TSTP Solution File: GRP283-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP283-1 : TPTP v3.4.2. Released v2.5.0.
% Transfm : add_equality:r
% Format : otter:hypothesis:set(auto),clear(print_given)
% Command : gandalf-wrapper -time %d %s
% Computer : art06.cs.miami.edu
% Model : i686 unknown
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 1000MB
% OS : Linux 2.4.22-21mdk-i686-up-4GB
% CPULimit : 600s
% Result : Unsatisfiable 298.2s
% Output : Assurance 298.2s
% 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/GRP283-1+eq_r.in
% Using automatic strategy selection.
% Time limit in seconds: 600
%
% prove-all-passes started
%
% detected problem class: peq
%
% strategies selected:
% (hyper 30 #f 3 23)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 3 23)
% (binary-posweight-lex-big-order 30 #f 3 23)
% (binary 30 #t)
% (binary-posweight-kb-big-order 156 #f)
% (binary-posweight-lex-big-order 102 #f)
% (binary-posweight-firstpref-order 60 #f)
% (binary-order 30 #f)
% (binary-posweight-kb-small-order 48 #f)
% (binary-posweight-lex-small-order 30 #f)
%
%
% SOS clause
% -equal(multiply(sk_c8,sk_c7),sk_c6) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8) | -equal(multiply(sk_c7,sk_c6),sk_c8) | -equal(inverse(sk_c7),sk_c6) | -equal(multiply(U,sk_c7),sk_c8) | -equal(inverse(U),sk_c7) | -equal(multiply(V,sk_c8),sk_c6) | -equal(inverse(V),sk_c8).
% was split for some strategies as:
% -equal(multiply(V,sk_c8),sk_c6) | -equal(inverse(V),sk_c8).
% -equal(multiply(U,sk_c7),sk_c8) | -equal(inverse(U),sk_c7).
% -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8).
% -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8).
% -equal(multiply(sk_c8,sk_c7),sk_c6).
% -equal(multiply(sk_c7,sk_c6),sk_c8).
% -equal(inverse(sk_c7),sk_c6).
%
% Starting a split proof attempt with 7 components.
%
% Split component 1 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c8,sk_c7),sk_c6) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8) | -equal(multiply(sk_c7,sk_c6),sk_c8) | -equal(inverse(sk_c7),sk_c6) | -equal(multiply(U,sk_c7),sk_c8) | -equal(inverse(U),sk_c7) | -equal(multiply(V,sk_c8),sk_c6) | -equal(inverse(V),sk_c8).
% Split part used next: -equal(multiply(V,sk_c8),sk_c6) | -equal(inverse(V),sk_c8).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(41,40,0,87,0,0,862,50,7,908,0,7,2015,50,24,2061,0,24,3459,50,44,3505,0,44,5031,50,65,5077,0,65,6770,50,94,6816,0,94,8637,50,134,8683,0,134,10673,50,197,10719,0,197,12879,50,304,12925,0,304,15296,50,479,15342,0,479,17925,50,744,17971,0,744,20807,50,1247,20807,40,1247,20853,0,1247,31053,3,1548,31744,4,1698,32397,1,1848,32397,50,1848,32397,40,1848,32443,0,1848,32707,3,2163,32718,4,2320,32730,5,2449,32730,1,2449,32730,50,2449,32730,40,2449,32776,0,2449,63932,3,3956,64602,4,4700,65529,1,5450,65529,50,5451,65529,40,5451,65575,0,5451,82836,3,6202,83658,4,6577,84356,5,6952,84357,1,6952,84357,50,6952,84357,40,6952,84403,0,6952,94272,3,7707,95732,4,8078,97291,5,8453,97292,5,8453,97292,1,8453,97292,50,8453,97292,40,8453,97338,0,8453,161537,3,12355,162566,4,14304,163316,1,16254,163316,50,16256,163316,40,16256,163362,0,16256,214975,3,18807,215871,4,20082,216648,5,21357,216649,1,21357,216649,50,21359,216649,40,21359,216695,0,21359,255391,3,22860,256275,4,23610,256867,1,24360,256867,50,24361,256867,40,24361,256913,0,24361,265249,3,25121,266234,4,25489,266383,5,25862,266383,1,25862,266383,50,25862,266383,40,25862,266429,0,25862,295157,3,27063,295882,4,27663,296556,1,28263,296556,50,28264,296556,40,28264,296602,0,28264,318579,3,29015,319209,4,29390,319677,1,29765,319677,50,29765,319677,40,29765,319677,40,29765,319718,0,29765)
%
%
% START OF PROOF
% 319679 [] equal(multiply(identity,X),X).
% 319680 [] equal(multiply(inverse(X),X),identity).
% 319681 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 319682 [] -equal(multiply(X,sk_c8),sk_c6) | -equal(inverse(X),sk_c8).
% 319683 [] equal(inverse(sk_c2),sk_c8) | equal(inverse(sk_c5),sk_c8).
% 319684 [?] ?
% 319689 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(inverse(sk_c5),sk_c8).
% 319690 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(multiply(sk_c5,sk_c8),sk_c6).
% 319695 [] equal(multiply(sk_c8,sk_c3),sk_c7) | equal(inverse(sk_c5),sk_c8).
% 319696 [] equal(multiply(sk_c8,sk_c3),sk_c7) | equal(multiply(sk_c5,sk_c8),sk_c6).
% 319701 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c5),sk_c8).
% 319702 [?] ?
% 319707 [] equal(multiply(sk_c1,sk_c8),sk_c7) | equal(inverse(sk_c5),sk_c8).
% 319708 [] equal(multiply(sk_c1,sk_c8),sk_c7) | equal(multiply(sk_c5,sk_c8),sk_c6).
% 319713 [] equal(multiply(sk_c8,sk_c7),sk_c6) | equal(inverse(sk_c5),sk_c8).
% 319714 [] equal(multiply(sk_c8,sk_c7),sk_c6) | equal(multiply(sk_c5,sk_c8),sk_c6).
% 319722 [hyper:319682,319683,binarycut:319684] equal(inverse(sk_c2),sk_c8).
