TSTP Solution File: SET581+3 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SET581+3 : TPTP v5.0.0. Released v2.2.0.
% 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 02:57:48 EST 2010

% Result   : Theorem 0.17s
% Output   : CNFRefutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   31 (  16 unt;   0 def)
%            Number of atoms       :   70 (  10 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   66 (  27   ~;  18   |;  17   &)
%                                         (   2 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :   46 (   1 sgn  31   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
    file('/tmp/tmp4pLK6C/sel_SET581+3.p_1',commutativity_of_intersection) ).

fof(3,axiom,
    ! [X1,X2] :
      ( not_equal(X1,X2)
    <=> X1 != X2 ),
    file('/tmp/tmp4pLK6C/sel_SET581+3.p_1',not_equal_defn) ).

fof(5,conjecture,
    ! [X1,X2,X3] :
      ( ( member(X1,X2)
        & member(X1,X3) )
     => not_equal(intersection(X2,X3),empty_set) ),
    file('/tmp/tmp4pLK6C/sel_SET581+3.p_1',prove_th24) ).

fof(6,axiom,
    ! [X1,X2,X3] :
      ( member(X3,intersection(X1,X2))
    <=> ( member(X3,X1)
        & member(X3,X2) ) ),
    file('/tmp/tmp4pLK6C/sel_SET581+3.p_1',intersection_defn) ).

fof(7,axiom,
    ! [X1] : ~ member(X1,empty_set),
    file('/tmp/tmp4pLK6C/sel_SET581+3.p_1',empty_set_defn) ).

fof(8,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( ( member(X1,X2)
          & member(X1,X3) )
       => not_equal(intersection(X2,X3),empty_set) ),
    inference(assume_negation,[status(cth)],[5]) ).

fof(10,plain,
    ! [X1] : ~ member(X1,empty_set),
    inference(fof_simplification,[status(thm)],[7,theory(equality)]) ).

fof(11,plain,
    ! [X3,X4] : intersection(X3,X4) = intersection(X4,X3),
    inference(variable_rename,[status(thm)],[1]) ).

cnf(12,plain,
    intersection(X1,X2) = intersection(X2,X1),
    inference(split_conjunct,[status(thm)],[11]) ).

fof(19,plain,
    ! [X1,X2] :
      ( ( ~ not_equal(X1,X2)
        | X1 != X2 )
      & ( X1 = X2
        | not_equal(X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[3]) ).

fof(20,plain,
    ! [X3,X4] :
      ( ( ~ not_equal(X3,X4)
        | X3 != X4 )
      & ( X3 = X4
        | not_equal(X3,X4) ) ),
    inference(variable_rename,[status(thm)],[19]) ).

cnf(21,plain,
    ( not_equal(X1,X2)
    | X1 = X2 ),
    inference(split_conjunct,[status(thm)],[20]) ).

fof(32,negated_conjecture,
    ? [X1,X2,X3] :
      ( member(X1,X2)
      & member(X1,X3)
      & ~ not_equal(intersection(X2,X3),empty_set) ),
    inference(fof_nnf,[status(thm)],[8]) ).

fof(33,negated_conjecture,
    ? [X4,X5,X6] :
      ( member(X4,X5)
      & member(X4,X6)
      & ~ not_equal(intersection(X5,X6),empty_set) ),
    inference(variable_rename,[status(thm)],[32]) ).

fof(34,negated_conjecture,
    ( member(esk3_0,esk4_0)
    & member(esk3_0,esk5_0)
    & ~ not_equal(intersection(esk4_0,esk5_0),empty_set) ),
    inference(skolemize,[status(esa)],[33]) ).

cnf(35,negated_conjecture,
    ~ not_equal(intersection(esk4_0,esk5_0),empty_set),
    inference(split_conjunct,[status(thm)],[34]) ).

cnf(36,negated_conjecture,
    member(esk3_0,esk5_0),
    inference(split_conjunct,[status(thm)],[34]) ).

cnf(37,negated_conjecture,
    member(esk3_0,esk4_0),
    inference(split_conjunct,[status(thm)],[34]) ).

fof(38,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)],[6]) ).

fof(39,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)],[38]) ).

fof(40,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)],[39]) ).

cnf(41,plain,
    ( member(X1,intersection(X2,X3))
    | ~ member(X1,X3)
    | ~ member(X1,X2) ),
    inference(split_conjunct,[status(thm)],[40]) ).

fof(44,plain,
    ! [X2] : ~ member(X2,empty_set),
    inference(variable_rename,[status(thm)],[10]) ).

cnf(45,plain,
    ~ member(X1,empty_set),
    inference(split_conjunct,[status(thm)],[44]) ).

cnf(49,negated_conjecture,
    intersection(esk4_0,esk5_0) = empty_set,
    inference(spm,[status(thm)],[35,21,theory(equality)]) ).

cnf(69,negated_conjecture,
    ( member(esk3_0,intersection(X1,esk4_0))
    | ~ member(esk3_0,X1) ),
    inference(spm,[status(thm)],[41,37,theory(equality)]) ).

cnf(75,negated_conjecture,
    member(esk3_0,intersection(esk5_0,esk4_0)),
    inference(spm,[status(thm)],[69,36,theory(equality)]) ).

cnf(76,negated_conjecture,
    member(esk3_0,intersection(esk4_0,esk5_0)),
    inference(rw,[status(thm)],[75,12,theory(equality)]) ).

cnf(102,negated_conjecture,
    member(esk3_0,empty_set),
    inference(rw,[status(thm)],[76,49,theory(equality)]) ).

cnf(103,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[102,45,theory(equality)]) ).

cnf(104,negated_conjecture,
    $false,
    103,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET581+3.p
% --creating new selector for []
% -running prover on /tmp/tmp4pLK6C/sel_SET581+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET581+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET581+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET581+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
% 
%------------------------------------------------------------------------------