%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SEU028+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n019.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri May 19 12:02:06 EDT 2023

% Result   : Theorem 0.45s 1.37s
% Output   : Proof 0.45s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem  : SEU028+1 : TPTP v8.1.2. Released v3.2.0.
% 0.10/0.12  % Command  : nanocop.sh %s %d
% 0.11/0.33  % Computer : n019.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 300
% 0.11/0.33  % DateTime : Thu May 18 13:39:42 EDT 2023
% 0.11/0.33  % CPUTime  : 
% 0.45/1.37  
% 0.45/1.37  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 0.45/1.37  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.45/1.37  %-----------------------------------------------------
% 0.45/1.37  ncf(matrix, plain, [(555 ^ _86810) ^ [] : [-(relation(553 ^ []))], (557 ^ _86810) ^ [] : [-(function(553 ^ []))], (559 ^ _86810) ^ [] : [-(one_to_one(553 ^ []))], (561 ^ _86810) ^ [] : [relation_composition(553 ^ [], function_inverse(553 ^ [])) = identity_relation(relation_dom(553 ^ [])), relation_composition(function_inverse(553 ^ []), 553 ^ []) = identity_relation(relation_rng(553 ^ []))], (112 ^ _86810) ^ [_90413, _90415, _90417, _90419] : [-(apply(_90419, _90415) = apply(_90417, _90413)), _90419 = _90417, _90415 = _90413], (122 ^ _86810) ^ [_90744, _90746] : [_90746 = _90744, -(powerset(_90746) = powerset(_90744))], (128 ^ _86810) ^ [_90962, _90964] : [_90964 = _90962, -(relation_dom(_90964) = relation_dom(_90962))], (134 ^ _86810) ^ [_91208, _91210, _91212, _91214] : [-(relation_composition(_91214, _91210) = relation_composition(_91212, _91208)), _91214 = _91212, _91210 = _91208], (144 ^ _86810) ^ [_91539, _91541] : [_91541 = _91539, -(function_inverse(_91541) = function_inverse(_91539))], (150 ^ _86810) ^ [_91757, _91759] : [_91759 = _91757, -(identity_relation(_91759) = identity_relation(_91757))], (156 ^ _86810) ^ [_91955, _91957] : [_91957 = _91955, -(relation_rng(_91957) = relation_rng(_91955))], (2 ^ _86810) ^ [_86954] : [-(_86954 = _86954)], (4 ^ _86810) ^ [_87061, _87063] : [_87063 = _87061, -(_87061 = _87063)], (10 ^ _86810) ^ [_87265, _87267, _87269] : [-(_87269 = _87265), _87269 = _87267, _87267 = _87265], (20 ^ _86810) ^ [_87578, _87580] : [-(relation_empty_yielding(_87578)), _87580 = _87578, relation_empty_yielding(_87580)], (30 ^ _86810) ^ [_87901, _87903, _87905, _87907] : [-(subset(_87905, _87901)), subset(_87907, _87903), _87907 = _87905, _87903 = _87901], (44 ^ _86810) ^ [_88345, _88347, _88349, _88351] : [-(element(_88349, _88345)), element(_88351, _88347), _88351 = _88349, _88347 = _88345], (58 ^ _86810) ^ [_88789, _88791, _88793, _88795] : [-(in(_88793, _88789)), in(_88795, _88791), _88795 = _88793, _88791 = _88789], (72 ^ _86810) ^ [_89205, _89207] : [-(empty(_89205)), _89207 = _89205, empty(_89207)], (82 ^ _86810) ^ [_89500, _89502] : [-(relation(_89500)), _89502 = _89500, relation(_89502)], (92 ^ _86810) ^ [_89795, _89797] : [-(function(_89795)), _89797 = _89795, function(_89797)], (102 ^ _86810) ^ [_90070, _90072] : [-(one_to_one(_90070)), _90072 = _90070, one_to_one(_90072)], (162 ^ _86810) ^ [_92199, _92201] : [in(_92201, _92199), in(_92199, _92201)], (168 ^ _86810) ^ [_92396] : [empty(_92396), -(function(_92396))], (174 ^ _86810) ^ [_92582] : [empty(_92582), -(relation(_92582))], (180 ^ _86810) ^ [_92768] : [191 ^ _86810 : [(192 ^ _86810) ^ [] : [-(relation(_92768))], (194 ^ _86810) ^ [] : [-(function(_92768))], (196 ^ _86810) ^ [] : [-(one_to_one(_92768))]], relation(_92768), empty(_92768), function(_92768)], (198 ^ _86810) ^ [_93261] : [205 ^ _86810 : [(206 ^ _86810) ^ [] : [-(relation(function_inverse(_93261)))], (208 ^ _86810) ^ [] : [-(function(function_inverse(_93261)))]], relation(_93261), function(_93261)], (210 ^ _86810) ^ [_93623, _93625] : [-(relation(relation_composition(_93625, _93623))), relation(_93625), relation(_93623)], (220 ^ _86810) ^ [_93893] : [-(relation(identity_relation(_93893)))], (223 ^ _86810) ^ [_94011] : [-(element(221 ^ [_94011], _94011))], (225 ^ _86810) ^ [_94123, _94125] : [232 ^ _86810 : [(233 ^ _86810) ^ [] : [-(empty(relation_composition(_94123, _94125)))], (235 ^ _86810) ^ [] : [-(relation(relation_composition(_94123, _94125)))]], empty(_94125), relation(_94123)], (237 ^ _86810) ^ [] : [-(empty(empty_set))], (239 ^ _86810) ^ [] : [-(relation(empty_set))], (241 ^ _86810) ^ [] : [-(relation_empty_yielding(empty_set))], (243 ^ _86810) ^ [_94664, _94666] : [258 ^ _86810 : [(259 ^ _86810) ^ [] : [-(relation(relation_composition(_94666, _94664)))], (261 ^ _86810) ^ [] : [-(function(relation_composition(_94666, _94664)))]], relation(_94666), function(_94666), relation(_94664), function(_94664)], (263 ^ _86810) ^ [_95186] : [empty(powerset(_95186))], (265 ^ _86810) ^ [] : [-(empty(empty_set))], (267 ^ _86810) ^ [_95338] : [-(relation(identity_relation(_95338)))], (269 ^ _86810) ^ [_95383] : [-(function(identity_relation(_95383)))], (271 ^ _86810) ^ [] : [-(empty(empty_set))], (273 ^ _86810) ^ [] : [-(relation(empty_set))], (275 ^ _86810) ^ [_95587] : [empty(relation_dom(_95587)), -(empty(_95587)), relation(_95587)], (285 ^ _86810) ^ [_95864] : [empty(relation_rng(_95864)), -(empty(_95864)), relation(_95864)], (295 ^ _86810) ^ [_96141] : [empty(_96141), 298 ^ _86810 : [(299 ^ _86810) ^ [] : [-(empty(relation_dom(_96141)))], (301 ^ _86810) ^ [] : [-(relation(relation_dom(_96141)))]]], (303 ^ _86810) ^ [_96406] : [empty(_96406), 306 ^ _86810 : [(307 ^ _86810) ^ [] : [-(empty(relation_rng(_96406)))], (309 ^ _86810) ^ [] : [-(relation(relation_rng(_96406)))]]], (311 ^ _86810) ^ [_96685, _96687] : [318 ^ _86810 : [(319 ^ _86810) ^ [] : [-(empty(relation_composition(_96687, _96685)))], (321 ^ _86810) ^ [] : [-(relation(relation_composition(_96687, _96685)))]], empty(_96687), relation(_96685)], (324 ^ _86810) ^ [] : [-(relation(322 ^ []))], (326 ^ _86810) ^ [] : [-(function(322 ^ []))], (329 ^ _86810) ^ [] : [-(empty(327 ^ []))], (331 ^ _86810) ^ [] : [-(relation(327 ^ []))], (333 ^ _86810) ^ [_97347] : [-(empty(_97347)), 337 ^ _86810 : [(338 ^ _86810) ^ [] : [-(element(336 ^ [_97347], powerset(_97347)))], (340 ^ _86810) ^ [] : [empty(336 ^ [_97347])]]], (343 ^ _86810) ^ [] : [-(empty(341 ^ []))], (346 ^ _86810) ^ [] : [-(relation(344 ^ []))], (348 ^ _86810) ^ [] : [-(empty(344 ^ []))], (350 ^ _86810) ^ [] : [-(function(344 ^ []))], (353 ^ _86810) ^ [] : [empty(351 ^ [])], (355 ^ _86810) ^ [] : [-(relation(351 ^ []))], (358 ^ _86810) ^ [_98178] : [-(element(356 ^ [_98178], powerset(_98178)))], (360 ^ _86810) ^ [_98229] : [-(empty(356 ^ [_98229]))], (363 ^ _86810) ^ [] : [empty(361 ^ [])], (366 ^ _86810) ^ [] : [-(relation(364 ^ []))], (368 ^ _86810) ^ [] : [-(function(364 ^ []))], (370 ^ _86810) ^ [] : [-(one_to_one(364 ^ []))], (373 ^ _86810) ^ [] : [-(relation(371 ^ []))], (375 ^ _86810) ^ [] : [-(relation_empty_yielding(371 ^ []))], (377 ^ _86810) ^ [_98775, _98777] : [-(subset(_98777, _98777))], (379 ^ _86810) ^ [_98884, _98886] : [in(_98886, _98884), -(element(_98886, _98884))], (385 ^ _86810) ^ [_99094, _99096] : [element(_99096, _99094), -(empty(_99094)), -(in(_99096, _99094))], (395 ^ _86810) ^ [_99392, _99394] : [relation(_99392), function(_99392), 402 ^ _86810 : [(403 ^ _86810) ^ [] : [_99392 = identity_relation(_99394), 406 ^ _86810 : [(407 ^ _86810) ^ [] : [-(relation_dom(_99392) = _99394)], (409 ^ _86810) ^ [_99811] : [in(_99811, _99394), -(apply(_99392, _99811) = _99811)]]], (415 ^ _86810) ^ [] : [-(_99392 = identity_relation(_99394)), relation_dom(_99392) = _99394, 421 ^ _86810 : [(422 ^ _86810) ^ [] : [-(in(420 ^ [_99392, _99394], _99394))], (424 ^ _86810) ^ [] : [apply(_99392, 420 ^ [_99392, _99394]) = 420 ^ [_99392, _99394]]]]]], (428 ^ _86810) ^ [_100445, _100447] : [element(_100447, powerset(_100445)), -(subset(_100447, _100445))], (434 ^ _86810) ^ [_100611, _100613] : [subset(_100613, _100611), -(element(_100613, powerset(_100611)))], (440 ^ _86810) ^ [_100841, _100843, _100845] : [-(element(_100845, _100841)), in(_100845, _100843), element(_100843, powerset(_100841))], (450 ^ _86810) ^ [_101154, _101156] : [relation(_101154), function(_101154), 465 ^ _86810 : [(466 ^ _86810) ^ [] : [-(_101156 = apply(function_inverse(_101154), apply(_101154, _101156)))], (468 ^ _86810) ^ [] : [-(_101156 = apply(relation_composition(_101154, function_inverse(_101154)), _101156))]], one_to_one(_101154), in(_101156, relation_dom(_101154))], (470 ^ _86810) ^ [_101738, _101740] : [relation(_101738), function(_101738), 485 ^ _86810 : [(486 ^ _86810) ^ [] : [-(_101740 = apply(_101738, apply(function_inverse(_101738), _101740)))], (488 ^ _86810) ^ [] : [-(_101740 = apply(relation_composition(function_inverse(_101738), _101738), _101740))]], one_to_one(_101738), in(_101740, relation_rng(_101738))], (490 ^ _86810) ^ [_102308] : [relation(_102308), function(_102308), one_to_one(_102308), 501 ^ _86810 : [(502 ^ _86810) ^ [] : [-(relation_dom(relation_composition(_102308, function_inverse(_102308))) = relation_dom(_102308))], (504 ^ _86810) ^ [] : [-(relation_rng(relation_composition(_102308, function_inverse(_102308))) = relation_dom(_102308))]]], (506 ^ _86810) ^ [_102773] : [relation(_102773), function(_102773), one_to_one(_102773), 517 ^ _86810 : [(518 ^ _86810) ^ [] : [-(relation_dom(relation_composition(function_inverse(_102773), _102773)) = relation_rng(_102773))], (520 ^ _86810) ^ [] : [-(relation_rng(relation_composition(function_inverse(_102773), _102773)) = relation_rng(_102773))]]], (522 ^ _86810) ^ [_103266, _103268, _103270] : [in(_103270, _103268), element(_103268, powerset(_103266)), empty(_103266)], (532 ^ _86810) ^ [_103562] : [empty(_103562), -(_103562 = empty_set)], (538 ^ _86810) ^ [_103764, _103766] : [in(_103766, _103764), empty(_103764)], (544 ^ _86810) ^ [_103951, _103953] : [empty(_103953), -(_103953 = _103951), empty(_103951)]], input).
% 0.45/1.37  ncf('1',plain,[relation_composition(553 ^ [], function_inverse(553 ^ [])) = identity_relation(relation_dom(553 ^ [])), relation_composition(function_inverse(553 ^ []), 553 ^ []) = identity_relation(relation_rng(553 ^ []))],start(561 ^ 0)).
% 0.45/1.37  ncf('1.1',plain,[-(relation_composition(553 ^ [], function_inverse(553 ^ [])) = identity_relation(relation_dom(553 ^ []))), 415 : relation_dom(relation_composition(553 ^ [], function_inverse(553 ^ []))) = relation_dom(553 ^ []), 422 : -(in(420 ^ [relation_composition(553 ^ [], function_inverse(553 ^ [])), relation_dom(553 ^ [])], relation_dom(553 ^ []))), 415 : relation(relation_composition(553 ^ [], function_inverse(553 ^ []))), 415 : function(relation_composition(553 ^ [], function_inverse(553 ^ [])))],extension(395 ^ 1,bind([[_99392, _99394], [relation_composition(553 ^ [], function_inverse(553 ^ [])), relation_dom(553 ^ [])]]))).
% 0.45/1.37  ncf('1.1.1',plain,[-(relation_dom(relation_composition(553 ^ [], function_inverse(553 ^ []))) = relation_dom(553 ^ [])), relation(553 ^ []), function(553 ^ []), one_to_one(553 ^ [])],extension(490 ^ 4,bind([[_102308], [553 ^ []]]))).
% 0.45/1.37  ncf('1.1.1.1',plain,[-(relation(553 ^ []))],extension(555 ^ 5)).
% 0.45/1.37  ncf('1.1.1.2',plain,[-(function(553 ^ []))],extension(557 ^ 5)).
% 0.45/1.37  ncf('1.1.1.3',plain,[-(one_to_one(553 ^ []))],extension(559 ^ 5)).
% 0.45/1.37  ncf('1.1.2',plain,[in(420 ^ [relation_composition(553 ^ [], function_inverse(553 ^ [])), relation_dom(553 ^ [])], relation_dom(553 ^ [])), relation(553 ^ []), function(553 ^ []), 468 : -(420 ^ [relation_composition(553 ^ [], function_inverse(553 ^ [])), relation_dom(553 ^ [])] = apply(relation_composition(553 ^ [], function_inverse(553 ^ [])), 420 ^ [relation_composition(553 ^ [], function_inverse(553 ^ [])), relation_dom(553 ^ [])])), 468 : one_to_one(553 ^ [])],extension(450 ^ 6,bind([[_101154, _101156], [553 ^ [], 420 ^ [relation_composition(553 ^ [], function_inverse(553 ^ [])), relation_dom(553 ^ [])]]]))).
