TSTP Solution File: GRP282-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP282-1 : 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 : art02.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 298.4s
% Output : Assurance 298.4s
% 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/GRP282-1+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 27)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 3 27)
% (binary-posweight-lex-big-order 30 #f 3 27)
% (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(sk_c9,sk_c8),sk_c7) | -equal(multiply(X,sk_c9),sk_c8) | -equal(inverse(X),sk_c9) | -equal(multiply(sk_c9,Y),sk_c8) | -equal(multiply(Z,sk_c9),Y) | -equal(inverse(Z),sk_c9) | -equal(multiply(sk_c8,sk_c9),sk_c7) | -equal(multiply(sk_c8,sk_c7),sk_c9) | -equal(inverse(sk_c9),sk_c7) | -equal(inverse(U),sk_c9) | -equal(multiply(U,sk_c7),sk_c9) | -equal(multiply(V,W),sk_c7) | -equal(inverse(V),W) | -equal(multiply(W,sk_c9),sk_c7).
% was split for some strategies as:
% -equal(multiply(V,W),sk_c7) | -equal(inverse(V),W) | -equal(multiply(W,sk_c9),sk_c7).
% -equal(inverse(U),sk_c9) | -equal(multiply(U,sk_c7),sk_c9).
% -equal(multiply(sk_c9,Y),sk_c8) | -equal(multiply(Z,sk_c9),Y) | -equal(inverse(Z),sk_c9).
% -equal(multiply(X,sk_c9),sk_c8) | -equal(inverse(X),sk_c9).
% -equal(multiply(sk_c9,sk_c8),sk_c7).
% -equal(multiply(sk_c8,sk_c9),sk_c7).
% -equal(multiply(sk_c8,sk_c7),sk_c9).
% -equal(inverse(sk_c9),sk_c7).
%
% Starting a split proof attempt with 8 components.
%
% Split component 1 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c9,sk_c8),sk_c7) | -equal(multiply(X,sk_c9),sk_c8) | -equal(inverse(X),sk_c9) | -equal(multiply(sk_c9,Y),sk_c8) | -equal(multiply(Z,sk_c9),Y) | -equal(inverse(Z),sk_c9) | -equal(multiply(sk_c8,sk_c9),sk_c7) | -equal(multiply(sk_c8,sk_c7),sk_c9) | -equal(inverse(sk_c9),sk_c7) | -equal(inverse(U),sk_c9) | -equal(multiply(U,sk_c7),sk_c9) | -equal(multiply(V,W),sk_c7) | -equal(inverse(V),W) | -equal(multiply(W,sk_c9),sk_c7).
% Split part used next: -equal(multiply(V,W),sk_c7) | -equal(inverse(V),W) | -equal(multiply(W,sk_c9),sk_c7).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(53,40,0,111,0,0,3323,50,39,3381,0,39,11844,50,159,11902,0,159,20546,50,297,20604,0,297,31034,50,483,31092,0,484,42933,50,723,42991,0,723,57134,50,1054,57134,40,1054,57192,0,1054,64622,3,1355,65677,4,1506,66533,1,1655,66533,50,1655,66533,40,1655,66591,0,1655,67902,3,1972,67920,4,2111,67937,5,2256,67937,1,2256,67937,50,2256,67937,40,2256,67995,0,2256,103367,3,3768,103892,4,4507,104386,1,5257,104386,50,5258,104386,40,5258,104444,0,5258,126208,3,6009,126749,4,6384,127111,1,6759,127111,50,6759,127111,40,6759,127169,0,6759,135735,3,7515,137891,4,7885,139750,5,8260,139751,1,8260,139751,50,8260,139751,40,8260,139809,0,8260,200004,3,12161,201026,4,14112,201403,1,16062,201403,50,16064,201403,40,16064,201461,0,16064,248462,3,18617,249320,4,19890,249768,1,21165,249768,50,21166,249768,40,21166,249826,0,21167,293123,3,22669,293652,4,23418,294203,5,24168,294204,1,24168,294204,50,24170,294204,40,24170,294262,0,24170,302655,3,24927,303589,4,25302,303700,5,25671,303700,1,25671,303700,50,25671,303700,40,25671,303758,0,25671,335349,3,26873,335906,4,27472,336339,1,28072,336339,50,28073,336339,40,28073,336397,0,28073,361509,3,28824,361949,4,29199,362364,1,29574,362364,50,29575,362364,40,29575,362364,40,29575,362417,0,29575)
%
%
% START OF PROOF
% 362366 [] equal(multiply(identity,X),X).
% 362367 [] equal(multiply(inverse(X),X),identity).
% 362368 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 362369 [] -equal(multiply(X,sk_c9),sk_c7) | -equal(multiply(Y,X),sk_c7) | -equal(inverse(Y),X).
% 362370 [?] ?
% 362371 [] equal(inverse(sk_c2),sk_c9) | equal(inverse(sk_c5),sk_c6).
% 362372 [?] ?
% 362378 [] equal(multiply(sk_c2,sk_c9),sk_c3) | equal(multiply(sk_c6,sk_c9),sk_c7).
% 362379 [] equal(multiply(sk_c2,sk_c9),sk_c3) | equal(inverse(sk_c5),sk_c6).
% 362380 [] equal(multiply(sk_c2,sk_c9),sk_c3) | equal(multiply(sk_c5,sk_c6),sk_c7).
% 362386 [] equal(multiply(sk_c9,sk_c3),sk_c8) | equal(multiply(sk_c6,sk_c9),sk_c7).
% 362387 [] equal(multiply(sk_c9,sk_c3),sk_c8) | equal(inverse(sk_c5),sk_c6).
% 362388 [] equal(multiply(sk_c9,sk_c3),sk_c8) | equal(multiply(sk_c5,sk_c6),sk_c7).
% 362394 [?] ?
% 362395 [] equal(inverse(sk_c1),sk_c9) | equal(inverse(sk_c5),sk_c6).
% 362396 [?] ?
% 362402 [] equal(multiply(sk_c1,sk_c9),sk_c8) | equal(multiply(sk_c6,sk_c9),sk_c7).
% 362403 [] equal(multiply(sk_c1,sk_c9),sk_c8) | equal(inverse(sk_c5),sk_c6).
% 362404 [] equal(multiply(sk_c1,sk_c9),sk_c8) | equal(multiply(sk_c5,sk_c6),sk_c7).
% 362410 [] equal(multiply(sk_c9,sk_c8),sk_c7) | equal(multiply(sk_c6,sk_c9),sk_c7).
% 362411 [] equal(multiply(sk_c9,sk_c8),sk_c7) | equal(inverse(sk_c5),sk_c6).
% 362412 [] equal(multiply(sk_c9,sk_c8),sk_c7) | equal(multiply(sk_c5,sk_c6),sk_c7).
% 362423 [hyper:362369,362371,binarycut:362372,binarycut:362370] equal(inverse(sk_c2),sk_c9).
% 362425 [para:362423.1.1,362367.1.1.1] equal(multiply(sk_c9,sk_c2),identity).
% 362430 [hyper:362369,362395,binarycut:362396,binarycut:362394] equal(inverse(sk_c1),sk_c9).
% 362433 [para:362430.1.1,362367.1.1.1] equal(multiply(sk_c9,sk_c1),identity).
% 362459 [hyper:362369,362380,362378,362379] equal(multiply(sk_c2,sk_c9),sk_c3).
% 362491 [hyper:362369,362388,362386,362387] equal(multiply(sk_c9,sk_c3),sk_c8).
% 362506 [hyper:362369,362404,362402,362403] equal(multiply(sk_c1,sk_c9),sk_c8).
% 362519 [hyper:362369,362412,362410,362411] equal(multiply(sk_c9,sk_c8),sk_c7).
% 362521 [para:362367.1.1,362368.1.1.1,demod:362366] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 362522 [para:362425.1.1,362368.1.1.1,demod:362366] equal(X,multiply(sk_c9,multiply(sk_c2,X))).
% 362523 [para:362433.1.1,362368.1.1.1,demod:362366] equal(X,multiply(sk_c9,multiply(sk_c1,X))).
% 362524 [para:362459.1.1,362368.1.1.1] equal(multiply(sk_c3,X),multiply(sk_c2,multiply(sk_c9,X))).
% 362525 [para:362491.1.1,362368.1.1.1] equal(multiply(sk_c8,X),multiply(sk_c9,multiply(sk_c3,X))).
