%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP370-1 : TPTP v3.4.2. Released v2.5.0.
% Transfm : add_equality:r
% Format : otter:hypothesis:set(auto),clear(print_given)
% Command : gandalf-wrapper -time %d %s
% Computer : art08.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 248.6s
% Output : Assurance 248.6s
% 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/GRP370-1+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 3 21)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 3 21)
% (binary-posweight-lex-big-order 30 #f 3 21)
% (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(sk_c7,sk_c8),sk_c9) | -equal(multiply(X,Y),sk_c8) | -equal(inverse(X),Y) | -equal(multiply(Y,sk_c7),sk_c8) | -equal(multiply(Z,sk_c9),sk_c8) | -equal(inverse(Z),sk_c9) | -equal(multiply(U,sk_c7),sk_c8) | -equal(inverse(U),sk_c7) | -equal(multiply(sk_c9,V),sk_c7) | -equal(multiply(W,sk_c9),V) | -equal(inverse(W),sk_c9).
% was split for some strategies as:
% -equal(multiply(sk_c9,V),sk_c7) | -equal(multiply(W,sk_c9),V) | -equal(inverse(W),sk_c9).
% -equal(multiply(U,sk_c7),sk_c8) | -equal(inverse(U),sk_c7).
% -equal(multiply(Z,sk_c9),sk_c8) | -equal(inverse(Z),sk_c9).
% -equal(multiply(X,Y),sk_c8) | -equal(inverse(X),Y) | -equal(multiply(Y,sk_c7),sk_c8).
% -equal(multiply(sk_c7,sk_c8),sk_c9).
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(33,40,1,71,0,1,2324,50,23,2362,0,23,5100,50,51,5138,0,51,8192,50,86,8230,0,86,11434,50,110,11472,0,110,14809,50,139,14847,0,139,18390,50,177,18428,0,177,22159,50,232,22197,0,232,26190,50,324,26228,0,324,30465,50,492,30503,0,492,35058,50,744,35096,0,745,39951,50,1173,39951,40,1173,39989,0,1173,50362,3,1474,51097,4,1624,51785,5,1774,51786,1,1774,51786,50,1774,51786,40,1774,51824,0,1774,52394,3,2077,52406,4,2229,52457,5,2375,52457,1,2375,52457,50,2375,52457,40,2375,52495,0,2375,81905,3,3878,82560,4,4626,83029,5,5376,83030,1,5376,83030,50,5377,83030,40,5377,83068,0,5377,104063,3,6128,104531,4,6503,104834,1,6878,104834,50,6878,104834,40,6878,104872,0,6879,124031,3,7676,124705,4,8005,125566,1,8380,125566,50,8380,125566,40,8380,125604,0,8380,170135,3,12281,171025,4,14231,171676,5,16181,171677,1,16181,171677,50,16183,171677,40,16183,171715,0,16183,210587,3,18734,211600,4,20009,212462,5,21284,212463,1,21284,212463,50,21286,212463,40,21286,212501,0,21286,247625,3,22795,248739,4,23537,249459,5,24287,249460,1,24287,249460,50,24288,249460,40,24288,249498,0,24288,265779,3,25039,266187,4,25414)
%
%
% START OF PROOF
% 249461 [] equal(X,X).
% 249462 [] equal(multiply(identity,X),X).
% 249463 [] equal(multiply(inverse(X),X),identity).
% 249464 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 249469 [] equal(multiply(sk_c2,sk_c7),sk_c8) | equal(inverse(sk_c4),sk_c7).
% 249476 [] equal(inverse(sk_c1),sk_c2) | equal(inverse(sk_c4),sk_c7).
% 249477 [] equal(multiply(sk_c4,sk_c7),sk_c8) | equal(inverse(sk_c1),sk_c2).
% 249478 [] equal(inverse(sk_c1),sk_c2) | equal(inverse(sk_c3),sk_c9).
% 249479 [] equal(multiply(sk_c3,sk_c9),sk_c8) | equal(inverse(sk_c1),sk_c2).
% 249483 [] equal(multiply(sk_c1,sk_c2),sk_c8) | equal(inverse(sk_c4),sk_c7).
% 249484 [] equal(multiply(sk_c1,sk_c2),sk_c8) | equal(multiply(sk_c4,sk_c7),sk_c8).
% 249487 [] equal(multiply(sk_c7,sk_c8),sk_c9) | equal(inverse(sk_c5),sk_c9).
% 249488 [] equal(multiply(sk_c7,sk_c8),sk_c9) | equal(multiply(sk_c5,sk_c9),sk_c6).
% 249489 [] equal(multiply(sk_c7,sk_c8),sk_c9) | equal(multiply(sk_c9,sk_c6),sk_c7).
% 249490 [] equal(multiply(sk_c7,sk_c8),sk_c9) | equal(inverse(sk_c4),sk_c7).
