TSTP Solution File: COM021+4 by nanoCoP---2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : nanoCoP---2.0
% Problem : COM021+4 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : nanocop.sh %s %d
% Computer : n015.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 10:14:35 EDT 2023
% Result : Theorem 2.19s 2.41s
% Output : Proof 2.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : COM021+4 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.12 % Command : nanocop.sh %s %d
% 0.12/0.33 % Computer : n015.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 03:30:22 EDT 2023
% 0.12/0.33 % CPUTime :
% 2.19/2.41
% 2.19/2.41 /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 2.19/2.41 Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.19/2.41 %-----------------------------------------------------
% 2.19/2.41 ncf(matrix, plain, [(936 ^ _124017) ^ [] : [xb = xd], (938 ^ _124017) ^ [] : [aReductOfIn0(xd, xb, xR)], (950 ^ _124017) ^ [] : [sdtmndtplgtdt0(xb, xR, xd)], (952 ^ _124017) ^ [] : [sdtmndtasgtdt0(xb, xR, xd)], (940 ^ _124017) ^ [_153526] : [aElement0(_153526), aReductOfIn0(_153526, xb, xR), sdtmndtplgtdt0(_153526, xR, xd)], (2 ^ _124017) ^ [_124141] : [-(_124141 = _124141)], (4 ^ _124017) ^ [_124248, _124250] : [_124250 = _124248, -(_124248 = _124250)], (10 ^ _124017) ^ [_124452, _124454, _124456] : [-(_124456 = _124452), _124456 = _124454, _124454 = _124452], (20 ^ _124017) ^ [_124765, _124767] : [-(isConfluent0(_124765)), _124767 = _124765, isConfluent0(_124767)], (30 ^ _124017) ^ [_125060, _125062] : [-(aRewritingSystem0(_125060)), _125062 = _125060, aRewritingSystem0(_125062)], (40 ^ _124017) ^ [_125355, _125357] : [-(isLocallyConfluent0(_125355)), _125357 = _125355, isLocallyConfluent0(_125357)], (50 ^ _124017) ^ [_125650, _125652] : [-(isTerminating0(_125650)), _125652 = _125650, isTerminating0(_125652)], (60 ^ _124017) ^ [_125973, _125975, _125977, _125979] : [-(iLess0(_125977, _125973)), iLess0(_125979, _125975), _125979 = _125977, _125975 = _125973], (74 ^ _124017) ^ [_126445, _126447, _126449, _126451, _126453, _126455] : [-(aNormalFormOfIn0(_126453, _126449, _126445)), aNormalFormOfIn0(_126455, _126451, _126447), _126455 = _126453, _126451 = _126449, _126447 = _126445], (92 ^ _124017) ^ [_126998, _127000] : [-(aElement0(_126998)), _127000 = _126998, aElement0(_127000)], (102 ^ _124017) ^ [_127349, _127351, _127353, _127355, _127357, _127359] : [-(aReductOfIn0(_127357, _127353, _127349)), aReductOfIn0(_127359, _127355, _127351), _127359 = _127357, _127355 = _127353, _127351 = _127349], (120 ^ _124017) ^ [_127958, _127960, _127962, _127964, _127966, _127968] : [-(sdtmndtplgtdt0(_127966, _127962, _127958)), sdtmndtplgtdt0(_127968, _127964, _127960), _127968 = _127966, _127964 = _127962, _127960 = _127958], (138 ^ _124017) ^ [_128547, _128549, _128551, _128553, _128555, _128557] : [-(sdtmndtasgtdt0(_128555, _128551, _128547)), sdtmndtasgtdt0(_128557, _128553, _128549), _128557 = _128555, _128553 = _128551, _128549 = _128547], (156 ^ _124017) ^ [_129110] : [aElement0(_129110), true___, -(true___)], (166 ^ _124017) ^ [_129365] : [aRewritingSystem0(_129365), true___, -(true___)], (176 ^ _124017) ^ [_129634, _129636] : [aElement0(_129636), aRewritingSystem0(_129634), 183 ^ _124017 : [(184 ^ _124017) ^ [_129856] : [aReductOfIn0(_129856, _129636, _129634), -(aElement0(_129856))]]], (190 ^ _124017) ^ [_130083, _130085] : [aElement0(_130085), aElement0(_130083), iLess0(_130085, _130083), true___, -(true___)], (208 ^ _124017) ^ [_130557, _130559, _130561] : [aElement0(_130561), aRewritingSystem0(_130559), aElement0(_130557), sdtmndtplgtdt0(_130561, _130559, _130557), true___, -(true___)], (230 ^ _124017) ^ [_131144, _131146, _131148] : [aElement0(_131148), aRewritingSystem0(_131146), aElement0(_131144), 241 ^ _124017 : [(242 ^ _124017) ^ [] : [sdtmndtplgtdt0(_131148, _131146, _131144), -(aReductOfIn0(_131144, _131148, _131146)), 250 ^ _124017 : [(251 ^ _124017) ^ [] : [-(aElement0(249 ^ [_131144, _131146, _131148]))], (253 ^ _124017) ^ [] : [-(aReductOfIn0(249 ^ [_131144, _131146, _131148], _131148, _131146))], (255 ^ _124017) ^ [] : [-(sdtmndtplgtdt0(249 ^ [_131144, _131146, _131148], _131146, _131144))]]], (257 ^ _124017) ^ [] : [-(sdtmndtplgtdt0(_131148, _131146, _131144)), 258 ^ _124017 : [(259 ^ _124017) ^ [] : [aReductOfIn0(_131144, _131148, _131146)], (261 ^ _124017) ^ [_132075] : [aElement0(_132075), aReductOfIn0(_132075, _131148, _131146), sdtmndtplgtdt0(_132075, _131146, _131144)]]]]], (273 ^ _124017) ^ [_132496, _132498, _132500, _132502] : [-(sdtmndtplgtdt0(_132502, _132500, _132496)), sdtmndtplgtdt0(_132502, _132500, _132498), sdtmndtplgtdt0(_132498, _132500, _132496), aElement0(_132502), aRewritingSystem0(_132500), aElement0(_132498), aElement0(_132496)], (299 ^ _124017) ^ [_133219, _133221, _133223] : [aElement0(_133223), aRewritingSystem0(_133221), aElement0(_133219), 310 ^ _124017 : [(321 ^ _124017) ^ [] : [322 ^ _124017 : [(323 ^ _124017) ^ [] : [_133223 = _133219], (325 ^ _124017) ^ [] : [sdtmndtplgtdt0(_133223, _133221, _133219)]], -(sdtmndtasgtdt0(_133223, _133221, _133219))], (311 ^ _124017) ^ [] : [sdtmndtasgtdt0(_133223, _133221, _133219), -(_133223 = _133219), -(sdtmndtplgtdt0(_133223, _133221, _133219))]]], (329 ^ _124017) ^ [_134077, _134079, _134081, _134083] : [-(sdtmndtasgtdt0(_134083, _134081, _134077)), sdtmndtasgtdt0(_134083, _134081, _134079), sdtmndtasgtdt0(_134079, _134081, _134077), aElement0(_134083), aRewritingSystem0(_134081), aElement0(_134079), aElement0(_134077)], (355 ^ _124017) ^ [_134772] : [aRewritingSystem0(_134772), 358 ^ _124017 : [(390 ^ _124017) ^ [] : [-(isConfluent0(_134772)), 394 ^ _124017 : [(395 ^ _124017) ^ [] : [-(aElement0(391 ^ [_134772]))], (397 ^ _124017) ^ [] : [-(aElement0(392 ^ [_134772]))], (399 ^ _124017) ^ [] : [-(aElement0(393 ^ [_134772]))], (401 ^ _124017) ^ [] : [-(sdtmndtasgtdt0(391 ^ [_134772], _134772, 392 ^ [_134772]))], (403 ^ _124017) ^ [] : [-(sdtmndtasgtdt0(391 ^ [_134772], _134772, 393 ^ [_134772]))], (405 ^ _124017) ^ [_136652] : [aElement0(_136652), sdtmndtasgtdt0(392 ^ [_134772], _134772, _136652), sdtmndtasgtdt0(393 ^ [_134772], _134772, _136652)]]], (359 ^ _124017) ^ [] : [isConfluent0(_134772), 362 ^ _124017 : [(363 ^ _124017) ^ [_135090, _135092, _135094] : [383 ^ _124017 : [(384 ^ _124017) ^ [] : [-(aElement0(382 ^ [_134772, _135090, _135092, _135094]))], (386 ^ _124017) ^ [] : [-(sdtmndtasgtdt0(_135092, _134772, 382 ^ [_134772, _135090, _135092, _135094]))], (388 ^ _124017) ^ [] : [-(sdtmndtasgtdt0(_135090, _134772, 382 ^ [_134772, _135090, _135092, _135094]))]], aElement0(_135094), aElement0(_135092), aElement0(_135090), sdtmndtasgtdt0(_135094, _134772, _135092), sdtmndtasgtdt0(_135094, _134772, _135090)]]]]], (417 ^ _124017) ^ [_137025] : [aRewritingSystem0(_137025), 420 ^ _124017 : [(452 ^ _124017) ^ [] : [-(isLocallyConfluent0(_137025)), 456 ^ _124017 : [(457 ^ _124017) ^ [] : [-(aElement0(453 ^ [_137025]))], (459 ^ _124017) ^ [] : [-(aElement0(454 ^ [_137025]))], (461 ^ _124017) ^ [] : [-(aElement0(455 ^ [_137025]))], (463 ^ _124017) ^ [] : [-(aReductOfIn0(454 ^ [_137025], 453 ^ [_137025], _137025))], (465 ^ _124017) ^ [] : [-(aReductOfIn0(455 ^ [_137025], 453 ^ [_137025], _137025))], (467 ^ _124017) ^ [_138905] : [aElement0(_138905), sdtmndtasgtdt0(454 ^ [_137025], _137025, _138905), sdtmndtasgtdt0(455 ^ [_137025], _137025, _138905)]]], (421 ^ _124017) ^ [] : [isLocallyConfluent0(_137025), 424 ^ _124017 : [(425 ^ _124017) ^ [_137343, _137345, _137347] : [445 ^ _124017 : [(446 ^ _124017) ^ [] : [-(aElement0(444 ^ [_137025, _137343, _137345, _137347]))], (448 ^ _124017) ^ [] : [-(sdtmndtasgtdt0(_137345, _137025, 444 ^ [_137025, _137343, _137345, _137347]))], (450 ^ _124017) ^ [] : [-(sdtmndtasgtdt0(_137343, _137025, 444 ^ [_137025, _137343, _137345, _137347]))]], aElement0(_137347), aElement0(_137345), aElement0(_137343), aReductOfIn0(_137345, _137347, _137025), aReductOfIn0(_137343, _137347, _137025)]]]]], (479 ^ _124017) ^ [_139278] : [aRewritingSystem0(_139278), 482 ^ _124017 : [(501 ^ _124017) ^ [] : [504 ^ _124017 : [(505 ^ _124017) ^ [] : [-(aElement0(502 ^ [_139278]))], (507 ^ _124017) ^ [] : [-(aElement0(503 ^ [_139278]))], (509 ^ _124017) ^ [] : [-(sdtmndtplgtdt0(502 ^ [_139278], _139278, 503 ^ [_139278]))], (511 ^ _124017) ^ [] : [iLess0(503 ^ [_139278], 502 ^ [_139278])]], -(isTerminating0(_139278))], (483 ^ _124017) ^ [] : [isTerminating0(_139278), 486 ^ _124017 : [(487 ^ _124017) ^ [_139547, _139549] : [aElement0(_139549), aElement0(_139547), sdtmndtplgtdt0(_139549, _139278, _139547), -(iLess0(_139547, _139549))]]]]], (515 ^ _124017) ^ [_140451, _140453] : [aElement0(_140453), aRewritingSystem0(_140451), 522 ^ _124017 : [(523 ^ _124017) ^ [_140723] : [aNormalFormOfIn0(_140723, _140453, _140451), 526 ^ _124017 : [(527 ^ _124017) ^ [] : [-(aElement0(_140723))], (529 ^ _124017) ^ [] : [-(sdtmndtasgtdt0(_140453, _140451, _140723))], (531 ^ _124017) ^ [_140999] : [aReductOfIn0(_140999, _140723, _140451)]]], (533 ^ _124017) ^ [_141074] : [-(aNormalFormOfIn0(_141074, _140453, _140451)), aElement0(_141074), sdtmndtasgtdt0(_140453, _140451, _141074), -(aReductOfIn0(542 ^ [_140451, _140453, _141074], _141074, _140451))]]], (548 ^ _124017) ^ [_141546] : [aRewritingSystem0(_141546), isTerminating0(_141546), 555 ^ _124017 : [(556 ^ _124017) ^ [_141765] : [aElement0(_141765), -(aNormalFormOfIn0(559 ^ [_141546, _141765], _141765, _141546))]]], (563 ^ _124017) ^ [] : [-(aRewritingSystem0(xR))], (626 ^ _124017) ^ [] : [-(isLocallyConfluent0(xR))], (654 ^ _124017) ^ [] : [-(isTerminating0(xR))], (628 ^ _124017) ^ [_144391, _144393] : [aElement0(_144393), aElement0(_144391), -(iLess0(_144391, _144393)), 637 ^ _124017 : [(638 ^ _124017) ^ [] : [aReductOfIn0(_144391, _144393, xR)], (650 ^ _124017) ^ [] : [sdtmndtplgtdt0(_144393, xR, _144391)], (640 ^ _124017) ^ [_144760] : [aElement0(_144760), aReductOfIn0(_144760, _144393, xR), sdtmndtplgtdt0(_144760, xR, _144391)]]], (565 ^ _124017) ^ [_142129, _142131, _142133] : [aElement0(_142133), aElement0(_142131), aElement0(_142129), aReductOfIn0(_142131, _142133, xR), aReductOfIn0(_142129, _142133, xR), 585 ^ _124017 : [(586 ^ _124017) ^ [] : [-(aElement0(584 ^ [_142129, _142131, _142133]))], (588 ^ _124017) ^ [] : [-(_142131 = 584 ^ [_142129, _142131, _142133]), 591 ^ _124017 : [(603 ^ _124017) ^ [] : [-(sdtmndtplgtdt0(_142131, xR, 