TSTP Solution File: GRP298-1 by Gandalf---c-2.6
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP298-1 : 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 : art09.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 30.0s
% Output : Assurance 30.0s
% 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/GRP298-1+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 23)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 3 23)
% (binary-posweight-lex-big-order 30 #f 3 23)
% (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_c8,sk_c7),sk_c6) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(sk_c6,sk_c8),sk_c7) | -equal(multiply(Y,sk_c8),sk_c7) | -equal(inverse(Y),sk_c8) | -equal(multiply(sk_c8,sk_c6),sk_c7) | -equal(inverse(Z),sk_c8) | -equal(multiply(Z,sk_c7),sk_c8) | -equal(multiply(U,V),sk_c7) | -equal(inverse(U),V) | -equal(multiply(V,sk_c6),sk_c7).
% was split for some strategies as:
% -equal(multiply(U,V),sk_c7) | -equal(inverse(U),V) | -equal(multiply(V,sk_c6),sk_c7).
% -equal(inverse(Z),sk_c8) | -equal(multiply(Z,sk_c7),sk_c8).
% -equal(multiply(Y,sk_c8),sk_c7) | -equal(inverse(Y),sk_c8).
% -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8).
% -equal(multiply(sk_c8,sk_c7),sk_c6).
% -equal(multiply(sk_c6,sk_c8),sk_c7).
% -equal(multiply(sk_c8,sk_c6),sk_c7).
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(37,40,1,79,0,1,1143,50,11,1185,0,11,2968,50,31,3010,0,31,5124,50,56,5166,0,56,7479,50,78,7521,0,78,10034,50,107,10076,0,107,12853,50,147,12895,0,147,15938,50,210,15980,0,210,19353,50,317,19395,0,317,23099,50,500,23141,0,500,27241,50,771,27241,40,771,27283,0,771,39278,3,1072,39906,4,1222,40553,5,1372,40554,1,1372,40554,50,1372,40554,40,1372,40596,0,1372,40791,3,1674,40801,4,1834,40809,5,1973,40809,1,1973,40809,50,1973,40809,40,1973,40851,0,1973)
%
%
% START OF PROOF
% 40810 [] equal(X,X).
% 40811 [] equal(multiply(identity,X),X).
% 40812 [] equal(multiply(inverse(X),X),identity).
% 40813 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 40815 [] equal(multiply(sk_c6,sk_c8),sk_c7) | equal(multiply(sk_c5,sk_c6),sk_c7).
% 40816 [] equal(multiply(sk_c6,sk_c8),sk_c7) | equal(inverse(sk_c4),sk_c5).
% 40818 [] equal(multiply(sk_c6,sk_c8),sk_c7) | equal(multiply(sk_c3,sk_c7),sk_c8).
% 40819 [] equal(multiply(sk_c6,sk_c8),sk_c7) | equal(inverse(sk_c3),sk_c8).
% 40821 [] equal(multiply(sk_c6,sk_c8),sk_c7) | equal(inverse(sk_c2),sk_c8).
% 40823 [] equal(multiply(sk_c5,sk_c6),sk_c7) | equal(inverse(sk_c1),sk_c8).
% 40824 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c4),sk_c5).
% 40825 [] equal(multiply(sk_c4,sk_c5),sk_c7) | equal(inverse(sk_c1),sk_c8).
% 40826 [] equal(multiply(sk_c3,sk_c7),sk_c8) | equal(inverse(sk_c1),sk_c8).
% 40827 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c3),sk_c8).
% 40828 [] equal(multiply(sk_c8,sk_c6),sk_c7) | equal(inverse(sk_c1),sk_c8).
% 40829 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c2),sk_c8).
% 40830 [] equal(multiply(sk_c2,sk_c8),sk_c7) | equal(inverse(sk_c1),sk_c8).
% 40832 [] equal(multiply(sk_c1,sk_c8),sk_c7) | equal(inverse(sk_c4),sk_c5).
% 40834 [] equal(multiply(sk_c1,sk_c8),sk_c7) | equal(multiply(sk_c3,sk_c7),sk_c8).
% 40835 [] equal(multiply(sk_c1,sk_c8),sk_c7) | equal(inverse(sk_c3),sk_c8).
% 40837 [] equal(multiply(sk_c1,sk_c8),sk_c7) | equal(inverse(sk_c2),sk_c8).
% 40838 [] equal(multiply(sk_c1,sk_c8),sk_c7) | equal(multiply(sk_c2,sk_c8),sk_c7).
% 40840 [] equal(multiply(sk_c8,sk_c7),sk_c6) | equal(inverse(sk_c4),sk_c5).
% 40841 [] equal(multiply(sk_c8,sk_c7),sk_c6) | equal(multiply(sk_c4,sk_c5),sk_c7).
% 40842 [] equal(multiply(sk_c8,sk_c7),sk_c6) | equal(multiply(sk_c3,sk_c7),sk_c8).
% 40843 [] equal(multiply(sk_c8,sk_c7),sk_c6) | equal(inverse(sk_c3),sk_c8).
