TSTP Solution File: SEU245+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SEU245+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 06:12:35 EST 2010

% Result   : Theorem 0.20s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   46 (   7 unt;   0 def)
%            Number of atoms       :  194 (  25 equ)
%            Maximal formula atoms :   20 (   4 avg)
%            Number of connectives :  237 (  89   ~; 101   |;  40   &)
%                                         (   4 <=>;   3  =>;   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    :    7 (   7 usr;   3 con; 0-3 aty)
%            Number of variables   :   79 (   5 sgn  38   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(3,axiom,
    ! [X1] :
      ( relation(X1)
     => ! [X2] : relation_restriction(X1,X2) = set_intersection2(X1,cartesian_product2(X2,X2)) ),
    file('/tmp/tmp3XCZTP/sel_SEU245+1.p_1',d6_wellord1) ).

fof(6,conjecture,
    ! [X1,X2,X3] :
      ( relation(X3)
     => ( in(X1,relation_restriction(X3,X2))
      <=> ( in(X1,X3)
          & in(X1,cartesian_product2(X2,X2)) ) ) ),
    file('/tmp/tmp3XCZTP/sel_SEU245+1.p_1',t16_wellord1) ).

fof(17,axiom,
    ! [X1,X2,X3] :
      ( X3 = set_intersection2(X1,X2)
    <=> ! [X4] :
          ( in(X4,X3)
        <=> ( in(X4,X1)
            & in(X4,X2) ) ) ),
    file('/tmp/tmp3XCZTP/sel_SEU245+1.p_1',d3_xboole_0) ).

fof(27,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( relation(X3)
       => ( in(X1,relation_restriction(X3,X2))
        <=> ( in(X1,X3)
            & in(X1,cartesian_product2(X2,X2)) ) ) ),
    inference(assume_negation,[status(cth)],[6]) ).

fof(35,plain,
    ! [X1] :
      ( ~ relation(X1)
      | ! [X2] : relation_restriction(X1,X2) = set_intersection2(X1,cartesian_product2(X2,X2)) ),
    inference(fof_nnf,[status(thm)],[3]) ).

fof(36,plain,
    ! [X3] :
      ( ~ relation(X3)
      | ! [X4] : relation_restriction(X3,X4) = set_intersection2(X3,cartesian_product2(X4,X4)) ),
    inference(variable_rename,[status(thm)],[35]) ).

fof(37,plain,
    ! [X3,X4] :
      ( relation_restriction(X3,X4) = set_intersection2(X3,cartesian_product2(X4,X4))
      | ~ relation(X3) ),
    inference(shift_quantors,[status(thm)],[36]) ).

cnf(38,plain,
    ( relation_restriction(X1,X2) = set_intersection2(X1,cartesian_product2(X2,X2))
    | ~ relation(X1) ),
    inference(split_conjunct,[status(thm)],[37]) ).

fof(46,negated_conjecture,
    ? [X1,X2,X3] :
      ( relation(X3)
      & ( ~ in(X1,relation_restriction(X3,X2))
        | ~ in(X1,X3)
        | ~ in(X1,cartesian_product2(X2,X2)) )
      & ( in(X1,relation_restriction(X3,X2))
        | ( in(X1,X3)
          & in(X1,cartesian_product2(X2,X2)) ) ) ),
    inference(fof_nnf,[status(thm)],[27]) ).

fof(47,negated_conjecture,
    ? [X4,X5,X6] :
      ( relation(X6)
      & ( ~ in(X4,relation_restriction(X6,X5))
        | ~ in(X4,X6)
        | ~ in(X4,cartesian_product2(X5,X5)) )
      & ( in(X4,relation_restriction(X6,X5))
        | ( in(X4,X6)
          & in(X4,cartesian_product2(X5,X5)) ) ) ),
    inference(variable_rename,[status(thm)],[46]) ).

fof(48,negated_conjecture,
    ( relation(esk5_0)
    & ( ~ in(esk3_0,relation_restriction(esk5_0,esk4_0))
      | ~ in(esk3_0,esk5_0)
      | ~ in(esk3_0,cartesian_product2(esk4_0,esk4_0)) )
    & ( in(esk3_0,relation_restriction(esk5_0,esk4_0))
      | ( in(esk3_0,esk5_0)
        & in(esk3_0,cartesian_product2(esk4_0,esk4_0)) ) ) ),
    inference(skolemize,[status(esa)],[47]) ).