584 ^ [_142129, _142131, _142133]))], (592 ^ _124017) ^ [] : [-(aReductOfIn0(584 ^ [_142129, _142131, _142133], _142131, xR)), 596 ^ _124017 : [(597 ^ _124017) ^ [] : [-(aElement0(595 ^ [_142129, _142131, _142133]))], (599 ^ _124017) ^ [] : [-(aReductOfIn0(595 ^ [_142129, _142131, _142133], _142131, xR))], (601 ^ _124017) ^ [] : [-(sdtmndtplgtdt0(595 ^ [_142129, _142131, _142133], xR, 584 ^ [_142129, _142131, _142133]))]]]]], (605 ^ _124017) ^ [] : [-(sdtmndtasgtdt0(_142131, xR, 584 ^ [_142129, _142131, _142133]))], (624 ^ _124017) ^ [] : [-(sdtmndtasgtdt0(_142129, xR, 584 ^ [_142129, _142131, _142133]))], (607 ^ _124017) ^ [] : [-(_142129 = 584 ^ [_142129, _142131, _142133]), 610 ^ _124017 : [(622 ^ _124017) ^ [] : [-(sdtmndtplgtdt0(_142129, xR, 584 ^ [_142129, _142131, _142133]))], (611 ^ _124017) ^ [] : [-(aReductOfIn0(584 ^ [_142129, _142131, _142133], _142129, xR)), 615 ^ _124017 : [(616 ^ _124017) ^ [] : [-(aElement0(614 ^ [_142129, _142131, _142133]))], (618 ^ _124017) ^ [] : [-(aReductOfIn0(614 ^ [_142129, _142131, _142133], _142129, xR))], (620 ^ _124017) ^ [] : [-(sdtmndtplgtdt0(614 ^ [_142129, _142131, _142133], xR, 584 ^ [_142129, _142131, _142133]))]]]]]]], (656 ^ _124017) ^ [] : [-(aElement0(xa))], (658 ^ _124017) ^ [] : [-(aElement0(xb))], (660 ^ _124017) ^ [] : [-(aElement0(xc))], (662 ^ _124017) ^ [_145401, _145403, _145405] : [aElement0(_145405), aElement0(_145403), aElement0(_145401), 677 ^ _124017 : [(678 ^ _124017) ^ [] : [_145405 = _145403], (680 ^ _124017) ^ [] : [aReductOfIn0(_145403, _145405, xR)], (692 ^ _124017) ^ [] : [sdtmndtplgtdt0(_145405, xR, _145403)], (694 ^ _124017) ^ [] : [sdtmndtasgtdt0(_145405, xR, _145403)], (682 ^ _124017) ^ [_146144] : [aElement0(_146144), aReductOfIn0(_146144, _145405, xR), sdtmndtplgtdt0(_146144, xR, _145403)]], 695 ^ _124017 : [(696 ^ _124017) ^ [] : [_145405 = _145401], (698 ^ _124017) ^ [] : [aReductOfIn0(_145401, _145405, xR)], (710 ^ _124017) ^ [] : [sdtmndtplgtdt0(_145405, xR, _145401)], (712 ^ _124017) ^ [] : [sdtmndtasgtdt0(_145405, xR, _145401)], (700 ^ _124017) ^ [_146717] : [aElement0(_146717), aReductOfIn0(_146717, _145405, xR), sdtmndtplgtdt0(_146717, xR, _145401)]], iLess0(_145405, xa), 718 ^ _124017 : [(719 ^ _124017) ^ [] : [-(aElement0(717 ^ [_145401, _145403, _145405]))], (721 ^ _124017) ^ [] : [-(_145403 = 717 ^ [_145401, _145403, _145405]), 724 ^ _124017 : [(736 ^ _124017) ^ [] : [-(sdtmndtplgtdt0(_145403, xR, 717 ^ [_145401, _145403, _145405]))], (725 ^ _124017) ^ [] : [-(aReductOfIn0(717 ^ [_145401, _145403, _145405], _145403, xR)), 729 ^ _124017 : [(730 ^ _124017) ^ [] : [-(aElement0(728 ^ [_145401, _145403, _145405]))], (732 ^ _124017) ^ [] : [-(aReductOfIn0(728 ^ [_145401, _145403, _145405], _145403, xR))], (734 ^ _124017) ^ [] : [-(sdtmndtplgtdt0(728 ^ [_145401, _145403, _145405], xR, 717 ^ [_145401, _145403, _145405]))]]]]], (738 ^ _124017) ^ [] : [-(sdtmndtasgtdt0(_145403, xR, 717 ^ [_145401, _145403, _145405]))], (757 ^ _124017) ^ [] : [-(sdtmndtasgtdt0(_145401, xR, 717 ^ [_145401, _145403, _145405]))], (740 ^ _124017) ^ [] : [-(_145401 = 717 ^ [_145401, _145403, _145405]), 743 ^ _124017 : [(755 ^ _124017) ^ [] : [-(sdtmndtplgtdt0(_145401, xR, 717 ^ [_145401, _145403, _145405]))], (744 ^ _124017) ^ [] : [-(aReductOfIn0(717 ^ [_145401, _145403, _145405], _145401, xR)), 748 ^ _124017 : [(749 ^ _124017) ^ [] : [-(aElement0(747 ^ [_145401, _145403, _145405]))], (751 ^ _124017) ^ [] : [-(aReductOfIn0(747 ^ [_145401, _145403, _145405], _145401, xR))], (753 ^ _124017) ^ [] : [-(sdtmndtplgtdt0(747 ^ [_145401, _145403, _145405], xR, 717 ^ [_145401, _145403, _145405]))]]]]]]], (759 ^ _124017) ^ [] : [-(aReductOfIn0(xb, xa, xR)), 763 ^ _124017 : [(764 ^ _124017) ^ [] : [-(aElement0(762 ^ []))], (766 ^ _124017) ^ [] : [-(aReductOfIn0(762 ^ [], xa, xR))], (768 ^ _124017) ^ [] : [-(sdtmndtplgtdt0(762 ^ [], xR, xb))]]], (770 ^ _124017) ^ [] : [-(sdtmndtplgtdt0(xa, xR, xb))], (783 ^ _124017) ^ [] : [-(sdtmndtplgtdt0(xa, xR, xc))], (772 ^ _124017) ^ [] : [-(aReductOfIn0(xc, xa, xR)), 776 ^ _124017 : [(777 ^ _124017) ^ [] : [-(aElement0(775 ^ []))], (779 ^ _124017) ^ [] : [-(aReductOfIn0(775 ^ [], xa, xR))], (781 ^ _124017) ^ [] : [-(sdtmndtplgtdt0(775 ^ [], xR, xc))]]], (785 ^ _124017) ^ [] : [-(aElement0(xu))], (787 ^ _124017) ^ [] : [-(aReductOfIn0(xu, xa, xR))], (806 ^ _124017) ^ [] : [-(sdtmndtasgtdt0(xu, xR, xb))], (789 ^ _124017) ^ [] : [-(xu = xb), 792 ^ _124017 : [(804 ^ _124017) ^ [] : [-(sdtmndtplgtdt0(xu, xR, xb))], (793 ^ _124017) ^ [] : [-(aReductOfIn0(xb, xu, xR)), 797 ^ _124017 : [(798 ^ _124017) ^ [] : [-(aElement0(796 ^ []))], (800 ^ _124017) ^ [] : [-(aReductOfIn0(796 ^ [], xu, xR))], (802 ^ _124017) ^ [] : [-(sdtmndtplgtdt0(796 ^ [], xR, xb))]]]]], (808 ^ _124017) ^ [] : [-(aElement0(xv))], (810 ^ _124017) ^ [] : [-(aReductOfIn0(xv, xa, xR))], (829 ^ _124017) ^ [] : [-(sdtmndtasgtdt0(xv, xR, xc))], (812 ^ _124017) ^ [] : [-(xv = xc), 815 ^ _124017 : [(827 ^ _124017) ^ [] : [-(sdtmndtplgtdt0(xv, xR, xc))], (816 ^ _124017) ^ [] : [-(aReductOfIn0(xc, xv, xR)), 820 ^ _124017 : [(821 ^ _124017) ^ [] : [-(aElement0(819 ^ []))], (823 ^ _124017) ^ [] : [-(aReductOfIn0(819 ^ [], xv, xR))], (825 ^ _124017) ^ [] : [-(sdtmndtplgtdt0(819 ^ [], xR, xc))]]]]], (831 ^ _124017) ^ [] : [-(aElement0(xw))], (833 ^ _124017) ^ [] : [-(xu = xw), 836 ^ _124017 : [(848 ^ _124017) ^ [] : [-(sdtmndtplgtdt0(xu, xR, xw))], (837 ^ _124017) ^ [] : [-(aReductOfIn0(xw, xu, xR)), 841 ^ _124017 : [(842 ^ _124017) ^ [] : [-(aElement0(840 ^ []))], (844 ^ _124017) ^ [] : [-(aReductOfIn0(840 ^ [], xu, xR))], (846 ^ _124017) ^ [] : [-(sdtmndtplgtdt0(840 ^ [], xR, xw))]]]]], (850 ^ _124017) ^ [] : [-(sdtmndtasgtdt0(xu, xR, xw))], (869 ^ _124017) ^ [] : [-(sdtmndtasgtdt0(xv, xR, xw))], (852 ^ _124017) ^ [] : [-(xv = xw), 855 ^ _124017 : [(867 ^ _124017) ^ [] : [-(sdtmndtplgtdt0(xv, xR, xw))], (856 ^ _124017) ^ [] : [-(aReductOfIn0(xw, xv, xR)), 860 ^ _124017 : [(861 ^ _124017) ^ [] : [-(aElement0(859 ^ []))], (863 ^ _124017) ^ [] : [-(aReductOfIn0(859 ^ [], xv, xR))], (865 ^ _124017) ^ [] : [-(sdtmndtplgtdt0(859 ^ [], xR, xw))]]]]], (871 ^ _124017) ^ [] : [-(aElement0(xd))], (890 ^ _124017) ^ [] : [-(sdtmndtasgtdt0(xw, xR, xd))], (892 ^ _124017) ^ [_152130] : [aReductOfIn0(_152130, xd, xR)], (894 ^ _124017) ^ [] : [-(aNormalFormOfIn0(xd, xw, xR))], (873 ^ _124017) ^ [] : [-(xw = xd), 876 ^ _124017 : [(888 ^ _124017) ^ [] : [-(sdtmndtplgtdt0(xw, xR, xd))], (877 ^ _124017) ^ [] : [-(aReductOfIn0(xd, xw, xR)), 881 ^ _124017 : [(882 ^ _124017) ^ [] : [-(aElement0(880 ^ []))], (884 ^ _124017) ^ [] : [-(aReductOfIn0(880 ^ [], xw, xR))], (886 ^ _124017) ^ [] : [-(sdtmndtplgtdt0(880 ^ [], xR, xd))]]]]], (896 ^ _124017) ^ [] : [-(aElement0(xx))], (898 ^ _124017) ^ [] : [-(xb = xx), 901 ^ _124017 : [(913 ^ _124017) ^ [] : [-(sdtmndtplgtdt0(xb, xR, xx))], (902 ^ _124017) ^ [] : [-(aReductOfIn0(xx, xb, xR)), 906 ^ _124017 : [(907 ^ _124017) ^ [] : [-(aElement0(905 ^ []))], (909 ^ _124017) ^ [] : [-(aReductOfIn0(905 ^ [], xb, xR))], (911 ^ _124017) ^ [] : [-(sdtmndtplgtdt0(905 ^ [], xR, xx))]]]]], (915 ^ _124017) ^ [] : [-(sdtmndtasgtdt0(xb, xR, xx))], (934 ^ _124017) ^ [] : [-(sdtmndtasgtdt0(xd, xR, xx))], (917 ^ _124017) ^ [] : [-(xd = xx), 920 ^ _124017 : [(932 ^ _124017) ^ [] : [-(sdtmndtplgtdt0(xd, xR, xx))], (921 ^ _124017) ^ [] : [-(aReductOfIn0(xx, xd, xR)), 925 ^ _124017 : [(926 ^ _124017) ^ [] : [-(aElement0(924 ^ []))], (928 ^ _124017) ^ [] : [-(aReductOfIn0(924 ^ [], xd, xR))], (930 ^ _124017) ^ [] : [-(sdtmndtplgtdt0(924 ^ [], xR, xx))]]]]]], input).
% 2.19/2.41 ncf('1',plain,[aReductOfIn0(xx, xd, xR)],start(892 ^ 0,bind([[_152130], [xx]]))).
% 2.19/2.41 ncf('1.1',plain,[-(aReductOfIn0(xx, xd, xR)), 928 : -(aReductOfIn0(924 ^ [], xd, xR)), 921 : -(xd = xx)],extension(917 ^ 1)).
