TSTP Solution File: SET984+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SET984+1 : TPTP v5.0.0. Released v3.2.0.
% 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 03:58:31 EST 2010

% Result   : Theorem 0.86s
% Output   : CNFRefutation 0.86s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   59 (  23 unt;   0 def)
%            Number of atoms       :  150 ( 117 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  142 (  51   ~;  68   |;  18   &)
%                                         (   1 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :  120 (  19 sgn  54   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
    file('/tmp/tmp2ycPs2/sel_SET984+1.p_1',commutativity_k3_xboole_0) ).

fof(3,axiom,
    ! [X1,X2] :
      ( subset(X1,X2)
     => set_intersection2(X1,X2) = X1 ),
    file('/tmp/tmp2ycPs2/sel_SET984+1.p_1',t28_xboole_1) ).

fof(5,axiom,
    ! [X1,X2] : subset(set_intersection2(X1,X2),X1),
    file('/tmp/tmp2ycPs2/sel_SET984+1.p_1',t17_xboole_1) ).

fof(6,axiom,
    ! [X1,X2,X3,X4] : cartesian_product2(set_intersection2(X1,X2),set_intersection2(X3,X4)) = set_intersection2(cartesian_product2(X1,X3),cartesian_product2(X2,X4)),
    file('/tmp/tmp2ycPs2/sel_SET984+1.p_1',t123_zfmisc_1) ).

fof(7,axiom,
    ! [X1,X2] :
      ( cartesian_product2(X1,X2) = empty_set
    <=> ( X1 = empty_set
        | X2 = empty_set ) ),
    file('/tmp/tmp2ycPs2/sel_SET984+1.p_1',t113_zfmisc_1) ).

fof(8,conjecture,
    ! [X1,X2,X3,X4] :
      ( subset(cartesian_product2(X1,X2),cartesian_product2(X3,X4))
     => ( cartesian_product2(X1,X2) = empty_set
        | ( subset(X1,X3)
          & subset(X2,X4) ) ) ),
    file('/tmp/tmp2ycPs2/sel_SET984+1.p_1',t138_zfmisc_1) ).

fof(10,axiom,
    ! [X1,X2,X3,X4] :
      ( cartesian_product2(X1,X2) = cartesian_product2(X3,X4)
     => ( X1 = empty_set
        | X2 = empty_set
        | ( X1 = X3
          & X2 = X4 ) ) ),
    file('/tmp/tmp2ycPs2/sel_SET984+1.p_1',t134_zfmisc_1) ).

fof(13,negated_conjecture,
    ~ ! [X1,X2,X3,X4] :
        ( subset(cartesian_product2(X1,X2),cartesian_product2(X3,X4))
       => ( cartesian_product2(X1,X2) = empty_set
          | ( subset(X1,X3)
            & subset(X2,X4) ) ) ),
    inference(assume_negation,[status(cth)],[8]) ).

fof(15,plain,
    ! [X3,X4] : set_intersection2(X3,X4) = set_intersection2(X4,X3),
    inference(variable_rename,[status(thm)],[1]) ).

cnf(16,plain,
    set_intersection2(X1,X2) = set_intersection2(X2,X1),
    inference(split_conjunct,[status(thm)],[15]) ).

fof(19,plain,
    ! [X1,X2] :
      ( ~ subset(X1,X2)
      | set_intersection2(X1,X2) = X1 ),
    inference(fof_nnf,[status(thm)],[3]) ).

fof(20,plain,
    ! [X3,X4] :
      ( ~ subset(X3,X4)
      | set_intersection2(X3,X4) = X3 ),
    inference(variable_rename,[status(thm)],[19]) ).

cnf(21,plain,
    ( set_intersection2(X1,X2) = X1
    | ~ subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[20]) ).

fof(25,plain,
    ! [X3,X4] : subset(set_intersection2(X3,X4),X3),
    inference(variable_rename,[status(thm)],[5]) ).

cnf(26,plain,
    subset(set_intersection2(X1,X2),X1),
    inference(split_conjunct,[status(thm)],[25]) ).

