%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SEU340+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n027.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 12:03:12 EDT 2023

% Result   : Theorem 98.54s 95.47s
% Output   : Proof 98.54s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.12  % Problem  : SEU340+1 : TPTP v8.1.2. Released v3.3.0.
% 0.02/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n027.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 13:41:50 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 98.54/95.47  
% 98.54/95.47  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 98.54/95.47  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 98.54/95.47  %-----------------------------------------------------
% 98.54/95.47  ncf(matrix, plain, [(578 ^ _123767) ^ [] : [-(element(576 ^ [], the_carrier(571 ^ [])))], (586 ^ _123767) ^ [] : [-(related(571 ^ [], 576 ^ [], 579 ^ []))], (573 ^ _123767) ^ [] : [-(transitive_relstr(571 ^ []))], (588 ^ _123767) ^ [] : [-(related(571 ^ [], 579 ^ [], 582 ^ []))], (581 ^ _123767) ^ [] : [-(element(579 ^ [], the_carrier(571 ^ [])))], (584 ^ _123767) ^ [] : [-(element(582 ^ [], the_carrier(571 ^ [])))], (590 ^ _123767) ^ [] : [related(571 ^ [], 576 ^ [], 582 ^ [])], (575 ^ _123767) ^ [] : [-(rel_str(571 ^ []))], !, (476 ^ _104628) ^ [_120343, _120345, _120347] : [relation_of2(_120343, _120347, _120345), -(relation_of2_as_subset(_120343, _120347, _120345))], (4 ^ _104628) ^ [_104859, _104861] : [_104861 = _104859, -(_104859 = _104861)], (228 ^ _104628) ^ [_112173, _112175] : [_112175 = _112173, -(the_carrier(_112175) = the_carrier(_112173))], (381 ^ _104628) ^ [] : [true___, -(true___)], (192 ^ _104628) ^ [_110926, _110928, _110930, _110932] : [-(unordered_pair(_110932, _110928) = unordered_pair(_110930, _110926)), _110932 = _110930, _110928 = _110926], (427 ^ _104628) ^ [_118550] : [-(element(425 ^ [_118550], _118550))], (432 ^ _104628) ^ [_118776] : [empty(powerset(_118776))], (180 ^ _104628) ^ [_110462, _110464] : [_110464 = _110462, -(the_InternalRel(_110464) = the_InternalRel(_110462))], (222 ^ _104628) ^ [_111975, _111977] : [_111977 = _111975, -(powerset(_111977) = powerset(_111975))], (2 ^ _104628) ^ [_104752] : [-(_104752 = _104752)], (468 ^ _104628) ^ [] : [empty(466 ^ [])], (530 ^ _104628) ^ [_122247, _122249, _122251] : [-(element(_122251, _122247)), in(_122251, _122249), element(_122249, powerset(_122247))], (460 ^ _104628) ^ [] : [-(empty(458 ^ []))], (104 ^ _104628) ^ [_108100, _108102, _108104, _108106] : [-(in(_108104, _108100)), in(_108106, _108102), _108106 = _108104, _108102 = _108100], (508 ^ _104628) ^ [_121524, _121526] : [element(_121526, _121524), -(empty(_121524)), -(in(_121526, _121524))], (484 ^ _104628) ^ [_120716, _120718, _120720, _120722] : [in(ordered_pair(_120722, _120720), cartesian_product2(_120718, _120716)), 487 ^ _104628 : [(490 ^ _104628) ^ [] : [-(in(_120720, _120716))], (488 ^ _104628) ^ [] : [-(in(_120722, _120718))]]], (421 ^ _104628) ^ [] : [-(one_sorted_str(419 ^ []))], (434 ^ _104628) ^ [] : [-(empty(empty_set))], (430 ^ _104628) ^ [_118689, _118691] : [-(relation_of2_as_subset(428 ^ [_118689, _118691], _118691, _118689))], (138 ^ _104628) ^ [_109106, _109108] : [-(rel_str(_109106)), _109108 = _109106, rel_str(_109108)], (399 ^ _104628) ^ [_117669, _117671, _117673] : [relation_of2_as_subset(_117669, _117673, _117671), -(element(_117669, powerset(cartesian_product2(_117673, _117671))))], (10 ^ _104628) ^ [_105063, _105065, _105067] : [-(_105067 = _105063), _105067 = _105065, _105065 = _105063], (524 ^ _104628) ^ [_122017, _122019] : [subset(_122019, _122017), -(element(_122019, powerset(_122017)))], (118 ^ _104628) ^ [_108516, _108518] : [-(empty(_108516)), _108518 = _108516, empty(_108518)], (72 ^ _104628) ^ [_107075, _107077, _107079, _107081, _107083, _107085] : [-(relation_of2(_107083, _107079, _107075)), relation_of2(_107085, _107081, _107077), _107085 = _107083, _107081 = _107079, _107077 = _107075], (375 ^ _104628) ^ [_117098] : [rel_str(_117098), -(one_sorted_str(_117098))], (248 ^ _104628) ^ [_112984] : [rel_str(_112984), 251 ^ _104628 : [(258 ^ _104628) ^ [] : [is_transitive_in(the_InternalRel(_112984), the_carrier(_112984)), -(transitive_relstr(_112984))], (252 ^ _104628) ^ [] : [transitive_relstr(_112984), -(is_transitive_in(the_InternalRel(_112984), the_carrier(_112984)))]]], (315 ^ _104628) ^ [_115571] : [rel_str(_115571), 318 ^ _104628 : [(319 ^ _104628) ^ [_115729] : [element(_115729, the_carrier(_115571)), 322 ^ _104628 : [(323 ^ _104628) ^ [_115886] : [element(_115886, the_carrier(_115571)), 326 ^ _104628 : [(333 ^ _104628) ^ [] : [in(ordered_pair(_115729, _115886), the_InternalRel(_115571)), -(related(_115571, _115729, _115886))], (327 ^ _104628) ^ [] : [related(_115571, _115729, _115886), -(in(ordered_pair(_115729, _115886), the_InternalRel(_115571)))]]]]]]], (351 ^ _104628) ^ [] : [true___, -(true___)], (234 ^ _104628) ^ [_112449, _112451] : [in(_112451, _112449), in(_112449, _112451)], (246 ^ _104628) ^ [_112883, _112885] : [-(unordered_pair(_112885, _112883) = unordered_pair(_112883, _112885))], (44 ^ _104628) ^ [_106115, _106117] : [-(one_sorted_str(_106115)), _106117 = _106115, one_sorted_str(_106117)], (502 ^ _104628) ^ [_121314, _121316] : [in(_121316, _121314), -(element(_121316, _121314))], (264 ^ _104628) ^ [_113420, _113422] : [-(ordered_pair(_113422, _113420) = unordered_pair(unordered_pair(_113422, _113420), singleton(_113422)))], (148 ^ _104628) ^ [_109429, _109431, _109433, _109435] : [-(element(_109433, _109429)), element(_109435, _109431), _109435 = _109433, _109431 = _109429], (186 ^ _104628) ^ [_110680, _110682] : [_110682 = _110680, -(singleton(_110682) = singleton(_110680))], (387 ^ _104628) ^ [] : [true___, -(true___)], (436 ^ _104628) ^ [_118907] : [empty(singleton(_118907))], (20 ^ _104628) ^ [_105376, _105378] : [-(relation(_105376)), _105378 = _105376, relation(_105378)], (450 ^ _104628) ^ [_119402] : [-(empty(_119402)), 454 ^ _104628 : [(457 ^ _104628) ^ [] : [empty(453 ^ [_119402])], (455 ^ _104628) ^ [] : [-(element(453 ^ [_119402], powerset(_119402)))]]], (470 ^ _104628) ^ [_120171, _120173, _120175] : [relation_of2_as_subset(_120171, _120175, _120173), -(relation_of2(_120171, _120175, _120173))], (202 ^ _104628) ^ [_111285, _111287, _111289, _111291] : [-(ordered_pair(_111291, _111287) = ordered_pair(_111289, _111285)), _111291 = _111289, _111287 = _111285], (240 ^ _104628) ^ [_112674, _112676, _112678] : [element(_112674, powerset(cartesian_product2(_112678, _112676))), -(relation(_112674))], (54 ^ _104628) ^ [_106466, _106468, _106470, _106472, _106474, _106476] : [-(relation_of2_as_subset(_106474, _106470, _106466)), relation_of2_as_subset(_106476, _106472, _106468), _106476 = _106474, _106472 = _106470, _106468 = _106466], (345 ^ _104628) ^ [] : [true___, -(true___)], (465 ^ _104628) ^ [_119925] : [-(empty(461 ^ [_119925]))], (550 ^ _104628) ^ [_122870] : [empty(_122870), -(_122870 = empty_set)], (411 ^ _104628) ^ [] : [true___, -(true___)], (393 ^ _104628) ^ [] : [true___, -(true___)], (440 ^ _104628) ^ [_119110, _119112] : [empty(cartesian_product2(_119112, _119110)), -(empty(_119112)), -(empty(_119110))], (492 ^ _104628) ^ [_120981, _120983, _120985, _120987] : [-(in(ordered_pair(_120987, _120985), cartesian_product2(_120983, _120981))), in(_120987, _120983), in(_120985, _120981)], (357 ^ _104628) ^ [] : [true___, -(true___)], (212 ^ _104628) ^ [_111644, _111646, _111648, _111650] : [-(cartesian_product2(_111650, _111646) = cartesian_product2(_111648, _111644)), _111650 = _111648, _111646 = _111644], (128 ^ _104628) ^ [_108811, _108813] : [-(transitive_relstr(_108811)), _108813 = _108811, transitive_relstr(_108813)], (438 ^ _104628) ^ [_118999, _119001] : [empty(unordered_pair(_119001, _118999))], (339 ^ _104628) ^ [] : [true___, -(true___)], (540 ^ _104628) ^ [_122574, _122576, _122578] : [in(_122578, _122576), element(_122576, powerset(_122574)), empty(_122574)], (363 ^ _104628) ^ [] : [true___, -(true___)], (518 ^ _104628) ^ [_121851, _121853] : [element(_121853, powerset(_121851)), -(subset(_121853, _121851))], (556 ^ _104628) ^ [_123072, _123074] : [in(_123074, _123072), empty(_123072)], (369 ^ _104628) ^ [] : [true___, -(true___)], (482 ^ _104628) ^ [_120550, _120552] : [-(subset(_120552, _120552))], (30 ^ _104628) ^ [_105699, _105701, _105703, _105705] : [-(is_transitive_in(_105703, _105699)), is_transitive_in(_105705, _105701), _105705 = _105703, _105701 = _105699], (424 ^ _104628) ^ [_118423, _118425] : [-(relation_of2(422 ^ [_118423, _118425], _118425, _118423))], (405 ^ _104628) ^ [_117883] : [rel_str(_117883), -(relation_of2_as_subset(the_InternalRel(_117883), the_carrier(_117883), the_carrier(_117883)))], (266 ^ _104628) ^ [_113526] : [relation(_113526), 269 ^ _104628 : [(270 ^ _104628) ^ [_113740] : [is_transitive_in(_113526, _113740), 273 ^ _104628 : [(274 ^ _104628) ^ [_113950, _113952, _113954] : [-(in(ordered_pair(_113954, _113950), _113526)), in(_113954, _113740), in(_113952, _113740), in(_113950, _113740), in(ordered_pair(_113954, _113952), _113526), in(ordered_pair(_113952, _113950), _113526)]]], (296 ^ _104628) ^ [_114561] : [300 ^ _104628 : [(303 ^ _104628) ^ [] : [-(in(298 ^ [_113526, _114561], _114561))], (301 ^ _104628) ^ [] : [-(in(297 ^ [_113526, _114561], _114561))], (311 ^ _104628) ^ [] : [in(ordered_pair(297 ^ [_113526, _114561], 299 ^ [_113526, _114561]), _113526)], (307 ^ _104628) ^ [] : [-(in(ordered_pair(297 ^ [_113526, _114561], 298 ^ [_113526, _114561]), _113526))], (309 ^ _104628) ^ [] : [-(in(ordered_pair(298 ^ [_113526, _114561], 299 ^ [_113526, _114561]), _113526))], (305 ^ _104628) ^ [] : [-(in(299 ^ [_113526, _114561], _114561))]], -(is_transitive_in(_113526, _114561))]]], (162 ^ _104628) ^ [_109881, _109883, _109885, _109887, _109889, _109891] : [-(related(_109889, _109885, _109881)), related(_109891, _109887, _109883), _109891 = _109889, _109887 = _109885, _109883 = _109881], (463 ^ _104628) ^ [_119874] : [-(element(461 ^ [_119874], powerset(_119874)))], (90 ^ _104628) ^ [_107656, _107658, _107660, _107662] : [-(subset(_107660, _107656)), subset(_107662, _107658), _107662 = _107660, _107658 = _107656], (418 ^ _104628) ^ [] : [-(rel_str(416 ^ []))], (562 ^ _104628) ^ [_123259, _123261] : [empty(_123261), -(_123261 = _123259), empty(_123259)]], input).
% 98.54/95.47  ncf('1',plain,[-(related(571 ^ [], 576 ^ [], 579 ^ []))],start(586 ^ 0)).
% 98.54/95.47  ncf('1.1',plain,[related(571 ^ [], 576 ^ [], 579 ^ []), 327 : -(in(ordered_pair(576 ^ [], 579 ^ []), the_InternalRel(571 ^ []))), 327 : element(579 ^ [], the_carrier(571 ^ [])), 323 : element(576 ^ [], the_carrier(571 ^ [])), 319 : rel_str(571 ^ [])],extension(315 ^ 1,bind([[_115571, _115729, _115886], [571 ^ [], 576 ^ [], 579 ^ []]]))).
% 98.54/95.47  ncf('1.1.1',plain,[in(ordered_pair(576 ^ [], 579 ^ []), the_InternalRel(571 ^ [])), 274 : -(in(ordered_pair(576 ^ [], 582 ^ []), the_InternalRel(571 ^ []))), 274 : in(576 ^ [], the_carrier(571 ^ [])), 274 : in(579 ^ [], the_carrier(571 ^ [])), 274 : in(582 ^ [], the_carrier(571 ^ [])), 274 : in(ordered_pair(579 ^ [], 582 ^ []), the_InternalRel(571 ^ [])), 274 : is_transitive_in(the_InternalRel(571 ^ []), the_carrier(571 ^ [])), 270 : relation(the_InternalRel(571 ^ []))],extension(266 ^ 8,bind([[_113526, _113740, _113950, _113952, _113954], [the_InternalRel(571 ^ []), the_carrier(571 ^ []), 582 ^ [], 579 ^ [], 576 ^ []]]))).
% 98.54/95.47  ncf('1.1.1.1',plain,[in(ordered_pair(576 ^ [], 582 ^ []), the_InternalRel(571 ^ [])), 333 : -(related(571 ^ [], 576 ^ [], 582 ^ [])), 333 : element(582 ^ [], the_carrier(571 ^ []))],extension(323 ^ 13,bind([[_115886], [582 ^ []]]))).
% 98.54/95.47  ncf('1.1.1.1.1',plain,[related(571 ^ [], 576 ^ [], 582 ^ [])],extension(590 ^ 16)).
% 98.54/95.47  ncf('1.1.1.1.2',plain,[-(element(582 ^ [], the_carrier(571 ^ [])))],extension(584 ^ 14)).
% 98.54/95.47  ncf('1.1.1.2',plain,[-(in(576 ^ [], the_carrier(571 ^ []))), in(ordered_pair(576 ^ [], 579 ^ []), cartesian_product2(the_carrier(571 ^ []), the_carrier(571 ^ [])))],extension(484 ^ 13,bind([[_120716, _120718, _120720, _120722], [the_carrier(571 ^ []), the_carrier(571 ^ []), 579 ^ [], 576 ^ []]]))).
% 98.54/95.47  ncf('1.1.1.2.1',plain,[-(in(ordered_pair(576 ^ [], 579 ^ []), cartesian_product2(the_carrier(571 ^ []), the_carrier(571 ^ [])))), element(ordered_pair(576 ^ [], 579 ^ []), cartesian_product2(the_carrier(571 ^ []), the_carrier(571 ^ []))), -(empty(cartesian_product2(the_carrier(571 ^ []), the_carrier(571 ^ []))))],extension(508 ^ 14,bind([[_121524, _121526], [cartesian_product2(the_carrier(571 ^ []), the_carrier(571 ^ [])), ordered_pair(576 ^ [], 579 ^ [])]]))).
