TSTP Solution File: SET879+1 by Faust---1.0

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%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : SET879+1 : TPTP v3.4.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art02.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 15:40:22 EDT 2009

% Result   : Theorem 0.1s
% Output   : Refutation 0.1s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   17 (   4 unt;   0 def)
%            Number of atoms       :   56 (   0 equ)
%            Maximal formula atoms :   18 (   3 avg)
%            Number of connectives :   64 (  25   ~;  30   |;   9   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-3 aty)
%            Number of variables   :   20 (   0 sgn   5   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(t20_zfmisc_1,plain,
    ( ( ~ $equal(b,a)
      | $equal(set_difference(singleton(a),singleton(b)),singleton(a)) )
    & ( ~ $equal(set_difference(singleton(a),singleton(b)),singleton(a))
      | $equal(set_difference(singleton(a),singleton(b)),singleton(a)) )
    & ( ~ $equal(b,a)
      | $equal(b,a) )
    & ( ~ $equal(set_difference(singleton(a),singleton(b)),singleton(a))
      | $equal(b,a) ) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET879+1.tptp',unknown),
    [] ).

cnf(160061640,plain,
    ( ~ $equal(b,a)
    | $equal(set_difference(singleton(a),singleton(b)),singleton(a)) ),
    inference(rewrite,[status(thm)],[t20_zfmisc_1]),
    [] ).

cnf(160055552,plain,
    ( ~ $equal(set_difference(singleton(a),singleton(b)),singleton(a))
    | $equal(b,a) ),
    inference(rewrite,[status(thm)],[t20_zfmisc_1]),
    [] ).

fof(l34_zfmisc_1,plain,
    ! [A,B] :
      ( ( ~ $equal(set_difference(singleton(A),B),singleton(A))
        | ~ in(A,B) )
      & ( $equal(set_difference(singleton(A),B),singleton(A))
        | in(A,B) ) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET879+1.tptp',unknown),
    [] ).

cnf(159958568,plain,
    ( $equal(set_difference(singleton(A),B),singleton(A))
    | in(A,B) ),
    inference(rewrite,[status(thm)],[l34_zfmisc_1]),
    [] ).

cnf(173632856,plain,
    ( $equal(b,a)
    | in(a,singleton(b)) ),
    inference(resolution,[status(thm)],[160055552,159958568]),
    [] ).

fof(d1_tarski,plain,
    ! [C,B,A] :
      ( ( in(C,B)
        | ~ $equal(A,C)
        | ~ $equal(singleton(A),B) )
      & ( ~ in(C,B)
        | $equal(A,C)
        | ~ $equal(singleton(A),B) )
      & ( $equal(c(A,B,C),A)
        | ~ $equal(c(A,B,C),A)
        | $equal(singleton(A),B) )
      & ( ~ in(c(A,B,C),B)
        | ~ $equal(c(A,B,C),A)
        | $equal(singleton(A),B) )
      & ( $equal(c(A,B,C),A)
        | in(c(A,B,C),B)
        | $equal(singleton(A),B) )
      & ( ~ in(c(A,B,C),B)
        | in(c(A,B,C),B)
        | $equal(singleton(A),B) ) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET879+1.tptp',unknown),
    [] ).

cnf(159941056,plain,
    ( ~ in(C,B)
    | $equal(A,C)
    | ~ $equal(singleton(A),B) ),
    inference(rewrite,[status(thm)],[d1_tarski]),
    [] ).

cnf(170497752,plain,
    ( ~ in(B,singleton(A))
    | $equal(A,B) ),
    inference(equality_resolution,[status(thm)],[159941056]),
    [] ).

cnf(173842680,plain,
    $equal(b,a),
    inference(resolution,[status(thm)],[173632856,170497752]),
    [] ).

cnf(174383240,plain,
    $equal(set_difference(singleton(a),singleton(b)),singleton(a)),
    inference(resolution,[status(thm)],[160061640,173842680]),
    [] ).

cnf(159952992,plain,
    ( in(C,B)
    | ~ $equal(A,C)
    | ~ $equal(singleton(A),B) ),
    inference(rewrite,[status(thm)],[d1_tarski]),
    [] ).

cnf(170610136,plain,
    ( in(A,B)
    | ~ $equal(singleton(A),B) ),
    inference(equality_resolution,[status(thm)],[159952992]),
    [] ).

cnf(174578024,plain,
    ( in(a,A)
    | ~ $equal(set_difference(singleton(a),singleton(b)),A) ),
    inference(forward_subsumption_resolution__paramodulation,[status(thm)],[173842680,160061640,170610136,theory(equality)]),
    [] ).

