%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SEU360+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n006.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 12:03:16 EDT 2023

% Result   : Theorem 0.58s 1.37s
% Output   : Proof 0.58s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : SEU360+1 : TPTP v8.1.2. Released v3.3.0.
% 0.06/0.11  % Command  : nanocop.sh %s %d
% 0.11/0.32  % Computer : n006.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 300
% 0.11/0.32  % DateTime : Thu May 18 13:40:06 EDT 2023
% 0.11/0.32  % CPUTime  : 
% 0.58/1.37  
% 0.58/1.37  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 0.58/1.37  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.58/1.37  %-----------------------------------------------------
% 0.58/1.37  ncf(matrix, plain, [(484 ^ _77891) ^ [] : [empty_carrier(482 ^ [])], (486 ^ _77891) ^ [] : [-(antisymmetric_relstr(482 ^ []))], (488 ^ _77891) ^ [] : [-(lower_bounded_relstr(482 ^ []))], (490 ^ _77891) ^ [] : [-(rel_str(482 ^ []))], (492 ^ _77891) ^ [] : [ex_sup_of_relstr_set(482 ^ [], empty_set), ex_inf_of_relstr_set(482 ^ [], the_carrier(482 ^ []))], (200 ^ _77891) ^ [_84319, _84321] : [_84321 = _84319, -(the_carrier(_84321) = the_carrier(_84319))], (2 ^ _77891) ^ [_78035] : [-(_78035 = _78035)], (4 ^ _77891) ^ [_78142, _78144] : [_78144 = _78142, -(_78142 = _78144)], (10 ^ _77891) ^ [_78346, _78348, _78350] : [-(_78350 = _78346), _78350 = _78348, _78348 = _78346], (20 ^ _77891) ^ [_78659, _78661] : [-(finite(_78659)), _78661 = _78659, finite(_78661)], (30 ^ _77891) ^ [_78954, _78956] : [-(one_sorted_str(_78954)), _78956 = _78954, one_sorted_str(_78956)], (40 ^ _77891) ^ [_79305, _79307, _79309, _79311, _79313, _79315] : [-(related(_79313, _79309, _79305)), related(_79315, _79311, _79307), _79315 = _79313, _79311 = _79309, _79307 = _79305], (58 ^ _77891) ^ [_79886, _79888, _79890, _79892] : [-(element(_79890, _79886)), element(_79892, _79888), _79892 = _79890, _79888 = _79886], (72 ^ _77891) ^ [_80358, _80360, _80362, _80364, _80366, _80368] : [-(relstr_set_smaller(_80366, _80362, _80358)), relstr_set_smaller(_80368, _80364, _80360), _80368 = _80366, _80364 = _80362, _80360 = _80358], (90 ^ _77891) ^ [_80967, _80969, _80971, _80973, _80975, _80977] : [-(relstr_element_smaller(_80975, _80971, _80967)), relstr_element_smaller(_80977, _80973, _80969), _80977 = _80975, _80973 = _80971, _80969 = _80967], (108 ^ _77891) ^ [_81548, _81550, _81552, _81554] : [-(in(_81552, _81548)), in(_81554, _81550), _81554 = _81552, _81550 = _81548], (122 ^ _77891) ^ [_81964, _81966] : [-(empty(_81964)), _81966 = _81964, empty(_81966)], (132 ^ _77891) ^ [_82259, _82261] : [-(empty_carrier(_82259)), _82261 = _82259, empty_carrier(_82261)], (142 ^ _77891) ^ [_82554, _82556] : [-(antisymmetric_relstr(_82554)), _82556 = _82554, antisymmetric_relstr(_82556)], (152 ^ _77891) ^ [_82849, _82851] : [-(lower_bounded_relstr(_82849)), _82851 = _82849, lower_bounded_relstr(_82851)], (162 ^ _77891) ^ [_83144, _83146] : [-(rel_str(_83144)), _83146 = _83144, rel_str(_83146)], (172 ^ _77891) ^ [_83467, _83469, _83471, _83473] : [-(ex_sup_of_relstr_set(_83471, _83467)), ex_sup_of_relstr_set(_83473, _83469), _83473 = _83471, _83469 = _83467], (186 ^ _77891) ^ [_83891, _83893, _83895, _83897] : [-(ex_inf_of_relstr_set(_83895, _83891)), ex_inf_of_relstr_set(_83897, _83893), _83897 = _83895, _83893 = _83891], (206 ^ _77891) ^ [_84539, _84541] : [in(_84541, _84539), in(_84539, _84541)], (212 ^ _77891) ^ [_84736] : [empty(_84736), -(finite(_84736))], (218 ^ _77891) ^ [_84922] : [rel_str(_84922), 221 ^ _77891 : [(222 ^ _77891) ^ [] : [lower_bounded_relstr(_84922), 226 ^ _77891 : [(227 ^ _77891) ^ [] : [-(element(225 ^ [_84922], the_carrier(_84922)))], (229 ^ _77891) ^ [] : [-(relstr_element_smaller(_84922, the_carrier(_84922), 225 ^ [_84922]))]]], (231 ^ _77891) ^ [] : [-(lower_bounded_relstr(_84922)), 232 ^ _77891 : [(233 ^ _77891) ^ [_85380] : [element(_85380, the_carrier(_84922)), relstr_element_smaller(_84922, the_carrier(_84922), _85380)]]]]], (241 ^ _77891) ^ [_85642] : [rel_str(_85642), 244 ^ _77891 : [(245 ^ _77891) ^ [_85821, _85823] : [element(_85821, the_carrier(_85642)), 