%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : COL019-1 : TPTP v3.4.2. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art05.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 11:31:35 EDT 2009
% Result : Unsatisfiable 0.2s
% Output : Refutation 0.2s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 12 ( 12 unt; 0 def)
% Number of atoms : 12 ( 0 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 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 : 23 ( 0 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(prove_fixed_point,plain,
! [A] : ~ $equal(apply(combinator,A),A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL019-1.tptp',unknown),
[] ).
cnf(161217104,plain,
~ $equal(apply(combinator,A),A),
inference(rewrite,[status(thm)],[prove_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/COL019-1.tptp',unknown),
[] ).
cnf(161204336,plain,
$equal(apply(apply(apply(b,A),B),C),apply(A,apply(B,C))),
inference(rewrite,[status(thm)],[b_definition]),
[] ).
cnf(169037256,plain,
~ $equal(apply(apply(apply(b,combinator),A),B),apply(A,B)),
inference(paramodulation,[status(thm)],[161217104,161204336,theory(equality)]),
[] ).
fof(t_definition,plain,
! [A,B] : $equal(apply(apply(t,A),B),apply(B,A)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL019-1.tptp',unknown),
[] ).
cnf(161208328,plain,
$equal(apply(apply(t,A),B),apply(B,A)),
inference(rewrite,[status(thm)],[t_definition]),
[] ).
cnf(169438496,plain,
~ $equal(apply(apply(t,B),apply(apply(b,combinator),A)),apply(A,B)),
inference(paramodulation,[status(thm)],[169037256,161208328,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/COL019-1.tptp',unknown),
[] ).
cnf(161200120,plain,
$equal(apply(apply(apply(s,A),B),C),apply(apply(A,C),apply(B,C))),
inference(rewrite,[status(thm)],[s_definition]),
[] ).
cnf(172371192,plain,
~ $equal(apply(apply(apply(s,t),apply(b,combinator)),A),apply(A,A)),
inference(paramodulation,[status(thm)],[169438496,161200120,theory(equality)]),
[] ).
cnf(contradiction,plain,
$false,
inference(equality_resolution,[status(thm)],[172371192]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(prove_fixed_point,plain,(~$equal(apply(combinator,A),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL019-1.tptp',unknown),[]).
%
% cnf(161217104,plain,(~$equal(apply(combinator,A),A)),inference(rewrite,[status(thm)],[prove_fixed_point]),[]).
%
% fof(b_definition,plain,($equal(apply(apply(apply(b,A),B),C),apply(A,apply(B,C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL019-1.tptp',unknown),[]).
%
% cnf(161204336,plain,($equal(apply(apply(apply(b,A),B),C),apply(A,apply(B,C)))),inference(rewrite,[status(thm)],[b_definition]),[]).
%
% cnf(169037256,plain,(~$equal(apply(apply(apply(b,combinator),A),B),apply(A,B))),inference(paramodulation,[status(thm)],[161217104,161204336,theory(equality)]),[]).
%
% fof(t_definition,plain,($equal(apply(apply(t,A),B),apply(B,A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL019-1.tptp',unknown),[]).
%
% cnf(161208328,plain,($equal(apply(apply(t,A),B),apply(B,A))),inference(rewrite,[status(thm)],[t_definition]),[]).
%
% cnf(169438496,plain,(~$equal(apply(apply(t,B),apply(apply(b,combinator),A)),apply(A,B))),inference(paramodulation,[status(thm)],[169037256,161208328,theory(equality)]),[]).
%
% fof(s_definition,plain,($equal(apply(apply(apply(s,A),B),C),apply(apply(A,C),apply(B,C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL019-1.tptp',unknown),[]).
%
% cnf(161200120,plain,($equal(apply(apply(apply(s,A),B),C),apply(apply(A,C),apply(B,C)))),inference(rewrite,[status(thm)],[s_definition]),[]).
%
% cnf(172371192,plain,(~$equal(apply(apply(apply(s,t),apply(b,combinator)),A),apply(A,A))),inference(paramodulation,[status(thm)],[169438496,161200120,theory(equality)]),[]).
%
% cnf(contradiction,plain,$false,inference(equality_resolution,[status(thm)],[172371192]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------