TSTP Solution File: GRP232-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP232-1 : 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 : art06.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 296.9s
% Output : Assurance 296.9s
% 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/GRP232-1+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(inverse(sk_c8),sk_c7) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(Y,Z),sk_c8) | -equal(inverse(Y),Z) | -equal(multiply(Z,sk_c7),sk_c8) | -equal(inverse(U),sk_c8) | -equal(multiply(U,sk_c7),sk_c8) | -equal(multiply(sk_c8,V),sk_c7) | -equal(multiply(W,sk_c8),V) | -equal(inverse(W),sk_c8).
% was split for some strategies as:
% -equal(multiply(sk_c8,V),sk_c7) | -equal(multiply(W,sk_c8),V) | -equal(inverse(W),sk_c8).
% -equal(inverse(U),sk_c8) | -equal(multiply(U,sk_c7),sk_c8).
% -equal(multiply(Y,Z),sk_c8) | -equal(inverse(Y),Z) | -equal(multiply(Z,sk_c7),sk_c8).
% -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8).
% -equal(inverse(sk_c8),sk_c7).
%
% Starting a split proof attempt with 5 components.
%
% Split component 1 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c8),sk_c7) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(Y,Z),sk_c8) | -equal(inverse(Y),Z) | -equal(multiply(Z,sk_c7),sk_c8) | -equal(inverse(U),sk_c8) | -equal(multiply(U,sk_c7),sk_c8) | -equal(multiply(sk_c8,V),sk_c7) | -equal(multiply(W,sk_c8),V) | -equal(inverse(W),sk_c8).
% Split part used next: -equal(multiply(sk_c8,V),sk_c7) | -equal(multiply(W,sk_c8),V) | -equal(inverse(W),sk_c8).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,75,0,0,57051,50,922,57051,40,922,57091,0,922,66177,3,1228,66945,4,1373,67652,5,1523,67653,1,1523,67653,50,1523,67653,40,1523,67693,0,1523,69386,3,1834,69396,4,1984,69561,5,2124,69561,1,2124,69561,50,2124,69561,40,2124,69601,0,2124,97668,3,3626,98415,4,4375,99228,1,5125,99228,50,5126,99228,40,5126,99268,0,5126,121836,3,5878,122326,4,6252,122882,1,6627,122882,50,6627,122882,40,6627,122922,0,6627,140288,3,7402,140961,4,7753,141918,5,8128,141919,5,8128,141920,1,8128,141920,50,8128,141920,40,8128,141960,0,8128,213821,3,12030,214696,4,13979,215427,5,15929,215428,1,15929,215428,50,15932,215428,40,15932,215468,0,15932,276860,3,18483,277476,4,19758,277961,1,21034,277961,50,21036,277961,40,21036,278001,0,21036,310897,3,22538,311908,4,23287,312803,5,24037,312804,1,24037,312804,50,24038,312804,40,24038,312844,0,24038,327349,3,24797,328602,4,25164,329467,5,25539,329467,1,25539,329467,50,25539,329467,40,25539,329507,0,25539,362527,3,26741,363230,4,27340,363580,1,27940,363580,50,27941,363580,40,27941,363620,0,27941,383682,3,28692,384367,4,29067,384792,1,29442,384792,50,29442,384792,40,29442,384792,40,29442,384827,0,29443)
%
%
% START OF PROOF
% 384793 [] equal(X,X).
% 384794 [] equal(multiply(identity,X),X).
% 384795 [] equal(multiply(inverse(X),X),identity).
% 384796 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 384797 [] -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8).
% 384798 [] equal(multiply(sk_c3,sk_c7),sk_c8) | equal(inverse(sk_c5),sk_c8).
% 384799 [] equal(multiply(sk_c3,sk_c7),sk_c8) | equal(multiply(sk_c5,sk_c8),sk_c6).
% 384800 [] equal(multiply(sk_c3,sk_c7),sk_c8) | equal(multiply(sk_c8,sk_c6),sk_c7).
% 384803 [] equal(inverse(sk_c2),sk_c3) | equal(inverse(sk_c5),sk_c8).
