TSTP Solution File: GRP357-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP357-1 : 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 : art07.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 297.9s
% Output : Assurance 297.9s
% 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/GRP357-1+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_c6),sk_c8) | -equal(inverse(sk_c8),sk_c6) | -equal(multiply(X,Y),sk_c8) | -equal(inverse(X),Y) | -equal(multiply(Y,sk_c7),sk_c8) | -equal(multiply(sk_c8,sk_c7),sk_c6) | -equal(multiply(Z,sk_c8),sk_c7) | -equal(inverse(Z),sk_c8) | -equal(multiply(sk_c8,U),sk_c7) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% was split for some strategies as:
% -equal(multiply(sk_c8,U),sk_c7) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% -equal(multiply(Z,sk_c8),sk_c7) | -equal(inverse(Z),sk_c8).
% -equal(multiply(X,Y),sk_c8) | -equal(inverse(X),Y) | -equal(multiply(Y,sk_c7),sk_c8).
% -equal(multiply(sk_c7,sk_c6),sk_c8).
% -equal(inverse(sk_c8),sk_c6).
% -equal(multiply(sk_c8,sk_c7),sk_c6).
%
% Starting a split proof attempt with 6 components.
%
% Split component 1 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c7,sk_c6),sk_c8) | -equal(inverse(sk_c8),sk_c6) | -equal(multiply(X,Y),sk_c8) | -equal(inverse(X),Y) | -equal(multiply(Y,sk_c7),sk_c8) | -equal(multiply(sk_c8,sk_c7),sk_c6) | -equal(multiply(Z,sk_c8),sk_c7) | -equal(inverse(Z),sk_c8) | -equal(multiply(sk_c8,U),sk_c7) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% Split part used next: -equal(multiply(sk_c8,U),sk_c7) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,1,74,0,1,787,50,8,826,0,8,2559,50,31,2598,0,31,5028,50,67,5067,0,67,7834,50,98,7873,0,99,11046,50,141,11085,0,141,14638,50,200,14677,0,200,18680,50,287,18719,0,287,23214,50,427,23253,0,427,28309,50,653,28348,0,653,34008,50,970,34008,40,970,34047,0,970,43813,3,1271,44570,4,1421,45318,1,1571,45318,50,1571,45318,40,1571,45357,0,1571,45806,3,1881,45820,4,2043,45877,5,2172,45877,1,2172,45877,50,2172,45877,40,2172,45916,0,2172,75337,3,3674,75884,4,4423,76480,5,5173,76481,1,5173,76481,50,5174,76481,40,5174,76520,0,5174,96042,3,5925,96563,4,6300,97105,5,6675,97106,1,6675,97106,50,6675,97106,40,6675,97145,0,6676,107433,3,7433,108905,4,7802,110598,5,8177,110599,1,8177,110599,50,8177,110599,40,8177,110638,0,8177,161523,3,12078,162802,4,14029,162926,1,15978,162926,50,15980,162926,40,15980,162965,0,15980,207353,3,18532,208385,4,19806,208424,1,21081,208424,50,21083,208424,40,21083,208463,0,21083,243083,3,22585,244015,4,23334,244859,5,24084,244860,1,24084,244860,50,24085,244860,40,24085,244899,0,24085,256375,3,24844,257622,4,25211,258674,5,25586,258675,5,25586,258675,1,25586,258675,50,25586,258675,40,25586,258714,0,25586,286684,3,26788,287511,4,27387,287885,5,27987,287886,1,27987,287886,50,27988,287886,40,27988,287925,0,27988,307994,3,28740,308592,4,29115,309123,1,29489,309123,50,29489,309123,40,29489,309123,40,29489,309158,0,29489)
%
%
% START OF PROOF
% 309124 [] equal(X,X).
% 309125 [] equal(multiply(identity,X),X).
% 309126 [] equal(multiply(inverse(X),X),identity).
% 309127 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 309128 [] -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8).
% 309129 [] equal(multiply(sk_c2,sk_c7),sk_c8) | equal(inverse(sk_c4),sk_c8).
% 309130 [] equal(multiply(sk_c2,sk_c7),sk_c8) | equal(multiply(sk_c4,sk_c8),sk_c5).
% 309131 [] equal(multiply(sk_c2,sk_c7),sk_c8) | equal(multiply(sk_c8,sk_c5),sk_c7).
% 309135 [] equal(inverse(sk_c1),sk_c2) | equal(inverse(sk_c4),sk_c8).
% 309136 [] equal(multiply(sk_c4,sk_c8),sk_c5) | equal(inverse(sk_c1),sk_c2).
% 309137 [?] ?
% 309141 [] equal(multiply(sk_c1,sk_c2),sk_c8) | equal(inverse(sk_c4),sk_c8).
% 309142 [] equal(multiply(sk_c1,sk_c2),sk_c8) | equal(multiply(sk_c4,sk_c8),sk_c5).
% 309143 [] equal(multiply(sk_c1,sk_c2),sk_c8) | equal(multiply(sk_c8,sk_c5),sk_c7).
% 309147 [] equal(inverse(sk_c8),sk_c6) | equal(inverse(sk_c4),sk_c8).
% 309148 [] equal(multiply(sk_c4,sk_c8),sk_c5) | equal(inverse(sk_c8),sk_c6).
