TSTP Solution File: GRP335-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP335-1 : 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 : art02.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 298.1s
% Output : Assurance 298.1s
% 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/GRP335-1+eq_r.in
% Using automatic strategy selection.
% Time limit in seconds: 600
%
% prove-all-passes started
%
% detected problem class: peq
%
% strategies selected:
% (hyper 30 #f 3 21)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 3 21)
% (binary-posweight-lex-big-order 30 #f 3 21)
% (binary 30 #t)
% (binary-posweight-kb-big-order 156 #f)
% (binary-posweight-lex-big-order 102 #f)
% (binary-posweight-firstpref-order 60 #f)
% (binary-order 30 #f)
% (binary-posweight-kb-small-order 48 #f)
% (binary-posweight-lex-small-order 30 #f)
%
%
% SOS clause
% -equal(multiply(sk_c7,sk_c8),sk_c6) | -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7) | -equal(multiply(Y,sk_c7),sk_c8) | -equal(inverse(Y),sk_c7) | -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(Y,sk_c7),sk_c8) | -equal(inverse(Y),sk_c7).
% -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7).
% -equal(multiply(sk_c7,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_c8),sk_c6) | -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7) | -equal(multiply(Y,sk_c7),sk_c8) | -equal(inverse(Y),sk_c7) | -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(35,40,0,75,0,0,763,50,6,803,0,6,1832,50,20,1872,0,20,3082,50,38,3122,0,38,4426,50,54,4466,0,54,5865,50,74,5905,0,74,7444,50,104,7484,0,104,9163,50,150,9203,0,150,11068,50,232,11108,0,232,13159,50,388,13199,0,388,15482,50,629,15522,0,629,18037,50,1051,18037,40,1051,18077,0,1051,28753,3,1352,29416,4,1502,30097,5,1652,30098,1,1652,30098,50,1652,30098,40,1652,30138,0,1652,30490,3,1966,30502,4,2128,30520,5,2253,30520,1,2253,30520,50,2253,30520,40,2253,30560,0,2253,54109,3,3761,54929,4,4504,55542,1,5254,55542,50,5255,55542,40,5255,55582,0,5255,73722,3,6006,74197,4,6381,74749,1,6756,74749,50,6756,74749,40,6756,74789,0,6756,86490,3,7510,87688,4,7882,89085,1,8257,89085,50,8257,89085,40,8257,89125,0,8257,127360,3,12158,129206,4,14108,130631,5,16058,130632,1,16058,130632,50,16059,130632,40,16059,130672,0,16059,163162,3,18613,164626,4,19885,165588,5,21160,165589,1,21160,165589,50,21161,165589,40,21161,165629,0,21162,193866,3,22663,194884,4,23413,195601,5,24163,195602,1,24163,195602,50,24164,195602,40,24164,195642,0,24164,205446,3,24927,206581,4,25299,206962,5,25665,206962,1,25665,206962,50,25665,206962,40,25665,207002,0,25665,230864,3,26866,231732,4,27466,232442,5,28066,232443,1,28066,232443,50,28067,232443,40,28067,232483,0,28067,250300,3,28818,250935,4,29193,251366,1,29568,251366,50,29568,251366,40,29568,251366,40,29568,251401,0,29568)
%
%
% START OF PROOF
% 251368 [] equal(multiply(identity,X),X).
% 251369 [] equal(multiply(inverse(X),X),identity).
% 251370 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 251371 [] -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8).
% 251372 [] equal(inverse(sk_c2),sk_c7) | equal(inverse(sk_c4),sk_c8).
% 251373 [] equal(multiply(sk_c4,sk_c8),sk_c5) | equal(inverse(sk_c2),sk_c7).
% 251374 [?] ?
% 251378 [] equal(multiply(sk_c2,sk_c7),sk_c8) | equal(inverse(sk_c4),sk_c8).
% 251379 [] equal(multiply(sk_c2,sk_c7),sk_c8) | equal(multiply(sk_c4,sk_c8),sk_c5).
% 251380 [] equal(multiply(sk_c2,sk_c7),sk_c8) | equal(multiply(sk_c8,sk_c5),sk_c7).
% 251384 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c4),sk_c8).
% 251385 [] equal(multiply(sk_c4,sk_c8),sk_c5) | equal(inverse(sk_c1),sk_c7).
% 251386 [?] ?
% 251390 [] equal(multiply(sk_c1,sk_c7),sk_c6) | equal(inverse(sk_c4),sk_c8).
% 251391 [] equal(multiply(sk_c1,sk_c7),sk_c6) | equal(multiply(sk_c4,sk_c8),sk_c5).
% 251392 [] equal(multiply(sk_c1,sk_c7),sk_c6) | equal(multiply(sk_c8,sk_c5),sk_c7).
% 251396 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(inverse(sk_c4),sk_c8).
% 251397 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(multiply(sk_c4,sk_c8),sk_c5).
% 251398 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(multiply(sk_c8,sk_c5),sk_c7).
% 251425 [hyper:251371,251373,251372,binarycut:251374] equal(inverse(sk_c2),sk_c7).
% 251426 [para:251425.1.1,251369.1.1.1] equal(multiply(sk_c7,sk_c2),identity).
% 251440 [hyper:251371,251385,251384,binarycut:251386] equal(inverse(sk_c1),sk_c7).
% 251444 [para:251440.1.1,251369.1.1.1] equal(multiply(sk_c7,sk_c1),identity).
% 251470 [hyper:251371,251380,251379,251378] equal(multiply(sk_c2,sk_c7),sk_c8).
% 251485 [hyper:251371,251392,251391,251390] equal(multiply(sk_c1,sk_c7),sk_c6).
% 251496 [hyper:251371,251398,251397,251396] equal(multiply(sk_c7,sk_c8),sk_c6).
