TSTP Solution File: GRP221-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP221-1 : 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 : art04.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/GRP221-1+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 27)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 3 27)
% (binary-posweight-lex-big-order 30 #f 3 27)
% (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_c10) | -equal(multiply(X,sk_c9),sk_c10) | -equal(multiply(Y,Z),sk_c9) | -equal(inverse(Y),Z) | -equal(multiply(Z,sk_c10),sk_c9) | -equal(multiply(sk_c10,U),sk_c9) | -equal(multiply(V,sk_c10),U) | -equal(inverse(V),sk_c10) | -equal(inverse(sk_c10),sk_c9) | -equal(inverse(W),sk_c10) | -equal(multiply(W,sk_c9),sk_c10) | -equal(multiply(sk_c10,X1),sk_c9) | -equal(multiply(X2,sk_c10),X1) | -equal(inverse(X2),sk_c10).
% was split for some strategies as:
% -equal(multiply(sk_c10,X1),sk_c9) | -equal(multiply(X2,sk_c10),X1) | -equal(inverse(X2),sk_c10).
% -equal(inverse(W),sk_c10) | -equal(multiply(W,sk_c9),sk_c10).
% -equal(multiply(sk_c10,U),sk_c9) | -equal(multiply(V,sk_c10),U) | -equal(inverse(V),sk_c10).
% -equal(multiply(Y,Z),sk_c9) | -equal(inverse(Y),Z) | -equal(multiply(Z,sk_c10),sk_c9).
% -equal(inverse(X),sk_c10) | -equal(multiply(X,sk_c9),sk_c10).
% -equal(inverse(sk_c10),sk_c9).
%
% 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_c10) | -equal(multiply(X,sk_c9),sk_c10) | -equal(multiply(Y,Z),sk_c9) | -equal(inverse(Y),Z) | -equal(multiply(Z,sk_c10),sk_c9) | -equal(multiply(sk_c10,U),sk_c9) | -equal(multiply(V,sk_c10),U) | -equal(inverse(V),sk_c10) | -equal(inverse(sk_c10),sk_c9) | -equal(inverse(W),sk_c10) | -equal(multiply(W,sk_c9),sk_c10) | -equal(multiply(sk_c10,X1),sk_c9) | -equal(multiply(X2,sk_c10),X1) | -equal(inverse(X2),sk_c10).
% Split part used next: -equal(multiply(sk_c10,X1),sk_c9) | -equal(multiply(X2,sk_c10),X1) | -equal(inverse(X2),sk_c10).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(53,40,0,112,0,0,342519,5,1501,342519,1,1501,342519,50,1501,342519,40,1501,342578,0,1501,354924,3,1802,355593,4,1952,356173,5,2102,356174,1,2102,356174,50,2102,356174,40,2102,356233,0,2102,356920,3,2420,356931,4,2584,356954,5,2703,356954,1,2703,356954,50,2703,356954,40,2703,357013,0,2703,378299,3,4204,379179,4,4954,379805,1,5704,379805,50,5704,379805,40,5704,379864,0,5704,396380,3,6455,397093,4,6830,397486,1,7205,397486,50,7205,397486,40,7205,397545,0,7205,408547,3,7967,409679,4,8331,411194,5,8706,411194,1,8706,411194,50,8706,411194,40,8706,411253,0,8706,476731,3,12608,477637,4,14558,478088,5,16507,478089,1,16507,478089,50,16509,478089,40,16509,478148,0,16509,525736,3,19060,526539,4,20335,527047,1,21610,527047,50,21611,527047,40,21611,527106,0,21611,575610,3,23116,576105,4,23862,576758,5,24612,576759,1,24612,576759,50,24614,576759,40,24614,576818,0,24614,585271,3,25384,586853,4,25740,587138,5,26115,587138,1,26115,587138,50,26115,587138,40,26115,587197,0,26115,608021,3,27316,608966,4,27916,609762,1,28516,609762,50,28516,609762,40,28516,609821,0,28516,626624,3,29267,627409,4,29642,628156,1,30017,628156,50,30017,628156,40,30017,628156,40,30017,628209,0,30017)
%
%
% START OF PROOF
% 628157 [] equal(X,X).
