TSTP Solution File: GRP376-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP376-1 : 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 298.3s
% Output : Assurance 298.3s
% 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/GRP376-1+eq_r.in
% Using automatic strategy selection.
% Time limit in seconds: 600
%
% prove-all-passes started
%
% detected problem class: peq
%
% strategies selected:
% (hyper 30 #f 3 21)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 3 21)
% (binary-posweight-lex-big-order 30 #f 3 21)
% (binary 30 #t)
% (binary-posweight-kb-big-order 156 #f)
% (binary-posweight-lex-big-order 102 #f)
% (binary-posweight-firstpref-order 60 #f)
% (binary-order 30 #f)
% (binary-posweight-kb-small-order 48 #f)
% (binary-posweight-lex-small-order 30 #f)
%
%
% SOS clause
% -equal(inverse(sk_c7),sk_c6) | -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7) | -equal(multiply(sk_c5,sk_c6),sk_c7) | -equal(multiply(Y,sk_c5),sk_c7) | -equal(inverse(Y),sk_c5) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(U),sk_c6) | -equal(multiply(U,sk_c5),sk_c6).
% was split for some strategies as:
% -equal(inverse(U),sk_c6) | -equal(multiply(U,sk_c5),sk_c6).
% -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7).
% -equal(multiply(Y,sk_c5),sk_c7) | -equal(inverse(Y),sk_c5).
% -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7).
% -equal(inverse(sk_c7),sk_c6).
% -equal(multiply(sk_c5,sk_c6),sk_c7).
% -equal(multiply(sk_c6,sk_c7),sk_c5).
%
% 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(inverse(sk_c7),sk_c6) | -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7) | -equal(multiply(sk_c5,sk_c6),sk_c7) | -equal(multiply(Y,sk_c5),sk_c7) | -equal(inverse(Y),sk_c5) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(U),sk_c6) | -equal(multiply(U,sk_c5),sk_c6).
% Split part used next: -equal(inverse(U),sk_c6) | -equal(multiply(U,sk_c5),sk_c6).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,75,0,0,587,50,4,627,0,4,1154,50,8,1194,0,8,1732,50,15,1772,0,15,2317,50,21,2357,0,21,2909,50,29,2949,0,29,3509,50,43,3549,0,43,4118,50,72,4158,0,72,4737,50,132,4777,0,133,5367,50,268,5407,0,268,6009,50,483,6049,0,483,6664,50,904,6664,40,904,6704,0,904,17182,3,1205,17913,4,1355,18613,5,1505,18614,1,1505,18614,50,1505,18614,40,1505,18654,0,1505,18827,3,1814,18835,4,1971,18843,5,2106,18843,1,2106,18843,50,2106,18843,40,2106,18883,0,2106,40704,3,3611,42141,4,4357,43465,1,5107,43465,50,5107,43465,40,5107,43505,0,5107,55441,3,5858,56712,4,6233,58003,5,6608,58004,1,6608,58004,50,6608,58004,40,6608,58044,0,6608,68009,3,7380,69092,4,7734,70334,1,8109,70334,50,8109,70334,40,8109,70374,0,8109,175429,3,12015,176480,4,13961,177424,1,15911,177424,50,15914,177424,40,15914,177464,0,15914,253189,3,18467,253918,4,19740,254521,5,21015,254522,1,21015,254522,50,21017,254522,40,21017,254562,0,21017,289828,3,22519,290801,4,23268,291692,5,24018,291693,1,24018,291693,50,24019,291693,40,24019,291733,0,24019,302321,3,24772,303572,4,25145,304213,5,25520,304213,1,25520,304213,50,25520,304213,40,25520,304253,0,25520,333317,3,26723,334217,4,27321,334764,5,27921,334765,1,27921,334765,50,27922,334765,40,27922,334805,0,27922,356009,3,28674,356738,4,29048,357249,1,29423,357249,50,29423,357249,40,29423,357249,40,29423,357284,0,29423)
%
%
% START OF PROOF
% 357251 [] equal(multiply(identity,X),X).
% 357252 [] equal(multiply(inverse(X),X),identity).
% 357253 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 357254 [] -equal(multiply(X,sk_c5),sk_c6) | -equal(inverse(X),sk_c6).
% 357255 [?] ?
% 357256 [] equal(inverse(sk_c2),sk_c5) | equal(inverse(sk_c4),sk_c6).
% 357260 [] equal(multiply(sk_c2,sk_c5),sk_c7) | equal(multiply(sk_c4,sk_c5),sk_c6).
% 357261 [] equal(multiply(sk_c2,sk_c5),sk_c7) | equal(inverse(sk_c4),sk_c6).
% 357265 [] equal(multiply(sk_c5,sk_c6),sk_c7) | equal(multiply(sk_c4,sk_c5),sk_c6).
% 357266 [] equal(multiply(sk_c5,sk_c6),sk_c7) | equal(inverse(sk_c4),sk_c6).
% 357270 [?] ?
% 357271 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c4),sk_c6).
% 357275 [] equal(multiply(sk_c1,sk_c7),sk_c6) | equal(multiply(sk_c4,sk_c5),sk_c6).
% 357276 [] equal(multiply(sk_c1,sk_c7),sk_c6) | equal(inverse(sk_c4),sk_c6).
% 357280 [?] ?
% 357281 [] equal(inverse(sk_c7),sk_c6) | equal(inverse(sk_c4),sk_c6).
