%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : HAL003+3 : TPTP v8.1.2. Released v2.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n017.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 11:16:46 EDT 2023

% Result   : Theorem 3.96s 4.47s
% Output   : Proof 3.96s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : HAL003+3 : TPTP v8.1.2. Released v2.6.0.
% 0.03/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n017.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Thu May 18 22:36:15 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 3.96/4.47  
% 3.96/4.47  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 3.96/4.47  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.96/4.47  %-----------------------------------------------------
% 3.96/4.47  ncf(matrix, plain, [(469 ^ _86915) ^ [] : [surjection(g)], (108 ^ _86915) ^ [_90556, _90558] : [_90558 = _90556, -(zero(_90558) = zero(_90556))], (114 ^ _86915) ^ [_90802, _90804, _90806, _90808] : [-(apply(_90808, _90804) = apply(_90806, _90802)), _90808 = _90806, _90804 = _90802], (124 ^ _86915) ^ [_91169, _91171, _91173, _91175, _91177, _91179] : [-(subtract(_91179, _91175, _91171) = subtract(_91177, _91173, _91169)), _91179 = _91177, _91175 = _91173, _91171 = _91169], (2 ^ _86915) ^ [_87059] : [-(_87059 = _87059)], (4 ^ _86915) ^ [_87166, _87168] : [_87168 = _87166, -(_87166 = _87168)], (10 ^ _86915) ^ [_87370, _87372, _87374] : [-(_87374 = _87370), _87374 = _87372, _87372 = _87370], (20 ^ _86915) ^ [_87739, _87741, _87743, _87745, _87747, _87749] : [-(morphism(_87747, _87743, _87739)), morphism(_87749, _87745, _87741), _87749 = _87747, _87745 = _87743, _87741 = _87739], (38 ^ _86915) ^ [_88292, _88294] : [-(injection(_88292)), _88294 = _88292, injection(_88294)], (48 ^ _86915) ^ [_88615, _88617, _88619, _88621] : [-(exact(_88619, _88615)), exact(_88621, _88617), _88621 = _88619, _88617 = _88615], (62 ^ _86915) ^ [_89115, _89117, _89119, _89121, _89123, _89125, _89127, _89129] : [-(commute(_89127, _89123, _89119, _89115)), commute(_89129, _89125, _89121, _89117), _89129 = _89127, _89125 = _89123, _89121 = _89119, _89117 = _89115], (98 ^ _86915) ^ [_90245, _90247] : [-(surjection(_90245)), _90247 = _90245, surjection(_90247)], (84 ^ _86915) ^ [_89849, _89851, _89853, _89855] : [-(element(_89853, _89849)), element(_89855, _89851), _89855 = _89853, _89851 = _89849], (388 ^ _86915) ^ [] : [-(morphism(alpha, a, b))], (390 ^ _86915) ^ [] : [-(morphism(beta, b, c))], (392 ^ _86915) ^ [] : [-(morphism(gamma, d, e))], (394 ^ _86915) ^ [] : [-(morphism(delta, e, r))], (396 ^ _86915) ^ [] : [-(morphism(f, a, d))], (398 ^ _86915) ^ [] : [-(morphism(g, b, e))], (400 ^ _86915) ^ [] : [-(morphism(h, c, r))], (402 ^ _86915) ^ [] : [-(injection(alpha))], (404 ^ _86915) ^ [] : [-(injection(gamma))], (406 ^ _86915) ^ [] : [-(surjection(beta))], (408 ^ _86915) ^ [] : [-(surjection(delta))], (410 ^ _86915) ^ [] : [-(exact(alpha, beta))], (412 ^ _86915) ^ [] : [-(exact(gammma, delta))], (414 ^ _86915) ^ [] : [-(commute(alpha, g, f, gamma))], (416 ^ _86915) ^ [] : [-(commute(beta, h, g, delta))], (418 ^ _86915) ^ [] : [-(surjection(f))], (420 ^ _86915) ^ [] : [-(surjection(h))], (422 ^ _86915) ^ [_102427] : [element(_102427, e), 427 ^ _86915 : [(428 ^ _86915) ^ [] : [-(element(425 ^ [_102427], r))], (430 ^ _86915) ^ [] : [-(apply(delta, _102427) = 425 ^ [_102427])], (432 ^ _86915) ^ [] : [-(element(426 ^ [_102427], b))], (434 ^ _86915) ^ [] : [-(apply(h, apply(beta, 426 ^ [_102427])) = 425 ^ [_102427])], (436 ^ _86915) ^ [] : [-(apply(delta, apply(g, 426 ^ [_102427])) = 425 ^ [_102427])]]], (438 ^ _86915) ^ [_103166] : [element(_103166, e), 444 ^ _86915 : [(445 ^ _86915) ^ [] : [-(element(441 ^ [_103166], b))], (447 ^ _86915) ^ [] : [-(element(442 ^ [_103166], e))], (449 ^ _86915) ^ [] : [-(subtract(e, apply(g, 441 ^ [_103166]), _103166) = 442 ^ [_103166])], (451 ^ _86915) ^ [] : [-(element(443 ^ [_103166], a))], (453 ^ _86915) ^ [] : [-(apply(gamma, apply(f, 443 ^ [_103166])) = 442 ^ [_103166])], (455 ^ _86915) ^ [] : [-(apply(g, apply(alpha, 443 ^ [_103166])) = 442 ^ [_103166])]]], (457 ^ _86915) ^ [_104120] : [element(_104120, e), 462 ^ _86915 : [(463 ^ _86915) ^ [] : [-(element(460 ^ [_104120], b))], (465 ^ _86915) ^ [] : [-(element(461 ^ [_104120], b))], (467 ^ _86915) ^ [] : [-(apply(g, subtract(b, 460 ^ [_104120], 461 ^ [_104120])) = _104120)]]], (138 ^ _86915) ^ [_91673, _91675, _91677] : [morphism(_91677, _91675, _91673), 141 ^ _86915 : [(148 ^ _86915) ^ [] : [-(apply(_91677, zero(_91675)) = zero(_91673))], (142 ^ _86915) ^ [_91852] : [element(_91852, _91675), -(element(apply(_91677, _91852), _91673))]]], (150 ^ _86915) ^ [_92162, _92164, _92166] : [injection(_92166), morphism(_92166, _92164, _92162), 157 ^ _86915 : [(158 ^ _86915) ^ [_92433, _92435] : [-(_92435 = _92433), element(_92435, _92164), element(_92433, _92164), apply(_92166, _92435) = apply(_92166, _92433)]]], (172 ^ _86915) ^ [_92902, _92904, _92906] : [-(injection(_92906)), morphism(_92906, _92904, _92902), 179 ^ _86915 : [(180 ^ _86915) ^ [] : [-(element(177 ^ [_92902, _92904, _92906], _92904))], (182 ^ _86915) ^ [] : [-(element(178 ^ [_92902, _92904, _92906], _92904))], (184 ^ _86915) ^ [] : [-(apply(_92906, 177 ^ [_92902, _92904, _92906]) = apply(_92906, 178 ^ [_92902, _92904, _92906]))], (186 ^ _86915) ^ [] : [177 ^ [_92902, _92904, _92906] = 178 ^ [_92902, _92904, _92906]]]], (190 ^ _86915) ^ [_93712, _93714, _93716] : [surjection(_93716), morphism(_93716, _93714, _93712), 197 ^ _86915 : [(198 ^ _86915) ^ [_93960] : [element(_93960, _93712), 202 ^ _86915 : [(203 ^ _86915) ^ [] : [-(element(201 ^ [_93712, _93714, _93716, _93960], _93714))], (205 ^ _86915) ^ [] : [-(apply(_93716, 201 ^ [_93712, _93714, _93716, _93960]) = _93960)]]]]], (207 ^ _86915) ^ [_94383, _94385, _94387] : [-(surjection(_94387)), morphism(_94387, _94385, _94383), 213 ^ _86915 : [(214 ^ _86915) ^ [] : [-(element(212 ^ [_94383, _94385, _94387], _94383))], (216 ^ _86915) ^ [_94727] : [element(_94727, _94385), apply(_94387, _94727) = 212 ^ [_94383, _94385, _94387]]]], (224 ^ _86915) ^ [_95078, _95080, _95082, _95084, _95086] : [exact(_95086, _95084), morphism(_95086, _95082, _95080), morphism(_95084, _95080, _95078), 235 ^ _86915 : [(236 ^ _86915) ^ [_95487] : [244 ^ _86915 : [(245 ^ _86915) ^ [] : [-(element(243 ^ [_95078, _95080, _95082, _95084, _95086, _95487], _95082))], (247 ^ _86915) ^ [] : [-(apply(_95086, 243 ^ [_95078, _95080, _95082, _95084, _95086, _95487]) = _95487)]], element(_95487, _95080), apply(_95084, _95487) = zero(_95078)], (249 ^ _86915) ^ [_95992] : [256 ^ _86915 : [(257 ^ _86915) ^ [] : [-(element(_95992, _95080))], (259 ^ _86915) ^ [] : [-(apply(_95084, _95992) = zero(_95078))]], 250 ^ _86915 : [(251 ^ _86915) ^ [_96116] : [element(_96116, _95082), apply(_95086, _96116) = _95992]]]]], (261 ^ _86915) ^ [_96567, _96569, _96571, _96573, _96575] : [-(exact(_96575, _96573)), morphism(_96575, _96571, _96569), morphism(_96573, _96569, _96567), 273 ^ _86915 : [(274 ^ _86915) ^ [] : [-(element(270 ^ [_96567, _96569, _96571, _96573, _96575], _96569))], (276 ^ _86915) ^ [] : [-(apply(_96573, 270 ^ [_96567, _96569, _96571, _96573, _96575]) = zero(_96567))], (278 ^ _86915) ^ [_97202] : [element(_97202, _96571), apply(_96575, _97202) = 270 ^ [_96567, _96569, _96571, _96573, _96575]]], 284 ^ _86915 : [(285 ^ _86915) ^ [] : [-(element(283 ^ [_96567, _96569, _96571, _96573, _96575], _96571))], (287 ^ _86915) ^ [] : [-(apply(_96575, 283 ^ [_96567, _96569, _96571, _96573, _96575]) = 270 ^ [_96567, _96569, _96571, _96573, _96575])], (289 ^ _86915) ^ [] : [element(270 ^ [_96567, _96569, _96571, _96573, _96575], _96569), apply(_96573, 270 ^ [_96567, _96569, _96571, _96573, _96575]) = zero(_96567)]]], (297 ^ _86915) ^ [_98083, _98085, _98087, _98089, _98091, _98093, _98095, _98097] : [316 ^ _86915 : [(317 ^ _86915) ^ [_98720] : [element(_98720, _98089), -(apply(_98095, apply(_98097, _98720)) = apply(_98091, apply(_98093, _98720)))]], commute(_98097, _98095, _98093, _98091), morphism(_98097, _98089, _98087), morphism(_98095, _98087, _98083), morphism(_98093, _98089, _98085), morphism(_98091, _98085, _98083)], (323 ^ _86915) ^ [_99101, _99103, _99105, _99107, _99109, _99111, _99113, _99115] : [-(commute(_99115, _99113, _99111, _99109)), morphism(_99115, _99107, _99105), morphism(_99113, _99105, _99101), morphism(_99111, _99107, _99103), morphism(_99109, _99103, _99101), 341 ^ _86915 : [(342 ^ _86915) ^ [] : [-(element(340 ^ [_99101, _99103, _99105, _99107, _99109, _99111, _99113, _99115], _99107))], (344 ^ _86915) ^ [] : [apply(_99113, apply(_99115, 340 ^ [_99101, _99103, _99105, _99107, _99109, _99111, _99113, _99115])) = apply(_99109, apply(_99111, 340 ^ [_99101, _99103, _99105, _99107, _99109, _99111, _99113, _99115]))]]], (348 ^ _86915) ^ [_100085, _100087, _100089] : [-(element(subtract(_100089, _100087, _100085), _100089)), element(_100087, _100089), element(_100085, _100089)], (358 ^ _86915) ^ [_100402, _100404] : [element(_100402, _100404), -(subtract(_100404, _100402, _100402) = zero(_100404))], (364 ^ _86915) ^ [_100638, _100640, _100642] : [-(subtract(_100642, _100640, subtract(_100642, _100640, _100638)) = _100638), element(_100640, _100642), element(_100638, _100642)], (374 ^ _86915) ^ [_100957, _100959, _100961] : [morphism(_100961, _100959, _100957), 377 ^ _86915 : [(378 ^ _86915) ^ [_101142, _101144] : [-(apply(_100961, subtract(_100959, _101144, _101142)) = subtract(_100957, apply(_100961, _101144), apply(_100961, _101142))), element(_101144, _100959), element(_101142, _100959)]]]], input).
% 3.96/4.47  ncf('1',plain,[surjection(g)],start(469 ^ 0)).
% 3.96/4.47  ncf('1.1',plain,[-(surjection(g)), morphism(g, b, e), 214 : -(element(212 ^ [e, b, g], e))],extension(207 ^ 1,bind([[_94383, _94385, _94387], [e, b, g]]))).
% 3.96/4.47  ncf('1.1.1',plain,[-(morphism(g, b, e))],extension(398 ^ 2)).
% 3.96/4.47  ncf('1.1.2',plain,[element(212 ^ [e, b, g], e), 463 : -(element(460 ^ [212 ^ [e, b, g]], b))],extension(457 ^ 4,bind([[_104120], [212 ^ [e, b, g]]]))).
% 3.96/4.47  ncf('1.1.2.1',plain,[element(460 ^ [212 ^ [e, b, g]], b), -(element(subtract(b, 460 ^ [212 ^ [e, b, g]], 461 ^ [212 ^ [e, b, g]]), b)), element(461 ^ [212 ^ [e, b, g]], b)],extension(348 ^ 7,bind([[_100085, _100087, _100089], [461 ^ [212 ^ [e, b, g]], 460 ^ [212 ^ [e, b, g]], b]]))).
% 3.96/4.47  ncf('1.1.2.1.1',plain,[element(subtract(b, 460 ^ [212 ^ [e, b, g]], 461 ^ [212 ^ [e, b, g]]), b), apply(g, subtract(b, 460 ^ [212 ^ [e, b, g]], 461 ^ [212 ^ [e, b, g]])) = 212 ^ [e, b, g]],extension(216 ^ 8,bind([[_94727], [subtract(b, 460 ^ [212 ^ [e, b, g]], 461 ^ [212 ^ [e, b, g]])]]))).
% 3.96/4.47  ncf('1.1.2.1.1.1',plain,[-(apply(g, subtract(b, 460 ^ [212 ^ [e, b, g]], 461 ^ [212 ^ [e, b, g]])) = 212 ^ [e, b, g])],extension(467 ^ 9)).
% 3.96/4.47  ncf('1.1.2.1.2',plain,[-(element(461 ^ [212 ^ [e, b, g]], b))],extension(465 ^ 8)).
% 3.96/4.47  %-----------------------------------------------------
% 3.96/4.47  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------