% 319724 [para:319722.1.1,319680.1.1.1] equal(multiply(sk_c8,sk_c2),identity).
% 319732 [hyper:319682,319701,binarycut:319702] equal(inverse(sk_c1),sk_c8).
% 319735 [para:319732.1.1,319680.1.1.1] equal(multiply(sk_c8,sk_c1),identity).
% 319740 [hyper:319682,319690,319689] equal(multiply(sk_c2,sk_c8),sk_c3).
% 319746 [hyper:319682,319696,319695] equal(multiply(sk_c8,sk_c3),sk_c7).
% 319752 [hyper:319682,319708,319707] equal(multiply(sk_c1,sk_c8),sk_c7).
% 319760 [hyper:319682,319714,319713] equal(multiply(sk_c8,sk_c7),sk_c6).
% 319761 [para:319680.1.1,319681.1.1.1,demod:319679] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 319762 [para:319724.1.1,319681.1.1.1,demod:319679] equal(X,multiply(sk_c8,multiply(sk_c2,X))).
% 319768 [para:319740.1.1,319762.1.2.2,demod:319746] equal(sk_c8,sk_c7).
% 319772 [para:319768.1.1,319746.1.1.1] equal(multiply(sk_c7,sk_c3),sk_c7).
% 319778 [para:319724.1.1,319761.1.2.2] equal(sk_c2,multiply(inverse(sk_c8),identity)).
% 319779 [para:319735.1.1,319761.1.2.2,demod:319778] equal(sk_c1,sk_c2).
% 319781 [para:319752.1.1,319761.1.2.2,demod:319760,319732] equal(sk_c8,sk_c6).
% 319785 [para:319779.1.2,319740.1.1.1,demod:319752] equal(sk_c7,sk_c3).
% 319786 [para:319781.1.1,319724.1.1.1] equal(multiply(sk_c6,sk_c2),identity).
% 319793 [para:319781.1.1,319768.1.1] equal(sk_c6,sk_c7).
% 319798 [para:319793.1.2,319785.1.1] equal(sk_c6,sk_c3).
% 319805 [para:319772.1.1,319761.1.2.2,demod:319680] equal(sk_c3,identity).
% 319809 [para:319805.1.1,319798.1.2] equal(sk_c6,identity).
% 319823 [para:319809.1.1,319786.1.1.1,demod:319679] equal(sk_c2,identity).
% 319824 [para:319823.1.1,319722.1.1.1] equal(inverse(identity),sk_c8).
% 319832 [hyper:319682,319824,demod:319679,cut:319781] 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 23
% 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_c8,sk_c7),sk_c6) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8) | -equal(multiply(sk_c7,sk_c6),sk_c8) | -equal(inverse(sk_c7),sk_c6) | -equal(multiply(U,sk_c7),sk_c8) | -equal(inverse(U),sk_c7) | -equal(multiply(V,sk_c8),sk_c6) | -equal(inverse(V),sk_c8).
% Split part used next: -equal(multiply(U,sk_c7),sk_c8) | -equal(inverse(U),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 23
% 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 23
% clause depth limited to 4
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(41,40,0,87,0,0,862,50,7,908,0,7,2015,50,24,2061,0,24,3459,50,44,3505,0,44,5031,50,65,5077,0,65,6770,50,94,6816,0,94,8637,50,134,8683,0,134,10673,50,197,10719,0,197,12879,50,304,12925,0,304,15296,50,479,15342,0,479,17925,50,744,17971,0,744,20807,50,1247,20807,40,1247,20853,0,1247,31053,3,1548,31744,4,1698,32397,1,1848,32397,50,1848,32397,40,1848,32443,0,1848,32707,3,2163,32718,4,2320,32730,5,2449,32730,1,2449,32730,50,2449,32730,40,2449,32776,0,2449,63932,3,3956,64602,4,4700,65529,1,5450,65529,50,5451,65529,40,5451,65575,0,5451,82836,3,6202,83658,4,6577,84356,5,6952,84357,1,6952,84357,50,6952,84357,40,6952,84403,0,6952,94272,3,7707,95732,4,8078,97291,5,8453,97292,5,8453,97292,1,8453,97292,50,8453,97292,40,8453,97338,0,8453,161537,3,12355,162566,4,14304,163316,1,16254,163316,50,16256,163316,40,16256,163362,0,16256,214975,3,18807,215871,4,20082,216648,5,21357,216649,1,21357,216649,50,21359,216649,40,21359,216695,0,21359,255391,3,22860,256275,4,23610,256867,1,24360,256867,50,24361,256867,40,24361,256913,0,24361,265249,3,25121,266234,4,25489,266383,5,25862,266383,1,25862,266383,50,25862,266383,40,25862,266429,0,25862,295157,3,27063,295882,4,27663,296556,1,28263,296556,50,28264,296556,40,28264,296602,0,28264,318579,3,29015,319209,4,29390,319677,1,29765,319677,50,29765,319677,40,29765,319677,40,29765,319718,0,29765,319831,50,29765,319831,30,29765,319831,40,29765,319872,0,29765,320009,50,29766,320050,0,29771)
%
%
% START OF PROOF
% 320011 [] equal(multiply(identity,X),X).
% 320012 [] equal(multiply(inverse(X),X),identity).
% 320013 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 320014 [] -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c7).
% 320017 [] equal(inverse(sk_c2),sk_c8) | equal(inverse(sk_c4),sk_c7).
% 320018 [?] ?
% 320023 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(inverse(sk_c4),sk_c7).
% 320024 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(multiply(sk_c4,sk_c7),sk_c8).
% 320029 [] equal(multiply(sk_c8,sk_c3),sk_c7) | equal(inverse(sk_c4),sk_c7).
% 320030 [] equal(multiply(sk_c8,sk_c3),sk_c7) | equal(multiply(sk_c4,sk_c7),sk_c8).
% 320035 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c4),sk_c7).
% 320036 [?] ?
% 320041 [] equal(multiply(sk_c1,sk_c8),sk_c7) | equal(inverse(sk_c4),sk_c7).
