TSTP Solution File: GRP365-1 by Gandalf---c-2.6
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP365-1 : 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 : art10.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 298.1s
% Output : Assurance 298.1s
% 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/GRP365-1+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 21)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 3 21)
% (binary-posweight-lex-big-order 30 #f 3 21)
% (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_c6,sk_c8),sk_c7) | -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8) | -equal(multiply(Z,sk_c6),sk_c8) | -equal(inverse(Z),sk_c6) | -equal(multiply(sk_c8,sk_c7),sk_c6) | -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8) | -equal(multiply(V,sk_c8),sk_c6) | -equal(inverse(V),sk_c8).
% was split for some strategies as:
% -equal(multiply(V,sk_c8),sk_c6) | -equal(inverse(V),sk_c8).
% -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8).
% -equal(multiply(Z,sk_c6),sk_c8) | -equal(inverse(Z),sk_c6).
% -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8).
% -equal(multiply(sk_c6,sk_c8),sk_c7).
% -equal(multiply(sk_c8,sk_c7),sk_c6).
%
% 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(sk_c6,sk_c8),sk_c7) | -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8) | -equal(multiply(Z,sk_c6),sk_c8) | -equal(inverse(Z),sk_c6) | -equal(multiply(sk_c8,sk_c7),sk_c6) | -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8) | -equal(multiply(V,sk_c8),sk_c6) | -equal(inverse(V),sk_c8).
% Split part used next: -equal(multiply(V,sk_c8),sk_c6) | -equal(inverse(V),sk_c8).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,75,0,0,855,50,6,895,0,7,1875,50,19,1915,0,19,2997,50,35,3037,0,35,4173,50,48,4213,0,48,5404,50,65,5444,0,65,6715,50,90,6755,0,90,8106,50,130,8146,0,130,9603,50,204,9643,0,204,11206,50,346,11246,0,347,12941,50,572,12981,0,572,14808,50,974,14808,40,974,14848,0,974,24634,3,1275,25378,4,1425,26131,5,1575,26132,1,1575,26132,50,1575,26132,40,1575,26172,0,1575,26508,3,1885,26519,4,2048,26539,5,2176,26539,1,2176,26539,50,2176,26539,40,2176,26579,0,2176,51915,3,3682,52513,4,4427,53573,5,5177,53574,1,5177,53574,50,5178,53574,40,5178,53614,0,5178,72541,3,5929,72778,4,6304,73480,5,6679,73481,1,6679,73481,50,6679,73481,40,6679,73521,0,6679,84093,3,7440,85404,4,7805,86834,1,8180,86834,50,8180,86834,40,8180,86874,0,8180,146822,3,12081,148099,4,14031,148751,1,15981,148751,50,15983,148751,40,15983,148791,0,15983,197239,3,18535,198253,4,19809,199032,1,21084,199032,50,21086,199032,40,21086,199072,0,21086,231678,3,22588,232639,4,23337,233483,1,24087,233483,50,24088,233483,40,24088,233523,0,24088,242850,3,24839,244067,4,25215,244819,5,25589,244820,5,25589,244821,1,25589,244821,50,25589,244821,40,25589,244861,0,25589,270460,3,26791,271173,4,27390,271701,5,27990,271702,1,27990,271702,50,27991,271702,40,27991,271742,0,27991,292227,3,28742,292792,4,29117,293346,5,29492,293347,1,29492,293347,50,29492,293347,40,29492,293347,40,29492,293382,0,29492)
%
%
% START OF PROOF
% 293349 [] equal(multiply(identity,X),X).
% 293350 [] equal(multiply(inverse(X),X),identity).
% 293351 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 293352 [] -equal(multiply(X,sk_c8),sk_c6) | -equal(inverse(X),sk_c8).
% 293353 [] equal(inverse(sk_c3),sk_c6) | equal(inverse(sk_c5),sk_c8).
% 293354 [?] ?
% 293358 [] equal(multiply(sk_c3,sk_c6),sk_c8) | equal(inverse(sk_c5),sk_c8).
% 293359 [] equal(multiply(sk_c3,sk_c6),sk_c8) | equal(multiply(sk_c5,sk_c8),sk_c6).
% 293363 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c5),sk_c8).
% 293364 [?] ?
% 293368 [] equal(multiply(sk_c1,sk_c8),sk_c2) | equal(inverse(sk_c5),sk_c8).
% 293369 [] equal(multiply(sk_c1,sk_c8),sk_c2) | equal(multiply(sk_c5,sk_c8),sk_c6).
% 293373 [] equal(multiply(sk_c8,sk_c2),sk_c7) | equal(inverse(sk_c5),sk_c8).
% 293374 [] equal(multiply(sk_c8,sk_c2),sk_c7) | equal(multiply(sk_c5,sk_c8),sk_c6).
% 293378 [] equal(multiply(sk_c6,sk_c8),sk_c7) | equal(inverse(sk_c5),sk_c8).
% 293379 [] equal(multiply(sk_c6,sk_c8),sk_c7) | equal(multiply(sk_c5,sk_c8),sk_c6).
% 293385 [hyper:293352,293353,binarycut:293354] equal(inverse(sk_c3),sk_c6).
