TSTP Solution File: SET183+3 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SET183+3 : TPTP v5.0.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art03.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 02:54:03 EST 2010

% Result   : Theorem 0.20s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   53 (  17 unt;   0 def)
%            Number of atoms       :  143 (  24 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  146 (  56   ~;  57   |;  27   &)
%                                         (   3 <=>;   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    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   95 (   4 sgn  50   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
    file('/tmp/tmp27CJ_-/sel_SET183+3.p_1',commutativity_of_intersection) ).

fof(2,axiom,
    ! [X1,X2] :
      ( subset(X1,X2)
    <=> ! [X3] :
          ( member(X3,X1)
         => member(X3,X2) ) ),
    file('/tmp/tmp27CJ_-/sel_SET183+3.p_1',subset_defn) ).

fof(3,axiom,
    ! [X1,X2] : subset(intersection(X1,X2),X1),
    file('/tmp/tmp27CJ_-/sel_SET183+3.p_1',intersection_is_subset) ).

fof(4,axiom,
    ! [X1,X2] :
      ( X1 = X2
    <=> ( subset(X1,X2)
        & subset(X2,X1) ) ),
    file('/tmp/tmp27CJ_-/sel_SET183+3.p_1',equal_defn) ).

fof(5,conjecture,
    ! [X1,X2] :
      ( subset(X1,X2)
     => intersection(X1,X2) = X1 ),
    file('/tmp/tmp27CJ_-/sel_SET183+3.p_1',prove_subset_intersection) ).

fof(7,axiom,
    ! [X1,X2,X3] :
      ( member(X3,intersection(X1,X2))
    <=> ( member(X3,X1)
        & member(X3,X2) ) ),
    file('/tmp/tmp27CJ_-/sel_SET183+3.p_1',intersection_defn) ).

fof(9,negated_conjecture,
    ~ ! [X1,X2] :
        ( subset(X1,X2)
       => intersection(X1,X2) = X1 ),
    inference(assume_negation,[status(cth)],[5]) ).

fof(10,plain,
    ! [X3,X4] : intersection(X3,X4) = intersection(X4,X3),
    inference(variable_rename,[status(thm)],[1]) ).

cnf(11,plain,
    intersection(X1,X2) = intersection(X2,X1),
    inference(split_conjunct,[status(thm)],[10]) ).

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

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

fof(15,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)],[14]) ).

fof(16,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)],[15]) ).

cnf(17,plain,
    ( subset(X1,X2)
    | ~ member(esk1_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[16]) ).

cnf(18,plain,
    ( subset(X1,X2)
    | member(esk1_2(X1,X2),X1) ),
    inference(split_conjunct,[status(thm)],[16]) ).

cnf(19,plain,
    ( member(X3,X2)
    | ~ subset(X1,X2)
    | ~ member(X3,X1) ),
    inference(split_conjunct,[status(thm)],[16]) ).

fof(20,plain,
    ! [X3,X4] : subset(intersection(X3,X4),X3),
    inference(variable_rename,[status(thm)],[3]) ).

cnf(21,plain,
    subset(intersection(X1,X2),X1),
    inference(split_conjunct,[status(thm)],[20]) ).

fof(22,plain,
    ! [X1,X2] :
      ( ( X1 != X2
        | ( subset(X1,X2)
          & subset(X2,X1) ) )
      & ( ~ subset(X1,X2)
        | ~ subset(X2,X1)
        | X1 = X2 ) ),
    inference(fof_nnf,[status(thm)],[4]) ).

fof(23,plain,
    ! [X3,X4] :
      ( ( X3 != X4
        | ( subset(X3,X4)
          & subset(X4,X3) ) )
      & ( ~ subset(X3,X4)
        | ~ subset(X4,X3)
        | X3 = X4 ) ),
    inference(variable_rename,[status(thm)],[22]) ).

fof(24,plain,
    ! [X3,X4] :
      ( ( subset(X3,X4)
        | X3 != X4 )
      & ( subset(X4,X3)
        | X3 != X4 )
      & ( ~ subset(X3,X4)
        | ~ subset(X4,X3)
        | X3 = X4 ) ),
    inference(distribute,[status(thm)],[23]) ).

cnf(25,plain,
    ( X1 = X2
    | ~ subset(X2,X1)
    | ~ subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[24]) ).

fof(28,negated_conjecture,
    ? [X1,X2] :
      ( subset(X1,X2)
      & intersection(X1,X2) != X1 ),
    inference(fof_nnf,[status(thm)],[9]) ).

fof(29,negated_conjecture,
    ? [X3,X4] :
      ( subset(X3,X4)
      & intersection(X3,X4) != X3 ),
    inference(variable_rename,[status(thm)],[28]) ).

