TSTP Solution File: GRP224-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP224-1 : 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 : art01.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 298.7s
% Output : Assurance 298.7s
% 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/GRP224-1+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 29)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 3 29)
% (binary-posweight-lex-big-order 30 #f 3 29)
% (binary 30 #t)
% (binary-posweight-kb-big-order 156 #f)
% (binary-posweight-lex-big-order 102 #f)
% (binary-posweight-firstpref-order 60 #f)
% (binary-order 30 #f)
% (binary-posweight-kb-small-order 48 #f)
% (binary-posweight-lex-small-order 30 #f)
%
%
% SOS clause
% -equal(inverse(X),sk_c11) | -equal(multiply(X,sk_c10),sk_c11) | -equal(multiply(sk_c11,Y),sk_c10) | -equal(multiply(Z,sk_c11),Y) | -equal(inverse(Z),sk_c11) | -equal(multiply(U,V),sk_c11) | -equal(inverse(U),V) | -equal(multiply(V,sk_c10),sk_c11) | -equal(inverse(W),sk_c11) | -equal(multiply(W,sk_c10),sk_c11) | -equal(multiply(X1,X2),sk_c10) | -equal(inverse(X1),X2) | -equal(multiply(X2,sk_c11),sk_c10) | -equal(inverse(X3),sk_c10) | -equal(multiply(X3,sk_c11),sk_c10).
% was split for some strategies as:
% -equal(inverse(X3),sk_c10) | -equal(multiply(X3,sk_c11),sk_c10).
% -equal(multiply(X1,X2),sk_c10) | -equal(inverse(X1),X2) | -equal(multiply(X2,sk_c11),sk_c10).
% -equal(inverse(W),sk_c11) | -equal(multiply(W,sk_c10),sk_c11).
% -equal(multiply(U,V),sk_c11) | -equal(inverse(U),V) | -equal(multiply(V,sk_c10),sk_c11).
% -equal(multiply(sk_c11,Y),sk_c10) | -equal(multiply(Z,sk_c11),Y) | -equal(inverse(Z),sk_c11).
% -equal(inverse(X),sk_c11) | -equal(multiply(X,sk_c10),sk_c11).
%
% 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(inverse(X),sk_c11) | -equal(multiply(X,sk_c10),sk_c11) | -equal(multiply(sk_c11,Y),sk_c10) | -equal(multiply(Z,sk_c11),Y) | -equal(inverse(Z),sk_c11) | -equal(multiply(U,V),sk_c11) | -equal(inverse(U),V) | -equal(multiply(V,sk_c10),sk_c11) | -equal(inverse(W),sk_c11) | -equal(multiply(W,sk_c10),sk_c11) | -equal(multiply(X1,X2),sk_c10) | -equal(inverse(X1),X2) | -equal(multiply(X2,sk_c11),sk_c10) | -equal(inverse(X3),sk_c10) | -equal(multiply(X3,sk_c11),sk_c10).
% Split part used next: -equal(inverse(X3),sk_c10) | -equal(multiply(X3,sk_c11),sk_c10).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(55,40,1,117,0,1,312697,5,1502,312697,1,1502,312697,50,1502,312697,40,1502,312759,0,1502,313258,5,2105,313260,1,2106,313260,50,2106,313260,40,2106,313322,0,2106,313820,5,2707,313821,1,2707,313821,50,2707,313821,40,2707,313883,0,2707,338503,3,4208,339444,4,4958,340556,1,5708,340556,50,5709,340556,40,5709,340618,0,5709,356148,3,6464,356828,4,6835,357681,5,7210,357682,1,7210,357682,50,7210,357682,40,7210,357744,0,7210,358659,3,8677,358659,4,8677,358821,50,8678,358821,40,8678,358883,0,8678,414525,3,12582,415935,4,14529,417286,1,16479,417286,50,16481,417286,40,16481,417348,0,16481,462293,3,19036,463468,4,20307,464590,1,21582,464590,50,21583,464590,40,21583,464652,0,21583,486028,3,23085,487378,4,23834,490653,1,24584,490653,50,24584,490653,40,24584,490715,0,24585,495435,3,26069,495435,4,26069,495575,5,26086,495575,1,26086,495575,50,26086,495575,40,26086,495637,0,26086,517668,3,27290,518683,4,27887,519793,5,28487,519794,1,28487,519794,50,28488,519794,40,28488,519856,0,28488,531829,3,29239,533056,4,29614,533969,1,29989,533969,50,29989,533969,40,29989,533969,40,29989,534024,0,29989,534114,50,29990,534169,0,29990)
%
%
% START OF PROOF
% 534116 [] equal(multiply(identity,X),X).
% 534117 [] equal(multiply(inverse(X),X),identity).
% 534118 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 534119 [] -equal(multiply(X,sk_c11),sk_c10) | -equal(inverse(X),sk_c10).
% 534120 [?] ?
% 534121 [] equal(inverse(sk_c2),sk_c11) | equal(inverse(sk_c9),sk_c10).
% 534130 [] equal(multiply(sk_c2,sk_c11),sk_c3) | equal(multiply(sk_c9,sk_c11),sk_c10).
