TSTP Solution File: SET867+1 by SInE---0.4

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%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SET867+1 : TPTP v5.0.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art09.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 03:42:10 EST 2010

% Result   : Theorem 0.29s
% Output   : CNFRefutation 0.29s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   23 (   6 unt;   0 def)
%            Number of atoms       :  119 (  38 equ)
%            Maximal formula atoms :   20 (   5 avg)
%            Number of connectives :  153 (  57   ~;  62   |;  30   &)
%                                         (   4 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   1 con; 0-3 aty)
%            Number of variables   :   58 (   1 sgn  40   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1,X2] :
      ( X2 = union(X1)
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ? [X4] :
              ( in(X3,X4)
              & in(X4,X1) ) ) ),
    file('/tmp/tmpxLXc3S/sel_SET867+1.p_1',d4_tarski) ).

fof(2,conjecture,
    union(empty_set) = empty_set,
    file('/tmp/tmpxLXc3S/sel_SET867+1.p_1',t2_zfmisc_1) ).

fof(6,axiom,
    ! [X1] :
      ( X1 = empty_set
    <=> ! [X2] : ~ in(X2,X1) ),
    file('/tmp/tmpxLXc3S/sel_SET867+1.p_1',d1_xboole_0) ).

fof(8,negated_conjecture,
    union(empty_set) != empty_set,
    inference(assume_negation,[status(cth)],[2]) ).

fof(9,negated_conjecture,
    union(empty_set) != empty_set,
    inference(fof_simplification,[status(thm)],[8,theory(equality)]) ).

fof(12,plain,
    ! [X1] :
      ( X1 = empty_set
    <=> ! [X2] : ~ in(X2,X1) ),
    inference(fof_simplification,[status(thm)],[6,theory(equality)]) ).

fof(13,plain,
    ! [X1,X2] :
      ( ( X2 != union(X1)
        | ! [X3] :
            ( ( ~ in(X3,X2)
              | ? [X4] :
                  ( in(X3,X4)
                  & in(X4,X1) ) )
            & ( ! [X4] :
                  ( ~ in(X3,X4)
                  | ~ in(X4,X1) )
              | in(X3,X2) ) ) )
      & ( ? [X3] :
            ( ( ~ in(X3,X2)
              | ! [X4] :
                  ( ~ in(X3,X4)
                  | ~ in(X4,X1) ) )
            & ( in(X3,X2)
              | ? [X4] :
                  ( in(X3,X4)
                  & in(X4,X1) ) ) )
        | X2 = union(X1) ) ),
    inference(fof_nnf,[status(thm)],[1]) ).

fof(14,plain,
    ! [X5,X6] :
      ( ( X6 != union(X5)
        | ! [X7] :
            ( ( ~ in(X7,X6)
              | ? [X8] :
                  ( in(X7,X8)
                  & in(X8,X5) ) )
            & ( ! [X9] :
                  ( ~ in(X7,X9)
                  | ~ in(X9,X5) )
              | in(X7,X6) ) ) )
      & ( ? [X10] :
            ( ( ~ in(X10,X6)
              | ! [X11] :
                  ( ~ in(X10,X11)
                  | ~ in(X11,X5) ) )
            & ( in(X10,X6)
              | ? [X12] :
                  ( in(X10,X12)
                  & in(X12,X5) ) ) )
        | X6 = union(X5) ) ),
    inference(variable_rename,[status(thm)],[13]) ).

fof(15,plain,
    ! [X5,X6] :
      ( ( X6 != union(X5)
        | ! [X7] :
            ( ( ~ in(X7,X6)
              | ( in(X7,esk1_3(X5,X6,X7))
                & in(esk1_3(X5,X6,X7),X5) ) )
            & ( ! [X9] :
                  ( ~ in(X7,X9)
                  | ~ in(X9,X5) )
              | in(X7,X6) ) ) )
      & ( ( ( ~ in(esk2_2(X5,X6),X6)
            | ! [X11] :
                ( ~ in(esk2_2(X5,X6),X11)
                | ~ in(X11,X5) ) )
          & ( in(esk2_2(X5,X6),X6)
            | ( in(esk2_2(X5,X6),esk3_2(X5,X6))
              & in(esk3_2(X5,X6),X5) ) ) )
        | X6 = union(X5) ) ),
    inference(skolemize,[status(esa)],[14]) ).

