TSTP Solution File: SET200+3 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SET200+3 : 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 02:54:51 EST 2010

% Result   : Theorem 0.24s
% Output   : CNFRefutation 0.24s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   39 (  10 unt;   0 def)
%            Number of atoms       :  112 (   3 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  114 (  41   ~;  44   |;  24   &)
%                                         (   2 <=>;   3  =>;   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    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   87 (   2 sgn  42   !;  10   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1,X2] :
      ( subset(X1,X2)
    <=> ! [X3] :
          ( member(X3,X1)
         => member(X3,X2) ) ),
    file('/tmp/tmpw7fVjV/sel_SET200+3.p_1',subset_defn) ).

fof(2,axiom,
    ! [X1,X2,X3] :
      ( member(X3,union(X1,X2))
    <=> ( member(X3,X1)
        | member(X3,X2) ) ),
    file('/tmp/tmpw7fVjV/sel_SET200+3.p_1',union_defn) ).

fof(3,axiom,
    ! [X1,X2] : union(X1,X2) = union(X2,X1),
    file('/tmp/tmpw7fVjV/sel_SET200+3.p_1',commutativity_of_union) ).

fof(5,conjecture,
    ! [X1,X2,X3,X4] :
      ( ( subset(X1,X2)
        & subset(X3,X4) )
     => subset(union(X1,X3),union(X2,X4)) ),
    file('/tmp/tmpw7fVjV/sel_SET200+3.p_1',prove_th34) ).

fof(7,negated_conjecture,
    ~ ! [X1,X2,X3,X4] :
        ( ( subset(X1,X2)
          & subset(X3,X4) )
       => subset(union(X1,X3),union(X2,X4)) ),
    inference(assume_negation,[status(cth)],[5]) ).

fof(8,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(9,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)],[8]) ).

fof(10,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)],[9]) ).

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

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

cnf(13,plain,
    ( subset(X1,X2)
    | ~ member(esk1_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[12]) ).

cnf(14,plain,
    ( subset(X1,X2)
    | member(esk1_2(X1,X2),X1) ),
    inference(split_conjunct,[status(thm)],[12]) ).

cnf(15,plain,
    ( member(X3,X2)
    | ~ subset(X1,X2)
    | ~ member(X3,X1) ),
    inference(split_conjunct,[status(thm)],[12]) ).

fof(16,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)],[2]) ).

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

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

cnf(19,plain,
    ( member(X1,union(X2,X3))
    | ~ member(X1,X3) ),
    inference(split_conjunct,[status(thm)],[18]) ).

cnf(20,plain,
    ( member(X1,union(X2,X3))
    | ~ member(X1,X2) ),
    inference(split_conjunct,[status(thm)],[18]) ).

cnf(21,plain,
    ( member(X1,X2)
    | member(X1,X3)
    | ~ member(X1,union(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[18]) ).

fof(22,plain,
    ! [X3,X4] : union(X3,X4) = union(X4,X3),
    inference(variable_rename,[status(thm)],[3]) ).

cnf(23,plain,
    union(X1,X2) = union(X2,X1),
    inference(split_conjunct,[status(thm)],[22]) ).

fof(33,negated_conjecture,
    ? [X1,X2,X3,X4] :
      ( subset(X1,X2)
      & subset(X3,X4)
      & ~ subset(union(X1,X3),union(X2,X4)) ),
    inference(fof_nnf,[status(thm)],[7]) ).

fof(34,negated_conjecture,
    ? [X5,X6,X7,X8] :
      ( subset(X5,X6)
      & subset(X7,X8)
      & ~ subset(union(X5,X7),union(X6,X8)) ),
    inference(variable_rename,[status(thm)],[33]) ).

fof(35,negated_conjecture,
    ( subset(esk3_0,esk4_0)
    & subset(esk5_0,esk6_0)
    & ~ subset(union(esk3_0,esk5_0),union(esk4_0,esk6_0)) ),
    inference(skolemize,[status(esa)],[34]) ).

cnf(36,negated_conjecture,
    ~ subset(union(esk3_0,esk5_0),union(esk4_0,esk6_0)),
    inference(split_conjunct,[status(thm)],[35]) ).

cnf(37,negated_conjecture,
    subset(esk5_0,esk6_0),
    inference(split_conjunct,[status(thm)],[35]) ).

cnf(38,negated_conjecture,
    subset(esk3_0,esk4_0),
    inference(split_conjunct,[status(thm)],[35]) ).

cnf(45,negated_conjecture,
    ( member(X1,esk4_0)
    | ~ member(X1,esk3_0) ),
    inference(spm,[status(thm)],[15,38,theory(equality)]) ).

cnf(46,negated_conjecture,
    ( member(X1,esk6_0)
    | ~ member(X1,esk5_0) ),
    inference(spm,[status(thm)],[15,37,theory(equality)]) ).

cnf(49,plain,
    ( subset(X1,union(X2,X3))
    | ~ member(esk1_2(X1,union(X2,X3)),X3) ),
    inference(spm,[status(thm)],[13,19,theory(equality)]) ).

cnf(50,plain,
    ( subset(X1,union(X2,X3))
    | ~ member(esk1_2(X1,union(X2,X3)),X2) ),
    inference(spm,[status(thm)],[13,20,theory(equality)]) ).

cnf(54,plain,
    ( member(esk1_2(union(X1,X2),X3),X2)
    | member(esk1_2(union(X1,X2),X3),X1)
    | subset(union(X1,X2),X3) ),
    inference(spm,[status(thm)],[21,14,theory(equality)]) ).

cnf(77,negated_conjecture,
    ( subset(X1,union(X2,esk4_0))
    | ~ member(esk1_2(X1,union(X2,esk4_0)),esk3_0) ),
    inference(spm,[status(thm)],[49,45,theory(equality)]) ).

cnf(93,negated_conjecture,
    ( subset(X1,union(esk6_0,X2))
    | ~ member(esk1_2(X1,union(esk6_0,X2)),esk5_0) ),
    inference(spm,[status(thm)],[50,46,theory(equality)]) ).

cnf(131,negated_conjecture,
    ( subset(union(esk3_0,X1),union(X2,esk4_0))
    | member(esk1_2(union(esk3_0,X1),union(X2,esk4_0)),X1) ),
    inference(spm,[status(thm)],[77,54,theory(equality)]) ).

cnf(2149,negated_conjecture,
    subset(union(esk3_0,esk5_0),union(esk6_0,esk4_0)),
    inference(spm,[status(thm)],[93,131,theory(equality)]) ).

cnf(2165,negated_conjecture,
    subset(union(esk3_0,esk5_0),union(esk4_0,esk6_0)),
    inference(rw,[status(thm)],[2149,23,theory(equality)]) ).

cnf(2166,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[2165,36,theory(equality)]) ).

cnf(2167,negated_conjecture,
    $false,
    2166,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET200+3.p
% --creating new selector for []
% -running prover on /tmp/tmpw7fVjV/sel_SET200+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET200+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET200+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET200+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
% 
%------------------------------------------------------------------------------