TSTP Solution File: SET880+1 by SInE---0.4

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%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SET880+1 : TPTP v5.0.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art05.cs.miami.edu
% Model    : i686 i686
% CPU      : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory   : 2018MB
% OS       : Linux 2.6.26.8-57.fc8
% CPULimit : 300s
% DateTime : Sun Dec 26 03:43:07 EST 2010

% Result   : Theorem 0.17s
% Output   : CNFRefutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   23 (   6 unt;   0 def)
%            Number of atoms       :   88 (  57 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  104 (  39   ~;  40   |;  20   &)
%                                         (   3 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   40 (   0 sgn  28   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(3,conjecture,
    ! [X1,X2] :
      ( set_difference(singleton(X1),singleton(X2)) = empty_set
     => X1 = X2 ),
    file('/tmp/tmp5Xh7wB/sel_SET880+1.p_1',t21_zfmisc_1) ).

fof(4,axiom,
    ! [X1,X2] :
      ( X2 = singleton(X1)
    <=> ! [X3] :
          ( in(X3,X2)
        <=> X3 = X1 ) ),
    file('/tmp/tmp5Xh7wB/sel_SET880+1.p_1',d1_tarski) ).

fof(7,axiom,
    ! [X1,X2] :
      ( set_difference(singleton(X1),X2) = empty_set
    <=> in(X1,X2) ),
    file('/tmp/tmp5Xh7wB/sel_SET880+1.p_1',l36_zfmisc_1) ).

fof(8,negated_conjecture,
    ~ ! [X1,X2] :
        ( set_difference(singleton(X1),singleton(X2)) = empty_set
       => X1 = X2 ),
    inference(assume_negation,[status(cth)],[3]) ).

fof(15,negated_conjecture,
    ? [X1,X2] :
      ( set_difference(singleton(X1),singleton(X2)) = empty_set
      & X1 != X2 ),
    inference(fof_nnf,[status(thm)],[8]) ).

fof(16,negated_conjecture,
    ? [X3,X4] :
      ( set_difference(singleton(X3),singleton(X4)) = empty_set
      & X3 != X4 ),
    inference(variable_rename,[status(thm)],[15]) ).

fof(17,negated_conjecture,
    ( set_difference(singleton(esk2_0),singleton(esk3_0)) = empty_set
    & esk2_0 != esk3_0 ),
    inference(skolemize,[status(esa)],[16]) ).

cnf(18,negated_conjecture,
    esk2_0 != esk3_0,
    inference(split_conjunct,[status(thm)],[17]) ).

cnf(19,negated_conjecture,
    set_difference(singleton(esk2_0),singleton(esk3_0)) = empty_set,
    inference(split_conjunct,[status(thm)],[17]) ).

fof(20,plain,
    ! [X1,X2] :
      ( ( X2 != singleton(X1)
        | ! [X3] :
            ( ( ~ in(X3,X2)
              | X3 = X1 )
            & ( X3 != X1
              | in(X3,X2) ) ) )
      & ( ? [X3] :
            ( ( ~ in(X3,X2)
              | X3 != X1 )
            & ( in(X3,X2)
              | X3 = X1 ) )
        | X2 = singleton(X1) ) ),
    inference(fof_nnf,[status(thm)],[4]) ).

fof(21,plain,
    ! [X4,X5] :
      ( ( X5 != singleton(X4)
        | ! [X6] :
            ( ( ~ in(X6,X5)
              | X6 = X4 )
            & ( X6 != X4
              | in(X6,X5) ) ) )
      & ( ? [X7] :
            ( ( ~ in(X7,X5)
              | X7 != X4 )
            & ( in(X7,X5)
              | X7 = X4 ) )
        | X5 = singleton(X4) ) ),
    inference(variable_rename,[status(thm)],[20]) ).

fof(22,plain,
    ! [X4,X5] :
      ( ( X5 != singleton(X4)
        | ! [X6] :
            ( ( ~ in(X6,X5)
              | X6 = X4 )
            & ( X6 != X4
              | in(X6,X5) ) ) )
      & ( ( ( ~ in(esk4_2(X4,X5),X5)
            | esk4_2(X4,X5) != X4 )
          & ( in(esk4_2(X4,X5),X5)
            | esk4_2(X4,X5) = X4 ) )
        | X5 = singleton(X4) ) ),
    inference(skolemize,[status(esa)],[21]) ).

fof(23,plain,
    ! [X4,X5,X6] :
      ( ( ( ( ~ in(X6,X5)
            | X6 = X4 )
          & ( X6 != X4
            | in(X6,X5) ) )
        | X5 != singleton(X4) )
      & ( ( ( ~ in(esk4_2(X4,X5),X5)
            | esk4_2(X4,X5) != X4 )
          & ( in(esk4_2(X4,X5),X5)
            | esk4_2(X4,X5) = X4 ) )
        | X5 = singleton(X4) ) ),
    inference(shift_quantors,[status(thm)],[22]) ).

fof(24,plain,
    ! [X4,X5,X6] :
      ( ( ~ in(X6,X5)
        | X6 = X4
        | X5 != singleton(X4) )
      & ( X6 != X4
        | in(X6,X5)
        | X5 != singleton(X4) )
      & ( ~ in(esk4_2(X4,X5),X5)
        | esk4_2(X4,X5) != X4
        | X5 = singleton(X4) )
      & ( in(esk4_2(X4,X5),X5)
        | esk4_2(X4,X5) = X4
        | X5 = singleton(X4) ) ),
    inference(distribute,[status(thm)],[23]) ).

cnf(28,plain,
    ( X3 = X2
    | X1 != singleton(X2)
    | ~ in(X3,X1) ),
    inference(split_conjunct,[status(thm)],[24]) ).

fof(35,plain,
    ! [X1,X2] :
      ( ( set_difference(singleton(X1),X2) != empty_set
        | in(X1,X2) )
      & ( ~ in(X1,X2)
        | set_difference(singleton(X1),X2) = empty_set ) ),
    inference(fof_nnf,[status(thm)],[7]) ).

fof(36,plain,
    ! [X3,X4] :
      ( ( set_difference(singleton(X3),X4) != empty_set
        | in(X3,X4) )
      & ( ~ in(X3,X4)
        | set_difference(singleton(X3),X4) = empty_set ) ),
    inference(variable_rename,[status(thm)],[35]) ).

cnf(38,plain,
    ( in(X1,X2)
    | set_difference(singleton(X1),X2) != empty_set ),
    inference(split_conjunct,[status(thm)],[36]) ).

cnf(39,negated_conjecture,
    in(esk2_0,singleton(esk3_0)),
    inference(spm,[status(thm)],[38,19,theory(equality)]) ).

cnf(46,negated_conjecture,
    ( X1 = esk2_0
    | singleton(X1) != singleton(esk3_0) ),
    inference(spm,[status(thm)],[28,39,theory(equality)]) ).

cnf(47,negated_conjecture,
    esk3_0 = esk2_0,
    inference(er,[status(thm)],[46,theory(equality)]) ).

cnf(48,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[47,18,theory(equality)]) ).

cnf(49,negated_conjecture,
    $false,
    48,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET880+1.p
% --creating new selector for []
% -running prover on /tmp/tmp5Xh7wB/sel_SET880+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET880+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET880+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET880+1.p
% Solved 1 out of 1.
% # Problem is unsatisfiable (or provable), constructing proof object
% # SZS status Theorem
% # SZS output start CNFRefutation.
% See solution above
% # SZS output end CNFRefutation
% 
%------------------------------------------------------------------------------