TSTP Solution File: GRP271-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP271-1 : 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 : art05.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 299.1s
% Output : Assurance 299.1s
% 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/GRP271-1+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 29)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 3 29)
% (binary-posweight-lex-big-order 30 #f 3 29)
% (binary 30 #t)
% (binary-posweight-kb-big-order 156 #f)
% (binary-posweight-lex-big-order 102 #f)
% (binary-posweight-firstpref-order 60 #f)
% (binary-order 30 #f)
% (binary-posweight-kb-small-order 48 #f)
% (binary-posweight-lex-small-order 30 #f)
%
%
% SOS clause
% -equal(multiply(X,sk_c11),sk_c10) | -equal(inverse(X),sk_c11) | -equal(multiply(sk_c11,sk_c9),sk_c10) | -equal(multiply(Y,sk_c10),sk_c9) | -equal(inverse(Y),sk_c10) | -equal(multiply(Z,sk_c11),sk_c10) | -equal(inverse(Z),sk_c11) | -equal(multiply(U,sk_c10),sk_c9) | -equal(inverse(U),sk_c10) | -equal(multiply(V,W),sk_c11) | -equal(inverse(V),W) | -equal(multiply(W,sk_c10),sk_c11) | -equal(inverse(X1),X2) | -equal(inverse(X2),W) | -equal(multiply(X1,W),X2).
% was split for some strategies as:
% -equal(multiply(V,W),sk_c11) | -equal(inverse(V),W) | -equal(multiply(W,sk_c10),sk_c11) | -equal(inverse(X2),W) | -equal(inverse(X1),X2) | -equal(multiply(X1,W),X2).
% -equal(multiply(U,sk_c10),sk_c9) | -equal(inverse(U),sk_c10).
% -equal(multiply(Z,sk_c11),sk_c10) | -equal(inverse(Z),sk_c11).
% -equal(multiply(Y,sk_c10),sk_c9) | -equal(inverse(Y),sk_c10).
% -equal(multiply(X,sk_c11),sk_c10) | -equal(inverse(X),sk_c11).
% -equal(multiply(sk_c11,sk_c9),sk_c10).
%
% Starting a split proof attempt with 6 components.
%
% Split component 1 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(X,sk_c11),sk_c10) | -equal(inverse(X),sk_c11) | -equal(multiply(sk_c11,sk_c9),sk_c10) | -equal(multiply(Y,sk_c10),sk_c9) | -equal(inverse(Y),sk_c10) | -equal(multiply(Z,sk_c11),sk_c10) | -equal(inverse(Z),sk_c11) | -equal(multiply(U,sk_c10),sk_c9) | -equal(inverse(U),sk_c10) | -equal(multiply(V,W),sk_c11) | -equal(inverse(V),W) | -equal(multiply(W,sk_c10),sk_c11) | -equal(inverse(X1),X2) | -equal(inverse(X2),W) | -equal(multiply(X1,W),X2).
% Split part used next: -equal(multiply(V,W),sk_c11) | -equal(inverse(V),W) | -equal(multiply(W,sk_c10),sk_c11) | -equal(inverse(X2),W) | -equal(inverse(X1),X2) | -equal(multiply(X1,W),X2).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(55,40,1,119,0,2,106902,5,1503,106902,1,1503,106902,50,1503,106902,40,1503,106966,0,1503,119568,3,1804,120217,4,1954,120832,5,2104,120833,1,2104,120833,50,2104,120833,40,2104,120897,0,2104,121982,3,2418,122017,4,2572,122194,5,2705,122194,1,2705,122194,50,2705,122194,40,2705,122258,0,2705,151917,3,4206,152611,4,4956,153454,1,5706,153454,50,5707,153454,40,5707,153518,0,5707,172680,3,6461,173386,4,6833,174017,1,7208,174017,50,7208,174017,40,7208,174081,0,7208,192058,3,7962,192912,4,8334,194123,5,8709,194124,1,8709,194124,50,8709,194124,40,8709,194188,0,8709,247365,3,12611,248973,4,14560,250075,5,16510,250076,1,16510,250076,50,16512,250076,40,16512,250140,0,16512,294451,3,19064,295639,4,20338,296386,5,21613,296387,1,21613,296387,50,21614,296387,40,21614,296451,0,21614,328391,3,23117,329525,4,23865,330182,1,24615,330182,50,24616,330182,40,24616,330246,0,24616,346760,3,25380,347777,4,25742,349802,5,26117,349803,1,26117,349803,50,26117,349803,40,26117,349867,0,26117,378464,3,27319,379218,4,27918,379703,1,28518,379703,50,28519,379703,40,28519,379767,0,28519,400458,3,29270,400958,4,29645,401246,1,30020,401246,50,30020,401246,40,30020,401246,40,30020,401355,0,30021)
%
%
% START OF PROOF
% 401247 [] equal(X,X).
