TSTP Solution File: CAT006-1 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : CAT006-1 : TPTP v3.4.2. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art10.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 11:29:11 EDT 2009
% Result : Unsatisfiable 278.5s
% Output : Refutation 278.5s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of formulae : 28 ( 13 unt; 0 def)
% Number of atoms : 51 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 48 ( 25 ~; 23 |; 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 : 43 ( 6 sgn 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(codomain_is_an_identity_map,plain,
! [A] : identity_map(codomain(A)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT006-1.tptp',unknown),
[] ).
cnf(156795320,plain,
identity_map(codomain(A)),
inference(rewrite,[status(thm)],[codomain_is_an_identity_map]),
[] ).
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/CAT006-1.tptp',unknown),
[] ).
cnf(156771424,plain,
( ~ product(A,B,C)
| ~ defined(D,C)
| defined(D,A) ),
inference(rewrite,[status(thm)],[category_theory_axiom3]),
[] ).
fof(ha_defined,plain,
defined(h,a),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT006-1.tptp',unknown),
[] ).
cnf(156842776,plain,
defined(h,a),
inference(rewrite,[status(thm)],[ha_defined]),
[] ).
cnf(164794680,plain,
( ~ product(A,B,a)
| defined(h,A) ),
inference(resolution,[status(thm)],[156771424,156842776]),
[] ).
fof(product_on_codomain,plain,
! [A] : product(codomain(A),A,A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT006-1.tptp',unknown),
[] ).
cnf(156816456,plain,
product(codomain(A),A,A),
inference(rewrite,[status(thm)],[product_on_codomain]),
[] ).
cnf(172289056,plain,
defined(h,codomain(a)),
inference(resolution,[status(thm)],[164794680,156816456]),
[] ).
fof(identity2,plain,
! [A,B] :
( ~ defined(A,B)
| ~ identity_map(B)
| product(A,B,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT006-1.tptp',unknown),
[] ).
cnf(156827056,plain,
( ~ defined(A,B)
| ~ identity_map(B)
| product(A,B,A) ),
inference(rewrite,[status(thm)],[identity2]),
[] ).
cnf(172463920,plain,
product(h,codomain(a),h),
inference(forward_subsumption_resolution__resolution,[status(thm)],[156795320,172289056,156827056]),
[] ).
fof(prove_codomain_of_a_is_h,plain,
~ $equal(codomain(a),h),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT006-1.tptp',unknown),
[] ).
cnf(156851096,plain,
~ $equal(codomain(a),h),
inference(rewrite,[status(thm)],[prove_codomain_of_a_is_h]),
[] ).
fof(identity1,plain,
! [A,B] :
( ~ defined(A,B)
| ~ identity_map(A)
| product(A,B,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT006-1.tptp',unknown),
[] ).
cnf(156822792,plain,
( ~ defined(A,B)
| ~ identity_map(A)
| product(A,B,B) ),
inference(rewrite,[status(thm)],[identity1]),
[] ).
fof(h_is_the_identity_map,plain,
identity_map(h),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT006-1.tptp',unknown),
[] ).
cnf(156846616,plain,
identity_map(h),
inference(rewrite,[status(thm)],[h_is_the_identity_map]),
[] ).
cnf(164650800,plain,
( ~ defined(h,A)
| product(h,A,A) ),
inference(resolution,[status(thm)],[156822792,156846616]),
[] ).
fof(associative_property1,plain,
! [A,B,C] :
( ~ product(A,B,C)
| defined(A,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT006-1.tptp',unknown),
[] ).
cnf(156741544,plain,
( ~ product(A,B,C)
| defined(A,B) ),
inference(rewrite,[status(thm)],[associative_property1]),
[] ).
cnf(166159248,plain,
( product(h,A,A)
| ~ product(h,A,B) ),
inference(resolution,[status(thm)],[164650800,156741544]),
[] ).
cnf(180216840,plain,
( ~ product(h,A,B)
| defined(h,A) ),
inference(resolution,[status(thm)],[166159248,156741544]),
[] ).
