%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SEU353+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n009.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 12:03:15 EDT 2023

% Result   : Theorem 265.51s 256.83s
% Output   : Proof 265.51s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SEU353+1 : TPTP v8.1.2. Released v3.3.0.
% 0.11/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n009.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 13:36:33 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 265.51/256.83  
% 265.51/256.83  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 265.51/256.83  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 265.51/256.83  %-----------------------------------------------------
% 265.51/256.83  ncf(matrix, plain, [(622 ^ _144541) ^ [_164319] : [empty(the_carrier(_164319)), -(empty_carrier(_164319)), one_sorted_str(_164319)], (134 ^ _144541) ^ [_148906, _148908] : [-(function(_148906)), _148908 = _148906, function(_148908)], (665 ^ _144541) ^ [_165723, _165725] : [-(quasi_total(657 ^ [_165723, _165725], _165725, _165723))], (20 ^ _144541) ^ [_145309, _145311] : [-(one_to_one(_145309)), _145311 = _145309, one_to_one(_145311)], (873 ^ _144541) ^ [] : [apply_as_element(the_carrier(864 ^ []), the_carrier(864 ^ []), identity_on_carrier(864 ^ []), 869 ^ []) = 869 ^ []], (620 ^ _144541) ^ [_164216, _164218] : [-(relation_of2_as_subset(618 ^ [_164216, _164218], _164218, _164216))], (787 ^ _144541) ^ [_170025, _170027] : [-(subset(_170027, _170027))], (558 ^ _144541) ^ [_162493, _162495, _162497, _162499] : [-(element(apply_as_element(_162499, _162497, _162495, _162493), _162497)), -(empty(_162499)), function(_162495), quasi_total(_162495, _162499, _162497), relation_of2(_162495, _162499, _162497), element(_162493, _162499)], (106 ^ _144541) ^ [_148002, _148004] : [-(transitive(_148002)), _148004 = _148002, transitive(_148004)], (530 ^ _144541) ^ [] : [true___, -(true___)], (751 ^ _144541) ^ [_168835] : [-(identity_as_relation_of(_168835) = identity_relation(_168835))], (727 ^ _144541) ^ [_168052] : [-(antisymmetric(717 ^ [_168052]))], (10 ^ _144541) ^ [_144996, _144998, _145000] : [-(_145000 = _144996), _145000 = _144998, _144998 = _144996], (76 ^ _144541) ^ [_147117, _147119] : [-(reflexive(_147117)), _147119 = _147117, reflexive(_147119)], (646 ^ _144541) ^ [_165037] : [-(transitive(identity_relation(_165037)))], (144 ^ _144541) ^ [_149257, _149259, _149261, _149263, _149265, _149267] : [-(quasi_total(_149265, _149261, _149257)), quasi_total(_149267, _149263, _149259), _149267 = _149265, _149263 = _149261, _149259 = _149257], (738 ^ _144541) ^ [_168429] : [746 ^ _144541 : [(747 ^ _144541) ^ [] : [-(element(745 ^ [_168429], powerset(the_carrier(_168429))))], (749 ^ _144541) ^ [] : [empty(745 ^ [_168429])]], -(empty_carrier(_168429)), one_sorted_str(_168429)], (302 ^ _144541) ^ [_154465, _154467] : [_154467 = _154465, -(powerset(_154467) = powerset(_154465))], (638 ^ _144541) ^ [_164797] : [-(function(identity_relation(_164797)))], (518 ^ _144541) ^ [] : [true___, -(true___)], (833 ^ _144541) ^ [_171614, _171616, _171618] : [in(_171618, _171616), element(_171616, powerset(_171614)), empty(_171614)], (212 ^ _144541) ^ [_151500, _151502, _151504, _151506] : [-(in(_151504, _151500)), in(_151506, _151502), _151506 = _151504, _151502 = _151500], (296 ^ _144541) ^ [_154247, _154249] : [_154249 = _154247, -(identity_relation(_154249) = identity_relation(_154247))], (753 ^ _144541) ^ [_168974, _168976, _168978, _168980] : [-(apply_as_element(_168980, _168978, _168976, _168974) = apply(_168976, _168974)), -(empty(_168980)), function(_168976), quasi_total(_168976, _168980, _168978), relation_of2(_168976, _168980, _168978), element(_168974, _168980)], (544 ^ _144541) ^ [_161911] : [-(relation_of2_as_subset(identity_as_relation_of(_161911), _161911, _161911))], (611 ^ _144541) ^ [] : [-(one_sorted_str(609 ^ []))], (719 ^ _144541) ^ [_167778] : [-(relation_of2(717 ^ [_167778], _167778, _167778))], (546 ^ _144541) ^ [_161994] : [-(relation(identity_relation(_161994)))], (695 ^ _144541) ^ [_166809] : [-(one_to_one(687 ^ [_166809]))], (344 ^ _144541) ^ [_156049, _156051, _156053] : [relation_of2(_156049, _156053, _156051), 355 ^ _144541 : [(356 ^ _144541) ^ [] : [-(function(_156049))], (358 ^ _144541) ^ [] : [-(quasi_total(_156049, _156053, _156051))]], function(_156049), v1_partfun1(_156049, _156053, _156051)], (711 ^ _144541) ^ [_167461] : [-(element(709 ^ [_167461], powerset(_167461)))], (866 ^ _144541) ^ [] : [empty_carrier(864 ^ [])], (634 ^ _144541) ^ [] : [-(empty(empty_set))], (716 ^ _144541) ^ [] : [empty(714 ^ [])], (871 ^ _144541) ^ [] : [-(element(869 ^ [], the_carrier(864 ^ [])))], (524 ^ _144541) ^ [] : [true___, -(true___)], (360 ^ _144541) ^ [_156516] : [371 ^ _144541 : [(372 ^ _144541) ^ [] : [-(relation(_156516))], (374 ^ _144541) ^ [] : [-(reflexive(_156516))]], relation(_156516), symmetric(_156516), transitive(_156516)], (270 ^ _144541) ^ [_153339, _153341, _153343, _153345] : [-(cartesian_product2(_153345, _153341) = cartesian_product2(_153343, _153339)), _153345 = _153343, _153341 = _153339], (256 ^ _144541) ^ [_152809, _152811, _152813, _152815] : [-(element(_152813, _152809)), element(_152815, _152811), _152815 = _152813, _152811 = _152809], (376 ^ _144541) ^ [_156967, _156969, _156971] : [element(_156967, powerset(cartesian_product2(_156971, _156969))), -(relation(_156967))], (699 ^ _144541) ^ [_166947] : [-(onto(687 ^ [_166947], _166947, _166947))], (246 ^ _144541) ^ [_152506, _152508] : [-(one_sorted_str(_152506)), _152508 = _152506, one_sorted_str(_152508)], (116 ^ _144541) ^ [_148353, _148355, _148357, _148359, _148361, _148363] : [-(v1_partfun1(_148361, _148357, _148353)), v1_partfun1(_148363, _148359, _148355), _148363 = _148361, _148359 = _148357, _148355 = _148353], (512 ^ _144541) ^ [_161183] : [one_sorted_str(_161183), -(identity_on_carrier(_161183) = identity_as_relation_of(the_carrier(_161183)))], (723 ^ _144541) ^ [_167916] : [-(reflexive(717 ^ [_167916]))], (736 ^ _144541) ^ [] : [empty_carrier(732 ^ [])], (721 ^ _144541) ^ [_167848] : [-(relation(717 ^ [_167848]))], (598 ^ _144541) ^ [_163487, _163489, _163491] : [relation_of2_as_subset(_163487, _163491, _163489), -(element(_163487, powerset(cartesian_product2(_163491, _163489))))], (734 ^ _144541) ^ [] : [-(one_sorted_str(732 ^ []))], (236 ^ _144541) ^ [_152211, _152213] : [-(empty_carrier(_152211)), _152213 = _152211, empty_carrier(_152213)], (697 ^ _144541) ^ [_166877] : [-(quasi_total(687 ^ [_166877], _166877, _166877))], (48 ^ _144541) ^ [_146269, _146271, _146273, _146275, _146277, _146279] : [-(bijective(_146277, _146273, _146269)), bijective(_146279, _146275, _146271), _146279 = _146277, _146275 = _146273, _146271 = _146269], (180 ^ _144541) ^ [_150475, _150477, _150479, _150481, _150483, _150485] : [-(relation_of2(_150483, _150479, _150475)), relation_of2(_150485, _150481, _150477), _150485 = _150483, _150481 = _150479, _150477 = _150475], (823 ^ _144541) ^ [_171287, _171289, _171291] : [-(element(_171291, _171287)), in(_171291, _171289), element(_171289, powerset(_171287))], (775 ^ _144541) ^ [_169646, _169648, _169650] : [relation_of2_as_subset(_169646, _169650, _169648), -(relation_of2(_169646, _169650, _169648))], (462 ^ _144541) ^ [_159559, _159561] : [-(empty(_159559)), 465 ^ _144541 : [(466 ^ _144541) ^ [_159723] : [relation_of2(_159723, _159561, _159559), 477 ^ _144541 : [(480 ^ _144541) ^ [] : [-(v1_partfun1(_159723, _159561, _159559))], (482 ^ _144541) ^ [] : [-(quasi_total(_159723, _159561, _159559))], (478 ^ _144541) ^ [] : [-(function(_159723))]], function(_159723), quasi_total(_159723, _159561, _159559)]]], (286 ^ _144541) ^ [_153916, _153918, _153920, _153922] : [-(apply(_153922, _153918) = apply(_153920, _153916)), _153922 = _153920, _153918 = _153916], (642 ^ _144541) ^ [_164927] : [-(symmetric(identity_relation(_164927)))], (326 ^ _144541) ^ [_155372, _155374] : [_155374 = _155372, -(the_carrier(_155374) = the_carrier(_155372))], (280 ^ _144541) ^ [_153670, _153672] : [_153672 = _153670, -(identity_as_relation_of(_153672) = identity_as_relation_of(_153670))], (676 ^ _144541) ^ [_166101] : [-(empty(_166101)), 680 ^ _144541 : [(681 ^ _144541) ^ [] : [-(element(679 ^ [_166101], powerset(_166101)))], (683 ^ _144541) ^ [] : [empty(679 ^ [_166101])]]], (2 ^ _144541) ^ [_144685] : [-(_144685 = _144685)], (706 ^ _144541) ^ [_167253, _167255] : [-(relation(702 ^ [_167253, _167255]))], (332 ^ _144541) ^ [_155570, _155572] : [_155572 = _155570, -(identity_on_carrier(_155572) = identity_on_carrier(_155570))], (96 ^ _144541) ^ [_147707, _147709] : [-(antisymmetric(_147707)), _147709 = _147707, antisymmetric(_147709)], (849 ^ _144541) ^ [_172112, _172114] : [in(_172114, _172112), empty(_172112)], (843 ^ _144541) ^ [_171910] : [empty(_171910), -(_171910 = empty_set)], (636 ^ _144541) ^ [_164732] : [-(relation(identity_relation(_164732)))], (4 ^ _144541) ^ [_144792, _144794] : [_144794 = _144792, -(_144792 = _144794)], (226 ^ _144541) ^ [_151916, _151918] : [-(empty(_151916)), _151918 = _151916, empty(_151918)], (66 ^ _144541) ^ [_146822, _146824] : [-(relation(_146822)), _146824 = _146822, relation(_146824)], (338 ^ _144541) ^ [_155824, _155826] : [in(_155826, _155824), in(_155824, _155826)], (781 ^ _144541) ^ [_169818, _169820, _169822] : [relation_of2(_169818, _169822, _169820), -(relation_of2_as_subset(_169818, _169822, _169820))], (86 ^ _144541) ^ [_147412, _147414] : [-(symmetric(_147412)), _147414 = _147412, symmetric(_147414)], (659 ^ _144541) ^ [_165525, _165527] : [-(relation_of2(657 ^ [_165525, _165527], _165527, _165525))], (817 ^ _144541) ^ [_171057, _171059] : [subset(_171059, _171057), -(element(_171059, powerset(_171057)))], (789 ^ _144541) ^ [_170134, _170136] : [in(_170136, _170134), -(element(_170136, _170134))], (592 ^ _144541) ^ [] : [true___, -(true___)], (640 ^ _144541) ^ [_164862] : [-(reflexive(identity_relation(_164862)))], (198 ^ _144541) ^ [_151056, _151058, _151060, _151062] : [-(subset(_151060, _151056)), subset(_151062, _151058), _151062 = _151060, _151058 = _151056], (580 ^ _144541) ^ [] : [true___, -(true___)], (632 ^ _144541) ^ [_164580] : [empty(powerset(_164580))], (432 ^ _144541) ^ [_158692, _158694] : [relation_of2(_158692, _158694, _158694), 451 ^ _144541 : [(460 ^ _144541) ^ [] : [-(bijective(_158692, _158694, _158694))], (458 ^ _144541) ^ [] : [-(onto(_158692, _158694, _158694))], (456 ^ _144541) ^ [] : [-(quasi_total(_158692, _158694, _158694))], (454 ^ _144541) ^ [] : [-(one_to_one(_158692))], (452 ^ _144541) ^ [] : [-(function(_158692))]], function(_158692), v1_partfun1(_158692, _158694, _158694), reflexive(_158692), quasi_total(_158692, _158694, _158694)], (668 ^ _144541) ^ [] : [-(relation(666 ^ []))], (725 ^ _144541) ^ [_167984] : [-(symmetric(717 ^ [_167984]))], (693 ^ _144541) ^ [_166741] : [-(function(687 ^ [_166741]))], (548 ^ _144541) ^ [_162088] : [one_sorted_str(_162088), 551 ^ _144541 : [(554 ^ _144541) ^ [] : [-(quasi_total(identity_on_carrier(_162088), the_carrier(_162088), the_carrier(_162088)))], (556 ^ _144541) ^ [] : [-(relation_of2_as_subset(identity_on_carrier(_162088), the_carrier(_162088), the_carrier(_162088)))], (552 ^ _144541) ^ [] : [-(function(identity_on_carrier(_162088)))]]], (661 ^ _144541) ^ [_165599, _165601] : [-(relation(657 ^ [_165599, _165601]))], (868 ^ _144541) ^ [] : [-(one_sorted_str(864 ^ []))], (704 ^ _144541) ^ [_167179, _167181] : [-(relation_of2(702 ^ [_167179, _167181], _167181, _167179))], (663 ^ _144541) ^ [_165671, _165673] : [-(function(657 ^ [_165671, _165673]))], (674 ^ _144541) ^ [] : [-(empty(666 ^ []))], (617 ^ _144541) ^ [_164077] : [-(element(615 ^ [_164077], _164077))], (672 ^ _144541) ^ [] : [-(one_to_one(666 ^ []))], (805 ^ _144541) ^ [_170642, _170644] : [in(_170642, _170644), -(apply(identity_relation(_170644), _170642) = _170642)], (689 ^ _144541) ^ [_166603] : [-(relation_of2(687 ^ [_166603], _166603, _166603))], (604 ^ _144541) ^ [] : [true___, -(true___)], (729 ^ _144541) ^ [_168120] : [-(transitive(717 ^ [_168120]))], (484 ^ _144541) ^ [_160291, _160293] : [-(empty(_160293)), -(empty(_160291)), 491 ^ _144541 : [(492 ^ _144541) ^ [_160552] : [relation_of2(_160552, _160293, _160291), 503 ^ _144541 : [(504 ^ _144541) ^ [] : [-(function(_160552))], (506 ^ _144541) ^ [] : [empty(_160552)], (508 ^ _144541) ^ [] : [-(v1_partfun1(_160552, _160293, _160291))], (510 ^ _144541) ^ [] : [-(quasi_total(_160552, _160293, _160291))]], function(_160552), quasi_total(_160552, _160293, _160291)]]], (162 ^ _144541) ^ [_149866, _149868, _149870, _149872, _149874, _149876] : [-(relation_of2_as_subset(_149874, _149870, _149866)), relation_of2_as_subset(_149876, _149872, _149868), _149876 = _149874, _149872 = _149870, _149868 = _149866], (731 ^ _144541) ^ [_168168] : [-(v1_partfun1(717 ^ [_168168], _168168, _168168))], (670 ^ _144541) ^ [] : [-(function(666 ^ []))], (542 ^ _144541) ^ [_161864] : [-(v1_partfun1(identity_as_relation_of(_161864), _161864, _161864))], (648 ^ _144541) ^ [_165155, _165157] : [empty(cartesian_product2(_165157, _165155)), -(empty(_165157)), -(empty(_165155))], (691 ^ _144541) ^ [_166673] : [-(relation(687 ^ [_166673]))], (586 ^ _144541) ^ [] : [true___, -(true___)], (811 ^ _144541) ^ [_170891, _170893] : [element(_170893, powerset(_170891)), -(subset(_170893, _170891))], (713 ^ _144541) ^ [_167512] : [-(empty(709 ^ [_167512]))], (614 ^ _144541) ^ [_163950, _163952] : [-(relation_of2(612 ^ [_163950, _163952], _163952, _163950))], (795 ^ _144541) ^ [_170344, _170346] : [element(_170346, _170344), -(empty(_170344)), -(in(_170346, _170344))], (644 ^ _144541) ^ [_164992] : [-(antisymmetric(identity_relation(_164992)))], (708 ^ _144541) ^ [_167305, _167307] : [-(function(702 ^ [_167305, _167307]))], (382 ^ _144541) ^ [_157205, _157207, _157209] : [relation_of2(_157205, _157209, _157207), 397 ^ _144541 : [(398 ^ _144541) ^ [] : [-(function(_157205))], (400 ^ _144541) ^ [] : [-(one_to_one(_157205))], (402 ^ _144541) ^ [] : [-(quasi_total(_157205, _157209, _157207))], (404 ^ _144541) ^ [] : [-(onto(_157205, _157209, _157207))]], function(_157205), quasi_total(_157205, _157209, _157207), bijective(_157205, _157209, _157207)], (686 ^ _144541) ^ [] : [-(empty(684 ^ []))], (701 ^ _144541) ^ [_166997] : [-(bijective(687 ^ [_166997], _166997, _166997))], (308 ^ _144541) ^ [_154767, _154769, _154771, _154773, _154775, _154777, _154779, _154781] : [-(apply_as_element(_154781, _154777, _154773, _154769) = apply_as_element(_154779, _154775, _154771, _154767)), _154781 = _154779, _154777 = _154775, _154773 = _154771, _154769 = _154767], (406 ^ _144541) ^ [_157947, _157949, _157951] : [relation_of2(_157947, _157951, _157949), 425 ^ _144541 : [(428 ^ _144541) ^ [] : [-(quasi_total(_157947, _157951, _157949))], (430 ^ _144541) ^ [] : [-(bijective(_157947, _157951, _157949))], (426 ^ _144541) ^ [] : [-(function(_157947))]], function(_157947), one_to_one(_157947), quasi_total(_157947, _157951, _157949), onto(_157947, _157951, _157949)], (30 ^ _144541) ^ [_145660, _145662, _145664, _145666, _145668, _145670] : [-(onto(_145668, _145664, _145660)), onto(_145670, _145666, _145662), _145670 = _145668, _145666 = _145664, _145662 = _145660], (536 ^ _144541) ^ [] : [true___, -(true___)], (855 ^ _144541) ^ [_172299, _172301] : [empty(_172301), -(_172301 = _172299), empty(_172299)]], input).
% 265.51/256.84  ncf('1',plain,[apply_as_element(the_carrier(864 ^ []), the_carrier(864 ^ []), identity_on_carrier(864 ^ []), 869 ^ []) = 869 ^ []],start(873 ^ 0)).
% 265.51/256.84  ncf('1.1',plain,[-(apply_as_element(the_carrier(864 ^ []), the_carrier(864 ^ []), identity_on_carrier(864 ^ []), 869 ^ []) = 869 ^ []), apply_as_element(the_carrier(864 ^ []), the_carrier(864 ^ []), identity_on_carrier(864 ^ []), 869 ^ []) = apply(identity_relation(the_carrier(864 ^ [])), 869 ^ []), apply(identity_relation(the_carrier(864 ^ [])), 869 ^ []) = 869 ^ []],extension(10 ^ 1,bind([[_144996, _144998, _145000], [869 ^ [], apply(identity_relation(the_carrier(864 ^ [])), 869 ^ []), apply_as_element(the_carrier(864 ^ []), the_carrier(864 ^ []), identity_on_carrier(864 ^ []), 869 ^ [])]]))).
% 265.51/256.84  ncf('1.1.1',plain,[-(apply_as_element(the_carrier(864 ^ []), the_carrier(864 ^ []), identity_on_carrier(864 ^ []), 869 ^ []) = apply(identity_relation(the_carrier(864 ^ [])), 869 ^ [])), apply_as_element(the_carrier(864 ^ []), the_carrier(864 ^ []), identity_on_carrier(864 ^ []), 869 ^ []) = apply(identity_on_carrier(864 ^ []), 869 ^ []), apply(identity_on_carrier(864 ^ []), 869 ^ []) = apply(identity_relation(the_carrier(864 ^ [])), 869 ^ [])],extension(10 ^ 2,bind([[_144996, _144998, _145000], [apply(identity_relation(the_carrier(864 ^ [])), 869 ^ []), apply(identity_on_carrier(864 ^ []), 869 ^ []), apply_as_element(the_carrier(864 ^ []), the_carrier(864 ^ []), identity_on_carrier(864 ^ []), 869 ^ [])]]))).
