%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SET802+4 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n032.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 11:56:27 EDT 2023

% Result   : Theorem 1.55s 2.34s
% Output   : Proof 1.55s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.08  % Problem  : SET802+4 : TPTP v8.1.2. Released v3.2.0.
% 0.05/0.09  % Command  : nanocop.sh %s %d
% 0.08/0.27  % Computer : n032.cluster.edu
% 0.08/0.27  % Model    : x86_64 x86_64
% 0.08/0.27  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.27  % Memory   : 8042.1875MB
% 0.08/0.27  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.08/0.27  % CPULimit : 300
% 0.08/0.27  % WCLimit  : 300
% 0.08/0.27  % DateTime : Thu May 18 19:22:19 EDT 2023
% 0.08/0.27  % CPUTime  : 
% 1.55/2.34  
% 1.55/2.34  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 1.55/2.34  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.55/2.34  %-----------------------------------------------------
% 1.55/2.34  ncf(matrix, plain, [(851 ^ _118722) ^ [] : [-(order(848 ^ [], 849 ^ []))], (854 ^ _118722) ^ [] : [-(subset(852 ^ [], 849 ^ []))], (857 ^ _118722) ^ [] : [866 ^ _118722 : [(867 ^ _118722) ^ [] : [-(member(855 ^ [], 852 ^ []))], (869 ^ _118722) ^ [] : [-(greatest_lower_bound(855 ^ [], 852 ^ [], 848 ^ [], 849 ^ []))], (871 ^ _118722) ^ [] : [least(855 ^ [], 848 ^ [], 852 ^ [])]], 858 ^ _118722 : [(859 ^ _118722) ^ [] : [-(least(855 ^ [], 848 ^ [], 852 ^ []))], (861 ^ _118722) ^ [] : [member(855 ^ [], 852 ^ []), greatest_lower_bound(855 ^ [], 852 ^ [], 848 ^ [], 849 ^ [])]]], (260 ^ _118722) ^ [_127601, _127603] : [_127603 = _127601, -(power_set(_127603) = power_set(_127601))], (266 ^ _118722) ^ [_127847, _127849, _127851, _127853] : [-(intersection(_127853, _127849) = intersection(_127851, _127847)), _127853 = _127851, _127849 = _127847], (276 ^ _118722) ^ [_128206, _128208, _128210, _128212] : [-(union(_128212, _128208) = union(_128210, _128206)), _128212 = _128210, _128208 = _128206], (286 ^ _118722) ^ [_128565, _128567, _128569, _128571] : [-(difference(_128571, _128567) = difference(_128569, _128565)), _128571 = _128569, _128567 = _128565], (296 ^ _118722) ^ [_128896, _128898] : [_128898 = _128896, -(singleton(_128898) = singleton(_128896))], (302 ^ _118722) ^ [_129142, _129144, _129146, _129148] : [-(unordered_pair(_129148, _129144) = unordered_pair(_129146, _129142)), _129148 = _129146, _129144 = _129142], (312 ^ _118722) ^ [_129473, _129475] : [_129475 = _129473, -(sum(_129475) = sum(_129473))], (318 ^ _118722) ^ [_129671, _129673] : [_129673 = _129671, -(product(_129673) = product(_129671))], (2 ^ _118722) ^ [_118866] : [-(_118866 = _118866)], (4 ^ _118722) ^ [_118973, _118975] : [_118975 = _118973, -(_118973 = _118975)], (10 ^ _118722) ^ [_119177, _119179, _119181] : [-(_119181 = _119177), _119181 = _119179, _119179 = _119177], (20 ^ _118722) ^ [_119518, _119520, _119522, _119524] : [-(equal_set(_119522, _119518)), equal_set(_119524, _119520), _119524 = _119522, _119520 = _119518], (34 ^ _118722) ^ [_119962, _119964, _119966, _119968] : [-(total_order(_119966, _119962)), total_order(_119968, _119964), _119968 = _119966, _119964 = _119962], (48 ^ _118722) ^ [_120434, _120436, _120438, _120440, _120442, _120444] : [-(greatest(_120442, _120438, _120434)), greatest(_120444, _120440, _120436), _120444 = _120442, _120440 = _120438, _120436 = _120434], (66 ^ _118722) ^ [_121043, _121045, _121047, _121049, _121051, _121053] : [-(max(_121051, _121047, _121043)), max(_121053, _121049, _121045), _121053 = _121051, _121049 = _121047, _121045 = _121043], (84 ^ _118722) ^ [_121652, _121654, _121656, _121658, _121660, _121662] : [-(min(_121660, _121656, _121652)), min(_121662, _121658, _121654), _121662 = _121660, _121658 = _121656, _121654 = _121652], (102 ^ _118722) ^ [_122289, _122291, _122293, _122295, _122297, _122299, _122301, _122303] : [-(least_upper_bound(_122301, _122297, _122293, _122289)), least_upper_bound(_122303, _122299, _122295, _122291), _122303 = _122301, _122299 = _122297, _122295 = _122293, _122291 = _122289], (124 ^ _118722) ^ [_123051, _123053, _123055, _123057, _123059, _123061] : [-(upper_bound(_123059, _123055, _123051)), upper_bound(_123061, _123057, _123053), _123061 = _123059, _123057 = _123055, _123053 = _123051], (142 ^ _118722) ^ [_123660, _123662, _123664, _123666, _123668, _123670] : [-(lower_bound(_123668, _123664, _123660)), lower_bound(_123670, _123666, _123662), _123670 = _123668, _123666 = _123664, _123662 = _123660], (160 ^ _118722) ^ [_124269, _124271, _124273, _124275, _124277, _124279] : [-(apply(_124277, _124273, _124269)), apply(_124279, _124275, _124271), _124279 = _124277, _124275 = _124273, _124271 = _124269], (178 ^ _118722) ^ [_124850, _124852, _124854, _124856] : [-(order(_124854, _124850)), order(_124856, _124852), _124856 = _124854, _124852 = _124850], (192 ^ _118722) ^ [_125294, _125296, _125298, _125300] : [-(subset(_125298, _125294)), subset(_125300, _125296), _125300 = _125298, _125296 = _125294], (206 ^ _118722) ^ [_125766, _125768, _125770, _125772, _125774, _125776] : [-(least(_125774, _125770, _125766)), least(_125776, _125772, _125768), _125776 = _125774, _125772 = _125770, _125768 = _125766], (224 ^ _118722) ^ [_126347, _126349, _126351, _126353] : [-(member(_126351, _126347)), member(_126353, _126349), _126353 = _126351, _126349 = _126347], (238 ^ _118722) ^ [_126827, _126829, _126831, _126833, _126835, _126837, _126839, _126841] : [-(greatest_lower_bound(_126839, _126835, _126831, _126827)), greatest_lower_bound(_126841, _126837, _126833, _126829), _126841 = _126839, _126837 = _126835, _126833 = _126831, _126829 = _126827], (334 ^ _118722) ^ [_130286, _130288] : [336 ^ _118722 : [(337 ^ _118722) ^ [] : [-(member(335 ^ [_130286, _130288], _130288))], (339 ^ _118722) ^ [] : [member(335 ^ [_130286, _130288], _130286)]], -(subset(_130288, _130286))], (324 ^ _118722) ^ [_129972, _129974] : [subset(_129974, _129972), 327 ^ _118722 : [(328 ^ _118722) ^ [_130109] : [member(_130109, _129974), -(member(_130109, _129972))]]], (343 ^ _118722) ^ [_130672, _130674] : [equal_set(_130674, _130672), 346 ^ _118722 : [(347 ^ _118722) ^ [] : [-(subset(_130674, _130672))], (349 ^ _118722) ^ [] : [-(subset(_130672, _130674))]]], (351 ^ _118722) ^ [_130909, _130911] : [-(equal_set(_130911, _130909)), subset(_130911, _130909), subset(_130909, _130911)], (361 ^ _118722) ^ [_131239, _131241] : [member(_131241, power_set(_131239)), -(subset(_131241, _131239))], (367 ^ _118722) ^ [_131405, _131407] : [subset(_131407, _131405), -(member(_131407, power_set(_131405)))], (373 ^ _118722) ^ [_131664, _131666, _131668] : [member(_131668, intersection(_131666, _131664)), 376 ^ _118722 : [(377 ^ _118722) ^ [] : [-(member(_131668, _131666))], (379 ^ _118722) ^ [] : [-(member(_131668, _131664))]]], (381 ^ _118722) ^ [_131915, _131917, _131919] : [-(member(_131919, intersection(_131917, _131915))), member(_131919, _131917), member(_131919, _131915)], (401 ^ _118722) ^ [_132543, _132545, _132547] : [402 ^ _118722 : [(403 ^ _118722) ^ [] : [member(_132547, _132545)], (405 ^ _118722) ^ [] : [member(_132547, _132543)]], -(member(_132547, union(_132545, _132543)))], (391 ^ _118722) ^ [_132275, _132277, _132279] : [member(_132279, union(_132277, _132275)), -(member(_132279, _132277)), -(member(_132279, _132275))], (409 ^ _118722) ^ [_132813] : [member(_132813, empty_set)], (411 ^ _118722) ^ [_132963, _132965, _132967] : [member(_132967, difference(_132963, _132965)), 414 ^ _118722 : [(415 ^ _118722) ^ [] : [-(member(_132967, _132963))], (417 ^ _118722) ^ [] : [member(_132967, _132965)]]], (419 ^ _118722) ^ [_133215, _133217, _133219] : [-(member(_133219, difference(_133215, _133217))), member(_133219, _133215), -(member(_133219, _133217))], (429 ^ _118722) ^ [_133564, _133566] : [member(_133566, singleton(_133564)), -(_133566 = _133564)], (435 ^ _118722) ^ [_133730, _133732] : [_133732 = _133730, -(member(_133732, singleton(_133730)))], (451 ^ _118722) ^ [_134257, _134259, _134261] : [452 ^ _118722 : [(453 ^ _118722) ^ [] : [_134261 = _134259], (455 ^ _118722) ^ [] : [_134261 = _134257]], -(member(_134261, unordered_pair(_134259, _134257)))], (441 ^ _118722) ^ [_133989, _133991, _133993] : [member(_133993, unordered_pair(_133991, _133989)), -(_133993 = _133991), -(_133993 = _133989)], (459 ^ _118722) ^ [_134586, _134588] : [member(_134588, sum(_134586)), 463 ^ _118722 : [(464 ^ _118722) ^ [] : [-(member(462 ^ [_134586, _134588], _134586))], (466 ^ _118722) ^ [] : [-(member(_134588, 462 ^ [_134586, _134588]))]]], (468 ^ _118722) ^ [_134897, _134899] : [-(member(_134899, sum(_134897))), 469 ^ _118722 : [(470 ^ _118722) ^ [_134991] : [member(_134991, _134897), member(_134899, _134991)]]], (488 ^ _118722) ^ [_135592, _135594] : [490 ^ _118722 : [(491 ^ _118722) ^ [] : [-(member(489 ^ [_135592, _135594], _135592))], (493 ^ _118722) ^ [] : [member(_135594, 489 ^ [_135592, _135594])]], -(member(_135594, product(_135592)))], (478 ^ _118722) ^ [_135274, _135276] : [member(_135276, product(_135274)), 