TSTP Solution File: GRP103-1 by Gandalf---c-2.6
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%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP103-1 : 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/GRP103-1+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 6 7)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 6 7)
% (binary-posweight-lex-big-order 30 #f 6 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),identity) | -equal(multiply(identity,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),identity).
% -equal(multiply(identity,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(6,40,0,12,0,0,1422,4,752)
%
%
% START OF PROOF
% 7 [] equal(X,X).
% 8 [] equal(double_divide(double_divide(X,double_divide(double_divide(identity,Y),double_divide(Z,double_divide(Y,X)))),double_divide(identity,identity)),Z).
% 9 [] equal(multiply(X,Y),double_divide(double_divide(Y,X),identity)).
% 10 [] equal(inverse(X),double_divide(X,identity)).
% 11 [] equal(identity,double_divide(X,inverse(X))).
% 12 [] -equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) | -equal(multiply(inverse(a1),a1),identity) | -equal(multiply(a4,b4),multiply(b4,a4)) | -equal(multiply(identity,a2),a2).
% 13 [para:9.1.2,10.1.2] equal(inverse(double_divide(X,Y)),multiply(Y,X)).
% 14 [para:10.1.2,9.1.2.1,demod:10] equal(multiply(identity,X),inverse(inverse(X))).
% 15 [para:11.1.2,9.1.2.1,demod:10] equal(multiply(inverse(X),X),inverse(identity)).
% 16 [para:9.1.2,9.1.2.1,demod:10] equal(multiply(identity,double_divide(X,Y)),inverse(multiply(Y,X))).
% 17 [para:14.1.2,11.1.2.2] equal(identity,double_divide(inverse(X),multiply(identity,X))).
% 18 [para:14.1.2,14.1.2.1] equal(multiply(identity,inverse(X)),inverse(multiply(identity,X))).
% 21 [para:13.1.1,11.1.2.2] equal(identity,double_divide(double_divide(X,Y),multiply(Y,X))).
% 22 [para:13.1.1,15.1.1.1] equal(multiply(multiply(X,Y),double_divide(Y,X)),inverse(identity)).
% 26 [para:10.1.2,8.1.1.1.2.1,demod:10] equal(double_divide(double_divide(X,double_divide(inverse(identity),double_divide(Y,double_divide(identity,X)))),inverse(identity)),Y).
% 27 [para:10.1.2,8.1.1.1.2.2.2,demod:10] equal(double_divide(double_divide(identity,double_divide(double_divide(identity,X),double_divide(Y,inverse(X)))),inverse(identity)),Y).
% 29 [para:11.1.2,8.1.1.1.2.2.2,demod:10] equal(double_divide(double_divide(inverse(X),double_divide(double_divide(identity,X),inverse(Y))),inverse(identity)),Y).
% 30 [para:8.1.1,9.1.2.1,demod:10] equal(multiply(inverse(identity),double_divide(X,double_divide(double_divide(identity,Y),double_divide(Z,double_divide(Y,X))))),inverse(Z)).
% 31 [para:9.1.2,8.1.1.1.2.2.2,demod:10] equal(double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(X,Y)),double_divide(Z,multiply(Y,X)))),inverse(identity)),Z).
% 34 [para:8.1.1,8.1.1.1.2.2,demod:10] equal(double_divide(double_divide(identity,double_divide(inverse(identity),X)),inverse(identity)),double_divide(Y,double_divide(double_divide(identity,Z),double_divide(X,double_divide(Z,Y))))).
% 42 [para:11.1.2,29.1.1.1.2,demod:14,10] equal(double_divide(multiply(identity,X),inverse(identity)),double_divide(identity,X)).
% 47 [para:42.1.1,9.1.2.1,demod:9] equal(multiply(inverse(identity),multiply(identity,X)),multiply(X,identity)).
% 50 [para:16.1.1,47.1.1.2] equal(multiply(inverse(identity),inverse(multiply(X,Y))),multiply(double_divide(Y,X),identity)).