248 ^ _77891 : [(263 ^ _77891) ^ [] : [265 ^ _77891 : [(266 ^ _77891) ^ [] : [-(element(264 ^ [_85642, _85821, _85823], the_carrier(_85642)))], (268 ^ _77891) ^ [] : [-(in(264 ^ [_85642, _85821, _85823], _85823))], (270 ^ _77891) ^ [] : [related(_85642, _85821, 264 ^ [_85642, _85821, _85823])]], -(relstr_element_smaller(_85642, _85823, _85821))], (249 ^ _77891) ^ [] : [relstr_element_smaller(_85642, _85823, _85821), 252 ^ _77891 : [(253 ^ _77891) ^ [_86097] : [element(_86097, the_carrier(_85642)), in(_86097, _85823), -(related(_85642, _85821, _86097))]]]]]]], (274 ^ _77891) ^ [] : [true___, -(true___)], (280 ^ _77891) ^ [_86921] : [rel_str(_86921), -(one_sorted_str(_86921))], (286 ^ _77891) ^ [] : [true___, -(true___)], (292 ^ _77891) ^ [] : [true___, -(true___)], (298 ^ _77891) ^ [] : [true___, -(true___)], (305 ^ _77891) ^ [] : [-(rel_str(303 ^ []))], (308 ^ _77891) ^ [] : [-(one_sorted_str(306 ^ []))], (311 ^ _77891) ^ [_87666] : [-(element(309 ^ [_87666], _87666))], (313 ^ _77891) ^ [_87764] : [empty(the_carrier(_87764)), -(empty_carrier(_87764)), one_sorted_str(_87764)], (323 ^ _77891) ^ [] : [-(empty(empty_set))], (326 ^ _77891) ^ [] : [empty(324 ^ [])], (328 ^ _77891) ^ [] : [-(finite(324 ^ []))], (331 ^ _77891) ^ [] : [-(empty(329 ^ []))], (334 ^ _77891) ^ [] : [empty(332 ^ [])], (337 ^ _77891) ^ [] : [-(one_sorted_str(335 ^ []))], (339 ^ _77891) ^ [] : [empty_carrier(335 ^ [])], (341 ^ _77891) ^ [_88573] : [antisymmetric_relstr(_88573), rel_str(_88573), 348 ^ _77891 : [(349 ^ _77891) ^ [_88857] : [ex_sup_of_relstr_set(_88573, _88857), 353 ^ _77891 : [(354 ^ _77891) ^ [] : [-(element(352 ^ [_88573, _88857], the_carrier(_88573)))], (356 ^ _77891) ^ [] : [-(relstr_set_smaller(_88573, _88857, 352 ^ [_88573, _88857]))], (358 ^ _77891) ^ [_89256] : [element(_89256, the_carrier(_88573)), relstr_set_smaller(_88573, _88857, _89256), -(related(_88573, 352 ^ [_88573, _88857], _89256))]]], (368 ^ _77891) ^ [_89552] : [-(ex_sup_of_relstr_set(_88573, _89552)), 369 ^ _77891 : [(370 ^ _77891) ^ [_89676] : [element(_89676, the_carrier(_88573)), relstr_set_smaller(_88573, _89552, _89676), 378 ^ _77891 : [(379 ^ _77891) ^ [] : [-(element(377 ^ [_88573, _89552, _89676], the_carrier(_88573)))], (381 ^ _77891) ^ [] : [-(relstr_set_smaller(_88573, _89552, 377 ^ [_88573, _89552, _89676]))], (383 ^ _77891) ^ [] : [related(_88573, _89676, 377 ^ [_88573, _89552, _89676])]]]]]]], (387 ^ _77891) ^ [_90298] : [antisymmetric_relstr(_90298), rel_str(_90298), 394 ^ _77891 : [(395 ^ _77891) ^ [_90582] : [ex_inf_of_relstr_set(_90298, _90582), 399 ^ _77891 : [(400 ^ _77891) ^ [] : [-(element(398 ^ [_90298, _90582], the_carrier(_90298)))], (402 ^ _77891) ^ [] : [-(relstr_element_smaller(_90298, _90582, 398 ^ [_90298, _90582]))], (404 ^ _77891) ^ [_90981] : [element(_90981, the_carrier(_90298)), relstr_element_smaller(_90298, _90582, _90981), -(related(_90298, _90981, 398 ^ [_90298, _90582]))]]], (414 ^ _77891) ^ [_91277] : [-(ex_inf_of_relstr_set(_90298, _91277)), 415 ^ _77891 : [(416 ^ _77891) ^ [_91401] : [element(_91401, the_carrier(_90298)), relstr_element_smaller(_90298, _91277, _91401), 424 ^ _77891 : [(425 ^ _77891) ^ [] : [-(element(423 ^ [_90298, _91277, _91401], the_carrier(_90298)))], (427 ^ _77891) ^ [] : [-(relstr_element_smaller(_90298, _91277, 423 ^ [_90298, _91277, _91401]))], (429 ^ _77891) ^ [] : [related(_90298, 423 ^ [_90298, _91277, _91401], _91401)]]]]]]], (433 ^ _77891) ^ [_92037, _92039] : [in(_92039, _92037), -(element(_92039, _92037))], (439 ^ _77891) ^ [_92247, _92249] : [element(_92249, _92247), -(empty(_92247)), -(in(_92249, _92247))], (449 ^ _77891) ^ [_92531] : [empty(_92531), -(_92531 = empty_set)], (455 ^ _77891) ^ [_92719] : [rel_str(_92719), 458 ^ _77891 : [(459 ^ _77891) ^ [_92860] : [element(_92860, the_carrier(_92719)), 462 ^ _77891 : [(463 ^ _77891) ^ [] : [-(relstr_set_smaller(_92719, empty_set, _92860))], (465 ^ _77891) ^ [] : [-(relstr_element_smaller(_92719, empty_set, _92860))]]]]], (467 ^ _77891) ^ [_93160, _93162] : [in(_93162, _93160), empty(_93160)], (473 ^ _77891) ^ [_93347, _93349] : [empty(_93349), -(_93349 = _93347), empty(_93347)]], input).