% 265.51/256.84  ncf('1.1.1.1',plain,[-(apply_as_element(the_carrier(864 ^ []), the_carrier(864 ^ []), identity_on_carrier(864 ^ []), 869 ^ []) = apply(identity_on_carrier(864 ^ []), 869 ^ [])), -(empty(the_carrier(864 ^ []))), function(identity_on_carrier(864 ^ [])), quasi_total(identity_on_carrier(864 ^ []), the_carrier(864 ^ []), the_carrier(864 ^ [])), relation_of2(identity_on_carrier(864 ^ []), the_carrier(864 ^ []), the_carrier(864 ^ [])), element(869 ^ [], the_carrier(864 ^ []))],extension(753 ^ 3,bind([[_168974, _168976, _168978, _168980], [869 ^ [], identity_on_carrier(864 ^ []), the_carrier(864 ^ []), the_carrier(864 ^ [])]]))).
% 265.51/256.84  ncf('1.1.1.1.1',plain,[empty(the_carrier(864 ^ [])), -(empty_carrier(864 ^ [])), one_sorted_str(864 ^ [])],extension(622 ^ 4,bind([[_164319], [864 ^ []]]))).
% 265.51/256.84  ncf('1.1.1.1.1.1',plain,[empty_carrier(864 ^ [])],extension(866 ^ 5)).
% 265.51/256.84  ncf('1.1.1.1.1.2',plain,[-(one_sorted_str(864 ^ []))],extension(868 ^ 5)).
% 265.51/256.84  ncf('1.1.1.1.2',plain,[-(function(identity_on_carrier(864 ^ []))), one_sorted_str(864 ^ [])],extension(548 ^ 4,bind([[_162088], [864 ^ []]]))).
% 265.51/256.84  ncf('1.1.1.1.2.1',plain,[-(one_sorted_str(864 ^ []))],extension(868 ^ 5)).
% 265.51/256.84  ncf('1.1.1.1.3',plain,[-(quasi_total(identity_on_carrier(864 ^ []), the_carrier(864 ^ []), the_carrier(864 ^ []))), one_sorted_str(864 ^ [])],extension(548 ^ 4,bind([[_162088], [864 ^ []]]))).
% 265.51/256.84  ncf('1.1.1.1.3.1',plain,[-(one_sorted_str(864 ^ []))],extension(868 ^ 5)).
% 265.51/256.84  ncf('1.1.1.1.4',plain,[-(relation_of2(identity_on_carrier(864 ^ []), the_carrier(864 ^ []), the_carrier(864 ^ []))), relation_of2_as_subset(identity_on_carrier(864 ^ []), the_carrier(864 ^ []), the_carrier(864 ^ []))],extension(775 ^ 4,bind([[_169646, _169648, _169650], [identity_on_carrier(864 ^ []), the_carrier(864 ^ []), the_carrier(864 ^ [])]]))).
% 265.51/256.84  ncf('1.1.1.1.4.1',plain,[-(relation_of2_as_subset(identity_on_carrier(864 ^ []), the_carrier(864 ^ []), the_carrier(864 ^ []))), one_sorted_str(864 ^ [])],extension(548 ^ 5,bind([[_162088], [864 ^ []]]))).
% 265.51/256.84  ncf('1.1.1.1.4.1.1',plain,[-(one_sorted_str(864 ^ []))],extension(868 ^ 6)).
% 265.51/256.84  ncf('1.1.1.1.5',plain,[-(element(869 ^ [], the_carrier(864 ^ [])))],extension(871 ^ 4)).
% 265.51/256.84  ncf('1.1.1.2',plain,[-(apply(identity_on_carrier(864 ^ []), 869 ^ []) = apply(identity_relation(the_carrier(864 ^ [])), 869 ^ [])), apply(identity_on_carrier(864 ^ []), 869 ^ []) = apply(identity_as_relation_of(the_carrier(864 ^ [])), 869 ^ []), apply(identity_as_relation_of(the_carrier(864 ^ [])), 869 ^ []) = apply(identity_relation(the_carrier(864 ^ [])), 869 ^ [])],extension(10 ^ 3,bind([[_144996, _144998, _145000], [apply(identity_relation(the_carrier(864 ^ [])), 869 ^ []), apply(identity_as_relation_of(the_carrier(864 ^ [])), 869 ^ []), apply(identity_on_carrier(864 ^ []), 869 ^ [])]]))).