% 51 [para:10.1.2,26.1.1.1.2.2.2] equal(double_divide(double_divide(identity,double_divide(inverse(identity),double_divide(X,inverse(identity)))),inverse(identity)),X).
% 71 [para:11.1.2,27.1.1.1.2.2,demod:9] equal(double_divide(double_divide(identity,multiply(X,identity)),inverse(identity)),X).
% 79 [para:15.1.1,71.1.1.1.2,demod:11] equal(identity,inverse(identity)).
% 83 [para:71.1.1,51.1.1.1.2.2,demod:9,79] equal(multiply(double_divide(identity,X),identity),double_divide(identity,multiply(X,identity))).
% 84 [para:79.1.2,14.1.2.1,demod:79] equal(multiply(identity,identity),identity).
% 85 [para:79.1.2,29.1.1.1.1,demod:83,9,79,10] equal(double_divide(identity,multiply(inverse(X),identity)),X).
% 88 [para:79.1.2,42.1.1.2,demod:18,10] equal(multiply(identity,inverse(X)),double_divide(identity,X)).
% 89 [para:79.1.2,47.1.1.1] equal(multiply(identity,multiply(identity,X)),multiply(X,identity)).
% 92 [para:79.1.2,50.1.1.1,demod:88] equal(double_divide(identity,multiply(X,Y)),multiply(double_divide(Y,X),identity)).
% 93 [para:79.1.2,71.1.1.2,demod:9] equal(multiply(multiply(X,identity),identity),X).
% 94 [para:93.1.1,21.1.2.2] equal(identity,double_divide(double_divide(identity,multiply(X,identity)),X)).
% 109 [para:13.1.1,85.1.1.2.1] equal(double_divide(identity,multiply(multiply(X,Y),identity)),double_divide(Y,X)).
% 116 [para:14.1.2,88.1.1.2,demod:89] equal(multiply(X,identity),double_divide(identity,inverse(X))).
% 120 [para:88.1.1,47.1.1.2,demod:16,79] equal(inverse(multiply(X,identity)),multiply(inverse(X),identity)).
% 147 [para:94.1.2,8.1.1.1.2.2,demod:92,79,10,9] equal(multiply(multiply(X,identity),Y),double_divide(identity,double_divide(identity,multiply(Y,X)))).
% 148 [para:94.1.2,8.1.1.1.2.2.2,demod:9,79,10,84,147] equal(multiply(double_divide(multiply(identity,X),inverse(Y)),X),Y).
% 149 [para:94.1.2,31.1.1.1.2.2,demod:109,10,79,147,92,9] equal(inverse(multiply(multiply(X,identity),Y)),double_divide(X,Y)).
% 176 [para:22.1.1,149.1.1.1,demod:79] equal(identity,double_divide(X,double_divide(identity,X))).
% 181 [para:93.1.1,149.1.1.1.1] equal(inverse(multiply(X,Y)),double_divide(multiply(X,identity),Y)).
% 188 [para:176.1.2,8.1.1.1.2.2,demod:14,79,10] equal(multiply(identity,X),X).
% 190 [para:176.1.2,30.1.1.2.2.2,demod:88,10,79] equal(double_divide(identity,X),inverse(X)).
% 193 [para:176.1.2,31.1.1.1.2.1,demod:188,14,181,79,120,190,116,10,84] equal(multiply(X,identity),X).
% 196 [para:188.1.1,17.1.2.2] equal(identity,double_divide(inverse(X),X)).
% 198 [para:188.1.1,16.1.1] equal(double_divide(X,Y),inverse(multiply(Y,X))).
% 199 [para:188.1.1,31.1.1.1.2.2.2,demod:198,79,13,190,193,116,10] equal(double_divide(X,double_divide(Y,X)),Y).
% 201 [para:193.1.1,149.1.1.1.1,demod:198] equal(double_divide(X,Y),double_divide(Y,X)).
% 223 [para:196.1.2,8.1.1.1.2.2,demod:13,9,79,188,14,10,190] equal(multiply(X,Y),multiply(Y,X)).
