TSTP Solution File: CAT005-4 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : CAT005-4 : TPTP v3.4.2. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art05.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 11:29:10 EDT 2009
% Result : Unsatisfiable 0.2s
% Output : Refutation 0.2s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of formulae : 28 ( 15 unt; 0 def)
% Number of atoms : 43 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 33 ( 18 ~; 15 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 23 ( 1 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(existence_and_equality_implies_equivalence1,plain,
! [A,B] :
( ~ there_exists(A)
| ~ $equal(B,A)
| equivalent(A,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT005-4.tptp',unknown),
[] ).
cnf(143447656,plain,
( ~ there_exists(A)
| ~ $equal(B,A)
| equivalent(A,B) ),
inference(rewrite,[status(thm)],[existence_and_equality_implies_equivalence1]),
[] ).
cnf(152722352,plain,
( ~ there_exists(A)
| equivalent(A,A) ),
inference(equality_resolution,[status(thm)],[143447656]),
[] ).
fof(composition_implies_domain,plain,
! [A,B] :
( ~ there_exists(compose(A,B))
| there_exists(domain(A)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT005-4.tptp',unknown),
[] ).
cnf(143472712,plain,
( ~ there_exists(compose(A,B))
| there_exists(domain(A)) ),
inference(rewrite,[status(thm)],[composition_implies_domain]),
[] ).
fof(ad_exists,plain,
there_exists(compose(a,d)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT005-4.tptp',unknown),
[] ).
cnf(143517600,plain,
there_exists(compose(a,d)),
inference(rewrite,[status(thm)],[ad_exists]),
[] ).
cnf(151316456,plain,
there_exists(domain(a)),
inference(resolution,[status(thm)],[143472712,143517600]),
[] ).
cnf(152867968,plain,
equivalent(domain(a),domain(a)),
inference(resolution,[status(thm)],[152722352,151316456]),
[] ).
fof(domain_codomain_composition1,plain,
! [A,B] :
( ~ there_exists(compose(A,B))
| $equal(codomain(B),domain(A)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT005-4.tptp',unknown),
[] ).
cnf(143485536,plain,
( ~ there_exists(compose(A,B))
| $equal(codomain(B),domain(A)) ),
inference(rewrite,[status(thm)],[domain_codomain_composition1]),
[] ).
cnf(151351024,plain,
$equal(codomain(d),domain(a)),
inference(resolution,[status(thm)],[143485536,143517600]),
[] ).
fof(compose_codomain,plain,
! [A] : $equal(compose(codomain(A),A),A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT005-4.tptp',unknown),
[] ).
cnf(143513168,plain,
$equal(compose(codomain(A),A),A),
inference(rewrite,[status(thm)],[compose_codomain]),
[] ).
cnf(154219864,plain,
$equal(compose(domain(a),d),d),
inference(paramodulation,[status(thm)],[151351024,143513168,theory(equality)]),
[] ).
fof(codomain_has_elements,plain,
! [A] :
( ~ there_exists(codomain(A))
| there_exists(A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT005-4.tptp',unknown),
[] ).
cnf(143463008,plain,
( ~ there_exists(codomain(A))
| there_exists(A) ),
inference(rewrite,[status(thm)],[codomain_has_elements]),
[] ).
cnf(154205496,plain,
there_exists(d),
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[151316456,151351024,143463008,theory(equality)]),
[] ).
cnf(154354560,plain,
there_exists(compose(domain(a),d)),
inference(paramodulation,[status(thm)],[154219864,154205496,theory(equality)]),
[] ).
fof(xd_equals_x,plain,
! [A] :
( ~ there_exists(compose(A,d))
| $equal(compose(A,d),A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT005-4.tptp',unknown),
[] ).
cnf(143523384,plain,
( ~ there_exists(compose(A,d))
| $equal(compose(A,d),A) ),
inference(rewrite,[status(thm)],[xd_equals_x]),
[] ).
cnf(157890768,plain,
$equal(d,domain(a)),
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[154354560,143523384,154219864,theory(equality)]),
[] ).
fof(equivalence_implies_existence2,plain,
! [A,B] :
( ~ equivalent(A,B)
| $equal(B,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT005-4.tptp',unknown),
[] ).
cnf(143435328,plain,
( ~ equivalent(A,B)
| $equal(B,A) ),
inference(rewrite,[status(thm)],[equivalence_implies_existence2]),
[] ).
fof(prove_domain_of_a_is_d,plain,
~ $equal(domain(a),d),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT005-4.tptp',unknown),
[] ).
cnf(143537504,plain,
~ $equal(domain(a),d),
inference(rewrite,[status(thm)],[prove_domain_of_a_is_d]),
[] ).
cnf(151443480,plain,
~ equivalent(d,domain(a)),
inference(resolution,[status(thm)],[143435328,143537504]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[152867968,157890768,151443480,theory(equality)]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(existence_and_equality_implies_equivalence1,plain,(~there_exists(A)|~$equal(B,A)|equivalent(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT005-4.tptp',unknown),[]).
