TSTP Solution File: SEU177+2 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SEU177+2 : TPTP v5.0.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art01.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 05:07:04 EST 2010

% Result   : Theorem 2.09s
% Output   : CNFRefutation 2.09s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   50 (  19 unt;   0 def)
%            Number of atoms       :  211 (  48 equ)
%            Maximal formula atoms :   16 (   4 avg)
%            Number of connectives :  266 ( 105   ~; 113   |;  38   &)
%                                         (   4 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 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   :  129 (   4 sgn  72   !;  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/tmpqyBnAY/sel_SEU177+2.p_1',d5_relat_1) ).

fof(36,conjecture,
    ! [X1,X2,X3] :
      ( relation(X3)
     => ( in(ordered_pair(X1,X2),X3)
       => ( in(X1,relation_dom(X3))
          & in(X2,relation_rng(X3)) ) ) ),
    file('/tmp/tmpqyBnAY/sel_SEU177+2.p_1',t20_relat_1) ).

fof(39,axiom,
    ! [X1] : unordered_pair(X1,X1) = singleton(X1),
    file('/tmp/tmpqyBnAY/sel_SEU177+2.p_1',t69_enumset1) ).

fof(80,axiom,
    ! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
    file('/tmp/tmpqyBnAY/sel_SEU177+2.p_1',commutativity_k2_tarski) ).

fof(88,axiom,
    ! [X1] :
      ( relation(X1)
     => ! [X2] :
          ( X2 = relation_dom(X1)
        <=> ! [X3] :
              ( in(X3,X2)
            <=> ? [X4] : in(ordered_pair(X3,X4),X1) ) ) ),
    file('/tmp/tmpqyBnAY/sel_SEU177+2.p_1',d4_relat_1) ).

fof(98,axiom,
    ! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
    file('/tmp/tmpqyBnAY/sel_SEU177+2.p_1',d5_tarski) ).

fof(143,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)],[36]) ).

fof(165,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(166,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)],[165]) ).

fof(167,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)],[166]) ).

fof(168,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)],[167]) ).

fof(169,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)],[168]) ).

cnf(171,plain,
    ( in(X3,X2)
    | ~ relation(X1)
    | X2 != relation_rng(X1)
    | ~ in(ordered_pair(X4,X3),X1) ),
    inference(split_conjunct,[status(thm)],[169]) ).

fof(284,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)],[143]) ).

fof(285,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)],[284]) ).

fof(286,negated_conjecture,
    ( relation(esk12_0)
    & in(ordered_pair(esk10_0,esk11_0),esk12_0)
    & ( ~ in(esk10_0,relation_dom(esk12_0))
      | ~ in(esk11_0,relation_rng(esk12_0)) ) ),
    inference(skolemize,[status(esa)],[285]) ).

cnf(287,negated_conjecture,
    ( ~ in(esk11_0,relation_rng(esk12_0))
    | ~ in(esk10_0,relation_dom(esk12_0)) ),
    inference(split_conjunct,[status(thm)],[286]) ).

cnf(288,negated_conjecture,
    in(ordered_pair(esk10_0,esk11_0),esk12_0),
    inference(split_conjunct,[status(thm)],[286]) ).

cnf(289,negated_conjecture,
    relation(esk12_0),
    inference(split_conjunct,[status(thm)],[286]) ).

fof(299,plain,
    ! [X2] : unordered_pair(X2,X2) = singleton(X2),
    inference(variable_rename,[status(thm)],[39]) ).

cnf(300,plain,
    unordered_pair(X1,X1) = singleton(X1),
    inference(split_conjunct,[status(thm)],[299]) ).

fof(450,plain,
    ! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
    inference(variable_rename,[status(thm)],[80]) ).

cnf(451,plain,
    unordered_pair(X1,X2) = unordered_pair(X2,X1),
    inference(split_conjunct,[status(thm)],[450]) ).

fof(477,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)],[88]) ).

fof(478,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)],[477]) ).

fof(479,plain,
    ! [X5] :
      ( ~ relation(X5)
      | ! [X6] :
          ( ( X6 != relation_dom(X5)
            | ! [X7] :
                ( ( ~ in(X7,X6)
                  | in(ordered_pair(X7,esk20_3(X5,X6,X7)),X5) )
                & ( ! [X9] : ~ in(ordered_pair(X7,X9),X5)
                  | in(X7,X6) ) ) )
          & ( ( ( ~ in(esk21_2(X5,X6),X6)
                | ! [X11] : ~ in(ordered_pair(esk21_2(X5,X6),X11),X5) )
              & ( in(esk21_2(X5,X6),X6)
                | in(ordered_pair(esk21_2(X5,X6),esk22_2(X5,X6)),X5) ) )
            | X6 = relation_dom(X5) ) ) ),
    inference(skolemize,[status(esa)],[478]) ).

fof(480,plain,
    ! [X5,X6,X7,X9,X11] :
      ( ( ( ( ( ~ in(ordered_pair(esk21_2(X5,X6),X11),X5)
              | ~ in(esk21_2(X5,X6),X6) )
            & ( in(esk21_2(X5,X6),X6)
              | in(ordered_pair(esk21_2(X5,X6),esk22_2(X5,X6)),X5) ) )
          | X6 = relation_dom(X5) )
        & ( ( ( ~ in(ordered_pair(X7,X9),X5)
              | in(X7,X6) )
            & ( ~ in(X7,X6)
              | in(ordered_pair(X7,esk20_3(X5,X6,X7)),X5) ) )
          | X6 != relation_dom(X5) ) )
      | ~ relation(X5) ),
    inference(shift_quantors,[status(thm)],[479]) ).

