TSTP Solution File: CAT012-1 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : CAT012-1 : 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 11:29:35 EDT 2009
% Result : Unsatisfiable 0.7s
% Output : Refutation 0.7s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 11
% Syntax : Number of formulae : 32 ( 17 unt; 0 def)
% Number of atoms : 57 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 52 ( 27 ~; 25 |; 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 : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 58 ( 5 sgn 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(category_theory_axiom3,plain,
! [A,B,C,D] :
( ~ product(A,B,C)
| ~ defined(D,C)
| defined(D,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT012-1.tptp',unknown),
[] ).
cnf(158093784,plain,
( ~ product(A,B,C)
| ~ defined(D,C)
| defined(D,A) ),
inference(rewrite,[status(thm)],[category_theory_axiom3]),
[] ).
fof(mapping_from_codomain_of_x_to_x,plain,
! [A] : defined(codomain(A),A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT012-1.tptp',unknown),
[] ).
cnf(158130152,plain,
defined(codomain(A),A),
inference(rewrite,[status(thm)],[mapping_from_codomain_of_x_to_x]),
[] ).
cnf(166188096,plain,
( ~ product(A,B,C)
| defined(codomain(C),A) ),
inference(resolution,[status(thm)],[158093784,158130152]),
[] ).
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/CAT012-1.tptp',unknown),
[] ).
cnf(158070696,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/CAT012-1.tptp',unknown),
[] ).
cnf(158122160,plain,
defined(A,domain(A)),
inference(rewrite,[status(thm)],[mapping_from_x_to_its_domain]),
[] ).
cnf(166067936,plain,
( ~ product(A,B,C)
| defined(B,domain(C)) ),
inference(resolution,[status(thm)],[158070696,158122160]),
[] ).
fof(product_on_domain,plain,
! [A] : product(A,domain(A),A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT012-1.tptp',unknown),
[] ).
cnf(158134680,plain,
product(A,domain(A),A),
inference(rewrite,[status(thm)],[product_on_domain]),
[] ).
cnf(167385904,plain,
defined(domain(A),domain(A)),
inference(resolution,[status(thm)],[166067936,158134680]),
[] ).
fof(identity1,plain,
! [A,B] :
( ~ defined(A,B)
| ~ identity_map(A)
| product(A,B,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT012-1.tptp',unknown),
[] ).
cnf(158144928,plain,
( ~ defined(A,B)
| ~ identity_map(A)
| product(A,B,B) ),
inference(rewrite,[status(thm)],[identity1]),
[] ).
fof(domain_is_an_identity_map,plain,
! [A] : identity_map(domain(A)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT012-1.tptp',unknown),
[] ).
cnf(158113648,plain,
identity_map(domain(A)),
inference(rewrite,[status(thm)],[domain_is_an_identity_map]),
[] ).
cnf(165961448,plain,
( ~ defined(domain(B),A)
| product(domain(B),A,A) ),
inference(resolution,[status(thm)],[158144928,158113648]),
[] ).
cnf(167576728,plain,
product(domain(A),domain(A),domain(A)),
inference(resolution,[status(thm)],[167385904,165961448]),
[] ).
cnf(170639632,plain,
defined(codomain(domain(A)),domain(A)),
inference(resolution,[status(thm)],[166188096,167576728]),
[] ).
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/CAT012-1.tptp',unknown),
[] ).
cnf(158053136,plain,
( ~ product(A,B,C)
| ~ product(A,B,D)
| $equal(D,C) ),
inference(rewrite,[status(thm)],[composition_is_well_defined]),
[] ).
fof(product_on_codomain,plain,
! [A] : product(codomain(A),A,A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT012-1.tptp',unknown),
[] ).
cnf(158138624,plain,
product(codomain(A),A,A),
inference(rewrite,[status(thm)],[product_on_codomain]),
[] ).
cnf(166403416,plain,
( ~ product(codomain(A),A,B)
| $equal(B,A) ),
inference(resolution,[status(thm)],[158053136,158138624]),
[] ).
fof(identity2,plain,
! [A,B] :
( ~ defined(A,B)
| ~ identity_map(B)
| product(A,B,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT012-1.tptp',unknown),
[] ).
cnf(158149160,plain,
( ~ defined(A,B)
| ~ identity_map(B)
| product(A,B,A) ),
inference(rewrite,[status(thm)],[identity2]),
[] ).
cnf(165984904,plain,
( ~ defined(A,domain(B))
| product(A,domain(B),A) ),
inference(resolution,[status(thm)],[158149160,158113648]),
[] ).
cnf(179756016,plain,
$equal(codomain(domain(A)),domain(A)),
inference(forward_subsumption_resolution__resolution,[status(thm)],[170639632,166403416,165984904]),
[] ).
fof(prove_codomain_of_domain_is_domain,plain,
~ $equal(codomain(domain(a)),domain(a)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT012-1.tptp',unknown),
[] ).
cnf(158161608,plain,
~ $equal(codomain(domain(a)),domain(a)),
inference(rewrite,[status(thm)],[prove_codomain_of_domain_is_domain]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[179756016,158161608]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 1 seconds
% START OF PROOF SEQUENCE
% fof(category_theory_axiom3,plain,(~product(A,B,C)|~defined(D,C)|defined(D,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT012-1.tptp',unknown),[]).