% 320042 [] equal(multiply(sk_c1,sk_c8),sk_c7) | equal(multiply(sk_c4,sk_c7),sk_c8).
% 320047 [] equal(multiply(sk_c8,sk_c7),sk_c6) | equal(inverse(sk_c4),sk_c7).
% 320048 [] equal(multiply(sk_c8,sk_c7),sk_c6) | equal(multiply(sk_c4,sk_c7),sk_c8).
% 320054 [hyper:320014,320017,binarycut:320018] equal(inverse(sk_c2),sk_c8).
% 320056 [para:320054.1.1,320012.1.1.1] equal(multiply(sk_c8,sk_c2),identity).
% 320061 [hyper:320014,320035,binarycut:320036] equal(inverse(sk_c1),sk_c8).
% 320062 [para:320061.1.1,320012.1.1.1] equal(multiply(sk_c8,sk_c1),identity).
% 320075 [hyper:320014,320024,320023] equal(multiply(sk_c2,sk_c8),sk_c3).
% 320089 [hyper:320014,320030,320029] equal(multiply(sk_c8,sk_c3),sk_c7).
% 320093 [hyper:320014,320042,320041] equal(multiply(sk_c1,sk_c8),sk_c7).
% 320097 [hyper:320014,320048,320047] equal(multiply(sk_c8,sk_c7),sk_c6).
% 320098 [para:320012.1.1,320013.1.1.1,demod:320011] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 320099 [para:320056.1.1,320013.1.1.1,demod:320011] equal(X,multiply(sk_c8,multiply(sk_c2,X))).
% 320100 [para:320062.1.1,320013.1.1.1,demod:320011] equal(X,multiply(sk_c8,multiply(sk_c1,X))).
% 320101 [para:320075.1.1,320013.1.1.1] equal(multiply(sk_c3,X),multiply(sk_c2,multiply(sk_c8,X))).
% 320105 [para:320075.1.1,320099.1.2.2,demod:320089] equal(sk_c8,sk_c7).
% 320109 [para:320105.1.1,320089.1.1.1] equal(multiply(sk_c7,sk_c3),sk_c7).
% 320115 [para:320012.1.1,320098.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 320116 [para:320056.1.1,320098.1.2.2] equal(sk_c2,multiply(inverse(sk_c8),identity)).
% 320117 [para:320062.1.1,320098.1.2.2,demod:320116] equal(sk_c1,sk_c2).
% 320118 [para:320089.1.1,320098.1.2.2] equal(sk_c3,multiply(inverse(sk_c8),sk_c7)).
% 320119 [para:320093.1.1,320098.1.2.2,demod:320097,320061] equal(sk_c8,sk_c6).
% 320120 [para:320013.1.1,320098.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 320122 [para:320099.1.2,320098.1.2.2] equal(multiply(sk_c2,X),multiply(inverse(sk_c8),X)).
% 320124 [para:320098.1.2,320098.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 320125 [para:320117.1.2,320075.1.1.1,demod:320093] equal(sk_c7,sk_c3).
% 320126 [para:320119.1.1,320056.1.1.1] equal(multiply(sk_c6,sk_c2),identity).
% 320128 [para:320119.1.1,320075.1.1.2] equal(multiply(sk_c2,sk_c6),sk_c3).
% 320133 [para:320119.1.1,320105.1.1] equal(sk_c6,sk_c7).
% 320138 [para:320133.1.2,320125.1.1] equal(sk_c6,sk_c3).
% 320140 [para:320100.1.2,320098.1.2.2,demod:320122] equal(multiply(sk_c1,X),multiply(sk_c2,X)).
% 320145 [para:320109.1.1,320098.1.2.2,demod:320012] equal(sk_c3,identity).
% 320148 [para:320145.1.1,320089.1.1.2] equal(multiply(sk_c8,identity),sk_c7).
% 320149 [para:320145.1.1,320138.1.2] equal(sk_c6,identity).
% 320155 [para:320099.1.2,320101.1.2.2,demod:320140] equal(multiply(sk_c3,multiply(sk_c1,X)),multiply(sk_c1,X)).
% 320164 [para:320149.1.1,320126.1.1.1,demod:320011] equal(sk_c2,identity).
% 320166 [para:320164.1.1,320056.1.1.2,demod:320148] equal(sk_c7,identity).
% 320167 [para:320164.1.1,320075.1.1.1,demod:320011] equal(sk_c8,sk_c3).
% 320172 [para:320167.1.1,320099.1.2.1,demod:320155,320140] equal(X,multiply(sk_c1,X)).
% 320180 [para:320166.1.1,320118.1.2.2,demod:320116] equal(sk_c3,sk_c2).
% 320182 [para:320180.1.2,320117.1.2] equal(sk_c1,sk_c3).
% 320184 [para:320182.1.2,320138.1.2] equal(sk_c6,sk_c1).
% 320188 [para:320075.1.1,320120.1.2.2.2] equal(sk_c8,multiply(inverse(multiply(X,sk_c2)),multiply(X,sk_c3))).
% 320202 [para:320128.1.1,320120.1.2.2.2,demod:320188] equal(sk_c6,sk_c8).
% 320204 [para:320184.1.2,320061.1.1.1] equal(inverse(sk_c6),sk_c8).
% 320205 [para:320202.1.2,320116.1.2.1.1,demod:320148,320204] equal(sk_c2,sk_c7).
% 320210 [para:320124.1.2,320012.1.1] equal(multiply(X,inverse(X)),identity).
% 320212 [para:320124.1.2,320115.1.2] equal(X,multiply(X,identity)).
% 320215 [para:320212.1.2,320115.1.2] equal(X,inverse(inverse(X))).
% 320217 [para:320212.1.2,320116.1.2] equal(sk_c2,inverse(sk_c8)).
% 320220 [para:320210.1.1,320120.1.2.2.2,demod:320212] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 320224 [para:320099.1.2,320220.1.2.1.1,demod:320172,320140] equal(inverse(X),multiply(inverse(X),sk_c8)).