% 628161 [] -equal(multiply(sk_c10,X),sk_c9) | -equal(multiply(Y,sk_c10),X) | -equal(inverse(Y),sk_c10).
% 628162 [] equal(inverse(sk_c4),sk_c10) | equal(inverse(sk_c7),sk_c10).
% 628163 [] equal(multiply(sk_c7,sk_c10),sk_c8) | equal(inverse(sk_c4),sk_c10).
% 628164 [?] ?
% 628168 [] equal(multiply(sk_c4,sk_c10),sk_c5) | equal(inverse(sk_c7),sk_c10).
% 628169 [] equal(multiply(sk_c4,sk_c10),sk_c5) | equal(multiply(sk_c7,sk_c10),sk_c8).
% 628170 [] equal(multiply(sk_c4,sk_c10),sk_c5) | equal(multiply(sk_c10,sk_c8),sk_c9).
% 628174 [?] ?
% 628175 [?] ?
% 628176 [?] ?
% 628252 [hyper:628161,628163,628162,binarycut:628164] equal(inverse(sk_c4),sk_c10).
% 628273 [hyper:628161,628168,demod:628252,cut:628157,binarycut:628174] equal(inverse(sk_c7),sk_c10).
% 628302 [hyper:628161,628169,demod:628252,cut:628157,binarycut:628175] equal(multiply(sk_c7,sk_c10),sk_c8).
% 628315 [hyper:628161,628170,demod:628252,cut:628157,binarycut:628176] equal(multiply(sk_c10,sk_c8),sk_c9).
% 628319 [hyper:628161,628315,628302,demod:628273,cut:628157] 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 27
% 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(inverse(X),sk_c10) | -equal(multiply(X,sk_c9),sk_c10) | -equal(multiply(Y,Z),sk_c9) | -equal(inverse(Y),Z) | -equal(multiply(Z,sk_c10),sk_c9) | -equal(multiply(sk_c10,U),sk_c9) | -equal(multiply(V,sk_c10),U) | -equal(inverse(V),sk_c10) | -equal(inverse(sk_c10),sk_c9) | -equal(inverse(W),sk_c10) | -equal(multiply(W,sk_c9),sk_c10) | -equal(multiply(sk_c10,X1),sk_c9) | -equal(multiply(X2,sk_c10),X1) | -equal(inverse(X2),sk_c10).
% Split part used next: -equal(inverse(W),sk_c10) | -equal(multiply(W,sk_c9),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 27
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(53,40,0,112,0,0,342519,5,1501,342519,1,1501,342519,50,1501,342519,40,1501,342578,0,1501,354924,3,1802,355593,4,1952,356173,5,2102,356174,1,2102,356174,50,2102,356174,40,2102,356233,0,2102,356920,3,2420,356931,4,2584,356954,5,2703,356954,1,2703,356954,50,2703,356954,40,2703,357013,0,2703,378299,3,4204,379179,4,4954,379805,1,5704,379805,50,5704,379805,40,5704,379864,0,5704,396380,3,6455,397093,4,6830,397486,1,7205,397486,50,7205,397486,40,7205,397545,0,7205,408547,3,7967,409679,4,8331,411194,5,8706,411194,1,8706,411194,50,8706,411194,40,8706,411253,0,8706,476731,3,12608,477637,4,14558,478088,5,16507,478089,1,16507,478089,50,16509,478089,40,16509,478148,0,16509,525736,3,19060,526539,4,20335,527047,1,21610,527047,50,21611,527047,40,21611,527106,0,21611,575610,3,23116,576105,4,23862,576758,5,24612,576759,1,24612,576759,50,24614,576759,40,24614,576818,0,24614,585271,3,25384,586853,4,25740,587138,5,26115,587138,1,26115,587138,50,26115,587138,40,26115,587197,0,26115,608021,3,27316,608966,4,27916,609762,1,28516,609762,50,28516,609762,40,28516,609821,0,28516,626624,3,29267,627409,4,29642,628156,1,30017,628156,50,30017,628156,40,30017,628156,40,30017,628209,0,30017,628318,50,30018,628318,30,30018,628318,40,30018,628371,0,30018)
%
%
% START OF PROOF
% 628319 [] equal(X,X).
