TSTP Solution File: SEU177+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SEU177+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 05:06:50 EST 2010

% Result   : Theorem 0.26s
% Output   : CNFRefutation 0.26s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   40 (  11 unt;   0 def)
%            Number of atoms       :  195 (  39 equ)
%            Maximal formula atoms :   16 (   4 avg)
%            Number of connectives :  254 (  99   ~; 107   |;  38   &)
%                                         (   4 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   14 (  14 usr;   3 con; 0-3 aty)
%            Number of variables   :  110 (   3 sgn  66   !;  20   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1] :
      ( relation(X1)
     => ! [X2] :
          ( X2 = relation_rng(X1)
        <=> ! [X3] :
              ( in(X3,X2)
            <=> ? [X4] : in(ordered_pair(X4,X3),X1) ) ) ),
    file('/tmp/tmphRY4t2/sel_SEU177+1.p_1',d5_relat_1) ).

fof(12,axiom,
    ! [X1] :
      ( relation(X1)
     => ! [X2] :
          ( X2 = relation_dom(X1)
        <=> ! [X3] :
              ( in(X3,X2)
            <=> ? [X4] : in(ordered_pair(X3,X4),X1) ) ) ),
    file('/tmp/tmphRY4t2/sel_SEU177+1.p_1',d4_relat_1) ).

fof(19,axiom,
    ! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
    file('/tmp/tmphRY4t2/sel_SEU177+1.p_1',d5_tarski) ).

fof(26,conjecture,
    ! [X1,X2,X3] :
      ( relation(X3)
     => ( in(ordered_pair(X1,X2),X3)
       => ( in(X1,relation_dom(X3))
          & in(X2,relation_rng(X3)) ) ) ),
    file('/tmp/tmphRY4t2/sel_SEU177+1.p_1',t20_relat_1) ).

fof(27,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( relation(X3)
       => ( in(ordered_pair(X1,X2),X3)
         => ( in(X1,relation_dom(X3))
            & in(X2,relation_rng(X3)) ) ) ),
    inference(assume_negation,[status(cth)],[26]) ).

fof(33,plain,
    ! [X1] :
      ( ~ relation(X1)
      | ! [X2] :
          ( ( X2 != relation_rng(X1)
            | ! [X3] :
                ( ( ~ in(X3,X2)
                  | ? [X4] : in(ordered_pair(X4,X3),X1) )
                & ( ! [X4] : ~ in(ordered_pair(X4,X3),X1)
                  | in(X3,X2) ) ) )
          & ( ? [X3] :
                ( ( ~ in(X3,X2)
                  | ! [X4] : ~ in(ordered_pair(X4,X3),X1) )
                & ( in(X3,X2)
                  | ? [X4] : in(ordered_pair(X4,X3),X1) ) )
            | X2 = relation_rng(X1) ) ) ),
    inference(fof_nnf,[status(thm)],[1]) ).

fof(34,plain,
    ! [X5] :
      ( ~ relation(X5)
      | ! [X6] :
          ( ( X6 != relation_rng(X5)
            | ! [X7] :
                ( ( ~ in(X7,X6)
                  | ? [X8] : in(ordered_pair(X8,X7),X5) )
                & ( ! [X9] : ~ in(ordered_pair(X9,X7),X5)
                  | in(X7,X6) ) ) )
          & ( ? [X10] :
                ( ( ~ in(X10,X6)
                  | ! [X11] : ~ in(ordered_pair(X11,X10),X5) )
                & ( in(X10,X6)
                  | ? [X12] : in(ordered_pair(X12,X10),X5) ) )
            | X6 = relation_rng(X5) ) ) ),
    inference(variable_rename,[status(thm)],[33]) ).

