TSTP Solution File: GRP386-1 by Gandalf---c-2.6
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP386-1 : 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 : art07.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 308.4s
% Output : Assurance 308.4s
% 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/GRP386-1+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(inverse(sk_c10),sk_c9) | -equal(multiply(sk_c9,sk_c8),sk_c10) | -equal(multiply(sk_c10,sk_c8),sk_c9) | -equal(inverse(X),sk_c10) | -equal(multiply(X,sk_c9),sk_c10) | -equal(multiply(Y,sk_c10),sk_c9) | -equal(inverse(Y),sk_c10) | -equal(multiply(Z,sk_c9),sk_c8) | -equal(inverse(Z),sk_c9) | -equal(multiply(U,V),sk_c10) | -equal(inverse(U),V) | -equal(multiply(V,sk_c9),sk_c10) | -equal(inverse(W),X1) | -equal(inverse(X1),V) | -equal(multiply(W,V),X1).
% was split for some strategies as:
% -equal(multiply(U,V),sk_c10) | -equal(inverse(U),V) | -equal(multiply(V,sk_c9),sk_c10) | -equal(inverse(X1),V) | -equal(inverse(W),X1) | -equal(multiply(W,V),X1).
% -equal(multiply(Z,sk_c9),sk_c8) | -equal(inverse(Z),sk_c9).
% -equal(multiply(Y,sk_c10),sk_c9) | -equal(inverse(Y),sk_c10).
% -equal(inverse(X),sk_c10) | -equal(multiply(X,sk_c9),sk_c10).
% -equal(inverse(sk_c10),sk_c9).
% -equal(multiply(sk_c9,sk_c8),sk_c10).
% -equal(multiply(sk_c10,sk_c8),sk_c9).
%
% 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_c10),sk_c9) | -equal(multiply(sk_c9,sk_c8),sk_c10) | -equal(multiply(sk_c10,sk_c8),sk_c9) | -equal(inverse(X),sk_c10) | -equal(multiply(X,sk_c9),sk_c10) | -equal(multiply(Y,sk_c10),sk_c9) | -equal(inverse(Y),sk_c10) | -equal(multiply(Z,sk_c9),sk_c8) | -equal(inverse(Z),sk_c9) | -equal(multiply(U,V),sk_c10) | -equal(inverse(U),V) | -equal(multiply(V,sk_c9),sk_c10) | -equal(inverse(W),X1) | -equal(inverse(X1),V) | -equal(multiply(W,V),X1).
% Split part used next: -equal(multiply(U,V),sk_c10) | -equal(inverse(U),V) | -equal(multiply(V,sk_c9),sk_c10) | -equal(inverse(X1),V) | -equal(inverse(W),X1) | -equal(multiply(W,V),X1).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(55,40,0,118,0,0,48849,50,295,48912,0,295,172318,4,1453,173652,5,1496,173656,1,1496,173656,50,1496,173656,40,1496,173719,0,1496,176029,3,1844,176371,4,1953,176469,5,2097,176469,1,2097,176469,50,2097,176469,40,2097,176532,0,2097,178842,3,2431,179227,4,2551,179284,5,2698,179284,1,2698,179284,50,2698,179284,40,2698,179347,0,2698,196273,3,4199,198300,4,4949,200593,5,5699,200594,1,5699,200594,50,5699,200594,40,5699,200657,0,5699,212954,3,6454,214284,4,6825,215883,1,7200,215883,50,7200,215883,40,7200,215946,0,7200,224119,3,8029,226261,4,8326,229138,5,8701,229139,5,8701,229140,1,8701,229140,50,8701,229140,40,8701,229203,0,8701,298908,3,12607,299900,4,14553,300616,1,16502,300616,50,16504,300616,40,16504,300679,0,16504,355039,3,19057,355808,4,20330,356529,1,21605,356529,50,21606,356529,40,21606,356592,0,21606,388894,3,23107,389725,4,23857,390689,1,24607,390689,50,24608,390689,40,24608,390752,0,24608,399156,3,25397,401462,4,25734,402905,5,26109,402905,1,26109,402905,50,26109,402905,40,26109,402968,0,26109,425948,3,27310,426831,4,27910,427762,1,28510,427762,50,28510,427762,40,28510,427825,0,28510,445408,3,29261,446075,4,29636,446594,5,30011,446595,1,30011,446595,50,30011,446595,40,30011,446595,40,30011,446704,0,30011)
%
%
% START OF PROOF
% 446597 [] equal(multiply(identity,X),X).
% 446598 [] equal(multiply(inverse(X),X),identity).
% 446599 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 446650 [] -equal(multiply(X,sk_c9),sk_c10) | -equal(multiply(Y,X),sk_c10) | -equal(multiply(Z,X),U) | -equal(inverse(Z),U) | -equal(inverse(U),X) | -equal(inverse(Y),X).
% 446651 [] -equal(multiply(X,Y),Z) | -equal(inverse(X),Z) | -equal(inverse(Z),Y) | $spltprd1($spltcnst85,Y).
% 446652 [] -equal(multiply(X,Y),sk_c10) | -equal(inverse(X),Y) | $spltprd1($spltcnst86,Y).
% 446653 [] -equal(multiply(X,sk_c9),sk_c10) | $spltprd1($spltcnst87,X).
% 446654 [] -$spltprd1($spltcnst86,X) | -$spltprd1($spltcnst85,X) | -$spltprd1($spltcnst87,X).
% 446655 [] equal(multiply(sk_c1,sk_c9),sk_c10) | equal(multiply(sk_c6,sk_c7),sk_c5).
% 446656 [] equal(multiply(sk_c1,sk_c9),sk_c10) | equal(inverse(sk_c5),sk_c7).
% 446657 [] equal(multiply(sk_c1,sk_c9),sk_c10) | equal(inverse(sk_c6),sk_c5).
% 446658 [] equal(multiply(sk_c1,sk_c9),sk_c10) | equal(multiply(sk_c7,sk_c9),sk_c10).
% 446659 [] equal(multiply(sk_c1,sk_c9),sk_c10) | equal(inverse(sk_c4),sk_c7).
% 446660 [] equal(multiply(sk_c1,sk_c9),sk_c10) | equal(multiply(sk_c4,sk_c7),sk_c10).
% 446665 [] equal(multiply(sk_c6,sk_c7),sk_c5) | equal(inverse(sk_c1),sk_c10).
% 446666 [] equal(inverse(sk_c1),sk_c10) | equal(inverse(sk_c5),sk_c7).
% 446667 [] equal(inverse(sk_c1),sk_c10) | equal(inverse(sk_c6),sk_c5).
% 446668 [] equal(multiply(sk_c7,sk_c9),sk_c10) | equal(inverse(sk_c1),sk_c10).
% 446669 [] equal(inverse(sk_c1),sk_c10) | equal(inverse(sk_c4),sk_c7).
% 446670 [?] ?
% 446675 [] equal(multiply(sk_c10,sk_c8),sk_c9) | equal(multiply(sk_c6,sk_c7),sk_c5).
% 446676 [] equal(multiply(sk_c10,sk_c8),sk_c9) | equal(inverse(sk_c5),sk_c7).