% 401248 [] equal(multiply(identity,X),X).
% 401249 [] equal(multiply(inverse(X),X),identity).
% 401250 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 401301 [] -equal(multiply(X,sk_c10),sk_c11) | -equal(multiply(Y,X),sk_c11) | -equal(multiply(Z,X),U) | -equal(inverse(Z),U) | -equal(inverse(U),X) | -equal(inverse(Y),X).
% 401302 [] -equal(multiply(X,Y),Z) | -equal(inverse(X),Z) | -equal(inverse(Z),Y) | $spltprd1($spltcnst97,Y).
% 401303 [] -equal(multiply(X,Y),sk_c11) | -equal(inverse(X),Y) | $spltprd1($spltcnst98,Y).
% 401304 [] -equal(multiply(X,sk_c10),sk_c11) | $spltprd1($spltcnst99,X).
% 401305 [] -$spltprd1($spltcnst98,X) | -$spltprd1($spltcnst97,X) | -$spltprd1($spltcnst99,X).
% 401306 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(inverse(sk_c2),sk_c10).
% 401307 [] equal(inverse(sk_c2),sk_c10) | equal(inverse(sk_c6),sk_c8).
% 401308 [] equal(inverse(sk_c2),sk_c10) | equal(inverse(sk_c7),sk_c6).
% 401309 [] equal(multiply(sk_c8,sk_c10),sk_c11) | equal(inverse(sk_c2),sk_c10).
% 401310 [] equal(inverse(sk_c2),sk_c10) | equal(inverse(sk_c5),sk_c8).
% 401311 [?] ?
% 401316 [] equal(multiply(sk_c2,sk_c10),sk_c9) | equal(multiply(sk_c7,sk_c8),sk_c6).
% 401317 [] equal(multiply(sk_c2,sk_c10),sk_c9) | equal(inverse(sk_c6),sk_c8).
% 401318 [] equal(multiply(sk_c2,sk_c10),sk_c9) | equal(inverse(sk_c7),sk_c6).
% 401319 [] equal(multiply(sk_c2,sk_c10),sk_c9) | equal(multiply(sk_c8,sk_c10),sk_c11).
% 401320 [] equal(multiply(sk_c2,sk_c10),sk_c9) | equal(inverse(sk_c5),sk_c8).
% 401321 [] equal(multiply(sk_c2,sk_c10),sk_c9) | equal(multiply(sk_c5,sk_c8),sk_c11).
% 401326 [] equal(multiply(sk_c11,sk_c9),sk_c10) | equal(multiply(sk_c7,sk_c8),sk_c6).
% 401327 [] equal(multiply(sk_c11,sk_c9),sk_c10) | equal(inverse(sk_c6),sk_c8).
% 401328 [] equal(multiply(sk_c11,sk_c9),sk_c10) | equal(inverse(sk_c7),sk_c6).
% 401329 [] equal(multiply(sk_c11,sk_c9),sk_c10) | equal(multiply(sk_c8,sk_c10),sk_c11).
% 401330 [] equal(multiply(sk_c11,sk_c9),sk_c10) | equal(inverse(sk_c5),sk_c8).
% 401331 [] equal(multiply(sk_c11,sk_c9),sk_c10) | equal(multiply(sk_c5,sk_c8),sk_c11).
% 401336 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(inverse(sk_c1),sk_c11).
% 401337 [] equal(inverse(sk_c1),sk_c11) | equal(inverse(sk_c6),sk_c8).
% 401338 [] equal(inverse(sk_c1),sk_c11) | equal(inverse(sk_c7),sk_c6).
% 401339 [] equal(multiply(sk_c8,sk_c10),sk_c11) | equal(inverse(sk_c1),sk_c11).
% 401340 [] equal(inverse(sk_c1),sk_c11) | equal(inverse(sk_c5),sk_c8).
% 401341 [?] ?
% 401346 [] equal(multiply(sk_c1,sk_c11),sk_c10) | equal(multiply(sk_c7,sk_c8),sk_c6).
