TSTP Solution File: SET699+4 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SET699+4 : 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 03:12:52 EST 2010

% Result   : Theorem 0.54s
% Output   : CNFRefutation 0.54s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   25
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   63 (  10 unt;   0 def)
%            Number of atoms       :  193 (   0 equ)
%            Maximal formula atoms :    7 (   3 avg)
%            Number of connectives :  206 (  76   ~;  85   |;  36   &)
%                                         (   6 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :  131 (  10 sgn  51   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1,X2] :
      ( subset(X1,X2)
    <=> ! [X3] :
          ( member(X3,X1)
         => member(X3,X2) ) ),
    file('/tmp/tmpFZicfr/sel_SET699+4.p_1',subset) ).

fof(2,axiom,
    ! [X2,X1,X4] :
      ( member(X2,difference(X4,X1))
    <=> ( member(X2,X4)
        & ~ member(X2,X1) ) ),
    file('/tmp/tmpFZicfr/sel_SET699+4.p_1',difference) ).

fof(3,axiom,
    ! [X3,X1,X2] :
      ( member(X3,intersection(X1,X2))
    <=> ( member(X3,X1)
        & member(X3,X2) ) ),
    file('/tmp/tmpFZicfr/sel_SET699+4.p_1',intersection) ).

fof(4,conjecture,
    ! [X1,X2,X4] :
      ( ( subset(X1,X4)
        & subset(X2,X4) )
     => ( subset(X1,X2)
      <=> subset(intersection(X1,difference(X4,X2)),difference(X4,X1)) ) ),
    file('/tmp/tmpFZicfr/sel_SET699+4.p_1',thI33) ).

fof(5,negated_conjecture,
    ~ ! [X1,X2,X4] :
        ( ( subset(X1,X4)
          & subset(X2,X4) )
       => ( subset(X1,X2)
        <=> subset(intersection(X1,difference(X4,X2)),difference(X4,X1)) ) ),
    inference(assume_negation,[status(cth)],[4]) ).

fof(6,plain,
    ! [X2,X1,X4] :
      ( member(X2,difference(X4,X1))
    <=> ( member(X2,X4)
        & ~ member(X2,X1) ) ),
    inference(fof_simplification,[status(thm)],[2,theory(equality)]) ).

fof(7,plain,
    ! [X1,X2] :
      ( ( ~ subset(X1,X2)
        | ! [X3] :
            ( ~ member(X3,X1)
            | member(X3,X2) ) )
      & ( ? [X3] :
            ( member(X3,X1)
            & ~ member(X3,X2) )
        | subset(X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[1]) ).

fof(8,plain,
    ! [X4,X5] :
      ( ( ~ subset(X4,X5)
        | ! [X6] :
            ( ~ member(X6,X4)
            | member(X6,X5) ) )
      & ( ? [X7] :
            ( member(X7,X4)
            & ~ member(X7,X5) )
        | subset(X4,X5) ) ),
    inference(variable_rename,[status(thm)],[7]) ).

fof(9,plain,
    ! [X4,X5] :
      ( ( ~ subset(X4,X5)
        | ! [X6] :
            ( ~ member(X6,X4)
            | member(X6,X5) ) )
      & ( ( member(esk1_2(X4,X5),X4)
          & ~ member(esk1_2(X4,X5),X5) )
        | subset(X4,X5) ) ),
    inference(skolemize,[status(esa)],[8]) ).

fof(10,plain,
    ! [X4,X5,X6] :
      ( ( ~ member(X6,X4)
        | member(X6,X5)
        | ~ subset(X4,X5) )
      & ( ( member(esk1_2(X4,X5),X4)
          & ~ member(esk1_2(X4,X5),X5) )
        | subset(X4,X5) ) ),
    inference(shift_quantors,[status(thm)],[9]) ).

fof(11,plain,
    ! [X4,X5,X6] :
      ( ( ~ member(X6,X4)
        | member(X6,X5)
        | ~ subset(X4,X5) )
      & ( member(esk1_2(X4,X5),X4)
        | subset(X4,X5) )
      & ( ~ member(esk1_2(X4,X5),X5)
        | subset(X4,X5) ) ),
    inference(distribute,[status(thm)],[10]) ).

cnf(12,plain,
    ( subset(X1,X2)
    | ~ member(esk1_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[11]) ).

