TSTP Solution File: SEU319+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SEU319+1 : TPTP v5.0.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art04.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 07:14:28 EST 2010

% Result   : Theorem 0.23s
% Output   : CNFRefutation 0.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   41 (   6 unt;   0 def)
%            Number of atoms       :  138 (   5 equ)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives :  166 (  69   ~;  72   |;  13   &)
%                                         (   3 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   2 con; 0-3 aty)
%            Number of variables   :   44 (   0 sgn  25   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1] :
      ( top_str(X1)
     => ! [X2] :
          ( element(X2,powerset(the_carrier(X1)))
         => ( closed_subset(X2,X1)
          <=> open_subset(subset_difference(the_carrier(X1),cast_as_carrier_subset(X1),X2),X1) ) ) ),
    file('/tmp/tmprK9VJP/sel_SEU319+1.p_1',d6_pre_topc) ).

fof(9,axiom,
    ! [X1] :
      ( one_sorted_str(X1)
     => ! [X2] :
          ( element(X2,powerset(the_carrier(X1)))
         => subset_complement(the_carrier(X1),X2) = subset_difference(the_carrier(X1),cast_as_carrier_subset(X1),X2) ) ),
    file('/tmp/tmprK9VJP/sel_SEU319+1.p_1',t17_pre_topc) ).

fof(13,axiom,
    ! [X1] :
      ( top_str(X1)
     => one_sorted_str(X1) ),
    file('/tmp/tmprK9VJP/sel_SEU319+1.p_1',dt_l1_pre_topc) ).

fof(17,conjecture,
    ! [X1] :
      ( top_str(X1)
     => ! [X2] :
          ( element(X2,powerset(the_carrier(X1)))
         => ( closed_subset(X2,X1)
          <=> open_subset(subset_complement(the_carrier(X1),X2),X1) ) ) ),
    file('/tmp/tmprK9VJP/sel_SEU319+1.p_1',t29_tops_1) ).

fof(20,negated_conjecture,
    ~ ! [X1] :
        ( top_str(X1)
       => ! [X2] :
            ( element(X2,powerset(the_carrier(X1)))
           => ( closed_subset(X2,X1)
            <=> open_subset(subset_complement(the_carrier(X1),X2),X1) ) ) ),
    inference(assume_negation,[status(cth)],[17]) ).

fof(21,plain,
    ! [X1] :
      ( ~ top_str(X1)
      | ! [X2] :
          ( ~ element(X2,powerset(the_carrier(X1)))
          | ( ( ~ closed_subset(X2,X1)
              | open_subset(subset_difference(the_carrier(X1),cast_as_carrier_subset(X1),X2),X1) )
            & ( ~ open_subset(subset_difference(the_carrier(X1),cast_as_carrier_subset(X1),X2),X1)
              | closed_subset(X2,X1) ) ) ) ),
    inference(fof_nnf,[status(thm)],[1]) ).

fof(22,plain,
    ! [X3] :
      ( ~ top_str(X3)
      | ! [X4] :
          ( ~ element(X4,powerset(the_carrier(X3)))
          | ( ( ~ closed_subset(X4,X3)
              | open_subset(subset_difference(the_carrier(X3),cast_as_carrier_subset(X3),X4),X3) )
            & ( ~ open_subset(subset_difference(the_carrier(X3),cast_as_carrier_subset(X3),X4),X3)
              | closed_subset(X4,X3) ) ) ) ),
    inference(variable_rename,[status(thm)],[21]) ).

fof(23,plain,
    ! [X3,X4] :
      ( ~ element(X4,powerset(the_carrier(X3)))
      | ( ( ~ closed_subset(X4,X3)
          | open_subset(subset_difference(the_carrier(X3),cast_as_carrier_subset(X3),X4),X3) )
        & ( ~ open_subset(subset_difference(the_carrier(X3),cast_as_carrier_subset(X3),X4),X3)
          | closed_subset(X4,X3) ) )
      | ~ top_str(X3) ),
    inference(shift_quantors,[status(thm)],[22]) ).

fof(24,plain,
    ! [X3,X4] :
      ( ( ~ closed_subset(X4,X3)
        | open_subset(subset_difference(the_carrier(X3),cast_as_carrier_subset(X3),X4),X3)
        | ~ element(X4,powerset(the_carrier(X3)))
        | ~ top_str(X3) )
      & ( ~ open_subset(subset_difference(the_carrier(X3),cast_as_carrier_subset(X3),X4),X3)
        | closed_subset(X4,X3)
        | ~ element(X4,powerset(the_carrier(X3)))
        | ~ top_str(X3) ) ),
    inference(distribute,[status(thm)],[23]) ).

