TSTP Solution File: GRP061-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP061-1 : TPTP v3.4.2. Released v1.0.0.
% Transfm : add_equality:r
% Format : otter:hypothesis:set(auto),clear(print_given)
% Command : gandalf-wrapper -time %d %s
% Computer : art04.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/GRP061-1+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(3,40,0,6,0,0,7,50,0,10,0,0,11,50,0,14,0,0,20,50,0,23,0,0,39,50,5,42,0,5,3025,4,682)
%
%
% START OF PROOF
% 40 [] equal(X,X).
% 41 [] equal(inverse(multiply(X,multiply(Y,multiply(multiply(inverse(Y),Z),inverse(multiply(U,multiply(X,Z))))))),U).
% 42 [] -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)).
% 43 [para:41.1.1,41.1.1.1.2.2.1.1] equal(inverse(multiply(X,multiply(multiply(Y,multiply(Z,multiply(multiply(inverse(Z),U),inverse(multiply(V,multiply(Y,U)))))),multiply(multiply(V,W),inverse(multiply(X1,multiply(X,W))))))),X1).
% 44 [para:41.1.1,41.1.1.1.2.2.2] equal(inverse(multiply(X,multiply(Y,multiply(multiply(inverse(Y),multiply(multiply(inverse(X),Z),inverse(multiply(U,multiply(V,Z))))),U)))),V).
% 46 [para:44.1.1,41.1.1.1.2.2.2] equal(inverse(multiply(X,multiply(Y,multiply(multiply(inverse(Y),multiply(multiply(inverse(X),multiply(multiply(inverse(Z),U),inverse(multiply(V,multiply(W,U))))),V)),W)))),Z).
% 51 [para:41.1.1,46.1.1.1.2.2.1.1] equal(inverse(multiply(X,multiply(multiply(Y,multiply(Z,multiply(multiply(inverse(Z),U),inverse(multiply(V,multiply(Y,U)))))),multiply(multiply(V,multiply(multiply(inverse(X),multiply(multiply(inverse(W),X1),inverse(multiply(X2,multiply(X3,X1))))),X2)),X3)))),W).
% 53 [para:41.1.1,46.1.1.1.2.2.1.2.1.2.1.1] equal(inverse(multiply(X,multiply(Y,multiply(multiply(inverse(Y),multiply(multiply(inverse(X),multiply(multiply(Z,U),inverse(multiply(V,multiply(W,U))))),V)),W)))),multiply(X1,multiply(X2,multiply(multiply(inverse(X2),X3),inverse(multiply(Z,multiply(X1,X3))))))).
% 57 [para:46.1.1,46.1.1.1.2.2.1.2.1.2.1.1] equal(inverse(multiply(X,multiply(Y,multiply(multiply(inverse(Y),multiply(multiply(inverse(X),multiply(multiply(Z,U),inverse(multiply(V,multiply(W,U))))),V)),W)))),multiply(X1,multiply(X2,multiply(multiply(inverse(X2),multiply(multiply(inverse(X1),multiply(multiply(inverse(Z),X3),inverse(multiply(X4,multiply(X5,X3))))),X4)),X5)))).
% 61 [para:43.1.1,44.1.1.1.2.2.1.2.1.1] equal(inverse(multiply(multiply(X,multiply(multiply(Y,multiply(Z,multiply(multiply(inverse(Z),U),inverse(multiply(V,multiply(Y,U)))))),multiply(multiply(V,W),inverse(multiply(X1,multiply(X,W)))))),multiply(X2,multiply(multiply(inverse(X2),multiply(multiply(X1,X3),inverse(multiply(X4,multiply(X5,X3))))),X4)))),X5).
