%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SWV180+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n008.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 0.30s 1.35s
% Output   : Proof 0.30s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10  % Problem  : SWV180+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.02/0.10  % Command  : nanocop.sh %s %d
% 0.11/0.31  % Computer : n008.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit : 300
% 0.11/0.31  % WCLimit  : 300
% 0.11/0.31  % DateTime : Fri May 19 02:24:39 EDT 2023
% 0.11/0.31  % CPUTime  : 
% 0.30/1.35  
% 0.30/1.35  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 0.30/1.35  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.30/1.35  %-----------------------------------------------------
% 0.30/1.35  ncf(matrix, plain, [(1189 ^ _212170) ^ [] : [a_select2(muold_init, pv86) = init], (1055 ^ _212170) ^ [] : [-(leq(n0, pv86))], (1057 ^ _212170) ^ [] : [-(leq(pv86, n4))], (1059 ^ _212170) ^ [_252592] : [leq(n0, _252592), leq(_252592, n135299), 1066 ^ _212170 : [(1067 ^ _212170) ^ [_252820] : [-(a_select3(q_init, _252592, _252820) = init), leq(n0, _252820), leq(_252820, n4)]]], (1077 ^ _212170) ^ [_253122] : [-(a_select2(rho_init, _253122) = init), leq(n0, _253122), leq(_253122, n4)], (1087 ^ _212170) ^ [_253403] : [-(a_select2(mu_init, _253403) = init), leq(n0, _253403), leq(_253403, n4)], (1097 ^ _212170) ^ [_253684] : [-(a_select2(sigma_init, _253684) = init), leq(n0, _253684), leq(_253684, n4)], (1107 ^ _212170) ^ [_253965] : [-(a_select3(center_init, _253965, n0) = init), leq(n0, _253965), leq(_253965, n4)], (1117 ^ _212170) ^ [] : [gt(loopcounter, n1), 1120 ^ _212170 : [(1121 ^ _212170) ^ [_254310] : [-(a_select2(muold_init, _254310) = init), leq(n0, _254310), leq(_254310, n4)]]], (1131 ^ _212170) ^ [] : [gt(loopcounter, n1), 1134 ^ _212170 : [(1135 ^ _212170) ^ [_254658] : [-(a_select2(rhoold_init, _254658) = init), leq(n0, _254658), leq(_254658, n4)]]], (1145 ^ _212170) ^ [] : [gt(loopcounter, n1), 1148 ^ _212170 : [(1149 ^ _212170) ^ [_255006] : [-(a_select2(sigmaold_init, _255006) = init), leq(n0, _255006), leq(_255006, n4)]]], (1159 ^ _212170) ^ [_255292] : [-(a_select2(muold_init, _255292) = init), leq(n0, _255292), leq(_255292, n4)], (1169 ^ _212170) ^ [_255573] : [-(a_select2(rhoold_init, _255573) = init), leq(n0, _255573), leq(_255573, n4)], (1179 ^ _212170) ^ [_255834] : [-(a_select2(sigmaold_init, _255834) = init), leq(n0, _255834), leq(_255834, n4)], (2 ^ _212170) ^ [_212314] : [-(_212314 = _212314)], (4 ^ _212170) ^ [_212421, _212423] : [_212423 = _212421, -(_212421 = _212423)], (10 ^ _212170) ^ [_212625, _212627, _212629] : [-(_212629 = _212625), _212629 = _212627, _212627 = _212625], (20 ^ _212170) ^ [_212966, _212968, _212970, _212972] : [-(lt(_212970, _212966)), lt(_212972, _212968), _212972 = _212970, _212968 = _212966], (34 ^ _212170) ^ [_213410, _213412, _213414, _213416] : [-(geq(_213414, _213410)), geq(_213416, _213412), _213416 = _213414, _213412 = _213410], (48 ^ _212170) ^ [_213854, _213856, _213858, _213860] : [-(gt(_213858, _213854)), gt(_213860, _213856), _213860 = _213858, _213856 = _213854], (62 ^ _212170) ^ [_214278, _214280, _214282, _214284] : [-(leq(_214282, _214278)), leq(_214284, _214280), _214284 = _214282, _214280 = _214278], (76 ^ _212170) ^ [_214734, _214736, _214738, _214740] : [-(uniform_int_rnd(_214740, _214736) = uniform_int_rnd(_214738, _214734)), _214740 = _214738, _214736 = _214734], (86 ^ _212170) ^ [_215093, _215095, _215097, _215099] : [-(tptp_const_array1(_215099, _215095) = tptp_const_array1(_215097, _215093)), _215099 = _215097, _215095 = _215093], (96 ^ _212170) ^ [_215480, _215482, _215484, _215486, _215488, _215490] : [-(tptp_const_array2(_215490, _215486, _215482) = tptp_const_array2(_215488, _215484, _215480)), _215490 = _215488, _215486 = _215484, _215482 = _215480], (110 ^ _212170) ^ [_215968, _215970, _215972, _215974] : [-(dim(_215974, _215970) = dim(_215972, _215968)), _215974 = _215972, _215970 = _215968], (120 ^ _212170) ^ [_216299, _216301] : [_216301 = _216299, -(inv(_216301) = inv(_216299))], (126 ^ _212170) ^ [_216545, _216547, _216549, _216551] : [-(tptp_msub(_216551, _216547) = tptp_msub(_216549, _216545)), _216551 = _216549, _216547 = _216545], (136 ^ _212170) ^ [_216904, _216906, _216908, _216910] : [-(tptp_madd(_216910, _216906) = tptp_madd(_216908, _216904)), _216910 = _216908, _216906 = _216904], (146 ^ _212170) ^ [_217263, _217265, _217267, _217269] : [-(tptp_mmul(_217269, _217265) = tptp_mmul(_217267, _217263)), _217269 = _217267, _217265 = _217263], (156 ^ _212170) ^ [_217594, _217596] : [_217596 = _217594, -(trans(_217596) = trans(_217594))], (162 ^ _212170) ^ [_217868, _217870, _217872, _217874, _217876, _217878] : [-(sum(_217878, _217874, _217870) = sum(_217876, _217872, _217868)), _217878 = _217876, _217874 = _217872, _217870 = _217868], (176 ^ _212170) ^ [_218356, _218358, _218360, _218362] : [-(plus(_218362, _218358) = plus(_218360, _218356)), _218362 = _218360, _218358 = _218356], (186 ^ _212170) ^ [_218687, _218689] : [_218689 = _218687, -(pred(_218689) = pred(_218687))], (192 ^ _212170) ^ [_218933, _218935, _218937, _218939] : [-(minus(_218939, _218935) = minus(_218937, _218933)), _218939 = _218937, _218935 = _218933], (202 ^ _212170) ^ [_219348, _219350, _219352, _219354, _219356, _219358, _219360, _219362] : [-(tptp_update3(_219362, _219358, _219354, _219350) = tptp_update3(_219360, _219356, _219352, _219348)), _219362 = _219360, _219358 = _219356, _219354 = _219352, _219350 = _219348], (220 ^ _212170) ^ [_220009, _220011, _220013, _220015, _220017, _220019] : [-(tptp_update2(_220019, _220015, _220011) = tptp_update2(_220017, _220013, _220009)), _220019 = _220017, _220015 = _220013, _220011 = _220009], (234 ^ _212170) ^ [_220469, _220471] : [_220471 = _220469, -(succ(_220471) = succ(_220469))], (254 ^ _212170) ^ [_221211, _221213, _221215, _221217] : [-(a_select2(_221217, _221213) = a_select2(_221215, _221211)), _221217 = _221215, _221213 = _221211], (240 ^ _212170) ^ [_220743, _220745, _220747, _220749, _220751, _220753] : [-(a_select3(_220753, _220749, _220745) = a_select3(_220751, _220747, _220743)), _220753 = _220751, _220749 = _220747, _220745 = _220743], (869 ^ _212170) ^ [] : [-(gt(n5, n4))], (871 ^ _212170) ^ [] : [-(gt(n135299, n4))], (873 ^ _212170) ^ [] : [-(gt(n135299, n5))], (875 ^ _212170) ^ [] : [-(gt(n4, tptp_minus_1))], (877 ^ _212170) ^ [] : [-(gt(n5, tptp_minus_1))], (879 ^ _212170) ^ [] : [-(gt(n135299, tptp_minus_1))], (881 ^ _212170) ^ [] : [-(gt(n0, tptp_minus_1))], (883 ^ _212170) ^ [] : [-(gt(n1, tptp_minus_1))], (885 ^ _212170) ^ [] : [-(gt(n2, tptp_minus_1))], (887 ^ _212170) ^ [] : [-(gt(n3, tptp_minus_1))], (889 ^ _212170) ^ [] : [-(gt(n4, n0))], (891 ^ _212170) ^ [] : [-(gt(n5, n0))], (893 ^ _212170) ^ [] : [-(gt(n135299, n0))], (895 ^ _212170) ^ [] : [-(gt(n1, n0))], (897 ^ _212170) ^ [] : [-(gt(n2, n0))], (899 ^ _212170) ^ [] : [-(gt(n3, n0))], (901 ^ _212170) ^ [] : [-(gt(n4, n1))], (903 ^ _212170) ^ [] : [-(gt(n5, n1))], (905 ^ _212170) ^ [] : [-(gt(n135299, n1))], (907 ^ _212170) ^ [] : [-(gt(n2, n1))], (909 ^ _212170) ^ [] : [-(gt(n3, n1))], (911 ^ _212170) ^ [] : [-(gt(n4, n2))], (913 ^ _212170) ^ [] : [-(gt(n5, n2))], (915 ^ _212170) ^ [] : [-(gt(n135299, n2))], (917 ^ _212170) ^ [] : [-(gt(n3, n2))], (919 ^ _212170) ^ [] : [-(gt(n4, n3))], (921 ^ _212170) ^ [] : [-(gt(n5, n3))], (923 ^ _212170) ^ [] : [-(gt(n135299, n3))], (925 ^ _212170) ^ [_249051] : [leq(n0, _249051), leq(_249051, n4), -(_249051 = n0), -(_249051 = n1), -(_249051 = n2), -(_249051 = n3), -(_249051 = n4)], (951 ^ _212170) ^ [_249672] : [leq(n0, _249672), leq(_249672, n5), -(_249672 = n0), -(_249672 = n1), -(_249672 = n2), -(_249672 = n3), -(_249672 = n4), -(_249672 = n5)], (981 ^ _212170) ^ [_250379] : [-(_250379 = n0), leq(n0, _250379), leq(_250379, n0)], (991 ^ _212170) ^ [_250654] : [leq(n0, _250654), leq(_250654, n1), -(_250654 = n0), -(_250654 = n1)], (1005 ^ _212170) ^ [_251017] : [leq(n0, _251017), leq(_251017, n2), -(_251017 = n0), -(_251017 = n1), -(_251017 = n2)], (1045 ^ _212170) ^ [] : [-(succ(succ(succ(succ(n0)))) = n4)], (1047 ^ _212170) ^ [] : [-(succ(succ(succ(succ(succ(n0))))) = n5)], (1049 ^ _212170) ^ [] : [-(succ(n0) = n1)], (1051 ^ _212170) ^ [] : [-(succ(succ(n0)) = n2)], (1053 ^ _212170) ^ [] : [-(succ(succ(succ(n0))) = n3)], (1023 ^ _212170) ^ [_251466] : [leq(n0, _251466), leq(_251466, n3), -(_251466 = n0), -(_251466 = n1), -(_251466 = n2), -(_251466 = n3)], (264 ^ _212170) ^ [_221642, _221644] : [-(gt(_221644, _221642)), -(gt(_221642, _221644)), -(_221644 = _221642)], (274 ^ _212170) ^ [_221957, _221959, _221961] : [-(gt(_221961, _221957)), gt(_221961, _221959), gt(_221959, _221957)], (284 ^ _212170) ^ [_222236] : [gt(_222236, _222236)], (286 ^ _212170) ^ [_222314] : [-(leq(_222314, _222314))], (288 ^ _212170) ^ [_222435, _222437, _222439] : [-(leq(_222439, _222435)), leq(_222439, _222437), leq(_222437, _222435)], (298 ^ _212170) ^ [_222773, _222775] : [lt(_222775, _222773), -(gt(_222773, _222775))], (304 ^ _212170) ^ [_222935, _222937] : [gt(_222935, _222937), -(lt(_222937, _222935))], (310 ^ _212170) ^ [_223176, _223178] : [geq(_223178, _223176), -(leq(_223176, _223178))], (316 ^ _212170) ^ [_223338, _223340] : [leq(_223338, _223340), -(geq(_223340, _223338))], (322 ^ _212170) ^ [_223550, _223552] : [gt(_223550, _223552), -(leq(_223552, _223550))], (328 ^ _212170) ^ [_223760, _223762] : [-(gt(_223760, _223762)), leq(_223762, _223760), -(_223762 = _223760)], (338 ^ _212170) ^ [_224091, _224093] : [leq(_224093, pred(_224091)), -(gt(_224091, _224093))], (344 ^ _212170) ^ [_224257, _224259] : [gt(_224257, _224259), -(leq(_224259, pred(_224257)))], (350 ^ _212170) ^ [_224444] : [-(gt(succ(_224444), _224444))], (352 ^ _212170) ^ [_224553, _224555] : [leq(_224555, _224553), -(leq(_224555, succ(_224553)))], (358 ^ _212170) ^ [_224796, _224798] : [leq(_224798, _224796), -(gt(succ(_224796), _224798))], (364 ^ _212170) ^ [_224962, _224964] : [gt(succ(_224962), _224964), -(leq(_224964, _224962))], (370 ^ _212170) ^ [_225178, _225180] : [leq(n0, _225180), -(leq(uniform_int_rnd(_225178, _225180), _225180))], (376 ^ _212170) ^ [_225394, _225396] : [leq(n0, _225396), -(leq(n0, uniform_int_rnd(_225394, _225396)))], (382 ^ _212170) ^ [_225638, _225640, _225642, _225644] : [-(a_select2(tptp_const_array1(dim(_225642, _225640), _225638), _225644) = _225638), leq(_225642, _225644), leq(_225644, _225640)], (392 ^ _212170) ^ [_226045, _226047, _226049, _226051, _226053, _226055, _226057] : [-(a_select3(tptp_const_array2(dim(_226055, _226053), dim(_226049, _226047), _226045), _226057, _226051) = _226045), leq(_226055, _226057), leq(_226057, _226053), leq(_226049, _226051), leq(_226051, _226047)], (410 ^ _212170) ^ [_226640, _226642] : [413 ^ _212170 : [(414 ^ _212170) ^ [] : [-(leq(n0, 411 ^ [_226640, _226642]))], (416 ^ _212170) ^ [] : [-(leq(411 ^ [_226640, _226642], _226640))], (418 ^ _212170) ^ [] : [-(leq(n0, 412 ^ [_226640, _226642]))], (420 ^ _212170) ^ [] : [-(leq(412 ^ [_226640, _226642], _226640))], (422 ^ _212170) ^ [] : [a_select3(_226642, 411 ^ [_226640, _226642], 412 ^ [_226640, _226642]) = a_select3(_226642, 412 ^ [_226640, _226642], 411 ^ [_226640, _226642])]], 423 ^ _212170 : [(424 ^ _212170) ^ [_227397, _227399] : [-(a_select3(trans(_226642), _227399, _227397) = a_select3(trans(_226642), _227397, _227399)), leq(n0, _227399), leq(_227399, _226640), leq(n0, _227397), leq(_227397, _226640)]]], (442 ^ _212170) ^ [_227944, _227946] : [445 ^ _212170 : [(446 ^ _212170) ^ [] : [-(leq(n0, 443 ^ [_227944, _227946]))], (448 ^ _212170) ^ [] : [-(leq(443 ^ [_227944, _227946], _227944))], (450 ^ _212170) ^ [] : [-(leq(n0, 444 ^ [_227944, _227946]))], (452 ^ _212170) ^ [] : [-(leq(444 ^ [_227944, _227946], _227944))], (454 ^ _212170) ^ [] : [a_select3(_227946, 443 ^ [_227944, _227946], 444 ^ [_227944, _227946]) = a_select3(_227946, 444 ^ [_227944, _227946], 443 ^ [_227944, _227946])]], 455 ^ _212170 : [(456 ^ _212170) ^ [_228701, _228703] : [-(a_select3(inv(_227946), _228703, _228701) = a_select3(inv(_227946), _228701, _228703)), leq(n0, _228703), leq(_228703, _227944), leq(n0, _228701), leq(_228701, _227944)]]], (474 ^ _212170) ^ [_229248, _229250] : [477 ^ _212170 : [(478 ^ _212170) ^ [] : [-(leq(n0, 475 ^ [_229248, _229250]))], (480 ^ _212170) ^ [] : [-(leq(475 ^ [_229248, _229250], _229248))], (482 ^ _212170) ^ [] : [-(leq(n0, 476 ^ [_229248, _229250]))], (484 ^ _212170) ^ [] : [-(leq(476 ^ [_229248, _229250], _229248))], (486 ^ _212170) ^ [] : [a_select3(_229250, 475 ^ [_229248, _229250], 