% 265.51/256.84  ncf('1.1.1.2.1',plain,[-(apply(identity_on_carrier(864 ^ []), 869 ^ []) = apply(identity_as_relation_of(the_carrier(864 ^ [])), 869 ^ [])), identity_on_carrier(864 ^ []) = identity_as_relation_of(the_carrier(864 ^ [])), 869 ^ [] = 869 ^ []],extension(286 ^ 4,bind([[_153916, _153918, _153920, _153922], [869 ^ [], 869 ^ [], identity_as_relation_of(the_carrier(864 ^ [])), identity_on_carrier(864 ^ [])]]))).
% 265.51/256.84  ncf('1.1.1.2.1.1',plain,[-(identity_on_carrier(864 ^ []) = identity_as_relation_of(the_carrier(864 ^ []))), one_sorted_str(864 ^ [])],extension(512 ^ 5,bind([[_161183], [864 ^ []]]))).
% 265.51/256.84  ncf('1.1.1.2.1.1.1',plain,[-(one_sorted_str(864 ^ []))],extension(868 ^ 6)).
% 265.51/256.84  ncf('1.1.1.2.1.2',plain,[-(869 ^ [] = 869 ^ [])],extension(2 ^ 5,bind([[_144685], [869 ^ []]]))).
% 265.51/256.84  ncf('1.1.1.2.2',plain,[-(apply(identity_as_relation_of(the_carrier(864 ^ [])), 869 ^ []) = apply(identity_relation(the_carrier(864 ^ [])), 869 ^ [])), identity_as_relation_of(the_carrier(864 ^ [])) = identity_relation(the_carrier(864 ^ [])), 869 ^ [] = 869 ^ []],extension(286 ^ 4,bind([[_153916, _153918, _153920, _153922], [869 ^ [], 869 ^ [], identity_relation(the_carrier(864 ^ [])), identity_as_relation_of(the_carrier(864 ^ []))]]))).
% 265.51/256.84  ncf('1.1.1.2.2.1',plain,[-(identity_as_relation_of(the_carrier(864 ^ [])) = identity_relation(the_carrier(864 ^ [])))],extension(751 ^ 5,bind([[_168835], [the_carrier(864 ^ [])]]))).
% 265.51/256.84  ncf('1.1.1.2.2.2',plain,[-(869 ^ [] = 869 ^ [])],extension(2 ^ 5,bind([[_144685], [869 ^ []]]))).
% 265.51/256.84  ncf('1.1.2',plain,[-(apply(identity_relation(the_carrier(864 ^ [])), 869 ^ []) = 869 ^ []), in(869 ^ [], the_carrier(864 ^ []))],extension(805 ^ 2,bind([[_170642, _170644], [869 ^ [], the_carrier(864 ^ [])]]))).
% 265.51/256.84  ncf('1.1.2.1',plain,[-(in(869 ^ [], the_carrier(864 ^ []))), element(869 ^ [], the_carrier(864 ^ [])), -(empty(the_carrier(864 ^ [])))],extension(795 ^ 3,bind([[_170344, _170346], [the_carrier(864 ^ []), 869 ^ []]]))).
% 265.51/256.84  ncf('1.1.2.1.1',plain,[-(element(869 ^ [], the_carrier(864 ^ [])))],extension(871 ^ 4)).
% 265.51/256.84  ncf('1.1.2.1.2',plain,[empty(the_carrier(864 ^ [])), -(empty_carrier(864 ^ [])), one_sorted_str(864 ^ [])],extension(622 ^ 4,bind([[_164319], [864 ^ []]]))).
% 265.51/256.84  ncf('1.1.2.1.2.1',plain,[empty_carrier(864 ^ [])],extension(866 ^ 5)).
% 265.51/256.84  ncf('1.1.2.1.2.2',plain,[-(one_sorted_str(864 ^ []))],extension(868 ^ 5)).
% 265.51/256.84  %-----------------------------------------------------
% 265.51/256.84  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------