TSTP Solution File: SEU160+3 by Faust---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : SEU160+3 : TPTP v3.4.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art10.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 15:50:05 EDT 2009

% Result   : Theorem 0.1s
% Output   : Refutation 0.1s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    2
% Syntax   : Number of formulae    :   14 (   5 unt;   0 def)
%            Number of atoms       :   64 (   0 equ)
%            Maximal formula atoms :   36 (   4 avg)
%            Number of connectives :   82 (  32   ~;  37   |;  13   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-1 aty)
%            Number of variables   :    8 (   1 sgn   2   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(l4_zfmisc_1,plain,
    ! [A,B] :
      ( ( ~ subset(A,singleton(B))
        | $equal(empty_set,A)
        | $equal(singleton(B),A) )
      & ( ~ $equal(singleton(B),A)
        | subset(A,singleton(B)) )
      & ( ~ $equal(empty_set,A)
        | subset(A,singleton(B)) ) ),
    file('/tmp/SystemOnTPTP10361/SEU160+3.p',unknown),
    [] ).

cnf(145648664,plain,
    ( ~ $equal(singleton(B),A)
    | subset(A,singleton(B)) ),
    inference(rewrite,[status(thm)],[l4_zfmisc_1]),
    [] ).

fof(t39_zfmisc_1,plain,
    ( ( ~ subset(a,singleton(b))
      | ~ subset(a,singleton(b))
      | subset(a,singleton(b)) )
    & ( $equal(empty_set,a)
      | ~ subset(a,singleton(b))
      | subset(a,singleton(b)) )
    & ( ~ subset(a,singleton(b))
      | $equal(singleton(b),a)
      | subset(a,singleton(b)) )
    & ( $equal(empty_set,a)
      | $equal(singleton(b),a)
      | subset(a,singleton(b)) )
    & ( ~ subset(a,singleton(b))
      | ~ subset(a,singleton(b))
      | ~ $equal(empty_set,a) )
    & ( $equal(empty_set,a)
      | ~ subset(a,singleton(b))
      | ~ $equal(empty_set,a) )
    & ( ~ subset(a,singleton(b))
      | $equal(singleton(b),a)
      | ~ $equal(empty_set,a) )
    & ( $equal(empty_set,a)
      | $equal(singleton(b),a)
      | ~ $equal(empty_set,a) )
    & ( ~ subset(a,singleton(b))
      | ~ subset(a,singleton(b))
      | ~ $equal(singleton(b),a) )
    & ( $equal(empty_set,a)
      | ~ subset(a,singleton(b))
      | ~ $equal(singleton(b),a) )
    & ( ~ subset(a,singleton(b))
      | $equal(singleton(b),a)
      | ~ $equal(singleton(b),a) )
    & ( $equal(empty_set,a)
      | $equal(singleton(b),a)
      | ~ $equal(singleton(b),a) ) ),
    file('/tmp/SystemOnTPTP10361/SEU160+3.p',unknown),
    [] ).

cnf(145608120,plain,
    ( ~ subset(a,singleton(b))
    | ~ $equal(singleton(b),a) ),
    inference(rewrite,[status(thm)],[t39_zfmisc_1]),
    [] ).

cnf(145612176,plain,
    ( ~ subset(a,singleton(b))
    | ~ $equal(empty_set,a) ),
    inference(rewrite__forward_subsumption_resolution,[status(thm)],[t39_zfmisc_1,145608120]),
    [] ).

cnf(145629080,plain,
    ( ~ $equal(empty_set,A)
    | subset(A,singleton(B)) ),
    inference(rewrite,[status(thm)],[l4_zfmisc_1]),
    [] ).

cnf(161385080,plain,
    ~ $equal(empty_set,a),
    inference(resolution,[status(thm)],[145612176,145629080]),
    [] ).

cnf(145622584,plain,
    ( $equal(empty_set,a)
    | $equal(singleton(b),a)
    | subset(a,singleton(b)) ),
    inference(rewrite,[status(thm)],[t39_zfmisc_1]),
    [] ).

cnf(161393712,plain,
    ( $equal(singleton(b),a)
    | subset(a,singleton(b)) ),
    inference(resolution,[status(thm)],[161385080,145622584]),
    [] ).

cnf(161436840,plain,
    subset(a,singleton(b)),
    inference(resolution,[status(thm)],[145648664,161393712]),
    [] ).

