%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : CAT007-1 : TPTP v3.4.2. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art07.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 11:29:16 EDT 2009
% Result : Unsatisfiable 0.9s
% Output : Refutation 0.9s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of formulae : 26 ( 17 unt; 0 def)
% Number of atoms : 42 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 37 ( 21 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 29 ( 3 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(associative_property1,plain,
! [A,B,C] :
( ~ product(A,B,C)
| defined(A,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT007-1.tptp',unknown),
[] ).
cnf(160542408,plain,
( ~ product(A,B,C)
| defined(A,B) ),
inference(rewrite,[status(thm)],[associative_property1]),
[] ).
fof(domain_is_an_identity_map,plain,
! [A] : identity_map(domain(A)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT007-1.tptp',unknown),
[] ).
cnf(160592184,plain,
identity_map(domain(A)),
inference(rewrite,[status(thm)],[domain_is_an_identity_map]),
[] ).
fof(category_theory_axiom6,plain,
! [A,B,C] :
( ~ defined(A,B)
| ~ defined(B,C)
| ~ identity_map(B)
| defined(A,C) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT007-1.tptp',unknown),
[] ).
cnf(160587416,plain,
( ~ defined(A,B)
| ~ defined(B,C)
| ~ identity_map(B)
| defined(A,C) ),
inference(rewrite,[status(thm)],[category_theory_axiom6]),
[] ).
fof(prove_ab_is_defined,plain,
~ defined(a,b),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT007-1.tptp',unknown),
[] ).
cnf(160648392,plain,
~ defined(a,b),
inference(rewrite,[status(thm)],[prove_ab_is_defined]),
[] ).
cnf(168774952,plain,
( ~ defined(a,A)
| ~ defined(A,b)
| ~ identity_map(A) ),
inference(resolution,[status(thm)],[160587416,160648392]),
[] ).
fof(mapping_from_x_to_its_domain,plain,
! [A] : defined(A,domain(A)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT007-1.tptp',unknown),
[] ).
cnf(160600728,plain,
defined(A,domain(A)),
inference(rewrite,[status(thm)],[mapping_from_x_to_its_domain]),
[] ).
cnf(168800704,plain,
~ defined(domain(a),b),
inference(forward_subsumption_resolution__resolution,[status(thm)],[160592184,168774952,160600728]),
[] ).
cnf(169199408,plain,
~ product(domain(a),b,A),
inference(resolution,[status(thm)],[160542408,168800704]),
[] ).
fof(identity1,plain,
! [A,B] :
( ~ defined(A,B)
| ~ identity_map(A)
| product(A,B,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT007-1.tptp',unknown),
[] ).
cnf(160623560,plain,
( ~ defined(A,B)
| ~ identity_map(A)
| product(A,B,B) ),
inference(rewrite,[status(thm)],[identity1]),
[] ).
fof(closure_of_composition,plain,
! [A,B] :
( ~ defined(A,B)
| product(A,B,compose(A,B)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT007-1.tptp',unknown),
[] ).
cnf(160535736,plain,
( ~ defined(A,B)
| product(A,B,compose(A,B)) ),
inference(rewrite,[status(thm)],[closure_of_composition]),
[] ).
fof(mapping_from_codomain_of_x_to_x,plain,
! [A] : defined(codomain(A),A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT007-1.tptp',unknown),
[] ).
cnf(160608752,plain,
defined(codomain(A),A),
inference(rewrite,[status(thm)],[mapping_from_codomain_of_x_to_x]),
[] ).
cnf(169369200,plain,
product(codomain(A),A,compose(codomain(A),A)),
inference(resolution,[status(thm)],[160535736,160608752]),
[] ).
fof(domain_of_a_equals_codomain_of_b,plain,
$equal(codomain(b),domain(a)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT007-1.tptp',unknown),
[] ).
cnf(160644360,plain,
$equal(codomain(b),domain(a)),
inference(rewrite,[status(thm)],[domain_of_a_equals_codomain_of_b]),
[] ).
cnf(169395248,plain,
product(domain(a),b,compose(codomain(b),b)),
inference(paramodulation,[status(thm)],[169369200,160644360,theory(equality)]),
[] ).
cnf(169414168,plain,
defined(domain(a),b),
inference(resolution,[status(thm)],[169395248,160542408]),
[] ).
cnf(169468848,plain,
product(domain(a),b,b),
inference(forward_subsumption_resolution__resolution,[status(thm)],[160592184,160623560,169414168]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[169199408,169468848]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 1 seconds
% START OF PROOF SEQUENCE
% fof(associative_property1,plain,(~product(A,B,C)|defined(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT007-1.tptp',unknown),[]).
