TSTP Solution File: GRP274-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP274-1 : TPTP v3.4.2. Released v2.5.0.
% Transfm : add_equality:r
% Format : otter:hypothesis:set(auto),clear(print_given)
% Command : gandalf-wrapper -time %d %s
% Computer : art09.cs.miami.edu
% Model : i686 unknown
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 1000MB
% OS : Linux 2.4.22-21mdk-i686-up-4GB
% CPULimit : 600s
% Result : Unsatisfiable 289.1s
% Output : Assurance 289.1s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
%
% Gandalf c-2.6 r1 starting to prove: /home/graph/tptp/TSTP/PreparedTPTP/otter:hypothesis:set(auto),clear(print_given)---add_equality:r/GRP/GRP274-1+eq_r.in
% Using automatic strategy selection.
% Time limit in seconds: 600
%
% prove-all-passes started
%
% detected problem class: peq
%
% strategies selected:
% (hyper 30 #f 3 19)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 3 19)
% (binary-posweight-lex-big-order 30 #f 3 19)
% (binary 30 #t)
% (binary-posweight-kb-big-order 156 #f)
% (binary-posweight-lex-big-order 102 #f)
% (binary-posweight-firstpref-order 60 #f)
% (binary-order 30 #f)
% (binary-posweight-kb-small-order 48 #f)
% (binary-posweight-lex-small-order 30 #f)
%
%
% SOS clause
% -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7) | -equal(multiply(sk_c7,sk_c5),sk_c6) | -equal(multiply(Y,sk_c5),sk_c7) | -equal(inverse(Y),sk_c5) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(U),sk_c6) | -equal(multiply(U,sk_c5),sk_c6).
% was split for some strategies as:
% -equal(inverse(U),sk_c6) | -equal(multiply(U,sk_c5),sk_c6).
% -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7).
% -equal(multiply(Y,sk_c5),sk_c7) | -equal(inverse(Y),sk_c5).
% -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7).
% -equal(multiply(sk_c7,sk_c5),sk_c6).
% -equal(multiply(sk_c6,sk_c7),sk_c5).
%
% Starting a split proof attempt with 6 components.
%
% Split component 1 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7) | -equal(multiply(sk_c7,sk_c5),sk_c6) | -equal(multiply(Y,sk_c5),sk_c7) | -equal(inverse(Y),sk_c5) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(U),sk_c6) | -equal(multiply(U,sk_c5),sk_c6).
% Split part used next: -equal(inverse(U),sk_c6) | -equal(multiply(U,sk_c5),sk_c6).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(30,40,0,65,0,0,484,50,3,519,0,3,953,50,6,988,0,7,1427,50,11,1462,0,11,1907,50,16,1942,0,16,2394,50,22,2429,0,22,2889,50,34,2924,0,34,3392,50,56,3427,0,56,3905,50,107,3940,0,107,4428,50,217,4463,0,217,4963,50,412,4998,0,412,5510,50,779,5510,40,779,5545,0,779,16500,3,1080,17202,4,1230,17844,5,1380,17845,1,1380,17845,50,1380,17845,40,1380,17880,0,1380,18033,3,1689,18041,4,1832,18049,5,1981,18049,1,1981,18049,50,1981,18049,40,1981,18084,0,1981,33051,3,3482,34230,4,4232,35185,50,4653,35185,40,4653,35220,0,4653,51511,3,5408,52538,4,5779,53443,5,6154,53444,1,6154,53444,50,6154,53444,40,6154,53479,0,6154,66038,3,6905,67447,4,7280,68896,5,7655,68897,1,7655,68897,50,7655,68897,40,7655,68932,0,7655,123105,3,11557,124264,4,13507,125063,5,15456,125064,1,15457,125064,50,15459,125064,40,15459,125099,0,15459,171035,3,18011,172070,4,19285,173022,1,20560,173022,50,20562,173022,40,20562,173057,0,20562,210331,3,22064,211285,4,22813,212121,1,23563,212121,50,23565,212121,40,23565,212156,0,23565,221858,3,24320,222482,4,24691,222741,5,25066,222742,1,25066,222742,50,25066,222742,40,25066,222777,0,25066,251711,3,26267,252655,4,26867,253281,5,27467,253282,1,27467,253282,50,27468,253282,40,27468,253317,0,27468,274134,3,28227,274870,4,28594,275476,1,28969,275476,50,28969,275476,40,28969,275476,40,28969,275506,0,28969)
%
%
% START OF PROOF
% 275478 [] equal(multiply(identity,X),X).
% 275479 [] equal(multiply(inverse(X),X),identity).
% 275480 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 275481 [] -equal(multiply(X,sk_c5),sk_c6) | -equal(inverse(X),sk_c6).
% 275482 [?] ?
% 275483 [] equal(inverse(sk_c2),sk_c5) | equal(inverse(sk_c4),sk_c6).
% 275487 [] equal(multiply(sk_c2,sk_c5),sk_c7) | equal(multiply(sk_c4,sk_c5),sk_c6).
% 275488 [] equal(multiply(sk_c2,sk_c5),sk_c7) | equal(inverse(sk_c4),sk_c6).
% 275492 [] equal(multiply(sk_c7,sk_c5),sk_c6) | equal(multiply(sk_c4,sk_c5),sk_c6).