% 293386 [para:293385.1.1,293350.1.1.1] equal(multiply(sk_c6,sk_c3),identity).
% 293394 [hyper:293352,293363,binarycut:293364] equal(inverse(sk_c1),sk_c8).
% 293397 [para:293394.1.1,293350.1.1.1] equal(multiply(sk_c8,sk_c1),identity).
% 293407 [hyper:293352,293359,293358] equal(multiply(sk_c3,sk_c6),sk_c8).
% 293422 [hyper:293352,293369,293368] equal(multiply(sk_c1,sk_c8),sk_c2).
% 293428 [hyper:293352,293374,293373] equal(multiply(sk_c8,sk_c2),sk_c7).
% 293431 [hyper:293352,293379,293378] equal(multiply(sk_c6,sk_c8),sk_c7).
% 293432 [para:293350.1.1,293351.1.1.1,demod:293349] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 293433 [para:293386.1.1,293351.1.1.1,demod:293349] equal(X,multiply(sk_c6,multiply(sk_c3,X))).
% 293439 [para:293407.1.1,293433.1.2.2,demod:293431] equal(sk_c6,sk_c7).
% 293440 [para:293439.1.1,293386.1.1.1] equal(multiply(sk_c7,sk_c3),identity).
% 293442 [para:293439.1.1,293431.1.1.1] equal(multiply(sk_c7,sk_c8),sk_c7).
% 293448 [para:293422.1.1,293432.1.2.2,demod:293428,293394] equal(sk_c8,sk_c7).
% 293458 [para:293442.1.1,293432.1.2.2,demod:293350] equal(sk_c8,identity).
% 293460 [para:293458.1.1,293397.1.1.1,demod:293349] equal(sk_c1,identity).
% 293464 [para:293458.1.1,293448.1.1] equal(identity,sk_c7).
% 293467 [para:293460.1.1,293394.1.1.1] equal(inverse(identity),sk_c8).
% 293475 [para:293464.1.2,293440.1.1.1,demod:293349] equal(sk_c3,identity).
% 293484 [para:293475.1.1,293385.1.1.1,demod:293467] equal(sk_c8,sk_c6).
% 293498 [hyper:293352,293467,demod:293349,cut:293484] 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 21
% 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(sk_c6,sk_c8),sk_c7) | -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8) | -equal(multiply(Z,sk_c6),sk_c8) | -equal(inverse(Z),sk_c6) | -equal(multiply(sk_c8,sk_c7),sk_c6) | -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8) | -equal(multiply(V,sk_c8),sk_c6) | -equal(inverse(V),sk_c8).
% Split part used next: -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8).
% 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 21
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,75,0,0,855,50,6,895,0,7,1875,50,19,1915,0,19,2997,50,35,3037,0,35,4173,50,48,4213,0,48,5404,50,65,5444,0,65,6715,50,90,6755,0,90,8106,50,130,8146,0,130,9603,50,204,9643,0,204,11206,50,346,11246,0,347,12941,50,572,12981,0,572,14808,50,974,14808,40,974,14848,0,974,24634,3,1275,25378,4,1425,26131,5,1575,26132,1,1575,26132,50,1575,26132,40,1575,26172,0,1575,26508,3,1885,26519,4,2048,26539,5,2176,26539,1,2176,26539,50,2176,26539,40,2176,26579,0,2176,51915,3,3682,52513,4,4427,53573,5,5177,53574,1,5177,53574,50,5178,53574,40,5178,53614,0,5178,72541,3,5929,72778,4,6304,73480,5,6679,73481,1,6679,73481,50,6679,73481,40,6679,73521,0,6679,84093,3,7440,85404,4,7805,86834,1,8180,86834,50,8180,86834,40,8180,86874,0,8180,146822,3,12081,148099,4,14031,148751,1,15981,148751,50,15983,148751,40,15983,148791,0,15983,197239,3,18535,198253,4,19809,199032,1,21084,199032,50,21086,199032,40,21086,199072,0,21086,231678,3,22588,232639,4,23337,233483,1,24087,233483,50,24088,233483,40,24088,233523,0,24088,242850,3,24839,244067,4,25215,244819,5,25589,244820,5,25589,244821,1,25589,244821,50,25589,244821,40,25589,244861,0,25589,270460,3,26791,271173,4,27390,271701,5,27990,271702,1,27990,271702,50,27991,271702,40,27991,271742,0,27991,292227,3,28742,292792,4,29117,293346,5,29492,293347,1,29492,293347,50,29492,293347,40,29492,293347,40,29492,293382,0,29492,293497,50,29492,293497,30,29492,293497,40,29492,293532,0,29492)
%
%
% START OF PROOF
% 293499 [] equal(multiply(identity,X),X).
% 293500 [] equal(multiply(inverse(X),X),identity).
% 293501 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 293502 [] -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8).
% 293505 [] equal(inverse(sk_c3),sk_c6) | equal(inverse(sk_c4),sk_c8).
% 293506 [?] ?
% 293510 [] equal(multiply(sk_c3,sk_c6),sk_c8) | equal(inverse(sk_c4),sk_c8).
% 293511 [] equal(multiply(sk_c3,sk_c6),sk_c8) | equal(multiply(sk_c4,sk_c8),sk_c7).
% 293515 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c4),sk_c8).
