TSTP Solution File: GRP097-1 by Gandalf---c-2.6
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% File : Gandalf---c-2.6
% Problem : GRP097-1 : 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 : 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
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%----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/GRP097-1+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(4,40,1,8,0,1,11,50,1,15,0,1,1888,4,758)
%
%
% START OF PROOF
% 13 [] equal(divide(X,inverse(divide(divide(Y,Z),divide(X,Z)))),Y).
% 14 [] equal(multiply(X,Y),divide(X,inverse(Y))).
% 15 [] -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)).
% 16 [para:13.1.1,14.1.2] equal(multiply(X,divide(divide(Y,Z),divide(X,Z))),Y).
% 17 [para:14.1.2,13.1.1.2.1.1,demod:14] equal(multiply(X,divide(multiply(Y,Z),multiply(X,Z))),Y).
% 18 [para:13.1.1,13.1.1.2.1.1,demod:14] equal(multiply(X,divide(Y,multiply(X,divide(divide(Y,Z),divide(U,Z))))),U).
% 19 [para:13.1.1,13.1.1.2.1.2,demod:14] equal(multiply(X,divide(multiply(Y,divide(divide(Z,U),divide(X,U))),Z)),Y).
% 20 [para:17.1.1,17.1.1.2.1] equal(multiply(X,divide(Y,multiply(X,divide(multiply(Y,Z),multiply(U,Z))))),U).
% 21 [para:17.1.1,17.1.1.2.2] equal(multiply(X,divide(multiply(Y,divide(multiply(Z,U),multiply(X,U))),Z)),Y).
% 23 [para:16.1.1,18.1.1.2.2] equal(multiply(X,divide(Y,Y)),X).
% 24 [para:14.1.2,23.1.1.2] equal(multiply(X,multiply(inverse(Y),Y)),X).
% 25 [para:23.1.1,17.1.1.2.1,demod:23] equal(multiply(X,divide(Y,X)),Y).
% 26 [para:14.1.2,25.1.1.2] equal(multiply(inverse(X),multiply(Y,X)),Y).
% 27 [para:13.1.1,25.1.1.2] equal(multiply(inverse(divide(divide(X,Y),divide(Z,Y))),X),Z).
% 34 [para:26.1.1,17.1.1.2.2] equal(multiply(inverse(X),divide(multiply(Y,multiply(Z,X)),Z)),Y).
% 36 [para:23.1.1,26.1.1.2] equal(multiply(inverse(divide(X,X)),Y),Y).
% 37 [para:25.1.1,26.1.1.2] equal(multiply(inverse(divide(X,Y)),X),Y).
% 39 [para:26.1.1,26.1.1.2] equal(multiply(inverse(multiply(X,Y)),X),inverse(Y)).
% 44 [para:36.1.1,17.1.1,demod:36] equal(divide(multiply(X,Y),Y),X).
% 53 [para:44.1.1,14.1.2] equal(multiply(multiply(X,inverse(Y)),Y),X).
% 54 [para:44.1.1,13.1.1.2.1.1,demod:14] equal(multiply(X,divide(Y,divide(X,Z))),multiply(Y,Z)).
% 56 [para:17.1.1,44.1.1.1] equal(divide(X,divide(multiply(X,Y),multiply(Z,Y))),Z).
% 60 [para:23.1.1,44.1.1.1] equal(divide(X,divide(Y,Y)),X).
% 61 [para:44.1.1,25.1.1.2] equal(multiply(X,Y),multiply(Y,X)).
% 62 [para:25.1.1,44.1.1.1] equal(divide(X,divide(X,Y)),Y).
% 64 [para:26.1.1,44.1.1.1] equal(divide(X,multiply(X,Y)),inverse(Y)).
% 78 [para:61.1.1,25.1.1] equal(multiply(divide(X,Y),Y),X).
% 79 [para:61.1.1,24.1.1] equal(multiply(multiply(inverse(X),X),Y),Y).
% 82 [para:61.1.1,26.1.1.2] equal(multiply(inverse(X),multiply(X,Y)),Y).
% 85 [para:61.1.1,44.1.1.1] equal(divide(multiply(X,Y),X),Y).
% 94 [para:62.1.1,18.1.1.2.2.2] equal(multiply(X,divide(Y,multiply(X,Z))),divide(Y,Z)).
% 97 [para:60.1.1,62.1.1.2] equal(divide(X,X),divide(Y,Y)).
% 104 [para:78.1.1,26.1.1.2] equal(multiply(inverse(X),Y),divide(Y,X)).
% 110 [para:16.1.1,85.1.1.1] equal(divide(X,Y),divide(divide(X,Z),divide(Y,Z))).
% 111 [para:17.1.1,85.1.1.1] equal(divide(X,Y),divide(multiply(X,Z),multiply(Y,Z))).
% 124 [para:78.1.1,21.1.1.2.1,demod:111] equal(multiply(X,divide(Y,Z)),divide(Y,divide(Z,X))).
% 128 [para:13.1.1,37.1.1.1.1,demod:110,104] equal(divide(X,Y),inverse(divide(Y,X))).
% 132 [para:53.1.1,17.1.1.2.1,demod:94] equal(divide(X,Y),multiply(X,inverse(Y))).
% 138 [para:44.1.1,27.1.1.1.1.2,demod:128] equal(multiply(divide(X,divide(Y,Z)),Y),multiply(X,Z)).
% 142 [para:26.1.1,64.1.1.2] equal(divide(inverse(X),Y),inverse(multiply(Y,X))).
% 157 [para:82.1.1,26.1.1.2,demod:142] equal(multiply(divide(inverse(X),Y),X),inverse(Y)).
% 169 [para:128.1.2,104.1.1.1] equal(multiply(divide(X,Y),Z),divide(Z,divide(Y,X))).
% 178 [para:39.1.1,19.1.1.2.1,demod:128,169,110,124] equal(divide(inverse(X),divide(Y,Z)),divide(divide(Z,Y),X)).
% 186 [para:142.1.2,14.1.2.2] equal(multiply(X,multiply(Y,Z)),divide(X,divide(inverse(Z),Y))).
% 187 [para:142.1.2,132.1.2.2,demod:178,124] equal(divide(X,multiply(Y,Z)),divide(divide(X,Y),Z)).
% 193 [para:34.1.1,20.1.1.2.2.2.2,demod:138,169,187,124] equal(divide(X,divide(multiply(Y,multiply(Z,U)),divide(Z,divide(X,Y)))),inverse(U)).
% 201 [para:54.1.1,85.1.1.1] equal(divide(multiply(X,Y),Z),divide(X,divide(Z,Y))).
% 204 [para:56.1.1,54.1.1.2] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Z,Y))).
% 217 [para:157.1.1,111.1.2.2,demod:201,186] equal(multiply(X,multiply(Y,Z)),multiply(X,multiply(Z,Y))).
% 1889 [input:15,cut:79,cut:61] -equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) | -equal(multiply(inverse(a1),a1),multiply(inverse(b1),b1)).
% 1890 [para:193.1.2,1889.2.1.1,demod:204,104,64,62,169,187,201,cut:97,cut:217] 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 6
% seconds given: 10
%
%
% ***GANDALF_FOUND_A_REFUTATION***
%
% Global statistics over all passes:
%
% given clauses: 302
% derived clauses: 182628
% kept clauses: 1870
% kept size sum: 40423
% kept mid-nuclei: 4
% kept new demods: 184
% forw unit-subs: 170458
% 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 : 7.59
% process. runtime: 7.58
% 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/GRP097-1+eq_r.in")
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