% 0.58/1.37  ncf('1',plain,[ex_sup_of_relstr_set(482 ^ [], empty_set), ex_inf_of_relstr_set(482 ^ [], the_carrier(482 ^ []))],start(492 ^ 0)).
% 0.58/1.37  ncf('1.1',plain,[-(ex_sup_of_relstr_set(482 ^ [], empty_set)), ex_sup_of_relstr_set(482 ^ [], empty_set), 482 ^ [] = 482 ^ [], empty_set = empty_set],extension(172 ^ 1,bind([[_83467, _83469, _83471, _83473], [empty_set, empty_set, 482 ^ [], 482 ^ []]]))).
% 0.58/1.37  ncf('1.1.1',plain,[-(ex_sup_of_relstr_set(482 ^ [], empty_set)), 370 : element(225 ^ [482 ^ []], the_carrier(482 ^ [])), 370 : relstr_set_smaller(482 ^ [], empty_set, 225 ^ [482 ^ []]), 379 : -(element(377 ^ [482 ^ [], empty_set, 225 ^ [482 ^ []]], the_carrier(482 ^ []))), 368 : antisymmetric_relstr(482 ^ []), 368 : rel_str(482 ^ [])],extension(341 ^ 2,bind([[_88573, _89552, _89676], [482 ^ [], empty_set, 225 ^ [482 ^ []]]]))).
% 0.58/1.37  ncf('1.1.1.1',plain,[-(element(225 ^ [482 ^ []], the_carrier(482 ^ []))), element(225 ^ [482 ^ []], the_carrier(482 ^ [])), 225 ^ [482 ^ []] = 225 ^ [482 ^ []], the_carrier(482 ^ []) = the_carrier(482 ^ [])],extension(58 ^ 7,bind([[_79886, _79888, _79890, _79892], [the_carrier(482 ^ []), the_carrier(482 ^ []), 225 ^ [482 ^ []], 225 ^ [482 ^ []]]]))).
% 0.58/1.37  ncf('1.1.1.1.1',plain,[-(element(225 ^ [482 ^ []], the_carrier(482 ^ []))), element(225 ^ [482 ^ []], the_carrier(482 ^ [])), 225 ^ [482 ^ []] = 225 ^ [482 ^ []], the_carrier(482 ^ []) = the_carrier(482 ^ [])],extension(58 ^ 8,bind([[_79886, _79888, _79890, _79892], [the_carrier(482 ^ []), the_carrier(482 ^ []), 225 ^ [482 ^ []], 225 ^ [482 ^ []]]]))).
% 0.58/1.37  ncf('1.1.1.1.1.1',plain,[-(element(225 ^ [482 ^ []], the_carrier(482 ^ []))), 222 : lower_bounded_relstr(482 ^ []), 222 : rel_str(482 ^ [])],extension(218 ^ 9,bind([[_84922], [482 ^ []]]))).
% 0.58/1.37  ncf('1.1.1.1.1.1.1',plain,[-(lower_bounded_relstr(482 ^ []))],extension(488 ^ 12)).
% 0.58/1.37  ncf('1.1.1.1.1.1.2',plain,[-(rel_str(482 ^ []))],extension(490 ^ 10)).
% 0.58/1.37  ncf('1.1.1.1.1.2',plain,[-(225 ^ [482 ^ []] = 225 ^ [482 ^ []])],extension(2 ^ 9,bind([[_78035], [225 ^ [482 ^ []]]]))).
% 0.58/1.37  ncf('1.1.1.1.1.3',plain,[-(the_carrier(482 ^ []) = the_carrier(482 ^ []))],extension(2 ^ 9,bind([[_78035], [the_carrier(482 ^ [])]]))).
% 0.58/1.37  ncf('1.1.1.1.2',plain,[-(225 ^ [482 ^ []] = 225 ^ [482 ^ []])],extension(2 ^ 8,bind([[_78035], [225 ^ [482 ^ []]]]))).