% 40844 [] equal(multiply(sk_c8,sk_c7),sk_c6) | equal(multiply(sk_c8,sk_c6),sk_c7).
% 40845 [] equal(multiply(sk_c8,sk_c7),sk_c6) | equal(inverse(sk_c2),sk_c8).
% 40847 [] -equal(multiply(sk_c6,sk_c8),sk_c7) | -equal(multiply(sk_c8,sk_c6),sk_c7) | -equal(multiply(sk_c8,sk_c7),sk_c6) | $spltprd0($spltcnst13) | -equal(multiply(X,sk_c6),sk_c7) | -equal(multiply(Y,X),sk_c7) | -equal(inverse(Y),X).
% 40848 [] $spltprd0($spltcnst14) | -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c8).
% 40849 [] $spltprd0($spltcnst15) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8).
% 40850 [] $spltprd0($spltcnst16) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8).
% 40851 [] -$spltprd0($spltcnst14) | -$spltprd0($spltcnst13) | -$spltprd0($spltcnst16) | -$spltprd0($spltcnst15).
% 40854 [input:40847,factor] -equal(multiply(sk_c8,sk_c6),sk_c7) | -equal(multiply(sk_c6,sk_c8),sk_c7) | -equal(multiply(sk_c8,sk_c7),sk_c6) | -equal(inverse(sk_c6),sk_c8) | $spltprd0($spltcnst13).
% 40856 [para:40824.1.1,40812.1.1.1] equal(multiply(sk_c8,sk_c1),identity) | equal(inverse(sk_c4),sk_c5).
% 40857 [para:40824.2.1,40812.1.1.1] equal(multiply(sk_c5,sk_c4),identity) | equal(inverse(sk_c1),sk_c8).
% 40860 [para:40827.2.1,40812.1.1.1] equal(multiply(sk_c8,sk_c3),identity) | equal(inverse(sk_c1),sk_c8).
% 40869 [para:40819.2.1,40812.1.1.1] equal(multiply(sk_c8,sk_c3),identity) | equal(multiply(sk_c6,sk_c8),sk_c7).
% 40871 [para:40821.2.1,40812.1.1.1] equal(multiply(sk_c8,sk_c2),identity) | equal(multiply(sk_c6,sk_c8),sk_c7).
% 40894 [para:40843.2.1,40812.1.1.1] equal(multiply(sk_c8,sk_c3),identity) | equal(multiply(sk_c8,sk_c7),sk_c6).
% 40951 [para:40826.1.1,40848.2.1,cut:40810] -equal(inverse(sk_c3),sk_c8) | equal(inverse(sk_c1),sk_c8) | $spltprd0($spltcnst14).
% 40954 [para:40818.2.1,40848.2.1,cut:40810] equal(multiply(sk_c6,sk_c8),sk_c7) | -equal(inverse(sk_c3),sk_c8) | $spltprd0($spltcnst14).
% 40956 [para:40834.2.1,40848.2.1,cut:40810] equal(multiply(sk_c1,sk_c8),sk_c7) | -equal(inverse(sk_c3),sk_c8) | $spltprd0($spltcnst14).
% 40960 [para:40842.2.1,40848.2.1,cut:40810] equal(multiply(sk_c8,sk_c7),sk_c6) | -equal(inverse(sk_c3),sk_c8) | $spltprd0($spltcnst14).
% 40967 [para:40827.2.1,40951.1.1,cut:40810] equal(inverse(sk_c1),sk_c8) | $spltprd0($spltcnst14).
% 40969 [para:40967.1.1,40812.1.1.1] equal(multiply(sk_c8,sk_c1),identity) | $spltprd0($spltcnst14).
% 40987 [para:40837.1.1,40849.2.1,cut:40810,binarycut:40829] equal(inverse(sk_c2),sk_c8) | $spltprd0($spltcnst15).
% 40999 [para:40838.2.1,40849.2.1,cut:40810,binarycut:40987] equal(multiply(sk_c1,sk_c8),sk_c7) | $spltprd0($spltcnst15).
% 41033 [para:40837.1.1,40850.2.1,cut:40810,binarycut:40829] equal(inverse(sk_c2),sk_c8) | $spltprd0($spltcnst16).
% 41045 [para:40838.2.1,40850.2.1,cut:40810,binarycut:41033] equal(multiply(sk_c1,sk_c8),sk_c7) | $spltprd0($spltcnst16).
% 41061 [para:40999.1.1,40849.2.1,cut:40810] -equal(inverse(sk_c1),sk_c8) | $spltprd0($spltcnst15).
% 41067 [para:40830.2.1,41061.1.1,cut:40810] equal(multiply(sk_c2,sk_c8),sk_c7) | $spltprd0($spltcnst15).
% 41069 [para:40812.1.1,40813.1.1.1,demod:40811] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 41090 [para:40856.1.1,40813.1.1.1,demod:40811] equal(inverse(sk_c4),sk_c5) | equal(X,multiply(sk_c8,multiply(sk_c1,X))).
