%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SWC131+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n020.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri May 19 12:12:37 EDT 2023

% Result   : Theorem 14.02s 13.80s
% Output   : Proof 14.02s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SWC131+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n020.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Fri May 19 01:22:32 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 14.02/13.80  
% 14.02/13.80  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 14.02/13.80  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.02/13.80  %-----------------------------------------------------
% 14.02/13.80  ncf(matrix, plain, [(1978 ^ _230414) ^ [] : [-(ssList(1976 ^ []))], (1981 ^ _230414) ^ [] : [-(ssList(1979 ^ []))], (1984 ^ _230414) ^ [] : [-(ssList(1982 ^ []))], (1987 ^ _230414) ^ [] : [-(ssList(1985 ^ []))], (1989 ^ _230414) ^ [] : [-(1979 ^ [] = 1985 ^ [])], (1991 ^ _230414) ^ [] : [-(1976 ^ [] = 1982 ^ [])], (1993 ^ _230414) ^ [] : [neq(1985 ^ [], nil)], (1995 ^ _230414) ^ [] : [cyclefreeP(1979 ^ [])], (246 ^ _230414) ^ [_238218, _238220, _238222, _238224] : [-(cons(_238224, _238220) = cons(_238222, _238218)), _238224 = _238222, _238220 = _238218], (256 ^ _230414) ^ [_238549, _238551] : [_238551 = _238549, -(hd(_238551) = hd(_238549))], (272 ^ _230414) ^ [_239106, _239108] : [_239108 = _239106, -(tl(_239108) = tl(_239106))], (262 ^ _230414) ^ [_238795, _238797, _238799, _238801] : [-(app(_238801, _238797) = app(_238799, _238795)), _238801 = _238799, _238797 = _238795], (2 ^ _230414) ^ [_230558] : [-(_230558 = _230558)], (4 ^ _230414) ^ [_230665, _230667] : [_230667 = _230665, -(_230665 = _230667)], (10 ^ _230414) ^ [_230869, _230871, _230873] : [-(_230873 = _230869), _230873 = _230871, _230871 = _230869], (20 ^ _230414) ^ [_231210, _231212, _231214, _231216] : [-(memberP(_231214, _231210)), memberP(_231216, _231212), _231216 = _231214, _231212 = _231210], (34 ^ _230414) ^ [_231626, _231628] : [-(singletonP(_231626)), _231628 = _231626, singletonP(_231628)], (44 ^ _230414) ^ [_231949, _231951, _231953, _231955] : [-(frontsegP(_231953, _231949)), frontsegP(_231955, _231951), _231955 = _231953, _231951 = _231949], (58 ^ _230414) ^ [_232393, _232395, _232397, _232399] : [-(rearsegP(_232397, _232393)), rearsegP(_232399, _232395), _232399 = _232397, _232395 = _232393], (72 ^ _230414) ^ [_232837, _232839, _232841, _232843] : [-(segmentP(_232841, _232837)), segmentP(_232843, _232839), _232843 = _232841, _232839 = _232837], (86 ^ _230414) ^ [_233253, _233255] : [-(totalorderP(_233253)), _233255 = _233253, totalorderP(_233255)], (96 ^ _230414) ^ [_233548, _233550] : [-(strictorderP(_233548)), _233550 = _233548, strictorderP(_233550)], (106 ^ _230414) ^ [_233843, _233845] : [-(totalorderedP(_233843)), _233845 = _233843, totalorderedP(_233845)], (116 ^ _230414) ^ [_234138, _234140] : [-(strictorderedP(_234138)), _234140 = _234138, strictorderedP(_234140)], (126 ^ _230414) ^ [_234433, _234435] : [-(duplicatefreeP(_234433)), _234435 = _234433, duplicatefreeP(_234435)], (136 ^ _230414) ^ [_234728, _234730] : [-(equalelemsP(_234728)), _234730 = _234728, equalelemsP(_234730)], (146 ^ _230414) ^ [_235051, _235053, _235055, _235057] : [-(geq(_235055, _235051)), geq(_235057, _235053), _235057 = _235055, _235053 = _235051], (160 ^ _230414) ^ [_235495, _235497, _235499, _235501] : [-(lt(_235499, _235495)), lt(_235501, _235497), _235501 = _235499, _235497 = _235495], (174 ^ _230414) ^ [_235939, _235941, _235943, _235945] : [-(leq(_235943, _235939)), leq(_235945, _235941), _235945 = _235943, _235941 = _235939], (188 ^ _230414) ^ [_236355, _236357] : [-(ssItem(_236355)), _236357 = _236355, ssItem(_236357)], (198 ^ _230414) ^ [_236678, _236680, _236682, _236684] : [-(gt(_236682, _236678)), gt(_236684, _236680), _236684 = _236682, _236680 = _236678], (212 ^ _230414) ^ [_237094, _237096] : [-(ssList(_237094)), _237096 = _237094, ssList(_237096)], (236 ^ _230414) ^ [_237813, _237815] : [-(cyclefreeP(_237813)), _237815 = _237813, cyclefreeP(_237815)], (222 ^ _230414) ^ [_237417, _237419, _237421, _237423] : [-(neq(_237421, _237417)), neq(_237423, _237419), _237423 = _237421, _237419 = _237417], (278 ^ _230414) ^ [_239328] : [ssItem(_239328), 281 ^ _230414 : [(282 ^ _230414) ^ [_239466] : [ssItem(_239466), 285 ^ _230414 : [(286 ^ _230414) ^ [] : [neq(_239328, _239466), _239328 = _239466], (292 ^ _230414) ^ [] : [-(_239328 = _239466), -(neq(_239328, _239466))]]]]], (299 ^ _230414) ^ [] : [-(ssItem(297 ^ []))], (302 ^ _230414) ^ [] : [-(ssItem(300 ^ []))], (304 ^ _230414) ^ [] : [297 ^ [] = 300 ^ []], (306 ^ _230414) ^ [_240179] : [ssList(_240179), 309 ^ _230414 : [(310 ^ _230414) ^ [_240341] : [ssItem(_240341), 313 ^ _230414 : [(314 ^ _230414) ^ [] : [memberP(_240179, _240341), 318 ^ _230414 : [(319 ^ _230414) ^ [] : [-(ssList(317 ^ [_240179, _240341]))], (322 ^ _230414) ^ [] : [-(ssList(320 ^ [_240179, _240341]))], (324 ^ _230414) ^ [] : [-(app(317 ^ [_240179, _240341], cons(_240341, 320 ^ [_240179, _240341])) = _240179)]]], (326 ^ _230414) ^ [] : [-(memberP(_240179, _240341)), 327 ^ _230414 : [(328 ^ _230414) ^ [_240989] : [ssList(_240989), 331 ^ _230414 : [(332 ^ _230414) ^ [_241137] : [ssList(_241137), app(_240989, cons(_240341, _241137)) = _240179]]]]]]]]], (340 ^ _230414) ^ [_241428] : [ssList(_241428), 343 ^ _230414 : [(344 ^ _230414) ^ [] : [singletonP(_241428), 348 ^ _230414 : [(349 ^ _230414) ^ [] : [-(ssItem(347 ^ [_241428]))], (351 ^ _230414) ^ [] : [-(cons(347 ^ [_241428], nil) = _241428)]]], (353 ^ _230414) ^ [] : [-(singletonP(_241428)), 354 ^ _230414 : [(355 ^ _230414) ^ [_241877] : [ssItem(_241877), cons(_241877, nil) = _241428]]]]], (363 ^ _230414) ^ [_242133] : [ssList(_242133), 366 ^ _230414 : [(367 ^ _230414) ^ [_242282] : [ssList(_242282), 370 ^ _230414 : [(371 ^ _230414) ^ [] : [frontsegP(_242133, _242282), 375 ^ _230414 : [(376 ^ _230414) ^ [] : [-(ssList(374 ^ [_242133, _242282]))], (378 ^ _230414) ^ [] : [-(app(_242282, 374 ^ [_242133, _242282]) = _242133)]]], (380 ^ _230414) ^ [] : [-(frontsegP(_242133, _242282)), 381 ^ _230414 : [(382 ^ _230414) ^ [_242757] : [ssList(_242757), app(_242282, _242757) = _242133]]]]]]], (390 ^ _230414) ^ [_243029] : [ssList(_243029), 393 ^ _230414 : [(394 ^ _230414) ^ [_243178] : [ssList(_243178), 397 ^ _230414 : [(398 ^ _230414) ^ [] : [rearsegP(_243029, _243178), 402 ^ _230414 : [(403 ^ _230414) ^ [] : [-(ssList(401 ^ [_243029, _243178]))], (405 ^ _230414) ^ [] : [-(app(401 ^ [_243029, _243178], _243178) = _243029)]]], (407 ^ _230414) ^ [] : [-(rearsegP(_243029, _243178)), 408 ^ _230414 : [(409 ^ _230414) ^ [_243653] : [ssList(_243653), app(_243653, _243178) = _243029]]]]]]], (417 ^ _230414) ^ [_243925] : [ssList(_243925), 420 ^ _230414 : [(421 ^ _230414) ^ [_244087] : [ssList(_244087), 424 ^ _230414 : [(425 ^ _230414) ^ [] : [segmentP(_243925, _244087), 429 ^ _230414 : [(430 ^ _230414) ^ [] : [-(ssList(428 ^ [_243925, _244087]))], (433 ^ _230414) ^ [] : [-(ssList(431 ^ [_243925, _244087]))], (435 ^ _230414) ^ [] : [-(app(app(428 ^ [_243925, _244087], _244087), 431 ^ [_243925, _244087]) = _243925)]]], (437 ^ _230414) ^ [] : [-(segmentP(_243925, _244087)), 438 ^ _230414 : [(439 ^ _230414) ^ [_244735] : [ssList(_244735), 442 ^ _230414 : [(443 ^ _230414) ^ [_244883] : [ssList(_244883), app(app(_244735, _244087), _244883) = _243925]]]]]]]]], (451 ^ _230414) ^ [_245174] : [ssList(_245174), 454 ^ _230414 : [(489 ^ _230414) ^ [] : [491 ^ _230414 : [(492 ^ _230414) ^ [] : [-(ssItem(490 ^ [_245174]))], (495 ^ _230414) ^ [] : [-(ssItem(493 ^ [_245174]))], (498 ^ _230414) ^ [] : [-(ssList(496 ^ [_245174]))], (501 ^ _230414) ^ [] : [-(ssList(499 ^ [_245174]))], (504 ^ _230414) ^ [] : [-(ssList(502 ^ [_245174]))], (506 ^ _230414) ^ [] : [-(app(app(496 ^ [_245174], cons(490 ^ [_245174], 499 ^ [_245174])), cons(493 ^ [_245174], 502 ^ [_245174])) = _245174)], (508 ^ _230414) ^ [] : [-(leq(490 ^ [_245174], 493 ^ [_245174]))], (510 ^ _230414) ^ [] : [-(leq(493 ^ [_245174], 490 ^ [_245174]))]], -(cyclefreeP(_245174))], (455 ^ _230414) ^ [] : [cyclefreeP(_245174), 458 ^ _230414 : [(459 ^ _230414) ^ [_245478] : [ssItem(_245478), 462 ^ _230414 : [(463 ^ _230414) ^ [_245670] : [ssItem(_245670), 466 ^ _230414 : [(467 ^ _230414) ^ [_245858] : [ssList(_245858), 470 ^ _230414 : [(471 ^ _230414) ^ [_246042] : [ssList(_246042), 474 ^ _230414 : [(475 ^ _230414) ^ [_246222] : [ssList(_246222), app(app(_245858, cons(_245478, _246042)), cons(_245670, _246222)) = _245174, leq(_245478, _245670), leq(_245670, _245478)]]]]]]]]]]]]], (514 ^ _230414) ^ [_247960] : [ssList(_247960), 517 ^ _230414 : [(552 ^ _230414) ^ [] : [554 ^ _230414 : [(555 ^ _230414) ^ [] : [-(ssItem(553 ^ [_247960]))], (558 ^ _230414) ^ [] : [-(ssItem(556 ^ [_247960]))], (561 ^ _230414) ^ [] : [-(ssList(559 ^ [_247960]))], (564 ^ _230414) ^ [] : [-(ssList(562 ^ [_247960]))], (567 ^ _230414) ^ [] : [-(ssList(565 ^ [_247960]))], (569 ^ _230414) ^ [] : [-(app(app(559 ^ [_247960], cons(553 ^ [_247960], 562 ^ [_247960])), cons(556 ^ [_247960], 565 ^ [_247960])) = _247960)], (571 ^ _230414) ^ [] : [leq(553 ^ [_247960], 556 ^ [_247960])], (573 ^ _230414) ^ [] : [leq(556 ^ [_247960], 553 ^ [_247960])]], -(totalorderP(_247960))], (518 ^ _230414) ^ [] : [totalorderP(_247960), 521 ^ _230414 : [(522 ^ _230414) ^ [_248262] : [ssItem(_248262), 525 ^ _230414 : [(526 ^ _230414) ^ [_248452] : [ssItem(_248452), 529 ^ _230414 : [(530 ^ _230414) ^ [_248638] : [ssList(_248638), 533 ^ _230414 : [(534 ^ _230414) ^ [_248820] : [ssList(_248820), 537 ^ _230414 : [(538 ^ _230414) ^ [_248998] : [ssList(_248998), app(app(_248638, cons(_248262, _248820)), cons(_248452, _248998)) = _247960, -(leq(_248262, _248452)), -(leq(_248452, _248262))]]]]]]]]]]]]], (577 ^ _230414) ^ [_250724] : [ssList(_250724), 580 ^ _230414 : [(615 ^ _230414) ^ [] : [617 ^ _230414 : [(618 ^ _230414) ^ [] : [-(ssItem(616 ^ [_250724]))], (621 ^ _230414) ^ [] : [-(ssItem(619 ^ [_250724]))], (624 ^ _230414) ^ [] : [-(ssList(622 ^ [_250724]))], (627 ^ _230414) ^ [] : [-(ssList(625 ^ [_250724]))], (630 ^ _230414) ^ [] : [-(ssList(628 ^ [_250724]))], (632 ^ _230414) ^ [] : [-(app(app(622 ^ [_250724], cons(616 ^ [_250724], 625 ^ [_250724])), cons(619 ^ [_250724], 628 ^ [_250724])) = _250724)], (634 ^ _230414) ^ [] : [lt(616 ^ [_250724], 619 ^ [_250724])], (636 ^ _230414) ^ [] : [lt(619 ^ [_250724], 616 ^ [_250724])]], -(strictorderP(_250724))], (581 ^ _230414) ^ [] : [strictorderP(_250724), 584 ^ _230414 : [(585 ^ _230414) ^ [_251026] : [ssItem(_251026), 588 ^ _230414 : [(589 ^ _230414) ^ [_251216] : [ssItem(_251216), 592 ^ _230414 : [(593 ^ _230414) ^ [_251402] : [ssList(_251402), 596 ^ _230414 : [(597 ^ _230414) ^ [_251584] : [ssList(_251584), 600 ^ _230414 : [(601 ^ _230414) ^ [_251762] : [ssList(_251762), app(app(_251402, cons(_251026, _251584)), cons(_251216, _251762)) = _250724, -(lt(_251026, _251216)), -(lt(_251216, _251026))]]]]]]]]]]]]], (640 ^ _230414) ^ [_253488] : [ssList(_253488), 643 ^ _230414 : [(674 ^ _230414) ^ [] : [676 ^ _230414 : [(677 ^ _230414) ^ [] : [-(ssItem(675 ^ [_253488]))], (680 ^ _230414) ^ [] : [-(ssItem(678 ^ [_253488]))], (683 ^ _230414) ^ [] : [-(ssList(681 ^ [_253488]))], (686 ^ _230414) ^ [] : [-(ssList(684 ^ [_253488]))], (689 ^ _230414) ^ [] : [-(ssList(687 ^ [_253488]))], (691 ^ _230414) ^ [] : [-(app(app(681 ^ [_253488], cons(675 ^ [_253488], 684 ^ [_253488])), cons(678 ^ [_253488], 687 ^ [_253488])) = _253488)], (693 ^ _230414) ^ [] : [leq(675 ^ [_253488], 678 ^ [_253488])]], -(totalorderedP(_253488))], (644 ^ _230414) ^ [] : [totalorderedP(_253488), 647 ^ _230414 : [(648 ^ _230414) ^ [_253784] : [ssItem(_253784), 651 ^ _230414 : [(652 ^ _230414) ^ [_253968] : [ssItem(_253968), 655 ^ _230414 : [(656 ^ _230414) ^ [_254148] : [ssList(_254148), 659 ^ _230414 : [(660 ^ _230414) ^ [_254324] : [ssList(_254324), 663 ^ _230414 : [(664 ^ _230414) ^ [_254496] : [ssList(_254496), app(app(_254148, cons(_253784, _254324)), cons(_253968, _254496)) = _253488, -(leq(_253784, _253968))]]]]]]]]]]]]], (697 ^ _230414) ^ [_255976] : [ssList(_255976), 700 ^ _230414 : [(731 ^ _230414) ^ [] : [733 ^ _230414 : [(734 ^ _230414) ^ [] : [-(ssItem(732 ^ [_255976]))], (737 ^ _230414) ^ [] : [-(ssItem(735 ^ [_255976]))], (740 ^ _230414) ^ [] : [-(ssList(738 ^ [_255976]))], (743 ^ _230414) ^ [] : [-(ssList(741 ^ [_255976]))], (746 ^ _230414) ^ [] : [-(ssList(744 ^ [_255976]))], (748 ^ _230414) ^ [] : [-(app(app(738 ^ [_255976], cons(732 ^ [_255976], 741 ^ [_255976])), cons(735 ^ [_255976], 744 ^ [_255976])) = _255976)], (750 ^ _230414) ^ [] : [lt(732 ^ [_255976], 735 ^ [_255976])]], -(strictorderedP(_255976))], (701 ^ _230414) ^ [] : [strictorderedP(_255976), 704 ^ _230414 : [(705 ^ _230414) ^ [_256272] : [ssItem(_256272), 708 ^ _230414 : [(709 ^ _230414) ^ [_256456] : [ssItem(_256456), 712 ^ _230414 : [(713 ^ _230414) ^ [_256636] : [ssList(_256636), 716 ^ _230414 : [(717 ^ _230414) ^ [_256812] : [ssList(_256812), 720 ^ _230414 : [(721 ^ _230414) ^ [_256984] : [ssList(_256984), app(app(_256636, cons(_256272, _256812)), cons(_256456, _256984)) = _255976, -(lt(_256272, _256456))]]]]]]]]]]]]], (754 ^ _230414) ^ [_258464] : [ssList(_258464), 757 ^ _230414 : [(788 ^ _230414) ^ [] : [790 ^ _230414 : [(791 ^ _230414) ^ [] : [-(ssItem(789 ^ [_258464]))], (794 ^ _230414) ^ [] : [-(ssItem(792 ^ [_258464]))], (797 ^ _230414) ^ [] : [-(ssList(795 ^ [_258464]))], (800 ^ _230414) ^ [] : [-(ssList(798 ^ [_258464]))], (803 ^ _230414) ^ [] : [-(ssList(801 ^ [_258464]))], (805 ^ _230414) ^ [] : [-(app(app(795 ^ [_258464], cons(789 ^ [_258464], 798 ^ [_258464])), cons(792 ^ [_258464], 801 ^ [_258464])) = _258464)], (807 ^ _230414) ^ [] : [-(789 ^ [_258464] = 792 ^ [_258464])]], -(duplicatefreeP(_258464))], (758 ^ _230414) ^ [] : [duplicatefreeP(_258464), 761 ^ _230414 : [(762 ^ _230414) ^ [_258762] : [ssItem(_258762), 765 ^ _230414 : [(766 ^ _230414) ^ [_258948] : [ssItem(_258948), 769 ^ _230414 : [(770 ^ _230414) ^ [_259130] : [ssList(_259130), 773 ^ _230414 : [(774 ^ _230414) ^ [_259308] : [ssList(_259308), 777 ^ _230414 : [(778 ^ _230414) ^ [_259482] : [ssList(_259482), app(app(_259130, cons(_258762, _259308)), cons(_258948, _259482)) = _258464, _258762 = _258948]]]]]]]]]]]]], (811 ^ _230414) ^ [_260974] : [ssList(_260974), 814 ^ _230414 : [(841 ^ _230414) ^ [] : [843 ^ _230414 : [(844 ^ _230414) ^ [] : [-(ssItem(842 ^ [_260974]))], (847 ^ _230414) ^ [] : [-(ssItem(845 ^ [_260974]))], (850 ^ _230414) ^ [] : [-(ssList(848 ^ [_260974]))], (853 ^ _230414) ^ [] : [-(ssList(851 ^ [_260974]))], (855 ^ _230414) ^ [] : [-(app(848 ^ [_260974], cons(842 ^ [_260974], cons(845 ^ [_260974], 851 ^ [_260974]))) = _260974)], (857 ^ _230414) ^ [] : [842 ^ [_260974] = 845 ^ [_260974]]], -(equalelemsP(_260974))], (815 ^ _230414) ^ [] : [equalelemsP(_260974), 818 ^ _230414 : [(819 ^ _230414) ^ [_261257] : [ssItem(_261257), 822 ^ _230414 : [(823 ^ _230414) ^ [_261428] : [ssItem(_261428), 826 ^ _230414 : [(827 ^ _230414) ^ [_261595] : [ssList(_261595), 830 ^ _230414 : [(831 ^ _230414) ^ [_261758] : [ssList(_261758), app(_261595, cons(_261257, cons(_261428, _261758))) = _260974, -(_261257 = _261428)]]]]]]]]]]], (861 ^ _230414) ^ [_262991] : [ssList(_262991), 864 ^ _230414 : [(865 ^ _230414) ^ [_263129] : [ssList(_263129), 868 ^ _230414 : [(869 ^ _230414) ^ [] : [neq(_262991, _263129), _262991 = _263129], (875 ^ _230414) ^ [] : [-(_262991 = _263129), -(neq(_262991, _263129))]]]]], (881 ^ _230414) ^ [_263582] : [ssList(_263582), 884 ^ _230414 : [(885 ^ _230414) ^ [_263714] : [ssItem(_263714), -(ssList(cons(_263714, _263582)))]]], (891 ^ _230414) ^ [] : [-(ssList(nil))], (893 ^ _230414) ^ [_263972] : [ssList(_263972), 896 ^ _230414 : [(897 ^ _230414) ^ [_264107] : [ssItem(_264107), cons(_264107, _263972) = _263972]]], (903 ^ _230414) ^ [_264315] : [ssList(_264315), 906 ^ _230414 : [(907 ^ _230414) ^ [_264483] : [ssList(_264483), 910 ^ _230414 : [(911 ^ _230414) ^ [_264647] : [ssItem(_264647), 914 ^ _230414 : [(915 ^ _230414) ^ [_264807] : [ssItem(_264807), cons(_264647, _264315) = cons(_264807, _264483), 922 ^ _230414 : [(923 ^ _230414) ^ [] : [-(_264647 = _264807)], (925 ^ _230414) ^ [] : [-(_264483 = _264315)]]]]]]]]], (927 ^ _230414) ^ [_265222] : [ssList(_265222), -(nil = _265222), 935 ^ _230414 : [(936 ^ _230414) ^ [] : [-(ssList(934 ^ [_265222]))], (939 ^ _230414) ^ [] : [-(ssItem(937 ^ [_265222]))], (941 ^ _230414) ^ [] : [-(cons(937 ^ [_265222], 934 ^ [_265222]) = _265222)]]], (943 ^ _230414) ^ [_265786] : [ssList(_265786), 946 ^ _230414 : [(947 ^ _230414) ^ [_265921] : [ssItem(_265921), nil = cons(_265921, _265786)]]], (953 ^ _230414) ^ [_266129] : [ssList(_266129), -(nil = _266129), -(ssItem(hd(_266129)))], (963 ^ _230414) ^ [_266407] : [ssList(_266407), 966 ^ _230414 : [(967 ^ _230414) ^ [_266542] : [ssItem(_266542), -(hd(cons(_266542, _266407)) = _266542)]]], (973 ^ _230414) ^ [_266753] : [ssList(_266753), -(nil = _266753), -(ssList(tl(_266753)))], (983 ^ _230414) ^ [_267031] : [ssList(_267031), 986 ^ _230414 : [(987 ^ _230414) ^ [_267166] : [ssItem(_267166), -(tl(cons(_267166, _267031)) = _267031)]]], (993 ^ _230414) ^ [_267377] : [ssList(_267377), 996 ^ _230414 : [(997 ^ _230414) ^ [_267509] : [ssList(_267509), -(ssList(app(_267377, _267509)))]]], (1003 ^ _230414) ^ [_267714] : [ssList(_267714), 1006 ^ _230414 : [(1007 ^ _230414) ^ [_267866] : [ssList(_267866), 1010 ^ _230414 : [(1011 ^ _230414) ^ [_268014] : [ssItem(_268014), -(cons(_268014, app(_267866, _267714)) = app(cons(_268014, _267866), _267714))]]]]], (1017 ^ _230414) ^ [_268252] : [ssList(_268252), -(app(nil, _268252) = _268252)], (1023 ^ _230414) ^ [_268446] : [ssItem(_268446), 1026 ^ _230414 : [(1027 ^ _230414) ^ [_268588] : [ssItem(_268588), -(_268446 = _268588), leq(_268446, _268588), leq(_268588, _268446)]]], (1041 ^ _230414) ^ [_268967] : [ssItem(_268967), 1044 ^ _230414 : [(1045 ^ _230414) ^ [_269119] : [ssItem(_269119), 1048 ^ _230414 : [(1049 ^ _230414) ^ [_269267] : [ssItem(_269267), -(leq(_268967, _269267)), leq(_268967, _269119), leq(_269119, _269267)]]]]], (1063 ^ _230414) ^ [_269667] : [ssItem(_269667), -(leq(_269667, _269667))], (1069 ^ _230414) ^ [_269855] : [ssItem(_269855), 1072 ^ _230414 : [(1073 ^ _230414) ^ [_269991] : [ssItem(_269991), 1076 ^ _230414 : [(1077 ^ _230414) ^ [] : [geq(_269855, _269991), -(leq(_269991, _269855))], (1083 ^ _230414) ^ [] : [leq(_269991, _269855), -(geq(_269855, _269991))]]]]], (1089 ^ _230414) ^ [_270442] : [ssItem(_270442), 1092 ^ _230414 : [(1093 ^ _230414) ^ [_270580] : [ssItem(_270580), lt(_270442, _270580), lt(_270580, _270442)]]], (1103 ^ _230414) ^ [_270871] : [ssItem(_270871), 1106 ^ _230414 : [(1107 ^ _230414) ^ [_271023] : [ssItem(_271023), 1110 ^ _230414 : [(1111 ^ _230414) ^ [_271171] : [ssItem(_271171), -(lt(_270871, _271171)), lt(_270871, _271023), lt(_271023, _271171)]]]]], (1125 ^ _230414) ^ [_271571] : [ssItem(_271571), 1128 ^ _230414 : [(1129 ^ _230414) ^ [_271707] : [ssItem(_271707), 1132 ^ _230414 : [(1133 ^ _230414) ^ [] : [gt(_271571, _271707), -(lt(_271707, _271571))], (1139 ^ _230414) ^ [] : [lt(_271707, _271571), -(gt(_271571, _271707))]]]]], (1145 ^ _230414) ^ [_272158] : [ssItem(_272158), 1148 ^ _230414 : [(1149 ^ _230414) ^ [_272313] : [ssList(_272313), 1152 ^ _230414 : [(1153 ^ _230414) ^ [_272464] : [ssList(_272464), 1156 ^ _230414 : [(1167 ^ _230414) ^ [] : [1168 ^ _230414 : [(1169 ^ _230414) ^ [] : [memberP(_272313, _272158)], (1171 ^ _230414) ^ [] : [memberP(_272464, _272158)]], -(memberP(app(_272313, _272464), _272158))], (1157 ^ _230414) ^ [] : [memberP(app(_272313, _272464), _272158), -(memberP(_272313, _272158)), -(memberP(_272464, _272158))]]]]]]], (1175 ^ _230414) ^ [_273111] : [ssItem(_273111), 1178 ^ _230414 : [(1179 ^ _230414) ^ [_273266] : [ssItem(_273266), 1182 ^ _230414 : [(1183 ^ _230414) ^ [_273417] : [ssList(_273417), 1186 ^ _230414 : [(1197 ^ _230414) ^ [] : [1198 ^ _230414 : [(1199 ^ _230414) ^ [] : [_273111 = _273266], (1201 ^ _230414) ^ [] : [memberP(_273417, _273111)]], -(memberP(cons(_273266, _273417), _273111))], (1187 ^ _230414) ^ [] : [memberP(cons(_273266, _273417), _273111), -(_273111 = _273266), -(memberP(_273417, _273111))]]]]]]], (1205 ^ _230414) ^ [_274064] : [ssItem(_274064), memberP(nil, _274064)], (1211 ^ _230414) ^ [] : [singletonP(nil)], (1213 ^ _230414) ^ [_274305] : [ssList(_274305), 1216 ^ _230414 : [(1217 ^ _230414) ^ [_274457] : [ssList(_274457), 1220 ^ _230414 : [(1221 ^ _230414) ^ [_274605] : [ssList(_274605), -(frontsegP(_274305, _274605)), frontsegP(_274305, _274457), frontsegP(_274457, _274605)]]]]], (1235 ^ _230414) ^ [_275005] : [ssList(_275005), 1238 ^ _230414 : [(1239 ^ _230414) ^ [_275147] : [ssList(_275147), -(_275005 = _275147), frontsegP(_275005, _275147), frontsegP(_275147, _275005)]]], (1253 ^ _230414) ^ [_275526] : [ssList(_275526), -(frontsegP(_275526, _275526))], (1259 ^ _230414) ^ [_275714] : [ssList(_275714), 1262 ^ _230414 : [(1263 ^ _230414) ^ [_275863] : [ssList(_275863), 1266 ^ _230414 : [(1267 ^ _230414) ^ [_276008] : [ssList(_276008), frontsegP(_275714, _275863), -(frontsegP(app(_275714, _276008), _275863))]]]]], (1277 ^ _230414) ^ [_276321] : [ssItem(_276321), 1280 ^ _230414 : [(1281 ^ _230414) ^ [_276489] : [ssItem(_276489), 1284 ^ _230414 : [(1285 ^ _230414) ^ [_276653] : [ssList(_276653), 1288 ^ _230414 : [(1289 ^ _230414) ^ [_276813] : [ssList(_276813), 1292 ^ _230414 : [(1293 ^ _230414) ^ [] : [frontsegP(cons(_276321, _276653), cons(_276489, _276813)), 1296 ^ _230414 : [(1297 ^ _230414) ^ [] : [-(_276321 = _276489)], (1299 ^ _230414) ^ [] : [-(frontsegP(_276653, _276813))]]], (1301 ^ _230414) ^ [] : [-(frontsegP(cons(_276321, _276653), cons(_276489, _276813))), _276321 = _276489, frontsegP(_276653, _276813)]]]]]]]]], (1311 ^ _230414) ^ [_277498] : [ssList(_277498), -(frontsegP(_277498, nil))], (1317 ^ _230414) ^ [_277686] : [ssList(_277686), 1320 ^ _230414 : [(1321 ^ _230414) ^ [] : [frontsegP(nil, _277686), -(nil = _277686)], (1327 ^ _230414) ^ [] : [nil = _277686, -(frontsegP(nil, _277686))]]], (1333 ^ _230414) ^ [_278114] : [ssList(_278114), 1336 ^ _230414 : [(1337 ^ _230414) ^ [_278266] : [ssList(_278266), 1340 ^ _230414 : [(1341 ^ _230414) ^ [_278414] : [ssList(_278414), -(rearsegP(_278114, _278414)), rearsegP(_278114, _278266), rearsegP(_278266, _278414)]]]]], (1355 ^ _230414) ^ [_278814] : [ssList(_278814), 1358 ^ _230414 : [(1359 ^ _230414) ^ [_278956] : [ssList(_278956), -(_278814 = _278956), rearsegP(_278814, _278956), rearsegP(_278956, _278814)]]], (1373 ^ _230414) ^ [_279335] : [ssList(_279335), -(rearsegP(_279335, _279335))], (1379 ^ _230414) ^ [_279523] : [ssList(_279523), 1382 ^ _230414 : [(1383 ^ _230414) ^ [_279672] : [ssList(_279672), 1386 ^ _230414 : [(1387 ^ _230414) ^ [_279817] : [ssList(_279817), rearsegP(_279523, _279672), -(rearsegP(app(_279817, _279523), _279672))]]]]], (1397 ^ _230414) ^ [_280130] : [ssList(_280130), -(rearsegP(_280130, nil))], (1403 ^ _230414) ^ [_280318] : [ssList(_280318), 1406 ^ _230414 : [(1407 ^ _230414) ^ [] : [rearsegP(nil, _280318), -(nil = _280318)], (1413 ^ _230414) ^ [] : [nil = _280318, -(rearsegP(nil, _280318))]]], (1419 ^ _230414) ^ [_280746] : [ssList(_280746), 1422 ^ _230414 : [(1423 ^ _230414) ^ [_280898] : [ssList(_280898), 1426 ^ _230414 : [(1427 ^ _230414) ^ [_281046] : [ssList(_281046), -(segmentP(_280746, _281046)), segmentP(_280746, _280898), segmentP(_280898, _281046)]]]]], (1441 ^ _230414) ^ [_281446] : [ssList(_281446), 1444 ^ _230414 : [(1445 ^ _230414) ^ [_281588] : [ssList(_281588), -(_281446 = _281588), segmentP(_281446, _281588), segmentP(_281588, _281446)]]], (1459 ^ _230414) ^ [_281967] : [ssList(_281967), -(segmentP(_281967, _281967))], (1465 ^ _230414) ^ [_282155] : [ssList(_282155), 1468 ^ _230414 : [(1469 ^ _230414) ^ [_282317] : [ssList(_282317), 1472 ^ _230414 : [(1473 ^ _230414) ^ [_282475] : [ssList(_282475), 1476 ^ _230414 : [(1477 ^ _230414) ^ [_282629] : [ssList(_282629), segmentP(_282155, _282317), -(segmentP(app(app(_282475, _282155), _282629), _282317))]]]]]]], (1487 ^ _230414) ^ [_282965] : [ssList(_282965), -(segmentP(_282965, nil))], (1493 ^ _230414) ^ [_283153] : [ssList(_283153), 1496 ^ _230414 : [(1497 ^ _230414) ^ [] : [segmentP(nil, _283153), -(nil = _283153)], (1503 ^ _230414) ^ [] : [nil = _283153, -(segmentP(nil, _283153))]]], (1509 ^ _230414) ^ [_283581] : [ssItem(_283581), -(cyclefreeP(cons(_283581, nil)))], (1515 ^ _230414) ^ [] : [-(cyclefreeP(nil))], (1517 ^ _230414) ^ [_283826] : [ssItem(_283826), -(totalorderP(cons(_283826, nil)))], (1523 ^ _230414) ^ [] : [-(totalorderP(nil))], (1525 ^ _230414) ^ [_284071] : [ssItem(_284071), -(strictorderP(cons(_284071, nil)))], (1531 ^ _230414) ^ [] : [-(strictorderP(nil))], (1533 ^ _230414) ^ [_284316] : [ssItem(_284316), -(totalorderedP(cons(_284316, nil)))], (1539 ^ _230414) ^ [] : [-(totalorderedP(nil))], (1541 ^ _230414) ^ [_284561] : [ssItem(_284561), 1544 ^ _230414 : [(1545 ^ _230414) ^ [_284720] : [ssList(_284720), 1548 ^ _230414 : [(1549 ^ _230414) ^ [] : [totalorderedP(cons(_284561, _284720)), -(nil = _284720), 1556 ^ _230414 : [(1557 ^ _230414) ^ [] : [nil = _284720], (1559 ^ _230414) ^ [] : [-(totalorderedP(_284720))], (1561 ^ _230414) ^ [] : [-(leq(_284561, hd(_284720)))]]], (1563 ^ _230414) ^ [] : [-(totalorderedP(cons(_284561, _284720))), 1564 ^ _230414 : [(1565 ^ _230414) ^ [] : [nil = _284720], (1567 ^ _230414) ^ [] : [-(nil = _284720), totalorderedP(_284720), leq(_284561, hd(_284720))]]]]]]], (1579 ^ _230414) ^ [_285655] : [ssItem(_285655), -(strictorderedP(cons(_285655, nil)))], (1585 ^ _230414) ^ [] : [-(strictorderedP(nil))], (1587 ^ _230414) ^ [_285900] : [ssItem(_285900), 1590 ^ _230414 : [(1591 ^ _230414) ^ [_286059] : [ssList(_286059), 1594 ^ _230414 : [(1595 ^ _230414) ^ [] : [strictorderedP(cons(_285900, _286059)), -(nil = _286059), 1602 ^ _230414 : [(1603 ^ _230414) ^ [] : [nil = _286059], (1605 ^ _230414) ^ [] : [-(strictorderedP(_286059))], (1607 ^ _230414) ^ [] : [-(lt(_285900, hd(_286059)))]]], (1609 ^ _230414) ^ [] : [-(strictorderedP(cons(_285900, _286059))), 1610 ^ _230414 : [(1611 ^ _230414) ^ [] : [nil = _286059], (1613 ^ _230414) ^ [] : [-(nil = _286059), strictorderedP(_286059), lt(_285900, hd(_286059))]]]]]]], (1625 ^ _230414) ^ [_286994] : [ssItem(_286994), -(duplicatefreeP(cons(_286994, nil)))], (1631 ^ _230414) ^ [] : [-(duplicatefreeP(nil))], (1633 ^ _230414) ^ [_287239] : [ssItem(_287239), -(equalelemsP(cons(_287239, nil)))], (1639 ^ _230414) ^ [] : [-(equalelemsP(nil))], (1641 ^ _230414) ^ [_287484] : [ssList(_287484), -(nil = _287484), 1649 ^ _230414 : [(1650 ^ _230414) ^ [] : [-(ssItem(1648 ^ [_287484]))], (1652 ^ _230414) ^ [] : [-(hd(_287484) = 1648 ^ [_287484])]]], (1654 ^ _230414) ^ [_287898] : [ssList(_287898), -(nil = _287898), 1662 ^ _230414 : [(1663 ^ _230414) ^ [] : [-(ssList(1661 ^ [_287898]))], (1665 ^ _230414) ^ [] : [-(tl(_287898) = 1661 ^ [_287898])]]], (1667 ^ _230414) ^ [_288312] : [ssList(_288312), 1670 ^ _230414 : [(1671 ^ _230414) ^ [_288478] : [ssList(_288478), -(_288478 = _288312), -(nil = _288478), -(nil = _288312), hd(_288478) = hd(_288312), tl(_288478) = tl(_288312)]]], (1693 ^ _230414) ^ [_289057] : [ssList(_289057), -(nil = _289057), -(cons(hd(_289057), tl(_289057)) = _289057)], (1703 ^ _230414) ^ [_289347] : [ssList(_289347), 1706 ^ _230414 : [(1707 ^ _230414) ^ [_289499] : [ssList(_289499), 1710 ^ _230414 : [(1711 ^ _230414) ^ [_289647] : [ssList(_289647), app(_289647, _289499) = app(_289347, _289499), -(_289647 = _289347)]]]]], (1721 ^ _230414) ^ [_289966] : [ssList(_289966), 1724 ^ _230414 : [(1725 ^ _230414) ^ [_290118] : [ssList(_290118), 1728 ^ _230414 : [(1729 ^ _230414) ^ [_290266] : [ssList(_290266), app(_290118, _290266) = app(_290118, _289966), -(_290266 = _289966)]]]]], (1739 ^ _230414) ^ [_290585] : [ssList(_290585), 1742 ^ _230414 : [(1743 ^ _230414) ^ [_290724] : [ssItem(_290724), -(cons(_290724, _290585) = app(cons(_290724, nil), _290585))]]], (1749 ^ _230414) ^ [_290943] : [ssList(_290943), 1752 ^ _230414 : [(1753 ^ _230414) ^ [_291095] : [ssList(_291095), 1756 ^ _230414 : [(1757 ^ _230414) ^ [_291243] : [ssList(_291243), -(app(app(_290943, _291095), _291243) = app(_290943, app(_291095, _291243)))]]]]], (1763 ^ _230414) ^ [_291481] : [ssList(_291481), 1766 ^ _230414 : [(1767 ^ _230414) ^ [_291626] : [ssList(_291626), 