% 0.58/1.37  ncf('1.1.1.1.3',plain,[-(the_carrier(482 ^ []) = the_carrier(482 ^ [])), 482 ^ [] = 482 ^ []],extension(200 ^ 8,bind([[_84319, _84321], [482 ^ [], 482 ^ []]]))).
% 0.58/1.37  ncf('1.1.1.1.3.1',plain,[-(482 ^ [] = 482 ^ [])],extension(2 ^ 9,bind([[_78035], [482 ^ []]]))).
% 0.58/1.37  ncf('1.1.1.2',plain,[-(relstr_set_smaller(482 ^ [], empty_set, 225 ^ [482 ^ []])), 459 : element(225 ^ [482 ^ []], the_carrier(482 ^ [])), 459 : rel_str(482 ^ [])],extension(455 ^ 7,bind([[_92719, _92860], [482 ^ [], 225 ^ [482 ^ []]]]))).
% 0.58/1.37  ncf('1.1.1.2.1',plain,[-(element(225 ^ [482 ^ []], the_carrier(482 ^ [])))],lemmata('[1, 1].x')).
% 0.58/1.37  ncf('1.1.1.2.2',plain,[-(rel_str(482 ^ []))],extension(490 ^ 8)).
% 0.58/1.37  ncf('1.1.1.3',plain,[element(377 ^ [482 ^ [], empty_set, 225 ^ [482 ^ []]], the_carrier(482 ^ [])), -(empty(the_carrier(482 ^ []))), -(in(377 ^ [482 ^ [], empty_set, 225 ^ [482 ^ []]], the_carrier(482 ^ [])))],extension(439 ^ 9,bind([[_92247, _92249], [the_carrier(482 ^ []), 377 ^ [482 ^ [], empty_set, 225 ^ [482 ^ []]]]]))).
% 0.58/1.37  ncf('1.1.1.3.1',plain,[empty(the_carrier(482 ^ [])), -(empty_carrier(482 ^ [])), one_sorted_str(482 ^ [])],extension(313 ^ 10,bind([[_87764], [482 ^ []]]))).
% 0.58/1.37  ncf('1.1.1.3.1.1',plain,[empty_carrier(482 ^ [])],extension(484 ^ 11)).
% 0.58/1.37  ncf('1.1.1.3.1.2',plain,[-(one_sorted_str(482 ^ [])), rel_str(482 ^ [])],extension(280 ^ 11,bind([[_86921], [482 ^ []]]))).
% 0.58/1.37  ncf('1.1.1.3.1.2.1',plain,[-(rel_str(482 ^ []))],extension(490 ^ 12)).
% 0.58/1.37  ncf('1.1.1.3.2',plain,[in(377 ^ [482 ^ [], empty_set, 225 ^ [482 ^ []]], the_carrier(482 ^ [])), 253 : element(377 ^ [482 ^ [], empty_set, 225 ^ [482 ^ []]], the_carrier(482 ^ [])), 253 : -(related(482 ^ [], 225 ^ [482 ^ []], 377 ^ [482 ^ [], empty_set, 225 ^ [482 ^ []]])), 253 : relstr_element_smaller(482 ^ [], the_carrier(482 ^ []), 225 ^ [482 ^ []]), 249 : element(225 ^ [482 ^ []], the_carrier(482 ^ [])), 245 : rel_str(482 ^ [])],extension(241 ^ 10,bind([[_85642, _85821, _85823, _86097], [482 ^ [], 225 ^ [482 ^ []], the_carrier(482 ^ []), 377 ^ [482 ^ [], empty_set, 225 ^ [482 ^ []]]]]))).
% 0.58/1.37  ncf('1.1.1.3.2.1',plain,[-(element(377 ^ [482 ^ [], empty_set, 225 ^ [482 ^ []]], the_carrier(482 ^ [])))],reduction('1.1.1')).
% 0.58/1.37  ncf('1.1.1.3.2.2',plain,[related(482 ^ [], 225 ^ [482 ^ []], 377 ^ [482 ^ [], empty_set, 225 ^ [482 ^ []]])],extension(383 ^ 17)).
% 0.58/1.37  ncf('1.1.1.3.2.3',plain,[-(relstr_element_smaller(482 ^ [], the_carrier(482 ^ []), 225 ^ [482 ^ []])), 222 : lower_bounded_relstr(482 ^ []), 222 : rel_str(482 ^ [])],extension(218 ^ 15,bind([[_84922], [482 ^ []]]))).
% 0.58/1.37  ncf('1.1.1.3.2.3.1',plain,[-(lower_bounded_relstr(482 ^ []))],extension(488 ^ 18)).
% 0.58/1.37  ncf('1.1.1.3.2.3.2',plain,[-(rel_str(482 ^ []))],extension(490 ^ 16)).
% 0.58/1.37  ncf('1.1.1.3.2.4',plain,[-(element(225 ^ [482 ^ []], the_carrier(482 ^ [])))],lemmata('[1, 1].x')).
% 0.58/1.37  ncf('1.1.1.3.2.5',plain,[-(rel_str(482 ^ []))],extension(490 ^ 11)).
% 0.58/1.37  ncf('1.1.1.4',plain,[-(antisymmetric_relstr(482 ^ []))],extension(486 ^ 3)).