%
% cnf(143447656,plain,(~there_exists(A)|~$equal(B,A)|equivalent(A,B)),inference(rewrite,[status(thm)],[existence_and_equality_implies_equivalence1]),[]).
%
% cnf(152722352,plain,(~there_exists(A)|equivalent(A,A)),inference(equality_resolution,[status(thm)],[143447656]),[]).
%
% fof(composition_implies_domain,plain,(~there_exists(compose(A,B))|there_exists(domain(A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT005-4.tptp',unknown),[]).
%
% cnf(143472712,plain,(~there_exists(compose(A,B))|there_exists(domain(A))),inference(rewrite,[status(thm)],[composition_implies_domain]),[]).
%
% fof(ad_exists,plain,(there_exists(compose(a,d))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT005-4.tptp',unknown),[]).
%
% cnf(143517600,plain,(there_exists(compose(a,d))),inference(rewrite,[status(thm)],[ad_exists]),[]).
%
% cnf(151316456,plain,(there_exists(domain(a))),inference(resolution,[status(thm)],[143472712,143517600]),[]).
%
% cnf(152867968,plain,(equivalent(domain(a),domain(a))),inference(resolution,[status(thm)],[152722352,151316456]),[]).
%
% fof(domain_codomain_composition1,plain,(~there_exists(compose(A,B))|$equal(codomain(B),domain(A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT005-4.tptp',unknown),[]).
%
% cnf(143485536,plain,(~there_exists(compose(A,B))|$equal(codomain(B),domain(A))),inference(rewrite,[status(thm)],[domain_codomain_composition1]),[]).
%
% cnf(151351024,plain,($equal(codomain(d),domain(a))),inference(resolution,[status(thm)],[143485536,143517600]),[]).
%
% fof(compose_codomain,plain,($equal(compose(codomain(A),A),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT005-4.tptp',unknown),[]).
%
% cnf(143513168,plain,($equal(compose(codomain(A),A),A)),inference(rewrite,[status(thm)],[compose_codomain]),[]).
%
% cnf(154219864,plain,($equal(compose(domain(a),d),d)),inference(paramodulation,[status(thm)],[151351024,143513168,theory(equality)]),[]).
%
% fof(codomain_has_elements,plain,(~there_exists(codomain(A))|there_exists(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT005-4.tptp',unknown),[]).
%
% cnf(143463008,plain,(~there_exists(codomain(A))|there_exists(A)),inference(rewrite,[status(thm)],[codomain_has_elements]),[]).
%
% cnf(154205496,plain,(there_exists(d)),inference(forward_subsumption_resolution__paramodulation,[status(thm)],[151316456,151351024,143463008,theory(equality)]),[]).
%
% cnf(154354560,plain,(there_exists(compose(domain(a),d))),inference(paramodulation,[status(thm)],[154219864,154205496,theory(equality)]),[]).
%
% fof(xd_equals_x,plain,(~there_exists(compose(A,d))|$equal(compose(A,d),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT005-4.tptp',unknown),[]).
%
% cnf(143523384,plain,(~there_exists(compose(A,d))|$equal(compose(A,d),A)),inference(rewrite,[status(thm)],[xd_equals_x]),[]).
%
% cnf(157890768,plain,($equal(d,domain(a))),inference(forward_subsumption_resolution__paramodulation,[status(thm)],[154354560,143523384,154219864,theory(equality)]),[]).
%
% fof(equivalence_implies_existence2,plain,(~equivalent(A,B)|$equal(B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT005-4.tptp',unknown),[]).
%
% cnf(143435328,plain,(~equivalent(A,B)|$equal(B,A)),inference(rewrite,[status(thm)],[equivalence_implies_existence2]),[]).
%
% fof(prove_domain_of_a_is_d,plain,(~$equal(domain(a),d)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT005-4.tptp',unknown),[]).
%
% cnf(143537504,plain,(~$equal(domain(a),d)),inference(rewrite,[status(thm)],[prove_domain_of_a_is_d]),[]).
%
% cnf(151443480,plain,(~equivalent(d,domain(a))),inference(resolution,[status(thm)],[143435328,143537504]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[152867968,157890768,151443480,theory(equality)]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------