% 275493 [] equal(multiply(sk_c7,sk_c5),sk_c6) | equal(inverse(sk_c4),sk_c6).
% 275497 [?] ?
% 275498 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c4),sk_c6).
% 275502 [] equal(multiply(sk_c1,sk_c7),sk_c6) | equal(multiply(sk_c4,sk_c5),sk_c6).
% 275503 [] equal(multiply(sk_c1,sk_c7),sk_c6) | equal(inverse(sk_c4),sk_c6).
% 275509 [hyper:275481,275483,binarycut:275482] equal(inverse(sk_c2),sk_c5).
% 275510 [para:275509.1.1,275479.1.1.1] equal(multiply(sk_c5,sk_c2),identity).
% 275517 [hyper:275481,275498,binarycut:275497] equal(inverse(sk_c1),sk_c7).
% 275518 [para:275517.1.1,275479.1.1.1] equal(multiply(sk_c7,sk_c1),identity).
% 275521 [hyper:275481,275488,275487] equal(multiply(sk_c2,sk_c5),sk_c7).
% 275536 [hyper:275481,275492,275493] equal(multiply(sk_c7,sk_c5),sk_c6).
% 275543 [hyper:275481,275502,275503] equal(multiply(sk_c1,sk_c7),sk_c6).
% 275544 [para:275479.1.1,275480.1.1.1,demod:275478] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 275545 [para:275510.1.1,275480.1.1.1,demod:275478] equal(X,multiply(sk_c5,multiply(sk_c2,X))).
% 275546 [para:275518.1.1,275480.1.1.1,demod:275478] equal(X,multiply(sk_c7,multiply(sk_c1,X))).
% 275547 [para:275521.1.1,275480.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c2,multiply(sk_c5,X))).
% 275550 [para:275521.1.1,275545.1.2.2] equal(sk_c5,multiply(sk_c5,sk_c7)).
% 275553 [para:275510.1.1,275544.1.2.2] equal(sk_c2,multiply(inverse(sk_c5),identity)).
% 275556 [para:275543.1.1,275544.1.2.2,demod:275517] equal(sk_c7,multiply(sk_c7,sk_c6)).
% 275559 [para:275556.1.2,275544.1.2.2,demod:275479] equal(sk_c6,identity).
% 275560 [para:275546.1.2,275544.1.2.2] equal(multiply(sk_c1,X),multiply(inverse(sk_c7),X)).
% 275561 [para:275559.1.1,275556.1.2.2] equal(sk_c7,multiply(sk_c7,identity)).
% 275565 [para:275550.1.2,275547.1.2.2,demod:275521] equal(multiply(sk_c7,sk_c7),sk_c7).
% 275567 [para:275565.1.1,275544.1.2.2,demod:275543,275560] equal(sk_c7,sk_c6).
% 275568 [para:275567.1.1,275518.1.1.1] equal(multiply(sk_c6,sk_c1),identity).
% 275569 [para:275567.1.1,275536.1.1.1] equal(multiply(sk_c6,sk_c5),sk_c6).
% 275575 [para:275567.1.1,275565.1.1.1] equal(multiply(sk_c6,sk_c7),sk_c7).
% 275577 [para:275559.1.1,275568.1.1.1,demod:275478] equal(sk_c1,identity).
% 275578 [para:275577.1.1,275517.1.1.1] equal(inverse(identity),sk_c7).
% 275579 [para:275577.1.1,275518.1.1.2,demod:275561] equal(sk_c7,identity).
% 275581 [para:275579.1.1,275536.1.1.1,demod:275478] equal(sk_c5,sk_c6).
% 275584 [para:275579.1.1,275546.1.2.1,demod:275478] equal(X,multiply(sk_c1,X)).
% 275590 [para:275581.1.1,275550.1.2.1,demod:275575] equal(sk_c5,sk_c7).
% 275596 [para:275590.1.2,275579.1.1] equal(sk_c5,identity).
% 275604 [para:275596.1.1,275553.1.2.1.1,demod:275561,275578] equal(sk_c2,sk_c7).
% 275605 [para:275604.1.2,275543.1.1.2,demod:275584] equal(sk_c2,sk_c6).
% 275610 [para:275605.1.1,275509.1.1.1] equal(inverse(sk_c6),sk_c5).
% 275616 [hyper:275481,275569,demod:275610,cut:275581] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 19
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 2 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7) | -equal(multiply(sk_c7,sk_c5),sk_c6) | -equal(multiply(Y,sk_c5),sk_c7) | -equal(inverse(Y),sk_c5) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(U),sk_c6) | -equal(multiply(U,sk_c5),sk_c6).
