TSTP Solution File: SEU230+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SEU230+1 : TPTP v5.0.0. Released v3.3.0.
% 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 05:58:36 EST 2010

% Result   : Theorem 0.18s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   31 (  15 unt;   0 def)
%            Number of atoms       :  160 (  56 equ)
%            Maximal formula atoms :   20 (   5 avg)
%            Number of connectives :  206 (  77   ~;  85   |;  40   &)
%                                         (   4 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   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;   1 con; 0-3 aty)
%            Number of variables   :   66 (   2 sgn  46   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(3,conjecture,
    ! [X1] : in(X1,succ(X1)),
    file('/tmp/tmptVRGyw/sel_SEU230+1.p_1',t10_ordinal1) ).

fof(19,axiom,
    ! [X1] : succ(X1) = set_union2(X1,singleton(X1)),
    file('/tmp/tmptVRGyw/sel_SEU230+1.p_1',d1_ordinal1) ).

fof(22,axiom,
    ! [X1,X2,X3] :
      ( X3 = set_union2(X1,X2)
    <=> ! [X4] :
          ( in(X4,X3)
        <=> ( in(X4,X1)
            | in(X4,X2) ) ) ),
    file('/tmp/tmptVRGyw/sel_SEU230+1.p_1',d2_xboole_0) ).

fof(34,axiom,
    ! [X1,X2] :
      ( X2 = singleton(X1)
    <=> ! [X3] :
          ( in(X3,X2)
        <=> X3 = X1 ) ),
    file('/tmp/tmptVRGyw/sel_SEU230+1.p_1',d1_tarski) ).

fof(39,negated_conjecture,
    ~ ! [X1] : in(X1,succ(X1)),
    inference(assume_negation,[status(cth)],[3]) ).

fof(53,negated_conjecture,
    ? [X1] : ~ in(X1,succ(X1)),
    inference(fof_nnf,[status(thm)],[39]) ).

fof(54,negated_conjecture,
    ? [X2] : ~ in(X2,succ(X2)),
    inference(variable_rename,[status(thm)],[53]) ).

fof(55,negated_conjecture,
    ~ in(esk3_0,succ(esk3_0)),
    inference(skolemize,[status(esa)],[54]) ).

cnf(56,negated_conjecture,
    ~ in(esk3_0,succ(esk3_0)),
    inference(split_conjunct,[status(thm)],[55]) ).

fof(104,plain,
    ! [X2] : succ(X2) = set_union2(X2,singleton(X2)),
    inference(variable_rename,[status(thm)],[19]) ).

cnf(105,plain,
    succ(X1) = set_union2(X1,singleton(X1)),
    inference(split_conjunct,[status(thm)],[104]) ).

fof(108,plain,
    ! [X1,X2,X3] :
      ( ( X3 != set_union2(X1,X2)
        | ! [X4] :
            ( ( ~ in(X4,X3)
              | in(X4,X1)
              | in(X4,X2) )
            & ( ( ~ in(X4,X1)
                & ~ in(X4,X2) )
              | in(X4,X3) ) ) )
      & ( ? [X4] :
            ( ( ~ in(X4,X3)
              | ( ~ in(X4,X1)
                & ~ in(X4,X2) ) )
            & ( in(X4,X3)
              | in(X4,X1)
              | in(X4,X2) ) )
        | X3 = set_union2(X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[22]) ).

fof(109,plain,
    ! [X5,X6,X7] :
      ( ( X7 != set_union2(X5,X6)
        | ! [X8] :
            ( ( ~ in(X8,X7)
              | in(X8,X5)
              | in(X8,X6) )
            & ( ( ~ in(X8,X5)
                & ~ in(X8,X6) )
              | in(X8,X7) ) ) )
      & ( ? [X9] :
            ( ( ~ in(X9,X7)
              | ( ~ in(X9,X5)
                & ~ in(X9,X6) ) )
            & ( in(X9,X7)
              | in(X9,X5)
              | in(X9,X6) ) )
        | X7 = set_union2(X5,X6) ) ),
    inference(variable_rename,[status(thm)],[108]) ).

fof(110,plain,
    ! [X5,X6,X7] :
      ( ( X7 != set_union2(X5,X6)
        | ! [X8] :
            ( ( ~ in(X8,X7)
              | in(X8,X5)
              | in(X8,X6) )
            & ( ( ~ in(X8,X5)
                & ~ in(X8,X6) )
              | in(X8,X7) ) ) )
      & ( ( ( ~ in(esk7_3(X5,X6,X7),X7)
            | ( ~ in(esk7_3(X5,X6,X7),X5)
              & ~ in(esk7_3(X5,X6,X7),X6) ) )
          & ( in(esk7_3(X5,X6,X7),X7)
            | in(esk7_3(X5,X6,X7),X5)
            | in(esk7_3(X5,X6,X7),X6) ) )
        | X7 = set_union2(X5,X6) ) ),
    inference(skolemize,[status(esa)],[109]) ).

