%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SEU215+3 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n004.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 12:02:42 EDT 2023

% Result   : Theorem 0.32s 1.37s
% Output   : Proof 0.32s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SEU215+3 : TPTP v8.1.2. Released v3.2.0.
% 0.11/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n004.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 12:54:09 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.32/1.37  
% 0.32/1.37  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 0.32/1.37  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.32/1.37  %-----------------------------------------------------
% 0.32/1.37  ncf(matrix, plain, [(487 ^ _75775) ^ [] : [-(relation(485 ^ []))], (489 ^ _75775) ^ [] : [-(function(485 ^ []))], (492 ^ _75775) ^ [] : [-(relation(490 ^ []))], (494 ^ _75775) ^ [] : [-(function(490 ^ []))], (496 ^ _75775) ^ [] : [-(in(484 ^ [], relation_dom(485 ^ [])))], (498 ^ _75775) ^ [] : [apply(relation_composition(485 ^ [], 490 ^ []), 484 ^ []) = apply(490 ^ [], apply(485 ^ [], 484 ^ []))], (102 ^ _75775) ^ [_79081, _79083, _79085, _79087] : [-(ordered_pair(_79087, _79083) = ordered_pair(_79085, _79081)), _79087 = _79085, _79083 = _79081], (112 ^ _75775) ^ [_79412, _79414] : [_79414 = _79412, -(singleton(_79414) = singleton(_79412))], (118 ^ _75775) ^ [_79658, _79660, _79662, _79664] : [-(unordered_pair(_79664, _79660) = unordered_pair(_79662, _79658)), _79664 = _79662, _79660 = _79658], (128 ^ _75775) ^ [_79989, _79991] : [_79991 = _79989, -(powerset(_79991) = powerset(_79989))], (134 ^ _75775) ^ [_80207, _80209] : [_80209 = _80207, -(relation_dom(_80209) = relation_dom(_80207))], (140 ^ _75775) ^ [_80453, _80455, _80457, _80459] : [-(relation_composition(_80459, _80455) = relation_composition(_80457, _80453)), _80459 = _80457, _80455 = _80453], (150 ^ _75775) ^ [_80792, _80794, _80796, _80798] : [-(apply(_80798, _80794) = apply(_80796, _80792)), _80798 = _80796, _80794 = _80792], (2 ^ _75775) ^ [_75919] : [-(_75919 = _75919)], (4 ^ _75775) ^ [_76026, _76028] : [_76028 = _76026, -(_76026 = _76028)], (10 ^ _75775) ^ [_76230, _76232, _76234] : [-(_76234 = _76230), _76234 = _76232, _76232 = _76230], (20 ^ _75775) ^ [_76543, _76545] : [-(relation_empty_yielding(_76543)), _76545 = _76543, relation_empty_yielding(_76545)], (30 ^ _75775) ^ [_76866, _76868, _76870, _76872] : [-(subset(_76870, _76866)), subset(_76872, _76868), _76872 = _76870, _76868 = _76866], (44 ^ _75775) ^ [_77310, _77312, _77314, _77316] : [-(element(_77314, _77310)), element(_77316, _77312), _77316 = _77314, _77312 = _77310], (58 ^ _75775) ^ [_77726, _77728] : [-(empty(_77726)), _77728 = _77726, empty(_77728)], (68 ^ _75775) ^ [_78021, _78023] : [-(relation(_78021)), _78023 = _78021, relation(_78023)], (78 ^ _75775) ^ [_78316, _78318] : [-(function(_78316)), _78318 = _78316, function(_78318)], (88 ^ _75775) ^ [_78619, _78621, _78623, _78625] : [-(in(_78623, _78619)), in(_78625, _78621), _78625 = _78623, _78621 = _78619], (160 ^ _75775) ^ [_81149, _81151] : [in(_81151, _81149), in(_81149, _81151)], (166 ^ _75775) ^ [_81346] : [empty(_81346), -(function(_81346))], (172 ^ _75775) ^ [_81532] : [empty(_81532), -(relation(_81532))], (178 ^ _75775) ^ [_81717, _81719] : [-(unordered_pair(_81719, _81717) = unordered_pair(_81717, _81719))], (180 ^ _75775) ^ [_81818] : [relation(_81818), function(_81818), 187 ^ _75775 : [(188 ^ _75775) ^ [_82110, _82112] : [in(_82112, relation_dom(_81818)), 191 ^ _75775 : [(192 ^ _75775) ^ [] : [_82110 = apply(_81818, _82112), -(in(ordered_pair(_82112, _82110), _81818))], (198 ^ _75775) ^ [] : [in(ordered_pair(_82112, _82110), _81818), -(_82110 = apply(_81818, _82112))]]], (204 ^ _75775) ^ [_82562, _82564] : [-(in(_82564, relation_dom(_81818))), 207 ^ _75775 : [(208 ^ _75775) ^ [] : [_82562 = apply(_81818, _82564), -(_82562 = empty_set)], (214 ^ _75775) ^ [] : [_82562 = empty_set, -(_82562 = apply(_81818, _82564))]]]]], (220 ^ _75775) ^ [_83050, _83052] : [-(ordered_pair(_83052, _83050) = unordered_pair(unordered_pair(_83052, _83050), singleton(_83052)))], (222 ^ _75775) ^ [_83170, _83172] : [-(relation(relation_composition(_83172, _83170))), relation(_83172), relation(_83170)], (233 ^ _75775) ^ [_83479] : [-(element(231 ^ [_83479], _83479))], (235 ^ _75775) ^ [_83591, _83593] : [242 ^ _75775 : [(243 ^ _75775) ^ [] : [-(empty(relation_composition(_83591, _83593)))], (245 ^ _75775) ^ [] : [-(relation(relation_composition(_83591, _83593)))]], empty(_83593), relation(_83591)], (247 ^ _75775) ^ [] : [-(empty(empty_set))], (249 ^ _75775) ^ [] : [-(relation(empty_set))], (251 ^ _75775) ^ [] : [-(relation_empty_yielding(empty_set))], (253 ^ _75775) ^ [_84132, _84134] : [268 ^ _75775 : [(269 ^ _75775) ^ [] : [-(relation(relation_composition(_84134, _84132)))], (271 ^ _75775) ^ [] : [-(function(relation_composition(_84134, _84132)))]], relation(_84134), function(_84134), relation(_84132), function(_84132)], (273 ^ _75775) ^ [_84654] : [empty(powerset(_84654))], (275 ^ _75775) ^ [] : [-(empty(empty_set))], (277 ^ _75775) ^ [_84799, _84801] : [empty(ordered_pair(_84801, _84799))], (279 ^ _75775) ^ [_84880] : [empty(singleton(_84880))], (281 ^ _75775) ^ [_84972, _84974] : [empty(unordered_pair(_84974, _84972))], (283 ^ _75775) ^ [] : [-(empty(empty_set))], (285 ^ _75775) ^ [] : [-(relation(empty_set))], (287 ^ _75775) ^ [_85177] : [empty(relation_dom(_85177)), -(empty(_85177)), relation(_85177)], (297 ^ _75775) ^ [_85454] : [empty(_85454), 300 ^ _75775 : [(301 ^ _75775) ^ [] : [-(empty(relation_dom(_85454)))], (303 ^ _75775) ^ [] : [-(relation(relation_dom(_85454)))]]], (305 ^ _75775) ^ [_85733, _85735] : [312 ^ _75775 : [(313 ^ _75775) ^ [] : [-(empty(relation_composition(_85735, _85733)))], (315 ^ _75775) ^ [] : [-(relation(relation_composition(_85735, _85733)))]], empty(_85735), relation(_85733)], (318 ^ _75775) ^ [] : [-(relation(316 ^ []))], (320 ^ _75775) ^ [] : [-(function(316 ^ []))], (323 ^ _75775) ^ [] : [-(empty(321 ^ []))], (325 ^ _75775) ^ [] : [-(relation(321 ^ []))], (327 ^ _75775) ^ [_86395] : [-(empty(_86395)), 331 ^ _75775 : [(332 ^ _75775) ^ [] : [-(element(330 ^ [_86395], powerset(_86395)))], (334 ^ _75775) ^ [] : [empty(330 ^ [_86395])]]], (337 ^ _75775) ^ [] : [-(empty(335 ^ []))], (340 ^ _75775) ^ [] : [empty(338 ^ [])], (342 ^ _75775) ^ [] : [-(relation(338 ^ []))], (345 ^ _75775) ^ [_87017] : [-(element(343 ^ [_87017], powerset(_87017)))], (347 ^ _75775) ^ [_87068] : [-(empty(343 ^ [_87068]))], (350 ^ _75775) ^ [] : [empty(348 ^ [])], (353 ^ _75775) ^ [] : [-(relation(351 ^ []))], (355 ^ _75775) ^ [] : [-(relation_empty_yielding(351 ^ []))], (357 ^ _75775) ^ [_87405, _87407] : [-(subset(_87407, _87407))], (359 ^ _75775) ^ [_87514, _87516] : [in(_87516, _87514), -(element(_87516, _87514))], (365 ^ _75775) ^ [_87724, _87726] : [relation(_87724), function(_87724), 372 ^ _75775 : [(373 ^ _75775) ^ [_87974] : [relation(_87974), function(_87974), 380 ^ _75775 : [(381 ^ _75775) ^ [] : [in(_87726, relation_dom(relation_composition(_87974, _87724))), 384 ^ _75775 : [(385 ^ _75775) ^ [] : [-(in(_87726, relation_dom(_87974)))], (387 ^ _75775) ^ [] : [-(in(apply(_87974, _87726), relation_dom(_87724)))]]], (389 ^ _75775) ^ [] : [-(in(_87726, relation_dom(relation_composition(_87974, _87724)))), in(_87726, relation_dom(_87974)), in(apply(_87974, _87726), relation_dom(_87724))]]]]], (399 ^ _75775) ^ [_88752, _88754] : [relation(_88752), function(_88752), 406 ^ _75775 : [(407 ^ _75775) ^ [_89001] : [relation(_89001), function(_89001), in(_88754, relation_dom(relation_composition(_89001, _88752))), -(apply(relation_composition(_89001, _88752), _88754) = apply(_88752, apply(_89001, _88754)))]]], (421 ^ _75775) ^ [_89446, _89448] : [element(_89448, _89446), -(empty(_89446)), -(in(_89448, _89446))], (431 ^ _75775) ^ [_89773, _89775] : [element(_89775, powerset(_89773)), -(subset(_89775, _89773))], (437 ^ _75775) ^ [_89939, _89941] : [subset(_89941, _89939), -(element(_89941, powerset(_89939)))], (443 ^ _75775) ^ [_90169, _90171, _90173] : [-(element(_90173, _90169)), in(_90173, _90171), element(_90171, powerset(_90169))], (453 ^ _75775) ^ [_90496, _90498, _90500] : [in(_90500, _90498), element(_90498, powerset(_90496)), empty(_90496)], (463 ^ _75775) ^ [_90792] : [empty(_90792), -(_90792 = empty_set)], (469 ^ _75775) ^ [_90994, _90996] : [in(_90996, _90994), empty(_90994)], (475 ^ _75775) ^ [_91181, _91183] : [empty(_91183), -(_91183 = _91181), empty(_91181)]], input).
% 0.32/1.37  ncf('1',plain,[apply(relation_composition(485 ^ [], 490 ^ []), 484 ^ []) = apply(490 ^ [], apply(485 ^ [], 484 ^ []))],start(498 ^ 0)).