% 534131 [] equal(multiply(sk_c2,sk_c11),sk_c3) | equal(inverse(sk_c9),sk_c10).
% 534140 [] equal(multiply(sk_c11,sk_c3),sk_c10) | equal(multiply(sk_c9,sk_c11),sk_c10).
% 534141 [] equal(multiply(sk_c11,sk_c3),sk_c10) | equal(inverse(sk_c9),sk_c10).
% 534150 [] equal(multiply(sk_c1,sk_c10),sk_c11) | equal(multiply(sk_c9,sk_c11),sk_c10).
% 534151 [] equal(multiply(sk_c1,sk_c10),sk_c11) | equal(inverse(sk_c9),sk_c10).
% 534160 [?] ?
% 534161 [] equal(inverse(sk_c1),sk_c11) | equal(inverse(sk_c9),sk_c10).
% 534172 [hyper:534119,534121,binarycut:534120] equal(inverse(sk_c2),sk_c11).
% 534173 [para:534172.1.1,534117.1.1.1] equal(multiply(sk_c11,sk_c2),identity).
% 534177 [hyper:534119,534161,binarycut:534160] equal(inverse(sk_c1),sk_c11).
% 534181 [para:534177.1.1,534117.1.1.1] equal(multiply(sk_c11,sk_c1),identity).
% 534184 [hyper:534119,534131,534130] equal(multiply(sk_c2,sk_c11),sk_c3).
% 534190 [hyper:534119,534141,534140] equal(multiply(sk_c11,sk_c3),sk_c10).
% 534196 [hyper:534119,534151,534150] equal(multiply(sk_c1,sk_c10),sk_c11).
% 534197 [para:534117.1.1,534118.1.1.1,demod:534116] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 534198 [para:534173.1.1,534118.1.1.1,demod:534116] equal(X,multiply(sk_c11,multiply(sk_c2,X))).
% 534199 [para:534181.1.1,534118.1.1.1,demod:534116] equal(X,multiply(sk_c11,multiply(sk_c1,X))).
% 534200 [para:534184.1.1,534118.1.1.1] equal(multiply(sk_c3,X),multiply(sk_c2,multiply(sk_c11,X))).
% 534203 [para:534184.1.1,534198.1.2.2,demod:534190] equal(sk_c11,sk_c10).
% 534204 [para:534203.1.1,534173.1.1.1] equal(multiply(sk_c10,sk_c2),identity).
% 534206 [para:534203.1.1,534184.1.1.2] equal(multiply(sk_c2,sk_c10),sk_c3).
% 534207 [para:534203.1.1,534190.1.1.1] equal(multiply(sk_c10,sk_c3),sk_c10).
% 534210 [para:534117.1.1,534197.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 534211 [para:534173.1.1,534197.1.2.2] equal(sk_c2,multiply(inverse(sk_c11),identity)).
% 534212 [para:534181.1.1,534197.1.2.2,demod:534211] equal(sk_c1,sk_c2).
% 534215 [para:534118.1.1,534197.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 534216 [para:534198.1.2,534197.1.2.2] equal(multiply(sk_c2,X),multiply(inverse(sk_c11),X)).
% 534218 [para:534197.1.2,534197.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 534219 [para:534212.1.1,534196.1.1.1,demod:534206] equal(sk_c3,sk_c11).
% 534220 [para:534219.1.2,534173.1.1.1] equal(multiply(sk_c3,sk_c2),identity).
% 534224 [para:534219.1.2,534198.1.2.1] equal(X,multiply(sk_c3,multiply(sk_c2,X))).
% 534225 [para:534219.1.2,534203.1.1] equal(sk_c3,sk_c10).
% 534229 [para:534199.1.2,534197.1.2.2,demod:534216] equal(multiply(sk_c1,X),multiply(sk_c2,X)).
% 534231 [para:534207.1.1,534197.1.2.2,demod:534117] equal(sk_c3,identity).
% 534233 [para:534231.1.1,534190.1.1.2] equal(multiply(sk_c11,identity),sk_c10).
% 534234 [para:534231.1.1,534225.1.1] equal(identity,sk_c10).
% 534237 [para:534234.1.2,534196.1.1.2,demod:534229] equal(multiply(sk_c2,identity),sk_c11).
% 534238 [para:534234.1.2,534204.1.1.1,demod:534116] equal(sk_c2,identity).
% 534241 [para:534238.1.1,534172.1.1.1] equal(inverse(identity),sk_c11).
% 534244 [para:534173.1.1,534200.1.2.2,demod:534237,534220] equal(identity,sk_c11).
% 534247 [para:534198.1.2,534200.1.2.2,demod:534224] equal(X,multiply(sk_c2,X)).
% 534255 [para:534244.1.2,534211.1.2.1.1,demod:534233,534241] equal(sk_c2,sk_c10).
% 534256 [para:534255.1.1,534172.1.1.1] equal(inverse(sk_c10),sk_c11).
% 534274 [para:534218.1.2,534117.1.1] equal(multiply(X,inverse(X)),identity).
% 534276 [para:534218.1.2,534210.1.2] equal(X,multiply(X,identity)).
