TSTP Solution File: GRP325-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP325-1 : 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/GRP325-1+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(sk_c9,sk_c10),sk_c8) | -equal(multiply(X,sk_c9),sk_c10) | -equal(inverse(X),sk_c9) | -equal(multiply(sk_c10,Y),sk_c9) | -equal(multiply(Z,sk_c10),Y) | -equal(inverse(Z),sk_c10) | -equal(multiply(U,sk_c10),sk_c9) | -equal(inverse(U),sk_c10) | -equal(inverse(sk_c9),sk_c8) | -equal(multiply(sk_c10,sk_c8),sk_c9) | -equal(inverse(V),sk_c9) | -equal(multiply(V,sk_c8),sk_c9) | -equal(inverse(W),X1) | -equal(inverse(X1),sk_c10) | -equal(multiply(W,sk_c10),X1).
% was split for some strategies as:
% -equal(inverse(W),X1) | -equal(inverse(X1),sk_c10) | -equal(multiply(W,sk_c10),X1).
% -equal(inverse(V),sk_c9) | -equal(multiply(V,sk_c8),sk_c9).
% -equal(multiply(U,sk_c10),sk_c9) | -equal(inverse(U),sk_c10).
% -equal(multiply(sk_c10,Y),sk_c9) | -equal(multiply(Z,sk_c10),Y) | -equal(inverse(Z),sk_c10).
% -equal(multiply(X,sk_c9),sk_c10) | -equal(inverse(X),sk_c9).
% -equal(multiply(sk_c9,sk_c10),sk_c8).
% -equal(inverse(sk_c9),sk_c8).
% -equal(multiply(sk_c10,sk_c8),sk_c9).
%
% Starting a split proof attempt with 8 components.
%
% Split component 1 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c9,sk_c10),sk_c8) | -equal(multiply(X,sk_c9),sk_c10) | -equal(inverse(X),sk_c9) | -equal(multiply(sk_c10,Y),sk_c9) | -equal(multiply(Z,sk_c10),Y) | -equal(inverse(Z),sk_c10) | -equal(multiply(U,sk_c10),sk_c9) | -equal(inverse(U),sk_c10) | -equal(inverse(sk_c9),sk_c8) | -equal(multiply(sk_c10,sk_c8),sk_c9) | -equal(inverse(V),sk_c9) | -equal(multiply(V,sk_c8),sk_c9) | -equal(inverse(W),X1) | -equal(inverse(X1),sk_c10) | -equal(multiply(W,sk_c10),X1).
% Split part used next: -equal(inverse(W),X1) | -equal(inverse(X1),sk_c10) | -equal(multiply(W,sk_c10),X1).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(51,40,0,108,0,0,296714,5,1501,296714,1,1501,296714,50,1501,296714,40,1501,296771,0,1501,302825,3,1806,304319,4,1952,304645,5,2102,304645,1,2102,304645,50,2102,304645,40,2102,304702,0,2102,307207,3,2406,307285,4,2556,307358,5,2703,307358,1,2703,307358,50,2703,307358,40,2703,307415,0,2703,327418,3,4204,328711,4,4954,329552,1,5704,329552,50,5704,329552,40,5704,329609,0,5704,343960,3,6456,344792,4,6830,345568,1,7205,345568,50,7205,345568,40,7205,345625,0,7205,359144,3,7997,360235,4,8331,361678,5,8706,361679,1,8706,361679,50,8706,361679,40,8706,361736,0,8706,459003,3,12609,459953,4,14557,460777,5,16507,460778,1,16507,460778,50,16510,460778,40,16510,460835,0,16510,525168,3,19080,525828,4,20337,526393,1,21611,526393,50,21614,526393,40,21614,526450,0,21614,590671,3,23118,591159,4,23866,591657,1,24615,591657,50,24617,591657,40,24617,591714,0,24617,604240,3,25375,605568,4,25743,606520,5,26118,606520,1,26118,606520,50,26118,606520,40,26118,606577,0,26118,656713,3,27319,657198,4,27919,657632,1,28519,657632,50,28521,657632,40,28521,657689,0,28521,697497,3,29273,697867,4,29647,698145,1,30022,698145,50,30023,698145,40,30023,698145,40,30023,698196,0,30023)
%
%
% START OF PROOF
% 698147 [] equal(multiply(identity,X),X).
% 698148 [] equal(multiply(inverse(X),X),identity).
% 698149 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 698150 [] -equal(multiply(X,sk_c10),Y) | -equal(inverse(Y),sk_c10) | -equal(inverse(X),Y).
% 698151 [?] ?
% 698152 [] equal(inverse(sk_c2),sk_c10) | equal(inverse(sk_c6),sk_c10).
% 698153 [] equal(inverse(sk_c2),sk_c10) | equal(inverse(sk_c7),sk_c6).
% 698160 [] equal(multiply(sk_c2,sk_c10),sk_c3) | equal(multiply(sk_c7,sk_c10),sk_c6).
% 698161 [] equal(multiply(sk_c2,sk_c10),sk_c3) | equal(inverse(sk_c6),sk_c10).
% 698162 [] equal(multiply(sk_c2,sk_c10),sk_c3) | equal(inverse(sk_c7),sk_c6).
% 698169 [] equal(multiply(sk_c10,sk_c3),sk_c9) | equal(multiply(sk_c7,sk_c10),sk_c6).
% 698170 [] equal(multiply(sk_c10,sk_c3),sk_c9) | equal(inverse(sk_c6),sk_c10).
% 698171 [] equal(multiply(sk_c10,sk_c3),sk_c9) | equal(inverse(sk_c7),sk_c6).
% 698178 [?] ?
% 698179 [] equal(inverse(sk_c1),sk_c9) | equal(inverse(sk_c6),sk_c10).
% 698180 [] equal(inverse(sk_c1),sk_c9) | equal(inverse(sk_c7),sk_c6).
% 698187 [] equal(multiply(sk_c1,sk_c9),sk_c10) | equal(multiply(sk_c7,sk_c10),sk_c6).
% 698188 [] equal(multiply(sk_c1,sk_c9),sk_c10) | equal(inverse(sk_c6),sk_c10).
% 698189 [] equal(multiply(sk_c1,sk_c9),sk_c10) | equal(inverse(sk_c7),sk_c6).
% 698196 [] equal(multiply(sk_c9,sk_c10),sk_c8).
% 698222 [hyper:698150,698153,698152,binarycut:698151] equal(inverse(sk_c2),sk_c10).
% 698227 [para:698222.1.1,698148.1.1.1] equal(multiply(sk_c10,sk_c2),identity).
% 698248 [hyper:698150,698180,698179,binarycut:698178] equal(inverse(sk_c1),sk_c9).
% 698251 [para:698248.1.1,698148.1.1.1] equal(multiply(sk_c9,sk_c1),identity).
% 698267 [hyper:698150,698162,698160,698161] equal(multiply(sk_c2,sk_c10),sk_c3).
% 698285 [hyper:698150,698171,698169,698170] equal(multiply(sk_c10,sk_c3),sk_c9).
% 698300 [hyper:698150,698189,698187,698188] equal(multiply(sk_c1,sk_c9),sk_c10).
% 698301 [para:698196.1.1,698149.1.1.1] equal(multiply(sk_c8,X),multiply(sk_c9,multiply(sk_c10,X))).
% 698302 [para:698148.1.1,698149.1.1.1,demod:698147] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 698303 [para:698227.1.1,698149.1.1.1,demod:698147] equal(X,multiply(sk_c10,multiply(sk_c2,X))).
% 698305 [para:698267.1.1,698149.1.1.1] equal(multiply(sk_c3,X),multiply(sk_c2,multiply(sk_c10,X))).
% 698312 [para:698267.1.1,698303.1.2.2,demod:698285] equal(sk_c10,sk_c9).
% 698317 [para:698303.1.2,698301.1.2.2] equal(multiply(sk_c8,multiply(sk_c2,X)),multiply(sk_c9,X)).