fof(35,plain,
    ! [X5] :
      ( ~ relation(X5)
      | ! [X6] :
          ( ( X6 != relation_rng(X5)
            | ! [X7] :
                ( ( ~ in(X7,X6)
                  | in(ordered_pair(esk1_3(X5,X6,X7),X7),X5) )
                & ( ! [X9] : ~ in(ordered_pair(X9,X7),X5)
                  | in(X7,X6) ) ) )
          & ( ( ( ~ in(esk2_2(X5,X6),X6)
                | ! [X11] : ~ in(ordered_pair(X11,esk2_2(X5,X6)),X5) )
              & ( in(esk2_2(X5,X6),X6)
                | in(ordered_pair(esk3_2(X5,X6),esk2_2(X5,X6)),X5) ) )
            | X6 = relation_rng(X5) ) ) ),
    inference(skolemize,[status(esa)],[34]) ).

fof(36,plain,
    ! [X5,X6,X7,X9,X11] :
      ( ( ( ( ( ~ in(ordered_pair(X11,esk2_2(X5,X6)),X5)
              | ~ in(esk2_2(X5,X6),X6) )
            & ( in(esk2_2(X5,X6),X6)
              | in(ordered_pair(esk3_2(X5,X6),esk2_2(X5,X6)),X5) ) )
          | X6 = relation_rng(X5) )
        & ( ( ( ~ in(ordered_pair(X9,X7),X5)
              | in(X7,X6) )
            & ( ~ in(X7,X6)
              | in(ordered_pair(esk1_3(X5,X6,X7),X7),X5) ) )
          | X6 != relation_rng(X5) ) )
      | ~ relation(X5) ),
    inference(shift_quantors,[status(thm)],[35]) ).

fof(37,plain,
    ! [X5,X6,X7,X9,X11] :
      ( ( ~ in(ordered_pair(X11,esk2_2(X5,X6)),X5)
        | ~ in(esk2_2(X5,X6),X6)
        | X6 = relation_rng(X5)
        | ~ relation(X5) )
      & ( in(esk2_2(X5,X6),X6)
        | in(ordered_pair(esk3_2(X5,X6),esk2_2(X5,X6)),X5)
        | X6 = relation_rng(X5)
        | ~ relation(X5) )
      & ( ~ in(ordered_pair(X9,X7),X5)
        | in(X7,X6)
        | X6 != relation_rng(X5)
        | ~ relation(X5) )
      & ( ~ in(X7,X6)
        | in(ordered_pair(esk1_3(X5,X6,X7),X7),X5)
        | X6 != relation_rng(X5)
        | ~ relation(X5) ) ),
    inference(distribute,[status(thm)],[36]) ).

cnf(39,plain,
    ( in(X3,X2)
    | ~ relation(X1)
    | X2 != relation_rng(X1)
    | ~ in(ordered_pair(X4,X3),X1) ),
    inference(split_conjunct,[status(thm)],[37]) ).

fof(66,plain,
    ! [X1] :
      ( ~ relation(X1)
      | ! [X2] :
          ( ( X2 != relation_dom(X1)
            | ! [X3] :
                ( ( ~ in(X3,X2)
                  | ? [X4] : in(ordered_pair(X3,X4),X1) )
                & ( ! [X4] : ~ in(ordered_pair(X3,X4),X1)
                  | in(X3,X2) ) ) )
          & ( ? [X3] :
                ( ( ~ in(X3,X2)
                  | ! [X4] : ~ in(ordered_pair(X3,X4),X1) )
                & ( in(X3,X2)
                  | ? [X4] : in(ordered_pair(X3,X4),X1) ) )
            | X2 = relation_dom(X1) ) ) ),
    inference(fof_nnf,[status(thm)],[12]) ).

fof(67,plain,
    ! [X5] :
      ( ~ relation(X5)
      | ! [X6] :
          ( ( X6 != relation_dom(X5)
            | ! [X7] :
                ( ( ~ in(X7,X6)
                  | ? [X8] : in(ordered_pair(X7,X8),X5) )
                & ( ! [X9] : ~ in(ordered_pair(X7,X9),X5)
                  | in(X7,X6) ) ) )
          & ( ? [X10] :
                ( ( ~ in(X10,X6)
                  | ! [X11] : ~ in(ordered_pair(X10,X11),X5) )
                & ( in(X10,X6)
                  | ? [X12] : in(ordered_pair(X10,X12),X5) ) )
            | X6 = relation_dom(X5) ) ) ),
    inference(variable_rename,[status(thm)],[66]) ).