% 309149 [?] ?
% 309153 [] equal(multiply(sk_c7,sk_c6),sk_c8) | equal(inverse(sk_c4),sk_c8).
% 309154 [] equal(multiply(sk_c7,sk_c6),sk_c8) | equal(multiply(sk_c4,sk_c8),sk_c5).
% 309155 [] equal(multiply(sk_c7,sk_c6),sk_c8) | equal(multiply(sk_c8,sk_c5),sk_c7).
% 309192 [hyper:309128,309136,309135,binarycut:309137] equal(inverse(sk_c1),sk_c2).
% 309196 [para:309192.1.1,309126.1.1.1] equal(multiply(sk_c2,sk_c1),identity).
% 309212 [hyper:309128,309148,309147,binarycut:309149] equal(inverse(sk_c8),sk_c6).
% 309217 [hyper:309128,309131,309130,309129] equal(multiply(sk_c2,sk_c7),sk_c8).
% 309221 [para:309212.1.1,309126.1.1.1] equal(multiply(sk_c6,sk_c8),identity).
% 309240 [hyper:309128,309143,309142,309141] equal(multiply(sk_c1,sk_c2),sk_c8).
% 309248 [hyper:309128,309155,309154,309153] equal(multiply(sk_c7,sk_c6),sk_c8).
% 309249 [para:309126.1.1,309127.1.1.1,demod:309125] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 309250 [para:309196.1.1,309127.1.1.1,demod:309125] equal(X,multiply(sk_c2,multiply(sk_c1,X))).
% 309251 [para:309217.1.1,309127.1.1.1] equal(multiply(sk_c8,X),multiply(sk_c2,multiply(sk_c7,X))).
% 309252 [para:309221.1.1,309127.1.1.1,demod:309125] equal(X,multiply(sk_c6,multiply(sk_c8,X))).
% 309253 [para:309240.1.1,309127.1.1.1] equal(multiply(sk_c8,X),multiply(sk_c1,multiply(sk_c2,X))).
% 309257 [para:309240.1.1,309250.1.2.2] equal(sk_c2,multiply(sk_c2,sk_c8)).
% 309264 [para:309196.1.1,309249.1.2.2] equal(sk_c1,multiply(inverse(sk_c2),identity)).
% 309265 [para:309217.1.1,309249.1.2.2] equal(sk_c7,multiply(inverse(sk_c2),sk_c8)).
% 309268 [para:309250.1.2,309249.1.2.2] equal(multiply(sk_c1,X),multiply(inverse(sk_c2),X)).
% 309274 [para:309248.1.1,309251.1.2.2,demod:309257] equal(multiply(sk_c8,sk_c6),sk_c2).
% 309284 [para:309257.1.2,309253.1.2.2,demod:309240] equal(multiply(sk_c8,sk_c8),sk_c8).
% 309289 [para:309284.1.1,309252.1.2.2,demod:309221] equal(sk_c8,identity).
% 309294 [para:309289.1.1,309274.1.1.1,demod:309125] equal(sk_c6,sk_c2).
% 309295 [para:309289.1.1,309265.1.2.2,demod:309264] equal(sk_c7,sk_c1).
% 309297 [para:309294.1.1,309221.1.1.1,demod:309257] equal(sk_c2,identity).
% 309304 [para:309295.1.1,309251.1.2.2.1,demod:309250] equal(multiply(sk_c8,X),X).
% 309309 [para:309297.1.1,309257.1.2.1,demod:309125] equal(sk_c2,sk_c8).
% 309325 [hyper:309128,309268,demod:309192,309304,309265,cut:309124,cut:309309] 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: 4
%
%
% Split component 2 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c7,sk_c6),sk_c8) | -equal(inverse(sk_c8),sk_c6) | -equal(multiply(X,Y),sk_c8) | -equal(inverse(X),Y) | -equal(multiply(Y,sk_c7),sk_c8) | -equal(multiply(sk_c8,sk_c7),sk_c6) | -equal(multiply(Z,sk_c8),sk_c7) | -equal(inverse(Z),sk_c8) | -equal(multiply(sk_c8,U),sk_c7) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% Split part used next: -equal(multiply(Z,sk_c8),sk_c7) | -equal(inverse(Z),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: 4
%
%
% 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: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,1,74,0,1,787,50,8,826,0,8,2559,50,31,2598,0,31,5028,50,67,5067,0,67,7834,50,98,7873,0,99,11046,50,141,11085,0,141,14638,50,200,14677,0,200,18680,50,287,18719,0,287,23214,50,427,23253,0,427,28309,50,653,28348,0,653,34008,50,970,34008,40,970,34047,0,970,43813,3,1271,44570,4,1421,45318,1,1571,45318,50,1571,45318,40,1571,45357,0,1571,45806,3,1881,45820,4,2043,45877,5,2172,45877,1,2172,45877,50,2172,45877,40,2172,45916,0,2172,75337,3,3674,75884,4,4423,76480,5,5173,76481,1,5173,76481,50,5174,76481,40,5174,76520,0,5174,96042,3,5925,96563,4,6300,97105,5,6675,97106,1,6675,97106,50,6675,97106,40,6675,97145,0,6676,107433,3,7433,108905,4,7802,110598,5,8177,110599,1,8177,110599,50,8177,110599,40,8177,110638,0,8177,161523,3,12078,162802,4,14029,162926,1,15978,162926,50,15980,162926,40,15980,162965,0,15980,207353,3,18532,208385,4,19806,208424,1,21081,208424,50,21083,208424,40,21083,208463,0,21083,243083,3,22585,244015,4,23334,244859,5,24084,244860,1,24084,244860,50,24085,244860,40,24085,244899,0,24085,256375,3,24844,257622,4,25211,258674,5,25586,258675,5,25586,258675,1,25586,258675,50,25586,258675,40,25586,258714,0,25586,286684,3,26788,287511,4,27387,287885,5,27987,287886,1,27987,287886,50,27988,287886,40,27988,287925,0,27988,307994,3,28740,308592,4,29115,309123,1,29489,309123,50,29489,309123,40,29489,309123,40,29489,309158,0,29489,309324,50,29489,309324,30,29489,309324,40,29489,309359,0,29489,309466,50,29489,309501,0,29495)
%
%
% START OF PROOF
% 309468 [] equal(multiply(identity,X),X).
