TSTP Solution File: SET971+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SET971+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 03:56:06 EST 2010

% Result   : Theorem 0.17s
% Output   : CNFRefutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   25 (  16 unt;   0 def)
%            Number of atoms       :   39 (  20 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   24 (  10   ~;   3   |;   8   &)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   42 (   0 sgn  26   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
    file('/tmp/tmp0YZ5s5/sel_SET971+1.p_1',commutativity_k3_xboole_0) ).

fof(2,conjecture,
    ! [X1,X2,X3,X4] :
      ( ( subset(X1,X2)
        & subset(X3,X4) )
     => set_intersection2(cartesian_product2(X1,X4),cartesian_product2(X2,X3)) = cartesian_product2(X1,X3) ),
    file('/tmp/tmp0YZ5s5/sel_SET971+1.p_1',t124_zfmisc_1) ).

fof(4,axiom,
    ! [X1,X2] :
      ( subset(X1,X2)
     => set_intersection2(X1,X2) = X1 ),
    file('/tmp/tmp0YZ5s5/sel_SET971+1.p_1',t28_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/tmp0YZ5s5/sel_SET971+1.p_1',t123_zfmisc_1) ).

fof(9,negated_conjecture,
    ~ ! [X1,X2,X3,X4] :
        ( ( subset(X1,X2)
          & subset(X3,X4) )
       => set_intersection2(cartesian_product2(X1,X4),cartesian_product2(X2,X3)) = cartesian_product2(X1,X3) ),
    inference(assume_negation,[status(cth)],[2]) ).

fof(11,plain,
    ! [X3,X4] : set_intersection2(X3,X4) = set_intersection2(X4,X3),
    inference(variable_rename,[status(thm)],[1]) ).

cnf(12,plain,
    set_intersection2(X1,X2) = set_intersection2(X2,X1),
    inference(split_conjunct,[status(thm)],[11]) ).

fof(13,negated_conjecture,
    ? [X1,X2,X3,X4] :
      ( subset(X1,X2)
      & subset(X3,X4)
      & set_intersection2(cartesian_product2(X1,X4),cartesian_product2(X2,X3)) != cartesian_product2(X1,X3) ),
    inference(fof_nnf,[status(thm)],[9]) ).

fof(14,negated_conjecture,
    ? [X5,X6,X7,X8] :
      ( subset(X5,X6)
      & subset(X7,X8)
      & set_intersection2(cartesian_product2(X5,X8),cartesian_product2(X6,X7)) != cartesian_product2(X5,X7) ),
    inference(variable_rename,[status(thm)],[13]) ).

fof(15,negated_conjecture,
    ( subset(esk1_0,esk2_0)
    & subset(esk3_0,esk4_0)
    & set_intersection2(cartesian_product2(esk1_0,esk4_0),cartesian_product2(esk2_0,esk3_0)) != cartesian_product2(esk1_0,esk3_0) ),
    inference(skolemize,[status(esa)],[14]) ).

cnf(16,negated_conjecture,
    set_intersection2(cartesian_product2(esk1_0,esk4_0),cartesian_product2(esk2_0,esk3_0)) != cartesian_product2(esk1_0,esk3_0),
    inference(split_conjunct,[status(thm)],[15]) ).

cnf(17,negated_conjecture,
    subset(esk3_0,esk4_0),
    inference(split_conjunct,[status(thm)],[15]) ).

cnf(18,negated_conjecture,
    subset(esk1_0,esk2_0),
    inference(split_conjunct,[status(thm)],[15]) ).

fof(21,plain,
    ! [X1,X2] :
      ( ~ subset(X1,X2)
      | set_intersection2(X1,X2) = X1 ),
    inference(fof_nnf,[status(thm)],[4]) ).

fof(22,plain,
    ! [X3,X4] :
      ( ~ subset(X3,X4)
      | set_intersection2(X3,X4) = X3 ),
    inference(variable_rename,[status(thm)],[21]) ).

cnf(23,plain,
    ( set_intersection2(X1,X2) = X1
    | ~ subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[22]) ).

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]) ).

cnf(38,negated_conjecture,
    set_intersection2(esk1_0,esk2_0) = esk1_0,
    inference(spm,[status(thm)],[23,18,theory(equality)]) ).

cnf(39,negated_conjecture,
    set_intersection2(esk3_0,esk4_0) = esk3_0,
    inference(spm,[status(thm)],[23,17,theory(equality)]) ).

cnf(45,negated_conjecture,
    cartesian_product2(set_intersection2(esk1_0,esk2_0),set_intersection2(esk3_0,esk4_0)) != cartesian_product2(esk1_0,esk3_0),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[16,28,theory(equality)]),12,theory(equality)]) ).

cnf(49,negated_conjecture,
    cartesian_product2(esk1_0,set_intersection2(esk3_0,esk4_0)) != cartesian_product2(esk1_0,esk3_0),
    inference(rw,[status(thm)],[45,38,theory(equality)]) ).

cnf(50,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[49,39,theory(equality)]) ).

cnf(51,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[50,theory(equality)]) ).

cnf(52,negated_conjecture,
    $false,
    51,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET971+1.p
% --creating new selector for []
% -running prover on /tmp/tmp0YZ5s5/sel_SET971+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET971+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET971+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET971+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
% 
%------------------------------------------------------------------------------