fof(27,plain,
    ! [X5,X6,X7,X8] : cartesian_product2(set_intersection2(X5,X6),set_intersection2(X7,X8)) = set_intersection2(cartesian_product2(X5,X7),cartesian_product2(X6,X8)),
    inference(variable_rename,[status(thm)],[6]) ).

cnf(28,plain,
    cartesian_product2(set_intersection2(X1,X2),set_intersection2(X3,X4)) = set_intersection2(cartesian_product2(X1,X3),cartesian_product2(X2,X4)),
    inference(split_conjunct,[status(thm)],[27]) ).

fof(29,plain,
    ! [X1,X2] :
      ( ( cartesian_product2(X1,X2) != empty_set
        | X1 = empty_set
        | X2 = empty_set )
      & ( ( X1 != empty_set
          & X2 != empty_set )
        | cartesian_product2(X1,X2) = empty_set ) ),
    inference(fof_nnf,[status(thm)],[7]) ).

fof(30,plain,
    ! [X3,X4] :
      ( ( cartesian_product2(X3,X4) != empty_set
        | X3 = empty_set
        | X4 = empty_set )
      & ( ( X3 != empty_set
          & X4 != empty_set )
        | cartesian_product2(X3,X4) = empty_set ) ),
    inference(variable_rename,[status(thm)],[29]) ).

fof(31,plain,
    ! [X3,X4] :
      ( ( cartesian_product2(X3,X4) != empty_set
        | X3 = empty_set
        | X4 = empty_set )
      & ( X3 != empty_set
        | cartesian_product2(X3,X4) = empty_set )
      & ( X4 != empty_set
        | cartesian_product2(X3,X4) = empty_set ) ),
    inference(distribute,[status(thm)],[30]) ).

cnf(32,plain,
    ( cartesian_product2(X1,X2) = empty_set
    | X2 != empty_set ),
    inference(split_conjunct,[status(thm)],[31]) ).

cnf(33,plain,
    ( cartesian_product2(X1,X2) = empty_set
    | X1 != empty_set ),
    inference(split_conjunct,[status(thm)],[31]) ).

fof(35,negated_conjecture,
    ? [X1,X2,X3,X4] :
      ( subset(cartesian_product2(X1,X2),cartesian_product2(X3,X4))
      & cartesian_product2(X1,X2) != empty_set
      & ( ~ subset(X1,X3)
        | ~ subset(X2,X4) ) ),
    inference(fof_nnf,[status(thm)],[13]) ).

fof(36,negated_conjecture,
    ? [X5,X6,X7,X8] :
      ( subset(cartesian_product2(X5,X6),cartesian_product2(X7,X8))
      & cartesian_product2(X5,X6) != empty_set
      & ( ~ subset(X5,X7)
        | ~ subset(X6,X8) ) ),
    inference(variable_rename,[status(thm)],[35]) ).

fof(37,negated_conjecture,
    ( subset(cartesian_product2(esk2_0,esk3_0),cartesian_product2(esk4_0,esk5_0))
    & cartesian_product2(esk2_0,esk3_0) != empty_set
    & ( ~ subset(esk2_0,esk4_0)
      | ~ subset(esk3_0,esk5_0) ) ),
    inference(skolemize,[status(esa)],[36]) ).

cnf(38,negated_conjecture,
    ( ~ subset(esk3_0,esk5_0)
    | ~ subset(esk2_0,esk4_0) ),
    inference(split_conjunct,[status(thm)],[37]) ).

cnf(39,negated_conjecture,
    cartesian_product2(esk2_0,esk3_0) != empty_set,
    inference(split_conjunct,[status(thm)],[37]) ).

cnf(40,negated_conjecture,
    subset(cartesian_product2(esk2_0,esk3_0),cartesian_product2(esk4_0,esk5_0)),
    inference(split_conjunct,[status(thm)],[37]) ).

fof(44,plain,
    ! [X1,X2,X3,X4] :
      ( cartesian_product2(X1,X2) != cartesian_product2(X3,X4)
      | X1 = empty_set
      | X2 = empty_set
      | ( X1 = X3
        & X2 = X4 ) ),
    inference(fof_nnf,[status(thm)],[10]) ).