cnf(13,plain,
    ( subset(X1,X2)
    | member(esk1_2(X1,X2),X1) ),
    inference(split_conjunct,[status(thm)],[11]) ).

cnf(14,plain,
    ( member(X3,X2)
    | ~ subset(X1,X2)
    | ~ member(X3,X1) ),
    inference(split_conjunct,[status(thm)],[11]) ).

fof(15,plain,
    ! [X2,X1,X4] :
      ( ( ~ member(X2,difference(X4,X1))
        | ( member(X2,X4)
          & ~ member(X2,X1) ) )
      & ( ~ member(X2,X4)
        | member(X2,X1)
        | member(X2,difference(X4,X1)) ) ),
    inference(fof_nnf,[status(thm)],[6]) ).

fof(16,plain,
    ! [X5,X6,X7] :
      ( ( ~ member(X5,difference(X7,X6))
        | ( member(X5,X7)
          & ~ member(X5,X6) ) )
      & ( ~ member(X5,X7)
        | member(X5,X6)
        | member(X5,difference(X7,X6)) ) ),
    inference(variable_rename,[status(thm)],[15]) ).

fof(17,plain,
    ! [X5,X6,X7] :
      ( ( member(X5,X7)
        | ~ member(X5,difference(X7,X6)) )
      & ( ~ member(X5,X6)
        | ~ member(X5,difference(X7,X6)) )
      & ( ~ member(X5,X7)
        | member(X5,X6)
        | member(X5,difference(X7,X6)) ) ),
    inference(distribute,[status(thm)],[16]) ).

cnf(18,plain,
    ( member(X1,difference(X2,X3))
    | member(X1,X3)
    | ~ member(X1,X2) ),
    inference(split_conjunct,[status(thm)],[17]) ).

cnf(19,plain,
    ( ~ member(X1,difference(X2,X3))
    | ~ member(X1,X3) ),
    inference(split_conjunct,[status(thm)],[17]) ).

cnf(20,plain,
    ( member(X1,X2)
    | ~ member(X1,difference(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[17]) ).

fof(21,plain,
    ! [X3,X1,X2] :
      ( ( ~ 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)],[3]) ).

fof(22,plain,
    ! [X4,X5,X6] :
      ( ( ~ member(X4,intersection(X5,X6))
        | ( member(X4,X5)
          & member(X4,X6) ) )
      & ( ~ member(X4,X5)
        | ~ member(X4,X6)
        | member(X4,intersection(X5,X6)) ) ),
    inference(variable_rename,[status(thm)],[21]) ).

fof(23,plain,
    ! [X4,X5,X6] :
      ( ( member(X4,X5)
        | ~ member(X4,intersection(X5,X6)) )
      & ( member(X4,X6)
        | ~ member(X4,intersection(X5,X6)) )
      & ( ~ member(X4,X5)
        | ~ member(X4,X6)
        | member(X4,intersection(X5,X6)) ) ),
    inference(distribute,[status(thm)],[22]) ).

cnf(24,plain,
    ( member(X1,intersection(X2,X3))
    | ~ member(X1,X3)
    | ~ member(X1,X2) ),
    inference(split_conjunct,[status(thm)],[23]) ).

cnf(25,plain,
    ( member(X1,X3)
    | ~ member(X1,intersection(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[23]) ).

cnf(26,plain,
    ( member(X1,X2)
    | ~ member(X1,intersection(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[23]) ).

fof(27,negated_conjecture,
    ? [X1,X2,X4] :
      ( subset(X1,X4)
      & subset(X2,X4)
      & ( ~ subset(X1,X2)
        | ~ subset(intersection(X1,difference(X4,X2)),difference(X4,X1)) )
      & ( subset(X1,X2)
        | subset(intersection(X1,difference(X4,X2)),difference(X4,X1)) ) ),
    inference(fof_nnf,[status(thm)],[5]) ).

fof(28,negated_conjecture,
    ? [X5,X6,X7] :
      ( subset(X5,X7)
      & subset(X6,X7)
      & ( ~ subset(X5,X6)
        | ~ subset(intersection(X5,difference(X7,X6)),difference(X7,X5)) )
      & ( subset(X5,X6)
        | subset(intersection(X5,difference(X7,X6)),difference(X7,X5)) ) ),
    inference(variable_rename,[status(thm)],[27]) ).

