TSTP Solution File: SEU186+2 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SEU186+2 : TPTP v5.0.0. Released v3.3.0.
% 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 05:17:24 EST 2010

% Result   : Theorem 0.52s
% Output   : CNFRefutation 0.52s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   45 (  18 unt;   0 def)
%            Number of atoms       :  114 (  45 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  128 (  59   ~;  37   |;  23   &)
%                                         (   3 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   2 con; 0-2 aty)
%            Number of variables   :   97 (   4 sgn  63   !;  10   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(25,axiom,
    ! [X1] :
      ( X1 = empty_set
    <=> ! [X2] : ~ in(X2,X1) ),
    file('/tmp/tmpjxhKK_/sel_SEU186+2.p_1',d1_xboole_0) ).

fof(43,axiom,
    ! [X1] : unordered_pair(X1,X1) = singleton(X1),
    file('/tmp/tmpjxhKK_/sel_SEU186+2.p_1',t69_enumset1) ).

fof(60,axiom,
    ! [X1] :
      ( relation(X1)
    <=> ! [X2] :
          ~ ( in(X2,X1)
            & ! [X3,X4] : X2 != ordered_pair(X3,X4) ) ),
    file('/tmp/tmpjxhKK_/sel_SEU186+2.p_1',d1_relat_1) ).

fof(85,conjecture,
    ! [X1] :
      ( relation(X1)
     => ( ! [X2,X3] : ~ in(ordered_pair(X2,X3),X1)
       => X1 = empty_set ) ),
    file('/tmp/tmpjxhKK_/sel_SEU186+2.p_1',t56_relat_1) ).

fof(93,axiom,
    ! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
    file('/tmp/tmpjxhKK_/sel_SEU186+2.p_1',commutativity_k2_tarski) ).

fof(115,axiom,
    ! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
    file('/tmp/tmpjxhKK_/sel_SEU186+2.p_1',d5_tarski) ).

fof(165,negated_conjecture,
    ~ ! [X1] :
        ( relation(X1)
       => ( ! [X2,X3] : ~ in(ordered_pair(X2,X3),X1)
         => X1 = empty_set ) ),
    inference(assume_negation,[status(cth)],[85]) ).

fof(171,plain,
    ! [X1] :
      ( X1 = empty_set
    <=> ! [X2] : ~ in(X2,X1) ),
    inference(fof_simplification,[status(thm)],[25,theory(equality)]) ).

fof(176,negated_conjecture,
    ~ ! [X1] :
        ( relation(X1)
       => ( ! [X2,X3] : ~ in(ordered_pair(X2,X3),X1)
         => X1 = empty_set ) ),
    inference(fof_simplification,[status(thm)],[165,theory(equality)]) ).

fof(285,plain,
    ! [X1] :
      ( ( X1 != empty_set
        | ! [X2] : ~ in(X2,X1) )
      & ( ? [X2] : in(X2,X1)
        | X1 = empty_set ) ),
    inference(fof_nnf,[status(thm)],[171]) ).

fof(286,plain,
    ! [X3] :
      ( ( X3 != empty_set
        | ! [X4] : ~ in(X4,X3) )
      & ( ? [X5] : in(X5,X3)
        | X3 = empty_set ) ),
    inference(variable_rename,[status(thm)],[285]) ).

fof(287,plain,
    ! [X3] :
      ( ( X3 != empty_set
        | ! [X4] : ~ in(X4,X3) )
      & ( in(esk10_1(X3),X3)
        | X3 = empty_set ) ),
    inference(skolemize,[status(esa)],[286]) ).

fof(288,plain,
    ! [X3,X4] :
      ( ( ~ in(X4,X3)
        | X3 != empty_set )
      & ( in(esk10_1(X3),X3)
        | X3 = empty_set ) ),
    inference(shift_quantors,[status(thm)],[287]) ).