% 320234 [para:320224.1.2,320124.1.2,demod:320215] equal(multiply(X,sk_c8),X).
% 320237 [para:320105.1.1,320234.1.1.2] equal(multiply(X,sk_c7),X).
% 320242 [hyper:320014,320237,demod:320217,cut:320205] 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 23
% 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_c8,sk_c7),sk_c6) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8) | -equal(multiply(sk_c7,sk_c6),sk_c8) | -equal(inverse(sk_c7),sk_c6) | -equal(multiply(U,sk_c7),sk_c8) | -equal(inverse(U),sk_c7) | -equal(multiply(V,sk_c8),sk_c6) | -equal(inverse(V),sk_c8).
% Split part used next: -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -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 23
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(41,40,0,87,0,0,862,50,7,908,0,7,2015,50,24,2061,0,24,3459,50,44,3505,0,44,5031,50,65,5077,0,65,6770,50,94,6816,0,94,8637,50,134,8683,0,134,10673,50,197,10719,0,197,12879,50,304,12925,0,304,15296,50,479,15342,0,479,17925,50,744,17971,0,744,20807,50,1247,20807,40,1247,20853,0,1247,31053,3,1548,31744,4,1698,32397,1,1848,32397,50,1848,32397,40,1848,32443,0,1848,32707,3,2163,32718,4,2320,32730,5,2449,32730,1,2449,32730,50,2449,32730,40,2449,32776,0,2449,63932,3,3956,64602,4,4700,65529,1,5450,65529,50,5451,65529,40,5451,65575,0,5451,82836,3,6202,83658,4,6577,84356,5,6952,84357,1,6952,84357,50,6952,84357,40,6952,84403,0,6952,94272,3,7707,95732,4,8078,97291,5,8453,97292,5,8453,97292,1,8453,97292,50,8453,97292,40,8453,97338,0,8453,161537,3,12355,162566,4,14304,163316,1,16254,163316,50,16256,163316,40,16256,163362,0,16256,214975,3,18807,215871,4,20082,216648,5,21357,216649,1,21357,216649,50,21359,216649,40,21359,216695,0,21359,255391,3,22860,256275,4,23610,256867,1,24360,256867,50,24361,256867,40,24361,256913,0,24361,265249,3,25121,266234,4,25489,266383,5,25862,266383,1,25862,266383,50,25862,266383,40,25862,266429,0,25862,295157,3,27063,295882,4,27663,296556,1,28263,296556,50,28264,296556,40,28264,296602,0,28264,318579,3,29015,319209,4,29390,319677,1,29765,319677,50,29765,319677,40,29765,319677,40,29765,319718,0,29765,319831,50,29765,319831,30,29765,319831,40,29765,319872,0,29765,320009,50,29766,320050,0,29771,320241,50,29773,320241,30,29773,320241,40,29773,320282,0,29773)
%
%
% START OF PROOF
% 320242 [] equal(X,X).
% 320243 [] equal(multiply(identity,X),X).
% 320244 [] equal(multiply(inverse(X),X),identity).
% 320245 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 320246 [] -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8).
% 320247 [] equal(inverse(sk_c2),sk_c8) | equal(inverse(sk_c5),sk_c8).
% 320248 [] equal(multiply(sk_c5,sk_c8),sk_c6) | equal(inverse(sk_c2),sk_c8).
% 320249 [] equal(inverse(sk_c2),sk_c8) | equal(inverse(sk_c4),sk_c7).
% 320250 [] equal(multiply(sk_c4,sk_c7),sk_c8) | equal(inverse(sk_c2),sk_c8).
% 320251 [] equal(inverse(sk_c2),sk_c8) | equal(inverse(sk_c7),sk_c6).
% 320253 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(inverse(sk_c5),sk_c8).
% 320254 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(multiply(sk_c5,sk_c8),sk_c6).
% 320255 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(inverse(sk_c4),sk_c7).
% 320256 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(multiply(sk_c4,sk_c7),sk_c8).
% 320257 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(inverse(sk_c7),sk_c6).
% 320259 [?] ?
% 320260 [?] ?
% 320261 [?] ?
% 320262 [?] ?
% 320263 [?] ?
% 320338 [hyper:320246,320253,binarycut:320259,binarycut:320247] equal(inverse(sk_c5),sk_c8).
% 320348 [para:320338.1.1,320244.1.1.1] equal(multiply(sk_c8,sk_c5),identity).
% 320354 [hyper:320246,320255,binarycut:320261,binarycut:320249] equal(inverse(sk_c4),sk_c7).
% 320359 [hyper:320246,320254,320248,binarycut:320260] equal(multiply(sk_c5,sk_c8),sk_c6).
% 320362 [para:320354.1.1,320244.1.1.1] equal(multiply(sk_c7,sk_c4),identity).
% 320367 [hyper:320246,320257,binarycut:320263,binarycut:320251] equal(inverse(sk_c7),sk_c6).
% 320368 [para:320367.1.1,320244.1.1.1] equal(multiply(sk_c6,sk_c7),identity).
% 320372 [hyper:320246,320256,320250,binarycut:320262] equal(multiply(sk_c4,sk_c7),sk_c8).
% 320382 [para:320244.1.1,320245.1.1.1,demod:320243] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 320383 [para:320348.1.1,320245.1.1.1,demod:320243] equal(X,multiply(sk_c8,multiply(sk_c5,X))).
% 320391 [para:320359.1.1,320383.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c6)).
% 320397 [para:320362.1.1,320382.1.2.2,demod:320367] equal(sk_c4,multiply(sk_c6,identity)).
% 320399 [para:320372.1.1,320382.1.2.2,demod:320354] equal(sk_c7,multiply(sk_c7,sk_c8)).
% 320405 [para:320399.1.2,320382.1.2.2,demod:320368,320367] equal(sk_c8,identity).
% 320406 [para:320405.1.1,320348.1.1.1,demod:320243] equal(sk_c5,identity).
% 320409 [para:320405.1.1,320391.1.2.1,demod:320243] equal(sk_c8,sk_c6).