% Split part used next: -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 19
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(30,40,0,65,0,0,484,50,3,519,0,3,953,50,6,988,0,7,1427,50,11,1462,0,11,1907,50,16,1942,0,16,2394,50,22,2429,0,22,2889,50,34,2924,0,34,3392,50,56,3427,0,56,3905,50,107,3940,0,107,4428,50,217,4463,0,217,4963,50,412,4998,0,412,5510,50,779,5510,40,779,5545,0,779,16500,3,1080,17202,4,1230,17844,5,1380,17845,1,1380,17845,50,1380,17845,40,1380,17880,0,1380,18033,3,1689,18041,4,1832,18049,5,1981,18049,1,1981,18049,50,1981,18049,40,1981,18084,0,1981,33051,3,3482,34230,4,4232,35185,50,4653,35185,40,4653,35220,0,4653,51511,3,5408,52538,4,5779,53443,5,6154,53444,1,6154,53444,50,6154,53444,40,6154,53479,0,6154,66038,3,6905,67447,4,7280,68896,5,7655,68897,1,7655,68897,50,7655,68897,40,7655,68932,0,7655,123105,3,11557,124264,4,13507,125063,5,15456,125064,1,15457,125064,50,15459,125064,40,15459,125099,0,15459,171035,3,18011,172070,4,19285,173022,1,20560,173022,50,20562,173022,40,20562,173057,0,20562,210331,3,22064,211285,4,22813,212121,1,23563,212121,50,23565,212121,40,23565,212156,0,23565,221858,3,24320,222482,4,24691,222741,5,25066,222742,1,25066,222742,50,25066,222742,40,25066,222777,0,25066,251711,3,26267,252655,4,26867,253281,5,27467,253282,1,27467,253282,50,27468,253282,40,27468,253317,0,27468,274134,3,28227,274870,4,28594,275476,1,28969,275476,50,28969,275476,40,28969,275476,40,28969,275506,0,28969,275615,50,28970,275615,30,28970,275615,40,28970,275645,0,28970)
%
%
% START OF PROOF
% 275617 [] equal(multiply(identity,X),X).
% 275618 [] equal(multiply(inverse(X),X),identity).
% 275619 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 275620 [] -equal(multiply(X,sk_c6),sk_c7) | -equal(inverse(X),sk_c7).
% 275623 [?] ?
% 275624 [] equal(inverse(sk_c2),sk_c5) | equal(inverse(sk_c3),sk_c7).
% 275628 [] equal(multiply(sk_c2,sk_c5),sk_c7) | equal(multiply(sk_c3,sk_c6),sk_c7).
% 275629 [] equal(multiply(sk_c2,sk_c5),sk_c7) | equal(inverse(sk_c3),sk_c7).
% 275633 [] equal(multiply(sk_c7,sk_c5),sk_c6) | equal(multiply(sk_c3,sk_c6),sk_c7).
% 275634 [] equal(multiply(sk_c7,sk_c5),sk_c6) | equal(inverse(sk_c3),sk_c7).
% 275638 [?] ?
% 275639 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c3),sk_c7).
% 275643 [] equal(multiply(sk_c1,sk_c7),sk_c6) | equal(multiply(sk_c3,sk_c6),sk_c7).
% 275644 [] equal(multiply(sk_c1,sk_c7),sk_c6) | equal(inverse(sk_c3),sk_c7).
% 275649 [hyper:275620,275624,binarycut:275623] equal(inverse(sk_c2),sk_c5).
% 275651 [para:275649.1.1,275618.1.1.1] equal(multiply(sk_c5,sk_c2),identity).
% 275659 [hyper:275620,275639,binarycut:275638] equal(inverse(sk_c1),sk_c7).
% 275662 [para:275659.1.1,275618.1.1.1] equal(multiply(sk_c7,sk_c1),identity).
% 275670 [hyper:275620,275629,275628] equal(multiply(sk_c2,sk_c5),sk_c7).
% 275682 [hyper:275620,275633,275634] equal(multiply(sk_c7,sk_c5),sk_c6).
% 275686 [hyper:275620,275643,275644] equal(multiply(sk_c1,sk_c7),sk_c6).
% 275687 [para:275618.1.1,275619.1.1.1,demod:275617] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 275688 [para:275651.1.1,275619.1.1.1,demod:275617] equal(X,multiply(sk_c5,multiply(sk_c2,X))).
% 275689 [para:275662.1.1,275619.1.1.1,demod:275617] equal(X,multiply(sk_c7,multiply(sk_c1,X))).
% 275690 [para:275670.1.1,275619.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c2,multiply(sk_c5,X))).
% 275693 [para:275670.1.1,275688.1.2.2] equal(sk_c5,multiply(sk_c5,sk_c7)).
% 275699 [para:275686.1.1,275687.1.2.2,demod:275659] equal(sk_c7,multiply(sk_c7,sk_c6)).
% 275702 [para:275699.1.2,275687.1.2.2,demod:275618] equal(sk_c6,identity).
% 275703 [para:275689.1.2,275687.1.2.2] equal(multiply(sk_c1,X),multiply(inverse(sk_c7),X)).
% 275704 [para:275702.1.1,275699.1.2.2] equal(sk_c7,multiply(sk_c7,identity)).
% 275708 [para:275693.1.2,275690.1.2.2,demod:275670] equal(multiply(sk_c7,sk_c7),sk_c7).
% 275710 [para:275708.1.1,275687.1.2.2,demod:275686,275703] equal(sk_c7,sk_c6).
% 275711 [para:275710.1.1,275662.1.1.1] equal(multiply(sk_c6,sk_c1),identity).
% 275718 [para:275710.1.1,275708.1.1.1] equal(multiply(sk_c6,sk_c7),sk_c7).
% 275720 [para:275702.1.1,275711.1.1.1,demod:275617] equal(sk_c1,identity).
% 275721 [para:275720.1.1,275659.1.1.1] equal(inverse(identity),sk_c7).