% 698319 [para:698312.1.2,698251.1.1.1] equal(multiply(sk_c10,sk_c1),identity).
% 698320 [para:698312.1.2,698300.1.1.2] equal(multiply(sk_c1,sk_c10),sk_c10).
% 698335 [para:698196.1.1,698302.1.2.2] equal(sk_c10,multiply(inverse(sk_c9),sk_c8)).
% 698338 [para:698227.1.1,698302.1.2.2] equal(sk_c2,multiply(inverse(sk_c10),identity)).
% 698345 [para:698319.1.1,698302.1.2.2,demod:698338] equal(sk_c1,sk_c2).
% 698346 [para:698320.1.1,698302.1.2.2,demod:698196,698248] equal(sk_c10,sk_c8).
% 698353 [para:698345.1.2,698267.1.1.1,demod:698320] equal(sk_c10,sk_c3).
% 698354 [para:698346.1.1,698285.1.1.1] equal(multiply(sk_c8,sk_c3),sk_c9).
% 698355 [para:698346.1.1,698303.1.2.1,demod:698317] equal(X,multiply(sk_c9,X)).
% 698359 [para:698353.1.1,698227.1.1.1] equal(multiply(sk_c3,sk_c2),identity).
% 698362 [para:698353.1.1,698303.1.2.1] equal(X,multiply(sk_c3,multiply(sk_c2,X))).
% 698377 [para:698355.1.2,698301.1.2] equal(multiply(sk_c8,X),multiply(sk_c10,X)).
% 698378 [para:698312.1.2,698355.1.2.1,demod:698377] equal(X,multiply(sk_c8,X)).
% 698385 [para:698303.1.2,698305.1.2.2,demod:698362] equal(X,multiply(sk_c2,X)).
% 698395 [para:698378.1.2,698302.1.2.2] equal(X,multiply(inverse(sk_c8),X)).
% 698408 [para:698354.1.1,698302.1.2.2,demod:698395] equal(sk_c3,sk_c9).
% 698411 [para:698408.1.2,698335.1.2.1.1] equal(sk_c10,multiply(inverse(sk_c3),sk_c8)).
% 698412 [para:698359.1.1,698302.1.2.2] equal(sk_c2,multiply(inverse(sk_c3),identity)).
% 698426 [para:698395.1.2,698148.1.1] equal(sk_c8,identity).
% 698433 [para:698426.1.1,698411.1.2.2,demod:698412] equal(sk_c10,sk_c2).
% 698447 [para:698433.1.1,698267.1.1.2,demod:698385] equal(sk_c2,sk_c3).
% 698455 [para:698447.1.1,698222.1.1.1] equal(inverse(sk_c3),sk_c10).
% 698460 [hyper:698150,698455,698267,demod:698222,cut:698353] 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: 2
%
%
% Split component 2 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c9,sk_c10),sk_c8) | -equal(multiply(X,sk_c9),sk_c10) | -equal(inverse(X),sk_c9) | -equal(multiply(sk_c10,Y),sk_c9) | -equal(multiply(Z,sk_c10),Y) | -equal(inverse(Z),sk_c10) | -equal(multiply(U,sk_c10),sk_c9) | -equal(inverse(U),sk_c10) | -equal(inverse(sk_c9),sk_c8) | -equal(multiply(sk_c10,sk_c8),sk_c9) | -equal(inverse(V),sk_c9) | -equal(multiply(V,sk_c8),sk_c9) | -equal(inverse(W),X1) | -equal(inverse(X1),sk_c10) | -equal(multiply(W,sk_c10),X1).
% Split part used next: -equal(inverse(V),sk_c9) | -equal(multiply(V,sk_c8),sk_c9).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 3
% seconds given: 2
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(51,40,0,108,0,0,296714,5,1501,296714,1,1501,296714,50,1501,296714,40,1501,296771,0,1501,302825,3,1806,304319,4,1952,304645,5,2102,304645,1,2102,304645,50,2102,304645,40,2102,304702,0,2102,307207,3,2406,307285,4,2556,307358,5,2703,307358,1,2703,307358,50,2703,307358,40,2703,307415,0,2703,327418,3,4204,328711,4,4954,329552,1,5704,329552,50,5704,329552,40,5704,329609,0,5704,343960,3,6456,344792,4,6830,345568,1,7205,345568,50,7205,345568,40,7205,345625,0,7205,359144,3,7997,360235,4,8331,361678,5,8706,361679,1,8706,361679,50,8706,361679,40,8706,361736,0,8706,459003,3,12609,459953,4,14557,460777,5,16507,460778,1,16507,460778,50,16510,460778,40,16510,460835,0,16510,525168,3,19080,525828,4,20337,526393,1,21611,526393,50,21614,526393,40,21614,526450,0,21614,590671,3,23118,591159,4,23866,591657,1,24615,591657,50,24617,591657,40,24617,591714,0,24617,604240,3,25375,605568,4,25743,606520,5,26118,606520,1,26118,606520,50,26118,606520,40,26118,606577,0,26118,656713,3,27319,657198,4,27919,657632,1,28519,657632,50,28521,657632,40,28521,657689,0,28521,697497,3,29273,697867,4,29647,698145,1,30022,698145,50,30023,698145,40,30023,698145,40,30023,698196,0,30023,698459,50,30024,698459,30,30024,698459,40,30024,698510,0,30024)
%
%
% START OF PROOF
% 698461 [] equal(multiply(identity,X),X).
% 698462 [] equal(multiply(inverse(X),X),identity).
% 698463 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 698464 [] -equal(multiply(X,sk_c8),sk_c9) | -equal(inverse(X),sk_c9).
% 698468 [?] ?
% 698469 [] equal(inverse(sk_c2),sk_c10) | equal(inverse(sk_c5),sk_c9).
% 698477 [] equal(multiply(sk_c2,sk_c10),sk_c3) | equal(multiply(sk_c5,sk_c8),sk_c9).
% 698478 [] equal(multiply(sk_c2,sk_c10),sk_c3) | equal(inverse(sk_c5),sk_c9).
% 698486 [] equal(multiply(sk_c10,sk_c3),sk_c9) | equal(multiply(sk_c5,sk_c8),sk_c9).
% 698487 [] equal(multiply(sk_c10,sk_c3),sk_c9) | equal(inverse(sk_c5),sk_c9).
% 698495 [?] ?
% 698496 [] equal(inverse(sk_c1),sk_c9) | equal(inverse(sk_c5),sk_c9).
% 698504 [] equal(multiply(sk_c1,sk_c9),sk_c10) | equal(multiply(sk_c5,sk_c8),sk_c9).
% 698505 [] equal(multiply(sk_c1,sk_c9),sk_c10) | equal(inverse(sk_c5),sk_c9).
% 698510 [] equal(multiply(sk_c9,sk_c10),sk_c8).
% 698516 [hyper:698464,698469,binarycut:698468] equal(inverse(sk_c2),sk_c10).
% 698517 [para:698516.1.1,698462.1.1.1] equal(multiply(sk_c10,sk_c2),identity).
% 698528 [hyper:698464,698496,binarycut:698495] equal(inverse(sk_c1),sk_c9).
% 698531 [para:698528.1.1,698462.1.1.1] equal(multiply(sk_c9,sk_c1),identity).
% 698544 [hyper:698464,698477,698478] equal(multiply(sk_c2,sk_c10),sk_c3).
% 698555 [hyper:698464,698486,698487] equal(multiply(sk_c10,sk_c3),sk_c9).
% 698564 [hyper:698464,698504,698505] equal(multiply(sk_c1,sk_c9),sk_c10).
% 698565 [para:698510.1.1,698463.1.1.1] equal(multiply(sk_c8,X),multiply(sk_c9,multiply(sk_c10,X))).
% 698566 [para:698462.1.1,698463.1.1.1,demod:698461] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 698567 [para:698517.1.1,698463.1.1.1,demod:698461] equal(X,multiply(sk_c10,multiply(sk_c2,X))).
