptp_mmul(_236940, trans(_236942))), _237795, _237793) = a_select3(tptp_mmul(_236942, tptp_mmul(_236940, trans(_236942))), _237793, _237795)), leq(n0, _237795), leq(_237795, _236938), leq(n0, _237793), leq(_237793, _236938)]]], (670 ^ _212604) ^ [_238488, _238490, _238492, _238494, _238496, _238498, _238500, _238502] : [675 ^ _212604 : [(676 ^ _212604) ^ [] : [-(leq(n0, 673 ^ [_238488, _238490, _238492, _238494, _238496, _238498, _238500, _238502]))], (678 ^ _212604) ^ [] : [-(leq(673 ^ [_238488, _238490, _238492, _238494, _238496, _238498, _238500, _238502], _238488))], (680 ^ _212604) ^ [] : [-(leq(n0, 674 ^ [_238488, _238490, _238492, _238494, _238496, _238498, _238500, _238502]))], (682 ^ _212604) ^ [] : [-(leq(674 ^ [_238488, _238490, _238492, _238494, _238496, _238498, _238500, _238502], _238488))], (684 ^ _212604) ^ [] : [a_select3(_238496, 673 ^ [_238488, _238490, _238492, _238494, _238496, _238498, _238500, _238502], 674 ^ [_238488, _238490, _238492, _238494, _238496, _238498, _238500, _238502]) = a_select3(_238496, 674 ^ [_238488, _238490, _238492, _238494, _238496, _238498, _238500, _238502], 673 ^ [_238488, _238490, _238492, _238494, _238496, _238498, _238500, _238502])]], 689 ^ _212604 : [(690 ^ _212604) ^ [] : [-(leq(n0, 687 ^ [_238488, _238490, _238492, _238494, _238496, _238498, _238500, _238502]))], (692 ^ _212604) ^ [] : [-(leq(687 ^ [_238488, _238490, _238492, _238494, _238496, _238498, _238500, _238502], _238490))], (694 ^ _212604) ^ [] : [-(leq(n0, 688 ^ [_238488, _238490, _238492, _238494, _238496, _238498, _238500, _238502]))], (696 ^ _212604) ^ [] : [-(leq(688 ^ [_238488, _238490, _238492, _238494, _238496, _238498, _238500, _238502], _238490))], (698 ^ _212604) ^ [] : [a_select3(_238502, 687 ^ [_238488, _238490, _238492, _238494, _238496, _238498, _238500, _238502], 688 ^ [_238488, _238490, _238492, _238494, _238496, _238498, _238500, _238502]) = a_select3(_238502, 688 ^ [_238488, _238490, _238492, _238494, _238496, _238498, _238500, _238502], 687 ^ [_238488, _238490, _238492, _238494, _238496, _238498, _238500, _238502])]], 701 ^ _212604 : [(702 ^ _212604) ^ [] : [-(leq(n0, 699 ^ [_238488, _238490, _238492, _238494, _238496, _238498, _238500, _238502]))], (704 ^ _212604) ^ [] : [-(leq(699 ^ [_238488, _238490, _238492, _238494, _238496, _238498, _238500, _238502], _238490))], (706 ^ _212604) ^ [] : [-(leq(n0, 700 ^ [_238488, _238490, _238492, _238494, _238496, _238498, _238500, _238502]))], (708 ^ _212604) ^ [] : [-(leq(700 ^ [_238488, _238490, _238492, _238494, _238496, _238498, _238500, _238502], _238490))], (710 ^ _212604) ^ [] : [a_select3(_238492, 699 ^ [_238488, _238490, _238492, _238494, _238496, _238498, _238500, _238502], 700 ^ [_238488, _238490, _238492, _238494, _238496, _238498, _238500, _238502]) = a_select3(_238492, 700 ^ [_238488, _238490, _238492, _238494, _238496, _238498, _238500, _238502], 699 ^ [_238488, _238490, _238492, _238494, _238496, _238498, _238500, _238502])]], 711 ^ _212604 : [(712 ^ _212604) ^ [_241416, _241418] : [-(a_select3(tptp_madd(_238502, tptp_mmul(_238500, tptp_mmul(tptp_madd(tptp_mmul(_238498, tptp_mmul(_238496, trans(_238498))), tptp_mmul(_238494, tptp_mmul(_238492, trans(_238494)))), trans(_238500)))), _241418, _241416) = a_select3(tptp_madd(_238502, tptp_mmul(_238500, tptp_mmul(tptp_madd(tptp_mmul(_238498, tptp_mmul(_238496, trans(_238498))), tptp_mmul(_238494, tptp_mmul(_238492, trans(_238494)))), trans(_238500)))), _241416, _241418)), leq(n0, _241418), leq(_241418, _238490), leq(n0, _241416), leq(_241416, _238490)]]], (730 ^ _212604) ^ [_242169] : [-(sum(n0, tptp_minus_1, _242169) = n0)], (732 ^ _212604) ^ [_242251] : [-(tptp_float_0_0 = sum(n0, tptp_minus_1, _242251))], (734 ^ _212604) ^ [] : [-(succ(tptp_minus_1) = n0)], (736 ^ _212604) ^ [_242386] : [-(plus(_242386, n1) = succ(_242386))], (738 ^ _212604) ^ [_242469] : [-(plus(n1, _242469) = succ(_242469))], (740 ^ _212604) ^ [_242552] : [-(plus(_242552, n2) = succ(succ(_242552)))], (742 ^ _212604) ^ [_242637] : [-(plus(n2, _242637) = succ(succ(_242637)))], (744 ^ _212604) ^ [_242722] : [-(plus(_242722, n3) = succ(succ(succ(_242722))))], (746 ^ _212604) ^ [_242809] : [-(plus(n3, _242809) = succ(succ(succ(_242809))))], (748 ^ _212604) ^ [_242896] : [-(plus(_242896, n4) = succ(succ(succ(succ(_242896)))))], (750 ^ _212604) ^ [_242985] : [-(plus(n4, _242985) = succ(succ(succ(succ(_242985)))))], (752 ^ _212604) ^ [_243074] : [-(plus(_243074, n5) = succ(succ(succ(succ(succ(_243074))))))], (754 ^ _212604) ^ [_243165] : [-(plus(n5, _243165) = succ(succ(succ(succ(succ(_243165))))))], (756 ^ _212604) ^ [_243256] : [-(minus(_243256, n1) = pred(_243256))], (758 ^ _212604) ^ [_243339] : [-(pred(succ(_243339)) = _243339)], (760 ^ _212604) ^ [_243421] : [-(succ(pred(_243421)) = _243421)], (762 ^ _212604) ^ [_243561, _243563] : [leq(succ(_243563), succ(_243561)), -(leq(_243563, _243561))], (768 ^ _212604) ^ [_243731, _243733] : [leq(_243733, _243731), -(leq(succ(_243733), succ(_243731)))], (774 ^ _212604) ^ [_243951, _243953] : [leq(succ(_243953), _243951), -(gt(_243951, _243953))], (780 ^ _212604) ^ [_244165, _244167] : [leq(minus(_244167, _244165), _244167), -(leq(n0, _244165))], (786 ^ _212604) ^ [_244394, _244396, _244398, _244400] : [-(a_select3(tptp_update3(_244400, _244398, _244396, _244394), _244398, _244396) = _244394)], (788 ^ _212604) ^ [_244586, _244588, _244590, _244592, _244594, _244596, _244598] : [-(a_select3(tptp_update3(_244590, _244598, _244596, _244586), _244594, _244592) = _244588), -(_244598 = _244594), _244596 = _244592, a_select3(_244590, _244594, _244592) = _244588], (802 ^ _212604) ^ [_245129, _245131, _245133, _245135, _245137, _245139] : [-(a_select3(tptp_update3(_245131, _245135, _245133, _245129), _245139, _245137) = _245129), 807 ^ _212604 : [(808 ^ _212604) ^ [] : [-(leq(n0, 805 ^ [_245129, _245131, _245133, _245135, _245137, _245139]))], (810 ^ _212604) ^ [] : [-(leq(n0, 806 ^ [_245129, _245131, _245133, _245135, _245137, _245139]))], (812 ^ _212604) ^ [] : [-(leq(805 ^ [_245129, _245131, _245133, _245135, _245137, _245139], _245135))], (814 ^ _212604) ^ [] : [-(leq(806 ^ [_245129, _245131, _245133, _245135, _245137, _245139], _245133))], (816 ^ _212604) ^ [] : [a_select3(_245131, 805 ^ [_245129, _245131, _245133, _245135, _245137, _245139], 806 ^ [_245129, _245131, _245133, _245135, _245137, _245139]) = _245129]], leq(n0, _245139), leq(_245139, _245135), leq(n0, _245137), leq(_245137, _245133)], (834 ^ _212604) ^ [_246471, _246473, _246475] : [-(a_select2(tptp_update2(_246475, _246473, _246471), _246473) = _246471)], (836 ^ _212604) ^ [_246631, _246633, _246635, _246637, _246639] : [-(a_select2(tptp_update2(_246635, _246639, _246631), _246637) = _246633), -(_246639 = _246637), a_select2(_246635, _246637) = _246633], (865 ^ _212604) ^ [] : [-(true)], (867 ^ _212604) ^ [] : [def = use], (846 ^ _212604) ^ [_247011, _247013, _247015, _247017] : [-(a_select2(tptp_update2(_247013, _247015, _247011), _247017) = _247011), 850 ^ _212604 : [(851 ^ _212604) ^ [] : [-(leq(n0, 849 ^ [_247011, _247013, _247015, _247017]))], (853 ^ _212604) ^ [] : [-(leq(849 ^ [_247011, _247013, _247015, _247017], _247015))], (855 ^ _212604) ^ [] : [a_select2(_247013, 849 ^ [_247011, _247013, _247015, _247017]) = _247011]], leq(n0, _247017), leq(_247017, _247015)]], input).
% 0.28/1.39  ncf('1',plain,[a_select2(mu_init, 1186 ^ []) = init],start(1192 ^ 0)).
% 0.28/1.39  ncf('1.1',plain,[-(a_select2(mu_init, 1186 ^ []) = init), leq(n0, 1186 ^ []), leq(1186 ^ [], n4)],extension(1085 ^ 1,bind([[_253784], [1186 ^ []]]))).
% 0.28/1.39  ncf('1.1.1',plain,[-(leq(n0, 1186 ^ []))],extension(1188 ^ 2)).
% 0.28/1.39  ncf('1.1.2',plain,[-(leq(1186 ^ [], n4))],extension(1190 ^ 2)).
% 0.28/1.39  %-----------------------------------------------------
% 0.28/1.39  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------