%
% cnf(160542408,plain,(~product(A,B,C)|defined(A,B)),inference(rewrite,[status(thm)],[associative_property1]),[]).
%
% fof(domain_is_an_identity_map,plain,(identity_map(domain(A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT007-1.tptp',unknown),[]).
%
% cnf(160592184,plain,(identity_map(domain(A))),inference(rewrite,[status(thm)],[domain_is_an_identity_map]),[]).
%
% fof(category_theory_axiom6,plain,(~defined(A,B)|~defined(B,C)|~identity_map(B)|defined(A,C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT007-1.tptp',unknown),[]).
%
% cnf(160587416,plain,(~defined(A,B)|~defined(B,C)|~identity_map(B)|defined(A,C)),inference(rewrite,[status(thm)],[category_theory_axiom6]),[]).
%
% fof(prove_ab_is_defined,plain,(~defined(a,b)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT007-1.tptp',unknown),[]).
%
% cnf(160648392,plain,(~defined(a,b)),inference(rewrite,[status(thm)],[prove_ab_is_defined]),[]).
%
% cnf(168774952,plain,(~defined(a,A)|~defined(A,b)|~identity_map(A)),inference(resolution,[status(thm)],[160587416,160648392]),[]).
%
% fof(mapping_from_x_to_its_domain,plain,(defined(A,domain(A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT007-1.tptp',unknown),[]).
%
% cnf(160600728,plain,(defined(A,domain(A))),inference(rewrite,[status(thm)],[mapping_from_x_to_its_domain]),[]).
%
% cnf(168800704,plain,(~defined(domain(a),b)),inference(forward_subsumption_resolution__resolution,[status(thm)],[160592184,168774952,160600728]),[]).
%
% cnf(169199408,plain,(~product(domain(a),b,A)),inference(resolution,[status(thm)],[160542408,168800704]),[]).
%
% fof(identity1,plain,(~defined(A,B)|~identity_map(A)|product(A,B,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT007-1.tptp',unknown),[]).
%
% cnf(160623560,plain,(~defined(A,B)|~identity_map(A)|product(A,B,B)),inference(rewrite,[status(thm)],[identity1]),[]).
%
% fof(closure_of_composition,plain,(~defined(A,B)|product(A,B,compose(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT007-1.tptp',unknown),[]).
%
% cnf(160535736,plain,(~defined(A,B)|product(A,B,compose(A,B))),inference(rewrite,[status(thm)],[closure_of_composition]),[]).
%
% fof(mapping_from_codomain_of_x_to_x,plain,(defined(codomain(A),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT007-1.tptp',unknown),[]).
%
% cnf(160608752,plain,(defined(codomain(A),A)),inference(rewrite,[status(thm)],[mapping_from_codomain_of_x_to_x]),[]).
%
% cnf(169369200,plain,(product(codomain(A),A,compose(codomain(A),A))),inference(resolution,[status(thm)],[160535736,160608752]),[]).
%
% fof(domain_of_a_equals_codomain_of_b,plain,($equal(codomain(b),domain(a))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT007-1.tptp',unknown),[]).
%
% cnf(160644360,plain,($equal(codomain(b),domain(a))),inference(rewrite,[status(thm)],[domain_of_a_equals_codomain_of_b]),[]).
%
% cnf(169395248,plain,(product(domain(a),b,compose(codomain(b),b))),inference(paramodulation,[status(thm)],[169369200,160644360,theory(equality)]),[]).
%
% cnf(169414168,plain,(defined(domain(a),b)),inference(resolution,[status(thm)],[169395248,160542408]),[]).
%
% cnf(169468848,plain,(product(domain(a),b,b)),inference(forward_subsumption_resolution__resolution,[status(thm)],[160592184,160623560,169414168]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[169199408,169468848]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------