% 309469 [] equal(multiply(inverse(X),X),identity).
% 309470 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 309471 [] -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8).
% 309475 [] equal(multiply(sk_c2,sk_c7),sk_c8) | equal(inverse(sk_c3),sk_c8).
% 309476 [] equal(multiply(sk_c2,sk_c7),sk_c8) | equal(multiply(sk_c3,sk_c8),sk_c7).
% 309481 [] equal(inverse(sk_c1),sk_c2) | equal(inverse(sk_c3),sk_c8).
% 309482 [?] ?
% 309487 [] equal(multiply(sk_c1,sk_c2),sk_c8) | equal(inverse(sk_c3),sk_c8).
% 309488 [] equal(multiply(sk_c1,sk_c2),sk_c8) | equal(multiply(sk_c3,sk_c8),sk_c7).
% 309493 [] equal(inverse(sk_c8),sk_c6) | equal(inverse(sk_c3),sk_c8).
% 309494 [?] ?
% 309499 [] equal(multiply(sk_c7,sk_c6),sk_c8) | equal(inverse(sk_c3),sk_c8).
% 309500 [] equal(multiply(sk_c7,sk_c6),sk_c8) | equal(multiply(sk_c3,sk_c8),sk_c7).
% 309506 [hyper:309471,309481,binarycut:309482] equal(inverse(sk_c1),sk_c2).
% 309508 [para:309506.1.1,309469.1.1.1] equal(multiply(sk_c2,sk_c1),identity).
% 309514 [hyper:309471,309493,binarycut:309494] equal(inverse(sk_c8),sk_c6).
% 309515 [para:309514.1.1,309469.1.1.1] equal(multiply(sk_c6,sk_c8),identity).
% 309538 [hyper:309471,309476,309475] equal(multiply(sk_c2,sk_c7),sk_c8).
% 309543 [hyper:309471,309488,309487] equal(multiply(sk_c1,sk_c2),sk_c8).
% 309548 [hyper:309471,309500,309499] equal(multiply(sk_c7,sk_c6),sk_c8).
% 309549 [para:309469.1.1,309470.1.1.1,demod:309468] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 309550 [para:309508.1.1,309470.1.1.1,demod:309468] equal(X,multiply(sk_c2,multiply(sk_c1,X))).
% 309551 [para:309515.1.1,309470.1.1.1,demod:309468] equal(X,multiply(sk_c6,multiply(sk_c8,X))).
% 309552 [para:309538.1.1,309470.1.1.1] equal(multiply(sk_c8,X),multiply(sk_c2,multiply(sk_c7,X))).
% 309553 [para:309543.1.1,309470.1.1.1] equal(multiply(sk_c8,X),multiply(sk_c1,multiply(sk_c2,X))).
% 309554 [para:309548.1.1,309470.1.1.1] equal(multiply(sk_c8,X),multiply(sk_c7,multiply(sk_c6,X))).
% 309555 [para:309543.1.1,309550.1.2.2] equal(sk_c2,multiply(sk_c2,sk_c8)).
% 309558 [para:309469.1.1,309549.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 309559 [para:309508.1.1,309549.1.2.2] equal(sk_c1,multiply(inverse(sk_c2),identity)).
% 309561 [para:309538.1.1,309549.1.2.2] equal(sk_c7,multiply(inverse(sk_c2),sk_c8)).
% 309563 [para:309470.1.1,309549.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 309566 [para:309549.1.2,309549.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 309567 [para:309548.1.1,309552.1.2.2,demod:309555] equal(multiply(sk_c8,sk_c6),sk_c2).
% 309575 [para:309555.1.2,309553.1.2.2,demod:309543] equal(multiply(sk_c8,sk_c8),sk_c8).
% 309578 [para:309575.1.1,309551.1.2.2,demod:309515] equal(sk_c8,identity).
% 309582 [para:309578.1.1,309551.1.2.2.1,demod:309468] equal(X,multiply(sk_c6,X)).
% 309583 [para:309578.1.1,309567.1.1.1,demod:309468] equal(sk_c6,sk_c2).