% 357287 [hyper:357254,357256,binarycut:357255] equal(inverse(sk_c2),sk_c5).
% 357288 [para:357287.1.1,357252.1.1.1] equal(multiply(sk_c5,sk_c2),identity).
% 357295 [hyper:357254,357271,binarycut:357270] equal(inverse(sk_c1),sk_c7).
% 357296 [para:357295.1.1,357252.1.1.1] equal(multiply(sk_c7,sk_c1),identity).
% 357300 [hyper:357254,357281,binarycut:357280] equal(inverse(sk_c7),sk_c6).
% 357303 [para:357300.1.1,357252.1.1.1] equal(multiply(sk_c6,sk_c7),identity).
% 357307 [hyper:357254,357261,357260] equal(multiply(sk_c2,sk_c5),sk_c7).
% 357313 [hyper:357254,357266,357265] equal(multiply(sk_c5,sk_c6),sk_c7).
% 357320 [hyper:357254,357275,357276] equal(multiply(sk_c1,sk_c7),sk_c6).
% 357321 [para:357252.1.1,357253.1.1.1,demod:357251] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 357322 [para:357288.1.1,357253.1.1.1,demod:357251] equal(X,multiply(sk_c5,multiply(sk_c2,X))).
% 357323 [para:357296.1.1,357253.1.1.1,demod:357251] equal(X,multiply(sk_c7,multiply(sk_c1,X))).
% 357328 [para:357307.1.1,357322.1.2.2] equal(sk_c5,multiply(sk_c5,sk_c7)).
% 357330 [para:357320.1.1,357323.1.2.2] equal(sk_c7,multiply(sk_c7,sk_c6)).
% 357339 [para:357330.1.2,357321.1.2.2,demod:357303,357300] equal(sk_c6,identity).
% 357340 [para:357339.1.1,357303.1.1.1,demod:357251] equal(sk_c7,identity).
% 357341 [para:357339.1.1,357313.1.1.2] equal(multiply(sk_c5,identity),sk_c7).
% 357343 [para:357340.1.1,357300.1.1.1] equal(inverse(identity),sk_c6).
% 357345 [para:357340.1.1,357328.1.2.2,demod:357341] equal(sk_c5,sk_c7).
% 357346 [para:357340.1.1,357323.1.2.1,demod:357251] equal(X,multiply(sk_c1,X)).
% 357352 [para:357345.1.2,357320.1.1.2,demod:357346] equal(sk_c5,sk_c6).
% 357378 [hyper:357254,357343,demod:357251,cut:357352] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 2 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c7),sk_c6) | -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7) | -equal(multiply(sk_c5,sk_c6),sk_c7) | -equal(multiply(Y,sk_c5),sk_c7) | -equal(inverse(Y),sk_c5) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(U),sk_c6) | -equal(multiply(U,sk_c5),sk_c6).
% Split part used next: -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 3
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 4
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,75,0,0,587,50,4,627,0,4,1154,50,8,1194,0,8,1732,50,15,1772,0,15,2317,50,21,2357,0,21,2909,50,29,2949,0,29,3509,50,43,3549,0,43,4118,50,72,4158,0,72,4737,50,132,4777,0,133,5367,50,268,5407,0,268,6009,50,483,6049,0,483,6664,50,904,6664,40,904,6704,0,904,17182,3,1205,17913,4,1355,18613,5,1505,18614,1,1505,18614,50,1505,18614,40,1505,18654,0,1505,18827,3,1814,18835,4,1971,18843,5,2106,18843,1,2106,18843,50,2106,18843,40,2106,18883,0,2106,40704,3,3611,42141,4,4357,43465,1,5107,43465,50,5107,43465,40,5107,43505,0,5107,55441,3,5858,56712,4,6233,58003,5,6608,58004,1,6608,58004,50,6608,58004,40,6608,58044,0,6608,68009,3,7380,69092,4,7734,70334,1,8109,70334,50,8109,70334,40,8109,70374,0,8109,175429,3,12015,176480,4,13961,177424,1,15911,177424,50,15914,177424,40,15914,177464,0,15914,253189,3,18467,253918,4,19740,254521,5,21015,254522,1,21015,254522,50,21017,254522,40,21017,254562,0,21017,289828,3,22519,290801,4,23268,291692,5,24018,291693,1,24018,291693,50,24019,291693,40,24019,291733,0,24019,302321,3,24772,303572,4,25145,304213,5,25520,304213,1,25520,304213,50,25520,304213,40,25520,304253,0,25520,333317,3,26723,334217,4,27321,334764,5,27921,334765,1,27921,334765,50,27922,334765,40,27922,334805,0,27922,356009,3,28674,356738,4,29048,357249,1,29423,357249,50,29423,357249,40,29423,357249,40,29423,357284,0,29423,357377,50,29423,357377,30,29423,357377,40,29423,357412,0,29423,357528,50,29424,357563,0,29429)
%
%
% START OF PROOF
% 357530 [] equal(multiply(identity,X),X).
% 357531 [] equal(multiply(inverse(X),X),identity).
% 357532 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 357533 [] -equal(multiply(X,sk_c6),sk_c7) | -equal(inverse(X),sk_c7).
% 357551 [?] ?
% 357552 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c3),sk_c7).
% 357556 [] equal(multiply(sk_c1,sk_c7),sk_c6) | equal(multiply(sk_c3,sk_c6),sk_c7).