% 401347 [] equal(multiply(sk_c1,sk_c11),sk_c10) | equal(inverse(sk_c6),sk_c8).
% 401348 [] equal(multiply(sk_c1,sk_c11),sk_c10) | equal(inverse(sk_c7),sk_c6).
% 401349 [] equal(multiply(sk_c1,sk_c11),sk_c10) | equal(multiply(sk_c8,sk_c10),sk_c11).
% 401350 [] equal(multiply(sk_c1,sk_c11),sk_c10) | equal(inverse(sk_c5),sk_c8).
% 401351 [] equal(multiply(sk_c1,sk_c11),sk_c10) | equal(multiply(sk_c5,sk_c8),sk_c11).
% 401422 [hyper:401303,401310,binarycut:401311] equal(inverse(sk_c2),sk_c10) | $spltprd1($spltcnst98,sk_c8).
% 401510 [hyper:401303,401340,binarycut:401341] equal(inverse(sk_c1),sk_c11) | $spltprd1($spltcnst98,sk_c8).
% 401572 [hyper:401302,401306,401307,401308] equal(inverse(sk_c2),sk_c10) | $spltprd1($spltcnst97,sk_c8).
% 401601 [hyper:401304,401309] equal(inverse(sk_c2),sk_c10) | $spltprd1($spltcnst99,sk_c8).
% 401612 [hyper:401305,401601,401572,401422] equal(inverse(sk_c2),sk_c10).
% 401619 [para:401612.1.1,401249.1.1.1] equal(multiply(sk_c10,sk_c2),identity).
% 401751 [hyper:401302,401336,401337,401338] equal(inverse(sk_c1),sk_c11) | $spltprd1($spltcnst97,sk_c8).
% 401778 [hyper:401304,401339] equal(inverse(sk_c1),sk_c11) | $spltprd1($spltcnst99,sk_c8).
% 401789 [hyper:401305,401778,401751,401510] equal(inverse(sk_c1),sk_c11).
% 401796 [para:401789.1.1,401249.1.1.1] equal(multiply(sk_c11,sk_c1),identity).
% 401955 [hyper:401301,401321,401319,401320,401317,401316,401318] equal(multiply(sk_c2,sk_c10),sk_c9).
% 402120 [hyper:401301,401331,401329,401330,401327,401326,401328] equal(multiply(sk_c11,sk_c9),sk_c10).
% 402197 [hyper:401301,401351,401349,401350,401347,401346,401348] equal(multiply(sk_c1,sk_c11),sk_c10).
% 402205 [para:401249.1.1,401250.1.1.1,demod:401248] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 402206 [para:401619.1.1,401250.1.1.1,demod:401248] equal(X,multiply(sk_c10,multiply(sk_c2,X))).
% 402207 [para:401796.1.1,401250.1.1.1,demod:401248] equal(X,multiply(sk_c11,multiply(sk_c1,X))).
% 402223 [para:401955.1.1,402206.1.2.2] equal(sk_c10,multiply(sk_c10,sk_c9)).
% 402245 [para:402197.1.1,402207.1.2.2] equal(sk_c11,multiply(sk_c11,sk_c10)).
% 402256 [para:401619.1.1,402205.1.2.2] equal(sk_c2,multiply(inverse(sk_c10),identity)).
% 402267 [para:402206.1.2,402205.1.2.2] equal(multiply(sk_c2,X),multiply(inverse(sk_c10),X)).
% 402288 [para:402267.1.2,401249.1.1,demod:401955] equal(sk_c9,identity).
% 402292 [para:402267.1.2,402256.1.2] equal(sk_c2,multiply(sk_c2,identity)).
% 402293 [para:402288.1.1,402120.1.1.2] equal(multiply(sk_c11,identity),sk_c10).
% 402316 [para:402293.1.1,401250.1.1.1,demod:401248] equal(multiply(sk_c10,X),multiply(sk_c11,X)).
% 402336 [para:402316.1.2,401796.1.1] equal(multiply(sk_c10,sk_c1),identity).
% 402340 [para:402316.1.2,402245.1.2] equal(sk_c11,multiply(sk_c10,sk_c10)).
% 402345 [para:402336.1.1,402205.1.2.2,demod:402256] equal(sk_c1,sk_c2).
% 402346 [para:402345.1.1,401789.1.1.1,demod:401612] equal(sk_c10,sk_c11).