% 41139 [para:40969.1.1,40813.1.1.1,demod:40811] $spltprd0($spltcnst14) | equal(X,multiply(sk_c8,multiply(sk_c1,X))).
% 41178 [para:41045.1.1,40850.2.1,cut:40810] -equal(inverse(sk_c1),sk_c8) | $spltprd0($spltcnst16).
% 41189 [para:40830.2.1,41178.1.1,cut:40810] equal(multiply(sk_c2,sk_c8),sk_c7) | $spltprd0($spltcnst16).
% 41216 [para:41067.1.1,40849.2.1,cut:40810,binarycut:40987] $spltprd0($spltcnst15).
% 41230 [para:41189.1.1,40850.2.1,cut:40810,binarycut:41033] $spltprd0($spltcnst16).
% 41232 [para:40816.1.1,41069.1.2.2] equal(sk_c8,multiply(inverse(sk_c6),sk_c7)) | equal(inverse(sk_c4),sk_c5).
% 41236 [para:40815.2.1,41069.1.2.2] equal(sk_c6,multiply(inverse(sk_c5),sk_c7)) | equal(multiply(sk_c6,sk_c8),sk_c7).
% 41237 [para:40823.1.1,41069.1.2.2] equal(sk_c6,multiply(inverse(sk_c5),sk_c7)) | equal(inverse(sk_c1),sk_c8).
% 41238 [para:40825.1.1,41069.1.2.2] equal(sk_c5,multiply(inverse(sk_c4),sk_c7)) | equal(inverse(sk_c1),sk_c8).
% 41239 [para:40826.1.1,41069.1.2.2] equal(sk_c7,multiply(inverse(sk_c3),sk_c8)) | equal(inverse(sk_c1),sk_c8).
% 41240 [para:40828.1.1,41069.1.2.2] equal(sk_c6,multiply(inverse(sk_c8),sk_c7)) | equal(inverse(sk_c1),sk_c8).
% 41244 [para:40832.1.1,41069.1.2.2] equal(sk_c8,multiply(inverse(sk_c1),sk_c7)) | equal(inverse(sk_c4),sk_c5).
% 41245 [para:40835.1.1,41069.1.2.2] equal(sk_c8,multiply(inverse(sk_c1),sk_c7)) | equal(inverse(sk_c3),sk_c8).
% 41246 [para:40837.1.1,41069.1.2.2] equal(sk_c8,multiply(inverse(sk_c1),sk_c7)) | equal(inverse(sk_c2),sk_c8).
% 41251 [para:40818.1.1,41069.1.2.2] equal(sk_c8,multiply(inverse(sk_c6),sk_c7)) | equal(multiply(sk_c3,sk_c7),sk_c8).
% 41257 [para:40857.1.1,41069.1.2.2] equal(sk_c4,multiply(inverse(sk_c5),identity)) | equal(inverse(sk_c1),sk_c8).
% 41261 [para:40860.1.1,41069.1.2.2] equal(sk_c3,multiply(inverse(sk_c8),identity)) | equal(inverse(sk_c1),sk_c8).
% 41293 [para:40869.1.1,41069.1.2.2] equal(sk_c3,multiply(inverse(sk_c8),identity)) | equal(multiply(sk_c6,sk_c8),sk_c7).
% 41295 [para:40871.1.1,41069.1.2.2] equal(sk_c2,multiply(inverse(sk_c8),identity)) | equal(multiply(sk_c6,sk_c8),sk_c7).
% 41309 [para:40969.1.1,41069.1.2.2] equal(sk_c1,multiply(inverse(sk_c8),identity)) | $spltprd0($spltcnst14).
% 41322 [para:41309.1.2,40813.1.1.1,demod:40811] $spltprd0($spltcnst14) | equal(multiply(sk_c1,X),multiply(inverse(sk_c8),X)).
% 41342 [para:40894.1.1,41069.1.2.2] equal(sk_c3,multiply(inverse(sk_c8),identity)) | equal(multiply(sk_c8,sk_c7),sk_c6).
% 41355 [para:41322.2.2,40812.1.1] equal(multiply(sk_c1,sk_c8),identity) | $spltprd0($spltcnst14).
% 41558 [para:40824.2.1,41238.1.2.1] equal(sk_c5,multiply(sk_c5,sk_c7)) | equal(inverse(sk_c1),sk_c8).
% 41566 [para:41558.1.2,41069.1.2.2,demod:40812] equal(inverse(sk_c1),sk_c8) | equal(sk_c7,identity).
% 41569 [para:41566.1.1,40812.1.1.1] equal(multiply(sk_c8,sk_c1),identity) | equal(sk_c7,identity).
% 41570 [para:41566.2.1,40826.1.1.2] equal(multiply(sk_c3,identity),sk_c8) | equal(inverse(sk_c1),sk_c8).