% 64 [para:43.1.1,46.1.1.1.2.2.1.2.1.2.1.1] equal(inverse(multiply(X,multiply(Y,multiply(multiply(inverse(Y),multiply(multiply(inverse(X),multiply(multiply(Z,U),inverse(multiply(V,multiply(W,U))))),V)),W)))),multiply(X1,multiply(multiply(X2,multiply(X3,multiply(multiply(inverse(X3),X4),inverse(multiply(X5,multiply(X2,X4)))))),multiply(multiply(X5,X6),inverse(multiply(Z,multiply(X1,X6))))))).
% 65 [para:43.1.1,43.1.1.1.2.1.2.2.2] equal(inverse(multiply(X,multiply(multiply(multiply(Y,multiply(Z,multiply(multiply(inverse(Z),U),inverse(multiply(V,multiply(Y,U)))))),multiply(W,multiply(multiply(inverse(W),multiply(multiply(V,X1),inverse(multiply(X2,multiply(X3,X1))))),X2))),multiply(multiply(X3,X4),inverse(multiply(X5,multiply(X,X4))))))),X5).
% 142 [para:53.1.1,46.1.1] equal(multiply(X,multiply(Y,multiply(multiply(inverse(Y),Z),inverse(multiply(inverse(U),multiply(X,Z)))))),U).
% 157 [para:142.1.1,41.1.1.1.2.2.2.1.2] equal(inverse(multiply(X,multiply(Y,multiply(multiply(inverse(Y),multiply(Z,multiply(multiply(inverse(Z),U),inverse(multiply(inverse(V),multiply(X,U)))))),inverse(multiply(W,V)))))),W).
% 159 [para:41.1.1,142.1.1.2.2.2] equal(multiply(X,multiply(Y,multiply(multiply(inverse(Y),multiply(multiply(inverse(X),Z),inverse(multiply(U,multiply(inverse(V),Z))))),U))),V).
% 161 [para:44.1.1,142.1.1.2.2.2] equal(multiply(X,multiply(Y,multiply(multiply(inverse(Y),multiply(multiply(inverse(X),multiply(multiply(inverse(inverse(Z)),U),inverse(multiply(V,multiply(W,U))))),V)),W))),Z).
% 273 [para:53.1.2,157.1.1.1.2.2.1,demod:46] equal(inverse(multiply(inverse(X),multiply(X,multiply(Y,inverse(multiply(Z,Y)))))),Z).
% 337 [para:273.1.1,53.1.2.2.2.2,demod:46] equal(X,multiply(X,multiply(Y,multiply(multiply(inverse(Y),multiply(Z,inverse(multiply(U,Z)))),U)))).
% 354 [para:273.1.1,157.1.1.1.2.2.1.2.2.2,demod:337] equal(inverse(multiply(X,multiply(Y,multiply(inverse(Y),inverse(multiply(Z,X)))))),Z).
% 357 [para:273.1.1,273.1.1.1.2.2.2] equal(inverse(multiply(inverse(X),multiply(X,multiply(multiply(Y,multiply(Z,inverse(multiply(U,Z)))),U)))),inverse(Y)).
% 359 [para:354.1.1,41.1.1.1.2.2.2] equal(inverse(multiply(X,multiply(Y,multiply(multiply(inverse(Y),multiply(inverse(X),inverse(multiply(Z,U)))),Z)))),U).
% 419 [para:354.1.1,142.1.1.2.2.2] equal(multiply(X,multiply(Y,multiply(multiply(inverse(Y),multiply(inverse(X),inverse(multiply(Z,inverse(U))))),Z))),U).
% 439 [para:354.1.1,273.1.1.1.2.2.2] equal(inverse(multiply(inverse(X),multiply(X,multiply(multiply(Y,multiply(inverse(Y),inverse(multiply(Z,U)))),Z)))),U).
% 443 [para:354.1.1,354.1.1.1.2.2.2] equal(inverse(multiply(multiply(X,multiply(inverse(X),inverse(multiply(Y,Z)))),multiply(U,multiply(inverse(U),Y)))),Z).
