%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : SET095+4 : TPTP v3.4.2. Released v2.2.0.
% 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 15:28:15 EDT 2009

% Result   : Theorem 0.1s
% Output   : Refutation 0.1s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   12 (   6 unt;   0 def)
%            Number of atoms       :   25 (   0 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   22 (   9   ~;   9   |;   4   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-3 aty)
%            Number of variables   :   15 (   4 sgn   5   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(thI44,plain,
    ( member(x,a)
    & ~ subset(singleton(x),a) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET095+4.tptp',unknown),
    [] ).

cnf(145071584,plain,
    member(x,a),
    inference(rewrite,[status(thm)],[thI44]),
    [] ).

fof(subset,plain,
    ! [A,B,C] :
      ( ( ~ subset(A,B)
        | ~ member(C,A)
        | member(C,B) )
      & ( ~ member(x(A,B,C),B)
        | subset(A,B) )
      & ( member(x(A,B,C),A)
        | subset(A,B) ) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET095+4.tptp',unknown),
    [] ).

cnf(144801624,plain,
    ( member(x(A,B,C),A)
    | subset(A,B) ),
    inference(rewrite,[status(thm)],[subset]),
    [] ).

cnf(145063688,plain,
    ~ subset(singleton(x),a),
    inference(rewrite,[status(thm)],[thI44]),
    [] ).

cnf(155916744,plain,
    member(x(singleton(x),a,A),singleton(x)),
    inference(resolution,[status(thm)],[144801624,145063688]),
    [] ).

fof(singleton,plain,
    ! [A,B] :
      ( ( ~ member(A,singleton(B))
        | $equal(B,A) )
      & ( member(A,singleton(B))
        | ~ $equal(B,A) ) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET095+4.tptp',unknown),
    [] ).

cnf(144952968,plain,
    ( ~ member(A,singleton(B))
    | $equal(B,A) ),
    inference(rewrite,[status(thm)],[singleton]),
    [] ).

cnf(158464680,plain,
    $equal(x,x(singleton(x),a,A)),
    inference(resolution,[status(thm)],[155916744,144952968]),
    [] ).

cnf(144808680,plain,
    ( ~ member(x(A,B,C),B)
    | subset(A,B) ),
    inference(rewrite,[status(thm)],[subset]),
    [] ).

cnf(160208824,plain,
    subset(singleton(x),a),
    inference(forward_subsumption_resolution__paramodulation,[status(thm)],[145071584,158464680,144808680,theory(equality)]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(resolution,[status(thm)],[160208824,145063688]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(thI44,plain,((member(x,a)&~subset(singleton(x),a))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET095+4.tptp',unknown),[]).
% 
% cnf(145071584,plain,(member(x,a)),inference(rewrite,[status(thm)],[thI44]),[]).
% 
% fof(subset,plain,(((~subset(A,B)|~member(C,A)|member(C,B))&(~member(x(A,B,C),B)|subset(A,B))&(member(x(A,B,C),A)|subset(A,B)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET095+4.tptp',unknown),[]).
% 
% cnf(144801624,plain,(member(x(A,B,C),A)|subset(A,B)),inference(rewrite,[status(thm)],[subset]),[]).
% 
% cnf(145063688,plain,(~subset(singleton(x),a)),inference(rewrite,[status(thm)],[thI44]),[]).
% 
% cnf(155916744,plain,(member(x(singleton(x),a,A),singleton(x))),inference(resolution,[status(thm)],[144801624,145063688]),[]).
% 
% fof(singleton,plain,(((~member(A,singleton(B))|$equal(B,A))&(member(A,singleton(B))|~$equal(B,A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET095+4.tptp',unknown),[]).
% 
% cnf(144952968,plain,(~member(A,singleton(B))|$equal(B,A)),inference(rewrite,[status(thm)],[singleton]),[]).
% 
% cnf(158464680,plain,($equal(x,x(singleton(x),a,A))),inference(resolution,[status(thm)],[155916744,144952968]),[]).
% 
% cnf(144808680,plain,(~member(x(A,B,C),B)|subset(A,B)),inference(rewrite,[status(thm)],[subset]),[]).
% 
% cnf(160208824,plain,(subset(singleton(x),a)),inference(forward_subsumption_resolution__paramodulation,[status(thm)],[145071584,158464680,144808680,theory(equality)]),[]).
% 
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[160208824,145063688]),[]).
% 
% END OF PROOF SEQUENCE
% faust: ../JJParser/Signature.c:39: void FreeSignatureList(SymbolNodeType**): Assertion `(*Symbols)->NumberOfUses == 0' failed.
% 
%------------------------------------------------------------------------------