%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP078-1 : TPTP v3.4.2. Bugfixed v2.3.0.
% Transfm : add_equality:r
% Format : otter:hypothesis:set(auto),clear(print_given)
% Command : gandalf-wrapper -time %d %s
% Computer : art05.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/GRP078-1+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 5)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 6 5)
% (binary-posweight-lex-big-order 30 #f 6 5)
% (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))).
% 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))).
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(6,40,1,12,0,1,311,4,778)
%
%
% START OF PROOF
% 7 [] equal(X,X).
% 8 [] equal(double_divide(double_divide(identity,X),double_divide(identity,double_divide(double_divide(double_divide(X,Y),identity),double_divide(Z,Y)))),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(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))).
% 21 [para:13.1.1,11.1.2.2] equal(identity,double_divide(double_divide(X,Y),multiply(Y,X))).
% 26 [para:10.1.2,8.1.1.1,demod:9] equal(double_divide(inverse(identity),double_divide(identity,double_divide(multiply(X,identity),double_divide(Y,X)))),Y).
% 27 [para:10.1.2,8.1.1.2.2.1,demod:13] equal(double_divide(double_divide(identity,X),double_divide(identity,double_divide(multiply(Y,X),double_divide(Z,Y)))),Z).
% 28 [para:10.1.2,8.1.1.2.2.1.1,demod:14,10] equal(double_divide(double_divide(identity,X),double_divide(identity,double_divide(multiply(identity,X),inverse(Y)))),Y).
% 31 [para:11.1.2,8.1.1.2.2.2,demod:10,9] equal(double_divide(double_divide(identity,X),double_divide(identity,inverse(multiply(inverse(Y),X)))),Y).
% 32 [para:8.1.1,9.1.2.1,demod:10,9] equal(multiply(double_divide(identity,double_divide(multiply(X,Y),double_divide(Z,X))),double_divide(identity,Y)),inverse(Z)).
% 34 [para:9.1.2,8.1.1.2.2.2,demod:14,10] equal(double_divide(double_divide(identity,X),double_divide(identity,double_divide(multiply(identity,X),multiply(Y,Z)))),double_divide(Z,Y)).
% 36 [para:17.1.2,8.1.1.2.2.2,demod:10,9] equal(double_divide(double_divide(identity,X),double_divide(identity,inverse(multiply(multiply(identity,Y),X)))),inverse(Y)).
% 46 [para:15.1.1,31.1.1.2.2.1,demod:14] equal(double_divide(double_divide(identity,X),double_divide(identity,multiply(identity,identity))),X).
% 47 [para:10.1.2,46.1.1.1] equal(double_divide(inverse(identity),double_divide(identity,multiply(identity,identity))),identity).
% 48 [para:11.1.2,46.1.1.1] equal(double_divide(identity,double_divide(identity,multiply(identity,identity))),inverse(identity)).
% 52 [para:48.1.1,46.1.1.1,demod:47] equal(identity,double_divide(identity,multiply(identity,identity))).
% 56 [para:52.1.2,8.1.1.2.2.2,demod:36,10,9] equal(inverse(identity),identity).
% 59 [para:52.1.2,46.1.1.2,demod:9] equal(multiply(X,identity),X).
% 62 [para:26.1.1,9.1.2.1,demod:10,56,59] equal(double_divide(identity,double_divide(X,double_divide(Y,X))),inverse(Y)).
% 65 [para:26.1.1,8.1.1.2.2.1.1,demod:62,59,10,56] equal(double_divide(identity,inverse(X)),X).
% 71 [para:59.1.1,21.1.2.2] equal(identity,double_divide(double_divide(identity,X),X)).
% 74 [para:13.1.1,65.1.1.2] equal(double_divide(identity,multiply(X,Y)),double_divide(Y,X)).
% 78 [para:71.1.2,8.1.1.2.2.1,demod:65,56,10] equal(double_divide(identity,double_divide(identity,X)),X).
% 79 [para:71.1.2,8.1.1.2.2.1.1,demod:56,10,78] equal(double_divide(X,double_divide(Y,X)),Y).
% 87 [para:11.1.2,79.1.1.2,demod:14,10] equal(multiply(identity,X),X).
% 88 [para:79.1.1,9.1.2.1,demod:10] equal(multiply(double_divide(X,Y),Y),inverse(X)).
% 89 [para:21.1.2,79.1.1.2,demod:10] equal(inverse(multiply(X,Y)),double_divide(Y,X)).
% 94 [para:79.1.1,26.1.1.2.2.2,demod:78,59,56] equal(double_divide(double_divide(X,Y),X),Y).
% 95 [para:65.1.1,79.1.1.2] equal(double_divide(inverse(X),X),identity).
% 96 [para:71.1.2,79.1.1.2,demod:10] equal(inverse(X),double_divide(identity,X)).
