TSTP Solution File: GRP259-1 by Gandalf---c-2.6
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP259-1 : 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 289.7s
% Output : Assurance 289.7s
% 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/GRP259-1+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 23)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 3 23)
% (binary-posweight-lex-big-order 30 #f 3 23)
% (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_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(Y,sk_c7),sk_c6) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c6,sk_c8),sk_c7) | -equal(multiply(Z,sk_c6),sk_c8) | -equal(inverse(Z),sk_c6) | -equal(multiply(sk_c7,sk_c8),sk_c6) | -equal(inverse(U),sk_c8) | -equal(multiply(U,sk_c7),sk_c8) | -equal(inverse(V),sk_c7) | -equal(multiply(V,sk_c6),sk_c7).
% was split for some strategies as:
% -equal(inverse(V),sk_c7) | -equal(multiply(V,sk_c6),sk_c7).
% -equal(inverse(U),sk_c8) | -equal(multiply(U,sk_c7),sk_c8).
% -equal(multiply(Z,sk_c6),sk_c8) | -equal(inverse(Z),sk_c6).
% -equal(multiply(Y,sk_c7),sk_c6) | -equal(inverse(Y),sk_c7).
% -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8).
% -equal(multiply(sk_c6,sk_c8),sk_c7).
% -equal(multiply(sk_c7,sk_c8),sk_c6).
%
% Starting a split proof attempt with 7 components.
%
% Split component 1 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(Y,sk_c7),sk_c6) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c6,sk_c8),sk_c7) | -equal(multiply(Z,sk_c6),sk_c8) | -equal(inverse(Z),sk_c6) | -equal(multiply(sk_c7,sk_c8),sk_c6) | -equal(inverse(U),sk_c8) | -equal(multiply(U,sk_c7),sk_c8) | -equal(inverse(V),sk_c7) | -equal(multiply(V,sk_c6),sk_c7).
% Split part used next: -equal(inverse(V),sk_c7) | -equal(multiply(V,sk_c6),sk_c7).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(40,40,0,86,0,0,793,50,7,839,0,7,1561,50,15,1607,0,15,2334,50,25,2380,0,25,3113,50,31,3159,0,31,3899,50,40,3945,0,40,4693,50,55,4739,0,55,5495,50,82,5541,0,82,6307,50,137,6353,0,137,7129,50,254,7175,0,254,7963,50,450,8009,0,450,8809,50,819,8809,40,819,8855,0,819,19252,3,1120,19959,4,1270,20638,1,1420,20638,50,1420,20638,40,1420,20684,0,1420,20861,3,1730,20869,4,1874,20877,5,2021,20877,1,2021,20877,50,2021,20877,40,2021,20923,0,2021,45949,3,3522,47046,4,4272,48038,5,5022,48039,1,5022,48039,50,5023,48039,40,5023,48085,0,5023,64432,3,5775,65273,4,6149,66044,5,6524,66045,1,6524,66045,50,6524,66045,40,6524,66091,0,6524,76645,3,7275,77799,4,7650,79061,5,8025,79062,1,8025,79062,50,8025,79062,40,8025,79108,0,8025,135496,3,11929,136794,4,13876,137983,1,15826,137983,50,15828,137983,40,15828,138029,0,15828,183492,3,18379,184665,4,19654,185456,1,20929,185456,50,20931,185456,40,20931,185502,0,20931,226694,3,22434,227360,4,23182,228206,5,23932,228207,1,23932,228207,50,23934,228207,40,23934,228253,0,23934,237533,3,24688,238580,4,25064,238639,5,25435,238639,1,25435,238639,50,25435,238639,40,25435,238685,0,25435,266059,3,26636,266979,4,27236,267486,1,27836,267486,50,27837,267486,40,27837,267532,0,27837,286980,3,28589,287751,4,28963,288373,5,29338,288374,1,29338,288374,50,29338,288374,40,29338,288374,40,29338,288414,0,29339)
%
%
% START OF PROOF
% 288376 [] equal(multiply(identity,X),X).
% 288377 [] equal(multiply(inverse(X),X),identity).
% 288378 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 288379 [] -equal(multiply(X,sk_c6),sk_c7) | -equal(inverse(X),sk_c7).
% 288380 [?] ?
% 288381 [] equal(inverse(sk_c3),sk_c6) | equal(inverse(sk_c5),sk_c7).
% 288385 [] equal(multiply(sk_c3,sk_c6),sk_c8) | equal(multiply(sk_c5,sk_c6),sk_c7).
% 288386 [] equal(multiply(sk_c3,sk_c6),sk_c8) | equal(inverse(sk_c5),sk_c7).
% 288390 [] equal(multiply(sk_c6,sk_c8),sk_c7) | equal(multiply(sk_c5,sk_c6),sk_c7).
% 288391 [] equal(multiply(sk_c6,sk_c8),sk_c7) | equal(inverse(sk_c5),sk_c7).
% 288395 [?] ?
% 288396 [] equal(inverse(sk_c2),sk_c7) | equal(inverse(sk_c5),sk_c7).
% 288400 [] equal(multiply(sk_c2,sk_c7),sk_c6) | equal(multiply(sk_c5,sk_c6),sk_c7).
% 288401 [] equal(multiply(sk_c2,sk_c7),sk_c6) | equal(inverse(sk_c5),sk_c7).
% 288405 [?] ?
% 288406 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c5),sk_c7).
% 288417 [hyper:288379,288381,binarycut:288380] equal(inverse(sk_c3),sk_c6).
% 288418 [para:288417.1.1,288377.1.1.1] equal(multiply(sk_c6,sk_c3),identity).
% 288426 [hyper:288379,288396,binarycut:288395] equal(inverse(sk_c2),sk_c7).
% 288429 [para:288426.1.1,288377.1.1.1] equal(multiply(sk_c7,sk_c2),identity).
% 288433 [hyper:288379,288406,binarycut:288405] equal(inverse(sk_c1),sk_c8).
% 288434 [para:288433.1.1,288377.1.1.1] equal(multiply(sk_c8,sk_c1),identity).
% 288437 [hyper:288379,288386,288385] equal(multiply(sk_c3,sk_c6),sk_c8).
% 288443 [hyper:288379,288391,288390] equal(multiply(sk_c6,sk_c8),sk_c7).
