TSTP Solution File: SET629+3 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SET629+3 : TPTP v5.0.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art04.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 03:05:35 EST 2010

% Result   : Theorem 0.16s
% Output   : CNFRefutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   41 (  11 unt;   0 def)
%            Number of atoms       :  126 (   0 equ)
%            Maximal formula atoms :    7 (   3 avg)
%            Number of connectives :  146 (  61   ~;  50   |;  28   &)
%                                         (   6 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   92 (   4 sgn  62   !;   7   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(2,conjecture,
    ! [X1,X2] : disjoint(intersection(X1,X2),difference(X1,X2)),
    file('/tmp/tmpDQGZ0v/sel_SET629+3.p_1',prove_intersection_and_difference_disjoint) ).

fof(3,axiom,
    ! [X1,X2] :
      ( intersect(X1,X2)
    <=> ? [X3] :
          ( member(X3,X1)
          & member(X3,X2) ) ),
    file('/tmp/tmpDQGZ0v/sel_SET629+3.p_1',intersect_defn) ).

fof(4,axiom,
    ! [X1,X2] :
      ( intersect(X1,X2)
     => intersect(X2,X1) ),
    file('/tmp/tmpDQGZ0v/sel_SET629+3.p_1',symmetry_of_intersect) ).

fof(6,axiom,
    ! [X1,X2] :
      ( disjoint(X1,X2)
    <=> ~ intersect(X1,X2) ),
    file('/tmp/tmpDQGZ0v/sel_SET629+3.p_1',disjoint_defn) ).

fof(7,axiom,
    ! [X1,X2,X3] :
      ( member(X3,intersection(X1,X2))
    <=> ( member(X3,X1)
        & member(X3,X2) ) ),
    file('/tmp/tmpDQGZ0v/sel_SET629+3.p_1',intersection_defn) ).

fof(8,axiom,
    ! [X1,X2,X3] :
      ( member(X3,difference(X1,X2))
    <=> ( member(X3,X1)
        & ~ member(X3,X2) ) ),
    file('/tmp/tmpDQGZ0v/sel_SET629+3.p_1',difference_defn) ).

fof(9,negated_conjecture,
    ~ ! [X1,X2] : disjoint(intersection(X1,X2),difference(X1,X2)),
    inference(assume_negation,[status(cth)],[2]) ).

fof(10,plain,
    ! [X1,X2] :
      ( disjoint(X1,X2)
    <=> ~ intersect(X1,X2) ),
    inference(fof_simplification,[status(thm)],[6,theory(equality)]) ).

fof(11,plain,
    ! [X1,X2,X3] :
      ( member(X3,difference(X1,X2))
    <=> ( member(X3,X1)
        & ~ member(X3,X2) ) ),
    inference(fof_simplification,[status(thm)],[8,theory(equality)]) ).

fof(14,negated_conjecture,
    ? [X1,X2] : ~ disjoint(intersection(X1,X2),difference(X1,X2)),
    inference(fof_nnf,[status(thm)],[9]) ).

fof(15,negated_conjecture,
    ? [X3,X4] : ~ disjoint(intersection(X3,X4),difference(X3,X4)),
    inference(variable_rename,[status(thm)],[14]) ).

fof(16,negated_conjecture,
    ~ disjoint(intersection(esk1_0,esk2_0),difference(esk1_0,esk2_0)),
    inference(skolemize,[status(esa)],[15]) ).

cnf(17,negated_conjecture,
    ~ disjoint(intersection(esk1_0,esk2_0),difference(esk1_0,esk2_0)),
    inference(split_conjunct,[status(thm)],[16]) ).

fof(18,plain,
    ! [X1,X2] :
      ( ( ~ intersect(X1,X2)
        | ? [X3] :
            ( member(X3,X1)
            & member(X3,X2) ) )
      & ( ! [X3] :
            ( ~ member(X3,X1)
            | ~ member(X3,X2) )
        | intersect(X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[3]) ).

fof(19,plain,
    ! [X4,X5] :
      ( ( ~ intersect(X4,X5)
        | ? [X6] :
            ( member(X6,X4)
            & member(X6,X5) ) )
      & ( ! [X7] :
            ( ~ member(X7,X4)
            | ~ member(X7,X5) )
        | intersect(X4,X5) ) ),
    inference(variable_rename,[status(thm)],[18]) ).

fof(20,plain,
    ! [X4,X5] :
      ( ( ~ intersect(X4,X5)
        | ( member(esk3_2(X4,X5),X4)
          & member(esk3_2(X4,X5),X5) ) )
      & ( ! [X7] :
            ( ~ member(X7,X4)
            | ~ member(X7,X5) )
        | intersect(X4,X5) ) ),
    inference(skolemize,[status(esa)],[19]) ).

fof(21,plain,
    ! [X4,X5,X7] :
      ( ( ~ member(X7,X4)
        | ~ member(X7,X5)
        | intersect(X4,X5) )
      & ( ~ intersect(X4,X5)
        | ( member(esk3_2(X4,X5),X4)
          & member(esk3_2(X4,X5),X5) ) ) ),
    inference(shift_quantors,[status(thm)],[20]) ).

fof(22,plain,
    ! [X4,X5,X7] :
      ( ( ~ member(X7,X4)
        | ~ member(X7,X5)
        | intersect(X4,X5) )
      & ( member(esk3_2(X4,X5),X4)
        | ~ intersect(X4,X5) )
      & ( member(esk3_2(X4,X5),X5)
        | ~ intersect(X4,X5) ) ),
    inference(distribute,[status(thm)],[21]) ).

