TSTP Solution File: SET717+4 by nanoCoP---2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : nanoCoP---2.0
% Problem : SET717+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : nanocop.sh %s %d
% Computer : n004.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 11:56:20 EDT 2023
% Result : Theorem 254.57s 246.59s
% Output : Proof 254.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET717+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.07/0.13 % Command : nanocop.sh %s %d
% 0.13/0.34 % Computer : n004.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu May 18 19:13:09 EDT 2023
% 0.13/0.34 % CPUTime :
% 254.57/246.59
% 254.57/246.59 /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 254.57/246.59 Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 254.57/246.59 %-----------------------------------------------------
% 254.57/246.59 ncf(matrix, plain, [(613 ^ _122844) ^ [_147370, _147372, _147374] : [-(member(_147370, inverse_image2(_147374, _147372))), 614 ^ _122844 : [(615 ^ _122844) ^ [_147468] : [member(_147468, _147372), apply(_147374, _147370, _147468)]]], (113 ^ _122844) ^ [_126764, _126766] : [_126766 = _126764, -(member(_126766, singleton(_126764)))], (175 ^ _122844) ^ [_129068, _129070, _129072] : [maps(_129072, _129070, _129068), 178 ^ _122844 : [(179 ^ _122844) ^ [_129296] : [member(_129296, _129070), 183 ^ _122844 : [(184 ^ _122844) ^ [] : [-(member(182 ^ [_129068, _129070, _129072, _129296], _129068))], (186 ^ _122844) ^ [] : [-(apply(_129072, _129296, 182 ^ [_129068, _129070, _129072, _129296]))]]], (188 ^ _122844) ^ [_129686, _129688, _129690] : [member(_129690, _129070), member(_129688, _129068), member(_129686, _129068), -(_129688 = _129686), apply(_129072, _129690, _129688), apply(_129072, _129690, _129686)]]], (2 ^ _122844) ^ [_123006, _123008] : [subset(_123008, _123006), 5 ^ _122844 : [(6 ^ _122844) ^ [_123143] : [member(_123143, _123008), -(member(_123143, _123006))]]], (51 ^ _122844) ^ [_124698, _124700, _124702] : [member(_124702, intersection(_124700, _124698)), 54 ^ _122844 : [(55 ^ _122844) ^ [] : [-(member(_124702, _124700))], (57 ^ _122844) ^ [] : [-(member(_124702, _124698))]]], (859 ^ _122844) ^ [] : [surjective(compose_function(846 ^ [], 845 ^ [], 847 ^ [], 848 ^ [], 849 ^ []), 847 ^ [], 849 ^ [])], (12 ^ _122844) ^ [_123320, _123322] : [14 ^ _122844 : [(15 ^ _122844) ^ [] : [-(member(13 ^ [_123320, _123322], _123322))], (17 ^ _122844) ^ [] : [member(13 ^ [_123320, _123322], _123320)]], -(subset(_123322, _123320))], (604 ^ _122844) ^ [_147038, _147040, _147042] : [member(_147038, inverse_image2(_147042, _147040)), 608 ^ _122844 : [(609 ^ _122844) ^ [] : [-(member(607 ^ [_147038, _147040, _147042], _147040))], (611 ^ _122844) ^ [] : [-(apply(_147042, _147038, 607 ^ [_147038, _147040, _147042]))]]], (388 ^ _122844) ^ [_138470, _138472] : [identity(_138472, _138470), 391 ^ _122844 : [(392 ^ _122844) ^ [_138608] : [member(_138608, _138470), -(apply(_138472, _138608, _138608))]]], (452 ^ _122844) ^ [_141118, _141120, _141122] : [surjective(_141122, _141120, _141118), 455 ^ _122844 : [(456 ^ _122844) ^ [_141273] : [member(_141273, _141118), 460 ^ _122844 : [(461 ^ _122844) ^ [] : [-(member(459 ^ [_141118, _141120, _141122, _141273], _141120))], (463 ^ _122844) ^ [] : [-(apply(_141122, 459 ^ [_141118, _141120, _141122, _141273], _141273))]]]]], (119 ^ _122844) ^ [_127023, _127025, _127027] : [member(_127027, unordered_pair(_127025, _127023)), -(_127027 = _127025), -(_127027 = _127023)], (407 ^ _122844) ^ [_139197, _139199, _139201] : [injective(_139201, _139199, _139197), 410 ^ _122844 : [(411 ^ _122844) ^ [_139404, _139406, _139408] : [member(_139408, _139199), member(_139406, _139199), member(_139404, _139197), -(_139408 = _139406), apply(_139201, _139408, _139404), apply(_139201, _139406, _139404)]]], (851 ^ _122844) ^ [] : [-(maps(845 ^ [], 847 ^ [], 848 ^ []))], (857 ^ _122844) ^ [] : [-(surjective(846 ^ [], 848 ^ [], 849 ^ []))], (369 ^ _122844) ^ [_137329, _137331, _137333, _137335] : [373 ^ _122844 : [(384 ^ _122844) ^ [] : [371 ^ [_137329, _137331, _137333, _137335] = 372 ^ [_137329, _137331, _137333, _137335]], (382 ^ _122844) ^ [] : [-(apply(_137333, 370 ^ [_137329, _137331, _137333, _137335], 372 ^ [_137329, _137331, _137333, _137335]))], (374 ^ _122844) ^ [] : [-(member(370 ^ [_137329, _137331, _137333, _137335], _137331))], (380 ^ _122844) ^ [] : [-(apply(_137335, 370 ^ [_137329, _137331, _137333, _137335], 371 ^ [_137329, _137331, _137333, _137335]))], (376 ^ _122844) ^ [] : [-(member(371 ^ [_137329, _137331, _137333, _137335], _137329))], (378 ^ _122844) ^ [] : [-(member(372 ^ [_137329, _137331, _137333, _137335], _137329))]], -(equal_maps(_137335, _137333, _137331, _137329))], (45 ^ _122844) ^ [_124439, _124441] : [subset(_124441, _124439), -(member(_124441, power_set(_124439)))], (107 ^ _122844) ^ [_126598, _126600] : [member(_126600, singleton(_126598)), -(_126600 = _126598)], (560 ^ _122844) ^ [_145297, _145299, _145301] : [member(_145297, image2(_145301, _145299)), 564 ^ _122844 : [(565 ^ _122844) ^ [] : [-(member(563 ^ [_145297, _145299, _145301], _145299))], (567 ^ _122844) ^ [] : [-(apply(_145301, 563 ^ [_145297, _145299, _145301], _145297))]]], (648 ^ _122844) ^ [_148807, _148809, _148811, _148813, _148815] : [increasing(_148815, _148813, _148811, _148809, _148807), 651 ^ _122844 : [(652 ^ _122844) ^ [_149059, _149061, _149063, _149065] : [-(apply(_148807, _149063, _149059)), member(_149065, _148813), member(_149063, _148809), member(_149061, _148813), member(_149059, _148809), apply(_148811, _149065, _149061), apply(_148815, _149065, _149063), apply(_148815, _149061, _149059)]]], (21 ^ _122844) ^ [_123706, _123708] : [equal_set(_123708, _123706), 24 ^ _122844 : [(25 ^ _122844) ^ [] : [-(subset(_123708, _123706))], (27 ^ _122844) ^ [] : [-(subset(_123706, _123708))]]], (486 ^ _122844) ^ [_142476, _142478, _142480] : [-(one_to_one(_142480, _142478, _142476)), injective(_142480, _142478, _142476), surjective(_142480, _142478, _142476)], (634 ^ _122844) ^ [_148240, _148242, _148244, _148246] : [-(member(_148240, inverse_image3(_148246, _148244, _148242))), member(_148240, _148242), 639 ^ _122844 : [(640 ^ _122844) ^ [_148434] : [member(_148434, _148244), apply(_148246, _148240, _148434)]]], (210 ^ _122844) ^ [_130313, _130315, _130317] : [-(maps(_130317, _130315, _130313)), 225 ^ _122844 : [(236 ^ _122844) ^ [] : [223 ^ [_130313, _130315, _130317] = 224 ^ [_130313, _130315, _130317]], (234 ^ _122844) ^ [] : [-(apply(_130317, 222 ^ [_130313, _130315, _130317], 224 ^ [_130313, _130315, _130317]))], (226 ^ _122844) ^ [] : [-(member(222 ^ [_130313, _130315, _130317], _130315))], (232 ^ _122844) ^ [] : [-(apply(_130317, 222 ^ [_130313, _130315, _130317], 223 ^ [_130313, _130315, _130317]))], (228 ^ _122844) ^ [] : [-(member(223 ^ [_130313, _130315, _130317], _130313))], (230 ^ _122844) ^ [] : [-(member(224 ^ [_130313, _130315, _130317], _130313))]], 214 ^ _122844 : [(215 ^ _122844) ^ [] : [-(member(213 ^ [_130313, _130315, _130317], _130315))], (217 ^ _122844) ^ [_130653] : [member(_130653, _130313), apply(_130317, 213 ^ [_130313, _130315, _130317], _130653)]]], (706 ^ _122844) ^ [_151728, _151730, _151732, _151734, _151736] : [decreasing(_151736, _151734, _151732, _151730, _151728), 709 ^ _122844 : [(710 ^ _122844) ^ [_151980, _151982, _151984, _151986] : [-(apply(_151728, _151980, _151984)), member(_151986, _151734), member(_151984, _151730), member(_151982, _151734), member(_151980, _151730), apply(_151732, _151986, _151982), apply(_151736, _151986, _151984), apply(_151736, _151982, _151980)]]], (89 ^ _122844) ^ [_125997, _125999, _126001] : [member(_126001, difference(_125997, _125999)), 92 ^ _122844 : [(93 ^ _122844) ^ [] : [-(member(_126001, _125997))], (95 ^ _122844) ^ [] : [member(_126001, _125999)]]], (398 ^ _122844) ^ [_138787, _138789] : [400 ^ _122844 : [(401 ^ _122844) ^ [] : [-(member(399 ^ [_138787, _138789], _138787))], (403 ^ _122844) ^ [] : [apply(_138789, 399 ^ [_138787, _138789], 399 ^ [_138787, _138789])]], -(identity(_138789, _138787))], (623 ^ _122844) ^ [_147812, _147814, _147816, _147818] : [member(_147812, inverse_image3(_147818, _147816, _147814)), 626 ^ _122844 : [(632 ^ _122844) ^ [] : [-(apply(_147818, _147812, 628 ^ [_147812, _147814, _147816, _147818]))], (627 ^ _122844) ^ [] : [-(member(_147812, _147814))], (630 ^ _122844) ^ [] : [-(member(628 ^ [_147812, _147814, _147816, _147818], _147816))]]], (855 ^ _122844) ^ [] : [-(surjective(845 ^ [], 847 ^ [], 848 ^ []))], (79 ^ _122844) ^ [_125577, _125579, _125581] : [80 ^ _122844 : [(81 ^ _122844) ^ [] : [member(_125581, _125579)], (83 ^ _122844) ^ [] : [member(_125581, _125577)]], -(member(_125581, union(_125579, _125577)))], (277 ^ _122844) ^ [_133348, _133350, _133352, _133354, _133356, _133358] : [-(compose_predicate(_133358, _133356, _133354, _133352, _133350, _133348)), 280 ^ _122844 : [(285 ^ _122844) ^ [] : [299 ^ _122844 : [(300 ^ _122844) ^ [] : [-(member(298 ^ [_133348, _133350, _133352, _133354, _133356, _133358], _133350))], (302 ^ _122844) ^ [] : [-(apply(_133354, 278 ^ [_133348, _133350, _133352, _133354, _133356, _133358], 298 ^ [_133348, _133350, _133352, _133354, _133356, _133358]))], (304 ^ _122844) ^ [] : [-(apply(_133356, 298 ^ [_133348, _133350, _133352, _133354, _133356, _133358], 279 ^ [_133348, _133350, _133352, _133354, _133356, _133358]))], (306 ^ _122844) ^ [] : [apply(_133358, 278 ^ [_133348, _133350, _133352, _133354, _133356, _133358], 279 ^ [_133348, _133350, _133352, _133354, _133356, _133358])]], 286 ^ _122844 : [(287 ^ _122844) ^ [] : [-(apply(_133358, 278 ^ [_133348, _133350, _133352, _133354, _133356, _133358], 279 ^ [_133348, _133350, _133352, _133354, _133356, _133358]))], (289 ^ _122844) ^ [_134073] : [member(_134073, _133350), apply(_133354, 278 ^ [_133348, _133350, _133352, _133354, _133356, _133358], _134073), apply(_133356, _134073, 279 ^ [_133348, _133350, _133352, _133354, _133356, _133358])]]], (281 ^ _122844) ^ [] : [-(member(278 ^ [_133348, _133350, _133352, _133354, _133356, _133358], _133352))], (283 ^ _122844) ^ [] : [-(member(279 ^ [_133348, _133350, _133352, _133354, _133356, _133358], _133348))]]], (853 ^ _122844) ^ [] : [-(maps(846 ^ [], 848 ^ [], 849 ^ []))], (740 ^ _122844) ^ [_152909, _152911, _152913, _152915, _152917] : [745 ^ _122844 : [(746 ^ _122844) ^ [] : [-(member(741 ^ [_152909, _152911, _152913, _152915, _152917], _152915))], (748 ^ _122844) ^ [] : [-(member(742 ^ [_152909, _152911, _152913, _152915, _152917], _152911))], (750 ^ _122844) ^ [] : [-(member(743 ^ [_152909, _152911, _152913, _152915, _152917], _152915))], (752 ^ _122844) ^ [] : [-(member(744 ^ [_152909, _152911, _152913, _152915, _152917], _152911))], (754 ^ _122844) ^ [] : [-(apply(_152913, 741 ^ [_152909, _152911, _152913, _152915, _152917], 743 ^ [_152909, _152911, _152913, _152915, _152917]))], (756 ^ _122844) ^ [] : [-(apply(_152917, 741 ^ [_152909, _152911, _152913, _152915, _152917], 742 ^ [_152909, _152911, _152913, _152915, _152917]))], (758 ^ _122844) ^ [] : [-(apply(_152917, 743 ^ [_152909, _152911, _152913, _152915, _152917], 744 ^ [_152909, _152911, _152913, _152915, _152917]))], (760 ^ _122844) ^ [] : [apply(_152909, 744 ^ [_152909, _152911, _152913, _152915, _152917], 742 ^ [_152909, _152911, _152913, _152915, _152917])]], -(decreasing(_152917, _152915, _152913, _152911, _152909))], (590 ^ _122844) ^ [_146499, _146501, _146503, _146505] : [-(member(_146499, image3(_146505, _146503, _146501))), member(_146499, _146501), 595 ^ _122844 : [(596 ^ _122844) ^ [_146693] : [member(_146693, _146503), apply(_146505, _146693, _146499)]]], (764 ^ _122844) ^ [_154629, _154631, _154633, _154635, _154637] : [isomorphism(_154637, _154635, _154633, _154631, _154629), 767 ^ _122844 : [(772 ^ _122844) ^ [_155041, _155043, _155045, _155047] : [795 ^ _122844 : [(796 ^ _122844) ^ [] : [apply(_154633, _155047, _155043), -(apply(_154629, _155045, _155041))], (802 ^ _122844) ^ [] : [apply(_154629, _155045, _155041), -(apply(_154633, _155047, _155043))]], member(_155047, _154635), member(_155045, _154631), member(_155043, _154635), member(_155041, _154631), apply(_154637, _155047, _155045), apply(_154637, _155043, _155041)], (768 ^ _122844) ^ [] : [-(maps(_154637, _154635, _154631))], (770 ^ _122844) ^ [] : [-(one_to_one(_154637, _154635, _154631))]]], (59 ^ _122844) ^ [_124949, _124951, _124953] : [-(member(_124953, intersection(_124951, _124949))), member(_124953, _124951), member(_124953, _124949)], (137 ^ _122844) ^ [_127620, _127622] : [member(_127622, sum(_127620)), 141 ^ _122844 : [(142 ^ _122844) ^ [] : [-(member(140 ^ [_127620, _127622], _127620))], (144 ^ _122844) ^ [] : [-(member(_127622, 140 ^ [_127620, _127622]))]]], (29 ^ _122844) ^ [_123943, _123945] : [-(equal_set(_123945, _123943)), subset(_123945, _123943), subset(_123943, _123945)], (682 ^ _122844) ^ [_149988, _149990, _149992, _149994, _149996] : [687 ^ _122844 : [(688 ^ _122844) ^ [] : [-(member(683 ^ [_149988, _149990, _149992, _149994, _149996], _149994))], (690 ^ _122844) ^ [] : [-(member(684 ^ [_149988, _149990, _149992, _149994, _149996], _149990))], (692 ^ _122844) ^ [] : [-(member(685 ^ [_149988, _149990, _149992, _149994, _149996], _149994))], (694 ^ _122844) ^ [] : [-(member(686 ^ [_149988, _149990, _149992, _149994, _149996], _149990))], (696 ^ _122844) ^ [] : [-(apply(_149992, 683 ^ [_149988, _149990, _149992, _149994, _149996], 685 ^ [_149988, _149990, _149992, _149994, _149996]))], (698 ^ _122844) ^ [] : [-(apply(_149996, 683 ^ [_149988, _149990, _149992, _149994, _149996], 684 ^ [_149988, _149990, _149992, _149994, _149996]))], (700 ^ _122844) ^ [] : [-(apply(_149996, 685 ^ [_149988, _149990, _149992, _149994, _149996], 686 ^ [_149988, _149990, _149992, _149994, _149996]))], (702 ^ _122844) ^ [] : [apply(_149988, 684 ^ [_149988, _149990, _149992, _149994, _149996], 686 ^ [_149988, _149990, _149992, _149994, _149996])]], -(increasing(_149996, _149994, _149992, _149990, _149988))], (87 ^ _122844) ^ [_125847] : [member(_125847, empty_set)], (343 ^ _122844) ^ [_136467, _136469, _136471, _136473] : [equal_maps(_136473, _136471, _136469, _136467), 346 ^ _122844 : [(347 ^ _122844) ^ [_136680, _136682, _136684] : [member(_136684, _136469), member(_136682, _136467), member(_136680, _136467), -(_136682 = _136680), apply(_136473, _136684, _136682), apply(_136471, _136684, _136680)]]], (496 ^ _122844) ^ [_142850, _142852, _142854, _142856] : [inverse_predicate(_142856, _142854, _142852, _142850), 499 ^ _122844 : [(500 ^ _122844) ^ [_143032, _143034] : [member(_143034, _142852), member(_143032, _142850), 507 ^ _122844 : [(508 ^ _122844) ^ [] : [apply(_142854, _143034, _143032), -(apply(_142856, _143032, _143034))], (514 ^ _122844) ^ [] : [apply(_142856, _143032, _143034), -(apply(_142854, _143034, _143032))]]]]], (540 ^ _122844) ^ [_144625, _144627, _144629, _144631, _144633] : [member(_144627, _144631), member(_144625, _144629), 547 ^ _122844 : [(548 ^ _122844) ^ [] : [apply(_144633, _144627, _144625), -(apply(inverse_function(_144633, _144631, _144629), _144625, _144627))], (554 ^ _122844) ^ [] : [apply(inverse_function(_144633, _144631, _144629), _144625, _144627), -(apply(_144633, _144627, _144625))]]], (97 ^ _122844) ^ [_126249, _126251, _126253] : [-(member(_126253, difference(_126249, _126251))), member(_126253, _126249), -(member(_126253, _126251))], (156 ^ _122844) ^ [_128308, _128310] : [member(_128310, product(_128308)), 159 ^ _122844 : [(160 ^ _122844) ^ [_128449] : [member(_128449, _128308), -(member(_128310, _128449))]]], (478 ^ _122844) ^ [_142225, _142227, _142229] : [one_to_one(_142229, _142227, _142225), 481 ^ _122844 : [(482 ^ _122844) ^ [] : [-(injective(_142229, _142227, _142225))], (484 ^ _122844) ^ [] : [-(surjective(_142229, _142227, _142225))]]], (129 ^ _122844) ^ [_127291, _127293, _127295] : [130 ^ _122844 : [(131 ^ _122844) ^ [] : [_127295 = _127293], (133 ^ _122844) ^ [] : [_127295 = _127291]], -(member(_127295, unordered_pair(_127293, _127291)))], (808 ^ _122844) ^ [_156179, _156181, _156183, _156185, _156187] : [-(isomorphism(_156187, _156185, _156183, _156181, _156179)), maps(_156187, _156185, _156181), one_to_one(_156187, _156185, _156181), 821 ^ _122844 : [(828 ^ _122844) ^ [] : [-(member(820 ^ [_156179, _156181, _156183, _156185, _156187], _156181))], (830 ^ _122844) ^ [] : [-(apply(_156187, 817 ^ [_156179, _156181, _156183, _156185, _156187], 818 ^ [_156179, _156181, _156183, _156185, _156187]))], (824 ^ _122844) ^ [] : [-(member(818 ^ [_156179, _156181, _156183, _156185, _156187], _156181))], (832 ^ _122844) ^ [] : [-(apply(_156187, 819 ^ [_156179, _156181, _156183, _156185, _156187], 820 ^ [_156179, _156181, _156183, _156185, _156187]))], (822 ^ _122844) ^ [] : [-(member(817 ^ [_156179, _156181, _156183, _156185, _156187], _156185))], (834 ^ _122844) ^ [] : [835 ^ _122844 : [(836 ^ _122844) ^ [] : [-(apply(_156183, 817 ^ [_156179, _156181, _156183, _156185, _156187], 819 ^ [_156179, _156181, _156183, _156185, _156187]))], (838 ^ _122844) ^ [] : [apply(_156179, 818 ^ [_156179, _156181, _156183, _156185, _156187], 820 ^ [_156179, _156181, _156183, _156185, _156187])]], 839 ^ _122844 : [(840 ^ _122844) ^ [] : [-(apply(_156179, 818 ^ [_156179, _156181, _156183, _156185, _156187], 820 ^ [_156179, _156181, _156183, _156185, _156187]))], (842 ^ _122844) ^ [] : [apply(_156183, 817 ^ [_156179, _156181, _156183, _156185, _156187], 819 ^ [_156179, _156181, _156183, _156185, _156187])]]], (826 ^ _122844) ^ [] : [-(member(819 ^ [_156179, _156181, _156183, _156185, _156187], _156185))]]], (579 ^ _122844) ^ [_146071, _146073, _146075, _146077] : [member(_146071, image3(_146077, _146075, _146073)), 582 ^ _122844 : [(588 ^ _122844) ^ [] : [-(apply(_146077, 584 ^ [_146071, _146073, _146075, _146077], _146071))], (583 ^ _122844) ^ [] : [-(member(_146071, _146073))], (586 ^ _122844) ^ [] : [-(member(584 ^ [_146071, _146073, _146075, _146077], _146075))]]], (433 ^ _122844) ^ [_140029, _140031, _140033] : [437 ^ _122844 : [(448 ^ _122844) ^ [] : [434 ^ [_140029, _140031, _140033] = 435 ^ [_140029, _140031, _140033]], (446 ^ _122844) ^ [] : [-(apply(_140033, 435 ^ [_140029, _140031, _140033], 436 ^ [_140029, _140031, _140033]))], (438 ^ _122844) ^ [] : [-(member(434 ^ [_140029, _140031, _140033], _140031))], (444 ^ _122844) ^ [] : [-(apply(_140033, 434 ^ [_140029, _140031, _140033], 436 ^ [_140029, _140031, _140033]))], (440 ^ _122844) ^ [] : [-(member(435 ^ [_140029, _140031, _140033], _140031))], (442 ^ _122844) ^ [] : [-(member(436 ^ [_140029, _140031, _140033], _140029))]], -(injective(_140033, _140031, _140029))], (520 ^ _122844) ^ [_143634, _143636, _143638, _143640] : [-(inverse_predicate(_143640, _143638, _143636, _143634)), 523 ^ _122844 : [(528 ^ _122844) ^ [] : [529 ^ _122844 : [(530 ^ _122844) ^ [] : [-(apply(_143638, 521 ^ [_143634, _143636, _143638, _143640], 522 ^ [_143634, _143636, _143638, _143640]))], (532 ^ _122844) ^ [] : [apply(_143640, 522 ^ [_143634, _143636, _143638, _143640], 521 ^ [_143634, _143636, _143638, _143640])]], 533 ^ _122844 : [(534 ^ _122844) ^ [] : [-(apply(_143640, 522 ^ [_143634, _143636, _143638, _143640], 521 ^ [_143634, _143636, _143638, _143640]))], (536 ^ _122844) ^ [] : [apply(_143638, 521 ^ [_143634, _143636, _143638, _143640], 522 ^ [_143634, _143636, _143638, _143640])]]], (524 ^ _122844) ^ [] : [-(member(521 ^ [_143634, _143636, _143638, _143640], _143636))], (526 ^ _122844) ^ [] : [-(member(522 ^ [_143634, _143636, _143638, _143640], _143634))]]], (146 ^ _122844) ^ [_127931, _127933] : [-(member(_127933, sum(_127931))), 147 ^ _122844 : [(148 ^ _122844) ^ [_128025] : [member(_128025, _127931), member(_127933, _128025)]]], (569 ^ _122844) ^ [_145629, _145631, _145633] : [-(member(_145629, image2(_145633, _145631))), 570 ^ _122844 : [(571 ^ _122844) ^ [_145727] : [member(_145727, _145631), apply(_145633, _145727, _145629)]]], (240 ^ _122844) ^ [_131873, _131875, _131877, _131879, _131881, _131883] : [compose_predicate(_131883, _131881, _131879, _131877, _131875, _131873), 243 ^ _122844 : [(244 ^ _122844) ^ [_132085, _132087] : [member(_132087, _131877), member(_132085, _131873), 251 ^ _122844 : [(252 ^ _122844) ^ [] : [apply(_131883, _132087, _132085), 256 ^ _122844 : [(261 ^ _122844) ^ [] : [-(apply(_131881, 255 ^ [_131873, _131875, _131877, _131879, _131881, _131883, _132085, _132087], _132085))], (257 ^ _122844) ^ [] : [-(member(255 ^ [_131873, _131875, _131877, _131879, _131881, _131883, _132085, _132087], _131875))], (259 ^ _122844) ^ [] : [-(apply(_131879, _132087, 255 ^ [_131873, _131875, _131877, _131879, _131881, _131883, _132085, _132087]))]]], (263 ^ _122844) ^ [] : [-(apply(_131883, _132087, _132085)), 264 ^ _122844 : [(265 ^ _122844) ^ [_132930] : [member(_132930, _131875), apply(_131879, _132087, _132930), apply(_131881, _132930, _132085)]]]]]]], (69 ^ _122844) ^ [_125309, _125311, _125313] : [member(_125313, union(_125311, _125309)), -(member(_125313, _125311)), -(member(_125313, _125309))], (166 ^ _122844) ^ [_128626, _128628] : [168 ^ _122844 : [(169 ^ _122844) ^ [] : [-(member(167 ^ [_128626, _128628], _128626))], (171 ^ _122844) ^ [] : [member(_128628, 167 ^ [_128626, _128628])]], -(member(_128628, product(_128626)))], (465 ^ _122844) ^ [_141626, _141628, _141630] : [-(surjective(_141630, _141628, _141626)), 467 ^ _122844 : [(468 ^ _122844) ^ [] : [-(member(466 ^ [_141626, _141628, _141630], _141626))], (470 ^ _122844) ^ [_141877] : [member(_141877, _141628), apply(_141630, _141877, 466 ^ [_141626, _141628, _141630])]]], (39 ^ _122844) ^ [_124273, _124275] : [member(_124275, power_set(_124273)), -(subset(_124275, _124273))], (310 ^ _122844) ^ [_135142, _135144, _135146, _135148, _135150, _135152, _135154] : [member(_135144, _135150), member(_135142, _135146), 317 ^ _122844 : [(318 ^ _122844) ^ [] : [apply(compose_function(_135154, _135152, _135150, _135148, _135146), _135144, _135142), 322 ^ _122844 : [(327 ^ _122844) ^ [] : [-(apply(_135154, 321 ^ [_135142, _135144, _135146, _135148, _135150, _135152, _135154], _135142))], (323 ^ _122844) ^ [] : [-(member(321 ^ [_135142, _135144, _135146, _135148, _135150, _135152, _135154], _135148))], (325 ^ _122844) ^ [] : [-(apply(_135152, _135144, 321 ^ [_135142, _135144, _135146, _135148, _135150, _135152, _135154]))]]], (329 ^ _122844) ^ [] : [-(apply(compose_function(_135154, _135152, _135150, _135148, _135146), _135144, _135142)), 330 ^ _122844 : [(331 ^ _122844) ^ [_135957] : [member(_135957, _135148), apply(_135152, _135144, _135957), apply(_135154, _135957, _135142)]]]]]], input).
% 254.57/246.59 ncf('1',plain,[surjective(compose_function(846 ^ [], 845 ^ [], 847 ^ [], 848 ^ [], 849 ^ []), 847 ^ [], 849 ^ [])],start(859 ^ 0)).
% 254.57/246.59 ncf('1.1',plain,[-(surjective(compose_function(846 ^ [], 845 ^ [], 847 ^ [], 848 ^ [], 849 ^ []), 847 ^ [], 849 ^ [])), 470 : member(459 ^ [848 ^ [], 847 ^ [], 845 ^ [], 459 ^ [849 ^ [], 848 ^ [], 846 ^ [], 466 ^ [849 ^ [], 847 ^ [], compose_function(846 ^ [], 845 ^ [], 847 ^ [], 848 ^ [], 849 ^ [])]]], 847 ^ []), 470 : apply(compose_function(846 ^ [], 845 ^ [], 847 ^ [], 848 ^ [], 849 ^ []), 459 ^ [848 ^ [], 847 ^ [], 845 ^ [], 459 ^ [849 ^ [], 848 ^ [], 846 ^ [], 466 ^ [849 ^ [], 847 ^ [], compose_function(846 ^ [], 845 ^ [], 847 ^ [], 848 ^ [], 849 ^ [])]]], 466 ^ [849 ^ [], 847 ^ [], compose_function(846 ^ [], 845 ^ [], 847 ^ [], 848 ^ [], 849 ^ [])])],extension(465 ^ 1,bind([[_141626, _141628, _141630, _141877], [849 ^ [], 847 ^ [], compose_function(846 ^ [], 845 ^ [], 847 ^ [], 848 ^ [], 849 ^ []), 459 ^ [848 ^ [], 847 ^ [], 845 ^ [], 459 ^ [849 ^ [], 848 ^ [], 846 ^ [], 466 ^ [849 ^ [], 847 ^ [], compose_function(846 ^ [], 845 ^ [], 847 ^ [], 848 ^ [], 849 ^ [])]]]]]))).
% 254.57/246.59 ncf('1.1.1',plain,[-(member(459 ^ [848 ^ [], 847 ^ [], 845 ^ [], 459 ^ [849 ^ [], 848 ^ [], 846 ^ [], 466 ^ [849 ^ [], 847 ^ [], compose_function(846 ^ [], 845 ^ [], 847 ^ [], 848 ^ [], 849 ^ [])]]], 847 ^ [])), 456 : member(459 ^ [849 ^ [], 848 ^ [], 846 ^ [], 466 ^ [849 ^ [], 847 ^ [], compose_function(846 ^ [], 845 ^ [], 847 ^ [], 848 ^ [], 849 ^ [])]], 848 ^ []), 456 : surjective(845 ^ [], 847 ^ [], 848 ^ [])],extension(452 ^ 4,bind([[_141118, _141120, _141122, _141273], [848 ^ [], 847 ^ [], 845 ^ [], 459 ^ [849 ^ [], 848 ^ [], 846 ^ [], 466 ^ [849 ^ [], 847 ^ [], compose_function(846 ^ [], 845 ^ [], 847 ^ [], 848 ^ [], 849 ^ [])]]]]))).