% 446677 [] equal(multiply(sk_c10,sk_c8),sk_c9) | equal(inverse(sk_c6),sk_c5).
% 446678 [] equal(multiply(sk_c10,sk_c8),sk_c9) | equal(multiply(sk_c7,sk_c9),sk_c10).
% 446679 [] equal(multiply(sk_c10,sk_c8),sk_c9) | equal(inverse(sk_c4),sk_c7).
% 446680 [] equal(multiply(sk_c10,sk_c8),sk_c9) | equal(multiply(sk_c4,sk_c7),sk_c10).
% 446685 [] equal(multiply(sk_c9,sk_c8),sk_c10) | equal(multiply(sk_c6,sk_c7),sk_c5).
% 446686 [] equal(multiply(sk_c9,sk_c8),sk_c10) | equal(inverse(sk_c5),sk_c7).
% 446687 [] equal(multiply(sk_c9,sk_c8),sk_c10) | equal(inverse(sk_c6),sk_c5).
% 446688 [] equal(multiply(sk_c9,sk_c8),sk_c10) | equal(multiply(sk_c7,sk_c9),sk_c10).
% 446689 [] equal(multiply(sk_c9,sk_c8),sk_c10) | equal(inverse(sk_c4),sk_c7).
% 446690 [] equal(multiply(sk_c9,sk_c8),sk_c10) | equal(multiply(sk_c4,sk_c7),sk_c10).
% 446695 [] equal(multiply(sk_c6,sk_c7),sk_c5) | equal(inverse(sk_c10),sk_c9).
% 446696 [] equal(inverse(sk_c10),sk_c9) | equal(inverse(sk_c5),sk_c7).
% 446697 [] equal(inverse(sk_c10),sk_c9) | equal(inverse(sk_c6),sk_c5).
% 446698 [] equal(multiply(sk_c7,sk_c9),sk_c10) | equal(inverse(sk_c10),sk_c9).
% 446699 [] equal(inverse(sk_c10),sk_c9) | equal(inverse(sk_c4),sk_c7).
% 446700 [?] ?
% 446771 [hyper:446652,446669,binarycut:446670] equal(inverse(sk_c1),sk_c10) | $spltprd1($spltcnst86,sk_c7).
% 446859 [hyper:446652,446699,binarycut:446700] equal(inverse(sk_c10),sk_c9) | $spltprd1($spltcnst86,sk_c7).
% 447162 [hyper:446651,446665,446666,446667] equal(inverse(sk_c1),sk_c10) | $spltprd1($spltcnst85,sk_c7).
% 447266 [hyper:446653,446668] equal(inverse(sk_c1),sk_c10) | $spltprd1($spltcnst87,sk_c7).
% 447314 [hyper:446654,447266,447162,446771] equal(inverse(sk_c1),sk_c10).
% 447358 [para:447314.1.1,446598.1.1.1] equal(multiply(sk_c10,sk_c1),identity).
% 447579 [hyper:446651,446695,446696,446697] equal(inverse(sk_c10),sk_c9) | $spltprd1($spltcnst85,sk_c7).
% 447656 [hyper:446653,446698] equal(inverse(sk_c10),sk_c9) | $spltprd1($spltcnst87,sk_c7).
% 447690 [hyper:446654,447656,447579,446859] equal(inverse(sk_c10),sk_c9).
% 447720 [para:447690.1.1,446598.1.1.1] equal(multiply(sk_c9,sk_c10),identity).
% 448039 [hyper:446650,446660,446658,446659,446656,446655,446657] equal(multiply(sk_c1,sk_c9),sk_c10).
% 448178 [hyper:446650,446680,446678,446679,446676,446675,446677] equal(multiply(sk_c10,sk_c8),sk_c9).
% 448267 [hyper:446650,446690,446688,446689,446686,446685,446687] equal(multiply(sk_c9,sk_c8),sk_c10).
% 448283 [para:447358.1.1,446599.1.1.1,demod:446597] equal(X,multiply(sk_c10,multiply(sk_c1,X))).
% 448284 [para:447720.1.1,446599.1.1.1,demod:446597] equal(X,multiply(sk_c9,multiply(sk_c10,X))).
% 448287 [para:448267.1.1,446599.1.1.1] equal(multiply(sk_c10,X),multiply(sk_c9,multiply(sk_c8,X))).
% 448304 [para:448039.1.1,448283.1.2.2] equal(sk_c9,multiply(sk_c10,sk_c10)).
% 448323 [para:448178.1.1,448284.1.2.2] equal(sk_c8,multiply(sk_c9,sk_c9)).
% 448325 [para:448304.1.2,448284.1.2.2,demod:448323] equal(sk_c10,sk_c8).
% 448327 [para:448325.1.1,447690.1.1.1] equal(inverse(sk_c8),sk_c9).
% 448328 [para:448325.1.1,447720.1.1.2,demod:448267] equal(sk_c10,identity).
% 448332 [para:448325.1.1,448284.1.2.2.1,demod:448287] equal(X,multiply(sk_c10,X)).
% 448334 [para:448328.1.1,447690.1.1.1] equal(inverse(identity),sk_c9).
% 448335 [para:448328.1.1,448178.1.1.1,demod:446597] equal(sk_c8,sk_c9).
% 448337 [para:448328.1.1,448304.1.2.1,demod:446597] equal(sk_c9,sk_c10).
% 448344 [para:448335.1.2,448284.1.2.1,demod:448332] equal(X,multiply(sk_c8,X)).
% 448345 [para:448337.1.2,447690.1.1.1] equal(inverse(sk_c9),sk_c9).
% 448346 [para:448337.1.2,448178.1.1.1,demod:448267] equal(sk_c10,sk_c9).
% 448378 [hyper:446650,448327,446597,demod:448345,448344,demod:448334,448332,cut:448337,cut:448337,cut:448337,cut:448346] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 2 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c10),sk_c9) | -equal(multiply(sk_c9,sk_c8),sk_c10) | -equal(multiply(sk_c10,sk_c8),sk_c9) | -equal(inverse(X),sk_c10) | -equal(multiply(X,sk_c9),sk_c10) | -equal(multiply(Y,sk_c10),sk_c9) | -equal(inverse(Y),sk_c10) | -equal(multiply(Z,sk_c9),sk_c8) | -equal(inverse(Z),sk_c9) | -equal(multiply(U,V),sk_c10) | -equal(inverse(U),V) | -equal(multiply(V,sk_c9),sk_c10) | -equal(inverse(W),X1) | -equal(inverse(X1),V) | -equal(multiply(W,V),X1).