% 0.58/1.37  ncf('1.1.1.5',plain,[-(rel_str(482 ^ []))],extension(490 ^ 3)).
% 0.58/1.37  ncf('1.1.2',plain,[-(482 ^ [] = 482 ^ [])],extension(2 ^ 2,bind([[_78035], [482 ^ []]]))).
% 0.58/1.37  ncf('1.1.3',plain,[-(empty_set = empty_set)],extension(2 ^ 2,bind([[_78035], [empty_set]]))).
% 0.58/1.37  ncf('1.2',plain,[-(ex_inf_of_relstr_set(482 ^ [], the_carrier(482 ^ []))), 416 : element(225 ^ [482 ^ []], the_carrier(482 ^ [])), 416 : relstr_element_smaller(482 ^ [], the_carrier(482 ^ []), 225 ^ [482 ^ []]), 425 : -(element(423 ^ [482 ^ [], the_carrier(482 ^ []), 225 ^ [482 ^ []]], the_carrier(482 ^ []))), 414 : antisymmetric_relstr(482 ^ []), 414 : rel_str(482 ^ [])],extension(387 ^ 1,bind([[_90298, _91277, _91401], [482 ^ [], the_carrier(482 ^ []), 225 ^ [482 ^ []]]]))).
% 0.58/1.37  ncf('1.2.1',plain,[-(element(225 ^ [482 ^ []], the_carrier(482 ^ []))), element(225 ^ [482 ^ []], the_carrier(482 ^ [])), 225 ^ [482 ^ []] = 225 ^ [482 ^ []], the_carrier(482 ^ []) = the_carrier(482 ^ [])],extension(58 ^ 6,bind([[_79886, _79888, _79890, _79892], [the_carrier(482 ^ []), the_carrier(482 ^ []), 225 ^ [482 ^ []], 225 ^ [482 ^ []]]]))).
% 0.58/1.37  ncf('1.2.1.1',plain,[-(element(225 ^ [482 ^ []], the_carrier(482 ^ []))), element(225 ^ [482 ^ []], the_carrier(482 ^ [])), 225 ^ [482 ^ []] = 225 ^ [482 ^ []], the_carrier(482 ^ []) = the_carrier(482 ^ [])],extension(58 ^ 7,bind([[_79886, _79888, _79890, _79892], [the_carrier(482 ^ []), the_carrier(482 ^ []), 225 ^ [482 ^ []], 225 ^ [482 ^ []]]]))).
% 0.58/1.37  ncf('1.2.1.1.1',plain,[-(element(225 ^ [482 ^ []], the_carrier(482 ^ []))), element(225 ^ [482 ^ []], the_carrier(482 ^ [])), 225 ^ [482 ^ []] = 225 ^ [482 ^ []], the_carrier(482 ^ []) = the_carrier(482 ^ [])],extension(58 ^ 8,bind([[_79886, _79888, _79890, _79892], [the_carrier(482 ^ []), the_carrier(482 ^ []), 225 ^ [482 ^ []], 225 ^ [482 ^ []]]]))).
% 0.58/1.37  ncf('1.2.1.1.1.1',plain,[-(element(225 ^ [482 ^ []], the_carrier(482 ^ []))), 222 : lower_bounded_relstr(482 ^ []), 222 : rel_str(482 ^ [])],extension(218 ^ 9,bind([[_84922], [482 ^ []]]))).
% 0.58/1.37  ncf('1.2.1.1.1.1.1',plain,[-(lower_bounded_relstr(482 ^ []))],extension(488 ^ 12)).
% 0.58/1.37  ncf('1.2.1.1.1.1.2',plain,[-(rel_str(482 ^ []))],extension(490 ^ 10)).
% 0.58/1.37  ncf('1.2.1.1.1.2',plain,[-(225 ^ [482 ^ []] = 225 ^ [482 ^ []])],extension(2 ^ 9,bind([[_78035], [225 ^ [482 ^ []]]]))).
% 0.58/1.37  ncf('1.2.1.1.1.3',plain,[-(the_carrier(482 ^ []) = the_carrier(482 ^ []))],extension(2 ^ 9,bind([[_78035], [the_carrier(482 ^ [])]]))).
% 0.58/1.37  ncf('1.2.1.1.2',plain,[-(225 ^ [482 ^ []] = 225 ^ [482 ^ []])],extension(2 ^ 8,bind([[_78035], [225 ^ [482 ^ []]]]))).
% 0.58/1.37  ncf('1.2.1.1.3',plain,[-(the_carrier(482 ^ []) = the_carrier(482 ^ [])), 482 ^ [] = 482 ^ []],extension(200 ^ 8,bind([[_84319, _84321], [482 ^ [], 482 ^ []]]))).
% 0.58/1.37  ncf('1.2.1.1.3.1',plain,[-(482 ^ [] = 482 ^ [])],extension(2 ^ 9,bind([[_78035], [482 ^ []]]))).
% 0.58/1.37  ncf('1.2.1.2',plain,[-(225 ^ [482 ^ []] = 225 ^ [482 ^ []])],extension(2 ^ 7,bind([[_78035], [225 ^ [482 ^ []]]]))).
