%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP088-1 : 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/GRP088-1+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 7)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 5 7)
% (binary-posweight-lex-big-order 30 #f 5 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(5,40,0,10,0,0,439,4,752)
%
%
% START OF PROOF
% 6 [] equal(X,X).
% 7 [] equal(divide(X,divide(Y,divide(Z,divide(X,Y)))),Z).
% 8 [] equal(multiply(X,Y),divide(X,divide(divide(Z,Z),Y))).
% 9 [] equal(inverse(X),divide(divide(Y,Y),X)).
% 10 [] -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)).
% 13 [para:7.1.1,9.1.2,demod:9] equal(inverse(divide(X,divide(Y,inverse(X)))),Y).
% 19 [para:9.1.2,13.1.1.1.2] equal(inverse(divide(X,inverse(inverse(X)))),divide(Y,Y)).
% 26 [para:19.1.1,19.1.1] equal(divide(X,X),divide(Y,Y)).
% 34 [para:26.1.1,7.1.1.2.2] equal(divide(X,divide(Y,divide(Z,Z))),divide(X,Y)).
% 35 [para:26.1.1,7.1.1.2.2.2,demod:34] equal(divide(X,divide(X,Y)),Y).
% 39 [para:35.1.1,7.1.1] equal(divide(X,divide(Y,Y)),X).
% 41 [para:7.1.1,35.1.1.2] equal(divide(X,Y),divide(Z,divide(Y,divide(X,Z)))).
% 47 [para:9.1.2,8.1.2.2] equal(multiply(X,Y),divide(X,inverse(Y))).
% 50 [para:8.1.2,7.1.1,demod:39] equal(multiply(X,divide(Y,X)),Y).
% 60 [para:8.1.2,35.1.1.2,demod:9] equal(divide(X,multiply(X,Y)),inverse(Y)).
% 61 [para:35.1.1,8.1.2.2,demod:9] equal(multiply(X,inverse(Y)),divide(X,Y)).
% 65 [para:7.1.1,50.1.1.2,demod:41] equal(multiply(divide(X,Y),Y),X).
% 66 [para:8.1.2,50.1.1.2,demod:9] equal(multiply(inverse(X),multiply(Y,X)),Y).
% 68 [para:8.1.2,65.1.1.1,demod:61,9] equal(divide(multiply(X,Y),Y),X).
% 70 [para:68.1.1,7.1.1.2.2] equal(divide(X,divide(Y,Z)),multiply(Z,divide(X,Y))).
% 72 [para:68.1.1,13.1.1.1.2,demod:61] equal(inverse(divide(X,Y)),divide(Y,X)).
% 73 [para:68.1.1,35.1.1.2] equal(divide(multiply(X,Y),X),Y).
% 74 [para:68.1.1,50.1.1.2] equal(multiply(X,Y),multiply(Y,X)).
% 76 [para:73.1.1,7.1.1.2.2] equal(divide(X,divide(Y,Z)),multiply(divide(X,Y),Z)).
% 78 [para:73.1.1,13.1.1.1.2,demod:72] equal(divide(X,Y),multiply(inverse(Y),X)).
% 85 [para:65.1.1,60.1.1.2] equal(divide(divide(X,Y),X),inverse(Y)).
% 89 [para:66.1.1,60.1.1.2] equal(divide(inverse(X),Y),inverse(multiply(Y,X))).
% 91 [para:72.1.1,47.1.2.2,demod:70] equal(divide(X,divide(Y,Z)),divide(Z,divide(Y,X))).
% 92 [para:78.1.2,61.1.1] equal(divide(inverse(X),Y),divide(inverse(Y),X)).
% 93 [para:85.1.1,7.1.1.2.2,demod:47] equal(divide(X,multiply(Y,Z)),divide(divide(X,Y),Z)).
% 95 [para:89.1.2,47.1.2.2] equal(multiply(X,multiply(Y,Z)),divide(X,divide(inverse(Z),Y))).
% 105 [para:8.1.2,76.1.2.1,demod:95,60,93] equal(multiply(X,multiply(Y,Z)),multiply(multiply(X,Z),Y)).
% 111 [para:92.1.1,91.1.2.2,demod:95] equal(multiply(X,multiply(Y,Z)),multiply(Y,multiply(Z,X))).
% 128 [para:74.1.1,105.1.2.1,demod:105] equal(multiply(X,multiply(Y,Z)),multiply(Z,multiply(Y,X))).
% 440 [input:10,cut:74] -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)).
% 441 [para:128.1.1,440.2.2,demod:35,76,78,105,cut:111,cut:6,cut:26] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using binary resolution
% not using sos 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 5
% seconds given: 10
%
%
% ***GANDALF_FOUND_A_REFUTATION***
%
% Global statistics over all passes:
%
% given clauses: 352
% derived clauses: 531787
% kept clauses: 426
% kept size sum: 7186
% kept mid-nuclei: 2
% kept new demods: 67
% forw unit-subs: 208593
% forw double-subs: 0
% forw overdouble-subs: 0
% backward subs: 0
% fast unit cutoff: 4
% full unit cutoff: 0
% dbl unit cutoff: 0
% real runtime : 7.53
% process. runtime: 7.53
% 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/GRP088-1+eq_r.in")
%
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