% 698568 [para:698531.1.1,698463.1.1.1,demod:698461] equal(X,multiply(sk_c9,multiply(sk_c1,X))).
% 698572 [para:698544.1.1,698567.1.2.2,demod:698555] equal(sk_c10,sk_c9).
% 698575 [para:698567.1.2,698565.1.2.2] equal(multiply(sk_c8,multiply(sk_c2,X)),multiply(sk_c9,X)).
% 698576 [para:698572.1.2,698510.1.1.1] equal(multiply(sk_c10,sk_c10),sk_c8).
% 698578 [para:698572.1.2,698564.1.1.2] equal(multiply(sk_c1,sk_c10),sk_c10).
% 698585 [para:698578.1.1,698568.1.2.2,demod:698510] equal(sk_c10,sk_c8).
% 698591 [para:698567.1.2,698566.1.2.2] equal(multiply(sk_c2,X),multiply(inverse(sk_c10),X)).
% 698593 [para:698576.1.1,698566.1.2.2,demod:698591] equal(sk_c10,multiply(sk_c2,sk_c8)).
% 698601 [para:698585.1.1,698544.1.1.2,demod:698593] equal(sk_c10,sk_c3).
% 698603 [para:698585.1.1,698567.1.2.1,demod:698575] equal(X,multiply(sk_c9,X)).
% 698604 [para:698585.1.1,698576.1.1.2] equal(multiply(sk_c10,sk_c8),sk_c8).
% 698606 [para:698601.1.1,698510.1.1.2,demod:698603] equal(sk_c3,sk_c8).
% 698620 [para:698606.1.1,698555.1.1.2,demod:698604] equal(sk_c8,sk_c9).
% 698622 [para:698603.1.2,698531.1.1] equal(sk_c1,identity).
% 698624 [para:698622.1.1,698528.1.1.1] equal(inverse(identity),sk_c9).
% 698625 [hyper:698464,698624,demod:698461,cut:698620] 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: 2
%
%
% Split component 3 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c9,sk_c10),sk_c8) | -equal(multiply(X,sk_c9),sk_c10) | -equal(inverse(X),sk_c9) | -equal(multiply(sk_c10,Y),sk_c9) | -equal(multiply(Z,sk_c10),Y) | -equal(inverse(Z),sk_c10) | -equal(multiply(U,sk_c10),sk_c9) | -equal(inverse(U),sk_c10) | -equal(inverse(sk_c9),sk_c8) | -equal(multiply(sk_c10,sk_c8),sk_c9) | -equal(inverse(V),sk_c9) | -equal(multiply(V,sk_c8),sk_c9) | -equal(inverse(W),X1) | -equal(inverse(X1),sk_c10) | -equal(multiply(W,sk_c10),X1).
% 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: 2
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(51,40,0,108,0,0,296714,5,1501,296714,1,1501,296714,50,1501,296714,40,1501,296771,0,1501,302825,3,1806,304319,4,1952,304645,5,2102,304645,1,2102,304645,50,2102,304645,40,2102,304702,0,2102,307207,3,2406,307285,4,2556,307358,5,2703,307358,1,2703,307358,50,2703,307358,40,2703,307415,0,2703,327418,3,4204,328711,4,4954,329552,1,5704,329552,50,5704,329552,40,5704,329609,0,5704,343960,3,6456,344792,4,6830,345568,1,7205,345568,50,7205,345568,40,7205,345625,0,7205,359144,3,7997,360235,4,8331,361678,5,8706,361679,1,8706,361679,50,8706,361679,40,8706,361736,0,8706,459003,3,12609,459953,4,14557,460777,5,16507,460778,1,16507,460778,50,16510,460778,40,16510,460835,0,16510,525168,3,19080,525828,4,20337,526393,1,21611,526393,50,21614,526393,40,21614,526450,0,21614,590671,3,23118,591159,4,23866,591657,1,24615,591657,50,24617,591657,40,24617,591714,0,24617,604240,3,25375,605568,4,25743,606520,5,26118,606520,1,26118,606520,50,26118,606520,40,26118,606577,0,26118,656713,3,27319,657198,4,27919,657632,1,28519,657632,50,28521,657632,40,28521,657689,0,28521,697497,3,29273,697867,4,29647,698145,1,30022,698145,50,30023,698145,40,30023,698145,40,30023,698196,0,30023,698459,50,30024,698459,30,30024,698459,40,30024,698510,0,30024,698624,50,30024,698624,30,30024,698624,40,30024,698675,0,30030)
%
%
% START OF PROOF
% 698626 [] equal(multiply(identity,X),X).
% 698627 [] equal(multiply(inverse(X),X),identity).
% 698628 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 698629 [] -equal(multiply(X,sk_c10),sk_c9) | -equal(inverse(X),sk_c10).
% 698637 [] equal(inverse(sk_c2),sk_c10) | equal(inverse(sk_c4),sk_c10).
% 698638 [?] ?
% 698646 [] equal(multiply(sk_c2,sk_c10),sk_c3) | equal(inverse(sk_c4),sk_c10).
% 698647 [] equal(multiply(sk_c2,sk_c10),sk_c3) | equal(multiply(sk_c4,sk_c10),sk_c9).
% 698655 [] equal(multiply(sk_c10,sk_c3),sk_c9) | equal(inverse(sk_c4),sk_c10).
% 698656 [] equal(multiply(sk_c10,sk_c3),sk_c9) | equal(multiply(sk_c4,sk_c10),sk_c9).
% 698664 [] equal(inverse(sk_c1),sk_c9) | equal(inverse(sk_c4),sk_c10).
% 698665 [?] ?
% 698673 [] equal(multiply(sk_c1,sk_c9),sk_c10) | equal(inverse(sk_c4),sk_c10).
% 698674 [] equal(multiply(sk_c1,sk_c9),sk_c10) | equal(multiply(sk_c4,sk_c10),sk_c9).
% 698675 [] equal(multiply(sk_c9,sk_c10),sk_c8).
% 698692 [hyper:698629,698637,binarycut:698638] equal(inverse(sk_c2),sk_c10).
% 698695 [para:698692.1.1,698627.1.1.1] equal(multiply(sk_c10,sk_c2),identity).
% 698706 [hyper:698629,698664,binarycut:698665] equal(inverse(sk_c1),sk_c9).
% 698707 [para:698706.1.1,698627.1.1.1] equal(multiply(sk_c9,sk_c1),identity).
% 698735 [hyper:698629,698647,698646] equal(multiply(sk_c2,sk_c10),sk_c3).
% 698745 [hyper:698629,698656,698655] equal(multiply(sk_c10,sk_c3),sk_c9).
% 698751 [hyper:698629,698674,698673] equal(multiply(sk_c1,sk_c9),sk_c10).
% 698752 [para:698675.1.1,698628.1.1.1] equal(multiply(sk_c8,X),multiply(sk_c9,multiply(sk_c10,X))).
% 698753 [para:698627.1.1,698628.1.1.1,demod:698626] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 698754 [para:698695.1.1,698628.1.1.1,demod:698626] equal(X,multiply(sk_c10,multiply(sk_c2,X))).
% 698755 [para:698707.1.1,698628.1.1.1,demod:698626] equal(X,multiply(sk_c9,multiply(sk_c1,X))).
% 698756 [para:698735.1.1,698628.1.1.1] equal(multiply(sk_c3,X),multiply(sk_c2,multiply(sk_c10,X))).
% 698759 [para:698735.1.1,698754.1.2.2,demod:698745] equal(sk_c10,sk_c9).
% 698762 [para:698754.1.2,698752.1.2.2] equal(multiply(sk_c8,multiply(sk_c2,X)),multiply(sk_c9,X)).
% 698763 [para:698759.1.2,698675.1.1.1] equal(multiply(sk_c10,sk_c10),sk_c8).
% 698764 [para:698759.1.2,698707.1.1.1] equal(multiply(sk_c10,sk_c1),identity).
% 698765 [para:698759.1.2,698751.1.1.2] equal(multiply(sk_c1,sk_c10),sk_c10).
% 698770 [?] ?
