%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : BOO035-1 : TPTP v3.4.2. Released v2.2.0.
% Transfm : add_equality:r
% Format : otter:hypothesis:set(auto),clear(print_given)
% Command : gandalf-wrapper -time %d %s
% Computer : art04.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/BOO035-1+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 5 9)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 5 9)
% (binary-posweight-lex-big-order 30 #f 5 9)
% (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(multiply(d,e,a),b,multiply(d,e,c)),multiply(d,e,multiply(a,b,c))) | -equal(multiply(b,a,a),a) | -equal(multiply(a,b,inverse(b)),a) | -equal(multiply(a,a,b),a) | -equal(multiply(inverse(b),b,a),a).
% was split for some strategies as:
% -equal(multiply(multiply(d,e,a),b,multiply(d,e,c)),multiply(d,e,multiply(a,b,c))).
% -equal(multiply(b,a,a),a).
% -equal(multiply(a,b,inverse(b)),a).
% -equal(multiply(a,a,b),a).
% -equal(multiply(inverse(b),b,a),a).
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(3,40,0,6,0,0,12,50,0,15,0,0,373,4,765,375,50,765,375,40,765,378,0,765)
%
%
% START OF PROOF
% 376 [] equal(X,X).
% 377 [] equal(multiply(multiply(X,inverse(X),Y),inverse(multiply(multiply(Z,U,V),W,multiply(Z,U,X1))),multiply(U,multiply(X1,W,V),Z)),Y).
% 378 [] -equal(multiply(multiply(d,e,a),b,multiply(d,e,c)),multiply(d,e,multiply(a,b,c))) | -equal(multiply(inverse(b),b,a),a) | -equal(multiply(a,b,inverse(b)),a) | -equal(multiply(a,a,b),a) | -equal(multiply(b,a,a),a).
% 379 [para:377.1.1,377.1.1.1] equal(multiply(multiply(X,Y,Z),inverse(multiply(multiply(U,V,W),X1,multiply(U,V,X2))),multiply(V,multiply(X2,X1,W),U)),multiply(Y,multiply(Z,inverse(multiply(X,Y,X3)),X3),X)).
% 383 [para:379.1.1,377.1.1] equal(multiply(inverse(X),multiply(Y,inverse(multiply(X,inverse(X),Z)),Z),X),Y).
% 384 [para:379.1.1,377.1.1.1] equal(multiply(multiply(X,multiply(multiply(Y,Z,U),inverse(multiply(multiply(Y,Z,V),X,W)),W),multiply(Y,Z,V)),inverse(multiply(multiply(X1,X2,X3),X4,multiply(X1,X2,X5))),multiply(X2,multiply(X5,X4,X3),X1)),multiply(Z,multiply(U,X,V),Y)).
% 399 [para:379.1.1,379.1.1] equal(multiply(X,multiply(Y,inverse(multiply(Z,X,U)),U),Z),multiply(X,multiply(Y,inverse(multiply(Z,X,V)),V),Z)).
% 417 [para:383.1.1,377.1.1.3.2] equal(multiply(multiply(X,inverse(X),Y),inverse(multiply(multiply(Z,U,V),multiply(W,inverse(multiply(V,inverse(V),X1)),X1),multiply(Z,U,inverse(V)))),multiply(U,W,Z)),Y).
% 487 [para:417.1.1,377.1.1.2.1] equal(multiply(multiply(X,inverse(X),Y),inverse(Z),multiply(inverse(U),multiply(V,inverse(multiply(multiply(V,U,W),multiply(inverse(U),inverse(multiply(W,inverse(W),X1)),X1),multiply(V,U,inverse(W)))),Z),U)),Y).
% 1019 [para:377.1.1,487.1.1.3.2,demod:383] equal(multiply(multiply(X,inverse(X),Y),inverse(multiply(Z,inverse(Z),multiply(U,inverse(U),V))),multiply(inverse(Z),V,Z)),Y).
% 1261 [para:1019.1.1,377.1.1.1,demod:377] equal(X,multiply(inverse(Y),X,Y)).