% Split part used next: -equal(multiply(Z,sk_c9),sk_c8) | -equal(inverse(Z),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: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(55,40,0,118,0,0,48849,50,295,48912,0,295,172318,4,1453,173652,5,1496,173656,1,1496,173656,50,1496,173656,40,1496,173719,0,1496,176029,3,1844,176371,4,1953,176469,5,2097,176469,1,2097,176469,50,2097,176469,40,2097,176532,0,2097,178842,3,2431,179227,4,2551,179284,5,2698,179284,1,2698,179284,50,2698,179284,40,2698,179347,0,2698,196273,3,4199,198300,4,4949,200593,5,5699,200594,1,5699,200594,50,5699,200594,40,5699,200657,0,5699,212954,3,6454,214284,4,6825,215883,1,7200,215883,50,7200,215883,40,7200,215946,0,7200,224119,3,8029,226261,4,8326,229138,5,8701,229139,5,8701,229140,1,8701,229140,50,8701,229140,40,8701,229203,0,8701,298908,3,12607,299900,4,14553,300616,1,16502,300616,50,16504,300616,40,16504,300679,0,16504,355039,3,19057,355808,4,20330,356529,1,21605,356529,50,21606,356529,40,21606,356592,0,21606,388894,3,23107,389725,4,23857,390689,1,24607,390689,50,24608,390689,40,24608,390752,0,24608,399156,3,25397,401462,4,25734,402905,5,26109,402905,1,26109,402905,50,26109,402905,40,26109,402968,0,26109,425948,3,27310,426831,4,27910,427762,1,28510,427762,50,28510,427762,40,28510,427825,0,28510,445408,3,29261,446075,4,29636,446594,5,30011,446595,1,30011,446595,50,30011,446595,40,30011,446595,40,30011,446704,0,30011,448377,50,30017,448377,30,30017,448377,40,30017,448432,0,30017)
%
%
% START OF PROOF
% 448379 [] equal(multiply(identity,X),X).
% 448380 [] equal(multiply(inverse(X),X),identity).
% 448381 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 448382 [] -equal(multiply(X,sk_c9),sk_c8) | -equal(inverse(X),sk_c9).
% 448389 [] equal(multiply(sk_c1,sk_c9),sk_c10) | equal(inverse(sk_c3),sk_c9).
% 448390 [] equal(multiply(sk_c1,sk_c9),sk_c10) | equal(multiply(sk_c3,sk_c9),sk_c8).
% 448399 [] equal(inverse(sk_c1),sk_c10) | equal(inverse(sk_c3),sk_c9).
% 448400 [?] ?
% 448409 [] equal(multiply(sk_c10,sk_c8),sk_c9) | equal(inverse(sk_c3),sk_c9).
% 448410 [] equal(multiply(sk_c10,sk_c8),sk_c9) | equal(multiply(sk_c3,sk_c9),sk_c8).
% 448419 [] equal(multiply(sk_c9,sk_c8),sk_c10) | equal(inverse(sk_c3),sk_c9).
% 448420 [] equal(multiply(sk_c9,sk_c8),sk_c10) | equal(multiply(sk_c3,sk_c9),sk_c8).
% 448429 [] equal(inverse(sk_c10),sk_c9) | equal(inverse(sk_c3),sk_c9).
% 448430 [?] ?
% 448439 [hyper:448382,448399,binarycut:448400] equal(inverse(sk_c1),sk_c10).
% 448440 [para:448439.1.1,448380.1.1.1] equal(multiply(sk_c10,sk_c1),identity).
% 448454 [hyper:448382,448429,binarycut:448430] equal(inverse(sk_c10),sk_c9).
% 448457 [para:448454.1.1,448380.1.1.1] equal(multiply(sk_c9,sk_c10),identity).
% 448484 [hyper:448382,448390,448389] equal(multiply(sk_c1,sk_c9),sk_c10).
% 448490 [hyper:448382,448410,448409] equal(multiply(sk_c10,sk_c8),sk_c9).
% 448496 [hyper:448382,448420,448419] equal(multiply(sk_c9,sk_c8),sk_c10).
% 448498 [para:448440.1.1,448381.1.1.1,demod:448379] equal(X,multiply(sk_c10,multiply(sk_c1,X))).
% 448499 [para:448457.1.1,448381.1.1.1,demod:448379] equal(X,multiply(sk_c9,multiply(sk_c10,X))).
% 448502 [para:448496.1.1,448381.1.1.1] equal(multiply(sk_c10,X),multiply(sk_c9,multiply(sk_c8,X))).
% 448503 [para:448484.1.1,448498.1.2.2] equal(sk_c9,multiply(sk_c10,sk_c10)).
% 448506 [para:448490.1.1,448499.1.2.2] equal(sk_c8,multiply(sk_c9,sk_c9)).
% 448508 [para:448503.1.2,448499.1.2.2,demod:448506] equal(sk_c10,sk_c8).
% 448514 [para:448508.1.1,448454.1.1.1] equal(inverse(sk_c8),sk_c9).
% 448515 [para:448508.1.1,448457.1.1.2,demod:448496] equal(sk_c10,identity).
% 448519 [para:448508.1.1,448499.1.2.2.1,demod:448502] equal(X,multiply(sk_c10,X)).
% 448522 [para:448515.1.1,448490.1.1.1,demod:448379] equal(sk_c8,sk_c9).
% 448524 [para:448515.1.1,448503.1.2.1,demod:448379] equal(sk_c9,sk_c10).
% 448529 [para:448522.1.2,448499.1.2.1,demod:448519] equal(X,multiply(sk_c8,X)).
% 448532 [para:448524.1.2,448508.1.1] equal(sk_c9,sk_c8).
% 448541 [hyper:448382,448514,demod:448529,cut:448532] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 3 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c10),sk_c9) | -equal(multiply(sk_c9,sk_c8),sk_c10) | -equal(multiply(sk_c10,sk_c8),sk_c9) | -equal(inverse(X),sk_c10) | -equal(multiply(X,sk_c9),sk_c10) | -equal(multiply(Y,sk_c10),sk_c9) | -equal(inverse(Y),sk_c10) | -equal(multiply(Z,sk_c9),sk_c8) | -equal(inverse(Z),sk_c9) | -equal(multiply(U,V),sk_c10) | -equal(inverse(U),V) | -equal(multiply(V,sk_c9),sk_c10) | -equal(inverse(W),X1) | -equal(inverse(X1),V) | -equal(multiply(W,V),X1).
% Split part used next: -equal(multiply(Y,sk_c10),sk_c9) | -equal(inverse(Y),sk_c10).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 3
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 4
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(55,40,0,118,0,0,48849,50,295,48912,0,295,172318,4,1453,173652,5,1496,173656,1,1496,173656,50,1496,173656,40,1496,173719,0,1496,176029,3,1844,176371,4,1953,176469,5,2097,176469,1,2097,176469,50,2097,176469,40,2097,176532,0,2097,178842,3,2431,179227,4,2551,179284,5,2698,179284,1,2698,179284,50,2698,179284,40,2698,179347,0,2698,196273,3,4199,198300,4,4949,200593,5,5699,200594,1,5699,200594,50,5699,200594,40,5699,200657,0,5699,212954,3,6454,214284,4,6825,215883,1,7200,215883,50,7200,215883,40,7200,215946,0,7200,224119,3,8029,226261,4,8326,229138,5,8701,229139,5,8701,229140,1,8701,229140,50,8701,229140,40,8701,229203,0,8701,298908,3,12607,299900,4,14553,300616,1,16502,300616,50,16504,300616,40,16504,300679,0,16504,355039,3,19057,355808,4,20330,356529,1,21605,356529,50,21606,356529,40,21606,356592,0,21606,388894,3,23107,389725,4,23857,390689,1,24607,390689,50,24608,390689,40,24608,390752,0,24608,399156,3,25397,401462,4,25734,402905,5,26109,402905,1,26109,402905,50,26109,402905,40,26109,402968,0,26109,425948,3,27310,426831,4,27910,427762,1,28510,427762,50,28510,427762,40,28510,427825,0,28510,445408,3,29261,446075,4,29636,446594,5,30011,446595,1,30011,446595,50,30011,446595,40,30011,446595,40,30011,446704,0,30011,448377,50,30017,448377,30,30017,448377,40,30017,448432,0,30017,448540,50,30017,448540,30,30017,448540,40,30017,448595,0,30023,448709,50,30023,448764,0,30023)
%
%
% START OF PROOF
% 448711 [] equal(multiply(identity,X),X).
