%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : BOO002-2 : TPTP v3.4.2. Released v1.1.0.
% Transfm : add_equality:r
% Format : otter:hypothesis:set(auto),clear(print_given)
% Command : gandalf-wrapper -time %d %s
% Computer : art06.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/BOO/BOO002-2+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 3 1)
% (binary-posweight-lex-big-order 30 #f 3 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(7,40,0,14,0,0,22,50,0,29,0,0)
%
%
% START OF PROOF
% 24 [] equal(multiply(multiply(X,Y,Z),U,multiply(X,Y,V)),multiply(X,Y,multiply(Z,U,V))).
% 25 [] equal(multiply(X,Y,Y),Y).
% 26 [] equal(multiply(X,X,Y),X).
% 27 [] equal(multiply(inverse(X),X,Y),Y).
% 28 [] equal(multiply(X,Y,X),X).
% 29 [] -equal(multiply(a,inverse(a),b),b).
% 30 [para:24.1.1,25.1.1] equal(multiply(X,Y,multiply(Z,multiply(X,Y,U),U)),multiply(X,Y,U)).
% 32 [para:25.1.1,24.1.1.3] equal(multiply(multiply(X,Y,Z),U,Y),multiply(X,Y,multiply(Z,U,Y))).
% 33 [para:24.1.1,26.1.1] equal(multiply(X,Y,multiply(Z,multiply(X,Y,Z),U)),multiply(X,Y,Z)).
% 34 [para:28.1.1,24.1.1.1] equal(multiply(X,Y,multiply(X,Z,U)),multiply(X,Z,multiply(X,Y,U))).
% 35 [para:28.1.1,24.1.1.3] equal(multiply(multiply(X,Y,Z),U,X),multiply(X,Y,multiply(Z,U,X))).
% 38 [para:26.1.1,30.1.1.3] equal(multiply(X,Y,multiply(X,Y,Z)),multiply(X,Y,Z)).
% 40 [para:38.1.1,24.1.1.3,demod:24] equal(multiply(X,Y,multiply(Z,U,V)),multiply(X,Y,multiply(Z,U,multiply(X,Y,V)))).
% 60 [para:28.1.1,32.1.1.1] equal(multiply(X,Y,Z),multiply(X,Z,multiply(X,Y,Z))).
% 105 [para:35.1.1,32.1.1.1] equal(multiply(multiply(X,Y,multiply(Z,U,X)),V,U),multiply(multiply(X,Y,Z),U,multiply(X,V,U))).
% 126 [para:33.1.1,40.1.2.3,demod:25] equal(multiply(X,multiply(Y,Z,X),multiply(Y,Z,U)),multiply(Y,Z,X)).
% 127 [para:25.1.1,126.1.1.3] equal(multiply(X,multiply(Y,Z,X),Z),multiply(Y,Z,X)).
% 128 [para:28.1.1,126.1.1.3] equal(multiply(X,multiply(Y,Z,X),Y),multiply(Y,Z,X)).
% 144 [para:60.1.2,126.1.1.3] equal(multiply(X,multiply(Y,Z,X),multiply(Y,U,Z)),multiply(Y,Z,X)).
% 188 [para:128.1.1,34.1.1.3] equal(multiply(X,Y,multiply(Z,U,X)),multiply(X,multiply(Z,U,X),multiply(X,Y,Z))).
% 189 [para:128.1.1,35.1.1.1] equal(multiply(multiply(X,Y,Z),U,Z),multiply(Z,multiply(X,Y,Z),multiply(X,U,Z))).
% 334 [para:144.1.1,128.1.1.2,demod:144] equal(multiply(multiply(X,Y,Z),multiply(X,Z,U),U),multiply(X,Z,U)).
% 576 [para:127.1.1,334.1.1.2,demod:127,105] equal(multiply(multiply(X,Y,Z),U,multiply(Z,U,X)),multiply(Z,U,X)).
% 666 [para:127.1.1,576.1.1.1] equal(multiply(multiply(X,Y,Z),U,multiply(Y,U,Z)),multiply(Y,U,Z)).
% 680 [para:27.1.1,666.1.1.3,demod:27] equal(multiply(multiply(X,inverse(Y),Z),Y,Z),Z).
% 1782 [para:128.1.1,188.1.2.3,demod:189] equal(multiply(multiply(X,Y,Z),U,Z),multiply(multiply(X,U,Z),Y,Z)).
% 1881 [para:1782.1.1,680.1.1] equal(multiply(multiply(X,Y,Z),inverse(Y),Z),Z).
% 1923 [para:26.1.1,1881.1.1.1,slowcut:29] 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 4
% seconds given: 60
%
%
% ***GANDALF_FOUND_A_REFUTATION***
%
% Global statistics over all passes:
%
% given clauses: 141
% derived clauses: 39450
% kept clauses: 1900
% kept size sum: 45184
% kept mid-nuclei: 0
% kept new demods: 1758
% forw unit-subs: 21666
% forw double-subs: 0
% forw overdouble-subs: 0
% backward subs: 1
% fast unit cutoff: 0
% full unit cutoff: 0
% dbl unit cutoff: 0
% real runtime : 1.82
% process. runtime: 1.80
% 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/BOO/BOO002-2+eq_r.in")
%
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