% 251500 [para:251369.1.1,251370.1.1.1,demod:251368] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 251501 [para:251426.1.1,251370.1.1.1,demod:251368] equal(X,multiply(sk_c7,multiply(sk_c2,X))).
% 251502 [para:251444.1.1,251370.1.1.1,demod:251368] equal(X,multiply(sk_c7,multiply(sk_c1,X))).
% 251503 [para:251470.1.1,251370.1.1.1] equal(multiply(sk_c8,X),multiply(sk_c2,multiply(sk_c7,X))).
% 251505 [para:251496.1.1,251370.1.1.1] equal(multiply(sk_c6,X),multiply(sk_c7,multiply(sk_c8,X))).
% 251508 [para:251470.1.1,251501.1.2.2,demod:251496] equal(sk_c7,sk_c6).
% 251509 [para:251508.1.1,251426.1.1.1] equal(multiply(sk_c6,sk_c2),identity).
% 251511 [para:251508.1.1,251470.1.1.2] equal(multiply(sk_c2,sk_c6),sk_c8).
% 251513 [para:251508.1.1,251496.1.1.1] equal(multiply(sk_c6,sk_c8),sk_c6).
% 251520 [para:251426.1.1,251500.1.2.2] equal(sk_c2,multiply(inverse(sk_c7),identity)).
% 251521 [para:251444.1.1,251500.1.2.2,demod:251520] equal(sk_c1,sk_c2).
% 251522 [para:251485.1.1,251500.1.2.2,demod:251440] equal(sk_c7,multiply(sk_c7,sk_c6)).
% 251523 [para:251496.1.1,251500.1.2.2] equal(sk_c8,multiply(inverse(sk_c7),sk_c6)).
% 251524 [para:251501.1.2,251500.1.2.2] equal(multiply(sk_c2,X),multiply(inverse(sk_c7),X)).
% 251526 [para:251521.1.2,251470.1.1.1,demod:251485] equal(sk_c6,sk_c8).
% 251532 [para:251513.1.1,251500.1.2.2,demod:251369] equal(sk_c8,identity).
% 251536 [para:251502.1.2,251500.1.2.2,demod:251524] equal(multiply(sk_c1,X),multiply(sk_c2,X)).
% 251538 [para:251532.1.1,251526.1.2] equal(sk_c6,identity).
% 251540 [para:251538.1.1,251509.1.1.1,demod:251368] equal(sk_c2,identity).
% 251542 [para:251538.1.1,251511.1.1.2,demod:251536] equal(multiply(sk_c1,identity),sk_c8).
% 251545 [para:251540.1.1,251470.1.1.1,demod:251368] equal(sk_c7,sk_c8).
% 251546 [para:251540.1.1,251501.1.2.2.1,demod:251368] equal(X,multiply(sk_c7,X)).
% 251550 [para:251426.1.1,251503.1.2.2,demod:251542,251536] equal(multiply(sk_c8,sk_c2),sk_c8).
% 251552 [para:251496.1.1,251503.1.2.2,demod:251511] equal(multiply(sk_c8,sk_c8),sk_c8).
% 251554 [para:251503.1.2,251501.1.2.2,demod:251505,251546] equal(X,multiply(sk_c6,X)).
% 251556 [para:251508.1.1,251503.1.2.2.1,demod:251536,251554] equal(multiply(sk_c8,X),multiply(sk_c1,X)).
% 251557 [para:251540.1.1,251503.1.2.1,demod:251368,251546,251556] equal(multiply(sk_c1,X),X).
% 251570 [para:251532.1.1,251550.1.1.1,demod:251368] equal(sk_c2,sk_c8).
% 251571 [para:251570.1.2,251526.1.2] equal(sk_c6,sk_c2).
% 251574 [para:251571.1.2,251425.1.1.1] equal(inverse(sk_c6),sk_c7).
% 251594 [para:251508.1.1,251523.1.2.1.1,demod:251522,251574] equal(sk_c8,sk_c7).
% 251597 [hyper:251371,251524,demod:251425,251552,251557,251536,251524,cut:251594,cut:251545] 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_c8),sk_c6) | -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7) | -equal(multiply(Y,sk_c7),sk_c8) | -equal(inverse(Y),sk_c7) | -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(35,40,0,75,0,0,763,50,6,803,0,6,1832,50,20,1872,0,20,3082,50,38,3122,0,38,4426,50,54,4466,0,54,5865,50,74,5905,0,74,7444,50,104,7484,0,104,9163,50,150,9203,0,150,11068,50,232,11108,0,232,13159,50,388,13199,0,388,15482,50,629,15522,0,629,18037,50,1051,18037,40,1051,18077,0,1051,28753,3,1352,29416,4,1502,30097,5,1652,30098,1,1652,30098,50,1652,30098,40,1652,30138,0,1652,30490,3,1966,30502,4,2128,30520,5,2253,30520,1,2253,30520,50,2253,30520,40,2253,30560,0,2253,54109,3,3761,54929,4,4504,55542,1,5254,55542,50,5255,55542,40,5255,55582,0,5255,73722,3,6006,74197,4,6381,74749,1,6756,74749,50,6756,74749,40,6756,74789,0,6756,86490,3,7510,87688,4,7882,89085,1,8257,89085,50,8257,89085,40,8257,89125,0,8257,127360,3,12158,129206,4,14108,130631,5,16058,130632,1,16058,130632,50,16059,130632,40,16059,130672,0,16059,163162,3,18613,164626,4,19885,165588,5,21160,165589,1,21160,165589,50,21161,165589,40,21161,165629,0,21162,193866,3,22663,194884,4,23413,195601,5,24163,195602,1,24163,195602,50,24164,195602,40,24164,195642,0,24164,205446,3,24927,206581,4,25299,206962,5,25665,206962,1,25665,206962,50,25665,206962,40,25665,207002,0,25665,230864,3,26866,231732,4,27466,232442,5,28066,232443,1,28066,232443,50,28067,232443,40,28067,232483,0,28067,250300,3,28818,250935,4,29193,251366,1,29568,251366,50,29568,251366,40,29568,251366,40,29568,251401,0,29568,251596,50,29569,251596,30,29569,251596,40,29569,251631,0,29569,251745,50,29569,251780,0,29571)
%
%
% START OF PROOF
% 251747 [] equal(multiply(identity,X),X).