% 293516 [?] ?
% 293520 [] equal(multiply(sk_c1,sk_c8),sk_c2) | equal(inverse(sk_c4),sk_c8).
% 293521 [] equal(multiply(sk_c1,sk_c8),sk_c2) | equal(multiply(sk_c4,sk_c8),sk_c7).
% 293525 [] equal(multiply(sk_c8,sk_c2),sk_c7) | equal(inverse(sk_c4),sk_c8).
% 293526 [] equal(multiply(sk_c8,sk_c2),sk_c7) | equal(multiply(sk_c4,sk_c8),sk_c7).
% 293530 [] equal(multiply(sk_c6,sk_c8),sk_c7) | equal(inverse(sk_c4),sk_c8).
% 293531 [] equal(multiply(sk_c6,sk_c8),sk_c7) | equal(multiply(sk_c4,sk_c8),sk_c7).
% 293537 [hyper:293502,293505,binarycut:293506] equal(inverse(sk_c3),sk_c6).
% 293539 [para:293537.1.1,293500.1.1.1] equal(multiply(sk_c6,sk_c3),identity).
% 293551 [hyper:293502,293515,binarycut:293516] equal(inverse(sk_c1),sk_c8).
% 293554 [para:293551.1.1,293500.1.1.1] equal(multiply(sk_c8,sk_c1),identity).
% 293579 [hyper:293502,293511,293510] equal(multiply(sk_c3,sk_c6),sk_c8).
% 293588 [hyper:293502,293521,293520] equal(multiply(sk_c1,sk_c8),sk_c2).
% 293592 [hyper:293502,293526,293525] equal(multiply(sk_c8,sk_c2),sk_c7).
% 293599 [hyper:293502,293531,293530] equal(multiply(sk_c6,sk_c8),sk_c7).
% 293601 [para:293500.1.1,293501.1.1.1,demod:293499] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 293602 [para:293539.1.1,293501.1.1.1,demod:293499] equal(X,multiply(sk_c6,multiply(sk_c3,X))).
% 293610 [para:293579.1.1,293602.1.2.2,demod:293599] equal(sk_c6,sk_c7).
% 293613 [para:293610.1.1,293599.1.1.1] equal(multiply(sk_c7,sk_c8),sk_c7).
% 293619 [para:293588.1.1,293601.1.2.2,demod:293592,293551] equal(sk_c8,sk_c7).
% 293631 [para:293613.1.1,293601.1.2.2,demod:293500] equal(sk_c8,identity).
% 293633 [para:293631.1.1,293554.1.1.1,demod:293499] equal(sk_c1,identity).
% 293640 [para:293633.1.1,293551.1.1.1] equal(inverse(identity),sk_c8).
% 293671 [hyper:293502,293640,demod:293499,cut:293619] 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 21
% 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(sk_c6,sk_c8),sk_c7) | -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8) | -equal(multiply(Z,sk_c6),sk_c8) | -equal(inverse(Z),sk_c6) | -equal(multiply(sk_c8,sk_c7),sk_c6) | -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8) | -equal(multiply(V,sk_c8),sk_c6) | -equal(inverse(V),sk_c8).
% Split part used next: -equal(multiply(Z,sk_c6),sk_c8) | -equal(inverse(Z),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 21
% 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 21
% clause depth limited to 4
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,75,0,0,855,50,6,895,0,7,1875,50,19,1915,0,19,2997,50,35,3037,0,35,4173,50,48,4213,0,48,5404,50,65,5444,0,65,6715,50,90,6755,0,90,8106,50,130,8146,0,130,9603,50,204,9643,0,204,11206,50,346,11246,0,347,12941,50,572,12981,0,572,14808,50,974,14808,40,974,14848,0,974,24634,3,1275,25378,4,1425,26131,5,1575,26132,1,1575,26132,50,1575,26132,40,1575,26172,0,1575,26508,3,1885,26519,4,2048,26539,5,2176,26539,1,2176,26539,50,2176,26539,40,2176,26579,0,2176,51915,3,3682,52513,4,4427,53573,5,5177,53574,1,5177,53574,50,5178,53574,40,5178,53614,0,5178,72541,3,5929,72778,4,6304,73480,5,6679,73481,1,6679,73481,50,6679,73481,40,6679,73521,0,6679,84093,3,7440,85404,4,7805,86834,1,8180,86834,50,8180,86834,40,8180,86874,0,8180,146822,3,12081,148099,4,14031,148751,1,15981,148751,50,15983,148751,40,15983,148791,0,15983,197239,3,18535,198253,4,19809,199032,1,21084,199032,50,21086,199032,40,21086,199072,0,21086,231678,3,22588,232639,4,23337,233483,1,24087,233483,50,24088,233483,40,24088,233523,0,24088,242850,3,24839,244067,4,25215,244819,5,25589,244820,5,25589,244821,1,25589,244821,50,25589,244821,40,25589,244861,0,25589,270460,3,26791,271173,4,27390,271701,5,27990,271702,1,27990,271702,50,27991,271702,40,27991,271742,0,27991,292227,3,28742,292792,4,29117,293346,5,29492,293347,1,29492,293347,50,29492,293347,40,29492,293347,40,29492,293382,0,29492,293497,50,29492,293497,30,29492,293497,40,29492,293532,0,29492,293670,50,29492,293670,30,29492,293670,40,29492,293705,0,29497,293786,50,29498,293821,0,29498)
%
%
% START OF PROOF
% 293788 [] equal(multiply(identity,X),X).