% 275722 [para:275720.1.1,275662.1.1.2,demod:275704] equal(sk_c7,identity).
% 275724 [para:275722.1.1,275682.1.1.1,demod:275617] equal(sk_c5,sk_c6).
% 275733 [para:275724.1.1,275693.1.2.1,demod:275718] equal(sk_c5,sk_c7).
% 275738 [para:275733.1.2,275708.1.1.2,demod:275682] equal(sk_c6,sk_c7).
% 275758 [hyper:275620,275721,demod:275617,cut:275738] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 19
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 3 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7) | -equal(multiply(sk_c7,sk_c5),sk_c6) | -equal(multiply(Y,sk_c5),sk_c7) | -equal(inverse(Y),sk_c5) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(U),sk_c6) | -equal(multiply(U,sk_c5),sk_c6).
% Split part used next: -equal(multiply(Y,sk_c5),sk_c7) | -equal(inverse(Y),sk_c5).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 19
% clause depth limited to 3
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 19
% clause depth limited to 4
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(30,40,0,65,0,0,484,50,3,519,0,3,953,50,6,988,0,7,1427,50,11,1462,0,11,1907,50,16,1942,0,16,2394,50,22,2429,0,22,2889,50,34,2924,0,34,3392,50,56,3427,0,56,3905,50,107,3940,0,107,4428,50,217,4463,0,217,4963,50,412,4998,0,412,5510,50,779,5510,40,779,5545,0,779,16500,3,1080,17202,4,1230,17844,5,1380,17845,1,1380,17845,50,1380,17845,40,1380,17880,0,1380,18033,3,1689,18041,4,1832,18049,5,1981,18049,1,1981,18049,50,1981,18049,40,1981,18084,0,1981,33051,3,3482,34230,4,4232,35185,50,4653,35185,40,4653,35220,0,4653,51511,3,5408,52538,4,5779,53443,5,6154,53444,1,6154,53444,50,6154,53444,40,6154,53479,0,6154,66038,3,6905,67447,4,7280,68896,5,7655,68897,1,7655,68897,50,7655,68897,40,7655,68932,0,7655,123105,3,11557,124264,4,13507,125063,5,15456,125064,1,15457,125064,50,15459,125064,40,15459,125099,0,15459,171035,3,18011,172070,4,19285,173022,1,20560,173022,50,20562,173022,40,20562,173057,0,20562,210331,3,22064,211285,4,22813,212121,1,23563,212121,50,23565,212121,40,23565,212156,0,23565,221858,3,24320,222482,4,24691,222741,5,25066,222742,1,25066,222742,50,25066,222742,40,25066,222777,0,25066,251711,3,26267,252655,4,26867,253281,5,27467,253282,1,27467,253282,50,27468,253282,40,27468,253317,0,27468,274134,3,28227,274870,4,28594,275476,1,28969,275476,50,28969,275476,40,28969,275476,40,28969,275506,0,28969,275615,50,28970,275615,30,28970,275615,40,28970,275645,0,28970,275757,50,28970,275757,30,28970,275757,40,28970,275787,0,28975,275871,50,28975,275901,0,28975)
%
%
% START OF PROOF
% 275873 [] equal(multiply(identity,X),X).
% 275874 [] equal(multiply(inverse(X),X),identity).
% 275875 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 275876 [] -equal(multiply(X,sk_c5),sk_c7) | -equal(inverse(X),sk_c5).
% 275877 [] equal(multiply(sk_c4,sk_c5),sk_c6) | equal(inverse(sk_c2),sk_c5).
% 275878 [] equal(inverse(sk_c2),sk_c5) | equal(inverse(sk_c4),sk_c6).
% 275879 [] equal(multiply(sk_c3,sk_c6),sk_c7) | equal(inverse(sk_c2),sk_c5).
% 275880 [] equal(inverse(sk_c2),sk_c5) | equal(inverse(sk_c3),sk_c7).
% 275881 [] equal(multiply(sk_c6,sk_c7),sk_c5) | equal(inverse(sk_c2),sk_c5).
% 275882 [?] ?
% 275883 [?] ?
% 275884 [?] ?
% 275885 [?] ?
% 275886 [?] ?
% 275904 [hyper:275876,275878,binarycut:275883] equal(inverse(sk_c4),sk_c6).
% 275905 [para:275904.1.1,275874.1.1.1] equal(multiply(sk_c6,sk_c4),identity).
% 275909 [hyper:275876,275880,binarycut:275885] equal(inverse(sk_c3),sk_c7).
% 275910 [para:275909.1.1,275874.1.1.1] equal(multiply(sk_c7,sk_c3),identity).
% 275913 [hyper:275876,275877,binarycut:275882] equal(multiply(sk_c4,sk_c5),sk_c6).
% 275916 [hyper:275876,275879,binarycut:275884] equal(multiply(sk_c3,sk_c6),sk_c7).
% 275919 [hyper:275876,275881,binarycut:275886] equal(multiply(sk_c6,sk_c7),sk_c5).
% 275920 [para:275874.1.1,275875.1.1.1,demod:275873] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 275921 [para:275905.1.1,275875.1.1.1,demod:275873] equal(X,multiply(sk_c6,multiply(sk_c4,X))).
% 275922 [para:275910.1.1,275875.1.1.1,demod:275873] equal(X,multiply(sk_c7,multiply(sk_c3,X))).
