TSTP Solution File: SEU186+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SEU186+1 : 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 05:17:05 EST 2010

% Result   : Theorem 0.17s
% Output   : CNFRefutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   47 (  19 unt;   0 def)
%            Number of atoms       :  113 (  33 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  118 (  52   ~;  38   |;  19   &)
%                                         (   1 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   2 con; 0-2 aty)
%            Number of variables   :   95 (   4 sgn  61   !;  10   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(4,conjecture,
    ! [X1] :
      ( relation(X1)
     => ( ! [X2,X3] : ~ in(ordered_pair(X2,X3),X1)
       => X1 = empty_set ) ),
    file('/tmp/tmpUM9HV5/sel_SEU186+1.p_1',t56_relat_1) ).

fof(8,axiom,
    ! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
    file('/tmp/tmpUM9HV5/sel_SEU186+1.p_1',commutativity_k2_tarski) ).

fof(14,axiom,
    ! [X1] :
      ( relation(X1)
    <=> ! [X2] :
          ~ ( in(X2,X1)
            & ! [X3,X4] : X2 != ordered_pair(X3,X4) ) ),
    file('/tmp/tmpUM9HV5/sel_SEU186+1.p_1',d1_relat_1) ).

fof(15,axiom,
    ! [X1,X2] :
      ( element(X1,X2)
     => ( empty(X2)
        | in(X1,X2) ) ),
    file('/tmp/tmpUM9HV5/sel_SEU186+1.p_1',t2_subset) ).

fof(21,axiom,
    ! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
    file('/tmp/tmpUM9HV5/sel_SEU186+1.p_1',d5_tarski) ).

fof(22,axiom,
    ! [X1] :
      ( empty(X1)
     => X1 = empty_set ),
    file('/tmp/tmpUM9HV5/sel_SEU186+1.p_1',t6_boole) ).

fof(23,axiom,
    ! [X1] :
    ? [X2] : element(X2,X1),
    file('/tmp/tmpUM9HV5/sel_SEU186+1.p_1',existence_m1_subset_1) ).

fof(27,negated_conjecture,
    ~ ! [X1] :
        ( relation(X1)
       => ( ! [X2,X3] : ~ in(ordered_pair(X2,X3),X1)
         => X1 = empty_set ) ),
    inference(assume_negation,[status(cth)],[4]) ).

fof(29,negated_conjecture,
    ~ ! [X1] :
        ( relation(X1)
       => ( ! [X2,X3] : ~ in(ordered_pair(X2,X3),X1)
         => X1 = empty_set ) ),
    inference(fof_simplification,[status(thm)],[27,theory(equality)]) ).

fof(45,negated_conjecture,
    ? [X1] :
      ( relation(X1)
      & ! [X2,X3] : ~ in(ordered_pair(X2,X3),X1)
      & X1 != empty_set ),
    inference(fof_nnf,[status(thm)],[29]) ).

fof(46,negated_conjecture,
    ? [X4] :
      ( relation(X4)
      & ! [X5,X6] : ~ in(ordered_pair(X5,X6),X4)
      & X4 != empty_set ),
    inference(variable_rename,[status(thm)],[45]) ).

fof(47,negated_conjecture,
    ( relation(esk3_0)
    & ! [X5,X6] : ~ in(ordered_pair(X5,X6),esk3_0)
    & esk3_0 != empty_set ),
    inference(skolemize,[status(esa)],[46]) ).

fof(48,negated_conjecture,
    ! [X5,X6] :
      ( ~ in(ordered_pair(X5,X6),esk3_0)
      & esk3_0 != empty_set
      & relation(esk3_0) ),
    inference(shift_quantors,[status(thm)],[47]) ).

cnf(49,negated_conjecture,
    relation(esk3_0),
    inference(split_conjunct,[status(thm)],[48]) ).

cnf(50,negated_conjecture,
    esk3_0 != empty_set,
    inference(split_conjunct,[status(thm)],[48]) ).

cnf(51,negated_conjecture,
    ~ in(ordered_pair(X1,X2),esk3_0),
    inference(split_conjunct,[status(thm)],[48]) ).

fof(59,plain,
    ! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
    inference(variable_rename,[status(thm)],[8]) ).

cnf(60,plain,
    unordered_pair(X1,X2) = unordered_pair(X2,X1),
    inference(split_conjunct,[status(thm)],[59]) ).

fof(74,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)],[14]) ).

fof(75,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)],[74]) ).

fof(76,plain,
    ! [X5] :
      ( ( ~ relation(X5)
        | ! [X6] :
            ( ~ in(X6,X5)
            | X6 = ordered_pair(esk5_2(X5,X6),esk6_2(X5,X6)) ) )
      & ( ( in(esk7_1(X5),X5)
          & ! [X10,X11] : esk7_1(X5) != ordered_pair(X10,X11) )
        | relation(X5) ) ),
    inference(skolemize,[status(esa)],[75]) ).

fof(77,plain,
    ! [X5,X6,X10,X11] :
      ( ( ( esk7_1(X5) != ordered_pair(X10,X11)
          & in(esk7_1(X5),X5) )
        | relation(X5) )
      & ( ~ in(X6,X5)
        | X6 = ordered_pair(esk5_2(X5,X6),esk6_2(X5,X6))
        | ~ relation(X5) ) ),
    inference(shift_quantors,[status(thm)],[76]) ).

