%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SWV153+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n027.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 12:20:04 EDT 2023

% Result   : Theorem 1.14s 1.38s
% Output   : Proof 1.14s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SWV153+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.07/0.13  % Command  : nanocop.sh %s %d
% 0.13/0.34  % Computer : n027.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 02:43:51 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 1.14/1.38  
% 1.14/1.38  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 1.14/1.38  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.14/1.38  %-----------------------------------------------------
% 1.14/1.38  ncf(matrix, plain, [(1112 ^ _214774) ^ [] : [-(leq(n0, 1110 ^ []))], (1114 ^ _214774) ^ [] : [-(leq(1110 ^ [], pv12))], (1116 ^ _214774) ^ [] : [pv12 = 1110 ^ []], (1118 ^ _214774) ^ [] : [a_select3(q, pv10, 1110 ^ []) = divide(sqrt(times(minus(a_select3(center, 1110 ^ [], n0), a_select2(x, pv10)), minus(a_select3(center, 1110 ^ [], n0), a_select2(x, pv10)))), sum(n0, n4, sqrt(times(minus(a_select3(center, tptp_sum_index, n0), a_select2(x, pv10)), minus(a_select3(center, tptp_sum_index, n0), a_select2(x, pv10))))))], (1081 ^ _214774) ^ [] : [-(pv70 = sum(n0, n4, sqrt(times(minus(a_select3(center, tptp_sum_index, n0), a_select2(x, pv10)), minus(a_select3(center, tptp_sum_index, n0), a_select2(x, pv10))))))], (1083 ^ _214774) ^ [] : [-(leq(n0, pv10))], (1085 ^ _214774) ^ [] : [-(leq(n0, pv12))], (1087 ^ _214774) ^ [] : [-(leq(pv10, n135299))], (1089 ^ _214774) ^ [] : [-(leq(pv12, n4))], (1091 ^ _214774) ^ [_256311] : [-(a_select3(q, pv10, _256311) = divide(sqrt(times(minus(a_select3(center, _256311, n0), a_select2(x, pv10)), minus(a_select3(center, _256311, n0), a_select2(x, pv10)))), sum(n0, n4, sqrt(times(minus(a_select3(center, tptp_sum_index, n0), a_select2(x, pv10)), minus(a_select3(center, tptp_sum_index, n0), a_select2(x, pv10))))))), leq(n0, _256311), leq(_256311, pred(pv12))], (1101 ^ _214774) ^ [_256618] : [-(sum(n0, n4, a_select3(q, _256618, tptp_sum_index)) = n1), leq(n0, _256618), leq(_256618, pred(pv10))], (2 ^ _214774) ^ [_214918] : [-(_214918 = _214918)], (4 ^ _214774) ^ [_215025, _215027] : [_215027 = _215025, -(_215025 = _215027)], (10 ^ _214774) ^ [_215229, _215231, _215233] : [-(_215233 = _215229), _215233 = _215231, _215231 = _215229], (20 ^ _214774) ^ [_215570, _215572, _215574, _215576] : [-(lt(_215574, _215570)), lt(_215576, _215572), _215576 = _215574, _215572 = _215570], (34 ^ _214774) ^ [_216014, _216016, _216018, _216020] : [-(geq(_216018, _216014)), geq(_216020, _216016), _216020 = _216018, _216016 = _216014], (48 ^ _214774) ^ [_216458, _216460, _216462, _216464] : [-(gt(_216462, _216458)), gt(_216464, _216460), _216464 = _216462, _216460 = _216458], (62 ^ _214774) ^ [_216882, _216884, _216886, _216888] : [-(leq(_216886, _216882)), leq(_216888, _216884), _216888 = _216886, _216884 = _216882], (76 ^ _214774) ^ [_217338, _217340, _217342, _217344] : [-(uniform_int_rnd(_217344, _217340) = uniform_int_rnd(_217342, _217338)), _217344 = _217342, _217340 = _217338], (86 ^ _214774) ^ [_217697, _217699, _217701, _217703] : [-(tptp_const_array1(_217703, _217699) = tptp_const_array1(_217701, _217697)), _217703 = _217701, _217699 = _217697], (96 ^ _214774) ^ [_218084, _218086, _218088, _218090, _218092, _218094] : [-(tptp_const_array2(_218094, _218090, _218086) = tptp_const_array2(_218092, _218088, _218084)), _218094 = _218092, _218090 = _218088, _218086 = _218084], (110 ^ _214774) ^ [_218572, _218574, _218576, _218578] : [-(dim(_218578, _218574) = dim(_218576, _218572)), _218578 = _218576, _218574 = _218572], (120 ^ _214774) ^ [_218903, _218905] : [_218905 = _218903, -(inv(_218905) = inv(_218903))], (126 ^ _214774) ^ [_219149, _219151, _219153, _219155] : [-(tptp_msub(_219155, _219151) = tptp_msub(_219153, _219149)), _219155 = _219153, _219151 = _219149], (136 ^ _214774) ^ [_219508, _219510, _219512, _219514] : [-(tptp_madd(_219514, _219510) = tptp_madd(_219512, _219508)), _219514 = _219512, _219510 = _219508], (146 ^ _214774) ^ [_219867, _219869, _219871, _219873] : [-(tptp_mmul(_219873, _219869) = tptp_mmul(_219871, _219867)), _219873 = _219871, _219869 = _219867], (156 ^ _214774) ^ [_220198, _220200] : [_220200 = _220198, -(trans(_220200) = trans(_220198))], (162 ^ _214774) ^ [_220444, _220446, _220448, _220450] : [-(plus(_220450, _220446) = plus(_220448, _220444)), _220450 = _220448, _220446 = _220444], (172 ^ _214774) ^ [_220859, _220861, _220863, _220865, _220867, _220869, _220871, _220873] : [-(tptp_update3(_220873, _220869, _220865, _220861) = tptp_update3(_220871, _220867, _220863, _220859)), _220873 = _220871, _220869 = _220867, _220865 = _220863, _220861 = _220859], (190 ^ _214774) ^ [_221520, _221522, _221524, _221526, _221528, _221530] : [-(tptp_update2(_221530, _221526, _221522) = tptp_update2(_221528, _221524, _221520)), _221530 = _221528, _221526 = _221524, _221522 = _221520], (204 ^ _214774) ^ [_221980, _221982] : [_221982 = _221980, -(succ(_221982) = succ(_221980))], (210 ^ _214774) ^ [_222198, _222200] : [_222200 = _222198, -(pred(_222200) = pred(_222198))], (216 ^ _214774) ^ [_222444, _222446, _222448, _222450] : [-(divide(_222450, _222446) = divide(_222448, _222444)), _222450 = _222448, _222446 = _222444], (226 ^ _214774) ^ [_222831, _222833, _222835, _222837, _222839, _222841] : [-(sum(_222841, _222837, _222833) = sum(_222839, _222835, _222831)), _222841 = _222839, _222837 = _222835, _222833 = _222831], (240 ^ _214774) ^ [_223291, _223293] : [_223293 = _223291, -(sqrt(_223293) = sqrt(_223291))], (246 ^ _214774) ^ [_223537, _223539, _223541, _223543] : [-(times(_223543, _223539) = times(_223541, _223537)), _223543 = _223541, _223539 = _223537], (256 ^ _214774) ^ [_223896, _223898, _223900, _223902] : [-(minus(_223902, _223898) = minus(_223900, _223896)), _223902 = _223900, _223898 = _223896], (280 ^ _214774) ^ [_224751, _224753, _224755, _224757] : [-(a_select2(_224757, _224753) = a_select2(_224755, _224751)), _224757 = _224755, _224753 = _224751], (266 ^ _214774) ^ [_224283, _224285, _224287, _224289, _224291, _224293] : [-(a_select3(_224293, _224289, _224285) = a_select3(_224291, _224287, _224283)), _224293 = _224291, _224289 = _224287, _224285 = _224283], (895 ^ _214774) ^ [] : [-(gt(n5, n4))], (897 ^ _214774) ^ [] : [-(gt(n135299, n4))], (899 ^ _214774) ^ [] : [-(gt(n135299, n5))], (901 ^ _214774) ^ [] : [-(gt(n4, tptp_minus_1))], (903 ^ _214774) ^ [] : [-(gt(n5, tptp_minus_1))], (905 ^ _214774) ^ [] : [-(gt(n135299, tptp_minus_1))], (907 ^ _214774) ^ [] : [-(gt(n0, tptp_minus_1))], (909 ^ _214774) ^ [] : [-(gt(n1, tptp_minus_1))], (911 ^ _214774) ^ [] : [-(gt(n2, tptp_minus_1))], (913 ^ _214774) ^ [] : [-(gt(n3, tptp_minus_1))], (915 ^ _214774) ^ [] : [-(gt(n4, n0))], (917 ^ _214774) ^ [] : [-(gt(n5, n0))], (919 ^ _214774) ^ [] : [-(gt(n135299, n0))], (921 ^ _214774) ^ [] : [-(gt(n1, n0))], (923 ^ _214774) ^ [] : [-(gt(n2, n0))], (925 ^ _214774) ^ [] : [-(gt(n3, n0))], (927 ^ _214774) ^ [] : [-(gt(n4, n1))], (929 ^ _214774) ^ [] : [-(gt(n5, n1))], (931 ^ _214774) ^ [] : [-(gt(n135299, n1))], (933 ^ _214774) ^ [] : [-(gt(n2, n1))], (935 ^ _214774) ^ [] : [-(gt(n3, n1))], (937 ^ _214774) ^ [] : [-(gt(n4, n2))], (939 ^ _214774) ^ [] : [-(gt(n5, n2))], (941 ^ _214774) ^ [] : [-(gt(n135299, n2))], (943 ^ _214774) ^ [] : [-(gt(n3, n2))], (945 ^ _214774) ^ [] : [-(gt(n4, n3))], (947 ^ _214774) ^ [] : [-(gt(n5, n3))], (949 ^ _214774) ^ [] : [-(gt(n135299, n3))], (951 ^ _214774) ^ [_252605] : [leq(n0, _252605), leq(_252605, n4), -(_252605 = n0), -(_252605 = n1), -(_252605 = n2), -(_252605 = n3), -(_252605 = n4)], (977 ^ _214774) ^ [_253226] : [leq(n0, _253226), leq(_253226, n5), -(_253226 = n0), -(_253226 = n1), -(_253226 = n2), -(_253226 = n3), -(_253226 = n4), -(_253226 = n5)], (1007 ^ _214774) ^ [_253933] : [-(_253933 = n0), leq(n0, _253933), leq(_253933, n0)], (1017 ^ _214774) ^ [_254208] : [leq(n0, _254208), leq(_254208, n1), -(_254208 = n0), -(_254208 = n1)], (1031 ^ _214774) ^ [_254571] : [leq(n0, _254571), leq(_254571, n2), -(_254571 = n0), -(_254571 = n1), -(_254571 = n2)], (1071 ^ _214774) ^ [] : [-(succ(succ(succ(succ(n0)))) = n4)], (1073 ^ _214774) ^ [] : [-(succ(succ(succ(succ(succ(n0))))) = n5)], (1075 ^ _214774) ^ [] : [-(succ(n0) = n1)], (1077 ^ _214774) ^ [] : [-(succ(succ(n0)) = n2)], (1079 ^ _214774) ^ [] : [-(succ(succ(succ(n0))) = n3)], (1049 ^ _214774) ^ [_255020] : [leq(n0, _255020), leq(_255020, n3), -(_255020 = n0), -(_255020 = n1), -(_255020 = n2), -(_255020 = n3)], (290 ^ _214774) ^ [_225196, _225198] : [-(gt(_225198, _225196)), -(gt(_225196, _225198)), -(_225198 = _225196)], (300 ^ _214774) ^ [_225511, _225513, _225515] : [-(gt(_225515, _225511)), gt(_225515, _225513), gt(_225513, _225511)], (310 ^ _214774) ^ [_225790] : [gt(_225790, _225790)], (312 ^ _214774) ^ [_225868] : [-(leq(_225868, _225868))], (314 ^ _214774) ^ [_225989, _225991, _225993] : [-(leq(_225993, _225989)), leq(_225993, _225991), leq(_225991, _225989)], (324 ^ _214774) ^ [_226327, _226329] : [lt(_226329, _226327), -(gt(_226327, _226329))], (330 ^ _214774) ^ [_226489, _226491] : [gt(_226489, _226491), -(lt(_226491, _226489))], (336 ^ _214774) ^ [_226730, _226732] : [geq(_226732, _226730), -(leq(_226730, _226732))], (342 ^ _214774) ^ [_226892, _226894] : [leq(_226892, _226894), -(geq(_226894, _226892))], (348 ^ _214774) ^ [_227104, _227106] : [gt(_227104, _227106), -(leq(_227106, _227104))], (354 ^ _214774) ^ [_227314, _227316] : [-(gt(_227314, _227316)), leq(_227316, _227314), -(_227316 = _227314)], (364 ^ _214774) ^ [_227645, _227647] : [leq(_227647, pred(_227645)), -(gt(_227645, _227647))], (370 ^ _214774) ^ [_227811, _227813] : [gt(_227811, _227813), -(leq(_227813, pred(_227811)))], (376 ^ _214774) ^ [_227998] : [-(gt(succ(_227998), _227998))], (378 ^ _214774) ^ [_228107, _228109] : [leq(_228109, _228107), -(leq(_228109, succ(_228107)))], (384 ^ _214774) ^ [_228350, _228352] : [leq(_228352, _228350), -(gt(succ(_228350), _228352))], (390 ^ _214774) ^ [_228516, _228518] : [gt(succ(_228516), _228518), -(leq(_228518, _228516))], (396 ^ _214774) ^ [_228732, _228734] : [leq(n0, _228734), -(leq(uniform_int_rnd(_228732, _228734), _228734))], (402 ^ _214774) ^ [_228948, _228950] : [leq(n0, _228950), -(leq(n0, uniform_int_rnd(_228948, _228950)))], (408 ^ _214774) ^ [_229192, _229194, _229196, _229198] : [-(a_select2(tptp_const_array1(dim(_229196, _229194), _229192), _229198) = _229192), leq(_229196, _229198), leq(_229198, _229194)], (418 ^ _214774) ^ [_229599, _229601, _229603, _229605, _229607, _229609, _229611] : [-(a_select3(tptp_const_array2(dim(_229609, _229607), dim(_229603, _229601), _229599), _229611, _229605) = _229599), leq(_229609, _229611), leq(_229611, _229607), leq(_229603, _229605), leq(_229605, _229601)], (436 ^ _214774) ^ [_230194, _230196] : [439 ^ _214774 : [(440 ^ _214774) ^ [] : [-(leq(n0, 437 ^ [_230194, _230196]))], (442 ^ _214774) ^ [] : [-(leq(437 ^ [_230194, _230196], _230194))], (444 ^ _214774) ^ [] : [-(leq(n0, 438 ^ [_230194, _230196]))], (446 ^ _214774) ^ [] : [-(leq(438 ^ [_230194, _230196], _230194))], (448 ^ _214774) ^ [] : [a_select3(_230196, 437 ^ [_230194, _230196], 438 ^ [_230194, _230196]) = a_select3(_230196, 438 ^ [_230194, _230196], 437 ^ [_230194, _230196])]], 449 ^ _214774 : [(450 ^ _214774) ^ [_230951, _230953] : [-(a_select3(trans(_230196), _230953, _230951) = a_select3(trans(_230196), _230951, _230953)), leq(n0, _230953), leq(_230953, _230194), leq(n0, _230951), leq(_230951, _230194)]]], (468 ^ _214774) ^ [_231498, _231500] : [471 ^ _214774 : [(472 ^ _214774) ^ [] : [-(leq(n0, 469 ^ [_231498, _231500]))], (474 ^ _214774) ^ [] : [-(leq(469 ^ [_231498, _231500], _231498))], (476 ^ _214774) ^ [] : [-(leq(n0, 470 ^ [_231498, _231500]))], (478 ^ _214774) ^ [] : [-(leq(470 ^ [_231498, _231500], _231498))], (480 ^ _214774) ^ [] : [a_select3(_231500, 469 ^ [_231498, _231500], 470 ^ [_231498, _231500]) = a_select3(_231500, 470 ^ [_231498, _231500], 469 ^ [_231498, _231500])]], 481 ^ _214774 : [(482 ^ _214774) ^ [_232255, _232257] : [-(a_select3(inv(_231500), _232257, _232255) = a_select3(inv(_231500), _232255, _232257)), leq(n0, _232257), leq(_232257, _231498), leq(n0, _232255), leq(_232255, _231498)]]], (500 ^ _214774) ^ [_232802, _232804] : [503 ^ _214774 : [(504 ^ _214774) ^ [] : [-(leq(n0, 501 ^ [_232802, _232804]))], (506 ^ _214774) ^ [] : [-(leq(501 ^ [_232802, _232804], _232802))], (508 ^ _214774) ^ [] : [-(leq(n0, 502 ^ [_232802, _232804]))], (510 ^ _214774) ^ [] : [-(leq(502 ^ [_232802, _232804], _232802))], (512 ^ _214774) ^ [] : [a_select3(_232804, 501 ^ [_232802, _232804], 502 ^ [_232802, _232804]) = a_select3(_232804, 502 ^ [_232802, _232804], 501 ^ [_232802, _232804])]], 513 ^ _214774 : [(514 ^ _214774) ^ [_233615, _233617, _233619, _233621] : [-(a_select3(tptp_update3(_232804, _233617, _233617, _233615), _233621, _233619) = a_select3(tptp_update3(_232804, _233617, _233617, _233615), _233619, _233621)), leq(n0, _233621), leq(_233621, _232802), leq(n0, _233619), leq(_233619, _232802), leq(n0, _233617), leq(_233617, _232802)]]], (540 ^ _214774) ^ [_234434, _234436, _234438] : [545 ^ _214774 : [(546 ^ _214774) ^ [] : [-(leq(n0, 543 ^ [_234434, _234436, _234438]))], (548 ^ _214774) ^ [] : [-(leq(543 ^ [_234434, _234436, _234438], _234434))], (550 ^ _214774) ^ [] : [-(leq(n0, 544 ^ [_234434, _234436, _234438]))], (552 ^ _214774) ^ [] : [-(leq(544 ^ [_234434, _234436, _234438], _234434))], (554 ^ _214774) ^ [] : [a_select3(_234438, 543 ^ [_234434, _234436, _234438], 544 ^ [_234434, _234436, _234438]) = a_select3(_234438, 544 ^ [_234434, _234436, _234438], 543 ^ [_234434, _234436, _234438])]], 557 ^ _214774 : [(558 ^ _214774) ^ [] : [-(leq(n0, 555 ^ [_234434, _234436, _234438]))], (560 ^ _214774) ^ [] : [-(leq(555 ^ [_234434, _234436, _234438], _234434))], (562 ^ _214774) ^ [] : [-(leq(n0, 556 ^ [_234434, _234436, _234438]))], (564 ^ _214774) ^ [] : [-(leq(556 ^ [_234434, _234436, _234438], _234434))], (566 ^ _214774) ^ [] : [a_select3(_234436, 555 ^ [_234434, _234436, _234438], 556 ^ [_234434, _234436, _234438]) = a_select3(_234436, 