TSTP Solution File: CAT018-1 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : CAT018-1 : 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 11:30:00 EDT 2009
% Result : Unsatisfiable 1.1s
% Output : Refutation 1.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 11
% Syntax : Number of formulae : 30 ( 17 unt; 0 def)
% Number of atoms : 56 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 55 ( 29 ~; 26 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 44 ( 2 sgn 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(assume_bc_exists,plain,
defined(b,c),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT018-1.tptp',unknown),
[] ).
cnf(171229768,plain,
defined(b,c),
inference(rewrite,[status(thm)],[assume_bc_exists]),
[] ).
fof(domain_is_an_identity_map,plain,
! [A] : identity_map(domain(A)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT018-1.tptp',unknown),
[] ).
cnf(171174312,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/CAT018-1.tptp',unknown),
[] ).
cnf(171169512,plain,
( ~ defined(A,B)
| ~ defined(B,C)
| ~ identity_map(B)
| defined(A,C) ),
inference(rewrite,[status(thm)],[category_theory_axiom6]),
[] ).
fof(mapping_from_x_to_its_domain,plain,
! [A] : defined(A,domain(A)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT018-1.tptp',unknown),
[] ).
cnf(171186976,plain,
defined(A,domain(A)),
inference(rewrite,[status(thm)],[mapping_from_x_to_its_domain]),
[] ).
cnf(179310384,plain,
( ~ defined(domain(A),B)
| defined(A,B) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[171174312,171169512,171186976]),
[] ).
fof(prove_a_bc_exists,plain,
~ defined(a,compose(b,c)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT018-1.tptp',unknown),
[] ).
cnf(171233688,plain,
~ defined(a,compose(b,c)),
inference(rewrite,[status(thm)],[prove_a_bc_exists]),
[] ).
cnf(179669048,plain,
~ defined(domain(a),compose(b,c)),
inference(resolution,[status(thm)],[179310384,171233688]),
[] ).
fof(category_theory_axiom1,plain,
! [A,B,C,D,E] :
( ~ product(A,B,C)
| ~ product(B,D,E)
| ~ defined(C,D)
| defined(A,E) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT018-1.tptp',unknown),
[] ).
cnf(171139528,plain,
( ~ product(A,B,C)
| ~ product(B,D,E)
| ~ defined(C,D)
| defined(A,E) ),
inference(rewrite,[status(thm)],[category_theory_axiom1]),
[] ).
fof(identity1,plain,
! [A,B] :
( ~ defined(A,B)
| ~ identity_map(A)
| product(A,B,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT018-1.tptp',unknown),
[] ).
cnf(171205784,plain,
( ~ defined(A,B)
| ~ identity_map(A)
| product(A,B,B) ),
inference(rewrite,[status(thm)],[identity1]),
[] ).
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/CAT018-1.tptp',unknown),
[] ).
cnf(171131104,plain,
( ~ product(A,B,C)
| ~ defined(C,D)
| defined(B,D) ),
inference(rewrite,[status(thm)],[associative_property2]),
[] ).
fof(product_on_domain,plain,
! [A] : product(A,domain(A),A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT018-1.tptp',unknown),
[] ).
cnf(171195472,plain,
product(A,domain(A),A),
inference(rewrite,[status(thm)],[product_on_domain]),
[] ).
cnf(180923352,plain,
( ~ defined(A,B)
| defined(domain(A),B) ),
inference(resolution,[status(thm)],[171131104,171195472]),
[] ).
fof(assume_ab_exists,plain,
defined(a,b),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT018-1.tptp',unknown),
[] ).
cnf(171225832,plain,
defined(a,b),
inference(rewrite,[status(thm)],[assume_ab_exists]),
[] ).
cnf(180931744,plain,
defined(domain(a),b),
inference(resolution,[status(thm)],[180923352,171225832]),
[] ).
cnf(181246888,plain,
product(domain(a),b,b),
inference(forward_subsumption_resolution__resolution,[status(thm)],[171174312,171205784,180931744]),
[] ).
cnf(184849024,plain,
( ~ product(b,A,B)
| ~ defined(b,A)
| defined(domain(a),B) ),
inference(resolution,[status(thm)],[171139528,181246888]),
[] ).
