%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP065-1 : 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/GRP065-1+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 8 5)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 8 5)
% (binary-posweight-lex-big-order 30 #f 8 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(5,40,0,10,0,0,1300,4,752)
%
%
% START OF PROOF
% 6 [] equal(X,X).
% 7 [] equal(divide(divide(divide(X,X),divide(X,divide(Y,divide(divide(divide(X,X),X),Z)))),Z),Y).
% 8 [] equal(multiply(X,Y),divide(X,divide(divide(Z,Z),Y))).
% 9 [] equal(inverse(X),divide(divide(Y,Y),X)).
% 10 [] -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)).
% 11 [para:9.1.2,9.1.2.1] equal(inverse(X),divide(inverse(divide(Y,Y)),X)).
% 12 [para:11.1.2,9.1.2.1] equal(inverse(X),divide(inverse(inverse(divide(Y,Y))),X)).
% 16 [para:8.1.2,9.1.2,demod:9] equal(inverse(inverse(X)),multiply(divide(Y,Y),X)).
% 19 [para:9.1.2,8.1.2.2] equal(multiply(X,Y),divide(X,inverse(Y))).
% 20 [para:8.1.2,11.1.2,demod:9] equal(inverse(inverse(X)),multiply(inverse(divide(Y,Y)),X)).
% 24 [para:8.1.2,8.1.2.2,demod:9] equal(multiply(X,inverse(Y)),divide(X,multiply(divide(Z,Z),Y))).
% 29 [para:16.1.1,16.1.1] equal(multiply(divide(X,X),Y),multiply(divide(Z,Z),Y)).
% 30 [para:16.1.1,16.1.1.1] equal(inverse(multiply(divide(X,X),Y)),multiply(divide(Z,Z),inverse(Y))).
% 37 [para:9.1.2,7.1.1.1,demod:9] equal(divide(inverse(divide(X,divide(Y,divide(inverse(X),Z)))),Z),Y).
% 38 [para:9.1.2,7.1.1.1.1,demod:19,11,9] equal(divide(inverse(inverse(multiply(X,Y))),Y),X).
% 39 [para:9.1.2,7.1.1.1.2.2,demod:19,9] equal(divide(inverse(multiply(X,divide(inverse(X),Y))),Y),divide(Z,Z)).
% 42 [para:7.1.1,8.1.2,demod:19,9] equal(multiply(inverse(divide(X,divide(Y,multiply(inverse(X),Z)))),Z),Y).
% 44 [para:7.1.1,7.1.1.1.2.2,demod:9] equal(divide(inverse(divide(X,Y)),Z),inverse(divide(U,divide(Y,divide(inverse(U),divide(inverse(X),Z)))))).
% 45 [para:38.1.1,8.1.2,demod:9] equal(multiply(inverse(inverse(multiply(X,inverse(Y)))),Y),X).
% 60 [para:45.1.1,38.1.1.1.1.1] equal(divide(inverse(inverse(X)),Y),inverse(inverse(multiply(X,inverse(Y))))).
% 76 [para:29.1.1,38.1.1.1.1.1,demod:38] equal(divide(X,X),divide(Y,Y)).
% 77 [para:29.1.1,45.1.1.1.1.1,demod:12,60] equal(multiply(inverse(X),X),divide(Y,Y)).
% 82 [para:76.1.1,12.1.2] equal(inverse(inverse(inverse(divide(X,X)))),divide(Y,Y)).
% 104 [para:77.1.2,8.1.2,demod:9] equal(multiply(inverse(X),X),multiply(inverse(Y),Y)).
% 182 [para:24.1.2,11.1.2,demod:20] equal(inverse(multiply(divide(X,X),Y)),inverse(inverse(inverse(Y)))).
% 926 [para:30.1.1,182.1.2.1.1,demod:12,60] equal(inverse(multiply(divide(X,X),multiply(divide(Y,Y),Z))),inverse(Z)).
% 994 [para:182.1.1,182.1.2.1.1,demod:926] equal(inverse(X),inverse(inverse(inverse(inverse(inverse(X)))))).
% 996 [para:994.1.2,19.1.2.2,demod:19] equal(multiply(X,inverse(inverse(inverse(inverse(Y))))),multiply(X,Y)).
% 999 [para:994.1.2,45.1.1.1.1.1.2,demod:996,60] equal(multiply(divide(inverse(inverse(X)),Y),Y),X).
% 1003 [para:999.1.1,16.1.2] equal(inverse(inverse(inverse(inverse(X)))),X).
% 1007 [para:999.1.1,24.1.2.2] equal(multiply(X,inverse(inverse(inverse(Y)))),divide(X,Y)).
% 1008 [para:999.1.1,30.1.2] equal(inverse(multiply(divide(X,X),inverse(Y))),Y).
% 1030 [para:16.1.1,1003.1.1.1.1] equal(inverse(inverse(multiply(divide(X,X),Y))),Y).
% 1033 [para:1003.1.1,999.1.1.1.1] equal(multiply(divide(X,Y),Y),inverse(inverse(X))).
% 1106 [para:1033.1.2,182.1.2.1.1,demod:1008] equal(X,inverse(inverse(multiply(divide(X,Y),Y)))).