fof(68,plain,
    ! [X5] :
      ( ~ relation(X5)
      | ! [X6] :
          ( ( X6 != relation_dom(X5)
            | ! [X7] :
                ( ( ~ in(X7,X6)
                  | in(ordered_pair(X7,esk6_3(X5,X6,X7)),X5) )
                & ( ! [X9] : ~ in(ordered_pair(X7,X9),X5)
                  | in(X7,X6) ) ) )
          & ( ( ( ~ in(esk7_2(X5,X6),X6)
                | ! [X11] : ~ in(ordered_pair(esk7_2(X5,X6),X11),X5) )
              & ( in(esk7_2(X5,X6),X6)
                | in(ordered_pair(esk7_2(X5,X6),esk8_2(X5,X6)),X5) ) )
            | X6 = relation_dom(X5) ) ) ),
    inference(skolemize,[status(esa)],[67]) ).

fof(69,plain,
    ! [X5,X6,X7,X9,X11] :
      ( ( ( ( ( ~ in(ordered_pair(esk7_2(X5,X6),X11),X5)
              | ~ in(esk7_2(X5,X6),X6) )
            & ( in(esk7_2(X5,X6),X6)
              | in(ordered_pair(esk7_2(X5,X6),esk8_2(X5,X6)),X5) ) )
          | X6 = relation_dom(X5) )
        & ( ( ( ~ in(ordered_pair(X7,X9),X5)
              | in(X7,X6) )
            & ( ~ in(X7,X6)
              | in(ordered_pair(X7,esk6_3(X5,X6,X7)),X5) ) )
          | X6 != relation_dom(X5) ) )
      | ~ relation(X5) ),
    inference(shift_quantors,[status(thm)],[68]) ).

fof(70,plain,
    ! [X5,X6,X7,X9,X11] :
      ( ( ~ in(ordered_pair(esk7_2(X5,X6),X11),X5)
        | ~ in(esk7_2(X5,X6),X6)
        | X6 = relation_dom(X5)
        | ~ relation(X5) )
      & ( in(esk7_2(X5,X6),X6)
        | in(ordered_pair(esk7_2(X5,X6),esk8_2(X5,X6)),X5)
        | X6 = relation_dom(X5)
        | ~ relation(X5) )
      & ( ~ in(ordered_pair(X7,X9),X5)
        | in(X7,X6)
        | X6 != relation_dom(X5)
        | ~ relation(X5) )
      & ( ~ in(X7,X6)
        | in(ordered_pair(X7,esk6_3(X5,X6,X7)),X5)
        | X6 != relation_dom(X5)
        | ~ relation(X5) ) ),
    inference(distribute,[status(thm)],[69]) ).

cnf(72,plain,
    ( in(X3,X2)
    | ~ relation(X1)
    | X2 != relation_dom(X1)
    | ~ in(ordered_pair(X3,X4),X1) ),
    inference(split_conjunct,[status(thm)],[70]) ).

fof(84,plain,
    ! [X3,X4] : ordered_pair(X3,X4) = unordered_pair(unordered_pair(X3,X4),singleton(X3)),
    inference(variable_rename,[status(thm)],[19]) ).

cnf(85,plain,
    ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
    inference(split_conjunct,[status(thm)],[84]) ).

fof(100,negated_conjecture,
    ? [X1,X2,X3] :
      ( relation(X3)
      & in(ordered_pair(X1,X2),X3)
      & ( ~ in(X1,relation_dom(X3))
        | ~ in(X2,relation_rng(X3)) ) ),
    inference(fof_nnf,[status(thm)],[27]) ).

fof(101,negated_conjecture,
    ? [X4,X5,X6] :
      ( relation(X6)
      & in(ordered_pair(X4,X5),X6)
      & ( ~ in(X4,relation_dom(X6))
        | ~ in(X5,relation_rng(X6)) ) ),
    inference(variable_rename,[status(thm)],[100]) ).