% 402347 [para:402345.1.1,402197.1.1.1] equal(multiply(sk_c2,sk_c11),sk_c10).
% 402355 [para:402346.1.2,402347.1.1.2,demod:401955] equal(sk_c9,sk_c10).
% 402357 [para:402355.1.1,402288.1.1] equal(sk_c10,identity).
% 402378 [para:402357.1.1,401619.1.1.1,demod:401248] equal(sk_c2,identity).
% 402379 [para:402357.1.1,401955.1.1.2,demod:402292] equal(sk_c2,sk_c9).
% 402380 [para:402357.1.1,402223.1.2.1,demod:401248] equal(sk_c10,sk_c9).
% 402383 [para:402378.1.1,401612.1.1.1] equal(inverse(identity),sk_c10).
% 402384 [para:402379.1.1,401612.1.1.1] equal(inverse(sk_c9),sk_c10).
% 402437 [hyper:401301,402383,401955,demod:402340,401248,cut:402346,cut:401247,demod:401612,402384,cut:401247,cut:402380] 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 29
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 2 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(X,sk_c11),sk_c10) | -equal(inverse(X),sk_c11) | -equal(multiply(sk_c11,sk_c9),sk_c10) | -equal(multiply(Y,sk_c10),sk_c9) | -equal(inverse(Y),sk_c10) | -equal(multiply(Z,sk_c11),sk_c10) | -equal(inverse(Z),sk_c11) | -equal(multiply(U,sk_c10),sk_c9) | -equal(inverse(U),sk_c10) | -equal(multiply(V,W),sk_c11) | -equal(inverse(V),W) | -equal(multiply(W,sk_c10),sk_c11) | -equal(inverse(X1),X2) | -equal(inverse(X2),W) | -equal(multiply(X1,W),X2).
% Split part used next: -equal(multiply(U,sk_c10),sk_c9) | -equal(inverse(U),sk_c10).
% 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 29
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(55,40,1,119,0,2,106902,5,1503,106902,1,1503,106902,50,1503,106902,40,1503,106966,0,1503,119568,3,1804,120217,4,1954,120832,5,2104,120833,1,2104,120833,50,2104,120833,40,2104,120897,0,2104,121982,3,2418,122017,4,2572,122194,5,2705,122194,1,2705,122194,50,2705,122194,40,2705,122258,0,2705,151917,3,4206,152611,4,4956,153454,1,5706,153454,50,5707,153454,40,5707,153518,0,5707,172680,3,6461,173386,4,6833,174017,1,7208,174017,50,7208,174017,40,7208,174081,0,7208,192058,3,7962,192912,4,8334,194123,5,8709,194124,1,8709,194124,50,8709,194124,40,8709,194188,0,8709,247365,3,12611,248973,4,14560,250075,5,16510,250076,1,16510,250076,50,16512,250076,40,16512,250140,0,16512,294451,3,19064,295639,4,20338,296386,5,21613,296387,1,21613,296387,50,21614,296387,40,21614,296451,0,21614,328391,3,23117,329525,4,23865,330182,1,24615,330182,50,24616,330182,40,24616,330246,0,24616,346760,3,25380,347777,4,25742,349802,5,26117,349803,1,26117,349803,50,26117,349803,40,26117,349867,0,26117,378464,3,27319,379218,4,27918,379703,1,28518,379703,50,28519,379703,40,28519,379767,0,28519,400458,3,29270,400958,4,29645,401246,1,30020,401246,50,30020,401246,40,30020,401246,40,30020,401355,0,30021,402436,50,30028,402436,30,30028,402436,40,30028,402491,0,30028)
%
%
% START OF PROOF
% 402437 [] equal(X,X).
% 402441 [] -equal(multiply(X,sk_c10),sk_c9) | -equal(inverse(X),sk_c10).
% 402448 [] equal(inverse(sk_c2),sk_c10) | equal(inverse(sk_c4),sk_c10).
% 402449 [?] ?
% 402458 [?] ?
% 402459 [] equal(multiply(sk_c2,sk_c10),sk_c9) | equal(multiply(sk_c4,sk_c10),sk_c9).
% 402510 [hyper:402441,402448,binarycut:402458] equal(inverse(sk_c4),sk_c10).
% 402512 [hyper:402441,402448,binarycut:402449] equal(inverse(sk_c2),sk_c10).
% 402530 [hyper:402441,402459,demod:402512,cut:402437] equal(multiply(sk_c4,sk_c10),sk_c9).