% 456 [para:337.1.2,142.1.1.2.2.1,demod:337] equal(multiply(X,multiply(Y,multiply(inverse(Y),inverse(multiply(inverse(Z),X))))),Z).
% 461 [para:273.1.1,337.1.2.2.2.1.2.2] equal(X,multiply(X,multiply(Y,multiply(multiply(inverse(Y),multiply(multiply(Z,multiply(U,inverse(multiply(V,U)))),V)),inverse(Z))))).
% 464 [para:354.1.1,337.1.2.2.2.1.2.2] equal(X,multiply(X,multiply(Y,multiply(multiply(inverse(Y),multiply(multiply(Z,multiply(inverse(Z),inverse(multiply(U,V)))),U)),V)))).
% 508 [para:273.1.1,456.1.1.2.2.2] equal(multiply(multiply(X,multiply(Y,inverse(multiply(Z,Y)))),multiply(U,multiply(inverse(U),Z))),X).
% 511 [para:354.1.1,456.1.1.2.2.2] equal(multiply(multiply(X,multiply(inverse(X),inverse(multiply(Y,inverse(Z))))),multiply(U,multiply(inverse(U),Y))),Z).
% 633 [para:357.1.1,46.1.1.1.2.2.1.2.1.2.1.1,demod:46] equal(X,multiply(inverse(Y),multiply(Y,multiply(multiply(X,multiply(Z,inverse(multiply(U,Z)))),U)))).
% 1290 [para:337.1.2,464.1.2.2.2,demod:337] equal(X,multiply(X,multiply(Y,multiply(inverse(Y),multiply(multiply(Z,multiply(inverse(Z),inverse(U))),U))))).
% 1375 [para:1290.1.2,508.1.1] equal(multiply(X,multiply(Y,inverse(multiply(multiply(multiply(Z,multiply(inverse(Z),inverse(U))),U),Y)))),X).
% 1445 [para:1375.1.1,41.1.1.1.2] equal(inverse(multiply(inverse(X),X)),multiply(multiply(Y,multiply(inverse(Y),inverse(Z))),Z)).
% 1582 [para:1445.1.1,53.1.2.2.2.2,demod:46] equal(multiply(X,Y),multiply(X,multiply(Z,multiply(multiply(inverse(Z),Y),multiply(multiply(U,multiply(inverse(U),inverse(V))),V))))).
% 1669 [para:1445.1.2,443.1.1.1] equal(inverse(inverse(multiply(inverse(X),X))),multiply(inverse(Y),Y)).
% 1693 [para:1445.1.1,461.1.2.2.2.2,demod:1582] equal(X,multiply(X,multiply(multiply(multiply(inverse(Y),Y),multiply(Z,inverse(multiply(U,Z)))),U))).
% 1867 [para:1669.1.1,337.1.2.2.2.1.1,demod:1693] equal(X,multiply(X,inverse(multiply(inverse(Y),Y)))).
% 2001 [para:1669.1.1,1669.1.1] equal(multiply(inverse(X),X),multiply(inverse(Y),Y)).
% 2036 [para:1867.1.2,53.1.2.2.2,demod:46] equal(multiply(X,Y),multiply(X,multiply(Z,multiply(inverse(Z),Y)))).
% 2038 [para:1867.1.2,142.1.1.2.2.1,demod:2036,1867] equal(multiply(X,inverse(multiply(inverse(Y),X))),Y).
% 2048 [para:1867.1.2,273.1.1.1.2.2] equal(inverse(multiply(inverse(X),multiply(X,Y))),inverse(Y)).
% 2049 [para:1867.1.2,273.1.1.1.2.2.2.1,demod:2048] equal(inverse(multiply(inverse(multiply(inverse(X),X)),inverse(Y))),Y).
% 2053 [para:1867.1.2,337.1.2.2.2,demod:2036,2038] equal(X,multiply(X,multiply(inverse(Y),Y))).
% 2063 [para:1867.1.2,508.1.1.1.2,demod:2036] equal(multiply(multiply(X,Y),inverse(Y)),X).
