%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SEU348+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n019.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 12:03:14 EDT 2023

% Result   : Theorem 100.73s 97.81s
% Output   : Proof 100.76s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem  : SEU348+1 : TPTP v8.1.2. Released v3.3.0.
% 0.10/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n019.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 13:44:57 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 100.73/97.81  
% 100.73/97.81  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 100.73/97.81  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 100.73/97.81  %-----------------------------------------------------
% 100.73/97.81  ncf(matrix, plain, [(1096 ^ _201308) ^ [] : [empty_carrier(1094 ^ [])], (1100 ^ _201308) ^ [] : [-(latt_str(1094 ^ []))], (1105 ^ _201308) ^ [] : [1106 ^ _201308 : [(1109 ^ _201308) ^ [] : [latt_set_smaller(1094 ^ [], cast_to_el_of_lattice(1094 ^ [], 1101 ^ []), 1093 ^ [])], (1107 ^ _201308) ^ [] : [-(relstr_element_smaller(poset_of_lattice(1094 ^ []), 1093 ^ [], 1101 ^ []))]], 1110 ^ _201308 : [(1113 ^ _201308) ^ [] : [relstr_element_smaller(poset_of_lattice(1094 ^ []), 1093 ^ [], 1101 ^ [])], (1111 ^ _201308) ^ [] : [-(latt_set_smaller(1094 ^ [], cast_to_el_of_lattice(1094 ^ [], 1101 ^ []), 1093 ^ []))]]], (1103 ^ _201308) ^ [] : [-(element(1101 ^ [], the_carrier(poset_of_lattice(1094 ^ []))))], (1098 ^ _201308) ^ [] : [-(lattice(1094 ^ []))], !, (774 ^ _166996) ^ [] : [-(join_semilatt_str(772 ^ []))], (292 ^ _166996) ^ [_176064, _176066] : [-(empty_carrier(_176064)), _176066 = _176064, empty_carrier(_176066)], (236 ^ _166996) ^ [_174328, _174330, _174332, _174334, _174336, _174338] : [-(relation_of2(_174336, _174332, _174328)), relation_of2(_174338, _174334, _174330), _174338 = _174336, _174334 = _174332, _174330 = _174328], (953 ^ _166996) ^ [] : [empty_carrier(949 ^ [])], (943 ^ _166996) ^ [_195998] : [-(element(941 ^ [_195998], powerset(_195998)))], (398 ^ _166996) ^ [_179679, _179681] : [_179681 = _179679, -(k2_lattice3(_179681) = k2_lattice3(_179679))], (780 ^ _166996) ^ [_190818, _190820] : [-(relation_of2(778 ^ [_190818, _190820], _190820, _190818))], (602 ^ _166996) ^ [_185799] : [613 ^ _166996 : [(614 ^ _166996) ^ [] : [-(reflexive(k2_lattice3(_185799)))], (618 ^ _166996) ^ [] : [-(transitive(k2_lattice3(_185799)))], (622 ^ _166996) ^ [] : [-(relation_of2_as_subset(k2_lattice3(_185799), the_carrier(_185799), the_carrier(_185799)))], (620 ^ _166996) ^ [] : [-(v1_partfun1(k2_lattice3(_185799), the_carrier(_185799), the_carrier(_185799)))], (616 ^ _166996) ^ [] : [-(antisymmetric(k2_lattice3(_185799)))]], -(empty_carrier(_185799)), lattice(_185799), latt_str(_185799)], (458 ^ _166996) ^ [_181795, _181797] : [in(_181797, _181795), in(_181795, _181797)], (464 ^ _166996) ^ [_181992] : [latt_str(_181992), 475 ^ _166996 : [(480 ^ _166996) ^ [] : [-(join_associative(_181992))], (486 ^ _166996) ^ [] : [-(meet_absorbing(_181992))], (488 ^ _166996) ^ [] : [-(join_absorbing(_181992))], (482 ^ _166996) ^ [] : [-(meet_commutative(_181992))], (476 ^ _166996) ^ [] : [empty_carrier(_181992)], (478 ^ _166996) ^ [] : [-(join_commutative(_181992))], (484 ^ _166996) ^ [] : [-(meet_associative(_181992))]], -(empty_carrier(_181992)), lattice(_181992)], (913 ^ _166996) ^ [] : [-(rel_str(911 ^ []))], (1062 ^ _166996) ^ [_199820, _199822, _199824] : [in(_199824, _199822), element(_199822, powerset(_199820)), empty(_199820)], (254 ^ _166996) ^ [_174909, _174911, _174913, _174915] : [-(subset(_174913, _174909)), subset(_174915, _174911), _174915 = _174913, _174911 = _174909], (688 ^ _166996) ^ [_188238] : [-(relation(relation_of_lattice(_188238))), -(empty_carrier(_188238)), lattice(_188238), latt_str(_188238)], (158 ^ _166996) ^ [_171893, _171895] : [-(rel_str(_171893)), _171895 = _171893, rel_str(_171895)], (968 ^ _166996) ^ [_196809] : [-(k2_lattice3(_196809) = relation_of_lattice(_196809)), -(empty_carrier(_196809)), lattice(_196809), latt_str(_196809)], (1030 ^ _166996) ^ [_198770, _198772] : [element(_198772, _198770), -(empty(_198770)), -(in(_198772, _198770))], (564 ^ _166996) ^ [_184742] : [575 ^ _166996 : [(576 ^ _166996) ^ [_185049] : [element(_185049, the_carrier(poset_of_lattice(_184742))), -(cast_to_el_of_lattice(_184742, _185049) = _185049)]], -(empty_carrier(_184742)), lattice(_184742), latt_str(_184742)], (800 ^ _166996) ^ [_191573] : [empty(the_carrier(_191573)), -(empty_carrier(_191573)), one_sorted_str(_191573)], (448 ^ _166996) ^ [_181496] : [rel_str(_181496), strict_rel_str(_181496), -(_181496 = rel_str_of(the_carrier(_181496), the_InternalRel(_181496)))], (890 ^ _166996) ^ [_194203, _194205] : [empty(cartesian_product2(_194205, _194203)), -(empty(_194205)), -(empty(_194203))], (432 ^ _166996) ^ [_180910, _180912] : [_180912 = _180910, -(poset_of_lattice(_180912) = poset_of_lattice(_180910))], (788 ^ _166996) ^ [_191201, _191203] : [795 ^ _166996 : [(798 ^ _166996) ^ [] : [-(strict_rel_str(rel_str_of(_191203, _191201)))], (796 ^ _166996) ^ [] : [empty_carrier(rel_str_of(_191203, _191201))]], -(empty(_191203)), relation_of2(_191201, _191203, _191203)], (218 ^ _166996) ^ [_173719, _173721, _173723, _173725, _173727, _173729] : [-(relation_of2_as_subset(_173727, _173723, _173719)), relation_of2_as_subset(_173729, _173725, _173721), _173729 = _173727, _173725 = _173723, _173721 = _173719], (582 ^ _166996) ^ [_185280, _185282] : [relation_of2(_185280, _185282, _185282), 585 ^ _166996 : [(588 ^ _166996) ^ [] : [-(rel_str(rel_str_of(_185282, _185280)))], (586 ^ _166996) ^ [] : [-(strict_rel_str(rel_str_of(_185282, _185280)))]]], (40 ^ _166996) ^ [_168334, _168336] : [-(meet_commutative(_168334)), _168336 = _168334, meet_commutative(_168336)], (936 ^ _166996) ^ [] : [-(reflexive_relstr(928 ^ []))], (940 ^ _166996) ^ [] : [-(antisymmetric_relstr(928 ^ []))], (814 ^ _166996) ^ [_191981] : [829 ^ _166996 : [(830 ^ _166996) ^ [] : [-(relation(the_InternalRel(_191981)))], (834 ^ _166996) ^ [] : [-(antisymmetric(the_InternalRel(_191981)))], (838 ^ _166996) ^ [] : [-(v1_partfun1(the_InternalRel(_191981), the_carrier(_191981), the_carrier(_191981)))], (836 ^ _166996) ^ [] : [-(transitive(the_InternalRel(_191981)))], (832 ^ _166996) ^ [] : [-(reflexive(the_InternalRel(_191981)))]], reflexive_relstr(_191981), transitive_relstr(_191981), antisymmetric_relstr(_191981), rel_str(_191981)], (378 ^ _166996) ^ [_178989, _178991, _178993, _178995] : [-(cartesian_product2(_178995, _178991) = cartesian_product2(_178993, _178989)), _178995 = _178993, _178991 = _178989], (90 ^ _166996) ^ [_169809, _169811] : [-(join_semilatt_str(_169809)), _169811 = _169809, join_semilatt_str(_169811)], (302 ^ _166996) ^ [_176359, _176361] : [-(lattice(_176359)), _176361 = _176359, lattice(_176361)], (208 ^ _166996) ^ [_173368, _173370] : [-(one_sorted_str(_173368)), _173370 = _173368, one_sorted_str(_173370)], (354 ^ _166996) ^ [_178038, _178040, _178042, _178044, _178046, _178048] : [-(latt_set_smaller(_178046, _178042, _178038)), latt_set_smaller(_178048, _178044, _178040), _178048 = _178046, _178044 = _178042, _178040 = _178038], (768 ^ _166996) ^ [] : [-(rel_str(766 ^ []))], (546 ^ _166996) ^ [_184224] : [557 ^ _166996 : [(558 ^ _166996) ^ [_184529] : [element(_184529, the_carrier(_184224)), -(cast_to_el_of_LattPOSet(_184224, _184529) = _184529)]], -(empty_carrier(_184224)), lattice(_184224), latt_str(_184224)], (927 ^ _166996) ^ [] : [-(empty(925 ^ []))], (777 ^ _166996) ^ [] : [-(latt_str(775 ^ []))], (426 ^ _166996) ^ [_180692, _180694] : [_180694 = _180692, -(the_carrier(_180694) = the_carrier(_180692))], (496 ^ _166996) ^ [_183007] : [latt_str(_183007), 