476 ^ [_229248, _229250]) = a_select3(_229250, 476 ^ [_229248, _229250], 475 ^ [_229248, _229250])]], 487 ^ _212170 : [(488 ^ _212170) ^ [_230061, _230063, _230065, _230067] : [-(a_select3(tptp_update3(_229250, _230063, _230063, _230061), _230067, _230065) = a_select3(tptp_update3(_229250, _230063, _230063, _230061), _230065, _230067)), leq(n0, _230067), leq(_230067, _229248), leq(n0, _230065), leq(_230065, _229248), leq(n0, _230063), leq(_230063, _229248)]]], (514 ^ _212170) ^ [_230880, _230882, _230884] : [519 ^ _212170 : [(520 ^ _212170) ^ [] : [-(leq(n0, 517 ^ [_230880, _230882, _230884]))], (522 ^ _212170) ^ [] : [-(leq(517 ^ [_230880, _230882, _230884], _230880))], (524 ^ _212170) ^ [] : [-(leq(n0, 518 ^ [_230880, _230882, _230884]))], (526 ^ _212170) ^ [] : [-(leq(518 ^ [_230880, _230882, _230884], _230880))], (528 ^ _212170) ^ [] : [a_select3(_230884, 517 ^ [_230880, _230882, _230884], 518 ^ [_230880, _230882, _230884]) = a_select3(_230884, 518 ^ [_230880, _230882, _230884], 517 ^ [_230880, _230882, _230884])]], 531 ^ _212170 : [(532 ^ _212170) ^ [] : [-(leq(n0, 529 ^ [_230880, _230882, _230884]))], (534 ^ _212170) ^ [] : [-(leq(529 ^ [_230880, _230882, _230884], _230880))], (536 ^ _212170) ^ [] : [-(leq(n0, 530 ^ [_230880, _230882, _230884]))], (538 ^ _212170) ^ [] : [-(leq(530 ^ [_230880, _230882, _230884], _230880))], (540 ^ _212170) ^ [] : [a_select3(_230882, 529 ^ [_230880, _230882, _230884], 530 ^ [_230880, _230882, _230884]) = a_select3(_230882, 530 ^ [_230880, _230882, _230884], 529 ^ [_230880, _230882, _230884])]], 541 ^ _212170 : [(542 ^ _212170) ^ [_232389, _232391] : [-(a_select3(tptp_madd(_230884, _230882), _232391, _232389) = a_select3(tptp_madd(_230884, _230882), _232389, _232391)), leq(n0, _232391), leq(_232391, _230880), leq(n0, _232389), leq(_232389, _230880)]]], (560 ^ _212170) ^ [_232975, _232977, _232979] : [565 ^ _212170 : [(566 ^ _212170) ^ [] : [-(leq(n0, 563 ^ [_232975, _232977, _232979]))], (568 ^ _212170) ^ [] : [-(leq(563 ^ [_232975, _232977, _232979], _232975))], (570 ^ _212170) ^ [] : [-(leq(n0, 564 ^ [_232975, _232977, _232979]))], (572 ^ _212170) ^ [] : [-(leq(564 ^ [_232975, _232977, _232979], _232975))], (574 ^ _212170) ^ [] : [a_select3(_232979, 563 ^ [_232975, _232977, _232979], 564 ^ [_232975, _232977, _232979]) = a_select3(_232979, 564 ^ [_232975, _232977, _232979], 563 ^ [_232975, _232977, _232979])]], 577 ^ _212170 : [(578 ^ _212170) ^ [] : [-(leq(n0, 575 ^ [_232975, _232977, _232979]))], (580 ^ _212170) ^ [] : [-(leq(575 ^ [_232975, _232977, _232979], _232975))], (582 ^ _212170) ^ [] : [-(leq(n0, 576 ^ [_232975, _232977, _232979]))], (584 ^ _212170) ^ [] : [-(leq(576 ^ [_232975, _232977, _232979], _232975))], (586 ^ _212170) ^ [] : [a_select3(_232977, 575 ^ [_232975, _232977, _232979], 576 ^ [_232975, _232977, _232979]) = a_select3(_232977, 576 ^ [_232975, _232977, _232979], 575 ^ [_232975, _232977, _232979])]], 587 ^ _212170 : [(588 ^ _212170) ^ [_234484, _234486] : [-(a_select3(tptp_msub(_232979, _232977), _234486, _234484) = a_select3(tptp_msub(_232979, _232977), _234484, _234486)), leq(n0, _234486), leq(_234486, _232975), leq(n0, _234484), leq(_234484, _232975)]]], (606 ^ _212170) ^ [_235070, _235072, _235074] : [609 ^ _212170 : [(610 ^ _212170) ^ [] : [-(leq(n0, 607 ^ [_235070, _235072, _235074]))], (612 ^ _212170) ^ [] : [-(leq(607 ^ [_235070, _235072, _235074], _235070))], (614 ^ _212170) ^ [] : [-(leq(n0, 608 ^ [_235070, _235072, _235074]))], (616 ^ _212170) ^ [] : [-(leq(608 ^ [_235070, _235072, _235074], _235070))], (618 ^ _212170) ^ [] : [a_select3(_235072, 607 ^ [_235070, _235072, _235074], 608 ^ [_235070, _235072, _235074]) = a_select3(_235072, 608 ^ [_235070, _235072, _235074], 607 ^ [_235070, _235072, _235074])]], 619 ^ _212170 : [(620 ^ _212170) ^ [_235883, _235885] : [-(a_select3(tptp_mmul(_235074, tptp_mmul(_235072, trans(_235074))), _235885, _235883) = a_select3(tptp_mmul(_235074, tptp_mmul(_235072, trans(_235074))), _235883, _235885)), leq(n0, _235885), leq(_235885, _235070), leq(n0, _235883), leq(_235883, _235070)]]], (638 ^ _212170) ^ [_236502, _236504, _236506, _236508] : [641 ^ _212170 : [(642 ^ _212170) ^ [] : [-(leq(n0, 639 ^ [_236502, _236504, _236506, _236508]))], (644 ^ _212170) ^ [] : [-(leq(639 ^ [_236502, _236504, _236506, _236508], _236502))], (646 ^ _212170) ^ [] : [-(leq(n0, 640 ^ [_236502, _236504, _236506, _236508]))], (648 ^ _212170) ^ [] : [-(leq(640 ^ [_236502, _236504, _236506, _236508], _236502))], (650 ^ _212170) ^ [] : [a_select3(_236506, 639 ^ [_236502, _236504, _236506, _236508], 640 ^ [_236502, _236504, _236506, _236508]) = a_select3(_236506, 640 ^ [_236502, _236504, _236506, _236508], 639 ^ [_236502, _236504, _236506, _236508])]], 651 ^ _212170 : [(652 ^ _212170) ^ [_237359, _237361] : [-(a_select3(tptp_mmul(_236508, tptp_mmul(_236506, trans(_236508))), _237361, _237359) = a_select3(tptp_mmul(_236508, tptp_mmul(_236506, trans(_236508))), _237359, _237361)), leq(n0, _237361), leq(_237361, _236504), leq(n0, _237359), leq(_237359, _236504)]]], (670 ^ _212170) ^ [_238054, _238056, _238058, _238060, _238062, _238064, _238066, _238068] : [675 ^ _212170 : [(676 ^ _212170) ^ [] : [-(leq(n0, 673 ^ [_238054, _238056, _238058, _238060, _238062, _238064, _238066, _238068]))], (678 ^ _212170) ^ [] : [-(leq(673 ^ [_238054, _238056, _238058, _238060, _238062, _238064, _238066, _238068], _238054))], (680 ^ _212170) ^ [] : [-(leq(n0, 674 ^ [_238054, _238056, _238058, _238060, _238062, _238064, _238066, _238068]))], (682 ^ _212170) ^ [] : [-(leq(674 ^ [_238054, _238056, _238058, _238060, _238062, _238064, _238066, _238068], _238054))], (684 ^ _212170) ^ [] : [a_select3(_238062, 673 ^ [_238054, _238056, _238058, _238060, _238062, _238064, _238066, _238068], 674 ^ [_238054, _238056, _238058, _238060, _238062, _238064, _238066, _238068]) = a_select3(_238062, 674 ^ [_238054, _238056, _238058, _238060, _238062, _238064, _238066, _238068], 673 ^ [_238054, _238056, _238058, _238060, _238062, _238064, _238066, _238068])]], 689 ^ _212170 : [(690 ^ _212170) ^ [] : [-(leq(n0, 687 ^ [_238054, _238056, _238058, _238060, _238062, _238064, _238066, _238068]))], (692 ^ _212170) ^ [] : [-(leq(687 ^ [_238054, _238056, _238058, _238060, _238062, _238064, _238066, _238068], _238056))], (694 ^ _212170) ^ [] : [-(leq(n0, 688 ^ [_238054, _238056, _238058, _238060, _238062, _238064, _238066, _238068]))], (696 ^ _212170) ^ [] : [-(leq(688 ^ [_238054, _238056, _238058, _238060, _238062, _238064, _238066, _238068], _238056))], (698 ^ _212170) ^ [] : [a_select3(_238068, 687 ^ [_238054, _238056, _238058, _238060, _238062, _238064, _238066, _238068], 688 ^ [_238054, _238056, _238058, _238060, _238062, _238064, _238066, _238068]) = a_select3(_238068, 688 ^ [_238054, _238056, _238058, _238060, _238062, _238064, _238066, _238068], 687 ^ [_238054, _238056, _238058, _238060, _238062, _238064, _238066, _238068])]], 701 ^ _212170 : [(702 ^ _212170) ^ [] : [-(leq(n0, 699 ^ [_238054, _238056, _238058, _238060, _238062, _238064, _238066, _238068]))], (704 ^ _212170) ^ [] : [-(leq(699 ^ [_238054, _238056, _238058, _238060, _238062, _238064, _238066, _238068], _238056))], (706 ^ _212170) ^ [] : [-(leq(n0, 700 ^ [_238054, _238056, _238058, _238060, _238062, _238064, _238066, _238068]))], (708 ^ _212170) ^ [] : [-(leq(700 ^ [_238054, _238056, _238058, _238060, _238062, _238064, _238066, _238068], _238056))], (710 ^ _212170) ^ [] : [a_select3(_238058, 699 ^ [_238054, _238056, _238058, _238060, _238062, _238064, _238066, _238068], 700 ^ [_238054, _238056, _238058, _238060, _238062, _238064, _238066, _238068]) = a_select3(_238058, 700 ^ [_238054, _238056, _238058, _238060, _238062, _238064, _238066, _238068], 699 ^ [_238054, _238056, _238058, _238060, _238062, _238064, _238066, _238068])]], 711 ^ _212170 : [(712 ^ _212170) ^ [_240982, _240984] : [-(a_select3(tptp_madd(_238068, tptp_mmul(_238066, tptp_mmul(tptp_madd(tptp_mmul(_238064, tptp_mmul(_238062, trans(_238064))), tptp_mmul(_238060, tptp_mmul(_238058, trans(_238060)))), trans(_238066)))), _240984, _240982) = a_select3(tptp_madd(_238068, tptp_mmul(_238066, tptp_mmul(tptp_madd(tptp_mmul(_238064, tptp_mmul(_238062, trans(_238064))), tptp_mmul(_238060, tptp_mmul(_238058, trans(_238060)))), trans(_238066)))), _240982, _240984)), leq(n0, _240984), leq(_240984, _238056), leq(n0, _240982), leq(_240982, _238056)]]], (730 ^ _212170) ^ [_241735] : [-(sum(n0, tptp_minus_1, _241735) = n0)], (732 ^ _212170) ^ [_241817] : [-(tptp_float_0_0 = sum(n0, tptp_minus_1, _241817))], (734 ^ _212170) ^ [] : [-(succ(tptp_minus_1) = n0)], (736 ^ _212170) ^ [_241952] : [-(plus(_241952, n1) = succ(_241952))], (738 ^ _212170) ^ [_242035] : [-(plus(n1, _242035) = succ(_242035))], (740 ^ _212170) ^ [_242118] : [-(plus(_242118, n2) = succ(succ(_242118)))], (742 ^ _212170) ^ [_242203] : [-(plus(n2, _242203) = succ(succ(_242203)))], (744 ^ _212170) ^ [_242288] : [-(plus(_242288, n3) = succ(succ(succ(_242288))))], (746 ^ _212170) ^ [_242375] : [-(plus(n3, _242375) = succ(succ(succ(_242375))))], (748 ^ _212170) ^ [_242462] : [-(plus(_242462, n4) = succ(succ(succ(succ(_242462)))))], (750 ^ _212170) ^ [_242551] : [-(plus(n4, _242551) = succ(succ(succ(succ(_242551)))))], (752 ^ _212170) ^ [_242640] : [-(plus(_242640, n5) = succ(succ(succ(succ(succ(_242640))))))], (754 ^ _212170) ^ [_242731] : [-(plus(n5, _242731) = succ(succ(succ(succ(succ(_242731))))))], (756 ^ _212170) ^ [_242822] : [-(minus(_242822, n1) = pred(_242822))], (758 ^ _212170) ^ [_242905] : [-(pred(succ(_242905)) = _242905)], (760 ^ _212170) ^ [_242987] : [-(succ(pred(_242987)) = _242987)], (762 ^ _212170) ^ [_243127, _243129] : [leq(succ(_243129), succ(_243127)), -(leq(_243129, _243127))], (768 ^ _212170) ^ [_243297, _243299] : [leq(_243299, _243297), -(leq(succ(_243299), succ(_243297)))], (774 ^ _212170) ^ [_243517, _243519] : [leq(succ(_243519), _243517), -(gt(_243517, _243519))], (780 ^ _212170) ^ [_243731, _243733] : [leq(minus(_243733, _243731), _243733), -(leq(n0, _243731))], (786 ^ _212170) ^ [_243960, _243962, _243964, _243966] : [-(a_select3(tptp_update3(_243966, _243964, _243962, _243960), _243964, _243962) = _243960)], (788 ^ _212170) ^ [_244152, _244154, _244156, _244158, _244160, _244162, _244164] : [-(a_select3(tptp_update3(_244156, _244164, _244162, _244152), _244160, _244158) = _244154), -(_244164 = _244160), _244162 = _244158, a_select3(_244156, _244160, _244158) = _244154], (802 ^ _212170) ^ [_244695, _244697, _244699, _244701, _244703, _244705] : [-(a_select3(tptp_update3(_244697, _244701, _244699, _244695), _244705, _244703) = _244695), 807 ^ _212170 : [(808 ^ _212170) ^ [] : [-(leq(n0, 805 ^ [_244695, _244697, _244699, _244701, _244703, _244705]))], (810 ^ _212170) ^ [] : [-(leq(n0, 806 ^ [_244695, _244697, _244699, _244701, _244703, _244705]))], (812 ^ _212170) ^ [] : [-(leq(805 ^ [_244695, _244697, _244699, _244701, _244703, _244705], _244701))], (814 ^ _212170) ^ [] : [-(leq(806 ^ [_244695, _244697, _244699, _244701, _244703, _244705], _244699))], (816 ^ _212170) ^ [] : [a_select3(_244697, 805 ^ [_244695, _244697, _244699, _244701, _244703, _244705], 806 ^ [_244695, _244697, _244699, _244701, _244703, _244705]) = _244695]], leq(n0, _244705), leq(_244705, _244701), leq(n0, _244703), leq(_244703, _244699)], (834 ^ _212170) ^ [_246037, _246039, _246041] : [-(a_select2(tptp_update2(_246041, _246039, _246037), _246039) = _246037)], (836 ^ _212170) ^ [_246197, _246199, _246201, _246203, _246205] : [-(a_select2(tptp_update2(_246201, _246205, _246197), _246203) = _246199), -(_246205 = _246203), a_select2(_246201, _246203) = _246199], (865 ^ _212170) ^ [] : [-(true)], (867 ^ _212170) ^ [] : [def = use], (846 ^ _212170) ^ [_246577, _246579, _246581, _246583] : [-(a_select2(tptp_update2(_246579, _246581, _246577), _246583) = _246577), 850 ^ _212170 : [(851 ^ _212170) ^ [] : [-(leq(n0, 849 ^ [_246577, _246579, _246581, _246583]))], (853 ^ _212170) ^ [] : [-(leq(849 ^ [_246577, _246579, _246581, _246583], _246581))], (855 ^ _212170) ^ [] : [a_select2(_246579, 849 ^ [_246577, _246579, _246581, _246583]) = _246577]], leq(n0, _246583), leq(_246583, _246581)]], input).
% 0.30/1.35  ncf('1',plain,[a_select2(muold_init, pv86) = init],start(1189 ^ 0)).
% 0.30/1.35  ncf('1.1',plain,[-(a_select2(muold_init, pv86) = init), leq(n0, pv86), leq(pv86, n4)],extension(1159 ^ 1,bind([[_255292], [pv86]]))).
% 0.30/1.35  ncf('1.1.1',plain,[-(leq(n0, pv86))],extension(1055 ^ 2)).
% 0.30/1.35  ncf('1.1.2',plain,[-(leq(pv86, n4))],extension(1057 ^ 2)).
% 0.30/1.35  %-----------------------------------------------------
% 0.30/1.35  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------