TSTP Solution File: COL042-8 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : COL042-8 : TPTP v3.4.2. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art04.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2794MHz
% Memory : 1003MB
% OS : Linux 2.6.11-1.1369_FC4
% CPULimit : 600s
% DateTime : Wed May 6 11:32:21 EDT 2009
% Result : Unsatisfiable 517.9s
% Output : Refutation 517.9s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 4
% Syntax : Number of formulae : 26 ( 26 unt; 0 def)
% Number of atoms : 26 ( 0 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 19 ( 19 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 10 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(b_definition,plain,
! [A,B,C] : $equal(apply(apply(apply(b,A),B),C),apply(A,apply(B,C))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL042-8.tptp',unknown),
[] ).
cnf(164165008,plain,
$equal(apply(apply(apply(b,A),B),C),apply(A,apply(B,C))),
inference(rewrite,[status(thm)],[b_definition]),
[] ).
fof(prove_strong_fixed_point,plain,
~ $equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(strong_fixed_point,fixed_pt)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL042-8.tptp',unknown),
[] ).
cnf(164182344,plain,
~ $equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(strong_fixed_point,fixed_pt)),
inference(rewrite,[status(thm)],[prove_strong_fixed_point]),
[] ).
fof(strong_fixed_point,plain,
$equal(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b))),b),strong_fixed_point),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL042-8.tptp',unknown),
[] ).
cnf(164173592,plain,
$equal(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b))),b),strong_fixed_point),
inference(rewrite,[status(thm)],[strong_fixed_point]),
[] ).
cnf(172014840,plain,
~ $equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b))),b),fixed_pt)),
inference(paramodulation,[status(thm)],[164182344,164173592,theory(equality)]),
[] ).
cnf(172483112,plain,
~ $equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b)),apply(b,fixed_pt))),
inference(paramodulation,[status(thm)],[172014840,164165008,theory(equality)]),
[] ).
cnf(174062880,plain,
~ $equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(apply(w1,w1),apply(apply(apply(b,apply(b,w1)),b),apply(b,fixed_pt)))),
inference(paramodulation,[status(thm)],[172483112,164165008,theory(equality)]),
[] ).
cnf(176223024,plain,
~ $equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,fixed_pt))))),
inference(paramodulation,[status(thm)],[174062880,164165008,theory(equality)]),
[] ).
fof(w1_definition,plain,
! [A,B] : $equal(apply(apply(w1,A),B),apply(apply(B,A),A)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL042-8.tptp',unknown),
[] ).
cnf(164169208,plain,
$equal(apply(apply(w1,A),B),apply(apply(B,A),A)),
inference(rewrite,[status(thm)],[w1_definition]),
[] ).
cnf(176425936,plain,
~ $equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(apply(apply(apply(b,w1),apply(b,apply(b,fixed_pt))),w1),w1)),
inference(paramodulation,[status(thm)],[176223024,164169208,theory(equality)]),
[] ).
cnf(176499760,plain,
~ $equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(apply(w1,apply(apply(b,apply(b,fixed_pt)),w1)),w1)),
inference(paramodulation,[status(thm)],[176425936,164165008,theory(equality)]),
[] ).
cnf(176552464,plain,
~ $equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(apply(w1,apply(apply(b,apply(b,fixed_pt)),w1)),apply(apply(b,apply(b,fixed_pt)),w1))),
inference(paramodulation,[status(thm)],[176499760,164169208,theory(equality)]),
[] ).
cnf(181127824,plain,
~ $equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(apply(apply(apply(b,apply(b,fixed_pt)),w1),apply(apply(b,apply(b,fixed_pt)),w1)),apply(apply(b,apply(b,fixed_pt)),w1))),
inference(paramodulation,[status(thm)],[176552464,164169208,theory(equality)]),
[] ).
cnf(225321696,plain,
~ $equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(apply(apply(b,fixed_pt),apply(w1,apply(apply(b,apply(b,fixed_pt)),w1))),apply(apply(b,apply(b,fixed_pt)),w1))),
inference(paramodulation,[status(thm)],[181127824,164165008,theory(equality)]),
[] ).