% 448712 [] equal(multiply(inverse(X),X),identity).
% 448713 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 448714 [] -equal(multiply(X,sk_c10),sk_c9) | -equal(inverse(X),sk_c10).
% 448723 [] equal(multiply(sk_c1,sk_c9),sk_c10) | equal(inverse(sk_c2),sk_c10).
% 448724 [] equal(multiply(sk_c1,sk_c9),sk_c10) | equal(multiply(sk_c2,sk_c10),sk_c9).
% 448733 [] equal(inverse(sk_c1),sk_c10) | equal(inverse(sk_c2),sk_c10).
% 448734 [?] ?
% 448743 [] equal(multiply(sk_c10,sk_c8),sk_c9) | equal(inverse(sk_c2),sk_c10).
% 448744 [] equal(multiply(sk_c10,sk_c8),sk_c9) | equal(multiply(sk_c2,sk_c10),sk_c9).
% 448753 [] equal(multiply(sk_c9,sk_c8),sk_c10) | equal(inverse(sk_c2),sk_c10).
% 448754 [] equal(multiply(sk_c9,sk_c8),sk_c10) | equal(multiply(sk_c2,sk_c10),sk_c9).
% 448763 [] equal(inverse(sk_c10),sk_c9) | equal(inverse(sk_c2),sk_c10).
% 448764 [?] ?
% 448779 [hyper:448714,448733,binarycut:448734] equal(inverse(sk_c1),sk_c10).
% 448782 [para:448779.1.1,448712.1.1.1] equal(multiply(sk_c10,sk_c1),identity).
% 448791 [hyper:448714,448763,binarycut:448764] equal(inverse(sk_c10),sk_c9).
% 448793 [para:448791.1.1,448712.1.1.1] equal(multiply(sk_c9,sk_c10),identity).
% 448819 [hyper:448714,448724,448723] equal(multiply(sk_c1,sk_c9),sk_c10).
% 448826 [hyper:448714,448744,448743] equal(multiply(sk_c10,sk_c8),sk_c9).
% 448833 [hyper:448714,448754,448753] equal(multiply(sk_c9,sk_c8),sk_c10).
% 448834 [para:448712.1.1,448713.1.1.1,demod:448711] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 448835 [para:448782.1.1,448713.1.1.1,demod:448711] equal(X,multiply(sk_c10,multiply(sk_c1,X))).
% 448836 [para:448793.1.1,448713.1.1.1,demod:448711] equal(X,multiply(sk_c9,multiply(sk_c10,X))).
% 448840 [para:448819.1.1,448835.1.2.2] equal(sk_c9,multiply(sk_c10,sk_c10)).
% 448843 [para:448826.1.1,448836.1.2.2] equal(sk_c8,multiply(sk_c9,sk_c9)).
% 448845 [para:448840.1.2,448836.1.2.2,demod:448843] equal(sk_c10,sk_c8).
% 448847 [para:448712.1.1,448834.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 448850 [para:448713.1.1,448834.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 448852 [para:448834.1.2,448834.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 448855 [para:448845.1.1,448793.1.1.2,demod:448833] equal(sk_c10,identity).
% 448863 [para:448855.1.1,448835.1.2.1,demod:448711] equal(X,multiply(sk_c1,X)).
% 448864 [para:448855.1.1,448840.1.2.1,demod:448711] equal(sk_c9,sk_c10).
% 448870 [para:448864.1.2,448791.1.1.1] equal(inverse(sk_c9),sk_c9).
% 448892 [para:448852.1.2,448712.1.1] equal(multiply(X,inverse(X)),identity).
% 448894 [para:448852.1.2,448847.1.2] equal(X,multiply(X,identity)).
% 448895 [para:448894.1.2,448847.1.2] equal(X,inverse(inverse(X))).
% 448896 [para:448892.1.1,448850.1.2.2.2,demod:448894] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 448898 [para:448835.1.2,448896.1.2.1.1,demod:448863] equal(inverse(X),multiply(inverse(X),sk_c10)).
% 448905 [para:448898.1.2,448852.1.2,demod:448895] equal(multiply(X,sk_c10),X).
% 448906 [hyper:448714,448905,demod:448870,cut:448864] 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: 4
%
%
% Split component 4 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c10),sk_c9) | -equal(multiply(sk_c9,sk_c8),sk_c10) | -equal(multiply(sk_c10,sk_c8),sk_c9) | -equal(inverse(X),sk_c10) | -equal(multiply(X,sk_c9),sk_c10) | -equal(multiply(Y,sk_c10),sk_c9) | -equal(inverse(Y),sk_c10) | -equal(multiply(Z,sk_c9),sk_c8) | -equal(inverse(Z),sk_c9) | -equal(multiply(U,V),sk_c10) | -equal(inverse(U),V) | -equal(multiply(V,sk_c9),sk_c10) | -equal(inverse(W),X1) | -equal(inverse(X1),V) | -equal(multiply(W,V),X1).
% Split part used next: -equal(inverse(X),sk_c10) | -equal(multiply(X,sk_c9),sk_c10).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(55,40,0,118,0,0,48849,50,295,48912,0,295,172318,4,1453,173652,5,1496,173656,1,1496,173656,50,1496,173656,40,1496,173719,0,1496,176029,3,1844,176371,4,1953,176469,5,2097,176469,1,2097,176469,50,2097,176469,40,2097,176532,0,2097,178842,3,2431,179227,4,2551,179284,5,2698,179284,1,2698,179284,50,2698,179284,40,2698,179347,0,2698,196273,3,4199,198300,4,4949,200593,5,5699,200594,1,5699,200594,50,5699,200594,40,5699,200657,0,5699,212954,3,6454,214284,4,6825,215883,1,7200,215883,50,7200,215883,40,7200,215946,0,7200,224119,3,8029,226261,4,8326,229138,5,8701,229139,5,8701,229140,1,8701,229140,50,8701,229140,40,8701,229203,0,8701,298908,3,12607,299900,4,14553,300616,1,16502,300616,50,16504,300616,40,16504,300679,0,16504,355039,3,19057,355808,4,20330,356529,1,21605,356529,50,21606,356529,40,21606,356592,0,21606,388894,3,23107,389725,4,23857,390689,1,24607,390689,50,24608,390689,40,24608,390752,0,24608,399156,3,25397,401462,4,25734,402905,5,26109,402905,1,26109,402905,50,26109,402905,40,26109,402968,0,26109,425948,3,27310,426831,4,27910,427762,1,28510,427762,50,28510,427762,40,28510,427825,0,28510,445408,3,29261,446075,4,29636,446594,5,30011,446595,1,30011,446595,50,30011,446595,40,30011,446595,40,30011,446704,0,30011,448377,50,30017,448377,30,30017,448377,40,30017,448432,0,30017,448540,50,30017,448540,30,30017,448540,40,30017,448595,0,30023,448709,50,30023,448764,0,30023,448905,50,30024,448905,30,30024,448905,40,30024,448960,0,30028)
%
%
% START OF PROOF
% 448907 [] equal(multiply(identity,X),X).
