%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SEU227+3 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n002.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 12:02:46 EDT 2023

% Result   : Theorem 45.43s 44.88s
% Output   : Proof 45.43s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : SEU227+3 : TPTP v8.1.2. Released v3.2.0.
% 0.12/0.13  % Command  : nanocop.sh %s %d
% 0.13/0.34  % Computer : n002.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 13:37:49 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 45.43/44.88  
% 45.43/44.88  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 45.43/44.88  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 45.43/44.88  %-----------------------------------------------------
% 45.43/44.88  ncf(matrix, plain, [(537 ^ _101635) ^ [] : [subset(530 ^ [], relation_inverse_image(531 ^ [], relation_image(531 ^ [], 530 ^ [])))], (535 ^ _101635) ^ [] : [-(subset(530 ^ [], relation_dom(531 ^ [])))], (533 ^ _101635) ^ [] : [-(relation(531 ^ []))], !, (452 ^ _82907) ^ [] : [-(one_to_one(446 ^ []))], (4 ^ _82907) ^ [_83138, _83140] : [_83140 = _83138, -(_83138 = _83140)], (160 ^ _82907) ^ [_88201, _88203, _88205, _88207] : [-(relation_image(_88207, _88203) = relation_image(_88205, _88201)), _88207 = _88205, _88203 = _88201], (379 ^ _82907) ^ [_96499] : [empty(singleton(_96499))], (128 ^ _82907) ^ [_87067, _87069, _87071, _87073] : [-(unordered_pair(_87073, _87069) = unordered_pair(_87071, _87067)), _87073 = _87071, _87069 = _87067], (413 ^ _82907) ^ [] : [-(relation(409 ^ []))], (425 ^ _82907) ^ [] : [-(empty(423 ^ []))], (112 ^ _82907) ^ [_86490, _86492, _86494, _86496] : [-(ordered_pair(_86496, _86492) = ordered_pair(_86494, _86490)), _86496 = _86494, _86492 = _86490], (150 ^ _82907) ^ [_87862, _87864, _87866, _87868] : [-(relation_inverse_image(_87868, _87864) = relation_inverse_image(_87866, _87862)), _87868 = _87866, _87864 = _87862], (2 ^ _82907) ^ [_83031] : [-(_83031 = _83031)], (448 ^ _82907) ^ [] : [-(relation(446 ^ []))], (489 ^ _82907) ^ [_100106, _100108, _100110] : [-(element(_100110, _100106)), in(_100110, _100108), element(_100108, powerset(_100106))], (440 ^ _82907) ^ [_98467] : [-(element(438 ^ [_98467], powerset(_98467)))], (88 ^ _82907) ^ [_85723, _85725] : [-(relation(_85723)), _85725 = _85723, relation(_85725)], (467 ^ _82907) ^ [_99383, _99385] : [element(_99385, _99383), -(empty(_99383)), -(in(_99385, _99383))], (457 ^ _82907) ^ [] : [-(relation_empty_yielding(453 ^ []))], (408 ^ _82907) ^ [] : [-(function(404 ^ []))], (428 ^ _82907) ^ [] : [-(relation(426 ^ []))], (415 ^ _82907) ^ [_97636] : [-(empty(_97636)), 419 ^ _82907 : [(422 ^ _82907) ^ [] : [empty(418 ^ [_97636])], (420 ^ _82907) ^ [] : [-(element(418 ^ [_97636], powerset(_97636)))]]], (176 ^ _82907) ^ [_88755] : [empty(_88755), -(function(_88755))], (385 ^ _82907) ^ [] : [-(relation(empty_set))], (10 ^ _82907) ^ [_83342, _83344, _83346] : [-(_83346 = _83342), _83346 = _83344, _83344 = _83342], (483 ^ _82907) ^ [_99876, _99878] : [subset(_99878, _99876), -(element(_99878, powerset(_99876)))], (98 ^ _82907) ^ [_86026, _86028, _86030, _86032] : [-(subset(_86030, _86026)), subset(_86032, _86028), _86032 = _86030, _86028 = _86026], (64 ^ _82907) ^ [_85012, _85014, _85016, _85018] : [-(in(_85016, _85012)), in(_85018, _85014), _85018 = _85016, _85014 = _85012], (377 ^ _82907) ^ [_96418, _96420] : [empty(ordered_pair(_96420, _96418))], (316 ^ _82907) ^ [_94115, _94117] : [318 ^ _82907 : [(321 ^ _82907) ^ [] : [in(317 ^ [_94115, _94117], _94115)], (319 ^ _82907) ^ [] : [-(in(317 ^ [_94115, _94117], _94117))]], -(subset(_94117, _94115))], (362 ^ _82907) ^ [_95898, _95900] : [-(ordered_pair(_95900, _95898) = unordered_pair(unordered_pair(_95900, _95898), singleton(_95900)))], (369 ^ _82907) ^ [] : [-(relation(empty_set))], (206 ^ _82907) ^ [_89619, _89621] : [-(unordered_pair(_89621, _89619) = unordered_pair(_89619, _89621))], (257 ^ _82907) ^ [_91739] : [relation(_91739), 260 ^ _82907 : [(261 ^ _82907) ^ [_91946, _91948] : [_91946 = relation_inverse_image(_91739, _91948), 264 ^ _82907 : [(274 ^ _82907) ^ [_92492] : [-(in(_92492, _91946)), 275 ^ _82907 : [(276 ^ _82907) ^ [_92597] : [in(ordered_pair(_92492, _92597), _91739), in(_92597, _91948)]]], (265 ^ _82907) ^ [_92138] : [in(_92138, _91946), 269 ^ _82907 : [(272 ^ _82907) ^ [] : [-(in(268 ^ [_91739, _91946, _91948, _92138], _91948))], (270 ^ _82907) ^ [] : [-(in(ordered_pair(_92138, 268 ^ [_91739, _91946, _91948, _92138]), _91739))]]]]], (284 ^ _82907) ^ [_92852, _92854] : [-(_92852 = relation_inverse_image(_91739, _92854)), 297 ^ _82907 : [(302 ^ _82907) ^ [] : [in(285 ^ [_91739, _92852, _92854], _92852)], (300 ^ _82907) ^ [] : [-(in(296 ^ [_91739, _92852, _92854], _92854))], (298 ^ _82907) ^ [] : [-(in(ordered_pair(285 ^ [_91739, _92852, _92854], 296 ^ [_91739, _92852, _92854]), _91739))]], 288 ^ _82907 : [(291 ^ _82907) ^ [_93156] : [in(ordered_pair(285 ^ [_91739, _92852, _92854], _93156), _91739), in(_93156, _92854)], (289 ^ _82907) ^ [] : [-(in(285 ^ [_91739, _92852, _92854], _92852))]]]]], (40 ^ _82907) ^ [_84245, _84247] : [-(relation_empty_yielding(_84245)), _84247 = _84245, relation_empty_yielding(_84247)], (461 ^ _82907) ^ [_99173, _99175] : [in(_99175, _99173), -(element(_99175, _99173))], (306 ^ _82907) ^ [_93801, _93803] : [subset(_93803, _93801), 309 ^ _82907 : [(310 ^ _82907) ^ [_93938] : [in(_93938, _93803), -(in(_93938, _93801))]]], (182 ^ _82907) ^ [_88941] : [empty(_88941), -(relation(_88941))], (122 ^ _82907) ^ [_86821, _86823] : [_86823 = _86821, -(singleton(_86823) = singleton(_86821))], (381 ^ _82907) ^ [_96591, _96593] : [empty(unordered_pair(_96593, _96591))], (430 ^ _82907) ^ [] : [-(empty(426 ^ []))], (20 ^ _82907) ^ [_83655, _83657] : [-(function(_83655)), _83657 = _83655, function(_83657)], (437 ^ _82907) ^ [] : [-(relation(433 ^ []))], (450 ^ _82907) ^ [] : [-(function(446 ^ []))], (138 ^ _82907) ^ [_87398, _87400] : [_87400 = _87398, -(powerset(_87400) = powerset(_87398))], (208 ^ _82907) ^ [_89720] : [relation(_89720), 211 ^ _82907 : [(212 ^ _82907) ^ [_89927, _89929] : [_89927 = relation_image(_89720, _89929), 215 ^ _82907 : [(225 ^ _82907) ^ [_90473] : [-(in(_90473, _89927)), 226 ^ _82907 : [(227 ^ _82907) ^ [_90578] : [in(ordered_pair(_90578, _90473), _89720), in(_90578, _89929)]]], (216 ^ _82907) ^ [_90119] : [in(_90119, _89927), 220 ^ _82907 : [(223 ^ _82907) ^ [] : [-(in(219 ^ [_89720, _89927, _89929, _90119], _89929))], (221 ^ _82907) ^ [] : [-(in(ordered_pair(219 ^ [_89720, _89927, _89929, _90119], _90119), _89720))]]]]], (235 ^ _82907) ^ [_90833, _90835] : [-(_90833 = relation_image(_89720, _90835)), 248 ^ _82907 : [(253 ^ _82907) ^ [] : [in(236 ^ [_89720, _90833, _90835], _90833)], (251 ^ _82907) ^ [] : [-(in(247 ^ [_89720, _90833, _90835], _90835))], (249 ^ _82907) ^ [] : [-(in(ordered_pair(247 ^ [_89720, _90833, _90835], 236 ^ [_89720, _90833, _90835]), _89720))]], 239 ^ _82907 : [(242 ^ _82907) ^ [_91137] : [in(ordered_pair(_91137, 236 ^ [_89720, _90833, _90835]), _89720), in(_91137, _90835)], (240 ^ _82907) ^ [] : [-(in(236 ^ [_89720, _90833, _90835], _90833))]]]]], (50 ^ _82907) ^ [_84568, _84570, _84572, _84574] : [-(element(_84572, _84568)), element(_84574, _84570), _84574 = _84572, _84570 = _84568], (367 ^ _82907) ^ [] : [-(empty(empty_set))], (445 ^ _82907) ^ [] : [empty(443 ^ [])], (509 ^ _82907) ^ [_100729] : [empty(_100729), -(_100729 = empty_set)], (397 ^ _82907) ^ [_97073] : [empty(_97073), 400 ^ _82907 : [(403 ^ _82907) ^ [] : [-(relation(relation_dom(_97073)))], (401 ^ _82907) ^ [] : [-(empty(relation_dom(_97073)))]]], (383 ^ _82907) ^ [] : [-(empty(empty_set))], (435 ^ _82907) ^ [] : [empty(433 ^ [])], (459 ^ _82907) ^ [_99064, _99066] : [-(subset(_99066, _99066))], (371 ^ _82907) ^ [] : [-(relation_empty_yielding(empty_set))], (144 ^ _82907) ^ [_87616, _87618] : [_87618 = _87616, -(relation_dom(_87618) = relation_dom(_87616))], (170 ^ _82907) ^ [_88558, _88560] : [in(_88560, _88558), in(_88558, _88560)], (432 ^ _82907) ^ [] : [-(function(426 ^ []))], (365 ^ _82907) ^ [_96028] : [-(element(363 ^ [_96028], _96028))], (499 ^ _82907) ^ [_100433, _100435, _100437] : [in(_100437, _100435), element(_100435, powerset(_100433)), empty(_100433)], (373 ^ _82907) ^ [_96273] : [empty(powerset(_96273))], (477 ^ _82907) ^ [_99710, _99712] : [element(_99712, powerset(_99710)), -(subset(_99712, _99710))], (515 ^ _82907) ^ [_100931, _100933] : [in(_100933, _100931), empty(_100931)], (375 ^ _82907) ^ [] : [-(empty(empty_set))], (455 ^ _82907) ^ [] : [-(relation(453 ^ []))], (30 ^ _82907) ^ [_83950, _83952] : [-(one_to_one(_83950)), _83952 = _83950, one_to_one(_83952)], (411 ^ _82907) ^ [] : [-(empty(409 ^ []))], (387 ^ _82907) ^ [_96796] : [empty(relation_dom(_96796)), -(empty(_96796)), relation(_96796)], (325 ^ _82907) ^ [_94458] : [relation(_94458), 328 ^ _82907 : [(329 ^ _82907) ^ [_94639] : [_94639 = relation_dom(_94458), 332 ^ _82907 : [(340 ^ _82907) ^ [_95063] : [341 ^ _82907 : [(342 ^ _82907) ^ [_95142] : [in(ordered_pair(_95063, _95142), _94458)]], -(in(_95063, _94639))], (333 ^ _82907) ^ [_94819] : [in(_94819, _94639), -(in(ordered_pair(_94819, 336 ^ [_94458, _94639, _94819]), _94458))]]], (346 ^ _82907) ^ [_95270] : [-(_95270 = relation_dom(_94458)), 350 ^ _82907 : [(353 ^ _82907) ^ [_95533] : [in(ordered_pair(347 ^ [_94458, _95270], _95533), _94458)], (351 ^ _82907) ^ [] : [-(in(347 ^ [_94458, _95270], _95270))]], 355 ^ _82907 : [(358 ^ _82907) ^ [] : [in(347 ^ [_94458, _95270], _95270)], (356 ^ _82907) ^ [] : [-(in(ordered_pair(347 ^ [_94458, _95270], 354 ^ [_94458, _95270]), _94458))]]]]], (188 ^ _82907) ^ [_89127] : [199 ^ _82907 : [(204 ^ _82907) ^ [] : [-(one_to_one(_89127))], (202 ^ _82907) ^ [] : [-(function(_89127))], (200 ^ _82907) ^ [] : [-(relation(_89127))]], relation(_89127), empty(_89127), function(_89127)], (442 ^ _82907) ^ [_98518] : [-(empty(438 ^ [_98518]))], (78 ^ _82907) ^ [_85428, _85430] : [-(empty(_85428)), _85430 = _85428, empty(_85430)], (406 ^ _82907) ^ [] : [-(relation(404 ^ []))], (521 ^ _82907) ^ [_101118, _101120] : [empty(_101120), -(_101120 = _101118), empty(_101118)]], input).
% 45.43/44.88  ncf('1',plain,[-(relation(531 ^ []))],start(533 ^ 0)).
% 45.43/44.88  ncf('1.1',plain,[relation(531 ^ []), 329 : relation_dom(531 ^ []) = relation_dom(531 ^ []), 333 : in(317 ^ [relation_inverse_image(531 ^ [], relation_image(531 ^ [], 530 ^ [])), 530 ^ []], relation_dom(531 ^ [])), 333 : -(in(ordered_pair(317 ^ [relation_inverse_image(531 ^ [], relation_image(531 ^ [], 530 ^ [])), 530 ^ []], 336 ^ [531 ^ [], relation_dom(531 ^ []), 317 ^ [relation_inverse_image(531 ^ [], relation_image(531 ^ [], 530 ^ [])), 530 ^ []]]), 531 ^ []))],extension(325 ^ 1,bind([[_94458, _94639, _94819], [531 ^ [], relation_dom(531 ^ []), 317 ^ [relation_inverse_image(531 ^ [], relation_image(531 ^ [], 530 ^ [])), 530 ^ []]]]))).
% 45.43/44.88  ncf('1.1.1',plain,[-(relation_dom(531 ^ []) = relation_dom(531 ^ [])), relation_dom(531 ^ []) = relation_dom(531 ^ [])],extension(4 ^ 4,bind([[_83138, _83140], [relation_dom(531 ^ []), relation_dom(531 ^ [])]]))).
% 45.43/44.88  ncf('1.1.1.1',plain,[-(relation_dom(531 ^ []) = relation_dom(531 ^ []))],extension(2 ^ 5,bind([[_83031], [relation_dom(531 ^ [])]]))).
% 45.43/44.88  ncf('1.1.2',plain,[-(in(317 ^ [relation_inverse_image(531 ^ [], relation_image(531 ^ [], 530 ^ [])), 530 ^ []], relation_dom(531 ^ []))), element(317 ^ [relation_inverse_image(531 ^ [], relation_image(531 ^ [], 530 ^ [])), 530 ^ []], relation_dom(531 ^ [])), -(empty(relation_dom(531 ^ [])))],extension(467 ^ 6,bind([[_99383, _99385], [relation_dom(531 ^ []), 317 ^ [relation_inverse_image(531 ^ [], relation_image(531 ^ [], 530 ^ [])), 530 ^ []]]]))).
% 45.43/44.88  ncf('1.1.2.1',plain,[-(element(317 ^ [relation_inverse_image(531 ^ [], relation_image(531 ^ [], 530 ^ [])), 530 ^ []], relation_dom(531 ^ []))), in(317 ^ [relation_inverse_image(531 ^ [], relation_image(531 ^ [], 530 ^ [])), 530 ^ []], 530 ^ []), element(530 ^ [], powerset(relation_dom(531 ^ [])))],extension(489 ^ 7,bind([[_100106, _100108, _100110], [relation_dom(531 ^ []), 530 ^ [], 317 ^ [relation_inverse_image(531 ^ [], relation_image(531 ^ [], 530 ^ [])), 530 ^ []]]]))).
