TSTP Solution File: COM021+1 by nanoCoP---2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : nanoCoP---2.0
% Problem : COM021+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : nanocop.sh %s %d
% Computer : n023.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 10:14:34 EDT 2023
% Result : Theorem 194.03s 187.06s
% Output : Proof 194.03s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : COM021+1 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.12 % Command : nanocop.sh %s %d
% 0.12/0.33 % Computer : n023.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 03:37:28 EDT 2023
% 0.12/0.33 % CPUTime :
% 194.03/187.06
% 194.03/187.06 /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 194.03/187.06 Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 194.03/187.06 %-----------------------------------------------------
% 194.03/187.06 ncf(matrix, plain, [(636 ^ _117006) ^ [] : [sdtmndtasgtdt0(xb, xR, xd)], !, (299 ^ _96856) ^ [_106038, _106040, _106042] : [aElement0(_106042), aRewritingSystem0(_106040), aElement0(_106038), 310 ^ _96856 : [(311 ^ _96856) ^ [] : [sdtmndtasgtdt0(_106042, _106040, _106038), -(_106042 = _106038), -(sdtmndtplgtdt0(_106042, _106040, _106038))], (321 ^ _96856) ^ [] : [322 ^ _96856 : [(325 ^ _96856) ^ [] : [sdtmndtplgtdt0(_106042, _106040, _106038)], (323 ^ _96856) ^ [] : [_106042 = _106038]], -(sdtmndtasgtdt0(_106042, _106040, _106038))]]], (606 ^ _96856) ^ [] : [-(sdtmndtplgtdt0(xa, xR, xb))], (156 ^ _96856) ^ [_101929] : [aElement0(_101929), true___, -(true___)], (10 ^ _96856) ^ [_97271, _97273, _97275] : [-(_97275 = _97271), _97275 = _97273, _97273 = _97271], (355 ^ _96856) ^ [_107591] : [aRewritingSystem0(_107591), 358 ^ _96856 : [(359 ^ _96856) ^ [] : [isConfluent0(_107591), 362 ^ _96856 : [(363 ^ _96856) ^ [_107909, _107911, _107913] : [383 ^ _96856 : [(388 ^ _96856) ^ [] : [-(sdtmndtasgtdt0(_107909, _107591, 382 ^ [_107591, _107909, _107911, _107913]))], (386 ^ _96856) ^ [] : [-(sdtmndtasgtdt0(_107911, _107591, 382 ^ [_107591, _107909, _107911, _107913]))], (384 ^ _96856) ^ [] : [-(aElement0(382 ^ [_107591, _107909, _107911, _107913]))]], aElement0(_107913), aElement0(_107911), aElement0(_107909), sdtmndtasgtdt0(_107913, _107591, _107911), sdtmndtasgtdt0(_107913, _107591, _107909)]]], (390 ^ _96856) ^ [] : [-(isConfluent0(_107591)), 394 ^ _96856 : [(403 ^ _96856) ^ [] : [-(sdtmndtasgtdt0(391 ^ [_107591], _107591, 393 ^ [_107591]))], (401 ^ _96856) ^ [] : [-(sdtmndtasgtdt0(391 ^ [_107591], _107591, 392 ^ [_107591]))], (405 ^ _96856) ^ [_109471] : [aElement0(_109471), sdtmndtasgtdt0(392 ^ [_107591], _107591, _109471), sdtmndtasgtdt0(393 ^ [_107591], _107591, _109471)], (395 ^ _96856) ^ [] : [-(aElement0(391 ^ [_107591]))], (397 ^ _96856) ^ [] : [-(aElement0(392 ^ [_107591]))], (399 ^ _96856) ^ [] : [-(aElement0(393 ^ [_107591]))]]]]], (166 ^ _96856) ^ [_102184] : [aRewritingSystem0(_102184), true___, -(true___)], (138 ^ _96856) ^ [_101366, _101368, _101370, _101372, _101374, _101376] : [-(sdtmndtasgtdt0(_101374, _101370, _101366)), sdtmndtasgtdt0(_101376, _101372, _101368), _101376 = _101374, _101372 = _101370, _101368 = _101366], (622 ^ _96856) ^ [] : [-(aElement0(xw))], (20 ^ _96856) ^ [_97584, _97586] : [-(isConfluent0(_97584)), _97586 = _97584, isConfluent0(_97586)], (618 ^ _96856) ^ [] : [-(aReductOfIn0(xv, xa, xR))], (612 ^ _96856) ^ [] : [-(aReductOfIn0(xu, xa, xR))], (4 ^ _96856) ^ [_97067, _97069] : [_97069 = _97067, -(_97067 = _97069)], (608 ^ _96856) ^ [] : [-(sdtmndtplgtdt0(xa, xR, xc))], (2 ^ _96856) ^ [_96960] : [-(_96960 = _96960)], (628 ^ _96856) ^ [] : [-(aNormalFormOfIn0(xd, xw, xR))], (614 ^ _96856) ^ [] : [-(sdtmndtasgtdt0(xu, xR, xb))], (92 ^ _96856) ^ [_99873, _99875, _99877, _99879, _99881, _99883] : [-(aReductOfIn0(_99881, _99877, _99873)), aReductOfIn0(_99883, _99879, _99875), _99883 = _99881, _99879 = _99877, _99875 = _99873], (632 ^ _96856) ^ [] : [-(sdtmndtasgtdt0(xb, xR, xx))], (128 ^ _96856) ^ [_101035, _101037] : [-(aElement0(_101035)), _101037 = _101035, aElement0(_101037)], (573 ^ _96856) ^ [] : [-(aElement0(xc))], (190 ^ _96856) ^ [_102902, _102904] : [aElement0(_102904), aElement0(_102902), iLess0(_102904, _102902), true___, -(true___)], (74 ^ _96856) ^ [_99264, _99266, _99268, _99270, _99272, _99274] : [-(sdtmndtplgtdt0(_99272, _99268, _99264)), sdtmndtplgtdt0(_99274, _99270, _99266), _99274 = _99272, _99270 = _99268, _99266 = _99264], (479 ^ _96856) ^ [_112097] : [aRewritingSystem0(_112097), 482 ^ _96856 : [(483 ^ _96856) ^ [] : [isTerminating0(_112097), 486 ^ _96856 : [(487 ^ _96856) ^ [_112366, _112368] : [aElement0(_112368), aElement0(_112366), sdtmndtplgtdt0(_112368, _112097, _112366), -(iLess0(_112366, _112368))]]], (501 ^ _96856) ^ [] : [504 ^ _96856 : [(511 ^ _96856) ^ [] : [iLess0(503 ^ [_112097], 502 ^ [_112097])], (505 ^ _96856) ^ [] : [-(aElement0(502 ^ [_112097]))], (509 ^ _96856) ^ [] : [-(sdtmndtplgtdt0(502 ^ [_112097], _112097, 503 ^ [_112097]))], (507 ^ _96856) ^ [] : [-(aElement0(503 ^ [_112097]))]], -(isTerminating0(_112097))]]], (60 ^ _96856) ^ [_98792, _98794, _98796, _98798] : [-(iLess0(_98796, _98792)), iLess0(_98798, _98794), _98798 = _98796, _98794 = _98792], (634 ^ _96856) ^ [] : [-(sdtmndtasgtdt0(xd, xR, xx))], (110 ^ _96856) ^ [_100482, _100484, _100486, _100488, _100490, _100492] : [-(aNormalFormOfIn0(_100490, _100486, _100482)), aNormalFormOfIn0(_100492, _100488, _100484), _100492 = _100490, _100488 = _100486, _100484 = _100482], (329 ^ _96856) ^ [_106896, _106898, _106900, _106902] : [-(sdtmndtasgtdt0(_106902, _106900, _106896)), sdtmndtasgtdt0(_106902, _106900, _106898), sdtmndtasgtdt0(_106898, _106900, _106896), aElement0(_106902), aRewritingSystem0(_106900), aElement0(_106898), aElement0(_106896)], (630 ^ _96856) ^ [] : [-(aElement0(xx))], (569 ^ _96856) ^ [] : [-(aElement0(xa))], (548 ^ _96856) ^ [_114365] : [aRewritingSystem0(_114365), isTerminating0(_114365), 555 ^ _96856 : [(556 ^ _96856) ^ [_114584] : [aElement0(_114584), -(aNormalFormOfIn0(559 ^ [_114365, _114584], _114584, _114365))]]], (230 ^ _96856) ^ [_103963, _103965, _103967] : [aElement0(_103967), aRewritingSystem0(_103965), aElement0(_103963), 241 ^ _96856 : [(257 ^ _96856) ^ [] : [-(sdtmndtplgtdt0(_103967, _103965, _103963)), 258 ^ _96856 : [(261 ^ _96856) ^ [_104894] : [aElement0(_104894), aReductOfIn0(_104894, _103967, _103965), sdtmndtplgtdt0(_104894, _103965, _103963)], (259 ^ _96856) ^ [] : [aReductOfIn0(_103963, _103967, _103965)]]], (242 ^ _96856) ^ [] : [sdtmndtplgtdt0(_103967, _103965, _103963), -(aReductOfIn0(_103963, _103967, _103965)), 250 ^ _96856 : [(255 ^ _96856) ^ [] : [-(sdtmndtplgtdt0(249 ^ [_103963, _103965, _103967], _103965, _103963))], (253 ^ _96856) ^ [] : [-(aReductOfIn0(249 ^ [_103963, _103965, _103967], _103967, _103965))], (251 ^ _96856) ^ [] : [-(aElement0(249 ^ [_103963, _103965, _103967]))]]]]], (571 ^ _96856) ^ [] : [-(aElement0(xb))], (30 ^ _96856) ^ [_97879, _97881] : [-(aRewritingSystem0(_97879)), _97881 = _97879, aRewritingSystem0(_97881)], (565 ^ _96856) ^ [] : [-(isLocallyConfluent0(xR))], (176 ^ _96856) ^ [_102453, _102455] : [aElement0(_102455), aRewritingSystem0(_102453), 183 ^ _96856 : [(184 ^ _96856) ^ [_102675] : [aReductOfIn0(_102675, _102455, _102453), -(aElement0(_102675))]]], (616 ^ _96856) ^ [] : [-(aElement0(xv))], (273 ^ _96856) ^ [_105315, _105317, _105319, _105321] : [-(sdtmndtplgtdt0(_105321, _105319, _105315)), sdtmndtplgtdt0(_105321, _105319, _105317), sdtmndtplgtdt0(_105317, _105319, _105315), aElement0(_105321), aRewritingSystem0(_105319), aElement0(_105317), aElement0(_105315)], (624 ^ _96856) ^ [] : [-(sdtmndtasgtdt0(xu, xR, xw))], (40 ^ _96856) ^ [_98174, _98176] : [-(isLocallyConfluent0(_98174)), _98176 = _98174, isLocallyConfluent0(_98176)], (515 ^ _96856) ^ [_113270, _113272] : [aElement0(_113272), aRewritingSystem0(_113270), 522 ^ _96856 : [(533 ^ _96856) ^ [_113893] : [-(aNormalFormOfIn0(_113893, _113272, _113270)), aElement0(_113893), sdtmndtasgtdt0(_113272, _113270, _113893), -(aReductOfIn0(542 ^ [_113270, _113272, _113893], _113893, _113270))], (523 ^ _96856) ^ [_113542] : [aNormalFormOfIn0(_113542, _113272, _113270), 526 ^ _96856 : [(531 ^ _96856) ^ [_113818] : [aReductOfIn0(_113818, _113542, _113270)], (529 ^ _96856) ^ [] : [-(sdtmndtasgtdt0(_113272, _113270, _113542))], (527 ^ _96856) ^ [] : [-(aElement0(_113542))]]]]], (567 ^ _96856) ^ [] : [-(isTerminating0(xR))], (610 ^ _96856) ^ [] : [-(aElement0(xu))], (417 ^ _96856) ^ [_109844] : [aRewritingSystem0(_109844), 420 ^ _96856 : [(421 ^ _96856) ^ [] : [isLocallyConfluent0(_109844), 424 ^ _96856 : [(425 ^ _96856) ^ [_110162, _110164, _110166] : [445 ^ _96856 : [(450 ^ _96856) ^ [] : [-(sdtmndtasgtdt0(_110162, _109844, 444 ^ [_109844, _110162, _110164, _110166]))], (448 ^ _96856) ^ [] : [-(sdtmndtasgtdt0(_110164, _109844, 444 ^ [_109844, _110162, _110164, _110166]))], (446 ^ _96856) ^ [] : [-(aElement0(444 ^ [_109844, _110162, _110164, _110166]))]], aElement0(_110166), aElement0(_110164), aElement0(_110162), aReductOfIn0(_110164, _110166, _109844), aReductOfIn0(_110162, _110166, _109844)]]], (452 ^ _96856) ^ [] : [-(isLocallyConfluent0(_109844)), 456 ^ _96856 : [(465 ^ _96856) ^ [] : [-(aReductOfIn0(455 ^ [_109844], 453 ^ [_109844], _109844))], (463 ^ _96856) ^ [] : [-(aReductOfIn0(454 ^ [_109844], 453 ^ [_109844], _109844))], (467 ^ _96856) ^ [_111724] : [aElement0(_111724), sdtmndtasgtdt0(454 ^ [_109844], _109844, _111724), sdtmndtasgtdt0(455 ^ [_109844], _109844, _111724)], (457 ^ _96856) ^ [] : [-(aElement0(453 ^ [_109844]))], (459 ^ _96856) ^ [] : [-(aElement0(454 ^ [_109844]))], (461 ^ _96856) ^ [] : [-(aElement0(455 ^ [_109844]))]]]]], (575 ^ _96856) ^ [_115199, _115201, _115203] : [iLess0(_115203, xa), 599 ^ _96856 : [(604 ^ _96856) ^ [] : [-(sdtmndtasgtdt0(_115199, xR, 598 ^ [_115199, _115201, _115203]))], (602 ^ _96856) ^ [] : [-(sdtmndtasgtdt0(_115201, xR, 598 ^ [_115199, _115201, _115203]))], (600 ^ _96856) ^ [] : [-(aElement0(598 ^ [_115199, _115201, _115203]))]], aElement0(_115203), aElement0(_115201), aElement0(_115199), sdtmndtasgtdt0(_115203, xR, _115201), sdtmndtasgtdt0(_115203, xR, _115199)], (620 ^ _96856) ^ [] : [-(sdtmndtasgtdt0(xv, xR, xc))], (626 ^ _96856) ^ [] : [-(sdtmndtasgtdt0(xv, xR, xw))], (563 ^ _96856) ^ [] : [-(aRewritingSystem0(xR))], (50 ^ _96856) ^ [_98469, _98471] : [-(isTerminating0(_98469)), _98471 = _98469, isTerminating0(_98471)], (208 ^ _96856) ^ [_103376, _103378, _103380] : [aElement0(_103380), aRewritingSystem0(_103378), aElement0(_103376), sdtmndtplgtdt0(_103380, _103378, _103376), true___, -(true___)]], input).
% 194.03/187.06 ncf('1',plain,[sdtmndtasgtdt0(xb, xR, xd)],start(636 ^ 0)).
% 194.03/187.06 ncf('1.1',plain,[-(sdtmndtasgtdt0(xb, xR, xd)), sdtmndtasgtdt0(xb, xR, xx), sdtmndtasgtdt0(xx, xR, xd), aElement0(xb), aRewritingSystem0(xR), aElement0(xx), aElement0(xd)],extension(329 ^ 1,bind([[_106896, _106898, _106900, _106902], [xd, xx, xR, xb]]))).
