%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SWV170+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n012.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri May 19 12:20:06 EDT 2023

% Result   : Theorem 0.35s 1.37s
% Output   : Proof 0.35s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11  % Problem  : SWV170+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.07/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n012.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 02:32:46 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.35/1.37  
% 0.35/1.37  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 0.35/1.37  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.35/1.37  %-----------------------------------------------------
% 0.35/1.37  ncf(matrix, plain, [(1170 ^ _210886) ^ [] : [-(leq(n0, 1168 ^ []))], (1172 ^ _210886) ^ [] : [-(leq(1168 ^ [], n4))], (1174 ^ _210886) ^ [] : [a_select2(muold_init, 1168 ^ []) = init], (1055 ^ _210886) ^ [] : [-(leq(n0, pv10))], (1057 ^ _210886) ^ [] : [-(leq(n0, pv52))], (1059 ^ _210886) ^ [] : [-(leq(n0, pv54))], (1061 ^ _210886) ^ [] : [-(leq(pv10, n135299))], (1063 ^ _210886) ^ [] : [-(leq(pv52, n4))], (1065 ^ _210886) ^ [] : [-(leq(pv54, n4))], (1067 ^ _210886) ^ [] : [-(gt(loopcounter, n1))], (1069 ^ _210886) ^ [_251573] : [leq(n0, _251573), leq(_251573, n135299), 1076 ^ _210886 : [(1077 ^ _210886) ^ [_251801] : [-(a_select3(q_init, _251573, _251801) = init), leq(n0, _251801), leq(_251801, n4)]]], (1087 ^ _210886) ^ [_252103] : [-(a_select2(rho_init, _252103) = init), leq(n0, _252103), leq(_252103, n4)], (1097 ^ _210886) ^ [_252384] : [-(a_select2(mu_init, _252384) = init), leq(n0, _252384), leq(_252384, n4)], (1107 ^ _210886) ^ [_252665] : [-(a_select2(sigma_init, _252665) = init), leq(n0, _252665), leq(_252665, n4)], (1117 ^ _210886) ^ [_252946] : [-(a_select3(center_init, _252946, n0) = init), leq(n0, _252946), leq(_252946, n4)], (1127 ^ _210886) ^ [] : [gt(loopcounter, n1), 1130 ^ _210886 : [(1131 ^ _210886) ^ [_253291] : [-(a_select2(muold_init, _253291) = init), leq(n0, _253291), leq(_253291, n4)]]], (1141 ^ _210886) ^ [] : [gt(loopcounter, n1), 1144 ^ _210886 : [(1145 ^ _210886) ^ [_253639] : [-(a_select2(rhoold_init, _253639) = init), leq(n0, _253639), leq(_253639, n4)]]], (1155 ^ _210886) ^ [] : [gt(loopcounter, n1), 1158 ^ _210886 : [(1159 ^ _210886) ^ [_253967] : [-(a_select2(sigmaold_init, _253967) = init), leq(n0, _253967), leq(_253967, n4)]]], (2 ^ _210886) ^ [_211030] : [-(_211030 = _211030)], (4 ^ _210886) ^ [_211137, _211139] : [_211139 = _211137, -(_211137 = _211139)], (10 ^ _210886) ^ [_211341, _211343, _211345] : [-(_211345 = _211341), _211345 = _211343, _211343 = _211341], (20 ^ _210886) ^ [_211682, _211684, _211686, _211688] : [-(lt(_211686, _211682)), lt(_211688, _211684), _211688 = _211686, _211684 = _211682], (34 ^ _210886) ^ [_212126, _212128, _212130, _212132] : [-(geq(_212130, _212126)), geq(_212132, _212128), _212132 = _212130, _212128 = _212126], (48 ^ _210886) ^ [_212570, _212572, _212574, _212576] : [-(gt(_212574, _212570)), gt(_212576, _212572), _212576 = _212574, _212572 = _212570], (62 ^ _210886) ^ [_212994, _212996, _212998, _213000] : [-(leq(_212998, _212994)), leq(_213000, _212996), _213000 = _212998, _212996 = _212994], (76 ^ _210886) ^ [_213450, _213452, _213454, _213456] : [-(uniform_int_rnd(_213456, _213452) = uniform_int_rnd(_213454, _213450)), _213456 = _213454, _213452 = _213450], (86 ^ _210886) ^ [_213809, _213811, _213813, _213815] : [-(tptp_const_array1(_213815, _213811) = tptp_const_array1(_213813, _213809)), _213815 = _213813, _213811 = _213809], (96 ^ _210886) ^ [_214196, _214198, _214200, _214202, _214204, _214206] : [-(tptp_const_array2(_214206, _214202, _214198) = tptp_const_array2(_214204, _214200, _214196)), _214206 = _214204, _214202 = _214200, _214198 = _214196], (110 ^ _210886) ^ [_214684, _214686, _214688, _214690] : [-(dim(_214690, _214686) = dim(_214688, _214684)), _214690 = _214688, _214686 = _214684], (120 ^ _210886) ^ [_215015, _215017] : [_215017 = _215015, -(inv(_215017) = inv(_215015))], (126 ^ _210886) ^ [_215261, _215263, _215265, _215267] : [-(tptp_msub(_215267, _215263) = tptp_msub(_215265, _215261)), _215267 = _215265, _215263 = _215261], (136 ^ _210886) ^ [_215620, _215622, _215624, _215626] : [-(tptp_madd(_215626, _215622) = tptp_madd(_215624, _215620)), _215626 = _215624, _215622 = _215620], (146 ^ _210886) ^ [_215979, _215981, _215983, _215985] : [-(tptp_mmul(_215985, _215981) = tptp_mmul(_215983, _215979)), _215985 = _215983, _215981 = _215979], (156 ^ _210886) ^ [_216310, _216312] : [_216312 = _216310, -(trans(_216312) = trans(_216310))], (162 ^ _210886) ^ [_216584, _216586, _216588, _216590, _216592, _216594] : [-(sum(_216594, _216590, _216586) = sum(_216592, _216588, _216584)), _216594 = _216592, _216590 = _216588, _216586 = _216584], (176 ^ _210886) ^ [_217072, _217074, _217076, _217078] : [-(plus(_217078, _217074) = plus(_217076, _217072)), _217078 = _217076, _217074 = _217072], (186 ^ _210886) ^ [_217403, _217405] : [_217405 = _217403, -(pred(_217405) = pred(_217403))], (192 ^ _210886) ^ [_217649, _217651, _217653, _217655] : [-(minus(_217655, _217651) = minus(_217653, _217649)), _217655 = _217653, _217651 = _217649], (202 ^ _210886) ^ [_218064, _218066, _218068, _218070, _218072, _218074, _218076, _218078] : [-(tptp_update3(_218078, _218074, _218070, _218066) = tptp_update3(_218076, _218072, _218068, _218064)), _218078 = _218076, _218074 = _218072, _218070 = _218068, _218066 = _218064], (220 ^ _210886) ^ [_218725, _218727, _218729, _218731, _218733, _218735] : [-(tptp_update2(_218735, _218731, _218727) = tptp_update2(_218733, _218729, _218725)), _218735 = _218733, _218731 = _218729, _218727 = _218725], (234 ^ _210886) ^ [_219185, _219187] : [_219187 = _219185, -(succ(_219187) = succ(_219185))], (254 ^ _210886) ^ [_219927, _219929, _219931, _219933] : [-(a_select2(_219933, _219929) = a_select2(_219931, _219927)), _219933 = _219931, _219929 = _219927], (240 ^ _210886) ^ [_219459, _219461, _219463, _219465, _219467, _219469] : [-(a_select3(_219469, _219465, _219461) = a_select3(_219467, _219463, _219459)), _219469 = _219467, _219465 = _219463, _219461 = _219459], (869 ^ _210886) ^ [] : [-(gt(n5, n4))], (871 ^ _210886) ^ [] : [-(gt(n135299, n4))], (873 ^ _210886) ^ [] : [-(gt(n135299, n5))], (875 ^ _210886) ^ [] : [-(gt(n4, tptp_minus_1))], (877 ^ _210886) ^ [] : [-(gt(n5, tptp_minus_1))], (879 ^ _210886) ^ [] : [-(gt(n135299, tptp_minus_1))], (881 ^ _210886) ^ [] : [-(gt(n0, tptp_minus_1))], (883 ^ _210886) ^ [] : [-(gt(n1, tptp_minus_1))], (885 ^ _210886) ^ [] : [-(gt(n2, tptp_minus_1))], (887 ^ _210886) ^ [] : [-(gt(n3, tptp_minus_1))], (889 ^ _210886) ^ [] : [-(gt(n4, n0))], (891 ^ _210886) ^ [] : [-(gt(n5, n0))], (893 ^ _210886) ^ [] : [-(gt(n135299, n0))], (895 ^ _210886) ^ [] : [-(gt(n1, n0))], (897 ^ _210886) ^ [] : [-(gt(n2, n0))], (899 ^ _210886) ^ [] : [-(gt(n3, n0))], (901 ^ _210886) ^ [] : [-(gt(n4, n1))], (903 ^ _210886) ^ [] : [-(gt(n5, n1))], (905 ^ _210886) ^ [] : [-(gt(n135299, n1))], (907 ^ _210886) ^ [] : [-(gt(n2, n1))], (909 ^ _210886) ^ [] : [-(gt(n3, n1))], (911 ^ _210886) ^ [] : [-(gt(n4, n2))], (913 ^ _210886) ^ [] : [-(gt(n5, n2))], (915 ^ _210886) ^ [] : [-(gt(n135299, n2))], (917 ^ _210886) ^ [] : [-(gt(n3, n2))], (919 ^ _210886) ^ [] : [-(gt(n4, n3))], (921 ^ _210886) ^ [] : [-(gt(n5, n3))], (923 ^ _210886) ^ [] : [-(gt(n135299, n3))], (925 ^ _210886) ^ [_247767] : [leq(n0, _247767), leq(_247767, n4), -(_247767 = n0), -(_247767 = n1), -(_247767 = n2), -(_247767 = n3), -(_247767 = n4)], (951 ^ _210886) ^ [_248388] : [leq(n0, _248388), leq(_248388, n5), -(_248388 = n0), -(_248388 = n1), -(_248388 = n2), -(_248388 = n3), -(_248388 = n4), -(_248388 = n5)], (981 ^ _210886) ^ [_249095] : [-(_249095 = n0), leq(n0, _249095), leq(_249095, n0)], (991 ^ _210886) ^ [_249370] : [leq(n0, _249370), leq(_249370, n1), -(_249370 = n0), -(_249370 = n1)], (1005 ^ _210886) ^ [_249733] : [leq(n0, _249733), leq(_249733, n2), -(_249733 = n0), -(_249733 = n1), -(_249733 = n2)], (1045 ^ _210886) ^ [] : [-(succ(succ(succ(succ(n0)))) = n4)], (1047 ^ _210886) ^ [] : [-(succ(succ(succ(succ(succ(n0))))) = n5)], (1049 ^ _210886) ^ [] : [-(succ(n0) = n1)], (1051 ^ _210886) ^ [] : [-(succ(succ(n0)) = n2)], (1053 ^ _210886) ^ [] : [-(succ(succ(succ(n0))) = n3)], (1023 ^ _210886) ^ [_250182] : [leq(n0, _250182), leq(_250182, n3), -(_250182 = n0), -(_250182 = n1), -(_250182 = n2), -(_250182 = n3)], (264 ^ _210886) ^ [_220358, _220360] : [-(gt(_220360, _220358)), -(gt(_220358, _220360)), -(_220360 = _220358)], (274 ^ _210886) ^ [_220673, _220675, _220677] : [-(gt(_220677, _220673)), gt(_220677, _220675), gt(_220675, _220673)], (284 ^ _210886) ^ [_220952] : [gt(_220952, _220952)], (286 ^ _210886) ^ [_221030] : [-(leq(_221030, _221030))], (288 ^ _210886) ^ [_221151, _221153, _221155] : [-(leq(_221155, _221151)), leq(_221155, _221153), leq(_221153, _221151)], (298 ^ _210886) ^ [_221489, _221491] : [lt(_221491, _221489), -(gt(_221489, _221491))], (304 ^ _210886) ^ [_221651, _221653] : [gt(_221651, _221653), -(lt(_221653, _221651))], (310 ^ _210886) ^ [_221892, _221894] : [geq(_221894, _221892), -(leq(_221892, _221894))], (316 ^ _210886) ^ [_222054, _222056] : [leq(_222054, _222056), -(geq(_222056, _222054))], (322 ^ _210886) ^ [_222266, _222268] : [gt(_222266, _222268), -(leq(_222268, _222266))], (328 ^ _210886) ^ [_222476, _222478] : [-(gt(_222476, _222478)), leq(_222478, _222476), -(_222478 = _222476)], (338 ^ _210886) ^ [_222807, _222809] : [leq(_222809, pred(_222807)), -(gt(_222807, _222809))], (344 ^ _210886) ^ [_222973, _222975] : [gt(_222973, _222975), -(leq(_222975, pred(_222973)))], (350 ^ _210886) ^ [_223160] : [-(gt(succ(_223160), _223160))], (352 ^ _210886) ^ [_223269, _223271] : [leq(_223271, _223269), -(leq(_223271, succ(_223269)))], (358 ^ _210886) ^ [_223512, _223514] : [leq(_223514, _223512), -(gt(succ(_223512), _223514))], (364 ^ _210886) ^ [_223678, _223680] : [gt(succ(_223678), _223680), -(leq(_223680, _223678))], (370 ^ _210886) ^ [_223894, _223896] : [leq(n0, _223896), -(leq(uniform_int_rnd(_223894, _223896), _223896))], (376 ^ _210886) ^ [_224110, _224112] : [leq(n0, _224112), -(leq(n0, uniform_int_rnd(_224110, _224112)))], (382 ^ _210886) ^ [_224354, _224356, _224358, _224360] : [-(a_select2(tptp_const_array1(dim(_224358, _224356), _224354), _224360) = _224354), leq(_224358, _224360), leq(_224360, _224356)], (392 ^ _210886) ^ [_224761, _224763, _224765, _224767, _224769, _224771, _224773] : [-(a_select3(tptp_const_array2(dim(_224771, _224769), dim(_224765, _224763), _224761), _224773, _224767) = _224761), leq(_224771, _224773), leq(_224773, _224769), leq(_224765, _224767), leq(_224767, _224763)], (410 ^ _210886) ^ [_225356, _225358] : [413 ^ _210886 : [(414 ^ _210886) ^ [] : [-(leq(n0, 411 ^ [_225356, _225358]))], (416 ^ _210886) ^ [] : [-(leq(411 ^ [_225356, _225358], _225356))], (418 ^ _210886) ^ [] : [-(leq(n0, 412 ^ [_225356, _225358]))], (420 ^ _210886) ^ [] : [-(leq(412 ^ [_225356, _225358], _225356))], (422 ^ _210886) ^ [] : [a_select3(_225358, 411 ^ [_225356, _225358], 412 ^ [_225356, _225358]) = a_select3(_225358, 412 ^ [_225356, _225358], 411 ^ [_225356, _225358])]], 423 ^ _210886 : [(424 ^ _210886) ^ [_226113, _226115] : [-(a_select3(trans(_225358), _226115, _226113) = a_select3(trans(_225358), _226113, _226115)), leq(n0, _226115), leq(_226115, _225356), leq(n0, _226113), leq(_226113, _225356)]]], (442 ^ _210886) ^ [_226660, _226662] : [445 ^ _210886 : [(446 ^ _210886) ^ [] : [-(leq(n0, 443 ^ [_226660, _226662]))], (448 ^ _210886) ^ [] : [-(leq(443 ^ [_226660, _226662], _226660))], (450 ^ _210886) ^ [] : [-(leq(n0, 444 ^ [_226660, _226662]))], (452 ^ _210886) ^ [] : [-(leq(444 ^ [_226660, _226662], _226660))], (454 ^ _210886) ^ [] : [a_select3(_226662, 443 ^ [_226660, _226662], 444 ^ [_226660, _226662]) = a_select3(_226662, 444 ^ [_226660, _226662], 443 ^ [_226660, _226662])]], 455 ^ _210886 : [(456 ^ _210886) ^ [_227417, _227419] : [-(a_select3(inv(_226662), _227419, _227417) = a_select3(inv(_226662), _227417, _227419)), leq(n0, _227419), leq(_227419, _226660), leq(n0, _227417), leq(_227417, _226660)]]], (474 ^ _210886) ^ [_227964, _227966] : [477 ^ _210886 : [(478 ^ _210886) ^ [] : [-(leq(n0, 475 ^ [_227964, _227966]))], (480 ^ _210886) ^ [] : [-(leq(475 ^ [_227964, _227966], _227964))], (482 ^ _210886) ^ [] : [-(leq(n0, 476 ^ [_227964, _227966]))], (484 ^ _210886) ^ [] : [-(leq(476 ^ [_227964, _227966], _227964))], (486 ^ _210886) ^ [] : [a_select3(_227966, 475 ^ [_227964, _227966], 476 ^ [_227964, _227966]) = a_select3(_227966, 476 ^ [_227964, _227966], 475 ^ [_227964, _227966])]], 