cnf(289,plain,
    ( X1 = empty_set
    | in(esk10_1(X1),X1) ),
    inference(split_conjunct,[status(thm)],[288]) ).

fof(341,plain,
    ! [X2] : unordered_pair(X2,X2) = singleton(X2),
    inference(variable_rename,[status(thm)],[43]) ).

cnf(342,plain,
    unordered_pair(X1,X1) = singleton(X1),
    inference(split_conjunct,[status(thm)],[341]) ).

fof(418,plain,
    ! [X1] :
      ( ( ~ relation(X1)
        | ! [X2] :
            ( ~ in(X2,X1)
            | ? [X3,X4] : X2 = ordered_pair(X3,X4) ) )
      & ( ? [X2] :
            ( in(X2,X1)
            & ! [X3,X4] : X2 != ordered_pair(X3,X4) )
        | relation(X1) ) ),
    inference(fof_nnf,[status(thm)],[60]) ).

fof(419,plain,
    ! [X5] :
      ( ( ~ relation(X5)
        | ! [X6] :
            ( ~ in(X6,X5)
            | ? [X7,X8] : X6 = ordered_pair(X7,X8) ) )
      & ( ? [X9] :
            ( in(X9,X5)
            & ! [X10,X11] : X9 != ordered_pair(X10,X11) )
        | relation(X5) ) ),
    inference(variable_rename,[status(thm)],[418]) ).

fof(420,plain,
    ! [X5] :
      ( ( ~ relation(X5)
        | ! [X6] :
            ( ~ in(X6,X5)
            | X6 = ordered_pair(esk20_2(X5,X6),esk21_2(X5,X6)) ) )
      & ( ( in(esk22_1(X5),X5)
          & ! [X10,X11] : esk22_1(X5) != ordered_pair(X10,X11) )
        | relation(X5) ) ),
    inference(skolemize,[status(esa)],[419]) ).

fof(421,plain,
    ! [X5,X6,X10,X11] :
      ( ( ( esk22_1(X5) != ordered_pair(X10,X11)
          & in(esk22_1(X5),X5) )
        | relation(X5) )
      & ( ~ in(X6,X5)
        | X6 = ordered_pair(esk20_2(X5,X6),esk21_2(X5,X6))
        | ~ relation(X5) ) ),
    inference(shift_quantors,[status(thm)],[420]) ).

fof(422,plain,
    ! [X5,X6,X10,X11] :
      ( ( esk22_1(X5) != ordered_pair(X10,X11)
        | relation(X5) )
      & ( in(esk22_1(X5),X5)
        | relation(X5) )
      & ( ~ in(X6,X5)
        | X6 = ordered_pair(esk20_2(X5,X6),esk21_2(X5,X6))
        | ~ relation(X5) ) ),
    inference(distribute,[status(thm)],[421]) ).

cnf(423,plain,
    ( X2 = ordered_pair(esk20_2(X1,X2),esk21_2(X1,X2))
    | ~ relation(X1)
    | ~ in(X2,X1) ),
    inference(split_conjunct,[status(thm)],[422]) ).

fof(521,negated_conjecture,
    ? [X1] :
      ( relation(X1)
      & ! [X2,X3] : ~ in(ordered_pair(X2,X3),X1)
      & X1 != empty_set ),
    inference(fof_nnf,[status(thm)],[176]) ).

fof(522,negated_conjecture,
    ? [X4] :
      ( relation(X4)
      & ! [X5,X6] : ~ in(ordered_pair(X5,X6),X4)
      & X4 != empty_set ),
    inference(variable_rename,[status(thm)],[521]) ).

fof(523,negated_conjecture,
    ( relation(esk27_0)
    & ! [X5,X6] : ~ in(ordered_pair(X5,X6),esk27_0)
    & esk27_0 != empty_set ),
    inference(skolemize,[status(esa)],[522]) ).