% 384804 [] equal(multiply(sk_c5,sk_c8),sk_c6) | equal(inverse(sk_c2),sk_c3).
% 384805 [?] ?
% 384808 [] equal(multiply(sk_c2,sk_c3),sk_c8) | equal(inverse(sk_c5),sk_c8).
% 384809 [] equal(multiply(sk_c2,sk_c3),sk_c8) | equal(multiply(sk_c5,sk_c8),sk_c6).
% 384810 [] equal(multiply(sk_c2,sk_c3),sk_c8) | equal(multiply(sk_c8,sk_c6),sk_c7).
% 384813 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c5),sk_c8).
% 384814 [] equal(multiply(sk_c5,sk_c8),sk_c6) | equal(inverse(sk_c1),sk_c8).
% 384815 [?] ?
% 384818 [] equal(multiply(sk_c1,sk_c8),sk_c7) | equal(inverse(sk_c5),sk_c8).
% 384819 [] equal(multiply(sk_c1,sk_c8),sk_c7) | equal(multiply(sk_c5,sk_c8),sk_c6).
% 384820 [] equal(multiply(sk_c1,sk_c8),sk_c7) | equal(multiply(sk_c8,sk_c6),sk_c7).
% 384823 [] equal(inverse(sk_c8),sk_c7) | equal(inverse(sk_c5),sk_c8).
% 384824 [] equal(multiply(sk_c5,sk_c8),sk_c6) | equal(inverse(sk_c8),sk_c7).
% 384825 [?] ?
% 384882 [hyper:384797,384804,384803,binarycut:384805] equal(inverse(sk_c2),sk_c3).
% 384899 [hyper:384797,384800,384799,384798] equal(multiply(sk_c3,sk_c7),sk_c8).
% 384911 [hyper:384797,384814,384813,binarycut:384815] equal(inverse(sk_c1),sk_c8).
% 384918 [para:384911.1.1,384795.1.1.1] equal(multiply(sk_c8,sk_c1),identity).
% 384943 [hyper:384797,384810,384809,384808] equal(multiply(sk_c2,sk_c3),sk_c8).
% 384947 [hyper:384797,384824,384823,binarycut:384825] equal(inverse(sk_c8),sk_c7).
% 384953 [para:384947.1.1,384795.1.1.1] equal(multiply(sk_c7,sk_c8),identity).
% 384961 [hyper:384797,384820,384819,384818] equal(multiply(sk_c1,sk_c8),sk_c7).
% 384965 [para:384795.1.1,384796.1.1.1,demod:384794] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 384967 [para:384899.1.1,384796.1.1.1] equal(multiply(sk_c8,X),multiply(sk_c3,multiply(sk_c7,X))).
% 384968 [para:384918.1.1,384796.1.1.1,demod:384794] equal(X,multiply(sk_c8,multiply(sk_c1,X))).
% 384970 [para:384953.1.1,384796.1.1.1,demod:384794] equal(X,multiply(sk_c7,multiply(sk_c8,X))).
% 384977 [para:384918.1.1,384965.1.2.2,demod:384947] equal(sk_c1,multiply(sk_c7,identity)).
% 384978 [para:384943.1.1,384965.1.2.2,demod:384882] equal(sk_c3,multiply(sk_c3,sk_c8)).
% 384981 [para:384977.1.2,384796.1.1.1,demod:384794] equal(multiply(sk_c1,X),multiply(sk_c7,X)).
% 384984 [para:384978.1.2,384965.1.2.2,demod:384795] equal(sk_c8,identity).
% 384985 [para:384984.1.1,384918.1.1.1,demod:384794] equal(sk_c1,identity).
% 384986 [para:384984.1.1,384947.1.1.1] equal(inverse(identity),sk_c7).
% 384989 [para:384985.1.1,384911.1.1.1,demod:384986] equal(sk_c7,sk_c8).
% 384994 [para:384989.1.2,384953.1.1.2,demod:384981] equal(multiply(sk_c1,sk_c7),identity).
% 384995 [para:384989.1.2,384961.1.1.2,demod:384994] equal(identity,sk_c7).