% 288450 [hyper:288379,288400,288401] equal(multiply(sk_c2,sk_c7),sk_c6).
% 288458 [para:288377.1.1,288378.1.1.1,demod:288376] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 288459 [para:288418.1.1,288378.1.1.1,demod:288376] equal(X,multiply(sk_c6,multiply(sk_c3,X))).
% 288461 [para:288434.1.1,288378.1.1.1,demod:288376] equal(X,multiply(sk_c8,multiply(sk_c1,X))).
% 288462 [para:288437.1.1,288378.1.1.1] equal(multiply(sk_c8,X),multiply(sk_c3,multiply(sk_c6,X))).
% 288466 [para:288437.1.1,288459.1.2.2,demod:288443] equal(sk_c6,sk_c7).
% 288467 [para:288466.1.1,288418.1.1.1] equal(multiply(sk_c7,sk_c3),identity).
% 288468 [para:288466.1.1,288437.1.1.2] equal(multiply(sk_c3,sk_c7),sk_c8).
% 288469 [para:288466.1.1,288443.1.1.1] equal(multiply(sk_c7,sk_c8),sk_c7).
% 288473 [para:288429.1.1,288458.1.2.2] equal(sk_c2,multiply(inverse(sk_c7),identity)).
% 288479 [para:288467.1.1,288458.1.2.2,demod:288473] equal(sk_c3,sk_c2).
% 288485 [para:288479.1.1,288468.1.1.1,demod:288450] equal(sk_c6,sk_c8).
% 288487 [para:288485.1.2,288443.1.1.2] equal(multiply(sk_c6,sk_c6),sk_c7).
% 288490 [para:288469.1.1,288458.1.2.2,demod:288377] equal(sk_c8,identity).
% 288492 [para:288490.1.1,288434.1.1.1,demod:288376] equal(sk_c1,identity).
% 288495 [para:288490.1.1,288485.1.2] equal(sk_c6,identity).
% 288501 [para:288495.1.1,288437.1.1.2] equal(multiply(sk_c3,identity),sk_c8).
% 288516 [para:288492.1.1,288461.1.2.2.1,demod:288376] equal(X,multiply(sk_c8,X)).
% 288521 [para:288418.1.1,288462.1.2.2,demod:288501,288516] equal(sk_c3,sk_c8).
% 288523 [para:288521.1.2,288485.1.2] equal(sk_c6,sk_c3).
% 288529 [para:288523.1.2,288417.1.1.1] equal(inverse(sk_c6),sk_c6).
% 288537 [hyper:288379,288487,demod:288529,cut:288466] 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 23
% 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_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(Y,sk_c7),sk_c6) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c6,sk_c8),sk_c7) | -equal(multiply(Z,sk_c6),sk_c8) | -equal(inverse(Z),sk_c6) | -equal(multiply(sk_c7,sk_c8),sk_c6) | -equal(inverse(U),sk_c8) | -equal(multiply(U,sk_c7),sk_c8) | -equal(inverse(V),sk_c7) | -equal(multiply(V,sk_c6),sk_c7).
% Split part used next: -equal(inverse(U),sk_c8) | -equal(multiply(U,sk_c7),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 23
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(40,40,0,86,0,0,793,50,7,839,0,7,1561,50,15,1607,0,15,2334,50,25,2380,0,25,3113,50,31,3159,0,31,3899,50,40,3945,0,40,4693,50,55,4739,0,55,5495,50,82,5541,0,82,6307,50,137,6353,0,137,7129,50,254,7175,0,254,7963,50,450,8009,0,450,8809,50,819,8809,40,819,8855,0,819,19252,3,1120,19959,4,1270,20638,1,1420,20638,50,1420,20638,40,1420,20684,0,1420,20861,3,1730,20869,4,1874,20877,5,2021,20877,1,2021,20877,50,2021,20877,40,2021,20923,0,2021,45949,3,3522,47046,4,4272,48038,5,5022,48039,1,5022,48039,50,5023,48039,40,5023,48085,0,5023,64432,3,5775,65273,4,6149,66044,5,6524,66045,1,6524,66045,50,6524,66045,40,6524,66091,0,6524,76645,3,7275,77799,4,7650,79061,5,8025,79062,1,8025,79062,50,8025,79062,40,8025,79108,0,8025,135496,3,11929,136794,4,13876,137983,1,15826,137983,50,15828,137983,40,15828,138029,0,15828,183492,3,18379,184665,4,19654,185456,1,20929,185456,50,20931,185456,40,20931,185502,0,20931,226694,3,22434,227360,4,23182,228206,5,23932,228207,1,23932,228207,50,23934,228207,40,23934,228253,0,23934,237533,3,24688,238580,4,25064,238639,5,25435,238639,1,25435,238639,50,25435,238639,40,25435,238685,0,25435,266059,3,26636,266979,4,27236,267486,1,27836,267486,50,27837,267486,40,27837,267532,0,27837,286980,3,28589,287751,4,28963,288373,5,29338,288374,1,29338,288374,50,29338,288374,40,29338,288374,40,29338,288414,0,29339,288536,50,29339,288536,30,29339,288536,40,29339,288576,0,29339)
%
%
% START OF PROOF
% 288538 [] equal(multiply(identity,X),X).
% 288539 [] equal(multiply(inverse(X),X),identity).
% 288540 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 288541 [] -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c8).
% 288544 [?] ?
% 288545 [] equal(inverse(sk_c3),sk_c6) | equal(inverse(sk_c4),sk_c8).
% 288549 [] equal(multiply(sk_c3,sk_c6),sk_c8) | equal(multiply(sk_c4,sk_c7),sk_c8).
% 288550 [] equal(multiply(sk_c3,sk_c6),sk_c8) | equal(inverse(sk_c4),sk_c8).
% 288554 [] equal(multiply(sk_c6,sk_c8),sk_c7) | equal(multiply(sk_c4,sk_c7),sk_c8).
% 288555 [] equal(multiply(sk_c6,sk_c8),sk_c7) | equal(inverse(sk_c4),sk_c8).
% 288559 [?] ?
% 288560 [] equal(inverse(sk_c2),sk_c7) | equal(inverse(sk_c4),sk_c8).
% 288564 [] equal(multiply(sk_c2,sk_c7),sk_c6) | equal(multiply(sk_c4,sk_c7),sk_c8).