fof(111,plain,
    ! [X5,X6,X7,X8] :
      ( ( ( ( ~ in(X8,X7)
            | in(X8,X5)
            | in(X8,X6) )
          & ( ( ~ in(X8,X5)
              & ~ in(X8,X6) )
            | in(X8,X7) ) )
        | X7 != set_union2(X5,X6) )
      & ( ( ( ~ in(esk7_3(X5,X6,X7),X7)
            | ( ~ in(esk7_3(X5,X6,X7),X5)
              & ~ in(esk7_3(X5,X6,X7),X6) ) )
          & ( in(esk7_3(X5,X6,X7),X7)
            | in(esk7_3(X5,X6,X7),X5)
            | in(esk7_3(X5,X6,X7),X6) ) )
        | X7 = set_union2(X5,X6) ) ),
    inference(shift_quantors,[status(thm)],[110]) ).

fof(112,plain,
    ! [X5,X6,X7,X8] :
      ( ( ~ in(X8,X7)
        | in(X8,X5)
        | in(X8,X6)
        | X7 != set_union2(X5,X6) )
      & ( ~ in(X8,X5)
        | in(X8,X7)
        | X7 != set_union2(X5,X6) )
      & ( ~ in(X8,X6)
        | in(X8,X7)
        | X7 != set_union2(X5,X6) )
      & ( ~ in(esk7_3(X5,X6,X7),X5)
        | ~ in(esk7_3(X5,X6,X7),X7)
        | X7 = set_union2(X5,X6) )
      & ( ~ in(esk7_3(X5,X6,X7),X6)
        | ~ in(esk7_3(X5,X6,X7),X7)
        | X7 = set_union2(X5,X6) )
      & ( in(esk7_3(X5,X6,X7),X7)
        | in(esk7_3(X5,X6,X7),X5)
        | in(esk7_3(X5,X6,X7),X6)
        | X7 = set_union2(X5,X6) ) ),
    inference(distribute,[status(thm)],[111]) ).

cnf(116,plain,
    ( in(X4,X1)
    | X1 != set_union2(X2,X3)
    | ~ in(X4,X3) ),
    inference(split_conjunct,[status(thm)],[112]) ).

fof(143,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)],[34]) ).

fof(144,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)],[143]) ).

fof(145,plain,
    ! [X4,X5] :
      ( ( X5 != singleton(X4)
        | ! [X6] :
            ( ( ~ in(X6,X5)
              | X6 = X4 )
            & ( X6 != X4
              | in(X6,X5) ) ) )
      & ( ( ( ~ in(esk9_2(X4,X5),X5)
            | esk9_2(X4,X5) != X4 )
          & ( in(esk9_2(X4,X5),X5)
            | esk9_2(X4,X5) = X4 ) )
        | X5 = singleton(X4) ) ),
    inference(skolemize,[status(esa)],[144]) ).

fof(146,plain,
    ! [X4,X5,X6] :
      ( ( ( ( ~ in(X6,X5)
            | X6 = X4 )
          & ( X6 != X4
            | in(X6,X5) ) )
        | X5 != singleton(X4) )
      & ( ( ( ~ in(esk9_2(X4,X5),X5)
            | esk9_2(X4,X5) != X4 )
          & ( in(esk9_2(X4,X5),X5)
            | esk9_2(X4,X5) = X4 ) )
        | X5 = singleton(X4) ) ),
    inference(shift_quantors,[status(thm)],[145]) ).

fof(147,plain,
    ! [X4,X5,X6] :
      ( ( ~ in(X6,X5)
        | X6 = X4
        | X5 != singleton(X4) )
      & ( X6 != X4
        | in(X6,X5)
        | X5 != singleton(X4) )
      & ( ~ in(esk9_2(X4,X5),X5)
        | esk9_2(X4,X5) != X4
        | X5 = singleton(X4) )
      & ( in(esk9_2(X4,X5),X5)
        | esk9_2(X4,X5) = X4
        | X5 = singleton(X4) ) ),
    inference(distribute,[status(thm)],[146]) ).

cnf(150,plain,
    ( in(X3,X1)
    | X1 != singleton(X2)
    | X3 != X2 ),
    inference(split_conjunct,[status(thm)],[147]) ).

cnf(171,negated_conjecture,
    ~ in(esk3_0,set_union2(esk3_0,singleton(esk3_0))),
    inference(rw,[status(thm)],[56,105,theory(equality)]),
    [unfolding] ).

cnf(188,plain,
    ( in(X1,X2)
    | singleton(X1) != X2 ),
    inference(er,[status(thm)],[150,theory(equality)]) ).

cnf(198,plain,
    ( in(X1,set_union2(X2,X3))
    | ~ in(X1,X3) ),
    inference(er,[status(thm)],[116,theory(equality)]) ).

cnf(316,plain,
    in(X1,singleton(X1)),
    inference(er,[status(thm)],[188,theory(equality)]) ).

cnf(335,negated_conjecture,
    ~ in(esk3_0,singleton(esk3_0)),
    inference(spm,[status(thm)],[171,198,theory(equality)]) ).

cnf(343,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[335,316,theory(equality)]) ).

cnf(344,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[343,theory(equality)]) ).

cnf(345,negated_conjecture,
    $false,
    344,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU230+1.p
% --creating new selector for []
% -running prover on /tmp/tmptVRGyw/sel_SEU230+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU230+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU230+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU230+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
% 
%------------------------------------------------------------------------------