%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : CAT014-2 : 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 11:29:47 EDT 2009

% Result   : Unsatisfiable 0.1s
% Output   : Refutation 0.1s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    3
% Syntax   : Number of formulae    :    8 (   8 unt;   0 def)
%            Number of atoms       :    8 (   0 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    3 (   3   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    2 (   2 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   1 con; 0-1 aty)
%            Number of variables   :    4 (   0 sgn   2   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(domain_of_codomain_is_codomain,plain,
    ! [A] : $equal(domain(codomain(A)),codomain(A)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT014-2.tptp',unknown),
    [] ).

cnf(141948752,plain,
    $equal(domain(codomain(A)),codomain(A)),
    inference(rewrite,[status(thm)],[domain_of_codomain_is_codomain]),
    [] ).

fof(prove_codomain_is_idempotent,plain,
    ~ $equal(codomain(codomain(a)),codomain(a)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT014-2.tptp',unknown),
    [] ).

cnf(141990256,plain,
    ~ $equal(codomain(codomain(a)),codomain(a)),
    inference(rewrite,[status(thm)],[prove_codomain_is_idempotent]),
    [] ).

cnf(149796536,plain,
    ~ $equal(codomain(domain(codomain(a))),codomain(a)),
    inference(paramodulation,[status(thm)],[141990256,141948752,theory(equality)]),
    [] ).

fof(codomain_of_domain_is_domain,plain,
    ! [A] : $equal(codomain(domain(A)),domain(A)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT014-2.tptp',unknown),
    [] ).

cnf(141944792,plain,
    $equal(codomain(domain(A)),domain(A)),
    inference(rewrite,[status(thm)],[codomain_of_domain_is_domain]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__paramodulation,[status(thm)],[141948752,149796536,141944792,theory(equality)]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(domain_of_codomain_is_codomain,plain,($equal(domain(codomain(A)),codomain(A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT014-2.tptp',unknown),[]).
% 
% cnf(141948752,plain,($equal(domain(codomain(A)),codomain(A))),inference(rewrite,[status(thm)],[domain_of_codomain_is_codomain]),[]).
% 
% fof(prove_codomain_is_idempotent,plain,(~$equal(codomain(codomain(a)),codomain(a))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT014-2.tptp',unknown),[]).
% 
% cnf(141990256,plain,(~$equal(codomain(codomain(a)),codomain(a))),inference(rewrite,[status(thm)],[prove_codomain_is_idempotent]),[]).
% 
% cnf(149796536,plain,(~$equal(codomain(domain(codomain(a))),codomain(a))),inference(paramodulation,[status(thm)],[141990256,141948752,theory(equality)]),[]).
% 
% fof(codomain_of_domain_is_domain,plain,($equal(codomain(domain(A)),domain(A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT014-2.tptp',unknown),[]).
% 
% cnf(141944792,plain,($equal(codomain(domain(A)),domain(A))),inference(rewrite,[status(thm)],[codomain_of_domain_is_domain]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[141948752,149796536,141944792,theory(equality)]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------