% 254.57/246.59 ncf('1.1.1.1',plain,[-(member(459 ^ [849 ^ [], 848 ^ [], 846 ^ [], 466 ^ [849 ^ [], 847 ^ [], compose_function(846 ^ [], 845 ^ [], 847 ^ [], 848 ^ [], 849 ^ [])]], 848 ^ [])), 456 : member(466 ^ [849 ^ [], 847 ^ [], compose_function(846 ^ [], 845 ^ [], 847 ^ [], 848 ^ [], 849 ^ [])], 849 ^ []), 456 : surjective(846 ^ [], 848 ^ [], 849 ^ [])],extension(452 ^ 7,bind([[_141118, _141120, _141122, _141273], [849 ^ [], 848 ^ [], 846 ^ [], 466 ^ [849 ^ [], 847 ^ [], compose_function(846 ^ [], 845 ^ [], 847 ^ [], 848 ^ [], 849 ^ [])]]]))).
% 254.57/246.59 ncf('1.1.1.1.1',plain,[-(member(466 ^ [849 ^ [], 847 ^ [], compose_function(846 ^ [], 845 ^ [], 847 ^ [], 848 ^ [], 849 ^ [])], 849 ^ []))],extension(468 ^ 10)).
% 254.57/246.59 ncf('1.1.1.1.2',plain,[-(surjective(846 ^ [], 848 ^ [], 849 ^ []))],extension(857 ^ 8)).
% 254.57/246.59 ncf('1.1.1.2',plain,[-(surjective(845 ^ [], 847 ^ [], 848 ^ []))],extension(855 ^ 5)).
% 254.57/246.59 ncf('1.1.2',plain,[-(apply(compose_function(846 ^ [], 845 ^ [], 847 ^ [], 848 ^ [], 849 ^ []), 459 ^ [848 ^ [], 847 ^ [], 845 ^ [], 459 ^ [849 ^ [], 848 ^ [], 846 ^ [], 466 ^ [849 ^ [], 847 ^ [], compose_function(846 ^ [], 845 ^ [], 847 ^ [], 848 ^ [], 849 ^ [])]]], 466 ^ [849 ^ [], 847 ^ [], compose_function(846 ^ [], 845 ^ [], 847 ^ [], 848 ^ [], 849 ^ [])])), 331 : member(459 ^ [849 ^ [], 848 ^ [], 846 ^ [], 466 ^ [849 ^ [], 847 ^ [], compose_function(846 ^ [], 845 ^ [], 847 ^ [], 848 ^ [], 849 ^ [])]], 848 ^ []), 331 : apply(845 ^ [], 459 ^ [848 ^ [], 847 ^ [], 845 ^ [], 459 ^ [849 ^ [], 848 ^ [], 846 ^ [], 466 ^ [849 ^ [], 847 ^ [], compose_function(846 ^ [], 845 ^ [], 847 ^ [], 848 ^ [], 849 ^ [])]]], 459 ^ [849 ^ [], 848 ^ [], 846 ^ [], 466 ^ [849 ^ [], 847 ^ [], compose_function(846 ^ [], 845 ^ [], 847 ^ [], 848 ^ [], 849 ^ [])]]), 331 : apply(846 ^ [], 459 ^ [849 ^ [], 848 ^ [], 846 ^ [], 466 ^ [849 ^ [], 847 ^ [], compose_function(846 ^ [], 845 ^ [], 847 ^ [], 848 ^ [], 849 ^ [])]], 466 ^ [849 ^ [], 847 ^ [], compose_function(846 ^ [], 845 ^ [], 847 ^ [], 848 ^ [], 849 ^ [])]), 329 : member(459 ^ [848 ^ [], 847 ^ [], 845 ^ [], 459 ^ [849 ^ [], 848 ^ [], 846 ^ [], 466 ^ [849 ^ [], 847 ^ [], compose_function(846 ^ [], 845 ^ [], 847 ^ [], 848 ^ [], 849 ^ [])]]], 847 ^ []), 329 : member(466 ^ [849 ^ [], 847 ^ [], compose_function(846 ^ [], 845 ^ [], 847 ^ [], 848 ^ [], 849 ^ [])], 849 ^ [])],extension(310 ^ 4,bind([[_135142, _135144, _135146, _135148, _135150, _135152, _135154, _135957], [466 ^ [849 ^ [], 847 ^ [], compose_function(846 ^ [], 845 ^ [], 847 ^ [], 848 ^ [], 849 ^ [])], 459 ^ [848 ^ [], 847 ^ [], 845 ^ [], 459 ^ [849 ^ [], 848 ^ [], 846 ^ [], 466 ^ [849 ^ [], 847 ^ [], compose_function(846 ^ [], 845 ^ [], 847 ^ [], 848 ^ [], 849 ^ [])]]], 849 ^ [], 848 ^ [], 847 ^ [], 845 ^ [], 846 ^ [], 459 ^ [849 ^ [], 848 ^ [], 846 ^ [], 466 ^ [849 ^ [], 847 ^ [], compose_function(846 ^ [], 845 ^ [], 847 ^ [], 848 ^ [], 849 ^ [])]]]]))).