% 251748 [] equal(multiply(inverse(X),X),identity).
% 251749 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 251750 [] -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8).
% 251754 [] equal(inverse(sk_c2),sk_c7) | equal(inverse(sk_c3),sk_c8).
% 251755 [?] ?
% 251760 [] equal(multiply(sk_c2,sk_c7),sk_c8) | equal(inverse(sk_c3),sk_c8).
% 251761 [] equal(multiply(sk_c2,sk_c7),sk_c8) | equal(multiply(sk_c3,sk_c8),sk_c7).
% 251766 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c3),sk_c8).
% 251767 [?] ?
% 251772 [] equal(multiply(sk_c1,sk_c7),sk_c6) | equal(inverse(sk_c3),sk_c8).
% 251773 [] equal(multiply(sk_c1,sk_c7),sk_c6) | equal(multiply(sk_c3,sk_c8),sk_c7).
% 251778 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(inverse(sk_c3),sk_c8).
% 251779 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(multiply(sk_c3,sk_c8),sk_c7).
% 251785 [hyper:251750,251754,binarycut:251755] equal(inverse(sk_c2),sk_c7).
% 251787 [para:251785.1.1,251748.1.1.1] equal(multiply(sk_c7,sk_c2),identity).
% 251796 [hyper:251750,251766,binarycut:251767] equal(inverse(sk_c1),sk_c7).
% 251797 [para:251796.1.1,251748.1.1.1] equal(multiply(sk_c7,sk_c1),identity).
% 251817 [hyper:251750,251761,251760] equal(multiply(sk_c2,sk_c7),sk_c8).
% 251822 [hyper:251750,251773,251772] equal(multiply(sk_c1,sk_c7),sk_c6).
% 251827 [hyper:251750,251779,251778] equal(multiply(sk_c7,sk_c8),sk_c6).
% 251828 [para:251748.1.1,251749.1.1.1,demod:251747] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 251829 [para:251787.1.1,251749.1.1.1,demod:251747] equal(X,multiply(sk_c7,multiply(sk_c2,X))).
% 251830 [para:251797.1.1,251749.1.1.1,demod:251747] equal(X,multiply(sk_c7,multiply(sk_c1,X))).
% 251831 [para:251817.1.1,251749.1.1.1] equal(multiply(sk_c8,X),multiply(sk_c2,multiply(sk_c7,X))).
% 251833 [para:251827.1.1,251749.1.1.1] equal(multiply(sk_c6,X),multiply(sk_c7,multiply(sk_c8,X))).
% 251834 [para:251817.1.1,251829.1.2.2,demod:251827] equal(sk_c7,sk_c6).
% 251835 [para:251834.1.1,251787.1.1.1] equal(multiply(sk_c6,sk_c2),identity).
% 251837 [para:251834.1.1,251817.1.1.2] equal(multiply(sk_c2,sk_c6),sk_c8).
% 251839 [para:251834.1.1,251827.1.1.1] equal(multiply(sk_c6,sk_c8),sk_c6).
% 251844 [para:251748.1.1,251828.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 251845 [para:251787.1.1,251828.1.2.2] equal(sk_c2,multiply(inverse(sk_c7),identity)).
% 251846 [para:251797.1.1,251828.1.2.2,demod:251845] equal(sk_c1,sk_c2).
% 251849 [para:251749.1.1,251828.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 251850 [para:251829.1.2,251828.1.2.2] equal(multiply(sk_c2,X),multiply(inverse(sk_c7),X)).
% 251852 [para:251828.1.2,251828.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 251853 [para:251846.1.2,251817.1.1.1,demod:251822] equal(sk_c6,sk_c8).
% 251857 [para:251839.1.1,251828.1.2.2,demod:251748] equal(sk_c8,identity).
% 251859 [para:251830.1.2,251828.1.2.2,demod:251850] equal(multiply(sk_c1,X),multiply(sk_c2,X)).
% 251861 [para:251857.1.1,251853.1.2] equal(sk_c6,identity).
% 251863 [para:251861.1.1,251835.1.1.1,demod:251747] equal(sk_c2,identity).
% 251865 [para:251861.1.1,251837.1.1.2,demod:251859] equal(multiply(sk_c1,identity),sk_c8).
% 251868 [para:251863.1.1,251817.1.1.1,demod:251747] equal(sk_c7,sk_c8).
% 251869 [para:251863.1.1,251829.1.2.2.1,demod:251747] equal(X,multiply(sk_c7,X)).
% 251871 [para:251787.1.1,251831.1.2.2,demod:251865,251859] equal(multiply(sk_c8,sk_c2),sk_c8).
% 251875 [para:251831.1.2,251829.1.2.2,demod:251833,251869] equal(X,multiply(sk_c6,X)).
% 251877 [para:251834.1.1,251831.1.2.2.1,demod:251859,251875] equal(multiply(sk_c8,X),multiply(sk_c1,X)).
% 251878 [para:251863.1.1,251831.1.2.1,demod:251747,251869,251877] equal(multiply(sk_c1,X),X).
% 251881 [para:251857.1.1,251871.1.1.1,demod:251747] equal(sk_c2,sk_c8).