% 105 [para:95.1.1,8.1.1.2.2.2,demod:13,89,10,9,96] equal(double_divide(inverse(X),multiply(Y,X)),inverse(Y)).
% 113 [para:28.1.1,26.1.1.2.2.2,demod:74,59,13,96,87,56] equal(double_divide(multiply(inverse(X),Y),X),inverse(Y)).
% 117 [para:8.1.1,94.1.1.1,demod:13,9,96] equal(double_divide(X,inverse(Y)),multiply(double_divide(X,Z),multiply(Z,Y))).
% 118 [para:31.1.1,94.1.1.1,demod:13,89,96] equal(double_divide(X,inverse(Y)),multiply(inverse(X),Y)).
% 124 [para:17.1.2,32.1.1.1.2.2,demod:14,13,96,89,10,87] equal(multiply(multiply(X,Y),inverse(Y)),X).
% 133 [para:124.1.1,27.1.1.2.2.1,demod:13,96,65] equal(double_divide(X,multiply(double_divide(Y,multiply(Z,X)),Z)),Y).
% 134 [para:89.1.1,124.1.1.2] equal(multiply(multiply(X,multiply(Y,Z)),double_divide(Z,Y)),X).
% 139 [para:105.1.1,94.1.1.1] equal(double_divide(inverse(X),inverse(Y)),multiply(X,Y)).
% 145 [para:89.1.1,113.1.1.1.1] equal(double_divide(multiply(double_divide(X,Y),Z),multiply(Y,X)),inverse(Z)).
% 161 [para:89.1.1,139.1.1.2] equal(double_divide(inverse(X),double_divide(Y,Z)),multiply(X,multiply(Z,Y))).
% 162 [para:34.1.1,88.1.1.1,demod:14,13,96,87] equal(multiply(double_divide(X,Y),multiply(multiply(Y,X),Z)),Z).
% 169 [para:133.1.1,94.1.1.1] equal(double_divide(X,Y),multiply(double_divide(X,multiply(Z,Y)),Z)).
% 170 [para:94.1.1,133.1.1.2.1] equal(double_divide(X,multiply(Y,Z)),double_divide(multiply(Z,X),Y)).
% 172 [para:133.1.1,34.1.1.2.2,demod:87,139,96] equal(multiply(X,Y),double_divide(Z,double_divide(Y,multiply(Z,X)))).
% 175 [para:9.1.2,162.1.1.1,demod:89,16] equal(multiply(multiply(X,Y),multiply(double_divide(Y,X),Z)),Z).
% 188 [para:169.1.2,105.1.1.2,demod:13,161] equal(multiply(X,multiply(Y,Z)),multiply(multiply(X,Y),Z)).
% 192 [para:169.1.2,134.1.1.1,demod:188] equal(multiply(double_divide(X,Y),double_divide(Z,U)),double_divide(X,multiply(U,multiply(Z,Y)))).
% 203 [para:162.1.1,172.1.2.2.2,demod:188] equal(multiply(X,multiply(Y,multiply(Z,U))),double_divide(double_divide(Y,X),double_divide(U,Z))).
% 210 [para:162.1.1,117.1.2.2,demod:170,89,188] equal(double_divide(X,double_divide(Y,multiply(Z,U))),multiply(double_divide(X,double_divide(U,Z)),Y)).
% 211 [para:175.1.1,117.1.2.2,demod:89] equal(double_divide(X,double_divide(Y,double_divide(Z,U))),multiply(double_divide(X,multiply(U,Z)),Y)).
% 239 [para:192.1.1,145.1.1.2,demod:210] equal(double_divide(double_divide(double_divide(X,Y),double_divide(Z,multiply(U,V))),double_divide(V,multiply(Y,multiply(X,U)))),inverse(Z)).
% 250 [para:203.1.1,170.1.2.1,demod:203,188,170] equal(double_divide(X,double_divide(double_divide(Y,Z),double_divide(U,V))),double_divide(double_divide(double_divide(V,Y),double_divide(X,U)),Z)).
% 312 [input:12,cut:87] -equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) | -equal(multiply(inverse(a1),a1),identity).
% 313 [para:239.1.2,312.2.1.1,demod:118,10,11,88,79,211,170,188,172,250,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 5
% clause depth limited to 6
% seconds given: 10
%
%
% ***GANDALF_FOUND_A_REFUTATION***
%
% Global statistics over all passes:
%
% given clauses: 292
% derived clauses: 118830
% kept clauses: 296
% kept size sum: 4629
% kept mid-nuclei: 2
% kept new demods: 281
% forw unit-subs: 89257
% forw double-subs: 0
% forw overdouble-subs: 0
% backward subs: 8
% fast unit cutoff: 4
% full unit cutoff: 0
% dbl unit cutoff: 0
% real runtime : 7.80
% process. runtime: 7.78
% 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/GRP078-1+eq_r.in")
%
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