%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP085-1 : TPTP v3.4.2. Bugfixed v2.7.0.
% Transfm : add_equality:r
% Format : otter:hypothesis:set(auto),clear(print_given)
% Command : gandalf-wrapper -time %d %s
% Computer : art09.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/GRP085-1+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 4 7)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 4 7)
% (binary-posweight-lex-big-order 30 #f 4 7)
% (binary 30 #t)
% (binary-posweight-kb-big-order 156 #f)
% (binary-posweight-lex-big-order 102 #f)
% (binary-posweight-firstpref-order 60 #f)
% (binary-order 30 #f)
% (binary-posweight-kb-small-order 48 #f)
% (binary-posweight-lex-small-order 30 #f)
%
%
% SOS clause
% -equal(multiply(inverse(a1),a1),multiply(inverse(b1),b1)) | -equal(multiply(multiply(inverse(b2),b2),a2),a2) | -equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) | -equal(multiply(a4,b4),multiply(b4,a4)).
% was split for some strategies as:
% -equal(multiply(inverse(a1),a1),multiply(inverse(b1),b1)).
% -equal(multiply(multiply(inverse(b2),b2),a2),a2).
% -equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))).
% -equal(multiply(a4,b4),multiply(b4,a4)).
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(3,40,1,6,0,1,7,50,1,10,0,1,11,50,1,14,0,2)
%
%
% START OF PROOF
% 13 [] equal(multiply(multiply(multiply(X,Y),Z),inverse(multiply(X,Z))),Y).
% 14 [] -equal(multiply(multiply(inverse(b2),b2),a2),a2) | -equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) | -equal(multiply(inverse(a1),a1),multiply(inverse(b1),b1)) | -equal(multiply(a4,b4),multiply(b4,a4)).
% 15 [para:13.1.1,13.1.1.1] equal(multiply(X,inverse(multiply(multiply(Y,X),inverse(multiply(Y,Z))))),Z).
% 16 [para:13.1.1,13.1.1.1.1] equal(multiply(multiply(X,Y),inverse(multiply(multiply(multiply(Z,X),U),Y))),inverse(multiply(Z,U))).
% 17 [para:13.1.1,13.1.1.2.1] equal(multiply(multiply(multiply(multiply(multiply(X,Y),Z),U),inverse(multiply(X,Z))),inverse(Y)),U).
% 18 [para:15.1.1,13.1.1.1.1] equal(multiply(multiply(X,Y),inverse(multiply(Z,Y))),inverse(multiply(multiply(U,Z),inverse(multiply(U,X))))).
% 22 [para:13.1.1,16.1.1.2.1] equal(multiply(multiply(X,inverse(multiply(Y,Z))),inverse(X)),inverse(multiply(Y,Z))).
% 24 [para:13.1.1,22.1.1.1] equal(multiply(X,inverse(multiply(multiply(Y,X),Z))),inverse(multiply(Y,Z))).
% 25 [para:13.1.1,22.1.1.1.2.1,demod:13] equal(multiply(multiply(X,inverse(Y)),inverse(X)),inverse(Y)).
% 26 [para:22.1.1,15.1.1.2.1.1,demod:24] equal(multiply(inverse(X),inverse(inverse(multiply(X,Y)))),Y).
% 28 [para:15.1.1,22.1.1.1] equal(multiply(X,inverse(Y)),inverse(multiply(multiply(Z,Y),inverse(multiply(Z,X))))).
% 29 [para:15.1.1,22.1.1.1.2.1,demod:28,25] equal(inverse(X),inverse(multiply(Y,multiply(X,inverse(Y))))).
% 42 [para:26.1.1,13.1.1.1.1] equal(multiply(multiply(X,Y),inverse(multiply(inverse(Z),Y))),inverse(inverse(multiply(Z,X)))).
% 46 [para:15.1.1,26.1.1.2.1.1,demod:28] equal(multiply(inverse(X),inverse(inverse(Y))),multiply(Y,inverse(X))).
% 48 [para:26.1.1,25.1.1.1] equal(multiply(X,inverse(inverse(Y))),inverse(inverse(multiply(Y,X)))).
% 51 [para:29.1.2,15.1.1.2.1.2,demod:24] equal(inverse(multiply(X,inverse(Y))),multiply(Y,inverse(X))).