% 402533 [hyper:402441,402530,demod:402510,cut:402437] 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 29
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 3 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(X,sk_c11),sk_c10) | -equal(inverse(X),sk_c11) | -equal(multiply(sk_c11,sk_c9),sk_c10) | -equal(multiply(Y,sk_c10),sk_c9) | -equal(inverse(Y),sk_c10) | -equal(multiply(Z,sk_c11),sk_c10) | -equal(inverse(Z),sk_c11) | -equal(multiply(U,sk_c10),sk_c9) | -equal(inverse(U),sk_c10) | -equal(multiply(V,W),sk_c11) | -equal(inverse(V),W) | -equal(multiply(W,sk_c10),sk_c11) | -equal(inverse(X1),X2) | -equal(inverse(X2),W) | -equal(multiply(X1,W),X2).
% Split part used next: -equal(multiply(Z,sk_c11),sk_c10) | -equal(inverse(Z),sk_c11).
% 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 29
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(55,40,1,119,0,2,106902,5,1503,106902,1,1503,106902,50,1503,106902,40,1503,106966,0,1503,119568,3,1804,120217,4,1954,120832,5,2104,120833,1,2104,120833,50,2104,120833,40,2104,120897,0,2104,121982,3,2418,122017,4,2572,122194,5,2705,122194,1,2705,122194,50,2705,122194,40,2705,122258,0,2705,151917,3,4206,152611,4,4956,153454,1,5706,153454,50,5707,153454,40,5707,153518,0,5707,172680,3,6461,173386,4,6833,174017,1,7208,174017,50,7208,174017,40,7208,174081,0,7208,192058,3,7962,192912,4,8334,194123,5,8709,194124,1,8709,194124,50,8709,194124,40,8709,194188,0,8709,247365,3,12611,248973,4,14560,250075,5,16510,250076,1,16510,250076,50,16512,250076,40,16512,250140,0,16512,294451,3,19064,295639,4,20338,296386,5,21613,296387,1,21613,296387,50,21614,296387,40,21614,296451,0,21614,328391,3,23117,329525,4,23865,330182,1,24615,330182,50,24616,330182,40,24616,330246,0,24616,346760,3,25380,347777,4,25742,349802,5,26117,349803,1,26117,349803,50,26117,349803,40,26117,349867,0,26117,378464,3,27319,379218,4,27918,379703,1,28518,379703,50,28519,379703,40,28519,379767,0,28519,400458,3,29270,400958,4,29645,401246,1,30020,401246,50,30020,401246,40,30020,401246,40,30020,401355,0,30021,402436,50,30028,402436,30,30028,402436,40,30028,402491,0,30028,402532,50,30028,402532,30,30028,402532,40,30028,402587,0,30028)
%
%
% START OF PROOF
% 402533 [] equal(X,X).
% 402537 [] -equal(multiply(X,sk_c11),sk_c10) | -equal(inverse(X),sk_c11).
% 402576 [] equal(inverse(sk_c1),sk_c11) | equal(inverse(sk_c3),sk_c11).
% 402577 [?] ?
% 402586 [?] ?
% 402587 [] equal(multiply(sk_c1,sk_c11),sk_c10) | equal(multiply(sk_c3,sk_c11),sk_c10).
% 402619 [hyper:402537,402576,binarycut:402586] equal(inverse(sk_c3),sk_c11).
% 402621 [hyper:402537,402576,binarycut:402577] equal(inverse(sk_c1),sk_c11).
% 402645 [hyper:402537,402587,demod:402621,cut:402533] equal(multiply(sk_c3,sk_c11),sk_c10).
% 402647 [hyper:402537,402645,demod:402619,cut:402533] 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 29
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 4 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(X,sk_c11),sk_c10) | -equal(inverse(X),sk_c11) | -equal(multiply(sk_c11,sk_c9),sk_c10) | -equal(multiply(Y,sk_c10),sk_c9) | -equal(inverse(Y),sk_c10) | -equal(multiply(Z,sk_c11),sk_c10) | -equal(inverse(Z),sk_c11) | -equal(multiply(U,sk_c10),sk_c9) | -equal(inverse(U),sk_c10) | -equal(multiply(V,W),sk_c11) | -equal(inverse(V),W) | -equal(multiply(W,sk_c10),sk_c11) | -equal(inverse(X1),X2) | -equal(inverse(X2),W) | -equal(multiply(X1,W),X2).