% 0.58/1.37  ncf('1.2.1.3',plain,[-(the_carrier(482 ^ []) = the_carrier(482 ^ [])), 482 ^ [] = 482 ^ []],extension(200 ^ 7,bind([[_84319, _84321], [482 ^ [], 482 ^ []]]))).
% 0.58/1.37  ncf('1.2.1.3.1',plain,[-(482 ^ [] = 482 ^ [])],extension(2 ^ 8,bind([[_78035], [482 ^ []]]))).
% 0.58/1.37  ncf('1.2.2',plain,[-(relstr_element_smaller(482 ^ [], the_carrier(482 ^ []), 225 ^ [482 ^ []])), relstr_element_smaller(482 ^ [], the_carrier(482 ^ []), 225 ^ [482 ^ []]), 482 ^ [] = 482 ^ [], the_carrier(482 ^ []) = the_carrier(482 ^ []), 225 ^ [482 ^ []] = 225 ^ [482 ^ []]],extension(90 ^ 6,bind([[_80967, _80969, _80971, _80973, _80975, _80977], [225 ^ [482 ^ []], 225 ^ [482 ^ []], the_carrier(482 ^ []), the_carrier(482 ^ []), 482 ^ [], 482 ^ []]]))).
% 0.58/1.37  ncf('1.2.2.1',plain,[-(relstr_element_smaller(482 ^ [], the_carrier(482 ^ []), 225 ^ [482 ^ []])), relstr_element_smaller(482 ^ [], the_carrier(482 ^ []), 225 ^ [482 ^ []]), 482 ^ [] = 482 ^ [], the_carrier(482 ^ []) = the_carrier(482 ^ []), 225 ^ [482 ^ []] = 225 ^ [482 ^ []]],extension(90 ^ 7,bind([[_80967, _80969, _80971, _80973, _80975, _80977], [225 ^ [482 ^ []], 225 ^ [482 ^ []], the_carrier(482 ^ []), the_carrier(482 ^ []), 482 ^ [], 482 ^ []]]))).
% 0.58/1.37  ncf('1.2.2.1.1',plain,[-(relstr_element_smaller(482 ^ [], the_carrier(482 ^ []), 225 ^ [482 ^ []])), relstr_element_smaller(482 ^ [], the_carrier(482 ^ []), 225 ^ [482 ^ []]), 482 ^ [] = 482 ^ [], the_carrier(482 ^ []) = the_carrier(482 ^ []), 225 ^ [482 ^ []] = 225 ^ [482 ^ []]],extension(90 ^ 8,bind([[_80967, _80969, _80971, _80973, _80975, _80977], [225 ^ [482 ^ []], 225 ^ [482 ^ []], the_carrier(482 ^ []), the_carrier(482 ^ []), 482 ^ [], 482 ^ []]]))).
% 0.58/1.37  ncf('1.2.2.1.1.1',plain,[-(relstr_element_smaller(482 ^ [], the_carrier(482 ^ []), 225 ^ [482 ^ []])), 222 : lower_bounded_relstr(482 ^ []), 222 : rel_str(482 ^ [])],extension(218 ^ 9,bind([[_84922], [482 ^ []]]))).
% 0.58/1.37  ncf('1.2.2.1.1.1.1',plain,[-(lower_bounded_relstr(482 ^ []))],extension(488 ^ 12)).
% 0.58/1.37  ncf('1.2.2.1.1.1.2',plain,[-(rel_str(482 ^ []))],extension(490 ^ 10)).
% 0.58/1.37  ncf('1.2.2.1.1.2',plain,[-(482 ^ [] = 482 ^ [])],extension(2 ^ 9,bind([[_78035], [482 ^ []]]))).
% 0.58/1.37  ncf('1.2.2.1.1.3',plain,[-(the_carrier(482 ^ []) = the_carrier(482 ^ []))],extension(2 ^ 9,bind([[_78035], [the_carrier(482 ^ [])]]))).
% 0.58/1.37  ncf('1.2.2.1.1.4',plain,[-(225 ^ [482 ^ []] = 225 ^ [482 ^ []])],extension(2 ^ 9,bind([[_78035], [225 ^ [482 ^ []]]]))).
% 0.58/1.37  ncf('1.2.2.1.2',plain,[-(482 ^ [] = 482 ^ [])],extension(2 ^ 8,bind([[_78035], [482 ^ []]]))).
% 0.58/1.37  ncf('1.2.2.1.3',plain,[-(the_carrier(482 ^ []) = the_carrier(482 ^ [])), 482 ^ [] = 482 ^ []],extension(200 ^ 8,bind([[_84319, _84321], [482 ^ [], 482 ^ []]]))).
% 0.58/1.37  ncf('1.2.2.1.3.1',plain,[-(482 ^ [] = 482 ^ [])],extension(2 ^ 9,bind([[_78035], [482 ^ []]]))).
% 0.58/1.37  ncf('1.2.2.1.4',plain,[-(225 ^ [482 ^ []] = 225 ^ [482 ^ []])],extension(2 ^ 8,bind([[_78035], [225 ^ [482 ^ []]]]))).
% 0.58/1.37  ncf('1.2.2.2',plain,[-(482 ^ [] = 482 ^ [])],extension(2 ^ 7,bind([[_78035], [482 ^ []]]))).