% 275924 [para:275916.1.1,275875.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c3,multiply(sk_c6,X))).
% 275925 [para:275919.1.1,275875.1.1.1] equal(multiply(sk_c5,X),multiply(sk_c6,multiply(sk_c7,X))).
% 275926 [para:275913.1.1,275921.1.2.2] equal(sk_c5,multiply(sk_c6,sk_c6)).
% 275929 [para:275874.1.1,275920.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 275930 [para:275905.1.1,275920.1.2.2] equal(sk_c4,multiply(inverse(sk_c6),identity)).
% 275931 [para:275910.1.1,275920.1.2.2] equal(sk_c3,multiply(inverse(sk_c7),identity)).
% 275932 [para:275916.1.1,275920.1.2.2,demod:275909] equal(sk_c6,multiply(sk_c7,sk_c7)).
% 275933 [para:275875.1.1,275920.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 275934 [para:275919.1.1,275920.1.2.2] equal(sk_c7,multiply(inverse(sk_c6),sk_c5)).
% 275936 [para:275926.1.2,275920.1.2.2,demod:275934] equal(sk_c6,sk_c7).
% 275937 [para:275920.1.2,275920.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 275938 [para:275936.1.2,275910.1.1.1] equal(multiply(sk_c6,sk_c3),identity).
% 275945 [para:275938.1.1,275920.1.2.2,demod:275930] equal(sk_c3,sk_c4).
% 275954 [para:275938.1.1,275924.1.2.2,demod:275910] equal(identity,multiply(sk_c3,identity)).
% 275955 [para:275954.1.2,275875.1.1.1,demod:275873] equal(X,multiply(sk_c3,X)).
% 275957 [para:275955.1.2,275920.1.2.2,demod:275909] equal(X,multiply(sk_c7,X)).
% 275958 [para:275955.1.2,275924.1.2,demod:275957] equal(X,multiply(sk_c6,X)).
% 275963 [para:275936.1.2,275925.1.2.2.1,demod:275958] equal(multiply(sk_c5,X),X).
% 275964 [para:275932.1.2,275925.1.2.2,demod:275926,275963] equal(sk_c7,sk_c5).
% 275967 [para:275963.1.1,275920.1.2.2] equal(X,multiply(inverse(sk_c5),X)).
% 275969 [para:275967.1.2,275874.1.1] equal(sk_c5,identity).
% 275974 [para:275969.1.1,275934.1.2.2,demod:275930] equal(sk_c7,sk_c4).
% 275989 [para:275974.1.1,275964.1.1] equal(sk_c4,sk_c5).
% 275996 [para:275989.1.1,275945.1.2] equal(sk_c3,sk_c5).
% 275999 [para:275937.1.2,275874.1.1] equal(multiply(X,inverse(X)),identity).
% 276001 [para:275937.1.2,275929.1.2] equal(X,multiply(X,identity)).
% 276003 [para:276001.1.2,275929.1.2] equal(X,inverse(inverse(X))).
% 276004 [para:276001.1.2,275931.1.2] equal(sk_c3,inverse(sk_c7)).
% 276006 [para:275999.1.1,275933.1.2.2.2,demod:276001] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 276011 [para:275922.1.2,276006.1.2.1.1,demod:275955] equal(inverse(X),multiply(inverse(X),sk_c7)).
% 276019 [para:276011.1.2,275937.1.2,demod:276003] equal(multiply(X,sk_c7),X).
% 276020 [para:275964.1.1,276019.1.1.2] equal(multiply(X,sk_c5),X).
% 276023 [hyper:275876,276020,demod:276004,cut:275996] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 19
% clause depth limited to 4
% seconds given: 4
%
%
% Split component 4 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7) | -equal(multiply(sk_c7,sk_c5),sk_c6) | -equal(multiply(Y,sk_c5),sk_c7) | -equal(inverse(Y),sk_c5) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(U),sk_c6) | -equal(multiply(U,sk_c5),sk_c6).
% Split part used next: -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 19
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(30,40,0,65,0,0,484,50,3,519,0,3,953,50,6,988,0,7,1427,50,11,1462,0,11,1907,50,16,1942,0,16,2394,50,22,2429,0,22,2889,50,34,2924,0,34,3392,50,56,3427,0,56,3905,50,107,3940,0,107,4428,50,217,4463,0,217,4963,50,412,4998,0,412,5510,50,779,5510,40,779,5545,0,779,16500,3,1080,17202,4,1230,17844,5,1380,17845,1,1380,17845,50,1380,17845,40,1380,17880,0,1380,18033,3,1689,18041,4,1832,18049,5,1981,18049,1,1981,18049,50,1981,18049,40,1981,18084,0,1981,33051,3,3482,34230,4,4232,35185,50,4653,35185,40,4653,35220,0,4653,51511,3,5408,52538,4,5779,53443,5,6154,53444,1,6154,53444,50,6154,53444,40,6154,53479,0,6154,66038,3,6905,67447,4,7280,68896,5,7655,68897,1,7655,68897,50,7655,68897,40,7655,68932,0,7655,123105,3,11557,124264,4,13507,125063,5,15456,125064,1,15457,125064,50,15459,125064,40,15459,125099,0,15459,171035,3,18011,172070,4,19285,173022,1,20560,173022,50,20562,173022,40,20562,173057,0,20562,210331,3,22064,211285,4,22813,212121,1,23563,212121,50,23565,212121,40,23565,212156,0,23565,221858,3,24320,222482,4,24691,222741,5,25066,222742,1,25066,222742,50,25066,222742,40,25066,222777,0,25066,251711,3,26267,252655,4,26867,253281,5,27467,253282,1,27467,253282,50,27468,253282,40,27468,253317,0,27468,274134,3,28227,274870,4,28594,275476,1,28969,275476,50,28969,275476,40,28969,275476,40,28969,275506,0,28969,275615,50,28970,275615,30,28970,275615,40,28970,275645,0,28970,275757,50,28970,275757,30,28970,275757,40,28970,275787,0,28975,275871,50,28975,275901,0,28975,276022,50,28976,276022,30,28976,276022,40,28976,276052,0,28976)
%
%
% START OF PROOF
% 276024 [] equal(multiply(identity,X),X).