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/CAT018-1.tptp',unknown),
[] ).
cnf(171117672,plain,
( ~ defined(A,B)
| product(A,B,compose(A,B)) ),
inference(rewrite,[status(thm)],[closure_of_composition]),
[] ).
cnf(180408984,plain,
product(b,c,compose(b,c)),
inference(resolution,[status(thm)],[171117672,171229768]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[171229768,179669048,184849024,180408984]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 1 seconds
% START OF PROOF SEQUENCE
% fof(assume_bc_exists,plain,(defined(b,c)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT018-1.tptp',unknown),[]).
%
% cnf(171229768,plain,(defined(b,c)),inference(rewrite,[status(thm)],[assume_bc_exists]),[]).
%
% fof(domain_is_an_identity_map,plain,(identity_map(domain(A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT018-1.tptp',unknown),[]).
%
% cnf(171174312,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/CAT018-1.tptp',unknown),[]).
%
% cnf(171169512,plain,(~defined(A,B)|~defined(B,C)|~identity_map(B)|defined(A,C)),inference(rewrite,[status(thm)],[category_theory_axiom6]),[]).
%
% fof(mapping_from_x_to_its_domain,plain,(defined(A,domain(A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT018-1.tptp',unknown),[]).
%
% cnf(171186976,plain,(defined(A,domain(A))),inference(rewrite,[status(thm)],[mapping_from_x_to_its_domain]),[]).
%
% cnf(179310384,plain,(~defined(domain(A),B)|defined(A,B)),inference(forward_subsumption_resolution__resolution,[status(thm)],[171174312,171169512,171186976]),[]).
%
% fof(prove_a_bc_exists,plain,(~defined(a,compose(b,c))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT018-1.tptp',unknown),[]).
%
% cnf(171233688,plain,(~defined(a,compose(b,c))),inference(rewrite,[status(thm)],[prove_a_bc_exists]),[]).
%
% cnf(179669048,plain,(~defined(domain(a),compose(b,c))),inference(resolution,[status(thm)],[179310384,171233688]),[]).
%
% fof(category_theory_axiom1,plain,(~product(A,B,C)|~product(B,D,E)|~defined(C,D)|defined(A,E)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT018-1.tptp',unknown),[]).
%
% cnf(171139528,plain,(~product(A,B,C)|~product(B,D,E)|~defined(C,D)|defined(A,E)),inference(rewrite,[status(thm)],[category_theory_axiom1]),[]).
%
% fof(identity1,plain,(~defined(A,B)|~identity_map(A)|product(A,B,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT018-1.tptp',unknown),[]).
%
% cnf(171205784,plain,(~defined(A,B)|~identity_map(A)|product(A,B,B)),inference(rewrite,[status(thm)],[identity1]),[]).
%
% fof(associative_property2,plain,(~product(A,B,C)|~defined(C,D)|defined(B,D)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT018-1.tptp',unknown),[]).
%
% cnf(171131104,plain,(~product(A,B,C)|~defined(C,D)|defined(B,D)),inference(rewrite,[status(thm)],[associative_property2]),[]).
%
% fof(product_on_domain,plain,(product(A,domain(A),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT018-1.tptp',unknown),[]).
%
% cnf(171195472,plain,(product(A,domain(A),A)),inference(rewrite,[status(thm)],[product_on_domain]),[]).
%
% cnf(180923352,plain,(~defined(A,B)|defined(domain(A),B)),inference(resolution,[status(thm)],[171131104,171195472]),[]).
%
% fof(assume_ab_exists,plain,(defined(a,b)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT018-1.tptp',unknown),[]).
%
% cnf(171225832,plain,(defined(a,b)),inference(rewrite,[status(thm)],[assume_ab_exists]),[]).
%
% cnf(180931744,plain,(defined(domain(a),b)),inference(resolution,[status(thm)],[180923352,171225832]),[]).
%
% cnf(181246888,plain,(product(domain(a),b,b)),inference(forward_subsumption_resolution__resolution,[status(thm)],[171174312,171205784,180931744]),[]).
%
% cnf(184849024,plain,(~product(b,A,B)|~defined(b,A)|defined(domain(a),B)),inference(resolution,[status(thm)],[171139528,181246888]),[]).
%
% fof(closure_of_composition,plain,(~defined(A,B)|product(A,B,compose(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT018-1.tptp',unknown),[]).
%
% cnf(171117672,plain,(~defined(A,B)|product(A,B,compose(A,B))),inference(rewrite,[status(thm)],[closure_of_composition]),[]).
%
% cnf(180408984,plain,(product(b,c,compose(b,c))),inference(resolution,[status(thm)],[171117672,171229768]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[171229768,179669048,184849024,180408984]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------