% 357557 [] equal(multiply(sk_c1,sk_c7),sk_c6) | equal(inverse(sk_c3),sk_c7).
% 357561 [?] ?
% 357562 [] equal(inverse(sk_c7),sk_c6) | equal(inverse(sk_c3),sk_c7).
% 357577 [hyper:357533,357552,binarycut:357551] equal(inverse(sk_c1),sk_c7).
% 357580 [para:357577.1.1,357531.1.1.1] equal(multiply(sk_c7,sk_c1),identity).
% 357586 [hyper:357533,357562,binarycut:357561] equal(inverse(sk_c7),sk_c6).
% 357587 [para:357586.1.1,357531.1.1.1] equal(multiply(sk_c6,sk_c7),identity).
% 357619 [hyper:357533,357556,357557] equal(multiply(sk_c1,sk_c7),sk_c6).
% 357620 [para:357531.1.1,357532.1.1.1,demod:357530] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 357622 [para:357580.1.1,357532.1.1.1,demod:357530] equal(X,multiply(sk_c7,multiply(sk_c1,X))).
% 357629 [para:357619.1.1,357622.1.2.2] equal(sk_c7,multiply(sk_c7,sk_c6)).
% 357631 [para:357531.1.1,357620.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 357636 [para:357532.1.1,357620.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 357639 [para:357620.1.2,357620.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 357641 [para:357629.1.2,357620.1.2.2,demod:357587,357586] equal(sk_c6,identity).
% 357642 [para:357641.1.1,357587.1.1.1,demod:357530] equal(sk_c7,identity).
% 357644 [para:357642.1.1,357580.1.1.1,demod:357530] equal(sk_c1,identity).
% 357645 [para:357642.1.1,357586.1.1.1] equal(inverse(identity),sk_c6).
% 357648 [para:357642.1.1,357622.1.2.1,demod:357530] equal(X,multiply(sk_c1,X)).
% 357649 [para:357642.1.1,357629.1.2.1,demod:357530] equal(sk_c7,sk_c6).
% 357650 [para:357644.1.1,357577.1.1.1,demod:357645] equal(sk_c6,sk_c7).
% 357683 [para:357639.1.2,357531.1.1] equal(multiply(X,inverse(X)),identity).
% 357685 [para:357639.1.2,357631.1.2] equal(X,multiply(X,identity)).
% 357686 [para:357685.1.2,357631.1.2] equal(X,inverse(inverse(X))).
% 357698 [para:357683.1.1,357636.1.2.2.2,demod:357685] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 357701 [para:357622.1.2,357698.1.2.1.1,demod:357648] equal(inverse(X),multiply(inverse(X),sk_c7)).
% 357712 [para:357701.1.2,357639.1.2,demod:357686] equal(multiply(X,sk_c7),X).
% 357713 [para:357649.1.1,357712.1.1.2] equal(multiply(X,sk_c6),X).
% 357716 [hyper:357533,357713,demod:357586,cut:357650] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 4
% seconds given: 4
%
%
% Split component 3 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c7),sk_c6) | -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7) | -equal(multiply(sk_c5,sk_c6),sk_c7) | -equal(multiply(Y,sk_c5),sk_c7) | -equal(inverse(Y),sk_c5) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(U),sk_c6) | -equal(multiply(U,sk_c5),sk_c6).
% Split part used next: -equal(multiply(Y,sk_c5),sk_c7) | -equal(inverse(Y),sk_c5).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 3
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 4
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,75,0,0,587,50,4,627,0,4,1154,50,8,1194,0,8,1732,50,15,1772,0,15,2317,50,21,2357,0,21,2909,50,29,2949,0,29,3509,50,43,3549,0,43,4118,50,72,4158,0,72,4737,50,132,4777,0,133,5367,50,268,5407,0,268,6009,50,483,6049,0,483,6664,50,904,6664,40,904,6704,0,904,17182,3,1205,17913,4,1355,18613,5,1505,18614,1,1505,18614,50,1505,18614,40,1505,18654,0,1505,18827,3,1814,18835,4,1971,18843,5,2106,18843,1,2106,18843,50,2106,18843,40,2106,18883,0,2106,40704,3,3611,42141,4,4357,43465,1,5107,43465,50,5107,43465,40,5107,43505,0,5107,55441,3,5858,56712,4,6233,58003,5,6608,58004,1,6608,58004,50,6608,58004,40,6608,58044,0,6608,68009,3,7380,69092,4,7734,70334,1,8109,70334,50,8109,70334,40,8109,70374,0,8109,175429,3,12015,176480,4,13961,177424,1,15911,177424,50,15914,177424,40,15914,177464,0,15914,253189,3,18467,253918,4,19740,254521,5,21015,254522,1,21015,254522,50,21017,254522,40,21017,254562,0,21017,289828,3,22519,290801,4,23268,291692,5,24018,291693,1,24018,291693,50,24019,291693,40,24019,291733,0,24019,302321,3,24772,303572,4,25145,304213,5,25520,304213,1,25520,304213,50,25520,304213,40,25520,304253,0,25520,333317,3,26723,334217,4,27321,334764,5,27921,334765,1,27921,334765,50,27922,334765,40,27922,334805,0,27922,356009,3,28674,356738,4,29048,357249,1,29423,357249,50,29423,357249,40,29423,357249,40,29423,357284,0,29423,357377,50,29423,357377,30,29423,357377,40,29423,357412,0,29423,357528,50,29424,357563,0,29429,357715,50,29429,357715,30,29429,357715,40,29429,357750,0,29429,357839,50,29429,357874,0,29429)
%
%
% START OF PROOF
% 357825 [?] ?