% 384996 [para:384989.1.2,384978.1.2.2,demod:384899] equal(sk_c3,sk_c8).
% 385002 [para:384996.1.2,384947.1.1.1] equal(inverse(sk_c3),sk_c7).
% 385005 [para:384996.1.2,384984.1.1] equal(sk_c3,identity).
% 385014 [para:384967.1.2,384965.1.2.2,demod:384970,385002,384981] equal(multiply(sk_c1,X),X).
% 385015 [para:384995.1.2,384967.1.2.2.1,demod:384794] equal(multiply(sk_c8,X),multiply(sk_c3,X)).
% 385016 [para:385005.1.1,384967.1.2.1,demod:384794,385014,384981,385015] equal(multiply(sk_c3,X),X).
% 385023 [hyper:384797,384968,384961,demod:385016,385015,385014,demod:384911,cut:384793] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 3
% seconds given: 6
%
%
% Split component 2 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c8),sk_c7) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(Y,Z),sk_c8) | -equal(inverse(Y),Z) | -equal(multiply(Z,sk_c7),sk_c8) | -equal(inverse(U),sk_c8) | -equal(multiply(U,sk_c7),sk_c8) | -equal(multiply(sk_c8,V),sk_c7) | -equal(multiply(W,sk_c8),V) | -equal(inverse(W),sk_c8).
% Split part used next: -equal(inverse(U),sk_c8) | -equal(multiply(U,sk_c7),sk_c8).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 3
% seconds given: 6
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 4
% seconds given: 6
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 5
% seconds given: 6
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 6
% seconds given: 6
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 7
% seconds given: 6
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 8
% seconds given: 6
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 9
% seconds given: 6
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 10
% seconds given: 6
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 11
% seconds given: 6
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 12
% seconds given: 6
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
% proof attempt stopped: sos exhausted
%
%
% timer checkpoints: c(35,40,0,75,0,0,57051,50,922,57051,40,922,57091,0,922,66177,3,1228,66945,4,1373,67652,5,1523,67653,1,1523,67653,50,1523,67653,40,1523,67693,0,1523,69386,3,1834,69396,4,1984,69561,5,2124,69561,1,2124,69561,50,2124,69561,40,2124,69601,0,2124,97668,3,3626,98415,4,4375,99228,1,5125,99228,50,5126,99228,40,5126,99268,0,5126,121836,3,5878,122326,4,6252,122882,1,6627,122882,50,6627,122882,40,6627,122922,0,6627,140288,3,7402,140961,4,7753,141918,5,8128,141919,5,8128,141920,1,8128,141920,50,8128,141920,40,8128,141960,0,8128,213821,3,12030,214696,4,13979,215427,5,15929,215428,1,15929,215428,50,15932,215428,40,15932,215468,0,15932,276860,3,18483,277476,4,19758,277961,1,21034,277961,50,21036,277961,40,21036,278001,0,21036,310897,3,22538,311908,4,23287,312803,5,24037,312804,1,24037,312804,50,24038,312804,40,24038,312844,0,24038,327349,3,24797,328602,4,25164,329467,5,25539,329467,1,25539,329467,50,25539,329467,40,25539,329507,0,25539,362527,3,26741,363230,4,27340,363580,1,27940,363580,50,27941,363580,40,27941,363620,0,27941,383682,3,28692,384367,4,29067,384792,1,29442,384792,50,29442,384792,40,29442,384792,40,29442,384827,0,29443,385022,50,29443,385022,30,29443,385022,40,29443,385057,0,29443,385189,50,29443,385224,0,29447,385392,50,29449,385427,0,29449,385608,50,29452,385643,0,29452,385831,50,29457,385866,0,29461,386061,50,29469,386096,0,29470,386299,50,29485,386334,0,29490,386546,50,29520,386581,0,29520,386803,50,29584,386838,0,29584,387071,50,29706,387106,0,29706,387351,4,29938)
%
%
% START OF PROOF
% 387076 [?] ?
% 387165 [?] ?
% 387209 [?] ?
% 387211 [?] ?