fof(16,plain,
    ! [X5,X6,X7,X9,X11] :
      ( ( ( ( ~ in(esk2_2(X5,X6),X11)
            | ~ in(X11,X5)
            | ~ in(esk2_2(X5,X6),X6) )
          & ( in(esk2_2(X5,X6),X6)
            | ( in(esk2_2(X5,X6),esk3_2(X5,X6))
              & in(esk3_2(X5,X6),X5) ) ) )
        | X6 = union(X5) )
      & ( ( ( ~ in(X7,X9)
            | ~ in(X9,X5)
            | in(X7,X6) )
          & ( ~ in(X7,X6)
            | ( in(X7,esk1_3(X5,X6,X7))
              & in(esk1_3(X5,X6,X7),X5) ) ) )
        | X6 != union(X5) ) ),
    inference(shift_quantors,[status(thm)],[15]) ).

fof(17,plain,
    ! [X5,X6,X7,X9,X11] :
      ( ( ~ in(esk2_2(X5,X6),X11)
        | ~ in(X11,X5)
        | ~ in(esk2_2(X5,X6),X6)
        | X6 = union(X5) )
      & ( in(esk2_2(X5,X6),esk3_2(X5,X6))
        | in(esk2_2(X5,X6),X6)
        | X6 = union(X5) )
      & ( in(esk3_2(X5,X6),X5)
        | in(esk2_2(X5,X6),X6)
        | X6 = union(X5) )
      & ( ~ in(X7,X9)
        | ~ in(X9,X5)
        | in(X7,X6)
        | X6 != union(X5) )
      & ( in(X7,esk1_3(X5,X6,X7))
        | ~ in(X7,X6)
        | X6 != union(X5) )
      & ( in(esk1_3(X5,X6,X7),X5)
        | ~ in(X7,X6)
        | X6 != union(X5) ) ),
    inference(distribute,[status(thm)],[16]) ).

cnf(21,plain,
    ( X1 = union(X2)
    | in(esk2_2(X2,X1),X1)
    | in(esk3_2(X2,X1),X2) ),
    inference(split_conjunct,[status(thm)],[17]) ).

cnf(24,negated_conjecture,
    union(empty_set) != empty_set,
    inference(split_conjunct,[status(thm)],[9]) ).

fof(34,plain,
    ! [X1] :
      ( ( X1 != empty_set
        | ! [X2] : ~ in(X2,X1) )
      & ( ? [X2] : in(X2,X1)
        | X1 = empty_set ) ),
    inference(fof_nnf,[status(thm)],[12]) ).

fof(35,plain,
    ! [X3] :
      ( ( X3 != empty_set
        | ! [X4] : ~ in(X4,X3) )
      & ( ? [X5] : in(X5,X3)
        | X3 = empty_set ) ),
    inference(variable_rename,[status(thm)],[34]) ).

fof(36,plain,
    ! [X3] :
      ( ( X3 != empty_set
        | ! [X4] : ~ in(X4,X3) )
      & ( in(esk6_1(X3),X3)
        | X3 = empty_set ) ),
    inference(skolemize,[status(esa)],[35]) ).

fof(37,plain,
    ! [X3,X4] :
      ( ( ~ in(X4,X3)
        | X3 != empty_set )
      & ( in(esk6_1(X3),X3)
        | X3 = empty_set ) ),
    inference(shift_quantors,[status(thm)],[36]) ).

cnf(39,plain,
    ( X1 != empty_set
    | ~ in(X2,X1) ),
    inference(split_conjunct,[status(thm)],[37]) ).

cnf(50,plain,
    ( union(X1) = X2
    | in(esk2_2(X1,X2),X2)
    | empty_set != X1 ),
    inference(spm,[status(thm)],[39,21,theory(equality)]) ).

cnf(62,plain,
    ( union(X2) = X1
    | empty_set != X1
    | empty_set != X2 ),
    inference(spm,[status(thm)],[39,50,theory(equality)]) ).

cnf(66,plain,
    ( union(X1) = empty_set
    | empty_set != X1 ),
    inference(er,[status(thm)],[62,theory(equality)]) ).

cnf(67,negated_conjecture,
    $false,
    inference(spm,[status(thm)],[24,66,theory(equality)]) ).

cnf(68,negated_conjecture,
    $false,
    67,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET867+1.p
% --creating new selector for []
% -running prover on /tmp/tmpxLXc3S/sel_SET867+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET867+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET867+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET867+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
% 
%------------------------------------------------------------------------------