cnf(25,plain,
    ( closed_subset(X2,X1)
    | ~ top_str(X1)
    | ~ element(X2,powerset(the_carrier(X1)))
    | ~ open_subset(subset_difference(the_carrier(X1),cast_as_carrier_subset(X1),X2),X1) ),
    inference(split_conjunct,[status(thm)],[24]) ).

cnf(26,plain,
    ( open_subset(subset_difference(the_carrier(X1),cast_as_carrier_subset(X1),X2),X1)
    | ~ top_str(X1)
    | ~ element(X2,powerset(the_carrier(X1)))
    | ~ closed_subset(X2,X1) ),
    inference(split_conjunct,[status(thm)],[24]) ).

fof(44,plain,
    ! [X1] :
      ( ~ one_sorted_str(X1)
      | ! [X2] :
          ( ~ element(X2,powerset(the_carrier(X1)))
          | subset_complement(the_carrier(X1),X2) = subset_difference(the_carrier(X1),cast_as_carrier_subset(X1),X2) ) ),
    inference(fof_nnf,[status(thm)],[9]) ).

fof(45,plain,
    ! [X3] :
      ( ~ one_sorted_str(X3)
      | ! [X4] :
          ( ~ element(X4,powerset(the_carrier(X3)))
          | subset_complement(the_carrier(X3),X4) = subset_difference(the_carrier(X3),cast_as_carrier_subset(X3),X4) ) ),
    inference(variable_rename,[status(thm)],[44]) ).

fof(46,plain,
    ! [X3,X4] :
      ( ~ element(X4,powerset(the_carrier(X3)))
      | subset_complement(the_carrier(X3),X4) = subset_difference(the_carrier(X3),cast_as_carrier_subset(X3),X4)
      | ~ one_sorted_str(X3) ),
    inference(shift_quantors,[status(thm)],[45]) ).

cnf(47,plain,
    ( subset_complement(the_carrier(X1),X2) = subset_difference(the_carrier(X1),cast_as_carrier_subset(X1),X2)
    | ~ one_sorted_str(X1)
    | ~ element(X2,powerset(the_carrier(X1))) ),
    inference(split_conjunct,[status(thm)],[46]) ).

fof(51,plain,
    ! [X1] :
      ( ~ top_str(X1)
      | one_sorted_str(X1) ),
    inference(fof_nnf,[status(thm)],[13]) ).

fof(52,plain,
    ! [X2] :
      ( ~ top_str(X2)
      | one_sorted_str(X2) ),
    inference(variable_rename,[status(thm)],[51]) ).

cnf(53,plain,
    ( one_sorted_str(X1)
    | ~ top_str(X1) ),
    inference(split_conjunct,[status(thm)],[52]) ).

fof(62,negated_conjecture,
    ? [X1] :
      ( top_str(X1)
      & ? [X2] :
          ( element(X2,powerset(the_carrier(X1)))
          & ( ~ closed_subset(X2,X1)
            | ~ open_subset(subset_complement(the_carrier(X1),X2),X1) )
          & ( closed_subset(X2,X1)
            | open_subset(subset_complement(the_carrier(X1),X2),X1) ) ) ),
    inference(fof_nnf,[status(thm)],[20]) ).

fof(63,negated_conjecture,
    ? [X3] :
      ( top_str(X3)
      & ? [X4] :
          ( element(X4,powerset(the_carrier(X3)))
          & ( ~ closed_subset(X4,X3)
            | ~ open_subset(subset_complement(the_carrier(X3),X4),X3) )
          & ( closed_subset(X4,X3)
            | open_subset(subset_complement(the_carrier(X3),X4),X3) ) ) ),
    inference(variable_rename,[status(thm)],[62]) ).

fof(64,negated_conjecture,
    ( top_str(esk4_0)
    & element(esk5_0,powerset(the_carrier(esk4_0)))
    & ( ~ closed_subset(esk5_0,esk4_0)
      | ~ open_subset(subset_complement(the_carrier(esk4_0),esk5_0),esk4_0) )
    & ( closed_subset(esk5_0,esk4_0)
      | open_subset(subset_complement(the_carrier(esk4_0),esk5_0),esk4_0) ) ),
    inference(skolemize,[status(esa)],[63]) ).

cnf(65,negated_conjecture,
    ( open_subset(subset_complement(the_carrier(esk4_0),esk5_0),esk4_0)
    | closed_subset(esk5_0,esk4_0) ),
    inference(split_conjunct,[status(thm)],[64]) ).

