TSTP Solution File: SEU094+1 by SInE---0.4

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%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SEU094+1 : TPTP v5.0.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art01.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 04:34:57 EST 2010

% Result   : Theorem 0.27s
% Output   : CNFRefutation 0.27s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   53 (  10 unt;   0 def)
%            Number of atoms       :  162 (   0 equ)
%            Maximal formula atoms :   11 (   3 avg)
%            Number of connectives :  179 (  70   ~;  75   |;  25   &)
%                                         (   3 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-1 aty)
%            Number of variables   :   52 (   0 sgn  32   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(9,axiom,
    ! [X1,X2] :
      ( ( subset(X1,X2)
        & finite(X2) )
     => finite(X1) ),
    file('/tmp/tmpxvW0PK/sel_SEU094+1.p_1',t13_finset_1) ).

fof(35,axiom,
    ! [X1] :
      ( finite(X1)
    <=> finite(powerset(X1)) ),
    file('/tmp/tmpxvW0PK/sel_SEU094+1.p_1',t24_finset_1) ).

fof(38,axiom,
    ! [X1] : subset(X1,powerset(union(X1))),
    file('/tmp/tmpxvW0PK/sel_SEU094+1.p_1',t100_zfmisc_1) ).

fof(46,axiom,
    ! [X1,X2] :
      ( in(X1,X2)
     => subset(X1,union(X2)) ),
    file('/tmp/tmpxvW0PK/sel_SEU094+1.p_1',t92_zfmisc_1) ).

fof(48,axiom,
    ! [X1] :
      ( ( finite(X1)
        & ! [X2] :
            ( in(X2,X1)
           => finite(X2) ) )
     => finite(union(X1)) ),
    file('/tmp/tmpxvW0PK/sel_SEU094+1.p_1',l22_finset_1) ).

fof(52,conjecture,
    ! [X1] :
      ( ( finite(X1)
        & ! [X2] :
            ( in(X2,X1)
           => finite(X2) ) )
    <=> finite(union(X1)) ),
    file('/tmp/tmpxvW0PK/sel_SEU094+1.p_1',t25_finset_1) ).

fof(61,negated_conjecture,
    ~ ! [X1] :
        ( ( finite(X1)
          & ! [X2] :
              ( in(X2,X1)
             => finite(X2) ) )
      <=> finite(union(X1)) ),
    inference(assume_negation,[status(cth)],[52]) ).

fof(105,plain,
    ! [X1,X2] :
      ( ~ subset(X1,X2)
      | ~ finite(X2)
      | finite(X1) ),
    inference(fof_nnf,[status(thm)],[9]) ).

fof(106,plain,
    ! [X3,X4] :
      ( ~ subset(X3,X4)
      | ~ finite(X4)
      | finite(X3) ),
    inference(variable_rename,[status(thm)],[105]) ).

cnf(107,plain,
    ( finite(X1)
    | ~ finite(X2)
    | ~ subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[106]) ).

fof(231,plain,
    ! [X1] :
      ( ( ~ finite(X1)
        | finite(powerset(X1)) )
      & ( ~ finite(powerset(X1))
        | finite(X1) ) ),
    inference(fof_nnf,[status(thm)],[35]) ).

fof(232,plain,
    ! [X2] :
      ( ( ~ finite(X2)
        | finite(powerset(X2)) )
      & ( ~ finite(powerset(X2))
        | finite(X2) ) ),
    inference(variable_rename,[status(thm)],[231]) ).

cnf(234,plain,
    ( finite(powerset(X1))
    | ~ finite(X1) ),
    inference(split_conjunct,[status(thm)],[232]) ).

fof(244,plain,
    ! [X2] : subset(X2,powerset(union(X2))),
    inference(variable_rename,[status(thm)],[38]) ).

cnf(245,plain,
    subset(X1,powerset(union(X1))),
    inference(split_conjunct,[status(thm)],[244]) ).

fof(278,plain,
    ! [X1,X2] :
      ( ~ in(X1,X2)
      | subset(X1,union(X2)) ),
    inference(fof_nnf,[status(thm)],[46]) ).

fof(279,plain,
    ! [X3,X4] :
      ( ~ in(X3,X4)
      | subset(X3,union(X4)) ),
    inference(variable_rename,[status(thm)],[278]) ).