% 276025 [] equal(multiply(inverse(X),X),identity).
% 276026 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 276027 [] -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7).
% 276043 [] equal(multiply(sk_c4,sk_c5),sk_c6) | equal(inverse(sk_c1),sk_c7).
% 276044 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c4),sk_c6).
% 276045 [] equal(multiply(sk_c3,sk_c6),sk_c7) | equal(inverse(sk_c1),sk_c7).
% 276046 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c3),sk_c7).
% 276047 [] equal(multiply(sk_c6,sk_c7),sk_c5) | equal(inverse(sk_c1),sk_c7).
% 276048 [?] ?
% 276049 [?] ?
% 276050 [?] ?
% 276051 [?] ?
% 276052 [?] ?
% 276059 [hyper:276027,276044,binarycut:276049] equal(inverse(sk_c4),sk_c6).
% 276060 [para:276059.1.1,276025.1.1.1] equal(multiply(sk_c6,sk_c4),identity).
% 276063 [hyper:276027,276046,binarycut:276051] equal(inverse(sk_c3),sk_c7).
% 276067 [para:276063.1.1,276025.1.1.1] equal(multiply(sk_c7,sk_c3),identity).
% 276074 [hyper:276027,276043,binarycut:276048] equal(multiply(sk_c4,sk_c5),sk_c6).
% 276077 [hyper:276027,276045,binarycut:276050] equal(multiply(sk_c3,sk_c6),sk_c7).
% 276081 [hyper:276027,276047,binarycut:276052] equal(multiply(sk_c6,sk_c7),sk_c5).
% 276082 [para:276025.1.1,276026.1.1.1,demod:276024] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 276083 [para:276060.1.1,276026.1.1.1,demod:276024] equal(X,multiply(sk_c6,multiply(sk_c4,X))).
% 276086 [para:276077.1.1,276026.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c3,multiply(sk_c6,X))).
% 276088 [para:276074.1.1,276083.1.2.2] equal(sk_c5,multiply(sk_c6,sk_c6)).
% 276091 [para:276060.1.1,276082.1.2.2] equal(sk_c4,multiply(inverse(sk_c6),identity)).
% 276094 [para:276081.1.1,276082.1.2.2] equal(sk_c7,multiply(inverse(sk_c6),sk_c5)).
% 276096 [para:276088.1.2,276082.1.2.2,demod:276094] equal(sk_c6,sk_c7).
% 276097 [para:276096.1.2,276067.1.1.1] equal(multiply(sk_c6,sk_c3),identity).
% 276104 [para:276097.1.1,276082.1.2.2,demod:276091] equal(sk_c3,sk_c4).
% 276105 [para:276104.1.2,276059.1.1.1,demod:276063] equal(sk_c7,sk_c6).
% 276113 [para:276097.1.1,276086.1.2.2,demod:276067] equal(identity,multiply(sk_c3,identity)).
% 276114 [para:276113.1.2,276026.1.1.1,demod:276024] equal(X,multiply(sk_c3,X)).
% 276116 [para:276114.1.2,276082.1.2.2,demod:276063] equal(X,multiply(sk_c7,X)).
% 276118 [para:276116.1.2,276067.1.1] equal(sk_c3,identity).
% 276119 [para:276118.1.1,276063.1.1.1] equal(inverse(identity),sk_c7).
% 276120 [hyper:276027,276119,demod:276024,cut:276105] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 19
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 5 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7) | -equal(multiply(sk_c7,sk_c5),sk_c6) | -equal(multiply(Y,sk_c5),sk_c7) | -equal(inverse(Y),sk_c5) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(U),sk_c6) | -equal(multiply(U,sk_c5),sk_c6).
