%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP064-1 : 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 : art07.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/GRP064-1+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),multiply(inverse(b1),b1)) | -equal(multiply(multiply(inverse(b2),b2),a2),a2) | -equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))).
% 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))).
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(5,40,1,10,0,1,248,50,81,253,0,81,513,50,236,518,0,236,783,50,377,788,0,377,1056,50,551,1056,40,551,1061,0,551)
%
%
% START OF PROOF
% 1057 [] equal(X,X).
% 1058 [] equal(divide(X,divide(divide(divide(divide(Y,Y),Y),Z),divide(divide(divide(Y,Y),X),Z))),Y).
% 1059 [] equal(multiply(X,Y),divide(X,divide(divide(Z,Z),Y))).
% 1060 [] equal(inverse(X),divide(divide(Y,Y),X)).
% 1061 [] -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)).
% 1062 [para:1060.1.2,1060.1.2.1] equal(inverse(X),divide(inverse(divide(Y,Y)),X)).
% 1067 [para:1059.1.2,1060.1.2,demod:1060] equal(inverse(inverse(X)),multiply(divide(Y,Y),X)).
% 1070 [para:1060.1.2,1059.1.2.2] equal(multiply(X,Y),divide(X,inverse(Y))).
% 1071 [para:1059.1.2,1062.1.2,demod:1060] equal(inverse(inverse(X)),multiply(inverse(divide(Y,Y)),X)).
% 1088 [para:1058.1.1,1060.1.2,demod:1070,1062,1060] equal(inverse(multiply(divide(inverse(X),Y),Y)),X).
% 1089 [para:1060.1.2,1058.1.1.2,demod:1070,1060] equal(multiply(X,multiply(inverse(X),Y)),Y).
% 1096 [para:1059.1.2,1058.1.1.2.2.1,demod:1060] equal(divide(inverse(X),divide(divide(inverse(Y),Z),divide(multiply(divide(Y,Y),X),Z))),Y).
% 1101 [para:1089.1.1,1067.1.2,demod:1071] equal(inverse(inverse(inverse(inverse(X)))),X).
% 1103 [para:1071.1.2,1089.1.1.2] equal(multiply(divide(X,X),inverse(inverse(Y))),Y).
% 1104 [para:1089.1.1,1089.1.1.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 1108 [para:1101.1.1,1089.1.1.2.1,demod:1104] equal(multiply(inverse(X),multiply(X,Y)),Y).
% 1110 [para:1062.1.2,1088.1.1.1.1] equal(inverse(multiply(inverse(X),X)),divide(Y,Y)).
% 1153 [para:1110.1.2,1058.1.1.2,demod:1070] equal(multiply(X,multiply(inverse(Y),Y)),X).
% 1154 [para:1110.1.2,1058.1.1.2.2,demod:1153,1070,1060] equal(divide(X,multiply(inverse(Y),X)),Y).
% 1160 [para:1110.1.1,1110.1.1] equal(divide(X,X),divide(Y,Y)).
% 1165 [para:1160.1.1,1059.1.2,demod:1060] equal(multiply(inverse(X),X),divide(Y,Y)).
% 1168 [para:1160.1.1,1058.1.1.2] equal(divide(X,divide(Y,Y)),X).
% 1169 [para:1060.1.2,1168.1.1.2,demod:1070] equal(multiply(X,divide(Y,Y)),X).
% 1176 [para:1168.1.1,1088.1.1.1.1,demod:1169] equal(inverse(inverse(X)),X).
% 1177 [para:1168.1.1,1103.1.1.1,demod:1176] equal(multiply(divide(X,X),Y),Y).
% 1178 [para:1176.1.1,1070.1.2.2] equal(multiply(X,inverse(Y)),divide(X,Y)).
% 1182 [para:1153.1.1,1108.1.1.2] equal(multiply(inverse(X),X),multiply(inverse(Y),Y)).
% 1183 [para:1067.1.1,1154.1.1.2.1,demod:1177] equal(divide(X,multiply(Y,X)),inverse(Y)).
% 1187 [para:1089.1.1,1154.1.1.2,demod:1176] equal(divide(multiply(X,Y),Y),X).
% 1189 [para:1187.1.1,1059.1.2,demod:1178,1060] equal(multiply(divide(X,Y),Y),X).
% 1193 [para:1165.1.1,1061.1.1.1,demod:1177,cut:1057,cut:1182] -equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))).
% 1194 [para:1178.1.1,1089.1.1.2] equal(multiply(X,divide(inverse(X),Y)),inverse(Y)).
% 1199 [para:1189.1.1,1183.1.1.2] equal(divide(X,Y),inverse(divide(Y,X))).
% 1203 [para:1059.1.2,1199.1.2.1,demod:1060] equal(divide(inverse(X),Y),inverse(multiply(Y,X))).
% 1204 [para:1199.1.2,1070.1.2.2] equal(multiply(X,divide(Y,Z)),divide(X,divide(Z,Y))).
% 1209 [para:1199.1.2,1194.1.1.2.1,demod:1204] equal(divide(divide(X,Y),divide(Z,divide(Y,X))),inverse(Z)).
% 1210 [para:1203.1.2,1070.1.2.2] equal(multiply(X,multiply(Y,Z)),divide(X,divide(inverse(Z),Y))).
% 1265 [para:1096.1.1,1209.1.1.2,demod:1176,1210,1177] equal(divide(multiply(divide(X,Y),multiply(Y,Z)),Z),X).
% 1269 [para:1108.1.1,1265.1.1.1.2,demod:1070] equal(divide(multiply(multiply(X,Y),Z),multiply(Y,Z)),X).
% 1286 [para:1269.1.1,1189.1.1.1] equal(multiply(X,multiply(Y,Z)),multiply(multiply(X,Y),Z)).
% 1305 [para:1286.1.2,1193.1.1,cut:1057] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 4
%
%
% ***GANDALF_FOUND_A_REFUTATION***
%
% Global statistics over all passes:
%
% given clauses: 1158
% derived clauses: 306927
% kept clauses: 1261
% kept size sum: 15654
% kept mid-nuclei: 8
% kept new demods: 964
% forw unit-subs: 304366
% forw double-subs: 0
% forw overdouble-subs: 0
% backward subs: 23
% fast unit cutoff: 10
% full unit cutoff: 0
% dbl unit cutoff: 0
% real runtime : 5.74
% process. runtime: 5.72
% 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/GRP064-1+eq_r.in")
%
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