487 ^ _210886 : [(488 ^ _210886) ^ [_228777, _228779, _228781, _228783] : [-(a_select3(tptp_update3(_227966, _228779, _228779, _228777), _228783, _228781) = a_select3(tptp_update3(_227966, _228779, _228779, _228777), _228781, _228783)), leq(n0, _228783), leq(_228783, _227964), leq(n0, _228781), leq(_228781, _227964), leq(n0, _228779), leq(_228779, _227964)]]], (514 ^ _210886) ^ [_229596, _229598, _229600] : [519 ^ _210886 : [(520 ^ _210886) ^ [] : [-(leq(n0, 517 ^ [_229596, _229598, _229600]))], (522 ^ _210886) ^ [] : [-(leq(517 ^ [_229596, _229598, _229600], _229596))], (524 ^ _210886) ^ [] : [-(leq(n0, 518 ^ [_229596, _229598, _229600]))], (526 ^ _210886) ^ [] : [-(leq(518 ^ [_229596, _229598, _229600], _229596))], (528 ^ _210886) ^ [] : [a_select3(_229600, 517 ^ [_229596, _229598, _229600], 518 ^ [_229596, _229598, _229600]) = a_select3(_229600, 518 ^ [_229596, _229598, _229600], 517 ^ [_229596, _229598, _229600])]], 531 ^ _210886 : [(532 ^ _210886) ^ [] : [-(leq(n0, 529 ^ [_229596, _229598, _229600]))], (534 ^ _210886) ^ [] : [-(leq(529 ^ [_229596, _229598, _229600], _229596))], (536 ^ _210886) ^ [] : [-(leq(n0, 530 ^ [_229596, _229598, _229600]))], (538 ^ _210886) ^ [] : [-(leq(530 ^ [_229596, _229598, _229600], _229596))], (540 ^ _210886) ^ [] : [a_select3(_229598, 529 ^ [_229596, _229598, _229600], 530 ^ [_229596, _229598, _229600]) = a_select3(_229598, 530 ^ [_229596, _229598, _229600], 529 ^ [_229596, _229598, _229600])]], 541 ^ _210886 : [(542 ^ _210886) ^ [_231105, _231107] : [-(a_select3(tptp_madd(_229600, _229598), _231107, _231105) = a_select3(tptp_madd(_229600, _229598), _231105, _231107)), leq(n0, _231107), leq(_231107, _229596), leq(n0, _231105), leq(_231105, _229596)]]], (560 ^ _210886) ^ [_231691, _231693, _231695] : [565 ^ _210886 : [(566 ^ _210886) ^ [] : [-(leq(n0, 563 ^ [_231691, _231693, _231695]))], (568 ^ _210886) ^ [] : [-(leq(563 ^ [_231691, _231693, _231695], _231691))], (570 ^ _210886) ^ [] : [-(leq(n0, 564 ^ [_231691, _231693, _231695]))], (572 ^ _210886) ^ [] : [-(leq(564 ^ [_231691, _231693, _231695], _231691))], (574 ^ _210886) ^ [] : [a_select3(_231695, 563 ^ [_231691, _231693, _231695], 564 ^ [_231691, _231693, _231695]) = a_select3(_231695, 564 ^ [_231691, _231693, _231695], 563 ^ [_231691, _231693, _231695])]], 577 ^ _210886 : [(578 ^ _210886) ^ [] : [-(leq(n0, 575 ^ [_231691, _231693, _231695]))], (580 ^ _210886) ^ [] : [-(leq(575 ^ [_231691, _231693, _231695], _231691))], (582 ^ _210886) ^ [] : [-(leq(n0, 576 ^ [_231691, _231693, _231695]))], (584 ^ _210886) ^ [] : [-(leq(576 ^ [_231691, _231693, _231695], _231691))], (586 ^ _210886) ^ [] : [a_select3(_231693, 575 ^ [_231691, _231693, _231695], 576 ^ [_231691, _231693, _231695]) = a_select3(_231693, 576 ^ [_231691, _231693, _231695], 575 ^ [_231691, _231693, _231695])]], 587 ^ _210886 : [(588 ^ _210886) ^ [_233200, _233202] : [-(a_select3(tptp_msub(_231695, _231693), _233202, _233200) = a_select3(tptp_msub(_231695, _231693), _233200, _233202)), leq(n0, _233202), leq(_233202, _231691), leq(n0, _233200), leq(_233200, _231691)]]], (606 ^ _210886) ^ [_233786, _233788, _233790] : [609 ^ _210886 : [(610 ^ _210886) ^ [] : [-(leq(n0, 607 ^ [_233786, _233788, _233790]))], (612 ^ _210886) ^ [] : [-(leq(607 ^ [_233786, _233788, _233790], _233786))], (614 ^ _210886) ^ [] : [-(leq(n0, 608 ^ [_233786, _233788, _233790]))], (616 ^ _210886) ^ [] : [-(leq(608 ^ [_233786, _233788, _233790], _233786))], (618 ^ _210886) ^ [] : [a_select3(_233788, 607 ^ [_233786, _233788, _233790], 608 ^ [_233786, _233788, _233790]) = a_select3(_233788, 608 ^ [_233786, _233788, _233790], 607 ^ [_233786, _233788, _233790])]], 619 ^ _210886 : [(620 ^ _210886) ^ [_234599, _234601] : [-(a_select3(tptp_mmul(_233790, tptp_mmul(_233788, trans(_233790))), _234601, _234599) = a_select3(tptp_mmul(_233790, tptp_mmul(_233788, trans(_233790))), _234599, _234601)), leq(n0, _234601), leq(_234601, _233786), leq(n0, _234599), leq(_234599, _233786)]]], (638 ^ _210886) ^ [_235218, _235220, _235222, _235224] : [641 ^ _210886 : [(642 ^ _210886) ^ [] : [-(leq(n0, 639 ^ [_235218, _235220, _235222, _235224]))], (644 ^ _210886) ^ [] : [-(leq(639 ^ [_235218, _235220, _235222, _235224], _235218))], (646 ^ _210886) ^ [] : [-(leq(n0, 640 ^ [_235218, _235220, _235222, _235224]))], (648 ^ _210886) ^ [] : [-(leq(640 ^ [_235218, _235220, _235222, _235224], _235218))], (650 ^ _210886) ^ [] : [a_select3(_235222, 639 ^ [_235218, _235220, _235222, _235224], 640 ^ [_235218, _235220, _235222, _235224]) = a_select3(_235222, 640 ^ [_235218, _235220, _235222, _235224], 639 ^ [_235218, _235220, _235222, _235224])]], 651 ^ _210886 : [(652 ^ _210886) ^ [_236075, _236077] : [-(a_select3(tptp_mmul(_235224, tptp_mmul(_235222, trans(_235224))), _236077, _236075) = a_select3(tptp_mmul(_235224, tptp_mmul(_235222, trans(_235224))), _236075, _236077)), leq(n0, _236077), leq(_236077, _235220), leq(n0, _236075), leq(_236075, _235220)]]], (670 ^ _210886) ^ [_236770, _236772, _236774, _236776, _236778, _236780, _236782, _236784] : [675 ^ _210886 : [(676 ^ _210886) ^ [] : [-(leq(n0, 673 ^ [_236770, _236772, _236774, _236776, _236778, _236780, _236782, _236784]))], (678 ^ _210886) ^ [] : [-(leq(673 ^ [_236770, _236772, _236774, _236776, _236778, _236780, _236782, _236784], _236770))], (680 ^ _210886) ^ [] : [-(leq(n0, 674 ^ [_236770, _236772, _236774, _236776, _236778, _236780, _236782, _236784]))], (682 ^ _210886) ^ [] : [-(leq(674 ^ [_236770, _236772, _236774, _236776, _236778, _236780, _236782, _236784], _236770))], (684 ^ _210886) ^ [] : [a_select3(_236778, 673 ^ [_236770, _236772, _236774, _236776, _236778, _236780, _236782, _236784], 674 ^ [_236770, _236772, _236774, _236776, _236778, _236780, _236782, _236784]) = a_select3(_236778, 674 ^ [_236770, _236772, _236774, _236776, _236778, _236780, _236782, _236784], 673 ^ [_236770, _236772, _236774, _236776, _236778, _236780, _236782, _236784])]], 689 ^ _210886 : [(690 ^ _210886) ^ [] : [-(leq(n0, 687 ^ [_236770, _236772, _236774, _236776, _236778, _236780, _236782, _236784]))], (692 ^ _210886) ^ [] : [-(leq(687 ^ [_236770, _236772, _236774, _236776, _236778, _236780, _236782, _236784], _236772))], (694 ^ _210886) ^ [] : [-(leq(n0, 688 ^ [_236770, _236772, _236774, _236776, _236778, _236780, _236782, _236784]))], (696 ^ _210886) ^ [] : [-(leq(688 ^ [_236770, _236772, _236774, _236776, _236778, _236780, _236782, _236784], _236772))], (698 ^ _210886) ^ [] : [a_select3(_236784, 687 ^ [_236770, _236772, _236774, _236776, _236778, _236780, _236782, _236784], 688 ^ [_236770, _236772, _236774, _236776, _236778, _236780, _236782, _236784]) = a_select3(_236784, 688 ^ [_236770, _236772, _236774, _236776, _236778, _236780, _236782, _236784], 687 ^ [_236770, _236772, _236774, _236776, _236778, _236780, _236782, _236784])]], 701 ^ _210886 : [(702 ^ _210886) ^ [] : [-(leq(n0, 699 ^ [_236770, _236772, _236774, _236776, _236778, _236780, _236782, _236784]))], (704 ^ _210886) ^ [] : [-(leq(699 ^ [_236770, _236772, _236774, _236776, _236778, _236780, _236782, _236784], _236772))], (706 ^ _210886) ^ [] : [-(leq(n0, 700 ^ [_236770, _236772, _236774, _236776, _236778, _236780, _236782, _236784]))], (708 ^ _210886) ^ [] : [-(leq(700 ^ [_236770, _236772, _236774, _236776, _236778, _236780, _236782, _236784], _236772))], (710 ^ _210886) ^ [] : [a_select3(_236774, 699 ^ [_236770, _236772, _236774, _236776, _236778, _236780, _236782, _236784], 700 ^ [_236770, _236772, _236774, _236776, _236778, _236780, _236782, _236784]) = a_select3(_236774, 700 ^ [_236770, _236772, _236774, _236776, _236778, _236780, _236782, _236784], 699 ^ [_236770, _236772, _236774, _236776, _236778, _236780, _236782, _236784])]], 711 ^ _210886 : [(712 ^ _210886) ^ [_239698, _239700] : [-(a_select3(tptp_madd(_236784, tptp_mmul(_236782, tptp_mmul(tptp_madd(tptp_mmul(_236780, tptp_mmul(_236778, trans(_236780))), tptp_mmul(_236776, tptp_mmul(_236774, trans(_236776)))), trans(_236782)))), _239700, _239698) = a_select3(tptp_madd(_236784, tptp_mmul(_236782, tptp_mmul(tptp_madd(tptp_mmul(_236780, tptp_mmul(_236778, trans(_236780))), tptp_mmul(_236776, tptp_mmul(_236774, trans(_236776)))), trans(_236782)))), _239698, _239700)), leq(n0, _239700), leq(_239700, _236772), leq(n0, _239698), leq(_239698, _236772)]]], (730 ^ _210886) ^ [_240451] : [-(sum(n0, tptp_minus_1, _240451) = n0)], (732 ^ _210886) ^ [_240533] : [-(tptp_float_0_0 = sum(n0, tptp_minus_1, _240533))], (734 ^ _210886) ^ [] : [-(succ(tptp_minus_1) = n0)], (736 ^ _210886) ^ [_240668] : [-(plus(_240668, n1) = succ(_240668))], (738 ^ _210886) ^ [_240751] : [-(plus(n1, _240751) = succ(_240751))], (740 ^ _210886) ^ [_240834] : [-(plus(_240834, n2) = succ(succ(_240834)))], (742 ^ _210886) ^ [_240919] : [-(plus(n2, _240919) = succ(succ(_240919)))], (744 ^ _210886) ^ [_241004] : [-(plus(_241004, n3) = succ(succ(succ(_241004))))], (746 ^ _210886) ^ [_241091] : [-(plus(n3, _241091) = succ(succ(succ(_241091))))], (748 ^ _210886) ^ [_241178] : [-(plus(_241178, n4) = succ(succ(succ(succ(_241178)))))], (750 ^ _210886) ^ [_241267] : [-(plus(n4, _241267) = succ(succ(succ(succ(_241267)))))], (752 ^ _210886) ^ [_241356] : [-(plus(_241356, n5) = succ(succ(succ(succ(succ(_241356))))))], (754 ^ _210886) ^ [_241447] : [-(plus(n5, _241447) = succ(succ(succ(succ(succ(_241447))))))], (756 ^ _210886) ^ [_241538] : [-(minus(_241538, n1) = pred(_241538))], (758 ^ _210886) ^ [_241621] : [-(pred(succ(_241621)) = _241621)], (760 ^ _210886) ^ [_241703] : [-(succ(pred(_241703)) = _241703)], (762 ^ _210886) ^ [_241843, _241845] : [leq(succ(_241845), succ(_241843)), -(leq(_241845, _241843))], (768 ^ _210886) ^ [_242013, _242015] : [leq(_242015, _242013), -(leq(succ(_242015), succ(_242013)))], (774 ^ _210886) ^ [_242233, _242235] : [leq(succ(_242235), _242233), -(gt(_242233, _242235))], (780 ^ _210886) ^ [_242447, _242449] : [leq(minus(_242449, _242447), _242449), -(leq(n0, _242447))], (786 ^ _210886) ^ [_242676, _242678, _242680, _242682] : [-(a_select3(tptp_update3(_242682, _242680, _242678, _242676), _242680, _242678) = _242676)], (788 ^ _210886) ^ [_242868, _242870, _242872, _242874, _242876, _242878, _242880] : [-(a_select3(tptp_update3(_242872, _242880, _242878, _242868), _242876, _242874) = _242870), -(_242880 = _242876), _242878 = _242874, a_select3(_242872, _242876, _242874) = _242870], (802 ^ _210886) ^ [_243411, _243413, _243415, _243417, _243419, _243421] : [-(a_select3(tptp_update3(_243413, _243417, _243415, _243411), _243421, _243419) = _243411), 807 ^ _210886 : [(808 ^ _210886) ^ [] : [-(leq(n0, 805 ^ [_243411, _243413, _243415, _243417, _243419, _243421]))], (810 ^ _210886) ^ [] : [-(leq(n0, 806 ^ [_243411, _243413, _243415, _243417, _243419, _243421]))], (812 ^ _210886) ^ [] : [-(leq(805 ^ [_243411, _243413, _243415, _243417, _243419, _243421], _243417))], (814 ^ _210886) ^ [] : [-(leq(806 ^ [_243411, _243413, _243415, _243417, _243419, _243421], _243415))], (816 ^ _210886) ^ [] : [a_select3(_243413, 805 ^ [_243411, _243413, _243415, _243417, _243419, _243421], 806 ^ [_243411, _243413, _243415, _243417, _243419, _243421]) = _243411]], leq(n0, _243421), leq(_243421, _243417), leq(n0, _243419), leq(_243419, _243415)], (834 ^ _210886) ^ [_244753, _244755, _244757] : [-(a_select2(tptp_update2(_244757, _244755, _244753), _244755) = _244753)], (836 ^ _210886) ^ [_244913, _244915, _244917, _244919, _244921] : [-(a_select2(tptp_update2(_244917, _244921, _244913), _244919) = _244915), -(_244921 = _244919), a_select2(_244917, _244919) = _244915], (865 ^ _210886) ^ [] : [-(true)], (867 ^ _210886) ^ [] : [def = use], (846 ^ _210886) ^ [_245293, _245295, _245297, _245299] : [-(a_select2(tptp_update2(_245295, _245297, _245293), _245299) = _245293), 850 ^ _210886 : [(851 ^ _210886) ^ [] : [-(leq(n0, 849 ^ [_245293, _245295, _245297, _245299]))], (853 ^ _210886) ^ [] : [-(leq(849 ^ [_245293, _245295, _245297, _245299], _245297))], (855 ^ _210886) ^ [] : [a_select2(_245295, 849 ^ [_245293, _245295, _245297, _245299]) = _245293]], leq(n0, _245299), leq(_245299, _245297)]], input).
% 0.35/1.37  ncf('1',plain,[a_select2(muold_init, 1168 ^ []) = init],start(1174 ^ 0)).
% 0.35/1.37  ncf('1.1',plain,[-(a_select2(muold_init, 1168 ^ []) = init), 1131 : leq(n0, 1168 ^ []), 1131 : leq(1168 ^ [], n4), 1131 : gt(loopcounter, n1)],extension(1127 ^ 1,bind([[_253291], [1168 ^ []]]))).
% 0.35/1.37  ncf('1.1.1',plain,[-(leq(n0, 1168 ^ []))],extension(1170 ^ 4)).
% 0.35/1.37  ncf('1.1.2',plain,[-(leq(1168 ^ [], n4))],extension(1172 ^ 4)).
% 0.35/1.37  ncf('1.1.3',plain,[-(gt(loopcounter, n1))],extension(1067 ^ 2)).
% 0.35/1.37  %-----------------------------------------------------
% 0.35/1.37  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------