cnf(280,plain,
    ( subset(X1,union(X2))
    | ~ in(X1,X2) ),
    inference(split_conjunct,[status(thm)],[279]) ).

fof(285,plain,
    ! [X1] :
      ( ~ finite(X1)
      | ? [X2] :
          ( in(X2,X1)
          & ~ finite(X2) )
      | finite(union(X1)) ),
    inference(fof_nnf,[status(thm)],[48]) ).

fof(286,plain,
    ! [X3] :
      ( ~ finite(X3)
      | ? [X4] :
          ( in(X4,X3)
          & ~ finite(X4) )
      | finite(union(X3)) ),
    inference(variable_rename,[status(thm)],[285]) ).

fof(287,plain,
    ! [X3] :
      ( ~ finite(X3)
      | ( in(esk22_1(X3),X3)
        & ~ finite(esk22_1(X3)) )
      | finite(union(X3)) ),
    inference(skolemize,[status(esa)],[286]) ).

fof(288,plain,
    ! [X3] :
      ( ( in(esk22_1(X3),X3)
        | ~ finite(X3)
        | finite(union(X3)) )
      & ( ~ finite(esk22_1(X3))
        | ~ finite(X3)
        | finite(union(X3)) ) ),
    inference(distribute,[status(thm)],[287]) ).

cnf(289,plain,
    ( finite(union(X1))
    | ~ finite(X1)
    | ~ finite(esk22_1(X1)) ),
    inference(split_conjunct,[status(thm)],[288]) ).

cnf(290,plain,
    ( finite(union(X1))
    | in(esk22_1(X1),X1)
    | ~ finite(X1) ),
    inference(split_conjunct,[status(thm)],[288]) ).

fof(305,negated_conjecture,
    ? [X1] :
      ( ( ~ finite(X1)
        | ? [X2] :
            ( in(X2,X1)
            & ~ finite(X2) )
        | ~ finite(union(X1)) )
      & ( ( finite(X1)
          & ! [X2] :
              ( ~ in(X2,X1)
              | finite(X2) ) )
        | finite(union(X1)) ) ),
    inference(fof_nnf,[status(thm)],[61]) ).

fof(306,negated_conjecture,
    ? [X3] :
      ( ( ~ finite(X3)
        | ? [X4] :
            ( in(X4,X3)
            & ~ finite(X4) )
        | ~ finite(union(X3)) )
      & ( ( finite(X3)
          & ! [X5] :
              ( ~ in(X5,X3)
              | finite(X5) ) )
        | finite(union(X3)) ) ),
    inference(variable_rename,[status(thm)],[305]) ).

fof(307,negated_conjecture,
    ( ( ~ finite(esk24_0)
      | ( in(esk25_0,esk24_0)
        & ~ finite(esk25_0) )
      | ~ finite(union(esk24_0)) )
    & ( ( finite(esk24_0)
        & ! [X5] :
            ( ~ in(X5,esk24_0)
            | finite(X5) ) )
      | finite(union(esk24_0)) ) ),
    inference(skolemize,[status(esa)],[306]) ).

fof(308,negated_conjecture,
    ! [X5] :
      ( ( ( ( ~ in(X5,esk24_0)
            | finite(X5) )
          & finite(esk24_0) )
        | finite(union(esk24_0)) )
      & ( ~ finite(esk24_0)
        | ( in(esk25_0,esk24_0)
          & ~ finite(esk25_0) )
        | ~ finite(union(esk24_0)) ) ),
    inference(shift_quantors,[status(thm)],[307]) ).

fof(309,negated_conjecture,
    ! [X5] :
      ( ( ~ in(X5,esk24_0)
        | finite(X5)
        | finite(union(esk24_0)) )
      & ( finite(esk24_0)
        | finite(union(esk24_0)) )
      & ( in(esk25_0,esk24_0)
        | ~ finite(esk24_0)
        | ~ finite(union(esk24_0)) )
      & ( ~ finite(esk25_0)
        | ~ finite(esk24_0)
        | ~ finite(union(esk24_0)) ) ),
    inference(distribute,[status(thm)],[308]) ).

cnf(310,negated_conjecture,
    ( ~ finite(union(esk24_0))
    | ~ finite(esk24_0)
    | ~ finite(esk25_0) ),
    inference(split_conjunct,[status(thm)],[309]) ).