fof(30,negated_conjecture,
    ( subset(esk2_0,esk3_0)
    & intersection(esk2_0,esk3_0) != esk2_0 ),
    inference(skolemize,[status(esa)],[29]) ).

cnf(31,negated_conjecture,
    intersection(esk2_0,esk3_0) != esk2_0,
    inference(split_conjunct,[status(thm)],[30]) ).

cnf(32,negated_conjecture,
    subset(esk2_0,esk3_0),
    inference(split_conjunct,[status(thm)],[30]) ).

fof(42,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)],[7]) ).

fof(43,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)],[42]) ).

fof(44,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)],[43]) ).

cnf(45,plain,
    ( member(X1,intersection(X2,X3))
    | ~ member(X1,X3)
    | ~ member(X1,X2) ),
    inference(split_conjunct,[status(thm)],[44]) ).

cnf(46,plain,
    ( member(X1,X3)
    | ~ member(X1,intersection(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[44]) ).

cnf(60,plain,
    ( member(esk1_2(intersection(X1,X2),X3),X2)
    | subset(intersection(X1,X2),X3) ),
    inference(spm,[status(thm)],[46,18,theory(equality)]) ).

cnf(66,negated_conjecture,
    ( member(X1,esk3_0)
    | ~ member(X1,esk2_0) ),
    inference(spm,[status(thm)],[19,32,theory(equality)]) ).

cnf(73,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)],[17,45,theory(equality)]) ).

cnf(89,negated_conjecture,
    ( subset(X1,esk3_0)
    | ~ member(esk1_2(X1,esk3_0),esk2_0) ),
    inference(spm,[status(thm)],[17,66,theory(equality)]) ).

cnf(102,negated_conjecture,
    subset(intersection(X1,esk2_0),esk3_0),
    inference(spm,[status(thm)],[89,60,theory(equality)]) ).

cnf(107,negated_conjecture,
    ( member(X1,esk3_0)
    | ~ member(X1,intersection(X2,esk2_0)) ),
    inference(spm,[status(thm)],[19,102,theory(equality)]) ).

cnf(129,negated_conjecture,
    ( member(esk1_2(intersection(X1,esk2_0),X2),esk3_0)
    | subset(intersection(X1,esk2_0),X2) ),
    inference(spm,[status(thm)],[107,18,theory(equality)]) ).

cnf(155,plain,
    ( subset(X1,intersection(X2,X1))
    | ~ member(esk1_2(X1,intersection(X2,X1)),X2) ),
    inference(spm,[status(thm)],[73,18,theory(equality)]) ).

cnf(773,plain,
    subset(X1,intersection(X1,X1)),
    inference(spm,[status(thm)],[155,18,theory(equality)]) ).

cnf(778,negated_conjecture,
    subset(intersection(X1,esk2_0),intersection(esk3_0,intersection(X1,esk2_0))),
    inference(spm,[status(thm)],[155,129,theory(equality)]) ).

cnf(790,plain,
    ( intersection(X1,X1) = X1
    | ~ subset(intersection(X1,X1),X1) ),
    inference(spm,[status(thm)],[25,773,theory(equality)]) ).

cnf(796,plain,
    ( intersection(X1,X1) = X1
    | $false ),
    inference(rw,[status(thm)],[790,21,theory(equality)]) ).

cnf(797,plain,
    intersection(X1,X1) = X1,
    inference(cn,[status(thm)],[796,theory(equality)]) ).

cnf(931,negated_conjecture,
    subset(esk2_0,intersection(esk3_0,esk2_0)),
    inference(spm,[status(thm)],[778,797,theory(equality)]) ).

cnf(937,negated_conjecture,
    subset(esk2_0,intersection(esk2_0,esk3_0)),
    inference(rw,[status(thm)],[931,11,theory(equality)]) ).

cnf(940,negated_conjecture,
    ( intersection(esk2_0,esk3_0) = esk2_0
    | ~ subset(intersection(esk2_0,esk3_0),esk2_0) ),
    inference(spm,[status(thm)],[25,937,theory(equality)]) ).

cnf(943,negated_conjecture,
    ( intersection(esk2_0,esk3_0) = esk2_0
    | $false ),
    inference(rw,[status(thm)],[940,21,theory(equality)]) ).

cnf(944,negated_conjecture,
    intersection(esk2_0,esk3_0) = esk2_0,
    inference(cn,[status(thm)],[943,theory(equality)]) ).

cnf(945,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[944,31,theory(equality)]) ).

cnf(946,negated_conjecture,
    $false,
    945,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET183+3.p
% --creating new selector for []
% -running prover on /tmp/tmp27CJ_-/sel_SET183+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET183+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET183+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET183+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
% 
%------------------------------------------------------------------------------