% 293789 [] equal(multiply(inverse(X),X),identity).
% 293790 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 293791 [] -equal(multiply(X,sk_c6),sk_c8) | -equal(inverse(X),sk_c6).
% 293792 [] equal(inverse(sk_c3),sk_c6) | equal(inverse(sk_c5),sk_c8).
% 293793 [] equal(multiply(sk_c5,sk_c8),sk_c6) | equal(inverse(sk_c3),sk_c6).
% 293794 [] equal(inverse(sk_c3),sk_c6) | equal(inverse(sk_c4),sk_c8).
% 293795 [] equal(multiply(sk_c4,sk_c8),sk_c7) | equal(inverse(sk_c3),sk_c6).
% 293796 [] equal(multiply(sk_c8,sk_c7),sk_c6) | equal(inverse(sk_c3),sk_c6).
% 293797 [?] ?
% 293798 [?] ?
% 293799 [?] ?
% 293800 [?] ?
% 293801 [?] ?
% 293824 [hyper:293791,293792,binarycut:293797] equal(inverse(sk_c5),sk_c8).
% 293825 [para:293824.1.1,293789.1.1.1] equal(multiply(sk_c8,sk_c5),identity).
% 293829 [hyper:293791,293794,binarycut:293799] equal(inverse(sk_c4),sk_c8).
% 293830 [para:293829.1.1,293789.1.1.1] equal(multiply(sk_c8,sk_c4),identity).
% 293833 [hyper:293791,293793,binarycut:293798] equal(multiply(sk_c5,sk_c8),sk_c6).
% 293836 [hyper:293791,293795,binarycut:293800] equal(multiply(sk_c4,sk_c8),sk_c7).
% 293839 [hyper:293791,293796,binarycut:293801] equal(multiply(sk_c8,sk_c7),sk_c6).
% 293840 [para:293789.1.1,293790.1.1.1,demod:293788] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 293841 [para:293825.1.1,293790.1.1.1,demod:293788] equal(X,multiply(sk_c8,multiply(sk_c5,X))).
% 293842 [para:293830.1.1,293790.1.1.1,demod:293788] equal(X,multiply(sk_c8,multiply(sk_c4,X))).
% 293843 [para:293833.1.1,293790.1.1.1] equal(multiply(sk_c6,X),multiply(sk_c5,multiply(sk_c8,X))).
% 293844 [para:293836.1.1,293790.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c4,multiply(sk_c8,X))).
% 293846 [para:293833.1.1,293841.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c6)).
% 293848 [para:293836.1.1,293842.1.2.2,demod:293839] equal(sk_c8,sk_c6).
% 293852 [para:293789.1.1,293840.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 293853 [para:293825.1.1,293840.1.2.2] equal(sk_c5,multiply(inverse(sk_c8),identity)).
% 293854 [para:293830.1.1,293840.1.2.2,demod:293853] equal(sk_c4,sk_c5).
% 293855 [para:293839.1.1,293840.1.2.2] equal(sk_c7,multiply(inverse(sk_c8),sk_c6)).
% 293856 [para:293790.1.1,293840.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 293857 [para:293841.1.2,293840.1.2.2] equal(multiply(sk_c5,X),multiply(inverse(sk_c8),X)).
% 293858 [para:293842.1.2,293840.1.2.2,demod:293857] equal(multiply(sk_c4,X),multiply(sk_c5,X)).
% 293859 [para:293840.1.2,293840.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 293860 [para:293854.1.2,293833.1.1.1,demod:293836] equal(sk_c7,sk_c6).
% 293861 [para:293860.1.2,293848.1.2] equal(sk_c8,sk_c7).
% 293863 [para:293861.1.1,293825.1.1.1] equal(multiply(sk_c7,sk_c5),identity).
% 293868 [para:293861.1.1,293841.1.2.1,demod:293858] equal(X,multiply(sk_c7,multiply(sk_c4,X))).
% 293875 [para:293846.1.2,293843.1.2.2,demod:293833] equal(multiply(sk_c6,sk_c6),sk_c6).
% 293877 [para:293854.1.2,293843.1.2.1,demod:293844] equal(multiply(sk_c6,X),multiply(sk_c7,X)).
% 293879 [para:293863.1.1,293840.1.2.2] equal(sk_c5,multiply(inverse(sk_c7),identity)).
% 293886 [para:293841.1.2,293844.1.2.2,demod:293868,293858] equal(X,multiply(sk_c4,X)).
% 293887 [para:293842.1.2,293844.1.2.2,demod:293886] equal(multiply(sk_c7,X),X).
% 293895 [para:293875.1.1,293840.1.2.2,demod:293789] equal(sk_c6,identity).
% 293901 [para:293895.1.1,293855.1.2.2,demod:293853] equal(sk_c7,sk_c5).
% 293902 [para:293901.1.2,293824.1.1.1] equal(inverse(sk_c7),sk_c8).
