TSTP Solution File: SET080-6 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET080-6 : TPTP v3.4.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art06.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 1003MB
% OS : Linux 2.6.17-1.2142_FC4
% CPULimit : 600s
% DateTime : Wed May 6 15:27:32 EDT 2009
% Result : Unsatisfiable 0.3s
% Output : Refutation 0.3s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of formulae : 19 ( 12 unt; 0 def)
% Number of atoms : 28 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 21 ( 12 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 17 ( 2 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(subclass_members,plain,
! [A,B,C] :
( ~ subclass(A,B)
| ~ member(C,A)
| member(C,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET080-6.tptp',unknown),
[] ).
cnf(146769560,plain,
( ~ subclass(A,B)
| ~ member(C,A)
| member(C,B) ),
inference(rewrite,[status(thm)],[subclass_members]),
[] ).
fof(inductive1,plain,
! [A] :
( ~ inductive(A)
| member(null_class,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET080-6.tptp',unknown),
[] ).
cnf(147160752,plain,
( ~ inductive(A)
| member(null_class,A) ),
inference(rewrite,[status(thm)],[inductive1]),
[] ).
fof(omega_is_inductive1,plain,
inductive(omega),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET080-6.tptp',unknown),
[] ).
cnf(147189896,plain,
inductive(omega),
inference(rewrite,[status(thm)],[omega_is_inductive1]),
[] ).
cnf(155729624,plain,
member(null_class,omega),
inference(resolution,[status(thm)],[147160752,147189896]),
[] ).
cnf(156362792,plain,
( ~ subclass(omega,A)
| member(null_class,A) ),
inference(resolution,[status(thm)],[146769560,155729624]),
[] ).
fof(class_elements_are_sets,plain,
! [A] : subclass(A,universal_class),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET080-6.tptp',unknown),
[] ).
cnf(146799536,plain,
subclass(A,universal_class),
inference(rewrite,[status(thm)],[class_elements_are_sets]),
[] ).
cnf(156372640,plain,
member(null_class,universal_class),
inference(resolution,[status(thm)],[156362792,146799536]),
[] ).
fof(unordered_pair2,plain,
! [A,B] :
( ~ member(A,universal_class)
| member(A,unordered_pair(A,B)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET080-6.tptp',unknown),
[] ).
cnf(146850424,plain,
( ~ member(A,universal_class)
| member(A,unordered_pair(A,B)) ),
inference(rewrite,[status(thm)],[unordered_pair2]),
[] ).
fof(prove_null_class_in_its_singleton_1,plain,
~ member(null_class,singleton(null_class)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET080-6.tptp',unknown),
[] ).
cnf(147700224,plain,
~ member(null_class,singleton(null_class)),
inference(rewrite,[status(thm)],[prove_null_class_in_its_singleton_1]),
[] ).
fof(singleton_set,plain,
! [A] : $equal(singleton(A),unordered_pair(A,A)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET080-6.tptp',unknown),
[] ).
cnf(146873632,plain,
$equal(singleton(A),unordered_pair(A,A)),
inference(rewrite,[status(thm)],[singleton_set]),
[] ).
cnf(157645248,plain,
~ member(null_class,unordered_pair(null_class,null_class)),
inference(paramodulation,[status(thm)],[147700224,146873632,theory(equality)]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[156372640,146850424,157645248]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 1 seconds
% START OF PROOF SEQUENCE
% fof(subclass_members,plain,(~subclass(A,B)|~member(C,A)|member(C,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET080-6.tptp',unknown),[]).
%
% cnf(146769560,plain,(~subclass(A,B)|~member(C,A)|member(C,B)),inference(rewrite,[status(thm)],[subclass_members]),[]).
%
% fof(inductive1,plain,(~inductive(A)|member(null_class,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET080-6.tptp',unknown),[]).
%
% cnf(147160752,plain,(~inductive(A)|member(null_class,A)),inference(rewrite,[status(thm)],[inductive1]),[]).
%
% fof(omega_is_inductive1,plain,(inductive(omega)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET080-6.tptp',unknown),[]).
%
% cnf(147189896,plain,(inductive(omega)),inference(rewrite,[status(thm)],[omega_is_inductive1]),[]).
%
% cnf(155729624,plain,(member(null_class,omega)),inference(resolution,[status(thm)],[147160752,147189896]),[]).
%
% cnf(156362792,plain,(~subclass(omega,A)|member(null_class,A)),inference(resolution,[status(thm)],[146769560,155729624]),[]).
%
% fof(class_elements_are_sets,plain,(subclass(A,universal_class)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET080-6.tptp',unknown),[]).
%
% cnf(146799536,plain,(subclass(A,universal_class)),inference(rewrite,[status(thm)],[class_elements_are_sets]),[]).
%
% cnf(156372640,plain,(member(null_class,universal_class)),inference(resolution,[status(thm)],[156362792,146799536]),[]).
%
% fof(unordered_pair2,plain,(~member(A,universal_class)|member(A,unordered_pair(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET080-6.tptp',unknown),[]).
%
% cnf(146850424,plain,(~member(A,universal_class)|member(A,unordered_pair(A,B))),inference(rewrite,[status(thm)],[unordered_pair2]),[]).
%
% fof(prove_null_class_in_its_singleton_1,plain,(~member(null_class,singleton(null_class))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET080-6.tptp',unknown),[]).
%
% cnf(147700224,plain,(~member(null_class,singleton(null_class))),inference(rewrite,[status(thm)],[prove_null_class_in_its_singleton_1]),[]).
%
% fof(singleton_set,plain,($equal(singleton(A),unordered_pair(A,A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET080-6.tptp',unknown),[]).
%
% cnf(146873632,plain,($equal(singleton(A),unordered_pair(A,A))),inference(rewrite,[status(thm)],[singleton_set]),[]).
%
% cnf(157645248,plain,(~member(null_class,unordered_pair(null_class,null_class))),inference(paramodulation,[status(thm)],[147700224,146873632,theory(equality)]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[156372640,146850424,157645248]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------