TSTP Solution File: COM018+4 by nanoCoP---2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : nanoCoP---2.0
% Problem : COM018+4 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : nanocop.sh %s %d
% Computer : n026.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 10:14:33 EDT 2023
% Result : Theorem 0.37s 1.40s
% Output : Proof 0.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : COM018+4 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : nanocop.sh %s %d
% 0.13/0.35 % Computer : n026.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri May 19 03:33:50 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.37/1.40
% 0.37/1.40 /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 0.37/1.40 Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.37/1.40 %-----------------------------------------------------
% 0.37/1.40 ncf(matrix, plain, [(898 ^ _112214) ^ [_140781] : [aNormalFormOfIn0(_140781, xw, xR)], (871 ^ _112214) ^ [_139966] : [aElement0(_139966), -(aReductOfIn0(894 ^ [_139966], _139966, xR)), 876 ^ _112214 : [(877 ^ _112214) ^ [] : [xw = _139966], (879 ^ _112214) ^ [] : [aReductOfIn0(_139966, xw, xR)], (891 ^ _112214) ^ [] : [sdtmndtplgtdt0(xw, xR, _139966)], (893 ^ _112214) ^ [] : [sdtmndtasgtdt0(xw, xR, _139966)], (881 ^ _112214) ^ [_140324] : [aElement0(_140324), aReductOfIn0(_140324, xw, xR), sdtmndtplgtdt0(_140324, xR, _139966)]]], (2 ^ _112214) ^ [_112338] : [-(_112338 = _112338)], (4 ^ _112214) ^ [_112445, _112447] : [_112447 = _112445, -(_112445 = _112447)], (10 ^ _112214) ^ [_112649, _112651, _112653] : [-(_112653 = _112649), _112653 = _112651, _112651 = _112649], (20 ^ _112214) ^ [_112962, _112964] : [-(isConfluent0(_112962)), _112964 = _112962, isConfluent0(_112964)], (30 ^ _112214) ^ [_113257, _113259] : [-(aRewritingSystem0(_113257)), _113259 = _113257, aRewritingSystem0(_113259)], (40 ^ _112214) ^ [_113552, _113554] : [-(isLocallyConfluent0(_113552)), _113554 = _113552, isLocallyConfluent0(_113554)], (50 ^ _112214) ^ [_113847, _113849] : [-(isTerminating0(_113847)), _113849 = _113847, isTerminating0(_113849)], (60 ^ _112214) ^ [_114170, _114172, _114174, _114176] : [-(iLess0(_114174, _114170)), iLess0(_114176, _114172), _114176 = _114174, _114172 = _114170], (74 ^ _112214) ^ [_114586, _114588] : [-(aElement0(_114586)), _114588 = _114586, aElement0(_114588)], (84 ^ _112214) ^ [_114937, _114939, _114941, _114943, _114945, _114947] : [-(sdtmndtplgtdt0(_114945, _114941, _114937)), sdtmndtplgtdt0(_114947, _114943, _114939), _114947 = _114945, _114943 = _114941, _114939 = _114937], (102 ^ _112214) ^ [_115546, _115548, _115550, _115552, _115554, _115556] : [-(sdtmndtasgtdt0(_115554, _115550, _115546)), sdtmndtasgtdt0(_115556, _115552, _115548), _115556 = _115554, _115552 = _115550, _115548 = _115546], (120 ^ _112214) ^ [_116155, _116157, _116159, _116161, _116163, _116165] : [-(aReductOfIn0(_116163, _116159, _116155)), aReductOfIn0(_116165, _116161, _116157), _116165 = _116163, _116161 = _116159, _116157 = _116155], (138 ^ _112214) ^ [_116744, _116746, _116748, _116750, _116752, _116754] : [-(aNormalFormOfIn0(_116752, _116748, _116744)), aNormalFormOfIn0(_116754, _116750, _116746), _116754 = _116752, _116750 = _116748, _116746 = _116744], (156 ^ _112214) ^ [_117307] : [aElement0(_117307), true___, -(true___)], (166 ^ _112214) ^ [_117562] : [aRewritingSystem0(_117562), true___, -(true___)], (176 ^ _112214) ^ [_117831, _117833] : [aElement0(_117833), aRewritingSystem0(_117831), 183 ^ _112214 : [(184 ^ _112214) ^ [_118053] : [aReductOfIn0(_118053, _117833, _117831), -(aElement0(_118053))]]], (190 ^ _112214) ^ [_118280, _118282] : [aElement0(_118282), aElement0(_118280), iLess0(_118282, _118280), true___, -(true___)], (208 ^ _112214) ^ [_118754, _118756, _118758] : [aElement0(_118758), aRewritingSystem0(_118756), aElement0(_118754), sdtmndtplgtdt0(_118758, _118756, _118754), true___, -(true___)], (230 ^ _112214) ^ [_119341, _119343, _119345] : [aElement0(_119345), aRewritingSystem0(_119343), aElement0(_119341), 241 ^ _112214 : [(242 ^ _112214) ^ [] : [sdtmndtplgtdt0(_119345, _119343, _119341), -(aReductOfIn0(_119341, _119345, _119343)), 250 ^ _112214 : [(251 ^ _112214) ^ [] : [-(aElement0(249 ^ [_119341, _119343, _119345]))], (253 ^ _112214) ^ [] : [-(aReductOfIn0(249 ^ [_119341, _119343, _119345], _119345, _119343))], (255 ^ _112214) ^ [] : [-(sdtmndtplgtdt0(249 ^ [_119341, _119343, _119345], _119343, _119341))]]], (257 ^ _112214) ^ [] : [-(sdtmndtplgtdt0(_119345, _119343, _119341)), 258 ^ _112214 : [(259 ^ _112214) ^ [] : [aReductOfIn0(_119341, _119345, _119343)], (261 ^ _112214) ^ [_120272] : [aElement0(_120272), aReductOfIn0(_120272, _119345, _119343), sdtmndtplgtdt0(_120272, _119343, _119341)]]]]], (273 ^ _112214) ^ [_120693, _120695, _120697, _120699] : [-(sdtmndtplgtdt0(_120699, _120697, _120693)), sdtmndtplgtdt0(_120699, _120697, _120695), sdtmndtplgtdt0(_120695, _120697, _120693), aElement0(_120699), aRewritingSystem0(_120697), aElement0(_120695), aElement0(_120693)], (299 ^ _112214) ^ [_121416, _121418, _121420] : [aElement0(_121420), aRewritingSystem0(_121418), aElement0(_121416), 310 ^ _112214 : [(321 ^ _112214) ^ [] : [322 ^ _112214 : [(323 ^ _112214) ^ [] : [_121420 = _121416], (325 ^ _112214) ^ [] : [sdtmndtplgtdt0(_121420, _121418, _121416)]], -(sdtmndtasgtdt0(_121420, _121418, _121416))], (311 ^ _112214) ^ [] : [sdtmndtasgtdt0(_121420, _121418, _121416), -(_121420 = _121416), -(sdtmndtplgtdt0(_121420, _121418, _121416))]]], (329 ^ _112214) ^ [_122274, _122276, _122278, _122280] : [-(sdtmndtasgtdt0(_122280, _122278, _122274)), sdtmndtasgtdt0(_122280, _122278, _122276), sdtmndtasgtdt0(_122276, _122278, _122274), aElement0(_122280), aRewritingSystem0(_122278), aElement0(_122276), aElement0(_122274)], (355 ^ _112214) ^ [_122969] : [aRewritingSystem0(_122969), 