TSTP Solution File: SET062-6 by Faust---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : SET062-6 : 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 15:26:25 EDT 2009

% Result   : Unsatisfiable 0.3s
% Output   : Refutation 0.3s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   19 (   9 unt;   0 def)
%            Number of atoms       :   29 (   0 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   20 (  10   ~;  10   |;   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   :   20 (   1 sgn  10   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(regularity2,plain,
    ! [A] :
      ( $equal(null_class,A)
      | $equal(intersection(A,regular(A)),null_class) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET062-6.tptp',unknown),
    [] ).

cnf(155555200,plain,
    ( $equal(null_class,A)
    | $equal(intersection(A,regular(A)),null_class) ),
    inference(rewrite,[status(thm)],[regularity2]),
    [] ).

fof(equal_implies_subclass2,plain,
    ! [B,A] :
      ( ~ $equal(B,A)
      | subclass(B,A) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET062-6.tptp',unknown),
    [] ).

cnf(155048640,plain,
    ( ~ $equal(B,A)
    | subclass(B,A) ),
    inference(rewrite,[status(thm)],[equal_implies_subclass2]),
    [] ).

fof(prove_null_class_is_subclass_1,plain,
    ~ subclass(null_class,x),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET062-6.tptp',unknown),
    [] ).

cnf(154981504,plain,
    ~ subclass(null_class,x),
    inference(rewrite,[status(thm)],[prove_null_class_is_subclass_1]),
    [] ).

cnf(164655272,plain,
    ~ $equal(null_class,x),
    inference(resolution,[status(thm)],[155048640,154981504]),
    [] ).

cnf(164803712,plain,
    $equal(intersection(x,regular(x)),null_class),
    inference(resolution,[status(thm)],[155555200,164655272]),
    [] ).

fof(not_subclass_members1,plain,
    ! [A,B] :
      ( member(not_subclass_element(A,B),A)
      | subclass(A,B) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET062-6.tptp',unknown),
    [] ).

cnf(155001648,plain,
    ( member(not_subclass_element(A,B),A)
    | subclass(A,B) ),
    inference(rewrite,[status(thm)],[not_subclass_members1]),
    [] ).

cnf(164668656,plain,
    member(not_subclass_element(null_class,x),null_class),
    inference(resolution,[status(thm)],[155001648,154981504]),
    [] ).

cnf(166012976,plain,
    member(not_subclass_element(null_class,x),intersection(x,regular(x))),
    inference(paramodulation,[status(thm)],[164803712,164668656,theory(equality)]),
    [] ).

fof(intersection1,plain,
    ! [A,B,C] :
      ( ~ member(A,intersection(B,C))
      | member(A,B) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET062-6.tptp',unknown),
    [] ).

cnf(155175312,plain,
    ( ~ member(A,intersection(B,C))
    | member(A,B) ),
    inference(rewrite,[status(thm)],[intersection1]),
    [] ).

cnf(178322376,plain,
    member(not_subclass_element(null_class,x),x),
    inference(resolution,[status(thm)],[166012976,155175312]),
    [] ).

fof(not_subclass_members2,plain,
    ! [A,B] :
      ( ~ member(not_subclass_element(A,B),B)
      | subclass(A,B) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET062-6.tptp',unknown),
    [] ).

cnf(155013768,plain,
    ( ~ member(not_subclass_element(A,B),B)
    | subclass(A,B) ),
    inference(rewrite,[status(thm)],[not_subclass_members2]),
    [] ).

cnf(172294744,plain,
    ~ member(not_subclass_element(null_class,x),x),
    inference(resolution,[status(thm)],[155013768,154981504]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(resolution,[status(thm)],[178322376,172294744]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(regularity2,plain,($equal(null_class,A)|$equal(intersection(A,regular(A)),null_class)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET062-6.tptp',unknown),[]).
% 
% cnf(155555200,plain,($equal(null_class,A)|$equal(intersection(A,regular(A)),null_class)),inference(rewrite,[status(thm)],[regularity2]),[]).
% 
% fof(equal_implies_subclass2,plain,(~$equal(B,A)|subclass(B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET062-6.tptp',unknown),[]).
% 
% cnf(155048640,plain,(~$equal(B,A)|subclass(B,A)),inference(rewrite,[status(thm)],[equal_implies_subclass2]),[]).
% 
% fof(prove_null_class_is_subclass_1,plain,(~subclass(null_class,x)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET062-6.tptp',unknown),[]).
% 
% cnf(154981504,plain,(~subclass(null_class,x)),inference(rewrite,[status(thm)],[prove_null_class_is_subclass_1]),[]).
% 
% cnf(164655272,plain,(~$equal(null_class,x)),inference(resolution,[status(thm)],[155048640,154981504]),[]).
% 
% cnf(164803712,plain,($equal(intersection(x,regular(x)),null_class)),inference(resolution,[status(thm)],[155555200,164655272]),[]).
% 
% fof(not_subclass_members1,plain,(member(not_subclass_element(A,B),A)|subclass(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET062-6.tptp',unknown),[]).
% 
% cnf(155001648,plain,(member(not_subclass_element(A,B),A)|subclass(A,B)),inference(rewrite,[status(thm)],[not_subclass_members1]),[]).
% 
% cnf(164668656,plain,(member(not_subclass_element(null_class,x),null_class)),inference(resolution,[status(thm)],[155001648,154981504]),[]).
% 
% cnf(166012976,plain,(member(not_subclass_element(null_class,x),intersection(x,regular(x)))),inference(paramodulation,[status(thm)],[164803712,164668656,theory(equality)]),[]).
% 
% fof(intersection1,plain,(~member(A,intersection(B,C))|member(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET062-6.tptp',unknown),[]).
% 
% cnf(155175312,plain,(~member(A,intersection(B,C))|member(A,B)),inference(rewrite,[status(thm)],[intersection1]),[]).
% 
% cnf(178322376,plain,(member(not_subclass_element(null_class,x),x)),inference(resolution,[status(thm)],[166012976,155175312]),[]).
% 
% fof(not_subclass_members2,plain,(~member(not_subclass_element(A,B),B)|subclass(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET062-6.tptp',unknown),[]).
% 
% cnf(155013768,plain,(~member(not_subclass_element(A,B),B)|subclass(A,B)),inference(rewrite,[status(thm)],[not_subclass_members2]),[]).
% 
% cnf(172294744,plain,(~member(not_subclass_element(null_class,x),x)),inference(resolution,[status(thm)],[155013768,154981504]),[]).
% 
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[178322376,172294744]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------