% 1325 [para:1261.1.2,383.1.1.2,demod:1261] equal(inverse(multiply(X,inverse(X),Y)),inverse(Y)).
% 1327 [para:383.1.1,1261.1.2,demod:1325] equal(multiply(X,inverse(Y),Y),X).
% 1329 [para:1261.1.2,399.1.1.2.2.1] equal(multiply(X,multiply(Y,inverse(X),Z),inverse(Z)),multiply(X,multiply(Y,inverse(multiply(inverse(Z),X,U)),U),inverse(Z))).
% 1360 [para:1261.1.2,1019.1.1.1,demod:1327,1261,1325] equal(inverse(inverse(X)),X).
% 1362 [para:1261.1.2,1019.1.1.2.1.3,demod:1327,1261,1325,1360] equal(multiply(X,inverse(X),Y),Y).
% 1364 [para:1360.1.1,383.1.1.1,demod:1327,1329,1360] equal(multiply(X,Y,inverse(X)),Y).
% 1375 [para:1360.1.1,1019.1.1.1.2,demod:1327,1261,1362] equal(multiply(inverse(X),X,Y),Y).
% 1377 [para:1327.1.1,377.1.1.2.1,demod:1362] equal(multiply(X,inverse(multiply(Y,Z,U)),multiply(Z,multiply(V,inverse(multiply(Y,Z,V)),U),Y)),X).
% 1382 [para:1327.1.1,379.1.1.2.1,demod:1377] equal(multiply(X,Y,Z),multiply(Y,multiply(Z,inverse(multiply(X,Y,U)),U),X)).
% 1408 [para:1327.1.1,1019.1.1.3,demod:1360,1362] equal(multiply(X,Y,inverse(Y)),X).
% 1411 [para:1362.1.1,379.1.1,demod:1382] equal(multiply(X,multiply(Y,Z,U),V),multiply(multiply(V,X,U),Z,multiply(V,X,Y))).
% 1412 [para:1362.1.1,379.1.2.2,demod:1327,1411] equal(multiply(X,Y,multiply(X,Y,Z)),multiply(Y,Z,X)).
% 1503 [para:1362.1.1,384.1.1.1.2.1,demod:1261,1327,1411,1382,1362] equal(multiply(X,Y,Z),multiply(Z,Y,X)).
% 1520 [para:1503.1.1,378.4.1,demod:1411,1375,1408,cut:376] -equal(multiply(e,multiply(c,b,a),d),multiply(d,e,multiply(a,b,c))) | -equal(multiply(b,a,a),a).
% 1560 [para:377.1.1,1412.1.1.3,demod:1375,1411,1362] equal(multiply(X,inverse(multiply(Y,multiply(Z,U,V),W)),X),X).
% 1562 [para:379.1.1,1412.1.1.3,demod:1375,1560,1382,1411] equal(multiply(X,Y,Z),multiply(Z,X,Y)).
% 1580 [para:1364.1.1,1412.1.1.3,demod:1327] equal(multiply(X,Y,Y),Y).
% 1651 [para:1580.1.1,1520.2.1,cut:376] -equal(multiply(e,multiply(c,b,a),d),multiply(d,e,multiply(a,b,c))).
% 1812 [para:1503.1.1,1651.1.1.2,cut:1562] 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: 4
%
%
% ***GANDALF_FOUND_A_REFUTATION***
%
% Global statistics over all passes:
%
% given clauses: 180
% derived clauses: 272418
% kept clauses: 1793
% kept size sum: 124963
% kept mid-nuclei: 0
% kept new demods: 1015
% forw unit-subs: 15623
% forw double-subs: 10
% forw overdouble-subs: 12
% backward subs: 41
% fast unit cutoff: 26
% full unit cutoff: 0
% dbl unit cutoff: 0
% real runtime : 7.92
% process. runtime: 7.90
% specific non-discr-tree subsumption statistics:
% tried: 12
% 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/BOO035-1+eq_r.in")
%
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