cnf(174892712,plain,
    in(a,singleton(b)),
    inference(forward_subsumption_resolution__paramodulation,[status(thm)],[174578024,173632856,160061640,173632856,theory(equality)]),
    [] ).

cnf(159965200,plain,
    ( ~ $equal(set_difference(singleton(A),B),singleton(A))
    | ~ in(A,B) ),
    inference(rewrite,[status(thm)],[l34_zfmisc_1]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__resolution,[status(thm)],[174383240,174892712,159965200]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(t20_zfmisc_1,plain,(((~$equal(b,a)|$equal(set_difference(singleton(a),singleton(b)),singleton(a)))&(~$equal(set_difference(singleton(a),singleton(b)),singleton(a))|$equal(set_difference(singleton(a),singleton(b)),singleton(a)))&(~$equal(b,a)|$equal(b,a))&(~$equal(set_difference(singleton(a),singleton(b)),singleton(a))|$equal(b,a)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET879+1.tptp',unknown),[]).
% 
% cnf(160061640,plain,(~$equal(b,a)|$equal(set_difference(singleton(a),singleton(b)),singleton(a))),inference(rewrite,[status(thm)],[t20_zfmisc_1]),[]).
% 
% cnf(160055552,plain,(~$equal(set_difference(singleton(a),singleton(b)),singleton(a))|$equal(b,a)),inference(rewrite,[status(thm)],[t20_zfmisc_1]),[]).
% 
% fof(l34_zfmisc_1,plain,(((~$equal(set_difference(singleton(A),B),singleton(A))|~in(A,B))&($equal(set_difference(singleton(A),B),singleton(A))|in(A,B)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET879+1.tptp',unknown),[]).
% 
% cnf(159958568,plain,($equal(set_difference(singleton(A),B),singleton(A))|in(A,B)),inference(rewrite,[status(thm)],[l34_zfmisc_1]),[]).
% 
% cnf(173632856,plain,($equal(b,a)|in(a,singleton(b))),inference(resolution,[status(thm)],[160055552,159958568]),[]).
% 
% fof(d1_tarski,plain,(((in(C,B)|~$equal(A,C)|~$equal(singleton(A),B))&(~in(C,B)|$equal(A,C)|~$equal(singleton(A),B))&($equal(c(A,B,C),A)|~$equal(c(A,B,C),A)|$equal(singleton(A),B))&(~in(c(A,B,C),B)|~$equal(c(A,B,C),A)|$equal(singleton(A),B))&($equal(c(A,B,C),A)|in(c(A,B,C),B)|$equal(singleton(A),B))&(~in(c(A,B,C),B)|in(c(A,B,C),B)|$equal(singleton(A),B)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET879+1.tptp',unknown),[]).
% 
% cnf(159941056,plain,(~in(C,B)|$equal(A,C)|~$equal(singleton(A),B)),inference(rewrite,[status(thm)],[d1_tarski]),[]).
% 
% cnf(170497752,plain,(~in(B,singleton(A))|$equal(A,B)),inference(equality_resolution,[status(thm)],[159941056]),[]).
% 
% cnf(173842680,plain,($equal(b,a)),inference(resolution,[status(thm)],[173632856,170497752]),[]).
% 
% cnf(174383240,plain,($equal(set_difference(singleton(a),singleton(b)),singleton(a))),inference(resolution,[status(thm)],[160061640,173842680]),[]).
% 
% cnf(159952992,plain,(in(C,B)|~$equal(A,C)|~$equal(singleton(A),B)),inference(rewrite,[status(thm)],[d1_tarski]),[]).
% 
% cnf(170610136,plain,(in(A,B)|~$equal(singleton(A),B)),inference(equality_resolution,[status(thm)],[159952992]),[]).
% 
% cnf(174578024,plain,(in(a,A)|~$equal(set_difference(singleton(a),singleton(b)),A)),inference(forward_subsumption_resolution__paramodulation,[status(thm)],[173842680,160061640,170610136,theory(equality)]),[]).
% 
% cnf(174892712,plain,(in(a,singleton(b))),inference(forward_subsumption_resolution__paramodulation,[status(thm)],[174578024,173632856,160061640,173632856,theory(equality)]),[]).
% 
% cnf(159965200,plain,(~$equal(set_difference(singleton(A),B),singleton(A))|~in(A,B)),inference(rewrite,[status(thm)],[l34_zfmisc_1]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[174383240,174892712,159965200]),[]).
% 
% END OF PROOF SEQUENCE
% faust: ../JJParser/Signature.c:39: void FreeSignatureList(SymbolNodeType**): Assertion `(*Symbols)->NumberOfUses == 0' failed.
% 
%------------------------------------------------------------------------------