%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : NUM925+5 : TPTP v8.1.2. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n016.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 1.33s 2.42s
% Output   : Proof 1.33s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : NUM925+5 : TPTP v8.1.2. Released v5.3.0.
% 0.03/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.34  % Computer : n016.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Thu May 18 17:44:11 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 1.33/2.42  
% 1.33/2.42  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 1.33/2.42  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.33/2.42  %-----------------------------------------------------
% 1.33/2.42  ncf(matrix, plain, [(1334 ^ _235892) ^ [] : [-(power_power(int, plus_plus(int, one_one(int), semiring_1_of_nat(int, n)), number_number_of(nat, bit0(bit1(pls)))) = zero_zero(int))], (168 ^ _235892) ^ [_241116, _241118] : [_241118 = _241116, -(undefined(_241118) = undefined(_241116))], (174 ^ _235892) ^ [_241362, _241364, _241366, _241368] : [-(ti(_241368, _241364) = ti(_241366, _241362)), _241368 = _241366, _241364 = _241362], (184 ^ _235892) ^ [_241749, _241751, _241753, _241755, _241757, _241759] : [-(power_power(_241759, _241755, _241751) = power_power(_241757, _241753, _241749)), _241759 = _241757, _241755 = _241753, _241751 = _241749], (198 ^ _235892) ^ [_242265, _242267, _242269, _242271, _242273, _242275] : [-(plus_plus(_242275, _242271, _242267) = plus_plus(_242273, _242269, _242265)), _242275 = _242273, _242271 = _242269, _242267 = _242265], (212 ^ _235892) ^ [_242725, _242727] : [_242727 = _242725, -(one_one(_242727) = one_one(_242725))], (218 ^ _235892) ^ [_242971, _242973, _242975, _242977] : [-(semiring_1_of_nat(_242977, _242973) = semiring_1_of_nat(_242975, _242971)), _242977 = _242975, _242973 = _242971], (228 ^ _235892) ^ [_243330, _243332, _243334, _243336] : [-(number_number_of(_243336, _243332) = number_number_of(_243334, _243330)), _243336 = _243334, _243332 = _243330], (238 ^ _235892) ^ [_243661, _243663] : [_243663 = _243661, -(bit0(_243663) = bit0(_243661))], (244 ^ _235892) ^ [_243879, _243881] : [_243881 = _243879, -(bit1(_243881) = bit1(_243879))], (250 ^ _235892) ^ [_244077, _244079] : [_244079 = _244077, -(zero_zero(_244079) = zero_zero(_244077))], (2 ^ _235892) ^ [_236036] : [-(_236036 = _236036)], (4 ^ _235892) ^ [_236143, _236145] : [_236145 = _236143, -(_236143 = _236145)], (10 ^ _235892) ^ [_236347, _236349, _236351] : [-(_236351 = _236347), _236351 = _236349, _236349 = _236347], (20 ^ _235892) ^ [_236716, _236718, _236720, _236722, _236724, _236726] : [-(ord_less(_236724, _236720, _236716)), ord_less(_236726, _236722, _236718), _236726 = _236724, _236722 = _236720, _236718 = _236716], (38 ^ _235892) ^ [_237269, _237271] : [-(linord219039673up_add(_237269)), _237271 = _237269, linord219039673up_add(_237271)], (48 ^ _235892) ^ [_237564, _237566] : [-(ring_11004092258visors(_237564)), _237566 = _237564, ring_11004092258visors(_237566)], (58 ^ _235892) ^ [_237859, _237861] : [-(linordered_idom(_237859)), _237861 = _237859, linordered_idom(_237861)], (68 ^ _235892) ^ [_238154, _238156] : [-(ring_char_0(_238154)), _238156 = _238154, ring_char_0(_238156)], (78 ^ _235892) ^ [_238449, _238451] : [-(number_ring(_238449)), _238451 = _238449, number_ring(_238451)], (88 ^ _235892) ^ [_238744, _238746] : [-(no_zero_divisors(_238744)), _238746 = _238744, no_zero_divisors(_238746)], (98 ^ _235892) ^ [_239039, _239041] : [-(number_semiring(_239039)), _239041 = _239039, number_semiring(_239041)], (108 ^ _235892) ^ [_239334, _239336] : [-(zero_neq_one(_239334)), _239336 = _239334, zero_neq_one(_239336)], (118 ^ _235892) ^ [_239629, _239631] : [-(semiring_1(_239629)), _239631 = _239629, semiring_1(_239631)], (128 ^ _235892) ^ [_239924, _239926] : [-(semiring_0(_239924)), _239926 = _239924, semiring_0(_239926)], (138 ^ _235892) ^ [_240219, _240221] : [-(mult_zero(_240219)), _240221 = _240219, mult_zero(_240221)], (148 ^ _235892) ^ [_240514, _240516] : [-(power(_240514)), _240516 = _240514, power(_240516)], (158 ^ _235892) ^ [_240789, _240791] : [-(number(_240789)), _240791 = _240789, number(_240791)], (256 ^ _235892) ^ [_244351] : [-(ti(_244351, one_one(_244351)) = one_one(_244351)), power(_244351), semiring_0(_244351)], (266 ^ _235892) ^ [_244664, _244666, _244668] : [linord219039673up_add(_244664), -(plus_plus(_244664, ti(_244664, _244668), _244666) = plus_plus(_244664, _244668, _244666))], (272 ^ _235892) ^ [_244914, _244916, _244918] : [linord219039673up_add(_244914), -(plus_plus(_244914, _244918, ti(_244914, _244916)) = plus_plus(_244914, _244918, _244916))], (278 ^ _235892) ^ [_245164, _245166, _245168] : [linord219039673up_add(_245164), -(ti(_245164, plus_plus(_245164, _245168, _245166)) = plus_plus(_245164, _245168, _245166))], (284 ^ _235892) ^ [_245414, _245416, _245418] : [number_semiring(_245414), -(plus_plus(_245414, ti(_245414, _245418), _245416) = plus_plus(_245414, _245418, _245416))], (290 ^ _235892) ^ [_245664, _245666, _245668] : [number_semiring(_245664), -(plus_plus(_245664, _245668, ti(_245664, _245666)) = plus_plus(_245664, _245668, _245666))], (296 ^ _235892) ^ [_245914, _245916, _245918] : [number_semiring(_245914), -(ti(_245914, plus_plus(_245914, _245918, _245916)) = plus_plus(_245914, _245918, _245916))], (302 ^ _235892) ^ [_246136] : [-(ti(_246136, zero_zero(_246136)) = zero_zero(_246136)), power(_246136), mult_zero(_246136), no_zero_divisors(_246136), zero_neq_one(_246136)], (320 ^ _235892) ^ [_246587] : [linord219039673up_add(_246587), -(ti(_246587, zero_zero(_246587)) = zero_zero(_246587))], (326 ^ _235892) ^ [_246789] : [-(ti(_246789, zero_zero(_246789)) = zero_zero(_246789)), power(_246789), semiring_0(_246789)], (336 ^ _235892) ^ [_247059] : [-(ti(_247059, undefined(_247059)) = undefined(_247059))], (338 ^ _235892) ^ [_247144] : [-(bit0(ti(int, _247144)) = bit0(_247144))], (340 ^ _235892) ^ [_247229] : [-(ti(int, bit0(_247229)) = bit0(_247229))], (342 ^ _235892) ^ [_247314] : [-(bit1(ti(int, _247314)) = bit1(_247314))], (344 ^ _235892) ^ [_247399] : [-(ti(int, bit1(_247399)) = bit1(_247399))], (346 ^ _235892) ^ [] : [-(ti(int, pls) = pls)], (348 ^ _235892) ^ [_247566, _247568] : [number(_247566), -(number_number_of(_247566, ti(int, _247568)) = number_number_of(_247566, _247568))], (354 ^ _235892) ^ [_247792, _247794] : [number(_247792), -(ti(_247792, number_number_of(_247792, _247794)) = number_number_of(_247792, _247794))], (360 ^ _235892) ^ [_248018, _248020] : [number_semiring(_248018), -(semiring_1_of_nat(_248018, ti(nat, _248020)) = semiring_1_of_nat(_248018, _248020))], (366 ^ _235892) ^ [_248244, _248246] : [number_semiring(_248244), -(ti(_248244, semiring_1_of_nat(_248244, _248246)) = semiring_1_of_nat(_248244, _248246))], (372 ^ _235892) ^ [_248484, _248486, _248488] : [linordered_idom(_248484), 375 ^ _235892 : [(376 ^ _235892) ^ [] : [ord_less(_248484, ti(_248484, _248488), _248486), -(ord_less(_248484, _248488, _248486))], (382 ^ _235892) ^ [] : [ord_less(_248484, _248488, _248486), -(ord_less(_248484, ti(_248484, _248488), _248486))]]], (388 ^ _235892) ^ [_248987, _248989, _248991] : [linordered_idom(_248987), 391 ^ _235892 : [(392 ^ _235892) ^ [] : [ord_less(_248987, _248991, ti(_248987, _248989)), -(ord_less(_248987, _248991, _248989))], (398 ^ _235892) ^ [] : [ord_less(_248987, _248991, _248989), -(ord_less(_248987, _248991, ti(_248987, _248989)))]]], (404 ^ _235892) ^ [_249505, _249507] : [ord_less(nat, ti(nat, _249507), _249505), -(ord_less(nat, _249507, _249505))], (410 ^ _235892) ^ [_249677, _249679] : [ord_less(nat, _249679, _249677), -(ord_less(nat, ti(nat, _249679), _249677))], (416 ^ _235892) ^ [_249928, _249930] : [ord_less(nat, _249930, ti(nat, _249928)), -(ord_less(nat, _249930, _249928))], (422 ^ _235892) ^ [_250100, _250102] : [ord_less(nat, _250102, _250100), -(ord_less(nat, _250102, ti(nat, _250100)))], (428 ^ _235892) ^ [_250336, _250338, _250340] : [-(power_power(_250336, ti(_250336, _250340), _250338) = power_power(_250336, _250340, _250338)), power(_250336), mult_zero(_250336), no_zero_divisors(_250336), zero_neq_one(_250336)], (446 ^ _235892) ^ [_250859, _250861, _250863] : [-(power_power(_250859, _250863, ti(nat, _250861)) = power_power(_250859, _250863, _250861)), power(_250859), mult_zero(_250859), no_zero_divisors(_250859), zero_neq_one(_250859)], (464 ^ _235892) ^ [_251382, _251384, _251386] : [-(ti(_251382, power_power(_251382, _251386, _251384)) = power_power(_251382, _251386, _251384)), power(_251382), mult_zero(_251382), no_zero_divisors(_251382), zero_neq_one(_251382)], (482 ^ _235892) ^ [_251905, _251907, _251909] : [-(power_power(_251905, ti(_251905, _251909), _251907) = power_power(_251905, _251909, _251907)), power(_251905), semiring_0(_251905)], (492 ^ _235892) ^ [_252246, _252248, _252250] : [-(power_power(_252246, _252250, ti(nat, _252248)) = power_power(_252246, _252250, _252248)), power(_252246), semiring_0(_252246)], (502 ^ _235892) ^ [_252587, _252589, _252591] : [-(ti(_252587, power_power(_252587, _252591, _252589)) = power_power(_252587, _252591, _252589)), power(_252587), semiring_0(_252587)], (512 ^ _235892) ^ [] : [-(ti(nat, n) = n)], (514 ^ _235892) ^ [] : [-(ti(int, t) = t)], (516 ^ _235892) ^ [] : [-(ord_less(int, zero_zero(int), plus_plus(int, one_one(int), semiring_1_of_nat(int, n))))], (518 ^ _235892) ^ [] : [-(ord_less(int, one_one(int), t))], (520 ^ _235892) ^ [_253112] : [linordered_idom(_253112), 523 ^ _235892 : [(524 ^ _235892) ^ [_253321, _253323] : [plus_plus(_253112, power_power(_253112, _253323, number_number_of(nat, bit0(bit1(pls)))), power_power(_253112, _253321, number_number_of(nat, bit0(bit1(pls))))) = zero_zero(_253112), 527 ^ _235892 : [(528 ^ _235892) ^ [] : [-(ti(_253112, _253323) = zero_zero(_253112))], (530 ^ _235892) ^ [] : [-(ti(_253112, _253321) = zero_zero(_253112))]]], (532 ^ _235892) ^ [_253616, _253618] : [-(plus_plus(_253112, power_power(_253112, _253618, number_number_of(nat, bit0(bit1(pls)))), power_power(_253112, _253616, number_number_of(nat, bit0(bit1(pls))))) = zero_zero(_253112)), ti(_253112, _253618) = zero_zero(_253112), ti(_253112, _253616) = zero_zero(_253112)]]], (542 ^ _235892) ^ [_253968] : [semiring_1(_253968), -(power_power(_253968, one_one(_253968), number_number_of(nat, bit0(bit1(pls)))) = one_one(_253968))], (548 ^ _235892) ^ [_254172] : [semiring_1(_254172), -(power_power(_254172, zero_zero(_254172), number_number_of(nat, bit0(bit1(pls)))) = zero_zero(_254172))], (554 ^ _235892) ^ [_254376] : [ring_11004092258visors(_254376), 557 ^ _235892 : [(558 ^ _235892) ^ [_254547] : [power_power(_254376, _254547, number_number_of(nat, bit0(bit1(pls)))) = zero_zero(_254376), -(ti(_254376, _254547) = zero_zero(_254376))], (564 ^ _235892) ^ [_254733] : [ti(_254376, _254733) = zero_zero(_254376), -(power_power(_254376, _254733, number_number_of(nat, bit0(bit1(pls)))) = zero_zero(_254376))]]], (570 ^ _235892) ^ [_254960] : [number_ring(_254960), 573 ^ _235892 : [(574 ^ _235892) ^ [_255086] : [-(plus_plus(_254960, one_one(_254960), number_number_of(_254960, _255086)) = number_number_of(_254960, plus_plus(int, bit1(pls), _255086)))]]], (576 ^ _235892) ^ [_255202] : [number_ring(_255202), 579 ^ _235892 : [(580 ^ _235892) ^ [_255328] : [-(plus_plus(_255202, number_number_of(_255202, _255328), one_one(_255202)) = number_number_of(_255202, plus_plus(int, _255328, bit1(pls))))]]], (582 ^ _235892) ^ [_255444] : [number_ring(_255444), -(plus_plus(_255444, one_one(_255444), one_one(_255444)) = number_number_of(_255444, bit0(bit1(pls))))], (588 ^ _235892) ^ [_255654] : [number_semiring(_255654), -(plus_plus(_255654, one_one(_255654), one_one(_255654)) = number_number_of(_255654, bit0(bit1(pls))))], (594 ^ _235892) ^ [_255849] : [-(power_power(int, power_power(int, _255849, number_number_of(nat, bit0(bit1(pls)))), number_number_of(nat, bit0(bit1(pls)))) = power_power(int, _255849, number_number_of(nat, bit0(bit0(bit1(pls))))))], (596 ^ _235892) ^ [_255954] : [power(_255954), semiring_0(_255954), 603 ^ _235892 : [(604 ^ _235892) ^ [_256230] : [number_number_of(nat, _256230) = zero_zero(nat), -(power_power(_255954, zero_zero(_255954), number_number_of(nat, _256230)) = one_one(_255954))], (610 ^ _235892) ^ [_256422] : [-(number_number_of(nat, _256422) = zero_zero(nat)), -(power_power(_255954, zero_zero(_255954), number_number_of(nat, _256422)) = zero_zero(_255954))]]], (616 ^ _235892) ^ [_256660] : [number_ring(_256660), -(one_one(_256660) = number_number_of(_256660, bit1(pls)))], (622 ^ _235892) ^ [_256858] : [number_ring(_256858), -(number_number_of(_256858, bit1(pls)) = one_one(_256858))], (628 ^ _235892) ^ [] : [-(ord_less(nat, zero_zero(nat), n))], (630 ^ _235892) ^ [_257123, _257125] : [-(ord_less(int, _257125, _257123)), -(_257125 = _257123), -(ord_less(int, _257123, _257125))], (640 ^ _235892) ^ [_257457, _257459] : [ord_less(int, number_number_of(int, _257459), number_number_of(int, _257457)), -(ord_less(int, _257459, _257457))], (646 ^ _235892) ^ [_257635, _257637] : [ord_less(int, _257637, _257635), -(ord_less(int, number_number_of(int, _257637), number_number_of(int, _257635)))], (652 ^ _235892) ^ [_257848, _257850] : [-(plus_plus(int, number_number_of(int, _257850), number_number_of(int, _257848)) = number_number_of(int, plus_plus(int, _257850, _257848)))], (654 ^ _235892) ^ [_257960] : [number_ring(_257960), linordered_idom(_257960), 661 ^ _235892 : [(662 ^ _235892) ^ [_258230, _258232] : [ord_less(_257960, number_number_of(_257960, _258232), number_number_of(_257960, _258230)), -(ord_less(int, _258232, _258230))], (668 ^ _235892) ^ [_258416, _258418] : [ord_less(int, _258418, _258416), -(ord_less(_257960, number_number_of(_257960, _258418), number_number_of(_257960, _258416)))]]], (674 ^ _235892) ^ [] : [-(zero_zero(int) = number_number_of(int, pls))], (676 ^ _235892) ^ [_258697, _258699] : [-(power_power(int, semiring_1_of_nat(int, _258699), _258697) = semiring_1_of_nat(int, power_power(nat, _258699, _258697)))], (678 ^ _235892) ^ [_258805, _258807] : [-(semiring_1_of_nat(int, power_power(nat, _258807, _258805)) = power_power(int, semiring_1_of_nat(int, _258807), _258805))], (680 ^ _235892) ^ [_258927, _258929, _258931] : [-(plus_plus(int, semiring_1_of_nat(int, _258931), plus_plus(int, semiring_1_of_nat(int, _258929), _258927)) = plus_plus(int, semiring_1_of_nat(int, plus_plus(nat, _258931, _258929)), _258927))], (682 ^ _235892) ^ [_259048, _259050] : [-(plus_plus(int, semiring_1_of_nat(int, _259050), semiring_1_of_nat(int, _259048)) = semiring_1_of_nat(int, plus_plus(nat, _259050, _259048)))], (684 ^ _235892) ^ [] : [-(semiring_1_of_nat(int, one_one(nat)) = one_one(int))], (686 ^ _235892) ^ [] : [-(number_number_of(nat, pls) = zero_zero(nat))], (688 ^ _235892) ^ [] : [-(zero_zero(nat) = number_number_of(nat, pls))], (690 ^ _235892) ^ [_259348] : [semiring_1_of_nat(int, _259348) = zero_zero(int), -(_259348 = zero_zero(nat))], (696 ^ _235892) ^ [_259510] : [_259510 = zero_zero(nat), -(semiring_1_of_nat(int, _259510) = zero_zero(int))], (702 ^ _235892) ^ [] : [-(semiring_1_of_nat(int, zero_zero(nat)) = zero_zero(int))], (704 ^ _235892) ^ [] : [-(plus_plus(nat, one_one(nat), one_one(nat)) = number_number_of(nat, bit0(bit1(pls))))], (706 ^ _235892) ^ [_259857, _259859] : [ord_less(int, bit1(_259859), bit1(_259857)), -(ord_less(int, _259859, _259857))], (712 ^ _235892) ^ [_260031, _260033] : [ord_less(int, _260033, _260031), -(ord_less(int, bit1(_260033), bit1(_260031)))], (718 ^ _235892) ^ [_260284, _260286] : [ord_less(int, bit1(_260286), bit1(_260284)), -(ord_less(int, _260286, _260284))], (724 ^ _235892) ^ [_260458, _260460] : [ord_less(int, _260460, _260458), -(ord_less(int, bit1(_260460), bit1(_260458)))], (730 ^ _235892) ^ [] : [ord_less(int, pls, pls)], (732 ^ _235892) ^ [_260763, _260765] : [ord_less(int, bit0(_260765), bit0(_260763)), -(ord_less(int, _260765, _260763))], (738 ^ _235892) ^ [_260937, _260939] : [ord_less(int, _260939, _260937), -(ord_less(int, bit0(_260939), bit0(_260937)))], (744 ^ _235892) ^ [_261190, _261192] : [ord_less(int, bit0(_261192), bit0(_261190)), -(ord_less(int, _261192, _261190))], (750 ^ _235892) ^ [_261364, _261366] : [ord_less(int, _261366, _261364), -(ord_less(int, bit0(_261366), bit0(_261364)))], (756 ^ _235892) ^ [_261602, _261604, _261606] : [ord_less(int, _261604, _261602), -(ord_less(int, plus_plus(int, _261604, _261606), plus_plus(int, _261602, _261606)))], (762 ^ _235892) ^ [_261858, _261860] : [ord_less(int, _261858, pls), -(plus_plus(nat, number_number_of(nat, _261858), number_number_of(nat, _261860)) = number_number_of(nat, _261860))], (768 ^ _235892) ^ [_262048, _262050] : [-(ord_less(int, _262048, pls)), 771 ^ _235892 : [(772 ^ _235892) ^ [] : [ord_less(int, _262050, pls), -(plus_plus(nat, number_number_of(nat, _262048), number_number_of(nat, _262050)) = number_number_of(nat, _262048))], (778 ^ _235892) ^ [] : [-(ord_less(int, _262050, pls)), -(plus_plus(nat, number_number_of(nat, _262048), number_number_of(nat, _262050)) = number_number_of(nat, plus_plus(int, _262048, _262050)))]]], (784 ^ _235892) ^ [] : [-(one_one(int) = number_number_of(int, bit1(pls)))], (786 ^ _235892) ^ [] : [-(number_number_of(nat, bit1(pls)) = one_one(nat))], (788 ^ _235892) ^ [] : [-(one_one(nat) = number_number_of(nat, bit1(pls)))], (790 ^ _235892) ^ [_262730] : [number_ring(_262730), ring_char_0(_262730), 797 ^ _235892 : [(798 ^ _235892) ^ [_262998, _263000] : [number_number_of(_262730, _263000) = number_number_of(_262730, _262998), -(_263000 = _262998)], (804 ^ _235892) ^ [_263180, _263182] : [_263182 = _263180, -(number_number_of(_262730, _263182) = number_number_of(_262730, _263180))]]], (810 ^ _235892) ^ [_263405] : [number(_263405), 813 ^ _235892 : [(814 ^ _235892) ^ [_263596, _263598] : [number_number_of(_263405, _263598) = ti(_263405, _263596), -(ti(_263405, _263596) = number_number_of(_263405, _263598))], (820 ^ _235892) ^ [_263790, _263792] : [ti(_263405, _263790) = number_number_of(_263405, _263792), -(number_number_of(_263405, _263792) = ti(_263405, _263790))]]], (826 ^ _235892) ^ [_264068, _264070] : [bit1(_264070) = bit1(_264068), -(_264070 = _264068)], (832 ^ _235892) ^ [_264238, _264240] : [_264240 = _264238, -(bit1(_264240) = bit1(_264238))], (838 ^ _235892) ^ [_264487, _264489] : [bit0(_264489) = bit0(_264487), -(_264489 = _264487)], (844 ^ _235892) ^ [_264657, _264659] : [_264659 = _264657, -(bit0(_264659) = bit0(_264657))], (850 ^ _235892) ^ [_264863] : [linordered_idom(_264863), 853 ^ _235892 : [(854 ^ _235892) ^ [_265033] : [ord_less(_264863, plus_plus(_264863, _265033, _265033), zero_zero(_264863)), -(ord_less(_264863, _265033, zero_zero(_264863)))], (860 ^ _235892) ^ [_265217] : [ord_less(_264863, _265217, zero_zero(_264863)), -(ord_less(_264863, plus_plus(_264863, _265217, _265217), zero_zero(_264863)))]]], (866 ^ _235892) ^ [_265455, _265457, _265459] : [-(plus_plus(int, plus_plus(int, _265459, _265457), _265455) = plus_plus(int, _265459, plus_plus(int, _265457, _265455)))], (868 ^ _235892) ^ [_265581, _265583, _265585] : [-(plus_plus(int, _265585, plus_plus(int, _265583, _265581)) = plus_plus(int, _265583, plus_plus(int, _265585, _265581)))], (870 ^ _235892) ^ [_265693, _265695] : [-(plus_plus(int, _265695, _265693) = plus_plus(int, _265693, _265695))], (872 ^ _235892) ^ [_265839, _265841] : [semiring_1_of_nat(int, _265841) = semiring_1_of_nat(int, _265839), -(_265841 = _265839)], (878 ^ _235892) ^ [_266013, _266015] : [_266015 = _266013, -(semiring_1_of_nat(int, _266015) = semiring_1_of_nat(int, _266013))], (884 ^ _235892) ^ [_266223] : [number_ring(_266223), linordered_idom(_266223), 891 ^ _235892 : [(892 ^ _235892) ^ [_266473] : [ord_less(_266223, number_number_of(_266223, _266473), zero_zero(_266223)), -(ord_less(int, _266473, pls))], (898 ^ _235892) ^ [_266651] : [ord_less(int, _266651, pls), -(ord_less(_266223, number_number_of(_266223, _266651), zero_zero(_266223)))]]], (904 ^ _235892) ^ [_266872] : [number_ring(_266872), linordered_idom(_266872), 911 ^ _235892 : [(912 ^ _235892) ^ [_267122] : [ord_less(_266872, zero_zero(_266872), number_number_of(_266872, _267122)), -(ord_less(int, pls, _267122))], (918 ^ _235892) ^ [_267300] : [ord_less(int, pls, _267300), -(ord_less(_266872, zero_zero(_266872), number_number_of(_266872, _267300)))]]], (924 ^ _235892) ^ [_267550] : [ord_less(int, bit1(_267550), pls), -(ord_less(int, _267550, pls))], (930 ^ _235892) ^ [_267714] : [ord_less(int, _267714, pls), -(ord_less(int, bit1(_267714), pls))], (936 ^ _235892) ^ [_267957, _267959] : [ord_less(int, bit1(_267959), bit0(_267957)), -(ord_less(int, _267959, _267957))], (942 ^ _235892) ^ [_268131, _268133] : [ord_less(int, _268133, _268131), -(ord_less(int, bit1(_268133), bit0(_268131)))], (948 ^ _235892) ^ [_268384, _268386] : [ord_less(int, bit1(_268386), bit0(_268384)), -(ord_less(int, _268386, _268384))], (954 ^ _235892) ^ [_268558, _268560] : [ord_less(int, _268560, _268558), -(ord_less(int, bit1(_268560), bit0(_268558)))], (960 ^ _235892) ^ [_268797] : [ord_less(int, bit0(_268797), pls), -(ord_less(int, _268797, pls))], (966 ^ _235892) ^ [_268961] : [ord_less(int, _268961, pls), -(ord_less(int, bit0(_268961), pls))], (972 ^ _235892) ^ [_269190] : [ord_less(int, pls, bit0(_269190)), -(ord_less(int, pls, _269190))], (978 ^ _235892) ^ [_269354] : [ord_less(int, pls, _269354), -(ord_less(int, pls, bit0(_269354)))], (984 ^ _235892) ^ [_269583] : [ord_less(int, bit1(_269583), zero_zero(int)), -(ord_less(int, _269583, zero_zero(int)))], (990 ^ _235892) ^ [_269747] : [ord_less(int, _269747, zero_zero(int)), -(ord_less(int, bit1(_269747), zero_zero(int)))], (996 ^ _235892) ^ [] : [ord_less(int, pls, zero_zero(int))], (998 ^ _235892) ^ [_270028] : [ord_less(int, bit0(_270028), zero_zero(int)), -(ord_less(int, _270028, zero_zero(int)))], (1004 ^ _235892) ^ [_270192] : [ord_less(int, _270192, zero_zero(int)), -(ord_less(int, bit0(_270192), zero_zero(int)))], (1010 ^ _235892) ^ [] : [-(ord_less(int, zero_zero(int), one_one(int)))], (1022 ^ _235892) ^ [_270752, _270754] : [1023 ^ _235892 : [(1024 ^ _235892) ^ [] : [ord_less(int, _270754, _270752)], (1026 ^ _235892) ^ [] : [_270754 = _270752]], -(ord_less(int, _270754, plus_plus(int, _270752, one_one(int))))], (1012 ^ _235892) ^ [_270488, _270490] : [ord_less(int, _270490, plus_plus(int, _270488, one_one(int))), -(ord_less(int, _270490, _270488)), -(_270490 = _270488)], (1030 ^ _235892) ^ [_271020] : [ord_less(int, semiring_1_of_nat(int, _271020), zero_zero(int))], (1032 ^ _235892) ^ [_271117] : [number_ring(_271117), linordered_idom(_271117), 1039 ^ _235892 : [(1040 ^ _235892) ^ [_271367] : [ord_less(_271117, number_number_of(_271117, _271367), one_one(_271117)), -(ord_less(int, _271367, bit1(pls)))], (1046 ^ _235892) ^ [_271545] : [ord_less(int, _271545, bit1(pls)), -(ord_less(_271117, number_number_of(_271117, _271545), one_one(_271117)))]]], (1052 ^ _235892) ^ [_271766] : [number_ring(_271766), linordered_idom(_271766), 1059 ^ _235892 : [(1060 ^ _235892) ^ [_272016] : [ord_less(_271766, one_one(_271766), number_number_of(_271766, _272016)), -(ord_less(int, bit1(pls), _272016))], (1066 ^ _235892) ^ [_272194] : [ord_less(int, bit1(pls), _272194), -(ord_less(_271766, one_one(_271766), number_number_of(_271766, _272194)))]]], (1072 ^ _235892) ^ [_272444] : [ord_less(int, plus_plus(int, plus_plus(int, one_one(int), _272444), _272444), zero_zero(int)), -(ord_less(int, _272444, zero_zero(int)))], (1078 ^ _235892) ^ [_272620] : [ord_less(int, _272620, zero_zero(int)), -(ord_less(int, plus_plus(int, plus_plus(int, one_one(int), _272620), _272620), zero_zero(int)))], (1084 ^ _235892) ^ [_272832] : [linord219039673up_add(_272832), 1087 ^ _235892 : [(1088 ^ _235892) ^ [_273003] : [plus_plus(_272832, _273003, _273003) = zero_zero(_272832), -(ti(_272832, _273003) = zero_zero(_272832))], (1094 ^ _235892) ^ [_273189] : [ti(_272832, _273189) = zero_zero(_272832), -(plus_plus(_272832, _273189, _273189) = zero_zero(_272832))]]], (1100 ^ _235892) ^ [_273400] : [bit1(_273400) = pls], (1102 ^ _235892) ^ [_273479] : [pls = bit1(_273479)], (1104 ^ _235892) ^ [_273572, _273574] : [bit1(_273574) = bit0(_273572)], (1106 ^ _235892) ^ [_273669, _273671] : [bit0(_273671) = bit1(_273669)], (1108 ^ _235892) ^ [_273797] : [bit0(_273797) = pls, -(_273797 = pls)], (1114 ^ _235892) ^ [_273957] : [_273957 = pls, -(bit0(_273957) = pls)], (1120 ^ _235892) ^ [_274182] : [pls = bit0(_274182), -(pls = _274182)], (1126 ^ _235892) ^ [_274342] : [pls = _274342, -(pls = bit0(_274342))], (1132 ^ _235892) ^ [] : [-(bit0(pls) = pls)], (1134 ^ _235892) ^ [] : [-(pls = zero_zero(int))], (1136 ^ _235892) ^ [] : [zero_zero(int) = one_one(int)], (1138 ^ _235892) ^ [_274681] : [-(plus_plus(int, _274681, pls) = _274681)], (1140 ^ _235892) ^ [_274763] : [-(plus_plus(int, pls, _274763) = _274763)], (1142 ^ _235892) ^ [_274859, _274861] : [-(plus_plus(int, bit0(_274861), bit0(_274859)) = bit0(plus_plus(int, _274861, _274859)))], (1144 ^ _235892) ^ [_274953] : [-(bit0(_274953) = plus_plus(int, _274953, _274953))], (1146 ^ _235892) ^ [_275037] : [-(plus_plus(int, _275037, zero_zero(int)) = _275037)], (1148 ^ _235892) ^ [_275119] : [-(plus_plus(int, zero_zero(int), _275119) = _275119)], (1150 ^ _235892) ^ [_275216] : [number_semiring(_275216), -(number_number_of(_275216, pls) = zero_zero(_275216))], (1156 ^ _235892) ^ [_275414] : [number_ring(_275414), -(number_number_of(_275414, pls) = zero_zero(_275414))], (1162 ^ _235892) ^ [_275612] : [number_ring(_275612), -(zero_zero(_275612) = number_number_of(_275612, pls))], (1168 ^ _235892) ^ [_275810] : [number_ring(_275810), 1171 ^ _235892 : [(1172 ^ _235892) ^ [_275930] : [-(plus_plus(_275810, number_number_of(_275810, pls), _275930) = ti(_275810, _275930))]]], (1174 ^ _235892) ^ [_276040] : [number_ring(_276040), 1177 ^ _235892 : [(1178 ^ _235892) ^ [_276160] : [-(plus_plus(_276040, _276160, number_number_of(_276040, pls)) = ti(_276040, _276160))]]], (1180 ^ _235892) ^ [_276270] : [power(_276270), mult_zero(_276270), no_zero_divisors(_276270), zero_neq_one(_276270), 1195 ^ _235892 : [(1196 ^ _235892) ^ [_276723, _276725] : [power_power(_276270, _276725, number_number_of(nat, _276723)) = zero_zero(_276270), 1199 ^ _235892 : [(1200 ^ _235892) ^ [] : [-(ti(_276270, _276725) = zero_zero(_276270))], (1202 ^ _235892) ^ [] : [number_number_of(nat, _276723) = zero_zero(nat)]]], (1204 ^ _235892) ^ [_277005, _277007] : [-(power_power(_276270, _277007, number_number_of(nat, _277005)) = zero_zero(_276270)), ti(_276270, _277007) = zero_zero(_276270), -(number_number_of(nat, _277005) = zero_zero(nat))]]], (1214 ^ _235892) ^ [_277352] : [number_ring(_277352), 1217 ^ _235892 : [(1218 ^ _235892) ^ [_277525, _277527, _277529] : [-(plus_plus(_277352, number_number_of(_277352, _277529), plus_plus(_277352, number_number_of(_277352, _277527), _277525)) = plus_plus(_277352, number_number_of(_277352, plus_plus(int, _277529, _277527)), _277525))]]], (1220 ^ _235892) ^ [_277654] : [number_ring(_277654), 1223 ^ _235892 : [(1224 ^ _235892) ^ [_277800, _277802] : [-(plus_plus(_277654, number_number_of(_277654, _277802), number_number_of(_277654, _277800)) = number_number_of(_277654, plus_plus(int, _277802, _277800)))]]], (1226 ^ _235892) ^ [_277919] : [number_ring(_277919), 1229 ^ _235892 : [(1230 ^ _235892) ^ [_278065, _278067] : [-(number_number_of(_277919, plus_plus(int, _278067, _278065)) = plus_plus(_277919, number_number_of(_277919, _278067), number_number_of(_277919, _278065)))]]], (1232 ^ _235892) ^ [_278183, _278185] : [-(plus_plus(int, bit1(_278185), bit0(_278183)) = bit1(plus_plus(int, _278185, _278183)))], (1234 ^ _235892) ^ [_278291, _278293] : [-(plus_plus(int, bit0(_278293), bit1(_278291)) = bit1(plus_plus(int, _278293, _278291)))], (1236 ^ _235892) ^ [_278385] : [-(bit1(_278385) = plus_plus(int, plus_plus(int, one_one(int), _278385), _278385))], (1238 ^ _235892) ^ [_278472] : [plus_plus(int, plus_plus(int, one_one(int), _278472), _278472) = zero_zero(int)], (1240 ^ _235892) ^ [_278573] : [number_semiring(_278573), 1243 ^ _235892 : [(1244 ^ _235892) ^ [_278692] : [-(number_number_of(_278573, semiring_1_of_nat(int, _278692)) = semiring_1_of_nat(_278573, _278692))]]], (1246 ^ _235892) ^ [_278801] : [linordered_idom(_278801), 1249 ^ _235892 : [(1250 ^ _235892) ^ [_278975] : [ord_less(_278801, zero_zero(_278801), power_power(_278801, _278975, number_number_of(nat, bit0(bit1(pls))))), ti(_278801, _278975) = zero_zero(_278801)], (1256 ^ _235892) ^ [_279164] : [-(ti(_278801, _279164) = zero_zero(_278801)), -(ord_less(_278801, zero_zero(_278801), power_power(_278801, _279164, number_number_of(nat, bit0(bit1(pls))))))]]], (1262 ^ _235892) ^ [_279396] : [linordered_idom(_279396), 1265 ^ _235892 : [(1266 ^ _235892) ^ [_279514] : [ord_less(_279396, power_power(_279396, _279514, number_number_of(nat, bit0(bit1(pls)))), zero_zero(_279396))]]], (1290 ^ _235892) ^ [] : [-(linord219039673up_add(int))], (1292 ^ _235892) ^ [] : [-(ring_11004092258visors(int))], (1294 ^ _235892) ^ [] : [-(no_zero_divisors(int))], (1296 ^ _235892) ^ [] : [-(linordered_idom(int))], (1298 ^ _235892) ^ [] : [-(number_semiring(int))], (1300 ^ _235892) ^ [] : [-(zero_neq_one(int))], (1302 ^ _235892) ^ [] : [-(semiring_1(int))], (1304 ^ _235892) ^ [] : [-(semiring_0(int))], (1306 ^ _235892) ^ [] : [-(mult_zero(int))], (1308 ^ _235892) ^ [] : [-(ring_char_0(int))], (1310 ^ _235892) ^ [] : [-(number_ring(int))], (1312 ^ _235892) ^ [] : [-(power(int))], (1314 ^ _235892) ^ [] : [-(number(int))], (1316 ^ _235892) ^ [] : [-(no_zero_divisors(nat))], (1318 ^ _235892) ^ [] : [-(number_semiring(nat))], (1320 ^ _235892) ^ [] : [-(zero_neq_one(nat))], (1322 ^ _235892) ^ [] : [-(semiring_1(nat))], (1324 ^ _235892) ^ [] : [-(semiring_0(nat))], (1326 ^ _235892) ^ [] : [-(mult_zero(nat))], (1328 ^ _235892) ^ [] : [-(power(nat))], (1330 ^ _235892) ^ [] : [-(number(nat))], (1332 ^ _235892) ^ [_281586, _281588] : [-(ti(_281588, ti(_281588, _281586)) = ti(_281588, _281586))], (1268 ^ _235892) ^ [_279621] : [linordered_idom(_279621), 1271 ^ _235892 : [(1282 ^ _235892) ^ [_280151, _280153] : [1283 ^ _235892 : [(1284 ^ _235892) ^ [] : [-(ti(_279621, _280153) = zero_zero(_279621))], (1286 ^ _235892) ^ [] : [-(ti(_279621, _280151) = zero_zero(_279621))]], -(ord_less(_279621, zero_zero(_279621), plus_plus(_279621, power_power(_279621, _280153, number_number_of(nat, bit0(bit1(pls)))), power_power(_279621, _280151, number_number_of(nat, bit0(bit1(pls)))))))], (1272 ^ _235892) ^ [_279835, _279837] : [ord_less(_279621, zero_zero(_279621), plus_plus(_279621, power_power(_279621, _279837, number_number_of(nat, bit0(bit1(pls)))), power_power(_279621, _279835, number_number_of(nat, bit0(bit1(pls)))))), ti(_279621, _279837) = zero_zero(_279621), ti(_279621, _279835) = zero_zero(_279621)]]]], input).