527 ^ _166996 : [(530 ^ _166996) ^ [] : [-(lattice(_183007))], (528 ^ _166996) ^ [] : [empty_carrier(_183007)]], -(empty_carrier(_183007)), join_commutative(_183007), join_associative(_183007), meet_commutative(_183007), meet_associative(_183007), meet_absorbing(_183007), join_absorbing(_183007)], (50 ^ _166996) ^ [_168629, _168631] : [-(meet_associative(_168629)), _168631 = _168629, meet_associative(_168631)], (20 ^ _166996) ^ [_167744, _167746] : [-(join_commutative(_167744)), _167746 = _167744, join_commutative(_167746)], (994 ^ _166996) ^ [_197610, _197612] : [-(subset(_197612, _197612))], (955 ^ _166996) ^ [_196388] : [963 ^ _166996 : [(966 ^ _166996) ^ [] : [empty(962 ^ [_196388])], (964 ^ _166996) ^ [] : [-(element(962 ^ [_196388], powerset(the_carrier(_196388))))]], -(empty_carrier(_196388)), one_sorted_str(_196388)], (624 ^ _166996) ^ [] : [true___, -(true___)], (420 ^ _166996) ^ [_180474, _180476] : [_180476 = _180474, -(powerset(_180476) = powerset(_180474))], (596 ^ _166996) ^ [] : [true___, -(true___)], (630 ^ _166996) ^ [_186598] : [641 ^ _166996 : [(642 ^ _166996) ^ [] : [-(strict_rel_str(poset_of_lattice(_186598)))], (646 ^ _166996) ^ [] : [-(transitive_relstr(poset_of_lattice(_186598)))], (650 ^ _166996) ^ [] : [-(rel_str(poset_of_lattice(_186598)))], (648 ^ _166996) ^ [] : [-(antisymmetric_relstr(poset_of_lattice(_186598)))], (644 ^ _166996) ^ [] : [-(reflexive_relstr(poset_of_lattice(_186598)))]], -(empty_carrier(_186598)), lattice(_186598), latt_str(_186598)], (765 ^ _166996) ^ [] : [-(meet_semilatt_str(763 ^ []))], (746 ^ _166996) ^ [_189797, _189799, _189801] : [relation_of2_as_subset(_189797, _189801, _189799), -(element(_189797, powerset(cartesian_product2(_189801, _189799))))], (996 ^ _166996) ^ [_197719, _197721] : [in(_197721, _197719), -(element(_197721, _197719))], (1040 ^ _166996) ^ [_199097, _199099] : [element(_199099, powerset(_199097)), -(subset(_199099, _199097))], (438 ^ _166996) ^ [_181136, _181138, _181140, _181142] : [-(cast_to_el_of_lattice(_181142, _181138) = cast_to_el_of_lattice(_181140, _181136)), _181142 = _181140, _181138 = _181136], (917 ^ _166996) ^ [_195136] : [-(empty(_195136)), 921 ^ _166996 : [(924 ^ _166996) ^ [] : [empty(920 ^ [_195136])], (922 ^ _166996) ^ [] : [-(element(920 ^ [_195136], powerset(_195136)))]]], (168 ^ _166996) ^ [_172188, _172190] : [-(strict_rel_str(_172188)), _172190 = _172188, strict_rel_str(_172190)], (951 ^ _166996) ^ [] : [-(one_sorted_str(949 ^ []))], (930 ^ _166996) ^ [] : [-(rel_str(928 ^ []))], (708 ^ _166996) ^ [_188783] : [rel_str(_188783), -(one_sorted_str(_188783))], (336 ^ _166996) ^ [_177449, _177451, _177453, _177455, _177457, _177459] : [-(relstr_element_smaller(_177457, _177453, _177449)), relstr_element_smaller(_177459, _177455, _177451), _177459 = _177457, _177455 = _177453, _177451 = _177449], (4 ^ _166996) ^ [_167227, _167229] : [_167229 = _167227, -(_167227 = _167229)], (30 ^ _166996) ^ [_168039, _168041] : [-(join_associative(_168039)), _168041 = _168039, join_associative(_168041)], (702 ^ _166996) ^ [_188597] : [meet_semilatt_str(_188597), -(one_sorted_str(_188597))], (100 ^ _166996) ^ [_170104, _170106] : [-(relation(_170104)), _170106 = _170104, relation(_170106)], (268 ^ _166996) ^ [_175353, _175355, _175357, _175359] : [-(in(_175357, _175353)), in(_175359, _175355), _175359 = _175357, _175355 = _175353], (372 ^ _166996) ^ [_178743, _178745] : [_178745 = _178743, -(the_InternalRel(_178745) = the_InternalRel(_178743))], (110 ^ _166996) ^ [_170399, _170401] : [-(reflexive(_170399)), _170401 = _170399, reflexive(_170401)], (714 ^ _166996) ^ [] : [true___, -(true___)], (948 ^ _166996) ^ [] : [empty(946 ^ [])], (10 ^ _166996) ^ [_167431, _167433, _167435] : [-(_167435 = _167431), _167435 = _167433, _167433 = _167431], (1078 ^ _166996) ^ [_200318, _200320] : [in(_200320, _200318), empty(_200318)], (726 ^ _166996) ^ [_189274] : [latt_str(_189274), 729 ^ _166996 : [(732 ^ _166996) ^ [] : [-(join_semilatt_str(_189274))], (730 ^ _166996) ^ [] : [-(meet_semilatt_str(_189274))]]], (988 ^ _166996) ^ [_197403, _197405, _197407] : [relation_of2(_197403, _197407, _197405), -(relation_of2_as_subset(_197403, _197407, _197405))], (740 ^ _166996) ^ [] : [true___, -(true___)], (282 ^ _166996) ^ [_175769, _175771] : [-(empty(_175769)), _175771 = _175769, empty(_175771)], (868 ^ _166996) ^ [_193532] : [879 ^ _166996 : [(880 ^ _166996) ^ [] : [empty_carrier(poset_of_lattice(_193532))], (884 ^ _166996) ^ [] : [-(reflexive_relstr(poset_of_lattice(_193532)))], (888 ^ _166996) ^ [] : [-(antisymmetric_relstr(poset_of_lattice(_193532)))], (886 ^ _166996) ^ [] : [-(transitive_relstr(poset_of_lattice(_193532)))], (882 ^ _166996) ^ [] : [-(strict_rel_str(poset_of_lattice(_193532)))]], -(empty_carrier(_193532)), lattice(_193532), latt_str(_193532)], (120 ^ _166996) ^ [_170694, _170696] : [-(antisymmetric(_170694)), _170696 = _170694, antisymmetric(_170696)], (1046 ^ _166996) ^ [_199263, _199265] : [subset(_199265, _199263), -(element(_199265, powerset(_199263)))], (752 ^ _166996) ^ [_190011] : [rel_str(_190011), -(relation_of2_as_subset(the_InternalRel(_190011), the_carrier(_190011), the_carrier(_190011)))], (840 ^ _166996) ^ [_192743, _192745] : [859 ^ _166996 : [(862 ^ _166996) ^ [] : [-(reflexive_relstr(rel_str_of(_192745, _192743)))], (864 ^ _166996) ^ [] : [-(transitive_relstr(rel_str_of(_192745, _192743)))], (866 ^ _166996) ^ [] : [-(antisymmetric_relstr(rel_str_of(_192745, _192743)))], (860 ^ _166996) ^ [] : [-(strict_rel_str(rel_str_of(_192745, _192743)))]], reflexive(_192743), antisymmetric(_192743), transitive(_192743), v1_partfun1(_192743, _192745, _192745), relation_of2(_192743, _192745, _192745)], (130 ^ _166996) ^ [_170989, _170991] : [-(transitive(_170989)), _170991 = _170989, transitive(_170991)], (490 ^ _166996) ^ [_182797, _182799, _182801] : [element(_182797, powerset(cartesian_product2(_182801, _182799))), -(relation(_182797))], (178 ^ _166996) ^ [_172483, _172485] : [-(reflexive_relstr(_172483)), _172485 = _172483, reflexive_relstr(_172485)], (80 ^ _166996) ^ [_169514, _169516] : [-(meet_semilatt_str(_169514)), _169516 = _169514, meet_semilatt_str(_169516)], (810 ^ _166996) ^ [_191834] : [empty(powerset(_191834))], (188 ^ _166996) ^ [_172778, _172780] : [-(transitive_relstr(_172778)), _172780 = _172778, transitive_relstr(_172780)], (938 ^ _166996) ^ [] : [-(transitive_relstr(928 ^ []))], (1084 ^ _166996) ^ [_200505, _200507] : [empty(_200507), -(_200507 = _200505), empty(_200505)], (652 ^ _166996) ^ [_187268, _187270] : [-(element(cast_to_el_of_LattPOSet(_187270, _187268), the_carrier(poset_of_lattice(_187270)))), -(empty_carrier(_187270)), lattice(_187270), latt_str(_187270), element(_187268, the_carrier(_187270))], (670 ^ _166996) ^ [_187760, _187762] : [-(element(cast_to_el_of_lattice(_187762, _187760), the_carrier(_187762))), -(empty_carrier(_187762)), lattice(_187762), latt_str(_187762), element(_187760, the_carrier(poset_of_lattice(_187762)))], (945 ^ _166996) ^ [_196049] : [-(empty(941 ^ [_196049]))], (312 ^ _166996) ^ [_176654, _176656] : [-(latt_str(_176654)), _176656 = _176654, latt_str(_176656)], (1052 ^ _166996) ^ [_199493, _199495, _199497] : [-(element(_199497, _199493)), in(_199497, _199495), element(_199495, powerset(_199493))], (734 ^ _166996) ^ [] : [true___, -(true___)], (410 ^ _166996) ^ [_180143, _180145, _180147, _180149] : [-(cast_to_el_of_LattPOSet(_180149, _180145) = cast_to_el_of_LattPOSet(_180147, _180143)), _180149 = _180147, _180145 = _180143], (720 ^ _166996) ^ [_189088] : [join_semilatt_str(_189088), -(one_sorted_str(_189088))], (590 ^ _166996) ^ [] : [true___, -(true___)], (1002 ^ _166996) ^ [_197929, _197931] : [-(empty_carrier(_197929)), lattice(_197929), latt_str(_197929), 