% 628323 [] -equal(multiply(X,sk_c9),sk_c10) | -equal(inverse(X),sk_c10).
% 628363 [] equal(multiply(sk_c1,sk_c9),sk_c10) | equal(multiply(sk_c6,sk_c9),sk_c10).
% 628364 [?] ?
% 628369 [?] ?
% 628370 [] equal(inverse(sk_c1),sk_c10) | equal(inverse(sk_c6),sk_c10).
% 628404 [hyper:628323,628370,binarycut:628364] equal(inverse(sk_c6),sk_c10).
% 628406 [hyper:628323,628370,binarycut:628369] equal(inverse(sk_c1),sk_c10).
% 628440 [hyper:628323,628363,demod:628406,cut:628319] equal(multiply(sk_c6,sk_c9),sk_c10).
% 628442 [hyper:628323,628440,demod:628404,cut:628319] 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 27
% 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_c10) | -equal(multiply(X,sk_c9),sk_c10) | -equal(multiply(Y,Z),sk_c9) | -equal(inverse(Y),Z) | -equal(multiply(Z,sk_c10),sk_c9) | -equal(multiply(sk_c10,U),sk_c9) | -equal(multiply(V,sk_c10),U) | -equal(inverse(V),sk_c10) | -equal(inverse(sk_c10),sk_c9) | -equal(inverse(W),sk_c10) | -equal(multiply(W,sk_c9),sk_c10) | -equal(multiply(sk_c10,X1),sk_c9) | -equal(multiply(X2,sk_c10),X1) | -equal(inverse(X2),sk_c10).
% Split part used next: -equal(multiply(sk_c10,U),sk_c9) | -equal(multiply(V,sk_c10),U) | -equal(inverse(V),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 27
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(53,40,0,112,0,0,342519,5,1501,342519,1,1501,342519,50,1501,342519,40,1501,342578,0,1501,354924,3,1802,355593,4,1952,356173,5,2102,356174,1,2102,356174,50,2102,356174,40,2102,356233,0,2102,356920,3,2420,356931,4,2584,356954,5,2703,356954,1,2703,356954,50,2703,356954,40,2703,357013,0,2703,378299,3,4204,379179,4,4954,379805,1,5704,379805,50,5704,379805,40,5704,379864,0,5704,396380,3,6455,397093,4,6830,397486,1,7205,397486,50,7205,397486,40,7205,397545,0,7205,408547,3,7967,409679,4,8331,411194,5,8706,411194,1,8706,411194,50,8706,411194,40,8706,411253,0,8706,476731,3,12608,477637,4,14558,478088,5,16507,478089,1,16507,478089,50,16509,478089,40,16509,478148,0,16509,525736,3,19060,526539,4,20335,527047,1,21610,527047,50,21611,527047,40,21611,527106,0,21611,575610,3,23116,576105,4,23862,576758,5,24612,576759,1,24612,576759,50,24614,576759,40,24614,576818,0,24614,585271,3,25384,586853,4,25740,587138,5,26115,587138,1,26115,587138,50,26115,587138,40,26115,587197,0,26115,608021,3,27316,608966,4,27916,609762,1,28516,609762,50,28516,609762,40,28516,609821,0,28516,626624,3,29267,627409,4,29642,628156,1,30017,628156,50,30017,628156,40,30017,628156,40,30017,628209,0,30017,628318,50,30018,628318,30,30018,628318,40,30018,628371,0,30018,628441,50,30018,628441,30,30018,628441,40,30018,628494,0,30024)
%
%
% START OF PROOF
% 628442 [] equal(X,X).
