%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : CAT005-1 : 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 11:29:07 EDT 2009
% Result : Unsatisfiable 122.7s
% Output : Refutation 122.7s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 38 ( 20 unt; 0 def)
% Number of atoms : 64 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 55 ( 29 ~; 26 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 50 ( 6 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(domain_is_an_identity_map,plain,
! [A] : identity_map(domain(A)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT005-1.tptp',unknown),
[] ).
cnf(166322704,plain,
identity_map(domain(A)),
inference(rewrite,[status(thm)],[domain_is_an_identity_map]),
[] ).
fof(associative_property2,plain,
! [A,B,C,D] :
( ~ product(A,B,C)
| ~ defined(C,D)
| defined(B,D) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT005-1.tptp',unknown),
[] ).
cnf(166279624,plain,
( ~ product(A,B,C)
| ~ defined(C,D)
| defined(B,D) ),
inference(rewrite,[status(thm)],[associative_property2]),
[] ).
fof(mapping_from_x_to_its_domain,plain,
! [A] : defined(A,domain(A)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT005-1.tptp',unknown),
[] ).
cnf(166331280,plain,
defined(A,domain(A)),
inference(rewrite,[status(thm)],[mapping_from_x_to_its_domain]),
[] ).
cnf(174385384,plain,
( ~ product(A,B,C)
| defined(B,domain(C)) ),
inference(resolution,[status(thm)],[166279624,166331280]),
[] ).
fof(identity2,plain,
! [A,B] :
( ~ defined(A,B)
| ~ identity_map(B)
| product(A,B,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT005-1.tptp',unknown),
[] ).
cnf(166358440,plain,
( ~ defined(A,B)
| ~ identity_map(B)
| product(A,B,A) ),
inference(rewrite,[status(thm)],[identity2]),
[] ).
fof(d_is_identity_map,plain,
identity_map(d),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT005-1.tptp',unknown),
[] ).
cnf(166378000,plain,
identity_map(d),
inference(rewrite,[status(thm)],[d_is_identity_map]),
[] ).
cnf(174204008,plain,
( ~ defined(A,d)
| product(A,d,A) ),
inference(resolution,[status(thm)],[166358440,166378000]),
[] ).
fof(ad_defined,plain,
defined(a,d),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT005-1.tptp',unknown),
[] ).
cnf(166374160,plain,
defined(a,d),
inference(rewrite,[status(thm)],[ad_defined]),
[] ).
cnf(174243856,plain,
product(a,d,a),
inference(resolution,[status(thm)],[174204008,166374160]),
[] ).
cnf(175631584,plain,
( ~ defined(a,A)
| defined(d,A) ),
inference(resolution,[status(thm)],[166279624,174243856]),
[] ).
cnf(176067736,plain,
defined(d,domain(a)),
inference(resolution,[status(thm)],[175631584,166331280]),
[] ).
cnf(176151096,plain,
product(d,domain(a),d),
inference(forward_subsumption_resolution__resolution,[status(thm)],[166322704,176067736,166358440]),
[] ).
cnf(176224456,plain,
defined(domain(a),domain(d)),
inference(resolution,[status(thm)],[174385384,176151096]),
[] ).
cnf(176492312,plain,
product(domain(a),domain(d),domain(a)),
inference(forward_subsumption_resolution__resolution,[status(thm)],[166322704,176224456,166358440]),
[] ).
fof(identity1,plain,
! [A,B] :
( ~ defined(A,B)
| ~ identity_map(A)
| product(A,B,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT005-1.tptp',unknown),
[] ).
cnf(166354176,plain,
( ~ defined(A,B)
| ~ identity_map(A)
| product(A,B,B) ),
inference(rewrite,[status(thm)],[identity1]),
[] ).
cnf(174182984,plain,
( ~ defined(d,A)
| product(d,A,A) ),
inference(resolution,[status(thm)],[166354176,166378000]),
[] ).