% 288565 [] equal(multiply(sk_c2,sk_c7),sk_c6) | equal(inverse(sk_c4),sk_c8).
% 288569 [?] ?
% 288570 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c4),sk_c8).
% 288580 [hyper:288541,288545,binarycut:288544] equal(inverse(sk_c3),sk_c6).
% 288582 [para:288580.1.1,288539.1.1.1] equal(multiply(sk_c6,sk_c3),identity).
% 288587 [hyper:288541,288560,binarycut:288559] equal(inverse(sk_c2),sk_c7).
% 288588 [para:288587.1.1,288539.1.1.1] equal(multiply(sk_c7,sk_c2),identity).
% 288596 [hyper:288541,288570,binarycut:288569] equal(inverse(sk_c1),sk_c8).
% 288599 [para:288596.1.1,288539.1.1.1] equal(multiply(sk_c8,sk_c1),identity).
% 288607 [hyper:288541,288549,288550] equal(multiply(sk_c3,sk_c6),sk_c8).
% 288622 [hyper:288541,288554,288555] equal(multiply(sk_c6,sk_c8),sk_c7).
% 288626 [hyper:288541,288564,288565] equal(multiply(sk_c2,sk_c7),sk_c6).
% 288631 [para:288539.1.1,288540.1.1.1,demod:288538] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 288632 [para:288582.1.1,288540.1.1.1,demod:288538] equal(X,multiply(sk_c6,multiply(sk_c3,X))).
% 288639 [para:288607.1.1,288632.1.2.2,demod:288622] equal(sk_c6,sk_c7).
% 288640 [para:288639.1.1,288582.1.1.1] equal(multiply(sk_c7,sk_c3),identity).
% 288641 [para:288639.1.1,288607.1.1.2] equal(multiply(sk_c3,sk_c7),sk_c8).
% 288642 [para:288639.1.1,288622.1.1.1] equal(multiply(sk_c7,sk_c8),sk_c7).
% 288646 [para:288588.1.1,288631.1.2.2] equal(sk_c2,multiply(inverse(sk_c7),identity)).
% 288652 [para:288640.1.1,288631.1.2.2,demod:288646] equal(sk_c3,sk_c2).
% 288660 [para:288652.1.1,288641.1.1.1,demod:288626] equal(sk_c6,sk_c8).
% 288665 [para:288642.1.1,288631.1.2.2,demod:288539] equal(sk_c8,identity).
% 288667 [para:288665.1.1,288599.1.1.1,demod:288538] equal(sk_c1,identity).
% 288670 [para:288665.1.1,288660.1.2] equal(sk_c6,identity).
% 288672 [para:288667.1.1,288596.1.1.1] equal(inverse(identity),sk_c8).
% 288675 [para:288670.1.1,288582.1.1.1,demod:288538] equal(sk_c3,identity).
% 288688 [para:288675.1.1,288641.1.1.1,demod:288538] equal(sk_c7,sk_c8).
% 288707 [hyper:288541,288672,demod:288538,cut:288688] 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 23
% 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_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(Y,sk_c7),sk_c6) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c6,sk_c8),sk_c7) | -equal(multiply(Z,sk_c6),sk_c8) | -equal(inverse(Z),sk_c6) | -equal(multiply(sk_c7,sk_c8),sk_c6) | -equal(inverse(U),sk_c8) | -equal(multiply(U,sk_c7),sk_c8) | -equal(inverse(V),sk_c7) | -equal(multiply(V,sk_c6),sk_c7).
% 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 23
% 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 23
% clause depth limited to 4
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(40,40,0,86,0,0,793,50,7,839,0,7,1561,50,15,1607,0,15,2334,50,25,2380,0,25,3113,50,31,3159,0,31,3899,50,40,3945,0,40,4693,50,55,4739,0,55,5495,50,82,5541,0,82,6307,50,137,6353,0,137,7129,50,254,7175,0,254,7963,50,450,8009,0,450,8809,50,819,8809,40,819,8855,0,819,19252,3,1120,19959,4,1270,20638,1,1420,20638,50,1420,20638,40,1420,20684,0,1420,20861,3,1730,20869,4,1874,20877,5,2021,20877,1,2021,20877,50,2021,20877,40,2021,20923,0,2021,45949,3,3522,47046,4,4272,48038,5,5022,48039,1,5022,48039,50,5023,48039,40,5023,48085,0,5023,64432,3,5775,65273,4,6149,66044,5,6524,66045,1,6524,66045,50,6524,66045,40,6524,66091,0,6524,76645,3,7275,77799,4,7650,79061,5,8025,79062,1,8025,79062,50,8025,79062,40,8025,79108,0,8025,135496,3,11929,136794,4,13876,137983,1,15826,137983,50,15828,137983,40,15828,138029,0,15828,183492,3,18379,184665,4,19654,185456,1,20929,185456,50,20931,185456,40,20931,185502,0,20931,226694,3,22434,227360,4,23182,228206,5,23932,228207,1,23932,228207,50,23934,228207,40,23934,228253,0,23934,237533,3,24688,238580,4,25064,238639,5,25435,238639,1,25435,238639,50,25435,238639,40,25435,238685,0,25435,266059,3,26636,266979,4,27236,267486,1,27836,267486,50,27837,267486,40,27837,267532,0,27837,286980,3,28589,287751,4,28963,288373,5,29338,288374,1,29338,288374,50,29338,288374,40,29338,288374,40,29338,288414,0,29339,288536,50,29339,288536,30,29339,288536,40,29339,288576,0,29339,288706,50,29339,288706,30,29339,288706,40,29339,288746,0,29344,288828,50,29345,288868,0,29345)
%
%
% START OF PROOF
% 288830 [] equal(multiply(identity,X),X).
% 288831 [] equal(multiply(inverse(X),X),identity).
% 288832 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 288833 [] -equal(multiply(X,sk_c6),sk_c8) | -equal(inverse(X),sk_c6).
% 288834 [] equal(multiply(sk_c5,sk_c6),sk_c7) | equal(inverse(sk_c3),sk_c6).
% 288835 [] equal(inverse(sk_c3),sk_c6) | equal(inverse(sk_c5),sk_c7).
% 288836 [] equal(multiply(sk_c4,sk_c7),sk_c8) | equal(inverse(sk_c3),sk_c6).
% 288837 [] equal(inverse(sk_c3),sk_c6) | equal(inverse(sk_c4),sk_c8).