% 698771 [para:698751.1.1,698755.1.2.2,demod:698675] equal(sk_c9,sk_c8).
% 698772 [para:698765.1.1,698755.1.2.2,demod:698675] equal(sk_c10,sk_c8).
% 698775 [para:698695.1.1,698753.1.2.2] equal(sk_c2,multiply(inverse(sk_c10),identity)).
% 698777 [para:698745.1.1,698753.1.2.2] equal(sk_c3,multiply(inverse(sk_c10),sk_c9)).
% 698778 [para:698754.1.2,698753.1.2.2] equal(multiply(sk_c2,X),multiply(inverse(sk_c10),X)).
% 698780 [para:698763.1.1,698753.1.2.2,demod:698778] equal(sk_c10,multiply(sk_c2,sk_c8)).
% 698781 [para:698764.1.1,698753.1.2.2,demod:698775] equal(sk_c1,sk_c2).
% 698783 [para:698771.1.1,698675.1.1.1] equal(multiply(sk_c8,sk_c10),sk_c8).
% 698788 [para:698772.1.1,698735.1.1.2,demod:698780] equal(sk_c10,sk_c3).
% 698790 [para:698772.1.1,698754.1.2.1,demod:698762] equal(X,multiply(sk_c9,X)).
% 698791 [para:698772.1.1,698763.1.1.2] equal(multiply(sk_c10,sk_c8),sk_c8).
% 698792 [para:698781.1.2,698692.1.1.1,demod:698706] equal(sk_c9,sk_c10).
% 698793 [para:698788.1.1,698675.1.1.2,demod:698790] equal(sk_c3,sk_c8).
% 698797 [para:698788.1.1,698754.1.2.1] equal(X,multiply(sk_c3,multiply(sk_c2,X))).
% 698798 [para:698788.1.1,698752.1.2.2.1,demod:698790] equal(multiply(sk_c8,X),multiply(sk_c3,X)).
% 698801 [para:698771.1.1,698792.1.1] equal(sk_c8,sk_c10).
% 698802 [?] ?
% 698805 [para:698754.1.2,698756.1.2.2,demod:698797] equal(X,multiply(sk_c2,X)).
% 698806 [para:698781.1.2,698756.1.2.1,demod:698770,698798] equal(multiply(sk_c8,X),multiply(sk_c10,X)).
% 698807 [para:698793.1.1,698745.1.1.2,demod:698791] equal(sk_c8,sk_c9).
% 698808 [para:698801.1.2,698754.1.2.1,demod:698805] equal(X,multiply(sk_c8,X)).
% 698812 [para:698808.1.2,698753.1.2.2] equal(X,multiply(inverse(sk_c8),X)).
% 698820 [para:698812.1.2,698627.1.1] equal(sk_c8,identity).
% 698821 [para:698820.1.1,698780.1.2.2,demod:698802] equal(sk_c10,identity).
% 698824 [para:698821.1.1,698735.1.1.2,demod:698802] equal(identity,sk_c3).
% 698826 [para:698824.1.2,698745.1.1.2,demod:698808,698806] equal(identity,sk_c9).
% 698837 [para:698826.1.2,698777.1.2.2,demod:698775] equal(sk_c3,sk_c2).
% 698839 [para:698837.1.2,698692.1.1.1] equal(inverse(sk_c3),sk_c10).
% 698840 [hyper:698629,698839,demod:698783,698798,cut:698807] 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: 2
%
%
% Split component 4 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c9,sk_c10),sk_c8) | -equal(multiply(X,sk_c9),sk_c10) | -equal(inverse(X),sk_c9) | -equal(multiply(sk_c10,Y),sk_c9) | -equal(multiply(Z,sk_c10),Y) | -equal(inverse(Z),sk_c10) | -equal(multiply(U,sk_c10),sk_c9) | -equal(inverse(U),sk_c10) | -equal(inverse(sk_c9),sk_c8) | -equal(multiply(sk_c10,sk_c8),sk_c9) | -equal(inverse(V),sk_c9) | -equal(multiply(V,sk_c8),sk_c9) | -equal(inverse(W),X1) | -equal(inverse(X1),sk_c10) | -equal(multiply(W,sk_c10),X1).
% Split part used next: -equal(multiply(sk_c10,Y),sk_c9) | -equal(multiply(Z,sk_c10),Y) | -equal(inverse(Z),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: 2
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(51,40,0,108,0,0,296714,5,1501,296714,1,1501,296714,50,1501,296714,40,1501,296771,0,1501,302825,3,1806,304319,4,1952,304645,5,2102,304645,1,2102,304645,50,2102,304645,40,2102,304702,0,2102,307207,3,2406,307285,4,2556,307358,5,2703,307358,1,2703,307358,50,2703,307358,40,2703,307415,0,2703,327418,3,4204,328711,4,4954,329552,1,5704,329552,50,5704,329552,40,5704,329609,0,5704,343960,3,6456,344792,4,6830,345568,1,7205,345568,50,7205,345568,40,7205,345625,0,7205,359144,3,7997,360235,4,8331,361678,5,8706,361679,1,8706,361679,50,8706,361679,40,8706,361736,0,8706,459003,3,12609,459953,4,14557,460777,5,16507,460778,1,16507,460778,50,16510,460778,40,16510,460835,0,16510,525168,3,19080,525828,4,20337,526393,1,21611,526393,50,21614,526393,40,21614,526450,0,21614,590671,3,23118,591159,4,23866,591657,1,24615,591657,50,24617,591657,40,24617,591714,0,24617,604240,3,25375,605568,4,25743,606520,5,26118,606520,1,26118,606520,50,26118,606520,40,26118,606577,0,26118,656713,3,27319,657198,4,27919,657632,1,28519,657632,50,28521,657632,40,28521,657689,0,28521,697497,3,29273,697867,4,29647,698145,1,30022,698145,50,30023,698145,40,30023,698145,40,30023,698196,0,30023,698459,50,30024,698459,30,30024,698459,40,30024,698510,0,30024,698624,50,30024,698624,30,30024,698624,40,30024,698675,0,30030,698839,50,30031,698839,30,30031,698839,40,30031,698890,0,30031)
%
%
% START OF PROOF
% 698840 [] equal(X,X).
% 698841 [] equal(multiply(identity,X),X).
% 698842 [] equal(multiply(inverse(X),X),identity).
% 698843 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 698844 [] -equal(multiply(sk_c10,X),sk_c9) | -equal(multiply(Y,sk_c10),X) | -equal(inverse(Y),sk_c10).
% 698845 [] equal(multiply(sk_c7,sk_c10),sk_c6) | equal(inverse(sk_c2),sk_c10).
% 698846 [] equal(inverse(sk_c2),sk_c10) | equal(inverse(sk_c6),sk_c10).
% 698847 [] equal(inverse(sk_c2),sk_c10) | equal(inverse(sk_c7),sk_c6).
% 698848 [] equal(multiply(sk_c5,sk_c8),sk_c9) | equal(inverse(sk_c2),sk_c10).
% 698849 [] equal(inverse(sk_c2),sk_c10) | equal(inverse(sk_c5),sk_c9).
% 698850 [] equal(multiply(sk_c10,sk_c8),sk_c9) | equal(inverse(sk_c2),sk_c10).
% 698851 [] equal(inverse(sk_c2),sk_c10) | equal(inverse(sk_c9),sk_c8).
% 698852 [] equal(inverse(sk_c2),sk_c10) | equal(inverse(sk_c4),sk_c10).
% 698853 [] equal(multiply(sk_c4,sk_c10),sk_c9) | equal(inverse(sk_c2),sk_c10).
% 698854 [] equal(multiply(sk_c2,sk_c10),sk_c3) | equal(multiply(sk_c7,sk_c10),sk_c6).
% 698855 [] equal(multiply(sk_c2,sk_c10),sk_c3) | equal(inverse(sk_c6),sk_c10).
% 698856 [] equal(multiply(sk_c2,sk_c10),sk_c3) | equal(inverse(sk_c7),sk_c6).