fof(associative_property1,plain,
! [A,B,C] :
( ~ product(A,B,C)
| defined(A,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT005-1.tptp',unknown),
[] ).
cnf(166272928,plain,
( ~ product(A,B,C)
| defined(A,B) ),
inference(rewrite,[status(thm)],[associative_property1]),
[] ).
cnf(175291176,plain,
( product(d,A,A)
| ~ product(d,A,B) ),
inference(resolution,[status(thm)],[174182984,166272928]),
[] ).
cnf(175500208,plain,
( ~ product(d,A,B)
| defined(d,A) ),
inference(resolution,[status(thm)],[175291176,166272928]),
[] ).
fof(composition_is_well_defined,plain,
! [A,B,C,D] :
( ~ product(A,B,C)
| ~ product(A,B,D)
| $equal(D,C) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT005-1.tptp',unknown),
[] ).
cnf(166262000,plain,
( ~ product(A,B,C)
| ~ product(A,B,D)
| $equal(D,C) ),
inference(rewrite,[status(thm)],[composition_is_well_defined]),
[] ).
cnf(201510992,plain,
( ~ product(d,A,B)
| $equal(B,A) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[175500208,166262000,174182984]),
[] ).
cnf(618204080,plain,
$equal(d,domain(a)),
inference(resolution,[status(thm)],[201510992,176151096]),
[] ).
fof(product_on_domain,plain,
! [A] : product(A,domain(A),A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT005-1.tptp',unknown),
[] ).
cnf(166343864,plain,
product(A,domain(A),A),
inference(rewrite,[status(thm)],[product_on_domain]),
[] ).
cnf(174572184,plain,
( ~ product(A,domain(A),B)
| $equal(B,A) ),
inference(resolution,[status(thm)],[166262000,166343864]),
[] ).
fof(prove_domain_of_a_is_d,plain,
~ $equal(domain(a),d),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT005-1.tptp',unknown),
[] ).
cnf(166382480,plain,
~ $equal(domain(a),d),
inference(rewrite,[status(thm)],[prove_domain_of_a_is_d]),
[] ).
cnf(174774856,plain,
~ product(d,domain(d),domain(a)),
inference(resolution,[status(thm)],[174572184,166382480]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[176492312,618204080,174774856,theory(equality)]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 121 seconds
% START OF PROOF SEQUENCE
% fof(domain_is_an_identity_map,plain,(identity_map(domain(A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT005-1.tptp',unknown),[]).
%
% cnf(166322704,plain,(identity_map(domain(A))),inference(rewrite,[status(thm)],[domain_is_an_identity_map]),[]).
%
% fof(associative_property2,plain,(~product(A,B,C)|~defined(C,D)|defined(B,D)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT005-1.tptp',unknown),[]).
%
% cnf(166279624,plain,(~product(A,B,C)|~defined(C,D)|defined(B,D)),inference(rewrite,[status(thm)],[associative_property2]),[]).
%
% fof(mapping_from_x_to_its_domain,plain,(defined(A,domain(A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT005-1.tptp',unknown),[]).
%
% cnf(166331280,plain,(defined(A,domain(A))),inference(rewrite,[status(thm)],[mapping_from_x_to_its_domain]),[]).
%
% cnf(174385384,plain,(~product(A,B,C)|defined(B,domain(C))),inference(resolution,[status(thm)],[166279624,166331280]),[]).
%
% fof(identity2,plain,(~defined(A,B)|~identity_map(B)|product(A,B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT005-1.tptp',unknown),[]).
%
% cnf(166358440,plain,(~defined(A,B)|~identity_map(B)|product(A,B,A)),inference(rewrite,[status(thm)],[identity2]),[]).
%
% fof(d_is_identity_map,plain,(identity_map(d)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT005-1.tptp',unknown),[]).
%
% cnf(166378000,plain,(identity_map(d)),inference(rewrite,[status(thm)],[d_is_identity_map]),[]).
