%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : CAT007-3 : 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 11:29:18 EDT 2009

% Result   : Unsatisfiable 0.1s
% Output   : Refutation 0.1s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :    4
% Syntax   : Number of formulae    :    9 (   7 unt;   0 def)
%            Number of atoms       :   13 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   10 (   6   ~;   4   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :    4 (   0 sgn   2   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(prove_c1_c2_is_defined,plain,
    ~ there_exists(compose(c2,c1)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT007-3.tptp',unknown),
    [] ).

cnf(163665712,plain,
    ~ there_exists(compose(c2,c1)),
    inference(rewrite,[status(thm)],[prove_c1_c2_is_defined]),
    [] ).

fof(domain_of_c2_exists,plain,
    there_exists(domain(c2)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT007-3.tptp',unknown),
    [] ).

cnf(163649896,plain,
    there_exists(domain(c2)),
    inference(rewrite,[status(thm)],[domain_of_c2_exists]),
    [] ).

fof(domain_codomain_composition2,plain,
    ! [A,B] :
      ( ~ there_exists(domain(A))
      | ~ equalish(domain(A),codomain(B))
      | there_exists(compose(A,B)) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT007-3.tptp',unknown),
    [] ).

cnf(163609488,plain,
    ( ~ there_exists(domain(A))
    | ~ equalish(domain(A),codomain(B))
    | there_exists(compose(A,B)) ),
    inference(rewrite,[status(thm)],[domain_codomain_composition2]),
    [] ).

fof(domain_of_c2_equals_codomain_of_c1,plain,
    equalish(domain(c2),codomain(c1)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT007-3.tptp',unknown),
    [] ).

cnf(163661912,plain,
    equalish(domain(c2),codomain(c1)),
    inference(rewrite,[status(thm)],[domain_of_c2_equals_codomain_of_c1]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__resolution,[status(thm)],[163665712,163649896,163609488,163661912]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(prove_c1_c2_is_defined,plain,(~there_exists(compose(c2,c1))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT007-3.tptp',unknown),[]).
% 
% cnf(163665712,plain,(~there_exists(compose(c2,c1))),inference(rewrite,[status(thm)],[prove_c1_c2_is_defined]),[]).
% 
% fof(domain_of_c2_exists,plain,(there_exists(domain(c2))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT007-3.tptp',unknown),[]).
% 
% cnf(163649896,plain,(there_exists(domain(c2))),inference(rewrite,[status(thm)],[domain_of_c2_exists]),[]).
% 
% fof(domain_codomain_composition2,plain,(~there_exists(domain(A))|~equalish(domain(A),codomain(B))|there_exists(compose(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT007-3.tptp',unknown),[]).
% 
% cnf(163609488,plain,(~there_exists(domain(A))|~equalish(domain(A),codomain(B))|there_exists(compose(A,B))),inference(rewrite,[status(thm)],[domain_codomain_composition2]),[]).
% 
% fof(domain_of_c2_equals_codomain_of_c1,plain,(equalish(domain(c2),codomain(c1))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT007-3.tptp',unknown),[]).
% 
% cnf(163661912,plain,(equalish(domain(c2),codomain(c1))),inference(rewrite,[status(thm)],[domain_of_c2_equals_codomain_of_c1]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[163665712,163649896,163609488,163661912]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------