% 1110 [para:1033.1.2,1003.1.1.1] equal(inverse(multiply(divide(inverse(X),Y),Y)),X).
% 1142 [para:39.1.1,1106.1.2.1.1.1,demod:1030] equal(inverse(multiply(X,divide(inverse(X),Y))),Y).
% 1150 [para:37.1.1,1110.1.1.1.1] equal(inverse(multiply(X,Y)),divide(Z,divide(X,divide(inverse(Z),Y)))).
% 1162 [para:1142.1.1,38.1.1.1.1] equal(divide(inverse(X),divide(inverse(Y),X)),Y).
% 1169 [para:82.1.2,1142.1.1.1.2,demod:1007] equal(inverse(divide(X,divide(Y,Y))),inverse(X)).
% 1192 [para:1162.1.1,11.1.2,demod:1169] equal(inverse(inverse(X)),X).
% 1193 [para:8.1.2,1162.1.1.2,demod:1192,9] equal(divide(X,multiply(inverse(Y),X)),Y).
% 1195 [para:16.1.1,1162.1.1.2.1] equal(divide(inverse(X),divide(multiply(divide(Y,Y),Z),X)),inverse(Z)).
% 1196 [para:38.1.1,1162.1.1.2] equal(divide(inverse(X),Y),inverse(multiply(Y,X))).
% 1200 [para:30.1.1,1162.1.1.2.1,demod:1192,1195] equal(X,multiply(divide(Y,Y),X)).
% 1203 [para:1162.1.1,999.1.1.1,demod:19] equal(multiply(X,multiply(inverse(X),Y)),Y).
% 1204 [para:1003.1.1,1162.1.1.2.1,demod:1192] equal(divide(inverse(X),divide(Y,X)),inverse(Y)).
% 1208 [para:9.1.2,42.1.1.1.1,demod:1192,20] equal(multiply(divide(X,Y),Y),X).
% 1218 [para:1192.1.1,19.1.2.2] equal(multiply(X,inverse(Y)),divide(X,Y)).
% 1221 [para:7.1.1,1208.1.1.1,demod:1196,1150,9] equal(multiply(X,Y),inverse(divide(inverse(Y),X))).
% 1223 [para:16.1.1,1193.1.1.2.1,demod:1200] equal(divide(X,multiply(Y,X)),inverse(Y)).
% 1224 [para:45.1.1,1193.1.1.2,demod:1218] equal(divide(X,Y),inverse(divide(Y,X))).
% 1228 [para:1203.1.1,42.1.1.1.1.2.2,demod:1192,1224] equal(multiply(divide(divide(X,Y),Z),multiply(Z,Y)),X).
% 1230 [para:9.1.2,44.1.2.1,demod:1221,9,1224] equal(divide(divide(X,Y),Z),divide(X,multiply(Z,Y))).
% 1248 [para:1224.1.2,19.1.2.2] equal(multiply(X,divide(Y,Z)),divide(X,divide(Z,Y))).
% 1249 [para:1224.1.2,999.1.1.1.1.1,demod:1230,1224] equal(multiply(divide(X,multiply(Y,Z)),Y),divide(X,Z)).
% 1251 [para:1224.1.2,1162.1.1.2.1,demod:1230] equal(divide(inverse(X),divide(Y,multiply(X,Z))),divide(Z,Y)).
% 1255 [para:1196.1.2,19.1.2.2] equal(multiply(X,multiply(Y,Z)),divide(X,divide(inverse(Z),Y))).
% 1269 [para:7.1.1,1204.1.1.2,demod:1224,1255,1223,1230] equal(divide(inverse(X),Y),divide(Z,multiply(Y,multiply(X,Z)))).
% 1277 [para:1196.1.2,1221.1.2.1.1,demod:1221,1230] equal(multiply(X,multiply(Y,Z)),multiply(multiply(X,Y),Z)).
% 1280 [para:7.1.1,1228.1.1.1.1,demod:1221,1269,1255,1223,1230] equal(multiply(divide(X,Y),multiply(Y,Z)),multiply(X,Z)).
% 1296 [para:1251.1.1,1280.1.1.1] equal(multiply(divide(X,Y),multiply(divide(Y,multiply(Z,X)),U)),multiply(inverse(Z),U)).
% 1301 [input:10,cut:104] -equal(multiply(multiply(inverse(b2),b2),a2),a2) | -equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))).
% 1302 [para:1296.1.2,1301.1.1.1,demod:1277,1200,1208,1230,1248,1249,cut:6,cut:6] 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 8
% seconds given: 10
%
%
% ***GANDALF_FOUND_A_REFUTATION***
%
% Global statistics over all passes:
%
% given clauses: 564
% derived clauses: 457800
% kept clauses: 1287
% kept size sum: 18819
% kept mid-nuclei: 2
% kept new demods: 360
% forw unit-subs: 456045
% forw double-subs: 0
% forw overdouble-subs: 0
% backward subs: 2
% fast unit cutoff: 2
% full unit cutoff: 0
% dbl unit cutoff: 0
% real runtime : 7.53
% process. runtime: 7.52
% 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/GRP065-1+eq_r.in")
%
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