%
% cnf(174204008,plain,(~defined(A,d)|product(A,d,A)),inference(resolution,[status(thm)],[166358440,166378000]),[]).
%
% fof(ad_defined,plain,(defined(a,d)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT005-1.tptp',unknown),[]).
%
% cnf(166374160,plain,(defined(a,d)),inference(rewrite,[status(thm)],[ad_defined]),[]).
%
% cnf(174243856,plain,(product(a,d,a)),inference(resolution,[status(thm)],[174204008,166374160]),[]).
%
% cnf(175631584,plain,(~defined(a,A)|defined(d,A)),inference(resolution,[status(thm)],[166279624,174243856]),[]).
%
% cnf(176067736,plain,(defined(d,domain(a))),inference(resolution,[status(thm)],[175631584,166331280]),[]).
%
% cnf(176151096,plain,(product(d,domain(a),d)),inference(forward_subsumption_resolution__resolution,[status(thm)],[166322704,176067736,166358440]),[]).
%
% cnf(176224456,plain,(defined(domain(a),domain(d))),inference(resolution,[status(thm)],[174385384,176151096]),[]).
%
% cnf(176492312,plain,(product(domain(a),domain(d),domain(a))),inference(forward_subsumption_resolution__resolution,[status(thm)],[166322704,176224456,166358440]),[]).
%
% fof(identity1,plain,(~defined(A,B)|~identity_map(A)|product(A,B,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT005-1.tptp',unknown),[]).
%
% cnf(166354176,plain,(~defined(A,B)|~identity_map(A)|product(A,B,B)),inference(rewrite,[status(thm)],[identity1]),[]).
%
% cnf(174182984,plain,(~defined(d,A)|product(d,A,A)),inference(resolution,[status(thm)],[166354176,166378000]),[]).
%
% fof(associative_property1,plain,(~product(A,B,C)|defined(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT005-1.tptp',unknown),[]).
%
% cnf(166272928,plain,(~product(A,B,C)|defined(A,B)),inference(rewrite,[status(thm)],[associative_property1]),[]).
%
% cnf(175291176,plain,(product(d,A,A)|~product(d,A,B)),inference(resolution,[status(thm)],[174182984,166272928]),[]).
%
% cnf(175500208,plain,(~product(d,A,B)|defined(d,A)),inference(resolution,[status(thm)],[175291176,166272928]),[]).
%
% fof(composition_is_well_defined,plain,(~product(A,B,C)|~product(A,B,D)|$equal(D,C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT005-1.tptp',unknown),[]).
%
% cnf(166262000,plain,(~product(A,B,C)|~product(A,B,D)|$equal(D,C)),inference(rewrite,[status(thm)],[composition_is_well_defined]),[]).
%
% cnf(201510992,plain,(~product(d,A,B)|$equal(B,A)),inference(forward_subsumption_resolution__resolution,[status(thm)],[175500208,166262000,174182984]),[]).
%
% cnf(618204080,plain,($equal(d,domain(a))),inference(resolution,[status(thm)],[201510992,176151096]),[]).
%
% fof(product_on_domain,plain,(product(A,domain(A),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT005-1.tptp',unknown),[]).
%
% cnf(166343864,plain,(product(A,domain(A),A)),inference(rewrite,[status(thm)],[product_on_domain]),[]).
%
% cnf(174572184,plain,(~product(A,domain(A),B)|$equal(B,A)),inference(resolution,[status(thm)],[166262000,166343864]),[]).
%
% fof(prove_domain_of_a_is_d,plain,(~$equal(domain(a),d)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT005-1.tptp',unknown),[]).
%
% cnf(166382480,plain,(~$equal(domain(a),d)),inference(rewrite,[status(thm)],[prove_domain_of_a_is_d]),[]).
%
% cnf(174774856,plain,(~product(d,domain(d),domain(a))),inference(resolution,[status(thm)],[174572184,166382480]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[176492312,618204080,174774856,theory(equality)]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------