TSTP Solution File: SET586+3 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SET586+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 02:58:42 EST 2010

% Result   : Theorem 0.26s
% Output   : CNFRefutation 0.26s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   38 (  11 unt;   0 def)
%            Number of atoms       :  104 (   3 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  108 (  42   ~;  41   |;  20   &)
%                                         (   2 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   81 (   4 sgn  40   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
    file('/tmp/tmp9-HL9o/sel_SET586+3.p_1',commutativity_of_intersection) ).

fof(2,axiom,
    ! [X1,X2] :
      ( subset(X1,X2)
    <=> ! [X3] :
          ( member(X3,X1)
         => member(X3,X2) ) ),
    file('/tmp/tmp9-HL9o/sel_SET586+3.p_1',subset_defn) ).

fof(3,conjecture,
    ! [X1,X2,X3] :
      ( subset(X1,X2)
     => subset(intersection(X1,X3),intersection(X2,X3)) ),
    file('/tmp/tmp9-HL9o/sel_SET586+3.p_1',prove_intersection_of_subset) ).

fof(5,axiom,
    ! [X1,X2,X3] :
      ( member(X3,intersection(X1,X2))
    <=> ( member(X3,X1)
        & member(X3,X2) ) ),
    file('/tmp/tmp9-HL9o/sel_SET586+3.p_1',intersection_defn) ).

fof(7,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( subset(X1,X2)
       => subset(intersection(X1,X3),intersection(X2,X3)) ),
    inference(assume_negation,[status(cth)],[3]) ).

fof(8,plain,
    ! [X3,X4] : intersection(X3,X4) = intersection(X4,X3),
    inference(variable_rename,[status(thm)],[1]) ).

cnf(9,plain,
    intersection(X1,X2) = intersection(X2,X1),
    inference(split_conjunct,[status(thm)],[8]) ).

fof(10,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)],[2]) ).

fof(11,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)],[10]) ).

fof(12,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)],[11]) ).

fof(13,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)],[12]) ).

fof(14,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)],[13]) ).

cnf(15,plain,
    ( subset(X1,X2)
    | ~ member(esk1_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[14]) ).

cnf(16,plain,
    ( subset(X1,X2)
    | member(esk1_2(X1,X2),X1) ),
    inference(split_conjunct,[status(thm)],[14]) ).

cnf(17,plain,
    ( member(X3,X2)
    | ~ subset(X1,X2)
    | ~ member(X3,X1) ),
    inference(split_conjunct,[status(thm)],[14]) ).

fof(18,negated_conjecture,
    ? [X1,X2,X3] :
      ( subset(X1,X2)
      & ~ subset(intersection(X1,X3),intersection(X2,X3)) ),
    inference(fof_nnf,[status(thm)],[7]) ).

fof(19,negated_conjecture,
    ? [X4,X5,X6] :
      ( subset(X4,X5)
      & ~ subset(intersection(X4,X6),intersection(X5,X6)) ),
    inference(variable_rename,[status(thm)],[18]) ).

fof(20,negated_conjecture,
    ( subset(esk2_0,esk3_0)
    & ~ subset(intersection(esk2_0,esk4_0),intersection(esk3_0,esk4_0)) ),
    inference(skolemize,[status(esa)],[19]) ).

cnf(21,negated_conjecture,
    ~ subset(intersection(esk2_0,esk4_0),intersection(esk3_0,esk4_0)),
    inference(split_conjunct,[status(thm)],[20]) ).

cnf(22,negated_conjecture,
    subset(esk2_0,esk3_0),
    inference(split_conjunct,[status(thm)],[20]) ).

fof(32,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)],[5]) ).

fof(33,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)],[32]) ).

fof(34,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)],[33]) ).

cnf(35,plain,
    ( member(X1,intersection(X2,X3))
    | ~ member(X1,X3)
    | ~ member(X1,X2) ),
    inference(split_conjunct,[status(thm)],[34]) ).

cnf(36,plain,
    ( member(X1,X3)
    | ~ member(X1,intersection(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[34]) ).

cnf(42,plain,
    ( member(esk1_2(intersection(X1,X2),X3),X2)
    | subset(intersection(X1,X2),X3) ),
    inference(spm,[status(thm)],[36,16,theory(equality)]) ).

cnf(48,negated_conjecture,
    ( member(X1,esk3_0)
    | ~ member(X1,esk2_0) ),
    inference(spm,[status(thm)],[17,22,theory(equality)]) ).

cnf(54,plain,
    ( subset(X1,intersection(X2,X3))
    | ~ member(esk1_2(X1,intersection(X2,X3)),X3)
    | ~ member(esk1_2(X1,intersection(X2,X3)),X2) ),
    inference(spm,[status(thm)],[15,35,theory(equality)]) ).

cnf(63,negated_conjecture,
    ( subset(X1,esk3_0)
    | ~ member(esk1_2(X1,esk3_0),esk2_0) ),
    inference(spm,[status(thm)],[15,48,theory(equality)]) ).

cnf(72,negated_conjecture,
    subset(intersection(X1,esk2_0),esk3_0),
    inference(spm,[status(thm)],[63,42,theory(equality)]) ).

cnf(73,negated_conjecture,
    subset(intersection(esk2_0,X1),esk3_0),
    inference(spm,[status(thm)],[72,9,theory(equality)]) ).

cnf(81,negated_conjecture,
    ( member(X1,esk3_0)
    | ~ member(X1,intersection(esk2_0,X2)) ),
    inference(spm,[status(thm)],[17,73,theory(equality)]) ).

cnf(109,negated_conjecture,
    ( member(esk1_2(intersection(esk2_0,X1),X2),esk3_0)
    | subset(intersection(esk2_0,X1),X2) ),
    inference(spm,[status(thm)],[81,16,theory(equality)]) ).

cnf(130,plain,
    ( subset(intersection(X1,X2),intersection(X3,X2))
    | ~ member(esk1_2(intersection(X1,X2),intersection(X3,X2)),X3) ),
    inference(spm,[status(thm)],[54,42,theory(equality)]) ).

cnf(941,negated_conjecture,
    subset(intersection(esk2_0,X1),intersection(esk3_0,X1)),
    inference(spm,[status(thm)],[130,109,theory(equality)]) ).

cnf(962,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[21,941,theory(equality)]) ).

cnf(963,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[962,theory(equality)]) ).

cnf(964,negated_conjecture,
    $false,
    963,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET586+3.p
% --creating new selector for []
% -running prover on /tmp/tmp9-HL9o/sel_SET586+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET586+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET586+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET586+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
% 
%------------------------------------------------------------------------------