%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SWV164+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n012.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 25.51s 25.27s
% Output   : Proof 25.51s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SWV164+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.03/0.13  % Command  : nanocop.sh %s %d
% 0.13/0.35  % Computer : n012.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 02:42:46 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 25.51/25.27  
% 25.51/25.27  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 25.51/25.27  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 25.51/25.27  %-----------------------------------------------------
% 25.51/25.27  ncf(matrix, plain, [(1118 ^ _213182) ^ [] : [-(leq(n0, 1116 ^ []))], (1120 ^ _213182) ^ [] : [-(leq(1116 ^ [], tptp_minus_1))], (1122 ^ _213182) ^ [] : [a_select3(q, pv10, 1116 ^ []) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, 1116 ^ [])), minus(a_select2(x, pv10), a_select2(mu, 1116 ^ []))), tptp_minus_2), times(a_select2(sigma, 1116 ^ []), a_select2(sigma, 1116 ^ [])))), a_select2(rho, 1116 ^ [])), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, 1116 ^ []))), 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 ^ _213182) ^ [] : [-(leq(n0, pv10))], (1105 ^ _213182) ^ [] : [-(leq(pv10, n135299))], (1107 ^ _213182) ^ [_255218] : [-(sum(n0, n4, a_select3(q, _255218, tptp_sum_index)) = n1), leq(n0, _255218), leq(_255218, pred(pv10))], (2 ^ _213182) ^ [_213326] : [-(_213326 = _213326)], (4 ^ _213182) ^ [_213433, _213435] : [_213435 = _213433, -(_213433 = _213435)], (10 ^ _213182) ^ [_213637, _213639, _213641] : [-(_213641 = _213637), _213641 = _213639, _213639 = _213637], (20 ^ _213182) ^ [_213978, _213980, _213982, _213984] : [-(lt(_213982, _213978)), lt(_213984, _213980), _213984 = _213982, _213980 = _213978], (34 ^ _213182) ^ [_214422, _214424, _214426, _214428] : [-(geq(_214426, _214422)), geq(_214428, _214424), _214428 = _214426, _214424 = _214422], (48 ^ _213182) ^ [_214866, _214868, _214870, _214872] : [-(gt(_214870, _214866)), gt(_214872, _214868), _214872 = _214870, _214868 = _214866], (62 ^ _213182) ^ [_215290, _215292, _215294, _215296] : [-(leq(_215294, _215290)), leq(_215296, _215292), _215296 = _215294, _215292 = _215290], (76 ^ _213182) ^ [_215746, _215748, _215750, _215752] : [-(uniform_int_rnd(_215752, _215748) = uniform_int_rnd(_215750, _215746)), _215752 = _215750, _215748 = _215746], (86 ^ _213182) ^ [_216105, _216107, _216109, _216111] : [-(tptp_const_array1(_216111, _216107) = tptp_const_array1(_216109, _216105)), _216111 = _216109, _216107 = _216105], (96 ^ _213182) ^ [_216492, _216494, _216496, _216498, _216500, _216502] : [-(tptp_const_array2(_216502, _216498, _216494) = tptp_const_array2(_216500, _216496, _216492)), _216502 = _216500, _216498 = _216496, _216494 = _216492], (110 ^ _213182) ^ [_216980, _216982, _216984, _216986] : [-(dim(_216986, _216982) = dim(_216984, _216980)), _216986 = _216984, _216982 = _216980], (120 ^ _213182) ^ [_217311, _217313] : [_217313 = _217311, -(inv(_217313) = inv(_217311))], (126 ^ _213182) ^ [_217557, _217559, _217561, _217563] : [-(tptp_msub(_217563, _217559) = tptp_msub(_217561, _217557)), _217563 = _217561, _217559 = _217557], (136 ^ _213182) ^ [_217916, _217918, _217920, _217922] : [-(tptp_madd(_217922, _217918) = tptp_madd(_217920, _217916)), _217922 = _217920, _217918 = _217916], (146 ^ _213182) ^ [_218275, _218277, _218279, _218281] : [-(tptp_mmul(_218281, _218277) = tptp_mmul(_218279, _218275)), _218281 = _218279, _218277 = _218275], (156 ^ _213182) ^ [_218606, _218608] : [_218608 = _218606, -(trans(_218608) = trans(_218606))], (162 ^ _213182) ^ [_218852, _218854, _218856, _218858] : [-(plus(_218858, _218854) = plus(_218856, _218852)), _218858 = _218856, _218854 = _218852], (172 ^ _213182) ^ [_219267, _219269, _219271, _219273, _219275, _219277, _219279, _219281] : [-(tptp_update3(_219281, _219277, _219273, _219269) = tptp_update3(_219279, _219275, _219271, _219267)), _219281 = _219279, _219277 = _219275, _219273 = _219271, _219269 = _219267], (190 ^ _213182) ^ [_219928, _219930, _219932, _219934, _219936, _219938] : [-(tptp_update2(_219938, _219934, _219930) = tptp_update2(_219936, _219932, _219928)), _219938 = _219936, _219934 = _219932, _219930 = _219928], (204 ^ _213182) ^ [_220388, _220390] : [_220390 = _220388, -(succ(_220390) = succ(_220388))], (210 ^ _213182) ^ [_220606, _220608] : [_220608 = _220606, -(pred(_220608) = pred(_220606))], (216 ^ _213182) ^ [_220880, _220882, _220884, _220886, _220888, _220890] : [-(a_select3(_220890, _220886, _220882) = a_select3(_220888, _220884, _220880)), _220890 = _220888, _220886 = _220884, _220882 = _220880], (230 ^ _213182) ^ [_221396, _221398, _221400, _221402, _221404, _221406] : [-(sum(_221406, _221402, _221398) = sum(_221404, _221400, _221396)), _221406 = _221404, _221402 = _221400, _221398 = _221396], (244 ^ _213182) ^ [_221856, _221858] : [_221858 = _221856, -(exp(_221858) = exp(_221856))], (250 ^ _213182) ^ [_222102, _222104, _222106, _222108] : [-(divide(_222108, _222104) = divide(_222106, _222102)), _222108 = _222106, _222104 = _222102], (260 ^ _213182) ^ [_222461, _222463, _222465, _222467] : [-(minus(_222467, _222463) = minus(_222465, _222461)), _222467 = _222465, _222463 = _222461], (270 ^ _213182) ^ [_222792, _222794] : [_222794 = _222792, -(sqrt(_222794) = sqrt(_222792))], (276 ^ _213182) ^ [_223038, _223040, _223042, _223044] : [-(times(_223044, _223040) = times(_223042, _223038)), _223044 = _223042, _223040 = _223038], (286 ^ _213182) ^ [_223377, _223379, _223381, _223383] : [-(a_select2(_223383, _223379) = a_select2(_223381, _223377)), _223383 = _223381, _223379 = _223377], (901 ^ _213182) ^ [] : [-(gt(n5, n4))], (903 ^ _213182) ^ [] : [-(gt(n135299, n4))], (905 ^ _213182) ^ [] : [-(gt(n135299, n5))], (907 ^ _213182) ^ [] : [-(gt(n4, tptp_minus_1))], (909 ^ _213182) ^ [] : [-(gt(n5, tptp_minus_1))], (911 ^ _213182) ^ [] : [-(gt(n135299, tptp_minus_1))], (913 ^ _213182) ^ [] : [-(gt(n0, tptp_minus_1))], (915 ^ _213182) ^ [] : [-(gt(n1, tptp_minus_1))], (917 ^ _213182) ^ [] : [-(gt(n2, tptp_minus_1))], (919 ^ _213182) ^ [] : [-(gt(n3, tptp_minus_1))], (921 ^ _213182) ^ [] : [-(gt(n4, tptp_minus_2))], (923 ^ _213182) ^ [] : [-(gt(n5, tptp_minus_2))], (925 ^ _213182) ^ [] : [-(gt(tptp_minus_1, tptp_minus_2))], (927 ^ _213182) ^ [] : [-(gt(n135299, tptp_minus_2))], (929 ^ _213182) ^ [] : [-(gt(n0, tptp_minus_2))], (931 ^ _213182) ^ [] : [-(gt(n1, tptp_minus_2))], (933 ^ _213182) ^ [] : [-(gt(n2, tptp_minus_2))], (935 ^ _213182) ^ [] : [-(gt(n3, tptp_minus_2))], (937 ^ _213182) ^ [] : [-(gt(n4, n0))], (939 ^ _213182) ^ [] : [-(gt(n5, n0))], (941 ^ _213182) ^ [] : [-(gt(n135299, n0))], (943 ^ _213182) ^ [] : [-(gt(n1, n0))], (945 ^ _213182) ^ [] : [-(gt(n2, n0))], (947 ^ _213182) ^ [] : [-(gt(n3, n0))], (949 ^ _213182) ^ [] : [-(gt(n4, n1))], (951 ^ _213182) ^ [] : [-(gt(n5, n1))], (953 ^ _213182) ^ [] : [-(gt(n135299, n1))], (955 ^ _213182) ^ [] : [-(gt(n2, n1))], (957 ^ _213182) ^ [] : [-(gt(n3, n1))], (959 ^ _213182) ^ [] : [-(gt(n4, n2))], (961 ^ _213182) ^ [] : [-(gt(n5, n2))], (963 ^ _213182) ^ [] : [-(gt(n135299, n2))], (965 ^ _213182) ^ [] : [-(gt(n3, n2))], (967 ^ _213182) ^ [] : [-(gt(n4, n3))], (969 ^ _213182) ^ [] : [-(gt(n5, n3))], (971 ^ _213182) ^ [] : [-(gt(n135299, n3))], (973 ^ _213182) ^ [_251657] : [leq(n0, _251657), leq(_251657, n4), -(_251657 = n0), -(_251657 = n1), -(_251657 = n2), -(_251657 = n3), -(_251657 = n4)], (999 ^ _213182) ^ [_252278] : [leq(n0, _252278), leq(_252278, n5), -(_252278 = n0), -(_252278 = n1), -(_252278 = n2), -(_252278 = n3), -(_252278 = n4), -(_252278 = n5)], (1029 ^ _213182) ^ [_252985] : [-(_252985 = n0), leq(n0, _252985), leq(_252985, n0)], (1039 ^ _213182) ^ [_253260] : [leq(n0, _253260), leq(_253260, n1), -(_253260 = n0), -(_253260 = n1)], (1053 ^ _213182) ^ [_253623] : [leq(n0, _253623), leq(_253623, n2), -(_253623 = n0), -(_253623 = n1), -(_253623 = n2)], (1093 ^ _213182) ^ [] : [-(succ(succ(succ(succ(n0)))) = n4)], (1095 ^ _213182) ^ [] : [-(succ(succ(succ(succ(succ(n0))))) = n5)], (1097 ^ _213182) ^ [] : [-(succ(n0) = n1)], (1099 ^ _213182) ^ [] : [-(succ(succ(n0)) = n2)], (1101 ^ _213182) ^ [] : [-(succ(succ(succ(n0))) = n3)], (1071 ^ _213182) ^ [_254072] : [leq(n0, _254072), leq(_254072, n3), -(_254072 = n0), -(_254072 = n1), -(_254072 = n2), -(_254072 = n3)], (296 ^ _213182) ^ [_223824, _223826] : [-(gt(_223826, _223824)), -(gt(_223824, _223826)), -(_223826 = _223824)], (306 ^ _213182) ^ [_224139, _224141, _224143] : [-(gt(_224143, _224139)), gt(_224143, _224141), gt(_224141, _224139)], (316 ^ _213182) ^ [_224418] : [gt(_224418, _224418)], (318 ^ _213182) ^ [_224496] : [-(leq(_224496, _224496))], (320 ^ _213182) ^ [_224617, _224619, _224621] : [-(leq(_224621, _224617)), leq(_224621, _224619), leq(_224619, _224617)], (330 ^ _213182) ^ [_224955, _224957] : [lt(_224957, _224955), -(gt(_224955, _224957))], (336 ^ _213182) ^ [_225117, _225119] : [gt(_225117, _225119), -(lt(_225119, _225117))], (342 ^ _213182) ^ [_225358, _225360] : [geq(_225360, _225358), -(leq(_225358, _225360))], (348 ^ _213182) ^ [_225520, _225522] : [leq(_225520, _225522), -(geq(_225522, _225520))], (354 ^ _213182) ^ [_225732, _225734] : [gt(_225732, _225734), -(leq(_225734, _225732))], (360 ^ _213182) ^ [_225942, _225944] : [-(gt(_225942, _225944)), leq(_225944, _225942), -(_225944 = _225942)], (370 ^ _213182) ^ [_226273, _226275] : [leq(_226275, pred(_226273)), -(gt(_226273, _226275))], (376 ^ _213182) ^ [_226439, _226441] : [gt(_226439, _226441), -(leq(_226441, pred(_226439)))], (382 ^ _213182) ^ [_226626] : [-(gt(succ(_226626), _226626))], (384 ^ _213182) ^ [_226735, _226737] : [leq(_226737, _226735), -(leq(_226737, succ(_226735)))], (390 ^ _213182) ^ [_226978, _226980] : [leq(_226980, _226978), -(gt(succ(_226978), _226980))], (396 ^ _213182) ^ [_227144, _227146] : [gt(succ(_227144), _227146), -(leq(_227146, _227144))], (402 ^ _213182) ^ [_227360, _227362] : [leq(n0, _227362), -(leq(uniform_int_rnd(_227360, _227362), _227362))], (408 ^ _213182) ^ [_227576, _227578] : [leq(n0, _227578), -(leq(n0, uniform_int_rnd(_227576, _227578)))], (414 ^ _213182) ^ [_227820, _227822, _227824, _227826] : [-(a_select2(tptp_const_array1(dim(_227824, _227822), _227820), _227826) = _227820), leq(_227824, _227826), leq(_227826, _227822)], (424 ^ _213182) ^ [_228227, _228229, _228231, _228233, _228235, _228237, _228239] : [-(a_select3(tptp_const_array2(dim(_228237, _228235), dim(_228231, _228229), _228227), _228239, _228233) = _228227), leq(_228237, _228239), leq(_228239, _228235), leq(_228231, _228233), leq(_228233, _228229)], (442 ^ _213182) ^ [_228822, _228824] : [445 ^ _213182 : [(446 ^ _213182) ^ [] : [-(leq(n0, 443 ^ [_228822, _228824]))], (448 ^ _213182) ^ [] : [-(leq(443 ^ [_228822, _228824], _228822))], (450 ^ _213182) ^ [] : [-(leq(n0, 444 ^ [_228822, _228824]))], (452 ^ _213182) ^ [] : [-(leq(444 ^ [_228822, _228824], _228822))], (454 ^ _213182) ^ [] : [a_select3(_228824, 443 ^ [_228822, _228824], 444 ^ [_228822, _228824]) = a_select3(_228824, 444 ^ [_228822, _228824], 443 ^ [_228822, _228824])]], 455 ^ _213182 : [(456 ^ _213182) ^ [_229579, _229581] : [-(a_select3(trans(_228824), _229581, _229579) = a_select3(trans(_228824), _229579, _229581)), leq(n0, _229581), leq(_229581, _228822), leq(n0, _229579), leq(_229579, _228822)]]], (474 ^ _213182) ^ [_230126, _230128] : [477 ^ _213182 : [(478 ^ _213182) ^ [] : [-(leq(n0, 475 ^ [_230126, _230128]))], (480 ^ _213182) ^ [] : [-(leq(475 ^ [_230126, _230128], _230126))], (482 ^ _213182) ^ [] : [-(leq(n0, 476 ^ [_230126, _230128]))], (484 ^ _213182) ^ [] : [-(leq(476 ^ [_230126, _230128], _230126))], (486 ^ _213182) ^ [] : [a_select3(_230128, 475 ^ [_230126, _230128], 476 ^ [_230126, _230128]) = a_select3(_230128, 476 ^ [_230126, _230128], 475 ^ [_230126, _230128])]], 487 ^ _213182 : [(488 ^ _213182) ^ [_230883, _230885] : [-(a_select3(inv(_230128), _230885, _230883) = a_select3(inv(_230128), _230883, _230885)), leq(n0, _230885), leq(_230885, _230126), leq(n0, _230883), leq(_230883, _230126)]]], (506 ^ _213182) ^ [_231430, _231432] : [509 ^ _213182 : [(510 ^ _213182) ^ [] : [-(leq(n0, 507 ^ [_231430, _231432]))], (512 ^ _213182) ^ [] : [-(leq(507 ^ [_231430, _231432], _231430))], (514 ^ _213182) ^ [] : [-(leq(n0, 508 ^ [_231430, _231432]))], (516 ^ _213182) ^ [] : [-(leq(508 ^ [_231430, _231432], _231430))], (518 ^ _213182) ^ [] : [a_select3(_231432, 507 ^ [_231430, _231432], 508 ^ [_231430, _231432]) = a_select3(_231432, 508 ^ [_231430, _231432], 507 ^ [_231430, _231432])]], 519 ^ _213182 : [(520 ^ _213182) ^ [_232243, _232245, _232247, _232249] : [-(a_select3(tptp_update3(_231432, _232245, _232245, _232243), _232249, _232247) = a_select3(tptp_update3(_231432, _232245, _232245, _232243), _232247, _232249)), leq(n0, _232249), leq(_232249, _231430), leq(n0, _232247), leq(_232247, _231430), leq(n0, _232245), leq(_232245, _231430)]]], (546 ^ _213182) ^ [_233062, _233064, _233066] : [551 ^ _213182 : [(552 ^ _213182) ^ [] : [-(leq(n0, 549 ^ [_233062, _233064, _233066]))], (554 ^ _213182) ^ [] : [-(leq(549 ^ [_233062, _233064, _233066], _233062))], (556 ^ _213182) ^ [] : [-(leq(n0, 550 ^ [_233062, _233064, _233066]))], (558 ^ _213182) ^ [] : [-(leq(550 ^ [_233062, _233064, _233066], _233062))], (560 ^ _213182) ^ [] : [a_select3(_233066, 549 ^ [_233062, _233064, _233066], 550 ^ [_233062, _233064, _233066]) = a_select3(_233066, 550 ^ [_233062, _233064, _233066], 549 ^ [_233062, _233064, _233066])]], 563 ^ _213182 : [(564 ^ _213182) ^ [] : [-(leq(n0, 561 ^ [_233062, _233064, _233066]))], (566 ^ _213182) ^ [] : [-(leq(561 ^ [_233062, _233064, _233066], _233062))], (568 ^ _213182) ^ [] : [-(leq(n0, 562 ^ [_233062, _233064, _233066]))], (570 ^ _213182) ^ [] : [-(leq(562 ^ [_233062, _233064, _233066], _233062))], (572 ^ _213182) ^ [] : [a_select3(_233064, 561 ^ [_233062, _233064, _233066], 562 ^ [_233062, _233064, _233066]) = a_select3(_233064, 562 ^ [_233062, _233064, _233066], 561 ^ [_233062, _233064, _233066])]], 573 ^ _213182 : [(574 ^ _213182) ^ [_234571, _234573] : [-(a_select3(tptp_madd(_233066, _233064), _234573, _234571) = a_select3(tptp_madd(_233066, _233064), _234571, _234573)), leq(n0, _234573), leq(_234573, _233062), leq(n0, _234571), leq(_234571, _233062)]]], (592 ^ _213182) ^ [_235157, _235159, _235161] : [597 ^ _213182 : [(598 ^ _213182) ^ [] : [-(leq(n0, 595 ^ [_235157, _235159, _235161]))], (600 ^ _213182) ^ [] : [-(leq(595 ^ [_235157, _235159, _235161], _235157))], (602 ^ _213182) ^ [] : [-(leq(n0, 596 ^ [_235157, _235159, _235161]))], (604 ^ _213182) ^ [] : [-(leq(596 ^ [_235157, _235159, _235161], _235157))], (606 ^ _213182) ^ [] : [a_select3(_235161, 595 ^ [_235157, _235159, _235161], 596 ^ [_235157, _235159, _235161]) = a_select3(_235161, 596 ^ [_235157, _235159, _235161], 595 ^ [_235157, _235159, _235161])]], 609 ^ _213182 : [(610 ^ _213182) ^ [] : [-(leq(n0, 607 ^ [_235157, _235159, _235161]))], (612 ^ _213182) ^ [] : [-(leq(607 ^ [_235157, _235159, _235161], _235157))], (614 ^ _213182) ^ [] : [-(leq(n0, 608 ^ [_235157, _235159, _235161]))], (616 ^ _213182) ^ [] : [-(leq(608 ^ [_235157, _235159, _235161], _235157))], (618 ^ _213182) ^ [] : [a_select3(_235159, 607 ^ [_235157, _235159, _235161], 608 ^ [_235157, _235159, _235161]) = a_select3(_235159, 608 ^ [_235157, _235159, _235161], 607 ^ [_235157, _235159, _235161])]], 619 ^ _213182 : [(620 ^ _213182) ^ [_236666, _236668] : [-(a_select3(tptp_msub(_235161, _235159), _236668, _236666) = a_select3(tptp_msub(_235161, _235159), _236666, _236668)), leq(n0, _236668), leq(_236668, _235157), leq(n0, _236666), leq(_236666, _235157)]]], (638 ^ _213182) ^ [_237252, _237254, _237256] : [641 ^ _213182 : [(642 ^ _213182) ^ [] : [-(leq(n0, 639 ^ [_237252, _237254, _237256]))], (644 ^ _213182) ^ [] : [-(leq(639 ^ [_237252, _237254, _237256], _237252))], (646 ^ _213182) ^ [] : [-(leq(n0, 640 ^ [_237252, _237254, _237256]))], (648 ^ _213182) ^ [] : [-(leq(640 ^ [_237252, _237254, _237256], _237252))], (650 ^ _213182) ^ [] : [a_select3(_237254, 639 ^ [_237252, _237254, _237256], 