% 293920 [para:293859.1.2,293789.1.1] equal(multiply(X,inverse(X)),identity).
% 293922 [para:293859.1.2,293852.1.2] equal(X,multiply(X,identity)).
% 293923 [para:293922.1.2,293852.1.2] equal(X,inverse(inverse(X))).
% 293924 [para:293922.1.2,293853.1.2] equal(sk_c5,inverse(sk_c8)).
% 293926 [para:293922.1.2,293879.1.2,demod:293902] equal(sk_c5,sk_c8).
% 293928 [para:293926.1.2,293833.1.1.2,demod:293886,293858] equal(sk_c5,sk_c6).
% 293931 [para:293920.1.1,293856.1.2.2.2,demod:293922] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 293940 [para:293877.1.1,293931.1.2.1.1,demod:293887] equal(inverse(X),multiply(inverse(X),sk_c6)).
% 293952 [para:293940.1.2,293859.1.2,demod:293923] equal(multiply(X,sk_c6),X).
% 293953 [hyper:293791,293952,demod:293924,cut:293928] 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 21
% 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(sk_c6,sk_c8),sk_c7) | -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8) | -equal(multiply(Z,sk_c6),sk_c8) | -equal(inverse(Z),sk_c6) | -equal(multiply(sk_c8,sk_c7),sk_c6) | -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8) | -equal(multiply(V,sk_c8),sk_c6) | -equal(inverse(V),sk_c8).
% Split part used next: -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8).
% 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 21
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,75,0,0,855,50,6,895,0,7,1875,50,19,1915,0,19,2997,50,35,3037,0,35,4173,50,48,4213,0,48,5404,50,65,5444,0,65,6715,50,90,6755,0,90,8106,50,130,8146,0,130,9603,50,204,9643,0,204,11206,50,346,11246,0,347,12941,50,572,12981,0,572,14808,50,974,14808,40,974,14848,0,974,24634,3,1275,25378,4,1425,26131,5,1575,26132,1,1575,26132,50,1575,26132,40,1575,26172,0,1575,26508,3,1885,26519,4,2048,26539,5,2176,26539,1,2176,26539,50,2176,26539,40,2176,26579,0,2176,51915,3,3682,52513,4,4427,53573,5,5177,53574,1,5177,53574,50,5178,53574,40,5178,53614,0,5178,72541,3,5929,72778,4,6304,73480,5,6679,73481,1,6679,73481,50,6679,73481,40,6679,73521,0,6679,84093,3,7440,85404,4,7805,86834,1,8180,86834,50,8180,86834,40,8180,86874,0,8180,146822,3,12081,148099,4,14031,148751,1,15981,148751,50,15983,148751,40,15983,148791,0,15983,197239,3,18535,198253,4,19809,199032,1,21084,199032,50,21086,199032,40,21086,199072,0,21086,231678,3,22588,232639,4,23337,233483,1,24087,233483,50,24088,233483,40,24088,233523,0,24088,242850,3,24839,244067,4,25215,244819,5,25589,244820,5,25589,244821,1,25589,244821,50,25589,244821,40,25589,244861,0,25589,270460,3,26791,271173,4,27390,271701,5,27990,271702,1,27990,271702,50,27991,271702,40,27991,271742,0,27991,292227,3,28742,292792,4,29117,293346,5,29492,293347,1,29492,293347,50,29492,293347,40,29492,293347,40,29492,293382,0,29492,293497,50,29492,293497,30,29492,293497,40,29492,293532,0,29492,293670,50,29492,293670,30,29492,293670,40,29492,293705,0,29497,293786,50,29498,293821,0,29498,293952,50,29499,293952,30,29499,293952,40,29499,293987,0,29499)
%
%
% START OF PROOF
% 293953 [] equal(X,X).
% 293954 [] equal(multiply(identity,X),X).
% 293955 [] equal(multiply(inverse(X),X),identity).
% 293956 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 293957 [] -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8).
% 293968 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c5),sk_c8).
% 293969 [] equal(multiply(sk_c5,sk_c8),sk_c6) | equal(inverse(sk_c1),sk_c8).
% 293970 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c4),sk_c8).
% 293971 [] equal(multiply(sk_c4,sk_c8),sk_c7) | equal(inverse(sk_c1),sk_c8).
% 293972 [] equal(multiply(sk_c8,sk_c7),sk_c6) | equal(inverse(sk_c1),sk_c8).
% 293973 [] equal(multiply(sk_c1,sk_c8),sk_c2) | equal(inverse(sk_c5),sk_c8).
% 293974 [] equal(multiply(sk_c1,sk_c8),sk_c2) | equal(multiply(sk_c5,sk_c8),sk_c6).
% 293975 [] equal(multiply(sk_c1,sk_c8),sk_c2) | equal(inverse(sk_c4),sk_c8).
% 293976 [] equal(multiply(sk_c1,sk_c8),sk_c2) | equal(multiply(sk_c4,sk_c8),sk_c7).
% 293977 [] equal(multiply(sk_c1,sk_c8),sk_c2) | equal(multiply(sk_c8,sk_c7),sk_c6).
% 293978 [?] ?
% 293979 [?] ?
% 293980 [?] ?
% 293981 [?] ?
% 293982 [?] ?
