TSTP Solution File: SET603+3 by SInE---0.4

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%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SET603+3 : TPTP v5.0.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art11.cs.miami.edu
% Model    : i686 i686
% CPU      : Intel(R) Pentium(R) 4 CPU 3.00GHz @ 3000MHz
% Memory   : 2006MB
% OS       : Linux 2.6.31.5-127.fc12.i686.PAE
% CPULimit : 300s
% DateTime : Sun Dec 26 03:04:58 EST 2010

% Result   : Theorem 0.23s
% Output   : CNFRefutation 0.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   41 (  16 unt;   0 def)
%            Number of atoms       :  120 (  18 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  131 (  52   ~;  49   |;  25   &)
%                                         (   4 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   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   :   77 (   3 sgn  46   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1,X2] :
      ( subset(X1,X2)
    <=> ! [X3] :
          ( member(X3,X1)
         => member(X3,X2) ) ),
    file('/tmp/tmp4MohZk/sel_SET603+3.p_1',subset_defn) ).

fof(3,conjecture,
    ! [X1] : difference(X1,empty_set) = X1,
    file('/tmp/tmp4MohZk/sel_SET603+3.p_1',prove_th74) ).

fof(4,axiom,
    ! [X1,X2] :
      ( X1 = X2
    <=> ( subset(X1,X2)
        & subset(X2,X1) ) ),
    file('/tmp/tmp4MohZk/sel_SET603+3.p_1',equal_defn) ).

fof(7,axiom,
    ! [X1,X2,X3] :
      ( member(X3,difference(X1,X2))
    <=> ( member(X3,X1)
        & ~ member(X3,X2) ) ),
    file('/tmp/tmp4MohZk/sel_SET603+3.p_1',difference_defn) ).

fof(9,axiom,
    ! [X1] : ~ member(X1,empty_set),
    file('/tmp/tmp4MohZk/sel_SET603+3.p_1',empty_set_defn) ).

fof(10,negated_conjecture,
    ~ ! [X1] : difference(X1,empty_set) = X1,
    inference(assume_negation,[status(cth)],[3]) ).

fof(12,plain,
    ! [X1,X2,X3] :
      ( member(X3,difference(X1,X2))
    <=> ( member(X3,X1)
        & ~ member(X3,X2) ) ),
    inference(fof_simplification,[status(thm)],[7,theory(equality)]) ).

fof(13,plain,
    ! [X1] : ~ member(X1,empty_set),
    inference(fof_simplification,[status(thm)],[9,theory(equality)]) ).

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

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

fof(17,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)],[16]) ).

fof(18,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)],[17]) ).

cnf(19,plain,
    ( subset(X1,X2)
    | ~ member(esk1_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[18]) ).

cnf(20,plain,
    ( subset(X1,X2)
    | member(esk1_2(X1,X2),X1) ),
    inference(split_conjunct,[status(thm)],[18]) ).

fof(28,negated_conjecture,
    ? [X1] : difference(X1,empty_set) != X1,
    inference(fof_nnf,[status(thm)],[10]) ).

fof(29,negated_conjecture,
    ? [X2] : difference(X2,empty_set) != X2,
    inference(variable_rename,[status(thm)],[28]) ).

fof(30,negated_conjecture,
    difference(esk3_0,empty_set) != esk3_0,
    inference(skolemize,[status(esa)],[29]) ).

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

fof(32,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(33,plain,
    ! [X3,X4] :
      ( ( X3 != X4
        | ( subset(X3,X4)
          & subset(X4,X3) ) )
      & ( ~ subset(X3,X4)
        | ~ subset(X4,X3)
        | X3 = X4 ) ),
    inference(variable_rename,[status(thm)],[32]) ).

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

cnf(35,plain,
    ( X1 = X2
    | ~ subset(X2,X1)
    | ~ subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[34]) ).

fof(53,plain,
    ! [X1,X2,X3] :
      ( ( ~ member(X3,difference(X1,X2))
        | ( member(X3,X1)
          & ~ member(X3,X2) ) )
      & ( ~ member(X3,X1)
        | member(X3,X2)
        | member(X3,difference(X1,X2)) ) ),
    inference(fof_nnf,[status(thm)],[12]) ).

fof(54,plain,
    ! [X4,X5,X6] :
      ( ( ~ member(X6,difference(X4,X5))
        | ( member(X6,X4)
          & ~ member(X6,X5) ) )
      & ( ~ member(X6,X4)
        | member(X6,X5)
        | member(X6,difference(X4,X5)) ) ),
    inference(variable_rename,[status(thm)],[53]) ).

fof(55,plain,
    ! [X4,X5,X6] :
      ( ( member(X6,X4)
        | ~ member(X6,difference(X4,X5)) )
      & ( ~ member(X6,X5)
        | ~ member(X6,difference(X4,X5)) )
      & ( ~ member(X6,X4)
        | member(X6,X5)
        | member(X6,difference(X4,X5)) ) ),
    inference(distribute,[status(thm)],[54]) ).

cnf(56,plain,
    ( member(X1,difference(X2,X3))
    | member(X1,X3)
    | ~ member(X1,X2) ),
    inference(split_conjunct,[status(thm)],[55]) ).

cnf(58,plain,
    ( member(X1,X2)
    | ~ member(X1,difference(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[55]) ).

fof(61,plain,
    ! [X2] : ~ member(X2,empty_set),
    inference(variable_rename,[status(thm)],[13]) ).

cnf(62,plain,
    ~ member(X1,empty_set),
    inference(split_conjunct,[status(thm)],[61]) ).

cnf(82,plain,
    ( member(esk1_2(difference(X1,X2),X3),X1)
    | subset(difference(X1,X2),X3) ),
    inference(spm,[status(thm)],[58,20,theory(equality)]) ).

cnf(90,plain,
    ( member(esk1_2(X1,X2),difference(X1,X3))
    | member(esk1_2(X1,X2),X3)
    | subset(X1,X2) ),
    inference(spm,[status(thm)],[56,20,theory(equality)]) ).

cnf(403,plain,
    subset(difference(X1,X2),X1),
    inference(spm,[status(thm)],[19,82,theory(equality)]) ).

cnf(701,plain,
    ( subset(X1,difference(X1,X2))
    | member(esk1_2(X1,difference(X1,X2)),X2) ),
    inference(spm,[status(thm)],[19,90,theory(equality)]) ).

cnf(948,plain,
    subset(X1,difference(X1,empty_set)),
    inference(spm,[status(thm)],[62,701,theory(equality)]) ).

cnf(981,plain,
    ( difference(X1,empty_set) = X1
    | ~ subset(difference(X1,empty_set),X1) ),
    inference(spm,[status(thm)],[35,948,theory(equality)]) ).

cnf(994,plain,
    ( difference(X1,empty_set) = X1
    | $false ),
    inference(rw,[status(thm)],[981,403,theory(equality)]) ).

cnf(995,plain,
    difference(X1,empty_set) = X1,
    inference(cn,[status(thm)],[994,theory(equality)]) ).

cnf(1034,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[31,995,theory(equality)]) ).

cnf(1035,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[1034,theory(equality)]) ).

cnf(1036,negated_conjecture,
    $false,
    1035,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% /home/graph/tptp/Systems/SInE---0.4/Source/sine.py:10: DeprecationWarning: the sets module is deprecated
%   from sets import Set
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET603+3.p
% --creating new selector for []
% -running prover on /tmp/tmp4MohZk/sel_SET603+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET603+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET603+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET603+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
% 
%------------------------------------------------------------------------------