% Split part used next: -equal(multiply(Y,sk_c10),sk_c9) | -equal(inverse(Y),sk_c10).
% 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 29
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(55,40,1,119,0,2,106902,5,1503,106902,1,1503,106902,50,1503,106902,40,1503,106966,0,1503,119568,3,1804,120217,4,1954,120832,5,2104,120833,1,2104,120833,50,2104,120833,40,2104,120897,0,2104,121982,3,2418,122017,4,2572,122194,5,2705,122194,1,2705,122194,50,2705,122194,40,2705,122258,0,2705,151917,3,4206,152611,4,4956,153454,1,5706,153454,50,5707,153454,40,5707,153518,0,5707,172680,3,6461,173386,4,6833,174017,1,7208,174017,50,7208,174017,40,7208,174081,0,7208,192058,3,7962,192912,4,8334,194123,5,8709,194124,1,8709,194124,50,8709,194124,40,8709,194188,0,8709,247365,3,12611,248973,4,14560,250075,5,16510,250076,1,16510,250076,50,16512,250076,40,16512,250140,0,16512,294451,3,19064,295639,4,20338,296386,5,21613,296387,1,21613,296387,50,21614,296387,40,21614,296451,0,21614,328391,3,23117,329525,4,23865,330182,1,24615,330182,50,24616,330182,40,24616,330246,0,24616,346760,3,25380,347777,4,25742,349802,5,26117,349803,1,26117,349803,50,26117,349803,40,26117,349867,0,26117,378464,3,27319,379218,4,27918,379703,1,28518,379703,50,28519,379703,40,28519,379767,0,28519,400458,3,29270,400958,4,29645,401246,1,30020,401246,50,30020,401246,40,30020,401246,40,30020,401355,0,30021,402436,50,30028,402436,30,30028,402436,40,30028,402491,0,30028,402532,50,30028,402532,30,30028,402532,40,30028,402587,0,30028,402646,50,30029,402646,30,30029,402646,40,30029,402701,0,30033)
%
%
% START OF PROOF
% 402647 [] equal(X,X).
% 402651 [] -equal(multiply(X,sk_c10),sk_c9) | -equal(inverse(X),sk_c10).
% 402658 [] equal(inverse(sk_c2),sk_c10) | equal(inverse(sk_c4),sk_c10).
% 402659 [?] ?
% 402668 [?] ?
% 402669 [] equal(multiply(sk_c2,sk_c10),sk_c9) | equal(multiply(sk_c4,sk_c10),sk_c9).
% 402720 [hyper:402651,402658,binarycut:402668] equal(inverse(sk_c4),sk_c10).
% 402722 [hyper:402651,402658,binarycut:402659] equal(inverse(sk_c2),sk_c10).
% 402740 [hyper:402651,402669,demod:402722,cut:402647] equal(multiply(sk_c4,sk_c10),sk_c9).
% 402743 [hyper:402651,402740,demod:402720,cut:402647] 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 29
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 5 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(X,sk_c11),sk_c10) | -equal(inverse(X),sk_c11) | -equal(multiply(sk_c11,sk_c9),sk_c10) | -equal(multiply(Y,sk_c10),sk_c9) | -equal(inverse(Y),sk_c10) | -equal(multiply(Z,sk_c11),sk_c10) | -equal(inverse(Z),sk_c11) | -equal(multiply(U,sk_c10),sk_c9) | -equal(inverse(U),sk_c10) | -equal(multiply(V,W),sk_c11) | -equal(inverse(V),W) | -equal(multiply(W,sk_c10),sk_c11) | -equal(inverse(X1),X2) | -equal(inverse(X2),W) | -equal(multiply(X1,W),X2).
% Split part used next: -equal(multiply(X,sk_c11),sk_c10) | -equal(inverse(X),sk_c11).