% 698857 [] equal(multiply(sk_c2,sk_c10),sk_c3) | equal(multiply(sk_c5,sk_c8),sk_c9).
% 698858 [] equal(multiply(sk_c2,sk_c10),sk_c3) | equal(inverse(sk_c5),sk_c9).
% 698859 [] equal(multiply(sk_c2,sk_c10),sk_c3) | equal(multiply(sk_c10,sk_c8),sk_c9).
% 698860 [] equal(multiply(sk_c2,sk_c10),sk_c3) | equal(inverse(sk_c9),sk_c8).
% 698861 [] equal(multiply(sk_c2,sk_c10),sk_c3) | equal(inverse(sk_c4),sk_c10).
% 698862 [] equal(multiply(sk_c2,sk_c10),sk_c3) | equal(multiply(sk_c4,sk_c10),sk_c9).
% 698863 [?] ?
% 698864 [?] ?
% 698865 [?] ?
% 698866 [?] ?
% 698867 [?] ?
% 698868 [?] ?
% 698869 [?] ?
% 698870 [?] ?
% 698871 [?] ?
% 698890 [] equal(multiply(sk_c9,sk_c10),sk_c8).
% 698970 [hyper:698844,698855,binarycut:698864,binarycut:698846] equal(inverse(sk_c6),sk_c10).
% 698980 [para:698970.1.1,698842.1.1.1] equal(multiply(sk_c10,sk_c6),identity).
% 698986 [hyper:698844,698856,binarycut:698865,binarycut:698847] equal(inverse(sk_c7),sk_c6).
% 698993 [hyper:698844,698854,698845,binarycut:698863] equal(multiply(sk_c7,sk_c10),sk_c6).
% 698996 [para:698986.1.1,698842.1.1.1] equal(multiply(sk_c6,sk_c7),identity).
% 699001 [hyper:698844,698858,binarycut:698867,binarycut:698849] equal(inverse(sk_c5),sk_c9).
% 699002 [para:699001.1.1,698842.1.1.1] equal(multiply(sk_c9,sk_c5),identity).
% 699008 [hyper:698844,698857,698848,binarycut:698866] equal(multiply(sk_c5,sk_c8),sk_c9).
% 699011 [hyper:698844,698860,binarycut:698869,binarycut:698851] equal(inverse(sk_c9),sk_c8).
% 699012 [para:699011.1.1,698842.1.1.1] equal(multiply(sk_c8,sk_c9),identity).
% 699017 [hyper:698844,698859,698850,binarycut:698868] equal(multiply(sk_c10,sk_c8),sk_c9).
% 699034 [hyper:698844,698861,binarycut:698870,binarycut:698852] equal(inverse(sk_c4),sk_c10).
% 699055 [hyper:698844,698862,698853,binarycut:698871] equal(multiply(sk_c4,sk_c10),sk_c9).
% 699061 [para:698842.1.1,698843.1.1.1,demod:698841] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 699062 [para:698980.1.1,698843.1.1.1,demod:698841] equal(X,multiply(sk_c10,multiply(sk_c6,X))).
% 699065 [para:699002.1.1,698843.1.1.1,demod:698841] equal(X,multiply(sk_c9,multiply(sk_c5,X))).
% 699067 [para:699012.1.1,698843.1.1.1,demod:698841] equal(X,multiply(sk_c8,multiply(sk_c9,X))).
% 699073 [para:698996.1.1,699062.1.2.2] equal(sk_c7,multiply(sk_c10,identity)).
% 699074 [para:699073.1.2,698843.1.1.1,demod:698841] equal(multiply(sk_c7,X),multiply(sk_c10,X)).
% 699081 [para:699008.1.1,699065.1.2.2] equal(sk_c8,multiply(sk_c9,sk_c9)).
% 699084 [para:698890.1.1,699067.1.2.2] equal(sk_c10,multiply(sk_c8,sk_c8)).
% 699087 [para:699065.1.2,699067.1.2.2] equal(multiply(sk_c5,X),multiply(sk_c8,X)).
% 699088 [para:699081.1.2,699067.1.2.2,demod:699084] equal(sk_c9,sk_c10).
% 699089 [para:699088.1.1,698890.1.1.1,demod:698993,699074] equal(sk_c6,sk_c8).
% 699097 [para:699089.1.1,698980.1.1.2,demod:699017] equal(sk_c9,identity).
% 699101 [para:699097.1.1,698890.1.1.1,demod:698841] equal(sk_c10,sk_c8).
% 699104 [para:699097.1.1,699065.1.2.1,demod:698841,699087] equal(X,multiply(sk_c8,X)).
% 699110 [para:699101.1.1,699017.1.1.1,demod:699084] equal(sk_c10,sk_c9).
% 699123 [para:699110.1.2,699065.1.2.1,demod:699074,699104,699087] equal(X,multiply(sk_c7,X)).
% 699146 [hyper:698844,699061,699055,demod:699123,699074,699061,demod:699034,cut:698840] 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: 2
%
%
% Split component 5 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c9,sk_c10),sk_c8) | -equal(multiply(X,sk_c9),sk_c10) | -equal(inverse(X),sk_c9) | -equal(multiply(sk_c10,Y),sk_c9) | -equal(multiply(Z,sk_c10),Y) | -equal(inverse(Z),sk_c10) | -equal(multiply(U,sk_c10),sk_c9) | -equal(inverse(U),sk_c10) | -equal(inverse(sk_c9),sk_c8) | -equal(multiply(sk_c10,sk_c8),sk_c9) | -equal(inverse(V),sk_c9) | -equal(multiply(V,sk_c8),sk_c9) | -equal(inverse(W),X1) | -equal(inverse(X1),sk_c10) | -equal(multiply(W,sk_c10),X1).
% Split part used next: -equal(multiply(X,sk_c9),sk_c10) | -equal(inverse(X),sk_c9).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 3
% seconds given: 2
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 4
% seconds given: 2
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(51,40,0,108,0,0,296714,5,1501,296714,1,1501,296714,50,1501,296714,40,1501,296771,0,1501,302825,3,1806,304319,4,1952,304645,5,2102,304645,1,2102,304645,50,2102,304645,40,2102,304702,0,2102,307207,3,2406,307285,4,2556,307358,5,2703,307358,1,2703,307358,50,2703,307358,40,2703,307415,0,2703,327418,3,4204,328711,4,4954,329552,1,5704,329552,50,5704,329552,40,5704,329609,0,5704,343960,3,6456,344792,4,6830,345568,1,7205,345568,50,7205,345568,40,7205,345625,0,7205,359144,3,7997,360235,4,8331,361678,5,8706,361679,1,8706,361679,50,8706,361679,40,8706,361736,0,8706,459003,3,12609,459953,4,14557,460777,5,16507,460778,1,16507,460778,50,16510,460778,40,16510,460835,0,16510,525168,3,19080,525828,4,20337,526393,1,21611,526393,50,21614,526393,40,21614,526450,0,21614,590671,3,23118,591159,4,23866,591657,1,24615,591657,50,24617,591657,40,24617,591714,0,24617,604240,3,25375,605568,4,25743,606520,5,26118,606520,1,26118,606520,50,26118,606520,40,26118,606577,0,26118,656713,3,27319,657198,4,27919,657632,1,28519,657632,50,28521,657632,40,28521,657689,0,28521,697497,3,29273,697867,4,29647,698145,1,30022,698145,50,30023,698145,40,30023,698145,40,30023,698196,0,30023,698459,50,30024,698459,30,30024,698459,40,30024,698510,0,30024,698624,50,30024,698624,30,30024,698624,40,30024,698675,0,30030,698839,50,30031,698839,30,30031,698839,40,30031,698890,0,30031,699145,50,30031,699145,30,30031,699145,40,30031,699196,0,30031,699353,50,30032,699404,0,30037)
%
%
% START OF PROOF
% 699355 [] equal(multiply(identity,X),X).
% 699356 [] equal(multiply(inverse(X),X),identity).