% 0.45/1.37  ncf('1.1.2.1',plain,[-(relation(553 ^ []))],extension(555 ^ 7)).
% 0.45/1.37  ncf('1.1.2.2',plain,[-(function(553 ^ []))],extension(557 ^ 7)).
% 0.45/1.37  ncf('1.1.2.3',plain,[420 ^ [relation_composition(553 ^ [], function_inverse(553 ^ [])), relation_dom(553 ^ [])] = apply(relation_composition(553 ^ [], function_inverse(553 ^ [])), 420 ^ [relation_composition(553 ^ [], function_inverse(553 ^ [])), relation_dom(553 ^ [])]), -(apply(relation_composition(553 ^ [], function_inverse(553 ^ [])), 420 ^ [relation_composition(553 ^ [], function_inverse(553 ^ [])), relation_dom(553 ^ [])]) = 420 ^ [relation_composition(553 ^ [], function_inverse(553 ^ [])), relation_dom(553 ^ [])])],extension(4 ^ 9,bind([[_87061, _87063], [apply(relation_composition(553 ^ [], function_inverse(553 ^ [])), 420 ^ [relation_composition(553 ^ [], function_inverse(553 ^ [])), relation_dom(553 ^ [])]), 420 ^ [relation_composition(553 ^ [], function_inverse(553 ^ [])), relation_dom(553 ^ [])]]]))).
% 0.45/1.37  ncf('1.1.2.3.1',plain,[apply(relation_composition(553 ^ [], function_inverse(553 ^ [])), 420 ^ [relation_composition(553 ^ [], function_inverse(553 ^ [])), relation_dom(553 ^ [])]) = 420 ^ [relation_composition(553 ^ [], function_inverse(553 ^ [])), relation_dom(553 ^ [])]],extension(424 ^ 10)).
% 0.45/1.37  ncf('1.1.2.4',plain,[-(one_to_one(553 ^ []))],extension(559 ^ 7)).
% 0.45/1.37  ncf('1.1.3',plain,[-(relation(relation_composition(553 ^ [], function_inverse(553 ^ [])))), relation(553 ^ []), relation(function_inverse(553 ^ []))],extension(210 ^ 2,bind([[_93623, _93625], [function_inverse(553 ^ []), 553 ^ []]]))).
% 0.45/1.37  ncf('1.1.3.1',plain,[-(relation(553 ^ []))],extension(555 ^ 3)).
% 0.45/1.37  ncf('1.1.3.2',plain,[-(relation(function_inverse(553 ^ []))), relation(553 ^ []), function(553 ^ [])],extension(198 ^ 3,bind([[_93261], [553 ^ []]]))).
% 0.45/1.37  ncf('1.1.3.2.1',plain,[-(relation(553 ^ []))],lemmata('[1, 1].x')).
% 0.45/1.37  ncf('1.1.3.2.2',plain,[-(function(553 ^ []))],extension(557 ^ 4)).
% 0.45/1.37  ncf('1.1.4',plain,[-(function(relation_composition(553 ^ [], function_inverse(553 ^ [])))), relation(553 ^ []), function(553 ^ []), relation(function_inverse(553 ^ [])), function(function_inverse(553 ^ []))],extension(243 ^ 2,bind([[_94664, _94666], [function_inverse(553 ^ []), 553 ^ []]]))).
% 0.45/1.37  ncf('1.1.4.1',plain,[-(relation(553 ^ []))],extension(555 ^ 3)).
% 0.45/1.37  ncf('1.1.4.2',plain,[-(function(553 ^ []))],extension(557 ^ 3)).
% 0.45/1.37  ncf('1.1.4.3',plain,[-(relation(function_inverse(553 ^ []))), relation(553 ^ []), function(553 ^ [])],extension(198 ^ 3,bind([[_93261], [553 ^ []]]))).