cnf(305969808,plain,
~ $equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(fixed_pt,apply(apply(w1,apply(apply(b,apply(b,fixed_pt)),w1)),apply(apply(b,apply(b,fixed_pt)),w1)))),
inference(paramodulation,[status(thm)],[225321696,164165008,theory(equality)]),
[] ).
cnf(330738216,plain,
~ $equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(fixed_pt,apply(apply(w1,apply(apply(b,apply(b,fixed_pt)),w1)),w1))),
inference(paramodulation,[status(thm)],[305969808,164169208,theory(equality)]),
[] ).
cnf(330863840,plain,
~ $equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(fixed_pt,apply(apply(apply(apply(b,w1),apply(b,apply(b,fixed_pt))),w1),w1))),
inference(paramodulation,[status(thm)],[330738216,164165008,theory(equality)]),
[] ).
cnf(331023136,plain,
~ $equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(fixed_pt,apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,fixed_pt)))))),
inference(paramodulation,[status(thm)],[330863840,164169208,theory(equality)]),
[] ).
cnf(331122808,plain,
~ $equal(apply(apply(apply(b,fixed_pt),strong_fixed_point),fixed_pt),apply(fixed_pt,apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,fixed_pt)))))),
inference(paramodulation,[status(thm)],[331023136,164165008,theory(equality)]),
[] ).
cnf(331730008,plain,
~ $equal(apply(apply(apply(b,fixed_pt),strong_fixed_point),fixed_pt),apply(fixed_pt,apply(apply(w1,w1),apply(apply(apply(b,apply(b,w1)),b),apply(b,fixed_pt))))),
inference(paramodulation,[status(thm)],[331122808,164165008,theory(equality)]),
[] ).
cnf(360647928,plain,
~ $equal(apply(apply(apply(b,fixed_pt),strong_fixed_point),fixed_pt),apply(fixed_pt,apply(apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b)),apply(b,fixed_pt)))),
inference(paramodulation,[status(thm)],[331730008,164165008,theory(equality)]),
[] ).
cnf(550852336,plain,
~ $equal(apply(apply(apply(b,fixed_pt),strong_fixed_point),fixed_pt),apply(fixed_pt,apply(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b))),b),fixed_pt))),
inference(paramodulation,[status(thm)],[360647928,164165008,theory(equality)]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[164165008,550852336,164173592,theory(equality)]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 518 seconds
% START OF PROOF SEQUENCE
% fof(b_definition,plain,($equal(apply(apply(apply(b,A),B),C),apply(A,apply(B,C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL042-8.tptp',unknown),[]).
%
% cnf(164165008,plain,($equal(apply(apply(apply(b,A),B),C),apply(A,apply(B,C)))),inference(rewrite,[status(thm)],[b_definition]),[]).
%
% fof(prove_strong_fixed_point,plain,(~$equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(strong_fixed_point,fixed_pt))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL042-8.tptp',unknown),[]).
%
% cnf(164182344,plain,(~$equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(strong_fixed_point,fixed_pt))),inference(rewrite,[status(thm)],[prove_strong_fixed_point]),[]).
%
% fof(strong_fixed_point,plain,($equal(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b))),b),strong_fixed_point)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL042-8.tptp',unknown),[]).
%
% cnf(164173592,plain,($equal(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b))),b),strong_fixed_point)),inference(rewrite,[status(thm)],[strong_fixed_point]),[]).
%
% cnf(172014840,plain,(~$equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b))),b),fixed_pt))),inference(paramodulation,[status(thm)],[164182344,164173592,theory(equality)]),[]).
%
% cnf(172483112,plain,(~$equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b)),apply(b,fixed_pt)))),inference(paramodulation,[status(thm)],[172014840,164165008,theory(equality)]),[]).
%
% cnf(174062880,plain,(~$equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(apply(w1,w1),apply(apply(apply(b,apply(b,w1)),b),apply(b,fixed_pt))))),inference(paramodulation,[status(thm)],[172483112,164165008,theory(equality)]),[]).
%
% cnf(176223024,plain,(~$equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,fixed_pt)))))),inference(paramodulation,[status(thm)],[174062880,164165008,theory(equality)]),[]).