% 45.43/44.88  ncf('1.1.2.1.1',plain,[-(in(317 ^ [relation_inverse_image(531 ^ [], relation_image(531 ^ [], 530 ^ [])), 530 ^ []], 530 ^ [])), -(subset(530 ^ [], relation_inverse_image(531 ^ [], relation_image(531 ^ [], 530 ^ []))))],extension(316 ^ 8,bind([[_94115, _94117], [relation_inverse_image(531 ^ [], relation_image(531 ^ [], 530 ^ [])), 530 ^ []]]))).
% 45.43/44.88  ncf('1.1.2.1.1.1',plain,[subset(530 ^ [], relation_inverse_image(531 ^ [], relation_image(531 ^ [], 530 ^ [])))],extension(537 ^ 9)).
% 45.43/44.88  ncf('1.1.2.1.2',plain,[-(element(530 ^ [], powerset(relation_dom(531 ^ [])))), subset(530 ^ [], relation_dom(531 ^ []))],extension(483 ^ 8,bind([[_99876, _99878], [relation_dom(531 ^ []), 530 ^ []]]))).
% 45.43/44.88  ncf('1.1.2.1.2.1',plain,[-(subset(530 ^ [], relation_dom(531 ^ [])))],extension(535 ^ 9)).
% 45.43/44.88  ncf('1.1.2.2',plain,[empty(relation_dom(531 ^ [])), in(317 ^ [relation_inverse_image(531 ^ [], relation_image(531 ^ [], 530 ^ [])), 530 ^ []], 530 ^ []), element(530 ^ [], powerset(relation_dom(531 ^ [])))],extension(499 ^ 7,bind([[_100433, _100435, _100437], [relation_dom(531 ^ []), 530 ^ [], 317 ^ [relation_inverse_image(531 ^ [], relation_image(531 ^ [], 530 ^ [])), 530 ^ []]]]))).
% 45.43/44.88  ncf('1.1.2.2.1',plain,[-(in(317 ^ [relation_inverse_image(531 ^ [], relation_image(531 ^ [], 530 ^ [])), 530 ^ []], 530 ^ [])), -(subset(530 ^ [], relation_inverse_image(531 ^ [], relation_image(531 ^ [], 530 ^ []))))],extension(316 ^ 8,bind([[_94115, _94117], [relation_inverse_image(531 ^ [], relation_image(531 ^ [], 530 ^ [])), 530 ^ []]]))).
% 45.43/44.88  ncf('1.1.2.2.1.1',plain,[subset(530 ^ [], relation_inverse_image(531 ^ [], relation_image(531 ^ [], 530 ^ [])))],extension(537 ^ 9)).
% 45.43/44.88  ncf('1.1.2.2.2',plain,[-(element(530 ^ [], powerset(relation_dom(531 ^ [])))), subset(530 ^ [], relation_dom(531 ^ []))],extension(483 ^ 8,bind([[_99876, _99878], [relation_dom(531 ^ []), 530 ^ []]]))).
% 45.43/44.88  ncf('1.1.2.2.2.1',plain,[-(subset(530 ^ [], relation_dom(531 ^ [])))],extension(535 ^ 9)).
% 45.43/44.88  ncf('1.1.3',plain,[in(ordered_pair(317 ^ [relation_inverse_image(531 ^ [], relation_image(531 ^ [], 530 ^ [])), 530 ^ []], 336 ^ [531 ^ [], relation_dom(531 ^ []), 317 ^ [relation_inverse_image(531 ^ [], relation_image(531 ^ [], 530 ^ [])), 530 ^ []]]), 531 ^ []), 276 : in(336 ^ [531 ^ [], relation_dom(531 ^ []), 317 ^ [relation_inverse_image(531 ^ [], relation_image(531 ^ [], 530 ^ [])), 530 ^ []]], relation_image(531 ^ [], 530 ^ [])), 276 : -(in(317 ^ [relation_inverse_image(531 ^ [], relation_image(531 ^ [], 530 ^ [])), 530 ^ []], relation_inverse_image(531 ^ [], relation_image(531 ^ [], 530 ^ [])))), 274 : relation_inverse_image(531 ^ [], relation_image(531 ^ [], 530 ^ [])) = relation_inverse_image(531 ^ [], relation_image(531 ^ [], 530 ^ [])), 261 : relation(531 ^ [])],extension(257 ^ 6,bind([[_91739, _91946, _91948, _92492, _92597], [531 ^ [], relation_inverse_image(531 ^ [], relation_image(531 ^ [], 530 ^ [])), relation_image(531 ^ [], 530 ^ []), 317 ^ [relation_inverse_image(531 ^ [], relation_image(531 ^ [], 530 ^ [])), 530 ^ []], 336 ^ [531 ^ [], relation_dom(531 ^ []), 317 ^ [relation_inverse_image(531 ^ [], relation_image(531 ^ [], 530 ^ [])), 530 ^ []]]]]))).