fof(49,negated_conjecture,
    ( relation(esk5_0)
    & ( ~ in(esk3_0,relation_restriction(esk5_0,esk4_0))
      | ~ in(esk3_0,esk5_0)
      | ~ in(esk3_0,cartesian_product2(esk4_0,esk4_0)) )
    & ( in(esk3_0,esk5_0)
      | in(esk3_0,relation_restriction(esk5_0,esk4_0)) )
    & ( in(esk3_0,cartesian_product2(esk4_0,esk4_0))
      | in(esk3_0,relation_restriction(esk5_0,esk4_0)) ) ),
    inference(distribute,[status(thm)],[48]) ).

cnf(50,negated_conjecture,
    ( in(esk3_0,relation_restriction(esk5_0,esk4_0))
    | in(esk3_0,cartesian_product2(esk4_0,esk4_0)) ),
    inference(split_conjunct,[status(thm)],[49]) ).

cnf(51,negated_conjecture,
    ( in(esk3_0,relation_restriction(esk5_0,esk4_0))
    | in(esk3_0,esk5_0) ),
    inference(split_conjunct,[status(thm)],[49]) ).

cnf(52,negated_conjecture,
    ( ~ in(esk3_0,cartesian_product2(esk4_0,esk4_0))
    | ~ in(esk3_0,esk5_0)
    | ~ in(esk3_0,relation_restriction(esk5_0,esk4_0)) ),
    inference(split_conjunct,[status(thm)],[49]) ).

cnf(53,negated_conjecture,
    relation(esk5_0),
    inference(split_conjunct,[status(thm)],[49]) ).

fof(81,plain,
    ! [X1,X2,X3] :
      ( ( X3 != set_intersection2(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_intersection2(X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[17]) ).

fof(82,plain,
    ! [X5,X6,X7] :
      ( ( X7 != set_intersection2(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_intersection2(X5,X6) ) ),
    inference(variable_rename,[status(thm)],[81]) ).

fof(83,plain,
    ! [X5,X6,X7] :
      ( ( X7 != set_intersection2(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_intersection2(X5,X6) ) ),
    inference(skolemize,[status(esa)],[82]) ).

fof(84,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_intersection2(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_intersection2(X5,X6) ) ),
    inference(shift_quantors,[status(thm)],[83]) ).

fof(85,plain,
    ! [X5,X6,X7,X8] :
      ( ( in(X8,X5)
        | ~ in(X8,X7)
        | X7 != set_intersection2(X5,X6) )
      & ( in(X8,X6)
        | ~ in(X8,X7)
        | X7 != set_intersection2(X5,X6) )
      & ( ~ in(X8,X5)
        | ~ in(X8,X6)
        | in(X8,X7)
        | X7 != set_intersection2(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_intersection2(X5,X6) )
      & ( in(esk7_3(X5,X6,X7),X5)
        | in(esk7_3(X5,X6,X7),X7)
        | X7 = set_intersection2(X5,X6) )
      & ( in(esk7_3(X5,X6,X7),X6)
        | in(esk7_3(X5,X6,X7),X7)
        | X7 = set_intersection2(X5,X6) ) ),
    inference(distribute,[status(thm)],[84]) ).

cnf(89,plain,
    ( in(X4,X1)
    | X1 != set_intersection2(X2,X3)
    | ~ in(X4,X3)
    | ~ in(X4,X2) ),
    inference(split_conjunct,[status(thm)],[85]) ).

cnf(90,plain,
    ( in(X4,X3)
    | X1 != set_intersection2(X2,X3)
    | ~ in(X4,X1) ),
    inference(split_conjunct,[status(thm)],[85]) ).

cnf(91,plain,
    ( in(X4,X2)
    | X1 != set_intersection2(X2,X3)
    | ~ in(X4,X1) ),
    inference(split_conjunct,[status(thm)],[85]) ).

cnf(135,plain,
    ( in(X1,X2)
    | ~ in(X1,set_intersection2(X3,X2)) ),
    inference(er,[status(thm)],[90,theory(equality)]) ).

cnf(141,plain,
    ( in(X1,X2)
    | ~ in(X1,set_intersection2(X2,X3)) ),
    inference(er,[status(thm)],[91,theory(equality)]) ).

cnf(158,plain,
    ( in(X1,X2)
    | relation_restriction(X3,X4) != X2
    | ~ in(X1,cartesian_product2(X4,X4))
    | ~ in(X1,X3)
    | ~ relation(X3) ),
    inference(spm,[status(thm)],[89,38,theory(equality)]) ).

