%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SWV097+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n006.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 0.36s 1.38s
% Output   : Proof 0.36s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SWV097+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.03/0.12  % Command  : nanocop.sh %s %d
% 0.13/0.34  % Computer : n006.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 02:21:06 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.36/1.38  
% 0.36/1.38  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 0.36/1.38  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.36/1.38  %-----------------------------------------------------
% 0.36/1.38  ncf(matrix, plain, [(1055 ^ _254912) ^ [] : [-(a_select2(rho_defuse, n0) = use)], (1057 ^ _254912) ^ [] : [-(a_select2(rho_defuse, n1) = use)], (1059 ^ _254912) ^ [] : [-(a_select2(rho_defuse, n2) = use)], (1061 ^ _254912) ^ [] : [-(a_select2(sigma_defuse, n0) = use)], (1063 ^ _254912) ^ [] : [-(a_select2(sigma_defuse, n1) = use)], (1065 ^ _254912) ^ [] : [-(a_select2(sigma_defuse, n2) = use)], (1067 ^ _254912) ^ [] : [-(a_select2(sigma_defuse, n3) = use)], (1069 ^ _254912) ^ [] : [-(a_select2(sigma_defuse, n4) = use)], (1071 ^ _254912) ^ [] : [-(a_select2(sigma_defuse, n5) = use)], (1073 ^ _254912) ^ [] : [-(a_select3(u_defuse, n0, n0) = use)], (1075 ^ _254912) ^ [] : [-(a_select3(u_defuse, n1, n0) = use)], (1077 ^ _254912) ^ [] : [-(a_select3(u_defuse, n2, n0) = use)], (1079 ^ _254912) ^ [] : [-(a_select2(xinit_defuse, n3) = use)], (1081 ^ _254912) ^ [] : [-(a_select2(xinit_defuse, n4) = use)], (1083 ^ _254912) ^ [] : [-(a_select2(xinit_defuse, n5) = use)], (1085 ^ _254912) ^ [] : [-(a_select2(xinit_mean_defuse, n0) = use)], (1087 ^ _254912) ^ [] : [-(a_select2(xinit_mean_defuse, n1) = use)], (1089 ^ _254912) ^ [] : [-(a_select2(xinit_mean_defuse, n2) = use)], (1091 ^ _254912) ^ [] : [-(a_select2(xinit_mean_defuse, n3) = use)], (1093 ^ _254912) ^ [] : [-(a_select2(xinit_mean_defuse, n4) = use)], (1095 ^ _254912) ^ [] : [-(a_select2(xinit_mean_defuse, n5) = use)], (1097 ^ _254912) ^ [] : [-(a_select2(xinit_noise_defuse, n0) = use)], (1099 ^ _254912) ^ [] : [-(a_select2(xinit_noise_defuse, n1) = use)], (1101 ^ _254912) ^ [] : [-(a_select2(xinit_noise_defuse, n2) = use)], (1103 ^ _254912) ^ [] : [-(a_select2(xinit_noise_defuse, n3) = use)], (1105 ^ _254912) ^ [] : [-(a_select2(xinit_noise_defuse, n4) = use)], (1107 ^ _254912) ^ [] : [-(a_select2(xinit_noise_defuse, n5) = use)], (1109 ^ _254912) ^ [] : [-(leq(n0, pv5))], (1111 ^ _254912) ^ [] : [-(leq(pv5, minus(n999, n1)))], (1113 ^ _254912) ^ [_296779, _296781] : [1128 ^ _254912 : [(1129 ^ _254912) ^ [] : [-(a_select3(u_defuse, _296781, _296779) = use)], (1131 ^ _254912) ^ [] : [-(a_select3(z_defuse, _296781, _296779) = use)]], leq(n0, _296781), leq(n0, _296779), leq(_296781, n2), leq(_296779, pv5)], (1133 ^ _254912) ^ [_297327, _297329] : [1148 ^ _254912 : [(1149 ^ _254912) ^ [] : [-(a_select3(u_defuse, _297329, _297327) = use)], (1151 ^ _254912) ^ [] : [-(a_select3(z_defuse, _297329, _297327) = use)]], leq(n0, _297329), leq(n0, _297327), leq(_297329, n2), leq(_297327, minus(pv5, n1))], (1153 ^ _254912) ^ [] : [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)), 1272 ^ _254912 : [(1273 ^ _254912) ^ [] : [-(leq(n0, 1270 ^ []))], (1275 ^ _254912) ^ [] : [-(leq(n0, 1271 ^ []))], (1277 ^ _254912) ^ [] : [-(leq(1270 ^ [], n2))], (1279 ^ _254912) ^ [] : [-(leq(1271 ^ [], pv5))], (1281 ^ _254912) ^ [] : [a_select3(u_defuse, 1270 ^ [], 1271 ^ []) = use, a_select3(z_defuse, 1270 ^ [], 1271 ^ []) = use]], 1288 ^ _254912 : [(1289 ^ _254912) ^ [] : [-(leq(n0, 1286 ^ []))], (1291 ^ _254912) ^ [] : [-(leq(n0, 1287 ^ []))], (1293 ^ _254912) ^ [] : [-(leq(1286 ^ [], n2))], (1295 ^ _254912) ^ [] : [-(leq(1287 ^ [], minus(pv5, n1)))], (1297 ^ _254912) ^ [] : [a_select3(u_defuse, 1286 ^ [], 1287 ^ []) = use, a_select3(z_defuse, 1286 ^ [], 1287 ^ []) = use]]], (2 ^ _254912) ^ [_255056] : [-(_255056 = _255056)], (4 ^ _254912) ^ [_255163, _255165] : [_255165 = _255163, -(_255163 = _255165)], (10 ^ _254912) ^ [_255367, _255369, _255371] : [-(_255371 = _255367), _255371 = _255369, _255369 = _255367], (20 ^ _254912) ^ [_255708, _255710, _255712, _255714] : [-(lt(_255712, _255708)), lt(_255714, _255710), _255714 = _255712, _255710 = _255708], (34 ^ _254912) ^ [_256152, _256154, _256156, _256158] : [-(geq(_256156, _256152)), geq(_256158, _256154), _256158 = _256156, _256154 = _256152], (48 ^ _254912) ^ [_256596, _256598, _256600, _256602] : [-(gt(_256600, _256596)), gt(_256602, _256598), _256602 = _256600, _256598 = _256596], (62 ^ _254912) ^ [_257020, _257022, _257024, _257026] : [-(leq(_257024, _257020)), leq(_257026, _257022), _257026 = _257024, _257022 = _257020], (76 ^ _254912) ^ [_257476, _257478, _257480, _257482] : [-(uniform_int_rnd(_257482, _257478) = uniform_int_rnd(_257480, _257476)), _257482 = _257480, _257478 = _257476], (86 ^ _254912) ^ [_257835, _257837, _257839, _257841] : [-(tptp_const_array1(_257841, _257837) = tptp_const_array1(_257839, _257835)), _257841 = _257839, _257837 = _257835], (96 ^ _254912) ^ [_258222, _258224, _258226, _258228, _258230, _258232] : [-(tptp_const_array2(_258232, _258228, _258224) = tptp_const_array2(_258230, _258226, _258222)), _258232 = _258230, _258228 = _258226, _258224 = _258222], (110 ^ _254912) ^ [_258710, _258712, _258714, _258716] : [-(dim(_258716, _258712) = dim(_258714, _258710)), _258716 = _258714, _258712 = _258710], (120 ^ _254912) ^ [_259041, _259043] : [_259043 = _259041, -(inv(_259043) = inv(_259041))], (126 ^ _254912) ^ [_259287, _259289, _259291, _259293] : [-(tptp_msub(_259293, _259289) = tptp_msub(_259291, _259287)), _259293 = _259291, _259289 = _259287], (136 ^ _254912) ^ [_259646, _259648, _259650, _259652] : [-(tptp_madd(_259652, _259648) = tptp_madd(_259650, _259646)), _259652 = _259650, _259648 = _259646], (146 ^ _254912) ^ [_260005, _260007, _260009, _260011] : [-(tptp_mmul(_260011, _260007) = tptp_mmul(_260009, _260005)), _260011 = _260009, _260007 = _260005], (156 ^ _254912) ^ [_260336, _260338] : [_260338 = _260336, -(trans(_260338) = trans(_260336))], (162 ^ _254912) ^ [_260610, _260612, _260614, _260616, _260618, _260620] : [-(sum(_260620, _260616, _260612) = sum(_260618, _260614, _260610)), _260620 = _260618, _260616 = _260614, _260612 = _260610], (176 ^ _254912) ^ [_261098, _261100, _261102, _261104] : [-(plus(_261104, _261100) = plus(_261102, _261098)), _261104 = _261102, _261100 = _261098], (186 ^ _254912) ^ [_261429, _261431] : [_261431 = _261429, -(pred(_261431) = pred(_261429))], (192 ^ _254912) ^ [_261731, _261733, _261735, _261737, _261739, _261741, _261743, _261745] : [-(tptp_update3(_261745, _261741, _261737, _261733) = tptp_update3(_261743, _261739, _261735, _261731)), _261745 = _261743, _261741 = _261739, _261737 = _261735, _261733 = _261731], (210 ^ _254912) ^ [_262392, _262394, _262396, _262398, _262400, _262402] : [-(tptp_update2(_262402, _262398, _262394) = tptp_update2(_262400, _262396, _262392)), _262402 = _262400, _262398 = _262396, _262394 = _262392], (224 ^ _254912) ^ [_262852, _262854] : [_262854 = _262852, -(succ(_262854) = succ(_262852))], (230 ^ _254912) ^ [_263098, _263100, _263102, _263104] : [-(a_select2(_263104, _263100) = a_select2(_263102, _263098)), _263104 = _263102, _263100 = _263098], (240 ^ _254912) ^ [_263457, _263459, _263461, _263463] : [-(minus(_263463, _263459) = minus(_263461, _263457)), _263463 = _263461, _263459 = _263457], (250 ^ _254912) ^ [_263824, _263826, _263828, _263830, _263832, _263834] : [-(a_select3(_263834, _263830, _263826) = a_select3(_263832, _263828, _263824)), _263834 = _263832, _263830 = _263828, _263826 = _263824], (869 ^ _254912) ^ [] : [-(gt(n5, n4))], (871 ^ _254912) ^ [] : [-(gt(n999, n4))], (873 ^ _254912) ^ [] : [-(gt(n999, n5))], (875 ^ _254912) ^ [] : [-(gt(n4, tptp_minus_1))], (877 ^ _254912) ^ [] : [-(gt(n5, tptp_minus_1))], (879 ^ _254912) ^ [] : [-(gt(n999, tptp_minus_1))], (881 ^ _254912) ^ [] : [-(gt(n0, tptp_minus_1))], (883 ^ _254912) ^ [] : [-(gt(n1, tptp_minus_1))], (885 ^ _254912) ^ [] : [-(gt(n2, tptp_minus_1))], (887 ^ _254912) ^ [] : [-(gt(n3, tptp_minus_1))], (889 ^ _254912) ^ [] : [-(gt(n4, n0))], (891 ^ _254912) ^ [] : [-(gt(n5, n0))], (893 ^ _254912) ^ [] : [-(gt(n999, n0))], (895 ^ _254912) ^ [] : [-(gt(n1, n0))], (897 ^ _254912) ^ [] : [-(gt(n2, n0))], (899 ^ _254912) ^ [] : [-(gt(n3, n0))], (901 ^ _254912) ^ [] : [-(gt(n4, n1))], (903 ^ _254912) ^ [] : [-(gt(n5, n1))], (905 ^ _254912) ^ [] : [-(gt(n999, n1))], (907 ^ _254912) ^ [] : [-(gt(n2, n1))], (909 ^ _254912) ^ [] : [-(gt(n3, n1))], (911 ^ _254912) ^ [] : [-(gt(n4, n2))], (913 ^ _254912) ^ [] : [-(gt(n5, n2))], (915 ^ _254912) ^ [] : [-(gt(n999, n2))], (917 ^ _254912) ^ [] : [-(gt(n3, n2))], (919 ^ _254912) ^ [] : [-(gt(n4, n3))], (921 ^ _254912) ^ [] : [-(gt(n5, n3))], (923 ^ _254912) ^ [] : [-(gt(n999, n3))], (925 ^ _254912) ^ [_291793] : [leq(n0, _291793), leq(_291793, n4), -(_291793 = n0), -(_291793 = n1), -(_291793 = n2), -(_291793 = n3), -(_291793 = n4)], (951 ^ _254912) ^ [_292414] : [leq(n0, _292414), leq(_292414, n5), -(_292414 = n0), -(_292414 = n1), -(_292414 = n2), -(_292414 = n3), -(_292414 = n4), -(_292414 = n5)], (981 ^ _254912) ^ [_293121] : [-(_293121 = n0), leq(n0, _293121), leq(_293121, n0)], (991 ^ _254912) ^ [_293396] : [leq(n0, _293396), leq(_293396, n1), -(_293396 = n0), -(_293396 = n1)], (1005 ^ _254912) ^ [_293759] : [leq(n0, _293759), leq(_293759, n2), -(_293759 = n0), -(_293759 = n1), -(_293759 = n2)], (1045 ^ _254912) ^ [] : [-(succ(succ(succ(succ(n0)))) = n4)], (1047 ^ _254912) ^ [] : [-(succ(succ(succ(succ(succ(n0))))) = n5)], (1049 ^ _254912) ^ [] : [-(succ(n0) = n1)], (1051 ^ _254912) ^ [] : [-(succ(succ(n0)) = n2)], (1053 ^ _254912) ^ [] : [-(succ(succ(succ(n0))) = n3)], (1023 ^ _254912) ^ [_294208] : [leq(n0, _294208), leq(_294208, n3), -(_294208 = n0), -(_294208 = n1), -(_294208 = n2), -(_294208 = n3)], (264 ^ _254912) ^ [_264384, _264386] : [-(gt(_264386, _264384)), -(gt(_264384, _264386)), -(_264386 = _264384)], (274 ^ _254912) ^ [_264699, _264701, _264703] : [-(gt(_264703, _264699)), gt(_264703, _264701), gt(_264701, _264699)], (284 ^ _254912) ^ [_264978] : [gt(_264978, _264978)], (286 ^ _254912) ^ [_265056] : [-(leq(_265056, _265056))], (288 ^ _254912) ^ [_265177, _265179, _265181] : [-(leq(_265181, _265177)), leq(_265181, _265179), leq(_265179, _265177)], (298 ^ _254912) ^ [_265515, _265517] : [lt(_265517, _265515), -(gt(_265515, _265517))], (304 ^ _254912) ^ [_265677, _265679] : [gt(_265677, _265679), -(lt(_265679, _265677))], (310 ^ _254912) ^ [_265918, _265920] : [geq(_265920, _265918), -(leq(_265918, _265920))], (316 ^ _254912) ^ [_266080, _266082] : [leq(_266080, _266082), -(geq(_266082, _266080))], (322 ^ _254912) ^ [_266292, _266294] : [gt(_266292, _266294), -(leq(_266294, _266292))], (328 ^ _254912) ^ [_266502, _266504] : [-(gt(_266502, _266504)), leq(_266504, _266502), -(_266504 = _266502)], (338 ^ _254912) ^ [_266833, _266835] : [leq(_266835, pred(_266833)), -(gt(_266833, _266835))], (344 ^ _254912) ^ [_266999, _267001] : [gt(_266999, _267001), -(leq(_267001, pred(_266999)))], (350 ^ _254912) ^ [_267186] : [-(gt(succ(_267186), _267186))], (352 ^ _254912) ^ [_267295, _267297] : [leq(_267297, _267295), -(leq(_267297, succ(_267295)))], (358 ^ _254912) ^ [_267538, _267540] : [leq(_267540, _267538), -(gt(succ(_267538), _267540))], (364 ^ _254912) ^ [_267704, _267706] : [gt(succ(_267704), _267706), -(leq(_267706, _267704))], (370 ^ _254912) ^ [_267920, _267922] : [leq(n0, _267922), -(leq(uniform_int_rnd(_267920, _267922), _267922))], (376 ^ _254912) ^ [_268136, _268138] : [leq(n0, _268138), -(leq(n0, uniform_int_rnd(_268136, _268138)))], (382 ^ _254912) ^ [_268380, _268382, _268384, _268386] : [-(a_select2(tptp_const_array1(dim(_268384, _268382), _268380), _268386) = _268380), leq(_268384, _268386), leq(_268386, _268382)], (392 ^ _254912) ^ [_268787, _268789, _268791, _268793, _268795, _268797, _268799] : [-(a_select3(tptp_const_array2(dim(_268797, _268795), dim(_268791, _268789), _268787), _268799, _268793) = _268787), leq(_268797, _268799), leq(_268799, _268795), leq(_268791, _268793), leq(_268793, _268789)], (410 ^ _254912) ^ [_269382, _269384] : [413 ^ _254912 : [(414 ^ _254912) ^ [] : [-(leq(n0, 411 ^ [_269382, _269384]))], (416 ^ _254912) ^ [] : [-(leq(411 ^ [_269382, _269384], _269382))], (418 ^ _254912) ^ [] : [-(leq(n0, 412 ^ [_269382, _269384]))], (420 ^ _254912) ^ [] : [-(leq(412 ^ [_269382, _269384], _269382))], (422 ^ _254912) ^ [] : [a_select3(_269384, 411 ^ [_269382, _269384], 412 ^ [_269382, _269384]) = a_select3(_269384, 412 ^ [_269382, _269384], 411 ^ [_269382, _269384])]], 423 ^ _254912 : [(424 ^ _254912) ^ [_270139, _270141] : [-(a_select3(trans(_269384), _270141, _270139) = a_select3(trans(_269384), _270139, _270141)), leq(n0, _270141), leq(_270141, _269382), leq(n0, _270139), leq(_270139, _269382)]]], (442 ^ _254912) ^ [_270686, _270688] : [445 ^ _254912 : [(446 ^ _254912) ^ [] : [-(leq(n0, 443 ^ [_270686, _270688]))], (448 ^ _254912) ^ [] : [-(leq(443 ^ [_270686, _270688], _270686))], (450 ^ _254912) ^ [] : [-(leq(n0, 444 ^ [_270686, _270688]))], (452 ^ _254912) ^ [] : [-(leq(444 ^ [_270686, _270688], _270686))], (454 ^ _254912) ^ [] : [a_select3(_270688, 443 ^ [_270686, _270688], 444 ^ [_270686, _270688]) = a_select3(_270688, 444 ^ [_270686, _270688], 443 ^ [_270686, _270688])]], 455 ^ _254912 : [(456 ^ _254912) ^ [_271443, _271445] : [-(a_select3(inv(_270688), _271445, _271443) = a_select3(inv(_270688), _271443, _271445)), leq(n0, _271445), leq(_271445, _270686), leq(n0, _271443), leq(_271443, _270686)]]], (474 ^ _254912) ^ [_271990, _271992] : [477 ^ _254912 : [(478 ^ _254912) ^ [] : [-(leq(n0, 475 ^ [_271990, _271992]))], (480 ^ _254912) ^ [] : [-(leq(475 ^ [_271990, _271992], _271990))], (482 ^ _254912) ^ [] : [-(leq(n0, 476 ^ [_271990, _271992]))], (484 ^ _254912) ^ [] : [-(leq(476 ^ [_271990, _271992], _271990))], (486 ^ _254912) ^ [] : [a_select3(_271992, 475 ^ [_271990, _271992], 476 ^ [_271990, _271992]) = a_select3(_271992, 476 ^ [_271990, _271992], 475 ^ [_271990, _271992])]], 487 ^ _254912 : [(488 ^ _254912) ^ [_272803, _272805, _272807, _272809] : [-(a_select3(tptp_update3(_271992, _272805, _272805, _272803), _272809, _272807) = a_select3(tptp_update3(_271992, _272805, _272805, _272803), _272807, _272809)), leq(n0, _272809), leq(_272809, _271990), leq(n0, _272807), leq(_272807, _271990), leq(n0, _272805), leq(_272805, _271990)]]], (514 ^ _254912) ^ [_273622, _273624, _273626] : [519 ^ _254912 : [(520 ^ _254912) ^ [] : [-(leq(n0, 517 ^ [_273622, _273624, _273626]))], (522 ^ _254912) ^ [] : [-(leq(517 ^ [_273622, _273624, _273626], _273622))], (524 ^ _254912) ^ [] : [-(leq(n0, 518 ^ [_273622, _273624, _273626]))], (526 ^ _254912) ^ [] : [-(leq(518 ^ [_273622, _273624, _273626], _273622))], (528 ^ _254912) ^ [] : [a_select3(_273626, 517 ^ [_273622, _273624, _273626], 518 ^ [_273622, _273624, _273626]) = a_select3(_273626, 518 ^ [_273622, _273624, _273626], 517 ^ [_273622, _273624, _273626])]], 531 ^ _254912 : [(532 ^ _254912) ^ [] : [-(leq(n0, 529 ^ [_273622, _273624, _273626]))], (534 ^ _254912) ^ [] : [-(leq(529 ^ [_273622, _273624, _273626], _273622))], (536 ^ _254912) ^ [] : [-(leq(n0, 530 ^ [_273622, _273624, _273626]))], (538 ^ _254912) ^ [] : [-(leq(530 ^ [_273622, _273624, _273626], _273622))], (540 ^ _254912) ^ [] : [a_select3(_273624, 529 ^ [_273622, _273624, _273626], 530 ^ [_273622, _273624, _273626]) = a_select3(_273624, 530 ^ [_273622, _273624, _273626], 529 ^ [_273622, _273624, _273626])]], 541 ^ _254912 : [(542 ^ _254912) ^ [_275131, _275133] : [-(a_select3(tptp_madd(_273626, _273624), _275133, _275131) = a_select3(tptp_madd(_273626, _273624), _275131, _275133)), leq(n0, _275133), leq(_275133, _273622), leq(n0, _275131), leq(_275131, _273622)]]], (560 ^ _254912) ^ [_275717, _275719, _275721] : [565 ^ _254912 : [(566 ^ _254912) ^ [] : [-(leq(n0, 563 ^ [_275717, _275719, _275721]))], (568 ^ _254912) ^ [] : [-(leq(563 ^ [_275717, _275719, _275721], _275717))], (570 ^ _254912) ^ [] : [-(leq(n0, 564 ^ [_275717, _275719, _275721]))], (572 ^ _254912) ^ [] : [-(leq(564 ^ [_275717, _275719, _275721], _275717))], (574 ^ _254912) ^ [] : [a_select3(_275721, 563 ^ [_275717, _275719, _275721], 564 ^ [_275717, _275719, _275721]) = a_select3(_275721, 564 ^ [_275717, _275719, _275721], 563 ^ [_275717, _275719, _275721])]], 577 ^ _254912 : [(578 ^ _254912) ^ [] : [-(leq(n0, 575 ^ [_275717, _275719, _275721]))], (580 ^ _254912) ^ [] : [-(leq(575 ^ [_275717, _275719, _275721], _275717))], (582 ^ _254912) ^ [] : [-(leq(n0, 576 ^ [_275717, _275719, _275721]))], (584 ^ _254912) ^ [] : [-(leq(576 ^ [_275717, _275719, _275721], _275717))], (586 ^ _254912) ^ [] : [a_select3(_275719, 575 ^ [_275717, _275719, _275721], 576 ^ [_275717, _275719, _275721]) = a_select3(_275719, 576 ^ [_275717, _275719, _275721], 575 ^ [_275717, _275719, _275721])]], 587 ^ _254912 : [(588 ^ _254912) ^ [_277226, _277228] : [-(a_select3(tptp_msub(_275721, _275719), _277228, _277226) = a_select3(tptp_msub(_275721, _275719), _277226, _277228)), leq(n0, _277228), leq(_277228, _275717), leq(n0, _277226), leq(_277226, _275717)]]], (606 ^ _254912) ^ [_277812, _277814, _277816] : [609 ^ _254912 : [(610 ^ _254912) ^ [] : [-(leq(n0, 607 ^ [_277812, _277814, _277816]))], (612 ^ _254912) ^ [] : [-(leq(607 ^ [_277812, _277814, _277816], _277812))], (614 ^ _254912) ^ [] : [-(leq(n0, 608 ^ [_277812, _277814, _277816]))], (616 ^ _254912) ^ [] : [-(leq(608 ^ [_277812, _277814, _277816], _277812))], (618 ^ _254912) ^ [] : [a_select3(_277814, 607 ^ [_277812, _277814, _277816], 608 ^ [_277812, _277814, _277816]) = a_select3(_277814, 608 ^ [_277812, _277814, _277816], 607 ^ [_277812, _277814, _277816])]], 619 ^ _254912 : [(620 ^ _254912) ^ [_278625, _278627] : [-(a_select3(tptp_mmul(_277816, tptp_mmul(_277814, trans(_277816))), _278627, _278625) = a_select3(tptp_mmul(_277816, tptp_mmul(_277814, trans(_277816))), _278625, _278627)), leq(n0, _278627), leq(_278627, _277812), leq(n0, _278625), leq(_278625, _277812)]]], (638 ^ _254912) ^ [_279244, _279246, _279248, _279250] : [641 ^ _254912 : [(642 ^ _254912) ^ [] : [-(leq(n0, 639 ^ [_279244, _279246, _279248, _279250]))], (644 ^ _254912) ^ [] : [-(leq(639 ^ [_279244, _279246, _279248, _279250], _279244))], (646 ^ _254912) ^ [] : [-(leq(n0, 640 ^ [_279244, _279246, _279248, _279250]))], (648 ^ _254912) ^ [] : [-(leq(640 ^ [_279244, _279246, _279248, _279250], _279244))], (650 ^ _254912) ^ [] : [a_select3(_279248, 639 ^ [_279244, _279246, _279248, _279250], 640 ^ [_279244, _279246, _279248, _279250]) = a_select3(_279248, 640 ^ [_279244, _279246, _279248, _279250], 639 ^ [_279244, _279246, _279248, _279250])]], 651 ^ _254912 : [(652 ^ _254912) ^ [_280101, _280103] : [-(a_select3(tptp_mmul(_279250, tptp_mmul(_279248, trans(_279250))), _280103, _280101) = a_select3(tptp_mmul(_279250, tptp_mmul(_279248, trans(_279250))), _280101, _280103)), leq(n0, _280103), leq(_280103, _279246), leq(n0, _280101), leq(_280101, _279246)]]], (670 ^ _254912) ^ [_280796, _280798, _280800, _280802, _280804, _280806, _280808, _280810] : [675 ^ _254912 : [(676 ^ _254912) ^ [] : [-(leq(n0, 673 ^ [_280796, _280798, _280800, _280802, _280804, _280806, _280808, _280810]))], (678 ^ _254912) ^ [] : [-(leq(673 ^ [_280796, _280798, _280800, _280802, _280804, _280806, _280808, _280810], _280796))], (680 ^ _254912) ^ [] : [-(leq(n0, 674 ^ [_280796, _280798, _280800, _280802, _280804, _280806, _280808, _280810]))], (682 ^ _254912) ^ [] : [-(leq(674 ^ [_280796, _280798, _280800, _280802, _280804, _280806, _280808, _280810], _280796))], (684 ^ _254912) ^ [] : [a_select3(_280804, 673 ^ [_280796, _280798, _280800, _280802, _280804, _280806, _280808, _280810], 674 ^ [_280796, _280798, _280800, _280802, _280804, _280806, _280808, _280810]) = a_select3(_280804, 674 ^ [_280796, _280798, _280800, _280802, _280804, _280806, _280808, _280810], 673 ^ [_280796, _280798, _280800, _280802, _280804, _280806, _280808, _280810])]], 689 ^ _254912 : [(690 ^ _254912) ^ [] : [-(leq(n0, 687 ^ [_280796, _280798, _280800, _280802, _280804, _280806, _280808, _280810]))], (692 ^ _254912) ^ [] : [-(leq(687 ^ [_280796, _280798, _280800, _280802, _280804, _280806, _280808, _280810], _280798))], (694 ^ _254912) ^ [] : [-(leq(n0, 688 ^ [_280796, _280798, _280800, _280802, _280804, _280806, _280808, _280810]))], (696 ^ _254912) ^ [] : [-(leq(688 ^ [_280796, _280798, _280800, _280802, _280804, _280806, _280808, _280810], _280798))], (698 ^ _254912) ^ [] : [a_select3(_280810, 687 ^ [_280796, _280798, _280800, _280802, _280804, _280806, _280808, _280810], 688 ^ [_280796, _280798, _280800, _280802, _280804, _280806, _280808, _280810]) = a_select3(_280810, 688 ^ [_280796, _280798, _280800, _280802, _280804, _280806, _280808, _280810], 687 ^ [_280796, _280798, _280800, _280802, _280804, _280806, _280808, _280810])]], 701 ^ _254912 : [(702 ^ _254912) ^ [] : [-(leq(n0, 699 ^ [_280796, _280798, _280800, _280802, _280804, _280806, _280808, _280810]))], (704 ^ _254912) ^ [] : [-(leq(699 ^ [_280796, _280798, _280800, _280802, _280804, _280806, _280808, _280810], _280798))], (706 ^ _254912) ^ [] : [-(leq(n0, 700 ^ [_280796, _280798, _280800, _280802, _280804, _280806, _280808, _280810]))], (708 ^ _254912) ^ [] : [-(leq(700 ^ [_280796, _280798, _280800, _280802, _280804, _280806, _280808, _280810], _280798))], (710 ^ _254912) ^ [] : [a_select3(_280800, 699 ^ [_280796, _280798, _280800, _280802, _280804, _280806, _280808, _280810], 700 ^ [_280796, _280798, _280800, _280802, _280804, _280806, _280808, _280810]) = a_select3(_280800, 700 ^ [_280796, _280798, _280800, _280802, _280804, _280806, _280808, _280810], 699 ^ [_280796, _280798, _280800, _280802, _280804, _280806, _280808, _280810])]], 711 ^ _254912 : [(712 ^ _254912) ^ [_283724, _283726] : [-(a_select3(tptp_madd(_280810, tptp_mmul(_280808, tptp_mmul(tptp_madd(tptp_mmul(_280806, tptp_mmul(_280804, trans(_280806))), tptp_mmul(_280802, tptp_mmul(_280800, trans(_280802)))), trans(_280808)))), _283726, _283724) = a_select3(tptp_madd(_280810, tptp_mmul(_280808, tptp_mmul(tptp_madd(tptp_mmul(_280806, tptp_mmul(_280804, trans(_280806))), tptp_mmul(_280802, tptp_mmul(_280800, trans(_280802)))), trans(_280808)))), _283724, _283726)), leq(n0, _283726), leq(_283726, _280798), leq(n0, _283724), leq(_283724, _280798)]]], (730 ^ _254912) ^ [_284477] : [-(sum(n0, tptp_minus_1, _284477) = n0)], (732 ^ _254912) ^ [_284559] : [-(tptp_float_0_0 = sum(n0, tptp_minus_1, _284559))], (734 ^ _254912) ^ [] : [-(succ(tptp_minus_1) = n0)], (736 ^ _254912) ^ [_284694] : [-(plus(_284694, n1) = succ(_284694))], (738 ^ _254912) ^ [_284777] : [-(plus(n1, _284777) = succ(_284777))], (740 ^ _254912) ^ [_284860] : [-(plus(_284860, n2) = succ(succ(_284860)))], (742 ^ _254912) ^ [_284945] : [-(plus(n2, _284945) = succ(succ(_284945)))], (744 ^ _254912) ^ [_285030] : [-(plus(_285030, n3) = succ(succ(succ(_285030))))], (746 ^ _254912) ^ [_285117] : [-(plus(n3, _285117) = succ(succ(succ(_285117))))], (748 ^ _254912) ^ [_285204] : [-(plus(_285204, n4) = succ(succ(succ(succ(_285204)))))], (750 ^ _254912) ^ [_285293] : [-(plus(n4, _285293) = succ(succ(succ(succ(_285293)))))], (752 ^ _254912) ^ [_285382] : [-(plus(_285382, n5) = succ(succ(succ(succ(succ(_285382))))))], (754 ^ _254912) ^ [_285473] : [-(plus(n5, _285473) = succ(succ(succ(succ(succ(_285473))))))], (756 ^ _254912) ^ [_285564] : [-(minus(_285564, n1) = pred(_285564))], (758 ^ _254912) ^ [_285647] : [-(pred(succ(_285647)) = _285647)], (760 ^ _254912) ^ [_285729] : [-(succ(pred(_285729)) = _285729)], (762 ^ _254912) ^ [_285869, _285871] : [leq(succ(_285871), succ(_285869)), -(leq(_285871, _285869))], (768 ^ _254912) ^ [_286039, _286041] : [leq(_286041, _286039), -(leq(succ(_286041), succ(_286039)))], (774 ^ _254912) ^ [_286259, _286261] : [leq(succ(_286261), _286259), -(gt(_286259, _286261))], (780 ^ _254912) ^ [_286473, _286475] : [leq(minus(_286475, _286473), _286475), -(leq(n0, _286473))], (786 ^ _254912) ^ [_286702, _286704, _286706, _286708] : [-(a_select3(tptp_update3(_286708, _286706, _286704, _286702), _286706, _286704) = _286702)], (788 ^ _254912) ^ [_286894, _286896, _286898, _286900, _286902, _286904, _286906] : [-(a_select3(tptp_update3(_286898, _286906, _286904, _286894), _286902, _286900) = _286896), -(_286906 = _286902), _286904 = _286900, a_select3(_286898, _286902, _286900) = _286896], (802 ^ _254912) ^ [_287437, _287439, _287441, _287443, _287445, _287447] : [-(a_select3(tptp_update3(_287439, _287443, _287441, _287437), _287447, _287445) = _287437), 807 ^ _254912 : [(808 ^ _254912) ^ [] : [-(leq(n0, 805 ^ [_287437, _287439, _287441, _287443, _287445, _287447]))], (810 ^ _254912) ^ [] : [-(leq(n0, 806 ^ [_287437, _287439, _287441, _287443, _287445, _287447]))], (812 ^ _254912) ^ [] : [-(leq(805 ^ [_287437, _287439, _287441, _287443, _287445, _287447], _287443))], (814 ^ _254912) ^ [] : [-(leq(806 ^ [_287437, _287439, _287441, _287443, _287445, _287447], _287441))], (816 ^ _254912) ^ [] : [a_select3(_287439, 805 ^ [_287437, _287439, _287441, _287443, _287445, _287447], 806 ^ [_287437, _287439, _287441, _287443, _287445, _287447]) = _287437]], leq(n0, _287447), leq(_287447, _287443), leq(n0, _287445), leq(_287445, _287441)], (834 ^ _254912) ^ [_288779, _288781, _288783] : [-(a_select2(tptp_update2(_288783, _288781, _288779), _288781) = _288779)], (836 ^ _254912) ^ [_288939, _288941, _288943, _288945, _288947] : [-(a_select2(tptp_update2(_288943, _288947, _288939), _288945) = _288941), -(_288947 = _288945), a_select2(_288943, _288945) = _288941], (865 ^ _254912) ^ [] : [-(true)], (867 ^ _254912) ^ [] : [def = use], (846 ^ _254912) ^ [_289319, _289321, _289323, _289325] : [-(a_select2(tptp_update2(_289321, _289323, _289319), _289325) = _289319), 850 ^ _254912 : [(851 ^ _254912) ^ [] : [-(leq(n0, 849 ^ [_289319, _289321, _289323, _289325]))], (853 ^ _254912) ^ [] : [-(leq(849 ^ [_289319, _289321, _289323, _289325], _289323))], (855 ^ _254912) ^ [] : [a_select2(_289321, 849 ^ [_289319, _289321, _289323, _289325]) = _289319]], leq(n0, _289325), leq(_289325, _289323)]], input).
% 0.36/1.38  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)), 1281 : a_select3(u_defuse, 1270 ^ [], 1271 ^ []) = use, 1281 : a_select3(z_defuse, 1270 ^ [], 1271 ^ []) = use, 1297 : a_select3(u_defuse, 1286 ^ [], 1287 ^ []) = use, 1297 : a_select3(z_defuse, 1286 ^ [], 1287 ^ []) = use],start(1153 ^ 0)).
% 0.36/1.38  ncf('1.1',plain,[-(a_select2(rho_defuse, n0) = use)],extension(1055 ^ 1)).
% 0.36/1.38  ncf('1.2',plain,[-(a_select2(rho_defuse, n1) = use)],extension(1057 ^ 1)).
% 0.36/1.38  ncf('1.3',plain,[-(a_select2(rho_defuse, n2) = use)],extension(1059 ^ 1)).
% 0.36/1.38  ncf('1.4',plain,[-(a_select2(sigma_defuse, n0) = use)],extension(1061 ^ 1)).
% 0.36/1.38  ncf('1.5',plain,[-(a_select2(sigma_defuse, n1) = use)],extension(1063 ^ 1)).
% 0.36/1.38  ncf('1.6',plain,[-(a_select2(sigma_defuse, n2) = use)],extension(1065 ^ 1)).
% 0.36/1.38  ncf('1.7',plain,[-(a_select2(sigma_defuse, n3) = use)],extension(1067 ^ 1)).
% 0.36/1.38  ncf('1.8',plain,[-(a_select2(sigma_defuse, n4) = use)],extension(1069 ^ 1)).
% 0.36/1.38  ncf('1.9',plain,[-(a_select2(sigma_defuse, n5) = use)],extension(1071 ^ 1)).
% 0.36/1.38  ncf('1.10',plain,[-(a_select3(u_defuse, n0, n0) = use)],extension(1073 ^ 1)).
% 0.36/1.38  ncf('1.11',plain,[-(a_select3(u_defuse, n1, n0) = use)],extension(1075 ^ 1)).
% 0.36/1.38  ncf('1.12',plain,[-(a_select3(u_defuse, n2, n0) = use)],extension(1077 ^ 1)).
% 0.36/1.38  ncf('1.13',plain,[-(a_select2(xinit_defuse, n3) = use)],extension(1079 ^ 1)).
% 0.36/1.38  ncf('1.14',plain,[-(a_select2(xinit_defuse, n4) = use)],extension(1081 ^ 1)).
% 0.36/1.38  ncf('1.15',plain,[-(a_select2(xinit_defuse, n5) = use)],extension(1083 ^ 1)).
% 0.36/1.38  ncf('1.16',plain,[-(a_select2(xinit_mean_defuse, n0) = use)],extension(1085 ^ 1)).
% 0.36/1.38  ncf('1.17',plain,[-(a_select2(xinit_mean_defuse, n1) = use)],extension(1087 ^ 1)).
% 0.36/1.38  ncf('1.18',plain,[-(a_select2(xinit_mean_defuse, n2) = use)],extension(1089 ^ 1)).