1013 ^ _166996 : [(1014 ^ _166996) ^ [_198256] : [element(_198256, the_carrier(_197929)), 1017 ^ _166996 : [(1024 ^ _166996) ^ [] : [relstr_element_smaller(poset_of_lattice(_197929), _197931, cast_to_el_of_LattPOSet(_197929, _198256)), -(latt_set_smaller(_197929, _198256, _197931))], (1018 ^ _166996) ^ [] : [latt_set_smaller(_197929, _198256, _197931), -(relstr_element_smaller(poset_of_lattice(_197929), _197931, cast_to_el_of_LattPOSet(_197929, _198256)))]]]]], (771 ^ _166996) ^ [] : [-(one_sorted_str(769 ^ []))], (934 ^ _166996) ^ [] : [-(strict_rel_str(928 ^ []))], (404 ^ _166996) ^ [_179897, _179899] : [_179899 = _179897, -(relation_of_lattice(_179899) = relation_of_lattice(_179897))], (786 ^ _166996) ^ [_191084, _191086] : [-(relation_of2_as_subset(784 ^ [_191084, _191086], _191086, _191084))], (198 ^ _166996) ^ [_173073, _173075] : [-(antisymmetric_relstr(_173073)), _173075 = _173073, antisymmetric_relstr(_173075)], (532 ^ _166996) ^ [_183849] : [-(poset_of_lattice(_183849) = rel_str_of(the_carrier(_183849), k2_lattice3(_183849))), -(empty_carrier(_183849)), lattice(_183849), latt_str(_183849)], (60 ^ _166996) ^ [_168924, _168926] : [-(meet_absorbing(_168924)), _168926 = _168924, meet_absorbing(_168926)], (783 ^ _166996) ^ [_190945] : [-(element(781 ^ [_190945], _190945))], (1072 ^ _166996) ^ [_200116] : [empty(_200116), -(_200116 = empty_set)], (140 ^ _166996) ^ [_171340, _171342, _171344, _171346, _171348, _171350] : [-(v1_partfun1(_171348, _171344, _171340)), v1_partfun1(_171350, _171346, _171342), _171350 = _171348, _171346 = _171344, _171342 = _171340], (2 ^ _166996) ^ [_167120] : [-(_167120 = _167120)], (932 ^ _166996) ^ [] : [empty_carrier(928 ^ [])], (758 ^ _166996) ^ [] : [true___, -(true___)], (915 ^ _166996) ^ [] : [-(strict_rel_str(911 ^ []))], (322 ^ _166996) ^ [_176977, _176979, _176981, _176983] : [-(element(_176981, _176977)), element(_176983, _176979), _176983 = _176981, _176979 = _176977], (812 ^ _166996) ^ [] : [-(empty(empty_set))], (70 ^ _166996) ^ [_169219, _169221] : [-(join_absorbing(_169219)), _169221 = _169219, join_absorbing(_169221)], (388 ^ _166996) ^ [_179348, _179350, _179352, _179354] : [-(rel_str_of(_179354, _179350) = rel_str_of(_179352, _179348)), _179354 = _179352, _179350 = _179348], (900 ^ _166996) ^ [_194509, _194511] : [relation_of2(_194509, _194511, _194511), 903 ^ _166996 : [(904 ^ _166996) ^ [_194679, _194681] : [rel_str_of(_194511, _194509) = rel_str_of(_194681, _194679), 907 ^ _166996 : [(910 ^ _166996) ^ [] : [-(_194509 = _194679)], (908 ^ _166996) ^ [] : [-(_194511 = _194681)]]]]], (982 ^ _166996) ^ [_197231, _197233, _197235] : [relation_of2_as_subset(_197231, _197235, _197233), -(relation_of2(_197231, _197235, _197233))]], input).
% 100.73/97.81  ncf('1',plain,[empty_carrier(1094 ^ [])],start(1096 ^ 0)).
% 100.73/97.81  ncf('1.1',plain,[-(empty_carrier(1094 ^ [])), 558 : element(cast_to_el_of_lattice(1094 ^ [], 1101 ^ []), the_carrier(1094 ^ [])), 558 : -(cast_to_el_of_LattPOSet(1094 ^ [], cast_to_el_of_lattice(1094 ^ [], 1101 ^ [])) = cast_to_el_of_lattice(1094 ^ [], 1101 ^ [])), 558 : lattice(1094 ^ []), 558 : latt_str(1094 ^ [])],extension(546 ^ 1,bind([[_184224, _184529], [1094 ^ [], cast_to_el_of_lattice(1094 ^ [], 1101 ^ [])]]))).
% 100.73/97.81  ncf('1.1.1',plain,[-(element(cast_to_el_of_lattice(1094 ^ [], 1101 ^ []), the_carrier(1094 ^ []))), -(empty_carrier(1094 ^ [])), lattice(1094 ^ []), latt_str(1094 ^ []), element(1101 ^ [], the_carrier(poset_of_lattice(1094 ^ [])))],extension(670 ^ 4,bind([[_187760, _187762], [1101 ^ [], 1094 ^ []]]))).
% 100.73/97.81  ncf('1.1.1.1',plain,[empty_carrier(1094 ^ [])],reduction('1')).
% 100.73/97.81  ncf('1.1.1.2',plain,[-(lattice(1094 ^ []))],extension(1098 ^ 5)).
% 100.73/97.81  ncf('1.1.1.3',plain,[-(latt_str(1094 ^ []))],extension(1100 ^ 5)).