cnf(215,plain,
    ( in(X1,cartesian_product2(X2,X2))
    | ~ in(X1,relation_restriction(X3,X2))
    | ~ relation(X3) ),
    inference(spm,[status(thm)],[135,38,theory(equality)]) ).

cnf(275,plain,
    ( in(X1,X2)
    | ~ in(X1,relation_restriction(X2,X3))
    | ~ relation(X2) ),
    inference(spm,[status(thm)],[141,38,theory(equality)]) ).

cnf(292,negated_conjecture,
    ( in(esk3_0,esk5_0)
    | ~ relation(esk5_0) ),
    inference(spm,[status(thm)],[275,51,theory(equality)]) ).

cnf(302,negated_conjecture,
    ( in(esk3_0,esk5_0)
    | $false ),
    inference(rw,[status(thm)],[292,53,theory(equality)]) ).

cnf(303,negated_conjecture,
    in(esk3_0,esk5_0),
    inference(cn,[status(thm)],[302,theory(equality)]) ).

cnf(310,negated_conjecture,
    ( ~ in(esk3_0,relation_restriction(esk5_0,esk4_0))
    | ~ in(esk3_0,cartesian_product2(esk4_0,esk4_0))
    | $false ),
    inference(rw,[status(thm)],[52,303,theory(equality)]) ).

cnf(311,negated_conjecture,
    ( ~ in(esk3_0,relation_restriction(esk5_0,esk4_0))
    | ~ in(esk3_0,cartesian_product2(esk4_0,esk4_0)) ),
    inference(cn,[status(thm)],[310,theory(equality)]) ).

cnf(531,negated_conjecture,
    ( in(esk3_0,X1)
    | in(esk3_0,relation_restriction(esk5_0,esk4_0))
    | relation_restriction(X2,esk4_0) != X1
    | ~ in(esk3_0,X2)
    | ~ relation(X2) ),
    inference(spm,[status(thm)],[158,50,theory(equality)]) ).

cnf(647,negated_conjecture,
    ( in(esk3_0,relation_restriction(esk5_0,esk4_0))
    | in(esk3_0,relation_restriction(X1,esk4_0))
    | ~ in(esk3_0,X1)
    | ~ relation(X1) ),
    inference(er,[status(thm)],[531,theory(equality)]) ).

cnf(663,negated_conjecture,
    ( in(esk3_0,relation_restriction(esk5_0,esk4_0))
    | ~ relation(esk5_0) ),
    inference(spm,[status(thm)],[647,303,theory(equality)]) ).

cnf(667,negated_conjecture,
    ( in(esk3_0,relation_restriction(esk5_0,esk4_0))
    | $false ),
    inference(rw,[status(thm)],[663,53,theory(equality)]) ).

cnf(668,negated_conjecture,
    in(esk3_0,relation_restriction(esk5_0,esk4_0)),
    inference(cn,[status(thm)],[667,theory(equality)]) ).

cnf(674,negated_conjecture,
    ( in(esk3_0,cartesian_product2(esk4_0,esk4_0))
    | ~ relation(esk5_0) ),
    inference(spm,[status(thm)],[215,668,theory(equality)]) ).

cnf(679,negated_conjecture,
    ( $false
    | ~ in(esk3_0,cartesian_product2(esk4_0,esk4_0)) ),
    inference(rw,[status(thm)],[311,668,theory(equality)]) ).

cnf(680,negated_conjecture,
    ~ in(esk3_0,cartesian_product2(esk4_0,esk4_0)),
    inference(cn,[status(thm)],[679,theory(equality)]) ).

cnf(689,negated_conjecture,
    ( in(esk3_0,cartesian_product2(esk4_0,esk4_0))
    | $false ),
    inference(rw,[status(thm)],[674,53,theory(equality)]) ).

cnf(690,negated_conjecture,
    in(esk3_0,cartesian_product2(esk4_0,esk4_0)),
    inference(cn,[status(thm)],[689,theory(equality)]) ).

cnf(724,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[690,680,theory(equality)]) ).

cnf(725,negated_conjecture,
    $false,
    724,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU245+1.p
% --creating new selector for []
% -running prover on /tmp/tmp3XCZTP/sel_SEU245+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU245+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU245+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU245+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
% 
%------------------------------------------------------------------------------