% 251909 [para:251852.1.2,251748.1.1] equal(multiply(X,inverse(X)),identity).
% 251911 [para:251852.1.2,251844.1.2] equal(X,multiply(X,identity)).
% 251913 [para:251911.1.2,251845.1.2] equal(sk_c2,inverse(sk_c7)).
% 251914 [para:251911.1.2,251844.1.2] equal(X,inverse(inverse(X))).
% 251918 [para:251909.1.1,251849.1.2.2.2,demod:251911] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 251920 [para:251829.1.2,251918.1.2.1.1,demod:251878,251859] equal(inverse(X),multiply(inverse(X),sk_c7)).
% 251929 [para:251920.1.2,251852.1.2,demod:251914] equal(multiply(X,sk_c7),X).
% 251931 [para:251868.1.1,251929.1.1.2] equal(multiply(X,sk_c8),X).
% 251935 [hyper:251750,251931,demod:251913,cut:251881] 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_c8),sk_c6) | -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7) | -equal(multiply(Y,sk_c7),sk_c8) | -equal(inverse(Y),sk_c7) | -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(Y,sk_c7),sk_c8) | -equal(inverse(Y),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: 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(35,40,0,75,0,0,763,50,6,803,0,6,1832,50,20,1872,0,20,3082,50,38,3122,0,38,4426,50,54,4466,0,54,5865,50,74,5905,0,74,7444,50,104,7484,0,104,9163,50,150,9203,0,150,11068,50,232,11108,0,232,13159,50,388,13199,0,388,15482,50,629,15522,0,629,18037,50,1051,18037,40,1051,18077,0,1051,28753,3,1352,29416,4,1502,30097,5,1652,30098,1,1652,30098,50,1652,30098,40,1652,30138,0,1652,30490,3,1966,30502,4,2128,30520,5,2253,30520,1,2253,30520,50,2253,30520,40,2253,30560,0,2253,54109,3,3761,54929,4,4504,55542,1,5254,55542,50,5255,55542,40,5255,55582,0,5255,73722,3,6006,74197,4,6381,74749,1,6756,74749,50,6756,74749,40,6756,74789,0,6756,86490,3,7510,87688,4,7882,89085,1,8257,89085,50,8257,89085,40,8257,89125,0,8257,127360,3,12158,129206,4,14108,130631,5,16058,130632,1,16058,130632,50,16059,130632,40,16059,130672,0,16059,163162,3,18613,164626,4,19885,165588,5,21160,165589,1,21160,165589,50,21161,165589,40,21161,165629,0,21162,193866,3,22663,194884,4,23413,195601,5,24163,195602,1,24163,195602,50,24164,195602,40,24164,195642,0,24164,205446,3,24927,206581,4,25299,206962,5,25665,206962,1,25665,206962,50,25665,206962,40,25665,207002,0,25665,230864,3,26866,231732,4,27466,232442,5,28066,232443,1,28066,232443,50,28067,232443,40,28067,232483,0,28067,250300,3,28818,250935,4,29193,251366,1,29568,251366,50,29568,251366,40,29568,251366,40,29568,251401,0,29568,251596,50,29569,251596,30,29569,251596,40,29569,251631,0,29569,251745,50,29569,251780,0,29571,251934,50,29572,251934,30,29572,251934,40,29572,251969,0,29573,252070,50,29573,252105,0,29573)
%
%
% START OF PROOF
% 252072 [] equal(multiply(identity,X),X).
% 252073 [] equal(multiply(inverse(X),X),identity).
% 252074 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 252075 [] -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c7).
% 252076 [] equal(inverse(sk_c2),sk_c7) | equal(inverse(sk_c4),sk_c8).
% 252077 [] equal(multiply(sk_c4,sk_c8),sk_c5) | equal(inverse(sk_c2),sk_c7).
% 252078 [] equal(multiply(sk_c8,sk_c5),sk_c7) | equal(inverse(sk_c2),sk_c7).
% 252079 [] equal(inverse(sk_c2),sk_c7) | equal(inverse(sk_c3),sk_c8).
% 252080 [] equal(multiply(sk_c3,sk_c8),sk_c7) | equal(inverse(sk_c2),sk_c7).
% 252081 [] equal(multiply(sk_c8,sk_c7),sk_c6) | equal(inverse(sk_c2),sk_c7).
% 252082 [?] ?
% 252083 [?] ?
% 252084 [?] ?
% 252085 [?] ?
% 252086 [?] ?
% 252087 [?] ?
% 252108 [hyper:252075,252076,binarycut:252082] equal(inverse(sk_c4),sk_c8).
% 252109 [para:252108.1.1,252073.1.1.1] equal(multiply(sk_c8,sk_c4),identity).
% 252113 [hyper:252075,252079,binarycut:252085] equal(inverse(sk_c3),sk_c8).
% 252114 [para:252113.1.1,252073.1.1.1] equal(multiply(sk_c8,sk_c3),identity).
% 252117 [hyper:252075,252077,binarycut:252083] equal(multiply(sk_c4,sk_c8),sk_c5).
% 252120 [hyper:252075,252078,binarycut:252084] equal(multiply(sk_c8,sk_c5),sk_c7).
% 252123 [hyper:252075,252080,binarycut:252086] equal(multiply(sk_c3,sk_c8),sk_c7).
% 252126 [hyper:252075,252081,binarycut:252087] equal(multiply(sk_c8,sk_c7),sk_c6).
% 252127 [para:252073.1.1,252074.1.1.1,demod:252072] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 252128 [para:252109.1.1,252074.1.1.1,demod:252072] equal(X,multiply(sk_c8,multiply(sk_c4,X))).
% 252129 [para:252114.1.1,252074.1.1.1,demod:252072] equal(X,multiply(sk_c8,multiply(sk_c3,X))).