% 534278 [para:534276.1.2,534210.1.2] equal(X,inverse(inverse(X))).
% 534281 [para:534274.1.1,534215.1.2.2.2,demod:534276] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 534284 [para:534198.1.2,534281.1.2.1.1,demod:534247] equal(inverse(X),multiply(inverse(X),sk_c11)).
% 534292 [para:534284.1.2,534218.1.2,demod:534278] equal(multiply(X,sk_c11),X).
% 534294 [hyper:534119,534292,demod:534256,cut:534203] 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 29
% clause depth limited to 4
% seconds given: 4
%
%
% Split component 2 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(X),sk_c11) | -equal(multiply(X,sk_c10),sk_c11) | -equal(multiply(sk_c11,Y),sk_c10) | -equal(multiply(Z,sk_c11),Y) | -equal(inverse(Z),sk_c11) | -equal(multiply(U,V),sk_c11) | -equal(inverse(U),V) | -equal(multiply(V,sk_c10),sk_c11) | -equal(inverse(W),sk_c11) | -equal(multiply(W,sk_c10),sk_c11) | -equal(multiply(X1,X2),sk_c10) | -equal(inverse(X1),X2) | -equal(multiply(X2,sk_c11),sk_c10) | -equal(inverse(X3),sk_c10) | -equal(multiply(X3,sk_c11),sk_c10).
% Split part used next: -equal(multiply(X1,X2),sk_c10) | -equal(inverse(X1),X2) | -equal(multiply(X2,sk_c11),sk_c10).
% 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 29
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(55,40,1,117,0,1,312697,5,1502,312697,1,1502,312697,50,1502,312697,40,1502,312759,0,1502,313258,5,2105,313260,1,2106,313260,50,2106,313260,40,2106,313322,0,2106,313820,5,2707,313821,1,2707,313821,50,2707,313821,40,2707,313883,0,2707,338503,3,4208,339444,4,4958,340556,1,5708,340556,50,5709,340556,40,5709,340618,0,5709,356148,3,6464,356828,4,6835,357681,5,7210,357682,1,7210,357682,50,7210,357682,40,7210,357744,0,7210,358659,3,8677,358659,4,8677,358821,50,8678,358821,40,8678,358883,0,8678,414525,3,12582,415935,4,14529,417286,1,16479,417286,50,16481,417286,40,16481,417348,0,16481,462293,3,19036,463468,4,20307,464590,1,21582,464590,50,21583,464590,40,21583,464652,0,21583,486028,3,23085,487378,4,23834,490653,1,24584,490653,50,24584,490653,40,24584,490715,0,24585,495435,3,26069,495435,4,26069,495575,5,26086,495575,1,26086,495575,50,26086,495575,40,26086,495637,0,26086,517668,3,27290,518683,4,27887,519793,5,28487,519794,1,28487,519794,50,28488,519794,40,28488,519856,0,28488,531829,3,29239,533056,4,29614,533969,1,29989,533969,50,29989,533969,40,29989,533969,40,29989,534024,0,29989,534114,50,29990,534169,0,29990,534293,50,29991,534293,30,29991,534293,40,29991,534348,0,29995)
%
%
% START OF PROOF
% 534294 [] equal(X,X).
% 534295 [] equal(multiply(identity,X),X).
% 534296 [] equal(multiply(inverse(X),X),identity).
% 534297 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 534298 [] -equal(multiply(X,sk_c11),sk_c10) | -equal(multiply(Y,X),sk_c10) | -equal(inverse(Y),X).
% 534301 [?] ?
% 534302 [] equal(inverse(sk_c2),sk_c11) | equal(inverse(sk_c7),sk_c8).
% 534303 [?] ?
% 534311 [] equal(multiply(sk_c2,sk_c11),sk_c3) | equal(multiply(sk_c8,sk_c11),sk_c10).
% 534312 [] equal(multiply(sk_c2,sk_c11),sk_c3) | equal(inverse(sk_c7),sk_c8).
% 534313 [] equal(multiply(sk_c2,sk_c11),sk_c3) | equal(multiply(sk_c7,sk_c8),sk_c10).
% 534321 [] equal(multiply(sk_c11,sk_c3),sk_c10) | equal(multiply(sk_c8,sk_c11),sk_c10).
% 534322 [] equal(multiply(sk_c11,sk_c3),sk_c10) | equal(inverse(sk_c7),sk_c8).
% 534323 [] equal(multiply(sk_c11,sk_c3),sk_c10) | equal(multiply(sk_c7,sk_c8),sk_c10).
% 534331 [] equal(multiply(sk_c1,sk_c10),sk_c11) | equal(multiply(sk_c8,sk_c11),sk_c10).
% 534332 [] equal(multiply(sk_c1,sk_c10),sk_c11) | equal(inverse(sk_c7),sk_c8).
% 534333 [] equal(multiply(sk_c1,sk_c10),sk_c11) | equal(multiply(sk_c7,sk_c8),sk_c10).
% 534341 [?] ?
% 534342 [] equal(inverse(sk_c1),sk_c11) | equal(inverse(sk_c7),sk_c8).
% 534343 [?] ?