% 357841 [] equal(multiply(identity,X),X).
% 357842 [] equal(multiply(inverse(X),X),identity).
% 357843 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 357844 [] -equal(multiply(X,sk_c5),sk_c7) | -equal(inverse(X),sk_c5).
% 357845 [] equal(multiply(sk_c4,sk_c5),sk_c6) | equal(inverse(sk_c2),sk_c5).
% 357846 [] equal(inverse(sk_c2),sk_c5) | equal(inverse(sk_c4),sk_c6).
% 357847 [] equal(multiply(sk_c3,sk_c6),sk_c7) | equal(inverse(sk_c2),sk_c5).
% 357848 [] equal(inverse(sk_c2),sk_c5) | equal(inverse(sk_c3),sk_c7).
% 357849 [] equal(multiply(sk_c6,sk_c7),sk_c5) | equal(inverse(sk_c2),sk_c5).
% 357850 [?] ?
% 357851 [?] ?
% 357852 [?] ?
% 357853 [?] ?
% 357854 [?] ?
% 357877 [hyper:357844,357846,binarycut:357851] equal(inverse(sk_c4),sk_c6).
% 357878 [para:357877.1.1,357842.1.1.1] equal(multiply(sk_c6,sk_c4),identity).
% 357882 [hyper:357844,357848,binarycut:357853] equal(inverse(sk_c3),sk_c7).
% 357883 [para:357882.1.1,357842.1.1.1] equal(multiply(sk_c7,sk_c3),identity).
% 357886 [hyper:357844,357845,binarycut:357850] equal(multiply(sk_c4,sk_c5),sk_c6).
% 357889 [hyper:357844,357847,binarycut:357852] equal(multiply(sk_c3,sk_c6),sk_c7).
% 357892 [hyper:357844,357849,binarycut:357854] equal(multiply(sk_c6,sk_c7),sk_c5).
% 357893 [para:357842.1.1,357843.1.1.1,demod:357841] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 357894 [para:357878.1.1,357843.1.1.1,demod:357841] equal(X,multiply(sk_c6,multiply(sk_c4,X))).
% 357895 [para:357883.1.1,357843.1.1.1,demod:357841] equal(X,multiply(sk_c7,multiply(sk_c3,X))).
% 357899 [para:357886.1.1,357894.1.2.2] equal(sk_c5,multiply(sk_c6,sk_c6)).
% 357901 [para:357889.1.1,357895.1.2.2] equal(sk_c6,multiply(sk_c7,sk_c7)).
% 357907 [para:357892.1.1,357893.1.2.2] equal(sk_c7,multiply(inverse(sk_c6),sk_c5)).
% 357910 [para:357899.1.2,357893.1.2.2,demod:357907] equal(sk_c6,sk_c7).
% 357915 [para:357910.1.2,357901.1.2.1,demod:357892] equal(sk_c6,sk_c5).
% 357918 [para:357915.1.1,357889.1.1.2] equal(multiply(sk_c3,sk_c5),sk_c7).
% 357934 [hyper:357844,357918,demod:357882,cut:357825] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 4
% seconds given: 4
%
%
% Split component 4 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c7),sk_c6) | -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7) | -equal(multiply(sk_c5,sk_c6),sk_c7) | -equal(multiply(Y,sk_c5),sk_c7) | -equal(inverse(Y),sk_c5) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(U),sk_c6) | -equal(multiply(U,sk_c5),sk_c6).
% Split part used next: -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,75,0,0,587,50,4,627,0,4,1154,50,8,1194,0,8,1732,50,15,1772,0,15,2317,50,21,2357,0,21,2909,50,29,2949,0,29,3509,50,43,3549,0,43,4118,50,72,4158,0,72,4737,50,132,4777,0,133,5367,50,268,5407,0,268,6009,50,483,6049,0,483,6664,50,904,6664,40,904,6704,0,904,17182,3,1205,17913,4,1355,18613,5,1505,18614,1,1505,18614,50,1505,18614,40,1505,18654,0,1505,18827,3,1814,18835,4,1971,18843,5,2106,18843,1,2106,18843,50,2106,18843,40,2106,18883,0,2106,40704,3,3611,42141,4,4357,43465,1,5107,43465,50,5107,43465,40,5107,43505,0,5107,55441,3,5858,56712,4,6233,58003,5,6608,58004,1,6608,58004,50,6608,58004,40,6608,58044,0,6608,68009,3,7380,69092,4,7734,70334,1,8109,70334,50,8109,70334,40,8109,70374,0,8109,175429,3,12015,176480,4,13961,177424,1,15911,177424,50,15914,177424,40,15914,177464,0,15914,253189,3,18467,253918,4,19740,254521,5,21015,254522,1,21015,254522,50,21017,254522,40,21017,254562,0,21017,289828,3,22519,290801,4,23268,291692,5,24018,291693,1,24018,291693,50,24019,291693,40,24019,291733,0,24019,302321,3,24772,303572,4,25145,304213,5,25520,304213,1,25520,304213,50,25520,304213,40,25520,304253,0,25520,333317,3,26723,334217,4,27321,334764,5,27921,334765,1,27921,334765,50,27922,334765,40,27922,334805,0,27922,356009,3,28674,356738,4,29048,357249,1,29423,357249,50,29423,357249,40,29423,357249,40,29423,357284,0,29423,357377,50,29423,357377,30,29423,357377,40,29423,357412,0,29423,357528,50,29424,357563,0,29429,357715,50,29429,357715,30,29429,357715,40,29429,357750,0,29429,357839,50,29429,357874,0,29429,357933,50,29429,357933,30,29429,357933,40,29429,357968,0,29434)
%
%
% START OF PROOF
% 357935 [] equal(multiply(identity,X),X).
