%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SEU350+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n015.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 75.10s 72.90s
% Output   : Proof 75.10s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU350+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.13  % Command  : nanocop.sh %s %d
% 0.12/0.34  % Computer : n015.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Thu May 18 13:14:52 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 75.10/72.90  
% 75.10/72.90  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 75.10/72.90  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 75.10/72.90  %-----------------------------------------------------
% 75.10/72.90  ncf(matrix, plain, [(1096 ^ _199493) ^ [] : [empty_carrier(1094 ^ [])], (1100 ^ _199493) ^ [] : [-(latt_str(1094 ^ []))], (1105 ^ _199493) ^ [] : [1106 ^ _199493 : [(1109 ^ _199493) ^ [] : [latt_element_smaller(1094 ^ [], cast_to_el_of_lattice(1094 ^ [], 1101 ^ []), 1093 ^ [])], (1107 ^ _199493) ^ [] : [-(relstr_set_smaller(poset_of_lattice(1094 ^ []), 1093 ^ [], 1101 ^ []))]], 1110 ^ _199493 : [(1113 ^ _199493) ^ [] : [relstr_set_smaller(poset_of_lattice(1094 ^ []), 1093 ^ [], 1101 ^ [])], (1111 ^ _199493) ^ [] : [-(latt_element_smaller(1094 ^ [], cast_to_el_of_lattice(1094 ^ [], 1101 ^ []), 1093 ^ []))]]], (1103 ^ _199493) ^ [] : [-(element(1101 ^ [], the_carrier(poset_of_lattice(1094 ^ []))))], (1098 ^ _199493) ^ [] : [-(lattice(1094 ^ []))], !, (774 ^ _165181) ^ [] : [-(join_semilatt_str(772 ^ []))], (292 ^ _165181) ^ [_174249, _174251] : [-(empty_carrier(_174249)), _174251 = _174249, empty_carrier(_174251)], (236 ^ _165181) ^ [_172513, _172515, _172517, _172519, _172521, _172523] : [-(relation_of2(_172521, _172517, _172513)), relation_of2(_172523, _172519, _172515), _172523 = _172521, _172519 = _172517, _172515 = _172513], (953 ^ _165181) ^ [] : [empty_carrier(949 ^ [])], (943 ^ _165181) ^ [_194183] : [-(element(941 ^ [_194183], powerset(_194183)))], (398 ^ _165181) ^ [_177864, _177866] : [_177866 = _177864, -(k2_lattice3(_177866) = k2_lattice3(_177864))], (780 ^ _165181) ^ [_189003, _189005] : [-(relation_of2(778 ^ [_189003, _189005], _189005, _189003))], (602 ^ _165181) ^ [_183984] : [613 ^ _165181 : [(614 ^ _165181) ^ [] : [-(reflexive(k2_lattice3(_183984)))], (618 ^ _165181) ^ [] : [-(transitive(k2_lattice3(_183984)))], (622 ^ _165181) ^ [] : [-(relation_of2_as_subset(k2_lattice3(_183984), the_carrier(_183984), the_carrier(_183984)))], (620 ^ _165181) ^ [] : [-(v1_partfun1(k2_lattice3(_183984), the_carrier(_183984), the_carrier(_183984)))], (616 ^ _165181) ^ [] : [-(antisymmetric(k2_lattice3(_183984)))]], -(empty_carrier(_183984)), lattice(_183984), latt_str(_183984)], (458 ^ _165181) ^ [_179980, _179982] : [in(_179982, _179980), in(_179980, _179982)], (464 ^ _165181) ^ [_180177] : [latt_str(_180177), 475 ^ _165181 : [(480 ^ _165181) ^ [] : [-(join_associative(_180177))], (486 ^ _165181) ^ [] : [-(meet_absorbing(_180177))], (488 ^ _165181) ^ [] : [-(join_absorbing(_180177))], (482 ^ _165181) ^ [] : [-(meet_commutative(_180177))], (476 ^ _165181) ^ [] : [empty_carrier(_180177)], (478 ^ _165181) ^ [] : [-(join_commutative(_180177))], (484 ^ _165181) ^ [] : [-(meet_associative(_180177))]], -(empty_carrier(_180177)), lattice(_180177)], (913 ^ _165181) ^ [] : [-(rel_str(911 ^ []))], (1062 ^ _165181) ^ [_198005, _198007, _198009] : [in(_198009, _198007), element(_198007, powerset(_198005)), empty(_198005)], (254 ^ _165181) ^ [_173094, _173096, _173098, _173100] : [-(subset(_173098, _173094)), subset(_173100, _173096), _173100 = _173098, _173096 = _173094], (688 ^ _165181) ^ [_186423] : [-(relation(relation_of_lattice(_186423))), -(empty_carrier(_186423)), lattice(_186423), latt_str(_186423)], (158 ^ _165181) ^ [_170078, _170080] : [-(rel_str(_170078)), _170080 = _170078, rel_str(_170080)], (968 ^ _165181) ^ [_194994] : [-(k2_lattice3(_194994) = relation_of_lattice(_194994)), -(empty_carrier(_194994)), lattice(_194994), latt_str(_194994)], (1012 ^ _165181) ^ [_196412, _196414] : [-(empty_carrier(_196412)), lattice(_196412), latt_str(_196412), 1023 ^ _165181 : [(1024 ^ _165181) ^ [_196739] : [element(_196739, the_carrier(_196412)), 1027 ^ _165181 : [(1034 ^ _165181) ^ [] : [relstr_set_smaller(poset_of_lattice(_196412), _196414, cast_to_el_of_LattPOSet(_196412, _196739)), -(latt_element_smaller(_196412, _196739, _196414))], (1028 ^ _165181) ^ [] : [latt_element_smaller(_196412, _196739, _196414), -(relstr_set_smaller(poset_of_lattice(_196412), _196414, cast_to_el_of_LattPOSet(_196412, _196739)))]]]]], (564 ^ _165181) ^ [_182927] : [575 ^ _165181 : [(576 ^ _165181) ^ [_183234] : [element(_183234, the_carrier(poset_of_lattice(_182927))), -(cast_to_el_of_lattice(_182927, _183234) = _183234)]], -(empty_carrier(_182927)), lattice(_182927), latt_str(_182927)], (800 ^ _165181) ^ [_189758] : [empty(the_carrier(_189758)), -(empty_carrier(_189758)), one_sorted_str(_189758)], (448 ^ _165181) ^ [_179681] : [rel_str(_179681), strict_rel_str(_179681), -(_179681 = rel_str_of(the_carrier(_179681), the_InternalRel(_179681)))], (890 ^ _165181) ^ [_192388, _192390] : [empty(cartesian_product2(_192390, _192388)), -(empty(_192390)), -(empty(_192388))], (432 ^ _165181) ^ [_179095, _179097] : [_179097 = _179095, -(poset_of_lattice(_179097) = poset_of_lattice(_179095))], (788 ^ _165181) ^ [_189386, _189388] : [795 ^ _165181 : [(798 ^ _165181) ^ [] : [-(strict_rel_str(rel_str_of(_189388, _189386)))], (796 ^ _165181) ^ [] : [empty_carrier(rel_str_of(_189388, _189386))]], -(empty(_189388)), relation_of2(_189386, _189388, _189388)], (218 ^ _165181) ^ [_171904, _171906, _171908, _171910, _171912, _171914] : [-(relation_of2_as_subset(_171912, _171908, _171904)), relation_of2_as_subset(_171914, _171910, _171906), _171914 = _171912, _171910 = _171908, _171906 = _171904], (582 ^ _165181) ^ [_183465, _183467] : [relation_of2(_183465, _183467, _183467), 585 ^ _165181 : [(588 ^ _165181) ^ [] : [-(rel_str(rel_str_of(_183467, _183465)))], (586 ^ _165181) ^ [] : [-(strict_rel_str(rel_str_of(_183467, _183465)))]]], (40 ^ _165181) ^ [_166519, _166521] : [-(meet_commutative(_166519)), _166521 = _166519, meet_commutative(_166521)], (936 ^ _165181) ^ [] : [-(reflexive_relstr(928 ^ []))], (940 ^ _165181) ^ [] : [-(antisymmetric_relstr(928 ^ []))], (814 ^ _165181) ^ [_190166] : [829 ^ _165181 : [(830 ^ _165181) ^ [] : [-(relation(the_InternalRel(_190166)))], (834 ^ _165181) ^ [] : [-(antisymmetric(the_InternalRel(_190166)))], (838 ^ _165181) ^ [] : [-(v1_partfun1(the_InternalRel(_190166), the_carrier(_190166), the_carrier(_190166)))], (836 ^ _165181) ^ [] : [-(transitive(the_InternalRel(_190166)))], (832 ^ _165181) ^ [] : [-(reflexive(the_InternalRel(_190166)))]], reflexive_relstr(_190166), transitive_relstr(_190166), antisymmetric_relstr(_190166), rel_str(_190166)], (378 ^ _165181) ^ [_177174, _177176, _177178, _177180] : [-(cartesian_product2(_177180, _177176) = cartesian_product2(_177178, _177174)), _177180 = _177178, _177176 = _177174], (90 ^ _165181) ^ [_167994, _167996] : [-(join_semilatt_str(_167994)), _167996 = _167994, join_semilatt_str(_167996)], (302 ^ _165181) ^ [_174544, _174546] : [-(lattice(_174544)), _174546 = _174544, lattice(_174546)], (208 ^ _165181) ^ [_171553, _171555] : [-(one_sorted_str(_171553)), _171555 = _171553, one_sorted_str(_171555)], (354 ^ _165181) ^ [_176223, _176225, _176227, _176229, _176231, _176233] : [-(latt_element_smaller(_176231, _176227, _176223)), latt_element_smaller(_176233, _176229, _176225), _176233 = _176231, _176229 = _176227, _176225 = _176223], (768 ^ _165181) ^ [] : [-(rel_str(766 ^ []))], (546 ^ _165181) ^ [_182409] : [557 ^ _165181 : [(558 ^ _165181) ^ [_182714] : [element(_182714, the_carrier(_182409)), -(cast_to_el_of_LattPOSet(_182409, _182714) = _182714)]], -(empty_carrier(_182409)), lattice(_182409), latt_str(_182409)], (927 ^ _165181) ^ [] : [-(empty(925 ^ []))], (777 ^ _165181) ^ [] : [-(latt_str(775 ^ []))], (426 ^ _165181) ^ [_178877, _178879] : [_178879 = _178877, -(the_carrier(_178879) = the_carrier(_178877))], (496 ^ _165181) ^ [_181192] : [latt_str(_181192), 527 ^ _165181 : [(530 ^ _165181) ^ [] : [-(lattice(_181192))], (528 ^ _165181) ^ [] : [empty_carrier(_181192)]], -(empty_carrier(_181192)), join_commutative(_181192), join_associative(_181192), meet_commutative(_181192), meet_associative(_181192), meet_absorbing(_181192), join_absorbing(_181192)], (50 ^ _165181) ^ [_166814, _166816] : [-(meet_associative(_166814)), _166816 = _166814, meet_associative(_166816)], (20 ^ _165181) ^ [_165929, _165931] : [-(join_commutative(_165929)), _165931 = _165929, join_commutative(_165931)], (994 ^ _165181) ^ [_195795, _195797] : [-(subset(_195797, _195797))], (955 ^ _165181) ^ [_194573] : [963 ^ _165181 : [(966 ^ _165181) ^ [] : [empty(962 ^ [_194573])], (964 ^ _165181) ^ [] : [-(element(962 ^ [_194573], powerset(the_carrier(_194573))))]], -(empty_carrier(_194573)), one_sorted_str(_194573)], (624 ^ _165181) ^ [] : [true___, -(true___)], (420 ^ _165181) ^ [_178659, _178661] : [_178661 = _178659, -(powerset(_178661) = powerset(_178659))], (596 ^ _165181) ^ [] : [true___, -(true___)], (630 ^ _165181) ^ [_184783] : [641 ^ _165181 : [(642 ^ _165181) ^ [] : [-(strict_rel_str(poset_of_lattice(_184783)))], (646 ^ _165181) ^ [] : [-(transitive_relstr(poset_of_lattice(_184783)))], (650 ^ _165181) ^ [] : [-(rel_str(poset_of_lattice(_184783)))], (648 ^ _165181) ^ [] : [-(antisymmetric_relstr(poset_of_lattice(_184783)))], (644 ^ _165181) ^ [] : [-(reflexive_relstr(poset_of_lattice(_184783)))]], -(empty_carrier(_184783)), lattice(_184783), latt_str(_184783)], (765 ^ _165181) ^ [] : [-(meet_semilatt_str(763 ^ []))], (746 ^ _165181) ^ [_187982, _187984, _187986] : [relation_of2_as_subset(_187982, _187986, _187984), -(element(_187982, powerset(cartesian_product2(_187986, _187984))))], (996 ^ _165181) ^ [_195904, _195906] : [in(_195906, _195904), -(element(_195906, _195904))], (1040 ^ _165181) ^ [_197282, _197284] : [element(_197284, powerset(_197282)), -(subset(_197284, _197282))], (438 ^ _165181) ^ [_179321, _179323, _179325, _179327] : [-(cast_to_el_of_lattice(_179327, _179323) = cast_to_el_of_lattice(_179325, _179321)), _179327 = _179325, _179323 = _179321], (917 ^ _165181) ^ [_193321] : [-(empty(_193321)), 921 ^ _165181 : [(924 ^ _165181) ^ [] : [empty(920 ^ [_193321])], (922 ^ _165181) ^ [] : [-(element(920 ^ [_193321], powerset(_193321)))]]], (168 ^ _165181) ^ [_170373, _170375] : [-(strict_rel_str(_170373)), _170375 = _170373, strict_rel_str(_170375)], (951 ^ _165181) ^ [] : [-(one_sorted_str(949 ^ []))], (930 ^ _165181) ^ [] : [-(rel_str(928 ^ []))], (708 ^ _165181) ^ [_186968] : [rel_str(_186968), -(one_sorted_str(_186968))], (336 ^ _165181) ^ [_175634, _175636, _175638, _175640, _175642, _175644] : [-(relstr_set_smaller(_175642, _175638, _175634)), relstr_set_smaller(_175644, _175640, _175636), _175644 = _175642, _175640 = _175638, _175636 = _175634], (4 ^ _165181) ^ [_165412, _165414] : [_165414 = _165412, -(_165412 = _165414)], (30 ^ _165181) ^ [_166224, _166226] : [-(join_associative(_166224)), _166226 = _166224, join_associative(_166226)], (702 ^ _165181) ^ [_186782] : [meet_semilatt_str(_186782), -(one_sorted_str(_186782))], (100 ^ _165181) ^ [_168289, _168291] : [-(relation(_168289)), _168291 = _168289, relation(_168291)], (268 ^ _165181) ^ [_173538, _173540, _173542, _173544] : [-(in(_173542, _173538)), in(_173544, _173540), _173544 = _173542, _173540 = _173538], (372 ^ _165181) ^ [_176928, _176930] : [_176930 = _176928, -(the_InternalRel(_176930) = the_InternalRel(_176928))], (110 ^ _165181) ^ [_168584, _168586] : [-(reflexive(_168584)), _168586 = _168584, reflexive(_168586)], (714 ^ _165181) ^ [] : [true___, -(true___)], (948 ^ _165181) ^ [] : [empty(946 ^ [])], (10 ^ _165181) ^ [_165616, _165618, _165620] : [-(_165620 = _165616), _165620 = _165618, _165618 = _165616], (1078 ^ _165181) ^ [_198503, _198505] : [in(_198505, _198503), empty(_198503)], (726 ^ _165181) ^ [_187459] : [latt_str(_187459), 729 ^ _165181 : [(732 ^ _165181) ^ [] : [-(join_semilatt_str(_187459))], (730 ^ _165181) ^ [] : [-(meet_semilatt_str(_187459))]]], (988 ^ _165181) ^ [_195588, _195590, _195592] : [relation_of2(_195588, _195592, _195590), -(relation_of2_as_subset(_195588, _195592, _195590))], (740 ^ _165181) ^ [] : [true___, -(true___)], (282 ^ _165181) ^ [_173954, _173956] : [-(empty(_173954)), _173956 = _173954, empty(_173956)], (868 ^ _165181) ^ [_191717] : [879 ^ _165181 : [(880 ^ _165181) ^ [] : [empty_carrier(poset_of_lattice(_191717))], (884 ^ _165181) ^ [] : [-(reflexive_relstr(poset_of_lattice(_191717)))], (888 ^ _165181) ^ [] : [-(antisymmetric_relstr(poset_of_lattice(_191717)))], (886 ^ _165181) ^ [] : [-(transitive_relstr(poset_of_lattice(_191717)))], (882 ^ _165181) ^ [] : [-(strict_rel_str(poset_of_lattice(_191717)))]], -(empty_carrier(_191717)), lattice(_191717), latt_str(_191717)], (120 ^ _165181) ^ [_168879, _168881] : [-(antisymmetric(_168879)), _168881 = _168879, antisymmetric(_168881)], (1046 ^ _165181) ^ [_197448, _197450] : [subset(_197450, _197448), -(element(_197450, powerset(_197448)))], (752 ^ _165181) ^ [_188196] : [rel_str(_188196), -(relation_of2_as_subset(the_InternalRel(_188196), the_carrier(_188196), the_carrier(_188196)))], (840 ^ _165181) ^ [_190928, _190930] : [859 ^ _165181 : [(862 ^ _165181) ^ [] : [-(reflexive_relstr(rel_str_of(_190930, _190928)))], (864 ^ _165181) ^ [] : [-(transitive_relstr(rel_str_of(_190930, _190928)))], (866 ^ _165181) ^ [] : [-(antisymmetric_relstr(rel_str_of(_190930, _190928)))], (860 ^ _165181) ^ [] : [-(strict_rel_str(rel_str_of(_190930, _190928)))]], reflexive(_190928), antisymmetric(_190928), transitive(_190928), v1_partfun1(_190928, _190930, _190930), relation_of2(_190928, _190930, _190930)], (130 ^ _165181) ^ [_169174, _169176] : [-(transitive(_169174)), _169176 = _169174, transitive(_169176)], (490 ^ _165181) ^ [_180982, _180984, _180986] : [element(_180982, powerset(cartesian_product2(_180986, _180984))), -(relation(_180982))], (178 ^ _165181) ^ [_170668, _170670] : [-(reflexive_relstr(_170668)), _170670 = _170668, reflexive_relstr(_170670)], (80 ^ _165181) ^ [_167699, _167701] : [-(meet_semilatt_str(_167699)), _167701 = _167699, meet_semilatt_str(_167701)], (810 ^ _165181) ^ [_190019] : [empty(powerset(_190019))], (188 ^ _165181) ^ [_170963, _170965] : [-(transitive_relstr(_170963)), _170965 = _170963, transitive_relstr(_170965)], (938 ^ _165181) ^ [] : [-(transitive_relstr(928 ^ []))], (1084 ^ _165181) ^ [_198690, _198692] : [empty(_198692), -(_198692 = _198690), empty(_198690)], (652 ^ _165181) ^ [_185453, _185455] : [-(element(cast_to_el_of_LattPOSet(_185455, _185453), the_carrier(poset_of_lattice(_185455)))), -(empty_carrier(_185455)), lattice(_185455), latt_str(_185455), element(_185453, the_carrier(_185455))], (670 ^ _165181) ^ [_185945, _185947] : [-(element(cast_to_el_of_lattice(_185947, _185945), the_carrier(_185947))), -(empty_carrier(_185947)), lattice(_185947), latt_str(_185947), element(_185945, the_carrier(poset_of_lattice(_185947)))], (945 ^ _165181) ^ [_194234] : [-(empty(941 ^ [_194234]))], (312 ^ _165181) ^ [_174839, _174841] : [-(latt_str(_174839)), _174841 = _174839, latt_str(_174841)], (1052 ^ _165181) ^ [_197678, _197680, _197682] : [-(element(_197682, _197678)), in(_197682, _197680), element(_197680, powerset(_197678))], (734 ^ _165181) ^ [] : [true___, -(true___)], (410 ^ _165181) ^ [_178328, _178330, _178332, _178334] : [-(cast_to_el_of_LattPOSet(_178334, _178330) = cast_to_el_of_LattPOSet(_178332, _178328)), _178334 = _178332, _178330 = _178328], (720 ^ _165181) ^ [_187273] : [join_semilatt_str(_187273), -(one_sorted_str(_187273))], (590 ^ _165181) ^ [] : [true___, -(true___)], (1002 ^ _165181) ^ [_196114, _196116] : [element(_196116, _196114), -(empty(_196114)), -(in(_196116, _196114))], (771 ^ _165181) ^ [] : [-(one_sorted_str(769 ^ []))], (934 ^ _165181) ^ [] : [-(strict_rel_str(928 ^ []))], (404 ^ _165181) ^ [_178082, _178084] : [_178084 = _178082, -(relation_of_lattice(_178084) = relation_of_lattice(_178082))], (786 ^ _165181) ^ [_189269, _189271] : [-(relation_of2_as_subset(784 ^ [_189269, _189271], _189271, _189269))], (198 ^ _165181) ^ [_171258, _171260] : [-(antisymmetric_relstr(_171258)), _171260 = _171258, antisymmetric_relstr(_171260)], (532 ^ _165181) ^ [_182034] : [-(poset_of_lattice(_182034) = rel_str_of(the_carrier(_182034), k2_lattice3(_182034))), -(empty_carrier(_182034)), lattice(_182034), latt_str(_182034)], (60 ^ _165181) ^ [_167109, _167111] : [-(meet_absorbing(_167109)), _167111 = _167109, meet_absorbing(_167111)], (783 ^ _165181) ^ [_189130] : [-(element(781 ^ [_189130], _189130))], (1072 ^ _165181) ^ [_198301] : [empty(_198301), -(_198301 = empty_set)], (140 ^ _165181) ^ [_169525, _169527, _169529, _169531, _169533, _169535] : [-(v1_partfun1(_169533, _169529, _169525)), v1_partfun1(_169535, _169531, _169527), _169535 = _169533, _169531 = _169529, _169527 = _169525], (2 ^ _165181) ^ [_165305] : [-(_165305 = _165305)], (932 ^ _165181) ^ [] : [empty_carrier(928 ^ [])], (758 ^ _165181) ^ [] : [true___, -(true___)], (915 ^ _165181) ^ [] : [-(strict_rel_str(911 ^ []))], (322 ^ _165181) ^ [_175162, _175164, _175166, _175168] : [-(element(_175166, _175162)), element(_175168, _175164), _175168 = _175166, _175164 = _175162], (812 ^ _165181) ^ [] : [-(empty(empty_set))], (70 ^ _165181) ^ [_167404, _167406] : [-(join_absorbing(_167404)), _167406 = _167404, join_absorbing(_167406)], (388 ^ _165181) ^ [_177533, _177535, _177537, _177539] : [-(rel_str_of(_177539, _177535) = rel_str_of(_177537, _177533)), _177539 = _177537, _177535 = _177533], (900 ^ _165181) ^ [_192694, _192696] : [relation_of2(_192694, _192696, _192696), 903 ^ _165181 : [(904 ^ _165181) ^ [_192864, _192866] : [rel_str_of(_192696, _192694) = rel_str_of(_192866, _192864), 907 ^ _165181 : [(910 ^ _165181) ^ [] : [-(_192694 = _192864)], (908 ^ _165181) ^ [] : [-(_192696 = _192866)]]]]], (982 ^ _165181) ^ [_195416, _195418, _195420] : [relation_of2_as_subset(_195416, _195420, _195418), -(relation_of2(_195416, _195420, _195418))]], input).