% 98.54/95.47  ncf('1.1.1.2.1.1',plain,[-(element(ordered_pair(576 ^ [], 579 ^ []), cartesian_product2(the_carrier(571 ^ []), the_carrier(571 ^ [])))), in(ordered_pair(576 ^ [], 579 ^ []), the_InternalRel(571 ^ [])), element(the_InternalRel(571 ^ []), powerset(cartesian_product2(the_carrier(571 ^ []), the_carrier(571 ^ []))))],extension(530 ^ 15,bind([[_122247, _122249, _122251], [cartesian_product2(the_carrier(571 ^ []), the_carrier(571 ^ [])), the_InternalRel(571 ^ []), ordered_pair(576 ^ [], 579 ^ [])]]))).
% 98.54/95.48  ncf('1.1.1.2.1.1.1',plain,[-(in(ordered_pair(576 ^ [], 579 ^ []), the_InternalRel(571 ^ [])))],reduction('1.1')).
% 98.54/95.48  ncf('1.1.1.2.1.1.2',plain,[-(element(the_InternalRel(571 ^ []), powerset(cartesian_product2(the_carrier(571 ^ []), the_carrier(571 ^ []))))), relation_of2_as_subset(the_InternalRel(571 ^ []), the_carrier(571 ^ []), the_carrier(571 ^ []))],extension(399 ^ 16,bind([[_117669, _117671, _117673], [the_InternalRel(571 ^ []), the_carrier(571 ^ []), the_carrier(571 ^ [])]]))).
% 98.54/95.48  ncf('1.1.1.2.1.1.2.1',plain,[-(relation_of2_as_subset(the_InternalRel(571 ^ []), the_carrier(571 ^ []), the_carrier(571 ^ []))), rel_str(571 ^ [])],extension(405 ^ 17,bind([[_117883], [571 ^ []]]))).
% 98.54/95.48  ncf('1.1.1.2.1.1.2.1.1',plain,[-(rel_str(571 ^ []))],extension(575 ^ 18)).
% 98.54/95.48  ncf('1.1.1.2.1.2',plain,[empty(cartesian_product2(the_carrier(571 ^ []), the_carrier(571 ^ []))), in(ordered_pair(576 ^ [], 579 ^ []), the_InternalRel(571 ^ [])), element(the_InternalRel(571 ^ []), powerset(cartesian_product2(the_carrier(571 ^ []), the_carrier(571 ^ []))))],extension(540 ^ 15,bind([[_122574, _122576, _122578], [cartesian_product2(the_carrier(571 ^ []), the_carrier(571 ^ [])), the_InternalRel(571 ^ []), ordered_pair(576 ^ [], 579 ^ [])]]))).
% 98.54/95.48  ncf('1.1.1.2.1.2.1',plain,[-(in(ordered_pair(576 ^ [], 579 ^ []), the_InternalRel(571 ^ [])))],reduction('1.1')).
% 98.54/95.48  ncf('1.1.1.2.1.2.2',plain,[-(element(the_InternalRel(571 ^ []), powerset(cartesian_product2(the_carrier(571 ^ []), the_carrier(571 ^ []))))), relation_of2_as_subset(the_InternalRel(571 ^ []), the_carrier(571 ^ []), the_carrier(571 ^ []))],extension(399 ^ 16,bind([[_117669, _117671, _117673], [the_InternalRel(571 ^ []), the_carrier(571 ^ []), the_carrier(571 ^ [])]]))).
% 98.54/95.48  ncf('1.1.1.2.1.2.2.1',plain,[-(relation_of2_as_subset(the_InternalRel(571 ^ []), the_carrier(571 ^ []), the_carrier(571 ^ []))), rel_str(571 ^ [])],extension(405 ^ 17,bind([[_117883], [571 ^ []]]))).
% 98.54/95.48  ncf('1.1.1.2.1.2.2.1.1',plain,[-(rel_str(571 ^ []))],extension(575 ^ 18)).
% 98.54/95.48  ncf('1.1.1.3',plain,[-(in(579 ^ [], the_carrier(571 ^ []))), in(ordered_pair(576 ^ [], 579 ^ []), cartesian_product2(the_carrier(571 ^ []), the_carrier(571 ^ [])))],extension(484 ^ 13,bind([[_120716, _120718, _120720, _120722], [the_carrier(571 ^ []), the_carrier(571 ^ []), 579 ^ [], 576 ^ []]]))).
% 98.54/95.48  ncf('1.1.1.3.1',plain,[-(in(ordered_pair(576 ^ [], 579 ^ []), cartesian_product2(the_carrier(571 ^ []), the_carrier(571 ^ [])))), element(ordered_pair(576 ^ [], 579 ^ []), cartesian_product2(the_carrier(571 ^ []), the_carrier(571 ^ []))), -(empty(cartesian_product2(the_carrier(571 ^ []), the_carrier(571 ^ []))))],extension(508 ^ 14,bind([[_121524, _121526], [cartesian_product2(the_carrier(571 ^ []), the_carrier(571 ^ [])), ordered_pair(576 ^ [], 579 ^ [])]]))).
% 98.54/95.48  ncf('1.1.1.3.1.1',plain,[-(element(ordered_pair(576 ^ [], 579 ^ []), cartesian_product2(the_carrier(571 ^ []), the_carrier(571 ^ [])))), in(ordered_pair(576 ^ [], 579 ^ []), the_InternalRel(571 ^ [])), element(the_InternalRel(571 ^ []), powerset(cartesian_product2(the_carrier(571 ^ []), the_carrier(571 ^ []))))],extension(530 ^ 15,bind([[_122247, _122249, _122251], [cartesian_product2(the_carrier(571 ^ []), the_carrier(571 ^ [])), the_InternalRel(571 ^ []), ordered_pair(576 ^ [], 579 ^ [])]]))).