fof(78,plain,
    ! [X5,X6,X10,X11] :
      ( ( esk7_1(X5) != ordered_pair(X10,X11)
        | relation(X5) )
      & ( in(esk7_1(X5),X5)
        | relation(X5) )
      & ( ~ in(X6,X5)
        | X6 = ordered_pair(esk5_2(X5,X6),esk6_2(X5,X6))
        | ~ relation(X5) ) ),
    inference(distribute,[status(thm)],[77]) ).

cnf(79,plain,
    ( X2 = ordered_pair(esk5_2(X1,X2),esk6_2(X1,X2))
    | ~ relation(X1)
    | ~ in(X2,X1) ),
    inference(split_conjunct,[status(thm)],[78]) ).

fof(82,plain,
    ! [X1,X2] :
      ( ~ element(X1,X2)
      | empty(X2)
      | in(X1,X2) ),
    inference(fof_nnf,[status(thm)],[15]) ).

fof(83,plain,
    ! [X3,X4] :
      ( ~ element(X3,X4)
      | empty(X4)
      | in(X3,X4) ),
    inference(variable_rename,[status(thm)],[82]) ).

cnf(84,plain,
    ( in(X1,X2)
    | empty(X2)
    | ~ element(X1,X2) ),
    inference(split_conjunct,[status(thm)],[83]) ).

fof(91,plain,
    ! [X3,X4] : ordered_pair(X3,X4) = unordered_pair(unordered_pair(X3,X4),singleton(X3)),
    inference(variable_rename,[status(thm)],[21]) ).

cnf(92,plain,
    ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
    inference(split_conjunct,[status(thm)],[91]) ).

fof(93,plain,
    ! [X1] :
      ( ~ empty(X1)
      | X1 = empty_set ),
    inference(fof_nnf,[status(thm)],[22]) ).

fof(94,plain,
    ! [X2] :
      ( ~ empty(X2)
      | X2 = empty_set ),
    inference(variable_rename,[status(thm)],[93]) ).

cnf(95,plain,
    ( X1 = empty_set
    | ~ empty(X1) ),
    inference(split_conjunct,[status(thm)],[94]) ).

fof(96,plain,
    ! [X3] :
    ? [X4] : element(X4,X3),
    inference(variable_rename,[status(thm)],[23]) ).

fof(97,plain,
    ! [X3] : element(esk8_1(X3),X3),
    inference(skolemize,[status(esa)],[96]) ).

cnf(98,plain,
    element(esk8_1(X1),X1),
    inference(split_conjunct,[status(thm)],[97]) ).

cnf(107,plain,
    ( unordered_pair(unordered_pair(esk5_2(X1,X2),esk6_2(X1,X2)),singleton(esk5_2(X1,X2))) = X2
    | ~ relation(X1)
    | ~ in(X2,X1) ),
    inference(rw,[status(thm)],[79,92,theory(equality)]),
    [unfolding] ).

cnf(109,negated_conjecture,
    ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),esk3_0),
    inference(rw,[status(thm)],[51,92,theory(equality)]),
    [unfolding] ).

cnf(124,plain,
    ( in(esk8_1(X1),X1)
    | empty(X1) ),
    inference(spm,[status(thm)],[84,98,theory(equality)]) ).

cnf(126,plain,
    ( unordered_pair(singleton(esk5_2(X1,X2)),unordered_pair(esk5_2(X1,X2),esk6_2(X1,X2))) = X2
    | ~ relation(X1)
    | ~ in(X2,X1) ),
    inference(rw,[status(thm)],[107,60,theory(equality)]) ).

cnf(130,negated_conjecture,
    ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),esk3_0),
    inference(spm,[status(thm)],[109,60,theory(equality)]) ).

cnf(159,negated_conjecture,
    ( ~ in(X2,esk3_0)
    | ~ in(X2,X1)
    | ~ relation(X1) ),
    inference(spm,[status(thm)],[130,126,theory(equality)]) ).

cnf(171,negated_conjecture,
    ( empty(esk3_0)
    | ~ in(esk8_1(esk3_0),X1)
    | ~ relation(X1) ),
    inference(spm,[status(thm)],[159,124,theory(equality)]) ).

cnf(173,negated_conjecture,
    ( empty(esk3_0)
    | ~ relation(esk3_0) ),
    inference(spm,[status(thm)],[171,124,theory(equality)]) ).

cnf(174,negated_conjecture,
    empty(esk3_0),
    inference(spm,[status(thm)],[173,49,theory(equality)]) ).

cnf(176,negated_conjecture,
    empty_set = esk3_0,
    inference(spm,[status(thm)],[95,174,theory(equality)]) ).

cnf(180,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[176,50,theory(equality)]) ).

cnf(181,negated_conjecture,
    $false,
    180,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU186+1.p
% --creating new selector for []
% -running prover on /tmp/tmpUM9HV5/sel_SEU186+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU186+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU186+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU186+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
% 
%------------------------------------------------------------------------------