% 387352 [binary:387165,387076,demod:387211,cut:387209] 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 21
% clause depth limited to 12
% seconds given: 6
%
%
% Split component 3 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c8),sk_c7) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(Y,Z),sk_c8) | -equal(inverse(Y),Z) | -equal(multiply(Z,sk_c7),sk_c8) | -equal(inverse(U),sk_c8) | -equal(multiply(U,sk_c7),sk_c8) | -equal(multiply(sk_c8,V),sk_c7) | -equal(multiply(W,sk_c8),V) | -equal(inverse(W),sk_c8).
% Split part used next: -equal(multiply(Y,Z),sk_c8) | -equal(inverse(Y),Z) | -equal(multiply(Z,sk_c7),sk_c8).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 3
% seconds given: 6
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,75,0,0,57051,50,922,57051,40,922,57091,0,922,66177,3,1228,66945,4,1373,67652,5,1523,67653,1,1523,67653,50,1523,67653,40,1523,67693,0,1523,69386,3,1834,69396,4,1984,69561,5,2124,69561,1,2124,69561,50,2124,69561,40,2124,69601,0,2124,97668,3,3626,98415,4,4375,99228,1,5125,99228,50,5126,99228,40,5126,99268,0,5126,121836,3,5878,122326,4,6252,122882,1,6627,122882,50,6627,122882,40,6627,122922,0,6627,140288,3,7402,140961,4,7753,141918,5,8128,141919,5,8128,141920,1,8128,141920,50,8128,141920,40,8128,141960,0,8128,213821,3,12030,214696,4,13979,215427,5,15929,215428,1,15929,215428,50,15932,215428,40,15932,215468,0,15932,276860,3,18483,277476,4,19758,277961,1,21034,277961,50,21036,277961,40,21036,278001,0,21036,310897,3,22538,311908,4,23287,312803,5,24037,312804,1,24037,312804,50,24038,312804,40,24038,312844,0,24038,327349,3,24797,328602,4,25164,329467,5,25539,329467,1,25539,329467,50,25539,329467,40,25539,329507,0,25539,362527,3,26741,363230,4,27340,363580,1,27940,363580,50,27941,363580,40,27941,363620,0,27941,383682,3,28692,384367,4,29067,384792,1,29442,384792,50,29442,384792,40,29442,384792,40,29442,384827,0,29443,385022,50,29443,385022,30,29443,385022,40,29443,385057,0,29443,385189,50,29443,385224,0,29447,385392,50,29449,385427,0,29449,385608,50,29452,385643,0,29452,385831,50,29457,385866,0,29461,386061,50,29469,386096,0,29470,386299,50,29485,386334,0,29490,386546,50,29520,386581,0,29520,386803,50,29584,386838,0,29584,387071,50,29706,387106,0,29706,387351,4,29938,387351,50,29939,387351,30,29939,387351,40,29939,387386,0,29939)
%
%
% START OF PROOF
% 387352 [] equal(X,X).
% 387353 [] equal(multiply(identity,X),X).
% 387354 [] equal(multiply(inverse(X),X),identity).
% 387355 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 387356 [] -equal(multiply(X,sk_c7),sk_c8) | -equal(multiply(Y,X),sk_c8) | -equal(inverse(Y),X).
% 387357 [?] ?
% 387358 [] equal(multiply(sk_c3,sk_c7),sk_c8) | equal(multiply(sk_c5,sk_c8),sk_c6).
% 387359 [?] ?
% 387360 [] equal(multiply(sk_c3,sk_c7),sk_c8) | equal(multiply(sk_c4,sk_c7),sk_c8).
% 387361 [?] ?
% 387362 [] equal(inverse(sk_c2),sk_c3) | equal(inverse(sk_c5),sk_c8).
% 387363 [] equal(multiply(sk_c5,sk_c8),sk_c6) | equal(inverse(sk_c2),sk_c3).
% 387364 [] equal(multiply(sk_c8,sk_c6),sk_c7) | equal(inverse(sk_c2),sk_c3).
% 387365 [] equal(multiply(sk_c4,sk_c7),sk_c8) | equal(inverse(sk_c2),sk_c3).