% 45.43/44.88  ncf('1.1.3.1',plain,[-(in(336 ^ [531 ^ [], relation_dom(531 ^ []), 317 ^ [relation_inverse_image(531 ^ [], relation_image(531 ^ [], 530 ^ [])), 530 ^ []]], relation_image(531 ^ [], 530 ^ []))), 227 : in(ordered_pair(317 ^ [relation_inverse_image(531 ^ [], relation_image(531 ^ [], 530 ^ [])), 530 ^ []], 336 ^ [531 ^ [], relation_dom(531 ^ []), 317 ^ [relation_inverse_image(531 ^ [], relation_image(531 ^ [], 530 ^ [])), 530 ^ []]]), 531 ^ []), 227 : in(317 ^ [relation_inverse_image(531 ^ [], relation_image(531 ^ [], 530 ^ [])), 530 ^ []], 530 ^ []), 225 : relation_image(531 ^ [], 530 ^ []) = relation_image(531 ^ [], 530 ^ []), 212 : relation(531 ^ [])],extension(208 ^ 13,bind([[_89720, _89927, _89929, _90473, _90578], [531 ^ [], relation_image(531 ^ [], 530 ^ []), 530 ^ [], 336 ^ [531 ^ [], relation_dom(531 ^ []), 317 ^ [relation_inverse_image(531 ^ [], relation_image(531 ^ [], 530 ^ [])), 530 ^ []]], 317 ^ [relation_inverse_image(531 ^ [], relation_image(531 ^ [], 530 ^ [])), 530 ^ []]]]))).
% 45.43/44.88  ncf('1.1.3.1.1',plain,[-(in(ordered_pair(317 ^ [relation_inverse_image(531 ^ [], relation_image(531 ^ [], 530 ^ [])), 530 ^ []], 336 ^ [531 ^ [], relation_dom(531 ^ []), 317 ^ [relation_inverse_image(531 ^ [], relation_image(531 ^ [], 530 ^ [])), 530 ^ []]]), 531 ^ []))],reduction('1.1')).
% 45.43/44.88  ncf('1.1.3.1.2',plain,[-(in(317 ^ [relation_inverse_image(531 ^ [], relation_image(531 ^ [], 530 ^ [])), 530 ^ []], 530 ^ [])), -(subset(530 ^ [], relation_inverse_image(531 ^ [], relation_image(531 ^ [], 530 ^ []))))],extension(316 ^ 20,bind([[_94115, _94117], [relation_inverse_image(531 ^ [], relation_image(531 ^ [], 530 ^ [])), 530 ^ []]]))).
% 45.43/44.88  ncf('1.1.3.1.2.1',plain,[subset(530 ^ [], relation_inverse_image(531 ^ [], relation_image(531 ^ [], 530 ^ [])))],extension(537 ^ 21)).
% 45.43/44.88  ncf('1.1.3.1.3',plain,[-(relation_image(531 ^ [], 530 ^ []) = relation_image(531 ^ [], 530 ^ []))],extension(2 ^ 16,bind([[_83031], [relation_image(531 ^ [], 530 ^ [])]]))).
% 45.43/44.88  ncf('1.1.3.1.4',plain,[-(relation(531 ^ []))],reduction('1')).