% Split part used next: -equal(multiply(sk_c7,sk_c5),sk_c6).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 19
% clause depth limited to 3
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 19
% clause depth limited to 4
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 19
% clause depth limited to 5
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 19
% clause depth limited to 6
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 19
% clause depth limited to 7
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 19
% clause depth limited to 8
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 19
% clause depth limited to 9
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 19
% clause depth limited to 10
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 19
% clause depth limited to 11
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(30,40,0,65,0,0,484,50,3,519,0,3,953,50,6,988,0,7,1427,50,11,1462,0,11,1907,50,16,1942,0,16,2394,50,22,2429,0,22,2889,50,34,2924,0,34,3392,50,56,3427,0,56,3905,50,107,3940,0,107,4428,50,217,4463,0,217,4963,50,412,4998,0,412,5510,50,779,5510,40,779,5545,0,779,16500,3,1080,17202,4,1230,17844,5,1380,17845,1,1380,17845,50,1380,17845,40,1380,17880,0,1380,18033,3,1689,18041,4,1832,18049,5,1981,18049,1,1981,18049,50,1981,18049,40,1981,18084,0,1981,33051,3,3482,34230,4,4232,35185,50,4653,35185,40,4653,35220,0,4653,51511,3,5408,52538,4,5779,53443,5,6154,53444,1,6154,53444,50,6154,53444,40,6154,53479,0,6154,66038,3,6905,67447,4,7280,68896,5,7655,68897,1,7655,68897,50,7655,68897,40,7655,68932,0,7655,123105,3,11557,124264,4,13507,125063,5,15456,125064,1,15457,125064,50,15459,125064,40,15459,125099,0,15459,171035,3,18011,172070,4,19285,173022,1,20560,173022,50,20562,173022,40,20562,173057,0,20562,210331,3,22064,211285,4,22813,212121,1,23563,212121,50,23565,212121,40,23565,212156,0,23565,221858,3,24320,222482,4,24691,222741,5,25066,222742,1,25066,222742,50,25066,222742,40,25066,222777,0,25066,251711,3,26267,252655,4,26867,253281,5,27467,253282,1,27467,253282,50,27468,253282,40,27468,253317,0,27468,274134,3,28227,274870,4,28594,275476,1,28969,275476,50,28969,275476,40,28969,275476,40,28969,275506,0,28969,275615,50,28970,275615,30,28970,275615,40,28970,275645,0,28970,275757,50,28970,275757,30,28970,275757,40,28970,275787,0,28975,275871,50,28975,275901,0,28975,276022,50,28976,276022,30,28976,276022,40,28976,276052,0,28976,276119,50,28976,276119,30,28976,276119,40,28976,276149,0,28981,276247,50,28981,276277,0,28981,276431,50,28983,276461,0,28988,276634,50,28991,276664,0,28991,276850,50,28995,276880,0,28995,277072,50,29002,277102,0,29006,277302,50,29019,277332,0,29019,277540,50,29044,277570,0,29048,277788,50,29100,277818,0,29100,278046,50,29206,278046,40,29206,278076,0,29206)
%
%
% START OF PROOF
% 277990 [?] ?
% 278048 [] equal(multiply(identity,X),X).
% 278049 [] equal(multiply(inverse(X),X),identity).
% 278050 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 278051 [] -equal(multiply(sk_c7,sk_c5),sk_c6).
% 278062 [?] ?
% 278063 [?] ?
% 278066 [?] ?
% 278100 [input:278063,cut:278051] equal(inverse(sk_c4),sk_c6).
% 278101 [para:278100.1.1,278049.1.1.1] equal(multiply(sk_c6,sk_c4),identity).
% 278116 [input:278062,cut:278051] equal(multiply(sk_c4,sk_c5),sk_c6).
% 278120 [input:278066,cut:278051] equal(multiply(sk_c6,sk_c7),sk_c5).
% 278124 [para:278049.1.1,278050.1.1.1,demod:278048] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 278132 [para:278101.1.1,278050.1.1.1,demod:278048] equal(X,multiply(sk_c6,multiply(sk_c4,X))).
% 278156 [para:278116.1.1,278132.1.2.2] equal(sk_c5,multiply(sk_c6,sk_c6)).
% 278196 [para:278120.1.1,278124.1.2.2] equal(sk_c7,multiply(inverse(sk_c6),sk_c5)).
% 278203 [para:278156.1.2,278124.1.2.2,demod:278196] equal(sk_c6,sk_c7).
% 278207 [para:278203.1.2,278051.1.1.1,cut:277990] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% Split component 6 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7) | -equal(multiply(sk_c7,sk_c5),sk_c6) | -equal(multiply(Y,sk_c5),sk_c7) | -equal(inverse(Y),sk_c5) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(U),sk_c6) | -equal(multiply(U,sk_c5),sk_c6).
