TSTP Solution File: SET065-6 by Faust---1.0
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%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET065-6 : TPTP v3.4.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art03.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 15:26:47 EDT 2009
% Result : Unsatisfiable 0.7s
% Output : Refutation 0.7s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 14 ( 9 unt; 0 def)
% Number of atoms : 21 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 16 ( 9 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 12 ( 2 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(prove_null_class_is_a_set_1,plain,
~ member(null_class,universal_class),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET065-6.tptp',unknown),
[] ).
cnf(161634776,plain,
~ member(null_class,universal_class),
inference(rewrite,[status(thm)],[prove_null_class_is_a_set_1]),
[] ).
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/SET065-6.tptp',unknown),
[] ).
cnf(160704136,plain,
( ~ subclass(A,B)
| ~ member(C,A)
| member(C,B) ),
inference(rewrite,[status(thm)],[subclass_members]),
[] ).
fof(class_elements_are_sets,plain,
! [A] : subclass(A,universal_class),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET065-6.tptp',unknown),
[] ).
cnf(160734112,plain,
subclass(A,universal_class),
inference(rewrite,[status(thm)],[class_elements_are_sets]),
[] ).
cnf(169870312,plain,
( ~ member(B,A)
| member(B,universal_class) ),
inference(resolution,[status(thm)],[160704136,160734112]),
[] ).
fof(inductive1,plain,
! [A] :
( ~ inductive(A)
| member(null_class,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET065-6.tptp',unknown),
[] ).
cnf(161095304,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/SET065-6.tptp',unknown),
[] ).
cnf(161124448,plain,
inductive(omega),
inference(rewrite,[status(thm)],[omega_is_inductive1]),
[] ).
cnf(169664160,plain,
member(null_class,omega),
inference(resolution,[status(thm)],[161095304,161124448]),
[] ).
cnf(196590336,plain,
member(null_class,universal_class),
inference(resolution,[status(thm)],[169870312,169664160]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[161634776,196590336]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(prove_null_class_is_a_set_1,plain,(~member(null_class,universal_class)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET065-6.tptp',unknown),[]).
%
% cnf(161634776,plain,(~member(null_class,universal_class)),inference(rewrite,[status(thm)],[prove_null_class_is_a_set_1]),[]).
%
% fof(subclass_members,plain,(~subclass(A,B)|~member(C,A)|member(C,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET065-6.tptp',unknown),[]).
%
% cnf(160704136,plain,(~subclass(A,B)|~member(C,A)|member(C,B)),inference(rewrite,[status(thm)],[subclass_members]),[]).
%
% fof(class_elements_are_sets,plain,(subclass(A,universal_class)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET065-6.tptp',unknown),[]).
%
% cnf(160734112,plain,(subclass(A,universal_class)),inference(rewrite,[status(thm)],[class_elements_are_sets]),[]).
%
% cnf(169870312,plain,(~member(B,A)|member(B,universal_class)),inference(resolution,[status(thm)],[160704136,160734112]),[]).
%
% fof(inductive1,plain,(~inductive(A)|member(null_class,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET065-6.tptp',unknown),[]).
%
% cnf(161095304,plain,(~inductive(A)|member(null_class,A)),inference(rewrite,[status(thm)],[inductive1]),[]).
%
% fof(omega_is_inductive1,plain,(inductive(omega)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET065-6.tptp',unknown),[]).
%
% cnf(161124448,plain,(inductive(omega)),inference(rewrite,[status(thm)],[omega_is_inductive1]),[]).
%
% cnf(169664160,plain,(member(null_class,omega)),inference(resolution,[status(thm)],[161095304,161124448]),[]).
%
% cnf(196590336,plain,(member(null_class,universal_class)),inference(resolution,[status(thm)],[169870312,169664160]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[161634776,196590336]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------