% 362526 [para:362506.1.1,362368.1.1.1] equal(multiply(sk_c8,X),multiply(sk_c1,multiply(sk_c9,X))).
% 362532 [para:362459.1.1,362522.1.2.2,demod:362491] equal(sk_c9,sk_c8).
% 362534 [para:362532.1.1,362433.1.1.1] equal(multiply(sk_c8,sk_c1),identity).
% 362535 [para:362532.1.1,362459.1.1.2] equal(multiply(sk_c2,sk_c8),sk_c3).
% 362537 [para:362532.1.1,362506.1.1.2] equal(multiply(sk_c1,sk_c8),sk_c8).
% 362540 [para:362534.1.1,362368.1.1.1,demod:362366] equal(X,multiply(sk_c8,multiply(sk_c1,X))).
% 362544 [para:362425.1.1,362521.1.2.2] equal(sk_c2,multiply(inverse(sk_c9),identity)).
% 362545 [para:362433.1.1,362521.1.2.2,demod:362544] equal(sk_c1,sk_c2).
% 362547 [para:362506.1.1,362521.1.2.2,demod:362519,362430] equal(sk_c9,sk_c7).
% 362549 [para:362522.1.2,362521.1.2.2] equal(multiply(sk_c2,X),multiply(inverse(sk_c9),X)).
% 362551 [para:362545.1.2,362459.1.1.1,demod:362506] equal(sk_c8,sk_c3).
% 362552 [para:362547.1.1,362425.1.1.1] equal(multiply(sk_c7,sk_c2),identity).
% 362559 [para:362547.1.1,362532.1.1] equal(sk_c7,sk_c8).
% 362564 [para:362559.1.2,362551.1.1] equal(sk_c7,sk_c3).
% 362568 [para:362523.1.2,362521.1.2.2,demod:362549] equal(multiply(sk_c1,X),multiply(sk_c2,X)).
% 362570 [para:362535.1.1,362368.1.1.1,demod:362568] equal(multiply(sk_c3,X),multiply(sk_c1,multiply(sk_c8,X))).
% 362582 [para:362524.1.2,362522.1.2.2,demod:362525] equal(multiply(sk_c9,X),multiply(sk_c8,X)).
% 362588 [para:362537.1.1,362368.1.1.1,demod:362570] equal(multiply(sk_c8,X),multiply(sk_c3,X)).
% 362590 [para:362522.1.2,362526.1.2.2,demod:362540,362568] equal(X,multiply(sk_c1,X)).
% 362591 [para:362523.1.2,362526.1.2.2,demod:362588,362590] equal(multiply(sk_c3,X),X).
% 362597 [para:362564.1.2,362591.1.1.1] equal(multiply(sk_c7,X),X).
% 362600 [para:362597.1.1,362521.1.2.2] equal(X,multiply(inverse(sk_c7),X)).
% 362604 [para:362552.1.1,362521.1.2.2,demod:362600] equal(sk_c2,identity).
% 362607 [para:362604.1.1,362423.1.1.1] equal(inverse(identity),sk_c9).
% 362616 [hyper:362369,362607,demod:362591,362588,362582,362366,cut:362547,cut:362547] 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 27
% clause depth limited to 3
% seconds given: 2
%
%
% Split component 2 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c9,sk_c8),sk_c7) | -equal(multiply(X,sk_c9),sk_c8) | -equal(inverse(X),sk_c9) | -equal(multiply(sk_c9,Y),sk_c8) | -equal(multiply(Z,sk_c9),Y) | -equal(inverse(Z),sk_c9) | -equal(multiply(sk_c8,sk_c9),sk_c7) | -equal(multiply(sk_c8,sk_c7),sk_c9) | -equal(inverse(sk_c9),sk_c7) | -equal(inverse(U),sk_c9) | -equal(multiply(U,sk_c7),sk_c9) | -equal(multiply(V,W),sk_c7) | -equal(inverse(V),W) | -equal(multiply(W,sk_c9),sk_c7).
% Split part used next: -equal(inverse(U),sk_c9) | -equal(multiply(U,sk_c7),sk_c9).
% 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 27
% clause depth limited to 3
% seconds given: 2
%
%
% 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 27
% clause depth limited to 4
% seconds given: 2
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(53,40,0,111,0,0,3323,50,39,3381,0,39,11844,50,159,11902,0,159,20546,50,297,20604,0,297,31034,50,483,31092,0,484,42933,50,723,42991,0,723,57134,50,1054,57134,40,1054,57192,0,1054,64622,3,1355,65677,4,1506,66533,1,1655,66533,50,1655,66533,40,1655,66591,0,1655,67902,3,1972,67920,4,2111,67937,5,2256,67937,1,2256,67937,50,2256,67937,40,2256,67995,0,2256,103367,3,3768,103892,4,4507,104386,1,5257,104386,50,5258,104386,40,5258,104444,0,5258,126208,3,6009,126749,4,6384,127111,1,6759,127111,50,6759,127111,40,6759,127169,0,6759,135735,3,7515,137891,4,7885,139750,5,8260,139751,1,8260,139751,50,8260,139751,40,8260,139809,0,8260,200004,3,12161,201026,4,14112,201403,1,16062,201403,50,16064,201403,40,16064,201461,0,16064,248462,3,18617,249320,4,19890,249768,1,21165,249768,50,21166,249768,40,21166,249826,0,21167,293123,3,22669,293652,4,23418,294203,5,24168,294204,1,24168,294204,50,24170,294204,40,24170,294262,0,24170,302655,3,24927,303589,4,25302,303700,5,25671,303700,1,25671,303700,50,25671,303700,40,25671,303758,0,25671,335349,3,26873,335906,4,27472,336339,1,28072,336339,50,28073,336339,40,28073,336397,0,28073,361509,3,28824,361949,4,29199,362364,1,29574,362364,50,29575,362364,40,29575,362364,40,29575,362417,0,29575,362615,50,29575,362615,30,29575,362615,40,29575,362668,0,29575,362824,50,29576,362877,0,29582)
%
%
% START OF PROOF
% 362826 [] equal(multiply(identity,X),X).
% 362827 [] equal(multiply(inverse(X),X),identity).
% 362828 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 362829 [] -equal(multiply(X,sk_c7),sk_c9) | -equal(inverse(X),sk_c9).
% 362833 [?] ?
% 362834 [] equal(inverse(sk_c2),sk_c9) | equal(inverse(sk_c4),sk_c9).
% 362841 [] equal(multiply(sk_c2,sk_c9),sk_c3) | equal(multiply(sk_c4,sk_c7),sk_c9).
% 362842 [] equal(multiply(sk_c2,sk_c9),sk_c3) | equal(inverse(sk_c4),sk_c9).
% 362849 [] equal(multiply(sk_c9,sk_c3),sk_c8) | equal(multiply(sk_c4,sk_c7),sk_c9).
% 362850 [] equal(multiply(sk_c9,sk_c3),sk_c8) | equal(inverse(sk_c4),sk_c9).
% 362857 [?] ?
% 362858 [] equal(inverse(sk_c1),sk_c9) | equal(inverse(sk_c4),sk_c9).
% 362865 [] equal(multiply(sk_c1,sk_c9),sk_c8) | equal(multiply(sk_c4,sk_c7),sk_c9).
% 362866 [] equal(multiply(sk_c1,sk_c9),sk_c8) | equal(inverse(sk_c4),sk_c9).
% 362873 [] equal(multiply(sk_c9,sk_c8),sk_c7) | equal(multiply(sk_c4,sk_c7),sk_c9).
% 362874 [] equal(multiply(sk_c9,sk_c8),sk_c7) | equal(inverse(sk_c4),sk_c9).
% 362883 [hyper:362829,362834,binarycut:362833] equal(inverse(sk_c2),sk_c9).
% 362886 [para:362883.1.1,362827.1.1.1] equal(multiply(sk_c9,sk_c2),identity).
% 362894 [hyper:362829,362858,binarycut:362857] equal(inverse(sk_c1),sk_c9).
% 362897 [para:362894.1.1,362827.1.1.1] equal(multiply(sk_c9,sk_c1),identity).
% 362918 [hyper:362829,362841,362842] equal(multiply(sk_c2,sk_c9),sk_c3).
% 362928 [hyper:362829,362849,362850] equal(multiply(sk_c9,sk_c3),sk_c8).
% 362933 [hyper:362829,362865,362866] equal(multiply(sk_c1,sk_c9),sk_c8).