cnf(66,negated_conjecture,
    ( ~ open_subset(subset_complement(the_carrier(esk4_0),esk5_0),esk4_0)
    | ~ closed_subset(esk5_0,esk4_0) ),
    inference(split_conjunct,[status(thm)],[64]) ).

cnf(67,negated_conjecture,
    element(esk5_0,powerset(the_carrier(esk4_0))),
    inference(split_conjunct,[status(thm)],[64]) ).

cnf(68,negated_conjecture,
    top_str(esk4_0),
    inference(split_conjunct,[status(thm)],[64]) ).

cnf(85,plain,
    ( open_subset(subset_complement(the_carrier(X1),X2),X1)
    | ~ closed_subset(X2,X1)
    | ~ element(X2,powerset(the_carrier(X1)))
    | ~ top_str(X1)
    | ~ one_sorted_str(X1) ),
    inference(spm,[status(thm)],[26,47,theory(equality)]) ).

cnf(87,plain,
    ( closed_subset(X1,X2)
    | ~ open_subset(subset_complement(the_carrier(X2),X1),X2)
    | ~ element(X1,powerset(the_carrier(X2)))
    | ~ top_str(X2)
    | ~ one_sorted_str(X2) ),
    inference(spm,[status(thm)],[25,47,theory(equality)]) ).

cnf(90,plain,
    ( open_subset(subset_complement(the_carrier(X1),X2),X1)
    | ~ closed_subset(X2,X1)
    | ~ element(X2,powerset(the_carrier(X1)))
    | ~ top_str(X1) ),
    inference(csr,[status(thm)],[85,53]) ).

cnf(96,plain,
    ( closed_subset(X1,X2)
    | ~ open_subset(subset_complement(the_carrier(X2),X1),X2)
    | ~ element(X1,powerset(the_carrier(X2)))
    | ~ top_str(X2) ),
    inference(csr,[status(thm)],[87,53]) ).

cnf(97,negated_conjecture,
    ( closed_subset(esk5_0,esk4_0)
    | ~ element(esk5_0,powerset(the_carrier(esk4_0)))
    | ~ top_str(esk4_0) ),
    inference(spm,[status(thm)],[96,65,theory(equality)]) ).

cnf(100,negated_conjecture,
    ( closed_subset(esk5_0,esk4_0)
    | $false
    | ~ top_str(esk4_0) ),
    inference(rw,[status(thm)],[97,67,theory(equality)]) ).

cnf(101,negated_conjecture,
    ( closed_subset(esk5_0,esk4_0)
    | $false
    | $false ),
    inference(rw,[status(thm)],[100,68,theory(equality)]) ).

cnf(102,negated_conjecture,
    closed_subset(esk5_0,esk4_0),
    inference(cn,[status(thm)],[101,theory(equality)]) ).

cnf(103,negated_conjecture,
    ( ~ open_subset(subset_complement(the_carrier(esk4_0),esk5_0),esk4_0)
    | $false ),
    inference(rw,[status(thm)],[66,102,theory(equality)]) ).

cnf(104,negated_conjecture,
    ~ open_subset(subset_complement(the_carrier(esk4_0),esk5_0),esk4_0),
    inference(cn,[status(thm)],[103,theory(equality)]) ).

cnf(108,negated_conjecture,
    ( ~ closed_subset(esk5_0,esk4_0)
    | ~ element(esk5_0,powerset(the_carrier(esk4_0)))
    | ~ top_str(esk4_0) ),
    inference(spm,[status(thm)],[104,90,theory(equality)]) ).

cnf(109,negated_conjecture,
    ( $false
    | ~ element(esk5_0,powerset(the_carrier(esk4_0)))
    | ~ top_str(esk4_0) ),
    inference(rw,[status(thm)],[108,102,theory(equality)]) ).

cnf(110,negated_conjecture,
    ( $false
    | $false
    | ~ top_str(esk4_0) ),
    inference(rw,[status(thm)],[109,67,theory(equality)]) ).

cnf(111,negated_conjecture,
    ( $false
    | $false
    | $false ),
    inference(rw,[status(thm)],[110,68,theory(equality)]) ).

cnf(112,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[111,theory(equality)]) ).

cnf(113,negated_conjecture,
    $false,
    112,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU319+1.p
% --creating new selector for []
% -running prover on /tmp/tmprK9VJP/sel_SEU319+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU319+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU319+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU319+1.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
% 
%------------------------------------------------------------------------------