% 387366 [] equal(inverse(sk_c2),sk_c3) | equal(inverse(sk_c4),sk_c8).
% 387367 [?] ?
% 387368 [?] ?
% 387369 [?] ?
% 387370 [?] ?
% 387371 [?] ?
% 387391 [hyper:387356,387362,binarycut:387367,binarycut:387357] equal(inverse(sk_c5),sk_c8).
% 387394 [para:387391.1.1,387354.1.1.1] equal(multiply(sk_c8,sk_c5),identity).
% 387398 [hyper:387356,387366,binarycut:387371,binarycut:387361] equal(inverse(sk_c4),sk_c8).
% 387402 [para:387398.1.1,387354.1.1.1] equal(multiply(sk_c8,sk_c4),identity).
% 387411 [hyper:387356,387363,binarycut:387368,binarycut:387358] equal(multiply(sk_c5,sk_c8),sk_c6).
% 387414 [hyper:387356,387364,binarycut:387369,binarycut:387359] equal(multiply(sk_c8,sk_c6),sk_c7).
% 387428 [hyper:387356,387365,binarycut:387370,binarycut:387360] equal(multiply(sk_c4,sk_c7),sk_c8).
% 387435 [para:387354.1.1,387355.1.1.1,demod:387353] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 387436 [para:387394.1.1,387355.1.1.1,demod:387353] equal(X,multiply(sk_c8,multiply(sk_c5,X))).
% 387443 [para:387411.1.1,387436.1.2.2,demod:387414] equal(sk_c8,sk_c7).
% 387446 [para:387443.1.1,387411.1.1.2] equal(multiply(sk_c5,sk_c7),sk_c6).
% 387447 [para:387443.1.1,387414.1.1.1] equal(multiply(sk_c7,sk_c6),sk_c7).
% 387454 [para:387394.1.1,387435.1.2.2] equal(sk_c5,multiply(inverse(sk_c8),identity)).
% 387455 [para:387402.1.1,387435.1.2.2,demod:387454] equal(sk_c4,sk_c5).
% 387457 [para:387428.1.1,387435.1.2.2,demod:387398] equal(sk_c7,multiply(sk_c8,sk_c8)).
% 387461 [para:387455.1.2,387446.1.1.1,demod:387428] equal(sk_c8,sk_c6).
% 387462 [para:387461.1.1,387394.1.1.1] equal(multiply(sk_c6,sk_c5),identity).
% 387471 [para:387447.1.1,387435.1.2.2,demod:387354] equal(sk_c6,identity).
% 387480 [para:387443.1.1,387457.1.2.2] equal(sk_c7,multiply(sk_c8,sk_c7)).
% 387484 [para:387471.1.1,387462.1.1.1,demod:387353] equal(sk_c5,identity).
% 387485 [para:387484.1.1,387391.1.1.1] equal(inverse(identity),sk_c8).
% 387488 [para:387484.1.1,387455.1.2] equal(sk_c4,identity).
% 387497 [para:387488.1.1,387428.1.1.1,demod:387353] equal(sk_c7,sk_c8).
% 387499 [hyper:387356,387485,demod:387480,387353,cut:387352,cut:387497] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 3
% seconds given: 6
%
%
% Split component 4 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c8),sk_c7) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(Y,Z),sk_c8) | -equal(inverse(Y),Z) | -equal(multiply(Z,sk_c7),sk_c8) | -equal(inverse(U),sk_c8) | -equal(multiply(U,sk_c7),sk_c8) | -equal(multiply(sk_c8,V),sk_c7) | -equal(multiply(W,sk_c8),V) | -equal(inverse(W),sk_c8).
