TSTP Solution File: GRP091-1 by Gandalf---c-2.6
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% File : Gandalf---c-2.6
% Problem : GRP091-1 : 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 : art08.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/GRP091-1+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(6,40,1,12,0,1,450,4,756)
%
%
% START OF PROOF
% 7 [] equal(X,X).
% 8 [] equal(divide(divide(X,divide(divide(X,Y),Z)),Y),Z).
% 9 [] equal(multiply(X,Y),divide(X,divide(divide(Z,Z),Y))).
% 10 [] equal(inverse(X),divide(divide(Y,Y),X)).
% 11 [] equal(identity,divide(X,X)).
% 12 [] -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)).
% 14 [para:11.1.2,10.1.2.1] equal(inverse(X),divide(identity,X)).
% 17 [para:11.1.2,8.1.1.1.2.1,demod:14] equal(divide(divide(X,inverse(Y)),X),Y).
% 20 [para:11.1.2,17.1.1.1,demod:14] equal(inverse(inverse(X)),X).
% 21 [para:10.1.2,17.1.1.1,demod:11,20] equal(divide(X,identity),X).
% 22 [para:17.1.1,8.1.1.1.2] equal(divide(divide(X,Y),inverse(Y)),X).
% 25 [para:20.1.1,17.1.1.1.2] equal(divide(divide(X,Y),X),inverse(Y)).
% 26 [para:21.1.1,8.1.1,demod:21] equal(divide(X,divide(X,Y)),Y).
% 33 [para:11.1.2,9.1.2.2.1,demod:14] equal(multiply(X,Y),divide(X,inverse(Y))).
% 34 [para:9.1.2,10.1.2,demod:20,14,11] equal(X,multiply(identity,X)).
% 35 [para:9.1.2,8.1.1,demod:33,14,11] equal(multiply(divide(X,divide(multiply(X,Y),Z)),Y),Z).
% 36 [para:9.1.2,8.1.1.1] equal(divide(multiply(X,Y),X),Y).
% 39 [para:17.1.1,9.1.2.2] equal(multiply(X,inverse(Y)),divide(X,Y)).
% 40 [para:9.1.2,26.1.1.2,demod:14,11] equal(divide(X,multiply(X,Y)),inverse(Y)).
% 43 [para:36.1.1,26.1.1.2] equal(divide(multiply(X,Y),Y),X).
% 45 [para:43.1.1,9.1.2,demod:39,14,11] equal(multiply(divide(X,Y),Y),X).
% 46 [para:8.1.1,45.1.1.1] equal(multiply(X,Y),divide(Z,divide(divide(Z,Y),X))).
% 47 [para:17.1.1,45.1.1.1,demod:33] equal(multiply(X,Y),multiply(Y,X)).
% 48 [para:26.1.1,45.1.1.1] equal(multiply(X,divide(Y,X)),Y).
% 53 [para:22.1.1,48.1.1.2] equal(multiply(inverse(X),Y),divide(Y,X)).
% 56 [para:17.1.1,25.1.1.1,demod:33] equal(divide(X,multiply(Y,X)),inverse(Y)).
% 64 [para:40.1.1,25.1.1.1] equal(divide(inverse(X),Y),inverse(multiply(Y,X))).
% 108 [para:64.1.2,33.1.2.2] equal(multiply(X,multiply(Y,Z)),divide(X,divide(inverse(Z),Y))).
% 114 [para:56.1.1,35.1.1.1.2,demod:33] equal(multiply(multiply(X,Y),Z),multiply(Y,multiply(X,Z))).
% 117 [para:40.1.1,46.1.2.2.1,demod:108] equal(multiply(X,multiply(Y,Z)),multiply(Y,multiply(X,Z))).
% 451 [input:12,cut:47] -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)).
% 452 [para:108.1.1,451.2.2,demod:34,11,53,108,114,cut:117,cut:7,cut:7] 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: 319
% derived clauses: 354845
% kept clauses: 435
% kept size sum: 7356
% kept mid-nuclei: 2
% kept new demods: 98
% forw unit-subs: 172731
% 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 : 7.56
% process. runtime: 7.55
% 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/GRP091-1+eq_r.in")
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