%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SWC262+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n023.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 12:13:02 EDT 2023

% Result   : Theorem 8.59s 8.61s
% Output   : Proof 8.59s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SWC262+1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.12  % Command  : nanocop.sh %s %d
% 0.13/0.33  % Computer : n023.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Fri May 19 01:12:13 EDT 2023
% 0.13/0.33  % CPUTime  : 
% 8.59/8.61  
% 8.59/8.61  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 8.59/8.61  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.59/8.61  %-----------------------------------------------------
% 8.59/8.61  ncf(matrix, plain, [(1978 ^ _229964) ^ [] : [-(ssList(1976 ^ []))], (1981 ^ _229964) ^ [] : [-(ssList(1979 ^ []))], (1984 ^ _229964) ^ [] : [-(ssList(1982 ^ []))], (1987 ^ _229964) ^ [] : [-(ssList(1985 ^ []))], (1989 ^ _229964) ^ [] : [-(1979 ^ [] = 1985 ^ [])], (1991 ^ _229964) ^ [] : [-(1976 ^ [] = 1982 ^ [])], (1993 ^ _229964) ^ [] : [-(totalorderedP(1982 ^ []))], (1995 ^ _229964) ^ [] : [totalorderedP(1976 ^ [])], (246 ^ _229964) ^ [_237768, _237770, _237772, _237774] : [-(cons(_237774, _237770) = cons(_237772, _237768)), _237774 = _237772, _237770 = _237768], (256 ^ _229964) ^ [_238099, _238101] : [_238101 = _238099, -(hd(_238101) = hd(_238099))], (272 ^ _229964) ^ [_238656, _238658] : [_238658 = _238656, -(tl(_238658) = tl(_238656))], (262 ^ _229964) ^ [_238345, _238347, _238349, _238351] : [-(app(_238351, _238347) = app(_238349, _238345)), _238351 = _238349, _238347 = _238345], (2 ^ _229964) ^ [_230108] : [-(_230108 = _230108)], (4 ^ _229964) ^ [_230215, _230217] : [_230217 = _230215, -(_230215 = _230217)], (10 ^ _229964) ^ [_230419, _230421, _230423] : [-(_230423 = _230419), _230423 = _230421, _230421 = _230419], (20 ^ _229964) ^ [_230760, _230762, _230764, _230766] : [-(neq(_230764, _230760)), neq(_230766, _230762), _230766 = _230764, _230762 = _230760], (34 ^ _229964) ^ [_231204, _231206, _231208, _231210] : [-(memberP(_231208, _231204)), memberP(_231210, _231206), _231210 = _231208, _231206 = _231204], (48 ^ _229964) ^ [_231620, _231622] : [-(singletonP(_231620)), _231622 = _231620, singletonP(_231622)], (58 ^ _229964) ^ [_231943, _231945, _231947, _231949] : [-(frontsegP(_231947, _231943)), frontsegP(_231949, _231945), _231949 = _231947, _231945 = _231943], (72 ^ _229964) ^ [_232387, _232389, _232391, _232393] : [-(rearsegP(_232391, _232387)), rearsegP(_232393, _232389), _232393 = _232391, _232389 = _232387], (86 ^ _229964) ^ [_232831, _232833, _232835, _232837] : [-(segmentP(_232835, _232831)), segmentP(_232837, _232833), _232837 = _232835, _232833 = _232831], (100 ^ _229964) ^ [_233247, _233249] : [-(cyclefreeP(_233247)), _233249 = _233247, cyclefreeP(_233249)], (110 ^ _229964) ^ [_233542, _233544] : [-(totalorderP(_233542)), _233544 = _233542, totalorderP(_233544)], (120 ^ _229964) ^ [_233837, _233839] : [-(strictorderP(_233837)), _233839 = _233837, strictorderP(_233839)], (130 ^ _229964) ^ [_234132, _234134] : [-(strictorderedP(_234132)), _234134 = _234132, strictorderedP(_234134)], (140 ^ _229964) ^ [_234427, _234429] : [-(duplicatefreeP(_234427)), _234429 = _234427, duplicatefreeP(_234429)], (150 ^ _229964) ^ [_234722, _234724] : [-(equalelemsP(_234722)), _234724 = _234722, equalelemsP(_234724)], (160 ^ _229964) ^ [_235045, _235047, _235049, _235051] : [-(geq(_235049, _235045)), geq(_235051, _235047), _235051 = _235049, _235047 = _235045], (174 ^ _229964) ^ [_235489, _235491, _235493, _235495] : [-(lt(_235493, _235489)), lt(_235495, _235491), _235495 = _235493, _235491 = _235489], (188 ^ _229964) ^ [_235933, _235935, _235937, _235939] : [-(leq(_235937, _235933)), leq(_235939, _235935), _235939 = _235937, _235935 = _235933], (202 ^ _229964) ^ [_236349, _236351] : [-(ssItem(_236349)), _236351 = _236349, ssItem(_236351)], (212 ^ _229964) ^ [_236672, _236674, _236676, _236678] : [-(gt(_236676, _236672)), gt(_236678, _236674), _236678 = _236676, _236674 = _236672], (226 ^ _229964) ^ [_237088, _237090] : [-(ssList(_237088)), _237090 = _237088, ssList(_237090)], (236 ^ _229964) ^ [_237363, _237365] : [-(totalorderedP(_237363)), _237365 = _237363, totalorderedP(_237365)], (278 ^ _229964) ^ [_238878] : [ssItem(_238878), 281 ^ _229964 : [(282 ^ _229964) ^ [_239016] : [ssItem(_239016), 285 ^ _229964 : [(286 ^ _229964) ^ [] : [neq(_238878, _239016), _238878 = _239016], (292 ^ _229964) ^ [] : [-(_238878 = _239016), -(neq(_238878, _239016))]]]]], (299 ^ _229964) ^ [] : [-(ssItem(297 ^ []))], (302 ^ _229964) ^ [] : [-(ssItem(300 ^ []))], (304 ^ _229964) ^ [] : [297 ^ [] = 300 ^ []], (306 ^ _229964) ^ [_239729] : [ssList(_239729), 309 ^ _229964 : [(310 ^ _229964) ^ [_239891] : [ssItem(_239891), 313 ^ _229964 : [(314 ^ _229964) ^ [] : [memberP(_239729, _239891), 318 ^ _229964 : [(319 ^ _229964) ^ [] : [-(ssList(317 ^ [_239729, _239891]))], (322 ^ _229964) ^ [] : [-(ssList(320 ^ [_239729, _239891]))], (324 ^ _229964) ^ [] : [-(app(317 ^ [_239729, _239891], cons(_239891, 320 ^ [_239729, _239891])) = _239729)]]], (326 ^ _229964) ^ [] : [-(memberP(_239729, _239891)), 327 ^ _229964 : [(328 ^ _229964) ^ [_240539] : [ssList(_240539), 331 ^ _229964 : [(332 ^ _229964) ^ [_240687] : [ssList(_240687), app(_240539, cons(_239891, _240687)) = _239729]]]]]]]]], (340 ^ _229964) ^ [_240978] : [ssList(_240978), 343 ^ _229964 : [(344 ^ _229964) ^ [] : [singletonP(_240978), 348 ^ _229964 : [(349 ^ _229964) ^ [] : [-(ssItem(347 ^ [_240978]))], (351 ^ _229964) ^ [] : [-(cons(347 ^ [_240978], nil) = _240978)]]], (353 ^ _229964) ^ [] : [-(singletonP(_240978)), 354 ^ _229964 : [(355 ^ _229964) ^ [_241427] : [ssItem(_241427), cons(_241427, nil) = _240978]]]]], (363 ^ _229964) ^ [_241683] : [ssList(_241683), 366 ^ _229964 : [(367 ^ _229964) ^ [_241832] : [ssList(_241832), 370 ^ _229964 : [(371 ^ _229964) ^ [] : [frontsegP(_241683, _241832), 375 ^ _229964 : [(376 ^ _229964) ^ [] : [-(ssList(374 ^ [_241683, _241832]))], (378 ^ _229964) ^ [] : [-(app(_241832, 374 ^ [_241683, _241832]) = _241683)]]], (380 ^ _229964) ^ [] : [-(frontsegP(_241683, _241832)), 381 ^ _229964 : [(382 ^ _229964) ^ [_242307] : [ssList(_242307), app(_241832, _242307) = _241683]]]]]]], (390 ^ _229964) ^ [_242579] : [ssList(_242579), 393 ^ _229964 : [(394 ^ _229964) ^ [_242728] : [ssList(_242728), 397 ^ _229964 : [(398 ^ _229964) ^ [] : [rearsegP(_242579, _242728), 402 ^ _229964 : [(403 ^ _229964) ^ [] : [-(ssList(401 ^ [_242579, _242728]))], (405 ^ _229964) ^ [] : [-(app(401 ^ [_242579, _242728], _242728) = _242579)]]], (407 ^ _229964) ^ [] : [-(rearsegP(_242579, _242728)), 408 ^ _229964 : [(409 ^ _229964) ^ [_243203] : [ssList(_243203), app(_243203, _242728) = _242579]]]]]]], (417 ^ _229964) ^ [_243475] : [ssList(_243475), 420 ^ _229964 : [(421 ^ _229964) ^ [_243637] : [ssList(_243637), 424 ^ _229964 : [(425 ^ _229964) ^ [] : [segmentP(_243475, _243637), 429 ^ _229964 : [(430 ^ _229964) ^ [] : [-(ssList(428 ^ [_243475, _243637]))], (433 ^ _229964) ^ [] : [-(ssList(431 ^ [_243475, _243637]))], (435 ^ _229964) ^ [] : [-(app(app(428 ^ [_243475, _243637], _243637), 431 ^ [_243475, _243637]) = _243475)]]], (437 ^ _229964) ^ [] : [-(segmentP(_243475, _243637)), 438 ^ _229964 : [(439 ^ _229964) ^ [_244285] : [ssList(_244285), 442 ^ _229964 : [(443 ^ _229964) ^ [_244433] : [ssList(_244433), app(app(_244285, _243637), _244433) = _243475]]]]]]]]], (451 ^ _229964) ^ [_244724] : [ssList(_244724), 454 ^ _229964 : [(489 ^ _229964) ^ [] : [491 ^ _229964 : [(492 ^ _229964) ^ [] : [-(ssItem(490 ^ [_244724]))], (495 ^ _229964) ^ [] : [-(ssItem(493 ^ [_244724]))], (498 ^ _229964) ^ [] : [-(ssList(496 ^ [_244724]))], (501 ^ _229964) ^ [] : [-(ssList(499 ^ [_244724]))], (504 ^ _229964) ^ [] : [-(ssList(502 ^ [_244724]))], (506 ^ _229964) ^ [] : [-(app(app(496 ^ [_244724], cons(490 ^ [_244724], 499 ^ [_244724])), cons(493 ^ [_244724], 502 ^ [_244724])) = _244724)], (508 ^ _229964) ^ [] : [-(leq(490 ^ [_244724], 493 ^ [_244724]))], (510 ^ _229964) ^ [] : [-(leq(493 ^ [_244724], 490 ^ [_244724]))]], -(cyclefreeP(_244724))], (455 ^ _229964) ^ [] : [cyclefreeP(_244724), 458 ^ _229964 : [(459 ^ _229964) ^ [_245028] : [ssItem(_245028), 462 ^ _229964 : [(463 ^ _229964) ^ [_245220] : [ssItem(_245220), 466 ^ _229964 : [(467 ^ _229964) ^ [_245408] : [ssList(_245408), 470 ^ _229964 : [(471 ^ _229964) ^ [_245592] : [ssList(_245592), 474 ^ _229964 : [(475 ^ _229964) ^ [_245772] : [ssList(_245772), app(app(_245408, cons(_245028, _245592)), cons(_245220, _245772)) = _244724, leq(_245028, _245220), leq(_245220, _245028)]]]]]]]]]]]]], (514 ^ _229964) ^ [_247510] : [ssList(_247510), 517 ^ _229964 : [(552 ^ _229964) ^ [] : [554 ^ _229964 : [(555 ^ _229964) ^ [] : [-(ssItem(553 ^ [_247510]))], (558 ^ _229964) ^ [] : [-(ssItem(556 ^ [_247510]))], (561 ^ _229964) ^ [] : [-(ssList(559 ^ [_247510]))], (564 ^ _229964) ^ [] : [-(ssList(562 ^ [_247510]))], (567 ^ _229964) ^ [] : [-(ssList(565 ^ [_247510]))], (569 ^ _229964) ^ [] : [-(app(app(559 ^ [_247510], cons(553 ^ [_247510], 562 ^ [_247510])), cons(556 ^ [_247510], 565 ^ [_247510])) = _247510)], (571 ^ _229964) ^ [] : [leq(553 ^ [_247510], 556 ^ [_247510])], (573 ^ _229964) ^ [] : [leq(556 ^ [_247510], 553 ^ [_247510])]], -(totalorderP(_247510))], (518 ^ _229964) ^ [] : [totalorderP(_247510), 521 ^ _229964 : [(522 ^ _229964) ^ [_247812] : [ssItem(_247812), 525 ^ _229964 : [(526 ^ _229964) ^ [_248002] : [ssItem(_248002), 529 ^ _229964 : [(530 ^ _229964) ^ [_248188] : [ssList(_248188), 533 ^ _229964 : [(534 ^ _229964) ^ [_248370] : [ssList(_248370), 537 ^ _229964 : [(538 ^ _229964) ^ [_248548] : [ssList(_248548), app(app(_248188, cons(_247812, _248370)), cons(_248002, _248548)) = _247510, -(leq(_247812, _248002)), -(leq(_248002, _247812))]]]]]]]]]]]]], (577 ^ _229964) ^ [_250274] : [ssList(_250274), 580 ^ _229964 : [(615 ^ _229964) ^ [] : [617 ^ _229964 : [(618 ^ _229964) ^ [] : [-(ssItem(616 ^ [_250274]))], (621 ^ _229964) ^ [] : [-(ssItem(619 ^ [_250274]))], (624 ^ _229964) ^ [] : [-(ssList(622 ^ [_250274]))], (627 ^ _229964) ^ [] : [-(ssList(625 ^ [_250274]))], (630 ^ _229964) ^ [] : [-(ssList(628 ^ [_250274]))], (632 ^ _229964) ^ [] : [-(app(app(622 ^ [_250274], cons(616 ^ [_250274], 625 ^ [_250274])), cons(619 ^ [_250274], 628 ^ [_250274])) = _250274)], (634 ^ _229964) ^ [] : [lt(616 ^ [_250274], 619 ^ [_250274])], (636 ^ _229964) ^ [] : [lt(619 ^ [_250274], 616 ^ [_250274])]], -(strictorderP(_250274))], (581 ^ _229964) ^ [] : [strictorderP(_250274), 584 ^ _229964 : [(585 ^ _229964) ^ [_250576] : [ssItem(_250576), 588 ^ _229964 : [(589 ^ _229964) ^ [_250766] : [ssItem(_250766), 592 ^ _229964 : [(593 ^ _229964) ^ [_250952] : [ssList(_250952), 596 ^ _229964 : [(597 ^ _229964) ^ [_251134] : [ssList(_251134), 600 ^ _229964 : [(601 ^ _229964) ^ [_251312] : [ssList(_251312), app(app(_250952, cons(_250576, _251134)), cons(_250766, _251312)) = _250274, -(lt(_250576, _250766)), -(lt(_250766, _250576))]]]]]]]]]]]]], (640 ^ _229964) ^ [_253038] : [ssList(_253038), 643 ^ _229964 : [(674 ^ _229964) ^ [] : [676 ^ _229964 : [(677 ^ _229964) ^ [] : [-(ssItem(675 ^ [_253038]))], (680 ^ _229964) ^ [] : [-(ssItem(678 ^ [_253038]))], (683 ^ _229964) ^ [] : [-(ssList(681 ^ [_253038]))], (686 ^ _229964) ^ [] : [-(ssList(684 ^ [_253038]))], (689 ^ _229964) ^ [] : [-(ssList(687 ^ [_253038]))], (691 ^ _229964) ^ [] : [-(app(app(681 ^ [_253038], cons(675 ^ [_253038], 684 ^ [_253038])), cons(678 ^ [_253038], 687 ^ [_253038])) = _253038)], (693 ^ _229964) ^ [] : [leq(675 ^ [_253038], 678 ^ [_253038])]], -(totalorderedP(_253038))], (644 ^ _229964) ^ [] : [totalorderedP(_253038), 647 ^ _229964 : [(648 ^ _229964) ^ [_253334] : [ssItem(_253334), 651 ^ _229964 : [(652 ^ _229964) ^ [_253518] : [ssItem(_253518), 655 ^ _229964 : [(656 ^ _229964) ^ [_253698] : [ssList(_253698), 659 ^ _229964 : [(660 ^ _229964) ^ [_253874] : [ssList(_253874), 663 ^ _229964 : [(664 ^ _229964) ^ [_254046] : [ssList(_254046), app(app(_253698, cons(_253334, _253874)), cons(_253518, _254046)) = _253038, -(leq(_253334, _253518))]]]]]]]]]]]]], (697 ^ _229964) ^ [_255526] : [ssList(_255526), 