556 ^ [_234434, _234436, _234438], 555 ^ [_234434, _234436, _234438])]], 567 ^ _214774 : [(568 ^ _214774) ^ [_235943, _235945] : [-(a_select3(tptp_madd(_234438, _234436), _235945, _235943) = a_select3(tptp_madd(_234438, _234436), _235943, _235945)), leq(n0, _235945), leq(_235945, _234434), leq(n0, _235943), leq(_235943, _234434)]]], (586 ^ _214774) ^ [_236529, _236531, _236533] : [591 ^ _214774 : [(592 ^ _214774) ^ [] : [-(leq(n0, 589 ^ [_236529, _236531, _236533]))], (594 ^ _214774) ^ [] : [-(leq(589 ^ [_236529, _236531, _236533], _236529))], (596 ^ _214774) ^ [] : [-(leq(n0, 590 ^ [_236529, _236531, _236533]))], (598 ^ _214774) ^ [] : [-(leq(590 ^ [_236529, _236531, _236533], _236529))], (600 ^ _214774) ^ [] : [a_select3(_236533, 589 ^ [_236529, _236531, _236533], 590 ^ [_236529, _236531, _236533]) = a_select3(_236533, 590 ^ [_236529, _236531, _236533], 589 ^ [_236529, _236531, _236533])]], 603 ^ _214774 : [(604 ^ _214774) ^ [] : [-(leq(n0, 601 ^ [_236529, _236531, _236533]))], (606 ^ _214774) ^ [] : [-(leq(601 ^ [_236529, _236531, _236533], _236529))], (608 ^ _214774) ^ [] : [-(leq(n0, 602 ^ [_236529, _236531, _236533]))], (610 ^ _214774) ^ [] : [-(leq(602 ^ [_236529, _236531, _236533], _236529))], (612 ^ _214774) ^ [] : [a_select3(_236531, 601 ^ [_236529, _236531, _236533], 602 ^ [_236529, _236531, _236533]) = a_select3(_236531, 602 ^ [_236529, _236531, _236533], 601 ^ [_236529, _236531, _236533])]], 613 ^ _214774 : [(614 ^ _214774) ^ [_238038, _238040] : [-(a_select3(tptp_msub(_236533, _236531), _238040, _238038) = a_select3(tptp_msub(_236533, _236531), _238038, _238040)), leq(n0, _238040), leq(_238040, _236529), leq(n0, _238038), leq(_238038, _236529)]]], (632 ^ _214774) ^ [_238624, _238626, _238628] : [635 ^ _214774 : [(636 ^ _214774) ^ [] : [-(leq(n0, 633 ^ [_238624, _238626, _238628]))], (638 ^ _214774) ^ [] : [-(leq(633 ^ [_238624, _238626, _238628], _238624))], (640 ^ _214774) ^ [] : [-(leq(n0, 634 ^ [_238624, _238626, _238628]))], (642 ^ _214774) ^ [] : [-(leq(634 ^ [_238624, _238626, _238628], _238624))], (644 ^ _214774) ^ [] : [a_select3(_238626, 633 ^ [_238624, _238626, _238628], 634 ^ [_238624, _238626, _238628]) = a_select3(_238626, 634 ^ [_238624, _238626, _238628], 633 ^ [_238624, _238626, _238628])]], 645 ^ _214774 : [(646 ^ _214774) ^ [_239437, _239439] : [-(a_select3(tptp_mmul(_238628, tptp_mmul(_238626, trans(_238628))), _239439, _239437) = a_select3(tptp_mmul(_238628, tptp_mmul(_238626, trans(_238628))), _239437, _239439)), leq(n0, _239439), leq(_239439, _238624), leq(n0, _239437), leq(_239437, _238624)]]], (664 ^ _214774) ^ [_240056, _240058, _240060, _240062] : [667 ^ _214774 : [(668 ^ _214774) ^ [] : [-(leq(n0, 665 ^ [_240056, _240058, _240060, _240062]))], (670 ^ _214774) ^ [] : [-(leq(665 ^ [_240056, _240058, _240060, _240062], _240056))], (672 ^ _214774) ^ [] : [-(leq(n0, 666 ^ [_240056, _240058, _240060, _240062]))], (674 ^ _214774) ^ [] : [-(leq(666 ^ [_240056, _240058, _240060, _240062], _240056))], (676 ^ _214774) ^ [] : [a_select3(_240060, 665 ^ [_240056, _240058, _240060, _240062], 666 ^ [_240056, _240058, _240060, _240062]) = a_select3(_240060, 666 ^ [_240056, _240058, _240060, _240062], 665 ^ [_240056, _240058, _240060, _240062])]], 677 ^ _214774 : [(678 ^ _214774) ^ [_240913, _240915] : [-(a_select3(tptp_mmul(_240062, tptp_mmul(_240060, trans(_240062))), _240915, _240913) = a_select3(tptp_mmul(_240062, tptp_mmul(_240060, trans(_240062))), _240913, _240915)), leq(n0, _240915), leq(_240915, _240058), leq(n0, _240913), leq(_240913, _240058)]]], (696 ^ _214774) ^ [_241608, _241610, _241612, _241614, _241616, _241618, _241620, _241622] : [701 ^ _214774 : [(702 ^ _214774) ^ [] : [-(leq(n0, 699 ^ [_241608, _241610, _241612, _241614, _241616, _241618, _241620, _241622]))], (704 ^ _214774) ^ [] : [-(leq(699 ^ [_241608, _241610, _241612, _241614, _241616, _241618, _241620, _241622], _241608))], (706 ^ _214774) ^ [] : [-(leq(n0, 700 ^ [_241608, _241610, _241612, _241614, _241616, _241618, _241620, _241622]))], (708 ^ _214774) ^ [] : [-(leq(700 ^ [_241608, _241610, _241612, _241614, _241616, _241618, _241620, _241622], _241608))], (710 ^ _214774) ^ [] : [a_select3(_241616, 699 ^ [_241608, _241610, _241612, _241614, _241616, _241618, _241620, _241622], 700 ^ [_241608, _241610, _241612, _241614, _241616, _241618, _241620, _241622]) = a_select3(_241616, 700 ^ [_241608, _241610, _241612, _241614, _241616, _241618, _241620, _241622], 699 ^ [_241608, _241610, _241612, _241614, _241616, _241618, _241620, _241622])]], 715 ^ _214774 : [(716 ^ _214774) ^ [] : [-(leq(n0, 713 ^ [_241608, _241610, _241612, _241614, _241616, _241618, _241620, _241622]))], (718 ^ _214774) ^ [] : [-(leq(713 ^ [_241608, _241610, _241612, _241614, _241616, _241618, _241620, _241622], _241610))], (720 ^ _214774) ^ [] : [-(leq(n0, 714 ^ [_241608, _241610, _241612, _241614, _241616, _241618, _241620, _241622]))], (722 ^ _214774) ^ [] : [-(leq(714 ^ [_241608, _241610, _241612, _241614, _241616, _241618, _241620, _241622], _241610))], (724 ^ _214774) ^ [] : [a_select3(_241622, 713 ^ [_241608, _241610, _241612, _241614, _241616, _241618, _241620, _241622], 714 ^ [_241608, _241610, _241612, _241614, _241616, _241618, _241620, _241622]) = a_select3(_241622, 714 ^ [_241608, _241610, _241612, _241614, _241616, _241618, _241620, _241622], 713 ^ [_241608, _241610, _241612, _241614, _241616, _241618, _241620, _241622])]], 727 ^ _214774 : [(728 ^ _214774) ^ [] : [-(leq(n0, 725 ^ [_241608, _241610, _241612, _241614, _241616, _241618, _241620, _241622]))], (730 ^ _214774) ^ [] : [-(leq(725 ^ [_241608, _241610, _241612, _241614, _241616, _241618, _241620, _241622], _241610))], (732 ^ _214774) ^ [] : [-(leq(n0, 726 ^ [_241608, _241610, _241612, _241614, _241616, _241618, _241620, _241622]))], (734 ^ _214774) ^ [] : [-(leq(726 ^ [_241608, _241610, _241612, _241614, _241616, _241618, _241620, _241622], _241610))], (736 ^ _214774) ^ [] : [a_select3(_241612, 725 ^ [_241608, _241610, _241612, _241614, _241616, _241618, _241620, _241622], 726 ^ [_241608, _241610, _241612, _241614, _241616, _241618, _241620, _241622]) = a_select3(_241612, 726 ^ [_241608, _241610, _241612, _241614, _241616, _241618, _241620, _241622], 725 ^ [_241608, _241610, _241612, _241614, _241616, _241618, _241620, _241622])]], 737 ^ _214774 : [(738 ^ _214774) ^ [_244536, _244538] : [-(a_select3(tptp_madd(_241622, tptp_mmul(_241620, tptp_mmul(tptp_madd(tptp_mmul(_241618, tptp_mmul(_241616, trans(_241618))), tptp_mmul(_241614, tptp_mmul(_241612, trans(_241614)))), trans(_241620)))), _244538, _244536) = a_select3(tptp_madd(_241622, tptp_mmul(_241620, tptp_mmul(tptp_madd(tptp_mmul(_241618, tptp_mmul(_241616, trans(_241618))), tptp_mmul(_241614, tptp_mmul(_241612, trans(_241614)))), trans(_241620)))), _244536, _244538)), leq(n0, _244538), leq(_244538, _241610), leq(n0, _244536), leq(_244536, _241610)]]], (756 ^ _214774) ^ [_245289] : [-(sum(n0, tptp_minus_1, _245289) = n0)], (758 ^ _214774) ^ [_245371] : [-(tptp_float_0_0 = sum(n0, tptp_minus_1, _245371))], (760 ^ _214774) ^ [] : [-(succ(tptp_minus_1) = n0)], (762 ^ _214774) ^ [_245506] : [-(plus(_245506, n1) = succ(_245506))], (764 ^ _214774) ^ [_245589] : [-(plus(n1, _245589) = succ(_245589))], (766 ^ _214774) ^ [_245672] : [-(plus(_245672, n2) = succ(succ(_245672)))], (768 ^ _214774) ^ [_245757] : [-(plus(n2, _245757) = succ(succ(_245757)))], (770 ^ _214774) ^ [_245842] : [-(plus(_245842, n3) = succ(succ(succ(_245842))))], (772 ^ _214774) ^ [_245929] : [-(plus(n3, _245929) = succ(succ(succ(_245929))))], (774 ^ _214774) ^ [_246016] : [-(plus(_246016, n4) = succ(succ(succ(succ(_246016)))))], (776 ^ _214774) ^ [_246105] : [-(plus(n4, _246105) = succ(succ(succ(succ(_246105)))))], (778 ^ _214774) ^ [_246194] : [-(plus(_246194, n5) = succ(succ(succ(succ(succ(_246194))))))], (780 ^ _214774) ^ [_246285] : [-(plus(n5, _246285) = succ(succ(succ(succ(succ(_246285))))))], (782 ^ _214774) ^ [_246376] : [-(minus(_246376, n1) = pred(_246376))], (784 ^ _214774) ^ [_246459] : [-(pred(succ(_246459)) = _246459)], (786 ^ _214774) ^ [_246541] : [-(succ(pred(_246541)) = _246541)], (788 ^ _214774) ^ [_246681, _246683] : [leq(succ(_246683), succ(_246681)), -(leq(_246683, _246681))], (794 ^ _214774) ^ [_246851, _246853] : [leq(_246853, _246851), -(leq(succ(_246853), succ(_246851)))], (800 ^ _214774) ^ [_247071, _247073] : [leq(succ(_247073), _247071), -(gt(_247071, _247073))], (806 ^ _214774) ^ [_247285, _247287] : [leq(minus(_247287, _247285), _247287), -(leq(n0, _247285))], (812 ^ _214774) ^ [_247514, _247516, _247518, _247520] : [-(a_select3(tptp_update3(_247520, _247518, _247516, _247514), _247518, _247516) = _247514)], (814 ^ _214774) ^ [_247706, _247708, _247710, _247712, _247714, _247716, _247718] : [-(a_select3(tptp_update3(_247710, _247718, _247716, _247706), _247714, _247712) = _247708), -(_247718 = _247714), _247716 = _247712, a_select3(_247710, _247714, _247712) = _247708], (828 ^ _214774) ^ [_248249, _248251, _248253, _248255, _248257, _248259] : [-(a_select3(tptp_update3(_248251, _248255, _248253, _248249), _248259, _248257) = _248249), 833 ^ _214774 : [(834 ^ _214774) ^ [] : [-(leq(n0, 831 ^ [_248249, _248251, _248253, _248255, _248257, _248259]))], (836 ^ _214774) ^ [] : [-(leq(n0, 832 ^ [_248249, _248251, _248253, _248255, _248257, _248259]))], (838 ^ _214774) ^ [] : [-(leq(831 ^ [_248249, _248251, _248253, _248255, _248257, _248259], _248255))], (840 ^ _214774) ^ [] : [-(leq(832 ^ [_248249, _248251, _248253, _248255, _248257, _248259], _248253))], (842 ^ _214774) ^ [] : [a_select3(_248251, 831 ^ [_248249, _248251, _248253, _248255, _248257, _248259], 832 ^ [_248249, _248251, _248253, _248255, _248257, _248259]) = _248249]], leq(n0, _248259), leq(_248259, _248255), leq(n0, _248257), leq(_248257, _248253)], (860 ^ _214774) ^ [_249591, _249593, _249595] : [-(a_select2(tptp_update2(_249595, _249593, _249591), _249593) = _249591)], (862 ^ _214774) ^ [_249751, _249753, _249755, _249757, _249759] : [-(a_select2(tptp_update2(_249755, _249759, _249751), _249757) = _249753), -(_249759 = _249757), a_select2(_249755, _249757) = _249753], (891 ^ _214774) ^ [] : [-(true)], (893 ^ _214774) ^ [] : [def = use], (872 ^ _214774) ^ [_250131, _250133, _250135, _250137] : [-(a_select2(tptp_update2(_250133, _250135, _250131), _250137) = _250131), 876 ^ _214774 : [(877 ^ _214774) ^ [] : [-(leq(n0, 875 ^ [_250131, _250133, _250135, _250137]))], (879 ^ _214774) ^ [] : [-(leq(875 ^ [_250131, _250133, _250135, _250137], _250135))], (881 ^ _214774) ^ [] : [a_select2(_250133, 875 ^ [_250131, _250133, _250135, _250137]) = _250131]], leq(n0, _250137), leq(_250137, _250135)]], input).