% 699357 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 699358 [] -equal(multiply(X,sk_c9),sk_c10) | -equal(inverse(X),sk_c9).
% 699387 [] equal(inverse(sk_c1),sk_c9) | equal(inverse(sk_c6),sk_c10).
% 699388 [] equal(inverse(sk_c1),sk_c9) | equal(inverse(sk_c7),sk_c6).
% 699389 [] equal(multiply(sk_c5,sk_c8),sk_c9) | equal(inverse(sk_c1),sk_c9).
% 699390 [] equal(inverse(sk_c1),sk_c9) | equal(inverse(sk_c5),sk_c9).
% 699391 [] equal(multiply(sk_c10,sk_c8),sk_c9) | equal(inverse(sk_c1),sk_c9).
% 699392 [] equal(inverse(sk_c1),sk_c9) | equal(inverse(sk_c9),sk_c8).
% 699396 [?] ?
% 699397 [?] ?
% 699398 [?] ?
% 699399 [?] ?
% 699400 [?] ?
% 699401 [?] ?
% 699404 [] equal(multiply(sk_c9,sk_c10),sk_c8).
% 699415 [hyper:699358,699387,binarycut:699396] equal(inverse(sk_c6),sk_c10).
% 699417 [para:699415.1.1,699356.1.1.1] equal(multiply(sk_c10,sk_c6),identity).
% 699420 [hyper:699358,699388,binarycut:699397] equal(inverse(sk_c7),sk_c6).
% 699421 [para:699420.1.1,699356.1.1.1] equal(multiply(sk_c6,sk_c7),identity).
% 699425 [hyper:699358,699390,binarycut:699399] equal(inverse(sk_c5),sk_c9).
% 699429 [para:699425.1.1,699356.1.1.1] equal(multiply(sk_c9,sk_c5),identity).
% 699433 [hyper:699358,699392,binarycut:699401] equal(inverse(sk_c9),sk_c8).
% 699434 [para:699433.1.1,699356.1.1.1] equal(multiply(sk_c8,sk_c9),identity).
% 699447 [hyper:699358,699389,binarycut:699398] equal(multiply(sk_c5,sk_c8),sk_c9).
% 699450 [hyper:699358,699391,binarycut:699400] equal(multiply(sk_c10,sk_c8),sk_c9).
% 699454 [para:699404.1.1,699357.1.1.1] equal(multiply(sk_c8,X),multiply(sk_c9,multiply(sk_c10,X))).
% 699455 [para:699356.1.1,699357.1.1.1,demod:699355] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 699456 [para:699417.1.1,699357.1.1.1,demod:699355] equal(X,multiply(sk_c10,multiply(sk_c6,X))).
% 699458 [para:699429.1.1,699357.1.1.1,demod:699355] equal(X,multiply(sk_c9,multiply(sk_c5,X))).
% 699459 [para:699434.1.1,699357.1.1.1,demod:699355] equal(X,multiply(sk_c8,multiply(sk_c9,X))).
% 699468 [para:699421.1.1,699456.1.2.2] equal(sk_c7,multiply(sk_c10,identity)).
% 699469 [para:699456.1.2,699454.1.2.2] equal(multiply(sk_c8,multiply(sk_c6,X)),multiply(sk_c9,X)).
% 699470 [para:699468.1.2,699357.1.1.1,demod:699355] equal(multiply(sk_c7,X),multiply(sk_c10,X)).
% 699474 [?] ?
% 699476 [para:699404.1.1,699455.1.2.2,demod:699474,699433] equal(sk_c10,sk_c8).
% 699477 [para:699356.1.1,699455.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 699479 [para:699429.1.1,699455.1.2.2,demod:699433] equal(sk_c5,multiply(sk_c8,identity)).
% 699484 [para:699357.1.1,699455.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 699485 [para:699454.1.2,699455.1.2.2,demod:699433,699470] equal(multiply(sk_c7,X),multiply(sk_c8,multiply(sk_c8,X))).
% 699487 [para:699458.1.2,699455.1.2.2,demod:699433] equal(multiply(sk_c5,X),multiply(sk_c8,X)).
% 699488 [para:699455.1.2,699455.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 699492 [para:699476.1.1,699450.1.1.1,demod:699474] equal(sk_c8,sk_c9).
% 699495 [para:699476.1.1,699456.1.2.1,demod:699469] equal(X,multiply(sk_c9,X)).
% 699496 [para:699476.1.1,699468.1.2.1,demod:699479] equal(sk_c7,sk_c5).
% 699503 [para:699492.1.2,699433.1.1.1] equal(inverse(sk_c8),sk_c8).
% 699504 [para:699492.1.2,699434.1.1.2,demod:699474] equal(sk_c8,identity).
% 699506 [para:699492.1.2,699458.1.2.1,demod:699485,699487] equal(X,multiply(sk_c7,X)).
% 699507 [para:699496.1.1,699420.1.1.1,demod:699425] equal(sk_c9,sk_c6).
% 699512 [para:699504.1.1,699447.1.1.2,demod:699479,699487] equal(sk_c5,sk_c9).
% 699515 [para:699459.1.2,699455.1.2.2,demod:699503,699495] equal(X,multiply(sk_c8,X)).
% 699531 [para:699512.1.2,699507.1.1] equal(sk_c5,sk_c6).
% 699544 [para:699531.1.2,699415.1.1.1,demod:699425] equal(sk_c9,sk_c10).
% 699553 [para:699544.1.1,699433.1.1.1] equal(inverse(sk_c10),sk_c8).
% 699582 [para:699488.1.2,699356.1.1] equal(multiply(X,inverse(X)),identity).
% 699584 [para:699488.1.2,699477.1.2] equal(X,multiply(X,identity)).
% 699585 [para:699584.1.2,699477.1.2] equal(X,inverse(inverse(X))).
% 699586 [para:699582.1.1,699484.1.2.2.2,demod:699584] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 699588 [para:699454.1.2,699586.1.2.1.1,demod:699515,699506,699470] equal(inverse(X),multiply(inverse(X),sk_c9)).
% 699598 [para:699588.1.2,699488.1.2,demod:699585] equal(multiply(X,sk_c9),X).
% 699599 [hyper:699358,699598,demod:699553,cut:699492] 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 4
% seconds given: 2
%
%
% Split component 6 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c9,sk_c10),sk_c8) | -equal(multiply(X,sk_c9),sk_c10) | -equal(inverse(X),sk_c9) | -equal(multiply(sk_c10,Y),sk_c9) | -equal(multiply(Z,sk_c10),Y) | -equal(inverse(Z),sk_c10) | -equal(multiply(U,sk_c10),sk_c9) | -equal(inverse(U),sk_c10) | -equal(inverse(sk_c9),sk_c8) | -equal(multiply(sk_c10,sk_c8),sk_c9) | -equal(inverse(V),sk_c9) | -equal(multiply(V,sk_c8),sk_c9) | -equal(inverse(W),X1) | -equal(inverse(X1),sk_c10) | -equal(multiply(W,sk_c10),X1).