% 448908 [] equal(multiply(inverse(X),X),identity).
% 448909 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 448910 [] -equal(multiply(X,sk_c9),sk_c10) | -equal(inverse(X),sk_c10).
% 448911 [] equal(multiply(sk_c1,sk_c9),sk_c10) | equal(multiply(sk_c6,sk_c7),sk_c5).
% 448912 [?] ?
% 448913 [?] ?
% 448914 [] equal(multiply(sk_c1,sk_c9),sk_c10) | equal(multiply(sk_c7,sk_c9),sk_c10).
% 448915 [?] ?
% 448916 [] equal(multiply(sk_c1,sk_c9),sk_c10) | equal(multiply(sk_c4,sk_c7),sk_c10).
% 448919 [?] ?
% 448920 [] equal(multiply(sk_c1,sk_c9),sk_c10) | equal(multiply(sk_c2,sk_c10),sk_c9).
% 448921 [] equal(multiply(sk_c6,sk_c7),sk_c5) | equal(inverse(sk_c1),sk_c10).
% 448922 [] equal(inverse(sk_c1),sk_c10) | equal(inverse(sk_c5),sk_c7).
% 448923 [] equal(inverse(sk_c1),sk_c10) | equal(inverse(sk_c6),sk_c5).
% 448924 [] equal(multiply(sk_c7,sk_c9),sk_c10) | equal(inverse(sk_c1),sk_c10).
% 448925 [] equal(inverse(sk_c1),sk_c10) | equal(inverse(sk_c4),sk_c7).
% 448926 [] equal(multiply(sk_c4,sk_c7),sk_c10) | equal(inverse(sk_c1),sk_c10).
% 448929 [] equal(inverse(sk_c1),sk_c10) | equal(inverse(sk_c2),sk_c10).
% 448930 [] equal(multiply(sk_c2,sk_c10),sk_c9) | equal(inverse(sk_c1),sk_c10).
% 448963 [hyper:448910,448922,binarycut:448912] equal(inverse(sk_c5),sk_c7).
% 448964 [para:448963.1.1,448908.1.1.1] equal(multiply(sk_c7,sk_c5),identity).
% 448968 [hyper:448910,448923,binarycut:448913] equal(inverse(sk_c6),sk_c5).
% 448969 [para:448968.1.1,448908.1.1.1] equal(multiply(sk_c5,sk_c6),identity).
% 448972 [hyper:448910,448925,binarycut:448915] equal(inverse(sk_c4),sk_c7).
% 448976 [para:448972.1.1,448908.1.1.1] equal(multiply(sk_c7,sk_c4),identity).
% 448988 [hyper:448910,448929,binarycut:448919] equal(inverse(sk_c2),sk_c10).
% 448992 [para:448988.1.1,448908.1.1.1] equal(multiply(sk_c10,sk_c2),identity).
% 448999 [hyper:448910,448921,binarycut:448911] equal(multiply(sk_c6,sk_c7),sk_c5).
% 449003 [hyper:448910,448924,binarycut:448914] equal(multiply(sk_c7,sk_c9),sk_c10).
% 449012 [hyper:448910,448926,binarycut:448916] equal(multiply(sk_c4,sk_c7),sk_c10).
% 449021 [hyper:448910,448930,binarycut:448920] equal(multiply(sk_c2,sk_c10),sk_c9).
% 449022 [para:448908.1.1,448909.1.1.1,demod:448907] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 449023 [para:448964.1.1,448909.1.1.1,demod:448907] equal(X,multiply(sk_c7,multiply(sk_c5,X))).
% 449024 [para:448969.1.1,448909.1.1.1,demod:448907] equal(X,multiply(sk_c5,multiply(sk_c6,X))).
% 449025 [para:448976.1.1,448909.1.1.1,demod:448907] equal(X,multiply(sk_c7,multiply(sk_c4,X))).
% 449030 [para:449012.1.1,448909.1.1.1] equal(multiply(sk_c10,X),multiply(sk_c4,multiply(sk_c7,X))).
% 449033 [para:448969.1.1,449023.1.2.2] equal(sk_c6,multiply(sk_c7,identity)).
% 449035 [para:448964.1.1,449022.1.2.2] equal(sk_c5,multiply(inverse(sk_c7),identity)).
% 449036 [para:448976.1.1,449022.1.2.2,demod:449035] equal(sk_c4,sk_c5).
% 449039 [para:448999.1.1,449022.1.2.2,demod:448968] equal(sk_c7,multiply(sk_c5,sk_c5)).
% 449041 [para:449012.1.1,449022.1.2.2,demod:448972] equal(sk_c7,multiply(sk_c7,sk_c10)).
% 449044 [para:449023.1.2,449022.1.2.2] equal(multiply(sk_c5,X),multiply(inverse(sk_c7),X)).
% 449046 [para:449033.1.2,448909.1.1.1,demod:448907] equal(multiply(sk_c6,X),multiply(sk_c7,X)).
% 449048 [para:449039.1.2,449023.1.2.2] equal(sk_c5,multiply(sk_c7,sk_c7)).
% 449055 [para:449036.1.2,449024.1.2.1,demod:449030,449046] equal(X,multiply(sk_c10,X)).
% 449057 [para:449025.1.2,449022.1.2.2,demod:449044] equal(multiply(sk_c4,X),multiply(sk_c5,X)).
% 449058 [para:449055.1.2,448992.1.1] equal(sk_c2,identity).
% 449060 [para:449058.1.1,448988.1.1.1] equal(inverse(identity),sk_c10).
% 449061 [para:449058.1.1,449021.1.1.1,demod:448907] equal(sk_c10,sk_c9).
% 449064 [para:449061.1.1,449041.1.2.2,demod:449003] equal(sk_c7,sk_c10).
% 449069 [para:449064.1.2,449041.1.2.2,demod:449048] equal(sk_c7,sk_c5).
% 449070 [para:449064.1.2,449055.1.2.1] equal(X,multiply(sk_c7,X)).
% 449074 [para:449069.1.2,448969.1.1.1,demod:449070] equal(sk_c6,identity).
% 449075 [para:449069.1.2,449036.1.2] equal(sk_c4,sk_c7).
% 449087 [para:449074.1.1,449024.1.2.2.1,demod:449057,448907] equal(X,multiply(sk_c4,X)).