481 ^ _118722 : [(482 ^ _118722) ^ [_135415] : [member(_135415, _135274), -(member(_135276, _135415))]]], (547 ^ _118722) ^ [_137620, _137622] : [-(order(_137622, _137620)), 551 ^ _118722 : [(552 ^ _118722) ^ [] : [-(member(550 ^ [_137620, _137622], _137620))], (554 ^ _118722) ^ [] : [apply(_137622, 550 ^ [_137620, _137622], 550 ^ [_137620, _137622])]], 559 ^ _118722 : [(560 ^ _118722) ^ [] : [-(member(557 ^ [_137620, _137622], _137620))], (562 ^ _118722) ^ [] : [-(member(558 ^ [_137620, _137622], _137620))], (564 ^ _118722) ^ [] : [-(apply(_137622, 557 ^ [_137620, _137622], 558 ^ [_137620, _137622]))], (566 ^ _118722) ^ [] : [-(apply(_137622, 558 ^ [_137620, _137622], 557 ^ [_137620, _137622]))], (568 ^ _118722) ^ [] : [557 ^ [_137620, _137622] = 558 ^ [_137620, _137622]]], 572 ^ _118722 : [(573 ^ _118722) ^ [] : [-(member(569 ^ [_137620, _137622], _137620))], (575 ^ _118722) ^ [] : [-(member(570 ^ [_137620, _137622], _137620))], (577 ^ _118722) ^ [] : [-(member(571 ^ [_137620, _137622], _137620))], (579 ^ _118722) ^ [] : [-(apply(_137622, 569 ^ [_137620, _137622], 570 ^ [_137620, _137622]))], (581 ^ _118722) ^ [] : [-(apply(_137622, 570 ^ [_137620, _137622], 571 ^ [_137620, _137622]))], (583 ^ _118722) ^ [] : [apply(_137622, 569 ^ [_137620, _137622], 571 ^ [_137620, _137622])]]], (497 ^ _118722) ^ [_136020, _136022] : [order(_136022, _136020), 500 ^ _118722 : [(501 ^ _118722) ^ [_136274] : [member(_136274, _136020), -(apply(_136022, _136274, _136274))], (507 ^ _118722) ^ [_136496, _136498] : [member(_136498, _136020), member(_136496, _136020), -(_136498 = _136496), apply(_136022, _136498, _136496), apply(_136022, _136496, _136498)], (525 ^ _118722) ^ [_137013, _137015, _137017] : [member(_137017, _136020), member(_137015, _136020), member(_137013, _136020), -(apply(_136022, _137017, _137013)), apply(_136022, _137017, _137015), apply(_136022, _137015, _137013)]]], (607 ^ _118722) ^ [_140141, _140143] : [-(total_order(_140143, _140141)), order(_140143, _140141), 614 ^ _118722 : [(615 ^ _118722) ^ [] : [-(member(612 ^ [_140141, _140143], _140141))], (617 ^ _118722) ^ [] : [-(member(613 ^ [_140141, _140143], _140141))], (619 ^ _118722) ^ [] : [apply(_140143, 612 ^ [_140141, _140143], 613 ^ [_140141, _140143])], (621 ^ _118722) ^ [] : [apply(_140143, 613 ^ [_140141, _140143], 612 ^ [_140141, _140143])]]], (587 ^ _118722) ^ [_139513, _139515] : [total_order(_139515, _139513), 590 ^ _118722 : [(591 ^ _118722) ^ [] : [-(order(_139515, _139513))], (593 ^ _118722) ^ [_139755, _139757] : [member(_139757, _139513), member(_139755, _139513), -(apply(_139515, _139757, _139755)), -(apply(_139515, _139755, _139757))]]], (635 ^ _118722) ^ [_141252, _141254, _141256] : [637 ^ _118722 : [(638 ^ _118722) ^ [] : [-(member(636 ^ [_141252, _141254, _141256], _141254))], (640 ^ _118722) ^ [] : [apply(_141256, 636 ^ [_141252, _141254, _141256], _141252)]], -(upper_bound(_141252, _141256, _141254))], (625 ^ _118722) ^ [_140921, _140923, _140925] : [upper_bound(_140921, _140925, _140923), 628 ^ _118722 : [(629 ^ _118722) ^ [_141065] : [member(_141065, _140923), -(apply(_140925, _141065, _140921))]]], (654 ^ _118722) ^ [_142004, _142006, _142008] : [656 ^ _118722 : [(657 ^ _118722) ^ [] : [-(member(655 ^ [_142004, _142006, _142008], _142006))], (659 ^ _118722) ^ [] : [apply(_142008, _142004, 655 ^ [_142004, _142006, _142008])]], -(lower_bound(_142004, _142008, _142006))], (644 ^ _118722) ^ [_141673, _141675, _141677] : [lower_bound(_141673, _141677, _141675), 647 ^ _118722 : [(648 ^ _118722) ^ [_141817] : [member(_141817, _141675), -(apply(_141677, _141673, _141817))]]], (663 ^ _118722) ^ [_142425, _142427, _142429] : [greatest(_142425, _142429, _142427), 666 ^ _118722 : [(667 ^ _118722) ^ [] : [-(member(_142425, _142427))], (669 ^ _118722) ^ [_142643] : [member(_142643, _142427), -(apply(_142429, _142643, _142425))]]], (675 ^ _118722) ^ [_142832, _142834, _142836] : [-(greatest(_142832, _142836, _142834)), member(_142832, _142834), 681 ^ _118722 : [(682 ^ _118722) ^ [] : [-(member(680 ^ [_142832, _142834, _142836], _142834))], (684 ^ _118722) ^ [] : [apply(_142836, 680 ^ [_142832, _142834, _142836], _142832)]]], (688 ^ _118722) ^ [_143346, _143348, _143350] : [least(_143346, _143350, _143348), 691 ^ _118722 : [(692 ^ _118722) ^ [] : [-(member(_143346, _143348))], (694 ^ _118722) ^ [_143564] : [member(_143564, _143348), -(apply(_143350, _143346, _143564))]]], (700 ^ _118722) ^ [_143753, _143755, _143757] : [-(least(_143753, _143757, _143755)), member(_143753, _143755), 706 ^ _118722 : [(707 ^ _118722) ^ [] : [-(member(705 ^ [_143753, _143755, _143757], _143755))], (709 ^ _118722) ^ [] : [apply(_143757, _143753, 705 ^ [_143753, _143755, _143757])]]], (729 ^ _118722) ^ [_144777, _144779, _144781] : [-(max(_144777, _144781, _144779)), member(_144777, _144779), 735 ^ _118722 : [(736 ^ _118722) ^ [] : [-(member(734 ^ [_144777, _144779, _144781], _144779))], (738 ^ _118722) ^ [] : [-(apply(_144781, _144777, 734 ^ [_144777, _144779, _144781]))], (740 ^ _118722) ^ [] : [_144777 = 734 ^ [_144777, _144779, _144781]]]], (713 ^ _118722) ^ [_144267, _144269, _144271] : [max(_144267, _144271, _144269), 716 ^ _118722 : [(717 ^ _118722) ^ [] : [-(member(_144267, _144269))], (719 ^ _118722) ^ [_144491] : [-(_144267 = _144491), member(_144491, _144269), apply(_144271, _144267, _144491)]]], (760 ^ _118722) ^ [_145894, _145896, _145898] : [-(min(_145894, _145898, _145896)), member(_145894, _145896), 766 ^ _118722 : [(767 ^ _118722) ^ [] : [-(member(765 ^ [_145894, _145896, _145898], _145896))], (769 ^ _118722) ^ [] : [-(apply(_145898, 765 ^ [_145894, _145896, _145898], _145894))], (771 ^ _118722) ^ [] : [_145894 = 765 ^ [_145894, _145896, _145898]]]], (744 ^ _118722) ^ [_145384, _145386, _145388] : [min(_145384, _145388, _145386), 747 ^ _118722 : [(748 ^ _118722) ^ [] : [-(member(_145384, _145386))], (750 ^ _118722) ^ [_145608] : [-(_145384 = _145608), member(_145608, _145386), apply(_145388, _145608, _145384)]]], (775 ^ _118722) ^ [_146515, _146517, _146519, _146521] : [least_upper_bound(_146521, _146519, _146517, _146515), 778 ^ _118722 : [(779 ^ _118722) ^ [] : [-(member(_146521, _146519))], (781 ^ _118722) ^ [] : [-(upper_bound(_146521, _146517, _146519))], (783 ^ _118722) ^ [_146826] : [-(apply(_146517, _146521, _146826)), member(_146826, _146515), upper_bound(_146826, _146517, _146519)]]], (793 ^ _118722) ^ [_147128, _147130, _147132, _147134] : [-(least_upper_bound(_147134, _147132, _147130, _147128)), member(_147134, _147132), upper_bound(_147134, _147130, _147132), 803 ^ _118722 : [(804 ^ _118722) ^ [] : [-(member(802 ^ [_147128, _147130, _147132, _147134], _147128))], (806 ^ _118722) ^ [] : [-(upper_bound(802 ^ [_147128, _147130, _147132, _147134], _147130, _147132))], (808 ^ _118722) ^ [] : [apply(_147130, _147134, 802 ^ [_147128, _147130, _147132, _147134])]]], (812 ^ _118722) ^ [_147857, _147859, _147861, _147863] : [greatest_lower_bound(_147863, _147861, _147859, _147857), 815 ^ _118722 : [(816 ^ _118722) ^ [] : [-(member(_147863, _147861))], (818 ^ _118722) ^ [] : [-(lower_bound(_147863, _147859, _147861))], (820 ^ _118722) ^ [_148168] : [-(apply(_147859, _148168, _147863)), member(_148168, _147857), lower_bound(_148168, _147859, _147861)]]], (830 ^ _118722) ^ [_148470, _148472, _148474, _148476] : [-(greatest_lower_bound(_148476, _148474, _148472, _148470)), member(_148476, _148474), lower_bound(_148476, _148472, _148474), 840 ^ _118722 : [(841 ^ _118722) ^ [] : [-(member(839 ^ [_148470, _148472, _148474, _148476], _148470))], (843 ^ _118722) ^ [] : [-(lower_bound(839 ^ [_148470, _148472, _148474, _148476], _148472, _148474))], (845 ^ _118722) ^ [] : [apply(_148472, 839 ^ [_148470, _148472, _148474, _148476], _148476)]]]], input).
% 1.55/2.34  ncf('1',plain,[871 : least(855 ^ [], 848 ^ [], 852 ^ []), 861 : member(855 ^ [], 852 ^ []), 861 : greatest_lower_bound(855 ^ [], 852 ^ [], 848 ^ [], 849 ^ [])],start(857 ^ 0)).
% 1.55/2.34  ncf('1.1',plain,[-(least(855 ^ [], 848 ^ [], 852 ^ [])), least(855 ^ [], 848 ^ [], 852 ^ []), 855 ^ [] = 855 ^ [], 848 ^ [] = 848 ^ [], 852 ^ [] = 852 ^ []],extension(206 ^ 3,bind([[_125766, _125768, _125770, _125772, _125774, _125776], [852 ^ [], 852 ^ [], 848 ^ [], 848 ^ [], 855 ^ [], 855 ^ []]]))).
% 1.55/2.34  ncf('1.1.1',plain,[-(least(855 ^ [], 848 ^ [], 852 ^ [])), member(855 ^ [], 852 ^ []), 707 : -(member(705 ^ [855 ^ [], 852 ^ [], 848 ^ []], 852 ^ []))],extension(700 ^ 4,bind([[_143753, _143755, _143757], [855 ^ [], 852 ^ [], 848 ^ []]]))).
% 1.55/2.34  ncf('1.1.1.1',plain,[-(member(855 ^ [], 852 ^ []))],extension(867 ^ 5)).
% 1.55/2.34  ncf('1.1.1.2',plain,[member(705 ^ [855 ^ [], 852 ^ [], 848 ^ []], 852 ^ []), 648 : -(apply(848 ^ [], 855 ^ [], 705 ^ [855 ^ [], 852 ^ [], 848 ^ []])), 648 : lower_bound(855 ^ [], 848 ^ [], 852 ^ [])],extension(644 ^ 7,bind([[_141673, _141675, _141677, _141817], [855 ^ [], 852 ^ [], 848 ^ [], 705 ^ [855 ^ [], 852 ^ [], 848 ^ []]]]))).
% 1.55/2.34  ncf('1.1.1.2.1',plain,[apply(848 ^ [], 855 ^ [], 705 ^ [855 ^ [], 852 ^ [], 848 ^ []])],extension(709 ^ 10)).