% 362938 [hyper:362829,362873,362874] equal(multiply(sk_c9,sk_c8),sk_c7).
% 362939 [para:362827.1.1,362828.1.1.1,demod:362826] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 362940 [para:362886.1.1,362828.1.1.1,demod:362826] equal(X,multiply(sk_c9,multiply(sk_c2,X))).
% 362941 [para:362897.1.1,362828.1.1.1,demod:362826] equal(X,multiply(sk_c9,multiply(sk_c1,X))).
% 362944 [para:362933.1.1,362828.1.1.1] equal(multiply(sk_c8,X),multiply(sk_c1,multiply(sk_c9,X))).
% 362945 [para:362938.1.1,362828.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c9,multiply(sk_c8,X))).
% 362946 [para:362918.1.1,362940.1.2.2,demod:362928] equal(sk_c9,sk_c8).
% 362947 [para:362946.1.1,362886.1.1.1] equal(multiply(sk_c8,sk_c2),identity).
% 362948 [para:362946.1.1,362897.1.1.1] equal(multiply(sk_c8,sk_c1),identity).
% 362949 [para:362946.1.1,362918.1.1.2] equal(multiply(sk_c2,sk_c8),sk_c3).
% 362950 [para:362946.1.1,362928.1.1.1] equal(multiply(sk_c8,sk_c3),sk_c8).
% 362951 [para:362946.1.1,362933.1.1.2] equal(multiply(sk_c1,sk_c8),sk_c8).
% 362954 [para:362948.1.1,362828.1.1.1,demod:362826] equal(X,multiply(sk_c8,multiply(sk_c1,X))).
% 362957 [para:362886.1.1,362939.1.2.2] equal(sk_c2,multiply(inverse(sk_c9),identity)).
% 362959 [para:362928.1.1,362939.1.2.2] equal(sk_c3,multiply(inverse(sk_c9),sk_c8)).
% 362960 [para:362933.1.1,362939.1.2.2,demod:362938,362894] equal(sk_c9,sk_c7).
% 362961 [para:362828.1.1,362939.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 362963 [para:362940.1.2,362939.1.2.2] equal(multiply(sk_c2,X),multiply(inverse(sk_c9),X)).
% 362967 [para:362960.1.1,362886.1.1.1] equal(multiply(sk_c7,sk_c2),identity).
% 362969 [para:362960.1.1,362918.1.1.2] equal(multiply(sk_c2,sk_c7),sk_c3).
% 362981 [para:362941.1.2,362939.1.2.2,demod:362963] equal(multiply(sk_c1,X),multiply(sk_c2,X)).
% 362983 [para:362949.1.1,362828.1.1.1,demod:362981] equal(multiply(sk_c3,X),multiply(sk_c1,multiply(sk_c8,X))).
% 362986 [para:362950.1.1,362939.1.2.2,demod:362827] equal(sk_c3,identity).
% 362989 [para:362986.1.1,362928.1.1.2] equal(multiply(sk_c9,identity),sk_c8).
% 363001 [para:362951.1.1,362828.1.1.1,demod:362983] equal(multiply(sk_c8,X),multiply(sk_c3,X)).
% 363004 [para:362940.1.2,362944.1.2.2,demod:362954,362981] equal(X,multiply(sk_c1,X)).
% 363005 [para:362941.1.2,362944.1.2.2,demod:363001,363004] equal(multiply(sk_c3,X),X).
% 363012 [para:362947.1.1,362945.1.2.2,demod:362989,362967] equal(identity,sk_c8).
% 363022 [para:363012.1.2,362959.1.2.2,demod:362957] equal(sk_c3,sk_c2).
% 363023 [para:363022.1.2,362883.1.1.1] equal(inverse(sk_c3),sk_c9).
% 363028 [para:362918.1.1,362961.1.2.2.2] equal(sk_c9,multiply(inverse(multiply(X,sk_c2)),multiply(X,sk_c3))).
% 363041 [para:362969.1.1,362961.1.2.2.2,demod:363028] equal(sk_c7,sk_c9).
% 363050 [hyper:362829,363023,demod:363005,cut:363041] 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 27
% clause depth limited to 4
% seconds given: 2
%
%
% Split component 3 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c9,sk_c8),sk_c7) | -equal(multiply(X,sk_c9),sk_c8) | -equal(inverse(X),sk_c9) | -equal(multiply(sk_c9,Y),sk_c8) | -equal(multiply(Z,sk_c9),Y) | -equal(inverse(Z),sk_c9) | -equal(multiply(sk_c8,sk_c9),sk_c7) | -equal(multiply(sk_c8,sk_c7),sk_c9) | -equal(inverse(sk_c9),sk_c7) | -equal(inverse(U),sk_c9) | -equal(multiply(U,sk_c7),sk_c9) | -equal(multiply(V,W),sk_c7) | -equal(inverse(V),W) | -equal(multiply(W,sk_c9),sk_c7).
% Split part used next: -equal(multiply(sk_c9,Y),sk_c8) | -equal(multiply(Z,sk_c9),Y) | -equal(inverse(Z),sk_c9).
% 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 27
% clause depth limited to 3
% seconds given: 2
%
%
% 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 27
% clause depth limited to 4
% seconds given: 2
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(53,40,0,111,0,0,3323,50,39,3381,0,39,11844,50,159,11902,0,159,20546,50,297,20604,0,297,31034,50,483,31092,0,484,42933,50,723,42991,0,723,57134,50,1054,57134,40,1054,57192,0,1054,64622,3,1355,65677,4,1506,66533,1,1655,66533,50,1655,66533,40,1655,66591,0,1655,67902,3,1972,67920,4,2111,67937,5,2256,67937,1,2256,67937,50,2256,67937,40,2256,67995,0,2256,103367,3,3768,103892,4,4507,104386,1,5257,104386,50,5258,104386,40,5258,104444,0,5258,126208,3,6009,126749,4,6384,127111,1,6759,127111,50,6759,127111,40,6759,127169,0,6759,135735,3,7515,137891,4,7885,139750,5,8260,139751,1,8260,139751,50,8260,139751,40,8260,139809,0,8260,200004,3,12161,201026,4,14112,201403,1,16062,201403,50,16064,201403,40,16064,201461,0,16064,248462,3,18617,249320,4,19890,249768,1,21165,249768,50,21166,249768,40,21166,249826,0,21167,293123,3,22669,293652,4,23418,294203,5,24168,294204,1,24168,294204,50,24170,294204,40,24170,294262,0,24170,302655,3,24927,303589,4,25302,303700,5,25671,303700,1,25671,303700,50,25671,303700,40,25671,303758,0,25671,335349,3,26873,335906,4,27472,336339,1,28072,336339,50,28073,336339,40,28073,336397,0,28073,361509,3,28824,361949,4,29199,362364,1,29574,362364,50,29575,362364,40,29575,362364,40,29575,362417,0,29575,362615,50,29575,362615,30,29575,362615,40,29575,362668,0,29575,362824,50,29576,362877,0,29582,363049,50,29583,363049,30,29583,363049,40,29583,363102,0,29583,363355,50,29583,363408,0,29584)
%
%
% START OF PROOF
% 363357 [] equal(multiply(identity,X),X).
% 363358 [] equal(multiply(inverse(X),X),identity).
% 363359 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 363360 [] -equal(multiply(sk_c9,X),sk_c8) | -equal(multiply(Y,sk_c9),X) | -equal(inverse(Y),sk_c9).
% 363361 [] equal(multiply(sk_c6,sk_c9),sk_c7) | equal(inverse(sk_c2),sk_c9).
% 363362 [] equal(inverse(sk_c2),sk_c9) | equal(inverse(sk_c5),sk_c6).
% 363363 [] equal(multiply(sk_c5,sk_c6),sk_c7) | equal(inverse(sk_c2),sk_c9).
% 363364 [] equal(multiply(sk_c4,sk_c7),sk_c9) | equal(inverse(sk_c2),sk_c9).
% 363365 [] equal(inverse(sk_c2),sk_c9) | equal(inverse(sk_c4),sk_c9).
% 363366 [] equal(inverse(sk_c2),sk_c9) | equal(inverse(sk_c9),sk_c7).
% 363367 [] equal(multiply(sk_c8,sk_c7),sk_c9) | equal(inverse(sk_c2),sk_c9).
% 363369 [] equal(multiply(sk_c2,sk_c9),sk_c3) | equal(multiply(sk_c6,sk_c9),sk_c7).
