TSTP Solution File: SET009+3 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SET009+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 02:36:22 EST 2010

% Result   : Theorem 0.20s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   34 (   6 unt;   0 def)
%            Number of atoms       :  102 (   0 equ)
%            Maximal formula atoms :    7 (   3 avg)
%            Number of connectives :  111 (  43   ~;  41   |;  21   &)
%                                         (   3 <=>;   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    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   79 (   2 sgn  39   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,conjecture,
    ! [X1,X2,X3] :
      ( subset(X1,X2)
     => subset(difference(X3,X2),difference(X3,X1)) ),
    file('/tmp/tmpnJooE2/sel_SET009+3.p_1',prove_subset_difference) ).

fof(2,axiom,
    ! [X1,X2,X3] :
      ( member(X3,difference(X1,X2))
    <=> ( member(X3,X1)
        & ~ member(X3,X2) ) ),
    file('/tmp/tmpnJooE2/sel_SET009+3.p_1',difference_defn) ).

fof(3,axiom,
    ! [X1,X2] :
      ( subset(X1,X2)
    <=> ! [X3] :
          ( member(X3,X1)
         => member(X3,X2) ) ),
    file('/tmp/tmpnJooE2/sel_SET009+3.p_1',subset_defn) ).

fof(5,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( subset(X1,X2)
       => subset(difference(X3,X2),difference(X3,X1)) ),
    inference(assume_negation,[status(cth)],[1]) ).

fof(6,plain,
    ! [X1,X2,X3] :
      ( member(X3,difference(X1,X2))
    <=> ( member(X3,X1)
        & ~ member(X3,X2) ) ),
    inference(fof_simplification,[status(thm)],[2,theory(equality)]) ).

fof(7,negated_conjecture,
    ? [X1,X2,X3] :
      ( subset(X1,X2)
      & ~ subset(difference(X3,X2),difference(X3,X1)) ),
    inference(fof_nnf,[status(thm)],[5]) ).

fof(8,negated_conjecture,
    ? [X4,X5,X6] :
      ( subset(X4,X5)
      & ~ subset(difference(X6,X5),difference(X6,X4)) ),
    inference(variable_rename,[status(thm)],[7]) ).

fof(9,negated_conjecture,
    ( subset(esk1_0,esk2_0)
    & ~ subset(difference(esk3_0,esk2_0),difference(esk3_0,esk1_0)) ),
    inference(skolemize,[status(esa)],[8]) ).

cnf(10,negated_conjecture,
    ~ subset(difference(esk3_0,esk2_0),difference(esk3_0,esk1_0)),
    inference(split_conjunct,[status(thm)],[9]) ).

cnf(11,negated_conjecture,
    subset(esk1_0,esk2_0),
    inference(split_conjunct,[status(thm)],[9]) ).

fof(12,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)],[6]) ).

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

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

cnf(15,plain,
    ( member(X1,difference(X2,X3))
    | member(X1,X3)
    | ~ member(X1,X2) ),
    inference(split_conjunct,[status(thm)],[14]) ).

cnf(16,plain,
    ( ~ member(X1,difference(X2,X3))
    | ~ member(X1,X3) ),
    inference(split_conjunct,[status(thm)],[14]) ).

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

fof(18,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)],[3]) ).

fof(19,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)],[18]) ).

fof(20,plain,
    ! [X4,X5] :
      ( ( ~ subset(X4,X5)
        | ! [X6] :
            ( ~ member(X6,X4)
            | member(X6,X5) ) )
      & ( ( member(esk4_2(X4,X5),X4)
          & ~ member(esk4_2(X4,X5),X5) )
        | subset(X4,X5) ) ),
    inference(skolemize,[status(esa)],[19]) ).

fof(21,plain,
    ! [X4,X5,X6] :
      ( ( ~ member(X6,X4)
        | member(X6,X5)
        | ~ subset(X4,X5) )
      & ( ( member(esk4_2(X4,X5),X4)
          & ~ member(esk4_2(X4,X5),X5) )
        | subset(X4,X5) ) ),
    inference(shift_quantors,[status(thm)],[20]) ).

fof(22,plain,
    ! [X4,X5,X6] :
      ( ( ~ member(X6,X4)
        | member(X6,X5)
        | ~ subset(X4,X5) )
      & ( member(esk4_2(X4,X5),X4)
        | subset(X4,X5) )
      & ( ~ member(esk4_2(X4,X5),X5)
        | subset(X4,X5) ) ),
    inference(distribute,[status(thm)],[21]) ).

cnf(23,plain,
    ( subset(X1,X2)
    | ~ member(esk4_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[22]) ).

cnf(24,plain,
    ( subset(X1,X2)
    | member(esk4_2(X1,X2),X1) ),
    inference(split_conjunct,[status(thm)],[22]) ).

cnf(25,plain,
    ( member(X3,X2)
    | ~ subset(X1,X2)
    | ~ member(X3,X1) ),
    inference(split_conjunct,[status(thm)],[22]) ).

cnf(30,plain,
    ( member(esk4_2(difference(X1,X2),X3),X1)
    | subset(difference(X1,X2),X3) ),
    inference(spm,[status(thm)],[17,24,theory(equality)]) ).

cnf(31,negated_conjecture,
    ( member(X1,esk2_0)
    | ~ member(X1,esk1_0) ),
    inference(spm,[status(thm)],[25,11,theory(equality)]) ).

cnf(33,plain,
    ( subset(difference(X1,X2),X3)
    | ~ member(esk4_2(difference(X1,X2),X3),X2) ),
    inference(spm,[status(thm)],[16,24,theory(equality)]) ).

cnf(34,plain,
    ( subset(X1,difference(X2,X3))
    | member(esk4_2(X1,difference(X2,X3)),X3)
    | ~ member(esk4_2(X1,difference(X2,X3)),X2) ),
    inference(spm,[status(thm)],[23,15,theory(equality)]) ).

cnf(42,negated_conjecture,
    ( subset(difference(X1,esk2_0),X2)
    | ~ member(esk4_2(difference(X1,esk2_0),X2),esk1_0) ),
    inference(spm,[status(thm)],[33,31,theory(equality)]) ).

cnf(60,plain,
    ( member(esk4_2(difference(X1,X2),difference(X1,X3)),X3)
    | subset(difference(X1,X2),difference(X1,X3)) ),
    inference(spm,[status(thm)],[34,30,theory(equality)]) ).

cnf(602,negated_conjecture,
    subset(difference(X1,esk2_0),difference(X1,esk1_0)),
    inference(spm,[status(thm)],[42,60,theory(equality)]) ).

cnf(615,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[10,602,theory(equality)]) ).

cnf(616,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[615,theory(equality)]) ).

cnf(617,negated_conjecture,
    $false,
    616,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET009+3.p
% --creating new selector for []
% -running prover on /tmp/tmpnJooE2/sel_SET009+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET009+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET009+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET009+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
% 
%------------------------------------------------------------------------------