% 252130 [para:252117.1.1,252074.1.1.1] equal(multiply(sk_c5,X),multiply(sk_c4,multiply(sk_c8,X))).
% 252131 [para:252120.1.1,252074.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c8,multiply(sk_c5,X))).
% 252132 [para:252123.1.1,252074.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c3,multiply(sk_c8,X))).
% 252134 [para:252117.1.1,252128.1.2.2,demod:252120] equal(sk_c8,sk_c7).
% 252137 [para:252123.1.1,252129.1.2.2,demod:252126] equal(sk_c8,sk_c6).
% 252139 [para:252073.1.1,252127.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 252140 [para:252109.1.1,252127.1.2.2] equal(sk_c4,multiply(inverse(sk_c8),identity)).
% 252141 [para:252114.1.1,252127.1.2.2,demod:252140] equal(sk_c3,sk_c4).
% 252143 [para:252074.1.1,252127.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 252144 [para:252126.1.1,252127.1.2.2] equal(sk_c7,multiply(inverse(sk_c8),sk_c6)).
% 252145 [para:252128.1.2,252127.1.2.2] equal(multiply(sk_c4,X),multiply(inverse(sk_c8),X)).
% 252146 [para:252129.1.2,252127.1.2.2,demod:252145] equal(multiply(sk_c3,X),multiply(sk_c4,X)).
% 252147 [para:252127.1.2,252127.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 252150 [para:252137.1.1,252117.1.1.2,demod:252146] equal(multiply(sk_c3,sk_c6),sk_c5).
% 252152 [para:252137.1.1,252123.1.1.2,demod:252150] equal(sk_c5,sk_c7).
% 252158 [para:252152.1.2,252126.1.1.2,demod:252120] equal(sk_c7,sk_c6).
% 252159 [para:252152.1.2,252134.1.2] equal(sk_c8,sk_c5).
% 252161 [para:252158.1.1,252152.1.2] equal(sk_c5,sk_c6).
% 252165 [para:252120.1.1,252130.1.2.2,demod:252146] equal(multiply(sk_c5,sk_c5),multiply(sk_c3,sk_c7)).
% 252167 [para:252130.1.2,252128.1.2.2,demod:252131] equal(multiply(sk_c8,X),multiply(sk_c7,X)).
% 252168 [para:252128.1.2,252130.1.2.2,demod:252146] equal(multiply(sk_c5,multiply(sk_c3,X)),multiply(sk_c3,X)).
% 252171 [para:252141.1.2,252130.1.2.1,demod:252167,252132] equal(multiply(sk_c5,X),multiply(sk_c8,X)).
% 252174 [para:252159.1.1,252120.1.1.1,demod:252165] equal(multiply(sk_c3,sk_c7),sk_c7).
% 252175 [para:252159.1.1,252128.1.2.1,demod:252168,252146] equal(X,multiply(sk_c3,X)).
% 252176 [para:252159.1.1,252129.1.2.1,demod:252175] equal(X,multiply(sk_c5,X)).
% 252180 [para:252176.1.2,252127.1.2.2] equal(X,multiply(inverse(sk_c5),X)).
% 252187 [para:252180.1.2,252073.1.1] equal(sk_c5,identity).
% 252189 [para:252187.1.1,252161.1.1] equal(identity,sk_c6).
% 252233 [para:252189.1.2,252144.1.2.2,demod:252140] equal(sk_c7,sk_c4).
% 252237 [para:252233.1.1,252174.1.1.2,demod:252175] equal(sk_c4,sk_c7).
% 252242 [para:252147.1.2,252073.1.1] equal(multiply(X,inverse(X)),identity).
% 252244 [para:252147.1.2,252139.1.2] equal(X,multiply(X,identity)).
% 252245 [para:252244.1.2,252139.1.2] equal(X,inverse(inverse(X))).
% 252246 [para:252244.1.2,252140.1.2] equal(sk_c4,inverse(sk_c8)).
% 252250 [para:252242.1.1,252143.1.2.2.2,demod:252244] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 252260 [para:252167.1.2,252250.1.2.1.1,demod:252176,252171] equal(inverse(X),multiply(inverse(X),sk_c7)).
% 252273 [para:252260.1.2,252147.1.2,demod:252245] equal(multiply(X,sk_c7),X).
% 252274 [hyper:252075,252273,demod:252246,cut:252237] 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 4 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c7,sk_c8),sk_c6) | -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7) | -equal(multiply(Y,sk_c7),sk_c8) | -equal(inverse(Y),sk_c7) | -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,sk_c7),sk_c6) | -equal(inverse(X),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: 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(35,40,0,75,0,0,763,50,6,803,0,6,1832,50,20,1872,0,20,3082,50,38,3122,0,38,4426,50,54,4466,0,54,5865,50,74,5905,0,74,7444,50,104,7484,0,104,9163,50,150,9203,0,150,11068,50,232,11108,0,232,13159,50,388,13199,0,388,15482,50,629,15522,0,629,18037,50,1051,18037,40,1051,18077,0,1051,28753,3,1352,29416,4,1502,30097,5,1652,30098,1,1652,30098,50,1652,30098,40,1652,30138,0,1652,30490,3,1966,30502,4,2128,30520,5,2253,30520,1,2253,30520,50,2253,30520,40,2253,30560,0,2253,54109,3,3761,54929,4,4504,55542,1,5254,55542,50,5255,55542,40,5255,55582,0,5255,73722,3,6006,74197,4,6381,74749,1,6756,74749,50,6756,74749,40,6756,74789,0,6756,86490,3,7510,87688,4,7882,89085,1,8257,89085,50,8257,89085,40,8257,89125,0,8257,127360,3,12158,129206,4,14108,130631,5,16058,130632,1,16058,130632,50,16059,130632,40,16059,130672,0,16059,163162,3,18613,164626,4,19885,165588,5,21160,165589,1,21160,165589,50,21161,165589,40,21161,165629,0,21162,193866,3,22663,194884,4,23413,195601,5,24163,195602,1,24163,195602,50,24164,195602,40,24164,195642,0,24164,205446,3,24927,206581,4,25299,206962,5,25665,206962,1,25665,206962,50,25665,206962,40,25665,207002,0,25665,230864,3,26866,231732,4,27466,232442,5,28066,232443,1,28066,232443,50,28067,232443,40,28067,232483,0,28067,250300,3,28818,250935,4,29193,251366,1,29568,251366,50,29568,251366,40,29568,251366,40,29568,251401,0,29568,251596,50,29569,251596,30,29569,251596,40,29569,251631,0,29569,251745,50,29569,251780,0,29571,251934,50,29572,251934,30,29572,251934,40,29572,251969,0,29573,252070,50,29573,252105,0,29573,252273,50,29575,252273,30,29575,252273,40,29575,252308,0,29577,252435,50,29578,252470,0,29578)
%
%
% START OF PROOF
% 252437 [] equal(multiply(identity,X),X).