% 309584 [para:309578.1.1,309561.1.2.2,demod:309559] equal(sk_c7,sk_c1).
% 309586 [para:309583.1.1,309515.1.1.1,demod:309555] equal(sk_c2,identity).
% 309591 [para:309584.1.1,309538.1.1.2,demod:309508] equal(identity,sk_c8).
% 309593 [para:309584.1.1,309552.1.2.2.1,demod:309550] equal(multiply(sk_c8,X),X).
% 309597 [para:309586.1.1,309550.1.2.1,demod:309468] equal(X,multiply(sk_c1,X)).
% 309598 [para:309586.1.1,309555.1.2.1,demod:309468] equal(sk_c2,sk_c8).
% 309602 [para:309554.1.2,309549.1.2.2,demod:309593,309582] equal(X,multiply(inverse(sk_c7),X)).
% 309622 [para:309566.1.2,309469.1.1] equal(multiply(X,inverse(X)),identity).
% 309624 [para:309566.1.2,309558.1.2] equal(X,multiply(X,identity)).
% 309628 [para:309624.1.2,309558.1.2] equal(X,inverse(inverse(X))).
% 309630 [para:309624.1.2,309602.1.2] equal(identity,inverse(sk_c7)).
% 309639 [para:309622.1.1,309563.1.2.2.2,demod:309624] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 309641 [para:309550.1.2,309639.1.2.1.1,demod:309597] equal(inverse(X),multiply(inverse(X),sk_c2)).
% 309650 [para:309641.1.2,309566.1.2,demod:309628] equal(multiply(X,sk_c2),X).
% 309651 [para:309598.1.1,309650.1.1.2] equal(multiply(X,sk_c8),X).
% 309653 [hyper:309471,309651,demod:309630,cut:309591] 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 4
% seconds given: 4
%
%
% Split component 3 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c7,sk_c6),sk_c8) | -equal(inverse(sk_c8),sk_c6) | -equal(multiply(X,Y),sk_c8) | -equal(inverse(X),Y) | -equal(multiply(Y,sk_c7),sk_c8) | -equal(multiply(sk_c8,sk_c7),sk_c6) | -equal(multiply(Z,sk_c8),sk_c7) | -equal(inverse(Z),sk_c8) | -equal(multiply(sk_c8,U),sk_c7) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% Split part used next: -equal(multiply(X,Y),sk_c8) | -equal(inverse(X),Y) | -equal(multiply(Y,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: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,1,74,0,1,787,50,8,826,0,8,2559,50,31,2598,0,31,5028,50,67,5067,0,67,7834,50,98,7873,0,99,11046,50,141,11085,0,141,14638,50,200,14677,0,200,18680,50,287,18719,0,287,23214,50,427,23253,0,427,28309,50,653,28348,0,653,34008,50,970,34008,40,970,34047,0,970,43813,3,1271,44570,4,1421,45318,1,1571,45318,50,1571,45318,40,1571,45357,0,1571,45806,3,1881,45820,4,2043,45877,5,2172,45877,1,2172,45877,50,2172,45877,40,2172,45916,0,2172,75337,3,3674,75884,4,4423,76480,5,5173,76481,1,5173,76481,50,5174,76481,40,5174,76520,0,5174,96042,3,5925,96563,4,6300,97105,5,6675,97106,1,6675,97106,50,6675,97106,40,6675,97145,0,6676,107433,3,7433,108905,4,7802,110598,5,8177,110599,1,8177,110599,50,8177,110599,40,8177,110638,0,8177,161523,3,12078,162802,4,14029,162926,1,15978,162926,50,15980,162926,40,15980,162965,0,15980,207353,3,18532,208385,4,19806,208424,1,21081,208424,50,21083,208424,40,21083,208463,0,21083,243083,3,22585,244015,4,23334,244859,5,24084,244860,1,24084,244860,50,24085,244860,40,24085,244899,0,24085,256375,3,24844,257622,4,25211,258674,5,25586,258675,5,25586,258675,1,25586,258675,50,25586,258675,40,25586,258714,0,25586,286684,3,26788,287511,4,27387,287885,5,27987,287886,1,27987,287886,50,27988,287886,40,27988,287925,0,27988,307994,3,28740,308592,4,29115,309123,1,29489,309123,50,29489,309123,40,29489,309123,40,29489,309158,0,29489,309324,50,29489,309324,30,29489,309324,40,29489,309359,0,29489,309466,50,29489,309501,0,29495,309652,50,29496,309652,30,29496,309652,40,29496,309687,0,29496)
%
%
% START OF PROOF
% 309653 [] equal(X,X).
% 309654 [] equal(multiply(identity,X),X).
% 309655 [] equal(multiply(inverse(X),X),identity).
% 309656 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 309657 [] -equal(multiply(X,sk_c7),sk_c8) | -equal(multiply(Y,X),sk_c8) | -equal(inverse(Y),X).
% 309658 [?] ?
% 309659 [] equal(multiply(sk_c2,sk_c7),sk_c8) | equal(multiply(sk_c4,sk_c8),sk_c5).
% 309660 [?] ?
% 309661 [?] ?
% 309662 [] equal(multiply(sk_c2,sk_c7),sk_c8) | equal(multiply(sk_c3,sk_c8),sk_c7).