% 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 29
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(55,40,1,119,0,2,106902,5,1503,106902,1,1503,106902,50,1503,106902,40,1503,106966,0,1503,119568,3,1804,120217,4,1954,120832,5,2104,120833,1,2104,120833,50,2104,120833,40,2104,120897,0,2104,121982,3,2418,122017,4,2572,122194,5,2705,122194,1,2705,122194,50,2705,122194,40,2705,122258,0,2705,151917,3,4206,152611,4,4956,153454,1,5706,153454,50,5707,153454,40,5707,153518,0,5707,172680,3,6461,173386,4,6833,174017,1,7208,174017,50,7208,174017,40,7208,174081,0,7208,192058,3,7962,192912,4,8334,194123,5,8709,194124,1,8709,194124,50,8709,194124,40,8709,194188,0,8709,247365,3,12611,248973,4,14560,250075,5,16510,250076,1,16510,250076,50,16512,250076,40,16512,250140,0,16512,294451,3,19064,295639,4,20338,296386,5,21613,296387,1,21613,296387,50,21614,296387,40,21614,296451,0,21614,328391,3,23117,329525,4,23865,330182,1,24615,330182,50,24616,330182,40,24616,330246,0,24616,346760,3,25380,347777,4,25742,349802,5,26117,349803,1,26117,349803,50,26117,349803,40,26117,349867,0,26117,378464,3,27319,379218,4,27918,379703,1,28518,379703,50,28519,379703,40,28519,379767,0,28519,400458,3,29270,400958,4,29645,401246,1,30020,401246,50,30020,401246,40,30020,401246,40,30020,401355,0,30021,402436,50,30028,402436,30,30028,402436,40,30028,402491,0,30028,402532,50,30028,402532,30,30028,402532,40,30028,402587,0,30028,402646,50,30029,402646,30,30029,402646,40,30029,402701,0,30033,402742,50,30033,402742,30,30033,402742,40,30033,402797,0,30033)
%
%
% START OF PROOF
% 402743 [] equal(X,X).
% 402747 [] -equal(multiply(X,sk_c11),sk_c10) | -equal(inverse(X),sk_c11).
% 402786 [] equal(inverse(sk_c1),sk_c11) | equal(inverse(sk_c3),sk_c11).
% 402787 [?] ?
% 402796 [?] ?
% 402797 [] equal(multiply(sk_c1,sk_c11),sk_c10) | equal(multiply(sk_c3,sk_c11),sk_c10).
% 402829 [hyper:402747,402786,binarycut:402796] equal(inverse(sk_c3),sk_c11).
% 402831 [hyper:402747,402786,binarycut:402787] equal(inverse(sk_c1),sk_c11).
% 402855 [hyper:402747,402797,demod:402831,cut:402743] equal(multiply(sk_c3,sk_c11),sk_c10).
% 402857 [hyper:402747,402855,demod:402829,cut:402743] 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 29
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 6 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(X,sk_c11),sk_c10) | -equal(inverse(X),sk_c11) | -equal(multiply(sk_c11,sk_c9),sk_c10) | -equal(multiply(Y,sk_c10),sk_c9) | -equal(inverse(Y),sk_c10) | -equal(multiply(Z,sk_c11),sk_c10) | -equal(inverse(Z),sk_c11) | -equal(multiply(U,sk_c10),sk_c9) | -equal(inverse(U),sk_c10) | -equal(multiply(V,W),sk_c11) | -equal(inverse(V),W) | -equal(multiply(W,sk_c10),sk_c11) | -equal(inverse(X1),X2) | -equal(inverse(X2),W) | -equal(multiply(X1,W),X2).
% Split part used next: -equal(multiply(sk_c11,sk_c9),sk_c10).
% 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 29
% 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 29
% 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 29
% 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 29
% 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 29
% 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 29
% 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 29
% 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 29
% clause depth limited to 10
% 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(55,40,1,119,0,2,106902,5,1503,106902,1,1503,106902,50,1503,106902,40,1503,106966,0,1503,119568,3,1804,120217,4,1954,120832,5,2104,120833,1,2104,120833,50,2104,120833,40,2104,120897,0,2104,121982,3,2418,122017,4,2572,122194,5,2705,122194,1,2705,122194,50,2705,122194,40,2705,122258,0,2705,151917,3,4206,152611,4,4956,153454,1,5706,153454,50,5707,153454,40,5707,153518,0,5707,172680,3,6461,173386,4,6833,174017,1,7208,174017,50,7208,174017,40,7208,174081,0,7208,192058,3,7962,192912,4,8334,194123,5,8709,194124,1,8709,194124,50,8709,194124,40,8709,194188,0,8709,247365,3,12611,248973,4,14560,250075,5,16510,250076,1,16510,250076,50,16512,250076,40,16512,250140,0,16512,294451,3,19064,295639,4,20338,296386,5,21613,296387,1,21613,296387,50,21614,296387,40,21614,296451,0,21614,328391,3,23117,329525,4,23865,330182,1,24615,330182,50,24616,330182,40,24616,330246,0,24616,346760,3,25380,347777,4,25742,349802,5,26117,349803,1,26117,349803,50,26117,349803,40,26117,349867,0,26117,378464,3,27319,379218,4,27918,379703,1,28518,379703,50,28519,379703,40,28519,379767,0,28519,400458,3,29270,400958,4,29645,401246,1,30020,401246,50,30020,401246,40,30020,401246,40,30020,401355,0,30021,402436,50,30028,402436,30,30028,402436,40,30028,402491,0,30028,402532,50,30028,402532,30,30028,402532,40,30028,402587,0,30028,402646,50,30029,402646,30,30029,402646,40,30029,402701,0,30033,402742,50,30033,402742,30,30033,402742,40,30033,402797,0,30033,402856,50,30033,402856,30,30033,402856,40,30033,402911,0,30039,403101,50,30040,403156,0,30040,403421,50,30046,403476,0,30051,403751,50,30059,403806,0,30059,404101,50,30070,404156,0,30075,404457,50,30090,404512,0,30090,404821,50,30115,404876,0,30119,405194,50,30162,405249,0,30162,405577,50,30244,405577,40,30244,405632,0,30244)
%
%
% START OF PROOF
% 405358 [?] ?