% 628446 [] -equal(multiply(sk_c10,X),sk_c9) | -equal(multiply(Y,sk_c10),X) | -equal(inverse(Y),sk_c10).
% 628447 [] equal(inverse(sk_c4),sk_c10) | equal(inverse(sk_c7),sk_c10).
% 628448 [] equal(multiply(sk_c7,sk_c10),sk_c8) | equal(inverse(sk_c4),sk_c10).
% 628449 [?] ?
% 628453 [] equal(multiply(sk_c4,sk_c10),sk_c5) | equal(inverse(sk_c7),sk_c10).
% 628454 [] equal(multiply(sk_c4,sk_c10),sk_c5) | equal(multiply(sk_c7,sk_c10),sk_c8).
% 628455 [] equal(multiply(sk_c4,sk_c10),sk_c5) | equal(multiply(sk_c10,sk_c8),sk_c9).
% 628459 [?] ?
% 628460 [?] ?
% 628461 [?] ?
% 628537 [hyper:628446,628448,628447,binarycut:628449] equal(inverse(sk_c4),sk_c10).
% 628558 [hyper:628446,628453,demod:628537,cut:628442,binarycut:628459] equal(inverse(sk_c7),sk_c10).
% 628587 [hyper:628446,628454,demod:628537,cut:628442,binarycut:628460] equal(multiply(sk_c7,sk_c10),sk_c8).
% 628600 [hyper:628446,628455,demod:628537,cut:628442,binarycut:628461] equal(multiply(sk_c10,sk_c8),sk_c9).
% 628604 [hyper:628446,628600,628587,demod:628558,cut:628442] 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 27
% 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_c10) | -equal(multiply(X,sk_c9),sk_c10) | -equal(multiply(Y,Z),sk_c9) | -equal(inverse(Y),Z) | -equal(multiply(Z,sk_c10),sk_c9) | -equal(multiply(sk_c10,U),sk_c9) | -equal(multiply(V,sk_c10),U) | -equal(inverse(V),sk_c10) | -equal(inverse(sk_c10),sk_c9) | -equal(inverse(W),sk_c10) | -equal(multiply(W,sk_c9),sk_c10) | -equal(multiply(sk_c10,X1),sk_c9) | -equal(multiply(X2,sk_c10),X1) | -equal(inverse(X2),sk_c10).
% Split part used next: -equal(multiply(Y,Z),sk_c9) | -equal(inverse(Y),Z) | -equal(multiply(Z,sk_c10),sk_c9).
% 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 27
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(53,40,0,112,0,0,342519,5,1501,342519,1,1501,342519,50,1501,342519,40,1501,342578,0,1501,354924,3,1802,355593,4,1952,356173,5,2102,356174,1,2102,356174,50,2102,356174,40,2102,356233,0,2102,356920,3,2420,356931,4,2584,356954,5,2703,356954,1,2703,356954,50,2703,356954,40,2703,357013,0,2703,378299,3,4204,379179,4,4954,379805,1,5704,379805,50,5704,379805,40,5704,379864,0,5704,396380,3,6455,397093,4,6830,397486,1,7205,397486,50,7205,397486,40,7205,397545,0,7205,408547,3,7967,409679,4,8331,411194,5,8706,411194,1,8706,411194,50,8706,411194,40,8706,411253,0,8706,476731,3,12608,477637,4,14558,478088,5,16507,478089,1,16507,478089,50,16509,478089,40,16509,478148,0,16509,525736,3,19060,526539,4,20335,527047,1,21610,527047,50,21611,527047,40,21611,527106,0,21611,575610,3,23116,576105,4,23862,576758,5,24612,576759,1,24612,576759,50,24614,576759,40,24614,576818,0,24614,585271,3,25384,586853,4,25740,587138,5,26115,587138,1,26115,587138,50,26115,587138,40,26115,587197,0,26115,608021,3,27316,608966,4,27916,609762,1,28516,609762,50,28516,609762,40,28516,609821,0,28516,626624,3,29267,627409,4,29642,628156,1,30017,628156,50,30017,628156,40,30017,628156,40,30017,628209,0,30017,628318,50,30018,628318,30,30018,628318,40,30018,628371,0,30018,628441,50,30018,628441,30,30018,628441,40,30018,628494,0,30024,628603,50,30024,628603,30,30024,628603,40,30024,628656,0,30024)
%
%
% START OF PROOF
% 628604 [] equal(X,X).