% 41579 [para:41566.2.1,41237.1.2.2] equal(sk_c6,multiply(inverse(sk_c5),identity)) | equal(inverse(sk_c1),sk_c8).
% 41590 [para:41569.1.1,41069.1.2.2] equal(sk_c1,multiply(inverse(sk_c8),identity)) | equal(sk_c7,identity).
% 41594 [para:41570.1.1,41069.1.2.2] equal(identity,multiply(inverse(sk_c3),sk_c8)) | equal(inverse(sk_c1),sk_c8).
% 41636 [para:40827.2.1,41239.1.2.1] equal(sk_c7,multiply(sk_c8,sk_c8)) | equal(inverse(sk_c1),sk_c8).
% 41642 [para:41636.1.2,41069.1.2.2] equal(sk_c8,multiply(inverse(sk_c8),sk_c7)) | equal(inverse(sk_c1),sk_c8).
% 41648 [para:41566.2.1,41240.1.2.2] equal(sk_c6,multiply(inverse(sk_c8),identity)) | equal(inverse(sk_c1),sk_c8).
% 41665 [para:40824.1.1,41244.1.2.1] equal(sk_c8,multiply(sk_c8,sk_c7)) | equal(inverse(sk_c4),sk_c5).
% 41672 [para:41665.1.2,40840.1.1] equal(inverse(sk_c4),sk_c5) | equal(sk_c8,sk_c6).
% 41675 [para:41665.1.2,41069.1.2.2,demod:40812] equal(inverse(sk_c4),sk_c5) | equal(sk_c7,identity).
% 41685 [para:41672.2.1,40816.1.1.2] equal(multiply(sk_c6,sk_c6),sk_c7) | equal(inverse(sk_c4),sk_c5).
% 41686 [para:41672.2.1,40832.1.1.2] equal(multiply(sk_c1,sk_c6),sk_c7) | equal(inverse(sk_c4),sk_c5).
% 41688 [para:41672.2.1,40856.1.1.1] equal(multiply(sk_c6,sk_c1),identity) | equal(inverse(sk_c4),sk_c5).
% 41719 [para:41675.2.1,41232.1.2.2] equal(sk_c8,multiply(inverse(sk_c6),identity)) | equal(inverse(sk_c4),sk_c5).
% 41808 [para:40819.2.1,40954.2.1,cut:40810] equal(multiply(sk_c6,sk_c8),sk_c7) | $spltprd0($spltcnst14).
% 41813 [para:41808.1.1,41069.1.2.2] equal(sk_c8,multiply(inverse(sk_c6),sk_c7)) | $spltprd0($spltcnst14).
% 41845 [para:41688.1.1,41069.1.2.2] equal(sk_c1,multiply(inverse(sk_c6),identity)) | equal(inverse(sk_c4),sk_c5).
% 41855 [para:40835.2.1,40956.2.1,cut:40810] equal(multiply(sk_c1,sk_c8),sk_c7) | $spltprd0($spltcnst14).
% 41860 [para:41855.1.1,41139.2.2.2] equal(sk_c8,multiply(sk_c8,sk_c7)) | $spltprd0($spltcnst14).
% 41861 [para:41855.1.1,41355.1.1] equal(sk_c7,identity) | $spltprd0($spltcnst14).
% 41882 [para:41861.1.1,41813.1.2.2] equal(sk_c8,multiply(inverse(sk_c6),identity)) | $spltprd0($spltcnst14).
% 41900 [para:41860.1.2,40848.2.1,cut:40810] -equal(inverse(sk_c8),sk_c8) | $spltprd0($spltcnst14).
% 41949 [para:40843.2.1,40960.2.1,cut:40810] equal(multiply(sk_c8,sk_c7),sk_c6) | $spltprd0($spltcnst14).
% 41957 [para:41949.1.1,41860.1.2] equal(sk_c8,sk_c6) | $spltprd0($spltcnst14).
% 41990 [para:41957.1.1,41309.1.2.1.1] equal(sk_c1,multiply(inverse(sk_c6),identity)) | $spltprd0($spltcnst14).
% 42142 [para:41990.1.2,41882.1.2] equal(sk_c8,sk_c1) | $spltprd0($spltcnst14).
% 42225 [para:42142.1.1,41900.1.1.1,binarycut:40967] $spltprd0($spltcnst14).
% 42226 [binary:40851,42225,cut:41230,cut:41216] -$spltprd0($spltcnst13).
% 42362 [para:40827.1.1,41245.1.2.1] equal(sk_c8,multiply(sk_c8,sk_c7)) | equal(inverse(sk_c3),sk_c8).
% 42370 [para:42362.1.2,40843.1.1] equal(inverse(sk_c3),sk_c8) | equal(sk_c8,sk_c6).
% 42372 [para:42362.1.2,41069.1.2.2,demod:40812] equal(inverse(sk_c3),sk_c8) | equal(sk_c7,identity).
% 42383 [para:42370.2.1,40819.1.1.2] equal(multiply(sk_c6,sk_c6),sk_c7) | equal(inverse(sk_c3),sk_c8).