%
% fof(w1_definition,plain,($equal(apply(apply(w1,A),B),apply(apply(B,A),A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL042-8.tptp',unknown),[]).
%
% cnf(164169208,plain,($equal(apply(apply(w1,A),B),apply(apply(B,A),A))),inference(rewrite,[status(thm)],[w1_definition]),[]).
%
% cnf(176425936,plain,(~$equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(apply(apply(apply(b,w1),apply(b,apply(b,fixed_pt))),w1),w1))),inference(paramodulation,[status(thm)],[176223024,164169208,theory(equality)]),[]).
%
% cnf(176499760,plain,(~$equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(apply(w1,apply(apply(b,apply(b,fixed_pt)),w1)),w1))),inference(paramodulation,[status(thm)],[176425936,164165008,theory(equality)]),[]).
%
% cnf(176552464,plain,(~$equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(apply(w1,apply(apply(b,apply(b,fixed_pt)),w1)),apply(apply(b,apply(b,fixed_pt)),w1)))),inference(paramodulation,[status(thm)],[176499760,164169208,theory(equality)]),[]).
%
% cnf(181127824,plain,(~$equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(apply(apply(apply(b,apply(b,fixed_pt)),w1),apply(apply(b,apply(b,fixed_pt)),w1)),apply(apply(b,apply(b,fixed_pt)),w1)))),inference(paramodulation,[status(thm)],[176552464,164169208,theory(equality)]),[]).
%
% cnf(225321696,plain,(~$equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(apply(apply(b,fixed_pt),apply(w1,apply(apply(b,apply(b,fixed_pt)),w1))),apply(apply(b,apply(b,fixed_pt)),w1)))),inference(paramodulation,[status(thm)],[181127824,164165008,theory(equality)]),[]).
%
% cnf(305969808,plain,(~$equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(fixed_pt,apply(apply(w1,apply(apply(b,apply(b,fixed_pt)),w1)),apply(apply(b,apply(b,fixed_pt)),w1))))),inference(paramodulation,[status(thm)],[225321696,164165008,theory(equality)]),[]).
%
% cnf(330738216,plain,(~$equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(fixed_pt,apply(apply(w1,apply(apply(b,apply(b,fixed_pt)),w1)),w1)))),inference(paramodulation,[status(thm)],[305969808,164169208,theory(equality)]),[]).
%
% cnf(330863840,plain,(~$equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(fixed_pt,apply(apply(apply(apply(b,w1),apply(b,apply(b,fixed_pt))),w1),w1)))),inference(paramodulation,[status(thm)],[330738216,164165008,theory(equality)]),[]).
%
% cnf(331023136,plain,(~$equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(fixed_pt,apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,fixed_pt))))))),inference(paramodulation,[status(thm)],[330863840,164169208,theory(equality)]),[]).
%
% cnf(331122808,plain,(~$equal(apply(apply(apply(b,fixed_pt),strong_fixed_point),fixed_pt),apply(fixed_pt,apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,fixed_pt))))))),inference(paramodulation,[status(thm)],[331023136,164165008,theory(equality)]),[]).
%
% cnf(331730008,plain,(~$equal(apply(apply(apply(b,fixed_pt),strong_fixed_point),fixed_pt),apply(fixed_pt,apply(apply(w1,w1),apply(apply(apply(b,apply(b,w1)),b),apply(b,fixed_pt)))))),inference(paramodulation,[status(thm)],[331122808,164165008,theory(equality)]),[]).
%
% cnf(360647928,plain,(~$equal(apply(apply(apply(b,fixed_pt),strong_fixed_point),fixed_pt),apply(fixed_pt,apply(apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b)),apply(b,fixed_pt))))),inference(paramodulation,[status(thm)],[331730008,164165008,theory(equality)]),[]).
%
% cnf(550852336,plain,(~$equal(apply(apply(apply(b,fixed_pt),strong_fixed_point),fixed_pt),apply(fixed_pt,apply(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b))),b),fixed_pt)))),inference(paramodulation,[status(thm)],[360647928,164165008,theory(equality)]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[164165008,550852336,164173592,theory(equality)]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------