%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SWV157+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n007.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 0.96s 1.33s
% Output   : Proof 0.96s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem  : SWV157+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.00/0.09  % Command  : nanocop.sh %s %d
% 0.08/0.30  % Computer : n007.cluster.edu
% 0.08/0.30  % Model    : x86_64 x86_64
% 0.08/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.30  % Memory   : 8042.1875MB
% 0.08/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.08/0.30  % CPULimit : 300
% 0.08/0.30  % WCLimit  : 300
% 0.08/0.30  % DateTime : Fri May 19 02:21:23 EDT 2023
% 0.08/0.30  % CPUTime  : 
% 0.96/1.33  
% 0.96/1.33  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 0.96/1.33  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.96/1.33  %-----------------------------------------------------
% 0.96/1.33  ncf(matrix, plain, [(1134 ^ _223975) ^ [] : [-(leq(n0, 1132 ^ []))], (1136 ^ _223975) ^ [] : [-(leq(1132 ^ [], pv47))], (1138 ^ _223975) ^ [] : [pv47 = 1132 ^ []], (1140 ^ _223975) ^ [] : [a_select3(q, pv10, 1132 ^ []) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, 1132 ^ [])), minus(a_select2(x, pv10), a_select2(mu, 1132 ^ []))), tptp_minus_2), times(a_select2(sigma, 1132 ^ []), a_select2(sigma, 1132 ^ [])))), a_select2(rho, 1132 ^ [])), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, 1132 ^ []))), sum(n0, n4, divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, tptp_sum_index)), minus(a_select2(x, pv10), a_select2(mu, tptp_sum_index))), tptp_minus_2), times(a_select2(sigma, tptp_sum_index), a_select2(sigma, tptp_sum_index)))), a_select2(rho, tptp_sum_index)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, tptp_sum_index)))))], (1103 ^ _223975) ^ [] : [-(pv84 = sum(n0, n4, divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, tptp_sum_index)), minus(a_select2(x, pv10), a_select2(mu, tptp_sum_index))), tptp_minus_2), times(a_select2(sigma, tptp_sum_index), a_select2(sigma, tptp_sum_index)))), a_select2(rho, tptp_sum_index)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, tptp_sum_index)))))], (1105 ^ _223975) ^ [] : [-(leq(n0, pv10))], (1107 ^ _223975) ^ [] : [-(leq(n0, pv47))], (1109 ^ _223975) ^ [] : [-(leq(pv10, n135299))], (1111 ^ _223975) ^ [] : [-(leq(pv47, n4))], (1113 ^ _223975) ^ [_266190] : [-(a_select3(q, pv10, _266190) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, _266190)), minus(a_select2(x, pv10), a_select2(mu, _266190))), tptp_minus_2), times(a_select2(sigma, _266190), a_select2(sigma, _266190)))), a_select2(rho, _266190)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, _266190))), sum(n0, n4, divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, tptp_sum_index)), minus(a_select2(x, pv10), a_select2(mu, tptp_sum_index))), tptp_minus_2), times(a_select2(sigma, tptp_sum_index), a_select2(sigma, tptp_sum_index)))), a_select2(rho, tptp_sum_index)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, tptp_sum_index)))))), leq(n0, _266190), leq(_266190, pred(pv47))], (1123 ^ _223975) ^ [_266553] : [-(sum(n0, n4, a_select3(q, _266553, tptp_sum_index)) = n1), leq(n0, _266553), leq(_266553, pred(pv10))], (2 ^ _223975) ^ [_224119] : [-(_224119 = _224119)], (4 ^ _223975) ^ [_224226, _224228] : [_224228 = _224226, -(_224226 = _224228)], (10 ^ _223975) ^ [_224430, _224432, _224434] : [-(_224434 = _224430), _224434 = _224432, _224432 = _224430], (20 ^ _223975) ^ [_224771, _224773, _224775, _224777] : [-(lt(_224775, _224771)), lt(_224777, _224773), _224777 = _224775, _224773 = _224771], (34 ^ _223975) ^ [_225215, _225217, _225219, _225221] : [-(geq(_225219, _225215)), geq(_225221, _225217), _225221 = _225219, _225217 = _225215], (48 ^ _223975) ^ [_225659, _225661, _225663, _225665] : [-(gt(_225663, _225659)), gt(_225665, _225661), _225665 = _225663, _225661 = _225659], (62 ^ _223975) ^ [_226083, _226085, _226087, _226089] : [-(leq(_226087, _226083)), leq(_226089, _226085), _226089 = _226087, _226085 = _226083], (76 ^ _223975) ^ [_226539, _226541, _226543, _226545] : [-(uniform_int_rnd(_226545, _226541) = uniform_int_rnd(_226543, _226539)), _226545 = _226543, _226541 = _226539], (86 ^ _223975) ^ [_226898, _226900, _226902, _226904] : [-(tptp_const_array1(_226904, _226900) = tptp_const_array1(_226902, _226898)), _226904 = _226902, _226900 = _226898], (96 ^ _223975) ^ [_227285, _227287, _227289, _227291, _227293, _227295] : [-(tptp_const_array2(_227295, _227291, _227287) = tptp_const_array2(_227293, _227289, _227285)), _227295 = _227293, _227291 = _227289, _227287 = _227285], (110 ^ _223975) ^ [_227773, _227775, _227777, _227779] : [-(dim(_227779, _227775) = dim(_227777, _227773)), _227779 = _227777, _227775 = _227773], (120 ^ _223975) ^ [_228104, _228106] : [_228106 = _228104, -(inv(_228106) = inv(_228104))], (126 ^ _223975) ^ [_228350, _228352, _228354, _228356] : [-(tptp_msub(_228356, _228352) = tptp_msub(_228354, _228350)), _228356 = _228354, _228352 = _228350], (136 ^ _223975) ^ [_228709, _228711, _228713, _228715] : [-(tptp_madd(_228715, _228711) = tptp_madd(_228713, _228709)), _228715 = _228713, _228711 = _228709], (146 ^ _223975) ^ [_229068, _229070, _229072, _229074] : [-(tptp_mmul(_229074, _229070) = tptp_mmul(_229072, _229068)), _229074 = _229072, _229070 = _229068], (156 ^ _223975) ^ [_229399, _229401] : [_229401 = _229399, -(trans(_229401) = trans(_229399))], (162 ^ _223975) ^ [_229645, _229647, _229649, _229651] : [-(plus(_229651, _229647) = plus(_229649, _229645)), _229651 = _229649, _229647 = _229645], (172 ^ _223975) ^ [_230060, _230062, _230064, _230066, _230068, _230070, _230072, _230074] : [-(tptp_update3(_230074, _230070, _230066, _230062) = tptp_update3(_230072, _230068, _230064, _230060)), _230074 = _230072, _230070 = _230068, _230066 = _230064, _230062 = _230060], (190 ^ _223975) ^ [_230721, _230723, _230725, _230727, _230729, _230731] : [-(tptp_update2(_230731, _230727, _230723) = tptp_update2(_230729, _230725, _230721)), _230731 = _230729, _230727 = _230725, _230723 = _230721], (204 ^ _223975) ^ [_231181, _231183] : [_231183 = _231181, -(succ(_231183) = succ(_231181))], (210 ^ _223975) ^ [_231399, _231401] : [_231401 = _231399, -(pred(_231401) = pred(_231399))], (216 ^ _223975) ^ [_231673, _231675, _231677, _231679, _231681, _231683] : [-(a_select3(_231683, _231679, _231675) = a_select3(_231681, _231677, _231673)), _231683 = _231681, _231679 = _231677, _231675 = _231673], (230 ^ _223975) ^ [_232189, _232191, _232193, _232195, _232197, _232199] : [-(sum(_232199, _232195, _232191) = sum(_232197, _232193, _232189)), _232199 = _232197, _232195 = _232193, _232191 = _232189], (244 ^ _223975) ^ [_232649, _232651] : [_232651 = _232649, -(exp(_232651) = exp(_232649))], (250 ^ _223975) ^ [_232895, _232897, _232899, _232901] : [-(divide(_232901, _232897) = divide(_232899, _232895)), _232901 = _232899, _232897 = _232895], (260 ^ _223975) ^ [_233254, _233256, _233258, _233260] : [-(minus(_233260, _233256) = minus(_233258, _233254)), _233260 = _233258, _233256 = _233254], (270 ^ _223975) ^ [_233585, _233587] : [_233587 = _233585, -(sqrt(_233587) = sqrt(_233585))], (276 ^ _223975) ^ [_233831, _233833, _233835, _233837] : [-(times(_233837, _233833) = times(_233835, _233831)), _233837 = _233835, _233833 = _233831], (286 ^ _223975) ^ [_234170, _234172, _234174, _234176] : [-(a_select2(_234176, _234172) = a_select2(_234174, _234170)), _234176 = _234174, _234172 = _234170], (901 ^ _223975) ^ [] : [-(gt(n5, n4))], (903 ^ _223975) ^ [] : [-(gt(n135299, n4))], (905 ^ _223975) ^ [] : [-(gt(n135299, n5))], (907 ^ _223975) ^ [] : [-(gt(n4, tptp_minus_1))], (909 ^ _223975) ^ [] : [-(gt(n5, tptp_minus_1))], (911 ^ _223975) ^ [] : [-(gt(n135299, tptp_minus_1))], (913 ^ _223975) ^ [] : [-(gt(n0, tptp_minus_1))], (915 ^ _223975) ^ [] : [-(gt(n1, tptp_minus_1))], (917 ^ _223975) ^ [] : [-(gt(n2, tptp_minus_1))], (919 ^ _223975) ^ [] : [-(gt(n3, tptp_minus_1))], (921 ^ _223975) ^ [] : [-(gt(n4, tptp_minus_2))], (923 ^ _223975) ^ [] : [-(gt(n5, tptp_minus_2))], (925 ^ _223975) ^ [] : [-(gt(tptp_minus_1, tptp_minus_2))], (927 ^ _223975) ^ [] : [-(gt(n135299, tptp_minus_2))], (929 ^ _223975) ^ [] : [-(gt(n0, tptp_minus_2))], (931 ^ _223975) ^ [] : [-(gt(n1, tptp_minus_2))], (933 ^ _223975) ^ [] : [-(gt(n2, tptp_minus_2))], (935 ^ _223975) ^ [] : [-(gt(n3, tptp_minus_2))], (937 ^ _223975) ^ [] : [-(gt(n4, n0))], (939 ^ _223975) ^ [] : [-(gt(n5, n0))], (941 ^ _223975) ^ [] : [-(gt(n135299, n0))], (943 ^ _223975) ^ [] : [-(gt(n1, n0))], (945 ^ _223975) ^ [] : [-(gt(n2, n0))], (947 ^ _223975) ^ [] : [-(gt(n3, n0))], (949 ^ _223975) ^ [] : [-(gt(n4, n1))], (951 ^ _223975) ^ [] : [-(gt(n5, n1))], (953 ^ _223975) ^ [] : [-(gt(n135299, n1))], (955 ^ _223975) ^ [] : [-(gt(n2, n1))], (957 ^ _223975) ^ [] : [-(gt(n3, n1))], (959 ^ _223975) ^ [] : [-(gt(n4, n2))], (961 ^ _223975) ^ [] : [-(gt(n5, n2))], (963 ^ _223975) ^ [] : [-(gt(n135299, n2))], (965 ^ _223975) ^ [] : [-(gt(n3, n2))], (967 ^ _223975) ^ [] : [-(gt(n4, n3))], (969 ^ _223975) ^ [] : [-(gt(n5, n3))], (971 ^ _223975) ^ [] : [-(gt(n135299, n3))], (973 ^ _223975) ^ [_262450] : [leq(n0, _262450), leq(_262450, n4), -(_262450 = n0), -(_262450 = n1), -(_262450 = n2), -(_262450 = n3), -(_262450 = n4)], (999 ^ _223975) ^ [_263071] : [leq(n0, _263071), leq(_263071, n5), -(_263071 = n0), -(_263071 = n1), -(_263071 = n2), -(_263071 = n3), -(_263071 = n4), -(_263071 = n5)], (1029 ^ _223975) ^ [_263778] : [-(_263778 = n0), leq(n0, _263778), leq(_263778, n0)], (1039 ^ _223975) ^ [_264053] : [leq(n0, _264053), leq(_264053, n1), -(_264053 = n0), -(_264053 = n1)], (1053 ^ _223975) ^ [_264416] : [leq(n0, _264416), leq(_264416, n2), -(_264416 = n0), -(_264416 = n1), -(_264416 = n2)], (1093 ^ _223975) ^ [] : [-(succ(succ(succ(succ(n0)))) = n4)], (1095 ^ _223975) ^ [] : [-(succ(succ(succ(succ(succ(n0))))) = n5)], (1097 ^ _223975) ^ [] : [-(succ(n0) = n1)], (1099 ^ _223975) ^ [] : [-(succ(succ(n0)) = n2)], (1101 ^ _223975) ^ [] : [-(succ(succ(succ(n0))) = n3)], (1071 ^ _223975) ^ [_264865] : [leq(n0, _264865), leq(_264865, n3), -(_264865 = n0), -(_264865 = n1), -(_264865 = n2), -(_264865 = n3)], (296 ^ _223975) ^ [_234617, _234619] : [-(gt(_234619, _234617)), -(gt(_234617, _234619)), -(_234619 = _234617)], (306 ^ _223975) ^ [_234932, _234934, _234936] : [-(gt(_234936, _234932)), gt(_234936, _234934), gt(_234934, _234932)], (316 ^ _223975) ^ [_235211] : [gt(_235211, _235211)], (318 ^ _223975) ^ [_235289] : [-(leq(_235289, _235289))], (320 ^ _223975) ^ [_235410, _235412, _235414] : [-(leq(_235414, _235410)), leq(_235414, _235412), leq(_235412, _235410)], (330 ^ _223975) ^ [_235748, _235750] : [lt(_235750, _235748), -(gt(_235748, _235750))], (336 ^ _223975) ^ [_235910, _235912] : [gt(_235910, _235912), -(lt(_235912, _235910))], (342 ^ _223975) ^ [_236151, _236153] : [geq(_236153, _236151), -(leq(_236151, _236153))], (348 ^ _223975) ^ [_236313, _236315] : [leq(_236313, _236315), -(geq(_236315, _236313))], (354 ^ _223975) ^ [_236525, _236527] : [gt(_236525, _236527), -(leq(_236527, _236525))], (360 ^ _223975) ^ [_236735, _236737] : [-(gt(_236735, _236737)), leq(_236737, _236735), -(_236737 = _236735)], (370 ^ _223975) ^ [_237066, _237068] : [leq(_237068, pred(_237066)), -(gt(_237066, _237068))], (376 ^ _223975) ^ [_237232, _237234] : [gt(_237232, _237234), -(leq(_237234, pred(_237232)))], (382 ^ _223975) ^ [_237419] : [-(gt(succ(_237419), _237419))], (384 ^ _223975) ^ [_237528, _237530] : [leq(_237530, _237528), -(leq(_237530, succ(_237528)))], (390 ^ _223975) ^ [_237771, _237773] : [leq(_237773, _237771), -(gt(succ(_237771), _237773))], (396 ^ _223975) ^ [_237937, _237939] : [gt(succ(_237937), _237939), -(leq(_237939, _237937))], (402 ^ _223975) ^ [_238153, _238155] : [leq(n0, _238155), -(leq(uniform_int_rnd(_238153, _238155), _238155))], (408 ^ _223975) ^ [_238369, _238371] : [leq(n0, _238371), -(leq(n0, uniform_int_rnd(_238369, _238371)))], (414 ^ _223975) ^ [_238613, _238615, _238617, _238619] : [-(a_select2(tptp_const_array1(dim(_238617, _238615), _238613), _238619) = _238613), leq(_238617, _238619), leq(_238619, _238615)], (424 ^ _223975) ^ [_239020, _239022, _239024, _239026, _239028, _239030, _239032] : [-(a_select3(tptp_const_array2(dim(_239030, _239028), dim(_239024, _239022), _239020), _239032, _239026) = _239020), leq(_239030, _239032), leq(_239032, _239028), leq(_239024, _239026), leq(_239026, _239022)], (442 ^ _223975) ^ [_239615, _239617] : [445 ^ _223975 : [(446 ^ _223975) ^ [] : [-(leq(n0, 443 ^ [_239615, _239617]))], (448 ^ _223975) ^ [] : [-(leq(443 ^ [_239615, _239617], _239615))], (450 ^ _223975) ^ [] : [-(leq(n0, 444 ^ [_239615, _239617]))], (452 ^ _223975) ^ [] : [-(leq(444 ^ [_239615, _239617], _239615))], (454 ^ _223975) ^ [] : [a_select3(_239617, 443 ^ [_239615, _239617], 444 ^ [_239615, _239617]) = a_select3(_239617, 444 ^ [_239615, _239617], 443 ^ [_239615, _239617])]], 455 ^ _223975 : [(456 ^ _223975) ^ [_240372, _240374] : [-(a_select3(trans(_239617), _240374, _240372) = a_select3(trans(_239617), _240372, _240374)), leq(n0, _240374), leq(_240374, _239615), leq(n0, _240372), leq(_240372, _239615)]]], (474 ^ _223975) ^ [_240919, _240921] : [477 ^ _223975 : [(478 ^ _223975) ^ [] : [-(leq(n0, 475 ^ [_240919, _240921]))], (480 ^ _223975) ^ [] : [-(leq(475 ^ [_240919, _240921], _240919))], (482 ^ _223975) ^ [] : [-(leq(n0, 476 ^ [_240919, _240921]))], (484 ^ _223975) ^ [] : [-(leq(476 ^ [_240919, _240921], _240919))], (486 ^ _223975) ^ [] : [a_select3(_240921, 475 ^ [_240919, _240921], 476 ^ [_240919, _240921]) = a_select3(_240921, 476 ^ [_240919, _240921], 475 ^ [_240919, _240921])]], 487 ^ _223975 : [(488 ^ _223975) ^ [_241676, _241678] : [-(a_select3(inv(_240921), _241678, _241676) = a_select3(inv(_240921), _241676, _241678)), leq(n0, _241678), leq(_241678, _240919), leq(n0, _241676), leq(_241676, _240919)]]], (506 ^ _223975) ^ [_242223, _242225] : [509 ^ _223975 : [(510 ^ _223975) ^ [] : [-(leq(n0, 507 ^ [_242223, _242225]))], (512 ^ _223975) ^ [] : [-(leq(507 ^ [_242223, _242225], _242223))], (514 ^ _223975) ^ [] : [-(leq(n0, 508 ^ [_242223, _242225]))], (516 ^ _223975) ^ [] : [-(leq(508 ^ [_242223, _242225], _242223))], (518 ^ _223975) ^ [] : [a_select3(_242225, 507 ^ [_242223, _242225], 508 ^ [_242223, _242225]) = a_select3(_242225, 508 ^ [_242223, _242225], 507 ^ [_242223, _242225])]], 519 ^ _223975 : [(520 ^ _223975) ^ [_243036, _243038, _243040, _243042] : [-(a_select3(tptp_update3(_242225, _243038, _243038, _243036), _243042, _243040) = a_select3(tptp_update3(_242225, _243038, _243038, _243036), _243040, _243042)), leq(n0, _243042), leq(_243042, _242223), leq(n0, _243040), leq(_243040, _242223), leq(n0, _243038), leq(_243038, _242223)]]], (546 ^ _223975) ^ [_243855, _243857, _243859] : [551 ^ _223975 : [(552 ^ _223975) ^ [] : [-(leq(n0, 549 ^ [_243855, _243857, _243859]))], (554 ^ _223975) ^ [] : [-(leq(549 ^ [_243855, _243857, _243859], _243855))], (556 ^ _223975) ^ [] : [-(leq(n0, 550 ^ [_243855, _243857, _243859]))], (558 ^ _223975) ^ [] : [-(leq(550 ^ [_243855, _243857, _243859], _243855))], (560 ^ _223975) ^ [] : [a_select3(_243859, 549 ^ [_243855, _243857, _243859], 550 ^ [_243855, _243857, _243859]) = a_select3(_243859, 550 ^ [_243855, _243857, _243859], 549 ^ [_243855, _243857, _243859])]], 563 ^ _223975 : [(564 ^ _223975) ^ [] : [-(leq(n0, 561 ^ [_243855, _243857, _243859]))], (566 ^ _223975) ^ [] : [-(leq(561 ^ [_243855, _243857, _243859], _243855))], (568 ^ _223975) ^ [] : [-(leq(n0, 562 ^ [_243855, _243857, _243859]))], (570 ^ _223975) ^ [] : [-(leq(562 ^ [_243855, _243857, _243859], _243855))], (572 ^ _223975) ^ [] : [a_select3(_243857, 561 ^ [_243855, _243857, _243859], 562 ^ [_243855, _243857, _243859]) = a_select3(_243857, 562 ^ [_243855, _243857, _243859], 561 ^ [_243855, _243857, _243859])]], 573 ^ _223975 : [(574 ^ _223975) ^ [_245364, _245366] : [-(a_select3(tptp_madd(_243859, _243857), _245366, _245364) = a_select3(tptp_madd(_243859, _243857), _245364, _245366)), leq(n0, _245366), leq(_245366, _243855), leq(n0, _245364), leq(_245364, _243855)]]], (592 ^ _223975) ^ [_245950, _245952, _245954] : [597 ^ _223975 : [(598 ^ _223975) ^ [] : [-(leq(n0, 595 ^ [_245950, _245952, _245954]))], (600 ^ _223975) ^ [] : [-(leq(595 ^ [_245950, _245952, _245954], _245950))], (602 ^ _223975) ^ [] : [-(leq(n0, 596 ^ [_245950, _245952, _245954]))], (604 ^ _223975) ^ [] : [-(leq(596 ^ [_245950, _245952, _245954], _245950))], (606 ^ _223975) ^ [] : [a_select3(_245954, 595 ^ [_245950, _245952, _245954], 596 ^ [_245950, _245952, _245954]) = a_select3(_245954, 596 ^ [_245950, _245952, _245954], 595 ^ [_245950, _245952, _245954])]], 609 ^ _223975 : [(610 ^ _223975) ^ [] : [-(leq(n0, 607 ^ [_245950, _245952, _245954]))], (612 ^ _223975) ^ [] : [-(leq(607 ^ [_245950, _245952, _245954], _245950))], (614 ^ _223975) ^ [] : [-(leq(n0, 608 ^ [_245950, _245952, _245954]))], (616 ^ _223975) ^ [] : [-(leq(608 ^ [_245950, _245952, _245954], _245950))], (618 ^ _223975) ^ [] : [a_select3(_245952, 607 ^ [_245950, _245952, _245954], 608 ^ [_245950, _245952, _245954]) = a_select3(_245952, 608 ^ [_245950, _245952, _245954], 607 ^ [_245950, _245952, _245954])]], 619 ^ _223975 : [(620 ^ _223975) ^ [_247459, _247461] : [-(a_select3(tptp_msub(_245954, _245952), _247461, _247459) = a_select3(tptp_msub(_245954, _245952), _247459, _247461)), leq(n0, _247461), leq(_247461, _245950), leq(n0, _247459), leq(_247459, _245950)]]], (638 ^ _223975) ^ [_248045, _248047, _248049] : [641 ^ _223975 : [(642 ^ _223975) ^ [] : [-(leq(n0, 639 ^ [_248045, _248047, _248049]))], (644 ^ _223975) ^ [] : [-(leq(639 ^ [_248045, _248047, _248049], _248045))], (646 ^ _223975) ^ [] : [-(leq(n0, 640 ^ [_248045, _248047, _248049]))], (648 ^ _223975) ^ [] : [-(leq(640 ^ [_248045, _248047, _248049], _248045))], (650 ^ _223975) ^ [] : [a_select3(_248047, 639 ^ [_248045, _248047, _248049], 640 ^ [_248045, _248047, _248049]) = a_select3(_248047, 640 ^ [_248045, _248047, _248049], 639 ^ [_248045, _248047, _248049])]], 651 ^ _223975 : [(652 ^ _223975) ^ [_248858, _248860] : [-(a_select3(tptp_mmul(_248049, tptp_mmul(_248047, trans(_248049))), _248860, _248858) = a_select3(tptp_mmul(_248049, tptp_mmul(_248047, trans(_248049))), _248858, _248860)), leq(n0, _248860), leq(_248860, _248045), leq(n0, _248858), leq(_248858, _248045)]]], (670 ^ _223975) ^ [_249477, _249479, _249481, _249483] : [673 ^ _223975 : [(674 ^ _223975) ^ [] : [-(leq(n0, 671 ^ [_249477, _249479, _249481, _249483]))], (676 ^ _223975) ^ [] : [-(leq(671 ^ [_249477, _249479, _249481, _249483], _249477))], (678 ^ _223975) ^ [] : [-(leq(n0, 672 ^ [_249477, _249479, _249481, _249483]))], (680 ^ _223975) ^ [] : [-(leq(672 ^ [_249477, _249479, _249481, _249483], _249477))], (682 ^ _223975) ^ [] : [a_select3(_249481, 671 ^ [_249477, _249479, _249481, _249483], 672 ^ [_249477, _249479, _249481, _249483]) = a_select3(_249481, 672 ^ [_249477, _249479, _249481, _249483], 671 ^ [_249477, _249479, _249481, _249483])]], 683 ^ _223975 : [(684 ^ _223975) ^ [_250334, _250336] : [-(a_select3(tptp_mmul(_249483, tptp_mmul(_249481, trans(_249483))), _250336, _250334) = a_select3(tptp_mmul(_249483, tptp_mmul(_249481, trans(_249483))), _250334, _250336)), leq(n0, _250336), leq(_250336, _249479), leq(n0, _250334), leq(_250334, _249479)]]], (702 ^ _223975) ^ [_251029, _251031, _251033, _251035, _251037, _251039, _251041, _251043] : [707 ^ _223975 : [(708 ^ _223975) ^ [] : [-(leq(n0, 705 ^ [_251029, _251031, _251033, _251035, _251037, _251039, _251041, _251043]))], (710 ^ _223975) ^ [] : [-(leq(705 ^ [_251029, _251031, _251033, _251035, _251037, _251039, _251041, _251043], _251029))], (712 ^ _223975) ^ [] : [-(leq(n0, 706 ^ [_251029, _251031, _251033, _251035, _251037, _251039, _251041, _251043]))], (714 ^ _223975) ^ [] : [-(leq(706 ^ [_251029, _251031, _251033, _251035, _251037, _251039, _251041, _251043], _251029))], (716 ^ _223975) ^ [] : [a_select3(_251037, 705 ^ [_251029, _251031, _251033, _251035, _251037, _251039, _251041, _251043], 706 ^ [_251029, _251031, _251033, _251035, _251037, _251039, _251041, _251043]) = a_select3(_251037, 706 ^ [_251029, _251031, _251033, _251035, _251037, _251039, _251041, _251043], 705 ^ [_251029, _251031, _251033, _251035, _251037, _251039, _251041, _251043])]], 721 ^ _223975 : [(722 ^ _223975) ^ [] : [-(leq(n0, 719 ^ [_251029, _251031, _251033, _251035, _251037, _251039, _251041, _251043]))], (724 ^ _223975) ^ [] : [-(leq(719 ^ [_251029, _251031, _251033, _251035, _251037, _251039, _251041, _251043], _251031))], (726 ^ _223975) ^ [] : [-(leq(n0, 720 ^ [_251029, _251031, _251033, _251035, _251037, _251039, _251041, _251043]))], (728 ^ _223975) ^ [] : [-(leq(720 ^ [_251029, _251031, _251033, _251035, _251037, _251039, _251041, _251043], _251031))], (730 ^ _223975) ^ [] : [a_select3(_251043, 719 ^ [_251029, _251031, _251033, _251035, _251037, _251039, _251041, _251043], 720 ^ [_251029, _251031, _251033, _251035, _251037, _251039, _251041, _251043]) = a_select3(_251043, 720 ^ [_251029, _251031, _251033, _251035, _251037, _251039, _251041, _251043], 719 ^ [_251029, _251031, _251033, _251035, _251037, _251039, _251041, _251043])]], 733 ^ _223975 : [(734 ^ _223975) ^ [] : [-(leq(n0, 731 ^ [_251029, _251031, _251033, _251035, _251037, _251039, _251041, _251043]))], (736 ^ _223975) ^ [] : [-(leq(731 ^ [_251029, _251031, _251033, _251035, _251037, _251039, _251041, _251043], _251031))], (738 ^ _223975) ^ [] : [-(leq(n0, 732 ^ [_251029, _251031, _251033, _251035, _251037, _251039, _251041, _251043]))], (740 ^ _223975) ^ [] : [-(leq(732 ^ [_251029, _251031, _251033, _251035, _251037, _251039, _251041, _251043], _251031))], (742 ^ _223975) ^ [] : [a_select3(_251033, 731 ^ [_251029, _251031, _251033, _251035, _251037, _251039, _251041, _251043], 732 ^ [_251029, _251031, _251033, _251035, _251037, _251039, _251041, _251043]) = a_select3(_251033, 732 ^ [_251029, _251031, _251033, _251035, _251037, _251039, _251041, _251043], 731 ^ [_251029, _251031, _251033, _251035, _251037, _251039, _251041, _251043])]], 743 ^ _223975 : [(744 ^ _223975) ^ [_253957, _253959] : [-(a_select3(tptp_madd(_251043, tptp_mmul(_251041, tptp_mmul(tptp_madd(tptp_mmul(_251039, tptp_mmul(_251037, trans(_251039))), tptp_mmul(_251035, tptp_mmul(_251033, trans(_251035)))), trans(_251041)))), _253959, _253957) = a_select3(tptp_madd(_251043, tptp_mmul(_251041, tptp_mmul(tptp_madd(tptp_mmul(_251039, tptp_mmul(_251037, trans(_251039))), tptp_mmul(_251035, tptp_mmul(_251033, trans(_251035)))), trans(_251041)))), _253957, _253959)), leq(n0, _253959), leq(_253959, _251031), leq(n0, _253957), leq(_253957, _251031)]]], (762 ^ _223975) ^ [_254710] : [-(sum(n0, tptp_minus_1, _254710) = n0)], (764 ^ _223975) ^ [_254792] : [-(tptp_float_0_0 = sum(n0, tptp_minus_1, _254792))], (766 ^ _223975) ^ [] : [-(succ(tptp_minus_1) = n0)], (768 ^ _223975) ^ [_254927] : [-(plus(_254927, n1) = succ(_254927))], (770 ^ _223975) ^ [_255010] : [-(plus(n1, _255010) = succ(_255010))], (772 ^ _223975) ^ [_255093] : [-(plus(_255093, n2) = succ(succ(_255093)))], (774 ^ _223975) ^ [_255178] : [-(plus(n2, _255178) = succ(succ(_255178)))], (776 ^ _223975) ^ [_255263] : [-(plus(_255263, n3) = succ(succ(succ(_255263))))], (778 ^ _223975) ^ [_255350] : [-(plus(n3, _255350) = succ(succ(succ(_255350))))], (780 ^ _223975) ^ [_255437] : [-(plus(_255437, n4) = succ(succ(succ(succ(_255437)))))], (782 ^ _223975) ^ [_255526] : [-(plus(n4, _255526) = succ(succ(succ(succ(_255526)))))], (784 ^ _223975) ^ [_255615] : [-(plus(_255615, n5) = succ(succ(succ(succ(succ(_255615))))))], (786 ^ _223975) ^ [_255706] : [-(plus(n5, _255706) = succ(succ(succ(succ(succ(_255706))))))], (788 ^ _223975) ^ [_255797] : [-(minus(_255797, n1) = pred(_255797))], (790 ^ _223975) ^ [_255880] : [-(pred(succ(_255880)) = _255880)], (792 ^ _223975) ^ [_255962] : [-(succ(pred(_255962)) = _255962)], (794 ^ _223975) ^ [_256102, _256104] : [leq(succ(_256104), succ(_256102)), -(leq(_256104, _256102))], (800 ^ _223975) ^ [_256272, _256274] : [leq(_256274, _256272), -(leq(succ(_256274), succ(_256272)))], (806 ^ _223975) ^ [_256492, _256494] : [leq(succ(_256494), _256492), -(gt(_256492, _256494))], (812 ^ _223975) ^ [_256706, _256708] : [leq(minus(_256708, _256706), _256708), -(leq(n0, _256706))], (818 ^ _223975) ^ [_256935, _256937, _256939, _256941] : [-(a_select3(tptp_update3(_256941, _256939, _256937, _256935), _256939, _256937) = _256935)], (820 ^ _223975) ^ [_257127, _257129, _257131, _257133, _257135, _257137, _257139] : [-(a_select3(tptp_update3(_257131, _257139, _257137, _257127), _257135, _257133) = _257129), -(_257139 = _257135), _257137 = _257133, a_select3(_257131, _257135, _257133) = _257129], (834 ^ _223975) ^ [_257670, _257672, _257674, _257676, _257678, _257680] : [-(a_select3(tptp_update3(_257672, _257676, _257674, _257670), _257680, _257678) = _257670), 839 ^ _223975 : [(840 ^ _223975) ^ [] : [-(leq(n0, 837 ^ [_257670, _257672, _257674, _257676, _257678, _257680]))], (842 ^ _223975) ^ [] : [-(leq(n0, 838 ^ [_257670, _257672, _257674, _257676, _257678, _257680]))], (844 ^ _223975) ^ [] : [-(leq(837 ^ [_257670, _257672, _257674, _257676, _257678, _257680], _257676))], (846 ^ _223975) ^ [] : [-(leq(838 ^ [_257670, _257672, _257674, _257676, _257678, _257680], _257674))], (848 ^ _223975) ^ [] : [a_select3(_257672, 837 ^ [_257670, _257672, _257674, _257676, _257678, _257680], 838 ^ [_257670, _257672, _257674, _257676, _257678, _257680]) = _257670]], leq(n0, _257680), leq(_257680, _257676), leq(n0, _257678), leq(_257678, _257674)], (866 ^ _223975) ^ [_259012, _259014, _259016] : [-(a_select2(tptp_update2(_259016, _259014, _259012), _259014) = _259012)], (868 ^ _223975) ^ [_259172, _259174, _259176, _259178, _259180] : [-(a_select2(tptp_update2(_259176, _259180, _259172), _259178) = _259174), -(_259180 = _259178), a_select2(_259176, _259178) = _259174], (897 ^ _223975) ^ [] : [-(true)], (899 ^ _223975) ^ [] : [def = use], (878 ^ _223975) ^ [_259552, _259554, _259556, _259558] : [-(a_select2(tptp_update2(_259554, _259556, _259552), _259558) = _259552), 882 ^ _223975 : [(883 ^ _223975) ^ [] : [-(leq(n0, 881 ^ [_259552, _259554, _259556, _259558]))], (885 ^ _223975) ^ [] : [-(leq(881 ^ [_259552, _259554, _259556, _259558], _259556))], (887 ^ _223975) ^ [] : [a_select2(_259554, 881 ^ [_259552, _259554, _259556, _259558]) = _259552]], leq(n0, _259558), leq(_259558, _259556)]], input).