% 194.03/187.06 ncf('1.1.1',plain,[-(sdtmndtasgtdt0(xb, xR, xx)), 325 : sdtmndtplgtdt0(xb, xR, xx), 321 : aElement0(xb), 321 : aRewritingSystem0(xR), 321 : aElement0(xx)],extension(299 ^ 2,bind([[_106038, _106040, _106042], [xx, xR, xb]]))).
% 194.03/187.06 ncf('1.1.1.1',plain,[-(sdtmndtplgtdt0(xb, xR, xx)), sdtmndtplgtdt0(xb, xR, xx), sdtmndtplgtdt0(xx, xR, xx), aElement0(xb), aRewritingSystem0(xR), aElement0(xx), aElement0(xx)],extension(273 ^ 7,bind([[_105315, _105317, _105319, _105321], [xx, xx, xR, xb]]))).
% 194.03/187.06 ncf('1.1.1.1.1',plain,[-(sdtmndtplgtdt0(xb, xR, xx)), 311 : sdtmndtasgtdt0(xb, xR, xx), 311 : -(xb = xx), 311 : aElement0(xb), 311 : aRewritingSystem0(xR), 311 : aElement0(xx)],extension(299 ^ 8,bind([[_106038, _106040, _106042], [xx, xR, xb]]))).
% 194.03/187.06 ncf('1.1.1.1.1.1',plain,[-(sdtmndtasgtdt0(xb, xR, xx)), 323 : xb = xx],extension(321 ^ 11)).
% 194.03/187.06 ncf('1.1.1.1.1.1.1',plain,[-(xb = xx), 311 : sdtmndtasgtdt0(xb, xR, xx), 311 : -(sdtmndtplgtdt0(xb, xR, xx)), 311 : aElement0(xb), 311 : aRewritingSystem0(xR), 311 : aElement0(xx)],extension(299 ^ 14,bind([[_106038, _106040, _106042], [xx, xR, xb]]))).
% 194.03/187.06 ncf('1.1.1.1.1.1.1.1',plain,[-(sdtmndtasgtdt0(xb, xR, xx))],extension(632 ^ 17)).
% 194.03/187.06 ncf('1.1.1.1.1.1.1.2',plain,[sdtmndtplgtdt0(xb, xR, xx)],reduction('1.1.1.1')).
% 194.03/187.06 ncf('1.1.1.1.1.1.1.3',plain,[-(aElement0(xb))],extension(571 ^ 15)).
% 194.03/187.06 ncf('1.1.1.1.1.1.1.4',plain,[-(aRewritingSystem0(xR))],extension(563 ^ 15)).
% 194.03/187.06 ncf('1.1.1.1.1.1.1.5',plain,[-(aElement0(xx))],extension(630 ^ 15)).
% 194.03/187.06 ncf('1.1.1.1.1.2',plain,[xb = xx, -(sdtmndtasgtdt0(xb, xR, xx))],extension(321 ^ 11)).
% 194.03/187.06 ncf('1.1.1.1.1.2.1',plain,[sdtmndtasgtdt0(xb, xR, xx)],reduction('1.1')).
% 194.03/187.06 ncf('1.1.1.1.1.3',plain,[-(aElement0(xb))],extension(571 ^ 9)).
% 194.03/187.06 ncf('1.1.1.1.1.4',plain,[-(aRewritingSystem0(xR))],extension(563 ^ 9)).
% 194.03/187.06 ncf('1.1.1.1.1.5',plain,[-(aElement0(xx))],extension(630 ^ 9)).
% 194.03/187.06 ncf('1.1.1.1.2',plain,[-(sdtmndtplgtdt0(xx, xR, xx)), 311 : sdtmndtasgtdt0(xx, xR, xx), 311 : -(xx = xx), 311 : aElement0(xx), 311 : aRewritingSystem0(xR), 311 : aElement0(xx)],extension(299 ^ 8,bind([[_106038, _106040, _106042], [xx, xR, xx]]))).
% 194.03/187.06 ncf('1.1.1.1.2.1',plain,[-(sdtmndtasgtdt0(xx, xR, xx)), 323 : xx = xx],extension(321 ^ 11)).