% 294058 [hyper:293957,293973,binarycut:293978,binarycut:293968] equal(inverse(sk_c5),sk_c8).
% 294075 [para:294058.1.1,293955.1.1.1] equal(multiply(sk_c8,sk_c5),identity).
% 294083 [hyper:293957,293975,binarycut:293980,binarycut:293970] equal(inverse(sk_c4),sk_c8).
% 294096 [para:294083.1.1,293955.1.1.1] equal(multiply(sk_c8,sk_c4),identity).
% 294108 [hyper:293957,293974,293969,binarycut:293979] equal(multiply(sk_c5,sk_c8),sk_c6).
% 294116 [hyper:293957,293976,293971,binarycut:293981] equal(multiply(sk_c4,sk_c8),sk_c7).
% 294124 [hyper:293957,293977,293972,binarycut:293982] equal(multiply(sk_c8,sk_c7),sk_c6).
% 294125 [para:293955.1.1,293956.1.1.1,demod:293954] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 294126 [para:294075.1.1,293956.1.1.1,demod:293954] equal(X,multiply(sk_c8,multiply(sk_c5,X))).
% 294127 [para:294096.1.1,293956.1.1.1,demod:293954] equal(X,multiply(sk_c8,multiply(sk_c4,X))).
% 294128 [para:294108.1.1,293956.1.1.1] equal(multiply(sk_c6,X),multiply(sk_c5,multiply(sk_c8,X))).
% 294129 [para:294116.1.1,293956.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c4,multiply(sk_c8,X))).
% 294133 [para:294108.1.1,294126.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c6)).
% 294137 [para:294116.1.1,294127.1.2.2,demod:294124] equal(sk_c8,sk_c6).
% 294143 [para:294075.1.1,294125.1.2.2] equal(sk_c5,multiply(inverse(sk_c8),identity)).
% 294144 [para:294096.1.1,294125.1.2.2,demod:294143] equal(sk_c4,sk_c5).
% 294146 [para:294126.1.2,294125.1.2.2] equal(multiply(sk_c5,X),multiply(inverse(sk_c8),X)).
% 294147 [para:294127.1.2,294125.1.2.2,demod:294146] equal(multiply(sk_c4,X),multiply(sk_c5,X)).
% 294148 [para:294144.1.2,294108.1.1.1,demod:294116] equal(sk_c7,sk_c6).
% 294149 [para:294148.1.2,294137.1.2] equal(sk_c8,sk_c7).
% 294155 [para:294149.1.1,294124.1.1.1] equal(multiply(sk_c7,sk_c7),sk_c6).
% 294156 [para:294149.1.1,294126.1.2.1,demod:294147] equal(X,multiply(sk_c7,multiply(sk_c4,X))).
% 294157 [para:294149.1.1,294133.1.2.1] equal(sk_c8,multiply(sk_c7,sk_c6)).
% 294167 [para:294144.1.2,294128.1.2.1,demod:294129] equal(multiply(sk_c6,X),multiply(sk_c7,X)).
% 294170 [para:294155.1.1,293956.1.1.1,demod:294167] equal(multiply(sk_c7,X),multiply(sk_c7,multiply(sk_c7,X))).
% 294172 [para:294157.1.2,293956.1.1.1,demod:294170,294167] equal(multiply(sk_c8,X),multiply(sk_c7,X)).
% 294178 [para:294126.1.2,294129.1.2.2,demod:294156,294147] equal(X,multiply(sk_c4,X)).
% 294179 [para:294127.1.2,294129.1.2.2,demod:294178] equal(multiply(sk_c7,X),X).
% 294181 [hyper:293957,294178,294116,demod:294179,294172,294178,demod:294083,cut:293953] 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 21
% 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(sk_c6,sk_c8),sk_c7) | -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8) | -equal(multiply(Z,sk_c6),sk_c8) | -equal(inverse(Z),sk_c6) | -equal(multiply(sk_c8,sk_c7),sk_c6) | -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8) | -equal(multiply(V,sk_c8),sk_c6) | -equal(inverse(V),sk_c8).
