%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : COL002-3 : TPTP v3.4.2. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art09.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 1003MB
% OS : Linux 2.6.11-1.1369_FC4
% CPULimit : 600s
% DateTime : Wed May 6 11:30:35 EDT 2009
% Result : Unsatisfiable 10.0s
% Output : Refutation 10.0s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 15 ( 10 unt; 0 def)
% Number of atoms : 20 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 12 ( 7 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 28 ( 0 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(weak_fixed_point,plain,
! [A] :
( ~ $equal(apply(fixed_pt,A),A)
| fixed_point(A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL002-3.tptp',unknown),
[] ).
cnf(168281296,plain,
( ~ $equal(apply(fixed_pt,A),A)
| fixed_point(A) ),
inference(rewrite,[status(thm)],[weak_fixed_point]),
[] ).
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/COL002-3.tptp',unknown),
[] ).
cnf(168262888,plain,
$equal(apply(apply(apply(b,A),B),C),apply(A,apply(B,C))),
inference(rewrite,[status(thm)],[b_definition]),
[] ).
cnf(176113384,plain,
( ~ $equal(apply(apply(apply(b,fixed_pt),A),B),apply(A,B))
| fixed_point(apply(A,B)) ),
inference(paramodulation,[status(thm)],[168281296,168262888,theory(equality)]),
[] ).
fof(c_definition,plain,
! [A,B,C] : $equal(apply(apply(apply(c,A),B),C),apply(apply(A,C),B)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL002-3.tptp',unknown),
[] ).
cnf(168266928,plain,
$equal(apply(apply(apply(c,A),B),C),apply(apply(A,C),B)),
inference(rewrite,[status(thm)],[c_definition]),
[] ).
cnf(176373008,plain,
( ~ $equal(apply(apply(apply(c,apply(b,fixed_pt)),B),A),apply(A,B))
| fixed_point(apply(A,B)) ),
inference(paramodulation,[status(thm)],[176113384,168266928,theory(equality)]),
[] ).
fof(s_definition,plain,
! [A,B,C] : $equal(apply(apply(apply(s,A),B),C),apply(apply(A,C),apply(B,C))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL002-3.tptp',unknown),
[] ).
cnf(168258576,plain,
$equal(apply(apply(apply(s,A),B),C),apply(apply(A,C),apply(B,C))),
inference(rewrite,[status(thm)],[s_definition]),
[] ).
cnf(177233824,plain,
( ~ $equal(apply(apply(apply(s,apply(c,apply(b,fixed_pt))),B),A),apply(apply(B,A),A))
| fixed_point(apply(apply(B,A),A)) ),
inference(paramodulation,[status(thm)],[176373008,168258576,theory(equality)]),
[] ).
cnf(191211184,plain,
fixed_point(apply(apply(apply(s,apply(c,apply(b,fixed_pt))),apply(s,apply(c,apply(b,fixed_pt)))),apply(s,apply(c,apply(b,fixed_pt))))),
inference(equality_resolution,[status(thm)],[177233824]),
[] ).
fof(prove_weak_fixed_point,plain,
! [A] : ~ fixed_point(apply(apply(apply(s,apply(c,apply(b,A))),apply(s,apply(c,apply(b,A)))),apply(s,apply(c,apply(b,A))))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL002-3.tptp',unknown),
[] ).
cnf(168286456,plain,
~ fixed_point(apply(apply(apply(s,apply(c,apply(b,A))),apply(s,apply(c,apply(b,A)))),apply(s,apply(c,apply(b,A))))),
inference(rewrite,[status(thm)],[prove_weak_fixed_point]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[191211184,168286456]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 9 seconds
% START OF PROOF SEQUENCE
% fof(weak_fixed_point,plain,(~$equal(apply(fixed_pt,A),A)|fixed_point(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL002-3.tptp',unknown),[]).
%
% cnf(168281296,plain,(~$equal(apply(fixed_pt,A),A)|fixed_point(A)),inference(rewrite,[status(thm)],[weak_fixed_point]),[]).
%
% fof(b_definition,plain,($equal(apply(apply(apply(b,A),B),C),apply(A,apply(B,C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL002-3.tptp',unknown),[]).
%
% cnf(168262888,plain,($equal(apply(apply(apply(b,A),B),C),apply(A,apply(B,C)))),inference(rewrite,[status(thm)],[b_definition]),[]).
%
% cnf(176113384,plain,(~$equal(apply(apply(apply(b,fixed_pt),A),B),apply(A,B))|fixed_point(apply(A,B))),inference(paramodulation,[status(thm)],[168281296,168262888,theory(equality)]),[]).
%
% fof(c_definition,plain,($equal(apply(apply(apply(c,A),B),C),apply(apply(A,C),B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL002-3.tptp',unknown),[]).
%
% cnf(168266928,plain,($equal(apply(apply(apply(c,A),B),C),apply(apply(A,C),B))),inference(rewrite,[status(thm)],[c_definition]),[]).
%
% cnf(176373008,plain,(~$equal(apply(apply(apply(c,apply(b,fixed_pt)),B),A),apply(A,B))|fixed_point(apply(A,B))),inference(paramodulation,[status(thm)],[176113384,168266928,theory(equality)]),[]).
%
% fof(s_definition,plain,($equal(apply(apply(apply(s,A),B),C),apply(apply(A,C),apply(B,C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL002-3.tptp',unknown),[]).
%
% cnf(168258576,plain,($equal(apply(apply(apply(s,A),B),C),apply(apply(A,C),apply(B,C)))),inference(rewrite,[status(thm)],[s_definition]),[]).
%
% cnf(177233824,plain,(~$equal(apply(apply(apply(s,apply(c,apply(b,fixed_pt))),B),A),apply(apply(B,A),A))|fixed_point(apply(apply(B,A),A))),inference(paramodulation,[status(thm)],[176373008,168258576,theory(equality)]),[]).
%
% cnf(191211184,plain,(fixed_point(apply(apply(apply(s,apply(c,apply(b,fixed_pt))),apply(s,apply(c,apply(b,fixed_pt)))),apply(s,apply(c,apply(b,fixed_pt)))))),inference(equality_resolution,[status(thm)],[177233824]),[]).
%
% fof(prove_weak_fixed_point,plain,(~fixed_point(apply(apply(apply(s,apply(c,apply(b,A))),apply(s,apply(c,apply(b,A)))),apply(s,apply(c,apply(b,A)))))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL002-3.tptp',unknown),[]).
%
% cnf(168286456,plain,(~fixed_point(apply(apply(apply(s,apply(c,apply(b,A))),apply(s,apply(c,apply(b,A)))),apply(s,apply(c,apply(b,A)))))),inference(rewrite,[status(thm)],[prove_weak_fixed_point]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[191211184,168286456]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------