fof(29,negated_conjecture,
    ( subset(esk2_0,esk4_0)
    & subset(esk3_0,esk4_0)
    & ( ~ subset(esk2_0,esk3_0)
      | ~ subset(intersection(esk2_0,difference(esk4_0,esk3_0)),difference(esk4_0,esk2_0)) )
    & ( subset(esk2_0,esk3_0)
      | subset(intersection(esk2_0,difference(esk4_0,esk3_0)),difference(esk4_0,esk2_0)) ) ),
    inference(skolemize,[status(esa)],[28]) ).

cnf(30,negated_conjecture,
    ( subset(intersection(esk2_0,difference(esk4_0,esk3_0)),difference(esk4_0,esk2_0))
    | subset(esk2_0,esk3_0) ),
    inference(split_conjunct,[status(thm)],[29]) ).

cnf(31,negated_conjecture,
    ( ~ subset(intersection(esk2_0,difference(esk4_0,esk3_0)),difference(esk4_0,esk2_0))
    | ~ subset(esk2_0,esk3_0) ),
    inference(split_conjunct,[status(thm)],[29]) ).

cnf(33,negated_conjecture,
    subset(esk2_0,esk4_0),
    inference(split_conjunct,[status(thm)],[29]) ).

cnf(35,plain,
    ( member(esk1_2(intersection(X1,X2),X3),X2)
    | subset(intersection(X1,X2),X3) ),
    inference(spm,[status(thm)],[25,13,theory(equality)]) ).

cnf(36,plain,
    ( member(esk1_2(difference(X1,X2),X3),X1)
    | subset(difference(X1,X2),X3) ),
    inference(spm,[status(thm)],[20,13,theory(equality)]) ).

cnf(37,plain,
    ( member(esk1_2(intersection(X1,X2),X3),X1)
    | subset(intersection(X1,X2),X3) ),
    inference(spm,[status(thm)],[26,13,theory(equality)]) ).

cnf(38,negated_conjecture,
    ( member(X1,esk4_0)
    | ~ member(X1,esk2_0) ),
    inference(spm,[status(thm)],[14,33,theory(equality)]) ).

cnf(40,negated_conjecture,
    ( member(X1,difference(esk4_0,esk2_0))
    | subset(esk2_0,esk3_0)
    | ~ member(X1,intersection(esk2_0,difference(esk4_0,esk3_0))) ),
    inference(spm,[status(thm)],[14,30,theory(equality)]) ).

cnf(41,plain,
    ( subset(difference(X1,X2),X3)
    | ~ member(esk1_2(difference(X1,X2),X3),X2) ),
    inference(spm,[status(thm)],[19,13,theory(equality)]) ).

cnf(50,negated_conjecture,
    ( subset(X1,esk4_0)
    | ~ member(esk1_2(X1,esk4_0),esk2_0) ),
    inference(spm,[status(thm)],[12,38,theory(equality)]) ).

cnf(58,plain,
    ( subset(intersection(X1,difference(X2,X3)),X4)
    | ~ member(esk1_2(intersection(X1,difference(X2,X3)),X4),X3) ),
    inference(spm,[status(thm)],[19,35,theory(equality)]) ).

cnf(61,plain,
    ( subset(difference(X1,difference(X2,X3)),X4)
    | member(esk1_2(difference(X1,difference(X2,X3)),X4),X3)
    | ~ member(esk1_2(difference(X1,difference(X2,X3)),X4),X2) ),
    inference(spm,[status(thm)],[41,18,theory(equality)]) ).

cnf(80,negated_conjecture,
    subset(difference(esk2_0,X1),esk4_0),
    inference(spm,[status(thm)],[50,36,theory(equality)]) ).

cnf(96,negated_conjecture,
    ( member(X1,esk4_0)
    | ~ member(X1,difference(esk2_0,X2)) ),
    inference(spm,[status(thm)],[14,80,theory(equality)]) ).

cnf(134,negated_conjecture,
    ( member(X1,difference(esk4_0,esk2_0))
    | subset(esk2_0,esk3_0)
    | ~ member(X1,difference(esk4_0,esk3_0))
    | ~ member(X1,esk2_0) ),
    inference(spm,[status(thm)],[40,24,theory(equality)]) ).