cnf(23,plain,
    ( member(esk3_2(X1,X2),X2)
    | ~ intersect(X1,X2) ),
    inference(split_conjunct,[status(thm)],[22]) ).

cnf(24,plain,
    ( member(esk3_2(X1,X2),X1)
    | ~ intersect(X1,X2) ),
    inference(split_conjunct,[status(thm)],[22]) ).

fof(26,plain,
    ! [X1,X2] :
      ( ~ intersect(X1,X2)
      | intersect(X2,X1) ),
    inference(fof_nnf,[status(thm)],[4]) ).

fof(27,plain,
    ! [X3,X4] :
      ( ~ intersect(X3,X4)
      | intersect(X4,X3) ),
    inference(variable_rename,[status(thm)],[26]) ).

cnf(28,plain,
    ( intersect(X1,X2)
    | ~ intersect(X2,X1) ),
    inference(split_conjunct,[status(thm)],[27]) ).

fof(38,plain,
    ! [X1,X2] :
      ( ( ~ disjoint(X1,X2)
        | ~ intersect(X1,X2) )
      & ( intersect(X1,X2)
        | disjoint(X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[10]) ).

fof(39,plain,
    ! [X3,X4] :
      ( ( ~ disjoint(X3,X4)
        | ~ intersect(X3,X4) )
      & ( intersect(X3,X4)
        | disjoint(X3,X4) ) ),
    inference(variable_rename,[status(thm)],[38]) ).

cnf(40,plain,
    ( disjoint(X1,X2)
    | intersect(X1,X2) ),
    inference(split_conjunct,[status(thm)],[39]) ).

fof(42,plain,
    ! [X1,X2,X3] :
      ( ( ~ member(X3,intersection(X1,X2))
        | ( member(X3,X1)
          & member(X3,X2) ) )
      & ( ~ member(X3,X1)
        | ~ member(X3,X2)
        | member(X3,intersection(X1,X2)) ) ),
    inference(fof_nnf,[status(thm)],[7]) ).

fof(43,plain,
    ! [X4,X5,X6] :
      ( ( ~ member(X6,intersection(X4,X5))
        | ( member(X6,X4)
          & member(X6,X5) ) )
      & ( ~ member(X6,X4)
        | ~ member(X6,X5)
        | member(X6,intersection(X4,X5)) ) ),
    inference(variable_rename,[status(thm)],[42]) ).

fof(44,plain,
    ! [X4,X5,X6] :
      ( ( member(X6,X4)
        | ~ member(X6,intersection(X4,X5)) )
      & ( member(X6,X5)
        | ~ member(X6,intersection(X4,X5)) )
      & ( ~ member(X6,X4)
        | ~ member(X6,X5)
        | member(X6,intersection(X4,X5)) ) ),
    inference(distribute,[status(thm)],[43]) ).

cnf(46,plain,
    ( member(X1,X3)
    | ~ member(X1,intersection(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[44]) ).

fof(48,plain,
    ! [X1,X2,X3] :
      ( ( ~ member(X3,difference(X1,X2))
        | ( member(X3,X1)
          & ~ member(X3,X2) ) )
      & ( ~ member(X3,X1)
        | member(X3,X2)
        | member(X3,difference(X1,X2)) ) ),
    inference(fof_nnf,[status(thm)],[11]) ).

fof(49,plain,
    ! [X4,X5,X6] :
      ( ( ~ member(X6,difference(X4,X5))
        | ( member(X6,X4)
          & ~ member(X6,X5) ) )
      & ( ~ member(X6,X4)
        | member(X6,X5)
        | member(X6,difference(X4,X5)) ) ),
    inference(variable_rename,[status(thm)],[48]) ).

fof(50,plain,
    ! [X4,X5,X6] :
      ( ( member(X6,X4)
        | ~ member(X6,difference(X4,X5)) )
      & ( ~ member(X6,X5)
        | ~ member(X6,difference(X4,X5)) )
      & ( ~ member(X6,X4)
        | member(X6,X5)
        | member(X6,difference(X4,X5)) ) ),
    inference(distribute,[status(thm)],[49]) ).

cnf(52,plain,
    ( ~ member(X1,difference(X2,X3))
    | ~ member(X1,X3) ),
    inference(split_conjunct,[status(thm)],[50]) ).

cnf(54,negated_conjecture,
    intersect(intersection(esk1_0,esk2_0),difference(esk1_0,esk2_0)),
    inference(spm,[status(thm)],[17,40,theory(equality)]) ).

cnf(60,plain,
    ( member(esk3_2(X1,intersection(X2,X3)),X3)
    | ~ intersect(X1,intersection(X2,X3)) ),
    inference(spm,[status(thm)],[46,23,theory(equality)]) ).

cnf(69,plain,
    ( ~ member(esk3_2(difference(X1,X2),X3),X2)
    | ~ intersect(difference(X1,X2),X3) ),
    inference(spm,[status(thm)],[52,24,theory(equality)]) ).

cnf(93,negated_conjecture,
    intersect(difference(esk1_0,esk2_0),intersection(esk1_0,esk2_0)),
    inference(spm,[status(thm)],[28,54,theory(equality)]) ).

cnf(109,plain,
    ~ intersect(difference(X1,X2),intersection(X3,X2)),
    inference(spm,[status(thm)],[69,60,theory(equality)]) ).

cnf(112,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[93,109,theory(equality)]) ).

cnf(113,negated_conjecture,
    $false,
    112,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET629+3.p
% --creating new selector for []
% -running prover on /tmp/tmpDQGZ0v/sel_SET629+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET629+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET629+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET629+3.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
% 
%------------------------------------------------------------------------------