% 320411 [para:320406.1.1,320338.1.1.1] equal(inverse(identity),sk_c8).
% 320413 [para:320406.1.1,320383.1.2.2.1,demod:320243] equal(X,multiply(sk_c8,X)).
% 320417 [para:320409.1.1,320405.1.1] equal(sk_c6,identity).
% 320425 [para:320417.1.1,320397.1.2.1,demod:320243] equal(sk_c4,identity).
% 320431 [para:320425.1.1,320354.1.1.1,demod:320411] equal(sk_c8,sk_c7).
% 320447 [hyper:320246,320411,320242,demod:320413,320243,cut:320431] 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 23
% 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_c8,sk_c7),sk_c6) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8) | -equal(multiply(sk_c7,sk_c6),sk_c8) | -equal(inverse(sk_c7),sk_c6) | -equal(multiply(U,sk_c7),sk_c8) | -equal(inverse(U),sk_c7) | -equal(multiply(V,sk_c8),sk_c6) | -equal(inverse(V),sk_c8).
% Split part used next: -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(41,40,0,87,0,0,862,50,7,908,0,7,2015,50,24,2061,0,24,3459,50,44,3505,0,44,5031,50,65,5077,0,65,6770,50,94,6816,0,94,8637,50,134,8683,0,134,10673,50,197,10719,0,197,12879,50,304,12925,0,304,15296,50,479,15342,0,479,17925,50,744,17971,0,744,20807,50,1247,20807,40,1247,20853,0,1247,31053,3,1548,31744,4,1698,32397,1,1848,32397,50,1848,32397,40,1848,32443,0,1848,32707,3,2163,32718,4,2320,32730,5,2449,32730,1,2449,32730,50,2449,32730,40,2449,32776,0,2449,63932,3,3956,64602,4,4700,65529,1,5450,65529,50,5451,65529,40,5451,65575,0,5451,82836,3,6202,83658,4,6577,84356,5,6952,84357,1,6952,84357,50,6952,84357,40,6952,84403,0,6952,94272,3,7707,95732,4,8078,97291,5,8453,97292,5,8453,97292,1,8453,97292,50,8453,97292,40,8453,97338,0,8453,161537,3,12355,162566,4,14304,163316,1,16254,163316,50,16256,163316,40,16256,163362,0,16256,214975,3,18807,215871,4,20082,216648,5,21357,216649,1,21357,216649,50,21359,216649,40,21359,216695,0,21359,255391,3,22860,256275,4,23610,256867,1,24360,256867,50,24361,256867,40,24361,256913,0,24361,265249,3,25121,266234,4,25489,266383,5,25862,266383,1,25862,266383,50,25862,266383,40,25862,266429,0,25862,295157,3,27063,295882,4,27663,296556,1,28263,296556,50,28264,296556,40,28264,296602,0,28264,318579,3,29015,319209,4,29390,319677,1,29765,319677,50,29765,319677,40,29765,319677,40,29765,319718,0,29765,319831,50,29765,319831,30,29765,319831,40,29765,319872,0,29765,320009,50,29766,320050,0,29771,320241,50,29773,320241,30,29773,320241,40,29773,320282,0,29773,320446,50,29773,320446,30,29773,320446,40,29773,320487,0,29773)
%
%
% START OF PROOF
% 320448 [] equal(multiply(identity,X),X).
% 320449 [] equal(multiply(inverse(X),X),identity).
% 320450 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 320451 [] -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8).
% 320470 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c5),sk_c8).
% 320471 [] equal(multiply(sk_c5,sk_c8),sk_c6) | equal(inverse(sk_c1),sk_c8).
% 320472 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c4),sk_c7).
% 320473 [] equal(multiply(sk_c4,sk_c7),sk_c8) | equal(inverse(sk_c1),sk_c8).
% 320474 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c7),sk_c6).
% 320475 [] equal(multiply(sk_c7,sk_c6),sk_c8) | equal(inverse(sk_c1),sk_c8).
% 320476 [?] ?
% 320477 [?] ?
% 320478 [?] ?
% 320479 [?] ?
% 320480 [?] ?
% 320481 [?] ?
% 320499 [hyper:320451,320470,binarycut:320476] equal(inverse(sk_c5),sk_c8).
% 320503 [para:320499.1.1,320449.1.1.1] equal(multiply(sk_c8,sk_c5),identity).
% 320507 [hyper:320451,320472,binarycut:320478] equal(inverse(sk_c4),sk_c7).
% 320511 [para:320507.1.1,320449.1.1.1] equal(multiply(sk_c7,sk_c4),identity).
% 320514 [hyper:320451,320474,binarycut:320480] equal(inverse(sk_c7),sk_c6).
% 320515 [para:320514.1.1,320449.1.1.1] equal(multiply(sk_c6,sk_c7),identity).
% 320524 [hyper:320451,320471,binarycut:320477] equal(multiply(sk_c5,sk_c8),sk_c6).
% 320528 [hyper:320451,320473,binarycut:320479] equal(multiply(sk_c4,sk_c7),sk_c8).
% 320531 [hyper:320451,320475,binarycut:320481] equal(multiply(sk_c7,sk_c6),sk_c8).
% 320532 [para:320449.1.1,320450.1.1.1,demod:320448] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 320533 [para:320503.1.1,320450.1.1.1,demod:320448] equal(X,multiply(sk_c8,multiply(sk_c5,X))).
% 320534 [para:320511.1.1,320450.1.1.1,demod:320448] equal(X,multiply(sk_c7,multiply(sk_c4,X))).
% 320539 [para:320524.1.1,320533.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c6)).
% 320541 [para:320528.1.1,320534.1.2.2] equal(sk_c7,multiply(sk_c7,sk_c8)).
% 320550 [para:320541.1.2,320532.1.2.2,demod:320515,320514] equal(sk_c8,identity).
% 320551 [para:320550.1.1,320503.1.1.1,demod:320448] equal(sk_c5,identity).
% 320553 [para:320550.1.1,320533.1.2.1,demod:320448] equal(X,multiply(sk_c5,X)).