% 0.45/1.37  ncf('1.1.4.3.1',plain,[-(relation(553 ^ []))],lemmata('[1, 1].x')).
% 0.45/1.37  ncf('1.1.4.3.2',plain,[-(function(553 ^ []))],lemmata('[1, 1].x')).
% 0.45/1.37  ncf('1.1.4.4',plain,[-(function(function_inverse(553 ^ []))), relation(553 ^ []), function(553 ^ [])],extension(198 ^ 3,bind([[_93261], [553 ^ []]]))).
% 0.45/1.37  ncf('1.1.4.4.1',plain,[-(relation(553 ^ []))],lemmata('[1, 1].x')).
% 0.45/1.37  ncf('1.1.4.4.2',plain,[-(function(553 ^ []))],lemmata('[1, 1].x')).
% 0.45/1.37  ncf('1.2',plain,[-(relation_composition(function_inverse(553 ^ []), 553 ^ []) = identity_relation(relation_rng(553 ^ []))), 415 : relation_dom(relation_composition(function_inverse(553 ^ []), 553 ^ [])) = relation_rng(553 ^ []), 422 : -(in(420 ^ [relation_composition(function_inverse(553 ^ []), 553 ^ []), relation_rng(553 ^ [])], relation_rng(553 ^ []))), 415 : relation(relation_composition(function_inverse(553 ^ []), 553 ^ [])), 415 : function(relation_composition(function_inverse(553 ^ []), 553 ^ []))],extension(395 ^ 1,bind([[_99392, _99394], [relation_composition(function_inverse(553 ^ []), 553 ^ []), relation_rng(553 ^ [])]]))).
% 0.45/1.37  ncf('1.2.1',plain,[-(relation_dom(relation_composition(function_inverse(553 ^ []), 553 ^ [])) = relation_rng(553 ^ [])), relation(553 ^ []), function(553 ^ []), one_to_one(553 ^ [])],extension(506 ^ 4,bind([[_102773], [553 ^ []]]))).
% 0.45/1.37  ncf('1.2.1.1',plain,[-(relation(553 ^ []))],extension(555 ^ 5)).
% 0.45/1.37  ncf('1.2.1.2',plain,[-(function(553 ^ []))],extension(557 ^ 5)).
% 0.45/1.37  ncf('1.2.1.3',plain,[-(one_to_one(553 ^ []))],extension(559 ^ 5)).
% 0.45/1.37  ncf('1.2.2',plain,[in(420 ^ [relation_composition(function_inverse(553 ^ []), 553 ^ []), relation_rng(553 ^ [])], relation_rng(553 ^ [])), relation(553 ^ []), function(553 ^ []), 488 : -(420 ^ [relation_composition(function_inverse(553 ^ []), 553 ^ []), relation_rng(553 ^ [])] = apply(relation_composition(function_inverse(553 ^ []), 553 ^ []), 420 ^ [relation_composition(function_inverse(553 ^ []), 553 ^ []), relation_rng(553 ^ [])])), 488 : one_to_one(553 ^ [])],extension(470 ^ 6,bind([[_101738, _101740], [553 ^ [], 420 ^ [relation_composition(function_inverse(553 ^ []), 553 ^ []), relation_rng(553 ^ [])]]]))).
% 0.45/1.37  ncf('1.2.2.1',plain,[-(relation(553 ^ []))],extension(555 ^ 7)).
% 0.45/1.37  ncf('1.2.2.2',plain,[-(function(553 ^ []))],extension(557 ^ 7)).