% 0.32/1.37  ncf('1.1',plain,[-(apply(relation_composition(485 ^ [], 490 ^ []), 484 ^ []) = apply(490 ^ [], apply(485 ^ [], 484 ^ []))), 214 : apply(relation_composition(485 ^ [], 490 ^ []), 484 ^ []) = empty_set, 214 : -(in(apply(485 ^ [], 484 ^ []), relation_dom(490 ^ []))), 204 : relation(490 ^ []), 204 : function(490 ^ [])],extension(180 ^ 1,bind([[_81818, _82562, _82564], [490 ^ [], apply(relation_composition(485 ^ [], 490 ^ []), 484 ^ []), apply(485 ^ [], 484 ^ [])]]))).
% 0.32/1.37  ncf('1.1.1',plain,[-(apply(relation_composition(485 ^ [], 490 ^ []), 484 ^ []) = empty_set), 208 : apply(relation_composition(485 ^ [], 490 ^ []), 484 ^ []) = apply(relation_composition(485 ^ [], 490 ^ []), 484 ^ []), 208 : -(in(484 ^ [], relation_dom(relation_composition(485 ^ [], 490 ^ [])))), 204 : relation(relation_composition(485 ^ [], 490 ^ [])), 204 : function(relation_composition(485 ^ [], 490 ^ []))],extension(180 ^ 6,bind([[_81818, _82562, _82564], [relation_composition(485 ^ [], 490 ^ []), apply(relation_composition(485 ^ [], 490 ^ []), 484 ^ []), 484 ^ []]]))).
% 0.32/1.37  ncf('1.1.1.1',plain,[-(apply(relation_composition(485 ^ [], 490 ^ []), 484 ^ []) = apply(relation_composition(485 ^ [], 490 ^ []), 484 ^ []))],extension(2 ^ 11,bind([[_75919], [apply(relation_composition(485 ^ [], 490 ^ []), 484 ^ [])]]))).
% 0.32/1.37  ncf('1.1.1.2',plain,[in(484 ^ [], relation_dom(relation_composition(485 ^ [], 490 ^ []))), 407 : relation(485 ^ []), 407 : function(485 ^ []), 407 : -(apply(relation_composition(485 ^ [], 490 ^ []), 484 ^ []) = apply(490 ^ [], apply(485 ^ [], 484 ^ []))), 407 : relation(490 ^ []), 407 : function(490 ^ [])],extension(399 ^ 9,bind([[_88752, _88754, _89001], [490 ^ [], 484 ^ [], 485 ^ []]]))).
% 0.32/1.37  ncf('1.1.1.2.1',plain,[-(relation(485 ^ []))],extension(487 ^ 12)).
% 0.32/1.37  ncf('1.1.1.2.2',plain,[-(function(485 ^ []))],extension(489 ^ 12)).
% 0.32/1.37  ncf('1.1.1.2.3',plain,[apply(relation_composition(485 ^ [], 490 ^ []), 484 ^ []) = apply(490 ^ [], apply(485 ^ [], 484 ^ []))],reduction('1')).
% 0.32/1.37  ncf('1.1.1.2.4',plain,[-(relation(490 ^ []))],extension(492 ^ 10)).
% 0.32/1.37  ncf('1.1.1.2.5',plain,[-(function(490 ^ []))],extension(494 ^ 10)).
% 0.32/1.37  ncf('1.1.1.3',plain,[-(relation(relation_composition(485 ^ [], 490 ^ []))), relation(485 ^ []), relation(490 ^ [])],extension(222 ^ 7,bind([[_83170, _83172], [490 ^ [], 485 ^ []]]))).
% 0.32/1.37  ncf('1.1.1.3.1',plain,[-(relation(485 ^ []))],extension(487 ^ 8)).
% 0.32/1.37  ncf('1.1.1.3.2',plain,[-(relation(490 ^ []))],extension(492 ^ 8)).