% 194.03/187.06 ncf('1.1.1.1.2.1.1',plain,[-(xx = xx)],extension(2 ^ 14,bind([[_96960], [xx]]))).
% 194.03/187.06 ncf('1.1.1.1.2.2',plain,[xx = xx, -(xb = xx), xb = xx],extension(10 ^ 11,bind([[_97271, _97273, _97275], [xx, xx, xb]]))).
% 194.03/187.06 ncf('1.1.1.1.2.2.1',plain,[xb = xx, 321 : -(sdtmndtasgtdt0(xb, xR, xx)), 321 : aElement0(xb), 321 : aRewritingSystem0(xR), 321 : aElement0(xx)],extension(299 ^ 12,bind([[_106038, _106040, _106042], [xx, xR, xb]]))).
% 194.03/187.06 ncf('1.1.1.1.2.2.1.1',plain,[sdtmndtasgtdt0(xb, xR, xx)],reduction('1.1')).
% 194.03/187.06 ncf('1.1.1.1.2.2.1.2',plain,[-(aElement0(xb))],extension(571 ^ 13)).
% 194.03/187.06 ncf('1.1.1.1.2.2.1.3',plain,[-(aRewritingSystem0(xR))],extension(563 ^ 13)).
% 194.03/187.06 ncf('1.1.1.1.2.2.1.4',plain,[-(aElement0(xx))],extension(630 ^ 13)).
% 194.03/187.06 ncf('1.1.1.1.2.2.2',plain,[-(xb = xx), 311 : sdtmndtasgtdt0(xb, xR, xx), 311 : -(sdtmndtplgtdt0(xb, xR, xx)), 311 : aElement0(xb), 311 : aRewritingSystem0(xR), 311 : aElement0(xx)],extension(299 ^ 12,bind([[_106038, _106040, _106042], [xx, xR, xb]]))).
% 194.03/187.06 ncf('1.1.1.1.2.2.2.1',plain,[-(sdtmndtasgtdt0(xb, xR, xx))],extension(632 ^ 15)).
% 194.03/187.06 ncf('1.1.1.1.2.2.2.2',plain,[sdtmndtplgtdt0(xb, xR, xx)],reduction('1.1.1')).
% 194.03/187.06 ncf('1.1.1.1.2.2.2.3',plain,[-(aElement0(xb))],extension(571 ^ 13)).
% 194.03/187.06 ncf('1.1.1.1.2.2.2.4',plain,[-(aRewritingSystem0(xR))],extension(563 ^ 13)).
% 194.03/187.06 ncf('1.1.1.1.2.2.2.5',plain,[-(aElement0(xx))],extension(630 ^ 13)).
% 194.03/187.06 ncf('1.1.1.1.2.3',plain,[-(aElement0(xx))],extension(630 ^ 9)).
% 194.03/187.06 ncf('1.1.1.1.2.4',plain,[-(aRewritingSystem0(xR))],extension(563 ^ 9)).
% 194.03/187.06 ncf('1.1.1.1.2.5',plain,[-(aElement0(xx))],lemmata('[1, 1, 1, 1].x')).
% 194.03/187.06 ncf('1.1.1.1.3',plain,[-(aElement0(xb))],extension(571 ^ 8)).
% 194.03/187.06 ncf('1.1.1.1.4',plain,[-(aRewritingSystem0(xR))],extension(563 ^ 8)).
% 194.03/187.06 ncf('1.1.1.1.5',plain,[-(aElement0(xx))],extension(630 ^ 8)).
% 194.03/187.06 ncf('1.1.1.1.6',plain,[-(aElement0(xx))],lemmata('[1, 1, 1].x')).
% 194.03/187.06 ncf('1.1.1.2',plain,[-(aElement0(xb))],extension(571 ^ 3)).
% 194.03/187.06 ncf('1.1.1.3',plain,[-(aRewritingSystem0(xR))],extension(563 ^ 3)).