% 288838 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(inverse(sk_c3),sk_c6).
% 288839 [?] ?
% 288840 [?] ?
% 288841 [?] ?
% 288842 [?] ?
% 288843 [?] ?
% 288871 [hyper:288833,288835,binarycut:288840] equal(inverse(sk_c5),sk_c7).
% 288872 [para:288871.1.1,288831.1.1.1] equal(multiply(sk_c7,sk_c5),identity).
% 288876 [hyper:288833,288837,binarycut:288842] equal(inverse(sk_c4),sk_c8).
% 288877 [para:288876.1.1,288831.1.1.1] equal(multiply(sk_c8,sk_c4),identity).
% 288880 [hyper:288833,288834,binarycut:288839] equal(multiply(sk_c5,sk_c6),sk_c7).
% 288883 [hyper:288833,288836,binarycut:288841] equal(multiply(sk_c4,sk_c7),sk_c8).
% 288886 [hyper:288833,288838,binarycut:288843] equal(multiply(sk_c7,sk_c8),sk_c6).
% 288887 [para:288831.1.1,288832.1.1.1,demod:288830] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 288888 [para:288872.1.1,288832.1.1.1,demod:288830] equal(X,multiply(sk_c7,multiply(sk_c5,X))).
% 288889 [para:288877.1.1,288832.1.1.1,demod:288830] equal(X,multiply(sk_c8,multiply(sk_c4,X))).
% 288890 [para:288880.1.1,288832.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c5,multiply(sk_c6,X))).
% 288891 [para:288883.1.1,288832.1.1.1] equal(multiply(sk_c8,X),multiply(sk_c4,multiply(sk_c7,X))).
% 288894 [para:288831.1.1,288887.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 288896 [para:288877.1.1,288887.1.2.2] equal(sk_c4,multiply(inverse(sk_c8),identity)).
% 288897 [para:288880.1.1,288887.1.2.2,demod:288871] equal(sk_c6,multiply(sk_c7,sk_c7)).
% 288898 [para:288883.1.1,288887.1.2.2,demod:288876] equal(sk_c7,multiply(sk_c8,sk_c8)).
% 288899 [para:288886.1.1,288887.1.2.2] equal(sk_c8,multiply(inverse(sk_c7),sk_c6)).
% 288900 [para:288832.1.1,288887.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 288901 [para:288887.1.2,288887.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 288903 [para:288897.1.2,288887.1.2.2,demod:288899] equal(sk_c7,sk_c8).
% 288904 [para:288903.1.2,288877.1.1.1] equal(multiply(sk_c7,sk_c4),identity).
% 288906 [para:288898.1.2,288887.1.2.2] equal(sk_c8,multiply(inverse(sk_c8),sk_c7)).
% 288910 [para:288904.1.1,288832.1.1.1,demod:288830] equal(X,multiply(sk_c7,multiply(sk_c4,X))).
% 288912 [para:288888.1.2,288887.1.2.2] equal(multiply(sk_c5,X),multiply(inverse(sk_c7),X)).
% 288919 [para:288889.1.2,288887.1.2.2] equal(multiply(sk_c4,X),multiply(inverse(sk_c8),X)).
% 288920 [para:288899.1.2,288832.1.1.1,demod:288890,288912] equal(multiply(sk_c8,X),multiply(sk_c7,X)).
% 288921 [para:288910.1.2,288887.1.2.2,demod:288912] equal(multiply(sk_c4,X),multiply(sk_c5,X)).
% 288922 [para:288920.1.1,288887.1.2.2,demod:288920,288891,288919] equal(X,multiply(sk_c7,X)).
% 288924 [para:288922.1.2,288886.1.1] equal(sk_c8,sk_c6).
% 288925 [para:288922.1.2,288887.1.2.2,demod:288921,288912] equal(X,multiply(sk_c4,X)).
% 288938 [para:288886.1.1,288900.1.2.1.1,demod:288922,288920] equal(X,multiply(inverse(sk_c6),X)).
% 288947 [para:288938.1.2,288831.1.1] equal(sk_c6,identity).
% 288948 [para:288901.1.2,288831.1.1] equal(multiply(X,inverse(X)),identity).
% 288950 [para:288901.1.2,288894.1.2] equal(X,multiply(X,identity)).
% 288951 [para:288947.1.1,288880.1.1.2,demod:288925,288921] equal(identity,sk_c7).
% 288955 [para:288951.1.2,288906.1.2.2,demod:288896] equal(sk_c8,sk_c4).
% 288963 [para:288955.1.1,288924.1.1] equal(sk_c4,sk_c6).
% 288969 [para:288950.1.2,288896.1.2] equal(sk_c4,inverse(sk_c8)).
% 288970 [para:288950.1.2,288894.1.2] equal(X,inverse(inverse(X))).
% 288973 [para:288948.1.1,288900.1.2.2.2,demod:288950] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 288977 [para:288889.1.2,288973.1.2.1.1,demod:288925] equal(inverse(X),multiply(inverse(X),sk_c8)).
% 288984 [para:288977.1.2,288901.1.2,demod:288970] equal(multiply(X,sk_c8),X).
% 288985 [para:288924.1.1,288984.1.1.2] equal(multiply(X,sk_c6),X).
% 288988 [hyper:288833,288985,demod:288969,cut:288963] 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 23
% clause depth limited to 4
% seconds given: 4
%
%
% Split component 4 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(Y,sk_c7),sk_c6) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c6,sk_c8),sk_c7) | -equal(multiply(Z,sk_c6),sk_c8) | -equal(inverse(Z),sk_c6) | -equal(multiply(sk_c7,sk_c8),sk_c6) | -equal(inverse(U),sk_c8) | -equal(multiply(U,sk_c7),sk_c8) | -equal(inverse(V),sk_c7) | -equal(multiply(V,sk_c6),sk_c7).