% 254.57/246.59 ncf('1.1.2.1',plain,[-(member(459 ^ [849 ^ [], 848 ^ [], 846 ^ [], 466 ^ [849 ^ [], 847 ^ [], compose_function(846 ^ [], 845 ^ [], 847 ^ [], 848 ^ [], 849 ^ [])]], 848 ^ [])), 456 : member(466 ^ [849 ^ [], 847 ^ [], compose_function(846 ^ [], 845 ^ [], 847 ^ [], 848 ^ [], 849 ^ [])], 849 ^ []), 456 : surjective(846 ^ [], 848 ^ [], 849 ^ [])],extension(452 ^ 9,bind([[_141118, _141120, _141122, _141273], [849 ^ [], 848 ^ [], 846 ^ [], 466 ^ [849 ^ [], 847 ^ [], compose_function(846 ^ [], 845 ^ [], 847 ^ [], 848 ^ [], 849 ^ [])]]]))).
% 254.57/246.59 ncf('1.1.2.1.1',plain,[-(member(466 ^ [849 ^ [], 847 ^ [], compose_function(846 ^ [], 845 ^ [], 847 ^ [], 848 ^ [], 849 ^ [])], 849 ^ []))],extension(468 ^ 12)).
% 254.57/246.59 ncf('1.1.2.1.2',plain,[-(surjective(846 ^ [], 848 ^ [], 849 ^ []))],extension(857 ^ 10)).
% 254.57/246.59 ncf('1.1.2.2',plain,[-(apply(845 ^ [], 459 ^ [848 ^ [], 847 ^ [], 845 ^ [], 459 ^ [849 ^ [], 848 ^ [], 846 ^ [], 466 ^ [849 ^ [], 847 ^ [], compose_function(846 ^ [], 845 ^ [], 847 ^ [], 848 ^ [], 849 ^ [])]]], 459 ^ [849 ^ [], 848 ^ [], 846 ^ [], 466 ^ [849 ^ [], 847 ^ [], compose_function(846 ^ [], 845 ^ [], 847 ^ [], 848 ^ [], 849 ^ [])]])), 456 : member(459 ^ [849 ^ [], 848 ^ [], 846 ^ [], 466 ^ [849 ^ [], 847 ^ [], compose_function(846 ^ [], 845 ^ [], 847 ^ [], 848 ^ [], 849 ^ [])]], 848 ^ []), 456 : surjective(845 ^ [], 847 ^ [], 848 ^ [])],extension(452 ^ 9,bind([[_141118, _141120, _141122, _141273], [848 ^ [], 847 ^ [], 845 ^ [], 459 ^ [849 ^ [], 848 ^ [], 846 ^ [], 466 ^ [849 ^ [], 847 ^ [], compose_function(846 ^ [], 845 ^ [], 847 ^ [], 848 ^ [], 849 ^ [])]]]]))).
% 254.57/246.59 ncf('1.1.2.2.1',plain,[-(member(459 ^ [849 ^ [], 848 ^ [], 846 ^ [], 466 ^ [849 ^ [], 847 ^ [], compose_function(846 ^ [], 845 ^ [], 847 ^ [], 848 ^ [], 849 ^ [])]], 848 ^ []))],lemmata('[1, 1].x')).
% 254.57/246.59 ncf('1.1.2.2.2',plain,[-(surjective(845 ^ [], 847 ^ [], 848 ^ []))],extension(855 ^ 10)).
% 254.57/246.59 ncf('1.1.2.3',plain,[-(apply(846 ^ [], 459 ^ [849 ^ [], 848 ^ [], 846 ^ [], 466 ^ [849 ^ [], 847 ^ [], compose_function(846 ^ [], 845 ^ [], 847 ^ [], 848 ^ [], 849 ^ [])]], 466 ^ [849 ^ [], 847 ^ [], compose_function(846 ^ [], 845 ^ [], 847 ^ [], 848 ^ [], 849 ^ [])])), 456 : member(466 ^ [849 ^ [], 847 ^ [], compose_function(846 ^ [], 845 ^ [], 847 ^ [], 848 ^ [], 849 ^ [])], 849 ^ []), 456 : surjective(846 ^ [], 848 ^ [], 849 ^ [])],extension(452 ^ 9,bind([[_141118, _141120, _141122, _141273], [849 ^ [], 848 ^ [], 846 ^ [], 466 ^ [849 ^ [], 847 ^ [], compose_function(846 ^ [], 845 ^ [], 847 ^ [], 848 ^ [], 849 ^ [])]]]))).
% 254.57/246.59 ncf('1.1.2.3.1',plain,[-(member(466 ^ [849 ^ [], 847 ^ [], compose_function(846 ^ [], 845 ^ [], 847 ^ [], 848 ^ [], 849 ^ [])], 849 ^ []))],extension(468 ^ 12)).
% 254.57/246.59 ncf('1.1.2.3.2',plain,[-(surjective(846 ^ [], 848 ^ [], 849 ^ []))],extension(857 ^ 10)).
% 254.57/246.59 ncf('1.1.2.4',plain,[-(member(459 ^ [848 ^ [], 847 ^ [], 845 ^ [], 459 ^ [849 ^ [], 848 ^ [], 846 ^ [], 466 ^ [849 ^ [], 847 ^ [], compose_function(846 ^ [], 845 ^ [], 847 ^ [], 848 ^ [], 849 ^ [])]]], 847 ^ []))],lemmata('[1].x')).
% 254.57/246.59 ncf('1.1.2.5',plain,[-(member(466 ^ [849 ^ [], 847 ^ [], compose_function(846 ^ [], 845 ^ [], 847 ^ [], 848 ^ [], 849 ^ [])], 849 ^ []))],extension(468 ^ 5)).
% 254.57/246.59 %-----------------------------------------------------
% 254.57/246.59 End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------