% 2.19/2.41 ncf('1.1.1',plain,[aReductOfIn0(924 ^ [], xd, xR), 523 : aNormalFormOfIn0(xd, xw, xR), 523 : aElement0(xw), 523 : aRewritingSystem0(xR)],extension(515 ^ 6,bind([[_140451, _140453, _140723, _140999], [xR, xw, xd, 924 ^ []]]))).
% 2.19/2.41 ncf('1.1.1.1',plain,[-(aNormalFormOfIn0(xd, xw, xR))],extension(894 ^ 9)).
% 2.19/2.41 ncf('1.1.1.2',plain,[-(aElement0(xw))],extension(831 ^ 7)).
% 2.19/2.41 ncf('1.1.1.3',plain,[-(aRewritingSystem0(xR))],extension(563 ^ 7)).
% 2.19/2.41 ncf('1.1.2',plain,[xd = xx, -(sdtmndtasgtdt0(xx, xR, xd)), sdtmndtasgtdt0(xd, xR, xx), xR = xR, xx = xd],extension(138 ^ 2,bind([[_128547, _128549, _128551, _128553, _128555, _128557], [xd, xx, xR, xR, xx, xd]]))).
% 2.19/2.41 ncf('1.1.2.1',plain,[sdtmndtasgtdt0(xx, xR, xd), -(sdtmndtasgtdt0(xb, xR, xd)), sdtmndtasgtdt0(xb, xR, xx), aElement0(xb), aRewritingSystem0(xR), aElement0(xx), aElement0(xd)],extension(329 ^ 3,bind([[_134077, _134079, _134081, _134083], [xd, xx, xR, xb]]))).
% 2.19/2.41 ncf('1.1.2.1.1',plain,[sdtmndtasgtdt0(xb, xR, xd)],extension(952 ^ 4)).
% 2.19/2.41 ncf('1.1.2.1.2',plain,[-(sdtmndtasgtdt0(xb, xR, xx))],extension(915 ^ 4)).
% 2.19/2.41 ncf('1.1.2.1.3',plain,[-(aElement0(xb))],extension(658 ^ 4)).
% 2.19/2.41 ncf('1.1.2.1.4',plain,[-(aRewritingSystem0(xR))],extension(563 ^ 4)).
% 2.19/2.41 ncf('1.1.2.1.5',plain,[-(aElement0(xx))],extension(896 ^ 4)).
% 2.19/2.41 ncf('1.1.2.1.6',plain,[-(aElement0(xd))],extension(871 ^ 4)).
% 2.19/2.41 ncf('1.1.2.2',plain,[-(sdtmndtasgtdt0(xd, xR, xx)), 323 : xd = xx, 321 : aElement0(xd), 321 : aRewritingSystem0(xR), 321 : aElement0(xx)],extension(299 ^ 3,bind([[_133219, _133221, _133223], [xx, xR, xd]]))).
% 2.19/2.41 ncf('1.1.2.2.1',plain,[-(xd = xx)],reduction('1.1')).
% 2.19/2.41 ncf('1.1.2.2.2',plain,[-(aElement0(xd))],extension(871 ^ 4)).
% 2.19/2.41 ncf('1.1.2.2.3',plain,[-(aRewritingSystem0(xR))],extension(563 ^ 4)).
% 2.19/2.41 ncf('1.1.2.2.4',plain,[-(aElement0(xx))],extension(896 ^ 4)).
% 2.19/2.41 ncf('1.1.2.3',plain,[-(xR = xR)],extension(2 ^ 3,bind([[_124141], [xR]]))).
% 2.19/2.41 ncf('1.1.2.4',plain,[-(xx = xd), xd = xx],extension(4 ^ 3,bind([[_124248, _124250], [xx, xd]]))).
% 2.19/2.41 ncf('1.1.2.4.1',plain,[-(xd = xx)],reduction('1.1')).
% 2.19/2.41 %-----------------------------------------------------
% 2.19/2.41 End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------