% Split part used next: -equal(multiply(sk_c6,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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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(35,40,0,75,0,0,855,50,6,895,0,7,1875,50,19,1915,0,19,2997,50,35,3037,0,35,4173,50,48,4213,0,48,5404,50,65,5444,0,65,6715,50,90,6755,0,90,8106,50,130,8146,0,130,9603,50,204,9643,0,204,11206,50,346,11246,0,347,12941,50,572,12981,0,572,14808,50,974,14808,40,974,14848,0,974,24634,3,1275,25378,4,1425,26131,5,1575,26132,1,1575,26132,50,1575,26132,40,1575,26172,0,1575,26508,3,1885,26519,4,2048,26539,5,2176,26539,1,2176,26539,50,2176,26539,40,2176,26579,0,2176,51915,3,3682,52513,4,4427,53573,5,5177,53574,1,5177,53574,50,5178,53574,40,5178,53614,0,5178,72541,3,5929,72778,4,6304,73480,5,6679,73481,1,6679,73481,50,6679,73481,40,6679,73521,0,6679,84093,3,7440,85404,4,7805,86834,1,8180,86834,50,8180,86834,40,8180,86874,0,8180,146822,3,12081,148099,4,14031,148751,1,15981,148751,50,15983,148751,40,15983,148791,0,15983,197239,3,18535,198253,4,19809,199032,1,21084,199032,50,21086,199032,40,21086,199072,0,21086,231678,3,22588,232639,4,23337,233483,1,24087,233483,50,24088,233483,40,24088,233523,0,24088,242850,3,24839,244067,4,25215,244819,5,25589,244820,5,25589,244821,1,25589,244821,50,25589,244821,40,25589,244861,0,25589,270460,3,26791,271173,4,27390,271701,5,27990,271702,1,27990,271702,50,27991,271702,40,27991,271742,0,27991,292227,3,28742,292792,4,29117,293346,5,29492,293347,1,29492,293347,50,29492,293347,40,29492,293347,40,29492,293382,0,29492,293497,50,29492,293497,30,29492,293497,40,29492,293532,0,29492,293670,50,29492,293670,30,29492,293670,40,29492,293705,0,29497,293786,50,29498,293821,0,29498,293952,50,29499,293952,30,29499,293952,40,29499,293987,0,29499,294180,50,29501,294180,30,29501,294180,40,29501,294215,0,29505,294306,50,29505,294341,0,29505,294480,50,29508,294515,0,29512,294662,50,29515,294697,0,29515,294852,50,29520,294887,0,29520,295048,50,29528,295083,0,29533,295252,50,29547,295287,0,29547,295464,50,29575,295499,0,29580,295686,50,29635,295721,0,29635,295918,50,29749,295918,40,29749,295953,0,29749)
%
%
% START OF PROOF
% 295791 [?] ?
% 295920 [] equal(multiply(identity,X),X).
% 295921 [] equal(multiply(inverse(X),X),identity).
% 295922 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 295923 [] -equal(multiply(sk_c6,sk_c8),sk_c7).
% 295949 [?] ?
% 295950 [?] ?
% 295951 [?] ?
% 295952 [?] ?
% 295953 [?] ?
% 295991 [input:295949,cut:295923] equal(inverse(sk_c5),sk_c8).
% 295992 [para:295991.1.1,295921.1.1.1] equal(multiply(sk_c8,sk_c5),identity).
% 295994 [input:295951,cut:295923] equal(inverse(sk_c4),sk_c8).
% 295995 [para:295994.1.1,295921.1.1.1] equal(multiply(sk_c8,sk_c4),identity).
% 296007 [input:295950,cut:295923] equal(multiply(sk_c5,sk_c8),sk_c6).
% 296008 [input:295952,cut:295923] equal(multiply(sk_c4,sk_c8),sk_c7).
% 296009 [input:295953,cut:295923] equal(multiply(sk_c8,sk_c7),sk_c6).
% 296028 [para:295992.1.1,295922.1.1.1,demod:295920] equal(X,multiply(sk_c8,multiply(sk_c5,X))).
% 296031 [para:295995.1.1,295922.1.1.1,demod:295920] equal(X,multiply(sk_c8,multiply(sk_c4,X))).
% 296061 [para:296007.1.1,296028.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c6)).
% 296068 [para:296008.1.1,296031.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c7)).
% 296074 [para:296068.1.2,296009.1.1] equal(sk_c8,sk_c6).
% 296076 [para:296074.1.2,295923.1.1.1] -equal(multiply(sk_c8,sk_c8),sk_c7).
% 296085 [para:296074.1.2,296061.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c8)).
% 296087 [para:296085.1.2,296076.1.1,cut:295791] 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_c6,sk_c8),sk_c7) | -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8) | -equal(multiply(Z,sk_c6),sk_c8) | -equal(inverse(Z),sk_c6) | -equal(multiply(sk_c8,sk_c7),sk_c6) | -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8) | -equal(multiply(V,sk_c8),sk_c6) | -equal(inverse(V),sk_c8).