% 98.54/95.48  ncf('1.1.1.3.1.1.1',plain,[-(in(ordered_pair(576 ^ [], 579 ^ []), the_InternalRel(571 ^ [])))],reduction('1.1')).
% 98.54/95.48  ncf('1.1.1.3.1.1.2',plain,[-(element(the_InternalRel(571 ^ []), powerset(cartesian_product2(the_carrier(571 ^ []), the_carrier(571 ^ []))))), relation_of2_as_subset(the_InternalRel(571 ^ []), the_carrier(571 ^ []), the_carrier(571 ^ []))],extension(399 ^ 16,bind([[_117669, _117671, _117673], [the_InternalRel(571 ^ []), the_carrier(571 ^ []), the_carrier(571 ^ [])]]))).
% 98.54/95.48  ncf('1.1.1.3.1.1.2.1',plain,[-(relation_of2_as_subset(the_InternalRel(571 ^ []), the_carrier(571 ^ []), the_carrier(571 ^ []))), rel_str(571 ^ [])],extension(405 ^ 17,bind([[_117883], [571 ^ []]]))).
% 98.54/95.48  ncf('1.1.1.3.1.1.2.1.1',plain,[-(rel_str(571 ^ []))],extension(575 ^ 18)).
% 98.54/95.48  ncf('1.1.1.3.1.2',plain,[empty(cartesian_product2(the_carrier(571 ^ []), the_carrier(571 ^ []))), in(ordered_pair(576 ^ [], 579 ^ []), the_InternalRel(571 ^ [])), element(the_InternalRel(571 ^ []), powerset(cartesian_product2(the_carrier(571 ^ []), the_carrier(571 ^ []))))],extension(540 ^ 15,bind([[_122574, _122576, _122578], [cartesian_product2(the_carrier(571 ^ []), the_carrier(571 ^ [])), the_InternalRel(571 ^ []), ordered_pair(576 ^ [], 579 ^ [])]]))).
% 98.54/95.48  ncf('1.1.1.3.1.2.1',plain,[-(in(ordered_pair(576 ^ [], 579 ^ []), the_InternalRel(571 ^ [])))],reduction('1.1')).
% 98.54/95.48  ncf('1.1.1.3.1.2.2',plain,[-(element(the_InternalRel(571 ^ []), powerset(cartesian_product2(the_carrier(571 ^ []), the_carrier(571 ^ []))))), relation_of2_as_subset(the_InternalRel(571 ^ []), the_carrier(571 ^ []), the_carrier(571 ^ []))],extension(399 ^ 16,bind([[_117669, _117671, _117673], [the_InternalRel(571 ^ []), the_carrier(571 ^ []), the_carrier(571 ^ [])]]))).
% 98.54/95.48  ncf('1.1.1.3.1.2.2.1',plain,[-(relation_of2_as_subset(the_InternalRel(571 ^ []), the_carrier(571 ^ []), the_carrier(571 ^ []))), rel_str(571 ^ [])],extension(405 ^ 17,bind([[_117883], [571 ^ []]]))).
% 98.54/95.48  ncf('1.1.1.3.1.2.2.1.1',plain,[-(rel_str(571 ^ []))],extension(575 ^ 18)).
% 98.54/95.48  ncf('1.1.1.4',plain,[-(in(582 ^ [], the_carrier(571 ^ []))), in(ordered_pair(579 ^ [], 582 ^ []), cartesian_product2(the_carrier(571 ^ []), the_carrier(571 ^ [])))],extension(484 ^ 13,bind([[_120716, _120718, _120720, _120722], [the_carrier(571 ^ []), the_carrier(571 ^ []), 582 ^ [], 579 ^ []]]))).
% 98.54/95.48  ncf('1.1.1.4.1',plain,[-(in(ordered_pair(579 ^ [], 582 ^ []), cartesian_product2(the_carrier(571 ^ []), the_carrier(571 ^ [])))), element(ordered_pair(579 ^ [], 582 ^ []), cartesian_product2(the_carrier(571 ^ []), the_carrier(571 ^ []))), -(empty(cartesian_product2(the_carrier(571 ^ []), the_carrier(571 ^ []))))],extension(508 ^ 14,bind([[_121524, _121526], [cartesian_product2(the_carrier(571 ^ []), the_carrier(571 ^ [])), ordered_pair(579 ^ [], 582 ^ [])]]))).
% 98.54/95.48  ncf('1.1.1.4.1.1',plain,[-(element(ordered_pair(579 ^ [], 582 ^ []), cartesian_product2(the_carrier(571 ^ []), the_carrier(571 ^ [])))), in(ordered_pair(579 ^ [], 582 ^ []), the_InternalRel(571 ^ [])), element(the_InternalRel(571 ^ []), powerset(cartesian_product2(the_carrier(571 ^ []), the_carrier(571 ^ []))))],extension(530 ^ 15,bind([[_122247, _122249, _122251], [cartesian_product2(the_carrier(571 ^ []), the_carrier(571 ^ [])), the_InternalRel(571 ^ []), ordered_pair(579 ^ [], 582 ^ [])]]))).
% 98.54/95.48  ncf('1.1.1.4.1.1.1',plain,[-(in(ordered_pair(579 ^ [], 582 ^ []), the_InternalRel(571 ^ []))), 327 : related(571 ^ [], 579 ^ [], 582 ^ []), 327 : element(582 ^ [], the_carrier(571 ^ [])), 323 : element(579 ^ [], the_carrier(571 ^ []))],extension(319 ^ 16,bind([[_115729, _115886], [579 ^ [], 582 ^ []]]))).