% 1.55/2.34  ncf('1.1.1.2.2',plain,[-(lower_bound(855 ^ [], 848 ^ [], 852 ^ [])), greatest_lower_bound(855 ^ [], 852 ^ [], 848 ^ [], 849 ^ [])],extension(812 ^ 8,bind([[_147857, _147859, _147861, _147863], [849 ^ [], 848 ^ [], 852 ^ [], 855 ^ []]]))).
% 1.55/2.34  ncf('1.1.1.2.2.1',plain,[-(greatest_lower_bound(855 ^ [], 852 ^ [], 848 ^ [], 849 ^ []))],extension(869 ^ 9)).
% 1.55/2.34  ncf('1.1.2',plain,[-(855 ^ [] = 855 ^ [])],extension(2 ^ 4,bind([[_118866], [855 ^ []]]))).
% 1.55/2.34  ncf('1.1.3',plain,[-(848 ^ [] = 848 ^ [])],extension(2 ^ 4,bind([[_118866], [848 ^ []]]))).
% 1.55/2.34  ncf('1.1.4',plain,[-(852 ^ [] = 852 ^ [])],extension(2 ^ 4,bind([[_118866], [852 ^ []]]))).
% 1.55/2.34  ncf('1.2',plain,[-(member(855 ^ [], 852 ^ [])), member(855 ^ [], intersection(852 ^ [], _81194))],extension(373 ^ 3,bind([[_131664, _131666, _131668], [_81194, 852 ^ [], 855 ^ []]]))).
% 1.55/2.34  ncf('1.2.1',plain,[-(member(855 ^ [], intersection(852 ^ [], _81194))), member(855 ^ [], union(intersection(852 ^ [], _81194), 852 ^ [])), -(member(855 ^ [], 852 ^ []))],extension(391 ^ 4,bind([[_132275, _132277, _132279], [852 ^ [], intersection(852 ^ [], _81194), 855 ^ []]]))).
% 1.55/2.34  ncf('1.2.1.1',plain,[-(member(855 ^ [], union(intersection(852 ^ [], _81194), 852 ^ []))), 405 : member(855 ^ [], 852 ^ [])],extension(401 ^ 5,bind([[_132543, _132545, _132547], [852 ^ [], intersection(852 ^ [], _81194), 855 ^ []]]))).
% 1.55/2.34  ncf('1.2.1.1.1',plain,[-(member(855 ^ [], 852 ^ [])), least(855 ^ [], 848 ^ [], 852 ^ [])],extension(688 ^ 8,bind([[_143346, _143348, _143350], [855 ^ [], 852 ^ [], 848 ^ []]]))).
% 1.55/2.34  ncf('1.2.1.1.1.1',plain,[-(least(855 ^ [], 848 ^ [], 852 ^ []))],extension(859 ^ 9)).
% 1.55/2.34  ncf('1.2.1.2',plain,[member(855 ^ [], 852 ^ [])],reduction('1')).
% 1.55/2.34  ncf('1.3',plain,[-(greatest_lower_bound(855 ^ [], 852 ^ [], 848 ^ [], 849 ^ [])), member(855 ^ [], 852 ^ []), lower_bound(855 ^ [], 848 ^ [], 852 ^ []), 843 : -(lower_bound(839 ^ [849 ^ [], 848 ^ [], 852 ^ [], 855 ^ []], 848 ^ [], 852 ^ []))],extension(830 ^ 3,bind([[_148470, _148472, _148474, _148476], [849 ^ [], 848 ^ [], 852 ^ [], 855 ^ []]]))).
% 1.55/2.34  ncf('1.3.1',plain,[-(member(855 ^ [], 852 ^ []))],lemmata('x')).
% 1.55/2.34  ncf('1.3.2',plain,[-(lower_bound(855 ^ [], 848 ^ [], 852 ^ [])), 657 : -(member(655 ^ [855 ^ [], 852 ^ [], 848 ^ []], 852 ^ []))],extension(654 ^ 4,bind([[_142004, _142006, _142008], [855 ^ [], 852 ^ [], 848 ^ []]]))).