% 2065 [para:1867.1.2,633.1.2.2.2,demod:2053,2038] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 2074 [para:1867.1.2,419.1.1.2.2,demod:2036,2049] equal(multiply(X,multiply(inverse(X),Y)),Y).
% 2109 [para:2053.1.2,41.1.1.1.2.2.1,demod:2074,2053] equal(inverse(multiply(X,inverse(multiply(Y,X)))),Y).
% 2166 [para:2053.1.2,273.1.1.1,demod:2109] equal(inverse(inverse(X)),X).
% 2172 [para:2053.1.2,456.1.1.2.2.2.1,demod:2074,2166] equal(multiply(multiply(inverse(X),X),Y),Y).
% 2178 [para:2053.1.2,359.1.1.1.2.2.1,demod:2074] equal(inverse(multiply(inverse(multiply(X,Y)),X)),Y).
% 2222 [para:61.1.1,161.1.1.2.2.1.1,demod:2166] equal(multiply(X,multiply(multiply(multiply(Y,multiply(multiply(Z,multiply(U,multiply(multiply(inverse(U),V),inverse(multiply(W,multiply(Z,V)))))),multiply(multiply(W,X1),inverse(multiply(X2,multiply(Y,X1)))))),multiply(X3,multiply(multiply(inverse(X3),multiply(multiply(X2,X4),inverse(multiply(X5,multiply(X6,X4))))),X5))),multiply(multiply(X6,multiply(multiply(inverse(X),multiply(multiply(X7,X8),inverse(multiply(X9,multiply(X10,X8))))),X9)),X10))),X7).
% 2290 [para:61.1.1,57.1.2.2.2.1.1,demod:2222] equal(inverse(multiply(X,multiply(Y,multiply(multiply(inverse(Y),multiply(multiply(inverse(X),multiply(multiply(Z,U),inverse(multiply(V,multiply(W,U))))),V)),W)))),inverse(Z)).
% 2291 [para:61.1.1,57.1.2.2.2.1.2.1.2.1.1,demod:61,2290] equal(X,multiply(Y,multiply(Z,multiply(multiply(inverse(Z),multiply(multiply(inverse(Y),multiply(multiply(X,U),inverse(multiply(V,multiply(W,U))))),V)),W)))).
% 2350 [para:354.1.1,2166.1.1.1,demod:2074] equal(inverse(X),multiply(Y,inverse(multiply(X,Y)))).
% 2356 [para:439.1.1,2166.1.1.1,demod:2065,2074] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 2447 [para:511.1.1,2063.1.1.1,demod:2074] equal(multiply(X,inverse(Y)),inverse(multiply(Y,inverse(X)))).
% 2495 [para:53.1.2,2065.1.2.2,demod:2291] equal(multiply(X,multiply(multiply(inverse(X),Y),inverse(multiply(Z,multiply(U,Y))))),multiply(inverse(U),inverse(Z))).
% 2511 [para:456.1.1,2065.1.2.2,demod:2074] equal(inverse(multiply(inverse(X),Y)),multiply(inverse(Y),X)).
% 2549 [para:161.1.1,2074.1.1.2,demod:2166] equal(multiply(X,Y),multiply(Z,multiply(multiply(inverse(Z),multiply(multiply(X,multiply(multiply(Y,U),inverse(multiply(V,multiply(W,U))))),V)),W))).
% 2703 [para:2172.1.1,53.1.2.2,demod:2172,2511,2074,2549] equal(inverse(X),multiply(Y,multiply(Z,inverse(multiply(X,multiply(Y,Z)))))).
% 2735 [para:2001.1.1,43.1.1.1.2.2.2.1.2,demod:2447,2511,2053,2074,2495] equal(multiply(multiply(multiply(X,inverse(multiply(Y,Z))),Y),Z),X).