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/CAT006-1.tptp',unknown),
[] ).
cnf(156730616,plain,
( ~ product(A,B,C)
| ~ product(A,B,D)
| $equal(D,C) ),
inference(rewrite,[status(thm)],[composition_is_well_defined]),
[] ).
cnf(192771952,plain,
( ~ product(h,A,B)
| $equal(A,B) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[180216840,156730616,164650800]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[172463920,156851096,192771952]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 276 seconds
% START OF PROOF SEQUENCE
% fof(codomain_is_an_identity_map,plain,(identity_map(codomain(A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT006-1.tptp',unknown),[]).
%
% cnf(156795320,plain,(identity_map(codomain(A))),inference(rewrite,[status(thm)],[codomain_is_an_identity_map]),[]).
%
% fof(category_theory_axiom3,plain,(~product(A,B,C)|~defined(D,C)|defined(D,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT006-1.tptp',unknown),[]).
%
% cnf(156771424,plain,(~product(A,B,C)|~defined(D,C)|defined(D,A)),inference(rewrite,[status(thm)],[category_theory_axiom3]),[]).
%
% fof(ha_defined,plain,(defined(h,a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT006-1.tptp',unknown),[]).
%
% cnf(156842776,plain,(defined(h,a)),inference(rewrite,[status(thm)],[ha_defined]),[]).
%
% cnf(164794680,plain,(~product(A,B,a)|defined(h,A)),inference(resolution,[status(thm)],[156771424,156842776]),[]).
%
% fof(product_on_codomain,plain,(product(codomain(A),A,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT006-1.tptp',unknown),[]).
%
% cnf(156816456,plain,(product(codomain(A),A,A)),inference(rewrite,[status(thm)],[product_on_codomain]),[]).
%
% cnf(172289056,plain,(defined(h,codomain(a))),inference(resolution,[status(thm)],[164794680,156816456]),[]).
%
% fof(identity2,plain,(~defined(A,B)|~identity_map(B)|product(A,B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT006-1.tptp',unknown),[]).
%
% cnf(156827056,plain,(~defined(A,B)|~identity_map(B)|product(A,B,A)),inference(rewrite,[status(thm)],[identity2]),[]).
%
% cnf(172463920,plain,(product(h,codomain(a),h)),inference(forward_subsumption_resolution__resolution,[status(thm)],[156795320,172289056,156827056]),[]).
%
% fof(prove_codomain_of_a_is_h,plain,(~$equal(codomain(a),h)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT006-1.tptp',unknown),[]).
%
% cnf(156851096,plain,(~$equal(codomain(a),h)),inference(rewrite,[status(thm)],[prove_codomain_of_a_is_h]),[]).
%
% fof(identity1,plain,(~defined(A,B)|~identity_map(A)|product(A,B,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT006-1.tptp',unknown),[]).
%
% cnf(156822792,plain,(~defined(A,B)|~identity_map(A)|product(A,B,B)),inference(rewrite,[status(thm)],[identity1]),[]).
%
% fof(h_is_the_identity_map,plain,(identity_map(h)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT006-1.tptp',unknown),[]).
%
% cnf(156846616,plain,(identity_map(h)),inference(rewrite,[status(thm)],[h_is_the_identity_map]),[]).
%
% cnf(164650800,plain,(~defined(h,A)|product(h,A,A)),inference(resolution,[status(thm)],[156822792,156846616]),[]).
%
% fof(associative_property1,plain,(~product(A,B,C)|defined(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT006-1.tptp',unknown),[]).
%
% cnf(156741544,plain,(~product(A,B,C)|defined(A,B)),inference(rewrite,[status(thm)],[associative_property1]),[]).
%
% cnf(166159248,plain,(product(h,A,A)|~product(h,A,B)),inference(resolution,[status(thm)],[164650800,156741544]),[]).
%
% cnf(180216840,plain,(~product(h,A,B)|defined(h,A)),inference(resolution,[status(thm)],[166159248,156741544]),[]).
%
% fof(composition_is_well_defined,plain,(~product(A,B,C)|~product(A,B,D)|$equal(D,C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT006-1.tptp',unknown),[]).
%
% cnf(156730616,plain,(~product(A,B,C)|~product(A,B,D)|$equal(D,C)),inference(rewrite,[status(thm)],[composition_is_well_defined]),[]).
%
% cnf(192771952,plain,(~product(h,A,B)|$equal(A,B)),inference(forward_subsumption_resolution__resolution,[status(thm)],[180216840,156730616,164650800]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[172463920,156851096,192771952]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------