% Split part used next: -equal(multiply(sk_c9,sk_c10),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 29
% clause depth limited to 3
% seconds given: 2
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(51,40,0,108,0,0,296714,5,1501,296714,1,1501,296714,50,1501,296714,40,1501,296771,0,1501,302825,3,1806,304319,4,1952,304645,5,2102,304645,1,2102,304645,50,2102,304645,40,2102,304702,0,2102,307207,3,2406,307285,4,2556,307358,5,2703,307358,1,2703,307358,50,2703,307358,40,2703,307415,0,2703,327418,3,4204,328711,4,4954,329552,1,5704,329552,50,5704,329552,40,5704,329609,0,5704,343960,3,6456,344792,4,6830,345568,1,7205,345568,50,7205,345568,40,7205,345625,0,7205,359144,3,7997,360235,4,8331,361678,5,8706,361679,1,8706,361679,50,8706,361679,40,8706,361736,0,8706,459003,3,12609,459953,4,14557,460777,5,16507,460778,1,16507,460778,50,16510,460778,40,16510,460835,0,16510,525168,3,19080,525828,4,20337,526393,1,21611,526393,50,21614,526393,40,21614,526450,0,21614,590671,3,23118,591159,4,23866,591657,1,24615,591657,50,24617,591657,40,24617,591714,0,24617,604240,3,25375,605568,4,25743,606520,5,26118,606520,1,26118,606520,50,26118,606520,40,26118,606577,0,26118,656713,3,27319,657198,4,27919,657632,1,28519,657632,50,28521,657632,40,28521,657689,0,28521,697497,3,29273,697867,4,29647,698145,1,30022,698145,50,30023,698145,40,30023,698145,40,30023,698196,0,30023,698459,50,30024,698459,30,30024,698459,40,30024,698510,0,30024,698624,50,30024,698624,30,30024,698624,40,30024,698675,0,30030,698839,50,30031,698839,30,30031,698839,40,30031,698890,0,30031,699145,50,30031,699145,30,30031,699145,40,30031,699196,0,30031,699353,50,30032,699404,0,30037,699598,50,30039,699598,30,30039,699598,40,30039,699649,0,30039)
%
%
% START OF PROOF
% 699603 [] -equal(multiply(sk_c9,sk_c10),sk_c8).
% 699649 [] equal(multiply(sk_c9,sk_c10),sk_c8).
% 699650 [hyper:699603,699649] 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: 2
%
%
% Split component 7 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c9,sk_c10),sk_c8) | -equal(multiply(X,sk_c9),sk_c10) | -equal(inverse(X),sk_c9) | -equal(multiply(sk_c10,Y),sk_c9) | -equal(multiply(Z,sk_c10),Y) | -equal(inverse(Z),sk_c10) | -equal(multiply(U,sk_c10),sk_c9) | -equal(inverse(U),sk_c10) | -equal(inverse(sk_c9),sk_c8) | -equal(multiply(sk_c10,sk_c8),sk_c9) | -equal(inverse(V),sk_c9) | -equal(multiply(V,sk_c8),sk_c9) | -equal(inverse(W),X1) | -equal(inverse(X1),sk_c10) | -equal(multiply(W,sk_c10),X1).
% Split part used next: -equal(inverse(sk_c9),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 29
% clause depth limited to 3
% seconds given: 2
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 4
% seconds given: 2
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 5
% seconds given: 2
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 6
% seconds given: 2
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 7
% seconds given: 2
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 8
% seconds given: 2
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 9
% seconds given: 2
%
%
% proof attempt stopped: sos exhausted
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(51,40,0,108,0,0,296714,5,1501,296714,1,1501,296714,50,1501,296714,40,1501,296771,0,1501,302825,3,1806,304319,4,1952,304645,5,2102,304645,1,2102,304645,50,2102,304645,40,2102,304702,0,2102,307207,3,2406,307285,4,2556,307358,5,2703,307358,1,2703,307358,50,2703,307358,40,2703,307415,0,2703,327418,3,4204,328711,4,4954,329552,1,5704,329552,50,5704,329552,40,5704,329609,0,5704,343960,3,6456,344792,4,6830,345568,1,7205,345568,50,7205,345568,40,7205,345625,0,7205,359144,3,7997,360235,4,8331,361678,5,8706,361679,1,8706,361679,50,8706,361679,40,8706,361736,0,8706,459003,3,12609,459953,4,14557,460777,5,16507,460778,1,16507,460778,50,16510,460778,40,16510,460835,0,16510,525168,3,19080,525828,4,20337,526393,1,21611,526393,50,21614,526393,40,21614,526450,0,21614,590671,3,23118,591159,4,23866,591657,1,24615,591657,50,24617,591657,40,24617,591714,0,24617,604240,3,25375,605568,4,25743,606520,5,26118,606520,1,26118,606520,50,26118,606520,40,26118,606577,0,26118,656713,3,27319,657198,4,27919,657632,1,28519,657632,50,28521,657632,40,28521,657689,0,28521,697497,3,29273,697867,4,29647,698145,1,30022,698145,50,30023,698145,40,30023,698145,40,30023,698196,0,30023,698459,50,30024,698459,30,30024,698459,40,30024,698510,0,30024,698624,50,30024,698624,30,30024,698624,40,30024,698675,0,30030,698839,50,30031,698839,30,30031,698839,40,30031,698890,0,30031,699145,50,30031,699145,30,30031,699145,40,30031,699196,0,30031,699353,50,30032,699404,0,30037,699598,50,30039,699598,30,30039,699598,40,30039,699649,0,30039,699649,50,30039,699649,30,30039,699649,40,30039,699700,0,30044,699847,50,30045,699898,0,30045,700099,50,30049,700150,0,30049,700361,50,30054,700412,0,30059,700635,50,30067,700686,0,30068,700915,50,30080,700966,0,30085,701203,50,30105,701254,0,30105,701500,50,30142,701500,40,30142,701551,0,30142)
%
%
% START OF PROOF
% 701502 [] equal(multiply(identity,X),X).
% 701503 [] equal(multiply(inverse(X),X),identity).
% 701504 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 701505 [] -equal(inverse(sk_c9),sk_c8).
% 701512 [?] ?
% 701521 [?] ?
% 701530 [?] ?
% 701539 [?] ?
% 701548 [?] ?
% 701551 [] equal(multiply(sk_c9,sk_c10),sk_c8).
% 701563 [input:701512,cut:701505] equal(inverse(sk_c2),sk_c10).
% 701564 [para:701563.1.1,701503.1.1.1] equal(multiply(sk_c10,sk_c2),identity).
% 701577 [input:701539,cut:701505] equal(inverse(sk_c1),sk_c9).
% 701578 [para:701577.1.1,701503.1.1.1] equal(multiply(sk_c9,sk_c1),identity).
% 701590 [input:701521,cut:701505] equal(multiply(sk_c2,sk_c10),sk_c3).
% 701600 [input:701530,cut:701505] equal(multiply(sk_c10,sk_c3),sk_c9).
% 701616 [input:701548,cut:701505] equal(multiply(sk_c1,sk_c9),sk_c10).
% 701639 [para:701503.1.1,701504.1.1.1,demod:701502] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 701641 [para:701564.1.1,701504.1.1.1,demod:701502] equal(X,multiply(sk_c10,multiply(sk_c2,X))).
% 701644 [para:701578.1.1,701504.1.1.1,demod:701502] equal(X,multiply(sk_c9,multiply(sk_c1,X))).
% 701656 [para:701600.1.1,701504.1.1.1] equal(multiply(sk_c9,X),multiply(sk_c10,multiply(sk_c3,X))).
% 701691 [para:701590.1.1,701641.1.2.2] equal(sk_c10,multiply(sk_c10,sk_c3)).
% 701695 [para:701691.1.2,701600.1.1] equal(sk_c10,sk_c9).
% 701696 [para:701691.1.2,701504.1.1.1,demod:701656] equal(multiply(sk_c10,X),multiply(sk_c9,X)).
% 701698 [para:701695.1.2,701551.1.1.1] equal(multiply(sk_c10,sk_c10),sk_c8).
% 701699 [para:701695.1.2,701578.1.1.1] equal(multiply(sk_c10,sk_c1),identity).
% 701703 [para:701695.1.2,701616.1.1.2] equal(multiply(sk_c1,sk_c10),sk_c10).
% 701709 [para:701699.1.1,701504.1.1.1,demod:701502] equal(X,multiply(sk_c10,multiply(sk_c1,X))).
% 701715 [para:701616.1.1,701644.1.2.2,demod:701551] equal(sk_c9,sk_c8).
% 701716 [para:701703.1.1,701644.1.2.2,demod:701551] equal(sk_c10,sk_c8).
% 701717 [para:701715.1.1,701505.1.1.1] -equal(inverse(sk_c8),sk_c8).
% 701718 [para:701715.1.1,701551.1.1.1] equal(multiply(sk_c8,sk_c10),sk_c8).