% 363370 [] equal(multiply(sk_c2,sk_c9),sk_c3) | equal(inverse(sk_c5),sk_c6).
% 363371 [] equal(multiply(sk_c2,sk_c9),sk_c3) | equal(multiply(sk_c5,sk_c6),sk_c7).
% 363372 [] equal(multiply(sk_c2,sk_c9),sk_c3) | equal(multiply(sk_c4,sk_c7),sk_c9).
% 363373 [] equal(multiply(sk_c2,sk_c9),sk_c3) | equal(inverse(sk_c4),sk_c9).
% 363374 [] equal(multiply(sk_c2,sk_c9),sk_c3) | equal(inverse(sk_c9),sk_c7).
% 363375 [] equal(multiply(sk_c2,sk_c9),sk_c3) | equal(multiply(sk_c8,sk_c7),sk_c9).
% 363377 [?] ?
% 363378 [?] ?
% 363379 [?] ?
% 363380 [?] ?
% 363381 [?] ?
% 363382 [?] ?
% 363383 [?] ?
% 363476 [hyper:363360,363370,binarycut:363378,binarycut:363362] equal(inverse(sk_c5),sk_c6).
% 363477 [para:363476.1.1,363358.1.1.1] equal(multiply(sk_c6,sk_c5),identity).
% 363483 [hyper:363360,363369,363361,binarycut:363377] equal(multiply(sk_c6,sk_c9),sk_c7).
% 363490 [hyper:363360,363373,binarycut:363381,binarycut:363365] equal(inverse(sk_c4),sk_c9).
% 363497 [para:363490.1.1,363358.1.1.1] equal(multiply(sk_c9,sk_c4),identity).
% 363504 [hyper:363360,363371,363363,binarycut:363379] equal(multiply(sk_c5,sk_c6),sk_c7).
% 363507 [hyper:363360,363374,binarycut:363382,binarycut:363366] equal(inverse(sk_c9),sk_c7).
% 363508 [para:363507.1.1,363358.1.1.1] equal(multiply(sk_c7,sk_c9),identity).
% 363519 [hyper:363360,363372,363364,binarycut:363380] equal(multiply(sk_c4,sk_c7),sk_c9).
% 363535 [hyper:363360,363375,363367,binarycut:363383] equal(multiply(sk_c8,sk_c7),sk_c9).
% 363543 [para:363358.1.1,363359.1.1.1,demod:363357] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 363545 [para:363477.1.1,363359.1.1.1,demod:363357] equal(X,multiply(sk_c6,multiply(sk_c5,X))).
% 363546 [para:363483.1.1,363359.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c6,multiply(sk_c9,X))).
% 363547 [para:363497.1.1,363359.1.1.1,demod:363357] equal(X,multiply(sk_c9,multiply(sk_c4,X))).
% 363548 [para:363504.1.1,363359.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c5,multiply(sk_c6,X))).
% 363557 [para:363504.1.1,363545.1.2.2] equal(sk_c6,multiply(sk_c6,sk_c7)).
% 363561 [para:363519.1.1,363547.1.2.2] equal(sk_c7,multiply(sk_c9,sk_c9)).
% 363565 [para:363358.1.1,363543.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 363569 [para:363497.1.1,363543.1.2.2,demod:363507] equal(sk_c4,multiply(sk_c7,identity)).
% 363572 [para:363359.1.1,363543.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 363575 [para:363547.1.2,363543.1.2.2,demod:363507] equal(multiply(sk_c4,X),multiply(sk_c7,X)).
% 363576 [para:363561.1.2,363543.1.2.2,demod:363507] equal(sk_c9,multiply(sk_c7,sk_c7)).
% 363577 [para:363543.1.2,363543.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 363579 [para:363576.1.2,363359.1.1.1] equal(multiply(sk_c9,X),multiply(sk_c7,multiply(sk_c7,X))).
% 363587 [para:363547.1.2,363546.1.2.2,demod:363579,363575] equal(multiply(sk_c9,X),multiply(sk_c6,X)).
% 363588 [para:363561.1.2,363546.1.2.2,demod:363557,363508] equal(identity,sk_c6).
% 363591 [para:363588.1.2,363504.1.1.2] equal(multiply(sk_c5,identity),sk_c7).
% 363592 [para:363588.1.2,363545.1.2.1,demod:363357] equal(X,multiply(sk_c5,X)).
% 363593 [para:363588.1.2,363557.1.2.1,demod:363357] equal(sk_c6,sk_c7).
% 363594 [para:363588.1.2,363546.1.2.1,demod:363357,363587] equal(multiply(sk_c7,X),multiply(sk_c6,X)).
% 363597 [para:363477.1.1,363548.1.2.2,demod:363591] equal(multiply(sk_c7,sk_c5),sk_c7).
% 363598 [para:363483.1.1,363548.1.2.2,demod:363592,363508] equal(identity,sk_c7).
% 363599 [para:363545.1.2,363548.1.2.2,demod:363592] equal(multiply(sk_c7,X),X).
% 363610 [para:363598.1.2,363519.1.1.2,demod:363569,363575] equal(sk_c4,sk_c9).
% 363611 [para:363598.1.2,363535.1.1.2] equal(multiply(sk_c8,identity),sk_c9).
% 363666 [para:363477.1.1,363572.1.2.2.2] equal(sk_c5,multiply(inverse(multiply(X,sk_c6)),multiply(X,identity))).
% 363688 [para:363577.1.2,363358.1.1] equal(multiply(X,inverse(X)),identity).
% 363691 [para:363577.1.2,363565.1.2] equal(X,multiply(X,identity)).
% 363694 [para:363691.1.2,363565.1.2] equal(X,inverse(inverse(X))).
% 363696 [para:363691.1.2,363611.1.1] equal(sk_c8,sk_c9).
% 363704 [para:363696.1.2,363610.1.2] equal(sk_c4,sk_c8).
% 363712 [para:363593.1.1,363666.1.2.1.1.2,demod:363691] equal(sk_c5,multiply(inverse(multiply(X,sk_c7)),X)).
% 363716 [para:363688.1.1,363572.1.2.2.2,demod:363691] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 363720 [para:363712.1.2,363543.1.2.2,demod:363597,363359,363694] equal(X,multiply(X,sk_c7)).
% 363721 [para:363712.1.2,363572.1.2.2,demod:363694,363716,363720,363359] equal(X,multiply(X,sk_c5)).
% 363725 [hyper:363360,363721,363490,demod:363599,363594,363691,363477,363587,363359,cut:363704] 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 27
% clause depth limited to 4
% seconds given: 2
%
%
% Split component 4 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c9,sk_c8),sk_c7) | -equal(multiply(X,sk_c9),sk_c8) | -equal(inverse(X),sk_c9) | -equal(multiply(sk_c9,Y),sk_c8) | -equal(multiply(Z,sk_c9),Y) | -equal(inverse(Z),sk_c9) | -equal(multiply(sk_c8,sk_c9),sk_c7) | -equal(multiply(sk_c8,sk_c7),sk_c9) | -equal(inverse(sk_c9),sk_c7) | -equal(inverse(U),sk_c9) | -equal(multiply(U,sk_c7),sk_c9) | -equal(multiply(V,W),sk_c7) | -equal(inverse(V),W) | -equal(multiply(W,sk_c9),sk_c7).
% Split part used next: -equal(multiply(X,sk_c9),sk_c8) | -equal(inverse(X),sk_c9).