640 ^ [_237252, _237254, _237256]) = a_select3(_237254, 640 ^ [_237252, _237254, _237256], 639 ^ [_237252, _237254, _237256])]], 651 ^ _213182 : [(652 ^ _213182) ^ [_238065, _238067] : [-(a_select3(tptp_mmul(_237256, tptp_mmul(_237254, trans(_237256))), _238067, _238065) = a_select3(tptp_mmul(_237256, tptp_mmul(_237254, trans(_237256))), _238065, _238067)), leq(n0, _238067), leq(_238067, _237252), leq(n0, _238065), leq(_238065, _237252)]]], (670 ^ _213182) ^ [_238684, _238686, _238688, _238690] : [673 ^ _213182 : [(674 ^ _213182) ^ [] : [-(leq(n0, 671 ^ [_238684, _238686, _238688, _238690]))], (676 ^ _213182) ^ [] : [-(leq(671 ^ [_238684, _238686, _238688, _238690], _238684))], (678 ^ _213182) ^ [] : [-(leq(n0, 672 ^ [_238684, _238686, _238688, _238690]))], (680 ^ _213182) ^ [] : [-(leq(672 ^ [_238684, _238686, _238688, _238690], _238684))], (682 ^ _213182) ^ [] : [a_select3(_238688, 671 ^ [_238684, _238686, _238688, _238690], 672 ^ [_238684, _238686, _238688, _238690]) = a_select3(_238688, 672 ^ [_238684, _238686, _238688, _238690], 671 ^ [_238684, _238686, _238688, _238690])]], 683 ^ _213182 : [(684 ^ _213182) ^ [_239541, _239543] : [-(a_select3(tptp_mmul(_238690, tptp_mmul(_238688, trans(_238690))), _239543, _239541) = a_select3(tptp_mmul(_238690, tptp_mmul(_238688, trans(_238690))), _239541, _239543)), leq(n0, _239543), leq(_239543, _238686), leq(n0, _239541), leq(_239541, _238686)]]], (702 ^ _213182) ^ [_240236, _240238, _240240, _240242, _240244, _240246, _240248, _240250] : [707 ^ _213182 : [(708 ^ _213182) ^ [] : [-(leq(n0, 705 ^ [_240236, _240238, _240240, _240242, _240244, _240246, _240248, _240250]))], (710 ^ _213182) ^ [] : [-(leq(705 ^ [_240236, _240238, _240240, _240242, _240244, _240246, _240248, _240250], _240236))], (712 ^ _213182) ^ [] : [-(leq(n0, 706 ^ [_240236, _240238, _240240, _240242, _240244, _240246, _240248, _240250]))], (714 ^ _213182) ^ [] : [-(leq(706 ^ [_240236, _240238, _240240, _240242, _240244, _240246, _240248, _240250], _240236))], (716 ^ _213182) ^ [] : [a_select3(_240244, 705 ^ [_240236, _240238, _240240, _240242, _240244, _240246, _240248, _240250], 706 ^ [_240236, _240238, _240240, _240242, _240244, _240246, _240248, _240250]) = a_select3(_240244, 706 ^ [_240236, _240238, _240240, _240242, _240244, _240246, _240248, _240250], 705 ^ [_240236, _240238, _240240, _240242, _240244, _240246, _240248, _240250])]], 721 ^ _213182 : [(722 ^ _213182) ^ [] : [-(leq(n0, 719 ^ [_240236, _240238, _240240, _240242, _240244, _240246, _240248, _240250]))], (724 ^ _213182) ^ [] : [-(leq(719 ^ [_240236, _240238, _240240, _240242, _240244, _240246, _240248, _240250], _240238))], (726 ^ _213182) ^ [] : [-(leq(n0, 720 ^ [_240236, _240238, _240240, _240242, _240244, _240246, _240248, _240250]))], (728 ^ _213182) ^ [] : [-(leq(720 ^ [_240236, _240238, _240240, _240242, _240244, _240246, _240248, _240250], _240238))], (730 ^ _213182) ^ [] : [a_select3(_240250, 719 ^ [_240236, _240238, _240240, _240242, _240244, _240246, _240248, _240250], 720 ^ [_240236, _240238, _240240, _240242, _240244, _240246, _240248, _240250]) = a_select3(_240250, 720 ^ [_240236, _240238, _240240, _240242, _240244, _240246, _240248, _240250], 719 ^ [_240236, _240238, _240240, _240242, _240244, _240246, _240248, _240250])]], 733 ^ _213182 : [(734 ^ _213182) ^ [] : [-(leq(n0, 731 ^ [_240236, _240238, _240240, _240242, _240244, _240246, _240248, _240250]))], (736 ^ _213182) ^ [] : [-(leq(731 ^ [_240236, _240238, _240240, _240242, _240244, _240246, _240248, _240250], _240238))], (738 ^ _213182) ^ [] : [-(leq(n0, 732 ^ [_240236, _240238, _240240, _240242, _240244, _240246, _240248, _240250]))], (740 ^ _213182) ^ [] : [-(leq(732 ^ [_240236, _240238, _240240, _240242, _240244, _240246, _240248, _240250], _240238))], (742 ^ _213182) ^ [] : [a_select3(_240240, 731 ^ [_240236, _240238, _240240, _240242, _240244, _240246, _240248, _240250], 732 ^ [_240236, _240238, _240240, _240242, _240244, _240246, _240248, _240250]) = a_select3(_240240, 732 ^ [_240236, _240238, _240240, _240242, _240244, _240246, _240248, _240250], 731 ^ [_240236, _240238, _240240, _240242, _240244, _240246, _240248, _240250])]], 743 ^ _213182 : [(744 ^ _213182) ^ [_243164, _243166] : [-(a_select3(tptp_madd(_240250, tptp_mmul(_240248, tptp_mmul(tptp_madd(tptp_mmul(_240246, tptp_mmul(_240244, trans(_240246))), tptp_mmul(_240242, tptp_mmul(_240240, trans(_240242)))), trans(_240248)))), _243166, _243164) = a_select3(tptp_madd(_240250, tptp_mmul(_240248, tptp_mmul(tptp_madd(tptp_mmul(_240246, tptp_mmul(_240244, trans(_240246))), tptp_mmul(_240242, tptp_mmul(_240240, trans(_240242)))), trans(_240248)))), _243164, _243166)), leq(n0, _243166), leq(_243166, _240238), leq(n0, _243164), leq(_243164, _240238)]]], (762 ^ _213182) ^ [_243917] : [-(sum(n0, tptp_minus_1, _243917) = n0)], (764 ^ _213182) ^ [_243999] : [-(tptp_float_0_0 = sum(n0, tptp_minus_1, _243999))], (766 ^ _213182) ^ [] : [-(succ(tptp_minus_1) = n0)], (768 ^ _213182) ^ [_244134] : [-(plus(_244134, n1) = succ(_244134))], (770 ^ _213182) ^ [_244217] : [-(plus(n1, _244217) = succ(_244217))], (772 ^ _213182) ^ [_244300] : [-(plus(_244300, n2) = succ(succ(_244300)))], (774 ^ _213182) ^ [_244385] : [-(plus(n2, _244385) = succ(succ(_244385)))], (776 ^ _213182) ^ [_244470] : [-(plus(_244470, n3) = succ(succ(succ(_244470))))], (778 ^ _213182) ^ [_244557] : [-(plus(n3, _244557) = succ(succ(succ(_244557))))], (780 ^ _213182) ^ [_244644] : [-(plus(_244644, n4) = succ(succ(succ(succ(_244644)))))], (782 ^ _213182) ^ [_244733] : [-(plus(n4, _244733) = succ(succ(succ(succ(_244733)))))], (784 ^ _213182) ^ [_244822] : [-(plus(_244822, n5) = succ(succ(succ(succ(succ(_244822))))))], (786 ^ _213182) ^ [_244913] : [-(plus(n5, _244913) = succ(succ(succ(succ(succ(_244913))))))], (788 ^ _213182) ^ [_245004] : [-(minus(_245004, n1) = pred(_245004))], (790 ^ _213182) ^ [_245087] : [-(pred(succ(_245087)) = _245087)], (792 ^ _213182) ^ [_245169] : [-(succ(pred(_245169)) = _245169)], (794 ^ _213182) ^ [_245309, _245311] : [leq(succ(_245311), succ(_245309)), -(leq(_245311, _245309))], (800 ^ _213182) ^ [_245479, _245481] : [leq(_245481, _245479), -(leq(succ(_245481), succ(_245479)))], (806 ^ _213182) ^ [_245699, _245701] : [leq(succ(_245701), _245699), -(gt(_245699, _245701))], (812 ^ _213182) ^ [_245913, _245915] : [leq(minus(_245915, _245913), _245915), -(leq(n0, _245913))], (818 ^ _213182) ^ [_246142, _246144, _246146, _246148] : [-(a_select3(tptp_update3(_246148, _246146, _246144, _246142), _246146, _246144) = _246142)], (820 ^ _213182) ^ [_246334, _246336, _246338, _246340, _246342, _246344, _246346] : [-(a_select3(tptp_update3(_246338, _246346, _246344, _246334), _246342, _246340) = _246336), -(_246346 = _246342), _246344 = _246340, a_select3(_246338, _246342, _246340) = _246336], (834 ^ _213182) ^ [_246877, _246879, _246881, _246883, _246885, _246887] : [-(a_select3(tptp_update3(_246879, _246883, _246881, _246877), _246887, _246885) = _246877), 839 ^ _213182 : [(840 ^ _213182) ^ [] : [-(leq(n0, 837 ^ [_246877, _246879, _246881, _246883, _246885, _246887]))], (842 ^ _213182) ^ [] : [-(leq(n0, 838 ^ [_246877, _246879, _246881, _246883, _246885, _246887]))], (844 ^ _213182) ^ [] : [-(leq(837 ^ [_246877, _246879, _246881, _246883, _246885, _246887], _246883))], (846 ^ _213182) ^ [] : [-(leq(838 ^ [_246877, _246879, _246881, _246883, _246885, _246887], _246881))], (848 ^ _213182) ^ [] : [a_select3(_246879, 837 ^ [_246877, _246879, _246881, _246883, _246885, _246887], 838 ^ [_246877, _246879, _246881, _246883, _246885, _246887]) = _246877]], leq(n0, _246887), leq(_246887, _246883), leq(n0, _246885), leq(_246885, _246881)], (866 ^ _213182) ^ [_248219, _248221, _248223] : [-(a_select2(tptp_update2(_248223, _248221, _248219), _248221) = _248219)], (868 ^ _213182) ^ [_248379, _248381, _248383, _248385, _248387] : [-(a_select2(tptp_update2(_248383, _248387, _248379), _248385) = _248381), -(_248387 = _248385), a_select2(_248383, _248385) = _248381], (897 ^ _213182) ^ [] : [-(true)], (899 ^ _213182) ^ [] : [def = use], (878 ^ _213182) ^ [_248759, _248761, _248763, _248765] : [-(a_select2(tptp_update2(_248761, _248763, _248759), _248765) = _248759), 882 ^ _213182 : [(883 ^ _213182) ^ [] : [-(leq(n0, 881 ^ [_248759, _248761, _248763, _248765]))], (885 ^ _213182) ^ [] : [-(leq(881 ^ [_248759, _248761, _248763, _248765], _248763))], (887 ^ _213182) ^ [] : [a_select2(_248761, 881 ^ [_248759, _248761, _248763, _248765]) = _248759]], leq(n0, _248765), leq(_248765, _248763)]], input).
% 25.51/25.27  ncf('1',plain,[gt(n0, n0)],start(316 ^ 0,bind([[_224418], [n0]]))).
% 25.51/25.27  ncf('1.1',plain,[-(gt(n0, n0)), leq(n0, pred(n0))],extension(370 ^ 1,bind([[_226273, _226275], [n0, n0]]))).
% 25.51/25.27  ncf('1.1.1',plain,[-(leq(n0, pred(n0))), leq(n0, 1116 ^ []), leq(1116 ^ [], pred(n0))],extension(320 ^ 2,bind([[_224617, _224619, _224621], [pred(n0), 1116 ^ [], n0]]))).
% 25.51/25.27  ncf('1.1.1.1',plain,[-(leq(n0, 1116 ^ []))],extension(1118 ^ 3)).
% 25.51/25.27  ncf('1.1.1.2',plain,[-(leq(1116 ^ [], pred(n0))), leq(1116 ^ [], tptp_minus_1), leq(tptp_minus_1, pred(n0))],extension(320 ^ 3,bind([[_224617, _224619, _224621], [pred(n0), tptp_minus_1, 1116 ^ []]]))).
% 25.51/25.27  ncf('1.1.1.2.1',plain,[-(leq(1116 ^ [], tptp_minus_1))],extension(1120 ^ 4)).
% 25.51/25.27  ncf('1.1.1.2.2',plain,[-(leq(tptp_minus_1, pred(n0))), gt(n0, tptp_minus_1)],extension(376 ^ 4,bind([[_226439, _226441], [n0, tptp_minus_1]]))).
% 25.51/25.27  ncf('1.1.1.2.2.1',plain,[-(gt(n0, tptp_minus_1))],extension(913 ^ 5)).
% 25.51/25.27  %-----------------------------------------------------
% 25.51/25.27  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------