% 98.54/95.48  ncf('1.1.1.4.1.1.1.1',plain,[-(related(571 ^ [], 579 ^ [], 582 ^ []))],extension(588 ^ 21)).
% 98.54/95.48  ncf('1.1.1.4.1.1.1.2',plain,[-(element(582 ^ [], the_carrier(571 ^ [])))],extension(584 ^ 19)).
% 98.54/95.48  ncf('1.1.1.4.1.1.1.3',plain,[-(element(579 ^ [], the_carrier(571 ^ [])))],extension(581 ^ 17)).
% 98.54/95.48  ncf('1.1.1.4.1.1.2',plain,[-(element(the_InternalRel(571 ^ []), powerset(cartesian_product2(the_carrier(571 ^ []), the_carrier(571 ^ []))))), relation_of2_as_subset(the_InternalRel(571 ^ []), the_carrier(571 ^ []), the_carrier(571 ^ []))],extension(399 ^ 16,bind([[_117669, _117671, _117673], [the_InternalRel(571 ^ []), the_carrier(571 ^ []), the_carrier(571 ^ [])]]))).
% 98.54/95.48  ncf('1.1.1.4.1.1.2.1',plain,[-(relation_of2_as_subset(the_InternalRel(571 ^ []), the_carrier(571 ^ []), the_carrier(571 ^ []))), rel_str(571 ^ [])],extension(405 ^ 17,bind([[_117883], [571 ^ []]]))).
% 98.54/95.48  ncf('1.1.1.4.1.1.2.1.1',plain,[-(rel_str(571 ^ []))],extension(575 ^ 18)).
% 98.54/95.48  ncf('1.1.1.4.1.2',plain,[empty(cartesian_product2(the_carrier(571 ^ []), the_carrier(571 ^ []))), in(ordered_pair(576 ^ [], 579 ^ []), the_InternalRel(571 ^ [])), element(the_InternalRel(571 ^ []), powerset(cartesian_product2(the_carrier(571 ^ []), the_carrier(571 ^ []))))],extension(540 ^ 15,bind([[_122574, _122576, _122578], [cartesian_product2(the_carrier(571 ^ []), the_carrier(571 ^ [])), the_InternalRel(571 ^ []), ordered_pair(576 ^ [], 579 ^ [])]]))).
% 98.54/95.48  ncf('1.1.1.4.1.2.1',plain,[-(in(ordered_pair(576 ^ [], 579 ^ []), the_InternalRel(571 ^ [])))],reduction('1.1')).
% 98.54/95.48  ncf('1.1.1.4.1.2.2',plain,[-(element(the_InternalRel(571 ^ []), powerset(cartesian_product2(the_carrier(571 ^ []), the_carrier(571 ^ []))))), relation_of2_as_subset(the_InternalRel(571 ^ []), the_carrier(571 ^ []), the_carrier(571 ^ []))],extension(399 ^ 16,bind([[_117669, _117671, _117673], [the_InternalRel(571 ^ []), the_carrier(571 ^ []), the_carrier(571 ^ [])]]))).
% 98.54/95.48  ncf('1.1.1.4.1.2.2.1',plain,[-(relation_of2_as_subset(the_InternalRel(571 ^ []), the_carrier(571 ^ []), the_carrier(571 ^ []))), rel_str(571 ^ [])],extension(405 ^ 17,bind([[_117883], [571 ^ []]]))).
% 98.54/95.48  ncf('1.1.1.4.1.2.2.1.1',plain,[-(rel_str(571 ^ []))],extension(575 ^ 18)).
% 98.54/95.48  ncf('1.1.1.5',plain,[-(in(ordered_pair(579 ^ [], 582 ^ []), the_InternalRel(571 ^ []))), in(ordered_pair(ordered_pair(576 ^ [], 579 ^ []), ordered_pair(579 ^ [], 582 ^ [])), cartesian_product2(the_InternalRel(571 ^ []), the_InternalRel(571 ^ [])))],extension(484 ^ 13,bind([[_120716, _120718, _120720, _120722], [the_InternalRel(571 ^ []), the_InternalRel(571 ^ []), ordered_pair(579 ^ [], 582 ^ []), ordered_pair(576 ^ [], 579 ^ [])]]))).
% 98.54/95.48  ncf('1.1.1.5.1',plain,[-(in(ordered_pair(ordered_pair(576 ^ [], 579 ^ []), ordered_pair(579 ^ [], 582 ^ [])), cartesian_product2(the_InternalRel(571 ^ []), the_InternalRel(571 ^ [])))), element(ordered_pair(ordered_pair(576 ^ [], 579 ^ []), ordered_pair(579 ^ [], 582 ^ [])), cartesian_product2(the_InternalRel(571 ^ []), the_InternalRel(571 ^ []))), -(empty(cartesian_product2(the_InternalRel(571 ^ []), the_InternalRel(571 ^ []))))],extension(508 ^ 14,bind([[_121524, _121526], [cartesian_product2(the_InternalRel(571 ^ []), the_InternalRel(571 ^ [])), ordered_pair(ordered_pair(576 ^ [], 579 ^ []), ordered_pair(579 ^ [], 582 ^ []))]]))).