% 100.73/97.81  ncf('1.1.1.4',plain,[-(element(1101 ^ [], the_carrier(poset_of_lattice(1094 ^ []))))],extension(1103 ^ 5)).
% 100.73/97.81  ncf('1.1.2',plain,[cast_to_el_of_LattPOSet(1094 ^ [], cast_to_el_of_lattice(1094 ^ [], 1101 ^ [])) = cast_to_el_of_lattice(1094 ^ [], 1101 ^ []), -(cast_to_el_of_LattPOSet(1094 ^ [], cast_to_el_of_lattice(1094 ^ [], 1101 ^ [])) = 1101 ^ []), cast_to_el_of_lattice(1094 ^ [], 1101 ^ []) = 1101 ^ []],extension(10 ^ 4,bind([[_167431, _167433, _167435], [1101 ^ [], cast_to_el_of_lattice(1094 ^ [], 1101 ^ []), cast_to_el_of_LattPOSet(1094 ^ [], cast_to_el_of_lattice(1094 ^ [], 1101 ^ []))]]))).
% 100.73/97.81  ncf('1.1.2.1',plain,[cast_to_el_of_LattPOSet(1094 ^ [], cast_to_el_of_lattice(1094 ^ [], 1101 ^ [])) = 1101 ^ [], -(relstr_element_smaller(poset_of_lattice(1094 ^ []), 1093 ^ [], 1101 ^ [])), relstr_element_smaller(rel_str_of(the_carrier(1094 ^ []), k2_lattice3(1094 ^ [])), 1093 ^ [], cast_to_el_of_LattPOSet(1094 ^ [], cast_to_el_of_lattice(1094 ^ [], 1101 ^ []))), rel_str_of(the_carrier(1094 ^ []), k2_lattice3(1094 ^ [])) = poset_of_lattice(1094 ^ []), 1093 ^ [] = 1093 ^ []],extension(336 ^ 5,bind([[_177449, _177451, _177453, _177455, _177457, _177459], [1101 ^ [], cast_to_el_of_LattPOSet(1094 ^ [], cast_to_el_of_lattice(1094 ^ [], 1101 ^ [])), 1093 ^ [], 1093 ^ [], poset_of_lattice(1094 ^ []), rel_str_of(the_carrier(1094 ^ []), k2_lattice3(1094 ^ []))]]))).
% 100.73/97.81  ncf('1.1.2.1.1',plain,[relstr_element_smaller(poset_of_lattice(1094 ^ []), 1093 ^ [], 1101 ^ []), -(relstr_element_smaller(poset_of_lattice(1094 ^ []), 1093 ^ [], cast_to_el_of_LattPOSet(1094 ^ [], cast_to_el_of_lattice(1094 ^ [], 1101 ^ [])))), poset_of_lattice(1094 ^ []) = poset_of_lattice(1094 ^ []), 1093 ^ [] = 1093 ^ [], 1101 ^ [] = cast_to_el_of_LattPOSet(1094 ^ [], cast_to_el_of_lattice(1094 ^ [], 1101 ^ []))],extension(336 ^ 6,bind([[_177449, _177451, _177453, _177455, _177457, _177459], [cast_to_el_of_LattPOSet(1094 ^ [], cast_to_el_of_lattice(1094 ^ [], 1101 ^ [])), 1101 ^ [], 1093 ^ [], 1093 ^ [], poset_of_lattice(1094 ^ []), poset_of_lattice(1094 ^ [])]]))).
% 100.73/97.81  ncf('1.1.2.1.1.1',plain,[relstr_element_smaller(poset_of_lattice(1094 ^ []), 1093 ^ [], cast_to_el_of_LattPOSet(1094 ^ [], cast_to_el_of_lattice(1094 ^ [], 1101 ^ []))), 1024 : -(latt_set_smaller(1094 ^ [], cast_to_el_of_lattice(1094 ^ [], 1101 ^ []), 1093 ^ [])), 1024 : element(cast_to_el_of_lattice(1094 ^ [], 1101 ^ []), the_carrier(1094 ^ [])), 1014 : -(empty_carrier(1094 ^ [])), 1014 : lattice(1094 ^ []), 1014 : latt_str(1094 ^ [])],extension(1002 ^ 7,bind([[_197929, _197931, _198256], [1094 ^ [], 1093 ^ [], cast_to_el_of_lattice(1094 ^ [], 1101 ^ [])]]))).
% 100.73/97.81  ncf('1.1.2.1.1.1.1',plain,[latt_set_smaller(1094 ^ [], cast_to_el_of_lattice(1094 ^ [], 1101 ^ []), 1093 ^ []), 1113 : relstr_element_smaller(poset_of_lattice(1094 ^ []), 1093 ^ [], 1101 ^ [])],extension(1105 ^ 12)).
% 100.73/97.81  ncf('1.1.2.1.1.1.1.1',plain,[-(relstr_element_smaller(poset_of_lattice(1094 ^ []), 1093 ^ [], 1101 ^ []))],reduction('1.1.2.1')).
% 100.76/97.81  ncf('1.1.2.1.1.1.2',plain,[-(element(cast_to_el_of_lattice(1094 ^ [], 1101 ^ []), the_carrier(1094 ^ [])))],lemmata('[1].x')).