% Split part used next: -equal(multiply(Y,sk_c7),sk_c6) | -equal(inverse(Y),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 23
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(40,40,0,86,0,0,793,50,7,839,0,7,1561,50,15,1607,0,15,2334,50,25,2380,0,25,3113,50,31,3159,0,31,3899,50,40,3945,0,40,4693,50,55,4739,0,55,5495,50,82,5541,0,82,6307,50,137,6353,0,137,7129,50,254,7175,0,254,7963,50,450,8009,0,450,8809,50,819,8809,40,819,8855,0,819,19252,3,1120,19959,4,1270,20638,1,1420,20638,50,1420,20638,40,1420,20684,0,1420,20861,3,1730,20869,4,1874,20877,5,2021,20877,1,2021,20877,50,2021,20877,40,2021,20923,0,2021,45949,3,3522,47046,4,4272,48038,5,5022,48039,1,5022,48039,50,5023,48039,40,5023,48085,0,5023,64432,3,5775,65273,4,6149,66044,5,6524,66045,1,6524,66045,50,6524,66045,40,6524,66091,0,6524,76645,3,7275,77799,4,7650,79061,5,8025,79062,1,8025,79062,50,8025,79062,40,8025,79108,0,8025,135496,3,11929,136794,4,13876,137983,1,15826,137983,50,15828,137983,40,15828,138029,0,15828,183492,3,18379,184665,4,19654,185456,1,20929,185456,50,20931,185456,40,20931,185502,0,20931,226694,3,22434,227360,4,23182,228206,5,23932,228207,1,23932,228207,50,23934,228207,40,23934,228253,0,23934,237533,3,24688,238580,4,25064,238639,5,25435,238639,1,25435,238639,50,25435,238639,40,25435,238685,0,25435,266059,3,26636,266979,4,27236,267486,1,27836,267486,50,27837,267486,40,27837,267532,0,27837,286980,3,28589,287751,4,28963,288373,5,29338,288374,1,29338,288374,50,29338,288374,40,29338,288374,40,29338,288414,0,29339,288536,50,29339,288536,30,29339,288536,40,29339,288576,0,29339,288706,50,29339,288706,30,29339,288706,40,29339,288746,0,29344,288828,50,29345,288868,0,29345,288987,50,29346,288987,30,29346,288987,40,29346,289027,0,29346)
%
%
% START OF PROOF
% 288989 [] equal(multiply(identity,X),X).
% 288990 [] equal(multiply(inverse(X),X),identity).
% 288991 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 288992 [] -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7).
% 289008 [] equal(multiply(sk_c5,sk_c6),sk_c7) | equal(inverse(sk_c2),sk_c7).
% 289009 [] equal(inverse(sk_c2),sk_c7) | equal(inverse(sk_c5),sk_c7).
% 289010 [] equal(multiply(sk_c4,sk_c7),sk_c8) | equal(inverse(sk_c2),sk_c7).
% 289011 [] equal(inverse(sk_c2),sk_c7) | equal(inverse(sk_c4),sk_c8).
% 289012 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(inverse(sk_c2),sk_c7).
% 289013 [?] ?
% 289014 [?] ?
% 289015 [?] ?
% 289016 [?] ?
% 289017 [?] ?
% 289034 [hyper:288992,289009,binarycut:289014] equal(inverse(sk_c5),sk_c7).
% 289038 [para:289034.1.1,288990.1.1.1] equal(multiply(sk_c7,sk_c5),identity).
% 289042 [hyper:288992,289011,binarycut:289016] equal(inverse(sk_c4),sk_c8).
% 289043 [para:289042.1.1,288990.1.1.1] equal(multiply(sk_c8,sk_c4),identity).
% 289049 [hyper:288992,289008,binarycut:289013] equal(multiply(sk_c5,sk_c6),sk_c7).
% 289052 [hyper:288992,289010,binarycut:289015] equal(multiply(sk_c4,sk_c7),sk_c8).
% 289056 [hyper:288992,289012,binarycut:289017] equal(multiply(sk_c7,sk_c8),sk_c6).
% 289057 [para:288990.1.1,288991.1.1.1,demod:288989] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 289058 [para:289038.1.1,288991.1.1.1,demod:288989] equal(X,multiply(sk_c7,multiply(sk_c5,X))).
% 289059 [para:289043.1.1,288991.1.1.1,demod:288989] equal(X,multiply(sk_c8,multiply(sk_c4,X))).
% 289060 [para:289049.1.1,288991.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c5,multiply(sk_c6,X))).
% 289061 [para:289052.1.1,288991.1.1.1] equal(multiply(sk_c8,X),multiply(sk_c4,multiply(sk_c7,X))).
% 289066 [para:289049.1.1,289057.1.2.2,demod:289034] equal(sk_c6,multiply(sk_c7,sk_c7)).
% 289067 [para:289052.1.1,289057.1.2.2,demod:289042] equal(sk_c7,multiply(sk_c8,sk_c8)).
% 289068 [para:289056.1.1,289057.1.2.2] equal(sk_c8,multiply(inverse(sk_c7),sk_c6)).
% 289070 [para:289066.1.2,289057.1.2.2,demod:289068] equal(sk_c7,sk_c8).
% 289074 [para:289070.1.2,289067.1.2.1,demod:289056] equal(sk_c7,sk_c6).
% 289079 [para:289058.1.2,289057.1.2.2] equal(multiply(sk_c5,X),multiply(inverse(sk_c7),X)).
% 289086 [para:289059.1.2,289057.1.2.2] equal(multiply(sk_c4,X),multiply(inverse(sk_c8),X)).
% 289087 [para:289068.1.2,288991.1.1.1,demod:289060,289079] equal(multiply(sk_c8,X),multiply(sk_c7,X)).
% 289089 [para:289087.1.1,289057.1.2.2,demod:289087,289061,289086] equal(X,multiply(sk_c7,X)).
% 289090 [para:289089.1.2,289038.1.1] equal(sk_c5,identity).
% 289094 [para:289090.1.1,289034.1.1.1] equal(inverse(identity),sk_c7).
% 289098 [hyper:288992,289094,demod:288989,cut:289074] 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 23
% 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_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(Y,sk_c7),sk_c6) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c6,sk_c8),sk_c7) | -equal(multiply(Z,sk_c6),sk_c8) | -equal(inverse(Z),sk_c6) | -equal(multiply(sk_c7,sk_c8),sk_c6) | -equal(inverse(U),sk_c8) | -equal(multiply(U,sk_c7),sk_c8) | -equal(inverse(V),sk_c7) | -equal(multiply(V,sk_c6),sk_c7).