% 0.45/1.37  ncf('1.2.2.3',plain,[420 ^ [relation_composition(function_inverse(553 ^ []), 553 ^ []), relation_rng(553 ^ [])] = apply(relation_composition(function_inverse(553 ^ []), 553 ^ []), 420 ^ [relation_composition(function_inverse(553 ^ []), 553 ^ []), relation_rng(553 ^ [])]), -(apply(relation_composition(function_inverse(553 ^ []), 553 ^ []), 420 ^ [relation_composition(function_inverse(553 ^ []), 553 ^ []), relation_rng(553 ^ [])]) = 420 ^ [relation_composition(function_inverse(553 ^ []), 553 ^ []), relation_rng(553 ^ [])])],extension(4 ^ 9,bind([[_87061, _87063], [apply(relation_composition(function_inverse(553 ^ []), 553 ^ []), 420 ^ [relation_composition(function_inverse(553 ^ []), 553 ^ []), relation_rng(553 ^ [])]), 420 ^ [relation_composition(function_inverse(553 ^ []), 553 ^ []), relation_rng(553 ^ [])]]]))).
% 0.45/1.37  ncf('1.2.2.3.1',plain,[apply(relation_composition(function_inverse(553 ^ []), 553 ^ []), 420 ^ [relation_composition(function_inverse(553 ^ []), 553 ^ []), relation_rng(553 ^ [])]) = 420 ^ [relation_composition(function_inverse(553 ^ []), 553 ^ []), relation_rng(553 ^ [])]],extension(424 ^ 10)).
% 0.45/1.37  ncf('1.2.2.4',plain,[-(one_to_one(553 ^ []))],extension(559 ^ 7)).
% 0.45/1.37  ncf('1.2.3',plain,[-(relation(relation_composition(function_inverse(553 ^ []), 553 ^ []))), relation(function_inverse(553 ^ [])), relation(553 ^ [])],extension(210 ^ 2,bind([[_93623, _93625], [553 ^ [], function_inverse(553 ^ [])]]))).
% 0.45/1.37  ncf('1.2.3.1',plain,[-(relation(function_inverse(553 ^ []))), relation(553 ^ []), function(553 ^ [])],extension(198 ^ 3,bind([[_93261], [553 ^ []]]))).
% 0.45/1.37  ncf('1.2.3.1.1',plain,[-(relation(553 ^ []))],extension(555 ^ 4)).
% 0.45/1.37  ncf('1.2.3.1.2',plain,[-(function(553 ^ []))],extension(557 ^ 4)).
% 0.45/1.37  ncf('1.2.3.2',plain,[-(relation(553 ^ []))],extension(555 ^ 3)).
% 0.45/1.37  ncf('1.2.4',plain,[-(function(relation_composition(function_inverse(553 ^ []), 553 ^ []))), relation(function_inverse(553 ^ [])), function(function_inverse(553 ^ [])), relation(553 ^ []), function(553 ^ [])],extension(243 ^ 2,bind([[_94664, _94666], [553 ^ [], function_inverse(553 ^ [])]]))).
% 0.45/1.37  ncf('1.2.4.1',plain,[-(relation(function_inverse(553 ^ []))), relation(553 ^ []), function(553 ^ [])],extension(198 ^ 3,bind([[_93261], [553 ^ []]]))).
% 0.45/1.37  ncf('1.2.4.1.1',plain,[-(relation(553 ^ []))],extension(555 ^ 4)).
% 0.45/1.37  ncf('1.2.4.1.2',plain,[-(function(553 ^ []))],extension(557 ^ 4)).
% 0.45/1.37  ncf('1.2.4.2',plain,[-(function(function_inverse(553 ^ []))), relation(553 ^ []), function(553 ^ [])],extension(198 ^ 3,bind([[_93261], [553 ^ []]]))).
% 0.45/1.37  ncf('1.2.4.2.1',plain,[-(relation(553 ^ []))],extension(555 ^ 4)).
% 0.45/1.37  ncf('1.2.4.2.2',plain,[-(function(553 ^ []))],extension(557 ^ 4)).
% 0.45/1.37  ncf('1.2.4.3',plain,[-(relation(553 ^ []))],extension(555 ^ 3)).
% 0.45/1.37  ncf('1.2.4.4',plain,[-(function(553 ^ []))],extension(557 ^ 3)).
% 0.45/1.37  %-----------------------------------------------------
% 0.45/1.37  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------