% 100.76/97.81  ncf('1.1.2.1.1.1.3',plain,[empty_carrier(1094 ^ [])],reduction('1')).
% 100.76/97.81  ncf('1.1.2.1.1.1.4',plain,[-(lattice(1094 ^ []))],extension(1098 ^ 8)).
% 100.76/97.81  ncf('1.1.2.1.1.1.5',plain,[-(latt_str(1094 ^ []))],extension(1100 ^ 8)).
% 100.76/97.81  ncf('1.1.2.1.1.2',plain,[-(poset_of_lattice(1094 ^ []) = poset_of_lattice(1094 ^ []))],extension(2 ^ 7,bind([[_167120], [poset_of_lattice(1094 ^ [])]]))).
% 100.76/97.81  ncf('1.1.2.1.1.3',plain,[-(1093 ^ [] = 1093 ^ [])],extension(2 ^ 7,bind([[_167120], [1093 ^ []]]))).
% 100.76/97.81  ncf('1.1.2.1.1.4',plain,[-(1101 ^ [] = cast_to_el_of_LattPOSet(1094 ^ [], cast_to_el_of_lattice(1094 ^ [], 1101 ^ []))), cast_to_el_of_LattPOSet(1094 ^ [], cast_to_el_of_lattice(1094 ^ [], 1101 ^ [])) = 1101 ^ []],extension(4 ^ 7,bind([[_167227, _167229], [1101 ^ [], cast_to_el_of_LattPOSet(1094 ^ [], cast_to_el_of_lattice(1094 ^ [], 1101 ^ []))]]))).
% 100.76/97.81  ncf('1.1.2.1.1.4.1',plain,[-(cast_to_el_of_LattPOSet(1094 ^ [], cast_to_el_of_lattice(1094 ^ [], 1101 ^ [])) = 1101 ^ [])],reduction('1.1.2')).
% 100.76/97.81  ncf('1.1.2.1.2',plain,[-(relstr_element_smaller(rel_str_of(the_carrier(1094 ^ []), k2_lattice3(1094 ^ [])), 1093 ^ [], cast_to_el_of_LattPOSet(1094 ^ [], cast_to_el_of_lattice(1094 ^ [], 1101 ^ [])))), relstr_element_smaller(poset_of_lattice(1094 ^ []), 1093 ^ [], cast_to_el_of_LattPOSet(1094 ^ [], cast_to_el_of_lattice(1094 ^ [], 1101 ^ []))), poset_of_lattice(1094 ^ []) = rel_str_of(the_carrier(1094 ^ []), k2_lattice3(1094 ^ [])), 1093 ^ [] = 1093 ^ [], cast_to_el_of_LattPOSet(1094 ^ [], cast_to_el_of_lattice(1094 ^ [], 1101 ^ [])) = cast_to_el_of_LattPOSet(1094 ^ [], cast_to_el_of_lattice(1094 ^ [], 1101 ^ []))],extension(336 ^ 6,bind([[_177449, _177451, _177453, _177455, _177457, _177459], [cast_to_el_of_LattPOSet(1094 ^ [], cast_to_el_of_lattice(1094 ^ [], 1101 ^ [])), cast_to_el_of_LattPOSet(1094 ^ [], cast_to_el_of_lattice(1094 ^ [], 1101 ^ [])), 1093 ^ [], 1093 ^ [], rel_str_of(the_carrier(1094 ^ []), k2_lattice3(1094 ^ [])), poset_of_lattice(1094 ^ [])]]))).
% 100.76/97.81  ncf('1.1.2.1.2.1',plain,[-(relstr_element_smaller(poset_of_lattice(1094 ^ []), 1093 ^ [], cast_to_el_of_LattPOSet(1094 ^ [], cast_to_el_of_lattice(1094 ^ [], 1101 ^ [])))), 1018 : latt_set_smaller(1094 ^ [], cast_to_el_of_lattice(1094 ^ [], 1101 ^ []), 1093 ^ []), 1018 : element(cast_to_el_of_lattice(1094 ^ [], 1101 ^ []), the_carrier(1094 ^ [])), 1014 : -(empty_carrier(1094 ^ [])), 1014 : lattice(1094 ^ []), 1014 : latt_str(1094 ^ [])],extension(1002 ^ 7,bind([[_197929, _197931, _198256], [1094 ^ [], 1093 ^ [], cast_to_el_of_lattice(1094 ^ [], 1101 ^ [])]]))).
% 100.76/97.81  ncf('1.1.2.1.2.1.1',plain,[-(latt_set_smaller(1094 ^ [], cast_to_el_of_lattice(1094 ^ [], 1101 ^ []), 1093 ^ [])), 1107 : -(relstr_element_smaller(poset_of_lattice(1094 ^ []), 1093 ^ [], 1101 ^ []))],extension(1105 ^ 12)).
% 100.76/97.81  ncf('1.1.2.1.2.1.1.1',plain,[relstr_element_smaller(poset_of_lattice(1094 ^ []), 1093 ^ [], 1101 ^ [])],lemmata('[2, 1, 1].x')).
% 100.76/97.81  ncf('1.1.2.1.2.1.2',plain,[-(element(cast_to_el_of_lattice(1094 ^ [], 1101 ^ []), the_carrier(1094 ^ [])))],lemmata('[1].x')).
