%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP002-3 : TPTP v3.4.2. Released v1.0.0.
% 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 0.0s
% Output : Assurance 0.0s
% 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/GRP002-3+eq_r.in
% Using automatic strategy selection.
% Time limit in seconds: 600
%
% prove-all-passes started
%
% detected problem class: ueq
%
% strategies selected:
% (binary-posweight-kb-big-order 60 #f 5 1)
% (binary-posweight-lex-big-order 30 #f 5 1)
% (binary 30 #t)
% (binary-posweight-kb-big-order 180 #f)
% (binary-posweight-lex-big-order 120 #f)
% (binary-posweight-firstpref-order 60 #f)
% (binary-posweight-kb-small-order 60 #f)
% (binary-posweight-lex-small-order 60 #f)
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(7,40,0,14,0,0)
%
%
% START OF PROOF
% 8 [] equal(X,X).
% 9 [] equal(multiply(identity,X),X).
% 10 [] equal(multiply(inverse(X),X),identity).
% 11 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 12 [] equal(commutator(X,Y),multiply(X,multiply(Y,multiply(inverse(X),inverse(Y))))).
% 13 [] equal(multiply(X,multiply(X,X)),identity).
% 14 [] -equal(commutator(commutator(a,b),b),identity).
% 15 [para:10.1.1,11.1.1.1,demod:9] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 16 [para:13.1.1,11.1.1.1,demod:11,9] equal(X,multiply(Y,multiply(Y,multiply(Y,X)))).
% 17 [para:9.1.1,15.1.2.2] equal(X,multiply(inverse(identity),X)).
% 18 [para:10.1.1,15.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 19 [para:13.1.1,15.1.2.2] equal(multiply(X,X),multiply(inverse(X),identity)).
% 20 [para:11.1.1,15.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 21 [para:15.1.2,15.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 22 [para:17.1.2,13.1.1,demod:17] equal(inverse(identity),identity).
% 25 [para:19.1.1,11.1.1.1,demod:9,11] equal(multiply(inverse(X),Y),multiply(X,multiply(X,Y))).
% 29 [para:19.1.2,18.1.2] equal(X,multiply(inverse(X),inverse(X))).
% 30 [para:12.1.2,9.1.1,demod:9,22] equal(commutator(identity,X),multiply(X,inverse(X))).
% 32 [para:10.1.1,12.1.2.2.2,demod:15] equal(commutator(inverse(X),X),identity).
% 33 [para:12.1.2,15.1.2,demod:32,30,21] equal(commutator(identity,X),identity).
% 34 [para:12.1.2,15.1.2.2] equal(multiply(X,multiply(inverse(Y),inverse(X))),multiply(inverse(Y),commutator(Y,X))).
% 38 [para:29.1.2,15.1.2.2,demod:21] equal(inverse(X),multiply(X,X)).
% 39 [para:13.1.1,16.1.2.2] equal(X,multiply(X,identity)).
% 41 [para:39.1.2,18.1.2] equal(X,inverse(inverse(X))).
% 43 [para:41.1.2,15.1.2.1] equal(X,multiply(Y,multiply(inverse(Y),X))).
% 44 [para:41.1.2,12.1.2.2.2.1] equal(commutator(inverse(X),Y),multiply(inverse(X),multiply(Y,multiply(X,inverse(Y))))).
% 45 [para:41.1.2,12.1.2.2.2.2] equal(commutator(X,inverse(Y)),multiply(X,multiply(inverse(Y),multiply(inverse(X),Y)))).
% 52 [para:10.1.1,20.1.2.2,demod:39] equal(X,inverse(multiply(inverse(multiply(Y,X)),Y))).
% 53 [para:10.1.1,20.1.2.2.2,demod:39] equal(X,multiply(inverse(multiply(Y,inverse(X))),Y)).
% 58 [para:19.1.1,20.1.2.2.2,demod:39] equal(X,multiply(inverse(multiply(Y,X)),multiply(Y,inverse(X)))).
% 59 [para:12.1.2,20.1.2.2] equal(multiply(inverse(X),inverse(Y)),multiply(inverse(multiply(X,Y)),commutator(X,Y))).
% 65 [para:30.1.2,20.1.2.2.2,demod:39,33] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 66 [para:15.1.2,52.1.2.1.1.1] equal(multiply(X,Y),inverse(multiply(inverse(Y),inverse(X)))).
% 69 [para:43.1.2,52.1.2.1.1.1] equal(multiply(inverse(X),Y),inverse(multiply(inverse(Y),X))).
% 72 [para:15.1.2,65.1.2.1.1] equal(inverse(multiply(X,Y)),multiply(inverse(Y),inverse(X))).
% 76 [para:52.1.2,65.1.2.1] equal(inverse(X),multiply(Y,inverse(multiply(X,Y)))).
