%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP422-1 : TPTP v3.4.2. Released v2.6.0.
% Transfm : add_equality:r
% Format : otter:hypothesis:set(auto),clear(print_given)
% Command : gandalf-wrapper -time %d %s
% Computer : art02.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 9.6s
% Output : Assurance 9.6s
% 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/GRP422-1+eq_r.in
% Using automatic strategy selection.
% Time limit in seconds: 600
%
% prove-all-passes started
%
% detected problem class: ueq
%
% strategies selected:
% (binary-posweight-kb-big-order 60 #f 11 1)
% (binary-posweight-lex-big-order 30 #f 11 1)
% (binary 30 #t)
% (binary-posweight-kb-big-order 180 #f)
% (binary-posweight-lex-big-order 120 #f)
% (binary-posweight-firstpref-order 60 #f)
% (binary-posweight-kb-small-order 60 #f)
% (binary-posweight-lex-small-order 60 #f)
%
%
% **** EMPTY CLAUSE DERIVED ****
%
%
% timer checkpoints: c(3,40,1,6,0,1)
%
%
% START OF PROOF
% 5 [] equal(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(Y),multiply(inverse(Z),inverse(multiply(inverse(Z),Z))))))),multiply(X,Z))),Y).
% 6 [] -equal(multiply(multiply(inverse(b2),b2),a2),a2).
% 7 [para:5.1.1,5.1.1.1.1.1.2] equal(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),multiply(inverse(Z),inverse(multiply(inverse(Y),multiply(inverse(inverse(multiply(inverse(Z),Z))),inverse(multiply(inverse(inverse(multiply(inverse(Z),Z))),inverse(multiply(inverse(Z),Z))))))))).
% 8 [para:5.1.1,5.1.1.1.1.1.2.1.1] equal(inverse(multiply(inverse(multiply(X,inverse(multiply(Y,multiply(inverse(Z),inverse(multiply(inverse(Z),Z))))))),multiply(X,Z))),multiply(inverse(multiply(U,inverse(multiply(inverse(Y),multiply(inverse(V),inverse(multiply(inverse(V),V))))))),multiply(U,V))).
% 10 [para:7.1.2,5.1.1.1.1.1] equal(inverse(multiply(inverse(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z)))),multiply(inverse(Z),inverse(multiply(inverse(Z),Z))))),Y).
% 11 [para:7.1.2,7.1.2] equal(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),inverse(multiply(inverse(multiply(U,Y)),multiply(U,Z)))).
% 12 [para:11.1.1,5.1.1.1.1.1.2] equal(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(multiply(Y,Z)),multiply(Y,inverse(multiply(inverse(U),U))))))),multiply(X,U))),multiply(inverse(U),Z)).
% 13 [para:11.1.1,5.1.1.1.1.1.2.1.1,demod:5] equal(multiply(inverse(multiply(X,Y)),multiply(X,Z)),multiply(inverse(multiply(U,Y)),multiply(U,Z))).
% 20 [para:8.1.1,5.1.1] equal(multiply(inverse(multiply(X,inverse(multiply(inverse(inverse(Y)),multiply(inverse(Z),inverse(multiply(inverse(Z),Z))))))),multiply(X,Z)),Y).
% 30 [para:5.1.1,13.1.1.1] equal(multiply(X,multiply(inverse(multiply(Y,inverse(multiply(inverse(X),multiply(inverse(Z),inverse(multiply(inverse(Z),Z))))))),U)),multiply(inverse(multiply(V,multiply(Y,Z))),multiply(V,U))).
% 34 [para:11.1.1,13.1.1.1] equal(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),multiply(inverse(multiply(U,Y)),V)),multiply(inverse(multiply(W,multiply(U,Z))),multiply(W,V))).
% 39 [para:13.1.1,13.1.1.2] equal(multiply(inverse(multiply(inverse(multiply(X,Y)),Z)),multiply(inverse(multiply(U,Y)),multiply(U,V))),multiply(inverse(multiply(W,Z)),multiply(W,multiply(X,V)))).
% 69 [para:11.1.1,12.1.1.1.1.1.2.1.1] equal(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(Y,Z)),multiply(Y,U))),multiply(inverse(multiply(V,Z)),inverse(multiply(inverse(W),W))))))),multiply(X,W))),multiply(inverse(W),multiply(V,U))).