% 42390 [para:42370.2.1,40854.1.1.1,cut:42226,binarycut:40843,binarycut:40819,binarycut:42383] -equal(inverse(sk_c6),sk_c8) | equal(inverse(sk_c3),sk_c8).
% 42391 [para:42370.1.1,41069.1.2.1] equal(sk_c8,sk_c6) | equal(X,multiply(sk_c8,multiply(sk_c3,X))).
% 42402 [para:42370.2.1,42362.1.2.1] equal(sk_c8,multiply(sk_c6,sk_c7)) | equal(inverse(sk_c3),sk_c8).
% 42506 [para:42372.2.1,42402.1.2.2] equal(sk_c8,multiply(sk_c6,identity)) | equal(inverse(sk_c3),sk_c8).
% 42688 [para:40829.1.1,41246.1.2.1] equal(sk_c8,multiply(sk_c8,sk_c7)) | equal(inverse(sk_c2),sk_c8).
% 42702 [para:42688.1.2,40845.1.1] equal(inverse(sk_c2),sk_c8) | equal(sk_c8,sk_c6).
% 42704 [para:42688.1.2,41069.1.2.2,demod:40812] equal(inverse(sk_c2),sk_c8) | equal(sk_c7,identity).
% 42713 [para:42702.1.1,40812.1.1.1] equal(multiply(sk_c8,sk_c2),identity) | equal(sk_c8,sk_c6).
% 42727 [para:42702.1.1,41069.1.2.1] equal(sk_c8,sk_c6) | equal(X,multiply(sk_c8,multiply(sk_c2,X))).
% 42738 [para:42704.1.1,40812.1.1.1] equal(multiply(sk_c8,sk_c2),identity) | equal(sk_c7,identity).
% 42789 [para:42713.1.1,41069.1.2.2] equal(sk_c2,multiply(inverse(sk_c8),identity)) | equal(sk_c8,sk_c6).
% 42808 [para:42738.1.1,41069.1.2.2] equal(sk_c2,multiply(inverse(sk_c8),identity)) | equal(sk_c7,identity).
% 43108 [para:42808.1.2,41590.1.2] equal(sk_c1,sk_c2) | equal(sk_c7,identity).
% 43120 [para:43108.1.1,40838.1.1.1] equal(multiply(sk_c2,sk_c8),sk_c7) | equal(sk_c7,identity).
% 43211 [para:43120.1.1,41069.1.2.2] equal(sk_c8,multiply(inverse(sk_c2),sk_c7)) | equal(sk_c7,identity).
% 43250 [para:42688.2.1,43211.1.2.1] equal(sk_c8,multiply(sk_c8,sk_c7)) | equal(sk_c7,identity).
% 43277 [para:43250.1.2,41069.1.2.2,demod:40812] equal(sk_c7,identity).
% 43514 [para:41579.1.2,41257.1.2] equal(inverse(sk_c1),sk_c8) | equal(sk_c4,sk_c6).
% 43515 [para:41257.1.2,41579.1.2] equal(inverse(sk_c1),sk_c8) | equal(sk_c6,sk_c4).
% 43518 [para:40824.2.1,43514.2.1.1] equal(inverse(sk_c6),sk_c5) | equal(inverse(sk_c1),sk_c8).
% 43528 [para:43515.1.1,40812.1.1.1] equal(multiply(sk_c8,sk_c1),identity) | equal(sk_c6,sk_c4).
% 43549 [para:43528.1.1,41069.1.2.2] equal(sk_c1,multiply(inverse(sk_c8),identity)) | equal(sk_c6,sk_c4).
% 44723 [para:40827.2.1,41594.1.2.1] equal(identity,multiply(sk_c8,sk_c8)) | equal(inverse(sk_c1),sk_c8).
% 44753 [para:41240.1.2,41642.1.2] equal(inverse(sk_c1),sk_c8) | equal(sk_c8,sk_c6).
% 44782 [para:44753.1.1,40812.1.1.1] equal(multiply(sk_c8,sk_c1),identity) | equal(sk_c8,sk_c6).
% 44821 [para:44782.1.1,41069.1.2.2] equal(sk_c1,multiply(inverse(sk_c8),identity)) | equal(sk_c8,sk_c6).
% 45007 [para:44821.1.2,42789.1.2] equal(sk_c2,sk_c1) | equal(sk_c8,sk_c6).
% 45183 [para:45007.1.2,40838.1.1.1] equal(multiply(sk_c2,sk_c8),sk_c7) | equal(sk_c8,sk_c6).
% 45349 [para:42727.1.1,45183.2.2.2] equal(sk_c8,multiply(sk_c8,sk_c7)) | equal(sk_c8,sk_c6).
% 45381 [para:45349.1.2,40842.1.1] equal(multiply(sk_c3,sk_c7),sk_c8) | equal(sk_c8,sk_c6).
% 45383 [para:45349.1.2,40844.1.1] equal(multiply(sk_c8,sk_c6),sk_c7) | equal(sk_c8,sk_c6).