% 449090 [para:449075.1.2,449003.1.1.1,demod:449087] equal(sk_c9,sk_c10).
% 449165 [hyper:448910,449060,demod:448907,cut:449090] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 5 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c10),sk_c9) | -equal(multiply(sk_c9,sk_c8),sk_c10) | -equal(multiply(sk_c10,sk_c8),sk_c9) | -equal(inverse(X),sk_c10) | -equal(multiply(X,sk_c9),sk_c10) | -equal(multiply(Y,sk_c10),sk_c9) | -equal(inverse(Y),sk_c10) | -equal(multiply(Z,sk_c9),sk_c8) | -equal(inverse(Z),sk_c9) | -equal(multiply(U,V),sk_c10) | -equal(inverse(U),V) | -equal(multiply(V,sk_c9),sk_c10) | -equal(inverse(W),X1) | -equal(inverse(X1),V) | -equal(multiply(W,V),X1).
% Split part used next: -equal(inverse(sk_c10),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: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 4
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 5
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 6
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 7
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 8
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 9
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 10
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using 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 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(55,40,0,118,0,0,48849,50,295,48912,0,295,172318,4,1453,173652,5,1496,173656,1,1496,173656,50,1496,173656,40,1496,173719,0,1496,176029,3,1844,176371,4,1953,176469,5,2097,176469,1,2097,176469,50,2097,176469,40,2097,176532,0,2097,178842,3,2431,179227,4,2551,179284,5,2698,179284,1,2698,179284,50,2698,179284,40,2698,179347,0,2698,196273,3,4199,198300,4,4949,200593,5,5699,200594,1,5699,200594,50,5699,200594,40,5699,200657,0,5699,212954,3,6454,214284,4,6825,215883,1,7200,215883,50,7200,215883,40,7200,215946,0,7200,224119,3,8029,226261,4,8326,229138,5,8701,229139,5,8701,229140,1,8701,229140,50,8701,229140,40,8701,229203,0,8701,298908,3,12607,299900,4,14553,300616,1,16502,300616,50,16504,300616,40,16504,300679,0,16504,355039,3,19057,355808,4,20330,356529,1,21605,356529,50,21606,356529,40,21606,356592,0,21606,388894,3,23107,389725,4,23857,390689,1,24607,390689,50,24608,390689,40,24608,390752,0,24608,399156,3,25397,401462,4,25734,402905,5,26109,402905,1,26109,402905,50,26109,402905,40,26109,402968,0,26109,425948,3,27310,426831,4,27910,427762,1,28510,427762,50,28510,427762,40,28510,427825,0,28510,445408,3,29261,446075,4,29636,446594,5,30011,446595,1,30011,446595,50,30011,446595,40,30011,446595,40,30011,446704,0,30011,448377,50,30017,448377,30,30017,448377,40,30017,448432,0,30017,448540,50,30017,448540,30,30017,448540,40,30017,448595,0,30023,448709,50,30023,448764,0,30023,448905,50,30024,448905,30,30024,448905,40,30024,448960,0,30028,449164,50,30029,449164,30,30029,449164,40,30029,449219,0,30029,449423,50,30032,449478,0,30037,449746,50,30042,449801,0,30042,450077,50,30049,450132,0,30053,450416,50,30063,450471,0,30063,450761,50,30076,450816,0,30080,451114,50,30101,451169,0,30101,451475,50,30137,451530,0,30142,451846,50,30210,451901,0,30210,452227,50,30346,452227,40,30346,452282,0,30346)
%
%
% START OF PROOF
% 452229 [] equal(multiply(identity,X),X).
% 452230 [] equal(multiply(inverse(X),X),identity).
% 452231 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 452232 [] -equal(inverse(sk_c10),sk_c9).
% 452273 [?] ?
% 452274 [?] ?
% 452275 [?] ?
% 452276 [?] ?
% 452277 [?] ?
% 452278 [?] ?
% 452279 [?] ?
% 452280 [?] ?
% 452281 [?] ?
% 452282 [?] ?
% 452299 [input:452274,cut:452232] equal(inverse(sk_c5),sk_c7).
% 452300 [para:452299.1.1,452230.1.1.1] equal(multiply(sk_c7,sk_c5),identity).
% 452302 [input:452275,cut:452232] equal(inverse(sk_c6),sk_c5).
% 452303 [para:452302.1.1,452230.1.1.1] equal(multiply(sk_c5,sk_c6),identity).
% 452304 [input:452277,cut:452232] equal(inverse(sk_c4),sk_c7).
% 452305 [para:452304.1.1,452230.1.1.1] equal(multiply(sk_c7,sk_c4),identity).
% 452307 [input:452279,cut:452232] equal(inverse(sk_c3),sk_c9).
% 452308 [para:452307.1.1,452230.1.1.1] equal(multiply(sk_c9,sk_c3),identity).
% 452309 [input:452281,cut:452232] equal(inverse(sk_c2),sk_c10).
% 452310 [para:452309.1.1,452230.1.1.1] equal(multiply(sk_c10,sk_c2),identity).
% 452339 [input:452273,cut:452232] equal(multiply(sk_c6,sk_c7),sk_c5).
% 452340 [input:452276,cut:452232] equal(multiply(sk_c7,sk_c9),sk_c10).
% 452342 [input:452278,cut:452232] equal(multiply(sk_c4,sk_c7),sk_c10).
% 452343 [input:452280,cut:452232] equal(multiply(sk_c3,sk_c9),sk_c8).
% 452344 [input:452282,cut:452232] equal(multiply(sk_c2,sk_c10),sk_c9).
% 452364 [para:452300.1.1,452231.1.1.1,demod:452229] equal(X,multiply(sk_c7,multiply(sk_c5,X))).
% 452365 [para:452303.1.1,452231.1.1.1,demod:452229] equal(X,multiply(sk_c5,multiply(sk_c6,X))).
% 452366 [para:452305.1.1,452231.1.1.1,demod:452229] equal(X,multiply(sk_c7,multiply(sk_c4,X))).
% 452368 [para:452308.1.1,452231.1.1.1,demod:452229] equal(X,multiply(sk_c9,multiply(sk_c3,X))).
% 452369 [para:452310.1.1,452231.1.1.1,demod:452229] equal(X,multiply(sk_c10,multiply(sk_c2,X))).
% 452401 [para:452342.1.1,452231.1.1.1] equal(multiply(sk_c10,X),multiply(sk_c4,multiply(sk_c7,X))).
% 452419 [para:452303.1.1,452364.1.2.2] equal(sk_c6,multiply(sk_c7,identity)).
% 452420 [para:452419.1.2,452231.1.1.1,demod:452229] equal(multiply(sk_c6,X),multiply(sk_c7,X)).
% 452424 [para:452339.1.1,452365.1.2.2] equal(sk_c7,multiply(sk_c5,sk_c5)).
% 452427 [para:452424.1.2,452364.1.2.2] equal(sk_c5,multiply(sk_c7,sk_c7)).
% 452433 [para:452342.1.1,452366.1.2.2] equal(sk_c7,multiply(sk_c7,sk_c10)).