% 194.03/187.06 ncf('1.1.1.4',plain,[-(aElement0(xx))],extension(630 ^ 3)).
% 194.03/187.06 ncf('1.1.2',plain,[-(sdtmndtasgtdt0(xx, xR, xd)), 323 : xx = xd, 321 : aElement0(xx), 321 : aRewritingSystem0(xR), 321 : aElement0(xd)],extension(299 ^ 2,bind([[_106038, _106040, _106042], [xd, xR, xx]]))).
% 194.03/187.06 ncf('1.1.2.1',plain,[-(xx = xd), xd = xx],extension(4 ^ 7,bind([[_97067, _97069], [xx, xd]]))).
% 194.03/187.06 ncf('1.1.2.1.1',plain,[-(xd = xx), 311 : sdtmndtasgtdt0(xd, xR, xx), 311 : -(sdtmndtplgtdt0(xd, xR, xx)), 311 : aElement0(xd), 311 : aRewritingSystem0(xR), 311 : aElement0(xx)],extension(299 ^ 8,bind([[_106038, _106040, _106042], [xx, xR, xd]]))).
% 194.03/187.06 ncf('1.1.2.1.1.1',plain,[-(sdtmndtasgtdt0(xd, xR, xx))],extension(634 ^ 11)).
% 194.03/187.06 ncf('1.1.2.1.1.2',plain,[sdtmndtplgtdt0(xd, xR, xx), 242 : -(aReductOfIn0(xx, xd, xR)), 253 : -(aReductOfIn0(249 ^ [xx, xR, xd], xd, xR)), 242 : aElement0(xd), 242 : aRewritingSystem0(xR), 242 : aElement0(xx)],extension(230 ^ 11,bind([[_103963, _103965, _103967], [xx, xR, xd]]))).
% 194.03/187.06 ncf('1.1.2.1.1.2.1',plain,[aReductOfIn0(xx, xd, xR), 523 : aNormalFormOfIn0(xd, xw, xR), 523 : aElement0(xw), 523 : aRewritingSystem0(xR)],extension(515 ^ 14,bind([[_113270, _113272, _113542, _113818], [xR, xw, xd, xx]]))).
% 194.03/187.06 ncf('1.1.2.1.1.2.1.1',plain,[-(aNormalFormOfIn0(xd, xw, xR))],extension(628 ^ 17)).
% 194.03/187.06 ncf('1.1.2.1.1.2.1.2',plain,[-(aElement0(xw))],extension(622 ^ 15)).
% 194.03/187.06 ncf('1.1.2.1.1.2.1.3',plain,[-(aRewritingSystem0(xR))],extension(563 ^ 15)).
% 194.03/187.06 ncf('1.1.2.1.1.2.2',plain,[aReductOfIn0(249 ^ [xx, xR, xd], xd, xR), 523 : aNormalFormOfIn0(xd, xw, xR), 523 : aElement0(xw), 523 : aRewritingSystem0(xR)],extension(515 ^ 16,bind([[_113270, _113272, _113542, _113818], [xR, xw, xd, 249 ^ [xx, xR, xd]]]))).
% 194.03/187.06 ncf('1.1.2.1.1.2.2.1',plain,[-(aNormalFormOfIn0(xd, xw, xR))],extension(628 ^ 19)).
% 194.03/187.06 ncf('1.1.2.1.1.2.2.2',plain,[-(aElement0(xw))],extension(622 ^ 17)).
% 194.03/187.06 ncf('1.1.2.1.1.2.2.3',plain,[-(aRewritingSystem0(xR))],extension(563 ^ 17)).
% 194.03/187.06 ncf('1.1.2.1.1.2.3',plain,[-(aElement0(xd)), 523 : aNormalFormOfIn0(xd, xw, xR), 523 : aElement0(xw), 523 : aRewritingSystem0(xR)],extension(515 ^ 12,bind([[_113270, _113272, _113542], [xR, xw, xd]]))).
% 194.03/187.06 ncf('1.1.2.1.1.2.3.1',plain,[-(aNormalFormOfIn0(xd, xw, xR))],extension(628 ^ 15)).
