TSTP Solution File: SEU117+1 by SInE---0.4

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%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SEU117+1 : TPTP v5.0.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art07.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 04:42:06 EST 2010

% Result   : Theorem 0.19s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   35 (   6 unt;   0 def)
%            Number of atoms       :  167 (  22 equ)
%            Maximal formula atoms :   26 (   4 avg)
%            Number of connectives :  209 (  77   ~;  85   |;  40   &)
%                                         (   3 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   10 (   8 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   60 (   2 sgn  37   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(20,axiom,
    ! [X1,X2] :
      ( preboolean(X2)
     => ( X2 = finite_subsets(X1)
      <=> ! [X3] :
            ( in(X3,X2)
          <=> ( subset(X3,X1)
              & finite(X3) ) ) ) ),
    file('/tmp/tmpKYEga4/sel_SEU117+1.p_1',d5_finsub_1) ).

fof(21,axiom,
    ! [X1,X2] :
      ( element(X1,X2)
     => ( empty(X2)
        | in(X1,X2) ) ),
    file('/tmp/tmpKYEga4/sel_SEU117+1.p_1',t2_subset) ).

fof(22,conjecture,
    ! [X1,X2] :
      ( element(X2,finite_subsets(X1))
     => element(X2,powerset(X1)) ),
    file('/tmp/tmpKYEga4/sel_SEU117+1.p_1',t32_finsub_1) ).

fof(24,axiom,
    ! [X1,X2] :
      ( element(X1,powerset(X2))
    <=> subset(X1,X2) ),
    file('/tmp/tmpKYEga4/sel_SEU117+1.p_1',t3_subset) ).

fof(25,axiom,
    ! [X1] :
      ( ~ empty(finite_subsets(X1))
      & cup_closed(finite_subsets(X1))
      & diff_closed(finite_subsets(X1))
      & preboolean(finite_subsets(X1)) ),
    file('/tmp/tmpKYEga4/sel_SEU117+1.p_1',fc2_finsub_1) ).

fof(33,negated_conjecture,
    ~ ! [X1,X2] :
        ( element(X2,finite_subsets(X1))
       => element(X2,powerset(X1)) ),
    inference(assume_negation,[status(cth)],[22]) ).

fof(42,plain,
    ! [X1] :
      ( ~ empty(finite_subsets(X1))
      & cup_closed(finite_subsets(X1))
      & diff_closed(finite_subsets(X1))
      & preboolean(finite_subsets(X1)) ),
    inference(fof_simplification,[status(thm)],[25,theory(equality)]) ).

fof(123,plain,
    ! [X1,X2] :
      ( ~ preboolean(X2)
      | ( ( X2 != finite_subsets(X1)
          | ! [X3] :
              ( ( ~ in(X3,X2)
                | ( subset(X3,X1)
                  & finite(X3) ) )
              & ( ~ subset(X3,X1)
                | ~ finite(X3)
                | in(X3,X2) ) ) )
        & ( ? [X3] :
              ( ( ~ in(X3,X2)
                | ~ subset(X3,X1)
                | ~ finite(X3) )
              & ( in(X3,X2)
                | ( subset(X3,X1)
                  & finite(X3) ) ) )
          | X2 = finite_subsets(X1) ) ) ),
    inference(fof_nnf,[status(thm)],[20]) ).

fof(124,plain,
    ! [X4,X5] :
      ( ~ preboolean(X5)
      | ( ( X5 != finite_subsets(X4)
          | ! [X6] :
              ( ( ~ in(X6,X5)
                | ( subset(X6,X4)
                  & finite(X6) ) )
              & ( ~ subset(X6,X4)
                | ~ finite(X6)
                | in(X6,X5) ) ) )
        & ( ? [X7] :
              ( ( ~ in(X7,X5)
                | ~ subset(X7,X4)
                | ~ finite(X7) )
              & ( in(X7,X5)
                | ( subset(X7,X4)
                  & finite(X7) ) ) )
          | X5 = finite_subsets(X4) ) ) ),
    inference(variable_rename,[status(thm)],[123]) ).