% 252438 [] equal(multiply(inverse(X),X),identity).
% 252439 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 252440 [] -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7).
% 252453 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c4),sk_c8).
% 252454 [] equal(multiply(sk_c4,sk_c8),sk_c5) | equal(inverse(sk_c1),sk_c7).
% 252455 [] equal(multiply(sk_c8,sk_c5),sk_c7) | equal(inverse(sk_c1),sk_c7).
% 252456 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c3),sk_c8).
% 252457 [] equal(multiply(sk_c3,sk_c8),sk_c7) | equal(inverse(sk_c1),sk_c7).
% 252458 [] equal(multiply(sk_c8,sk_c7),sk_c6) | equal(inverse(sk_c1),sk_c7).
% 252459 [?] ?
% 252460 [?] ?
% 252461 [?] ?
% 252462 [?] ?
% 252463 [?] ?
% 252464 [?] ?
% 252478 [hyper:252440,252453,binarycut:252459] equal(inverse(sk_c4),sk_c8).
% 252479 [para:252478.1.1,252438.1.1.1] equal(multiply(sk_c8,sk_c4),identity).
% 252482 [hyper:252440,252456,binarycut:252462] equal(inverse(sk_c3),sk_c8).
% 252483 [para:252482.1.1,252438.1.1.1] equal(multiply(sk_c8,sk_c3),identity).
% 252501 [hyper:252440,252454,binarycut:252460] equal(multiply(sk_c4,sk_c8),sk_c5).
% 252504 [hyper:252440,252455,binarycut:252461] equal(multiply(sk_c8,sk_c5),sk_c7).
% 252508 [hyper:252440,252457,binarycut:252463] equal(multiply(sk_c3,sk_c8),sk_c7).
% 252512 [hyper:252440,252458,binarycut:252464] equal(multiply(sk_c8,sk_c7),sk_c6).
% 252514 [para:252438.1.1,252439.1.1.1,demod:252437] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 252515 [para:252479.1.1,252439.1.1.1,demod:252437] equal(X,multiply(sk_c8,multiply(sk_c4,X))).
% 252516 [para:252483.1.1,252439.1.1.1,demod:252437] equal(X,multiply(sk_c8,multiply(sk_c3,X))).
% 252517 [para:252501.1.1,252439.1.1.1] equal(multiply(sk_c5,X),multiply(sk_c4,multiply(sk_c8,X))).
% 252518 [para:252504.1.1,252439.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c8,multiply(sk_c5,X))).
% 252519 [para:252508.1.1,252439.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c3,multiply(sk_c8,X))).
% 252523 [para:252501.1.1,252515.1.2.2,demod:252504] equal(sk_c8,sk_c7).
% 252526 [para:252508.1.1,252516.1.2.2,demod:252512] equal(sk_c8,sk_c6).
% 252528 [para:252438.1.1,252514.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 252529 [para:252479.1.1,252514.1.2.2] equal(sk_c4,multiply(inverse(sk_c8),identity)).
% 252530 [para:252483.1.1,252514.1.2.2,demod:252529] equal(sk_c3,sk_c4).
% 252531 [para:252504.1.1,252514.1.2.2] equal(sk_c5,multiply(inverse(sk_c8),sk_c7)).
% 252532 [para:252439.1.1,252514.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 252534 [para:252515.1.2,252514.1.2.2] equal(multiply(sk_c4,X),multiply(inverse(sk_c8),X)).
% 252535 [para:252516.1.2,252514.1.2.2,demod:252534] equal(multiply(sk_c3,X),multiply(sk_c4,X)).
% 252536 [para:252514.1.2,252514.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 252539 [para:252526.1.1,252501.1.1.2,demod:252535] equal(multiply(sk_c3,sk_c6),sk_c5).
% 252541 [para:252526.1.1,252508.1.1.2,demod:252539] equal(sk_c5,sk_c7).
% 252547 [para:252541.1.2,252512.1.1.2,demod:252504] equal(sk_c7,sk_c6).
% 252548 [para:252541.1.2,252523.1.2] equal(sk_c8,sk_c5).
% 252550 [para:252547.1.1,252541.1.2] equal(sk_c5,sk_c6).
% 252556 [para:252517.1.2,252515.1.2.2,demod:252518] equal(multiply(sk_c8,X),multiply(sk_c7,X)).
% 252557 [para:252515.1.2,252517.1.2.2,demod:252535] equal(multiply(sk_c5,multiply(sk_c3,X)),multiply(sk_c3,X)).
% 252560 [para:252530.1.2,252517.1.2.1,demod:252556,252519] equal(multiply(sk_c5,X),multiply(sk_c8,X)).