% 357936 [] equal(multiply(inverse(X),X),identity).
% 357937 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 357938 [] -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7).
% 357954 [] equal(multiply(sk_c4,sk_c5),sk_c6) | equal(inverse(sk_c1),sk_c7).
% 357955 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c4),sk_c6).
% 357956 [] equal(multiply(sk_c3,sk_c6),sk_c7) | equal(inverse(sk_c1),sk_c7).
% 357957 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c3),sk_c7).
% 357958 [] equal(multiply(sk_c6,sk_c7),sk_c5) | equal(inverse(sk_c1),sk_c7).
% 357959 [?] ?
% 357960 [?] ?
% 357961 [?] ?
% 357962 [?] ?
% 357963 [?] ?
% 357975 [hyper:357938,357955,binarycut:357960] equal(inverse(sk_c4),sk_c6).
% 357976 [para:357975.1.1,357936.1.1.1] equal(multiply(sk_c6,sk_c4),identity).
% 357979 [hyper:357938,357957,binarycut:357962] equal(inverse(sk_c3),sk_c7).
% 357983 [para:357979.1.1,357936.1.1.1] equal(multiply(sk_c7,sk_c3),identity).
% 357990 [hyper:357938,357954,binarycut:357959] equal(multiply(sk_c4,sk_c5),sk_c6).
% 357993 [hyper:357938,357956,binarycut:357961] equal(multiply(sk_c3,sk_c6),sk_c7).
% 357997 [hyper:357938,357958,binarycut:357963] equal(multiply(sk_c6,sk_c7),sk_c5).
% 357998 [para:357936.1.1,357937.1.1.1,demod:357935] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 357999 [para:357976.1.1,357937.1.1.1,demod:357935] equal(X,multiply(sk_c6,multiply(sk_c4,X))).
% 358000 [para:357983.1.1,357937.1.1.1,demod:357935] equal(X,multiply(sk_c7,multiply(sk_c3,X))).
% 358004 [para:357990.1.1,357999.1.2.2] equal(sk_c5,multiply(sk_c6,sk_c6)).
% 358006 [para:357993.1.1,358000.1.2.2] equal(sk_c6,multiply(sk_c7,sk_c7)).
% 358009 [para:357976.1.1,357998.1.2.2] equal(sk_c4,multiply(inverse(sk_c6),identity)).
% 358011 [para:357997.1.1,357998.1.2.2] equal(sk_c7,multiply(inverse(sk_c6),sk_c5)).
% 358013 [para:358004.1.2,357998.1.2.2,demod:358011] equal(sk_c6,sk_c7).
% 358015 [para:358013.1.2,357983.1.1.1] equal(multiply(sk_c6,sk_c3),identity).
% 358017 [para:358013.1.2,358006.1.2.1,demod:357997] equal(sk_c6,sk_c5).
% 358021 [para:358017.1.1,357997.1.1.1] equal(multiply(sk_c5,sk_c7),sk_c5).
% 358025 [para:358015.1.1,357998.1.2.2,demod:358009] equal(sk_c3,sk_c4).
% 358027 [para:358025.1.2,357975.1.1.1,demod:357979] equal(sk_c7,sk_c6).
% 358038 [para:358021.1.1,357998.1.2.2,demod:357936] equal(sk_c7,identity).
% 358041 [para:358038.1.1,357983.1.1.1,demod:357935] equal(sk_c3,identity).
% 358046 [para:358041.1.1,357979.1.1.1] equal(inverse(identity),sk_c7).
% 358054 [hyper:357938,358046,demod:357935,cut:358027] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 5 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c7),sk_c6) | -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7) | -equal(multiply(sk_c5,sk_c6),sk_c7) | -equal(multiply(Y,sk_c5),sk_c7) | -equal(inverse(Y),sk_c5) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(U),sk_c6) | -equal(multiply(U,sk_c5),sk_c6).