% 0.36/1.38  ncf('1.19',plain,[-(a_select2(xinit_mean_defuse, n3) = use)],extension(1091 ^ 1)).
% 0.36/1.38  ncf('1.20',plain,[-(a_select2(xinit_mean_defuse, n4) = use)],extension(1093 ^ 1)).
% 0.36/1.38  ncf('1.21',plain,[-(a_select2(xinit_mean_defuse, n5) = use)],extension(1095 ^ 1)).
% 0.36/1.38  ncf('1.22',plain,[-(a_select2(xinit_noise_defuse, n0) = use)],extension(1097 ^ 1)).
% 0.36/1.38  ncf('1.23',plain,[-(a_select2(xinit_noise_defuse, n1) = use)],extension(1099 ^ 1)).
% 0.36/1.38  ncf('1.24',plain,[-(a_select2(xinit_noise_defuse, n2) = use)],extension(1101 ^ 1)).
% 0.36/1.38  ncf('1.25',plain,[-(a_select2(xinit_noise_defuse, n3) = use)],extension(1103 ^ 1)).
% 0.36/1.38  ncf('1.26',plain,[-(a_select2(xinit_noise_defuse, n4) = use)],extension(1105 ^ 1)).
% 0.36/1.38  ncf('1.27',plain,[-(a_select2(xinit_noise_defuse, n5) = use)],extension(1107 ^ 1)).
% 0.36/1.38  ncf('1.28',plain,[-(leq(n0, pv5))],extension(1109 ^ 1)).
% 0.36/1.38  ncf('1.29',plain,[-(leq(pv5, minus(n999, n1)))],extension(1111 ^ 1)).
% 0.36/1.38  ncf('1.30',plain,[-(a_select3(u_defuse, 1270 ^ [], 1271 ^ []) = use), leq(n0, 1270 ^ []), leq(n0, 1271 ^ []), leq(1270 ^ [], n2), leq(1271 ^ [], pv5)],extension(1113 ^ 3,bind([[_296779, _296781], [1271 ^ [], 1270 ^ []]]))).
% 0.36/1.38  ncf('1.30.1',plain,[-(leq(n0, 1270 ^ []))],extension(1273 ^ 4)).
% 0.36/1.38  ncf('1.30.2',plain,[-(leq(n0, 1271 ^ []))],extension(1275 ^ 4)).
% 0.36/1.38  ncf('1.30.3',plain,[-(leq(1270 ^ [], n2))],extension(1277 ^ 4)).
% 0.36/1.38  ncf('1.30.4',plain,[-(leq(1271 ^ [], pv5))],extension(1279 ^ 4)).
% 0.36/1.38  ncf('1.31',plain,[-(a_select3(z_defuse, 1270 ^ [], 1271 ^ []) = use), leq(n0, 1270 ^ []), leq(n0, 1271 ^ []), leq(1270 ^ [], n2), leq(1271 ^ [], pv5)],extension(1113 ^ 3,bind([[_296779, _296781], [1271 ^ [], 1270 ^ []]]))).
% 0.36/1.38  ncf('1.31.1',plain,[-(leq(n0, 1270 ^ []))],extension(1273 ^ 4)).
% 0.36/1.38  ncf('1.31.2',plain,[-(leq(n0, 1271 ^ []))],extension(1275 ^ 4)).
% 0.36/1.38  ncf('1.31.3',plain,[-(leq(1270 ^ [], n2))],extension(1277 ^ 4)).
% 0.36/1.38  ncf('1.31.4',plain,[-(leq(1271 ^ [], pv5))],extension(1279 ^ 4)).
% 0.36/1.38  ncf('1.32',plain,[-(a_select3(u_defuse, 1286 ^ [], 1287 ^ []) = use), leq(n0, 1286 ^ []), leq(n0, 1287 ^ []), leq(1286 ^ [], n2), leq(1287 ^ [], minus(pv5, n1))],extension(1133 ^ 3,bind([[_297327, _297329], [1287 ^ [], 1286 ^ []]]))).
% 0.36/1.38  ncf('1.32.1',plain,[-(leq(n0, 1286 ^ []))],extension(1289 ^ 4)).
% 0.36/1.38  ncf('1.32.2',plain,[-(leq(n0, 1287 ^ []))],extension(1291 ^ 4)).
% 0.36/1.38  ncf('1.32.3',plain,[-(leq(1286 ^ [], n2))],extension(1293 ^ 4)).
% 0.36/1.38  ncf('1.32.4',plain,[-(leq(1287 ^ [], minus(pv5, n1)))],extension(1295 ^ 4)).
% 0.36/1.38  ncf('1.33',plain,[-(a_select3(z_defuse, 1286 ^ [], 1287 ^ []) = use), leq(n0, 1286 ^ []), leq(n0, 1287 ^ []), leq(1286 ^ [], n2), leq(1287 ^ [], minus(pv5, n1))],extension(1133 ^ 3,bind([[_297327, _297329], [1287 ^ [], 1286 ^ []]]))).
% 0.36/1.38  ncf('1.33.1',plain,[-(leq(n0, 1286 ^ []))],extension(1289 ^ 4)).
% 0.36/1.38  ncf('1.33.2',plain,[-(leq(n0, 1287 ^ []))],extension(1291 ^ 4)).
% 0.36/1.38  ncf('1.33.3',plain,[-(leq(1286 ^ [], n2))],extension(1293 ^ 4)).
% 0.36/1.38  ncf('1.33.4',plain,[-(leq(1287 ^ [], minus(pv5, n1)))],extension(1295 ^ 4)).
% 0.36/1.38  %-----------------------------------------------------
% 0.36/1.38  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------