TSTP Solution File: SEU143+1 by SInE---0.4

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%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SEU143+1 : TPTP v5.0.0. Released v3.3.0.
% 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 04:51:28 EST 2010

% Result   : Theorem 0.22s
% Output   : CNFRefutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   25 (  10 unt;   0 def)
%            Number of atoms       :   92 (  54 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  111 (  44   ~;  44   |;  19   &)
%                                         (   4 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   46 (   1 sgn  32   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(4,axiom,
    ! [X1,X2] :
      ( X2 = singleton(X1)
    <=> ! [X3] :
          ( in(X3,X2)
        <=> X3 = X1 ) ),
    file('/tmp/tmpZBGhx3/sel_SEU143+1.p_1',d1_tarski) ).

fof(5,conjecture,
    ! [X1] : singleton(X1) != empty_set,
    file('/tmp/tmpZBGhx3/sel_SEU143+1.p_1',l1_zfmisc_1) ).

fof(8,axiom,
    ! [X1] :
      ( X1 = empty_set
    <=> ! [X2] : ~ in(X2,X1) ),
    file('/tmp/tmpZBGhx3/sel_SEU143+1.p_1',d1_xboole_0) ).

fof(10,negated_conjecture,
    ~ ! [X1] : singleton(X1) != empty_set,
    inference(assume_negation,[status(cth)],[5]) ).

fof(13,plain,
    ! [X1] :
      ( X1 = empty_set
    <=> ! [X2] : ~ in(X2,X1) ),
    inference(fof_simplification,[status(thm)],[8,theory(equality)]) ).

fof(19,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(20,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)],[19]) ).

fof(21,plain,
    ! [X4,X5] :
      ( ( X5 != singleton(X4)
        | ! [X6] :
            ( ( ~ in(X6,X5)
              | X6 = X4 )
            & ( X6 != X4
              | in(X6,X5) ) ) )
      & ( ( ( ~ in(esk2_2(X4,X5),X5)
            | esk2_2(X4,X5) != X4 )
          & ( in(esk2_2(X4,X5),X5)
            | esk2_2(X4,X5) = X4 ) )
        | X5 = singleton(X4) ) ),
    inference(skolemize,[status(esa)],[20]) ).

fof(22,plain,
    ! [X4,X5,X6] :
      ( ( ( ( ~ in(X6,X5)
            | X6 = X4 )
          & ( X6 != X4
            | in(X6,X5) ) )
        | X5 != singleton(X4) )
      & ( ( ( ~ in(esk2_2(X4,X5),X5)
            | esk2_2(X4,X5) != X4 )
          & ( in(esk2_2(X4,X5),X5)
            | esk2_2(X4,X5) = X4 ) )
        | X5 = singleton(X4) ) ),
    inference(shift_quantors,[status(thm)],[21]) ).

fof(23,plain,
    ! [X4,X5,X6] :
      ( ( ~ in(X6,X5)
        | X6 = X4
        | X5 != singleton(X4) )
      & ( X6 != X4
        | in(X6,X5)
        | X5 != singleton(X4) )
      & ( ~ in(esk2_2(X4,X5),X5)
        | esk2_2(X4,X5) != X4
        | X5 = singleton(X4) )
      & ( in(esk2_2(X4,X5),X5)
        | esk2_2(X4,X5) = X4
        | X5 = singleton(X4) ) ),
    inference(distribute,[status(thm)],[22]) ).

cnf(26,plain,
    ( in(X3,X1)
    | X1 != singleton(X2)
    | X3 != X2 ),
    inference(split_conjunct,[status(thm)],[23]) ).

fof(28,negated_conjecture,
    ? [X1] : singleton(X1) = empty_set,
    inference(fof_nnf,[status(thm)],[10]) ).

fof(29,negated_conjecture,
    ? [X2] : singleton(X2) = empty_set,
    inference(variable_rename,[status(thm)],[28]) ).

fof(30,negated_conjecture,
    singleton(esk3_0) = empty_set,
    inference(skolemize,[status(esa)],[29]) ).

cnf(31,negated_conjecture,
    singleton(esk3_0) = empty_set,
    inference(split_conjunct,[status(thm)],[30]) ).

fof(38,plain,
    ! [X1] :
      ( ( X1 != empty_set
        | ! [X2] : ~ in(X2,X1) )
      & ( ? [X2] : in(X2,X1)
        | X1 = empty_set ) ),
    inference(fof_nnf,[status(thm)],[13]) ).

fof(39,plain,
    ! [X3] :
      ( ( X3 != empty_set
        | ! [X4] : ~ in(X4,X3) )
      & ( ? [X5] : in(X5,X3)
        | X3 = empty_set ) ),
    inference(variable_rename,[status(thm)],[38]) ).

fof(40,plain,
    ! [X3] :
      ( ( X3 != empty_set
        | ! [X4] : ~ in(X4,X3) )
      & ( in(esk5_1(X3),X3)
        | X3 = empty_set ) ),
    inference(skolemize,[status(esa)],[39]) ).

fof(41,plain,
    ! [X3,X4] :
      ( ( ~ in(X4,X3)
        | X3 != empty_set )
      & ( in(esk5_1(X3),X3)
        | X3 = empty_set ) ),
    inference(shift_quantors,[status(thm)],[40]) ).

cnf(43,plain,
    ( X1 != empty_set
    | ~ in(X2,X1) ),
    inference(split_conjunct,[status(thm)],[41]) ).

cnf(45,plain,
    ( in(X1,X2)
    | singleton(X1) != X2 ),
    inference(er,[status(thm)],[26,theory(equality)]) ).

cnf(54,plain,
    in(X1,singleton(X1)),
    inference(er,[status(thm)],[45,theory(equality)]) ).

cnf(56,negated_conjecture,
    in(esk3_0,empty_set),
    inference(spm,[status(thm)],[54,31,theory(equality)]) ).

cnf(61,negated_conjecture,
    $false,
    inference(spm,[status(thm)],[43,56,theory(equality)]) ).

cnf(63,negated_conjecture,
    $false,
    61,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU143+1.p
% --creating new selector for []
% -running prover on /tmp/tmpZBGhx3/sel_SEU143+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU143+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU143+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU143+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
% 
%------------------------------------------------------------------------------