% 75.10/72.90  ncf('1',plain,[empty_carrier(1094 ^ [])],start(1096 ^ 0)).
% 75.10/72.90  ncf('1.1',plain,[-(empty_carrier(1094 ^ [])), lattice(1094 ^ []), latt_str(1094 ^ []), 1024 : element(cast_to_el_of_lattice(1094 ^ [], 1101 ^ []), the_carrier(1094 ^ [])), 1034 : relstr_set_smaller(poset_of_lattice(1094 ^ []), 1093 ^ [], cast_to_el_of_LattPOSet(1094 ^ [], cast_to_el_of_lattice(1094 ^ [], 1101 ^ []))), 1034 : -(latt_element_smaller(1094 ^ [], cast_to_el_of_lattice(1094 ^ [], 1101 ^ []), 1093 ^ []))],extension(1012 ^ 1,bind([[_196412, _196414, _196739], [1094 ^ [], 1093 ^ [], cast_to_el_of_lattice(1094 ^ [], 1101 ^ [])]]))).
% 75.10/72.90  ncf('1.1.1',plain,[-(lattice(1094 ^ []))],extension(1098 ^ 2)).
% 75.10/72.90  ncf('1.1.2',plain,[-(latt_str(1094 ^ []))],extension(1100 ^ 2)).
% 75.10/72.90  ncf('1.1.3',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([[_185945, _185947], [1101 ^ [], 1094 ^ []]]))).
% 75.10/72.90  ncf('1.1.3.1',plain,[empty_carrier(1094 ^ [])],reduction('1')).
% 75.10/72.90  ncf('1.1.3.2',plain,[-(lattice(1094 ^ []))],lemmata('[1].x')).
% 75.10/72.90  ncf('1.1.3.3',plain,[-(latt_str(1094 ^ []))],lemmata('[1].x')).
% 75.10/72.90  ncf('1.1.3.4',plain,[-(element(1101 ^ [], the_carrier(poset_of_lattice(1094 ^ []))))],extension(1103 ^ 5)).
% 75.10/72.90  ncf('1.1.4',plain,[-(relstr_set_smaller(poset_of_lattice(1094 ^ []), 1093 ^ [], cast_to_el_of_LattPOSet(1094 ^ [], cast_to_el_of_lattice(1094 ^ [], 1101 ^ [])))), relstr_set_smaller(poset_of_lattice(1094 ^ []), 1093 ^ [], 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([[_175634, _175636, _175638, _175640, _175642, _175644], [cast_to_el_of_LattPOSet(1094 ^ [], cast_to_el_of_lattice(1094 ^ [], 1101 ^ [])), 1101 ^ [], 1093 ^ [], 1093 ^ [], poset_of_lattice(1094 ^ []), poset_of_lattice(1094 ^ [])]]))).
% 75.10/72.90  ncf('1.1.4.1',plain,[-(relstr_set_smaller(poset_of_lattice(1094 ^ []), 1093 ^ [], 1101 ^ [])), 1111 : -(latt_element_smaller(1094 ^ [], cast_to_el_of_lattice(1094 ^ [], 1101 ^ []), 1093 ^ []))],extension(1105 ^ 7)).
% 75.10/72.90  ncf('1.1.4.1.1',plain,[latt_element_smaller(1094 ^ [], cast_to_el_of_lattice(1094 ^ [], 1101 ^ []), 1093 ^ []), -(relstr_set_smaller(poset_of_lattice(1094 ^ []), 1093 ^ [], cast_to_el_of_LattPOSet(1094 ^ [], cast_to_el_of_lattice(1094 ^ [], 1101 ^ []))))],extension(1028 ^ 10)).
% 75.10/72.90  ncf('1.1.4.1.1.1',plain,[relstr_set_smaller(poset_of_lattice(1094 ^ []), 1093 ^ [], cast_to_el_of_LattPOSet(1094 ^ [], cast_to_el_of_lattice(1094 ^ [], 1101 ^ [])))],reduction('1.1')).
% 75.10/72.90  ncf('1.1.4.2',plain,[-(poset_of_lattice(1094 ^ []) = poset_of_lattice(1094 ^ [])), 1094 ^ [] = 1094 ^ []],extension(432 ^ 7,bind([[_179095, _179097], [1094 ^ [], 1094 ^ []]]))).