% 252564 [para:252548.1.1,252515.1.2.1,demod:252557,252535] equal(X,multiply(sk_c3,X)).
% 252565 [para:252548.1.1,252516.1.2.1,demod:252564] equal(X,multiply(sk_c5,X)).
% 252569 [para:252565.1.2,252514.1.2.2] equal(X,multiply(inverse(sk_c5),X)).
% 252578 [para:252569.1.2,252438.1.1] equal(sk_c5,identity).
% 252579 [para:252578.1.1,252504.1.1.2,demod:252565,252560] equal(identity,sk_c7).
% 252585 [para:252579.1.2,252531.1.2.2,demod:252529] equal(sk_c5,sk_c4).
% 252588 [para:252585.1.2,252530.1.2] equal(sk_c3,sk_c5).
% 252590 [para:252588.1.2,252550.1.1] equal(sk_c3,sk_c6).
% 252592 [para:252590.1.1,252482.1.1.1] equal(inverse(sk_c6),sk_c8).
% 252633 [para:252536.1.2,252438.1.1] equal(multiply(X,inverse(X)),identity).
% 252635 [para:252536.1.2,252528.1.2] equal(X,multiply(X,identity)).
% 252636 [para:252635.1.2,252528.1.2] equal(X,inverse(inverse(X))).
% 252641 [para:252633.1.1,252532.1.2.2.2,demod:252635] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 252651 [para:252556.1.2,252641.1.2.1.1,demod:252565,252560] equal(inverse(X),multiply(inverse(X),sk_c7)).
% 252664 [para:252651.1.2,252536.1.2,demod:252636] equal(multiply(X,sk_c7),X).
% 252665 [hyper:252440,252664,demod:252592,cut:252523] 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 5 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c7,sk_c8),sk_c6) | -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7) | -equal(multiply(Y,sk_c7),sk_c8) | -equal(inverse(Y),sk_c7) | -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_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(35,40,0,75,0,0,763,50,6,803,0,6,1832,50,20,1872,0,20,3082,50,38,3122,0,38,4426,50,54,4466,0,54,5865,50,74,5905,0,74,7444,50,104,7484,0,104,9163,50,150,9203,0,150,11068,50,232,11108,0,232,13159,50,388,13199,0,388,15482,50,629,15522,0,629,18037,50,1051,18037,40,1051,18077,0,1051,28753,3,1352,29416,4,1502,30097,5,1652,30098,1,1652,30098,50,1652,30098,40,1652,30138,0,1652,30490,3,1966,30502,4,2128,30520,5,2253,30520,1,2253,30520,50,2253,30520,40,2253,30560,0,2253,54109,3,3761,54929,4,4504,55542,1,5254,55542,50,5255,55542,40,5255,55582,0,5255,73722,3,6006,74197,4,6381,74749,1,6756,74749,50,6756,74749,40,6756,74789,0,6756,86490,3,7510,87688,4,7882,89085,1,8257,89085,50,8257,89085,40,8257,89125,0,8257,127360,3,12158,129206,4,14108,130631,5,16058,130632,1,16058,130632,50,16059,130632,40,16059,130672,0,16059,163162,3,18613,164626,4,19885,165588,5,21160,165589,1,21160,165589,50,21161,165589,40,21161,165629,0,21162,193866,3,22663,194884,4,23413,195601,5,24163,195602,1,24163,195602,50,24164,195602,40,24164,195642,0,24164,205446,3,24927,206581,4,25299,206962,5,25665,206962,1,25665,206962,50,25665,206962,40,25665,207002,0,25665,230864,3,26866,231732,4,27466,232442,5,28066,232443,1,28066,232443,50,28067,232443,40,28067,232483,0,28067,250300,3,28818,250935,4,29193,251366,1,29568,251366,50,29568,251366,40,29568,251366,40,29568,251401,0,29568,251596,50,29569,251596,30,29569,251596,40,29569,251631,0,29569,251745,50,29569,251780,0,29571,251934,50,29572,251934,30,29572,251934,40,29572,251969,0,29573,252070,50,29573,252105,0,29573,252273,50,29575,252273,30,29575,252273,40,29575,252308,0,29577,252435,50,29578,252470,0,29578,252664,50,29579,252664,30,29579,252664,40,29579,252699,0,29581,252825,50,29582,252860,0,29582,253051,50,29584,253086,0,29584,253294,50,29588,253329,0,29590,253550,50,29595,253585,0,29595,253812,50,29603,253847,0,29605,254082,50,29619,254117,0,29619,254360,50,29648,254395,0,29648,254648,50,29708,254683,0,29708,254946,50,29822,254946,40,29822,254981,0,29822)
%
%
% START OF PROOF
% 254738 [?] ?
% 254948 [] equal(multiply(identity,X),X).
% 254949 [] equal(multiply(inverse(X),X),identity).
% 254950 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 254951 [] -equal(multiply(sk_c7,sk_c8),sk_c6).
% 254976 [?] ?
% 254977 [?] ?
% 254978 [?] ?
% 255019 [input:254976,cut:254951] equal(inverse(sk_c4),sk_c8).
% 255020 [para:255019.1.1,254949.1.1.1] equal(multiply(sk_c8,sk_c4),identity).
% 255034 [input:254977,cut:254951] equal(multiply(sk_c4,sk_c8),sk_c5).
% 255035 [input:254978,cut:254951] equal(multiply(sk_c8,sk_c5),sk_c7).
% 255056 [para:255020.1.1,254950.1.1.1,demod:254948] equal(X,multiply(sk_c8,multiply(sk_c4,X))).
% 255087 [para:255034.1.1,255056.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c5)).
% 255092 [para:255087.1.2,255035.1.1] equal(sk_c8,sk_c7).