% Split part used next: -equal(multiply(sk_c8,sk_c7),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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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(35,40,0,75,0,0,855,50,6,895,0,7,1875,50,19,1915,0,19,2997,50,35,3037,0,35,4173,50,48,4213,0,48,5404,50,65,5444,0,65,6715,50,90,6755,0,90,8106,50,130,8146,0,130,9603,50,204,9643,0,204,11206,50,346,11246,0,347,12941,50,572,12981,0,572,14808,50,974,14808,40,974,14848,0,974,24634,3,1275,25378,4,1425,26131,5,1575,26132,1,1575,26132,50,1575,26132,40,1575,26172,0,1575,26508,3,1885,26519,4,2048,26539,5,2176,26539,1,2176,26539,50,2176,26539,40,2176,26579,0,2176,51915,3,3682,52513,4,4427,53573,5,5177,53574,1,5177,53574,50,5178,53574,40,5178,53614,0,5178,72541,3,5929,72778,4,6304,73480,5,6679,73481,1,6679,73481,50,6679,73481,40,6679,73521,0,6679,84093,3,7440,85404,4,7805,86834,1,8180,86834,50,8180,86834,40,8180,86874,0,8180,146822,3,12081,148099,4,14031,148751,1,15981,148751,50,15983,148751,40,15983,148791,0,15983,197239,3,18535,198253,4,19809,199032,1,21084,199032,50,21086,199032,40,21086,199072,0,21086,231678,3,22588,232639,4,23337,233483,1,24087,233483,50,24088,233483,40,24088,233523,0,24088,242850,3,24839,244067,4,25215,244819,5,25589,244820,5,25589,244821,1,25589,244821,50,25589,244821,40,25589,244861,0,25589,270460,3,26791,271173,4,27390,271701,5,27990,271702,1,27990,271702,50,27991,271702,40,27991,271742,0,27991,292227,3,28742,292792,4,29117,293346,5,29492,293347,1,29492,293347,50,29492,293347,40,29492,293347,40,29492,293382,0,29492,293497,50,29492,293497,30,29492,293497,40,29492,293532,0,29492,293670,50,29492,293670,30,29492,293670,40,29492,293705,0,29497,293786,50,29498,293821,0,29498,293952,50,29499,293952,30,29499,293952,40,29499,293987,0,29499,294180,50,29501,294180,30,29501,294180,40,29501,294215,0,29505,294306,50,29505,294341,0,29505,294480,50,29508,294515,0,29512,294662,50,29515,294697,0,29515,294852,50,29520,294887,0,29520,295048,50,29528,295083,0,29533,295252,50,29547,295287,0,29547,295464,50,29575,295499,0,29580,295686,50,29635,295721,0,29635,295918,50,29749,295918,40,29749,295953,0,29749,296086,50,29749,296086,30,29749,296086,40,29749,296121,0,29749,296239,50,29750,296274,0,29754,296442,50,29757,296477,0,29757,296653,50,29762,296688,0,29762,296872,50,29768,296907,0,29772,297097,50,29782,297132,0,29782,297330,50,29798,297365,0,29803,297571,50,29833,297606,0,29833,297822,50,29896,297857,0,29896,298083,50,30013,298083,40,30013,298118,0,30014)
%
%
% START OF PROOF
% 298084 [] equal(X,X).
% 298085 [] equal(multiply(identity,X),X).
% 298086 [] equal(multiply(inverse(X),X),identity).
% 298087 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 298088 [] -equal(multiply(sk_c8,sk_c7),sk_c6).
% 298093 [?] ?
% 298098 [?] ?
% 298103 [?] ?
% 298108 [?] ?
% 298113 [?] ?
% 298118 [?] ?
% 298135 [input:298093,cut:298088] equal(inverse(sk_c3),sk_c6).
% 298136 [para:298135.1.1,298086.1.1.1] equal(multiply(sk_c6,sk_c3),identity).
% 298145 [input:298103,cut:298088] equal(inverse(sk_c1),sk_c8).
% 298146 [para:298145.1.1,298086.1.1.1] equal(multiply(sk_c8,sk_c1),identity).
% 298162 [input:298098,cut:298088] equal(multiply(sk_c3,sk_c6),sk_c8).
% 298168 [input:298108,cut:298088] equal(multiply(sk_c1,sk_c8),sk_c2).
% 298171 [input:298113,cut:298088] equal(multiply(sk_c8,sk_c2),sk_c7).
% 298174 [input:298118,cut:298088] equal(multiply(sk_c6,sk_c8),sk_c7).
% 298180 [para:298136.1.1,298087.1.1.1,demod:298085] equal(X,multiply(sk_c6,multiply(sk_c3,X))).
% 298186 [para:298146.1.1,298087.1.1.1,demod:298085] equal(X,multiply(sk_c8,multiply(sk_c1,X))).
% 298214 [para:298174.1.1,298087.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c6,multiply(sk_c8,X))).
% 298220 [para:298162.1.1,298180.1.2.2] equal(sk_c6,multiply(sk_c6,sk_c8)).
% 298225 [para:298220.1.2,298174.1.1] equal(sk_c6,sk_c7).
% 298226 [para:298220.1.2,298087.1.1.1,demod:298214] equal(multiply(sk_c6,X),multiply(sk_c7,X)).
% 298227 [para:298225.1.1,298088.1.2] -equal(multiply(sk_c8,sk_c7),sk_c7).
% 298250 [para:298168.1.1,298186.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c2)).
% 298255 [para:298250.1.2,298171.1.1] equal(sk_c8,sk_c7).
% 298285 [para:298255.1.1,298174.1.1.2,demod:298226] equal(multiply(sk_c7,sk_c7),sk_c7).
% 298287 [para:298255.1.1,298227.1.1.1,demod:298285,cut:298084] 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: 34175
% derived clauses: 6962768
% kept clauses: 248158
% kept size sum: 290035
% kept mid-nuclei: 11249
% kept new demods: 4123
% forw unit-subs: 3329834
% forw double-subs: 3127781
% forw overdouble-subs: 206733
% backward subs: 11020
% fast unit cutoff: 21736
% full unit cutoff: 0
% dbl unit cutoff: 6024
% real runtime : 302.34
% process. runtime: 300.14
% specific non-discr-tree subsumption statistics:
% tried: 42877000
% length fails: 5109526
% strength fails: 13900630
% predlist fails: 4004007
% aux str. fails: 5832790
% by-lit fails: 7517893
% full subs tried: 1833395
% full subs fail: 1729950
%
% ; 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/GRP365-1+eq_r.in")
%
%------------------------------------------------------------------------------