% 0.32/1.37  ncf('1.1.1.4',plain,[-(function(relation_composition(485 ^ [], 490 ^ []))), relation(485 ^ []), function(485 ^ []), relation(490 ^ []), function(490 ^ [])],extension(253 ^ 7,bind([[_84132, _84134], [490 ^ [], 485 ^ []]]))).
% 0.32/1.37  ncf('1.1.1.4.1',plain,[-(relation(485 ^ []))],extension(487 ^ 8)).
% 0.32/1.37  ncf('1.1.1.4.2',plain,[-(function(485 ^ []))],extension(489 ^ 8)).
% 0.32/1.37  ncf('1.1.1.4.3',plain,[-(relation(490 ^ []))],extension(492 ^ 8)).
% 0.32/1.37  ncf('1.1.1.4.4',plain,[-(function(490 ^ []))],extension(494 ^ 8)).
% 0.32/1.37  ncf('1.1.2',plain,[in(apply(485 ^ [], 484 ^ []), relation_dom(490 ^ [])), 389 : -(in(484 ^ [], relation_dom(relation_composition(485 ^ [], 490 ^ [])))), 389 : in(484 ^ [], relation_dom(485 ^ [])), 389 : relation(485 ^ []), 389 : function(485 ^ []), 373 : relation(490 ^ []), 373 : function(490 ^ [])],extension(365 ^ 4,bind([[_87724, _87726, _87974], [490 ^ [], 484 ^ [], 485 ^ []]]))).
% 0.32/1.37  ncf('1.1.2.1',plain,[in(484 ^ [], relation_dom(relation_composition(485 ^ [], 490 ^ []))), 407 : relation(485 ^ []), 407 : function(485 ^ []), 407 : -(apply(relation_composition(485 ^ [], 490 ^ []), 484 ^ []) = apply(490 ^ [], apply(485 ^ [], 484 ^ []))), 407 : relation(490 ^ []), 407 : function(490 ^ [])],extension(399 ^ 9,bind([[_88752, _88754, _89001], [490 ^ [], 484 ^ [], 485 ^ []]]))).
% 0.32/1.37  ncf('1.1.2.1.1',plain,[-(relation(485 ^ []))],extension(487 ^ 12)).
% 0.32/1.37  ncf('1.1.2.1.2',plain,[-(function(485 ^ []))],extension(489 ^ 12)).
% 0.32/1.37  ncf('1.1.2.1.3',plain,[apply(relation_composition(485 ^ [], 490 ^ []), 484 ^ []) = apply(490 ^ [], apply(485 ^ [], 484 ^ []))],reduction('1')).
% 0.32/1.37  ncf('1.1.2.1.4',plain,[-(relation(490 ^ []))],extension(492 ^ 10)).
% 0.32/1.37  ncf('1.1.2.1.5',plain,[-(function(490 ^ []))],extension(494 ^ 10)).
% 0.32/1.37  ncf('1.1.2.2',plain,[-(in(484 ^ [], relation_dom(485 ^ [])))],extension(496 ^ 9)).
% 0.32/1.37  ncf('1.1.2.3',plain,[-(relation(485 ^ []))],extension(487 ^ 7)).
% 0.32/1.37  ncf('1.1.2.4',plain,[-(function(485 ^ []))],extension(489 ^ 7)).
% 0.32/1.37  ncf('1.1.2.5',plain,[-(relation(490 ^ []))],extension(492 ^ 5)).
% 0.32/1.37  ncf('1.1.2.6',plain,[-(function(490 ^ []))],extension(494 ^ 5)).
% 0.32/1.37  ncf('1.1.3',plain,[-(relation(490 ^ []))],extension(492 ^ 2)).
% 0.32/1.37  ncf('1.1.4',plain,[-(function(490 ^ []))],extension(494 ^ 2)).
% 0.32/1.37  %-----------------------------------------------------
% 0.32/1.37  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------