% 69 [para:26.1.1,51.1.1.1,demod:46] equal(inverse(X),multiply(Y,inverse(multiply(Y,X)))).
% 79 [para:69.1.2,16.1.1.2.1.1,demod:51,48,42] equal(multiply(X,inverse(inverse(Y))),multiply(multiply(multiply(Z,X),Y),inverse(Z))).
% 82 [para:69.1.2,25.1.1.1] equal(multiply(inverse(X),inverse(Y)),inverse(multiply(Y,X))).
% 85 [para:69.1.2,51.1.1.1] equal(inverse(inverse(X)),multiply(multiply(Y,X),inverse(Y))).
% 89 [para:15.1.1,17.1.1.1.1,demod:28] equal(multiply(multiply(X,inverse(multiply(Y,Z))),inverse(U)),multiply(X,inverse(multiply(multiply(Y,U),Z)))).
% 91 [?] ?
% 95 [para:25.1.1,17.1.1.1.1.1,demod:79,51] equal(multiply(X,multiply(Y,inverse(Y))),X).
% 96 [para:25.1.1,17.1.1.1.1.1.1,demod:91,85,89] equal(inverse(inverse(X)),X).
% 102 [para:69.1.2,17.1.1.1.1,demod:82] equal(inverse(multiply(X,multiply(multiply(Y,Z),U))),inverse(multiply(multiply(multiply(Y,X),Z),U))).
% 107 [para:96.1.1,26.1.1.2] equal(multiply(inverse(X),multiply(X,Y)),Y).
% 110 [para:95.1.1,15.1.1.2.1.1,demod:96,69] equal(multiply(multiply(X,inverse(X)),Y),Y).
% 115 [para:96.1.1,95.1.1.2.2] equal(multiply(X,multiply(inverse(Y),Y)),X).
% 116 [para:107.1.1,13.1.1.1.1,demod:96,48,42] equal(multiply(X,Y),multiply(Y,X)).
% 132 [para:116.1.1,15.1.1,demod:28] equal(multiply(multiply(X,inverse(Y)),Y),X).
% 144 [para:116.1.1,51.1.1.1] equal(inverse(multiply(inverse(X),Y)),multiply(X,inverse(Y))).
% 156 [para:13.1.1,18.1.2.1.1,demod:96,48,69,102,144] equal(multiply(multiply(X,Y),multiply(multiply(Z,U),inverse(Y))),multiply(X,multiply(U,Z))).
% 171 [para:18.1.2,25.1.1.1.2,demod:28,51,85] equal(multiply(multiply(X,Y),inverse(multiply(Z,Y))),multiply(X,inverse(Z))).
% 184 [para:18.1.2,51.1.1,demod:171] equal(multiply(X,inverse(Y)),multiply(multiply(Z,X),inverse(multiply(Z,Y)))).
% 186 [para:18.1.1,69.1.2.2.1,demod:51,184,96,48] equal(multiply(X,Y),multiply(multiply(Z,X),multiply(Y,inverse(Z)))).
% 189 [para:69.1.2,18.1.2.1.1,demod:96,48,82,156,144] equal(multiply(X,multiply(Y,Z)),multiply(Y,multiply(X,Z))).
% 204 [para:51.1.1,110.1.1.1.2,demod:186] equal(multiply(multiply(inverse(X),X),Y),Y).
% 206 [para:115.1.1,26.1.1.2.1.1,demod:96] equal(multiply(inverse(X),X),multiply(inverse(Y),Y)).
% 210 [para:13.1.1,132.1.1.1] equal(multiply(X,multiply(Y,Z)),multiply(multiply(Y,X),Z)).
% 228 [hyper:14,204,demod:210,cut:189,cut:206,cut:116] 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 7
% clause depth limited to 6
% seconds given: 10
%
%
% ***GANDALF_FOUND_A_REFUTATION***
%
% Global statistics over all passes:
%
% given clauses: 31
% derived clauses: 935
% kept clauses: 210
% kept size sum: 2925
% kept mid-nuclei: 2
% kept new demods: 190
% forw unit-subs: 638
% 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 : 0.4
% process. runtime: 0.3
% specific non-discr-tree subsumption statistics:
% tried: 2
% length fails: 0
% strength fails: 2
% 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/GRP085-1+eq_r.in")
%
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