TSTP Solution File: SET812+4 by nanoCoP---2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : nanoCoP---2.0
% Problem : SET812+4 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : nanocop.sh %s %d
% Computer : n020.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 11:56:28 EDT 2023
% Result : Theorem 6.23s 6.54s
% Output : Proof 6.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET812+4 : TPTP v8.1.2. Released v3.2.0.
% 0.03/0.12 % Command : nanocop.sh %s %d
% 0.12/0.33 % Computer : n020.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 19:00:17 EDT 2023
% 0.12/0.33 % CPUTime :
% 6.23/6.54
% 6.23/6.54 /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 6.23/6.54 Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.23/6.54 %-----------------------------------------------------
% 6.23/6.54 ncf(matrix, plain, [(612 ^ _78606) ^ [] : [-(member(610 ^ [], on))], (614 ^ _78606) ^ [] : [equal_set(610 ^ [], intersection(610 ^ [], power_set(610 ^ [])))], (136 ^ _78606) ^ [_83135, _83137, _83139, _83141] : [-(difference(_83141, _83137) = difference(_83139, _83135)), _83141 = _83139, _83137 = _83135], (146 ^ _78606) ^ [_83494, _83496, _83498, _83500] : [-(unordered_pair(_83500, _83496) = unordered_pair(_83498, _83494)), _83500 = _83498, _83496 = _83494], (156 ^ _78606) ^ [_83825, _83827] : [_83827 = _83825, -(sum(_83827) = sum(_83825))], (162 ^ _78606) ^ [_84043, _84045] : [_84045 = _84043, -(product(_84045) = product(_84043))], (168 ^ _78606) ^ [_84317, _84319, _84321, _84323, _84325, _84327] : [-(initial_segment(_84327, _84323, _84319) = initial_segment(_84325, _84321, _84317)), _84327 = _84325, _84323 = _84321, _84319 = _84317], (182 ^ _78606) ^ [_84777, _84779] : [_84779 = _84777, -(suc(_84779) = suc(_84777))], (188 ^ _78606) ^ [_85023, _85025, _85027, _85029] : [-(union(_85029, _85025) = union(_85027, _85023)), _85029 = _85027, _85025 = _85023], (198 ^ _78606) ^ [_85354, _85356] : [_85356 = _85354, -(singleton(_85356) = singleton(_85354))], (214 ^ _78606) ^ [_85911, _85913] : [_85913 = _85911, -(power_set(_85913) = power_set(_85911))], (204 ^ _78606) ^ [_85600, _85602, _85604, _85606] : [-(intersection(_85606, _85602) = intersection(_85604, _85600)), _85606 = _85604, _85602 = _85600], (2 ^ _78606) ^ [_78750] : [-(_78750 = _78750)], (4 ^ _78606) ^ [_78857, _78859] : [_78859 = _78857, -(_78857 = _78859)], (10 ^ _78606) ^ [_79061, _79063, _79065] : [-(_79065 = _79061), _79065 = _79063, _79063 = _79061], (20 ^ _78606) ^ [_79402, _79404, _79406, _79408] : [-(strict_well_order(_79406, _79402)), strict_well_order(_79408, _79404), _79408 = _79406, _79404 = _79402], (34 ^ _78606) ^ [_79846, _79848, _79850, _79852] : [-(subset(_79850, _79846)), subset(_79852, _79848), _79852 = _79850, _79848 = _79846], (48 ^ _78606) ^ [_80318, _80320, _80322, _80324, _80326, _80328] : [-(least(_80326, _80322, _80318)), least(_80328, _80324, _80320), _80328 = _80326, _80324 = _80322, _80320 = _80318], (66 ^ _78606) ^ [_80899, _80901, _80903, _80905] : [-(strict_order(_80903, _80899)), strict_order(_80905, _80901), _80905 = _80903, _80901 = _80899], (80 ^ _78606) ^ [_81315, _81317] : [-(set(_81315)), _81317 = _81315, set(_81317)], (90 ^ _78606) ^ [_81666, _81668, _81670, _81672, _81674, _81676] : [-(apply(_81674, _81670, _81666)), apply(_81676, _81672, _81668), _81676 = _81674, _81672 = _81670, _81668 = _81666], (108 ^ _78606) ^ [_82247, _82249, _82251, _82253] : [-(member(_82251, _82247)), member(_82253, _82249), _82253 = _82251, _82249 = _82247], (122 ^ _78606) ^ [_82671, _82673, _82675, _82677] : [-(equal_set(_82675, _82671)), equal_set(_82677, _82673), _82677 = _82675, _82673 = _82671], (230 ^ _78606) ^ [_86562, _86564] : [232 ^ _78606 : [(233 ^ _78606) ^ [] : [-(member(231 ^ [_86562, _86564], _86564))], (235 ^ _78606) ^ [] : [member(231 ^ [_86562, _86564], _86562)]], -(subset(_86564, _86562))], (220 ^ _78606) ^ [_86248, _86250] : [subset(_86250, _86248), 223 ^ _78606 : [(224 ^ _78606) ^ [_86385] : [member(_86385, _86250), -(member(_86385, _86248))]]], (239 ^ _78606) ^ [_86948, _86950] : [equal_set(_86950, _86948), 242 ^ _78606 : [(243 ^ _78606) ^ [] : [-(subset(_86950, _86948))], (245 ^ _78606) ^ [] : [-(subset(_86948, _86950))]]], (247 ^ _78606) ^ [_87185, _87187] : [-(equal_set(_87187, _87185)), subset(_87187, _87185), subset(_87185, _87187)], (257 ^ _78606) ^ [_87515, _87517] : [member(_87517, power_set(_87515)), -(subset(_87517, _87515))], (263 ^ _78606) ^ [_87681, _87683] : [subset(_87683, _87681), -(member(_87683, power_set(_87681)))], (269 ^ _78606) ^ [_87940, _87942, _87944] : [member(_87944, intersection(_87942, _87940)), 272 ^ _78606 : [(273 ^ _78606) ^ [] : [-(member(_87944, _87942))], (275 ^ _78606) ^ [] : [-(member(_87944, _87940))]]], (277 ^ _78606) ^ [_88191, _88193, _88195] : [-(member(_88195, intersection(_88193, _88191))), member(_88195, _88193), member(_88195, _88191)], (297 ^ _78606) ^ [_88819, _88821, _88823] : [298 ^ _78606 : [(299 ^ _78606) ^ [] : [member(_88823, _88821)], (301 ^ _78606) ^ [] : [member(_88823, _88819)]], -(member(_88823, union(_88821, _88819)))], (287 ^ _78606) ^ [_88551, _88553, _88555] : [member(_88555, union(_88553, _88551)), -(member(_88555, _88553)), -(member(_88555, _88551))], (305 ^ _78606) ^ [_89089] : [member(_89089, empty_set)], (307 ^ _78606) ^ [_89239, _89241, _89243] : [member(_89243, difference(_89239, _89241)), 310 ^ _78606 : [(311 ^ _78606) ^ [] : [-(member(_89243, _89239))], (313 ^ _78606) ^ [] : [member(_89243, _89241)]]], (315 ^ _78606) ^ [_89491, _89493, _89495] : [-(member(_89495, difference(_89491, _89493))), member(_89495, _89491), -(member(_89495, _89493))], (325 ^ _78606) ^ [_89840, _89842] : [member(_89842, singleton(_89840)), -(_89842 = _89840)], (331 ^ _78606) ^ [_90006, _90008] : [_90008 = _90006, -(member(_90008, singleton(_90006)))], (347 ^ _78606) ^ [_90533, _90535, _90537] : [348 ^ _78606 : [(349 ^ _78606) ^ [] : [_90537 = _90535], (351 ^ _78606) ^ [] : [_90537 = _90533]], -(member(_90537, unordered_pair(_90535, _90533)))], (337 ^ _78606) ^ [_90265, _90267, _90269] : [member(_90269, unordered_pair(_90267, _90265)), -(_90269 = _90267), -(_90269 = _90265)], (355 ^ _78606) ^ [_90862, _90864] : [member(_90864, sum(_90862)), 359 ^ _78606 : [(360 ^ _78606) ^ [] : [-(member(358 ^ [_90862, _90864], _90862))], (362 ^ _78606) ^ [] : [-(member(_90864, 358 ^ [_90862, _90864]))]]], (364 ^ _78606) ^ [_91173, _91175] : [-(member(_91175, sum(_91173))), 365 ^ _78606 : [(366 ^ _78606) ^ [_91267] : [member(_91267, _91173), member(_91175, _91267)]]], (384 ^ _78606) ^ [_91868, _91870] : [386 ^ _78606 : [(387 ^ _78606) ^ [] : [-(member(385 ^ [_91868, _91870], _91868))], (389 ^ _78606) ^ [] : [member(_91870, 385 ^ [_91868, _91870])]], -(member(_91870, product(_91868)))], (374 ^ _78606) ^ [_91550, _91552] : [member(_91552, product(_91550)), 377 ^ _78606 : [(378 ^ _78606) ^ [_91691] : [member(_91691, _91550), -(member(_91552, _91691))]]], (393 ^ _78606) ^ [_92282] : [member(_92282, on), 396 ^ _78606 : [(397 ^ _78606) ^ [] : [-(set(_92282))], (399 ^ _78606) ^ [] : [-(strict_well_order(member_predicate, _92282))], (401 ^ _78606) ^ [_92553] : [member(_92553, _92282), -(subset(_92553, _92282))]]], (407 ^ _78606) ^ [_92726] : [-(member(_92726, on)), set(_92726), strict_well_order(member_predicate, _92726), 417 ^ _78606 : [(418 ^ _78606) ^ [] : [-(member(416 ^ [_92726], _92726))], (420 ^ _78606) ^ [] : [subset(416 ^ [_92726], _92726)]]], (441 ^ _78606) ^ [_93850, _93852] : [-(strict_well_order(_93852, _93850)), strict_order(_93852, _93850), 447 ^ _78606 : [(448 ^ _78606) ^ [] : [-(subset(446 ^ [_93850, _93852], _93850))], (451 ^ _78606) ^ [] : [-(member(449 ^ [_93850, _93852], 446 ^ [_93850, _93852]))], (453 ^ _78606) ^ [_94303] : [least(_94303, _93852, 446 ^ [_93850, _93852])]]], (424 ^ _78606) ^ [_93264, _93266] : [strict_well_order(_93266, _93264), 427 ^ _78606 : [(428 ^ _78606) ^ [] : [-(strict_order(_93266, _93264))], (430 ^ _78606) ^ [_93490] : [-(least(437 ^ [_93264, _93266, _93490], _93266, _93490)), subset(_93490, _93264), 435 ^ _78606 : [(436 ^ _78606) ^ [_93661] : [member(_93661, _93490)]]]]], (473 ^ _78606) ^ [_95037, _95039, _95041] : [-(least(_95037, _95041, _95039)), member(_95037, _95039), 479 ^ _78606 : [(480 ^ _78606) ^ [] : [-(member(478 ^ [_95037, _95039, _95041], _95039))], (482 ^ _78606) ^ [] : [_95037 = 478 ^ [_95037, _95039, _95041]], (484 ^ _78606) ^ [] : [apply(_95041, _95037, 478 ^ [_95037, _95039, _95041])]]], (457 ^ _78606) ^ [_94526, _94528, _94530] : [least(_94526, _94530, _94528), 460 ^ _78606 : [(461 ^ _78606) ^ [] : [-(member(_94526, _94528))], (463 ^ _78606) ^ [_94750] : [member(_94750, _94528), -(_94526 = _94750), -(apply(_94530, _94526, _94750))]]], (488 ^ _78606) ^ [_95627, _95629] : [apply(member_predicate, _95629, _95627), -(member(_95629, _95627))], (494 ^ _78606) ^ [_95791, _95793] : [member(_95793, _95791), -(apply(member_predicate, _95793, _95791))], (571 ^ _78606) ^ [_98810] : [set(_98810), 574 ^ _78606 : [(575 ^ _78606) ^ [_98940] : [member(_98940, _98810), -(set(_98940))]]], (599 ^ _78606) ^ [_99815, _99817] : [member(_99815, suc(_99817)), -(member(_99815, union(_99817, singleton(_99817))))], (605 ^ _78606) ^ [_99991, _99993] : [member(_99991, union(_99993, singleton(_99993))), -(member(_99991, suc(_99993)))], (581 ^ _78606) ^ [_99212, _99214, _99216, _99218] : [member(_99212, initial_segment(_99218, _99216, _99214)), 584 ^ _78606 : [(585 ^ _78606) ^ [] : [-(member(_99212, _99214))], (587 ^ _78606) ^ [] : [-(apply(_99216, _99212, _99218))]]], (589 ^ _78606) ^ [_99475, _99477, _99479, _99481] : [-(member(_99475, initial_segment(_99481, _99479, _99477))), member(_99475, _99477), apply(_99479, _99475, _99481)], (540 ^ _78606) ^ [_97306, _97308] : [-(strict_order(_97308, _97306)), 545 ^ _78606 : [(546 ^ _78606) ^ [] : [-(member(543 ^ [_97306, _97308], _97306))], (548 ^ _78606) ^ [] : [-(member(544 ^ [_97306, _97308], _97306))], (550 ^ _78606) ^ [] : [-(apply(_97308, 543 ^ [_97306, _97308], 544 ^ [_97306, _97308]))], (552 ^ _78606) ^ [] : [-(apply(_97308, 544 ^ [_97306, _97308], 543 ^ [_97306, _97308]))]], 556 ^ _78606 : [(557 ^ _78606) ^ [] : [-(member(553 ^ [_97306, _97308], _97306))], (559 ^ _78606) ^ [] : [-(member(554 ^ [_97306, _97308], _97306))], (561 ^ _78606) ^ [] : [-(member(555 ^ [_97306, _97308], _97306))], (563 ^ _78606) ^ [] : [-(apply(_97308, 553 ^ [_97306, _97308], 554 ^ [_97306, _97308]))], (565 ^ _78606) ^ [] : [-(apply(_97308, 554 ^ [_97306, _97308], 555 ^ [_97306, _97308]))], (567 ^ _78606) ^ [] : [apply(_97308, 553 ^ [_97306, _97308], 555 ^ [_97306, _97308])]]], (500 ^ _78606) ^ [_96034, _96036] : [strict_order(_96036, _96034), 503 ^ _78606 : [(504 ^ _78606) ^ [_96280, _96282] : [member(_96282, _96034), member(_96280, _96034), apply(_96036, _96282, _96280), apply(_96036, _96280, _96282)], (518 ^ _78606) ^ [_96701, _96703, _96705] : [member(_96705, _96034), member(_96703, _96034), member(_96701, _96034), -(apply(_96036, _96705, _96701)), apply(_96036, _96705, _96703), apply(_96036, _96703, _96701)]]]], input).
% 6.23/6.54 ncf('1',plain,[equal_set(610 ^ [], intersection(610 ^ [], power_set(610 ^ [])))],start(614 ^ 0)).
% 6.23/6.54 ncf('1.1',plain,[-(equal_set(610 ^ [], intersection(610 ^ [], power_set(610 ^ [])))), subset(610 ^ [], intersection(610 ^ [], power_set(610 ^ []))), subset(intersection(610 ^ [], power_set(610 ^ [])), 610 ^ [])],extension(247 ^ 1,bind([[_87185, _87187], [intersection(610 ^ [], power_set(610 ^ [])), 610 ^ []]]))).