% 75.10/72.90  ncf('1.1.4.2.1',plain,[-(1094 ^ [] = 1094 ^ [])],extension(2 ^ 8,bind([[_165305], [1094 ^ []]]))).
% 75.10/72.90  ncf('1.1.4.3',plain,[-(1093 ^ [] = 1093 ^ [])],extension(2 ^ 7,bind([[_165305], [1093 ^ []]]))).
% 75.10/72.90  ncf('1.1.4.4',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([[_165412, _165414], [1101 ^ [], cast_to_el_of_LattPOSet(1094 ^ [], cast_to_el_of_lattice(1094 ^ [], 1101 ^ []))]]))).
% 75.10/72.90  ncf('1.1.4.4.1',plain,[-(cast_to_el_of_LattPOSet(1094 ^ [], cast_to_el_of_lattice(1094 ^ [], 1101 ^ [])) = 1101 ^ []), cast_to_el_of_LattPOSet(1094 ^ [], cast_to_el_of_lattice(1094 ^ [], 1101 ^ [])) = cast_to_el_of_lattice(1094 ^ [], 1101 ^ []), cast_to_el_of_lattice(1094 ^ [], 1101 ^ []) = 1101 ^ []],extension(10 ^ 8,bind([[_165616, _165618, _165620], [1101 ^ [], cast_to_el_of_lattice(1094 ^ [], 1101 ^ []), cast_to_el_of_LattPOSet(1094 ^ [], cast_to_el_of_lattice(1094 ^ [], 1101 ^ []))]]))).
% 75.10/72.90  ncf('1.1.4.4.1.1',plain,[-(cast_to_el_of_LattPOSet(1094 ^ [], cast_to_el_of_lattice(1094 ^ [], 1101 ^ [])) = cast_to_el_of_lattice(1094 ^ [], 1101 ^ [])), 558 : element(cast_to_el_of_lattice(1094 ^ [], 1101 ^ []), the_carrier(1094 ^ [])), 558 : -(empty_carrier(1094 ^ [])), 558 : lattice(1094 ^ []), 558 : latt_str(1094 ^ [])],extension(546 ^ 9,bind([[_182409, _182714], [1094 ^ [], cast_to_el_of_lattice(1094 ^ [], 1101 ^ [])]]))).
% 75.10/72.90  ncf('1.1.4.4.1.1.1',plain,[-(element(cast_to_el_of_lattice(1094 ^ [], 1101 ^ []), the_carrier(1094 ^ [])))],lemmata('[1].x')).
% 75.10/72.90  ncf('1.1.4.4.1.1.2',plain,[empty_carrier(1094 ^ [])],reduction('1')).
% 75.10/72.90  ncf('1.1.4.4.1.1.3',plain,[-(lattice(1094 ^ []))],lemmata('[1].x')).
% 75.10/72.90  ncf('1.1.4.4.1.1.4',plain,[-(latt_str(1094 ^ []))],lemmata('[1].x')).
% 75.10/72.90  ncf('1.1.4.4.1.2',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 ^ 9,bind([[_182927, _183234], [1094 ^ [], 1101 ^ []]]))).
% 75.10/72.90  ncf('1.1.4.4.1.2.1',plain,[-(element(1101 ^ [], the_carrier(poset_of_lattice(1094 ^ []))))],extension(1103 ^ 12)).
% 75.10/72.90  ncf('1.1.4.4.1.2.2',plain,[empty_carrier(1094 ^ [])],reduction('1')).
% 75.10/72.90  ncf('1.1.4.4.1.2.3',plain,[-(lattice(1094 ^ []))],lemmata('[1].x')).
% 75.10/72.90  ncf('1.1.4.4.1.2.4',plain,[-(latt_str(1094 ^ []))],lemmata('[1].x')).
% 75.10/72.90  ncf('1.1.5',plain,[latt_element_smaller(1094 ^ [], cast_to_el_of_lattice(1094 ^ [], 1101 ^ []), 1093 ^ []), 1113 : relstr_set_smaller(poset_of_lattice(1094 ^ []), 1093 ^ [], 1101 ^ [])],extension(1105 ^ 6)).
% 75.10/72.90  ncf('1.1.5.1',plain,[-(relstr_set_smaller(poset_of_lattice(1094 ^ []), 1093 ^ [], 1101 ^ [])), relstr_set_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 ^ [], cast_to_el_of_LattPOSet(1094 ^ [], cast_to_el_of_lattice(1094 ^ [], 1101 ^ [])) = 1101 ^ []],extension(336 ^ 9,bind([[_175634, _175636, _175638, _175640, _175642, _175644], [1101 ^ [], cast_to_el_of_LattPOSet(1094 ^ [], cast_to_el_of_lattice(1094 ^ [], 1101 ^ [])), 1093 ^ [], 1093 ^ [], poset_of_lattice(1094 ^ []), poset_of_lattice(1094 ^ [])]]))).