% 2777 [para:41.1.1,2178.1.1.1.1,demod:2495] equal(inverse(multiply(X,Y)),multiply(inverse(Y),inverse(X))).
% 2792 [para:2178.1.1,53.1.2.2.2.2,demod:2166,2350,2777,2549] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(U,multiply(multiply(inverse(U),Y),Z)))).
% 2801 [para:359.1.1,2178.1.1.1.1,demod:2777] equal(inverse(multiply(X,Y)),multiply(Z,multiply(inverse(multiply(multiply(multiply(U,X),Y),Z)),U))).
% 2943 [para:2356.1.2,46.1.1.1.2.2.1.2.1.2.1,demod:2511,2801,2792,2777] equal(multiply(inverse(X),multiply(multiply(X,Y),Z)),multiply(Y,Z)).
% 2945 [para:2356.1.2,43.1.1.1.2.2.2.1,demod:2943,2166,2350,2777,2495] equal(inverse(multiply(X,multiply(Y,Z))),inverse(multiply(multiply(X,Y),Z))).
% 2969 [para:2356.1.2,51.1.1.1.2.2.1.2.1.2.1,demod:2447,2943,2356,2945,2350,2777,2495] equal(multiply(multiply(X,multiply(Y,Z)),inverse(Z)),multiply(X,Y)).
% 2978 [para:2356.1.2,53.1.2.2.2.2.1,demod:2792,2166,2969,2447,2777,2549,2945] equal(multiply(X,multiply(Y,Z)),multiply(multiply(X,Y),Z)).
% 2986 [para:2356.1.2,64.1.2.2.2.2.1,demod:2065,2166,2703,2074,2777,2350,2356,2978] equal(inverse(multiply(X,multiply(Y,inverse(multiply(Z,multiply(U,multiply(V,multiply(X,Y)))))))),multiply(Z,multiply(U,V))).
% 2994 [para:65.1.1,359.1.1.1.2.2.1.2.2,demod:2065,2350,2356,2703,2074,2978] equal(inverse(multiply(X,Y)),multiply(Z,inverse(multiply(X,multiply(Y,Z))))).
% 3010 [para:2511.1.1,159.1.1.2.2.1.2.2.1.2.1,demod:2074,2511,2356,2978] equal(multiply(X,multiply(inverse(multiply(Y,X)),Z)),multiply(inverse(Y),Z)).
% 3011 [para:2511.1.1,2447.1.2.1.2,demod:2978] equal(multiply(inverse(X),multiply(Y,inverse(Z))),inverse(multiply(Z,multiply(inverse(Y),X)))).
% 3012 [para:2511.1.1,2511.1.1.1.1,demod:2511,2978] equal(multiply(inverse(multiply(X,Y)),Z),multiply(inverse(Y),multiply(inverse(X),Z))).
% 3014 [para:2735.1.1,53.1.1.1.2.2.1.2.1.2,demod:3011,2166,2994,2074,3010,3012,2978] equal(inverse(multiply(X,multiply(Y,Z))),multiply(U,multiply(V,inverse(multiply(X,multiply(Y,multiply(Z,multiply(U,V)))))))).
% 3026 [input:42,cut:2172,cut:2001] -equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))).
% 3027 [para:2986.1.2,3026.1.2,demod:2166,3014,2978,cut:40] 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 12
% seconds given: 10
%
%
% ***GANDALF_FOUND_A_REFUTATION***
%
% Global statistics over all passes:
%
% given clauses: 217
% derived clauses: 113749
% kept clauses: 2998
% kept size sum: 116831
% kept mid-nuclei: 4
% kept new demods: 2206
% forw unit-subs: 104420
% forw double-subs: 0
% forw overdouble-subs: 0
% backward subs: 1
% fast unit cutoff: 6
% full unit cutoff: 0
% dbl unit cutoff: 0
% real runtime : 6.87
% process. runtime: 6.84
% 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/GRP061-1+eq_r.in")
%
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