%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SWV096+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n003.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 12:19:58 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
% 0.03/0.12  % Problem  : SWV096+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.03/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.34  % Computer : n003.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Fri May 19 02:24:30 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.35/1.38  
% 0.35/1.38  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 0.35/1.38  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.35/1.38  %-----------------------------------------------------
% 0.35/1.38  ncf(matrix, plain, [(1107 ^ _243280) ^ [] : [-(a_select2(rho_defuse, n0) = use)], (1109 ^ _243280) ^ [] : [-(a_select2(rho_defuse, n1) = use)], (1111 ^ _243280) ^ [] : [-(a_select2(rho_defuse, n2) = use)], (1113 ^ _243280) ^ [] : [-(a_select2(sigma_defuse, n0) = use)], (1115 ^ _243280) ^ [] : [-(a_select2(sigma_defuse, n1) = use)], (1117 ^ _243280) ^ [] : [-(a_select2(sigma_defuse, n2) = use)], (1119 ^ _243280) ^ [] : [-(a_select2(sigma_defuse, n3) = use)], (1121 ^ _243280) ^ [] : [-(a_select2(sigma_defuse, n4) = use)], (1123 ^ _243280) ^ [] : [-(a_select2(sigma_defuse, n5) = use)], (1125 ^ _243280) ^ [] : [-(a_select3(u_defuse, n0, n0) = use)], (1127 ^ _243280) ^ [] : [-(a_select3(u_defuse, n1, n0) = use)], (1129 ^ _243280) ^ [] : [-(a_select3(u_defuse, n2, n0) = use)], (1131 ^ _243280) ^ [] : [-(a_select2(xinit_defuse, n3) = use)], (1133 ^ _243280) ^ [] : [-(a_select2(xinit_defuse, n4) = use)], (1135 ^ _243280) ^ [] : [-(a_select2(xinit_defuse, n5) = use)], (1137 ^ _243280) ^ [] : [-(a_select2(xinit_mean_defuse, n0) = use)], (1139 ^ _243280) ^ [] : [-(a_select2(xinit_mean_defuse, n1) = use)], (1141 ^ _243280) ^ [] : [-(a_select2(xinit_mean_defuse, n2) = use)], (1143 ^ _243280) ^ [] : [-(a_select2(xinit_mean_defuse, n3) = use)], (1145 ^ _243280) ^ [] : [-(a_select2(xinit_mean_defuse, n4) = use)], (1147 ^ _243280) ^ [] : [-(a_select2(xinit_mean_defuse, n5) = use)], (1149 ^ _243280) ^ [] : [-(a_select2(xinit_noise_defuse, n0) = use)], (1151 ^ _243280) ^ [] : [-(a_select2(xinit_noise_defuse, n1) = use)], (1153 ^ _243280) ^ [] : [-(a_select2(xinit_noise_defuse, n2) = use)], (1155 ^ _243280) ^ [] : [-(a_select2(xinit_noise_defuse, n3) = use)], (1157 ^ _243280) ^ [] : [-(a_select2(xinit_noise_defuse, n4) = use)], (1159 ^ _243280) ^ [] : [-(a_select2(xinit_noise_defuse, n5) = use)], (1161 ^ _243280) ^ [] : [-(leq(n0, pv5))], (1163 ^ _243280) ^ [] : [-(leq(n0, pv51))], (1165 ^ _243280) ^ [] : [-(leq(pv5, minus(n999, n1)))], (1167 ^ _243280) ^ [] : [-(leq(pv51, minus(n6, n1)))], (1169 ^ _243280) ^ [_286545, _286547] : [1184 ^ _243280 : [(1185 ^ _243280) ^ [] : [-(a_select3(u_defuse, _286547, _286545) = use)], (1187 ^ _243280) ^ [] : [-(a_select3(z_defuse, _286547, _286545) = use)]], leq(n0, _286547), leq(n0, _286545), leq(_286547, n2), leq(_286545, minus(pv5, n1))], (1189 ^ _243280) ^ [] : [a_select2(rho_defuse, n0) = use, a_select2(rho_defuse, n1) = use, a_select2(rho_defuse, n2) = use, a_select2(sigma_defuse, n0) = use, a_select2(sigma_defuse, n1) = use, a_select2(sigma_defuse, n2) = use, a_select2(sigma_defuse, n3) = use, a_select2(sigma_defuse, n4) = use, a_select2(sigma_defuse, n5) = use, a_select3(u_defuse, n0, n0) = use, a_select3(u_defuse, n1, n0) = use, a_select3(u_defuse, n2, n0) = use, a_select2(xinit_defuse, n3) = use, a_select2(xinit_defuse, n4) = use, a_select2(xinit_defuse, n5) = use, a_select2(xinit_mean_defuse, n0) = use, a_select2(xinit_mean_defuse, n1) = use, a_select2(xinit_mean_defuse, n2) = use, a_select2(xinit_mean_defuse, n3) = use, a_select2(xinit_mean_defuse, n4) = use, a_select2(xinit_mean_defuse, n5) = use, a_select2(xinit_noise_defuse, n0) = use, a_select2(xinit_noise_defuse, n1) = use, a_select2(xinit_noise_defuse, n2) = use, a_select2(xinit_noise_defuse, n3) = use, a_select2(xinit_noise_defuse, n4) = use, a_select2(xinit_noise_defuse, n5) = use, leq(n0, pv5), leq(pv5, minus(n999, n1)), 1306 ^ _243280 : [(1307 ^ _243280) ^ [] : [-(leq(n0, 1304 ^ []))], (1309 ^ _243280) ^ [] : [-(leq(n0, 1305 ^ []))], (1311 ^ _243280) ^ [] : [-(leq(1304 ^ [], n2))], (1313 ^ _243280) ^ [] : [-(leq(1305 ^ [], minus(pv5, n1)))], (1315 ^ _243280) ^ [] : [a_select3(u_defuse, 1304 ^ [], 1305 ^ []) = use, a_select3(z_defuse, 1304 ^ [], 1305 ^ []) = use]]], (2 ^ _243280) ^ [_243424] : [-(_243424 = _243424)], (4 ^ _243280) ^ [_243531, _243533] : [_243533 = _243531, -(_243531 = _243533)], (10 ^ _243280) ^ [_243735, _243737, _243739] : [-(_243739 = _243735), _243739 = _243737, _243737 = _243735], (20 ^ _243280) ^ [_244076, _244078, _244080, _244082] : [-(lt(_244080, _244076)), lt(_244082, _244078), _244082 = _244080, _244078 = _244076], (34 ^ _243280) ^ [_244520, _244522, _244524, _244526] : [-(geq(_244524, _244520)), geq(_244526, _244522), _244526 = _244524, _244522 = _244520], (48 ^ _243280) ^ [_244964, _244966, _244968, _244970] : [-(gt(_244968, _244964)), gt(_244970, _244966), _244970 = _244968, _244966 = _244964], (62 ^ _243280) ^ [_245388, _245390, _245392, _245394] : [-(leq(_245392, _245388)), leq(_245394, _245390), _245394 = _245392, _245390 = _245388], (76 ^ _243280) ^ [_245844, _245846, _245848, _245850] : [-(uniform_int_rnd(_245850, _245846) = uniform_int_rnd(_245848, _245844)), _245850 = _245848, _245846 = _245844], (86 ^ _243280) ^ [_246203, _246205, _246207, _246209] : [-(tptp_const_array1(_246209, _246205) = tptp_const_array1(_246207, _246203)), _246209 = _246207, _246205 = _246203], (96 ^ _243280) ^ [_246590, _246592, _246594, _246596, _246598, _246600] : [-(tptp_const_array2(_246600, _246596, _246592) = tptp_const_array2(_246598, _246594, _246590)), _246600 = _246598, _246596 = _246594, _246592 = _246590], (110 ^ _243280) ^ [_247078, _247080, _247082, _247084] : [-(dim(_247084, _247080) = dim(_247082, _247078)), _247084 = _247082, _247080 = _247078], (120 ^ _243280) ^ [_247409, _247411] : [_247411 = _247409, -(inv(_247411) = inv(_247409))], (126 ^ _243280) ^ [_247655, _247657, _247659, _247661] : [-(tptp_msub(_247661, _247657) = tptp_msub(_247659, _247655)), _247661 = _247659, _247657 = _247655], (136 ^ _243280) ^ [_248014, _248016, _248018, _248020] : [-(tptp_madd(_248020, _248016) = tptp_madd(_248018, _248014)), _248020 = _248018, _248016 = _248014], (146 ^ _243280) ^ [_248373, _248375, _248377, _248379] : [-(tptp_mmul(_248379, _248375) = tptp_mmul(_248377, _248373)), _248379 = _248377, _248375 = _248373], (156 ^ _243280) ^ [_248704, _248706] : [_248706 = _248704, -(trans(_248706) = trans(_248704))], (162 ^ _243280) ^ [_248978, _248980, _248982, _248984, _248986, _248988] : [-(sum(_248988, _248984, _248980) = sum(_248986, _248982, _248978)), _248988 = _248986, _248984 = _248982, _248980 = _248978], (176 ^ _243280) ^ [_249466, _249468, _249470, _249472] : [-(plus(_249472, _249468) = plus(_249470, _249466)), _249472 = _249470, _249468 = _249466], (186 ^ _243280) ^ [_249797, _249799] : [_249799 = _249797, -(pred(_249799) = pred(_249797))], (192 ^ _243280) ^ [_250099, _250101, _250103, _250105, _250107, _250109, _250111, _250113] : [-(tptp_update3(_250113, _250109, _250105, _250101) = tptp_update3(_250111, _250107, _250103, _250099)), _250113 = _250111, _250109 = _250107, _250105 = _250103, _250101 = _250099], (210 ^ _243280) ^ [_250760, _250762, _250764, _250766, _250768, _250770] : [-(tptp_update2(_250770, _250766, _250762) = tptp_update2(_250768, _250764, _250760)), _250770 = _250768, _250766 = _250764, _250762 = _250760], (224 ^ _243280) ^ [_251220, _251222] : [_251222 = _251220, -(succ(_251222) = succ(_251220))], (230 ^ _243280) ^ [_251466, _251468, _251470, _251472] : [-(a_select2(_251472, _251468) = a_select2(_251470, _251466)), _251472 = _251470, _251468 = _251466], (240 ^ _243280) ^ [_251825, _251827, _251829, _251831] : [-(minus(_251831, _251827) = minus(_251829, _251825)), _251831 = _251829, _251827 = _251825], (250 ^ _243280) ^ [_252192, _252194, _252196, _252198, _252200, _252202] : [-(a_select3(_252202, _252198, _252194) = a_select3(_252200, _252196, _252192)), _252202 = _252200, _252198 = _252196, _252194 = _252192], (869 ^ _243280) ^ [] : [-(gt(n5, n4))], (871 ^ _243280) ^ [] : [-(gt(n6, n4))], (873 ^ _243280) ^ [] : [-(gt(n999, n4))], (875 ^ _243280) ^ [] : [-(gt(n6, n5))], (877 ^ _243280) ^ [] : [-(gt(n999, n5))], (879 ^ _243280) ^ [] : [-(gt(n999, n6))], (881 ^ _243280) ^ [] : [-(gt(n4, tptp_minus_1))], (883 ^ _243280) ^ [] : [-(gt(n5, tptp_minus_1))], (885 ^ _243280) ^ [] : [-(gt(n6, tptp_minus_1))], (887 ^ _243280) ^ [] : [-(gt(n999, tptp_minus_1))], (889 ^ _243280) ^ [] : [-(gt(n0, tptp_minus_1))], (891 ^ _243280) ^ [] : [-(gt(n1, tptp_minus_1))], (893 ^ _243280) ^ [] : [-(gt(n2, tptp_minus_1))], (895 ^ _243280) ^ [] : [-(gt(n3, tptp_minus_1))], (897 ^ _243280) ^ [] : [-(gt(n4, n0))], (899 ^ _243280) ^ [] : [-(gt(n5, n0))], (901 ^ _243280) ^ [] : [-(gt(n6, n0))], (903 ^ _243280) ^ [] : [-(gt(n999, n0))], (905 ^ _243280) ^ [] : [-(gt(n1, n0))], (907 ^ _243280) ^ [] : [-(gt(n2, n0))], (909 ^ _243280) ^ [] : [-(gt(n3, n0))], (911 ^ _243280) ^ [] : [-(gt(n4, n1))], (913 ^ _243280) ^ [] : [-(gt(n5, n1))], (915 ^ _243280) ^ [] : [-(gt(n6, n1))], (917 ^ _243280) ^ [] : [-(gt(n999, n1))], (919 ^ _243280) ^ [] : [-(gt(n2, n1))], (921 ^ _243280) ^ [] : [-(gt(n3, n1))], (923 ^ _243280) ^ [] : [-(gt(n4, n2))], (925 ^ _243280) ^ [] : [-(gt(n5, n2))], (927 ^ _243280) ^ [] : [-(gt(n6, n2))], (929 ^ _243280) ^ [] : [-(gt(n999, n2))], (931 ^ _243280) ^ [] : [-(gt(n3, n2))], (933 ^ _243280) ^ [] : [-(gt(n4, n3))], (935 ^ _243280) ^ [] : [-(gt(n5, n3))], (937 ^ _243280) ^ [] : [-(gt(n6, n3))], (939 ^ _243280) ^ [] : [-(gt(n999, n3))], (941 ^ _243280) ^ [_280585] : [leq(n0, _280585), leq(_280585, n4), -(_280585 = n0), -(_280585 = n1), -(_280585 = n2), -(_280585 = n3), -(_280585 = n4)], (967 ^ _243280) ^ [_281206] : [leq(n0, _281206), leq(_281206, n5), -(_281206 = n0), -(_281206 = n1), -(_281206 = n2), -(_281206 = n3), -(_281206 = n4), -(_281206 = n5)], (997 ^ _243280) ^ [_281913] : [leq(n0, _281913), leq(_281913, n6), -(_281913 = n0), -(_281913 = n1), -(_281913 = n2), -(_281913 = n3), -(_281913 = n4), -(_281913 = n5), -(_281913 = n6)], (1031 ^ _243280) ^ [_282706] : [-(_282706 = n0), leq(n0, _282706), leq(_282706, n0)], (1041 ^ _243280) ^ [_282981] : [leq(n0, _282981), leq(_282981, n1), -(_282981 = n0), -(_282981 = n1)], (1055 ^ _243280) ^ [_283344] : [leq(n0, _283344), leq(_283344, n2), -(_283344 = n0), -(_283344 = n1), -(_283344 = n2)], (1095 ^ _243280) ^ [] : [-(succ(succ(succ(succ(n0)))) = n4)], (1097 ^ _243280) ^ [] : [-(succ(succ(succ(succ(succ(n0))))) = n5)], (1099 ^ _243280) ^ [] : [-(succ(succ(succ(succ(succ(succ(n0)))))) = n6)], (1101 ^ _243280) ^ [] : [-(succ(n0) = n1)], (1103 ^ _243280) ^ [] : [-(succ(succ(n0)) = n2)], (1105 ^ _243280) ^ [] : [-(succ(succ(succ(n0))) = n3)], (1073 ^ _243280) ^ [_283793] : [leq(n0, _283793), leq(_283793, n3), -(_283793 = n0), -(_283793 = n1), -(_283793 = n2), -(_283793 = n3)], (264 ^ _243280) ^ [_252752, _252754] : [-(gt(_252754, _252752)), -(gt(_252752, _252754)), -(_252754 = _252752)], (274 ^ _243280) ^ [_253067, _253069, _253071] : [-(gt(_253071, _253067)), gt(_253071, _253069), gt(_253069, _253067)], (284 ^ _243280) ^ [_253346] : [gt(_253346, _253346)], (286 ^ _243280) ^ [_253424] : [-(leq(_253424, _253424))], (288 ^ _243280) ^ [_253545, _253547, _253549] : [-(leq(_253549, _253545)), leq(_253549, _253547), leq(_253547, _253545)], (298 ^ _243280) ^ [_253883, _253885] : [lt(_253885, _253883), -(gt(_253883, _253885))], (304 ^ _243280) ^ [_254045, _254047] : [gt(_254045, _254047), -(lt(_254047, _254045))], (310 ^ _243280) ^ [_254286, _254288] : [geq(_254288, _254286), -(leq(_254286, _254288))], (316 ^ _243280) ^ [_254448, _254450] : [leq(_254448, _254450), -(geq(_254450, _254448))], (322 ^ _243280) ^ [_254660, _254662] : [gt(_254660, _254662), -(leq(_254662, _254660))], (328 ^ _243280) ^ [_254870, _254872] : [-(gt(_254870, _254872)), leq(_254872, _254870), -(_254872 = _254870)], (338 ^ _243280) ^ [_255201, _255203] : [leq(_255203, pred(_255201)), -(gt(_255201, _255203))], (344 ^ _243280) ^ [_255367, _255369] : [gt(_255367, _255369), -(leq(_255369, pred(_255367)))], (350 ^ _243280) ^ [_255554] : [-(gt(succ(_255554), _255554))], (352 ^ _243280) ^ [_255663, _255665] : [leq(_255665, _255663), -(leq(_255665, succ(_255663)))], (358 ^ _243280) ^ [_255906, _255908] : [leq(_255908, _255906), -(gt(succ(_255906), _255908))], (364 ^ _243280) ^ [_256072, _256074] : [gt(succ(_256072), _256074), -(leq(_256074, _256072))], (370 ^ _243280) ^ [_256288, _256290] : [leq(n0, _256290), -(leq(uniform_int_rnd(_256288, _256290), _256290))], (376 ^ _243280) ^ [_256504, _256506] : [leq(n0, _256506), -(leq(n0, uniform_int_rnd(_256504, _256506)))], (382 ^ _243280) ^ [_256748, _256750, _256752, _256754] : [-(a_select2(tptp_const_array1(dim(_256752, _256750), _256748), _256754) = _256748), leq(_256752, _256754), leq(_256754, _256750)], (392 ^ _243280) ^ [_257155, _257157, _257159, _257161, _257163, _257165, _257167] : [-(a_select3(tptp_const_array2(dim(_257165, _257163), dim(_257159, _257157), _257155), _257167, _257161) = _257155), leq(_257165, _257167), leq(_257167, _257163), leq(_257159, _257161), leq(_257161, _257157)], (410 ^ _243280) ^ [_257750, _257752] : [413 ^ _243280 : [(414 ^ _243280) ^ [] : [-(leq(n0, 411 ^ [_257750, _257752]))], (416 ^ _243280) ^ [] : [-(leq(411 ^ [_257750, _257752], _257750))], (418 ^ _243280) ^ [] : [-(leq(n0, 412 ^ [_257750, _257752]))], (420 ^ _243280) ^ [] : [-(leq(412 ^ [_257750, _257752], _257750))], (422 ^ _243280) ^ [] : [a_select3(_257752, 411 ^ [_257750, _257752], 412 ^ [_257750, _257752]) = a_select3(_257752, 412 ^ [_257750, _257752], 411 ^ [_257750, _257752])]], 423 ^ _243280 : [(424 ^ _243280) ^ [_258507, _258509] : [-(a_select3(trans(_257752), _258509, _258507) = a_select3(trans(_257752), _258507, _258509)), leq(n0, _258509), leq(_258509, _257750), leq(n0, _258507), leq(_258507, _257750)]]], (442 ^ _243280) ^ [_259054, _259056] : [445 ^ _243280 : [(446 ^ _243280) ^ [] : [-(leq(n0, 443 ^ [_259054, _259056]))], (448 ^ _243280) ^ [] : [-(leq(443 ^ [_259054, _259056], _259054))], (450 ^ _243280) ^ [] : [-(leq(n0, 444 ^ [_259054, _259056]))], (452 ^ _243280) ^ [] : [-(leq(444 ^ [_259054, _259056], _259054))], (454 ^ _243280) ^ [] : [a_select3(_259056, 443 ^ [_259054, _259056], 444 ^ [_259054, _259056]) = a_select3(_259056, 444 ^ [_259054, _259056], 443 ^ [_259054, _259056])]], 455 ^ _243280 : [(456 ^ _243280) ^ [_259811, _259813] : [-(a_select3(inv(_259056), _259813, _259811) = a_select3(inv(_259056), _259811, _259813)), leq(n0, _259813), leq(_259813, _259054), leq(n0, _259811), leq(_259811, _259054)]]], (474 ^ _243280) ^ [_260358, _260360] : [477 ^ _243280 : [(478 ^ _243280) ^ [] : [-(leq(n0, 475 ^ [_260358, _260360]))], (480 ^ _243280) ^ [] : [-(leq(475 ^ [_260358, _260360], _260358))], (482 ^ _243280) ^ [] : [-(leq(n0, 476 ^ [_260358, _260360]))], (484 ^ _243280) ^ [] : [-(leq(476 ^ [_260358, _260360], _260358))], (486 ^ _243280) ^ [] : [a_select3(_260360, 475 ^ [_260358, _260360], 476 ^ [_260358, _260360]) = a_select3(_260360, 476 ^ [_260358, _260360], 475 ^ [_260358, _260360])]], 487 ^ _243280 : [(488 ^ _243280) ^ [_261171, _261173, _261175, _261177] : [-(a_select3(tptp_update3(_260360, _261173, _261173, _261171), _261177, _261175) = a_select3(tptp_update3(_260360, _261173, _261173, _261171), _261175, _261177)), leq(n0, _261177), leq(_261177, _260358), leq(n0, _261175), leq(_261175, _260358), leq(n0, _261173), leq(_261173, _260358)]]], (514 ^ _243280) ^ [_261990, _261992, _261994] : [519 ^ _243280 : [(520 ^ _243280) ^ [] : [-(leq(n0, 517 ^ [_261990, _261992, _261994]))], (522 ^ _243280) ^ [] : [-(leq(517 ^ [_261990, _261992, _261994], _261990))], (524 ^ _243280) ^ [] : [-(leq(n0, 518 ^ [_261990, _261992, _261994]))], (526 ^ _243280) ^ [] : [-(leq(518 ^ [_261990, _261992, _261994], _261990))], (528 ^ _243280) ^ [] : [a_select3(_261994, 517 ^ [_261990, _261992, _261994], 518 ^ [_261990, _261992, _261994]) = a_select3(_261994, 518 ^ [_261990, _261992, _261994], 517 ^ [_261990, _261992, _261994])]], 531 ^ _243280 : [(532 ^ _243280) ^ [] : [-(leq(n0, 529 ^ [_261990, _261992, _261994]))], (534 ^ _243280) ^ [] : [-(leq(529 ^ [_261990, _261992, _261994], _261990))], (536 ^ _243280) ^ [] : [-(leq(n0, 530 ^ [_261990, _261992, _261994]))], (538 ^ _243280) ^ [] : [-(leq(530 ^ [_261990, _261992, _261994], _261990))], (540 ^ _243280) ^ [] : [a_select3(_261992, 529 ^ [_261990, _261992, _261994], 530 ^ [_261990, _261992, _261994]) = a_select3(_261992, 530 ^ [_261990, _261992, _261994], 529 ^ [_261990, _261992, _261994])]], 541 ^ _243280 : [(542 ^ _243280) ^ [_263499, _263501] : [-(a_select3(tptp_madd(_261994, _261992), _263501, _263499) = a_select3(tptp_madd(_261994, _261992), _263499, _263501)), leq(n0, _263501), leq(_263501, _261990), leq(n0, _263499), leq(_263499, _261990)]]], (560 ^ _243280) ^ [_264085, _264087, _264089] : [565 ^ _243280 : [(566 ^ _243280) ^ [] : [-(leq(n0, 563 ^ [_264085, _264087, _264089]))], (568 ^ _243280) ^ [] : [-(leq(563 ^ [_264085, _264087, _264089], _264085))], (570 ^ _243280) ^ [] : [-(leq(n0, 564 ^ [_264085, _264087, _264089]))], (572 ^ _243280) ^ [] : [-(leq(564 ^ [_264085, _264087, _264089], _264085))], (574 ^ _243280) ^ [] : [a_select3(_264089, 563 ^ [_264085, _264087, _264089], 564 ^ [_264085, _264087, _264089]) = a_select3(_264089, 564 ^ [_264085, _264087, _264089], 563 ^ [_264085, _264087, _264089])]], 577 ^ _243280 : [(578 ^ _243280) ^ [] : [-(leq(n0, 575 ^ [_264085, _264087, _264089]))], (580 ^ _243280) ^ [] : [-(leq(575 ^ [_264085, _264087, _264089], _264085))], (582 ^ _243280) ^ [] : [-(leq(n0, 576 ^ [_264085, _264087, _264089]))], (584 ^ _243280) ^ [] : [-(leq(576 ^ [_264085, _264087, _264089], _264085))], (586 ^ _243280) ^ [] : [a_select3(_264087, 575 ^ [_264085, _264087, _264089], 576 ^ [_264085, _264087, _264089]) = a_select3(_264087, 576 ^ [_264085, _264087, _264089], 575 ^ [_264085, _264087, _264089])]], 587 ^ _243280 : [(588 ^ _243280) ^ [_265594, _265596] : [-(a_select3(tptp_msub(_264089, _264087), _265596, _265594) = a_select3(tptp_msub(_264089, _264087), _265594, _265596)), leq(n0, _265596), leq(_265596, _264085), leq(n0, _265594), leq(_265594, _264085)]]], (606 ^ _243280) ^ [_266180, _266182, _266184] : [609 ^ _243280 : [(610 ^ _243280) ^ [] : [-(leq(n0, 607 ^ [_266180, _266182, _266184]))], (612 ^ _243280) ^ [] : [-(leq(607 ^ [_266180, _266182, _266184], _266180))], (614 ^ _243280) ^ [] : [-(leq(n0, 608 ^ [_266180, _266182, _266184]))], (616 ^ _243280) ^ [] : [-(leq(608 ^ [_266180, _266182, _266184], _266180))], (618 ^ _243280) ^ [] : [a_select3(_266182, 607 ^ [_266180, _266182, _266184], 608 ^ [_266180, _266182, _266184]) = a_select3(_266182, 608 ^ [_266180, _266182, _266184], 607 ^ [_266180, _266182, _266184])]], 619 ^ _243280 : [(620 ^ _243280) ^ [_266993, _266995] : [-(a_select3(tptp_mmul(_266184, tptp_mmul(_266182, trans(_266184))), _266995, _266993) = a_select3(tptp_mmul(_266184, tptp_mmul(_266182, trans(_266184))), _266993, _266995)), leq(n0, _266995), leq(_266995, _266180), leq(n0, _266993), leq(_266993, _266180)]]], (638 ^ _243280) ^ [_267612, _267614, _267616, _267618] : [641 ^ _243280 : [(642 ^ _243280) ^ [] : [-(leq(n0, 639 ^ [_267612, _267614, _267616, _267618]))], (644 ^ _243280) ^ [] : [-(leq(639 ^ [_267612, _267614, _267616, _267618], _267612))], (646 ^ _243280) ^ [] : [-(leq(n0, 640 ^ [_267612, _267614, _267616, _267618]))], (648 ^ _243280) ^ [] : [-(leq(640 ^ [_267612, _267614, _267616, _267618], _267612))], (650 ^ _243280) ^ [] : [a_select3(_267616, 639 ^ [_267612, _267614, _267616, _267618], 640 ^ [_267612, _267614, _267616, _267618]) = a_select3(_267616, 640 ^ [_267612, _267614, _267616, _267618], 639 ^ [_267612, _267614, _267616, _267618])]], 651 ^ _243280 : [(652 ^ _243280) ^ [_268469, _268471] : [-(a_select3(tptp_mmul(_267618, tptp_mmul(_267616, trans(_267618))), _268471, _268469) = a_select3(tptp_mmul(_267618, tptp_mmul(_267616, trans(_267618))), _268469, _268471)), leq(n0, _268471), leq(_268471, _267614), leq(n0, _268469), leq(_268469, _267614)]]], (670 ^ _243280) ^ [_269164, _269166, _269168, _269170, _269172, _269174, _269176, _269178] : [675 ^ _243280 : [(676 ^ _243280) ^ [] : [-(leq(n0, 673 ^ [_269164, _269166, _269168, _269170, _269172, _269174, _269176, _269178]))], (678 ^ _243280) ^ [] : [-(leq(673 ^ [_269164, _269166, _269168, _269170, _269172, _269174, _269176, _269178], _269164))], (680 ^ _243280) ^ [] : [-(leq(n0, 674 ^ [_269164, _269166, _269168, _269170, _269172, _269174, _269176, _269178]))], (682 ^ _243280) ^ [] : [-(leq(674 ^ [_269164, _269166, _269168, _269170, _269172, _269174, _269176, _269178], _269164))], (684 ^ _243280) ^ [] : [a_select3(_269172, 673 ^ [_269164, _269166, _269168, _269170, _269172, _269174, _269176, _269178], 674 ^ [_269164, _269166, _269168, _269170, _269172, _269174, _269176, _269178]) = a_select3(_269172, 674 ^ [_269164, _269166, _269168, _269170, _269172, _269174, _269176, _269178], 673 ^ [_269164, _269166, _269168, _269170, _269172, _269174, _269176, _269178])]], 689 ^ _243280 : [(690 ^ _243280) ^ [] : [-(leq(n0, 687 ^ [_269164, _269166, _269168, _269170, _269172, _269174, _269176, _269178]))], (692 ^ _243280) ^ [] : [-(leq(687 ^ [_269164, _269166, _269168, _269170, _269172, _269174, _269176, _269178], _269166))], (694 ^ _243280) ^ [] : [-(leq(n0, 688 ^ [_269164, _269166, _269168, _269170, _269172, _269174, _269176, _269178]))], (696 ^ _243280) ^ [] : [-(leq(688 ^ [_269164, _269166, _269168, _269170, _269172, _269174, _269176, _269178], _269166))], (698 ^ _243280) ^ [] : [a_select3(_269178, 687 ^ [_269164, _269166, _269168, _269170, _269172, _269174, _269176, _269178], 688 ^ [_269164, _269166, _269168, _269170, _269172, _269174, _269176, _269178]) = a_select3(_269178, 688 ^ [_269164, _269166, _269168, _269170, _269172, _269174, _269176, _269178], 687 ^ [_269164, _269166, _269168, _269170, _269172, _269174, _269176, _269178])]], 701 ^ _243280 : [(702 ^ _243280) ^ [] : [-(leq(n0, 699 ^ [_269164, _269166, _269168, _269170, _269172, _269174, _269176, _269178]))], (704 ^ _243280) ^ [] : [-(leq(699 ^ [_269164, _269166, _269168, _269170, _269172, _269174, _269176, _269178], _269166))], (706 ^ _243280) ^ [] : [-(leq(n0, 700 ^ [_269164, _269166, _269168, _269170, _269172, _269174, _269176, _269178]))], (708 ^ _243280) ^ [] : [-(leq(700 ^ [_269164, _269166, _269168, _269170, _269172, _269174, _269176, _269178], _269166))], (710 ^ _243280) ^ [] : [a_select3(_269168, 699 ^ [_269164, _269166, _269168, _269170, _269172, _269174, _269176, _269178], 700 ^ [_269164, _269166, _269168, _269170, _269172, _269174, _269176, _269178]) = a_select3(_269168, 700 ^ [_269164, _269166, _269168, _269170, _269172, _269174, _269176, _269178], 699 ^ [_269164, _269166, _269168, _269170, _269172, _269174, _269176, _269178])]], 711 ^ _243280 : [(712 ^ _243280) ^ [_272092, _272094] : [-(a_select3(tptp_madd(_269178, tptp_mmul(_269176, tptp_mmul(tptp_madd(tptp_mmul(_269174, tptp_mmul(_269172, trans(_269174))), tptp_mmul(_269170, tptp_mmul(_269168, trans(_269170)))), trans(_269176)))), _272094, _272092) = a_select3(tptp_madd(_269178, tptp_mmul(_269176, tptp_mmul(tptp_madd(tptp_mmul(_269174, tptp_mmul(_269172, trans(_269174))), tptp_mmul(_269170, tptp_mmul(_269168, trans(_269170)))), trans(_269176)))), _272092, _272094)), leq(n0, _272094), leq(_272094, _269166), leq(n0, _272092), leq(_272092, _269166)]]], (730 ^ _243280) ^ [_272845] : [-(sum(n0, tptp_minus_1, _272845) = n0)], (732 ^ _243280) ^ [_272927] : [-(tptp_float_0_0 = sum(n0, tptp_minus_1, _272927))], (734 ^ _243280) ^ [] : [-(succ(tptp_minus_1) = n0)], (736 ^ _243280) ^ [_273062] : [-(plus(_273062, n1) = succ(_273062))], (738 ^ _243280) ^ [_273145] : [-(plus(n1, _273145) = succ(_273145))], (740 ^ _243280) ^ [_273228] : [-(plus(_273228, n2) = succ(succ(_273228)))], (742 ^ _243280) ^ [_273313] : [-(plus(n2, _273313) = succ(succ(_273313)))], (744 ^ _243280) ^ [_273398] : [-(plus(_273398, n3) = succ(succ(succ(_273398))))], (746 ^ _243280) ^ [_273485] : [-(plus(n3, _273485) = succ(succ(succ(_273485))))], (748 ^ _243280) ^ [_273572] : [-(plus(_273572, n4) = succ(succ(succ(succ(_273572)))))], (750 ^ _243280) ^ [_273661] : [-(plus(n4, _273661) = succ(succ(succ(succ(_273661)))))], (752 ^ _243280) ^ [_273750] : [-(plus(_273750, n5) = succ(succ(succ(succ(succ(_273750))))))], (754 ^ _243280) ^ [_273841] : [-(plus(n5, _273841) = succ(succ(succ(succ(succ(_273841))))))], (756 ^ _243280) ^ [_273932] : [-(minus(_273932, n1) = pred(_273932))], (758 ^ _243280) ^ [_274015] : [-(pred(succ(_274015)) = _274015)], (760 ^ _243280) ^ [_274097] : [-(succ(pred(_274097)) = _274097)], (762 ^ _243280) ^ [_274237, _274239] : [leq(succ(_274239), succ(_274237)), -(leq(_274239, _274237))], (768 ^ _243280) ^ [_274407, _274409] : [leq(_274409, _274407), -(leq(succ(_274409), succ(_274407)))], (774 ^ _243280) ^ [_274627, _274629] : [leq(succ(_274629), _274627), -(gt(_274627, _274629))], (780 ^ _243280) ^ [_274841, _274843] : [leq(minus(_274843, _274841), _274843), -(leq(n0, _274841))], (786 ^ _243280) ^ [_275070, _275072, _275074, _275076] : [-(a_select3(tptp_update3(_275076, _275074, _275072, _275070), _275074, _275072) = _275070)], (788 ^ _243280) ^ [_275262, _275264, _275266, _275268, _275270, _275272, _275274] : [-(a_select3(tptp_update3(_275266, _275274, _275272, _275262), _275270, _275268) = _275264), -(_275274 = _275270), _275272 = _275268, a_select3(_275266, _275270, _275268) = _275264], (802 ^ _243280) ^ [_275805, _275807, _275809, _275811, _275813, _275815] : [-(a_select3(tptp_update3(_275807, _275811, _275809, _275805), _275815, _275813) = _275805), 807 ^ _243280 : [(808 ^ _243280) ^ [] : [-(leq(n0, 805 ^ [_275805, _275807, _275809, _275811, _275813, _275815]))], (810 ^ _243280) ^ [] : [-(leq(n0, 806 ^ [_275805, _275807, _275809, _275811, _275813, _275815]))], (812 ^ _243280) ^ [] : [-(leq(805 ^ [_275805, _275807, _275809, _275811, _275813, _275815], _275811))], (814 ^ _243280) ^ [] : [-(leq(806 ^ [_275805, _275807, _275809, _275811, _275813, _275815], _275809))], (816 ^ _243280) ^ [] : [a_select3(_275807, 805 ^ [_275805, _275807, _275809, _275811, _275813, _275815], 806 ^ [_275805, _275807, _275809, _275811, _275813, _275815]) = _275805]], leq(n0, _275815), leq(_275815, _275811), leq(n0, _275813), leq(_275813, _275809)], (834 ^ _243280) ^ [_277147, _277149, _277151] : [-(a_select2(tptp_update2(_277151, _277149, _277147), _277149) = _277147)], (836 ^ _243280) ^ [_277307, _277309, _277311, _277313, _277315] : [-(a_select2(tptp_update2(_277311, _277315, _277307), _277313) = _277309), -(_277315 = _277313), a_select2(_277311, _277313) = _277309], (865 ^ _243280) ^ [] : [-(true)], (867 ^ _243280) ^ [] : [def = use], (846 ^ _243280) ^ [_277687, _277689, _277691, _277693] : [-(a_select2(tptp_update2(_277689, _277691, _277687), _277693) = _277687), 850 ^ _243280 : [(851 ^ _243280) ^ [] : [-(leq(n0, 849 ^ [_277687, _277689, _277691, _277693]))], (853 ^ _243280) ^ [] : [-(leq(849 ^ [_277687, _277689, _277691, _277693], _277691))], (855 ^ _243280) ^ [] : [a_select2(_277689, 849 ^ [_277687, _277689, _277691, _277693]) = _277687]], leq(n0, _277693), leq(_277693, _277691)]], input).
% 0.35/1.38  ncf('1',plain,[a_select2(rho_defuse, n0) = use, a_select2(rho_defuse, n1) = use, a_select2(rho_defuse, n2) = use, a_select2(sigma_defuse, n0) = use, a_select2(sigma_defuse, n1) = use, a_select2(sigma_defuse, n2) = use, a_select2(sigma_defuse, n3) = use, a_select2(sigma_defuse, n4) = use, a_select2(sigma_defuse, n5) = use, a_select3(u_defuse, n0, n0) = use, a_select3(u_defuse, n1, n0) = use, a_select3(u_defuse, n2, n0) = use, a_select2(xinit_defuse, n3) = use, a_select2(xinit_defuse, n4) = use, a_select2(xinit_defuse, n5) = use, a_select2(xinit_mean_defuse, n0) = use, a_select2(xinit_mean_defuse, n1) = use, a_select2(xinit_mean_defuse, n2) = use, a_select2(xinit_mean_defuse, n3) = use, a_select2(xinit_mean_defuse, n4) = use, a_select2(xinit_mean_defuse, n5) = use, a_select2(xinit_noise_defuse, n0) = use, a_select2(xinit_noise_defuse, n1) = use, a_select2(xinit_noise_defuse, n2) = use, a_select2(xinit_noise_defuse, n3) = use, a_select2(xinit_noise_defuse, n4) = use, a_select2(xinit_noise_defuse, n5) = use, leq(n0, pv5), leq(pv5, minus(n999, n1)), 1315 : a_select3(u_defuse, 1304 ^ [], 1305 ^ []) = use, 1315 : a_select3(z_defuse, 1304 ^ [], 1305 ^ []) = use],start(1189 ^ 0)).
% 0.35/1.38  ncf('1.1',plain,[-(a_select2(rho_defuse, n0) = use)],extension(1107 ^ 1)).
% 0.35/1.38  ncf('1.2',plain,[-(a_select2(rho_defuse, n1) = use)],extension(1109 ^ 1)).
% 0.35/1.38  ncf('1.3',plain,[-(a_select2(rho_defuse, n2) = use)],extension(1111 ^ 1)).
% 0.35/1.38  ncf('1.4',plain,[-(a_select2(sigma_defuse, n0) = use)],extension(1113 ^ 1)).