% 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 27
% clause depth limited to 3
% seconds given: 2
%
%
% 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 27
% clause depth limited to 4
% seconds given: 2
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(53,40,0,111,0,0,3323,50,39,3381,0,39,11844,50,159,11902,0,159,20546,50,297,20604,0,297,31034,50,483,31092,0,484,42933,50,723,42991,0,723,57134,50,1054,57134,40,1054,57192,0,1054,64622,3,1355,65677,4,1506,66533,1,1655,66533,50,1655,66533,40,1655,66591,0,1655,67902,3,1972,67920,4,2111,67937,5,2256,67937,1,2256,67937,50,2256,67937,40,2256,67995,0,2256,103367,3,3768,103892,4,4507,104386,1,5257,104386,50,5258,104386,40,5258,104444,0,5258,126208,3,6009,126749,4,6384,127111,1,6759,127111,50,6759,127111,40,6759,127169,0,6759,135735,3,7515,137891,4,7885,139750,5,8260,139751,1,8260,139751,50,8260,139751,40,8260,139809,0,8260,200004,3,12161,201026,4,14112,201403,1,16062,201403,50,16064,201403,40,16064,201461,0,16064,248462,3,18617,249320,4,19890,249768,1,21165,249768,50,21166,249768,40,21166,249826,0,21167,293123,3,22669,293652,4,23418,294203,5,24168,294204,1,24168,294204,50,24170,294204,40,24170,294262,0,24170,302655,3,24927,303589,4,25302,303700,5,25671,303700,1,25671,303700,50,25671,303700,40,25671,303758,0,25671,335349,3,26873,335906,4,27472,336339,1,28072,336339,50,28073,336339,40,28073,336397,0,28073,361509,3,28824,361949,4,29199,362364,1,29574,362364,50,29575,362364,40,29575,362364,40,29575,362417,0,29575,362615,50,29575,362615,30,29575,362615,40,29575,362668,0,29575,362824,50,29576,362877,0,29582,363049,50,29583,363049,30,29583,363049,40,29583,363102,0,29583,363355,50,29583,363408,0,29584,363724,50,29585,363724,30,29585,363724,40,29585,363777,0,29589,363912,50,29589,363965,0,29589)
%
%
% START OF PROOF
% 363914 [] equal(multiply(identity,X),X).
% 363915 [] equal(multiply(inverse(X),X),identity).
% 363916 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 363917 [] -equal(multiply(X,sk_c9),sk_c8) | -equal(inverse(X),sk_c9).
% 363942 [] equal(multiply(sk_c6,sk_c9),sk_c7) | equal(inverse(sk_c1),sk_c9).
% 363943 [] equal(inverse(sk_c1),sk_c9) | equal(inverse(sk_c5),sk_c6).
% 363944 [] equal(multiply(sk_c5,sk_c6),sk_c7) | equal(inverse(sk_c1),sk_c9).
% 363945 [] equal(multiply(sk_c4,sk_c7),sk_c9) | equal(inverse(sk_c1),sk_c9).
% 363946 [] equal(inverse(sk_c1),sk_c9) | equal(inverse(sk_c4),sk_c9).
% 363947 [] equal(inverse(sk_c1),sk_c9) | equal(inverse(sk_c9),sk_c7).
% 363948 [] equal(multiply(sk_c8,sk_c7),sk_c9) | equal(inverse(sk_c1),sk_c9).
% 363949 [] equal(multiply(sk_c8,sk_c9),sk_c7) | equal(inverse(sk_c1),sk_c9).
% 363950 [?] ?
% 363951 [?] ?
% 363952 [?] ?
% 363953 [?] ?
% 363954 [?] ?
% 363955 [?] ?
% 363956 [?] ?
% 363957 [?] ?
% 363977 [hyper:363917,363943,binarycut:363951] equal(inverse(sk_c5),sk_c6).
% 363978 [para:363977.1.1,363915.1.1.1] equal(multiply(sk_c6,sk_c5),identity).
% 363981 [hyper:363917,363946,binarycut:363954] equal(inverse(sk_c4),sk_c9).
% 363988 [para:363981.1.1,363915.1.1.1] equal(multiply(sk_c9,sk_c4),identity).
% 363992 [hyper:363917,363947,binarycut:363955] equal(inverse(sk_c9),sk_c7).
% 363993 [para:363992.1.1,363915.1.1.1] equal(multiply(sk_c7,sk_c9),identity).
% 364008 [hyper:363917,363942,binarycut:363950] equal(multiply(sk_c6,sk_c9),sk_c7).
% 364011 [hyper:363917,363944,binarycut:363952] equal(multiply(sk_c5,sk_c6),sk_c7).
% 364014 [hyper:363917,363945,binarycut:363953] equal(multiply(sk_c4,sk_c7),sk_c9).
% 364017 [hyper:363917,363948,binarycut:363956] equal(multiply(sk_c8,sk_c7),sk_c9).
% 364021 [hyper:363917,363949,binarycut:363957] equal(multiply(sk_c8,sk_c9),sk_c7).
% 364022 [para:363915.1.1,363916.1.1.1,demod:363914] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 364023 [para:363978.1.1,363916.1.1.1,demod:363914] equal(X,multiply(sk_c6,multiply(sk_c5,X))).
% 364024 [para:363988.1.1,363916.1.1.1,demod:363914] equal(X,multiply(sk_c9,multiply(sk_c4,X))).
% 364026 [para:364008.1.1,363916.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c6,multiply(sk_c9,X))).
% 364027 [para:364011.1.1,363916.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c5,multiply(sk_c6,X))).
% 364031 [para:364011.1.1,364023.1.2.2] equal(sk_c6,multiply(sk_c6,sk_c7)).
% 364033 [para:363915.1.1,364022.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 364035 [para:363988.1.1,364022.1.2.2,demod:363992] equal(sk_c4,multiply(sk_c7,identity)).
% 364038 [para:364014.1.1,364022.1.2.2,demod:363981] equal(sk_c7,multiply(sk_c9,sk_c9)).
% 364039 [para:364017.1.1,364022.1.2.2] equal(sk_c7,multiply(inverse(sk_c8),sk_c9)).
% 364040 [para:364021.1.1,364022.1.2.2] equal(sk_c9,multiply(inverse(sk_c8),sk_c7)).
% 364041 [para:363916.1.1,364022.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 364043 [para:364022.1.2,364022.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 364045 [para:364035.1.2,363916.1.1.1,demod:363914] equal(multiply(sk_c4,X),multiply(sk_c7,X)).
% 364059 [para:364038.1.2,364026.1.2.2,demod:364031,363993] equal(identity,sk_c6).
% 364064 [para:364059.1.2,364008.1.1.1,demod:363914] equal(sk_c9,sk_c7).
% 364066 [para:364059.1.2,364023.1.2.1,demod:363914] equal(X,multiply(sk_c5,X)).
% 364070 [para:364008.1.1,364027.1.2.2,demod:364066,363993] equal(identity,sk_c7).
% 364071 [para:364023.1.2,364027.1.2.2,demod:364066] equal(multiply(sk_c7,X),X).
% 364077 [para:364064.1.1,364039.1.2.2,demod:364040] equal(sk_c7,sk_c9).
% 364082 [para:364070.1.2,364017.1.1.2] equal(multiply(sk_c8,identity),sk_c9).
% 364125 [para:364043.1.2,363915.1.1] equal(multiply(X,inverse(X)),identity).
% 364127 [para:364043.1.2,364033.1.2] equal(X,multiply(X,identity)).
% 364128 [para:364127.1.2,364033.1.2] equal(X,inverse(inverse(X))).
% 364131 [para:364127.1.2,364082.1.1] equal(sk_c8,sk_c9).
% 364132 [para:364131.1.2,363992.1.1.1] equal(inverse(sk_c8),sk_c7).
% 364140 [para:364125.1.1,364041.1.2.2.2,demod:364127] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 364145 [para:364024.1.2,364140.1.2.1.1,demod:364071,364045] equal(inverse(X),multiply(inverse(X),sk_c9)).
% 364157 [para:364145.1.2,364043.1.2,demod:364128] equal(multiply(X,sk_c9),X).
% 364158 [hyper:363917,364157,demod:364132,cut:364077] 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 27
% clause depth limited to 4
% seconds given: 2
%
%
% Split component 5 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c9,sk_c8),sk_c7) | -equal(multiply(X,sk_c9),sk_c8) | -equal(inverse(X),sk_c9) | -equal(multiply(sk_c9,Y),sk_c8) | -equal(multiply(Z,sk_c9),Y) | -equal(inverse(Z),sk_c9) | -equal(multiply(sk_c8,sk_c9),sk_c7) | -equal(multiply(sk_c8,sk_c7),sk_c9) | -equal(inverse(sk_c9),sk_c7) | -equal(inverse(U),sk_c9) | -equal(multiply(U,sk_c7),sk_c9) | -equal(multiply(V,W),sk_c7) | -equal(inverse(V),W) | -equal(multiply(W,sk_c9),sk_c7).