cnf(311,negated_conjecture,
    ( in(esk25_0,esk24_0)
    | ~ finite(union(esk24_0))
    | ~ finite(esk24_0) ),
    inference(split_conjunct,[status(thm)],[309]) ).

cnf(312,negated_conjecture,
    ( finite(union(esk24_0))
    | finite(esk24_0) ),
    inference(split_conjunct,[status(thm)],[309]) ).

cnf(313,negated_conjecture,
    ( finite(union(esk24_0))
    | finite(X1)
    | ~ in(X1,esk24_0) ),
    inference(split_conjunct,[status(thm)],[309]) ).

cnf(378,plain,
    ( finite(X1)
    | ~ finite(powerset(union(X1))) ),
    inference(spm,[status(thm)],[107,245,theory(equality)]) ).

cnf(379,plain,
    ( finite(X1)
    | ~ finite(union(X2))
    | ~ in(X1,X2) ),
    inference(spm,[status(thm)],[107,280,theory(equality)]) ).

cnf(380,negated_conjecture,
    ( finite(union(esk24_0))
    | finite(esk22_1(esk24_0))
    | ~ finite(esk24_0) ),
    inference(spm,[status(thm)],[313,290,theory(equality)]) ).

cnf(605,negated_conjecture,
    ( finite(union(esk24_0))
    | finite(esk22_1(esk24_0)) ),
    inference(csr,[status(thm)],[380,312]) ).

cnf(606,negated_conjecture,
    ( finite(union(esk24_0))
    | ~ finite(esk24_0) ),
    inference(spm,[status(thm)],[289,605,theory(equality)]) ).

cnf(613,negated_conjecture,
    finite(union(esk24_0)),
    inference(csr,[status(thm)],[606,312]) ).

cnf(615,negated_conjecture,
    ( $false
    | ~ finite(esk24_0)
    | ~ finite(esk25_0) ),
    inference(rw,[status(thm)],[310,613,theory(equality)]) ).

cnf(616,negated_conjecture,
    ( ~ finite(esk24_0)
    | ~ finite(esk25_0) ),
    inference(cn,[status(thm)],[615,theory(equality)]) ).

cnf(618,negated_conjecture,
    ( in(esk25_0,esk24_0)
    | $false
    | ~ finite(esk24_0) ),
    inference(rw,[status(thm)],[311,613,theory(equality)]) ).

cnf(619,negated_conjecture,
    ( in(esk25_0,esk24_0)
    | ~ finite(esk24_0) ),
    inference(cn,[status(thm)],[618,theory(equality)]) ).

cnf(640,plain,
    ( finite(X1)
    | ~ finite(union(X1)) ),
    inference(spm,[status(thm)],[378,234,theory(equality)]) ).

cnf(642,negated_conjecture,
    ( finite(X1)
    | ~ in(X1,esk24_0) ),
    inference(spm,[status(thm)],[379,613,theory(equality)]) ).

cnf(654,negated_conjecture,
    finite(esk24_0),
    inference(spm,[status(thm)],[640,613,theory(equality)]) ).

cnf(666,negated_conjecture,
    ( $false
    | ~ finite(esk25_0) ),
    inference(rw,[status(thm)],[616,654,theory(equality)]) ).

cnf(667,negated_conjecture,
    ~ finite(esk25_0),
    inference(cn,[status(thm)],[666,theory(equality)]) ).

cnf(670,negated_conjecture,
    ( in(esk25_0,esk24_0)
    | $false ),
    inference(rw,[status(thm)],[619,654,theory(equality)]) ).

cnf(671,negated_conjecture,
    in(esk25_0,esk24_0),
    inference(cn,[status(thm)],[670,theory(equality)]) ).

cnf(682,negated_conjecture,
    finite(esk25_0),
    inference(spm,[status(thm)],[642,671,theory(equality)]) ).

cnf(685,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[682,667,theory(equality)]) ).

cnf(686,negated_conjecture,
    $false,
    685,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU094+1.p
% --creating new selector for []
% -running prover on /tmp/tmpxvW0PK/sel_SEU094+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU094+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU094+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU094+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
% 
%------------------------------------------------------------------------------