% 628605 [] equal(multiply(identity,X),X).
% 628606 [] equal(multiply(inverse(X),X),identity).
% 628607 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 628608 [] -equal(multiply(X,sk_c10),sk_c9) | -equal(multiply(Y,X),sk_c9) | -equal(inverse(Y),X).
% 628627 [?] ?
% 628628 [?] ?
% 628629 [?] ?
% 628630 [?] ?
% 628631 [?] ?
% 628632 [?] ?
% 628633 [] equal(inverse(sk_c2),sk_c3) | equal(inverse(sk_c7),sk_c10).
% 628634 [] equal(multiply(sk_c7,sk_c10),sk_c8) | equal(inverse(sk_c2),sk_c3).
% 628635 [] equal(multiply(sk_c10,sk_c8),sk_c9) | equal(inverse(sk_c2),sk_c3).
% 628636 [] equal(multiply(sk_c6,sk_c9),sk_c10) | equal(inverse(sk_c2),sk_c3).
% 628637 [] equal(inverse(sk_c2),sk_c3) | equal(inverse(sk_c6),sk_c10).
% 628638 [] equal(inverse(sk_c2),sk_c3) | equal(inverse(sk_c10),sk_c9).
% 628639 [?] ?
% 628640 [?] ?
% 628641 [?] ?
% 628642 [?] ?
% 628643 [?] ?
% 628644 [?] ?
% 628673 [hyper:628608,628633,binarycut:628639,binarycut:628627] equal(inverse(sk_c7),sk_c10).
% 628677 [para:628673.1.1,628606.1.1.1] equal(multiply(sk_c10,sk_c7),identity).
% 628681 [hyper:628608,628637,binarycut:628643,binarycut:628631] equal(inverse(sk_c6),sk_c10).
% 628688 [para:628681.1.1,628606.1.1.1] equal(multiply(sk_c10,sk_c6),identity).
% 628692 [hyper:628608,628638,binarycut:628644,binarycut:628632] equal(inverse(sk_c10),sk_c9).
% 628696 [para:628692.1.1,628606.1.1.1] equal(multiply(sk_c9,sk_c10),identity).
% 628708 [hyper:628608,628634,binarycut:628640,binarycut:628628] equal(multiply(sk_c7,sk_c10),sk_c8).
% 628715 [hyper:628608,628635,binarycut:628641,binarycut:628629] equal(multiply(sk_c10,sk_c8),sk_c9).
% 628721 [hyper:628608,628636,binarycut:628642,binarycut:628630] equal(multiply(sk_c6,sk_c9),sk_c10).
% 628722 [para:628606.1.1,628607.1.1.1,demod:628605] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 628723 [para:628677.1.1,628607.1.1.1,demod:628605] equal(X,multiply(sk_c10,multiply(sk_c7,X))).
% 628731 [para:628708.1.1,628723.1.2.2,demod:628715] equal(sk_c10,sk_c9).
% 628734 [para:628731.1.1,628692.1.1.1] equal(inverse(sk_c9),sk_c9).
% 628735 [para:628731.1.1,628696.1.1.2] equal(multiply(sk_c9,sk_c9),identity).
% 628744 [para:628677.1.1,628722.1.2.2,demod:628692] equal(sk_c7,multiply(sk_c9,identity)).
