TSTP Solution File: SET593+3 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SET593+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 03:03:48 EST 2010

% Result   : Theorem 0.29s
% Output   : CNFRefutation 0.29s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   46 (   7 unt;   0 def)
%            Number of atoms       :  146 (   0 equ)
%            Maximal formula atoms :    7 (   3 avg)
%            Number of connectives :  161 (  61   ~;  64   |;  29   &)
%                                         (   4 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    3 (   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   :   94 (   4 sgn  51   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1,X2] :
      ( subset(X1,X2)
    <=> ! [X3] :
          ( member(X3,X1)
         => member(X3,X2) ) ),
    file('/tmp/tmpgmU2Jb/sel_SET593+3.p_1',subset_defn) ).

fof(2,conjecture,
    ! [X1,X2,X3] :
      ( subset(X1,union(X2,X3))
     => ( subset(difference(X1,X2),X3)
        & subset(difference(X1,X3),X2) ) ),
    file('/tmp/tmpgmU2Jb/sel_SET593+3.p_1',prove_th52) ).

fof(3,axiom,
    ! [X1,X2,X3] :
      ( member(X3,union(X1,X2))
    <=> ( member(X3,X1)
        | member(X3,X2) ) ),
    file('/tmp/tmpgmU2Jb/sel_SET593+3.p_1',union_defn) ).

fof(6,axiom,
    ! [X1,X2,X3] :
      ( member(X3,difference(X1,X2))
    <=> ( member(X3,X1)
        & ~ member(X3,X2) ) ),
    file('/tmp/tmpgmU2Jb/sel_SET593+3.p_1',difference_defn) ).

fof(8,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( subset(X1,union(X2,X3))
       => ( subset(difference(X1,X2),X3)
          & subset(difference(X1,X3),X2) ) ),
    inference(assume_negation,[status(cth)],[2]) ).

fof(9,plain,
    ! [X1,X2,X3] :
      ( member(X3,difference(X1,X2))
    <=> ( member(X3,X1)
        & ~ member(X3,X2) ) ),
    inference(fof_simplification,[status(thm)],[6,theory(equality)]) ).

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)],[1]) ).

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,union(X2,X3))
      & ( ~ subset(difference(X1,X2),X3)
        | ~ subset(difference(X1,X3),X2) ) ),
    inference(fof_nnf,[status(thm)],[8]) ).

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

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

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

cnf(22,negated_conjecture,
    subset(esk2_0,union(esk3_0,esk4_0)),
    inference(split_conjunct,[status(thm)],[20]) ).

fof(23,plain,
    ! [X1,X2,X3] :
      ( ( ~ member(X3,union(X1,X2))
        | member(X3,X1)
        | member(X3,X2) )
      & ( ( ~ member(X3,X1)
          & ~ member(X3,X2) )
        | member(X3,union(X1,X2)) ) ),
    inference(fof_nnf,[status(thm)],[3]) ).

fof(24,plain,
    ! [X4,X5,X6] :
      ( ( ~ member(X6,union(X4,X5))
        | member(X6,X4)
        | member(X6,X5) )
      & ( ( ~ member(X6,X4)
          & ~ member(X6,X5) )
        | member(X6,union(X4,X5)) ) ),
    inference(variable_rename,[status(thm)],[23]) ).

fof(25,plain,
    ! [X4,X5,X6] :
      ( ( ~ member(X6,union(X4,X5))
        | member(X6,X4)
        | member(X6,X5) )
      & ( ~ member(X6,X4)
        | member(X6,union(X4,X5)) )
      & ( ~ member(X6,X5)
        | member(X6,union(X4,X5)) ) ),
    inference(distribute,[status(thm)],[24]) ).

cnf(28,plain,
    ( member(X1,X2)
    | member(X1,X3)
    | ~ member(X1,union(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[25]) ).

fof(40,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)],[9]) ).

fof(41,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)],[40]) ).

fof(42,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)],[41]) ).

cnf(44,plain,
    ( ~ member(X1,difference(X2,X3))
    | ~ member(X1,X3) ),
    inference(split_conjunct,[status(thm)],[42]) ).

cnf(45,plain,
    ( member(X1,X2)
    | ~ member(X1,difference(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[42]) ).