% 0.58/1.37  ncf('1.2.2.3',plain,[-(the_carrier(482 ^ []) = the_carrier(482 ^ [])), 482 ^ [] = 482 ^ []],extension(200 ^ 7,bind([[_84319, _84321], [482 ^ [], 482 ^ []]]))).
% 0.58/1.37  ncf('1.2.2.3.1',plain,[-(482 ^ [] = 482 ^ [])],lemmata('[2, 1].x')).
% 0.58/1.37  ncf('1.2.2.4',plain,[-(225 ^ [482 ^ []] = 225 ^ [482 ^ []])],extension(2 ^ 7,bind([[_78035], [225 ^ [482 ^ []]]]))).
% 0.58/1.37  ncf('1.2.3',plain,[element(423 ^ [482 ^ [], the_carrier(482 ^ []), 225 ^ [482 ^ []]], the_carrier(482 ^ [])), 253 : in(423 ^ [482 ^ [], the_carrier(482 ^ []), 225 ^ [482 ^ []]], the_carrier(482 ^ [])), 253 : -(related(482 ^ [], 423 ^ [482 ^ [], the_carrier(482 ^ []), 423 ^ [482 ^ [], the_carrier(482 ^ []), 225 ^ [482 ^ []]]], 423 ^ [482 ^ [], the_carrier(482 ^ []), 225 ^ [482 ^ []]])), 253 : relstr_element_smaller(482 ^ [], the_carrier(482 ^ []), 423 ^ [482 ^ [], the_carrier(482 ^ []), 423 ^ [482 ^ [], the_carrier(482 ^ []), 225 ^ [482 ^ []]]]), 249 : element(423 ^ [482 ^ [], the_carrier(482 ^ []), 423 ^ [482 ^ [], the_carrier(482 ^ []), 225 ^ [482 ^ []]]], the_carrier(482 ^ [])), 245 : rel_str(482 ^ [])],extension(241 ^ 8,bind([[_85642, _85821, _85823, _86097], [482 ^ [], 423 ^ [482 ^ [], the_carrier(482 ^ []), 423 ^ [482 ^ [], the_carrier(482 ^ []), 225 ^ [482 ^ []]]], the_carrier(482 ^ []), 423 ^ [482 ^ [], the_carrier(482 ^ []), 225 ^ [482 ^ []]]]]))).
% 0.58/1.37  ncf('1.2.3.1',plain,[-(in(423 ^ [482 ^ [], the_carrier(482 ^ []), 225 ^ [482 ^ []]], the_carrier(482 ^ []))), element(423 ^ [482 ^ [], the_carrier(482 ^ []), 225 ^ [482 ^ []]], the_carrier(482 ^ [])), -(empty(the_carrier(482 ^ [])))],extension(439 ^ 15,bind([[_92247, _92249], [the_carrier(482 ^ []), 423 ^ [482 ^ [], the_carrier(482 ^ []), 225 ^ [482 ^ []]]]]))).
% 0.58/1.37  ncf('1.2.3.1.1',plain,[-(element(423 ^ [482 ^ [], the_carrier(482 ^ []), 225 ^ [482 ^ []]], the_carrier(482 ^ [])))],reduction('1.2')).
% 0.58/1.37  ncf('1.2.3.1.2',plain,[empty(the_carrier(482 ^ [])), -(empty_carrier(482 ^ [])), one_sorted_str(482 ^ [])],extension(313 ^ 16,bind([[_87764], [482 ^ []]]))).
% 0.58/1.37  ncf('1.2.3.1.2.1',plain,[empty_carrier(482 ^ [])],extension(484 ^ 17)).
% 0.58/1.37  ncf('1.2.3.1.2.2',plain,[-(one_sorted_str(482 ^ [])), rel_str(482 ^ [])],extension(280 ^ 17,bind([[_86921], [482 ^ []]]))).
% 0.58/1.37  ncf('1.2.3.1.2.2.1',plain,[-(rel_str(482 ^ []))],extension(490 ^ 18)).
% 0.58/1.37  ncf('1.2.3.2',plain,[related(482 ^ [], 423 ^ [482 ^ [], the_carrier(482 ^ []), 423 ^ [482 ^ [], the_carrier(482 ^ []), 225 ^ [482 ^ []]]], 423 ^ [482 ^ [], the_carrier(482 ^ []), 225 ^ [482 ^ []]]), element(423 ^ [482 ^ [], the_carrier(482 ^ []), 225 ^ [482 ^ []]], the_carrier(482 ^ [])), relstr_element_smaller(482 ^ [], the_carrier(482 ^ []), 423 ^ [482 ^ [], the_carrier(482 ^ []), 225 ^ [482 ^ []]])],extension(416 ^ 15,bind([[_91401], [423 ^ [482 ^ [], the_carrier(482 ^ []), 225 ^ [482 ^ []]]]]))).
% 0.58/1.37  ncf('1.2.3.2.1',plain,[-(element(423 ^ [482 ^ [], the_carrier(482 ^ []), 225 ^ [482 ^ []]], the_carrier(482 ^ [])))],reduction('1.2')).