% Split part used next: -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 3
% seconds given: 6
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,75,0,0,57051,50,922,57051,40,922,57091,0,922,66177,3,1228,66945,4,1373,67652,5,1523,67653,1,1523,67653,50,1523,67653,40,1523,67693,0,1523,69386,3,1834,69396,4,1984,69561,5,2124,69561,1,2124,69561,50,2124,69561,40,2124,69601,0,2124,97668,3,3626,98415,4,4375,99228,1,5125,99228,50,5126,99228,40,5126,99268,0,5126,121836,3,5878,122326,4,6252,122882,1,6627,122882,50,6627,122882,40,6627,122922,0,6627,140288,3,7402,140961,4,7753,141918,5,8128,141919,5,8128,141920,1,8128,141920,50,8128,141920,40,8128,141960,0,8128,213821,3,12030,214696,4,13979,215427,5,15929,215428,1,15929,215428,50,15932,215428,40,15932,215468,0,15932,276860,3,18483,277476,4,19758,277961,1,21034,277961,50,21036,277961,40,21036,278001,0,21036,310897,3,22538,311908,4,23287,312803,5,24037,312804,1,24037,312804,50,24038,312804,40,24038,312844,0,24038,327349,3,24797,328602,4,25164,329467,5,25539,329467,1,25539,329467,50,25539,329467,40,25539,329507,0,25539,362527,3,26741,363230,4,27340,363580,1,27940,363580,50,27941,363580,40,27941,363620,0,27941,383682,3,28692,384367,4,29067,384792,1,29442,384792,50,29442,384792,40,29442,384792,40,29442,384827,0,29443,385022,50,29443,385022,30,29443,385022,40,29443,385057,0,29443,385189,50,29443,385224,0,29447,385392,50,29449,385427,0,29449,385608,50,29452,385643,0,29452,385831,50,29457,385866,0,29461,386061,50,29469,386096,0,29470,386299,50,29485,386334,0,29490,386546,50,29520,386581,0,29520,386803,50,29584,386838,0,29584,387071,50,29706,387106,0,29706,387351,4,29938,387351,50,29939,387351,30,29939,387351,40,29939,387386,0,29939,387498,50,29939,387498,30,29939,387498,40,29939,387533,0,29943)
%
%
% START OF PROOF
% 387500 [] equal(multiply(identity,X),X).
% 387501 [] equal(multiply(inverse(X),X),identity).
% 387502 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 387503 [] -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8).
% 387519 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c5),sk_c8).
% 387520 [] equal(multiply(sk_c5,sk_c8),sk_c6) | equal(inverse(sk_c1),sk_c8).
% 387521 [] equal(multiply(sk_c8,sk_c6),sk_c7) | equal(inverse(sk_c1),sk_c8).
% 387522 [] equal(multiply(sk_c4,sk_c7),sk_c8) | equal(inverse(sk_c1),sk_c8).
% 387523 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c4),sk_c8).
% 387524 [?] ?
% 387525 [?] ?
% 387526 [?] ?
% 387527 [?] ?
% 387528 [?] ?
% 387541 [hyper:387503,387519,binarycut:387524] equal(inverse(sk_c5),sk_c8).
% 387545 [para:387541.1.1,387501.1.1.1] equal(multiply(sk_c8,sk_c5),identity).
% 387549 [hyper:387503,387523,binarycut:387528] equal(inverse(sk_c4),sk_c8).
% 387554 [para:387549.1.1,387501.1.1.1] equal(multiply(sk_c8,sk_c4),identity).
% 387562 [hyper:387503,387520,binarycut:387525] equal(multiply(sk_c5,sk_c8),sk_c6).
% 387565 [hyper:387503,387521,binarycut:387526] equal(multiply(sk_c8,sk_c6),sk_c7).
% 387568 [hyper:387503,387522,binarycut:387527] equal(multiply(sk_c4,sk_c7),sk_c8).
% 387569 [para:387501.1.1,387502.1.1.1,demod:387500] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 387570 [para:387545.1.1,387502.1.1.1,demod:387500] equal(X,multiply(sk_c8,multiply(sk_c5,X))).
% 387575 [para:387562.1.1,387570.1.2.2,demod:387565] equal(sk_c8,sk_c7).
% 387578 [para:387575.1.1,387562.1.1.2] equal(multiply(sk_c5,sk_c7),sk_c6).
% 387579 [para:387575.1.1,387565.1.1.1] equal(multiply(sk_c7,sk_c6),sk_c7).
