%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SWC351+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n024.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri May 19 12:13:18 EDT 2023

% Result   : Theorem 95.16s 92.37s
% Output   : Proof 95.16s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SWC351+1 : TPTP v8.1.2. Released v2.4.0.
% 0.03/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n024.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 01:24:21 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 95.16/92.37  
% 95.16/92.37  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 95.16/92.37  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 95.16/92.37  %-----------------------------------------------------
% 95.16/92.37  ncf(matrix, plain, [(1991 ^ _323934) ^ [] : [-(1976 ^ [] = 1982 ^ [])], (1981 ^ _323934) ^ [] : [-(ssList(1979 ^ []))], (2002 ^ _323934) ^ [_325199] : [ssItem(_325199), 2005 ^ _323934 : [(2006 ^ _323934) ^ [_325373] : [ssList(_325373), app(cons(_325199, nil), _325373) = 1994 ^ [], 2013 ^ _323934 : [(2014 ^ _323934) ^ [_325628] : [ssItem(_325628), 2017 ^ _323934 : [(2018 ^ _323934) ^ [_325782] : [ssList(_325782), app(_325782, cons(_325628, nil)) = 1982 ^ [], lt(_325628, _325199)]]]]]]], (1996 ^ _323934) ^ [] : [-(ssList(1994 ^ []))], (1989 ^ _323934) ^ [] : [-(1979 ^ [] = 1985 ^ [])], (1984 ^ _323934) ^ [] : [-(ssList(1982 ^ []))], (2028 ^ _323934) ^ [] : [frontsegP(1979 ^ [], 1976 ^ [])], (2000 ^ _323934) ^ [] : [-(strictorderedP(1982 ^ []))], (1993 ^ _323934) ^ [] : [-(neq(1979 ^ [], nil))], (1998 ^ _323934) ^ [] : [-(app(1982 ^ [], 1994 ^ []) = 1985 ^ [])], (2030 ^ _323934) ^ [] : [-(nil = 1985 ^ []), nil = 1982 ^ []], (1987 ^ _323934) ^ [] : [-(ssList(1985 ^ []))], (1978 ^ _323934) ^ [] : [-(ssList(1976 ^ []))], !, (861 ^ _255529) ^ [_288086] : [ssList(_288086), 864 ^ _255529 : [(865 ^ _255529) ^ [_288224] : [ssList(_288224), 868 ^ _255529 : [(875 ^ _255529) ^ [] : [-(_288086 = _288224), -(neq(_288086, _288224))], (869 ^ _255529) ^ [] : [neq(_288086, _288224), _288086 = _288224]]]]], (252 ^ _255529) ^ [_263503, _263505] : [_263505 = _263503, -(tl(_263505) = tl(_263503))], (72 ^ _255529) ^ [_257904, _257906] : [-(cyclefreeP(_257904)), _257906 = _257904, cyclefreeP(_257906)], (1355 ^ _255529) ^ [_303909] : [ssList(_303909), 1358 ^ _255529 : [(1359 ^ _255529) ^ [_304051] : [ssList(_304051), -(_303909 = _304051), rearsegP(_303909, _304051), rearsegP(_304051, _303909)]]], (1459 ^ _255529) ^ [_307062] : [ssList(_307062), -(segmentP(_307062, _307062))], (102 ^ _255529) ^ [_258789, _258791] : [-(totalorderedP(_258789)), _258791 = _258789, totalorderedP(_258791)], (58 ^ _255529) ^ [_257488, _257490, _257492, _257494] : [-(segmentP(_257492, _257488)), segmentP(_257494, _257490), _257494 = _257492, _257490 = _257488], (943 ^ _255529) ^ [_290881] : [ssList(_290881), 946 ^ _255529 : [(947 ^ _255529) ^ [_291016] : [ssItem(_291016), nil = cons(_291016, _290881)]]], (1869 ^ _255529) ^ [_319855] : [ssItem(_319855), lt(_319855, _319855)], (132 ^ _255529) ^ [_259702, _259704, _259706, _259708] : [-(geq(_259706, _259702)), geq(_259708, _259704), _259708 = _259706, _259704 = _259702], (232 ^ _255529) ^ [_262787, _262789, _262791, _262793] : [-(frontsegP(_262791, _262787)), frontsegP(_262793, _262789), _262793 = _262791, _262789 = _262787], (2 ^ _255529) ^ [_255653] : [-(_255653 = _255653)], (1633 ^ _255529) ^ [_312334] : [ssItem(_312334), -(equalelemsP(cons(_312334, nil)))], (268 ^ _255529) ^ [_264088, _264090, _264092, _264094] : [-(cons(_264094, _264090) = cons(_264092, _264088)), _264094 = _264092, _264090 = _264088], (1145 ^ _255529) ^ [_297253] : [ssItem(_297253), 1148 ^ _255529 : [(1149 ^ _255529) ^ [_297408] : [ssList(_297408), 1152 ^ _255529 : [(1153 ^ _255529) ^ [_297559] : [ssList(_297559), 1156 ^ _255529 : [(1157 ^ _255529) ^ [] : [memberP(app(_297408, _297559), _297253), -(memberP(_297408, _297253)), -(memberP(_297559, _297253))], (1167 ^ _255529) ^ [] : [1168 ^ _255529 : [(1171 ^ _255529) ^ [] : [memberP(_297559, _297253)], (1169 ^ _255529) ^ [] : [memberP(_297408, _297253)]], -(memberP(app(_297408, _297559), _297253))]]]]]]], (278 ^ _255529) ^ [_264423] : [ssItem(_264423), 281 ^ _255529 : [(282 ^ _255529) ^ [_264561] : [ssItem(_264561), 285 ^ _255529 : [(292 ^ _255529) ^ [] : [-(_264423 = _264561), -(neq(_264423, _264561))], (286 ^ _255529) ^ [] : [neq(_264423, _264561), _264423 = _264561]]]]], (1213 ^ _255529) ^ [_299400] : [ssList(_299400), 1216 ^ _255529 : [(1217 ^ _255529) ^ [_299552] : [ssList(_299552), 1220 ^ _255529 : [(1221 ^ _255529) ^ [_299700] : [ssList(_299700), -(frontsegP(_299400, _299700)), frontsegP(_299400, _299552), frontsegP(_299552, _299700)]]]]], (390 ^ _255529) ^ [_268124] : [ssList(_268124), 393 ^ _255529 : [(394 ^ _255529) ^ [_268273] : [ssList(_268273), 397 ^ _255529 : [(407 ^ _255529) ^ [] : [-(rearsegP(_268124, _268273)), 408 ^ _255529 : [(409 ^ _255529) ^ [_268748] : [ssList(_268748), app(_268748, _268273) = _268124]]], (398 ^ _255529) ^ [] : [rearsegP(_268124, _268273), 402 ^ _255529 : [(405 ^ _255529) ^ [] : [-(app(401 ^ [_268124, _268273], _268273) = _268124)], (403 ^ _255529) ^ [] : [-(ssList(401 ^ [_268124, _268273]))]]]]]]], (1017 ^ _255529) ^ [_293347] : [ssList(_293347), -(app(nil, _293347) = _293347)], (1063 ^ _255529) ^ [_294762] : [ssItem(_294762), -(leq(_294762, _294762))], (1749 ^ _255529) ^ [_316038] : [ssList(_316038), 1752 ^ _255529 : [(1753 ^ _255529) ^ [_316190] : [ssList(_316190), 1756 ^ _255529 : [(1757 ^ _255529) ^ [_316338] : [ssList(_316338), -(app(app(_316038, _316190), _316338) = app(_316038, app(_316190, _316338)))]]]]], (1465 ^ _255529) ^ [_307250] : [ssList(_307250), 1468 ^ _255529 : [(1469 ^ _255529) ^ [_307412] : [ssList(_307412), 1472 ^ _255529 : [(1473 ^ _255529) ^ [_307570] : [ssList(_307570), 1476 ^ _255529 : [(1477 ^ _255529) ^ [_307724] : [ssList(_307724), segmentP(_307250, _307412), -(segmentP(app(app(_307570, _307250), _307724), _307412))]]]]]]], (1809 ^ _255529) ^ [_317985] : [ssList(_317985), 1812 ^ _255529 : [(1813 ^ _255529) ^ [_318133] : [ssList(_318133), -(nil = _317985), -(tl(app(_317985, _318133)) = app(tl(_317985), _318133))]]], (1211 ^ _255529) ^ [] : [singletonP(nil)], (1379 ^ _255529) ^ [_304618] : [ssList(_304618), 1382 ^ _255529 : [(1383 ^ _255529) ^ [_304767] : [ssList(_304767), 1386 ^ _255529 : [(1387 ^ _255529) ^ [_304912] : [ssList(_304912), rearsegP(_304618, _304767), -(rearsegP(app(_304912, _304618), _304767))]]]]], (993 ^ _255529) ^ [_292472] : [ssList(_292472), 996 ^ _255529 : [(997 ^ _255529) ^ [_292604] : [ssList(_292604), -(ssList(app(_292472, _292604)))]]], (1517 ^ _255529) ^ [_308921] : [ssItem(_308921), -(totalorderP(cons(_308921, nil)))], (1253 ^ _255529) ^ [_300621] : [ssList(_300621), -(frontsegP(_300621, _300621))], (1487 ^ _255529) ^ [_308060] : [ssList(_308060), -(segmentP(_308060, nil))], (34 ^ _255529) ^ [_256721, _256723] : [-(singletonP(_256721)), _256723 = _256721, singletonP(_256723)], (1311 ^ _255529) ^ [_302593] : [ssList(_302593), -(frontsegP(_302593, nil))], (1023 ^ _255529) ^ [_293541] : [ssItem(_293541), 1026 ^ _255529 : [(1027 ^ _255529) ^ [_293683] : [ssItem(_293683), -(_293541 = _293683), leq(_293541, _293683), leq(_293683, _293541)]]], (1403 ^ _255529) ^ [_305413] : [ssList(_305413), 1406 ^ _255529 : [(1413 ^ _255529) ^ [] : [nil = _305413, -(rearsegP(nil, _305413))], (1407 ^ _255529) ^ [] : [rearsegP(nil, _305413), -(nil = _305413)]]], (1579 ^ _255529) ^ [_310750] : [ssItem(_310750), -(strictorderedP(cons(_310750, nil)))], (188 ^ _255529) ^ [_261450, _261452] : [-(strictorderedP(_261450)), _261452 = _261450, strictorderedP(_261452)], (754 ^ _255529) ^ [_283559] : [ssList(_283559), 757 ^ _255529 : [(758 ^ _255529) ^ [] : [duplicatefreeP(_283559), 761 ^ _255529 : [(762 ^ _255529) ^ [_283857] : [ssItem(_283857), 765 ^ _255529 : [(766 ^ _255529) ^ [_284043] : [ssItem(_284043), 769 ^ _255529 : [(770 ^ _255529) ^ [_284225] : [ssList(_284225), 773 ^ _255529 : [(774 ^ _255529) ^ [_284403] : [ssList(_284403), 777 ^ _255529 : [(778 ^ _255529) ^ [_284577] : [ssList(_284577), app(app(_284225, cons(_283857, _284403)), cons(_284043, _284577)) = _283559, _283857 = _284043]]]]]]]]]]], (788 ^ _255529) ^ [] : [790 ^ _255529 : [(797 ^ _255529) ^ [] : [-(ssList(795 ^ [_283559]))], (805 ^ _255529) ^ [] : [-(app(app(795 ^ [_283559], cons(789 ^ [_283559], 798 ^ [_283559])), cons(792 ^ [_283559], 801 ^ [_283559])) = _283559)], (807 ^ _255529) ^ [] : [-(789 ^ [_283559] = 792 ^ [_283559])], (800 ^ _255529) ^ [] : [-(ssList(798 ^ [_283559]))], (791 ^ _255529) ^ [] : [-(ssItem(789 ^ [_283559]))], (794 ^ _255529) ^ [] : [-(ssItem(792 ^ [_283559]))], (803 ^ _255529) ^ [] : [-(ssList(801 ^ [_283559]))]], -(duplicatefreeP(_283559))]]], (963 ^ _255529) ^ [_291502] : [ssList(_291502), 966 ^ _255529 : [(967 ^ _255529) ^ [_291637] : [ssItem(_291637), -(hd(cons(_291637, _291502)) = _291637)]]], (1089 ^ _255529) ^ [_295537] : [ssItem(_295537), 1092 ^ _255529 : [(1093 ^ _255529) ^ [_295675] : [ssItem(_295675), lt(_295537, _295675), lt(_295675, _295537)]]], (1739 ^ _255529) ^ [_315680] : [ssList(_315680), 1742 ^ _255529 : [(1743 ^ _255529) ^ [_315819] : [ssItem(_315819), -(cons(_315819, _315680) = app(cons(_315819, nil), _315680))]]], (1441 ^ _255529) ^ [_306541] : [ssList(_306541), 1444 ^ _255529 : [(1445 ^ _255529) ^ [_306683] : [ssList(_306683), -(_306541 = _306683), segmentP(_306541, _306683), segmentP(_306683, _306541)]]], (1259 ^ _255529) ^ [_300809] : [ssList(_300809), 1262 ^ _255529 : [(1263 ^ _255529) ^ [_300958] : [ssList(_300958), 1266 ^ _255529 : [(1267 ^ _255529) ^ [_301103] : [ssList(_301103), frontsegP(_300809, _300958), -(frontsegP(app(_300809, _301103), _300958))]]]]], (1875 ^ _255529) ^ [_320044] : [ssItem(_320044), 1878 ^ _255529 : [(1879 ^ _255529) ^ [_320196] : [ssItem(_320196), 1882 ^ _255529 : [(1883 ^ _255529) ^ [_320344] : [ssItem(_320344), -(lt(_320044, _320344)), leq(_320044, _320196), lt(_320196, _320344)]]]]], (1541 ^ _255529) ^ [_309656] : [ssItem(_309656), 1544 ^ _255529 : [(1545 ^ _255529) ^ [_309815] : [ssList(_309815), 1548 ^ _255529 : [(1563 ^ _255529) ^ [] : [-(totalorderedP(cons(_309656, _309815))), 1564 ^ _255529 : [(1567 ^ _255529) ^ [] : [-(nil = _309815), totalorderedP(_309815), leq(_309656, hd(_309815))], (1565 ^ _255529) ^ [] : [nil = _309815]]], (1549 ^ _255529) ^ [] : [totalorderedP(cons(_309656, _309815)), -(nil = _309815), 1556 ^ _255529 : [(1561 ^ _255529) ^ [] : [-(leq(_309656, hd(_309815)))], (1559 ^ _255529) ^ [] : [-(totalorderedP(_309815))], (1557 ^ _255529) ^ [] : [nil = _309815]]]]]]], (1721 ^ _255529) ^ [_315061] : [ssList(_315061), 1724 ^ _255529 : [(1725 ^ _255529) ^ [_315213] : [ssList(_315213), 1728 ^ _255529 : [(1729 ^ _255529) ^ [_315361] : [ssList(_315361), app(_315213, _315361) = app(_315213, _315061), -(_315361 = _315061)]]]]], (340 ^ _255529) ^ [_266523] : [ssList(_266523), 343 ^ _255529 : [(353 ^ _255529) ^ [] : [-(singletonP(_266523)), 354 ^ _255529 : [(355 ^ _255529) ^ [_266972] : [ssItem(_266972), cons(_266972, nil) = _266523]]], (344 ^ _255529) ^ [] : [singletonP(_266523), 348 ^ _255529 : [(351 ^ _255529) ^ [] : [-(cons(347 ^ [_266523], nil) = _266523)], (349 ^ _255529) ^ [] : [-(ssItem(347 ^ [_266523]))]]]]], (1041 ^ _255529) ^ [_294062] : [ssItem(_294062), 1044 ^ _255529 : [(1045 ^ _255529) ^ [_294214] : [ssItem(_294214), 1048 ^ _255529 : [(1049 ^ _255529) ^ [_294362] : [ssItem(_294362), -(leq(_294062, _294362)), leq(_294062, _294214), leq(_294214, _294362)]]]]], (246 ^ _255529) ^ [_263285, _263287] : [_263287 = _263285, -(hd(_263287) = hd(_263285))], (1533 ^ _255529) ^ [_309411] : [ssItem(_309411), -(totalorderedP(cons(_309411, nil)))], (927 ^ _255529) ^ [_290317] : [ssList(_290317), -(nil = _290317), 935 ^ _255529 : [(941 ^ _255529) ^ [] : [-(cons(937 ^ [_290317], 934 ^ [_290317]) = _290317)], (939 ^ _255529) ^ [] : [-(ssItem(937 ^ [_290317]))], (936 ^ _255529) ^ [] : [-(ssList(934 ^ [_290317]))]]], (1493 ^ _255529) ^ [_308248] : [ssList(_308248), 1496 ^ _255529 : [(1503 ^ _255529) ^ [] : [nil = _308248, -(segmentP(nil, _308248))], (1497 ^ _255529) ^ [] : [segmentP(nil, _308248), -(nil = _308248)]]], (363 ^ _255529) ^ [_267228] : [ssList(_267228), 366 ^ _255529 : [(367 ^ _255529) ^ [_267377] : [ssList(_267377), 370 ^ _255529 : [(380 ^ _255529) ^ [] : [-(frontsegP(_267228, _267377)), 381 ^ _255529 : [(382 ^ _255529) ^ [_267852] : [ssList(_267852), app(_267377, _267852) = _267228]]], (371 ^ _255529) ^ [] : [frontsegP(_267228, _267377), 375 ^ _255529 : [(378 ^ _255529) ^ [] : [-(app(_267377, 374 ^ [_267228, _267377]) = _267228)], (376 ^ _255529) ^ [] : [-(ssList(374 ^ [_267228, _267377]))]]]]]]], (306 ^ _255529) ^ [_265274] : [ssList(_265274), 309 ^ _255529 : [(310 ^ _255529) ^ [_265436] : [ssItem(_265436), 313 ^ _255529 : [(326 ^ _255529) ^ [] : [-(memberP(_265274, _265436)), 327 ^ _255529 : [(328 ^ _255529) ^ [_266084] : [ssList(_266084), 331 ^ _255529 : [(332 ^ _255529) ^ [_266232] : [ssList(_266232), app(_266084, cons(_265436, _266232)) = _265274]]]]], (314 ^ _255529) ^ [] : [memberP(_265274, _265436), 318 ^ _255529 : [(324 ^ _255529) ^ [] : [-(app(317 ^ [_265274, _265436], cons(_265436, 320 ^ [_265274, _265436])) = _265274)], (322 ^ _255529) ^ [] : [-(ssList(320 ^ [_265274, _265436]))], (319 ^ _255529) ^ [] : [-(ssList(317 ^ [_265274, _265436]))]]]]]]], (1693 ^ _255529) ^ [_314152] : [ssList(_314152), -(nil = _314152), -(cons(hd(_314152), tl(_314152)) = _314152)], (811 ^ _255529) ^ [_286069] : [ssList(_286069), 814 ^ _255529 : [(815 ^ _255529) ^ [] : [equalelemsP(_286069), 818 ^ _255529 : [(819 ^ _255529) ^ [_286352] : [ssItem(_286352), 822 ^ _255529 : [(823 ^ _255529) ^ [_286523] : [ssItem(_286523), 826 ^ _255529 : [(827 ^ _255529) ^ [_286690] : [ssList(_286690), 830 ^ _255529 : [(831 ^ _255529) ^ [_286853] : [ssList(_286853), app(_286690, cons(_286352, cons(_286523, _286853))) = _286069, -(_286352 = _286523)]]]]]]]]], (841 ^ _255529) ^ [] : [843 ^ _255529 : [(847 ^ _255529) ^ [] : [-(ssItem(845 ^ [_286069]))], (844 ^ _255529) ^ [] : [-(ssItem(842 ^ [_286069]))], (857 ^ _255529) ^ [] : [842 ^ [_286069] = 845 ^ [_286069]], (853 ^ _255529) ^ [] : [-(ssList(851 ^ [_286069]))], (855 ^ _255529) ^ [] : [-(app(848 ^ [_286069], cons(842 ^ [_286069], cons(845 ^ [_286069], 851 ^ [_286069]))) = _286069)], (850 ^ _255529) ^ [] : [-(ssList(848 ^ [_286069]))]], -(equalelemsP(_286069))]]], (1125 ^ _255529) ^ [_296666] : [ssItem(_296666), 1128 ^ _255529 : [(1129 ^ _255529) ^ [_296802] : [ssItem(_296802), 1132 ^ _255529 : [(1139 ^ _255529) ^ [] : [lt(_296802, _296666), -(gt(_296666, _296802))], (1133 ^ _255529) ^ [] : [gt(_296666, _296802), -(lt(_296802, _296666))]]]]], (973 ^ _255529) ^ [_291848] : [ssList(_291848), -(nil = _291848), -(ssList(tl(_291848)))], (1823 ^ _255529) ^ [_318446] : [ssItem(_318446), 1826 ^ _255529 : [(1827 ^ _255529) ^ [_318588] : [ssItem(_318588), -(_318446 = _318588), geq(_318446, _318588), geq(_318588, _318446)]]], (953 ^ _255529) ^ [_291224] : [ssList(_291224), -(nil = _291224), -(ssItem(hd(_291224)))], (1667 ^ _255529) ^ [_313407] : [ssList(_313407), 1670 ^ _255529 : [(1671 ^ _255529) ^ [_313573] : [ssList(_313573), -(_313573 = _313407), -(nil = _313573), -(nil = _313407), hd(_313573) = hd(_313407), tl(_313573) = tl(_313407)]]], (1841 ^ _255529) ^ [_318967] : [ssItem(_318967), 1844 ^ _255529 : [(1845 ^ _255529) ^ [_319119] : [ssItem(_319119), 1848 ^ _255529 : [(1849 ^ _255529) ^ [_319267] : [ssItem(_319267), -(geq(_318967, _319267)), geq(_318967, _319119), geq(_319119, _319267)]]]]], (1897 ^ _255529) ^ [_320744] : [ssItem(_320744), 1900 ^ _255529 : [(1901 ^ _255529) ^ [_320886] : [ssItem(_320886), leq(_320744, _320886), -(_320744 = _320886), -(lt(_320744, _320886))]]], (1639 ^ _255529) ^ [] : [-(equalelemsP(nil))], (1863 ^ _255529) ^ [_319667] : [ssItem(_319667), -(geq(_319667, _319667))], (1625 ^ _255529) ^ [_312089] : [ssItem(_312089), -(duplicatefreeP(cons(_312089, nil)))], (577 ^ _255529) ^ [_275819] : [ssList(_275819), 580 ^ _255529 : [(581 ^ _255529) ^ [] : [strictorderP(_275819), 584 ^ _255529 : [(585 ^ _255529) ^ [_276121] : [ssItem(_276121), 588 ^ _255529 : [(589 ^ _255529) ^ [_276311] : [ssItem(_276311), 592 ^ _255529 : [(593 ^ _255529) ^ [_276497] : [ssList(_276497), 596 ^ _255529 : [(597 ^ _255529) ^ [_276679] : [ssList(_276679), 600 ^ _255529 : [(601 ^ _255529) ^ [_276857] : [ssList(_276857), app(app(_276497, cons(_276121, _276679)), cons(_276311, _276857)) = _275819, -(lt(_276121, _276311)), -(lt(_276311, _276121))]]]]]]]]]]], (615 ^ _255529) ^ [] : [617 ^ _255529 : [(624 ^ _255529) ^ [] : [-(ssList(622 ^ [_275819]))], (632 ^ _255529) ^ [] : [-(app(app(622 ^ [_275819], cons(616 ^ [_275819], 625 ^ [_275819])), cons(619 ^ [_275819], 628 ^ [_275819])) = _275819)], (618 ^ _255529) ^ [] : [-(ssItem(616 ^ [_275819]))], (634 ^ _255529) ^ [] : [lt(616 ^ [_275819], 619 ^ [_275819])], (627 ^ _255529) ^ [] : [-(ssList(625 ^ [_275819]))], (630 ^ _255529) ^ [] : [-(ssList(628 ^ [_275819]))], (636 ^ _255529) ^ [] : [lt(619 ^ [_275819], 616 ^ [_275819])], (621 ^ _255529) ^ [] : [-(ssItem(619 ^ [_275819]))]], -(strictorderP(_275819))]]], (44 ^ _255529) ^ [_257044, _257046, _257048, _257050] : [-(rearsegP(_257048, _257044)), rearsegP(_257050, _257046), _257050 = _257048, _257046 = _257044], (1795 ^ _255529) ^ [_317533] : [ssList(_317533), 1798 ^ _255529 : [(1799 ^ _255529) ^ [_317678] : [ssList(_317678), -(nil = _317533), -(hd(app(_317533, _317678)) = hd(_317533))]]], (20 ^ _255529) ^ [_256305, _256307, _256309, _256311] : [-(memberP(_256309, _256305)), memberP(_256311, _256307), _256311 = _256309, _256307 = _256305], (1523 ^ _255529) ^ [] : [-(totalorderP(nil))], (1789 ^ _255529) ^ [_317339] : [ssList(_317339), -(app(_317339, nil) = _317339)], (697 ^ _255529) ^ [_281071] : [ssList(_281071), 700 ^ _255529 : [(701 ^ _255529) ^ [] : [strictorderedP(_281071), 704 ^ _255529 : [(705 ^ _255529) ^ [_281367] : [ssItem(_281367), 708 ^ _255529 : [(709 ^ _255529) ^ [_281551] : [ssItem(_281551), 712 ^ _255529 : [(713 ^ _255529) ^ [_281731] : [ssList(_281731), 716 ^ _255529 : [(717 ^ _255529) ^ [_281907] : [ssList(_281907), 720 ^ _255529 : [(721 ^ _255529) ^ [_282079] : [ssList(_282079), app(app(_281731, cons(_281367, _281907)), cons(_281551, _282079)) = _281071, -(lt(_281367, _281551))]]]]]]]]]]], (731 ^ _255529) ^ [] : [733 ^ _255529 : [(740 ^ _255529) ^ [] : [-(ssList(738 ^ [_281071]))], (748 ^ _255529) ^ [] : [-(app(app(738 ^ [_281071], cons(732 ^ [_281071], 741 ^ [_281071])), cons(735 ^ [_281071], 744 ^ [_281071])) = _281071)], (750 ^ _255529) ^ [] : [lt(732 ^ [_281071], 735 ^ [_281071])], (743 ^ _255529) ^ [] : [-(ssList(741 ^ [_281071]))], (734 ^ _255529) ^ [] : [-(ssItem(732 ^ [_281071]))], (737 ^ _255529) ^ [] : [-(ssItem(735 ^ [_281071]))], (746 ^ _255529) ^ [] : [-(ssList(744 ^ [_281071]))]], -(strictorderedP(_281071))]]], (198 ^ _255529) ^ [_261745, _261747] : [-(ssItem(_261745)), _261747 = _261745, ssItem(_261747)], (1373 ^ _255529) ^ [_304430] : [ssList(_304430), -(rearsegP(_304430, _304430))], (112 ^ _255529) ^ [_259084, _259086] : [-(duplicatefreeP(_259084)), _259086 = _259084, duplicatefreeP(_259086)], (10 ^ _255529) ^ [_255964, _255966, _255968] : [-(_255968 = _255964), _255968 = _255966, _255966 = _255964], (1941 ^ _255529) ^ [_322021] : [ssItem(_322021), 1944 ^ _255529 : [(1945 ^ _255529) ^ [_322159] : [ssItem(_322159), gt(_322021, _322159), gt(_322159, _322021)]]], (1587 ^ _255529) ^ [_310995] : [ssItem(_310995), 1590 ^ _255529 : [(1591 ^ _255529) ^ [_311154] : [ssList(_311154), 1594 ^ _255529 : [(1609 ^ _255529) ^ [] : [-(strictorderedP(cons(_310995, _311154))), 1610 ^ _255529 : [(1613 ^ _255529) ^ [] : [-(nil = _311154), strictorderedP(_311154), lt(_310995, hd(_311154))], (1611 ^ _255529) ^ [] : [nil = _311154]]], (1595 ^ _255529) ^ [] : [strictorderedP(cons(_310995, _311154)), -(nil = _311154), 1602 ^ _255529 : [(1607 ^ _255529) ^ [] : [-(lt(_310995, hd(_311154)))], (1605 ^ _255529) ^ [] : [-(strictorderedP(_311154))], (1603 ^ _255529) ^ [] : [nil = _311154]]]]]]], (299 ^ _255529) ^ [] : [-(ssItem(297 ^ []))], (451 ^ _255529) ^ [_270269] : [ssList(_270269), 454 ^ _255529 : [(455 ^ _255529) ^ [] : [cyclefreeP(_270269), 458 ^ _255529 : [(459 ^ _255529) ^ [_270573] : [ssItem(_270573), 462 ^ _255529 : [(463 ^ _255529) ^ [_270765] : [ssItem(_270765), 466 ^ _255529 : [(467 ^ _255529) ^ [_270953] : [ssList(_270953), 470 ^ _255529 : [(471 ^ _255529) ^ [_271137] : [ssList(_271137), 474 ^ _255529 : [(475 ^ _255529) ^ [_271317] : [ssList(_271317), app(app(_270953, cons(_270573, _271137)), cons(_270765, _271317)) = _270269, leq(_270573, _270765), leq(_270765, _270573)]]]]]]]]]]], (489 ^ _255529) ^ [] : [491 ^ _255529 : [(498 ^ _255529) ^ [] : [-(ssList(496 ^ [_270269]))], (506 ^ _255529) ^ [] : [-(app(app(496 ^ [_270269], cons(490 ^ [_270269], 499 ^ [_270269])), cons(493 ^ [_270269], 502 ^ [_270269])) = _270269)], (492 ^ _255529) ^ [] : [-(ssItem(490 ^ [_270269]))], (508 ^ _255529) ^ [] : [-(leq(490 ^ [_270269], 493 ^ [_270269]))], (501 ^ _255529) ^ [] : [-(ssList(499 ^ [_270269]))], (504 ^ _255529) ^ [] : [-(ssList(502 ^ [_270269]))], (510 ^ _255529) ^ [] : [-(leq(493 ^ [_270269], 490 ^ [_270269]))], (495 ^ _255529) ^ [] : [-(ssItem(493 ^ [_270269]))]], -(cyclefreeP(_270269))]]], (1515 ^ _255529) ^ [] : [-(cyclefreeP(nil))], (1333 ^ _255529) ^ [_303209] : [ssList(_303209), 1336 ^ _255529 : [(1337 ^ _255529) ^ [_303361] : [ssList(_303361), 1340 ^ _255529 : [(1341 ^ _255529) ^ [_303509] : [ssList(_303509), -(rearsegP(_303209, _303509)), rearsegP(_303209, _303361), rearsegP(_303361, _303509)]]]]], (302 ^ _255529) ^ [] : [-(ssItem(300 ^ []))], (174 ^ _255529) ^ [_261034, _261036, _261038, _261040] : [-(neq(_261038, _261034)), neq(_261040, _261036), _261040 = _261038, _261036 = _261034], (1103 ^ _255529) ^ [_295966] : [ssItem(_295966), 1106 ^ _255529 : [(1107 ^ _255529) ^ [_296118] : [ssItem(_296118), 1110 ^ _255529 : [(1111 ^ _255529) ^ [_296266] : [ssItem(_296266), -(lt(_295966, _296266)), lt(_295966, _296118), lt(_296118, _296266)]]]]], (1955 ^ _255529) ^ [_322430] : [ssItem(_322430), 1958 ^ _255529 : [(1959 ^ _255529) ^ [_322582] : [ssItem(_322582), 1962 ^ _255529 : [(1963 ^ _255529) ^ [_322730] : [ssItem(_322730), -(gt(_322430, _322730)), gt(_322430, _322582), gt(_322582, _322730)]]]]], (893 ^ _255529) ^ [_289067] : [ssList(_289067), 896 ^ _255529 : [(897 ^ _255529) ^ [_289202] : [ssItem(_289202), cons(_289202, _289067) = _289067]]], (1205 ^ _255529) ^ [_299159] : [ssItem(_299159), memberP(nil, _299159)], (640 ^ _255529) ^ [_278583] : [ssList(_278583), 643 ^ _255529 : [(644 ^ _255529) ^ [] : [totalorderedP(_278583), 647 ^ _255529 : [(648 ^ _255529) ^ [_278879] : [ssItem(_278879), 651 ^ _255529 : [(652 ^ _255529) ^ [_279063] : [ssItem(_279063), 655 ^ _255529 : [(656 ^ _255529) ^ [_279243] : [ssList(_279243), 659 ^ _255529 : [(660 ^ _255529) ^ [_279419] : [ssList(_279419), 663 ^ _255529 : [(664 ^ _255529) ^ [_279591] : [ssList(_279591), app(app(_279243, cons(_278879, _279419)), cons(_279063, _279591)) = _278583, -(leq(_278879, _279063))]]]]]]]]]]], (674 ^ _255529) ^ [] : [676 ^ _255529 : [(683 ^ _255529) ^ [] : [-(ssList(681 ^ [_278583]))], (691 ^ _255529) ^ [] : [-(app(app(681 ^ [_278583], cons(675 ^ [_278583], 684 ^ [_278583])), cons(678 ^ [_278583], 687 ^ [_278583])) = _278583)], (693 ^ _255529) ^ [] : [leq(675 ^ [_278583], 678 ^ [_278583])], (686 ^ _255529) ^ [] : [-(ssList(684 ^ [_278583]))], (677 ^ _255529) ^ [] : [-(ssItem(675 ^ [_278583]))], (680 ^ _255529) ^ [] : [-(ssItem(678 ^ [_278583]))], (689 ^ _255529) ^ [] : [-(ssList(687 ^ [_278583]))]], -(totalorderedP(_278583))]]], (1654 ^ _255529) ^ [_312993] : [ssList(_312993), -(nil = _312993), 1662 ^ _255529 : [(1665 ^ _255529) ^ [] : [-(tl(_312993) = 1661 ^ [_312993])], (1663 ^ _255529) ^ [] : [-(ssList(1661 ^ [_312993]))]]], (4 ^ _255529) ^ [_255760, _255762] : [_255762 = _255760, -(_255760 = _255762)], (417 ^ _255529) ^ [_269020] : [ssList(_269020), 420 ^ _255529 : [(421 ^ _255529) ^ [_269182] : [ssList(_269182), 424 ^ _255529 : [(437 ^ _255529) ^ [] : [-(segmentP(_269020, _269182)), 438 ^ _255529 : [(439 ^ _255529) ^ [_269830] : [ssList(_269830), 442 ^ _255529 : [(443 ^ _255529) ^ [_269978] : [ssList(_269978), app(app(_269830, _269182), _269978) = _269020]]]]], (425 ^ _255529) ^ [] : [segmentP(_269020, _269182), 429 ^ _255529 : [(435 ^ _255529) ^ [] : [-(app(app(428 ^ [_269020, _269182], _269182), 431 ^ [_269020, _269182]) = _269020)], (433 ^ _255529) ^ [] : [-(ssList(431 ^ [_269020, _269182]))], (430 ^ _255529) ^ [] : [-(ssList(428 ^ [_269020, _269182]))]]]]]]], (1069 ^ _255529) ^ [_294950] : [ssItem(_294950), 1072 ^ _255529 : [(1073 ^ _255529) ^ [_295086] : [ssItem(_295086), 1076 ^ _255529 : [(1083 ^ _255529) ^ [] : [leq(_295086, _294950), -(geq(_294950, _295086))], (1077 ^ _255529) ^ [] : [geq(_294950, _295086), -(leq(_295086, _294950))]]]]], (208 ^ _255529) ^ [_262040, _262042] : [-(ssList(_262040)), _262042 = _262040, ssList(_262042)], (1175 ^ _255529) ^ [_298206] : [ssItem(_298206), 1178 ^ _255529 : [(1179 ^ _255529) ^ [_298361] : [ssItem(_298361), 1182 ^ _255529 : [(1183 ^ _255529) ^ [_298512] : [ssList(_298512), 1186 ^ _255529 : [(1187 ^ _255529) ^ [] : [memberP(cons(_298361, _298512), _298206), -(_298206 = _298361), -(memberP(_298512, _298206))], (1197 ^ _255529) ^ [] : [1198 ^ _255529 : [(1201 ^ _255529) ^ [] : [memberP(_298512, _298206)], (1199 ^ _255529) ^ [] : [_298206 = _298361]], -(memberP(cons(_298361, _298512), _298206))]]]]]]], (258 ^ _255529) ^ [_263749, _263751, _263753, _263755] : [-(app(_263755, _263751) = app(_263753, _263749)), _263755 = _263753, _263751 = _263749], (1531 ^ _255529) ^ [] : [-(strictorderP(nil))], (1763 ^ _255529) ^ [_316576] : [ssList(_316576), 1766 ^ _255529 : [(1767 ^ _255529) ^ [_316721] : [ssList(_316721), 1770 ^ _255529 : [(1779 ^ _255529) ^ [] : [-(nil = app(_316576, _316721)), nil = _316721, nil = _316576], (1771 ^ _255529) ^ [] : [nil = app(_316576, _316721), 1774 ^ _255529 : [(1777 ^ _255529) ^ [] : [-(nil = _316576)], (1775 ^ _255529) ^ [] : [-(nil = _316721)]]]]]]], (1003 ^ _255529) ^ [_292809] : [ssList(_292809), 1006 ^ _255529 : [(1007 ^ _255529) ^ [_292961] : [ssList(_292961), 1010 ^ _255529 : [(1011 ^ _255529) ^ [_293109] : [ssItem(_293109), -(cons(_293109, app(_292961, _292809)) = app(cons(_293109, _292961), _292809))]]]]], (1509 ^ _255529) ^ [_308676] : [ssItem(_308676), -(cyclefreeP(cons(_308676, nil)))], (1539 ^ _255529) ^ [] : [-(totalorderedP(nil))], (1317 ^ _255529) ^ [_302781] : [ssList(_302781), 1320 ^ _255529 : [(1327 ^ _255529) ^ [] : [nil = _302781, -(frontsegP(nil, _302781))], (1321 ^ _255529) ^ [] : [frontsegP(nil, _302781), -(nil = _302781)]]], (1397 ^ _255529) ^ [_305225] : [ssList(_305225), -(rearsegP(_305225, nil))], (1585 ^ _255529) ^ [] : [-(strictorderedP(nil))], (92 ^ _255529) ^ [_258494, _258496] : [-(strictorderP(_258494)), _258496 = _258494, strictorderP(_258496)], (146 ^ _255529) ^ [_260146, _260148, _260150, _260152] : [-(leq(_260150, _260146)), leq(_260152, _260148), _260152 = _260150, _260148 = _260146], (881 ^ _255529) ^ [_288677] : [ssList(_288677), 884 ^ _255529 : [(885 ^ _255529) ^ [_288809] : [ssItem(_288809), -(ssList(cons(_288809, _288677)))]]], (1235 ^ _255529) ^ [_300100] : [ssList(_300100), 1238 ^ _255529 : [(1239 ^ _255529) ^ [_300242] : [ssList(_300242), -(_300100 = _300242), frontsegP(_300100, _300242), frontsegP(_300242, _300100)]]], (1915 ^ _255529) ^ [_321266] : [ssItem(_321266), 1918 ^ _255529 : [(1919 ^ _255529) ^ [_321410] : [ssItem(_321410), 1922 ^ _255529 : [(1931 ^ _255529) ^ [] : [-(lt(_321266, _321410)), -(_321266 = _321410), leq(_321266, _321410)], (1923 ^ _255529) ^ [] : [lt(_321266, _321410), 1926 ^ _255529 : [(1929 ^ _255529) ^ [] : [-(leq(_321266, _321410))], (1927 ^ _255529) ^ [] : [_321266 = _321410]]]]]]], (903 ^ _255529) ^ [_289410] : [ssList(_289410), 906 ^ _255529 : [(907 ^ _255529) ^ [_289578] : [ssList(_289578), 910 ^ _255529 : [(911 ^ _255529) ^ [_289742] : [ssItem(_289742), 914 ^ _255529 : [(915 ^ _255529) ^ [_289902] : [ssItem(_289902), cons(_289742, _289410) = cons(_289902, _289578), 922 ^ _255529 : [(925 ^ _255529) ^ [] : [-(_289578 = _289410)], (923 ^ _255529) ^ [] : [-(_289742 = _289902)]]]]]]]]], (304 ^ _255529) ^ [] : [297 ^ [] = 300 ^ []], (1631 ^ _255529) ^ [] : [-(duplicatefreeP(nil))], (1525 ^ _255529) ^ [_309166] : [ssItem(_309166), -(strictorderP(cons(_309166, nil)))], (160 ^ _255529) ^ [_260590, _260592, _260594, _260596] : [-(gt(_260594, _260590)), gt(_260596, _260592), _260596 = _260594, _260592 = _260590], (891 ^ _255529) ^ [] : [-(ssList(nil))], (983 ^ _255529) ^ [_292126] : [ssList(_292126), 986 ^ _255529 : [(987 ^ _255529) ^ [_292261] : [ssItem(_292261), -(tl(cons(_292261, _292126)) = _292126)]]], (82 ^ _255529) ^ [_258199, _258201] : [-(totalorderP(_258199)), _258201 = _258199, totalorderP(_258201)], (1277 ^ _255529) ^ [_301416] : [ssItem(_301416), 1280 ^ _255529 : [(1281 ^ _255529) ^ [_301584] : [ssItem(_301584), 1284 ^ _255529 : [(1285 ^ _255529) ^ [_301748] : [ssList(_301748), 1288 ^ _255529 : [(1289 ^ _255529) ^ [_301908] : [ssList(_301908), 