% 701723 [para:701715.1.1,701616.1.1.2] equal(multiply(sk_c1,sk_c8),sk_c10).
% 701739 [para:701716.1.1,701590.1.1.2] equal(multiply(sk_c2,sk_c8),sk_c3).
% 701761 [para:701723.1.1,701504.1.1.1] equal(multiply(sk_c10,X),multiply(sk_c1,multiply(sk_c8,X))).
% 701775 [para:701715.1.1,701696.1.2.1] equal(multiply(sk_c10,X),multiply(sk_c8,X)).
% 701850 [para:701641.1.2,701639.1.2.2] equal(multiply(sk_c2,X),multiply(inverse(sk_c10),X)).
% 701852 [para:701698.1.1,701639.1.2.2,demod:701739,701850] equal(sk_c10,sk_c3).
% 701854 [para:701644.1.2,701639.1.2.2] equal(multiply(sk_c1,X),multiply(inverse(sk_c9),X)).
% 701855 [para:701718.1.1,701639.1.2.2,demod:701503] equal(sk_c10,identity).
% 701862 [para:701696.1.2,701639.1.2.2,demod:701761,701854,701775] equal(X,multiply(sk_c8,X)).
% 701863 [para:701709.1.2,701639.1.2.2,demod:701850] equal(multiply(sk_c1,X),multiply(sk_c2,X)).
% 701866 [para:701775.1.1,701639.1.2.2,demod:701863,701850,701862] equal(X,multiply(sk_c1,X)).
% 701888 [para:701852.1.1,701641.1.2.1,demod:701866,701863] equal(X,multiply(sk_c3,X)).
% 701890 [para:701852.1.1,701699.1.1.1,demod:701888] equal(sk_c1,identity).
% 701900 [para:701855.1.1,701551.1.1.2,demod:701862,701775,701696] equal(identity,sk_c8).
% 701930 [para:701890.1.1,701577.1.1.1] equal(inverse(identity),sk_c9).
% 701944 [para:701900.1.2,701717.1.1.1,demod:701930,cut:701715] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% Split component 8 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c9,sk_c10),sk_c8) | -equal(multiply(X,sk_c9),sk_c10) | -equal(inverse(X),sk_c9) | -equal(multiply(sk_c10,Y),sk_c9) | -equal(multiply(Z,sk_c10),Y) | -equal(inverse(Z),sk_c10) | -equal(multiply(U,sk_c10),sk_c9) | -equal(inverse(U),sk_c10) | -equal(inverse(sk_c9),sk_c8) | -equal(multiply(sk_c10,sk_c8),sk_c9) | -equal(inverse(V),sk_c9) | -equal(multiply(V,sk_c8),sk_c9) | -equal(inverse(W),X1) | -equal(inverse(X1),sk_c10) | -equal(multiply(W,sk_c10),X1).
% Split part used next: -equal(multiply(sk_c10,sk_c8),sk_c9).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 3
% seconds given: 2
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 4
% seconds given: 2
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 5
% seconds given: 2
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 6
% seconds given: 2
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 7
% seconds given: 2
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 8
% seconds given: 2
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 9
% seconds given: 2
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 10
% seconds given: 2
%
%
% proof attempt stopped: sos exhausted
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(51,40,0,108,0,0,296714,5,1501,296714,1,1501,296714,50,1501,296714,40,1501,296771,0,1501,302825,3,1806,304319,4,1952,304645,5,2102,304645,1,2102,304645,50,2102,304645,40,2102,304702,0,2102,307207,3,2406,307285,4,2556,307358,5,2703,307358,1,2703,307358,50,2703,307358,40,2703,307415,0,2703,327418,3,4204,328711,4,4954,329552,1,5704,329552,50,5704,329552,40,5704,329609,0,5704,343960,3,6456,344792,4,6830,345568,1,7205,345568,50,7205,345568,40,7205,345625,0,7205,359144,3,7997,360235,4,8331,361678,5,8706,361679,1,8706,361679,50,8706,361679,40,8706,361736,0,8706,459003,3,12609,459953,4,14557,460777,5,16507,460778,1,16507,460778,50,16510,460778,40,16510,460835,0,16510,525168,3,19080,525828,4,20337,526393,1,21611,526393,50,21614,526393,40,21614,526450,0,21614,590671,3,23118,591159,4,23866,591657,1,24615,591657,50,24617,591657,40,24617,591714,0,24617,604240,3,25375,605568,4,25743,606520,5,26118,606520,1,26118,606520,50,26118,606520,40,26118,606577,0,26118,656713,3,27319,657198,4,27919,657632,1,28519,657632,50,28521,657632,40,28521,657689,0,28521,697497,3,29273,697867,4,29647,698145,1,30022,698145,50,30023,698145,40,30023,698145,40,30023,698196,0,30023,698459,50,30024,698459,30,30024,698459,40,30024,698510,0,30024,698624,50,30024,698624,30,30024,698624,40,30024,698675,0,30030,698839,50,30031,698839,30,30031,698839,40,30031,698890,0,30031,699145,50,30031,699145,30,30031,699145,40,30031,699196,0,30031,699353,50,30032,699404,0,30037,699598,50,30039,699598,30,30039,699598,40,30039,699649,0,30039,699649,50,30039,699649,30,30039,699649,40,30039,699700,0,30044,699847,50,30045,699898,0,30045,700099,50,30049,700150,0,30049,700361,50,30054,700412,0,30059,700635,50,30067,700686,0,30068,700915,50,30080,700966,0,30085,701203,50,30105,701254,0,30105,701500,50,30142,701500,40,30142,701551,0,30142,701943,50,30143,701943,30,30143,701943,40,30143,701994,0,30148,702146,50,30149,702197,0,30149,702395,50,30153,702446,0,30157,702652,50,30162,702703,0,30162,702917,50,30169,702968,0,30169,703188,50,30180,703239,0,30185,703467,50,30203,703518,0,30203,703754,50,30236,703805,0,30240,704051,50,30304,704051,40,30304,704102,0,30304)
%
%
% START OF PROOF
% 704004 [?] ?
% 704053 [] equal(multiply(identity,X),X).
% 704054 [] equal(multiply(inverse(X),X),identity).
% 704055 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 704056 [] -equal(multiply(sk_c10,sk_c8),sk_c9).
% 704062 [?] ?
% 704071 [?] ?
% 704080 [?] ?
% 704137 [input:704062,cut:704056] equal(inverse(sk_c2),sk_c10).
% 704138 [para:704137.1.1,704054.1.1.1] equal(multiply(sk_c10,sk_c2),identity).
% 704168 [input:704071,cut:704056] equal(multiply(sk_c2,sk_c10),sk_c3).
% 704186 [input:704080,cut:704056] equal(multiply(sk_c10,sk_c3),sk_c9).
% 704206 [para:704138.1.1,704055.1.1.1,demod:704053] equal(X,multiply(sk_c10,multiply(sk_c2,X))).
% 704265 [para:704168.1.1,704206.1.2.2] equal(sk_c10,multiply(sk_c10,sk_c3)).
% 704275 [para:704265.1.2,704186.1.1] equal(sk_c10,sk_c9).
% 704277 [para:704275.1.2,704056.1.2,cut:704004] 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: 31243
% derived clauses: 4224463
% kept clauses: 346899
% kept size sum: 609482
% kept mid-nuclei: 296780
% kept new demods: 3950
% forw unit-subs: 1257810
% forw double-subs: 1905094
% forw overdouble-subs: 361176
% backward subs: 14367
% fast unit cutoff: 20746
% full unit cutoff: 0
% dbl unit cutoff: 5872
% real runtime : 305.34
% process. runtime: 303.5
% specific non-discr-tree subsumption statistics:
% tried: 51913148
% length fails: 6517159
% strength fails: 17418603
% predlist fails: 2551424
% aux str. fails: 6286720
% by-lit fails: 7866507
% full subs tried: 3499273
% full subs fail: 3292671
%
% ; 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/GRP325-1+eq_r.in")
%
%------------------------------------------------------------------------------