%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SWV188+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n014.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 18.78s 18.96s
% Output   : Proof 18.78s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : SWV188+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.10/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n014.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 02:14:57 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 18.78/18.96  
% 18.78/18.96  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 18.78/18.96  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 18.78/18.96  %-----------------------------------------------------
% 18.78/18.96  ncf(matrix, plain, [(1136 ^ _208097) ^ [] : [-(leq(n0, 1134 ^ []))], (1138 ^ _208097) ^ [] : [-(leq(1134 ^ [], tptp_minus_1))], (1140 ^ _208097) ^ [] : [a_select2(mu_init, 1134 ^ []) = init], (1055 ^ _208097) ^ [_248413] : [leq(n0, _248413), leq(_248413, n135299), 1062 ^ _208097 : [(1063 ^ _208097) ^ [_248641] : [-(a_select3(q_init, _248413, _248641) = init), leq(n0, _248641), leq(_248641, n4)]]], (1073 ^ _208097) ^ [_248943] : [-(a_select2(rho_init, _248943) = init), leq(n0, _248943), leq(_248943, n4)], (1083 ^ _208097) ^ [_249224] : [-(a_select3(center_init, _249224, n0) = init), leq(n0, _249224), leq(_249224, n4)], (1093 ^ _208097) ^ [] : [gt(loopcounter, n1), 1096 ^ _208097 : [(1097 ^ _208097) ^ [_249569] : [-(a_select2(muold_init, _249569) = init), leq(n0, _249569), leq(_249569, n4)]]], (1107 ^ _208097) ^ [] : [gt(loopcounter, n1), 1110 ^ _208097 : [(1111 ^ _208097) ^ [_249917] : [-(a_select2(rhoold_init, _249917) = init), leq(n0, _249917), leq(_249917, n4)]]], (1121 ^ _208097) ^ [] : [gt(loopcounter, n1), 1124 ^ _208097 : [(1125 ^ _208097) ^ [_250245] : [-(a_select2(sigmaold_init, _250245) = init), leq(n0, _250245), leq(_250245, n4)]]], (2 ^ _208097) ^ [_208241] : [-(_208241 = _208241)], (4 ^ _208097) ^ [_208348, _208350] : [_208350 = _208348, -(_208348 = _208350)], (10 ^ _208097) ^ [_208552, _208554, _208556] : [-(_208556 = _208552), _208556 = _208554, _208554 = _208552], (20 ^ _208097) ^ [_208893, _208895, _208897, _208899] : [-(lt(_208897, _208893)), lt(_208899, _208895), _208899 = _208897, _208895 = _208893], (34 ^ _208097) ^ [_209337, _209339, _209341, _209343] : [-(geq(_209341, _209337)), geq(_209343, _209339), _209343 = _209341, _209339 = _209337], (48 ^ _208097) ^ [_209781, _209783, _209785, _209787] : [-(gt(_209785, _209781)), gt(_209787, _209783), _209787 = _209785, _209783 = _209781], (62 ^ _208097) ^ [_210205, _210207, _210209, _210211] : [-(leq(_210209, _210205)), leq(_210211, _210207), _210211 = _210209, _210207 = _210205], (76 ^ _208097) ^ [_210661, _210663, _210665, _210667] : [-(uniform_int_rnd(_210667, _210663) = uniform_int_rnd(_210665, _210661)), _210667 = _210665, _210663 = _210661], (86 ^ _208097) ^ [_211020, _211022, _211024, _211026] : [-(tptp_const_array1(_211026, _211022) = tptp_const_array1(_211024, _211020)), _211026 = _211024, _211022 = _211020], (96 ^ _208097) ^ [_211407, _211409, _211411, _211413, _211415, _211417] : [-(tptp_const_array2(_211417, _211413, _211409) = tptp_const_array2(_211415, _211411, _211407)), _211417 = _211415, _211413 = _211411, _211409 = _211407], (110 ^ _208097) ^ [_211895, _211897, _211899, _211901] : [-(dim(_211901, _211897) = dim(_211899, _211895)), _211901 = _211899, _211897 = _211895], (120 ^ _208097) ^ [_212226, _212228] : [_212228 = _212226, -(inv(_212228) = inv(_212226))], (126 ^ _208097) ^ [_212472, _212474, _212476, _212478] : [-(tptp_msub(_212478, _212474) = tptp_msub(_212476, _212472)), _212478 = _212476, _212474 = _212472], (136 ^ _208097) ^ [_212831, _212833, _212835, _212837] : [-(tptp_madd(_212837, _212833) = tptp_madd(_212835, _212831)), _212837 = _212835, _212833 = _212831], (146 ^ _208097) ^ [_213190, _213192, _213194, _213196] : [-(tptp_mmul(_213196, _213192) = tptp_mmul(_213194, _213190)), _213196 = _213194, _213192 = _213190], (156 ^ _208097) ^ [_213521, _213523] : [_213523 = _213521, -(trans(_213523) = trans(_213521))], (162 ^ _208097) ^ [_213795, _213797, _213799, _213801, _213803, _213805] : [-(sum(_213805, _213801, _213797) = sum(_213803, _213799, _213795)), _213805 = _213803, _213801 = _213799, _213797 = _213795], (176 ^ _208097) ^ [_214283, _214285, _214287, _214289] : [-(plus(_214289, _214285) = plus(_214287, _214283)), _214289 = _214287, _214285 = _214283], (186 ^ _208097) ^ [_214614, _214616] : [_214616 = _214614, -(pred(_214616) = pred(_214614))], (192 ^ _208097) ^ [_214860, _214862, _214864, _214866] : [-(minus(_214866, _214862) = minus(_214864, _214860)), _214866 = _214864, _214862 = _214860], (202 ^ _208097) ^ [_215275, _215277, _215279, _215281, _215283, _215285, _215287, _215289] : [-(tptp_update3(_215289, _215285, _215281, _215277) = tptp_update3(_215287, _215283, _215279, _215275)), _215289 = _215287, _215285 = _215283, _215281 = _215279, _215277 = _215275], (220 ^ _208097) ^ [_215936, _215938, _215940, _215942, _215944, _215946] : [-(tptp_update2(_215946, _215942, _215938) = tptp_update2(_215944, _215940, _215936)), _215946 = _215944, _215942 = _215940, _215938 = _215936], (234 ^ _208097) ^ [_216396, _216398] : [_216398 = _216396, -(succ(_216398) = succ(_216396))], (254 ^ _208097) ^ [_217138, _217140, _217142, _217144] : [-(a_select2(_217144, _217140) = a_select2(_217142, _217138)), _217144 = _217142, _217140 = _217138], (240 ^ _208097) ^ [_216670, _216672, _216674, _216676, _216678, _216680] : [-(a_select3(_216680, _216676, _216672) = a_select3(_216678, _216674, _216670)), _216680 = _216678, _216676 = _216674, _216672 = _216670], (869 ^ _208097) ^ [] : [-(gt(n5, n4))], (871 ^ _208097) ^ [] : [-(gt(n135299, n4))], (873 ^ _208097) ^ [] : [-(gt(n135299, n5))], (875 ^ _208097) ^ [] : [-(gt(n4, tptp_minus_1))], (877 ^ _208097) ^ [] : [-(gt(n5, tptp_minus_1))], (879 ^ _208097) ^ [] : [-(gt(n135299, tptp_minus_1))], (881 ^ _208097) ^ [] : [-(gt(n0, tptp_minus_1))], (883 ^ _208097) ^ [] : [-(gt(n1, tptp_minus_1))], (885 ^ _208097) ^ [] : [-(gt(n2, tptp_minus_1))], (887 ^ _208097) ^ [] : [-(gt(n3, tptp_minus_1))], (889 ^ _208097) ^ [] : [-(gt(n4, n0))], (891 ^ _208097) ^ [] : [-(gt(n5, n0))], (893 ^ _208097) ^ [] : [-(gt(n135299, n0))], (895 ^ _208097) ^ [] : [-(gt(n1, n0))], (897 ^ _208097) ^ [] : [-(gt(n2, n0))], (899 ^ _208097) ^ [] : [-(gt(n3, n0))], (901 ^ _208097) ^ [] : [-(gt(n4, n1))], (903 ^ _208097) ^ [] : [-(gt(n5, n1))], (905 ^ _208097) ^ [] : [-(gt(n135299, n1))], (907 ^ _208097) ^ [] : [-(gt(n2, n1))], (909 ^ _208097) ^ [] : [-(gt(n3, n1))], (911 ^ _208097) ^ [] : [-(gt(n4, n2))], (913 ^ _208097) ^ [] : [-(gt(n5, n2))], (915 ^ _208097) ^ [] : [-(gt(n135299, n2))], (917 ^ _208097) ^ [] : [-(gt(n3, n2))], (919 ^ _208097) ^ [] : [-(gt(n4, n3))], (921 ^ _208097) ^ [] : [-(gt(n5, n3))], (923 ^ _208097) ^ [] : [-(gt(n135299, n3))], (925 ^ _208097) ^ [_244978] : [leq(n0, _244978), leq(_244978, n4), -(_244978 = n0), -(_244978 = n1), -(_244978 = n2), -(_244978 = n3), -(_244978 = n4)], (951 ^ _208097) ^ [_245599] : [leq(n0, _245599), leq(_245599, n5), -(_245599 = n0), -(_245599 = n1), -(_245599 = n2), -(_245599 = n3), -(_245599 = n4), -(_245599 = n5)], (981 ^ _208097) ^ [_246306] : [-(_246306 = n0), leq(n0, _246306), leq(_246306, n0)], (991 ^ _208097) ^ [_246581] : [leq(n0, _246581), leq(_246581, n1), -(_246581 = n0), -(_246581 = n1)], (1005 ^ _208097) ^ [_246944] : [leq(n0, _246944), leq(_246944, n2), -(_246944 = n0), -(_246944 = n1), -(_246944 = n2)], (1045 ^ _208097) ^ [] : [-(succ(succ(succ(succ(n0)))) = n4)], (1047 ^ _208097) ^ [] : [-(succ(succ(succ(succ(succ(n0))))) = n5)], (1049 ^ _208097) ^ [] : [-(succ(n0) = n1)], (1051 ^ _208097) ^ [] : [-(succ(succ(n0)) = n2)], (1053 ^ _208097) ^ [] : [-(succ(succ(succ(n0))) = n3)], (1023 ^ _208097) ^ [_247393] : [leq(n0, _247393), leq(_247393, n3), -(_247393 = n0), -(_247393 = n1), -(_247393 = n2), -(_247393 = n3)], (264 ^ _208097) ^ [_217569, _217571] : [-(gt(_217571, _217569)), -(gt(_217569, _217571)), -(_217571 = _217569)], (274 ^ _208097) ^ [_217884, _217886, _217888] : [-(gt(_217888, _217884)), gt(_217888, _217886), gt(_217886, _217884)], (284 ^ _208097) ^ [_218163] : [gt(_218163, _218163)], (286 ^ _208097) ^ [_218241] : [-(leq(_218241, _218241))], (288 ^ _208097) ^ [_218362, _218364, _218366] : [-(leq(_218366, _218362)), leq(_218366, _218364), leq(_218364, _218362)], (298 ^ _208097) ^ [_218700, _218702] : [lt(_218702, _218700), -(gt(_218700, _218702))], (304 ^ _208097) ^ [_218862, _218864] : [gt(_218862, _218864), -(lt(_218864, _218862))], (310 ^ _208097) ^ [_219103, _219105] : [geq(_219105, _219103), -(leq(_219103, _219105))], (316 ^ _208097) ^ [_219265, _219267] : [leq(_219265, _219267), -(geq(_219267, _219265))], (322 ^ _208097) ^ [_219477, _219479] : [gt(_219477, _219479), -(leq(_219479, _219477))], (328 ^ _208097) ^ [_219687, _219689] : [-(gt(_219687, _219689)), leq(_219689, _219687), -(_219689 = _219687)], (338 ^ _208097) ^ [_220018, _220020] : [leq(_220020, pred(_220018)), -(gt(_220018, _220020))], (344 ^ _208097) ^ [_220184, _220186] : [gt(_220184, _220186), -(leq(_220186, pred(_220184)))], (350 ^ _208097) ^ [_220371] : [-(gt(succ(_220371), _220371))], (352 ^ _208097) ^ [_220480, _220482] : [leq(_220482, _220480), -(leq(_220482, succ(_220480)))], (358 ^ _208097) ^ [_220723, _220725] : [leq(_220725, _220723), -(gt(succ(_220723), _220725))], (364 ^ _208097) ^ [_220889, _220891] : [gt(succ(_220889), _220891), -(leq(_220891, _220889))], (370 ^ _208097) ^ [_221105, _221107] : [leq(n0, _221107), -(leq(uniform_int_rnd(_221105, _221107), _221107))], (376 ^ _208097) ^ [_221321, _221323] : [leq(n0, _221323), -(leq(n0, uniform_int_rnd(_221321, _221323)))], (382 ^ _208097) ^ [_221565, _221567, _221569, _221571] : [-(a_select2(tptp_const_array1(dim(_221569, _221567), _221565), _221571) = _221565), leq(_221569, _221571), leq(_221571, _221567)], (392 ^ _208097) ^ [_221972, _221974, _221976, _221978, _221980, _221982, _221984] : [-(a_select3(tptp_const_array2(dim(_221982, _221980), dim(_221976, _221974), _221972), _221984, _221978) = _221972), leq(_221982, _221984), leq(_221984, _221980), leq(_221976, _221978), leq(_221978, _221974)], (410 ^ _208097) ^ [_222567, _222569] : [413 ^ _208097 : [(414 ^ _208097) ^ [] : [-(leq(n0, 411 ^ [_222567, _222569]))], (416 ^ _208097) ^ [] : [-(leq(411 ^ [_222567, _222569], _222567))], (418 ^ _208097) ^ [] : [-(leq(n0, 412 ^ [_222567, _222569]))], (420 ^ _208097) ^ [] : [-(leq(412 ^ [_222567, _222569], _222567))], (422 ^ _208097) ^ [] : [a_select3(_222569, 411 ^ [_222567, _222569], 412 ^ [_222567, _222569]) = a_select3(_222569, 412 ^ [_222567, _222569], 411 ^ [_222567, _222569])]], 423 ^ _208097 : [(424 ^ _208097) ^ [_223324, _223326] : [-(a_select3(trans(_222569), _223326, _223324) = a_select3(trans(_222569), _223324, _223326)), leq(n0, _223326), leq(_223326, _222567), leq(n0, _223324), leq(_223324, _222567)]]], (442 ^ _208097) ^ [_223871, _223873] : [445 ^ _208097 : [(446 ^ _208097) ^ [] : [-(leq(n0, 443 ^ [_223871, _223873]))], (448 ^ _208097) ^ [] : [-(leq(443 ^ [_223871, _223873], _223871))], (450 ^ _208097) ^ [] : [-(leq(n0, 444 ^ [_223871, _223873]))], (452 ^ _208097) ^ [] : [-(leq(444 ^ [_223871, _223873], _223871))], (454 ^ _208097) ^ [] : [a_select3(_223873, 443 ^ [_223871, _223873], 444 ^ [_223871, _223873]) = a_select3(_223873, 444 ^ [_223871, _223873], 443 ^ [_223871, _223873])]], 455 ^ _208097 : [(456 ^ _208097) ^ [_224628, _224630] : [-(a_select3(inv(_223873), _224630, _224628) = a_select3(inv(_223873), _224628, _224630)), leq(n0, _224630), leq(_224630, _223871), leq(n0, _224628), leq(_224628, _223871)]]], (474 ^ _208097) ^ [_225175, _225177] : [477 ^ _208097 : [(478 ^ _208097) ^ [] : [-(leq(n0, 475 ^ [_225175, _225177]))], (480 ^ _208097) ^ [] : [-(leq(475 ^ [_225175, _225177], _225175))], (482 ^ _208097) ^ [] : [-(leq(n0, 476 ^ [_225175, _225177]))], (484 ^ _208097) ^ [] : [-(leq(476 ^ [_225175, _225177], _225175))], (486 ^ _208097) ^ [] : [a_select3(_225177, 475 ^ [_225175, _225177], 476 ^ [_225175, _225177]) = a_select3(_225177, 476 ^ [_225175, _225177], 475 ^ [_225175, _225177])]], 487 ^ _208097 : [(488 ^ _208097) ^ [_225988, _225990, _225992, _225994] : [-(a_select3(tptp_update3(_225177, _225990, _225990, _225988), _225994, _225992) = a_select3(tptp_update3(_225177, _225990, _225990, _225988), _225992, _225994)), leq(n0, _225994), leq(_225994, _225175), leq(n0, _225992), leq(_225992, _225175), leq(n0, _225990), leq(_225990, _225175)]]], (514 ^ _208097) ^ [_226807, _226809, _226811] : [519 ^ _208097 : [(520 ^ _208097) ^ [] : [-(leq(n0, 517 ^ [_226807, _226809, _226811]))], (522 ^ _208097) ^ [] : [-(leq(517 ^ [_226807, _226809, _226811], _226807))], (524 ^ _208097) ^ [] : [-(leq(n0, 518 ^ [_226807, _226809, _226811]))], (526 ^ _208097) ^ [] : [-(leq(518 ^ [_226807, _226809, _226811], _226807))], (528 ^ _208097) ^ [] : [a_select3(_226811, 517 ^ [_226807, _226809, _226811], 518 ^ [_226807, _226809, _226811]) = a_select3(_226811, 518 ^ [_226807, _226809, _226811], 517 ^ [_226807, _226809, _226811])]], 531 ^ _208097 : [(532 ^ _208097) ^ [] : [-(leq(n0, 529 ^ [_226807, _226809, _226811]))], (534 ^ _208097) ^ [] : [-(leq(529 ^ [_226807, _226809, _226811], _226807))], (536 ^ _208097) ^ [] : [-(leq(n0, 530 ^ [_226807, _226809, _226811]))], (538 ^ _208097) ^ [] : [-(leq(530 ^ [_226807, _226809, _226811], _226807))], (540 ^ _208097) ^ [] : [a_select3(_226809, 529 ^ [_226807, _226809, _226811], 530 ^ [_226807, _226809, _226811]) = a_select3(_226809, 530 ^ [_226807, _226809, _226811], 529 ^ [_226807, _226809, _226811])]], 541 ^ _208097 : [(542 ^ _208097) ^ [_228316, _228318] : [-(a_select3(tptp_madd(_226811, _226809), _228318, _228316) = a_select3(tptp_madd(_226811, _226809), _228316, _228318)), leq(n0, _228318), leq(_228318, _226807), leq(n0, _228316), leq(_228316, _226807)]]], (560 ^ _208097) ^ [_228902, _228904, _228906] : [565 ^ _208097 : [(566 ^ _208097) ^ [] : [-(leq(n0, 563 ^ [_228902, _228904, _228906]))], (568 ^ _208097) ^ [] : [-(leq(563 ^ [_228902, _228904, _228906], _228902))], (570 ^ _208097) ^ [] : [-(leq(n0, 564 ^ [_228902, _228904, _228906]))], (572 ^ _208097) ^ [] : [-(leq(564 ^ [_228902, _228904, _228906], _228902))], (574 ^ _208097) ^ [] : [a_select3(_228906, 563 ^ [_228902, _228904, _228906], 564 ^ [_228902, _228904, _228906]) = a_select3(_228906, 564 ^ [_228902, _228904, _228906], 563 ^ [_228902, _228904, _228906])]], 577 ^ _208097 : [(578 ^ _208097) ^ [] : [-(leq(n0, 575 ^ [_228902, _228904, _228906]))], (580 ^ _208097) ^ [] : [-(leq(575 ^ [_228902, _228904, _228906], _228902))], (582 ^ _208097) ^ [] : [-(leq(n0, 576 ^ [_228902, _228904, _228906]))], (584 ^ _208097) ^ [] : [-(leq(576 ^ [_228902, _228904, _228906], _228902))], (586 ^ _208097) ^ [] : [a_select3(_228904, 575 ^ [_228902, _228904, _228906], 576 ^ [_228902, _228904, _228906]) = a_select3(_228904, 576 ^ [_228902, _228904, _228906], 575 ^ [_228902, _228904, _228906])]], 587 ^ _208097 : [(588 ^ _208097) ^ [_230411, _230413] : [-(a_select3(tptp_msub(_228906, _228904), _230413, _230411) = a_select3(tptp_msub(_228906, _228904), _230411, _230413)), leq(n0, _230413), leq(_230413, _228902), leq(n0, _230411), leq(_230411, _228902)]]], (606 ^ _208097) ^ [_230997, _230999, _231001] : [609 ^ _208097 : [(610 ^ _208097) ^ [] : [-(leq(n0, 607 ^ [_230997, _230999, _231001]))], (612 ^ _208097) ^ [] : [-(leq(607 ^ [_230997, _230999, _231001], _230997))], (614 ^ _208097) ^ [] : [-(leq(n0, 608 ^ [_230997, _230999, _231001]))], (616 ^ _208097) ^ [] : [-(leq(608 ^ [_230997, _230999, _231001], _230997))], (618 ^ _208097) ^ [] : [a_select3(_230999, 607 ^ [_230997, _230999, _231001], 608 ^ [_230997, _230999, _231001]) = a_select3(_230999, 608 ^ [_230997, _230999, _231001], 607 ^ [_230997, _230999, _231001])]], 619 ^ _208097 : [(620 ^ _208097) ^ [_231810, _231812] : [-(a_select3(tptp_mmul(_231001, tptp_mmul(_230999, trans(_231001))), _231812, _231810) = a_select3(tptp_mmul(_231001, tptp_mmul(_230999, trans(_231001))), _231810, _231812)), leq(n0, _231812), leq(_231812, _230997), leq(n0, _231810), leq(_231810, _230997)]]], (638 ^ _208097) ^ [_232429, _232431, _232433, _232435] : [641 ^ _208097 : [(642 ^ _208097) ^ [] : [-(leq(n0, 639 ^ [_232429, _232431, _232433, _232435]))], (644 ^ _208097) ^ [] : [-(leq(639 ^ [_232429, _232431, _232433, _232435], _232429))], (646 ^ _208097) ^ [] : [-(leq(n0, 640 ^ [_232429, _232431, _232433, _232435]))], (648 ^ _208097) ^ [] : [-(leq(640 ^ [_232429, _232431, _232433, _232435], _232429))], (650 ^ _208097) ^ [] : [a_select3(_232433, 639 ^ [_232429, _232431, _232433, _232435], 640 ^ [_232429, _232431, _232433, _232435]) = a_select3(_232433, 640 ^ [_232429, _232431, _232433, _232435], 639 ^ [_232429, _232431, _232433, _232435])]], 651 ^ _208097 : [(652 ^ _208097) ^ [_233286, _233288] : [-(a_select3(tptp_mmul(_232435, tptp_mmul(_232433, trans(_232435))), _233288, _233286) = a_select3(tptp_mmul(_232435, tptp_mmul(_232433, trans(_232435))), _233286, _233288)), leq(n0, _233288), leq(_233288, _232431), leq(n0, _233286), leq(_233286, _232431)]]], (670 ^ _208097) ^ [_233981, _233983, _233985, _233987, _233989, _233991, _233993, _233995] : [675 ^ _208097 : [(676 ^ _208097) ^ [] : [-(leq(n0, 673 ^ [_233981, _233983, _233985, _233987, _233989, _233991, _233993, _233995]))], (678 ^ _208097) ^ [] : [-(leq(673 ^ [_233981, _233983, _233985, _233987, _233989, _233991, _233993, _233995], _233981))], (680 ^ _208097) ^ [] : [-(leq(n0, 674 ^ [_233981, _233983, _233985, _233987, _233989, _233991, _233993, _233995]))], (682 ^ _208097) ^ [] : [-(leq(674 ^ [_233981, _233983, _233985, _233987, _233989, _233991, _233993, _233995], _233981))], (684 ^ _208097) ^ [] : [a_select3(_233989, 673 ^ [_233981, _233983, _233985, _233987, _233989, _233991, _233993, _233995], 674 ^ [_233981, _233983, _233985, _233987, _233989, _233991, _233993, _233995]) = a_select3(_233989, 674 ^ [_233981, _233983, _233985, _233987, _233989, _233991, _233993, _233995], 673 ^ [_233981, _233983, _233985, _233987, _233989, _233991, _233993, _233995])]], 689 ^ _208097 : [(690 ^ _208097) ^ [] : [-(leq(n0, 687 ^ [_233981, _233983, _233985, _233987, _233989, _233991, _233993, _233995]))], (692 ^ _208097) ^ [] : [-(leq(687 ^ [_233981, _233983, _233985, _233987, _233989, _233991, _233993, _233995], _233983))], (694 ^ _208097) ^ [] : [-(leq(n0, 688 ^ [_233981, _233983, _233985, _233987, _233989, _233991, _233993, _233995]))], (696 ^ _208097) ^ [] : [-(leq(688 ^ [_233981, _233983, _233985, _233987, _233989, _233991, _233993, _233995], _233983))], (698 ^ _208097) ^ [] : [a_select3(_233995, 687 ^ [_233981, _233983, _233985, _233987, _233989, _233991, _233993, _233995], 688 ^ [_233981, _233983, _233985, _233987, _233989, _233991, _233993, _233995]) = a_select3(_233995, 688 ^ [_233981, _233983, _233985, _233987, _233989, _233991, _233993, _233995], 687 ^ [_233981, _233983, _233985, _233987, _233989, _233991, _233993, _233995])]], 701 ^ _208097 : [(702 ^ _208097) ^ [] : [-(leq(n0, 699 ^ [_233981, _233983, _233985, _233987, _233989, _233991, _233993, _233995]))], (704 ^ _208097) ^ [] : [-(leq(699 ^ [_233981, _233983, _233985, _233987, _233989, _233991, _233993, _233995], _233983))], (706 ^ _208097) ^ [] : [-(leq(n0, 700 ^ [_233981, _233983, _233985, _233987, _233989, _233991, _233993, _233995]))], (708 ^ _208097) ^ [] : [-(leq(700 ^ [_233981, _233983, _233985, _233987, _233989, _233991, _233993, _233995], _233983))], (710 ^ _208097) ^ [] : [a_select3(_233985, 699 ^ [_233981, _233983, _233985, _233987, _233989, _233991, _233993, _233995], 700 ^ [_233981, _233983, _233985, _233987, _233989, _233991, _233993, _233995]) = a_select3(_233985, 700 ^ [_233981, _233983, _233985, _233987, _233989, _233991, _233993, _233995], 699 ^ [_233981, _233983, _233985, _233987, _233989, _233991, _233993, _233995])]], 711 ^ _208097 : [(712 ^ _208097) ^ [_236909, _236911] : [-(a_select3(tptp_madd(_233995, tptp_mmul(_233993, tptp_mmul(tptp_madd(tptp_mmul(_233991, tptp_mmul(_233989, trans(_233991))), tptp_mmul(_233987, tptp_mmul(_233985, trans(_233987)))), trans(_233993)))), _236911, _236909) = a_select3(tptp_madd(_233995, tptp_mmul(_233993, tptp_mmul(tptp_madd(tptp_mmul(_233991, tptp_mmul(_233989, trans(_233991))), tptp_mmul(_233987, tptp_mmul(_233985, trans(_233987)))), trans(_233993)))), _236909, _236911)), leq(n0, _236911), leq(_236911, _233983), leq(n0, _236909), leq(_236909, _233983)]]], (730 ^ _208097) ^ [_237662] : [-(sum(n0, tptp_minus_1, _237662) = n0)], (732 ^ _208097) ^ [_237744] : [-(tptp_float_0_0 = sum(n0, tptp_minus_1, _237744))], (734 ^ _208097) ^ [] : [-(succ(tptp_minus_1) = n0)], (736 ^ _208097) ^ [_237879] : [-(plus(_237879, n1) = succ(_237879))], (738 ^ _208097) ^ [_237962] : [-(plus(n1, _237962) = succ(_237962))], (740 ^ _208097) ^ [_238045] : [-(plus(_238045, n2) = succ(succ(_238045)))], (742 ^ _208097) ^ [_238130] : [-(plus(n2, _238130) = succ(succ(_238130)))], (744 ^ _208097) ^ [_238215] : [-(plus(_238215, n3) = succ(succ(succ(_238215))))], (746 ^ _208097) ^ [_238302] : [-(plus(n3, _238302) = succ(succ(succ(_238302))))], (748 ^ _208097) ^ [_238389] : [-(plus(_238389, n4) = succ(succ(succ(succ(_238389)))))], (750 ^ _208097) ^ [_238478] : [-(plus(n4, _238478) = succ(succ(succ(succ(_238478)))))], (752 ^ _208097) ^ [_238567] : [-(plus(_238567, n5) = succ(succ(succ(succ(succ(_238567))))))], (754 ^ _208097) ^ [_238658] : [-(plus(n5, _238658) = succ(succ(succ(succ(succ(_238658))))))], (756 ^ _208097) ^ [_238749] : [-(minus(_238749, n1) = pred(_238749))], (758 ^ _208097) ^ [_238832] : [-(pred(succ(_238832)) = _238832)], (760 ^ _208097) ^ [_238914] : [-(succ(pred(_238914)) = _238914)], (762 ^ _208097) ^ [_239054, _239056] : [leq(succ(_239056), succ(_239054)), -(leq(_239056, _239054))], (768 ^ _208097) ^ [_239224, _239226] : [leq(_239226, _239224), -(leq(succ(_239226), succ(_239224)))], (774 ^ _208097) ^ [_239444, _239446] : [leq(succ(_239446), _239444), -(gt(_239444, _239446))], (780 ^ _208097) ^ [_239658, _239660] : [leq(minus(_239660, _239658), _239660), -(leq(n0, _239658))], (786 ^ _208097) ^ [_239887, _239889, _239891, _239893] : [-(a_select3(tptp_update3(_239893, _239891, _239889, _239887), _239891, _239889) = _239887)], (788 ^ _208097) ^ [_240079, _240081, _240083, _240085, _240087, _240089, _240091] : [-(a_select3(tptp_update3(_240083, _240091, _240089, _240079), _240087, _240085) = _240081), -(_240091 = _240087), _240089 = _240085, a_select3(_240083, _240087, _240085) = _240081], (802 ^ _208097) ^ [_240622, _240624, _240626, _240628, _240630, _240632] : [-(a_select3(tptp_update3(_240624, _240628, _240626, _240622), _240632, _240630) = _240622), 807 ^ _208097 : [(808 ^ _208097) ^ [] : [-(leq(n0, 805 ^ [_240622, _240624, _240626, _240628, _240630, _240632]))], (810 ^ _208097) ^ [] : [-(leq(n0, 806 ^ [_240622, _240624, _240626, _240628, _240630, _240632]))], (812 ^ _208097) ^ [] : [-(leq(805 ^ [_240622, _240624, _240626, _240628, _240630, _240632], _240628))], (814 ^ _208097) ^ [] : [-(leq(806 ^ [_240622, _240624, _240626, _240628, _240630, _240632], _240626))], (816 ^ _208097) ^ [] : [a_select3(_240624, 805 ^ [_240622, _240624, _240626, _240628, _240630, _240632], 806 ^ [_240622, _240624, _240626, _240628, _240630, _240632]) = _240622]], leq(n0, _240632), leq(_240632, _240628), leq(n0, _240630), leq(_240630, _240626)], (834 ^ _208097) ^ [_241964, _241966, _241968] : [-(a_select2(tptp_update2(_241968, _241966, _241964), _241966) = _241964)], (836 ^ _208097) ^ [_242124, _242126, _242128, _242130, _242132] : [-(a_select2(tptp_update2(_242128, _242132, _242124), _242130) = _242126), -(_242132 = _242130), a_select2(_242128, _242130) = _242126], (865 ^ _208097) ^ [] : [-(true)], (867 ^ _208097) ^ [] : [def = use], (846 ^ _208097) ^ [_242504, _242506, _242508, _242510] : [-(a_select2(tptp_update2(_242506, _242508, _242504), _242510) = _242504), 850 ^ _208097 : [(851 ^ _208097) ^ [] : [-(leq(n0, 849 ^ [_242504, _242506, _242508, _242510]))], (853 ^ _208097) ^ [] : [-(leq(849 ^ [_242504, _242506, _242508, _242510], _242508))], (855 ^ _208097) ^ [] : [a_select2(_242506, 849 ^ [_242504, _242506, _242508, _242510]) = _242504]], leq(n0, _242510), leq(_242510, _242508)]], input).
% 18.78/18.96  ncf('1',plain,[gt(n0, n0)],start(284 ^ 0,bind([[_218163], [n0]]))).
% 18.78/18.96  ncf('1.1',plain,[-(gt(n0, n0)), leq(n0, pred(n0))],extension(338 ^ 1,bind([[_220018, _220020], [n0, n0]]))).
% 18.78/18.96  ncf('1.1.1',plain,[-(leq(n0, pred(n0))), leq(n0, 1134 ^ []), leq(1134 ^ [], pred(n0))],extension(288 ^ 2,bind([[_218362, _218364, _218366], [pred(n0), 1134 ^ [], n0]]))).
% 18.78/18.96  ncf('1.1.1.1',plain,[-(leq(n0, 1134 ^ []))],extension(1136 ^ 3)).
% 18.78/18.96  ncf('1.1.1.2',plain,[-(leq(1134 ^ [], pred(n0))), leq(1134 ^ [], tptp_minus_1), leq(tptp_minus_1, pred(n0))],extension(288 ^ 3,bind([[_218362, _218364, _218366], [pred(n0), tptp_minus_1, 1134 ^ []]]))).
% 18.78/18.96  ncf('1.1.1.2.1',plain,[-(leq(1134 ^ [], tptp_minus_1))],extension(1138 ^ 4)).
% 18.78/18.96  ncf('1.1.1.2.2',plain,[-(leq(tptp_minus_1, pred(n0))), gt(n0, tptp_minus_1)],extension(344 ^ 4,bind([[_220184, _220186], [n0, tptp_minus_1]]))).
% 18.78/18.96  ncf('1.1.1.2.2.1',plain,[-(gt(n0, tptp_minus_1))],extension(881 ^ 5)).
% 18.78/18.96  %-----------------------------------------------------
% 18.78/18.96  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------