% 192 [para:39.1.1,12.1.1.1.1.1.2.1.1.1,demod:69] equal(multiply(inverse(X),multiply(inverse(multiply(Y,Z)),multiply(Y,U))),multiply(inverse(X),multiply(inverse(multiply(V,Z)),multiply(V,U)))).
% 195 [para:39.1.1,34.1.1] equal(multiply(inverse(multiply(X,multiply(Y,Z))),multiply(X,multiply(Y,U))),multiply(inverse(multiply(V,multiply(W,Z))),multiply(V,multiply(W,U)))).
% 250 [para:5.1.1,192.1.1.1,demod:5] equal(multiply(X,multiply(inverse(multiply(Y,Z)),multiply(Y,U))),multiply(X,multiply(inverse(multiply(V,Z)),multiply(V,U)))).
% 381 [para:195.1.1,11.1.1.1] equal(inverse(multiply(inverse(multiply(X,multiply(Y,Z))),multiply(X,multiply(Y,U)))),inverse(multiply(inverse(multiply(V,multiply(W,Z))),multiply(V,multiply(W,U))))).
% 895 [para:20.1.1,30.1.1.2] equal(multiply(inverse(X),X),multiply(inverse(multiply(Y,multiply(Z,U))),multiply(Y,multiply(Z,U)))).
% 973 [para:20.1.1,895.1.2.1.1,demod:20] equal(multiply(inverse(X),X),multiply(inverse(Y),Y)).
% 1230 [para:973.1.1,6.1.1.1] -equal(multiply(multiply(inverse(X),X),a2),a2).
% 1233 [para:973.1.1,5.1.1.1.1.1.2.1.2.2.1] equal(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(Y),multiply(inverse(Z),inverse(multiply(inverse(U),U))))))),multiply(X,Z))),Y).
% 1242 [para:973.1.1,11.1.1.1] equal(inverse(multiply(inverse(X),X)),inverse(multiply(inverse(multiply(Y,Z)),multiply(Y,Z)))).
% 1243 [para:973.1.1,11.1.1.1.1.1] equal(inverse(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Z))),inverse(multiply(inverse(multiply(U,Y)),multiply(U,Z)))).
% 1244 [para:973.1.1,11.1.1.1.2] equal(inverse(multiply(inverse(multiply(inverse(X),Y)),multiply(inverse(Z),Z))),inverse(multiply(inverse(multiply(U,Y)),multiply(U,X)))).
% 1260 [para:973.1.1,10.1.1.1.1.1.1] equal(inverse(multiply(inverse(inverse(multiply(inverse(X),X))),multiply(inverse(Y),inverse(multiply(inverse(Y),Y))))),Y).
% 1263 [para:973.1.1,10.1.1.1.2.2.1] equal(inverse(multiply(inverse(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z)))),multiply(inverse(Z),inverse(multiply(inverse(U),U))))),Y).
% 1309 [para:973.1.1,250.1.1.2] equal(multiply(X,multiply(inverse(Y),Y)),multiply(X,multiply(inverse(multiply(Z,U)),multiply(Z,U)))).
% 1429 [para:973.1.1,1242.1.2.1] equal(inverse(multiply(inverse(X),X)),inverse(multiply(inverse(Y),Y))).
% 1430 [para:973.1.1,1242.1.2.1.1.1] equal(inverse(multiply(inverse(X),X)),inverse(multiply(inverse(multiply(inverse(Y),Y)),multiply(inverse(Z),Z)))).
% 1441 [para:1429.1.1,1230.1.1.1.1] -equal(multiply(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Y)),a2),a2).
% 1474 [para:1429.1.1,1441.1.1.1.2.1] -equal(multiply(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(multiply(inverse(Y),Y)),multiply(inverse(Z),Z))),a2),a2).
% 1843 [para:973.1.1,1309.1.2.2] equal(multiply(X,multiply(inverse(Y),Y)),multiply(X,multiply(inverse(Z),Z))).
% 2084 [para:973.1.1,1260.1.1.1.2.2.1] equal(inverse(multiply(inverse(inverse(multiply(inverse(X),X))),multiply(inverse(Y),inverse(multiply(inverse(Z),Z))))),Y).
% 2159 [para:973.1.1,2084.1.1.1.2] equal(inverse(multiply(inverse(inverse(multiply(inverse(X),X))),multiply(inverse(Y),Y))),inverse(multiply(inverse(Z),Z))).