% 405579 [] equal(multiply(identity,X),X).
% 405580 [] equal(multiply(inverse(X),X),identity).
% 405581 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 405582 [] -equal(multiply(sk_c11,sk_c9),sk_c10).
% 405604 [?] ?
% 405605 [?] ?
% 405607 [?] ?
% 405608 [?] ?
% 405684 [input:405604,cut:405582] equal(inverse(sk_c6),sk_c8).
% 405685 [para:405684.1.1,405580.1.1.1] equal(multiply(sk_c8,sk_c6),identity).
% 405686 [input:405605,cut:405582] equal(inverse(sk_c7),sk_c6).
% 405687 [para:405686.1.1,405580.1.1.1] equal(multiply(sk_c6,sk_c7),identity).
% 405689 [input:405607,cut:405582] equal(inverse(sk_c5),sk_c8).
% 405690 [para:405689.1.1,405580.1.1.1] equal(multiply(sk_c8,sk_c5),identity).
% 405719 [input:405608,cut:405582] equal(multiply(sk_c5,sk_c8),sk_c11).
% 405746 [para:405685.1.1,405581.1.1.1,demod:405579] equal(X,multiply(sk_c8,multiply(sk_c6,X))).
% 405747 [para:405687.1.1,405581.1.1.1,demod:405579] equal(X,multiply(sk_c6,multiply(sk_c7,X))).
% 405775 [para:405719.1.1,405581.1.1.1] equal(multiply(sk_c11,X),multiply(sk_c5,multiply(sk_c8,X))).
% 405789 [para:405687.1.1,405746.1.2.2] equal(sk_c7,multiply(sk_c8,identity)).
% 405790 [para:405789.1.2,405581.1.1.1,demod:405579] equal(multiply(sk_c7,X),multiply(sk_c8,X)).
% 405818 [para:405790.1.1,405747.1.2.2] equal(X,multiply(sk_c6,multiply(sk_c8,X))).
% 405820 [para:405685.1.1,405818.1.2.2] equal(sk_c6,multiply(sk_c6,identity)).
% 405822 [para:405690.1.1,405818.1.2.2,demod:405820] equal(sk_c5,sk_c6).
% 405830 [para:405822.1.2,405747.1.2.1,demod:405775,405790] equal(X,multiply(sk_c11,X)).
% 405833 [para:405830.1.2,405582.1.1,cut:405358] 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: 34467
% derived clauses: 4646604
% kept clauses: 251204
% kept size sum: 14597
% kept mid-nuclei: 91534
% kept new demods: 2533
% forw unit-subs: 1593621
% forw double-subs: 2473106
% forw overdouble-subs: 182970
% backward subs: 15338
% fast unit cutoff: 29337
% full unit cutoff: 0
% dbl unit cutoff: 27539
% real runtime : 303.73
% process. runtime: 302.43
% specific non-discr-tree subsumption statistics:
% tried: 29590161
% length fails: 3703893
% strength fails: 12102101
% predlist fails: 2349883
% aux str. fails: 1746625
% by-lit fails: 4003092
% full subs tried: 1917946
% full subs fail: 1822544
%
% ; 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/GRP271-1+eq_r.in")
%
%------------------------------------------------------------------------------