% 255094 [para:255092.1.2,254951.1.1.1,cut:254738] 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_c8),sk_c6) | -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7) | -equal(multiply(Y,sk_c7),sk_c8) | -equal(inverse(Y),sk_c7) | -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(35,40,0,75,0,0,763,50,6,803,0,6,1832,50,20,1872,0,20,3082,50,38,3122,0,38,4426,50,54,4466,0,54,5865,50,74,5905,0,74,7444,50,104,7484,0,104,9163,50,150,9203,0,150,11068,50,232,11108,0,232,13159,50,388,13199,0,388,15482,50,629,15522,0,629,18037,50,1051,18037,40,1051,18077,0,1051,28753,3,1352,29416,4,1502,30097,5,1652,30098,1,1652,30098,50,1652,30098,40,1652,30138,0,1652,30490,3,1966,30502,4,2128,30520,5,2253,30520,1,2253,30520,50,2253,30520,40,2253,30560,0,2253,54109,3,3761,54929,4,4504,55542,1,5254,55542,50,5255,55542,40,5255,55582,0,5255,73722,3,6006,74197,4,6381,74749,1,6756,74749,50,6756,74749,40,6756,74789,0,6756,86490,3,7510,87688,4,7882,89085,1,8257,89085,50,8257,89085,40,8257,89125,0,8257,127360,3,12158,129206,4,14108,130631,5,16058,130632,1,16058,130632,50,16059,130632,40,16059,130672,0,16059,163162,3,18613,164626,4,19885,165588,5,21160,165589,1,21160,165589,50,21161,165589,40,21161,165629,0,21162,193866,3,22663,194884,4,23413,195601,5,24163,195602,1,24163,195602,50,24164,195602,40,24164,195642,0,24164,205446,3,24927,206581,4,25299,206962,5,25665,206962,1,25665,206962,50,25665,206962,40,25665,207002,0,25665,230864,3,26866,231732,4,27466,232442,5,28066,232443,1,28066,232443,50,28067,232443,40,28067,232483,0,28067,250300,3,28818,250935,4,29193,251366,1,29568,251366,50,29568,251366,40,29568,251366,40,29568,251401,0,29568,251596,50,29569,251596,30,29569,251596,40,29569,251631,0,29569,251745,50,29569,251780,0,29571,251934,50,29572,251934,30,29572,251934,40,29572,251969,0,29573,252070,50,29573,252105,0,29573,252273,50,29575,252273,30,29575,252273,40,29575,252308,0,29577,252435,50,29578,252470,0,29578,252664,50,29579,252664,30,29579,252664,40,29579,252699,0,29581,252825,50,29582,252860,0,29582,253051,50,29584,253086,0,29584,253294,50,29588,253329,0,29590,253550,50,29595,253585,0,29595,253812,50,29603,253847,0,29605,254082,50,29619,254117,0,29619,254360,50,29648,254395,0,29648,254648,50,29708,254683,0,29708,254946,50,29822,254946,40,29822,254981,0,29822,255093,50,29823,255093,30,29823,255093,40,29823,255128,0,29823,255228,50,29823,255263,0,29825,255408,50,29827,255443,0,29827,255596,50,29830,255631,0,29830,255792,50,29836,255827,0,29837,255994,50,29846,256029,0,29846,256204,50,29863,256239,0,29863,256422,50,29894,256457,0,29894,256650,50,29954,256685,0,29954,256888,50,30072,256888,40,30072,256923,0,30072)
%
%
% START OF PROOF
% 256890 [] equal(multiply(identity,X),X).
% 256891 [] equal(multiply(inverse(X),X),identity).
% 256892 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 256893 [] -equal(multiply(sk_c8,sk_c7),sk_c6).
% 256899 [?] ?
% 256905 [?] ?
% 256923 [?] ?
% 256942 [input:256899,cut:256893] equal(inverse(sk_c2),sk_c7).
% 256943 [para:256942.1.1,256891.1.1.1] equal(multiply(sk_c7,sk_c2),identity).
% 256971 [input:256905,cut:256893] equal(multiply(sk_c2,sk_c7),sk_c8).
% 256979 [input:256923,cut:256893] equal(multiply(sk_c7,sk_c8),sk_c6).
% 256980 [para:256891.1.1,256892.1.1.1,demod:256890] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 256984 [para:256943.1.1,256892.1.1.1,demod:256890] equal(X,multiply(sk_c7,multiply(sk_c2,X))).
% 257025 [para:256971.1.1,256984.1.2.2] equal(sk_c7,multiply(sk_c7,sk_c8)).
% 257031 [para:257025.1.2,256979.1.1] equal(sk_c7,sk_c6).
% 257053 [para:257031.1.1,256979.1.1.1] equal(multiply(sk_c6,sk_c8),sk_c6).
% 257116 [para:257053.1.1,256980.1.2.2,demod:256891] equal(sk_c8,identity).
% 257131 [para:257116.1.1,256893.1.1.1,demod:256890,cut:257031] 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: 36906
% derived clauses: 6007219
% kept clauses: 199115
% kept size sum: 868018
% kept mid-nuclei: 14621
% kept new demods: 4440
% forw unit-subs: 2392203
% forw double-subs: 3211575
% forw overdouble-subs: 150058
% backward subs: 15531
% fast unit cutoff: 32470
% full unit cutoff: 0
% dbl unit cutoff: 7475
% real runtime : 302.97
% process. runtime: 300.73
% specific non-discr-tree subsumption statistics:
% tried: 37596401
% length fails: 3939941
% strength fails: 12091423
% predlist fails: 4513655
% aux str. fails: 5841843
% by-lit fails: 6579914
% full subs tried: 1306080
% full subs fail: 1210878
%
% ; 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/GRP335-1+eq_r.in")
%
%------------------------------------------------------------------------------