% 231 [para:199.1.1,199.1.1.2] equal(double_divide(double_divide(X,Y),X),Y).
% 236 [para:201.1.1,26.1.1.1,demod:9,13,190,79] equal(multiply(X,multiply(inverse(X),Y)),Y).
% 237 [para:201.1.1,26.1.1.1.2.2,demod:9,13,190,79] equal(multiply(multiply(X,inverse(Y)),Y),X).
% 247 [para:201.1.1,199.1.1] equal(double_divide(double_divide(X,Y),Y),X).
% 256 [para:231.1.1,26.1.1.1.2.2,demod:9,190,79] equal(multiply(inverse(X),Y),double_divide(inverse(Y),X)).
% 259 [para:34.1.2,231.1.1.1,demod:10,193,116,190,79] equal(double_divide(inverse(X),Y),double_divide(inverse(Z),double_divide(X,double_divide(Z,Y)))).
% 261 [para:247.1.1,8.1.1.1.2.2.2,demod:9,79,13,190] equal(multiply(double_divide(multiply(X,Y),double_divide(Z,Y)),X),Z).
% 271 [para:13.1.1,237.1.1.1.2] equal(multiply(multiply(X,multiply(Y,Z)),double_divide(Z,Y)),X).
% 272 [para:148.1.1,237.1.1.1,demod:190,88] equal(multiply(X,Y),double_divide(inverse(Y),inverse(X))).
% 290 [para:13.1.1,256.1.1.1] equal(multiply(multiply(X,Y),Z),double_divide(inverse(Z),double_divide(Y,X))).
% 297 [para:272.1.2,8.1.1.1.2.2.2,demod:198,10,79,190,290,193,116] equal(double_divide(X,multiply(double_divide(Y,multiply(X,Z)),Z)),Y).
% 298 [para:149.1.1,272.1.2.1,demod:193] equal(multiply(X,multiply(Y,Z)),double_divide(double_divide(Y,Z),inverse(X))).
% 302 [para:198.1.2,272.1.2.1,demod:298] equal(multiply(X,multiply(Y,Z)),multiply(X,multiply(Z,Y))).
% 326 [para:181.1.2,8.1.1.1,demod:9,79,198,290,193,190] equal(multiply(X,multiply(multiply(double_divide(Y,X),Z),Y)),Z).
% 442 [para:261.1.1,271.1.1.1] equal(multiply(X,double_divide(Y,Z)),double_divide(multiply(multiply(Z,Y),U),double_divide(X,U))).
% 519 [para:231.1.1,297.1.1.2.1] equal(double_divide(X,multiply(Y,Z)),double_divide(multiply(X,Z),Y)).
% 604 [para:236.1.1,326.1.1.2.1,demod:13] equal(multiply(X,multiply(Y,Z)),multiply(multiply(X,Z),Y)).
% 1251 [para:442.1.2,259.1.2.2.2,demod:519,198,604,290] equal(multiply(X,multiply(Y,Z)),double_divide(double_divide(X,multiply(U,V)),double_divide(Y,multiply(Z,double_divide(V,U))))).
% 1423 [input:12,cut:223,cut:188] -equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) | -equal(multiply(inverse(a1),a1),identity).
% 1424 [para:1251.1.1,1423.1.2,demod:196,256,1251,604,cut:302,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 6
% seconds given: 10
%
%
% ***GANDALF_FOUND_A_REFUTATION***
%
% Global statistics over all passes:
%
% given clauses: 572
% derived clauses: 308654
% kept clauses: 1405
% kept size sum: 20853
% kept mid-nuclei: 4
% kept new demods: 979
% forw unit-subs: 307176
% forw double-subs: 0
% forw overdouble-subs: 0
% backward subs: 16
% fast unit cutoff: 6
% full unit cutoff: 0
% dbl unit cutoff: 0
% real runtime : 7.55
% 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/GRP103-1+eq_r.in")
%
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