fof(524,negated_conjecture,
    ! [X5,X6] :
      ( ~ in(ordered_pair(X5,X6),esk27_0)
      & esk27_0 != empty_set
      & relation(esk27_0) ),
    inference(shift_quantors,[status(thm)],[523]) ).

cnf(525,negated_conjecture,
    relation(esk27_0),
    inference(split_conjunct,[status(thm)],[524]) ).

cnf(526,negated_conjecture,
    esk27_0 != empty_set,
    inference(split_conjunct,[status(thm)],[524]) ).

cnf(527,negated_conjecture,
    ~ in(ordered_pair(X1,X2),esk27_0),
    inference(split_conjunct,[status(thm)],[524]) ).

fof(552,plain,
    ! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
    inference(variable_rename,[status(thm)],[93]) ).

cnf(553,plain,
    unordered_pair(X1,X2) = unordered_pair(X2,X1),
    inference(split_conjunct,[status(thm)],[552]) ).

fof(627,plain,
    ! [X3,X4] : ordered_pair(X3,X4) = unordered_pair(unordered_pair(X3,X4),singleton(X3)),
    inference(variable_rename,[status(thm)],[115]) ).

cnf(628,plain,
    ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
    inference(split_conjunct,[status(thm)],[627]) ).

cnf(832,plain,
    unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)) = ordered_pair(X1,X2),
    inference(rw,[status(thm)],[628,342,theory(equality)]),
    [unfolding] ).

cnf(886,plain,
    ( unordered_pair(unordered_pair(esk20_2(X1,X2),esk21_2(X1,X2)),unordered_pair(esk20_2(X1,X2),esk20_2(X1,X2))) = X2
    | ~ relation(X1)
    | ~ in(X2,X1) ),
    inference(rw,[status(thm)],[423,832,theory(equality)]),
    [unfolding] ).

cnf(913,negated_conjecture,
    ~ in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),esk27_0),
    inference(rw,[status(thm)],[527,832,theory(equality)]),
    [unfolding] ).

cnf(1013,negated_conjecture,
    ~ in(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,X2)),esk27_0),
    inference(spm,[status(thm)],[913,553,theory(equality)]) ).

cnf(3208,plain,
    ( unordered_pair(unordered_pair(esk20_2(X1,X2),esk20_2(X1,X2)),unordered_pair(esk20_2(X1,X2),esk21_2(X1,X2))) = X2
    | ~ relation(X1)
    | ~ in(X2,X1) ),
    inference(rw,[status(thm)],[886,553,theory(equality)]) ).

cnf(5272,negated_conjecture,
    ( ~ in(X2,esk27_0)
    | ~ in(X2,X1)
    | ~ relation(X1) ),
    inference(spm,[status(thm)],[1013,3208,theory(equality)]) ).

cnf(5283,negated_conjecture,
    ( empty_set = esk27_0
    | ~ in(esk10_1(esk27_0),X1)
    | ~ relation(X1) ),
    inference(spm,[status(thm)],[5272,289,theory(equality)]) ).

cnf(5320,negated_conjecture,
    ( ~ in(esk10_1(esk27_0),X1)
    | ~ relation(X1) ),
    inference(sr,[status(thm)],[5283,526,theory(equality)]) ).

cnf(5336,negated_conjecture,
    ( empty_set = esk27_0
    | ~ relation(esk27_0) ),
    inference(spm,[status(thm)],[5320,289,theory(equality)]) ).

cnf(5342,negated_conjecture,
    ~ relation(esk27_0),
    inference(sr,[status(thm)],[5336,526,theory(equality)]) ).

cnf(5344,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[525,5342,theory(equality)]) ).

cnf(5345,negated_conjecture,
    $false,
    5344,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU186+2.p
% --creating new selector for []
% -running prover on /tmp/tmpjxhKK_/sel_SEU186+2.p_1 with time limit 29
% -prover status Theorem
% Problem SEU186+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU186+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU186+2.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
% 
%------------------------------------------------------------------------------