% 8425 [para:973.1.1,1263.1.1.1.1.1.1.1.1] equal(inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Z)))),multiply(inverse(Z),inverse(multiply(inverse(U),U))))),Y).
% 8462 [para:2159.1.1,1263.1.1.1.1.1.1.1,demod:8425] equal(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Y)).
% 8903 [para:8462.1.2,1843.1.1.2] equal(multiply(X,inverse(multiply(inverse(Y),Y))),multiply(X,multiply(inverse(Z),Z))).
% 8905 [para:8462.1.2,1843.1.2.2] equal(multiply(X,multiply(inverse(Y),Y)),multiply(X,inverse(multiply(inverse(Z),Z)))).
% 8922 [para:8462.1.1,2084.1.1.1.1.1] equal(inverse(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),inverse(multiply(inverse(Z),Z))))),Y).
% 9214 [para:8462.1.2,8462.1.1.1] equal(inverse(inverse(multiply(inverse(X),X))),multiply(inverse(Y),Y)).
% 9735 [para:9214.1.2,9214.1.2] equal(inverse(inverse(multiply(inverse(X),X))),inverse(inverse(multiply(inverse(Y),Y)))).
% 11396 [para:9735.1.1,1474.1.1.1.2.1.1.1] -equal(multiply(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(multiply(inverse(inverse(multiply(inverse(Y),Y))),inverse(multiply(inverse(Z),Z)))),multiply(inverse(U),U))),a2),a2).
% 12113 [para:8903.1.2,1243.1.1.1.2,demod:8922] equal(X,inverse(multiply(inverse(multiply(Y,X)),multiply(Y,multiply(inverse(Z),Z))))).
% 12161 [para:8905.1.1,11.1.1.1.2,demod:12113] equal(inverse(multiply(inverse(multiply(X,Y)),multiply(X,inverse(multiply(inverse(Z),Z))))),Y).
% 12168 [para:8905.1.1,381.1.1.1.2,demod:12161] equal(multiply(inverse(X),Y),inverse(multiply(inverse(multiply(Z,multiply(U,Y))),multiply(Z,multiply(U,X))))).
% 12169 [para:8905.1.1,381.1.2.1,demod:12168] equal(multiply(inverse(X),Y),inverse(multiply(inverse(multiply(inverse(multiply(Z,X)),multiply(Z,Y))),inverse(multiply(inverse(U),U))))).
% 12204 [para:8905.1.1,1244.1.2.1.2,demod:12161] equal(inverse(multiply(inverse(multiply(inverse(multiply(inverse(X),X)),Y)),multiply(inverse(Z),Z))),Y).
% 12212 [para:8905.1.1,1263.1.1.1,demod:12161] equal(inverse(multiply(inverse(X),inverse(multiply(inverse(Y),Y)))),X).
% 12292 [para:11.1.1,12212.1.1.1.1,demod:12169] equal(multiply(inverse(X),Y),multiply(inverse(multiply(Z,X)),multiply(Z,Y))).
% 12332 [para:1430.1.1,12212.1.1.1.2.1.1,demod:12204] equal(inverse(multiply(inverse(X),multiply(inverse(Y),Y))),X).
% 12374 [para:12212.1.1,1244.1.1.1.1.1.1,demod:12292,12332] equal(multiply(X,Y),inverse(multiply(inverse(Y),multiply(inverse(X),inverse(multiply(inverse(Z),Z)))))).
% 12394 [para:12212.1.1,1233.1.1.1.1.1.2.1.2.2,demod:12292,12374] equal(inverse(multiply(inverse(multiply(X,Y)),X)),Y).
% 12493 [para:8903.1.2,12394.1.1.1,demod:12212,slowcut:11396] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using binary resolution
% using first neg lit preferred strategy
% not using sos strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% clause length limited to 1
% clause depth limited to 11
% seconds given: 60
%
%
% ***GANDALF_FOUND_A_REFUTATION***
%
% Global statistics over all passes:
%
% given clauses: 135
% derived clauses: 81628
% kept clauses: 12485
% kept size sum: 435953
% kept mid-nuclei: 0
% kept new demods: 545
% forw unit-subs: 53398
% forw double-subs: 0
% forw overdouble-subs: 0
% backward subs: 68
% fast unit cutoff: 0
% full unit cutoff: 0
% dbl unit cutoff: 0
% real runtime : 11.54
% process. runtime: 11.3
% 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/GRP422-1+eq_r.in")
%
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