% 628745 [para:628688.1.1,628722.1.2.2,demod:628744,628692] equal(sk_c6,sk_c7).
% 628746 [para:628696.1.1,628722.1.2.2,demod:628744,628734] equal(sk_c10,sk_c7).
% 628753 [para:628746.1.1,628731.1.1] equal(sk_c7,sk_c9).
% 628759 [para:628753.1.1,628745.1.2] equal(sk_c6,sk_c9).
% 628765 [para:628759.1.1,628721.1.1.1,demod:628735] equal(identity,sk_c10).
% 628768 [para:628765.1.2,628692.1.1.1] equal(inverse(identity),sk_c9).
% 628772 [para:628765.1.2,628731.1.1] equal(identity,sk_c9).
% 628792 [hyper:628608,628768,demod:628696,628605,cut:628604,cut:628772] 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 27
% 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_c10) | -equal(multiply(X,sk_c9),sk_c10) | -equal(multiply(Y,Z),sk_c9) | -equal(inverse(Y),Z) | -equal(multiply(Z,sk_c10),sk_c9) | -equal(multiply(sk_c10,U),sk_c9) | -equal(multiply(V,sk_c10),U) | -equal(inverse(V),sk_c10) | -equal(inverse(sk_c10),sk_c9) | -equal(inverse(W),sk_c10) | -equal(multiply(W,sk_c9),sk_c10) | -equal(multiply(sk_c10,X1),sk_c9) | -equal(multiply(X2,sk_c10),X1) | -equal(inverse(X2),sk_c10).
% Split part used next: -equal(inverse(X),sk_c10) | -equal(multiply(X,sk_c9),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 27
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(53,40,0,112,0,0,342519,5,1501,342519,1,1501,342519,50,1501,342519,40,1501,342578,0,1501,354924,3,1802,355593,4,1952,356173,5,2102,356174,1,2102,356174,50,2102,356174,40,2102,356233,0,2102,356920,3,2420,356931,4,2584,356954,5,2703,356954,1,2703,356954,50,2703,356954,40,2703,357013,0,2703,378299,3,4204,379179,4,4954,379805,1,5704,379805,50,5704,379805,40,5704,379864,0,5704,396380,3,6455,397093,4,6830,397486,1,7205,397486,50,7205,397486,40,7205,397545,0,7205,408547,3,7967,409679,4,8331,411194,5,8706,411194,1,8706,411194,50,8706,411194,40,8706,411253,0,8706,476731,3,12608,477637,4,14558,478088,5,16507,478089,1,16507,478089,50,16509,478089,40,16509,478148,0,16509,525736,3,19060,526539,4,20335,527047,1,21610,527047,50,21611,527047,40,21611,527106,0,21611,575610,3,23116,576105,4,23862,576758,5,24612,576759,1,24612,576759,50,24614,576759,40,24614,576818,0,24614,585271,3,25384,586853,4,25740,587138,5,26115,587138,1,26115,587138,50,26115,587138,40,26115,587197,0,26115,608021,3,27316,608966,4,27916,609762,1,28516,609762,50,28516,609762,40,28516,609821,0,28516,626624,3,29267,627409,4,29642,628156,1,30017,628156,50,30017,628156,40,30017,628156,40,30017,628209,0,30017,628318,50,30018,628318,30,30018,628318,40,30018,628371,0,30018,628441,50,30018,628441,30,30018,628441,40,30018,628494,0,30024,628603,50,30024,628603,30,30024,628603,40,30024,628656,0,30024,628791,50,30024,628791,30,30024,628791,40,30024,628844,0,30024)
%
%
% START OF PROOF
% 628792 [] equal(X,X).
% 628796 [] -equal(multiply(X,sk_c9),sk_c10) | -equal(inverse(X),sk_c10).
% 628836 [] equal(multiply(sk_c1,sk_c9),sk_c10) | equal(multiply(sk_c6,sk_c9),sk_c10).