cnf(145660056,plain,
    ( ~ subset(A,singleton(B))
    | $equal(empty_set,A)
    | $equal(singleton(B),A) ),
    inference(rewrite,[status(thm)],[l4_zfmisc_1]),
    [] ).

cnf(161455768,plain,
    ~ $equal(singleton(b),a),
    inference(resolution,[status(thm)],[145608120,161436840]),
    [] ).

cnf(161497704,plain,
    $equal(empty_set,a),
    inference(forward_subsumption_resolution__resolution,[status(thm)],[161436840,145660056,161455768]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(resolution,[status(thm)],[161497704,161385080]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(l4_zfmisc_1,plain,(((~subset(A,singleton(B))|$equal(empty_set,A)|$equal(singleton(B),A))&(~$equal(singleton(B),A)|subset(A,singleton(B)))&(~$equal(empty_set,A)|subset(A,singleton(B))))),file('/tmp/SystemOnTPTP10361/SEU160+3.p',unknown),[]).
% 
% cnf(145648664,plain,(~$equal(singleton(B),A)|subset(A,singleton(B))),inference(rewrite,[status(thm)],[l4_zfmisc_1]),[]).
% 
% fof(t39_zfmisc_1,plain,(((~subset(a,singleton(b))|~subset(a,singleton(b))|subset(a,singleton(b)))&($equal(empty_set,a)|~subset(a,singleton(b))|subset(a,singleton(b)))&(~subset(a,singleton(b))|$equal(singleton(b),a)|subset(a,singleton(b)))&($equal(empty_set,a)|$equal(singleton(b),a)|subset(a,singleton(b)))&(~subset(a,singleton(b))|~subset(a,singleton(b))|~$equal(empty_set,a))&($equal(empty_set,a)|~subset(a,singleton(b))|~$equal(empty_set,a))&(~subset(a,singleton(b))|$equal(singleton(b),a)|~$equal(empty_set,a))&($equal(empty_set,a)|$equal(singleton(b),a)|~$equal(empty_set,a))&(~subset(a,singleton(b))|~subset(a,singleton(b))|~$equal(singleton(b),a))&($equal(empty_set,a)|~subset(a,singleton(b))|~$equal(singleton(b),a))&(~subset(a,singleton(b))|$equal(singleton(b),a)|~$equal(singleton(b),a))&($equal(empty_set,a)|$equal(singleton(b),a)|~$equal(singleton(b),a)))),file('/tmp/SystemOnTPTP10361/SEU160+3.p',unknown),[]).
% 
% cnf(145608120,plain,(~subset(a,singleton(b))|~$equal(singleton(b),a)),inference(rewrite,[status(thm)],[t39_zfmisc_1]),[]).
% 
% cnf(145612176,plain,(~subset(a,singleton(b))|~$equal(empty_set,a)),inference(rewrite__forward_subsumption_resolution,[status(thm)],[t39_zfmisc_1,145608120]),[]).
% 
% cnf(145629080,plain,(~$equal(empty_set,A)|subset(A,singleton(B))),inference(rewrite,[status(thm)],[l4_zfmisc_1]),[]).
% 
% cnf(161385080,plain,(~$equal(empty_set,a)),inference(resolution,[status(thm)],[145612176,145629080]),[]).
% 
% cnf(145622584,plain,($equal(empty_set,a)|$equal(singleton(b),a)|subset(a,singleton(b))),inference(rewrite,[status(thm)],[t39_zfmisc_1]),[]).
% 
% cnf(161393712,plain,($equal(singleton(b),a)|subset(a,singleton(b))),inference(resolution,[status(thm)],[161385080,145622584]),[]).
% 
% cnf(161436840,plain,(subset(a,singleton(b))),inference(resolution,[status(thm)],[145648664,161393712]),[]).
% 
% cnf(145660056,plain,(~subset(A,singleton(B))|$equal(empty_set,A)|$equal(singleton(B),A)),inference(rewrite,[status(thm)],[l4_zfmisc_1]),[]).
% 
% cnf(161455768,plain,(~$equal(singleton(b),a)),inference(resolution,[status(thm)],[145608120,161436840]),[]).
% 
% cnf(161497704,plain,($equal(empty_set,a)),inference(forward_subsumption_resolution__resolution,[status(thm)],[161436840,145660056,161455768]),[]).
% 
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[161497704,161385080]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------