% 45469 [para:41686.1.1,41090.2.2.2] equal(sk_c6,multiply(sk_c8,sk_c7)) | equal(inverse(sk_c4),sk_c5).
% 45515 [para:42391.1.1,45381.2.2.2] equal(sk_c7,multiply(sk_c8,sk_c8)) | equal(sk_c8,sk_c6).
% 45541 [para:45383.1.1,41069.1.2.2] equal(sk_c6,multiply(inverse(sk_c8),sk_c7)) | equal(sk_c8,sk_c6).
% 45660 [para:45515.1.2,41069.1.2.2] equal(sk_c8,multiply(inverse(sk_c8),sk_c7)) | equal(sk_c8,sk_c6).
% 46137 [para:41665.1.2,45469.1.2] equal(inverse(sk_c4),sk_c5) | equal(sk_c6,sk_c8).
% 46145 [para:46137.2.2,40854.1.1.1,cut:42226,binarycut:40840,binarycut:40816,binarycut:41685] -equal(inverse(sk_c6),sk_c8) | equal(inverse(sk_c4),sk_c5).
% 46343 [para:45541.1.2,45660.1.2] equal(sk_c8,sk_c6).
% 46375 [para:46343.1.1,43549.1.2.1.1] equal(sk_c1,multiply(inverse(sk_c6),identity)) | equal(sk_c6,sk_c4).
% 47215 [para:41648.1.2,41261.1.2] equal(inverse(sk_c1),sk_c8) | equal(sk_c3,sk_c6).
% 47221 [para:40827.2.1,47215.2.1.1] equal(inverse(sk_c6),sk_c8) | equal(inverse(sk_c1),sk_c8).
% 47246 [para:47221.1.1,43518.1.1] equal(inverse(sk_c1),sk_c8) | equal(sk_c8,sk_c5).
% 47247 [para:43518.1.1,47221.1.1] equal(inverse(sk_c1),sk_c8) | equal(sk_c5,sk_c8).
% 47249 [para:47246.1.1,40812.1.1.1] equal(multiply(sk_c8,sk_c1),identity) | equal(sk_c8,sk_c5).
% 47263 [para:47246.2.1,44723.1.2.1] equal(identity,multiply(sk_c5,sk_c8)) | equal(inverse(sk_c1),sk_c8).
% 47277 [para:47247.1.1,40812.1.1.1] equal(multiply(sk_c8,sk_c1),identity) | equal(sk_c5,sk_c8).
% 47363 [para:46343.1.1,47249.1.1.1] equal(multiply(sk_c6,sk_c1),identity) | equal(sk_c8,sk_c5).
% 47371 [para:46343.1.1,47277.1.1.1] equal(multiply(sk_c6,sk_c1),identity) | equal(sk_c5,sk_c8).
% 47484 [para:47363.1.1,41069.1.2.2] equal(sk_c1,multiply(inverse(sk_c6),identity)) | equal(sk_c8,sk_c5).
% 47524 [para:47371.1.1,41069.1.2.2] equal(sk_c1,multiply(inverse(sk_c6),identity)) | equal(sk_c5,sk_c8).
% 48509 [para:41845.1.2,41719.1.2] equal(inverse(sk_c4),sk_c5) | equal(sk_c8,sk_c1).
% 48540 [para:48509.2.1,46343.1.1] equal(inverse(sk_c4),sk_c5) | equal(sk_c1,sk_c6).
% 48549 [para:48540.2.1,40824.1.1.1,binarycut:46145] equal(inverse(sk_c4),sk_c5).
% 48551 [para:48549.1.1,40812.1.1.1] equal(multiply(sk_c5,sk_c4),identity).
% 48552 [para:48549.1.1,41069.1.2.1] equal(X,multiply(sk_c5,multiply(sk_c4,X))).
% 48553 [para:48551.1.1,41069.1.2.2] equal(sk_c4,multiply(inverse(sk_c5),identity)).
% 48560 [para:48553.1.2,40813.1.1.1,demod:40811] equal(multiply(sk_c4,X),multiply(inverse(sk_c5),X)).
% 48585 [para:48560.1.2,40812.1.1] equal(multiply(sk_c4,sk_c5),identity).
% 48586 [para:48560.1.2,41069.1.2] equal(X,multiply(sk_c4,multiply(sk_c5,X))).
% 48600 [para:48560.1.2,48553.1.2] equal(sk_c4,multiply(sk_c4,identity)).
% 48603 [para:40841.1.1,48585.2.1] equal(multiply(sk_c8,sk_c7),sk_c6) | equal(identity,sk_c7).
% 48604 [para:48585.1.1,41069.1.2.2,demod:48549] equal(sk_c5,multiply(sk_c5,identity)).
% 48679 [para:47263.1.2,48586.1.2.2,demod:48600] equal(inverse(sk_c1),sk_c8) | equal(sk_c8,sk_c4).