% 452439 [para:452343.1.1,452368.1.2.2] equal(sk_c9,multiply(sk_c9,sk_c8)).
% 452454 [para:452344.1.1,452369.1.2.2] equal(sk_c10,multiply(sk_c10,sk_c9)).
% 452456 [para:452420.1.1,452365.1.2.2] equal(X,multiply(sk_c5,multiply(sk_c7,X))).
% 452457 [para:452300.1.1,452456.1.2.2] equal(sk_c5,multiply(sk_c5,identity)).
% 452458 [para:452305.1.1,452456.1.2.2,demod:452457] equal(sk_c4,sk_c5).
% 452466 [para:452458.1.2,452365.1.2.1,demod:452401,452420] equal(X,multiply(sk_c10,X)).
% 452543 [para:452466.1.2,452369.1.2] equal(X,multiply(sk_c2,X)).
% 452544 [para:452466.1.2,452454.1.2] equal(sk_c10,sk_c9).
% 452555 [para:452544.1.1,452433.1.2.2] equal(sk_c7,multiply(sk_c7,sk_c9)).
% 452556 [para:452544.1.1,452369.1.2.1,demod:452543] equal(X,multiply(sk_c9,X)).
% 452567 [para:452556.1.2,452439.1.2] equal(sk_c9,sk_c8).
% 452582 [para:452567.1.1,452340.1.1.2] equal(multiply(sk_c7,sk_c8),sk_c10).
% 452585 [para:452567.1.1,452454.1.2.2,demod:452466] equal(sk_c10,sk_c8).
% 452588 [para:452585.1.1,452433.1.2.2,demod:452582] equal(sk_c7,sk_c10).
% 452593 [para:452588.1.2,452344.1.1.2,demod:452543] equal(sk_c7,sk_c9).
% 452598 [para:452588.1.2,452433.1.2.2,demod:452427] equal(sk_c7,sk_c5).
% 452600 [para:452588.1.2,452454.1.2.1,demod:452555] equal(sk_c10,sk_c7).
% 452618 [para:452598.1.2,452299.1.1.1] equal(inverse(sk_c7),sk_c7).
% 452624 [para:452600.1.1,452232.1.1.1,demod:452618,cut:452593] 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_c10),sk_c9) | -equal(multiply(sk_c9,sk_c8),sk_c10) | -equal(multiply(sk_c10,sk_c8),sk_c9) | -equal(inverse(X),sk_c10) | -equal(multiply(X,sk_c9),sk_c10) | -equal(multiply(Y,sk_c10),sk_c9) | -equal(inverse(Y),sk_c10) | -equal(multiply(Z,sk_c9),sk_c8) | -equal(inverse(Z),sk_c9) | -equal(multiply(U,V),sk_c10) | -equal(inverse(U),V) | -equal(multiply(V,sk_c9),sk_c10) | -equal(inverse(W),X1) | -equal(inverse(X1),V) | -equal(multiply(W,V),X1).
% Split part used next: -equal(multiply(sk_c9,sk_c8),sk_c10).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 3
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 4
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 5
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 6
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 7
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 8
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 9
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 10
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using 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 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(55,40,0,118,0,0,48849,50,295,48912,0,295,172318,4,1453,173652,5,1496,173656,1,1496,173656,50,1496,173656,40,1496,173719,0,1496,176029,3,1844,176371,4,1953,176469,5,2097,176469,1,2097,176469,50,2097,176469,40,2097,176532,0,2097,178842,3,2431,179227,4,2551,179284,5,2698,179284,1,2698,179284,50,2698,179284,40,2698,179347,0,2698,196273,3,4199,198300,4,4949,200593,5,5699,200594,1,5699,200594,50,5699,200594,40,5699,200657,0,5699,212954,3,6454,214284,4,6825,215883,1,7200,215883,50,7200,215883,40,7200,215946,0,7200,224119,3,8029,226261,4,8326,229138,5,8701,229139,5,8701,229140,1,8701,229140,50,8701,229140,40,8701,229203,0,8701,298908,3,12607,299900,4,14553,300616,1,16502,300616,50,16504,300616,40,16504,300679,0,16504,355039,3,19057,355808,4,20330,356529,1,21605,356529,50,21606,356529,40,21606,356592,0,21606,388894,3,23107,389725,4,23857,390689,1,24607,390689,50,24608,390689,40,24608,390752,0,24608,399156,3,25397,401462,4,25734,402905,5,26109,402905,1,26109,402905,50,26109,402905,40,26109,402968,0,26109,425948,3,27310,426831,4,27910,427762,1,28510,427762,50,28510,427762,40,28510,427825,0,28510,445408,3,29261,446075,4,29636,446594,5,30011,446595,1,30011,446595,50,30011,446595,40,30011,446595,40,30011,446704,0,30011,448377,50,30017,448377,30,30017,448377,40,30017,448432,0,30017,448540,50,30017,448540,30,30017,448540,40,30017,448595,0,30023,448709,50,30023,448764,0,30023,448905,50,30024,448905,30,30024,448905,40,30024,448960,0,30028,449164,50,30029,449164,30,30029,449164,40,30029,449219,0,30029,449423,50,30032,449478,0,30037,449746,50,30042,449801,0,30042,450077,50,30049,450132,0,30053,450416,50,30063,450471,0,30063,450761,50,30076,450816,0,30080,451114,50,30101,451169,0,30101,451475,50,30137,451530,0,30142,451846,50,30210,451901,0,30210,452227,50,30346,452227,40,30346,452282,0,30346,452623,50,30347,452623,30,30347,452623,40,30347,452678,0,30347,452882,50,30350,452937,0,30354,453205,50,30359,453260,0,30359,453536,50,30366,453591,0,30371,453875,50,30380,453930,0,30380,454220,50,30393,454275,0,30397,454573,50,30418,454628,0,30418,454934,50,30454,454989,0,30459,455305,50,30529,455360,0,30529,455686,50,30665,455686,40,30665,455741,0,30665)
%
%
% START OF PROOF
% 455477 [?] ?
% 455688 [] equal(multiply(identity,X),X).
% 455689 [] equal(multiply(inverse(X),X),identity).
% 455690 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 455691 [] -equal(multiply(sk_c9,sk_c8),sk_c10).
% 455728 [?] ?
% 455729 [?] ?
% 455815 [input:455728,cut:455691] equal(inverse(sk_c3),sk_c9).
% 455816 [para:455815.1.1,455689.1.1.1] equal(multiply(sk_c9,sk_c3),identity).
% 455845 [input:455729,cut:455691] equal(multiply(sk_c3,sk_c9),sk_c8).
% 455880 [para:455816.1.1,455690.1.1.1,demod:455688] equal(X,multiply(sk_c9,multiply(sk_c3,X))).
% 455929 [para:455845.1.1,455880.1.2.2] equal(sk_c9,multiply(sk_c9,sk_c8)).