% 309663 [?] ?
% 309664 [] equal(inverse(sk_c1),sk_c2) | equal(inverse(sk_c4),sk_c8).
% 309665 [] equal(multiply(sk_c4,sk_c8),sk_c5) | equal(inverse(sk_c1),sk_c2).
% 309666 [] equal(multiply(sk_c8,sk_c5),sk_c7) | equal(inverse(sk_c1),sk_c2).
% 309667 [] equal(inverse(sk_c1),sk_c2) | equal(inverse(sk_c3),sk_c8).
% 309668 [] equal(multiply(sk_c3,sk_c8),sk_c7) | equal(inverse(sk_c1),sk_c2).
% 309669 [] equal(multiply(sk_c8,sk_c7),sk_c6) | equal(inverse(sk_c1),sk_c2).
% 309670 [?] ?
% 309671 [?] ?
% 309672 [?] ?
% 309673 [?] ?
% 309674 [?] ?
% 309675 [?] ?
% 309692 [hyper:309657,309664,binarycut:309670,binarycut:309658] equal(inverse(sk_c4),sk_c8).
% 309695 [para:309692.1.1,309655.1.1.1] equal(multiply(sk_c8,sk_c4),identity).
% 309699 [hyper:309657,309667,binarycut:309673,binarycut:309661] equal(inverse(sk_c3),sk_c8).
% 309703 [para:309699.1.1,309655.1.1.1] equal(multiply(sk_c8,sk_c3),identity).
% 309712 [hyper:309657,309665,binarycut:309671,binarycut:309659] equal(multiply(sk_c4,sk_c8),sk_c5).
% 309715 [hyper:309657,309666,binarycut:309672,binarycut:309660] equal(multiply(sk_c8,sk_c5),sk_c7).
% 309723 [hyper:309657,309668,binarycut:309674,binarycut:309662] equal(multiply(sk_c3,sk_c8),sk_c7).
% 309726 [hyper:309657,309669,binarycut:309675,binarycut:309663] equal(multiply(sk_c8,sk_c7),sk_c6).
% 309727 [para:309655.1.1,309656.1.1.1,demod:309654] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 309728 [para:309695.1.1,309656.1.1.1,demod:309654] equal(X,multiply(sk_c8,multiply(sk_c4,X))).
% 309729 [para:309703.1.1,309656.1.1.1,demod:309654] equal(X,multiply(sk_c8,multiply(sk_c3,X))).
% 309730 [para:309712.1.1,309656.1.1.1] equal(multiply(sk_c5,X),multiply(sk_c4,multiply(sk_c8,X))).
% 309731 [para:309715.1.1,309656.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c8,multiply(sk_c5,X))).
% 309732 [para:309723.1.1,309656.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c3,multiply(sk_c8,X))).
% 309736 [para:309712.1.1,309728.1.2.2,demod:309715] equal(sk_c8,sk_c7).
% 309737 [para:309736.1.2,309726.1.1.2] equal(multiply(sk_c8,sk_c8),sk_c6).
% 309745 [para:309695.1.1,309727.1.2.2] equal(sk_c4,multiply(inverse(sk_c8),identity)).
% 309746 [para:309703.1.1,309727.1.2.2,demod:309745] equal(sk_c3,sk_c4).
% 309749 [para:309728.1.2,309727.1.2.2] equal(multiply(sk_c4,X),multiply(inverse(sk_c8),X)).
% 309750 [para:309729.1.2,309727.1.2.2,demod:309749] equal(multiply(sk_c3,X),multiply(sk_c4,X)).
% 309751 [para:309746.1.2,309712.1.1.1,demod:309723] equal(sk_c7,sk_c5).
% 309753 [para:309751.1.1,309736.1.2] equal(sk_c8,sk_c5).
% 309757 [para:309753.1.2,309715.1.1.2,demod:309737] equal(sk_c6,sk_c7).
% 309762 [para:309730.1.2,309728.1.2.2,demod:309731] equal(multiply(sk_c8,X),multiply(sk_c7,X)).
% 309767 [para:309736.1.2,309757.1.2] equal(sk_c6,sk_c8).
% 309776 [para:309728.1.2,309732.1.2.2,demod:309729,309762,309750] equal(X,multiply(sk_c3,X)).
% 309777 [para:309729.1.2,309732.1.2.2,demod:309762,309776] equal(multiply(sk_c8,X),X).
% 309782 [para:309777.1.1,309695.1.1] equal(sk_c4,identity).
% 309787 [para:309782.1.1,309692.1.1.1] equal(inverse(identity),sk_c8).