% 249494 [] -equal(multiply(sk_c7,sk_c8),sk_c9) | $spltprd0($spltcnst37) | -equal(multiply(sk_c9,X),sk_c7) | -equal(multiply(Y,sk_c9),X) | -equal(inverse(Y),sk_c9).
% 249495 [] $spltprd0($spltcnst38) | -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c7).
% 249496 [] $spltprd0($spltcnst39) | -equal(multiply(X,sk_c9),sk_c8) | -equal(inverse(X),sk_c9).
% 249497 [] $spltprd0($spltcnst40) | -equal(multiply(X,sk_c7),sk_c8) | -equal(multiply(Y,X),sk_c8) | -equal(inverse(Y),X).
% 249498 [] -$spltprd0($spltcnst38) | -$spltprd0($spltcnst37) | -$spltprd0($spltcnst40) | -$spltprd0($spltcnst39).
% 249766 [para:249463.1.1,249464.1.1.1,demod:249462] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 249830 [para:249476.2.1,249495.3.1,cut:249461,binarycut:249477] equal(inverse(sk_c1),sk_c2) | $spltprd0($spltcnst38).
% 249845 [para:249830.1.1,249463.1.1.1] equal(multiply(sk_c2,sk_c1),identity) | $spltprd0($spltcnst38).
% 249852 [para:249463.1.1,249766.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 249900 [para:249845.1.1,249766.1.2.2] equal(sk_c1,multiply(inverse(sk_c2),identity)) | $spltprd0($spltcnst38).
% 249901 [para:249766.1.2,249766.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 249924 [para:249478.2.1,249496.3.1,cut:249461,binarycut:249479] equal(inverse(sk_c1),sk_c2) | $spltprd0($spltcnst39).
% 249977 [para:249483.1.1,249497.3.1,cut:249461,binarycut:249469,binarycut:249476] equal(inverse(sk_c4),sk_c7) | $spltprd0($spltcnst40).
% 250041 [para:249977.1.1,249463.1.1.1] equal(multiply(sk_c7,sk_c4),identity) | $spltprd0($spltcnst40).
% 250045 [para:249977.1.1,249852.1.2.1.1] equal(sk_c4,multiply(inverse(sk_c7),identity)) | $spltprd0($spltcnst40).
% 250445 [para:249901.1.2,249463.1.1] equal(multiply(X,inverse(X)),identity).
% 250469 [para:249901.1.2,249852.1.2] equal(X,multiply(X,identity)).
% 250510 [para:250469.1.2,249852.1.2] equal(X,inverse(inverse(X))).
% 250511 [para:250469.1.2,249900.1.2] equal(sk_c1,inverse(sk_c2)) | $spltprd0($spltcnst38).
% 250526 [para:250045.1.2,250469.1.2] equal(inverse(sk_c7),sk_c4) | $spltprd0($spltcnst40).
% 250548 [para:250511.1.2,249463.1.1.1] equal(multiply(sk_c1,sk_c2),identity) | $spltprd0($spltcnst38).
% 250697 [para:249476.1.1,250445.1.1.2] equal(multiply(sk_c1,sk_c2),identity) | equal(inverse(sk_c4),sk_c7).
% 250705 [para:249924.1.1,250445.1.1.2] equal(multiply(sk_c1,sk_c2),identity) | $spltprd0($spltcnst39).
% 250708 [para:249977.1.1,250445.1.1.2] equal(multiply(sk_c4,sk_c7),identity) | $spltprd0($spltcnst40).
% 256238 [para:250697.1.1,249483.1.1] equal(inverse(sk_c4),sk_c7) | equal(identity,sk_c8).
% 256261 [para:256238.1.1,250445.1.1.2] equal(multiply(sk_c4,sk_c7),identity) | equal(identity,sk_c8).
% 256498 [para:256261.1.1,249477.1.1] equal(inverse(sk_c1),sk_c2) | equal(identity,sk_c8).
% 256500 [para:249484.1.1,256261.2.1] equal(multiply(sk_c1,sk_c2),sk_c8) | equal(identity,sk_c8).
% 256762 [para:256498.1.1,250445.1.1.2] equal(multiply(sk_c1,sk_c2),identity) | equal(identity,sk_c8).
% 257573 [para:250548.1.1,256500.1.1] equal(identity,sk_c8) | $spltprd0($spltcnst38).
% 257575 [para:250705.1.1,256500.1.1] equal(identity,sk_c8) | $spltprd0($spltcnst39).
% 257647 [para:257573.1.2,249495.2.2] $spltprd0($spltcnst38) | -equal(multiply(X,sk_c7),identity) | -equal(inverse(X),sk_c7).