% 1.33/2.42  ncf('1',plain,[ord_less(int, pls, zero_zero(int))],start(996 ^ 0)).
% 1.33/2.42  ncf('1.1',plain,[-(ord_less(int, pls, zero_zero(int))), -(ord_less(int, zero_zero(int), pls)), -(zero_zero(int) = pls)],extension(630 ^ 1,bind([[_257123, _257125], [pls, zero_zero(int)]]))).
% 1.33/2.42  ncf('1.1.1',plain,[ord_less(int, zero_zero(int), pls), -(ord_less(int, pls, zero_zero(int))), int = int, zero_zero(int) = pls, pls = zero_zero(int)],extension(20 ^ 2,bind([[_236716, _236718, _236720, _236722, _236724, _236726], [zero_zero(int), pls, pls, zero_zero(int), int, int]]))).
% 1.33/2.42  ncf('1.1.1.1',plain,[ord_less(int, pls, zero_zero(int))],reduction('1')).
% 1.33/2.42  ncf('1.1.1.2',plain,[-(int = int)],extension(2 ^ 3,bind([[_236036], [int]]))).
% 1.33/2.42  ncf('1.1.1.3',plain,[-(zero_zero(int) = pls), pls = zero_zero(int)],extension(4 ^ 3,bind([[_236143, _236145], [zero_zero(int), pls]]))).
% 1.33/2.42  ncf('1.1.1.3.1',plain,[-(pls = zero_zero(int))],extension(1134 ^ 4)).
% 1.33/2.42  ncf('1.1.1.4',plain,[-(pls = zero_zero(int)), zero_zero(int) = pls],extension(4 ^ 3,bind([[_236143, _236145], [pls, zero_zero(int)]]))).
% 1.33/2.42  ncf('1.1.1.4.1',plain,[-(zero_zero(int) = pls)],lemmata('[1, 1].x')).
% 1.33/2.42  ncf('1.1.2',plain,[zero_zero(int) = pls, -(ord_less(int, pls, zero_zero(int))), ord_less(int, zero_zero(int), ti(int, plus_plus(int, one_one(int), semiring_1_of_nat(int, n)))), int = int, ti(int, plus_plus(int, one_one(int), semiring_1_of_nat(int, n))) = zero_zero(int)],extension(20 ^ 2,bind([[_236716, _236718, _236720, _236722, _236724, _236726], [zero_zero(int), ti(int, plus_plus(int, one_one(int), semiring_1_of_nat(int, n))), pls, zero_zero(int), int, int]]))).
% 1.33/2.42  ncf('1.1.2.1',plain,[ord_less(int, pls, zero_zero(int))],reduction('1')).
% 1.33/2.42  ncf('1.1.2.2',plain,[-(ord_less(int, zero_zero(int), ti(int, plus_plus(int, one_one(int), semiring_1_of_nat(int, n))))), 398 : ord_less(int, zero_zero(int), plus_plus(int, one_one(int), semiring_1_of_nat(int, n))), 398 : linordered_idom(int)],extension(388 ^ 3,bind([[_248987, _248989, _248991], [int, plus_plus(int, one_one(int), semiring_1_of_nat(int, n)), zero_zero(int)]]))).
% 1.33/2.42  ncf('1.1.2.2.1',plain,[-(ord_less(int, zero_zero(int), plus_plus(int, one_one(int), semiring_1_of_nat(int, n))))],extension(516 ^ 6)).
% 1.33/2.42  ncf('1.1.2.2.2',plain,[-(linordered_idom(int))],extension(1296 ^ 4)).
% 1.33/2.42  ncf('1.1.2.3',plain,[-(int = int)],extension(2 ^ 3,bind([[_236036], [int]]))).
% 1.33/2.42  ncf('1.1.2.4',plain,[-(ti(int, plus_plus(int, one_one(int), semiring_1_of_nat(int, n))) = zero_zero(int)), 558 : power_power(int, plus_plus(int, one_one(int), semiring_1_of_nat(int, n)), number_number_of(nat, bit0(bit1(pls)))) = zero_zero(int), 558 : ring_11004092258visors(int)],extension(554 ^ 3,bind([[_254376, _254547], [int, plus_plus(int, one_one(int), semiring_1_of_nat(int, n))]]))).
% 1.33/2.42  ncf('1.1.2.4.1',plain,[-(power_power(int, plus_plus(int, one_one(int), semiring_1_of_nat(int, n)), number_number_of(nat, bit0(bit1(pls)))) = zero_zero(int))],extension(1334 ^ 6)).
% 1.33/2.42  ncf('1.1.2.4.2',plain,[-(ring_11004092258visors(int))],extension(1292 ^ 4)).
% 1.33/2.42  %-----------------------------------------------------
% 1.33/2.42  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------