% 309788 [hyper:309657,309787,demod:309726,309654,cut:309653,cut:309767] 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: 4
%
%
% Split component 4 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c7,sk_c6),sk_c8) | -equal(inverse(sk_c8),sk_c6) | -equal(multiply(X,Y),sk_c8) | -equal(inverse(X),Y) | -equal(multiply(Y,sk_c7),sk_c8) | -equal(multiply(sk_c8,sk_c7),sk_c6) | -equal(multiply(Z,sk_c8),sk_c7) | -equal(inverse(Z),sk_c8) | -equal(multiply(sk_c8,U),sk_c7) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% Split part used next: -equal(multiply(sk_c7,sk_c6),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: 4
%
%
% 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: 4
%
%
% 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: 4
%
%
% 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: 4
%
%
% 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: 4
%
%
% 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: 4
%
%
% 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: 4
%
%
% 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: 4
%
%
% 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: 4
%
%
% 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(35,40,1,74,0,1,787,50,8,826,0,8,2559,50,31,2598,0,31,5028,50,67,5067,0,67,7834,50,98,7873,0,99,11046,50,141,11085,0,141,14638,50,200,14677,0,200,18680,50,287,18719,0,287,23214,50,427,23253,0,427,28309,50,653,28348,0,653,34008,50,970,34008,40,970,34047,0,970,43813,3,1271,44570,4,1421,45318,1,1571,45318,50,1571,45318,40,1571,45357,0,1571,45806,3,1881,45820,4,2043,45877,5,2172,45877,1,2172,45877,50,2172,45877,40,2172,45916,0,2172,75337,3,3674,75884,4,4423,76480,5,5173,76481,1,5173,76481,50,5174,76481,40,5174,76520,0,5174,96042,3,5925,96563,4,6300,97105,5,6675,97106,1,6675,97106,50,6675,97106,40,6675,97145,0,6676,107433,3,7433,108905,4,7802,110598,5,8177,110599,1,8177,110599,50,8177,110599,40,8177,110638,0,8177,161523,3,12078,162802,4,14029,162926,1,15978,162926,50,15980,162926,40,15980,162965,0,15980,207353,3,18532,208385,4,19806,208424,1,21081,208424,50,21083,208424,40,21083,208463,0,21083,243083,3,22585,244015,4,23334,244859,5,24084,244860,1,24084,244860,50,24085,244860,40,24085,244899,0,24085,256375,3,24844,257622,4,25211,258674,5,25586,258675,5,25586,258675,1,25586,258675,50,25586,258675,40,25586,258714,0,25586,286684,3,26788,287511,4,27387,287885,5,27987,287886,1,27987,287886,50,27988,287886,40,27988,287925,0,27988,307994,3,28740,308592,4,29115,309123,1,29489,309123,50,29489,309123,40,29489,309123,40,29489,309158,0,29489,309324,50,29489,309324,30,29489,309324,40,29489,309359,0,29489,309466,50,29489,309501,0,29495,309652,50,29496,309652,30,29496,309652,40,29496,309687,0,29496,309787,50,29496,309787,30,29496,309787,40,29496,309822,0,29496,309928,50,29496,309963,0,29502,310120,50,29505,310155,0,29505,310320,50,29509,310355,0,29514,310528,50,29520,310563,0,29520,310742,50,29529,310777,0,29529,310964,50,29545,310999,0,29549,311194,50,29579,311229,0,29579,311434,50,29642,311469,0,29642,311684,50,29769,311684,40,29769,311719,0,29769)
%
%
% START OF PROOF
% 311630 [?] ?
% 311686 [] equal(multiply(identity,X),X).
% 311687 [] equal(multiply(inverse(X),X),identity).
% 311688 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 311689 [] -equal(multiply(sk_c7,sk_c6),sk_c8).
% 311714 [?] ?
% 311715 [?] ?
% 311716 [?] ?
% 311758 [input:311714,cut:311689] equal(inverse(sk_c4),sk_c8).
% 311759 [para:311758.1.1,311687.1.1.1] equal(multiply(sk_c8,sk_c4),identity).
% 311772 [input:311715,cut:311689] equal(multiply(sk_c4,sk_c8),sk_c5).
% 311773 [input:311716,cut:311689] equal(multiply(sk_c8,sk_c5),sk_c7).
% 311796 [para:311759.1.1,311688.1.1.1,demod:311686] equal(X,multiply(sk_c8,multiply(sk_c4,X))).
% 311821 [para:311772.1.1,311796.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c5)).
% 311826 [para:311821.1.2,311773.1.1] equal(sk_c8,sk_c7).
% 311828 [para:311826.1.2,311689.1.1.1,cut:311630] 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 component 5 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c7,sk_c6),sk_c8) | -equal(inverse(sk_c8),sk_c6) | -equal(multiply(X,Y),sk_c8) | -equal(inverse(X),Y) | -equal(multiply(Y,sk_c7),sk_c8) | -equal(multiply(sk_c8,sk_c7),sk_c6) | -equal(multiply(Z,sk_c8),sk_c7) | -equal(inverse(Z),sk_c8) | -equal(multiply(sk_c8,U),sk_c7) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% Split part used next: -equal(inverse(sk_c8),sk_c6).