% 98.54/95.48  ncf('1.1.1.5.1.1',plain,[-(element(ordered_pair(ordered_pair(576 ^ [], 579 ^ []), ordered_pair(579 ^ [], 582 ^ [])), cartesian_product2(the_InternalRel(571 ^ []), the_InternalRel(571 ^ [])))), in(ordered_pair(ordered_pair(576 ^ [], 579 ^ []), ordered_pair(579 ^ [], 582 ^ [])), cartesian_product2(the_InternalRel(571 ^ []), the_InternalRel(571 ^ []))), element(cartesian_product2(the_InternalRel(571 ^ []), the_InternalRel(571 ^ [])), powerset(cartesian_product2(the_InternalRel(571 ^ []), the_InternalRel(571 ^ []))))],extension(530 ^ 15,bind([[_122247, _122249, _122251], [cartesian_product2(the_InternalRel(571 ^ []), the_InternalRel(571 ^ [])), cartesian_product2(the_InternalRel(571 ^ []), the_InternalRel(571 ^ [])), ordered_pair(ordered_pair(576 ^ [], 579 ^ []), ordered_pair(579 ^ [], 582 ^ []))]]))).
% 98.54/95.48  ncf('1.1.1.5.1.1.1',plain,[-(in(ordered_pair(ordered_pair(576 ^ [], 579 ^ []), ordered_pair(579 ^ [], 582 ^ [])), cartesian_product2(the_InternalRel(571 ^ []), the_InternalRel(571 ^ [])))), in(ordered_pair(576 ^ [], 579 ^ []), the_InternalRel(571 ^ [])), in(ordered_pair(579 ^ [], 582 ^ []), the_InternalRel(571 ^ []))],extension(492 ^ 16,bind([[_120981, _120983, _120985, _120987], [the_InternalRel(571 ^ []), the_InternalRel(571 ^ []), ordered_pair(579 ^ [], 582 ^ []), ordered_pair(576 ^ [], 579 ^ [])]]))).
% 98.54/95.48  ncf('1.1.1.5.1.1.1.1',plain,[-(in(ordered_pair(576 ^ [], 579 ^ []), the_InternalRel(571 ^ [])))],reduction('1.1')).
% 98.54/95.48  ncf('1.1.1.5.1.1.1.2',plain,[-(in(ordered_pair(579 ^ [], 582 ^ []), the_InternalRel(571 ^ []))), 327 : related(571 ^ [], 579 ^ [], 582 ^ []), 327 : element(582 ^ [], the_carrier(571 ^ [])), 323 : element(579 ^ [], the_carrier(571 ^ []))],extension(319 ^ 17,bind([[_115729, _115886], [579 ^ [], 582 ^ []]]))).
% 98.54/95.48  ncf('1.1.1.5.1.1.1.2.1',plain,[-(related(571 ^ [], 579 ^ [], 582 ^ []))],extension(588 ^ 22)).
% 98.54/95.48  ncf('1.1.1.5.1.1.1.2.2',plain,[-(element(582 ^ [], the_carrier(571 ^ [])))],extension(584 ^ 20)).
% 98.54/95.48  ncf('1.1.1.5.1.1.1.2.3',plain,[-(element(579 ^ [], the_carrier(571 ^ [])))],extension(581 ^ 18)).
% 98.54/95.48  ncf('1.1.1.5.1.1.2',plain,[-(element(cartesian_product2(the_InternalRel(571 ^ []), the_InternalRel(571 ^ [])), powerset(cartesian_product2(the_InternalRel(571 ^ []), the_InternalRel(571 ^ []))))), subset(cartesian_product2(the_InternalRel(571 ^ []), the_InternalRel(571 ^ [])), cartesian_product2(the_InternalRel(571 ^ []), the_InternalRel(571 ^ [])))],extension(524 ^ 16,bind([[_122017, _122019], [cartesian_product2(the_InternalRel(571 ^ []), the_InternalRel(571 ^ [])), cartesian_product2(the_InternalRel(571 ^ []), the_InternalRel(571 ^ []))]]))).
% 98.54/95.48  ncf('1.1.1.5.1.1.2.1',plain,[-(subset(cartesian_product2(the_InternalRel(571 ^ []), the_InternalRel(571 ^ [])), cartesian_product2(the_InternalRel(571 ^ []), the_InternalRel(571 ^ []))))],extension(482 ^ 17,bind([[_120550, _120552], [_77909, cartesian_product2(the_InternalRel(571 ^ []), the_InternalRel(571 ^ []))]]))).
% 98.54/95.48  ncf('1.1.1.5.1.2',plain,[empty(cartesian_product2(the_InternalRel(571 ^ []), the_InternalRel(571 ^ []))), -(empty(the_InternalRel(571 ^ []))), -(empty(the_InternalRel(571 ^ [])))],extension(440 ^ 15,bind([[_119110, _119112], [the_InternalRel(571 ^ []), the_InternalRel(571 ^ [])]]))).
% 98.54/95.48  ncf('1.1.1.5.1.2.1',plain,[empty(the_InternalRel(571 ^ [])), in(ordered_pair(576 ^ [], 579 ^ []), the_InternalRel(571 ^ []))],extension(556 ^ 16,bind([[_123072, _123074], [the_InternalRel(571 ^ []), ordered_pair(576 ^ [], 579 ^ [])]]))).
% 98.54/95.48  ncf('1.1.1.5.1.2.1.1',plain,[-(in(ordered_pair(576 ^ [], 579 ^ []), the_InternalRel(571 ^ [])))],reduction('1.1')).
% 98.54/95.48  ncf('1.1.1.5.1.2.2',plain,[empty(the_InternalRel(571 ^ []))],lemmata('[1, 5, 1, 1, 1].x')).
% 98.54/95.48  ncf('1.1.1.6',plain,[-(is_transitive_in(the_InternalRel(571 ^ []), the_carrier(571 ^ []))), 252 : transitive_relstr(571 ^ []), 252 : rel_str(571 ^ [])],extension(248 ^ 11,bind([[_112984], [571 ^ []]]))).
