%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SWV172+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 1.38s
% Output   : Proof 0.35s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SWV172+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.07/0.13  % Command  : nanocop.sh %s %d
% 0.13/0.34  % Computer : n012.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Fri May 19 02:37:31 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.35/1.38  
% 0.35/1.38  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 0.35/1.38  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.35/1.38  %-----------------------------------------------------
% 0.35/1.38  ncf(matrix, plain, [(1163 ^ _209071) ^ [] : [a_select2(rho_init, pv54) = init], (1055 ^ _209071) ^ [] : [-(leq(n0, pv10))], (1057 ^ _209071) ^ [] : [-(leq(n0, pv54))], (1059 ^ _209071) ^ [] : [-(leq(pv10, n135299))], (1061 ^ _209071) ^ [] : [-(leq(pv54, n4))], (1063 ^ _209071) ^ [_249599] : [leq(n0, _249599), leq(_249599, n135299), 1070 ^ _209071 : [(1071 ^ _209071) ^ [_249827] : [-(a_select3(q_init, _249599, _249827) = init), leq(n0, _249827), leq(_249827, n4)]]], (1081 ^ _209071) ^ [_250129] : [-(a_select2(rho_init, _250129) = init), leq(n0, _250129), leq(_250129, n4)], (1091 ^ _209071) ^ [_250410] : [-(a_select2(mu_init, _250410) = init), leq(n0, _250410), leq(_250410, n4)], (1101 ^ _209071) ^ [_250691] : [-(a_select2(sigma_init, _250691) = init), leq(n0, _250691), leq(_250691, n4)], (1111 ^ _209071) ^ [_250972] : [-(a_select3(center_init, _250972, n0) = init), leq(n0, _250972), leq(_250972, n4)], (1121 ^ _209071) ^ [] : [gt(loopcounter, n1), 1124 ^ _209071 : [(1125 ^ _209071) ^ [_251317] : [-(a_select2(muold_init, _251317) = init), leq(n0, _251317), leq(_251317, n4)]]], (1135 ^ _209071) ^ [] : [gt(loopcounter, n1), 1138 ^ _209071 : [(1139 ^ _209071) ^ [_251665] : [-(a_select2(rhoold_init, _251665) = init), leq(n0, _251665), leq(_251665, n4)]]], (1149 ^ _209071) ^ [] : [gt(loopcounter, n1), 1152 ^ _209071 : [(1153 ^ _209071) ^ [_251993] : [-(a_select2(sigmaold_init, _251993) = init), leq(n0, _251993), leq(_251993, n4)]]], (2 ^ _209071) ^ [_209215] : [-(_209215 = _209215)], (4 ^ _209071) ^ [_209322, _209324] : [_209324 = _209322, -(_209322 = _209324)], (10 ^ _209071) ^ [_209526, _209528, _209530] : [-(_209530 = _209526), _209530 = _209528, _209528 = _209526], (20 ^ _209071) ^ [_209867, _209869, _209871, _209873] : [-(lt(_209871, _209867)), lt(_209873, _209869), _209873 = _209871, _209869 = _209867], (34 ^ _209071) ^ [_210311, _210313, _210315, _210317] : [-(geq(_210315, _210311)), geq(_210317, _210313), _210317 = _210315, _210313 = _210311], (48 ^ _209071) ^ [_210755, _210757, _210759, _210761] : [-(gt(_210759, _210755)), gt(_210761, _210757), _210761 = _210759, _210757 = _210755], (62 ^ _209071) ^ [_211179, _211181, _211183, _211185] : [-(leq(_211183, _211179)), leq(_211185, _211181), _211185 = _211183, _211181 = _211179], (76 ^ _209071) ^ [_211635, _211637, _211639, _211641] : [-(uniform_int_rnd(_211641, _211637) = uniform_int_rnd(_211639, _211635)), _211641 = _211639, _211637 = _211635], (86 ^ _209071) ^ [_211994, _211996, _211998, _212000] : [-(tptp_const_array1(_212000, _211996) = tptp_const_array1(_211998, _211994)), _212000 = _211998, _211996 = _211994], (96 ^ _209071) ^ [_212381, _212383, _212385, _212387, _212389, _212391] : [-(tptp_const_array2(_212391, _212387, _212383) = tptp_const_array2(_212389, _212385, _212381)), _212391 = _212389, _212387 = _212385, _212383 = _212381], (110 ^ _209071) ^ [_212869, _212871, _212873, _212875] : [-(dim(_212875, _212871) = dim(_212873, _212869)), _212875 = _212873, _212871 = _212869], (120 ^ _209071) ^ [_213200, _213202] : [_213202 = _213200, -(inv(_213202) = inv(_213200))], (126 ^ _209071) ^ [_213446, _213448, _213450, _213452] : [-(tptp_msub(_213452, _213448) = tptp_msub(_213450, _213446)), _213452 = _213450, _213448 = _213446], (136 ^ _209071) ^ [_213805, _213807, _213809, _213811] : [-(tptp_madd(_213811, _213807) = tptp_madd(_213809, _213805)), _213811 = _213809, _213807 = _213805], (146 ^ _209071) ^ [_214164, _214166, _214168, _214170] : [-(tptp_mmul(_214170, _214166) = tptp_mmul(_214168, _214164)), _214170 = _214168, _214166 = _214164], (156 ^ _209071) ^ [_214495, _214497] : [_214497 = _214495, -(trans(_214497) = trans(_214495))], (162 ^ _209071) ^ [_214769, _214771, _214773, _214775, _214777, _214779] : [-(sum(_214779, _214775, _214771) = sum(_214777, _214773, _214769)), _214779 = _214777, _214775 = _214773, _214771 = _214769], (176 ^ _209071) ^ [_215257, _215259, _215261, _215263] : [-(plus(_215263, _215259) = plus(_215261, _215257)), _215263 = _215261, _215259 = _215257], (186 ^ _209071) ^ [_215588, _215590] : [_215590 = _215588, -(pred(_215590) = pred(_215588))], (192 ^ _209071) ^ [_215834, _215836, _215838, _215840] : [-(minus(_215840, _215836) = minus(_215838, _215834)), _215840 = _215838, _215836 = _215834], (202 ^ _209071) ^ [_216249, _216251, _216253, _216255, _216257, _216259, _216261, _216263] : [-(tptp_update3(_216263, _216259, _216255, _216251) = tptp_update3(_216261, _216257, _216253, _216249)), _216263 = _216261, _216259 = _216257, _216255 = _216253, _216251 = _216249], (220 ^ _209071) ^ [_216910, _216912, _216914, _216916, _216918, _216920] : [-(tptp_update2(_216920, _216916, _216912) = tptp_update2(_216918, _216914, _216910)), _216920 = _216918, _216916 = _216914, _216912 = _216910], (234 ^ _209071) ^ [_217370, _217372] : [_217372 = _217370, -(succ(_217372) = succ(_217370))], (254 ^ _209071) ^ [_218112, _218114, _218116, _218118] : [-(a_select2(_218118, _218114) = a_select2(_218116, _218112)), _218118 = _218116, _218114 = _218112], (240 ^ _209071) ^ [_217644, _217646, _217648, _217650, _217652, _217654] : [-(a_select3(_217654, _217650, _217646) = a_select3(_217652, _217648, _217644)), _217654 = _217652, _217650 = _217648, _217646 = _217644], (869 ^ _209071) ^ [] : [-(gt(n5, n4))], (871 ^ _209071) ^ [] : [-(gt(n135299, n4))], (873 ^ _209071) ^ [] : [-(gt(n135299, n5))], (875 ^ _209071) ^ [] : [-(gt(n4, tptp_minus_1))], (877 ^ _209071) ^ [] : [-(gt(n5, tptp_minus_1))], (879 ^ _209071) ^ [] : [-(gt(n135299, tptp_minus_1))], (881 ^ _209071) ^ [] : [-(gt(n0, tptp_minus_1))], (883 ^ _209071) ^ [] : [-(gt(n1, tptp_minus_1))], (885 ^ _209071) ^ [] : [-(gt(n2, tptp_minus_1))], (887 ^ _209071) ^ [] : [-(gt(n3, tptp_minus_1))], (889 ^ _209071) ^ [] : [-(gt(n4, n0))], (891 ^ _209071) ^ [] : [-(gt(n5, n0))], (893 ^ _209071) ^ [] : [-(gt(n135299, n0))], (895 ^ _209071) ^ [] : [-(gt(n1, n0))], (897 ^ _209071) ^ [] : [-(gt(n2, n0))], (899 ^ _209071) ^ [] : [-(gt(n3, n0))], (901 ^ _209071) ^ [] : [-(gt(n4, n1))], (903 ^ _209071) ^ [] : [-(gt(n5, n1))], (905 ^ _209071) ^ [] : [-(gt(n135299, n1))], (907 ^ _209071) ^ [] : [-(gt(n2, n1))], (909 ^ _209071) ^ [] : [-(gt(n3, n1))], (911 ^ _209071) ^ [] : [-(gt(n4, n2))], (913 ^ _209071) ^ [] : [-(gt(n5, n2))], (915 ^ _209071) ^ [] : [-(gt(n135299, n2))], (917 ^ _209071) ^ [] : [-(gt(n3, n2))], (919 ^ _209071) ^ [] : [-(gt(n4, n3))], (921 ^ _209071) ^ [] : [-(gt(n5, n3))], (923 ^ _209071) ^ [] : [-(gt(n135299, n3))], (925 ^ _209071) ^ [_245952] : [leq(n0, _245952), leq(_245952, n4), -(_245952 = n0), -(_245952 = n1), -(_245952 = n2), -(_245952 = n3), -(_245952 = n4)], (951 ^ _209071) ^ [_246573] : [leq(n0, _246573), leq(_246573, n5), -(_246573 = n0), -(_246573 = n1), -(_246573 = n2), -(_246573 = n3), -(_246573 = n4), -(_246573 = n5)], (981 ^ _209071) ^ [_247280] : [-(_247280 = n0), leq(n0, _247280), leq(_247280, n0)], (991 ^ _209071) ^ [_247555] : [leq(n0, _247555), leq(_247555, n1), -(_247555 = n0), -(_247555 = n1)], (1005 ^ _209071) ^ [_247918] : [leq(n0, _247918), leq(_247918, n2), -(_247918 = n0), -(_247918 = n1), -(_247918 = n2)], (1045 ^ _209071) ^ [] : [-(succ(succ(succ(succ(n0)))) = n4)], (1047 ^ _209071) ^ [] : [-(succ(succ(succ(succ(succ(n0))))) = n5)], (1049 ^ _209071) ^ [] : [-(succ(n0) = n1)], (1051 ^ _209071) ^ [] : [-(succ(succ(n0)) = n2)], (1053 ^ _209071) ^ [] : [-(succ(succ(succ(n0))) = n3)], (1023 ^ _209071) ^ [_248367] : [leq(n0, _248367), leq(_248367, n3), -(_248367 = n0), -(_248367 = n1), -(_248367 = n2), -(_248367 = n3)], (264 ^ _209071) ^ [_218543, _218545] : [-(gt(_218545, _218543)), -(gt(_218543, _218545)), -(_218545 = _218543)], (274 ^ _209071) ^ [_218858, _218860, _218862] : [-(gt(_218862, _218858)), gt(_218862, _218860), gt(_218860, _218858)], (284 ^ _209071) ^ [_219137] : [gt(_219137, _219137)], (286 ^ _209071) ^ [_219215] : [-(leq(_219215, _219215))], (288 ^ _209071) ^ [_219336, _219338, _219340] : [-(leq(_219340, _219336)), leq(_219340, _219338), leq(_219338, _219336)], (298 ^ _209071) ^ [_219674, _219676] : [lt(_219676, _219674), -(gt(_219674, _219676))], (304 ^ _209071) ^ [_219836, _219838] : [gt(_219836, _219838), -(lt(_219838, _219836))], (310 ^ _209071) ^ [_220077, _220079] : [geq(_220079, _220077), -(leq(_220077, _220079))], (316 ^ _209071) ^ [_220239, _220241] : [leq(_220239, _220241), -(geq(_220241, _220239))], (322 ^ _209071) ^ [_220451, _220453] : [gt(_220451, _220453), -(leq(_220453, _220451))], (328 ^ _209071) ^ [_220661, _220663] : [-(gt(_220661, _220663)), leq(_220663, _220661), -(_220663 = _220661)], (338 ^ _209071) ^ [_220992, _220994] : [leq(_220994, pred(_220992)), -(gt(_220992, _220994))], (344 ^ _209071) ^ [_221158, _221160] : [gt(_221158, _221160), -(leq(_221160, pred(_221158)))], (350 ^ _209071) ^ [_221345] : [-(gt(succ(_221345), _221345))], (352 ^ _209071) ^ [_221454, _221456] : [leq(_221456, _221454), -(leq(_221456, succ(_221454)))], (358 ^ _209071) ^ [_221697, _221699] : [leq(_221699, _221697), -(gt(succ(_221697), _221699))], (364 ^ _209071) ^ [_221863, _221865] : [gt(succ(_221863), _221865), -(leq(_221865, _221863))], (370 ^ _209071) ^ [_222079, _222081] : [leq(n0, _222081), -(leq(uniform_int_rnd(_222079, _222081), _222081))], (376 ^ _209071) ^ [_222295, _222297] : [leq(n0, _222297), -(leq(n0, uniform_int_rnd(_222295, _222297)))], (382 ^ _209071) ^ [_222539, _222541, _222543, _222545] : [-(a_select2(tptp_const_array1(dim(_222543, _222541), _222539), _222545) = _222539), leq(_222543, _222545), leq(_222545, _222541)], (392 ^ _209071) ^ [_222946, _222948, _222950, _222952, _222954, _222956, _222958] : [-(a_select3(tptp_const_array2(dim(_222956, _222954), dim(_222950, _222948), _222946), _222958, _222952) = _222946), leq(_222956, _222958), leq(_222958, _222954), leq(_222950, _222952), leq(_222952, _222948)], (410 ^ _209071) ^ [_223541, _223543] : [413 ^ _209071 : [(414 ^ _209071) ^ [] : [-(leq(n0, 411 ^ [_223541, _223543]))], (416 ^ _209071) ^ [] : [-(leq(411 ^ [_223541, _223543], _223541))], (418 ^ _209071) ^ [] : [-(leq(n0, 412 ^ [_223541, _223543]))], (420 ^ _209071) ^ [] : [-(leq(412 ^ [_223541, _223543], _223541))], (422 ^ _209071) ^ [] : [a_select3(_223543, 411 ^ [_223541, _223543], 412 ^ [_223541, _223543]) = a_select3(_223543, 412 ^ [_223541, _223543], 411 ^ [_223541, _223543])]], 423 ^ _209071 : [(424 ^ _209071) ^ [_224298, _224300] : [-(a_select3(trans(_223543), _224300, _224298) = a_select3(trans(_223543), _224298, _224300)), leq(n0, _224300), leq(_224300, _223541), leq(n0, _224298), leq(_224298, _223541)]]], (442 ^ _209071) ^ [_224845, _224847] : [445 ^ _209071 : [(446 ^ _209071) ^ [] : [-(leq(n0, 443 ^ [_224845, _224847]))], (448 ^ _209071) ^ [] : [-(leq(443 ^ [_224845, _224847], _224845))], (450 ^ _209071) ^ [] : [-(leq(n0, 444 ^ [_224845, _224847]))], (452 ^ _209071) ^ [] : [-(leq(444 ^ [_224845, _224847], _224845))], (454 ^ _209071) ^ [] : [a_select3(_224847, 443 ^ [_224845, _224847], 444 ^ [_224845, _224847]) = a_select3(_224847, 444 ^ [_224845, _224847], 443 ^ [_224845, _224847])]], 455 ^ _209071 : [(456 ^ _209071) ^ [_225602, _225604] : [-(a_select3(inv(_224847), _225604, _225602) = a_select3(inv(_224847), _225602, _225604)), leq(n0, _225604), leq(_225604, _224845), leq(n0, _225602), leq(_225602, _224845)]]], (474 ^ _209071) ^ [_226149, _226151] : [477 ^ _209071 : [(478 ^ _209071) ^ [] : [-(leq(n0, 475 ^ [_226149, _226151]))], (480 ^ _209071) ^ [] : [-(leq(475 ^ [_226149, _226151], _226149))], (482 ^ _209071) ^ [] : [-(leq(n0, 476 ^ [_226149, _226151]))], (484 ^ _209071) ^ [] : [-(leq(476 ^ [_226149, _226151], _226149))], (486 ^ _209071) ^ [] : [a_select3(_226151, 475 ^ [_226149, _226151], 476 ^ [_226149, _226151]) = a_select3(_226151, 476 ^ [_226149, _226151], 475 ^ [_226149, _226151])]], 487 ^ _209071 : [(488 ^ _209071) ^ [_226962, _226964, _226966, _226968] : [-(a_select3(tptp_update3(_226151, _226964, _226964, _226962), _226968, _226966) = a_select3(tptp_update3(_226151, _226964, _226964, _226962), _226966, _226968)), leq(n0, _226968), leq(_226968, _226149), leq(n0, _226966), leq(_226966, _226149), leq(n0, _226964), leq(_226964, _226149)]]], (514 ^ _209071) ^ [_227781, _227783, _227785] : [519 ^ _209071 : [(520 ^ _209071) ^ [] : [-(leq(n0, 517 ^ [_227781, _227783, _227785]))], (522 ^ _209071) ^ [] : [-(leq(517 ^ [_227781, _227783, _227785], _227781))], (524 ^ _209071) ^ [] : [-(leq(n0, 518 ^ [_227781, _227783, _227785]))], (526 ^ _209071) ^ [] : [-(leq(518 ^ [_227781, _227783, _227785], _227781))], (528 ^ _209071) ^ [] : [a_select3(_227785, 517 ^ [_227781, _227783, _227785], 518 ^ [_227781, _227783, _227785]) = a_select3(_227785, 518 ^ [_227781, _227783, _227785], 517 ^ [_227781, _227783, _227785])]], 531 ^ _209071 : [(532 ^ _209071) ^ [] : [-(leq(n0, 529 ^ [_227781, _227783, _227785]))], (534 ^ _209071) ^ [] : [-(leq(529 ^ [_227781, _227783, _227785], _227781))], (536 ^ _209071) ^ [] : [-(leq(n0, 530 ^ [_227781, _227783, _227785]))], (538 ^ _209071) ^ [] : [-(leq(530 ^ [_227781, _227783, _227785], _227781))], (540 ^ _209071) ^ [] : [a_select3(_227783, 529 ^ [_227781, _227783, _227785], 530 ^ [_227781, _227783, _227785]) = a_select3(_227783, 530 ^ [_227781, _227783, _227785], 529 ^ [_227781, _227783, _227785])]], 541 ^ _209071 : [(542 ^ _209071) ^ [_229290, _229292] : [-(a_select3(tptp_madd(_227785, _227783), _229292, _229290) = a_select3(tptp_madd(_227785, _227783), _229290, _229292)), leq(n0, _229292), leq(_229292, _227781), leq(n0, _229290), leq(_229290, _227781)]]], (560 ^ _209071) ^ [_229876, _229878, _229880] : [565 ^ _209071 : [(566 ^ _209071) ^ [] : [-(leq(n0, 563 ^ [_229876, _229878, _229880]))], (568 ^ _209071) ^ [] : [-(leq(563 ^ [_229876, _229878, _229880], _229876))], (570 ^ _209071) ^ [] : [-(leq(n0, 564 ^ [_229876, _229878, _229880]))], (572 ^ _209071) ^ [] : [-(leq(564 ^ [_229876, _229878, _229880], _229876))], (574 ^ _209071) ^ [] : [a_select3(_229880, 563 ^ [_229876, _229878, _229880], 564 ^ [_229876, _229878, _229880]) = a_select3(_229880, 564 ^ [_229876, _229878, _229880], 563 ^ [_229876, _229878, _229880])]], 577 ^ _209071 : [(578 ^ _209071) ^ [] : [-(leq(n0, 575 ^ [_229876, _229878, _229880]))], (580 ^ _209071) ^ [] : [-(leq(575 ^ [_229876, _229878, _229880], _229876))], (582 ^ _209071) ^ [] : [-(leq(n0, 576 ^ [_229876, _229878, _229880]))], (584 ^ _209071) ^ [] : [-(leq(576 ^ [_229876, _229878, _229880], _229876))], (586 ^ _209071) ^ [] : [a_select3(_229878, 575 ^ [_229876, _229878, _229880], 576 ^ [_229876, _229878, _229880]) = a_select3(_229878, 576 ^ [_229876, _229878, _229880], 575 ^ [_229876, _229878, _229880])]], 587 ^ _209071 : [(588 ^ _209071) ^ [_231385, _231387] : [-(a_select3(tptp_msub(_229880, _229878), _231387, _231385) = a_select3(tptp_msub(_229880, _229878), _231385, _231387)), leq(n0, _231387), leq(_231387, _229876), leq(n0, _231385), leq(_231385, _229876)]]], (606 ^ _209071) ^ [_231971, _231973, _231975] : [609 ^ _209071 : [(610 ^ _209071) ^ [] : [-(leq(n0, 607 ^ [_231971, _231973, _231975]))], (612 ^ _209071) ^ [] : [-(leq(607 ^ [_231971, _231973, _231975], _231971))], (614 ^ _209071) ^ [] : [-(leq(n0, 608 ^ [_231971, _231973, _231975]))], (616 ^ _209071) ^ [] : [-(leq(608 ^ [_231971, _231973, _231975], _231971))], (618 ^ _209071) ^ [] : [a_select3(_231973, 607 ^ [_231971, _231973, _231975], 608 ^ [_231971, _231973, _231975]) = a_select3(_231973, 608 ^ [_231971, _231973, _231975], 607 ^ [_231971, _231973, _231975])]], 619 ^ _209071 : [(620 ^ _209071) ^ [_232784, _232786] : [-(a_select3(tptp_mmul(_231975, tptp_mmul(_231973, trans(_231975))), _232786, _232784) = a_select3(tptp_mmul(_231975, tptp_mmul(_231973, trans(_231975))), _232784, _232786)), leq(n0, _232786), leq(_232786, _231971), leq(n0, _232784), leq(_232784, _231971)]]], (638 ^ _209071) ^ [_233403, _233405, _233407, _233409] : [641 ^ _209071 : [(642 ^ _209071) ^ [] : [-(leq(n0, 639 ^ [_233403, _233405, _233407, _233409]))], (644 ^ _209071) ^ [] : [-(leq(639 ^ [_233403, _233405, _233407, _233409], _233403))], (646 ^ _209071) ^ [] : [-(leq(n0, 640 ^ [_233403, _233405, _233407, _233409]))], (648 ^ _209071) ^ [] : [-(leq(640 ^ [_233403, _233405, _233407, _233409], _233403))], (650 ^ _209071) ^ [] : [a_select3(_233407, 639 ^ [_233403, _233405, _233407, _233409], 640 ^ [_233403, _233405, _233407, _233409]) = a_select3(_233407, 640 ^ [_233403, _233405, _233407, _233409], 639 ^ [_233403, _233405, _233407, _233409])]], 651 ^ _209071 : [(652 ^ _209071) ^ [_234260, _234262] : [-(a_select3(tptp_mmul(_233409, tptp_mmul(_233407, trans(_233409))), _234262, _234260) = a_select3(tptp_mmul(_233409, tptp_mmul(_233407, trans(_233409))), _234260, _234262)), leq(n0, _234262), leq(_234262, _233405), leq(n0, _234260), leq(_234260, _233405)]]], (670 ^ _209071) ^ [_234955, _234957, _234959, _234961, _234963, _234965, _234967, _234969] : [675 ^ _209071 : [(676 ^ _209071) ^ [] : [-(leq(n0, 673 ^ [_234955, _234957, _234959, _234961, _234963, _234965, _234967, _234969]))], (678 ^ _209071) ^ [] : [-(leq(673 ^ [_234955, _234957, _234959, _234961, _234963, _234965, _234967, _234969], _234955))], (680 ^ _209071) ^ [] : [-(leq(n0, 674 ^ [_234955, _234957, _234959, _234961, _234963, _234965, _234967, _234969]))], (682 ^ _209071) ^ [] : [-(leq(674 ^ [_234955, _234957, _234959, _234961, _234963, _234965, _234967, _234969], _234955))], (684 ^ _209071) ^ [] : [a_select3(_234963, 673 ^ [_234955, _234957, _234959, _234961, _234963, _234965, _234967, _234969], 674 ^ [_234955, _234957, _234959, _234961, _234963, _234965, _234967, _234969]) = a_select3(_234963, 674 ^ [_234955, _234957, _234959, _234961, _234963, _234965, _234967, _234969], 673 ^ [_234955, _234957, _234959, _234961, _234963, _234965, _234967, _234969])]], 689 ^ _209071 : [(690 ^ _209071) ^ [] : [-(leq(n0, 687 ^ [_234955, _234957, _234959, _234961, _234963, _234965, _234967, _234969]))], (692 ^ _209071) ^ [] : [-(leq(687 ^ [_234955, _234957, _234959, _234961, _234963, _234965, _234967, _234969], _234957))], (694 ^ _209071) ^ [] : [-(leq(n0, 688 ^ [_234955, _234957, _234959, _234961, _234963, _234965, _234967, _234969]))], (696 ^ _209071) ^ [] : [-(leq(688 ^ [_234955, _234957, _234959, _234961, _234963, _234965, _234967, _234969], _234957))], (698 ^ _209071) ^ [] : [a_select3(_234969, 687 ^ [_234955, _234957, _234959, _234961, _234963, _234965, _234967, _234969], 688 ^ [_234955, _234957, _234959, _234961, _234963, _234965, _234967, _234969]) = a_select3(_234969, 688 ^ [_234955, _234957, _234959, _234961, _234963, _234965, _234967, _234969], 687 ^ [_234955, _234957, _234959, _234961, _234963, _234965, _234967, _234969])]], 701 ^ _209071 : [(702 ^ _209071) ^ [] : [-(leq(n0, 699 ^ [_234955, _234957, _234959, _234961, _234963, _234965, _234967, _234969]))], (704 ^ _209071) ^ [] : [-(leq(699 ^ [_234955, _234957, _234959, _234961, _234963, _234965, _234967, _234969], _234957))], (706 ^ _209071) ^ [] : [-(leq(n0, 700 ^ [_234955, _234957, _234959, _234961, _234963, _234965, _234967, _234969]))], (708 ^ _209071) ^ [] : [-(leq(700 ^ [_234955, _234957, _234959, _234961, _234963, _234965, _234967, _234969], _234957))], (710 ^ _209071) ^ [] : [a_select3(_234959, 699 ^ [_234955, _234957, _234959, _234961, _234963, _234965, _234967, _234969], 700 ^ [_234955, _234957, _234959, _234961, _234963, _234965, _234967, _234969]) = a_select3(_234959, 700 ^ [_234955, _234957, _234959, _234961, _234963, _234965, _234967, _234969], 699 ^ [_234955, _234957, _234959, _234961, _234963, _234965, _234967, _234969])]], 711 ^ _209071 : [(712 ^ _209071) ^ [_237883, _237885] : [-(a_select3(tptp_madd(_234969, tptp_mmul(_234967, tptp_mmul(tptp_madd(tptp_mmul(_234965, tptp_mmul(_234963, trans(_234965))), tptp_mmul(_234961, tptp_mmul(_234959, trans(_234961)))), trans(_234967)))), _237885, _237883) = a_select3(tptp_madd(_234969, tptp_mmul(_234967, tptp_mmul(tptp_madd(tptp_mmul(_234965, tptp_mmul(_234963, trans(_234965))), tptp_mmul(_234961, tptp_mmul(_234959, trans(_234961)))), trans(_234967)))), _237883, _237885)), leq(n0, _237885), leq(_237885, _234957), leq(n0, _237883), leq(_237883, _234957)]]], (730 ^ _209071) ^ [_238636] : [-(sum(n0, tptp_minus_1, _238636) = n0)], (732 ^ _209071) ^ [_238718] : [-(tptp_float_0_0 = sum(n0, tptp_minus_1, _238718))], (734 ^ _209071) ^ [] : [-(succ(tptp_minus_1) = n0)], (736 ^ _209071) ^ [_238853] : [-(plus(_238853, n1) = succ(_238853))], (738 ^ _209071) ^ [_238936] : [-(plus(n1, _238936) = succ(_238936))], (740 ^ _209071) ^ [_239019] : [-(plus(_239019, n2) = succ(succ(_239019)))], (742 ^ _209071) ^ [_239104] : [-(plus(n2, _239104) = succ(succ(_239104)))], (744 ^ _209071) ^ [_239189] : [-(plus(_239189, n3) = succ(succ(succ(_239189))))], (746 ^ _209071) ^ [_239276] : [-(plus(n3, _239276) = succ(succ(succ(_239276))))], (748 ^ _209071) ^ [_239363] : [-(plus(_239363, n4) = succ(succ(succ(succ(_239363)))))], (750 ^ _209071) ^ [_239452] : [-(plus(n4, _239452) = succ(succ(succ(succ(_239452)))))], (752 ^ _209071) ^ [_239541] : [-(plus(_239541, n5) = succ(succ(succ(succ(succ(_239541))))))], (754 ^ _209071) ^ [_239632] : [-(plus(n5, _239632) = succ(succ(succ(succ(succ(_239632))))))], (756 ^ _209071) ^ [_239723] : [-(minus(_239723, n1) = pred(_239723))], (758 ^ _209071) ^ [_239806] : [-(pred(succ(_239806)) = _239806)], (760 ^ _209071) ^ [_239888] : [-(succ(pred(_239888)) = _239888)], (762 ^ _209071) ^ [_240028, _240030] : [leq(succ(_240030), succ(_240028)), -(leq(_240030, _240028))], (768 ^ _209071) ^ [_240198, _240200] : [leq(_240200, _240198), -(leq(succ(_240200), succ(_240198)))], (774 ^ _209071) ^ [_240418, _240420] : [leq(succ(_240420), _240418), -(gt(_240418, _240420))], (780 ^ _209071) ^ [_240632, _240634] : [leq(minus(_240634, _240632), _240634), -(leq(n0, _240632))], (786 ^ _209071) ^ [_240861, _240863, _240865, _240867] : [-(a_select3(tptp_update3(_240867, _240865, _240863, _240861), _240865, _240863) = _240861)], (788 ^ _209071) ^ [_241053, _241055, _241057, _241059, _241061, _241063, _241065] : [-(a_select3(tptp_update3(_241057, _241065, _241063, _241053), _241061, _241059) = _241055), -(_241065 = _241061), _241063 = _241059, a_select3(_241057, _241061, _241059) = _241055], (802 ^ _209071) ^ [_241596, _241598, _241600, _241602, _241604, _241606] : [-(a_select3(tptp_update3(_241598, _241602, _241600, _241596), _241606, _241604) = _241596), 807 ^ _209071 : [(808 ^ _209071) ^ [] : [-(leq(n0, 805 ^ [_241596, _241598, _241600, _241602, _241604, _241606]))], (810 ^ _209071) ^ [] : [-(leq(n0, 806 ^ [_241596, _241598, _241600, _241602, _241604, _241606]))], (812 ^ _209071) ^ [] : [-(leq(805 ^ [_241596, _241598, _241600, _241602, _241604, _241606], _241602))], (814 ^ _209071) ^ [] : [-(leq(806 ^ [_241596, _241598, _241600, _241602, _241604, _241606], _241600))], (816 ^ _209071) ^ [] : [a_select3(_241598, 805 ^ [_241596, _241598, _241600, _241602, _241604, _241606], 806 ^ [_241596, _241598, _241600, _241602, _241604, _241606]) = _241596]], leq(n0, _241606), leq(_241606, _241602), leq(n0, _241604), leq(_241604, _241600)], (834 ^ _209071) ^ [_242938, _242940, _242942] : [-(a_select2(tptp_update2(_242942, _242940, _242938), _242940) = _242938)], (836 ^ _209071) ^ [_243098, _243100, _243102, _243104, _243106] : [-(a_select2(tptp_update2(_243102, _243106, _243098), _243104) = _243100), -(_243106 = _243104), a_select2(_243102, _243104) = _243100], (865 ^ _209071) ^ [] : [-(true)], (867 ^ _209071) ^ [] : [def = use], (846 ^ _209071) ^ [_243478, _243480, _243482, _243484] : [-(a_select2(tptp_update2(_243480, _243482, _243478), _243484) = _243478), 850 ^ _209071 : [(851 ^ _209071) ^ [] : [-(leq(n0, 849 ^ [_243478, _243480, _243482, _243484]))], (853 ^ _209071) ^ [] : [-(leq(849 ^ [_243478, _243480, _243482, _243484], _243482))], (855 ^ _209071) ^ [] : [a_select2(_243480, 849 ^ [_243478, _243480, _243482, _243484]) = _243478]], leq(n0, _243484), leq(_243484, _243482)]], input).
% 0.35/1.38  ncf('1',plain,[a_select2(rho_init, pv54) = init],start(1163 ^ 0)).
% 0.35/1.38  ncf('1.1',plain,[-(a_select2(rho_init, pv54) = init), leq(n0, pv54), leq(pv54, n4)],extension(1081 ^ 1,bind([[_250129], [pv54]]))).
% 0.35/1.38  ncf('1.1.1',plain,[-(leq(n0, pv54))],extension(1057 ^ 2)).
% 0.35/1.38  ncf('1.1.2',plain,[-(leq(pv54, n4))],extension(1061 ^ 2)).
% 0.35/1.38  %-----------------------------------------------------
% 0.35/1.38  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------