% 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: 4
%
%
% 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: 4
%
%
% 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: 4
%
%
% 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: 4
%
%
% 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: 4
%
%
% 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: 4
%
%
% 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: 4
%
%
% 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: 4
%
%
% 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: 4
%
%
% 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(35,40,1,74,0,1,787,50,8,826,0,8,2559,50,31,2598,0,31,5028,50,67,5067,0,67,7834,50,98,7873,0,99,11046,50,141,11085,0,141,14638,50,200,14677,0,200,18680,50,287,18719,0,287,23214,50,427,23253,0,427,28309,50,653,28348,0,653,34008,50,970,34008,40,970,34047,0,970,43813,3,1271,44570,4,1421,45318,1,1571,45318,50,1571,45318,40,1571,45357,0,1571,45806,3,1881,45820,4,2043,45877,5,2172,45877,1,2172,45877,50,2172,45877,40,2172,45916,0,2172,75337,3,3674,75884,4,4423,76480,5,5173,76481,1,5173,76481,50,5174,76481,40,5174,76520,0,5174,96042,3,5925,96563,4,6300,97105,5,6675,97106,1,6675,97106,50,6675,97106,40,6675,97145,0,6676,107433,3,7433,108905,4,7802,110598,5,8177,110599,1,8177,110599,50,8177,110599,40,8177,110638,0,8177,161523,3,12078,162802,4,14029,162926,1,15978,162926,50,15980,162926,40,15980,162965,0,15980,207353,3,18532,208385,4,19806,208424,1,21081,208424,50,21083,208424,40,21083,208463,0,21083,243083,3,22585,244015,4,23334,244859,5,24084,244860,1,24084,244860,50,24085,244860,40,24085,244899,0,24085,256375,3,24844,257622,4,25211,258674,5,25586,258675,5,25586,258675,1,25586,258675,50,25586,258675,40,25586,258714,0,25586,286684,3,26788,287511,4,27387,287885,5,27987,287886,1,27987,287886,50,27988,287886,40,27988,287925,0,27988,307994,3,28740,308592,4,29115,309123,1,29489,309123,50,29489,309123,40,29489,309123,40,29489,309158,0,29489,309324,50,29489,309324,30,29489,309324,40,29489,309359,0,29489,309466,50,29489,309501,0,29495,309652,50,29496,309652,30,29496,309652,40,29496,309687,0,29496,309787,50,29496,309787,30,29496,309787,40,29496,309822,0,29496,309928,50,29496,309963,0,29502,310120,50,29505,310155,0,29505,310320,50,29509,310355,0,29514,310528,50,29520,310563,0,29520,310742,50,29529,310777,0,29529,310964,50,29545,310999,0,29549,311194,50,29579,311229,0,29579,311434,50,29642,311469,0,29642,311684,50,29769,311684,40,29769,311719,0,29769,311827,50,29769,311827,30,29769,311827,40,29769,311862,0,29769,311968,50,29770,312003,0,29774,312160,50,29777,312195,0,29777,312360,50,29781,312395,0,29781,312568,50,29787,312603,0,29791,312782,50,29800,312817,0,29800,313004,50,29816,313039,0,29821,313234,50,29850,313269,0,29850,313474,50,29913,313509,0,29913,313724,50,30030,313724,40,30030,313759,0,30031)
%
%
% START OF PROOF
% 313618 [?] ?
% 313726 [] equal(multiply(identity,X),X).
% 313727 [] equal(multiply(inverse(X),X),identity).
% 313728 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 313729 [] -equal(inverse(sk_c8),sk_c6).
% 313751 [?] ?
% 313752 [?] ?
% 313753 [?] ?
% 313770 [input:313751,cut:313729] equal(inverse(sk_c3),sk_c8).
% 313771 [para:313770.1.1,313727.1.1.1] equal(multiply(sk_c8,sk_c3),identity).
% 313787 [input:313752,cut:313729] equal(multiply(sk_c3,sk_c8),sk_c7).
% 313789 [input:313753,cut:313729] equal(multiply(sk_c8,sk_c7),sk_c6).
% 313806 [para:313771.1.1,313728.1.1.1,demod:313726] equal(X,multiply(sk_c8,multiply(sk_c3,X))).
% 313857 [para:313787.1.1,313806.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c7)).
% 313861 [para:313857.1.2,313789.1.1] equal(sk_c8,sk_c6).
% 313863 [para:313861.1.2,313729.1.2,cut:313618] 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 component 6 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c7,sk_c6),sk_c8) | -equal(inverse(sk_c8),sk_c6) | -equal(multiply(X,Y),sk_c8) | -equal(inverse(X),Y) | -equal(multiply(Y,sk_c7),sk_c8) | -equal(multiply(sk_c8,sk_c7),sk_c6) | -equal(multiply(Z,sk_c8),sk_c7) | -equal(inverse(Z),sk_c8) | -equal(multiply(sk_c8,U),sk_c7) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% Split part used next: -equal(multiply(sk_c8,sk_c7),sk_c6).