% 257738 [para:257575.1.2,249496.2.2] $spltprd0($spltcnst39) | -equal(multiply(X,sk_c9),identity) | -equal(inverse(X),sk_c9).
% 258643 [para:256762.1.1,256500.1.1] equal(identity,sk_c8).
% 258651 [para:258643.1.2,249487.1.1.2,demod:250469] equal(inverse(sk_c5),sk_c9) | equal(sk_c7,sk_c9).
% 258652 [para:258643.1.2,249490.1.1.2,demod:250469] equal(inverse(sk_c4),sk_c7) | equal(sk_c7,sk_c9).
% 258654 [para:258643.1.2,249488.1.1.2,demod:250469] equal(multiply(sk_c5,sk_c9),sk_c6) | equal(sk_c7,sk_c9).
% 258655 [para:258643.1.2,249489.1.1.2,demod:250469] equal(multiply(sk_c9,sk_c6),sk_c7) | equal(sk_c7,sk_c9).
% 258814 [para:258651.1.1,250445.1.1.2] equal(multiply(sk_c5,sk_c9),identity) | equal(sk_c7,sk_c9).
% 258871 [para:258652.1.1,249852.1.2.1.1,demod:250469] equal(sk_c4,inverse(sk_c7)) | equal(sk_c7,sk_c9).
% 259086 [para:258871.1.2,249852.1.2.1.1,demod:250469] equal(sk_c7,inverse(sk_c4)) | equal(sk_c7,sk_c9).
% 261207 [para:258814.1.1,258654.1.1] equal(identity,sk_c6) | equal(sk_c7,sk_c9).
% 261507 [para:261207.1.2,258655.1.1.2,demod:250469] equal(sk_c9,sk_c7) | equal(sk_c7,sk_c9).
% 262337 [para:261507.1.2,258871.1.2.1] equal(sk_c4,inverse(sk_c9)) | equal(sk_c7,sk_c9).
% 262344 [para:262337.1.2,249852.1.2.1.1,demod:250469] equal(sk_c9,inverse(sk_c4)) | equal(sk_c7,sk_c9).
% 263633 [para:262344.1.2,259086.1.2] equal(sk_c7,sk_c9).
% 263691 [para:263633.1.1,250041.1.1.1] equal(multiply(sk_c9,sk_c4),identity) | $spltprd0($spltcnst40).
% 263750 [para:263633.1.1,250526.1.1.1] equal(inverse(sk_c9),sk_c4) | $spltprd0($spltcnst40).
% 264282 [para:263691.1.1,249497.3.1,cut:258643,binarycut:263750] -equal(multiply(sk_c4,sk_c7),sk_c8) | $spltprd0($spltcnst40).
% 264567 [para:250708.1.1,264282.1.1,cut:258643] $spltprd0($spltcnst40).
% 264568 [binary:249498.3,264567] -$spltprd0($spltcnst38) | -$spltprd0($spltcnst39) | -$spltprd0($spltcnst37).
% 266046 [binary:249463,257647.2,demod:250510,cut:249461] $spltprd0($spltcnst38).
% 266047 [binary:264568,266046] -$spltprd0($spltcnst39) | -$spltprd0($spltcnst37).
% 266050 [binary:249463,257738.2,demod:250510,cut:249461] $spltprd0($spltcnst39).
% 266051 [binary:266047,266050] -$spltprd0($spltcnst37).
% 266297 [para:258643.1.2,249494.1.1.2,demod:250469,cut:263633,cut:266051] -equal(multiply(sk_c9,X),sk_c7) | -equal(multiply(Y,sk_c9),X) | -equal(inverse(Y),sk_c9).
% 266300 [binary:249463,266297.2,demod:250510,250469,cut:249461] -equal(sk_c9,sk_c7).
% 266304 [para:263633.1.1,266300.1.2,cut:249461] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using binary resolution
% using term-depth-order strategy
% not using sos strategy
% using unit paramodulation 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: 15
%
%
% ***GANDALF_FOUND_A_REFUTATION***
%
% Global statistics over all passes:
%
% given clauses: 22647
% derived clauses: 4291073
% kept clauses: 198826
% kept size sum: 518259
% kept mid-nuclei: 35038
% kept new demods: 1143
% forw unit-subs: 1866244
% forw double-subs: 1988899
% forw overdouble-subs: 168159
% backward subs: 13992
% fast unit cutoff: 24872
% full unit cutoff: 0
% dbl unit cutoff: 8094
% real runtime : 257.9
% process. runtime: 255.40
% specific non-discr-tree subsumption statistics:
% tried: 15026579
% length fails: 1499808
% strength fails: 4909977
% predlist fails: 734088
% aux str. fails: 1660987
% by-lit fails: 2760409
% full subs tried: 1710167
% full subs fail: 1606883
%
% ; 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/GRP370-1+eq_r.in")
%
%------------------------------------------------------------------------------