fof(45,plain,
    ! [X5,X6,X7,X8] :
      ( cartesian_product2(X5,X6) != cartesian_product2(X7,X8)
      | X5 = empty_set
      | X6 = empty_set
      | ( X5 = X7
        & X6 = X8 ) ),
    inference(variable_rename,[status(thm)],[44]) ).

fof(46,plain,
    ! [X5,X6,X7,X8] :
      ( ( X5 = X7
        | X5 = empty_set
        | X6 = empty_set
        | cartesian_product2(X5,X6) != cartesian_product2(X7,X8) )
      & ( X6 = X8
        | X5 = empty_set
        | X6 = empty_set
        | cartesian_product2(X5,X6) != cartesian_product2(X7,X8) ) ),
    inference(distribute,[status(thm)],[45]) ).

cnf(47,plain,
    ( X2 = empty_set
    | X1 = empty_set
    | X2 = X4
    | cartesian_product2(X1,X2) != cartesian_product2(X3,X4) ),
    inference(split_conjunct,[status(thm)],[46]) ).

cnf(48,plain,
    ( X2 = empty_set
    | X1 = empty_set
    | X1 = X3
    | cartesian_product2(X1,X2) != cartesian_product2(X3,X4) ),
    inference(split_conjunct,[status(thm)],[46]) ).

cnf(54,negated_conjecture,
    empty_set != esk3_0,
    inference(spm,[status(thm)],[39,32,theory(equality)]) ).

cnf(61,negated_conjecture,
    set_intersection2(cartesian_product2(esk2_0,esk3_0),cartesian_product2(esk4_0,esk5_0)) = cartesian_product2(esk2_0,esk3_0),
    inference(spm,[status(thm)],[21,40,theory(equality)]) ).

cnf(68,plain,
    subset(set_intersection2(X2,X1),X1),
    inference(spm,[status(thm)],[26,16,theory(equality)]) ).

cnf(88,plain,
    ( set_intersection2(cartesian_product2(X1,X3),cartesian_product2(X2,X4)) = empty_set
    | empty_set != set_intersection2(X3,X4) ),
    inference(spm,[status(thm)],[32,28,theory(equality)]) ).

cnf(89,plain,
    ( set_intersection2(cartesian_product2(X1,X3),cartesian_product2(X2,X4)) = empty_set
    | empty_set != set_intersection2(X1,X2) ),
    inference(spm,[status(thm)],[33,28,theory(equality)]) ).

cnf(91,plain,
    ( empty_set = set_intersection2(X1,X2)
    | empty_set = set_intersection2(X3,X4)
    | set_intersection2(X3,X4) = X5
    | set_intersection2(cartesian_product2(X1,X3),cartesian_product2(X2,X4)) != cartesian_product2(X6,X5) ),
    inference(spm,[status(thm)],[47,28,theory(equality)]) ).

cnf(93,plain,
    ( empty_set = set_intersection2(X1,X2)
    | empty_set = set_intersection2(X3,X4)
    | set_intersection2(X1,X2) = X5
    | set_intersection2(cartesian_product2(X1,X3),cartesian_product2(X2,X4)) != cartesian_product2(X5,X6) ),
    inference(spm,[status(thm)],[48,28,theory(equality)]) ).

cnf(691,negated_conjecture,
    ( empty_set = cartesian_product2(esk2_0,esk3_0)
    | set_intersection2(esk3_0,esk5_0) != empty_set ),
    inference(spm,[status(thm)],[61,88,theory(equality)]) ).

cnf(713,negated_conjecture,
    set_intersection2(esk3_0,esk5_0) != empty_set,
    inference(sr,[status(thm)],[691,39,theory(equality)]) ).

cnf(747,negated_conjecture,
    ( empty_set = cartesian_product2(esk2_0,esk3_0)
    | set_intersection2(esk2_0,esk4_0) != empty_set ),
    inference(spm,[status(thm)],[61,89,theory(equality)]) ).