% Split part used next: -equal(multiply(sk_c6,sk_c7),sk_c5).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 19
% clause depth limited to 3
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 19
% clause depth limited to 4
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 19
% clause depth limited to 5
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 19
% clause depth limited to 6
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 19
% clause depth limited to 7
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 19
% clause depth limited to 8
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 19
% clause depth limited to 9
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 19
% clause depth limited to 10
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 19
% clause depth limited to 11
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(30,40,0,65,0,0,484,50,3,519,0,3,953,50,6,988,0,7,1427,50,11,1462,0,11,1907,50,16,1942,0,16,2394,50,22,2429,0,22,2889,50,34,2924,0,34,3392,50,56,3427,0,56,3905,50,107,3940,0,107,4428,50,217,4463,0,217,4963,50,412,4998,0,412,5510,50,779,5510,40,779,5545,0,779,16500,3,1080,17202,4,1230,17844,5,1380,17845,1,1380,17845,50,1380,17845,40,1380,17880,0,1380,18033,3,1689,18041,4,1832,18049,5,1981,18049,1,1981,18049,50,1981,18049,40,1981,18084,0,1981,33051,3,3482,34230,4,4232,35185,50,4653,35185,40,4653,35220,0,4653,51511,3,5408,52538,4,5779,53443,5,6154,53444,1,6154,53444,50,6154,53444,40,6154,53479,0,6154,66038,3,6905,67447,4,7280,68896,5,7655,68897,1,7655,68897,50,7655,68897,40,7655,68932,0,7655,123105,3,11557,124264,4,13507,125063,5,15456,125064,1,15457,125064,50,15459,125064,40,15459,125099,0,15459,171035,3,18011,172070,4,19285,173022,1,20560,173022,50,20562,173022,40,20562,173057,0,20562,210331,3,22064,211285,4,22813,212121,1,23563,212121,50,23565,212121,40,23565,212156,0,23565,221858,3,24320,222482,4,24691,222741,5,25066,222742,1,25066,222742,50,25066,222742,40,25066,222777,0,25066,251711,3,26267,252655,4,26867,253281,5,27467,253282,1,27467,253282,50,27468,253282,40,27468,253317,0,27468,274134,3,28227,274870,4,28594,275476,1,28969,275476,50,28969,275476,40,28969,275476,40,28969,275506,0,28969,275615,50,28970,275615,30,28970,275615,40,28970,275645,0,28970,275757,50,28970,275757,30,28970,275757,40,28970,275787,0,28975,275871,50,28975,275901,0,28975,276022,50,28976,276022,30,28976,276022,40,28976,276052,0,28976,276119,50,28976,276119,30,28976,276119,40,28976,276149,0,28981,276247,50,28981,276277,0,28981,276431,50,28983,276461,0,28988,276634,50,28991,276664,0,28991,276850,50,28995,276880,0,28995,277072,50,29002,277102,0,29006,277302,50,29019,277332,0,29019,277540,50,29044,277570,0,29048,277788,50,29100,277818,0,29100,278046,50,29206,278046,40,29206,278076,0,29206,278206,50,29206,278206,30,29206,278206,40,29206,278236,0,29206,278344,50,29207,278374,0,29212,278524,50,29214,278554,0,29214,278712,50,29218,278742,0,29218,278908,50,29224,278938,0,29228,279110,50,29237,279140,0,29237,279320,50,29253,279350,0,29257,279538,50,29286,279568,0,29286,279766,50,29348,279796,0,29348,280004,50,29465,280004,40,29465,280034,0,29465)
%
%
% START OF PROOF
% 279948 [?] ?
% 280006 [] equal(multiply(identity,X),X).
% 280007 [] equal(multiply(inverse(X),X),identity).
% 280008 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 280009 [] -equal(multiply(sk_c6,sk_c7),sk_c5).
% 280014 [?] ?
% 280019 [?] ?
% 280024 [?] ?
% 280051 [input:280014,cut:280009] equal(inverse(sk_c2),sk_c5).
% 280052 [para:280051.1.1,280007.1.1.1] equal(multiply(sk_c5,sk_c2),identity).
% 280071 [input:280019,cut:280009] equal(multiply(sk_c2,sk_c5),sk_c7).
% 280080 [input:280024,cut:280009] equal(multiply(sk_c7,sk_c5),sk_c6).
% 280084 [para:280007.1.1,280008.1.1.1,demod:280006] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 280089 [para:280052.1.1,280008.1.1.1,demod:280006] equal(X,multiply(sk_c5,multiply(sk_c2,X))).
% 280120 [para:280071.1.1,280089.1.2.2] equal(sk_c5,multiply(sk_c5,sk_c7)).
% 280168 [para:280089.1.2,280084.1.2.2] equal(multiply(sk_c2,X),multiply(inverse(sk_c5),X)).
% 280169 [para:280120.1.2,280084.1.2.2,demod:280168] equal(sk_c7,multiply(sk_c2,sk_c5)).
% 280187 [para:280168.1.2,280007.1.1,demod:280169] equal(sk_c7,identity).
% 280200 [para:280187.1.1,280080.1.1.1,demod:280006] equal(sk_c5,sk_c6).
% 280215 [para:280200.1.1,280009.1.2,cut:279948] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% Split attempt finished with SUCCESS.
%
% ***GANDALF_FOUND_A_REFUTATION***
%
% Global statistics over all passes:
%
% given clauses: 37838
% derived clauses: 6710880
% kept clauses: 237347
% kept size sum: 978152
% kept mid-nuclei: 2656
% kept new demods: 4134
% forw unit-subs: 2853264
% forw double-subs: 3378906
% forw overdouble-subs: 195687
% backward subs: 17963
% fast unit cutoff: 31406
% full unit cutoff: 0
% dbl unit cutoff: 4103
% real runtime : 295.90
% process. runtime: 294.65
% specific non-discr-tree subsumption statistics:
% tried: 21935336
% length fails: 1897713
% strength fails: 3340158
% predlist fails: 2043213
% aux str. fails: 4226346
% by-lit fails: 4992105
% full subs tried: 1106760
% full subs fail: 1034801
%
% ; program args: ("/home/graph/tptp/Systems/Gandalf---c-2.6/gandalf" "-time" "600" "/home/graph/tptp/TSTP/PreparedTPTP/otter:hypothesis:set(auto),clear(print_given)---add_equality:r/GRP/GRP274-1+eq_r.in")
%
%------------------------------------------------------------------------------