TSTP Solution File: CAT014-1 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : CAT014-1 : 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 11:29:45 EDT 2009
% Result : Unsatisfiable 18.9s
% Output : Refutation 18.9s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of formulae : 16 ( 10 unt; 0 def)
% Number of atoms : 26 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 22 ( 12 ~; 10 |; 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 : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 23 ( 1 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(identity2,plain,
! [A,B] :
( ~ defined(A,B)
| ~ identity_map(B)
| product(A,B,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT014-1.tptp',unknown),
[] ).
cnf(150276648,plain,
( ~ defined(A,B)
| ~ identity_map(B)
| product(A,B,A) ),
inference(rewrite,[status(thm)],[identity2]),
[] ).
fof(codomain_is_an_identity_map,plain,
! [A] : identity_map(codomain(A)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT014-1.tptp',unknown),
[] ).
cnf(150245104,plain,
identity_map(codomain(A)),
inference(rewrite,[status(thm)],[codomain_is_an_identity_map]),
[] ).
cnf(158169552,plain,
( ~ defined(A,codomain(B))
| product(A,codomain(B),A) ),
inference(resolution,[status(thm)],[150276648,150245104]),
[] ).
fof(mapping_from_codomain_of_x_to_x,plain,
! [A] : defined(codomain(A),A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT014-1.tptp',unknown),
[] ).
cnf(150257640,plain,
defined(codomain(A),A),
inference(rewrite,[status(thm)],[mapping_from_codomain_of_x_to_x]),
[] ).
cnf(159400760,plain,
product(codomain(codomain(A)),codomain(A),codomain(codomain(A))),
inference(resolution,[status(thm)],[158169552,150257640]),
[] ).
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/CAT014-1.tptp',unknown),
[] ).
cnf(150180624,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/CAT014-1.tptp',unknown),
[] ).
cnf(150266112,plain,
product(codomain(A),A,A),
inference(rewrite,[status(thm)],[product_on_codomain]),
[] ).
cnf(169142680,plain,
( ~ product(codomain(A),A,B)
| $equal(B,A) ),
inference(resolution,[status(thm)],[150180624,150266112]),
[] ).
fof(prove_codomain_is_idempotent,plain,
~ $equal(codomain(codomain(a)),codomain(a)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT014-1.tptp',unknown),
[] ).
cnf(150289096,plain,
~ $equal(codomain(codomain(a)),codomain(a)),
inference(rewrite,[status(thm)],[prove_codomain_is_idempotent]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[159400760,169142680,150289096]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 19 seconds
% START OF PROOF SEQUENCE
% fof(identity2,plain,(~defined(A,B)|~identity_map(B)|product(A,B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT014-1.tptp',unknown),[]).
%
% cnf(150276648,plain,(~defined(A,B)|~identity_map(B)|product(A,B,A)),inference(rewrite,[status(thm)],[identity2]),[]).
%
% fof(codomain_is_an_identity_map,plain,(identity_map(codomain(A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT014-1.tptp',unknown),[]).
%
% cnf(150245104,plain,(identity_map(codomain(A))),inference(rewrite,[status(thm)],[codomain_is_an_identity_map]),[]).
%
% cnf(158169552,plain,(~defined(A,codomain(B))|product(A,codomain(B),A)),inference(resolution,[status(thm)],[150276648,150245104]),[]).
%
% fof(mapping_from_codomain_of_x_to_x,plain,(defined(codomain(A),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT014-1.tptp',unknown),[]).
%
% cnf(150257640,plain,(defined(codomain(A),A)),inference(rewrite,[status(thm)],[mapping_from_codomain_of_x_to_x]),[]).
%
% cnf(159400760,plain,(product(codomain(codomain(A)),codomain(A),codomain(codomain(A)))),inference(resolution,[status(thm)],[158169552,150257640]),[]).
%
% fof(composition_is_well_defined,plain,(~product(A,B,C)|~product(A,B,D)|$equal(D,C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT014-1.tptp',unknown),[]).
%
% cnf(150180624,plain,(~product(A,B,C)|~product(A,B,D)|$equal(D,C)),inference(rewrite,[status(thm)],[composition_is_well_defined]),[]).
%
% fof(product_on_codomain,plain,(product(codomain(A),A,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT014-1.tptp',unknown),[]).
%
% cnf(150266112,plain,(product(codomain(A),A,A)),inference(rewrite,[status(thm)],[product_on_codomain]),[]).
%
% cnf(169142680,plain,(~product(codomain(A),A,B)|$equal(B,A)),inference(resolution,[status(thm)],[150180624,150266112]),[]).
%
% fof(prove_codomain_is_idempotent,plain,(~$equal(codomain(codomain(a)),codomain(a))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT014-1.tptp',unknown),[]).
%
% cnf(150289096,plain,(~$equal(codomain(codomain(a)),codomain(a))),inference(rewrite,[status(thm)],[prove_codomain_is_idempotent]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[159400760,169142680,150289096]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------