fof(102,negated_conjecture,
    ( relation(esk13_0)
    & in(ordered_pair(esk11_0,esk12_0),esk13_0)
    & ( ~ in(esk11_0,relation_dom(esk13_0))
      | ~ in(esk12_0,relation_rng(esk13_0)) ) ),
    inference(skolemize,[status(esa)],[101]) ).

cnf(103,negated_conjecture,
    ( ~ in(esk12_0,relation_rng(esk13_0))
    | ~ in(esk11_0,relation_dom(esk13_0)) ),
    inference(split_conjunct,[status(thm)],[102]) ).

cnf(104,negated_conjecture,
    in(ordered_pair(esk11_0,esk12_0),esk13_0),
    inference(split_conjunct,[status(thm)],[102]) ).

cnf(105,negated_conjecture,
    relation(esk13_0),
    inference(split_conjunct,[status(thm)],[102]) ).

cnf(106,negated_conjecture,
    in(unordered_pair(unordered_pair(esk11_0,esk12_0),singleton(esk11_0)),esk13_0),
    inference(rw,[status(thm)],[104,85,theory(equality)]),
    [unfolding] ).

cnf(109,plain,
    ( in(X3,X2)
    | relation_rng(X1) != X2
    | ~ relation(X1)
    | ~ in(unordered_pair(unordered_pair(X4,X3),singleton(X4)),X1) ),
    inference(rw,[status(thm)],[39,85,theory(equality)]),
    [unfolding] ).

cnf(110,plain,
    ( in(X3,X2)
    | relation_dom(X1) != X2
    | ~ relation(X1)
    | ~ in(unordered_pair(unordered_pair(X3,X4),singleton(X3)),X1) ),
    inference(rw,[status(thm)],[72,85,theory(equality)]),
    [unfolding] ).

cnf(127,negated_conjecture,
    ( in(esk12_0,X1)
    | relation_rng(esk13_0) != X1
    | ~ relation(esk13_0) ),
    inference(spm,[status(thm)],[109,106,theory(equality)]) ).

cnf(132,negated_conjecture,
    ( in(esk12_0,X1)
    | relation_rng(esk13_0) != X1
    | $false ),
    inference(rw,[status(thm)],[127,105,theory(equality)]) ).

cnf(133,negated_conjecture,
    ( in(esk12_0,X1)
    | relation_rng(esk13_0) != X1 ),
    inference(cn,[status(thm)],[132,theory(equality)]) ).

cnf(134,negated_conjecture,
    ( in(esk11_0,X1)
    | relation_dom(esk13_0) != X1
    | ~ relation(esk13_0) ),
    inference(spm,[status(thm)],[110,106,theory(equality)]) ).

cnf(139,negated_conjecture,
    ( in(esk11_0,X1)
    | relation_dom(esk13_0) != X1
    | $false ),
    inference(rw,[status(thm)],[134,105,theory(equality)]) ).

cnf(140,negated_conjecture,
    ( in(esk11_0,X1)
    | relation_dom(esk13_0) != X1 ),
    inference(cn,[status(thm)],[139,theory(equality)]) ).

cnf(181,negated_conjecture,
    in(esk12_0,relation_rng(esk13_0)),
    inference(er,[status(thm)],[133,theory(equality)]) ).

cnf(186,negated_conjecture,
    ( ~ in(esk11_0,relation_dom(esk13_0))
    | $false ),
    inference(rw,[status(thm)],[103,181,theory(equality)]) ).

cnf(187,negated_conjecture,
    ~ in(esk11_0,relation_dom(esk13_0)),
    inference(cn,[status(thm)],[186,theory(equality)]) ).

cnf(188,negated_conjecture,
    in(esk11_0,relation_dom(esk13_0)),
    inference(er,[status(thm)],[140,theory(equality)]) ).

cnf(194,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[188,187,theory(equality)]) ).

cnf(195,negated_conjecture,
    $false,
    194,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU177+1.p
% --creating new selector for []
% -running prover on /tmp/tmphRY4t2/sel_SEU177+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU177+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU177+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU177+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
% 
%------------------------------------------------------------------------------