% 628837 [?] ?
% 628842 [?] ?
% 628843 [] equal(inverse(sk_c1),sk_c10) | equal(inverse(sk_c6),sk_c10).
% 628877 [hyper:628796,628843,binarycut:628837] equal(inverse(sk_c6),sk_c10).
% 628879 [hyper:628796,628843,binarycut:628842] equal(inverse(sk_c1),sk_c10).
% 628913 [hyper:628796,628836,demod:628879,cut:628792] equal(multiply(sk_c6,sk_c9),sk_c10).
% 628915 [hyper:628796,628913,demod:628877,cut:628792] 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 27
% 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_c10) | -equal(multiply(X,sk_c9),sk_c10) | -equal(multiply(Y,Z),sk_c9) | -equal(inverse(Y),Z) | -equal(multiply(Z,sk_c10),sk_c9) | -equal(multiply(sk_c10,U),sk_c9) | -equal(multiply(V,sk_c10),U) | -equal(inverse(V),sk_c10) | -equal(inverse(sk_c10),sk_c9) | -equal(inverse(W),sk_c10) | -equal(multiply(W,sk_c9),sk_c10) | -equal(multiply(sk_c10,X1),sk_c9) | -equal(multiply(X2,sk_c10),X1) | -equal(inverse(X2),sk_c10).
% Split part used next: -equal(inverse(sk_c10),sk_c9).
% 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 27
% 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 27
% 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 27
% 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 27
% 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 27
% 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 27
% 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 27
% 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 27
% 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 27
% 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(53,40,0,112,0,0,342519,5,1501,342519,1,1501,342519,50,1501,342519,40,1501,342578,0,1501,354924,3,1802,355593,4,1952,356173,5,2102,356174,1,2102,356174,50,2102,356174,40,2102,356233,0,2102,356920,3,2420,356931,4,2584,356954,5,2703,356954,1,2703,356954,50,2703,356954,40,2703,357013,0,2703,378299,3,4204,379179,4,4954,379805,1,5704,379805,50,5704,379805,40,5704,379864,0,5704,396380,3,6455,397093,4,6830,397486,1,7205,397486,50,7205,397486,40,7205,397545,0,7205,408547,3,7967,409679,4,8331,411194,5,8706,411194,1,8706,411194,50,8706,411194,40,8706,411253,0,8706,476731,3,12608,477637,4,14558,478088,5,16507,478089,1,16507,478089,50,16509,478089,40,16509,478148,0,16509,525736,3,19060,526539,4,20335,527047,1,21610,527047,50,21611,527047,40,21611,527106,0,21611,575610,3,23116,576105,4,23862,576758,5,24612,576759,1,24612,576759,50,24614,576759,40,24614,576818,0,24614,585271,3,25384,586853,4,25740,587138,5,26115,587138,1,26115,587138,50,26115,587138,40,26115,587197,0,26115,608021,3,27316,608966,4,27916,609762,1,28516,609762,50,28516,609762,40,28516,609821,0,28516,626624,3,29267,627409,4,29642,628156,1,30017,628156,50,30017,628156,40,30017,628156,40,30017,628209,0,30017,628318,50,30018,628318,30,30018,628318,40,30018,628371,0,30018,628441,50,30018,628441,30,30018,628441,40,30018,628494,0,30024,628603,50,30024,628603,30,30024,628603,40,30024,628656,0,30024,628791,50,30024,628791,30,30024,628791,40,30024,628844,0,30024,628914,50,30025,628914,30,30025,628914,40,30025,628967,0,30030,629127,50,30031,629180,0,30031,629396,50,30035,629449,0,30040,629673,50,30046,629726,0,30046,629958,50,30053,630011,0,30054,630249,50,30065,630302,0,30069,630548,50,30088,630601,0,30088,630855,50,30122,630908,0,30126,631172,50,30191,631225,0,30191,631499,50,30322,631499,40,30322,631552,0,30322)
%
%
% START OF PROOF
% 631501 [] equal(multiply(identity,X),X).