% 320554 [para:320550.1.1,320539.1.2.1,demod:320448] equal(sk_c8,sk_c6).
% 320556 [para:320551.1.1,320499.1.1.1] equal(inverse(identity),sk_c8).
% 320560 [para:320554.1.1,320533.1.2.1,demod:320553] equal(X,multiply(sk_c6,X)).
% 320561 [para:320554.1.1,320541.1.2.2,demod:320531] equal(sk_c7,sk_c8).
% 320565 [para:320561.1.2,320524.1.1.2,demod:320553] equal(sk_c7,sk_c6).
% 320569 [para:320565.1.1,320511.1.1.1,demod:320560] equal(sk_c4,identity).
% 320573 [para:320569.1.1,320507.1.1.1,demod:320556] equal(sk_c8,sk_c7).
% 320582 [hyper:320451,320556,demod:320448,cut:320573] 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 23
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 5 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c8,sk_c7),sk_c6) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8) | -equal(multiply(sk_c7,sk_c6),sk_c8) | -equal(inverse(sk_c7),sk_c6) | -equal(multiply(U,sk_c7),sk_c8) | -equal(inverse(U),sk_c7) | -equal(multiply(V,sk_c8),sk_c6) | -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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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(41,40,0,87,0,0,862,50,7,908,0,7,2015,50,24,2061,0,24,3459,50,44,3505,0,44,5031,50,65,5077,0,65,6770,50,94,6816,0,94,8637,50,134,8683,0,134,10673,50,197,10719,0,197,12879,50,304,12925,0,304,15296,50,479,15342,0,479,17925,50,744,17971,0,744,20807,50,1247,20807,40,1247,20853,0,1247,31053,3,1548,31744,4,1698,32397,1,1848,32397,50,1848,32397,40,1848,32443,0,1848,32707,3,2163,32718,4,2320,32730,5,2449,32730,1,2449,32730,50,2449,32730,40,2449,32776,0,2449,63932,3,3956,64602,4,4700,65529,1,5450,65529,50,5451,65529,40,5451,65575,0,5451,82836,3,6202,83658,4,6577,84356,5,6952,84357,1,6952,84357,50,6952,84357,40,6952,84403,0,6952,94272,3,7707,95732,4,8078,97291,5,8453,97292,5,8453,97292,1,8453,97292,50,8453,97292,40,8453,97338,0,8453,161537,3,12355,162566,4,14304,163316,1,16254,163316,50,16256,163316,40,16256,163362,0,16256,214975,3,18807,215871,4,20082,216648,5,21357,216649,1,21357,216649,50,21359,216649,40,21359,216695,0,21359,255391,3,22860,256275,4,23610,256867,1,24360,256867,50,24361,256867,40,24361,256913,0,24361,265249,3,25121,266234,4,25489,266383,5,25862,266383,1,25862,266383,50,25862,266383,40,25862,266429,0,25862,295157,3,27063,295882,4,27663,296556,1,28263,296556,50,28264,296556,40,28264,296602,0,28264,318579,3,29015,319209,4,29390,319677,1,29765,319677,50,29765,319677,40,29765,319677,40,29765,319718,0,29765,319831,50,29765,319831,30,29765,319831,40,29765,319872,0,29765,320009,50,29766,320050,0,29771,320241,50,29773,320241,30,29773,320241,40,29773,320282,0,29773,320446,50,29773,320446,30,29773,320446,40,29773,320487,0,29773,320581,50,29773,320581,30,29773,320581,40,29773,320622,0,29777,320728,50,29777,320769,0,29777,320916,50,29780,320957,0,29784,321112,50,29788,321153,0,29788,321316,50,29793,321357,0,29793,321526,50,29801,321567,0,29805,321744,50,29819,321785,0,29820,321970,50,29847,322011,0,29852,322206,50,29908,322247,0,29908,322452,50,30029,322452,40,30029,322493,0,30029)
%
%
% START OF PROOF
% 322335 [?] ?
% 322454 [] equal(multiply(identity,X),X).
% 322455 [] equal(multiply(inverse(X),X),identity).
% 322456 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 322457 [] -equal(multiply(sk_c8,sk_c7),sk_c6).
% 322490 [?] ?
% 322491 [?] ?
% 322492 [?] ?
% 322547 [input:322490,cut:322457] equal(inverse(sk_c4),sk_c7).
% 322548 [para:322547.1.1,322455.1.1.1] equal(multiply(sk_c7,sk_c4),identity).
% 322549 [input:322492,cut:322457] equal(inverse(sk_c7),sk_c6).
% 322550 [para:322549.1.1,322455.1.1.1] equal(multiply(sk_c6,sk_c7),identity).
% 322564 [input:322491,cut:322457] equal(multiply(sk_c4,sk_c7),sk_c8).
% 322592 [para:322548.1.1,322456.1.1.1,demod:322454] equal(X,multiply(sk_c7,multiply(sk_c4,X))).
% 322593 [para:322550.1.1,322456.1.1.1,demod:322454] equal(X,multiply(sk_c6,multiply(sk_c7,X))).
% 322630 [para:322564.1.1,322592.1.2.2] equal(sk_c7,multiply(sk_c7,sk_c8)).
% 322640 [para:322630.1.2,322593.1.2.2,demod:322550] equal(sk_c8,identity).