700 ^ _229964 : [(731 ^ _229964) ^ [] : [733 ^ _229964 : [(734 ^ _229964) ^ [] : [-(ssItem(732 ^ [_255526]))], (737 ^ _229964) ^ [] : [-(ssItem(735 ^ [_255526]))], (740 ^ _229964) ^ [] : [-(ssList(738 ^ [_255526]))], (743 ^ _229964) ^ [] : [-(ssList(741 ^ [_255526]))], (746 ^ _229964) ^ [] : [-(ssList(744 ^ [_255526]))], (748 ^ _229964) ^ [] : [-(app(app(738 ^ [_255526], cons(732 ^ [_255526], 741 ^ [_255526])), cons(735 ^ [_255526], 744 ^ [_255526])) = _255526)], (750 ^ _229964) ^ [] : [lt(732 ^ [_255526], 735 ^ [_255526])]], -(strictorderedP(_255526))], (701 ^ _229964) ^ [] : [strictorderedP(_255526), 704 ^ _229964 : [(705 ^ _229964) ^ [_255822] : [ssItem(_255822), 708 ^ _229964 : [(709 ^ _229964) ^ [_256006] : [ssItem(_256006), 712 ^ _229964 : [(713 ^ _229964) ^ [_256186] : [ssList(_256186), 716 ^ _229964 : [(717 ^ _229964) ^ [_256362] : [ssList(_256362), 720 ^ _229964 : [(721 ^ _229964) ^ [_256534] : [ssList(_256534), app(app(_256186, cons(_255822, _256362)), cons(_256006, _256534)) = _255526, -(lt(_255822, _256006))]]]]]]]]]]]]], (754 ^ _229964) ^ [_258014] : [ssList(_258014), 757 ^ _229964 : [(788 ^ _229964) ^ [] : [790 ^ _229964 : [(791 ^ _229964) ^ [] : [-(ssItem(789 ^ [_258014]))], (794 ^ _229964) ^ [] : [-(ssItem(792 ^ [_258014]))], (797 ^ _229964) ^ [] : [-(ssList(795 ^ [_258014]))], (800 ^ _229964) ^ [] : [-(ssList(798 ^ [_258014]))], (803 ^ _229964) ^ [] : [-(ssList(801 ^ [_258014]))], (805 ^ _229964) ^ [] : [-(app(app(795 ^ [_258014], cons(789 ^ [_258014], 798 ^ [_258014])), cons(792 ^ [_258014], 801 ^ [_258014])) = _258014)], (807 ^ _229964) ^ [] : [-(789 ^ [_258014] = 792 ^ [_258014])]], -(duplicatefreeP(_258014))], (758 ^ _229964) ^ [] : [duplicatefreeP(_258014), 761 ^ _229964 : [(762 ^ _229964) ^ [_258312] : [ssItem(_258312), 765 ^ _229964 : [(766 ^ _229964) ^ [_258498] : [ssItem(_258498), 769 ^ _229964 : [(770 ^ _229964) ^ [_258680] : [ssList(_258680), 773 ^ _229964 : [(774 ^ _229964) ^ [_258858] : [ssList(_258858), 777 ^ _229964 : [(778 ^ _229964) ^ [_259032] : [ssList(_259032), app(app(_258680, cons(_258312, _258858)), cons(_258498, _259032)) = _258014, _258312 = _258498]]]]]]]]]]]]], (811 ^ _229964) ^ [_260524] : [ssList(_260524), 814 ^ _229964 : [(841 ^ _229964) ^ [] : [843 ^ _229964 : [(844 ^ _229964) ^ [] : [-(ssItem(842 ^ [_260524]))], (847 ^ _229964) ^ [] : [-(ssItem(845 ^ [_260524]))], (850 ^ _229964) ^ [] : [-(ssList(848 ^ [_260524]))], (853 ^ _229964) ^ [] : [-(ssList(851 ^ [_260524]))], (855 ^ _229964) ^ [] : [-(app(848 ^ [_260524], cons(842 ^ [_260524], cons(845 ^ [_260524], 851 ^ [_260524]))) = _260524)], (857 ^ _229964) ^ [] : [842 ^ [_260524] = 845 ^ [_260524]]], -(equalelemsP(_260524))], (815 ^ _229964) ^ [] : [equalelemsP(_260524), 818 ^ _229964 : [(819 ^ _229964) ^ [_260807] : [ssItem(_260807), 822 ^ _229964 : [(823 ^ _229964) ^ [_260978] : [ssItem(_260978), 826 ^ _229964 : [(827 ^ _229964) ^ [_261145] : [ssList(_261145), 830 ^ _229964 : [(831 ^ _229964) ^ [_261308] : [ssList(_261308), app(_261145, cons(_260807, cons(_260978, _261308))) = _260524, -(_260807 = _260978)]]]]]]]]]]], (861 ^ _229964) ^ [_262541] : [ssList(_262541), 864 ^ _229964 : [(865 ^ _229964) ^ [_262679] : [ssList(_262679), 868 ^ _229964 : [(869 ^ _229964) ^ [] : [neq(_262541, _262679), _262541 = _262679], (875 ^ _229964) ^ [] : [-(_262541 = _262679), -(neq(_262541, _262679))]]]]], (881 ^ _229964) ^ [_263132] : [ssList(_263132), 884 ^ _229964 : [(885 ^ _229964) ^ [_263264] : [ssItem(_263264), -(ssList(cons(_263264, _263132)))]]], (891 ^ _229964) ^ [] : [-(ssList(nil))], (893 ^ _229964) ^ [_263522] : [ssList(_263522), 896 ^ _229964 : [(897 ^ _229964) ^ [_263657] : [ssItem(_263657), cons(_263657, _263522) = _263522]]], (903 ^ _229964) ^ [_263865] : [ssList(_263865), 906 ^ _229964 : [(907 ^ _229964) ^ [_264033] : [ssList(_264033), 910 ^ _229964 : [(911 ^ _229964) ^ [_264197] : [ssItem(_264197), 914 ^ _229964 : [(915 ^ _229964) ^ [_264357] : [ssItem(_264357), cons(_264197, _263865) = cons(_264357, _264033), 922 ^ _229964 : [(923 ^ _229964) ^ [] : [-(_264197 = _264357)], (925 ^ _229964) ^ [] : [-(_264033 = _263865)]]]]]]]]], (927 ^ _229964) ^ [_264772] : [ssList(_264772), -(nil = _264772), 935 ^ _229964 : [(936 ^ _229964) ^ [] : [-(ssList(934 ^ [_264772]))], (939 ^ _229964) ^ [] : [-(ssItem(937 ^ [_264772]))], (941 ^ _229964) ^ [] : [-(cons(937 ^ [_264772], 934 ^ [_264772]) = _264772)]]], (943 ^ _229964) ^ [_265336] : [ssList(_265336), 946 ^ _229964 : [(947 ^ _229964) ^ [_265471] : [ssItem(_265471), nil = cons(_265471, _265336)]]], (953 ^ _229964) ^ [_265679] : [ssList(_265679), -(nil = _265679), -(ssItem(hd(_265679)))], (963 ^ _229964) ^ [_265957] : [ssList(_265957), 966 ^ _229964 : [(967 ^ _229964) ^ [_266092] : [ssItem(_266092), -(hd(cons(_266092, _265957)) = _266092)]]], (973 ^ _229964) ^ [_266303] : [ssList(_266303), -(nil = _266303), -(ssList(tl(_266303)))], (983 ^ _229964) ^ [_266581] : [ssList(_266581), 986 ^ _229964 : [(987 ^ _229964) ^ [_266716] : [ssItem(_266716), -(tl(cons(_266716, _266581)) = _266581)]]], (993 ^ _229964) ^ [_266927] : [ssList(_266927), 996 ^ _229964 : [(997 ^ _229964) ^ [_267059] : [ssList(_267059), -(ssList(app(_266927, _267059)))]]], (1003 ^ _229964) ^ [_267264] : [ssList(_267264), 1006 ^ _229964 : [(1007 ^ _229964) ^ [_267416] : [ssList(_267416), 1010 ^ _229964 : [(1011 ^ _229964) ^ [_267564] : [ssItem(_267564), -(cons(_267564, app(_267416, _267264)) = app(cons(_267564, _267416), _267264))]]]]], (1017 ^ _229964) ^ [_267802] : [ssList(_267802), -(app(nil, _267802) = _267802)], (1023 ^ _229964) ^ [_267996] : [ssItem(_267996), 1026 ^ _229964 : [(1027 ^ _229964) ^ [_268138] : [ssItem(_268138), -(_267996 = _268138), leq(_267996, _268138), leq(_268138, _267996)]]], (1041 ^ _229964) ^ [_268517] : [ssItem(_268517), 1044 ^ _229964 : [(1045 ^ _229964) ^ [_268669] : [ssItem(_268669), 1048 ^ _229964 : [(1049 ^ _229964) ^ [_268817] : [ssItem(_268817), -(leq(_268517, _268817)), leq(_268517, _268669), leq(_268669, _268817)]]]]], (1063 ^ _229964) ^ [_269217] : [ssItem(_269217), -(leq(_269217, _269217))], (1069 ^ _229964) ^ [_269405] : [ssItem(_269405), 1072 ^ _229964 : [(1073 ^ _229964) ^ [_269541] : [ssItem(_269541), 1076 ^ _229964 : [(1077 ^ _229964) ^ [] : [geq(_269405, _269541), -(leq(_269541, _269405))], (1083 ^ _229964) ^ [] : [leq(_269541, _269405), -(geq(_269405, _269541))]]]]], (1089 ^ _229964) ^ [_269992] : [ssItem(_269992), 1092 ^ _229964 : [(1093 ^ _229964) ^ [_270130] : [ssItem(_270130), lt(_269992, _270130), lt(_270130, _269992)]]], (1103 ^ _229964) ^ [_270421] : [ssItem(_270421), 1106 ^ _229964 : [(1107 ^ _229964) ^ [_270573] : [ssItem(_270573), 1110 ^ _229964 : [(1111 ^ _229964) ^ [_270721] : [ssItem(_270721), -(lt(_270421, _270721)), lt(_270421, _270573), lt(_270573, _270721)]]]]], (1125 ^ _229964) ^ [_271121] : [ssItem(_271121), 1128 ^ _229964 : [(1129 ^ _229964) ^ [_271257] : [ssItem(_271257), 1132 ^ _229964 : [(1133 ^ _229964) ^ [] : [gt(_271121, _271257), -(lt(_271257, _271121))], (1139 ^ _229964) ^ [] : [lt(_271257, _271121), -(gt(_271121, _271257))]]]]], (1145 ^ _229964) ^ [_271708] : [ssItem(_271708), 1148 ^ _229964 : [(1149 ^ _229964) ^ [_271863] : [ssList(_271863), 1152 ^ _229964 : [(1153 ^ _229964) ^ [_272014] : [ssList(_272014), 1156 ^ _229964 : [(1167 ^ _229964) ^ [] : [1168 ^ _229964 : [(1169 ^ _229964) ^ [] : [memberP(_271863, _271708)], (1171 ^ _229964) ^ [] : [memberP(_272014, _271708)]], -(memberP(app(_271863, _272014), _271708))], (1157 ^ _229964) ^ [] : [memberP(app(_271863, _272014), _271708), -(memberP(_271863, _271708)), -(memberP(_272014, _271708))]]]]]]], (1175 ^ _229964) ^ [_272661] : [ssItem(_272661), 1178 ^ _229964 : [(1179 ^ _229964) ^ [_272816] : [ssItem(_272816), 1182 ^ _229964 : [(1183 ^ _229964) ^ [_272967] : [ssList(_272967), 1186 ^ _229964 : [(1197 ^ _229964) ^ [] : [1198 ^ _229964 : [(1199 ^ _229964) ^ [] : [_272661 = _272816], (1201 ^ _229964) ^ [] : [memberP(_272967, _272661)]], -(memberP(cons(_272816, _272967), _272661))], (1187 ^ _229964) ^ [] : [memberP(cons(_272816, _272967), _272661), -(_272661 = _272816), -(memberP(_272967, _272661))]]]]]]], (1205 ^ _229964) ^ [_273614] : [ssItem(_273614), memberP(nil, _273614)], (1211 ^ _229964) ^ [] : [singletonP(nil)], (1213 ^ _229964) ^ [_273855] : [ssList(_273855), 1216 ^ _229964 : [(1217 ^ _229964) ^ [_274007] : [ssList(_274007), 1220 ^ _229964 : [(1221 ^ _229964) ^ [_274155] : [ssList(_274155), -(frontsegP(_273855, _274155)), frontsegP(_273855, _274007), frontsegP(_274007, _274155)]]]]], (1235 ^ _229964) ^ [_274555] : [ssList(_274555), 1238 ^ _229964 : [(1239 ^ _229964) ^ [_274697] : [ssList(_274697), -(_274555 = _274697), frontsegP(_274555, _274697), frontsegP(_274697, _274555)]]], (1253 ^ _229964) ^ [_275076] : [ssList(_275076), -(frontsegP(_275076, _275076))], (1259 ^ _229964) ^ [_275264] : [ssList(_275264), 1262 ^ _229964 : [(1263 ^ _229964) ^ [_275413] : [ssList(_275413), 1266 ^ _229964 : [(1267 ^ _229964) ^ [_275558] : [ssList(_275558), frontsegP(_275264, _275413), -(frontsegP(app(_275264, _275558), _275413))]]]]], (1277 ^ _229964) ^ [_275871] : [ssItem(_275871), 1280 ^ _229964 : [(1281 ^ _229964) ^ [_276039] : [ssItem(_276039), 1284 ^ _229964 : [(1285 ^ _229964) ^ [_276203] : [ssList(_276203), 1288 ^ _229964 : [(1289 ^ _229964) ^ [_276363] : [ssList(_276363), 1292 ^ _229964 : [(1293 ^ _229964) ^ [] : [frontsegP(cons(_275871, _276203), cons(_276039, _276363)), 1296 ^ _229964 : [(1297 ^ _229964) ^ [] : [-(_275871 = _276039)], (1299 ^ _229964) ^ [] : [-(frontsegP(_276203, _276363))]]], (1301 ^ _229964) ^ [] : [-(frontsegP(cons(_275871, _276203), cons(_276039, _276363))), _275871 = _276039, frontsegP(_276203, _276363)]]]]]]]]], (1311 ^ _229964) ^ [_277048] : [ssList(_277048), -(frontsegP(_277048, nil))], (1317 ^ _229964) ^ [_277236] : [ssList(_277236), 1320 ^ _229964 : [(1321 ^ _229964) ^ [] : [frontsegP(nil, _277236), -(nil = _277236)], (1327 ^ _229964) ^ [] : [nil = _277236, -(frontsegP(nil, _277236))]]], (1333 ^ _229964) ^ [_277664] : [ssList(_277664), 1336 ^ _229964 : [(1337 ^ _229964) ^ [_277816] : [ssList(_277816), 1340 ^ _229964 : [(1341 ^ _229964) ^ [_277964] : [ssList(_277964), -(rearsegP(_277664, _277964)), rearsegP(_277664, _277816), rearsegP(_277816, _277964)]]]]], (1355 ^ _229964) ^ [_278364] : [ssList(_278364), 1358 ^ _229964 : [(1359 ^ _229964) ^ [_278506] : [ssList(_278506), -(_278364 = _278506), rearsegP(_278364, _278506), rearsegP(_278506, _278364)]]], (1373 ^ _229964) ^ [_278885] : [ssList(_278885), -(rearsegP(_278885, _278885))], (1379 ^ _229964) ^ [_279073] : [ssList(_279073), 1382 ^ _229964 : [(1383 ^ _229964) ^ [_279222] : [ssList(_279222), 1386 ^ _229964 : [(1387 ^ _229964) ^ [_279367] : [ssList(_279367), rearsegP(_279073, _279222), -(rearsegP(app(_279367, _279073), _279222))]]]]], (1397 ^ _229964) ^ [_279680] : [ssList(_279680), -(rearsegP(_279680, nil))], (1403 ^ _229964) ^ [_279868] : [ssList(_279868), 1406 ^ _229964 : [(1407 ^ _229964) ^ [] : [rearsegP(nil, _279868), -(nil = _279868)], (1413 ^ _229964) ^ [] : [nil = _279868, -(rearsegP(nil, _279868))]]], (1419 ^ _229964) ^ [_280296] : [ssList(_280296), 1422 ^ _229964 : [(1423 ^ _229964) ^ [_280448] : [ssList(_280448), 1426 ^ _229964 : [(1427 ^ _229964) ^ [_280596] : [ssList(_280596), -(segmentP(_280296, _280596)), segmentP(_280296, _280448), segmentP(_280448, _280596)]]]]], (1441 ^ _229964) ^ [_280996] : [ssList(_280996), 1444 ^ _229964 : [(1445 ^ _229964) ^ [_281138] : [ssList(_281138), -(_280996 = _281138), segmentP(_280996, _281138), segmentP(_281138, _280996)]]], (1459 ^ _229964) ^ [_281517] : [ssList(_281517), -(segmentP(_281517, _281517))], (1465 ^ _229964) ^ [_281705] : [ssList(_281705), 1468 ^ _229964 : [(1469 ^ _229964) ^ [_281867] : [ssList(_281867), 1472 ^ _229964 : [(1473 ^ _229964) ^ [_282025] : [ssList(_282025), 1476 ^ _229964 : [(1477 ^ _229964) ^ [_282179] : [ssList(_282179), segmentP(_281705, _281867), -(segmentP(app(app(_282025, _281705), _282179), _281867))]]]]]]], (1487 ^ _229964) ^ [_282515] : [ssList(_282515), -(segmentP(_282515, nil))], (1493 ^ _229964) ^ [_282703] : [ssList(_282703), 1496 ^ _229964 : [(1497 ^ _229964) ^ [] : [segmentP(nil, _282703), -(nil = _282703)], (1503 ^ _229964) ^ [] : [nil = _282703, -(segmentP(nil, _282703))]]], (1509 ^ _229964) ^ [_283131] : [ssItem(_283131), -(cyclefreeP(cons(_283131, nil)))], (1515 ^ _229964) ^ [] : [-(cyclefreeP(nil))], (1517 ^ _229964) ^ [_283376] : [ssItem(_283376), -(totalorderP(cons(_283376, nil)))], (1523 ^ _229964) ^ [] : [-(totalorderP(nil))], (1525 ^ _229964) ^ [_283621] : [ssItem(_283621), -(strictorderP(cons(_283621, nil)))], (1531 ^ _229964) ^ [] : [-(strictorderP(nil))], (1533 ^ _229964) ^ [_283866] : [ssItem(_283866), -(totalorderedP(cons(_283866, nil)))], (1539 ^ _229964) ^ [] : [-(totalorderedP(nil))], (1541 ^ _229964) ^ [_284111] : [ssItem(_284111), 1544 ^ _229964 : [(1545 ^ _229964) ^ [_284270] : [ssList(_284270), 1548 ^ _229964 : [(1549 ^ _229964) ^ [] : [totalorderedP(cons(_284111, _284270)), -(nil = _284270), 1556 ^ _229964 : [(1557 ^ _229964) ^ [] : [nil = _284270], (1559 ^ _229964) ^ [] : [-(totalorderedP(_284270))], (1561 ^ _229964) ^ [] : [-(leq(_284111, hd(_284270)))]]], (1563 ^ _229964) ^ [] : [-(totalorderedP(cons(_284111, _284270))), 1564 ^ _229964 : [(1565 ^ _229964) ^ [] : [nil = _284270], (1567 ^ _229964) ^ [] : [-(nil = _284270), totalorderedP(_284270), leq(_284111, hd(_284270))]]]]]]], (1579 ^ _229964) ^ [_285205] : [ssItem(_285205), -(strictorderedP(cons(_285205, nil)))], (1585 ^ _229964) ^ [] : [-(strictorderedP(nil))], (1587 ^ _229964) ^ [_285450] : [ssItem(_285450), 1590 ^ _229964 : [(1591 ^ _229964) ^ [_285609] : [ssList(_285609), 1594 ^ _229964 : [(1595 ^ _229964) ^ [] : [strictorderedP(cons(_285450, _285609)), -(nil = _285609), 1602 ^ _229964 : [(1603 ^ _229964) ^ [] : [nil = _285609], (1605 ^ _229964) ^ [] : [-(strictorderedP(_285609))], (1607 ^ _229964) ^ [] : [-(lt(_285450, hd(_285609)))]]], (1609 ^ _229964) ^ [] : [-(strictorderedP(cons(_285450, _285609))), 1610 ^ _229964 : [(1611 ^ _229964) ^ [] : [nil = _285609], (1613 ^ _229964) ^ [] : [-(nil = _285609), strictorderedP(_285609), lt(_285450, hd(_285609))]]]]]]], (1625 ^ _229964) ^ [_286544] : [ssItem(_286544), -(duplicatefreeP(cons(_286544, nil)))], (1631 ^ _229964) ^ [] : [-(duplicatefreeP(nil))], (1633 ^ _229964) ^ [_286789] : [ssItem(_286789), -(equalelemsP(cons(_286789, nil)))], (1639 ^ _229964) ^ [] : [-(equalelemsP(nil))], (1641 ^ _229964) ^ [_287034] : [ssList(_287034), -(nil = _287034), 1649 ^ _229964 : [(1650 ^ _229964) ^ [] : [-(ssItem(1648 ^ [_287034]))], (1652 ^ _229964) ^ [] : [-(hd(_287034) = 1648 ^ [_287034])]]], (1654 ^ _229964) ^ [_287448] : [ssList(_287448), -(nil = _287448), 1662 ^ _229964 : [(1663 ^ _229964) ^ [] : [-(ssList(1661 ^ [_287448]))], (1665 ^ _229964) ^ [] : [-(tl(_287448) = 1661 ^ [_287448])]]], (1667 ^ _229964) ^ [_287862] : [ssList(_287862), 1670 ^ _229964 : [(1671 ^ _229964) ^ [_288028] : [ssList(_288028), -(_288028 = _287862), -(nil = _288028), -(nil = _287862), hd(_288028) = hd(_287862), tl(_288028) = tl(_287862)]]], (1693 ^ _229964) ^ [_288607] : [ssList(_288607), -(nil = _288607), -(cons(hd(_288607), tl(_288607)) = _288607)], (1703 ^ _229964) ^ [_288897] : [ssList(_288897), 1706 ^ _229964 : [(1707 ^ _229964) ^ [_289049] : [ssList(_289049), 1710 ^ _229964 : [(1711 ^ _229964) ^ [_289197] : [ssList(_289197), app(_289197, _289049) = app(_288897, _289049), -(_289197 = _288897)]]]]], (1721 ^ _229964) ^ [_289516] : [ssList(_289516), 1724 ^ _229964 : [(1725 ^ _229964) ^ [_289668] : [ssList(_289668), 1728 ^ _229964 : [(1729 ^ _229964) ^ [_289816] : [ssList(_289816), app(_289668, _289816) = app(_289668, _289516), -(_289816 = _289516)]]]]], (1739 ^ _229964) ^ [_290135] : [ssList(_290135), 1742 ^ _229964 : [(1743 ^ _229964) ^ [_290274] : [ssItem(_290274), -(cons(_290274, _290135) = app(cons(_290274, nil), _290135))]]], (1749 ^ _229964) ^ [_290493] : [ssList(_290493), 1752 ^ _229964 : [(1753 ^ _229964) ^ [_290645] : [ssList(_290645), 1756 ^ _229964 : [(1757 ^ _229964) ^ [_290793] : [ssList(_290793), -(app(app(_290493, _290645), _290793) = app(_290493, app(_290645, _290793)))]]]]], (1763 ^ _229964) ^ [_291031] : [ssList(_291031), 1766 ^ _229964 : [(1767 ^ _229964) ^ [_291176] : [ssList(_291176), 1770 ^ _229964 : [(1771 ^ _229964) ^ [] : [nil = app(_291031, _291176), 1774 ^ _229964 : [(1775 ^ _229964) ^ [] : [-(nil = _291176)], (1777 ^ _229964) ^ [] : [-(nil = _291031)]]], (1779 ^ _229964) ^ [] : [-(nil = app(_291031, _291176)), nil = _291176, nil = _291031]]]]], (1789 ^ _229964) ^ [_291794] : [ssList(_291794), -(app(_291794, nil) = _291794)], (1795 ^ _229964) ^ [_291988] : [ssList(_291988), 1798 ^ _229964 : [(1799 ^ _229964) ^ [_292133] : [ssList(_292133), -(nil = _291988), -(hd(app(_291988, _292133)) = hd(_291988))]]], (1809 ^ _229964) ^ [_292440] : [ssList(_292440), 1812 ^ _229964 : [(1813 ^ _229964) ^ [_292588] : [ssList(_292588), -(nil = _292440), -(tl(app(_292440, _292588)) = app(tl(_292440), _292588))]]], (1823 ^ _229964) ^ [_292901] : [ssItem(_292901), 1826 ^ _229964 : [(1827 ^ _229964) ^ [_293043] : [ssItem(_293043), -(_292901 = _293043), geq(_292901, _293043), geq(_293043, _292901)]]], (1841 ^ _229964) ^ [_293422] : [ssItem(_293422), 1844 ^ _229964 : [(1845 ^ _229964) ^ [_293574] : [ssItem(_293574), 1848 ^ _229964 : [(1849 ^ _229964) ^ [_293722] : [ssItem(_293722), -(geq(_293422, _293722)), geq(_293422, _293574), geq(_293574, _293722)]]]]], (1863 ^ _229964) ^ [_294122] : [ssItem(_294122), -(geq(_294122, _294122))], (1869 ^ _229964) ^ [_294310] : [ssItem(_294310), lt(_294310, _294310)], (1875 ^ _229964) ^ [_294499] : [ssItem(_294499), 1878 ^ _229964 : [(1879 ^ _229964) ^ [_294651] : [ssItem(_294651), 1882 ^ _229964 : [(1883 ^ _229964) ^ [_294799] : [ssItem(_294799), -(lt(_294499, _294799)), leq(_294499, _294651), lt(_294651, _294799)]]]]], (1897 ^ _229964) ^ [_295199] : [ssItem(_295199), 1900 ^ _229964 : [(1901 ^ _229964) ^ [_295341] : [ssItem(_295341), leq(_295199, _295341), -(_295199 = _295341), -(lt(_295199, _295341))]]], (1915 ^ _229964) ^ [_295721] : [ssItem(_295721), 1918 ^ _229964 : [(1919 ^ _229964) ^ [_295865] : [ssItem(_295865), 1922 ^ _229964 : [(1923 ^ _229964) ^ [] : [lt(_295721, _295865), 1926 ^ _229964 : [(1927 ^ _229964) ^ [] : [_295721 = _295865], (1929 ^ _229964) ^ [] : [-(leq(_295721, _295865))]]], (1931 ^ _229964) ^ [] : [-(lt(_295721, _295865)), -(_295721 = _295865), leq(_295721, _295865)]]]]], (1941 ^ _229964) ^ [_296476] : [ssItem(_296476), 1944 ^ _229964 : [(1945 ^ _229964) ^ [_296614] : [ssItem(_296614), gt(_296476, _296614), gt(_296614, _296476)]]], (1955 ^ _229964) ^ [_296885] : [ssItem(_296885), 1958 ^ _229964 : [(1959 ^ _229964) ^ [_297037] : [ssItem(_297037), 1962 ^ _229964 : [(1963 ^ _229964) ^ [_297185] : [ssItem(_297185), -(gt(_296885, _297185)), gt(_296885, _297037), gt(_297037, _297185)]]]]]], input).
% 8.59/8.61  ncf('1',plain,[ssList(1976 ^ []), 865 : ssList(1976 ^ []), 869 : neq(1976 ^ [], 1976 ^ []), 869 : 1976 ^ [] = 1976 ^ []],start(861 ^ 0,bind([[_262541, _262679], [1976 ^ [], 1976 ^ []]]))).
% 8.59/8.61  ncf('1.1',plain,[-(ssList(1976 ^ []))],extension(1978 ^ 1)).
% 8.59/8.61  ncf('1.2',plain,[-(ssList(1976 ^ []))],extension(1978 ^ 3)).
% 8.59/8.61  ncf('1.3',plain,[-(neq(1976 ^ [], 1976 ^ [])), -(1976 ^ [] = 1976 ^ [])],extension(875 ^ 5)).
% 8.59/8.61  ncf('1.3.1',plain,[1976 ^ [] = 1976 ^ [], -(1982 ^ [] = 1976 ^ []), 1982 ^ [] = 1976 ^ []],extension(10 ^ 6,bind([[_230419, _230421, _230423], [1976 ^ [], 1976 ^ [], 1982 ^ []]]))).
% 8.59/8.61  ncf('1.3.1.1',plain,[1982 ^ [] = 1976 ^ [], -(totalorderedP(1976 ^ [])), totalorderedP(1982 ^ [])],extension(236 ^ 7,bind([[_237363, _237365], [1976 ^ [], 1982 ^ []]]))).
% 8.59/8.61  ncf('1.3.1.1.1',plain,[totalorderedP(1976 ^ [])],extension(1995 ^ 8)).
% 8.59/8.61  ncf('1.3.1.1.2',plain,[-(totalorderedP(1982 ^ []))],extension(1993 ^ 8)).
% 8.59/8.61  ncf('1.3.1.2',plain,[-(1982 ^ [] = 1976 ^ []), 1976 ^ [] = 1982 ^ []],extension(4 ^ 7,bind([[_230215, _230217], [1982 ^ [], 1976 ^ []]]))).
% 8.59/8.61  ncf('1.3.1.2.1',plain,[-(1976 ^ [] = 1982 ^ [])],extension(1991 ^ 8)).
% 8.59/8.61  ncf('1.4',plain,[-(1976 ^ [] = 1976 ^ [])],extension(2 ^ 5,bind([[_230108], [1976 ^ []]]))).
% 8.59/8.61  %-----------------------------------------------------
% 8.59/8.61  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------