%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SWC411+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n007.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 12:13:29 EDT 2023

% Result   : Theorem 44.00s 42.72s
% Output   : Proof 44.00s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : SWC411+1 : TPTP v8.1.2. Released v2.4.0.
% 0.10/0.13  % Command  : nanocop.sh %s %d
% 0.12/0.34  % Computer : n007.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 : Fri May 19 01:04:08 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 44.00/42.72  
% 44.00/42.72  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 44.00/42.72  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 44.00/42.72  %-----------------------------------------------------
% 44.00/42.72  ncf(matrix, plain, [(1987 ^ _317539) ^ [] : [-(ssList(1985 ^ []))], (1993 ^ _317539) ^ [_318261] : [ssItem(_318261), -(memberP(1982 ^ [], _318261)), memberP(1985 ^ [], _318261)], (1981 ^ _317539) ^ [] : [-(ssList(1979 ^ []))], (1978 ^ _317539) ^ [] : [-(ssList(1976 ^ []))], (1991 ^ _317539) ^ [] : [-(1976 ^ [] = 1982 ^ [])], (2008 ^ _317539) ^ [] : [memberP(1976 ^ [], 2002 ^ [])], (1984 ^ _317539) ^ [] : [-(ssList(1982 ^ []))], (2006 ^ _317539) ^ [] : [-(memberP(1979 ^ [], 2002 ^ []))], (1989 ^ _317539) ^ [] : [-(1979 ^ [] = 1985 ^ [])], (2004 ^ _317539) ^ [] : [-(ssItem(2002 ^ []))], !, (861 ^ _249212) ^ [_281769] : [ssList(_281769), 864 ^ _249212 : [(865 ^ _249212) ^ [_281907] : [ssList(_281907), 868 ^ _249212 : [(875 ^ _249212) ^ [] : [-(_281769 = _281907), -(neq(_281769, _281907))], (869 ^ _249212) ^ [] : [neq(_281769, _281907), _281769 = _281907]]]]], (256 ^ _249212) ^ [_257327, _257329] : [_257329 = _257327, -(hd(_257329) = hd(_257327))], (72 ^ _249212) ^ [_251615, _251617, _251619, _251621] : [-(segmentP(_251619, _251615)), segmentP(_251621, _251617), _251621 = _251619, _251617 = _251615], (1355 ^ _249212) ^ [_297592] : [ssList(_297592), 1358 ^ _249212 : [(1359 ^ _249212) ^ [_297734] : [ssList(_297734), -(_297592 = _297734), rearsegP(_297592, _297734), rearsegP(_297734, _297592)]]], (1459 ^ _249212) ^ [_300745] : [ssList(_300745), -(segmentP(_300745, _300745))], (106 ^ _249212) ^ [_252621, _252623] : [-(strictorderP(_252621)), _252623 = _252621, strictorderP(_252623)], (58 ^ _249212) ^ [_251171, _251173, _251175, _251177] : [-(rearsegP(_251175, _251171)), rearsegP(_251177, _251173), _251177 = _251175, _251173 = _251171], (943 ^ _249212) ^ [_284564] : [ssList(_284564), 946 ^ _249212 : [(947 ^ _249212) ^ [_284699] : [ssItem(_284699), nil = cons(_284699, _284564)]]], (1869 ^ _249212) ^ [_313538] : [ssItem(_313538), lt(_313538, _313538)], (136 ^ _249212) ^ [_253506, _253508] : [-(duplicatefreeP(_253506)), _253508 = _253506, duplicatefreeP(_253508)], (232 ^ _249212) ^ [_256470, _256472, _256474, _256476] : [-(memberP(_256474, _256470)), memberP(_256476, _256472), _256476 = _256474, _256472 = _256470], (2 ^ _249212) ^ [_249336] : [-(_249336 = _249336)], (1633 ^ _249212) ^ [_306017] : [ssItem(_306017), -(equalelemsP(cons(_306017, nil)))], (262 ^ _249212) ^ [_257573, _257575, _257577, _257579] : [-(app(_257579, _257575) = app(_257577, _257573)), _257579 = _257577, _257575 = _257573], (1145 ^ _249212) ^ [_290936] : [ssItem(_290936), 1148 ^ _249212 : [(1149 ^ _249212) ^ [_291091] : [ssList(_291091), 1152 ^ _249212 : [(1153 ^ _249212) ^ [_291242] : [ssList(_291242), 1156 ^ _249212 : [(1157 ^ _249212) ^ [] : [memberP(app(_291091, _291242), _290936), -(memberP(_291091, _290936)), -(memberP(_291242, _290936))], (1167 ^ _249212) ^ [] : [1168 ^ _249212 : [(1171 ^ _249212) ^ [] : [memberP(_291242, _290936)], (1169 ^ _249212) ^ [] : [memberP(_291091, _290936)]], -(memberP(app(_291091, _291242), _290936))]]]]]]], (278 ^ _249212) ^ [_258106] : [ssItem(_258106), 281 ^ _249212 : [(282 ^ _249212) ^ [_258244] : [ssItem(_258244), 285 ^ _249212 : [(292 ^ _249212) ^ [] : [-(_258106 = _258244), -(neq(_258106, _258244))], (286 ^ _249212) ^ [] : [neq(_258106, _258244), _258106 = _258244]]]]], (1213 ^ _249212) ^ [_293083] : [ssList(_293083), 1216 ^ _249212 : [(1217 ^ _249212) ^ [_293235] : [ssList(_293235), 1220 ^ _249212 : [(1221 ^ _249212) ^ [_293383] : [ssList(_293383), -(frontsegP(_293083, _293383)), frontsegP(_293083, _293235), frontsegP(_293235, _293383)]]]]], (390 ^ _249212) ^ [_261807] : [ssList(_261807), 393 ^ _249212 : [(394 ^ _249212) ^ [_261956] : [ssList(_261956), 397 ^ _249212 : [(407 ^ _249212) ^ [] : [-(rearsegP(_261807, _261956)), 408 ^ _249212 : [(409 ^ _249212) ^ [_262431] : [ssList(_262431), app(_262431, _261956) = _261807]]], (398 ^ _249212) ^ [] : [rearsegP(_261807, _261956), 402 ^ _249212 : [(405 ^ _249212) ^ [] : [-(app(401 ^ [_261807, _261956], _261956) = _261807)], (403 ^ _249212) ^ [] : [-(ssList(401 ^ [_261807, _261956]))]]]]]]], (1017 ^ _249212) ^ [_287030] : [ssList(_287030), -(app(nil, _287030) = _287030)], (1063 ^ _249212) ^ [_288445] : [ssItem(_288445), -(leq(_288445, _288445))], (1749 ^ _249212) ^ [_309721] : [ssList(_309721), 1752 ^ _249212 : [(1753 ^ _249212) ^ [_309873] : [ssList(_309873), 1756 ^ _249212 : [(1757 ^ _249212) ^ [_310021] : [ssList(_310021), -(app(app(_309721, _309873), _310021) = app(_309721, app(_309873, _310021)))]]]]], (1465 ^ _249212) ^ [_300933] : [ssList(_300933), 1468 ^ _249212 : [(1469 ^ _249212) ^ [_301095] : [ssList(_301095), 1472 ^ _249212 : [(1473 ^ _249212) ^ [_301253] : [ssList(_301253), 1476 ^ _249212 : [(1477 ^ _249212) ^ [_301407] : [ssList(_301407), segmentP(_300933, _301095), -(segmentP(app(app(_301253, _300933), _301407), _301095))]]]]]]], (1809 ^ _249212) ^ [_311668] : [ssList(_311668), 1812 ^ _249212 : [(1813 ^ _249212) ^ [_311816] : [ssList(_311816), -(nil = _311668), -(tl(app(_311668, _311816)) = app(tl(_311668), _311816))]]], (1211 ^ _249212) ^ [] : [singletonP(nil)], (1379 ^ _249212) ^ [_298301] : [ssList(_298301), 1382 ^ _249212 : [(1383 ^ _249212) ^ [_298450] : [ssList(_298450), 1386 ^ _249212 : [(1387 ^ _249212) ^ [_298595] : [ssList(_298595), rearsegP(_298301, _298450), -(rearsegP(app(_298595, _298301), _298450))]]]]], (993 ^ _249212) ^ [_286155] : [ssList(_286155), 996 ^ _249212 : [(997 ^ _249212) ^ [_286287] : [ssList(_286287), -(ssList(app(_286155, _286287)))]]], (1517 ^ _249212) ^ [_302604] : [ssItem(_302604), -(totalorderP(cons(_302604, nil)))], (1253 ^ _249212) ^ [_294304] : [ssList(_294304), -(frontsegP(_294304, _294304))], (1487 ^ _249212) ^ [_301743] : [ssList(_301743), -(segmentP(_301743, nil))], (34 ^ _249212) ^ [_250404, _250406] : [-(singletonP(_250404)), _250406 = _250404, singletonP(_250406)], (1311 ^ _249212) ^ [_296276] : [ssList(_296276), -(frontsegP(_296276, nil))], (1023 ^ _249212) ^ [_287224] : [ssItem(_287224), 1026 ^ _249212 : [(1027 ^ _249212) ^ [_287366] : [ssItem(_287366), -(_287224 = _287366), leq(_287224, _287366), leq(_287366, _287224)]]], (1403 ^ _249212) ^ [_299096] : [ssList(_299096), 1406 ^ _249212 : [(1413 ^ _249212) ^ [] : [nil = _299096, -(rearsegP(nil, _299096))], (1407 ^ _249212) ^ [] : [rearsegP(nil, _299096), -(nil = _299096)]]], (1579 ^ _249212) ^ [_304433] : [ssItem(_304433), -(strictorderedP(cons(_304433, nil)))], (184 ^ _249212) ^ [_255012, _255014, _255016, _255018] : [-(leq(_255016, _255012)), leq(_255018, _255014), _255018 = _255016, _255014 = _255012], (754 ^ _249212) ^ [_277242] : [ssList(_277242), 757 ^ _249212 : [(758 ^ _249212) ^ [] : [duplicatefreeP(_277242), 761 ^ _249212 : [(762 ^ _249212) ^ [_277540] : [ssItem(_277540), 765 ^ _249212 : [(766 ^ _249212) ^ [_277726] : [ssItem(_277726), 769 ^ _249212 : [(770 ^ _249212) ^ [_277908] : [ssList(_277908), 773 ^ _249212 : [(774 ^ _249212) ^ [_278086] : [ssList(_278086), 777 ^ _249212 : [(778 ^ _249212) ^ [_278260] : [ssList(_278260), app(app(_277908, cons(_277540, _278086)), cons(_277726, _278260)) = _277242, _277540 = _277726]]]]]]]]]]], (788 ^ _249212) ^ [] : [790 ^ _249212 : [(797 ^ _249212) ^ [] : [-(ssList(795 ^ [_277242]))], (805 ^ _249212) ^ [] : [-(app(app(795 ^ [_277242], cons(789 ^ [_277242], 798 ^ [_277242])), cons(792 ^ [_277242], 801 ^ [_277242])) = _277242)], (807 ^ _249212) ^ [] : [-(789 ^ [_277242] = 792 ^ [_277242])], (800 ^ _249212) ^ [] : [-(ssList(798 ^ [_277242]))], (791 ^ _249212) ^ [] : [-(ssItem(789 ^ [_277242]))], (794 ^ _249212) ^ [] : [-(ssItem(792 ^ [_277242]))], (803 ^ _249212) ^ [] : [-(ssList(801 ^ [_277242]))]], -(duplicatefreeP(_277242))]]], (963 ^ _249212) ^ [_285185] : [ssList(_285185), 966 ^ _249212 : [(967 ^ _249212) ^ [_285320] : [ssItem(_285320), -(hd(cons(_285320, _285185)) = _285320)]]], (1089 ^ _249212) ^ [_289220] : [ssItem(_289220), 1092 ^ _249212 : [(1093 ^ _249212) ^ [_289358] : [ssItem(_289358), lt(_289220, _289358), lt(_289358, _289220)]]], (1739 ^ _249212) ^ [_309363] : [ssList(_309363), 1742 ^ _249212 : [(1743 ^ _249212) ^ [_309502] : [ssItem(_309502), -(cons(_309502, _309363) = app(cons(_309502, nil), _309363))]]], (1441 ^ _249212) ^ [_300224] : [ssList(_300224), 1444 ^ _249212 : [(1445 ^ _249212) ^ [_300366] : [ssList(_300366), -(_300224 = _300366), segmentP(_300224, _300366), segmentP(_300366, _300224)]]], (1259 ^ _249212) ^ [_294492] : [ssList(_294492), 1262 ^ _249212 : [(1263 ^ _249212) ^ [_294641] : [ssList(_294641), 1266 ^ _249212 : [(1267 ^ _249212) ^ [_294786] : [ssList(_294786), frontsegP(_294492, _294641), -(frontsegP(app(_294492, _294786), _294641))]]]]], (1875 ^ _249212) ^ [_313727] : [ssItem(_313727), 1878 ^ _249212 : [(1879 ^ _249212) ^ [_313879] : [ssItem(_313879), 1882 ^ _249212 : [(1883 ^ _249212) ^ [_314027] : [ssItem(_314027), -(lt(_313727, _314027)), leq(_313727, _313879), lt(_313879, _314027)]]]]], (1541 ^ _249212) ^ [_303339] : [ssItem(_303339), 1544 ^ _249212 : [(1545 ^ _249212) ^ [_303498] : [ssList(_303498), 1548 ^ _249212 : [(1563 ^ _249212) ^ [] : [-(totalorderedP(cons(_303339, _303498))), 1564 ^ _249212 : [(1567 ^ _249212) ^ [] : [-(nil = _303498), totalorderedP(_303498), leq(_303339, hd(_303498))], (1565 ^ _249212) ^ [] : [nil = _303498]]], (1549 ^ _249212) ^ [] : [totalorderedP(cons(_303339, _303498)), -(nil = _303498), 1556 ^ _249212 : [(1561 ^ _249212) ^ [] : [-(leq(_303339, hd(_303498)))], (1559 ^ _249212) ^ [] : [-(totalorderedP(_303498))], (1557 ^ _249212) ^ [] : [nil = _303498]]]]]]], (1721 ^ _249212) ^ [_308744] : [ssList(_308744), 1724 ^ _249212 : [(1725 ^ _249212) ^ [_308896] : [ssList(_308896), 1728 ^ _249212 : [(1729 ^ _249212) ^ [_309044] : [ssList(_309044), app(_308896, _309044) = app(_308896, _308744), -(_309044 = _308744)]]]]], (340 ^ _249212) ^ [_260206] : [ssList(_260206), 343 ^ _249212 : [(353 ^ _249212) ^ [] : [-(singletonP(_260206)), 354 ^ _249212 : [(355 ^ _249212) ^ [_260655] : [ssItem(_260655), cons(_260655, nil) = _260206]]], (344 ^ _249212) ^ [] : [singletonP(_260206), 348 ^ _249212 : [(351 ^ _249212) ^ [] : [-(cons(347 ^ [_260206], nil) = _260206)], (349 ^ _249212) ^ [] : [-(ssItem(347 ^ [_260206]))]]]]], (1041 ^ _249212) ^ [_287745] : [ssItem(_287745), 1044 ^ _249212 : [(1045 ^ _249212) ^ [_287897] : [ssItem(_287897), 1048 ^ _249212 : [(1049 ^ _249212) ^ [_288045] : [ssItem(_288045), -(leq(_287745, _288045)), leq(_287745, _287897), leq(_287897, _288045)]]]]], (246 ^ _249212) ^ [_256996, _256998, _257000, _257002] : [-(cons(_257002, _256998) = cons(_257000, _256996)), _257002 = _257000, _256998 = _256996], (1533 ^ _249212) ^ [_303094] : [ssItem(_303094), -(totalorderedP(cons(_303094, nil)))], (927 ^ _249212) ^ [_284000] : [ssList(_284000), -(nil = _284000), 935 ^ _249212 : [(941 ^ _249212) ^ [] : [-(cons(937 ^ [_284000], 934 ^ [_284000]) = _284000)], (939 ^ _249212) ^ [] : [-(ssItem(937 ^ [_284000]))], (936 ^ _249212) ^ [] : [-(ssList(934 ^ [_284000]))]]], (1493 ^ _249212) ^ [_301931] : [ssList(_301931), 1496 ^ _249212 : [(1503 ^ _249212) ^ [] : [nil = _301931, -(segmentP(nil, _301931))], (1497 ^ _249212) ^ [] : [segmentP(nil, _301931), -(nil = _301931)]]], (363 ^ _249212) ^ [_260911] : [ssList(_260911), 366 ^ _249212 : [(367 ^ _249212) ^ [_261060] : [ssList(_261060), 370 ^ _249212 : [(380 ^ _249212) ^ [] : [-(frontsegP(_260911, _261060)), 381 ^ _249212 : [(382 ^ _249212) ^ [_261535] : [ssList(_261535), app(_261060, _261535) = _260911]]], (371 ^ _249212) ^ [] : [frontsegP(_260911, _261060), 375 ^ _249212 : [(378 ^ _249212) ^ [] : [-(app(_261060, 374 ^ [_260911, _261060]) = _260911)], (376 ^ _249212) ^ [] : [-(ssList(374 ^ [_260911, _261060]))]]]]]]], (306 ^ _249212) ^ [_258957] : [ssList(_258957), 309 ^ _249212 : [(310 ^ _249212) ^ [_259119] : [ssItem(_259119), 313 ^ _249212 : [(326 ^ _249212) ^ [] : [-(memberP(_258957, _259119)), 327 ^ _249212 : [(328 ^ _249212) ^ [_259767] : [ssList(_259767), 331 ^ _249212 : [(332 ^ _249212) ^ [_259915] : [ssList(_259915), app(_259767, cons(_259119, _259915)) = _258957]]]]], (314 ^ _249212) ^ [] : [memberP(_258957, _259119), 318 ^ _249212 : [(324 ^ _249212) ^ [] : [-(app(317 ^ [_258957, _259119], cons(_259119, 320 ^ [_258957, _259119])) = _258957)], (322 ^ _249212) ^ [] : [-(ssList(320 ^ [_258957, _259119]))], (319 ^ _249212) ^ [] : [-(ssList(317 ^ [_258957, _259119]))]]]]]]], (1693 ^ _249212) ^ [_307835] : [ssList(_307835), -(nil = _307835), -(cons(hd(_307835), tl(_307835)) = _307835)], (811 ^ _249212) ^ [_279752] : [ssList(_279752), 814 ^ _249212 : [(815 ^ _249212) ^ [] : [equalelemsP(_279752), 818 ^ _249212 : [(819 ^ _249212) ^ [_280035] : [ssItem(_280035), 822 ^ _249212 : [(823 ^ _249212) ^ [_280206] : [ssItem(_280206), 826 ^ _249212 : [(827 ^ _249212) ^ [_280373] : [ssList(_280373), 830 ^ _249212 : [(831 ^ _249212) ^ [_280536] : [ssList(_280536), app(_280373, cons(_280035, cons(_280206, _280536))) = _279752, -(_280035 = _280206)]]]]]]]]], (841 ^ _249212) ^ [] : [843 ^ _249212 : [(847 ^ _249212) ^ [] : [-(ssItem(845 ^ [_279752]))], (844 ^ _249212) ^ [] : [-(ssItem(842 ^ [_279752]))], (857 ^ _249212) ^ [] : [842 ^ [_279752] = 845 ^ [_279752]], (853 ^ _249212) ^ [] : [-(ssList(851 ^ [_279752]))], (855 ^ _249212) ^ [] : [-(app(848 ^ [_279752], cons(842 ^ [_279752], cons(845 ^ [_279752], 851 ^ [_279752]))) = _279752)], (850 ^ _249212) ^ [] : [-(ssList(848 ^ [_279752]))]], -(equalelemsP(_279752))]]], (1125 ^ _249212) ^ [_290349] : [ssItem(_290349), 1128 ^ _249212 : [(1129 ^ _249212) ^ [_290485] : [ssItem(_290485), 1132 ^ _249212 : [(1139 ^ _249212) ^ [] : [lt(_290485, _290349), -(gt(_290349, _290485))], (1133 ^ _249212) ^ [] : [gt(_290349, _290485), -(lt(_290485, _290349))]]]]], (973 ^ _249212) ^ [_285531] : [ssList(_285531), -(nil = _285531), -(ssList(tl(_285531)))], (1823 ^ _249212) ^ [_312129] : [ssItem(_312129), 1826 ^ _249212 : [(1827 ^ _249212) ^ [_312271] : [ssItem(_312271), -(_312129 = _312271), geq(_312129, _312271), geq(_312271, _312129)]]], (953 ^ _249212) ^ [_284907] : [ssList(_284907), -(nil = _284907), -(ssItem(hd(_284907)))], (1667 ^ _249212) ^ [_307090] : [ssList(_307090), 1670 ^ _249212 : [(1671 ^ _249212) ^ [_307256] : [ssList(_307256), -(_307256 = _307090), -(nil = _307256), -(nil = _307090), hd(_307256) = hd(_307090), tl(_307256) = tl(_307090)]]], (1841 ^ _249212) ^ [_312650] : [ssItem(_312650), 1844 ^ _249212 : [(1845 ^ _249212) ^ [_312802] : [ssItem(_312802), 1848 ^ _249212 : [(1849 ^ _249212) ^ [_312950] : [ssItem(_312950), -(geq(_312650, _312950)), geq(_312650, _312802), geq(_312802, _312950)]]]]], (1897 ^ _249212) ^ [_314427] : [ssItem(_314427), 1900 ^ _249212 : [(1901 ^ _249212) ^ [_314569] : [ssItem(_314569), leq(_314427, _314569), -(_314427 = _314569), -(lt(_314427, _314569))]]], (1639 ^ _249212) ^ [] : [-(equalelemsP(nil))], (1863 ^ _249212) ^ [_313350] : [ssItem(_313350), -(geq(_313350, _313350))], (1625 ^ _249212) ^ [_305772] : [ssItem(_305772), -(duplicatefreeP(cons(_305772, nil)))], (577 ^ _249212) ^ [_269502] : [ssList(_269502), 580 ^ _249212 : [(581 ^ _249212) ^ [] : [strictorderP(_269502), 584 ^ _249212 : [(585 ^ _249212) ^ [_269804] : [ssItem(_269804), 588 ^ _249212 : [(589 ^ _249212) ^ [_269994] : [ssItem(_269994), 592 ^ _249212 : [(593 ^ _249212) ^ [_270180] : [ssList(_270180), 596 ^ _249212 : [(597 ^ _249212) ^ [_270362] : [ssList(_270362), 600 ^ _249212 : [(601 ^ _249212) ^ [_270540] : [ssList(_270540), app(app(_270180, cons(_269804, _270362)), cons(_269994, _270540)) = _269502, -(lt(_269804, _269994)), -(lt(_269994, _269804))]]]]]]]]]]], (615 ^ _249212) ^ [] : [617 ^ _249212 : [(624 ^ _249212) ^ [] : [-(ssList(622 ^ [_269502]))], (632 ^ _249212) ^ [] : [-(app(app(622 ^ [_269502], cons(616 ^ [_269502], 625 ^ [_269502])), cons(619 ^ [_269502], 628 ^ [_269502])) = _269502)], (618 ^ _249212) ^ [] : [-(ssItem(616 ^ [_269502]))], (634 ^ _249212) ^ [] : [lt(616 ^ [_269502], 619 ^ [_269502])], (627 ^ _249212) ^ [] : [-(ssList(625 ^ [_269502]))], (630 ^ _249212) ^ [] : [-(ssList(628 ^ [_269502]))], (636 ^ _249212) ^ [] : [lt(619 ^ [_269502], 616 ^ [_269502])], (621 ^ _249212) ^ [] : [-(ssItem(619 ^ [_269502]))]], -(strictorderP(_269502))]]], (44 ^ _249212) ^ [_250727, _250729, _250731, _250733] : [-(frontsegP(_250731, _250727)), frontsegP(_250733, _250729), _250733 = _250731, _250729 = _250727], (1795 ^ _249212) ^ [_311216] : [ssList(_311216), 1798 ^ _249212 : [(1799 ^ _249212) ^ [_311361] : [ssList(_311361), -(nil = _311216), -(hd(app(_311216, _311361)) = hd(_311216))]]], (20 ^ _249212) ^ [_249988, _249990, _249992, _249994] : [-(neq(_249992, _249988)), neq(_249994, _249990), _249994 = _249992, _249990 = _249988], (1523 ^ _249212) ^ [] : [-(totalorderP(nil))], (1789 ^ _249212) ^ [_311022] : [ssList(_311022), -(app(_311022, nil) = _311022)], (697 ^ _249212) ^ [_274754] : [ssList(_274754), 700 ^ _249212 : [(701 ^ _249212) ^ [] : [strictorderedP(_274754), 704 ^ _249212 : [(705 ^ _249212) ^ [_275050] : [ssItem(_275050), 708 ^ _249212 : [(709 ^ _249212) ^ [_275234] : [ssItem(_275234), 712 ^ _249212 : [(713 ^ _249212) ^ [_275414] : [ssList(_275414), 716 ^ _249212 : [(717 ^ _249212) ^ [_275590] : [ssList(_275590), 720 ^ _249212 : [(721 ^ _249212) ^ [_275762] : [ssList(_275762), app(app(_275414, cons(_275050, _275590)), cons(_275234, _275762)) = _274754, -(lt(_275050, _275234))]]]]]]]]]]], (731 ^ _249212) ^ [] : [733 ^ _249212 : [(740 ^ _249212) ^ [] : [-(ssList(738 ^ [_274754]))], (748 ^ _249212) ^ [] : [-(app(app(738 ^ [_274754], cons(732 ^ [_274754], 741 ^ [_274754])), cons(735 ^ [_274754], 744 ^ [_274754])) = _274754)], (750 ^ _249212) ^ [] : [lt(732 ^ [_274754], 735 ^ [_274754])], (743 ^ _249212) ^ [] : [-(ssList(741 ^ [_274754]))], (734 ^ _249212) ^ [] : [-(ssItem(732 ^ [_274754]))], (737 ^ _249212) ^ [] : [-(ssItem(735 ^ [_274754]))], (746 ^ _249212) ^ [] : [-(ssList(744 ^ [_274754]))]], -(strictorderedP(_274754))]]], (198 ^ _249212) ^ [_255456, _255458, _255460, _255462] : [-(gt(_255460, _255456)), gt(_255462, _255458), _255462 = _255460, _255458 = _255456], (1373 ^ _249212) ^ [_298113] : [ssList(_298113), -(rearsegP(_298113, _298113))], (116 ^ _249212) ^ [_252916, _252918] : [-(totalorderedP(_252916)), _252918 = _252916, totalorderedP(_252918)], (10 ^ _249212) ^ [_249647, _249649, _249651] : [-(_249651 = _249647), _249651 = _249649, _249649 = _249647], (1941 ^ _249212) ^ [_315704] : [ssItem(_315704), 1944 ^ _249212 : [(1945 ^ _249212) ^ [_315842] : [ssItem(_315842), gt(_315704, _315842), gt(_315842, _315704)]]], (1587 ^ _249212) ^ [_304678] : [ssItem(_304678), 1590 ^ _249212 : [(1591 ^ _249212) ^ [_304837] : [ssList(_304837), 1594 ^ _249212 : [(1609 ^ _249212) ^ [] : [-(strictorderedP(cons(_304678, _304837))), 1610 ^ _249212 : [(1613 ^ _249212) ^ [] : [-(nil = _304837), strictorderedP(_304837), lt(_304678, hd(_304837))], (1611 ^ _249212) ^ [] : [nil = _304837]]], (1595 ^ _249212) ^ [] : [strictorderedP(cons(_304678, _304837)), -(nil = _304837), 1602 ^ _249212 : [(1607 ^ _249212) ^ [] : [-(lt(_304678, hd(_304837)))], (1605 ^ _249212) ^ [] : [-(strictorderedP(_304837))], (1603 ^ _249212) ^ [] : [nil = _304837]]]]]]], (299 ^ _249212) ^ [] : [-(ssItem(297 ^ []))], (451 ^ _249212) ^ [_263952] : [ssList(_263952), 454 ^ _249212 : [(455 ^ _249212) ^ [] : [cyclefreeP(_263952), 458 ^ _249212 : [(459 ^ _249212) ^ [_264256] : [ssItem(_264256), 462 ^ _249212 : [(463 ^ _249212) ^ [_264448] : [ssItem(_264448), 466 ^ _249212 : [(467 ^ _249212) ^ [_264636] : [ssList(_264636), 470 ^ _249212 : [(471 ^ _249212) ^ [_264820] : [ssList(_264820), 474 ^ _249212 : [(475 ^ _249212) ^ [_265000] : [ssList(_265000), app(app(_264636, cons(_264256, _264820)), cons(_264448, _265000)) = _263952, leq(_264256, _264448), leq(_264448, _264256)]]]]]]]]]]], (489 ^ _249212) ^ [] : [491 ^ _249212 : [(498 ^ _249212) ^ [] : [-(ssList(496 ^ [_263952]))], (506 ^ _249212) ^ [] : [-(app(app(496 ^ [_263952], cons(490 ^ [_263952], 