% 1.55/2.34  ncf('1.3.2.1',plain,[member(655 ^ [855 ^ [], 852 ^ [], 848 ^ []], 852 ^ []), 694 : -(apply(848 ^ [], 855 ^ [], 655 ^ [855 ^ [], 852 ^ [], 848 ^ []])), 694 : least(855 ^ [], 848 ^ [], 852 ^ [])],extension(688 ^ 7,bind([[_143346, _143348, _143350, _143564], [855 ^ [], 852 ^ [], 848 ^ [], 655 ^ [855 ^ [], 852 ^ [], 848 ^ []]]]))).
% 1.55/2.34  ncf('1.3.2.1.1',plain,[apply(848 ^ [], 855 ^ [], 655 ^ [855 ^ [], 852 ^ [], 848 ^ []])],extension(659 ^ 10)).
% 1.55/2.34  ncf('1.3.2.1.2',plain,[-(least(855 ^ [], 848 ^ [], 852 ^ []))],extension(859 ^ 8)).
% 1.55/2.34  ncf('1.3.3',plain,[lower_bound(839 ^ [849 ^ [], 848 ^ [], 852 ^ [], 855 ^ []], 848 ^ [], 852 ^ []), 648 : member(855 ^ [], 852 ^ []), 648 : -(apply(848 ^ [], 839 ^ [849 ^ [], 848 ^ [], 852 ^ [], 855 ^ []], 855 ^ []))],extension(644 ^ 6,bind([[_141673, _141675, _141677, _141817], [839 ^ [849 ^ [], 848 ^ [], 852 ^ [], 855 ^ []], 852 ^ [], 848 ^ [], 855 ^ []]]))).
% 1.55/2.34  ncf('1.3.3.1',plain,[-(member(855 ^ [], 852 ^ [])), least(855 ^ [], 848 ^ [], 852 ^ [])],extension(688 ^ 9,bind([[_143346, _143348, _143350], [855 ^ [], 852 ^ [], 848 ^ []]]))).
% 1.55/2.34  ncf('1.3.3.1.1',plain,[-(least(855 ^ [], 848 ^ [], 852 ^ []))],extension(859 ^ 10)).
% 1.55/2.34  ncf('1.3.3.2',plain,[apply(848 ^ [], 839 ^ [849 ^ [], 848 ^ [], 852 ^ [], 855 ^ []], 855 ^ []), -(apply(848 ^ [], 839 ^ [849 ^ [], 848 ^ [], 852 ^ [], 855 ^ []], 855 ^ [])), 848 ^ [] = 848 ^ [], 839 ^ [849 ^ [], 848 ^ [], 852 ^ [], 855 ^ []] = 839 ^ [849 ^ [], 848 ^ [], 852 ^ [], 855 ^ []], 855 ^ [] = 855 ^ []],extension(160 ^ 9,bind([[_124269, _124271, _124273, _124275, _124277, _124279], [855 ^ [], 855 ^ [], 839 ^ [849 ^ [], 848 ^ [], 852 ^ [], 855 ^ []], 839 ^ [849 ^ [], 848 ^ [], 852 ^ [], 855 ^ []], 848 ^ [], 848 ^ []]]))).
% 1.55/2.34  ncf('1.3.3.2.1',plain,[apply(848 ^ [], 839 ^ [849 ^ [], 848 ^ [], 852 ^ [], 855 ^ []], 855 ^ [])],extension(845 ^ 10)).
% 1.55/2.34  ncf('1.3.3.2.2',plain,[-(848 ^ [] = 848 ^ [])],extension(2 ^ 10,bind([[_118866], [848 ^ []]]))).
% 1.55/2.34  ncf('1.3.3.2.3',plain,[-(839 ^ [849 ^ [], 848 ^ [], 852 ^ [], 855 ^ []] = 839 ^ [849 ^ [], 848 ^ [], 852 ^ [], 855 ^ []])],extension(2 ^ 10,bind([[_118866], [839 ^ [849 ^ [], 848 ^ [], 852 ^ [], 855 ^ []]]]))).
% 1.55/2.34  ncf('1.3.3.2.4',plain,[-(855 ^ [] = 855 ^ [])],extension(2 ^ 10,bind([[_118866], [855 ^ []]]))).
% 1.55/2.34  %-----------------------------------------------------
% 1.55/2.34  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------