%------------------------------------------------------------------------------
% File : nanoCoP---2.0
% Problem : SWC128+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : nanocop.sh %s %d
% Computer : n018.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 12:12:36 EDT 2023
% Result : Theorem 0.32s 1.38s
% Output : Proof 0.32s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWC128+1 : TPTP v8.1.2. Released v2.4.0.
% 0.11/0.12 % Command : nanocop.sh %s %d
% 0.12/0.33 % Computer : n018.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 01:27:58 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.32/1.38
% 0.32/1.38 /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 0.32/1.38 Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.32/1.38 %-----------------------------------------------------
% 0.32/1.38 ncf(matrix, plain, [(1977 ^ _225329) ^ [] : [-(true___)], (1979 ^ _225329) ^ [] : [true___], (246 ^ _225329) ^ [_233133, _233135, _233137, _233139] : [-(cons(_233139, _233135) = cons(_233137, _233133)), _233139 = _233137, _233135 = _233133], (256 ^ _225329) ^ [_233464, _233466] : [_233466 = _233464, -(hd(_233466) = hd(_233464))], (272 ^ _225329) ^ [_234021, _234023] : [_234023 = _234021, -(tl(_234023) = tl(_234021))], (262 ^ _225329) ^ [_233710, _233712, _233714, _233716] : [-(app(_233716, _233712) = app(_233714, _233710)), _233716 = _233714, _233712 = _233710], (2 ^ _225329) ^ [_225473] : [-(_225473 = _225473)], (4 ^ _225329) ^ [_225580, _225582] : [_225582 = _225580, -(_225580 = _225582)], (10 ^ _225329) ^ [_225784, _225786, _225788] : [-(_225788 = _225784), _225788 = _225786, _225786 = _225784], (20 ^ _225329) ^ [_226125, _226127, _226129, _226131] : [-(neq(_226129, _226125)), neq(_226131, _226127), _226131 = _226129, _226127 = _226125], (34 ^ _225329) ^ [_226569, _226571, _226573, _226575] : [-(memberP(_226573, _226569)), memberP(_226575, _226571), _226575 = _226573, _226571 = _226569], (48 ^ _225329) ^ [_226985, _226987] : [-(singletonP(_226985)), _226987 = _226985, singletonP(_226987)], (58 ^ _225329) ^ [_227308, _227310, _227312, _227314] : [-(frontsegP(_227312, _227308)), frontsegP(_227314, _227310), _227314 = _227312, _227310 = _227308], (72 ^ _225329) ^ [_227752, _227754, _227756, _227758] : [-(rearsegP(_227756, _227752)), rearsegP(_227758, _227754), _227758 = _227756, _227754 = _227752], (86 ^ _225329) ^ [_228196, _228198, _228200, _228202] : [-(segmentP(_228200, _228196)), segmentP(_228202, _228198), _228202 = _228200, _228198 = _228196], (100 ^ _225329) ^ [_228612, _228614] : [-(cyclefreeP(_228612)), _228614 = _228612, cyclefreeP(_228614)], (110 ^ _225329) ^ [_228907, _228909] : [-(totalorderP(_228907)), _228909 = _228907, totalorderP(_228909)], (120 ^ _225329) ^ [_229202, _229204] : [-(strictorderP(_229202)), _229204 = _229202, strictorderP(_229204)], (130 ^ _225329) ^ [_229497, _229499] : [-(totalorderedP(_229497)), _229499 = _229497, totalorderedP(_229499)], (140 ^ _225329) ^ [_229792, _229794] : [-(strictorderedP(_229792)), _229794 = _229792, strictorderedP(_229794)], (150 ^ _225329) ^ [_230087, _230089] : [-(duplicatefreeP(_230087)), _230089 = _230087, duplicatefreeP(_230089)], (160 ^ _225329) ^ [_230382, _230384] : [-(equalelemsP(_230382)), _230384 = _230382, equalelemsP(_230384)], (170 ^ _225329) ^ [_230677, _230679] : [-(ssList(_230677)), _230679 = _230677, ssList(_230679)], (180 ^ _225329) ^ [_231000, _231002, _231004, _231006] : [-(geq(_231004, _231000)), geq(_231006, _231002), _231006 = _231004, _231002 = _231000], (194 ^ _225329) ^ [_231444, _231446, _231448, _231450] : [-(lt(_231448, _231444)), lt(_231450, _231446), _231450 = _231448, _231446 = _231444], (208 ^ _225329) ^ [_231888, _231890, _231892, _231894] : [-(leq(_231892, _231888)), leq(_231894, _231890), _231894 = _231892, _231890 = _231888], (222 ^ _225329) ^ [_232304, _232306] : [-(ssItem(_232304)), _232306 = _232304, ssItem(_232306)], (232 ^ _225329) ^ [_232607, _232609, _232611, _232613] : [-(gt(_232611, _232607)), gt(_232613, _232609), _232613 = _232611, _232609 = _232607], (278 ^ _225329) ^ [_234243] : [ssItem(_234243), 281 ^ _225329 : [(282 ^ _225329) ^ [_234381] : [ssItem(_234381), 285 ^ _225329 : [(286 ^ _225329) ^ [] : [neq(_234243, _234381), _234243 = _234381], (292 ^ _225329) ^ [] : [-(_234243 = _234381), -(neq(_234243, _234381))]]]]], (299 ^ _225329) ^ [] : [-(ssItem(297 ^ []))], (302 ^ _225329) ^ [] : [-(ssItem(300 ^ []))], (304 ^ _225329) ^ [] : [297 ^ [] = 300 ^ []], (306 ^ _225329) ^ [_235094] : [ssList(_235094), 309 ^ _225329 : [(310 ^ _225329) ^ [_235256] : [ssItem(_235256), 313 ^ _225329 : [(314 ^ _225329) ^ [] : [memberP(_235094, _235256), 318 ^ _225329 : [(319 ^ _225329) ^ [] : [-(ssList(317 ^ [_235094, _235256]))], (322 ^ _225329) ^ [] : [-(ssList(320 ^ [_235094, _235256]))], (324 ^ _225329) ^ [] : [-(app(317 ^ [_235094, _235256], cons(_235256, 320 ^ [_235094, _235256])) = _235094)]]], (326 ^ _225329) ^ [] : [-(memberP(_235094, _235256)), 327 ^ _225329 : [(328 ^ _225329) ^ [_235904] : [ssList(_235904), 331 ^ _225329 : [(332 ^ _225329) ^ [_236052] : [ssList(_236052), app(_235904, cons(_235256, _236052)) = _235094]]]]]]]]], (340 ^ _225329) ^ [_236343] : [ssList(_236343), 343 ^ _225329 : [(344 ^ _225329) ^ [] : [singletonP(_236343), 348 ^ _225329 : [(349 ^ _225329) ^ [] : [-(ssItem(347 ^ [_236343]))], (351 ^ _225329) ^ [] : [-(cons(347 ^ [_236343], nil) = _236343)]]], (353 ^ _225329) ^ [] : [-(singletonP(_236343)), 354 ^ _225329 : [(355 ^ _225329) ^ [_236792] : [ssItem(_236792), cons(_236792, nil) = _236343]]]]], (363 ^ _225329) ^ [_237048] : [ssList(_237048), 366 ^ _225329 : [(367 ^ _225329) ^ [_237197] : [ssList(_237197), 370 ^ _225329 : [(371 ^ _225329) ^ [] : [frontsegP(_237048, _237197), 375 ^ _225329 : [(376 ^ _225329) ^ [] : [-(ssList(374 ^ [_237048, _237197]))], (378 ^ _225329) ^ [] : [-(app(_237197, 374 ^ [_237048, _237197]) = _237048)]]], (380 ^ _225329) ^ [] : [-(frontsegP(_237048, _237197)), 381 ^ _225329 : [(382 ^ _225329) ^ [_237672] : [ssList(_237672), app(_237197, _237672) = _237048]]]]]]], (390 ^ _225329) ^ [_237944] : [ssList(_237944), 393 ^ _225329 : [(394 ^ _225329) ^ [_238093] : [ssList(_238093), 397 ^ _225329 : [(398 ^ _225329) ^ [] : [rearsegP(_237944, _238093), 402 ^ _225329 : [(403 ^ _225329) ^ [] : [-(ssList(401 ^ [_237944, _238093]))], (405 ^ _225329) ^ [] : [-(app(401 ^ [_237944, _238093], _238093) = _237944)]]], (407 ^ _225329) ^ [] : [-(rearsegP(_237944, _238093)), 408 ^ _225329 : [(409 ^ _225329) ^ [_238568] : [ssList(_238568), app(_238568, _238093) = _237944]]]]]]], (417 ^ _225329) ^ [_238840] : [ssList(_238840), 420 ^ _225329 : [(421 ^ _225329) ^ [_239002] : [ssList(_239002), 424 ^ _225329 : [(425 ^ _225329) ^ [] : [segmentP(_238840, _239002), 429 ^ _225329 : [(430 ^ _225329) ^ [] : [-(ssList(428 ^ [_238840, _239002]))], (433 ^ _225329) ^ [] : [-(ssList(431 ^ [_238840, _239002]))], (435 ^ _225329) ^ [] : [-(app(app(428 ^ [_238840, _239002], _239002), 431 ^ [_238840, _239002]) = _238840)]]], (437 ^ _225329) ^ [] : [-(segmentP(_238840, _239002)), 438 ^ _225329 : [(439 ^ _225329) ^ [_239650] : [ssList(_239650), 442 ^ _225329 : [(443 ^ _225329) ^ [_239798] : [ssList(_239798), app(app(_239650, _239002), _239798) = _238840]]]]]]]]], (451 ^ _225329) ^ [_240089] : [ssList(_240089), 454 ^ _225329 : [(489 ^ _225329) ^ [] : [491 ^ _225329 : [(492 ^ _225329) ^ [] : [-(ssItem(490 ^ [_240089]))], (495 ^ _225329) ^ [] : [-(ssItem(493 ^ [_240089]))], (498 ^ _225329) ^ [] : [-(ssList(496 ^ [_240089]))], (501 ^ _225329) ^ [] : [-(ssList(499 ^ [_240089]))], (504 ^ _225329) ^ [] : [-(ssList(502 ^ [_240089]))], (506 ^ _225329) ^ [] : [-(app(app(496 ^ [_240089], cons(490 ^ [_240089], 499 ^ [_240089])), cons(493 ^ [_240089], 502 ^ [_240089])) = _240089)], (508 ^ _225329) ^ [] : [-(leq(490 ^ [_240089], 493 ^ [_240089]))], (510 ^ _225329) ^ [] : [-(leq(493 ^ [_240089], 490 ^ [_240089]))]], -(cyclefreeP(_240089))], (455 ^ _225329) ^ [] : [cyclefreeP(_240089), 458 ^ _225329 : [(459 ^ _225329) ^ [_240393] : [ssItem(_240393), 462 ^ _225329 : [(463 ^ _225329) ^ [_240585] : [ssItem(_240585), 466 ^ _225329 : [(467 ^ _225329) ^ [_240773] : [ssList(_240773), 470 ^ _225329 : [(471 ^ _225329) ^ [_240957] : [ssList(_240957), 474 ^ _225329 : [(475 ^ _225329) ^ [_241137] : [ssList(_241137), app(app(_240773, cons(_240393, _240957)), cons(_240585, _241137)) = _240089, leq(_240393, _240585), leq(_240585, _240393)]]]]]]]]]]]]], (514 ^ _225329) ^ [_242875] : [ssList(_242875), 517 ^ _225329 : [(552 ^ _225329) ^ [] : [554 ^ _225329 : [(555 ^ _225329) ^ [] : [-(ssItem(553 ^ [_242875]))], (558 ^ _225329) ^ [] : [-(ssItem(556 ^ [_242875]))], (561 ^ _225329) ^ [] : [-(ssList(559 ^ [_242875]))], (564 ^ _225329) ^ [] : [-(ssList(562 ^ [_242875]))], (567 ^ _225329) ^ [] : [-(ssList(565 ^ [_242875]))], (569 ^ _225329) ^ [] : [-(app(app(559 ^ [_242875], cons(553 ^ [_242875], 562 ^ [_242875])), cons(556 ^ [_242875], 565 ^ [_242875])) = _242875)], (571 ^ _225329) ^ [] : [leq(553 ^ [_242875], 556 ^ [_242875])], (573 ^ _225329) ^ [] : [leq(556 ^ [_242875], 553 ^ [_242875])]], -(totalorderP(_242875))], (518 ^ _225329) ^ [] : [totalorderP(_242875), 521 ^ _225329 : [(522 ^ _225329) ^ [_243177] : [ssItem(_243177), 525 ^ _225329 : [(526 ^ _225329) ^ [_243367] : [ssItem(_243367), 529 ^ _225329 : [(530 ^ _225329) ^ [_243553] : [ssList(_243553), 533 ^ _225329 : [(534 ^ _225329) ^ [_243735] : [ssList(_243735), 537 ^ _225329 : [(538 ^ _225329) ^ [_243913] : [ssList(_243913), app(app(_243553, cons(_243177, _243735)), cons(_243367, _243913)) = _242875, -(leq(_243177, _243367)), -(leq(_243367, _243177))]]]]]]]]]]]]], (577 ^ _225329) ^ [_245639] : [ssList(_245639), 580 ^ _225329 : [(615 ^ _225329) ^ [] : [617 ^ _225329 : [(618 ^ _225329) ^ [] : [-(ssItem(616 ^ [_245639]))], (621 ^ _225329) ^ [] : [-(ssItem(619 ^ [_245639]))], (624 ^ _225329) ^ [] : [-(ssList(622 ^ [_245639]))], (627 ^ _225329) ^ [] : [-(ssList(625 ^ [_245639]))], (630 ^ _225329) ^ [] : [-(ssList(628 ^ [_245639]))], (632 ^ _225329) ^ [] : [-(app(app(622 ^ [_245639], cons(616 ^ [_245639], 625 ^ [_245639])), cons(619 ^ [_245639], 628 ^ [_245639])) = _245639)], (634 ^ _225329) ^ [] : [lt(616 ^ [_245639], 619 ^ [_245639])], (636 ^ _225329) ^ [] : [lt(619 ^ [_245639], 616 ^ [_245639])]], -(strictorderP(_245639))], (581 ^ _225329) ^ [] : [strictorderP(_245639), 584 ^ _225329 : [(585 ^ _225329) ^ [_245941] : [ssItem(_245941), 588 ^ _225329 : [(589 ^ _225329) ^ [_246131] : [ssItem(_246131), 592 ^ _225329 : [(593 ^ _225329) ^ [_246317] : [ssList(_246317), 596 ^ _225329 : [(597 ^ _225329) ^ [_246499] : [ssList(_246499), 600 ^ _225329 : [(601 ^ _225329) ^ [_246677] : [ssList(_246677), app(app(_246317, cons(_245941, _246499)), cons(_246131, _246677)) = _245639, -(lt(_245941, _246131)), -(lt(_246131, _245941))]]]]]]]]]]]]], (640 ^ _225329) ^ [_248403] : [ssList(_248403), 643 ^ _225329 : [(674 ^ _225329) ^ [] : [676 ^ _225329 : [(677 ^ _225329) ^ [] : [-(ssItem(675 ^ [_248403]))], (680 ^ _225329) ^ [] : [-(ssItem(678 ^ [_248403]))], (683 ^ _225329) ^ [] : [-(ssList(681 ^ [_248403]))], (686 ^ _225329) ^ [] : [-(ssList(684 ^ [_248403]))], (689 ^ _225329) ^ [] : [-(ssList(687 ^ [_248403]))], (691 ^ _225329) ^ [] : [-(app(app(681 ^ [_248403], cons(675 ^ [_248403], 684 ^ [_248403])), cons(678 ^ [_248403], 687 ^ [_248403])) = _248403)], (693 ^ _225329) ^ [] : [leq(675 ^ [_248403], 678 ^ [_248403])]], -(totalorderedP(_248403))], (644 ^ _225329) ^ [] : [totalorderedP(_248403), 647 ^ _225329 : [(648 ^ _225329) ^ [_248699] : [ssItem(_248699), 651 ^ _225329 : [(652 ^ _225329) ^ [_248883] : [ssItem(_248883), 655 ^ _225329 : [(656 ^ _225329) ^ [_249063] : [ssList(_249063), 