% 387584 [para:387545.1.1,387569.1.2.2] equal(sk_c5,multiply(inverse(sk_c8),identity)).
% 387585 [para:387554.1.1,387569.1.2.2,demod:387584] equal(sk_c4,sk_c5).
% 387591 [para:387585.1.2,387578.1.1.1,demod:387568] equal(sk_c8,sk_c6).
% 387592 [para:387591.1.1,387545.1.1.1] equal(multiply(sk_c6,sk_c5),identity).
% 387601 [para:387579.1.1,387569.1.2.2,demod:387501] equal(sk_c6,identity).
% 387612 [para:387601.1.1,387592.1.1.1,demod:387500] equal(sk_c5,identity).
% 387613 [para:387612.1.1,387541.1.1.1] equal(inverse(identity),sk_c8).
% 387627 [hyper:387503,387613,demod:387500,cut:387575] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 3
% seconds given: 6
%
%
% Split component 5 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c8),sk_c7) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(Y,Z),sk_c8) | -equal(inverse(Y),Z) | -equal(multiply(Z,sk_c7),sk_c8) | -equal(inverse(U),sk_c8) | -equal(multiply(U,sk_c7),sk_c8) | -equal(multiply(sk_c8,V),sk_c7) | -equal(multiply(W,sk_c8),V) | -equal(inverse(W),sk_c8).
% Split part used next: -equal(inverse(sk_c8),sk_c7).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 3
% seconds given: 6
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 4
% seconds given: 6
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 5
% seconds given: 6
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 6
% seconds given: 6
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 7
% seconds given: 6
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 8
% seconds given: 6
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 9
% seconds given: 6
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 10
% seconds given: 6
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 11
% seconds given: 6
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 12
% seconds given: 6
%
%
% proof attempt stopped: sos exhausted
%
% using binary resolution
% not using sos 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: 2
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,75,0,0,57051,50,922,57051,40,922,57091,0,922,66177,3,1228,66945,4,1373,67652,5,1523,67653,1,1523,67653,50,1523,67653,40,1523,67693,0,1523,69386,3,1834,69396,4,1984,69561,5,2124,69561,1,2124,69561,50,2124,69561,40,2124,69601,0,2124,97668,3,3626,98415,4,4375,99228,1,5125,99228,50,5126,99228,40,5126,99268,0,5126,121836,3,5878,122326,4,6252,122882,1,6627,122882,50,6627,122882,40,6627,122922,0,6627,140288,3,7402,140961,4,7753,141918,5,8128,141919,5,8128,141920,1,8128,141920,50,8128,141920,40,8128,141960,0,8128,213821,3,12030,214696,4,13979,215427,5,15929,215428,1,15929,215428,50,15932,215428,40,15932,215468,0,15932,276860,3,18483,277476,4,19758,277961,1,21034,277961,50,21036,277961,40,21036,278001,0,21036,310897,3,22538,311908,4,23287,312803,5,24037,312804,1,24037,312804,50,24038,312804,40,24038,312844,0,24038,327349,3,24797,328602,4,25164,329467,5,25539,329467,1,25539,329467,50,25539,329467,40,25539,329507,0,25539,362527,3,26741,363230,4,27340,363580,1,27940,363580,50,27941,363580,40,27941,363620,0,27941,383682,3,28692,384367,4,29067,384792,1,29442,384792,50,29442,384792,40,29442,384792,40,29442,384827,0,29443,385022,50,29443,385022,30,29443,385022,40,29443,385057,0,29443,385189,50,29443,385224,0,29447,385392,50,29449,385427,0,29449,385608,50,29452,385643,0,29452,385831,50,29457,385866,0,29461,386061,50,29469,386096,0,29470,386299,50,29485,386334,0,29490,386546,50,29520,386581,0,29520,386803,50,29584,386838,0,29584,387071,50,29706,387106,0,29706,387351,4,29938,387351,50,29939,387351,30,29939,387351,40,29939,387386,0,29939,387498,50,29939,387498,30,29939,387498,40,29939,387533,0,29943,387626,50,29944,387626,30,29944,387626,40,29944,387661,0,29944,387767,50,29944,387802,0,29944,387949,50,29947,387984,0,29952,388139,50,29955,388174,0,29955,388337,50,29960,388372,0,29964,388541,50,29973,388576,0,29973,388753,50,29988,388788,0,29988,388973,50,30016,389008,0,30021,389203,50,30077,389238,0,30077,389443,50,30191,389478,0,30191,389695,50,30426,389695,40,30426,389730,0,30426)
%
%
% START OF PROOF
% 389697 [] equal(multiply(identity,X),X).
