%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SWV177+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n013.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 12:20:07 EDT 2023

% Result   : Theorem 0.36s 1.41s
% Output   : Proof 0.36s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SWV177+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.07/0.14  % Command  : nanocop.sh %s %d
% 0.13/0.35  % Computer : n013.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Fri May 19 02:31:50 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.36/1.41  
% 0.36/1.41  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 0.36/1.41  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.36/1.41  %-----------------------------------------------------
% 0.36/1.41  ncf(matrix, plain, [(1166 ^ _210494) ^ [] : [-(leq(n0, 1164 ^ []))], (1168 ^ _210494) ^ [] : [-(leq(1164 ^ [], n4))], (1170 ^ _210494) ^ [] : [a_select2(rhoold_init, 1164 ^ []) = init], (1055 ^ _210494) ^ [] : [-(leq(n0, pv40))], (1057 ^ _210494) ^ [] : [-(leq(n0, pv45))], (1059 ^ _210494) ^ [] : [-(leq(pv40, n4))], (1061 ^ _210494) ^ [] : [-(leq(pv45, n135299))], (1063 ^ _210494) ^ [] : [-(gt(loopcounter, n1))], (1065 ^ _210494) ^ [_251075] : [leq(n0, _251075), leq(_251075, n135299), 1072 ^ _210494 : [(1073 ^ _210494) ^ [_251303] : [-(a_select3(q_init, _251075, _251303) = init), leq(n0, _251303), leq(_251303, n4)]]], (1083 ^ _210494) ^ [_251605] : [-(a_select2(rho_init, _251605) = init), leq(n0, _251605), leq(_251605, n4)], (1093 ^ _210494) ^ [_251886] : [-(a_select2(mu_init, _251886) = init), leq(n0, _251886), leq(_251886, pred(pv40))], (1103 ^ _210494) ^ [_252167] : [-(a_select2(sigma_init, _252167) = init), leq(n0, _252167), leq(_252167, pred(pv40))], (1113 ^ _210494) ^ [_252448] : [-(a_select3(center_init, _252448, n0) = init), leq(n0, _252448), leq(_252448, n4)], (1123 ^ _210494) ^ [] : [gt(loopcounter, n1), 1126 ^ _210494 : [(1127 ^ _210494) ^ [_252793] : [-(a_select2(muold_init, _252793) = init), leq(n0, _252793), leq(_252793, n4)]]], (1137 ^ _210494) ^ [] : [gt(loopcounter, n1), 1140 ^ _210494 : [(1141 ^ _210494) ^ [_253141] : [-(a_select2(rhoold_init, _253141) = init), leq(n0, _253141), leq(_253141, n4)]]], (1151 ^ _210494) ^ [] : [gt(loopcounter, n1), 1154 ^ _210494 : [(1155 ^ _210494) ^ [_253469] : [-(a_select2(sigmaold_init, _253469) = init), leq(n0, _253469), leq(_253469, n4)]]], (2 ^ _210494) ^ [_210638] : [-(_210638 = _210638)], (4 ^ _210494) ^ [_210745, _210747] : [_210747 = _210745, -(_210745 = _210747)], (10 ^ _210494) ^ [_210949, _210951, _210953] : [-(_210953 = _210949), _210953 = _210951, _210951 = _210949], (20 ^ _210494) ^ [_211290, _211292, _211294, _211296] : [-(lt(_211294, _211290)), lt(_211296, _211292), _211296 = _211294, _211292 = _211290], (34 ^ _210494) ^ [_211734, _211736, _211738, _211740] : [-(geq(_211738, _211734)), geq(_211740, _211736), _211740 = _211738, _211736 = _211734], (48 ^ _210494) ^ [_212178, _212180, _212182, _212184] : [-(gt(_212182, _212178)), gt(_212184, _212180), _212184 = _212182, _212180 = _212178], (62 ^ _210494) ^ [_212602, _212604, _212606, _212608] : [-(leq(_212606, _212602)), leq(_212608, _212604), _212608 = _212606, _212604 = _212602], (76 ^ _210494) ^ [_213058, _213060, _213062, _213064] : [-(uniform_int_rnd(_213064, _213060) = uniform_int_rnd(_213062, _213058)), _213064 = _213062, _213060 = _213058], (86 ^ _210494) ^ [_213417, _213419, _213421, _213423] : [-(tptp_const_array1(_213423, _213419) = tptp_const_array1(_213421, _213417)), _213423 = _213421, _213419 = _213417], (96 ^ _210494) ^ [_213804, _213806, _213808, _213810, _213812, _213814] : [-(tptp_const_array2(_213814, _213810, _213806) = tptp_const_array2(_213812, _213808, _213804)), _213814 = _213812, _213810 = _213808, _213806 = _213804], (110 ^ _210494) ^ [_214292, _214294, _214296, _214298] : [-(dim(_214298, _214294) = dim(_214296, _214292)), _214298 = _214296, _214294 = _214292], (120 ^ _210494) ^ [_214623, _214625] : [_214625 = _214623, -(inv(_214625) = inv(_214623))], (126 ^ _210494) ^ [_214869, _214871, _214873, _214875] : [-(tptp_msub(_214875, _214871) = tptp_msub(_214873, _214869)), _214875 = _214873, _214871 = _214869], (136 ^ _210494) ^ [_215228, _215230, _215232, _215234] : [-(tptp_madd(_215234, _215230) = tptp_madd(_215232, _215228)), _215234 = _215232, _215230 = _215228], (146 ^ _210494) ^ [_215587, _215589, _215591, _215593] : [-(tptp_mmul(_215593, _215589) = tptp_mmul(_215591, _215587)), _215593 = _215591, _215589 = _215587], (156 ^ _210494) ^ [_215918, _215920] : [_215920 = _215918, -(trans(_215920) = trans(_215918))], (162 ^ _210494) ^ [_216192, _216194, _216196, _216198, _216200, _216202] : [-(sum(_216202, _216198, _216194) = sum(_216200, _216196, _216192)), _216202 = _216200, _216198 = _216196, _216194 = _216192], (176 ^ _210494) ^ [_216680, _216682, _216684, _216686] : [-(plus(_216686, _216682) = plus(_216684, _216680)), _216686 = _216684, _216682 = _216680], (186 ^ _210494) ^ [_217039, _217041, _217043, _217045] : [-(minus(_217045, _217041) = minus(_217043, _217039)), _217045 = _217043, _217041 = _217039], (196 ^ _210494) ^ [_217454, _217456, _217458, _217460, _217462, _217464, _217466, _217468] : [-(tptp_update3(_217468, _217464, _217460, _217456) = tptp_update3(_217466, _217462, _217458, _217454)), _217468 = _217466, _217464 = _217462, _217460 = _217458, _217456 = _217454], (214 ^ _210494) ^ [_218115, _218117, _218119, _218121, _218123, _218125] : [-(tptp_update2(_218125, _218121, _218117) = tptp_update2(_218123, _218119, _218115)), _218125 = _218123, _218121 = _218119, _218117 = _218115], (228 ^ _210494) ^ [_218575, _218577] : [_218577 = _218575, -(succ(_218577) = succ(_218575))], (234 ^ _210494) ^ [_218793, _218795] : [_218795 = _218793, -(pred(_218795) = pred(_218793))], (254 ^ _210494) ^ [_219535, _219537, _219539, _219541] : [-(a_select2(_219541, _219537) = a_select2(_219539, _219535)), _219541 = _219539, _219537 = _219535], (240 ^ _210494) ^ [_219067, _219069, _219071, _219073, _219075, _219077] : [-(a_select3(_219077, _219073, _219069) = a_select3(_219075, _219071, _219067)), _219077 = _219075, _219073 = _219071, _219069 = _219067], (869 ^ _210494) ^ [] : [-(gt(n5, n4))], (871 ^ _210494) ^ [] : [-(gt(n135299, n4))], (873 ^ _210494) ^ [] : [-(gt(n135299, n5))], (875 ^ _210494) ^ [] : [-(gt(n4, tptp_minus_1))], (877 ^ _210494) ^ [] : [-(gt(n5, tptp_minus_1))], (879 ^ _210494) ^ [] : [-(gt(n135299, tptp_minus_1))], (881 ^ _210494) ^ [] : [-(gt(n0, tptp_minus_1))], (883 ^ _210494) ^ [] : [-(gt(n1, tptp_minus_1))], (885 ^ _210494) ^ [] : [-(gt(n2, tptp_minus_1))], (887 ^ _210494) ^ [] : [-(gt(n3, tptp_minus_1))], (889 ^ _210494) ^ [] : [-(gt(n4, n0))], (891 ^ _210494) ^ [] : [-(gt(n5, n0))], (893 ^ _210494) ^ [] : [-(gt(n135299, n0))], (895 ^ _210494) ^ [] : [-(gt(n1, n0))], (897 ^ _210494) ^ [] : [-(gt(n2, n0))], (899 ^ _210494) ^ [] : [-(gt(n3, n0))], (901 ^ _210494) ^ [] : [-(gt(n4, n1))], (903 ^ _210494) ^ [] : [-(gt(n5, n1))], (905 ^ _210494) ^ [] : [-(gt(n135299, n1))], (907 ^ _210494) ^ [] : [-(gt(n2, n1))], (909 ^ _210494) ^ [] : [-(gt(n3, n1))], (911 ^ _210494) ^ [] : [-(gt(n4, n2))], (913 ^ _210494) ^ [] : [-(gt(n5, n2))], (915 ^ _210494) ^ [] : [-(gt(n135299, n2))], (917 ^ _210494) ^ [] : [-(gt(n3, n2))], (919 ^ _210494) ^ [] : [-(gt(n4, n3))], (921 ^ _210494) ^ [] : [-(gt(n5, n3))], (923 ^ _210494) ^ [] : [-(gt(n135299, n3))], (925 ^ _210494) ^ [_247375] : [leq(n0, _247375), leq(_247375, n4), -(_247375 = n0), -(_247375 = n1), -(_247375 = n2), -(_247375 = n3), -(_247375 = n4)], (951 ^ _210494) ^ [_247996] : [leq(n0, _247996), leq(_247996, n5), -(_247996 = n0), -(_247996 = n1), -(_247996 = n2), -(_247996 = n3), -(_247996 = n4), -(_247996 = n5)], (981 ^ _210494) ^ [_248703] : [-(_248703 = n0), leq(n0, _248703), leq(_248703, n0)], (991 ^ _210494) ^ [_248978] : [leq(n0, _248978), leq(_248978, n1), -(_248978 = n0), -(_248978 = n1)], (1005 ^ _210494) ^ [_249341] : [leq(n0, _249341), leq(_249341, n2), -(_249341 = n0), -(_249341 = n1), -(_249341 = n2)], (1045 ^ _210494) ^ [] : [-(succ(succ(succ(succ(n0)))) = n4)], (1047 ^ _210494) ^ [] : [-(succ(succ(succ(succ(succ(n0))))) = n5)], (1049 ^ _210494) ^ [] : [-(succ(n0) = n1)], (1051 ^ _210494) ^ [] : [-(succ(succ(n0)) = n2)], (1053 ^ _210494) ^ [] : [-(succ(succ(succ(n0))) = n3)], (1023 ^ _210494) ^ [_249790] : [leq(n0, _249790), leq(_249790, n3), -(_249790 = n0), -(_249790 = n1), -(_249790 = n2), -(_249790 = n3)], (264 ^ _210494) ^ [_219966, _219968] : [-(gt(_219968, _219966)), -(gt(_219966, _219968)), -(_219968 = _219966)], (274 ^ _210494) ^ [_220281, _220283, _220285] : [-(gt(_220285, _220281)), gt(_220285, _220283), gt(_220283, _220281)], (284 ^ _210494) ^ [_220560] : [gt(_220560, _220560)], (286 ^ _210494) ^ [_220638] : [-(leq(_220638, _220638))], (288 ^ _210494) ^ [_220759, _220761, _220763] : [-(leq(_220763, _220759)), leq(_220763, _220761), leq(_220761, _220759)], (298 ^ _210494) ^ [_221097, _221099] : [lt(_221099, _221097), -(gt(_221097, _221099))], (304 ^ _210494) ^ [_221259, _221261] : [gt(_221259, _221261), -(lt(_221261, _221259))], (310 ^ _210494) ^ [_221500, _221502] : [geq(_221502, _221500), -(leq(_221500, _221502))], (316 ^ _210494) ^ [_221662, _221664] : [leq(_221662, _221664), -(geq(_221664, _221662))], (322 ^ _210494) ^ [_221874, _221876] : [gt(_221874, _221876), -(leq(_221876, _221874))], (328 ^ _210494) ^ [_222084, _222086] : [-(gt(_222084, _222086)), leq(_222086, _222084), -(_222086 = _222084)], (338 ^ _210494) ^ [_222415, _222417] : [leq(_222417, pred(_222415)), -(gt(_222415, _222417))], (344 ^ _210494) ^ [_222581, _222583] : [gt(_222581, _222583), -(leq(_222583, pred(_222581)))], (350 ^ _210494) ^ [_222768] : [-(gt(succ(_222768), _222768))], (352 ^ _210494) ^ [_222877, _222879] : [leq(_222879, _222877), -(leq(_222879, succ(_222877)))], (358 ^ _210494) ^ [_223120, _223122] : [leq(_223122, _223120), -(gt(succ(_223120), _223122))], (364 ^ _210494) ^ [_223286, _223288] : [gt(succ(_223286), _223288), -(leq(_223288, _223286))], (370 ^ _210494) ^ [_223502, _223504] : [leq(n0, _223504), -(leq(uniform_int_rnd(_223502, _223504), _223504))], (376 ^ _210494) ^ [_223718, _223720] : [leq(n0, _223720), -(leq(n0, uniform_int_rnd(_223718, _223720)))], (382 ^ _210494) ^ [_223962, _223964, _223966, _223968] : [-(a_select2(tptp_const_array1(dim(_223966, _223964), _223962), _223968) = _223962), leq(_223966, _223968), leq(_223968, _223964)], (392 ^ _210494) ^ [_224369, _224371, _224373, _224375, _224377, _224379, _224381] : [-(a_select3(tptp_const_array2(dim(_224379, _224377), dim(_224373, _224371), _224369), _224381, _224375) = _224369), leq(_224379, _224381), leq(_224381, _224377), leq(_224373, _224375), leq(_224375, _224371)], (410 ^ _210494) ^ [_224964, _224966] : [413 ^ _210494 : [(414 ^ _210494) ^ [] : [-(leq(n0, 411 ^ [_224964, _224966]))], (416 ^ _210494) ^ [] : [-(leq(411 ^ [_224964, _224966], _224964))], (418 ^ _210494) ^ [] : [-(leq(n0, 412 ^ [_224964, _224966]))], (420 ^ _210494) ^ [] : [-(leq(412 ^ [_224964, _224966], _224964))], (422 ^ _210494) ^ [] : [a_select3(_224966, 411 ^ [_224964, _224966], 412 ^ [_224964, _224966]) = a_select3(_224966, 412 ^ [_224964, _224966], 411 ^ [_224964, _224966])]], 423 ^ _210494 : [(424 ^ _210494) ^ [_225721, _225723] : [-(a_select3(trans(_224966), _225723, _225721) = a_select3(trans(_224966), _225721, _225723)), leq(n0, _225723), leq(_225723, _224964), leq(n0, _225721), leq(_225721, _224964)]]], (442 ^ _210494) ^ [_226268, _226270] : [445 ^ _210494 : [(446 ^ _210494) ^ [] : [-(leq(n0, 443 ^ [_226268, _226270]))], (448 ^ _210494) ^ [] : [-(leq(443 ^ [_226268, _226270], _226268))], (450 ^ _210494) ^ [] : [-(leq(n0, 444 ^ [_226268, _226270]))], (452 ^ _210494) ^ [] : [-(leq(444 ^ [_226268, _226270], _226268))], (454 ^ _210494) ^ [] : [a_select3(_226270, 443 ^ [_226268, _226270], 444 ^ [_226268, _226270]) = a_select3(_226270, 444 ^ [_226268, _226270], 443 ^ [_226268, _226270])]], 455 ^ _210494 : [(456 ^ _210494) ^ [_227025, _227027] : [-(a_select3(inv(_226270), _227027, _227025) = a_select3(inv(_226270), _227025, _227027)), leq(n0, _227027), leq(_227027, _226268), leq(n0, _227025), leq(_227025, _226268)]]], (474 ^ _210494) ^ [_227572, _227574] : [477 ^ _210494 : [(478 ^ _210494) ^ [] : [-(leq(n0, 475 ^ [_227572, _227574]))], (480 ^ _210494) ^ [] : [-(leq(475 ^ [_227572, _227574], _227572))], (482 ^ _210494) ^ [] : [-(leq(n0, 476 ^ [_227572, _227574]))], (484 ^ _210494) ^ [] : [-(leq(476 ^ [_227572, _227574], _227572))], (486 ^ _210494) ^ [] : [a_select3(_227574, 475 ^ [_227572, _227574], 476 ^ [_227572, _227574]) = a_select3(_227574, 476 ^ [_227572, _227574], 475 ^ [_227572, _227574])]], 487 ^ _210494 : [(488 ^ _210494) ^ [_228385, _228387, _228389, _228391] : [-(a_select3(tptp_update3(_227574, _228387, _228387, _228385), _228391, _228389) = a_select3(tptp_update3(_227574, _228387, _228387, _228385), _228389, _228391)), leq(n0, _228391), leq(_228391, _227572), leq(n0, _228389), leq(_228389, _227572), leq(n0, _228387), leq(_228387, _227572)]]], (514 ^ _210494) ^ [_229204, _229206, _229208] : [519 ^ _210494 : [(520 ^ _210494) ^ [] : [-(leq(n0, 517 ^ [_229204, _229206, _229208]))], (522 ^ _210494) ^ [] : [-(leq(517 ^ [_229204, _229206, _229208], _229204))], (524 ^ _210494) ^ [] : [-(leq(n0, 518 ^ [_229204, _229206, _229208]))], (526 ^ _210494) ^ [] : [-(leq(518 ^ [_229204, _229206, _229208], _229204))], (528 ^ _210494) ^ [] : [a_select3(_229208, 517 ^ [_229204, _229206, _229208], 518 ^ [_229204, _229206, _229208]) = a_select3(_229208, 518 ^ [_229204, _229206, _229208], 517 ^ [_229204, _229206, _229208])]], 531 ^ _210494 : [(532 ^ _210494) ^ [] : [-(leq(n0, 529 ^ [_229204, _229206, _229208]))], (534 ^ _210494) ^ [] : [-(leq(529 ^ [_229204, _229206, _229208], _229204))], (536 ^ _210494) ^ [] : [-(leq(n0, 530 ^ [_229204, _229206, _229208]))], (538 ^ _210494) ^ [] : [-(leq(530 ^ [_229204, _229206, _229208], _229204))], (540 ^ _210494) ^ [] : [a_select3(_229206, 529 ^ [_229204, _229206, _229208], 530 ^ [_229204, _229206, _229208]) = a_select3(_229206, 530 ^ [_229204, _229206, _229208], 529 ^ [_229204, _229206, _229208])]], 541 ^ _210494 : [(542 ^ _210494) ^ [_230713, _230715] : [-(a_select3(tptp_madd(_229208, _229206), _230715, _230713) = a_select3(tptp_madd(_229208, _229206), _230713, _230715)), leq(n0, _230715), leq(_230715, _229204), leq(n0, _230713), leq(_230713, _229204)]]], (560 ^ _210494) ^ [_231299, _231301, _231303] : [565 ^ _210494 : [(566 ^ _210494) ^ [] : [-(leq(n0, 563 ^ [_231299, _231301, _231303]))], (568 ^ _210494) ^ [] : [-(leq(563 ^ [_231299, _231301, _231303], _231299))], (570 ^ _210494) ^ [] : [-(leq(n0, 564 ^ [_231299, _231301, _231303]))], (572 ^ _210494) ^ [] : [-(leq(564 ^ [_231299, _231301, _231303], _231299))], (574 ^ _210494) ^ [] : [a_select3(_231303, 563 ^ [_231299, _231301, _231303], 564 ^ [_231299, _231301, _231303]) = a_select3(_231303, 564 ^ [_231299, _231301, _231303], 563 ^ [_231299, _231301, _231303])]], 577 ^ _210494 : [(578 ^ _210494) ^ [] : [-(leq(n0, 575 ^ [_231299, _231301, _231303]))], (580 ^ _210494) ^ [] : [-(leq(575 ^ [_231299, _231301, _231303], _231299))], (582 ^ _210494) ^ [] : [-(leq(n0, 576 ^ [_231299, _231301, _231303]))], (584 ^ _210494) ^ [] : [-(leq(576 ^ [_231299, _231301, _231303], _231299))], (586 ^ _210494) ^ [] : [a_select3(_231301, 575 ^ [_231299, _231301, _231303], 576 ^ [_231299, _231301, _231303]) = a_select3(_231301, 576 ^ [_231299, _231301, _231303], 575 ^ [_231299, _231301, _231303])]], 587 ^ _210494 : [(588 ^ _210494) ^ [_232808, _232810] : [-(a_select3(tptp_msub(_231303, _231301), _232810, _232808) = a_select3(tptp_msub(_231303, _231301), _232808, _232810)), leq(n0, _232810), leq(_232810, _231299), leq(n0, _232808), leq(_232808, _231299)]]], (606 ^ _210494) ^ [_233394, _233396, _233398] : [609 ^ _210494 : [(610 ^ _210494) ^ [] : [-(leq(n0, 607 ^ [_233394, _233396, _233398]))], (612 ^ _210494) ^ [] : [-(leq(607 ^ [_233394, _233396, _233398], _233394))], (614 ^ _210494) ^ [] : [-(leq(n0, 608 ^ [_233394, _233396, _233398]))], (616 ^ _210494) ^ [] : [-(leq(608 ^ [_233394, _233396, _233398], _233394))], (618 ^ _210494) ^ [] : [a_select3(_233396, 607 ^ [_233394, _233396, _233398], 608 ^ [_233394, _233396, _233398]) = a_select3(_233396, 608 ^ [_233394, _233396, _233398], 607 ^ [_233394, _233396, _233398])]], 619 ^ _210494 : [(620 ^ _210494) ^ [_234207, _234209] : [-(a_select3(tptp_mmul(_233398, tptp_mmul(_233396, trans(_233398))), _234209, _234207) = a_select3(tptp_mmul(_233398, tptp_mmul(_233396, trans(_233398))), _234207, _234209)), leq(n0, _234209), leq(_234209, _233394), leq(n0, _234207), leq(_234207, _233394)]]], (638 ^ _210494) ^ [_234826, _234828, _234830, _234832] : [641 ^ _210494 : [(642 ^ _210494) ^ [] : [-(leq(n0, 639 ^ [_234826, _234828, _234830, _234832]))], (644 ^ _210494) ^ [] : [-(leq(639 ^ [_234826, _234828, _234830, _234832], _234826))], (646 ^ _210494) ^ [] : [-(leq(n0, 640 ^ [_234826, _234828, _234830, _234832]))], (648 ^ _210494) ^ [] : [-(leq(640 ^ [_234826, _234828, _234830, _234832], _234826))], (650 ^ _210494) ^ [] : [a_select3(_234830, 639 ^ [_234826, _234828, _234830, _234832], 640 ^ [_234826, _234828, _234830, _234832]) = a_select3(_234830, 640 ^ [_234826, _234828, _234830, _234832], 639 ^ [_234826, _234828, _234830, _234832])]], 651 ^ _210494 : [(652 ^ _210494) ^ [_235683, _235685] : [-(a_select3(tptp_mmul(_234832, tptp_mmul(_234830, trans(_234832))), _235685, _235683) = a_select3(tptp_mmul(_234832, tptp_mmul(_234830, trans(_234832))), _235683, _235685)), leq(n0, _235685), leq(_235685, _234828), leq(n0, _235683), leq(_235683, _234828)]]], (670 ^ _210494) ^ [_236378, _236380, _236382, _236384, _236386, _236388, _236390, _236392] : [675 ^ _210494 : [(676 ^ _210494) ^ [] : [-(leq(n0, 673 ^ [_236378, _236380, _236382, _236384, _236386, _236388, _236390, _236392]))], (678 ^ _210494) ^ [] : [-(leq(673 ^ [_236378, _236380, _236382, _236384, _236386, _236388, _236390, _236392], _236378))], (680 ^ _210494) ^ [] : [-(leq(n0, 674 ^ [_236378, _236380, _236382, _236384, _236386, _236388, _236390, _236392]))], (682 ^ _210494) ^ [] : [-(leq(674 ^ [_236378, _236380, _236382, _236384, _236386, _236388, _236390, _236392], _236378))], (684 ^ _210494) ^ [] : [a_select3(_236386, 673 ^ [_236378, _236380, _236382, _236384, _236386, _236388, _236390, _236392], 674 ^ [_236378, _236380, _236382, _236384, _236386, _236388, _236390, _236392]) = a_select3(_236386, 674 ^ [_236378, _236380, _236382, _236384, _236386, _236388, _236390, _236392], 673 ^ [_236378, _236380, _236382, _236384, _236386, _236388, _236390, _236392])]], 689 ^ _210494 : [(690 ^ _210494) ^ [] : [-(leq(n0, 687 ^ [_236378, _236380, _236382, _236384, _236386, _236388, _236390, _236392]))], (692 ^ _210494) ^ [] : [-(leq(687 ^ [_236378, _236380, _236382, _236384, _236386, _236388, _236390, _236392], _236380))], (694 ^ _210494) ^ [] : [-(leq(n0, 688 ^ [_236378, _236380, _236382, _236384, _236386, _236388, _236390, _236392]))], (696 ^ _210494) ^ [] : [-(leq(688 ^ [_236378, _236380, _236382, _236384, _236386, _236388, _236390, _236392], _236380))], (698 ^ _210494) ^ [] : [a_select3(_236392, 687 ^ [_236378, _236380, _236382, _236384, _236386, _236388, _236390, _236392], 688 ^ [_236378, _236380, _236382, _236384, _236386, _236388, _236390, _236392]) = a_select3(_236392, 688 ^ [_236378, _236380, _236382, _236384, _236386, _236388, _236390, _236392], 687 ^ [_236378, _236380, _236382, _236384, _236386, _236388, _236390, _236392])]], 701 ^ _210494 : [(702 ^ _210494) ^ [] : [-(leq(n0, 699 ^ [_236378, _236380, _236382, _236384, _236386, _236388, _236390, _236392]))], (704 ^ _210494) ^ [] : [-(leq(699 ^ [_236378, _236380, _236382, _236384, _236386, _236388, _236390, _236392], _236380))], (706 ^ _210494) ^ [] : [-(leq(n0, 700 ^ [_236378, _236380, _236382, _236384, _236386, _236388, _236390, _236392]))], (708 ^ _210494) ^ [] : [-(leq(700 ^ [_236378, _236380, _236382, _236384, _236386, _236388, _236390, _236392], _236380))], (710 ^ _210494) ^ [] : [a_select3(_236382, 699 ^ [_236378, _236380, _236382, _236384, _236386, _236388, _236390, _236392], 700 ^ [_236378, _236380, _236382, _236384, _236386, _236388, _236390, _236392]) = a_select3(_236382, 700 ^ [_236378, _236380, _236382, _236384, _236386, _236388, _236390, _236392], 699 ^ [_236378, _236380, _236382, _236384, _236386, _236388, _236390, _236392])]], 711 ^ _210494 : [(712 ^ _210494) ^ [_239306, _239308] : [-(a_select3(tptp_madd(_236392, tptp_mmul(_236390, tptp_mmul(tptp_madd(tptp_mmul(_236388, tptp_mmul(_236386, trans(_236388))), tptp_mmul(_236384, tptp_mmul(_236382, trans(_236384)))), trans(_236390)))), _239308, _239306) = a_select3(tptp_madd(_236392, tptp_mmul(_236390, tptp_mmul(tptp_madd(tptp_mmul(_236388, tptp_mmul(_236386, trans(_236388))), tptp_mmul(_236384, tptp_mmul(_236382, trans(_236384)))), trans(_236390)))), _239306, _239308)), leq(n0, _239308), leq(_239308, _236380), leq(n0, _239306), leq(_239306, _236380)]]], (730 ^ _210494) ^ [_240059] : [-(sum(n0, tptp_minus_1, _240059) = n0)], (732 ^ _210494) ^ [_240141] : [-(tptp_float_0_0 = sum(n0, tptp_minus_1, _240141))], (734 ^ _210494) ^ [] : [-(succ(tptp_minus_1) = n0)], (736 ^ _210494) ^ [_240276] : [-(plus(_240276, n1) = succ(_240276))], (738 ^ _210494) ^ [_240359] : [-(plus(n1, _240359) = succ(_240359))], (740 ^ _210494) ^ [_240442] : [-(plus(_240442, n2) = succ(succ(_240442)))], (742 ^ _210494) ^ [_240527] : [-(plus(n2, _240527) = succ(succ(_240527)))], (744 ^ _210494) ^ [_240612] : [-(plus(_240612, n3) = succ(succ(succ(_240612))))], (746 ^ _210494) ^ [_240699] : [-(plus(n3, _240699) = succ(succ(succ(_240699))))], (748 ^ _210494) ^ [_240786] : [-(plus(_240786, n4) = succ(succ(succ(succ(_240786)))))], (750 ^ _210494) ^ [_240875] : [-(plus(n4, _240875) = succ(succ(succ(succ(_240875)))))], (752 ^ _210494) ^ [_240964] : [-(plus(_240964, n5) = succ(succ(succ(succ(succ(_240964))))))], (754 ^ _210494) ^ [_241055] : [-(plus(n5, _241055) = succ(succ(succ(succ(succ(_241055))))))], (756 ^ _210494) ^ [_241146] : [-(minus(_241146, n1) = pred(_241146))], (758 ^ _210494) ^ [_241229] : [-(pred(succ(_241229)) = _241229)], (760 ^ _210494) ^ [_241311] : [-(succ(pred(_241311)) = _241311)], (762 ^ _210494) ^ [_241451, _241453] : [leq(succ(_241453), succ(_241451)), -(leq(_241453, _241451))], (768 ^ _210494) ^ [_241621, _241623] : [leq(_241623, _241621), -(leq(succ(_241623), succ(_241621)))], (774 ^ _210494) ^ [_241841, _241843] : [leq(succ(_241843), _241841), -(gt(_241841, _241843))], (780 ^ _210494) ^ [_242055, _242057] : [leq(minus(_242057, _242055), _242057), -(leq(n0, _242055))], (786 ^ _210494) ^ [_242284, _242286, _242288, _242290] : [-(a_select3(tptp_update3(_242290, _242288, _242286, _242284), _242288, _242286) = _242284)], (788 ^ _210494) ^ [_242476, _242478, _242480, _242482, _242484, _242486, _242488] : [-(a_select3(tptp_update3(_242480, _242488, _242486, _242476), _242484, _242482) = _242478), -(_242488 = _242484), _242486 = _242482, a_select3(_242480, _242484, _242482) = _242478], (802 ^ _210494) ^ [_243019, _243021, _243023, _243025, _243027, _243029] : [-(a_select3(tptp_update3(_243021, _243025, _243023, _243019), _243029, _243027) = _243019), 807 ^ _210494 : [(808 ^ _210494) ^ [] : [-(leq(n0, 805 ^ [_243019, _243021, _243023, _243025, _243027, _243029]))], (810 ^ _210494) ^ [] : [-(leq(n0, 806 ^ [_243019, _243021, _243023, _243025, _243027, _243029]))], (812 ^ _210494) ^ [] : [-(leq(805 ^ [_243019, _243021, _243023, _243025, _243027, _243029], _243025))], (814 ^ _210494) ^ [] : [-(leq(806 ^ [_243019, _243021, _243023, _243025, _243027, _243029], _243023))], (816 ^ _210494) ^ [] : [a_select3(_243021, 805 ^ [_243019, _243021, _243023, _243025, _243027, _243029], 806 ^ [_243019, _243021, _243023, _243025, _243027, _243029]) = _243019]], leq(n0, _243029), leq(_243029, _243025), leq(n0, _243027), leq(_243027, _243023)], (834 ^ _210494) ^ [_244361, _244363, _244365] : [-(a_select2(tptp_update2(_244365, _244363, _244361), _244363) = _244361)], (836 ^ _210494) ^ [_244521, _244523, _244525, _244527, _244529] : [-(a_select2(tptp_update2(_244525, _244529, _244521), _244527) = _244523), -(_244529 = _244527), a_select2(_244525, _244527) = _244523], (865 ^ _210494) ^ [] : [-(true)], (867 ^ _210494) ^ [] : [def = use], (846 ^ _210494) ^ [_244901, _244903, _244905, _244907] : [-(a_select2(tptp_update2(_244903, _244905, _244901), _244907) = _244901), 850 ^ _210494 : [(851 ^ _210494) ^ [] : [-(leq(n0, 849 ^ [_244901, _244903, _244905, _244907]))], (853 ^ _210494) ^ [] : [-(leq(849 ^ [_244901, _244903, _244905, _244907], _244905))], (855 ^ _210494) ^ [] : [a_select2(_244903, 849 ^ [_244901, _244903, _244905, _244907]) = _244901]], leq(n0, _244907), leq(_244907, _244905)]], input).
% 0.36/1.41  ncf('1',plain,[a_select2(rhoold_init, 1164 ^ []) = init],start(1170 ^ 0)).
% 0.36/1.41  ncf('1.1',plain,[-(a_select2(rhoold_init, 1164 ^ []) = init), 1141 : leq(n0, 1164 ^ []), 1141 : leq(1164 ^ [], n4), 1141 : gt(loopcounter, n1)],extension(1137 ^ 1,bind([[_253141], [1164 ^ []]]))).
% 0.36/1.41  ncf('1.1.1',plain,[-(leq(n0, 1164 ^ []))],extension(1166 ^ 4)).
% 0.36/1.41  ncf('1.1.2',plain,[-(leq(1164 ^ [], n4))],extension(1168 ^ 4)).
% 0.36/1.41  ncf('1.1.3',plain,[-(gt(loopcounter, n1))],extension(1063 ^ 2)).
% 0.36/1.41  %-----------------------------------------------------
% 0.36/1.41  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------