cnf(52,plain,
    ( member(esk1_2(difference(X1,X2),X3),X1)
    | subset(difference(X1,X2),X3) ),
    inference(spm,[status(thm)],[45,16,theory(equality)]) ).

cnf(54,negated_conjecture,
    ( member(X1,union(esk3_0,esk4_0))
    | ~ member(X1,esk2_0) ),
    inference(spm,[status(thm)],[17,22,theory(equality)]) ).

cnf(59,plain,
    ( subset(difference(X1,X2),X3)
    | ~ member(esk1_2(difference(X1,X2),X3),X2) ),
    inference(spm,[status(thm)],[44,16,theory(equality)]) ).

cnf(80,negated_conjecture,
    ( subset(X1,union(esk3_0,esk4_0))
    | ~ member(esk1_2(X1,union(esk3_0,esk4_0)),esk2_0) ),
    inference(spm,[status(thm)],[15,54,theory(equality)]) ).

cnf(81,negated_conjecture,
    ( member(X1,esk4_0)
    | member(X1,esk3_0)
    | ~ member(X1,esk2_0) ),
    inference(spm,[status(thm)],[28,54,theory(equality)]) ).

cnf(83,negated_conjecture,
    ( subset(X1,esk4_0)
    | member(esk1_2(X1,esk4_0),esk3_0)
    | ~ member(esk1_2(X1,esk4_0),esk2_0) ),
    inference(spm,[status(thm)],[15,81,theory(equality)]) ).

cnf(91,negated_conjecture,
    subset(difference(esk2_0,X1),union(esk3_0,esk4_0)),
    inference(spm,[status(thm)],[80,52,theory(equality)]) ).

cnf(93,negated_conjecture,
    ( member(X1,union(esk3_0,esk4_0))
    | ~ member(X1,difference(esk2_0,X2)) ),
    inference(spm,[status(thm)],[17,91,theory(equality)]) ).

cnf(121,negated_conjecture,
    ( member(esk1_2(difference(esk2_0,X1),X2),union(esk3_0,esk4_0))
    | subset(difference(esk2_0,X1),X2) ),
    inference(spm,[status(thm)],[93,16,theory(equality)]) ).

cnf(138,negated_conjecture,
    ( member(esk1_2(difference(esk2_0,X1),X2),esk4_0)
    | member(esk1_2(difference(esk2_0,X1),X2),esk3_0)
    | subset(difference(esk2_0,X1),X2) ),
    inference(spm,[status(thm)],[28,121,theory(equality)]) ).

cnf(164,negated_conjecture,
    ( subset(difference(X1,esk3_0),esk4_0)
    | ~ member(esk1_2(difference(X1,esk3_0),esk4_0),esk2_0) ),
    inference(spm,[status(thm)],[59,83,theory(equality)]) ).

cnf(167,negated_conjecture,
    subset(difference(esk2_0,esk3_0),esk4_0),
    inference(spm,[status(thm)],[164,52,theory(equality)]) ).

cnf(169,negated_conjecture,
    ( $false
    | ~ subset(difference(esk2_0,esk4_0),esk3_0) ),
    inference(rw,[status(thm)],[21,167,theory(equality)]) ).

cnf(170,negated_conjecture,
    ~ subset(difference(esk2_0,esk4_0),esk3_0),
    inference(cn,[status(thm)],[169,theory(equality)]) ).

cnf(2231,negated_conjecture,
    ( subset(difference(esk2_0,esk4_0),X1)
    | member(esk1_2(difference(esk2_0,esk4_0),X1),esk3_0) ),
    inference(spm,[status(thm)],[59,138,theory(equality)]) ).

cnf(2241,negated_conjecture,
    subset(difference(esk2_0,esk4_0),esk3_0),
    inference(spm,[status(thm)],[15,2231,theory(equality)]) ).

cnf(2251,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[2241,170,theory(equality)]) ).

cnf(2252,negated_conjecture,
    $false,
    2251,
    [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/SET593+3.p
% --creating new selector for []
% -running prover on /tmp/tmpgmU2Jb/sel_SET593+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET593+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET593+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET593+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
% 
%------------------------------------------------------------------------------