% 6.23/6.54 ncf('1.1.1',plain,[-(subset(610 ^ [], intersection(610 ^ [], power_set(610 ^ [])))), 233 : -(member(231 ^ [intersection(610 ^ [], power_set(610 ^ [])), 610 ^ []], 610 ^ []))],extension(230 ^ 2,bind([[_86562, _86564], [intersection(610 ^ [], power_set(610 ^ [])), 610 ^ []]]))).
% 6.23/6.54 ncf('1.1.1.1',plain,[member(231 ^ [intersection(610 ^ [], power_set(610 ^ [])), 610 ^ []], 610 ^ []), -(member(231 ^ [intersection(610 ^ [], power_set(610 ^ [])), 610 ^ []], intersection(610 ^ [], power_set(610 ^ [])))), member(231 ^ [intersection(610 ^ [], power_set(610 ^ [])), 610 ^ []], power_set(610 ^ []))],extension(277 ^ 5,bind([[_88191, _88193, _88195], [power_set(610 ^ []), 610 ^ [], 231 ^ [intersection(610 ^ [], power_set(610 ^ [])), 610 ^ []]]]))).
% 6.23/6.54 ncf('1.1.1.1.1',plain,[member(231 ^ [intersection(610 ^ [], power_set(610 ^ [])), 610 ^ []], intersection(610 ^ [], power_set(610 ^ []))), -(member(231 ^ [intersection(610 ^ [], power_set(610 ^ [])), 610 ^ []], intersection(610 ^ [], power_set(610 ^ [])))), 231 ^ [intersection(610 ^ [], power_set(610 ^ [])), 610 ^ []] = 231 ^ [intersection(610 ^ [], power_set(610 ^ [])), 610 ^ []], intersection(610 ^ [], power_set(610 ^ [])) = intersection(610 ^ [], power_set(610 ^ []))],extension(108 ^ 6,bind([[_82247, _82249, _82251, _82253], [intersection(610 ^ [], power_set(610 ^ [])), intersection(610 ^ [], power_set(610 ^ [])), 231 ^ [intersection(610 ^ [], power_set(610 ^ [])), 610 ^ []], 231 ^ [intersection(610 ^ [], power_set(610 ^ [])), 610 ^ []]]]))).
% 6.23/6.54 ncf('1.1.1.1.1.1',plain,[member(231 ^ [intersection(610 ^ [], power_set(610 ^ [])), 610 ^ []], intersection(610 ^ [], power_set(610 ^ [])))],extension(235 ^ 7)).
% 6.23/6.54 ncf('1.1.1.1.1.2',plain,[-(231 ^ [intersection(610 ^ [], power_set(610 ^ [])), 610 ^ []] = 231 ^ [intersection(610 ^ [], power_set(610 ^ [])), 610 ^ []])],extension(2 ^ 7,bind([[_78750], [231 ^ [intersection(610 ^ [], power_set(610 ^ [])), 610 ^ []]]]))).
% 6.23/6.54 ncf('1.1.1.1.1.3',plain,[-(intersection(610 ^ [], power_set(610 ^ [])) = intersection(610 ^ [], power_set(610 ^ [])))],extension(2 ^ 7,bind([[_78750], [intersection(610 ^ [], power_set(610 ^ []))]]))).
% 6.23/6.54 ncf('1.1.1.1.2',plain,[-(member(231 ^ [intersection(610 ^ [], power_set(610 ^ [])), 610 ^ []], power_set(610 ^ []))), subset(231 ^ [intersection(610 ^ [], power_set(610 ^ [])), 610 ^ []], 610 ^ [])],extension(263 ^ 6,bind([[_87681, _87683], [610 ^ [], 231 ^ [intersection(610 ^ [], power_set(610 ^ [])), 610 ^ []]]]))).
