%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SWV181+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n002.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 0.73s 1.37s
% Output   : Proof 0.73s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SWV181+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.07/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n002.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 02:43:19 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.73/1.37  
% 0.73/1.37  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 0.73/1.37  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.73/1.37  %-----------------------------------------------------
% 0.73/1.37  ncf(matrix, plain, [(1132 ^ _207138) ^ [] : [-(leq(n0, 1130 ^ []))], (1134 ^ _207138) ^ [] : [-(leq(1130 ^ [], n4))], (1136 ^ _207138) ^ [] : [a_select2(muold_init, 1130 ^ []) = init], (1055 ^ _207138) ^ [] : [-(leq(tptp_float_0_001, pv76))], (1057 ^ _207138) ^ [] : [-(leq(n1, loopcounter))], (1059 ^ _207138) ^ [] : [-(gt(n1, loopcounter))], (1061 ^ _207138) ^ [_247613] : [leq(n0, _247613), leq(_247613, n135299), 1068 ^ _207138 : [(1069 ^ _207138) ^ [_247841] : [-(a_select3(q_init, _247613, _247841) = init), leq(n0, _247841), leq(_247841, n4)]]], (1079 ^ _207138) ^ [_248143] : [-(a_select3(center_init, _248143, n0) = init), leq(n0, _248143), leq(_248143, n4)], (1089 ^ _207138) ^ [] : [gt(loopcounter, n0), 1092 ^ _207138 : [(1093 ^ _207138) ^ [_248488] : [-(a_select2(mu_init, _248488) = init), leq(n0, _248488), leq(_248488, n4)]]], (1103 ^ _207138) ^ [] : [gt(loopcounter, n0), 1106 ^ _207138 : [(1107 ^ _207138) ^ [_248836] : [-(a_select2(rho_init, _248836) = init), leq(n0, _248836), leq(_248836, n4)]]], (1117 ^ _207138) ^ [] : [gt(loopcounter, n0), 1120 ^ _207138 : [(1121 ^ _207138) ^ [_249164] : [-(a_select2(sigma_init, _249164) = init), leq(n0, _249164), leq(_249164, n4)]]], (2 ^ _207138) ^ [_207282] : [-(_207282 = _207282)], (4 ^ _207138) ^ [_207389, _207391] : [_207391 = _207389, -(_207389 = _207391)], (10 ^ _207138) ^ [_207593, _207595, _207597] : [-(_207597 = _207593), _207597 = _207595, _207595 = _207593], (20 ^ _207138) ^ [_207934, _207936, _207938, _207940] : [-(lt(_207938, _207934)), lt(_207940, _207936), _207940 = _207938, _207936 = _207934], (34 ^ _207138) ^ [_208378, _208380, _208382, _208384] : [-(geq(_208382, _208378)), geq(_208384, _208380), _208384 = _208382, _208380 = _208378], (48 ^ _207138) ^ [_208822, _208824, _208826, _208828] : [-(gt(_208826, _208822)), gt(_208828, _208824), _208828 = _208826, _208824 = _208822], (62 ^ _207138) ^ [_209246, _209248, _209250, _209252] : [-(leq(_209250, _209246)), leq(_209252, _209248), _209252 = _209250, _209248 = _209246], (76 ^ _207138) ^ [_209702, _209704, _209706, _209708] : [-(uniform_int_rnd(_209708, _209704) = uniform_int_rnd(_209706, _209702)), _209708 = _209706, _209704 = _209702], (86 ^ _207138) ^ [_210061, _210063, _210065, _210067] : [-(tptp_const_array1(_210067, _210063) = tptp_const_array1(_210065, _210061)), _210067 = _210065, _210063 = _210061], (96 ^ _207138) ^ [_210448, _210450, _210452, _210454, _210456, _210458] : [-(tptp_const_array2(_210458, _210454, _210450) = tptp_const_array2(_210456, _210452, _210448)), _210458 = _210456, _210454 = _210452, _210450 = _210448], (110 ^ _207138) ^ [_210936, _210938, _210940, _210942] : [-(dim(_210942, _210938) = dim(_210940, _210936)), _210942 = _210940, _210938 = _210936], (120 ^ _207138) ^ [_211267, _211269] : [_211269 = _211267, -(inv(_211269) = inv(_211267))], (126 ^ _207138) ^ [_211513, _211515, _211517, _211519] : [-(tptp_msub(_211519, _211515) = tptp_msub(_211517, _211513)), _211519 = _211517, _211515 = _211513], (136 ^ _207138) ^ [_211872, _211874, _211876, _211878] : [-(tptp_madd(_211878, _211874) = tptp_madd(_211876, _211872)), _211878 = _211876, _211874 = _211872], (146 ^ _207138) ^ [_212231, _212233, _212235, _212237] : [-(tptp_mmul(_212237, _212233) = tptp_mmul(_212235, _212231)), _212237 = _212235, _212233 = _212231], (156 ^ _207138) ^ [_212562, _212564] : [_212564 = _212562, -(trans(_212564) = trans(_212562))], (162 ^ _207138) ^ [_212836, _212838, _212840, _212842, _212844, _212846] : [-(sum(_212846, _212842, _212838) = sum(_212844, _212840, _212836)), _212846 = _212844, _212842 = _212840, _212838 = _212836], (176 ^ _207138) ^ [_213324, _213326, _213328, _213330] : [-(plus(_213330, _213326) = plus(_213328, _213324)), _213330 = _213328, _213326 = _213324], (186 ^ _207138) ^ [_213655, _213657] : [_213657 = _213655, -(pred(_213657) = pred(_213655))], (192 ^ _207138) ^ [_213901, _213903, _213905, _213907] : [-(minus(_213907, _213903) = minus(_213905, _213901)), _213907 = _213905, _213903 = _213901], (202 ^ _207138) ^ [_214316, _214318, _214320, _214322, _214324, _214326, _214328, _214330] : [-(tptp_update3(_214330, _214326, _214322, _214318) = tptp_update3(_214328, _214324, _214320, _214316)), _214330 = _214328, _214326 = _214324, _214322 = _214320, _214318 = _214316], (220 ^ _207138) ^ [_214977, _214979, _214981, _214983, _214985, _214987] : [-(tptp_update2(_214987, _214983, _214979) = tptp_update2(_214985, _214981, _214977)), _214987 = _214985, _214983 = _214981, _214979 = _214977], (234 ^ _207138) ^ [_215437, _215439] : [_215439 = _215437, -(succ(_215439) = succ(_215437))], (254 ^ _207138) ^ [_216179, _216181, _216183, _216185] : [-(a_select2(_216185, _216181) = a_select2(_216183, _216179)), _216185 = _216183, _216181 = _216179], (240 ^ _207138) ^ [_215711, _215713, _215715, _215717, _215719, _215721] : [-(a_select3(_215721, _215717, _215713) = a_select3(_215719, _215715, _215711)), _215721 = _215719, _215717 = _215715, _215713 = _215711], (869 ^ _207138) ^ [] : [-(gt(n5, n4))], (871 ^ _207138) ^ [] : [-(gt(n135299, n4))], (873 ^ _207138) ^ [] : [-(gt(n135299, n5))], (875 ^ _207138) ^ [] : [-(gt(n4, tptp_minus_1))], (877 ^ _207138) ^ [] : [-(gt(n5, tptp_minus_1))], (879 ^ _207138) ^ [] : [-(gt(n135299, tptp_minus_1))], (881 ^ _207138) ^ [] : [-(gt(n0, tptp_minus_1))], (883 ^ _207138) ^ [] : [-(gt(n1, tptp_minus_1))], (885 ^ _207138) ^ [] : [-(gt(n2, tptp_minus_1))], (887 ^ _207138) ^ [] : [-(gt(n3, tptp_minus_1))], (889 ^ _207138) ^ [] : [-(gt(n4, n0))], (891 ^ _207138) ^ [] : [-(gt(n5, n0))], (893 ^ _207138) ^ [] : [-(gt(n135299, n0))], (895 ^ _207138) ^ [] : [-(gt(n1, n0))], (897 ^ _207138) ^ [] : [-(gt(n2, n0))], (899 ^ _207138) ^ [] : [-(gt(n3, n0))], (901 ^ _207138) ^ [] : [-(gt(n4, n1))], (903 ^ _207138) ^ [] : [-(gt(n5, n1))], (905 ^ _207138) ^ [] : [-(gt(n135299, n1))], (907 ^ _207138) ^ [] : [-(gt(n2, n1))], (909 ^ _207138) ^ [] : [-(gt(n3, n1))], (911 ^ _207138) ^ [] : [-(gt(n4, n2))], (913 ^ _207138) ^ [] : [-(gt(n5, n2))], (915 ^ _207138) ^ [] : [-(gt(n135299, n2))], (917 ^ _207138) ^ [] : [-(gt(n3, n2))], (919 ^ _207138) ^ [] : [-(gt(n4, n3))], (921 ^ _207138) ^ [] : [-(gt(n5, n3))], (923 ^ _207138) ^ [] : [-(gt(n135299, n3))], (925 ^ _207138) ^ [_244019] : [leq(n0, _244019), leq(_244019, n4), -(_244019 = n0), -(_244019 = n1), -(_244019 = n2), -(_244019 = n3), -(_244019 = n4)], (951 ^ _207138) ^ [_244640] : [leq(n0, _244640), leq(_244640, n5), -(_244640 = n0), -(_244640 = n1), -(_244640 = n2), -(_244640 = n3), -(_244640 = n4), -(_244640 = n5)], (981 ^ _207138) ^ [_245347] : [-(_245347 = n0), leq(n0, _245347), leq(_245347, n0)], (991 ^ _207138) ^ [_245622] : [leq(n0, _245622), leq(_245622, n1), -(_245622 = n0), -(_245622 = n1)], (1005 ^ _207138) ^ [_245985] : [leq(n0, _245985), leq(_245985, n2), -(_245985 = n0), -(_245985 = n1), -(_245985 = n2)], (1045 ^ _207138) ^ [] : [-(succ(succ(succ(succ(n0)))) = n4)], (1047 ^ _207138) ^ [] : [-(succ(succ(succ(succ(succ(n0))))) = n5)], (1049 ^ _207138) ^ [] : [-(succ(n0) = n1)], (1051 ^ _207138) ^ [] : [-(succ(succ(n0)) = n2)], (1053 ^ _207138) ^ [] : [-(succ(succ(succ(n0))) = n3)], (1023 ^ _207138) ^ [_246434] : [leq(n0, _246434), leq(_246434, n3), -(_246434 = n0), -(_246434 = n1), -(_246434 = n2), -(_246434 = n3)], (264 ^ _207138) ^ [_216610, _216612] : [-(gt(_216612, _216610)), -(gt(_216610, _216612)), -(_216612 = _216610)], (274 ^ _207138) ^ [_216925, _216927, _216929] : [-(gt(_216929, _216925)), gt(_216929, _216927), gt(_216927, _216925)], (284 ^ _207138) ^ [_217204] : [gt(_217204, _217204)], (286 ^ _207138) ^ [_217282] : [-(leq(_217282, _217282))], (288 ^ _207138) ^ [_217403, _217405, _217407] : [-(leq(_217407, _217403)), leq(_217407, _217405), leq(_217405, _217403)], (298 ^ _207138) ^ [_217741, _217743] : [lt(_217743, _217741), -(gt(_217741, _217743))], (304 ^ _207138) ^ [_217903, _217905] : [gt(_217903, _217905), -(lt(_217905, _217903))], (310 ^ _207138) ^ [_218144, _218146] : [geq(_218146, _218144), -(leq(_218144, _218146))], (316 ^ _207138) ^ [_218306, _218308] : [leq(_218306, _218308), -(geq(_218308, _218306))], (322 ^ _207138) ^ [_218518, _218520] : [gt(_218518, _218520), -(leq(_218520, _218518))], (328 ^ _207138) ^ [_218728, _218730] : [-(gt(_218728, _218730)), leq(_218730, _218728), -(_218730 = _218728)], (338 ^ _207138) ^ [_219059, _219061] : [leq(_219061, pred(_219059)), -(gt(_219059, _219061))], (344 ^ _207138) ^ [_219225, _219227] : [gt(_219225, _219227), -(leq(_219227, pred(_219225)))], (350 ^ _207138) ^ [_219412] : [-(gt(succ(_219412), _219412))], (352 ^ _207138) ^ [_219521, _219523] : [leq(_219523, _219521), -(leq(_219523, succ(_219521)))], (358 ^ _207138) ^ [_219764, _219766] : [leq(_219766, _219764), -(gt(succ(_219764), _219766))], (364 ^ _207138) ^ [_219930, _219932] : [gt(succ(_219930), _219932), -(leq(_219932, _219930))], (370 ^ _207138) ^ [_220146, _220148] : [leq(n0, _220148), -(leq(uniform_int_rnd(_220146, _220148), _220148))], (376 ^ _207138) ^ [_220362, _220364] : [leq(n0, _220364), -(leq(n0, uniform_int_rnd(_220362, _220364)))], (382 ^ _207138) ^ [_220606, _220608, _220610, _220612] : [-(a_select2(tptp_const_array1(dim(_220610, _220608), _220606), _220612) = _220606), leq(_220610, _220612), leq(_220612, _220608)], (392 ^ _207138) ^ [_221013, _221015, _221017, _221019, _221021, _221023, _221025] : [-(a_select3(tptp_const_array2(dim(_221023, _221021), dim(_221017, _221015), _221013), _221025, _221019) = _221013), leq(_221023, _221025), leq(_221025, _221021), leq(_221017, _221019), leq(_221019, _221015)], (410 ^ _207138) ^ [_221608, _221610] : [413 ^ _207138 : [(414 ^ _207138) ^ [] : [-(leq(n0, 411 ^ [_221608, _221610]))], (416 ^ _207138) ^ [] : [-(leq(411 ^ [_221608, _221610], _221608))], (418 ^ _207138) ^ [] : [-(leq(n0, 412 ^ [_221608, _221610]))], (420 ^ _207138) ^ [] : [-(leq(412 ^ [_221608, _221610], _221608))], (422 ^ _207138) ^ [] : [a_select3(_221610, 411 ^ [_221608, _221610], 412 ^ [_221608, _221610]) = a_select3(_221610, 412 ^ [_221608, _221610], 411 ^ [_221608, _221610])]], 423 ^ _207138 : [(424 ^ _207138) ^ [_222365, _222367] : [-(a_select3(trans(_221610), _222367, _222365) = a_select3(trans(_221610), _222365, _222367)), leq(n0, _222367), leq(_222367, _221608), leq(n0, _222365), leq(_222365, _221608)]]], (442 ^ _207138) ^ [_222912, _222914] : [445 ^ _207138 : [(446 ^ _207138) ^ [] : [-(leq(n0, 443 ^ [_222912, _222914]))], (448 ^ _207138) ^ [] : [-(leq(443 ^ [_222912, _222914], _222912))], (450 ^ _207138) ^ [] : [-(leq(n0, 444 ^ [_222912, _222914]))], (452 ^ _207138) ^ [] : [-(leq(444 ^ [_222912, _222914], _222912))], (454 ^ _207138) ^ [] : [a_select3(_222914, 443 ^ [_222912, _222914], 444 ^ [_222912, _222914]) = a_select3(_222914, 444 ^ [_222912, _222914], 443 ^ [_222912, _222914])]], 455 ^ _207138 : [(456 ^ _207138) ^ [_223669, _223671] : [-(a_select3(inv(_222914), _223671, _223669) = a_select3(inv(_222914), _223669, _223671)), leq(n0, _223671), leq(_223671, _222912), leq(n0, _223669), leq(_223669, _222912)]]], (474 ^ _207138) ^ [_224216, _224218] : [477 ^ _207138 : [(478 ^ _207138) ^ [] : [-(leq(n0, 475 ^ [_224216, _224218]))], (480 ^ _207138) ^ [] : [-(leq(475 ^ [_224216, _224218], _224216))], (482 ^ _207138) ^ [] : [-(leq(n0, 476 ^ [_224216, _224218]))], (484 ^ _207138) ^ [] : [-(leq(476 ^ [_224216, _224218], _224216))], (486 ^ _207138) ^ [] : [a_select3(_224218, 475 ^ [_224216, _224218], 476 ^ [_224216, _224218]) = a_select3(_224218, 476 ^ [_224216, _224218], 475 ^ [_224216, _224218])]], 487 ^ _207138 : [(488 ^ _207138) ^ [_225029, _225031, _225033, _225035] : [-(a_select3(tptp_update3(_224218, _225031, _225031, _225029), _225035, _225033) = a_select3(tptp_update3(_224218, _225031, _225031, _225029), _225033, _225035)), leq(n0, _225035), leq(_225035, _224216), leq(n0, _225033), leq(_225033, _224216), leq(n0, _225031), leq(_225031, _224216)]]], (514 ^ _207138) ^ [_225848, _225850, _225852] : [519 ^ _207138 : [(520 ^ _207138) ^ [] : [-(leq(n0, 517 ^ [_225848, _225850, _225852]))], (522 ^ _207138) ^ [] : [-(leq(517 ^ [_225848, _225850, _225852], _225848))], (524 ^ _207138) ^ [] : [-(leq(n0, 518 ^ [_225848, _225850, _225852]))], (526 ^ _207138) ^ [] : [-(leq(518 ^ [_225848, _225850, _225852], _225848))], (528 ^ _207138) ^ [] : [a_select3(_225852, 517 ^ [_225848, _225850, _225852], 518 ^ [_225848, _225850, _225852]) = a_select3(_225852, 518 ^ [_225848, _225850, _225852], 517 ^ [_225848, _225850, _225852])]], 531 ^ _207138 : [(532 ^ _207138) ^ [] : [-(leq(n0, 529 ^ [_225848, _225850, _225852]))], (534 ^ _207138) ^ [] : [-(leq(529 ^ [_225848, _225850, _225852], _225848))], (536 ^ _207138) ^ [] : [-(leq(n0, 530 ^ [_225848, _225850, _225852]))], (538 ^ _207138) ^ [] : [-(leq(530 ^ [_225848, _225850, _225852], _225848))], (540 ^ _207138) ^ [] : [a_select3(_225850, 529 ^ [_225848, _225850, _225852], 530 ^ [_225848, _225850, _225852]) = a_select3(_225850, 530 ^ [_225848, _225850, _225852], 529 ^ [_225848, _225850, _225852])]], 541 ^ _207138 : [(542 ^ _207138) ^ [_227357, _227359] : [-(a_select3(tptp_madd(_225852, _225850), _227359, _227357) = a_select3(tptp_madd(_225852, _225850), _227357, _227359)), leq(n0, _227359), leq(_227359, _225848), leq(n0, _227357), leq(_227357, _225848)]]], (560 ^ _207138) ^ [_227943, _227945, _227947] : [565 ^ _207138 : [(566 ^ _207138) ^ [] : [-(leq(n0, 563 ^ [_227943, _227945, _227947]))], (568 ^ _207138) ^ [] : [-(leq(563 ^ [_227943, _227945, _227947], _227943))], (570 ^ _207138) ^ [] : [-(leq(n0, 564 ^ [_227943, _227945, _227947]))], (572 ^ _207138) ^ [] : [-(leq(564 ^ [_227943, _227945, _227947], _227943))], (574 ^ _207138) ^ [] : [a_select3(_227947, 563 ^ [_227943, _227945, _227947], 564 ^ [_227943, _227945, _227947]) = a_select3(_227947, 564 ^ [_227943, _227945, _227947], 563 ^ [_227943, _227945, _227947])]], 577 ^ _207138 : [(578 ^ _207138) ^ [] : [-(leq(n0, 575 ^ [_227943, _227945, _227947]))], (580 ^ _207138) ^ [] : [-(leq(575 ^ [_227943, _227945, _227947], _227943))], (582 ^ _207138) ^ [] : [-(leq(n0, 576 ^ [_227943, _227945, _227947]))], (584 ^ _207138) ^ [] : [-(leq(576 ^ [_227943, _227945, _227947], _227943))], (586 ^ _207138) ^ [] : [a_select3(_227945, 575 ^ [_227943, _227945, _227947], 576 ^ [_227943, _227945, _227947]) = a_select3(_227945, 576 ^ [_227943, _227945, _227947], 575 ^ [_227943, _227945, _227947])]], 587 ^ _207138 : [(588 ^ _207138) ^ [_229452, _229454] : [-(a_select3(tptp_msub(_227947, _227945), _229454, _229452) = a_select3(tptp_msub(_227947, _227945), _229452, _229454)), leq(n0, _229454), leq(_229454, _227943), leq(n0, _229452), leq(_229452, _227943)]]], (606 ^ _207138) ^ [_230038, _230040, _230042] : [609 ^ _207138 : [(610 ^ _207138) ^ [] : [-(leq(n0, 607 ^ [_230038, _230040, _230042]))], (612 ^ _207138) ^ [] : [-(leq(607 ^ [_230038, _230040, _230042], _230038))], (614 ^ _207138) ^ [] : [-(leq(n0, 608 ^ [_230038, _230040, _230042]))], (616 ^ _207138) ^ [] : [-(leq(608 ^ [_230038, _230040, _230042], _230038))], (618 ^ _207138) ^ [] : [a_select3(_230040, 607 ^ [_230038, _230040, _230042], 608 ^ [_230038, _230040, _230042]) = a_select3(_230040, 608 ^ [_230038, _230040, _230042], 607 ^ [_230038, _230040, _230042])]], 619 ^ _207138 : [(620 ^ _207138) ^ [_230851, _230853] : [-(a_select3(tptp_mmul(_230042, tptp_mmul(_230040, trans(_230042))), _230853, _230851) = a_select3(tptp_mmul(_230042, tptp_mmul(_230040, trans(_230042))), _230851, _230853)), leq(n0, _230853), leq(_230853, _230038), leq(n0, _230851), leq(_230851, _230038)]]], (638 ^ _207138) ^ [_231470, _231472, _231474, _231476] : [641 ^ _207138 : [(642 ^ _207138) ^ [] : [-(leq(n0, 639 ^ [_231470, _231472, _231474, _231476]))], (644 ^ _207138) ^ [] : [-(leq(639 ^ [_231470, _231472, _231474, _231476], _231470))], (646 ^ _207138) ^ [] : [-(leq(n0, 640 ^ [_231470, _231472, _231474, _231476]))], (648 ^ _207138) ^ [] : [-(leq(640 ^ [_231470, _231472, _231474, _231476], _231470))], (650 ^ _207138) ^ [] : [a_select3(_231474, 639 ^ [_231470, _231472, _231474, _231476], 640 ^ [_231470, _231472, _231474, _231476]) = a_select3(_231474, 640 ^ [_231470, _231472, _231474, _231476], 639 ^ [_231470, _231472, _231474, _231476])]], 651 ^ _207138 : [(652 ^ _207138) ^ [_232327, _232329] : [-(a_select3(tptp_mmul(_231476, tptp_mmul(_231474, trans(_231476))), _232329, _232327) = a_select3(tptp_mmul(_231476, tptp_mmul(_231474, trans(_231476))), _232327, _232329)), leq(n0, _232329), leq(_232329, _231472), leq(n0, _232327), leq(_232327, _231472)]]], (670 ^ _207138) ^ [_233022, _233024, _233026, _233028, _233030, _233032, _233034, _233036] : [675 ^ _207138 : [(676 ^ _207138) ^ [] : [-(leq(n0, 673 ^ [_233022, _233024, _233026, _233028, _233030, _233032, _233034, _233036]))], (678 ^ _207138) ^ [] : [-(leq(673 ^ [_233022, _233024, _233026, _233028, _233030, _233032, _233034, _233036], _233022))], (680 ^ _207138) ^ [] : [-(leq(n0, 674 ^ [_233022, _233024, _233026, _233028, _233030, _233032, _233034, _233036]))], (682 ^ _207138) ^ [] : [-(leq(674 ^ [_233022, _233024, _233026, _233028, _233030, _233032, _233034, _233036], _233022))], (684 ^ _207138) ^ [] : [a_select3(_233030, 673 ^ [_233022, _233024, _233026, _233028, _233030, _233032, _233034, _233036], 674 ^ [_233022, _233024, _233026, _233028, _233030, _233032, _233034, _233036]) = a_select3(_233030, 674 ^ [_233022, _233024, _233026, _233028, _233030, _233032, _233034, _233036], 673 ^ [_233022, _233024, _233026, _233028, _233030, _233032, _233034, _233036])]], 689 ^ _207138 : [(690 ^ _207138) ^ [] : [-(leq(n0, 687 ^ [_233022, _233024, _233026, _233028, _233030, _233032, _233034, _233036]))], (692 ^ _207138) ^ [] : [-(leq(687 ^ [_233022, _233024, _233026, _233028, _233030, _233032, _233034, _233036], _233024))], (694 ^ _207138) ^ [] : [-(leq(n0, 688 ^ [_233022, _233024, _233026, _233028, _233030, _233032, _233034, _233036]))], (696 ^ _207138) ^ [] : [-(leq(688 ^ [_233022, _233024, _233026, _233028, _233030, _233032, _233034, _233036], _233024))], (698 ^ _207138) ^ [] : [a_select3(_233036, 687 ^ [_233022, _233024, _233026, _233028, _233030, _233032, _233034, _233036], 688 ^ [_233022, _233024, _233026, _233028, _233030, _233032, _233034, _233036]) = a_select3(_233036, 688 ^ [_233022, _233024, _233026, _233028, _233030, _233032, _233034, _233036], 687 ^ [_233022, _233024, _233026, _233028, _233030, _233032, _233034, _233036])]], 701 ^ _207138 : [(702 ^ _207138) ^ [] : [-(leq(n0, 699 ^ [_233022, _233024, _233026, _233028, _233030, _233032, _233034, _233036]))], (704 ^ _207138) ^ [] : [-(leq(699 ^ [_233022, _233024, _233026, _233028, _233030, _233032, _233034, _233036], _233024))], (706 ^ _207138) ^ [] : [-(leq(n0, 700 ^ [_233022, _233024, _233026, _233028, _233030, _233032, _233034, _233036]))], (708 ^ _207138) ^ [] : [-(leq(700 ^ [_233022, _233024, _233026, _233028, _233030, _233032, _233034, _233036], _233024))], (710 ^ _207138) ^ [] : [a_select3(_233026, 699 ^ [_233022, _233024, _233026, _233028, _233030, _233032, _233034, _233036], 700 ^ [_233022, _233024, _233026, _233028, _233030, _233032, _233034, _233036]) = a_select3(_233026, 700 ^ [_233022, _233024, _233026, _233028, _233030, _233032, _233034, _233036], 699 ^ [_233022, _233024, _233026, _233028, _233030, _233032, _233034, _233036])]], 711 ^ _207138 : [(712 ^ _207138) ^ [_235950, _235952] : [-(a_select3(tptp_madd(_233036, tptp_mmul(_233034, tptp_mmul(tptp_madd(tptp_mmul(_233032, tptp_mmul(_233030, trans(_233032))), tptp_mmul(_233028, tptp_mmul(_233026, trans(_233028)))), trans(_233034)))), _235952, _235950) = a_select3(tptp_madd(_233036, tptp_mmul(_233034, tptp_mmul(tptp_madd(tptp_mmul(_233032, tptp_mmul(_233030, trans(_233032))), tptp_mmul(_233028, tptp_mmul(_233026, trans(_233028)))), trans(_233034)))), _235950, _235952)), leq(n0, _235952), leq(_235952, _233024), leq(n0, _235950), leq(_235950, _233024)]]], (730 ^ _207138) ^ [_236703] : [-(sum(n0, tptp_minus_1, _236703) = n0)], (732 ^ _207138) ^ [_236785] : [-(tptp_float_0_0 = sum(n0, tptp_minus_1, _236785))], (734 ^ _207138) ^ [] : [-(succ(tptp_minus_1) = n0)], (736 ^ _207138) ^ [_236920] : [-(plus(_236920, n1) = succ(_236920))], (738 ^ _207138) ^ [_237003] : [-(plus(n1, _237003) = succ(_237003))], (740 ^ _207138) ^ [_237086] : [-(plus(_237086, n2) = succ(succ(_237086)))], (742 ^ _207138) ^ [_237171] : [-(plus(n2, _237171) = succ(succ(_237171)))], (744 ^ _207138) ^ [_237256] : [-(plus(_237256, n3) = succ(succ(succ(_237256))))], (746 ^ _207138) ^ [_237343] : [-(plus(n3, _237343) = succ(succ(succ(_237343))))], (748 ^ _207138) ^ [_237430] : [-(plus(_237430, n4) = succ(succ(succ(succ(_237430)))))], (750 ^ _207138) ^ [_237519] : [-(plus(n4, _237519) = succ(succ(succ(succ(_237519)))))], (752 ^ _207138) ^ [_237608] : [-(plus(_237608, n5) = succ(succ(succ(succ(succ(_237608))))))], (754 ^ _207138) ^ [_237699] : [-(plus(n5, _237699) = succ(succ(succ(succ(succ(_237699))))))], (756 ^ _207138) ^ [_237790] : [-(minus(_237790, n1) = pred(_237790))], (758 ^ _207138) ^ [_237873] : [-(pred(succ(_237873)) = _237873)], (760 ^ _207138) ^ [_237955] : [-(succ(pred(_237955)) = _237955)], (762 ^ _207138) ^ [_238095, _238097] : [leq(succ(_238097), succ(_238095)), -(leq(_238097, _238095))], (768 ^ _207138) ^ [_238265, _238267] : [leq(_238267, _238265), -(leq(succ(_238267), succ(_238265)))], (774 ^ _207138) ^ [_238485, _238487] : [leq(succ(_238487), _238485), -(gt(_238485, _238487))], (780 ^ _207138) ^ [_238699, _238701] : [leq(minus(_238701, _238699), _238701), -(leq(n0, _238699))], (786 ^ _207138) ^ [_238928, _238930, _238932, _238934] : [-(a_select3(tptp_update3(_238934, _238932, _238930, _238928), _238932, _238930) = _238928)], (788 ^ _207138) ^ [_239120, _239122, _239124, _239126, _239128, _239130, _239132] : [-(a_select3(tptp_update3(_239124, _239132, _239130, _239120), _239128, _239126) = _239122), -(_239132 = _239128), _239130 = _239126, a_select3(_239124, _239128, _239126) = _239122], (802 ^ _207138) ^ [_239663, _239665, _239667, _239669, _239671, _239673] : [-(a_select3(tptp_update3(_239665, _239669, _239667, _239663), _239673, _239671) = _239663), 807 ^ _207138 : [(808 ^ _207138) ^ [] : [-(leq(n0, 805 ^ [_239663, _239665, _239667, _239669, _239671, _239673]))], (810 ^ _207138) ^ [] : [-(leq(n0, 806 ^ [_239663, _239665, _239667, _239669, _239671, _239673]))], (812 ^ _207138) ^ [] : [-(leq(805 ^ [_239663, _239665, _239667, _239669, _239671, _239673], _239669))], (814 ^ _207138) ^ [] : [-(leq(806 ^ [_239663, _239665, _239667, _239669, _239671, _239673], _239667))], (816 ^ _207138) ^ [] : [a_select3(_239665, 805 ^ [_239663, _239665, _239667, _239669, _239671, _239673], 806 ^ [_239663, _239665, _239667, _239669, _239671, _239673]) = _239663]], leq(n0, _239673), leq(_239673, _239669), leq(n0, _239671), leq(_239671, _239667)], (834 ^ _207138) ^ [_241005, _241007, _241009] : [-(a_select2(tptp_update2(_241009, _241007, _241005), _241007) = _241005)], (836 ^ _207138) ^ [_241165, _241167, _241169, _241171, _241173] : [-(a_select2(tptp_update2(_241169, _241173, _241165), _241171) = _241167), -(_241173 = _241171), a_select2(_241169, _241171) = _241167], (865 ^ _207138) ^ [] : [-(true)], (867 ^ _207138) ^ [] : [def = use], (846 ^ _207138) ^ [_241545, _241547, _241549, _241551] : [-(a_select2(tptp_update2(_241547, _241549, _241545), _241551) = _241545), 850 ^ _207138 : [(851 ^ _207138) ^ [] : [-(leq(n0, 849 ^ [_241545, _241547, _241549, _241551]))], (853 ^ _207138) ^ [] : [-(leq(849 ^ [_241545, _241547, _241549, _241551], _241549))], (855 ^ _207138) ^ [] : [a_select2(_241547, 849 ^ [_241545, _241547, _241549, _241551]) = _241545]], leq(n0, _241551), leq(_241551, _241549)]], input).
% 0.73/1.37  ncf('1',plain,[gt(n1, n1)],start(284 ^ 0,bind([[_217204], [n1]]))).
% 0.73/1.37  ncf('1.1',plain,[-(gt(n1, n1)), gt(n1, loopcounter), gt(loopcounter, n1)],extension(274 ^ 1,bind([[_216925, _216927, _216929], [n1, loopcounter, n1]]))).
% 0.73/1.37  ncf('1.1.1',plain,[-(gt(n1, loopcounter))],extension(1059 ^ 2)).
% 0.73/1.37  ncf('1.1.2',plain,[-(gt(loopcounter, n1)), gt(n1, loopcounter), n1 = loopcounter, loopcounter = n1],extension(48 ^ 2,bind([[_208822, _208824, _208826, _208828], [n1, loopcounter, loopcounter, n1]]))).
% 0.73/1.37  ncf('1.1.2.1',plain,[-(gt(n1, loopcounter))],extension(1059 ^ 3)).
% 0.73/1.37  ncf('1.1.2.2',plain,[-(n1 = loopcounter), -(gt(loopcounter, n1)), leq(n1, loopcounter)],extension(328 ^ 3,bind([[_218728, _218730], [loopcounter, n1]]))).
% 0.73/1.37  ncf('1.1.2.2.1',plain,[gt(loopcounter, n1)],reduction('1.1')).
% 0.73/1.37  ncf('1.1.2.2.2',plain,[-(leq(n1, loopcounter))],extension(1057 ^ 4)).
% 0.73/1.37  ncf('1.1.2.3',plain,[-(loopcounter = n1), n1 = loopcounter],extension(4 ^ 3,bind([[_207389, _207391], [loopcounter, n1]]))).
% 0.73/1.37  ncf('1.1.2.3.1',plain,[-(n1 = loopcounter)],lemmata('[1, 1].x')).
% 0.73/1.37  %-----------------------------------------------------
% 0.73/1.37  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------