% 534357 [hyper:534298,534302,binarycut:534303,binarycut:534301] equal(inverse(sk_c2),sk_c11).
% 534360 [para:534357.1.1,534296.1.1.1] equal(multiply(sk_c11,sk_c2),identity).
% 534375 [hyper:534298,534342,binarycut:534343,binarycut:534341] equal(inverse(sk_c1),sk_c11).
% 534378 [para:534375.1.1,534296.1.1.1] equal(multiply(sk_c11,sk_c1),identity).
% 534416 [hyper:534298,534313,534311,534312] equal(multiply(sk_c2,sk_c11),sk_c3).
% 534453 [hyper:534298,534323,534321,534322] equal(multiply(sk_c11,sk_c3),sk_c10).
% 534471 [hyper:534298,534333,534331,534332] equal(multiply(sk_c1,sk_c10),sk_c11).
% 534472 [para:534296.1.1,534297.1.1.1,demod:534295] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 534473 [para:534360.1.1,534297.1.1.1,demod:534295] equal(X,multiply(sk_c11,multiply(sk_c2,X))).
% 534480 [para:534416.1.1,534473.1.2.2,demod:534453] equal(sk_c11,sk_c10).
% 534481 [para:534480.1.1,534360.1.1.1] equal(multiply(sk_c10,sk_c2),identity).
% 534483 [para:534480.1.1,534416.1.1.2] equal(multiply(sk_c2,sk_c10),sk_c3).
% 534484 [para:534480.1.1,534453.1.1.1] equal(multiply(sk_c10,sk_c3),sk_c10).
% 534489 [para:534360.1.1,534472.1.2.2] equal(sk_c2,multiply(inverse(sk_c11),identity)).
% 534490 [para:534378.1.1,534472.1.2.2,demod:534489] equal(sk_c1,sk_c2).
% 534492 [para:534471.1.1,534472.1.2.2,demod:534375] equal(sk_c10,multiply(sk_c11,sk_c11)).
% 534495 [para:534490.1.1,534471.1.1.1,demod:534483] equal(sk_c3,sk_c11).
% 534501 [para:534495.1.2,534480.1.1] equal(sk_c3,sk_c10).
% 534511 [para:534484.1.1,534472.1.2.2,demod:534296] equal(sk_c3,identity).
% 534514 [para:534511.1.1,534501.1.1] equal(identity,sk_c10).
% 534518 [para:534514.1.2,534481.1.1.1,demod:534295] equal(sk_c2,identity).
% 534521 [para:534518.1.1,534357.1.1.1] equal(inverse(identity),sk_c11).
% 534532 [hyper:534298,534521,demod:534492,534295,cut:534480,cut:534294] 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 29
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 3 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(X),sk_c11) | -equal(multiply(X,sk_c10),sk_c11) | -equal(multiply(sk_c11,Y),sk_c10) | -equal(multiply(Z,sk_c11),Y) | -equal(inverse(Z),sk_c11) | -equal(multiply(U,V),sk_c11) | -equal(inverse(U),V) | -equal(multiply(V,sk_c10),sk_c11) | -equal(inverse(W),sk_c11) | -equal(multiply(W,sk_c10),sk_c11) | -equal(multiply(X1,X2),sk_c10) | -equal(inverse(X1),X2) | -equal(multiply(X2,sk_c11),sk_c10) | -equal(inverse(X3),sk_c10) | -equal(multiply(X3,sk_c11),sk_c10).
% Split part used next: -equal(inverse(W),sk_c11) | -equal(multiply(W,sk_c10),sk_c11).
% 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 29
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(55,40,1,117,0,1,312697,5,1502,312697,1,1502,312697,50,1502,312697,40,1502,312759,0,1502,313258,5,2105,313260,1,2106,313260,50,2106,313260,40,2106,313322,0,2106,313820,5,2707,313821,1,2707,313821,50,2707,313821,40,2707,313883,0,2707,338503,3,4208,339444,4,4958,340556,1,5708,340556,50,5709,340556,40,5709,340618,0,5709,356148,3,6464,356828,4,6835,357681,5,7210,357682,1,7210,357682,50,7210,357682,40,7210,357744,0,7210,358659,3,8677,358659,4,8677,358821,50,8678,358821,40,8678,358883,0,8678,414525,3,12582,415935,4,14529,417286,1,16479,417286,50,16481,417286,40,16481,417348,0,16481,462293,3,19036,463468,4,20307,464590,1,21582,464590,50,21583,464590,40,21583,464652,0,21583,486028,3,23085,487378,4,23834,490653,1,24584,490653,50,24584,490653,40,24584,490715,0,24585,495435,3,26069,495435,4,26069,495575,5,26086,495575,1,26086,495575,50,26086,495575,40,26086,495637,0,26086,517668,3,27290,518683,4,27887,519793,5,28487,519794,1,28487,519794,50,28488,519794,40,28488,519856,0,28488,531829,3,29239,533056,4,29614,533969,1,29989,533969,50,29989,533969,40,29989,533969,40,29989,534024,0,29989,534114,50,29990,534169,0,29990,534293,50,29991,534293,30,29991,534293,40,29991,534348,0,29995,534531,50,29995,534531,30,29995,534531,40,29995,534586,0,29995)
%
%
% START OF PROOF
% 534532 [] equal(X,X).