499 ^ [_263952])), cons(493 ^ [_263952], 502 ^ [_263952])) = _263952)], (492 ^ _249212) ^ [] : [-(ssItem(490 ^ [_263952]))], (508 ^ _249212) ^ [] : [-(leq(490 ^ [_263952], 493 ^ [_263952]))], (501 ^ _249212) ^ [] : [-(ssList(499 ^ [_263952]))], (504 ^ _249212) ^ [] : [-(ssList(502 ^ [_263952]))], (510 ^ _249212) ^ [] : [-(leq(493 ^ [_263952], 490 ^ [_263952]))], (495 ^ _249212) ^ [] : [-(ssItem(493 ^ [_263952]))]], -(cyclefreeP(_263952))]]], (1515 ^ _249212) ^ [] : [-(cyclefreeP(nil))], (1333 ^ _249212) ^ [_296892] : [ssList(_296892), 1336 ^ _249212 : [(1337 ^ _249212) ^ [_297044] : [ssList(_297044), 1340 ^ _249212 : [(1341 ^ _249212) ^ [_297192] : [ssList(_297192), -(rearsegP(_296892, _297192)), rearsegP(_296892, _297044), rearsegP(_297044, _297192)]]]]], (302 ^ _249212) ^ [] : [-(ssItem(300 ^ []))], (170 ^ _249212) ^ [_254568, _254570, _254572, _254574] : [-(lt(_254572, _254568)), lt(_254574, _254570), _254574 = _254572, _254570 = _254568], (1103 ^ _249212) ^ [_289649] : [ssItem(_289649), 1106 ^ _249212 : [(1107 ^ _249212) ^ [_289801] : [ssItem(_289801), 1110 ^ _249212 : [(1111 ^ _249212) ^ [_289949] : [ssItem(_289949), -(lt(_289649, _289949)), lt(_289649, _289801), lt(_289801, _289949)]]]]], (1955 ^ _249212) ^ [_316113] : [ssItem(_316113), 1958 ^ _249212 : [(1959 ^ _249212) ^ [_316265] : [ssItem(_316265), 1962 ^ _249212 : [(1963 ^ _249212) ^ [_316413] : [ssItem(_316413), -(gt(_316113, _316413)), gt(_316113, _316265), gt(_316265, _316413)]]]]], (893 ^ _249212) ^ [_282750] : [ssList(_282750), 896 ^ _249212 : [(897 ^ _249212) ^ [_282885] : [ssItem(_282885), cons(_282885, _282750) = _282750]]], (1205 ^ _249212) ^ [_292842] : [ssItem(_292842), memberP(nil, _292842)], (640 ^ _249212) ^ [_272266] : [ssList(_272266), 643 ^ _249212 : [(644 ^ _249212) ^ [] : [totalorderedP(_272266), 647 ^ _249212 : [(648 ^ _249212) ^ [_272562] : [ssItem(_272562), 651 ^ _249212 : [(652 ^ _249212) ^ [_272746] : [ssItem(_272746), 655 ^ _249212 : [(656 ^ _249212) ^ [_272926] : [ssList(_272926), 659 ^ _249212 : [(660 ^ _249212) ^ [_273102] : [ssList(_273102), 663 ^ _249212 : [(664 ^ _249212) ^ [_273274] : [ssList(_273274), app(app(_272926, cons(_272562, _273102)), cons(_272746, _273274)) = _272266, -(leq(_272562, _272746))]]]]]]]]]]], (674 ^ _249212) ^ [] : [676 ^ _249212 : [(683 ^ _249212) ^ [] : [-(ssList(681 ^ [_272266]))], (691 ^ _249212) ^ [] : [-(app(app(681 ^ [_272266], cons(675 ^ [_272266], 684 ^ [_272266])), cons(678 ^ [_272266], 687 ^ [_272266])) = _272266)], (693 ^ _249212) ^ [] : [leq(675 ^ [_272266], 678 ^ [_272266])], (686 ^ _249212) ^ [] : [-(ssList(684 ^ [_272266]))], (677 ^ _249212) ^ [] : [-(ssItem(675 ^ [_272266]))], (680 ^ _249212) ^ [] : [-(ssItem(678 ^ [_272266]))], (689 ^ _249212) ^ [] : [-(ssList(687 ^ [_272266]))]], -(totalorderedP(_272266))]]], (1654 ^ _249212) ^ [_306676] : [ssList(_306676), -(nil = _306676), 1662 ^ _249212 : [(1665 ^ _249212) ^ [] : [-(tl(_306676) = 1661 ^ [_306676])], (1663 ^ _249212) ^ [] : [-(ssList(1661 ^ [_306676]))]]], (4 ^ _249212) ^ [_249443, _249445] : [_249445 = _249443, -(_249443 = _249445)], (417 ^ _249212) ^ [_262703] : [ssList(_262703), 420 ^ _249212 : [(421 ^ _249212) ^ [_262865] : [ssList(_262865), 424 ^ _249212 : [(437 ^ _249212) ^ [] : [-(segmentP(_262703, _262865)), 438 ^ _249212 : [(439 ^ _249212) ^ [_263513] : [ssList(_263513), 442 ^ _249212 : [(443 ^ _249212) ^ [_263661] : [ssList(_263661), app(app(_263513, _262865), _263661) = _262703]]]]], (425 ^ _249212) ^ [] : [segmentP(_262703, _262865), 429 ^ _249212 : [(435 ^ _249212) ^ [] : [-(app(app(428 ^ [_262703, _262865], _262865), 431 ^ [_262703, _262865]) = _262703)], (433 ^ _249212) ^ [] : [-(ssList(431 ^ [_262703, _262865]))], (430 ^ _249212) ^ [] : [-(ssList(428 ^ [_262703, _262865]))]]]]]]], (1069 ^ _249212) ^ [_288633] : [ssItem(_288633), 1072 ^ _249212 : [(1073 ^ _249212) ^ [_288769] : [ssItem(_288769), 1076 ^ _249212 : [(1083 ^ _249212) ^ [] : [leq(_288769, _288633), -(geq(_288633, _288769))], (1077 ^ _249212) ^ [] : [geq(_288633, _288769), -(leq(_288769, _288633))]]]]], (212 ^ _249212) ^ [_255872, _255874] : [-(ssList(_255872)), _255874 = _255872, ssList(_255874)], (1175 ^ _249212) ^ [_291889] : [ssItem(_291889), 1178 ^ _249212 : [(1179 ^ _249212) ^ [_292044] : [ssItem(_292044), 1182 ^ _249212 : [(1183 ^ _249212) ^ [_292195] : [ssList(_292195), 1186 ^ _249212 : [(1187 ^ _249212) ^ [] : [memberP(cons(_292044, _292195), _291889), -(_291889 = _292044), -(memberP(_292195, _291889))], (1197 ^ _249212) ^ [] : [1198 ^ _249212 : [(1201 ^ _249212) ^ [] : [memberP(_292195, _291889)], (1199 ^ _249212) ^ [] : [_291889 = _292044]], -(memberP(cons(_292044, _292195), _291889))]]]]]]], (272 ^ _249212) ^ [_257884, _257886] : [_257886 = _257884, -(tl(_257886) = tl(_257884))], (1531 ^ _249212) ^ [] : [-(strictorderP(nil))], (1763 ^ _249212) ^ [_310259] : [ssList(_310259), 1766 ^ _249212 : [(1767 ^ _249212) ^ [_310404] : [ssList(_310404), 1770 ^ _249212 : [(1779 ^ _249212) ^ [] : [-(nil = app(_310259, _310404)), nil = _310404, nil = _310259], (1771 ^ _249212) ^ [] : [nil = app(_310259, _310404), 1774 ^ _249212 : [(1777 ^ _249212) ^ [] : [-(nil = _310259)], (1775 ^ _249212) ^ [] : [-(nil = _310404)]]]]]]], (1003 ^ _249212) ^ [_286492] : [ssList(_286492), 1006 ^ _249212 : [(1007 ^ _249212) ^ [_286644] : [ssList(_286644), 1010 ^ _249212 : [(1011 ^ _249212) ^ [_286792] : [ssItem(_286792), -(cons(_286792, app(_286644, _286492)) = app(cons(_286792, _286644), _286492))]]]]], (1509 ^ _249212) ^ [_302359] : [ssItem(_302359), -(cyclefreeP(cons(_302359, nil)))], (1539 ^ _249212) ^ [] : [-(totalorderedP(nil))], (1317 ^ _249212) ^ [_296464] : [ssList(_296464), 1320 ^ _249212 : [(1327 ^ _249212) ^ [] : [nil = _296464, -(frontsegP(nil, _296464))], (1321 ^ _249212) ^ [] : [frontsegP(nil, _296464), -(nil = _296464)]]], (1397 ^ _249212) ^ [_298908] : [ssList(_298908), -(rearsegP(_298908, nil))], (1585 ^ _249212) ^ [] : [-(strictorderedP(nil))], (96 ^ _249212) ^ [_252326, _252328] : [-(totalorderP(_252326)), _252328 = _252326, totalorderP(_252328)], (146 ^ _249212) ^ [_253801, _253803] : [-(equalelemsP(_253801)), _253803 = _253801, equalelemsP(_253803)], (881 ^ _249212) ^ [_282360] : [ssList(_282360), 884 ^ _249212 : [(885 ^ _249212) ^ [_282492] : [ssItem(_282492), -(ssList(cons(_282492, _282360)))]]], (1235 ^ _249212) ^ [_293783] : [ssList(_293783), 1238 ^ _249212 : [(1239 ^ _249212) ^ [_293925] : [ssList(_293925), -(_293783 = _293925), frontsegP(_293783, _293925), frontsegP(_293925, _293783)]]], (1915 ^ _249212) ^ [_314949] : [ssItem(_314949), 1918 ^ _249212 : [(1919 ^ _249212) ^ [_315093] : [ssItem(_315093), 1922 ^ _249212 : [(1931 ^ _249212) ^ [] : [-(lt(_314949, _315093)), -(_314949 = _315093), leq(_314949, _315093)], (1923 ^ _249212) ^ [] : [lt(_314949, _315093), 1926 ^ _249212 : [(1929 ^ _249212) ^ [] : [-(leq(_314949, _315093))], (1927 ^ _249212) ^ [] : [_314949 = _315093]]]]]]], (903 ^ _249212) ^ [_283093] : [ssList(_283093), 906 ^ _249212 : [(907 ^ _249212) ^ [_283261] : [ssList(_283261), 910 ^ _249212 : [(911 ^ _249212) ^ [_283425] : [ssItem(_283425), 914 ^ _249212 : [(915 ^ _249212) ^ [_283585] : [ssItem(_283585), cons(_283425, _283093) = cons(_283585, _283261), 922 ^ _249212 : [(925 ^ _249212) ^ [] : [-(_283261 = _283093)], (923 ^ _249212) ^ [] : [-(_283425 = _283585)]]]]]]]]], (304 ^ _249212) ^ [] : [297 ^ [] = 300 ^ []], (1631 ^ _249212) ^ [] : [-(duplicatefreeP(nil))], (1525 ^ _249212) ^ [_302849] : [ssItem(_302849), -(strictorderP(cons(_302849, nil)))], (156 ^ _249212) ^ [_254124, _254126, _254128, _254130] : [-(geq(_254128, _254124)), geq(_254130, _254126), _254130 = _254128, _254126 = _254124], (891 ^ _249212) ^ [] : [-(ssList(nil))], (983 ^ _249212) ^ [_285809] : [ssList(_285809), 986 ^ _249212 : [(987 ^ _249212) ^ [_285944] : [ssItem(_285944), -(tl(cons(_285944, _285809)) = _285809)]]], (86 ^ _249212) ^ [_252031, _252033] : [-(cyclefreeP(_252031)), _252033 = _252031, cyclefreeP(_252033)], (1277 ^ _249212) ^ [_295099] : [ssItem(_295099), 1280 ^ _249212 : [(1281 ^ _249212) ^ [_295267] : [ssItem(_295267), 1284 ^ _249212 : [(1285 ^ _249212) ^ [_295431] : [ssList(_295431), 1288 ^ _249212 : [(1289 ^ _249212) ^ [_295591] : [ssList(_295591), 1292 ^ _249212 : [(1301 ^ _249212) ^ [] : [-(frontsegP(cons(_295099, _295431), cons(_295267, _295591))), _295099 = _295267, frontsegP(_295431, _295591)], (1293 ^ _249212) ^ [] : [frontsegP(cons(_295099, _295431), cons(_295267, _295591)), 1296 ^ _249212 : [(1299 ^ _249212) ^ [] : [-(frontsegP(_295431, _295591))], (1297 ^ _249212) ^ [] : [-(_295099 = _295267)]]]]]]]]]]], (1703 ^ _249212) ^ [_308125] : [ssList(_308125), 1706 ^ _249212 : [(1707 ^ _249212) ^ [_308277] : [ssList(_308277), 1710 ^ _249212 : [(1711 ^ _249212) ^ [_308425] : [ssList(_308425), app(_308425, _308277) = app(_308125, _308277), -(_308425 = _308125)]]]]], (514 ^ _249212) ^ [_266738] : [ssList(_266738), 517 ^ _249212 : [(518 ^ _249212) ^ [] : [totalorderP(_266738), 521 ^ _249212 : [(522 ^ _249212) ^ [_267040] : [ssItem(_267040), 525 ^ _249212 : [(526 ^ _249212) ^ [_267230] : [ssItem(_267230), 529 ^ _249212 : [(530 ^ _249212) ^ [_267416] : [ssList(_267416), 533 ^ _249212 : [(534 ^ _249212) ^ [_267598] : [ssList(_267598), 537 ^ _249212 : [(538 ^ _249212) ^ [_267776] : [ssList(_267776), app(app(_267416, cons(_267040, _267598)), cons(_267230, _267776)) = _266738, -(leq(_267040, _267230)), -(leq(_267230, _267040))]]]]]]]]]]], (552 ^ _249212) ^ [] : [554 ^ _249212 : [(561 ^ _249212) ^ [] : [-(ssList(559 ^ [_266738]))], (569 ^ _249212) ^ [] : [-(app(app(559 ^ [_266738], cons(553 ^ [_266738], 562 ^ [_266738])), cons(556 ^ [_266738], 565 ^ [_266738])) = _266738)], (555 ^ _249212) ^ [] : [-(ssItem(553 ^ [_266738]))], (571 ^ _249212) ^ [] : [leq(553 ^ [_266738], 556 ^ [_266738])], (564 ^ _249212) ^ [] : [-(ssList(562 ^ [_266738]))], (567 ^ _249212) ^ [] : [-(ssList(565 ^ [_266738]))], (573 ^ _249212) ^ [] : [leq(556 ^ [_266738], 553 ^ [_266738])], (558 ^ _249212) ^ [] : [-(ssItem(556 ^ [_266738]))]], -(totalorderP(_266738))]]], (1419 ^ _249212) ^ [_299524] : [ssList(_299524), 1422 ^ _249212 : [(1423 ^ _249212) ^ [_299676] : [ssList(_299676), 1426 ^ _249212 : [(1427 ^ _249212) ^ [_299824] : [ssList(_299824), -(segmentP(_299524, _299824)), segmentP(_299524, _299676), segmentP(_299676, _299824)]]]]], (1641 ^ _249212) ^ [_306262] : [ssList(_306262), -(nil = _306262), 1649 ^ _249212 : [(1652 ^ _249212) ^ [] : [-(hd(_306262) = 1648 ^ [_306262])], (1650 ^ _249212) ^ [] : [-(ssItem(1648 ^ [_306262]))]]], (222 ^ _249212) ^ [_256167, _256169] : [-(ssItem(_256167)), _256169 = _256167, ssItem(_256169)], (126 ^ _249212) ^ [_253211, _253213] : [-(strictorderedP(_253211)), _253213 = _253211, strictorderedP(_253213)]], input).
% 44.00/42.72  ncf('1',plain,[ssItem(2002 ^ []), -(memberP(1982 ^ [], 2002 ^ [])), memberP(1985 ^ [], 2002 ^ [])],start(1993 ^ 0,bind([[_318261], [2002 ^ []]]))).
% 44.00/42.72  ncf('1.1',plain,[-(ssItem(2002 ^ []))],extension(2004 ^ 1)).
% 44.00/42.72  ncf('1.2',plain,[memberP(1982 ^ [], 2002 ^ []), -(memberP(1976 ^ [], 2002 ^ [])), 1982 ^ [] = 1976 ^ [], 2002 ^ [] = 2002 ^ []],extension(232 ^ 1,bind([[_256470, _256472, _256474, _256476], [2002 ^ [], 2002 ^ [], 1976 ^ [], 1982 ^ []]]))).
% 44.00/42.72  ncf('1.2.1',plain,[memberP(1976 ^ [], 2002 ^ [])],extension(2008 ^ 2)).
% 44.00/42.72  ncf('1.2.2',plain,[-(1982 ^ [] = 1976 ^ []), 1976 ^ [] = 1982 ^ []],extension(4 ^ 2,bind([[_249443, _249445], [1982 ^ [], 1976 ^ []]]))).
% 44.00/42.72  ncf('1.2.2.1',plain,[-(1976 ^ [] = 1982 ^ [])],extension(1991 ^ 3)).
% 44.00/42.72  ncf('1.2.3',plain,[-(2002 ^ [] = 2002 ^ [])],extension(2 ^ 2,bind([[_249336], [2002 ^ []]]))).
% 44.00/42.72  ncf('1.3',plain,[-(memberP(1985 ^ [], 2002 ^ [])), memberP(1979 ^ [], 2002 ^ []), 1979 ^ [] = 1985 ^ [], 2002 ^ [] = 2002 ^ []],extension(232 ^ 1,bind([[_256470, _256472, _256474, _256476], [2002 ^ [], 2002 ^ [], 1985 ^ [], 1979 ^ []]]))).
% 44.00/42.72  ncf('1.3.1',plain,[-(memberP(1979 ^ [], 2002 ^ []))],extension(2006 ^ 2)).
% 44.00/42.72  ncf('1.3.2',plain,[-(1979 ^ [] = 1985 ^ [])],extension(1989 ^ 2)).
% 44.00/42.72  ncf('1.3.3',plain,[-(2002 ^ [] = 2002 ^ [])],extension(2 ^ 2,bind([[_249336], [2002 ^ []]]))).
% 44.00/42.72  %-----------------------------------------------------
% 44.00/42.72  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------