% 1.14/1.38  ncf('1',plain,[pv12 = 1110 ^ []],start(1116 ^ 0)).
% 1.14/1.38  ncf('1.1',plain,[-(pv12 = 1110 ^ []), 1110 ^ [] = pv12],extension(4 ^ 1,bind([[_215025, _215027], [pv12, 1110 ^ []]]))).
% 1.14/1.38  ncf('1.1.1',plain,[-(1110 ^ [] = pv12), -(gt(1110 ^ [], pv12)), -(gt(pv12, 1110 ^ []))],extension(290 ^ 2,bind([[_225196, _225198], [pv12, 1110 ^ []]]))).
% 1.14/1.38  ncf('1.1.1.1',plain,[gt(1110 ^ [], pv12), -(gt(1110 ^ [], 1110 ^ [])), gt(pv12, 1110 ^ [])],extension(300 ^ 3,bind([[_225511, _225513, _225515], [1110 ^ [], pv12, 1110 ^ []]]))).
% 1.14/1.38  ncf('1.1.1.1.1',plain,[gt(1110 ^ [], 1110 ^ [])],extension(310 ^ 4,bind([[_225790], [1110 ^ []]]))).
% 1.14/1.38  ncf('1.1.1.1.2',plain,[-(gt(pv12, 1110 ^ [])), leq(1110 ^ [], pv12), -(1110 ^ [] = pv12)],extension(354 ^ 4,bind([[_227314, _227316], [pv12, 1110 ^ []]]))).
% 1.14/1.38  ncf('1.1.1.1.2.1',plain,[-(leq(1110 ^ [], pv12))],extension(1114 ^ 5)).
% 1.14/1.38  ncf('1.1.1.1.2.2',plain,[1110 ^ [] = pv12],reduction('1.1')).
% 1.14/1.38  ncf('1.1.1.2',plain,[gt(pv12, 1110 ^ []), -(leq(1110 ^ [], pred(pv12)))],extension(370 ^ 3,bind([[_227811, _227813], [pv12, 1110 ^ []]]))).
% 1.14/1.38  ncf('1.1.1.2.1',plain,[leq(1110 ^ [], pred(pv12)), -(a_select3(q, pv10, 1110 ^ []) = divide(sqrt(times(minus(a_select3(center, 1110 ^ [], n0), a_select2(x, pv10)), minus(a_select3(center, 1110 ^ [], n0), a_select2(x, pv10)))), sum(n0, n4, sqrt(times(minus(a_select3(center, tptp_sum_index, n0), a_select2(x, pv10)), minus(a_select3(center, tptp_sum_index, n0), a_select2(x, pv10))))))), leq(n0, 1110 ^ [])],extension(1091 ^ 4,bind([[_256311], [1110 ^ []]]))).
% 1.14/1.38  ncf('1.1.1.2.1.1',plain,[a_select3(q, pv10, 1110 ^ []) = divide(sqrt(times(minus(a_select3(center, 1110 ^ [], n0), a_select2(x, pv10)), minus(a_select3(center, 1110 ^ [], n0), a_select2(x, pv10)))), sum(n0, n4, sqrt(times(minus(a_select3(center, tptp_sum_index, n0), a_select2(x, pv10)), minus(a_select3(center, tptp_sum_index, n0), a_select2(x, pv10))))))],extension(1118 ^ 5)).
% 1.14/1.38  ncf('1.1.1.2.1.2',plain,[-(leq(n0, 1110 ^ []))],extension(1112 ^ 5)).
% 1.14/1.38  %-----------------------------------------------------
% 1.14/1.38  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------