% 534536 [] -equal(multiply(X,sk_c10),sk_c11) | -equal(inverse(X),sk_c11).
% 534572 [] equal(multiply(sk_c1,sk_c10),sk_c11) | equal(multiply(sk_c6,sk_c10),sk_c11).
% 534573 [?] ?
% 534582 [?] ?
% 534583 [] equal(inverse(sk_c1),sk_c11) | equal(inverse(sk_c6),sk_c11).
% 534612 [hyper:534536,534583,binarycut:534573] equal(inverse(sk_c6),sk_c11).
% 534614 [hyper:534536,534583,binarycut:534582] equal(inverse(sk_c1),sk_c11).
% 534641 [hyper:534536,534572,demod:534614,cut:534532] equal(multiply(sk_c6,sk_c10),sk_c11).
% 534655 [hyper:534536,534641,demod:534612,cut:534532] 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 29
% 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(inverse(X),sk_c11) | -equal(multiply(X,sk_c10),sk_c11) | -equal(multiply(sk_c11,Y),sk_c10) | -equal(multiply(Z,sk_c11),Y) | -equal(inverse(Z),sk_c11) | -equal(multiply(U,V),sk_c11) | -equal(inverse(U),V) | -equal(multiply(V,sk_c10),sk_c11) | -equal(inverse(W),sk_c11) | -equal(multiply(W,sk_c10),sk_c11) | -equal(multiply(X1,X2),sk_c10) | -equal(inverse(X1),X2) | -equal(multiply(X2,sk_c11),sk_c10) | -equal(inverse(X3),sk_c10) | -equal(multiply(X3,sk_c11),sk_c10).
% Split part used next: -equal(multiply(U,V),sk_c11) | -equal(inverse(U),V) | -equal(multiply(V,sk_c10),sk_c11).
% 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 29
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(55,40,1,117,0,1,312697,5,1502,312697,1,1502,312697,50,1502,312697,40,1502,312759,0,1502,313258,5,2105,313260,1,2106,313260,50,2106,313260,40,2106,313322,0,2106,313820,5,2707,313821,1,2707,313821,50,2707,313821,40,2707,313883,0,2707,338503,3,4208,339444,4,4958,340556,1,5708,340556,50,5709,340556,40,5709,340618,0,5709,356148,3,6464,356828,4,6835,357681,5,7210,357682,1,7210,357682,50,7210,357682,40,7210,357744,0,7210,358659,3,8677,358659,4,8677,358821,50,8678,358821,40,8678,358883,0,8678,414525,3,12582,415935,4,14529,417286,1,16479,417286,50,16481,417286,40,16481,417348,0,16481,462293,3,19036,463468,4,20307,464590,1,21582,464590,50,21583,464590,40,21583,464652,0,21583,486028,3,23085,487378,4,23834,490653,1,24584,490653,50,24584,490653,40,24584,490715,0,24585,495435,3,26069,495435,4,26069,495575,5,26086,495575,1,26086,495575,50,26086,495575,40,26086,495637,0,26086,517668,3,27290,518683,4,27887,519793,5,28487,519794,1,28487,519794,50,28488,519794,40,28488,519856,0,28488,531829,3,29239,533056,4,29614,533969,1,29989,533969,50,29989,533969,40,29989,533969,40,29989,534024,0,29989,534114,50,29990,534169,0,29990,534293,50,29991,534293,30,29991,534293,40,29991,534348,0,29995,534531,50,29995,534531,30,29995,534531,40,29995,534586,0,29995,534654,50,29996,534654,30,29996,534654,40,29996,534709,0,30001)
%
%
% START OF PROOF
% 534655 [] equal(X,X).
% 534656 [] equal(multiply(identity,X),X).
% 534657 [] equal(multiply(inverse(X),X),identity).
% 534658 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 534659 [] -equal(multiply(X,sk_c10),sk_c11) | -equal(multiply(Y,X),sk_c11) | -equal(inverse(Y),X).
% 534667 [?] ?
% 534668 [] equal(inverse(sk_c2),sk_c11) | equal(inverse(sk_c4),sk_c5).
% 534669 [?] ?
% 534677 [] equal(multiply(sk_c2,sk_c11),sk_c3) | equal(multiply(sk_c5,sk_c10),sk_c11).
% 534678 [] equal(multiply(sk_c2,sk_c11),sk_c3) | equal(inverse(sk_c4),sk_c5).
% 534679 [] equal(multiply(sk_c2,sk_c11),sk_c3) | equal(multiply(sk_c4,sk_c5),sk_c11).
% 534687 [] equal(multiply(sk_c11,sk_c3),sk_c10) | equal(multiply(sk_c5,sk_c10),sk_c11).
% 534688 [] equal(multiply(sk_c11,sk_c3),sk_c10) | equal(inverse(sk_c4),sk_c5).
% 534689 [] equal(multiply(sk_c11,sk_c3),sk_c10) | equal(multiply(sk_c4,sk_c5),sk_c11).