% 45.43/44.88  ncf('1.1.3.2',plain,[in(317 ^ [relation_inverse_image(531 ^ [], relation_image(531 ^ [], 530 ^ [])), 530 ^ []], relation_inverse_image(531 ^ [], relation_image(531 ^ [], 530 ^ []))), -(in(317 ^ [relation_inverse_image(531 ^ [], relation_image(531 ^ [], 530 ^ [])), 530 ^ []], relation_inverse_image(531 ^ [], relation_image(531 ^ [], 530 ^ [])))), 317 ^ [relation_inverse_image(531 ^ [], relation_image(531 ^ [], 530 ^ [])), 530 ^ []] = 317 ^ [relation_inverse_image(531 ^ [], relation_image(531 ^ [], 530 ^ [])), 530 ^ []], relation_inverse_image(531 ^ [], relation_image(531 ^ [], 530 ^ [])) = relation_inverse_image(531 ^ [], relation_image(531 ^ [], 530 ^ []))],extension(64 ^ 11,bind([[_85012, _85014, _85016, _85018], [relation_inverse_image(531 ^ [], relation_image(531 ^ [], 530 ^ [])), relation_inverse_image(531 ^ [], relation_image(531 ^ [], 530 ^ [])), 317 ^ [relation_inverse_image(531 ^ [], relation_image(531 ^ [], 530 ^ [])), 530 ^ []], 317 ^ [relation_inverse_image(531 ^ [], relation_image(531 ^ [], 530 ^ [])), 530 ^ []]]]))).
% 45.43/44.88  ncf('1.1.3.2.1',plain,[in(317 ^ [relation_inverse_image(531 ^ [], relation_image(531 ^ [], 530 ^ [])), 530 ^ []], relation_inverse_image(531 ^ [], relation_image(531 ^ [], 530 ^ []))), -(subset(530 ^ [], relation_inverse_image(531 ^ [], relation_image(531 ^ [], 530 ^ []))))],extension(316 ^ 12,bind([[_94115, _94117], [relation_inverse_image(531 ^ [], relation_image(531 ^ [], 530 ^ [])), 530 ^ []]]))).
% 45.43/44.88  ncf('1.1.3.2.1.1',plain,[subset(530 ^ [], relation_inverse_image(531 ^ [], relation_image(531 ^ [], 530 ^ [])))],extension(537 ^ 13)).
% 45.43/44.88  ncf('1.1.3.2.2',plain,[-(317 ^ [relation_inverse_image(531 ^ [], relation_image(531 ^ [], 530 ^ [])), 530 ^ []] = 317 ^ [relation_inverse_image(531 ^ [], relation_image(531 ^ [], 530 ^ [])), 530 ^ []])],extension(2 ^ 12,bind([[_83031], [317 ^ [relation_inverse_image(531 ^ [], relation_image(531 ^ [], 530 ^ [])), 530 ^ []]]]))).
% 45.43/44.88  ncf('1.1.3.2.3',plain,[-(relation_inverse_image(531 ^ [], relation_image(531 ^ [], 530 ^ [])) = relation_inverse_image(531 ^ [], relation_image(531 ^ [], 530 ^ [])))],extension(2 ^ 12,bind([[_83031], [relation_inverse_image(531 ^ [], relation_image(531 ^ [], 530 ^ []))]]))).
% 45.43/44.88  ncf('1.1.3.3',plain,[-(relation_inverse_image(531 ^ [], relation_image(531 ^ [], 530 ^ [])) = relation_inverse_image(531 ^ [], relation_image(531 ^ [], 530 ^ []))), 531 ^ [] = 531 ^ [], relation_image(531 ^ [], 530 ^ []) = relation_image(531 ^ [], 530 ^ [])],extension(150 ^ 9,bind([[_87862, _87864, _87866, _87868], [relation_image(531 ^ [], 530 ^ []), relation_image(531 ^ [], 530 ^ []), 531 ^ [], 531 ^ []]]))).
% 45.43/44.88  ncf('1.1.3.3.1',plain,[-(531 ^ [] = 531 ^ [])],extension(2 ^ 10,bind([[_83031], [531 ^ []]]))).
% 45.43/44.88  ncf('1.1.3.3.2',plain,[-(relation_image(531 ^ [], 530 ^ []) = relation_image(531 ^ [], 530 ^ []))],extension(2 ^ 10,bind([[_83031], [relation_image(531 ^ [], 530 ^ [])]]))).
% 45.43/44.88  ncf('1.1.3.4',plain,[-(relation(531 ^ []))],reduction('1')).
% 45.43/44.88  %-----------------------------------------------------
% 45.43/44.88  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
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