cnf(273,negated_conjecture,
    ( member(esk1_2(difference(esk2_0,X1),X2),esk4_0)
    | subset(difference(esk2_0,X1),X2) ),
    inference(spm,[status(thm)],[96,13,theory(equality)]) ).

cnf(459,negated_conjecture,
    ( member(esk1_2(difference(esk2_0,difference(esk4_0,X1)),X2),X1)
    | subset(difference(esk2_0,difference(esk4_0,X1)),X2) ),
    inference(spm,[status(thm)],[61,273,theory(equality)]) ).

cnf(1101,negated_conjecture,
    ( subset(esk2_0,esk3_0)
    | ~ member(X1,difference(esk4_0,esk3_0))
    | ~ member(X1,esk2_0) ),
    inference(csr,[status(thm)],[134,19]) ).

cnf(1318,negated_conjecture,
    subset(difference(esk2_0,difference(esk4_0,X1)),X1),
    inference(spm,[status(thm)],[12,459,theory(equality)]) ).

cnf(1349,negated_conjecture,
    ( member(X1,X2)
    | ~ member(X1,difference(esk2_0,difference(esk4_0,X2))) ),
    inference(spm,[status(thm)],[14,1318,theory(equality)]) ).

cnf(1422,negated_conjecture,
    ( member(X1,X2)
    | member(X1,difference(esk4_0,X2))
    | ~ member(X1,esk2_0) ),
    inference(spm,[status(thm)],[1349,18,theory(equality)]) ).

cnf(3403,negated_conjecture,
    ( subset(esk2_0,esk3_0)
    | member(X1,esk3_0)
    | ~ member(X1,esk2_0) ),
    inference(spm,[status(thm)],[1101,1422,theory(equality)]) ).

cnf(3439,negated_conjecture,
    ( member(X1,esk3_0)
    | ~ member(X1,esk2_0) ),
    inference(csr,[status(thm)],[3403,14]) ).

cnf(3440,negated_conjecture,
    ( subset(X1,esk3_0)
    | ~ member(esk1_2(X1,esk3_0),esk2_0) ),
    inference(spm,[status(thm)],[12,3439,theory(equality)]) ).

cnf(3472,negated_conjecture,
    subset(esk2_0,esk3_0),
    inference(spm,[status(thm)],[3440,13,theory(equality)]) ).

cnf(3475,negated_conjecture,
    subset(intersection(esk2_0,X1),esk3_0),
    inference(spm,[status(thm)],[3440,37,theory(equality)]) ).

cnf(3509,negated_conjecture,
    ( ~ subset(intersection(esk2_0,difference(esk4_0,esk3_0)),difference(esk4_0,esk2_0))
    | $false ),
    inference(rw,[status(thm)],[31,3472,theory(equality)]) ).

cnf(3510,negated_conjecture,
    ~ subset(intersection(esk2_0,difference(esk4_0,esk3_0)),difference(esk4_0,esk2_0)),
    inference(cn,[status(thm)],[3509,theory(equality)]) ).

cnf(3514,negated_conjecture,
    ( member(X1,esk3_0)
    | ~ member(X1,intersection(esk2_0,X2)) ),
    inference(spm,[status(thm)],[14,3475,theory(equality)]) ).

cnf(3811,negated_conjecture,
    ( member(esk1_2(intersection(esk2_0,X1),X2),esk3_0)
    | subset(intersection(esk2_0,X1),X2) ),
    inference(spm,[status(thm)],[3514,13,theory(equality)]) ).

cnf(4461,negated_conjecture,
    subset(intersection(esk2_0,difference(X1,esk3_0)),X2),
    inference(spm,[status(thm)],[58,3811,theory(equality)]) ).

cnf(4483,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[3510,4461,theory(equality)]) ).

cnf(4484,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[4483,theory(equality)]) ).

cnf(4485,negated_conjecture,
    $false,
    4484,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET699+4.p
% --creating new selector for [SET006+0.ax]
% -running prover on /tmp/tmpFZicfr/sel_SET699+4.p_1 with time limit 29
% -prover status Theorem
% Problem SET699+4.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET699+4.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET699+4.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
% 
%------------------------------------------------------------------------------