fof(125,plain,
    ! [X4,X5] :
      ( ~ preboolean(X5)
      | ( ( X5 != finite_subsets(X4)
          | ! [X6] :
              ( ( ~ in(X6,X5)
                | ( subset(X6,X4)
                  & finite(X6) ) )
              & ( ~ subset(X6,X4)
                | ~ finite(X6)
                | in(X6,X5) ) ) )
        & ( ( ( ~ in(esk7_2(X4,X5),X5)
              | ~ subset(esk7_2(X4,X5),X4)
              | ~ finite(esk7_2(X4,X5)) )
            & ( in(esk7_2(X4,X5),X5)
              | ( subset(esk7_2(X4,X5),X4)
                & finite(esk7_2(X4,X5)) ) ) )
          | X5 = finite_subsets(X4) ) ) ),
    inference(skolemize,[status(esa)],[124]) ).

fof(126,plain,
    ! [X4,X5,X6] :
      ( ( ( ( ( ~ in(X6,X5)
              | ( subset(X6,X4)
                & finite(X6) ) )
            & ( ~ subset(X6,X4)
              | ~ finite(X6)
              | in(X6,X5) ) )
          | X5 != finite_subsets(X4) )
        & ( ( ( ~ in(esk7_2(X4,X5),X5)
              | ~ subset(esk7_2(X4,X5),X4)
              | ~ finite(esk7_2(X4,X5)) )
            & ( in(esk7_2(X4,X5),X5)
              | ( subset(esk7_2(X4,X5),X4)
                & finite(esk7_2(X4,X5)) ) ) )
          | X5 = finite_subsets(X4) ) )
      | ~ preboolean(X5) ),
    inference(shift_quantors,[status(thm)],[125]) ).

fof(127,plain,
    ! [X4,X5,X6] :
      ( ( subset(X6,X4)
        | ~ in(X6,X5)
        | X5 != finite_subsets(X4)
        | ~ preboolean(X5) )
      & ( finite(X6)
        | ~ in(X6,X5)
        | X5 != finite_subsets(X4)
        | ~ preboolean(X5) )
      & ( ~ subset(X6,X4)
        | ~ finite(X6)
        | in(X6,X5)
        | X5 != finite_subsets(X4)
        | ~ preboolean(X5) )
      & ( ~ in(esk7_2(X4,X5),X5)
        | ~ subset(esk7_2(X4,X5),X4)
        | ~ finite(esk7_2(X4,X5))
        | X5 = finite_subsets(X4)
        | ~ preboolean(X5) )
      & ( subset(esk7_2(X4,X5),X4)
        | in(esk7_2(X4,X5),X5)
        | X5 = finite_subsets(X4)
        | ~ preboolean(X5) )
      & ( finite(esk7_2(X4,X5))
        | in(esk7_2(X4,X5),X5)
        | X5 = finite_subsets(X4)
        | ~ preboolean(X5) ) ),
    inference(distribute,[status(thm)],[126]) ).

cnf(133,plain,
    ( subset(X3,X2)
    | ~ preboolean(X1)
    | X1 != finite_subsets(X2)
    | ~ in(X3,X1) ),
    inference(split_conjunct,[status(thm)],[127]) ).

fof(134,plain,
    ! [X1,X2] :
      ( ~ element(X1,X2)
      | empty(X2)
      | in(X1,X2) ),
    inference(fof_nnf,[status(thm)],[21]) ).

fof(135,plain,
    ! [X3,X4] :
      ( ~ element(X3,X4)
      | empty(X4)
      | in(X3,X4) ),
    inference(variable_rename,[status(thm)],[134]) ).

cnf(136,plain,
    ( in(X1,X2)
    | empty(X2)
    | ~ element(X1,X2) ),
    inference(split_conjunct,[status(thm)],[135]) ).

fof(137,negated_conjecture,
    ? [X1,X2] :
      ( element(X2,finite_subsets(X1))
      & ~ element(X2,powerset(X1)) ),
    inference(fof_nnf,[status(thm)],[33]) ).