% 48729 [para:47246.2.1,48679.2.1] equal(inverse(sk_c1),sk_c8) | equal(sk_c4,sk_c5).
% 48808 [para:48729.1.1,40812.1.1.1] equal(multiply(sk_c8,sk_c1),identity) | equal(sk_c4,sk_c5).
% 48854 [para:48603.1.1,41069.1.2.2] equal(sk_c7,multiply(inverse(sk_c8),sk_c6)) | equal(identity,sk_c7).
% 48855 [para:43277.1.1,48603.1.1.2] equal(multiply(sk_c8,identity),sk_c6) | equal(identity,sk_c7).
% 48997 [para:46343.1.1,48808.1.1.1] equal(multiply(sk_c6,sk_c1),identity) | equal(sk_c4,sk_c5).
% 49055 [para:48855.1.1,41069.1.2.2] equal(identity,multiply(inverse(sk_c8),sk_c6)) | equal(identity,sk_c7).
% 49224 [para:48997.1.1,41069.1.2.2] equal(sk_c1,multiply(inverse(sk_c6),identity)) | equal(sk_c4,sk_c5).
% 49636 [para:43277.1.1,41236.1.2.2,demod:48553] equal(multiply(sk_c6,sk_c8),sk_c7) | equal(sk_c6,sk_c4).
% 49665 [para:49636.1.1,41069.1.2.2] equal(sk_c8,multiply(inverse(sk_c6),sk_c7)) | equal(sk_c6,sk_c4).
% 50076 [para:48854.1.2,49055.1.2] equal(identity,sk_c7).
% 51251 [para:43277.1.1,49665.1.2.2] equal(sk_c8,multiply(inverse(sk_c6),identity)) | equal(sk_c6,sk_c4).
% 52523 [para:41295.1.2,41293.1.2] equal(multiply(sk_c6,sk_c8),sk_c7) | equal(sk_c3,sk_c2).
% 52864 [para:51251.1.2,46375.1.2] equal(sk_c1,sk_c8) | equal(sk_c6,sk_c4).
% 52917 [?] ?
% 52966 [para:52864.1.2,46343.1.1] equal(sk_c1,sk_c6) | equal(sk_c6,sk_c4).
% 53089 [para:41579.1.1,52966.2.1.1,demod:48553,binarycut:52917] equal(sk_c6,sk_c4).
% 53102 [para:53089.1.2,48549.1.1.1] equal(inverse(sk_c6),sk_c5).
% 53103 [para:53089.1.2,48551.1.1.2] equal(multiply(sk_c5,sk_c6),identity).
% 53104 [para:53089.1.2,48552.1.2.2.1] equal(X,multiply(sk_c5,multiply(sk_c6,X))).
% 53106 [para:53089.1.2,48600.1.2.1] equal(sk_c4,multiply(sk_c6,identity)).
% 53127 [para:53102.1.1,47484.1.2.1,demod:48604] equal(sk_c1,sk_c5) | equal(sk_c8,sk_c5).
% 53128 [para:53102.1.1,47524.1.2.1,demod:48604] equal(sk_c1,sk_c5) | equal(sk_c5,sk_c8).
% 53139 [para:53102.1.1,49224.1.2.1,demod:48604] equal(sk_c1,sk_c5) | equal(sk_c4,sk_c5).
% 53194 [para:53106.1.2,40813.1.1.1,demod:40811] equal(multiply(sk_c4,X),multiply(sk_c6,X)).
% 53196 [para:53106.1.2,42506.1.2] equal(inverse(sk_c3),sk_c8) | equal(sk_c8,sk_c4).
% 53871 [para:53127.2.1,42390.1.2,demod:53102,cut:40810] equal(inverse(sk_c3),sk_c8) | equal(sk_c1,sk_c5).
% 54060 [para:47221.1.1,53128.2.1.1,demod:53102] equal(inverse(sk_c5),sk_c8) | equal(sk_c5,sk_c8).
% 55142 [para:53139.1.1,48729.1.1.1] equal(inverse(sk_c5),sk_c8) | equal(sk_c4,sk_c5).
% 56862 [para:52523.1.1,53104.1.2.2] equal(sk_c8,multiply(sk_c5,sk_c7)) | equal(sk_c3,sk_c2).
% 57042 [para:53196.1.1,40812.1.1.1] equal(multiply(sk_c8,sk_c3),identity) | equal(sk_c8,sk_c4).
% 57279 [para:53871.2.1,40827.1.1.1] equal(inverse(sk_c5),sk_c8) | equal(inverse(sk_c3),sk_c8).
% 57801 [para:55142.1.1,48553.1.2.1] equal(sk_c4,multiply(sk_c8,identity)) | equal(sk_c4,sk_c5).
% 58614 [para:46343.1.1,41342.1.2.1.1,demod:48604,53102] equal(multiply(sk_c8,sk_c7),sk_c6) | equal(sk_c3,sk_c5).
% 59636 [?] ?
% 60024 [para:43277.1.1,56862.1.2.2,demod:48604] equal(sk_c8,sk_c5) | equal(sk_c3,sk_c2).