% 534697 [] equal(multiply(sk_c1,sk_c10),sk_c11) | equal(multiply(sk_c5,sk_c10),sk_c11).
% 534698 [] equal(multiply(sk_c1,sk_c10),sk_c11) | equal(inverse(sk_c4),sk_c5).
% 534699 [] equal(multiply(sk_c1,sk_c10),sk_c11) | equal(multiply(sk_c4,sk_c5),sk_c11).
% 534707 [?] ?
% 534708 [] equal(inverse(sk_c1),sk_c11) | equal(inverse(sk_c4),sk_c5).
% 534709 [?] ?
% 534727 [hyper:534659,534668,binarycut:534669,binarycut:534667] equal(inverse(sk_c2),sk_c11).
% 534730 [para:534727.1.1,534657.1.1.1] equal(multiply(sk_c11,sk_c2),identity).
% 534751 [hyper:534659,534708,binarycut:534709,binarycut:534707] equal(inverse(sk_c1),sk_c11).
% 534754 [para:534751.1.1,534657.1.1.1] equal(multiply(sk_c11,sk_c1),identity).
% 534824 [hyper:534659,534679,534677,534678] equal(multiply(sk_c2,sk_c11),sk_c3).
% 534842 [hyper:534659,534689,534687,534688] equal(multiply(sk_c11,sk_c3),sk_c10).
% 534882 [hyper:534659,534699,534697,534698] equal(multiply(sk_c1,sk_c10),sk_c11).
% 534889 [para:534657.1.1,534658.1.1.1,demod:534656] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 534890 [para:534730.1.1,534658.1.1.1,demod:534656] equal(X,multiply(sk_c11,multiply(sk_c2,X))).
% 534897 [para:534824.1.1,534890.1.2.2,demod:534842] equal(sk_c11,sk_c10).
% 534898 [para:534897.1.1,534730.1.1.1] equal(multiply(sk_c10,sk_c2),identity).
% 534899 [para:534897.1.1,534754.1.1.1] equal(multiply(sk_c10,sk_c1),identity).
% 534900 [para:534897.1.1,534824.1.1.2] equal(multiply(sk_c2,sk_c10),sk_c3).
% 534901 [para:534897.1.1,534842.1.1.1] equal(multiply(sk_c10,sk_c3),sk_c10).
% 534906 [para:534730.1.1,534889.1.2.2] equal(sk_c2,multiply(inverse(sk_c11),identity)).
% 534907 [para:534754.1.1,534889.1.2.2,demod:534906] equal(sk_c1,sk_c2).
% 534912 [para:534907.1.1,534882.1.1.1,demod:534900] equal(sk_c3,sk_c11).
% 534918 [para:534912.1.2,534897.1.1] equal(sk_c3,sk_c10).
% 534919 [para:534918.1.1,534842.1.1.2] equal(multiply(sk_c11,sk_c10),sk_c10).
% 534926 [para:534901.1.1,534889.1.2.2,demod:534657] equal(sk_c3,identity).
% 534929 [para:534926.1.1,534918.1.1] equal(identity,sk_c10).
% 534933 [para:534929.1.2,534898.1.1.1,demod:534656] equal(sk_c2,identity).
% 534934 [para:534929.1.2,534899.1.1.1,demod:534656] equal(sk_c1,identity).
% 534936 [para:534933.1.1,534727.1.1.1] equal(inverse(identity),sk_c11).
% 534944 [para:534934.1.1,534882.1.1.1,demod:534656] equal(sk_c10,sk_c11).
% 534947 [hyper:534659,534936,demod:534919,534656,cut:534655,cut:534944] 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 29
% 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(inverse(X),sk_c11) | -equal(multiply(X,sk_c10),sk_c11) | -equal(multiply(sk_c11,Y),sk_c10) | -equal(multiply(Z,sk_c11),Y) | -equal(inverse(Z),sk_c11) | -equal(multiply(U,V),sk_c11) | -equal(inverse(U),V) | -equal(multiply(V,sk_c10),sk_c11) | -equal(inverse(W),sk_c11) | -equal(multiply(W,sk_c10),sk_c11) | -equal(multiply(X1,X2),sk_c10) | -equal(inverse(X1),X2) | -equal(multiply(X2,sk_c11),sk_c10) | -equal(inverse(X3),sk_c10) | -equal(multiply(X3,sk_c11),sk_c10).
% Split part used next: -equal(multiply(sk_c11,Y),sk_c10) | -equal(multiply(Z,sk_c11),Y) | -equal(inverse(Z),sk_c11).