% 631502 [] equal(multiply(inverse(X),X),identity).
% 631503 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 631504 [] -equal(inverse(sk_c10),sk_c9).
% 631510 [?] ?
% 631516 [?] ?
% 631522 [?] ?
% 631528 [?] ?
% 631534 [?] ?
% 631540 [?] ?
% 631552 [?] ?
% 631561 [input:631510,cut:631504] equal(inverse(sk_c4),sk_c10).
% 631562 [para:631561.1.1,631502.1.1.1] equal(multiply(sk_c10,sk_c4),identity).
% 631570 [input:631534,cut:631504] equal(inverse(sk_c2),sk_c3).
% 631571 [para:631570.1.1,631502.1.1.1] equal(multiply(sk_c3,sk_c2),identity).
% 631578 [input:631552,cut:631504] equal(inverse(sk_c1),sk_c10).
% 631579 [para:631578.1.1,631502.1.1.1] equal(multiply(sk_c10,sk_c1),identity).
% 631585 [input:631516,cut:631504] equal(multiply(sk_c4,sk_c10),sk_c5).
% 631591 [input:631522,cut:631504] equal(multiply(sk_c10,sk_c5),sk_c9).
% 631596 [input:631528,cut:631504] equal(multiply(sk_c3,sk_c10),sk_c9).
% 631606 [input:631540,cut:631504] equal(multiply(sk_c2,sk_c3),sk_c9).
% 631636 [para:631502.1.1,631503.1.1.1,demod:631501] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 631638 [para:631562.1.1,631503.1.1.1,demod:631501] equal(X,multiply(sk_c10,multiply(sk_c4,X))).
% 631640 [para:631571.1.1,631503.1.1.1,demod:631501] equal(X,multiply(sk_c3,multiply(sk_c2,X))).
% 631690 [para:631585.1.1,631638.1.2.2] equal(sk_c10,multiply(sk_c10,sk_c5)).
% 631693 [para:631690.1.2,631591.1.1] equal(sk_c10,sk_c9).
% 631695 [para:631693.1.1,631504.1.1.1] -equal(inverse(sk_c9),sk_c9).
% 631709 [para:631693.1.1,631596.1.1.2] equal(multiply(sk_c3,sk_c9),sk_c9).
% 631746 [para:631606.1.1,631640.1.2.2,demod:631709] equal(sk_c3,sk_c9).
% 631750 [para:631746.1.1,631596.1.1.1] equal(multiply(sk_c9,sk_c10),sk_c9).
% 631854 [para:631750.1.1,631636.1.2.2,demod:631502] equal(sk_c10,identity).
% 631879 [para:631854.1.1,631579.1.1.1,demod:631501] equal(sk_c1,identity).
% 631903 [para:631854.1.1,631693.1.1] equal(identity,sk_c9).
% 631922 [para:631879.1.1,631578.1.1.1] equal(inverse(identity),sk_c10).
% 631925 [para:631903.1.2,631695.1.1.1,demod:631922,cut:631693] 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: 33894
% derived clauses: 4437791
% kept clauses: 251631
% kept size sum: 597293
% kept mid-nuclei: 342582
% kept new demods: 2409
% forw unit-subs: 993541
% forw double-subs: 2506625
% forw overdouble-subs: 305959
% backward subs: 20947
% fast unit cutoff: 32609
% full unit cutoff: 0
% dbl unit cutoff: 2727
% real runtime : 304.86
% process. runtime: 303.23
% specific non-discr-tree subsumption statistics:
% tried: 11006256
% length fails: 1171024
% strength fails: 2709803
% predlist fails: 437914
% aux str. fails: 1638433
% by-lit fails: 1459120
% full subs tried: 1657034
% full subs fail: 1403782
%
% ; 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/GRP221-1+eq_r.in")
%
%------------------------------------------------------------------------------