659 ^ _225329 : [(660 ^ _225329) ^ [_249239] : [ssList(_249239), 663 ^ _225329 : [(664 ^ _225329) ^ [_249411] : [ssList(_249411), app(app(_249063, cons(_248699, _249239)), cons(_248883, _249411)) = _248403, -(leq(_248699, _248883))]]]]]]]]]]]]], (697 ^ _225329) ^ [_250891] : [ssList(_250891), 700 ^ _225329 : [(731 ^ _225329) ^ [] : [733 ^ _225329 : [(734 ^ _225329) ^ [] : [-(ssItem(732 ^ [_250891]))], (737 ^ _225329) ^ [] : [-(ssItem(735 ^ [_250891]))], (740 ^ _225329) ^ [] : [-(ssList(738 ^ [_250891]))], (743 ^ _225329) ^ [] : [-(ssList(741 ^ [_250891]))], (746 ^ _225329) ^ [] : [-(ssList(744 ^ [_250891]))], (748 ^ _225329) ^ [] : [-(app(app(738 ^ [_250891], cons(732 ^ [_250891], 741 ^ [_250891])), cons(735 ^ [_250891], 744 ^ [_250891])) = _250891)], (750 ^ _225329) ^ [] : [lt(732 ^ [_250891], 735 ^ [_250891])]], -(strictorderedP(_250891))], (701 ^ _225329) ^ [] : [strictorderedP(_250891), 704 ^ _225329 : [(705 ^ _225329) ^ [_251187] : [ssItem(_251187), 708 ^ _225329 : [(709 ^ _225329) ^ [_251371] : [ssItem(_251371), 712 ^ _225329 : [(713 ^ _225329) ^ [_251551] : [ssList(_251551), 716 ^ _225329 : [(717 ^ _225329) ^ [_251727] : [ssList(_251727), 720 ^ _225329 : [(721 ^ _225329) ^ [_251899] : [ssList(_251899), app(app(_251551, cons(_251187, _251727)), cons(_251371, _251899)) = _250891, -(lt(_251187, _251371))]]]]]]]]]]]]], (754 ^ _225329) ^ [_253379] : [ssList(_253379), 757 ^ _225329 : [(788 ^ _225329) ^ [] : [790 ^ _225329 : [(791 ^ _225329) ^ [] : [-(ssItem(789 ^ [_253379]))], (794 ^ _225329) ^ [] : [-(ssItem(792 ^ [_253379]))], (797 ^ _225329) ^ [] : [-(ssList(795 ^ [_253379]))], (800 ^ _225329) ^ [] : [-(ssList(798 ^ [_253379]))], (803 ^ _225329) ^ [] : [-(ssList(801 ^ [_253379]))], (805 ^ _225329) ^ [] : [-(app(app(795 ^ [_253379], cons(789 ^ [_253379], 798 ^ [_253379])), cons(792 ^ [_253379], 801 ^ [_253379])) = _253379)], (807 ^ _225329) ^ [] : [-(789 ^ [_253379] = 792 ^ [_253379])]], -(duplicatefreeP(_253379))], (758 ^ _225329) ^ [] : [duplicatefreeP(_253379), 761 ^ _225329 : [(762 ^ _225329) ^ [_253677] : [ssItem(_253677), 765 ^ _225329 : [(766 ^ _225329) ^ [_253863] : [ssItem(_253863), 769 ^ _225329 : [(770 ^ _225329) ^ [_254045] : [ssList(_254045), 773 ^ _225329 : [(774 ^ _225329) ^ [_254223] : [ssList(_254223), 777 ^ _225329 : [(778 ^ _225329) ^ [_254397] : [ssList(_254397), app(app(_254045, cons(_253677, _254223)), cons(_253863, _254397)) = _253379, _253677 = _253863]]]]]]]]]]]]], (811 ^ _225329) ^ [_255889] : [ssList(_255889), 814 ^ _225329 : [(841 ^ _225329) ^ [] : [843 ^ _225329 : [(844 ^ _225329) ^ [] : [-(ssItem(842 ^ [_255889]))], (847 ^ _225329) ^ [] : [-(ssItem(845 ^ [_255889]))], (850 ^ _225329) ^ [] : [-(ssList(848 ^ [_255889]))], (853 ^ _225329) ^ [] : [-(ssList(851 ^ [_255889]))], (855 ^ _225329) ^ [] : [-(app(848 ^ [_255889], cons(842 ^ [_255889], cons(845 ^ [_255889], 851 ^ [_255889]))) = _255889)], (857 ^ _225329) ^ [] : [842 ^ [_255889] = 845 ^ [_255889]]], -(equalelemsP(_255889))], (815 ^ _225329) ^ [] : [equalelemsP(_255889), 818 ^ _225329 : [(819 ^ _225329) ^ [_256172] : [ssItem(_256172), 822 ^ _225329 : [(823 ^ _225329) ^ [_256343] : [ssItem(_256343), 826 ^ _225329 : [(827 ^ _225329) ^ [_256510] : [ssList(_256510), 830 ^ _225329 : [(831 ^ _225329) ^ [_256673] : [ssList(_256673), app(_256510, cons(_256172, cons(_256343, _256673))) = _255889, -(_256172 = _256343)]]]]]]]]]]], (861 ^ _225329) ^ [_257906] : [ssList(_257906), 864 ^ _225329 : [(865 ^ _225329) ^ [_258044] : [ssList(_258044), 868 ^ _225329 : [(869 ^ _225329) ^ [] : [neq(_257906, _258044), _257906 = _258044], (875 ^ _225329) ^ [] : [-(_257906 = _258044), -(neq(_257906, _258044))]]]]], (881 ^ _225329) ^ [_258497] : [ssList(_258497), 884 ^ _225329 : [(885 ^ _225329) ^ [_258629] : [ssItem(_258629), -(ssList(cons(_258629, _258497)))]]], (891 ^ _225329) ^ [] : [-(ssList(nil))], (893 ^ _225329) ^ [_258887] : [ssList(_258887), 896 ^ _225329 : [(897 ^ _225329) ^ [_259022] : [ssItem(_259022), cons(_259022, _258887) = _258887]]], (903 ^ _225329) ^ [_259230] : [ssList(_259230), 906 ^ _225329 : [(907 ^ _225329) ^ [_259398] : [ssList(_259398), 910 ^ _225329 : [(911 ^ _225329) ^ [_259562] : [ssItem(_259562), 914 ^ _225329 : [(915 ^ _225329) ^ [_259722] : [ssItem(_259722), cons(_259562, _259230) = cons(_259722, _259398), 922 ^ _225329 : [(923 ^ _225329) ^ [] : [-(_259562 = _259722)], (925 ^ _225329) ^ [] : [-(_259398 = _259230)]]]]]]]]], (927 ^ _225329) ^ [_260137] : [ssList(_260137), -(nil = _260137), 935 ^ _225329 : [(936 ^ _225329) ^ [] : [-(ssList(934 ^ [_260137]))], (939 ^ _225329) ^ [] : [-(ssItem(937 ^ [_260137]))], (941 ^ _225329) ^ [] : [-(cons(937 ^ [_260137], 934 ^ [_260137]) = _260137)]]], (943 ^ _225329) ^ [_260701] : [ssList(_260701), 946 ^ _225329 : [(947 ^ _225329) ^ [_260836] : [ssItem(_260836), nil = cons(_260836, _260701)]]], (953 ^ _225329) ^ [_261044] : [ssList(_261044), -(nil = _261044), -(ssItem(hd(_261044)))], (963 ^ _225329) ^ [_261322] : [ssList(_261322), 966 ^ _225329 : [(967 ^ _225329) ^ [_261457] : [ssItem(_261457), -(hd(cons(_261457, _261322)) = _261457)]]], (973 ^ _225329) ^ [_261668] : [ssList(_261668), -(nil = _261668), -(ssList(tl(_261668)))], (983 ^ _225329) ^ [_261946] : [ssList(_261946), 986 ^ _225329 : [(987 ^ _225329) ^ [_262081] : [ssItem(_262081), -(tl(cons(_262081, _261946)) = _261946)]]], (993 ^ _225329) ^ [_262292] : [ssList(_262292), 996 ^ _225329 : [(997 ^ _225329) ^ [_262424] : [ssList(_262424), -(ssList(app(_262292, _262424)))]]], (1003 ^ _225329) ^ [_262629] : [ssList(_262629), 1006 ^ _225329 : [(1007 ^ _225329) ^ [_262781] : [ssList(_262781), 1010 ^ _225329 : [(1011 ^ _225329) ^ [_262929] : [ssItem(_262929), -(cons(_262929, app(_262781, _262629)) = app(cons(_262929, _262781), _262629))]]]]], (1017 ^ _225329) ^ [_263167] : [ssList(_263167), -(app(nil, _263167) = _263167)], (1023 ^ _225329) ^ [_263361] : [ssItem(_263361), 1026 ^ _225329 : [(1027 ^ _225329) ^ [_263503] : [ssItem(_263503), -(_263361 = _263503), leq(_263361, _263503), leq(_263503, _263361)]]], (1041 ^ _225329) ^ [_263882] : [ssItem(_263882), 1044 ^ _225329 : [(1045 ^ _225329) ^ [_264034] : [ssItem(_264034), 1048 ^ _225329 : [(1049 ^ _225329) ^ [_264182] : [ssItem(_264182), -(leq(_263882, _264182)), leq(_263882, _264034), leq(_264034, _264182)]]]]], (1063 ^ _225329) ^ [_264582] : [ssItem(_264582), -(leq(_264582, _264582))], (1069 ^ _225329) ^ [_264770] : [ssItem(_264770), 1072 ^ _225329 : [(1073 ^ _225329) ^ [_264906] : [ssItem(_264906), 1076 ^ _225329 : [(1077 ^ _225329) ^ [] : [geq(_264770, _264906), -(leq(_264906, _264770))], (1083 ^ _225329) ^ [] : [leq(_264906, _264770), -(geq(_264770, _264906))]]]]], (1089 ^ _225329) ^ [_265357] : [ssItem(_265357), 1092 ^ _225329 : [(1093 ^ _225329) ^ [_265495] : [ssItem(_265495), lt(_265357, _265495), lt(_265495, _265357)]]], (1103 ^ _225329) ^ [_265786] : [ssItem(_265786), 1106 ^ _225329 : [(1107 ^ _225329) ^ [_265938] : [ssItem(_265938), 1110 ^ _225329 : [(1111 ^ _225329) ^ [_266086] : [ssItem(_266086), -(lt(_265786, _266086)), lt(_265786, _265938), lt(_265938, _266086)]]]]], (1125 ^ _225329) ^ [_266486] : [ssItem(_266486), 1128 ^ _225329 : [(1129 ^ _225329) ^ [_266622] : [ssItem(_266622), 1132 ^ _225329 : [(1133 ^ _225329) ^ [] : [gt(_266486, _266622), -(lt(_266622, _266486))], (1139 ^ _225329) ^ [] : [lt(_266622, _266486), -(gt(_266486, _266622))]]]]], (1145 ^ _225329) ^ [_267073] : [ssItem(_267073), 1148 ^ _225329 : [(1149 ^ _225329) ^ [_267228] : [ssList(_267228), 1152 ^ _225329 : [(1153 ^ _225329) ^ [_267379] : [ssList(_267379), 1156 ^ _225329 : [(1167 ^ _225329) ^ [] : [1168 ^ _225329 : [(1169 ^ _225329) ^ [] : [memberP(_267228, _267073)], (1171 ^ _225329) ^ [] : [memberP(_267379, _267073)]], -(memberP(app(_267228, _267379), _267073))], (1157 ^ _225329) ^ [] : [memberP(app(_267228, _267379), _267073), -(memberP(_267228, _267073)), -(memberP(_267379, _267073))]]]]]]], (1175 ^ _225329) ^ [_268026] : [ssItem(_268026), 1178 ^ _225329 : [(1179 ^ _225329) ^ [_268181] : [ssItem(_268181), 1182 ^ _225329 : [(1183 ^ _225329) ^ [_268332] : [ssList(_268332), 1186 ^ _225329 : [(1197 ^ _225329) ^ [] : [1198 ^ _225329 : [(1199 ^ _225329) ^ [] : [_268026 = _268181], (1201 ^ _225329) ^ [] : [memberP(_268332, _268026)]], -(memberP(cons(_268181, _268332), _268026))], (1187 ^ _225329) ^ [] : [memberP(cons(_268181, _268332), _268026), -(_268026 = _268181), -(memberP(_268332, _268026))]]]]]]], (1205 ^ _225329) ^ [_268979] : [ssItem(_268979), memberP(nil, _268979)], (1211 ^ _225329) ^ [] : [singletonP(nil)], (1213 ^ _225329) ^ [_269220] : [ssList(_269220), 1216 ^ _225329 : [(1217 ^ _225329) ^ [_269372] : [ssList(_269372), 1220 ^ _225329 : [(1221 ^ _225329) ^ [_269520] : [ssList(_269520), -(frontsegP(_269220, _269520)), frontsegP(_269220, _269372), frontsegP(_269372, _269520)]]]]], (1235 ^ _225329) ^ [_269920] : [ssList(_269920), 1238 ^ _225329 : [(1239 ^ _225329) ^ [_270062] : [ssList(_270062), -(_269920 = _270062), frontsegP(_269920, _270062), frontsegP(_270062, _269920)]]], (1253 ^ _225329) ^ [_270441] : [ssList(_270441), -(frontsegP(_270441, _270441))], (1259 ^ _225329) ^ [_270629] : [ssList(_270629), 1262 ^ _225329 : [(1263 ^ _225329) ^ [_270778] : [ssList(_270778), 1266 ^ _225329 : [(1267 ^ _225329) ^ [_270923] : [ssList(_270923), frontsegP(_270629, _270778), -(frontsegP(app(_270629, _270923), _270778))]]]]], (1277 ^ _225329) ^ [_271236] : [ssItem(_271236), 1280 ^ _225329 : [(1281 ^ _225329) ^ [_271404] : [ssItem(_271404), 1284 ^ _225329 : [(1285 ^ _225329) ^ [_271568] : [ssList(_271568), 1288 ^ _225329 : [(1289 ^ _225329) ^ [_271728] : [ssList(_271728), 1292 ^ _225329 : [(1293 ^ _225329) ^ [] : [frontsegP(cons(_271236, _271568), cons(_271404, _271728)), 1296 ^ _225329 : [(1297 ^ _225329) ^ [] : [-(_271236 = _271404)], (1299 ^ _225329) ^ [] : [-(frontsegP(_271568, _271728))]]], (1301 ^ _225329) ^ [] : [-(frontsegP(cons(_271236, _271568), cons(_271404, _271728))), _271236 = _271404, frontsegP(_271568, _271728)]]]]]]]]], (1311 ^ _225329) ^ [_272413] : [ssList(_272413), -(frontsegP(_272413, nil))], (1317 ^ _225329) ^ [_272601] : [ssList(_272601), 1320 ^ _225329 : [(1321 ^ _225329) ^ [] : [frontsegP(nil, _272601), -(nil = _272601)], (1327 ^ _225329) ^ [] : [nil = _272601, -(frontsegP(nil, _272601))]]], (1333 ^ _225329) ^ [_273029] : [ssList(_273029), 1336 ^ _225329 : [(1337 ^ _225329) ^ [_273181] : [ssList(_273181), 1340 ^ _225329 : [(1341 ^ _225329) ^ [_273329] : [ssList(_273329), -(rearsegP(_273029, _273329)), rearsegP(_273029, _273181), rearsegP(_273181, _273329)]]]]], (1355 ^ _225329) ^ [_273729] : [ssList(_273729), 1358 ^ _225329 : [(1359 ^ _225329) ^ [_273871] : [ssList(_273871), -(_273729 = _273871), rearsegP(_273729, _273871), rearsegP(_273871, _273729)]]], (1373 ^ _225329) ^ [_274250] : [ssList(_274250), -(rearsegP(_274250, _274250))], (1379 ^ _225329) ^ [_274438] : [ssList(_274438), 1382 ^ _225329 : [(1383 ^ _225329) ^ [_274587] : [ssList(_274587), 1386 ^ _225329 : [(1387 ^ _225329) ^ [_274732] : [ssList(_274732), rearsegP(_274438, _274587), -(rearsegP(app(_274732, _274438), _274587))]]]]], (1397 ^ _225329) ^ [_275045] : [ssList(_275045), -(rearsegP(_275045, nil))], (1403 ^ _225329) ^ [_275233] : [ssList(_275233), 1406 ^ _225329 : [(1407 ^ _225329) ^ [] : [rearsegP(nil, _275233), -(nil = _275233)], (1413 ^ _225329) ^ [] : [nil = _275233, -(rearsegP(nil, _275233))]]], (1419 ^ _225329) ^ [_275661] : [ssList(_275661), 1422 ^ _225329 : [(1423 ^ _225329) ^ [_275813] : [ssList(_275813), 1426 ^ _225329 : [(1427 ^ _225329) ^ [_275961] : [ssList(_275961), -(segmentP(_275661, _275961)), segmentP(_275661, _275813), segmentP(_275813, _275961)]]]]], (1441 ^ _225329) ^ [_276361] : [ssList(_276361), 1444 ^ _225329 : [(1445 ^ _225329) ^ [_276503] : [ssList(_276503), -(_276361 = _276503), segmentP(_276361, _276503), segmentP(_276503, _276361)]]], (1459 ^ _225329) ^ [_276882] : [ssList(_276882), -(segmentP(_276882, _276882))], (1465 ^ _225329) ^ [_277070] : [ssList(_277070), 1468 ^ _225329 : [(1469 ^ _225329) ^ [_277232] : [ssList(_277232), 1472 ^ _225329 : [(1473 ^ _225329) ^ [_277390] : [ssList(_277390), 1476 ^ _225329 : [(1477 ^ _225329) ^ [_277544] : [ssList(_277544), segmentP(_277070, _277232), -(segmentP(app(app(_277390, _277070), _277544), _277232))]]]]]]], (1487 ^ _225329) ^ [_277880] : [ssList(_277880), -(segmentP(_277880, nil))], (1493 ^ _225329) ^ [_278068] : [ssList(_278068), 1496 ^ _225329 : [(1497 ^ _225329) ^ [] : [segmentP(nil, _278068), -(nil = _278068)], (1503 ^ _225329) ^ [] : [nil = _278068, -(segmentP(nil, _278068))]]], (1509 ^ _225329) ^ [_278496] : [ssItem(_278496), -(cyclefreeP(cons(_278496, nil)))], (1515 ^ _225329) ^ [] : [-(cyclefreeP(nil))], (1517 ^ _225329) ^ [_278741] : [ssItem(_278741), -(totalorderP(cons(_278741, nil)))], (1523 ^ _225329) ^ [] : [-(totalorderP(nil))], (1525 ^ _225329) ^ [_278986] : [ssItem(_278986), -(strictorderP(cons(_278986, nil)))], (1531 ^ _225329) ^ [] : [-(strictorderP(nil))], (1533 ^ _225329) ^ [_279231] : [ssItem(_279231), -(totalorderedP(cons(_279231, nil)))], (1539 ^ _225329) ^ [] : [-(totalorderedP(nil))], (1541 ^ _225329) ^ [_279476] : [ssItem(_279476), 1544 ^ _225329 : [(1545 ^ _225329) ^ [_279635] : [ssList(_279635), 1548 ^ _225329 : [(1549 ^ _225329) ^ [] : [totalorderedP(cons(_279476, _279635)), -(nil = _279635), 1556 ^ _225329 : [(1557 ^ _225329) ^ [] : [nil = _279635], (1559 ^ _225329) ^ [] : [-(totalorderedP(_279635))], (1561 ^ _225329) ^ [] : [-(leq(_279476, hd(_279635)))]]], (1563 ^ _225329) ^ [] : [-(totalorderedP(cons(_279476, _279635))), 1564 ^ _225329 : [(1565 ^ _225329) ^ [] : [nil = _279635], (1567 ^ _225329) ^ [] : [-(nil = _279635), totalorderedP(_279635), leq(_279476, hd(_279635))]]]]]]], (1579 ^ _225329) ^ [_280570] : [ssItem(_280570), -(strictorderedP(cons(_280570, nil)))], (1585 ^ _225329) ^ [] : [-(strictorderedP(nil))], (1587 ^ _225329) ^ [_280815] : [ssItem(_280815), 1590 ^ _225329 : [(1591 ^ _225329) ^ [_280974] : [ssList(_280974), 1594 ^ _225329 : [(1595 ^ _225329) ^ [] : [strictorderedP(cons(_280815, _280974)), -(nil = _280974), 1602 ^ _225329 : [(1603 ^ _225329) ^ [] : [nil = _280974], (1605 ^ _225329) ^ [] : [-(strictorderedP(_280974))], (1607 ^ _225329) ^ [] : [-(lt(_280815, hd(_280974)))]]], (1609 ^ _225329) ^ [] : [-(strictorderedP(cons(_280815, _280974))), 1610 ^ _225329 : [(1611 ^ _225329) ^ [] : [nil = _280974], (1613 ^ _225329) ^ [] : [-(nil = _280974), strictorderedP(_280974), lt(_280815, hd(_280974))]]]]]]], (1625 ^ _225329) ^ [_281909] : [ssItem(_281909), -(duplicatefreeP(cons(_281909, nil)))], (1631 ^ _225329) ^ [] : [-(duplicatefreeP(nil))], (1633 ^ _225329) ^ [_282154] : [ssItem(_282154), -(equalelemsP(cons(_282154, nil)))], (1639 ^ _225329) ^ [] : [-(equalelemsP(nil))], (1641 ^ _225329) ^ [_282399] : [ssList(_282399), -(nil = _282399), 1649 ^ _225329 : [(1650 ^ _225329) ^ [] : [-(ssItem(1648 ^ [_282399]))], (1652 ^ _225329) ^ [] : [-(hd(_282399) = 1648 ^ [_282399])]]], (1654 ^ _225329) ^ [_282813] : [ssList(_282813), -(nil = _282813), 1662 ^ _225329 : [(1663 ^ _225329) ^ [] : [-(ssList(1661 ^ [_282813]))], (1665 ^ _225329) ^ [] : [-(tl(_282813) = 1661 ^ [_282813])]]], (1667 ^ _225329) ^ [_283227] : [ssList(_283227), 1670 ^ _225329 : [(1671 ^ _225329) ^ [_283393] : [ssList(_283393), -(_283393 = _283227), -(nil = _283393), -(nil = _283227), hd(_283393) = hd(_283227), tl(_283393) = tl(_283227)]]], (1693 ^ _225329) ^ [_283972] : [ssList(_283972), -(nil = _283972), -(cons(hd(_283972), tl(_283972)) = _283972)], (1703 ^ _225329) ^ [_284262] : [ssList(_284262), 1706 ^ _225329 : [(1707 ^ _225329) ^ [_284414] : [ssList(_284414), 1710 ^ _225329 : [(1711 ^ _225329) ^ [_284562] : [ssList(_284562), app(_284562, _284414) = app(_284262, _284414), -(_284562 = _284262)]]]]], (1721 ^ _225329) ^ [_284881] : [ssList(_284881), 1724 ^ _225329 : [(1725 ^ _225329) ^ [_285033] : [ssList(_285033), 1728 ^ _225329 : [(1729 ^ _225329) ^ [_285181] : [ssList(_285181), app(_285033, _285181) = app(_285033, _284881), -(_285181 = _284881)]]]]], (1739 ^ _225329) ^ [_285500] : [ssList(_285500), 1742 ^ _225329 : [(1743 ^ _225329) ^ [_285639] : [ssItem(_285639), -(cons(_285639, _285500) = app(cons(_285639, nil), _285500))]]], (1749 ^ _225329) ^ [_285858] : [ssList(_285858), 1752 ^ _225329 : [(1753 ^ _225329) ^ [_286010] : [ssList(_286010), 1756 ^ _225329 : [(1757 ^ _225329) ^ [_286158] : [ssList(_286158), -(app(app(_285858, _286010), _286158) = app(_285858, app(_286010, _286158)))]]]]], (1763 ^ _225329) ^ [_286396] : [ssList(_286396), 1766 ^ _225329 : [(1767 ^ _225329) ^ [_286541] : [ssList(_286541), 1770 ^ _225329 : [(1771 ^ _225329) ^ [] : [nil = app(_286396, _286541), 1774 ^ _225329 : [(1775 ^ _225329) ^ [] : [-(nil = _286541)], (1777 ^ _225329) ^ [] : [-(nil = _286396)]]], (1779 ^ _225329) ^ [] : [-(nil = app(_286396, _286541)), nil = _286541, nil = _286396]]]]], (1789 ^ _225329) ^ [_287159] : [ssList(_287159), -(app(_287159, nil) = _287159)], (1795 ^ _225329) ^ [_287353] : [ssList(_287353), 1798 ^ _225329 : [(1799 ^ _225329) ^ [_287498] : [ssList(_287498), -(nil = _287353), -(hd(app(_287353, _287498)) = hd(_287353))]]], (1809 ^ _225329) ^ [_287805] : [ssList(_287805), 1812 ^ _225329 : [(1813 ^ _225329) ^ [_287953] : [ssList(_287953), -(nil = _287805), -(tl(app(_287805, _287953)) = app(tl(_287805), _287953))]]], (1823 ^ _225329) ^ [_288266] : [ssItem(_288266), 1826 ^ _225329 : [(1827 ^ _225329) ^ [_288408] : [ssItem(_288408), -(_288266 = _288408), geq(_288266, _288408), geq(_288408, _288266)]]], (1841 ^ _225329) ^ [_288787] : [ssItem(_288787), 1844 ^ _225329 : [(1845 ^ _225329) ^ [_288939] : [ssItem(_288939), 1848 ^ _225329 : [(1849 ^ _225329) ^ [_289087] : [ssItem(_289087), -(geq(_288787, _289087)), geq(_288787, _288939), geq(_288939, _289087)]]]]], (1863 ^ _225329) ^ [_289487] : [ssItem(_289487), -(geq(_289487, _289487))], (1869 ^ _225329) ^ [_289675] : [ssItem(_289675), lt(_289675, _289675)], (1875 ^ _225329) ^ [_289864] : [ssItem(_289864), 1878 ^ _225329 : [(1879 ^ _225329) ^ [_290016] : [ssItem(_290016), 1882 ^ _225329 : [(1883 ^ _225329) ^ [_290164] : [ssItem(_290164), -(lt(_289864, _290164)), leq(_289864, _290016), lt(_290016, _290164)]]]]], (1897 ^ _225329) ^ [_290564] : [ssItem(_290564), 1900 ^ _225329 : [(1901 ^ _225329) ^ [_290706] : [ssItem(_290706), leq(_290564, _290706), -(_290564 = _290706), -(lt(_290564, _290706))]]], (1915 ^ _225329) ^ [_291086] : [ssItem(_291086), 1918 ^ _225329 : [(1919 ^ _225329) ^ [_291230] : [ssItem(_291230), 1922 ^ _225329 : [(1923 ^ _225329) ^ [] : [lt(_291086, _291230), 1926 ^ _225329 : [(1927 ^ _225329) ^ [] : [_291086 = _291230], (1929 ^ _225329) ^ [] : [-(leq(_291086, _291230))]]], (1931 ^ _225329) ^ [] : [-(lt(_291086, _291230)), -(_291086 = _291230), leq(_291086, _291230)]]]]], (1941 ^ _225329) ^ [_291841] : [ssItem(_291841), 1944 ^ _225329 : [(1945 ^ _225329) ^ [_291979] : [ssItem(_291979), gt(_291841, _291979), gt(_291979, _291841)]]], (1955 ^ _225329) ^ [_292250] : [ssItem(_292250), 1958 ^ _225329 : [(1959 ^ _225329) ^ [_292402] : [ssItem(_292402), 1962 ^ _225329 : [(1963 ^ _225329) ^ [_292550] : [ssItem(_292550), -(gt(_292250, _292550)), gt(_292250, _292402), gt(_292402, _292550)]]]]]], input).
% 0.32/1.38 ncf('1',plain,[true___],start(1979 ^ 0)).
% 0.32/1.38 ncf('1.1',plain,[-(true___)],extension(1977 ^ 1)).
% 0.32/1.38 %-----------------------------------------------------
% 0.32/1.38 End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------