% Split part used next: -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),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 23
% 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 23
% clause depth limited to 4
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(40,40,0,86,0,0,793,50,7,839,0,7,1561,50,15,1607,0,15,2334,50,25,2380,0,25,3113,50,31,3159,0,31,3899,50,40,3945,0,40,4693,50,55,4739,0,55,5495,50,82,5541,0,82,6307,50,137,6353,0,137,7129,50,254,7175,0,254,7963,50,450,8009,0,450,8809,50,819,8809,40,819,8855,0,819,19252,3,1120,19959,4,1270,20638,1,1420,20638,50,1420,20638,40,1420,20684,0,1420,20861,3,1730,20869,4,1874,20877,5,2021,20877,1,2021,20877,50,2021,20877,40,2021,20923,0,2021,45949,3,3522,47046,4,4272,48038,5,5022,48039,1,5022,48039,50,5023,48039,40,5023,48085,0,5023,64432,3,5775,65273,4,6149,66044,5,6524,66045,1,6524,66045,50,6524,66045,40,6524,66091,0,6524,76645,3,7275,77799,4,7650,79061,5,8025,79062,1,8025,79062,50,8025,79062,40,8025,79108,0,8025,135496,3,11929,136794,4,13876,137983,1,15826,137983,50,15828,137983,40,15828,138029,0,15828,183492,3,18379,184665,4,19654,185456,1,20929,185456,50,20931,185456,40,20931,185502,0,20931,226694,3,22434,227360,4,23182,228206,5,23932,228207,1,23932,228207,50,23934,228207,40,23934,228253,0,23934,237533,3,24688,238580,4,25064,238639,5,25435,238639,1,25435,238639,50,25435,238639,40,25435,238685,0,25435,266059,3,26636,266979,4,27236,267486,1,27836,267486,50,27837,267486,40,27837,267532,0,27837,286980,3,28589,287751,4,28963,288373,5,29338,288374,1,29338,288374,50,29338,288374,40,29338,288374,40,29338,288414,0,29339,288536,50,29339,288536,30,29339,288536,40,29339,288576,0,29339,288706,50,29339,288706,30,29339,288706,40,29339,288746,0,29344,288828,50,29345,288868,0,29345,288987,50,29346,288987,30,29346,288987,40,29346,289027,0,29346,289097,50,29347,289097,30,29347,289097,40,29347,289137,0,29352,289238,50,29352,289278,0,29352)
%
%
% START OF PROOF
% 289240 [] equal(multiply(identity,X),X).
% 289241 [] equal(multiply(inverse(X),X),identity).
% 289242 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 289243 [] -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8).
% 289269 [] equal(multiply(sk_c5,sk_c6),sk_c7) | equal(inverse(sk_c1),sk_c8).
% 289270 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c5),sk_c7).
% 289271 [] equal(multiply(sk_c4,sk_c7),sk_c8) | equal(inverse(sk_c1),sk_c8).
% 289272 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c4),sk_c8).
% 289273 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(inverse(sk_c1),sk_c8).
% 289274 [?] ?
% 289275 [?] ?
% 289276 [?] ?
% 289277 [?] ?
% 289278 [?] ?
% 289289 [hyper:289243,289270,binarycut:289275] equal(inverse(sk_c5),sk_c7).
% 289290 [para:289289.1.1,289241.1.1.1] equal(multiply(sk_c7,sk_c5),identity).
% 289294 [hyper:289243,289272,binarycut:289277] equal(inverse(sk_c4),sk_c8).
% 289298 [para:289294.1.1,289241.1.1.1] equal(multiply(sk_c8,sk_c4),identity).
% 289308 [hyper:289243,289269,binarycut:289274] equal(multiply(sk_c5,sk_c6),sk_c7).
% 289312 [hyper:289243,289271,binarycut:289276] equal(multiply(sk_c4,sk_c7),sk_c8).
% 289315 [hyper:289243,289273,binarycut:289278] equal(multiply(sk_c7,sk_c8),sk_c6).
% 289316 [para:289241.1.1,289242.1.1.1,demod:289240] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 289317 [para:289290.1.1,289242.1.1.1,demod:289240] equal(X,multiply(sk_c7,multiply(sk_c5,X))).
% 289318 [para:289298.1.1,289242.1.1.1,demod:289240] equal(X,multiply(sk_c8,multiply(sk_c4,X))).
% 289319 [para:289308.1.1,289242.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c5,multiply(sk_c6,X))).
% 289320 [para:289312.1.1,289242.1.1.1] equal(multiply(sk_c8,X),multiply(sk_c4,multiply(sk_c7,X))).
% 289323 [para:289241.1.1,289316.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 289324 [para:289290.1.1,289316.1.2.2] equal(sk_c5,multiply(inverse(sk_c7),identity)).
% 289326 [para:289308.1.1,289316.1.2.2,demod:289289] equal(sk_c6,multiply(sk_c7,sk_c7)).
% 289328 [para:289315.1.1,289316.1.2.2] equal(sk_c8,multiply(inverse(sk_c7),sk_c6)).
% 289329 [para:289242.1.1,289316.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 289330 [para:289316.1.2,289316.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 289332 [para:289326.1.2,289316.1.2.2,demod:289328] equal(sk_c7,sk_c8).
% 289333 [para:289332.1.2,289298.1.1.1] equal(multiply(sk_c7,sk_c4),identity).
% 289339 [para:289333.1.1,289242.1.1.1,demod:289240] equal(X,multiply(sk_c7,multiply(sk_c4,X))).
% 289341 [para:289317.1.2,289316.1.2.2] equal(multiply(sk_c5,X),multiply(inverse(sk_c7),X)).
% 289348 [para:289318.1.2,289316.1.2.2] equal(multiply(sk_c4,X),multiply(inverse(sk_c8),X)).
% 289349 [para:289328.1.2,289242.1.1.1,demod:289319,289341] equal(multiply(sk_c8,X),multiply(sk_c7,X)).
% 289350 [para:289339.1.2,289316.1.2.2,demod:289341] equal(multiply(sk_c4,X),multiply(sk_c5,X)).
% 289351 [para:289349.1.1,289316.1.2.2,demod:289349,289320,289348] equal(X,multiply(sk_c7,X)).
% 289354 [para:289351.1.2,289316.1.2.2,demod:289350,289341] equal(X,multiply(sk_c4,X)).
% 289367 [para:289315.1.1,289329.1.2.1.1,demod:289351,289349] equal(X,multiply(inverse(sk_c6),X)).