% 322641 [para:322640.1.1,322457.1.1.1,demod:322454,cut:322335] 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_c8,sk_c7),sk_c6) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8) | -equal(multiply(sk_c7,sk_c6),sk_c8) | -equal(inverse(sk_c7),sk_c6) | -equal(multiply(U,sk_c7),sk_c8) | -equal(inverse(U),sk_c7) | -equal(multiply(V,sk_c8),sk_c6) | -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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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(41,40,0,87,0,0,862,50,7,908,0,7,2015,50,24,2061,0,24,3459,50,44,3505,0,44,5031,50,65,5077,0,65,6770,50,94,6816,0,94,8637,50,134,8683,0,134,10673,50,197,10719,0,197,12879,50,304,12925,0,304,15296,50,479,15342,0,479,17925,50,744,17971,0,744,20807,50,1247,20807,40,1247,20853,0,1247,31053,3,1548,31744,4,1698,32397,1,1848,32397,50,1848,32397,40,1848,32443,0,1848,32707,3,2163,32718,4,2320,32730,5,2449,32730,1,2449,32730,50,2449,32730,40,2449,32776,0,2449,63932,3,3956,64602,4,4700,65529,1,5450,65529,50,5451,65529,40,5451,65575,0,5451,82836,3,6202,83658,4,6577,84356,5,6952,84357,1,6952,84357,50,6952,84357,40,6952,84403,0,6952,94272,3,7707,95732,4,8078,97291,5,8453,97292,5,8453,97292,1,8453,97292,50,8453,97292,40,8453,97338,0,8453,161537,3,12355,162566,4,14304,163316,1,16254,163316,50,16256,163316,40,16256,163362,0,16256,214975,3,18807,215871,4,20082,216648,5,21357,216649,1,21357,216649,50,21359,216649,40,21359,216695,0,21359,255391,3,22860,256275,4,23610,256867,1,24360,256867,50,24361,256867,40,24361,256913,0,24361,265249,3,25121,266234,4,25489,266383,5,25862,266383,1,25862,266383,50,25862,266383,40,25862,266429,0,25862,295157,3,27063,295882,4,27663,296556,1,28263,296556,50,28264,296556,40,28264,296602,0,28264,318579,3,29015,319209,4,29390,319677,1,29765,319677,50,29765,319677,40,29765,319677,40,29765,319718,0,29765,319831,50,29765,319831,30,29765,319831,40,29765,319872,0,29765,320009,50,29766,320050,0,29771,320241,50,29773,320241,30,29773,320241,40,29773,320282,0,29773,320446,50,29773,320446,30,29773,320446,40,29773,320487,0,29773,320581,50,29773,320581,30,29773,320581,40,29773,320622,0,29777,320728,50,29777,320769,0,29777,320916,50,29780,320957,0,29784,321112,50,29788,321153,0,29788,321316,50,29793,321357,0,29793,321526,50,29801,321567,0,29805,321744,50,29819,321785,0,29820,321970,50,29847,322011,0,29852,322206,50,29908,322247,0,29908,322452,50,30029,322452,40,30029,322493,0,30029,322640,50,30030,322640,30,30030,322640,40,30030,322681,0,30030,322821,50,30031,322862,0,30036,323052,50,30040,323093,0,30040,323291,50,30045,323332,0,30045,323538,50,30053,323579,0,30057,323791,50,30068,323832,0,30068,324052,50,30087,324093,0,30092,324321,50,30126,324362,0,30126,324600,50,30195,324641,0,30196,324889,50,30324,324889,40,30324,324930,0,30324)
%
%
% START OF PROOF
% 324832 [?] ?
% 324891 [] equal(multiply(identity,X),X).
% 324892 [] equal(multiply(inverse(X),X),identity).
% 324893 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 324894 [] -equal(multiply(sk_c7,sk_c6),sk_c8).
% 324900 [?] ?
% 324906 [?] ?
% 324912 [?] ?
% 324953 [input:324900,cut:324894] equal(inverse(sk_c2),sk_c8).
% 324954 [para:324953.1.1,324892.1.1.1] equal(multiply(sk_c8,sk_c2),identity).
% 324981 [input:324906,cut:324894] equal(multiply(sk_c2,sk_c8),sk_c3).
% 324993 [input:324912,cut:324894] equal(multiply(sk_c8,sk_c3),sk_c7).
% 325009 [para:324954.1.1,324893.1.1.1,demod:324891] equal(X,multiply(sk_c8,multiply(sk_c2,X))).
% 325059 [para:324981.1.1,325009.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c3)).
% 325065 [para:325059.1.2,324993.1.1] equal(sk_c8,sk_c7).
% 325067 [para:325065.1.1,324894.1.2,cut:324832] 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 7 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c8,sk_c7),sk_c6) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8) | -equal(multiply(sk_c7,sk_c6),sk_c8) | -equal(inverse(sk_c7),sk_c6) | -equal(multiply(U,sk_c7),sk_c8) | -equal(inverse(U),sk_c7) | -equal(multiply(V,sk_c8),sk_c6) | -equal(inverse(V),sk_c8).