%
% cnf(158093784,plain,(~product(A,B,C)|~defined(D,C)|defined(D,A)),inference(rewrite,[status(thm)],[category_theory_axiom3]),[]).
%
% fof(mapping_from_codomain_of_x_to_x,plain,(defined(codomain(A),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT012-1.tptp',unknown),[]).
%
% cnf(158130152,plain,(defined(codomain(A),A)),inference(rewrite,[status(thm)],[mapping_from_codomain_of_x_to_x]),[]).
%
% cnf(166188096,plain,(~product(A,B,C)|defined(codomain(C),A)),inference(resolution,[status(thm)],[158093784,158130152]),[]).
%
% fof(associative_property2,plain,(~product(A,B,C)|~defined(C,D)|defined(B,D)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT012-1.tptp',unknown),[]).
%
% cnf(158070696,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/CAT012-1.tptp',unknown),[]).
%
% cnf(158122160,plain,(defined(A,domain(A))),inference(rewrite,[status(thm)],[mapping_from_x_to_its_domain]),[]).
%
% cnf(166067936,plain,(~product(A,B,C)|defined(B,domain(C))),inference(resolution,[status(thm)],[158070696,158122160]),[]).
%
% fof(product_on_domain,plain,(product(A,domain(A),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT012-1.tptp',unknown),[]).
%
% cnf(158134680,plain,(product(A,domain(A),A)),inference(rewrite,[status(thm)],[product_on_domain]),[]).
%
% cnf(167385904,plain,(defined(domain(A),domain(A))),inference(resolution,[status(thm)],[166067936,158134680]),[]).
%
% fof(identity1,plain,(~defined(A,B)|~identity_map(A)|product(A,B,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT012-1.tptp',unknown),[]).
%
% cnf(158144928,plain,(~defined(A,B)|~identity_map(A)|product(A,B,B)),inference(rewrite,[status(thm)],[identity1]),[]).
%
% fof(domain_is_an_identity_map,plain,(identity_map(domain(A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT012-1.tptp',unknown),[]).
%
% cnf(158113648,plain,(identity_map(domain(A))),inference(rewrite,[status(thm)],[domain_is_an_identity_map]),[]).
%
% cnf(165961448,plain,(~defined(domain(B),A)|product(domain(B),A,A)),inference(resolution,[status(thm)],[158144928,158113648]),[]).
%
% cnf(167576728,plain,(product(domain(A),domain(A),domain(A))),inference(resolution,[status(thm)],[167385904,165961448]),[]).
%
% cnf(170639632,plain,(defined(codomain(domain(A)),domain(A))),inference(resolution,[status(thm)],[166188096,167576728]),[]).
%
% 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/CAT012-1.tptp',unknown),[]).
%
% cnf(158053136,plain,(~product(A,B,C)|~product(A,B,D)|$equal(D,C)),inference(rewrite,[status(thm)],[composition_is_well_defined]),[]).
%
% fof(product_on_codomain,plain,(product(codomain(A),A,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT012-1.tptp',unknown),[]).
%
% cnf(158138624,plain,(product(codomain(A),A,A)),inference(rewrite,[status(thm)],[product_on_codomain]),[]).
%
% cnf(166403416,plain,(~product(codomain(A),A,B)|$equal(B,A)),inference(resolution,[status(thm)],[158053136,158138624]),[]).
%
% fof(identity2,plain,(~defined(A,B)|~identity_map(B)|product(A,B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT012-1.tptp',unknown),[]).
%
% cnf(158149160,plain,(~defined(A,B)|~identity_map(B)|product(A,B,A)),inference(rewrite,[status(thm)],[identity2]),[]).
%
% cnf(165984904,plain,(~defined(A,domain(B))|product(A,domain(B),A)),inference(resolution,[status(thm)],[158149160,158113648]),[]).
%
% cnf(179756016,plain,($equal(codomain(domain(A)),domain(A))),inference(forward_subsumption_resolution__resolution,[status(thm)],[170639632,166403416,165984904]),[]).
%
% fof(prove_codomain_of_domain_is_domain,plain,(~$equal(codomain(domain(a)),domain(a))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT012-1.tptp',unknown),[]).
%
% cnf(158161608,plain,(~$equal(codomain(domain(a)),domain(a))),inference(rewrite,[status(thm)],[prove_codomain_of_domain_is_domain]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[179756016,158161608]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------