%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : NUM926+5 : TPTP v8.1.2. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n015.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 11:45:59 EDT 2023

% Result   : Theorem 1.86s 2.42s
% Output   : Proof 1.86s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : NUM926+5 : TPTP v8.1.2. Released v5.3.0.
% 0.04/0.13  % Command  : nanocop.sh %s %d
% 0.13/0.34  % Computer : n015.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Thu May 18 17:57:07 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 1.86/2.42  
% 1.86/2.42  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 1.86/2.42  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.86/2.42  %-----------------------------------------------------
% 1.86/2.42  ncf(matrix, plain, [(1253 ^ _256258) ^ [_301917, _301919] : [plus_plus(int, power_power(int, _301919, number_number_of(nat, bit0(bit1(pls)))), power_power(int, _301917, 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))], (166 ^ _256258) ^ [_261499, _261501] : [_261501 = _261499, -(undefined(_261501) = undefined(_261499))], (172 ^ _256258) ^ [_261745, _261747, _261749, _261751] : [-(ti(_261751, _261747) = ti(_261749, _261745)), _261751 = _261749, _261747 = _261745], (182 ^ _256258) ^ [_262132, _262134, _262136, _262138, _262140, _262142] : [-(power_power(_262142, _262138, _262134) = power_power(_262140, _262136, _262132)), _262142 = _262140, _262138 = _262136, _262134 = _262132], (196 ^ _256258) ^ [_262648, _262650, _262652, _262654, _262656, _262658] : [-(plus_plus(_262658, _262654, _262650) = plus_plus(_262656, _262652, _262648)), _262658 = _262656, _262654 = _262652, _262650 = _262648], (210 ^ _256258) ^ [_263164, _263166, _263168, _263170, _263172, _263174] : [-(times_times(_263174, _263170, _263166) = times_times(_263172, _263168, _263164)), _263174 = _263172, _263170 = _263168, _263166 = _263164], (224 ^ _256258) ^ [_263652, _263654, _263656, _263658] : [-(number_number_of(_263658, _263654) = number_number_of(_263656, _263652)), _263658 = _263656, _263654 = _263652], (234 ^ _256258) ^ [_263983, _263985] : [_263985 = _263983, -(bit0(_263985) = bit0(_263983))], (240 ^ _256258) ^ [_264201, _264203] : [_264203 = _264201, -(bit1(_264203) = bit1(_264201))], (246 ^ _256258) ^ [_264399, _264401] : [_264401 = _264399, -(one_one(_264401) = one_one(_264399))], (2 ^ _256258) ^ [_256402] : [-(_256402 = _256402)], (4 ^ _256258) ^ [_256509, _256511] : [_256511 = _256509, -(_256509 = _256511)], (10 ^ _256258) ^ [_256713, _256715, _256717] : [-(_256717 = _256713), _256717 = _256715, _256715 = _256713], (20 ^ _256258) ^ [_257026, _257028] : [-(zprime(_257026)), _257028 = _257026, zprime(_257028)], (30 ^ _256258) ^ [_257321, _257323] : [-(twoSqu33214720sum2sq(_257321)), _257323 = _257321, twoSqu33214720sum2sq(_257323)], (40 ^ _256258) ^ [_257672, _257674, _257676, _257678, _257680, _257682] : [-(ord_less(_257680, _257676, _257672)), ord_less(_257682, _257678, _257674), _257682 = _257680, _257678 = _257676, _257674 = _257672], (58 ^ _256258) ^ [_258281, _258283, _258285, _258287, _258289, _258291] : [-(ord_less_eq(_258289, _258285, _258281)), ord_less_eq(_258291, _258287, _258283), _258291 = _258289, _258287 = _258285, _258283 = _258281], (76 ^ _256258) ^ [_258834, _258836] : [-(linordered_idom(_258834)), _258836 = _258834, linordered_idom(_258836)], (86 ^ _256258) ^ [_259129, _259131] : [-(ring_char_0(_259129)), _259131 = _259129, ring_char_0(_259131)], (96 ^ _256258) ^ [_259424, _259426] : [-(number_ring(_259424)), _259426 = _259424, number_ring(_259426)], (106 ^ _256258) ^ [_259719, _259721] : [-(comm_semiring_1(_259719)), _259721 = _259719, comm_semiring_1(_259721)], (116 ^ _256258) ^ [_260014, _260016] : [-(number_semiring(_260014)), _260016 = _260014, number_semiring(_260016)], (126 ^ _256258) ^ [_260309, _260311] : [-(linorder(_260309)), _260311 = _260309, linorder(_260311)], (136 ^ _256258) ^ [_260604, _260606] : [-(monoid_mult(_260604)), _260606 = _260604, monoid_mult(_260606)], (146 ^ _256258) ^ [_260899, _260901] : [-(semiring_1(_260899)), _260901 = _260899, semiring_1(_260901)], (156 ^ _256258) ^ [_261174, _261176] : [-(number(_261174)), _261176 = _261174, number(_261176)], (252 ^ _256258) ^ [_264669] : [semiring_1(_264669), -(ti(_264669, one_one(_264669)) = one_one(_264669))], (258 ^ _256258) ^ [_264899, _264901, _264903] : [comm_semiring_1(_264899), -(plus_plus(_264899, ti(_264899, _264903), _264901) = plus_plus(_264899, _264903, _264901))], (264 ^ _256258) ^ [_265149, _265151, _265153] : [comm_semiring_1(_265149), -(plus_plus(_265149, _265153, ti(_265149, _265151)) = plus_plus(_265149, _265153, _265151))], (270 ^ _256258) ^ [_265399, _265401, _265403] : [comm_semiring_1(_265399), -(ti(_265399, plus_plus(_265399, _265403, _265401)) = plus_plus(_265399, _265403, _265401))], (276 ^ _256258) ^ [_265649, _265651, _265653] : [monoid_mult(_265649), -(times_times(_265649, ti(_265649, _265653), _265651) = times_times(_265649, _265653, _265651))], (282 ^ _256258) ^ [_265899, _265901, _265903] : [monoid_mult(_265899), -(times_times(_265899, _265903, ti(_265899, _265901)) = times_times(_265899, _265903, _265901))], (288 ^ _256258) ^ [_266149, _266151, _266153] : [monoid_mult(_266149), -(ti(_266149, times_times(_266149, _266153, _266151)) = times_times(_266149, _266153, _266151))], (294 ^ _256258) ^ [_266356] : [-(ti(_266356, undefined(_266356)) = undefined(_266356))], (296 ^ _256258) ^ [_266485] : [zprime(ti(int, _266485)), -(zprime(_266485))], (302 ^ _256258) ^ [_266643] : [zprime(_266643), -(zprime(ti(int, _266643)))], (308 ^ _256258) ^ [_266822] : [-(bit0(ti(int, _266822)) = bit0(_266822))], (310 ^ _256258) ^ [_266907] : [-(ti(int, bit0(_266907)) = bit0(_266907))], (312 ^ _256258) ^ [_266992] : [-(bit1(ti(int, _266992)) = bit1(_266992))], (314 ^ _256258) ^ [_267077] : [-(ti(int, bit1(_267077)) = bit1(_267077))], (316 ^ _256258) ^ [] : [-(ti(int, pls) = pls)], (318 ^ _256258) ^ [_267244, _267246] : [number(_267244), -(number_number_of(_267244, ti(int, _267246)) = number_number_of(_267244, _267246))], (324 ^ _256258) ^ [_267470, _267472] : [number(_267470), -(ti(_267470, number_number_of(_267470, _267472)) = number_number_of(_267470, _267472))], (330 ^ _256258) ^ [_267710, _267712, _267714] : [number(_267710), linorder(_267710), 337 ^ _256258 : [(338 ^ _256258) ^ [] : [ord_less(_267710, ti(_267710, _267714), _267712), -(ord_less(_267710, _267714, _267712))], (344 ^ _256258) ^ [] : [ord_less(_267710, _267714, _267712), -(ord_less(_267710, ti(_267710, _267714), _267712))]]], (350 ^ _256258) ^ [_268306, _268308, _268310] : [number(_268306), linorder(_268306), 357 ^ _256258 : [(358 ^ _256258) ^ [] : [ord_less(_268306, _268310, ti(_268306, _268308)), -(ord_less(_268306, _268310, _268308))], (364 ^ _256258) ^ [] : [ord_less(_268306, _268310, _268308), -(ord_less(_268306, _268310, ti(_268306, _268308)))]]], (370 ^ _256258) ^ [_268902, _268904, _268906] : [number(_268902), linorder(_268902), 377 ^ _256258 : [(378 ^ _256258) ^ [] : [ord_less_eq(_268902, ti(_268902, _268906), _268904), -(ord_less_eq(_268902, _268906, _268904))], (384 ^ _256258) ^ [] : [ord_less_eq(_268902, _268906, _268904), -(ord_less_eq(_268902, ti(_268902, _268906), _268904))]]], (390 ^ _256258) ^ [_269498, _269500, _269502] : [number(_269498), linorder(_269498), 397 ^ _256258 : [(398 ^ _256258) ^ [] : [ord_less_eq(_269498, _269502, ti(_269498, _269500)), -(ord_less_eq(_269498, _269502, _269500))], (404 ^ _256258) ^ [] : [ord_less_eq(_269498, _269502, _269500), -(ord_less_eq(_269498, _269502, ti(_269498, _269500)))]]], (410 ^ _256258) ^ [_270094, _270096, _270098] : [monoid_mult(_270094), -(power_power(_270094, ti(_270094, _270098), _270096) = power_power(_270094, _270098, _270096))], (416 ^ _256258) ^ [_270344, _270346, _270348] : [monoid_mult(_270344), -(power_power(_270344, _270348, ti(nat, _270346)) = power_power(_270344, _270348, _270346))], (422 ^ _256258) ^ [_270594, _270596, _270598] : [monoid_mult(_270594), -(ti(_270594, power_power(_270594, _270598, _270596)) = power_power(_270594, _270598, _270596))], (428 ^ _256258) ^ [_270845] : [twoSqu33214720sum2sq(ti(int, _270845)), -(twoSqu33214720sum2sq(_270845))], (434 ^ _256258) ^ [_271003] : [twoSqu33214720sum2sq(_271003), -(twoSqu33214720sum2sq(ti(int, _271003)))], (440 ^ _256258) ^ [] : [-(ti(int, m) = m)], (442 ^ _256258) ^ [] : [-(ti(int, s) = s)], (444 ^ _256258) ^ [] : [-(ti(int, t) = t)], (446 ^ _256258) ^ [] : [-(ord_less_eq(int, one_one(int), t))], (448 ^ _256258) ^ [] : [t = one_one(int), -(plus_plus(int, power_power(int, 451 ^ [], number_number_of(nat, bit0(bit1(pls)))), power_power(int, 452 ^ [], 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)))], (456 ^ _256258) ^ [] : [ord_less(int, one_one(int), t), -(plus_plus(int, power_power(int, 459 ^ [], number_number_of(nat, bit0(bit1(pls)))), power_power(int, 460 ^ [], 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)))], (464 ^ _256258) ^ [] : [-(ord_less(int, t, plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int))))], (466 ^ _256258) ^ [] : [-(zprime(plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int))))], (468 ^ _256258) ^ [] : [-(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))], (470 ^ _256258) ^ [] : [-(twoSqu33214720sum2sq(times_times(int, plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int)), t)))], (472 ^ _256258) ^ [_272056, _272058] : [-(power_power(int, plus_plus(int, _272058, _272056), number_number_of(nat, bit0(bit1(pls)))) = plus_plus(int, plus_plus(int, power_power(int, _272058, number_number_of(nat, bit0(bit1(pls)))), times_times(int, times_times(int, number_number_of(int, bit0(bit1(pls))), _272058), _272056)), power_power(int, _272056, number_number_of(nat, bit0(bit1(pls))))))], (474 ^ _256258) ^ [_272182, _272184] : [-(power_power(int, plus_plus(int, _272184, _272182), number_number_of(nat, bit1(bit1(pls)))) = plus_plus(int, plus_plus(int, plus_plus(int, power_power(int, _272184, number_number_of(nat, bit1(bit1(pls)))), times_times(int, times_times(int, number_number_of(int, bit1(bit1(pls))), power_power(int, _272184, number_number_of(nat, bit0(bit1(pls))))), _272182)), times_times(int, times_times(int, number_number_of(int, bit1(bit1(pls))), _272184), power_power(int, _272182, number_number_of(nat, bit0(bit1(pls)))))), power_power(int, _272182, number_number_of(nat, bit1(bit1(pls))))))], (476 ^ _256258) ^ [_272329] : [number_semiring(_272329), 479 ^ _256258 : [(480 ^ _256258) ^ [_272493, _272495] : [-(power_power(_272329, plus_plus(_272329, _272495, _272493), number_number_of(nat, bit0(bit1(pls)))) = plus_plus(_272329, plus_plus(_272329, power_power(_272329, _272495, number_number_of(nat, bit0(bit1(pls)))), power_power(_272329, _272493, number_number_of(nat, bit0(bit1(pls))))), times_times(_272329, times_times(_272329, number_number_of(_272329, bit0(bit1(pls))), _272495), _272493)))]]], (482 ^ _256258) ^ [_272630] : [489 ^ _256258 : [(490 ^ _256258) ^ [_272840] : [-(power_power(_272630, number_number_of(_272630, _272840), number_number_of(nat, bit0(bit1(pls)))) = times_times(_272630, number_number_of(_272630, _272840), number_number_of(_272630, _272840)))]], monoid_mult(_272630), number(_272630)], (492 ^ _256258) ^ [_272942] : [-(times_times(int, _272942, power_power(int, _272942, number_number_of(nat, bit0(bit1(pls))))) = power_power(int, _272942, number_number_of(nat, bit1(bit1(pls)))))], (494 ^ _256258) ^ [_273047] : [semiring_1(_273047), -(power_power(_273047, one_one(_273047), number_number_of(nat, bit0(bit1(pls)))) = one_one(_273047))], (500 ^ _256258) ^ [_273251] : [comm_semiring_1(_273251), 503 ^ _256258 : [(504 ^ _256258) ^ [_273369] : [-(times_times(_273251, _273369, _273369) = power_power(_273251, _273369, number_number_of(nat, bit0(bit1(pls)))))]]], (506 ^ _256258) ^ [_273477] : [monoid_mult(_273477), 509 ^ _256258 : [(510 ^ _256258) ^ [_273595] : [-(power_power(_273477, _273595, number_number_of(nat, bit0(bit1(pls)))) = times_times(_273477, _273595, _273595))]]], (512 ^ _256258) ^ [_273703] : [comm_semiring_1(_273703), 515 ^ _256258 : [(516 ^ _256258) ^ [_273852, _273854] : [-(power_power(_273703, _273854, times_times(nat, number_number_of(nat, bit0(bit1(pls))), _273852)) = times_times(_273703, power_power(_273703, _273854, _273852), power_power(_273703, _273854, _273852)))]]], (518 ^ _256258) ^ [_273974] : [number_ring(_273974), 521 ^ _256258 : [(522 ^ _256258) ^ [_274100] : [-(plus_plus(_273974, one_one(_273974), number_number_of(_273974, _274100)) = number_number_of(_273974, plus_plus(int, bit1(pls), _274100)))]]], (524 ^ _256258) ^ [_274216] : [number_ring(_274216), 527 ^ _256258 : [(528 ^ _256258) ^ [_274342] : [-(plus_plus(_274216, number_number_of(_274216, _274342), one_one(_274216)) = number_number_of(_274216, plus_plus(int, _274342, bit1(pls))))]]], (530 ^ _256258) ^ [_274458] : [number_ring(_274458), -(plus_plus(_274458, one_one(_274458), one_one(_274458)) = number_number_of(_274458, bit0(bit1(pls))))], (537 ^ _256258) ^ [] : [-(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)), 535 ^ []))], (539 ^ _256258) ^ [_274749] : [-(ord_less_eq(int, _274749, _274749))], (541 ^ _256258) ^ [_274857, _274859] : [-(ord_less_eq(int, _274859, _274857)), -(ord_less_eq(int, _274857, _274859))], (547 ^ _256258) ^ [_275101, _275103] : [ord_less(int, _275103, _275101), 550 ^ _256258 : [(551 ^ _256258) ^ [] : [-(ord_less_eq(int, _275103, _275101))], (553 ^ _256258) ^ [] : [_275103 = _275101]]], (555 ^ _256258) ^ [_275343, _275345] : [-(ord_less(int, _275345, _275343)), ord_less_eq(int, _275345, _275343), -(_275345 = _275343)], (565 ^ _256258) ^ [_275651, _275653] : [-(ord_less(int, _275653, _275651)), -(_275653 = _275651), -(ord_less(int, _275651, _275653))], (575 ^ _256258) ^ [_275970, _275972, _275974] : [ord_less_eq(int, _275972, _275970), ord_less_eq(int, _275970, _275974), -(ord_less_eq(int, _275972, _275974))], (585 ^ _256258) ^ [_276285, _276287] : [ord_less_eq(int, _276287, _276285), ord_less_eq(int, _276285, _276287), -(_276287 = _276285)], (595 ^ _256258) ^ [_276574] : [comm_semiring_1(_276574), 598 ^ _256258 : [(599 ^ _256258) ^ [_276738, _276740, _276742] : [-(power_power(_276574, power_power(_276574, _276742, _276740), _276738) = power_power(_276574, _276742, times_times(nat, _276740, _276738)))]]], (601 ^ _256258) ^ [_276858] : [comm_semiring_1(_276858), 604 ^ _256258 : [(605 ^ _256258) ^ [_276975] : [-(power_power(_276858, _276975, one_one(nat)) = ti(_276858, _276975))]]], (607 ^ _256258) ^ [_277095, _277097, _277099] : [-(power_power(int, power_power(int, _277099, _277097), _277095) = power_power(int, _277099, times_times(nat, _277097, _277095)))], (609 ^ _256258) ^ [_277208] : [number(_277208), linorder(_277208), 616 ^ _256258 : [(617 ^ _256258) ^ [_277486, _277488] : [ord_less_eq(_277208, number_number_of(_277208, _277488), number_number_of(_277208, _277486)), ord_less(_277208, number_number_of(_277208, _277486), number_number_of(_277208, _277488))], (623 ^ _256258) ^ [_277685, _277687] : [-(ord_less(_277208, number_number_of(_277208, _277685), number_number_of(_277208, _277687))), -(ord_less_eq(_277208, number_number_of(_277208, _277687), number_number_of(_277208, _277685)))]]], (629 ^ _256258) ^ [_277929] : [number_ring(_277929), linordered_idom(_277929), 636 ^ _256258 : [(637 ^ _256258) ^ [_278199, _278201] : [ord_less(_277929, number_number_of(_277929, _278201), number_number_of(_277929, _278199)), -(ord_less(int, _278201, _278199))], (643 ^ _256258) ^ [_278385, _278387] : [ord_less(int, _278387, _278385), -(ord_less(_277929, number_number_of(_277929, _278387), number_number_of(_277929, _278385)))]]], (649 ^ _256258) ^ [_278614] : [number_ring(_278614), linordered_idom(_278614), 656 ^ _256258 : [(657 ^ _256258) ^ [_278884, _278886] : [ord_less_eq(_278614, number_number_of(_278614, _278886), number_number_of(_278614, _278884)), -(ord_less_eq(int, _278886, _278884))], (663 ^ _256258) ^ [_279070, _279072] : [ord_less_eq(int, _279072, _279070), -(ord_less_eq(_278614, number_number_of(_278614, _279072), number_number_of(_278614, _279070)))]]], (669 ^ _256258) ^ [_279341, _279343, _279345, _279347] : [ord_less(int, _279343, _279341), ord_less_eq(int, _279347, _279345), -(ord_less(int, plus_plus(int, _279343, _279347), plus_plus(int, _279341, _279345)))], (679 ^ _256258) ^ [_279668] : [comm_semiring_1(_279668), 682 ^ _256258 : [(683 ^ _256258) ^ [_279836, _279838, _279840] : [-(times_times(_279668, power_power(_279668, _279840, _279838), power_power(_279668, _279840, _279836)) = power_power(_279668, _279840, plus_plus(nat, _279838, _279836)))]]], (685 ^ _256258) ^ [_279973, _279975, _279977] : [-(power_power(int, _279977, plus_plus(nat, _279975, _279973)) = times_times(int, power_power(int, _279977, _279975), power_power(int, _279977, _279973)))], (687 ^ _256258) ^ [_280075] : [-(times_times(nat, number_number_of(nat, bit0(bit1(pls))), _280075) = plus_plus(nat, _280075, _280075))], (689 ^ _256258) ^ [_280161] : [-(times_times(nat, _280161, number_number_of(nat, bit0(bit1(pls)))) = plus_plus(nat, _280161, _280161))], (691 ^ _256258) ^ [] : [-(plus_plus(nat, one_one(nat), one_one(nat)) = number_number_of(nat, bit0(bit1(pls))))], (693 ^ _256258) ^ [_280358, _280360] : [ord_less(int, bit1(_280360), bit1(_280358)), -(ord_less(int, _280360, _280358))], (699 ^ _256258) ^ [_280532, _280534] : [ord_less(int, _280534, _280532), -(ord_less(int, bit1(_280534), bit1(_280532)))], (705 ^ _256258) ^ [_280785, _280787] : [ord_less(int, bit1(_280787), bit1(_280785)), -(ord_less(int, _280787, _280785))], (711 ^ _256258) ^ [_280959, _280961] : [ord_less(int, _280961, _280959), -(ord_less(int, bit1(_280961), bit1(_280959)))], (717 ^ _256258) ^ [_281212, _281214] : [ord_less_eq(int, bit1(_281214), bit1(_281212)), -(ord_less_eq(int, _281214, _281212))], (723 ^ _256258) ^ [_281386, _281388] : [ord_less_eq(int, _281388, _281386), -(ord_less_eq(int, bit1(_281388), bit1(_281386)))], (729 ^ _256258) ^ [_281639, _281641] : [ord_less_eq(int, bit1(_281641), bit1(_281639)), -(ord_less_eq(int, _281641, _281639))], (735 ^ _256258) ^ [_281813, _281815] : [ord_less_eq(int, _281815, _281813), -(ord_less_eq(int, bit1(_281815), bit1(_281813)))], (741 ^ _256258) ^ [] : [ord_less(int, pls, pls)], (743 ^ _256258) ^ [_282118, _282120] : [ord_less(int, bit0(_282120), bit0(_282118)), -(ord_less(int, _282120, _282118))], (749 ^ _256258) ^ [_282292, _282294] : [ord_less(int, _282294, _282292), -(ord_less(int, bit0(_282294), bit0(_282292)))], (755 ^ _256258) ^ [_282545, _282547] : [ord_less(int, bit0(_282547), bit0(_282545)), -(ord_less(int, _282547, _282545))], (761 ^ _256258) ^ [_282719, _282721] : [ord_less(int, _282721, _282719), -(ord_less(int, bit0(_282721), bit0(_282719)))], (767 ^ _256258) ^ [] : [-(ord_less_eq(int, pls, pls))], (769 ^ _256258) ^ [_283025, _283027] : [ord_less_eq(int, bit0(_283027), bit0(_283025)), -(ord_less_eq(int, _283027, _283025))], (775 ^ _256258) ^ [_283199, _283201] : [ord_less_eq(int, _283201, _283199), -(ord_less_eq(int, bit0(_283201), bit0(_283199)))], (781 ^ _256258) ^ [_283452, _283454] : [ord_less_eq(int, bit0(_283454), bit0(_283452)), -(ord_less_eq(int, _283454, _283452))], (787 ^ _256258) ^ [_283626, _283628] : [ord_less_eq(int, _283628, _283626), -(ord_less_eq(int, bit0(_283628), bit0(_283626)))], (793 ^ _256258) ^ [_283879, _283881] : [ord_less(int, number_number_of(int, _283881), number_number_of(int, _283879)), -(ord_less(int, _283881, _283879))], (799 ^ _256258) ^ [_284057, _284059] : [ord_less(int, _284059, _284057), -(ord_less(int, number_number_of(int, _284059), number_number_of(int, _284057)))], (805 ^ _256258) ^ [_284314, _284316] : [ord_less_eq(int, number_number_of(int, _284316), number_number_of(int, _284314)), -(ord_less_eq(int, _284316, _284314))], (811 ^ _256258) ^ [_284492, _284494] : [ord_less_eq(int, _284494, _284492), -(ord_less_eq(int, number_number_of(int, _284494), number_number_of(int, _284492)))], (817 ^ _256258) ^ [_284734, _284736, _284738] : [ord_less(int, _284736, _284734), -(ord_less(int, plus_plus(int, _284736, _284738), plus_plus(int, _284734, _284738)))], (823 ^ _256258) ^ [_284984, _284986, _284988] : [ord_less_eq(int, _284986, _284984), -(ord_less_eq(int, plus_plus(int, _284988, _284986), plus_plus(int, _284988, _284984)))], (829 ^ _256258) ^ [_285240, _285242] : [ord_less(int, _285240, pls), -(plus_plus(nat, number_number_of(nat, _285240), number_number_of(nat, _285242)) = number_number_of(nat, _285242))], (835 ^ _256258) ^ [_285430, _285432] : [-(ord_less(int, _285430, pls)), 838 ^ _256258 : [(839 ^ _256258) ^ [] : [ord_less(int, _285432, pls), -(plus_plus(nat, number_number_of(nat, _285430), number_number_of(nat, _285432)) = number_number_of(nat, _285430))], (845 ^ _256258) ^ [] : [-(ord_less(int, _285432, pls)), -(plus_plus(nat, number_number_of(nat, _285430), number_number_of(nat, _285432)) = number_number_of(nat, plus_plus(int, _285430, _285432)))]]], (851 ^ _256258) ^ [] : [-(number_number_of(nat, bit1(pls)) = one_one(nat))], (853 ^ _256258) ^ [] : [-(one_one(nat) = number_number_of(nat, bit1(pls)))], (855 ^ _256258) ^ [_286088] : [ord_less_eq(int, bit1(_286088), pls), -(ord_less(int, _286088, pls))], (861 ^ _256258) ^ [_286252] : [ord_less(int, _286252, pls), -(ord_less_eq(int, bit1(_286252), pls))], (867 ^ _256258) ^ [_286481] : [ord_less(int, pls, bit1(_286481)), -(ord_less_eq(int, pls, _286481))], (873 ^ _256258) ^ [_286645] : [ord_less_eq(int, pls, _286645), -(ord_less(int, pls, bit1(_286645)))], (879 ^ _256258) ^ [_286888, _286890] : [ord_less_eq(int, bit1(_286890), bit0(_286888)), -(ord_less(int, _286890, _286888))], (885 ^ _256258) ^ [_287062, _287064] : [ord_less(int, _287064, _287062), -(ord_less_eq(int, bit1(_287064), bit0(_287062)))], (891 ^ _256258) ^ [_287315, _287317] : [ord_less_eq(int, bit1(_287317), bit0(_287315)), -(ord_less(int, _287317, _287315))], (897 ^ _256258) ^ [_287489, _287491] : [ord_less(int, _287491, _287489), -(ord_less_eq(int, bit1(_287491), bit0(_287489)))], (903 ^ _256258) ^ [_287742, _287744] : [ord_less(int, bit0(_287744), bit1(_287742)), -(ord_less_eq(int, _287744, _287742))], (909 ^ _256258) ^ [_287916, _287918] : [ord_less_eq(int, _287918, _287916), -(ord_less(int, bit0(_287918), bit1(_287916)))], (915 ^ _256258) ^ [_288169, _288171] : [ord_less(int, bit0(_288171), bit1(_288169)), -(ord_less_eq(int, _288171, _288169))], (921 ^ _256258) ^ [_288343, _288345] : [ord_less_eq(int, _288345, _288343), -(ord_less(int, bit0(_288345), bit1(_288343)))], (927 ^ _256258) ^ [_288567, _288569] : [ord_less(int, _288569, _288567), -(ord_less_eq(int, plus_plus(int, _288569, one_one(int)), _288567))], (933 ^ _256258) ^ [_288818, _288820] : [ord_less_eq(int, plus_plus(int, _288820, one_one(int)), _288818), -(ord_less(int, _288820, _288818))], (939 ^ _256258) ^ [_288992, _288994] : [ord_less(int, _288994, _288992), -(ord_less_eq(int, plus_plus(int, _288994, one_one(int)), _288992))], (945 ^ _256258) ^ [_289245, _289247] : [ord_less(int, _289247, plus_plus(int, _289245, one_one(int))), -(ord_less_eq(int, _289247, _289245))], (951 ^ _256258) ^ [_289419, _289421] : [ord_less_eq(int, _289421, _289419), -(ord_less(int, _289421, plus_plus(int, _289419, one_one(int))))], (957 ^ _256258) ^ [] : [-(zprime(number_number_of(int, bit0(bit1(pls)))))], (959 ^ _256258) ^ [_289696, _289698] : [twoSqu33214720sum2sq(_289696), twoSqu33214720sum2sq(_289698), -(twoSqu33214720sum2sq(times_times(int, _289696, _289698)))], (969 ^ _256258) ^ [_289983] : [comm_semiring_1(_289983), 972 ^ _256258 : [(973 ^ _256258) ^ [_290174, _290176, _290178, _290180] : [-(times_times(_289983, times_times(_289983, _290180, _290178), times_times(_289983, _290176, _290174)) = times_times(_289983, times_times(_289983, _290180, _290176), times_times(_289983, _290178, _290174)))]]], (975 ^ _256258) ^ [_290304] : [comm_semiring_1(_290304), 978 ^ _256258 : [(979 ^ _256258) ^ [_290495, _290497, _290499, _290501] : [-(times_times(_290304, times_times(_290304, _290501, _290499), times_times(_290304, _290497, _290495)) = times_times(_290304, _290497, times_times(_290304, times_times(_290304, _290501, _290499), _290495)))]]], (981 ^ _256258) ^ [_290625] : [comm_semiring_1(_290625), 984 ^ _256258 : [(985 ^ _256258) ^ [_290816, _290818, _290820, _290822] : [-(times_times(_290625, times_times(_290625, _290822, _290820), times_times(_290625, _290818, _290816)) = times_times(_290625, _290822, times_times(_290625, _290820, times_times(_290625, _290818, _290816))))]]], (987 ^ _256258) ^ [_290946] : [comm_semiring_1(_290946), 990 ^ _256258 : [(991 ^ _256258) ^ [_291110, _291112, _291114] : [-(times_times(_290946, times_times(_290946, _291114, _291112), _291110) = times_times(_290946, times_times(_290946, _291114, _291110), _291112))]]], (993 ^ _256258) ^ [_291230] : [comm_semiring_1(_291230), 996 ^ _256258 : [(997 ^ _256258) ^ [_291394, _291396, _291398] : [-(times_times(_291230, times_times(_291230, _291398, _291396), _291394) = times_times(_291230, _291398, times_times(_291230, _291396, _291394)))]]], (999 ^ _256258) ^ [_291514] : [comm_semiring_1(_291514), 1002 ^ _256258 : [(1003 ^ _256258) ^ [_291678, _291680, _291682] : [-(times_times(_291514, _291682, times_times(_291514, _291680, _291678)) = times_times(_291514, times_times(_291514, _291682, _291680), _291678))]]], (1005 ^ _256258) ^ [_291798] : [comm_semiring_1(_291798), 1008 ^ _256258 : [(1009 ^ _256258) ^ [_291962, _291964, _291966] : [-(times_times(_291798, _291966, times_times(_291798, _291964, _291962)) = times_times(_291798, _291964, times_times(_291798, _291966, _291962)))]]], (1011 ^ _256258) ^ [_292082] : [comm_semiring_1(_292082), 1014 ^ _256258 : [(1015 ^ _256258) ^ [_292219, _292221] : [-(times_times(_292082, _292221, _292219) = times_times(_292082, _292219, _292221))]]], (1017 ^ _256258) ^ [_292329] : [comm_semiring_1(_292329), 1020 ^ _256258 : [(1021 ^ _256258) ^ [_292520, _292522, _292524, _292526] : [-(plus_plus(_292329, plus_plus(_292329, _292526, _292524), plus_plus(_292329, _292522, _292520)) = plus_plus(_292329, plus_plus(_292329, _292526, _292522), plus_plus(_292329, _292524, _292520)))]]], (1023 ^ _256258) ^ [_292650] : [comm_semiring_1(_292650), 1026 ^ _256258 : [(1027 ^ _256258) ^ [_292814, _292816, _292818] : [-(plus_plus(_292650, plus_plus(_292650, _292818, _292816), _292814) = plus_plus(_292650, plus_plus(_292650, _292818, _292814), _292816))]]], (1029 ^ _256258) ^ [_292934] : [comm_semiring_1(_292934), 1032 ^ _256258 : [(1033 ^ _256258) ^ [_293098, _293100, _293102] : [-(plus_plus(_292934, plus_plus(_292934, _293102, _293100), _293098) = plus_plus(_292934, _293102, plus_plus(_292934, _293100, _293098)))]]], (1035 ^ _256258) ^ [_293218] : [comm_semiring_1(_293218), 1038 ^ _256258 : [(1039 ^ _256258) ^ [_293382, _293384, _293386] : [-(plus_plus(_293218, _293386, plus_plus(_293218, _293384, _293382)) = plus_plus(_293218, plus_plus(_293218, _293386, _293384), _293382))]]], (1041 ^ _256258) ^ [_293502] : [comm_semiring_1(_293502), 1044 ^ _256258 : [(1045 ^ _256258) ^ [_293666, _293668, _293670] : [-(plus_plus(_293502, _293670, plus_plus(_293502, _293668, _293666)) = plus_plus(_293502, _293668, plus_plus(_293502, _293670, _293666)))]]], (1047 ^ _256258) ^ [_293786] : [comm_semiring_1(_293786), 1050 ^ _256258 : [(1051 ^ _256258) ^ [_293923, _293925] : [-(plus_plus(_293786, _293925, _293923) = plus_plus(_293786, _293923, _293925))]]], (1053 ^ _256258) ^ [_294033] : [number_ring(_294033), ring_char_0(_294033), 1060 ^ _256258 : [(1061 ^ _256258) ^ [_294301, _294303] : [number_number_of(_294033, _294303) = number_number_of(_294033, _294301), -(_294303 = _294301)], (1067 ^ _256258) ^ [_294483, _294485] : [_294485 = _294483, -(number_number_of(_294033, _294485) = number_number_of(_294033, _294483))]]], (1073 ^ _256258) ^ [_294708] : [number(_294708), 1076 ^ _256258 : [(1077 ^ _256258) ^ [_294899, _294901] : [number_number_of(_294708, _294901) = ti(_294708, _294899), -(ti(_294708, _294899) = number_number_of(_294708, _294901))], (1083 ^ _256258) ^ [_295093, _295095] : [ti(_294708, _295093) = number_number_of(_294708, _295095), -(number_number_of(_294708, _295095) = ti(_294708, _295093))]]], (1089 ^ _256258) ^ [_295371, _295373] : [bit1(_295373) = bit1(_295371), -(_295373 = _295371)], (1095 ^ _256258) ^ [_295541, _295543] : [_295543 = _295541, -(bit1(_295543) = bit1(_295541))], (1101 ^ _256258) ^ [_295790, _295792] : [bit0(_295792) = bit0(_295790), -(_295792 = _295790)], (1107 ^ _256258) ^ [_295960, _295962] : [_295962 = _295960, -(bit0(_295962) = bit0(_295960))], (1113 ^ _256258) ^ [_296179, _296181, _296183] : [-(times_times(int, times_times(int, _296183, _296181), _296179) = times_times(int, _296183, times_times(int, _296181, _296179)))], (1115 ^ _256258) ^ [_296291, _296293] : [-(times_times(int, _296293, _296291) = times_times(int, _296291, _296293))], (1117 ^ _256258) ^ [_296379] : [-(number_number_of(int, _296379) = _296379)], (1119 ^ _256258) ^ [_296488, _296490, _296492] : [-(plus_plus(int, plus_plus(int, _296492, _296490), _296488) = plus_plus(int, _296492, plus_plus(int, _296490, _296488)))], (1121 ^ _256258) ^ [_296614, _296616, _296618] : [-(plus_plus(int, _296618, plus_plus(int, _296616, _296614)) = plus_plus(int, _296616, plus_plus(int, _296618, _296614)))], (1123 ^ _256258) ^ [_296726, _296728] : [-(plus_plus(int, _296728, _296726) = plus_plus(int, _296726, _296728))], (1125 ^ _256258) ^ [_296858] : [ord_less(int, bit1(_296858), pls), -(ord_less(int, _296858, pls))], (1131 ^ _256258) ^ [_297022] : [ord_less(int, _297022, pls), -(ord_less(int, bit1(_297022), pls))], (1137 ^ _256258) ^ [_297265, _297267] : [ord_less(int, bit1(_297267), bit0(_297265)), -(ord_less(int, _297267, _297265))], (1143 ^ _256258) ^ [_297439, _297441] : [ord_less(int, _297441, _297439), -(ord_less(int, bit1(_297441), bit0(_297439)))], (1149 ^ _256258) ^ [_297692, _297694] : [ord_less(int, bit1(_297694), bit0(_297692)), -(ord_less(int, _297694, _297692))], (1155 ^ _256258) ^ [_297866, _297868] : [ord_less(int, _297868, _297866), -(ord_less(int, bit1(_297868), bit0(_297866)))], (1161 ^ _256258) ^ [_298105] : [ord_less(int, bit0(_298105), pls), -(ord_less(int, _298105, pls))], (1167 ^ _256258) ^ [_298269] : [ord_less(int, _298269, pls), -(ord_less(int, bit0(_298269), pls))], (1173 ^ _256258) ^ [_298498] : [ord_less(int, pls, bit0(_298498)), -(ord_less(int, pls, _298498))], (1179 ^ _256258) ^ [_298662] : [ord_less(int, pls, _298662), -(ord_less(int, pls, bit0(_298662)))], (1185 ^ _256258) ^ [_298891] : [ord_less_eq(int, pls, bit1(_298891)), -(ord_less_eq(int, pls, _298891))], (1191 ^ _256258) ^ [_299055] : [ord_less_eq(int, pls, _299055), -(ord_less_eq(int, pls, bit1(_299055)))], (1197 ^ _256258) ^ [_299298, _299300] : [ord_less_eq(int, bit0(_299300), bit1(_299298)), -(ord_less_eq(int, _299300, _299298))], (1203 ^ _256258) ^ [_299472, _299474] : [ord_less_eq(int, _299474, _299472), -(ord_less_eq(int, bit0(_299474), bit1(_299472)))], (1221 ^ _256258) ^ [] : [-(linordered_idom(int))], (1223 ^ _256258) ^ [] : [-(comm_semiring_1(int))], (1225 ^ _256258) ^ [] : [-(number_semiring(int))], (1227 ^ _256258) ^ [] : [-(linorder(int))], (1229 ^ _256258) ^ [] : [-(monoid_mult(int))], (1231 ^ _256258) ^ [] : [-(semiring_1(int))], (1233 ^ _256258) ^ [] : [-(ring_char_0(int))], (1235 ^ _256258) ^ [] : [-(number_ring(int))], (1237 ^ _256258) ^ [] : [-(number(int))], (1239 ^ _256258) ^ [] : [-(comm_semiring_1(nat))], (1241 ^ _256258) ^ [] : [-(number_semiring(nat))], (1243 ^ _256258) ^ [] : [-(linorder(nat))], (1245 ^ _256258) ^ [] : [-(monoid_mult(nat))], (1247 ^ _256258) ^ [] : [-(semiring_1(nat))], (1249 ^ _256258) ^ [] : [-(number(nat))], (1251 ^ _256258) ^ [_300883, _300885] : [-(ti(_300885, ti(_300885, _300883)) = ti(_300885, _300883))], (1209 ^ _256258) ^ [_299725, _299727] : [ord_less_eq(int, bit0(_299727), bit1(_299725)), -(ord_less_eq(int, _299727, _299725))], (1215 ^ _256258) ^ [_299899, _299901] : [ord_less_eq(int, _299901, _299899), -(ord_less_eq(int, bit0(_299901), bit1(_299899)))]], input).
% 1.86/2.42  ncf('1',plain,[plus_plus(int, power_power(int, 451 ^ [], number_number_of(nat, bit0(bit1(pls)))), power_power(int, 452 ^ [], 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(1253 ^ 0,bind([[_301917, _301919], [452 ^ [], 451 ^ []]]))).
% 1.86/2.42  ncf('1.1',plain,[-(plus_plus(int, power_power(int, 451 ^ [], number_number_of(nat, bit0(bit1(pls)))), power_power(int, 452 ^ [], 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(448 ^ 1)).
% 1.86/2.42  ncf('1.1.1',plain,[-(t = one_one(int)), -(ord_less(int, t, one_one(int))), -(ord_less(int, one_one(int), t))],extension(565 ^ 2,bind([[_275651, _275653], [one_one(int), t]]))).
% 1.86/2.42  ncf('1.1.1.1',plain,[ord_less(int, t, one_one(int)), 551 : -(ord_less_eq(int, t, one_one(int)))],extension(547 ^ 3,bind([[_275101, _275103], [one_one(int), t]]))).
% 1.86/2.42  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(585 ^ 6,bind([[_276285, _276287], [one_one(int), t]]))).
% 1.86/2.42  ncf('1.1.1.1.1.1',plain,[-(ord_less_eq(int, one_one(int), t))],extension(446 ^ 7)).
% 1.86/2.42  ncf('1.1.1.1.1.2',plain,[t = one_one(int)],reduction('1.1')).
% 1.86/2.42  ncf('1.1.1.2',plain,[ord_less(int, one_one(int), t), -(plus_plus(int, power_power(int, 459 ^ [], number_number_of(nat, bit0(bit1(pls)))), power_power(int, 460 ^ [], 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(456 ^ 3)).
% 1.86/2.42  ncf('1.1.1.2.1',plain,[plus_plus(int, power_power(int, 459 ^ [], number_number_of(nat, bit0(bit1(pls)))), power_power(int, 460 ^ [], 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(1253 ^ 4,bind([[_301917, _301919], [460 ^ [], 459 ^ []]]))).
% 1.86/2.42  %-----------------------------------------------------
% 1.86/2.42  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
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