% 289376 [para:289367.1.2,289241.1.1] equal(sk_c6,identity).
% 289377 [para:289330.1.2,289241.1.1] equal(multiply(X,inverse(X)),identity).
% 289379 [para:289330.1.2,289323.1.2] equal(X,multiply(X,identity)).
% 289382 [para:289376.1.1,289328.1.2.2,demod:289324] equal(sk_c8,sk_c5).
% 289386 [para:289382.1.1,289332.1.2] equal(sk_c7,sk_c5).
% 289395 [para:289386.1.2,289289.1.1.1] equal(inverse(sk_c7),sk_c7).
% 289399 [para:289379.1.2,289323.1.2] equal(X,inverse(inverse(X))).
% 289402 [para:289377.1.1,289329.1.2.2.2,demod:289379] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 289406 [para:289318.1.2,289402.1.2.1.1,demod:289354] equal(inverse(X),multiply(inverse(X),sk_c8)).
% 289413 [para:289406.1.2,289330.1.2,demod:289399] equal(multiply(X,sk_c8),X).
% 289414 [hyper:289243,289413,demod:289395,cut:289332] 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 23
% clause depth limited to 4
% seconds given: 4
%
%
% Split component 6 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(Y,sk_c7),sk_c6) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c6,sk_c8),sk_c7) | -equal(multiply(Z,sk_c6),sk_c8) | -equal(inverse(Z),sk_c6) | -equal(multiply(sk_c7,sk_c8),sk_c6) | -equal(inverse(U),sk_c8) | -equal(multiply(U,sk_c7),sk_c8) | -equal(inverse(V),sk_c7) | -equal(multiply(V,sk_c6),sk_c7).
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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(40,40,0,86,0,0,793,50,7,839,0,7,1561,50,15,1607,0,15,2334,50,25,2380,0,25,3113,50,31,3159,0,31,3899,50,40,3945,0,40,4693,50,55,4739,0,55,5495,50,82,5541,0,82,6307,50,137,6353,0,137,7129,50,254,7175,0,254,7963,50,450,8009,0,450,8809,50,819,8809,40,819,8855,0,819,19252,3,1120,19959,4,1270,20638,1,1420,20638,50,1420,20638,40,1420,20684,0,1420,20861,3,1730,20869,4,1874,20877,5,2021,20877,1,2021,20877,50,2021,20877,40,2021,20923,0,2021,45949,3,3522,47046,4,4272,48038,5,5022,48039,1,5022,48039,50,5023,48039,40,5023,48085,0,5023,64432,3,5775,65273,4,6149,66044,5,6524,66045,1,6524,66045,50,6524,66045,40,6524,66091,0,6524,76645,3,7275,77799,4,7650,79061,5,8025,79062,1,8025,79062,50,8025,79062,40,8025,79108,0,8025,135496,3,11929,136794,4,13876,137983,1,15826,137983,50,15828,137983,40,15828,138029,0,15828,183492,3,18379,184665,4,19654,185456,1,20929,185456,50,20931,185456,40,20931,185502,0,20931,226694,3,22434,227360,4,23182,228206,5,23932,228207,1,23932,228207,50,23934,228207,40,23934,228253,0,23934,237533,3,24688,238580,4,25064,238639,5,25435,238639,1,25435,238639,50,25435,238639,40,25435,238685,0,25435,266059,3,26636,266979,4,27236,267486,1,27836,267486,50,27837,267486,40,27837,267532,0,27837,286980,3,28589,287751,4,28963,288373,5,29338,288374,1,29338,288374,50,29338,288374,40,29338,288374,40,29338,288414,0,29339,288536,50,29339,288536,30,29339,288536,40,29339,288576,0,29339,288706,50,29339,288706,30,29339,288706,40,29339,288746,0,29344,288828,50,29345,288868,0,29345,288987,50,29346,288987,30,29346,288987,40,29346,289027,0,29346,289097,50,29347,289097,30,29347,289097,40,29347,289137,0,29352,289238,50,29352,289278,0,29352,289413,50,29353,289413,30,29353,289413,40,29353,289453,0,29358,289562,50,29359,289602,0,29359,289750,50,29361,289790,0,29361,289946,50,29364,289986,0,29369,290150,50,29374,290190,0,29374,290360,50,29383,290400,0,29387,290578,50,29403,290618,0,29403,290804,50,29431,290844,0,29431,291040,50,29493,291080,0,29493,291286,50,29608,291286,40,29608,291326,0,29608)
%
%
% START OF PROOF
% 291287 [] equal(X,X).
% 291288 [] equal(multiply(identity,X),X).
% 291289 [] equal(multiply(inverse(X),X),identity).
% 291290 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 291291 [] -equal(multiply(sk_c6,sk_c8),sk_c7).
% 291302 [?] ?
% 291303 [?] ?
% 291304 [?] ?
% 291305 [?] ?
% 291306 [?] ?
% 291355 [input:291303,cut:291291] equal(inverse(sk_c5),sk_c7).
% 291356 [para:291355.1.1,291289.1.1.1] equal(multiply(sk_c7,sk_c5),identity).
% 291358 [input:291305,cut:291291] equal(inverse(sk_c4),sk_c8).
% 291359 [para:291358.1.1,291289.1.1.1] equal(multiply(sk_c8,sk_c4),identity).
% 291380 [input:291302,cut:291291] equal(multiply(sk_c5,sk_c6),sk_c7).
% 291382 [input:291304,cut:291291] equal(multiply(sk_c4,sk_c7),sk_c8).
% 291384 [input:291306,cut:291291] equal(multiply(sk_c7,sk_c8),sk_c6).
% 291393 [para:291289.1.1,291290.1.1.1,demod:291288] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 291399 [para:291356.1.1,291290.1.1.1,demod:291288] equal(X,multiply(sk_c7,multiply(sk_c5,X))).
% 291402 [para:291359.1.1,291290.1.1.1,demod:291288] equal(X,multiply(sk_c8,multiply(sk_c4,X))).
% 291436 [para:291380.1.1,291399.1.2.2] equal(sk_c6,multiply(sk_c7,sk_c7)).
% 291442 [para:291382.1.1,291402.1.2.2] equal(sk_c7,multiply(sk_c8,sk_c8)).
