%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SWV159+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n004.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 12:20:05 EDT 2023

% Result   : Theorem 0.36s 1.37s
% Output   : Proof 0.36s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SWV159+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.11/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n004.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Fri May 19 02:46:54 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.36/1.37  
% 0.36/1.37  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 0.36/1.37  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.36/1.37  %-----------------------------------------------------
% 0.36/1.37  ncf(matrix, plain, [(1134 ^ _216503) ^ [] : [-(leq(n0, 1132 ^ []))], (1136 ^ _216503) ^ [] : [-(leq(1132 ^ [], pred(pv10)))], (1138 ^ _216503) ^ [] : [pv10 = 1132 ^ []], (1140 ^ _216503) ^ [] : [sum(n0, n4, a_select3(q, 1132 ^ [], tptp_sum_index)) = n1], (1103 ^ _216503) ^ [] : [-(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 ^ _216503) ^ [] : [-(leq(n0, pv10))], (1107 ^ _216503) ^ [] : [-(leq(n0, pv47))], (1109 ^ _216503) ^ [] : [-(leq(pv10, n135299))], (1111 ^ _216503) ^ [] : [-(leq(pv47, n4))], (1113 ^ _216503) ^ [_258718] : [-(a_select3(q, pv10, _258718) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, _258718)), minus(a_select2(x, pv10), a_select2(mu, _258718))), tptp_minus_2), times(a_select2(sigma, _258718), a_select2(sigma, _258718)))), a_select2(rho, _258718)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, _258718))), 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, _258718), leq(_258718, pred(pv47))], (1123 ^ _216503) ^ [_259081] : [-(sum(n0, n4, a_select3(q, _259081, tptp_sum_index)) = n1), leq(n0, _259081), leq(_259081, pred(pv10))], (2 ^ _216503) ^ [_216647] : [-(_216647 = _216647)], (4 ^ _216503) ^ [_216754, _216756] : [_216756 = _216754, -(_216754 = _216756)], (10 ^ _216503) ^ [_216958, _216960, _216962] : [-(_216962 = _216958), _216962 = _216960, _216960 = _216958], (20 ^ _216503) ^ [_217299, _217301, _217303, _217305] : [-(lt(_217303, _217299)), lt(_217305, _217301), _217305 = _217303, _217301 = _217299], (34 ^ _216503) ^ [_217743, _217745, _217747, _217749] : [-(geq(_217747, _217743)), geq(_217749, _217745), _217749 = _217747, _217745 = _217743], (48 ^ _216503) ^ [_218187, _218189, _218191, _218193] : [-(gt(_218191, _218187)), gt(_218193, _218189), _218193 = _218191, _218189 = _218187], (62 ^ _216503) ^ [_218611, _218613, _218615, _218617] : [-(leq(_218615, _218611)), leq(_218617, _218613), _218617 = _218615, _218613 = _218611], (76 ^ _216503) ^ [_219067, _219069, _219071, _219073] : [-(uniform_int_rnd(_219073, _219069) = uniform_int_rnd(_219071, _219067)), _219073 = _219071, _219069 = _219067], (86 ^ _216503) ^ [_219426, _219428, _219430, _219432] : [-(tptp_const_array1(_219432, _219428) = tptp_const_array1(_219430, _219426)), _219432 = _219430, _219428 = _219426], (96 ^ _216503) ^ [_219813, _219815, _219817, _219819, _219821, _219823] : [-(tptp_const_array2(_219823, _219819, _219815) = tptp_const_array2(_219821, _219817, _219813)), _219823 = _219821, _219819 = _219817, _219815 = _219813], (110 ^ _216503) ^ [_220301, _220303, _220305, _220307] : [-(dim(_220307, _220303) = dim(_220305, _220301)), _220307 = _220305, _220303 = _220301], (120 ^ _216503) ^ [_220632, _220634] : [_220634 = _220632, -(inv(_220634) = inv(_220632))], (126 ^ _216503) ^ [_220878, _220880, _220882, _220884] : [-(tptp_msub(_220884, _220880) = tptp_msub(_220882, _220878)), _220884 = _220882, _220880 = _220878], (136 ^ _216503) ^ [_221237, _221239, _221241, _221243] : [-(tptp_madd(_221243, _221239) = tptp_madd(_221241, _221237)), _221243 = _221241, _221239 = _221237], (146 ^ _216503) ^ [_221596, _221598, _221600, _221602] : [-(tptp_mmul(_221602, _221598) = tptp_mmul(_221600, _221596)), _221602 = _221600, _221598 = _221596], (156 ^ _216503) ^ [_221927, _221929] : [_221929 = _221927, -(trans(_221929) = trans(_221927))], (162 ^ _216503) ^ [_222173, _222175, _222177, _222179] : [-(plus(_222179, _222175) = plus(_222177, _222173)), _222179 = _222177, _222175 = _222173], (172 ^ _216503) ^ [_222588, _222590, _222592, _222594, _222596, _222598, _222600, _222602] : [-(tptp_update3(_222602, _222598, _222594, _222590) = tptp_update3(_222600, _222596, _222592, _222588)), _222602 = _222600, _222598 = _222596, _222594 = _222592, _222590 = _222588], (190 ^ _216503) ^ [_223249, _223251, _223253, _223255, _223257, _223259] : [-(tptp_update2(_223259, _223255, _223251) = tptp_update2(_223257, _223253, _223249)), _223259 = _223257, _223255 = _223253, _223251 = _223249], (204 ^ _216503) ^ [_223709, _223711] : [_223711 = _223709, -(succ(_223711) = succ(_223709))], (210 ^ _216503) ^ [_223927, _223929] : [_223929 = _223927, -(exp(_223929) = exp(_223927))], (216 ^ _216503) ^ [_224173, _224175, _224177, _224179] : [-(divide(_224179, _224175) = divide(_224177, _224173)), _224179 = _224177, _224175 = _224173], (226 ^ _216503) ^ [_224532, _224534, _224536, _224538] : [-(minus(_224538, _224534) = minus(_224536, _224532)), _224538 = _224536, _224534 = _224532], (236 ^ _216503) ^ [_224863, _224865] : [_224865 = _224863, -(sqrt(_224865) = sqrt(_224863))], (242 ^ _216503) ^ [_225109, _225111, _225113, _225115] : [-(times(_225115, _225111) = times(_225113, _225109)), _225115 = _225113, _225111 = _225109], (252 ^ _216503) ^ [_225468, _225470, _225472, _225474] : [-(a_select2(_225474, _225470) = a_select2(_225472, _225468)), _225474 = _225472, _225470 = _225468], (262 ^ _216503) ^ [_225799, _225801] : [_225801 = _225799, -(pred(_225801) = pred(_225799))], (268 ^ _216503) ^ [_226073, _226075, _226077, _226079, _226081, _226083] : [-(sum(_226083, _226079, _226075) = sum(_226081, _226077, _226073)), _226083 = _226081, _226079 = _226077, _226075 = _226073], (282 ^ _216503) ^ [_226569, _226571, _226573, _226575, _226577, _226579] : [-(a_select3(_226579, _226575, _226571) = a_select3(_226577, _226573, _226569)), _226579 = _226577, _226575 = _226573, _226571 = _226569], (901 ^ _216503) ^ [] : [-(gt(n5, n4))], (903 ^ _216503) ^ [] : [-(gt(n135299, n4))], (905 ^ _216503) ^ [] : [-(gt(n135299, n5))], (907 ^ _216503) ^ [] : [-(gt(n4, tptp_minus_1))], (909 ^ _216503) ^ [] : [-(gt(n5, tptp_minus_1))], (911 ^ _216503) ^ [] : [-(gt(n135299, tptp_minus_1))], (913 ^ _216503) ^ [] : [-(gt(n0, tptp_minus_1))], (915 ^ _216503) ^ [] : [-(gt(n1, tptp_minus_1))], (917 ^ _216503) ^ [] : [-(gt(n2, tptp_minus_1))], (919 ^ _216503) ^ [] : [-(gt(n3, tptp_minus_1))], (921 ^ _216503) ^ [] : [-(gt(n4, tptp_minus_2))], (923 ^ _216503) ^ [] : [-(gt(n5, tptp_minus_2))], (925 ^ _216503) ^ [] : [-(gt(tptp_minus_1, tptp_minus_2))], (927 ^ _216503) ^ [] : [-(gt(n135299, tptp_minus_2))], (929 ^ _216503) ^ [] : [-(gt(n0, tptp_minus_2))], (931 ^ _216503) ^ [] : [-(gt(n1, tptp_minus_2))], (933 ^ _216503) ^ [] : [-(gt(n2, tptp_minus_2))], (935 ^ _216503) ^ [] : [-(gt(n3, tptp_minus_2))], (937 ^ _216503) ^ [] : [-(gt(n4, n0))], (939 ^ _216503) ^ [] : [-(gt(n5, n0))], (941 ^ _216503) ^ [] : [-(gt(n135299, n0))], (943 ^ _216503) ^ [] : [-(gt(n1, n0))], (945 ^ _216503) ^ [] : [-(gt(n2, n0))], (947 ^ _216503) ^ [] : [-(gt(n3, n0))], (949 ^ _216503) ^ [] : [-(gt(n4, n1))], (951 ^ _216503) ^ [] : [-(gt(n5, n1))], (953 ^ _216503) ^ [] : [-(gt(n135299, n1))], (955 ^ _216503) ^ [] : [-(gt(n2, n1))], (957 ^ _216503) ^ [] : [-(gt(n3, n1))], (959 ^ _216503) ^ [] : [-(gt(n4, n2))], (961 ^ _216503) ^ [] : [-(gt(n5, n2))], (963 ^ _216503) ^ [] : [-(gt(n135299, n2))], (965 ^ _216503) ^ [] : [-(gt(n3, n2))], (967 ^ _216503) ^ [] : [-(gt(n4, n3))], (969 ^ _216503) ^ [] : [-(gt(n5, n3))], (971 ^ _216503) ^ [] : [-(gt(n135299, n3))], (973 ^ _216503) ^ [_254978] : [leq(n0, _254978), leq(_254978, n4), -(_254978 = n0), -(_254978 = n1), -(_254978 = n2), -(_254978 = n3), -(_254978 = n4)], (999 ^ _216503) ^ [_255599] : [leq(n0, _255599), leq(_255599, n5), -(_255599 = n0), -(_255599 = n1), -(_255599 = n2), -(_255599 = n3), -(_255599 = n4), -(_255599 = n5)], (1029 ^ _216503) ^ [_256306] : [-(_256306 = n0), leq(n0, _256306), leq(_256306, n0)], (1039 ^ _216503) ^ [_256581] : [leq(n0, _256581), leq(_256581, n1), -(_256581 = n0), -(_256581 = n1)], (1053 ^ _216503) ^ [_256944] : [leq(n0, _256944), leq(_256944, n2), -(_256944 = n0), -(_256944 = n1), -(_256944 = n2)], (1093 ^ _216503) ^ [] : [-(succ(succ(succ(succ(n0)))) = n4)], (1095 ^ _216503) ^ [] : [-(succ(succ(succ(succ(succ(n0))))) = n5)], (1097 ^ _216503) ^ [] : [-(succ(n0) = n1)], (1099 ^ _216503) ^ [] : [-(succ(succ(n0)) = n2)], (1101 ^ _216503) ^ [] : [-(succ(succ(succ(n0))) = n3)], (1071 ^ _216503) ^ [_257393] : [leq(n0, _257393), leq(_257393, n3), -(_257393 = n0), -(_257393 = n1), -(_257393 = n2), -(_257393 = n3)], (296 ^ _216503) ^ [_227145, _227147] : [-(gt(_227147, _227145)), -(gt(_227145, _227147)), -(_227147 = _227145)], (306 ^ _216503) ^ [_227460, _227462, _227464] : [-(gt(_227464, _227460)), gt(_227464, _227462), gt(_227462, _227460)], (316 ^ _216503) ^ [_227739] : [gt(_227739, _227739)], (318 ^ _216503) ^ [_227817] : [-(leq(_227817, _227817))], (320 ^ _216503) ^ [_227938, _227940, _227942] : [-(leq(_227942, _227938)), leq(_227942, _227940), leq(_227940, _227938)], (330 ^ _216503) ^ [_228276, _228278] : [lt(_228278, _228276), -(gt(_228276, _228278))], (336 ^ _216503) ^ [_228438, _228440] : [gt(_228438, _228440), -(lt(_228440, _228438))], (342 ^ _216503) ^ [_228679, _228681] : [geq(_228681, _228679), -(leq(_228679, _228681))], (348 ^ _216503) ^ [_228841, _228843] : [leq(_228841, _228843), -(geq(_228843, _228841))], (354 ^ _216503) ^ [_229053, _229055] : [gt(_229053, _229055), -(leq(_229055, _229053))], (360 ^ _216503) ^ [_229263, _229265] : [-(gt(_229263, _229265)), leq(_229265, _229263), -(_229265 = _229263)], (370 ^ _216503) ^ [_229594, _229596] : [leq(_229596, pred(_229594)), -(gt(_229594, _229596))], (376 ^ _216503) ^ [_229760, _229762] : [gt(_229760, _229762), -(leq(_229762, pred(_229760)))], (382 ^ _216503) ^ [_229947] : [-(gt(succ(_229947), _229947))], (384 ^ _216503) ^ [_230056, _230058] : [leq(_230058, _230056), -(leq(_230058, succ(_230056)))], (390 ^ _216503) ^ [_230299, _230301] : [leq(_230301, _230299), -(gt(succ(_230299), _230301))], (396 ^ _216503) ^ [_230465, _230467] : [gt(succ(_230465), _230467), -(leq(_230467, _230465))], (402 ^ _216503) ^ [_230681, _230683] : [leq(n0, _230683), -(leq(uniform_int_rnd(_230681, _230683), _230683))], (408 ^ _216503) ^ [_230897, _230899] : [leq(n0, _230899), -(leq(n0, uniform_int_rnd(_230897, _230899)))], (414 ^ _216503) ^ [_231141, _231143, _231145, _231147] : [-(a_select2(tptp_const_array1(dim(_231145, _231143), _231141), _231147) = _231141), leq(_231145, _231147), leq(_231147, _231143)], (424 ^ _216503) ^ [_231548, _231550, _231552, _231554, _231556, _231558, _231560] : [-(a_select3(tptp_const_array2(dim(_231558, _231556), dim(_231552, _231550), _231548), _231560, _231554) = _231548), leq(_231558, _231560), leq(_231560, _231556), leq(_231552, _231554), leq(_231554, _231550)], (442 ^ _216503) ^ [_232143, _232145] : [445 ^ _216503 : [(446 ^ _216503) ^ [] : [-(leq(n0, 443 ^ [_232143, _232145]))], (448 ^ _216503) ^ [] : [-(leq(443 ^ [_232143, _232145], _232143))], (450 ^ _216503) ^ [] : [-(leq(n0, 444 ^ [_232143, _232145]))], (452 ^ _216503) ^ [] : [-(leq(444 ^ [_232143, _232145], _232143))], (454 ^ _216503) ^ [] : [a_select3(_232145, 443 ^ [_232143, _232145], 444 ^ [_232143, _232145]) = a_select3(_232145, 444 ^ [_232143, _232145], 443 ^ [_232143, _232145])]], 455 ^ _216503 : [(456 ^ _216503) ^ [_232900, _232902] : [-(a_select3(trans(_232145), _232902, _232900) = a_select3(trans(_232145), _232900, _232902)), leq(n0, _232902), leq(_232902, _232143), leq(n0, _232900), leq(_232900, _232143)]]], (474 ^ _216503) ^ [_233447, _233449] : [477 ^ _216503 : [(478 ^ _216503) ^ [] : [-(leq(n0, 475 ^ [_233447, _233449]))], (480 ^ _216503) ^ [] : [-(leq(475 ^ [_233447, _233449], _233447))], (482 ^ _216503) ^ [] : [-(leq(n0, 476 ^ [_233447, _233449]))], (484 ^ _216503) ^ [] : [-(leq(476 ^ [_233447, _233449], _233447))], (486 ^ _216503) ^ [] : [a_select3(_233449, 475 ^ [_233447, _233449], 476 ^ [_233447, _233449]) = a_select3(_233449, 476 ^ [_233447, _233449], 475 ^ [_233447, _233449])]], 487 ^ _216503 : [(488 ^ _216503) ^ [_234204, _234206] : [-(a_select3(inv(_233449), _234206, _234204) = a_select3(inv(_233449), _234204, _234206)), leq(n0, _234206), leq(_234206, _233447), leq(n0, _234204), leq(_234204, _233447)]]], (506 ^ _216503) ^ [_234751, _234753] : [509 ^ _216503 : [(510 ^ _216503) ^ [] : [-(leq(n0, 507 ^ [_234751, _234753]))], (512 ^ _216503) ^ [] : [-(leq(507 ^ [_234751, _234753], _234751))], (514 ^ _216503) ^ [] : [-(leq(n0, 508 ^ [_234751, _234753]))], (516 ^ _216503) ^ [] : [-(leq(508 ^ [_234751, _234753], _234751))], (518 ^ _216503) ^ [] : [a_select3(_234753, 507 ^ [_234751, _234753], 508 ^ [_234751, _234753]) = a_select3(_234753, 508 ^ [_234751, _234753], 507 ^ [_234751, _234753])]], 519 ^ _216503 : [(520 ^ _216503) ^ [_235564, _235566, _235568, _235570] : [-(a_select3(tptp_update3(_234753, _235566, _235566, _235564), _235570, _235568) = a_select3(tptp_update3(_234753, _235566, _235566, _235564), _235568, _235570)), leq(n0, _235570), leq(_235570, _234751), leq(n0, _235568), leq(_235568, _234751), leq(n0, _235566), leq(_235566, _234751)]]], (546 ^ _216503) ^ [_236383, _236385, _236387] : [551 ^ _216503 : [(552 ^ _216503) ^ [] : [-(leq(n0, 549 ^ [_236383, _236385, _236387]))], (554 ^ _216503) ^ [] : [-(leq(549 ^ [_236383, _236385, _236387], _236383))], (556 ^ _216503) ^ [] : [-(leq(n0, 550 ^ [_236383, _236385, _236387]))], (558 ^ _216503) ^ [] : [-(leq(550 ^ [_236383, _236385, _236387], _236383))], (560 ^ _216503) ^ [] : [a_select3(_236387, 549 ^ [_236383, _236385, _236387], 550 ^ [_236383, _236385, _236387]) = a_select3(_236387, 550 ^ [_236383, _236385, _236387], 549 ^ [_236383, _236385, _236387])]], 563 ^ _216503 : [(564 ^ _216503) ^ [] : [-(leq(n0, 561 ^ [_236383, _236385, _236387]))], (566 ^ _216503) ^ [] : [-(leq(561 ^ [_236383, _236385, _236387], _236383))], (568 ^ _216503) ^ [] : [-(leq(n0, 562 ^ [_236383, _236385, _236387]))], (570 ^ _216503) ^ [] : [-(leq(562 ^ [_236383, _236385, _236387], _236383))], (572 ^ _216503) ^ [] : [a_select3(_236385, 561 ^ [_236383, _236385, _236387], 562 ^ [_236383, _236385, _236387]) = a_select3(_236385, 562 ^ [_236383, _236385, _236387], 561 ^ [_236383, _236385, _236387])]], 573 ^ _216503 : [(574 ^ _216503) ^ [_237892, _237894] : [-(a_select3(tptp_madd(_236387, _236385), _237894, _237892) = a_select3(tptp_madd(_236387, _236385), _237892, _237894)), leq(n0, _237894), leq(_237894, _236383), leq(n0, _237892), leq(_237892, _236383)]]], (592 ^ _216503) ^ [_238478, _238480, _238482] : [597 ^ _216503 : [(598 ^ _216503) ^ [] : [-(leq(n0, 595 ^ [_238478, _238480, _238482]))], (600 ^ _216503) ^ [] : [-(leq(595 ^ [_238478, _238480, _238482], _238478))], (602 ^ _216503) ^ [] : [-(leq(n0, 596 ^ [_238478, _238480, _238482]))], (604 ^ _216503) ^ [] : [-(leq(596 ^ [_238478, _238480, _238482], _238478))], (606 ^ _216503) ^ [] : [a_select3(_238482, 595 ^ [_238478, _238480, _238482], 596 ^ [_238478, _238480, _238482]) = a_select3(_238482, 596 ^ [_238478, _238480, _238482], 595 ^ [_238478, _238480, _238482])]], 609 ^ _216503 : [(610 ^ _216503) ^ [] : [-(leq(n0, 607 ^ [_238478, _238480, _238482]))], (612 ^ _216503) ^ [] : [-(leq(607 ^ [_238478, _238480, _238482], _238478))], (614 ^ _216503) ^ [] : [-(leq(n0, 608 ^ [_238478, _238480, _238482]))], (616 ^ _216503) ^ [] : [-(leq(608 ^ [_238478, _238480, _238482], _238478))], (618 ^ _216503) ^ [] : [a_select3(_238480, 607 ^ [_238478, _238480, _238482], 608 ^ [_238478, _238480, _238482]) = a_select3(_238480, 608 ^ [_238478, _238480, _238482], 607 ^ [_238478, _238480, _238482])]], 619 ^ _216503 : [(620 ^ _216503) ^ [_239987, _239989] : [-(a_select3(tptp_msub(_238482, _238480), _239989, _239987) = a_select3(tptp_msub(_238482, _238480), _239987, _239989)), leq(n0, _239989), leq(_239989, _238478), leq(n0, _239987), leq(_239987, _238478)]]], (638 ^ _216503) ^ [_240573, _240575, _240577] : [641 ^ _216503 : [(642 ^ _216503) ^ [] : [-(leq(n0, 639 ^ [_240573, _240575, _240577]))], (644 ^ _216503) ^ [] : [-(leq(639 ^ [_240573, _240575, _240577], _240573))], (646 ^ _216503) ^ [] : [-(leq(n0, 640 ^ [_240573, _240575, _240577]))], (648 ^ _216503) ^ [] : [-(leq(640 ^ [_240573, _240575, _240577], _240573))], (650 ^ _216503) ^ [] : [a_select3(_240575, 639 ^ [_240573, _240575, _240577], 640 ^ [_240573, _240575, _240577]) = a_select3(_240575, 640 ^ [_240573, _240575, _240577], 639 ^ [_240573, _240575, _240577])]], 651 ^ _216503 : [(652 ^ _216503) ^ [_241386, _241388] : [-(a_select3(tptp_mmul(_240577, tptp_mmul(_240575, trans(_240577))), _241388, _241386) = a_select3(tptp_mmul(_240577, tptp_mmul(_240575, trans(_240577))), _241386, _241388)), leq(n0, _241388), leq(_241388, _240573), leq(n0, _241386), leq(_241386, _240573)]]], (670 ^ _216503) ^ [_242005, _242007, _242009, _242011] : [673 ^ _216503 : [(674 ^ _216503) ^ [] : [-(leq(n0, 671 ^ [_242005, _242007, _242009, _242011]))], (676 ^ _216503) ^ [] : [-(leq(671 ^ [_242005, _242007, _242009, _242011], _242005))], (678 ^ _216503) ^ [] : [-(leq(n0, 672 ^ [_242005, _242007, _242009, _242011]))], (680 ^ _216503) ^ [] : [-(leq(672 ^ [_242005, _242007, _242009, _242011], _242005))], (682 ^ _216503) ^ [] : [a_select3(_242009, 671 ^ [_242005, _242007, _242009, _242011], 672 ^ [_242005, _242007, _242009, _242011]) = a_select3(_242009, 672 ^ [_242005, _242007, _242009, _242011], 671 ^ [_242005, _242007, _242009, _242011])]], 683 ^ _216503 : [(684 ^ _216503) ^ [_242862, _242864] : [-(a_select3(tptp_mmul(_242011, tptp_mmul(_242009, trans(_242011))), _242864, _242862) = a_select3(tptp_mmul(_242011, tptp_mmul(_242009, trans(_242011))), _242862, _242864)), leq(n0, _242864), leq(_242864, _242007), leq(n0, _242862), leq(_242862, _242007)]]], (702 ^ _216503) ^ [_243557, _243559, _243561, _243563, _243565, _243567, _243569, _243571] : [707 ^ _216503 : [(708 ^ _216503) ^ [] : [-(leq(n0, 705 ^ [_243557, _243559, _243561, _243563, _243565, _243567, _243569, _243571]))], (710 ^ _216503) ^ [] : [-(leq(705 ^ [_243557, _243559, _243561, _243563, _243565, _243567, _243569, _243571], _243557))], (712 ^ _216503) ^ [] : [-(leq(n0, 706 ^ [_243557, _243559, _243561, _243563, _243565, _243567, _243569, _243571]))], (714 ^ _216503) ^ [] : [-(leq(706 ^ [_243557, _243559, _243561, _243563, _243565, _243567, _243569, _243571], _243557))], (716 ^ _216503) ^ [] : [a_select3(_243565, 705 ^ [_243557, _243559, _243561, _243563, _243565, _243567, _243569, _243571], 706 ^ [_243557, _243559, _243561, _243563, _243565, _243567, _243569, _243571]) = a_select3(_243565, 706 ^ [_243557, _243559, _243561, _243563, _243565, _243567, _243569, _243571], 705 ^ [_243557, _243559, _243561, _243563, _243565, _243567, _243569, _243571])]], 721 ^ _216503 : [(722 ^ _216503) ^ [] : [-(leq(n0, 719 ^ [_243557, _243559, _243561, _243563, _243565, _243567, _243569, _243571]))], (724 ^ _216503) ^ [] : [-(leq(719 ^ [_243557, _243559, _243561, _243563, _243565, _243567, _243569, _243571], _243559))], (726 ^ _216503) ^ [] : [-(leq(n0, 720 ^ [_243557, _243559, _243561, _243563, _243565, _243567, _243569, _243571]))], (728 ^ _216503) ^ [] : [-(leq(720 ^ [_243557, _243559, _243561, _243563, _243565, _243567, _243569, _243571], _243559))], (730 ^ _216503) ^ [] : [a_select3(_243571, 719 ^ [_243557, _243559, _243561, _243563, _243565, _243567, _243569, _243571], 720 ^ [_243557, _243559, _243561, _243563, _243565, _243567, _243569, _243571]) = a_select3(_243571, 720 ^ [_243557, _243559, _243561, _243563, _243565, _243567, _243569, _243571], 719 ^ [_243557, _243559, _243561, _243563, _243565, _243567, _243569, _243571])]], 733 ^ _216503 : [(734 ^ _216503) ^ [] : [-(leq(n0, 731 ^ [_243557, _243559, _243561, _243563, _243565, _243567, _243569, _243571]))], (736 ^ _216503) ^ [] : [-(leq(731 ^ [_243557, _243559, _243561, _243563, _243565, _243567, _243569, _243571], _243559))], (738 ^ _216503) ^ [] : [-(leq(n0, 732 ^ [_243557, _243559, _243561, _243563, _243565, _243567, _243569, _243571]))], (740 ^ _216503) ^ [] : [-(leq(732 ^ [_243557, _243559, _243561, _243563, _243565, _243567, _243569, _243571], _243559))], (742 ^ _216503) ^ [] : [a_select3(_243561, 731 ^ [_243557, _243559, _243561, _243563, _243565, _243567, _243569, _243571], 732 ^ [_243557, _243559, _243561, _243563, _243565, _243567, _243569, _243571]) = a_select3(_243561, 732 ^ [_243557, _243559, _243561, _243563, _243565, _243567, _243569, _243571], 731 ^ [_243557, _243559, _243561, _243563, _243565, _243567, _243569, _243571])]], 743 ^ _216503 : [(744 ^ _216503) ^ [_246485, _246487] : [-(a_select3(tptp_madd(_243571, tptp_mmul(_243569, tptp_mmul(tptp_madd(tptp_mmul(_243567, tptp_mmul(_243565, trans(_243567))), tptp_mmul(_243563, tptp_mmul(_243561, trans(_243563)))), trans(_243569)))), _246487, _246485) = a_select3(tptp_madd(_243571, tptp_mmul(_243569, tptp_mmul(tptp_madd(tptp_mmul(_243567, tptp_mmul(_243565, trans(_243567))), tptp_mmul(_243563, tptp_mmul(_243561, trans(_243563)))), trans(_243569)))), _246485, _246487)), leq(n0, _246487), leq(_246487, _243559), leq(n0, _246485), leq(_246485, _243559)]]], (762 ^ _216503) ^ [_247238] : [-(sum(n0, tptp_minus_1, _247238) = n0)], (764 ^ _216503) ^ [_247320] : [-(tptp_float_0_0 = sum(n0, tptp_minus_1, _247320))], (766 ^ _216503) ^ [] : [-(succ(tptp_minus_1) = n0)], (768 ^ _216503) ^ [_247455] : [-(plus(_247455, n1) = succ(_247455))], (770 ^ _216503) ^ [_247538] : [-(plus(n1, _247538) = succ(_247538))], (772 ^ _216503) ^ [_247621] : [-(plus(_247621, n2) = succ(succ(_247621)))], (774 ^ _216503) ^ [_247706] : [-(plus(n2, _247706) = succ(succ(_247706)))], (776 ^ _216503) ^ [_247791] : [-(plus(_247791, n3) = succ(succ(succ(_247791))))], (778 ^ _216503) ^ [_247878] : [-(plus(n3, _247878) = succ(succ(succ(_247878))))], (780 ^ _216503) ^ [_247965] : [-(plus(_247965, n4) = succ(succ(succ(succ(_247965)))))], (782 ^ _216503) ^ [_248054] : [-(plus(n4, _248054) = succ(succ(succ(succ(_248054)))))], (784 ^ _216503) ^ [_248143] : [-(plus(_248143, n5) = succ(succ(succ(succ(succ(_248143))))))], (786 ^ _216503) ^ [_248234] : [-(plus(n5, _248234) = succ(succ(succ(succ(succ(_248234))))))], (788 ^ _216503) ^ [_248325] : [-(minus(_248325, n1) = pred(_248325))], (790 ^ _216503) ^ [_248408] : [-(pred(succ(_248408)) = _248408)], (792 ^ _216503) ^ [_248490] : [-(succ(pred(_248490)) = _248490)], (794 ^ _216503) ^ [_248630, _248632] : [leq(succ(_248632), succ(_248630)), -(leq(_248632, _248630))], (800 ^ _216503) ^ [_248800, _248802] : [leq(_248802, _248800), -(leq(succ(_248802), succ(_248800)))], (806 ^ _216503) ^ [_249020, _249022] : [leq(succ(_249022), _249020), -(gt(_249020, _249022))], (812 ^ _216503) ^ [_249234, _249236] : [leq(minus(_249236, _249234), _249236), -(leq(n0, _249234))], (818 ^ _216503) ^ [_249463, _249465, _249467, _249469] : [-(a_select3(tptp_update3(_249469, _249467, _249465, _249463), _249467, _249465) = _249463)], (820 ^ _216503) ^ [_249655, _249657, _249659, _249661, _249663, _249665, _249667] : [-(a_select3(tptp_update3(_249659, _249667, _249665, _249655), _249663, _249661) = _249657), -(_249667 = _249663), _249665 = _249661, a_select3(_249659, _249663, _249661) = _249657], (834 ^ _216503) ^ [_250198, _250200, _250202, _250204, _250206, _250208] : [-(a_select3(tptp_update3(_250200, _250204, _250202, _250198), _250208, _250206) = _250198), 839 ^ _216503 : [(840 ^ _216503) ^ [] : [-(leq(n0, 837 ^ [_250198, _250200, _250202, _250204, _250206, _250208]))], (842 ^ _216503) ^ [] : [-(leq(n0, 838 ^ [_250198, _250200, _250202, _250204, _250206, _250208]))], (844 ^ _216503) ^ [] : [-(leq(837 ^ [_250198, _250200, _250202, _250204, _250206, _250208], _250204))], (846 ^ _216503) ^ [] : [-(leq(838 ^ [_250198, _250200, _250202, _250204, _250206, _250208], _250202))], (848 ^ _216503) ^ [] : [a_select3(_250200, 837 ^ [_250198, _250200, _250202, _250204, _250206, _250208], 838 ^ [_250198, _250200, _250202, _250204, _250206, _250208]) = _250198]], leq(n0, _250208), leq(_250208, _250204), leq(n0, _250206), leq(_250206, _250202)], (866 ^ _216503) ^ [_251540, _251542, _251544] : [-(a_select2(tptp_update2(_251544, _251542, _251540), _251542) = _251540)], (868 ^ _216503) ^ [_251700, _251702, _251704, _251706, _251708] : [-(a_select2(tptp_update2(_251704, _251708, _251700), _251706) = _251702), -(_251708 = _251706), a_select2(_251704, _251706) = _251702], (897 ^ _216503) ^ [] : [-(true)], (899 ^ _216503) ^ [] : [def = use], (878 ^ _216503) ^ [_252080, _252082, _252084, _252086] : [-(a_select2(tptp_update2(_252082, _252084, _252080), _252086) = _252080), 882 ^ _216503 : [(883 ^ _216503) ^ [] : [-(leq(n0, 881 ^ [_252080, _252082, _252084, _252086]))], (885 ^ _216503) ^ [] : [-(leq(881 ^ [_252080, _252082, _252084, _252086], _252084))], (887 ^ _216503) ^ [] : [a_select2(_252082, 881 ^ [_252080, _252082, _252084, _252086]) = _252080]], leq(n0, _252086), leq(_252086, _252084)]], input).
% 0.36/1.37  ncf('1',plain,[sum(n0, n4, a_select3(q, 1132 ^ [], tptp_sum_index)) = n1],start(1140 ^ 0)).
% 0.36/1.37  ncf('1.1',plain,[-(sum(n0, n4, a_select3(q, 1132 ^ [], tptp_sum_index)) = n1), leq(n0, 1132 ^ []), leq(1132 ^ [], pred(pv10))],extension(1123 ^ 1,bind([[_259081], [1132 ^ []]]))).
% 0.36/1.37  ncf('1.1.1',plain,[-(leq(n0, 1132 ^ []))],extension(1134 ^ 2)).
% 0.36/1.37  ncf('1.1.2',plain,[-(leq(1132 ^ [], pred(pv10)))],extension(1136 ^ 2)).
% 0.36/1.37  %-----------------------------------------------------
% 0.36/1.37  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------