fof(138,negated_conjecture,
    ? [X3,X4] :
      ( element(X4,finite_subsets(X3))
      & ~ element(X4,powerset(X3)) ),
    inference(variable_rename,[status(thm)],[137]) ).

fof(139,negated_conjecture,
    ( element(esk9_0,finite_subsets(esk8_0))
    & ~ element(esk9_0,powerset(esk8_0)) ),
    inference(skolemize,[status(esa)],[138]) ).

cnf(140,negated_conjecture,
    ~ element(esk9_0,powerset(esk8_0)),
    inference(split_conjunct,[status(thm)],[139]) ).

cnf(141,negated_conjecture,
    element(esk9_0,finite_subsets(esk8_0)),
    inference(split_conjunct,[status(thm)],[139]) ).

fof(145,plain,
    ! [X1,X2] :
      ( ( ~ element(X1,powerset(X2))
        | subset(X1,X2) )
      & ( ~ subset(X1,X2)
        | element(X1,powerset(X2)) ) ),
    inference(fof_nnf,[status(thm)],[24]) ).

fof(146,plain,
    ! [X3,X4] :
      ( ( ~ element(X3,powerset(X4))
        | subset(X3,X4) )
      & ( ~ subset(X3,X4)
        | element(X3,powerset(X4)) ) ),
    inference(variable_rename,[status(thm)],[145]) ).

cnf(147,plain,
    ( element(X1,powerset(X2))
    | ~ subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[146]) ).

fof(149,plain,
    ! [X2] :
      ( ~ empty(finite_subsets(X2))
      & cup_closed(finite_subsets(X2))
      & diff_closed(finite_subsets(X2))
      & preboolean(finite_subsets(X2)) ),
    inference(variable_rename,[status(thm)],[42]) ).

cnf(150,plain,
    preboolean(finite_subsets(X1)),
    inference(split_conjunct,[status(thm)],[149]) ).

cnf(153,plain,
    ~ empty(finite_subsets(X1)),
    inference(split_conjunct,[status(thm)],[149]) ).

cnf(221,plain,
    ( subset(X1,X2)
    | empty(X3)
    | finite_subsets(X2) != X3
    | ~ preboolean(X3)
    | ~ element(X1,X3) ),
    inference(spm,[status(thm)],[133,136,theory(equality)]) ).

cnf(401,negated_conjecture,
    ( subset(esk9_0,X1)
    | empty(finite_subsets(esk8_0))
    | finite_subsets(X1) != finite_subsets(esk8_0)
    | ~ preboolean(finite_subsets(esk8_0)) ),
    inference(spm,[status(thm)],[221,141,theory(equality)]) ).

cnf(410,negated_conjecture,
    ( subset(esk9_0,X1)
    | empty(finite_subsets(esk8_0))
    | finite_subsets(X1) != finite_subsets(esk8_0)
    | $false ),
    inference(rw,[status(thm)],[401,150,theory(equality)]) ).

cnf(411,negated_conjecture,
    ( subset(esk9_0,X1)
    | empty(finite_subsets(esk8_0))
    | finite_subsets(X1) != finite_subsets(esk8_0) ),
    inference(cn,[status(thm)],[410,theory(equality)]) ).

cnf(412,negated_conjecture,
    ( subset(esk9_0,X1)
    | finite_subsets(X1) != finite_subsets(esk8_0) ),
    inference(sr,[status(thm)],[411,153,theory(equality)]) ).

cnf(431,negated_conjecture,
    ( element(esk9_0,powerset(X1))
    | finite_subsets(X1) != finite_subsets(esk8_0) ),
    inference(spm,[status(thm)],[147,412,theory(equality)]) ).

cnf(435,negated_conjecture,
    $false,
    inference(spm,[status(thm)],[140,431,theory(equality)]) ).

cnf(442,negated_conjecture,
    $false,
    435,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU117+1.p
% --creating new selector for []
% -running prover on /tmp/tmpKYEga4/sel_SEU117+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU117+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU117+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU117+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
% 
%------------------------------------------------------------------------------