% 291484 [para:291384.1.1,291393.1.2.2] equal(sk_c8,multiply(inverse(sk_c7),sk_c6)).
% 291495 [para:291436.1.2,291393.1.2.2,demod:291484] equal(sk_c7,sk_c8).
% 291510 [para:291495.1.2,291442.1.2.1] equal(sk_c7,multiply(sk_c7,sk_c8)).
% 291534 [para:291510.1.2,291384.1.1] equal(sk_c7,sk_c6).
% 291537 [para:291534.1.2,291291.1.1.1,demod:291510,cut:291287] 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(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(Y,sk_c7),sk_c6) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c6,sk_c8),sk_c7) | -equal(multiply(Z,sk_c6),sk_c8) | -equal(inverse(Z),sk_c6) | -equal(multiply(sk_c7,sk_c8),sk_c6) | -equal(inverse(U),sk_c8) | -equal(multiply(U,sk_c7),sk_c8) | -equal(inverse(V),sk_c7) | -equal(multiply(V,sk_c6),sk_c7).
% Split part used next: -equal(multiply(sk_c7,sk_c8),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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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(40,40,0,86,0,0,793,50,7,839,0,7,1561,50,15,1607,0,15,2334,50,25,2380,0,25,3113,50,31,3159,0,31,3899,50,40,3945,0,40,4693,50,55,4739,0,55,5495,50,82,5541,0,82,6307,50,137,6353,0,137,7129,50,254,7175,0,254,7963,50,450,8009,0,450,8809,50,819,8809,40,819,8855,0,819,19252,3,1120,19959,4,1270,20638,1,1420,20638,50,1420,20638,40,1420,20684,0,1420,20861,3,1730,20869,4,1874,20877,5,2021,20877,1,2021,20877,50,2021,20877,40,2021,20923,0,2021,45949,3,3522,47046,4,4272,48038,5,5022,48039,1,5022,48039,50,5023,48039,40,5023,48085,0,5023,64432,3,5775,65273,4,6149,66044,5,6524,66045,1,6524,66045,50,6524,66045,40,6524,66091,0,6524,76645,3,7275,77799,4,7650,79061,5,8025,79062,1,8025,79062,50,8025,79062,40,8025,79108,0,8025,135496,3,11929,136794,4,13876,137983,1,15826,137983,50,15828,137983,40,15828,138029,0,15828,183492,3,18379,184665,4,19654,185456,1,20929,185456,50,20931,185456,40,20931,185502,0,20931,226694,3,22434,227360,4,23182,228206,5,23932,228207,1,23932,228207,50,23934,228207,40,23934,228253,0,23934,237533,3,24688,238580,4,25064,238639,5,25435,238639,1,25435,238639,50,25435,238639,40,25435,238685,0,25435,266059,3,26636,266979,4,27236,267486,1,27836,267486,50,27837,267486,40,27837,267532,0,27837,286980,3,28589,287751,4,28963,288373,5,29338,288374,1,29338,288374,50,29338,288374,40,29338,288374,40,29338,288414,0,29339,288536,50,29339,288536,30,29339,288536,40,29339,288576,0,29339,288706,50,29339,288706,30,29339,288706,40,29339,288746,0,29344,288828,50,29345,288868,0,29345,288987,50,29346,288987,30,29346,288987,40,29346,289027,0,29346,289097,50,29347,289097,30,29347,289097,40,29347,289137,0,29352,289238,50,29352,289278,0,29352,289413,50,29353,289413,30,29353,289413,40,29353,289453,0,29358,289562,50,29359,289602,0,29359,289750,50,29361,289790,0,29361,289946,50,29364,289986,0,29369,290150,50,29374,290190,0,29374,290360,50,29383,290400,0,29387,290578,50,29403,290618,0,29403,290804,50,29431,290844,0,29431,291040,50,29493,291080,0,29493,291286,50,29608,291286,40,29608,291326,0,29608,291536,50,29610,291536,30,29610,291536,40,29610,291576,0,29610,291701,50,29610,291741,0,29615,291919,50,29618,291959,0,29618,292145,50,29623,292185,0,29623,292379,50,29629,292419,0,29634,292619,50,29643,292659,0,29643,292867,50,29659,292907,0,29664,293123,50,29694,293163,0,29694,293389,50,29760,293429,0,29760,293665,50,29880,293665,40,29880,293705,0,29880)
%
%
% START OF PROOF
% 293481 [?] ?
% 293667 [] equal(multiply(identity,X),X).
% 293668 [] equal(multiply(inverse(X),X),identity).
% 293669 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 293670 [] -equal(multiply(sk_c7,sk_c8),sk_c6).
% 293675 [?] ?
% 293680 [?] ?
% 293685 [?] ?
% 293728 [input:293675,cut:293670] equal(inverse(sk_c3),sk_c6).
% 293729 [para:293728.1.1,293668.1.1.1] equal(multiply(sk_c6,sk_c3),identity).
% 293756 [input:293680,cut:293670] equal(multiply(sk_c3,sk_c6),sk_c8).
% 293766 [input:293685,cut:293670] equal(multiply(sk_c6,sk_c8),sk_c7).
% 293782 [para:293729.1.1,293669.1.1.1,demod:293667] equal(X,multiply(sk_c6,multiply(sk_c3,X))).
% 293830 [para:293756.1.1,293782.1.2.2] equal(sk_c6,multiply(sk_c6,sk_c8)).
% 293835 [para:293830.1.2,293766.1.1] equal(sk_c6,sk_c7).
% 293837 [para:293835.1.1,293670.1.2,cut:293481] 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: 37378
% derived clauses: 6253007
% kept clauses: 246885
% kept size sum: 257835
% kept mid-nuclei: 4631
% kept new demods: 4426
% forw unit-subs: 2644210
% forw double-subs: 3046571
% forw overdouble-subs: 269410
% backward subs: 11051
% fast unit cutoff: 23146
% full unit cutoff: 0
% dbl unit cutoff: 6779
% real runtime : 299.46
% process. runtime: 298.81
% specific non-discr-tree subsumption statistics:
% tried: 37728384
% length fails: 5372282
% strength fails: 9836426
% predlist fails: 1738602
% aux str. fails: 6079617
% by-lit fails: 7572748
% full subs tried: 1587360
% full subs fail: 1494437
%
% ; 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/GRP259-1+eq_r.in")
%
%------------------------------------------------------------------------------