% 98.54/95.48  ncf('1.1.1.6.1',plain,[-(transitive_relstr(571 ^ []))],extension(573 ^ 14)).
% 98.54/95.48  ncf('1.1.1.6.2',plain,[-(rel_str(571 ^ []))],extension(575 ^ 12)).
% 98.54/95.48  ncf('1.1.1.7',plain,[-(relation(the_InternalRel(571 ^ []))), element(the_InternalRel(571 ^ []), powerset(cartesian_product2(the_carrier(571 ^ []), the_carrier(571 ^ []))))],extension(240 ^ 9,bind([[_112674, _112676, _112678], [the_InternalRel(571 ^ []), the_carrier(571 ^ []), the_carrier(571 ^ [])]]))).
% 98.54/95.48  ncf('1.1.1.7.1',plain,[-(element(the_InternalRel(571 ^ []), powerset(cartesian_product2(the_carrier(571 ^ []), the_carrier(571 ^ []))))), in(the_InternalRel(571 ^ []), powerset(cartesian_product2(the_carrier(571 ^ []), the_carrier(571 ^ [])))), element(powerset(cartesian_product2(the_carrier(571 ^ []), the_carrier(571 ^ []))), powerset(powerset(cartesian_product2(the_carrier(571 ^ []), the_carrier(571 ^ [])))))],extension(530 ^ 10,bind([[_122247, _122249, _122251], [powerset(cartesian_product2(the_carrier(571 ^ []), the_carrier(571 ^ []))), powerset(cartesian_product2(the_carrier(571 ^ []), the_carrier(571 ^ []))), the_InternalRel(571 ^ [])]]))).
% 98.54/95.48  ncf('1.1.1.7.1.1',plain,[-(in(the_InternalRel(571 ^ []), powerset(cartesian_product2(the_carrier(571 ^ []), the_carrier(571 ^ []))))), element(the_InternalRel(571 ^ []), powerset(cartesian_product2(the_carrier(571 ^ []), the_carrier(571 ^ [])))), -(empty(powerset(cartesian_product2(the_carrier(571 ^ []), the_carrier(571 ^ [])))))],extension(508 ^ 11,bind([[_121524, _121526], [powerset(cartesian_product2(the_carrier(571 ^ []), the_carrier(571 ^ []))), the_InternalRel(571 ^ [])]]))).
% 98.54/95.48  ncf('1.1.1.7.1.1.1',plain,[-(element(the_InternalRel(571 ^ []), powerset(cartesian_product2(the_carrier(571 ^ []), the_carrier(571 ^ []))))), relation_of2_as_subset(the_InternalRel(571 ^ []), the_carrier(571 ^ []), the_carrier(571 ^ []))],extension(399 ^ 12,bind([[_117669, _117671, _117673], [the_InternalRel(571 ^ []), the_carrier(571 ^ []), the_carrier(571 ^ [])]]))).
% 98.54/95.48  ncf('1.1.1.7.1.1.1.1',plain,[-(relation_of2_as_subset(the_InternalRel(571 ^ []), the_carrier(571 ^ []), the_carrier(571 ^ []))), rel_str(571 ^ [])],extension(405 ^ 13,bind([[_117883], [571 ^ []]]))).
% 98.54/95.48  ncf('1.1.1.7.1.1.1.1.1',plain,[-(rel_str(571 ^ []))],extension(575 ^ 14)).
% 98.54/95.48  ncf('1.1.1.7.1.1.2',plain,[empty(powerset(cartesian_product2(the_carrier(571 ^ []), the_carrier(571 ^ []))))],extension(432 ^ 12,bind([[_118776], [cartesian_product2(the_carrier(571 ^ []), the_carrier(571 ^ []))]]))).
% 98.54/95.48  ncf('1.1.1.7.1.2',plain,[-(element(powerset(cartesian_product2(the_carrier(571 ^ []), the_carrier(571 ^ []))), powerset(powerset(cartesian_product2(the_carrier(571 ^ []), the_carrier(571 ^ [])))))), subset(powerset(cartesian_product2(the_carrier(571 ^ []), the_carrier(571 ^ []))), powerset(cartesian_product2(the_carrier(571 ^ []), the_carrier(571 ^ []))))],extension(524 ^ 11,bind([[_122017, _122019], [powerset(cartesian_product2(the_carrier(571 ^ []), the_carrier(571 ^ []))), powerset(cartesian_product2(the_carrier(571 ^ []), the_carrier(571 ^ [])))]]))).
% 98.54/95.48  ncf('1.1.1.7.1.2.1',plain,[-(subset(powerset(cartesian_product2(the_carrier(571 ^ []), the_carrier(571 ^ []))), powerset(cartesian_product2(the_carrier(571 ^ []), the_carrier(571 ^ [])))))],extension(482 ^ 12,bind([[_120550, _120552], [_81319, powerset(cartesian_product2(the_carrier(571 ^ []), the_carrier(571 ^ [])))]]))).
% 98.54/95.48  ncf('1.1.2',plain,[-(element(579 ^ [], the_carrier(571 ^ [])))],extension(581 ^ 6)).
% 98.54/95.48  ncf('1.1.3',plain,[-(element(576 ^ [], the_carrier(571 ^ [])))],extension(578 ^ 4)).
% 98.54/95.48  ncf('1.1.4',plain,[-(rel_str(571 ^ []))],extension(575 ^ 2)).
% 98.54/95.48  %-----------------------------------------------------
% 98.54/95.48  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------