% 389698 [] equal(multiply(inverse(X),X),identity).
% 389699 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 389700 [] -equal(inverse(sk_c8),sk_c7).
% 389726 [?] ?
% 389727 [?] ?
% 389728 [?] ?
% 389729 [?] ?
% 389730 [?] ?
% 389745 [input:389726,cut:389700] equal(inverse(sk_c5),sk_c8).
% 389746 [para:389745.1.1,389698.1.1.1] equal(multiply(sk_c8,sk_c5),identity).
% 389748 [input:389730,cut:389700] equal(inverse(sk_c4),sk_c8).
% 389749 [para:389748.1.1,389698.1.1.1] equal(multiply(sk_c8,sk_c4),identity).
% 389769 [input:389727,cut:389700] equal(multiply(sk_c5,sk_c8),sk_c6).
% 389770 [input:389728,cut:389700] equal(multiply(sk_c8,sk_c6),sk_c7).
% 389772 [input:389729,cut:389700] equal(multiply(sk_c4,sk_c7),sk_c8).
% 389784 [para:389698.1.1,389699.1.1.1,demod:389697] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 389786 [para:389746.1.1,389699.1.1.1,demod:389697] equal(X,multiply(sk_c8,multiply(sk_c5,X))).
% 389789 [para:389749.1.1,389699.1.1.1,demod:389697] equal(X,multiply(sk_c8,multiply(sk_c4,X))).
% 389806 [para:389770.1.1,389699.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c8,multiply(sk_c6,X))).
% 389823 [para:389769.1.1,389786.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c6)).
% 389827 [para:389823.1.2,389770.1.1] equal(sk_c8,sk_c7).
% 389828 [para:389823.1.2,389699.1.1.1,demod:389806] equal(multiply(sk_c8,X),multiply(sk_c7,X)).
% 389829 [para:389827.1.1,389700.1.1.1] -equal(inverse(sk_c7),sk_c7).
% 389856 [para:389772.1.1,389789.1.2.2,demod:389828] equal(sk_c7,multiply(sk_c7,sk_c8)).
% 389909 [para:389856.1.2,389784.1.2.2,demod:389698] equal(sk_c8,identity).
% 389930 [para:389909.1.1,389746.1.1.1,demod:389697] equal(sk_c5,identity).
% 389945 [para:389909.1.1,389827.1.1] equal(identity,sk_c7).
% 389959 [para:389930.1.1,389745.1.1.1] equal(inverse(identity),sk_c8).
% 389975 [para:389945.1.2,389829.1.1.1,demod:389959,cut:389827] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using binary resolution
% not using sos 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: 2
%
%
% Split attempt finished with SUCCESS.
%
% ***GANDALF_FOUND_A_REFUTATION***
%
% Global statistics over all passes:
%
% given clauses: 29654
% derived clauses: 5938231
% kept clauses: 296966
% kept size sum: 327804
% kept mid-nuclei: 51121
% kept new demods: 3584
% forw unit-subs: 1961777
% forw double-subs: 3316653
% forw overdouble-subs: 264252
% backward subs: 9335
% fast unit cutoff: 27700
% full unit cutoff: 0
% dbl unit cutoff: 11114
% real runtime : 307.78
% process. runtime: 304.27
% specific non-discr-tree subsumption statistics:
% tried: 26992939
% length fails: 3178368
% strength fails: 9640012
% predlist fails: 1685434
% aux str. fails: 2769425
% by-lit fails: 3278062
% full subs tried: 2412423
% full subs fail: 2264171
%
% ; 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/GRP232-1+eq_r.in")
%
%------------------------------------------------------------------------------