% 0.96/1.33  ncf('1',plain,[pv47 = 1132 ^ []],start(1138 ^ 0)).
% 0.96/1.33  ncf('1.1',plain,[-(pv47 = 1132 ^ []), 1132 ^ [] = pv47],extension(4 ^ 1,bind([[_224226, _224228], [pv47, 1132 ^ []]]))).
% 0.96/1.33  ncf('1.1.1',plain,[-(1132 ^ [] = pv47), -(gt(1132 ^ [], pv47)), -(gt(pv47, 1132 ^ []))],extension(296 ^ 2,bind([[_234617, _234619], [pv47, 1132 ^ []]]))).
% 0.96/1.33  ncf('1.1.1.1',plain,[gt(1132 ^ [], pv47), -(gt(1132 ^ [], 1132 ^ [])), gt(pv47, 1132 ^ [])],extension(306 ^ 3,bind([[_234932, _234934, _234936], [1132 ^ [], pv47, 1132 ^ []]]))).
% 0.96/1.33  ncf('1.1.1.1.1',plain,[gt(1132 ^ [], 1132 ^ [])],extension(316 ^ 4,bind([[_235211], [1132 ^ []]]))).
% 0.96/1.33  ncf('1.1.1.1.2',plain,[-(gt(pv47, 1132 ^ [])), leq(1132 ^ [], pv47), -(1132 ^ [] = pv47)],extension(360 ^ 4,bind([[_236735, _236737], [pv47, 1132 ^ []]]))).
% 0.96/1.33  ncf('1.1.1.1.2.1',plain,[-(leq(1132 ^ [], pv47))],extension(1136 ^ 5)).
% 0.96/1.33  ncf('1.1.1.1.2.2',plain,[1132 ^ [] = pv47],reduction('1.1')).
% 0.96/1.33  ncf('1.1.1.2',plain,[gt(pv47, 1132 ^ []), -(leq(1132 ^ [], pred(pv47)))],extension(376 ^ 3,bind([[_237232, _237234], [pv47, 1132 ^ []]]))).
% 0.96/1.33  ncf('1.1.1.2.1',plain,[leq(1132 ^ [], pred(pv47)), -(a_select3(q, pv10, 1132 ^ []) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, 1132 ^ [])), minus(a_select2(x, pv10), a_select2(mu, 1132 ^ []))), tptp_minus_2), times(a_select2(sigma, 1132 ^ []), a_select2(sigma, 1132 ^ [])))), a_select2(rho, 1132 ^ [])), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, 1132 ^ []))), sum(n0, n4, divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, tptp_sum_index)), minus(a_select2(x, pv10), a_select2(mu, tptp_sum_index))), tptp_minus_2), times(a_select2(sigma, tptp_sum_index), a_select2(sigma, tptp_sum_index)))), a_select2(rho, tptp_sum_index)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, tptp_sum_index)))))), leq(n0, 1132 ^ [])],extension(1113 ^ 4,bind([[_266190], [1132 ^ []]]))).
% 0.96/1.33  ncf('1.1.1.2.1.1',plain,[a_select3(q, pv10, 1132 ^ []) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, 1132 ^ [])), minus(a_select2(x, pv10), a_select2(mu, 1132 ^ []))), tptp_minus_2), times(a_select2(sigma, 1132 ^ []), a_select2(sigma, 1132 ^ [])))), a_select2(rho, 1132 ^ [])), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, 1132 ^ []))), sum(n0, n4, divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, tptp_sum_index)), minus(a_select2(x, pv10), a_select2(mu, tptp_sum_index))), tptp_minus_2), times(a_select2(sigma, tptp_sum_index), a_select2(sigma, tptp_sum_index)))), a_select2(rho, tptp_sum_index)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, tptp_sum_index)))))],extension(1140 ^ 5)).
% 0.96/1.33  ncf('1.1.1.2.1.2',plain,[-(leq(n0, 1132 ^ []))],extension(1134 ^ 5)).
% 0.96/1.33  %-----------------------------------------------------
% 0.96/1.33  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------