% 0.58/1.37  ncf('1.2.3.2.2',plain,[-(relstr_element_smaller(482 ^ [], the_carrier(482 ^ []), 423 ^ [482 ^ [], the_carrier(482 ^ []), 225 ^ [482 ^ []]])), element(225 ^ [482 ^ []], the_carrier(482 ^ [])), relstr_element_smaller(482 ^ [], the_carrier(482 ^ []), 225 ^ [482 ^ []])],extension(416 ^ 16,bind([[_91401], [225 ^ [482 ^ []]]]))).
% 0.58/1.37  ncf('1.2.3.2.2.1',plain,[-(element(225 ^ [482 ^ []], the_carrier(482 ^ [])))],lemmata('[1].x')).
% 0.58/1.37  ncf('1.2.3.2.2.2',plain,[-(relstr_element_smaller(482 ^ [], the_carrier(482 ^ []), 225 ^ [482 ^ []]))],lemmata('[1].x')).
% 0.58/1.37  ncf('1.2.3.3',plain,[-(relstr_element_smaller(482 ^ [], the_carrier(482 ^ []), 423 ^ [482 ^ [], the_carrier(482 ^ []), 423 ^ [482 ^ [], the_carrier(482 ^ []), 225 ^ [482 ^ []]]])), element(423 ^ [482 ^ [], the_carrier(482 ^ []), 225 ^ [482 ^ []]], the_carrier(482 ^ [])), relstr_element_smaller(482 ^ [], the_carrier(482 ^ []), 423 ^ [482 ^ [], the_carrier(482 ^ []), 225 ^ [482 ^ []]])],extension(416 ^ 13,bind([[_91401], [423 ^ [482 ^ [], the_carrier(482 ^ []), 225 ^ [482 ^ []]]]]))).
% 0.58/1.37  ncf('1.2.3.3.1',plain,[-(element(423 ^ [482 ^ [], the_carrier(482 ^ []), 225 ^ [482 ^ []]], the_carrier(482 ^ [])))],reduction('1.2')).
% 0.58/1.37  ncf('1.2.3.3.2',plain,[-(relstr_element_smaller(482 ^ [], the_carrier(482 ^ []), 423 ^ [482 ^ [], the_carrier(482 ^ []), 225 ^ [482 ^ []]])), element(225 ^ [482 ^ []], the_carrier(482 ^ [])), relstr_element_smaller(482 ^ [], the_carrier(482 ^ []), 225 ^ [482 ^ []])],extension(416 ^ 14,bind([[_91401], [225 ^ [482 ^ []]]]))).
% 0.58/1.37  ncf('1.2.3.3.2.1',plain,[-(element(225 ^ [482 ^ []], the_carrier(482 ^ [])))],lemmata('[1].x')).
% 0.58/1.37  ncf('1.2.3.3.2.2',plain,[-(relstr_element_smaller(482 ^ [], the_carrier(482 ^ []), 225 ^ [482 ^ []]))],lemmata('[1].x')).
% 0.58/1.37  ncf('1.2.3.4',plain,[-(element(423 ^ [482 ^ [], the_carrier(482 ^ []), 423 ^ [482 ^ [], the_carrier(482 ^ []), 225 ^ [482 ^ []]]], the_carrier(482 ^ []))), element(423 ^ [482 ^ [], the_carrier(482 ^ []), 225 ^ [482 ^ []]], the_carrier(482 ^ [])), relstr_element_smaller(482 ^ [], the_carrier(482 ^ []), 423 ^ [482 ^ [], the_carrier(482 ^ []), 225 ^ [482 ^ []]])],extension(416 ^ 11,bind([[_91401], [423 ^ [482 ^ [], the_carrier(482 ^ []), 225 ^ [482 ^ []]]]]))).
% 0.58/1.37  ncf('1.2.3.4.1',plain,[-(element(423 ^ [482 ^ [], the_carrier(482 ^ []), 225 ^ [482 ^ []]], the_carrier(482 ^ [])))],reduction('1.2')).
% 0.58/1.37  ncf('1.2.3.4.2',plain,[-(relstr_element_smaller(482 ^ [], the_carrier(482 ^ []), 423 ^ [482 ^ [], the_carrier(482 ^ []), 225 ^ [482 ^ []]])), element(225 ^ [482 ^ []], the_carrier(482 ^ [])), relstr_element_smaller(482 ^ [], the_carrier(482 ^ []), 225 ^ [482 ^ []])],extension(416 ^ 12,bind([[_91401], [225 ^ [482 ^ []]]]))).
% 0.58/1.37  ncf('1.2.3.4.2.1',plain,[-(element(225 ^ [482 ^ []], the_carrier(482 ^ [])))],lemmata('[1].x')).
% 0.58/1.37  ncf('1.2.3.4.2.2',plain,[-(relstr_element_smaller(482 ^ [], the_carrier(482 ^ []), 225 ^ [482 ^ []]))],lemmata('[1].x')).
% 0.58/1.37  ncf('1.2.3.5',plain,[-(rel_str(482 ^ []))],extension(490 ^ 9)).
% 0.58/1.37  ncf('1.2.4',plain,[-(antisymmetric_relstr(482 ^ []))],extension(486 ^ 2)).
% 0.58/1.37  ncf('1.2.5',plain,[-(rel_str(482 ^ []))],extension(490 ^ 2)).
% 0.58/1.37  %-----------------------------------------------------
% 0.58/1.37  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------