1292 ^ _255529 : [(1301 ^ _255529) ^ [] : [-(frontsegP(cons(_301416, _301748), cons(_301584, _301908))), _301416 = _301584, frontsegP(_301748, _301908)], (1293 ^ _255529) ^ [] : [frontsegP(cons(_301416, _301748), cons(_301584, _301908)), 1296 ^ _255529 : [(1299 ^ _255529) ^ [] : [-(frontsegP(_301748, _301908))], (1297 ^ _255529) ^ [] : [-(_301416 = _301584)]]]]]]]]]]], (1703 ^ _255529) ^ [_314442] : [ssList(_314442), 1706 ^ _255529 : [(1707 ^ _255529) ^ [_314594] : [ssList(_314594), 1710 ^ _255529 : [(1711 ^ _255529) ^ [_314742] : [ssList(_314742), app(_314742, _314594) = app(_314442, _314594), -(_314742 = _314442)]]]]], (514 ^ _255529) ^ [_273055] : [ssList(_273055), 517 ^ _255529 : [(518 ^ _255529) ^ [] : [totalorderP(_273055), 521 ^ _255529 : [(522 ^ _255529) ^ [_273357] : [ssItem(_273357), 525 ^ _255529 : [(526 ^ _255529) ^ [_273547] : [ssItem(_273547), 529 ^ _255529 : [(530 ^ _255529) ^ [_273733] : [ssList(_273733), 533 ^ _255529 : [(534 ^ _255529) ^ [_273915] : [ssList(_273915), 537 ^ _255529 : [(538 ^ _255529) ^ [_274093] : [ssList(_274093), app(app(_273733, cons(_273357, _273915)), cons(_273547, _274093)) = _273055, -(leq(_273357, _273547)), -(leq(_273547, _273357))]]]]]]]]]]], (552 ^ _255529) ^ [] : [554 ^ _255529 : [(561 ^ _255529) ^ [] : [-(ssList(559 ^ [_273055]))], (569 ^ _255529) ^ [] : [-(app(app(559 ^ [_273055], cons(553 ^ [_273055], 562 ^ [_273055])), cons(556 ^ [_273055], 565 ^ [_273055])) = _273055)], (555 ^ _255529) ^ [] : [-(ssItem(553 ^ [_273055]))], (571 ^ _255529) ^ [] : [leq(553 ^ [_273055], 556 ^ [_273055])], (564 ^ _255529) ^ [] : [-(ssList(562 ^ [_273055]))], (567 ^ _255529) ^ [] : [-(ssList(565 ^ [_273055]))], (573 ^ _255529) ^ [] : [leq(556 ^ [_273055], 553 ^ [_273055])], (558 ^ _255529) ^ [] : [-(ssItem(556 ^ [_273055]))]], -(totalorderP(_273055))]]], (1419 ^ _255529) ^ [_305841] : [ssList(_305841), 1422 ^ _255529 : [(1423 ^ _255529) ^ [_305993] : [ssList(_305993), 1426 ^ _255529 : [(1427 ^ _255529) ^ [_306141] : [ssList(_306141), -(segmentP(_305841, _306141)), segmentP(_305841, _305993), segmentP(_305993, _306141)]]]]], (1641 ^ _255529) ^ [_312579] : [ssList(_312579), -(nil = _312579), 1649 ^ _255529 : [(1652 ^ _255529) ^ [] : [-(hd(_312579) = 1648 ^ [_312579])], (1650 ^ _255529) ^ [] : [-(ssItem(1648 ^ [_312579]))]]], (218 ^ _255529) ^ [_262363, _262365, _262367, _262369] : [-(lt(_262367, _262363)), lt(_262369, _262365), _262369 = _262367, _262365 = _262363], (122 ^ _255529) ^ [_259379, _259381] : [-(equalelemsP(_259379)), _259381 = _259379, equalelemsP(_259381)]], input).
% 95.16/92.37  ncf('1',plain,[-(ssList(1994 ^ []))],start(1996 ^ 0)).
% 95.16/92.37  ncf('1.1',plain,[ssList(1994 ^ []), 382 : app(1982 ^ [], 1994 ^ []) = 1985 ^ [], 382 : -(frontsegP(1985 ^ [], 1982 ^ [])), 380 : ssList(1982 ^ []), 367 : ssList(1985 ^ [])],extension(363 ^ 1,bind([[_267228, _267377, _267852], [1985 ^ [], 1982 ^ [], 1994 ^ []]]))).
% 95.16/92.37  ncf('1.1.1',plain,[-(app(1982 ^ [], 1994 ^ []) = 1985 ^ [])],extension(1998 ^ 8)).
% 95.16/92.37  ncf('1.1.2',plain,[frontsegP(1985 ^ [], 1982 ^ []), -(frontsegP(1979 ^ [], 1976 ^ [])), 1985 ^ [] = 1979 ^ [], 1982 ^ [] = 1976 ^ []],extension(232 ^ 6,bind([[_262787, _262789, _262791, _262793], [1976 ^ [], 1982 ^ [], 1979 ^ [], 1985 ^ []]]))).
% 95.16/92.37  ncf('1.1.2.1',plain,[frontsegP(1979 ^ [], 1976 ^ [])],extension(2028 ^ 7)).
% 95.16/92.37  ncf('1.1.2.2',plain,[-(1985 ^ [] = 1979 ^ []), 1979 ^ [] = 1985 ^ []],extension(4 ^ 7,bind([[_255760, _255762], [1985 ^ [], 1979 ^ []]]))).
% 95.16/92.37  ncf('1.1.2.2.1',plain,[-(1979 ^ [] = 1985 ^ [])],extension(1989 ^ 8)).
% 95.16/92.37  ncf('1.1.2.3',plain,[-(1982 ^ [] = 1976 ^ []), 1976 ^ [] = 1982 ^ []],extension(4 ^ 7,bind([[_255760, _255762], [1982 ^ [], 1976 ^ []]]))).
% 95.16/92.37  ncf('1.1.2.3.1',plain,[-(1976 ^ [] = 1982 ^ [])],extension(1991 ^ 8)).
% 95.16/92.37  ncf('1.1.3',plain,[-(ssList(1982 ^ []))],extension(1984 ^ 4)).
% 95.16/92.37  ncf('1.1.4',plain,[-(ssList(1985 ^ []))],extension(1987 ^ 2)).
% 95.16/92.37  %-----------------------------------------------------
% 95.16/92.37  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------