% Split part used next: -equal(inverse(sk_c7),sk_c6).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 3
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 4
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 5
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 6
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 7
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 8
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 9
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 10
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 11
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,75,0,0,587,50,4,627,0,4,1154,50,8,1194,0,8,1732,50,15,1772,0,15,2317,50,21,2357,0,21,2909,50,29,2949,0,29,3509,50,43,3549,0,43,4118,50,72,4158,0,72,4737,50,132,4777,0,133,5367,50,268,5407,0,268,6009,50,483,6049,0,483,6664,50,904,6664,40,904,6704,0,904,17182,3,1205,17913,4,1355,18613,5,1505,18614,1,1505,18614,50,1505,18614,40,1505,18654,0,1505,18827,3,1814,18835,4,1971,18843,5,2106,18843,1,2106,18843,50,2106,18843,40,2106,18883,0,2106,40704,3,3611,42141,4,4357,43465,1,5107,43465,50,5107,43465,40,5107,43505,0,5107,55441,3,5858,56712,4,6233,58003,5,6608,58004,1,6608,58004,50,6608,58004,40,6608,58044,0,6608,68009,3,7380,69092,4,7734,70334,1,8109,70334,50,8109,70334,40,8109,70374,0,8109,175429,3,12015,176480,4,13961,177424,1,15911,177424,50,15914,177424,40,15914,177464,0,15914,253189,3,18467,253918,4,19740,254521,5,21015,254522,1,21015,254522,50,21017,254522,40,21017,254562,0,21017,289828,3,22519,290801,4,23268,291692,5,24018,291693,1,24018,291693,50,24019,291693,40,24019,291733,0,24019,302321,3,24772,303572,4,25145,304213,5,25520,304213,1,25520,304213,50,25520,304213,40,25520,304253,0,25520,333317,3,26723,334217,4,27321,334764,5,27921,334765,1,27921,334765,50,27922,334765,40,27922,334805,0,27922,356009,3,28674,356738,4,29048,357249,1,29423,357249,50,29423,357249,40,29423,357249,40,29423,357284,0,29423,357377,50,29423,357377,30,29423,357377,40,29423,357412,0,29423,357528,50,29424,357563,0,29429,357715,50,29429,357715,30,29429,357715,40,29429,357750,0,29429,357839,50,29429,357874,0,29429,357933,50,29429,357933,30,29429,357933,40,29429,357968,0,29434,358053,50,29434,358053,30,29434,358053,40,29434,358088,0,29434,358191,50,29435,358226,0,29440,358372,50,29442,358407,0,29442,358561,50,29446,358596,0,29446,358758,50,29452,358793,0,29456,358961,50,29465,358996,0,29465,359172,50,29480,359207,0,29485,359391,50,29514,359426,0,29514,359620,50,29575,359655,0,29576,359859,50,29692,359859,40,29692,359894,0,29692)
%
%
% START OF PROOF
% 359775 [?] ?
% 359861 [] equal(multiply(identity,X),X).
% 359862 [] equal(multiply(inverse(X),X),identity).
% 359863 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 359864 [] -equal(inverse(sk_c7),sk_c6).
% 359890 [?] ?
% 359891 [?] ?
% 359892 [?] ?
% 359893 [?] ?
% 359894 [?] ?
% 359909 [input:359891,cut:359864] equal(inverse(sk_c4),sk_c6).
% 359910 [para:359909.1.1,359862.1.1.1] equal(multiply(sk_c6,sk_c4),identity).
% 359913 [input:359893,cut:359864] equal(inverse(sk_c3),sk_c7).
% 359914 [para:359913.1.1,359862.1.1.1] equal(multiply(sk_c7,sk_c3),identity).
% 359931 [input:359890,cut:359864] equal(multiply(sk_c4,sk_c5),sk_c6).
% 359932 [input:359892,cut:359864] equal(multiply(sk_c3,sk_c6),sk_c7).
% 359933 [input:359894,cut:359864] equal(multiply(sk_c6,sk_c7),sk_c5).
% 359948 [para:359862.1.1,359863.1.1.1,demod:359861] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 359950 [para:359910.1.1,359863.1.1.1,demod:359861] equal(X,multiply(sk_c6,multiply(sk_c4,X))).
% 359952 [para:359914.1.1,359863.1.1.1,demod:359861] equal(X,multiply(sk_c7,multiply(sk_c3,X))).
% 359987 [para:359931.1.1,359950.1.2.2] equal(sk_c5,multiply(sk_c6,sk_c6)).
% 359992 [para:359932.1.1,359952.1.2.2] equal(sk_c6,multiply(sk_c7,sk_c7)).
% 360019 [para:359933.1.1,359948.1.2.2] equal(sk_c7,multiply(inverse(sk_c6),sk_c5)).
% 360036 [para:359987.1.2,359948.1.2.2,demod:360019] equal(sk_c6,sk_c7).
% 360042 [para:360036.1.2,359864.1.1.1] -equal(inverse(sk_c6),sk_c6).
% 360051 [para:360036.1.2,359992.1.2.1] equal(sk_c6,multiply(sk_c6,sk_c7)).
% 360069 [para:360051.1.2,359933.1.1] equal(sk_c6,sk_c5).
% 360083 [para:360069.1.1,360042.1.1.1,cut:359775] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% Split component 6 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c7),sk_c6) | -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7) | -equal(multiply(sk_c5,sk_c6),sk_c7) | -equal(multiply(Y,sk_c5),sk_c7) | -equal(inverse(Y),sk_c5) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(U),sk_c6) | -equal(multiply(U,sk_c5),sk_c6).