1770 ^ _230414 : [(1771 ^ _230414) ^ [] : [nil = app(_291481, _291626), 1774 ^ _230414 : [(1775 ^ _230414) ^ [] : [-(nil = _291626)], (1777 ^ _230414) ^ [] : [-(nil = _291481)]]], (1779 ^ _230414) ^ [] : [-(nil = app(_291481, _291626)), nil = _291626, nil = _291481]]]]], (1789 ^ _230414) ^ [_292244] : [ssList(_292244), -(app(_292244, nil) = _292244)], (1795 ^ _230414) ^ [_292438] : [ssList(_292438), 1798 ^ _230414 : [(1799 ^ _230414) ^ [_292583] : [ssList(_292583), -(nil = _292438), -(hd(app(_292438, _292583)) = hd(_292438))]]], (1809 ^ _230414) ^ [_292890] : [ssList(_292890), 1812 ^ _230414 : [(1813 ^ _230414) ^ [_293038] : [ssList(_293038), -(nil = _292890), -(tl(app(_292890, _293038)) = app(tl(_292890), _293038))]]], (1823 ^ _230414) ^ [_293351] : [ssItem(_293351), 1826 ^ _230414 : [(1827 ^ _230414) ^ [_293493] : [ssItem(_293493), -(_293351 = _293493), geq(_293351, _293493), geq(_293493, _293351)]]], (1841 ^ _230414) ^ [_293872] : [ssItem(_293872), 1844 ^ _230414 : [(1845 ^ _230414) ^ [_294024] : [ssItem(_294024), 1848 ^ _230414 : [(1849 ^ _230414) ^ [_294172] : [ssItem(_294172), -(geq(_293872, _294172)), geq(_293872, _294024), geq(_294024, _294172)]]]]], (1863 ^ _230414) ^ [_294572] : [ssItem(_294572), -(geq(_294572, _294572))], (1869 ^ _230414) ^ [_294760] : [ssItem(_294760), lt(_294760, _294760)], (1875 ^ _230414) ^ [_294949] : [ssItem(_294949), 1878 ^ _230414 : [(1879 ^ _230414) ^ [_295101] : [ssItem(_295101), 1882 ^ _230414 : [(1883 ^ _230414) ^ [_295249] : [ssItem(_295249), -(lt(_294949, _295249)), leq(_294949, _295101), lt(_295101, _295249)]]]]], (1897 ^ _230414) ^ [_295649] : [ssItem(_295649), 1900 ^ _230414 : [(1901 ^ _230414) ^ [_295791] : [ssItem(_295791), leq(_295649, _295791), -(_295649 = _295791), -(lt(_295649, _295791))]]], (1915 ^ _230414) ^ [_296171] : [ssItem(_296171), 1918 ^ _230414 : [(1919 ^ _230414) ^ [_296315] : [ssItem(_296315), 1922 ^ _230414 : [(1923 ^ _230414) ^ [] : [lt(_296171, _296315), 1926 ^ _230414 : [(1927 ^ _230414) ^ [] : [_296171 = _296315], (1929 ^ _230414) ^ [] : [-(leq(_296171, _296315))]]], (1931 ^ _230414) ^ [] : [-(lt(_296171, _296315)), -(_296171 = _296315), leq(_296171, _296315)]]]]], (1941 ^ _230414) ^ [_296926] : [ssItem(_296926), 1944 ^ _230414 : [(1945 ^ _230414) ^ [_297064] : [ssItem(_297064), gt(_296926, _297064), gt(_297064, _296926)]]], (1955 ^ _230414) ^ [_297335] : [ssItem(_297335), 1958 ^ _230414 : [(1959 ^ _230414) ^ [_297487] : [ssItem(_297487), 1962 ^ _230414 : [(1963 ^ _230414) ^ [_297635] : [ssItem(_297635), -(gt(_297335, _297635)), gt(_297335, _297487), gt(_297487, _297635)]]]]]], input).
% 14.02/13.80  ncf('1',plain,[neq(1985 ^ [], nil)],start(1993 ^ 0)).
% 14.02/13.80  ncf('1.1',plain,[-(neq(1985 ^ [], nil)), 875 : -(1985 ^ [] = nil), 875 : ssList(nil), 865 : ssList(1985 ^ [])],extension(861 ^ 1,bind([[_262991, _263129], [1985 ^ [], nil]]))).
% 14.02/13.80  ncf('1.1.1',plain,[1985 ^ [] = nil, -(nil = 1985 ^ [])],extension(4 ^ 6,bind([[_230665, _230667], [nil, 1985 ^ []]]))).
% 14.02/13.80  ncf('1.1.1.1',plain,[nil = 1985 ^ [], -(nil = 1979 ^ []), 1985 ^ [] = 1979 ^ []],extension(10 ^ 7,bind([[_230869, _230871, _230873], [1979 ^ [], 1985 ^ [], nil]]))).
% 14.02/13.80  ncf('1.1.1.1.1',plain,[nil = 1979 ^ [], -(cyclefreeP(1979 ^ [])), cyclefreeP(nil)],extension(236 ^ 8,bind([[_237813, _237815], [1979 ^ [], nil]]))).
% 14.02/13.80  ncf('1.1.1.1.1.1',plain,[cyclefreeP(1979 ^ [])],extension(1995 ^ 9)).
% 14.02/13.80  ncf('1.1.1.1.1.2',plain,[-(cyclefreeP(nil))],extension(1515 ^ 9)).
% 14.02/13.80  ncf('1.1.1.1.2',plain,[-(1985 ^ [] = 1979 ^ []), 1979 ^ [] = 1985 ^ []],extension(4 ^ 8,bind([[_230665, _230667], [1985 ^ [], 1979 ^ []]]))).
% 14.02/13.80  ncf('1.1.1.1.2.1',plain,[-(1979 ^ [] = 1985 ^ [])],extension(1989 ^ 9)).
% 14.02/13.80  ncf('1.1.2',plain,[-(ssList(nil))],extension(891 ^ 4)).
% 14.02/13.80  ncf('1.1.3',plain,[-(ssList(1985 ^ []))],extension(1987 ^ 2)).
% 14.02/13.80  %-----------------------------------------------------
% 14.02/13.80  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------