% Split part used next: -equal(multiply(sk_c9,sk_c8),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 27
% clause depth limited to 3
% seconds given: 2
%
%
% 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 27
% clause depth limited to 4
% seconds given: 2
%
%
% 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 27
% clause depth limited to 5
% seconds given: 2
%
%
% 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 27
% clause depth limited to 6
% seconds given: 2
%
%
% 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 27
% clause depth limited to 7
% seconds given: 2
%
%
% 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 27
% clause depth limited to 8
% seconds given: 2
%
%
% 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 27
% clause depth limited to 9
% seconds given: 2
%
%
% 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 27
% clause depth limited to 10
% seconds given: 2
%
%
% 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(53,40,0,111,0,0,3323,50,39,3381,0,39,11844,50,159,11902,0,159,20546,50,297,20604,0,297,31034,50,483,31092,0,484,42933,50,723,42991,0,723,57134,50,1054,57134,40,1054,57192,0,1054,64622,3,1355,65677,4,1506,66533,1,1655,66533,50,1655,66533,40,1655,66591,0,1655,67902,3,1972,67920,4,2111,67937,5,2256,67937,1,2256,67937,50,2256,67937,40,2256,67995,0,2256,103367,3,3768,103892,4,4507,104386,1,5257,104386,50,5258,104386,40,5258,104444,0,5258,126208,3,6009,126749,4,6384,127111,1,6759,127111,50,6759,127111,40,6759,127169,0,6759,135735,3,7515,137891,4,7885,139750,5,8260,139751,1,8260,139751,50,8260,139751,40,8260,139809,0,8260,200004,3,12161,201026,4,14112,201403,1,16062,201403,50,16064,201403,40,16064,201461,0,16064,248462,3,18617,249320,4,19890,249768,1,21165,249768,50,21166,249768,40,21166,249826,0,21167,293123,3,22669,293652,4,23418,294203,5,24168,294204,1,24168,294204,50,24170,294204,40,24170,294262,0,24170,302655,3,24927,303589,4,25302,303700,5,25671,303700,1,25671,303700,50,25671,303700,40,25671,303758,0,25671,335349,3,26873,335906,4,27472,336339,1,28072,336339,50,28073,336339,40,28073,336397,0,28073,361509,3,28824,361949,4,29199,362364,1,29574,362364,50,29575,362364,40,29575,362364,40,29575,362417,0,29575,362615,50,29575,362615,30,29575,362615,40,29575,362668,0,29575,362824,50,29576,362877,0,29582,363049,50,29583,363049,30,29583,363049,40,29583,363102,0,29583,363355,50,29583,363408,0,29584,363724,50,29585,363724,30,29585,363724,40,29585,363777,0,29589,363912,50,29589,363965,0,29589,364157,50,29591,364157,30,29591,364157,40,29592,364210,0,29596,364343,50,29597,364396,0,29597,364586,50,29601,364639,0,29601,364837,50,29605,364890,0,29610,365096,50,29617,365149,0,29617,365361,50,29627,365414,0,29631,365634,50,29648,365687,0,29648,365915,50,29680,365968,0,29680,366206,50,29747,366206,40,29747,366259,0,29747)
%
%
% START OF PROOF
% 366133 [?] ?
% 366208 [] equal(multiply(identity,X),X).
% 366209 [] equal(multiply(inverse(X),X),identity).
% 366210 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 366211 [] -equal(multiply(sk_c9,sk_c8),sk_c7).
% 366253 [?] ?
% 366254 [?] ?
% 366257 [?] ?
% 366319 [input:366253,cut:366211] equal(inverse(sk_c5),sk_c6).
% 366320 [para:366319.1.1,366209.1.1.1] equal(multiply(sk_c6,sk_c5),identity).
% 366324 [input:366257,cut:366211] equal(inverse(sk_c9),sk_c7).
% 366325 [para:366324.1.1,366209.1.1.1] equal(multiply(sk_c7,sk_c9),identity).
% 366344 [input:366254,cut:366211] equal(multiply(sk_c5,sk_c6),sk_c7).
% 366352 [para:366209.1.1,366210.1.1.1,demod:366208] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 366378 [para:366320.1.1,366210.1.1.1,demod:366208] equal(X,multiply(sk_c6,multiply(sk_c5,X))).
% 366425 [para:366344.1.1,366378.1.2.2] equal(sk_c6,multiply(sk_c6,sk_c7)).
% 366528 [para:366378.1.2,366352.1.2.2] equal(multiply(sk_c5,X),multiply(inverse(sk_c6),X)).
% 366529 [para:366425.1.2,366352.1.2.2,demod:366528] equal(sk_c7,multiply(sk_c5,sk_c6)).
% 366542 [para:366528.1.2,366209.1.1,demod:366529] equal(sk_c7,identity).
% 366553 [para:366542.1.1,366325.1.1.1,demod:366208] equal(sk_c9,identity).
% 366568 [para:366553.1.1,366211.1.1.1,demod:366208,cut:366133] 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(sk_c9,sk_c8),sk_c7) | -equal(multiply(X,sk_c9),sk_c8) | -equal(inverse(X),sk_c9) | -equal(multiply(sk_c9,Y),sk_c8) | -equal(multiply(Z,sk_c9),Y) | -equal(inverse(Z),sk_c9) | -equal(multiply(sk_c8,sk_c9),sk_c7) | -equal(multiply(sk_c8,sk_c7),sk_c9) | -equal(inverse(sk_c9),sk_c7) | -equal(inverse(U),sk_c9) | -equal(multiply(U,sk_c7),sk_c9) | -equal(multiply(V,W),sk_c7) | -equal(inverse(V),W) | -equal(multiply(W,sk_c9),sk_c7).
% Split part used next: -equal(multiply(sk_c8,sk_c9),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 27
% clause depth limited to 3
% seconds given: 2
%
%
% 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 27
% clause depth limited to 4
% seconds given: 2
%
%
% 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 27
% clause depth limited to 5
% seconds given: 2
%
%
% 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 27
% clause depth limited to 6
% seconds given: 2
%
%
% 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 27
% clause depth limited to 7
% seconds given: 2
%
%
% 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 27
% clause depth limited to 8
% seconds given: 2
%
%
% 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 27
% clause depth limited to 9
% seconds given: 2
%
%
% 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 27
% clause depth limited to 10
% seconds given: 2
%
%
% 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(53,40,0,111,0,0,3323,50,39,3381,0,39,11844,50,159,11902,0,159,20546,50,297,20604,0,297,31034,50,483,31092,0,484,42933,50,723,42991,0,723,57134,50,1054,57134,40,1054,57192,0,1054,64622,3,1355,65677,4,1506,66533,1,1655,66533,50,1655,66533,40,1655,66591,0,1655,67902,3,1972,67920,4,2111,67937,5,2256,67937,1,2256,67937,50,2256,67937,40,2256,67995,0,2256,103367,3,3768,103892,4,4507,104386,1,5257,104386,50,5258,104386,40,5258,104444,0,5258,126208,3,6009,126749,4,6384,127111,1,6759,127111,50,6759,127111,40,6759,127169,0,6759,135735,3,7515,137891,4,7885,139750,5,8260,139751,1,8260,139751,50,8260,139751,40,8260,139809,0,8260,200004,3,12161,201026,4,14112,201403,1,16062,201403,50,16064,201403,40,16064,201461,0,16064,248462,3,18617,249320,4,19890,249768,1,21165,249768,50,21166,249768,40,21166,249826,0,21167,293123,3,22669,293652,4,23418,294203,5,24168,294204,1,24168,294204,50,24170,294204,40,24170,294262,0,24170,302655,3,24927,303589,4,25302,303700,5,25671,303700,1,25671,303700,50,25671,303700,40,25671,303758,0,25671,335349,3,26873,335906,4,27472,336339,1,28072,336339,50,28073,336339,40,28073,336397,0,28073,361509,3,28824,361949,4,29199,362364,1,29574,362364,50,29575,362364,40,29575,362364,40,29575,362417,0,29575,362615,50,29575,362615,30,29575,362615,40,29575,362668,0,29575,362824,50,29576,362877,0,29582,363049,50,29583,363049,30,29583,363049,40,29583,363102,0,29583,363355,50,29583,363408,0,29584,363724,50,29585,363724,30,29585,363724,40,29585,363777,0,29589,363912,50,29589,363965,0,29589,364157,50,29591,364157,30,29591,364157,40,29592,364210,0,29596,364343,50,29597,364396,0,29597,364586,50,29601,364639,0,29601,364837,50,29605,364890,0,29610,365096,50,29617,365149,0,29617,365361,50,29627,365414,0,29631,365634,50,29648,365687,0,29648,365915,50,29680,365968,0,29680,366206,50,29747,366206,40,29747,366259,0,29747,366567,50,29748,366567,30,29748,366567,40,29748,366620,0,29748,366773,50,29749,366826,0,29755,367026,50,29758,367079,0,29758,367287,50,29763,367340,0,29763,367556,50,29770,367609,0,29775,367831,50,29785,367884,0,29785,368114,50,29803,368167,0,29807,368405,50,29839,368458,0,29839,368706,50,29907,368706,40,29907,368759,0,29908)
%
%
% START OF PROOF
% 368524 [?] ?