% Split part used next: -equal(multiply(sk_c5,sk_c6),sk_c7).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 3
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 4
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 5
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 6
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 7
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 8
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 9
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 10
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 11
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,75,0,0,587,50,4,627,0,4,1154,50,8,1194,0,8,1732,50,15,1772,0,15,2317,50,21,2357,0,21,2909,50,29,2949,0,29,3509,50,43,3549,0,43,4118,50,72,4158,0,72,4737,50,132,4777,0,133,5367,50,268,5407,0,268,6009,50,483,6049,0,483,6664,50,904,6664,40,904,6704,0,904,17182,3,1205,17913,4,1355,18613,5,1505,18614,1,1505,18614,50,1505,18614,40,1505,18654,0,1505,18827,3,1814,18835,4,1971,18843,5,2106,18843,1,2106,18843,50,2106,18843,40,2106,18883,0,2106,40704,3,3611,42141,4,4357,43465,1,5107,43465,50,5107,43465,40,5107,43505,0,5107,55441,3,5858,56712,4,6233,58003,5,6608,58004,1,6608,58004,50,6608,58004,40,6608,58044,0,6608,68009,3,7380,69092,4,7734,70334,1,8109,70334,50,8109,70334,40,8109,70374,0,8109,175429,3,12015,176480,4,13961,177424,1,15911,177424,50,15914,177424,40,15914,177464,0,15914,253189,3,18467,253918,4,19740,254521,5,21015,254522,1,21015,254522,50,21017,254522,40,21017,254562,0,21017,289828,3,22519,290801,4,23268,291692,5,24018,291693,1,24018,291693,50,24019,291693,40,24019,291733,0,24019,302321,3,24772,303572,4,25145,304213,5,25520,304213,1,25520,304213,50,25520,304213,40,25520,304253,0,25520,333317,3,26723,334217,4,27321,334764,5,27921,334765,1,27921,334765,50,27922,334765,40,27922,334805,0,27922,356009,3,28674,356738,4,29048,357249,1,29423,357249,50,29423,357249,40,29423,357249,40,29423,357284,0,29423,357377,50,29423,357377,30,29423,357377,40,29423,357412,0,29423,357528,50,29424,357563,0,29429,357715,50,29429,357715,30,29429,357715,40,29429,357750,0,29429,357839,50,29429,357874,0,29429,357933,50,29429,357933,30,29429,357933,40,29429,357968,0,29434,358053,50,29434,358053,30,29434,358053,40,29434,358088,0,29434,358191,50,29435,358226,0,29440,358372,50,29442,358407,0,29442,358561,50,29446,358596,0,29446,358758,50,29452,358793,0,29456,358961,50,29465,358996,0,29465,359172,50,29480,359207,0,29485,359391,50,29514,359426,0,29514,359620,50,29575,359655,0,29576,359859,50,29692,359859,40,29692,359894,0,29692,360082,50,29692,360082,30,29692,360082,40,29692,360117,0,29692,360220,50,29693,360255,0,29698,360401,50,29700,360436,0,29700,360590,50,29704,360625,0,29704,360787,50,29710,360822,0,29714,360990,50,29723,361025,0,29723,361201,50,29738,361236,0,29743,361420,50,29772,361455,0,29772,361649,50,29833,361684,0,29834,361888,50,29950,361888,40,29950,361923,0,29950)
%
%
% START OF PROOF
% 361889 [] equal(X,X).
% 361890 [] equal(multiply(identity,X),X).
% 361891 [] equal(multiply(inverse(X),X),identity).
% 361892 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 361893 [] -equal(multiply(sk_c5,sk_c6),sk_c7).
% 361904 [?] ?
% 361905 [?] ?
% 361906 [?] ?
% 361907 [?] ?
% 361908 [?] ?
% 361952 [input:361905,cut:361893] equal(inverse(sk_c4),sk_c6).
% 361953 [para:361952.1.1,361891.1.1.1] equal(multiply(sk_c6,sk_c4),identity).
% 361955 [input:361907,cut:361893] equal(inverse(sk_c3),sk_c7).
% 361956 [para:361955.1.1,361891.1.1.1] equal(multiply(sk_c7,sk_c3),identity).
% 361976 [input:361904,cut:361893] equal(multiply(sk_c4,sk_c5),sk_c6).
% 361978 [input:361906,cut:361893] equal(multiply(sk_c3,sk_c6),sk_c7).
% 361980 [input:361908,cut:361893] equal(multiply(sk_c6,sk_c7),sk_c5).
% 361996 [para:361891.1.1,361892.1.1.1,demod:361890] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 362000 [para:361953.1.1,361892.1.1.1,demod:361890] equal(X,multiply(sk_c6,multiply(sk_c4,X))).
% 362003 [para:361956.1.1,361892.1.1.1,demod:361890] equal(X,multiply(sk_c7,multiply(sk_c3,X))).
% 362027 [para:361976.1.1,362000.1.2.2] equal(sk_c5,multiply(sk_c6,sk_c6)).
% 362033 [para:361978.1.1,362003.1.2.2] equal(sk_c6,multiply(sk_c7,sk_c7)).
% 362056 [para:361980.1.1,361996.1.2.2] equal(sk_c7,multiply(inverse(sk_c6),sk_c5)).
% 362065 [para:362027.1.2,361996.1.2.2,demod:362056] equal(sk_c6,sk_c7).
% 362070 [para:362065.1.2,361893.1.2] -equal(multiply(sk_c5,sk_c6),sk_c6).
% 362077 [para:362065.1.2,362033.1.2.1] equal(sk_c6,multiply(sk_c6,sk_c7)).
% 362095 [para:362077.1.2,361980.1.1] equal(sk_c6,sk_c5).
% 362106 [para:362095.1.1,362027.1.2.1] equal(sk_c5,multiply(sk_c5,sk_c6)).