% Split part used next: -equal(inverse(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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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(41,40,0,87,0,0,862,50,7,908,0,7,2015,50,24,2061,0,24,3459,50,44,3505,0,44,5031,50,65,5077,0,65,6770,50,94,6816,0,94,8637,50,134,8683,0,134,10673,50,197,10719,0,197,12879,50,304,12925,0,304,15296,50,479,15342,0,479,17925,50,744,17971,0,744,20807,50,1247,20807,40,1247,20853,0,1247,31053,3,1548,31744,4,1698,32397,1,1848,32397,50,1848,32397,40,1848,32443,0,1848,32707,3,2163,32718,4,2320,32730,5,2449,32730,1,2449,32730,50,2449,32730,40,2449,32776,0,2449,63932,3,3956,64602,4,4700,65529,1,5450,65529,50,5451,65529,40,5451,65575,0,5451,82836,3,6202,83658,4,6577,84356,5,6952,84357,1,6952,84357,50,6952,84357,40,6952,84403,0,6952,94272,3,7707,95732,4,8078,97291,5,8453,97292,5,8453,97292,1,8453,97292,50,8453,97292,40,8453,97338,0,8453,161537,3,12355,162566,4,14304,163316,1,16254,163316,50,16256,163316,40,16256,163362,0,16256,214975,3,18807,215871,4,20082,216648,5,21357,216649,1,21357,216649,50,21359,216649,40,21359,216695,0,21359,255391,3,22860,256275,4,23610,256867,1,24360,256867,50,24361,256867,40,24361,256913,0,24361,265249,3,25121,266234,4,25489,266383,5,25862,266383,1,25862,266383,50,25862,266383,40,25862,266429,0,25862,295157,3,27063,295882,4,27663,296556,1,28263,296556,50,28264,296556,40,28264,296602,0,28264,318579,3,29015,319209,4,29390,319677,1,29765,319677,50,29765,319677,40,29765,319677,40,29765,319718,0,29765,319831,50,29765,319831,30,29765,319831,40,29765,319872,0,29765,320009,50,29766,320050,0,29771,320241,50,29773,320241,30,29773,320241,40,29773,320282,0,29773,320446,50,29773,320446,30,29773,320446,40,29773,320487,0,29773,320581,50,29773,320581,30,29773,320581,40,29773,320622,0,29777,320728,50,29777,320769,0,29777,320916,50,29780,320957,0,29784,321112,50,29788,321153,0,29788,321316,50,29793,321357,0,29793,321526,50,29801,321567,0,29805,321744,50,29819,321785,0,29820,321970,50,29847,322011,0,29852,322206,50,29908,322247,0,29908,322452,50,30029,322452,40,30029,322493,0,30029,322640,50,30030,322640,30,30030,322640,40,30030,322681,0,30030,322821,50,30031,322862,0,30036,323052,50,30040,323093,0,30040,323291,50,30045,323332,0,30045,323538,50,30053,323579,0,30057,323791,50,30068,323832,0,30068,324052,50,30087,324093,0,30092,324321,50,30126,324362,0,30126,324600,50,30195,324641,0,30196,324889,50,30324,324889,40,30324,324930,0,30324,325066,50,30325,325066,30,30325,325066,40,30325,325107,0,30325,325247,50,30326,325288,0,30330,325478,50,30334,325519,0,30334,325717,50,30339,325758,0,30339,325964,50,30347,326005,0,30351,326217,50,30362,326258,0,30362,326478,50,30381,326519,0,30387,326747,50,30421,326788,0,30421,327026,50,30491,327067,0,30491,327315,50,30620,327315,40,30620,327356,0,30620)
%
%
% START OF PROOF
% 327317 [] equal(multiply(identity,X),X).
% 327318 [] equal(multiply(inverse(X),X),identity).
% 327319 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 327320 [] -equal(inverse(sk_c7),sk_c6).
% 327325 [?] ?
% 327331 [?] ?
% 327337 [?] ?
% 327343 [?] ?
% 327349 [?] ?
% 327355 [?] ?
% 327365 [input:327325,cut:327320] equal(inverse(sk_c2),sk_c8).
% 327366 [para:327365.1.1,327318.1.1.1] equal(multiply(sk_c8,sk_c2),identity).
% 327374 [input:327343,cut:327320] equal(inverse(sk_c1),sk_c8).
% 327375 [para:327374.1.1,327318.1.1.1] equal(multiply(sk_c8,sk_c1),identity).
% 327382 [input:327331,cut:327320] equal(multiply(sk_c2,sk_c8),sk_c3).
% 327387 [input:327337,cut:327320] equal(multiply(sk_c8,sk_c3),sk_c7).
% 327396 [input:327349,cut:327320] equal(multiply(sk_c1,sk_c8),sk_c7).
% 327402 [input:327355,cut:327320] equal(multiply(sk_c8,sk_c7),sk_c6).
% 327418 [para:327318.1.1,327319.1.1.1,demod:327317] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 327420 [para:327366.1.1,327319.1.1.1,demod:327317] equal(X,multiply(sk_c8,multiply(sk_c2,X))).
% 327422 [para:327375.1.1,327319.1.1.1,demod:327317] equal(X,multiply(sk_c8,multiply(sk_c1,X))).
% 327431 [para:327387.1.1,327319.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c8,multiply(sk_c3,X))).
% 327461 [para:327382.1.1,327420.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c3)).
% 327464 [para:327461.1.2,327387.1.1] equal(sk_c8,sk_c7).
% 327465 [para:327461.1.2,327319.1.1.1,demod:327431] equal(multiply(sk_c8,X),multiply(sk_c7,X)).
% 327467 [para:327464.1.1,327366.1.1.1] equal(multiply(sk_c7,sk_c2),identity).
% 327480 [para:327464.1.1,327396.1.1.2] equal(multiply(sk_c1,sk_c7),sk_c7).
% 327483 [para:327464.1.1,327402.1.1.1] equal(multiply(sk_c7,sk_c7),sk_c6).
% 327499 [para:327396.1.1,327422.1.2.2,demod:327483,327465] equal(sk_c8,sk_c6).
% 327500 [para:327480.1.1,327422.1.2.2,demod:327483,327465] equal(sk_c7,sk_c6).
% 327518 [para:327499.1.1,327402.1.1.1] equal(multiply(sk_c6,sk_c7),sk_c6).
% 327526 [para:327500.1.1,327320.1.1.1] -equal(inverse(sk_c6),sk_c6).
% 327617 [para:327518.1.1,327418.1.2.2,demod:327318] equal(sk_c7,identity).
% 327636 [para:327617.1.1,327467.1.1.1,demod:327317] equal(sk_c2,identity).
% 327640 [para:327617.1.1,327500.1.1] equal(identity,sk_c6).
% 327662 [para:327636.1.1,327365.1.1.1] equal(inverse(identity),sk_c8).
% 327668 [para:327640.1.2,327526.1.1.1,demod:327662,cut:327499] 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: 35444
% derived clauses: 6304814
% kept clauses: 270749
% kept size sum: 339864
% kept mid-nuclei: 14547
% kept new demods: 6101
% forw unit-subs: 2540445
% forw double-subs: 3197487
% forw overdouble-subs: 234253
% backward subs: 9146
% fast unit cutoff: 16732
% full unit cutoff: 0
% dbl unit cutoff: 9775
% real runtime : 308.49
% process. runtime: 306.21
% specific non-discr-tree subsumption statistics:
% tried: 41878415
% length fails: 4267274
% strength fails: 13089867
% predlist fails: 3013958
% aux str. fails: 5282887
% by-lit fails: 8673297
% full subs tried: 1890769
% full subs fail: 1783110
%
% ; 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/GRP283-1+eq_r.in")
%
%------------------------------------------------------------------------------