% 0.35/1.38  ncf('1.5',plain,[-(a_select2(sigma_defuse, n1) = use)],extension(1115 ^ 1)).
% 0.35/1.38  ncf('1.6',plain,[-(a_select2(sigma_defuse, n2) = use)],extension(1117 ^ 1)).
% 0.35/1.38  ncf('1.7',plain,[-(a_select2(sigma_defuse, n3) = use)],extension(1119 ^ 1)).
% 0.35/1.38  ncf('1.8',plain,[-(a_select2(sigma_defuse, n4) = use)],extension(1121 ^ 1)).
% 0.35/1.38  ncf('1.9',plain,[-(a_select2(sigma_defuse, n5) = use)],extension(1123 ^ 1)).
% 0.35/1.38  ncf('1.10',plain,[-(a_select3(u_defuse, n0, n0) = use)],extension(1125 ^ 1)).
% 0.35/1.38  ncf('1.11',plain,[-(a_select3(u_defuse, n1, n0) = use)],extension(1127 ^ 1)).
% 0.35/1.38  ncf('1.12',plain,[-(a_select3(u_defuse, n2, n0) = use)],extension(1129 ^ 1)).
% 0.35/1.38  ncf('1.13',plain,[-(a_select2(xinit_defuse, n3) = use)],extension(1131 ^ 1)).
% 0.35/1.38  ncf('1.14',plain,[-(a_select2(xinit_defuse, n4) = use)],extension(1133 ^ 1)).
% 0.35/1.38  ncf('1.15',plain,[-(a_select2(xinit_defuse, n5) = use)],extension(1135 ^ 1)).
% 0.35/1.38  ncf('1.16',plain,[-(a_select2(xinit_mean_defuse, n0) = use)],extension(1137 ^ 1)).
% 0.35/1.38  ncf('1.17',plain,[-(a_select2(xinit_mean_defuse, n1) = use)],extension(1139 ^ 1)).
% 0.35/1.38  ncf('1.18',plain,[-(a_select2(xinit_mean_defuse, n2) = use)],extension(1141 ^ 1)).
% 0.35/1.38  ncf('1.19',plain,[-(a_select2(xinit_mean_defuse, n3) = use)],extension(1143 ^ 1)).
% 0.35/1.38  ncf('1.20',plain,[-(a_select2(xinit_mean_defuse, n4) = use)],extension(1145 ^ 1)).
% 0.35/1.38  ncf('1.21',plain,[-(a_select2(xinit_mean_defuse, n5) = use)],extension(1147 ^ 1)).
% 0.35/1.38  ncf('1.22',plain,[-(a_select2(xinit_noise_defuse, n0) = use)],extension(1149 ^ 1)).
% 0.35/1.38  ncf('1.23',plain,[-(a_select2(xinit_noise_defuse, n1) = use)],extension(1151 ^ 1)).
% 0.35/1.38  ncf('1.24',plain,[-(a_select2(xinit_noise_defuse, n2) = use)],extension(1153 ^ 1)).
% 0.35/1.38  ncf('1.25',plain,[-(a_select2(xinit_noise_defuse, n3) = use)],extension(1155 ^ 1)).
% 0.35/1.38  ncf('1.26',plain,[-(a_select2(xinit_noise_defuse, n4) = use)],extension(1157 ^ 1)).
% 0.35/1.38  ncf('1.27',plain,[-(a_select2(xinit_noise_defuse, n5) = use)],extension(1159 ^ 1)).
% 0.35/1.38  ncf('1.28',plain,[-(leq(n0, pv5))],extension(1161 ^ 1)).
% 0.35/1.38  ncf('1.29',plain,[-(leq(pv5, minus(n999, n1)))],extension(1165 ^ 1)).
% 0.35/1.38  ncf('1.30',plain,[-(a_select3(u_defuse, 1304 ^ [], 1305 ^ []) = use), leq(n0, 1304 ^ []), leq(n0, 1305 ^ []), leq(1304 ^ [], n2), leq(1305 ^ [], minus(pv5, n1))],extension(1169 ^ 3,bind([[_286545, _286547], [1305 ^ [], 1304 ^ []]]))).
% 0.35/1.38  ncf('1.30.1',plain,[-(leq(n0, 1304 ^ []))],extension(1307 ^ 4)).
% 0.35/1.38  ncf('1.30.2',plain,[-(leq(n0, 1305 ^ []))],extension(1309 ^ 4)).
% 0.35/1.38  ncf('1.30.3',plain,[-(leq(1304 ^ [], n2))],extension(1311 ^ 4)).
% 0.35/1.38  ncf('1.30.4',plain,[-(leq(1305 ^ [], minus(pv5, n1)))],extension(1313 ^ 4)).
% 0.35/1.38  ncf('1.31',plain,[-(a_select3(z_defuse, 1304 ^ [], 1305 ^ []) = use), leq(n0, 1304 ^ []), leq(n0, 1305 ^ []), leq(1304 ^ [], n2), leq(1305 ^ [], minus(pv5, n1))],extension(1169 ^ 3,bind([[_286545, _286547], [1305 ^ [], 1304 ^ []]]))).
% 0.35/1.38  ncf('1.31.1',plain,[-(leq(n0, 1304 ^ []))],extension(1307 ^ 4)).
% 0.35/1.38  ncf('1.31.2',plain,[-(leq(n0, 1305 ^ []))],extension(1309 ^ 4)).
% 0.35/1.38  ncf('1.31.3',plain,[-(leq(1304 ^ [], n2))],extension(1311 ^ 4)).
% 0.35/1.38  ncf('1.31.4',plain,[-(leq(1305 ^ [], minus(pv5, n1)))],extension(1313 ^ 4)).
% 0.35/1.38  %-----------------------------------------------------
% 0.35/1.38  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------