cnf(769,negated_conjecture,
    set_intersection2(esk2_0,esk4_0) != empty_set,
    inference(sr,[status(thm)],[747,39,theory(equality)]) ).

cnf(834,negated_conjecture,
    ( set_intersection2(esk3_0,esk5_0) = empty_set
    | set_intersection2(esk2_0,esk4_0) = empty_set
    | set_intersection2(esk3_0,esk5_0) = X1
    | cartesian_product2(esk2_0,esk3_0) != cartesian_product2(X2,X1) ),
    inference(spm,[status(thm)],[91,61,theory(equality)]) ).

cnf(857,negated_conjecture,
    ( set_intersection2(esk2_0,esk4_0) = empty_set
    | set_intersection2(esk3_0,esk5_0) = X1
    | cartesian_product2(esk2_0,esk3_0) != cartesian_product2(X2,X1) ),
    inference(sr,[status(thm)],[834,713,theory(equality)]) ).

cnf(858,negated_conjecture,
    ( set_intersection2(esk3_0,esk5_0) = X1
    | cartesian_product2(esk2_0,esk3_0) != cartesian_product2(X2,X1) ),
    inference(sr,[status(thm)],[857,769,theory(equality)]) ).

cnf(865,negated_conjecture,
    set_intersection2(esk3_0,esk5_0) = esk3_0,
    inference(er,[status(thm)],[858,theory(equality)]) ).

cnf(876,negated_conjecture,
    subset(esk3_0,esk5_0),
    inference(spm,[status(thm)],[68,865,theory(equality)]) ).

cnf(889,negated_conjecture,
    ( ~ subset(esk2_0,esk4_0)
    | $false ),
    inference(rw,[status(thm)],[38,876,theory(equality)]) ).

cnf(890,negated_conjecture,
    ~ subset(esk2_0,esk4_0),
    inference(cn,[status(thm)],[889,theory(equality)]) ).

cnf(1065,negated_conjecture,
    ( set_intersection2(esk3_0,esk5_0) = empty_set
    | set_intersection2(esk2_0,esk4_0) = empty_set
    | set_intersection2(esk2_0,esk4_0) = X1
    | cartesian_product2(esk2_0,esk3_0) != cartesian_product2(X1,X2) ),
    inference(spm,[status(thm)],[93,61,theory(equality)]) ).

cnf(1088,negated_conjecture,
    ( esk3_0 = empty_set
    | set_intersection2(esk2_0,esk4_0) = empty_set
    | set_intersection2(esk2_0,esk4_0) = X1
    | cartesian_product2(esk2_0,esk3_0) != cartesian_product2(X1,X2) ),
    inference(rw,[status(thm)],[1065,865,theory(equality)]) ).

cnf(1089,negated_conjecture,
    ( set_intersection2(esk2_0,esk4_0) = empty_set
    | set_intersection2(esk2_0,esk4_0) = X1
    | cartesian_product2(esk2_0,esk3_0) != cartesian_product2(X1,X2) ),
    inference(sr,[status(thm)],[1088,54,theory(equality)]) ).

cnf(1090,negated_conjecture,
    ( set_intersection2(esk2_0,esk4_0) = X1
    | cartesian_product2(esk2_0,esk3_0) != cartesian_product2(X1,X2) ),
    inference(sr,[status(thm)],[1089,769,theory(equality)]) ).

cnf(17578,negated_conjecture,
    set_intersection2(esk2_0,esk4_0) = esk2_0,
    inference(er,[status(thm)],[1090,theory(equality)]) ).

cnf(17600,negated_conjecture,
    subset(esk2_0,esk4_0),
    inference(spm,[status(thm)],[68,17578,theory(equality)]) ).

cnf(17640,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[17600,890,theory(equality)]) ).

cnf(17641,negated_conjecture,
    $false,
    17640,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET984+1.p
% --creating new selector for []
% -running prover on /tmp/tmp2ycPs2/sel_SET984+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET984+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET984+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET984+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
% 
%------------------------------------------------------------------------------