% 100.76/97.81  ncf('1.1.2.1.2.1.3',plain,[empty_carrier(1094 ^ [])],reduction('1')).
% 100.76/97.81  ncf('1.1.2.1.2.1.4',plain,[-(lattice(1094 ^ []))],extension(1098 ^ 8)).
% 100.76/97.81  ncf('1.1.2.1.2.1.5',plain,[-(latt_str(1094 ^ []))],extension(1100 ^ 8)).
% 100.76/97.81  ncf('1.1.2.1.2.2',plain,[-(poset_of_lattice(1094 ^ []) = rel_str_of(the_carrier(1094 ^ []), k2_lattice3(1094 ^ []))), -(empty_carrier(1094 ^ [])), lattice(1094 ^ []), latt_str(1094 ^ [])],extension(532 ^ 7,bind([[_183849], [1094 ^ []]]))).
% 100.76/97.81  ncf('1.1.2.1.2.2.1',plain,[empty_carrier(1094 ^ [])],reduction('1')).
% 100.76/97.81  ncf('1.1.2.1.2.2.2',plain,[-(lattice(1094 ^ []))],extension(1098 ^ 8)).
% 100.76/97.81  ncf('1.1.2.1.2.2.3',plain,[-(latt_str(1094 ^ []))],extension(1100 ^ 8)).
% 100.76/97.81  ncf('1.1.2.1.2.3',plain,[-(1093 ^ [] = 1093 ^ [])],extension(2 ^ 7,bind([[_167120], [1093 ^ []]]))).
% 100.76/97.81  ncf('1.1.2.1.2.4',plain,[-(cast_to_el_of_LattPOSet(1094 ^ [], cast_to_el_of_lattice(1094 ^ [], 1101 ^ [])) = cast_to_el_of_LattPOSet(1094 ^ [], cast_to_el_of_lattice(1094 ^ [], 1101 ^ [])))],extension(2 ^ 7,bind([[_167120], [cast_to_el_of_LattPOSet(1094 ^ [], cast_to_el_of_lattice(1094 ^ [], 1101 ^ []))]]))).
% 100.76/97.81  ncf('1.1.2.1.3',plain,[-(rel_str_of(the_carrier(1094 ^ []), k2_lattice3(1094 ^ [])) = poset_of_lattice(1094 ^ [])), poset_of_lattice(1094 ^ []) = rel_str_of(the_carrier(1094 ^ []), k2_lattice3(1094 ^ []))],extension(4 ^ 6,bind([[_167227, _167229], [rel_str_of(the_carrier(1094 ^ []), k2_lattice3(1094 ^ [])), poset_of_lattice(1094 ^ [])]]))).
% 100.76/97.81  ncf('1.1.2.1.3.1',plain,[-(poset_of_lattice(1094 ^ []) = rel_str_of(the_carrier(1094 ^ []), k2_lattice3(1094 ^ []))), -(empty_carrier(1094 ^ [])), lattice(1094 ^ []), latt_str(1094 ^ [])],extension(532 ^ 7,bind([[_183849], [1094 ^ []]]))).
% 100.76/97.81  ncf('1.1.2.1.3.1.1',plain,[empty_carrier(1094 ^ [])],reduction('1')).
% 100.76/97.81  ncf('1.1.2.1.3.1.2',plain,[-(lattice(1094 ^ []))],extension(1098 ^ 8)).
% 100.76/97.81  ncf('1.1.2.1.3.1.3',plain,[-(latt_str(1094 ^ []))],extension(1100 ^ 8)).
% 100.76/97.81  ncf('1.1.2.1.4',plain,[-(1093 ^ [] = 1093 ^ [])],extension(2 ^ 6,bind([[_167120], [1093 ^ []]]))).
% 100.76/97.81  ncf('1.1.2.2',plain,[-(cast_to_el_of_lattice(1094 ^ [], 1101 ^ []) = 1101 ^ []), 576 : element(1101 ^ [], the_carrier(poset_of_lattice(1094 ^ []))), 576 : -(empty_carrier(1094 ^ [])), 576 : lattice(1094 ^ []), 576 : latt_str(1094 ^ [])],extension(564 ^ 5,bind([[_184742, _185049], [1094 ^ [], 1101 ^ []]]))).
% 100.76/97.81  ncf('1.1.2.2.1',plain,[-(element(1101 ^ [], the_carrier(poset_of_lattice(1094 ^ []))))],extension(1103 ^ 8)).
% 100.76/97.81  ncf('1.1.2.2.2',plain,[empty_carrier(1094 ^ [])],reduction('1')).
% 100.76/97.81  ncf('1.1.2.2.3',plain,[-(lattice(1094 ^ []))],extension(1098 ^ 6)).
% 100.76/97.81  ncf('1.1.2.2.4',plain,[-(latt_str(1094 ^ []))],extension(1100 ^ 6)).
% 100.76/97.81  ncf('1.1.3',plain,[-(lattice(1094 ^ []))],extension(1098 ^ 2)).
% 100.76/97.81  ncf('1.1.4',plain,[-(latt_str(1094 ^ []))],extension(1100 ^ 2)).
% 100.76/97.81  %-----------------------------------------------------
% 100.76/97.81  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------