% 455930 [para:455929.1.2,455691.1.1,cut:455477] 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_c10),sk_c9) | -equal(multiply(sk_c9,sk_c8),sk_c10) | -equal(multiply(sk_c10,sk_c8),sk_c9) | -equal(inverse(X),sk_c10) | -equal(multiply(X,sk_c9),sk_c10) | -equal(multiply(Y,sk_c10),sk_c9) | -equal(inverse(Y),sk_c10) | -equal(multiply(Z,sk_c9),sk_c8) | -equal(inverse(Z),sk_c9) | -equal(multiply(U,V),sk_c10) | -equal(inverse(U),V) | -equal(multiply(V,sk_c9),sk_c10) | -equal(inverse(W),X1) | -equal(inverse(X1),V) | -equal(multiply(W,V),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: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 4
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 5
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 6
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 7
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 8
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 9
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 10
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(55,40,0,118,0,0,48849,50,295,48912,0,295,172318,4,1453,173652,5,1496,173656,1,1496,173656,50,1496,173656,40,1496,173719,0,1496,176029,3,1844,176371,4,1953,176469,5,2097,176469,1,2097,176469,50,2097,176469,40,2097,176532,0,2097,178842,3,2431,179227,4,2551,179284,5,2698,179284,1,2698,179284,50,2698,179284,40,2698,179347,0,2698,196273,3,4199,198300,4,4949,200593,5,5699,200594,1,5699,200594,50,5699,200594,40,5699,200657,0,5699,212954,3,6454,214284,4,6825,215883,1,7200,215883,50,7200,215883,40,7200,215946,0,7200,224119,3,8029,226261,4,8326,229138,5,8701,229139,5,8701,229140,1,8701,229140,50,8701,229140,40,8701,229203,0,8701,298908,3,12607,299900,4,14553,300616,1,16502,300616,50,16504,300616,40,16504,300679,0,16504,355039,3,19057,355808,4,20330,356529,1,21605,356529,50,21606,356529,40,21606,356592,0,21606,388894,3,23107,389725,4,23857,390689,1,24607,390689,50,24608,390689,40,24608,390752,0,24608,399156,3,25397,401462,4,25734,402905,5,26109,402905,1,26109,402905,50,26109,402905,40,26109,402968,0,26109,425948,3,27310,426831,4,27910,427762,1,28510,427762,50,28510,427762,40,28510,427825,0,28510,445408,3,29261,446075,4,29636,446594,5,30011,446595,1,30011,446595,50,30011,446595,40,30011,446595,40,30011,446704,0,30011,448377,50,30017,448377,30,30017,448377,40,30017,448432,0,30017,448540,50,30017,448540,30,30017,448540,40,30017,448595,0,30023,448709,50,30023,448764,0,30023,448905,50,30024,448905,30,30024,448905,40,30024,448960,0,30028,449164,50,30029,449164,30,30029,449164,40,30029,449219,0,30029,449423,50,30032,449478,0,30037,449746,50,30042,449801,0,30042,450077,50,30049,450132,0,30053,450416,50,30063,450471,0,30063,450761,50,30076,450816,0,30080,451114,50,30101,451169,0,30101,451475,50,30137,451530,0,30142,451846,50,30210,451901,0,30210,452227,50,30346,452227,40,30346,452282,0,30346,452623,50,30347,452623,30,30347,452623,40,30347,452678,0,30347,452882,50,30350,452937,0,30354,453205,50,30359,453260,0,30359,453536,50,30366,453591,0,30371,453875,50,30380,453930,0,30380,454220,50,30393,454275,0,30397,454573,50,30418,454628,0,30418,454934,50,30454,454989,0,30459,455305,50,30529,455360,0,30529,455686,50,30665,455686,40,30665,455741,0,30665,455929,50,30665,455929,30,30665,455929,40,30665,455984,0,30665,456188,50,30667,456243,0,30672,456511,50,30677,456566,0,30677,456842,50,30684,456897,0,30688,457181,50,30697,457236,0,30697,457526,50,30710,457581,0,30725,457879,50,30762,457934,0,30763,458240,50,30799,458295,0,30803,458611,50,30873,458611,40,30873,458666,0,30873)
%
%
% START OF PROOF
% 458409 [?] ?
% 458613 [] equal(multiply(identity,X),X).
% 458614 [] equal(multiply(inverse(X),X),identity).
% 458615 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 458616 [] -equal(multiply(sk_c10,sk_c8),sk_c9).
% 458638 [?] ?
% 458639 [?] ?
% 458641 [?] ?
% 458642 [?] ?
% 458720 [input:458638,cut:458616] equal(inverse(sk_c5),sk_c7).
% 458721 [para:458720.1.1,458614.1.1.1] equal(multiply(sk_c7,sk_c5),identity).
% 458723 [input:458639,cut:458616] equal(inverse(sk_c6),sk_c5).
% 458724 [para:458723.1.1,458614.1.1.1] equal(multiply(sk_c5,sk_c6),identity).
% 458725 [input:458641,cut:458616] equal(inverse(sk_c4),sk_c7).
% 458726 [para:458725.1.1,458614.1.1.1] equal(multiply(sk_c7,sk_c4),identity).
% 458741 [input:458642,cut:458616] equal(multiply(sk_c4,sk_c7),sk_c10).
% 458784 [para:458721.1.1,458615.1.1.1,demod:458613] equal(X,multiply(sk_c7,multiply(sk_c5,X))).
% 458787 [para:458724.1.1,458615.1.1.1,demod:458613] equal(X,multiply(sk_c5,multiply(sk_c6,X))).
% 458800 [para:458741.1.1,458615.1.1.1] equal(multiply(sk_c10,X),multiply(sk_c4,multiply(sk_c7,X))).
% 458820 [para:458724.1.1,458784.1.2.2] equal(sk_c6,multiply(sk_c7,identity)).
% 458821 [para:458820.1.2,458615.1.1.1,demod:458613] equal(multiply(sk_c6,X),multiply(sk_c7,X)).
% 458852 [para:458821.1.1,458787.1.2.2] equal(X,multiply(sk_c5,multiply(sk_c7,X))).
% 458855 [para:458721.1.1,458852.1.2.2] equal(sk_c5,multiply(sk_c5,identity)).
% 458856 [para:458726.1.1,458852.1.2.2,demod:458855] equal(sk_c4,sk_c5).
% 458862 [para:458856.1.2,458787.1.2.1,demod:458800,458821] equal(X,multiply(sk_c10,X)).
% 458865 [para:458862.1.2,458616.1.1,cut:458409] 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: 45151
% derived clauses: 3804134
% kept clauses: 226519
% kept size sum: 917416
% kept mid-nuclei: 159666
% kept new demods: 7228
% forw unit-subs: 1076666
% forw double-subs: 2067572
% forw overdouble-subs: 201670
% backward subs: 16282
% fast unit cutoff: 26232
% full unit cutoff: 0
% dbl unit cutoff: 23433
% real runtime : 310.68
% process. runtime: 308.74
% specific non-discr-tree subsumption statistics:
% tried: 43865649
% length fails: 4734380
% strength fails: 12382386
% predlist fails: 3551311
% aux str. fails: 5848522
% by-lit fails: 7879167
% full subs tried: 3093405
% full subs fail: 3008720
%
% ; 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/GRP386-1+eq_r.in")
%
%------------------------------------------------------------------------------