% 6.23/6.54 ncf('1.1.1.1.2.1',plain,[-(subset(231 ^ [intersection(610 ^ [], power_set(610 ^ [])), 610 ^ []], 610 ^ [])), 401 : member(231 ^ [intersection(610 ^ [], power_set(610 ^ [])), 610 ^ []], 610 ^ []), 401 : member(610 ^ [], on)],extension(393 ^ 7,bind([[_92282, _92553], [610 ^ [], 231 ^ [intersection(610 ^ [], power_set(610 ^ [])), 610 ^ []]]]))).
% 6.23/6.54 ncf('1.1.1.1.2.1.1',plain,[-(member(231 ^ [intersection(610 ^ [], power_set(610 ^ [])), 610 ^ []], 610 ^ []))],reduction('1.1.1')).
% 6.23/6.54 ncf('1.1.1.1.2.1.2',plain,[-(member(610 ^ [], on))],extension(612 ^ 8)).
% 6.23/6.54 ncf('1.1.2',plain,[-(subset(intersection(610 ^ [], power_set(610 ^ [])), 610 ^ [])), 233 : -(member(231 ^ [610 ^ [], intersection(610 ^ [], power_set(610 ^ []))], intersection(610 ^ [], power_set(610 ^ []))))],extension(230 ^ 2,bind([[_86562, _86564], [610 ^ [], intersection(610 ^ [], power_set(610 ^ []))]]))).
% 6.23/6.54 ncf('1.1.2.1',plain,[member(231 ^ [610 ^ [], intersection(610 ^ [], power_set(610 ^ []))], intersection(610 ^ [], power_set(610 ^ []))), 273 : -(member(231 ^ [610 ^ [], intersection(610 ^ [], power_set(610 ^ []))], 610 ^ []))],extension(269 ^ 5,bind([[_87940, _87942, _87944], [power_set(610 ^ []), 610 ^ [], 231 ^ [610 ^ [], intersection(610 ^ [], power_set(610 ^ []))]]]))).
% 6.23/6.54 ncf('1.1.2.1.1',plain,[member(231 ^ [610 ^ [], intersection(610 ^ [], power_set(610 ^ []))], 610 ^ []), -(member(231 ^ [610 ^ [], intersection(610 ^ [], power_set(610 ^ []))], 610 ^ [])), 231 ^ [610 ^ [], intersection(610 ^ [], power_set(610 ^ []))] = 231 ^ [610 ^ [], intersection(610 ^ [], power_set(610 ^ []))], 610 ^ [] = 610 ^ []],extension(108 ^ 8,bind([[_82247, _82249, _82251, _82253], [610 ^ [], 610 ^ [], 231 ^ [610 ^ [], intersection(610 ^ [], power_set(610 ^ []))], 231 ^ [610 ^ [], intersection(610 ^ [], power_set(610 ^ []))]]]))).
% 6.23/6.54 ncf('1.1.2.1.1.1',plain,[member(231 ^ [610 ^ [], intersection(610 ^ [], power_set(610 ^ []))], 610 ^ [])],extension(235 ^ 9)).
% 6.23/6.54 ncf('1.1.2.1.1.2',plain,[-(231 ^ [610 ^ [], intersection(610 ^ [], power_set(610 ^ []))] = 231 ^ [610 ^ [], intersection(610 ^ [], power_set(610 ^ []))])],extension(2 ^ 9,bind([[_78750], [231 ^ [610 ^ [], intersection(610 ^ [], power_set(610 ^ []))]]]))).
% 6.23/6.54 ncf('1.1.2.1.1.3',plain,[-(610 ^ [] = 610 ^ [])],extension(2 ^ 9,bind([[_78750], [610 ^ []]]))).
% 6.23/6.54 %-----------------------------------------------------
% 6.23/6.54 End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------