% 60054 [para:60024.1.1,40854.1.1.1,demod:53102,53103,cut:50076,cut:42226,binarycut:59636,binarycut:52523] -equal(sk_c5,sk_c8) | equal(sk_c3,sk_c2).
% 60072 [?] ?
% 60135 [para:46343.1.1,60054.1.2,binarycut:60072] equal(sk_c3,sk_c2).
% 60323 [para:46343.1.1,57042.1.1.1] equal(multiply(sk_c6,sk_c3),identity) | equal(sk_c8,sk_c4).
% 62851 [para:60323.1.1,41069.1.2.2,demod:48604,53102] equal(sk_c3,sk_c5) | equal(sk_c8,sk_c4).
% 62961 [para:62851.2.1,41293.1.2.1.1,demod:48604,48549] equal(multiply(sk_c6,sk_c8),sk_c7) | equal(sk_c3,sk_c5).
% 64457 [para:62961.1.1,41069.1.2.2,demod:53102] equal(sk_c8,multiply(sk_c5,sk_c7)) | equal(sk_c3,sk_c5).
% 66993 [para:43277.1.1,64457.1.2.2,demod:48604] equal(sk_c8,sk_c5) | equal(sk_c3,sk_c5).
% 67028 [para:66993.1.1,40854.1.1.1,demod:53102,53103,cut:50076,cut:42226,binarycut:58614,binarycut:62961] -equal(sk_c5,sk_c8) | equal(sk_c3,sk_c5).
% 67044 [?] ?
% 67160 [para:46343.1.1,67028.1.2,binarycut:67044] equal(sk_c3,sk_c5).
% 67168 [para:67160.1.2,48551.1.1.1] equal(multiply(sk_c3,sk_c4),identity).
% 67173 [para:67160.1.2,48604.1.2.1] equal(sk_c5,multiply(sk_c3,identity)).
% 67204 [para:67160.1.2,57279.1.1.1] equal(inverse(sk_c3),sk_c8).
% 67234 [para:60135.1.1,67204.1.1.1] equal(inverse(sk_c2),sk_c8).
% 67237 [para:67168.1.1,41069.1.2.2,demod:67204] equal(sk_c4,multiply(sk_c8,identity)).
% 67250 [para:67173.1.2,40813.1.1.1,demod:40811] equal(multiply(sk_c5,X),multiply(sk_c3,X)).
% 67252 [para:60135.1.1,67173.1.2.1] equal(sk_c5,multiply(sk_c2,identity)).
% 67280 [para:67237.1.2,40813.1.1.1,demod:40811,53194] equal(multiply(sk_c6,X),multiply(sk_c8,X)).
% 67345 [para:67252.1.2,40813.1.1.1,demod:40811,67250] equal(multiply(sk_c3,X),multiply(sk_c2,X)).
% 68024 [para:41251.2.1,67345.1.1,demod:67345,67250,53102] equal(sk_c8,multiply(sk_c2,sk_c7)).
% 68026 [para:68024.1.2,41069.1.2.2,demod:67280,67234] equal(sk_c7,multiply(sk_c6,sk_c8)).
% 68027 [para:43277.1.1,68024.1.2.2,demod:67252] equal(sk_c8,sk_c5).
% 68049 [para:68027.1.1,46343.1.1] equal(sk_c5,sk_c6).
% 68145 [para:68027.1.1,57801.1.2.1,demod:48604] equal(sk_c4,sk_c5).
% 68161 [para:68049.1.1,54060.1.1.1,demod:53102] equal(sk_c5,sk_c8).
% 68169 [para:68145.1.2,68049.1.1] equal(sk_c4,sk_c6).
% 68176 [para:68161.1.2,40854.1.1.1,demod:53102,67280,68026,53103,cut:50076,cut:40810,cut:68161,cut:42226] -equal(multiply(sk_c6,sk_c7),sk_c6).
% 68181 [para:43277.1.1,68176.1.1.2,demod:53106,cut:68169] 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 23
% clause depth limited to 3
% seconds given: 30
%
%
% ***GANDALF_FOUND_A_REFUTATION***
%
% Global statistics over all passes:
%
% given clauses: 5903
% derived clauses: 637650
% kept clauses: 36505
% kept size sum: 541052
% kept mid-nuclei: 15360
% kept new demods: 763
% forw unit-subs: 303129
% forw double-subs: 257220
% forw overdouble-subs: 12238
% backward subs: 1520
% fast unit cutoff: 2244
% full unit cutoff: 0
% dbl unit cutoff: 10299
% real runtime : 31.19
% process. runtime: 31.15
% specific non-discr-tree subsumption statistics:
% tried: 568333
% length fails: 51306
% strength fails: 95621
% predlist fails: 5995
% aux str. fails: 115390
% by-lit fails: 56636
% full subs tried: 37948
% full subs fail: 30796
%
% ; 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/GRP298-1+eq_r.in")
%
%------------------------------------------------------------------------------