% 368708 [] equal(multiply(identity,X),X).
% 368709 [] equal(multiply(inverse(X),X),identity).
% 368710 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 368711 [] -equal(multiply(sk_c8,sk_c9),sk_c7).
% 368719 [?] ?
% 368727 [?] ?
% 368735 [?] ?
% 368786 [input:368719,cut:368711] equal(inverse(sk_c2),sk_c9).
% 368787 [para:368786.1.1,368709.1.1.1] equal(multiply(sk_c9,sk_c2),identity).
% 368826 [input:368727,cut:368711] equal(multiply(sk_c2,sk_c9),sk_c3).
% 368837 [input:368735,cut:368711] equal(multiply(sk_c9,sk_c3),sk_c8).
% 368854 [para:368787.1.1,368710.1.1.1,demod:368708] equal(X,multiply(sk_c9,multiply(sk_c2,X))).
% 368922 [para:368826.1.1,368854.1.2.2] equal(sk_c9,multiply(sk_c9,sk_c3)).
% 368930 [para:368922.1.2,368837.1.1] equal(sk_c9,sk_c8).
% 368932 [para:368930.1.1,368711.1.1.2,cut:368524] 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 7 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c9,sk_c8),sk_c7) | -equal(multiply(X,sk_c9),sk_c8) | -equal(inverse(X),sk_c9) | -equal(multiply(sk_c9,Y),sk_c8) | -equal(multiply(Z,sk_c9),Y) | -equal(inverse(Z),sk_c9) | -equal(multiply(sk_c8,sk_c9),sk_c7) | -equal(multiply(sk_c8,sk_c7),sk_c9) | -equal(inverse(sk_c9),sk_c7) | -equal(inverse(U),sk_c9) | -equal(multiply(U,sk_c7),sk_c9) | -equal(multiply(V,W),sk_c7) | -equal(inverse(V),W) | -equal(multiply(W,sk_c9),sk_c7).
% Split part used next: -equal(multiply(sk_c8,sk_c7),sk_c9).
% 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 27
% clause depth limited to 3
% seconds given: 2
%
%
% 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 27
% clause depth limited to 4
% seconds given: 2
%
%
% 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 27
% clause depth limited to 5
% seconds given: 2
%
%
% 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 27
% clause depth limited to 6
% seconds given: 2
%
%
% 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 27
% clause depth limited to 7
% seconds given: 2
%
%
% 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 27
% clause depth limited to 8
% seconds given: 2
%
%
% 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 27
% clause depth limited to 9
% seconds given: 2
%
%
% 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 27
% clause depth limited to 10
% seconds given: 2
%
%
% 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(53,40,0,111,0,0,3323,50,39,3381,0,39,11844,50,159,11902,0,159,20546,50,297,20604,0,297,31034,50,483,31092,0,484,42933,50,723,42991,0,723,57134,50,1054,57134,40,1054,57192,0,1054,64622,3,1355,65677,4,1506,66533,1,1655,66533,50,1655,66533,40,1655,66591,0,1655,67902,3,1972,67920,4,2111,67937,5,2256,67937,1,2256,67937,50,2256,67937,40,2256,67995,0,2256,103367,3,3768,103892,4,4507,104386,1,5257,104386,50,5258,104386,40,5258,104444,0,5258,126208,3,6009,126749,4,6384,127111,1,6759,127111,50,6759,127111,40,6759,127169,0,6759,135735,3,7515,137891,4,7885,139750,5,8260,139751,1,8260,139751,50,8260,139751,40,8260,139809,0,8260,200004,3,12161,201026,4,14112,201403,1,16062,201403,50,16064,201403,40,16064,201461,0,16064,248462,3,18617,249320,4,19890,249768,1,21165,249768,50,21166,249768,40,21166,249826,0,21167,293123,3,22669,293652,4,23418,294203,5,24168,294204,1,24168,294204,50,24170,294204,40,24170,294262,0,24170,302655,3,24927,303589,4,25302,303700,5,25671,303700,1,25671,303700,50,25671,303700,40,25671,303758,0,25671,335349,3,26873,335906,4,27472,336339,1,28072,336339,50,28073,336339,40,28073,336397,0,28073,361509,3,28824,361949,4,29199,362364,1,29574,362364,50,29575,362364,40,29575,362364,40,29575,362417,0,29575,362615,50,29575,362615,30,29575,362615,40,29575,362668,0,29575,362824,50,29576,362877,0,29582,363049,50,29583,363049,30,29583,363049,40,29583,363102,0,29583,363355,50,29583,363408,0,29584,363724,50,29585,363724,30,29585,363724,40,29585,363777,0,29589,363912,50,29589,363965,0,29589,364157,50,29591,364157,30,29591,364157,40,29592,364210,0,29596,364343,50,29597,364396,0,29597,364586,50,29601,364639,0,29601,364837,50,29605,364890,0,29610,365096,50,29617,365149,0,29617,365361,50,29627,365414,0,29631,365634,50,29648,365687,0,29648,365915,50,29680,365968,0,29680,366206,50,29747,366206,40,29747,366259,0,29747,366567,50,29748,366567,30,29748,366567,40,29748,366620,0,29748,366773,50,29749,366826,0,29755,367026,50,29758,367079,0,29758,367287,50,29763,367340,0,29763,367556,50,29770,367609,0,29775,367831,50,29785,367884,0,29785,368114,50,29803,368167,0,29807,368405,50,29839,368458,0,29839,368706,50,29907,368706,40,29907,368759,0,29908,368931,50,29908,368931,30,29908,368931,40,29908,368984,0,29908,369137,50,29909,369190,0,29914,369390,50,29917,369443,0,29917,369651,50,29922,369704,0,29922,369920,50,29929,369973,0,29934,370195,50,29944,370248,0,29944,370478,50,29962,370531,0,29966,370769,50,29999,370822,0,29999,371070,50,30066,371070,40,30066,371123,0,30066)
%
%
% START OF PROOF
% 371023 [?] ?
% 371072 [] equal(multiply(identity,X),X).
% 371073 [] equal(multiply(inverse(X),X),identity).
% 371074 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 371075 [] -equal(multiply(sk_c8,sk_c7),sk_c9).
% 371082 [?] ?
% 371090 [?] ?
% 371098 [?] ?
% 371148 [input:371082,cut:371075] equal(inverse(sk_c2),sk_c9).
% 371149 [para:371148.1.1,371073.1.1.1] equal(multiply(sk_c9,sk_c2),identity).
% 371183 [input:371090,cut:371075] equal(multiply(sk_c2,sk_c9),sk_c3).
% 371198 [input:371098,cut:371075] equal(multiply(sk_c9,sk_c3),sk_c8).
% 371216 [para:371149.1.1,371074.1.1.1,demod:371072] equal(X,multiply(sk_c9,multiply(sk_c2,X))).
% 371281 [para:371183.1.1,371216.1.2.2] equal(sk_c9,multiply(sk_c9,sk_c3)).
% 371288 [para:371281.1.2,371198.1.1] equal(sk_c9,sk_c8).
% 371290 [para:371288.1.1,371075.1.2,cut:371023] 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 8 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c9,sk_c8),sk_c7) | -equal(multiply(X,sk_c9),sk_c8) | -equal(inverse(X),sk_c9) | -equal(multiply(sk_c9,Y),sk_c8) | -equal(multiply(Z,sk_c9),Y) | -equal(inverse(Z),sk_c9) | -equal(multiply(sk_c8,sk_c9),sk_c7) | -equal(multiply(sk_c8,sk_c7),sk_c9) | -equal(inverse(sk_c9),sk_c7) | -equal(inverse(U),sk_c9) | -equal(multiply(U,sk_c7),sk_c9) | -equal(multiply(V,W),sk_c7) | -equal(inverse(V),W) | -equal(multiply(W,sk_c9),sk_c7).