fof(481,plain,
    ! [X5,X6,X7,X9,X11] :
      ( ( ~ in(ordered_pair(esk21_2(X5,X6),X11),X5)
        | ~ in(esk21_2(X5,X6),X6)
        | X6 = relation_dom(X5)
        | ~ relation(X5) )
      & ( in(esk21_2(X5,X6),X6)
        | in(ordered_pair(esk21_2(X5,X6),esk22_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,esk20_3(X5,X6,X7)),X5)
        | X6 != relation_dom(X5)
        | ~ relation(X5) ) ),
    inference(distribute,[status(thm)],[480]) ).

cnf(483,plain,
    ( in(X3,X2)
    | ~ relation(X1)
    | X2 != relation_dom(X1)
    | ~ in(ordered_pair(X3,X4),X1) ),
    inference(split_conjunct,[status(thm)],[481]) ).

fof(512,plain,
    ! [X3,X4] : ordered_pair(X3,X4) = unordered_pair(unordered_pair(X3,X4),singleton(X3)),
    inference(variable_rename,[status(thm)],[98]) ).

cnf(513,plain,
    ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
    inference(split_conjunct,[status(thm)],[512]) ).

cnf(710,plain,
    unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)) = ordered_pair(X1,X2),
    inference(rw,[status(thm)],[513,300,theory(equality)]),
    [unfolding] ).

cnf(754,negated_conjecture,
    in(unordered_pair(unordered_pair(esk10_0,esk11_0),unordered_pair(esk10_0,esk10_0)),esk12_0),
    inference(rw,[status(thm)],[288,710,theory(equality)]),
    [unfolding] ).

cnf(767,plain,
    ( in(X3,X2)
    | relation_rng(X1) != X2
    | ~ relation(X1)
    | ~ in(unordered_pair(unordered_pair(X4,X3),unordered_pair(X4,X4)),X1) ),
    inference(rw,[status(thm)],[171,710,theory(equality)]),
    [unfolding] ).

cnf(768,plain,
    ( in(X3,X2)
    | relation_dom(X1) != X2
    | ~ relation(X1)
    | ~ in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),X1) ),
    inference(rw,[status(thm)],[483,710,theory(equality)]),
    [unfolding] ).

cnf(787,negated_conjecture,
    in(unordered_pair(unordered_pair(esk10_0,esk10_0),unordered_pair(esk10_0,esk11_0)),esk12_0),
    inference(rw,[status(thm)],[754,451,theory(equality)]) ).

cnf(1385,plain,
    ( in(X1,X2)
    | relation_rng(X3) != X2
    | ~ in(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,X1)),X3)
    | ~ relation(X3) ),
    inference(spm,[status(thm)],[767,451,theory(equality)]) ).

cnf(1394,plain,
    ( in(X1,X2)
    | relation_dom(X3) != X2
    | ~ in(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,X4)),X3)
    | ~ relation(X3) ),
    inference(spm,[status(thm)],[768,451,theory(equality)]) ).

cnf(31626,negated_conjecture,
    ( in(esk11_0,X1)
    | relation_rng(esk12_0) != X1
    | ~ relation(esk12_0) ),
    inference(spm,[status(thm)],[1385,787,theory(equality)]) ).

cnf(31780,negated_conjecture,
    ( in(esk11_0,X1)
    | relation_rng(esk12_0) != X1
    | $false ),
    inference(rw,[status(thm)],[31626,289,theory(equality)]) ).

cnf(31781,negated_conjecture,
    ( in(esk11_0,X1)
    | relation_rng(esk12_0) != X1 ),
    inference(cn,[status(thm)],[31780,theory(equality)]) ).

cnf(31784,negated_conjecture,
    in(esk11_0,relation_rng(esk12_0)),
    inference(er,[status(thm)],[31781,theory(equality)]) ).

cnf(31815,negated_conjecture,
    ( ~ in(esk10_0,relation_dom(esk12_0))
    | $false ),
    inference(rw,[status(thm)],[287,31784,theory(equality)]) ).

cnf(31816,negated_conjecture,
    ~ in(esk10_0,relation_dom(esk12_0)),
    inference(cn,[status(thm)],[31815,theory(equality)]) ).

cnf(32558,negated_conjecture,
    ( in(esk10_0,X1)
    | relation_dom(esk12_0) != X1
    | ~ relation(esk12_0) ),
    inference(spm,[status(thm)],[1394,787,theory(equality)]) ).

cnf(32712,negated_conjecture,
    ( in(esk10_0,X1)
    | relation_dom(esk12_0) != X1
    | $false ),
    inference(rw,[status(thm)],[32558,289,theory(equality)]) ).

cnf(32713,negated_conjecture,
    ( in(esk10_0,X1)
    | relation_dom(esk12_0) != X1 ),
    inference(cn,[status(thm)],[32712,theory(equality)]) ).

cnf(32729,negated_conjecture,
    in(esk10_0,relation_dom(esk12_0)),
    inference(er,[status(thm)],[32713,theory(equality)]) ).

cnf(32732,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[32729,31816,theory(equality)]) ).

cnf(32733,negated_conjecture,
    $false,
    32732,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU177+2.p
% --creating new selector for []
% -running prover on /tmp/tmpqyBnAY/sel_SEU177+2.p_1 with time limit 29
% -prover status Theorem
% Problem SEU177+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU177+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU177+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
% 
%------------------------------------------------------------------------------