% 194.03/187.06 ncf('1.1.2.1.1.2.3.2',plain,[-(aElement0(xw))],extension(622 ^ 13)).
% 194.03/187.06 ncf('1.1.2.1.1.2.3.3',plain,[-(aRewritingSystem0(xR))],extension(563 ^ 13)).
% 194.03/187.06 ncf('1.1.2.1.1.2.4',plain,[-(aRewritingSystem0(xR))],extension(563 ^ 12)).
% 194.03/187.06 ncf('1.1.2.1.1.2.5',plain,[-(aElement0(xx))],extension(630 ^ 12)).
% 194.03/187.06 ncf('1.1.2.1.1.3',plain,[-(aElement0(xd)), 523 : aNormalFormOfIn0(xd, xw, xR), 523 : aElement0(xw), 523 : aRewritingSystem0(xR)],extension(515 ^ 9,bind([[_113270, _113272, _113542], [xR, xw, xd]]))).
% 194.03/187.06 ncf('1.1.2.1.1.3.1',plain,[-(aNormalFormOfIn0(xd, xw, xR))],extension(628 ^ 12)).
% 194.03/187.06 ncf('1.1.2.1.1.3.2',plain,[-(aElement0(xw))],extension(622 ^ 10)).
% 194.03/187.06 ncf('1.1.2.1.1.3.3',plain,[-(aRewritingSystem0(xR))],extension(563 ^ 10)).
% 194.03/187.06 ncf('1.1.2.1.1.4',plain,[-(aRewritingSystem0(xR))],extension(563 ^ 9)).
% 194.03/187.06 ncf('1.1.2.1.1.5',plain,[-(aElement0(xx))],extension(630 ^ 9)).
% 194.03/187.06 ncf('1.1.2.2',plain,[-(aElement0(xx))],extension(630 ^ 3)).
% 194.03/187.06 ncf('1.1.2.3',plain,[-(aRewritingSystem0(xR))],extension(563 ^ 3)).
% 194.03/187.06 ncf('1.1.2.4',plain,[-(aElement0(xd)), 523 : aNormalFormOfIn0(xd, xw, xR), 523 : aElement0(xw), 523 : aRewritingSystem0(xR)],extension(515 ^ 3,bind([[_113270, _113272, _113542], [xR, xw, xd]]))).
% 194.03/187.06 ncf('1.1.2.4.1',plain,[-(aNormalFormOfIn0(xd, xw, xR))],extension(628 ^ 6)).
% 194.03/187.06 ncf('1.1.2.4.2',plain,[-(aElement0(xw))],extension(622 ^ 4)).
% 194.03/187.06 ncf('1.1.2.4.3',plain,[-(aRewritingSystem0(xR))],lemmata('[1, 1].x')).
% 194.03/187.06 ncf('1.1.3',plain,[-(aElement0(xb))],extension(571 ^ 2)).
% 194.03/187.06 ncf('1.1.4',plain,[-(aRewritingSystem0(xR))],extension(563 ^ 2)).
% 194.03/187.06 ncf('1.1.5',plain,[-(aElement0(xx))],extension(630 ^ 2)).
% 194.03/187.06 ncf('1.1.6',plain,[-(aElement0(xd)), 523 : aNormalFormOfIn0(xd, xw, xR), 523 : aElement0(xw), 523 : aRewritingSystem0(xR)],extension(515 ^ 2,bind([[_113270, _113272, _113542], [xR, xw, xd]]))).
% 194.03/187.06 ncf('1.1.6.1',plain,[-(aNormalFormOfIn0(xd, xw, xR))],extension(628 ^ 5)).
% 194.03/187.06 ncf('1.1.6.2',plain,[-(aElement0(xw))],extension(622 ^ 3)).
% 194.03/187.06 ncf('1.1.6.3',plain,[-(aRewritingSystem0(xR))],lemmata('[1].x')).
% 194.03/187.06 %-----------------------------------------------------
% 194.03/187.06 End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------