% 84 [para:76.1.2,12.1.2.2.2,demod:72,11] equal(commutator(X,multiply(Y,inverse(X))),multiply(X,multiply(Y,inverse(multiply(Y,X))))).
% 86 [para:76.1.2,16.1.2.2.2] equal(inverse(multiply(X,Y)),multiply(Y,multiply(Y,inverse(X)))).
% 87 [para:76.1.2,43.1.2.2] equal(inverse(multiply(X,inverse(Y))),multiply(Y,inverse(X))).
% 88 [para:25.1.1,12.1.2.2.2,demod:84,86] equal(commutator(X,Y),commutator(X,multiply(Y,inverse(X)))).
% 97 [para:66.1.2,66.1.2.1.1,demod:11,72] equal(multiply(X,inverse(multiply(Y,Z))),inverse(multiply(Y,multiply(Z,inverse(X))))).
% 98 [para:12.1.2,69.1.2.1,demod:11,97,41] equal(multiply(X,multiply(inverse(multiply(X,Y)),Y)),inverse(commutator(inverse(Y),X))).
% 107 [para:53.1.2,88.1.2.2,demod:41,72] equal(commutator(X,multiply(Y,X)),commutator(X,Y)).
% 109 [para:25.1.1,88.1.2.2,demod:86] equal(commutator(X,inverse(Y)),commutator(X,inverse(multiply(X,Y)))).
% 123 [para:34.1.2,52.1.2.1.1.1,demod:88,84,11,87,72] equal(commutator(X,Y),inverse(commutator(Y,X))).
% 161 [para:34.1.2,107.1.1.2,demod:72] equal(commutator(commutator(X,Y),multiply(Y,inverse(multiply(Y,X)))),commutator(commutator(X,Y),inverse(X))).
% 162 [para:107.1.1,123.1.2.1,demod:123] equal(commutator(multiply(X,Y),Y),commutator(X,Y)).
% 164 [para:15.1.2,162.1.1.1,demod:107] equal(commutator(X,Y),commutator(inverse(Y),multiply(Y,X))).
% 165 [para:12.1.2,162.1.1.1,demod:161,72] equal(commutator(commutator(X,Y),inverse(X)),commutator(X,multiply(Y,inverse(multiply(Y,X))))).
% 210 [para:15.1.2,164.1.2.2,demod:41] equal(commutator(multiply(X,Y),inverse(X)),commutator(X,Y)).
% 254 [para:58.1.2,25.1.2.2,demod:11,41] equal(multiply(X,multiply(Y,multiply(X,inverse(Y)))),multiply(inverse(multiply(X,Y)),Y)).
% 286 [para:38.1.1,44.1.2.1,demod:123,98,254,11] equal(commutator(inverse(X),Y),commutator(X,inverse(Y))).
% 303 [para:123.1.2,286.1.1.1] equal(commutator(commutator(X,Y),Z),commutator(commutator(Y,X),inverse(Z))).
% 307 [para:286.1.1,164.1.2,demod:109] equal(commutator(X,Y),commutator(Y,inverse(X))).
% 315 [para:123.1.2,307.1.2.2] equal(commutator(commutator(X,Y),Z),commutator(Z,commutator(Y,X))).
% 316 [para:307.1.2,210.1.1] equal(commutator(X,multiply(X,Y)),commutator(X,Y)).
% 327 [para:12.1.2,316.1.1.2,demod:303,165,72] equal(commutator(X,commutator(X,Y)),commutator(commutator(Y,X),X)).
% 334 [para:12.1.2,45.1.2.2.2,demod:33,30,76,72,59,11,307,286,327,303,165,97,41] equal(commutator(X,commutator(X,Y)),identity).
% 684 [para:315.1.1,14.1.1,demod:334,cut:8] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using binary resolution
% using first neg lit preferred strategy
% not using sos strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% clause length limited to 1
% clause depth limited to 5
% seconds given: 60
%
%
% ***GANDALF_FOUND_A_REFUTATION***
%
% Global statistics over all passes:
%
% given clauses: 121
% derived clauses: 11027
% kept clauses: 669
% kept size sum: 9358
% kept mid-nuclei: 0
% kept new demods: 506
% forw unit-subs: 9918
% forw double-subs: 0
% forw overdouble-subs: 0
% backward subs: 2
% fast unit cutoff: 1
% full unit cutoff: 0
% dbl unit cutoff: 0
% real runtime : 0.18
% process. runtime: 0.16
% specific non-discr-tree subsumption statistics:
% tried: 0
% length fails: 0
% strength fails: 0
% predlist fails: 0
% aux str. fails: 0
% by-lit fails: 0
% full subs tried: 0
% full subs fail: 0
%
% ; 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/GRP002-3+eq_r.in")
%
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