% 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 29
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(55,40,1,117,0,1,312697,5,1502,312697,1,1502,312697,50,1502,312697,40,1502,312759,0,1502,313258,5,2105,313260,1,2106,313260,50,2106,313260,40,2106,313322,0,2106,313820,5,2707,313821,1,2707,313821,50,2707,313821,40,2707,313883,0,2707,338503,3,4208,339444,4,4958,340556,1,5708,340556,50,5709,340556,40,5709,340618,0,5709,356148,3,6464,356828,4,6835,357681,5,7210,357682,1,7210,357682,50,7210,357682,40,7210,357744,0,7210,358659,3,8677,358659,4,8677,358821,50,8678,358821,40,8678,358883,0,8678,414525,3,12582,415935,4,14529,417286,1,16479,417286,50,16481,417286,40,16481,417348,0,16481,462293,3,19036,463468,4,20307,464590,1,21582,464590,50,21583,464590,40,21583,464652,0,21583,486028,3,23085,487378,4,23834,490653,1,24584,490653,50,24584,490653,40,24584,490715,0,24585,495435,3,26069,495435,4,26069,495575,5,26086,495575,1,26086,495575,50,26086,495575,40,26086,495637,0,26086,517668,3,27290,518683,4,27887,519793,5,28487,519794,1,28487,519794,50,28488,519794,40,28488,519856,0,28488,531829,3,29239,533056,4,29614,533969,1,29989,533969,50,29989,533969,40,29989,533969,40,29989,534024,0,29989,534114,50,29990,534169,0,29990,534293,50,29991,534293,30,29991,534293,40,29991,534348,0,29995,534531,50,29995,534531,30,29995,534531,40,29995,534586,0,29995,534654,50,29996,534654,30,29996,534654,40,29996,534709,0,30001,534946,50,30001,534946,30,30001,534946,40,30001,535001,0,30002)
%
%
% START OF PROOF
% 534948 [] equal(multiply(identity,X),X).
% 534949 [] equal(multiply(inverse(X),X),identity).
% 534950 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 534951 [] -equal(multiply(sk_c11,X),sk_c10) | -equal(multiply(Y,sk_c11),X) | -equal(inverse(Y),sk_c11).
% 534952 [] equal(multiply(sk_c9,sk_c11),sk_c10) | equal(inverse(sk_c2),sk_c11).
% 534953 [] equal(inverse(sk_c2),sk_c11) | equal(inverse(sk_c9),sk_c10).
% 534957 [] equal(multiply(sk_c6,sk_c10),sk_c11) | equal(inverse(sk_c2),sk_c11).
% 534958 [] equal(inverse(sk_c2),sk_c11) | equal(inverse(sk_c6),sk_c11).
% 534960 [] equal(inverse(sk_c2),sk_c11) | equal(inverse(sk_c4),sk_c5).
% 534961 [] equal(multiply(sk_c4,sk_c5),sk_c11) | equal(inverse(sk_c2),sk_c11).
% 534962 [] equal(multiply(sk_c2,sk_c11),sk_c3) | equal(multiply(sk_c9,sk_c11),sk_c10).
% 534963 [] equal(multiply(sk_c2,sk_c11),sk_c3) | equal(inverse(sk_c9),sk_c10).
% 534967 [] equal(multiply(sk_c2,sk_c11),sk_c3) | equal(multiply(sk_c6,sk_c10),sk_c11).
% 534968 [] equal(multiply(sk_c2,sk_c11),sk_c3) | equal(inverse(sk_c6),sk_c11).
% 534970 [] equal(multiply(sk_c2,sk_c11),sk_c3) | equal(inverse(sk_c4),sk_c5).
% 534971 [] equal(multiply(sk_c2,sk_c11),sk_c3) | equal(multiply(sk_c4,sk_c5),sk_c11).
% 534972 [?] ?
% 534973 [?] ?
% 534977 [?] ?
% 534978 [?] ?
% 534980 [?] ?
% 534981 [?] ?
% 535086 [hyper:534951,534963,binarycut:534973,binarycut:534953] equal(inverse(sk_c9),sk_c10).
% 535097 [hyper:534951,534962,534952,binarycut:534972] equal(multiply(sk_c9,sk_c11),sk_c10).
% 535104 [hyper:534951,534968,binarycut:534978,binarycut:534958] equal(inverse(sk_c6),sk_c11).
% 535111 [para:535104.1.1,534949.1.1.1] equal(multiply(sk_c11,sk_c6),identity).
% 535125 [hyper:534951,534970,binarycut:534980,binarycut:534960] equal(inverse(sk_c4),sk_c5).
% 535126 [para:535125.1.1,534949.1.1.1] equal(multiply(sk_c5,sk_c4),identity).
% 535149 [hyper:534951,534967,534957,binarycut:534977] equal(multiply(sk_c6,sk_c10),sk_c11).
% 535162 [hyper:534951,534971,534961,binarycut:534981] equal(multiply(sk_c4,sk_c5),sk_c11).
% 535163 [para:534949.1.1,534950.1.1.1,demod:534948] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 535167 [para:535111.1.1,534950.1.1.1,demod:534948] equal(X,multiply(sk_c11,multiply(sk_c6,X))).
% 535169 [para:535126.1.1,534950.1.1.1,demod:534948] equal(X,multiply(sk_c5,multiply(sk_c4,X))).
% 535184 [para:535149.1.1,535167.1.2.2] equal(sk_c10,multiply(sk_c11,sk_c11)).
% 535194 [para:535162.1.1,535163.1.2.2,demod:535125] equal(sk_c5,multiply(sk_c5,sk_c11)).
% 535205 [para:535194.1.2,535163.1.2.2,demod:534949] equal(sk_c11,identity).
% 535207 [para:535205.1.1,535111.1.1.1,demod:534948] equal(sk_c6,identity).