% 75.10/72.90  ncf('1.1.5.1.1',plain,[-(relstr_set_smaller(poset_of_lattice(1094 ^ []), 1093 ^ [], cast_to_el_of_LattPOSet(1094 ^ [], cast_to_el_of_lattice(1094 ^ [], 1101 ^ [])))), latt_element_smaller(1094 ^ [], cast_to_el_of_lattice(1094 ^ [], 1101 ^ []), 1093 ^ [])],extension(1028 ^ 10)).
% 75.10/72.90  ncf('1.1.5.1.1.1',plain,[-(latt_element_smaller(1094 ^ [], cast_to_el_of_lattice(1094 ^ [], 1101 ^ []), 1093 ^ []))],reduction('1.1')).
% 75.10/72.90  ncf('1.1.5.1.2',plain,[-(poset_of_lattice(1094 ^ []) = poset_of_lattice(1094 ^ [])), 1094 ^ [] = 1094 ^ []],extension(432 ^ 10,bind([[_179095, _179097], [1094 ^ [], 1094 ^ []]]))).
% 75.10/72.90  ncf('1.1.5.1.2.1',plain,[-(1094 ^ [] = 1094 ^ [])],extension(2 ^ 11,bind([[_165305], [1094 ^ []]]))).
% 75.10/72.90  ncf('1.1.5.1.3',plain,[-(1093 ^ [] = 1093 ^ [])],extension(2 ^ 10,bind([[_165305], [1093 ^ []]]))).
% 75.10/72.90  ncf('1.1.5.1.4',plain,[-(cast_to_el_of_LattPOSet(1094 ^ [], cast_to_el_of_lattice(1094 ^ [], 1101 ^ [])) = 1101 ^ []), cast_to_el_of_LattPOSet(1094 ^ [], cast_to_el_of_lattice(1094 ^ [], 1101 ^ [])) = cast_to_el_of_lattice(1094 ^ [], 1101 ^ []), cast_to_el_of_lattice(1094 ^ [], 1101 ^ []) = 1101 ^ []],extension(10 ^ 10,bind([[_165616, _165618, _165620], [1101 ^ [], cast_to_el_of_lattice(1094 ^ [], 1101 ^ []), cast_to_el_of_LattPOSet(1094 ^ [], cast_to_el_of_lattice(1094 ^ [], 1101 ^ []))]]))).
% 75.10/72.90  ncf('1.1.5.1.4.1',plain,[-(cast_to_el_of_LattPOSet(1094 ^ [], cast_to_el_of_lattice(1094 ^ [], 1101 ^ [])) = cast_to_el_of_lattice(1094 ^ [], 1101 ^ [])), 558 : element(cast_to_el_of_lattice(1094 ^ [], 1101 ^ []), the_carrier(1094 ^ [])), 558 : -(empty_carrier(1094 ^ [])), 558 : lattice(1094 ^ []), 558 : latt_str(1094 ^ [])],extension(546 ^ 11,bind([[_182409, _182714], [1094 ^ [], cast_to_el_of_lattice(1094 ^ [], 1101 ^ [])]]))).
% 75.10/72.90  ncf('1.1.5.1.4.1.1',plain,[-(element(cast_to_el_of_lattice(1094 ^ [], 1101 ^ []), the_carrier(1094 ^ [])))],lemmata('[1].x')).
% 75.10/72.90  ncf('1.1.5.1.4.1.2',plain,[empty_carrier(1094 ^ [])],reduction('1')).
% 75.10/72.90  ncf('1.1.5.1.4.1.3',plain,[-(lattice(1094 ^ []))],lemmata('[1].x')).
% 75.10/72.90  ncf('1.1.5.1.4.1.4',plain,[-(latt_str(1094 ^ []))],lemmata('[1].x')).
% 75.10/72.90  ncf('1.1.5.1.4.2',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 ^ 11,bind([[_182927, _183234], [1094 ^ [], 1101 ^ []]]))).
% 75.10/72.90  ncf('1.1.5.1.4.2.1',plain,[-(element(1101 ^ [], the_carrier(poset_of_lattice(1094 ^ []))))],extension(1103 ^ 14)).
% 75.10/72.90  ncf('1.1.5.1.4.2.2',plain,[empty_carrier(1094 ^ [])],reduction('1')).
% 75.10/72.90  ncf('1.1.5.1.4.2.3',plain,[-(lattice(1094 ^ []))],lemmata('[1].x')).
% 75.10/72.90  ncf('1.1.5.1.4.2.4',plain,[-(latt_str(1094 ^ []))],lemmata('[1].x')).
% 75.10/72.90  %-----------------------------------------------------
% 75.10/72.90  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------