% 362108 [para:362095.1.1,362070.1.2,demod:362106,cut:361889] 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(inverse(sk_c7),sk_c6) | -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7) | -equal(multiply(sk_c5,sk_c6),sk_c7) | -equal(multiply(Y,sk_c5),sk_c7) | -equal(inverse(Y),sk_c5) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(U),sk_c6) | -equal(multiply(U,sk_c5),sk_c6).
% Split part used next: -equal(multiply(sk_c6,sk_c7),sk_c5).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 3
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 4
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 5
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 6
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 7
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 8
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 9
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 10
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 11
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,75,0,0,587,50,4,627,0,4,1154,50,8,1194,0,8,1732,50,15,1772,0,15,2317,50,21,2357,0,21,2909,50,29,2949,0,29,3509,50,43,3549,0,43,4118,50,72,4158,0,72,4737,50,132,4777,0,133,5367,50,268,5407,0,268,6009,50,483,6049,0,483,6664,50,904,6664,40,904,6704,0,904,17182,3,1205,17913,4,1355,18613,5,1505,18614,1,1505,18614,50,1505,18614,40,1505,18654,0,1505,18827,3,1814,18835,4,1971,18843,5,2106,18843,1,2106,18843,50,2106,18843,40,2106,18883,0,2106,40704,3,3611,42141,4,4357,43465,1,5107,43465,50,5107,43465,40,5107,43505,0,5107,55441,3,5858,56712,4,6233,58003,5,6608,58004,1,6608,58004,50,6608,58004,40,6608,58044,0,6608,68009,3,7380,69092,4,7734,70334,1,8109,70334,50,8109,70334,40,8109,70374,0,8109,175429,3,12015,176480,4,13961,177424,1,15911,177424,50,15914,177424,40,15914,177464,0,15914,253189,3,18467,253918,4,19740,254521,5,21015,254522,1,21015,254522,50,21017,254522,40,21017,254562,0,21017,289828,3,22519,290801,4,23268,291692,5,24018,291693,1,24018,291693,50,24019,291693,40,24019,291733,0,24019,302321,3,24772,303572,4,25145,304213,5,25520,304213,1,25520,304213,50,25520,304213,40,25520,304253,0,25520,333317,3,26723,334217,4,27321,334764,5,27921,334765,1,27921,334765,50,27922,334765,40,27922,334805,0,27922,356009,3,28674,356738,4,29048,357249,1,29423,357249,50,29423,357249,40,29423,357249,40,29423,357284,0,29423,357377,50,29423,357377,30,29423,357377,40,29423,357412,0,29423,357528,50,29424,357563,0,29429,357715,50,29429,357715,30,29429,357715,40,29429,357750,0,29429,357839,50,29429,357874,0,29429,357933,50,29429,357933,30,29429,357933,40,29429,357968,0,29434,358053,50,29434,358053,30,29434,358053,40,29434,358088,0,29434,358191,50,29435,358226,0,29440,358372,50,29442,358407,0,29442,358561,50,29446,358596,0,29446,358758,50,29452,358793,0,29456,358961,50,29465,358996,0,29465,359172,50,29480,359207,0,29485,359391,50,29514,359426,0,29514,359620,50,29575,359655,0,29576,359859,50,29692,359859,40,29692,359894,0,29692,360082,50,29692,360082,30,29692,360082,40,29692,360117,0,29692,360220,50,29693,360255,0,29698,360401,50,29700,360436,0,29700,360590,50,29704,360625,0,29704,360787,50,29710,360822,0,29714,360990,50,29723,361025,0,29723,361201,50,29738,361236,0,29743,361420,50,29772,361455,0,29772,361649,50,29833,361684,0,29834,361888,50,29950,361888,40,29950,361923,0,29950,362107,50,29950,362107,30,29950,362107,40,29950,362142,0,29951,362260,50,29951,362295,0,29956,362451,50,29959,362486,0,29959,362650,50,29963,362685,0,29963,362857,50,29968,362892,0,29973,363070,50,29982,363105,0,29982,363291,50,29999,363326,0,30003,363520,50,30033,363555,0,30033,363759,50,30095,363794,0,30095,364008,50,30213,364008,40,30213,364043,0,30213)
%
%
% START OF PROOF
% 363894 [?] ?
% 364011 [] equal(multiply(inverse(X),X),identity).
% 364013 [] -equal(multiply(sk_c6,sk_c7),sk_c5).
% 364043 [?] ?
% 364092 [input:364043,cut:364013] equal(inverse(sk_c7),sk_c6).
% 364093 [para:364092.1.1,364011.1.1.1] equal(multiply(sk_c6,sk_c7),identity).
% 364095 [para:364093.1.1,364013.1.1,cut:363894] 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: 38524
% derived clauses: 6253450
% kept clauses: 293086
% kept size sum: 297383
% kept mid-nuclei: 3194
% kept new demods: 5490
% forw unit-subs: 2242734
% forw double-subs: 3316814
% forw overdouble-subs: 324485
% backward subs: 9023
% fast unit cutoff: 22869
% full unit cutoff: 0
% dbl unit cutoff: 6220
% real runtime : 304.21
% process. runtime: 302.13
% specific non-discr-tree subsumption statistics:
% tried: 40078789
% length fails: 4608318
% strength fails: 9921501
% predlist fails: 2137157
% aux str. fails: 5065363
% by-lit fails: 8533747
% full subs tried: 2012033
% full subs fail: 1890783
%
% ; 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/GRP376-1+eq_r.in")
%
%------------------------------------------------------------------------------