%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SWC203+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n026.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 12:12:51 EDT 2023

% Result   : Theorem 10.79s 10.69s
% Output   : Proof 10.79s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SWC203+1 : TPTP v8.1.2. Released v2.4.0.
% 0.11/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n026.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Fri May 19 01:36:05 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 10.79/10.69  
% 10.79/10.69  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 10.79/10.69  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.79/10.69  %-----------------------------------------------------
% 10.79/10.69  ncf(matrix, plain, [(1978 ^ _230097) ^ [] : [-(ssList(1976 ^ []))], (1981 ^ _230097) ^ [] : [-(ssList(1979 ^ []))], (1984 ^ _230097) ^ [] : [-(ssList(1982 ^ []))], (1987 ^ _230097) ^ [] : [-(ssList(1985 ^ []))], (1989 ^ _230097) ^ [] : [-(1979 ^ [] = 1985 ^ [])], (1991 ^ _230097) ^ [] : [-(1976 ^ [] = 1982 ^ [])], (1993 ^ _230097) ^ [] : [-(1985 ^ [] = 1982 ^ [])], (1995 ^ _230097) ^ [] : [-(neq(1979 ^ [], nil))], (1997 ^ _230097) ^ [] : [neq(1976 ^ [], nil)], (246 ^ _230097) ^ [_237901, _237903, _237905, _237907] : [-(cons(_237907, _237903) = cons(_237905, _237901)), _237907 = _237905, _237903 = _237901], (256 ^ _230097) ^ [_238232, _238234] : [_238234 = _238232, -(hd(_238234) = hd(_238232))], (272 ^ _230097) ^ [_238789, _238791] : [_238791 = _238789, -(tl(_238791) = tl(_238789))], (262 ^ _230097) ^ [_238478, _238480, _238482, _238484] : [-(app(_238484, _238480) = app(_238482, _238478)), _238484 = _238482, _238480 = _238478], (2 ^ _230097) ^ [_230241] : [-(_230241 = _230241)], (4 ^ _230097) ^ [_230348, _230350] : [_230350 = _230348, -(_230348 = _230350)], (10 ^ _230097) ^ [_230552, _230554, _230556] : [-(_230556 = _230552), _230556 = _230554, _230554 = _230552], (20 ^ _230097) ^ [_230893, _230895, _230897, _230899] : [-(memberP(_230897, _230893)), memberP(_230899, _230895), _230899 = _230897, _230895 = _230893], (34 ^ _230097) ^ [_231309, _231311] : [-(singletonP(_231309)), _231311 = _231309, singletonP(_231311)], (44 ^ _230097) ^ [_231632, _231634, _231636, _231638] : [-(frontsegP(_231636, _231632)), frontsegP(_231638, _231634), _231638 = _231636, _231634 = _231632], (58 ^ _230097) ^ [_232076, _232078, _232080, _232082] : [-(rearsegP(_232080, _232076)), rearsegP(_232082, _232078), _232082 = _232080, _232078 = _232076], (72 ^ _230097) ^ [_232520, _232522, _232524, _232526] : [-(segmentP(_232524, _232520)), segmentP(_232526, _232522), _232526 = _232524, _232522 = _232520], (86 ^ _230097) ^ [_232936, _232938] : [-(cyclefreeP(_232936)), _232938 = _232936, cyclefreeP(_232938)], (96 ^ _230097) ^ [_233231, _233233] : [-(totalorderP(_233231)), _233233 = _233231, totalorderP(_233233)], (106 ^ _230097) ^ [_233526, _233528] : [-(strictorderP(_233526)), _233528 = _233526, strictorderP(_233528)], (116 ^ _230097) ^ [_233821, _233823] : [-(totalorderedP(_233821)), _233823 = _233821, totalorderedP(_233823)], (126 ^ _230097) ^ [_234116, _234118] : [-(strictorderedP(_234116)), _234118 = _234116, strictorderedP(_234118)], (136 ^ _230097) ^ [_234411, _234413] : [-(duplicatefreeP(_234411)), _234413 = _234411, duplicatefreeP(_234413)], (146 ^ _230097) ^ [_234706, _234708] : [-(equalelemsP(_234706)), _234708 = _234706, equalelemsP(_234708)], (156 ^ _230097) ^ [_235029, _235031, _235033, _235035] : [-(geq(_235033, _235029)), geq(_235035, _235031), _235035 = _235033, _235031 = _235029], (170 ^ _230097) ^ [_235473, _235475, _235477, _235479] : [-(lt(_235477, _235473)), lt(_235479, _235475), _235479 = _235477, _235475 = _235473], (184 ^ _230097) ^ [_235917, _235919, _235921, _235923] : [-(leq(_235921, _235917)), leq(_235923, _235919), _235923 = _235921, _235919 = _235917], (198 ^ _230097) ^ [_236333, _236335] : [-(ssItem(_236333)), _236335 = _236333, ssItem(_236335)], (208 ^ _230097) ^ [_236656, _236658, _236660, _236662] : [-(gt(_236660, _236656)), gt(_236662, _236658), _236662 = _236660, _236658 = _236656], (222 ^ _230097) ^ [_237072, _237074] : [-(ssList(_237072)), _237074 = _237072, ssList(_237074)], (232 ^ _230097) ^ [_237375, _237377, _237379, _237381] : [-(neq(_237379, _237375)), neq(_237381, _237377), _237381 = _237379, _237377 = _237375], (278 ^ _230097) ^ [_239011] : [ssItem(_239011), 281 ^ _230097 : [(282 ^ _230097) ^ [_239149] : [ssItem(_239149), 285 ^ _230097 : [(286 ^ _230097) ^ [] : [neq(_239011, _239149), _239011 = _239149], (292 ^ _230097) ^ [] : [-(_239011 = _239149), -(neq(_239011, _239149))]]]]], (299 ^ _230097) ^ [] : [-(ssItem(297 ^ []))], (302 ^ _230097) ^ [] : [-(ssItem(300 ^ []))], (304 ^ _230097) ^ [] : [297 ^ [] = 300 ^ []], (306 ^ _230097) ^ [_239862] : [ssList(_239862), 309 ^ _230097 : [(310 ^ _230097) ^ [_240024] : [ssItem(_240024), 313 ^ _230097 : [(314 ^ _230097) ^ [] : [memberP(_239862, _240024), 318 ^ _230097 : [(319 ^ _230097) ^ [] : [-(ssList(317 ^ [_239862, _240024]))], (322 ^ _230097) ^ [] : [-(ssList(320 ^ [_239862, _240024]))], (324 ^ _230097) ^ [] : [-(app(317 ^ [_239862, _240024], cons(_240024, 320 ^ [_239862, _240024])) = _239862)]]], (326 ^ _230097) ^ [] : [-(memberP(_239862, _240024)), 327 ^ _230097 : [(328 ^ _230097) ^ [_240672] : [ssList(_240672), 331 ^ _230097 : [(332 ^ _230097) ^ [_240820] : [ssList(_240820), app(_240672, cons(_240024, _240820)) = _239862]]]]]]]]], (340 ^ _230097) ^ [_241111] : [ssList(_241111), 343 ^ _230097 : [(344 ^ _230097) ^ [] : [singletonP(_241111), 348 ^ _230097 : [(349 ^ _230097) ^ [] : [-(ssItem(347 ^ [_241111]))], (351 ^ _230097) ^ [] : [-(cons(347 ^ [_241111], nil) = _241111)]]], (353 ^ _230097) ^ [] : [-(singletonP(_241111)), 354 ^ _230097 : [(355 ^ _230097) ^ [_241560] : [ssItem(_241560), cons(_241560, nil) = _241111]]]]], (363 ^ _230097) ^ [_241816] : [ssList(_241816), 366 ^ _230097 : [(367 ^ _230097) ^ [_241965] : [ssList(_241965), 370 ^ _230097 : [(371 ^ _230097) ^ [] : [frontsegP(_241816, _241965), 375 ^ _230097 : [(376 ^ _230097) ^ [] : [-(ssList(374 ^ [_241816, _241965]))], (378 ^ _230097) ^ [] : [-(app(_241965, 374 ^ [_241816, _241965]) = _241816)]]], (380 ^ _230097) ^ [] : [-(frontsegP(_241816, _241965)), 381 ^ _230097 : [(382 ^ _230097) ^ [_242440] : [ssList(_242440), app(_241965, _242440) = _241816]]]]]]], (390 ^ _230097) ^ [_242712] : [ssList(_242712), 393 ^ _230097 : [(394 ^ _230097) ^ [_242861] : [ssList(_242861), 397 ^ _230097 : [(398 ^ _230097) ^ [] : [rearsegP(_242712, _242861), 402 ^ _230097 : [(403 ^ _230097) ^ [] : [-(ssList(401 ^ [_242712, _242861]))], (405 ^ _230097) ^ [] : [-(app(401 ^ [_242712, _242861], _242861) = _242712)]]], (407 ^ _230097) ^ [] : [-(rearsegP(_242712, _242861)), 408 ^ _230097 : [(409 ^ _230097) ^ [_243336] : [ssList(_243336), app(_243336, _242861) = _242712]]]]]]], (417 ^ _230097) ^ [_243608] : [ssList(_243608), 420 ^ _230097 : [(421 ^ _230097) ^ [_243770] : [ssList(_243770), 424 ^ _230097 : [(425 ^ _230097) ^ [] : [segmentP(_243608, _243770), 429 ^ _230097 : [(430 ^ _230097) ^ [] : [-(ssList(428 ^ [_243608, _243770]))], (433 ^ _230097) ^ [] : [-(ssList(431 ^ [_243608, _243770]))], (435 ^ _230097) ^ [] : [-(app(app(428 ^ [_243608, _243770], _243770), 431 ^ [_243608, _243770]) = _243608)]]], (437 ^ _230097) ^ [] : [-(segmentP(_243608, _243770)), 438 ^ _230097 : [(439 ^ _230097) ^ [_244418] : [ssList(_244418), 442 ^ _230097 : [(443 ^ _230097) ^ [_244566] : [ssList(_244566), app(app(_244418, _243770), _244566) = _243608]]]]]]]]], (451 ^ _230097) ^ [_244857] : [ssList(_244857), 454 ^ _230097 : [(489 ^ _230097) ^ [] : [491 ^ _230097 : [(492 ^ _230097) ^ [] : [-(ssItem(490 ^ [_244857]))], (495 ^ _230097) ^ [] : [-(ssItem(493 ^ [_244857]))], (498 ^ _230097) ^ [] : [-(ssList(496 ^ [_244857]))], (501 ^ _230097) ^ [] : [-(ssList(499 ^ [_244857]))], (504 ^ _230097) ^ [] : [-(ssList(502 ^ [_244857]))], (506 ^ _230097) ^ [] : [-(app(app(496 ^ [_244857], cons(490 ^ [_244857], 499 ^ [_244857])), cons(493 ^ [_244857], 502 ^ [_244857])) = _244857)], (508 ^ _230097) ^ [] : [-(leq(490 ^ [_244857], 493 ^ [_244857]))], (510 ^ _230097) ^ [] : [-(leq(493 ^ [_244857], 490 ^ [_244857]))]], -(cyclefreeP(_244857))], (455 ^ _230097) ^ [] : [cyclefreeP(_244857), 458 ^ _230097 : [(459 ^ _230097) ^ [_245161] : [ssItem(_245161), 462 ^ _230097 : [(463 ^ _230097) ^ [_245353] : [ssItem(_245353), 466 ^ _230097 : [(467 ^ _230097) ^ [_245541] : [ssList(_245541), 470 ^ _230097 : [(471 ^ _230097) ^ [_245725] : [ssList(_245725), 474 ^ _230097 : [(475 ^ _230097) ^ [_245905] : [ssList(_245905), app(app(_245541, cons(_245161, _245725)), cons(_245353, _245905)) = _244857, leq(_245161, _245353), leq(_245353, _245161)]]]]]]]]]]]]], (514 ^ _230097) ^ [_247643] : [ssList(_247643), 517 ^ _230097 : [(552 ^ _230097) ^ [] : [554 ^ _230097 : [(555 ^ _230097) ^ [] : [-(ssItem(553 ^ [_247643]))], (558 ^ _230097) ^ [] : [-(ssItem(556 ^ [_247643]))], (561 ^ _230097) ^ [] : [-(ssList(559 ^ [_247643]))], (564 ^ _230097) ^ [] : [-(ssList(562 ^ [_247643]))], (567 ^ _230097) ^ [] : [-(ssList(565 ^ [_247643]))], (569 ^ _230097) ^ [] : [-(app(app(559 ^ [_247643], cons(553 ^ [_247643], 562 ^ [_247643])), cons(556 ^ [_247643], 565 ^ [_247643])) = _247643)], (571 ^ _230097) ^ [] : [leq(553 ^ [_247643], 556 ^ [_247643])], (573 ^ _230097) ^ [] : [leq(556 ^ [_247643], 553 ^ [_247643])]], -(totalorderP(_247643))], (518 ^ _230097) ^ [] : [totalorderP(_247643), 521 ^ _230097 : [(522 ^ _230097) ^ [_247945] : [ssItem(_247945), 525 ^ _230097 : [(526 ^ _230097) ^ [_248135] : [ssItem(_248135), 529 ^ _230097 : [(530 ^ _230097) ^ [_248321] : [ssList(_248321), 533 ^ _230097 : [(534 ^ _230097) ^ [_248503] : [ssList(_248503), 537 ^ _230097 : [(538 ^ _230097) ^ [_248681] : [ssList(_248681), app(app(_248321, cons(_247945, _248503)), cons(_248135, _248681)) = _247643, -(leq(_247945, _248135)), -(leq(_248135, _247945))]]]]]]]]]]]]], (577 ^ _230097) ^ [_250407] : [ssList(_250407), 580 ^ _230097 : [(615 ^ _230097) ^ [] : [617 ^ _230097 : [(618 ^ _230097) ^ [] : [-(ssItem(616 ^ [_250407]))], (621 ^ _230097) ^ [] : [-(ssItem(619 ^ [_250407]))], (624 ^ _230097) ^ [] : [-(ssList(622 ^ [_250407]))], (627 ^ _230097) ^ [] : [-(ssList(625 ^ [_250407]))], (630 ^ _230097) ^ [] : [-(ssList(628 ^ [_250407]))], (632 ^ _230097) ^ [] : [-(app(app(622 ^ [_250407], cons(616 ^ [_250407], 625 ^ [_250407])), cons(619 ^ [_250407], 628 ^ [_250407])) = _250407)], (634 ^ _230097) ^ [] : [lt(616 ^ [_250407], 619 ^ [_250407])], (636 ^ _230097) ^ [] : [lt(619 ^ [_250407], 616 ^ [_250407])]], -(strictorderP(_250407))], (581 ^ _230097) ^ [] : [strictorderP(_250407), 584 ^ _230097 : [(585 ^ _230097) ^ [_250709] : [ssItem(_250709), 588 ^ _230097 : [(589 ^ _230097) ^ [_250899] : [ssItem(_250899), 592 ^ _230097 : [(593 ^ _230097) ^ [_251085] : [ssList(_251085), 596 ^ _230097 : [(597 ^ _230097) ^ [_251267] : [ssList(_251267), 600 ^ _230097 : [(601 ^ _230097) ^ [_251445] : [ssList(_251445), app(app(_251085, cons(_250709, _251267)), cons(_250899, _251445)) = _250407, -(lt(_250709, _250899)), -(lt(_250899, _250709))]]]]]]]]]]]]], (640 ^ _230097) ^ [_253171] : [ssList(_253171), 643 ^ _230097 : [(674 ^ _230097) ^ [] : [676 ^ _230097 : [(677 ^ _230097) ^ [] : [-(ssItem(675 ^ [_253171]))], (680 ^ _230097) ^ [] : [-(ssItem(678 ^ [_253171]))], (683 ^ _230097) ^ [] : [-(ssList(681 ^ [_253171]))], (686 ^ _230097) ^ [] : [-(ssList(684 ^ [_253171]))], (689 ^ _230097) ^ [] : [-(ssList(687 ^ [_253171]))], (691 ^ _230097) ^ [] : [-(app(app(681 ^ [_253171], cons(675 ^ [_253171], 684 ^ [_253171])), cons(678 ^ [_253171], 687 ^ [_253171])) = _253171)], (693 ^ _230097) ^ [] : [leq(675 ^ [_253171], 678 ^ [_253171])]], -(totalorderedP(_253171))], (644 ^ _230097) ^ [] : [totalorderedP(_253171), 647 ^ _230097 : [(648 ^ _230097) ^ [_253467] : [ssItem(_253467), 651 ^ _230097 : [(652 ^ _230097) ^ [_253651] : [ssItem(_253651), 655 ^ _230097 : [(656 ^ _230097) ^ [_253831] : [ssList(_253831), 659 ^ _230097 : [(660 ^ _230097) ^ [_254007] : [ssList(_254007), 663 ^ _230097 : [(664 ^ _230097) ^ [_254179] : [ssList(_254179), app(app(_253831, cons(_253467, _254007)), cons(_253651, _254179)) = _253171, -(leq(_253467, _253651))]]]]]]]]]]]]], (697 ^ _230097) ^ [_255659] : [ssList(_255659), 700 ^ _230097 : [(731 ^ _230097) ^ [] : [733 ^ _230097 : [(734 ^ _230097) ^ [] : [-(ssItem(732 ^ [_255659]))], (737 ^ _230097) ^ [] : [-(ssItem(735 ^ [_255659]))], (740 ^ _230097) ^ [] : [-(ssList(738 ^ [_255659]))], (743 ^ _230097) ^ [] : [-(ssList(741 ^ [_255659]))], (746 ^ _230097) ^ [] : [-(ssList(744 ^ [_255659]))], (748 ^ _230097) ^ [] : [-(app(app(738 ^ [_255659], cons(732 ^ [_255659], 741 ^ [_255659])), cons(735 ^ [_255659], 744 ^ [_255659])) = _255659)], (750 ^ _230097) ^ [] : [lt(732 ^ [_255659], 735 ^ [_255659])]], -(strictorderedP(_255659))], (701 ^ _230097) ^ [] : [strictorderedP(_255659), 704 ^ _230097 : [(705 ^ _230097) ^ [_255955] : [ssItem(_255955), 708 ^ _230097 : [(709 ^ _230097) ^ [_256139] : [ssItem(_256139), 712 ^ _230097 : [(713 ^ _230097) ^ [_256319] : [ssList(_256319), 716 ^ _230097 : [(717 ^ _230097) ^ [_256495] : [ssList(_256495), 720 ^ _230097 : [(721 ^ _230097) ^ [_256667] : [ssList(_256667), app(app(_256319, cons(_255955, _256495)), cons(_256139, _256667)) = _255659, -(lt(_255955, _256139))]]]]]]]]]]]]], (754 ^ _230097) ^ [_258147] : [ssList(_258147), 757 ^ _230097 : [(788 ^ _230097) ^ [] : [790 ^ _230097 : [(791 ^ _230097) ^ [] : [-(ssItem(789 ^ [_258147]))], (794 ^ _230097) ^ [] : [-(ssItem(792 ^ [_258147]))], (797 ^ _230097) ^ [] : [-(ssList(795 ^ [_258147]))], (800 ^ _230097) ^ [] : [-(ssList(798 ^ [_258147]))], (803 ^ _230097) ^ [] : [-(ssList(801 ^ [_258147]))], (805 ^ _230097) ^ [] : [-(app(app(795 ^ [_258147], cons(789 ^ [_258147], 798 ^ [_258147])), cons(792 ^ [_258147], 801 ^ [_258147])) = _258147)], (807 ^ _230097) ^ [] : [-(789 ^ [_258147] = 792 ^ [_258147])]], -(duplicatefreeP(_258147))], (758 ^ _230097) ^ [] : [duplicatefreeP(_258147), 761 ^ _230097 : [(762 ^ _230097) ^ [_258445] : [ssItem(_258445), 765 ^ _230097 : [(766 ^ _230097) ^ [_258631] : [ssItem(_258631), 769 ^ _230097 : [(770 ^ _230097) ^ [_258813] : [ssList(_258813), 773 ^ _230097 : [(774 ^ _230097) ^ [_258991] : [ssList(_258991), 777 ^ _230097 : [(778 ^ _230097) ^ [_259165] : [ssList(_259165), app(app(_258813, cons(_258445, _258991)), cons(_258631, _259165)) = _258147, _258445 = _258631]]]]]]]]]]]]], (811 ^ _230097) ^ [_260657] : [ssList(_260657), 814 ^ _230097 : [(841 ^ _230097) ^ [] : [843 ^ _230097 : [(844 ^ _230097) ^ [] : [-(ssItem(842 ^ [_260657]))], (847 ^ _230097) ^ [] : [-(ssItem(845 ^ [_260657]))], (850 ^ _230097) ^ [] : [-(ssList(848 ^ [_260657]))], (853 ^ _230097) ^ [] : [-(ssList(851 ^ [_260657]))], (855 ^ _230097) ^ [] : [-(app(848 ^ [_260657], cons(842 ^ [_260657], cons(845 ^ [_260657], 851 ^ [_260657]))) = _260657)], (857 ^ _230097) ^ [] : [842 ^ [_260657] = 845 ^ [_260657]]], -(equalelemsP(_260657))], (815 ^ _230097) ^ [] : [equalelemsP(_260657), 818 ^ _230097 : [(819 ^ _230097) ^ [_260940] : [ssItem(_260940), 822 ^ _230097 : [(823 ^ _230097) ^ [_261111] : [ssItem(_261111), 826 ^ _230097 : [(827 ^ _230097) ^ [_261278] : [ssList(_261278), 830 ^ _230097 : [(831 ^ _230097) ^ [_261441] : [ssList(_261441), app(_261278, cons(_260940, cons(_261111, _261441))) = _260657, -(_260940 = _261111)]]]]]]]]]]], (861 ^ _230097) ^ [_262674] : [ssList(_262674), 864 ^ _230097 : [(865 ^ _230097) ^ [_262812] : [ssList(_262812), 868 ^ _230097 : [(869 ^ _230097) ^ [] : [neq(_262674, _262812), _262674 = _262812], (875 ^ _230097) ^ [] : [-(_262674 = _262812), -(neq(_262674, _262812))]]]]], (881 ^ _230097) ^ [_263265] : [ssList(_263265), 884 ^ _230097 : [(885 ^ _230097) ^ [_263397] : [ssItem(_263397), -(ssList(cons(_263397, _263265)))]]], (891 ^ _230097) ^ [] : [-(ssList(nil))], (893 ^ _230097) ^ [_263655] : [ssList(_263655), 896 ^ _230097 : [(897 ^ _230097) ^ [_263790] : [ssItem(_263790), cons(_263790, _263655) = _263655]]], (903 ^ _230097) ^ [_263998] : [ssList(_263998), 906 ^ _230097 : [(907 ^ _230097) ^ [_264166] : [ssList(_264166), 910 ^ _230097 : [(911 ^ _230097) ^ [_264330] : [ssItem(_264330), 914 ^ _230097 : [(915 ^ _230097) ^ [_264490] : [ssItem(_264490), cons(_264330, _263998) = cons(_264490, _264166), 922 ^ _230097 : [(923 ^ _230097) ^ [] : [-(_264330 = _264490)], (925 ^ _230097) ^ [] : [-(_264166 = _263998)]]]]]]]]], (927 ^ _230097) ^ [_264905] : [ssList(_264905), -(nil = _264905), 935 ^ _230097 : [(936 ^ _230097) ^ [] : [-(ssList(934 ^ [_264905]))], (939 ^ _230097) ^ [] : [-(ssItem(937 ^ [_264905]))], (941 ^ _230097) ^ [] : [-(cons(937 ^ [_264905], 934 ^ [_264905]) = _264905)]]], (943 ^ _230097) ^ [_265469] : [ssList(_265469), 946 ^ _230097 : [(947 ^ _230097) ^ [_265604] : [ssItem(_265604), nil = cons(_265604, _265469)]]], (953 ^ _230097) ^ [_265812] : [ssList(_265812), -(nil = _265812), -(ssItem(hd(_265812)))], (963 ^ _230097) ^ [_266090] : [ssList(_266090), 966 ^ _230097 : [(967 ^ _230097) ^ [_266225] : [ssItem(_266225), -(hd(cons(_266225, _266090)) = _266225)]]], (973 ^ _230097) ^ [_266436] : [ssList(_266436), -(nil = _266436), -(ssList(tl(_266436)))], (983 ^ _230097) ^ [_266714] : [ssList(_266714), 986 ^ _230097 : [(987 ^ _230097) ^ [_266849] : [ssItem(_266849), -(tl(cons(_266849, _266714)) = _266714)]]], (993 ^ _230097) ^ [_267060] : [ssList(_267060), 996 ^ _230097 : [(997 ^ _230097) ^ [_267192] : [ssList(_267192), -(ssList(app(_267060, _267192)))]]], (1003 ^ _230097) ^ [_267397] : [ssList(_267397), 1006 ^ _230097 : [(1007 ^ _230097) ^ [_267549] : [ssList(_267549), 1010 ^ _230097 : [(1011 ^ _230097) ^ [_267697] : [ssItem(_267697), -(cons(_267697, app(_267549, _267397)) = app(cons(_267697, _267549), _267397))]]]]], (1017 ^ _230097) ^ [_267935] : [ssList(_267935), -(app(nil, _267935) = _267935)], (1023 ^ _230097) ^ [_268129] : [ssItem(_268129), 1026 ^ _230097 : [(1027 ^ _230097) ^ [_268271] : [ssItem(_268271), -(_268129 = _268271), leq(_268129, _268271), leq(_268271, _268129)]]], (1041 ^ _230097) ^ [_268650] : [ssItem(_268650), 1044 ^ _230097 : [(1045 ^ _230097) ^ [_268802] : [ssItem(_268802), 1048 ^ _230097 : [(1049 ^ _230097) ^ [_268950] : [ssItem(_268950), -(leq(_268650, _268950)), leq(_268650, _268802), leq(_268802, _268950)]]]]], (1063 ^ _230097) ^ [_269350] : [ssItem(_269350), -(leq(_269350, _269350))], (1069 ^ _230097) ^ [_269538] : [ssItem(_269538), 1072 ^ _230097 : [(1073 ^ _230097) ^ [_269674] : [ssItem(_269674), 1076 ^ _230097 : [(1077 ^ _230097) ^ [] : [geq(_269538, _269674), -(leq(_269674, _269538))], (1083 ^ _230097) ^ [] : [leq(_269674, _269538), -(geq(_269538, _269674))]]]]], (1089 ^ _230097) ^ [_270125] : [ssItem(_270125), 1092 ^ _230097 : [(1093 ^ _230097) ^ [_270263] : [ssItem(_270263), lt(_270125, _270263), lt(_270263, _270125)]]], (1103 ^ _230097) ^ [_270554] : [ssItem(_270554), 1106 ^ _230097 : [(1107 ^ _230097) ^ [_270706] : [ssItem(_270706), 1110 ^ _230097 : [(1111 ^ _230097) ^ [_270854] : [ssItem(_270854), -(lt(_270554, _270854)), lt(_270554, _270706), lt(_270706, _270854)]]]]], (1125 ^ _230097) ^ [_271254] : [ssItem(_271254), 1128 ^ _230097 : [(1129 ^ _230097) ^ [_271390] : [ssItem(_271390), 1132 ^ _230097 : [(1133 ^ _230097) ^ [] : [gt(_271254, _271390), -(lt(_271390, _271254))], (1139 ^ _230097) ^ [] : [lt(_271390, _271254), -(gt(_271254, _271390))]]]]], (1145 ^ _230097) ^ [_271841] : [ssItem(_271841), 1148 ^ _230097 : [(1149 ^ _230097) ^ [_271996] : [ssList(_271996), 1152 ^ _230097 : [(1153 ^ _230097) ^ [_272147] : [ssList(_272147), 1156 ^ _230097 : [(1167 ^ _230097) ^ [] : [1168 ^ _230097 : [(1169 ^ _230097) ^ [] : [memberP(_271996, _271841)], (1171 ^ _230097) ^ [] : [memberP(_272147, _271841)]], -(memberP(app(_271996, _272147), _271841))], (1157 ^ _230097) ^ [] : [memberP(app(_271996, _272147), _271841), -(memberP(_271996, _271841)), -(memberP(_272147, _271841))]]]]]]], (1175 ^ _230097) ^ [_272794] : [ssItem(_272794), 1178 ^ _230097 : [(1179 ^ _230097) ^ [_272949] : [ssItem(_272949), 1182 ^ _230097 : [(1183 ^ _230097) ^ [_273100] : [ssList(_273100), 1186 ^ _230097 : [(1197 ^ _230097) ^ [] : [1198 ^ _230097 : [(1199 ^ _230097) ^ [] : [_272794 = _272949], (1201 ^ _230097) ^ [] : [memberP(_273100, _272794)]], -(memberP(cons(_272949, _273100), _272794))], (1187 ^ _230097) ^ [] : [memberP(cons(_272949, _273100), _272794), -(_272794 = _272949), -(memberP(_273100, _272794))]]]]]]], (1205 ^ _230097) ^ [_273747] : [ssItem(_273747), memberP(nil, _273747)], (1211 ^ _230097) ^ [] : [singletonP(nil)], (1213 ^ _230097) ^ [_273988] : [ssList(_273988), 1216 ^ _230097 : [(1217 ^ _230097) ^ [_274140] : [ssList(_274140), 1220 ^ _230097 : [(1221 ^ _230097) ^ [_274288] : [ssList(_274288), -(frontsegP(_273988, _274288)), frontsegP(_273988, _274140), frontsegP(_274140, _274288)]]]]], (1235 ^ _230097) ^ [_274688] : [ssList(_274688), 1238 ^ _230097 : [(1239 ^ _230097) ^ [_274830] : [ssList(_274830), -(_274688 = _274830), frontsegP(_274688, _274830), frontsegP(_274830, _274688)]]], (1253 ^ _230097) ^ [_275209] : [ssList(_275209), -(frontsegP(_275209, _275209))], (1259 ^ _230097) ^ [_275397] : [ssList(_275397), 1262 ^ _230097 : [(1263 ^ _230097) ^ [_275546] : [ssList(_275546), 1266 ^ _230097 : [(1267 ^ _230097) ^ [_275691] : [ssList(_275691), frontsegP(_275397, _275546), -(frontsegP(app(_275397, _275691), _275546))]]]]], (1277 ^ _230097) ^ [_276004] : [ssItem(_276004), 1280 ^ _230097 : [(1281 ^ _230097) ^ [_276172] : [ssItem(_276172), 1284 ^ _230097 : [(1285 ^ _230097) ^ [_276336] : [ssList(_276336), 1288 ^ _230097 : [(1289 ^ _230097) ^ [_276496] : [ssList(_276496), 1292 ^ _230097 : [(1293 ^ _230097) ^ [] : [frontsegP(cons(_276004, _276336), cons(_276172, _276496)), 1296 ^ _230097 : [(1297 ^ _230097) ^ [] : [-(_276004 = _276172)], (1299 ^ _230097) ^ [] : [-(frontsegP(_276336, _276496))]]], (1301 ^ _230097) ^ [] : [-(frontsegP(cons(_276004, _276336), cons(_276172, _276496))), _276004 = _276172, frontsegP(_276336, _276496)]]]]]]]]], (1311 ^ _230097) ^ [_277181] : [ssList(_277181), -(frontsegP(_277181, nil))], (1317 ^ _230097) ^ [_277369] : [ssList(_277369), 1320 ^ _230097 : [(1321 ^ _230097) ^ [] : [frontsegP(nil, _277369), -(nil = _277369)], (1327 ^ _230097) ^ [] : [nil = _277369, -(frontsegP(nil, _277369))]]], (1333 ^ _230097) ^ [_277797] : [ssList(_277797), 1336 ^ _230097 : [(1337 ^ _230097) ^ [_277949] : [ssList(_277949), 1340 ^ _230097 : [(1341 ^ _230097) ^ [_278097] : [ssList(_278097), -(rearsegP(_277797, _278097)), rearsegP(_277797, _277949), rearsegP(_277949, _278097)]]]]], (1355 ^ _230097) ^ [_278497] : [ssList(_278497), 1358 ^ _230097 : [(1359 ^ _230097) ^ [_278639] : [ssList(_278639), -(_278497 = _278639), rearsegP(_278497, _278639), rearsegP(_278639, _278497)]]], (1373 ^ _230097) ^ [_279018] : [ssList(_279018), -(rearsegP(_279018, _279018))], (1379 ^ _230097) ^ [_279206] : [ssList(_279206), 1382 ^ _230097 : [(1383 ^ _230097) ^ [_279355] : [ssList(_279355), 1386 ^ _230097 : [(1387 ^ _230097) ^ [_279500] : [ssList(_279500), rearsegP(_279206, _279355), -(rearsegP(app(_279500, _279206), _279355))]]]]], (1397 ^ _230097) ^ [_279813] : [ssList(_279813), -(rearsegP(_279813, nil))], (1403 ^ _230097) ^ [_280001] : [ssList(_280001), 1406 ^ _230097 : [(1407 ^ _230097) ^ [] : [rearsegP(nil, _280001), -(nil = _280001)], (1413 ^ _230097) ^ [] : [nil = _280001, -(rearsegP(nil, _280001))]]], (1419 ^ _230097) ^ [_280429] : [ssList(_280429), 1422 ^ _230097 : [(1423 ^ _230097) ^ [_280581] : [ssList(_280581), 1426 ^ _230097 : [(1427 ^ _230097) ^ [_280729] : [ssList(_280729), -(segmentP(_280429, _280729)), segmentP(_280429, _280581), segmentP(_280581, _280729)]]]]], (1441 ^ _230097) ^ [_281129] : [ssList(_281129), 1444 ^ _230097 : [(1445 ^ _230097) ^ [_281271] : [ssList(_281271), -(_281129 = _281271), segmentP(_281129, _281271), segmentP(_281271, _281129)]]], (1459 ^ _230097) ^ [_281650] : [ssList(_281650), -(segmentP(_281650, _281650))], (1465 ^ _230097) ^ [_281838] : [ssList(_281838), 1468 ^ _230097 : [(1469 ^ _230097) ^ [_282000] : [ssList(_282000), 1472 ^ _230097 : [(1473 ^ _230097) ^ [_282158] : [ssList(_282158), 1476 ^ _230097 : [(1477 ^ _230097) ^ [_282312] : [ssList(_282312), segmentP(_281838, _282000), -(segmentP(app(app(_282158, _281838), _282312), _282000))]]]]]]], (1487 ^ _230097) ^ [_282648] : [ssList(_282648), -(segmentP(_282648, nil))], (1493 ^ _230097) ^ [_282836] : [ssList(_282836), 1496 ^ _230097 : [(1497 ^ _230097) ^ [] : [segmentP(nil, _282836), -(nil = _282836)], (1503 ^ _230097) ^ [] : [nil = _282836, -(segmentP(nil, _282836))]]], (1509 ^ _230097) ^ [_283264] : [ssItem(_283264), -(cyclefreeP(cons(_283264, nil)))], (1515 ^ _230097) ^ [] : [-(cyclefreeP(nil))], (1517 ^ _230097) ^ [_283509] : [ssItem(_283509), -(totalorderP(cons(_283509, nil)))], (1523 ^ _230097) ^ [] : [-(totalorderP(nil))], (1525 ^ _230097) ^ [_283754] : [ssItem(_283754), -(strictorderP(cons(_283754, nil)))], (1531 ^ _230097) ^ [] : [-(strictorderP(nil))], (1533 ^ _230097) ^ [_283999] : [ssItem(_283999), -(totalorderedP(cons(_283999, nil)))], (1539 ^ _230097) ^ [] : [-(totalorderedP(nil))], (1541 ^ _230097) ^ [_284244] : [ssItem(_284244), 1544 ^ _230097 : [(1545 ^ _230097) ^ [_284403] : [ssList(_284403), 1548 ^ _230097 : [(1549 ^ _230097) ^ [] : [totalorderedP(cons(_284244, _284403)), -(nil = _284403), 1556 ^ _230097 : [(1557 ^ _230097) ^ [] : [nil = _284403], (1559 ^ _230097) ^ [] : [-(totalorderedP(_284403))], (1561 ^ _230097) ^ [] : [-(leq(_284244, hd(_284403)))]]], (1563 ^ _230097) ^ [] : [-(totalorderedP(cons(_284244, _284403))), 1564 ^ _230097 : [(1565 ^ _230097) ^ [] : [nil = _284403], (1567 ^ _230097) ^ [] : [-(nil = _284403), totalorderedP(_284403), leq(_284244, hd(_284403))]]]]]]], (1579 ^ _230097) ^ [_285338] : [ssItem(_285338), -(strictorderedP(cons(_285338, nil)))], (1585 ^ _230097) ^ [] : [-(strictorderedP(nil))], (1587 ^ _230097) ^ [_285583] : [ssItem(_285583), 1590 ^ _230097 : [(1591 ^ _230097) ^ [_285742] : [ssList(_285742), 1594 ^ _230097 : [(1595 ^ _230097) ^ [] : [strictorderedP(cons(_285583, _285742)), -(nil = _285742), 1602 ^ _230097 : [(1603 ^ _230097) ^ [] : [nil = _285742], (1605 ^ _230097) ^ [] : [-(strictorderedP(_285742))], (1607 ^ _230097) ^ [] : [-(lt(_285583, hd(_285742)))]]], (1609 ^ _230097) ^ [] : [-(strictorderedP(cons(_285583, _285742))), 1610 ^ _230097 : [(1611 ^ _230097) ^ [] : [nil = _285742], (1613 ^ _230097) ^ [] : [-(nil = _285742), strictorderedP(_285742), lt(_285583, hd(_285742))]]]]]]], (1625 ^ _230097) ^ [_286677] : [ssItem(_286677), -(duplicatefreeP(cons(_286677, nil)))], (1631 ^ _230097) ^ [] : [-(duplicatefreeP(nil))], (1633 ^ _230097) ^ [_286922] : [ssItem(_286922), -(equalelemsP(cons(_286922, nil)))], (1639 ^ _230097) ^ [] : [-(equalelemsP(nil))], (1641 ^ _230097) ^ [_287167] : [ssList(_287167), -(nil = _287167), 1649 ^ _230097 : [(1650 ^ _230097) ^ [] : [-(ssItem(1648 ^ [_287167]))], (1652 ^ _230097) ^ [] : [-(hd(_287167) = 1648 ^ [_287167])]]], (1654 ^ _230097) ^ [_287581] : [ssList(_287581), -(nil = _287581), 1662 ^ _230097 : [(1663 ^ _230097) ^ [] : [-(ssList(1661 ^ [_287581]))], (1665 ^ _230097) ^ [] : [-(tl(_287581) = 1661 ^ [_287581])]]], (1667 ^ _230097) ^ [_287995] : [ssList(_287995), 1670 ^ _230097 : [(1671 ^ _230097) ^ [_288161] : [ssList(_288161), -(_288161 = _287995), -(nil = _288161), -(nil = _287995), hd(_288161) = hd(_287995), tl(_288161) = tl(_287995)]]], (1693 ^ _230097) ^ [_288740] : [ssList(_288740), -(nil = _288740), -(cons(hd(_288740), tl(_288740)) = _288740)], (1703 ^ _230097) ^ [_289030] : [ssList(_289030), 1706 ^ _230097 : [(1707 ^ _230097) ^ [_289182] : [ssList(_289182), 1710 ^ _230097 : [(1711 ^ _230097) ^ [_289330] : [ssList(_289330), app(_289330, _289182) = app(_289030, _289182), -(_289330 = _289030)]]]]], (1721 ^ _230097) ^ [_289649] : [ssList(_289649), 1724 ^ _230097 : [(1725 ^ _230097) ^ [_289801] : [ssList(_289801), 1728 ^ _230097 : [(1729 ^ _230097) ^ [_289949] : [ssList(_289949), app(_289801, _289949) = app(_289801, _289649), -(_289949 = _289649)]]]]], (1739 ^ _230097) ^ [_290268] : [ssList(_290268), 1742 ^ _230097 : [(1743 ^ _230097) ^ [_290407] : [ssItem(_290407), -(cons(_290407, _290268) = app(cons(_290407, nil), _290268))]]], (1749 ^ _230097) ^ [_290626] : [ssList(_290626), 1752 ^ _230097 : [(1753 ^ _230097) ^ [_290778] : [ssList(_290778), 1756 ^ _230097 : [(1757 ^ _230097) ^ [_290926] : [ssList(_290926), -(app(app(_290626, _290778), _290926) = app(_290626, app(_290778, _290926)))]]]]], (1763 ^ _230097) ^ [_291164] : [ssList(_291164), 1766 ^ _230097 : [(1767 ^ _230097) ^ [_291309] : [ssList(_291309), 1770 ^ _230097 : [(1771 ^ _230097) ^ [] : [nil = app(_291164, _291309), 1774 ^ _230097 : [(1775 ^ _230097) ^ [] : [-(nil = _291309)], (1777 ^ _230097) ^ [] : [-(nil = _291164)]]], (1779 ^ _230097) ^ [] : [-(nil = app(_291164, _291309)), nil = _291309, nil = _291164]]]]], (1789 ^ _230097) ^ [_291927] : [ssList(_291927), -(app(_291927, nil) = _291927)], (1795 ^ _230097) ^ [_292121] : [ssList(_292121), 1798 ^ _230097 : [(1799 ^ _230097) ^ [_292266] : [ssList(_292266), -(nil = _292121), -(hd(app(_292121, _292266)) = hd(_292121))]]], (1809 ^ _230097) ^ [_292573] : [ssList(_292573), 1812 ^ _230097 : [(1813 ^ _230097) ^ [_292721] : [ssList(_292721), -(nil = _292573), -(tl(app(_292573, _292721)) = app(tl(_292573), _292721))]]], (1823 ^ _230097) ^ [_293034] : [ssItem(_293034), 1826 ^ _230097 : [(1827 ^ _230097) ^ [_293176] : [ssItem(_293176), -(_293034 = _293176), geq(_293034, _293176), geq(_293176, _293034)]]], (1841 ^ _230097) ^ [_293555] : [ssItem(_293555), 1844 ^ _230097 : [(1845 ^ _230097) ^ [_293707] : [ssItem(_293707), 1848 ^ _230097 : [(1849 ^ _230097) ^ [_293855] : [ssItem(_293855), -(geq(_293555, _293855)), geq(_293555, _293707), geq(_293707, _293855)]]]]], (1863 ^ _230097) ^ [_294255] : [ssItem(_294255), -(geq(_294255, _294255))], (1869 ^ _230097) ^ [_294443] : [ssItem(_294443), lt(_294443, _294443)], (1875 ^ _230097) ^ [_294632] : [ssItem(_294632), 1878 ^ _230097 : [(1879 ^ _230097) ^ [_294784] : [ssItem(_294784), 1882 ^ _230097 : [(1883 ^ _230097) ^ [_294932] : [ssItem(_294932), -(lt(_294632, _294932)), leq(_294632, _294784), lt(_294784, _294932)]]]]], (1897 ^ _230097) ^ [_295332] : [ssItem(_295332), 1900 ^ _230097 : [(1901 ^ _230097) ^ [_295474] : [ssItem(_295474), leq(_295332, _295474), -(_295332 = _295474), -(lt(_295332, _295474))]]], (1915 ^ _230097) ^ [_295854] : [ssItem(_295854), 1918 ^ _230097 : [(1919 ^ _230097) ^ [_295998] : [ssItem(_295998), 1922 ^ _230097 : [(1923 ^ _230097) ^ [] : [lt(_295854, _295998), 1926 ^ _230097 : [(1927 ^ _230097) ^ [] : [_295854 = _295998], (1929 ^ _230097) ^ [] : [-(leq(_295854, _295998))]]], (1931 ^ _230097) ^ [] : [-(lt(_295854, _295998)), -(_295854 = _295998), leq(_295854, _295998)]]]]], (1941 ^ _230097) ^ [_296609] : [ssItem(_296609), 1944 ^ _230097 : [(1945 ^ _230097) ^ [_296747] : [ssItem(_296747), gt(_296609, _296747), gt(_296747, _296609)]]], (1955 ^ _230097) ^ [_297018] : [ssItem(_297018), 1958 ^ _230097 : [(1959 ^ _230097) ^ [_297170] : [ssItem(_297170), 1962 ^ _230097 : [(1963 ^ _230097) ^ [_297318] : [ssItem(_297318), -(gt(_297018, _297318)), gt(_297018, _297170), gt(_297170, _297318)]]]]]], input).
% 10.79/10.69  ncf('1',plain,[neq(1976 ^ [], nil)],start(1997 ^ 0)).
% 10.79/10.69  ncf('1.1',plain,[-(neq(1976 ^ [], nil)), neq(1979 ^ [], nil), 1979 ^ [] = 1976 ^ [], nil = nil],extension(232 ^ 1,bind([[_237375, _237377, _237379, _237381], [nil, nil, 1976 ^ [], 1979 ^ []]]))).
% 10.79/10.69  ncf('1.1.1',plain,[-(neq(1979 ^ [], nil))],extension(1995 ^ 2)).
% 10.79/10.69  ncf('1.1.2',plain,[-(1979 ^ [] = 1976 ^ []), 1979 ^ [] = 1985 ^ [], 1985 ^ [] = 1976 ^ []],extension(10 ^ 2,bind([[_230552, _230554, _230556], [1976 ^ [], 1985 ^ [], 1979 ^ []]]))).
% 10.79/10.69  ncf('1.1.2.1',plain,[-(1979 ^ [] = 1985 ^ [])],extension(1989 ^ 3)).
% 10.79/10.69  ncf('1.1.2.2',plain,[-(1985 ^ [] = 1976 ^ []), 1985 ^ [] = 1982 ^ [], 1982 ^ [] = 1976 ^ []],extension(10 ^ 3,bind([[_230552, _230554, _230556], [1976 ^ [], 1982 ^ [], 1985 ^ []]]))).
% 10.79/10.69  ncf('1.1.2.2.1',plain,[-(1985 ^ [] = 1982 ^ [])],extension(1993 ^ 4)).
% 10.79/10.69  ncf('1.1.2.2.2',plain,[-(1982 ^ [] = 1976 ^ []), 1976 ^ [] = 1982 ^ []],extension(4 ^ 4,bind([[_230348, _230350], [1982 ^ [], 1976 ^ []]]))).
% 10.79/10.69  ncf('1.1.2.2.2.1',plain,[-(1976 ^ [] = 1982 ^ [])],extension(1991 ^ 5)).
% 10.79/10.69  ncf('1.1.3',plain,[-(nil = nil)],extension(2 ^ 2,bind([[_230241], [nil]]))).
% 10.79/10.69  %-----------------------------------------------------
% 10.79/10.69  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------