% 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: 4
%
%
% 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: 4
%
%
% 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: 4
%
%
% 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: 4
%
%
% 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: 4
%
%
% 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: 4
%
%
% 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: 4
%
%
% 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: 4
%
%
% 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: 4
%
%
% 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(35,40,1,74,0,1,787,50,8,826,0,8,2559,50,31,2598,0,31,5028,50,67,5067,0,67,7834,50,98,7873,0,99,11046,50,141,11085,0,141,14638,50,200,14677,0,200,18680,50,287,18719,0,287,23214,50,427,23253,0,427,28309,50,653,28348,0,653,34008,50,970,34008,40,970,34047,0,970,43813,3,1271,44570,4,1421,45318,1,1571,45318,50,1571,45318,40,1571,45357,0,1571,45806,3,1881,45820,4,2043,45877,5,2172,45877,1,2172,45877,50,2172,45877,40,2172,45916,0,2172,75337,3,3674,75884,4,4423,76480,5,5173,76481,1,5173,76481,50,5174,76481,40,5174,76520,0,5174,96042,3,5925,96563,4,6300,97105,5,6675,97106,1,6675,97106,50,6675,97106,40,6675,97145,0,6676,107433,3,7433,108905,4,7802,110598,5,8177,110599,1,8177,110599,50,8177,110599,40,8177,110638,0,8177,161523,3,12078,162802,4,14029,162926,1,15978,162926,50,15980,162926,40,15980,162965,0,15980,207353,3,18532,208385,4,19806,208424,1,21081,208424,50,21083,208424,40,21083,208463,0,21083,243083,3,22585,244015,4,23334,244859,5,24084,244860,1,24084,244860,50,24085,244860,40,24085,244899,0,24085,256375,3,24844,257622,4,25211,258674,5,25586,258675,5,25586,258675,1,25586,258675,50,25586,258675,40,25586,258714,0,25586,286684,3,26788,287511,4,27387,287885,5,27987,287886,1,27987,287886,50,27988,287886,40,27988,287925,0,27988,307994,3,28740,308592,4,29115,309123,1,29489,309123,50,29489,309123,40,29489,309123,40,29489,309158,0,29489,309324,50,29489,309324,30,29489,309324,40,29489,309359,0,29489,309466,50,29489,309501,0,29495,309652,50,29496,309652,30,29496,309652,40,29496,309687,0,29496,309787,50,29496,309787,30,29496,309787,40,29496,309822,0,29496,309928,50,29496,309963,0,29502,310120,50,29505,310155,0,29505,310320,50,29509,310355,0,29514,310528,50,29520,310563,0,29520,310742,50,29529,310777,0,29529,310964,50,29545,310999,0,29549,311194,50,29579,311229,0,29579,311434,50,29642,311469,0,29642,311684,50,29769,311684,40,29769,311719,0,29769,311827,50,29769,311827,30,29769,311827,40,29769,311862,0,29769,311968,50,29770,312003,0,29774,312160,50,29777,312195,0,29777,312360,50,29781,312395,0,29781,312568,50,29787,312603,0,29791,312782,50,29800,312817,0,29800,313004,50,29816,313039,0,29821,313234,50,29850,313269,0,29850,313474,50,29913,313509,0,29913,313724,50,30030,313724,40,30030,313759,0,30031,313862,50,30031,313862,30,30031,313862,40,30031,313897,0,30031,313997,50,30032,314032,0,30036,314182,50,30039,314217,0,30039,314375,50,30042,314410,0,30042,314576,50,30048,314611,0,30052,314783,50,30061,314818,0,30061,314998,50,30076,315033,0,30080,315221,50,30109,315256,0,30109,315454,50,30170,315489,0,30170,315697,50,30285,315697,40,30285,315732,0,30285)
%
%
% START OF PROOF
% 315630 [?] ?
% 315699 [] equal(multiply(identity,X),X).
% 315700 [] equal(multiply(inverse(X),X),identity).
% 315701 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 315702 [] -equal(multiply(sk_c8,sk_c7),sk_c6).
% 315714 [?] ?
% 315720 [?] ?
% 315756 [input:315714,cut:315702] equal(inverse(sk_c1),sk_c2).
% 315757 [para:315756.1.1,315700.1.1.1] equal(multiply(sk_c2,sk_c1),identity).
% 315784 [input:315720,cut:315702] equal(multiply(sk_c1,sk_c2),sk_c8).
% 315791 [para:315700.1.1,315701.1.1.1,demod:315699] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 315799 [para:315757.1.1,315701.1.1.1,demod:315699] equal(X,multiply(sk_c2,multiply(sk_c1,X))).
% 315838 [para:315784.1.1,315799.1.2.2] equal(sk_c2,multiply(sk_c2,sk_c8)).
% 315899 [para:315799.1.2,315791.1.2.2] equal(multiply(sk_c1,X),multiply(inverse(sk_c2),X)).
% 315900 [para:315838.1.2,315791.1.2.2,demod:315899] equal(sk_c8,multiply(sk_c1,sk_c2)).
% 315908 [para:315899.1.2,315700.1.1,demod:315900] equal(sk_c8,identity).
% 315913 [para:315908.1.1,315702.1.1.1,demod:315699,cut:315630] 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: 32953
% derived clauses: 6697801
% kept clauses: 246355
% kept size sum: 288331
% kept mid-nuclei: 22620
% kept new demods: 5351
% forw unit-subs: 2301227
% forw double-subs: 3883175
% forw overdouble-subs: 202541
% backward subs: 11812
% fast unit cutoff: 16178
% full unit cutoff: 0
% dbl unit cutoff: 16287
% real runtime : 305.21
% process. runtime: 302.85
% specific non-discr-tree subsumption statistics:
% tried: 41971530
% length fails: 3700563
% strength fails: 11484392
% predlist fails: 3803332
% aux str. fails: 7932744
% by-lit fails: 8983707
% full subs tried: 1352902
% full subs fail: 1249565
%
% ; 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/GRP357-1+eq_r.in")
%
%------------------------------------------------------------------------------