%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : NUM926+1 : TPTP v8.1.2. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n027.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri May 19 11:45:58 EDT 2023

% Result   : Theorem 1.32s 2.41s
% Output   : Proof 1.32s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : NUM926+1 : TPTP v8.1.2. Released v5.3.0.
% 0.07/0.13  % Command  : nanocop.sh %s %d
% 0.13/0.33  % Computer : n027.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Thu May 18 17:06:05 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 1.32/2.41  
% 1.32/2.41  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 1.32/2.41  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.32/2.41  %-----------------------------------------------------
% 1.32/2.41  ncf(matrix, plain, [(881 ^ _186686) ^ [_219848, _219850] : [plus_plus_int(power_power_int(_219850, number_number_of_nat(bit0(bit1(pls)))), power_power_int(_219848, number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))), m), one_one_int)], (96 ^ _186686) ^ [_189844, _189846, _189848, _189850] : [-(power_power_nat(_189850, _189846) = power_power_nat(_189848, _189844)), _189850 = _189848, _189846 = _189844], (106 ^ _186686) ^ [_190203, _190205, _190207, _190209] : [-(times_times_nat(_190209, _190205) = times_times_nat(_190207, _190203)), _190209 = _190207, _190205 = _190203], (116 ^ _186686) ^ [_190562, _190564, _190566, _190568] : [-(plus_plus_nat(_190568, _190564) = plus_plus_nat(_190566, _190562)), _190568 = _190566, _190564 = _190562], (126 ^ _186686) ^ [_190921, _190923, _190925, _190927] : [-(power_power_int(_190927, _190923) = power_power_int(_190925, _190921)), _190927 = _190925, _190923 = _190921], (136 ^ _186686) ^ [_191252, _191254] : [_191254 = _191252, -(number_number_of_nat(_191254) = number_number_of_nat(_191252))], (142 ^ _186686) ^ [_191498, _191500, _191502, _191504] : [-(plus_plus_int(_191504, _191500) = plus_plus_int(_191502, _191498)), _191504 = _191502, _191500 = _191498], (152 ^ _186686) ^ [_191857, _191859, _191861, _191863] : [-(times_times_int(_191863, _191859) = times_times_int(_191861, _191857)), _191863 = _191861, _191859 = _191857], (162 ^ _186686) ^ [_192188, _192190] : [_192190 = _192188, -(number_number_of_int(_192190) = number_number_of_int(_192188))], (168 ^ _186686) ^ [_192406, _192408] : [_192408 = _192406, -(bit0(_192408) = bit0(_192406))], (174 ^ _186686) ^ [_192604, _192606] : [_192606 = _192604, -(bit1(_192606) = bit1(_192604))], (2 ^ _186686) ^ [_186830] : [-(_186830 = _186830)], (4 ^ _186686) ^ [_186937, _186939] : [_186939 = _186937, -(_186937 = _186939)], (10 ^ _186686) ^ [_187141, _187143, _187145] : [-(_187145 = _187141), _187145 = _187143, _187143 = _187141], (20 ^ _186686) ^ [_187482, _187484, _187486, _187488] : [-(ord_less_eq_nat(_187486, _187482)), ord_less_eq_nat(_187488, _187484), _187488 = _187486, _187484 = _187482], (34 ^ _186686) ^ [_187926, _187928, _187930, _187932] : [-(ord_less_nat(_187930, _187926)), ord_less_nat(_187932, _187928), _187932 = _187930, _187928 = _187926], (48 ^ _186686) ^ [_188342, _188344] : [-(zprime(_188342)), _188344 = _188342, zprime(_188344)], (58 ^ _186686) ^ [_188637, _188639] : [-(twoSqu526106917sum2sq(_188637)), _188639 = _188637, twoSqu526106917sum2sq(_188639)], (68 ^ _186686) ^ [_188960, _188962, _188964, _188966] : [-(ord_less_int(_188964, _188960)), ord_less_int(_188966, _188962), _188966 = _188964, _188962 = _188960], (82 ^ _186686) ^ [_189384, _189386, _189388, _189390] : [-(ord_less_eq_int(_189388, _189384)), ord_less_eq_int(_189390, _189386), _189390 = _189388, _189386 = _189384], (180 ^ _186686) ^ [] : [-(ord_less_eq_int(one_one_int, t))], (182 ^ _186686) ^ [] : [t = one_one_int, -(plus_plus_int(power_power_int(185 ^ [], number_number_of_nat(bit0(bit1(pls)))), power_power_int(186 ^ [], number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))), m), one_one_int))], (190 ^ _186686) ^ [] : [ord_less_int(one_one_int, t), -(plus_plus_int(power_power_int(193 ^ [], number_number_of_nat(bit0(bit1(pls)))), power_power_int(194 ^ [], number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))), m), one_one_int))], (198 ^ _186686) ^ [] : [-(ord_less_int(t, plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))), m), one_one_int)))], (200 ^ _186686) ^ [] : [-(zprime(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))), m), one_one_int)))], (202 ^ _186686) ^ [] : [-(plus_plus_int(power_power_int(s, number_number_of_nat(bit0(bit1(pls)))), one_one_int) = times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))), m), one_one_int), t))], (204 ^ _186686) ^ [] : [-(twoSqu526106917sum2sq(times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))), m), one_one_int), t)))], (206 ^ _186686) ^ [_193536, _193538] : [-(power_power_int(plus_plus_int(_193538, _193536), number_number_of_nat(bit0(bit1(pls)))) = plus_plus_int(plus_plus_int(power_power_int(_193538, number_number_of_nat(bit0(bit1(pls)))), times_times_int(times_times_int(number_number_of_int(bit0(bit1(pls))), _193538), _193536)), power_power_int(_193536, number_number_of_nat(bit0(bit1(pls))))))], (208 ^ _186686) ^ [_193654, _193656] : [-(power_power_int(plus_plus_int(_193656, _193654), number_number_of_nat(bit1(bit1(pls)))) = plus_plus_int(plus_plus_int(plus_plus_int(power_power_int(_193656, number_number_of_nat(bit1(bit1(pls)))), times_times_int(times_times_int(number_number_of_int(bit1(bit1(pls))), power_power_int(_193656, number_number_of_nat(bit0(bit1(pls))))), _193654)), times_times_int(times_times_int(number_number_of_int(bit1(bit1(pls))), _193656), power_power_int(_193654, number_number_of_nat(bit0(bit1(pls)))))), power_power_int(_193654, number_number_of_nat(bit1(bit1(pls))))))], (210 ^ _186686) ^ [_193787, _193789] : [-(power_power_nat(plus_plus_nat(_193789, _193787), number_number_of_nat(bit0(bit1(pls)))) = plus_plus_nat(plus_plus_nat(power_power_nat(_193789, number_number_of_nat(bit0(bit1(pls)))), power_power_nat(_193787, number_number_of_nat(bit0(bit1(pls))))), times_times_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls))), _193789), _193787)))], (212 ^ _186686) ^ [_193905, _193907] : [-(power_power_int(plus_plus_int(_193907, _193905), number_number_of_nat(bit0(bit1(pls)))) = plus_plus_int(plus_plus_int(power_power_int(_193907, number_number_of_nat(bit0(bit1(pls)))), power_power_int(_193905, number_number_of_nat(bit0(bit1(pls))))), times_times_int(times_times_int(number_number_of_int(bit0(bit1(pls))), _193907), _193905)))], (214 ^ _186686) ^ [_194009] : [-(power_power_int(number_number_of_int(_194009), number_number_of_nat(bit0(bit1(pls)))) = times_times_int(number_number_of_int(_194009), number_number_of_int(_194009)))], (216 ^ _186686) ^ [_194099] : [-(power_power_nat(number_number_of_nat(_194099), number_number_of_nat(bit0(bit1(pls)))) = times_times_nat(number_number_of_nat(_194099), number_number_of_nat(_194099)))], (218 ^ _186686) ^ [_194189] : [-(times_times_int(_194189, power_power_int(_194189, number_number_of_nat(bit0(bit1(pls))))) = power_power_int(_194189, number_number_of_nat(bit1(bit1(pls)))))], (220 ^ _186686) ^ [] : [-(power_power_nat(one_one_nat, number_number_of_nat(bit0(bit1(pls)))) = one_one_nat)], (222 ^ _186686) ^ [] : [-(power_power_int(one_one_int, number_number_of_nat(bit0(bit1(pls)))) = one_one_int)], (224 ^ _186686) ^ [_194382] : [-(times_times_int(_194382, _194382) = power_power_int(_194382, number_number_of_nat(bit0(bit1(pls)))))], (226 ^ _186686) ^ [_194466] : [-(times_times_nat(_194466, _194466) = power_power_nat(_194466, number_number_of_nat(bit0(bit1(pls)))))], (228 ^ _186686) ^ [_194550] : [-(power_power_int(_194550, number_number_of_nat(bit0(bit1(pls)))) = times_times_int(_194550, _194550))], (230 ^ _186686) ^ [_194634] : [-(power_power_nat(_194634, number_number_of_nat(bit0(bit1(pls)))) = times_times_nat(_194634, _194634))], (232 ^ _186686) ^ [_194732, _194734] : [-(power_power_int(_194734, times_times_nat(number_number_of_nat(bit0(bit1(pls))), _194732)) = times_times_int(power_power_int(_194734, _194732), power_power_int(_194734, _194732)))], (234 ^ _186686) ^ [_194841, _194843] : [-(power_power_nat(_194843, times_times_nat(number_number_of_nat(bit0(bit1(pls))), _194841)) = times_times_nat(power_power_nat(_194843, _194841), power_power_nat(_194843, _194841)))], (236 ^ _186686) ^ [_194936] : [-(plus_plus_int(one_one_int, number_number_of_int(_194936)) = number_number_of_int(plus_plus_int(bit1(pls), _194936)))], (238 ^ _186686) ^ [_195024] : [-(plus_plus_int(number_number_of_int(_195024), one_one_int) = number_number_of_int(plus_plus_int(_195024, bit1(pls))))], (240 ^ _186686) ^ [] : [-(plus_plus_int(one_one_int, one_one_int) = number_number_of_int(bit0(bit1(pls))))], (243 ^ _186686) ^ [] : [-(plus_plus_int(power_power_int(s, number_number_of_nat(bit0(bit1(pls)))), one_one_int) = times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))), m), one_one_int), 241 ^ []))], (245 ^ _186686) ^ [_195260] : [-(ord_less_eq_int(_195260, _195260))], (247 ^ _186686) ^ [_195367, _195369] : [-(ord_less_eq_int(_195369, _195367)), -(ord_less_eq_int(_195367, _195369))], (253 ^ _186686) ^ [_195607, _195609] : [ord_less_int(_195609, _195607), 256 ^ _186686 : [(257 ^ _186686) ^ [] : [-(ord_less_eq_int(_195609, _195607))], (259 ^ _186686) ^ [] : [_195609 = _195607]]], (261 ^ _186686) ^ [_195845, _195847] : [-(ord_less_int(_195847, _195845)), ord_less_eq_int(_195847, _195845), -(_195847 = _195845)], (271 ^ _186686) ^ [_196149, _196151] : [-(ord_less_int(_196151, _196149)), -(_196151 = _196149), -(ord_less_int(_196149, _196151))], (281 ^ _186686) ^ [_196464, _196466, _196468] : [ord_less_eq_int(_196466, _196464), ord_less_eq_int(_196464, _196468), -(ord_less_eq_int(_196466, _196468))], (291 ^ _186686) ^ [_196773, _196775] : [ord_less_eq_int(_196775, _196773), ord_less_eq_int(_196773, _196775), -(_196775 = _196773)], (301 ^ _186686) ^ [_197071, _197073, _197075] : [-(power_power_int(power_power_int(_197075, _197073), _197071) = power_power_int(_197075, times_times_nat(_197073, _197071)))], (303 ^ _186686) ^ [_197193, _197195, _197197] : [-(power_power_nat(power_power_nat(_197197, _197195), _197193) = power_power_nat(_197197, times_times_nat(_197195, _197193)))], (305 ^ _186686) ^ [_197287] : [-(power_power_int(_197287, one_one_nat) = _197287)], (307 ^ _186686) ^ [_197368] : [-(power_power_nat(_197368, one_one_nat) = _197368)], (309 ^ _186686) ^ [_197477, _197479, _197481] : [-(power_power_int(power_power_int(_197481, _197479), _197477) = power_power_int(_197481, times_times_nat(_197479, _197477)))], (311 ^ _186686) ^ [_197629, _197631] : [ord_less_eq_nat(number_number_of_nat(_197631), number_number_of_nat(_197629)), ord_less_nat(number_number_of_nat(_197629), number_number_of_nat(_197631))], (317 ^ _186686) ^ [_197808, _197810] : [-(ord_less_nat(number_number_of_nat(_197808), number_number_of_nat(_197810))), -(ord_less_eq_nat(number_number_of_nat(_197810), number_number_of_nat(_197808)))], (323 ^ _186686) ^ [_198068, _198070] : [ord_less_eq_int(number_number_of_int(_198070), number_number_of_int(_198068)), ord_less_int(number_number_of_int(_198068), number_number_of_int(_198070))], (329 ^ _186686) ^ [_198247, _198249] : [-(ord_less_int(number_number_of_int(_198247), number_number_of_int(_198249))), -(ord_less_eq_int(number_number_of_int(_198249), number_number_of_int(_198247)))], (335 ^ _186686) ^ [_198507, _198509] : [ord_less_int(number_number_of_int(_198509), number_number_of_int(_198507)), -(ord_less_int(_198509, _198507))], (341 ^ _186686) ^ [_198677, _198679] : [ord_less_int(_198679, _198677), -(ord_less_int(number_number_of_int(_198679), number_number_of_int(_198677)))], (347 ^ _186686) ^ [_198926, _198928] : [ord_less_eq_int(number_number_of_int(_198928), number_number_of_int(_198926)), -(ord_less_eq_int(_198928, _198926))], (353 ^ _186686) ^ [_199096, _199098] : [ord_less_eq_int(_199098, _199096), -(ord_less_eq_int(number_number_of_int(_199098), number_number_of_int(_199096)))], (359 ^ _186686) ^ [_199344, _199346, _199348, _199350] : [ord_less_int(_199346, _199344), ord_less_eq_int(_199350, _199348), -(ord_less_int(plus_plus_int(_199346, _199350), plus_plus_int(_199344, _199348)))], (369 ^ _186686) ^ [_199674, _199676, _199678] : [-(times_times_int(power_power_int(_199678, _199676), power_power_int(_199678, _199674)) = power_power_int(_199678, plus_plus_nat(_199676, _199674)))], (371 ^ _186686) ^ [_199799, _199801, _199803] : [-(times_times_nat(power_power_nat(_199803, _199801), power_power_nat(_199803, _199799)) = power_power_nat(_199803, plus_plus_nat(_199801, _199799)))], (373 ^ _186686) ^ [_199924, _199926, _199928] : [-(power_power_int(_199928, plus_plus_nat(_199926, _199924)) = times_times_int(power_power_int(_199928, _199926), power_power_int(_199928, _199924)))], (375 ^ _186686) ^ [_200021] : [-(times_times_nat(number_number_of_nat(bit0(bit1(pls))), _200021) = plus_plus_nat(_200021, _200021))], (377 ^ _186686) ^ [_200105] : [-(times_times_nat(_200105, number_number_of_nat(bit0(bit1(pls)))) = plus_plus_nat(_200105, _200105))], (379 ^ _186686) ^ [] : [-(plus_plus_nat(one_one_nat, one_one_nat) = number_number_of_nat(bit0(bit1(pls))))], (381 ^ _186686) ^ [_200300, _200302] : [ord_less_int(bit1(_200302), bit1(_200300)), -(ord_less_int(_200302, _200300))], (387 ^ _186686) ^ [_200470, _200472] : [ord_less_int(_200472, _200470), -(ord_less_int(bit1(_200472), bit1(_200470)))], (393 ^ _186686) ^ [_200719, _200721] : [ord_less_int(bit1(_200721), bit1(_200719)), -(ord_less_int(_200721, _200719))], (399 ^ _186686) ^ [_200889, _200891] : [ord_less_int(_200891, _200889), -(ord_less_int(bit1(_200891), bit1(_200889)))], (405 ^ _186686) ^ [_201138, _201140] : [ord_less_eq_int(bit1(_201140), bit1(_201138)), -(ord_less_eq_int(_201140, _201138))], (411 ^ _186686) ^ [_201308, _201310] : [ord_less_eq_int(_201310, _201308), -(ord_less_eq_int(bit1(_201310), bit1(_201308)))], (417 ^ _186686) ^ [_201557, _201559] : [ord_less_eq_int(bit1(_201559), bit1(_201557)), -(ord_less_eq_int(_201559, _201557))], (423 ^ _186686) ^ [_201727, _201729] : [ord_less_eq_int(_201729, _201727), -(ord_less_eq_int(bit1(_201729), bit1(_201727)))], (429 ^ _186686) ^ [] : [ord_less_int(pls, pls)], (431 ^ _186686) ^ [_202028, _202030] : [ord_less_int(bit0(_202030), bit0(_202028)), -(ord_less_int(_202030, _202028))], (437 ^ _186686) ^ [_202198, _202200] : [ord_less_int(_202200, _202198), -(ord_less_int(bit0(_202200), bit0(_202198)))], (443 ^ _186686) ^ [_202447, _202449] : [ord_less_int(bit0(_202449), bit0(_202447)), -(ord_less_int(_202449, _202447))], (449 ^ _186686) ^ [_202617, _202619] : [ord_less_int(_202619, _202617), -(ord_less_int(bit0(_202619), bit0(_202617)))], (455 ^ _186686) ^ [] : [-(ord_less_eq_int(pls, pls))], (457 ^ _186686) ^ [_202919, _202921] : [ord_less_eq_int(bit0(_202921), bit0(_202919)), -(ord_less_eq_int(_202921, _202919))], (463 ^ _186686) ^ [_203089, _203091] : [ord_less_eq_int(_203091, _203089), -(ord_less_eq_int(bit0(_203091), bit0(_203089)))], (469 ^ _186686) ^ [_203338, _203340] : [ord_less_eq_int(bit0(_203340), bit0(_203338)), -(ord_less_eq_int(_203340, _203338))], (475 ^ _186686) ^ [_203508, _203510] : [ord_less_eq_int(_203510, _203508), -(ord_less_eq_int(bit0(_203510), bit0(_203508)))], (481 ^ _186686) ^ [_203757, _203759] : [ord_less_int(number_number_of_int(_203759), number_number_of_int(_203757)), -(ord_less_int(_203759, _203757))], (487 ^ _186686) ^ [_203927, _203929] : [ord_less_int(_203929, _203927), -(ord_less_int(number_number_of_int(_203929), number_number_of_int(_203927)))], (493 ^ _186686) ^ [_204176, _204178] : [ord_less_eq_int(number_number_of_int(_204178), number_number_of_int(_204176)), -(ord_less_eq_int(_204178, _204176))], (499 ^ _186686) ^ [_204346, _204348] : [ord_less_eq_int(_204348, _204346), -(ord_less_eq_int(number_number_of_int(_204348), number_number_of_int(_204346)))], (505 ^ _186686) ^ [_204580, _204582, _204584] : [ord_less_int(_204582, _204580), -(ord_less_int(plus_plus_int(_204582, _204584), plus_plus_int(_204580, _204584)))], (511 ^ _186686) ^ [_204822, _204824, _204826] : [ord_less_eq_int(_204824, _204822), -(ord_less_eq_int(plus_plus_int(_204826, _204824), plus_plus_int(_204826, _204822)))], (517 ^ _186686) ^ [_205070, _205072] : [ord_less_int(_205070, pls), -(plus_plus_nat(number_number_of_nat(_205070), number_number_of_nat(_205072)) = number_number_of_nat(_205072))], (523 ^ _186686) ^ [_205250, _205252] : [-(ord_less_int(_205250, pls)), 526 ^ _186686 : [(527 ^ _186686) ^ [] : [ord_less_int(_205252, pls), -(plus_plus_nat(number_number_of_nat(_205250), number_number_of_nat(_205252)) = number_number_of_nat(_205250))], (533 ^ _186686) ^ [] : [-(ord_less_int(_205252, pls)), -(plus_plus_nat(number_number_of_nat(_205250), number_number_of_nat(_205252)) = number_number_of_nat(plus_plus_int(_205250, _205252)))]]], (539 ^ _186686) ^ [] : [-(number_number_of_nat(bit1(pls)) = one_one_nat)], (541 ^ _186686) ^ [] : [-(one_one_nat = number_number_of_nat(bit1(pls)))], (543 ^ _186686) ^ [_205884] : [ord_less_eq_int(bit1(_205884), pls), -(ord_less_int(_205884, pls))], (549 ^ _186686) ^ [_206044] : [ord_less_int(_206044, pls), -(ord_less_eq_int(bit1(_206044), pls))], (555 ^ _186686) ^ [_206269] : [ord_less_int(pls, bit1(_206269)), -(ord_less_eq_int(pls, _206269))], (561 ^ _186686) ^ [_206429] : [ord_less_eq_int(pls, _206429), -(ord_less_int(pls, bit1(_206429)))], (567 ^ _186686) ^ [_206668, _206670] : [ord_less_eq_int(bit1(_206670), bit0(_206668)), -(ord_less_int(_206670, _206668))], (573 ^ _186686) ^ [_206838, _206840] : [ord_less_int(_206840, _206838), -(ord_less_eq_int(bit1(_206840), bit0(_206838)))], (579 ^ _186686) ^ [_207087, _207089] : [ord_less_eq_int(bit1(_207089), bit0(_207087)), -(ord_less_int(_207089, _207087))], (585 ^ _186686) ^ [_207257, _207259] : [ord_less_int(_207259, _207257), -(ord_less_eq_int(bit1(_207259), bit0(_207257)))], (591 ^ _186686) ^ [_207506, _207508] : [ord_less_int(bit0(_207508), bit1(_207506)), -(ord_less_eq_int(_207508, _207506))], (597 ^ _186686) ^ [_207676, _207678] : [ord_less_eq_int(_207678, _207676), -(ord_less_int(bit0(_207678), bit1(_207676)))], (603 ^ _186686) ^ [_207925, _207927] : [ord_less_int(bit0(_207927), bit1(_207925)), -(ord_less_eq_int(_207927, _207925))], (609 ^ _186686) ^ [_208095, _208097] : [ord_less_eq_int(_208097, _208095), -(ord_less_int(bit0(_208097), bit1(_208095)))], (615 ^ _186686) ^ [_208315, _208317] : [ord_less_int(_208317, _208315), -(ord_less_eq_int(plus_plus_int(_208317, one_one_int), _208315))], (621 ^ _186686) ^ [_208560, _208562] : [ord_less_eq_int(plus_plus_int(_208562, one_one_int), _208560), -(ord_less_int(_208562, _208560))], (627 ^ _186686) ^ [_208728, _208730] : [ord_less_int(_208730, _208728), -(ord_less_eq_int(plus_plus_int(_208730, one_one_int), _208728))], (633 ^ _186686) ^ [_208975, _208977] : [ord_less_int(_208977, plus_plus_int(_208975, one_one_int)), -(ord_less_eq_int(_208977, _208975))], (639 ^ _186686) ^ [_209143, _209145] : [ord_less_eq_int(_209145, _209143), -(ord_less_int(_209145, plus_plus_int(_209143, one_one_int)))], (645 ^ _186686) ^ [] : [-(zprime(number_number_of_int(bit0(bit1(pls)))))], (647 ^ _186686) ^ [_209414, _209416] : [twoSqu526106917sum2sq(_209414), twoSqu526106917sum2sq(_209416), -(twoSqu526106917sum2sq(times_times_int(_209414, _209416)))], (657 ^ _186686) ^ [_209726, _209728, _209730, _209732] : [-(times_times_int(times_times_int(_209732, _209730), times_times_int(_209728, _209726)) = times_times_int(times_times_int(_209732, _209728), times_times_int(_209730, _209726)))], (659 ^ _186686) ^ [_209870, _209872, _209874, _209876] : [-(times_times_nat(times_times_nat(_209876, _209874), times_times_nat(_209872, _209870)) = times_times_nat(times_times_nat(_209876, _209872), times_times_nat(_209874, _209870)))], (661 ^ _186686) ^ [_210014, _210016, _210018, _210020] : [-(times_times_int(times_times_int(_210020, _210018), times_times_int(_210016, _210014)) = times_times_int(_210016, times_times_int(times_times_int(_210020, _210018), _210014)))], (663 ^ _186686) ^ [_210158, _210160, _210162, _210164] : [-(times_times_nat(times_times_nat(_210164, _210162), times_times_nat(_210160, _210158)) = times_times_nat(_210160, times_times_nat(times_times_nat(_210164, _210162), _210158)))], (665 ^ _186686) ^ [_210302, _210304, _210306, _210308] : [-(times_times_int(times_times_int(_210308, _210306), times_times_int(_210304, _210302)) = times_times_int(_210308, times_times_int(_210306, times_times_int(_210304, _210302))))], (667 ^ _186686) ^ [_210446, _210448, _210450, _210452] : [-(times_times_nat(times_times_nat(_210452, _210450), times_times_nat(_210448, _210446)) = times_times_nat(_210452, times_times_nat(_210450, times_times_nat(_210448, _210446))))], (669 ^ _186686) ^ [_210576, _210578, _210580] : [-(times_times_int(times_times_int(_210580, _210578), _210576) = times_times_int(times_times_int(_210580, _210576), _210578))], (671 ^ _186686) ^ [_210698, _210700, _210702] : [-(times_times_nat(times_times_nat(_210702, _210700), _210698) = times_times_nat(times_times_nat(_210702, _210698), _210700))], (673 ^ _186686) ^ [_210820, _210822, _210824] : [-(times_times_int(times_times_int(_210824, _210822), _210820) = times_times_int(_210824, times_times_int(_210822, _210820)))], (675 ^ _186686) ^ [_210942, _210944, _210946] : [-(times_times_nat(times_times_nat(_210946, _210944), _210942) = times_times_nat(_210946, times_times_nat(_210944, _210942)))], (677 ^ _186686) ^ [_211064, _211066, _211068] : [-(times_times_int(_211068, times_times_int(_211066, _211064)) = times_times_int(times_times_int(_211068, _211066), _211064))], (679 ^ _186686) ^ [_211186, _211188, _211190] : [-(times_times_nat(_211190, times_times_nat(_211188, _211186)) = times_times_nat(times_times_nat(_211190, _211188), _211186))], (681 ^ _186686) ^ [_211308, _211310, _211312] : [-(times_times_int(_211312, times_times_int(_211310, _211308)) = times_times_int(_211310, times_times_int(_211312, _211308)))], (683 ^ _186686) ^ [_211430, _211432, _211434] : [-(times_times_nat(_211434, times_times_nat(_211432, _211430)) = times_times_nat(_211432, times_times_nat(_211434, _211430)))], (685 ^ _186686) ^ [_211538, _211540] : [-(times_times_int(_211540, _211538) = times_times_int(_211538, _211540))], (687 ^ _186686) ^ [_211638, _211640] : [-(times_times_nat(_211640, _211638) = times_times_nat(_211638, _211640))], (689 ^ _186686) ^ [_211766, _211768, _211770, _211772] : [-(plus_plus_int(plus_plus_int(_211772, _211770), plus_plus_int(_211768, _211766)) = plus_plus_int(plus_plus_int(_211772, _211768), plus_plus_int(_211770, _211766)))], (691 ^ _186686) ^ [_211910, _211912, _211914, _211916] : [-(plus_plus_nat(plus_plus_nat(_211916, _211914), plus_plus_nat(_211912, _211910)) = plus_plus_nat(plus_plus_nat(_211916, _211912), plus_plus_nat(_211914, _211910)))], (693 ^ _186686) ^ [_212040, _212042, _212044] : [-(plus_plus_int(plus_plus_int(_212044, _212042), _212040) = plus_plus_int(plus_plus_int(_212044, _212040), _212042))], (695 ^ _186686) ^ [_212162, _212164, _212166] : [-(plus_plus_nat(plus_plus_nat(_212166, _212164), _212162) = plus_plus_nat(plus_plus_nat(_212166, _212162), _212164))], (697 ^ _186686) ^ [_212284, _212286, _212288] : [-(plus_plus_int(plus_plus_int(_212288, _212286), _212284) = plus_plus_int(_212288, plus_plus_int(_212286, _212284)))], (699 ^ _186686) ^ [_212406, _212408, _212410] : [-(plus_plus_nat(plus_plus_nat(_212410, _212408), _212406) = plus_plus_nat(_212410, plus_plus_nat(_212408, _212406)))], (701 ^ _186686) ^ [_212528, _212530, _212532] : [-(plus_plus_int(_212532, plus_plus_int(_212530, _212528)) = plus_plus_int(plus_plus_int(_212532, _212530), _212528))], (703 ^ _186686) ^ [_212650, _212652, _212654] : [-(plus_plus_nat(_212654, plus_plus_nat(_212652, _212650)) = plus_plus_nat(plus_plus_nat(_212654, _212652), _212650))], (705 ^ _186686) ^ [_212772, _212774, _212776] : [-(plus_plus_int(_212776, plus_plus_int(_212774, _212772)) = plus_plus_int(_212774, plus_plus_int(_212776, _212772)))], (707 ^ _186686) ^ [_212894, _212896, _212898] : [-(plus_plus_nat(_212898, plus_plus_nat(_212896, _212894)) = plus_plus_nat(_212896, plus_plus_nat(_212898, _212894)))], (709 ^ _186686) ^ [_213002, _213004] : [-(plus_plus_int(_213004, _213002) = plus_plus_int(_213002, _213004))], (711 ^ _186686) ^ [_213102, _213104] : [-(plus_plus_nat(_213104, _213102) = plus_plus_nat(_213102, _213104))], (713 ^ _186686) ^ [_213246, _213248] : [number_number_of_int(_213248) = number_number_of_int(_213246), -(_213248 = _213246)], (719 ^ _186686) ^ [_213416, _213418] : [_213418 = _213416, -(number_number_of_int(_213418) = number_number_of_int(_213416))], (725 ^ _186686) ^ [_213665, _213667] : [number_number_of_nat(_213667) = _213665, -(_213665 = number_number_of_nat(_213667))], (731 ^ _186686) ^ [_213835, _213837] : [_213835 = number_number_of_nat(_213837), -(number_number_of_nat(_213837) = _213835)], (737 ^ _186686) ^ [_214084, _214086] : [number_number_of_int(_214086) = _214084, -(_214084 = number_number_of_int(_214086))], (743 ^ _186686) ^ [_214254, _214256] : [_214254 = number_number_of_int(_214256), -(number_number_of_int(_214256) = _214254)], (749 ^ _186686) ^ [_214503, _214505] : [bit1(_214505) = bit1(_214503), -(_214505 = _214503)], (755 ^ _186686) ^ [_214673, _214675] : [_214675 = _214673, -(bit1(_214675) = bit1(_214673))], (761 ^ _186686) ^ [_214922, _214924] : [bit0(_214924) = bit0(_214922), -(_214924 = _214922)], (767 ^ _186686) ^ [_215092, _215094] : [_215094 = _215092, -(bit0(_215094) = bit0(_215092))], (773 ^ _186686) ^ [_215311, _215313, _215315] : [-(times_times_int(times_times_int(_215315, _215313), _215311) = times_times_int(_215315, times_times_int(_215313, _215311)))], (775 ^ _186686) ^ [_215419, _215421] : [-(times_times_int(_215421, _215419) = times_times_int(_215419, _215421))], (777 ^ _186686) ^ [_215505] : [-(number_number_of_int(_215505) = _215505)], (779 ^ _186686) ^ [_215613, _215615, _215617] : [-(plus_plus_int(plus_plus_int(_215617, _215615), _215613) = plus_plus_int(_215617, plus_plus_int(_215615, _215613)))], (781 ^ _186686) ^ [_215735, _215737, _215739] : [-(plus_plus_int(_215739, plus_plus_int(_215737, _215735)) = plus_plus_int(_215737, plus_plus_int(_215739, _215735)))], (783 ^ _186686) ^ [_215843, _215845] : [-(plus_plus_int(_215845, _215843) = plus_plus_int(_215843, _215845))], (785 ^ _186686) ^ [_215973] : [ord_less_int(bit1(_215973), pls), -(ord_less_int(_215973, pls))], (791 ^ _186686) ^ [_216133] : [ord_less_int(_216133, pls), -(ord_less_int(bit1(_216133), pls))], (797 ^ _186686) ^ [_216372, _216374] : [ord_less_int(bit1(_216374), bit0(_216372)), -(ord_less_int(_216374, _216372))], (803 ^ _186686) ^ [_216542, _216544] : [ord_less_int(_216544, _216542), -(ord_less_int(bit1(_216544), bit0(_216542)))], (809 ^ _186686) ^ [_216791, _216793] : [ord_less_int(bit1(_216793), bit0(_216791)), -(ord_less_int(_216793, _216791))], (815 ^ _186686) ^ [_216961, _216963] : [ord_less_int(_216963, _216961), -(ord_less_int(bit1(_216963), bit0(_216961)))], (821 ^ _186686) ^ [_217196] : [ord_less_int(bit0(_217196), pls), -(ord_less_int(_217196, pls))], (827 ^ _186686) ^ [_217356] : [ord_less_int(_217356, pls), -(ord_less_int(bit0(_217356), pls))], (833 ^ _186686) ^ [_217581] : [ord_less_int(pls, bit0(_217581)), -(ord_less_int(pls, _217581))], (839 ^ _186686) ^ [_217741] : [ord_less_int(pls, _217741), -(ord_less_int(pls, bit0(_217741)))], (845 ^ _186686) ^ [_217966] : [ord_less_eq_int(pls, bit1(_217966)), -(ord_less_eq_int(pls, _217966))], (851 ^ _186686) ^ [_218126] : [ord_less_eq_int(pls, _218126), -(ord_less_eq_int(pls, bit1(_218126)))], (857 ^ _186686) ^ [_218365, _218367] : [ord_less_eq_int(bit0(_218367), bit1(_218365)), -(ord_less_eq_int(_218367, _218365))], (863 ^ _186686) ^ [_218535, _218537] : [ord_less_eq_int(_218537, _218535), -(ord_less_eq_int(bit0(_218537), bit1(_218535)))], (869 ^ _186686) ^ [_218764, _218766] : [ord_less_eq_int(bit0(_218766), bit1(_218764)), -(ord_less_eq_int(_218766, _218764))], (875 ^ _186686) ^ [_218934, _218936] : [ord_less_eq_int(_218936, _218934), -(ord_less_eq_int(bit0(_218936), bit1(_218934)))]], input).
% 1.32/2.41  ncf('1',plain,[plus_plus_int(power_power_int(185 ^ [], number_number_of_nat(bit0(bit1(pls)))), power_power_int(186 ^ [], number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))), m), one_one_int)],start(881 ^ 0,bind([[_219848, _219850], [186 ^ [], 185 ^ []]]))).
% 1.32/2.41  ncf('1.1',plain,[-(plus_plus_int(power_power_int(185 ^ [], number_number_of_nat(bit0(bit1(pls)))), power_power_int(186 ^ [], number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))), m), one_one_int)), t = one_one_int],extension(182 ^ 1)).
% 1.32/2.41  ncf('1.1.1',plain,[-(t = one_one_int), -(ord_less_int(t, one_one_int)), -(ord_less_int(one_one_int, t))],extension(271 ^ 2,bind([[_196149, _196151], [one_one_int, t]]))).
% 1.32/2.41  ncf('1.1.1.1',plain,[ord_less_int(t, one_one_int), 257 : -(ord_less_eq_int(t, one_one_int))],extension(253 ^ 3,bind([[_195607, _195609], [one_one_int, t]]))).
% 1.32/2.41  ncf('1.1.1.1.1',plain,[ord_less_eq_int(t, one_one_int), ord_less_eq_int(one_one_int, t), -(t = one_one_int)],extension(291 ^ 6,bind([[_196773, _196775], [one_one_int, t]]))).
% 1.32/2.41  ncf('1.1.1.1.1.1',plain,[-(ord_less_eq_int(one_one_int, t))],extension(180 ^ 7)).
% 1.32/2.41  ncf('1.1.1.1.1.2',plain,[t = one_one_int],reduction('1.1')).
% 1.32/2.41  ncf('1.1.1.2',plain,[ord_less_int(one_one_int, t), -(plus_plus_int(power_power_int(193 ^ [], number_number_of_nat(bit0(bit1(pls)))), power_power_int(194 ^ [], number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))), m), one_one_int))],extension(190 ^ 3)).
% 1.32/2.41  ncf('1.1.1.2.1',plain,[plus_plus_int(power_power_int(193 ^ [], number_number_of_nat(bit0(bit1(pls)))), power_power_int(194 ^ [], number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))), m), one_one_int)],extension(881 ^ 4,bind([[_219848, _219850], [194 ^ [], 193 ^ []]]))).
% 1.32/2.41  %-----------------------------------------------------
% 1.32/2.41  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------