% 535210 [para:535205.1.1,535184.1.2.1,demod:534948] equal(sk_c10,sk_c11).
% 535216 [para:535207.1.1,535167.1.2.2.1,demod:534948] equal(X,multiply(sk_c11,X)).
% 535240 [hyper:534951,535169,535097,demod:535216,535169,demod:535086,cut:535210] 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 29
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 6 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(X),sk_c11) | -equal(multiply(X,sk_c10),sk_c11) | -equal(multiply(sk_c11,Y),sk_c10) | -equal(multiply(Z,sk_c11),Y) | -equal(inverse(Z),sk_c11) | -equal(multiply(U,V),sk_c11) | -equal(inverse(U),V) | -equal(multiply(V,sk_c10),sk_c11) | -equal(inverse(W),sk_c11) | -equal(multiply(W,sk_c10),sk_c11) | -equal(multiply(X1,X2),sk_c10) | -equal(inverse(X1),X2) | -equal(multiply(X2,sk_c11),sk_c10) | -equal(inverse(X3),sk_c10) | -equal(multiply(X3,sk_c11),sk_c10).
% Split part used next: -equal(inverse(X),sk_c11) | -equal(multiply(X,sk_c10),sk_c11).
% 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 29
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(55,40,1,117,0,1,312697,5,1502,312697,1,1502,312697,50,1502,312697,40,1502,312759,0,1502,313258,5,2105,313260,1,2106,313260,50,2106,313260,40,2106,313322,0,2106,313820,5,2707,313821,1,2707,313821,50,2707,313821,40,2707,313883,0,2707,338503,3,4208,339444,4,4958,340556,1,5708,340556,50,5709,340556,40,5709,340618,0,5709,356148,3,6464,356828,4,6835,357681,5,7210,357682,1,7210,357682,50,7210,357682,40,7210,357744,0,7210,358659,3,8677,358659,4,8677,358821,50,8678,358821,40,8678,358883,0,8678,414525,3,12582,415935,4,14529,417286,1,16479,417286,50,16481,417286,40,16481,417348,0,16481,462293,3,19036,463468,4,20307,464590,1,21582,464590,50,21583,464590,40,21583,464652,0,21583,486028,3,23085,487378,4,23834,490653,1,24584,490653,50,24584,490653,40,24584,490715,0,24585,495435,3,26069,495435,4,26069,495575,5,26086,495575,1,26086,495575,50,26086,495575,40,26086,495637,0,26086,517668,3,27290,518683,4,27887,519793,5,28487,519794,1,28487,519794,50,28488,519794,40,28488,519856,0,28488,531829,3,29239,533056,4,29614,533969,1,29989,533969,50,29989,533969,40,29989,533969,40,29989,534024,0,29989,534114,50,29990,534169,0,29990,534293,50,29991,534293,30,29991,534293,40,29991,534348,0,29995,534531,50,29995,534531,30,29995,534531,40,29995,534586,0,29995,534654,50,29996,534654,30,29996,534654,40,29996,534709,0,30001,534946,50,30001,534946,30,30001,534946,40,30001,535001,0,30002,535239,50,30002,535239,30,30002,535239,40,30002,535294,0,30007)
%
%
% START OF PROOF
% 535240 [] equal(X,X).
% 535244 [] -equal(multiply(X,sk_c10),sk_c11) | -equal(inverse(X),sk_c11).
% 535280 [] equal(multiply(sk_c1,sk_c10),sk_c11) | equal(multiply(sk_c6,sk_c10),sk_c11).
% 535281 [?] ?
% 535290 [?] ?
% 535291 [] equal(inverse(sk_c1),sk_c11) | equal(inverse(sk_c6),sk_c11).
% 535320 [hyper:535244,535291,binarycut:535281] equal(inverse(sk_c6),sk_c11).
% 535322 [hyper:535244,535291,binarycut:535290] equal(inverse(sk_c1),sk_c11).
% 535349 [hyper:535244,535280,demod:535322,cut:535240] equal(multiply(sk_c6,sk_c10),sk_c11).
% 535363 [hyper:535244,535349,demod:535320,cut:535240] 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 29
% clause depth limited to 3
% seconds given: 4
%
%
% Split attempt finished with SUCCESS.
%
% ***GANDALF_FOUND_A_REFUTATION***
%
% Global statistics over all passes:
%
% given clauses: 25925
% derived clauses: 6251687
% kept clauses: 185886
% kept size sum: 712496
% kept mid-nuclei: 312839
% kept new demods: 1495
% forw unit-subs: 3368322
% forw double-subs: 2079397
% forw overdouble-subs: 267617
% backward subs: 8726
% fast unit cutoff: 9450
% full unit cutoff: 0
% dbl unit cutoff: 3456
% real runtime : 301.72
% process. runtime: 300.7
% specific non-discr-tree subsumption statistics:
% tried: 101716081
% length fails: 19416161
% strength fails: 28871984
% predlist fails: 551373
% aux str. fails: 14907183
% by-lit fails: 14295501
% full subs tried: 7540894
% full subs fail: 7393310
%
% ; 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/GRP224-1+eq_r.in")
%
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