358 ^ _112214 : [(390 ^ _112214) ^ [] : [-(isConfluent0(_122969)), 394 ^ _112214 : [(395 ^ _112214) ^ [] : [-(aElement0(391 ^ [_122969]))], (397 ^ _112214) ^ [] : [-(aElement0(392 ^ [_122969]))], (399 ^ _112214) ^ [] : [-(aElement0(393 ^ [_122969]))], (401 ^ _112214) ^ [] : [-(sdtmndtasgtdt0(391 ^ [_122969], _122969, 392 ^ [_122969]))], (403 ^ _112214) ^ [] : [-(sdtmndtasgtdt0(391 ^ [_122969], _122969, 393 ^ [_122969]))], (405 ^ _112214) ^ [_124849] : [aElement0(_124849), sdtmndtasgtdt0(392 ^ [_122969], _122969, _124849), sdtmndtasgtdt0(393 ^ [_122969], _122969, _124849)]]], (359 ^ _112214) ^ [] : [isConfluent0(_122969), 362 ^ _112214 : [(363 ^ _112214) ^ [_123287, _123289, _123291] : [383 ^ _112214 : [(384 ^ _112214) ^ [] : [-(aElement0(382 ^ [_122969, _123287, _123289, _123291]))], (386 ^ _112214) ^ [] : [-(sdtmndtasgtdt0(_123289, _122969, 382 ^ [_122969, _123287, _123289, _123291]))], (388 ^ _112214) ^ [] : [-(sdtmndtasgtdt0(_123287, _122969, 382 ^ [_122969, _123287, _123289, _123291]))]], aElement0(_123291), aElement0(_123289), aElement0(_123287), sdtmndtasgtdt0(_123291, _122969, _123289), sdtmndtasgtdt0(_123291, _122969, _123287)]]]]], (417 ^ _112214) ^ [_125222] : [aRewritingSystem0(_125222), 420 ^ _112214 : [(452 ^ _112214) ^ [] : [-(isLocallyConfluent0(_125222)), 456 ^ _112214 : [(457 ^ _112214) ^ [] : [-(aElement0(453 ^ [_125222]))], (459 ^ _112214) ^ [] : [-(aElement0(454 ^ [_125222]))], (461 ^ _112214) ^ [] : [-(aElement0(455 ^ [_125222]))], (463 ^ _112214) ^ [] : [-(aReductOfIn0(454 ^ [_125222], 453 ^ [_125222], _125222))], (465 ^ _112214) ^ [] : [-(aReductOfIn0(455 ^ [_125222], 453 ^ [_125222], _125222))], (467 ^ _112214) ^ [_127102] : [aElement0(_127102), sdtmndtasgtdt0(454 ^ [_125222], _125222, _127102), sdtmndtasgtdt0(455 ^ [_125222], _125222, _127102)]]], (421 ^ _112214) ^ [] : [isLocallyConfluent0(_125222), 424 ^ _112214 : [(425 ^ _112214) ^ [_125540, _125542, _125544] : [445 ^ _112214 : [(446 ^ _112214) ^ [] : [-(aElement0(444 ^ [_125222, _125540, _125542, _125544]))], (448 ^ _112214) ^ [] : [-(sdtmndtasgtdt0(_125542, _125222, 444 ^ [_125222, _125540, _125542, _125544]))], (450 ^ _112214) ^ [] : [-(sdtmndtasgtdt0(_125540, _125222, 444 ^ [_125222, _125540, _125542, _125544]))]], aElement0(_125544), aElement0(_125542), aElement0(_125540), aReductOfIn0(_125542, _125544, _125222), aReductOfIn0(_125540, _125544, _125222)]]]]], (479 ^ _112214) ^ [_127475] : [aRewritingSystem0(_127475), 482 ^ _112214 : [(501 ^ _112214) ^ [] : [504 ^ _112214 : [(505 ^ _112214) ^ [] : [-(aElement0(502 ^ [_127475]))], (507 ^ _112214) ^ [] : [-(aElement0(503 ^ [_127475]))], (509 ^ _112214) ^ [] : [-(sdtmndtplgtdt0(502 ^ [_127475], _127475, 503 ^ [_127475]))], (511 ^ _112214) ^ [] : [iLess0(503 ^ [_127475], 502 ^ [_127475])]], -(isTerminating0(_127475))], (483 ^ _112214) ^ [] : [isTerminating0(_127475), 486 ^ _112214 : [(487 ^ _112214) ^ [_127744, _127746] : [aElement0(_127746), aElement0(_127744), sdtmndtplgtdt0(_127746, _127475, _127744), -(iLess0(_127744, _127746))]]]]], (515 ^ _112214) ^ [_128648, _128650] : [aElement0(_128650), aRewritingSystem0(_128648), 522 ^ _112214 : [(523 ^ _112214) ^ [_128920] : [aNormalFormOfIn0(_128920, _128650, _128648), 526 ^ _112214 : [(527 ^ _112214) ^ [] : [-(aElement0(_128920))], (529 ^ _112214) ^ [] : [-(sdtmndtasgtdt0(_128650, _128648, _128920))], (531 ^ _112214) ^ [_129196] : [aReductOfIn0(_129196, _128920, _128648)]]], (533 ^ _112214) ^ [_129271] : [-(aNormalFormOfIn0(_129271, _128650, _128648)), aElement0(_129271), sdtmndtasgtdt0(_128650, _128648, _129271), -(aReductOfIn0(542 ^ [_128648, _128650, _129271], _129271, _128648))]]], (548 ^ _112214) ^ [_129743] : [aRewritingSystem0(_129743), isTerminating0(_129743), 555 ^ _112214 : [(556 ^ _112214) ^ [_129962] : [aElement0(_129962), -(aNormalFormOfIn0(559 ^ [_129743, _129962], _129962, _129743))]]], (563 ^ _112214) ^ [] : [-(aRewritingSystem0(xR))], (626 ^ _112214) ^ [] : [-(isLocallyConfluent0(xR))], (654 ^ _112214) ^ [] : [-(isTerminating0(xR))], (628 ^ _112214) ^ [_132588, _132590] : [aElement0(_132590), aElement0(_132588), -(iLess0(_132588, _132590)), 637 ^ _112214 : [(638 ^ _112214) ^ [] : [aReductOfIn0(_132588, _132590, xR)], (650 ^ _112214) ^ [] : [sdtmndtplgtdt0(_132590, xR, _132588)], (640 ^ _112214) ^ [_132957] : [aElement0(_132957), aReductOfIn0(_132957, _132590, xR), sdtmndtplgtdt0(_132957, xR, _132588)]]], (565 ^ _112214) ^ [_130326, _130328, _130330] : [aElement0(_130330), aElement0(_130328), aElement0(_130326), aReductOfIn0(_130328, _130330, xR), aReductOfIn0(_130326, _130330, xR), 585 ^ _112214 : [(586 ^ _112214) ^ [] : [-(aElement0(584 ^ [_130326, _130328, _130330]))], (588 ^ _112214) ^ [] : [-(_130328 = 584 ^ [_130326, _130328, _130330]), 591 ^ _112214 : [(603 ^ _112214) ^ [] : [-(sdtmndtplgtdt0(_130328, xR, 584 ^ [_130326, _130328, _130330]))], (592 ^ _112214) ^ [] : [-(aReductOfIn0(584 ^ [_130326, _130328, _130330], _130328, xR)), 596 ^ _112214 : [(597 ^ _112214) ^ [] : [-(aElement0(595 ^ [_130326, _130328, _130330]))], (599 ^ _112214) ^ [] : [-(aReductOfIn0(595 ^ [_130326, _130328, _130330], _130328, xR))], (601 ^ _112214) ^ [] : [-(sdtmndtplgtdt0(595 ^ [_130326, _130328, _130330], xR, 584 ^ [_130326, _130328, _130330]))]]]]], (605 ^ _112214) ^ [] : [-(sdtmndtasgtdt0(_130328, xR, 584 ^ [_130326, _130328, _130330]))], (624 ^ _112214) ^ [] : [-(sdtmndtasgtdt0(_130326, xR, 584 ^ [_130326, _130328, _130330]))], (607 ^ _112214) ^ [] : [-(_130326 = 584 ^ [_130326, _130328, _130330]), 610 ^ _112214 : [(622 ^ _112214) ^ [] : [-(sdtmndtplgtdt0(_130326, xR, 584 ^ [_130326, _130328, _130330]))], (611 ^ _112214) ^ [] : [-(aReductOfIn0(584 ^ [_130326, _130328, _130330], _130326, xR)), 615 ^ _112214 : [(616 ^ _112214) ^ [] : [-(aElement0(614 ^ [_130326, _130328, _130330]))], (618 ^ _112214) ^ [] : [-(aReductOfIn0(614 ^ [_130326, _130328, _130330], _130326, xR))], (620 ^ _112214) ^ [] : [-(sdtmndtplgtdt0(614 ^ [_130326, _130328, _130330], xR, 584 ^ [_130326, _130328, _130330]))]]]]]]], (656 ^ _112214) ^ [] : [-(aElement0(xa))], (658 ^ _112214) ^ [] : [-(aElement0(xb))], (660 ^ _112214) ^ [] : [-(aElement0(xc))], (662 ^ _112214) ^ [_133598, _133600, _133602] : [aElement0(_133602), aElement0(_133600), aElement0(_133598), 677 ^ _112214 : [(678 ^ _112214) ^ [] : [_133602 = _133600], (680 ^ _112214) ^ [] : [aReductOfIn0(_133600, _133602, xR)], (692 ^ _112214) ^ [] : [sdtmndtplgtdt0(_133602, xR, _133600)], (694 ^ _112214) ^ [] : [sdtmndtasgtdt0(_133602, xR, _133600)], (682 ^ _112214) ^ [_134341] : [aElement0(_134341), aReductOfIn0(_134341, _133602, xR), sdtmndtplgtdt0(_134341, xR, _133600)]], 695 ^ _112214 : [(696 ^ _112214) ^ [] : [_133602 = _133598], (698 ^ _112214) ^ [] : [aReductOfIn0(_133598, _133602, xR)], (710 ^ _112214) ^ [] : [sdtmndtplgtdt0(_133602, xR, _133598)], (712 ^ _112214) ^ [] : [sdtmndtasgtdt0(_133602, xR, _133598)], (700 ^ _112214) ^ [_134914] : [aElement0(_134914), aReductOfIn0(_134914, _133602, xR), sdtmndtplgtdt0(_134914, xR, _133598)]], iLess0(_133602, xa), 718 ^ _112214 : [(719 ^ _112214) ^ [] : [-(aElement0(717 ^ [_133598, _133600, _133602]))], (721 ^ _112214) ^ [] : [-(_133600 = 717 ^ [_133598, _133600, _133602]), 724 ^ _112214 : [(736 ^ _112214) ^ [] : [-(sdtmndtplgtdt0(_133600, xR, 717 ^ [_133598, _133600, _133602]))], (725 ^ _112214) ^ [] : [-(aReductOfIn0(717 ^ [_133598, _133600, _133602], _133600, xR)), 729 ^ _112214 : [(730 ^ _112214) ^ [] : [-(aElement0(728 ^ [_133598, _133600, _133602]))], (732 ^ _112214) ^ [] : [-(aReductOfIn0(728 ^ [_133598, _133600, _133602], _133600, xR))], (734 ^ _112214) ^ [] : [-(sdtmndtplgtdt0(728 ^ [_133598, _133600, _133602], xR, 717 ^ [_133598, _133600, _133602]))]]]]], (738 ^ _112214) ^ [] : [-(sdtmndtasgtdt0(_133600, xR, 717 ^ [_133598, _133600, _133602]))], (757 ^ _112214) ^ [] : [-(sdtmndtasgtdt0(_133598, xR, 717 ^ [_133598, _133600, _133602]))], (740 ^ _112214) ^ [] : [-(_133598 = 717 ^ [_133598, _133600, _133602]), 743 ^ _112214 : [(755 ^ _112214) ^ [] : [-(sdtmndtplgtdt0(_133598, xR, 717 ^ [_133598, _133600, _133602]))], (744 ^ _112214) ^ [] : [-(aReductOfIn0(717 ^ [_133598, _133600, _133602], _133598, xR)), 748 ^ _112214 : [(749 ^ _112214) ^ [] : [-(aElement0(747 ^ [_133598, _133600, _133602]))], (751 ^ _112214) ^ [] : [-(aReductOfIn0(747 ^ [_133598, _133600, _133602], _133598, xR))], (753 ^ _112214) ^ [] : [-(sdtmndtplgtdt0(747 ^ [_133598, _133600, _133602], xR, 717 ^ [_133598, _133600, _133602]))]]]]]]], (759 ^ _112214) ^ [] : [-(aReductOfIn0(xb, xa, xR)), 763 ^ _112214 : [(764 ^ _112214) ^ [] : [-(aElement0(762 ^ []))], (766 ^ _112214) ^ [] : [-(aReductOfIn0(762 ^ [], xa, xR))], (768 ^ _112214) ^ [] : [-(sdtmndtplgtdt0(762 ^ [], xR, xb))]]], (770 ^ _112214) ^ [] : [-(sdtmndtplgtdt0(xa, xR, xb))], (783 ^ _112214) ^ [] : [-(sdtmndtplgtdt0(xa, xR, xc))], (772 ^ _112214) ^ [] : [-(aReductOfIn0(xc, xa, xR)), 776 ^ _112214 : [(777 ^ _112214) ^ [] : [-(aElement0(775 ^ []))], (779 ^ _112214) ^ [] : [-(aReductOfIn0(775 ^ [], xa, xR))], (781 ^ _112214) ^ [] : [-(sdtmndtplgtdt0(775 ^ [], xR, xc))]]], (785 ^ _112214) ^ [] : [-(aElement0(xu))], (787 ^ _112214) ^ [] : [-(aReductOfIn0(xu, xa, xR))], (806 ^ _112214) ^ [] : [-(sdtmndtasgtdt0(xu, xR, xb))], (789 ^ _112214) ^ [] : [-(xu = xb), 792 ^ _112214 : [(804 ^ _112214) ^ [] : [-(sdtmndtplgtdt0(xu, xR, xb))], (793 ^ _112214) ^ [] : [-(aReductOfIn0(xb, xu, xR)), 797 ^ _112214 : [(798 ^ _112214) ^ [] : [-(aElement0(796 ^ []))], (800 ^ _112214) ^ [] : [-(aReductOfIn0(796 ^ [], xu, xR))], (802 ^ _112214) ^ [] : [-(sdtmndtplgtdt0(796 ^ [], xR, xb))]]]]], (808 ^ _112214) ^ [] : [-(aElement0(xv))], (810 ^ _112214) ^ [] : [-(aReductOfIn0(xv, xa, xR))], (829 ^ _112214) ^ [] : [-(sdtmndtasgtdt0(xv, xR, xc))], (812 ^ _112214) ^ [] : [-(xv = xc), 815 ^ _112214 : [(827 ^ _112214) ^ [] : [-(sdtmndtplgtdt0(xv, xR, xc))], (816 ^ _112214) ^ [] : [-(aReductOfIn0(xc, xv, xR)), 820 ^ _112214 : [(821 ^ _112214) ^ [] : [-(aElement0(819 ^ []))], (823 ^ _112214) ^ [] : [-(aReductOfIn0(819 ^ [], xv, xR))], (825 ^ _112214) ^ [] : [-(sdtmndtplgtdt0(819 ^ [], xR, xc))]]]]], (831 ^ _112214) ^ [] : [-(aElement0(xw))], (833 ^ _112214) ^ [] : [-(xu = xw), 836 ^ _112214 : [(848 ^ _112214) ^ [] : [-(sdtmndtplgtdt0(xu, xR, xw))], (837 ^ _112214) ^ [] : [-(aReductOfIn0(xw, xu, xR)), 841 ^ _112214 : [(842 ^ _112214) ^ [] : [-(aElement0(840 ^ []))], (844 ^ _112214) ^ [] : [-(aReductOfIn0(840 ^ [], xu, xR))], (846 ^ _112214) ^ [] : [-(sdtmndtplgtdt0(840 ^ [], xR, xw))]]]]], (850 ^ _112214) ^ [] : [-(sdtmndtasgtdt0(xu, xR, xw))], (869 ^ _112214) ^ [] : [-(sdtmndtasgtdt0(xv, xR, xw))], (852 ^ _112214) ^ [] : [-(xv = xw), 855 ^ _112214 : [(867 ^ _112214) ^ [] : [-(sdtmndtplgtdt0(xv, xR, xw))], (856 ^ _112214) ^ [] : [-(aReductOfIn0(xw, xv, xR)), 860 ^ _112214 : [(861 ^ _112214) ^ [] : [-(aElement0(859 ^ []))], (863 ^ _112214) ^ [] : [-(aReductOfIn0(859 ^ [], xv, xR))], (865 ^ _112214) ^ [] : [-(sdtmndtplgtdt0(859 ^ [], xR, xw))]]]]]], input).
% 0.37/1.40 ncf('1',plain,[aNormalFormOfIn0(559 ^ [xR, xw], xw, xR)],start(898 ^ 0,bind([[_140781], [559 ^ [xR, xw]]]))).
% 0.37/1.40 ncf('1.1',plain,[-(aNormalFormOfIn0(559 ^ [xR, xw], xw, xR)), 556 : aElement0(xw), 556 : aRewritingSystem0(xR), 556 : isTerminating0(xR)],extension(548 ^ 1,bind([[_129743, _129962], [xR, xw]]))).
% 0.37/1.40 ncf('1.1.1',plain,[-(aElement0(xw))],extension(831 ^ 4)).
% 0.37/1.40 ncf('1.1.2',plain,[-(aRewritingSystem0(xR))],extension(563 ^ 2)).
% 0.37/1.40 ncf('1.1.3',plain,[-(isTerminating0(xR))],extension(654 ^ 2)).
% 0.37/1.40 %-----------------------------------------------------
% 0.37/1.40 End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------