%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SEU096+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n028.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 12:02:12 EDT 2023

% Result   : Theorem 43.26s 42.74s
% Output   : Proof 43.26s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU096+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.12  % Command  : nanocop.sh %s %d
% 0.13/0.33  % Computer : n028.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Thu May 18 13:26:48 EDT 2023
% 0.13/0.33  % CPUTime  : 
% 43.26/42.74  
% 43.26/42.74  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 43.26/42.74  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 43.26/42.74  %-----------------------------------------------------
% 43.26/42.74  ncf(matrix, plain, [(766 ^ _136779) ^ [] : [-(relation(764 ^ []))], (770 ^ _136779) ^ [] : [-(subset(763 ^ [], relation_rng(764 ^ [])))], (774 ^ _136779) ^ [] : [finite(763 ^ [])], (772 ^ _136779) ^ [] : [-(finite(relation_inverse_image(764 ^ [], 763 ^ [])))], (768 ^ _136779) ^ [] : [-(function(764 ^ []))], !, (568 ^ _112601) ^ [] : [-(empty(560 ^ []))], (636 ^ _112601) ^ [] : [-(ordinal(628 ^ []))], (222 ^ _112601) ^ [_119487, _119489, _119491, _119493] : [-(relation_image(_119493, _119489) = relation_image(_119491, _119487)), _119493 = _119491, _119489 = _119487], (212 ^ _112601) ^ [_119086, _119088] : [-(finite(_119086)), _119088 = _119086, finite(_119088)], (487 ^ _112601) ^ [] : [-(function(483 ^ []))], (605 ^ _112601) ^ [] : [-(epsilon_connected(597 ^ []))], (130 ^ _112601) ^ [_116594, _116596] : [-(relation_non_empty(_116594)), _116596 = _116594, relation_non_empty(_116596)], (506 ^ _112601) ^ [] : [-(empty(504 ^ []))], (540 ^ _112601) ^ [_129310] : [-(function(532 ^ [_129310]))], (482 ^ _112601) ^ [] : [-(function_yielding(476 ^ []))], (648 ^ _112601) ^ [] : [-(function(642 ^ []))], (110 ^ _112601) ^ [_116004, _116006] : [-(relation_empty_yielding(_116004)), _116006 = _116004, relation_empty_yielding(_116006)], (232 ^ _112601) ^ [_119818, _119820] : [_119820 = _119818, -(powerset(_119820) = powerset(_119818))], (748 ^ _112601) ^ [_135894, _135896] : [in(_135896, _135894), empty(_135894)], (508 ^ _112601) ^ [] : [-(relation(504 ^ []))], (154 ^ _112601) ^ [_117361, _117363, _117365, _117367] : [-(in(_117365, _117361)), in(_117367, _117363), _117367 = _117365, _117363 = _117361], (550 ^ _112601) ^ [_129650] : [-(natural(532 ^ [_129650]))], (722 ^ _112601) ^ [_135069, _135071, _135073] : [-(element(_135073, _135069)), in(_135073, _135071), element(_135071, powerset(_135069))], (538 ^ _112601) ^ [_129242] : [-(relation(532 ^ [_129242]))], (583 ^ _112601) ^ [] : [-(ordinal_yielding(575 ^ []))], (466 ^ _112601) ^ [] : [-(epsilon_connected(460 ^ []))], (694 ^ _112601) ^ [_134136, _134138] : [in(_134138, _134136), -(element(_134138, _134136))], (238 ^ _112601) ^ [_120036, _120038] : [_120038 = _120036, -(relation_rng(_120038) = relation_rng(_120036))], (529 ^ _112601) ^ [] : [-(epsilon_connected(521 ^ []))], (413 ^ _112601) ^ [] : [-(one_to_one(empty_set))], (385 ^ _112601) ^ [] : [-(relation(empty_set))], (473 ^ _112601) ^ [] : [empty(471 ^ [])], (10 ^ _112601) ^ [_113036, _113038, _113040] : [-(_113040 = _113036), _113040 = _113038, _113038 = _113036], (562 ^ _112601) ^ [] : [-(relation(560 ^ []))], (655 ^ _112601) ^ [] : [-(transfinite_sequence(649 ^ []))], (415 ^ _112601) ^ [] : [-(empty(empty_set))], (510 ^ _112601) ^ [_128260] : [-(empty(_128260)), 514 ^ _112601 : [(517 ^ _112601) ^ [] : [empty(513 ^ [_128260])], (515 ^ _112601) ^ [] : [-(element(513 ^ [_128260], powerset(_128260)))]]], (660 ^ _112601) ^ [] : [-(relation_non_empty(656 ^ []))], (742 ^ _112601) ^ [_135692] : [empty(_135692), -(_135692 = empty_set)], (566 ^ _112601) ^ [] : [-(one_to_one(560 ^ []))], (666 ^ _112601) ^ [_133346, _133348] : [relation(_133346), function(_133346), subset(_133348, relation_rng(_133346)), -(relation_image(_133346, relation_inverse_image(_133346, _133348)) = _133348)], (627 ^ _112601) ^ [] : [-(one_to_one(621 ^ []))], (354 ^ _112601) ^ [_123688] : [empty(_123688), 357 ^ _112601 : [(362 ^ _112601) ^ [] : [-(ordinal(_123688))], (360 ^ _112601) ^ [] : [-(epsilon_connected(_123688))], (358 ^ _112601) ^ [] : [-(epsilon_transitive(_123688))]]], (20 ^ _112601) ^ [_113349, _113351] : [-(with_non_empty_elements(_113349)), _113351 = _113349, with_non_empty_elements(_113351)], (381 ^ _112601) ^ [_124521] : [-(element(379 ^ [_124521], _124521))], (499 ^ _112601) ^ [] : [-(epsilon_connected(495 ^ []))], (475 ^ _112601) ^ [] : [-(finite(471 ^ []))], (316 ^ _112601) ^ [_122589] : [finite(_122589), 319 ^ _112601 : [(320 ^ _112601) ^ [_122721] : [element(_122721, powerset(_122589)), -(finite(_122721))]]], (588 ^ _112601) ^ [] : [-(relation(584 ^ []))], (630 ^ _112601) ^ [] : [empty(628 ^ [])], (40 ^ _112601) ^ [_113939, _113941] : [-(being_limit_ordinal(_113939)), _113941 = _113939, being_limit_ordinal(_113941)], (462 ^ _112601) ^ [] : [empty(460 ^ [])], (641 ^ _112601) ^ [] : [-(relation_empty_yielding(637 ^ []))], (651 ^ _112601) ^ [] : [-(relation(649 ^ []))], (423 ^ _112601) ^ [] : [-(empty(empty_set))], (50 ^ _112601) ^ [_114234, _114236] : [-(ordinal_yielding(_114234)), _114236 = _114234, ordinal_yielding(_114236)], (120 ^ _112601) ^ [_116299, _116301] : [-(transfinite_sequence(_116299)), _116301 = _116299, transfinite_sequence(_116301)], (625 ^ _112601) ^ [] : [-(function(621 ^ []))], (411 ^ _112601) ^ [] : [-(function(empty_set))], (557 ^ _112601) ^ [] : [-(empty(553 ^ []))], (662 ^ _112601) ^ [] : [-(function(656 ^ []))], (632 ^ _112601) ^ [] : [-(epsilon_transitive(628 ^ []))], (188 ^ _112601) ^ [_118367, _118369] : [-(function(_118367)), _118369 = _118367, function(_118369)], (603 ^ _112601) ^ [] : [-(epsilon_transitive(597 ^ []))], (700 ^ _112601) ^ [_134346, _134348] : [element(_134348, _134346), -(empty(_134346)), -(in(_134348, _134346))], (607 ^ _112601) ^ [] : [-(ordinal(597 ^ []))], (611 ^ _112601) ^ [_131571] : [-(empty(_131571)), 615 ^ _112601 : [(620 ^ _112601) ^ [] : [-(finite(614 ^ [_131571]))], (618 ^ _112601) ^ [] : [empty(614 ^ [_131571])], (616 ^ _112601) ^ [] : [-(element(614 ^ [_131571], powerset(_131571)))]]], (564 ^ _112601) ^ [] : [-(function(560 ^ []))], (531 ^ _112601) ^ [] : [-(ordinal(521 ^ []))], (478 ^ _112601) ^ [] : [-(relation(476 ^ []))], (591 ^ _112601) ^ [_130941] : [-(element(589 ^ [_130941], powerset(_130941)))], (468 ^ _112601) ^ [] : [-(ordinal(460 ^ []))], (710 ^ _112601) ^ [_134673, _134675] : [element(_134675, powerset(_134673)), -(subset(_134675, _134673))], (525 ^ _112601) ^ [] : [empty(521 ^ [])], (427 ^ _112601) ^ [_125845] : [-(with_non_empty_elements(relation_rng(_125845))), relation(_125845), relation_non_empty(_125845), function(_125845)], (492 ^ _112601) ^ [] : [-(epsilon_connected(488 ^ []))], (527 ^ _112601) ^ [] : [-(epsilon_transitive(521 ^ []))], (570 ^ _112601) ^ [] : [-(epsilon_transitive(560 ^ []))], (555 ^ _112601) ^ [] : [-(relation(553 ^ []))], (574 ^ _112601) ^ [] : [-(ordinal(560 ^ []))], (260 ^ _112601) ^ [_120808] : [ordinal(_120808), 263 ^ _112601 : [(264 ^ _112601) ^ [_120948] : [element(_120948, _120808), 267 ^ _112601 : [(272 ^ _112601) ^ [] : [-(ordinal(_120948))], (270 ^ _112601) ^ [] : [-(epsilon_connected(_120948))], (268 ^ _112601) ^ [] : [-(epsilon_transitive(_120948))]]]]], (364 ^ _112601) ^ [_124015] : [element(_124015, positive_rationals), ordinal(_124015), 371 ^ _112601 : [(374 ^ _112601) ^ [] : [-(epsilon_connected(_124015))], (376 ^ _112601) ^ [] : [-(ordinal(_124015))], (378 ^ _112601) ^ [] : [-(natural(_124015))], (372 ^ _112601) ^ [] : [-(epsilon_transitive(_124015))]]], (280 ^ _112601) ^ [_121480] : [empty(_121480), -(function(_121480))], (383 ^ _112601) ^ [] : [-(empty(empty_set))], (389 ^ _112601) ^ [_124796, _124798] : [-(finite(relation_image(_124798, _124796))), relation(_124798), function(_124798), finite(_124796)], (542 ^ _112601) ^ [_129378] : [-(one_to_one(532 ^ [_129378]))], (80 ^ _112601) ^ [_115119, _115121] : [-(epsilon_transitive(_115119)), _115121 = _115119, epsilon_transitive(_115121)], (501 ^ _112601) ^ [] : [-(ordinal(495 ^ []))], (403 ^ _112601) ^ [_125152] : [empty(powerset(_125152))], (417 ^ _112601) ^ [] : [-(epsilon_transitive(empty_set))], (198 ^ _112601) ^ [_118690, _118692, _118694, _118696] : [-(subset(_118694, _118690)), subset(_118696, _118692), _118696 = _118694, _118692 = _118690], (520 ^ _112601) ^ [] : [-(empty(518 ^ []))], (534 ^ _112601) ^ [_129103] : [-(element(532 ^ [_129103], powerset(_129103)))], (658 ^ _112601) ^ [] : [-(relation(656 ^ []))], (634 ^ _112601) ^ [] : [-(epsilon_connected(628 ^ []))], (623 ^ _112601) ^ [] : [-(relation(621 ^ []))], (254 ^ _112601) ^ [_120611, _120613] : [in(_120613, _120611), in(_120611, _120613)], (523 ^ _112601) ^ [] : [-(element(521 ^ [], positive_rationals))], (572 ^ _112601) ^ [] : [-(epsilon_connected(560 ^ []))], (60 ^ _112601) ^ [_114529, _114531] : [-(natural(_114529)), _114531 = _114529, natural(_114531)], (326 ^ _112601) ^ [_122926] : [337 ^ _112601 : [(342 ^ _112601) ^ [] : [-(one_to_one(_122926))], (340 ^ _112601) ^ [] : [-(function(_122926))], (338 ^ _112601) ^ [] : [-(relation(_122926))]], relation(_122926), empty(_122926), function(_122926)], (294 ^ _112601) ^ [_121923] : [empty(_121923), -(relation(_121923))], (421 ^ _112601) ^ [] : [-(ordinal(empty_set))], (100 ^ _112601) ^ [_115709, _115711] : [-(ordinal(_115709)), _115711 = _115709, ordinal(_115711)], (2 ^ _112601) ^ [_112725] : [-(_112725 = _112725)], (140 ^ _112601) ^ [_116917, _116919, _116921, _116923] : [-(element(_116921, _116917)), element(_116923, _116919), _116923 = _116921, _116919 = _116917], (754 ^ _112601) ^ [_136081, _136083] : [empty(_136083), -(_136083 = _136081), empty(_136081)], (581 ^ _112601) ^ [] : [-(transfinite_sequence(575 ^ []))], (405 ^ _112601) ^ [] : [-(empty(empty_set))], (546 ^ _112601) ^ [_129514] : [-(epsilon_connected(532 ^ [_129514]))], (286 ^ _112601) ^ [_121666] : [ordinal(_121666), 289 ^ _112601 : [(292 ^ _112601) ^ [] : [-(epsilon_connected(_121666))], (290 ^ _112601) ^ [] : [-(epsilon_transitive(_121666))]]], (644 ^ _112601) ^ [] : [-(relation(642 ^ []))], (451 ^ _112601) ^ [] : [empty(positive_rationals)], (90 ^ _112601) ^ [_115414, _115416] : [-(epsilon_connected(_115414)), _115416 = _115414, epsilon_connected(_115416)], (300 ^ _112601) ^ [_122109] : [307 ^ _112601 : [(310 ^ _112601) ^ [] : [-(epsilon_connected(_122109))], (312 ^ _112601) ^ [] : [-(ordinal(_122109))], (314 ^ _112601) ^ [] : [-(natural(_122109))], (308 ^ _112601) ^ [] : [-(epsilon_transitive(_122109))]], empty(_122109), ordinal(_122109)], (470 ^ _112601) ^ [] : [-(natural(460 ^ []))], (168 ^ _112601) ^ [_117777, _117779] : [-(empty(_117777)), _117779 = _117777, empty(_117779)], (601 ^ _112601) ^ [] : [-(empty(597 ^ []))], (646 ^ _112601) ^ [] : [-(relation_empty_yielding(642 ^ []))], (497 ^ _112601) ^ [] : [-(epsilon_transitive(495 ^ []))], (596 ^ _112601) ^ [] : [empty(594 ^ [])], (593 ^ _112601) ^ [_130992] : [-(empty(589 ^ [_130992]))], (536 ^ _112601) ^ [_129174] : [-(empty(532 ^ [_129174]))], (480 ^ _112601) ^ [] : [-(function(476 ^ []))], (552 ^ _112601) ^ [_129698] : [-(finite(532 ^ [_129698]))], (70 ^ _112601) ^ [_114824, _114826] : [-(one_to_one(_114824)), _114826 = _114824, one_to_one(_114826)], (664 ^ _112601) ^ [_133237, _133239] : [-(subset(_133239, _133239))], (544 ^ _112601) ^ [_129446] : [-(epsilon_transitive(532 ^ [_129446]))], (387 ^ _112601) ^ [] : [-(relation_empty_yielding(empty_set))], (494 ^ _112601) ^ [] : [-(ordinal(488 ^ []))], (464 ^ _112601) ^ [] : [-(epsilon_transitive(460 ^ []))], (599 ^ _112601) ^ [] : [-(element(597 ^ [], positive_rationals))], (639 ^ _112601) ^ [] : [-(relation(637 ^ []))], (244 ^ _112601) ^ [_120262, _120264, _120266, _120268] : [-(relation_inverse_image(_120268, _120264) = relation_inverse_image(_120266, _120262)), _120268 = _120266, _120264 = _120262], (441 ^ _112601) ^ [_126201] : [empty(relation_rng(_126201)), -(empty(_126201)), relation(_126201)], (559 ^ _112601) ^ [] : [-(function(553 ^ []))], (30 ^ _112601) ^ [_113644, _113646] : [-(function_yielding(_113644)), _113646 = _113644, function_yielding(_113646)], (419 ^ _112601) ^ [] : [-(epsilon_connected(empty_set))], (425 ^ _112601) ^ [] : [-(relation(empty_set))], (490 ^ _112601) ^ [] : [-(epsilon_transitive(488 ^ []))], (609 ^ _112601) ^ [] : [-(natural(597 ^ []))], (577 ^ _112601) ^ [] : [-(relation(575 ^ []))], (716 ^ _112601) ^ [_134839, _134841] : [subset(_134841, _134839), -(element(_134841, powerset(_134839)))], (653 ^ _112601) ^ [] : [-(function(649 ^ []))], (732 ^ _112601) ^ [_135396, _135398, _135400] : [in(_135400, _135398), element(_135398, powerset(_135396)), empty(_135396)], (4 ^ _112601) ^ [_112832, _112834] : [_112834 = _112832, -(_112832 = _112834)], (274 ^ _112601) ^ [_121294] : [empty(_121294), -(finite(_121294))], (178 ^ _112601) ^ [_118072, _118074] : [-(relation(_118072)), _118074 = _118072, relation(_118074)], (409 ^ _112601) ^ [] : [-(relation_empty_yielding(empty_set))], (680 ^ _112601) ^ [_133748, _133750] : [relation(_133748), function(_133748), finite(_133750), -(finite(relation_image(_133748, _133750)))], (503 ^ _112601) ^ [] : [-(being_limit_ordinal(495 ^ []))], (453 ^ _112601) ^ [_126530] : [empty(_126530), 456 ^ _112601 : [(459 ^ _112601) ^ [] : [-(relation(relation_rng(_126530)))], (457 ^ _112601) ^ [] : [-(empty(relation_rng(_126530)))]]], (344 ^ _112601) ^ [_123419] : [-(ordinal(_123419)), epsilon_transitive(_123419), epsilon_connected(_123419)], (579 ^ _112601) ^ [] : [-(function(575 ^ []))], (485 ^ _112601) ^ [] : [-(relation(483 ^ []))], (548 ^ _112601) ^ [_129582] : [-(ordinal(532 ^ [_129582]))], (407 ^ _112601) ^ [] : [-(relation(empty_set))], (586 ^ _112601) ^ [] : [empty(584 ^ [])]], input).
% 43.26/42.74  ncf('1',plain,[finite(763 ^ [])],start(774 ^ 0)).
% 43.26/42.74  ncf('1.1',plain,[-(finite(763 ^ [])), relation_image(764 ^ [], relation_inverse_image(764 ^ [], 763 ^ [])) = 763 ^ [], finite(relation_image(764 ^ [], relation_inverse_image(764 ^ [], 763 ^ [])))],extension(212 ^ 1,bind([[_119086, _119088], [763 ^ [], relation_image(764 ^ [], relation_inverse_image(764 ^ [], 763 ^ []))]]))).
% 43.26/42.74  ncf('1.1.1',plain,[-(relation_image(764 ^ [], relation_inverse_image(764 ^ [], 763 ^ [])) = 763 ^ []), relation(764 ^ []), function(764 ^ []), subset(763 ^ [], relation_rng(764 ^ []))],extension(666 ^ 2,bind([[_133346, _133348], [764 ^ [], 763 ^ []]]))).
% 43.26/42.74  ncf('1.1.1.1',plain,[-(relation(764 ^ []))],extension(766 ^ 3)).
% 43.26/42.74  ncf('1.1.1.2',plain,[-(function(764 ^ []))],extension(768 ^ 3)).
% 43.26/42.74  ncf('1.1.1.3',plain,[-(subset(763 ^ [], relation_rng(764 ^ [])))],extension(770 ^ 3)).
% 43.26/42.74  ncf('1.1.2',plain,[-(finite(relation_image(764 ^ [], relation_inverse_image(764 ^ [], 763 ^ [])))), relation(764 ^ []), function(764 ^ []), finite(relation_inverse_image(764 ^ [], 763 ^ []))],extension(389 ^ 2,bind([[_124796, _124798], [relation_inverse_image(764 ^ [], 763 ^ []), 764 ^ []]]))).
% 43.26/42.74  ncf('1.1.2.1',plain,[-(relation(764 ^ []))],extension(766 ^ 3)).
% 43.26/42.74  ncf('1.1.2.2',plain,[-(function(764 ^ []))],extension(768 ^ 3)).
% 43.26/42.74  ncf('1.1.2.3',plain,[-(finite(relation_inverse_image(764 ^ [], 763 ^ [])))],extension(772 ^ 3)).
% 43.26/42.74  %-----------------------------------------------------
% 43.26/42.74  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------