% Split part used next: -equal(inverse(sk_c9),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 27
% clause depth limited to 3
% seconds given: 2
%
%
% 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 27
% clause depth limited to 4
% seconds given: 2
%
%
% 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 27
% clause depth limited to 5
% seconds given: 2
%
%
% 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 27
% clause depth limited to 6
% seconds given: 2
%
%
% 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 27
% clause depth limited to 7
% seconds given: 2
%
%
% 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 27
% clause depth limited to 8
% seconds given: 2
%
%
% 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 27
% clause depth limited to 9
% seconds given: 2
%
%
% 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(53,40,0,111,0,0,3323,50,39,3381,0,39,11844,50,159,11902,0,159,20546,50,297,20604,0,297,31034,50,483,31092,0,484,42933,50,723,42991,0,723,57134,50,1054,57134,40,1054,57192,0,1054,64622,3,1355,65677,4,1506,66533,1,1655,66533,50,1655,66533,40,1655,66591,0,1655,67902,3,1972,67920,4,2111,67937,5,2256,67937,1,2256,67937,50,2256,67937,40,2256,67995,0,2256,103367,3,3768,103892,4,4507,104386,1,5257,104386,50,5258,104386,40,5258,104444,0,5258,126208,3,6009,126749,4,6384,127111,1,6759,127111,50,6759,127111,40,6759,127169,0,6759,135735,3,7515,137891,4,7885,139750,5,8260,139751,1,8260,139751,50,8260,139751,40,8260,139809,0,8260,200004,3,12161,201026,4,14112,201403,1,16062,201403,50,16064,201403,40,16064,201461,0,16064,248462,3,18617,249320,4,19890,249768,1,21165,249768,50,21166,249768,40,21166,249826,0,21167,293123,3,22669,293652,4,23418,294203,5,24168,294204,1,24168,294204,50,24170,294204,40,24170,294262,0,24170,302655,3,24927,303589,4,25302,303700,5,25671,303700,1,25671,303700,50,25671,303700,40,25671,303758,0,25671,335349,3,26873,335906,4,27472,336339,1,28072,336339,50,28073,336339,40,28073,336397,0,28073,361509,3,28824,361949,4,29199,362364,1,29574,362364,50,29575,362364,40,29575,362364,40,29575,362417,0,29575,362615,50,29575,362615,30,29575,362615,40,29575,362668,0,29575,362824,50,29576,362877,0,29582,363049,50,29583,363049,30,29583,363049,40,29583,363102,0,29583,363355,50,29583,363408,0,29584,363724,50,29585,363724,30,29585,363724,40,29585,363777,0,29589,363912,50,29589,363965,0,29589,364157,50,29591,364157,30,29591,364157,40,29592,364210,0,29596,364343,50,29597,364396,0,29597,364586,50,29601,364639,0,29601,364837,50,29605,364890,0,29610,365096,50,29617,365149,0,29617,365361,50,29627,365414,0,29631,365634,50,29648,365687,0,29648,365915,50,29680,365968,0,29680,366206,50,29747,366206,40,29747,366259,0,29747,366567,50,29748,366567,30,29748,366567,40,29748,366620,0,29748,366773,50,29749,366826,0,29755,367026,50,29758,367079,0,29758,367287,50,29763,367340,0,29763,367556,50,29770,367609,0,29775,367831,50,29785,367884,0,29785,368114,50,29803,368167,0,29807,368405,50,29839,368458,0,29839,368706,50,29907,368706,40,29907,368759,0,29908,368931,50,29908,368931,30,29908,368931,40,29908,368984,0,29908,369137,50,29909,369190,0,29914,369390,50,29917,369443,0,29917,369651,50,29922,369704,0,29922,369920,50,29929,369973,0,29934,370195,50,29944,370248,0,29944,370478,50,29962,370531,0,29966,370769,50,29999,370822,0,29999,371070,50,30066,371070,40,30066,371123,0,30066,371289,50,30067,371289,30,30067,371289,40,30067,371342,0,30067,371495,50,30068,371548,0,30073,371748,50,30076,371801,0,30076,372009,50,30087,372062,0,30087,372278,50,30103,372331,0,30113,372553,50,30126,372606,0,30126,372836,50,30144,372889,0,30148,373127,50,30182,373127,40,30182,373180,0,30182)
%
%
% START OF PROOF
% 373129 [] equal(multiply(identity,X),X).
% 373130 [] equal(multiply(inverse(X),X),identity).
% 373131 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 373132 [] -equal(inverse(sk_c9),sk_c7).
% 373138 [?] ?
% 373146 [?] ?
% 373154 [?] ?
% 373162 [?] ?
% 373170 [?] ?
% 373178 [?] ?
% 373189 [input:373138,cut:373132] equal(inverse(sk_c2),sk_c9).
% 373190 [para:373189.1.1,373130.1.1.1] equal(multiply(sk_c9,sk_c2),identity).
% 373198 [input:373162,cut:373132] equal(inverse(sk_c1),sk_c9).
% 373199 [para:373198.1.1,373130.1.1.1] equal(multiply(sk_c9,sk_c1),identity).
% 373208 [input:373146,cut:373132] equal(multiply(sk_c2,sk_c9),sk_c3).
% 373214 [input:373154,cut:373132] equal(multiply(sk_c9,sk_c3),sk_c8).
% 373225 [input:373170,cut:373132] equal(multiply(sk_c1,sk_c9),sk_c8).
% 373231 [input:373178,cut:373132] equal(multiply(sk_c9,sk_c8),sk_c7).
% 373254 [para:373130.1.1,373131.1.1.1,demod:373129] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 373256 [para:373190.1.1,373131.1.1.1,demod:373129] equal(X,multiply(sk_c9,multiply(sk_c2,X))).
% 373258 [para:373199.1.1,373131.1.1.1,demod:373129] equal(X,multiply(sk_c9,multiply(sk_c1,X))).
% 373270 [para:373214.1.1,373131.1.1.1] equal(multiply(sk_c8,X),multiply(sk_c9,multiply(sk_c3,X))).
% 373309 [para:373208.1.1,373256.1.2.2] equal(sk_c9,multiply(sk_c9,sk_c3)).
% 373312 [para:373309.1.2,373214.1.1] equal(sk_c9,sk_c8).
% 373313 [para:373309.1.2,373131.1.1.1,demod:373270] equal(multiply(sk_c9,X),multiply(sk_c8,X)).
% 373316 [para:373312.1.1,373190.1.1.1] equal(multiply(sk_c8,sk_c2),identity).
% 373331 [para:373312.1.1,373225.1.1.2] equal(multiply(sk_c1,sk_c8),sk_c8).
% 373334 [para:373312.1.1,373231.1.1.1] equal(multiply(sk_c8,sk_c8),sk_c7).
% 373352 [para:373225.1.1,373258.1.2.2,demod:373334,373313] equal(sk_c9,sk_c7).
% 373353 [para:373331.1.1,373258.1.2.2,demod:373334,373313] equal(sk_c8,sk_c7).
% 373354 [para:373352.1.1,373132.1.1.1] -equal(inverse(sk_c7),sk_c7).
% 373374 [para:373352.1.1,373231.1.1.1] equal(multiply(sk_c7,sk_c8),sk_c7).
% 373472 [para:373374.1.1,373254.1.2.2,demod:373130] equal(sk_c8,identity).
% 373488 [para:373472.1.1,373316.1.1.1,demod:373129] equal(sk_c2,identity).
% 373492 [para:373472.1.1,373353.1.1] equal(identity,sk_c7).
% 373515 [para:373488.1.1,373189.1.1.1] equal(inverse(identity),sk_c9).
% 373521 [para:373492.1.2,373354.1.1.1,demod:373515,cut:373352] 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: 34114
% derived clauses: 5212899
% kept clauses: 273648
% kept size sum: 48390
% kept mid-nuclei: 41543
% kept new demods: 6767
% forw unit-subs: 2149799
% forw double-subs: 2498395
% forw overdouble-subs: 186266
% backward subs: 16665
% fast unit cutoff: 18243
% full unit cutoff: 0
% dbl unit cutoff: 23574
% real runtime : 304.10
% process. runtime: 301.83
% specific non-discr-tree subsumption statistics:
% tried: 56500210
% length fails: 4856213
% strength fails: 18893795
% predlist fails: 4879183
% aux str. fails: 5580416
% by-lit fails: 12345346
% full subs tried: 2179219
% full subs fail: 2080014
%
% ; 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/GRP282-1+eq_r.in")
%
%------------------------------------------------------------------------------